Properties

Label 630.2.ce.c.107.6
Level $630$
Weight $2$
Character 630.107
Analytic conductor $5.031$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [630,2,Mod(53,630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(630, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("630.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.ce (of order \(12\), 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: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 107.6
Character \(\chi\) \(=\) 630.107
Dual form 630.2.ce.c.53.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.923861 + 2.03629i) q^{5} +(-2.56861 + 0.634242i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-0.923861 + 2.03629i) q^{5} +(-2.56861 + 0.634242i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.20602 - 0.365351i) q^{10} +(4.28438 - 2.47359i) q^{11} +(-4.34735 + 4.34735i) q^{13} +(-1.27744 - 2.31693i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-4.25035 - 1.13888i) q^{17} +(-3.22874 - 1.86412i) q^{19} +(-0.218058 - 2.22541i) q^{20} +(3.49819 + 3.49819i) q^{22} +(1.87844 - 0.503327i) q^{23} +(-3.29296 - 3.76250i) q^{25} +(-5.32440 - 3.07404i) q^{26} +(1.90736 - 1.83357i) q^{28} -3.56555 q^{29} +(-0.272207 - 0.471476i) q^{31} +(0.965926 + 0.258819i) q^{32} -4.40029i q^{34} +(1.08153 - 5.81638i) q^{35} +(-1.62530 + 0.435499i) q^{37} +(0.964938 - 3.60120i) q^{38} +(2.09314 - 0.786607i) q^{40} -0.268424i q^{41} +(-8.39666 + 8.39666i) q^{43} +(-2.47359 + 4.28438i) q^{44} +(0.972352 + 1.68416i) q^{46} +(0.240094 + 0.896043i) q^{47} +(6.19547 - 3.25824i) q^{49} +(2.78202 - 4.15456i) q^{50} +(1.59124 - 5.93859i) q^{52} +(2.06426 - 7.70392i) q^{53} +(1.07877 + 11.0095i) q^{55} +(2.26476 + 1.36780i) q^{56} +(-0.922831 - 3.44405i) q^{58} +(4.90077 + 8.48838i) q^{59} +(-5.71103 + 9.89179i) q^{61} +(0.384959 - 0.384959i) q^{62} +1.00000i q^{64} +(-4.83612 - 12.8688i) q^{65} +(-0.0109452 + 0.0408482i) q^{67} +(4.25035 - 1.13888i) q^{68} +(5.89811 - 0.460709i) q^{70} +16.3109i q^{71} +(8.42396 + 2.25719i) q^{73} +(-0.841319 - 1.45721i) q^{74} +3.72823 q^{76} +(-9.43604 + 9.07102i) q^{77} +(-6.93305 - 4.00280i) q^{79} +(1.30155 + 1.81823i) q^{80} +(0.259278 - 0.0694733i) q^{82} +(-1.30281 - 1.30281i) q^{83} +(6.24583 - 7.60279i) q^{85} +(-10.2838 - 5.93734i) q^{86} +(-4.77861 - 1.28042i) q^{88} +(-0.229324 + 0.397201i) q^{89} +(8.40936 - 13.9239i) q^{91} +(-1.37511 + 1.37511i) q^{92} +(-0.803371 + 0.463826i) q^{94} +(6.77880 - 4.85248i) q^{95} +(-10.6198 - 10.6198i) q^{97} +(4.75072 + 5.14107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85} - 16 q^{88} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.183013 + 0.683013i
\(3\) 0 0
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) −0.923861 + 2.03629i −0.413163 + 0.910657i
\(6\) 0 0
\(7\) −2.56861 + 0.634242i −0.970842 + 0.239721i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0 0
\(10\) −2.20602 0.365351i −0.697604 0.115534i
\(11\) 4.28438 2.47359i 1.29179 0.745816i 0.312819 0.949813i \(-0.398727\pi\)
0.978971 + 0.203997i \(0.0653933\pi\)
\(12\) 0 0
\(13\) −4.34735 + 4.34735i −1.20574 + 1.20574i −0.233344 + 0.972394i \(0.574967\pi\)
−0.972394 + 0.233344i \(0.925033\pi\)
\(14\) −1.27744 2.31693i −0.341409 0.619225i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −4.25035 1.13888i −1.03086 0.276219i −0.296541 0.955020i \(-0.595833\pi\)
−0.734322 + 0.678802i \(0.762500\pi\)
\(18\) 0 0
\(19\) −3.22874 1.86412i −0.740725 0.427658i 0.0816079 0.996665i \(-0.473994\pi\)
−0.822333 + 0.569007i \(0.807328\pi\)
\(20\) −0.218058 2.22541i −0.0487593 0.497617i
\(21\) 0 0
\(22\) 3.49819 + 3.49819i 0.745816 + 0.745816i
\(23\) 1.87844 0.503327i 0.391682 0.104951i −0.0576026 0.998340i \(-0.518346\pi\)
0.449284 + 0.893389i \(0.351679\pi\)
\(24\) 0 0
\(25\) −3.29296 3.76250i −0.658592 0.752500i
\(26\) −5.32440 3.07404i −1.04420 0.602869i
\(27\) 0 0
\(28\) 1.90736 1.83357i 0.360457 0.346513i
\(29\) −3.56555 −0.662105 −0.331053 0.943612i \(-0.607404\pi\)
−0.331053 + 0.943612i \(0.607404\pi\)
\(30\) 0 0
\(31\) −0.272207 0.471476i −0.0488898 0.0846796i 0.840545 0.541742i \(-0.182235\pi\)
−0.889435 + 0.457062i \(0.848902\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) 0 0
\(34\) 4.40029i 0.754644i
\(35\) 1.08153 5.81638i 0.182813 0.983148i
\(36\) 0 0
\(37\) −1.62530 + 0.435499i −0.267198 + 0.0715955i −0.389931 0.920844i \(-0.627501\pi\)
0.122732 + 0.992440i \(0.460834\pi\)
\(38\) 0.964938 3.60120i 0.156534 0.584191i
\(39\) 0 0
\(40\) 2.09314 0.786607i 0.330955 0.124373i
\(41\) 0.268424i 0.0419208i −0.999780 0.0209604i \(-0.993328\pi\)
0.999780 0.0209604i \(-0.00667239\pi\)
\(42\) 0 0
\(43\) −8.39666 + 8.39666i −1.28048 + 1.28048i −0.340084 + 0.940395i \(0.610455\pi\)
−0.940395 + 0.340084i \(0.889545\pi\)
\(44\) −2.47359 + 4.28438i −0.372908 + 0.645895i
\(45\) 0 0
\(46\) 0.972352 + 1.68416i 0.143366 + 0.248316i
\(47\) 0.240094 + 0.896043i 0.0350213 + 0.130701i 0.981223 0.192875i \(-0.0617813\pi\)
−0.946202 + 0.323577i \(0.895115\pi\)
\(48\) 0 0
\(49\) 6.19547 3.25824i 0.885068 0.465462i
\(50\) 2.78202 4.15456i 0.393436 0.587544i
\(51\) 0 0
\(52\) 1.59124 5.93859i 0.220665 0.823534i
\(53\) 2.06426 7.70392i 0.283548 1.05822i −0.666346 0.745643i \(-0.732143\pi\)
0.949894 0.312573i \(-0.101191\pi\)
\(54\) 0 0
\(55\) 1.07877 + 11.0095i 0.145462 + 1.48452i
\(56\) 2.26476 + 1.36780i 0.302641 + 0.182780i
\(57\) 0 0
\(58\) −0.922831 3.44405i −0.121174 0.452226i
\(59\) 4.90077 + 8.48838i 0.638026 + 1.10509i 0.985865 + 0.167539i \(0.0535820\pi\)
−0.347840 + 0.937554i \(0.613085\pi\)
\(60\) 0 0
\(61\) −5.71103 + 9.89179i −0.731222 + 1.26651i 0.225139 + 0.974327i \(0.427716\pi\)
−0.956361 + 0.292187i \(0.905617\pi\)
\(62\) 0.384959 0.384959i 0.0488898 0.0488898i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −4.83612 12.8688i −0.599847 1.59618i
\(66\) 0 0
\(67\) −0.0109452 + 0.0408482i −0.00133717 + 0.00499040i −0.966591 0.256323i \(-0.917489\pi\)
0.965254 + 0.261313i \(0.0841556\pi\)
\(68\) 4.25035 1.13888i 0.515431 0.138109i
\(69\) 0 0
\(70\) 5.89811 0.460709i 0.704959 0.0550652i
\(71\) 16.3109i 1.93574i 0.251443 + 0.967872i \(0.419095\pi\)
−0.251443 + 0.967872i \(0.580905\pi\)
\(72\) 0 0
\(73\) 8.42396 + 2.25719i 0.985950 + 0.264185i 0.715548 0.698563i \(-0.246177\pi\)
