Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(13,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(60\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 69.18 | ||
Character | \(\chi\) | \(=\) | 224.69 |
Dual form | 224.3.v.b.13.18 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33217 | + | 1.49175i | −0.666085 | + | 0.745876i | ||||
\(3\) | 2.62896 | − | 1.08895i | 0.876321 | − | 0.362984i | 0.101252 | − | 0.994861i | \(-0.467715\pi\) |
0.775069 | + | 0.631877i | \(0.217715\pi\) | |||||||
\(4\) | −0.450649 | − | 3.97453i | −0.112662 | − | 0.993633i | ||||
\(5\) | −2.38974 | + | 5.76934i | −0.477948 | + | 1.15387i | 0.482622 | + | 0.875829i | \(0.339685\pi\) |
−0.960570 | + | 0.278039i | \(0.910315\pi\) | |||||||
\(6\) | −1.87778 | + | 5.37243i | −0.312963 | + | 0.895405i | ||||
\(7\) | −5.98528 | − | 3.62994i | −0.855040 | − | 0.518562i | ||||
\(8\) | 6.52936 | + | 4.62250i | 0.816170 | + | 0.577812i | ||||
\(9\) | −0.638332 | + | 0.638332i | −0.0709257 | + | 0.0709257i | ||||
\(10\) | −5.42289 | − | 11.2506i | −0.542289 | − | 1.12506i | ||||
\(11\) | −4.95364 | + | 11.9592i | −0.450331 | + | 1.08720i | 0.521865 | + | 0.853028i | \(0.325236\pi\) |
−0.972196 | + | 0.234167i | \(0.924764\pi\) | |||||||
\(12\) | −5.51282 | − | 9.95817i | −0.459401 | − | 0.829847i | ||||
\(13\) | −6.06710 | − | 14.6473i | −0.466700 | − | 1.12671i | −0.965595 | − | 0.260051i | \(-0.916260\pi\) |
0.498895 | − | 0.866663i | \(-0.333740\pi\) | |||||||
\(14\) | 13.3884 | − | 4.09286i | 0.956312 | − | 0.292347i | ||||
\(15\) | 17.7697i | 1.18465i | ||||||||
\(16\) | −15.5938 | + | 3.58224i | −0.974614 | + | 0.223890i | ||||
\(17\) | −8.22837 | −0.484022 | −0.242011 | − | 0.970274i | \(-0.577807\pi\) | ||||
−0.242011 | + | 0.970274i | \(0.577807\pi\) | |||||||
\(18\) | −0.101867 | − | 1.80260i | −0.00565926 | − | 0.100144i | ||||
\(19\) | 8.30680 | + | 20.0544i | 0.437200 | + | 1.05549i | 0.976912 | + | 0.213644i | \(0.0685334\pi\) |
−0.539711 | + | 0.841850i | \(0.681467\pi\) | |||||||
\(20\) | 24.0074 | + | 6.89815i | 1.20037 | + | 0.344907i | ||||
\(21\) | −19.6879 | − | 3.02529i | −0.937519 | − | 0.144061i | ||||
\(22\) | −11.2410 | − | 23.3212i | −0.510954 | − | 1.06006i | ||||
\(23\) | −26.4453 | + | 26.4453i | −1.14979 | + | 1.14979i | −0.163202 | + | 0.986593i | \(0.552182\pi\) |
−0.986593 | + | 0.163202i | \(0.947818\pi\) | |||||||
\(24\) | 22.1991 | + | 5.04221i | 0.924963 | + | 0.210092i | ||||
\(25\) | −9.89676 | − | 9.89676i | −0.395870 | − | 0.395870i | ||||
\(26\) | 29.9325 | + | 10.4620i | 1.15125 | + | 0.402386i | ||||
\(27\) | −10.7836 | + | 26.0339i | −0.399393 | + | 0.964220i | ||||
\(28\) | −11.7300 | + | 25.4245i | −0.418930 | + | 0.908018i | ||||
\(29\) | 7.68667 | + | 18.5573i | 0.265057 | + | 0.639905i | 0.999237 | − | 0.0390498i | \(-0.0124331\pi\) |
−0.734180 | + | 0.678955i | \(0.762433\pi\) | |||||||
\(30\) | −26.5080 | − | 23.6722i | −0.883599 | − | 0.789075i | ||||
\(31\) | − | 59.4680i | − | 1.91832i | −0.282859 | − | 0.959162i | \(-0.591283\pi\) | ||
0.282859 | − | 0.959162i | \(-0.408717\pi\) | |||||||
\(32\) | 15.4298 | − | 28.0343i | 0.482182 | − | 0.876071i | ||||
\(33\) | 36.8344i | 1.11620i | ||||||||
\(34\) | 10.9616 | − | 12.2747i | 0.322400 | − | 0.361020i | ||||
\(35\) | 35.2456 | − | 25.8565i | 1.00702 | − | 0.738757i | ||||
\(36\) | 2.82473 | + | 2.24941i | 0.0784648 | + | 0.0624835i | ||||
\(37\) | −20.1216 | − | 8.33464i | −0.543827 | − | 0.225261i | 0.0938199 | − | 0.995589i | \(-0.470092\pi\) |
−0.637647 | + | 0.770329i | \(0.720092\pi\) | |||||||
\(38\) | −40.9823 | − | 14.3242i | −1.07848 | − | 0.376952i | ||||
\(39\) | −31.9004 | − | 31.9004i | −0.817958 | − | 0.817958i | ||||
\(40\) | −42.2722 | + | 26.6235i | −1.05681 | + | 0.665588i | ||||
\(41\) | −24.3694 | − | 24.3694i | −0.594376 | − | 0.594376i | 0.344435 | − | 0.938810i | \(-0.388071\pi\) |
−0.938810 | + | 0.344435i | \(0.888071\pi\) | |||||||
\(42\) | 30.7406 | − | 25.3393i | 0.731919 | − | 0.603316i | ||||
\(43\) | −14.7173 | + | 35.5306i | −0.342262 | + | 0.826294i | 0.655224 | + | 0.755434i | \(0.272574\pi\) |
−0.997486 | + | 0.0708592i | \(0.977426\pi\) | |||||||
\(44\) | 49.7644 | + | 14.2990i | 1.13101 | + | 0.324978i | ||||
\(45\) | −2.15731 | − | 5.20820i | −0.0479401 | − | 0.115738i | ||||
\(46\) | −4.22021 | − | 74.6794i | −0.0917436 | − | 1.62346i | ||||
\(47\) | 5.31825 | 0.113154 | 0.0565771 | − | 0.998398i | \(-0.481981\pi\) | ||||
0.0565771 | + | 0.998398i | \(0.481981\pi\) | |||||||
\(48\) | −37.0947 | + | 26.3985i | −0.772807 | + | 0.549969i | ||||
\(49\) | 22.6471 | + | 43.4524i | 0.462186 | + | 0.886783i | ||||
\(50\) | 27.9477 | − | 1.57935i | 0.558953 | − | 0.0315870i | ||||
\(51\) | −21.6321 | + | 8.96030i | −0.424159 | + | 0.175692i | ||||
\(52\) | −55.4820 | + | 30.7147i | −1.06696 | + | 0.590667i | ||||
\(53\) | 15.0826 | − | 36.4126i | 0.284577 | − | 0.687030i | −0.715354 | − | 0.698762i | \(-0.753735\pi\) |
0.999931 | + | 0.0117325i | \(0.00373464\pi\) | |||||||
\(54\) | −24.4706 | − | 50.7681i | −0.453159 | − | 0.940150i | ||||
\(55\) | −57.1585 | − | 57.1585i | −1.03925 | − | 1.03925i | ||||
\(56\) | −22.3007 | − | 51.3681i | −0.398226 | − | 0.917287i | ||||
\(57\) | 43.6766 | + | 43.6766i | 0.766255 | + | 0.766255i | ||||
\(58\) | −37.9228 | − | 13.2548i | −0.653841 | − | 0.228531i | ||||
\(59\) | −6.55591 | + | 15.8274i | −0.111117 | + | 0.268260i | −0.969650 | − | 0.244499i | \(-0.921377\pi\) |
0.858533 | + | 0.512759i | \(0.171377\pi\) | |||||||
\(60\) | 70.6262 | − | 8.00789i | 1.17710 | − | 0.133465i | ||||
\(61\) | 86.2481 | − | 35.7251i | 1.41390 | − | 0.585658i | 0.460583 | − | 0.887617i | \(-0.347640\pi\) |
0.953321 | + | 0.301959i | \(0.0976404\pi\) | |||||||
\(62\) | 88.7115 | + | 79.2215i | 1.43083 | + | 1.27777i | ||||
\(63\) | 6.13770 | − | 1.50349i | 0.0974238 | − | 0.0238649i | ||||
\(64\) | 21.2651 | + | 60.3639i | 0.332267 | + | 0.943185i | ||||
\(65\) | 99.0039 | 1.52314 | ||||||||
\(66\) | −54.9479 | − | 49.0697i | −0.832543 | − | 0.743481i | ||||
\(67\) | 3.59372 | + | 8.67602i | 0.0536377 | + | 0.129493i | 0.948427 | − | 0.316996i | \(-0.102674\pi\) |
−0.894789 | + | 0.446489i | \(0.852674\pi\) | |||||||
\(68\) | 3.70811 | + | 32.7039i | 0.0545310 | + | 0.480940i | ||||
\(69\) | −40.7260 | + | 98.3213i | −0.590232 | + | 1.42495i | ||||
\(70\) | −8.38161 | + | 87.0229i | −0.119737 | + | 1.24318i | ||||
\(71\) | 22.3288 | + | 22.3288i | 0.314490 | + | 0.314490i | 0.846646 | − | 0.532156i | \(-0.178618\pi\) |
−0.532156 | + | 0.846646i | \(0.678618\pi\) | |||||||
\(72\) | −7.11858 | + | 1.21721i | −0.0988692 | + | 0.0169057i | ||||
\(73\) | 92.1045 | + | 92.1045i | 1.26171 | + | 1.26171i | 0.950266 | + | 0.311440i | \(0.100811\pi\) |
0.311440 | + | 0.950266i | \(0.399189\pi\) | |||||||
\(74\) | 39.2386 | − | 18.9133i | 0.530252 | − | 0.255585i | ||||
\(75\) | −36.7953 | − | 15.2411i | −0.490604 | − | 0.203215i | ||||
\(76\) | 75.9634 | − | 42.0532i | 0.999519 | − | 0.553331i | ||||
\(77\) | 73.0599 | − | 53.5974i | 0.948830 | − | 0.696071i | ||||
\(78\) | 90.0842 | − | 5.09075i | 1.15493 | − | 0.0652660i | ||||
\(79\) | 125.782i | 1.59217i | 0.605183 | + | 0.796086i | \(0.293100\pi\) | ||||
−0.605183 | + | 0.796086i | \(0.706900\pi\) | |||||||
\(80\) | 16.5980 | − | 98.5267i | 0.207475 | − | 1.23158i | ||||
\(81\) | 72.0604i | 0.889635i | ||||||||
\(82\) | 68.8173 | − | 3.88894i | 0.839235 | − | 0.0474260i | ||||
\(83\) | −9.80373 | − | 23.6683i | −0.118117 | − | 0.285160i | 0.853753 | − | 0.520679i | \(-0.174321\pi\) |
−0.971870 | + | 0.235519i | \(0.924321\pi\) | |||||||
\(84\) | −3.15178 | + | 79.6136i | −0.0375211 | + | 0.947781i | ||||
\(85\) | 19.6637 | − | 47.4723i | 0.231337 | − | 0.558497i | ||||
\(86\) | −33.3970 | − | 69.2873i | −0.388337 | − | 0.805667i | ||||
\(87\) | 40.4159 | + | 40.4159i | 0.464551 | + | 0.464551i | ||||
\(88\) | −87.6252 | + | 55.1874i | −0.995741 | + | 0.627130i | ||||
\(89\) | 22.0951 | − | 22.0951i | 0.248259 | − | 0.248259i | −0.571997 | − | 0.820256i | \(-0.693831\pi\) |
0.820256 | + | 0.571997i | \(0.193831\pi\) | |||||||
\(90\) | 10.6432 | + | 3.72004i | 0.118258 | + | 0.0413337i | ||||
\(91\) | −16.8554 | + | 109.691i | −0.185224 | + | 1.20540i | ||||
\(92\) | 117.025 | + | 93.1901i | 1.27201 | + | 1.01294i | ||||
\(93\) | −64.7578 | − | 156.339i | −0.696321 | − | 1.68107i | ||||
\(94\) | −7.08481 | + | 7.93351i | −0.0753703 | + | 0.0843990i | ||||
\(95\) | −135.552 | −1.42686 | ||||||||
\(96\) | 10.0364 | − | 90.5034i | 0.104546 | − | 0.942744i | ||||
\(97\) | − | 126.184i | − | 1.30086i | −0.759566 | − | 0.650431i | \(-0.774589\pi\) | ||
0.759566 | − | 0.650431i | \(-0.225411\pi\) | |||||||
\(98\) | −94.9900 | − | 24.1020i | −0.969285 | − | 0.245939i | ||||
\(99\) | −4.47184 | − | 10.7960i | −0.0451701 | − | 0.109050i | ||||
\(100\) | −34.8750 | + | 43.7950i | −0.348750 | + | 0.437950i | ||||
\(101\) | −36.0209 | + | 86.9622i | −0.356643 | + | 0.861012i | 0.639125 | + | 0.769103i | \(0.279297\pi\) |
−0.995767 | + | 0.0919087i | \(0.970703\pi\) | |||||||
\(102\) | 15.4511 | − | 44.2064i | 0.151481 | − | 0.433396i | ||||
\(103\) | −62.5866 | + | 62.5866i | −0.607637 | + | 0.607637i | −0.942328 | − | 0.334691i | \(-0.891368\pi\) |
0.334691 | + | 0.942328i | \(0.391368\pi\) | |||||||
\(104\) | 28.0927 | − | 123.683i | 0.270122 | − | 1.18926i | ||||
\(105\) | 64.5029 | − | 106.357i | 0.614313 | − | 1.01292i | ||||
\(106\) | 34.2260 | + | 71.0072i | 0.322887 | + | 0.669879i | ||||
\(107\) | 76.7971 | − | 185.405i | 0.717730 | − | 1.73275i | 0.0380135 | − | 0.999277i | \(-0.487897\pi\) |
0.679716 | − | 0.733475i | \(-0.262103\pi\) | |||||||
\(108\) | 108.332 | + | 31.1276i | 1.00308 | + | 0.288219i | ||||
\(109\) | 70.2851 | − | 29.1130i | 0.644817 | − | 0.267092i | −0.0362167 | − | 0.999344i | \(-0.511531\pi\) |
0.681034 | + | 0.732252i | \(0.261531\pi\) | |||||||
\(110\) | 161.411 | − | 9.12151i | 1.46737 | − | 0.0829228i | ||||
\(111\) | −61.9750 | −0.558333 | ||||||||
\(112\) | 106.337 | + | 35.1639i | 0.949435 | + | 0.313964i | ||||
\(113\) | 35.3129i | 0.312504i | 0.987717 | + | 0.156252i | \(0.0499411\pi\) | ||||
−0.987717 | + | 0.156252i | \(0.950059\pi\) | |||||||
\(114\) | −123.339 | + | 6.97002i | −1.08192 | + | 0.0611405i | ||||
