Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,3,Mod(3,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.f (of order \(20\), degree \(8\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.36240132180\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 27.3 | ||
Character | \(\chi\) | \(=\) | 50.27 |
Dual form | 50.3.f.b.13.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(e\left(\frac{1}{20}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39680 | + | 0.221232i | 0.698401 | + | 0.110616i | ||||
\(3\) | 1.54417 | + | 3.03060i | 0.514722 | + | 1.01020i | 0.991369 | + | 0.131104i | \(0.0418521\pi\) |
−0.476647 | + | 0.879095i | \(0.658148\pi\) | |||||||
\(4\) | 1.90211 | + | 0.618034i | 0.475528 | + | 0.154508i | ||||
\(5\) | −4.51960 | − | 2.13851i | −0.903920 | − | 0.427702i | ||||
\(6\) | 1.48643 | + | 4.57476i | 0.247738 | + | 0.762460i | ||||
\(7\) | −2.71827 | − | 2.71827i | −0.388324 | − | 0.388324i | 0.485765 | − | 0.874089i | \(-0.338541\pi\) |
−0.874089 | + | 0.485765i | \(0.838541\pi\) | |||||||
\(8\) | 2.52015 | + | 1.28408i | 0.315018 | + | 0.160510i | ||||
\(9\) | −1.51000 | + | 2.07833i | −0.167778 | + | 0.230926i | ||||
\(10\) | −5.83988 | − | 3.98695i | −0.583988 | − | 0.398695i | ||||
\(11\) | 13.9453 | − | 10.1318i | 1.26775 | − | 0.921077i | 0.268643 | − | 0.963240i | \(-0.413425\pi\) |
0.999111 | + | 0.0421629i | \(0.0134249\pi\) | |||||||
\(12\) | 1.06417 | + | 6.71888i | 0.0886806 | + | 0.559907i | ||||
\(13\) | −8.27725 | + | 1.31099i | −0.636711 | + | 0.100845i | −0.466441 | − | 0.884552i | \(-0.654464\pi\) |
−0.170270 | + | 0.985397i | \(0.554464\pi\) | |||||||
\(14\) | −3.19552 | − | 4.39825i | −0.228251 | − | 0.314161i | ||||
\(15\) | −0.498051 | − | 16.9993i | −0.0332034 | − | 1.13329i | ||||
\(16\) | 3.23607 | + | 2.35114i | 0.202254 | + | 0.146946i | ||||
\(17\) | −4.91940 | + | 9.65487i | −0.289377 | + | 0.567933i | −0.989233 | − | 0.146350i | \(-0.953247\pi\) |
0.699856 | + | 0.714284i | \(0.253247\pi\) | |||||||
\(18\) | −2.56896 | + | 2.56896i | −0.142720 | + | 0.142720i | ||||
\(19\) | −31.3075 | + | 10.1724i | −1.64776 | + | 0.535391i | −0.978254 | − | 0.207412i | \(-0.933496\pi\) |
−0.669510 | + | 0.742803i | \(0.733496\pi\) | |||||||
\(20\) | −7.27512 | − | 6.86095i | −0.363756 | − | 0.343048i | ||||
\(21\) | 4.04052 | − | 12.4354i | 0.192406 | − | 0.592164i | ||||
\(22\) | 21.7203 | − | 11.0670i | 0.987286 | − | 0.503047i | ||||
\(23\) | −1.39020 | + | 8.77738i | −0.0604435 | + | 0.381625i | 0.938860 | + | 0.344300i | \(0.111884\pi\) |
−0.999303 | + | 0.0373252i | \(0.988116\pi\) | |||||||
\(24\) | 9.62038i | 0.400849i | ||||||||
\(25\) | 15.8536 | + | 19.3304i | 0.634142 | + | 0.773217i | ||||
\(26\) | −11.8517 | −0.455835 | ||||||||
\(27\) | 21.6047 | + | 3.42185i | 0.800174 | + | 0.126735i | ||||
\(28\) | −3.49047 | − | 6.85044i | −0.124660 | − | 0.244659i | ||||
\(29\) | −2.63851 | − | 0.857304i | −0.0909831 | − | 0.0295622i | 0.263172 | − | 0.964749i | \(-0.415231\pi\) |
−0.354155 | + | 0.935187i | \(0.615231\pi\) | |||||||
\(30\) | 3.06510 | − | 23.8548i | 0.102170 | − | 0.795161i | ||||
\(31\) | −14.1220 | − | 43.4631i | −0.455549 | − | 1.40204i | −0.870490 | − | 0.492187i | \(-0.836198\pi\) |
0.414941 | − | 0.909848i | \(-0.363802\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 52.2394 | + | 26.6173i | 1.58301 | + | 0.806585i | ||||
\(34\) | −9.00739 | + | 12.3976i | −0.264923 | + | 0.364636i | ||||
\(35\) | 6.47244 | + | 18.0985i | 0.184927 | + | 0.517101i | ||||
\(36\) | −4.15667 | + | 3.02000i | −0.115463 | + | 0.0838888i | ||||
\(37\) | 8.87405 | + | 56.0286i | 0.239839 | + | 1.51429i | 0.754162 | + | 0.656689i | \(0.228043\pi\) |
−0.514323 | + | 0.857597i | \(0.671957\pi\) | |||||||
\(38\) | −45.9809 | + | 7.28265i | −1.21002 | + | 0.191649i | ||||
\(39\) | −16.7545 | − | 23.0606i | −0.429603 | − | 0.591298i | ||||
\(40\) | −8.64404 | − | 11.1929i | −0.216101 | − | 0.279822i | ||||
\(41\) | 46.2281 | + | 33.5867i | 1.12752 | + | 0.819188i | 0.985331 | − | 0.170652i | \(-0.0545874\pi\) |
0.142184 | + | 0.989840i | \(0.454587\pi\) | |||||||
\(42\) | 8.39492 | − | 16.4760i | 0.199879 | − | 0.392285i | ||||
\(43\) | −6.00015 | + | 6.00015i | −0.139538 | + | 0.139538i | −0.773426 | − | 0.633887i | \(-0.781458\pi\) |
0.633887 | + | 0.773426i | \(0.281458\pi\) | |||||||
\(44\) | 32.7873 | − | 10.6533i | 0.745167 | − | 0.242119i | ||||
\(45\) | 11.2691 | − | 6.16409i | 0.250425 | − | 0.136980i | ||||
\(46\) | −3.88367 | + | 11.9527i | −0.0844276 | + | 0.259842i | ||||
\(47\) | 22.4520 | − | 11.4399i | 0.477702 | − | 0.243401i | −0.198523 | − | 0.980096i | \(-0.563615\pi\) |
0.676225 | + | 0.736695i | \(0.263615\pi\) | |||||||
\(48\) | −2.12833 | + | 13.4378i | −0.0443403 | + | 0.279953i | ||||
\(49\) | − | 34.2220i | − | 0.698409i | ||||||
\(50\) | 17.8678 | + | 30.5081i | 0.357355 | + | 0.610161i | ||||
\(51\) | −36.8564 | −0.722674 | ||||||||
\(52\) | −16.5545 | − | 2.62197i | −0.318356 | − | 0.0504226i | ||||
\(53\) | −13.6421 | − | 26.7742i | −0.257399 | − | 0.505174i | 0.725755 | − | 0.687953i | \(-0.241491\pi\) |
−0.983154 | + | 0.182779i | \(0.941491\pi\) | |||||||
\(54\) | 29.4205 | + | 9.55929i | 0.544824 | + | 0.177024i | ||||
\(55\) | −84.6942 | + | 15.9697i | −1.53989 | + | 0.290359i | ||||
\(56\) | −3.35997 | − | 10.3409i | −0.0599994 | − | 0.184659i | ||||
\(57\) | −79.1725 | − | 79.1725i | −1.38899 | − | 1.38899i | ||||
\(58\) | −3.49581 | − | 1.78121i | −0.0602726 | − | 0.0307104i | ||||
\(59\) | 38.3329 | − | 52.7607i | 0.649710 | − | 0.894249i | −0.349376 | − | 0.936982i | \(-0.613607\pi\) |
0.999087 | + | 0.0427332i | \(0.0136065\pi\) | |||||||
\(60\) | 9.55879 | − | 32.6424i | 0.159313 | − | 0.544040i | ||||
\(61\) | −68.2457 | + | 49.5834i | −1.11878 | + | 0.812842i | −0.984024 | − | 0.178036i | \(-0.943026\pi\) |
−0.134758 | + | 0.990879i | \(0.543026\pi\) | |||||||
\(62\) | −10.1102 | − | 63.8336i | −0.163069 | − | 1.02957i | ||||
\(63\) | 9.75405 | − | 1.54489i | 0.154826 | − | 0.0245221i | ||||
\(64\) | 4.70228 | + | 6.47214i | 0.0734732 | + | 0.101127i | ||||
\(65\) | 40.2134 | + | 11.7758i | 0.618668 | + | 0.181167i | ||||
\(66\) | 67.0795 | + | 48.7361i | 1.01636 | + | 0.738426i | ||||
\(67\) | −17.3215 | + | 33.9954i | −0.258530 | + | 0.507394i | −0.983391 | − | 0.181502i | \(-0.941904\pi\) |
0.724861 | + | 0.688896i | \(0.241904\pi\) | |||||||
\(68\) | −15.3243 | + | 15.3243i | −0.225357 | + | 0.225357i | ||||
\(69\) | −28.7474 | + | 9.34060i | −0.416629 | + | 0.135371i | ||||
\(70\) | 5.03675 | + | 26.7120i | 0.0719536 | + | 0.381600i | ||||
\(71\) | 33.5080 | − | 103.127i | 0.471943 | − | 1.45249i | −0.378093 | − | 0.925768i | \(-0.623420\pi\) |
0.850036 | − | 0.526725i | \(-0.176580\pi\) | |||||||
\(72\) | −6.47416 | + | 3.29875i | −0.0899189 | + | 0.0458160i | ||||
\(73\) | 12.6356 | − | 79.7780i | 0.173090 | − | 1.09285i | −0.736223 | − | 0.676739i | \(-0.763393\pi\) |
0.909314 | − | 0.416111i | \(-0.136607\pi\) | |||||||
\(74\) | 80.2240i | 1.08411i | ||||||||
\(75\) | −34.1022 | + | 77.8951i | −0.454696 | + | 1.03860i | ||||
\(76\) | −65.8373 | −0.866281 | ||||||||
\(77\) | −65.4481 | − | 10.3660i | −0.849976 | − | 0.134623i | ||||
\(78\) | −18.3010 | − | 35.9177i | −0.234628 | − | 0.460484i | ||||
\(79\) | 39.1289 | + | 12.7138i | 0.495303 | + | 0.160934i | 0.546008 | − | 0.837780i | \(-0.316147\pi\) |
−0.0507051 | + | 0.998714i | \(0.516147\pi\) | |||||||
\(80\) | −9.59779 | − | 17.5466i | −0.119972 | − | 0.219332i | ||||
\(81\) | 30.1357 | + | 92.7481i | 0.372045 | + | 1.14504i | ||||
\(82\) | 57.1411 | + | 57.1411i | 0.696843 | + | 0.696843i | ||||
\(83\) | 32.1640 | + | 16.3884i | 0.387518 | + | 0.197451i | 0.636885 | − | 0.770959i | \(-0.280222\pi\) |
−0.249367 | + | 0.968409i | \(0.580222\pi\) | |||||||
\(84\) | 15.3710 | − | 21.1564i | 0.182989 | − | 0.251862i | ||||
\(85\) | 42.8808 | − | 33.1159i | 0.504479 | − | 0.389599i | ||||
\(86\) | −9.70844 | + | 7.05360i | −0.112889 | + | 0.0820186i | ||||
\(87\) | −1.47615 | − | 9.32008i | −0.0169673 | − | 0.107127i | ||||
\(88\) | 48.1543 | − | 7.62689i | 0.547208 | − | 0.0866692i | ||||
\(89\) | 57.7869 | + | 79.5368i | 0.649291 | + | 0.893672i | 0.999068 | − | 0.0431607i | \(-0.0137427\pi\) |
−0.349777 | + | 0.936833i | \(0.613743\pi\) | |||||||
\(90\) | 17.1044 | − | 6.11693i | 0.190049 | − | 0.0679658i | ||||
\(91\) | 26.0634 | + | 18.9362i | 0.286411 | + | 0.208090i | ||||
\(92\) | −8.06904 | + | 15.8364i | −0.0877069 | + | 0.172135i | ||||
\(93\) | 109.912 | − | 109.912i | 1.18185 | − | 1.18185i | ||||
\(94\) | 33.8919 | − | 11.0121i | 0.360552 | − | 0.117150i | ||||
\(95\) | 163.251 | + | 20.9761i | 1.71843 | + | 0.220801i | ||||
\(96\) | −5.94572 | + | 18.2990i | −0.0619346 | + | 0.190615i | ||||
\(97\) | −72.8156 | + | 37.1014i | −0.750677 | + | 0.382489i | −0.787082 | − | 0.616848i | \(-0.788409\pi\) |
0.0364055 | + | 0.999337i | \(0.488409\pi\) | |||||||
\(98\) | 7.57100 | − | 47.8014i | 0.0772551 | − | 0.487769i | ||||
\(99\) | 44.2820i | 0.447293i | ||||||||
\(100\) | 18.2084 | + | 46.5667i | 0.182084 | + | 0.465667i | ||||
\(101\) | −24.9483 | −0.247013 | −0.123506 | − | 0.992344i | \(-0.539414\pi\) | ||||
−0.123506 | + | 0.992344i | \(0.539414\pi\) | |||||||
\(102\) | −51.4811 | − | 8.15380i | −0.504716 | − | 0.0799392i | ||||
\(103\) | −45.5971 | − | 89.4893i | −0.442690 | − | 0.868828i | −0.999276 | − | 0.0380385i | \(-0.987889\pi\) |
0.556586 | − | 0.830790i | \(-0.312111\pi\) | |||||||
\(104\) | −22.5433 | − | 7.32476i | −0.216762 | − | 0.0704304i | ||||
\(105\) | −44.8548 | + | 47.5625i | −0.427189 | + | 0.452976i | ||||
\(106\) | −13.1321 | − | 40.4164i | −0.123887 | − | 0.381286i | ||||
\(107\) | 22.8729 | + | 22.8729i | 0.213765 | + | 0.213765i | 0.805865 | − | 0.592100i | \(-0.201701\pi\) |
−0.592100 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(108\) | 38.9798 | + | 19.8612i | 0.360924 | + | 0.183900i | ||||
\(109\) | −8.46118 | + | 11.6458i | −0.0776255 | + | 0.106842i | −0.846064 | − | 0.533081i | \(-0.821034\pi\) |
0.768439 | + | 0.639924i | \(0.221034\pi\) | |||||||
\(110\) | −121.834 | + | 3.56953i | −1.10758 | + | 0.0324503i | ||||
\(111\) | −156.097 | + | 113.411i | −1.40628 | + | 1.02172i | ||||
\(112\) | −2.40547 | − | 15.1875i | −0.0214774 | − | 0.135603i | ||||
\(113\) | −204.622 | + | 32.4090i | −1.81082 | + | 0.286805i | −0.967918 | − | 0.251265i | \(-0.919154\pi\) |
−0.842900 | + | 0.538070i | \(0.819154\pi\) | |||||||
