Properties

Label 784.2.x.m.557.6
Level $784$
Weight $2$
Character 784.557
Analytic conductor $6.260$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), not 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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 557.6
Character \(\chi\) \(=\) 784.557
Dual form 784.2.x.m.373.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.16343 + 0.804007i) q^{2} +(1.90046 - 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(2.95714 + 0.792364i) q^{5} +(2.62048 + 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +O(q^{10})\) \(q+(1.16343 + 0.804007i) q^{2} +(1.90046 - 0.509227i) q^{3} +(0.707146 + 1.87081i) q^{4} +(2.95714 + 0.792364i) q^{5} +(2.62048 + 0.935533i) q^{6} +(-0.681431 + 2.74511i) q^{8} +(0.754366 - 0.435533i) q^{9} +(2.80337 + 3.29942i) q^{10} +(-1.13308 - 4.22870i) q^{11} +(2.29657 + 3.19531i) q^{12} +(-1.75410 - 1.75410i) q^{13} +6.02343 q^{15} +(-2.99989 + 2.64588i) q^{16} +(-2.60235 + 4.50740i) q^{17} +(1.22782 + 0.0998021i) q^{18} +(0.311715 - 1.16333i) q^{19} +(0.608766 + 6.09258i) q^{20} +(2.08165 - 5.83081i) q^{22} +(5.33038 - 3.07750i) q^{23} +(0.102853 + 5.56399i) q^{24} +(3.78672 + 2.18626i) q^{25} +(-0.630466 - 3.45108i) q^{26} +(-2.96185 + 2.96185i) q^{27} +(-6.24096 - 6.24096i) q^{29} +(7.00784 + 4.84288i) q^{30} +(-1.39123 + 2.40969i) q^{31} +(-5.61747 + 0.666365i) q^{32} +(-4.30674 - 7.45950i) q^{33} +(-6.65164 + 3.15175i) q^{34} +(1.34825 + 1.10329i) q^{36} +(-5.61713 - 1.50511i) q^{37} +(1.29799 - 1.10284i) q^{38} +(-4.22683 - 2.44036i) q^{39} +(-4.19022 + 7.57775i) q^{40} -6.32956i q^{41} +(3.05937 - 3.05937i) q^{43} +(7.10987 - 5.11009i) q^{44} +(2.57587 - 0.690201i) q^{45} +(8.67586 + 0.705206i) q^{46} +(1.80192 + 3.12101i) q^{47} +(-4.35382 + 6.55601i) q^{48} +(2.64782 + 5.58812i) q^{50} +(-2.65037 + 9.89133i) q^{51} +(2.04119 - 4.52199i) q^{52} +(1.93405 + 7.21798i) q^{53} +(-5.82725 + 1.06456i) q^{54} -13.4027i q^{55} -2.36961i q^{57} +(-2.24315 - 12.2787i) q^{58} +(2.61179 + 9.74734i) q^{59} +(4.25944 + 11.2687i) q^{60} +(-0.380638 + 1.42056i) q^{61} +(-3.55601 + 1.68495i) q^{62} +(-7.07130 - 3.74121i) q^{64} +(-3.79723 - 6.57700i) q^{65} +(0.986887 - 12.1413i) q^{66} +(1.32053 - 0.353834i) q^{67} +(-10.2728 - 1.68112i) q^{68} +(8.56304 - 8.56304i) q^{69} -10.0597i q^{71} +(0.681540 + 2.36761i) q^{72} +(13.1391 + 7.58585i) q^{73} +(-5.32503 - 6.26730i) q^{74} +(8.30982 + 2.22661i) q^{75} +(2.39681 - 0.239487i) q^{76} +(-2.95556 - 6.23759i) q^{78} +(3.30674 + 5.72745i) q^{79} +(-10.9676 + 5.44723i) q^{80} +(-5.42722 + 9.40022i) q^{81} +(5.08901 - 7.36400i) q^{82} +(7.41730 + 7.41730i) q^{83} +(-11.2670 + 11.2670i) q^{85} +(6.01912 - 1.09961i) q^{86} +(-15.0388 - 8.68264i) q^{87} +(12.3804 - 0.228856i) q^{88} +(-2.82449 + 1.63072i) q^{89} +(3.55177 + 1.26801i) q^{90} +(9.52678 + 7.79591i) q^{92} +(-1.41691 + 5.28798i) q^{93} +(-0.412907 + 5.07983i) q^{94} +(1.84357 - 3.19315i) q^{95} +(-10.3365 + 4.12697i) q^{96} +7.66352 q^{97} +(-2.69650 - 2.69650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16343 + 0.804007i 0.822670 + 0.568519i
\(3\) 1.90046 0.509227i 1.09723 0.294002i 0.335595 0.942006i \(-0.391063\pi\)
0.761637 + 0.648004i \(0.224396\pi\)
\(4\) 0.707146 + 1.87081i 0.353573 + 0.935407i
\(5\) 2.95714 + 0.792364i 1.32247 + 0.354356i 0.849904 0.526937i \(-0.176660\pi\)
0.472570 + 0.881293i \(0.343326\pi\)
\(6\) 2.62048 + 0.935533i 1.06981 + 0.381930i
\(7\) 0 0
\(8\) −0.681431 + 2.74511i −0.240922 + 0.970544i
\(9\) 0.754366 0.435533i 0.251455 0.145178i
\(10\) 2.80337 + 3.29942i 0.886502 + 1.04337i
\(11\) −1.13308 4.22870i −0.341636 1.27500i −0.896493 0.443057i \(-0.853894\pi\)
0.554858 0.831945i \(-0.312773\pi\)
\(12\) 2.29657 + 3.19531i 0.662963 + 0.922407i
\(13\) −1.75410 1.75410i −0.486499 0.486499i 0.420701 0.907200i \(-0.361784\pi\)
−0.907200 + 0.420701i \(0.861784\pi\)
\(14\) 0 0
\(15\) 6.02343 1.55524
\(16\) −2.99989 + 2.64588i −0.749972 + 0.661469i
\(17\) −2.60235 + 4.50740i −0.631163 + 1.09321i 0.356152 + 0.934428i \(0.384089\pi\)
−0.987314 + 0.158778i \(0.949245\pi\)
\(18\) 1.22782 + 0.0998021i 0.289401 + 0.0235236i
\(19\) 0.311715 1.16333i 0.0715122 0.266887i −0.920908 0.389781i \(-0.872551\pi\)
0.992420 + 0.122894i \(0.0392174\pi\)
\(20\) 0.608766 + 6.09258i 0.136124 + 1.36234i
\(21\) 0 0
\(22\) 2.08165 5.83081i 0.443809 1.24313i
\(23\) 5.33038 3.07750i 1.11146 0.641703i 0.172254 0.985053i \(-0.444895\pi\)
0.939208 + 0.343350i \(0.111562\pi\)
\(24\) 0.102853 + 5.56399i 0.0209947 + 1.13574i
\(25\) 3.78672 + 2.18626i 0.757344 + 0.437253i
\(26\) −0.630466 3.45108i −0.123645 0.676812i
\(27\) −2.96185 + 2.96185i −0.570007 + 0.570007i
\(28\) 0 0
\(29\) −6.24096 6.24096i −1.15892 1.15892i −0.984709 0.174208i \(-0.944264\pi\)
−0.174208 0.984709i \(-0.555736\pi\)
\(30\) 7.00784 + 4.84288i 1.27945 + 0.884184i
\(31\) −1.39123 + 2.40969i −0.249873 + 0.432793i −0.963490 0.267743i \(-0.913722\pi\)
0.713617 + 0.700536i \(0.247056\pi\)
\(32\) −5.61747 + 0.666365i −0.993038 + 0.117798i
\(33\) −4.30674 7.45950i −0.749708 1.29853i
\(34\) −6.65164 + 3.15175i −1.14075 + 0.540520i
\(35\) 0 0
\(36\) 1.34825 + 1.10329i 0.224708 + 0.183882i
\(37\) −5.61713 1.50511i −0.923450 0.247438i −0.234391 0.972142i \(-0.575310\pi\)
−0.689060 + 0.724705i \(0.741976\pi\)
\(38\) 1.29799 1.10284i 0.210561 0.178904i
\(39\) −4.22683 2.44036i −0.676834 0.390770i
\(40\) −4.19022 + 7.57775i −0.662532 + 1.19815i
\(41\) 6.32956i 0.988511i −0.869317 0.494255i \(-0.835441\pi\)
0.869317 0.494255i \(-0.164559\pi\)
\(42\) 0 0
\(43\) 3.05937 3.05937i 0.466549 0.466549i −0.434245 0.900795i \(-0.642985\pi\)
0.900795 + 0.434245i \(0.142985\pi\)
\(44\) 7.10987 5.11009i 1.07185 0.770375i
\(45\) 2.57587 0.690201i 0.383988 0.102889i
\(46\) 8.67586 + 0.705206i 1.27919 + 0.103977i
\(47\) 1.80192 + 3.12101i 0.262836 + 0.455246i 0.966994 0.254797i \(-0.0820087\pi\)
−0.704158 + 0.710043i \(0.748675\pi\)
\(48\) −4.35382 + 6.55601i −0.628420 + 0.946279i
\(49\) 0 0
\(50\) 2.64782 + 5.58812i 0.374458 + 0.790279i
\(51\) −2.65037 + 9.89133i −0.371127 + 1.38506i
\(52\) 2.04119 4.52199i 0.283062 0.627087i
\(53\) 1.93405 + 7.21798i 0.265662 + 0.991466i 0.961844 + 0.273600i \(0.0882144\pi\)
−0.696181 + 0.717866i \(0.745119\pi\)
\(54\) −5.82725 + 1.06456i −0.792988 + 0.144868i
\(55\) 13.4027i 1.80722i
\(56\) 0 0
\(57\) 2.36961i 0.313862i
\(58\) −2.24315 12.2787i −0.294541 1.61227i
\(59\) 2.61179 + 9.74734i 0.340026 + 1.26900i 0.898316 + 0.439350i \(0.144791\pi\)
−0.558290 + 0.829646i \(0.688542\pi\)
\(60\) 4.25944 + 11.2687i 0.549892 + 1.45478i
\(61\) −0.380638 + 1.42056i −0.0487357 + 0.181884i −0.986003 0.166727i \(-0.946680\pi\)
0.937267 + 0.348611i \(0.113347\pi\)
\(62\) −3.55601 + 1.68495i −0.451614 + 0.213988i
\(63\) 0 0
\(64\) −7.07130 3.74121i −0.883913 0.467652i
\(65\) −3.79723 6.57700i −0.470988 0.815776i
\(66\) 0.986887 12.1413i 0.121477 1.49449i
\(67\) 1.32053 0.353834i 0.161328 0.0432277i −0.177251 0.984166i \(-0.556720\pi\)
0.338579 + 0.940938i \(0.390054\pi\)
\(68\) −10.2728 1.68112i −1.24575 0.203866i
\(69\) 8.56304 8.56304i 1.03087 1.03087i
\(70\) 0 0
\(71\) 10.0597i 1.19386i −0.802291 0.596932i \(-0.796386\pi\)
0.802291 0.596932i \(-0.203614\pi\)
\(72\) 0.681540 + 2.36761i 0.0803203 + 0.279025i
