Properties

Label 891.2.k.a.404.1
Level $891$
Weight $2$
Character 891.404
Analytic conductor $7.115$
Analytic rank $0$
Dimension $80$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(161,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.k (of order \(10\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 404.1
Character \(\chi\) \(=\) 891.404
Dual form 891.2.k.a.161.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.17940 + 1.58343i) q^{2} +(1.62452 - 4.99975i) q^{4} +(-0.850459 + 1.17056i) q^{5} +(1.37298 + 0.446107i) q^{7} +(2.71136 + 8.34470i) q^{8} -3.89775i q^{10} +(0.371076 - 3.29580i) q^{11} +(-1.74976 - 2.40833i) q^{13} +(-3.69865 + 1.20176i) q^{14} +(-10.6163 - 7.71319i) q^{16} +(-3.35854 - 2.44012i) q^{17} +(-1.19136 + 0.387096i) q^{19} +(4.47090 + 6.15367i) q^{20} +(4.40994 + 7.77045i) q^{22} +5.80743i q^{23} +(0.898164 + 2.76426i) q^{25} +(7.62685 + 2.47811i) q^{26} +(4.46085 - 6.13983i) q^{28} +(-0.0300853 + 0.0925930i) q^{29} +(-3.30738 + 2.40295i) q^{31} +17.8022 q^{32} +11.1834 q^{34} +(-1.68985 + 1.22775i) q^{35} +(-3.08635 + 9.49880i) q^{37} +(1.98351 - 2.73007i) q^{38} +(-12.0738 - 3.92303i) q^{40} +(-1.41240 - 4.34693i) q^{41} +2.12626i q^{43} +(-15.8754 - 7.20937i) q^{44} +(-9.19566 - 12.6567i) q^{46} +(-6.90361 + 2.24312i) q^{47} +(-3.97707 - 2.88951i) q^{49} +(-6.33448 - 4.60227i) q^{50} +(-14.8836 + 4.83597i) q^{52} +(-0.197492 - 0.271824i) q^{53} +(3.54233 + 3.23731i) q^{55} +12.6666i q^{56} +(-0.0810465 - 0.249436i) q^{58} +(-2.87859 - 0.935310i) q^{59} +(0.187098 - 0.257518i) q^{61} +(3.40321 - 10.4740i) q^{62} +(-17.5657 + 12.7622i) q^{64} +4.30718 q^{65} +3.43656 q^{67} +(-17.6560 + 12.8278i) q^{68} +(1.73882 - 5.35153i) q^{70} +(-5.38901 + 7.41734i) q^{71} +(-6.75113 - 2.19358i) q^{73} +(-8.31428 - 25.5887i) q^{74} +6.58534i q^{76} +(1.97976 - 4.35952i) q^{77} +(-5.88983 - 8.10666i) q^{79} +(18.0574 - 5.86722i) q^{80} +(9.96124 + 7.23727i) q^{82} +(-4.82527 - 3.50577i) q^{83} +(5.71260 - 1.85614i) q^{85} +(-3.36679 - 4.63399i) q^{86} +(28.5086 - 5.83958i) q^{88} -5.11584i q^{89} +(-1.32800 - 4.08716i) q^{91} +(29.0357 + 9.43428i) q^{92} +(11.4939 - 15.8200i) q^{94} +(0.560084 - 1.72376i) q^{95} +(-4.88722 + 3.55077i) q^{97} +13.2430 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17940 + 1.58343i −1.54107 + 1.11965i −0.591412 + 0.806370i \(0.701429\pi\)
−0.949660 + 0.313284i \(0.898571\pi\)
\(3\) 0 0
\(4\) 1.62452 4.99975i 0.812259 2.49988i
\(5\) −0.850459 + 1.17056i −0.380337 + 0.523488i −0.955674 0.294428i \(-0.904871\pi\)
0.575337 + 0.817916i \(0.304871\pi\)
\(6\) 0 0
\(7\) 1.37298 + 0.446107i 0.518936 + 0.168613i 0.556763 0.830672i \(-0.312043\pi\)
−0.0378262 + 0.999284i \(0.512043\pi\)
\(8\) 2.71136 + 8.34470i 0.958610 + 2.95030i
\(9\) 0 0
\(10\) 3.89775i 1.23258i
\(11\) 0.371076 3.29580i 0.111883 0.993721i
\(12\) 0 0
\(13\) −1.74976 2.40833i −0.485295 0.667951i 0.494217 0.869339i \(-0.335455\pi\)
−0.979512 + 0.201388i \(0.935455\pi\)
\(14\) −3.69865 + 1.20176i −0.988506 + 0.321185i
\(15\) 0 0
\(16\) −10.6163 7.71319i −2.65408 1.92830i
\(17\) −3.35854 2.44012i −0.814566 0.591817i 0.100585 0.994928i \(-0.467929\pi\)
−0.915151 + 0.403112i \(0.867929\pi\)
\(18\) 0 0
\(19\) −1.19136 + 0.387096i −0.273317 + 0.0888059i −0.442468 0.896784i \(-0.645897\pi\)
0.169152 + 0.985590i \(0.445897\pi\)
\(20\) 4.47090 + 6.15367i 0.999724 + 1.37600i
\(21\) 0 0
\(22\) 4.40994 + 7.77045i 0.940203 + 1.65667i
\(23\) 5.80743i 1.21093i 0.795871 + 0.605467i \(0.207014\pi\)
−0.795871 + 0.605467i \(0.792986\pi\)
\(24\) 0 0
\(25\) 0.898164 + 2.76426i 0.179633 + 0.552853i
\(26\) 7.62685 + 2.47811i 1.49575 + 0.485998i
\(27\) 0 0
\(28\) 4.46085 6.13983i 0.843021 1.16032i
\(29\) −0.0300853 + 0.0925930i −0.00558670 + 0.0171941i −0.953811 0.300407i \(-0.902877\pi\)
0.948224 + 0.317601i \(0.102877\pi\)
\(30\) 0 0
\(31\) −3.30738 + 2.40295i −0.594023 + 0.431583i −0.843752 0.536733i \(-0.819658\pi\)
0.249730 + 0.968316i \(0.419658\pi\)
\(32\) 17.8022 3.14702
\(33\) 0 0
\(34\) 11.1834 1.91793
\(35\) −1.68985 + 1.22775i −0.285637 + 0.207528i
\(36\) 0 0
\(37\) −3.08635 + 9.49880i −0.507392 + 1.56159i 0.289319 + 0.957233i \(0.406571\pi\)
−0.796711 + 0.604360i \(0.793429\pi\)
\(38\) 1.98351 2.73007i 0.321768 0.442876i
\(39\) 0 0
\(40\) −12.0738 3.92303i −1.90904 0.620285i
\(41\) −1.41240 4.34693i −0.220580 0.678876i −0.998710 0.0507726i \(-0.983832\pi\)
0.778130 0.628103i \(-0.216168\pi\)
\(42\) 0 0
\(43\) 2.12626i 0.324252i 0.986770 + 0.162126i \(0.0518351\pi\)
−0.986770 + 0.162126i \(0.948165\pi\)
\(44\) −15.8754 7.20937i −2.39330 1.08685i
\(45\) 0 0
\(46\) −9.19566 12.6567i −1.35583 1.86614i
\(47\) −6.90361 + 2.24312i −1.00700 + 0.327193i −0.765657 0.643249i \(-0.777586\pi\)
−0.241338 + 0.970441i \(0.577586\pi\)
\(48\) 0 0
\(49\) −3.97707 2.88951i −0.568152 0.412787i
\(50\) −6.33448 4.60227i −0.895831 0.650859i
\(51\) 0 0
\(52\) −14.8836 + 4.83597i −2.06398 + 0.670628i
\(53\) −0.197492 0.271824i −0.0271276 0.0373379i 0.795238 0.606298i \(-0.207346\pi\)
−0.822365 + 0.568960i \(0.807346\pi\)
\(54\) 0 0
\(55\) 3.54233 + 3.23731i 0.477648 + 0.436518i
\(56\) 12.6666i 1.69265i
\(57\) 0 0
\(58\) −0.0810465 0.249436i −0.0106419 0.0327525i
\(59\) −2.87859 0.935310i −0.374760 0.121767i 0.115580 0.993298i \(-0.463127\pi\)
−0.490340 + 0.871531i \(0.663127\pi\)
\(60\) 0 0
\(61\) 0.187098 0.257518i 0.0239554 0.0329718i −0.796871 0.604149i \(-0.793513\pi\)
0.820827 + 0.571177i \(0.193513\pi\)
\(62\) 3.40321 10.4740i 0.432208 1.33020i
\(63\) 0 0
\(64\) −17.5657 + 12.7622i −2.19571 + 1.59527i
\(65\) 4.30718 0.534240
\(66\) 0 0
\(67\) 3.43656 0.419843 0.209922 0.977718i \(-0.432679\pi\)
0.209922 + 0.977718i \(0.432679\pi\)
\(68\) −17.6560 + 12.8278i −2.14111 + 1.55561i
\(69\) 0 0
\(70\) 1.73882 5.35153i 0.207828 0.639630i
\(71\) −5.38901 + 7.41734i −0.639558 + 0.880276i −0.998592 0.0530483i \(-0.983106\pi\)
0.359034 + 0.933325i \(0.383106\pi\)
\(72\) 0 0
\(73\) −6.75113 2.19358i −0.790160 0.256739i −0.113988 0.993482i \(-0.536363\pi\)
−0.676172 + 0.736743i \(0.736363\pi\)
\(74\) −8.31428 25.5887i −0.966516 2.97463i
