Properties

Label 441.2.u.c.64.2
Level $441$
Weight $2$
Character 441.64
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), degree \(6\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 64.2
Character \(\chi\) \(=\) 441.64
Dual form 441.2.u.c.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.271791 + 1.19079i) q^{2} +(0.457820 + 0.220474i) q^{4} +(0.164209 - 0.205912i) q^{5} +(2.60345 + 0.471214i) q^{7} +(-1.91005 + 2.39513i) q^{8} +O(q^{10})\) \(q+(-0.271791 + 1.19079i) q^{2} +(0.457820 + 0.220474i) q^{4} +(0.164209 - 0.205912i) q^{5} +(2.60345 + 0.471214i) q^{7} +(-1.91005 + 2.39513i) q^{8} +(0.200568 + 0.251504i) q^{10} +(-0.153939 + 0.674453i) q^{11} +(-0.135275 + 0.592678i) q^{13} +(-1.26871 + 2.97210i) q^{14} +(-1.69933 - 2.13089i) q^{16} +(3.45113 - 1.66198i) q^{17} -0.615297 q^{19} +(0.120576 - 0.0580665i) q^{20} +(-0.761295 - 0.366620i) q^{22} +(5.76051 + 2.77412i) q^{23} +(1.09717 + 4.80701i) q^{25} +(-0.668991 - 0.322169i) q^{26} +(1.08802 + 0.789725i) q^{28} +(-1.87727 + 0.904044i) q^{29} -5.96883 q^{31} +(-2.52090 + 1.21400i) q^{32} +(1.04108 + 4.56129i) q^{34} +(0.524539 - 0.458703i) q^{35} +(-2.85657 + 1.37565i) q^{37} +(0.167232 - 0.732692i) q^{38} +(0.179537 + 0.786604i) q^{40} +(-0.738263 + 0.925753i) q^{41} +(-5.16974 - 6.48265i) q^{43} +(-0.219176 + 0.274838i) q^{44} +(-4.86905 + 6.10560i) q^{46} +(2.14312 - 9.38961i) q^{47} +(6.55591 + 2.45357i) q^{49} -6.02236 q^{50} +(-0.192602 + 0.241515i) q^{52} +(-1.39064 - 0.669699i) q^{53} +(0.113599 + 0.142449i) q^{55} +(-6.10135 + 5.33556i) q^{56} +(-0.566305 - 2.48115i) q^{58} +(6.23715 + 7.82114i) q^{59} +(7.51520 - 3.61913i) q^{61} +(1.62227 - 7.10765i) q^{62} +(-1.97343 - 8.64618i) q^{64} +(0.0998260 + 0.125178i) q^{65} -10.7485 q^{67} +1.94642 q^{68} +(0.403656 + 0.749289i) q^{70} +(-4.67009 - 2.24899i) q^{71} +(-2.50573 - 10.9783i) q^{73} +(-0.861728 - 3.77548i) q^{74} +(-0.281695 - 0.135657i) q^{76} +(-0.718586 + 1.68337i) q^{77} +15.8299 q^{79} -0.717820 q^{80} +(-0.901727 - 1.13073i) q^{82} +(1.83820 + 8.05367i) q^{83} +(0.224486 - 0.983539i) q^{85} +(9.12458 - 4.39417i) q^{86} +(-1.32137 - 1.65694i) q^{88} +(-4.13037 - 18.0963i) q^{89} +(-0.631460 + 1.47927i) q^{91} +(2.02565 + 2.54009i) q^{92} +(10.5986 + 5.10402i) q^{94} +(-0.101037 + 0.126697i) q^{95} +12.1405 q^{97} +(-4.70353 + 7.13988i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - q^{2} - 3 q^{4} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - q^{2} - 3 q^{4} - 3 q^{8} - 30 q^{10} - 9 q^{11} + 21 q^{14} - 29 q^{16} - 5 q^{17} + 26 q^{19} + 13 q^{20} + 11 q^{22} - 4 q^{23} - 28 q^{25} + 22 q^{26} - 7 q^{28} - 6 q^{29} + 36 q^{31} - 14 q^{32} + 46 q^{34} + 7 q^{35} - 22 q^{37} + 45 q^{38} + 35 q^{40} + 11 q^{41} + 6 q^{43} - 82 q^{44} - 16 q^{46} - 29 q^{47} - 42 q^{49} + 48 q^{50} - 50 q^{52} - 28 q^{53} + 23 q^{55} - 21 q^{56} + 39 q^{58} + 15 q^{59} - 32 q^{61} + 8 q^{62} + 29 q^{64} + 21 q^{65} - 34 q^{67} + 22 q^{68} - 24 q^{71} - 15 q^{73} - 6 q^{74} + 7 q^{76} + 21 q^{77} - 34 q^{79} - 8 q^{80} + 14 q^{82} - 14 q^{83} + 20 q^{85} + 100 q^{86} - 108 q^{88} - 10 q^{89} + 84 q^{91} + 21 q^{92} + 99 q^{94} - 18 q^{95} - 64 q^{97} - 91 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{7}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.271791 + 1.19079i −0.192185 + 0.842018i 0.783246 + 0.621712i \(0.213563\pi\)
−0.975431 + 0.220306i \(0.929294\pi\)
\(3\) 0 0
\(4\) 0.457820 + 0.220474i 0.228910 + 0.110237i
\(5\) 0.164209 0.205912i 0.0734366 0.0920865i −0.743756 0.668451i \(-0.766958\pi\)
0.817193 + 0.576364i \(0.195529\pi\)
\(6\) 0 0
\(7\) 2.60345 + 0.471214i 0.984012 + 0.178102i
\(8\) −1.91005 + 2.39513i −0.675305 + 0.846806i
\(9\) 0 0
\(10\) 0.200568 + 0.251504i 0.0634251 + 0.0795326i
\(11\) −0.153939 + 0.674453i −0.0464145 + 0.203355i −0.992819 0.119630i \(-0.961829\pi\)
0.946404 + 0.322985i \(0.104686\pi\)
\(12\) 0 0
\(13\) −0.135275 + 0.592678i −0.0375185 + 0.164379i −0.990217 0.139539i \(-0.955438\pi\)
0.952698 + 0.303918i \(0.0982950\pi\)