\(73\) 13.1391 + 7.58585i 1.53781 + 0.887857i 0.998966 + 0.0454536i \(0.0144733\pi\)
0.538847 + 0.842404i \(0.318860\pi\)
\(74\) −5.32503 6.26730i −0.619022 0.728559i
\(75\) 8.30982 + 2.22661i 0.959535 + 0.257107i
\(76\) 2.39681 0.239487i 0.274933 0.0274711i
\(77\) 0 0
\(78\) −2.95556 6.23759i −0.334651 0.706268i
\(79\) 3.30674 + 5.72745i 0.372038 + 0.644388i 0.989879 0.141915i \(-0.0453259\pi\)
−0.617841 + 0.786303i \(0.711993\pi\)
\(80\) −10.9676 + 5.44723i −1.22621 + 0.609019i
\(81\) −5.42722 + 9.40022i −0.603025 + 1.04447i
\(82\) 5.08901 7.36400i 0.561987 0.813218i
\(83\) 7.41730 + 7.41730i 0.814154 + 0.814154i 0.985254 0.171100i \(-0.0547320\pi\)
−0.171100 + 0.985254i \(0.554732\pi\)
\(84\) 0 0
\(85\) −11.2670 + 11.2670i −1.22208 + 1.22208i
\(86\) 6.01912 1.09961i 0.649058 0.118574i
\(87\) −15.0388 8.68264i −1.61232 0.930876i
\(88\) 12.3804 0.228856i 1.31975 0.0243962i
\(89\) −2.82449 + 1.63072i −0.299396 + 0.172856i −0.642171 0.766561i \(-0.721966\pi\)
0.342776 + 0.939417i \(0.388633\pi\)
\(90\) 3.55177 + 1.26801i 0.374390 + 0.133660i
\(91\) 0 0
\(92\) 9.52678 + 7.79591i 0.993236 + 0.812780i
\(93\) −1.41691 + 5.28798i −0.146927 + 0.548337i
\(94\) −0.412907 + 5.07983i −0.0425881 + 0.523945i
\(95\) 1.84357 3.19315i 0.189146 0.327611i
\(96\) −10.3365 + 4.12697i −1.05496 + 0.421207i
\(97\) 7.66352 0.778112 0.389056 0.921214i \(-0.372801\pi\)
0.389056 + 0.921214i \(0.372801\pi\)
\(98\) 0 0
\(99\) −2.69650 2.69650i −0.271008 0.271008i
\(100\) −1.41233 + 8.63025i −0.141233 + 0.863025i
\(101\) −3.63555 13.5681i −0.361751 1.35007i −0.871772 0.489912i \(-0.837029\pi\)
0.510021 0.860162i \(-0.329638\pi\)
\(102\) −11.0362 + 9.37697i −1.09275 + 0.928458i
\(103\) 1.39602 0.805993i 0.137554 0.0794169i −0.429644 0.902998i \(-0.641361\pi\)
0.567198 + 0.823582i \(0.308028\pi\)
\(104\) 6.01049 3.61990i 0.589377 0.354960i
\(105\) 0 0
\(106\) −3.55317 + 9.95262i −0.345114 + 0.966684i
\(107\) −10.8240 2.90028i −1.04640 0.280381i −0.305634 0.952149i \(-0.598869\pi\)
−0.740762 + 0.671768i \(0.765535\pi\)
\(108\) −7.63552 3.44660i −0.734728 0.331650i
\(109\) −7.77240 + 2.08261i −0.744461 + 0.199478i −0.611060 0.791584i \(-0.709257\pi\)
−0.133401 + 0.991062i \(0.542590\pi\)
\(110\) 10.7759 15.5931i 1.02744 1.48674i
\(111\) −11.4416 −1.08599
\(112\) 0 0
\(113\) 15.2609 1.43563 0.717813 0.696235i \(-0.245143\pi\)
0.717813 + 0.696235i \(0.245143\pi\)
\(114\) 1.90518 2.75688i 0.178436 0.258205i
\(115\) 18.2012 4.87699i 1.69727 0.454782i
\(116\) 7.26240 16.0889i 0.674297 1.49382i
\(117\) −2.08720 0.559263i −0.192962 0.0517039i
\(118\) −4.79829 + 13.4403i −0.441718 + 1.23728i
\(119\) 0 0
\(120\) −4.10455 + 16.5350i −0.374693 + 1.50943i
\(121\) −7.07180 + 4.08290i −0.642891 + 0.371173i
\(122\) −1.58499 + 1.34669i −0.143498 + 0.121924i
\(123\) −3.22318 12.0291i −0.290624 1.08463i
\(124\) −5.49188 0.898739i −0.493186 0.0807092i
\(125\) −1.35834 1.35834i −0.121494 0.121494i
\(126\) 0 0
\(127\) −1.80529 −0.160193 −0.0800966 0.996787i \(-0.525523\pi\)
−0.0800966 + 0.996787i \(0.525523\pi\)
\(128\) −5.21902 10.0380i −0.461300 0.887244i
\(129\) 4.25630 7.37213i 0.374746 0.649080i
\(130\) 0.870132 10.7049i 0.0763157 0.938880i
\(131\) −3.39881 + 12.6845i −0.296956 + 1.10825i 0.642696 + 0.766121i \(0.277816\pi\)
−0.939652 + 0.342132i \(0.888851\pi\)
\(132\) 10.9098 13.3321i 0.949579 1.16041i
\(133\) 0 0
\(134\) 1.82083 + 0.650051i 0.157296 + 0.0561559i
\(135\) −11.1055 + 6.41174i −0.955805 + 0.551835i
\(136\) −10.6000 10.2152i −0.908943 0.875949i
\(137\) −6.87323 3.96826i −0.587220 0.339031i 0.176778 0.984251i \(-0.443433\pi\)
−0.763997 + 0.645219i \(0.776766\pi\)
\(138\) 16.8473 3.07777i 1.43413 0.261997i
\(139\) 2.06915 2.06915i 0.175503 0.175503i −0.613889 0.789392i \(-0.710396\pi\)
0.789392 + 0.613889i \(0.210396\pi\)
\(140\) 0 0
\(141\) 5.01377 + 5.01377i 0.422236 + 0.422236i
\(142\) 8.08806 11.7038i 0.678735 0.982157i
\(143\) −5.43003 + 9.40509i −0.454082 + 0.786493i
\(144\) −1.11065 + 3.30251i −0.0925539 + 0.275209i
\(145\) −13.5103 23.4005i −1.12197 1.94331i
\(146\) 9.18735 + 19.3895i 0.760350 + 1.60469i
\(147\) 0 0
\(148\) −1.15636 11.5729i −0.0950521 0.951289i
\(149\) −12.5060 3.35096i −1.02453 0.274521i −0.292840 0.956161i \(-0.594600\pi\)
−0.731688 + 0.681640i \(0.761267\pi\)
\(150\) 7.87770 + 9.27166i 0.643211 + 0.757028i
\(151\) −2.42743 1.40148i −0.197541 0.114051i 0.397967 0.917400i \(-0.369716\pi\)
−0.595508 + 0.803349i \(0.703049\pi\)
\(152\) 2.98107 + 1.64842i 0.241797 + 0.133705i
\(153\) 4.53364i 0.366523i
\(154\) 0 0
\(155\) −6.02343 + 6.02343i −0.483813 + 0.483813i
\(156\) 1.57648 9.63330i 0.126219 0.771281i
\(157\) 1.30974 0.350944i 0.104529 0.0280084i −0.206176 0.978515i \(-0.566102\pi\)
0.310704 + 0.950507i \(0.399435\pi\)
\(158\) −0.757737 + 9.32213i −0.0602823 + 0.741629i
\(159\) 7.35118 + 12.7326i 0.582987 + 1.00976i
\(160\) −17.1397 2.48054i −1.35501 0.196104i
\(161\) 0 0
\(162\) −13.8720 + 6.57299i −1.08989 + 0.516423i
\(163\) 4.72925 17.6498i 0.370423 1.38244i −0.489495 0.872006i \(-0.662819\pi\)
0.859918 0.510432i \(-0.170515\pi\)
\(164\) 11.8414 4.47592i 0.924660 0.349511i
\(165\) −6.82501 25.4713i −0.531326 1.98294i
\(166\) 2.66596 + 14.5931i 0.206919 + 1.13264i
\(167\) 1.96111i 0.151755i 0.997117 + 0.0758775i \(0.0241758\pi\)
−0.997117 + 0.0758775i \(0.975824\pi\)
\(168\) 0 0
\(169\) 6.84629i 0.526637i
\(170\) −22.1672 + 4.04964i −1.70014 + 0.310594i
\(171\) −0.271524 1.01334i −0.0207640 0.0774922i
\(172\) 7.88693 + 3.56009i 0.601373 + 0.271454i
\(173\) 1.51549 5.65589i 0.115221 0.430009i −0.884083 0.467330i \(-0.845216\pi\)
0.999303 + 0.0373213i \(0.0118825\pi\)
\(174\) −10.5157 22.1929i −0.797191 1.68244i
\(175\) 0 0
\(176\) 14.5877 + 9.68766i 1.09959 + 0.730235i
\(177\) 9.92722 + 17.1945i 0.746176 + 1.29241i
\(178\) −4.59722 0.373679i −0.344576 0.0280084i
\(179\) 12.9980 3.48281i 0.971519 0.260318i 0.262050 0.965054i \(-0.415602\pi\)
0.709469 + 0.704737i \(0.248935\pi\)
\(180\) 3.11275 + 4.33089i 0.232011 + 0.322806i
\(181\) −7.60424 + 7.60424i −0.565219 + 0.565219i −0.930785 0.365566i \(-0.880875\pi\)
0.365566 + 0.930785i \(0.380875\pi\)
\(182\) 0 0
\(183\) 2.89355i 0.213897i
\(184\) 4.81579 + 16.7296i 0.355025 + 1.23332i
\(185\) −15.4181 8.90162i −1.13356 0.654460i
\(186\) −5.90004 + 5.01299i −0.432612 + 0.367570i
\(187\) 22.0091 + 5.89733i 1.60947 + 0.431256i
\(188\) −4.56461 + 5.57806i −0.332908 + 0.406822i
\(189\) 0 0
\(190\) 4.71218 2.23277i 0.341858 0.161982i
\(191\) 10.2439 + 17.7430i 0.741223 + 1.28384i 0.951939 + 0.306289i \(0.0990873\pi\)
−0.210715 + 0.977547i \(0.567579\pi\)
\(192\) −15.3439 3.50913i −1.10735 0.253250i
\(193\) −6.35776 + 11.0120i −0.457642 + 0.792659i −0.998836 0.0482388i \(-0.984639\pi\)
0.541194 + 0.840898i \(0.317972\pi\)
\(194\) 8.91598 + 6.16152i 0.640130 + 0.442371i
\(195\) −10.5657 10.5657i −0.756624 0.756624i
\(196\) 0 0
\(197\) −12.8638 + 12.8638i −0.916509 + 0.916509i −0.996774 0.0802649i \(-0.974423\pi\)
0.0802649 + 0.996774i \(0.474423\pi\)
\(198\) −0.969187 5.30519i −0.0688771 0.377023i
\(199\) −1.27174 0.734237i −0.0901510 0.0520487i 0.454247 0.890876i \(-0.349908\pi\)
−0.544398 + 0.838827i \(0.683242\pi\)
\(200\) −8.58193 + 8.90519i −0.606834 + 0.629692i