\(75\) 0 0
\(76\) 6.58534i 0.755391i
\(77\) 1.97976 4.35952i 0.225614 0.496813i
\(78\) 0 0
\(79\) −5.88983 8.10666i −0.662658 0.912071i 0.336908 0.941538i \(-0.390619\pi\)
−0.999566 + 0.0294671i \(0.990619\pi\)
\(80\) 18.0574 5.86722i 2.01888 0.655975i
\(81\) 0 0
\(82\) 9.96124 + 7.23727i 1.10004 + 0.799222i
\(83\) −4.82527 3.50577i −0.529643 0.384808i 0.290581 0.956850i \(-0.406151\pi\)
−0.820224 + 0.572042i \(0.806151\pi\)
\(84\) 0 0
\(85\) 5.71260 1.85614i 0.619619 0.201326i
\(86\) −3.36679 4.63399i −0.363050 0.499696i
\(87\) 0 0
\(88\) 28.5086 5.83958i 3.03903 0.622501i
\(89\) 5.11584i 0.542278i −0.962540 0.271139i \(-0.912600\pi\)
0.962540 0.271139i \(-0.0874004\pi\)
\(90\) 0 0
\(91\) −1.32800 4.08716i −0.139212 0.428451i
\(92\) 29.0357 + 9.43428i 3.02718 + 0.983592i
\(93\) 0 0
\(94\) 11.4939 15.8200i 1.18551 1.63171i
\(95\) 0.560084 1.72376i 0.0574634 0.176854i
\(96\) 0 0
\(97\) −4.88722 + 3.55077i −0.496222 + 0.360526i −0.807572 0.589769i \(-0.799219\pi\)
0.311350 + 0.950295i \(0.399219\pi\)
\(98\) 13.2430 1.33774
\(99\) 0 0
\(100\) 15.2797 1.52797
\(101\) −9.41885 + 6.84320i −0.937211 + 0.680923i −0.947748 0.319021i \(-0.896646\pi\)
0.0105370 + 0.999944i \(0.496646\pi\)
\(102\) 0 0
\(103\) −1.03517 + 3.18593i −0.101999 + 0.313919i −0.989014 0.147820i \(-0.952774\pi\)
0.887016 + 0.461739i \(0.152774\pi\)
\(104\) 15.3526 21.1310i 1.50545 2.07207i
\(105\) 0 0
\(106\) 0.860829 + 0.279700i 0.0836111 + 0.0271669i
\(107\) −2.92166 8.99195i −0.282448 0.869285i −0.987152 0.159784i \(-0.948920\pi\)
0.704704 0.709501i \(-0.251080\pi\)
\(108\) 0 0
\(109\) 4.11325i 0.393978i −0.980406 0.196989i \(-0.936884\pi\)
0.980406 0.196989i \(-0.0631163\pi\)
\(110\) −12.8462 1.44636i −1.22484 0.137905i
\(111\) 0 0
\(112\) −11.1350 15.3260i −1.05216 1.44818i
\(113\) 19.2327 6.24909i 1.80926 0.587864i 0.809261 0.587449i \(-0.199868\pi\)
1.00000 0.000415145i \(-0.000132145\pi\)
\(114\) 0 0
\(115\) −6.79793 4.93898i −0.633910 0.460562i
\(116\) 0.414068 + 0.300838i 0.0384452 + 0.0279321i
\(117\) 0 0
\(118\) 7.75460 2.51962i 0.713869 0.231950i
\(119\) −3.52264 4.84850i −0.322920 0.444461i
\(120\) 0 0
\(121\) −10.7246 2.44598i −0.974964 0.222362i
\(122\) 0.857491i 0.0776336i
\(123\) 0 0
\(124\) 6.64126 + 20.4397i 0.596403 + 1.83554i
\(125\) −10.8799 3.53510i −0.973131 0.316189i
\(126\) 0 0
\(127\) −0.0604870 + 0.0832533i −0.00536736 + 0.00738753i −0.811692 0.584085i \(-0.801453\pi\)
0.806325 + 0.591473i \(0.201453\pi\)
\(128\) 7.07223 21.7661i 0.625103 1.92387i
\(129\) 0 0
\(130\) −9.38709 + 6.82012i −0.823302 + 0.598164i
\(131\) −15.3653 −1.34248 −0.671238 0.741242i \(-0.734237\pi\)
−0.671238 + 0.741242i \(0.734237\pi\)
\(132\) 0 0
\(133\) −1.80839 −0.156808
\(134\) −7.48966 + 5.44156i −0.647008 + 0.470079i
\(135\) 0 0
\(136\) 11.2559 34.6421i 0.965185 2.97053i
\(137\) −2.18861 + 3.01236i −0.186986 + 0.257364i −0.892210 0.451620i \(-0.850846\pi\)
0.705225 + 0.708984i \(0.250846\pi\)
\(138\) 0 0
\(139\) 16.1833 + 5.25827i 1.37265 + 0.446001i 0.900246 0.435381i \(-0.143386\pi\)
0.472404 + 0.881382i \(0.343386\pi\)
\(140\) 3.39325 + 10.4433i 0.286782 + 0.882624i
\(141\) 0 0
\(142\) 24.6985i 2.07265i
\(143\) −8.58668 + 4.87317i −0.718054 + 0.407515i
\(144\) 0 0
\(145\) −0.0827990 0.113963i −0.00687608 0.00946412i
\(146\) 18.1868 5.90925i 1.50515 0.489053i
\(147\) 0 0
\(148\) 42.4778 + 30.8619i 3.49166 + 2.53684i
\(149\) −9.26481 6.73128i −0.759003 0.551448i 0.139601 0.990208i \(-0.455418\pi\)
−0.898604 + 0.438760i \(0.855418\pi\)
\(150\) 0 0
\(151\) 1.01097 0.328485i 0.0822718 0.0267317i −0.267592 0.963532i \(-0.586228\pi\)
0.349864 + 0.936801i \(0.386228\pi\)
\(152\) −6.46040 8.89198i −0.524008 0.721235i
\(153\) 0 0
\(154\) 2.58830 + 12.6360i 0.208571 + 1.01823i
\(155\) 5.91508i 0.475111i
\(156\) 0 0
\(157\) −0.0263869 0.0812104i −0.00210590 0.00648129i 0.949998 0.312256i \(-0.101085\pi\)
−0.952104 + 0.305775i \(0.901085\pi\)
\(158\) 25.6727 + 8.34155i 2.04241 + 0.663618i
\(159\) 0 0
\(160\) −15.1401 + 20.8385i −1.19693 + 1.64743i
\(161\) −2.59074 + 7.97347i −0.204179 + 0.628398i
\(162\) 0 0
\(163\) −2.37021 + 1.72206i −0.185650 + 0.134882i −0.676728 0.736233i \(-0.736603\pi\)
0.491079 + 0.871115i \(0.336603\pi\)
\(164\) −24.0280 −1.87627
\(165\) 0 0
\(166\) 16.0674 1.24707
\(167\) −3.60309 + 2.61780i −0.278816 + 0.202571i −0.718401 0.695630i \(-0.755125\pi\)
0.439585 + 0.898201i \(0.355125\pi\)
\(168\) 0 0
\(169\) 1.27880 3.93575i 0.0983694 0.302750i
\(170\) −9.51100 + 13.0908i −0.729461 + 1.00402i
\(171\) 0 0
\(172\) 10.6308 + 3.45415i 0.810590 + 0.263377i
\(173\) 3.22935 + 9.93891i 0.245523 + 0.755641i 0.995550 + 0.0942343i \(0.0300403\pi\)
−0.750027 + 0.661407i \(0.769960\pi\)
\(174\) 0 0
\(175\) 4.19595i 0.317184i
\(176\) −29.3606 + 32.1270i −2.21314 + 2.42167i
\(177\) 0 0
\(178\) 8.10058 + 11.1495i 0.607164 + 0.835690i
\(179\) 9.58188 3.11334i 0.716183 0.232702i 0.0718157 0.997418i \(-0.477121\pi\)
0.644368 + 0.764716i \(0.277121\pi\)
\(180\) 0 0
\(181\) 12.5433 + 9.11327i 0.932339 + 0.677384i 0.946564 0.322515i \(-0.104528\pi\)
−0.0142256 + 0.999899i \(0.504528\pi\)
\(182\) 9.36598 + 6.80478i 0.694253 + 0.504404i
\(183\) 0 0
\(184\) −48.4613 + 15.7460i −3.57261 + 1.16081i
\(185\) −8.49407 11.6911i −0.624496 0.859545i
\(186\) 0 0
\(187\) −9.28843 + 10.1636i −0.679237 + 0.743237i
\(188\) 38.1603i 2.78313i
\(189\) 0 0
\(190\) 1.50881 + 4.64363i 0.109460 + 0.336884i
\(191\) −3.53297 1.14793i −0.255637 0.0830615i 0.178395 0.983959i \(-0.442910\pi\)
−0.434032 + 0.900897i \(0.642910\pi\)
\(192\) 0 0
\(193\) −14.6578 + 20.1747i −1.05509 + 1.45221i −0.170779 + 0.985309i \(0.554628\pi\)
−0.884311 + 0.466898i \(0.845372\pi\)
\(194\) 5.02883 15.4771i 0.361049 1.11119i
\(195\) 0 0
\(196\) −20.9076 + 15.1903i −1.49340 + 1.08502i
\(197\) 19.2214 1.36947 0.684733 0.728794i \(-0.259919\pi\)
0.684733 + 0.728794i \(0.259919\pi\)
\(198\) 0 0
\(199\) −26.0126 −1.84399 −0.921993 0.387206i \(-0.873440\pi\)
−0.921993 + 0.387206i \(0.873440\pi\)
\(200\) −20.6317 + 14.9898i −1.45888 + 1.05994i
\(201\) 0 0
\(202\) 9.69176 29.8282i 0.681910 2.09870i
