Properties

Label 891.2.k.a.161.20
Level $891$
Weight $2$
Character 891.161
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 161.20
Character \(\chi\) \(=\) 891.161
Dual form 891.2.k.a.404.20

$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

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 0.949660 + 0.313284i \(0.101429\pi\)
0.591412 + 0.806370i \(0.298571\pi\)
\(3\) 0 0
\(4\) 1.62452 + 4.99975i 0.812259 + 2.49988i
\(5\) 0.850459 + 1.17056i 0.380337 + 0.523488i 0.955674 0.294428i \(-0.0951291\pi\)
−0.575337 + 0.817916i \(0.695129\pi\)
\(6\) 0 0
\(7\) 1.37298 0.446107i 0.518936 0.168613i −0.0378262 0.999284i \(-0.512043\pi\)
0.556763 + 0.830672i \(0.312043\pi\)
\(8\) −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 −0.979512 0.201388i \(-0.935455\pi\)
0.494217 + 0.869339i \(0.335455\pi\)
\(14\) 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 \(-0.532071\pi\)
0.915151 + 0.403112i \(0.132071\pi\)
\(18\) 0 0
\(19\) −1.19136 0.387096i −0.273317 0.0888059i 0.169152 0.985590i \(-0.445897\pi\)
−0.442468 + 0.896784i \(0.645897\pi\)
\(20\) −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 \(-0.0971226\pi\)
−0.948224 + 0.317601i \(0.897123\pi\)
\(30\) 0 0
\(31\) −3.30738 2.40295i −0.594023 0.431583i 0.249730 0.968316i \(-0.419658\pi\)
−0.843752 + 0.536733i \(0.819658\pi\)
\(32\) −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 −0.796711 0.604360i \(-0.793429\pi\)
0.289319 0.957233i \(-0.406571\pi\)
\(38\) −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 −0.778130 0.628103i \(-0.783832\pi\)
0.998710 0.0507726i \(-0.0161684\pi\)
\(42\) 0 0
\(43\) 2.12626i 0.324252i −0.986770 0.162126i \(-0.948165\pi\)
0.986770 0.162126i \(-0.0518351\pi\)
\(44\) 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 \(-0.222414\pi\)
0.241338 + 0.970441i \(0.422414\pi\)
\(48\) 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 \(-0.792654\pi\)
0.822365 + 0.568960i \(0.192654\pi\)
\(54\) 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 \(-0.536873\pi\)
0.490340 + 0.871531i \(0.336873\pi\)
\(60\) 0 0
\(61\) 0.187098 + 0.257518i 0.0239554 + 0.0329718i 0.820827 0.571177i \(-0.193513\pi\)
−0.796871 + 0.604149i \(0.793513\pi\)
\(62\) −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 \(-0.0168937\pi\)
−0.359034 + 0.933325i \(0.616894\pi\)
\(72\) 0 0
\(73\) −6.75113 + 2.19358i −0.790160 + 0.256739i −0.676172 0.736743i \(-0.736363\pi\)
−0.113988 + 0.993482i \(0.536363\pi\)
\(74\) 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 −0.999566 0.0294671i \(-0.990619\pi\)
0.336908 + 0.941538i \(0.390619\pi\)
\(80\) −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 \(-0.593849\pi\)
0.820224 + 0.572042i \(0.193849\pi\)
\(84\) 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 0.311350 0.950295i \(-0.399219\pi\)
−0.807572 + 0.589769i \(0.799219\pi\)
\(98\) −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 \(-0.103354\pi\)
−0.0105370 + 0.999944i \(0.503354\pi\)
\(102\) 0 0
\(103\) −1.03517 3.18593i −0.101999 0.313919i 0.887016 0.461739i \(-0.152774\pi\)
−0.989014 + 0.147820i \(0.952774\pi\)
\(104\) −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 −0.704704 0.709501i \(-0.748920\pi\)
0.987152 0.159784i \(-0.0510797\pi\)
\(108\) 0 0
\(109\) 4.11325i 0.393978i 0.980406 + 0.196989i \(0.0631163\pi\)
−0.980406 + 0.196989i \(0.936884\pi\)
\(110\) 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 −1.00000 0.000415145i \(-0.999868\pi\)
−0.809261 0.587449i \(-0.800132\pi\)
\(114\) 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 0.806325 0.591473i \(-0.201453\pi\)
−0.811692 + 0.584085i \(0.801453\pi\)
\(128\) −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 \(-0.265763\pi\)
0.671238 + 0.741242i \(0.265763\pi\)
\(132\) 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 \(-0.149154\pi\)
−0.705225 + 0.708984i \(0.749154\pi\)
\(138\) 0 0
\(139\) 16.1833 5.25827i 1.37265 0.446001i 0.472404 0.881382i \(-0.343386\pi\)
0.900246 + 0.435381i \(0.143386\pi\)
\(140\) −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 \(-0.544582\pi\)