\(14\) −1.26871 + 2.97210i −0.339078 + 0.794327i
\(15\) 0 0
\(16\) −1.69933 2.13089i −0.424832 0.532722i
\(17\) 3.45113 1.66198i 0.837021 0.403088i 0.0342775 0.999412i \(-0.489087\pi\)
0.802744 + 0.596324i \(0.203373\pi\)
\(18\) 0 0
\(19\) −0.615297 −0.141159 −0.0705794 0.997506i \(-0.522485\pi\)
−0.0705794 + 0.997506i \(0.522485\pi\)
\(20\) 0.120576 0.0580665i 0.0269617 0.0129841i
\(21\) 0 0
\(22\) −0.761295 0.366620i −0.162309 0.0781637i
\(23\) 5.76051 + 2.77412i 1.20115 + 0.578443i 0.924003 0.382385i \(-0.124897\pi\)
0.277146 + 0.960828i \(0.410611\pi\)
\(24\) 0 0
\(25\) 1.09717 + 4.80701i 0.219434 + 0.961403i
\(26\) −0.668991 0.322169i −0.131200 0.0631825i
\(27\) 0 0
\(28\) 1.08802 + 0.789725i 0.205616 + 0.149244i
\(29\) −1.87727 + 0.904044i −0.348600 + 0.167877i −0.599987 0.800010i \(-0.704828\pi\)
0.251387 + 0.967887i \(0.419113\pi\)
\(30\) 0 0
\(31\) −5.96883 −1.07203 −0.536017 0.844207i \(-0.680072\pi\)
−0.536017 + 0.844207i \(0.680072\pi\)
\(32\) −2.52090 + 1.21400i −0.445636 + 0.214607i
\(33\) 0 0
\(34\) 1.04108 + 4.56129i 0.178544 + 0.782254i
\(35\) 0.524539 0.458703i 0.0886633 0.0775350i
\(36\) 0 0
\(37\) −2.85657 + 1.37565i −0.469617 + 0.226156i −0.653698 0.756755i \(-0.726783\pi\)
0.184081 + 0.982911i \(0.441069\pi\)
\(38\) 0.167232 0.732692i 0.0271286 0.118858i
\(39\) 0 0
\(40\) 0.179537 + 0.786604i 0.0283873 + 0.124373i
\(41\) −0.738263 + 0.925753i −0.115297 + 0.144578i −0.836131 0.548530i \(-0.815188\pi\)
0.720834 + 0.693108i \(0.243759\pi\)
\(42\) 0 0
\(43\) −5.16974 6.48265i −0.788378 0.988595i −0.999937 0.0112294i \(-0.996425\pi\)
0.211559 0.977365i \(-0.432146\pi\)
\(44\) −0.219176 + 0.274838i −0.0330420 + 0.0414334i
\(45\) 0 0
\(46\) −4.86905 + 6.10560i −0.717903 + 0.900221i
\(47\) 2.14312 9.38961i 0.312606 1.36962i −0.537615 0.843190i \(-0.680675\pi\)
0.850221 0.526426i \(-0.176468\pi\)
\(48\) 0 0
\(49\) 6.55591 + 2.45357i 0.936559 + 0.350510i
\(50\) −6.02236 −0.851690
\(51\) 0 0
\(52\) −0.192602 + 0.241515i −0.0267091 + 0.0334921i
\(53\) −1.39064 0.669699i −0.191020 0.0919902i 0.335929 0.941887i \(-0.390950\pi\)
−0.526949 + 0.849897i \(0.676664\pi\)
\(54\) 0 0
\(55\) 0.113599 + 0.142449i 0.0153178 + 0.0192079i
\(56\) −6.10135 + 5.33556i −0.815327 + 0.712994i
\(57\) 0 0
\(58\) −0.566305 2.48115i −0.0743596 0.325790i
\(59\) 6.23715 + 7.82114i 0.812008 + 1.01823i 0.999354 + 0.0359314i \(0.0114398\pi\)
−0.187347 + 0.982294i \(0.559989\pi\)
\(60\) 0 0
\(61\) 7.51520 3.61913i 0.962223 0.463382i 0.114268 0.993450i \(-0.463548\pi\)
0.847955 + 0.530068i \(0.177833\pi\)
\(62\) 1.62227 7.10765i 0.206029 0.902672i
\(63\) 0 0
\(64\) −1.97343 8.64618i −0.246679 1.08077i
\(65\) 0.0998260 + 0.125178i 0.0123819 + 0.0155264i
\(66\) 0 0
\(67\) −10.7485 −1.31313 −0.656566 0.754268i \(-0.727992\pi\)
−0.656566 + 0.754268i \(0.727992\pi\)
\(68\) 1.94642 0.236038
\(69\) 0 0
\(70\) 0.403656 + 0.749289i 0.0482461 + 0.0895571i
\(71\) −4.67009 2.24899i −0.554237 0.266907i 0.135732 0.990746i \(-0.456662\pi\)
−0.689969 + 0.723839i \(0.742376\pi\)
\(72\) 0 0
\(73\) −2.50573 10.9783i −0.293274 1.28492i −0.879939 0.475087i \(-0.842416\pi\)
0.586665 0.809830i \(-0.300441\pi\)
\(74\) −0.861728 3.77548i −0.100174 0.438890i
\(75\) 0 0
\(76\) −0.281695 0.135657i −0.0323126 0.0155609i
\(77\) −0.718586 + 1.68337i −0.0818904 + 0.191837i
\(78\) 0 0
\(79\) 15.8299 1.78101 0.890504 0.454975i \(-0.150352\pi\)
0.890504 + 0.454975i \(0.150352\pi\)
\(80\) −0.717820 −0.0802547
\(81\) 0 0
\(82\) −0.901727 1.13073i −0.0995791 0.124868i
\(83\) 1.83820 + 8.05367i 0.201768 + 0.884005i 0.969860 + 0.243665i \(0.0783497\pi\)
−0.768091 + 0.640341i \(0.778793\pi\)
\(84\) 0 0
\(85\) 0.224486 0.983539i 0.0243490 0.106680i
\(86\) 9.12458 4.39417i 0.983929 0.473835i
\(87\) 0 0
\(88\) −1.32137 1.65694i −0.140858 0.176631i
\(89\) −4.13037 18.0963i −0.437819 1.91821i −0.393847 0.919176i \(-0.628856\pi\)
−0.0439721 0.999033i \(-0.514001\pi\)
\(90\) 0 0
\(91\) −0.631460 + 1.47927i −0.0661950 + 0.155069i
\(92\) 2.02565 + 2.54009i 0.211189 + 0.264823i