\(203\) −0.0826128 + 0.113707i −0.00579828 + 0.00798065i
\(204\) 0 0
\(205\) 6.28951 + 2.04358i 0.439278 + 0.142730i
\(206\) −2.78864 8.58255i −0.194294 0.597975i
\(207\) 0 0
\(208\) 39.0638i 2.70859i
\(209\) 0.833707 + 4.07012i 0.0576687 + 0.281536i
\(210\) 0 0
\(211\) −13.3646 18.3948i −0.920057 1.26635i −0.963614 0.267299i \(-0.913869\pi\)
0.0435567 0.999051i \(-0.486131\pi\)
\(212\) −1.67988 + 0.545827i −0.115375 + 0.0374875i
\(213\) 0 0
\(214\) 20.6056 + 14.9708i 1.40857 + 1.02339i
\(215\) −2.48891 1.80830i −0.169742 0.123325i
\(216\) 0 0
\(217\) −5.61293 + 1.82375i −0.381030 + 0.123804i
\(218\) 6.51304 + 8.96443i 0.441119 + 0.607148i
\(219\) 0 0
\(220\) 21.9403 12.4517i 1.47922 0.839495i
\(221\) 12.3581i 0.831296i
\(222\) 0 0
\(223\) −7.02963 21.6350i −0.470739 1.44878i −0.851619 0.524161i \(-0.824379\pi\)
0.380881 0.924624i \(-0.375621\pi\)
\(224\) 24.4421 + 7.94170i 1.63310 + 0.530627i
\(225\) 0 0
\(226\) −32.0208 + 44.0729i −2.13000 + 2.93169i
\(227\) 2.51159 7.72987i 0.166700 0.513050i −0.832458 0.554089i \(-0.813067\pi\)
0.999158 + 0.0410390i \(0.0130668\pi\)
\(228\) 0 0
\(229\) −10.9974 + 7.99008i −0.726728 + 0.527999i −0.888527 0.458825i \(-0.848271\pi\)
0.161798 + 0.986824i \(0.448271\pi\)
\(230\) 22.6360 1.49257
\(231\) 0 0
\(232\) −0.854233 −0.0560831
\(233\) 4.09157 2.97270i 0.268048 0.194748i −0.445640 0.895212i \(-0.647024\pi\)
0.713687 + 0.700464i \(0.247024\pi\)
\(234\) 0 0
\(235\) 3.24554 9.98874i 0.211716 0.651594i
\(236\) −9.35264 + 12.8728i −0.608805 + 0.837948i
\(237\) 0 0
\(238\) 15.3545 + 4.98899i 0.995286 + 0.323388i
\(239\) 6.23162 + 19.1790i 0.403090 + 1.24058i 0.922480 + 0.386046i \(0.126159\pi\)
−0.519390 + 0.854538i \(0.673841\pi\)
\(240\) 0 0
\(241\) 28.3011i 1.82303i 0.411264 + 0.911516i \(0.365087\pi\)
−0.411264 + 0.911516i \(0.634913\pi\)
\(242\) 27.2463 11.6509i 1.75146 0.748947i
\(243\) 0 0
\(244\) −0.983581 1.35378i −0.0629674 0.0866671i
\(245\) 6.76466 2.19797i 0.432178 0.140423i
\(246\) 0 0
\(247\) 3.01684 + 2.19187i 0.191957 + 0.139465i
\(248\) −29.0194 21.0838i −1.84273 1.33882i
\(249\) 0 0
\(250\) 29.3093 9.52318i 1.85369 0.602299i
\(251\) 13.7475 + 18.9219i 0.867737 + 1.19434i 0.979669 + 0.200622i \(0.0642964\pi\)
−0.111931 + 0.993716i \(0.535704\pi\)
\(252\) 0 0
\(253\) 19.1401 + 2.15500i 1.20333 + 0.135483i
\(254\) 0.277219i 0.0173943i
\(255\) 0 0
\(256\) 5.63285 + 17.3361i 0.352053 + 1.08351i
\(257\) −0.396081 0.128695i −0.0247069 0.00802775i 0.296637 0.954990i \(-0.404135\pi\)
−0.321344 + 0.946962i \(0.604135\pi\)
\(258\) 0 0
\(259\) −8.47497 + 11.6648i −0.526609 + 0.724815i
\(260\) 6.99709 21.5348i 0.433941 1.33553i
\(261\) 0 0
\(262\) 33.4873 24.3299i 2.06885 1.50311i
\(263\) 28.1176 1.73380 0.866902 0.498478i \(-0.166108\pi\)
0.866902 + 0.498478i \(0.166108\pi\)
\(264\) 0 0
\(265\) 0.486144 0.0298636
\(266\) 3.94122 2.86347i 0.241652 0.175570i
\(267\) 0 0
\(268\) 5.58276 17.1820i 0.341021 1.04956i
\(269\) 7.97137 10.9716i 0.486023 0.668953i −0.493625 0.869675i \(-0.664329\pi\)
0.979648 + 0.200721i \(0.0643286\pi\)
\(270\) 0 0
\(271\) −10.5963 3.44294i −0.643678 0.209144i −0.0310533 0.999518i \(-0.509886\pi\)
−0.612624 + 0.790374i \(0.709886\pi\)
\(272\) 16.8341 + 51.8102i 1.02072 + 3.14145i
\(273\) 0 0
\(274\) 10.0307i 0.605975i
\(275\) 9.44375 1.93442i 0.569480 0.116650i
\(276\) 0 0
\(277\) −5.75105 7.91564i −0.345547 0.475605i 0.600504 0.799622i \(-0.294967\pi\)
−0.946051 + 0.324017i \(0.894967\pi\)
\(278\) −43.5961 + 14.1652i −2.61472 + 0.849573i
\(279\) 0 0
\(280\) −14.8270 10.7724i −0.886083 0.643777i
\(281\) −9.85777 7.16209i −0.588065 0.427254i 0.253558 0.967320i \(-0.418399\pi\)
−0.841623 + 0.540066i \(0.818399\pi\)
\(282\) 0 0
\(283\) 14.6399 4.75680i 0.870253 0.282762i 0.160348 0.987060i \(-0.448738\pi\)
0.709904 + 0.704298i \(0.248738\pi\)
\(284\) 28.3303 + 38.9933i 1.68109 + 2.31383i
\(285\) 0 0
\(286\) 10.9975 24.2170i 0.650296 1.43198i
\(287\) 6.59831i 0.389486i
\(288\) 0 0
\(289\) 0.0723102 + 0.222548i 0.00425354 + 0.0130911i
\(290\) 0.360905 + 0.117265i 0.0211931 + 0.00688604i
\(291\) 0 0
\(292\) −21.9347 + 30.1905i −1.28363 + 1.76676i
\(293\) −8.41119 + 25.8870i −0.491387 + 1.51233i 0.331125 + 0.943587i \(0.392572\pi\)
−0.822512 + 0.568747i \(0.807428\pi\)
\(294\) 0 0
\(295\) 3.54295 2.57411i 0.206279 0.149870i
\(296\) −87.6328 −5.09356
\(297\) 0 0
\(298\) 30.8503 1.78711
\(299\) 13.9862 10.1616i 0.808845 0.587660i
\(300\) 0 0
\(301\) −0.948542 + 2.91931i −0.0546730 + 0.168266i
\(302\) −1.68319 + 2.31671i −0.0968564 + 0.133311i
\(303\) 0 0
\(304\) 15.6336 + 5.07966i 0.896647 + 0.291338i
\(305\) 0.142320 + 0.438016i 0.00814923 + 0.0250807i
\(306\) 0 0
\(307\) 31.0795i 1.77380i −0.461960 0.886901i \(-0.652854\pi\)
0.461960 0.886901i \(-0.347146\pi\)
\(308\) −18.5804 16.9804i −1.05871 0.967549i
\(309\) 0 0
\(310\) 9.36611 + 12.8914i 0.531960 + 0.732179i
\(311\) −5.43478 + 1.76587i −0.308178 + 0.100133i −0.459023 0.888424i \(-0.651800\pi\)
0.150845 + 0.988557i \(0.451800\pi\)
\(312\) 0 0
\(313\) 21.3843 + 15.5366i 1.20871 + 0.878180i 0.995113 0.0987412i \(-0.0314816\pi\)
0.213598 + 0.976922i \(0.431482\pi\)
\(314\) 0.186099 + 0.135209i 0.0105021 + 0.00763026i
\(315\) 0 0
\(316\) −50.0994 + 16.2783i −2.81831 + 0.915725i
\(317\) 1.16373 + 1.60174i 0.0653617 + 0.0899627i 0.840446 0.541895i \(-0.182293\pi\)
−0.775085 + 0.631857i \(0.782293\pi\)
\(318\) 0 0
\(319\) 0.294004 + 0.133514i 0.0164611 + 0.00747536i
\(320\) 31.4153i 1.75617i
\(321\) 0 0
\(322\) −6.97917 21.4797i −0.388934 1.19701i
\(323\) 4.94579 + 1.60698i 0.275191 + 0.0894150i
\(324\) 0 0
\(325\) 5.08570 6.99986i 0.282104 0.388283i
\(326\) 2.43889 7.50614i 0.135078 0.415726i
\(327\) 0 0
\(328\) 32.4443 23.5721i 1.79143 1.30155i
\(329\) −10.4792 −0.577735
\(330\) 0 0
\(331\) −4.07717 −0.224101 −0.112051 0.993702i \(-0.535742\pi\)
−0.112051 + 0.993702i \(0.535742\pi\)
\(332\) −25.3667 + 18.4300i −1.39218 + 1.01148i
\(333\) 0 0
\(334\) 3.70749 11.4105i 0.202865 0.624354i
\(335\) −2.92266 + 4.02269i −0.159682 + 0.219783i
\(336\) 0 0
\(337\) −27.1314 8.81552i −1.47794 0.480212i −0.544444 0.838797i \(-0.683259\pi\)