0.270402 + 0.962748i \(0.412844\pi\)
\(74\) −0.841319 1.45721i −0.0978013 0.169397i
\(75\) 0 0
\(76\) 3.72823 0.427658
\(77\) −9.43604 + 9.07102i −1.07534 + 1.03374i
\(78\) 0 0
\(79\) −6.93305 4.00280i −0.780029 0.450350i 0.0564118 0.998408i \(-0.482034\pi\)
−0.836440 + 0.548058i \(0.815367\pi\)
\(80\) 1.30155 + 1.81823i 0.145518 + 0.203285i
\(81\) 0 0
\(82\) 0.259278 0.0694733i 0.0286324 0.00767204i
\(83\) −1.30281 1.30281i −0.143002 0.143002i 0.631981 0.774984i \(-0.282242\pi\)
−0.774984 + 0.631981i \(0.782242\pi\)
\(84\) 0 0
\(85\) 6.24583 7.60279i 0.677455 0.824639i
\(86\) −10.2838 5.93734i −1.10893 0.640239i
\(87\) 0 0
\(88\) −4.77861 1.28042i −0.509402 0.136494i
\(89\) −0.229324 + 0.397201i −0.0243083 + 0.0421033i −0.877924 0.478801i \(-0.841072\pi\)
0.853615 + 0.520904i \(0.174405\pi\)
\(90\) 0 0
\(91\) 8.40936 13.9239i 0.881540 1.45962i
\(92\) −1.37511 + 1.37511i −0.143366 + 0.143366i
\(93\) 0 0
\(94\) −0.803371 + 0.463826i −0.0828613 + 0.0478400i
\(95\) 6.77880 4.85248i 0.695490 0.497854i
\(96\) 0 0
\(97\) −10.6198 10.6198i −1.07828 1.07828i −0.996664 0.0816181i \(-0.973991\pi\)
−0.0816181 0.996664i \(-0.526009\pi\)
\(98\) 4.75072 + 5.14107i 0.479895 + 0.519327i
\(99\) 0 0
\(100\) 4.73304 + 1.61194i 0.473304 + 0.161194i
\(101\) 4.33656 2.50371i 0.431504 0.249129i −0.268483 0.963284i \(-0.586522\pi\)
0.699987 + 0.714156i \(0.253189\pi\)
\(102\) 0 0
\(103\) 4.73881 + 17.6855i 0.466929 + 1.74260i 0.650415 + 0.759579i \(0.274595\pi\)
−0.183486 + 0.983022i \(0.558738\pi\)
\(104\) 6.14808 0.602869
\(105\) 0 0
\(106\) 7.97569 0.774667
\(107\) 1.00810 + 3.76228i 0.0974568 + 0.363714i 0.997380 0.0723338i \(-0.0230447\pi\)
−0.899924 + 0.436047i \(0.856378\pi\)
\(108\) 0 0
\(109\) 7.47396 4.31509i 0.715875 0.413311i −0.0973573 0.995249i \(-0.531039\pi\)
0.813233 + 0.581939i \(0.197706\pi\)
\(110\) −10.3552 + 3.89148i −0.987326 + 0.371039i
\(111\) 0 0
\(112\) −0.735033 + 2.54160i −0.0694541 + 0.240159i
\(113\) 13.9091 + 13.9091i 1.30845 + 1.30845i 0.922530 + 0.385925i \(0.126118\pi\)
0.385925 + 0.922530i \(0.373882\pi\)
\(114\) 0 0
\(115\) −0.710499 + 4.29005i −0.0662544 + 0.400050i
\(116\) 3.08785 1.78277i 0.286700 0.165526i
\(117\) 0 0
\(118\) −6.93073 + 6.93073i −0.638026 + 0.638026i
\(119\) 11.6398 + 0.229577i 1.06702 + 0.0210453i
\(120\) 0 0
\(121\) 6.73730 11.6693i 0.612482 1.06085i
\(122\) −11.0329 2.95625i −0.998868 0.267646i
\(123\) 0 0
\(124\) 0.471476 + 0.272207i 0.0423398 + 0.0244449i
\(125\) 10.7038 3.22940i 0.957376 0.288846i
\(126\) 0 0
\(127\) −0.200145 0.200145i −0.0177600 0.0177600i 0.698171 0.715931i \(-0.253998\pi\)
−0.715931 + 0.698171i \(0.753998\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) 0 0
\(130\) 11.1786 8.00203i 0.980432 0.701824i
\(131\) −13.5876 7.84483i −1.18716 0.685406i −0.229498 0.973309i \(-0.573709\pi\)
−0.957660 + 0.287903i \(0.907042\pi\)
\(132\) 0 0
\(133\) 9.47568 + 2.74038i 0.821645 + 0.237621i
\(134\) −0.0422892 −0.00365323
\(135\) 0 0
\(136\) 2.20015 + 3.81076i 0.188661 + 0.326770i
\(137\) 2.44530 + 0.655217i 0.208916 + 0.0559789i 0.361759 0.932272i \(-0.382176\pi\)
−0.152843 + 0.988250i \(0.548843\pi\)
\(138\) 0 0
\(139\) 2.80784i 0.238158i −0.992885 0.119079i \(-0.962006\pi\)
0.992885 0.119079i \(-0.0379942\pi\)
\(140\) 1.97155 + 5.57790i 0.166627 + 0.471419i
\(141\) 0 0
\(142\) −15.7551 + 4.22156i −1.32214 + 0.354266i
\(143\) −7.87216 + 29.3793i −0.658303 + 2.45682i
\(144\) 0 0
\(145\) 3.29407 7.26049i 0.273558 0.602951i
\(146\) 8.72113i 0.721766i
\(147\) 0 0
\(148\) 1.18980 1.18980i 0.0978013 0.0978013i
\(149\) −9.80410 + 16.9812i −0.803184 + 1.39115i 0.114327 + 0.993443i \(0.463529\pi\)
−0.917510 + 0.397712i \(0.869804\pi\)
\(150\) 0 0
\(151\) 1.25264 + 2.16964i 0.101939 + 0.176563i 0.912483 0.409114i \(-0.134162\pi\)
−0.810545 + 0.585677i \(0.800829\pi\)
\(152\) 0.964938 + 3.60120i 0.0782668 + 0.292096i
\(153\) 0 0
\(154\) −11.2042 6.76676i −0.902857 0.545281i
\(155\) 1.21154 0.118714i 0.0973136 0.00953533i
\(156\) 0 0
\(157\) −5.05560 + 18.8678i −0.403481 + 1.50581i 0.403360 + 0.915042i \(0.367842\pi\)
−0.806840 + 0.590770i \(0.798824\pi\)
\(158\) 2.07200 7.73281i 0.164839 0.615189i
\(159\) 0 0
\(160\) −1.41941 + 1.72779i −0.112214 + 0.136594i
\(161\) −4.50574 + 2.48423i −0.355102 + 0.195785i
\(162\) 0 0
\(163\) 0.00961679 + 0.0358904i 0.000753245 + 0.00281115i 0.966301 0.257413i \(-0.0828701\pi\)
−0.965548 + 0.260224i \(0.916203\pi\)
\(164\) 0.134212 + 0.232462i 0.0104802 + 0.0181522i
\(165\) 0 0
\(166\) 0.921227 1.59561i 0.0715011 0.123844i
\(167\) 9.26150 9.26150i 0.716676 0.716676i −0.251247 0.967923i \(-0.580841\pi\)
0.967923 + 0.251247i \(0.0808405\pi\)
\(168\) 0 0
\(169\) 24.7989i 1.90761i
\(170\) 8.96027 + 4.06526i 0.687221 + 0.311791i
\(171\) 0 0
\(172\) 3.07339 11.4701i 0.234344 0.874583i
\(173\) 0.706925 0.189420i 0.0537465 0.0144013i −0.231846 0.972753i \(-0.574476\pi\)
0.285592 + 0.958351i \(0.407810\pi\)
\(174\) 0 0
\(175\) 10.8447 + 7.57585i 0.819779 + 0.572680i
\(176\) 4.94718i 0.372908i
\(177\) 0 0
\(178\) −0.443021 0.118707i −0.0332058 0.00889747i
\(179\) 3.20263 + 5.54712i 0.239376 + 0.414611i 0.960535 0.278158i \(-0.0897238\pi\)
−0.721159 + 0.692769i \(0.756390\pi\)
\(180\) 0 0
\(181\) −8.70196 −0.646812 −0.323406 0.946260i \(-0.604828\pi\)
−0.323406 + 0.946260i \(0.604828\pi\)
\(182\) 15.6260 + 4.51904i 1.15827 + 0.334974i
\(183\) 0 0
\(184\) −1.68416 0.972352i −0.124158 0.0716828i
\(185\) 0.614753 3.71193i 0.0451975 0.272907i
\(186\) 0 0
\(187\) −21.0273 + 5.63424i −1.53767 + 0.412016i
\(188\) −0.655949 0.655949i −0.0478400 0.0478400i
\(189\) 0 0
\(190\) 6.44162 + 5.29190i 0.467324 + 0.383915i
\(191\) 6.91128 + 3.99023i 0.500083 + 0.288723i 0.728748 0.684782i \(-0.240103\pi\)
−0.228665 + 0.973505i \(0.573436\pi\)
\(192\) 0 0
\(193\) −18.8317 5.04593i −1.35553 0.363214i −0.493358 0.869826i \(-0.664231\pi\)
−0.862174 + 0.506612i \(0.830898\pi\)
\(194\) 7.50936 13.0066i 0.539141 0.933819i
\(195\) 0 0
\(196\) −3.73632 + 5.91945i −0.266880 + 0.422818i
\(197\) −10.0960 + 10.0960i −0.719312 + 0.719312i −0.968464 0.249153i \(-0.919848\pi\)
0.249153 + 0.968464i \(0.419848\pi\)
\(198\) 0 0
\(199\) −11.0002 + 6.35098i −0.779785 + 0.450209i −0.836354 0.548190i \(-0.815317\pi\)
0.0565691 + 0.998399i \(0.481984\pi\)