\(114\) | −93.0729 | − | 128.104i | −0.816429 | − | 1.12372i | ||||
\(115\) | 25.0537 | − | 36.6973i | 0.217858 | − | 0.319107i | ||||
\(116\) | −4.48890 | − | 3.26138i | −0.0386974 | − | 0.0281153i | ||||
\(117\) | 9.77395 | − | 19.1825i | 0.0835381 | − | 0.163953i | ||||
\(118\) | 65.2158 | − | 65.2158i | 0.552676 | − | 0.552676i | ||||
\(119\) | 39.6168 | − | 12.8723i | 0.332914 | − | 0.108170i | ||||
\(120\) | 20.5733 | − | 43.4803i | 0.171444 | − | 0.362335i | ||||
\(121\) | 54.4257 | − | 167.505i | 0.449800 | − | 1.38434i | ||||
\(122\) | −106.295 | + | 54.1601i | −0.871271 | + | 0.443935i | ||||
\(123\) | −30.4038 | + | 191.962i | −0.247186 | + | 1.56067i | ||||
\(124\) | − | 91.3996i | − | 0.737094i | ||||||
\(125\) | −30.3134 | − | 121.269i | −0.242507 | − | 0.970150i | ||||
\(126\) | 13.9663 | 0.110843 | ||||||||
\(127\) | 168.207 | + | 26.6413i | 1.32446 | + | 0.209774i | 0.778293 | − | 0.627901i | \(-0.216086\pi\) |
0.546169 | + | 0.837675i | \(0.316086\pi\) | |||||||
\(128\) | 5.13632 | + | 10.0806i | 0.0401275 | + | 0.0787546i | ||||
\(129\) | −27.4492 | − | 8.91880i | −0.212785 | − | 0.0691380i | ||||
\(130\) | 53.5650 | + | 25.3450i | 0.412038 | + | 0.194961i | ||||
\(131\) | −1.22385 | − | 3.76662i | −0.00934236 | − | 0.0287528i | 0.946277 | − | 0.323358i | \(-0.104812\pi\) |
−0.955619 | + | 0.294605i | \(0.904812\pi\) | |||||||
\(132\) | 82.9148 | + | 82.9148i | 0.628142 | + | 0.628142i | ||||
\(133\) | 112.754 | + | 57.4508i | 0.847772 | + | 0.431961i | ||||
\(134\) | −31.7156 | + | 43.6528i | −0.236683 | + | 0.325767i | ||||
\(135\) | −90.3269 | − | 61.6672i | −0.669088 | − | 0.456794i | ||||
\(136\) | −24.7952 | + | 18.0148i | −0.182318 | + | 0.132462i | ||||
\(137\) | −33.2579 | − | 209.982i | −0.242758 | − | 1.53272i | −0.744456 | − | 0.667672i | \(-0.767291\pi\) |
0.501697 | − | 0.865043i | \(-0.332709\pi\) | |||||||
\(138\) | −42.2209 | + | 6.68713i | −0.305948 | + | 0.0484575i | ||||
\(139\) | 18.0245 | + | 24.8086i | 0.129672 | + | 0.178479i | 0.868916 | − | 0.494959i | \(-0.164817\pi\) |
−0.739244 | + | 0.673438i | \(0.764817\pi\) | |||||||
\(140\) | 1.12581 | + | 38.4256i | 0.00804148 | + | 0.274469i | ||||
\(141\) | 69.3392 | + | 50.3779i | 0.491768 | + | 0.357290i | ||||
\(142\) | 69.6190 | − | 136.635i | 0.490275 | − | 0.962218i | ||||
\(143\) | −102.146 | + | 102.146i | −0.714307 | + | 0.714307i | ||||
\(144\) | −9.77291 | + | 3.17541i | −0.0678674 | + | 0.0220515i | ||||
\(145\) | 10.0917 | + | 9.51715i | 0.0695976 | + | 0.0656355i | ||||
\(146\) | 35.2989 | − | 108.639i | 0.241773 | − | 0.744101i | ||||
\(147\) | 103.713 | − | 52.8445i | 0.705532 | − | 0.359486i | ||||
\(148\) | −17.7481 | + | 112.057i | −0.119920 | + | 0.757143i | ||||
\(149\) | 17.7382i | 0.119048i | 0.998227 | + | 0.0595242i | \(0.0189584\pi\) | ||||
−0.998227 | + | 0.0595242i | \(0.981042\pi\) | |||||||
\(150\) | −64.8668 | + | 101.260i | −0.432446 | + | 0.675064i | ||||
\(151\) | 82.5008 | 0.546363 | 0.273181 | − | 0.961963i | \(-0.411924\pi\) | ||||
0.273181 | + | 0.961963i | \(0.411924\pi\) | |||||||
\(152\) | −91.9617 | − | 14.5653i | −0.605011 | − | 0.0958244i | ||||
\(153\) | −12.6378 | − | 24.8030i | −0.0825997 | − | 0.162111i | ||||
\(154\) | −89.1248 | − | 28.9584i | −0.578733 | − | 0.188042i | ||||
\(155\) | −29.1204 | + | 226.636i | −0.187874 | + | 1.46217i | ||||
\(156\) | −17.6167 | − | 54.2187i | −0.112928 | − | 0.347556i | ||||
\(157\) | 49.4887 | + | 49.4887i | 0.315215 | + | 0.315215i | 0.846926 | − | 0.531711i | \(-0.178451\pi\) |
−0.531711 | + | 0.846926i | \(0.678451\pi\) | |||||||
\(158\) | 51.8427 | + | 26.4152i | 0.328118 | + | 0.167185i | ||||
\(159\) | 60.0761 | − | 82.6877i | 0.377837 | − | 0.520048i | ||||
\(160\) | −9.52436 | − | 26.6324i | −0.0595272 | − | 0.166453i | ||||
\(161\) | 27.6382 | − | 20.0803i | 0.171666 | − | 0.124723i | ||||
\(162\) | 21.5748 | + | 136.218i | 0.133178 | + | 0.840850i | ||||
\(163\) | −72.4915 | + | 11.4815i | −0.444733 | + | 0.0704388i | −0.374785 | − | 0.927112i | \(-0.622283\pi\) |
−0.0699483 | + | 0.997551i | \(0.522283\pi\) | |||||||
\(164\) | 67.1734 | + | 92.4563i | 0.409594 | + | 0.563758i | ||||
\(165\) | −179.180 | − | 232.014i | −1.08594 | − | 1.40614i | ||||
\(166\) | 41.3012 | + | 30.0071i | 0.248802 | + | 0.180765i | ||||
\(167\) | 2.01337 | − | 3.95145i | 0.0120561 | − | 0.0236614i | −0.884900 | − | 0.465781i | \(-0.845773\pi\) |
0.896956 | + | 0.442120i | \(0.145773\pi\) | |||||||
\(168\) | 26.1508 | − | 26.1508i | 0.155659 | − | 0.155659i | ||||
\(169\) | −93.9344 | + | 30.5212i | −0.555825 | + | 0.180599i | ||||
\(170\) | 67.2222 | − | 36.7698i | 0.395425 | − | 0.216293i | ||||
\(171\) | 26.1326 | − | 80.4278i | 0.152822 | − | 0.470338i | ||||
\(172\) | −15.1213 | + | 7.70466i | −0.0879143 | + | 0.0447946i | ||||
\(173\) | −48.0579 | + | 303.425i | −0.277791 | + | 1.75390i | 0.315509 | + | 0.948923i | \(0.397825\pi\) |
−0.593300 | + | 0.804981i | \(0.702175\pi\) | |||||||
\(174\) | − | 13.3449i | − | 0.0766947i | ||||||
\(175\) | 9.45105 | − | 95.6395i | 0.0540060 | − | 0.546511i | ||||
\(176\) | 68.9493 | 0.391757 | ||||||||
\(177\) | 219.089 | + | 34.7002i | 1.23779 | + | 0.196047i | ||||
\(178\) | 63.1208 | + | 123.882i | 0.354611 | + | 0.695964i | ||||
\(179\) | −41.8910 | − | 13.6112i | −0.234028 | − | 0.0760402i | 0.189655 | − | 0.981851i | \(-0.439263\pi\) |
−0.423683 | + | 0.905811i | \(0.639263\pi\) | |||||||
\(180\) | 25.2448 | − | 4.76009i | 0.140249 | − | 0.0264450i | ||||
\(181\) | 79.7074 | + | 245.314i | 0.440372 | + | 1.35533i | 0.887480 | + | 0.460847i | \(0.152454\pi\) |
−0.447107 | + | 0.894480i | \(0.647546\pi\) | |||||||
\(182\) | 32.2161 | + | 32.2161i | 0.177012 | + | 0.177012i | ||||
\(183\) | −255.650 | − | 130.260i | −1.39699 | − | 0.711804i | ||||
\(184\) | −14.7744 | + | 20.3352i | −0.0802954 | + | 0.110517i | ||||
\(185\) | 79.7105 | − | 272.204i | 0.430867 | − | 1.47137i | ||||
\(186\) | 177.842 | − | 129.210i | 0.956139 | − | 0.694676i | ||||
\(187\) | 29.2192 | + | 184.483i | 0.156252 | + | 0.986538i | ||||
\(188\) | 49.7765 | − | 7.88382i | 0.264769 | − | 0.0419352i | ||||
\(189\) | −49.4259 | − | 68.0289i | −0.261513 | − | 0.359941i | ||||
\(190\) | 223.389 | + | 65.4159i | 1.17573 | + | 0.344294i | ||||
\(191\) | −101.886 | − | 74.0247i | −0.533436 | − | 0.387564i | 0.288206 | − | 0.957569i | \(-0.406941\pi\) |
−0.821641 | + | 0.570005i | \(0.806941\pi\) | |||||||
\(192\) | −12.3533 | + | 24.2448i | −0.0643402 | + | 0.126275i | ||||
\(193\) | 159.169 | − | 159.169i | 0.824708 | − | 0.824708i | −0.162071 | − | 0.986779i | \(-0.551817\pi\) |
0.986779 | + | 0.162071i | \(0.0518174\pi\) | |||||||
\(194\) | −109.917 | + | 35.7142i | −0.566583 | + | 0.184094i | ||||
\(195\) | 26.4083 | + | 140.054i | 0.135427 | + | 0.718228i | ||||
\(196\) | 21.1504 | − | 65.0942i | 0.107910 | − | 0.332113i | ||||
\(197\) | 55.3779 | − | 28.2164i | 0.281106 | − | 0.143231i | −0.307753 | − | 0.951466i | \(-0.599577\pi\) |
0.588859 | + | 0.808235i | \(0.299577\pi\) | |||||||
\(198\) | −9.79659 | + | 61.8532i | −0.0494777 | + | 0.312390i | ||||
\(199\) | − | 137.580i | − | 0.691357i | −0.938353 | − | 0.345679i | \(-0.887649\pi\) | ||
0.938353 | − | 0.345679i | \(-0.112351\pi\) | |||||||
\(200\) | 15.1315 | + | 69.0727i | 0.0756575 | + | 0.345363i | ||||
\(201\) | −129.774 | −0.645640 | ||||||||
\(202\) | −34.8478 | − | 5.51935i | −0.172514 | − | 0.0273235i | ||||
\(203\) | 4.84180 | + | 9.50256i | 0.0238512 | + | 0.0468106i | ||||
\(204\) | −70.1050 | − | 22.7785i | −0.343652 | − | 0.111659i | ||||
\(205\) | −137.107 | − | 250.658i | −0.668815 | − | 1.22272i | ||||
\(206\) | −43.8922 | − | 135.086i | −0.213069 | − | 0.655759i | ||||
\(207\) | −16.1431 | − | 16.1431i | −0.0779861 | − | 0.0779861i | ||||
\(208\) | −29.8680 | − | 15.2185i | −0.143596 | − | 0.0731660i | ||||
\(209\) | −333.527 | + | 459.060i | −1.59582 | + | 2.19646i | ||||
\(210\) | −73.1757 | + | 56.5121i | −0.348455 | + | 0.269105i | ||||
\(211\) | −149.606 | + | 108.695i | −0.709033 | + | 0.515142i | −0.882861 | − | 0.469634i | \(-0.844386\pi\) |
0.173829 | + | 0.984776i | \(0.444386\pi\) | |||||||
\(212\) | −9.40152 | − | 59.3589i | −0.0443468 | − | 0.279995i | ||||
\(213\) | 364.278 | − | 57.6960i | 1.71023 | − | 0.270873i | ||||
\(214\) | 26.8887 | + | 37.0091i | 0.125648 | + | 0.172940i | ||||
\(215\) | 39.9496 | − | 14.2869i | 0.185812 | − | 0.0664506i | ||||
\(216\) | 50.0531 | + | 36.3657i | 0.231727 | + | 0.168360i | ||||
\(217\) | −79.7570 | + | 156.532i | −0.367544 | + | 0.721345i | ||||
\(218\) | −14.3950 | + | 14.3950i | −0.0660322 | + | 0.0660322i | ||||
\(219\) | 261.286 | − | 84.8971i | 1.19309 | − | 0.387658i | ||||
\(220\) | −170.968 | − | 21.9676i | −0.777126 | − | 0.0998528i | ||||
\(221\) | 28.0617 | − | 86.3650i | 0.126976 | − | 0.390792i | ||||
\(222\) | −243.127 | + | 123.879i | −1.09517 | + | 0.558015i | ||||
\(223\) | 44.3027 | − | 279.716i | 0.198667 | − | 1.25433i | −0.663681 | − | 0.748016i | \(-0.731007\pi\) |
0.862348 | − | 0.506316i | \(-0.168993\pi\) | |||||||
\(224\) | − | 21.7462i | − | 0.0970810i | ||||||
\(225\) | −64.1139 | + | 3.76009i | −0.284951 | + | 0.0167115i | ||||
\(226\) | −292.987 | −1.29640 | ||||||||
\(227\) | −86.9133 | − | 13.7657i | −0.382878 | − | 0.0606419i | −0.0379711 | − | 0.999279i | \(-0.512089\pi\) |
−0.344907 | + | 0.938637i | \(0.612089\pi\) | |||||||
\(228\) | −101.664 | − | 199.526i | −0.445894 | − | 0.875116i | ||||
\(229\) | −1.53872 | − | 0.499961i | −0.00671931 | − | 0.00218324i | 0.305655 | − | 0.952142i | \(-0.401124\pi\) |
−0.312375 | + | 0.949959i | \(0.601124\pi\) | |||||||
\(230\) | 43.1136 | − | 45.7162i | 0.187451 | − | 0.198766i | ||||
\(231\) | −69.6477 | − | 214.354i | −0.301505 | − | 0.927938i | ||||
\(232\) | −5.54859 | − | 5.54859i | −0.0239163 | − | 0.0239163i | ||||
\(233\) | −68.7608 | − | 35.0354i | −0.295111 | − | 0.150366i | 0.300166 | − | 0.953887i | \(-0.402958\pi\) |
−0.595277 | + | 0.803520i | \(0.702958\pi\) | |||||||
\(234\) | 17.8960 | − | 24.6318i | 0.0764788 | − | 0.105264i | ||||
\(235\) | −125.938 | + | 3.68978i | −0.535908 | + | 0.0157012i | ||||
\(236\) | 105.521 | − | 76.6658i | 0.447125 | − | 0.324855i | ||||
\(237\) | 21.8913 | + | 138.216i | 0.0923683 | + | 0.583190i | ||||
\(238\) | 58.1846 | − | 9.21553i | 0.244473 | − | 0.0387207i | ||||
\(239\) | 5.89389 | + | 8.11224i | 0.0246606 | + | 0.0339424i | 0.821169 | − | 0.570685i | \(-0.193322\pi\) |
−0.796509 | + | 0.604627i | \(0.793322\pi\) | |||||||