0.898604 + 0.438760i \(0.144582\pi\)
\(150\) 0 0
\(151\) 1.01097 + 0.328485i 0.0822718 + 0.0267317i 0.349864 0.936801i \(-0.386228\pi\)
−0.267592 + 0.963532i \(0.586228\pi\)
\(152\) 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 −0.952104 0.305775i \(-0.901085\pi\)
0.949998 + 0.312256i \(0.101085\pi\)
\(158\) −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 0.491079 0.871115i \(-0.336603\pi\)
−0.676728 + 0.736233i \(0.736603\pi\)
\(164\) 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 \(-0.244875\pi\)
−0.439585 + 0.898201i \(0.644875\pi\)
\(168\) 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 0.750027 + 0.661407i \(0.230040\pi\)
−0.995550 + 0.0942343i \(0.969960\pi\)
\(174\) 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 \(-0.522879\pi\)
−0.644368 + 0.764716i \(0.722879\pi\)
\(180\) 0 0
\(181\) 12.5433 9.11327i 0.932339 0.677384i −0.0142256 0.999899i \(-0.504528\pi\)
0.946564 + 0.322515i \(0.104528\pi\)
\(182\) −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 \(-0.557090\pi\)
0.434032 + 0.900897i \(0.357090\pi\)
\(192\) 0 0
\(193\) −14.6578 20.1747i −1.05509 1.45221i −0.884311 0.466898i \(-0.845372\pi\)
−0.170779 0.985309i \(-0.554628\pi\)
\(194\) −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 \(-0.740081\pi\)
−0.684733 + 0.728794i \(0.740081\pi\)
\(198\) 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 0.0435567 + 0.999051i \(0.486131\pi\)
−0.963614 + 0.267299i \(0.913869\pi\)
\(212\) 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 0.380881 + 0.924624i \(0.375621\pi\)
−0.851619 + 0.524161i \(0.824379\pi\)
\(224\) −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 \(-0.186933\pi\)
−0.999158 + 0.0410390i \(0.986933\pi\)
\(228\) 0 0
\(229\) −10.9974 7.99008i −0.726728 0.527999i 0.161798 0.986824i \(-0.448271\pi\)
−0.888527 + 0.458825i \(0.848271\pi\)
\(230\) −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 \(-0.352976\pi\)
−0.713687 + 0.700464i \(0.752976\pi\)
\(234\) 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 0.519390 + 0.854538i \(0.326159\pi\)
−0.922480 + 0.386046i \(0.873841\pi\)
\(240\) 0 0
\(241\) 28.3011i 1.82303i −0.411264 0.911516i \(-0.634913\pi\)
0.411264 0.911516i \(-0.365087\pi\)
\(242\) −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 0.111931 + 0.993716i \(0.464296\pi\)
−0.979669 + 0.200622i \(0.935704\pi\)
\(252\) 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 \(-0.595865\pi\)
0.321344 + 0.946962i \(0.395865\pi\)
\(258\) 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 \(-0.833892\pi\)
−0.866902 + 0.498478i \(0.833892\pi\)
\(264\) 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 \(-0.335671\pi\)
−0.979648 + 0.200721i \(0.935671\pi\)
\(270\) 0 0
\(271\) −10.5963 + 3.44294i −0.643678 + 0.209144i −0.612624 0.790374i \(-0.709886\pi\)
−0.0310533 + 0.999518i \(0.509886\pi\)
\(272\) −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 −0.946051 0.324017i \(-0.894967\pi\)
0.600504 + 0.799622i \(0.294967\pi\)
\(278\) 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 \(-0.581601\pi\)
0.841623 + 0.540066i \(0.181601\pi\)
\(282\) 0 0
\(283\) 14.6399 + 4.75680i 0.870253 + 0.282762i 0.709904 0.704298i \(-0.248738\pi\)
0.160348 + 0.987060i \(0.448738\pi\)
\(284\) −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 0.822512 + 0.568747i \(0.192572\pi\)
−0.331125 + 0.943587i \(0.607428\pi\)
\(294\) 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 \(0.347146\pi\)
−0.461960 + 0.886901i \(0.652854\pi\)
\(308\) 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 \(-0.348200\pi\)
−0.150845 + 0.988557i \(0.548200\pi\)
\(312\) 0 0
\(313\) 21.3843 15.5366i 1.20871 0.878180i 0.213598 0.976922i \(-0.431482\pi\)
0.995113 + 0.0987412i \(0.0314816\pi\)
\(314\) −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 \(-0.817707\pi\)
0.775085 + 0.631857i \(0.217707\pi\)
\(318\) 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 −0.933497 0.358585i \(-0.883259\pi\)
−0.544444 + 0.838797i \(0.683259\pi\)