\(200\) −0.332015 + 4.98896i −0.0234770 + 0.352773i
\(201\) 0 0
\(202\) 3.54078 + 3.54078i 0.249129 + 0.249129i
\(203\) 9.15848 2.26142i 0.642800 0.158721i
\(204\) 0 0
\(205\) 0.546590 + 0.247987i 0.0381755 + 0.0173201i
\(206\) −15.8564 + 9.15468i −1.10477 + 0.637837i
\(207\) 0 0
\(208\) 1.59124 + 5.93859i 0.110333 + 0.411767i
\(209\) −18.4442 −1.27582
\(210\) 0 0
\(211\) 18.8900 1.30044 0.650220 0.759746i \(-0.274677\pi\)
0.650220 + 0.759746i \(0.274677\pi\)
\(212\) 2.06426 + 7.70392i 0.141774 + 0.529108i
\(213\) 0 0
\(214\) −3.37317 + 1.94750i −0.230585 + 0.133128i
\(215\) −9.34069 24.8554i −0.637030 1.69512i
\(216\) 0 0
\(217\) 0.998223 + 1.03839i 0.0677638 + 0.0704906i
\(218\) 6.10246 + 6.10246i 0.413311 + 0.413311i
\(219\) 0 0
\(220\) −6.43900 8.99513i −0.434117 0.606451i
\(221\) 23.4289 13.5267i 1.57600 0.909903i
\(222\) 0 0
\(223\) 2.93799 2.93799i 0.196743 0.196743i −0.601859 0.798602i \(-0.705573\pi\)
0.798602 + 0.601859i \(0.205573\pi\)
\(224\) −2.64524 0.0521732i −0.176742 0.00348597i
\(225\) 0 0
\(226\) −9.83520 + 17.0351i −0.654227 + 1.13316i
\(227\) −0.861758 0.230907i −0.0571969 0.0153259i 0.230107 0.973165i \(-0.426092\pi\)
−0.287304 + 0.957839i \(0.592759\pi\)
\(228\) 0 0
\(229\) 17.8423 + 10.3013i 1.17905 + 0.680728i 0.955796 0.294032i \(-0.0949971\pi\)
0.223259 + 0.974759i \(0.428330\pi\)
\(230\) −4.32777 + 0.424059i −0.285364 + 0.0279616i
\(231\) 0 0
\(232\) 2.52122 + 2.52122i 0.165526 + 0.165526i
\(233\) −4.65452 + 1.24718i −0.304928 + 0.0817052i −0.408038 0.912965i \(-0.633787\pi\)
0.103111 + 0.994670i \(0.467120\pi\)
\(234\) 0 0
\(235\) −2.04642 0.338918i −0.133494 0.0221086i
\(236\) −8.48838 4.90077i −0.552547 0.319013i
\(237\) 0 0
\(238\) 2.79085 + 11.3026i 0.180904 + 0.732640i
\(239\) −15.7251 −1.01717 −0.508585 0.861012i \(-0.669831\pi\)
−0.508585 + 0.861012i \(0.669831\pi\)
\(240\) 0 0
\(241\) −3.64485 6.31306i −0.234785 0.406660i 0.724425 0.689354i \(-0.242105\pi\)
−0.959210 + 0.282693i \(0.908772\pi\)
\(242\) 13.0155 + 3.48748i 0.836666 + 0.224184i
\(243\) 0 0
\(244\) 11.4221i 0.731222i
\(245\) 0.910960 + 15.6259i 0.0581991 + 0.998305i
\(246\) 0 0
\(247\) 22.1405 5.93252i 1.40876 0.377477i
\(248\) −0.140905 + 0.525863i −0.00894746 + 0.0333924i
\(249\) 0 0
\(250\) 5.88970 + 9.50323i 0.372497 + 0.601037i
\(251\) 8.22912i 0.519418i −0.965687 0.259709i \(-0.916373\pi\)
0.965687 0.259709i \(-0.0836266\pi\)
\(252\) 0 0
\(253\) 6.80294 6.80294i 0.427697 0.427697i
\(254\) 0.141524 0.245127i 0.00888001 0.0153806i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.337836 + 1.26082i 0.0210736 + 0.0786479i 0.975662 0.219281i \(-0.0703710\pi\)
−0.954588 + 0.297928i \(0.903704\pi\)
\(258\) 0 0
\(259\) 3.89855 2.14946i 0.242244 0.133561i
\(260\) 10.6226 + 8.72666i 0.658787 + 0.541205i
\(261\) 0 0
\(262\) 4.06078 15.1550i 0.250876 0.936282i
\(263\) 3.82344 14.2693i 0.235763 0.879881i −0.742040 0.670356i \(-0.766141\pi\)
0.977803 0.209525i \(-0.0671919\pi\)
\(264\) 0 0
\(265\) 13.7803 + 11.3208i 0.846520 + 0.695431i
\(266\) −0.194514 + 9.86206i −0.0119264 + 0.604682i
\(267\) 0 0
\(268\) −0.0109452 0.0408482i −0.000668587 0.00249520i
\(269\) −10.5069 18.1984i −0.640615 1.10958i −0.985296 0.170858i \(-0.945346\pi\)
0.344680 0.938720i \(-0.387987\pi\)
\(270\) 0 0
\(271\) 4.95098 8.57534i 0.300750 0.520915i −0.675556 0.737309i \(-0.736096\pi\)
0.976306 + 0.216394i \(0.0694296\pi\)
\(272\) −3.11148 + 3.11148i −0.188661 + 0.188661i
\(273\) 0 0
\(274\) 2.53156i 0.152937i
\(275\) −23.4152 7.97456i −1.41199 0.480884i
\(276\) 0 0
\(277\) 5.36596 20.0261i 0.322410 1.20325i −0.594481 0.804110i \(-0.702642\pi\)
0.916890 0.399139i \(-0.130691\pi\)
\(278\) 2.71217 0.726722i 0.162665 0.0435859i
\(279\) 0 0
\(280\) −4.87756 + 3.34804i −0.291490 + 0.200084i
\(281\) 24.6495i 1.47046i −0.677816 0.735232i \(-0.737073\pi\)
0.677816 0.735232i \(-0.262927\pi\)
\(282\) 0 0
\(283\) −5.33016 1.42821i −0.316845 0.0848985i 0.0968916 0.995295i \(-0.469110\pi\)
−0.413737 + 0.910396i \(0.635777\pi\)
\(284\) −8.15543 14.1256i −0.483936 0.838202i
\(285\) 0 0
\(286\) −30.4157 −1.79852
\(287\) 0.170246 + 0.689476i 0.0100493 + 0.0406985i
\(288\) 0 0
\(289\) 2.04603 + 1.18128i 0.120355 + 0.0694870i
\(290\) 7.86566 + 1.30267i 0.461888 + 0.0764957i
\(291\) 0 0
\(292\) −8.42396 + 2.25719i −0.492975 + 0.132092i
\(293\) −13.1648 13.1648i −0.769096 0.769096i 0.208851 0.977947i \(-0.433028\pi\)
−0.977947 + 0.208851i \(0.933028\pi\)
\(294\) 0 0
\(295\) −21.8124 + 2.13731i −1.26997 + 0.124439i
\(296\) 1.45721 + 0.841319i 0.0846984 + 0.0489007i
\(297\) 0 0
\(298\) −18.9401 5.07498i −1.09717 0.293986i
\(299\) −5.97810 + 10.3544i −0.345723 + 0.598809i
\(300\) 0 0
\(301\) 16.2422 26.8932i 0.936185 1.55010i
\(302\) −1.77151 + 1.77151i −0.101939 + 0.101939i
\(303\) 0 0
\(304\) −3.22874 + 1.86412i −0.185181 + 0.106914i
\(305\) −14.8664 20.7680i −0.851245 1.18917i
\(306\) 0 0
\(307\) 16.9282 + 16.9282i 0.966145 + 0.966145i 0.999445 0.0333006i \(-0.0106019\pi\)
−0.0333006 + 0.999445i \(0.510602\pi\)
\(308\) 3.63634 12.5738i 0.207200 0.716456i
\(309\) 0 0
\(310\) 0.428240 + 1.13954i 0.0243224 + 0.0647213i
\(311\) 23.6318 13.6438i 1.34004 0.773671i 0.353225 0.935539i \(-0.385085\pi\)
0.986812 + 0.161868i \(0.0517518\pi\)
\(312\) 0 0
\(313\) 1.92449 + 7.18228i 0.108778 + 0.405967i 0.998746 0.0500564i \(-0.0159401\pi\)
−0.889968 + 0.456023i \(0.849273\pi\)
\(314\) −19.5333 −1.10233
\(315\) 0 0
\(316\) 8.00559 0.450350
\(317\) −8.08855 30.1869i −0.454298 1.69546i −0.690143 0.723673i \(-0.742452\pi\)
0.235845 0.971791i \(-0.424214\pi\)
\(318\) 0 0
\(319\) −15.2762 + 8.81970i −0.855302 + 0.493809i
\(320\) −2.03629 0.923861i −0.113832 0.0516454i
\(321\) 0 0
\(322\) −3.56576 3.70925i −0.198712 0.206708i
\(323\) 11.6003 + 11.6003i 0.645458 + 0.645458i
\(324\) 0 0
\(325\) 30.6726 + 2.04125i 1.70141 + 0.113228i
\(326\) −0.0321784 + 0.0185782i −0.00178220 + 0.00102895i
\(327\) 0 0
\(328\) −0.189805 + 0.189805i −0.0104802 + 0.0104802i
\(329\) −1.18502 2.14930i −0.0653320 0.118495i
\(330\) 0 0
\(331\) −5.38534 + 9.32768i −0.296005 + 0.512696i −0.975218 0.221245i \(-0.928988\pi\)
0.679213 + 0.733941i \(0.262321\pi\)
\(332\) 1.77967 + 0.476862i 0.0976723 + 0.0261712i
\(333\) 0 0
\(334\) 11.3430 + 6.54887i 0.620660 + 0.358338i