\(93\) 0 0
\(94\) 10.5986 + 5.10402i 1.09316 + 0.526439i
\(95\) −0.101037 + 0.126697i −0.0103662 + 0.0129988i
\(96\) 0 0
\(97\) 12.1405 1.23268 0.616339 0.787481i \(-0.288615\pi\)
0.616339 + 0.787481i \(0.288615\pi\)
\(98\) −4.70353 + 7.13988i −0.475128 + 0.721237i
\(99\) 0 0
\(100\) −0.557517 + 2.44264i −0.0557517 + 0.244264i
\(101\) 0.817165 1.02469i 0.0813110 0.101961i −0.739512 0.673143i \(-0.764944\pi\)
0.820823 + 0.571183i \(0.193515\pi\)
\(102\) 0 0
\(103\) 5.91684 7.41948i 0.583003 0.731063i −0.399619 0.916682i \(-0.630857\pi\)
0.982622 + 0.185618i \(0.0594288\pi\)
\(104\) −1.16116 1.45605i −0.113861 0.142777i
\(105\) 0 0
\(106\) 1.17544 1.47395i 0.114169 0.143163i
\(107\) −2.76501 12.1143i −0.267303 1.17113i −0.913137 0.407653i \(-0.866347\pi\)
0.645834 0.763478i \(-0.276510\pi\)
\(108\) 0 0
\(109\) −0.314606 + 1.37838i −0.0301338 + 0.132025i −0.987757 0.155998i \(-0.950141\pi\)
0.957624 + 0.288023i \(0.0929978\pi\)
\(110\) −0.200503 + 0.0965571i −0.0191172 + 0.00920636i
\(111\) 0 0
\(112\) −3.42001 6.34841i −0.323161 0.599869i
\(113\) −3.07242 13.4612i −0.289029 1.26632i −0.885860 0.463952i \(-0.846431\pi\)
0.596831 0.802367i \(-0.296426\pi\)
\(114\) 0 0
\(115\) 1.51715 0.730622i 0.141475 0.0681308i
\(116\) −1.05877 −0.0983041
\(117\) 0 0
\(118\) −11.0086 + 5.30144i −1.01342 + 0.488037i
\(119\) 9.76799 2.70065i 0.895430 0.247568i
\(120\) 0 0
\(121\) 9.47947 + 4.56507i 0.861770 + 0.415006i
\(122\) 2.26707 + 9.93270i 0.205251 + 0.899264i
\(123\) 0 0
\(124\) −2.73265 1.31597i −0.245399 0.118178i
\(125\) 2.35643 + 1.13480i 0.210766 + 0.101499i
\(126\) 0 0
\(127\) −19.3774 + 9.33165i −1.71946 + 0.828050i −0.729970 + 0.683480i \(0.760466\pi\)
−0.989494 + 0.144571i \(0.953820\pi\)
\(128\) 5.23619 0.462818
\(129\) 0 0
\(130\) −0.176193 + 0.0848500i −0.0154531 + 0.00744183i
\(131\) −4.11563 5.16083i −0.359584 0.450904i 0.568828 0.822457i \(-0.307397\pi\)
−0.928412 + 0.371552i \(0.878826\pi\)
\(132\) 0 0
\(133\) −1.60190 0.289937i −0.138902 0.0251407i
\(134\) 2.92133 12.7992i 0.252364 1.10568i
\(135\) 0 0
\(136\) −2.61119 + 11.4404i −0.223907 + 0.981002i
\(137\) 0.894004 + 1.12105i 0.0763799 + 0.0957774i 0.818553 0.574430i \(-0.194776\pi\)
−0.742174 + 0.670208i \(0.766205\pi\)
\(138\) 0 0
\(139\) 7.24276 9.08213i 0.614323 0.770337i −0.373210 0.927747i \(-0.621743\pi\)
0.987533 + 0.157410i \(0.0503145\pi\)
\(140\) 0.341277 0.0943560i 0.0288431 0.00797454i
\(141\) 0 0
\(142\) 3.94737 4.94985i 0.331256 0.415382i
\(143\) −0.378909 0.182473i −0.0316860 0.0152592i
\(144\) 0 0
\(145\) −0.122111 + 0.535003i −0.0101408 + 0.0444296i
\(146\) 13.7540 1.13829
\(147\) 0 0
\(148\) −1.61109 −0.132431
\(149\) 2.40170 10.5225i 0.196755 0.862039i −0.776098 0.630613i \(-0.782804\pi\)
0.972852 0.231426i \(-0.0743393\pi\)
\(150\) 0 0
\(151\) −0.299677 0.144317i −0.0243873 0.0117443i 0.421650 0.906759i \(-0.361451\pi\)
−0.446038 + 0.895014i \(0.647165\pi\)
\(152\) 1.17525 1.47372i 0.0953253 0.119534i
\(153\) 0 0
\(154\) −1.80924 1.31321i −0.145792 0.105822i
\(155\) −0.980137 + 1.22905i −0.0787265 + 0.0987199i
\(156\) 0 0
\(157\) −7.40382 9.28409i −0.590889 0.740951i 0.393038 0.919522i \(-0.371424\pi\)
−0.983927 + 0.178571i \(0.942853\pi\)
\(158\) −4.30243 + 18.8502i −0.342283 + 1.49964i
\(159\) 0 0
\(160\) −0.163978 + 0.718433i −0.0129636 + 0.0567971i
\(161\) 13.6900 + 9.93671i 1.07892 + 0.783122i
\(162\) 0 0
\(163\) −6.42527 8.05703i −0.503266 0.631076i 0.463697 0.885994i \(-0.346523\pi\)
−0.966963 + 0.254919i \(0.917951\pi\)
\(164\) −0.542096 + 0.261060i −0.0423306 + 0.0203853i
\(165\) 0 0
\(166\) −10.0899 −0.783125
\(167\) −2.56144 + 1.23352i −0.198210 + 0.0954529i −0.530356 0.847775i \(-0.677942\pi\)
0.332146 + 0.943228i \(0.392227\pi\)
\(168\) 0 0
\(169\) 11.3796 + 5.48014i 0.875356 + 0.421549i
\(170\) 1.11018 + 0.534634i 0.0851468 + 0.0410045i
\(171\) 0 0
\(172\) −0.937551 4.10768i −0.0714876 0.313207i
\(173\) 8.31687 + 4.00519i 0.632320 + 0.304509i 0.722452 0.691421i \(-0.243015\pi\)
−0.0901327 + 0.995930i \(0.528729\pi\)
