Properties

Label 630.2.ce.c.233.2
Level $630$
Weight $2$
Character 630.233
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 233.2
Character \(\chi\) \(=\) 630.233
Dual form 630.2.ce.c.557.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.30155 + 1.81823i) q^{5} +(0.634242 + 2.56861i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.30155 + 1.81823i) q^{5} +(0.634242 + 2.56861i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.786607 - 2.09314i) q^{10} +(-4.28438 + 2.47359i) q^{11} +(-4.34735 - 4.34735i) q^{13} +(-1.27744 - 2.31693i) q^{14} +(0.500000 - 0.866025i) q^{16} +(1.13888 - 4.25035i) q^{17} +(3.22874 + 1.86412i) q^{19} +(-0.218058 + 2.22541i) q^{20} +(3.49819 - 3.49819i) q^{22} +(-0.503327 - 1.87844i) q^{23} +(-1.61194 - 4.73304i) q^{25} +(5.32440 + 3.07404i) q^{26} +(1.83357 + 1.90736i) q^{28} -3.56555 q^{29} +(-0.272207 - 0.471476i) q^{31} +(-0.258819 + 0.965926i) q^{32} +4.40029i q^{34} +(-5.49582 - 2.18997i) q^{35} +(0.435499 + 1.62530i) q^{37} +(-3.60120 - 0.964938i) q^{38} +(-0.365351 - 2.20602i) q^{40} +0.268424i q^{41} +(-8.39666 - 8.39666i) q^{43} +(-2.47359 + 4.28438i) q^{44} +(0.972352 + 1.68416i) q^{46} +(-0.896043 + 0.240094i) q^{47} +(-6.19547 + 3.25824i) q^{49} +(2.78202 + 4.15456i) q^{50} +(-5.93859 - 1.59124i) q^{52} +(-7.70392 - 2.06426i) q^{53} +(1.07877 - 11.0095i) q^{55} +(-2.26476 - 1.36780i) q^{56} +(3.44405 - 0.922831i) q^{58} +(4.90077 + 8.48838i) q^{59} +(-5.71103 + 9.89179i) q^{61} +(0.384959 + 0.384959i) q^{62} -1.00000i q^{64} +(13.5628 - 2.24621i) q^{65} +(0.0408482 + 0.0109452i) q^{67} +(-1.13888 - 4.25035i) q^{68} +(5.87536 + 0.692922i) q^{70} -16.3109i q^{71} +(-2.25719 + 8.42396i) q^{73} +(-0.841319 - 1.45721i) q^{74} +3.72823 q^{76} +(-9.07102 - 9.43604i) q^{77} +(6.93305 + 4.00280i) q^{79} +(0.923861 + 2.03629i) q^{80} +(-0.0694733 - 0.259278i) q^{82} +(-1.30281 + 1.30281i) q^{83} +(6.24583 + 7.60279i) q^{85} +(10.2838 + 5.93734i) q^{86} +(1.28042 - 4.77861i) q^{88} +(-0.229324 + 0.397201i) q^{89} +(8.40936 - 13.9239i) q^{91} +(-1.37511 - 1.37511i) q^{92} +(0.803371 - 0.463826i) q^{94} +(-7.59177 + 3.44437i) q^{95} +(-10.6198 + 10.6198i) q^{97} +(5.14107 - 4.75072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 12 q^{7}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) 0 0
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) −1.30155 + 1.81823i −0.582070 + 0.813138i
\(6\) 0 0
\(7\) 0.634242 + 2.56861i 0.239721 + 0.970842i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0.786607 2.09314i 0.248747 0.661910i
\(11\) −4.28438 + 2.47359i −1.29179 + 0.745816i −0.978971 0.203997i \(-0.934607\pi\)
−0.312819 + 0.949813i \(0.601273\pi\)
\(12\) 0 0
\(13\) −4.34735 4.34735i −1.20574 1.20574i −0.972394 0.233344i \(-0.925033\pi\)
−0.233344 0.972394i \(-0.574967\pi\)
\(14\) −1.27744 2.31693i −0.341409 0.619225i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.13888 4.25035i 0.276219 1.03086i −0.678802 0.734322i \(-0.737500\pi\)
0.955020 0.296541i \(-0.0958330\pi\)
\(18\) 0 0
\(19\) 3.22874 + 1.86412i 0.740725 + 0.427658i 0.822333 0.569007i \(-0.192672\pi\)
−0.0816079 + 0.996665i \(0.526006\pi\)
\(20\) −0.218058 + 2.22541i −0.0487593 + 0.497617i
\(21\) 0 0
\(22\) 3.49819 3.49819i 0.745816 0.745816i
\(23\) −0.503327 1.87844i −0.104951 0.391682i 0.893389 0.449284i \(-0.148321\pi\)
−0.998340 + 0.0576026i \(0.981654\pi\)
\(24\) 0 0
\(25\) −1.61194 4.73304i −0.322388 0.946608i
\(26\) 5.32440 + 3.07404i 1.04420 + 0.602869i
\(27\) 0 0
\(28\) 1.83357 + 1.90736i 0.346513 + 0.360457i
\(29\) −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 \(0.848902\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) 0 0
\(34\) 4.40029i 0.754644i
\(35\) −5.49582 2.18997i −0.928963 0.370172i
\(36\) 0 0
\(37\) 0.435499 + 1.62530i 0.0715955 + 0.267198i 0.992440 0.122732i \(-0.0391657\pi\)
−0.920844 + 0.389931i \(0.872499\pi\)
\(38\) −3.60120 0.964938i −0.584191 0.156534i
\(39\) 0 0
\(40\) −0.365351 2.20602i −0.0577670 0.348802i
\(41\) 0.268424i 0.0419208i 0.999780 + 0.0209604i \(0.00667239\pi\)
−0.999780 + 0.0209604i \(0.993328\pi\)
\(42\) 0 0
\(43\) −8.39666 8.39666i −1.28048 1.28048i −0.940395 0.340084i \(-0.889545\pi\)
−0.340084 0.940395i \(-0.610455\pi\)
\(44\) −2.47359 + 4.28438i −0.372908 + 0.645895i
\(45\) 0 0
\(46\) 0.972352 + 1.68416i 0.143366 + 0.248316i
\(47\) −0.896043 + 0.240094i −0.130701 + 0.0350213i −0.323577 0.946202i \(-0.604885\pi\)
0.192875 + 0.981223i \(0.438219\pi\)
\(48\) 0 0
\(49\) −6.19547 + 3.25824i −0.885068 + 0.465462i
\(50\) 2.78202 + 4.15456i 0.393436 + 0.587544i
\(51\) 0 0
\(52\) −5.93859 1.59124i −0.823534 0.220665i
\(53\) −7.70392 2.06426i −1.05822 0.283548i −0.312573 0.949894i \(-0.601191\pi\)
−0.745643 + 0.666346i \(0.767857\pi\)
\(54\) 0 0
\(55\) 1.07877 11.0095i 0.145462 1.48452i
\(56\) −2.26476 1.36780i −0.302641 0.182780i
\(57\) 0 0
\(58\) 3.44405 0.922831i 0.452226 0.121174i
\(59\) 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
\(65\) 13.5628 2.24621i 1.68226 0.278607i
\(66\) 0 0
\(67\) 0.0408482 + 0.0109452i 0.00499040 + 0.00133717i 0.261313 0.965254i \(-0.415844\pi\)
−0.256323 + 0.966591i \(0.582511\pi\)
\(68\) −1.13888 4.25035i −0.138109 0.515431i
\(69\) 0 0
\(70\) 5.87536 + 0.692922i 0.702240 + 0.0828200i
