Properties

Label 162.3.f.a.17.1
Level $162$
Weight $3$
Character 162.17
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 17.1
Character \(\chi\) \(=\) 162.17
Dual form 162.3.f.a.143.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-5.90332 - 1.04091i) q^{5} +(5.59840 - 4.69762i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\) \(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(-5.90332 - 1.04091i) q^{5} +(5.59840 - 4.69762i) q^{7} +(2.44949 - 1.41421i) q^{8} +(4.23867 - 7.34160i) q^{10} +(20.3832 - 3.59412i) q^{11} +(6.40830 - 2.33243i) q^{13} +(3.53490 + 9.71205i) q^{14} +(0.694593 + 3.93923i) q^{16} +(-1.96510 - 1.13455i) q^{17} +(-12.1634 - 21.0675i) q^{19} +(7.70624 + 9.18394i) q^{20} +(-5.08285 + 28.8263i) q^{22} +(15.5320 - 18.5103i) q^{23} +(10.2734 + 3.73921i) q^{25} +9.64433i q^{26} -14.6164 q^{28} +(-6.32777 + 17.3854i) q^{29} +(16.6469 + 13.9684i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(2.45823 - 2.06270i) q^{34} +(-37.9390 + 21.9041i) q^{35} +(22.3832 - 38.7688i) q^{37} +(33.8805 - 5.97405i) q^{38} +(-15.9322 + 5.79885i) q^{40} +(-17.5398 - 48.1902i) q^{41} +(6.41470 + 36.3796i) q^{43} +(-35.8494 - 20.6977i) q^{44} +(17.0861 + 29.5941i) q^{46} +(-8.15595 - 9.71989i) q^{47} +(0.765740 - 4.34273i) q^{49} +(-9.93826 + 11.8440i) q^{50} +(-12.8166 - 4.66486i) q^{52} +17.7730i q^{53} -124.070 q^{55} +(7.06980 - 19.4241i) q^{56} +(-20.0432 - 16.8183i) q^{58} +(-64.9049 - 11.4445i) q^{59} +(32.3438 - 27.1396i) q^{61} +(-26.6150 + 15.3662i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-40.2581 + 7.09859i) q^{65} +(-111.190 + 40.4700i) q^{67} +(1.55216 + 4.26451i) q^{68} +(-10.7582 - 61.0129i) q^{70} +(46.1702 + 26.6564i) q^{71} +(33.8569 + 58.6419i) q^{73} +(40.6944 + 48.4976i) q^{74} +(-8.44858 + 47.9143i) q^{76} +(97.2298 - 115.874i) q^{77} +(104.610 + 38.0750i) q^{79} -23.9776i q^{80} +72.5250 q^{82} +(-8.63542 + 23.7256i) q^{83} +(10.4196 + 8.74311i) q^{85} +(-51.4485 - 9.07175i) q^{86} +(44.8457 - 37.6300i) q^{88} +(35.4447 - 20.4640i) q^{89} +(24.9194 - 43.1616i) q^{91} +(-47.5927 + 8.39188i) q^{92} +(16.8620 - 6.13725i) q^{94} +(49.8747 + 137.030i) q^{95} +(7.02010 + 39.8130i) q^{97} +(5.40078 + 3.11814i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{11}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.483690 + 1.32893i −0.241845 + 0.664463i
\(3\) 0 0
\(4\) −1.53209 1.28558i −0.383022 0.321394i
\(5\) −5.90332 1.04091i −1.18066 0.208183i −0.451341 0.892352i \(-0.649054\pi\)
−0.729324 + 0.684169i \(0.760165\pi\)
\(6\) 0 0
\(7\) 5.59840 4.69762i 0.799772 0.671088i −0.148371 0.988932i \(-0.547403\pi\)
0.948143 + 0.317844i \(0.102959\pi\)
\(8\) 2.44949 1.41421i 0.306186 0.176777i
\(9\) 0 0
\(10\) 4.23867 7.34160i 0.423867 0.734160i
\(11\) 20.3832 3.59412i 1.85302 0.326738i 0.867653 0.497170i \(-0.165628\pi\)
0.985369 + 0.170433i \(0.0545165\pi\)
\(12\) 0 0
\(13\) 6.40830 2.33243i 0.492946 0.179418i −0.0835725 0.996502i \(-0.526633\pi\)
0.576519 + 0.817084i \(0.304411\pi\)
\(14\) 3.53490 + 9.71205i 0.252493 + 0.693718i
\(15\) 0 0
\(16\) 0.694593 + 3.93923i 0.0434120 + 0.246202i
\(17\) −1.96510 1.13455i −0.115594 0.0667382i 0.441088 0.897464i \(-0.354593\pi\)
−0.556682 + 0.830725i \(0.687926\pi\)
\(18\) 0 0
\(19\) −12.1634 21.0675i −0.640176 1.10882i −0.985393 0.170295i \(-0.945528\pi\)
0.345217 0.938523i \(-0.387805\pi\)
\(20\) 7.70624 + 9.18394i 0.385312 + 0.459197i
\(21\) 0 0
\(22\) −5.08285 + 28.8263i −0.231039 + 1.31028i
\(23\) 15.5320 18.5103i 0.675303 0.804795i −0.314192 0.949359i \(-0.601734\pi\)
0.989495 + 0.144564i \(0.0461781\pi\)
\(24\) 0 0
\(25\) 10.2734 + 3.73921i 0.410935 + 0.149568i
\(26\) 9.64433i 0.370936i
\(27\) 0 0
\(28\) −14.6164 −0.522014
\(29\) −6.32777 + 17.3854i −0.218199 + 0.599497i −0.999702 0.0244045i \(-0.992231\pi\)
0.781503 + 0.623901i \(0.214453\pi\)
\(30\) 0 0
\(31\) 16.6469 + 13.9684i 0.536998 + 0.450595i 0.870510 0.492151i \(-0.163789\pi\)
−0.333512 + 0.942746i \(0.608234\pi\)
\(32\) −5.57091 0.982302i −0.174091 0.0306970i
\(33\) 0 0
\(34\) 2.45823 2.06270i 0.0723009 0.0606677i
\(35\) −37.9390 + 21.9041i −1.08397 + 0.625831i
\(36\) 0 0
\(37\) 22.3832 38.7688i 0.604951 1.04781i −0.387109 0.922034i \(-0.626526\pi\)
0.992059 0.125771i \(-0.0401405\pi\)
\(38\) 33.8805 5.97405i 0.891592 0.157212i
\(39\) 0 0
\(40\) −15.9322 + 5.79885i −0.398305 + 0.144971i
\(41\) −17.5398 48.1902i −0.427800 1.17537i −0.947145 0.320806i \(-0.896046\pi\)
0.519345 0.854565i \(-0.326176\pi\)
\(42\) 0 0
\(43\) 6.41470 + 36.3796i 0.149179 + 0.846036i 0.963916 + 0.266206i \(0.0857701\pi\)
−0.814737 + 0.579830i \(0.803119\pi\)
\(44\) −35.8494 20.6977i −0.814760 0.470402i
\(45\) 0 0
\(46\) 17.0861 + 29.5941i 0.371438 + 0.643350i
\(47\) −8.15595 9.71989i −0.173531 0.206806i 0.672268 0.740308i \(-0.265320\pi\)
−0.845799 + 0.533502i \(0.820876\pi\)
\(48\) 0 0
\(49\) 0.765740 4.34273i 0.0156273 0.0886271i
\(50\) −9.93826 + 11.8440i −0.198765 + 0.236879i
\(51\) 0 0
\(52\) −12.8166 4.66486i −0.246473 0.0897089i
\(53\) 17.7730i 0.335339i 0.985843 + 0.167670i \(0.0536242\pi\)
−0.985843 + 0.167670i \(0.946376\pi\)
\(54\) 0 0
\(55\) −124.070 −2.25582
\(56\) 7.06980 19.4241i 0.126246 0.346859i
\(57\) 0 0
\(58\) −20.0432 16.8183i −0.345573 0.289970i
\(59\) −64.9049 11.4445i −1.10008 0.193974i −0.406003 0.913872i \(-0.633078\pi\)
−0.694080 + 0.719897i \(0.744189\pi\)
\(60\) 0 0
\(61\) 32.3438 27.1396i 0.530226 0.444912i −0.337954 0.941163i \(-0.609735\pi\)
0.868179 + 0.496251i \(0.165290\pi\)
\(62\) −26.6150 + 15.3662i −0.429274 + 0.247841i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) −40.2581 + 7.09859i −0.619356 + 0.109209i
\(66\) 0 0
\(67\) −111.190 + 40.4700i −1.65956 + 0.604030i −0.990293 0.138993i \(-0.955613\pi\)
−0.669266 + 0.743023i \(0.733391\pi\)
\(68\) 1.55216 + 4.26451i 0.0228258 + 0.0627134i
\(69\) 0 0
\(70\) −10.7582 61.0129i −0.153689 0.871613i
\(71\) 46.1702 + 26.6564i 0.650284 + 0.375442i 0.788565 0.614951i \(-0.210824\pi\)
−0.138281 + 0.990393i \(0.544158\pi\)
\(72\) 0 0
\(73\) 33.8569 + 58.6419i 0.463793 + 0.803314i 0.999146 0.0413148i \(-0.0131546\pi\)
−0.535353 + 0.844629i \(0.679821\pi\)
\(74\) 40.6944 + 48.4976i 0.549924 + 0.655374i
