Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,3,Mod(53,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.g (of order \(8\), degree \(4\), 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: | \(2.77929869648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 59.6 | ||
Character | \(\chi\) | \(=\) | 102.59 |
Dual form | 102.3.g.a.83.6 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 2.79886 | + | 1.07998i | 0.932955 | + | 0.359994i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 2.45376 | − | 5.92389i | 0.490752 | − | 1.18478i | −0.463587 | − | 0.886051i | \(-0.653438\pi\) |
0.954338 | − | 0.298728i | \(-0.0965622\pi\) | |||||||
\(6\) | −1.71888 | − | 3.87885i | −0.286480 | − | 0.646474i | ||||
\(7\) | −2.42737 | + | 1.00545i | −0.346766 | + | 0.143635i | −0.549267 | − | 0.835647i | \(-0.685093\pi\) |
0.202501 | + | 0.979282i | \(0.435093\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 6.66728 | + | 6.04544i | 0.740809 | + | 0.671716i | ||||
\(10\) | −8.37765 | + | 3.47014i | −0.837765 | + | 0.347014i | ||||
\(11\) | 14.2208 | − | 5.89045i | 1.29280 | − | 0.535496i | 0.372982 | − | 0.927839i | \(-0.378335\pi\) |
0.919819 | + | 0.392343i | \(0.128335\pi\) | |||||||
\(12\) | −2.15996 | + | 5.59773i | −0.179997 | + | 0.466477i | ||||
\(13\) | 3.81184i | 0.293218i | 0.989195 | + | 0.146609i | \(0.0468359\pi\) | ||||
−0.989195 | + | 0.146609i | \(0.953164\pi\) | |||||||
\(14\) | 3.43281 | + | 1.42192i | 0.245201 | + | 0.101566i | ||||
\(15\) | 13.2654 | − | 13.9302i | 0.884362 | − | 0.928678i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −15.4293 | − | 7.13697i | −0.907607 | − | 0.419822i | ||||
\(18\) | −0.621836 | − | 12.7127i | −0.0345465 | − | 0.706262i | ||||
\(19\) | 9.95630 | − | 9.95630i | 0.524016 | − | 0.524016i | −0.394766 | − | 0.918782i | \(-0.629174\pi\) |
0.918782 | + | 0.394766i | \(0.129174\pi\) | |||||||
\(20\) | 11.8478 | + | 4.90752i | 0.592389 | + | 0.245376i | ||||
\(21\) | −7.87973 | + | 0.192601i | −0.375225 | + | 0.00917149i | ||||
\(22\) | −20.1113 | − | 8.33036i | −0.914148 | − | 0.378653i | ||||
\(23\) | −11.4276 | + | 4.73345i | −0.496850 | + | 0.205802i | −0.617014 | − | 0.786952i | \(-0.711658\pi\) |
0.120164 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(24\) | 7.75769 | − | 3.43776i | 0.323237 | − | 0.143240i | ||||
\(25\) | −11.3939 | − | 11.3939i | −0.455757 | − | 0.455757i | ||||
\(26\) | 3.81184 | − | 3.81184i | 0.146609 | − | 0.146609i | ||||
\(27\) | 12.1318 | + | 24.1209i | 0.449327 | + | 0.893367i | ||||
\(28\) | −2.01090 | − | 4.85473i | −0.0718177 | − | 0.173383i | ||||
\(29\) | −15.7748 | + | 38.0836i | −0.543957 | + | 1.31323i | 0.377953 | + | 0.925825i | \(0.376628\pi\) |
−0.921910 | + | 0.387404i | \(0.873372\pi\) | |||||||
\(30\) | −27.1956 | + | 0.664732i | −0.906520 | + | 0.0221577i | ||||
\(31\) | −10.0183 | + | 24.1863i | −0.323171 | + | 0.780204i | 0.675895 | + | 0.736998i | \(0.263757\pi\) |
−0.999066 | + | 0.0432061i | \(0.986243\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 46.1637 | − | 1.12836i | 1.39890 | − | 0.0341928i | ||||
\(34\) | 8.29234 | + | 22.5663i | 0.243892 | + | 0.663714i | ||||
\(35\) | 16.8466i | 0.481331i | ||||||||
\(36\) | −12.0909 | + | 13.3346i | −0.335858 | + | 0.370404i | ||||
\(37\) | −19.7992 | + | 47.7996i | −0.535115 | + | 1.29188i | 0.392983 | + | 0.919546i | \(0.371443\pi\) |
−0.928098 | + | 0.372336i | \(0.878557\pi\) | |||||||
\(38\) | −19.9126 | −0.524016 | ||||||||
\(39\) | −4.11671 | + | 10.6688i | −0.105557 | + | 0.273559i | ||||
\(40\) | −6.94027 | − | 16.7553i | −0.173507 | − | 0.418883i | ||||
\(41\) | −24.3029 | − | 58.6725i | −0.592754 | − | 1.43104i | −0.880832 | − | 0.473429i | \(-0.843016\pi\) |
0.288078 | − | 0.957607i | \(-0.406984\pi\) | |||||||
\(42\) | 8.07233 | + | 7.68713i | 0.192198 | + | 0.183027i | ||||
\(43\) | −4.47973 | − | 4.47973i | −0.104180 | − | 0.104180i | 0.653096 | − | 0.757275i | \(-0.273470\pi\) |
−0.757275 | + | 0.653096i | \(0.773470\pi\) | |||||||
\(44\) | 11.7809 | + | 28.4416i | 0.267748 | + | 0.646401i | ||||
\(45\) | 52.1725 | − | 24.6622i | 1.15939 | − | 0.548049i | ||||
\(46\) | 16.1610 | + | 6.69411i | 0.351326 | + | 0.145524i | ||||
\(47\) | −71.4076 | −1.51931 | −0.759656 | − | 0.650325i | \(-0.774633\pi\) | ||||
−0.759656 | + | 0.650325i | \(0.774633\pi\) | |||||||
\(48\) | −11.1955 | − | 4.31993i | −0.233239 | − | 0.0899985i | ||||
\(49\) | −29.7671 | + | 29.7671i | −0.607491 | + | 0.607491i | ||||
\(50\) | 22.7879i | 0.455757i | ||||||||
\(51\) | −35.4768 | − | 36.6388i | −0.695623 | − | 0.718407i | ||||
\(52\) | −7.62367 | −0.146609 | ||||||||
\(53\) | 28.1506 | + | 28.1506i | 0.531143 | + | 0.531143i | 0.920912 | − | 0.389770i | \(-0.127445\pi\) |
−0.389770 | + | 0.920912i | \(0.627445\pi\) | |||||||
\(54\) | 11.9891 | − | 36.2528i | 0.222020 | − | 0.671347i | ||||
\(55\) | − | 98.6963i | − | 1.79448i | ||||||
\(56\) | −2.84384 | + | 6.86563i | −0.0507828 | + | 0.122600i | ||||
\(57\) | 38.6189 | − | 17.1137i | 0.677525 | − | 0.300240i | ||||
\(58\) | 53.8584 | − | 22.3089i | 0.928593 | − | 0.384636i | ||||
\(59\) | 49.2340 | − | 49.2340i | 0.834475 | − | 0.834475i | −0.153650 | − | 0.988125i | \(-0.549103\pi\) |
0.988125 | + | 0.153650i | \(0.0491028\pi\) | |||||||
\(60\) | 27.8603 | + | 26.5309i | 0.464339 | + | 0.442181i | ||||
\(61\) | −34.7236 | + | 14.3830i | −0.569239 | + | 0.235786i | −0.648691 | − | 0.761052i | \(-0.724683\pi\) |
0.0794517 | + | 0.996839i | \(0.474683\pi\) | |||||||
\(62\) | 34.2046 | − | 14.1680i | 0.551687 | − | 0.228516i | ||||
\(63\) | −22.2623 | − | 7.97090i | −0.353370 | − | 0.126522i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 22.5809 | + | 9.35332i | 0.347399 | + | 0.143897i | ||||
\(66\) | −47.2921 | − | 45.0353i | −0.716546 | − | 0.682354i | ||||
\(67\) | 56.4378 | 0.842355 | 0.421177 | − | 0.906978i | \(-0.361617\pi\) | ||||
0.421177 | + | 0.906978i | \(0.361617\pi\) | |||||||
\(68\) | 14.2739 | − | 30.8586i | 0.209911 | − | 0.453803i | ||||
\(69\) | −37.0962 | + | 0.906729i | −0.537626 | + | 0.0131410i | ||||
\(70\) | 16.8466 | − | 16.8466i | 0.240665 | − | 0.240665i | ||||
\(71\) | 53.8186 | + | 22.2924i | 0.758008 | + | 0.313977i | 0.728004 | − | 0.685572i | \(-0.240448\pi\) |
0.0300040 | + | 0.999550i | \(0.490448\pi\) | |||||||
\(72\) | 25.4254 | − | 1.24367i | 0.353131 | − | 0.0172732i | ||||
\(73\) | 92.4089 | + | 38.2770i | 1.26587 | + | 0.524342i | 0.911708 | − | 0.410840i | \(-0.134764\pi\) |
0.354167 | + | 0.935182i | \(0.384764\pi\) | |||||||
\(74\) | 67.5989 | − | 28.0004i | 0.913498 | − | 0.378383i | ||||
\(75\) | −19.5848 | − | 44.1953i | −0.261131 | − | 0.589271i | ||||
\(76\) | 19.9126 | + | 19.9126i | 0.262008 | + | 0.262008i | ||||
\(77\) | −28.5966 | + | 28.5966i | −0.371384 | + | 0.371384i | ||||
\(78\) | 14.7855 | − | 6.55210i | 0.189558 | − | 0.0840012i | ||||
\(79\) | −44.0023 | − | 106.231i | −0.556991 | − | 1.34469i | −0.912138 | − | 0.409884i | \(-0.865569\pi\) |
0.355147 | − | 0.934811i | \(-0.384431\pi\) | |||||||
\(80\) | −9.81503 | + | 23.6956i | −0.122688 | + | 0.296195i | ||||
\(81\) | 7.90523 | + | 80.6133i | 0.0975955 | + | 0.995226i | ||||
\(82\) | −34.3695 | + | 82.9754i | −0.419141 | + | 1.01190i | ||||
\(83\) | −65.3290 | − | 65.3290i | −0.787097 | − | 0.787097i | 0.193920 | − | 0.981017i | \(-0.437880\pi\) |
−0.981017 | + | 0.193920i | \(0.937880\pi\) | |||||||
\(84\) | −0.385203 | − | 15.7595i | −0.00458575 | − | 0.187613i | ||||
\(85\) | −80.1384 | + | 73.8892i | −0.942805 | + | 0.869285i | ||||
\(86\) | 8.95947i | 0.104180i | ||||||||
\(87\) | −85.2810 | + | 89.5544i | −0.980241 | + | 1.02936i | ||||
\(88\) | 16.6607 | − | 40.2225i | 0.189326 | − | 0.457074i | ||||
\(89\) | 9.82979 | 0.110447 | 0.0552235 | − | 0.998474i | \(-0.482413\pi\) | ||||
0.0552235 | + | 0.998474i | \(0.482413\pi\) | |||||||
\(90\) | −76.8347 | − | 27.5102i | −0.853719 | − | 0.305669i | ||||
\(91\) | −3.83260 | − | 9.25272i | −0.0421165 | − | 0.101678i | ||||
\(92\) | −9.46690 | − | 22.8551i | −0.102901 | − | 0.248425i | ||||
\(93\) | −54.1606 | + | 56.8746i | −0.582373 | + | 0.611555i | ||||
\(94\) | 71.4076 | + | 71.4076i | 0.759656 | + | 0.759656i | ||||
\(95\) | −34.5497 | − | 83.4104i | −0.363681 | − | 0.878004i | ||||
\(96\) | 6.87553 | + | 15.5154i | 0.0716201 | + | 0.161619i | ||||
\(97\) | −101.603 | − | 42.0852i | −1.04745 | − | 0.433868i | −0.208469 | − | 0.978029i | \(-0.566848\pi\) |
−0.838981 | + | 0.544161i | \(0.816848\pi\) | |||||||
\(98\) | 59.5341 | 0.607491 | ||||||||
\(99\) | 130.425 | + | 46.6978i | 1.31742 | + | 0.471695i | ||||
\(100\) | 22.7879 | − | 22.7879i | 0.227879 | − | 0.227879i | ||||
\(101\) | 56.1901i | 0.556338i | 0.960532 | + | 0.278169i | \(0.0897275\pi\) | ||||
−0.960532 | + | 0.278169i | \(0.910273\pi\) | |||||||
\(102\) | −1.16202 | + | 72.1155i | −0.0113924 | + | 0.707015i | ||||
\(103\) | 175.554 | 1.70441 | 0.852204 | − | 0.523210i | \(-0.175266\pi\) | ||||
0.852204 | + | 0.523210i | \(0.175266\pi\) | |||||||
\(104\) | 7.62367 | + | 7.62367i | 0.0733045 | + | 0.0733045i | ||||
\(105\) | −18.1940 | + | 47.1513i | −0.173276 | + | 0.449060i | ||||
\(106\) | − | 56.3011i | − | 0.531143i | ||||||
\(107\) | 42.7135 | − | 103.119i | 0.399191 | − | 0.963733i | −0.588667 | − | 0.808376i | \(-0.700347\pi\) |
0.987858 | − | 0.155357i | \(-0.0496529\pi\) | |||||||
\(108\) | −48.2418 | + | 24.2637i | −0.446684 | + | 0.224664i | ||||
\(109\) | 194.837 | − | 80.7041i | 1.78750 | − | 0.740405i | 0.796811 | − | 0.604229i | \(-0.206519\pi\) |
0.990685 | − | 0.136176i | \(-0.0434814\pi\) | |||||||
\(110\) | −98.6963 | + | 98.6963i | −0.897239 | + | 0.897239i | ||||
\(111\) | −107.038 | + | 112.402i | −0.964307 | + | 1.01263i | ||||
\(112\) | 9.70946 | − | 4.02179i | 0.0866916 | − | 0.0359088i | ||||
\(113\) | −156.202 | + | 64.7009i | −1.38232 | + | 0.572574i | −0.945100 | − | 0.326782i | \(-0.894036\pi\) |
−0.437216 | + | 0.899356i | \(0.644036\pi\) | |||||||
\(114\) | −55.7326 | − | 21.5052i | −0.488883 | − | 0.188642i | ||||
\(115\) | 79.3104i | 0.689656i | ||||||||
\(116\) | −76.1672 | − | 31.5495i | −0.656614 | − | 0.271979i | ||||