\(174\) 0 0
\(175\) 0.591293 + 13.0318i 0.0446976 + 0.985114i
\(176\) 1.69878 0.818088i 0.128050 0.0616657i
\(177\) 0 0
\(178\) 22.6716 1.69931
\(179\) −15.3996 + 7.41607i −1.15102 + 0.554303i −0.909341 0.416052i \(-0.863413\pi\)
−0.241682 + 0.970356i \(0.577699\pi\)
\(180\) 0 0
\(181\) −0.831306 3.64219i −0.0617905 0.270722i 0.934590 0.355727i \(-0.115767\pi\)
−0.996381 + 0.0850048i \(0.972909\pi\)
\(182\) −1.58987 1.15399i −0.117849 0.0855394i
\(183\) 0 0
\(184\) −17.6472 + 8.49846i −1.30097 + 0.626515i
\(185\) −0.185812 + 0.814096i −0.0136612 + 0.0598536i
\(186\) 0 0
\(187\) 0.589659 + 2.58347i 0.0431202 + 0.188922i
\(188\) 3.05133 3.82625i 0.222541 0.279058i
\(189\) 0 0
\(190\) −0.123409 0.154750i −0.00895302 0.0112267i
\(191\) −15.2730 + 19.1518i −1.10512 + 1.38577i −0.190388 + 0.981709i \(0.560975\pi\)
−0.914730 + 0.404065i \(0.867597\pi\)
\(192\) 0 0
\(193\) −1.42392 + 1.78554i −0.102496 + 0.128526i −0.830434 0.557117i \(-0.811908\pi\)
0.727938 + 0.685643i \(0.240479\pi\)
\(194\) −3.29967 + 14.4568i −0.236902 + 1.03794i
\(195\) 0 0
\(196\) 2.46048 + 2.56870i 0.175748 + 0.183479i
\(197\) −15.8935 −1.13236 −0.566182 0.824280i \(-0.691580\pi\)
−0.566182 + 0.824280i \(0.691580\pi\)
\(198\) 0 0
\(199\) −6.66062 + 8.35215i −0.472159 + 0.592068i −0.959698 0.281033i \(-0.909323\pi\)
0.487539 + 0.873101i \(0.337895\pi\)
\(200\) −13.6091 6.55378i −0.962307 0.463423i
\(201\) 0 0
\(202\) 0.998099 + 1.25158i 0.0702260 + 0.0880606i
\(203\) −5.31337 + 1.46904i −0.372925 + 0.103106i
\(204\) 0 0
\(205\) 0.0693938 + 0.304034i 0.00484668 + 0.0212347i
\(206\) 7.22692 + 9.06228i 0.503524 + 0.631399i
\(207\) 0 0
\(208\) 1.49281 0.718898i 0.103508 0.0498466i
\(209\) 0.0947185 0.414989i 0.00655182 0.0287054i
\(210\) 0 0
\(211\) 3.30311 + 14.4719i 0.227396 + 0.996286i 0.951754 + 0.306862i \(0.0992790\pi\)
−0.724358 + 0.689424i \(0.757864\pi\)
\(212\) −0.489013 0.613203i −0.0335855 0.0421149i
\(213\) 0 0
\(214\) 15.1771 1.03749
\(215\) −2.18377 −0.148932
\(216\) 0 0
\(217\) −15.5396 2.81260i −1.05489 0.190932i
\(218\) −1.55586 0.749261i −0.105376 0.0507464i
\(219\) 0 0
\(220\) 0.0206017 + 0.0902618i 0.00138896 + 0.00608545i
\(221\) 0.518165 + 2.27023i 0.0348556 + 0.152712i
\(222\) 0 0
\(223\) −17.1603 8.26397i −1.14914 0.553396i −0.240364 0.970683i \(-0.577267\pi\)
−0.908775 + 0.417286i \(0.862981\pi\)
\(224\) −7.13510 + 1.97271i −0.476734 + 0.131807i
\(225\) 0 0
\(226\) 16.8645 1.12181
\(227\) −26.8831 −1.78429 −0.892147 0.451746i \(-0.850801\pi\)
−0.892147 + 0.451746i \(0.850801\pi\)
\(228\) 0 0
\(229\) −8.68270 10.8878i −0.573769 0.719484i 0.407267 0.913309i \(-0.366482\pi\)
−0.981036 + 0.193826i \(0.937910\pi\)
\(230\) 0.457672 + 2.00519i 0.0301780 + 0.132218i
\(231\) 0 0
\(232\) 1.42037 6.22307i 0.0932521 0.408564i
\(233\) 14.4360 6.95200i 0.945733 0.455441i 0.103545 0.994625i \(-0.466982\pi\)
0.842188 + 0.539184i \(0.181267\pi\)
\(234\) 0 0
\(235\) −1.58151 1.98315i −0.103166 0.129367i
\(236\) 1.13113 + 4.95580i 0.0736302 + 0.322595i
\(237\) 0 0
\(238\) 0.561067 + 12.3657i 0.0363686 + 0.801547i
\(239\) 5.61842 + 7.04528i 0.363425 + 0.455721i 0.929603 0.368562i \(-0.120150\pi\)
−0.566178 + 0.824283i \(0.691578\pi\)
\(240\) 0 0
\(241\) 14.1384 + 6.80872i 0.910737 + 0.438588i 0.829755 0.558128i \(-0.188480\pi\)
0.0809822 + 0.996716i \(0.474194\pi\)
\(242\) −8.01249 + 10.0473i −0.515062 + 0.645868i
\(243\) 0 0
\(244\) 4.23853 0.271344
\(245\) 1.58176 0.947042i 0.101055 0.0605043i
\(246\) 0 0
\(247\) 0.0832343 0.364673i 0.00529607 0.0232036i
\(248\) 11.4008 14.2961i 0.723951 0.907805i
\(249\) 0 0
\(250\) −1.99177 + 2.49760i −0.125970 + 0.157962i
\(251\) 17.1365 + 21.4885i 1.08165 + 1.35634i 0.929853 + 0.367930i \(0.119933\pi\)
0.151794 + 0.988412i \(0.451495\pi\)
\(252\) 0 0
\(253\) −2.75778 + 3.45815i −0.173380 + 0.217412i
\(254\) −5.84548 25.6107i −0.366778 1.60696i
\(255\) 0 0
\(256\) 2.52372 11.0571i 0.157732 0.691071i
\(257\) −14.2541 + 6.86442i −0.889147 + 0.428191i −0.821957 0.569550i \(-0.807118\pi\)
−0.0671899 + 0.997740i \(0.521403\pi\)