\(115\) | −89.3745 | − | 215.769i | −0.777169 | − | 1.87625i | ||||
\(116\) | 70.2924 | − | 38.9137i | 0.605969 | − | 0.335463i | ||||
\(117\) | 13.2226 | + | 5.47700i | 0.113014 | + | 0.0468120i | ||||
\(118\) | −14.8769 | − | 30.8645i | −0.126076 | − | 0.261564i | ||||
\(119\) | 49.2491 | + | 29.8685i | 0.413858 | + | 0.250996i | ||||
\(120\) | −82.1403 | + | 116.025i | −0.684503 | + | 0.966873i | ||||
\(121\) | −32.9228 | − | 32.9228i | −0.272089 | − | 0.272089i | ||||
\(122\) | −61.6041 | + | 176.253i | −0.504951 | + | 1.44470i | ||||
\(123\) | −90.6034 | − | 37.5292i | −0.736613 | − | 0.305115i | ||||
\(124\) | −236.358 | + | 26.7992i | −1.90611 | + | 0.216123i | ||||
\(125\) | −63.4851 | + | 26.2964i | −0.507880 | + | 0.210371i | ||||
\(126\) | −5.93362 | + | 11.1588i | −0.0470922 | + | 0.0885621i | ||||
\(127\) | −129.436 | −1.01918 | −0.509589 | − | 0.860418i | \(-0.670203\pi\) | ||||
−0.509589 | + | 0.860418i | \(0.670203\pi\) | |||||||
\(128\) | −118.377 | − | 48.6927i | −0.924817 | − | 0.380412i | ||||
\(129\) | 109.435i | 0.848334i | ||||||||
\(130\) | −131.890 | + | 147.689i | −1.01454 | + | 1.13607i | ||||
\(131\) | −45.8272 | + | 18.9823i | −0.349826 | + | 0.144903i | −0.550676 | − | 0.834719i | \(-0.685630\pi\) |
0.200849 | + | 0.979622i | \(0.435630\pi\) | |||||||
\(132\) | 146.400 | − | 16.5994i | 1.10909 | − | 0.125753i | ||||
\(133\) | 23.0777 | − | 150.184i | 0.173516 | − | 1.12921i | ||||
\(134\) | −17.7299 | − | 6.19698i | −0.132313 | − | 0.0462461i | ||||
\(135\) | −124.429 | − | 124.429i | −0.921693 | − | 0.921693i | ||||
\(136\) | −53.7260 | − | 38.0356i | −0.395044 | − | 0.279674i | ||||
\(137\) | −26.4380 | + | 26.4380i | −0.192978 | + | 0.192978i | −0.796982 | − | 0.604004i | \(-0.793571\pi\) |
0.604004 | + | 0.796982i | \(0.293571\pi\) | |||||||
\(138\) | −92.4170 | − | 191.734i | −0.669689 | − | 1.38937i | ||||
\(139\) | 158.211 | + | 65.5330i | 1.13821 | + | 0.471461i | 0.870563 | − | 0.492057i | \(-0.163755\pi\) |
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(140\) | −118.651 | − | 128.433i | −0.847507 | − | 0.917375i | ||||
\(141\) | 13.9815 | − | 5.79132i | 0.0991594 | − | 0.0410732i | ||||
\(142\) | −63.0547 | + | 3.56328i | −0.444047 | + | 0.0250935i | ||||
\(143\) | 205.223 | 1.43513 | ||||||||
\(144\) | 7.66738 | − | 12.2407i | 0.0532457 | − | 0.0850048i | ||||
\(145\) | −125.432 | −0.865050 | ||||||||
\(146\) | −260.096 | + | 14.6983i | −1.78148 | + | 0.100673i | ||||
\(147\) | 106.856 | + | 89.5730i | 0.726911 | + | 0.609340i | ||||
\(148\) | −24.0585 | + | 83.7300i | −0.162558 | + | 0.565743i | ||||
\(149\) | −24.8431 | + | 59.9766i | −0.166732 | + | 0.402527i | −0.985057 | − | 0.172229i | \(-0.944903\pi\) |
0.818325 | + | 0.574756i | \(0.194903\pi\) | |||||||
\(150\) | 71.7536 | − | 34.5857i | 0.478357 | − | 0.230572i | ||||
\(151\) | −153.458 | + | 153.458i | −1.01628 | + | 1.01628i | −0.0164134 | + | 0.999865i | \(0.505225\pi\) |
−0.999865 | + | 0.0164134i | \(0.994775\pi\) | |||||||
\(152\) | −38.4632 | + | 169.341i | −0.253048 | + | 1.11408i | ||||
\(153\) | 5.25243 | − | 5.25243i | 0.0343296 | − | 0.0343296i | ||||
\(154\) | −17.3741 | + | 180.388i | −0.112819 | + | 1.17135i | ||||
\(155\) | 343.091 | + | 142.113i | 2.21349 | + | 0.916858i | ||||
\(156\) | −112.413 | + | 141.165i | −0.720598 | + | 0.904904i | ||||
\(157\) | 75.7760 | − | 31.3875i | 0.482650 | − | 0.199920i | −0.128073 | − | 0.991765i | \(-0.540879\pi\) |
0.610723 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(158\) | −187.635 | − | 167.562i | −1.18756 | − | 1.06052i | ||||
\(159\) | − | 112.151i | − | 0.705355i | ||||||
\(160\) | 124.866 | + | 156.014i | 0.780413 | + | 0.975090i | ||||
\(161\) | 254.277 | − | 62.2876i | 1.57936 | − | 0.386880i | ||||
\(162\) | −107.496 | − | 95.9967i | −0.663557 | − | 0.592572i | ||||
\(163\) | −67.4334 | − | 162.799i | −0.413702 | − | 0.998764i | −0.984135 | − | 0.177420i | \(-0.943225\pi\) |
0.570434 | − | 0.821344i | \(-0.306775\pi\) | |||||||
\(164\) | −85.8750 | + | 107.839i | −0.523628 | + | 0.657555i | ||||
\(165\) | −212.510 | − | 88.0247i | −1.28794 | − | 0.533483i | ||||
\(166\) | 48.3675 | + | 16.9055i | 0.291370 | + | 0.101840i | ||||
\(167\) | 1.60311 | − | 1.60311i | 0.00959944 | − | 0.00959944i | −0.702291 | − | 0.711890i | \(-0.747839\pi\) |
0.711890 | + | 0.702291i | \(0.247839\pi\) | |||||||
\(168\) | −114.565 | − | 110.760i | −0.681935 | − | 0.659288i | ||||
\(169\) | −58.2321 | + | 58.2321i | −0.344569 | + | 0.344569i | ||||
\(170\) | 44.6215 | + | 92.5744i | 0.262480 | + | 0.544555i | ||||
\(171\) | −18.1039 | − | 7.49886i | −0.105870 | − | 0.0438530i | ||||
\(172\) | 147.850 | + | 42.4824i | 0.859593 | + | 0.246991i | ||||
\(173\) | 29.9048 | + | 72.1966i | 0.172860 | + | 0.417322i | 0.986438 | − | 0.164135i | \(-0.0524832\pi\) |
−0.813578 | + | 0.581456i | \(0.802483\pi\) | |||||||
\(174\) | −114.131 | + | 6.44968i | −0.655928 | + | 0.0370671i | ||||
\(175\) | 23.3102 | + | 95.1595i | 0.133201 | + | 0.543768i | ||||
\(176\) | 34.4057 | − | 204.234i | 0.195487 | − | 1.16042i | ||||
\(177\) | 48.7486i | 0.275416i | ||||||||
\(178\) | 3.52599 | + | 62.3948i | 0.0198090 | + | 0.350533i | ||||
\(179\) | −24.0549 | + | 9.96388i | −0.134385 | + | 0.0556641i | −0.448863 | − | 0.893601i | \(-0.648171\pi\) |
0.314477 | + | 0.949265i | \(0.398171\pi\) | |||||||
\(180\) | −19.7280 | + | 10.9214i | −0.109600 | + | 0.0606742i | ||||
\(181\) | −5.89024 | − | 2.43982i | −0.0325428 | − | 0.0134797i | 0.366353 | − | 0.930476i | \(-0.380606\pi\) |
−0.398895 | + | 0.916996i | \(0.630606\pi\) | |||||||
\(182\) | −141.178 | − | 171.271i | −0.775703 | − | 0.941052i | ||||
\(183\) | 187.840 | − | 187.840i | 1.02645 | − | 1.02645i | ||||
\(184\) | −294.914 | + | 50.4275i | −1.60279 | + | 0.274063i | ||||
\(185\) | 96.1708 | − | 96.1708i | 0.519842 | − | 0.519842i | ||||
\(186\) | 319.488 | + | 111.668i | 1.71768 | + | 0.600364i | ||||
\(187\) | 40.7604 | − | 98.4043i | 0.217970 | − | 0.526226i | ||||
\(188\) | −2.39666 | − | 21.1375i | −0.0127482 | − | 0.112434i | ||||
\(189\) | 159.044 | − | 116.676i | 0.841505 | − | 0.617336i | ||||
\(190\) | 180.578 | − | 202.210i | 0.950410 | − | 1.06426i | ||||
\(191\) | −66.9175 | −0.350353 | −0.175177 | − | 0.984537i | \(-0.556050\pi\) | ||||
−0.175177 | + | 0.984537i | \(0.556050\pi\) | |||||||
\(192\) | 121.638 | + | 135.538i | 0.633534 | + | 0.705926i | ||||
\(193\) | −57.1735 | −0.296236 | −0.148118 | − | 0.988970i | \(-0.547322\pi\) | ||||
−0.148118 | + | 0.988970i | \(0.547322\pi\) | |||||||
\(194\) | 188.235 | + | 168.098i | 0.970281 | + | 0.866484i | ||||
\(195\) | 260.278 | − | 107.811i | 1.33476 | − | 0.552875i | ||||
\(196\) | 162.497 | − | 109.593i | 0.829066 | − | 0.559150i | ||||
\(197\) | −219.277 | − | 90.8277i | −1.11308 | − | 0.461054i | −0.251085 | − | 0.967965i | \(-0.580787\pi\) |
−0.861998 | + | 0.506911i | \(0.830787\pi\) | |||||||
\(198\) | 22.0622 | + | 7.71119i | 0.111425 | + | 0.0389454i | ||||
\(199\) | −60.0935 | + | 60.0935i | −0.301977 | + | 0.301977i | −0.841787 | − | 0.539810i | \(-0.818496\pi\) |
0.539810 | + | 0.841787i | \(0.318496\pi\) | |||||||
\(200\) | −18.8718 | − | 110.367i | −0.0943589 | − | 0.551836i | ||||
\(201\) | 18.8955 | + | 18.8955i | 0.0940076 | + | 0.0940076i | ||||
\(202\) | −81.7401 | − | 169.583i | −0.404654 | − | 0.839518i | ||||
\(203\) | 21.3548 | − | 138.972i | 0.105196 | − | 0.684593i | ||||
\(204\) | 45.3615 | + | 81.9395i | 0.222360 | + | 0.401664i | ||||
\(205\) | 198.832 | − | 82.3589i | 0.969912 | − | 0.401751i | ||||
\(206\) | −9.98775 | − | 176.740i | −0.0484842 | − | 0.857960i | ||||
\(207\) | − | 33.7617i | − | 0.163100i | ||||||
\(208\) | 147.079 | + | 206.673i | 0.707113 | + | 0.993622i | ||||
\(209\) | −280.982 | −1.34441 | ||||||||
\(210\) | 72.7289 | + | 237.907i | 0.346328 | + | 1.13289i | ||||
\(211\) | −9.56309 | + | 3.96116i | −0.0453227 | + | 0.0187733i | −0.405230 | − | 0.914215i | \(-0.632808\pi\) |
0.359907 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(212\) | −151.520 | − | 43.5369i | −0.714717 | − | 0.205363i | ||||
\(213\) | 83.0164 | + | 34.3865i | 0.389748 | + | 0.161439i | ||||
\(214\) | 174.271 | + | 361.552i | 0.814350 | + | 1.68950i | ||||
\(215\) | −169.818 | − | 169.818i | −0.789850 | − | 0.789850i | ||||
\(216\) | −190.752 | + | 120.138i | −0.883110 | + | 0.556193i | ||||
\(217\) | −215.865 | + | 355.933i | −0.994770 | + | 1.64024i | ||||
\(218\) | −50.2022 | + | 143.631i | −0.230285 | + | 0.658860i | ||||
\(219\) | 342.437 | + | 141.842i | 1.56364 | + | 0.647680i | ||||
\(220\) | −201.420 | + | 252.937i | −0.915545 | + | 1.14971i | ||||
\(221\) | 49.9224 | + | 120.523i | 0.225893 | + | 0.545354i | ||||
\(222\) | 82.5612 | − | 92.4513i | 0.371897 | − | 0.416447i | ||||
\(223\) | 385.896i | 1.73047i | 0.501363 | + | 0.865237i | \(0.332832\pi\) | ||||
−0.501363 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(224\) | −194.114 | + | 111.784i | −0.866582 | + | 0.499034i | ||||
\(225\) | 12.6348 | 0.0561548 | ||||||||
\(226\) | −52.6781 | − | 47.0428i | −0.233089 | − | 0.208154i | ||||
\(227\) | −294.847 | + | 122.130i | −1.29889 | + | 0.538016i | −0.921622 | − | 0.388089i | \(-0.873135\pi\) |
−0.377265 | + | 0.926106i | \(0.623135\pi\) | |||||||
\(228\) | 153.911 | − | 193.277i | 0.675049 | − | 0.847705i | ||||
\(229\) | 112.540 | − | 271.695i | 0.491440 | − | 1.18644i | −0.462547 | − | 0.886595i | \(-0.653064\pi\) |
0.953987 | − | 0.299847i | \(-0.0969357\pi\) | |||||||
\(230\) | 440.936 | + | 154.116i | 1.91711 | + | 0.670071i | ||||
\(231\) | 133.707 | − | 220.464i | 0.578817 | − | 0.954391i | ||||
\(232\) | −35.5918 | + | 156.699i | −0.153413 | + | 0.675425i | ||||
\(233\) | −78.6743 | + | 78.6743i | −0.337658 | + | 0.337658i | −0.855485 | − | 0.517827i | \(-0.826741\pi\) |
0.517827 | + | 0.855485i | \(0.326741\pi\) | |||||||
\(234\) | −25.7851 | + | 12.4286i | −0.110193 | + | 0.0531138i | ||||
\(235\) | −12.7092 | + | 30.6828i | −0.0540818 | + | 0.130565i | ||||
\(236\) | 65.8608 | + | 18.9241i | 0.279071 | + | 0.0801868i | ||||
\(237\) | 136.970 | + | 330.675i | 0.577933 | + | 1.39525i | ||||
\(238\) | −110.165 | + | 33.6776i | −0.462876 | + | 0.141502i | ||||
\(239\) | 415.345i | 1.73785i | 0.494948 | + | 0.868923i | \(0.335187\pi\) | ||||