\(240\) | 38.3560 | − | 56.1819i | 0.159817 | − | 0.234091i | ||||
\(241\) | 172.450 | + | 125.292i | 0.715559 | + | 0.519884i | 0.884962 | − | 0.465663i | \(-0.154184\pi\) |
−0.169404 | + | 0.985547i | \(0.554184\pi\) | |||||||
\(242\) | 113.079 | − | 221.931i | 0.467271 | − | 0.917070i | ||||
\(243\) | −95.3421 | + | 95.3421i | −0.392355 | + | 0.392355i | ||||
\(244\) | −160.455 | + | 52.1351i | −0.657603 | + | 0.213668i | ||||
\(245\) | −73.1841 | + | 154.670i | −0.298711 | + | 0.631305i | ||||
\(246\) | −84.9363 | + | 261.407i | −0.345270 | + | 1.06263i | ||||
\(247\) | 245.804 | − | 125.243i | 0.995158 | − | 0.507058i | ||||
\(248\) | 20.2205 | − | 127.667i | 0.0815343 | − | 0.514787i | ||||
\(249\) | 122.783i | 0.493103i | ||||||||
\(250\) | −15.5134 | − | 176.095i | −0.0620534 | − | 0.704379i | ||||
\(251\) | 350.719 | 1.39729 | 0.698643 | − | 0.715471i | \(-0.253788\pi\) | ||||
0.698643 | + | 0.715471i | \(0.253788\pi\) | |||||||
\(252\) | 19.5081 | + | 3.08978i | 0.0774131 | + | 0.0122610i | ||||
\(253\) | 69.5443 | + | 136.488i | 0.274879 | + | 0.539480i | ||||
\(254\) | 229.058 | + | 74.4253i | 0.901802 | + | 0.293013i | ||||
\(255\) | 166.576 | + | 78.8177i | 0.653239 | + | 0.309089i | ||||
\(256\) | 4.94427 | + | 15.2169i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −351.169 | − | 351.169i | −1.36642 | − | 1.36642i | −0.865489 | − | 0.500928i | \(-0.832992\pi\) |
−0.500928 | − | 0.865489i | \(-0.667008\pi\) | |||||||
\(258\) | −36.3680 | − | 18.5304i | −0.140961 | − | 0.0718234i | ||||
\(259\) | 128.179 | − | 176.423i | 0.494898 | − | 0.681169i | ||||
\(260\) | 69.2125 | + | 47.2522i | 0.266202 | + | 0.181739i | ||||
\(261\) | 5.76591 | − | 4.18918i | 0.0220916 | − | 0.0160505i | ||||
\(262\) | −0.876179 | − | 5.53198i | −0.00334420 | − | 0.0211144i | ||||
\(263\) | −82.1738 | + | 13.0151i | −0.312448 | + | 0.0494869i | −0.310689 | − | 0.950512i | \(-0.600560\pi\) |
−0.00175874 | + | 0.999998i | \(0.500560\pi\) | |||||||
\(264\) | 97.4722 | + | 134.159i | 0.369213 | + | 0.508178i | ||||
\(265\) | 4.40010 | + | 150.183i | 0.0166041 | + | 0.566727i | ||||
\(266\) | 144.785 | + | 105.192i | 0.544303 | + | 0.395459i | ||||
\(267\) | −151.811 | + | 297.947i | −0.568582 | + | 1.11591i | ||||
\(268\) | −53.9578 | + | 53.9578i | −0.201335 | + | 0.201335i | ||||
\(269\) | 214.251 | − | 69.6142i | 0.796470 | − | 0.258789i | 0.117613 | − | 0.993059i | \(-0.462476\pi\) |
0.678857 | + | 0.734271i | \(0.262476\pi\) | |||||||
\(270\) | −112.526 | − | 106.120i | −0.416763 | − | 0.393038i | ||||
\(271\) | −108.531 | + | 334.023i | −0.400482 | + | 1.23256i | 0.524128 | + | 0.851640i | \(0.324391\pi\) |
−0.924610 | + | 0.380916i | \(0.875609\pi\) | |||||||
\(272\) | −38.6195 | + | 19.6776i | −0.141983 | + | 0.0723441i | ||||
\(273\) | −17.1417 | + | 108.228i | −0.0627900 | + | 0.396440i | ||||
\(274\) | − | 300.661i | − | 1.09730i | ||||||
\(275\) | 416.935 | + | 108.942i | 1.51613 | + | 0.396154i | ||||
\(276\) | −60.4536 | −0.219035 | ||||||||
\(277\) | −316.145 | − | 50.0724i | −1.14132 | − | 0.180767i | −0.442977 | − | 0.896533i | \(-0.646078\pi\) |
−0.698340 | + | 0.715766i | \(0.746078\pi\) | |||||||
\(278\) | 19.6882 | + | 38.6402i | 0.0708208 | + | 0.138994i | ||||
\(279\) | 111.655 | + | 36.2789i | 0.400197 | + | 0.130032i | ||||
\(280\) | −6.92844 | + | 53.9221i | −0.0247444 | + | 0.192579i | ||||
\(281\) | 28.9023 | + | 88.9520i | 0.102855 | + | 0.316555i | 0.989221 | − | 0.146430i | \(-0.0467783\pi\) |
−0.886366 | + | 0.462985i | \(0.846778\pi\) | |||||||
\(282\) | 85.7080 | + | 85.7080i | 0.303929 | + | 0.303929i | ||||
\(283\) | 30.4450 | + | 15.5125i | 0.107579 | + | 0.0548144i | 0.506952 | − | 0.861974i | \(-0.330772\pi\) |
−0.399373 | + | 0.916789i | \(0.630772\pi\) | |||||||
\(284\) | 127.472 | − | 175.450i | 0.448845 | − | 0.617782i | ||||
\(285\) | 188.517 | + | 527.139i | 0.661462 | + | 1.84961i | ||||
\(286\) | −165.275 | + | 120.080i | −0.577886 | + | 0.419859i | ||||
\(287\) | −34.3628 | − | 216.958i | −0.119731 | − | 0.755952i | ||||
\(288\) | −14.3533 | + | 2.27334i | −0.0498379 | + | 0.00789355i | ||||
\(289\) | 100.854 | + | 138.814i | 0.348976 | + | 0.480324i | ||||
\(290\) | 11.9905 | + | 15.5262i | 0.0413467 | + | 0.0535385i | ||||
\(291\) | −224.879 | − | 163.384i | −0.772779 | − | 0.561457i | ||||
\(292\) | 73.3399 | − | 143.938i | 0.251164 | − | 0.492937i | ||||
\(293\) | 115.262 | − | 115.262i | 0.393385 | − | 0.393385i | −0.482507 | − | 0.875892i | \(-0.660274\pi\) |
0.875892 | + | 0.482507i | \(0.160274\pi\) | |||||||
\(294\) | 156.558 | − | 50.8687i | 0.532509 | − | 0.173023i | ||||
\(295\) | −286.079 | + | 156.482i | −0.969758 | + | 0.530447i | ||||
\(296\) | −49.5812 | + | 152.595i | −0.167504 | + | 0.515524i | ||||
\(297\) | 335.953 | − | 171.177i | 1.13116 | − | 0.576353i | ||||
\(298\) | −3.92426 | + | 24.7768i | −0.0131687 | + | 0.0831436i | ||||
\(299\) | − | 74.4751i | − | 0.249081i | ||||||
\(300\) | −113.008 | + | 127.089i | −0.376693 | + | 0.423630i | ||||
\(301\) | 32.6200 | 0.108372 | ||||||||
\(302\) | 115.237 | + | 18.2518i | 0.381580 | + | 0.0604364i | ||||
\(303\) | −38.5243 | − | 75.6082i | −0.127143 | − | 0.249532i | ||||
\(304\) | −125.230 | − | 40.6897i | −0.411941 | − | 0.133848i | ||||
\(305\) | 414.478 | − | 78.1530i | 1.35894 | − | 0.256239i | ||||
\(306\) | −12.1652 | − | 37.4407i | −0.0397557 | − | 0.122355i | ||||
\(307\) | −363.925 | − | 363.925i | −1.18542 | − | 1.18542i | −0.978319 | − | 0.207103i | \(-0.933597\pi\) |
−0.207103 | − | 0.978319i | \(-0.566403\pi\) | |||||||
\(308\) | −118.083 | − | 60.1664i | −0.383387 | − | 0.195346i | ||||
\(309\) | 200.797 | − | 276.373i | 0.649827 | − | 0.894410i | ||||
\(310\) | −90.8145 | + | 310.123i | −0.292950 | + | 1.00040i | ||||
\(311\) | −52.7135 | + | 38.2986i | −0.169497 | + | 0.123147i | −0.669300 | − | 0.742993i | \(-0.733406\pi\) |
0.499803 | + | 0.866139i | \(0.333406\pi\) | |||||||
\(312\) | −12.6122 | − | 79.6302i | −0.0404237 | − | 0.255225i | ||||
\(313\) | −79.9313 | + | 12.6599i | −0.255371 | + | 0.0404469i | −0.282807 | − | 0.959177i | \(-0.591266\pi\) |
0.0274360 | + | 0.999624i | \(0.491266\pi\) | |||||||
\(314\) | 58.1775 | + | 80.0745i | 0.185279 | + | 0.255014i | ||||
\(315\) | −47.3882 | − | 13.8769i | −0.150439 | − | 0.0440535i | ||||
\(316\) | 66.5701 | + | 48.3660i | 0.210665 | + | 0.153057i | ||||
\(317\) | −123.024 | + | 241.447i | −0.388087 | + | 0.761664i | −0.999562 | − | 0.0296003i | \(-0.990577\pi\) |
0.611475 | + | 0.791264i | \(0.290577\pi\) | |||||||
\(318\) | 102.208 | − | 102.208i | 0.321407 | − | 0.321407i | ||||
\(319\) | −45.4808 | + | 14.7776i | −0.142573 | + | 0.0463248i | ||||
\(320\) | −7.41170 | − | 39.3073i | −0.0231616 | − | 0.122835i | ||||
\(321\) | −33.9989 | + | 104.638i | −0.105916 | + | 0.325975i | ||||
\(322\) | 43.0475 | − | 21.9338i | 0.133688 | − | 0.0681175i | ||||
\(323\) | 55.8008 | − | 352.312i | 0.172758 | − | 1.09075i | ||||
\(324\) | 195.042i | 0.601982i | ||||||||
\(325\) | −156.566 | − | 139.219i | −0.481740 | − | 0.428365i | ||||
\(326\) | −103.796 | −0.318394 | ||||||||
\(327\) | −48.3592 | − | 7.65935i | −0.147888 | − | 0.0234231i | ||||
\(328\) | 73.3737 | + | 144.004i | 0.223700 | + | 0.439037i | ||||
\(329\) | −92.1273 | − | 29.9340i | −0.280022 | − | 0.0909847i | ||||
\(330\) | −198.950 | − | 363.718i | −0.602878 | − | 1.10218i | ||||
\(331\) | −112.045 | − | 344.840i | −0.338506 | − | 1.04181i | −0.964969 | − | 0.262363i | \(-0.915498\pi\) |
0.626464 | − | 0.779451i | \(-0.284502\pi\) | |||||||
\(332\) | 51.0510 | + | 51.0510i | 0.153768 | + | 0.153768i | ||||
\(333\) | −129.846 | − | 66.1598i | −0.389927 | − | 0.198678i | ||||
\(334\) | 3.68646 | − | 5.07398i | 0.0110373 | − | 0.0151916i | ||||
\(335\) | 150.986 | − | 116.603i | 0.450704 | − | 0.348069i | ||||
\(336\) | 42.3129 | − | 30.7421i | 0.125931 | − | 0.0914943i | ||||
\(337\) | 27.6755 | + | 174.736i | 0.0821231 | + | 0.518505i | 0.994118 | + | 0.108303i | \(0.0345417\pi\) |
−0.911995 | + | 0.410202i | \(0.865458\pi\) | |||||||
\(338\) | −137.960 | + | 21.8507i | −0.408166 | + | 0.0646471i | ||||
\(339\) | −414.190 | − | 570.083i | −1.22180 | − | 1.68166i | ||||
\(340\) | 102.031 | − | 36.4885i | 0.300091 | − | 0.107319i | ||||
\(341\) | −637.297 | − | 463.023i | −1.86891 | − | 1.35784i | ||||
\(342\) | 54.2952 | − | 106.560i | 0.158758 | − | 0.311580i | ||||
\(343\) | −226.220 | + | 226.220i | −0.659533 | + | 0.659533i | ||||
\(344\) | −22.8259 | + | 7.41659i | −0.0663544 | + | 0.0215599i | ||||
\(345\) | 149.902 | + | 19.2608i | 0.434498 | + | 0.0558285i | ||||
\(346\) | −134.255 | + | 413.193i | −0.388019 | + | 1.19420i | ||||
\(347\) | −192.498 | + | 98.0825i | −0.554748 | + | 0.282658i | −0.708806 | − | 0.705403i | \(-0.750766\pi\) |
0.154058 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(348\) | 2.95231 | − | 18.6402i | 0.00848365 | − | 0.0535637i | ||||
\(349\) | 182.332i | 0.522441i | 0.965279 | + | 0.261220i | \(0.0841250\pi\) | ||||
−0.965279 | + | 0.261220i | \(0.915875\pi\) | |||||||
\(350\) | 34.3597 | − | 131.499i | 0.0981707 | − | 0.375710i | ||||
\(351\) | −183.313 | −0.522260 | ||||||||
\(352\) | 96.3085 | + | 15.2538i | 0.273604 | + | 0.0433346i | ||||
\(353\) | 57.6752 | + | 113.194i | 0.163386 | + | 0.320663i | 0.958155 | − | 0.286248i | \(-0.0924083\pi\) |
−0.794769 | + | 0.606911i | \(0.792408\pi\) | |||||||
\(354\) | 298.347 | + | 96.9388i | 0.842788 | + | 0.273838i | ||||
\(355\) | −371.981 | + | 394.435i | −1.04783 | + | 1.11109i | ||||
\(356\) | 60.7607 | + | 187.002i | 0.170676 | + | 0.525287i | ||||
\(357\) | 100.186 | + | 100.186i | 0.280632 | + | 0.280632i | ||||
\(358\) | −55.5022 | − | 28.2798i | −0.155034 | − | 0.0789938i | ||||
\(359\) | −138.854 | + | 191.116i | −0.386780 | + | 0.532358i | −0.957365 | − | 0.288881i | \(-0.906717\pi\) |
0.570584 | + | 0.821239i | \(0.306717\pi\) | |||||||
\(360\) | 36.3150 | − | 1.06397i | 0.100875 | − | 0.00295547i | ||||
\(361\) | 584.627 | − | 424.756i | 1.61946 | − | 1.17661i | ||||
\(362\) | 57.0642 | + | 360.289i | 0.157636 | + | 0.995274i | ||||
\(363\) | 591.683 | − | 93.7134i | 1.62998 | − | 0.258164i | ||||
\(364\) | 37.8723 | + | 52.1268i | 0.104045 | + | 0.143205i | ||||
\(365\) | −227.714 | + | 333.543i | −0.623874 | + | 0.913817i | ||||
\(366\) | −328.275 | − | 238.505i | −0.896925 | − | 0.651654i | ||||
\(367\) | −58.6290 | + | 115.066i | −0.159752 | + | 0.313531i | −0.956983 | − | 0.290143i | \(-0.906297\pi\) |