\(71\) 16.3109i 1.93574i −0.251443 0.967872i \(-0.580905\pi\)
0.251443 0.967872i \(-0.419095\pi\)
\(72\) 0 0
\(73\) −2.25719 + 8.42396i −0.264185 + 0.985950i 0.698563 + 0.715548i \(0.253823\pi\)
−0.962748 + 0.270402i \(0.912844\pi\)
\(74\) −0.841319 1.45721i −0.0978013 0.169397i
\(75\) 0 0
\(76\) 3.72823 0.427658
\(77\) −9.07102 9.43604i −1.03374 1.07534i
\(78\) 0 0
\(79\) 6.93305 + 4.00280i 0.780029 + 0.450350i 0.836440 0.548058i \(-0.184633\pi\)
−0.0564118 + 0.998408i \(0.517966\pi\)
\(80\) 0.923861 + 2.03629i 0.103291 + 0.227664i
\(81\) 0 0
\(82\) −0.0694733 0.259278i −0.00767204 0.0286324i
\(83\) −1.30281 + 1.30281i −0.143002 + 0.143002i −0.774984 0.631981i \(-0.782242\pi\)
0.631981 + 0.774984i \(0.282242\pi\)
\(84\) 0 0
\(85\) 6.24583 + 7.60279i 0.677455 + 0.824639i
\(86\) 10.2838 + 5.93734i 1.10893 + 0.640239i
\(87\) 0 0
\(88\) 1.28042 4.77861i 0.136494 0.509402i
\(89\) −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
\(95\) −7.59177 + 3.44437i −0.778899 + 0.353385i
\(96\) 0 0
\(97\) −10.6198 + 10.6198i −1.07828 + 1.07828i −0.0816181 + 0.996664i \(0.526009\pi\)
−0.996664 + 0.0816181i \(0.973991\pi\)
\(98\) 5.14107 4.75072i 0.519327 0.479895i
\(99\) 0 0
\(100\) −3.76250 3.29296i −0.376250 0.329296i
\(101\) −4.33656 + 2.50371i −0.431504 + 0.249129i −0.699987 0.714156i \(-0.746811\pi\)
0.268483 + 0.963284i \(0.413478\pi\)
\(102\) 0 0
\(103\) −17.6855 + 4.73881i −1.74260 + 0.466929i −0.983022 0.183486i \(-0.941262\pi\)
−0.759579 + 0.650415i \(0.774595\pi\)
\(104\) 6.14808 0.602869
\(105\) 0 0
\(106\) 7.97569 0.774667
\(107\) −3.76228 + 1.00810i −0.363714 + 0.0974568i −0.436047 0.899924i \(-0.643622\pi\)
0.0723338 + 0.997380i \(0.476955\pi\)
\(108\) 0 0
\(109\) −7.47396 + 4.31509i −0.715875 + 0.413311i −0.813233 0.581939i \(-0.802294\pi\)
0.0973573 + 0.995249i \(0.468961\pi\)
\(110\) 1.80746 + 10.9136i 0.172334 + 1.04057i
\(111\) 0 0
\(112\) 2.54160 + 0.735033i 0.240159 + 0.0694541i
\(113\) 13.9091 13.9091i 1.30845 1.30845i 0.385925 0.922530i \(-0.373882\pi\)
0.922530 0.385925i \(-0.126118\pi\)
\(114\) 0 0
\(115\) 4.07055 + 1.52972i 0.379580 + 0.142647i
\(116\) −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
\(122\) 2.95625 11.0329i 0.267646 0.998868i
\(123\) 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 −0.715931 0.698171i \(-0.753998\pi\)
0.698171 + 0.715931i \(0.253998\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) 0 0
\(130\) −12.5193 + 5.67997i −1.09801 + 0.498167i
\(131\) 13.5876 + 7.84483i 1.18716 + 0.685406i 0.957660 0.287903i \(-0.0929581\pi\)
0.229498 + 0.973309i \(0.426291\pi\)
\(132\) 0 0
\(133\) −2.74038 + 9.47568i −0.237621 + 0.821645i
\(134\) −0.0422892 −0.00365323
\(135\) 0 0
\(136\) 2.20015 + 3.81076i 0.188661 + 0.326770i
\(137\) −0.655217 + 2.44530i −0.0559789 + 0.208916i −0.988250 0.152843i \(-0.951157\pi\)
0.932272 + 0.361759i \(0.117824\pi\)
\(138\) 0 0
\(139\) 2.80784i 0.238158i 0.992885 + 0.119079i \(0.0379942\pi\)
−0.992885 + 0.119079i \(0.962006\pi\)
\(140\) −5.85450 + 0.851344i −0.494796 + 0.0719517i
\(141\) 0 0
\(142\) 4.22156 + 15.7551i 0.354266 + 1.32214i
\(143\) 29.3793 + 7.87216i 2.45682 + 0.658303i
\(144\) 0 0
\(145\) 4.64073 6.48299i 0.385392 0.538383i
\(146\) 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 \(0.800829\pi\)
\(152\) −3.60120 + 0.964938i −0.292096 + 0.0782668i
\(153\) 0 0
\(154\) 11.2042 + 6.76676i 0.902857 + 0.545281i
\(155\) 1.21154 + 0.118714i 0.0973136 + 0.00953533i
\(156\) 0 0
\(157\) 18.8678 + 5.05560i 1.50581 + 0.403481i 0.915042 0.403360i \(-0.132158\pi\)
0.590770 + 0.806840i \(0.298824\pi\)
\(158\) −7.73281 2.07200i −0.615189 0.164839i
\(159\) 0 0
\(160\) −1.41941 1.72779i −0.112214 0.136594i
\(161\) 4.50574 2.48423i 0.355102 0.195785i
\(162\) 0 0
\(163\) −0.0358904 + 0.00961679i −0.00281115 + 0.000753245i −0.260224 0.965548i \(-0.583797\pi\)
0.257413 + 0.966301i \(0.417130\pi\)
\(164\) 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 0.967923 0.251247i \(-0.0808405\pi\)
−0.251247 + 0.967923i \(0.580841\pi\)
\(168\) 0 0
\(169\) 24.7989i 1.90761i
\(170\) −8.00075 5.72719i −0.613630 0.439256i
\(171\) 0 0
\(172\) −11.4701 3.07339i −0.874583 0.234344i
\(173\) −0.189420 0.706925i −0.0144013 0.0537465i 0.958351 0.285592i \(-0.0921903\pi\)
−0.972753 + 0.231846i \(0.925524\pi\)
\(174\) 0 0
\(175\) 11.1349 7.14233i 0.841723 0.539910i
\(176\) 4.94718i 0.372908i
\(177\) 0 0
\(178\) 0.118707 0.443021i 0.00889747 0.0332058i
\(179\) 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 \(0.604828\pi\)
\(182\) −4.51904 + 15.6260i −0.334974 + 1.15827i
\(183\) 0 0
\(184\) 1.68416 + 0.972352i 0.124158 + 0.0716828i
\(185\) −3.52200 1.32357i −0.258943 0.0973111i
\(186\) 0 0
\(187\) 5.63424 + 21.0273i 0.412016 + 1.53767i
\(188\) −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 0.228665 0.973505i \(-0.426564\pi\)
−0.728748 + 0.684782i \(0.759897\pi\)
\(192\) 0 0
\(193\) 5.04593 18.8317i 0.363214 1.35553i −0.506612 0.862174i \(-0.669102\pi\)
0.869826 0.493358i \(-0.164231\pi\)
\(194\) 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 0.249153 0.968464i \(-0.419848\pi\)
−0.968464 + 0.249153i \(0.919848\pi\)
\(198\) 0 0
\(199\) 11.0002 6.35098i 0.779785 0.450209i −0.0565691 0.998399i \(-0.518016\pi\)