−0.494948 | + | 0.868923i | \(0.664813\pi\) | |||||||
\(240\) | −63.6553 | − | 277.098i | −0.265230 | − | 1.15457i | ||||
\(241\) | −105.572 | −0.438060 | −0.219030 | − | 0.975718i | \(-0.570289\pi\) | ||||
−0.219030 | + | 0.975718i | \(0.570289\pi\) | |||||||
\(242\) | 92.9714 | − | 5.25391i | 0.384179 | − | 0.0217104i | ||||
\(243\) | −18.5821 | − | 44.8612i | −0.0764696 | − | 0.184614i | ||||
\(244\) | −180.858 | − | 326.697i | −0.741223 | − | 1.33892i | ||||
\(245\) | −304.812 | + | 26.8191i | −1.24413 | + | 0.109466i | ||||
\(246\) | 176.683 | − | 85.1626i | 0.718225 | − | 0.346189i | ||||
\(247\) | 243.344 | − | 243.344i | 0.985199 | − | 0.985199i | ||||
\(248\) | 274.891 | − | 388.288i | 1.10843 | − | 1.56568i | ||||
\(249\) | −51.5473 | − | 51.5473i | −0.207017 | − | 0.207017i | ||||
\(250\) | 45.3452 | − | 129.735i | 0.181381 | − | 0.518941i | ||||
\(251\) | 8.51793 | − | 20.5641i | 0.0339360 | − | 0.0819287i | −0.906003 | − | 0.423271i | \(-0.860882\pi\) |
0.939939 | + | 0.341343i | \(0.110882\pi\) | |||||||
\(252\) | −8.74161 | − | 23.7169i | −0.0346889 | − | 0.0941148i | ||||
\(253\) | −185.263 | − | 447.263i | −0.732263 | − | 1.76784i | ||||
\(254\) | 172.430 | − | 193.086i | 0.678859 | − | 0.760181i | ||||
\(255\) | − | 146.216i | − | 0.573395i | ||||||
\(256\) | 230.335 | − | 111.722i | 0.899747 | − | 0.436413i | ||||
\(257\) | 252.000i | 0.980547i | 0.871569 | + | 0.490273i | \(0.163103\pi\) | ||||
−0.871569 | + | 0.490273i | \(0.836897\pi\) | |||||||
\(258\) | −163.250 | − | 145.786i | −0.632752 | − | 0.565062i | ||||
\(259\) | 90.1792 | + | 122.925i | 0.348182 | + | 0.474615i | ||||
\(260\) | −44.6160 | − | 393.494i | −0.171600 | − | 1.51344i | ||||
\(261\) | −16.7523 | − | 6.93904i | −0.0641852 | − | 0.0265864i | ||||
\(262\) | 32.7328 | − | 93.6505i | 0.124934 | − | 0.357445i | ||||
\(263\) | −37.2844 | − | 37.2844i | −0.141766 | − | 0.141766i | 0.632662 | − | 0.774428i | \(-0.281962\pi\) |
−0.774428 | + | 0.632662i | \(0.781962\pi\) | |||||||
\(264\) | −170.267 | + | 240.505i | −0.644951 | + | 0.911005i | ||||
\(265\) | 174.033 | + | 174.033i | 0.656728 | + | 0.656728i | ||||
\(266\) | 193.294 | + | 234.497i | 0.726671 | + | 0.881568i | ||||
\(267\) | 34.0267 | − | 82.1477i | 0.127441 | − | 0.307669i | ||||
\(268\) | 32.8636 | − | 18.1932i | 0.122625 | − | 0.0678851i | ||||
\(269\) | −73.4951 | − | 177.433i | −0.273216 | − | 0.659602i | 0.726401 | − | 0.687271i | \(-0.241192\pi\) |
−0.999617 | + | 0.0276690i | \(0.991192\pi\) | |||||||
\(270\) | 351.377 | − | 19.8566i | 1.30139 | − | 0.0735431i | ||||
\(271\) | −524.944 | −1.93706 | −0.968532 | − | 0.248889i | \(-0.919935\pi\) | ||||
−0.968532 | + | 0.248889i | \(0.919935\pi\) | |||||||
\(272\) | 128.312 | − | 29.4760i | 0.471735 | − | 0.108368i | ||||
\(273\) | 75.1363 | + | 306.729i | 0.275224 | + | 1.12355i | ||||
\(274\) | −4.21905 | − | 74.6588i | −0.0153980 | − | 0.272478i | ||||
\(275\) | 167.382 | − | 69.3318i | 0.608661 | − | 0.252116i | ||||
\(276\) | 409.134 | + | 117.558i | 1.48237 | + | 0.425936i | ||||
\(277\) | −152.184 | + | 367.404i | −0.549400 | + | 1.32637i | 0.368527 | + | 0.929617i | \(0.379862\pi\) |
−0.917926 | + | 0.396751i | \(0.870138\pi\) | |||||||
\(278\) | −308.523 | + | 148.710i | −1.10979 | + | 0.534929i | ||||
\(279\) | 37.9603 | + | 37.9603i | 0.136058 | + | 0.136058i | ||||
\(280\) | 349.653 | − | 5.90382i | 1.24876 | − | 0.0210851i | ||||
\(281\) | −164.515 | − | 164.515i | −0.585463 | − | 0.585463i | 0.350937 | − | 0.936399i | \(-0.385863\pi\) |
−0.936399 | + | 0.350937i | \(0.885863\pi\) | |||||||
\(282\) | −9.98648 | + | 28.5719i | −0.0354131 | + | 0.101319i | ||||
\(283\) | −15.6042 | + | 37.6718i | −0.0551384 | + | 0.133116i | −0.949048 | − | 0.315131i | \(-0.897951\pi\) |
0.893910 | + | 0.448247i | \(0.147951\pi\) | |||||||
\(284\) | 78.6840 | − | 98.8088i | 0.277056 | − | 0.347918i | ||||
\(285\) | −356.360 | + | 147.609i | −1.25039 | + | 0.517927i | ||||
\(286\) | −273.392 | + | 306.142i | −0.955917 | + | 1.07043i | ||||
\(287\) | 57.3983 | + | 234.317i | 0.199994 | + | 0.816436i | ||||
\(288\) | 8.04583 | + | 27.7445i | 0.0279369 | + | 0.0963351i | ||||
\(289\) | −221.294 | −0.765723 | ||||||||
\(290\) | 167.097 | − | 187.114i | 0.576196 | − | 0.645220i | ||||
\(291\) | −137.408 | − | 331.732i | −0.472192 | − | 1.13997i | ||||
\(292\) | 324.566 | − | 407.579i | 1.11153 | − | 1.39582i | ||||
\(293\) | 185.206 | − | 447.127i | 0.632103 | − | 1.52603i | −0.204871 | − | 0.978789i | \(-0.565677\pi\) |
0.836974 | − | 0.547243i | \(-0.184323\pi\) | |||||||
\(294\) | −275.971 | + | 40.0762i | −0.938677 | + | 0.136313i | ||||
\(295\) | −75.6465 | − | 75.6465i | −0.256429 | − | 0.256429i | ||||
\(296\) | −92.8544 | − | 147.432i | −0.313697 | − | 0.498081i | ||||
\(297\) | −257.926 | − | 257.926i | −0.868436 | − | 0.868436i | ||||
\(298\) | −56.3749 | − | 116.959i | −0.189178 | − | 0.392479i | ||||
\(299\) | 547.798 | + | 226.905i | 1.83210 | + | 0.758880i | ||||
\(300\) | −43.9946 | + | 153.113i | −0.146649 | + | 0.510375i | ||||
\(301\) | 217.061 | − | 159.238i | 0.721132 | − | 0.529030i | ||||
\(302\) | −24.4893 | − | 433.354i | −0.0810902 | − | 1.43495i | ||||
\(303\) | 267.845i | 0.883978i | ||||||||
\(304\) | −201.375 | − | 282.968i | −0.662416 | − | 0.930815i | ||||
\(305\) | 582.969i | 1.91137i | ||||||||
\(306\) | 0.838197 | + | 14.8325i | 0.00273921 | + | 0.0484721i | ||||
\(307\) | 55.1706 | + | 133.194i | 0.179709 | + | 0.433856i | 0.987905 | − | 0.155057i | \(-0.0495562\pi\) |
−0.808197 | + | 0.588913i | \(0.799556\pi\) | |||||||
\(308\) | −245.949 | − | 266.225i | −0.798536 | − | 0.864368i | ||||
\(309\) | −96.3841 | + | 232.692i | −0.311923 | + | 0.753048i | ||||
\(310\) | −669.053 | + | 322.488i | −2.15824 | + | 1.04029i | ||||
\(311\) | 281.152 | + | 281.152i | 0.904025 | + | 0.904025i | 0.995781 | − | 0.0917564i | \(-0.0292481\pi\) |
−0.0917564 | + | 0.995781i | \(0.529248\pi\) | |||||||
\(312\) | −60.8297 | − | 355.748i | −0.194967 | − | 1.14022i | ||||
\(313\) | 164.448 | − | 164.448i | 0.525394 | − | 0.525394i | −0.393801 | − | 0.919196i | \(-0.628840\pi\) |
0.919196 | + | 0.393801i | \(0.128840\pi\) | |||||||
\(314\) | −54.1242 | + | 154.853i | −0.172370 | + | 0.493161i | ||||
\(315\) | −5.99335 | + | 39.0034i | −0.0190265 | + | 0.123820i | ||||
\(316\) | 499.923 | − | 56.6834i | 1.58204 | − | 0.179378i | ||||
\(317\) | 102.453 | + | 247.344i | 0.323197 | + | 0.780267i | 0.999065 | + | 0.0432434i | \(0.0137691\pi\) |
−0.675868 | + | 0.737023i | \(0.736231\pi\) | |||||||
\(318\) | 167.302 | + | 149.405i | 0.526108 | + | 0.469826i | ||||
\(319\) | −260.006 | −0.815066 | ||||||||
\(320\) | −399.078 | − | 21.5684i | −1.24712 | − | 0.0674014i | ||||
\(321\) | − | 571.050i | − | 1.77897i | ||||||
\(322\) | −245.822 | + | 462.296i | −0.763423 | + | 1.43570i | ||||
\(323\) | −68.3515 | − | 165.015i | −0.211614 | − | 0.510882i | ||||
\(324\) | 286.407 | − | 32.4740i | 0.883971 | − | 0.100228i | ||||
\(325\) | −84.9160 | + | 205.005i | −0.261280 | + | 0.630785i | ||||
\(326\) | 332.688 | + | 116.281i | 1.02051 | + | 0.356691i | ||||
\(327\) | 153.074 | − | 153.074i | 0.468117 | − | 0.468117i | ||||
\(328\) | −46.4692 | − | 271.764i | −0.141674 | − | 0.828549i | ||||
\(329\) | −31.8312 | − | 19.3049i | −0.0967513 | − | 0.0586775i | ||||
\(330\) | 414.411 | − | 199.749i | 1.25579 | − | 0.605300i | ||||
\(331\) | −42.2185 | + | 101.924i | −0.127548 | + | 0.307929i | −0.974734 | − | 0.223368i | \(-0.928295\pi\) |
0.847186 | + | 0.531296i | \(0.178295\pi\) | |||||||
\(332\) | −89.6524 | + | 49.6314i | −0.270037 | + | 0.149492i | ||||
\(333\) | 18.1645 | − | 7.52399i | 0.0545481 | − | 0.0225946i | ||||
\(334\) | 0.255828 | + | 4.52704i | 0.000765952 | + | 0.0135540i | ||||
\(335\) | −58.6430 | −0.175054 | ||||||||
\(336\) | 317.847 | − | 23.3509i | 0.945974 | − | 0.0694968i | ||||
\(337\) | 84.3102i | 0.250179i | 0.992145 | + | 0.125089i | \(0.0399217\pi\) | ||||
−0.992145 | + | 0.125089i | \(0.960078\pi\) | |||||||
\(338\) | −9.29284 | − | 164.443i | −0.0274936 | − | 0.486518i | ||||
\(339\) | 38.4541 | + | 92.8364i | 0.113434 | + | 0.273854i | ||||
\(340\) | −197.542 | − | 56.7605i | −0.581005 | − | 0.166943i | ||||
\(341\) | 711.187 | + | 294.583i | 2.08559 | + | 0.863881i | ||||
\(342\) | 35.3038 | − | 17.0167i | 0.103228 | − | 0.0497564i | ||||
\(343\) | 22.1801 | − | 342.282i | 0.0646650 | − | 0.997907i | ||||
\(344\) | −260.334 | + | 163.962i | −0.756786 | + | 0.476633i | ||||
\(345\) | −469.924 | − | 469.924i | −1.36210 | − | 1.36210i | ||||
\(346\) | −147.538 | − | 51.5676i | −0.426410 | − | 0.149039i | ||||
\(347\) | 273.373 | + | 113.235i | 0.787818 | + | 0.326325i | 0.740066 | − | 0.672534i | \(-0.234794\pi\) |
0.0477521 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(348\) | 142.421 | − | 178.848i | 0.409256 | − | 0.513931i | ||||
\(349\) | −78.2311 | + | 32.4044i | −0.224158 | + | 0.0928492i | −0.491936 | − | 0.870631i | \(-0.663711\pi\) |
0.267778 | + | 0.963481i | \(0.413711\pi\) | |||||||
\(350\) | −173.008 | − | 91.9954i | −0.494307 | − | 0.262844i | ||||
\(351\) | 446.752 | 1.27280 | ||||||||
\(352\) | 258.832 | + | 323.399i | 0.735319 | + | 0.918748i | ||||
\(353\) | 47.5226i | 0.134625i | 0.997732 | + | 0.0673125i | \(0.0214424\pi\) | ||||
−0.997732 | + | 0.0673125i | \(0.978558\pi\) | |||||||
\(354\) | −72.7209 | − | 64.9414i | −0.205426 | − | 0.183450i | ||||
\(355\) | −182.182 | + | 75.4623i | −0.513189 | + | 0.212570i | ||||
\(356\) | −97.7748 | − | 77.8606i | −0.274648 | − | 0.218709i | ||||
\(357\) | 161.999 | + | 24.8932i | 0.453780 | + | 0.0697289i | ||||
\(358\) | 17.1816 | − | 49.1576i | 0.0479933 | − | 0.137312i | ||||
\(359\) | 285.648 | + | 285.648i | 0.795677 | + | 0.795677i | 0.982411 | − | 0.186734i | \(-0.0597902\pi\) |
−0.186734 | + | 0.982411i | \(0.559790\pi\) | |||||||
\(360\) | 9.98904 | − | 43.9783i | 0.0277473 | − | 0.122162i | ||||
\(361\) | −77.9103 | + | 77.9103i | −0.215818 | + | 0.215818i | ||||
\(362\) | 11.4864 | − | 5.53653i | 0.0317304 | − | 0.0152943i | ||||
\(363\) | −122.404 | − | 50.7014i | −0.337201 | − | 0.139673i | ||||
\(364\) | 443.567 | + | 17.5601i | 1.21859 | + | 0.0482421i | ||||
\(365\) | −751.488 | + | 311.277i | −2.05887 | + | 0.852812i | ||||