\(201\) 2.32943 1.34490i 0.164305 0.0948617i
\(202\) 6.67911 18.7085i 0.469940 1.31633i
\(203\) 0 0
\(204\) −20.3790 + 2.03626i −1.42682 + 0.142567i
\(205\) 5.01531 18.7174i 0.350284 1.30728i
\(206\) 2.27220 + 0.184693i 0.158312 + 0.0128681i
\(207\) 2.68070 4.64312i 0.186322 0.322719i
\(208\) 9.90322 + 0.620972i 0.686665 + 0.0430567i
\(209\) −5.27260 −0.364713
\(210\) 0 0
\(211\) 0.534767 + 0.534767i 0.0368149 + 0.0368149i 0.725275 0.688460i \(-0.241713\pi\)
−0.688460 + 0.725275i \(0.741713\pi\)
\(212\) −12.1358 + 8.72242i −0.833493 + 0.599058i
\(213\) −5.12266 19.1180i −0.350999 1.30995i
\(214\) −10.2611 12.0769i −0.701437 0.825557i
\(215\) 11.4711 6.62285i 0.782324 0.451675i
\(216\) −6.11231 10.1489i −0.415890 0.690545i
\(217\) 0 0
\(218\) −10.7171 3.82609i −0.725853 0.259136i
\(219\) 28.8333 + 7.72585i 1.94837 + 0.522064i
\(220\) 25.0739 9.47766i 1.69048 0.638983i
\(221\) 12.4712 3.34165i 0.838903 0.224784i
\(222\) −13.3115 9.19911i −0.893409 0.617404i
\(223\) 7.83775 0.524855 0.262427 0.964952i \(-0.415477\pi\)
0.262427 + 0.964952i \(0.415477\pi\)
\(224\) 0 0
\(225\) 3.80876 0.253917
\(226\) 17.7550 + 12.2699i 1.18105 + 0.816181i
\(227\) 0.338192 0.0906182i 0.0224466 0.00601454i −0.247578 0.968868i \(-0.579635\pi\)
0.270025 + 0.962853i \(0.412968\pi\)
\(228\) 4.43309 1.67566i 0.293589 0.110973i
\(229\) −21.3140 5.71108i −1.40847 0.377399i −0.527092 0.849808i \(-0.676718\pi\)
−0.881379 + 0.472409i \(0.843384\pi\)
\(230\) 25.0970 + 8.95983i 1.65485 + 0.590794i
\(231\) 0 0
\(232\) 21.3849 12.8794i 1.40399 0.845571i
\(233\) 8.24017 4.75746i 0.539831 0.311672i −0.205179 0.978724i \(-0.565778\pi\)
0.745011 + 0.667053i \(0.232444\pi\)
\(234\) −1.97866 2.32879i −0.129349 0.152238i
\(235\) 2.85554 + 10.6570i 0.186275 + 0.695188i
\(236\) −16.3885 + 11.7790i −1.06680 + 0.766746i
\(237\) 9.20091 + 9.20091i 0.597663 + 0.597663i
\(238\) 0 0
\(239\) 18.8469 1.21910 0.609552 0.792746i \(-0.291349\pi\)
0.609552 + 0.792746i \(0.291349\pi\)
\(240\) −18.0696 + 15.9372i −1.16639 + 1.02874i
\(241\) −3.19914 + 5.54108i −0.206075 + 0.356932i −0.950475 0.310802i \(-0.899402\pi\)
0.744400 + 0.667734i \(0.232736\pi\)
\(242\) −11.5102 0.935594i −0.739906 0.0601423i
\(243\) −2.27504 + 8.49058i −0.145944 + 0.544671i
\(244\) −2.92677 + 0.292441i −0.187367 + 0.0187216i
\(245\) 0 0
\(246\) 5.92151 16.5865i 0.377542 1.05751i
\(247\) −2.58738 + 1.49382i −0.164631 + 0.0950498i
\(248\) −5.66684 5.46113i −0.359845 0.346782i
\(249\) 17.8734 + 10.3192i 1.13268 + 0.653953i
\(250\) −0.488221 2.67245i −0.0308778 0.169021i
\(251\) 2.93159 2.93159i 0.185040 0.185040i −0.608508 0.793548i \(-0.708232\pi\)
0.793548 + 0.608508i \(0.208232\pi\)
\(252\) 0 0
\(253\) −19.0536 19.0536i −1.19789 1.19789i
\(254\) −2.10033 1.45146i −0.131786 0.0910728i
\(255\) −15.6751 + 27.1500i −0.981611 + 1.70020i
\(256\) 1.99867 15.8747i 0.124917 0.992167i
\(257\) 14.4838 + 25.0867i 0.903475 + 1.56487i 0.822951 + 0.568113i \(0.192326\pi\)
0.0805246 + 0.996753i \(0.474340\pi\)
\(258\) 10.8792 5.15487i 0.677306 0.320928i
\(259\) 0 0
\(260\) 9.61914 11.7548i 0.596554 0.729002i
\(261\) −7.42611 1.98982i −0.459665 0.123167i
\(262\) −14.1527 + 12.0249i −0.874359 + 0.742902i
\(263\) −0.298299 0.172223i −0.0183939 0.0106197i 0.490775 0.871286i \(-0.336714\pi\)
−0.509169 + 0.860667i \(0.670047\pi\)
\(264\) 23.4119 6.73936i 1.44090 0.414779i
\(265\) 22.8771i 1.40533i
\(266\) 0 0
\(267\) −4.53743 + 4.53743i −0.277686 + 0.277686i
\(268\) 1.59576 + 2.22025i 0.0974768 + 0.135623i
\(269\) −13.4946 + 3.61587i −0.822781 + 0.220463i −0.645562 0.763708i \(-0.723377\pi\)
−0.177219 + 0.984171i \(0.556710\pi\)
\(270\) −18.0755 1.46924i −1.10004 0.0894154i
\(271\) −6.24843 10.8226i −0.379565 0.657426i 0.611434 0.791296i \(-0.290593\pi\)
−0.990999 + 0.133869i \(0.957260\pi\)
\(272\) −4.11927 20.4072i −0.249767 1.23737i
\(273\) 0 0
\(274\) −4.80602 10.1429i −0.290342 0.612756i
\(275\) 4.95441 18.4901i 0.298762 1.11500i
\(276\) 22.0752 + 9.96454i 1.32877 + 0.599795i
\(277\) −2.19595 8.19541i −0.131942 0.492415i 0.868050 0.496477i \(-0.165373\pi\)
−0.999992 + 0.00406280i \(0.998707\pi\)
\(278\) 4.07093 0.743704i 0.244158 0.0446044i
\(279\) 2.42372i 0.145104i
\(280\) 0 0
\(281\) 9.56494i 0.570596i −0.958439 0.285298i \(-0.907907\pi\)
0.958439 0.285298i \(-0.0920926\pi\)
\(282\) 1.80207 + 9.86429i 0.107312 + 0.587410i
\(283\) −4.27803 15.9658i −0.254303 0.949070i −0.968477 0.249102i \(-0.919864\pi\)
0.714175 0.699968i \(-0.246802\pi\)
\(284\) 18.8198 7.11367i 1.11675 0.422118i
\(285\) 1.87759 7.00726i 0.111219 0.415074i
\(286\) −13.8792 + 6.57639i −0.820696 + 0.388870i
\(287\) 0 0
\(288\) −3.94740 + 2.94928i −0.232603 + 0.173788i
\(289\) −5.04445 8.73725i −0.296732 0.513956i
\(290\) 3.09587 38.0873i 0.181796 2.23656i
\(291\) 14.5642 3.90247i 0.853769 0.228767i
\(292\) −4.90047 + 29.9451i −0.286778 + 1.75240i
\(293\) 15.2913 15.2913i 0.893328 0.893328i −0.101507 0.994835i \(-0.532366\pi\)
0.994835 + 0.101507i \(0.0323664\pi\)
\(294\) 0 0
\(295\) 30.8938i 1.79870i
\(296\) 7.95937 14.3940i 0.462629 0.836636i
\(297\) 15.8808 + 9.16877i 0.921496 + 0.532026i
\(298\) −11.8556 13.9535i −0.686778 0.808304i
\(299\) −14.7482 3.95178i −0.852913 0.228537i
\(300\) 1.71068 + 17.1207i 0.0987663 + 0.988462i
\(301\) 0 0
\(302\) −1.69735 3.58219i −0.0976716 0.206132i
\(303\) −13.8185 23.9343i −0.793850 1.37499i
\(304\) 2.14293 + 4.31463i 0.122906 + 0.247461i
\(305\) −2.25120 + 3.89919i −0.128903 + 0.223267i
\(306\) −3.64508 + 5.27458i −0.208375 + 0.301528i
\(307\) 4.16259 + 4.16259i 0.237571 + 0.237571i 0.815844 0.578272i \(-0.196273\pi\)
−0.578272 + 0.815844i \(0.696273\pi\)
\(308\) 0 0
\(309\) 2.24265 2.24265i 0.127580 0.127580i
\(310\) −11.8507 + 2.16497i −0.673076 + 0.122962i
\(311\) 0.695092 + 0.401312i 0.0394151 + 0.0227563i 0.519578 0.854423i \(-0.326089\pi\)
−0.480163 + 0.877179i \(0.659422\pi\)
\(312\) 9.57936 9.94019i 0.542325 0.562752i
\(313\) −15.3533 + 8.86423i −0.867819 + 0.501036i −0.866623 0.498964i \(-0.833714\pi\)
−0.00119626 + 0.999999i \(0.500381\pi\)
\(314\) 1.80596 + 0.644742i 0.101916 + 0.0363849i
\(315\) 0 0
\(316\) −8.37664 + 10.2364i −0.471223 + 0.575845i
\(317\) 3.79534 14.1644i 0.213168 0.795552i −0.773636 0.633630i \(-0.781564\pi\)
0.986804 0.161922i \(-0.0517693\pi\)
\(318\) −1.68452 + 20.7239i −0.0944631 + 1.16214i
\(319\) −19.3197 + 33.4627i −1.08169 + 1.87355i
\(320\) −17.9464 16.6663i −1.00324 0.931677i
\(321\) −22.0475 −1.23057
\(322\) 0 0
\(323\) 4.43243 + 4.43243i 0.246627 + 0.246627i
\(324\) −21.4239 3.50599i −1.19022 0.194777i
\(325\) −2.80735 10.4772i −0.155724 0.581170i
\(326\) 19.6927 16.7320i 1.09068 0.926699i
\(327\) −13.7106 + 7.91584i −0.758200 + 0.437747i
\(328\) 17.3754 + 4.31316i 0.959393 + 0.238154i
\(329\) 0 0
\(330\) 12.5387 35.1215i 0.690230 1.93337i
\(331\) 0.304708 + 0.0816464i 0.0167483 + 0.00448769i 0.267183 0.963646i \(-0.413907\pi\)
−0.250435 + 0.968133i \(0.580574\pi\)
\(332\) −8.63127 + 19.1215i −0.473702 + 1.04943i
\(333\) −4.89289 + 1.31105i −0.268129 + 0.0718449i
\(334\) −1.57674 + 2.28161i −0.0862756 + 0.124844i
\(335\) 4.18535 0.228670
\(336\) 0 0
\(337\) −26.7633 −1.45789 −0.728944 0.684573i \(-0.759989\pi\)
−0.728944 + 0.684573i \(0.759989\pi\)
\(338\) 5.50446 7.96519i 0.299403 0.433249i