0.836354 + 0.548190i \(0.184683\pi\)
\(200\) 4.48658 + 2.20695i 0.317249 + 0.156055i
\(201\) 0 0
\(202\) 3.54078 3.54078i 0.249129 0.249129i
\(203\) −2.26142 9.15848i −0.158721 0.642800i
\(204\) 0 0
\(205\) −0.488058 0.349367i −0.0340874 0.0244009i
\(206\) 15.8564 9.15468i 1.10477 0.637837i
\(207\) 0 0
\(208\) −5.93859 + 1.59124i −0.411767 + 0.110333i
\(209\) −18.4442 −1.27582
\(210\) 0 0
\(211\) 18.8900 1.30044 0.650220 0.759746i \(-0.274677\pi\)
0.650220 + 0.759746i \(0.274677\pi\)
\(212\) −7.70392 + 2.06426i −0.529108 + 0.141774i
\(213\) 0 0
\(214\) 3.37317 1.94750i 0.230585 0.133128i
\(215\) 26.1957 4.33842i 1.78654 0.295878i
\(216\) 0 0
\(217\) 1.03839 0.998223i 0.0704906 0.0677638i
\(218\) 6.10246 6.10246i 0.413311 0.413311i
\(219\) 0 0
\(220\) −4.57051 10.0739i −0.308144 0.679182i
\(221\) −23.4289 + 13.5267i −1.57600 + 0.909903i
\(222\) 0 0
\(223\) 2.93799 + 2.93799i 0.196743 + 0.196743i 0.798602 0.601859i \(-0.205573\pi\)
−0.601859 + 0.798602i \(0.705573\pi\)
\(224\) −2.64524 0.0521732i −0.176742 0.00348597i
\(225\) 0 0
\(226\) −9.83520 + 17.0351i −0.654227 + 1.13316i
\(227\) 0.230907 0.861758i 0.0153259 0.0571969i −0.957839 0.287304i \(-0.907241\pi\)
0.973165 + 0.230107i \(0.0739077\pi\)
\(228\) 0 0
\(229\) −17.8423 10.3013i −1.17905 0.680728i −0.223259 0.974759i \(-0.571670\pi\)
−0.955796 + 0.294032i \(0.905003\pi\)
\(230\) −4.32777 0.424059i −0.285364 0.0279616i
\(231\) 0 0
\(232\) 2.52122 2.52122i 0.165526 0.165526i
\(233\) 1.24718 + 4.65452i 0.0817052 + 0.304928i 0.994670 0.103111i \(-0.0328796\pi\)
−0.912965 + 0.408038i \(0.866213\pi\)
\(234\) 0 0
\(235\) 0.729697 1.94171i 0.0476002 0.126663i
\(236\) 8.48838 + 4.90077i 0.552547 + 0.319013i
\(237\) 0 0
\(238\) −11.3026 + 2.79085i −0.732640 + 0.180904i
\(239\) −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 \(0.908772\pi\)
\(242\) −3.48748 + 13.0155i −0.224184 + 0.836666i
\(243\) 0 0
\(244\) 11.4221i 0.731222i
\(245\) 2.13948 15.5056i 0.136686 0.990614i
\(246\) 0 0
\(247\) −5.93252 22.1405i −0.377477 1.40876i
\(248\) 0.525863 + 0.140905i 0.0333924 + 0.00894746i
\(249\) 0 0
\(250\) −11.1749 0.349016i −0.706762 0.0220737i
\(251\) 8.22912i 0.519418i 0.965687 + 0.259709i \(0.0836266\pi\)
−0.965687 + 0.259709i \(0.916373\pi\)
\(252\) 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
\(257\) −1.26082 + 0.337836i −0.0786479 + 0.0210736i −0.297928 0.954588i \(-0.596296\pi\)
0.219281 + 0.975662i \(0.429629\pi\)
\(258\) 0 0
\(259\) −3.89855 + 2.14946i −0.242244 + 0.133561i
\(260\) 10.6226 8.72666i 0.658787 0.541205i
\(261\) 0 0
\(262\) −15.1550 4.06078i −0.936282 0.250876i
\(263\) −14.2693 3.82344i −0.879881 0.235763i −0.209525 0.977803i \(-0.567192\pi\)
−0.670356 + 0.742040i \(0.733859\pi\)
\(264\) 0 0
\(265\) 13.7803 11.3208i 0.846520 0.695431i
\(266\) 0.194514 9.86206i 0.0119264 0.604682i
\(267\) 0 0
\(268\) 0.0408482 0.0109452i 0.00249520 0.000668587i
\(269\) −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
\(275\) 18.6138 + 16.2909i 1.12245 + 0.982377i
\(276\) 0 0
\(277\) −20.0261 5.36596i −1.20325 0.322410i −0.399139 0.916890i \(-0.630691\pi\)
−0.804110 + 0.594481i \(0.797358\pi\)
\(278\) −0.726722 2.71217i −0.0435859 0.162665i
\(279\) 0 0
\(280\) 5.43467 2.33759i 0.324784 0.139698i
\(281\) 24.6495i 1.47046i 0.677816 + 0.735232i \(0.262927\pi\)
−0.677816 + 0.735232i \(0.737073\pi\)
\(282\) 0 0
\(283\) 1.42821 5.33016i 0.0848985 0.316845i −0.910396 0.413737i \(-0.864223\pi\)
0.995295 + 0.0968916i \(0.0308900\pi\)
\(284\) −8.15543 14.1256i −0.483936 0.838202i
\(285\) 0 0
\(286\) −30.4157 −1.79852
\(287\) −0.689476 + 0.170246i −0.0406985 + 0.0100493i
\(288\) 0 0
\(289\) −2.04603 1.18128i −0.120355 0.0694870i
\(290\) −2.80468 + 7.46320i −0.164697 + 0.438254i
\(291\) 0 0
\(292\) 2.25719 + 8.42396i 0.132092 + 0.492975i
\(293\) −13.1648 + 13.1648i −0.769096 + 0.769096i −0.977947 0.208851i \(-0.933028\pi\)
0.208851 + 0.977947i \(0.433028\pi\)
\(294\) 0 0
\(295\) −21.8124 2.13731i −1.26997 0.124439i
\(296\) −1.45721 0.841319i −0.0846984 0.0489007i
\(297\) 0 0
\(298\) 5.07498 18.9401i 0.293986 1.09717i
\(299\) −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
\(305\) −10.5524 23.2586i −0.604228 1.33178i
\(306\) 0 0
\(307\) 16.9282 16.9282i 0.966145 0.966145i −0.0333006 0.999445i \(-0.510602\pi\)
0.999445 + 0.0333006i \(0.0106019\pi\)
\(308\) −12.5738 3.63634i −0.716456 0.207200i
\(309\) 0 0
\(310\) −1.20099 + 0.198902i −0.0682115 + 0.0112969i
\(311\) −23.6318 + 13.6438i −1.34004 + 0.773671i −0.986812 0.161868i \(-0.948248\pi\)
−0.353225 + 0.935539i \(0.614915\pi\)
\(312\) 0 0
\(313\) −7.18228 + 1.92449i −0.405967 + 0.108778i −0.456023 0.889968i \(-0.650727\pi\)
0.0500564 + 0.998746i \(0.484060\pi\)
\(314\) −19.5333 −1.10233
\(315\) 0 0
\(316\) 8.00559 0.450350
\(317\) 30.1869 8.08855i 1.69546 0.454298i 0.723673 0.690143i \(-0.242452\pi\)
0.971791 + 0.235845i \(0.0757857\pi\)
\(318\) 0 0
\(319\) 15.2762 8.81970i 0.855302 0.493809i
\(320\) 1.81823 + 1.30155i 0.101642 + 0.0727588i
\(321\) 0 0
\(322\) −3.70925 + 3.56576i −0.206708 + 0.198712i
\(323\) 11.6003 11.6003i 0.645458 0.645458i
\(324\) 0 0
\(325\) −13.5685 + 27.5838i −0.752645 + 1.53008i
\(326\) 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 \(0.262321\pi\)