−0.933497 + 0.358585i \(0.883259\pi\)
\(338\) 3.44495 + 10.6025i 0.187381 + 0.576699i
\(339\) 0 0
\(340\) 31.5769i 1.71250i
\(341\) 6.69236 + 11.7921i 0.362412 + 0.638580i
\(342\) 0 0
\(343\) −10.1112 13.9169i −0.545954 0.751441i
\(344\) −17.7430 + 5.76506i −0.956640 + 0.310831i
\(345\) 0 0
\(346\) −22.7756 16.5474i −1.22442 0.889596i
\(347\) 8.36428 + 6.07700i 0.449018 + 0.326231i 0.789208 0.614126i \(-0.210491\pi\)
−0.340190 + 0.940357i \(0.610491\pi\)
\(348\) 0 0
\(349\) 17.5504 5.70248i 0.939453 0.305247i 0.201030 0.979585i \(-0.435571\pi\)
0.738423 + 0.674338i \(0.235571\pi\)
\(350\) −6.64399 9.14466i −0.355136 0.488803i
\(351\) 0 0
\(352\) 6.60597 58.6726i 0.352100 3.12726i
\(353\) 13.3918i 0.712772i 0.934339 + 0.356386i \(0.115991\pi\)
−0.934339 + 0.356386i \(0.884009\pi\)
\(354\) 0 0
\(355\) −4.09928 12.6163i −0.217567 0.669603i
\(356\) −25.5780 8.31078i −1.35563 0.440470i
\(357\) 0 0
\(358\) −15.9530 + 21.9575i −0.843144 + 1.16049i
\(359\) 1.92854 5.93545i 0.101785 0.313261i −0.887178 0.461428i \(-0.847337\pi\)
0.988962 + 0.148167i \(0.0473373\pi\)
\(360\) 0 0
\(361\) −14.1018 + 10.2456i −0.742202 + 0.539241i
\(362\) −41.7672 −2.19524
\(363\) 0 0
\(364\) −22.5922 −1.18415
\(365\) 8.30926 6.03703i 0.434927 0.315993i
\(366\) 0 0
\(367\) −2.37952 + 7.32341i −0.124210 + 0.382279i −0.993756 0.111572i \(-0.964411\pi\)
0.869546 + 0.493851i \(0.164411\pi\)
\(368\) 44.7939 61.6535i 2.33504 3.21391i
\(369\) 0 0
\(370\) 37.0240 + 12.0298i 1.92479 + 0.625401i
\(371\) −0.149889 0.461311i −0.00778185 0.0239501i
\(372\) 0 0
\(373\) 21.0593i 1.09041i 0.838304 + 0.545204i \(0.183548\pi\)
−0.838304 + 0.545204i \(0.816452\pi\)
\(374\) 4.14988 36.8582i 0.214585 1.90589i
\(375\) 0 0
\(376\) −37.4363 51.5267i −1.93063 2.65729i
\(377\) 0.275637 0.0895598i 0.0141960 0.00461256i
\(378\) 0 0
\(379\) 24.0003 + 17.4372i 1.23281 + 0.895691i 0.997098 0.0761314i \(-0.0242568\pi\)
0.235715 + 0.971822i \(0.424257\pi\)
\(380\) −7.70851 5.60056i −0.395438 0.287303i
\(381\) 0 0
\(382\) 9.51744 3.09241i 0.486955 0.158221i
\(383\) 1.56826 + 2.15852i 0.0801343 + 0.110295i 0.847202 0.531270i \(-0.178285\pi\)
−0.767068 + 0.641566i \(0.778285\pi\)
\(384\) 0 0
\(385\) 3.41936 + 6.02501i 0.174267 + 0.307063i
\(386\) 67.1784i 3.41929i
\(387\) 0 0
\(388\) 9.81361 + 30.2032i 0.498210 + 1.53333i
\(389\) 0.606242 + 0.196980i 0.0307377 + 0.00998729i 0.324346 0.945939i \(-0.394856\pi\)
−0.293608 + 0.955926i \(0.594856\pi\)
\(390\) 0 0
\(391\) 14.1709 19.5045i 0.716651 0.986385i
\(392\) 13.3288 41.0219i 0.673207 2.07192i
\(393\) 0 0
\(394\) −41.8911 + 30.4357i −2.11044 + 1.53333i
\(395\) 14.4984 0.729492
\(396\) 0 0
\(397\) −25.2145 −1.26548 −0.632741 0.774364i \(-0.718070\pi\)
−0.632741 + 0.774364i \(0.718070\pi\)
\(398\) 56.6920 41.1892i 2.84171 2.06463i
\(399\) 0 0
\(400\) 11.7861 36.2740i 0.589306 1.81370i
\(401\) 17.1458 23.5992i 0.856221 1.17849i −0.126236 0.992000i \(-0.540290\pi\)
0.982457 0.186487i \(-0.0597102\pi\)
\(402\) 0 0
\(403\) 11.5742 + 3.76069i 0.576552 + 0.187333i
\(404\) 18.9132 + 58.2088i 0.940966 + 2.89600i
\(405\) 0 0
\(406\) 0.378625i 0.0187908i
\(407\) 30.1609 + 13.6968i 1.49502 + 0.678923i
\(408\) 0 0
\(409\) 9.76208 + 13.4363i 0.482704 + 0.664384i 0.979022 0.203756i \(-0.0653150\pi\)
−0.496318 + 0.868141i \(0.665315\pi\)
\(410\) −16.9432 + 5.50520i −0.836767 + 0.271882i
\(411\) 0 0
\(412\) 14.2472 + 10.3512i 0.701910 + 0.509967i
\(413\) −3.53499 2.56832i −0.173945 0.126379i
\(414\) 0 0
\(415\) 8.20739 2.66674i 0.402885 0.130905i
\(416\) −31.1496 42.8737i −1.52723 2.10206i
\(417\) 0 0
\(418\) −8.26174 7.55033i −0.404095 0.369299i
\(419\) 9.37377i 0.457939i −0.973434 0.228969i \(-0.926464\pi\)
0.973434 0.228969i \(-0.0735356\pi\)
\(420\) 0 0
\(421\) −1.02317 3.14901i −0.0498664 0.153473i 0.923022 0.384746i \(-0.125711\pi\)
−0.972889 + 0.231273i \(0.925711\pi\)
\(422\) 58.2537 + 18.9278i 2.83575 + 0.921390i
\(423\) 0 0
\(424\) 1.73282 2.38502i 0.0841532 0.115827i
\(425\) 3.72862 11.4755i 0.180865 0.556645i
\(426\) 0 0
\(427\) 0.371761 0.270100i 0.0179908 0.0130711i
\(428\) −49.7038 −2.40252
\(429\) 0 0
\(430\) 8.28766 0.399666
\(431\) −1.72195 + 1.25107i −0.0829434 + 0.0602619i −0.628484 0.777822i \(-0.716324\pi\)
0.545541 + 0.838084i \(0.316324\pi\)
\(432\) 0 0
\(433\) −4.76068 + 14.6519i −0.228784 + 0.704124i 0.769102 + 0.639126i \(0.220704\pi\)
−0.997885 + 0.0649975i \(0.979296\pi\)
\(434\) 9.34505 12.8624i 0.448577 0.617413i
\(435\) 0 0
\(436\) −20.5652 6.68205i −0.984896 0.320012i
\(437\) −2.24803 6.91874i −0.107538 0.330968i
\(438\) 0 0
\(439\) 35.8053i 1.70889i −0.519539 0.854447i \(-0.673896\pi\)
0.519539 0.854447i \(-0.326104\pi\)
\(440\) −17.4098 + 38.3372i −0.829981 + 1.82765i
\(441\) 0 0
\(442\) −19.5682 26.9333i −0.930764 1.28109i
\(443\) −11.4104 + 3.70747i −0.542125 + 0.176147i −0.567263 0.823537i \(-0.691998\pi\)
0.0251376 + 0.999684i \(0.491998\pi\)
\(444\) 0 0
\(445\) 5.98838 + 4.35081i 0.283877 + 0.206248i
\(446\) 49.5779 + 36.0204i 2.34758 + 1.70562i
\(447\) 0 0
\(448\) −29.8105 + 9.68603i −1.40842 + 0.457622i
\(449\) 15.0088 + 20.6578i 0.708307 + 0.974901i 0.999832 + 0.0183378i \(0.00583742\pi\)
−0.291525 + 0.956563i \(0.594163\pi\)
\(450\) 0 0
\(451\) −14.8507 + 3.04196i −0.699292 + 0.143240i
\(452\) 106.310i 5.00043i
\(453\) 0 0
\(454\) 6.76595 + 20.8234i 0.317542 + 0.977292i
\(455\) 5.91366 + 1.92146i 0.277237 + 0.0900797i
\(456\) 0 0
\(457\) 0.599502 0.825144i 0.0280435 0.0385986i −0.794765 0.606917i \(-0.792406\pi\)
0.822809 + 0.568319i \(0.192406\pi\)
\(458\) 11.3160 34.8272i 0.528764 1.62737i
\(459\) 0 0
\(460\) −35.7370 + 25.9645i −1.66625 + 1.21060i
\(461\) −4.52405 −0.210706 −0.105353 0.994435i \(-0.533597\pi\)
−0.105353 + 0.994435i \(0.533597\pi\)
\(462\) 0 0
\(463\) −8.45187 −0.392792 −0.196396 0.980525i \(-0.562924\pi\)
−0.196396 + 0.980525i \(0.562924\pi\)
\(464\) 1.03358 0.750942i 0.0479829 0.0348616i
\(465\) 0 0
\(466\) −4.21012 + 12.9574i −0.195030 + 0.600241i
\(467\) 3.64591 5.01817i 0.168713 0.232213i −0.716286 0.697807i \(-0.754159\pi\)
0.884998 + 0.465594i \(0.154159\pi\)