\(339\) 29.0028 7.77128i 1.57522 0.422078i
\(340\) −29.0459 13.1111i −1.57524 0.711048i
\(341\) 11.7662 + 3.15275i 0.637178 + 0.170731i
\(342\) 0.498834 1.39726i 0.0269739 0.0755552i
\(343\) 0 0
\(344\) 6.31357 + 10.4831i 0.340405 + 0.565209i
\(345\) 32.1072 18.5371i 1.72859 0.998003i
\(346\) 6.31054 5.36177i 0.339257 0.288251i
\(347\) 9.00704 + 33.6147i 0.483523 + 1.80453i 0.586621 + 0.809861i \(0.300458\pi\)
−0.103098 + 0.994671i \(0.532876\pi\)
\(348\) 5.60899 34.2746i 0.300674 1.83731i
\(349\) −13.7818 13.7818i −0.737725 0.737725i 0.234412 0.972137i \(-0.424683\pi\)
−0.972137 + 0.234412i \(0.924683\pi\)
\(350\) 0 0
\(351\) 10.3907 0.554616
\(352\) 9.18289 + 22.9996i 0.489450 + 1.22588i
\(353\) −13.0221 + 22.5550i −0.693099 + 1.20048i 0.277718 + 0.960663i \(0.410422\pi\)
−0.970817 + 0.239820i \(0.922912\pi\)
\(354\) −2.27481 + 27.9861i −0.120905 + 1.48745i
\(355\) 7.97093 29.7479i 0.423053 1.57886i
\(356\) −5.04811 4.13094i −0.267549 0.218940i
\(357\) 0 0
\(358\) 17.9225 + 6.39850i 0.947235 + 0.338171i
\(359\) −18.2196 + 10.5191i −0.961593 + 0.555176i −0.896663 0.442714i \(-0.854016\pi\)
−0.0649297 + 0.997890i \(0.520682\pi\)
\(360\) 0.139405 + 7.54137i 0.00734730 + 0.397465i
\(361\) 15.1983 + 8.77474i 0.799911 + 0.461829i
\(362\) −14.9609 + 2.73315i −0.786326 + 0.143651i
\(363\) −11.3606 + 11.3606i −0.596274 + 0.596274i
\(364\) 0 0
\(365\) 32.8434 + 32.8434i 1.71910 + 1.71910i
\(366\) −2.32644 + 3.36645i −0.121605 + 0.175967i
\(367\) 3.70670 6.42020i 0.193488 0.335132i −0.752916 0.658117i \(-0.771353\pi\)
0.946404 + 0.322986i \(0.104687\pi\)
\(368\) −7.84788 + 23.3357i −0.409099 + 1.21646i
\(369\) −2.75673 4.77480i −0.143510 0.248566i
\(370\) −10.7809 22.7526i −0.560472 1.18285i
\(371\) 0 0
\(372\) −10.8948 + 1.08860i −0.564868 + 0.0564412i
\(373\) −5.12662 1.37367i −0.265446 0.0711261i 0.123641 0.992327i \(-0.460543\pi\)
−0.389087 + 0.921201i \(0.627210\pi\)
\(374\) 20.8646 + 24.5566i 1.07888 + 1.26979i
\(375\) −3.27318 1.88977i −0.169026 0.0975873i
\(376\) −9.79541 + 2.81971i −0.505160 + 0.145415i
\(377\) 21.8945i 1.12762i
\(378\) 0 0
\(379\) 18.8387 18.8387i 0.967677 0.967677i −0.0318167 0.999494i \(-0.510129\pi\)
0.999494 + 0.0318167i \(0.0101293\pi\)
\(380\) 7.27747 + 1.19095i 0.373326 + 0.0610943i
\(381\) −3.43087 + 0.919300i −0.175769 + 0.0470972i
\(382\) −2.34738 + 28.8789i −0.120103 + 1.47757i
\(383\) −2.47310 4.28353i −0.126369 0.218878i 0.795898 0.605431i \(-0.206999\pi\)
−0.922267 + 0.386553i \(0.873666\pi\)
\(384\) −15.0302 16.4192i −0.767005 0.837889i
\(385\) 0 0
\(386\) −16.2505 + 7.69999i −0.827130 + 0.391919i
\(387\) 0.975426 3.64034i 0.0495837 0.185049i
\(388\) 5.41922 + 14.3370i 0.275119 + 0.727851i
\(389\) 5.13412 + 19.1608i 0.260310 + 0.971491i 0.965059 + 0.262034i \(0.0843932\pi\)
−0.704748 + 0.709457i \(0.748940\pi\)
\(390\) −3.79756 20.7873i −0.192297 1.05261i
\(391\) 32.0349i 1.62007i
\(392\) 0 0
\(393\) 25.8372i 1.30332i
\(394\) −25.3088 + 4.62357i −1.27504 + 0.232932i
\(395\) 5.24028 + 19.5570i 0.263667 + 0.984020i
\(396\) 3.13783 6.95146i 0.157682 0.349324i
\(397\) 0.0233859 0.0872772i 0.00117370 0.00438032i −0.965336 0.261009i \(-0.915945\pi\)
0.966510 + 0.256628i \(0.0826116\pi\)
\(398\) −0.889246 1.87672i −0.0445739 0.0940714i
\(399\) 0 0
\(400\) −17.1443 + 3.46064i −0.857216 + 0.173032i
\(401\) 12.7052 + 22.0060i 0.634466 + 1.09893i 0.986628 + 0.162988i \(0.0521133\pi\)
−0.352162 + 0.935939i \(0.614553\pi\)
\(402\) 3.79144 + 0.308182i 0.189100 + 0.0153707i
\(403\) 6.66719 1.78647i 0.332116 0.0889903i
\(404\) 22.8125 16.3961i 1.13496 0.815734i
\(405\) −23.4975 + 23.4975i −1.16760 + 1.16760i
\(406\) 0 0
\(407\) 25.4586i 1.26194i
\(408\) −25.3468 14.0158i −1.25485 0.693888i
\(409\) 19.4037 + 11.2027i 0.959450 + 0.553939i 0.896004 0.444047i \(-0.146458\pi\)
0.0634462 + 0.997985i \(0.479791\pi\)
\(410\) 20.8839 17.7441i 1.03138 0.876317i
\(411\) −15.0831 4.04149i −0.743992 0.199352i
\(412\) 2.49505 + 2.04174i 0.122922 + 0.100589i
\(413\) 0 0
\(414\) 6.85191 3.24664i 0.336753 0.159564i
\(415\) 16.0568 + 27.8112i 0.788197 + 1.36520i
\(416\) 11.0225 + 8.68472i 0.540420 + 0.425803i
\(417\) 2.87867 4.98601i 0.140969 0.244166i
\(418\) −6.13430 4.23920i −0.300039 0.207346i
\(419\) 24.2758 + 24.2758i 1.18595 + 1.18595i 0.978177 + 0.207775i \(0.0666220\pi\)
0.207775 + 0.978177i \(0.433378\pi\)
\(420\) 0 0
\(421\) 16.0270 16.0270i 0.781108 0.781108i −0.198910 0.980018i \(-0.563740\pi\)
0.980018 + 0.198910i \(0.0637400\pi\)
\(422\) 0.192208 + 1.05212i 0.00935656 + 0.0512164i
\(423\) 2.71861 + 1.56959i 0.132183 + 0.0763160i
\(424\) −21.1321 + 0.390635i −1.02627 + 0.0189709i
\(425\) −19.7087 + 11.3788i −0.956014 + 0.551955i
\(426\) 9.41117 26.3612i 0.455973 1.27720i
\(427\) 0 0
\(428\) −2.22826 22.3006i −0.107707 1.07794i
\(429\) −5.53024 + 20.6391i −0.267002 + 0.996466i
\(430\) 18.6707 + 1.51762i 0.900380 + 0.0731862i
\(431\) 15.8307 27.4196i 0.762540 1.32076i −0.178998 0.983849i \(-0.557285\pi\)
0.941538 0.336908i \(-0.109381\pi\)
\(432\) 1.04853 16.7219i 0.0504474 0.804532i
\(433\) 11.6823 0.561413 0.280707 0.959794i \(-0.409431\pi\)
0.280707 + 0.959794i \(0.409431\pi\)
\(434\) 0 0
\(435\) −37.5920 37.5920i −1.80240 1.80240i
\(436\) −9.39240 13.0680i −0.449814 0.625844i
\(437\) −1.91860 7.16032i −0.0917792 0.342525i
\(438\) 27.3339 + 32.1706i 1.30606 + 1.53717i
\(439\) 11.3637 6.56086i 0.542362 0.313133i −0.203674 0.979039i \(-0.565288\pi\)
0.746036 + 0.665906i \(0.231955\pi\)
\(440\) 36.7919 + 9.13301i 1.75399 + 0.435399i
\(441\) 0 0
\(442\) 17.1961 + 6.13915i 0.817935 + 0.292010i
\(443\) 22.1569 + 5.93692i 1.05271 + 0.282071i 0.743369 0.668881i \(-0.233227\pi\)
0.309336 + 0.950953i \(0.399893\pi\)
\(444\) −8.09087 21.4051i −0.383976 1.01584i
\(445\) −9.64455 + 2.58425i −0.457196 + 0.122505i
\(446\) 9.11869 + 6.30160i 0.431782 + 0.298390i
\(447\) −25.4735 −1.20485
\(448\) 0 0
\(449\) −15.6396 −0.738077 −0.369038 0.929414i \(-0.620313\pi\)
−0.369038 + 0.929414i \(0.620313\pi\)
\(450\) 4.43123 + 3.06227i 0.208890 + 0.144357i
\(451\) −26.7658 + 7.17188i −1.26035 + 0.337711i
\(452\) 10.7917 + 28.5503i 0.507599 + 1.34290i
\(453\) −5.32691 1.42734i −0.250280 0.0670623i
\(454\) 0.466321 + 0.166480i 0.0218855 + 0.00781331i
\(455\) 0 0
\(456\) 6.50484 + 1.61472i 0.304617 + 0.0756164i
\(457\) −10.5919 + 6.11523i −0.495468 + 0.286058i −0.726840 0.686807i \(-0.759012\pi\)
0.231372 + 0.972865i \(0.425678\pi\)
\(458\) −20.2057 23.7811i −0.944150 1.11122i
\(459\) −5.64247 21.0580i −0.263368 0.982903i
\(460\) 21.9948 + 30.6023i 1.02552 + 1.42684i
\(461\) 13.4658 + 13.4658i 0.627163 + 0.627163i 0.947353 0.320191i \(-0.103747\pi\)
−0.320191 + 0.947353i \(0.603747\pi\)
\(462\) 0 0
\(463\) −24.7807 −1.15166 −0.575829 0.817570i \(-0.695321\pi\)
−0.575829 + 0.817570i \(0.695321\pi\)
\(464\) 35.2350 + 2.20938i 1.63574 + 0.102568i
\(465\) −8.38000 + 14.5146i −0.388613 + 0.673098i
\(466\) 13.4119 + 1.09017i 0.621295 + 0.0505011i
\(467\) −8.48020 + 31.6485i −0.392417 + 1.46452i 0.433718 + 0.901048i \(0.357201\pi\)
−0.826135 + 0.563472i \(0.809465\pi\)
\(468\) −0.429677 4.30024i −0.0198618 0.198779i
\(469\) 0 0
\(470\) −5.24610 + 14.6946i −0.241985 + 0.677812i
\(471\) 2.31040 1.33391i 0.106458 0.0614634i