0.797231 | + | 0.603674i | \(0.206297\pi\) | |||||||
\(368\) | −25.1356 | + | 25.1356i | −0.0683034 | + | 0.0683034i | ||||
\(369\) | −139.609 | + | 45.3616i | −0.378344 | + | 0.122931i | ||||
\(370\) | 171.560 | − | 362.580i | 0.463675 | − | 0.979947i | ||||
\(371\) | −35.6965 | + | 109.863i | −0.0962170 | + | 0.296125i | ||||
\(372\) | 276.995 | − | 141.136i | 0.744611 | − | 0.379398i | ||||
\(373\) | 78.9853 | − | 498.693i | 0.211757 | − | 1.33698i | −0.621205 | − | 0.783648i | \(-0.713356\pi\) |
0.832961 | − | 0.553331i | \(-0.186644\pi\) | |||||||
\(374\) | 264.150i | 0.706283i | ||||||||
\(375\) | 320.708 | − | 279.127i | 0.855220 | − | 0.744338i | ||||
\(376\) | 71.2721 | 0.189553 | ||||||||
\(377\) | 22.9635 | + | 3.63706i | 0.0609111 | + | 0.00964738i | ||||
\(378\) | −53.9880 | − | 105.957i | −0.142825 | − | 0.280311i | ||||
\(379\) | −89.7830 | − | 29.1723i | −0.236894 | − | 0.0769717i | 0.188164 | − | 0.982138i | \(-0.439746\pi\) |
−0.425058 | + | 0.905166i | \(0.639746\pi\) | |||||||
\(380\) | 297.558 | + | 140.794i | 0.783048 | + | 0.370510i | ||||
\(381\) | 179.000 | + | 550.905i | 0.469816 | + | 1.44595i | ||||
\(382\) | −125.938 | − | 125.938i | −0.329681 | − | 0.329681i | ||||
\(383\) | 325.615 | + | 165.909i | 0.850171 | + | 0.433184i | 0.824078 | − | 0.566476i | \(-0.191694\pi\) |
0.0260923 | + | 0.999660i | \(0.491694\pi\) | |||||||
\(384\) | −22.6189 | + | 31.1322i | −0.0589033 | + | 0.0810734i | ||||
\(385\) | 273.632 | + | 186.812i | 0.710732 | + | 0.485225i | ||||
\(386\) | 257.540 | − | 187.114i | 0.667203 | − | 0.484751i | ||||
\(387\) | −3.41010 | − | 21.5305i | −0.00881162 | − | 0.0556344i | ||||
\(388\) | −161.433 | + | 25.5686i | −0.416066 | + | 0.0658983i | ||||
\(389\) | −100.649 | − | 138.531i | −0.258737 | − | 0.356120i | 0.659810 | − | 0.751432i | \(-0.270637\pi\) |
−0.918547 | + | 0.395312i | \(0.870637\pi\) | |||||||
\(390\) | 5.90275 | + | 201.471i | 0.0151353 | + | 0.516591i | ||||
\(391\) | −77.9055 | − | 56.6017i | −0.199247 | − | 0.144761i | ||||
\(392\) | 43.9438 | − | 86.2445i | 0.112101 | − | 0.220012i | ||||
\(393\) | 9.52528 | − | 9.52528i | 0.0242373 | − | 0.0242373i | ||||
\(394\) | 83.5943 | − | 27.1614i | 0.212168 | − | 0.0689377i | ||||
\(395\) | −149.659 | − | 141.139i | −0.378882 | − | 0.357313i | ||||
\(396\) | −27.3678 | + | 84.2294i | −0.0691106 | + | 0.212701i | ||||
\(397\) | −170.110 | + | 86.6754i | −0.428489 | + | 0.218326i | −0.654915 | − | 0.755702i | \(-0.727296\pi\) |
0.226427 | + | 0.974028i | \(0.427296\pi\) | |||||||
\(398\) | 30.4371 | − | 192.172i | 0.0764751 | − | 0.482845i | ||||
\(399\) | 430.424i | 1.07876i | ||||||||
\(400\) | 5.85464 | + | 99.8285i | 0.0146366 | + | 0.249571i | ||||
\(401\) | 81.2535 | 0.202627 | 0.101314 | − | 0.994855i | \(-0.467695\pi\) | ||||
0.101314 | + | 0.994855i | \(0.467695\pi\) | |||||||
\(402\) | −181.268 | − | 28.7100i | −0.450915 | − | 0.0714180i | ||||
\(403\) | 173.871 | + | 341.241i | 0.431442 | + | 0.846752i | ||||
\(404\) | −47.4545 | − | 15.4189i | −0.117462 | − | 0.0381656i | ||||
\(405\) | 62.1415 | − | 483.630i | 0.153436 | − | 1.19415i | ||||
\(406\) | 4.66076 | + | 14.3444i | 0.0114797 | + | 0.0353309i | ||||
\(407\) | 691.424 | + | 691.424i | 1.69883 | + | 1.69883i | ||||
\(408\) | −92.8835 | − | 47.3265i | −0.227656 | − | 0.115996i | ||||
\(409\) | 142.583 | − | 196.249i | 0.348614 | − | 0.479825i | −0.598319 | − | 0.801258i | \(-0.704164\pi\) |
0.946932 | + | 0.321433i | \(0.104164\pi\) | |||||||
\(410\) | −136.058 | − | 380.452i | −0.331849 | − | 0.927931i | ||||
\(411\) | 585.015 | − | 425.038i | 1.42339 | − | 1.03416i | ||||
\(412\) | −31.4234 | − | 198.399i | −0.0762703 | − | 0.481552i | ||||
\(413\) | −247.617 | + | 39.2187i | −0.599557 | + | 0.0949605i | ||||
\(414\) | −18.9774 | − | 26.1201i | −0.0458391 | − | 0.0630921i | ||||
\(415\) | −110.322 | − | 142.852i | −0.265836 | − | 0.344222i | ||||
\(416\) | −38.3529 | − | 27.8650i | −0.0921945 | − | 0.0669833i | ||||
\(417\) | −47.3519 | + | 92.9334i | −0.113554 | + | 0.222862i | ||||
\(418\) | −567.430 | + | 567.430i | −1.35749 | + | 1.35749i | ||||
\(419\) | −313.535 | + | 101.874i | −0.748294 | + | 0.243136i | −0.658247 | − | 0.752802i | \(-0.728702\pi\) |
−0.0900473 | + | 0.995937i | \(0.528702\pi\) | |||||||
\(420\) | −114.714 | + | 62.7474i | −0.273129 | + | 0.149399i | ||||
\(421\) | −34.6749 | + | 106.718i | −0.0823633 | + | 0.253488i | −0.983755 | − | 0.179517i | \(-0.942547\pi\) |
0.901392 | + | 0.433005i | \(0.142547\pi\) | |||||||
\(422\) | −233.017 | + | 118.728i | −0.552172 | + | 0.281346i | ||||
\(423\) | −10.1266 | + | 63.9369i | −0.0239400 | + | 0.151151i | ||||
\(424\) | − | 84.9925i | − | 0.200454i | ||||||
\(425\) | −264.623 | + | 57.9699i | −0.622641 | + | 0.136400i | ||||
\(426\) | 521.589 | 1.22439 | ||||||||
\(427\) | 320.291 | + | 50.7291i | 0.750096 | + | 0.118804i | ||||
\(428\) | 29.3706 | + | 57.6430i | 0.0686229 | + | 0.134680i | ||||
\(429\) | −467.293 | − | 151.833i | −1.08926 | − | 0.353922i | ||||
\(430\) | 58.9625 | − | 11.1178i | 0.137122 | − | 0.0258554i | ||||
\(431\) | 65.2188 | + | 200.723i | 0.151320 | + | 0.465714i | 0.997769 | − | 0.0667544i | \(-0.0212644\pi\) |
−0.846450 | + | 0.532469i | \(0.821264\pi\) | |||||||
\(432\) | 61.8690 | + | 61.8690i | 0.143215 | + | 0.143215i | ||||
\(433\) | 58.0321 | + | 29.5688i | 0.134023 | + | 0.0682883i | 0.519716 | − | 0.854339i | \(-0.326038\pi\) |
−0.385693 | + | 0.922627i | \(0.626038\pi\) | |||||||
\(434\) | −146.035 | + | 200.999i | −0.336485 | + | 0.463132i | ||||
\(435\) | −13.2594 | + | 45.2798i | −0.0304815 | + | 0.104091i | ||||
\(436\) | −23.2916 | + | 16.9224i | −0.0534212 | + | 0.0388128i | ||||
\(437\) | −45.7635 | − | 288.940i | −0.104722 | − | 0.661189i | ||||
\(438\) | 383.747 | − | 60.7796i | 0.876136 | − | 0.138766i | ||||
\(439\) | 420.223 | + | 578.387i | 0.957228 | + | 1.31751i | 0.948241 | + | 0.317551i | \(0.102861\pi\) |
0.00898677 | + | 0.999960i | \(0.497139\pi\) | |||||||
\(440\) | −233.948 | − | 68.5079i | −0.531700 | − | 0.155700i | ||||
\(441\) | 71.1248 | + | 51.6752i | 0.161281 | + | 0.117177i | ||||
\(442\) | 58.3033 | − | 114.427i | 0.131908 | − | 0.258884i | ||||
\(443\) | −398.922 | + | 398.922i | −0.900500 | + | 0.900500i | −0.995479 | − | 0.0949791i | \(-0.969722\pi\) |
0.0949791 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(444\) | −367.006 | + | 119.247i | −0.826590 | + | 0.268575i | ||||
\(445\) | −91.0833 | − | 483.052i | −0.204682 | − | 1.08551i | ||||
\(446\) | 123.764 | − | 380.907i | 0.277498 | − | 0.854051i | ||||
\(447\) | −53.7574 | + | 27.3908i | −0.120263 | + | 0.0612769i | ||||
\(448\) | 4.81094 | − | 30.3751i | 0.0107387 | − | 0.0678015i | ||||
\(449\) | − | 524.459i | − | 1.16806i | −0.811732 | − | 0.584030i | \(-0.801475\pi\) | ||
0.811732 | − | 0.584030i | \(-0.198525\pi\) | |||||||
\(450\) | −90.3863 | − | 8.93193i | −0.200858 | − | 0.0198487i | ||||
\(451\) | 984.960 | 2.18395 | ||||||||
\(452\) | −409.245 | − | 64.8180i | −0.905409 | − | 0.143403i | ||||
\(453\) | 127.395 | + | 250.027i | 0.281225 | + | 0.551935i | ||||
\(454\) | −118.355 | − | 38.4560i | −0.260694 | − | 0.0847047i | ||||
\(455\) | −77.3009 | − | 141.321i | −0.169892 | − | 0.310595i | ||||
\(456\) | −97.8626 | − | 301.190i | −0.214611 | − | 0.660505i | ||||
\(457\) | 4.32110 | + | 4.32110i | 0.00945537 | + | 0.00945537i | 0.711819 | − | 0.702363i | \(-0.247872\pi\) |
−0.702363 | + | 0.711819i | \(0.747872\pi\) | |||||||
\(458\) | −2.03868 | − | 1.03876i | −0.00445127 | − | 0.00226804i | ||||
\(459\) | −139.320 | + | 191.757i | −0.303529 | + | 0.417771i | ||||
\(460\) | 70.3351 | − | 54.3184i | 0.152902 | − | 0.118083i | ||||
\(461\) | −281.522 | + | 204.538i | −0.610676 | + | 0.443682i | −0.849652 | − | 0.527343i | \(-0.823188\pi\) |
0.238976 | + | 0.971025i | \(0.423188\pi\) | |||||||
\(462\) | −49.8623 | − | 314.818i | −0.107927 | − | 0.681424i | ||||
\(463\) | 288.817 | − | 45.7442i | 0.623795 | − | 0.0987995i | 0.163468 | − | 0.986549i | \(-0.447732\pi\) |
0.460327 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(464\) | −6.52275 | − | 8.97780i | −0.0140577 | − | 0.0193487i | ||||
\(465\) | −731.808 | + | 261.711i | −1.57378 | + | 0.562820i | ||||
\(466\) | −88.2943 | − | 64.1496i | −0.189473 | − | 0.137660i | ||||
\(467\) | 285.147 | − | 559.633i | 0.610594 | − | 1.19836i | −0.354155 | − | 0.935187i | \(-0.615231\pi\) |
0.964749 | − | 0.263172i | \(-0.0847686\pi\) | |||||||
\(468\) | 30.4466 | − | 30.4466i | 0.0650568 | − | 0.0650568i | ||||
\(469\) | 139.493 | − | 45.3241i | 0.297427 | − | 0.0966398i | ||||
\(470\) | −176.727 | − | 22.7077i | −0.376015 | − | 0.0483142i | ||||
\(471\) | −73.5616 | + | 226.399i | −0.156182 | + | 0.480678i | ||||
\(472\) | 164.353 | − | 83.7423i | 0.348206 | − | 0.177420i | ||||
\(473\) | −22.8812 | + | 144.466i | −0.0483747 | + | 0.305426i | ||||
\(474\) | 197.904i | 0.417518i | ||||||||
\(475\) | −692.972 | − | 443.918i | −1.45889 | − | 0.934564i | ||||
\(476\) | 83.3111 | 0.175023 | ||||||||
\(477\) | 76.2454 | + | 12.0761i | 0.159844 | + | 0.0253167i | ||||
\(478\) | 6.43791 | + | 12.6351i | 0.0134684 | + | 0.0264333i | ||||
\(479\) | 402.767 | + | 130.867i | 0.840850 | + | 0.273209i | 0.697609 | − | 0.716479i | \(-0.254248\pi\) |
0.143241 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(480\) | 66.0050 | − | 69.9894i | 0.137510 | − | 0.145811i | ||||
\(481\) | −146.905 | − | 452.128i | −0.305417 | − | 0.939976i | ||||
\(482\) | 213.159 | + | 213.159i | 0.442240 | + | 0.442240i | ||||
\(483\) | 103.533 | + | 52.7529i | 0.214355 | + | 0.109219i | ||||
\(484\) | 207.048 | − | 284.977i | 0.427785 | − | 0.588795i | ||||
\(485\) | 408.439 | − | 11.9666i | 0.842143 | − | 0.0246734i | ||||
\(486\) | −154.267 | + | 112.081i | −0.317421 | + | 0.230620i | ||||
\(487\) | 47.1753 | + | 297.853i | 0.0968692 | + | 0.611608i | 0.987590 | + | 0.157056i | \(0.0502004\pi\) |
−0.890720 | + | 0.454551i | \(0.849800\pi\) | |||||||
\(488\) | −235.658 | + | 37.3246i | −0.482906 | + | 0.0764848i | ||||
\(489\) | −146.735 | − | 201.963i | −0.300071 | − | 0.413013i | ||||
\(490\) | −136.442 | + | 199.853i | −0.278452 | + | 0.407862i | ||||
\(491\) | −295.498 | − | 214.692i | −0.601830 | − | 0.437255i | 0.244698 | − | 0.969599i | \(-0.421311\pi\) |
−0.846528 | + | 0.532344i | \(0.821311\pi\) | |||||||
\(492\) | −176.471 | + | 346.343i | −0.358680 | + | 0.703950i | ||||