\(117\) | −23.0442 | + | 25.4146i | −0.196959 | + | 0.217219i | ||||
\(118\) | −98.4681 | −0.834475 | ||||||||
\(119\) | 44.6284 | + | 1.81066i | 0.375029 | + | 0.0152157i | ||||
\(120\) | −1.32946 | − | 54.3912i | −0.0110789 | − | 0.453260i | ||||
\(121\) | 81.9741 | − | 81.9741i | 0.677472 | − | 0.677472i | ||||
\(122\) | 49.1065 | + | 20.3406i | 0.402513 | + | 0.166726i | ||||
\(123\) | −4.65542 | − | 190.463i | −0.0378489 | − | 1.54848i | ||||
\(124\) | −48.3726 | − | 20.0366i | −0.390102 | − | 0.161586i | ||||
\(125\) | 52.6429 | − | 21.8054i | 0.421144 | − | 0.174443i | ||||
\(126\) | 14.2914 | + | 30.2332i | 0.113424 | + | 0.239946i | ||||
\(127\) | −72.4964 | − | 72.4964i | −0.570838 | − | 0.570838i | 0.361525 | − | 0.932362i | \(-0.382256\pi\) |
−0.932362 | + | 0.361525i | \(0.882256\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −7.70013 | − | 17.3762i | −0.0596910 | − | 0.134699i | ||||
\(130\) | −13.2276 | − | 31.9342i | −0.101751 | − | 0.245648i | ||||
\(131\) | −24.0772 | + | 58.1276i | −0.183796 | + | 0.443722i | −0.988743 | − | 0.149624i | \(-0.952194\pi\) |
0.804947 | + | 0.593346i | \(0.202194\pi\) | |||||||
\(132\) | 2.25672 | + | 92.3274i | 0.0170964 | + | 0.699450i | ||||
\(133\) | −14.1570 | + | 34.1781i | −0.106444 | + | 0.256978i | ||||
\(134\) | −56.4378 | − | 56.4378i | −0.421177 | − | 0.421177i | ||||
\(135\) | 172.658 | − | 12.6809i | 1.27895 | − | 0.0939324i | ||||
\(136\) | −45.1326 | + | 16.5847i | −0.331857 | + | 0.121946i | ||||
\(137\) | 99.8865i | 0.729098i | 0.931184 | + | 0.364549i | \(0.118777\pi\) | ||||
−0.931184 | + | 0.364549i | \(0.881223\pi\) | |||||||
\(138\) | 38.0030 | + | 36.1895i | 0.275384 | + | 0.262243i | ||||
\(139\) | −5.23734 | + | 12.6441i | −0.0376787 | + | 0.0909644i | −0.941599 | − | 0.336737i | \(-0.890677\pi\) |
0.903920 | + | 0.427702i | \(0.140677\pi\) | |||||||
\(140\) | −33.6932 | −0.240665 | ||||||||
\(141\) | −199.860 | − | 77.1189i | −1.41745 | − | 0.546943i | ||||
\(142\) | −31.5262 | − | 76.1110i | −0.222016 | − | 0.535993i | ||||
\(143\) | 22.4534 | + | 54.2074i | 0.157017 | + | 0.379073i | ||||
\(144\) | −26.6691 | − | 24.1818i | −0.185202 | − | 0.167929i | ||||
\(145\) | 186.896 | + | 186.896i | 1.28894 | + | 1.28894i | ||||
\(146\) | −54.1319 | − | 130.686i | −0.370766 | − | 0.895109i | ||||
\(147\) | −115.462 | + | 51.1661i | −0.785454 | + | 0.348068i | ||||
\(148\) | −95.5992 | − | 39.5985i | −0.645941 | − | 0.267557i | ||||
\(149\) | 72.5768 | 0.487093 | 0.243546 | − | 0.969889i | \(-0.421689\pi\) | ||||
0.243546 | + | 0.969889i | \(0.421689\pi\) | |||||||
\(150\) | −24.6105 | + | 63.7801i | −0.164070 | + | 0.425201i | ||||
\(151\) | −75.9450 | + | 75.9450i | −0.502947 | + | 0.502947i | −0.912353 | − | 0.409405i | \(-0.865736\pi\) |
0.409405 | + | 0.912353i | \(0.365736\pi\) | |||||||
\(152\) | − | 39.8252i | − | 0.262008i | ||||||
\(153\) | −59.7254 | − | 140.861i | −0.390362 | − | 0.920661i | ||||
\(154\) | 57.1931 | 0.371384 | ||||||||
\(155\) | 118.695 | + | 118.695i | 0.765772 | + | 0.765772i | ||||
\(156\) | −21.3376 | − | 8.23342i | −0.136780 | − | 0.0527784i | ||||
\(157\) | 70.9318i | 0.451795i | 0.974151 | + | 0.225897i | \(0.0725314\pi\) | ||||
−0.974151 | + | 0.225897i | \(0.927469\pi\) | |||||||
\(158\) | −62.2286 | + | 150.233i | −0.393852 | + | 0.950843i | ||||
\(159\) | 48.3875 | + | 109.192i | 0.304324 | + | 0.686740i | ||||
\(160\) | 33.5106 | − | 13.8805i | 0.209441 | − | 0.0867534i | ||||
\(161\) | 22.9796 | − | 22.9796i | 0.142731 | − | 0.142731i | ||||
\(162\) | 72.7081 | − | 88.5186i | 0.448815 | − | 0.546411i | ||||
\(163\) | −103.217 | + | 42.7538i | −0.633231 | + | 0.262293i | −0.676125 | − | 0.736787i | \(-0.736342\pi\) |
0.0428940 | + | 0.999080i | \(0.486342\pi\) | |||||||
\(164\) | 117.345 | − | 48.6059i | 0.715518 | − | 0.296377i | ||||
\(165\) | 106.590 | − | 276.238i | 0.646001 | − | 1.67417i | ||||
\(166\) | 130.658i | 0.787097i | ||||||||
\(167\) | −38.1651 | − | 15.8085i | −0.228533 | − | 0.0946616i | 0.265479 | − | 0.964117i | \(-0.414470\pi\) |
−0.494012 | + | 0.869455i | \(0.664470\pi\) | |||||||
\(168\) | −15.3743 | + | 16.1447i | −0.0915134 | + | 0.0960992i | ||||
\(169\) | 154.470 | 0.914023 | ||||||||
\(170\) | 154.028 | + | 6.24921i | 0.906045 | + | 0.0367600i | ||||
\(171\) | 126.572 | − | 6.19119i | 0.740185 | − | 0.0362058i | ||||
\(172\) | 8.95947 | − | 8.95947i | 0.0520899 | − | 0.0520899i | ||||
\(173\) | −225.559 | − | 93.4297i | −1.30381 | − | 0.540056i | −0.380739 | − | 0.924683i | \(-0.624330\pi\) |
−0.923072 | + | 0.384626i | \(0.874330\pi\) | |||||||
\(174\) | 174.835 | − | 4.27344i | 1.00480 | − | 0.0245600i | ||||
\(175\) | 39.1132 | + | 16.2012i | 0.223504 | + | 0.0925785i | ||||
\(176\) | −56.8832 | + | 23.5618i | −0.323200 | + | 0.133874i | ||||
\(177\) | 190.971 | − | 84.6275i | 1.07893 | − | 0.478122i | ||||
\(178\) | −9.82979 | − | 9.82979i | −0.0552235 | − | 0.0552235i | ||||
\(179\) | 152.283 | − | 152.283i | 0.850742 | − | 0.850742i | −0.139482 | − | 0.990225i | \(-0.544544\pi\) |
0.990225 | + | 0.139482i | \(0.0445439\pi\) | |||||||
\(180\) | 49.3244 | + | 104.345i | 0.274025 | + | 0.579694i | ||||
\(181\) | −93.8937 | − | 226.679i | −0.518750 | − | 1.25237i | −0.938672 | − | 0.344813i | \(-0.887942\pi\) |
0.419922 | − | 0.907560i | \(-0.362058\pi\) | |||||||
\(182\) | −5.42012 | + | 13.0853i | −0.0297809 | + | 0.0718973i | ||||
\(183\) | −112.720 | + | 2.75517i | −0.615956 | + | 0.0150556i | ||||
\(184\) | −13.3882 | + | 32.3220i | −0.0727621 | + | 0.175663i | ||||
\(185\) | 234.577 | + | 234.577i | 1.26799 | + | 1.26799i | ||||
\(186\) | 111.035 | − | 2.71399i | 0.596964 | − | 0.0145914i | ||||
\(187\) | −261.457 | − | 10.6078i | −1.39817 | − | 0.0567264i | ||||
\(188\) | − | 142.815i | − | 0.759656i | ||||||
\(189\) | −53.7007 | − | 46.3523i | −0.284131 | − | 0.245250i | ||||
\(190\) | −48.8607 | + | 117.960i | −0.257161 | + | 0.620843i | ||||
\(191\) | 73.2511 | 0.383514 | 0.191757 | − | 0.981442i | \(-0.438581\pi\) | ||||
0.191757 | + | 0.981442i | \(0.438581\pi\) | |||||||
\(192\) | 8.63985 | − | 22.3909i | 0.0449992 | − | 0.116619i | ||||
\(193\) | −12.1162 | − | 29.2511i | −0.0627783 | − | 0.151560i | 0.889377 | − | 0.457174i | \(-0.151138\pi\) |
−0.952156 | + | 0.305614i | \(0.901138\pi\) | |||||||
\(194\) | 59.5175 | + | 143.688i | 0.306791 | + | 0.740659i | ||||
\(195\) | 53.0995 | + | 50.5656i | 0.272305 | + | 0.259311i | ||||
\(196\) | −59.5341 | − | 59.5341i | −0.303745 | − | 0.303745i | ||||
\(197\) | −17.6628 | − | 42.6418i | −0.0896588 | − | 0.216456i | 0.872689 | − | 0.488276i | \(-0.162374\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(198\) | −83.7267 | − | 177.122i | −0.422862 | − | 0.894557i | ||||
\(199\) | 5.30033 | + | 2.19547i | 0.0266348 | + | 0.0110325i | 0.395961 | − | 0.918267i | \(-0.370412\pi\) |
−0.369326 | + | 0.929300i | \(0.620412\pi\) | |||||||
\(200\) | −45.5757 | −0.227879 | ||||||||
\(201\) | 157.962 | + | 60.9517i | 0.785879 | + | 0.303243i | ||||
\(202\) | 56.1901 | − | 56.1901i | 0.278169 | − | 0.278169i | ||||
\(203\) | − | 108.304i | − | 0.533515i | ||||||
\(204\) | 73.2776 | − | 70.9535i | 0.359204 | − | 0.347811i | ||||
\(205\) | −407.203 | −1.98636 | ||||||||
\(206\) | −175.554 | − | 175.554i | −0.852204 | − | 0.852204i | ||||
\(207\) | −104.807 | − | 37.5254i | −0.506312 | − | 0.181282i | ||||
\(208\) | − | 15.2473i | − | 0.0733045i | ||||||
\(209\) | 82.9395 | − | 200.234i | 0.396840 | − | 0.958056i | ||||
\(210\) | 65.3453 | − | 28.9573i | 0.311168 | − | 0.137892i | ||||
\(211\) | 158.876 | − | 65.8085i | 0.752966 | − | 0.311889i | 0.0270150 | − | 0.999635i | \(-0.491400\pi\) |
0.725951 | + | 0.687746i | \(0.241400\pi\) | |||||||
\(212\) | −56.3011 | + | 56.3011i | −0.265571 | + | 0.265571i | ||||
\(213\) | 126.556 | + | 120.516i | 0.594158 | + | 0.565805i | ||||
\(214\) | −145.833 | + | 60.4060i | −0.681462 | + | 0.282271i | ||||
\(215\) | −37.5296 | + | 15.5453i | −0.174556 | + | 0.0723037i | ||||
\(216\) | 72.5055 | + | 23.9781i | 0.335674 | + | 0.111010i | ||||
\(217\) | − | 68.7819i | − | 0.316967i | ||||||
\(218\) | −275.541 | − | 114.133i | −1.26395 | − | 0.523545i | ||||
\(219\) | 217.301 | + | 206.932i | 0.992244 | + | 0.944895i | ||||
\(220\) | 197.393 | 0.897239 | ||||||||
\(221\) | 27.2049 | − | 58.8140i | 0.123099 | − | 0.266127i | ||||
\(222\) | 219.440 | − | 5.36369i | 0.988468 | − | 0.0241608i | ||||
\(223\) | −70.7300 | + | 70.7300i | −0.317175 | + | 0.317175i | −0.847681 | − | 0.530506i | \(-0.822002\pi\) |
0.530506 | + | 0.847681i | \(0.322002\pi\) | |||||||
\(224\) | −13.7313 | − | 5.68767i | −0.0613002 | − | 0.0253914i | ||||
\(225\) | −7.08516 | − | 144.848i | −0.0314896 | − | 0.643769i | ||||
\(226\) | 220.903 | + | 91.5008i | 0.977445 | + | 0.404871i | ||||
\(227\) | −239.164 | + | 99.0651i | −1.05359 | + | 0.436410i | −0.841171 | − | 0.540769i | \(-0.818133\pi\) |
−0.212416 | + | 0.977179i | \(0.568133\pi\) | |||||||
\(228\) | 34.2274 | + | 77.2379i | 0.150120 | + | 0.338763i | ||||
\(229\) | −134.595 | − | 134.595i | −0.587752 | − | 0.587752i | 0.349270 | − | 0.937022i | \(-0.386430\pi\) |
−0.937022 | + | 0.349270i | \(0.886430\pi\) | |||||||
\(230\) | 79.3104 | − | 79.3104i | 0.344828 | − | 0.344828i | ||||
\(231\) | −110.922 | + | 49.1541i | −0.480180 | + | 0.212788i | ||||
\(232\) | 44.6177 | + | 107.717i | 0.192318 | + | 0.464296i | ||||
\(233\) | −99.0061 | + | 239.022i | −0.424919 | + | 1.02585i | 0.555957 | + | 0.831211i | \(0.312352\pi\) |
−0.980876 | + | 0.194634i | \(0.937648\pi\) | |||||||
\(234\) | 48.4588 | − | 2.37034i | 0.207089 | − | 0.0101296i | ||||
\(235\) | −175.217 | + | 423.011i | −0.745604 | + | 1.80005i | ||||
\(236\) | 98.4681 | + | 98.4681i | 0.417238 | + | 0.417238i | ||||
\(237\) | −8.42898 | − | 344.847i | −0.0355653 | − | 1.45505i | ||||
\(238\) | −42.8178 | − | 46.4391i | −0.179907 | − | 0.195122i | ||||
\(239\) | 172.033i | 0.719805i | 0.932990 | + | 0.359902i | \(0.117190\pi\) | ||||
−0.932990 | + | 0.359902i | \(0.882810\pi\) | |||||||
\(240\) | −53.0617 | + | 55.7207i | −0.221091 | + | 0.232169i | ||||