\(335\) −0.0730669 0.0600258i −0.00399207 0.00327956i
\(336\) 0 0
\(337\) −21.8140 21.8140i −1.18828 1.18828i −0.977542 0.210740i \(-0.932413\pi\)
−0.210740 0.977542i \(-0.567587\pi\)
\(338\) 23.9539 6.41843i 1.30292 0.349117i
\(339\) 0 0
\(340\) −1.60765 + 9.70712i −0.0871870 + 0.526443i
\(341\) −2.33248 1.34666i −0.126311 0.0729256i
\(342\) 0 0
\(343\) −13.8472 + 12.2986i −0.747680 + 0.664060i
\(344\) 11.8747 0.640239
\(345\) 0 0
\(346\) 0.365931 + 0.633812i 0.0196726 + 0.0340739i
\(347\) 5.94688 + 1.59346i 0.319245 + 0.0855415i 0.414883 0.909875i \(-0.363822\pi\)
−0.0956379 + 0.995416i \(0.530489\pi\)
\(348\) 0 0
\(349\) 0.197242i 0.0105581i 0.999986 + 0.00527907i \(0.00168039\pi\)
−0.999986 + 0.00527907i \(0.998320\pi\)
\(350\) −4.51090 + 12.4359i −0.241118 + 0.664727i
\(351\) 0 0
\(352\) 4.77861 1.28042i 0.254701 0.0682469i
\(353\) 2.64401 9.86759i 0.140727 0.525199i −0.859182 0.511670i \(-0.829027\pi\)
0.999908 0.0135287i \(-0.00430643\pi\)
\(354\) 0 0
\(355\) −33.2137 15.0690i −1.76280 0.799778i
\(356\) 0.458649i 0.0243083i
\(357\) 0 0
\(358\) −4.52921 + 4.52921i −0.239376 + 0.239376i
\(359\) 7.63203 13.2191i 0.402803 0.697676i −0.591260 0.806481i \(-0.701369\pi\)
0.994063 + 0.108805i \(0.0347026\pi\)
\(360\) 0 0
\(361\) −2.55014 4.41697i −0.134218 0.232472i
\(362\) −2.25223 8.40545i −0.118375 0.441781i
\(363\) 0 0
\(364\) −0.320765 + 16.2631i −0.0168127 + 0.852420i
\(365\) −12.3789 + 15.0683i −0.647940 + 0.788711i
\(366\) 0 0
\(367\) −6.14181 + 22.9216i −0.320600 + 1.19650i 0.598062 + 0.801450i \(0.295938\pi\)
−0.918662 + 0.395045i \(0.870729\pi\)
\(368\) 0.503327 1.87844i 0.0262377 0.0979205i
\(369\) 0 0
\(370\) 3.74456 0.366913i 0.194670 0.0190749i
\(371\) −0.416117 + 21.0976i −0.0216037 + 1.09533i
\(372\) 0 0
\(373\) 4.81825 + 17.9820i 0.249480 + 0.931071i 0.971079 + 0.238760i \(0.0767408\pi\)
−0.721599 + 0.692311i \(0.756593\pi\)
\(374\) −10.8845 18.8525i −0.562825 0.974841i
\(375\) 0 0
\(376\) 0.463826 0.803371i 0.0239200 0.0414307i
\(377\) 15.5007 15.5007i 0.798326 0.798326i
\(378\) 0 0
\(379\) 34.8805i 1.79169i 0.444367 + 0.895845i \(0.353429\pi\)
−0.444367 + 0.895845i \(0.646571\pi\)
\(380\) −3.44437 + 7.59177i −0.176692 + 0.389449i
\(381\) 0 0
\(382\) −2.06549 + 7.70853i −0.105680 + 0.394403i
\(383\) −30.0303 + 8.04661i −1.53448 + 0.411162i −0.924477 0.381238i \(-0.875498\pi\)
−0.610002 + 0.792400i \(0.708831\pi\)
\(384\) 0 0
\(385\) −9.75364 27.5949i −0.497091 1.40637i
\(386\) 19.4960i 0.992319i
\(387\) 0 0
\(388\) 14.5070 + 3.88713i 0.736480 + 0.197339i
\(389\) 9.96369 + 17.2576i 0.505179 + 0.874996i 0.999982 + 0.00599092i \(0.00190698\pi\)
−0.494803 + 0.869005i \(0.664760\pi\)
\(390\) 0 0
\(391\) −8.55726 −0.432759
\(392\) −6.68478 2.07694i −0.337633 0.104901i
\(393\) 0 0
\(394\) −12.3651 7.13897i −0.622942 0.359656i
\(395\) 14.5560 10.4197i 0.732393 0.524271i
\(396\) 0 0
\(397\) −12.5094 + 3.35189i −0.627831 + 0.168227i −0.558685 0.829380i \(-0.688694\pi\)
−0.0691456 + 0.997607i \(0.522027\pi\)
\(398\) −8.98164 8.98164i −0.450209 0.450209i
\(399\) 0 0
\(400\) −4.90490 + 0.970538i −0.245245 + 0.0485269i
\(401\) −1.57729 0.910650i −0.0787662 0.0454757i 0.460100 0.887867i \(-0.347814\pi\)
−0.538866 + 0.842392i \(0.681147\pi\)
\(402\) 0 0
\(403\) 3.23305 + 0.866294i 0.161050 + 0.0431532i
\(404\) −2.50371 + 4.33656i −0.124564 + 0.215752i
\(405\) 0 0
\(406\) 4.55475 + 8.26112i 0.226049 + 0.409992i
\(407\) −5.88618 + 5.88618i −0.291767 + 0.291767i
\(408\) 0 0
\(409\) −17.8771 + 10.3214i −0.883967 + 0.510359i −0.871964 0.489569i \(-0.837154\pi\)
−0.0120026 + 0.999928i \(0.503821\pi\)
\(410\) −0.0980689 + 0.592149i −0.00484328 + 0.0292441i
\(411\) 0 0
\(412\) −12.9467 12.9467i −0.637837 0.637837i
\(413\) −17.9718 18.6950i −0.884336 0.919922i
\(414\) 0 0
\(415\) 3.85652 1.44929i 0.189309 0.0711427i
\(416\) −5.32440 + 3.07404i −0.261050 + 0.150717i
\(417\) 0 0
\(418\) −4.77372 17.8158i −0.233490 0.871398i
\(419\) 12.8948 0.629954 0.314977 0.949099i \(-0.398003\pi\)
0.314977 + 0.949099i \(0.398003\pi\)
\(420\) 0 0
\(421\) −16.9311 −0.825170 −0.412585 0.910919i \(-0.635374\pi\)
−0.412585 + 0.910919i \(0.635374\pi\)
\(422\) 4.88909 + 18.2463i 0.237997 + 0.888217i
\(423\) 0 0
\(424\) −6.90715 + 3.98784i −0.335441 + 0.193667i
\(425\) 9.71122 + 19.7422i 0.471063 + 0.957639i
\(426\) 0 0
\(427\) 8.39559 29.0303i 0.406291 1.40487i
\(428\) −2.75418 2.75418i −0.133128 0.133128i
\(429\) 0 0
\(430\) 21.5909 15.4555i 1.04121 0.745329i
\(431\) 25.7429 14.8627i 1.23999 0.715910i 0.270901 0.962607i \(-0.412679\pi\)
0.969093 + 0.246697i \(0.0793452\pi\)
\(432\) 0 0
\(433\) 20.0190 20.0190i 0.962052 0.962052i −0.0372534 0.999306i \(-0.511861\pi\)
0.999306 + 0.0372534i \(0.0118609\pi\)
\(434\) −0.744650 + 1.23296i −0.0357444 + 0.0591842i
\(435\) 0 0
\(436\) −4.31509 + 7.47396i −0.206655 + 0.357938i
\(437\) −7.00326 1.87652i −0.335012 0.0897661i
\(438\) 0 0
\(439\) −5.54137 3.19931i −0.264475 0.152695i 0.361899 0.932217i \(-0.382128\pi\)
−0.626374 + 0.779522i \(0.715462\pi\)
\(440\) 7.02209 8.54771i 0.334765 0.407496i
\(441\) 0 0
\(442\) 19.1296 + 19.1296i 0.909903 + 0.909903i
\(443\) 0.328032 0.0878959i 0.0155853 0.00417606i −0.251018 0.967982i \(-0.580765\pi\)
0.266603 + 0.963806i \(0.414099\pi\)
\(444\) 0 0
\(445\) −0.596954 0.833930i −0.0282983 0.0395321i
\(446\) 3.59829 + 2.07747i 0.170384 + 0.0983713i
\(447\) 0 0
\(448\) −0.634242 2.56861i −0.0299651 0.121355i
\(449\) −11.8831 −0.560800 −0.280400 0.959883i \(-0.590467\pi\)
−0.280400 + 0.959883i \(0.590467\pi\)
\(450\) 0 0
\(451\) −0.663971 1.15003i −0.0312652 0.0541529i
\(452\) −19.0001 5.09107i −0.893691 0.239464i
\(453\) 0 0
\(454\) 0.892157i 0.0418710i
\(455\) 20.5840 + 29.9877i 0.964995 + 1.40584i
\(456\) 0 0
\(457\) 19.4777 5.21904i 0.911129 0.244136i 0.227340 0.973816i \(-0.426997\pi\)
0.683790 + 0.729679i \(0.260331\pi\)
\(458\) −5.33233 + 19.9005i −0.249164 + 0.929891i
\(459\) 0 0
\(460\) −1.52972 4.07055i −0.0713234 0.189790i
\(461\) 19.5952i 0.912638i 0.889816 + 0.456319i \(0.150832\pi\)
−0.889816 + 0.456319i \(0.849168\pi\)
\(462\) 0 0
\(463\) 19.2239 19.2239i 0.893411 0.893411i −0.101432 0.994843i \(-0.532342\pi\)
0.994843 + 0.101432i \(0.0323423\pi\)
\(464\) −1.78277 + 3.08785i −0.0827632 + 0.143350i
\(465\) 0 0
\(466\) −2.40936 4.17313i −0.111611 0.193316i