\(468\) 0 0
\(469\) 4.71832 + 1.53308i 0.217872 + 0.0707909i
\(470\) 8.74313 + 26.9086i 0.403290 + 1.24120i
\(471\) 0 0
\(472\) 26.5569i 1.22238i
\(473\) 7.00774 + 0.789005i 0.322216 + 0.0362785i
\(474\) 0 0
\(475\) −2.14007 2.94556i −0.0981932 0.135151i
\(476\) −29.9639 + 9.73586i −1.37339 + 0.446242i
\(477\) 0 0
\(478\) −43.9497 31.9314i −2.01021 1.46051i
\(479\) 18.0462 + 13.1113i 0.824550 + 0.599071i 0.918012 0.396552i \(-0.129793\pi\)
−0.0934623 + 0.995623i \(0.529793\pi\)
\(480\) 0 0
\(481\) 28.2766 9.18763i 1.28930 0.418920i
\(482\) −44.8128 61.6795i −2.04117 2.80942i
\(483\) 0 0
\(484\) −29.6516 + 49.6468i −1.34780 + 2.25667i
\(485\) 8.74055i 0.396888i
\(486\) 0 0
\(487\) 10.5290 + 32.4051i 0.477117 + 1.46841i 0.843082 + 0.537786i \(0.180739\pi\)
−0.365965 + 0.930629i \(0.619261\pi\)
\(488\) 2.65620 + 0.863051i 0.120240 + 0.0390685i
\(489\) 0 0
\(490\) −11.2626 + 15.5016i −0.508792 + 0.700292i
\(491\) −5.81717 + 17.9034i −0.262525 + 0.807970i 0.729728 + 0.683738i \(0.239647\pi\)
−0.992253 + 0.124232i \(0.960353\pi\)
\(492\) 0 0
\(493\) 0.326981 0.237566i 0.0147265 0.0106994i
\(494\) −10.0456 −0.451972
\(495\) 0 0
\(496\) 53.6466 2.40880
\(497\) −10.7079 + 7.77976i −0.480316 + 0.348970i
\(498\) 0 0
\(499\) 2.34788 7.22603i 0.105106 0.323482i −0.884650 0.466256i \(-0.845602\pi\)
0.989755 + 0.142775i \(0.0456024\pi\)
\(500\) −35.3493 + 48.6541i −1.58087 + 2.17588i
\(501\) 0 0
\(502\) −59.9229 19.4701i −2.67449 0.868995i
\(503\) −8.18033 25.1765i −0.364743 1.12256i −0.950142 0.311818i \(-0.899062\pi\)
0.585399 0.810745i \(-0.300938\pi\)
\(504\) 0 0
\(505\) 16.8451i 0.749599i
\(506\) −45.1264 + 25.6105i −2.00611 + 1.13852i
\(507\) 0 0
\(508\) 0.317983 + 0.437666i 0.0141082 + 0.0194183i
\(509\) 12.1254 3.93980i 0.537451 0.174628i −0.0276995 0.999616i \(-0.508818\pi\)
0.565150 + 0.824988i \(0.308818\pi\)
\(510\) 0 0
\(511\) −8.29058 6.02346i −0.366754 0.266462i
\(512\) −2.69612 1.95884i −0.119153 0.0865695i
\(513\) 0 0
\(514\) 1.06700 0.346689i 0.0470633 0.0152918i
\(515\) −2.84894 3.92123i −0.125539 0.172790i
\(516\) 0 0
\(517\) 4.83111 + 23.5853i 0.212472 + 1.03728i
\(518\) 38.8418i 1.70661i
\(519\) 0 0
\(520\) 11.6783 + 35.9421i 0.512128 + 1.57617i
\(521\) −6.80629 2.21150i −0.298189 0.0968875i 0.156102 0.987741i \(-0.450107\pi\)
−0.454291 + 0.890854i \(0.650107\pi\)
\(522\) 0 0
\(523\) 18.1933 25.0410i 0.795539 1.09497i −0.197857 0.980231i \(-0.563398\pi\)
0.993396 0.114734i \(-0.0366017\pi\)
\(524\) −24.9613 + 76.8229i −1.09044 + 3.35602i
\(525\) 0 0
\(526\) −61.2796 + 44.5222i −2.67192 + 1.94126i
\(527\) 16.9715 0.739289
\(528\) 0 0
\(529\) −10.7263 −0.466360
\(530\) −1.05950 + 0.769775i −0.0460219 + 0.0334369i
\(531\) 0 0
\(532\) −2.93777 + 9.04152i −0.127368 + 0.392000i
\(533\) −7.99748 + 11.0076i −0.346409 + 0.476792i
\(534\) 0 0
\(535\) 13.0103 + 4.22731i 0.562486 + 0.182763i
\(536\) 9.31775 + 28.6771i 0.402466 + 1.23866i
\(537\) 0 0
\(538\) 36.5338i 1.57508i
\(539\) −10.9990 + 12.0354i −0.473762 + 0.518401i
\(540\) 0 0
\(541\) 25.5272 + 35.1352i 1.09750 + 1.51058i 0.838656 + 0.544661i \(0.183342\pi\)
0.258845 + 0.965919i \(0.416658\pi\)
\(542\) 28.5452 9.27490i 1.22612 0.398391i
\(543\) 0 0
\(544\) −59.7895 43.4396i −2.56346 1.86246i
\(545\) 4.81479 + 3.49815i 0.206243 + 0.149844i
\(546\) 0 0
\(547\) 7.10797 2.30952i 0.303915 0.0987480i −0.153090 0.988212i \(-0.548922\pi\)
0.457005 + 0.889464i \(0.348922\pi\)
\(548\) 11.5056 + 15.8361i 0.491496 + 0.676487i
\(549\) 0 0
\(550\) −17.5187 + 19.1694i −0.747001 + 0.817386i
\(551\) 0.121957i 0.00519556i
\(552\) 0 0
\(553\) −4.47017 13.7578i −0.190091 0.585039i
\(554\) 25.0677 + 8.14499i 1.06503 + 0.346048i
\(555\) 0 0
\(556\) 52.5801 72.3703i 2.22989 3.06919i
\(557\) −8.26967 + 25.4514i −0.350397 + 1.07841i 0.608233 + 0.793758i \(0.291879\pi\)
−0.958631 + 0.284653i \(0.908121\pi\)
\(558\) 0 0
\(559\) 5.12075 3.72044i 0.216585 0.157358i
\(560\) 27.4099 1.15828
\(561\) 0 0
\(562\) 32.8247 1.38463
\(563\) 18.8904 13.7247i 0.796136 0.578427i −0.113642 0.993522i \(-0.536252\pi\)
0.909778 + 0.415095i \(0.136252\pi\)
\(564\) 0 0
\(565\) −9.04172 + 27.8275i −0.380388 + 1.17071i
\(566\) −24.3742 + 33.5483i −1.02453 + 1.41014i
\(567\) 0 0
\(568\) −76.5070 24.8586i −3.21016 1.04305i
\(569\) −1.67819 5.16494i −0.0703534 0.216526i 0.909698 0.415271i \(-0.136313\pi\)
−0.980051 + 0.198746i \(0.936313\pi\)
\(570\) 0 0
\(571\) 10.1542i 0.424940i 0.977168 + 0.212470i \(0.0681508\pi\)
−0.977168 + 0.212470i \(0.931849\pi\)
\(572\) 10.4154 + 50.8478i 0.435492 + 2.12605i
\(573\) 0 0
\(574\) 10.4480 + 14.3804i 0.436089 + 0.600225i
\(575\) −16.0533 + 5.21603i −0.669468 + 0.217523i
\(576\) 0 0
\(577\) 17.0075 + 12.3566i 0.708029 + 0.514414i 0.882537 0.470242i \(-0.155833\pi\)
−0.174508 + 0.984656i \(0.555833\pi\)
\(578\) −0.509982 0.370524i −0.0212125 0.0154118i
\(579\) 0 0
\(580\) −0.704295 + 0.228839i −0.0292443 + 0.00950204i
\(581\) −5.06104 6.96593i −0.209967 0.288995i
\(582\) 0 0
\(583\) −0.969163 + 0.550026i −0.0401386 + 0.0227798i
\(584\) 62.2837i 2.57732i
\(585\) 0 0
\(586\) −22.6588 69.7367i −0.936028 2.88080i
\(587\) −41.4845 13.4791i −1.71225 0.556343i −0.721543 0.692370i \(-0.756567\pi\)
−0.990705 + 0.136027i \(0.956567\pi\)
\(588\) 0 0
\(589\) 3.01010 4.14305i 0.124029 0.170711i
\(590\) −3.64561 + 11.2200i −0.150087 + 0.461921i
\(591\) 0 0
\(592\) 106.032 77.0365i 4.35788 3.16618i
\(593\) −37.0300 −1.52064 −0.760319 0.649549i \(-0.774958\pi\)
−0.760319 + 0.649549i \(0.774958\pi\)
\(594\) 0 0
\(595\) 8.67130 0.355489
\(596\) −48.7056 + 35.3867i −1.99506 + 1.44949i
\(597\) 0 0
\(598\) −14.3915 + 44.2924i −0.588511 + 1.81125i
\(599\) 14.1622 19.4926i 0.578652 0.796446i −0.414895 0.909869i \(-0.636182\pi\)
0.993547 + 0.113423i \(0.0361817\pi\)
\(600\) 0 0
\(601\) −17.7661 5.77256i −0.724694 0.235467i −0.0766371 0.997059i \(-0.524418\pi\)
−0.648057 + 0.761592i \(0.724418\pi\)
\(602\) −2.55527 7.86431i −0.104145 0.320525i
\(603\) 0 0
\(604\) 5.58824i 0.227382i
\(605\) 11.9840 10.4735i 0.487219 0.425810i
\(606\) 0 0
\(607\) −14.4621 19.9054i −0.587000 0.807936i 0.407441 0.913231i \(-0.366421\pi\)