\(241\) | 51.0444 | − | 123.232i | 0.211802 | − | 0.511336i | −0.781898 | − | 0.623407i | \(-0.785748\pi\) |
0.993700 | + | 0.112070i | \(0.0357482\pi\) | |||||||
\(242\) | −163.948 | −0.677472 | ||||||||
\(243\) | −64.9352 | + | 234.163i | −0.267223 | + | 0.963635i | ||||
\(244\) | −28.7659 | − | 69.4471i | −0.117893 | − | 0.284619i | ||||
\(245\) | 103.296 | + | 249.378i | 0.421615 | + | 1.01787i | ||||
\(246\) | −185.808 | + | 195.118i | −0.755315 | + | 0.793164i | ||||
\(247\) | 37.9518 | + | 37.9518i | 0.153651 | + | 0.153651i | ||||
\(248\) | 28.3360 | + | 68.4092i | 0.114258 | + | 0.275844i | ||||
\(249\) | −112.293 | − | 253.401i | −0.450976 | − | 1.01768i | ||||
\(250\) | −74.4484 | − | 30.8375i | −0.297793 | − | 0.123350i | ||||
\(251\) | 201.450 | 0.802591 | 0.401296 | − | 0.915949i | \(-0.368560\pi\) | ||||
0.401296 | + | 0.915949i | \(0.368560\pi\) | |||||||
\(252\) | 15.9418 | − | 44.5246i | 0.0632611 | − | 0.176685i | ||||
\(253\) | −134.627 | + | 134.627i | −0.532123 | + | 0.532123i | ||||
\(254\) | 144.993i | 0.570838i | ||||||||
\(255\) | −304.096 | + | 120.258i | −1.19253 | + | 0.471600i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −53.5444 | − | 53.5444i | −0.208344 | − | 0.208344i | 0.595219 | − | 0.803563i | \(-0.297065\pi\) |
−0.803563 | + | 0.595219i | \(0.797065\pi\) | |||||||
\(258\) | −9.67606 | + | 25.0763i | −0.0375041 | + | 0.0971951i | ||||
\(259\) | − | 135.934i | − | 0.524843i | ||||||
\(260\) | −18.7066 | + | 45.1618i | −0.0719486 | + | 0.173699i | ||||
\(261\) | −335.407 | + | 158.549i | −1.28508 | + | 0.607467i | ||||
\(262\) | 82.2048 | − | 34.0504i | 0.313759 | − | 0.129963i | ||||
\(263\) | 362.318 | − | 362.318i | 1.37764 | − | 1.37764i | 0.529040 | − | 0.848597i | \(-0.322552\pi\) |
0.848597 | − | 0.529040i | \(-0.177448\pi\) | |||||||
\(264\) | 90.0707 | − | 94.5841i | 0.341177 | − | 0.358273i | ||||
\(265\) | 235.836 | − | 97.6863i | 0.889946 | − | 0.368628i | ||||
\(266\) | 48.3351 | − | 20.0211i | 0.181711 | − | 0.0752672i | ||||
\(267\) | 27.5122 | + | 10.6160i | 0.103042 | + | 0.0397603i | ||||
\(268\) | 112.876i | 0.421177i | ||||||||
\(269\) | 0.511204 | + | 0.211748i | 0.00190039 | + | 0.000787166i | 0.383633 | − | 0.923485i | \(-0.374673\pi\) |
−0.381733 | + | 0.924273i | \(0.624673\pi\) | |||||||
\(270\) | −185.339 | − | 159.977i | −0.686442 | − | 0.592509i | ||||
\(271\) | 33.9197 | 0.125165 | 0.0625824 | − | 0.998040i | \(-0.480066\pi\) | ||||
0.0625824 | + | 0.998040i | \(0.480066\pi\) | |||||||
\(272\) | 61.7173 | + | 28.5479i | 0.226902 | + | 0.104955i | ||||
\(273\) | −0.734165 | − | 30.0362i | −0.00268925 | − | 0.110023i | ||||
\(274\) | 99.8865 | − | 99.8865i | 0.364549 | − | 0.364549i | ||||
\(275\) | −229.146 | − | 94.9156i | −0.833260 | − | 0.345147i | ||||
\(276\) | −1.81346 | − | 74.1925i | −0.00657050 | − | 0.268813i | ||||
\(277\) | −451.514 | − | 187.023i | −1.63002 | − | 0.675174i | −0.634781 | − | 0.772692i | \(-0.718910\pi\) |
−0.995234 | + | 0.0975175i | \(0.968910\pi\) | |||||||
\(278\) | 17.8814 | − | 7.40671i | 0.0643215 | − | 0.0266429i | ||||
\(279\) | −213.012 | + | 100.692i | −0.763483 | + | 0.360903i | ||||
\(280\) | 33.6932 | + | 33.6932i | 0.120333 | + | 0.120333i | ||||
\(281\) | −213.733 | + | 213.733i | −0.760615 | + | 0.760615i | −0.976433 | − | 0.215819i | \(-0.930758\pi\) |
0.215819 | + | 0.976433i | \(0.430758\pi\) | |||||||
\(282\) | 122.741 | + | 276.979i | 0.435253 | + | 0.982196i | ||||
\(283\) | 187.312 | + | 452.211i | 0.661880 | + | 1.59792i | 0.794855 | + | 0.606800i | \(0.207547\pi\) |
−0.132975 | + | 0.991119i | \(0.542453\pi\) | |||||||
\(284\) | −44.5848 | + | 107.637i | −0.156989 | + | 0.379004i | ||||
\(285\) | −6.61827 | − | 270.767i | −0.0232220 | − | 0.950061i | ||||
\(286\) | 31.7540 | − | 76.6608i | 0.111028 | − | 0.268045i | ||||
\(287\) | 117.984 | + | 117.984i | 0.411095 | + | 0.411095i | ||||
\(288\) | 2.48735 | + | 50.8509i | 0.00863661 | + | 0.176566i | ||||
\(289\) | 187.127 | + | 220.237i | 0.647500 | + | 0.762066i | ||||
\(290\) | − | 373.792i | − | 1.28894i | ||||||
\(291\) | −238.921 | − | 227.520i | −0.821034 | − | 0.781855i | ||||
\(292\) | −76.5540 | + | 184.818i | −0.262171 | + | 0.632937i | ||||
\(293\) | −411.302 | −1.40376 | −0.701881 | − | 0.712294i | \(-0.747656\pi\) | ||||
−0.701881 | + | 0.712294i | \(0.747656\pi\) | |||||||
\(294\) | 166.628 | + | 64.2957i | 0.566761 | + | 0.218693i | ||||
\(295\) | −170.849 | − | 412.466i | −0.579149 | − | 1.39819i | ||||
\(296\) | 56.0007 | + | 135.198i | 0.189192 | + | 0.456749i | ||||
\(297\) | 314.608 | + | 271.557i | 1.05929 | + | 0.914333i | ||||
\(298\) | −72.5768 | − | 72.5768i | −0.243546 | − | 0.243546i | ||||
\(299\) | −18.0431 | − | 43.5600i | −0.0603449 | − | 0.145686i | ||||
\(300\) | 88.3906 | − | 39.1697i | 0.294635 | − | 0.130566i | ||||
\(301\) | 15.3781 | + | 6.36981i | 0.0510900 | + | 0.0211622i | ||||
\(302\) | 151.890 | 0.502947 | ||||||||
\(303\) | −60.6843 | + | 157.268i | −0.200278 | + | 0.519038i | ||||
\(304\) | −39.8252 | + | 39.8252i | −0.131004 | + | 0.131004i | ||||
\(305\) | 240.991i | 0.790135i | ||||||||
\(306\) | −81.1358 | + | 200.587i | −0.265150 | + | 0.655512i | ||||
\(307\) | 238.599 | 0.777195 | 0.388597 | − | 0.921408i | \(-0.372960\pi\) | ||||
0.388597 | + | 0.921408i | \(0.372960\pi\) | |||||||
\(308\) | −57.1931 | − | 57.1931i | −0.185692 | − | 0.185692i | ||||
\(309\) | 491.352 | + | 189.595i | 1.59014 | + | 0.613576i | ||||
\(310\) | − | 237.389i | − | 0.765772i | ||||||
\(311\) | 205.626 | − | 496.425i | 0.661177 | − | 1.59622i | −0.134784 | − | 0.990875i | \(-0.543034\pi\) |
0.795961 | − | 0.605348i | \(-0.206966\pi\) | |||||||
\(312\) | 13.1042 | + | 29.5710i | 0.0420006 | + | 0.0947790i | ||||
\(313\) | 157.683 | − | 65.3145i | 0.503780 | − | 0.208672i | −0.116296 | − | 0.993215i | \(-0.537102\pi\) |
0.620075 | + | 0.784542i | \(0.287102\pi\) | |||||||
\(314\) | 70.9318 | − | 70.9318i | 0.225897 | − | 0.225897i | ||||
\(315\) | −101.845 | + | 112.321i | −0.323318 | + | 0.356574i | ||||
\(316\) | 212.462 | − | 88.0045i | 0.672347 | − | 0.278495i | ||||
\(317\) | 58.5858 | − | 24.2670i | 0.184813 | − | 0.0765522i | −0.288358 | − | 0.957523i | \(-0.593109\pi\) |
0.473171 | + | 0.880971i | \(0.343109\pi\) | |||||||
\(318\) | 60.8042 | − | 157.579i | 0.191208 | − | 0.495532i | ||||
\(319\) | 634.500i | 1.98903i | ||||||||
\(320\) | −47.3912 | − | 19.6301i | −0.148097 | − | 0.0613439i | ||||
\(321\) | 230.916 | − | 242.488i | 0.719365 | − | 0.755413i | ||||
\(322\) | −45.9593 | −0.142731 | ||||||||
\(323\) | −224.677 | + | 82.5610i | −0.695593 | + | 0.255607i | ||||
\(324\) | −161.227 | + | 15.8105i | −0.497613 | + | 0.0487977i | ||||
\(325\) | 43.4318 | − | 43.4318i | 0.133636 | − | 0.133636i | ||||
\(326\) | 145.970 | + | 60.4630i | 0.447762 | + | 0.185469i | ||||
\(327\) | 632.481 | − | 15.4595i | 1.93419 | − | 0.0472768i | ||||
\(328\) | −165.951 | − | 68.7391i | −0.505948 | − | 0.209570i | ||||
\(329\) | 173.332 | − | 71.7966i | 0.526846 | − | 0.218227i | ||||
\(330\) | −382.828 | + | 169.647i | −1.16008 | + | 0.514083i | ||||
\(331\) | −81.8846 | − | 81.8846i | −0.247386 | − | 0.247386i | 0.572511 | − | 0.819897i | \(-0.305969\pi\) |
−0.819897 | + | 0.572511i | \(0.805969\pi\) | |||||||
\(332\) | 130.658 | − | 130.658i | 0.393548 | − | 0.393548i | ||||
\(333\) | −420.977 | + | 198.998i | −1.26420 | + | 0.597592i | ||||
\(334\) | 22.3566 | + | 53.9736i | 0.0669359 | + | 0.161597i | ||||
\(335\) | 138.485 | − | 334.331i | 0.413387 | − | 0.998004i | ||||
\(336\) | 31.5189 | − | 0.770405i | 0.0938063 | − | 0.00229287i | ||||
\(337\) | 217.048 | − | 524.000i | 0.644059 | − | 1.55490i | −0.177099 | − | 0.984193i | \(-0.556671\pi\) |
0.821157 | − | 0.570702i | \(-0.193329\pi\) | |||||||
\(338\) | −154.470 | − | 154.470i | −0.457012 | − | 0.457012i | ||||
\(339\) | −507.063 | + | 12.3940i | −1.49576 | + | 0.0365603i | ||||
\(340\) | −147.778 | − | 160.277i | −0.434643 | − | 0.471403i | ||||
\(341\) | 402.961i | 1.18171i | ||||||||
\(342\) | −132.763 | − | 120.380i | −0.388195 | − | 0.351990i | ||||
\(343\) | 91.5932 | − | 221.126i | 0.267036 | − | 0.644681i | ||||
\(344\) | −17.9189 | −0.0520899 | ||||||||
\(345\) | −85.6538 | + | 221.979i | −0.248272 | + | 0.643418i | ||||
\(346\) | 132.130 | + | 318.989i | 0.381877 | + | 0.921934i | ||||
\(347\) | −176.782 | − | 426.790i | −0.509459 | − | 1.22994i | −0.944196 | − | 0.329385i | \(-0.893159\pi\) |
0.434737 | − | 0.900557i | \(-0.356841\pi\) | |||||||
\(348\) | −179.109 | − | 170.562i | −0.514681 | − | 0.490121i | ||||
\(349\) | −32.1059 | − | 32.1059i | −0.0919939 | − | 0.0919939i | 0.659612 | − | 0.751606i | \(-0.270721\pi\) |
−0.751606 | + | 0.659612i | \(0.770721\pi\) | |||||||
\(350\) | −22.9120 | − | 55.3145i | −0.0654629 | − | 0.158041i | ||||
\(351\) | −91.9449 | + | 46.2446i | −0.261951 | + | 0.131751i | ||||
\(352\) | 80.4451 | + | 33.3214i | 0.228537 | + | 0.0946632i | ||||
\(353\) | 33.3930 | 0.0945978 | 0.0472989 | − | 0.998881i | \(-0.484939\pi\) | ||||
0.0472989 | + | 0.998881i | \(0.484939\pi\) | |||||||
\(354\) | −275.599 | − | 106.344i | −0.778528 | − | 0.300406i | ||||
\(355\) | 264.116 | − | 264.116i | 0.743988 | − | 0.743988i | ||||
\(356\) | 19.6596i | 0.0552235i | ||||||||
\(357\) | 122.953 | + | 53.2657i | 0.344407 | + | 0.149204i | ||||
\(358\) | −304.566 | −0.850742 | ||||||||
\(359\) | 266.987 | + | 266.987i | 0.743697 | + | 0.743697i | 0.973287 | − | 0.229590i | \(-0.0737386\pi\) |
−0.229590 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(360\) | 55.0205 | − | 153.669i | 0.152835 | − | 0.426859i | ||||
\(361\) | 162.744i | 0.450815i | ||||||||
\(362\) | −132.786 | + | 320.573i | −0.366812 | + | 0.885561i | ||||
\(363\) | 317.965 | − | 140.904i | 0.875937 | − | 0.388165i | ||||
\(364\) | 18.5054 | − | 7.66520i | 0.0508391 | − | 0.0210582i | ||||
\(365\) | 453.498 | − | 453.498i | 1.24246 | − | 1.24246i | ||||
\(366\) | 115.475 | + | 109.965i | 0.315506 | + | 0.300450i | ||||
\(367\) | 512.700 | − | 212.367i | 1.39700 | − | 0.578657i | 0.448031 | − | 0.894018i | \(-0.352125\pi\) |