\(75\) 0 0
\(76\) −8.44858 + 47.9143i −0.111165 + 0.630451i
\(77\) 97.2298 115.874i 1.26273 1.50486i
\(78\) 0 0
\(79\) 104.610 + 38.0750i 1.32418 + 0.481962i 0.904795 0.425846i \(-0.140024\pi\)
0.419385 + 0.907809i \(0.362246\pi\)
\(80\) 23.9776i 0.299719i
\(81\) 0 0
\(82\) 72.5250 0.884452
\(83\) −8.63542 + 23.7256i −0.104041 + 0.285851i −0.980780 0.195115i \(-0.937492\pi\)
0.876739 + 0.480966i \(0.159714\pi\)
\(84\) 0 0
\(85\) 10.4196 + 8.74311i 0.122584 + 0.102860i
\(86\) −51.4485 9.07175i −0.598238 0.105486i
\(87\) 0 0
\(88\) 44.8457 37.6300i 0.509610 0.427614i
\(89\) 35.4447 20.4640i 0.398254 0.229932i −0.287476 0.957788i \(-0.592816\pi\)
0.685731 + 0.727855i \(0.259483\pi\)
\(90\) 0 0
\(91\) 24.9194 43.1616i 0.273839 0.474304i
\(92\) −47.5927 + 8.39188i −0.517312 + 0.0912161i
\(93\) 0 0
\(94\) 16.8620 6.13725i 0.179383 0.0652899i
\(95\) 49.8747 + 137.030i 0.524996 + 1.44242i
\(96\) 0 0
\(97\) 7.02010 + 39.8130i 0.0723722 + 0.410443i 0.999374 + 0.0353855i \(0.0112659\pi\)
−0.927002 + 0.375057i \(0.877623\pi\)
\(98\) 5.40078 + 3.11814i 0.0551100 + 0.0318178i
\(99\) 0 0
\(100\) −10.9327 18.9360i −0.109327 0.189360i
\(101\) −7.45688 8.88677i −0.0738305 0.0879878i 0.727865 0.685721i \(-0.240513\pi\)
−0.801695 + 0.597733i \(0.796068\pi\)
\(102\) 0 0
\(103\) 21.6451 122.756i 0.210147 1.19180i −0.678985 0.734152i \(-0.737580\pi\)
0.889132 0.457650i \(-0.151309\pi\)
\(104\) 12.3985 14.7760i 0.119216 0.142077i
\(105\) 0 0
\(106\) −23.6190 8.59660i −0.222820 0.0811000i
\(107\) 142.548i 1.33223i 0.745850 + 0.666113i \(0.232043\pi\)
−0.745850 + 0.666113i \(0.767957\pi\)
\(108\) 0 0
\(109\) −119.276 −1.09427 −0.547137 0.837043i \(-0.684282\pi\)
−0.547137 + 0.837043i \(0.684282\pi\)
\(110\) 60.0114 164.880i 0.545558 1.49891i
\(111\) 0 0
\(112\) 22.3936 + 18.7905i 0.199943 + 0.167772i
\(113\) 102.092 + 18.0016i 0.903471 + 0.159306i 0.606037 0.795436i \(-0.292758\pi\)
0.297434 + 0.954743i \(0.403869\pi\)
\(114\) 0 0
\(115\) −110.958 + 93.1047i −0.964851 + 0.809606i
\(116\) 32.0450 18.5012i 0.276250 0.159493i
\(117\) 0 0
\(118\) 46.6027 80.7183i 0.394938 0.684053i
\(119\) −16.3311 + 2.87961i −0.137236 + 0.0241984i
\(120\) 0 0
\(121\) 288.856 105.135i 2.38724 0.868885i
\(122\) 20.4222 + 56.1096i 0.167395 + 0.459915i
\(123\) 0 0
\(124\) −7.54711 42.8018i −0.0608638 0.345176i
\(125\) 73.0275 + 42.1624i 0.584220 + 0.337299i
\(126\) 0 0
\(127\) 109.770 + 190.127i 0.864329 + 1.49706i 0.867712 + 0.497067i \(0.165590\pi\)
−0.00338367 + 0.999994i \(0.501077\pi\)
\(128\) 7.27231 + 8.66680i 0.0568149 + 0.0677094i
\(129\) 0 0
\(130\) 10.0389 56.9336i 0.0772225 0.437951i
\(131\) −83.9745 + 100.077i −0.641027 + 0.763946i −0.984532 0.175205i \(-0.943941\pi\)
0.343505 + 0.939151i \(0.388386\pi\)
\(132\) 0 0
\(133\) −167.063 60.8058i −1.25611 0.457187i
\(134\) 167.339i 1.24880i
\(135\) 0 0
\(136\) −6.41798 −0.0471911
\(137\) −26.4097 + 72.5602i −0.192772 + 0.529636i −0.997992 0.0633396i \(-0.979825\pi\)
0.805220 + 0.592976i \(0.202047\pi\)
\(138\) 0 0
\(139\) −81.8517 68.6818i −0.588861 0.494113i 0.298982 0.954259i \(-0.403353\pi\)
−0.887844 + 0.460145i \(0.847797\pi\)
\(140\) 86.2852 + 15.2144i 0.616323 + 0.108674i
\(141\) 0 0
\(142\) −57.7564 + 48.4633i −0.406735 + 0.341291i
\(143\) 122.239 70.5747i 0.854818 0.493529i
\(144\) 0 0
\(145\) 55.4516 96.0450i 0.382425 0.662379i
\(146\) −94.3070 + 16.6289i −0.645938 + 0.113896i
\(147\) 0 0
\(148\) −84.1332 + 30.6220i −0.568468 + 0.206905i
\(149\) −53.0524 145.760i −0.356056 0.978257i −0.980384 0.197095i \(-0.936849\pi\)
0.624328 0.781162i \(-0.285373\pi\)
\(150\) 0 0
\(151\) −26.9250 152.699i −0.178311 1.01125i −0.934252 0.356614i \(-0.883931\pi\)
0.755940 0.654641i \(-0.227180\pi\)
\(152\) −59.5880 34.4032i −0.392026 0.226337i
\(153\) 0 0
\(154\) 106.959 + 185.258i 0.694538 + 1.20298i
\(155\) −83.7323 99.7883i −0.540208 0.643795i
\(156\) 0 0
\(157\) −21.0948 + 119.634i −0.134362 + 0.762003i 0.840941 + 0.541128i \(0.182002\pi\)
−0.975302 + 0.220875i \(0.929109\pi\)
\(158\) −101.198 + 120.603i −0.640492 + 0.763309i
\(159\) 0 0
\(160\) 31.8644 + 11.5977i 0.199153 + 0.0724856i
\(161\) 176.591i 1.09684i
\(162\) 0 0
\(163\) −66.9033 −0.410450 −0.205225 0.978715i \(-0.565793\pi\)
−0.205225 + 0.978715i \(0.565793\pi\)
\(164\) −35.0796 + 96.3804i −0.213900 + 0.587685i
\(165\) 0 0
\(166\) −27.3527 22.9517i −0.164776 0.138263i
\(167\) 7.14238 + 1.25939i 0.0427687 + 0.00754128i 0.194992 0.980805i \(-0.437532\pi\)
−0.152223 + 0.988346i \(0.548643\pi\)
\(168\) 0 0
\(169\) −93.8354 + 78.7373i −0.555239 + 0.465901i
\(170\) −16.6588 + 9.61798i −0.0979931 + 0.0565763i
\(171\) 0 0
\(172\) 36.9408 63.9833i 0.214772 0.371996i
\(173\) 71.4004 12.5898i 0.412719 0.0727735i 0.0365665 0.999331i \(-0.488358\pi\)
0.376153 + 0.926558i \(0.377247\pi\)
\(174\) 0 0
\(175\) 75.0799 27.3268i 0.429028 0.156153i
\(176\) 28.3161 + 77.7979i 0.160887 + 0.442033i
\(177\) 0 0
\(178\) 10.0509 + 57.0015i 0.0564658 + 0.320233i
\(179\) −219.366 126.651i −1.22551 0.707547i −0.259420 0.965765i \(-0.583531\pi\)
−0.966087 + 0.258218i \(0.916865\pi\)
\(180\) 0 0
\(181\) 19.4150 + 33.6278i 0.107265 + 0.185789i 0.914662 0.404221i \(-0.132457\pi\)
−0.807396 + 0.590010i \(0.799124\pi\)
\(182\) 45.3054 + 53.9928i 0.248931 + 0.296664i
\(183\) 0 0
\(184\) 11.8679 67.3063i 0.0644995 0.365795i
\(185\) −172.490 + 205.566i −0.932379 + 1.11117i
\(186\) 0 0
\(187\) −44.1328 16.0630i −0.236004 0.0858985i
\(188\) 25.3768i 0.134983i
\(189\) 0 0
\(190\) −206.226 −1.08540
\(191\) −67.8767 + 186.490i −0.355375 + 0.976385i 0.625238 + 0.780434i \(0.285002\pi\)
−0.980614 + 0.195951i \(0.937220\pi\)
\(192\) 0 0
\(193\) 43.6611 + 36.6360i 0.226223 + 0.189824i 0.748853 0.662736i \(-0.230605\pi\)
−0.522630 + 0.852560i \(0.675049\pi\)
\(194\) −56.3040 9.92792i −0.290227 0.0511748i
\(195\) 0 0
\(196\) −6.75608 + 5.66903i −0.0344698 + 0.0289236i
\(197\) 64.8251 37.4268i 0.329061 0.189984i −0.326363 0.945245i \(-0.605823\pi\)
0.655424 + 0.755261i \(0.272490\pi\)
\(198\) 0 0
\(199\) −65.2158 + 112.957i −0.327717 + 0.567623i −0.982059 0.188576i \(-0.939613\pi\)
0.654341 + 0.756200i \(0.272946\pi\)
\(200\) 30.4526 5.36961i 0.152263 0.0268481i
\(201\) 0 0