\(366\) | 29.9760 | + | 530.446i | 0.0819018 | + | 1.44931i | ||||
\(367\) | −48.7938 | −0.132953 | −0.0664765 | − | 0.997788i | \(-0.521176\pi\) | ||||
−0.0664765 | + | 0.997788i | \(0.521176\pi\) | |||||||
\(368\) | 317.650 | − | 507.116i | 0.863179 | − | 1.37803i | ||||
\(369\) | 31.1115 | 0.0843131 | ||||||||
\(370\) | 15.3472 | + | 271.579i | 0.0414789 | + | 0.733997i | ||||
\(371\) | −222.449 | + | 163.191i | −0.599592 | + | 0.439867i | ||||
\(372\) | −592.192 | + | 327.836i | −1.59192 | + | 0.881280i | ||||
\(373\) | 41.0112 | − | 99.0098i | 0.109950 | − | 0.265442i | −0.859322 | − | 0.511435i | \(-0.829114\pi\) |
0.969272 | + | 0.245993i | \(0.0791141\pi\) | |||||||
\(374\) | 92.4951 | + | 191.896i | 0.247313 | + | 0.513090i | ||||
\(375\) | −138.264 | + | 138.264i | −0.368705 | + | 0.368705i | ||||
\(376\) | 34.7247 | + | 24.5836i | 0.0923530 | + | 0.0653818i | ||||
\(377\) | 225.178 | − | 225.178i | 0.597288 | − | 0.597288i | ||||
\(378\) | −37.8217 | + | 392.688i | −0.100057 | + | 1.03886i | ||||
\(379\) | 301.152 | + | 124.741i | 0.794595 | + | 0.329132i | 0.742789 | − | 0.669525i | \(-0.233502\pi\) |
0.0518057 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(380\) | 61.0862 | + | 538.755i | 0.160753 | + | 1.41778i | ||||
\(381\) | −340.281 | + | 140.949i | −0.893127 | + | 0.369945i | ||||
\(382\) | 89.1454 | − | 99.8243i | 0.233365 | − | 0.261320i | ||||
\(383\) | − | 531.504i | − | 1.38774i | −0.720100 | − | 0.693870i | \(-0.755904\pi\) | ||
0.720100 | − | 0.693870i | \(-0.244096\pi\) | |||||||
\(384\) | −364.232 | + | 0.895203i | −0.948520 | + | 0.00233126i | ||||
\(385\) | 134.628 | + | 549.591i | 0.349682 | + | 1.42751i | ||||
\(386\) | 76.1648 | − | 85.2887i | 0.197318 | − | 0.220955i | ||||
\(387\) | −13.2858 | − | 32.0748i | −0.0343303 | − | 0.0828807i | ||||
\(388\) | −501.521 | + | 56.8645i | −1.29258 | + | 0.146558i | ||||
\(389\) | −122.261 | − | 50.6422i | −0.314296 | − | 0.130186i | 0.219959 | − | 0.975509i | \(-0.429408\pi\) |
−0.534255 | + | 0.845324i | \(0.679408\pi\) | |||||||
\(390\) | −185.907 | + | 531.892i | −0.476686 | + | 1.36382i | ||||
\(391\) | 217.602 | − | 217.602i | 0.556526 | − | 0.556526i | ||||
\(392\) | −52.9872 | + | 388.402i | −0.135171 | + | 0.990822i | ||||
\(393\) | −99.8073 | + | 99.8073i | −0.253963 | + | 0.253963i | ||||
\(394\) | 427.607 | − | 206.110i | 1.08530 | − | 0.523121i | ||||
\(395\) | −725.677 | − | 300.585i | −1.83716 | − | 0.760975i | ||||
\(396\) | −40.8937 | + | 22.6387i | −0.103267 | + | 0.0571683i | ||||
\(397\) | −94.5605 | − | 228.289i | −0.238188 | − | 0.575036i | 0.758908 | − | 0.651198i | \(-0.225733\pi\) |
−0.997095 | + | 0.0761623i | \(0.975733\pi\) | |||||||
\(398\) | −9.58988 | − | 169.699i | −0.0240952 | − | 0.426380i | ||||
\(399\) | −102.873 | − | 419.959i | −0.257828 | − | 1.05253i | ||||
\(400\) | 189.781 | + | 118.876i | 0.474452 | + | 0.297190i | ||||
\(401\) | 364.409i | 0.908751i | 0.890810 | + | 0.454375i | \(0.150138\pi\) | ||||
−0.890810 | + | 0.454375i | \(0.849862\pi\) | |||||||
\(402\) | −53.3595 | + | 3.01540i | −0.132735 | + | 0.00750100i | ||||
\(403\) | −871.045 | + | 360.799i | −2.16140 | + | 0.895282i | ||||
\(404\) | 361.867 | + | 103.977i | 0.895710 | + | 0.257369i | ||||
\(405\) | −415.741 | − | 172.206i | −1.02652 | − | 0.425199i | ||||
\(406\) | 178.864 | + | 216.991i | 0.440552 | + | 0.534460i | ||||
\(407\) | 199.351 | − | 199.351i | 0.489805 | − | 0.489805i | ||||
\(408\) | −182.663 | − | 41.4892i | −0.447703 | − | 0.101689i | ||||
\(409\) | 307.105 | − | 307.105i | 0.750867 | − | 0.750867i | −0.223774 | − | 0.974641i | \(-0.571838\pi\) |
0.974641 | + | 0.223774i | \(0.0718378\pi\) | |||||||
\(410\) | −142.019 | + | 406.324i | −0.346387 | + | 0.991034i | ||||
\(411\) | −40.7148 | + | 98.2942i | −0.0990628 | + | 0.239159i | ||||
\(412\) | 276.957 | + | 220.548i | 0.672226 | + | 0.535311i | ||||
\(413\) | 96.6913 | − | 70.9336i | 0.234119 | − | 0.171752i | ||||
\(414\) | 50.3641 | + | 44.9763i | 0.121652 | + | 0.108638i | ||||
\(415\) | 159.979 | 0.385491 | ||||||||
\(416\) | −504.240 | − | 55.9180i | −1.21212 | − | 0.134418i | ||||
\(417\) | 487.293 | 1.16857 | ||||||||
\(418\) | 374.316 | − | 419.156i | 0.895493 | − | 1.00277i | ||||
\(419\) | −260.334 | + | 107.834i | −0.621322 | + | 0.257360i | −0.671061 | − | 0.741402i | \(-0.734161\pi\) |
0.0497391 | + | 0.998762i | \(0.484161\pi\) | |||||||
\(420\) | −451.786 | − | 208.439i | −1.07568 | − | 0.496284i | ||||
\(421\) | −514.444 | − | 213.090i | −1.22196 | − | 0.506151i | −0.323926 | − | 0.946083i | \(-0.605003\pi\) |
−0.898031 | + | 0.439931i | \(0.855003\pi\) | |||||||
\(422\) | 6.83059 | − | 19.5427i | 0.0161862 | − | 0.0463097i | ||||
\(423\) | −3.39481 | + | 3.39481i | −0.00802554 | + | 0.00802554i | ||||
\(424\) | 266.796 | − | 168.032i | 0.629237 | − | 0.396301i | ||||
\(425\) | 81.4342 | + | 81.4342i | 0.191610 | + | 0.191610i | ||||
\(426\) | −161.888 | + | 78.0312i | −0.380019 | + | 0.183172i | ||||
\(427\) | −645.899 | − | 99.2504i | −1.51264 | − | 0.232436i | ||||
\(428\) | −771.505 | − | 221.680i | −1.80258 | − | 0.517944i | ||||
\(429\) | 539.525 | − | 223.478i | 1.25763 | − | 0.520929i | ||||
\(430\) | 479.552 | − | 27.1000i | 1.11524 | − | 0.0630232i | ||||
\(431\) | 410.006i | 0.951290i | 0.879637 | + | 0.475645i | \(0.157785\pi\) | ||||
−0.879637 | + | 0.475645i | \(0.842215\pi\) | |||||||
\(432\) | 74.8980 | − | 444.598i | 0.173375 | − | 1.02916i | ||||
\(433\) | 512.137 | 1.18277 | 0.591383 | − | 0.806391i | \(-0.298582\pi\) | ||||
0.591383 | + | 0.806391i | \(0.298582\pi\) | |||||||
\(434\) | −243.394 | − | 796.180i | −0.560816 | − | 1.83452i | ||||
\(435\) | −329.757 | + | 136.590i | −0.758061 | + | 0.313999i | ||||
\(436\) | −147.385 | − | 266.231i | −0.338038 | − | 0.610621i | ||||
\(437\) | −750.019 | − | 310.668i | −1.71629 | − | 0.710911i | ||||
\(438\) | −667.777 | + | 321.873i | −1.52460 | + | 0.734871i | ||||
\(439\) | 469.838 | + | 469.838i | 1.07025 | + | 1.07025i | 0.997339 | + | 0.0729066i | \(0.0232275\pi\) |
0.0729066 | + | 0.997339i | \(0.476773\pi\) | |||||||
\(440\) | −108.993 | − | 637.423i | −0.247712 | − | 1.44869i | ||||
\(441\) | −42.1934 | − | 13.2807i | −0.0956766 | − | 0.0301149i | ||||
\(442\) | −246.296 | − | 86.0856i | −0.557231 | − | 0.194764i | ||||
\(443\) | 86.8413 | + | 35.9709i | 0.196030 | + | 0.0811983i | 0.478539 | − | 0.878066i | \(-0.341167\pi\) |
−0.282509 | + | 0.959265i | \(0.591167\pi\) | |||||||
\(444\) | 27.9290 | + | 246.322i | 0.0629031 | + | 0.554779i | ||||
\(445\) | 74.6726 | + | 180.276i | 0.167804 | + | 0.405114i | ||||
\(446\) | −575.661 | − | 514.078i | −1.29072 | − | 1.15264i | ||||
\(447\) | 184.729i | 0.413264i | ||||||||
\(448\) | 91.8397 | − | 438.485i | 0.204999 | − | 0.978762i | ||||
\(449\) | 33.6621 | 0.0749712 | 0.0374856 | − | 0.999297i | \(-0.488065\pi\) | ||||
0.0374856 | + | 0.999297i | \(0.488065\pi\) | |||||||
\(450\) | −16.8317 | + | 18.8480i | −0.0374039 | + | 0.0418845i | ||||
\(451\) | 412.155 | − | 170.720i | 0.913869 | − | 0.378537i | ||||
\(452\) | 140.352 | − | 15.9137i | 0.310514 | − | 0.0352074i | ||||
\(453\) | −236.327 | + | 570.544i | −0.521693 | + | 1.25948i | ||||
\(454\) | 210.599 | − | 602.536i | 0.463875 | − | 1.32717i | ||||
\(455\) | −592.566 | − | 359.378i | −1.30234 | − | 0.789842i | ||||
\(456\) | 83.2853 | + | 487.075i | 0.182643 | + | 1.06815i | ||||
\(457\) | 621.540 | − | 621.540i | 1.36004 | − | 1.36004i | 0.486191 | − | 0.873853i | \(-0.338386\pi\) |
0.873853 | − | 0.486191i | \(-0.161614\pi\) | |||||||
\(458\) | 255.380 | + | 529.826i | 0.557598 | + | 1.15682i | ||||
\(459\) | 88.7315 | − | 214.217i | 0.193315 | − | 0.466703i | ||||
\(460\) | −817.305 | + | 452.458i | −1.77675 | + | 0.983604i | ||||
\(461\) | 284.099 | + | 685.876i | 0.616267 | + | 1.48780i | 0.856008 | + | 0.516963i | \(0.172938\pi\) |
−0.239741 | + | 0.970837i | \(0.577062\pi\) | |||||||
\(462\) | 150.758 | + | 493.153i | 0.326317 | + | 1.06743i | ||||
\(463\) | − | 342.743i | − | 0.740266i | −0.928979 | − | 0.370133i | \(-0.879312\pi\) | ||
0.928979 | − | 0.370133i | \(-0.120688\pi\) | |||||||
\(464\) | −186.341 | − | 261.843i | −0.401597 | − | 0.564317i | ||||
\(465\) | 1056.73 | 2.27253 | ||||||||
\(466\) | −12.5551 | − | 222.170i | −0.0269422 | − | 0.476760i | ||||
\(467\) | 73.9541 | + | 178.541i | 0.158360 | + | 0.382315i | 0.983067 | − | 0.183245i | \(-0.0586602\pi\) |
−0.824707 | + | 0.565560i | \(0.808660\pi\) | |||||||
\(468\) | 15.8097 | − | 55.0221i | 0.0337815 | − | 0.117569i | ||||
\(469\) | 9.98396 | − | 64.9734i | 0.0212878 | − | 0.138536i | ||||
\(470\) | −28.8403 | − | 59.8337i | −0.0613622 | − | 0.127306i | ||||
\(471\) | 165.033 | − | 165.033i | 0.350388 | − | 0.350388i | ||||
\(472\) | −115.968 | + | 73.0379i | −0.245695 | + | 0.154741i | ||||
\(473\) | −352.012 | − | 352.012i | −0.744211 | − | 0.744211i | ||||
\(474\) | −675.753 | − | 236.190i | −1.42564 | − | 0.498291i | ||||
\(475\) | 116.263 | − | 280.684i | 0.244764 | − | 0.590914i | ||||
\(476\) | 96.5192 | − | 209.202i | 0.202771 | − | 0.439501i | ||||
\(477\) | 13.6156 | + | 32.8710i | 0.0285442 | + | 0.0689119i | ||||
\(478\) | −619.592 | − | 553.310i | −1.29622 | − | 1.15755i | ||||
\(479\) | 326.700i | 0.682045i | 0.940055 | + | 0.341023i | \(0.110773\pi\) | ||||
−0.940055 | + | 0.341023i | \(0.889227\pi\) | |||||||
\(480\) | 498.160 | + | 274.183i | 1.03783 | + | 0.571215i | ||||
\(481\) | 345.294i | 0.717867i | ||||||||
\(482\) | 140.640 | − | 157.488i | 0.291785 | − | 0.326738i | ||||
\(483\) | 600.656 | − | 440.647i | 1.24360 | − | 0.912313i | ||||
\(484\) | −116.016 | + | 145.689i | −0.239703 | + | 0.301011i | ||||
\(485\) | 727.996 | + | 301.546i | 1.50102 | + | 0.621744i | ||||
\(486\) | 91.6762 | + | 32.0428i | 0.188634 | + | 0.0659316i | ||||
\(487\) | −254.213 | − | 254.213i | −0.521999 | − | 0.521999i | 0.396176 | − | 0.918175i | \(-0.370337\pi\) |
−0.918175 | + | 0.396176i | \(0.870337\pi\) | |||||||
\(488\) | 728.284 | + | 165.419i | 1.49239 | + | 0.338974i | ||||
\(489\) | −354.560 | − | 354.560i | −0.725071 | − | 0.725071i | ||||
\(490\) | 366.054 | − | 490.432i | 0.747049 | − | 1.00088i | ||||
\(491\) | −91.2679 | + | 220.340i | −0.185882 | + | 0.448758i | −0.989159 | − | 0.146847i | \(-0.953088\pi\) |