\(493\) | 21.2570 | − | 21.2570i | 0.0431177 | − | 0.0431177i | ||||
\(494\) | 371.047 | − | 120.561i | 0.751108 | − | 0.244050i | ||||
\(495\) | 94.6975 | − | 200.137i | 0.191308 | − | 0.404317i | ||||
\(496\) | 56.4881 | − | 173.852i | 0.113887 | − | 0.350509i | ||||
\(497\) | −371.411 | + | 189.243i | −0.747305 | + | 0.380771i | ||||
\(498\) | −27.1634 | + | 171.503i | −0.0545450 | + | 0.344384i | ||||
\(499\) | − | 94.7720i | − | 0.189924i | −0.995481 | − | 0.0949619i | \(-0.969727\pi\) | ||
0.995481 | − | 0.0949619i | \(-0.0302729\pi\) | |||||||
\(500\) | 17.2886 | − | 249.401i | 0.0345773 | − | 0.498803i | ||||
\(501\) | 15.0842 | 0.0301082 | ||||||||
\(502\) | 489.885 | + | 77.5901i | 0.975866 | + | 0.154562i | ||||
\(503\) | −98.1083 | − | 192.548i | −0.195046 | − | 0.382800i | 0.772683 | − | 0.634792i | \(-0.218914\pi\) |
−0.967729 | + | 0.251992i | \(0.918914\pi\) | |||||||
\(504\) | 26.5654 | + | 8.63162i | 0.0527091 | + | 0.0171262i | ||||
\(505\) | 112.756 | + | 53.3521i | 0.223280 | + | 0.105648i | ||||
\(506\) | 66.9441 | + | 206.033i | 0.132301 | + | 0.407179i | ||||
\(507\) | −237.548 | − | 237.548i | −0.468536 | − | 0.468536i | ||||
\(508\) | 303.483 | + | 154.632i | 0.597407 | + | 0.304394i | ||||
\(509\) | 83.6706 | − | 115.163i | 0.164382 | − | 0.226253i | −0.718877 | − | 0.695137i | \(-0.755344\pi\) |
0.883260 | + | 0.468884i | \(0.155344\pi\) | |||||||
\(510\) | 215.237 | + | 146.945i | 0.422033 | + | 0.288127i | ||||
\(511\) | −251.205 | + | 182.511i | −0.491595 | + | 0.357165i | ||||
\(512\) | 3.53971 | + | 22.3488i | 0.00691349 | + | 0.0436501i | ||||
\(513\) | −711.198 | + | 112.643i | −1.38635 | + | 0.219576i | ||||
\(514\) | −412.824 | − | 568.204i | −0.803160 | − | 1.10545i | ||||
\(515\) | 14.7068 | + | 501.966i | 0.0285568 | + | 0.974691i | ||||
\(516\) | −46.6994 | − | 33.9291i | −0.0905028 | − | 0.0657541i | ||||
\(517\) | 197.193 | − | 387.013i | 0.381417 | − | 0.748574i | ||||
\(518\) | 218.071 | − | 218.071i | 0.420986 | − | 0.420986i | ||||
\(519\) | −993.769 | + | 322.895i | −1.91478 | + | 0.622149i | ||||
\(520\) | 86.2225 | + | 81.3140i | 0.165813 | + | 0.156373i | ||||
\(521\) | 38.0795 | − | 117.197i | 0.0730892 | − | 0.224945i | −0.907838 | − | 0.419321i | \(-0.862268\pi\) |
0.980927 | + | 0.194376i | \(0.0622681\pi\) | |||||||
\(522\) | 8.98061 | − | 4.57585i | 0.0172042 | − | 0.00876599i | ||||
\(523\) | 0.194623 | − | 1.22880i | 0.000372128 | − | 0.00234952i | −0.987502 | − | 0.157609i | \(-0.949621\pi\) |
0.987874 | + | 0.155260i | \(0.0496214\pi\) | |||||||
\(524\) | − | 7.92092i | − | 0.0151163i | ||||||
\(525\) | 304.439 | − | 119.041i | 0.579883 | − | 0.226745i | ||||
\(526\) | −117.660 | −0.223688 | ||||||||
\(527\) | 489.102 | + | 77.4662i | 0.928088 | + | 0.146995i | ||||
\(528\) | 106.469 | + | 208.957i | 0.201646 | + | 0.395753i | ||||
\(529\) | 427.999 | + | 139.065i | 0.809072 | + | 0.262883i | ||||
\(530\) | −27.0791 | + | 210.749i | −0.0510926 | + | 0.397639i | ||||
\(531\) | 51.7718 | + | 159.337i | 0.0974986 | + | 0.300070i | ||||
\(532\) | 178.964 | + | 178.964i | 0.336398 | + | 0.336398i | ||||
\(533\) | −426.673 | − | 217.401i | −0.800513 | − | 0.407882i | ||||
\(534\) | −277.966 | + | 382.587i | −0.520535 | + | 0.716455i | ||||
\(535\) | −54.4624 | − | 152.290i | −0.101799 | − | 0.284654i | ||||
\(536\) | −87.3055 | + | 63.4312i | −0.162883 | + | 0.118342i | ||||
\(537\) | −23.4365 | − | 147.973i | −0.0436435 | − | 0.275554i | ||||
\(538\) | 314.666 | − | 49.8383i | 0.584882 | − | 0.0926362i | ||||
\(539\) | −346.732 | − | 477.236i | −0.643288 | − | 0.885410i | ||||
\(540\) | −133.700 | − | 173.123i | −0.247592 | − | 0.320598i | ||||
\(541\) | −363.946 | − | 264.422i | −0.672729 | − | 0.488766i | 0.198209 | − | 0.980160i | \(-0.436488\pi\) |
−0.870938 | + | 0.491394i | \(0.836488\pi\) | |||||||
\(542\) | −225.492 | + | 442.553i | −0.416037 | + | 0.816519i | ||||
\(543\) | −620.367 | + | 620.367i | −1.14248 | + | 1.14248i | ||||
\(544\) | −58.2971 | + | 18.9419i | −0.107164 | + | 0.0348196i | ||||
\(545\) | 63.1458 | − | 34.5401i | 0.115864 | − | 0.0633763i | ||||
\(546\) | −47.8870 | + | 147.381i | −0.0877052 | + | 0.269929i | ||||
\(547\) | −457.733 | + | 233.226i | −0.836806 | + | 0.426374i | −0.819225 | − | 0.573472i | \(-0.805596\pi\) |
−0.0175802 | + | 0.999845i | \(0.505596\pi\) | |||||||
\(548\) | 66.5158 | − | 419.964i | 0.121379 | − | 0.766358i | ||||
\(549\) | − | 216.708i | − | 0.394732i | ||||||
\(550\) | 558.274 | + | 244.410i | 1.01504 | + | 0.444383i | ||||
\(551\) | 91.3260 | 0.165746 | ||||||||
\(552\) | −84.4417 | − | 13.3743i | −0.152974 | − | 0.0242287i | ||||
\(553\) | −71.8035 | − | 140.922i | −0.129844 | − | 0.254832i | ||||
\(554\) | −430.514 | − | 139.883i | −0.777102 | − | 0.252496i | ||||
\(555\) | 948.026 | − | 178.758i | 1.70816 | − | 0.322086i | ||||
\(556\) | 18.9520 | + | 58.3284i | 0.0340864 | + | 0.104907i | ||||
\(557\) | 498.053 | + | 498.053i | 0.894171 | + | 0.894171i | 0.994913 | − | 0.100742i | \(-0.0321215\pi\) |
−0.100742 | + | 0.994913i | \(0.532122\pi\) | |||||||
\(558\) | 147.934 | + | 75.3761i | 0.265115 | + | 0.135083i | ||||
\(559\) | 41.7986 | − | 57.5308i | 0.0747738 | − | 0.102917i | ||||
\(560\) | −21.6069 | + | 73.7857i | −0.0385838 | + | 0.131760i | ||||
\(561\) | −513.973 | + | 373.423i | −0.916173 | + | 0.665638i | ||||
\(562\) | 20.6917 | + | 130.642i | 0.0368180 | + | 0.232460i | ||||
\(563\) | 918.854 | − | 145.532i | 1.63207 | − | 0.258494i | 0.727904 | − | 0.685679i | \(-0.240495\pi\) |
0.904164 | + | 0.427185i | \(0.140495\pi\) | |||||||
\(564\) | 100.756 | + | 138.678i | 0.178645 | + | 0.245884i | ||||
\(565\) | 994.119 | + | 291.111i | 1.75950 | + | 0.515241i | ||||
\(566\) | 39.0937 | + | 28.4033i | 0.0690702 | + | 0.0501824i | ||||
\(567\) | 170.197 | − | 334.031i | 0.300172 | − | 0.589120i | ||||
\(568\) | 216.868 | − | 216.868i | 0.381810 | − | 0.381810i | ||||
\(569\) | 829.779 | − | 269.612i | 1.45831 | − | 0.473834i | 0.530757 | − | 0.847524i | \(-0.321908\pi\) |
0.927554 | + | 0.373690i | \(0.121908\pi\) | |||||||
\(570\) | 146.701 | + | 778.015i | 0.257370 | + | 1.36494i | ||||
\(571\) | 43.0384 | − | 132.459i | 0.0753737 | − | 0.231977i | −0.906270 | − | 0.422699i | \(-0.861083\pi\) |
0.981644 | + | 0.190722i | \(0.0610829\pi\) | |||||||
\(572\) | −257.423 | + | 131.163i | −0.450040 | + | 0.229307i | ||||
\(573\) | 67.0097 | − | 423.082i | 0.116945 | − | 0.738364i | ||||
\(574\) | − | 310.650i | − | 0.541202i | ||||||
\(575\) | −191.710 | + | 112.280i | −0.333409 | + | 0.195269i | ||||
\(576\) | −20.5517 | −0.0356800 | ||||||||
\(577\) | 454.188 | + | 71.9363i | 0.787154 | + | 0.124673i | 0.537055 | − | 0.843547i | \(-0.319537\pi\) |
0.250099 | + | 0.968220i | \(0.419537\pi\) | |||||||
\(578\) | 110.163 | + | 216.207i | 0.190594 | + | 0.374061i | ||||
\(579\) | 728.159 | + | 236.593i | 1.25761 | + | 0.408624i | ||||
\(580\) | 13.3135 | + | 24.3397i | 0.0229544 | + | 0.0419650i | ||||
\(581\) | −42.8824 | − | 131.979i | −0.0738080 | − | 0.227158i | ||||
\(582\) | −277.965 | − | 277.965i | −0.477604 | − | 0.477604i | ||||
\(583\) | −461.516 | − | 235.154i | −0.791622 | − | 0.403352i | ||||
\(584\) | 134.285 | − | 184.827i | 0.229940 | − | 0.316485i | ||||
\(585\) | −85.1962 | + | 65.7953i | −0.145635 | + | 0.112471i | ||||
\(586\) | 186.497 | − | 135.498i | 0.318255 | − | 0.231226i | ||||
\(587\) | −35.6617 | − | 225.159i | −0.0607524 | − | 0.383576i | −0.999265 | − | 0.0383309i | \(-0.987796\pi\) |
0.938513 | − | 0.345245i | \(-0.112204\pi\) | |||||||
\(588\) | 229.934 | − | 36.4179i | 0.391044 | − | 0.0619353i | ||||
\(589\) | 884.250 | + | 1217.07i | 1.50127 | + | 2.06633i | ||||
\(590\) | −434.214 | + | 155.285i | −0.735956 | + | 0.263194i | ||||
\(591\) | 171.025 | + | 124.257i | 0.289383 | + | 0.210249i | ||||
\(592\) | −103.014 | + | 202.176i | −0.174010 | + | 0.341514i | ||||
\(593\) | 274.055 | − | 274.055i | 0.462150 | − | 0.462150i | −0.437210 | − | 0.899360i | \(-0.644033\pi\) |
0.899360 | + | 0.437210i | \(0.144033\pi\) | |||||||
\(594\) | 507.130 | − | 164.777i | 0.853755 | − | 0.277402i | ||||
\(595\) | −206.580 | − | 26.5434i | −0.347192 | − | 0.0446107i | ||||
\(596\) | −10.9628 | + | 33.7401i | −0.0183940 | + | 0.0566109i | ||||
\(597\) | 416.950 | − | 212.447i | 0.698408 | − | 0.355857i | ||||
\(598\) | 16.4763 | − | 104.027i | 0.0275523 | − | 0.173958i | ||||
\(599\) | 995.730i | 1.66232i | 0.556033 | + | 0.831160i | \(0.312323\pi\) | ||||
−0.556033 | + | 0.831160i | \(0.687677\pi\) | |||||||
\(600\) | −185.966 | + | 152.517i | −0.309943 | + | 0.254195i | ||||
\(601\) | −814.641 | −1.35548 | −0.677738 | − | 0.735303i | \(-0.737040\pi\) | ||||
−0.677738 | + | 0.735303i | \(0.737040\pi\) | |||||||
\(602\) | 45.5637 | + | 7.21659i | 0.0756873 | + | 0.0119877i | ||||
\(603\) | −44.4983 | − | 87.3328i | −0.0737949 | − | 0.144831i | ||||
\(604\) | 156.926 | + | 50.9883i | 0.259811 | + | 0.0844177i | ||||
\(605\) | −604.194 | + | 640.666i | −0.998668 | + | 1.05895i | ||||
\(606\) | −37.0839 | − | 114.132i | −0.0611945 | − | 0.188337i | ||||
\(607\) | −767.174 | − | 767.174i | −1.26388 | − | 1.26388i | −0.949198 | − | 0.314680i | \(-0.898103\pi\) |
−0.314680 | − | 0.949198i | \(-0.601897\pi\) | |||||||
\(608\) | −165.920 | − | 84.5403i | −0.272894 | − | 0.139047i | ||||
\(609\) | −21.3219 | + | 29.3471i | −0.0350113 | + | 0.0481889i | ||||
\(610\) | 596.233 | − | 17.4686i | 0.977431 | − | 0.0286371i | ||||
\(611\) | −170.843 | + | 124.125i | −0.279613 | + | 0.203150i | ||||
\(612\) | −8.70935 | − | 54.9886i | −0.0142310 | − | 0.0898507i | ||||
\(613\) | −1067.95 | + | 169.147i | −1.74217 | + | 0.275933i | −0.944821 | − | 0.327587i | \(-0.893765\pi\) |
−0.797349 | + | 0.603519i | \(0.793765\pi\) | |||||||
\(614\) | −427.819 | − | 588.842i | −0.696774 | − | 0.959027i | ||||
\(615\) | 547.926 | − | 802.574i | 0.890937 | − | 1.30500i | ||||
\(616\) | −151.628 | − | 110.164i | −0.246150 | − | 0.178838i | ||||
\(617\) | 241.065 | − | 473.116i | 0.390704 | − | 0.766800i | −0.608947 | − | 0.793211i | \(-0.708408\pi\) |
0.999651 | + | 0.0264106i | \(0.00840774\pi\) | |||||||
\(618\) | 341.615 | − | 341.615i | 0.552776 | − | 0.552776i | ||||
\(619\) | −694.267 | + | 225.581i | −1.12159 | + | 0.364428i | −0.810376 | − | 0.585910i | \(-0.800737\pi\) |
−0.311219 | + | 0.950338i | \(0.600737\pi\) | |||||||
\(620\) | −195.459 | + | 413.090i | −0.315256 | + | 0.666274i | ||||
\(621\) | −60.0697 | + | 184.876i | −0.0967307 | + | 0.297706i | ||||