\(258\) 0 0
\(259\) −8.08517 + 2.23539i −0.502388 + 0.138900i
\(260\) 0.0181038 + 0.0793179i 0.00112275 + 0.00491909i
\(261\) 0 0
\(262\) 7.26407 3.49819i 0.448776 0.216119i
\(263\) 7.40301 0.456489 0.228245 0.973604i \(-0.426701\pi\)
0.228245 + 0.973604i \(0.426701\pi\)
\(264\) 0 0
\(265\) −0.366255 + 0.176379i −0.0224989 + 0.0108349i
\(266\) 0.780636 1.82872i 0.0478638 0.112126i
\(267\) 0 0
\(268\) −4.92085 2.36976i −0.300589 0.144756i
\(269\) 4.09331 + 17.9339i 0.249573 + 1.09345i 0.931989 + 0.362487i \(0.118072\pi\)
−0.682415 + 0.730965i \(0.739070\pi\)
\(270\) 0 0
\(271\) −15.9708 7.69114i −0.970158 0.467203i −0.119449 0.992840i \(-0.538113\pi\)
−0.850709 + 0.525637i \(0.823827\pi\)
\(272\) −9.40608 4.52973i −0.570327 0.274655i
\(273\) 0 0
\(274\) −1.57791 + 0.759884i −0.0953253 + 0.0459063i
\(275\) −3.41100 −0.205691
\(276\) 0 0
\(277\) 13.0491 6.28413i 0.784046 0.377577i 0.00136453 0.999999i \(-0.499566\pi\)
0.782682 + 0.622422i \(0.213851\pi\)
\(278\) 8.84643 + 11.0931i 0.530574 + 0.665318i
\(279\) 0 0
\(280\) 0.0967573 + 2.13249i 0.00578235 + 0.127440i
\(281\) −0.791810 + 3.46915i −0.0472355 + 0.206952i −0.993039 0.117788i \(-0.962420\pi\)
0.945803 + 0.324740i \(0.105277\pi\)
\(282\) 0 0
\(283\) −6.35315 + 27.8350i −0.377655 + 1.65462i 0.326968 + 0.945035i \(0.393973\pi\)
−0.704624 + 0.709581i \(0.748884\pi\)
\(284\) −1.64221 2.05927i −0.0974473 0.122195i
\(285\) 0 0
\(286\) 0.320272 0.401608i 0.0189381 0.0237476i
\(287\) −2.35826 + 2.06227i −0.139204 + 0.121732i
\(288\) 0 0
\(289\) −1.45121 + 1.81976i −0.0853654 + 0.107045i
\(290\) −0.603890 0.290818i −0.0354616 0.0170774i
\(291\) 0 0
\(292\) 1.27327 5.57855i 0.0745123 0.326460i
\(293\) 27.2921 1.59442 0.797210 0.603702i \(-0.206308\pi\)
0.797210 + 0.603702i \(0.206308\pi\)
\(294\) 0 0
\(295\) 2.63466 0.153396
\(296\) 2.16133 9.46943i 0.125625 0.550399i
\(297\) 0 0
\(298\) 11.8774 + 5.71985i 0.688039 + 0.331342i
\(299\) −2.42341 + 3.03886i −0.140149 + 0.175742i
\(300\) 0 0
\(301\) −10.4044 19.3133i −0.599702 1.11320i
\(302\) 0.253301 0.317629i 0.0145758 0.0182775i
\(303\) 0 0
\(304\) 1.04559 + 1.31113i 0.0599688 + 0.0751985i
\(305\) 0.488844 2.14176i 0.0279911 0.122637i
\(306\) 0 0
\(307\) −0.201667 + 0.883562i −0.0115098 + 0.0504275i −0.980357 0.197233i \(-0.936805\pi\)
0.968847 + 0.247660i \(0.0796617\pi\)
\(308\) −0.700122 + 0.612248i −0.0398931 + 0.0348861i
\(309\) 0 0
\(310\) −1.19716 1.50119i −0.0679939 0.0852616i
\(311\) 1.50260 0.723613i 0.0852046 0.0410324i −0.390796 0.920477i \(-0.627800\pi\)
0.476001 + 0.879445i \(0.342086\pi\)
\(312\) 0 0
\(313\) 11.2183 0.634098 0.317049 0.948409i \(-0.397308\pi\)
0.317049 + 0.948409i \(0.397308\pi\)
\(314\) 13.0677 6.29308i 0.737454 0.355139i
\(315\) 0 0
\(316\) 7.24726 + 3.49010i 0.407690 + 0.196333i
\(317\) 11.4622 + 5.51988i 0.643779 + 0.310027i 0.727137 0.686492i \(-0.240850\pi\)
−0.0833585 + 0.996520i \(0.526565\pi\)
\(318\) 0 0
\(319\) −0.320749 1.40530i −0.0179585 0.0786814i
\(320\) −2.10441 1.01343i −0.117640 0.0566524i
\(321\) 0 0
\(322\) −15.5534 + 13.6013i −0.866756 + 0.757969i
\(323\) −2.12347 + 1.02261i −0.118153 + 0.0568995i
\(324\) 0 0
\(325\) −2.99743 −0.166268
\(326\) 11.3406 5.46134i 0.628097 0.302476i
\(327\) 0 0
\(328\) −0.807177 3.53647i −0.0445689 0.195269i
\(329\) 10.0040 23.4355i 0.551540 1.29204i
\(330\) 0 0
\(331\) −2.55863 + 1.23217i −0.140635 + 0.0677262i −0.502878 0.864358i \(-0.667725\pi\)
0.362243 + 0.932084i \(0.382011\pi\)
\(332\) −0.934065 + 4.09240i −0.0512634 + 0.224600i
\(333\) 0 0
\(334\) −0.772696 3.38540i −0.0422801 0.185241i
\(335\) −1.76499 + 2.21323i −0.0964319 + 0.120922i
\(336\) 0 0
\(337\) 11.8447 + 14.8528i 0.645221 + 0.809081i 0.991645 0.128997i \(-0.0411756\pi\)
−0.346424 + 0.938078i \(0.612604\pi\)
\(338\) −9.61859 + 12.0613i −0.523182 + 0.656050i
\(339\) 0 0
\(340\) 0.319619 0.400790i 0.0173338 0.0217359i
\(341\) 0.918839 4.02570i 0.0497579 0.218004i
\(342\) 0 0
\(343\) 15.9118 + 9.47698i 0.859159 + 0.511709i
\(344\) 25.4013 1.36954