0.948972 | + | 0.315361i | \(0.102125\pi\) | |||||||
\(368\) | 45.7102 | − | 18.9338i | 0.124213 | − | 0.0514505i | ||||
\(369\) | 192.667 | − | 538.108i | 0.522132 | − | 1.45829i | ||||
\(370\) | − | 469.155i | − | 1.26799i | ||||||
\(371\) | −96.6356 | − | 40.0278i | −0.260473 | − | 0.107892i | ||||
\(372\) | −113.749 | − | 108.321i | −0.305778 | − | 0.291186i | ||||
\(373\) | 64.7860 | 0.173689 | 0.0868445 | − | 0.996222i | \(-0.472322\pi\) | ||||
0.0868445 | + | 0.996222i | \(0.472322\pi\) | |||||||
\(374\) | 250.849 | + | 272.065i | 0.670721 | + | 0.727447i | ||||
\(375\) | 170.890 | − | 4.17700i | 0.455706 | − | 0.0111387i | ||||
\(376\) | −142.815 | + | 142.815i | −0.379828 | + | 0.379828i | ||||
\(377\) | −145.168 | − | 60.1308i | −0.385062 | − | 0.159498i | ||||
\(378\) | 7.34839 | + | 100.053i | 0.0194402 | + | 0.264691i | ||||
\(379\) | 519.297 | + | 215.100i | 1.37018 | + | 0.567546i | 0.941836 | − | 0.336072i | \(-0.109099\pi\) |
0.428340 | + | 0.903618i | \(0.359099\pi\) | |||||||
\(380\) | 166.821 | − | 69.0994i | 0.439002 | − | 0.181841i | ||||
\(381\) | −124.613 | − | 281.202i | −0.327068 | − | 0.738064i | ||||
\(382\) | −73.2511 | − | 73.2511i | −0.191757 | − | 0.191757i | ||||
\(383\) | 8.73334 | − | 8.73334i | 0.0228025 | − | 0.0228025i | −0.695614 | − | 0.718416i | \(-0.744867\pi\) |
0.718416 | + | 0.695614i | \(0.244867\pi\) | |||||||
\(384\) | −31.0308 | + | 13.7511i | −0.0808093 | + | 0.0358101i | ||||
\(385\) | 99.2340 | + | 239.572i | 0.257751 | + | 0.622265i | ||||
\(386\) | −17.1349 | + | 41.3673i | −0.0443909 | + | 0.107169i | ||||
\(387\) | −2.78566 | − | 56.9496i | −0.00719809 | − | 0.147157i | ||||
\(388\) | 84.1704 | − | 203.205i | 0.216934 | − | 0.523725i | ||||
\(389\) | 116.166 | + | 116.166i | 0.298628 | + | 0.298628i | 0.840476 | − | 0.541848i | \(-0.182275\pi\) |
−0.541848 | + | 0.840476i | \(0.682275\pi\) | |||||||
\(390\) | −2.53385 | − | 103.665i | −0.00649705 | − | 0.265808i | ||||
\(391\) | 210.102 | + | 8.52425i | 0.537345 | + | 0.0218011i | ||||
\(392\) | 119.068i | 0.303745i | ||||||||
\(393\) | −130.166 | + | 136.688i | −0.331210 | + | 0.347807i | ||||
\(394\) | −24.9790 | + | 60.3045i | −0.0633984 | + | 0.153057i | ||||
\(395\) | −737.272 | −1.86651 | ||||||||
\(396\) | −93.3956 | + | 260.849i | −0.235848 | + | 0.658710i | ||||
\(397\) | −43.2401 | − | 104.391i | −0.108917 | − | 0.262949i | 0.860018 | − | 0.510263i | \(-0.170452\pi\) |
−0.968935 | + | 0.247314i | \(0.920452\pi\) | |||||||
\(398\) | −3.10486 | − | 7.49580i | −0.00780116 | − | 0.0188337i | ||||
\(399\) | −76.5353 | + | 80.3705i | −0.191818 | + | 0.201430i | ||||
\(400\) | 45.5757 | + | 45.5757i | 0.113939 | + | 0.113939i | ||||
\(401\) | −175.483 | − | 423.654i | −0.437614 | − | 1.05649i | −0.976771 | − | 0.214287i | \(-0.931257\pi\) |
0.539157 | − | 0.842205i | \(-0.318743\pi\) | |||||||
\(402\) | −97.0099 | − | 218.913i | −0.241318 | − | 0.544561i | ||||
\(403\) | −92.1943 | − | 38.1881i | −0.228770 | − | 0.0947596i | ||||
\(404\) | −112.380 | −0.278169 | ||||||||
\(405\) | 496.942 | + | 150.976i | 1.22702 | + | 0.372780i | ||||
\(406\) | −108.304 | + | 108.304i | −0.266758 | + | 0.266758i | ||||
\(407\) | 796.376i | 1.95670i | ||||||||
\(408\) | −144.231 | − | 2.32405i | −0.353508 | − | 0.00569619i | ||||
\(409\) | −113.479 | −0.277454 | −0.138727 | − | 0.990331i | \(-0.544301\pi\) | ||||
−0.138727 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(410\) | 407.203 | + | 407.203i | 0.993178 | + | 0.993178i | ||||
\(411\) | −107.876 | + | 279.569i | −0.262471 | + | 0.680216i | ||||
\(412\) | 351.108i | 0.852204i | ||||||||
\(413\) | −70.0068 | + | 169.011i | −0.169508 | + | 0.409228i | ||||
\(414\) | 67.2811 | + | 142.332i | 0.162515 | + | 0.343797i | ||||
\(415\) | −547.304 | + | 226.701i | −1.31880 | + | 0.546267i | ||||
\(416\) | −15.2473 | + | 15.2473i | −0.0366523 | + | 0.0366523i | ||||
\(417\) | −28.3139 | + | 29.7328i | −0.0678991 | + | 0.0713016i | ||||
\(418\) | −283.173 | + | 117.294i | −0.677448 | + | 0.280608i | ||||
\(419\) | −332.032 | + | 137.532i | −0.792439 | + | 0.328239i | −0.741924 | − | 0.670484i | \(-0.766086\pi\) |
−0.0505152 | + | 0.998723i | \(0.516086\pi\) | |||||||
\(420\) | −94.3026 | − | 36.3880i | −0.224530 | − | 0.0866381i | ||||
\(421\) | − | 162.090i | − | 0.385011i | −0.981296 | − | 0.192506i | \(-0.938339\pi\) | ||
0.981296 | − | 0.192506i | \(-0.0616614\pi\) | |||||||
\(422\) | −224.684 | − | 93.0673i | −0.532427 | − | 0.220539i | ||||
\(423\) | −476.095 | − | 431.691i | −1.12552 | − | 1.02055i | ||||
\(424\) | 112.602 | 0.265571 | ||||||||
\(425\) | 94.4824 | + | 257.119i | 0.222312 | + | 0.604985i | ||||
\(426\) | −6.03909 | − | 247.072i | −0.0141763 | − | 0.579981i | ||||
\(427\) | 69.8255 | − | 69.8255i | 0.163526 | − | 0.163526i | ||||
\(428\) | 206.239 | + | 85.4269i | 0.481867 | + | 0.199596i | ||||
\(429\) | 4.30113 | + | 175.968i | 0.0100259 | + | 0.410183i | ||||
\(430\) | 53.0749 | + | 21.9844i | 0.123430 | + | 0.0511264i | ||||
\(431\) | 12.2065 | − | 5.05611i | 0.0283214 | − | 0.0117311i | −0.368478 | − | 0.929637i | \(-0.620121\pi\) |
0.396799 | + | 0.917905i | \(0.370121\pi\) | |||||||
\(432\) | −48.5274 | − | 96.4837i | −0.112332 | − | 0.223342i | ||||
\(433\) | 339.827 | + | 339.827i | 0.784819 | + | 0.784819i | 0.980640 | − | 0.195820i | \(-0.0627369\pi\) |
−0.195820 | + | 0.980640i | \(0.562737\pi\) | |||||||
\(434\) | −68.7819 | + | 68.7819i | −0.158484 | + | 0.158484i | ||||
\(435\) | 321.252 | + | 724.941i | 0.738511 | + | 1.66653i | ||||
\(436\) | 161.408 | + | 389.674i | 0.370202 | + | 0.893748i | ||||
\(437\) | −66.6485 | + | 160.904i | −0.152514 | + | 0.368201i | ||||
\(438\) | −10.3694 | − | 424.233i | −0.0236744 | − | 0.968569i | ||||
\(439\) | 30.4849 | − | 73.5970i | 0.0694416 | − | 0.167647i | −0.885348 | − | 0.464929i | \(-0.846080\pi\) |
0.954790 | + | 0.297282i | \(0.0960800\pi\) | |||||||
\(440\) | −197.393 | − | 197.393i | −0.448620 | − | 0.448620i | ||||
\(441\) | −378.420 | + | 18.5102i | −0.858096 | + | 0.0419733i | ||||
\(442\) | −86.0189 | + | 31.6090i | −0.194613 | + | 0.0715137i | ||||
\(443\) | 461.487i | 1.04173i | 0.853639 | + | 0.520866i | \(0.174391\pi\) | ||||
−0.853639 | + | 0.520866i | \(0.825609\pi\) | |||||||
\(444\) | −224.804 | − | 214.076i | −0.506314 | − | 0.482154i | ||||
\(445\) | 24.1199 | − | 58.2306i | 0.0542021 | − | 0.130855i | ||||
\(446\) | 141.460 | 0.317175 | ||||||||
\(447\) | 203.133 | + | 78.3816i | 0.454435 | + | 0.175350i | ||||
\(448\) | 8.04358 | + | 19.4189i | 0.0179544 | + | 0.0433458i | ||||
\(449\) | −219.513 | − | 529.951i | −0.488893 | − | 1.18029i | −0.955278 | − | 0.295710i | \(-0.904444\pi\) |
0.466385 | − | 0.884582i | \(-0.345556\pi\) | |||||||
\(450\) | −137.763 | + | 151.933i | −0.306139 | + | 0.337629i | ||||
\(451\) | −691.215 | − | 691.215i | −1.53263 | − | 1.53263i | ||||
\(452\) | −129.402 | − | 312.403i | −0.286287 | − | 0.691158i | ||||
\(453\) | −294.579 | + | 130.541i | −0.650285 | + | 0.288169i | ||||
\(454\) | 338.229 | + | 140.099i | 0.744999 | + | 0.308589i | ||||
\(455\) | −64.2164 | −0.141135 | ||||||||
\(456\) | 43.0105 | − | 111.465i | 0.0943212 | − | 0.244441i | ||||
\(457\) | −122.147 | + | 122.147i | −0.267280 | + | 0.267280i | −0.828003 | − | 0.560723i | \(-0.810523\pi\) |
0.560723 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(458\) | 269.190i | 0.587752i | ||||||||
\(459\) | −15.0358 | − | 458.754i | −0.0327577 | − | 0.999463i | ||||
\(460\) | −158.621 | −0.344828 | ||||||||
\(461\) | −174.620 | − | 174.620i | −0.378786 | − | 0.378786i | 0.491878 | − | 0.870664i | \(-0.336310\pi\) |
−0.870664 | + | 0.491878i | \(0.836310\pi\) | |||||||
\(462\) | 160.076 | + | 61.7675i | 0.346484 | + | 0.133696i | ||||
\(463\) | 708.905i | 1.53111i | 0.643369 | + | 0.765557i | \(0.277536\pi\) | ||||
−0.643369 | + | 0.765557i | \(0.722464\pi\) | |||||||
\(464\) | 63.0990 | − | 152.334i | 0.135989 | − | 0.328307i | ||||
\(465\) | 204.022 | + | 460.399i | 0.438758 | + | 0.990104i | ||||
\(466\) | 338.028 | − | 140.016i | 0.725382 | − | 0.300463i | ||||
\(467\) | −19.5872 | + | 19.5872i | −0.0419425 | + | 0.0419425i | −0.727767 | − | 0.685824i | \(-0.759442\pi\) |
0.685824 | + | 0.727767i | \(0.259442\pi\) | |||||||
\(468\) | −50.8291 | − | 46.0885i | −0.108609 | − | 0.0984796i | ||||
\(469\) | −136.995 | + | 56.7452i | −0.292100 | + | 0.120992i | ||||
\(470\) | 598.228 | − | 247.794i | 1.27283 | − | 0.527222i | ||||
\(471\) | −76.6050 | + | 198.528i | −0.162643 | + | 0.421504i | ||||
\(472\) | − | 196.936i | − | 0.417238i | ||||||
\(473\) | −90.0931 | − | 37.3178i | −0.190472 | − | 0.0788959i | ||||
\(474\) | −336.418 | + | 353.276i | −0.709744 | + | 0.745309i | ||||
\(475\) | −226.883 | −0.477648 | ||||||||
\(476\) | −3.62133 | + | 89.2569i | −0.00760783 | + | 0.187514i | ||||
\(477\) | 17.5050 | + | 357.870i | 0.0366982 | + | 0.750252i | ||||
\(478\) | 172.033 | − | 172.033i | 0.359902 | − | 0.359902i | ||||
\(479\) | 139.563 | + | 57.8090i | 0.291364 | + | 0.120687i | 0.523578 | − | 0.851978i | \(-0.324597\pi\) |
−0.232214 | + | 0.972665i | \(0.574597\pi\) | |||||||
\(480\) | 108.782 | − | 2.65893i | 0.226630 | − | 0.00553943i | ||||
\(481\) | −182.204 | − | 75.4715i | −0.378803 | − | 0.156905i | ||||
\(482\) | −174.276 | + | 72.1876i | −0.361569 | + | 0.149767i | ||||
\(483\) | 89.1344 | − | 39.4993i | 0.184543 | − | 0.0817790i | ||||
\(484\) | 163.948 | + | 163.948i | 0.338736 | + | 0.338736i | ||||
\(485\) | −498.617 | + | 498.617i | −1.02808 | + | 1.02808i | ||||
\(486\) | 299.098 | − | 169.228i | 0.615429 | − | 0.348206i | ||||
\(487\) | −175.108 | − | 422.748i | −0.359564 | − | 0.868065i | −0.995361 | − | 0.0962087i | \(-0.969328\pi\) |
0.635797 | − | 0.771856i | \(-0.280672\pi\) | |||||||
\(488\) | −40.6812 | + | 98.2131i | −0.0833631 | + | 0.201256i | ||||
\(489\) | −335.063 | + | 8.18982i | −0.685200 | + | 0.0167481i | ||||
\(490\) | 146.082 | − | 352.674i | 0.298127 | − | 0.719742i | ||||
\(491\) | −145.423 | − | 145.423i | −0.296177 | − | 0.296177i | 0.543337 | − | 0.839515i | \(-0.317161\pi\) |