\(622\) | −82.1031 | + | 41.8336i | −0.131999 | + | 0.0672567i | ||||
\(623\) | 59.1222 | − | 373.283i | 0.0948992 | − | 0.599170i | ||||
\(624\) | − | 114.018i | − | 0.182721i | ||||||
\(625\) | −122.330 | + | 612.911i | −0.195728 | + | 0.980658i | ||||
\(626\) | −114.449 | −0.182826 | ||||||||
\(627\) | −1906.25 | − | 301.920i | −3.04027 | − | 0.481531i | ||||
\(628\) | 63.5475 | + | 124.719i | 0.101190 | + | 0.198597i | ||||
\(629\) | −584.603 | − | 189.949i | −0.929417 | − | 0.301986i | ||||
\(630\) | −63.1219 | − | 29.8670i | −0.100193 | − | 0.0474079i | ||||
\(631\) | 232.185 | + | 714.593i | 0.367964 | + | 1.13248i | 0.948104 | + | 0.317960i | \(0.102998\pi\) |
−0.580140 | + | 0.814517i | \(0.697002\pi\) | |||||||
\(632\) | 82.2852 | + | 82.2852i | 0.130198 | + | 0.130198i | ||||
\(633\) | −560.427 | − | 285.552i | −0.885351 | − | 0.451109i | ||||
\(634\) | −225.255 | + | 310.037i | −0.355292 | + | 0.489018i | ||||
\(635\) | −703.254 | − | 480.120i | −1.10749 | − | 0.756094i | ||||
\(636\) | 165.375 | − | 120.152i | 0.260024 | − | 0.188919i | ||||
\(637\) | 44.8646 | + | 283.264i | 0.0704311 | + | 0.444685i | ||||
\(638\) | −66.7970 | + | 10.5796i | −0.104698 | + | 0.0165825i | ||||
\(639\) | 163.735 | + | 225.362i | 0.256237 | + | 0.352680i | ||||
\(640\) | −1.65665 | − | 56.5443i | −0.00258852 | − | 0.0883504i | ||||
\(641\) | 363.902 | + | 264.390i | 0.567710 | + | 0.412466i | 0.834273 | − | 0.551352i | \(-0.185888\pi\) |
−0.266563 | + | 0.963818i | \(0.585888\pi\) | |||||||
\(642\) | −70.6390 | + | 138.637i | −0.110030 | + | 0.215945i | ||||
\(643\) | 554.876 | − | 554.876i | 0.862949 | − | 0.862949i | −0.128731 | − | 0.991680i | \(-0.541090\pi\) |
0.991680 | + | 0.128731i | \(0.0410903\pi\) | |||||||
\(644\) | 64.9814 | − | 21.1137i | 0.100903 | − | 0.0327853i | ||||
\(645\) | 104.987 | + | 99.0099i | 0.162770 | + | 0.153504i | ||||
\(646\) | 155.885 | − | 479.766i | 0.241308 | − | 0.742671i | ||||
\(647\) | 207.914 | − | 105.937i | 0.321351 | − | 0.163736i | −0.285873 | − | 0.958268i | \(-0.592283\pi\) |
0.607223 | + | 0.794531i | \(0.292283\pi\) | |||||||
\(648\) | −43.1495 | + | 272.435i | −0.0665888 | + | 0.420425i | ||||
\(649\) | − | 1124.15i | − | 1.73212i | ||||||
\(650\) | −187.892 | − | 229.098i | −0.289064 | − | 0.352459i | ||||
\(651\) | −597.543 | −0.917884 | ||||||||
\(652\) | −144.983 | − | 22.9631i | −0.222367 | − | 0.0352194i | ||||
\(653\) | 296.217 | + | 581.359i | 0.453625 | + | 0.890290i | 0.998654 | + | 0.0518724i | \(0.0165189\pi\) |
−0.545028 | + | 0.838418i | \(0.683481\pi\) | |||||||
\(654\) | −65.8538 | − | 21.3972i | −0.100694 | − | 0.0327174i | ||||
\(655\) | −2.52365 | + | 19.6408i | −0.00385290 | + | 0.0299860i | ||||
\(656\) | 70.6303 | + | 217.378i | 0.107668 | + | 0.331369i | ||||
\(657\) | 146.726 | + | 146.726i | 0.223327 | + | 0.223327i | ||||
\(658\) | −122.061 | − | 62.1933i | −0.185503 | − | 0.0945187i | ||||
\(659\) | 652.592 | − | 898.216i | 0.990276 | − | 1.36300i | 0.0591706 | − | 0.998248i | \(-0.481154\pi\) |
0.931105 | − | 0.364750i | \(-0.118846\pi\) | |||||||
\(660\) | −197.428 | − | 552.056i | −0.299133 | − | 0.836448i | ||||
\(661\) | 889.686 | − | 646.395i | 1.34597 | − | 0.977904i | 0.346768 | − | 0.937951i | \(-0.387279\pi\) |
0.999202 | − | 0.0399532i | \(-0.0127209\pi\) | |||||||
\(662\) | −80.2156 | − | 506.461i | −0.121172 | − | 0.765048i | ||||
\(663\) | 305.069 | − | 48.3182i | 0.460135 | − | 0.0728782i | ||||
\(664\) | 60.0141 | + | 82.6023i | 0.0903827 | + | 0.124401i | ||||
\(665\) | −386.742 | − | 500.780i | −0.581567 | − | 0.753052i | ||||
\(666\) | −166.732 | − | 121.138i | −0.250349 | − | 0.181889i | ||||
\(667\) | 11.1929 | − | 21.9674i | 0.0167810 | − | 0.0329346i | ||||
\(668\) | 6.27178 | − | 6.27178i | 0.00938890 | − | 0.00938890i | ||||
\(669\) | 916.117 | − | 297.664i | 1.36938 | − | 0.444939i | ||||
\(670\) | 236.694 | − | 129.469i | 0.353274 | − | 0.193237i | ||||
\(671\) | −449.334 | + | 1382.91i | −0.669649 | + | 2.06097i | ||||
\(672\) | 65.9038 | − | 33.5797i | 0.0980712 | − | 0.0499697i | ||||
\(673\) | −90.6315 | + | 572.224i | −0.134668 | + | 0.850259i | 0.824178 | + | 0.566331i | \(0.191638\pi\) |
−0.958846 | + | 0.283928i | \(0.908362\pi\) | |||||||
\(674\) | 250.194i | 0.371208i | ||||||||
\(675\) | 276.365 | + | 471.876i | 0.409430 | + | 0.699076i | ||||
\(676\) | −197.537 | −0.292215 | ||||||||
\(677\) | −42.6461 | − | 6.75448i | −0.0629928 | − | 0.00997708i | 0.124858 | − | 0.992175i | \(-0.460152\pi\) |
−0.187851 | + | 0.982197i | \(0.560152\pi\) | |||||||
\(678\) | −452.421 | − | 887.925i | −0.667287 | − | 1.30962i | ||||
\(679\) | 298.784 | + | 97.0808i | 0.440035 | + | 0.142976i | ||||
\(680\) | 150.589 | − | 28.3948i | 0.221455 | − | 0.0417570i | ||||
\(681\) | −92.4902 | − | 284.656i | −0.135815 | − | 0.417996i | ||||
\(682\) | −787.742 | − | 787.742i | −1.15505 | − | 1.15505i | ||||
\(683\) | 831.566 | + | 423.704i | 1.21752 | + | 0.620357i | 0.940266 | − | 0.340440i | \(-0.110576\pi\) |
0.277253 | + | 0.960797i | \(0.410576\pi\) | |||||||
\(684\) | 99.4142 | − | 136.832i | 0.145342 | − | 0.200047i | ||||
\(685\) | −298.736 | + | 1020.16i | −0.436111 | + | 1.48928i | ||||
\(686\) | −366.031 | + | 265.937i | −0.533574 | + | 0.387664i | ||||
\(687\) | −0.860862 | − | 5.43527i | −0.00125307 | − | 0.00791159i | ||||
\(688\) | −33.5241 | + | 5.30969i | −0.0487269 | + | 0.00771758i | ||||
\(689\) | 148.020 | + | 203.732i | 0.214833 | + | 0.295692i | ||||
\(690\) | 205.122 | + | 60.0666i | 0.297278 | + | 0.0870531i | ||||
\(691\) | 880.749 | + | 639.902i | 1.27460 | + | 0.926052i | 0.999376 | − | 0.0353282i | \(-0.0112476\pi\) |
0.275225 | + | 0.961380i | \(0.411248\pi\) | |||||||
\(692\) | −278.939 | + | 547.448i | −0.403091 | + | 0.791110i | ||||
\(693\) | 120.370 | − | 120.370i | 0.173695 | − | 0.173695i | ||||
\(694\) | −290.580 | + | 94.4152i | −0.418703 | + | 0.136045i | ||||
\(695\) | −28.4100 | − | 150.670i | −0.0408777 | − | 0.216792i | ||||
\(696\) | 8.24759 | − | 25.3835i | 0.0118500 | − | 0.0364705i | ||||
\(697\) | −551.690 | + | 281.100i | −0.791521 | + | 0.403300i | ||||
\(698\) | −40.3376 | + | 254.682i | −0.0577903 | + | 0.364873i | ||||
\(699\) | − | 262.487i | − | 0.375517i | ||||||
\(700\) | 77.0854 | − | 176.076i | 0.110122 | − | 0.251537i | ||||
\(701\) | 93.0109 | 0.132683 | 0.0663416 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663416 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(702\) | −256.053 | − | 40.5547i | −0.364747 | − | 0.0577703i | ||||
\(703\) | −847.771 | − | 1663.84i | −1.20593 | − | 2.36678i | ||||
\(704\) | 131.149 | + | 42.6130i | 0.186292 | + | 0.0605298i | ||||
\(705\) | −205.652 | − | 375.971i | −0.291705 | − | 0.533292i | ||||
\(706\) | 55.5188 | + | 170.869i | 0.0786385 | + | 0.242024i | ||||
\(707\) | 67.8162 | + | 67.8162i | 0.0959210 | + | 0.0959210i | ||||
\(708\) | 395.286 | + | 201.408i | 0.558313 | + | 0.284475i | ||||
\(709\) | −512.727 | + | 705.708i | −0.723169 | + | 0.995357i | 0.276243 | + | 0.961088i | \(0.410910\pi\) |
−0.999413 | + | 0.0342694i | \(0.989090\pi\) | |||||||
\(710\) | −606.845 | + | 468.654i | −0.854711 | + | 0.660077i | ||||
\(711\) | −85.5080 | + | 62.1252i | −0.120264 | + | 0.0873772i | ||||
\(712\) | 43.4999 | + | 274.647i | 0.0610953 | + | 0.385741i | ||||
\(713\) | 401.125 | − | 63.5319i | 0.562587 | − | 0.0891050i | ||||
\(714\) | 117.775 | + | 162.104i | 0.164951 | + | 0.227036i | ||||
\(715\) | 680.098 | − | 243.218i | 0.951186 | − | 0.340166i | ||||
\(716\) | −71.2692 | − | 51.7801i | −0.0995379 | − | 0.0723185i | ||||
\(717\) | −15.4838 | + | 30.3886i | −0.0215952 | + | 0.0423831i | ||||
\(718\) | −236.233 | + | 236.233i | −0.329015 | + | 0.329015i | ||||
\(719\) | 924.330 | − | 300.333i | 1.28558 | − | 0.417709i | 0.415036 | − | 0.909805i | \(-0.363769\pi\) |
0.870541 | + | 0.492096i | \(0.163769\pi\) | |||||||
\(720\) | 50.9603 | + | 6.54788i | 0.0707782 | + | 0.00909428i | ||||
\(721\) | −119.311 | + | 367.201i | −0.165480 | + | 0.509294i | ||||
\(722\) | 910.577 | − | 463.962i | 1.26119 | − | 0.642607i | ||||
\(723\) | −113.419 | + | 716.097i | −0.156872 | + | 0.990452i | ||||
\(724\) | 515.877i | 0.712538i | ||||||||
\(725\) | −25.2577 | − | 64.5948i | −0.0348382 | − | 0.0890963i | ||||
\(726\) | 847.197 | 1.16694 | ||||||||
\(727\) | 613.184 | + | 97.1188i | 0.843444 | + | 0.133588i | 0.563180 | − | 0.826334i | \(-0.309578\pi\) |
0.280264 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(728\) | 41.3681 | + | 81.1894i | 0.0568243 | + | 0.111524i | ||||
\(729\) | 398.565 | + | 129.502i | 0.546728 | + | 0.177643i | ||||
\(730\) | −391.862 | + | 415.517i | −0.536797 | + | 0.569201i | ||||
\(731\) | −28.4135 | − | 87.4478i | −0.0388694 | − | 0.119628i | ||||
\(732\) | −405.770 | − | 405.770i | −0.554330 | − | 0.554330i | ||||
\(733\) | 15.0875 | + | 7.68746i | 0.0205832 | + | 0.0104877i | 0.464252 | − | 0.885703i | \(-0.346323\pi\) |
−0.443669 | + | 0.896191i | \(0.646323\pi\) | |||||||
\(734\) | −107.349 | + | 147.754i | −0.146252 | + | 0.201299i | ||||
\(735\) | −581.750 | + | 17.0443i | −0.791497 | + | 0.0231895i | ||||
\(736\) | −40.6703 | + | 29.5487i | −0.0552586 | + | 0.0401477i | ||||
\(737\) | 102.882 | + | 649.574i | 0.139596 | + | 0.881376i | ||||
\(738\) | −205.041 | + | 32.4754i | −0.277834 | + | 0.0440045i | ||||
\(739\) | 98.2185 | + | 135.186i | 0.132907 | + | 0.182931i | 0.870284 | − | 0.492551i | \(-0.163935\pi\) |
−0.737376 | + | 0.675482i | \(0.763935\pi\) | |||||||
\(740\) | 319.850 | − | 468.499i | 0.432229 | − | 0.633106i | ||||
\(741\) | 759.124 | + | 551.536i | 1.02446 | + | 0.744313i | ||||
\(742\) | −74.1660 | + | 145.559i | −0.0999542 | + | 0.196171i | ||||
\(743\) | 691.071 | − | 691.071i | 0.930108 | − | 0.930108i | −0.0676038 | − | 0.997712i | \(-0.521535\pi\) |
0.997712 | + | 0.0676038i | \(0.0215354\pi\) | |||||||
\(744\) | 418.131 | − | 135.859i | 0.562005 | − | 0.182606i | ||||
\(745\) | 37.9334 | − | 80.1697i | 0.0509173 | − | 0.107610i | ||||
\(746\) | 220.654 | − | 679.102i | 0.295782 | − | 0.910324i | ||||
\(747\) | −82.6282 | + | 42.1012i | −0.110613 | + | 0.0563603i | ||||
\(748\) | −58.4383 | + | 368.965i | −0.0781261 | + | 0.493269i | ||||
\(749\) | − | 124.349i | − | 0.166020i | ||||||
\(750\) | 509.717 | − | 318.934i | 0.679622 | − | 0.425245i | ||||
\(751\) | −958.191 | −1.27589 | −0.637944 | − | 0.770083i | \(-0.720215\pi\) | ||||