0.803278 | + | 0.595605i | \(0.203088\pi\) | |||||||
\(492\) | −108.331 | + | 377.019i | −0.220184 | + | 0.766298i | ||||
\(493\) | −63.2488 | − | 152.696i | −0.128294 | − | 0.309728i | ||||
\(494\) | 38.8335 | + | 687.185i | 0.0786104 | + | 1.39106i | ||||
\(495\) | 72.9721 | 0.147418 | ||||||||
\(496\) | 213.029 | + | 927.334i | 0.429493 | + | 1.86963i | ||||
\(497\) | −52.5918 | − | 214.696i | −0.105819 | − | 0.431984i | ||||
\(498\) | 145.566 | − | 8.22606i | 0.292300 | − | 0.0165182i | ||||
\(499\) | 531.863 | − | 220.305i | 1.06586 | − | 0.441493i | 0.220331 | − | 0.975425i | \(-0.429286\pi\) |
0.845527 | + | 0.533933i | \(0.179286\pi\) | |||||||
\(500\) | 133.125 | + | 240.473i | 0.266251 | + | 0.480946i | ||||
\(501\) | 2.46880 | − | 5.96021i | 0.00492774 | − | 0.0118966i | ||||
\(502\) | 19.3292 | + | 40.1015i | 0.0385044 | + | 0.0798834i | ||||
\(503\) | −529.745 | − | 529.745i | −1.05317 | − | 1.05317i | −0.998505 | − | 0.0546667i | \(-0.982590\pi\) |
−0.0546667 | − | 0.998505i | \(-0.517410\pi\) | |||||||
\(504\) | 47.0251 | + | 18.5547i | 0.0933038 | + | 0.0368148i | ||||
\(505\) | −415.634 | − | 415.634i | −0.823037 | − | 0.823037i | ||||
\(506\) | 914.007 | + | 319.465i | 1.80634 | + | 0.631353i | ||||
\(507\) | −89.6781 | + | 216.502i | −0.176880 | + | 0.427026i | ||||
\(508\) | 58.3300 | + | 514.446i | 0.114823 | + | 1.01269i | ||||
\(509\) | 97.2308 | − | 40.2743i | 0.191023 | − | 0.0791244i | −0.285121 | − | 0.958491i | \(-0.592034\pi\) |
0.476145 | + | 0.879367i | \(0.342034\pi\) | |||||||
\(510\) | 218.117 | + | 194.784i | 0.427681 | + | 0.381929i | ||||
\(511\) | −216.938 | − | 885.605i | −0.424535 | − | 1.73308i | ||||
\(512\) | −140.184 | + | 492.435i | −0.273798 | + | 0.961787i | ||||
\(513\) | −611.672 | −1.19234 | ||||||||
\(514\) | −375.922 | − | 335.707i | −0.731366 | − | 0.653127i | ||||
\(515\) | −211.518 | − | 510.649i | −0.410714 | − | 0.991552i | ||||
\(516\) | 434.953 | − | 49.3168i | 0.842933 | − | 0.0955752i | ||||
\(517\) | −26.3447 | + | 63.6017i | −0.0509568 | + | 0.123021i | ||||
\(518\) | −303.508 | − | 29.2324i | −0.585923 | − | 0.0564331i | ||||
\(519\) | 157.237 | + | 157.237i | 0.302962 | + | 0.302962i | ||||
\(520\) | 646.432 | + | 457.645i | 1.24314 | + | 0.880087i | ||||
\(521\) | −162.950 | − | 162.950i | −0.312764 | − | 0.312764i | 0.533215 | − | 0.845980i | \(-0.320984\pi\) |
−0.845980 | + | 0.533215i | \(0.820984\pi\) | |||||||
\(522\) | 32.6683 | − | 15.7463i | 0.0625829 | − | 0.0301654i | ||||
\(523\) | 445.079 | + | 184.358i | 0.851012 | + | 0.352501i | 0.765186 | − | 0.643809i | \(-0.222647\pi\) |
0.0858261 | + | 0.996310i | \(0.472647\pi\) | |||||||
\(524\) | 96.0976 | + | 173.588i | 0.183392 | + | 0.331274i | ||||
\(525\) | 164.906 | + | 224.787i | 0.314106 | + | 0.428166i | ||||
\(526\) | 105.288 | − | 5.94995i | 0.200168 | − | 0.0113117i | ||||
\(527\) | 489.325i | 0.928510i | ||||||||
\(528\) | −131.950 | − | 574.390i | −0.249905 | − | 1.08786i | ||||
\(529\) | − | 869.704i | − | 1.64405i | ||||||
\(530\) | −491.456 | + | 27.7727i | −0.927275 | + | 0.0524012i | ||||
\(531\) | −5.91826 | − | 14.2880i | −0.0111455 | − | 0.0269076i | ||||
\(532\) | −607.312 | − | 24.0425i | −1.14156 | − | 0.0451928i | ||||
\(533\) | −209.094 | + | 504.797i | −0.392296 | + | 0.947087i | ||||
\(534\) | 77.2147 | + | 160.194i | 0.144597 | + | 0.299989i | ||||
\(535\) | 886.137 | + | 886.137i | 1.65633 | + | 1.65633i | ||||
\(536\) | −16.6401 | + | 73.2608i | −0.0310450 | + | 0.136681i | ||||
\(537\) | −52.3893 | + | 52.3893i | −0.0975593 | + | 0.0975593i | ||||
\(538\) | 362.594 | + | 126.734i | 0.673967 | + | 0.235566i | ||||
\(539\) | −631.839 | + | 55.5928i | −1.17224 | + | 0.103141i | ||||
\(540\) | −438.472 | + | 550.619i | −0.811985 | + | 1.01967i | ||||
\(541\) | 111.898 | + | 270.145i | 0.206835 | + | 0.499344i | 0.992921 | − | 0.118773i | \(-0.0378959\pi\) |
−0.786086 | + | 0.618117i | \(0.787896\pi\) | |||||||
\(542\) | 699.315 | − | 783.087i | 1.29025 | − | 1.44481i | ||||
\(543\) | −18.1421 | −0.0334108 | ||||||||
\(544\) | −126.962 | + | 230.677i | −0.233386 | + | 0.424038i | ||||
\(545\) | 475.071i | 0.871690i | ||||||||
\(546\) | −557.658 | − | 296.530i | −1.02135 | − | 0.543096i | ||||
\(547\) | 389.555 | + | 940.469i | 0.712166 | + | 1.71932i | 0.694516 | + | 0.719477i | \(0.255619\pi\) |
0.0176505 | + | 0.999844i | \(0.494381\pi\) | |||||||
\(548\) | 116.993 | + | 93.1645i | 0.213491 | + | 0.170008i | ||||
\(549\) | −32.2504 | + | 77.8594i | −0.0587439 | + | 0.141820i | ||||
\(550\) | −119.555 | + | 342.054i | −0.217373 | + | 0.621916i | ||||
\(551\) | −308.303 | + | 308.303i | −0.559533 | + | 0.559533i | ||||
\(552\) | −720.404 | + | 453.719i | −1.30508 | + | 0.821955i | ||||
\(553\) | 456.579 | − | 752.838i | 0.825641 | − | 1.36137i | ||||
\(554\) | −345.341 | − | 716.465i | −0.623359 | − | 1.29326i | ||||
\(555\) | 148.104 | − | 357.555i | 0.266854 | − | 0.644243i | ||||
\(556\) | 189.166 | − | 658.346i | 0.340226 | − | 1.18408i | ||||
\(557\) | 962.583 | − | 398.715i | 1.72816 | − | 0.715825i | 0.728634 | − | 0.684904i | \(-0.240156\pi\) |
0.999522 | − | 0.0309216i | \(-0.00984422\pi\) | |||||||
\(558\) | −107.197 | + | 6.05781i | −0.192109 | + | 0.0108563i | ||||
\(559\) | 609.718 | 1.09073 | ||||||||
\(560\) | −456.990 | + | 529.460i | −0.816053 | + | 0.945464i | ||||
\(561\) | − | 303.088i | − | 0.540263i | ||||||
\(562\) | 464.577 | − | 26.2537i | 0.826650 | − | 0.0467149i | ||||
\(563\) | 40.2258 | + | 97.1136i | 0.0714490 | + | 0.172493i | 0.955570 | − | 0.294766i | \(-0.0952416\pi\) |
−0.884121 | + | 0.467259i | \(0.845242\pi\) | |||||||
\(564\) | −29.3185 | − | 52.9600i | −0.0519832 | − | 0.0939007i | ||||
\(565\) | −203.732 | − | 84.3886i | −0.360588 | − | 0.149360i | ||||
\(566\) | −35.4096 | − | 73.4627i | −0.0625611 | − | 0.129793i | ||||
\(567\) | 261.575 | − | 431.302i | 0.461331 | − | 0.760673i | ||||
\(568\) | 42.5779 | + | 249.007i | 0.0749611 | + | 0.438393i | ||||
\(569\) | 367.219 | + | 367.219i | 0.645377 | + | 0.645377i | 0.951872 | − | 0.306495i | \(-0.0991564\pi\) |
−0.306495 | + | 0.951872i | \(0.599156\pi\) | |||||||
\(570\) | 254.536 | − | 728.242i | 0.446554 | − | 1.27762i | ||||
\(571\) | −325.809 | − | 134.955i | −0.570595 | − | 0.236348i | 0.0786828 | − | 0.996900i | \(-0.474929\pi\) |
−0.649277 | + | 0.760552i | \(0.724929\pi\) | |||||||
\(572\) | −92.4837 | − | 815.667i | −0.161685 | − | 1.42599i | ||||
\(573\) | −175.924 | + | 72.8699i | −0.307022 | + | 0.127173i | ||||
\(574\) | −426.007 | − | 226.526i | −0.742173 | − | 0.394645i | ||||
\(575\) | 523.445 | 0.910339 | ||||||||
\(576\) | −52.1063 | − | 24.9580i | −0.0904624 | − | 0.0433299i | ||||
\(577\) | − | 268.418i | − | 0.465195i | −0.972573 | − | 0.232598i | \(-0.925278\pi\) | ||
0.972573 | − | 0.232598i | \(-0.0747225\pi\) | |||||||
\(578\) | 294.801 | − | 330.116i | 0.510036 | − | 0.571134i | ||||
\(579\) | −150.307 | + | 62.2592i | −0.259598 | + | 0.107529i | ||||
\(580\) | 56.5259 | + | 498.535i | 0.0974585 | + | 0.859542i | ||||
\(581\) | −27.2364 | + | 177.248i | −0.0468785 | + | 0.305075i | ||||
\(582\) | 677.912 | + | 236.945i | 1.16480 | + | 0.407121i | ||||
\(583\) | 360.750 | + | 360.750i | 0.618782 | + | 0.618782i | ||||
\(584\) | 175.631 | + | 1027.14i | 0.300738 | + | 1.75880i | ||||
\(585\) | −63.1974 | + | 63.1974i | −0.108030 | + | 0.108030i | ||||
\(586\) | 420.277 | + | 871.931i | 0.717197 | + | 1.48794i | ||||
\(587\) | −24.3962 | − | 10.1052i | −0.0415609 | − | 0.0172151i | 0.361806 | − | 0.932253i | \(-0.382160\pi\) |
−0.403367 | + | 0.915038i | \(0.632160\pi\) | |||||||
\(588\) | 307.857 | − | 465.069i | 0.523565 | − | 0.790933i | ||||
\(589\) | 1192.60 | − | 493.989i | 2.02478 | − | 0.838691i | ||||
\(590\) | 213.620 | − | 12.0719i | 0.362068 | − | 0.0204608i | ||||
\(591\) | −675.379 | −1.14277 | ||||||||
\(592\) | 343.630 | + | 57.8886i | 0.580456 | + | 0.0977848i | ||||
\(593\) | −1008.99 | −1.70150 | −0.850749 | − | 0.525572i | \(-0.823851\pi\) | ||||
−0.850749 | + | 0.525572i | \(0.823851\pi\) | |||||||
\(594\) | 728.362 | − | 41.1605i | 1.22620 | − | 0.0692937i | ||||
\(595\) | −290.014 | + | 212.757i | −0.487418 | + | 0.357575i | ||||
\(596\) | 249.574 | + | 71.7114i | 0.418749 | + | 0.120321i | ||||
\(597\) | −92.5446 | + | 223.422i | −0.155016 | + | 0.374242i | ||||
\(598\) | −1068.25 | + | 514.902i | −1.78636 | + | 0.861040i | ||||
\(599\) | 358.882 | − | 358.882i | 0.599135 | − | 0.599135i | −0.340948 | − | 0.940082i | \(-0.610748\pi\) |
0.940082 | + | 0.340948i | \(0.110748\pi\) | |||||||
\(600\) | −169.798 | − | 269.601i | −0.282996 | − | 0.449335i | ||||
\(601\) | −828.467 | + | 828.467i | −1.37848 | + | 1.37848i | −0.531292 | + | 0.847189i | \(0.678293\pi\) |
−0.847189 | + | 0.531292i | \(0.821707\pi\) | |||||||
\(602\) | −51.6183 | + | 535.933i | −0.0857447 | + | 0.890254i | ||||
\(603\) | −7.83216 | − | 3.24419i | −0.0129887 | − | 0.00538008i | ||||
\(604\) | 679.080 | + | 540.769i | 1.12430 | + | 0.895312i | ||||
\(605\) | 268.620 | − | 111.266i | 0.443999 | − | 0.183911i | ||||
\(606\) | −399.559 | − | 356.816i | −0.659338 | − | 0.588805i | ||||
\(607\) | − | 338.797i | − | 0.558149i | −0.960269 | − | 0.279075i | \(-0.909972\pi\) | ||
0.960269 | − | 0.279075i | \(-0.0900277\pi\) | |||||||
\(608\) | 690.383 | + | 76.5603i | 1.13550 | + | 0.125922i | ||||
\(609\) | −95.1933 | − | 388.608i | −0.156311 | − | 0.638108i | ||||
\(610\) | −869.645 | − | 776.613i | −1.42565 | − | 1.27314i | ||||
\(611\) | −32.2664 | − | 77.8979i | −0.0528091 | − | 0.127492i | ||||
\(612\) | −23.2430 | − | 18.5090i | −0.0379787 | − | 0.0302434i | ||||
\(613\) | 561.283 | + | 232.491i | 0.915634 | + | 0.379268i | 0.790211 | − | 0.612835i | \(-0.209971\pi\) |
0.125423 | + | 0.992103i | \(0.459971\pi\) | |||||||
\(614\) | −272.189 | − | 95.1356i | −0.443304 | − | 0.154944i | ||||
\(615\) | 433.037 | − | 433.037i | 0.704125 | − | 0.704125i | ||||
\(616\) | 724.788 | − | 12.2379i | 1.17660 | − | 0.0198667i | ||||
\(617\) | 178.617 | − | 178.617i | 0.289492 | − | 0.289492i | −0.547387 | − | 0.836879i | \(-0.684378\pi\) |
0.836879 | + | 0.547387i | \(0.184378\pi\) | |||||||
\(618\) | −218.719 | − | 453.766i | −0.353914 | − | 0.734249i | ||||