−0.839515 | + | 0.543337i | \(0.817161\pi\) | |||||||
\(492\) | 380.926 | − | 9.31083i | 0.774240 | − | 0.0189245i | ||||
\(493\) | 515.195 | − | 475.020i | 1.04502 | − | 0.963530i | ||||
\(494\) | − | 75.9035i | − | 0.153651i | ||||||
\(495\) | 596.663 | − | 658.036i | 1.20538 | − | 1.32937i | ||||
\(496\) | 40.0732 | − | 96.7453i | 0.0807928 | − | 0.195051i | ||||
\(497\) | −153.051 | −0.307950 | ||||||||
\(498\) | −141.108 | + | 365.694i | −0.283350 | + | 0.734326i | ||||
\(499\) | −10.8628 | − | 26.2252i | −0.0217692 | − | 0.0525555i | 0.912621 | − | 0.408806i | \(-0.134055\pi\) |
−0.934390 | + | 0.356251i | \(0.884055\pi\) | |||||||
\(500\) | 43.6108 | + | 105.286i | 0.0872217 | + | 0.210572i | ||||
\(501\) | −89.7460 | − | 85.4634i | −0.179134 | − | 0.170586i | ||||
\(502\) | −201.450 | − | 201.450i | −0.401296 | − | 0.401296i | ||||
\(503\) | −90.9750 | − | 219.633i | −0.180865 | − | 0.436646i | 0.807281 | − | 0.590168i | \(-0.200938\pi\) |
−0.988145 | + | 0.153522i | \(0.950938\pi\) | |||||||
\(504\) | −60.4664 | + | 28.5828i | −0.119973 | + | 0.0567119i | ||||
\(505\) | 332.864 | + | 137.877i | 0.659137 | + | 0.273024i | ||||
\(506\) | 269.254 | 0.532123 | ||||||||
\(507\) | 432.340 | + | 166.825i | 0.852742 | + | 0.329043i | ||||
\(508\) | 144.993 | − | 144.993i | 0.285419 | − | 0.285419i | ||||
\(509\) | − | 256.271i | − | 0.503479i | −0.967795 | − | 0.251739i | \(-0.918997\pi\) | ||
0.967795 | − | 0.251739i | \(-0.0810026\pi\) | |||||||
\(510\) | 424.353 | + | 183.838i | 0.832066 | + | 0.360466i | ||||
\(511\) | −262.796 | −0.514277 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 360.943 | + | 119.367i | 0.703593 | + | 0.232684i | ||||
\(514\) | 107.089i | 0.208344i | ||||||||
\(515\) | 430.767 | − | 1039.96i | 0.836441 | − | 2.01935i | ||||
\(516\) | 34.7524 | − | 15.4003i | 0.0673496 | − | 0.0298455i | ||||
\(517\) | −1015.47 | + | 420.623i | −1.96417 | + | 0.813585i | ||||
\(518\) | −135.934 | + | 135.934i | −0.262421 | + | 0.262421i | ||||
\(519\) | −530.407 | − | 505.097i | −1.02198 | − | 0.973212i | ||||
\(520\) | 63.8685 | − | 26.4552i | 0.122824 | − | 0.0508753i | ||||
\(521\) | 519.575 | − | 215.215i | 0.997265 | − | 0.413081i | 0.176472 | − | 0.984306i | \(-0.443532\pi\) |
0.820794 | + | 0.571225i | \(0.193532\pi\) | |||||||
\(522\) | 493.956 | + | 176.858i | 0.946276 | + | 0.338809i | ||||
\(523\) | − | 204.467i | − | 0.390950i | −0.980709 | − | 0.195475i | \(-0.937375\pi\) | ||
0.980709 | − | 0.195475i | \(-0.0626248\pi\) | |||||||
\(524\) | −116.255 | − | 48.1545i | −0.221861 | − | 0.0918979i | ||||
\(525\) | 91.9756 | + | 87.5866i | 0.175192 | + | 0.166832i | ||||
\(526\) | −724.637 | −1.37764 | ||||||||
\(527\) | 327.192 | − | 301.678i | 0.620859 | − | 0.572444i | ||||
\(528\) | −184.655 | + | 4.51345i | −0.349725 | + | 0.00854820i | ||||
\(529\) | −265.876 | + | 265.876i | −0.502601 | + | 0.502601i | ||||
\(530\) | −333.522 | − | 138.149i | −0.629287 | − | 0.260659i | ||||
\(531\) | 625.899 | − | 30.6155i | 1.17872 | − | 0.0576563i | ||||
\(532\) | −68.3562 | − | 28.3141i | −0.128489 | − | 0.0532219i | ||||
\(533\) | 223.650 | − | 92.6388i | 0.419606 | − | 0.173806i | ||||
\(534\) | −16.8963 | − | 38.1282i | −0.0316409 | − | 0.0714012i | ||||
\(535\) | −506.060 | − | 506.060i | −0.945907 | − | 0.945907i | ||||
\(536\) | 112.876 | − | 112.876i | 0.210589 | − | 0.210589i | ||||
\(537\) | 590.682 | − | 261.756i | 1.09997 | − | 0.487442i | ||||
\(538\) | −0.299456 | − | 0.722952i | −0.000556611 | − | 0.00134378i | ||||
\(539\) | −247.970 | + | 598.653i | −0.460056 | + | 1.11067i | ||||
\(540\) | 25.3618 | + | 345.317i | 0.0469662 | + | 0.639475i | ||||
\(541\) | −221.214 | + | 534.057i | −0.408898 | + | 0.987167i | 0.576530 | + | 0.817076i | \(0.304406\pi\) |
−0.985428 | + | 0.170091i | \(0.945594\pi\) | |||||||
\(542\) | −33.9197 | − | 33.9197i | −0.0625824 | − | 0.0625824i | ||||
\(543\) | −17.9861 | − | 735.849i | −0.0331235 | − | 1.35515i | ||||
\(544\) | −33.1694 | − | 90.2651i | −0.0609731 | − | 0.165929i | ||||
\(545\) | − | 1352.22i | − | 2.48114i | ||||||
\(546\) | −29.3021 | + | 30.7704i | −0.0536668 | + | 0.0563560i | ||||
\(547\) | −18.4696 | + | 44.5895i | −0.0337652 | + | 0.0815165i | −0.939863 | − | 0.341553i | \(-0.889047\pi\) |
0.906097 | + | 0.423069i | \(0.139047\pi\) | |||||||
\(548\) | −199.773 | −0.364549 | ||||||||
\(549\) | −318.463 | − | 114.024i | −0.580079 | − | 0.207694i | ||||
\(550\) | 134.231 | + | 324.062i | 0.244056 | + | 0.589204i | ||||
\(551\) | 222.114 | + | 536.230i | 0.403110 | + | 0.973194i | ||||
\(552\) | −72.3790 | + | 76.0059i | −0.131121 | + | 0.137692i | ||||
\(553\) | 213.619 | + | 213.619i | 0.386291 | + | 0.386291i | ||||
\(554\) | 264.491 | + | 638.537i | 0.477420 | + | 1.15259i | ||||
\(555\) | 403.211 | + | 909.889i | 0.726506 | + | 1.63944i | ||||
\(556\) | −25.2881 | − | 10.4747i | −0.0454822 | − | 0.0188393i | ||||
\(557\) | −110.295 | −0.198017 | −0.0990084 | − | 0.995087i | \(-0.531567\pi\) | ||||
−0.0990084 | + | 0.995087i | \(0.531567\pi\) | |||||||
\(558\) | 313.704 | + | 112.320i | 0.562193 | + | 0.201290i | ||||
\(559\) | 17.0760 | − | 17.0760i | 0.0305474 | − | 0.0305474i | ||||
\(560\) | − | 67.3863i | − | 0.120333i | ||||||
\(561\) | −720.327 | − | 312.059i | −1.28401 | − | 0.556255i | ||||
\(562\) | 427.465 | 0.760615 | ||||||||
\(563\) | 657.173 | + | 657.173i | 1.16727 | + | 1.16727i | 0.982847 | + | 0.184422i | \(0.0590414\pi\) |
0.184422 | + | 0.982847i | \(0.440959\pi\) | |||||||
\(564\) | 154.238 | − | 399.721i | 0.273471 | − | 0.708724i | ||||
\(565\) | 1084.08i | 1.91873i | ||||||||
\(566\) | 264.899 | − | 639.523i | 0.468020 | − | 1.12990i | ||||
\(567\) | −100.241 | − | 187.730i | −0.176793 | − | 0.331093i | ||||
\(568\) | 152.222 | − | 63.0524i | 0.267996 | − | 0.111008i | ||||
\(569\) | −78.2270 | + | 78.2270i | −0.137482 | + | 0.137482i | −0.772498 | − | 0.635017i | \(-0.780993\pi\) |
0.635017 | + | 0.772498i | \(0.280993\pi\) | |||||||
\(570\) | −264.149 | + | 277.386i | −0.463420 | + | 0.486642i | ||||
\(571\) | −78.1967 | + | 32.3901i | −0.136947 | + | 0.0567253i | −0.450104 | − | 0.892976i | \(-0.648613\pi\) |
0.313157 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(572\) | −108.415 | + | 44.9069i | −0.189536 | + | 0.0785085i | ||||
\(573\) | 205.020 | + | 79.1099i | 0.357801 | + | 0.138063i | ||||
\(574\) | − | 235.968i | − | 0.411095i | ||||||
\(575\) | 184.137 | + | 76.2722i | 0.320239 | + | 0.132647i | ||||
\(576\) | 48.3635 | − | 53.3382i | 0.0839645 | − | 0.0926011i | ||||
\(577\) | −899.323 | −1.55862 | −0.779310 | − | 0.626639i | \(-0.784430\pi\) | ||||
−0.779310 | + | 0.626639i | \(0.784430\pi\) | |||||||
\(578\) | 33.1097 | − | 407.364i | 0.0572831 | − | 0.704783i | ||||
\(579\) | −2.32095 | − | 94.9551i | −0.00400856 | − | 0.163999i | ||||
\(580\) | −373.792 | + | 373.792i | −0.644469 | + | 0.644469i | ||||
\(581\) | 224.262 | + | 92.8925i | 0.385994 | + | 0.159884i | ||||
\(582\) | 11.4010 | + | 466.441i | 0.0195894 | + | 0.801444i | ||||
\(583\) | 566.144 | + | 234.504i | 0.971087 | + | 0.402237i | ||||
\(584\) | 261.372 | − | 108.264i | 0.447554 | − | 0.185383i | ||||
\(585\) | 94.0083 | + | 198.873i | 0.160698 | + | 0.339954i | ||||
\(586\) | 411.302 | + | 411.302i | 0.701881 | + | 0.701881i | ||||
\(587\) | 604.970 | − | 604.970i | 1.03061 | − | 1.03061i | 0.0310964 | − | 0.999516i | \(-0.490100\pi\) |
0.999516 | − | 0.0310964i | \(-0.00989988\pi\) | |||||||
\(588\) | −102.332 | − | 230.924i | −0.174034 | − | 0.392727i | ||||
\(589\) | 141.061 | + | 340.551i | 0.239492 | + | 0.578186i | ||||
\(590\) | −241.617 | + | 583.315i | −0.409520 | + | 0.988669i | ||||
\(591\) | −3.38345 | − | 138.424i | −0.00572495 | − | 0.234220i | ||||
\(592\) | 79.1970 | − | 191.198i | 0.133779 | − | 0.322970i | ||||
\(593\) | 589.870 | + | 589.870i | 0.994721 | + | 0.994721i | 0.999986 | − | 0.00526513i | \(-0.00167595\pi\) |
−0.00526513 | + | 0.999986i | \(0.501676\pi\) | |||||||
\(594\) | −43.0508 | − | 586.165i | −0.0724761 | − | 0.986809i | ||||
\(595\) | 120.234 | − | 259.931i | 0.202073 | − | 0.436859i | ||||
\(596\) | 145.154i | 0.243546i | ||||||||
\(597\) | 12.4638 | + | 11.8691i | 0.0208775 | + | 0.0198812i | ||||
\(598\) | −25.5168 | + | 61.6031i | −0.0426703 | + | 0.103015i | ||||
\(599\) | −291.140 | −0.486043 | −0.243021 | − | 0.970021i | \(-0.578139\pi\) | ||||
−0.243021 | + | 0.970021i | \(0.578139\pi\) | |||||||
\(600\) | −127.560 | − | 49.2210i | −0.212600 | − | 0.0820349i | ||||
\(601\) | 162.891 | + | 393.255i | 0.271034 | + | 0.654334i | 0.999528 | − | 0.0307181i | \(-0.00977942\pi\) |
−0.728494 | + | 0.685052i | \(0.759779\pi\) | |||||||
\(602\) | −9.00827 | − | 21.7479i | −0.0149639 | − | 0.0361261i | ||||
\(603\) | 376.286 | + | 341.191i | 0.624024 | + | 0.565823i | ||||
\(604\) | −151.890 | − | 151.890i | −0.251474 | − | 0.251474i | ||||
\(605\) | −284.461 | − | 686.751i | −0.470184 | − | 1.13513i | ||||
\(606\) | 217.953 | − | 96.5842i | 0.359658 | − | 0.159380i | ||||
\(607\) | −355.623 | − | 147.304i | −0.585871 | − | 0.242676i | 0.0700023 | − | 0.997547i | \(-0.477699\pi\) |
−0.655873 | + | 0.754871i | \(0.727699\pi\) | |||||||
\(608\) | 79.6504 | 0.131004 | ||||||||
\(609\) | 116.966 | − | 303.127i | 0.192062 | − | 0.497745i | ||||
\(610\) | 240.991 | − | 240.991i | 0.395067 | − | 0.395067i | ||||
\(611\) | − | 272.194i | − | 0.445490i | ||||||
\(612\) | 281.722 | − | 119.451i | 0.460331 | − | 0.195181i | ||||
\(613\) | 380.042 | 0.619970 | 0.309985 | − | 0.950741i | \(-0.399676\pi\) | ||||
0.309985 | + | 0.950741i | \(0.399676\pi\) | |||||||
\(614\) | −238.599 | − | 238.599i | −0.388597 | − | 0.388597i | ||||
\(615\) | −1139.71 | − | 439.772i | −1.85318 | − | 0.715076i | ||||
\(616\) | 114.386i | 0.185692i | ||||||||
\(617\) | −380.704 | + | 919.101i | −0.617024 | + | 1.48963i | 0.238119 | + | 0.971236i | \(0.423469\pi\) |
−0.855143 | + | 0.518392i | \(0.826531\pi\) | |||||||
\(618\) | −301.757 | − | 680.947i | −0.488279 | − | 1.10186i | ||||
\(619\) | −661.524 | + | 274.012i | −1.06870 | + | 0.442669i | −0.846531 | − | 0.532339i | \(-0.821313\pi\) |