\(332\) −0.476862 + 1.77967i −0.0261712 + 0.0976723i
\(333\) 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 −0.210740 + 0.977542i \(0.567587\pi\)
−0.977542 + 0.210740i \(0.932413\pi\)
\(338\) −6.41843 23.9539i −0.349117 1.30292i
\(339\) 0 0
\(340\) 9.21044 + 3.46130i 0.499506 + 0.187715i
\(341\) 2.33248 + 1.34666i 0.126311 + 0.0729256i
\(342\) 0 0
\(343\) −12.2986 13.8472i −0.664060 0.747680i
\(344\) 11.8747 0.640239
\(345\) 0 0
\(346\) 0.365931 + 0.633812i 0.0196726 + 0.0340739i
\(347\) −1.59346 + 5.94688i −0.0855415 + 0.319245i −0.995416 0.0956379i \(-0.969511\pi\)
0.909875 + 0.414883i \(0.136178\pi\)
\(348\) 0 0
\(349\) 0.197242i 0.0105581i −0.999986 0.00527907i \(-0.998320\pi\)
0.999986 0.00527907i \(-0.00168039\pi\)
\(350\) −8.90696 + 9.78090i −0.476097 + 0.522811i
\(351\) 0 0
\(352\) −1.28042 4.77861i −0.0682469 0.254701i
\(353\) −9.86759 2.64401i −0.525199 0.140727i −0.0135287 0.999908i \(-0.504306\pi\)
−0.511670 + 0.859182i \(0.670973\pi\)
\(354\) 0 0
\(355\) 29.6570 + 21.2294i 1.57403 + 1.12674i
\(356\) 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
\(362\) 8.40545 2.25223i 0.441781 0.118375i
\(363\) 0 0
\(364\) 0.320765 16.2631i 0.0168127 0.852420i
\(365\) −12.3789 15.0683i −0.647940 0.788711i
\(366\) 0 0
\(367\) 22.9216 + 6.14181i 1.19650 + 0.320600i 0.801450 0.598062i \(-0.204062\pi\)
0.395045 + 0.918662i \(0.370729\pi\)
\(368\) −1.87844 0.503327i −0.0979205 0.0262377i
\(369\) 0 0
\(370\) 3.74456 + 0.366913i 0.194670 + 0.0190749i
\(371\) 0.416117 21.0976i 0.0216037 1.09533i
\(372\) 0 0
\(373\) −17.9820 + 4.81825i −0.931071 + 0.249480i −0.692311 0.721599i \(-0.743407\pi\)
−0.238760 + 0.971079i \(0.576741\pi\)
\(374\) −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 \(-0.646571\pi\)
0.444367 0.895845i \(-0.353429\pi\)
\(380\) −4.85248 + 6.77880i −0.248927 + 0.347745i
\(381\) 0 0
\(382\) 7.70853 + 2.06549i 0.394403 + 0.105680i
\(383\) 8.04661 + 30.0303i 0.411162 + 1.53448i 0.792400 + 0.610002i \(0.208831\pi\)
−0.381238 + 0.924477i \(0.624502\pi\)
\(384\) 0 0
\(385\) 28.9633 4.21175i 1.47611 0.214651i
\(386\) 19.4960i 0.992319i
\(387\) 0 0
\(388\) −3.88713 + 14.5070i −0.197339 + 0.736480i
\(389\) 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
\(392\) 2.07694 6.68478i 0.104901 0.337633i
\(393\) 0 0
\(394\) 12.3651 + 7.13897i 0.622942 + 0.359656i
\(395\) −16.3017 + 7.39606i −0.820228 + 0.372136i
\(396\) 0 0
\(397\) 3.35189 + 12.5094i 0.168227 + 0.627831i 0.997607 + 0.0691456i \(0.0220273\pi\)
−0.829380 + 0.558685i \(0.811306\pi\)
\(398\) −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 0.538866 0.842392i \(-0.318853\pi\)
−0.460100 + 0.887867i \(0.652186\pi\)
\(402\) 0 0
\(403\) −0.866294 + 3.23305i −0.0431532 + 0.161050i
\(404\) −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 0.0120026 0.999928i \(-0.496179\pi\)
0.871964 + 0.489569i \(0.162846\pi\)
\(410\) 0.561850 + 0.211144i 0.0277478 + 0.0104277i
\(411\) 0 0
\(412\) −12.9467 + 12.9467i −0.637837 + 0.637837i
\(413\) −18.6950 + 17.9718i −0.919922 + 0.884336i
\(414\) 0 0
\(415\) −0.673142 4.06449i −0.0330432 0.199518i
\(416\) 5.32440 3.07404i 0.261050 0.150717i
\(417\) 0 0
\(418\) 17.8158 4.77372i 0.871398 0.233490i
\(419\) 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 \(0.635374\pi\)
\(422\) −18.2463 + 4.88909i −0.888217 + 0.237997i
\(423\) 0 0
\(424\) 6.90715 3.98784i 0.335441 0.193667i
\(425\) −21.9529 + 1.46096i −1.06487 + 0.0708670i
\(426\) 0 0
\(427\) −29.0303 8.39559i −1.40487 0.406291i
\(428\) −2.75418 + 2.75418i −0.133128 + 0.133128i
\(429\) 0 0
\(430\) −24.1803 + 10.9705i −1.16608 + 0.529047i
\(431\) −25.7429 + 14.8627i −1.23999 + 0.715910i −0.969093 0.246697i \(-0.920655\pi\)
−0.270901 + 0.962607i \(0.587321\pi\)
\(432\) 0 0
\(433\) 20.0190 + 20.0190i 0.962052 + 0.962052i 0.999306 0.0372534i \(-0.0118609\pi\)
−0.0372534 + 0.999306i \(0.511861\pi\)
\(434\) −0.744650 + 1.23296i −0.0357444 + 0.0591842i
\(435\) 0 0
\(436\) −4.31509 + 7.47396i −0.206655 + 0.357938i
\(437\) 1.87652 7.00326i 0.0897661 0.335012i
\(438\) 0 0
\(439\) 5.54137 + 3.19931i 0.264475 + 0.152695i 0.626374 0.779522i \(-0.284538\pi\)
−0.361899 + 0.932217i \(0.617872\pi\)
\(440\) 7.02209 + 8.54771i 0.334765 + 0.407496i
\(441\) 0 0
\(442\) 19.1296 19.1296i 0.909903 0.909903i
\(443\) −0.0878959 0.328032i −0.00417606 0.0155853i 0.963806 0.266603i \(-0.0859013\pi\)
−0.967982 + 0.251018i \(0.919235\pi\)
\(444\) 0 0
\(445\) −0.423728 0.933942i −0.0200866 0.0442731i
\(446\) −3.59829 2.07747i −0.170384 0.0983713i
\(447\) 0 0
\(448\) 2.56861 0.634242i 0.121355 0.0299651i
\(449\) −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
\(452\) 5.09107 19.0001i 0.239464 0.893691i
\(453\) 0 0
\(454\) 0.892157i 0.0418710i
\(455\) 14.3717 + 33.4128i 0.673756 + 1.56642i
\(456\) 0 0
\(457\) −5.21904 19.4777i −0.244136 0.911129i −0.973816 0.227340i \(-0.926997\pi\)
0.729679 0.683790i \(-0.239669\pi\)
\(458\) 19.9005 + 5.33233i 0.929891 + 0.249164i
\(459\) 0 0
\(460\) 4.29005 0.710499i 0.200025 0.0331272i
\(461\) 19.5952i 0.912638i −0.889816 0.456319i \(-0.849168\pi\)
0.889816 0.456319i \(-0.150832\pi\)
\(462\) 0 0
\(463\) 19.2239 + 19.2239i 0.893411 + 0.893411i 0.994843 0.101432i \(-0.0323423\pi\)
−0.101432 + 0.994843i \(0.532342\pi\)