\(619\) | 267.269 | + | 110.707i | 0.431776 | + | 0.178847i | 0.587977 | − | 0.808878i | \(-0.299925\pi\) |
−0.156201 | + | 0.987725i | \(0.549925\pi\) | |||||||
\(620\) | 410.219 | − | 1427.67i | 0.661644 | − | 2.30269i | ||||
\(621\) | −403.299 | − | 973.650i | −0.649435 | − | 1.56787i | ||||
\(622\) | −793.951 | + | 44.8670i | −1.27645 | + | 0.0721334i | ||||
\(623\) | −212.449 | + | 52.0415i | −0.341010 | + | 0.0835337i | ||||
\(624\) | 611.724 | + | 383.174i | 0.980327 | + | 0.614061i | ||||
\(625\) | − | 779.012i | − | 1.24642i | ||||||
\(626\) | 26.2431 | + | 464.389i | 0.0419219 | + | 0.741836i | ||||
\(627\) | −738.692 | + | 305.976i | −1.17814 | + | 0.488001i | ||||
\(628\) | −158.899 | − | 287.030i | −0.253024 | − | 0.457054i | ||||
\(629\) | 165.568 | + | 68.5806i | 0.263224 | + | 0.109031i | ||||
\(630\) | −50.1992 | − | 60.8997i | −0.0796813 | − | 0.0966662i | ||||
\(631\) | 224.670 | − | 224.670i | 0.356054 | − | 0.356054i | −0.506302 | − | 0.862356i | \(-0.668988\pi\) |
0.862356 | + | 0.506302i | \(0.168988\pi\) | |||||||
\(632\) | −581.425 | + | 821.274i | −0.919976 | + | 1.29948i | ||||
\(633\) | −20.8275 | + | 20.8275i | −0.0329028 | + | 0.0329028i | ||||
\(634\) | −505.462 | − | 176.670i | −0.797259 | − | 0.278659i | ||||
\(635\) | 309.317 | − | 746.758i | 0.487114 | − | 1.17600i | ||||
\(636\) | −445.750 | + | 50.5410i | −0.700865 | + | 0.0794669i | ||||
\(637\) | 499.057 | − | 595.349i | 0.783449 | − | 0.934613i | ||||
\(638\) | 346.372 | − | 387.864i | 0.542903 | − | 0.607938i | ||||
\(639\) | −28.5063 | −0.0446108 | ||||||||
\(640\) | 563.814 | − | 566.592i | 0.880959 | − | 0.885300i | ||||
\(641\) | 983.789 | 1.53477 | 0.767386 | − | 0.641185i | \(-0.221557\pi\) | ||||
0.767386 | + | 0.641185i | \(0.221557\pi\) | |||||||
\(642\) | 851.865 | + | 760.735i | 1.32689 | + | 1.18495i | ||||
\(643\) | −597.032 | + | 247.299i | −0.928511 | + | 0.384602i | −0.795113 | − | 0.606461i | \(-0.792589\pi\) |
−0.133397 | + | 0.991063i | \(0.542589\pi\) | |||||||
\(644\) | −362.154 | − | 982.562i | −0.562351 | − | 1.52572i | ||||
\(645\) | −631.368 | − | 261.521i | −0.978865 | − | 0.405459i | ||||
\(646\) | 337.217 | + | 117.865i | 0.522008 | + | 0.182453i | ||||
\(647\) | −6.01032 | + | 6.01032i | −0.00928952 | + | 0.00928952i | −0.711736 | − | 0.702447i | \(-0.752091\pi\) |
0.702447 | + | 0.711736i | \(0.252091\pi\) | |||||||
\(648\) | −333.099 | + | 470.508i | −0.514042 | + | 0.726093i | ||||
\(649\) | −156.806 | − | 156.806i | −0.241612 | − | 0.241612i | ||||
\(650\) | −192.695 | − | 399.775i | −0.296453 | − | 0.615039i | ||||
\(651\) | −179.908 | + | 1170.80i | −0.276356 | + | 1.79846i | ||||
\(652\) | −616.660 | + | 341.381i | −0.945797 | + | 0.523591i | ||||
\(653\) | 12.8469 | − | 5.32137i | 0.0196737 | − | 0.00814911i | −0.372825 | − | 0.927902i | \(-0.621611\pi\) |
0.392499 | + | 0.919753i | \(0.371611\pi\) | |||||||
\(654\) | 24.4280 | + | 432.269i | 0.0373517 | + | 0.660962i | ||||
\(655\) | − | 309.756i | − | 0.472909i | ||||||
\(656\) | 467.309 | + | 292.715i | 0.712362 | + | 0.446212i | ||||
\(657\) | −117.586 | −0.178975 | ||||||||
\(658\) | 71.2027 | − | 21.7668i | 0.108211 | − | 0.0330803i | ||||
\(659\) | −536.835 | + | 222.364i | −0.814620 | + | 0.337427i | −0.750796 | − | 0.660535i | \(-0.770330\pi\) |
−0.0638243 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(660\) | −254.089 | + | 884.298i | −0.384984 | + | 1.33985i | ||||
\(661\) | 1131.08 | + | 468.510i | 1.71117 | + | 0.708790i | 0.999983 | + | 0.00578751i | \(0.00184223\pi\) |
0.711187 | + | 0.703003i | \(0.248158\pi\) | |||||||
\(662\) | −95.8038 | − | 198.760i | −0.144719 | − | 0.300242i | ||||
\(663\) | 262.488 | + | 262.488i | 0.395910 | + | 0.395910i | ||||
\(664\) | 45.3945 | − | 199.857i | 0.0683653 | − | 0.300989i | ||||
\(665\) | 811.315 | + | 492.044i | 1.22002 | + | 0.739916i | ||||
\(666\) | −12.9743 | + | 37.1202i | −0.0194809 | + | 0.0557361i | ||||
\(667\) | −694.027 | − | 287.476i | −1.04052 | − | 0.430998i | ||||
\(668\) | −7.09403 | − | 5.64916i | −0.0106198 | − | 0.00845682i | ||||
\(669\) | 420.222 | + | 1014.51i | 0.628134 | + | 1.51645i | ||||
\(670\) | 78.1224 | − | 87.4808i | 0.116601 | − | 0.130568i | ||||
\(671\) | 1208.42i | 1.80093i | ||||||||
\(672\) | −388.592 | + | 505.257i | −0.578263 | + | 0.751870i | ||||
\(673\) | −631.845 | −0.938848 | −0.469424 | − | 0.882973i | \(-0.655538\pi\) | ||||
−0.469424 | + | 0.882973i | \(0.655538\pi\) | |||||||
\(674\) | −125.770 | − | 112.315i | −0.186602 | − | 0.166640i | ||||
\(675\) | 364.374 | − | 150.929i | 0.539814 | − | 0.223598i | ||||
\(676\) | 257.688 | + | 205.203i | 0.381195 | + | 0.303555i | ||||
\(677\) | 383.762 | − | 926.483i | 0.566857 | − | 1.36851i | −0.337335 | − | 0.941385i | \(-0.609525\pi\) |
0.904191 | − | 0.427128i | \(-0.140475\pi\) | |||||||
\(678\) | −189.716 | − | 66.3098i | −0.279817 | − | 0.0978021i | ||||
\(679\) | −458.038 | + | 755.243i | −0.674578 | + | 1.11229i | ||||
\(680\) | 347.831 | − | 219.068i | 0.511517 | − | 0.322159i | ||||
\(681\) | −642.149 | + | 642.149i | −0.942950 | + | 0.942950i | ||||
\(682\) | −1386.87 | + | 668.480i | −2.03353 | + | 0.980176i | ||||
\(683\) | 66.5040 | − | 160.555i | 0.0973705 | − | 0.235073i | −0.867687 | − | 0.497110i | \(-0.834394\pi\) |
0.965058 | + | 0.262037i | \(0.0843944\pi\) | |||||||
\(684\) | −21.6460 | + | 75.3337i | −0.0316462 | + | 0.110137i | ||||
\(685\) | −89.3499 | − | 215.710i | −0.130438 | − | 0.314905i | ||||
\(686\) | 481.052 | + | 489.065i | 0.701243 | + | 0.712923i | ||||
\(687\) | − | 836.827i | − | 1.21809i | ||||||
\(688\) | 102.219 | − | 606.779i | 0.148575 | − | 0.881947i | ||||
\(689\) | −624.853 | −0.906898 | ||||||||
\(690\) | 1327.03 | − | 74.9918i | 1.92323 | − | 0.108684i | ||||
\(691\) | −450.399 | − | 1087.36i | −0.651807 | − | 1.57360i | −0.810153 | − | 0.586218i | \(-0.800616\pi\) |
0.158346 | − | 0.987384i | \(-0.449384\pi\) | |||||||
\(692\) | 273.471 | − | 151.393i | 0.395190 | − | 0.218776i | ||||
\(693\) | −12.4235 | + | 80.8494i | −0.0179271 | + | 0.116666i | ||||
\(694\) | −533.097 | + | 256.957i | −0.768152 | + | 0.370255i | ||||
\(695\) | −756.165 | + | 756.165i | −1.08801 | + | 1.08801i | ||||
\(696\) | 77.0677 | + | 450.712i | 0.110729 | + | 0.647575i | ||||
\(697\) | 200.521 | + | 200.521i | 0.287691 | + | 0.287691i | ||||
\(698\) | 55.8778 | − | 159.869i | 0.0800541 | − | 0.229039i | ||||
\(699\) | −121.159 | + | 292.504i | −0.173332 | + | 0.418461i | ||||
\(700\) | 367.710 | − | 135.531i | 0.525300 | − | 0.193616i | ||||
\(701\) | −22.9991 | − | 55.5246i | −0.0328089 | − | 0.0792077i | 0.906626 | − | 0.421936i | \(-0.138649\pi\) |
−0.939435 | + | 0.342728i | \(0.888649\pi\) | |||||||
\(702\) | −595.149 | + | 666.443i | −0.847790 | + | 0.949349i | ||||
\(703\) | − | 472.761i | − | 0.672491i | ||||||
\(704\) | −827.240 | − | 44.7088i | −1.17506 | − | 0.0635068i | ||||
\(705\) | 94.5036i | 0.134048i | ||||||||
\(706\) | −70.8919 | − | 63.3082i | −0.100414 | − | 0.0896716i | ||||
\(707\) | 531.263 | − | 389.739i | 0.751432 | − | 0.551258i | ||||
\(708\) | 193.753 | − | 21.9685i | 0.273662 | − | 0.0310290i | ||||
\(709\) | 437.459 | + | 181.202i | 0.617009 | + | 0.255574i | 0.669222 | − | 0.743062i | \(-0.266627\pi\) |
−0.0522130 | + | 0.998636i | \(0.516627\pi\) | |||||||
\(710\) | 130.126 | − | 372.299i | 0.183277 | − | 0.524365i | ||||
\(711\) | −80.2904 | − | 80.2904i | −0.112926 | − | 0.112926i | ||||
\(712\) | 246.401 | − | 42.1323i | 0.346069 | − | 0.0591746i | ||||
\(713\) | 1572.65 | + | 1572.65i | 2.20568 | + | 2.20568i | ||||
\(714\) | −252.945 | + | 208.501i | −0.354265 | + | 0.292018i | ||||
\(715\) | −490.430 | + | 1184.00i | −0.685916 | + | 1.65595i | ||||
\(716\) | 50.4421 | + | 91.1169i | 0.0704498 | + | 0.127258i | ||||
\(717\) | 452.291 | + | 1091.93i | 0.630810 | + | 1.52291i | ||||
\(718\) | −806.647 | + | 45.5845i | −1.12346 | + | 0.0634881i | ||||
\(719\) | 668.803 | 0.930184 | 0.465092 | − | 0.885262i | \(-0.346021\pi\) | ||||
0.465092 | + | 0.885262i | \(0.346021\pi\) | |||||||
\(720\) | 52.2977 | + | 73.4878i | 0.0726357 | + | 0.102066i | ||||
\(721\) | 601.784 | − | 147.413i | 0.834652 | − | 0.204456i | ||||
\(722\) | −12.4331 | − | 220.012i | −0.0172204 | − | 0.304726i | ||||
\(723\) | −277.546 | + | 114.963i | −0.383881 | + | 0.159009i | ||||
\(724\) | −7.04270 | + | 24.5105i | −0.00972749 | + | 0.0338542i | ||||
\(725\) | 107.584 | − | 259.730i | 0.148391 | − | 0.358248i | ||||
\(726\) | 238.697 | − | 115.054i | 0.328784 | − | 0.158476i | ||||
\(727\) | −570.615 | − | 570.615i | −0.784890 | − | 0.784890i | 0.195762 | − | 0.980651i | \(-0.437282\pi\) |
−0.980651 | + | 0.195762i | \(0.937282\pi\) | |||||||
\(728\) | −617.102 | + | 638.300i | −0.847668 | + | 0.876785i | ||||
\(729\) | −556.293 | − | 556.293i | −0.763091 | − | 0.763091i | ||||
\(730\) | 536.762 | − | 1535.71i | 0.735290 | − | 2.10371i | ||||
\(731\) | 121.099 | − | 292.359i | 0.165662 | − | 0.399944i | ||||
\(732\) | −831.227 | − | 661.927i | −1.13556 | − | 0.904272i | ||||
\(733\) | 205.500 | − | 85.1210i | 0.280355 | − | 0.116127i | −0.238075 | − | 0.971247i | \(-0.576517\pi\) |
0.518430 | + | 0.855120i | \(0.326517\pi\) | |||||||
\(734\) | 65.0016 | − | 72.7882i | 0.0885580 | − | 0.0991665i | ||||
\(735\) | −772.135 | + | 402.432i | −1.05052 | + | 0.547527i | ||||
\(736\) | 333.329 | + | 1149.42i | 0.452892 | + | 1.56171i | ||||
\(737\) | −121.560 | −0.164939 | ||||||||
\(738\) | −41.4458 | + | 46.4107i | −0.0561597 | + | 0.0628871i | ||||
\(739\) | −72.3032 | − | 174.555i | −0.0978393 | − | 0.236205i | 0.867380 | − | 0.497646i | \(-0.165802\pi\) |
−0.965219 | + | 0.261441i | \(0.915802\pi\) | |||||||
\(740\) | −425.573 | − | 338.895i | −0.575099 | − | 0.457966i | ||||
\(741\) | 374.753 | − | 904.733i | 0.505739 | − | 1.22096i | ||||
\(742\) | 52.8996 | − | 549.236i | 0.0712933 | − | 0.740210i | ||||
\(743\) | 244.158 | + | 244.158i | 0.328611 | + | 0.328611i | 0.852058 | − | 0.523447i | \(-0.175354\pi\) |
−0.523447 | + | 0.852058i | \(0.675354\pi\) | |||||||
\(744\) | 299.850 | − | 1320.14i | 0.403024 | − | 1.77438i | ||||
\(745\) | −286.657 | − | 286.657i | −0.384774 | − | 0.384774i | ||||
\(746\) | 93.0643 | + | 193.076i | 0.124751 | + | 0.258816i | ||||