\(472\) −28.5373 + 0.527524i −1.31354 + 0.0242812i
\(473\) −16.4037 9.47066i −0.754242 0.435462i
\(474\) 3.30703 + 18.1022i 0.151897 + 0.831462i
\(475\) 3.72373 3.72373i 0.170857 0.170857i
\(476\) 0 0
\(477\) 4.60265 + 4.60265i 0.210741 + 0.210741i
\(478\) 21.9271 + 15.1530i 1.00292 + 0.693084i
\(479\) 17.6824 30.6268i 0.807930 1.39938i −0.106365 0.994327i \(-0.533921\pi\)
0.914295 0.405049i \(-0.132746\pi\)
\(480\) −33.8364 + 4.01380i −1.54441 + 0.183204i
\(481\) 7.21289 + 12.4931i 0.328879 + 0.569636i
\(482\) −8.17705 + 3.87453i −0.372454 + 0.176480i
\(483\) 0 0
\(484\) −12.6391 10.3428i −0.574507 0.470128i
\(485\) 22.6621 + 6.07229i 1.02903 + 0.275729i
\(486\) −9.47334 + 8.04906i −0.429720 + 0.365113i
\(487\) −14.4850 8.36292i −0.656378 0.378960i 0.134517 0.990911i \(-0.457052\pi\)
−0.790896 + 0.611951i \(0.790385\pi\)
\(488\) −3.64022 2.01291i −0.164785 0.0911201i
\(489\) 35.9510i 1.62576i
\(490\) 0 0
\(491\) 5.93243 5.93243i 0.267727 0.267727i −0.560457 0.828184i \(-0.689374\pi\)
0.828184 + 0.560457i \(0.189374\pi\)
\(492\) 20.2249 14.5363i 0.911809 0.655346i
\(493\) 44.3717 11.8894i 1.99840 0.535470i
\(494\) −4.21128 0.342309i −0.189475 0.0154012i
\(495\) −5.83732 10.1105i −0.262368 0.454434i
\(496\) −2.20219 10.9098i −0.0988813 0.489866i
\(497\) 0 0
\(498\) 12.4977 + 26.3760i 0.560037 + 1.18194i
\(499\) −2.03391 + 7.59066i −0.0910504 + 0.339805i −0.996391 0.0848814i \(-0.972949\pi\)
0.905341 + 0.424686i \(0.139616\pi\)
\(500\) 1.58066 3.50175i 0.0706892 0.156603i
\(501\) 0.998649 + 3.72701i 0.0446164 + 0.166510i
\(502\) 5.76772 1.05368i 0.257426 0.0470282i
\(503\) 6.99765i 0.312010i 0.987756 + 0.156005i \(0.0498616\pi\)
−0.987756 + 0.156005i \(0.950138\pi\)
\(504\) 0 0
\(505\) 43.0034i 1.91363i
\(506\) −6.84832 37.4867i −0.304445 1.66649i
\(507\) −3.48631 13.0111i −0.154833 0.577843i
\(508\) −1.27660 3.37735i −0.0566400 0.149846i
\(509\) −1.30940 + 4.88676i −0.0580383 + 0.216602i −0.988854 0.148886i \(-0.952431\pi\)
0.930816 + 0.365488i \(0.119098\pi\)
\(510\) −40.0657 + 18.9843i −1.77414 + 0.840640i
\(511\) 0 0
\(512\) 15.0887 16.8622i 0.666831 0.745209i
\(513\) 2.52237 + 4.36887i 0.111365 + 0.192890i
\(514\) −3.31895 + 40.8317i −0.146393 + 1.80101i
\(515\) 4.76687 1.27728i 0.210053 0.0562837i
\(516\) 16.8017 + 2.74957i 0.739654 + 0.121043i
\(517\) 11.1561 11.1561i 0.490645 0.490645i
\(518\) 0 0
\(519\) 11.5205i 0.505695i
\(520\) 20.6422 5.94206i 0.905218 0.260577i
\(521\) 15.0383 + 8.68234i 0.658838 + 0.380380i 0.791834 0.610736i \(-0.209126\pi\)
−0.132996 + 0.991117i \(0.542460\pi\)
\(522\) −7.03994 8.28566i −0.308130 0.362654i
\(523\) −35.4526 9.49950i −1.55023 0.415384i −0.620679 0.784065i \(-0.713143\pi\)
−0.929556 + 0.368681i \(0.879810\pi\)
\(524\) −26.1339 + 2.61128i −1.14166 + 0.114074i
\(525\) 0 0
\(526\) −0.208582 0.440204i −0.00909461 0.0191938i
\(527\) −7.24096 12.5417i −0.315421 0.546325i
\(528\) 32.6567 + 10.9826i 1.42120 + 0.477954i
\(529\) 7.44198 12.8899i 0.323564 0.560430i
\(530\) −18.3933 + 26.6159i −0.798955 + 1.15612i
\(531\) 6.21554 + 6.21554i 0.269731 + 0.269731i
\(532\) 0 0
\(533\) −11.1027 + 11.1027i −0.480909 + 0.480909i
\(534\) −8.92712 + 1.63087i −0.386314 + 0.0705744i
\(535\) −29.7100 17.1531i −1.28448 0.741593i
\(536\) 0.0714666 + 3.86611i 0.00308689 + 0.166991i
\(537\) 22.9287 13.2379i 0.989448 0.571258i
\(538\) −18.6072 6.64294i −0.802215 0.286397i
\(539\) 0 0
\(540\) −19.8483 16.2422i −0.854137 0.698953i
\(541\) −4.14648 + 15.4749i −0.178271 + 0.665317i 0.817700 + 0.575644i \(0.195249\pi\)
−0.995971 + 0.0896726i \(0.971418\pi\)
\(542\) 1.43182 17.6151i 0.0615021 0.756635i
\(543\) −10.5793 + 18.3239i −0.454001 + 0.786352i
\(544\) 11.6150 27.0543i 0.497991 1.15994i
\(545\) −24.6343 −1.05522
\(546\) 0 0
\(547\) −10.8422 10.8422i −0.463578 0.463578i 0.436248 0.899826i \(-0.356307\pi\)
−0.899826 + 0.436248i \(0.856307\pi\)
\(548\) 2.56350 15.6647i 0.109507 0.669162i
\(549\) 0.331561 + 1.23740i 0.0141507 + 0.0528111i
\(550\) 20.6303 17.5286i 0.879679 0.747422i
\(551\) −9.20572 + 5.31493i −0.392177 + 0.226423i
\(552\) 17.6714 + 29.3416i 0.752145 + 1.24886i
\(553\) 0 0
\(554\) 4.03433 11.3004i 0.171402 0.480106i
\(555\) −33.8344 9.06589i −1.43619 0.384826i
\(556\) 5.33419 + 2.40781i 0.226220 + 0.102114i
\(557\) 21.5541 5.77540i 0.913275 0.244711i 0.228567 0.973528i \(-0.426596\pi\)
0.684709 + 0.728817i \(0.259929\pi\)
\(558\) −1.94868 + 2.81983i −0.0824944 + 0.119373i
\(559\) −10.7329 −0.453952
\(560\) 0 0
\(561\) 44.8306 1.89275
\(562\) 7.69028 11.1282i 0.324395 0.469413i
\(563\) 20.1711 5.40483i 0.850110 0.227786i 0.192643 0.981269i \(-0.438294\pi\)
0.657468 + 0.753483i \(0.271628\pi\)
\(564\) −5.83437 + 12.9253i −0.245671 + 0.544254i
\(565\) 45.1287 + 12.0922i 1.89858 + 0.508723i
\(566\) 7.85944 22.0147i 0.330357 0.925348i
\(567\) 0 0
\(568\) 27.6150 + 6.85498i 1.15870 + 0.287629i
\(569\) −15.2567 + 8.80848i −0.639596 + 0.369271i −0.784459 0.620181i \(-0.787059\pi\)
0.144863 + 0.989452i \(0.453726\pi\)
\(570\) 7.81833 6.64287i 0.327474 0.278239i
\(571\) −2.22250 8.29448i −0.0930087 0.347113i 0.903701 0.428164i \(-0.140839\pi\)
−0.996710 + 0.0810502i \(0.974173\pi\)
\(572\) −21.4350 3.50781i −0.896242 0.146669i
\(573\) 28.5034 + 28.5034i 1.19074 + 1.19074i
\(574\) 0 0
\(575\) 26.9129 1.12234
\(576\) −6.96377 + 0.257544i −0.290157 + 0.0107310i
\(577\) −17.6514 + 30.5732i −0.734838 + 1.27278i 0.219956 + 0.975510i \(0.429409\pi\)
−0.954794 + 0.297268i \(0.903925\pi\)
\(578\) 1.15593 14.2210i 0.0480804 0.591514i
\(579\) −6.47509 + 24.1654i −0.269096 + 1.00428i
\(580\) 34.2242 41.8228i 1.42108 1.73660i
\(581\) 0 0
\(582\) 20.0821 + 7.16947i 0.832429 + 0.297184i
\(583\) 28.3313 16.3571i 1.17336 0.677441i
\(584\) −29.7774 + 30.8991i −1.23220 + 1.27861i
\(585\) −5.72900 3.30764i −0.236865 0.136754i
\(586\) 30.0847 5.49608i 1.24279 0.227041i
\(587\) 2.38838 2.38838i 0.0985791 0.0985791i −0.656097 0.754676i \(-0.727794\pi\)
0.754676 + 0.656097i \(0.227794\pi\)
\(588\) 0 0
\(589\) 2.36961 + 2.36961i 0.0976379 + 0.0976379i
\(590\) −24.8388 + 35.9428i −1.02260 + 1.47974i
\(591\) −17.8966 + 30.9978i −0.736167 + 1.27508i
\(592\) 20.8331 10.3471i 0.856235 0.425263i
\(593\) 5.78207 + 10.0148i 0.237441 + 0.411260i 0.959979 0.280071i \(-0.0903580\pi\)
−0.722538 + 0.691331i \(0.757025\pi\)
\(594\) 11.1044 + 23.4355i 0.455621 + 0.961570i
\(595\) 0 0
\(596\) −2.57451 25.7659i −0.105456 1.05541i
\(597\) −2.79078 0.747787i −0.114219 0.0306049i
\(598\) −13.9813 16.4553i −0.571738 0.672908i
\(599\) −10.6273 6.13567i −0.434219 0.250697i 0.266923 0.963718i \(-0.413993\pi\)
−0.701142 + 0.713021i \(0.747326\pi\)
\(600\) −11.7749 + 21.2941i −0.480707 + 0.869329i
\(601\) 14.1538i 0.577347i −0.957428 0.288674i \(-0.906786\pi\)
0.957428 0.288674i \(-0.0932143\pi\)
\(602\) 0 0
\(603\) 0.842054 0.842054i 0.0342911 0.0342911i
\(604\) 0.905356 5.53232i 0.0368384 0.225107i
\(605\) −24.1474 + 6.47029i −0.981733 + 0.263055i
\(606\) 3.16649 38.9560i 0.128630 1.58248i
\(607\) −12.8174 22.2005i −0.520244 0.901089i −0.999723 0.0235358i \(-0.992508\pi\)
0.479479 0.877553i \(-0.340826\pi\)
\(608\) −0.975842 + 6.74271i −0.0395756 + 0.273453i
\(609\) 0 0
\(610\) −5.75410 + 2.72646i −0.232977 + 0.110391i
\(611\) 2.31382 8.63529i 0.0936071 0.349346i