\(202\) 15.4167 5.61121i 0.0763201 0.0277783i
\(203\) 46.2446 + 127.056i 0.227806 + 0.625891i
\(204\) 0 0
\(205\) 53.3812 + 302.740i 0.260396 + 1.47678i
\(206\) 152.664 + 88.1404i 0.741085 + 0.427866i
\(207\) 0 0
\(208\) 13.6391 + 23.6237i 0.0655728 + 0.113575i
\(209\) −323.648 385.708i −1.54855 1.84549i
\(210\) 0 0
\(211\) 5.49032 31.1372i 0.0260205 0.147570i −0.969030 0.246945i \(-0.920573\pi\)
0.995050 + 0.0993753i \(0.0316844\pi\)
\(212\) 22.8485 27.2298i 0.107776 0.128442i
\(213\) 0 0
\(214\) −189.436 68.9491i −0.885215 0.322192i
\(215\) 221.437i 1.02994i
\(216\) 0 0
\(217\) 158.815 0.731865
\(218\) 57.6925 158.509i 0.264644 0.727105i
\(219\) 0 0
\(220\) 190.086 + 159.501i 0.864029 + 0.725006i
\(221\) −15.2392 2.68708i −0.0689557 0.0121587i
\(222\) 0 0
\(223\) 78.1769 65.5982i 0.350569 0.294162i −0.450449 0.892802i \(-0.648736\pi\)
0.801019 + 0.598639i \(0.204292\pi\)
\(224\) −35.8027 + 20.6707i −0.159833 + 0.0922799i
\(225\) 0 0
\(226\) −73.3037 + 126.966i −0.324353 + 0.561796i
\(227\) 253.309 44.6652i 1.11590 0.196763i 0.414859 0.909886i \(-0.363831\pi\)
0.701039 + 0.713123i \(0.252720\pi\)
\(228\) 0 0
\(229\) −258.391 + 94.0468i −1.12835 + 0.410685i −0.837692 0.546143i \(-0.816095\pi\)
−0.290655 + 0.956828i \(0.593873\pi\)
\(230\) −70.0601 192.489i −0.304609 0.836907i
\(231\) 0 0
\(232\) 9.08687 + 51.5342i 0.0391675 + 0.222130i
\(233\) 223.311 + 128.928i 0.958414 + 0.553341i 0.895685 0.444690i \(-0.146686\pi\)
0.0627296 + 0.998031i \(0.480019\pi\)
\(234\) 0 0
\(235\) 38.0296 + 65.8693i 0.161828 + 0.280295i
\(236\) 84.7273 + 100.974i 0.359014 + 0.427856i
\(237\) 0 0
\(238\) 4.07239 23.0957i 0.0171109 0.0970406i
\(239\) 80.0566 95.4078i 0.334965 0.399196i −0.572102 0.820183i \(-0.693872\pi\)
0.907067 + 0.420987i \(0.138316\pi\)
\(240\) 0 0
\(241\) −61.5004 22.3843i −0.255188 0.0928809i 0.211258 0.977430i \(-0.432244\pi\)
−0.466447 + 0.884549i \(0.654466\pi\)
\(242\) 434.721i 1.79637i
\(243\) 0 0
\(244\) −84.4436 −0.346080
\(245\) −9.04081 + 24.8394i −0.0369013 + 0.101385i
\(246\) 0 0
\(247\) −127.085 106.637i −0.514514 0.431729i
\(248\) 60.5309 + 10.6732i 0.244076 + 0.0430372i
\(249\) 0 0
\(250\) −91.3534 + 76.6546i −0.365413 + 0.306618i
\(251\) −202.528 + 116.930i −0.806884 + 0.465855i −0.845873 0.533385i \(-0.820920\pi\)
0.0389884 + 0.999240i \(0.487586\pi\)
\(252\) 0 0
\(253\) 250.064 433.123i 0.988395 1.71195i
\(254\) −305.759 + 53.9135i −1.20378 + 0.212258i
\(255\) 0 0
\(256\) −15.0351 + 5.47232i −0.0587308 + 0.0213763i
\(257\) −25.7075 70.6309i −0.100029 0.274828i 0.879576 0.475758i \(-0.157826\pi\)
−0.979606 + 0.200929i \(0.935604\pi\)
\(258\) 0 0
\(259\) −56.8110 322.191i −0.219347 1.24398i
\(260\) 70.8048 + 40.8792i 0.272326 + 0.157228i
\(261\) 0 0
\(262\) −92.3773 160.002i −0.352585 0.610695i
\(263\) 97.3609 + 116.030i 0.370194 + 0.441180i 0.918694 0.394971i \(-0.129245\pi\)
−0.548500 + 0.836151i \(0.684801\pi\)
\(264\) 0 0
\(265\) 18.5001 104.920i 0.0698119 0.395923i
\(266\) 161.613 192.603i 0.607567 0.724070i
\(267\) 0 0
\(268\) 222.381 + 80.9400i 0.829780 + 0.302015i
\(269\) 170.868i 0.635198i 0.948225 + 0.317599i \(0.102877\pi\)
−0.948225 + 0.317599i \(0.897123\pi\)
\(270\) 0 0
\(271\) −8.46530 −0.0312373 −0.0156186 0.999878i \(-0.504972\pi\)
−0.0156186 + 0.999878i \(0.504972\pi\)
\(272\) 3.10431 8.52903i 0.0114129 0.0313567i
\(273\) 0 0
\(274\) −83.6530 70.1932i −0.305303 0.256180i
\(275\) 222.844 + 39.2934i 0.810342 + 0.142885i
\(276\) 0 0
\(277\) 382.880 321.274i 1.38224 1.15984i 0.413862 0.910340i \(-0.364180\pi\)
0.968376 0.249496i \(-0.0802649\pi\)
\(278\) 130.864 75.5542i 0.470733 0.271778i
\(279\) 0 0
\(280\) −61.9541 + 107.308i −0.221265 + 0.383242i
\(281\) 68.9552 12.1587i 0.245392 0.0432693i −0.0495990 0.998769i \(-0.515794\pi\)
0.294991 + 0.955500i \(0.404683\pi\)
\(282\) 0 0
\(283\) 33.6840 12.2600i 0.119025 0.0433214i −0.281821 0.959467i \(-0.590939\pi\)
0.400846 + 0.916145i \(0.368716\pi\)
\(284\) −36.4680 100.195i −0.128409 0.352800i
\(285\) 0 0
\(286\) 34.6628 + 196.583i 0.121199 + 0.687352i
\(287\) −324.574 187.393i −1.13092 0.652937i
\(288\) 0 0
\(289\) −141.926 245.822i −0.491092 0.850596i
\(290\) 100.815 + 120.147i 0.347639 + 0.414300i
\(291\) 0 0
\(292\) 23.5168 133.370i 0.0805369 0.456747i
\(293\) 21.9392 26.1461i 0.0748779 0.0892360i −0.727305 0.686314i \(-0.759227\pi\)
0.802183 + 0.597078i \(0.203672\pi\)
\(294\) 0 0
\(295\) 371.242 + 135.121i 1.25845 + 0.458037i
\(296\) 126.618i 0.427765i
\(297\) 0 0
\(298\) 219.366 0.736126
\(299\) 56.3596 154.847i 0.188494 0.517882i
\(300\) 0 0
\(301\) 206.809 + 173.534i 0.687074 + 0.576524i
\(302\) 215.950 + 38.0777i 0.715065 + 0.126085i
\(303\) 0 0
\(304\) 74.5414 62.5476i 0.245202 0.205749i
\(305\) −219.186 + 126.547i −0.718642 + 0.414908i
\(306\) 0 0
\(307\) −165.305 + 286.316i −0.538452 + 0.932627i 0.460535 + 0.887641i \(0.347657\pi\)
−0.998988 + 0.0449854i \(0.985676\pi\)
\(308\) −297.929 + 52.5330i −0.967303 + 0.170562i
\(309\) 0 0
\(310\) 173.112 63.0075i 0.558425 0.203250i
\(311\) −82.6437 227.062i −0.265735 0.730102i −0.998755 0.0498938i \(-0.984112\pi\)
0.733019 0.680208i \(-0.238111\pi\)
\(312\) 0 0
\(313\) −54.4006 308.521i −0.173804 0.985691i −0.939515 0.342507i \(-0.888724\pi\)
0.765712 0.643184i \(-0.222387\pi\)
\(314\) −148.782 85.8993i −0.473828 0.273565i
\(315\) 0 0
\(316\) −111.324 192.819i −0.352291 0.610186i
\(317\) 317.348 + 378.201i 1.00110 + 1.19306i 0.981147 + 0.193262i \(0.0619068\pi\)
0.0199518 + 0.999801i \(0.493649\pi\)
\(318\) 0 0
\(319\) −66.4953 + 377.114i −0.208449 + 1.18217i
\(320\) −30.8250 + 36.7358i −0.0963280 + 0.114799i
\(321\) 0 0
\(322\) 234.677 + 85.4154i 0.728810 + 0.265265i
\(323\) 55.1997i 0.170897i
\(324\) 0 0
\(325\) 74.5564 0.229404
\(326\) 32.3604 88.9096i 0.0992651 0.272729i
\(327\) 0 0
\(328\) −111.115 93.2364i −0.338765 0.284257i
\(329\) −91.3206 16.1023i −0.277570 0.0489431i
\(330\) 0 0
\(331\) 198.545 166.599i 0.599833 0.503320i −0.291559 0.956553i \(-0.594174\pi\)
0.891392 + 0.453233i \(0.149730\pi\)
\(332\) 43.7313 25.2483i 0.131721 0.0760491i
\(333\) 0 0
\(334\) −5.12833 + 8.88254i −0.0153543 + 0.0265944i
\(335\) 698.519 123.168i 2.08513 0.367665i
\(336\) 0 0