−0.222167 | + | 0.975009i | \(0.571313\pi\) | |||||||
\(620\) | −237.389 | + | 237.389i | −0.382886 | + | 0.382886i | ||||
\(621\) | −252.812 | − | 218.218i | −0.407105 | − | 0.351397i | ||||
\(622\) | −702.051 | + | 290.799i | −1.12870 | + | 0.467523i | ||||
\(623\) | −23.8605 | + | 9.88334i | −0.0382993 | + | 0.0158641i | ||||
\(624\) | 16.4668 | − | 42.6752i | 0.0263892 | − | 0.0683898i | ||||
\(625\) | − | 768.193i | − | 1.22911i | ||||||
\(626\) | −222.998 | − | 92.3686i | −0.356226 | − | 0.147554i | ||||
\(627\) | 448.385 | − | 470.854i | 0.715128 | − | 0.750963i | ||||
\(628\) | −141.864 | −0.225897 | ||||||||
\(629\) | 646.633 | − | 596.209i | 1.02803 | − | 0.947867i | ||||
\(630\) | 214.166 | − | 10.4758i | 0.339946 | − | 0.0166283i | ||||
\(631\) | 108.470 | − | 108.470i | 0.171902 | − | 0.171902i | −0.615912 | − | 0.787815i | \(-0.711213\pi\) |
0.787815 | + | 0.615912i | \(0.211213\pi\) | |||||||
\(632\) | −300.466 | − | 124.457i | −0.475421 | − | 0.196926i | ||||
\(633\) | 515.744 | − | 12.6061i | 0.814761 | − | 0.0199149i | ||||
\(634\) | −82.8528 | − | 34.3188i | −0.130683 | − | 0.0541305i | ||||
\(635\) | −607.349 | + | 251.572i | −0.956456 | + | 0.396177i | ||||
\(636\) | −218.383 | + | 96.7750i | −0.343370 | + | 0.152162i | ||||
\(637\) | −113.467 | − | 113.467i | −0.178127 | − | 0.178127i | ||||
\(638\) | 634.500 | − | 634.500i | 0.994515 | − | 0.994515i | ||||
\(639\) | 224.056 | + | 473.987i | 0.350636 | + | 0.741764i | ||||
\(640\) | 27.7611 | + | 67.0212i | 0.0433767 | + | 0.104721i | ||||
\(641\) | −448.406 | + | 1082.55i | −0.699542 | + | 1.68884i | 0.0250694 | + | 0.999686i | \(0.492019\pi\) |
−0.724611 | + | 0.689158i | \(0.757981\pi\) | |||||||
\(642\) | −473.404 | + | 11.5712i | −0.737389 | + | 0.0180237i | ||||
\(643\) | 395.823 | − | 955.602i | 0.615588 | − | 1.48616i | −0.241191 | − | 0.970478i | \(-0.577538\pi\) |
0.856779 | − | 0.515683i | \(-0.172462\pi\) | |||||||
\(644\) | 45.9593 | + | 45.9593i | 0.0713653 | + | 0.0713653i | ||||
\(645\) | −121.829 | + | 2.97782i | −0.188882 | + | 0.00461678i | ||||
\(646\) | 307.238 | + | 142.116i | 0.475600 | + | 0.219993i | ||||
\(647\) | 455.156i | 0.703488i | 0.936096 | + | 0.351744i | \(0.114411\pi\) | ||||
−0.936096 | + | 0.351744i | \(0.885589\pi\) | |||||||
\(648\) | 177.037 | + | 145.416i | 0.273205 | + | 0.224408i | ||||
\(649\) | 410.137 | − | 990.159i | 0.631953 | − | 1.52567i | ||||
\(650\) | −86.8636 | −0.133636 | ||||||||
\(651\) | 74.2832 | − | 192.511i | 0.114106 | − | 0.295716i | ||||
\(652\) | −85.5075 | − | 206.433i | −0.131147 | − | 0.316616i | ||||
\(653\) | 103.859 | + | 250.737i | 0.159049 | + | 0.383978i | 0.983235 | − | 0.182341i | \(-0.0583673\pi\) |
−0.824187 | + | 0.566318i | \(0.808367\pi\) | |||||||
\(654\) | −647.941 | − | 617.022i | −0.990735 | − | 0.943458i | ||||
\(655\) | 285.262 | + | 285.262i | 0.435515 | + | 0.435515i | ||||
\(656\) | 97.2117 | + | 234.690i | 0.148189 | + | 0.357759i | ||||
\(657\) | 384.714 | + | 813.856i | 0.585562 | + | 1.23875i | ||||
\(658\) | −245.129 | − | 101.536i | −0.372537 | − | 0.154310i | ||||
\(659\) | −886.843 | −1.34574 | −0.672870 | − | 0.739760i | \(-0.734939\pi\) | ||||
−0.672870 | + | 0.739760i | \(0.734939\pi\) | |||||||
\(660\) | 552.475 | + | 213.180i | 0.837084 | + | 0.323001i | ||||
\(661\) | 167.689 | − | 167.689i | 0.253690 | − | 0.253690i | −0.568791 | − | 0.822482i | \(-0.692589\pi\) |
0.822482 | + | 0.568791i | \(0.192589\pi\) | |||||||
\(662\) | 163.769i | 0.247386i | ||||||||
\(663\) | 139.661 | − | 135.232i | 0.210650 | − | 0.203969i | ||||
\(664\) | −261.316 | −0.393548 | ||||||||
\(665\) | 167.730 | + | 167.730i | 0.252225 | + | 0.252225i | ||||
\(666\) | 619.975 | + | 221.979i | 0.930894 | + | 0.333302i | ||||
\(667\) | − | 509.872i | − | 0.764426i | ||||||
\(668\) | 31.6170 | − | 76.3301i | 0.0473308 | − | 0.114267i | ||||
\(669\) | −274.351 | + | 121.577i | −0.410091 | + | 0.181729i | ||||
\(670\) | −472.816 | + | 195.847i | −0.705695 | + | 0.292309i | ||||
\(671\) | −409.075 | + | 409.075i | −0.609650 | + | 0.609650i | ||||
\(672\) | −32.2893 | − | 30.7485i | −0.0480496 | − | 0.0457567i | ||||
\(673\) | 83.8669 | − | 34.7388i | 0.124616 | − | 0.0516178i | −0.319504 | − | 0.947585i | \(-0.603516\pi\) |
0.444120 | + | 0.895967i | \(0.353516\pi\) | |||||||
\(674\) | −741.047 | + | 306.952i | −1.09948 | + | 0.455418i | ||||
\(675\) | 136.603 | − | 413.061i | 0.202374 | − | 0.611943i | ||||
\(676\) | 308.940i | 0.457012i | ||||||||
\(677\) | 36.0836 | + | 14.9463i | 0.0532993 | + | 0.0220773i | 0.409174 | − | 0.912456i | \(-0.365817\pi\) |
−0.355875 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(678\) | 519.457 | + | 494.669i | 0.766161 | + | 0.729600i | ||||
\(679\) | 288.941 | 0.425539 | ||||||||
\(680\) | −12.4984 | + | 308.055i | −0.0183800 | + | 0.453023i | ||||
\(681\) | −776.377 | + | 18.9767i | −1.14005 | + | 0.0278659i | ||||
\(682\) | 402.961 | − | 402.961i | 0.590853 | − | 0.590853i | ||||
\(683\) | −388.860 | − | 161.071i | −0.569341 | − | 0.235829i | 0.0793937 | − | 0.996843i | \(-0.474702\pi\) |
−0.648735 | + | 0.761015i | \(0.724702\pi\) | |||||||
\(684\) | 12.3824 | + | 253.143i | 0.0181029 | + | 0.370093i | ||||
\(685\) | 591.717 | + | 245.097i | 0.863820 | + | 0.357806i | ||||
\(686\) | −312.719 | + | 129.532i | −0.455858 | + | 0.188823i | ||||
\(687\) | −231.353 | − | 522.074i | −0.336759 | − | 0.759933i | ||||
\(688\) | 17.9189 | + | 17.9189i | 0.0260450 | + | 0.0260450i | ||||
\(689\) | −107.305 | + | 107.305i | −0.155741 | + | 0.155741i | ||||
\(690\) | 307.633 | − | 136.325i | 0.445845 | − | 0.197573i | ||||
\(691\) | −285.492 | − | 689.238i | −0.413157 | − | 0.997449i | −0.984285 | − | 0.176588i | \(-0.943494\pi\) |
0.571128 | − | 0.820861i | \(-0.306506\pi\) | |||||||
\(692\) | 186.859 | − | 451.119i | 0.270028 | − | 0.651906i | ||||
\(693\) | −363.540 | + | 17.7824i | −0.524589 | + | 0.0256600i | ||||
\(694\) | −250.008 | + | 603.572i | −0.360242 | + | 0.869701i | ||||
\(695\) | 62.0509 | + | 62.0509i | 0.0892818 | + | 0.0892818i | ||||
\(696\) | 8.54688 | + | 349.671i | 0.0122800 | + | 0.502401i | ||||
\(697\) | −43.7660 | + | 1078.73i | −0.0627920 | + | 1.54767i | ||||
\(698\) | 64.2118i | 0.0919939i | ||||||||
\(699\) | −535.244 | + | 562.065i | −0.765728 | + | 0.804099i | ||||
\(700\) | −32.4025 | + | 78.2265i | −0.0462892 | + | 0.111752i | ||||
\(701\) | −352.002 | −0.502142 | −0.251071 | − | 0.967969i | \(-0.580783\pi\) | ||||
−0.251071 | + | 0.967969i | \(0.580783\pi\) | |||||||
\(702\) | 138.190 | + | 45.7004i | 0.196851 | + | 0.0651002i | ||||
\(703\) | 278.780 | + | 673.034i | 0.396558 | + | 0.957375i | ||||
\(704\) | −47.1236 | − | 113.766i | −0.0669370 | − | 0.161600i | ||||
\(705\) | −947.253 | + | 994.720i | −1.34362 | + | 1.41095i | ||||
\(706\) | −33.3930 | − | 33.3930i | −0.0472989 | − | 0.0472989i | ||||
\(707\) | −56.4962 | − | 136.394i | −0.0799098 | − | 0.192919i | ||||
\(708\) | 169.255 | + | 381.943i | 0.239061 | + | 0.539467i | ||||
\(709\) | 1179.44 | + | 488.540i | 1.66352 | + | 0.689054i | 0.998338 | − | 0.0576229i | \(-0.0183521\pi\) |
0.665186 | + | 0.746677i | \(0.268352\pi\) | |||||||
\(710\) | −528.231 | −0.743988 | ||||||||
\(711\) | 348.837 | − | 974.284i | 0.490629 | − | 1.37030i | ||||
\(712\) | 19.6596 | − | 19.6596i | 0.0276118 | − | 0.0276118i | ||||
\(713\) | − | 323.812i | − | 0.454154i | ||||||
\(714\) | −69.6877 | − | 176.219i | −0.0976019 | − | 0.246805i | ||||
\(715\) | 376.214 | 0.526174 | ||||||||
\(716\) | 304.566 | + | 304.566i | 0.425371 | + | 0.425371i | ||||
\(717\) | −185.793 | + | 481.498i | −0.259125 | + | 0.671545i | ||||
\(718\) | − | 533.975i | − | 0.743697i | ||||||
\(719\) | −159.153 | + | 384.229i | −0.221353 | + | 0.534393i | −0.995074 | − | 0.0991328i | \(-0.968393\pi\) |
0.773721 | + | 0.633526i | \(0.218393\pi\) | |||||||
\(720\) | −208.690 | + | 98.6488i | −0.289847 | + | 0.137012i | ||||
\(721\) | −426.134 | + | 176.510i | −0.591031 | + | 0.244813i | ||||
\(722\) | 162.744 | − | 162.744i | 0.225408 | − | 0.225408i | ||||
\(723\) | 275.955 | − | 289.783i | 0.381680 | − | 0.400806i | ||||
\(724\) | 453.359 | − | 187.787i | 0.626186 | − | 0.259375i | ||||
\(725\) | 613.659 | − | 254.186i | 0.846426 | − | 0.350601i | ||||
\(726\) | −458.869 | − | 177.061i | −0.632051 | − | 0.243886i | ||||
\(727\) | − | 545.127i | − | 0.749830i | −0.927059 | − | 0.374915i | \(-0.877672\pi\) | ||
0.927059 | − | 0.374915i | \(-0.122328\pi\) | |||||||
\(728\) | −26.1706 | − | 10.8402i | −0.0359487 | − | 0.0148904i | ||||
\(729\) | −434.637 | + | 585.262i | −0.596210 | + | 0.802829i | ||||
\(730\) | −906.996 | −1.24246 | ||||||||
\(731\) | 37.1475 | + | 101.091i | 0.0508174 | + | 0.138291i | ||||
\(732\) | −5.51034 | − | 225.440i | −0.00752779 | − | 0.307978i | ||||
\(733\) | 141.391 | − | 141.391i | 0.192894 | − | 0.192894i | −0.604051 | − | 0.796945i | \(-0.706448\pi\) |
0.796945 | + | 0.604051i | \(0.206448\pi\) | |||||||
\(734\) | −725.067 | − | 300.333i | −0.987830 | − | 0.409173i | ||||
\(735\) | 19.7871 | + | 809.533i | 0.0269212 | + | 1.10141i | ||||
\(736\) | −64.6440 | − | 26.7764i | −0.0878316 | − | 0.0363810i | ||||
\(737\) | 802.591 | − | 332.444i | 1.08900 | − | 0.451077i | ||||
\(738\) | −730.774 | + | 345.441i | −0.990209 | + | 0.468077i | ||||
\(739\) | 366.745 | + | 366.745i | 0.496272 | + | 0.496272i | 0.910275 | − | 0.414003i | \(-0.135870\pi\) |
−0.414003 | + | 0.910275i | \(0.635870\pi\) | |||||||
\(740\) | −469.155 | + | 469.155i | −0.633993 | + | 0.633993i | ||||
\(741\) | 65.2346 | + | 147.209i | 0.0880359 | + | 0.198663i | ||||
\(742\) | 56.6079 | + | 136.663i | 0.0762909 | + | 0.184183i | ||||
\(743\) | 10.3633 | − | 25.0192i | 0.0139479 | − | 0.0336732i | −0.916752 | − | 0.399456i | \(-0.869199\pi\) |
0.930700 | + | 0.365783i | \(0.119199\pi\) | |||||||
\(744\) | 5.42799 | + | 222.071i | 0.00729568 | + | 0.298482i | ||||
\(745\) | 178.086 | − | 429.937i | 0.239041 | − | 0.577097i | ||||
\(746\) | −64.7860 | − | 64.7860i | −0.0868445 | − | 0.0868445i | ||||
\(747\) | −40.6240 | − | 830.510i | −0.0543828 | − | 1.11179i | ||||