\(612\) −8.48160 + 3.20594i −0.342848 + 0.129593i
\(613\) 2.49198 + 9.30020i 0.100650 + 0.375632i 0.997815 0.0660634i \(-0.0210440\pi\)
−0.897165 + 0.441695i \(0.854377\pi\)
\(614\) 1.49614 + 8.18963i 0.0603792 + 0.330507i
\(615\) 38.1256i 1.53737i
\(616\) 0 0
\(617\) 23.1951i 0.933800i 0.884310 + 0.466900i \(0.154629\pi\)
−0.884310 + 0.466900i \(0.845371\pi\)
\(618\) 4.41228 0.806064i 0.177488 0.0324247i
\(619\) −8.68871 32.4267i −0.349229 1.30334i −0.887594 0.460627i \(-0.847625\pi\)
0.538365 0.842712i \(-0.319042\pi\)
\(620\) −15.5282 7.00927i −0.623626 0.281499i
\(621\) −6.67270 + 24.9028i −0.267766 + 0.999317i
\(622\) 0.486035 + 1.02576i 0.0194882 + 0.0411291i
\(623\) 0 0
\(624\) 19.1369 3.86286i 0.766089 0.154638i
\(625\) −13.8718 24.0267i −0.554873 0.961068i
\(626\) −24.9894 2.03123i −0.998777 0.0811843i
\(627\) −10.0204 + 2.68495i −0.400175 + 0.107227i
\(628\) 1.58273 + 2.20211i 0.0631578 + 0.0878739i
\(629\) 21.4019 21.4019i 0.853348 0.853348i
\(630\) 0 0
\(631\) 30.2574i 1.20453i 0.798296 + 0.602265i \(0.205735\pi\)
−0.798296 + 0.602265i \(0.794265\pi\)
\(632\) −17.9758 + 5.17452i −0.715039 + 0.205832i
\(633\) 1.28862 + 0.743986i 0.0512181 + 0.0295708i
\(634\) 15.8039 13.4278i 0.627653 0.533287i
\(635\) −5.33848 1.43044i −0.211851 0.0567654i
\(636\) −18.6220 + 22.7565i −0.738411 + 0.902355i
\(637\) 0 0
\(638\) −49.3813 + 23.3984i −1.95503 + 0.926350i
\(639\) −4.38133 7.58868i −0.173323 0.300204i
\(640\) −7.47960 33.8192i −0.295657 1.33682i
\(641\) 3.34695 5.79709i 0.132197 0.228971i −0.792326 0.610097i \(-0.791130\pi\)
0.924523 + 0.381126i \(0.124464\pi\)
\(642\) −25.6508 17.7263i −1.01236 0.699603i
\(643\) −24.7491 24.7491i −0.976007 0.976007i 0.0237114 0.999719i \(-0.492452\pi\)
−0.999719 + 0.0237114i \(0.992452\pi\)
\(644\) 0 0
\(645\) 18.4279 18.4279i 0.725597 0.725597i
\(646\) 1.59312 + 8.72053i 0.0626806 + 0.343105i
\(647\) 37.7857 + 21.8156i 1.48551 + 0.857659i 0.999864 0.0164976i \(-0.00525159\pi\)
0.485645 + 0.874156i \(0.338585\pi\)
\(648\) −22.1064 21.3039i −0.868422 0.836898i
\(649\) 38.2593 22.0890i 1.50181 0.867069i
\(650\) 5.15757 14.4466i 0.202296 0.566643i
\(651\) 0 0
\(652\) 36.3637 3.63344i 1.42411 0.142296i
\(653\) −6.54748 + 24.4355i −0.256223 + 0.956236i 0.711184 + 0.703006i \(0.248159\pi\)
−0.967406 + 0.253230i \(0.918507\pi\)
\(654\) −22.3158 1.81391i −0.872616 0.0709294i
\(655\) −20.1015 + 34.8169i −0.785432 + 1.36041i
\(656\) 16.7472 + 18.9880i 0.653869 + 0.741356i
\(657\) 13.2156 0.515588
\(658\) 0 0
\(659\) −16.0357 16.0357i −0.624662 0.624662i 0.322058 0.946720i \(-0.395626\pi\)
−0.946720 + 0.322058i \(0.895626\pi\)
\(660\) 42.8258 30.7802i 1.66699 1.19812i
\(661\) −2.82150 10.5300i −0.109743 0.409568i 0.889097 0.457720i \(-0.151334\pi\)
−0.998840 + 0.0481514i \(0.984667\pi\)
\(662\) 0.288863 + 0.339978i 0.0112270 + 0.0132136i
\(663\) 21.9994 12.7013i 0.854385 0.493279i
\(664\) −25.4157 + 15.3069i −0.986321 + 0.594025i
\(665\) 0 0
\(666\) −6.74664 2.40861i −0.261427 0.0933316i
\(667\) −52.4732 14.0602i −2.03177 0.544412i
\(668\) −3.66887 + 1.38679i −0.141953 + 0.0536565i
\(669\) 14.8953 3.99120i 0.575887 0.154309i
\(670\) 4.86937 + 3.36505i 0.188120 + 0.130003i
\(671\) 6.43842 0.248553
\(672\) 0 0
\(673\) 1.82580 0.0703795 0.0351897 0.999381i \(-0.488796\pi\)
0.0351897 + 0.999381i \(0.488796\pi\)
\(674\) −31.1372 21.5178i −1.19936 0.828837i
\(675\) −17.6911 + 4.74030i −0.680929 + 0.182454i
\(676\) 12.8081 4.84132i 0.492620 0.186205i
\(677\) 26.1437 + 7.00518i 1.00478 + 0.269231i 0.723448 0.690379i \(-0.242556\pi\)
0.281335 + 0.959610i \(0.409223\pi\)
\(678\) 39.9909 + 14.2771i 1.53584 + 0.548309i
\(679\) 0 0
\(680\) −23.2516 38.6070i −0.891656 1.48051i
\(681\) 0.596575 0.344433i 0.0228608 0.0131987i
\(682\) 11.1544 + 13.1282i 0.427123 + 0.502703i
\(683\) −5.18175 19.3386i −0.198274 0.739970i −0.991395 0.130905i \(-0.958212\pi\)
0.793121 0.609065i \(-0.208455\pi\)
\(684\) 1.70377 1.22455i 0.0651452 0.0468219i
\(685\) −17.1808 17.1808i −0.656445 0.656445i
\(686\) 0 0
\(687\) −43.4148 −1.65638
\(688\) −1.08305 + 17.2725i −0.0412911 + 0.658507i
\(689\) 9.26852 16.0536i 0.353103 0.611592i
\(690\) 52.2584 + 4.24776i 1.98944 + 0.161709i
\(691\) 3.95994 14.7787i 0.150643 0.562208i −0.848796 0.528720i \(-0.822672\pi\)
0.999439 0.0334874i \(-0.0106614\pi\)
\(692\) 11.6528 1.16434i 0.442972 0.0442614i
\(693\) 0 0
\(694\) −16.5474 + 46.3501i −0.628130 + 1.75943i
\(695\) 7.75829 4.47925i 0.294289 0.169908i
\(696\) 34.0827 35.3665i 1.29190 1.34056i
\(697\) 28.5299 + 16.4717i 1.08065 + 0.623911i
\(698\) −4.95353 27.1149i −0.187494 1.02631i
\(699\) 13.2375 13.2375i 0.500688 0.500688i
\(700\) 0 0
\(701\) 2.64009 + 2.64009i 0.0997148 + 0.0997148i 0.755204 0.655490i \(-0.227538\pi\)
−0.655490 + 0.755204i \(0.727538\pi\)
\(702\) 12.0889 + 8.35422i 0.456266 + 0.315310i
\(703\) −3.50188 + 6.06544i −0.132076 + 0.228762i
\(704\) −7.80815 + 34.1415i −0.294281 + 1.28676i
\(705\) 10.8537 + 18.7992i 0.408774 + 0.708018i
\(706\) −33.2848 + 15.7713i −1.25269 + 0.593562i
\(707\) 0 0
\(708\) −25.1476 + 30.7310i −0.945106 + 1.15494i
\(709\) 27.6926 + 7.42020i 1.04002 + 0.278671i 0.738120 0.674669i \(-0.235714\pi\)
0.301896 + 0.953341i \(0.402380\pi\)
\(710\) 33.1912 28.2010i 1.24564 1.05836i
\(711\) 4.98899 + 2.88039i 0.187102 + 0.108023i
\(712\) −2.55182 8.86478i −0.0956335 0.332222i
\(713\) 17.1261i 0.641377i
\(714\) 0 0
\(715\) −23.5096 + 23.5096i −0.879210 + 0.879210i
\(716\) 15.7072 + 21.8541i 0.587006 + 0.816724i
\(717\) 35.8178 9.59735i 1.33764 0.358420i
\(718\) −29.6546 2.41044i −1.10670 0.0899568i
\(719\) 10.0679 + 17.4381i 0.375468 + 0.650330i 0.990397 0.138253i \(-0.0441486\pi\)
−0.614929 + 0.788583i \(0.710815\pi\)
\(720\) −5.90113 + 8.88595i −0.219922 + 0.331160i
\(721\) 0 0
\(722\) 10.6272 + 22.4284i 0.395505 + 0.834697i
\(723\) −3.25818 + 12.1597i −0.121173 + 0.452224i
\(724\) −19.6034 8.84882i −0.728556 0.328864i
\(725\) −9.98838 37.2771i −0.370959 1.38444i
\(726\) −22.3512 + 4.08326i −0.829530 + 0.151544i
\(727\) 30.0313i 1.11380i −0.830580 0.556900i \(-0.811991\pi\)
0.830580 0.556900i \(-0.188009\pi\)
\(728\) 0 0
\(729\) 15.2688i 0.565511i
\(730\) 11.8047 + 64.6173i 0.436912 + 2.39159i
\(731\) 5.82826 + 21.7514i 0.215566 + 0.804503i
\(732\) −5.41330 + 2.04616i −0.200081 + 0.0756284i
\(733\) 3.31347 12.3660i 0.122386 0.456750i −0.877347 0.479856i \(-0.840689\pi\)
0.999733 + 0.0231062i \(0.00735557\pi\)
\(734\) 9.47438 4.48925i 0.349706 0.165701i
\(735\) 0 0
\(736\) −27.8925 + 20.8397i −1.02813 + 0.768163i
\(737\) −2.99252 5.18320i −0.110231 0.190926i
\(738\) 0.631703 7.77158i 0.0232533 0.286076i
\(739\) −27.5947 + 7.39398i −1.01509 + 0.271992i −0.727754 0.685839i \(-0.759436\pi\)
−0.287334 + 0.957831i \(0.592769\pi\)
\(740\) 5.75046 35.1391i 0.211391 1.29174i
\(741\) −4.15652 + 4.15652i −0.152694 + 0.152694i
\(742\) 0 0
\(743\) 32.8469i 1.20504i −0.798106 0.602518i \(-0.794164\pi\)
0.798106 0.602518i \(-0.205836\pi\)
\(744\) −13.5506 7.49297i −0.496788 0.274706i
\(745\) −34.3267 19.8185i −1.25763 0.726095i
\(746\) −4.86003 5.72001i −0.177938 0.209424i
\(747\) 8.82583 + 2.36487i 0.322920 + 0.0865262i
\(748\) 4.53086 + 45.3453i 0.165665 + 1.65799i
\(749\) 0 0
\(750\) −2.28873 4.83028i −0.0835726 0.176377i