\(467\) 7.83232 + 29.2306i 0.362437 + 1.35263i 0.870863 + 0.491526i \(0.163561\pi\)
−0.508426 + 0.861105i \(0.669773\pi\)
\(468\) 0 0
\(469\) 0.00220636 0.111865i 0.000101880 0.00516544i
\(470\) −0.202282 2.06441i −0.00933058 0.0952240i
\(471\) 0 0
\(472\) 2.53682 9.46756i 0.116767 0.435780i
\(473\) −15.2046 + 56.7444i −0.699109 + 2.60911i
\(474\) 0 0
\(475\) 3.61839 + 18.2866i 0.166023 + 0.839048i
\(476\) −10.1952 + 5.62109i −0.467294 + 0.257642i
\(477\) 0 0
\(478\) −4.06995 15.1892i −0.186155 0.694740i
\(479\) −0.818104 1.41700i −0.0373801 0.0647443i 0.846730 0.532023i \(-0.178568\pi\)
−0.884110 + 0.467278i \(0.845235\pi\)
\(480\) 0 0
\(481\) 5.17250 8.95903i 0.235846 0.408497i
\(482\) 5.15460 5.15460i 0.234785 0.234785i
\(483\) 0 0
\(484\) 13.4746i 0.612482i
\(485\) 31.4364 11.8138i 1.42745 0.536438i
\(486\) 0 0
\(487\) −1.86735 + 6.96906i −0.0846178 + 0.315798i −0.995242 0.0974385i \(-0.968935\pi\)
0.910624 + 0.413237i \(0.135602\pi\)
\(488\) 11.0329 2.95625i 0.499434 0.133823i
\(489\) 0 0
\(490\) −14.8577 + 4.92421i −0.671204 + 0.222453i
\(491\) 23.4235i 1.05709i 0.848907 + 0.528543i \(0.177261\pi\)
−0.848907 + 0.528543i \(0.822739\pi\)
\(492\) 0 0
\(493\) 15.1548 + 4.06073i 0.682540 + 0.182886i
\(494\) 11.4607 + 19.8506i 0.515643 + 0.893120i
\(495\) 0 0
\(496\) −0.544414 −0.0244449
\(497\) −10.3450 41.8962i −0.464039 1.87930i
\(498\) 0 0
\(499\) 25.5933 + 14.7763i 1.14571 + 0.661477i 0.947838 0.318751i \(-0.103263\pi\)
0.197873 + 0.980228i \(0.436597\pi\)
\(500\) −7.65505 + 8.14863i −0.342344 + 0.364418i
\(501\) 0 0
\(502\) 7.94872 2.12985i 0.354769 0.0950600i
\(503\) −16.6368 16.6368i −0.741797 0.741797i 0.231127 0.972924i \(-0.425759\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(504\) 0 0
\(505\) 1.09191 + 11.1436i 0.0485893 + 0.495883i
\(506\) 8.33186 + 4.81040i 0.370396 + 0.213848i
\(507\) 0 0
\(508\) 0.273404 + 0.0732583i 0.0121303 + 0.00325031i
\(509\) 4.84247 8.38740i 0.214639 0.371765i −0.738522 0.674229i \(-0.764476\pi\)
0.953161 + 0.302464i \(0.0978093\pi\)
\(510\) 0 0
\(511\) −23.0694 0.455009i −1.02053 0.0201284i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) −1.13042 + 0.652649i −0.0498608 + 0.0287871i
\(515\) −40.3908 6.68933i −1.77983 0.294767i
\(516\) 0 0
\(517\) 3.24510 + 3.24510i 0.142719 + 0.142719i
\(518\) 3.08524 + 3.20939i 0.135558 + 0.141013i
\(519\) 0 0
\(520\) −5.67997 + 12.5193i −0.249083 + 0.549007i
\(521\) −18.3916 + 10.6184i −0.805750 + 0.465200i −0.845478 0.534011i \(-0.820684\pi\)
0.0397281 + 0.999211i \(0.487351\pi\)
\(522\) 0 0
\(523\) 0.0569475 + 0.212531i 0.00249014 + 0.00929332i 0.967160 0.254169i \(-0.0818021\pi\)
−0.964670 + 0.263463i \(0.915135\pi\)
\(524\) 15.6897 0.685406
\(525\) 0 0
\(526\) 14.7726 0.644118
\(527\) 0.620022 + 2.31395i 0.0270086 + 0.100797i
\(528\) 0 0
\(529\) −16.6434 + 9.60906i −0.723625 + 0.417785i
\(530\) −7.36843 + 16.2408i −0.320064 + 0.705456i
\(531\) 0 0
\(532\) −9.57636 + 2.36460i −0.415188 + 0.102519i
\(533\) 1.16693 + 1.16693i 0.0505455 + 0.0505455i
\(534\) 0 0
\(535\) −8.59245 1.42304i −0.371484 0.0615234i
\(536\) 0.0366235 0.0211446i 0.00158189 0.000913307i
\(537\) 0 0
\(538\) 14.8590 14.8590i 0.640615 0.640615i
\(539\) 18.4842 29.2846i 0.796173 1.26138i
\(540\) 0 0
\(541\) −21.0652 + 36.4861i −0.905666 + 1.56866i −0.0856442 + 0.996326i \(0.527295\pi\)
−0.820021 + 0.572333i \(0.806038\pi\)
\(542\) 9.56455 + 2.56281i 0.410833 + 0.110082i
\(543\) 0 0
\(544\) −3.81076 2.20015i −0.163385 0.0943305i
\(545\) 1.88188 + 19.2057i 0.0806110 + 0.822682i
\(546\) 0 0
\(547\) 10.6450 + 10.6450i 0.455147 + 0.455147i 0.897059 0.441911i \(-0.145699\pi\)
−0.441911 + 0.897059i \(0.645699\pi\)
\(548\) −2.44530 + 0.655217i −0.104458 + 0.0279895i
\(549\) 0 0
\(550\) 1.64254 24.6813i 0.0700380 1.05241i
\(551\) 11.5122 + 6.64660i 0.490438 + 0.283154i
\(552\) 0 0
\(553\) 20.3470 + 5.88438i 0.865243 + 0.250229i
\(554\) 20.7325 0.880839
\(555\) 0 0
\(556\) 1.40392 + 2.43166i 0.0595395 + 0.103125i
\(557\) 30.4049 + 8.14696i 1.28830 + 0.345198i 0.837013 0.547183i \(-0.184300\pi\)
0.451283 + 0.892381i \(0.350967\pi\)
\(558\) 0 0
\(559\) 73.0065i 3.08784i
\(560\) −4.49637 3.84483i −0.190006 0.162474i
\(561\) 0 0
\(562\) 23.8096 6.37975i 1.00435 0.269114i
\(563\) 0.0168462 0.0628710i 0.000709984 0.00264969i −0.965570 0.260144i \(-0.916230\pi\)
0.966280 + 0.257494i \(0.0828967\pi\)
\(564\) 0 0
\(565\) −41.1730 + 15.4729i −1.73216 + 0.650948i
\(566\) 5.51819i 0.231947i
\(567\) 0 0
\(568\) 11.5335 11.5335i 0.483936 0.483936i
\(569\) −13.5754 + 23.5133i −0.569110 + 0.985728i 0.427544 + 0.903995i \(0.359379\pi\)
−0.996654 + 0.0817335i \(0.973954\pi\)
\(570\) 0 0
\(571\) 13.3600 + 23.1403i 0.559101 + 0.968391i 0.997572 + 0.0696454i \(0.0221868\pi\)
−0.438471 + 0.898745i \(0.644480\pi\)
\(572\) −7.87216 29.3793i −0.329151 1.22841i
\(573\) 0 0
\(574\) −0.621920 + 0.342894i −0.0259584 + 0.0143121i
\(575\) −8.07940 5.41020i −0.336934 0.225621i
\(576\) 0 0
\(577\) 3.91412 14.6077i 0.162947 0.608127i −0.835346 0.549724i \(-0.814733\pi\)
0.998293 0.0584023i \(-0.0186006\pi\)
\(578\) −0.611475 + 2.28205i −0.0254340 + 0.0949210i
\(579\) 0 0
\(580\) 0.777496 + 7.93480i 0.0322838 + 0.329475i
\(581\) 4.17271 + 2.52011i 0.173113 + 0.104552i
\(582\) 0 0
\(583\) −10.2123 38.1127i −0.422949 1.57847i
\(584\) −4.36056 7.55272i −0.180441 0.312534i
\(585\) 0 0
\(586\) 9.30892 16.1235i 0.384548 0.666057i
\(587\) −0.814359 + 0.814359i −0.0336122 + 0.0336122i −0.723713 0.690101i \(-0.757566\pi\)
0.690101 + 0.723713i \(0.257566\pi\)
\(588\) 0 0
\(589\) 2.02970i 0.0836324i
\(590\) −7.70995 20.5160i −0.317414 0.844631i
\(591\) 0 0
\(592\) −0.435499 + 1.62530i −0.0178989 + 0.0667996i
\(593\) −0.591195 + 0.158410i −0.0242775 + 0.00650513i −0.270937 0.962597i \(-0.587334\pi\)
0.246660 + 0.969102i \(0.420667\pi\)
\(594\) 0 0
\(595\) −11.2211 + 23.4899i −0.460018 + 0.962994i
\(596\) 19.6082i 0.803184i
\(597\) 0 0
\(598\) −11.5488 3.09449i −0.472266 0.126543i
\(599\) 6.50281 + 11.2632i 0.265698 + 0.460202i 0.967746 0.251927i \(-0.0810644\pi\)
−0.702049 + 0.712129i \(0.747731\pi\)
\(600\) 0 0
\(601\) −12.4846 −0.509258 −0.254629 0.967039i \(-0.581953\pi\)
−0.254629 + 0.967039i \(0.581953\pi\)
\(602\) 30.1807 + 8.72828i 1.23007 + 0.355738i
\(603\) 0 0