\(337\) −431.168 + 156.932i −1.27943 + 0.465675i −0.890244 0.455484i \(-0.849466\pi\)
−0.389187 + 0.921159i \(0.627244\pi\)
\(338\) −59.2488 162.785i −0.175292 0.481612i
\(339\) 0 0
\(340\) −4.72388 26.7905i −0.0138938 0.0787955i
\(341\) 389.523 + 224.891i 1.14230 + 0.659505i
\(342\) 0 0
\(343\) 162.937 + 282.216i 0.475036 + 0.822786i
\(344\) 67.1612 + 80.0396i 0.195236 + 0.232673i
\(345\) 0 0
\(346\) −17.8047 + 100.975i −0.0514587 + 0.291837i
\(347\) −173.848 + 207.184i −0.501002 + 0.597071i −0.955980 0.293432i \(-0.905203\pi\)
0.454978 + 0.890503i \(0.349647\pi\)
\(348\) 0 0
\(349\) −314.152 114.342i −0.900148 0.327627i −0.149836 0.988711i \(-0.547875\pi\)
−0.750312 + 0.661084i \(0.770097\pi\)
\(350\) 112.993i 0.322838i
\(351\) 0 0
\(352\) −117.084 −0.332624
\(353\) −179.081 + 492.021i −0.507312 + 1.39383i 0.376688 + 0.926340i \(0.377063\pi\)
−0.884000 + 0.467487i \(0.845159\pi\)
\(354\) 0 0
\(355\) −244.810 205.420i −0.689607 0.578649i
\(356\) −80.6123 14.2141i −0.226439 0.0399273i
\(357\) 0 0
\(358\) 274.415 230.261i 0.766521 0.643188i
\(359\) 46.0527 26.5885i 0.128280 0.0740627i −0.434487 0.900678i \(-0.643070\pi\)
0.562767 + 0.826616i \(0.309737\pi\)
\(360\) 0 0
\(361\) −115.394 + 199.869i −0.319652 + 0.553653i
\(362\) −54.0798 + 9.53572i −0.149392 + 0.0263418i
\(363\) 0 0
\(364\) −93.6662 + 34.0917i −0.257325 + 0.0936586i
\(365\) −138.827 381.424i −0.380348 1.04500i
\(366\) 0 0
\(367\) 76.2686 + 432.541i 0.207816 + 1.17859i 0.892946 + 0.450164i \(0.148635\pi\)
−0.685129 + 0.728421i \(0.740254\pi\)
\(368\) 83.7047 + 48.3269i 0.227458 + 0.131323i
\(369\) 0 0
\(370\) −189.750 328.657i −0.512838 0.888261i
\(371\) 83.4906 + 99.5002i 0.225042 + 0.268195i
\(372\) 0 0
\(373\) −102.738 + 582.657i −0.275438 + 1.56208i 0.462131 + 0.886812i \(0.347085\pi\)
−0.737568 + 0.675272i \(0.764026\pi\)
\(374\) 42.6931 50.8797i 0.114153 0.136042i
\(375\) 0 0
\(376\) −33.7239 12.2745i −0.0896913 0.0326450i
\(377\) 126.170i 0.334668i
\(378\) 0 0
\(379\) 198.665 0.524183 0.262092 0.965043i \(-0.415588\pi\)
0.262092 + 0.965043i \(0.415588\pi\)
\(380\) 99.7493 274.059i 0.262498 0.721208i
\(381\) 0 0
\(382\) −215.000 180.406i −0.562826 0.472267i
\(383\) −31.8457 5.61525i −0.0831479 0.0146612i 0.131919 0.991260i \(-0.457886\pi\)
−0.215067 + 0.976599i \(0.568997\pi\)
\(384\) 0 0
\(385\) −694.594 + 582.833i −1.80414 + 1.51385i
\(386\) −69.8050 + 40.3019i −0.180842 + 0.104409i
\(387\) 0 0
\(388\) 40.4271 70.0219i 0.104194 0.180469i
\(389\) −215.378 + 37.9769i −0.553671 + 0.0976271i −0.443482 0.896284i \(-0.646257\pi\)
−0.110189 + 0.993911i \(0.535146\pi\)
\(390\) 0 0
\(391\) −51.5227 + 18.7527i −0.131772 + 0.0479610i
\(392\) −4.26587 11.7204i −0.0108823 0.0298989i
\(393\) 0 0
\(394\) 18.3822 + 104.251i 0.0466553 + 0.264596i
\(395\) −577.915 333.659i −1.46308 0.844707i
\(396\) 0 0
\(397\) −264.698 458.471i −0.666746 1.15484i −0.978809 0.204777i \(-0.934353\pi\)
0.312062 0.950062i \(-0.398980\pi\)
\(398\) −118.567 141.303i −0.297908 0.355033i
\(399\) 0 0
\(400\) −7.59378 + 43.0665i −0.0189844 + 0.107666i
\(401\) 167.829 200.011i 0.418526 0.498780i −0.515049 0.857161i \(-0.672226\pi\)
0.933576 + 0.358380i \(0.116671\pi\)
\(402\) 0 0
\(403\) 139.259 + 50.6862i 0.345556 + 0.125772i
\(404\) 23.2017i 0.0574299i
\(405\) 0 0
\(406\) −191.216 −0.470975
\(407\) 316.902 870.682i 0.778629 2.13927i
\(408\) 0 0
\(409\) 489.930 + 411.100i 1.19787 + 1.00513i 0.999688 + 0.0249695i \(0.00794888\pi\)
0.198184 + 0.980165i \(0.436496\pi\)
\(410\) −428.139 75.4924i −1.04424 0.184128i
\(411\) 0 0
\(412\) −190.974 + 160.246i −0.463529 + 0.388947i
\(413\) −417.126 + 240.828i −1.00999 + 0.583118i
\(414\) 0 0
\(415\) 75.6740 131.071i 0.182347 0.315834i
\(416\) −37.9912 + 6.69888i −0.0913251 + 0.0161031i
\(417\) 0 0
\(418\) 669.123 243.541i 1.60077 0.582634i
\(419\) 244.237 + 671.034i 0.582904 + 1.60151i 0.783194 + 0.621778i \(0.213589\pi\)
−0.200290 + 0.979737i \(0.564189\pi\)
\(420\) 0 0
\(421\) −12.1583 68.9530i −0.0288795 0.163784i 0.966957 0.254939i \(-0.0820553\pi\)
−0.995837 + 0.0911549i \(0.970944\pi\)
\(422\) 38.7234 + 22.3570i 0.0917616 + 0.0529786i
\(423\) 0 0
\(424\) 25.1348 + 43.5347i 0.0592801 + 0.102676i
\(425\) −15.9459 19.0036i −0.0375197 0.0447143i
\(426\) 0 0
\(427\) 53.5818 303.877i 0.125484 0.711656i
\(428\) 183.257 218.397i 0.428169 0.510272i
\(429\) 0 0
\(430\) 294.274 + 107.107i 0.684358 + 0.249086i
\(431\) 76.1177i 0.176607i −0.996094 0.0883036i \(-0.971855\pi\)
0.996094 0.0883036i \(-0.0281446\pi\)
\(432\) 0 0
\(433\) 109.713 0.253380 0.126690 0.991942i \(-0.459565\pi\)
0.126690 + 0.991942i \(0.459565\pi\)
\(434\) −76.8170 + 211.053i −0.176998 + 0.486297i
\(435\) 0 0
\(436\) 182.741 + 153.338i 0.419131 + 0.351693i
\(437\) −578.887 102.073i −1.32468 0.233578i
\(438\) 0 0
\(439\) 87.3258 73.2751i 0.198920 0.166914i −0.537887 0.843017i \(-0.680777\pi\)
0.736807 + 0.676103i \(0.236333\pi\)
\(440\) −303.908 + 175.461i −0.690701 + 0.398776i
\(441\) 0 0
\(442\) 10.9420 18.9521i 0.0247556 0.0428780i
\(443\) −170.087 + 29.9909i −0.383944 + 0.0676996i −0.362289 0.932066i \(-0.618005\pi\)
−0.0216549 + 0.999766i \(0.506893\pi\)
\(444\) 0 0
\(445\) −230.542 + 83.9106i −0.518073 + 0.188563i
\(446\) 49.3618 + 135.621i 0.110677 + 0.304082i
\(447\) 0 0
\(448\) −10.1524 57.5773i −0.0226617 0.128521i
\(449\) −164.941 95.2288i −0.367352 0.212091i 0.304949 0.952369i \(-0.401361\pi\)
−0.672301 + 0.740278i \(0.734694\pi\)
\(450\) 0 0
\(451\) −530.719 919.233i −1.17676 2.03821i
\(452\) −133.272 158.827i −0.294849 0.351388i
\(453\) 0 0
\(454\) −63.1661 + 358.233i −0.139132 + 0.789059i
\(455\) −192.035 + 228.858i −0.422054 + 0.502985i
\(456\) 0 0
\(457\) −135.071 49.1618i −0.295560 0.107575i 0.189984 0.981787i \(-0.439156\pi\)
−0.485544 + 0.874212i \(0.661379\pi\)
\(458\) 388.872i 0.849066i
\(459\) 0 0
\(460\) 289.690 0.629762
\(461\) −223.385 + 613.745i −0.484566 + 1.33133i 0.420974 + 0.907073i \(0.361688\pi\)
−0.905540 + 0.424261i \(0.860534\pi\)
\(462\) 0 0
\(463\) 17.1769 + 14.4132i 0.0370992 + 0.0311299i 0.661149 0.750255i \(-0.270069\pi\)
−0.624050 + 0.781385i \(0.714514\pi\)
\(464\) −72.8804 12.8508i −0.157070 0.0276956i
\(465\) 0 0
\(466\) −279.349 + 234.402i −0.599462 + 0.503008i