\(747\) | 21.3663 | + | 8.85020i | 0.0286028 | + | 0.0118477i | ||||
\(748\) | −409.480 | − | 117.658i | −0.547433 | − | 0.157297i | ||||
\(749\) | −1132.66 | + | 830.929i | −1.51223 | + | 1.10938i | ||||
\(750\) | −22.0646 | − | 390.448i | −0.0294195 | − | 0.520597i | ||||
\(751\) | 982.403i | 1.30813i | 0.756440 | + | 0.654063i | \(0.226937\pi\) | ||||
−0.756440 | + | 0.654063i | \(0.773063\pi\) | |||||||
\(752\) | −82.9318 | + | 19.0512i | −0.110282 | + | 0.0253341i | ||||
\(753\) | − | 63.3378i | − | 0.0841140i | ||||||
\(754\) | 35.9344 | + | 635.884i | 0.0476584 | + | 0.843347i | ||||
\(755\) | −518.627 | − | 1252.08i | −0.686923 | − | 1.65838i | ||||
\(756\) | −535.408 | − | 579.547i | −0.708211 | − | 0.766597i | ||||
\(757\) | 343.365 | − | 828.955i | 0.453586 | − | 1.09505i | −0.517363 | − | 0.855766i | \(-0.673086\pi\) |
0.970949 | − | 0.239287i | \(-0.0769137\pi\) | |||||||
\(758\) | −587.268 | + | 283.067i | −0.774759 | + | 0.373440i | ||||
\(759\) | −974.097 | − | 974.097i | −1.28339 | − | 1.28339i | ||||
\(760\) | −885.066 | − | 626.587i | −1.16456 | − | 0.824457i | ||||
\(761\) | 313.409 | − | 313.409i | 0.411838 | − | 0.411838i | −0.470540 | − | 0.882378i | \(-0.655941\pi\) |
0.882378 | + | 0.470540i | \(0.155941\pi\) | |||||||
\(762\) | 243.051 | − | 695.384i | 0.318965 | − | 0.912577i | ||||
\(763\) | −526.354 | − | 80.8808i | −0.689848 | − | 0.106004i | ||||
\(764\) | 30.1563 | + | 265.966i | 0.0394716 | + | 0.348123i | ||||
\(765\) | 17.7511 | + | 42.8550i | 0.0232041 | + | 0.0560196i | ||||
\(766\) | 792.873 | + | 708.054i | 1.03508 | + | 0.924352i | ||||
\(767\) | 271.603 | 0.354111 | ||||||||
\(768\) | 483.883 | − | 544.536i | 0.630056 | − | 0.709031i | ||||
\(769\) | − | 982.775i | − | 1.27799i | −0.769211 | − | 0.638995i | \(-0.779350\pi\) | ||
0.769211 | − | 0.638995i | \(-0.220650\pi\) | |||||||
\(770\) | −999.201 | − | 531.317i | −1.29766 | − | 0.690023i | ||||
\(771\) | 274.416 | + | 662.500i | 0.355923 | + | 0.859274i | ||||
\(772\) | 25.7652 | + | 227.238i | 0.0333746 | + | 0.294350i | ||||
\(773\) | −206.007 | + | 497.344i | −0.266503 | + | 0.643394i | −0.999314 | − | 0.0370377i | \(-0.988208\pi\) |
0.732811 | + | 0.680432i | \(0.238208\pi\) | |||||||
\(774\) | 65.5467 | + | 22.9099i | 0.0846856 | + | 0.0295994i | ||||
\(775\) | −588.541 | + | 588.541i | −0.759407 | + | 0.759407i | ||||
\(776\) | 583.283 | − | 823.898i | 0.751653 | − | 1.06172i | ||||
\(777\) | 370.938 | + | 224.965i | 0.477397 | + | 0.289531i | ||||
\(778\) | 238.418 | − | 114.919i | 0.306450 | − | 0.147711i | ||||
\(779\) | 286.282 | − | 691.146i | 0.367499 | − | 0.887222i | ||||
\(780\) | −545.791 | − | 985.898i | −0.699731 | − | 1.26397i | ||||
\(781\) | −377.642 | + | 156.424i | −0.483536 | + | 0.200287i | ||||
\(782\) | 34.7254 | + | 614.490i | 0.0444059 | + | 0.785792i | ||||
\(783\) | −566.008 | −0.722871 | ||||||||
\(784\) | −508.812 | − | 596.461i | −0.648995 | − | 0.760793i | ||||
\(785\) | 512.186i | 0.652466i | ||||||||
\(786\) | −15.9275 | − | 281.848i | −0.0202640 | − | 0.358585i | ||||
\(787\) | −98.7672 | − | 238.445i | −0.125498 | − | 0.302980i | 0.848626 | − | 0.528994i | \(-0.177431\pi\) |
−0.974124 | + | 0.226014i | \(0.927431\pi\) | |||||||
\(788\) | −262.180 | + | 912.457i | −0.332716 | + | 1.15794i | ||||
\(789\) | −138.620 | − | 57.4184i | −0.175691 | − | 0.0727737i | ||||
\(790\) | 1415.12 | − | 682.100i | 1.79130 | − | 0.863417i | ||||
\(791\) | 128.184 | − | 211.358i | 0.162053 | − | 0.267203i | ||||
\(792\) | 20.7061 | − | 91.1618i | 0.0261441 | − | 0.115103i | ||||
\(793\) | −1046.55 | − | 1046.55i | −1.31974 | − | 1.31974i | ||||
\(794\) | 466.521 | + | 163.059i | 0.587559 | + | 0.205364i | ||||
\(795\) | 647.040 | + | 268.013i | 0.813887 | + | 0.337123i | ||||
\(796\) | 265.925 | + | 211.762i | 0.334076 | + | 0.266033i | ||||
\(797\) | −448.362 | + | 185.718i | −0.562562 | + | 0.233021i | −0.645797 | − | 0.763509i | \(-0.723475\pi\) |
0.0832351 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(798\) | 763.520 | + | 405.996i | 0.956792 | + | 0.508767i | ||||
\(799\) | −43.7605 | −0.0547691 | ||||||||
\(800\) | −430.154 | + | 124.743i | −0.537692 | + | 0.155929i | ||||
\(801\) | 28.2080i | 0.0352160i | ||||||||
\(802\) | −543.608 | − | 485.455i | −0.677816 | − | 0.605305i | ||||
\(803\) | −1557.74 | + | 645.239i | −1.93991 | + | 0.803536i | ||||
\(804\) | 66.5857 | − | 83.6162i | 0.0828180 | − | 0.104000i | ||||
\(805\) | −248.297 | + | 1615.86i | −0.308443 | + | 2.00728i | ||||
\(806\) | 622.157 | − | 1780.03i | 0.771907 | − | 2.20847i | ||||
\(807\) | −386.432 | − | 386.432i | −0.478850 | − | 0.478850i | ||||
\(808\) | −637.176 | + | 401.301i | −0.788584 | + | 0.496660i | ||||
\(809\) | −664.079 | + | 664.079i | −0.820863 | + | 0.820863i | −0.986232 | − | 0.165368i | \(-0.947119\pi\) |
0.165368 | + | 0.986232i | \(0.447119\pi\) | |||||||
\(810\) | 810.726 | − | 390.776i | 1.00090 | − | 0.482439i | ||||
\(811\) | −268.042 | − | 111.027i | −0.330508 | − | 0.136901i | 0.211258 | − | 0.977430i | \(-0.432244\pi\) |
−0.541766 | + | 0.840529i | \(0.682244\pi\) | |||||||
\(812\) | −561.974 | − | 22.2477i | −0.692086 | − | 0.0273986i | ||||
\(813\) | −1380.06 | + | 571.639i | −1.69749 | + | 0.703123i | ||||
\(814\) | 31.8129 | + | 562.950i | 0.0390822 | + | 0.691585i | ||||
\(815\) | 1100.39 | 1.35017 | ||||||||
\(816\) | 305.229 | − | 217.217i | 0.374055 | − | 0.266197i | ||||
\(817\) | −834.799 | −1.02179 | ||||||||
\(818\) | 49.0086 | + | 867.239i | 0.0599127 | + | 1.06019i | ||||
\(819\) | −59.2601 | − | 80.7788i | −0.0723566 | − | 0.0986310i | ||||
\(820\) | −416.942 | − | 753.149i | −0.508465 | − | 0.918475i | ||||
\(821\) | −530.822 | + | 1281.52i | −0.646555 | + | 1.56092i | 0.171125 | + | 0.985249i | \(0.445260\pi\) |
−0.817680 | + | 0.575673i | \(0.804740\pi\) | |||||||
\(822\) | −92.3916 | − | 191.681i | −0.112399 | − | 0.233189i | ||||
\(823\) | −811.582 | + | 811.582i | −0.986127 | + | 0.986127i | −0.999905 | − | 0.0137784i | \(-0.995614\pi\) |
0.0137784 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(824\) | −697.957 | + | 119.344i | −0.847035 | + | 0.144835i | ||||
\(825\) | 364.542 | − | 364.542i | 0.441869 | − | 0.441869i | ||||
\(826\) | −22.9938 | + | 238.735i | −0.0278375 | + | 0.289026i | ||||
\(827\) | 158.098 | + | 65.4865i | 0.191171 | + | 0.0791856i | 0.476215 | − | 0.879329i | \(-0.342008\pi\) |
−0.285044 | + | 0.958514i | \(0.592008\pi\) | |||||||
\(828\) | −134.187 | + | 15.2147i | −0.162062 | + | 0.0183752i | ||||
\(829\) | −138.953 | + | 57.5564i | −0.167616 | + | 0.0694286i | −0.464913 | − | 0.885356i | \(-0.653915\pi\) |
0.297298 | + | 0.954785i | \(0.403915\pi\) | |||||||
\(830\) | −213.119 | + | 238.649i | −0.256770 | + | 0.287529i | ||||
\(831\) | 1131.61i | 1.36175i | ||||||||
\(832\) | 755.149 | − | 677.709i | 0.907631 | − | 0.814555i | ||||
\(833\) | −186.349 | − | 357.542i | −0.223708 | − | 0.429222i | ||||
\(834\) | −649.156 | + | 726.920i | −0.778365 | + | 0.871606i | ||||
\(835\) | 5.41786 | + | 13.0799i | 0.00648845 | + | 0.0156645i | ||||
\(836\) | 126.624 | + | 1116.77i | 0.151465 | + | 1.33585i | ||||
\(837\) | 1548.19 | + | 641.280i | 1.84968 | + | 0.766165i | ||||
\(838\) | 185.947 | − | 532.006i | 0.221894 | − | 0.634852i | ||||
\(839\) | 54.1600 | − | 54.1600i | 0.0645530 | − | 0.0645530i | −0.674093 | − | 0.738646i | \(-0.735465\pi\) |
0.738646 | + | 0.674093i | \(0.235465\pi\) | |||||||
\(840\) | 912.795 | − | 396.276i | 1.08666 | − | 0.471757i | ||||
\(841\) | 309.390 | − | 309.390i | 0.367883 | − | 0.367883i | ||||
\(842\) | 1003.20 | − | 483.551i | 1.19145 | − | 0.574289i | ||||
\(843\) | −611.653 | − | 253.355i | −0.725567 | − | 0.300540i | ||||
\(844\) | 20.0534 | + | 36.2237i | 0.0237599 | + | 0.0429191i | ||||
\(845\) | −196.801 | − | 475.120i | −0.232901 | − | 0.562273i | ||||
\(846\) | −0.541752 | − | 9.58666i | −0.000640369 | − | 0.0113318i | ||||
\(847\) | 77.5444 | + | 316.560i | 0.0915518 | + | 0.373742i | ||||
\(848\) | −104.757 | + | 621.841i | −0.123534 | + | 0.733303i | ||||
\(849\) | 116.030i | 0.136667i | ||||||||
\(850\) | −229.964 | + | 12.9955i | −0.270546 | + | 0.0152888i | ||||
\(851\) | 752.533 | − | 311.710i | 0.884293 | − | 0.366286i | ||||
\(852\) | 99.2591 | − | 345.448i | 0.116501 | − | 0.405455i | ||||
\(853\) | −383.190 | − | 158.722i | −0.449226 | − | 0.186075i | 0.146589 | − | 0.989198i | \(-0.453171\pi\) |
−0.595814 | + | 0.803122i | \(0.703171\pi\) | |||||||
\(854\) | 1008.50 | − | 831.303i | 1.18092 | − | 0.973423i | ||||
\(855\) | 86.5269 | − | 86.5269i | 0.101201 | − | 0.101201i | ||||
\(856\) | 1358.47 | − | 855.579i | 1.58699 | − | 0.999508i | ||||
\(857\) | −453.196 | + | 453.196i | −0.528817 | + | 0.528817i | −0.920220 | − | 0.391403i | \(-0.871990\pi\) |
0.391403 | + | 0.920220i | \(0.371990\pi\) | |||||||
\(858\) | −385.364 | + | 1102.55i | −0.449142 | + | 1.28502i | ||||
\(859\) | −378.413 | + | 913.570i | −0.440527 | + | 1.06353i | 0.535237 | + | 0.844702i | \(0.320222\pi\) |
−0.975764 | + | 0.218825i | \(0.929778\pi\) | |||||||
\(860\) | −598.418 | + | 751.475i | −0.695835 | + | 0.873808i | ||||
\(861\) | 406.058 | + | 553.507i | 0.471612 | + | 0.642865i | ||||
\(862\) | −611.627 | − | 546.198i | −0.709545 | − | 0.633640i | ||||
\(863\) | −47.7125 | −0.0552868 | −0.0276434 | − | 0.999618i | \(-0.508800\pi\) | ||||
−0.0276434 | + | 0.999618i | \(0.508800\pi\) | |||||||
\(864\) | 563.453 | + | 704.009i | 0.652145 | + | 0.814826i | ||||
\(865\) | −487.992 | −0.564152 | ||||||||
\(866\) | −682.254 | + | 763.982i | −0.787822 | + | 0.882196i | ||||
\(867\) | −581.773 | + | 240.978i | −0.671019 | + | 0.277945i | ||||
\(868\) | 1511.95 | + | 697.563i | 1.74187 | + | 0.803644i | ||||
\(869\) | −1504.24 | − | 623.077i | −1.73100 | − | 0.717005i | ||||
\(870\) | 235.534 | − | 673.876i | 0.270729 | − | 0.774570i | ||||
\(871\) | 105.277 | − | 105.277i | 0.120869 | − | 0.120869i | ||||
\(872\) | 593.491 | + | 134.803i | 0.680609 | + | 0.154591i | ||||
\(873\) | 80.5469 | + | 80.5469i | 0.0922645 | + | 0.0922645i | ||||
\(874\) | 1462.59 | − | 704.980i | 1.67345 | − | 0.806614i | ||||
\(875\) | 475.430 | + | 73.0557i | 0.543349 | + | 0.0834922i | ||||
\(876\) | 409.437 | − | 1424.95i | 0.467394 | − | 1.62665i | ||||