\(464\) −1.78277 + 3.08785i −0.0827632 + 0.143350i
\(465\) 0 0
\(466\) −2.40936 4.17313i −0.111611 0.193316i
\(467\) −29.2306 + 7.83232i −1.35263 + 0.362437i −0.861105 0.508426i \(-0.830227\pi\)
−0.491526 + 0.870863i \(0.663561\pi\)
\(468\) 0 0
\(469\) −0.00220636 + 0.111865i −0.000101880 + 0.00516544i
\(470\) −0.202282 + 2.06441i −0.00933058 + 0.0952240i
\(471\) 0 0
\(472\) −9.46756 2.53682i −0.435780 0.116767i
\(473\) 56.7444 + 15.2046i 2.60911 + 0.699109i
\(474\) 0 0
\(475\) 3.61839 18.2866i 0.166023 0.839048i
\(476\) 10.1952 5.62109i 0.467294 0.257642i
\(477\) 0 0
\(478\) 15.1892 4.06995i 0.694740 0.186155i
\(479\) −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
\(485\) −5.48710 33.1316i −0.249156 1.50443i
\(486\) 0 0
\(487\) 6.96906 + 1.86735i 0.315798 + 0.0846178i 0.413237 0.910624i \(-0.364398\pi\)
−0.0974385 + 0.995242i \(0.531065\pi\)
\(488\) −2.95625 11.0329i −0.133823 0.499434i
\(489\) 0 0
\(490\) 1.94656 + 15.5310i 0.0879365 + 0.701618i
\(491\) 23.4235i 1.05709i −0.848907 0.528543i \(-0.822739\pi\)
0.848907 0.528543i \(-0.177261\pi\)
\(492\) 0 0
\(493\) −4.06073 + 15.1548i −0.182886 + 0.682540i
\(494\) 11.4607 + 19.8506i 0.515643 + 0.893120i
\(495\) 0 0
\(496\) −0.544414 −0.0244449
\(497\) 41.8962 10.3450i 1.87930 0.464039i
\(498\) 0 0
\(499\) −25.5933 14.7763i −1.14571 0.661477i −0.197873 0.980228i \(-0.563403\pi\)
−0.947838 + 0.318751i \(0.896737\pi\)
\(500\) 10.8844 2.55515i 0.486767 0.114270i
\(501\) 0 0
\(502\) −2.12985 7.94872i −0.0950600 0.354769i
\(503\) −16.6368 + 16.6368i −0.741797 + 0.741797i −0.972924 0.231127i \(-0.925759\pi\)
0.231127 + 0.972924i \(0.425759\pi\)
\(504\) 0 0
\(505\) 1.09191 11.1436i 0.0485893 0.495883i
\(506\) −8.33186 4.81040i −0.370396 0.213848i
\(507\) 0 0
\(508\) −0.0732583 + 0.273404i −0.00325031 + 0.0121303i
\(509\) 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
\(515\) 14.4023 38.3241i 0.634639 1.68876i
\(516\) 0 0
\(517\) 3.24510 3.24510i 0.142719 0.142719i
\(518\) 3.20939 3.08524i 0.141013 0.135558i
\(519\) 0 0
\(520\) −8.00203 + 11.1786i −0.350912 + 0.490216i
\(521\) 18.3916 10.6184i 0.805750 0.465200i −0.0397281 0.999211i \(-0.512649\pi\)
0.845478 + 0.534011i \(0.179316\pi\)
\(522\) 0 0
\(523\) −0.212531 + 0.0569475i −0.00929332 + 0.00249014i −0.263463 0.964670i \(-0.584865\pi\)
0.254169 + 0.967160i \(0.418198\pi\)
\(524\) 15.6897 0.685406
\(525\) 0 0
\(526\) 14.7726 0.644118
\(527\) −2.31395 + 0.620022i −0.100797 + 0.0270086i
\(528\) 0 0
\(529\) 16.6434 9.60906i 0.723625 0.417785i
\(530\) −10.3808 + 14.5017i −0.450911 + 0.629912i
\(531\) 0 0
\(532\) 2.36460 + 9.57636i 0.102519 + 0.415188i
\(533\) 1.16693 1.16693i 0.0505455 0.0505455i
\(534\) 0 0
\(535\) 3.06383 8.15280i 0.132461 0.352476i
\(536\) −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 \(0.806038\pi\)
\(542\) −2.56281 + 9.56455i −0.110082 + 0.410833i
\(543\) 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 −0.441911 0.897059i \(-0.645699\pi\)
0.897059 + 0.441911i \(0.145699\pi\)
\(548\) 0.655217 + 2.44530i 0.0279895 + 0.104458i
\(549\) 0 0
\(550\) −22.1959 10.9182i −0.946437 0.465553i
\(551\) −11.5122 6.64660i −0.490438 0.283154i
\(552\) 0 0
\(553\) −5.88438 + 20.3470i −0.250229 + 0.865243i
\(554\) 20.7325 0.880839
\(555\) 0 0
\(556\) 1.40392 + 2.43166i 0.0595395 + 0.103125i
\(557\) −8.14696 + 30.4049i −0.345198 + 1.28830i 0.547183 + 0.837013i \(0.315700\pi\)
−0.892381 + 0.451283i \(0.850967\pi\)
\(558\) 0 0
\(559\) 73.0065i 3.08784i
\(560\) −4.64448 + 3.66454i −0.196265 + 0.154855i
\(561\) 0 0
\(562\) −6.37975 23.8096i −0.269114 1.00435i
\(563\) −0.0628710 0.0168462i −0.00264969 0.000709984i 0.257494 0.966280i \(-0.417103\pi\)
−0.260144 + 0.965570i \(0.583770\pi\)
\(564\) 0 0
\(565\) 7.18659 + 43.3933i 0.302342 + 1.82557i
\(566\) 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 \(0.644480\pi\)
\(572\) 29.3793 7.87216i 1.22841 0.329151i
\(573\) 0 0
\(574\) 0.621920 0.342894i 0.0259584 0.0143121i
\(575\) −8.07940 + 5.41020i −0.336934 + 0.225621i
\(576\) 0 0
\(577\) −14.6077 3.91412i −0.608127 0.162947i −0.0584023 0.998293i \(-0.518601\pi\)
−0.549724 + 0.835346i \(0.685267\pi\)
\(578\) 2.28205 + 0.611475i 0.0949210 + 0.0254340i
\(579\) 0 0
\(580\) 0.777496 7.93480i 0.0322838 0.329475i
\(581\) −4.17271 2.52011i −0.173113 0.104552i
\(582\) 0 0
\(583\) 38.1127 10.2123i 1.57847 0.422949i
\(584\) −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 0.690101 0.723713i \(-0.257566\pi\)
−0.723713 + 0.690101i \(0.757566\pi\)
\(588\) 0 0
\(589\) 2.02970i 0.0836324i
\(590\) 21.6224 3.58100i 0.890179 0.147427i
\(591\) 0 0
\(592\) 1.62530 + 0.435499i 0.0667996 + 0.0178989i
\(593\) 0.158410 + 0.591195i 0.00650513 + 0.0242775i 0.969102 0.246660i \(-0.0793330\pi\)
−0.962597 + 0.270937i \(0.912666\pi\)
\(594\) 0 0
\(595\) −15.5672 + 20.8651i −0.638193 + 0.855385i
\(596\) 19.6082i 0.803184i
\(597\) 0 0
\(598\) 3.09449 11.5488i 0.126543 0.472266i
\(599\) 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 \(0.581953\pi\)
\(602\) −8.72828 + 30.1807i −0.355738 + 1.23007i
\(603\) 0 0
\(604\) 2.16964 + 1.25264i 0.0882816 + 0.0509694i
\(605\) 12.4487 + 27.4382i 0.506110 + 1.11552i
\(606\) 0 0
\(607\) −2.30511 8.60280i −0.0935616 0.349177i 0.903236 0.429145i \(-0.141185\pi\)