\(345\) 0 0
\(346\) −7.02980 + 8.81510i −0.377925 + 0.473902i
\(347\) −7.80284 3.75765i −0.418878 0.201721i 0.212559 0.977148i \(-0.431820\pi\)
−0.631437 + 0.775427i \(0.717535\pi\)
\(348\) 0 0
\(349\) 12.2571 + 15.3699i 0.656108 + 0.822733i 0.992913 0.118841i \(-0.0379178\pi\)
−0.336805 + 0.941574i \(0.609346\pi\)
\(350\) −15.6789 2.83782i −0.838074 0.151688i
\(351\) 0 0
\(352\) −0.430721 1.88711i −0.0229575 0.100583i
\(353\) −4.89408 6.13699i −0.260486 0.326639i 0.634340 0.773054i \(-0.281272\pi\)
−0.894826 + 0.446415i \(0.852700\pi\)
\(354\) 0 0
\(355\) −1.22997 + 0.592320i −0.0652798 + 0.0314371i
\(356\) 2.09881 9.19550i 0.111237 0.487361i
\(357\) 0 0
\(358\) −4.64553 20.3534i −0.245524 1.07571i
\(359\) 5.31904 + 6.66987i 0.280728 + 0.352022i 0.902126 0.431473i \(-0.142006\pi\)
−0.621397 + 0.783496i \(0.713435\pi\)
\(360\) 0 0
\(361\) −18.6214 −0.980074
\(362\) 4.56304 0.239828
\(363\) 0 0
\(364\) −0.615235 + 0.538016i −0.0322471 + 0.0281997i
\(365\) −2.67203 1.28678i −0.139861 0.0673533i
\(366\) 0 0
\(367\) −5.26281 23.0579i −0.274717 1.20361i −0.904375 0.426740i \(-0.859662\pi\)
0.629658 0.776872i \(-0.283195\pi\)
\(368\) −3.87766 16.9891i −0.202137 0.885620i
\(369\) 0 0
\(370\) −0.918918 0.442528i −0.0477723 0.0230059i
\(371\) −3.30490 2.39882i −0.171582 0.124541i
\(372\) 0 0
\(373\) −5.03892 −0.260905 −0.130453 0.991455i \(-0.541643\pi\)
−0.130453 + 0.991455i \(0.541643\pi\)
\(374\) −3.23664 −0.167363
\(375\) 0 0
\(376\) 18.3959 + 23.0677i 0.948695 + 1.18963i
\(377\) −0.281860 1.23491i −0.0145165 0.0636010i
\(378\) 0 0
\(379\) 3.29768 14.4481i 0.169391 0.742149i −0.816852 0.576847i \(-0.804283\pi\)
0.986243 0.165302i \(-0.0528599\pi\)
\(380\) −0.0741903 + 0.0357282i −0.00380588 + 0.00183282i
\(381\) 0 0
\(382\) −18.6547 23.3923i −0.954459 1.19685i
\(383\) −4.89043 21.4264i −0.249889 1.09484i −0.931678 0.363286i \(-0.881655\pi\)
0.681789 0.731549i \(-0.261202\pi\)
\(384\) 0 0
\(385\) 0.228627 + 0.424389i 0.0116519 + 0.0216289i
\(386\) −1.73920 2.18089i −0.0885232 0.111005i
\(387\) 0 0
\(388\) 5.55815 + 2.67666i 0.282172 + 0.135887i
\(389\) 18.4408 23.1240i 0.934984 1.17243i −0.0498191 0.998758i \(-0.515864\pi\)
0.984803 0.173675i \(-0.0555641\pi\)
\(390\) 0 0
\(391\) 24.4908 1.23855
\(392\) −18.3987 + 11.0158i −0.929277 + 0.556383i
\(393\) 0 0
\(394\) 4.31970 18.9259i 0.217624 0.953471i
\(395\) 2.59942 3.25957i 0.130791 0.164007i
\(396\) 0 0
\(397\) 2.88602 3.61895i 0.144845 0.181630i −0.704117 0.710084i \(-0.748657\pi\)
0.848962 + 0.528454i \(0.177228\pi\)
\(398\) −8.13539 10.2015i −0.407790 0.511353i
\(399\) 0 0
\(400\) 8.37876 10.5066i 0.418938 0.525332i
\(401\) −5.61119 24.5842i −0.280210 1.22768i −0.897525 0.440963i \(-0.854637\pi\)
0.617316 0.786716i \(-0.288220\pi\)
\(402\) 0 0
\(403\) 0.807434 3.53760i 0.0402211 0.176220i
\(404\) 0.600033 0.288960i 0.0298527 0.0143763i
\(405\) 0 0
\(406\) −0.305197 6.72639i −0.0151467 0.333825i
\(407\) −0.488074 2.13839i −0.0241929 0.105996i
\(408\) 0 0
\(409\) 4.58112 2.20615i 0.226522 0.109087i −0.317181 0.948365i \(-0.602736\pi\)
0.543703 + 0.839278i \(0.317022\pi\)
\(410\) −0.380902 −0.0188114
\(411\) 0 0
\(412\) 4.34465 2.09227i 0.214045 0.103079i
\(413\) 12.5527 + 23.3010i 0.617677 + 1.14657i
\(414\) 0 0
\(415\) 1.96019 + 0.943980i 0.0962222 + 0.0463382i
\(416\) −0.378498 1.65831i −0.0185574 0.0813052i
\(417\) 0 0
\(418\) 0.468422 + 0.225580i 0.0229113 + 0.0110335i
\(419\) −24.4711 11.7847i −1.19549 0.575718i −0.273103 0.961985i \(-0.588050\pi\)
−0.922387 + 0.386267i \(0.873764\pi\)
\(420\) 0 0
\(421\) −10.5627 + 5.08674i −0.514796 + 0.247912i −0.673198 0.739462i \(-0.735080\pi\)
0.158403 + 0.987375i \(0.449366\pi\)
\(422\) −18.1308 −0.882592
\(423\) 0 0
\(424\) 4.26022 2.05161i 0.206895 0.0996352i
\(425\) 11.7756 + 14.7661i 0.571201 + 0.716263i
\(426\) 0 0
\(427\) 21.2709 5.88096i 1.02937 0.284600i
\(428\) 1.40501 6.15577i 0.0679139 0.297550i
\(429\) 0 0
\(430\) 0.593529 2.60042i 0.0286225 0.125403i
\(431\) 15.0594 + 18.8839i 0.725385 + 0.909604i 0.998629 0.0523404i \(-0.0166681\pi\)