\(877\) | −374.791 | + | 155.244i | −0.427356 | + | 0.177017i | −0.585985 | − | 0.810322i | \(-0.699292\pi\) |
0.158630 | + | 0.987338i | \(0.449292\pi\) | |||||||
\(878\) | −1326.78 | + | 74.9780i | −1.51114 | + | 0.0853963i | ||||
\(879\) | − | 1377.16i | − | 1.56674i | ||||||
\(880\) | 1096.08 | + | 686.564i | 1.24554 | + | 0.780187i | ||||
\(881\) | −1021.71 | −1.15971 | −0.579856 | − | 0.814719i | \(-0.696891\pi\) | ||||
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(882\) | 76.0202 | − | 45.2500i | 0.0861907 | − | 0.0513039i | ||||
\(883\) | 1333.96 | − | 552.545i | 1.51071 | − | 0.625758i | 0.535009 | − | 0.844846i | \(-0.320308\pi\) |
0.975705 | + | 0.219088i | \(0.0703081\pi\) | |||||||
\(884\) | 456.526 | − | 252.732i | 0.516433 | − | 0.285896i | ||||
\(885\) | −281.247 | − | 116.496i | −0.317794 | − | 0.131634i | ||||
\(886\) | −169.347 | + | 81.6265i | −0.191137 | + | 0.0921292i | ||||
\(887\) | −280.700 | − | 280.700i | −0.316460 | − | 0.316460i | 0.530946 | − | 0.847406i | \(-0.321837\pi\) |
−0.847406 | + | 0.530946i | \(0.821837\pi\) | |||||||
\(888\) | −404.657 | − | 286.479i | −0.455695 | − | 0.322612i | ||||
\(889\) | 774.708 | + | 469.843i | 0.871438 | + | 0.528508i | ||||
\(890\) | −368.403 | − | 128.765i | −0.413936 | − | 0.144679i | ||||
\(891\) | −861.782 | − | 356.962i | −0.967207 | − | 0.400630i | ||||
\(892\) | 1533.75 | − | 173.903i | 1.71946 | − | 0.194959i | ||||
\(893\) | 44.1776 | + | 106.654i | 0.0494710 | + | 0.119434i | ||||
\(894\) | −275.570 | − | 246.090i | −0.308244 | − | 0.275269i | ||||
\(895\) | − | 162.592i | − | 0.181667i | ||||||
\(896\) | 531.766 | + | 721.139i | 0.593488 | + | 0.804843i | ||||
\(897\) | 1687.23 | 1.88097 | ||||||||
\(898\) | −44.8436 | + | 50.2155i | −0.0499372 | + | 0.0559192i | ||||
\(899\) | 1103.56 | − | 457.111i | 1.22755 | − | 0.508466i | ||||
\(900\) | −5.69387 | − | 50.2175i | −0.00632653 | − | 0.0557973i | ||||
\(901\) | −124.105 | + | 299.616i | −0.137741 | + | 0.332537i | ||||
\(902\) | −294.388 | + | 842.261i | −0.326372 | + | 0.933770i | ||||
\(903\) | 397.242 | − | 654.999i | 0.439914 | − | 0.725359i | ||||
\(904\) | −163.234 | + | 230.571i | −0.180568 | + | 0.255056i | ||||
\(905\) | 28.1523 | − | 28.1523i | 0.0311075 | − | 0.0311075i | ||||
\(906\) | −536.283 | − | 1112.60i | −0.591923 | − | 1.22804i | ||||
\(907\) | −222.285 | + | 536.643i | −0.245077 | + | 0.591668i | −0.997773 | − | 0.0667002i | \(-0.978753\pi\) |
0.752696 | + | 0.658368i | \(0.228753\pi\) | |||||||
\(908\) | 618.281 | + | 1116.84i | 0.680926 | + | 1.23000i | ||||
\(909\) | −32.5174 | − | 78.5040i | −0.0357728 | − | 0.0863631i | ||||
\(910\) | 1325.50 | − | 405.209i | 1.45660 | − | 0.445285i | ||||
\(911\) | − | 549.528i | − | 0.603214i | −0.953432 | − | 0.301607i | \(-0.902477\pi\) | ||
0.953432 | − | 0.301607i | \(-0.0975231\pi\) | |||||||
\(912\) | −837.545 | − | 524.625i | −0.918360 | − | 0.575247i | ||||
\(913\) | 331.617 | 0.363217 | ||||||||
\(914\) | 99.1870 | + | 1755.18i | 0.108520 | + | 1.92033i | ||||
\(915\) | 634.825 | + | 1532.60i | 0.693798 | + | 1.67498i | ||||
\(916\) | −1130.58 | − | 324.854i | −1.23426 | − | 0.354644i | ||||
\(917\) | 343.193 | + | 52.7359i | 0.374257 | + | 0.0575091i | ||||
\(918\) | 201.353 | + | 417.739i | 0.219339 | + | 0.455053i | ||||
\(919\) | −432.452 | + | 432.452i | −0.470568 | + | 0.470568i | −0.902098 | − | 0.431531i | \(-0.857974\pi\) |
0.431531 | + | 0.902098i | \(0.357974\pi\) | |||||||
\(920\) | 413.833 | − | 1821.97i | 0.449819 | − | 1.98040i | ||||
\(921\) | 290.083 | + | 290.083i | 0.314965 | + | 0.314965i | ||||
\(922\) | −1401.62 | − | 489.897i | −1.52020 | − | 0.531342i | ||||
\(923\) | 191.585 | − | 462.527i | 0.207567 | − | 0.501112i | ||||
\(924\) | −936.498 | − | 432.070i | −1.01353 | − | 0.467608i | ||||
\(925\) | 116.653 | + | 281.625i | 0.126111 | + | 0.304459i | ||||
\(926\) | 511.288 | + | 456.592i | 0.552147 | + | 0.493080i | ||||
\(927\) | − | 79.9021i | − | 0.0861943i | ||||||
\(928\) | 638.843 | + | 70.8448i | 0.688408 | + | 0.0763414i | ||||
\(929\) | − | 614.862i | − | 0.661853i | −0.943657 | − | 0.330927i | \(-0.892639\pi\) | ||
0.943657 | − | 0.330927i | \(-0.107361\pi\) | |||||||
\(930\) | −1407.74 | + | 1576.38i | −1.51370 | + | 1.69503i | ||||
\(931\) | −683.286 | + | 815.124i | −0.733927 | + | 0.875536i | ||||
\(932\) | 348.148 | + | 277.239i | 0.373549 | + | 0.297467i | ||||
\(933\) | 1045.30 | + | 432.977i | 1.12036 | + | 0.464069i | ||||
\(934\) | −364.858 | − | 127.526i | −0.390641 | − | 0.136537i | ||||
\(935\) | 470.321 | + | 470.321i | 0.503017 | + | 0.503017i | ||||
\(936\) | 61.0180 | + | 96.8829i | 0.0651902 | + | 0.103507i | ||||
\(937\) | 840.986 | + | 840.986i | 0.897530 | + | 0.897530i | 0.995217 | − | 0.0976871i | \(-0.0311444\pi\) |
−0.0976871 | + | 0.995217i | \(0.531144\pi\) | |||||||
\(938\) | 83.6238 | + | 101.449i | 0.0891512 | + | 0.108155i | ||||
\(939\) | 253.252 | − | 611.405i | 0.269704 | − | 0.651124i | ||||
\(940\) | 127.677 | + | 36.6861i | 0.135827 | + | 0.0390277i | ||||
\(941\) | −341.284 | − | 823.933i | −0.362682 | − | 0.875593i | −0.994906 | − | 0.100807i | \(-0.967858\pi\) |
0.632224 | − | 0.774786i | \(-0.282142\pi\) | |||||||
\(942\) | 26.3364 | + | 466.040i | 0.0279580 | + | 0.494735i | ||||
\(943\) | 1288.91 | 1.36682 | ||||||||
\(944\) | 45.5343 | − | 270.294i | 0.0482355 | − | 0.286328i | ||||
\(945\) | 293.072 | + | 1196.41i | 0.310129 | + | 1.26604i | ||||
\(946\) | 994.054 | − | 56.1750i | 1.05080 | − | 0.0593816i | ||||
\(947\) | 1478.15 | − | 612.270i | 1.56088 | − | 0.646536i | 0.575635 | − | 0.817707i | \(-0.304755\pi\) |
0.985241 | + | 0.171170i | \(0.0547549\pi\) | |||||||
\(948\) | 1252.55 | − | 693.411i | 1.32126 | − | 0.731446i | ||||
\(949\) | 790.273 | − | 1907.89i | 0.832743 | − | 2.01042i | ||||
\(950\) | 263.829 | + | 547.354i | 0.277714 | + | 0.576162i | ||||
\(951\) | 538.693 | + | 538.693i | 0.566449 | + | 0.566449i | ||||
\(952\) | 183.498 | + | 422.676i | 0.192750 | + | 0.443987i | ||||
\(953\) | 1213.91 | + | 1213.91i | 1.27377 | + | 1.27377i | 0.944092 | + | 0.329682i | \(0.106941\pi\) |
0.329682 | + | 0.944092i | \(0.393059\pi\) | |||||||
\(954\) | −67.1737 | − | 23.4786i | −0.0704126 | − | 0.0246107i | ||||
\(955\) | 159.915 | − | 386.070i | 0.167451 | − | 0.404261i | ||||
\(956\) | 1650.80 | − | 187.175i | 1.72678 | − | 0.195790i | ||||
\(957\) | −683.546 | + | 283.134i | −0.714259 | + | 0.295856i | ||||
\(958\) | −487.355 | − | 435.219i | −0.508721 | − | 0.454300i | ||||
\(959\) | 254.207 | − | 62.2705i | 0.265075 | − | 0.0649328i | ||||
\(960\) | −1072.65 | + | 377.874i | −1.11734 | + | 0.393619i | ||||
\(961\) | −2575.45 | −2.67996 | ||||||||
\(962\) | −515.093 | − | 459.990i | −0.535440 | − | 0.478160i | ||||
\(963\) | 69.3276 | + | 167.372i | 0.0719913 | + | 0.173802i | ||||
\(964\) | 47.5761 | + | 419.601i | 0.0493528 | + | 0.435271i | ||||
\(965\) | 136.630 | − | 329.853i | 0.141585 | − | 0.341817i | ||||
\(966\) | −142.840 | + | 1483.05i | −0.147867 | + | 1.53525i | ||||
\(967\) | 597.026 | + | 597.026i | 0.617400 | + | 0.617400i | 0.944864 | − | 0.327464i | \(-0.106194\pi\) |
−0.327464 | + | 0.944864i | \(0.606194\pi\) | |||||||
\(968\) | −62.7793 | − | 367.150i | −0.0648546 | − | 0.379287i | ||||
\(969\) | −359.387 | − | 359.387i | −0.370884 | − | 0.370884i | ||||
\(970\) | −1419.64 | + | 684.279i | −1.46355 | + | 0.705442i | ||||
\(971\) | 876.015 | + | 362.857i | 0.902178 | + | 0.373694i | 0.785057 | − | 0.619423i | \(-0.212634\pi\) |
0.117121 | + | 0.993118i | \(0.462634\pi\) | |||||||
\(972\) | −169.928 | + | 94.0718i | −0.174823 | + | 0.0967817i | ||||
\(973\) | −709.055 | − | 966.529i | −0.728730 | − | 0.993349i | ||||
\(974\) | 717.879 | − | 40.5681i | 0.737042 | − | 0.0416510i | ||||
\(975\) | 631.421i | 0.647611i | ||||||||
\(976\) | −1216.96 | + | 866.053i | −1.24689 | + | 0.887350i | ||||
\(977\) | − | 1598.48i | − | 1.63611i | −0.575141 | − | 0.818054i | \(-0.695053\pi\) | ||
0.575141 | − | 0.818054i | \(-0.304947\pi\) | |||||||
\(978\) | 1001.25 | − | 56.5816i | 1.02377 | − | 0.0578544i | ||||
\(979\) | 154.787 | + | 373.690i | 0.158108 | + | 0.381706i | ||||
\(980\) | 243.957 | + | 1199.40i | 0.248935 | + | 1.22388i | ||||
\(981\) | −26.2814 | + | 63.4490i | −0.0267904 | + | 0.0646778i | ||||
\(982\) | −207.109 | − | 429.679i | −0.210905 | − | 0.437555i | ||||
\(983\) | −310.257 | − | 310.257i | −0.315623 | − | 0.315623i | 0.531461 | − | 0.847083i | \(-0.321643\pi\) |
−0.847083 | + | 0.531461i | \(0.821643\pi\) | |||||||
\(984\) | −418.104 | − | 663.855i | −0.424902 | − | 0.674649i | ||||
\(985\) | 1048.03 | − | 1048.03i | 1.06399 | − | 1.06399i | ||||
\(986\) | 312.043 | + | 109.065i | 0.316473 | + | 0.110614i | ||||
\(987\) | −104.705 | − | 16.0892i | −0.106084 | − | 0.0163011i | ||||
\(988\) | −1076.84 | − | 857.517i | −1.08992 | − | 0.867932i | ||||
\(989\) | −550.415 | − | 1328.82i | −0.556537 | − | 1.34360i | ||||
\(990\) | −97.2113 | + | 108.856i | −0.0981932 | + | 0.109956i | ||||
\(991\) | 149.424 | 0.150781 | 0.0753907 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753907 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(992\) | −1667.14 | − | 917.580i | −1.68059 | − | 0.924980i | ||||
\(993\) | 313.930i | 0.316143i | ||||||||
\(994\) | 390.334 | + | 207.557i | 0.392690 | + | 0.208810i | ||||
\(995\) | −203.092 | − | 490.307i | −0.204112 | − | 0.492771i | ||||
\(996\) | −181.647 | + | 228.106i | −0.182376 | + | 0.229022i | ||||
\(997\) | −519.496 | + | 1254.18i | −0.521059 | + | 1.25795i | 0.416186 | + | 0.909279i | \(0.363366\pi\) |
−0.937246 | + | 0.348670i | \(0.886634\pi\) | |||||||
\(998\) | −379.891 | + | 1086.89i | −0.380653 | + | 1.08907i | ||||
\(999\) | 433.967 | − | 433.967i | 0.434401 | − | 0.434401i |
(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 | 224.3.v.b.69.18 | yes | 240 | |
7.6 | odd | 2 | inner | 224.3.v.b.69.17 | yes | 240 | |
32.13 | even | 8 | inner | 224.3.v.b.13.17 | ✓ | 240 | |
224.13 | odd | 8 | inner | 224.3.v.b.13.18 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.b.13.17 | ✓ | 240 | 32.13 | even | 8 | inner | |
224.3.v.b.13.18 | yes | 240 | 224.13 | odd | 8 | inner | |
224.3.v.b.69.17 | yes | 240 | 7.6 | odd | 2 | inner | |
224.3.v.b.69.18 | yes | 240 | 1.1 | even | 1 | trivial |