−0.994441 + 0.105296i \(0.966421\pi\)
\(608\) −21.2089 + 6.89117i −0.860133 + 0.279474i
\(609\) 0 0
\(610\) −1.00374 0.729261i −0.0406403 0.0295269i
\(611\) 17.4818 + 12.7013i 0.707238 + 0.513839i
\(612\) 0 0
\(613\) 21.4976 6.98501i 0.868282 0.282122i 0.159199 0.987247i \(-0.449109\pi\)
0.709083 + 0.705125i \(0.249109\pi\)
\(614\) 49.2122 + 67.7348i 1.98604 + 2.73355i
\(615\) 0 0
\(616\) 41.7467 + 4.70028i 1.68202 + 0.189380i
\(617\) 9.43688i 0.379915i 0.981792 + 0.189957i \(0.0608349\pi\)
−0.981792 + 0.189957i \(0.939165\pi\)
\(618\) 0 0
\(619\) −4.13730 12.7333i −0.166292 0.511794i 0.832837 0.553518i \(-0.186715\pi\)
−0.999129 + 0.0417238i \(0.986715\pi\)
\(620\) −29.5739 9.60915i −1.18772 0.385913i
\(621\) 0 0
\(622\) 9.04845 12.4541i 0.362810 0.499365i
\(623\) 2.28222 7.02394i 0.0914350 0.281408i
\(624\) 0 0
\(625\) 1.63385 1.18706i 0.0653540 0.0474824i
\(626\) −71.2061 −2.84597
\(627\) 0 0
\(628\) −0.448898 −0.0179130
\(629\) 33.5439 24.3710i 1.33748 0.971737i
\(630\) 0 0
\(631\) −3.99811 + 12.3049i −0.159162 + 0.489851i −0.998559 0.0536685i \(-0.982909\pi\)
0.839397 + 0.543519i \(0.182909\pi\)
\(632\) 51.6782 71.1290i 2.05565 2.82936i
\(633\) 0 0
\(634\) −5.07249 1.64815i −0.201454 0.0654564i
\(635\) −0.0460109 0.141607i −0.00182589 0.00561950i
\(636\) 0 0
\(637\) 14.6340i 0.579821i
\(638\) −0.852164 + 0.174554i −0.0337375 + 0.00691065i
\(639\) 0 0
\(640\) 19.4638 + 26.7896i 0.769373 + 1.05895i
\(641\) 9.50152 3.08723i 0.375288 0.121938i −0.115299 0.993331i \(-0.536783\pi\)
0.490586 + 0.871393i \(0.336783\pi\)
\(642\) 0 0
\(643\) 10.2607 + 7.45486i 0.404644 + 0.293991i 0.771430 0.636314i \(-0.219542\pi\)
−0.366786 + 0.930305i \(0.619542\pi\)
\(644\) 35.6567 + 25.9061i 1.40507 + 1.02084i
\(645\) 0 0
\(646\) −13.3234 + 4.32904i −0.524203 + 0.170324i
\(647\) −19.3401 26.6193i −0.760337 1.04651i −0.997186 0.0749678i \(-0.976115\pi\)
0.236849 0.971547i \(-0.423885\pi\)
\(648\) 0 0
\(649\) −4.15077 + 9.14018i −0.162932 + 0.358784i
\(650\) 23.3084i 0.914230i
\(651\) 0 0
\(652\) 4.75943 + 14.6480i 0.186393 + 0.573660i
\(653\) 20.3171 + 6.60143i 0.795070 + 0.258334i 0.678262 0.734820i \(-0.262734\pi\)
0.116809 + 0.993154i \(0.462734\pi\)
\(654\) 0 0
\(655\) 13.0676 17.9860i 0.510593 0.702771i
\(656\) −18.5342 + 57.0424i −0.723639 + 2.22713i
\(657\) 0 0
\(658\) 22.8383 16.5930i 0.890331 0.646863i
\(659\) −10.6922 −0.416508 −0.208254 0.978075i \(-0.566778\pi\)
−0.208254 + 0.978075i \(0.566778\pi\)
\(660\) 0 0
\(661\) 29.2602 1.13809 0.569045 0.822306i \(-0.307313\pi\)
0.569045 + 0.822306i \(0.307313\pi\)
\(662\) 8.88580 6.45591i 0.345356 0.250916i
\(663\) 0 0
\(664\) 16.1715 49.7709i 0.627577 1.93148i
\(665\) 1.53796 2.11683i 0.0596397 0.0820870i
\(666\) 0 0
\(667\) −0.537728 0.174718i −0.0208209 0.00676512i
\(668\) 7.23506 + 22.2672i 0.279933 + 0.861544i
\(669\) 0 0
\(670\) 13.3949i 0.517490i
\(671\) −0.779300 0.712195i −0.0300845 0.0274940i
\(672\) 0 0
\(673\) −24.5320 33.7655i −0.945641 1.30156i −0.953437 0.301593i \(-0.902481\pi\)
0.00779576 0.999970i \(-0.497519\pi\)
\(674\) 73.0890 23.7481i 2.81528 0.914741i
\(675\) 0 0
\(676\) −17.6003 12.7874i −0.676935 0.491822i
\(677\) 24.0662 + 17.4851i 0.924940 + 0.672008i 0.944749 0.327796i \(-0.106306\pi\)
−0.0198090 + 0.999804i \(0.506306\pi\)
\(678\) 0 0
\(679\) −8.29406 + 2.69491i −0.318297 + 0.103421i
\(680\) 30.9778 + 42.6373i 1.18794 + 1.63507i
\(681\) 0 0
\(682\) −33.2574 15.1029i −1.27349 0.578322i
\(683\) 27.9122i 1.06803i 0.845475 + 0.534015i \(0.179317\pi\)
−0.845475 + 0.534015i \(0.820683\pi\)
\(684\) 0 0
\(685\) −1.66482 5.12378i −0.0636094 0.195770i
\(686\) 44.0728 + 14.3201i 1.68271 + 0.546745i
\(687\) 0 0
\(688\) 16.4003 22.5731i 0.625255 0.860590i
\(689\) −0.309081 + 0.951252i −0.0117750 + 0.0362398i
\(690\) 0 0
\(691\) −1.03840 + 0.754441i −0.0395026 + 0.0287003i −0.607361 0.794426i \(-0.707772\pi\)
0.567859 + 0.823126i \(0.307772\pi\)
\(692\) 54.9382 2.08844
\(693\) 0 0
\(694\) −27.8516 −1.05723
\(695\) −19.9183 + 14.4715i −0.755545 + 0.548936i
\(696\) 0 0
\(697\) −5.86342 + 18.0458i −0.222093 + 0.683532i
\(698\) −29.2200 + 40.2179i −1.10599 + 1.52227i
\(699\) 0 0
\(700\) 20.9787 + 6.81639i 0.792920 + 0.257635i
\(701\) 9.82030 + 30.2238i 0.370908 + 1.14154i 0.946198 + 0.323588i \(0.104889\pi\)
−0.575290 + 0.817949i \(0.695111\pi\)
\(702\) 0 0
\(703\) 12.5112i 0.471869i
\(704\) 35.5435 + 62.6286i 1.33959 + 2.36041i
\(705\) 0 0
\(706\) −21.2049 29.1861i −0.798058 1.09843i
\(707\) −15.9847 + 5.19373i −0.601165 + 0.195330i
\(708\) 0 0
\(709\) −0.387633 0.281632i −0.0145579 0.0105769i 0.580483 0.814273i \(-0.302864\pi\)
−0.595040 + 0.803696i \(0.702864\pi\)
\(710\) 28.9110 + 21.0050i 1.08501 + 0.788305i
\(711\) 0 0
\(712\) 42.6902 13.8709i 1.59988 0.519833i
\(713\) −13.9550 19.2074i −0.522618 0.719322i
\(714\) 0 0
\(715\) 1.59829 14.1956i 0.0597727 0.530886i
\(716\) 52.9647i 1.97938i
\(717\) 0 0
\(718\) 5.19529 + 15.9895i 0.193886 + 0.596721i
\(719\) −22.0526 7.16534i −0.822425 0.267222i −0.132574 0.991173i \(-0.542324\pi\)
−0.689851 + 0.723951i \(0.742324\pi\)
\(720\) 0 0
\(721\) −2.84253 + 3.91241i −0.105862 + 0.145706i
\(722\) 14.5104 44.6585i 0.540022 1.66202i
\(723\) 0 0
\(724\) 65.9409 47.9089i 2.45068 1.78052i
\(725\) −0.282973 −0.0105094
\(726\) 0 0
\(727\) 39.4438 1.46289 0.731444 0.681902i \(-0.238847\pi\)
0.731444 + 0.681902i \(0.238847\pi\)
\(728\) 30.5055 22.1635i 1.13061 0.821435i
\(729\) 0 0
\(730\) −8.55002 + 26.3143i −0.316450 + 0.973934i
\(731\) 5.18835 7.14114i 0.191898 0.264125i
\(732\) 0 0
\(733\) 9.29818 + 3.02116i 0.343436 + 0.111589i 0.475656 0.879631i \(-0.342211\pi\)
−0.132220 + 0.991220i \(0.542211\pi\)
\(734\) −6.41017 19.7285i −0.236604 0.728191i
\(735\) 0 0
\(736\) 103.385i 3.81083i
\(737\) 1.27523 11.3262i 0.0469735 0.417207i
\(738\) 0 0
\(739\) −14.0478 19.3351i −0.516757 0.711255i 0.468284 0.883578i \(-0.344873\pi\)
−0.985040 + 0.172324i \(0.944873\pi\)
\(740\) −72.2512 + 23.4759i −2.65601 + 0.862990i
\(741\) 0 0
\(742\) 1.05712 + 0.768044i 0.0388082 + 0.0281958i