−0.273244 + 0.961945i \(0.588097\pi\)
\(432\) 0 0
\(433\) −6.17402 + 7.74197i −0.296704 + 0.372056i −0.907730 0.419556i \(-0.862186\pi\)
0.611025 + 0.791611i \(0.290757\pi\)
\(434\) 7.57274 17.7400i 0.363503 0.851546i
\(435\) 0 0
\(436\) −0.447930 + 0.561686i −0.0214519 + 0.0268999i
\(437\) −3.54443 1.70691i −0.169553 0.0816524i
\(438\) 0 0
\(439\) −5.62609 + 24.6495i −0.268519 + 1.17646i 0.643218 + 0.765683i \(0.277599\pi\)
−0.911737 + 0.410775i \(0.865258\pi\)
\(440\) −0.558165 −0.0266095
\(441\) 0 0
\(442\) −2.84421 −0.135285
\(443\) −8.38096 + 36.7194i −0.398191 + 1.74459i 0.236318 + 0.971676i \(0.424059\pi\)
−0.634510 + 0.772915i \(0.718798\pi\)
\(444\) 0 0
\(445\) −4.40450 2.12109i −0.208793 0.100549i
\(446\) 14.5047 18.1883i 0.686817 0.861242i
\(447\) 0 0
\(448\) −1.06353 23.4398i −0.0502473 1.10743i
\(449\) −8.18839 + 10.2679i −0.386434 + 0.484573i −0.936559 0.350509i \(-0.886008\pi\)
0.550125 + 0.835082i \(0.314580\pi\)
\(450\) 0 0
\(451\) −0.510729 0.640434i −0.0240493 0.0301568i
\(452\) 1.56122 6.84017i 0.0734338 0.321735i
\(453\) 0 0
\(454\) 7.30657 32.0122i 0.342915 1.50241i
\(455\) 0.200907 + 0.372934i 0.00941864 + 0.0174834i
\(456\) 0 0
\(457\) −15.4622 19.3890i −0.723293 0.906981i 0.275226 0.961380i \(-0.411247\pi\)
−0.998519 + 0.0543984i \(0.982676\pi\)
\(458\) 15.3250 7.38011i 0.716088 0.344850i
\(459\) 0 0
\(460\) 0.855665 0.0398956
\(461\) −34.4853 + 16.6072i −1.60614 + 0.773476i −0.999764 0.0217023i \(-0.993091\pi\)
−0.606375 + 0.795178i \(0.707377\pi\)
\(462\) 0 0
\(463\) 15.9730 + 7.69218i 0.742327 + 0.357486i 0.766519 0.642222i \(-0.221987\pi\)
−0.0241922 + 0.999707i \(0.507701\pi\)
\(464\) 5.11651 + 2.46398i 0.237528 + 0.114387i
\(465\) 0 0
\(466\) 4.35483 + 19.0798i 0.201734 + 0.883853i
\(467\) −37.0828 17.8582i −1.71599 0.826377i −0.990397 0.138251i \(-0.955852\pi\)
−0.725592 0.688125i \(-0.758434\pi\)
\(468\) 0 0
\(469\) −27.9831 5.06482i −1.29214 0.233872i
\(470\) 2.79137 1.34425i 0.128756 0.0620057i
\(471\) 0 0
\(472\) −30.6459 −1.41059
\(473\) 5.16807 2.48881i 0.237628 0.114436i
\(474\) 0 0
\(475\) −0.675085 2.95774i −0.0309750 0.135711i
\(476\) 5.06740 + 0.917179i 0.232264 + 0.0420388i
\(477\) 0 0
\(478\) −9.91650 + 4.77554i −0.453570 + 0.218428i
\(479\) −0.656206 + 2.87503i −0.0299828 + 0.131363i −0.987704 0.156334i \(-0.950032\pi\)
0.957721 + 0.287697i \(0.0928896\pi\)
\(480\) 0 0
\(481\) −0.428897 1.87912i −0.0195560 0.0856804i
\(482\) −11.9505 + 14.9854i −0.544329 + 0.682567i
\(483\) 0 0
\(484\) 3.33340 + 4.17996i 0.151518 + 0.189998i
\(485\) 1.99358 2.49987i 0.0905237 0.113513i
\(486\) 0 0
\(487\) 1.39287 1.74660i 0.0631168 0.0791460i −0.749271 0.662264i \(-0.769596\pi\)
0.812388 + 0.583118i \(0.198167\pi\)
\(488\) −5.68614 + 24.9126i −0.257400 + 1.12774i
\(489\) 0 0
\(490\) 0.697823 + 2.14095i 0.0315244 + 0.0967181i
\(491\) 11.7506 0.530297 0.265148 0.964208i \(-0.414579\pi\)
0.265148 + 0.964208i \(0.414579\pi\)
\(492\) 0 0
\(493\) −4.97619 + 6.23994i −0.224116 + 0.281033i
\(494\) 0.411628 + 0.198230i 0.0185200 + 0.00891877i
\(495\) 0 0
\(496\) 10.1430 + 12.7189i 0.455434 + 0.571097i
\(497\) −11.0986 8.05576i −0.497839 0.361350i
\(498\) 0 0
\(499\) 5.23035 + 22.9157i 0.234143 + 1.02585i 0.946164 + 0.323688i \(0.104923\pi\)
−0.712021 + 0.702158i \(0.752220\pi\)
\(500\) 0.828627 + 1.03906i 0.0370573 + 0.0464684i
\(501\) 0 0
\(502\) −30.2459 + 14.5657i −1.34994 + 0.650097i
\(503\) 3.48579 15.2723i 0.155424 0.680956i −0.835830 0.548988i \(-0.815013\pi\)
0.991254 0.131968i \(-0.0421297\pi\)
\(504\) 0 0
\(505\) −0.0768103 0.336528i −0.00341801 0.0149753i
\(506\) −3.36840 4.22384i −0.149744 0.187773i
\(507\) 0 0
\(508\) −10.9287 −0.484884
\(509\) 24.4548 1.08394 0.541969 0.840398i \(-0.317679\pi\)
0.541969 + 0.840398i \(0.317679\pi\)
\(510\) 0 0
\(511\) −1.35041 29.7623i −0.0597384 1.31661i
\(512\) 21.9161 + 10.5542i 0.968565 + 0.466436i
\(513\) 0 0
\(514\) −4.29997 18.8394i −0.189663 0.830969i
\(515\) −0.556159 2.43669i −0.0245073 0.107374i