−0.996797 + 0.0799678i \(0.974518\pi\)
\(608\) −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
\(613\) 7.44173 27.7729i 0.300569 1.12174i −0.636125 0.771586i \(-0.719464\pi\)
0.936693 0.350151i \(-0.113870\pi\)
\(614\) −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 0.782502 0.622649i \(-0.213943\pi\)
−0.622649 + 0.782502i \(0.713943\pi\)
\(618\) 0 0
\(619\) −29.1348 + 16.8210i −1.17103 + 0.676092i −0.953921 0.300057i \(-0.902994\pi\)
−0.217104 + 0.976148i \(0.569661\pi\)
\(620\) 1.10859 0.502963i 0.0445218 0.0201995i
\(621\) 0 0
\(622\) 19.2953 19.2953i 0.773671 0.773671i
\(623\) −1.16570 0.337122i −0.0467028 0.0135065i
\(624\) 0 0
\(625\) −19.8033 + 15.2588i −0.792132 + 0.610350i
\(626\) 6.43946 3.71782i 0.257373 0.148594i
\(627\) 0 0
\(628\) 18.8678 5.05560i 0.752906 0.201740i
\(629\) 7.40409 0.295221
\(630\) 0 0
\(631\) −15.9081 −0.633292 −0.316646 0.948544i \(-0.602557\pi\)
−0.316646 + 0.948544i \(0.602557\pi\)
\(632\) −7.73281 + 2.07200i −0.307595 + 0.0824197i
\(633\) 0 0
\(634\) −27.0648 + 15.6259i −1.07488 + 0.620583i
\(635\) −0.103412 0.624410i −0.00410377 0.0247789i
\(636\) 0 0
\(637\) 41.0986 + 12.7692i 1.62839 + 0.505934i
\(638\) −12.4729 + 12.4729i −0.493809 + 0.493809i
\(639\) 0 0
\(640\) −2.09314 0.786607i −0.0827388 0.0310934i
\(641\) 31.4224 18.1417i 1.24111 0.716555i 0.271789 0.962357i \(-0.412385\pi\)
0.969320 + 0.245802i \(0.0790513\pi\)
\(642\) 0 0
\(643\) 2.60079 + 2.60079i 0.102565 + 0.102565i 0.756527 0.653962i \(-0.226894\pi\)
−0.653962 + 0.756527i \(0.726894\pi\)
\(644\) 2.65997 4.40428i 0.104818 0.173553i
\(645\) 0 0
\(646\) −8.20266 + 14.2074i −0.322729 + 0.558983i
\(647\) 2.05269 7.66073i 0.0806994 0.301174i −0.913766 0.406242i \(-0.866839\pi\)
0.994465 + 0.105067i \(0.0335058\pi\)
\(648\) 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
\(653\) −12.3118 45.9484i −0.481799 1.79810i −0.594060 0.804421i \(-0.702476\pi\)
0.112260 0.993679i \(-0.464191\pi\)
\(654\) 0 0
\(655\) −31.9487 + 14.4951i −1.24834 + 0.566369i
\(656\) 0.232462 + 0.134212i 0.00907612 + 0.00524010i
\(657\) 0 0
\(658\) 1.70092 + 1.76936i 0.0663087 + 0.0689770i
\(659\) 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 \(0.629489\pi\)
\(662\) 2.78766 10.4037i 0.108345 0.404350i
\(663\) 0 0
\(664\) 1.84245i 0.0715011i
\(665\) −13.6623 17.3157i −0.529799 0.671474i
\(666\) 0 0
\(667\) 1.79463 + 6.69767i 0.0694885 + 0.259335i
\(668\) 12.6514 + 3.38994i 0.489499 + 0.131161i
\(669\) 0 0
\(670\) 0.0550414 0.0768915i 0.00212644 0.00297058i
\(671\) 56.5070i 2.18143i
\(672\) 0 0
\(673\) 2.13524 + 2.13524i 0.0823073 + 0.0823073i 0.747062 0.664755i \(-0.231464\pi\)
−0.664755 + 0.747062i \(0.731464\pi\)
\(674\) 15.4248 26.7165i 0.594141 1.02908i
\(675\) 0 0
\(676\) 12.3995 + 21.4765i 0.476902 + 0.826019i
\(677\) −2.33327 + 0.625198i −0.0896749 + 0.0240283i −0.303378 0.952870i \(-0.598114\pi\)
0.213703 + 0.976899i \(0.431448\pi\)
\(678\) 0 0
\(679\) −34.0137 20.5426i −1.30533 0.788354i
\(680\) −9.79245 0.959519i −0.375523 0.0367959i
\(681\) 0 0
\(682\) −2.60154 0.697081i −0.0996182 0.0266926i
\(683\) 19.9200 + 5.33754i 0.762216 + 0.204235i 0.618930 0.785446i \(-0.287566\pi\)
0.143286 + 0.989681i \(0.454233\pi\)
\(684\) 0 0
\(685\) −3.59333 4.37402i −0.137294 0.167123i
\(686\) 15.4634 + 10.1923i 0.590396 + 0.389143i
\(687\) 0 0
\(688\) −11.4701 + 3.07339i −0.437292 + 0.117172i
\(689\) 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
\(695\) −5.10531 3.65454i −0.193655 0.138625i
\(696\) 0 0
\(697\) 1.14090 + 0.305703i 0.0432146 + 0.0115793i
\(698\) 0.0510501 + 0.190521i 0.00193227 + 0.00721134i
\(699\) 0 0
\(700\) 6.07198 11.7529i 0.229499 0.444218i
\(701\) 16.4455i 0.621140i 0.950551 + 0.310570i \(0.100520\pi\)
−0.950551 + 0.310570i \(0.899480\pi\)
\(702\) 0 0
\(703\) −1.62364 + 6.05951i −0.0612368 + 0.228539i
\(704\) 2.47359 + 4.28438i 0.0932270 + 0.161474i
\(705\) 0 0
\(706\) 10.2157 0.384472
\(707\) −9.18148 9.55095i −0.345305 0.359200i
\(708\) 0 0
\(709\) −17.3375 10.0098i −0.651122 0.375926i 0.137764 0.990465i \(-0.456009\pi\)
−0.788886 + 0.614539i \(0.789342\pi\)
\(710\) −34.1410 12.8302i −1.28129 0.481510i
\(711\) 0 0
\(712\) −0.118707 0.443021i −0.00444873 0.0166029i
\(713\) −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
\(718\) −3.95063 + 14.7440i −0.147436 + 0.550239i
\(719\) 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
\(725\) 5.74745 + 16.8759i 0.213455 + 0.626754i
\(726\) 0 0
\(727\) 17.5089 17.5089i 0.649368 0.649368i −0.303473 0.952840i \(-0.598146\pi\)
0.952840 + 0.303473i \(0.0981461\pi\)
\(728\) 3.89937 + 15.7920i 0.144520 + 0.585290i
\(729\) 0 0
\(730\) 15.8570 + 11.3510i 0.586895 + 0.420118i
\(731\) −45.2516 + 26.1260i −1.67369 + 0.966305i
\(732\) 0 0
\(733\) −5.09340 + 1.36477i −0.188129 + 0.0504090i −0.351653 0.936130i \(-0.614380\pi\)
0.163524 + 0.986539i \(0.447714\pi\)
\(734\) −23.7301 −0.875896
\(735\) 0 0
\(736\) 1.94470 0.0716828
\(737\) −0.202083 + 0.0541481i −0.00744384 + 0.00199457i
\(738\) 0 0
\(739\) −3.95782 + 2.28505i −0.145591 + 0.0840570i −0.571026 0.820932i \(-0.693454\pi\)
0.425435 + 0.904989i \(0.360121\pi\)
\(740\) −3.71193 + 0.614753i −0.136453 + 0.0225988i
\(741\) 0 0
\(742\) 5.05852 + 20.4864i 0.185704 + 0.752080i