\(604\) −2.16964 1.25264i −0.0882816 0.0509694i
\(605\) 17.5379 + 24.5000i 0.713015 + 0.996065i
\(606\) 0 0
\(607\) 8.60280 2.30511i 0.349177 0.0935616i −0.0799678 0.996797i \(-0.525482\pi\)
0.429145 + 0.903236i \(0.358815\pi\)
\(608\) −2.63626 2.63626i −0.106914 0.106914i
\(609\) 0 0
\(610\) 16.2126 19.7349i 0.656429 0.799045i
\(611\) −4.93919 2.85164i −0.199818 0.115365i
\(612\) 0 0
\(613\) −27.7729 7.44173i −1.12174 0.300569i −0.350151 0.936693i \(-0.613870\pi\)
−0.771586 + 0.636125i \(0.780536\pi\)
\(614\) −11.9701 + 20.7328i −0.483072 + 0.836706i
\(615\) 0 0
\(616\) 13.0865 + 0.258110i 0.527269 + 0.0103996i
\(617\) 3.97067 3.97067i 0.159853 0.159853i −0.622649 0.782502i \(-0.713943\pi\)
0.782502 + 0.622649i \(0.213943\pi\)
\(618\) 0 0
\(619\) 29.1348 16.8210i 1.17103 0.676092i 0.217104 0.976148i \(-0.430339\pi\)
0.953921 + 0.300057i \(0.0970056\pi\)
\(620\) −0.989871 + 0.708581i −0.0397542 + 0.0284573i
\(621\) 0 0
\(622\) 19.2953 + 19.2953i 0.773671 + 0.773671i
\(623\) 0.337122 1.16570i 0.0135065 0.0467028i
\(624\) 0 0
\(625\) −3.31282 + 24.7795i −0.132513 + 0.991181i
\(626\) −6.43946 + 3.71782i −0.257373 + 0.148594i
\(627\) 0 0
\(628\) −5.05560 18.8678i −0.201740 0.752906i
\(629\) 7.40409 0.295221
\(630\) 0 0
\(631\) −15.9081 −0.633292 −0.316646 0.948544i \(-0.602557\pi\)
−0.316646 + 0.948544i \(0.602557\pi\)
\(632\) 2.07200 + 7.73281i 0.0824197 + 0.307595i
\(633\) 0 0
\(634\) 27.0648 15.6259i 1.07488 0.620583i
\(635\) 0.592460 0.222648i 0.0235111 0.00883550i
\(636\) 0 0
\(637\) −12.7692 + 41.0986i −0.505934 + 1.62839i
\(638\) −12.4729 12.4729i −0.493809 0.493809i
\(639\) 0 0
\(640\) 0.365351 2.20602i 0.0144417 0.0872005i
\(641\) −31.4224 + 18.1417i −1.24111 + 0.716555i −0.969320 0.245802i \(-0.920949\pi\)
−0.271789 + 0.962357i \(0.587615\pi\)
\(642\) 0 0
\(643\) 2.60079 2.60079i 0.102565 0.102565i −0.653962 0.756527i \(-0.726894\pi\)
0.756527 + 0.653962i \(0.226894\pi\)
\(644\) 2.65997 4.40428i 0.104818 0.173553i
\(645\) 0 0
\(646\) −8.20266 + 14.2074i −0.322729 + 0.558983i
\(647\) −7.66073 2.05269i −0.301174 0.0806994i 0.105067 0.994465i \(-0.466494\pi\)
−0.406242 + 0.913766i \(0.633161\pi\)
\(648\) 0 0
\(649\) 41.9936 + 24.2450i 1.64839 + 0.951699i
\(650\) 5.96694 + 30.1557i 0.234043 + 1.18281i
\(651\) 0 0
\(652\) −0.0262736 0.0262736i −0.00102895 0.00102895i
\(653\) 45.9484 12.3118i 1.79810 0.481799i 0.804421 0.594060i \(-0.202476\pi\)
0.993679 + 0.112260i \(0.0358090\pi\)
\(654\) 0 0
\(655\) 28.5275 20.4209i 1.11466 0.797909i
\(656\) −0.232462 0.134212i −0.00907612 0.00524010i
\(657\) 0 0
\(658\) 1.76936 1.70092i 0.0689770 0.0663087i
\(659\) 40.4379 1.57524 0.787618 0.616164i \(-0.211314\pi\)
0.787618 + 0.616164i \(0.211314\pi\)
\(660\) 0 0
\(661\) 15.3620 + 26.6078i 0.597513 + 1.03492i 0.993187 + 0.116532i \(0.0371777\pi\)
−0.395674 + 0.918391i \(0.629489\pi\)
\(662\) −10.4037 2.78766i −0.404350 0.108345i
\(663\) 0 0
\(664\) 1.84245i 0.0715011i
\(665\) −14.3344 + 16.7635i −0.555865 + 0.650061i
\(666\) 0 0
\(667\) −6.69767 + 1.79463i −0.259335 + 0.0694885i
\(668\) −3.38994 + 12.6514i −0.131161 + 0.489499i
\(669\) 0 0
\(670\) 0.0390693 0.0861130i 0.00150938 0.00332684i
\(671\) 56.5070i 2.18143i
\(672\) 0 0
\(673\) 2.13524 2.13524i 0.0823073 0.0823073i −0.664755 0.747062i \(-0.731464\pi\)
0.747062 + 0.664755i \(0.231464\pi\)
\(674\) 15.4248 26.7165i 0.594141 1.02908i
\(675\) 0 0
\(676\) 12.3995 + 21.4765i 0.476902 + 0.826019i
\(677\) 0.625198 + 2.33327i 0.0240283 + 0.0896749i 0.976899 0.213703i \(-0.0685523\pi\)
−0.952870 + 0.303378i \(0.901886\pi\)
\(678\) 0 0
\(679\) 34.0137 + 20.5426i 1.30533 + 0.788354i
\(680\) −9.79245 + 0.959519i −0.375523 + 0.0367959i
\(681\) 0 0
\(682\) 0.697081 2.60154i 0.0266926 0.0996182i
\(683\) −5.33754 + 19.9200i −0.204235 + 0.762216i 0.785446 + 0.618930i \(0.212434\pi\)
−0.989681 + 0.143286i \(0.954233\pi\)
\(684\) 0 0
\(685\) −3.59333 + 4.37402i −0.137294 + 0.167123i
\(686\) −15.4634 10.1923i −0.590396 0.389143i
\(687\) 0 0
\(688\) 3.07339 + 11.4701i 0.117172 + 0.437292i
\(689\) 24.5176 + 42.4657i 0.934046 + 1.61782i
\(690\) 0 0
\(691\) 20.3078 35.1742i 0.772546 1.33809i −0.163617 0.986524i \(-0.552316\pi\)
0.936163 0.351566i \(-0.114351\pi\)
\(692\) −0.517505 + 0.517505i −0.0196726 + 0.0196726i
\(693\) 0 0
\(694\) 6.15667i 0.233704i
\(695\) 5.71758 + 2.59405i 0.216880 + 0.0983981i
\(696\) 0 0
\(697\) −0.305703 + 1.14090i −0.0115793 + 0.0432146i
\(698\) −0.190521 + 0.0510501i −0.00721134 + 0.00193227i
\(699\) 0 0
\(700\) −13.1797 1.13855i −0.498145 0.0430330i
\(701\) 16.4455i 0.621140i −0.950551 0.310570i \(-0.899480\pi\)
0.950551 0.310570i \(-0.100520\pi\)
\(702\) 0 0
\(703\) 6.05951 + 1.62364i 0.228539 + 0.0612368i
\(704\) 2.47359 + 4.28438i 0.0932270 + 0.161474i
\(705\) 0 0
\(706\) 10.2157 0.384472
\(707\) −9.55095 + 9.18148i −0.359200 + 0.345305i
\(708\) 0 0
\(709\) 17.3375 + 10.0098i 0.651122 + 0.375926i 0.788886 0.614539i \(-0.210658\pi\)
−0.137764 + 0.990465i \(0.543991\pi\)
\(710\) 5.95919 35.9821i 0.223644 1.35038i
\(711\) 0 0
\(712\) 0.443021 0.118707i 0.0166029 0.00444873i
\(713\) −0.748631 0.748631i −0.0280365 0.0280365i
\(714\) 0 0
\(715\) −52.5520 43.1724i −1.96533 1.61456i
\(716\) −5.54712 3.20263i −0.207306 0.119688i
\(717\) 0 0
\(718\) 14.7440 + 3.95063i 0.550239 + 0.147436i
\(719\) 20.2948 35.1516i 0.756868 1.31093i −0.187572 0.982251i \(-0.560062\pi\)
0.944440 0.328683i \(-0.106605\pi\)
\(720\) 0 0
\(721\) −23.3890 42.4215i −0.871052 1.57986i
\(722\) 3.60644 3.60644i 0.134218 0.134218i
\(723\) 0 0
\(724\) 7.53612 4.35098i 0.280078 0.161703i
\(725\) 11.7412 + 13.4154i 0.436057 + 0.498234i
\(726\) 0 0
\(727\) 17.5089 + 17.5089i 0.649368 + 0.649368i 0.952840 0.303473i \(-0.0981461\pi\)
−0.303473 + 0.952840i \(0.598146\pi\)
\(728\) −15.7920 + 3.89937i −0.585290 + 0.144520i
\(729\) 0 0
\(730\) −17.7587 8.05711i −0.657281 0.298207i
\(731\) 45.2516 26.1260i 1.67369 0.966305i
\(732\) 0 0
\(733\) 1.36477 + 5.09340i 0.0504090 + 0.188129i 0.986539 0.163524i \(-0.0522862\pi\)
−0.936130 + 0.351653i \(0.885620\pi\)
\(734\) −23.7301 −0.875896
\(735\) 0 0
\(736\) 1.94470 0.0716828
\(737\) 0.0541481 + 0.202083i 0.00199457 + 0.00744384i
\(738\) 0 0
\(739\) 3.95782 2.28505i 0.145591 0.0840570i −0.425435 0.904989i \(-0.639879\pi\)
0.571026 + 0.820932i \(0.306546\pi\)