−0.637944 | + | 0.770083i | \(0.720215\pi\) | |||||||
\(752\) | 99.5530 | + | 15.7676i | 0.132384 | + | 0.0209676i | ||||
\(753\) | 541.568 | + | 1062.89i | 0.719214 | + | 1.41154i | ||||
\(754\) | 31.2708 | + | 10.1605i | 0.0414733 | + | 0.0134755i | ||||
\(755\) | −372.870 | − | 176.429i | −0.493868 | − | 0.233680i | ||||
\(756\) | −51.9695 | − | 159.946i | −0.0687427 | − | 0.211568i | ||||
\(757\) | 105.145 | + | 105.145i | 0.138896 | + | 0.138896i | 0.773136 | − | 0.634240i | \(-0.218687\pi\) |
−0.634240 | + | 0.773136i | \(0.718687\pi\) | |||||||
\(758\) | −118.955 | − | 60.6107i | −0.156933 | − | 0.0799614i | ||||
\(759\) | −306.253 | + | 421.522i | −0.403496 | + | 0.555364i | ||||
\(760\) | 384.482 | + | 262.490i | 0.505897 | + | 0.345382i | ||||
\(761\) | −555.664 | + | 403.713i | −0.730176 | + | 0.530504i | −0.889619 | − | 0.456703i | \(-0.849030\pi\) |
0.159443 | + | 0.987207i | \(0.449030\pi\) | |||||||
\(762\) | 128.150 | + | 809.106i | 0.168176 | + | 1.06182i | ||||
\(763\) | 54.6562 | − | 8.65670i | 0.0716333 | − | 0.0113456i | ||||
\(764\) | −148.049 | − | 203.772i | −0.193782 | − | 0.266718i | ||||
\(765\) | 4.07615 | + | 139.126i | 0.00532829 | + | 0.181863i | ||||
\(766\) | 418.116 | + | 303.779i | 0.545843 | + | 0.396578i | ||||
\(767\) | −248.122 | + | 486.967i | −0.323497 | + | 0.634899i | ||||
\(768\) | −38.4815 | + | 38.4815i | −0.0501061 | + | 0.0501061i | ||||
\(769\) | −1224.25 | + | 397.783i | −1.59200 | + | 0.517273i | −0.965112 | − | 0.261836i | \(-0.915672\pi\) |
−0.626889 | + | 0.779109i | \(0.715672\pi\) | |||||||
\(770\) | 340.881 | + | 321.475i | 0.442702 | + | 0.417500i | ||||
\(771\) | 521.988 | − | 1606.52i | 0.677028 | − | 2.08368i | ||||
\(772\) | 401.128 | − | 204.385i | 0.519596 | − | 0.264748i | ||||
\(773\) | −72.9454 | + | 460.559i | −0.0943666 | + | 0.595808i | 0.894508 | + | 0.447053i | \(0.147526\pi\) |
−0.988874 | + | 0.148755i | \(0.952474\pi\) | |||||||
\(774\) | − | 30.8283i | − | 0.0398298i | ||||||
\(775\) | 616.276 | − | 962.029i | 0.795194 | − | 1.24133i | ||||
\(776\) | −231.147 | −0.297870 | ||||||||
\(777\) | 732.595 | + | 116.032i | 0.942851 | + | 0.149333i | ||||
\(778\) | −109.939 | − | 215.767i | −0.141309 | − | 0.277335i | ||||
\(779\) | −1788.95 | − | 581.264i | −2.29647 | − | 0.746167i | ||||
\(780\) | −36.3267 | + | 282.721i | −0.0465727 | + | 0.362462i | ||||
\(781\) | −577.588 | − | 1777.63i | −0.739549 | − | 2.27610i | ||||
\(782\) | −96.2965 | − | 96.2965i | −0.123141 | − | 0.123141i | ||||
\(783\) | −54.0706 | − | 27.5504i | −0.0690557 | − | 0.0351857i | ||||
\(784\) | 80.4608 | − | 110.745i | 0.102629 | − | 0.141256i | ||||
\(785\) | −117.837 | − | 329.501i | −0.150111 | − | 0.419747i | ||||
\(786\) | 15.4122 | − | 11.1976i | 0.0196084 | − | 0.0142464i | ||||
\(787\) | 22.5670 | + | 142.483i | 0.0286748 | + | 0.181045i | 0.997869 | − | 0.0652534i | \(-0.0207856\pi\) |
−0.969194 | + | 0.246299i | \(0.920786\pi\) | |||||||
\(788\) | 122.774 | − | 19.4454i | 0.155804 | − | 0.0246770i | ||||
\(789\) | −166.333 | − | 228.938i | −0.210815 | − | 0.290162i | ||||
\(790\) | −177.819 | − | 230.252i | −0.225087 | − | 0.291458i | ||||
\(791\) | 644.315 | + | 468.123i | 0.814558 | + | 0.591811i | ||||
\(792\) | −56.8616 | + | 111.597i | −0.0717950 | + | 0.140906i | ||||
\(793\) | 499.883 | − | 499.883i | 0.630369 | − | 0.630369i | ||||
\(794\) | −256.785 | + | 83.4346i | −0.323407 | + | 0.105081i | ||||
\(795\) | −448.348 | + | 245.242i | −0.563960 | + | 0.308480i | ||||
\(796\) | 85.0292 | − | 261.693i | 0.106821 | − | 0.328760i | ||||
\(797\) | 1020.72 | − | 520.082i | 1.28070 | − | 0.652549i | 0.324673 | − | 0.945826i | \(-0.394746\pi\) |
0.956027 | + | 0.293277i | \(0.0947459\pi\) | |||||||
\(798\) | −95.2235 | + | 601.218i | −0.119328 | + | 0.753406i | ||||
\(799\) | 273.049i | 0.341738i | ||||||||
\(800\) | −13.9075 | + | 140.736i | −0.0173843 | + | 0.175920i | ||||
\(801\) | −252.562 | −0.315309 | ||||||||
\(802\) | 113.495 | + | 17.9759i | 0.141515 | + | 0.0224138i | ||||
\(803\) | −632.092 | − | 1240.55i | −0.787163 | − | 1.54489i | ||||
\(804\) | −246.844 | − | 80.2045i | −0.307020 | − | 0.0997568i | ||||
\(805\) | −167.856 | + | 31.6505i | −0.208516 | + | 0.0393174i | ||||
\(806\) | 167.370 | + | 515.112i | 0.207655 | + | 0.639097i | ||||
\(807\) | 541.811 | + | 541.811i | 0.671389 | + | 0.671389i | ||||
\(808\) | −62.8733 | − | 32.0356i | −0.0778135 | − | 0.0396480i | ||||
\(809\) | −366.674 | + | 504.683i | −0.453243 | + | 0.623836i | −0.973090 | − | 0.230423i | \(-0.925989\pi\) |
0.519847 | + | 0.854259i | \(0.325989\pi\) | |||||||
\(810\) | 193.794 | − | 661.787i | 0.239251 | − | 0.817021i | ||||
\(811\) | 325.346 | − | 236.378i | 0.401166 | − | 0.291464i | −0.368850 | − | 0.929489i | \(-0.620248\pi\) |
0.770016 | + | 0.638025i | \(0.220248\pi\) | |||||||
\(812\) | 3.33674 | + | 21.0673i | 0.00410928 | + | 0.0259450i | ||||
\(813\) | −1179.88 | + | 186.874i | −1.45126 | + | 0.229857i | ||||
\(814\) | 812.818 | + | 1118.75i | 0.998547 | + | 1.37438i | ||||
\(815\) | 352.186 | + | 103.132i | 0.432130 | + | 0.126542i | ||||
\(816\) | −119.270 | − | 86.6545i | −0.146164 | − | 0.106194i | ||||
\(817\) | 126.814 | − | 248.886i | 0.155219 | − | 0.304634i | ||||
\(818\) | 242.577 | − | 242.577i | 0.296548 | − | 0.296548i | ||||
\(819\) | −78.7113 | + | 25.5749i | −0.0961066 | + | 0.0312269i | ||||
\(820\) | −105.878 | − | 561.516i | −0.129120 | − | 0.684776i | ||||
\(821\) | 202.953 | − | 624.625i | 0.247202 | − | 0.760810i | −0.748064 | − | 0.663626i | \(-0.769016\pi\) |
0.995266 | − | 0.0971839i | \(-0.0309835\pi\) | |||||||
\(822\) | 911.182 | − | 464.270i | 1.10849 | − | 0.564806i | ||||
\(823\) | −217.260 | + | 1371.72i | −0.263985 | + | 1.66674i | 0.398126 | + | 0.917331i | \(0.369661\pi\) |
−0.662111 | + | 0.749406i | \(0.730339\pi\) | |||||||
\(824\) | − | 284.077i | − | 0.344753i | ||||||
\(825\) | 313.656 | + | 1431.79i | 0.380190 | + | 1.73550i | ||||
\(826\) | −354.548 | −0.429235 | ||||||||
\(827\) | −788.480 | − | 124.883i | −0.953423 | − | 0.151007i | −0.339704 | − | 0.940532i | \(-0.610327\pi\) |
−0.613718 | + | 0.789525i | \(0.710327\pi\) | |||||||
\(828\) | −20.7291 | − | 40.6831i | −0.0250351 | − | 0.0491341i | ||||
\(829\) | −1412.70 | − | 459.014i | −1.70410 | − | 0.553696i | −0.714767 | − | 0.699363i | \(-0.753467\pi\) |
−0.989334 | + | 0.145667i | \(0.953467\pi\) | |||||||
\(830\) | −122.494 | − | 223.943i | −0.147584 | − | 0.269811i | ||||
\(831\) | −336.431 | − | 1035.43i | −0.404851 | − | 1.24600i | ||||
\(832\) | −47.4068 | − | 47.4068i | −0.0569794 | − | 0.0569794i | ||||
\(833\) | 330.409 | + | 168.352i | 0.396650 | + | 0.202103i | ||||
\(834\) | −86.7011 | + | 119.334i | −0.103958 | + | 0.143086i | ||||
\(835\) | −17.5498 | + | 13.5534i | −0.0210178 | + | 0.0162316i | ||||
\(836\) | −918.121 | + | 667.054i | −1.09823 | + | 0.797911i | ||||
\(837\) | −156.378 | − | 987.331i | −0.186831 | − | 1.17961i | ||||
\(838\) | −460.485 | + | 72.9336i | −0.549504 | + | 0.0870329i | ||||
\(839\) | −720.904 | − | 992.239i | −0.859241 | − | 1.18264i | −0.981750 | − | 0.190177i | \(-0.939094\pi\) |
0.122508 | − | 0.992467i | \(-0.460906\pi\) | |||||||
\(840\) | −174.115 | + | 62.2673i | −0.207279 | + | 0.0741278i | ||||
\(841\) | −674.157 | − | 489.803i | −0.801613 | − | 0.582406i | ||||
\(842\) | −72.0435 | + | 141.393i | −0.0855624 | + | 0.167926i | ||||
\(843\) | −224.948 | + | 224.948i | −0.266842 | + | 0.266842i | ||||
\(844\) | −351.744 | + | 114.289i | −0.416759 | + | 0.135413i | ||||
\(845\) | 489.816 | + | 62.9364i | 0.579664 | + | 0.0744809i | ||||
\(846\) | −28.2898 | + | 87.0669i | −0.0334394 | + | 0.102916i | ||||
\(847\) | −603.268 | + | 307.380i | −0.712241 | + | 0.362905i | ||||
\(848\) | 18.8030 | − | 118.718i | 0.0221734 | − | 0.139997i | ||||
\(849\) | 116.220i | 0.136891i | ||||||||
\(850\) | −382.450 | + | 22.4296i | −0.449941 | + | 0.0263877i | ||||
\(851\) | −504.121 | −0.592386 | ||||||||
\(852\) | 728.556 | + | 115.392i | 0.855113 | + | 0.135437i | ||||
\(853\) | 437.247 | + | 858.146i | 0.512599 | + | 1.00603i | 0.991736 | + | 0.128292i | \(0.0409496\pi\) |
−0.479137 | + | 0.877740i | \(0.659050\pi\) | |||||||
\(854\) | 436.160 | + | 141.717i | 0.510727 | + | 0.165945i | ||||
\(855\) | −290.104 | + | 307.617i | −0.339303 | + | 0.359785i | ||||
\(856\) | 28.2724 | + | 87.0136i | 0.0330285 | + | 0.101651i | ||||
\(857\) | 827.294 | + | 827.294i | 0.965338 | + | 0.965338i | 0.999419 | − | 0.0340814i | \(-0.0108506\pi\) |
−0.0340814 | + | 0.999419i | \(0.510851\pi\) | |||||||
\(858\) | −619.126 | − | 315.460i | −0.721592 | − | 0.367669i | ||||
\(859\) | 385.955 | − | 531.221i | 0.449307 | − | 0.618418i | −0.522941 | − | 0.852369i | \(-0.675165\pi\) |
0.972249 | + | 0.233950i | \(0.0751653\pi\) | |||||||
\(860\) | 84.8185 | − | 2.48504i | 0.0986262 | − | 0.00288958i | ||||
\(861\) | 604.451 | − | 439.159i | 0.702034 | − | 0.510057i | ||||
\(862\) | 46.6915 | + | 294.799i | 0.0541665 | + | 0.341994i | ||||
\(863\) | 49.3257 | − | 7.81243i | 0.0571561 | − | 0.00905264i | −0.127791 | − | 0.991801i | \(-0.540789\pi\) |
0.184947 | + | 0.982748i | \(0.440789\pi\) | |||||||
\(864\) | 72.7314 | + | 100.106i | 0.0841799 | + | 0.115864i | ||||
\(865\) | 866.080 | − | 1268.59i | 1.00125 | − | 1.46658i | ||||
\(866\) | 74.5178 | + | 54.1403i | 0.0860483 | + | 0.0625177i | ||||
\(867\) | −264.953 | + | 519.999i | −0.305597 | + | 0.599768i | ||||
\(868\) | −248.449 | + | 248.449i | −0.286231 | + | 0.286231i | ||||
\(869\) | 674.478 | − | 219.151i | 0.776154 | − | 0.252188i | ||||
\(870\) | −28.5381 | + | 60.3135i | −0.0328025 | + | 0.0693258i | ||||
\(871\) | 98.8069 | − | 304.096i | 0.113441 | − | 0.349135i | ||||
\(872\) | −36.2776 | + | 18.4843i | −0.0416027 | + | 0.0211976i | ||||
\(873\) | 32.8423 | − | 207.358i | 0.0376201 | − | 0.237524i | ||||
\(874\) | − | 413.716i | − | 0.473359i | ||||||
\(875\) | −247.241 | + | 412.041i | −0.282561 | + | 0.470904i | ||||
\(876\) | 549.466 | 0.627244 | ||||||||
\(877\) | −696.793 | − | 110.361i | −0.794518 | − | 0.125839i | −0.254036 | − | 0.967195i | \(-0.581758\pi\) |
−0.540482 | + | 0.841355i | \(0.681758\pi\) | |||||||
\(878\) | 459.011 | + | 900.859i | 0.522791 | + | 1.02604i | ||||
\(879\) | 527.295 | + | 171.328i | 0.599880 | + | 0.194913i | ||||
\(880\) | −311.623 | − | 147.449i | −0.354117 | − | 0.167555i | ||||
\(881\) | 83.4556 | + | 256.850i | 0.0947282 | + | 0.291544i | 0.987183 | − | 0.159594i | \(-0.0510184\pi\) |