\(467\) 413.326 238.634i 0.885065 0.510993i 0.0127402 0.999919i \(-0.495945\pi\)
0.872325 + 0.488926i \(0.162611\pi\)
\(468\) 0 0
\(469\) −432.376 + 748.898i −0.921911 + 1.59680i
\(470\) −105.930 + 18.6783i −0.225383 + 0.0397411i
\(471\) 0 0
\(472\) −175.169 + 63.7563i −0.371120 + 0.135077i
\(473\) 261.505 + 718.478i 0.552864 + 1.51898i
\(474\) 0 0
\(475\) −46.1829 261.916i −0.0972272 0.551403i
\(476\) 28.7226 + 16.5830i 0.0603417 + 0.0348383i
\(477\) 0 0
\(478\) 88.0673 + 152.537i 0.184241 + 0.319115i
\(479\) −383.849 457.454i −0.801356 0.955019i 0.198329 0.980136i \(-0.436449\pi\)
−0.999685 + 0.0251168i \(0.992004\pi\)
\(480\) 0 0
\(481\) 53.0126 300.649i 0.110213 0.625051i
\(482\) 59.4942 70.9024i 0.123432 0.147100i
\(483\) 0 0
\(484\) −577.712 210.270i −1.19362 0.434442i
\(485\) 242.336i 0.499662i
\(486\) 0 0
\(487\) 758.948 1.55842 0.779208 0.626766i \(-0.215622\pi\)
0.779208 + 0.626766i \(0.215622\pi\)
\(488\) 40.8445 112.219i 0.0836977 0.229957i
\(489\) 0 0
\(490\) −28.6368 24.0291i −0.0584425 0.0490391i
\(491\) −258.651 45.6071i −0.526783 0.0928861i −0.0960694 0.995375i \(-0.530627\pi\)
−0.430714 + 0.902489i \(0.641738\pi\)
\(492\) 0 0
\(493\) 32.1593 26.9849i 0.0652319 0.0547360i
\(494\) 203.182 117.307i 0.411300 0.237464i
\(495\) 0 0
\(496\) −43.4621 + 75.2785i −0.0876252 + 0.151771i
\(497\) 383.701 67.6568i 0.772033 0.136130i
\(498\) 0 0
\(499\) 85.4398 31.0975i 0.171222 0.0623197i −0.254987 0.966945i \(-0.582071\pi\)
0.426209 + 0.904625i \(0.359849\pi\)
\(500\) −57.6816 158.479i −0.115363 0.316958i
\(501\) 0 0
\(502\) −57.4301 325.702i −0.114403 0.648809i
\(503\) 368.263 + 212.617i 0.732134 + 0.422698i 0.819202 0.573505i \(-0.194417\pi\)
−0.0870685 + 0.996202i \(0.527750\pi\)
\(504\) 0 0
\(505\) 34.7700 + 60.2234i 0.0688515 + 0.119254i
\(506\) 454.636 + 541.814i 0.898490 + 1.07078i
\(507\) 0 0
\(508\) 76.2453 432.408i 0.150089 0.851198i
\(509\) 434.422 517.724i 0.853481 1.01714i −0.146130 0.989265i \(-0.546682\pi\)
0.999611 0.0278737i \(-0.00887363\pi\)
\(510\) 0 0
\(511\) 465.022 + 169.254i 0.910023 + 0.331221i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 106.298 0.206805
\(515\) −255.556 + 702.135i −0.496226 + 1.36337i
\(516\) 0 0
\(517\) −201.179 168.809i −0.389128 0.326517i
\(518\) 455.647 + 80.3428i 0.879627 + 0.155102i
\(519\) 0 0
\(520\) −88.5729 + 74.3215i −0.170333 + 0.142926i
\(521\) 677.597 391.211i 1.30057 0.750885i 0.320069 0.947394i \(-0.396294\pi\)
0.980502 + 0.196509i \(0.0629606\pi\)
\(522\) 0 0
\(523\) −342.909 + 593.936i −0.655658 + 1.13563i 0.326071 + 0.945345i \(0.394275\pi\)
−0.981729 + 0.190287i \(0.939058\pi\)
\(524\) 257.313 45.3712i 0.491055 0.0865863i
\(525\) 0 0
\(526\) −201.288 + 73.2629i −0.382677 + 0.139283i
\(527\) −16.8650 46.3362i −0.0320019 0.0879244i
\(528\) 0 0
\(529\) −9.52859 54.0393i −0.0180124 0.102154i
\(530\) 130.482 + 75.3338i 0.246192 + 0.142139i
\(531\) 0 0
\(532\) 177.784 + 307.931i 0.334181 + 0.578819i
\(533\) −224.801 267.907i −0.421765 0.502640i
\(534\) 0 0
\(535\) 148.381 841.508i 0.277347 1.57291i
\(536\) −215.127 + 256.378i −0.401356 + 0.478317i
\(537\) 0 0
\(538\) −227.071 82.6472i −0.422066 0.153619i
\(539\) 91.2710i 0.169334i
\(540\) 0 0
\(541\) 884.789 1.63547 0.817735 0.575595i \(-0.195229\pi\)
0.817735 + 0.575595i \(0.195229\pi\)
\(542\) 4.09458 11.2498i 0.00755457 0.0207560i
\(543\) 0 0
\(544\) 9.83292 + 8.25080i 0.0180752 + 0.0151669i
\(545\) 704.124 + 124.156i 1.29197 + 0.227809i
\(546\) 0 0
\(547\) 263.600 221.186i 0.481901 0.404363i −0.369212 0.929345i \(-0.620373\pi\)
0.851113 + 0.524982i \(0.175928\pi\)
\(548\) 133.744 77.2169i 0.244058 0.140907i
\(549\) 0 0
\(550\) −160.005 + 277.137i −0.290919 + 0.503886i
\(551\) 443.235 78.1542i 0.804419 0.141841i
\(552\) 0 0
\(553\) 764.512 278.260i 1.38248 0.503182i
\(554\) 241.755 + 664.216i 0.436381 + 1.19895i
\(555\) 0 0
\(556\) 37.1086 + 210.453i 0.0667420 + 0.378513i
\(557\) 274.575 + 158.526i 0.492953 + 0.284606i 0.725799 0.687907i \(-0.241470\pi\)
−0.232846 + 0.972514i \(0.574804\pi\)
\(558\) 0 0
\(559\) 125.960 + 218.169i 0.225331 + 0.390285i
\(560\) −112.637 134.236i −0.201138 0.239707i
\(561\) 0 0
\(562\) −17.1950 + 97.5174i −0.0305960 + 0.173519i
\(563\) −130.488 + 155.510i −0.231773 + 0.276216i −0.869379 0.494147i \(-0.835481\pi\)
0.637605 + 0.770363i \(0.279925\pi\)
\(564\) 0 0
\(565\) −583.945 212.539i −1.03353 0.376174i
\(566\) 50.6935i 0.0895646i
\(567\) 0 0
\(568\) 150.791 0.265477
\(569\) 80.4994 221.170i 0.141475 0.388700i −0.848637 0.528975i \(-0.822576\pi\)
0.990113 + 0.140275i \(0.0447987\pi\)
\(570\) 0 0
\(571\) 50.2848 + 42.1940i 0.0880645 + 0.0738949i 0.685757 0.727830i \(-0.259471\pi\)
−0.597693 + 0.801725i \(0.703916\pi\)
\(572\) −278.010 49.0207i −0.486031 0.0857005i
\(573\) 0 0
\(574\) 406.024 340.695i 0.707359 0.593545i
\(575\) 228.780 132.086i 0.397878 0.229715i
\(576\) 0 0
\(577\) 72.1281 124.930i 0.125005 0.216516i −0.796730 0.604336i \(-0.793439\pi\)
0.921735 + 0.387820i \(0.126772\pi\)
\(578\) 395.328 69.7069i 0.683958 0.120600i
\(579\) 0 0
\(580\) −208.430 + 75.8622i −0.359362 + 0.130797i
\(581\) 63.1094 + 173.392i 0.108622 + 0.298436i
\(582\) 0 0
\(583\) 63.8781 + 362.271i 0.109568 + 0.621391i
\(584\) 165.864 + 95.7618i 0.284014 + 0.163976i
\(585\) 0 0
\(586\) 24.1345 + 41.8022i 0.0411852 + 0.0713348i
\(587\) −364.747 434.688i −0.621375 0.740526i 0.359931 0.932979i \(-0.382800\pi\)
−0.981306 + 0.192453i \(0.938356\pi\)
\(588\) 0 0
\(589\) 91.7982 520.613i 0.155854 0.883894i
\(590\) −359.132 + 427.996i −0.608698 + 0.725418i
\(591\) 0 0
\(592\) 168.266 + 61.2440i 0.284234 + 0.103453i
\(593\) 174.635i 0.294494i −0.989100 0.147247i \(-0.952959\pi\)
0.989100 0.147247i \(-0.0470412\pi\)
\(594\) 0 0
\(595\) 99.4051 0.167067
\(596\) −106.105 + 291.521i −0.178028 + 0.489128i
\(597\) 0 0
\(598\) 178.519 + 149.796i 0.298527 + 0.250494i
\(599\) 424.905 + 74.9222i 0.709357 + 0.125079i 0.516674 0.856182i \(-0.327170\pi\)
0.192683 + 0.981261i \(0.438281\pi\)
\(600\) 0 0
\(601\) −636.447 + 534.042i −1.05898 + 0.888589i −0.994009 0.109298i \(-0.965140\pi\)
−0.0649703 + 0.997887i \(0.520695\pi\)
\(602\) −330.645 + 190.898i −0.549244 + 0.317106i
\(603\) 0 0