\(740\) 1.32357 + 3.52200i 0.0486555 + 0.129471i
\(741\) 0 0
\(742\) −20.4864 + 5.05852i −0.752080 + 0.185704i
\(743\) −12.0060 12.0060i −0.440459 0.440459i 0.451707 0.892166i \(-0.350815\pi\)
−0.892166 + 0.451707i \(0.850815\pi\)
\(744\) 0 0
\(745\) −25.5210 35.6523i −0.935019 1.30620i
\(746\) −16.1222 + 9.30815i −0.590275 + 0.340796i
\(747\) 0 0
\(748\) 15.3930 15.3930i 0.562825 0.562825i
\(749\) −4.97561 9.02444i −0.181805 0.329746i
\(750\) 0 0
\(751\) 7.40868 12.8322i 0.270347 0.468254i −0.698604 0.715509i \(-0.746195\pi\)
0.968951 + 0.247255i \(0.0795284\pi\)
\(752\) 0.896043 + 0.240094i 0.0326753 + 0.00875533i
\(753\) 0 0
\(754\) 18.9844 + 10.9606i 0.691370 + 0.399163i
\(755\) −5.57530 + 0.546299i −0.202906 + 0.0198818i
\(756\) 0 0
\(757\) −15.0073 15.0073i −0.545448 0.545448i 0.379673 0.925121i \(-0.376037\pi\)
−0.925121 + 0.379673i \(0.876037\pi\)
\(758\) −33.6920 + 9.02773i −1.22375 + 0.327902i
\(759\) 0 0
\(760\) −8.22455 1.36211i −0.298336 0.0494090i
\(761\) 2.48525 + 1.43486i 0.0900904 + 0.0520137i 0.544368 0.838846i \(-0.316769\pi\)
−0.454278 + 0.890860i \(0.650103\pi\)
\(762\) 0 0
\(763\) −16.4608 + 15.8241i −0.595922 + 0.572870i
\(764\) −7.98046 −0.288723
\(765\) 0 0
\(766\) −15.5448 26.9245i −0.561658 0.972821i
\(767\) −58.2073 15.5966i −2.10174 0.563161i
\(768\) 0 0
\(769\) 35.3321i 1.27411i 0.770819 + 0.637055i \(0.219847\pi\)
−0.770819 + 0.637055i \(0.780153\pi\)
\(770\) 24.1302 16.5634i 0.869591 0.596902i
\(771\) 0 0
\(772\) 18.8317 5.04593i 0.677766 0.181607i
\(773\) 3.63582 13.5691i 0.130771 0.488045i −0.869208 0.494446i \(-0.835371\pi\)
0.999980 + 0.00640103i \(0.00203753\pi\)
\(774\) 0 0
\(775\) −0.877563 + 2.57673i −0.0315230 + 0.0925589i
\(776\) 15.0187i 0.539141i
\(777\) 0 0
\(778\) −14.0908 + 14.0908i −0.505179 + 0.505179i
\(779\) −0.500374 + 0.866673i −0.0179278 + 0.0310518i
\(780\) 0 0
\(781\) 40.3464 + 69.8820i 1.44371 + 2.50058i
\(782\) −2.21478 8.26568i −0.0792005 0.295580i
\(783\) 0 0
\(784\) 0.276021 6.99456i 0.00985789 0.249806i
\(785\) −33.7496 27.7259i −1.20457 0.989579i
\(786\) 0 0
\(787\) −3.81054 + 14.2211i −0.135831 + 0.506929i 0.864162 + 0.503214i \(0.167849\pi\)
−0.999993 + 0.00371495i \(0.998817\pi\)
\(788\) 3.69540 13.7914i 0.131643 0.491299i
\(789\) 0 0
\(790\) 13.8320 + 11.3632i 0.492121 + 0.404286i
\(791\) −44.5486 26.9052i −1.58397 0.956639i
\(792\) 0 0
\(793\) −18.1752 67.8309i −0.645422 2.40875i
\(794\) −6.47536 11.2157i −0.229802 0.398029i
\(795\) 0 0
\(796\) 6.35098 11.0002i 0.225105 0.389892i
\(797\) 17.8544 17.8544i 0.632437 0.632437i −0.316242 0.948679i \(-0.602421\pi\)
0.948679 + 0.316242i \(0.102421\pi\)
\(798\) 0 0
\(799\) 4.08194i 0.144409i
\(800\) −2.20695 4.48658i −0.0780274 0.158624i
\(801\) 0 0
\(802\) 0.471387 1.75924i 0.0166453 0.0621210i
\(803\) 41.6749 11.1667i 1.47067 0.394066i
\(804\) 0 0
\(805\) −0.895942 11.4701i −0.0315778 0.404268i
\(806\) 3.34710i 0.117897i
\(807\) 0 0
\(808\) −4.83680 1.29602i −0.170158 0.0455937i
\(809\) −8.23813 14.2689i −0.289637 0.501666i 0.684086 0.729401i \(-0.260201\pi\)
−0.973723 + 0.227735i \(0.926868\pi\)
\(810\) 0 0
\(811\) −24.1358 −0.847522 −0.423761 0.905774i \(-0.639290\pi\)
−0.423761 + 0.905774i \(0.639290\pi\)
\(812\) −6.80077 + 6.53769i −0.238660 + 0.229428i
\(813\) 0 0
\(814\) −7.20907 4.16216i −0.252678 0.145884i
\(815\) −0.0819678 0.0135751i −0.00287121 0.000475516i
\(816\) 0 0
\(817\) 42.7630 11.4583i 1.49609 0.400876i
\(818\) −14.5966 14.5966i −0.510359 0.510359i
\(819\) 0 0
\(820\) −0.597354 + 0.0585321i −0.0208605 + 0.00204403i
\(821\) 22.7639 + 13.1427i 0.794464 + 0.458684i 0.841532 0.540207i \(-0.181654\pi\)
−0.0470674 + 0.998892i \(0.514988\pi\)
\(822\) 0 0
\(823\) 22.4829 + 6.02428i 0.783705 + 0.209993i 0.628417 0.777876i \(-0.283703\pi\)
0.155287 + 0.987869i \(0.450370\pi\)
\(824\) 9.15468 15.8564i 0.318918 0.552383i
\(825\) 0 0
\(826\) 13.4066 22.1981i 0.466474 0.772370i
\(827\) 3.56023 3.56023i 0.123801 0.123801i −0.642492 0.766293i \(-0.722099\pi\)
0.766293 + 0.642492i \(0.222099\pi\)
\(828\) 0 0
\(829\) −25.5490 + 14.7507i −0.887354 + 0.512314i −0.873076 0.487584i \(-0.837878\pi\)
−0.0142776 + 0.999898i \(0.504545\pi\)
\(830\) 2.39804 + 3.35001i 0.0832373 + 0.116281i
\(831\) 0 0
\(832\) −4.34735 4.34735i −0.150717 0.150717i
\(833\) −30.0437 + 6.79277i −1.04095 + 0.235355i
\(834\) 0 0
\(835\) 10.3028 + 27.4155i 0.356542 + 0.948751i
\(836\) 15.9732 9.22212i 0.552444 0.318954i
\(837\) 0 0
\(838\) 3.33743 + 12.4555i 0.115290 + 0.430267i
\(839\) 18.9600 0.654573 0.327286 0.944925i \(-0.393866\pi\)
0.327286 + 0.944925i \(0.393866\pi\)
\(840\) 0 0
\(841\) −16.2869 −0.561616
\(842\) −4.38208 16.3542i −0.151017 0.563601i
\(843\) 0 0
\(844\) −16.3592 + 9.44499i −0.563107 + 0.325110i
\(845\) 50.4978 + 22.9108i 1.73718 + 0.788154i
\(846\) 0 0
\(847\) −9.90428 + 34.2470i −0.340315 + 1.17674i
\(848\) −5.63966 5.63966i −0.193667 0.193667i
\(849\) 0 0
\(850\) −16.5561 + 14.4900i −0.567869 + 0.497002i
\(851\) −2.83384 + 1.63612i −0.0971427 + 0.0560854i
\(852\) 0 0
\(853\) 14.2865 14.2865i 0.489159 0.489159i −0.418882 0.908041i \(-0.637578\pi\)
0.908041 + 0.418882i \(0.137578\pi\)
\(854\) 30.2140 + 0.595925i 1.03390 + 0.0203921i
\(855\) 0 0
\(856\) 1.94750 3.37317i 0.0665642 0.115293i
\(857\) −14.9651 4.00989i −0.511199 0.136975i −0.00600644 0.999982i \(-0.501912\pi\)
−0.505193 + 0.863007i \(0.668579\pi\)
\(858\) 0 0
\(859\) −42.4333 24.4989i −1.44781 0.835891i −0.449455 0.893303i \(-0.648382\pi\)
−0.998351 + 0.0574123i \(0.981715\pi\)
\(860\) 20.5170 + 16.8551i 0.699623 + 0.574753i
\(861\) 0 0
\(862\) 21.0190 + 21.0190i 0.715910 + 0.715910i
\(863\) −50.5379 + 13.5416i −1.72033 + 0.460961i −0.977919 0.208984i \(-0.932984\pi\)
−0.742411 + 0.669945i \(0.766318\pi\)
\(864\) 0 0
\(865\) −0.267387 + 1.61450i −0.00909142 + 0.0548948i
\(866\) 24.5182 + 14.1556i 0.833162 + 0.481026i
\(867\) 0 0
\(868\) −1.38368 0.400162i −0.0469652 0.0135824i
\(869\) −39.6051 −1.34351
\(870\) 0 0
\(871\) −0.129999 0.225164i −0.00440484 0.00762940i
\(872\) −8.33612 2.23366i −0.282297 0.0756411i
\(873\) 0 0
\(874\) 7.25031i 0.245245i
\(875\) −25.4456 + 15.0838i −0.860218 + 0.509927i
\(876\) 0 0
\(877\) −19.1533 + 5.13210i −0.646760 + 0.173299i −0.567264 0.823536i \(-0.691998\pi\)