\(751\) −8.80060 15.2431i −0.321138 0.556228i 0.659585 0.751630i \(-0.270732\pi\)
−0.980723 + 0.195402i \(0.937399\pi\)
\(752\) −13.6634 4.59503i −0.498251 0.167564i
\(753\) 4.07852 7.06421i 0.148630 0.257434i
\(754\) −17.6033 + 25.4727i −0.641075 + 0.927663i
\(755\) −6.06777 6.06777i −0.220829 0.220829i
\(756\) 0 0
\(757\) −10.8261 + 10.8261i −0.393480 + 0.393480i −0.875926 0.482446i \(-0.839749\pi\)
0.482446 + 0.875926i \(0.339749\pi\)
\(758\) 37.0639 6.77108i 1.34622 0.245937i
\(759\) −45.9132 26.5080i −1.66654 0.962179i
\(760\) 7.50931 + 7.23672i 0.272391 + 0.262503i
\(761\) 1.13395 0.654687i 0.0411057 0.0237324i −0.479306 0.877648i \(-0.659112\pi\)
0.520412 + 0.853915i \(0.325778\pi\)
\(762\) −4.73071 1.68890i −0.171376 0.0611825i
\(763\) 0 0
\(764\) −25.9499 + 31.7113i −0.938833 + 1.14728i
\(765\) −3.59229 + 13.4066i −0.129880 + 0.484717i
\(766\) 0.566708 6.97198i 0.0204760 0.251908i
\(767\) 12.5164 21.6791i 0.451943 0.782788i
\(768\) −4.28542 31.1870i −0.154637 1.12536i
\(769\) −22.6761 −0.817720 −0.408860 0.912597i \(-0.634074\pi\)
−0.408860 + 0.912597i \(0.634074\pi\)
\(770\) 0 0
\(771\) 40.3008 + 40.3008i 1.45140 + 1.45140i
\(772\) −25.0972 4.10712i −0.903269 0.147819i
\(773\) 1.01468 + 3.78685i 0.0364956 + 0.136203i 0.981770 0.190073i \(-0.0608725\pi\)
−0.945274 + 0.326277i \(0.894206\pi\)
\(774\) 4.06170 3.45104i 0.145995 0.124045i
\(775\) −10.5364 + 6.08321i −0.378480 + 0.218515i
\(776\) −5.22216 + 21.0372i −0.187465 + 0.755192i
\(777\) 0 0
\(778\) −9.43222 + 26.4201i −0.338161 + 0.947208i
\(779\) −7.36339 1.97301i −0.263821 0.0706906i
\(780\) 12.2949 27.2379i 0.440229 0.975273i
\(781\) −42.5394 + 11.3984i −1.52218 + 0.407867i
\(782\) −25.7563 + 37.2704i −0.921043 + 1.33279i
\(783\) 36.9695 1.32118
\(784\) 0 0
\(785\) 4.15117 0.148161
\(786\) −20.7733 + 30.0599i −0.740960 + 1.07220i
\(787\) 30.0204 8.04395i 1.07011 0.286736i 0.319573 0.947562i \(-0.396460\pi\)
0.750539 + 0.660826i \(0.229794\pi\)
\(788\) −33.1624 14.9692i −1.18136 0.533256i
\(789\) −0.654607 0.175401i −0.0233046 0.00624445i
\(790\) −9.62726 + 26.9665i −0.342522 + 0.959424i
\(791\) 0 0
\(792\) 9.23967 5.56471i 0.328317 0.197733i
\(793\) 3.15948 1.82412i 0.112196 0.0647766i
\(794\) 0.0973794 0.0827387i 0.00345586 0.00293629i
\(795\) 11.6496 + 43.4770i 0.413170 + 1.54197i
\(796\) 0.474318 2.89839i 0.0168118 0.102731i
\(797\) −27.7986 27.7986i −0.984679 0.984679i 0.0152058 0.999884i \(-0.495160\pi\)
−0.999884 + 0.0152058i \(0.995160\pi\)
\(798\) 0 0
\(799\) −18.7569 −0.663570
\(800\) −22.7286 9.75793i −0.803578 0.344995i
\(801\) −1.42047 + 2.46032i −0.0501897 + 0.0869312i
\(802\) −2.91138 + 35.8175i −0.102804 + 1.26476i
\(803\) 17.1907 64.1567i 0.606648 2.26404i
\(804\) 4.16330 + 3.40689i 0.146828 + 0.120152i
\(805\) 0 0
\(806\) 9.19315 + 3.28203i 0.323815 + 0.115605i
\(807\) −23.8047 + 13.7436i −0.837964 + 0.483799i
\(808\) 39.7233 0.734301i 1.39746 0.0258326i
\(809\) −42.7813 24.6998i −1.50411 0.868398i −0.999989 0.00476483i \(-0.998483\pi\)
−0.504121 0.863633i \(-0.668183\pi\)
\(810\) −46.2298 + 8.44557i −1.62435 + 0.296747i
\(811\) 13.1428 13.1428i 0.461506 0.461506i −0.437643 0.899149i \(-0.644187\pi\)
0.899149 + 0.437643i \(0.144187\pi\)
\(812\) 0 0
\(813\) −17.3861 17.3861i −0.609756 0.609756i
\(814\) −20.4689 + 29.6193i −0.717434 + 1.03816i
\(815\) 27.9701 48.4457i 0.979750 1.69698i
\(816\) −18.2204 36.6855i −0.637842 1.28425i
\(817\) −2.60542 4.51272i −0.0911521 0.157880i
\(818\) 13.5678 + 28.6343i 0.474386 + 1.00117i
\(819\) 0 0
\(820\) 38.5633 3.85322i 1.34669 0.134560i
\(821\) −1.03860 0.278293i −0.0362475 0.00971248i 0.240650 0.970612i \(-0.422639\pi\)
−0.276897 + 0.960900i \(0.589306\pi\)
\(822\) −14.2987 16.8289i −0.498725 0.586975i
\(823\) 17.3926 + 10.0416i 0.606268 + 0.350029i 0.771504 0.636225i \(-0.219505\pi\)
−0.165235 + 0.986254i \(0.552838\pi\)
\(824\) 1.26125 + 4.38147i 0.0439377 + 0.152636i
\(825\) 37.6627i 1.31125i
\(826\) 0 0
\(827\) 6.99770 6.99770i 0.243334 0.243334i −0.574894 0.818228i \(-0.694957\pi\)
0.818228 + 0.574894i \(0.194957\pi\)
\(828\) 10.5821 + 1.73174i 0.367752 + 0.0601821i
\(829\) −44.6990 + 11.9771i −1.55246 + 0.415980i −0.930267 0.366884i \(-0.880425\pi\)
−0.622193 + 0.782864i \(0.713758\pi\)
\(830\) −3.67940 + 45.2662i −0.127714 + 1.57121i
\(831\) −8.34665 14.4568i −0.289542 0.501502i
\(832\) 5.84130 + 18.9662i 0.202511 + 0.657535i
\(833\) 0 0
\(834\) 7.35793 3.48641i 0.254784 0.120724i
\(835\) −1.55391 + 5.79927i −0.0537753 + 0.200692i
\(836\) −3.72849 9.86405i −0.128953 0.341155i
\(837\) −3.01650 11.2577i −0.104266 0.389125i
\(838\) 8.72533 + 47.7612i 0.301411 + 1.64988i
\(839\) 11.1872i 0.386225i 0.981177 + 0.193113i \(0.0618583\pi\)
−0.981177 + 0.193113i \(0.938142\pi\)
\(840\) 0 0
\(841\) 48.8991i 1.68618i
\(842\) 31.5321 5.76050i 1.08667 0.198520i
\(843\) −4.87073 18.1778i −0.167757 0.626077i
\(844\) −0.622291 + 1.37861i −0.0214201 + 0.0474536i
\(845\) 5.42475 20.2454i 0.186617 0.696464i
\(846\) 1.90095 + 4.01189i 0.0653561 + 0.137931i
\(847\) 0 0
\(848\) −24.8998 16.5359i −0.855064 0.567844i
\(849\) −16.2605 28.1640i −0.558058 0.966585i
\(850\) −32.0784 2.60745i −1.10028 0.0894349i
\(851\) −34.5734 + 9.26392i −1.18516 + 0.317563i
\(852\) 32.1438 23.1028i 1.10123 0.791489i
\(853\) 25.4369 25.4369i 0.870944 0.870944i −0.121632 0.992575i \(-0.538813\pi\)
0.992575 + 0.121632i \(0.0388127\pi\)
\(854\) 0 0
\(855\) 3.21174i 0.109839i
\(856\) 15.3374 27.7368i 0.524222 0.948024i
\(857\) −28.5281 16.4707i −0.974500 0.562628i −0.0738951 0.997266i \(-0.523543\pi\)
−0.900605 + 0.434638i \(0.856876\pi\)
\(858\) −23.0281 + 19.5659i −0.786165 + 0.667967i
\(859\) −40.8704 10.9512i −1.39448 0.373649i −0.518120 0.855308i \(-0.673368\pi\)
−0.876359 + 0.481659i \(0.840034\pi\)
\(860\) 20.5019 + 16.7770i 0.699108 + 0.572091i
\(861\) 0 0
\(862\) 40.4636 19.1729i 1.37819 0.653030i
\(863\) −10.9071 18.8916i −0.371281 0.643078i 0.618482 0.785799i \(-0.287748\pi\)
−0.989763 + 0.142721i \(0.954415\pi\)
\(864\) 14.6644 18.6117i 0.498893 0.633184i
\(865\) 8.96304 15.5244i 0.304752 0.527847i
\(866\) 13.5915 + 9.39261i 0.461858 + 0.319174i
\(867\) −14.0360 14.0360i −0.476689 0.476689i
\(868\) 0 0
\(869\) 20.4729 20.4729i 0.694495 0.694495i
\(870\) −13.5115 73.9599i −0.458082 2.50747i
\(871\) −2.93699 1.69567i −0.0995162 0.0574557i
\(872\) −0.420640 22.7553i −0.0142447 0.770591i
\(873\) 5.78109 3.33772i 0.195660 0.112965i
\(874\) 3.52478 9.87311i 0.119228 0.333963i
\(875\) 0 0
\(876\) 5.93570 + 59.4049i 0.200549 + 2.00711i
\(877\) 3.62186 13.5170i 0.122302 0.456435i −0.877428 0.479709i \(-0.840742\pi\)
0.999729 + 0.0232736i \(0.00740889\pi\)
\(878\) 18.4959 + 1.50342i 0.624207 + 0.0507378i
\(879\) 21.2738 36.8473i 0.717548 1.24283i
\(880\) 35.4619 + 40.2066i 1.19542 + 1.35536i
\(881\) 12.3319 0.415471 0.207735 0.978185i \(-0.433391\pi\)
0.207735 + 0.978185i \(0.433391\pi\)
\(882\) 0 0
\(883\) 24.3508 + 24.3508i 0.819469 + 0.819469i 0.986031 0.166562i \(-0.0532667\pi\)
−0.166562 + 0.986031i \(0.553267\pi\)
\(884\) 15.0706 + 20.9683i 0.506878 + 0.705239i
\(885\) 15.7319 + 58.7124i 0.528823 + 1.97360i
\(886\) 21.0047 + 24.7215i 0.705666 + 0.830534i
\(887\) 3.69725 2.13461i 0.124141 0.0716731i −0.436643 0.899635i \(-0.643833\pi\)