\(604\) −155.055 + 268.563i −0.256714 + 0.444641i
\(605\) −1814.65 + 319.971i −2.99942 + 0.528878i
\(606\) 0 0
\(607\) 352.792 128.406i 0.581205 0.211541i −0.0346516 0.999399i \(-0.511032\pi\)
0.615857 + 0.787858i \(0.288810\pi\)
\(608\) 47.0663 + 129.314i 0.0774117 + 0.212687i
\(609\) 0 0
\(610\) −62.1537 352.491i −0.101891 0.577854i
\(611\) −74.9368 43.2648i −0.122646 0.0708098i
\(612\) 0 0
\(613\) 192.466 + 333.361i 0.313974 + 0.543820i 0.979219 0.202806i \(-0.0650060\pi\)
−0.665245 + 0.746626i \(0.731673\pi\)
\(614\) −300.537 358.166i −0.489474 0.583333i
\(615\) 0 0
\(616\) 74.2929 421.336i 0.120605 0.683987i
\(617\) 106.165 126.523i 0.172066 0.205061i −0.673119 0.739534i \(-0.735046\pi\)
0.845185 + 0.534474i \(0.179490\pi\)
\(618\) 0 0
\(619\) −449.740 163.692i −0.726560 0.264446i −0.0478519 0.998854i \(-0.515238\pi\)
−0.678708 + 0.734408i \(0.737460\pi\)
\(620\) 260.529i 0.420208i
\(621\) 0 0
\(622\) 341.722 0.549392
\(623\) 102.301 281.071i 0.164208 0.451157i
\(624\) 0 0
\(625\) −596.591 500.599i −0.954545 0.800958i
\(626\) 436.315 + 76.9341i 0.696989 + 0.122898i
\(627\) 0 0
\(628\) 186.118 156.172i 0.296366 0.248681i
\(629\) −87.9703 + 50.7897i −0.139857 + 0.0807467i
\(630\) 0 0
\(631\) 124.618 215.844i 0.197493 0.342067i −0.750222 0.661186i \(-0.770053\pi\)
0.947715 + 0.319119i \(0.103387\pi\)
\(632\) 310.088 54.6769i 0.490645 0.0865140i
\(633\) 0 0
\(634\) −656.099 + 238.801i −1.03486 + 0.376657i
\(635\) −450.100 1236.64i −0.708819 1.94746i
\(636\) 0 0
\(637\) −5.22202 29.6155i −0.00819783 0.0464922i
\(638\) −468.993 270.773i −0.735099 0.424410i
\(639\) 0 0
\(640\) −33.9094 58.7328i −0.0529834 0.0917700i
\(641\) −144.405 172.096i −0.225282 0.268480i 0.641550 0.767081i \(-0.278292\pi\)
−0.866832 + 0.498601i \(0.833847\pi\)
\(642\) 0 0
\(643\) −63.2329 + 358.612i −0.0983404 + 0.557716i 0.895332 + 0.445399i \(0.146938\pi\)
−0.993672 + 0.112317i \(0.964173\pi\)
\(644\) −227.021 + 270.554i −0.352518 + 0.420114i
\(645\) 0 0
\(646\) −73.3564 26.6995i −0.113555 0.0413305i
\(647\) 1200.78i 1.85593i 0.372671 + 0.927964i \(0.378442\pi\)
−0.372671 + 0.927964i \(0.621558\pi\)
\(648\) 0 0
\(649\) −1364.11 −2.10186
\(650\) −36.0621 + 99.0799i −0.0554802 + 0.152431i
\(651\) 0 0
\(652\) 102.502 + 86.0092i 0.157211 + 0.131916i
\(653\) −626.194 110.415i −0.958949 0.169089i −0.327797 0.944748i \(-0.606306\pi\)
−0.631152 + 0.775659i \(0.717417\pi\)
\(654\) 0 0
\(655\) 599.900 503.376i 0.915878 0.768513i
\(656\) 177.649 102.566i 0.270807 0.156350i
\(657\) 0 0
\(658\) 65.5696 113.570i 0.0996498 0.172599i
\(659\) −1147.84 + 202.395i −1.74179 + 0.307125i −0.951965 0.306207i \(-0.900940\pi\)
−0.789825 + 0.613332i \(0.789829\pi\)
\(660\) 0 0
\(661\) 904.893 329.354i 1.36898 0.498266i 0.450158 0.892949i \(-0.351368\pi\)
0.918818 + 0.394683i \(0.129145\pi\)
\(662\) 125.363 + 344.433i 0.189371 + 0.520292i
\(663\) 0 0
\(664\) 12.4007 + 70.3280i 0.0186758 + 0.105916i
\(665\) 922.931 + 532.854i 1.38787 + 0.801285i
\(666\) 0 0
\(667\) 223.526 + 387.159i 0.335122 + 0.580448i
\(668\) −9.32371 11.1116i −0.0139577 0.0166341i
\(669\) 0 0
\(670\) −174.185 + 987.855i −0.259978 + 1.47441i
\(671\) 561.728 669.441i 0.837150 0.997677i
\(672\) 0 0
\(673\) 612.694 + 223.002i 0.910392 + 0.331355i 0.754409 0.656404i \(-0.227923\pi\)
0.155982 + 0.987760i \(0.450146\pi\)
\(674\) 648.897i 0.962755i
\(675\) 0 0
\(676\) 244.987 0.362407
\(677\) 258.040 708.958i 0.381152 1.04721i −0.589720 0.807608i \(-0.700762\pi\)
0.970872 0.239598i \(-0.0770158\pi\)
\(678\) 0 0
\(679\) 226.327 + 189.911i 0.333325 + 0.279693i
\(680\) 37.8874 + 6.68058i 0.0557168 + 0.00982438i
\(681\) 0 0
\(682\) −487.272 + 408.870i −0.714475 + 0.599516i
\(683\) 405.766 234.269i 0.594094 0.343000i −0.172621 0.984988i \(-0.555224\pi\)
0.766715 + 0.641988i \(0.221890\pi\)
\(684\) 0 0
\(685\) 231.434 400.856i 0.337860 0.585191i
\(686\) −453.855 + 80.0268i −0.661596 + 0.116657i
\(687\) 0 0
\(688\) −138.852 + 50.5380i −0.201820 + 0.0734563i
\(689\) 41.4542 + 113.895i 0.0601658 + 0.165304i
\(690\) 0 0
\(691\) 37.3428 + 211.781i 0.0540416 + 0.306485i 0.999833 0.0182903i \(-0.00582232\pi\)
−0.945791 + 0.324776i \(0.894711\pi\)
\(692\) −125.577 72.5019i −0.181470 0.104772i
\(693\) 0 0
\(694\) −191.243 331.243i −0.275567 0.477296i
\(695\) 411.705 + 490.651i 0.592382 + 0.705973i
\(696\) 0 0
\(697\) −20.2068 + 114.598i −0.0289911 + 0.164416i
\(698\) 303.904 362.178i 0.435392 0.518880i
\(699\) 0 0
\(700\) −150.160 54.6537i −0.214514 0.0780767i
\(701\) 848.227i 1.21002i −0.796216 0.605012i \(-0.793168\pi\)
0.796216 0.605012i \(-0.206832\pi\)
\(702\) 0 0
\(703\) −1089.02 −1.54910
\(704\) 56.6322 155.596i 0.0804435 0.221017i
\(705\) 0 0
\(706\) −567.240 475.971i −0.803456 0.674180i
\(707\) −83.4932 14.7221i −0.118095 0.0208234i
\(708\) 0 0
\(709\) −63.9344 + 53.6473i −0.0901754 + 0.0756662i −0.686761 0.726883i \(-0.740968\pi\)
0.596586 + 0.802549i \(0.296524\pi\)
\(710\) 391.401 225.975i 0.551268 0.318275i
\(711\) 0 0
\(712\) 57.8809 100.253i 0.0812934 0.140804i
\(713\) 517.120 91.1822i 0.725273 0.127885i
\(714\) 0 0
\(715\) −795.078 + 289.385i −1.11200 + 0.404734i
\(716\) 173.269 + 476.052i 0.241995 + 0.664876i
\(717\) 0 0
\(718\) 13.0590 + 74.0612i 0.0181880 + 0.103149i
\(719\) −1032.07 595.867i −1.43543 0.828744i −0.437899 0.899024i \(-0.644277\pi\)
−0.997527 + 0.0702802i \(0.977611\pi\)
\(720\) 0 0
\(721\) −455.481 788.916i −0.631735 1.09420i
\(722\) −209.796 250.025i −0.290576 0.346295i
\(723\) 0 0
\(724\) 13.4855 76.4803i 0.0186264 0.105636i
\(725\) −130.015 + 154.946i −0.179331 + 0.213719i
\(726\) 0 0
\(727\) −633.829 230.695i −0.871842 0.317325i −0.132929 0.991126i \(-0.542438\pi\)
−0.738913 + 0.673801i \(0.764661\pi\)
\(728\) 140.965i 0.193634i
\(729\) 0 0
\(730\) 574.034 0.786348
\(731\) 28.6689 78.7672i 0.0392188 0.107753i
\(732\) 0 0
\(733\) −149.604 125.532i −0.204098 0.171259i 0.535010 0.844846i \(-0.320308\pi\)
−0.739107 + 0.673588i \(0.764752\pi\)
\(734\) −611.705 107.860i −0.833386 0.146948i
\(735\) 0 0
\(736\) −104.710 + 87.8621i −0.142269 + 0.119378i
\(737\) −2120.97 + 1224.54i −2.87784 + 1.66152i
\(738\) 0 0
\(739\) −718.905 + 1245.18i −0.972807 + 1.68495i −0.285818 + 0.958284i \(0.592265\pi\)