−0.0794965 + 0.996835i \(0.525331\pi\)
\(878\) 1.65609 6.18060i 0.0558902 0.208585i
\(879\) 0 0
\(880\) 10.0739 + 4.57051i 0.339591 + 0.154072i
\(881\) 22.4079i 0.754943i 0.926021 + 0.377471i \(0.123206\pi\)
−0.926021 + 0.377471i \(0.876794\pi\)
\(882\) 0 0
\(883\) −24.7816 + 24.7816i −0.833966 + 0.833966i −0.988057 0.154091i \(-0.950755\pi\)
0.154091 + 0.988057i \(0.450755\pi\)
\(884\) −13.5267 + 23.4289i −0.454951 + 0.787999i
\(885\) 0 0
\(886\) 0.169802 + 0.294105i 0.00570460 + 0.00988066i
\(887\) 9.95542 + 37.1542i 0.334270 + 1.24751i 0.904658 + 0.426139i \(0.140126\pi\)
−0.570387 + 0.821376i \(0.693207\pi\)
\(888\) 0 0
\(889\) 0.641035 + 0.387154i 0.0214996 + 0.0129847i
\(890\) 0.651012 0.792450i 0.0218220 0.0265630i
\(891\) 0 0
\(892\) −1.07538 + 4.01337i −0.0360064 + 0.134378i
\(893\) 0.895127 3.34066i 0.0299543 0.111791i
\(894\) 0 0
\(895\) −14.2543 + 1.39672i −0.476470 + 0.0466872i
\(896\) 2.31693 1.27744i 0.0774032 0.0426761i
\(897\) 0 0
\(898\) −3.07558 11.4782i −0.102633 0.383033i
\(899\) 0.970567 + 1.68107i 0.0323702 + 0.0560668i
\(900\) 0 0
\(901\) −17.5477 + 30.3935i −0.584598 + 1.01255i
\(902\) 0.938997 0.938997i 0.0312652 0.0312652i
\(903\) 0 0
\(904\) 19.6704i 0.654227i
\(905\) 8.03940 17.7197i 0.267239 0.589023i
\(906\) 0 0
\(907\) 8.21125 30.6448i 0.272650 1.01754i −0.684750 0.728778i \(-0.740089\pi\)
0.957400 0.288766i \(-0.0932448\pi\)
\(908\) 0.861758 0.230907i 0.0285984 0.00766293i
\(909\) 0 0
\(910\) −23.6383 + 27.6440i −0.783602 + 0.916391i
\(911\) 38.5994i 1.27886i 0.768851 + 0.639428i \(0.220829\pi\)
−0.768851 + 0.639428i \(0.779171\pi\)
\(912\) 0 0
\(913\) −8.80437 2.35912i −0.291382 0.0780756i
\(914\) 10.0824 + 17.4632i 0.333496 + 0.577633i
\(915\) 0 0
\(916\) −20.6026 −0.680728
\(917\) 39.8768 + 11.5324i 1.31685 + 0.380834i
\(918\) 0 0
\(919\) −3.71713 2.14609i −0.122617 0.0707928i 0.437437 0.899249i \(-0.355886\pi\)
−0.560054 + 0.828456i \(0.689220\pi\)
\(920\) 3.53593 2.53113i 0.116576 0.0834488i
\(921\) 0 0
\(922\) −18.9275 + 5.07160i −0.623343 + 0.167024i
\(923\) −70.9091 70.9091i −2.33400 2.33400i
\(924\) 0 0
\(925\) 6.99062 + 4.68112i 0.229850 + 0.153914i
\(926\) 23.5444 + 13.5934i 0.773716 + 0.446705i
\(927\) 0 0
\(928\) −3.44405 0.922831i −0.113057 0.0302934i
\(929\) 8.99774 15.5845i 0.295206 0.511312i −0.679827 0.733373i \(-0.737945\pi\)
0.975033 + 0.222061i \(0.0712783\pi\)
\(930\) 0 0
\(931\) −26.0773 1.02907i −0.854650 0.0337264i
\(932\) 3.40735 3.40735i 0.111611 0.111611i
\(933\) 0 0
\(934\) −26.2075 + 15.1309i −0.857534 + 0.495098i
\(935\) 7.95333 48.0229i 0.260102 1.57052i
\(936\) 0 0
\(937\) 25.1463 + 25.1463i 0.821495 + 0.821495i 0.986322 0.164828i \(-0.0527068\pi\)
−0.164828 + 0.986322i \(0.552707\pi\)
\(938\) 0.108624 0.0268216i 0.00354671 0.000875756i
\(939\) 0 0
\(940\) 1.94171 0.729697i 0.0633316 0.0238001i
\(941\) 19.8371 11.4529i 0.646670 0.373355i −0.140509 0.990079i \(-0.544874\pi\)
0.787179 + 0.616724i \(0.211541\pi\)
\(942\) 0 0
\(943\) −0.135105 0.504219i −0.00439962 0.0164196i
\(944\) 9.80154 0.319013
\(945\) 0 0
\(946\) −58.7462 −1.91000
\(947\) 5.17572 + 19.3161i 0.168188 + 0.627687i 0.997612 + 0.0690674i \(0.0220023\pi\)
−0.829424 + 0.558620i \(0.811331\pi\)
\(948\) 0 0
\(949\) −46.4347 + 26.8091i −1.50733 + 0.870260i
\(950\) −16.7270 + 8.22802i −0.542696 + 0.266952i
\(951\) 0 0
\(952\) −8.06825 8.39292i −0.261494 0.272016i
\(953\) 5.12950 + 5.12950i 0.166161 + 0.166161i 0.785289 0.619129i \(-0.212514\pi\)
−0.619129 + 0.785289i \(0.712514\pi\)
\(954\) 0 0
\(955\) −14.5103 + 10.3870i −0.469543 + 0.336114i
\(956\) 13.6183 7.86253i 0.440448 0.254293i
\(957\) 0 0
\(958\) 1.15697 1.15697i 0.0373801 0.0373801i
\(959\) −6.69658 0.132080i −0.216244 0.00426508i
\(960\) 0 0
\(961\) 15.3518 26.5901i 0.495220 0.857745i
\(962\) 9.99250 + 2.67748i 0.322171 + 0.0863255i
\(963\) 0 0
\(964\) 6.31306 + 3.64485i 0.203330 + 0.117393i
\(965\) 27.6728 33.6850i 0.890819 1.08436i
\(966\) 0 0
\(967\) −19.0930 19.0930i −0.613989 0.613989i 0.329994 0.943983i \(-0.392953\pi\)
−0.943983 + 0.329994i \(0.892953\pi\)
\(968\) −13.0155 + 3.48748i −0.418333 + 0.112092i
\(969\) 0 0
\(970\) 19.5476 + 27.3075i 0.627636 + 0.876792i
\(971\) −38.4438 22.1955i −1.23372 0.712289i −0.265917 0.963996i \(-0.585675\pi\)
−0.967804 + 0.251707i \(0.919008\pi\)
\(972\) 0 0
\(973\) 1.78085 + 7.21223i 0.0570915 + 0.231214i
\(974\) −7.21490 −0.231180
\(975\) 0 0
\(976\) 5.71103 + 9.89179i 0.182806 + 0.316628i
\(977\) −8.10250 2.17106i −0.259222 0.0694583i 0.126868 0.991920i \(-0.459508\pi\)
−0.386089 + 0.922461i \(0.626174\pi\)
\(978\) 0 0
\(979\) 2.26902i 0.0725181i
\(980\) −8.60189 13.0770i −0.274777 0.417729i
\(981\) 0 0
\(982\) −22.6253 + 6.06244i −0.722003 + 0.193460i
\(983\) −0.734462 + 2.74105i −0.0234257 + 0.0874259i −0.976649 0.214841i \(-0.931077\pi\)
0.953223 + 0.302267i \(0.0977434\pi\)
\(984\) 0 0
\(985\) −11.2311 29.8858i −0.357853 0.952239i
\(986\) 15.6894i 0.499654i
\(987\) 0 0
\(988\) −16.2079 + 16.2079i −0.515643 + 0.515643i
\(989\) −11.5464 + 19.9989i −0.367153 + 0.635928i
\(990\) 0 0
\(991\) 17.4678 + 30.2552i 0.554884 + 0.961088i 0.997913 + 0.0645801i \(0.0205708\pi\)
−0.443028 + 0.896508i \(0.646096\pi\)
\(992\) −0.140905 0.525863i −0.00447373 0.0166962i
\(993\) 0 0
\(994\) 37.7911 20.8361i 1.19866 0.660880i
\(995\) −2.76977 28.2671i −0.0878075 0.896126i
\(996\) 0 0
\(997\) −0.417054 + 1.55647i −0.0132082 + 0.0492938i −0.972215 0.234088i \(-0.924790\pi\)
0.959007 + 0.283382i \(0.0914563\pi\)
\(998\) −7.64876 + 28.5456i −0.242117 + 0.903594i
\(999\) 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 630.2.ce.c.107.6 yes 32
3.2 odd 2 inner 630.2.ce.c.107.3 yes 32
5.3 odd 4 inner 630.2.ce.c.233.7 yes 32
7.4 even 3 inner 630.2.ce.c.557.2 yes 32
15.8 even 4 inner 630.2.ce.c.233.2 yes 32
21.11 odd 6 inner 630.2.ce.c.557.7 yes 32
35.18 odd 12 inner 630.2.ce.c.53.3 32
105.53 even 12 inner 630.2.ce.c.53.6 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.ce.c.53.3 32 35.18 odd 12 inner
630.2.ce.c.53.6 yes 32 105.53 even 12 inner
630.2.ce.c.107.3 yes 32 3.2 odd 2 inner
630.2.ce.c.107.6 yes 32 1.1 even 1 trivial
630.2.ce.c.233.2 yes 32 15.8 even 4 inner
630.2.ce.c.233.7 yes 32 5.3 odd 4 inner
630.2.ce.c.557.2 yes 32 7.4 even 3 inner
630.2.ce.c.557.7 yes 32 21.11 odd 6 inner