0.560785 + 0.827962i \(0.310500\pi\)
\(888\) 7.79665 31.4084i 0.261638 1.05400i
\(889\) 0 0
\(890\) −13.2985 4.74769i −0.445768 0.159143i
\(891\) 45.9002 + 12.2989i 1.53772 + 0.412030i
\(892\) 5.54243 + 14.6630i 0.185574 + 0.490953i
\(893\) 4.19246 1.12337i 0.140295 0.0375920i
\(894\) −29.6367 20.4809i −0.991198 0.684982i
\(895\) 41.1967 1.37705
\(896\) 0 0
\(897\) −30.0408 −1.00303
\(898\) −18.1956 12.5743i −0.607194 0.419610i
\(899\) 23.7214 6.35613i 0.791153 0.211989i
\(900\) 2.69335 + 7.12548i 0.0897783 + 0.237516i
\(901\) −37.5674 10.0662i −1.25155 0.335352i
\(902\) −36.9064 13.1759i −1.22885 0.438710i
\(903\) 0 0
\(904\) −10.3993 + 41.8930i −0.345875 + 1.39334i
\(905\) −28.5122 + 16.4615i −0.947776 + 0.547199i
\(906\) −5.04990 5.94348i −0.167772 0.197459i
\(907\) −8.71495 32.5246i −0.289375 1.07996i −0.945583 0.325382i \(-0.894507\pi\)
0.656208 0.754580i \(-0.272160\pi\)
\(908\) 0.408681 + 0.568613i 0.0135625 + 0.0188701i
\(909\) −8.65188 8.65188i −0.286965 0.286965i
\(910\) 0 0
\(911\) 4.22749 0.140063 0.0700315 0.997545i \(-0.477690\pi\)
0.0700315 + 0.997545i \(0.477690\pi\)
\(912\) 6.26969 + 7.10856i 0.207610 + 0.235388i
\(913\) 22.9612 39.7699i 0.759904 1.31619i
\(914\) −17.2396 1.40130i −0.570236 0.0463509i
\(915\) −2.29275 + 8.55664i −0.0757958 + 0.282874i
\(916\) −4.38777 43.9132i −0.144976 1.45093i
\(917\) 0 0
\(918\) 10.3661 29.0361i 0.342134 0.958335i
\(919\) −18.8641 + 10.8912i −0.622270 + 0.359268i −0.777752 0.628571i \(-0.783640\pi\)
0.155482 + 0.987839i \(0.450307\pi\)
\(920\) 0.985044 + 53.2877i 0.0324759 + 1.75684i
\(921\) 10.0305 + 5.79113i 0.330517 + 0.190824i
\(922\) 4.83992 + 26.4930i 0.159394 + 0.872502i
\(923\) −17.6457 + 17.6457i −0.580814 + 0.580814i
\(924\) 0 0
\(925\) −17.9799 17.9799i −0.591177 0.591177i
\(926\) −28.8307 19.9239i −0.947435 0.654739i
\(927\) 0.702074 1.21603i 0.0230591 0.0399396i
\(928\) 39.2171 + 30.8996i 1.28737 + 1.01433i
\(929\) −15.6683 27.1384i −0.514062 0.890381i −0.999867 0.0163141i \(-0.994807\pi\)
0.485805 0.874067i \(-0.338526\pi\)
\(930\) −21.4194 + 10.1491i −0.702369 + 0.332804i
\(931\) 0 0
\(932\) 14.7273 + 12.0516i 0.482410 + 0.394763i
\(933\) 1.52535 + 0.408718i 0.0499379 + 0.0133808i
\(934\) −35.3118 + 30.0028i −1.15544 + 0.981721i
\(935\) 60.4113 + 34.8785i 1.97566 + 1.14065i
\(936\) 2.95752 5.34850i 0.0966697 0.174821i
\(937\) 53.9341i 1.76195i 0.473162 + 0.880975i \(0.343113\pi\)
−0.473162 + 0.880975i \(0.656887\pi\)
\(938\) 0 0
\(939\) −24.6644 + 24.6644i −0.804893 + 0.804893i
\(940\) −17.9180 + 12.8783i −0.584422 + 0.420043i
\(941\) −47.8941 + 12.8332i −1.56130 + 0.418350i −0.933076 0.359680i \(-0.882886\pi\)
−0.628227 + 0.778030i \(0.716219\pi\)
\(942\) 3.76047 + 0.305665i 0.122523 + 0.00995910i
\(943\) −19.4792 33.7390i −0.634330 1.09869i
\(944\) −33.6254 22.3305i −1.09441 0.726795i
\(945\) 0 0
\(946\) −11.4701 24.2071i −0.372924 0.787042i
\(947\) 0.0235259 0.0877997i 0.000764488 0.00285311i −0.965543 0.260245i \(-0.916197\pi\)
0.966307 + 0.257392i \(0.0828632\pi\)
\(948\) −10.7068 + 23.7196i −0.347741 + 0.770376i
\(949\) −9.74091 36.3536i −0.316203 1.18009i
\(950\) 7.32621 1.33840i 0.237694 0.0434235i
\(951\) 28.8516i 0.935577i
\(952\) 0 0
\(953\) 45.4195i 1.47128i −0.677371 0.735641i \(-0.736881\pi\)
0.677371 0.735641i \(-0.263119\pi\)
\(954\) 1.65431 + 9.05544i 0.0535602 + 0.293181i
\(955\) 16.2338 + 60.5854i 0.525314 + 1.96050i
\(956\) 13.3275 + 35.2590i 0.431042 + 1.14036i
\(957\) −19.6762 + 73.4326i −0.636041 + 2.37374i
\(958\) 45.1965 21.4155i 1.46023 0.691902i
\(959\) 0 0
\(960\) −42.5935 22.5349i −1.37470 0.727312i
\(961\) 11.6289 + 20.1419i 0.375127 + 0.649739i
\(962\) −1.65283 + 20.3341i −0.0532893 + 0.655597i
\(963\) −9.42843 + 2.52634i −0.303827 + 0.0814102i
\(964\) −12.6286 2.06665i −0.406739 0.0665623i
\(965\) −27.5263 + 27.5263i −0.886103 + 0.886103i
\(966\) 0 0
\(967\) 60.1289i 1.93362i −0.255506 0.966808i \(-0.582242\pi\)
0.255506 0.966808i \(-0.417758\pi\)
\(968\) −6.38909 22.1951i −0.205353 0.713378i
\(969\) 10.6808 + 6.16655i 0.343116 + 0.198098i
\(970\) 21.4836 + 25.2852i 0.689798 + 0.811858i
\(971\) 36.4130 + 9.75682i 1.16855 + 0.313111i 0.790375 0.612624i \(-0.209886\pi\)
0.378173 + 0.925735i \(0.376552\pi\)
\(972\) −17.4931 + 1.74790i −0.561091 + 0.0560638i
\(973\) 0 0
\(974\) −10.1285 21.3757i −0.324537 0.684923i
\(975\) −10.6705 18.4819i −0.341731 0.591895i
\(976\) −2.61676 5.26865i −0.0837603 0.168645i
\(977\) 12.3444 21.3811i 0.394932 0.684042i −0.598161 0.801376i \(-0.704102\pi\)
0.993092 + 0.117334i \(0.0374349\pi\)
\(978\) 28.9049 41.8265i 0.924276 1.33747i
\(979\) 10.0962 + 10.0962i 0.322676 + 0.322676i
\(980\) 0 0
\(981\) −4.95619 + 4.95619i −0.158239 + 0.158239i
\(982\) 11.6717 2.13226i 0.372459 0.0680433i
\(983\) 4.43148 + 2.55852i 0.141342 + 0.0816041i 0.569004 0.822335i \(-0.307329\pi\)
−0.427661 + 0.903939i \(0.640662\pi\)
\(984\) 35.2176 0.651011i 1.12270 0.0207535i
\(985\) −48.2329 + 27.8473i −1.53683 + 0.887289i
\(986\) 61.1825 + 21.8427i 1.94845 + 0.695613i
\(987\) 0 0
\(988\) −4.62432 3.78415i −0.147119 0.120390i
\(989\) 6.89240 25.7228i 0.219166 0.817938i
\(990\) 1.33762 16.4561i 0.0425122 0.523011i
\(991\) 2.71965 4.71056i 0.0863924 0.149636i −0.819591 0.572949i \(-0.805799\pi\)
0.905984 + 0.423313i \(0.139133\pi\)
\(992\) 6.20948 14.4634i 0.197151 0.459214i
\(993\) 0.620663 0.0196961
\(994\) 0 0
\(995\) −3.17892 3.17892i −0.100779 0.100779i
\(996\) −6.66621 + 40.7349i −0.211227 + 1.29074i
\(997\) 3.12961 + 11.6799i 0.0991157 + 0.369905i 0.997611 0.0690777i \(-0.0220057\pi\)
−0.898496 + 0.438983i \(0.855339\pi\)
\(998\) −8.46926 + 7.19594i −0.268090 + 0.227783i
\(999\) 21.0950 12.1792i 0.667415 0.385332i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 784.2.x.m.557.6 24
7.2 even 3 inner 784.2.x.m.765.4 24
7.3 odd 6 112.2.m.d.29.1 12
7.4 even 3 784.2.m.h.589.1 12
7.5 odd 6 784.2.x.l.765.4 24
7.6 odd 2 784.2.x.l.557.6 24
16.5 even 4 inner 784.2.x.m.165.4 24
28.3 even 6 448.2.m.d.337.2 12
56.3 even 6 896.2.m.h.673.5 12
56.45 odd 6 896.2.m.g.673.2 12
112.3 even 12 896.2.m.h.225.5 12
112.5 odd 12 784.2.x.l.373.6 24
112.37 even 12 inner 784.2.x.m.373.6 24
112.45 odd 12 896.2.m.g.225.2 12
112.53 even 12 784.2.m.h.197.1 12
112.59 even 12 448.2.m.d.113.2 12
112.69 odd 4 784.2.x.l.165.4 24
112.101 odd 12 112.2.m.d.85.1 yes 12
224.59 even 24 7168.2.a.bi.1.10 12
224.101 odd 24 7168.2.a.bj.1.3 12
224.171 even 24 7168.2.a.bi.1.3 12
224.213 odd 24 7168.2.a.bj.1.10 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.d.29.1 12 7.3 odd 6
112.2.m.d.85.1 yes 12 112.101 odd 12
448.2.m.d.113.2 12 112.59 even 12
448.2.m.d.337.2 12 28.3 even 6
784.2.m.h.197.1 12 112.53 even 12
784.2.m.h.589.1 12 7.4 even 3
784.2.x.l.165.4 24 112.69 odd 4
784.2.x.l.373.6 24 112.5 odd 12
784.2.x.l.557.6 24 7.6 odd 2
784.2.x.l.765.4 24 7.5 odd 6
784.2.x.m.165.4 24 16.5 even 4 inner
784.2.x.m.373.6 24 112.37 even 12 inner
784.2.x.m.557.6 24 1.1 even 1 trivial
784.2.x.m.765.4 24 7.2 even 3 inner
896.2.m.g.225.2 12 112.45 odd 12
896.2.m.g.673.2 12 56.45 odd 6
896.2.m.h.225.5 12 112.3 even 12
896.2.m.h.673.5 12 56.3 even 6
7168.2.a.bi.1.3 12 224.171 even 24
7168.2.a.bi.1.10 12 224.59 even 24
7168.2.a.bj.1.3 12 224.101 odd 24
7168.2.a.bj.1.10 12 224.213 odd 24