−0.686989 + 0.726668i \(0.741068\pi\)
\(740\) 528.540 93.1959i 0.714244 0.125940i
\(741\) 0 0
\(742\) −172.612 + 62.8256i −0.232631 + 0.0846707i
\(743\) 342.663 + 941.458i 0.461188 + 1.26710i 0.924593 + 0.380957i \(0.124405\pi\)
−0.463405 + 0.886147i \(0.653372\pi\)
\(744\) 0 0
\(745\) 161.461 + 915.693i 0.216727 + 1.22912i
\(746\) −724.615 418.357i −0.971334 0.560800i
\(747\) 0 0
\(748\) 46.9651 + 81.3460i 0.0627876 + 0.108751i
\(749\) 669.637 + 798.043i 0.894042 + 1.06548i
\(750\) 0 0
\(751\) −129.904 + 736.724i −0.172975 + 0.980990i 0.767480 + 0.641073i \(0.221510\pi\)
−0.940455 + 0.339918i \(0.889601\pi\)
\(752\) 32.6238 38.8795i 0.0433827 0.0517015i
\(753\) 0 0
\(754\) −167.671 61.0271i −0.222375 0.0809378i
\(755\) 929.460i 1.23107i
\(756\) 0 0
\(757\) 788.946 1.04220 0.521100 0.853496i \(-0.325522\pi\)
0.521100 + 0.853496i \(0.325522\pi\)
\(758\) −96.0924 + 264.012i −0.126771 + 0.348300i
\(759\) 0 0
\(760\) 315.956 + 265.119i 0.415732 + 0.348841i
\(761\) −512.126 90.3016i −0.672965 0.118662i −0.173284 0.984872i \(-0.555438\pi\)
−0.499680 + 0.866210i \(0.666549\pi\)
\(762\) 0 0
\(763\) −667.754 + 560.312i −0.875170 + 0.734354i
\(764\) 343.739 198.458i 0.449921 0.259762i
\(765\) 0 0
\(766\) 22.8657 39.6045i 0.0298507 0.0517030i
\(767\) −442.624 + 78.0465i −0.577084 + 0.101756i
\(768\) 0 0
\(769\) 683.962 248.942i 0.889417 0.323721i 0.143413 0.989663i \(-0.454192\pi\)
0.746004 + 0.665942i \(0.231970\pi\)
\(770\) −438.575 1204.97i −0.569578 1.56490i
\(771\) 0 0
\(772\) −19.7943 112.259i −0.0256403 0.145414i
\(773\) 980.568 + 566.131i 1.26852 + 0.732382i 0.974708 0.223480i \(-0.0717419\pi\)
0.293814 + 0.955862i \(0.405075\pi\)
\(774\) 0 0
\(775\) 118.790 + 205.750i 0.153277 + 0.265483i
\(776\) 73.4997 + 87.5935i 0.0947161 + 0.112878i
\(777\) 0 0
\(778\) 53.7075 304.590i 0.0690328 0.391504i
\(779\) −801.907 + 955.675i −1.02941 + 1.22680i
\(780\) 0 0
\(781\) 1036.90 + 377.402i 1.32766 + 0.483229i
\(782\) 77.5404i 0.0991565i
\(783\) 0 0
\(784\) 17.6389 0.0224986
\(785\) 249.058 684.282i 0.317272 0.871697i
\(786\) 0 0
\(787\) −591.843 496.615i −0.752024 0.631023i 0.184013 0.982924i \(-0.441091\pi\)
−0.936037 + 0.351901i \(0.885536\pi\)
\(788\) −147.433 25.9964i −0.187097 0.0329903i
\(789\) 0 0
\(790\) 722.940 606.619i 0.915114 0.767872i
\(791\) 656.118 378.810i 0.829479 0.478900i
\(792\) 0 0
\(793\) 143.967 249.359i 0.181548 0.314450i
\(794\) 737.306 130.007i 0.928597 0.163737i
\(795\) 0 0
\(796\) 245.131 89.2204i 0.307954 0.112086i
\(797\) −383.656 1054.09i −0.481375 1.32257i −0.908315 0.418287i \(-0.862631\pi\)
0.426940 0.904280i \(-0.359592\pi\)
\(798\) 0 0
\(799\) 4.99955 + 28.3539i 0.00625726 + 0.0354867i
\(800\) −53.5591 30.9224i −0.0669489 0.0386530i
\(801\) 0 0
\(802\) 184.623 + 319.776i 0.230203 + 0.398723i
\(803\) 900.880 + 1073.63i 1.12189 + 1.33702i
\(804\) 0 0
\(805\) −183.817 + 1042.48i −0.228343 + 1.29500i
\(806\) −134.716 + 160.549i −0.167142 + 0.199192i
\(807\) 0 0
\(808\) −30.8333 11.2224i −0.0381601 0.0138891i
\(809\) 1053.93i 1.30275i −0.758754 0.651377i \(-0.774192\pi\)
0.758754 0.651377i \(-0.225808\pi\)
\(810\) 0 0
\(811\) −440.011 −0.542554 −0.271277 0.962501i \(-0.587446\pi\)
−0.271277 + 0.962501i \(0.587446\pi\)
\(812\) 92.4892 254.112i 0.113903 0.312946i
\(813\) 0 0
\(814\) 1003.79 + 842.279i 1.23316 + 1.03474i
\(815\) 394.952 + 69.6407i 0.484603 + 0.0854487i
\(816\) 0 0
\(817\) 688.404 577.639i 0.842600 0.707025i
\(818\) −783.295 + 452.236i −0.957574 + 0.552855i
\(819\) 0 0
\(820\) 307.410 532.450i 0.374890 0.649329i
\(821\) 293.175 51.6946i 0.357095 0.0629654i 0.00777691 0.999970i \(-0.497525\pi\)
0.349318 + 0.937004i \(0.386413\pi\)
\(822\) 0 0
\(823\) −452.037 + 164.528i −0.549255 + 0.199912i −0.601715 0.798711i \(-0.705516\pi\)
0.0524604 + 0.998623i \(0.483294\pi\)
\(824\) −120.583 331.299i −0.146339 0.402062i
\(825\) 0 0
\(826\) −118.283 670.815i −0.143199 0.812125i
\(827\) 271.357 + 156.668i 0.328122 + 0.189441i 0.655007 0.755623i \(-0.272666\pi\)
−0.326885 + 0.945064i \(0.605999\pi\)
\(828\) 0 0
\(829\) 320.622 + 555.333i 0.386757 + 0.669883i 0.992011 0.126149i \(-0.0402618\pi\)
−0.605254 + 0.796032i \(0.706928\pi\)
\(830\) 137.581 + 163.963i 0.165761 + 0.197546i
\(831\) 0 0
\(832\) 9.47365 53.7277i 0.0113866 0.0645766i
\(833\) −6.43179 + 7.66511i −0.00772124 + 0.00920182i
\(834\) 0 0
\(835\) −40.8528 14.8692i −0.0489255 0.0178074i
\(836\) 1007.01i 1.20456i
\(837\) 0 0
\(838\) −1009.89 −1.20512
\(839\) −301.891 + 829.438i −0.359822 + 0.988603i 0.619269 + 0.785179i \(0.287429\pi\)
−0.979091 + 0.203424i \(0.934793\pi\)
\(840\) 0 0
\(841\) 382.032 + 320.563i 0.454259 + 0.381168i
\(842\) 97.5142 + 17.1944i 0.115813 + 0.0204209i
\(843\) 0 0
\(844\) −48.4408 + 40.6467i −0.0573944 + 0.0481596i
\(845\) 635.899 367.137i 0.752544 0.434481i
\(846\) 0 0
\(847\) 1123.25 1945.52i 1.32615 2.29696i
\(848\) −70.0118 + 12.3450i −0.0825611 + 0.0145578i
\(849\) 0 0
\(850\) 32.9672 11.9991i 0.0387850 0.0141166i
\(851\) −369.967 1016.47i −0.434743 1.19445i
\(852\) 0 0
\(853\) −241.895 1371.85i −0.283581 1.60827i −0.710311 0.703888i \(-0.751446\pi\)
0.426730 0.904379i \(-0.359666\pi\)
\(854\) 377.913 + 218.188i 0.442522 + 0.255490i
\(855\) 0 0
\(856\) 201.594 + 349.171i 0.235507 + 0.407910i
\(857\) 81.1695 + 96.7341i 0.0947135 + 0.112875i 0.811319 0.584603i \(-0.198750\pi\)
−0.716606 + 0.697478i \(0.754305\pi\)
\(858\) 0 0
\(859\) 197.472 1119.92i 0.229886 1.30375i −0.623234 0.782035i \(-0.714182\pi\)
0.853120 0.521714i \(-0.174707\pi\)
\(860\) −284.674 + 339.262i −0.331017 + 0.394490i
\(861\) 0 0
\(862\) 101.155 + 36.8173i 0.117349 + 0.0427115i
\(863\) 458.427i 0.531202i −0.964083 0.265601i \(-0.914430\pi\)
0.964083 0.265601i \(-0.0855703\pi\)
\(864\) 0 0
\(865\) −434.605 −0.502433
\(866\) −53.0672 + 145.801i −0.0612786 + 0.168362i
\(867\) 0 0
\(868\) −243.318 204.168i −0.280321 0.235217i
\(869\) 2269.14 + 400.111i 2.61121 + 0.460427i
\(870\) 0 0
\(871\) −618.148 + 518.688i −0.709700 + 0.595509i
\(872\) −292.165 + 168.682i −0.335052 + 0.193442i
\(873\) 0 0
\(874\) 415.650 719.926i 0.475572 0.823714i
\(875\) 606.900 107.013i 0.693600 0.122300i
\(876\) 0 0