\(338\) −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 \(-0.789509\pi\)
0.340190 + 0.940357i \(0.389509\pi\)
\(348\) 0 0
\(349\) 17.5504 + 5.70248i 0.939453 + 0.305247i 0.738423 0.674338i \(-0.235571\pi\)
0.201030 + 0.979585i \(0.435571\pi\)
\(350\) 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 \(-0.152663\pi\)
−0.988962 + 0.148167i \(0.952663\pi\)
\(360\) 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 0.869546 0.493851i \(-0.164411\pi\)
−0.993756 + 0.111572i \(0.964411\pi\)
\(368\) −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 \(-0.816452\pi\)
0.838304 0.545204i \(-0.183548\pi\)
\(374\) −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 0.235715 0.971822i \(-0.424257\pi\)
0.997098 + 0.0761314i \(0.0242568\pi\)
\(380\) 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 \(-0.821715\pi\)
0.767068 + 0.641566i \(0.221715\pi\)
\(384\) 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 \(-0.605144\pi\)
0.293608 + 0.955926i \(0.405144\pi\)
\(390\) 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 −0.982457 0.186487i \(-0.940290\pi\)
0.126236 0.992000i \(-0.459710\pi\)
\(402\) 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 −0.496318 0.868141i \(-0.665315\pi\)
0.979022 + 0.203756i \(0.0653150\pi\)
\(410\) 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 −0.972889 0.231273i \(-0.925711\pi\)
0.923022 + 0.384746i \(0.125711\pi\)
\(422\) −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 \(-0.283676\pi\)
−0.545541 + 0.838084i \(0.683676\pi\)
\(432\) 0 0
\(433\) −4.76068 14.6519i −0.228784 0.704124i −0.997885 0.0649975i \(-0.979296\pi\)
0.769102 0.639126i \(-0.220704\pi\)
\(434\) −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 \(0.326104\pi\)
−0.519539 + 0.854447i \(0.673896\pi\)
\(440\) 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 \(-0.308002\pi\)
−0.0251376 + 0.999684i \(0.508002\pi\)
\(444\) 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 0.291525 + 0.956563i \(0.405837\pi\)
−0.999832 + 0.0183378i \(0.994163\pi\)
\(450\) 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 0.822809 0.568319i \(-0.192406\pi\)
−0.794765 + 0.606917i \(0.792406\pi\)
\(458\) −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 \(-0.466403\pi\)
0.105353 + 0.994435i \(0.466403\pi\)
\(462\) 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 \(-0.245841\pi\)
−0.884998 + 0.465594i \(0.845841\pi\)
\(468\) 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 \(-0.870207\pi\)
0.0934623 + 0.995623i \(0.470207\pi\)
\(480\) 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 −0.365965 0.930629i \(-0.619261\pi\)
0.843082 0.537786i \(-0.180739\pi\)
\(488\) −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 0.992253 + 0.124232i \(0.0396467\pi\)
−0.729728 + 0.683738i \(0.760353\pi\)
\(492\) 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 0.989755 0.142775i \(-0.0456024\pi\)
−0.884650 + 0.466256i \(0.845602\pi\)
\(500\) 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 −0.585399 0.810745i \(-0.699062\pi\)
0.950142 0.311818i \(-0.100938\pi\)
\(504\) 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 \(-0.491182\pi\)
−0.565150 + 0.824988i \(0.691182\pi\)
\(510\) 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 \(-0.549893\pi\)
0.454291 + 0.890854i \(0.349893\pi\)
\(522\) 0 0
\(523\) 18.1933 + 25.0410i 0.795539 + 1.09497i 0.993396 + 0.114734i \(0.0366017\pi\)
−0.197857 + 0.980231i \(0.563398\pi\)
\(524\) 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 0.258845 0.965919i \(-0.416658\pi\)
0.838656 0.544661i \(-0.183342\pi\)
\(542\) −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 0.457005 0.889464i \(-0.348922\pi\)
−0.153090 + 0.988212i \(0.548922\pi\)
\(548\) −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 0.958631 + 0.284653i \(0.0918785\pi\)
−0.608233 + 0.793758i \(0.708121\pi\)
\(558\) 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 \(-0.463748\pi\)
−0.909778 + 0.415095i \(0.863748\pi\)
\(564\) 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 \(-0.863687\pi\)