\(743\) −29.7914 21.6447i −1.09294 0.794067i −0.113046 0.993590i \(-0.536061\pi\)
−0.979893 + 0.199523i \(0.936061\pi\)
\(744\) 0 0
\(745\) 15.7587 5.12031i 0.577353 0.187593i
\(746\) −33.3459 45.8967i −1.22088 1.68040i
\(747\) 0 0
\(748\) 35.7263 + 62.9508i 1.30628 + 2.30171i
\(749\) 13.6491i 0.498728i
\(750\) 0 0
\(751\) −9.48714 29.1984i −0.346191 1.06547i −0.960943 0.276746i \(-0.910744\pi\)
0.614752 0.788720i \(-0.289256\pi\)
\(752\) 90.5924 + 29.4353i 3.30357 + 1.07339i
\(753\) 0 0
\(754\) −0.458912 + 0.631638i −0.0167126 + 0.0230029i
\(755\) −0.475281 + 1.46276i −0.0172972 + 0.0532354i
\(756\) 0 0
\(757\) −34.5971 + 25.1362i −1.25745 + 0.913592i −0.998630 0.0523331i \(-0.983334\pi\)
−0.258822 + 0.965925i \(0.583334\pi\)
\(758\) −79.9170 −2.90272
\(759\) 0 0
\(760\) 15.9029 0.576857
\(761\) −21.8523 + 15.8766i −0.792145 + 0.575527i −0.908599 0.417669i \(-0.862847\pi\)
0.116454 + 0.993196i \(0.462847\pi\)
\(762\) 0 0
\(763\) 1.83495 5.64740i 0.0664297 0.204450i
\(764\) −11.4788 + 15.7991i −0.415287 + 0.571593i
\(765\) 0 0
\(766\) −6.83574 2.22107i −0.246985 0.0802504i
\(767\) 2.78429 + 8.56916i 0.100535 + 0.309415i
\(768\) 0 0
\(769\) 48.3934i 1.74511i −0.488517 0.872555i \(-0.662462\pi\)
0.488517 0.872555i \(-0.337538\pi\)
\(770\) −16.9923 7.71661i −0.612361 0.278087i
\(771\) 0 0
\(772\) 77.0567 + 106.059i 2.77333 + 3.81716i
\(773\) −33.6456 + 10.9321i −1.21015 + 0.393201i −0.843485 0.537152i \(-0.819500\pi\)
−0.366664 + 0.930354i \(0.619500\pi\)
\(774\) 0 0
\(775\) −9.61296 6.98422i −0.345308 0.250881i
\(776\) −42.8811 31.1550i −1.53934 1.11840i
\(777\) 0 0
\(778\) −1.63315 + 0.530643i −0.0585513 + 0.0190245i
\(779\) 3.36536 + 4.63201i 0.120576 + 0.165959i
\(780\) 0 0
\(781\) 22.4463 + 20.5135i 0.803193 + 0.734031i
\(782\) 64.9467i 2.32249i
\(783\) 0 0
\(784\) 19.9344 + 61.3518i 0.711943 + 2.19113i
\(785\) 0.117502 + 0.0381788i 0.00419383 + 0.00136266i
\(786\) 0 0
\(787\) 15.1588 20.8643i 0.540353 0.743732i −0.448311 0.893878i \(-0.647974\pi\)
0.988664 + 0.150146i \(0.0479743\pi\)
\(788\) 31.2255 96.1021i 1.11236 3.42349i
\(789\) 0 0
\(790\) −31.5978 + 22.9571i −1.12420 + 0.816778i
\(791\) 29.1938 1.03801
\(792\) 0 0
\(793\) −0.947564 −0.0336490
\(794\) 54.9527 39.9254i 1.95020 1.41690i
\(795\) 0 0
\(796\) −42.2580 + 130.057i −1.49779 + 4.60974i
\(797\) −10.0269 + 13.8009i −0.355171 + 0.488851i −0.948795 0.315891i \(-0.897697\pi\)
0.593624 + 0.804742i \(0.297697\pi\)
\(798\) 0 0
\(799\) 28.6596 + 9.31205i 1.01390 + 0.329437i
\(800\) 15.9893 + 49.2101i 0.565308 + 1.73984i
\(801\) 0 0
\(802\) 78.5813i 2.77480i
\(803\) −9.73477 + 21.4364i −0.343533 + 0.756474i
\(804\) 0 0
\(805\) −7.13008 9.81371i −0.251302 0.345888i
\(806\) −31.1797 + 10.1309i −1.09826 + 0.356845i
\(807\) 0 0
\(808\) −82.6423 60.0431i −2.90735 2.11231i
\(809\) −38.7684 28.1669i −1.36302 0.990295i −0.998246 0.0592001i \(-0.981145\pi\)
−0.364778 0.931095i \(-0.618855\pi\)
\(810\) 0 0
\(811\) 45.0299 14.6311i 1.58121 0.513768i 0.618845 0.785513i \(-0.287601\pi\)
0.962369 + 0.271745i \(0.0876009\pi\)
\(812\) 0.434300 + 0.597762i 0.0152409 + 0.0209773i
\(813\) 0 0
\(814\) −87.4206 + 17.9069i −3.06409 + 0.627636i
\(815\) 4.23901i 0.148486i
\(816\) 0 0
\(817\) −0.823068 2.53314i −0.0287955 0.0886235i
\(818\) −42.5510 13.8257i −1.48776 0.483403i
\(819\) 0 0
\(820\) 20.4348 28.1261i 0.713615 0.982207i
\(821\) −5.43200 + 16.7180i −0.189578 + 0.583461i −0.999997 0.00238936i \(-0.999239\pi\)
0.810419 + 0.585851i \(0.199239\pi\)
\(822\) 0 0
\(823\) −23.1389 + 16.8114i −0.806571 + 0.586008i −0.912835 0.408330i \(-0.866111\pi\)
0.106263 + 0.994338i \(0.466111\pi\)
\(824\) −29.3924 −1.02393
\(825\) 0 0
\(826\) 11.7709 0.409562
\(827\) −13.0031 + 9.44733i −0.452163 + 0.328516i −0.790449 0.612527i \(-0.790153\pi\)
0.338286 + 0.941043i \(0.390153\pi\)
\(828\) 0 0
\(829\) 0.324003 0.997179i 0.0112531 0.0346335i −0.945272 0.326282i \(-0.894204\pi\)
0.956525 + 0.291649i \(0.0942039\pi\)
\(830\) −13.6646 + 18.8077i −0.474306 + 0.652826i
\(831\) 0 0
\(832\) 61.4712 + 19.9732i 2.13113 + 0.692446i
\(833\) 6.30639 + 19.4091i 0.218503 + 0.672484i
\(834\) 0 0
\(835\) 6.44395i 0.223002i
\(836\) 21.7040 + 2.44366i 0.750648 + 0.0845158i
\(837\) 0 0
\(838\) 14.8427 + 20.4292i 0.512733 + 0.705716i
\(839\) −19.9651 + 6.48707i −0.689273 + 0.223958i −0.632651 0.774437i \(-0.718033\pi\)
−0.0566224 + 0.998396i \(0.518033\pi\)
\(840\) 0 0
\(841\) 23.4538 + 17.0402i 0.808753 + 0.587593i
\(842\) 7.21614 + 5.24283i 0.248685 + 0.180680i
\(843\) 0 0
\(844\) −113.680 + 36.9370i −3.91304 + 1.27142i
\(845\) 3.51944 + 4.84410i 0.121073 + 0.166642i
\(846\) 0 0
\(847\) −13.6335 8.14260i −0.468451 0.279783i
\(848\) 4.40906i 0.151408i
\(849\) 0 0
\(850\) 10.0445 + 30.9138i 0.344524 + 1.06034i
\(851\) −55.1637 17.9238i −1.89099 0.614419i
\(852\) 0 0
\(853\) −3.11090 + 4.28178i −0.106515 + 0.146605i −0.858947 0.512065i \(-0.828881\pi\)
0.752432 + 0.658670i \(0.228881\pi\)
\(854\) −0.382533 + 1.17732i −0.0130900 + 0.0402869i
\(855\) 0 0
\(856\) 67.1135 48.7608i 2.29389 1.66661i
\(857\) 7.76042 0.265091 0.132545 0.991177i \(-0.457685\pi\)
0.132545 + 0.991177i \(0.457685\pi\)
\(858\) 0 0
\(859\) −48.6716 −1.66065 −0.830326 0.557278i \(-0.811846\pi\)
−0.830326 + 0.557278i \(0.811846\pi\)
\(860\) −13.0843 + 9.50632i −0.446172 + 0.324163i
\(861\) 0 0
\(862\) 1.77184 5.45317i 0.0603492 0.185736i
\(863\) 8.87079 12.2096i 0.301965 0.415619i −0.630889 0.775873i \(-0.717310\pi\)
0.932854 + 0.360253i \(0.117310\pi\)
\(864\) 0 0
\(865\) −14.3805 4.67250i −0.488951 0.158870i
\(866\) −12.8248 39.4705i −0.435803 1.34126i
\(867\) 0 0
\(868\) 31.0260i 1.05309i
\(869\) −28.9035 + 16.4035i −0.980485 + 0.556452i
\(870\) 0 0
\(871\) −6.01315 8.27639i −0.203748 0.280435i
\(872\) 34.3238 11.1525i 1.16235 0.377671i
\(873\) 0 0
\(874\) 15.8547 + 11.5191i 0.536294 + 0.389640i
\(875\) −13.3609 9.70723i −0.451679 0.328164i
\(876\) 0 0
\(877\) 21.0670 6.84508i 0.711382 0.231142i 0.0690993 0.997610i \(-0.477987\pi\)
0.642283 + 0.766468i \(0.277987\pi\)
\(878\) 56.6952 + 78.0342i 1.91337 + 2.63353i
\(879\) 0 0
\(880\) −12.6365 61.6909i −0.425977 2.07960i