\(743\) −12.0060 + 12.0060i −0.440459 + 0.440459i −0.892166 0.451707i \(-0.850815\pi\)
0.451707 + 0.892166i \(0.350815\pi\)
\(744\) 0 0
\(745\) −18.1153 39.9280i −0.663692 1.46285i
\(746\) 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 \(0.0795284\pi\)
\(752\) −0.240094 + 0.896043i −0.00875533 + 0.0326753i
\(753\) 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 −0.925121 0.379673i \(-0.876037\pi\)
0.379673 + 0.925121i \(0.376037\pi\)
\(758\) 9.02773 + 33.6920i 0.327902 + 1.22375i
\(759\) 0 0
\(760\) 2.93265 7.80373i 0.106378 0.283071i
\(761\) −2.48525 1.43486i −0.0900904 0.0520137i 0.454278 0.890860i \(-0.349897\pi\)
−0.544368 + 0.838846i \(0.683231\pi\)
\(762\) 0 0
\(763\) −15.8241 16.4608i −0.572870 0.595922i
\(764\) −7.98046 −0.288723
\(765\) 0 0
\(766\) −15.5448 26.9245i −0.561658 0.972821i
\(767\) 15.5966 58.2073i 0.563161 2.10174i
\(768\) 0 0
\(769\) 35.3321i 1.27411i −0.770819 0.637055i \(-0.780153\pi\)
0.770819 0.637055i \(-0.219847\pi\)
\(770\) −26.8863 + 11.5645i −0.968915 + 0.416755i
\(771\) 0 0
\(772\) −5.04593 18.8317i −0.181607 0.677766i
\(773\) −13.5691 3.63582i −0.488045 0.130771i 0.00640103 0.999980i \(-0.497962\pi\)
−0.494446 + 0.869208i \(0.664629\pi\)
\(774\) 0 0
\(775\) −1.79273 + 2.04836i −0.0643969 + 0.0735792i
\(776\) 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
\(782\) 8.26568 2.21478i 0.295580 0.0792005i
\(783\) 0 0
\(784\) −0.276021 + 6.99456i −0.00985789 + 0.249806i
\(785\) −33.7496 + 27.7259i −1.20457 + 0.989579i
\(786\) 0 0
\(787\) 14.2211 + 3.81054i 0.506929 + 0.135831i 0.503214 0.864162i \(-0.332151\pi\)
0.00371495 + 0.999993i \(0.498817\pi\)
\(788\) −13.7914 3.69540i −0.491299 0.131643i
\(789\) 0 0
\(790\) 13.8320 11.3632i 0.492121 0.404286i
\(791\) 44.5486 + 26.9052i 1.58397 + 0.956639i
\(792\) 0 0
\(793\) 67.8309 18.1752i 2.40875 0.645422i
\(794\) −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 0.948679 0.316242i \(-0.102421\pi\)
−0.316242 + 0.948679i \(0.602421\pi\)
\(798\) 0 0
\(799\) 4.08194i 0.144409i
\(800\) 4.98896 0.332015i 0.176387 0.0117385i
\(801\) 0 0
\(802\) −1.75924 0.471387i −0.0621210 0.0166453i
\(803\) −11.1667 41.6749i −0.394066 1.47067i
\(804\) 0 0
\(805\) −1.34753 + 11.4258i −0.0474941 + 0.402708i
\(806\) 3.34710i 0.117897i
\(807\) 0 0
\(808\) 1.29602 4.83680i 0.0455937 0.170158i
\(809\) −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 \(0.639290\pi\)
\(812\) −6.53769 6.80077i −0.229428 0.238660i
\(813\) 0 0
\(814\) 7.20907 + 4.16216i 0.252678 + 0.145884i
\(815\) 0.0292275 0.0777738i 0.00102379 0.00272430i
\(816\) 0 0
\(817\) −11.4583 42.7630i −0.400876 1.49609i
\(818\) −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 0.0470674 0.998892i \(-0.485012\pi\)
−0.841532 + 0.540207i \(0.818346\pi\)
\(822\) 0 0
\(823\) −6.02428 + 22.4829i −0.209993 + 0.783705i 0.777876 + 0.628417i \(0.216297\pi\)
−0.987869 + 0.155287i \(0.950370\pi\)
\(824\) 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 0.766293 0.642492i \(-0.222099\pi\)
−0.642492 + 0.766293i \(0.722099\pi\)
\(828\) 0 0
\(829\) 25.5490 14.7507i 0.887354 0.512314i 0.0142776 0.999898i \(-0.495455\pi\)
0.873076 + 0.487584i \(0.162122\pi\)
\(830\) 1.70217 + 3.75177i 0.0590832 + 0.130226i
\(831\) 0 0
\(832\) −4.34735 + 4.34735i −0.150717 + 0.150717i
\(833\) 6.79277 + 30.0437i 0.235355 + 1.04095i
\(834\) 0 0
\(835\) −28.8939 + 4.78527i −0.999913 + 0.165601i
\(836\) −15.9732 + 9.22212i −0.552444 + 0.318954i
\(837\) 0 0
\(838\) −12.4555 + 3.33743i −0.430267 + 0.115290i
\(839\) 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
\(842\) 16.3542 4.38208i 0.563601 0.151017i
\(843\) 0 0
\(844\) 16.3592 9.44499i 0.563107 0.325110i
\(845\) −45.0902 32.2770i −1.55115 1.11036i
\(846\) 0 0
\(847\) 34.2470 + 9.90428i 1.17674 + 0.340315i
\(848\) −5.63966 + 5.63966i −0.193667 + 0.193667i
\(849\) 0 0
\(850\) 20.8267 7.09301i 0.714351 0.243288i
\(851\) 2.83384 1.63612i 0.0971427 0.0560854i
\(852\) 0 0
\(853\) 14.2865 + 14.2865i 0.489159 + 0.489159i 0.908041 0.418882i \(-0.137578\pi\)
−0.418882 + 0.908041i \(0.637578\pi\)
\(854\) 30.2140 + 0.595925i 1.03390 + 0.0203921i
\(855\) 0 0
\(856\) 1.94750 3.37317i 0.0665642 0.115293i
\(857\) 4.00989 14.9651i 0.136975 0.511199i −0.863007 0.505193i \(-0.831421\pi\)
0.999982 0.00600644i \(-0.00191192\pi\)
\(858\) 0 0
\(859\) 42.4333 + 24.4989i 1.44781 + 0.835891i 0.998351 0.0574123i \(-0.0182850\pi\)
0.449455 + 0.893303i \(0.351618\pi\)
\(860\) 20.5170 16.8551i 0.699623 0.574753i
\(861\) 0 0
\(862\) 21.0190 21.0190i 0.715910 0.715910i
\(863\) 13.5416 + 50.5379i 0.460961 + 1.72033i 0.669945 + 0.742411i \(0.266318\pi\)
−0.208984 + 0.977919i \(0.567016\pi\)
\(864\) 0 0
\(865\) 1.53189 + 0.575688i 0.0520860 + 0.0195740i
\(866\) −24.5182 14.1556i −0.833162 0.481026i
\(867\) 0 0
\(868\) 0.400162 1.38368i 0.0135824 0.0469652i
\(869\) −39.6051 −1.34351
\(870\) 0 0
\(871\) −0.129999 0.225164i −0.00440484 0.00762940i
\(872\) 2.23366 8.33612i 0.0756411 0.282297i
\(873\) 0 0
\(874\) 7.25031i 0.245245i
\(875\) −1.50626 + 29.5420i −0.0509208 + 0.998703i
\(876\) 0 0
\(877\) 5.13210 + 19.1533i 0.173299 + 0.646760i 0.996835 + 0.0794965i \(0.0253313\pi\)
−0.823536 + 0.567264i \(0.808002\pi\)
\(878\) −6.18060 1.65609i −0.208585 0.0558902i
\(879\) 0 0