0.980051 + 0.198746i \(0.0636867\pi\)
\(570\) 0 0
\(571\) 10.1542i 0.424940i −0.977168 0.212470i \(-0.931849\pi\)
0.977168 0.212470i \(-0.0681508\pi\)
\(572\) −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 −0.174508 0.984656i \(-0.555833\pi\)
0.882537 + 0.470242i \(0.155833\pi\)
\(578\) 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 \(-0.243433\pi\)
0.990705 + 0.136027i \(0.0434334\pi\)
\(588\) 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 \(-0.225042\pi\)
0.760319 + 0.649549i \(0.225042\pi\)
\(594\) 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 \(-0.363818\pi\)
−0.993547 + 0.113423i \(0.963818\pi\)
\(600\) 0 0
\(601\) −17.7661 + 5.77256i −0.724694 + 0.235467i −0.648057 0.761592i \(-0.724418\pi\)
−0.0766371 + 0.997059i \(0.524418\pi\)
\(602\) 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 −0.994441 0.105296i \(-0.966421\pi\)
0.407441 + 0.913231i \(0.366421\pi\)
\(608\) 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 0.709083 0.705125i \(-0.249109\pi\)
0.159199 + 0.987247i \(0.449109\pi\)
\(614\) −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 −0.999129 0.0417238i \(-0.986715\pi\)
0.832837 + 0.553518i \(0.186715\pi\)
\(620\) 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 0.839397 0.543519i \(-0.182909\pi\)
−0.998559 + 0.0536685i \(0.982909\pi\)
\(632\) −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 \(-0.463217\pi\)
−0.490586 + 0.871393i \(0.663217\pi\)
\(642\) 0 0
\(643\) 10.2607 7.45486i 0.404644 0.293991i −0.366786 0.930305i \(-0.619542\pi\)
0.771430 + 0.636314i \(0.219542\pi\)
\(644\) −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 −0.236849 0.971547i \(-0.576115\pi\)
0.997186 0.0749678i \(-0.0238854\pi\)
\(648\) 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 \(-0.737266\pi\)
−0.116809 + 0.993154i \(0.537266\pi\)
\(654\) 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 \(-0.433222\pi\)
0.208254 + 0.978075i \(0.433222\pi\)
\(660\) 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 0.00779576 + 0.999970i \(0.497519\pi\)
−0.953437 + 0.301593i \(0.902481\pi\)
\(674\) −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 \(-0.893694\pi\)
0.0198090 + 0.999804i \(0.493694\pi\)
\(678\) 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 0.567859 0.823126i \(-0.307772\pi\)
−0.607361 + 0.794426i \(0.707772\pi\)
\(692\) −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 0.575290 + 0.817949i \(0.304889\pi\)
−0.946198 + 0.323588i \(0.895111\pi\)
\(702\) 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 −0.595040 0.803696i \(-0.702864\pi\)
0.580483 + 0.814273i \(0.302864\pi\)
\(710\) −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 \(-0.457676\pi\)
0.689851 + 0.723951i \(0.257676\pi\)
\(720\) 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 −0.132220 0.991220i \(-0.542211\pi\)
0.475656 + 0.879631i \(0.342211\pi\)
\(734\) 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 −0.985040 0.172324i \(-0.944873\pi\)
0.468284 + 0.883578i \(0.344873\pi\)
\(740\) 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 \(-0.463939\pi\)
0.979893 + 0.199523i \(0.0639392\pi\)
\(744\) 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 0.614752 + 0.788720i \(0.289256\pi\)
−0.960943 + 0.276746i \(0.910744\pi\)
\(752\) −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 −0.258822 0.965925i \(-0.583334\pi\)
−0.998630 + 0.0523331i \(0.983334\pi\)
\(758\) 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 \(-0.137153\pi\)
−0.116454 + 0.993196i \(0.537153\pi\)
\(762\) 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 \(0.337538\pi\)
−0.488517 + 0.872555i \(0.662462\pi\)
\(770\) 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 \(-0.180500\pi\)
0.366664 + 0.930354i \(0.380500\pi\)
\(774\) 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 0.988664 0.150146i \(-0.0479743\pi\)
−0.448311 + 0.893878i \(0.647974\pi\)
\(788\) −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 \(-0.102303\pi\)
−0.593624 + 0.804742i \(0.702303\pi\)