\(748\) | 21.2157 | − | 522.915i | 0.0283632 | − | 0.699084i | ||||
\(749\) | 293.255i | 0.391528i | ||||||||
\(750\) | −175.067 | − | 166.713i | −0.233423 | − | 0.222284i | ||||
\(751\) | −362.690 | + | 875.610i | −0.482942 | + | 1.16593i | 0.475263 | + | 0.879844i | \(0.342353\pi\) |
−0.958205 | + | 0.286082i | \(0.907647\pi\) | |||||||
\(752\) | 285.631 | 0.379828 | ||||||||
\(753\) | 563.832 | + | 217.563i | 0.748781 | + | 0.288928i | ||||
\(754\) | 85.0377 | + | 205.299i | 0.112782 | + | 0.272280i | ||||
\(755\) | 263.540 | + | 636.241i | 0.349059 | + | 0.842703i | ||||
\(756\) | 92.7047 | − | 107.401i | 0.122625 | − | 0.142065i | ||||
\(757\) | −517.194 | − | 517.194i | −0.683215 | − | 0.683215i | 0.277508 | − | 0.960723i | \(-0.410491\pi\) |
−0.960723 | + | 0.277508i | \(0.910491\pi\) | |||||||
\(758\) | −304.197 | − | 734.397i | −0.401315 | − | 0.968861i | ||||
\(759\) | −522.197 | + | 231.408i | −0.688007 | + | 0.304885i | ||||
\(760\) | −235.920 | − | 97.7214i | −0.310421 | − | 0.128581i | ||||
\(761\) | 1052.26 | 1.38273 | 0.691366 | − | 0.722504i | \(-0.257009\pi\) | ||||
0.691366 | + | 0.722504i | \(0.257009\pi\) | |||||||
\(762\) | −156.589 | + | 405.815i | −0.205498 | + | 0.532566i | ||||
\(763\) | −391.797 | + | 391.797i | −0.513495 | + | 0.513495i | ||||
\(764\) | 146.502i | 0.191757i | ||||||||
\(765\) | −980.999 | + | 8.16778i | −1.28235 | + | 0.0106768i | ||||
\(766\) | −17.4667 | −0.0228025 | ||||||||
\(767\) | 187.672 | + | 187.672i | 0.244683 | + | 0.244683i | ||||
\(768\) | 44.7818 | + | 17.2797i | 0.0583097 | + | 0.0224996i | ||||
\(769\) | − | 958.775i | − | 1.24678i | −0.781911 | − | 0.623391i | \(-0.785755\pi\) | ||
0.781911 | − | 0.623391i | \(-0.214245\pi\) | |||||||
\(770\) | 140.338 | − | 338.806i | 0.182257 | − | 0.440008i | ||||
\(771\) | −92.0365 | − | 207.690i | −0.119373 | − | 0.269378i | ||||
\(772\) | 58.5022 | − | 24.2324i | 0.0757801 | − | 0.0313891i | ||||
\(773\) | 95.4320 | − | 95.4320i | 0.123457 | − | 0.123457i | −0.642679 | − | 0.766136i | \(-0.722177\pi\) |
0.766136 | + | 0.642679i | \(0.222177\pi\) | |||||||
\(774\) | −54.1639 | + | 59.7353i | −0.0699793 | + | 0.0771773i | ||||
\(775\) | 389.725 | − | 161.429i | 0.502871 | − | 0.208296i | ||||
\(776\) | −287.376 | + | 119.035i | −0.370330 | + | 0.153396i | ||||
\(777\) | 146.806 | − | 380.461i | 0.188940 | − | 0.489654i | ||||
\(778\) | − | 232.333i | − | 0.298628i | ||||||
\(779\) | −826.128 | − | 342.193i | −1.06050 | − | 0.439273i | ||||
\(780\) | −101.131 | + | 106.199i | −0.129655 | + | 0.136153i | ||||
\(781\) | 896.656 | 1.14809 | ||||||||
\(782\) | −201.578 | − | 218.626i | −0.257772 | − | 0.279573i | ||||
\(783\) | −1109.99 | + | 81.5230i | −1.41761 | + | 0.104116i | ||||
\(784\) | 119.068 | − | 119.068i | 0.151873 | − | 0.151873i | ||||
\(785\) | 420.193 | + | 174.049i | 0.535277 | + | 0.221719i | ||||
\(786\) | 266.854 | − | 6.52261i | 0.339509 | − | 0.00829849i | ||||
\(787\) | −798.006 | − | 330.545i | −1.01398 | − | 0.420006i | −0.187078 | − | 0.982345i | \(-0.559902\pi\) |
−0.826907 | + | 0.562339i | \(0.809902\pi\) | |||||||
\(788\) | 85.2835 | − | 35.3256i | 0.108228 | − | 0.0448294i | ||||
\(789\) | 1405.38 | − | 622.783i | 1.78121 | − | 0.789332i | ||||
\(790\) | 737.272 | + | 737.272i | 0.933255 | + | 0.933255i | ||||
\(791\) | 314.105 | − | 314.105i | 0.397099 | − | 0.397099i | ||||
\(792\) | 354.245 | − | 167.453i | 0.447279 | − | 0.211431i | ||||
\(793\) | −54.8255 | − | 132.361i | −0.0691368 | − | 0.166911i | ||||
\(794\) | −61.1508 | + | 147.631i | −0.0770161 | + | 0.185933i | ||||
\(795\) | 765.572 | − | 18.7126i | 0.962983 | − | 0.0235378i | ||||
\(796\) | −4.39094 | + | 10.6007i | −0.00551626 | + | 0.0133174i | ||||
\(797\) | 94.1778 | + | 94.1778i | 0.118165 | + | 0.118165i | 0.763717 | − | 0.645551i | \(-0.223372\pi\) |
−0.645551 | + | 0.763717i | \(0.723372\pi\) | |||||||
\(798\) | 156.906 | − | 3.83519i | 0.196624 | − | 0.00480601i | ||||
\(799\) | 1101.77 | + | 509.634i | 1.37894 | + | 0.637840i | ||||
\(800\) | − | 91.1515i | − | 0.113939i | ||||||
\(801\) | 65.5380 | + | 59.4254i | 0.0818202 | + | 0.0741891i | ||||
\(802\) | −248.171 | + | 599.137i | −0.309440 | + | 0.747053i | ||||
\(803\) | 1539.60 | 1.91731 | ||||||||
\(804\) | −121.903 | + | 315.923i | −0.151621 | + | 0.392939i | ||||
\(805\) | −79.7425 | − | 192.515i | −0.0990590 | − | 0.239149i | ||||
\(806\) | 54.0061 | + | 130.382i | 0.0670051 | + | 0.161765i | ||||
\(807\) | 1.20211 | + | 1.14474i | 0.00148960 | + | 0.00141852i | ||||
\(808\) | 112.380 | + | 112.380i | 0.139084 | + | 0.139084i | ||||
\(809\) | −346.315 | − | 836.078i | −0.428078 | − | 1.03347i | −0.979896 | − | 0.199507i | \(-0.936066\pi\) |
0.551819 | − | 0.833964i | \(-0.313934\pi\) | |||||||
\(810\) | −345.967 | − | 647.918i | −0.427119 | − | 0.799899i | ||||
\(811\) | 1115.63 | + | 462.110i | 1.37562 | + | 0.569802i | 0.943308 | − | 0.331920i | \(-0.107696\pi\) |
0.432317 | + | 0.901722i | \(0.357696\pi\) | |||||||
\(812\) | 216.607 | 0.266758 | ||||||||
\(813\) | 94.9365 | + | 36.6326i | 0.116773 | + | 0.0450586i | ||||
\(814\) | 796.376 | − | 796.376i | 0.978349 | − | 0.978349i | ||||
\(815\) | 716.352i | 0.878960i | ||||||||
\(816\) | 141.907 | + | 146.555i | 0.173906 | + | 0.179602i | ||||
\(817\) | −89.2031 | −0.109184 | ||||||||
\(818\) | 113.479 | + | 113.479i | 0.138727 | + | 0.138727i | ||||
\(819\) | 30.3838 | − | 84.8602i | 0.0370986 | − | 0.103614i | ||||
\(820\) | − | 814.406i | − | 0.993178i | ||||||
\(821\) | 116.205 | − | 280.543i | 0.141540 | − | 0.341709i | −0.837174 | − | 0.546937i | \(-0.815794\pi\) |
0.978714 | + | 0.205228i | \(0.0657937\pi\) | |||||||
\(822\) | 387.444 | − | 171.693i | 0.471343 | − | 0.208872i | ||||
\(823\) | −473.961 | + | 196.321i | −0.575895 | + | 0.238543i | −0.651569 | − | 0.758589i | \(-0.725889\pi\) |
0.0756745 | + | 0.997133i | \(0.475889\pi\) | |||||||
\(824\) | 351.108 | − | 351.108i | 0.426102 | − | 0.426102i | ||||
\(825\) | −538.843 | − | 513.130i | −0.653143 | − | 0.621975i | ||||
\(826\) | 239.018 | − | 99.0045i | 0.289368 | − | 0.119860i | ||||
\(827\) | −269.956 | + | 111.819i | −0.326428 | + | 0.135211i | −0.539878 | − | 0.841743i | \(-0.681530\pi\) |
0.213450 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(828\) | 75.0509 | − | 209.613i | 0.0906411 | − | 0.253156i | ||||
\(829\) | − | 799.864i | − | 0.964854i | −0.875936 | − | 0.482427i | \(-0.839755\pi\) | ||
0.875936 | − | 0.482427i | \(-0.160245\pi\) | |||||||
\(830\) | 774.005 | + | 320.603i | 0.932536 | + | 0.386269i | ||||
\(831\) | −1061.75 | − | 1011.08i | −1.27767 | − | 1.21670i | ||||
\(832\) | 30.4947 | 0.0366523 | ||||||||
\(833\) | 671.732 | − | 246.839i | 0.806401 | − | 0.296325i | ||||
\(834\) | 58.0467 | − | 1.41881i | 0.0696004 | − | 0.00170122i | ||||
\(835\) | −187.296 | + | 187.296i | −0.224306 | + | 0.224306i | ||||
\(836\) | 400.467 | + | 165.879i | 0.479028 | + | 0.198420i | ||||
\(837\) | −704.937 | + | 51.7740i | −0.842218 | + | 0.0618566i | ||||
\(838\) | 469.564 | + | 194.500i | 0.560339 | + | 0.232100i | ||||
\(839\) | −312.662 | + | 129.509i | −0.372661 | + | 0.154361i | −0.561150 | − | 0.827714i | \(-0.689641\pi\) |
0.188489 | + | 0.982075i | \(0.439641\pi\) | |||||||
\(840\) | 57.9146 | + | 130.691i | 0.0689459 | + | 0.155584i | ||||
\(841\) | −606.843 | − | 606.843i | −0.721573 | − | 0.721573i | ||||
\(842\) | −162.090 | + | 162.090i | −0.192506 | + | 0.192506i | ||||
\(843\) | −829.036 | + | 367.381i | −0.983435 | + | 0.435802i | ||||
\(844\) | 131.617 | + | 317.752i | 0.155944 | + | 0.376483i | ||||
\(845\) | 379.032 | − | 915.064i | 0.448558 | − | 1.08292i | ||||
\(846\) | 44.4039 | + | 907.786i | 0.0524868 | + | 1.07303i | ||||
\(847\) | −116.560 | + | 281.402i | −0.137616 | + | 0.332234i | ||||
\(848\) | −112.602 | − | 112.602i | −0.132786 | − | 0.132786i | ||||
\(849\) | 35.8811 | + | 1467.97i | 0.0422628 | + | 1.72906i | ||||
\(850\) | 162.636 | − | 351.601i | 0.191337 | − | 0.413648i | ||||
\(851\) | − | 639.952i | − | 0.752000i | ||||||
\(852\) | −241.033 | + | 253.111i | −0.282903 | + | 0.297079i | ||||
\(853\) | 161.059 | − | 388.832i | 0.188815 | − | 0.455840i | −0.800917 | − | 0.598776i | \(-0.795654\pi\) |
0.989732 | + | 0.142935i | \(0.0456541\pi\) | |||||||
\(854\) | −139.651 | −0.163526 | ||||||||
\(855\) | 273.900 | − | 764.989i | 0.320351 | − | 0.894724i | ||||
\(856\) | −120.812 | − | 291.666i | −0.141135 | − | 0.340731i | ||||
\(857\) | −298.878 | − | 721.556i | −0.348749 | − | 0.841955i | −0.996768 | − | 0.0803310i | \(-0.974402\pi\) |
0.648019 | − | 0.761624i | \(-0.275598\pi\) | |||||||
\(858\) | 171.667 | − | 180.270i | 0.200078 | − | 0.210104i | ||||
\(859\) | 318.871 | + | 318.871i | 0.371212 | + | 0.371212i | 0.867919 | − | 0.496707i | \(-0.165457\pi\) |
−0.496707 | + | 0.867919i | \(0.665457\pi\) | |||||||
\(860\) | −31.0906 | − | 75.0593i | −0.0361518 | − | 0.0872782i | ||||
\(861\) | 202.801 | + | 457.642i | 0.235541 | + | 0.531524i | ||||
\(862\) | −17.2626 | − | 7.15041i | −0.0200262 | − | 0.00829514i | ||||
\(863\) | 1505.86 | 1.74492 | 0.872459 | − | 0.488687i | \(-0.162524\pi\) | ||||
0.872459 | + | 0.488687i | \(0.162524\pi\) | |||||||
\(864\) | −47.9563 | + | 145.011i | −0.0555050 | + | 0.167837i | ||||
\(865\) | −1106.94 | + | 1106.94i | −1.27969 | + | 1.27969i | ||||
\(866\) | − | 679.654i | − | 0.784819i | ||||||
\(867\) | 285.892 | + | 818.508i | 0.329749 | + | 0.944069i | ||||
\(868\) | 137.564 | 0.158484 | ||||||||
\(869\) | −1251.50 | − | 1251.50i | −1.44016 | − | 1.44016i | ||||
\(870\) | 403.688 | − | 1046.19i | 0.464010 | − | 1.20252i | ||||
\(871\) | 215.131i | 0.246994i | ||||||||
\(872\) | 228.266 | − | 551.082i | 0.261773 | − | 0.631975i | ||||
\(873\) | −422.990 | − | 894.827i | −0.484524 | − | 1.02500i | ||||
\(874\) | 227.552 | − | 94.2553i | 0.260357 | − | 0.107844i | ||||
\(875\) | −105.859 | + | 105.859i | −0.120982 | + | 0.120982i | ||||
\(876\) | −413.864 | + | 434.603i | −0.472447 | + | 0.496122i | ||||
\(877\) | −511.733 | + | 211.967i | −0.583503 | + | 0.241695i | −0.654853 | − | 0.755756i | \(-0.727269\pi\) |