\(877\) −1234.89 + 449.462i −1.40808 + 0.512500i −0.930566 0.366124i \(-0.880685\pi\)
−0.477515 + 0.878623i \(0.658462\pi\)
\(878\) 55.1386 + 151.492i 0.0628002 + 0.172542i
\(879\) 0 0
\(880\) −86.1781 488.740i −0.0979297 0.555387i
\(881\) −1313.98 758.626i −1.49146 0.861096i −0.491510 0.870872i \(-0.663555\pi\)
−0.999952 + 0.00977549i \(0.996888\pi\)
\(882\) 0 0
\(883\) −761.692 1319.29i −0.862619 1.49410i −0.869392 0.494123i \(-0.835489\pi\)
0.00677344 0.999977i \(-0.497844\pi\)
\(884\) 19.8934 + 23.7080i 0.0225038 + 0.0268190i
\(885\) 0 0
\(886\) 42.4136 240.539i 0.0478709 0.271489i
\(887\) 506.405 603.510i 0.570919 0.680394i −0.400901 0.916122i \(-0.631303\pi\)
0.971819 + 0.235727i \(0.0757472\pi\)
\(888\) 0 0
\(889\) 1507.68 + 548.750i 1.69593 + 0.617266i
\(890\) 346.960i 0.389843i
\(891\) 0 0
\(892\) −204.105 −0.228818
\(893\) −105.570 + 290.052i −0.118220 + 0.324807i
\(894\) 0 0
\(895\) 1163.15 + 976.002i 1.29961 + 1.09050i
\(896\) 81.4267 + 14.3577i 0.0908780 + 0.0160242i
\(897\) 0 0
\(898\) 206.332 173.133i 0.229769 0.192799i
\(899\) −348.185 + 201.025i −0.387303 + 0.223609i
\(900\) 0 0
\(901\) 20.1643 34.9256i 0.0223799 0.0387632i
\(902\) 1478.30 260.663i 1.63891 0.288984i
\(903\) 0 0
\(904\) 275.532 100.285i 0.304792 0.110935i
\(905\) −79.6095 218.725i −0.0879663 0.241685i
\(906\) 0 0
\(907\) 295.268 + 1674.55i 0.325544 + 1.84625i 0.505825 + 0.862636i \(0.331188\pi\)
−0.180281 + 0.983615i \(0.557701\pi\)
\(908\) −445.512 257.217i −0.490652 0.283278i
\(909\) 0 0
\(910\) −211.250 365.896i −0.232143 0.402084i
\(911\) 195.203 + 232.634i 0.214273 + 0.255361i 0.862466 0.506116i \(-0.168919\pi\)
−0.648192 + 0.761477i \(0.724475\pi\)
\(912\) 0 0
\(913\) −90.7453 + 514.642i −0.0993924 + 0.563682i
\(914\) 130.665 155.720i 0.142959 0.170372i
\(915\) 0 0
\(916\) 516.783 + 188.094i 0.564173 + 0.205342i
\(917\) 954.751i 1.04117i
\(918\) 0 0
\(919\) −682.579 −0.742741 −0.371370 0.928485i \(-0.621112\pi\)
−0.371370 + 0.928485i \(0.621112\pi\)
\(920\) −140.120 + 384.977i −0.152305 + 0.418453i
\(921\) 0 0
\(922\) −707.573 593.724i −0.767432 0.643952i
\(923\) 358.046 + 63.1332i 0.387916 + 0.0684001i
\(924\) 0 0
\(925\) 374.915 314.591i 0.405314 0.340099i
\(926\) −27.4623 + 15.8554i −0.0296570 + 0.0171224i
\(927\) 0 0
\(928\) 52.3292 90.6368i 0.0563892 0.0976690i
\(929\) 786.356 138.656i 0.846454 0.149253i 0.266432 0.963854i \(-0.414155\pi\)
0.580022 + 0.814601i \(0.303044\pi\)
\(930\) 0 0
\(931\) −100.805 + 36.6898i −0.108276 + 0.0394091i
\(932\) −176.384 484.612i −0.189254 0.519970i
\(933\) 0 0
\(934\) 117.205 + 664.704i 0.125487 + 0.711674i
\(935\) 243.810 + 140.764i 0.260759 + 0.150549i
\(936\) 0 0
\(937\) −386.927 670.176i −0.412942 0.715236i 0.582268 0.812997i \(-0.302165\pi\)
−0.995210 + 0.0977605i \(0.968832\pi\)
\(938\) −786.094 936.830i −0.838053 0.998753i
\(939\) 0 0
\(940\) 26.4151 149.808i 0.0281012 0.159370i
\(941\) −838.349 + 999.106i −0.890913 + 1.06175i 0.106808 + 0.994280i \(0.465937\pi\)
−0.997721 + 0.0674693i \(0.978508\pi\)
\(942\) 0 0
\(943\) −1164.44 423.822i −1.23483 0.449440i
\(944\) 263.625i 0.279263i
\(945\) 0 0
\(946\) −1081.29 −1.14301
\(947\) 282.223 775.402i 0.298018 0.818799i −0.696813 0.717253i \(-0.745399\pi\)
0.994831 0.101545i \(-0.0323787\pi\)
\(948\) 0 0
\(949\) 353.744 + 296.826i 0.372754 + 0.312778i
\(950\) 370.405 + 65.3125i 0.389901 + 0.0687500i
\(951\) 0 0
\(952\) −35.9305 + 30.1492i −0.0377421 + 0.0316694i
\(953\) −1058.27 + 610.995i −1.11047 + 0.641128i −0.938950 0.344054i \(-0.888200\pi\)
−0.171516 + 0.985181i \(0.554866\pi\)
\(954\) 0 0
\(955\) 594.817 1030.25i 0.622846 1.07880i
\(956\) −245.308 + 43.2544i −0.256598 + 0.0452452i
\(957\) 0 0
\(958\) 793.586 288.842i 0.828378 0.301505i
\(959\) 193.008 + 530.284i 0.201259 + 0.552955i
\(960\) 0 0
\(961\) −84.8726 481.336i −0.0883169 0.500870i
\(962\) 373.899 + 215.871i 0.388669 + 0.224398i
\(963\) 0 0
\(964\) 65.4473 + 113.358i 0.0678914 + 0.117591i
\(965\) −219.611 261.722i −0.227576 0.271214i
\(966\) 0 0
\(967\) −46.9384 + 266.201i −0.0485403 + 0.275286i −0.999412 0.0343010i \(-0.989080\pi\)
0.950871 + 0.309587i \(0.100191\pi\)
\(968\) 558.867 666.032i 0.577342 0.688049i
\(969\) 0 0
\(970\) 322.047 + 117.215i 0.332007 + 0.120841i
\(971\) 1817.80i 1.87209i 0.351883 + 0.936044i \(0.385542\pi\)
−0.351883 + 0.936044i \(0.614458\pi\)
\(972\) 0 0
\(973\) −780.879 −0.802548
\(974\) −367.095 + 1008.59i −0.376895 + 1.03551i
\(975\) 0 0
\(976\) 129.375 + 108.559i 0.132556 + 0.111228i
\(977\) −1295.60 228.448i −1.32610 0.233826i −0.534654 0.845071i \(-0.679558\pi\)
−0.791442 + 0.611245i \(0.790669\pi\)
\(978\) 0 0
\(979\) 648.927 544.514i 0.662847 0.556195i
\(980\) 45.7843 26.4336i 0.0467187 0.0269730i
\(981\) 0 0
\(982\) 185.715 321.668i 0.189119 0.327564i
\(983\) −623.860 + 110.003i −0.634649 + 0.111906i −0.481711 0.876330i \(-0.659984\pi\)
−0.152938 + 0.988236i \(0.548873\pi\)
\(984\) 0 0
\(985\) −421.641 + 153.465i −0.428062 + 0.155802i
\(986\) 20.3058 + 55.7896i 0.0205941 + 0.0565818i
\(987\) 0 0
\(988\) 57.6157 + 326.755i 0.0583155 + 0.330723i
\(989\) 773.029 + 446.309i 0.781627 + 0.451273i
\(990\) 0 0
\(991\) 817.383 + 1415.75i 0.824806 + 1.42861i 0.902067 + 0.431595i \(0.142049\pi\)
−0.0772613 + 0.997011i \(0.524618\pi\)
\(992\) −79.0175 94.1693i −0.0796547 0.0949288i
\(993\) 0 0
\(994\) −95.6811 + 542.635i −0.0962587 + 0.545910i
\(995\) 502.568 598.938i 0.505094 0.601947i
\(996\) 0 0
\(997\) 412.548 + 150.155i 0.413789 + 0.150607i 0.540522 0.841330i \(-0.318227\pi\)
−0.126733 + 0.991937i \(0.540449\pi\)
\(998\) 128.585i 0.128842i
\(999\) 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 162.3.f.a.17.1 36
3.2 odd 2 54.3.f.a.23.5 36
12.11 even 2 432.3.bc.c.401.2 36
27.7 even 9 54.3.f.a.47.5 yes 36
27.13 even 9 1458.3.b.c.1457.4 36
27.14 odd 18 1458.3.b.c.1457.33 36
27.20 odd 18 inner 162.3.f.a.143.1 36
108.7 odd 18 432.3.bc.c.209.2 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.23.5 36 3.2 odd 2
54.3.f.a.47.5 yes 36 27.7 even 9
162.3.f.a.17.1 36 1.1 even 1 trivial
162.3.f.a.143.1 36 27.20 odd 18 inner
432.3.bc.c.209.2 36 108.7 odd 18
432.3.bc.c.401.2 36 12.11 even 2
1458.3.b.c.1457.4 36 27.13 even 9
1458.3.b.c.1457.33 36 27.14 odd 18