\(880\) −8.99513 6.43900i −0.303226 0.217059i
\(881\) 22.4079i 0.754943i −0.926021 0.377471i \(-0.876794\pi\)
0.926021 0.377471i \(-0.123206\pi\)
\(882\) 0 0
\(883\) −24.7816 24.7816i −0.833966 0.833966i 0.154091 0.988057i \(-0.450755\pi\)
−0.988057 + 0.154091i \(0.950755\pi\)
\(884\) −13.5267 + 23.4289i −0.454951 + 0.787999i
\(885\) 0 0
\(886\) 0.169802 + 0.294105i 0.00570460 + 0.00988066i
\(887\) −37.1542 + 9.95542i −1.24751 + 0.334270i −0.821376 0.570387i \(-0.806793\pi\)
−0.426139 + 0.904658i \(0.640126\pi\)
\(888\) 0 0
\(889\) −0.641035 0.387154i −0.0214996 0.0129847i
\(890\) 0.651012 + 0.792450i 0.0218220 + 0.0265630i
\(891\) 0 0
\(892\) 4.01337 + 1.07538i 0.134378 + 0.0360064i
\(893\) −3.34066 0.895127i −0.111791 0.0299543i
\(894\) 0 0
\(895\) −14.2543 1.39672i −0.476470 0.0466872i
\(896\) −2.31693 + 1.27744i −0.0774032 + 0.0426761i
\(897\) 0 0
\(898\) 11.4782 3.07558i 0.383033 0.102633i
\(899\) 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
\(905\) 11.3260 15.8222i 0.376490 0.525947i
\(906\) 0 0
\(907\) −30.6448 8.21125i −1.01754 0.272650i −0.288766 0.957400i \(-0.593245\pi\)
−0.728778 + 0.684750i \(0.759911\pi\)
\(908\) −0.230907 0.861758i −0.00766293 0.0285984i
\(909\) 0 0
\(910\) −22.5299 28.5546i −0.746858 0.946577i
\(911\) 38.5994i 1.27886i −0.768851 0.639428i \(-0.779171\pi\)
0.768851 0.639428i \(-0.220829\pi\)
\(912\) 0 0
\(913\) 2.35912 8.80437i 0.0780756 0.291382i
\(914\) 10.0824 + 17.4632i 0.333496 + 0.577633i
\(915\) 0 0
\(916\) −20.6026 −0.680728
\(917\) −11.5324 + 39.8768i −0.380834 + 1.31685i
\(918\) 0 0
\(919\) 3.71713 + 2.14609i 0.122617 + 0.0707928i 0.560054 0.828456i \(-0.310780\pi\)
−0.437437 + 0.899249i \(0.644114\pi\)
\(920\) −3.95998 + 1.79664i −0.130557 + 0.0592334i
\(921\) 0 0
\(922\) 5.07160 + 18.9275i 0.167024 + 0.623343i
\(923\) −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
\(928\) 0.922831 3.44405i 0.0302934 0.113057i
\(929\) 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
\(935\) −45.5657 17.1237i −1.49016 0.560004i
\(936\) 0 0
\(937\) 25.1463 25.1463i 0.821495 0.821495i −0.164828 0.986322i \(-0.552707\pi\)
0.986322 + 0.164828i \(0.0527068\pi\)
\(938\) −0.0268216 0.108624i −0.000875756 0.00354671i
\(939\) 0 0
\(940\) −0.338918 2.04642i −0.0110543 0.0667468i
\(941\) −19.8371 + 11.4529i −0.646670 + 0.373355i −0.787179 0.616724i \(-0.788459\pi\)
0.140509 + 0.990079i \(0.455126\pi\)
\(942\) 0 0
\(943\) 0.504219 0.135105i 0.0164196 0.00439962i
\(944\) 9.80154 0.319013
\(945\) 0 0
\(946\) −58.7462 −1.91000
\(947\) −19.3161 + 5.17572i −0.627687 + 0.168188i −0.558620 0.829424i \(-0.688669\pi\)
−0.0690674 + 0.997612i \(0.522002\pi\)
\(948\) 0 0
\(949\) 46.4347 26.8091i 1.50733 0.870260i
\(950\) 1.23783 + 18.6000i 0.0401604 + 0.603464i
\(951\) 0 0
\(952\) −8.39292 + 8.06825i −0.272016 + 0.261494i
\(953\) 5.12950 5.12950i 0.166161 0.166161i −0.619129 0.785289i \(-0.712514\pi\)
0.785289 + 0.619129i \(0.212514\pi\)
\(954\) 0 0
\(955\) 16.2505 7.37283i 0.525855 0.238579i
\(956\) −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
\(962\) −2.67748 + 9.99250i −0.0863255 + 0.322171i
\(963\) 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 −0.943983 0.329994i \(-0.892953\pi\)
0.329994 + 0.943983i \(0.392953\pi\)
\(968\) 3.48748 + 13.0155i 0.112092 + 0.418333i
\(969\) 0 0
\(970\) 13.8752 + 30.5825i 0.445506 + 0.981945i
\(971\) 38.4438 + 22.1955i 1.23372 + 0.712289i 0.967804 0.251707i \(-0.0809918\pi\)
0.265917 + 0.963996i \(0.414325\pi\)
\(972\) 0 0
\(973\) −7.21223 + 1.78085i −0.231214 + 0.0570915i
\(974\) −7.21490 −0.231180
\(975\) 0 0
\(976\) 5.71103 + 9.89179i 0.182806 + 0.316628i
\(977\) 2.17106 8.10250i 0.0694583 0.259222i −0.922461 0.386089i \(-0.873826\pi\)
0.991920 + 0.126868i \(0.0404923\pi\)
\(978\) 0 0
\(979\) 2.26902i 0.0725181i
\(980\) −5.89994 14.4980i −0.188467 0.463120i
\(981\) 0 0
\(982\) 6.06244 + 22.6253i 0.193460 + 0.722003i
\(983\) 2.74105 + 0.734462i 0.0874259 + 0.0234257i 0.302267 0.953223i \(-0.402257\pi\)
−0.214841 + 0.976649i \(0.568923\pi\)
\(984\) 0 0
\(985\) 31.4974 5.21645i 1.00359 0.166210i
\(986\) 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 \(0.646096\pi\)
\(992\) 0.525863 0.140905i 0.0166962 0.00447373i
\(993\) 0 0
\(994\) −37.7911 + 20.8361i −1.19866 + 0.660880i
\(995\) −2.76977 + 28.2671i −0.0878075 + 0.896126i
\(996\) 0 0
\(997\) 1.55647 + 0.417054i 0.0492938 + 0.0132082i 0.283382 0.959007i \(-0.408544\pi\)
−0.234088 + 0.972215i \(0.575210\pi\)
\(998\) 28.5456 + 7.64876i 0.903594 + 0.242117i
\(999\) 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.233.2 yes 32
3.2 odd 2 inner 630.2.ce.c.233.7 yes 32
5.2 odd 4 inner 630.2.ce.c.107.3 yes 32
7.4 even 3 inner 630.2.ce.c.53.6 yes 32
15.2 even 4 inner 630.2.ce.c.107.6 yes 32
21.11 odd 6 inner 630.2.ce.c.53.3 32
35.32 odd 12 inner 630.2.ce.c.557.7 yes 32
105.32 even 12 inner 630.2.ce.c.557.2 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
630.2.ce.c.53.3 32 21.11 odd 6 inner
630.2.ce.c.53.6 yes 32 7.4 even 3 inner
630.2.ce.c.107.3 yes 32 5.2 odd 4 inner
630.2.ce.c.107.6 yes 32 15.2 even 4 inner
630.2.ce.c.233.2 yes 32 1.1 even 1 trivial
630.2.ce.c.233.7 yes 32 3.2 odd 2 inner
630.2.ce.c.557.2 yes 32 105.32 even 12 inner
630.2.ce.c.557.7 yes 32 35.32 odd 12 inner