\(881\) 18.8235i 0.634180i −0.948395 0.317090i \(-0.897294\pi\)
0.948395 0.317090i \(-0.102706\pi\)
\(882\) 0 0
\(883\) −11.7223 36.0776i −0.394488 1.21411i −0.929360 0.369175i \(-0.879640\pi\)
0.534872 0.844933i \(-0.320360\pi\)
\(884\) 61.7874 + 20.0760i 2.07814 + 0.675228i
\(885\) 0 0
\(886\) 18.9974 26.1477i 0.638230 0.878448i
\(887\) 8.99644 27.6882i 0.302071 0.929679i −0.678683 0.734431i \(-0.737449\pi\)
0.980754 0.195247i \(-0.0625510\pi\)
\(888\) 0 0
\(889\) −0.120187 + 0.0873211i −0.00403095 + 0.00292866i
\(890\) −19.9403 −0.668401
\(891\) 0 0
\(892\) −119.589 −4.00414
\(893\) 7.35638 5.34472i 0.246172 0.178854i
\(894\) 0 0
\(895\) −4.50465 + 13.8639i −0.150574 + 0.463419i
\(896\) 19.4200 26.7293i 0.648777 0.892965i
\(897\) 0 0
\(898\) −65.4203 21.2563i −2.18310 0.709333i
\(899\) −0.122993 0.378534i −0.00410205 0.0126248i
\(900\) 0 0
\(901\) 1.39484i 0.0464688i
\(902\) 27.5490 30.1447i 0.917280 1.00371i
\(903\) 0 0
\(904\) 104.293 + 143.548i 3.46875 + 4.77432i
\(905\) −21.3352 + 6.93222i −0.709205 + 0.230435i
\(906\) 0 0
\(907\) 15.0107 + 10.9059i 0.498423 + 0.362126i 0.808414 0.588614i \(-0.200326\pi\)
−0.309991 + 0.950739i \(0.600326\pi\)
\(908\) −34.5673 25.1146i −1.14716 0.833458i
\(909\) 0 0
\(910\) −15.9308 + 5.17622i −0.528100 + 0.171590i
\(911\) −19.5259 26.8751i −0.646922 0.890411i 0.352039 0.935985i \(-0.385488\pi\)
−0.998961 + 0.0455740i \(0.985488\pi\)
\(912\) 0 0
\(913\) −13.3449 + 14.6022i −0.441650 + 0.483264i
\(914\) 2.74759i 0.0908823i
\(915\) 0 0
\(916\) 22.0829 + 67.9643i 0.729640 + 2.24560i
\(917\) −21.0963 6.85459i −0.696660 0.226359i
\(918\) 0 0
\(919\) −10.8277 + 14.9031i −0.357173 + 0.491606i −0.949358 0.314195i \(-0.898265\pi\)
0.592185 + 0.805802i \(0.298265\pi\)
\(920\) 22.7827 70.1180i 0.751124 2.31172i
\(921\) 0 0
\(922\) 9.85973 7.16351i 0.324713 0.235918i
\(923\) 27.2929 0.898356
\(924\) 0 0
\(925\) −29.0292 −0.954476
\(926\) 18.4200 13.3829i 0.605320 0.439791i
\(927\) 0 0
\(928\) −0.535586 + 1.64836i −0.0175815 + 0.0541102i
\(929\) 17.2134 23.6922i 0.564752 0.777315i −0.427169 0.904172i \(-0.640489\pi\)
0.991921 + 0.126857i \(0.0404889\pi\)
\(930\) 0 0
\(931\) 5.85663 + 1.90293i 0.191943 + 0.0623662i
\(932\) −8.21593 25.2860i −0.269122 0.828272i
\(933\) 0 0
\(934\) 16.7097i 0.546757i
\(935\) −3.99765 19.5164i −0.130737 0.638253i
\(936\) 0 0
\(937\) −9.28756 12.7832i −0.303411 0.417610i 0.629901 0.776675i \(-0.283095\pi\)
−0.933312 + 0.359066i \(0.883095\pi\)
\(938\) −12.7106 + 4.12994i −0.415017 + 0.134847i
\(939\) 0 0
\(940\) −44.6688 32.4538i −1.45694 1.05853i
\(941\) −6.70118 4.86869i −0.218452 0.158715i 0.473177 0.880967i \(-0.343107\pi\)
−0.691630 + 0.722252i \(0.743107\pi\)
\(942\) 0 0
\(943\) 25.2445 8.20243i 0.822073 0.267108i
\(944\) 23.3457 + 32.1326i 0.759839 + 1.04583i
\(945\) 0 0
\(946\) −16.5220 + 9.37671i −0.537178 + 0.304863i
\(947\) 4.91237i 0.159631i 0.996810 + 0.0798154i \(0.0254331\pi\)
−0.996810 + 0.0798154i \(0.974567\pi\)
\(948\) 0 0
\(949\) 6.52997 + 20.0972i 0.211972 + 0.652382i
\(950\) 9.32816 + 3.03090i 0.302645 + 0.0983355i
\(951\) 0 0
\(952\) 30.9081 42.5414i 1.00174 1.37878i
\(953\) 1.81366 5.58186i 0.0587501 0.180814i −0.917375 0.398025i \(-0.869696\pi\)
0.976125 + 0.217211i \(0.0696958\pi\)
\(954\) 0 0
\(955\) 4.34837 3.15927i 0.140710 0.102232i
\(956\) 106.013 3.42872
\(957\) 0 0
\(958\) −60.0907 −1.94144
\(959\) −4.34875 + 3.15955i −0.140428 + 0.102027i
\(960\) 0 0
\(961\) −4.41495 + 13.5878i −0.142418 + 0.438317i
\(962\) −47.0782 + 64.7976i −1.51786 + 2.08916i
\(963\) 0 0
\(964\) 141.498 + 45.9756i 4.55735 + 1.48077i
\(965\) −11.1498 34.3155i −0.358924 1.10466i
\(966\) 0 0
\(967\) 17.5410i 0.564080i −0.959403 0.282040i \(-0.908989\pi\)
0.959403 0.282040i \(-0.0910110\pi\)
\(968\) −8.66725 96.1256i −0.278576 3.08959i
\(969\) 0 0
\(970\) 13.8400 + 19.0492i 0.444377 + 0.611633i
\(971\) 46.6836 15.1684i 1.49815 0.486778i 0.558672 0.829389i \(-0.311311\pi\)
0.939478 + 0.342610i \(0.111311\pi\)
\(972\) 0 0
\(973\) 19.8735 + 14.4390i 0.637117 + 0.462892i
\(974\) −74.2582 53.9518i −2.37939 1.72873i
\(975\) 0 0
\(976\) −3.97257 + 1.29077i −0.127159 + 0.0413164i
\(977\) 7.37573 + 10.1518i 0.235970 + 0.324785i 0.910536 0.413429i \(-0.135669\pi\)
−0.674566 + 0.738215i \(0.735669\pi\)
\(978\) 0 0
\(979\) −16.8608 1.89836i −0.538874 0.0606720i
\(980\) 37.3923i 1.19445i
\(981\) 0 0
\(982\) −15.6708 48.2298i −0.500076 1.53908i
\(983\) 20.0460 + 6.51333i 0.639367 + 0.207743i 0.610720 0.791847i \(-0.290880\pi\)
0.0286471 + 0.999590i \(0.490880\pi\)
\(984\) 0 0
\(985\) −16.3470 + 22.4997i −0.520858 + 0.716900i
\(986\) −0.336455 + 1.03550i −0.0107149 + 0.0329771i
\(987\) 0 0
\(988\) 15.8597 11.5227i 0.504564 0.366587i
\(989\) −12.3481 −0.392648
\(990\) 0 0
\(991\) 60.3045 1.91564 0.957818 0.287375i \(-0.0927826\pi\)
0.957818 + 0.287375i \(0.0927826\pi\)
\(992\) −58.8787 + 42.7779i −1.86940 + 1.35820i
\(993\) 0 0
\(994\) 11.0182 33.9105i 0.349475 1.07557i
\(995\) 22.1227 30.4492i 0.701336 0.965306i
\(996\) 0 0
\(997\) 53.4551 + 17.3686i 1.69294 + 0.550069i 0.987351 0.158553i \(-0.0506828\pi\)
0.705588 + 0.708622i \(0.250683\pi\)
\(998\) 6.32493 + 19.4661i 0.200212 + 0.616190i
\(999\) 0 0
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 891.2.k.a.404.1 80
3.2 odd 2 inner 891.2.k.a.404.20 80
9.2 odd 6 99.2.p.a.41.1 yes 80
9.4 even 3 99.2.p.a.74.1 yes 80
9.5 odd 6 297.2.t.a.8.10 80
9.7 even 3 297.2.t.a.206.10 80
11.7 odd 10 inner 891.2.k.a.161.20 80
33.29 even 10 inner 891.2.k.a.161.1 80
99.7 odd 30 297.2.t.a.260.10 80
99.29 even 30 99.2.p.a.95.1 yes 80
99.40 odd 30 99.2.p.a.29.1 80
99.95 even 30 297.2.t.a.62.10 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.1 80 99.40 odd 30
99.2.p.a.41.1 yes 80 9.2 odd 6
99.2.p.a.74.1 yes 80 9.4 even 3
99.2.p.a.95.1 yes 80 99.29 even 30
297.2.t.a.8.10 80 9.5 odd 6
297.2.t.a.62.10 80 99.95 even 30
297.2.t.a.206.10 80 9.7 even 3
297.2.t.a.260.10 80 99.7 odd 30
891.2.k.a.161.1 80 33.29 even 10 inner
891.2.k.a.161.20 80 11.7 odd 10 inner
891.2.k.a.404.1 80 1.1 even 1 trivial
891.2.k.a.404.20 80 3.2 odd 2 inner