\(798\) 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 0.364778 0.931095i \(-0.381145\pi\)
0.998246 0.0592001i \(-0.0188550\pi\)
\(810\) 0 0
\(811\) 45.0299 + 14.6311i 1.58121 + 0.513768i 0.962369 0.271745i \(-0.0876009\pi\)
0.618845 + 0.785513i \(0.287601\pi\)
\(812\) −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 \(-0.000760556\pi\)
−0.810419 + 0.585851i \(0.800761\pi\)
\(822\) 0 0
\(823\) −23.1389 16.8114i −0.806571 0.586008i 0.106263 0.994338i \(-0.466111\pi\)
−0.912835 + 0.408330i \(0.866111\pi\)
\(824\) 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 \(-0.209847\pi\)
−0.338286 + 0.941043i \(0.609847\pi\)
\(828\) 0 0
\(829\) 0.324003 + 0.997179i 0.0112531 + 0.0346335i 0.956525 0.291649i \(-0.0942039\pi\)
−0.945272 + 0.326282i \(0.894204\pi\)
\(830\) 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 \(-0.281967\pi\)
0.0566224 + 0.998396i \(0.481967\pi\)
\(840\) 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 0.752432 0.658670i \(-0.228881\pi\)
−0.858947 + 0.512065i \(0.828881\pi\)
\(854\) 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 \(-0.542315\pi\)
−0.132545 + 0.991177i \(0.542315\pi\)
\(858\) 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 \(-0.282690\pi\)
−0.932854 + 0.360253i \(0.882690\pi\)
\(864\) 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 0.642283 0.766468i \(-0.277987\pi\)
0.0690993 + 0.997610i \(0.477987\pi\)
\(878\) −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 0.534872 + 0.844933i \(0.320360\pi\)
−0.929360 + 0.369175i \(0.879640\pi\)
\(884\) −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 −0.980754 0.195247i \(-0.937449\pi\)
0.678683 0.734431i \(-0.262551\pi\)
\(888\) 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 −0.309991 0.950739i \(-0.600326\pi\)
0.808414 + 0.588614i \(0.200326\pi\)
\(908\) 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 \(-0.614512\pi\)
0.998961 + 0.0455740i \(0.0145117\pi\)
\(912\) 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 0.592185 0.805802i \(-0.298265\pi\)
−0.949358 + 0.314195i \(0.898265\pi\)
\(920\) −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 \(-0.359511\pi\)
−0.991921 + 0.126857i \(0.959511\pi\)
\(930\) 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 −0.933312 0.359066i \(-0.883095\pi\)
0.629901 + 0.776675i \(0.283095\pi\)
\(938\) 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 \(-0.656893\pi\)
0.691630 + 0.722252i \(0.256893\pi\)
\(942\) 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 \(-0.130304\pi\)
−0.976125 + 0.217211i \(0.930304\pi\)
\(954\) 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 \(0.0910110\pi\)
−0.959403 + 0.282040i \(0.908989\pi\)
\(968\) 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 \(-0.688689\pi\)
−0.939478 + 0.342610i \(0.888689\pi\)
\(972\) 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 \(-0.864331\pi\)
0.674566 + 0.738215i \(0.264331\pi\)
\(978\) 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 \(-0.709120\pi\)
−0.0286471 + 0.999590i \(0.509120\pi\)
\(984\) 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 0.705588 0.708622i \(-0.250683\pi\)
0.987351 + 0.158553i \(0.0506828\pi\)
\(998\) −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.161.20 80
3.2 odd 2 inner 891.2.k.a.161.1 80
9.2 odd 6 99.2.p.a.95.1 yes 80
9.4 even 3 99.2.p.a.29.1 80
9.5 odd 6 297.2.t.a.62.10 80
9.7 even 3 297.2.t.a.260.10 80
11.8 odd 10 inner 891.2.k.a.404.1 80
33.8 even 10 inner 891.2.k.a.404.20 80
99.41 even 30 297.2.t.a.8.10 80
99.52 odd 30 297.2.t.a.206.10 80
99.74 even 30 99.2.p.a.41.1 yes 80
99.85 odd 30 99.2.p.a.74.1 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.1 80 9.4 even 3
99.2.p.a.41.1 yes 80 99.74 even 30
99.2.p.a.74.1 yes 80 99.85 odd 30
99.2.p.a.95.1 yes 80 9.2 odd 6
297.2.t.a.8.10 80 99.41 even 30
297.2.t.a.62.10 80 9.5 odd 6
297.2.t.a.206.10 80 99.52 odd 30
297.2.t.a.260.10 80 9.7 even 3
891.2.k.a.161.1 80 3.2 odd 2 inner
891.2.k.a.161.20 80 1.1 even 1 trivial
891.2.k.a.404.1 80 11.8 odd 10 inner
891.2.k.a.404.20 80 33.8 even 10 inner