0.0713495 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(878\) | −104.082 | + | 43.1121i | −0.118544 | + | 0.0491027i | ||||
\(879\) | −1151.18 | − | 444.199i | −1.30965 | − | 0.505346i | ||||
\(880\) | 394.785i | 0.448620i | ||||||||
\(881\) | 62.8357 | + | 26.0274i | 0.0713232 | + | 0.0295430i | 0.418060 | − | 0.908420i | \(-0.362710\pi\) |
−0.346737 | + | 0.937963i | \(0.612710\pi\) | |||||||
\(882\) | 396.931 | + | 359.910i | 0.450035 | + | 0.408061i | ||||
\(883\) | 587.139 | 0.664936 | 0.332468 | − | 0.943114i | \(-0.392119\pi\) | ||||
0.332468 | + | 0.943114i | \(0.392119\pi\) | |||||||
\(884\) | 117.628 | + | 54.4099i | 0.133063 | + | 0.0615497i | ||||
\(885\) | −32.7274 | − | 1338.95i | −0.0369802 | − | 1.51294i | ||||
\(886\) | 461.487 | − | 461.487i | 0.520866 | − | 0.520866i | ||||
\(887\) | 366.285 | + | 151.720i | 0.412948 | + | 0.171048i | 0.579478 | − | 0.814988i | \(-0.303256\pi\) |
−0.166531 | + | 0.986036i | \(0.553256\pi\) | |||||||
\(888\) | 10.7274 | + | 438.880i | 0.0120804 | + | 0.494234i | ||||
\(889\) | 248.866 | + | 103.084i | 0.279940 | + | 0.115955i | ||||
\(890\) | −82.3506 | + | 34.1107i | −0.0925287 | + | 0.0383267i | ||||
\(891\) | 587.268 | + | 1099.82i | 0.659111 | + | 1.23437i | ||||
\(892\) | −141.460 | − | 141.460i | −0.158588 | − | 0.158588i | ||||
\(893\) | −710.956 | + | 710.956i | −0.796143 | + | 0.796143i | ||||
\(894\) | −124.751 | − | 281.514i | −0.139542 | − | 0.314893i | ||||
\(895\) | −528.442 | − | 1275.77i | −0.590438 | − | 1.42544i | ||||
\(896\) | 11.3753 | − | 27.4625i | 0.0126957 | − | 0.0306501i | ||||
\(897\) | −3.45630 | − | 141.405i | −0.00385318 | − | 0.157642i | ||||
\(898\) | −310.438 | + | 749.464i | −0.345699 | + | 0.834592i | ||||
\(899\) | −763.066 | − | 763.066i | −0.848795 | − | 0.848795i | ||||
\(900\) | 289.696 | − | 14.1703i | 0.321884 | − | 0.0157448i | ||||
\(901\) | −233.434 | − | 635.254i | −0.259083 | − | 0.705054i | ||||
\(902\) | 1382.43i | 1.53263i | ||||||||
\(903\) | 36.1619 | + | 34.4363i | 0.0400464 | + | 0.0381354i | ||||
\(904\) | −183.002 | + | 441.805i | −0.202435 | + | 0.488723i | ||||
\(905\) | −1573.22 | −1.73836 | ||||||||
\(906\) | 425.120 | + | 164.038i | 0.469227 | + | 0.181058i | ||||
\(907\) | 476.485 | + | 1150.34i | 0.525342 | + | 1.26829i | 0.934545 | + | 0.355845i | \(0.115807\pi\) |
−0.409203 | + | 0.912444i | \(0.634193\pi\) | |||||||
\(908\) | −198.130 | − | 478.329i | −0.218205 | − | 0.526794i | ||||
\(909\) | −339.694 | + | 374.635i | −0.373701 | + | 0.412140i | ||||
\(910\) | 64.2164 | + | 64.2164i | 0.0705675 | + | 0.0705675i | ||||
\(911\) | 300.980 | + | 726.630i | 0.330384 | + | 0.797619i | 0.998562 | + | 0.0536163i | \(0.0170748\pi\) |
−0.668177 | + | 0.744002i | \(0.732925\pi\) | |||||||
\(912\) | −154.476 | + | 68.4548i | −0.169381 | + | 0.0750601i | ||||
\(913\) | −1313.85 | − | 544.214i | −1.43905 | − | 0.596073i | ||||
\(914\) | 244.294 | 0.267280 | ||||||||
\(915\) | −260.266 | + | 674.501i | −0.284444 | + | 0.737160i | ||||
\(916\) | 269.190 | − | 269.190i | 0.293876 | − | 0.293876i | ||||
\(917\) | − | 165.305i | − | 0.180268i | ||||||
\(918\) | −443.718 | + | 473.789i | −0.483353 | + | 0.516111i | ||||
\(919\) | −962.138 | −1.04694 | −0.523470 | − | 0.852044i | \(-0.675363\pi\) | ||||
−0.523470 | + | 0.852044i | \(0.675363\pi\) | |||||||
\(920\) | 158.621 | + | 158.621i | 0.172414 | + | 0.172414i | ||||
\(921\) | 667.805 | + | 257.682i | 0.725087 | + | 0.279785i | ||||
\(922\) | 349.240i | 0.378786i | ||||||||
\(923\) | −84.9749 | + | 205.148i | −0.0920638 | + | 0.222262i | ||||
\(924\) | −98.3083 | − | 221.843i | −0.106394 | − | 0.240090i | ||||
\(925\) | 770.217 | − | 319.034i | 0.832667 | − | 0.344902i | ||||
\(926\) | 708.905 | − | 708.905i | 0.765557 | − | 0.765557i | ||||
\(927\) | 1170.47 | + | 1061.30i | 1.26264 | + | 1.14488i | ||||
\(928\) | −215.434 | + | 89.2355i | −0.232148 | + | 0.0961589i | ||||
\(929\) | −580.541 | + | 240.468i | −0.624910 | + | 0.258846i | −0.672588 | − | 0.740017i | \(-0.734818\pi\) |
0.0476790 | + | 0.998863i | \(0.484818\pi\) | |||||||
\(930\) | 256.376 | − | 664.421i | 0.275673 | − | 0.714431i | ||||
\(931\) | 592.739i | 0.636669i | ||||||||
\(932\) | −478.044 | − | 198.012i | −0.512923 | − | 0.212459i | ||||
\(933\) | 1111.65 | − | 1167.35i | 1.19148 | − | 1.25118i | ||||
\(934\) | 39.1743 | 0.0419425 | ||||||||
\(935\) | −704.393 | + | 1522.82i | −0.753361 | + | 1.62868i | ||||
\(936\) | 4.74067 | + | 96.9176i | 0.00506482 | + | 0.103544i | ||||
\(937\) | −780.874 | + | 780.874i | −0.833376 | + | 0.833376i | −0.987977 | − | 0.154601i | \(-0.950591\pi\) |
0.154601 | + | 0.987977i | \(0.450591\pi\) | |||||||
\(938\) | 193.740 | + | 80.2499i | 0.206546 | + | 0.0855542i | ||||
\(939\) | 511.872 | − | 12.5115i | 0.545124 | − | 0.0133243i | ||||
\(940\) | −846.023 | − | 350.434i | −0.900024 | − | 0.372802i | ||||
\(941\) | 740.966 | − | 306.918i | 0.787424 | − | 0.326162i | 0.0475166 | − | 0.998870i | \(-0.484869\pi\) |
0.739907 | + | 0.672709i | \(0.234869\pi\) | |||||||
\(942\) | 275.134 | − | 121.923i | 0.292074 | − | 0.129430i | ||||
\(943\) | 555.447 | + | 555.447i | 0.589021 | + | 0.589021i | ||||
\(944\) | −196.936 | + | 196.936i | −0.208619 | + | 0.208619i | ||||
\(945\) | −406.355 | + | 204.380i | −0.430005 | + | 0.216275i | ||||
\(946\) | 52.7753 | + | 127.411i | 0.0557879 | + | 0.134684i | ||||
\(947\) | −176.047 | + | 425.016i | −0.185900 | + | 0.448802i | −0.989163 | − | 0.146822i | \(-0.953095\pi\) |
0.803263 | + | 0.595625i | \(0.203095\pi\) | |||||||
\(948\) | 689.695 | − | 16.8580i | 0.727526 | − | 0.0177827i | ||||
\(949\) | −145.906 | + | 352.247i | −0.153747 | + | 0.371177i | ||||
\(950\) | 226.883 | + | 226.883i | 0.238824 | + | 0.238824i | ||||
\(951\) | 190.182 | − | 4.64854i | 0.199981 | − | 0.00488805i | ||||
\(952\) | 92.8782 | − | 85.6355i | 0.0975611 | − | 0.0899533i | ||||
\(953\) | 1130.14i | 1.18588i | 0.805248 | + | 0.592938i | \(0.202032\pi\) | ||||
−0.805248 | + | 0.592938i | \(0.797968\pi\) | |||||||
\(954\) | 340.365 | − | 375.375i | 0.356777 | − | 0.393475i | ||||
\(955\) | 179.740 | − | 433.932i | 0.188210 | − | 0.454379i | ||||
\(956\) | −344.067 | −0.359902 | ||||||||
\(957\) | −685.249 | + | 1775.88i | −0.716039 | + | 1.85567i | ||||
\(958\) | −81.7542 | − | 197.372i | −0.0853384 | − | 0.206025i | ||||
\(959\) | −100.431 | − | 242.461i | −0.104724 | − | 0.252827i | ||||
\(960\) | −111.441 | − | 106.123i | −0.116085 | − | 0.110545i | ||||
\(961\) | 194.918 | + | 194.918i | 0.202828 | + | 0.202828i | ||||
\(962\) | 106.733 | + | 257.676i | 0.110949 | + | 0.267854i | ||||
\(963\) | 908.185 | − | 429.304i | 0.943079 | − | 0.445799i | ||||
\(964\) | 246.464 | + | 102.089i | 0.255668 | + | 0.105901i | ||||
\(965\) | −203.011 | −0.210374 | ||||||||
\(966\) | −128.634 | − | 49.6351i | −0.133161 | − | 0.0513821i | ||||
\(967\) | 371.066 | − | 371.066i | 0.383729 | − | 0.383729i | −0.488715 | − | 0.872444i | \(-0.662534\pi\) |
0.872444 | + | 0.488715i | \(0.162534\pi\) | |||||||
\(968\) | − | 327.897i | − | 0.338736i | ||||||
\(969\) | −718.004 | − | 11.5695i | −0.740974 | − | 0.0119396i | ||||
\(970\) | 997.233 | 1.02808 | ||||||||
\(971\) | −174.991 | − | 174.991i | −0.180217 | − | 0.180217i | 0.611233 | − | 0.791451i | \(-0.290674\pi\) |
−0.791451 | + | 0.611233i | \(0.790674\pi\) | |||||||
\(972\) | −468.326 | − | 129.870i | −0.481817 | − | 0.133612i | ||||
\(973\) | − | 35.9576i | − | 0.0369554i | ||||||
\(974\) | −247.640 | + | 597.856i | −0.254250 | + | 0.613815i | ||||
\(975\) | 168.465 | − | 74.6542i | 0.172785 | − | 0.0765684i | ||||
\(976\) | 138.894 | − | 57.5319i | 0.142310 | − | 0.0589466i | ||||
\(977\) | 698.925 | − | 698.925i | 0.715379 | − | 0.715379i | −0.252276 | − | 0.967655i | \(-0.581179\pi\) |
0.967655 | + | 0.252276i | \(0.0811791\pi\) | |||||||
\(978\) | 343.253 | + | 326.873i | 0.350974 | + | 0.334226i | ||||
\(979\) | 139.788 | − | 57.9019i | 0.142786 | − | 0.0591439i | ||||
\(980\) | −498.756 | + | 206.592i | −0.508935 | + | 0.210808i | ||||
\(981\) | 1786.93 | + | 639.799i | 1.82153 | + | 0.652191i | ||||
\(982\) | 290.846i | 0.296177i | ||||||||
\(983\) | −1018.65 | − | 421.940i | −1.03627 | − | 0.429237i | −0.201298 | − | 0.979530i | \(-0.564516\pi\) |
−0.834971 | + | 0.550293i | \(0.814516\pi\) | |||||||
\(984\) | −390.237 | − | 371.615i | −0.396582 | − | 0.377658i | ||||
\(985\) | −295.945 | −0.300452 | ||||||||
\(986\) | −990.215 | − | 40.1750i | −1.00428 | − | 0.0407454i | ||||
\(987\) | 562.673 | − | 13.7532i | 0.570084 | − | 0.0139344i | ||||
\(988\) | −75.9035 | + | 75.9035i | −0.0768254 | + | 0.0768254i | ||||
\(989\) | 72.3970 | + | 29.9878i | 0.0732022 | + | 0.0303214i | ||||
\(990\) | −1254.70 | + | 61.3730i | −1.26737 | + | 0.0619929i | ||||
\(991\) | −1679.30 | − | 695.587i | −1.69455 | − | 0.701904i | −0.694697 | − | 0.719302i | \(-0.744462\pi\) |
−0.999849 | + | 0.0173980i | \(0.994462\pi\) | |||||||
\(992\) | −136.818 | + | 56.6721i | −0.137922 | + | 0.0571291i | ||||
\(993\) | −140.750 | − | 317.618i | −0.141742 | − | 0.319857i | ||||
\(994\) | 153.051 | + | 153.051i | 0.153975 | + | 0.153975i | ||||
\(995\) | 26.0115 | − | 26.0115i | 0.0261422 | − | 0.0261422i | ||||
\(996\) | 506.802 | − | 224.586i | 0.508838 | − | 0.225488i | ||||
\(997\) | −164.604 | − | 397.388i | −0.165099 | − | 0.398584i | 0.819579 | − | 0.572966i | \(-0.194207\pi\) |
−0.984678 | + | 0.174382i | \(0.944207\pi\) | |||||||
\(998\) | −15.3624 | + | 37.0880i | −0.0153932 | + | 0.0371624i | ||||
\(999\) | −1393.17 | + | 102.321i | −1.39457 | + | 0.102424i |
(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 | 102.3.g.a.59.6 | ✓ | 24 | |
3.2 | odd | 2 | 102.3.g.b.59.1 | yes | 24 | ||
17.15 | even | 8 | 102.3.g.b.83.1 | yes | 24 | ||
51.32 | odd | 8 | inner | 102.3.g.a.83.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.3.g.a.59.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
102.3.g.a.83.6 | yes | 24 | 51.32 | odd | 8 | inner | |
102.3.g.b.59.1 | yes | 24 | 3.2 | odd | 2 | ||
102.3.g.b.83.1 | yes | 24 | 17.15 | even | 8 |