−0.892455 | + | 0.451137i | \(0.851018\pi\) | |||||||
\(882\) | 87.9151 | + | 87.9151i | 0.0996769 | + | 0.0996769i | ||||
\(883\) | 730.774 | + | 372.348i | 0.827603 | + | 0.421685i | 0.815862 | − | 0.578246i | \(-0.196263\pi\) |
0.0117409 | + | 0.999931i | \(0.496263\pi\) | |||||||
\(884\) | 106.753 | − | 146.933i | 0.120761 | − | 0.166214i | ||||
\(885\) | −915.986 | − | 625.355i | −1.03501 | − | 0.706615i | ||||
\(886\) | −645.469 | + | 468.960i | −0.728520 | + | 0.529301i | ||||
\(887\) | −82.5838 | − | 521.413i | −0.0931046 | − | 0.587839i | −0.989494 | − | 0.144572i | \(-0.953819\pi\) |
0.896390 | − | 0.443267i | \(-0.146181\pi\) | |||||||
\(888\) | −539.016 | + | 85.3717i | −0.607000 | + | 0.0961394i | ||||
\(889\) | −384.813 | − | 529.649i | −0.432860 | − | 0.595781i | ||||
\(890\) | −20.3588 | − | 694.879i | −0.0228751 | − | 0.780763i | ||||
\(891\) | 1359.96 | + | 988.069i | 1.52633 | + | 1.10894i | ||||
\(892\) | 257.143 | − | 504.671i | 0.288277 | − | 0.565775i | ||||
\(893\) | −586.545 | + | 586.545i | −0.656826 | + | 0.656826i | ||||
\(894\) | −81.1482 | + | 26.3666i | −0.0907698 | + | 0.0294929i | ||||
\(895\) | 160.223 | + | 151.101i | 0.179020 | + | 0.168828i | ||||
\(896\) | 13.4399 | − | 41.3636i | 0.0149998 | − | 0.0461648i | ||||
\(897\) | 225.704 | − | 115.002i | 0.251621 | − | 0.128207i | ||||
\(898\) | 116.027 | − | 732.565i | 0.129206 | − | 0.815774i | ||||
\(899\) | 126.785i | 0.141029i | ||||||||
\(900\) | −124.276 | − | 32.4724i | −0.138084 | − | 0.0360805i | ||||
\(901\) | 325.613 | 0.361390 | ||||||||
\(902\) | 1375.79 | + | 217.904i | 1.52527 | + | 0.241579i | ||||
\(903\) | 50.3707 | + | 98.8581i | 0.0557816 | + | 0.109477i | ||||
\(904\) | −557.295 | − | 181.076i | −0.616476 | − | 0.200305i | ||||
\(905\) | 164.361 | − | 1279.18i | 0.181615 | − | 1.41346i | ||||
\(906\) | 122.632 | + | 377.421i | 0.135355 | + | 0.416580i | ||||
\(907\) | −78.0839 | − | 78.0839i | −0.0860903 | − | 0.0860903i | 0.662750 | − | 0.748841i | \(-0.269389\pi\) |
−0.748841 | + | 0.662750i | \(0.769389\pi\) | |||||||
\(908\) | −156.811 | − | 79.8993i | −0.172700 | − | 0.0879948i | ||||
\(909\) | 37.6718 | − | 51.8509i | 0.0414432 | − | 0.0570416i | ||||
\(910\) | −76.7095 | − | 214.499i | −0.0842961 | − | 0.235713i | ||||
\(911\) | 457.456 | − | 332.361i | 0.502147 | − | 0.364831i | −0.307690 | − | 0.951487i | \(-0.599556\pi\) |
0.809836 | + | 0.586656i | \(0.199556\pi\) | |||||||
\(912\) | −70.0619 | − | 442.353i | −0.0768222 | − | 0.485037i | ||||
\(913\) | 614.581 | − | 97.3401i | 0.673145 | − | 0.106616i | ||||
\(914\) | 5.07976 | + | 6.99169i | 0.00555773 | + | 0.00764956i | ||||
\(915\) | 876.872 | + | 1135.43i | 0.958330 | + | 1.24091i | ||||
\(916\) | −2.61783 | − | 1.90196i | −0.00285789 | − | 0.00207638i | ||||
\(917\) | −6.91194 | + | 13.5654i | −0.00753755 | + | 0.0147933i | ||||
\(918\) | −237.025 | + | 237.025i | −0.258197 | + | 0.258197i | ||||
\(919\) | −791.048 | + | 257.027i | −0.860771 | + | 0.279681i | −0.705950 | − | 0.708261i | \(-0.749480\pi\) |
−0.154820 | + | 0.987943i | \(0.549480\pi\) | |||||||
\(920\) | 110.261 | − | 60.3117i | 0.119849 | − | 0.0655562i | ||||
\(921\) | 540.948 | − | 1664.87i | 0.587349 | − | 1.80767i | ||||
\(922\) | −438.481 | + | 223.417i | −0.475575 | + | 0.242318i | ||||
\(923\) | −142.156 | + | 897.536i | −0.154015 | + | 0.972411i | ||||
\(924\) | − | 450.770i | − | 0.487846i | ||||||
\(925\) | −942.370 | + | 1059.79i | −1.01878 | + | 1.14572i | ||||
\(926\) | 413.541 | 0.446588 | ||||||||
\(927\) | 254.840 | + | 40.3627i | 0.274908 | + | 0.0435412i | ||||
\(928\) | −7.12482 | − | 13.9833i | −0.00767761 | − | 0.0150682i | ||||
\(929\) | 680.836 | + | 221.217i | 0.732869 | + | 0.238124i | 0.651594 | − | 0.758568i | \(-0.274101\pi\) |
0.0812754 | + | 0.996692i | \(0.474101\pi\) | |||||||
\(930\) | −1080.09 | + | 203.659i | −1.16139 | + | 0.218989i | ||||
\(931\) | 348.121 | + | 1071.41i | 0.373922 | + | 1.15081i | ||||
\(932\) | −109.138 | − | 109.138i | −0.117101 | − | 0.117101i | ||||
\(933\) | −197.466 | − | 100.614i | −0.211646 | − | 0.107839i | ||||
\(934\) | 522.103 | − | 718.613i | 0.558997 | − | 0.769393i | ||||
\(935\) | 262.459 | − | 896.273i | 0.280705 | − | 0.958580i | ||||
\(936\) | 49.2636 | − | 35.7921i | 0.0526320 | − | 0.0382394i | ||||
\(937\) | 259.512 | + | 1638.49i | 0.276960 | + | 1.74866i | 0.597910 | + | 0.801563i | \(0.295998\pi\) |
−0.320949 | + | 0.947096i | \(0.604002\pi\) | |||||||
\(938\) | 204.871 | − | 32.4485i | 0.218413 | − | 0.0345932i | ||||
\(939\) | −161.794 | − | 222.690i | −0.172305 | − | 0.237157i | ||||
\(940\) | −241.829 | − | 70.8158i | −0.257265 | − | 0.0753360i | ||||
\(941\) | 928.405 | + | 674.525i | 0.986615 | + | 0.716818i | 0.959177 | − | 0.282806i | \(-0.0912652\pi\) |
0.0274377 | + | 0.999624i | \(0.491265\pi\) | |||||||
\(942\) | −152.838 | + | 299.961i | −0.162248 | + | 0.318430i | ||||
\(943\) | −359.070 | + | 359.070i | −0.380774 | + | 0.380774i | ||||
\(944\) | 248.096 | − | 80.6112i | 0.262813 | − | 0.0853932i | ||||
\(945\) | 77.9047 | + | 413.161i | 0.0824389 | + | 0.437207i | ||||
\(946\) | −63.9211 | + | 196.729i | −0.0675699 | + | 0.207959i | ||||
\(947\) | −768.561 | + | 391.602i | −0.811575 | + | 0.413518i | −0.809963 | − | 0.586481i | \(-0.800513\pi\) |
−0.00161156 | + | 0.999999i | \(0.500513\pi\) | |||||||
\(948\) | −43.7826 | + | 276.432i | −0.0461841 | + | 0.291595i | ||||
\(949\) | 676.907i | 0.713285i | ||||||||
\(950\) | −869.737 | − | 773.373i | −0.915512 | − | 0.814077i | ||||
\(951\) | −921.698 | −0.969188 | ||||||||
\(952\) | 116.369 | + | 18.4311i | 0.122237 | + | 0.0193604i | ||||
\(953\) | −194.635 | − | 381.992i | −0.204234 | − | 0.400831i | 0.766057 | − | 0.642772i | \(-0.222216\pi\) |
−0.970291 | + | 0.241941i | \(0.922216\pi\) | |||||||
\(954\) | 103.828 | + | 33.7358i | 0.108834 | + | 0.0353625i | ||||
\(955\) | 302.182 | + | 552.447i | 0.316421 | + | 0.578478i | ||||
\(956\) | 6.19720 | + | 19.0730i | 0.00648243 | + | 0.0199509i | ||||
\(957\) | −115.015 | − | 115.015i | −0.120183 | − | 0.120183i | ||||
\(958\) | 533.634 | + | 271.900i | 0.557029 | + | 0.283821i | ||||
\(959\) | −480.384 | + | 661.191i | −0.500922 | + | 0.689459i | ||||
\(960\) | 107.680 | − | 83.1589i | 0.112166 | − | 0.0866239i | ||||
\(961\) | −912.144 | + | 662.711i | −0.949161 | + | 0.689606i | ||||
\(962\) | −105.173 | − | 664.034i | −0.109327 | − | 0.690264i | ||||
\(963\) | −82.0755 | + | 12.9995i | −0.0852289 | + | 0.0134989i | ||||
\(964\) | 250.584 | + | 344.899i | 0.259942 | + | 0.357779i | ||||
\(965\) | −1059.76 | + | 378.995i | −1.09820 | + | 0.392741i | ||||
\(966\) | 132.945 | + | 96.5903i | 0.137624 | + | 0.0999899i | ||||
\(967\) | 843.184 | − | 1654.84i | 0.871958 | − | 1.71131i | 0.187497 | − | 0.982265i | \(-0.439962\pi\) |
0.684461 | − | 0.729049i | \(-0.260038\pi\) | |||||||
\(968\) | 352.251 | − | 352.251i | 0.363895 | − | 0.363895i | ||||
\(969\) | 1153.88 | − | 374.919i | 1.19080 | − | 0.386913i | ||||
\(970\) | 573.156 | + | 73.6448i | 0.590883 | + | 0.0759224i | ||||
\(971\) | 173.464 | − | 533.869i | 0.178645 | − | 0.549813i | −0.821136 | − | 0.570733i | \(-0.806659\pi\) |
0.999781 | + | 0.0209193i | \(0.00665931\pi\) | |||||||
\(972\) | −240.276 | + | 122.427i | −0.247198 | + | 0.125954i | ||||
\(973\) | 18.4410 | − | 116.432i | 0.0189527 | − | 0.119663i | ||||
\(974\) | 426.478i | 0.437863i | ||||||||
\(975\) | 180.153 | − | 689.464i | 0.184772 | − | 0.707143i | ||||
\(976\) | −337.425 | −0.345722 | ||||||||
\(977\) | −1039.14 | − | 164.584i | −1.06361 | − | 0.168459i | −0.399981 | − | 0.916524i | \(-0.630983\pi\) |
−0.663625 | + | 0.748065i | \(0.730983\pi\) | |||||||
\(978\) | −160.279 | − | 314.565i | −0.163884 | − | 0.321641i | ||||
\(979\) | 1611.71 | + | 523.676i | 1.64628 | + | 0.534909i | ||||
\(980\) | −234.796 | + | 248.969i | −0.239587 | + | 0.254050i | ||||
\(981\) | −11.4275 | − | 35.1703i | −0.0116489 | − | 0.0358515i | ||||
\(982\) | −365.256 | − | 365.256i | −0.371951 | − | 0.371951i | ||||
\(983\) | 949.807 | + | 483.951i | 0.966233 | + | 0.492321i | 0.864578 | − | 0.502499i | \(-0.167586\pi\) |
0.101656 | + | 0.994820i | \(0.467586\pi\) | |||||||
\(984\) | −323.117 | + | 444.732i | −0.328371 | + | 0.451964i | ||||
\(985\) | −310.627 | + | 9.10085i | −0.315357 | + | 0.00923944i | ||||
\(986\) | 34.3946 | − | 24.9892i | 0.0348830 | − | 0.0253440i | ||||
\(987\) | −51.5420 | − | 325.423i | −0.0522209 | − | 0.329710i | ||||
\(988\) | 544.952 | − | 86.3119i | 0.551571 | − | 0.0873602i | ||||
\(989\) | −44.3242 | − | 61.0070i | −0.0448172 | − | 0.0616855i | ||||
\(990\) | 176.550 | − | 258.602i | 0.178334 | − | 0.261214i | ||||
\(991\) | 9.79794 | + | 7.11862i | 0.00988692 | + | 0.00718327i | 0.592718 | − | 0.805410i | \(-0.298055\pi\) |
−0.582831 | + | 0.812594i | \(0.698055\pi\) | |||||||
\(992\) | 117.364 | − | 230.340i | 0.118311 | − | 0.232198i | ||||
\(993\) | 872.055 | − | 872.055i | 0.878202 | − | 0.878202i | ||||
\(994\) | −560.654 | + | 182.167i | −0.564038 | + | 0.183267i | ||||
\(995\) | −294.216 | + | 621.807i | −0.295695 | + | 0.624932i | ||||
\(996\) | −75.8838 | + | 233.546i | −0.0761886 | + | 0.234484i | ||||
\(997\) | −872.430 | + | 444.525i | −0.875055 | + | 0.445863i | −0.833013 | − | 0.553253i | \(-0.813386\pi\) |
−0.0420419 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(998\) | 20.9666 | − | 132.378i | 0.0210086 | − | 0.132643i | ||||
\(999\) | 1240.85i | 1.24209i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 50.3.f.b.27.3 | yes | 24 | |
4.3 | odd | 2 | 400.3.bg.b.177.1 | 24 | |||
5.2 | odd | 4 | 250.3.f.d.93.3 | 24 | |||
5.3 | odd | 4 | 250.3.f.f.93.1 | 24 | |||
5.4 | even | 2 | 250.3.f.e.157.1 | 24 | |||
25.9 | even | 10 | 250.3.f.d.207.3 | 24 | |||
25.12 | odd | 20 | 250.3.f.e.43.1 | 24 | |||
25.13 | odd | 20 | inner | 50.3.f.b.13.3 | ✓ | 24 | |
25.16 | even | 5 | 250.3.f.f.207.1 | 24 | |||
100.63 | even | 20 | 400.3.bg.b.113.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.3.f.b.13.3 | ✓ | 24 | 25.13 | odd | 20 | inner | |
50.3.f.b.27.3 | yes | 24 | 1.1 | even | 1 | trivial | |
250.3.f.d.93.3 | 24 | 5.2 | odd | 4 | |||
250.3.f.d.207.3 | 24 | 25.9 | even | 10 | |||
250.3.f.e.43.1 | 24 | 25.12 | odd | 20 | |||
250.3.f.e.157.1 | 24 | 5.4 | even | 2 | |||
250.3.f.f.93.1 | 24 | 5.3 | odd | 4 | |||
250.3.f.f.207.1 | 24 | 25.16 | even | 5 | |||
400.3.bg.b.113.1 | 24 | 100.63 | even | 20 | |||
400.3.bg.b.177.1 | 24 | 4.3 | odd | 2 |