\(516\) 0 0
\(517\) 6.00294 + 2.89086i 0.264009 + 0.127140i
\(518\) −0.464407 10.2353i −0.0204049 0.449714i
\(519\) 0 0
\(520\) −0.490490 −0.0215094
\(521\) −27.7729 −1.21675 −0.608377 0.793648i \(-0.708179\pi\)
−0.608377 + 0.793648i \(0.708179\pi\)
\(522\) 0 0
\(523\) 9.15293 + 11.4774i 0.400230 + 0.501872i 0.940582 0.339567i \(-0.110280\pi\)
−0.540352 + 0.841439i \(0.681709\pi\)
\(524\) −0.746383 3.27012i −0.0326059 0.142856i
\(525\) 0 0
\(526\) −2.01207 + 8.81545i −0.0877304 + 0.384372i
\(527\) −20.5992 + 9.92005i −0.897315 + 0.432124i
\(528\) 0 0
\(529\) 11.1475 + 13.9785i 0.484674 + 0.607762i
\(530\) −0.110486 0.484073i −0.00479922 0.0210268i
\(531\) 0 0
\(532\) −0.669456 0.485916i −0.0290246 0.0210671i
\(533\) −0.448805 0.562784i −0.0194399 0.0243769i
\(534\) 0 0
\(535\) −2.94851 1.41993i −0.127475 0.0613889i
\(536\) 20.5301 25.7439i 0.886765 1.11197i
\(537\) 0 0
\(538\) −22.4681 −0.968671
\(539\) −2.66403 + 4.04395i −0.114748 + 0.174185i
\(540\) 0 0
\(541\) 3.02877 13.2699i 0.130217 0.570517i −0.867153 0.498041i \(-0.834053\pi\)
0.997370 0.0724760i \(-0.0230901\pi\)
\(542\) 13.4993 16.9276i 0.579843 0.727101i
\(543\) 0 0
\(544\) −6.68231 + 8.37935i −0.286502 + 0.359262i
\(545\) 0.232163 + 0.291123i 0.00994477 + 0.0124704i
\(546\) 0 0
\(547\) −17.9852 + 22.5528i −0.768992 + 0.964286i −0.999962 0.00867481i \(-0.997239\pi\)
0.230970 + 0.972961i \(0.425810\pi\)
\(548\) 0.162131 + 0.710341i 0.00692588 + 0.0303443i
\(549\) 0 0
\(550\) 0.927079 4.06180i 0.0395308 0.173196i
\(551\) 1.15508 0.556256i 0.0492079 0.0236973i
\(552\) 0 0
\(553\) 41.2125 + 7.45930i 1.75253 + 0.317202i
\(554\) 3.93646 + 17.2468i 0.167244 + 0.732745i
\(555\) 0 0
\(556\) 5.31825 2.56114i 0.225544 0.108616i
\(557\) 35.1166 1.48794 0.743970 0.668213i \(-0.232941\pi\)
0.743970 + 0.668213i \(0.232941\pi\)
\(558\) 0 0
\(559\) 4.54146 2.18705i 0.192083 0.0925024i
\(560\) −1.86881 0.338247i −0.0789716 0.0142936i
\(561\) 0 0
\(562\) −3.91583 1.88577i −0.165179 0.0795462i
\(563\) −7.50581 32.8851i −0.316332 1.38594i −0.843933 0.536449i \(-0.819765\pi\)
0.527600 0.849493i \(-0.323092\pi\)
\(564\) 0 0
\(565\) −3.27633 1.57780i −0.137836 0.0663784i
\(566\) −31.4190 15.1306i −1.32064 0.635985i
\(567\) 0 0
\(568\) 14.3067 6.88976i 0.600297 0.289088i
\(569\) 27.8808 1.16882 0.584412 0.811457i \(-0.301325\pi\)
0.584412 + 0.811457i \(0.301325\pi\)
\(570\) 0 0
\(571\) 7.32747 3.52872i 0.306645 0.147672i −0.274232 0.961663i \(-0.588424\pi\)
0.580878 + 0.813991i \(0.302709\pi\)
\(572\) −0.133241 0.167079i −0.00557111 0.00698594i
\(573\) 0 0
\(574\) −1.81479 3.36871i −0.0757477 0.140607i
\(575\) −7.01496 + 30.7345i −0.292544 + 1.28172i
\(576\) 0 0
\(577\) 2.38417 10.4457i 0.0992542 0.434861i −0.900746 0.434347i \(-0.856979\pi\)
1.00000 0.000514126i \(-0.000163652\pi\)
\(578\) −1.77253 2.22269i −0.0737277 0.0924516i
\(579\) 0 0
\(580\) −0.173859 + 0.218013i −0.00721911 + 0.00905248i
\(581\) 0.990653 + 21.8335i 0.0410992 + 0.905807i
\(582\) 0 0
\(583\) 0.665756 0.834831i 0.0275728 0.0345752i
\(584\) 31.0806 + 14.9676i 1.28613 + 0.619365i
\(585\) 0 0
\(586\) −7.41773 + 32.4992i −0.306424 + 1.34253i
\(587\) −18.6672 −0.770478 −0.385239 0.922817i \(-0.625881\pi\)
−0.385239 + 0.922817i \(0.625881\pi\)
\(588\) 0 0
\(589\) 3.67261 0.151327
\(590\) −0.716076 + 3.13734i −0.0294804 + 0.129162i
\(591\) 0 0
\(592\) 7.78561 + 3.74935i 0.319987 + 0.154098i
\(593\) −0.0838867 + 0.105191i −0.00344481 + 0.00431966i −0.783551 0.621328i \(-0.786594\pi\)
0.780106 + 0.625647i \(0.215165\pi\)
\(594\) 0 0
\(595\) 1.04790 2.45481i 0.0429596 0.100638i
\(596\) 3.41949 4.28791i 0.140068 0.175640i
\(597\) 0 0
\(598\) −2.95999 3.71172i −0.121043 0.151783i
\(599\) −0.0561486 + 0.246003i −0.00229417 + 0.0100514i −0.976062 0.217492i \(-0.930212\pi\)
0.973768 + 0.227544i \(0.0730694\pi\)
\(600\) 0 0
\(601\) −6.69428 + 29.3296i −0.273065 + 1.19638i 0.633308 + 0.773900i \(0.281697\pi\)
−0.906373 + 0.422478i \(0.861160\pi\)
\(602\) 25.8260 7.14036i 1.05259 0.291020i
\(603\) 0 0
\(604\) −0.105380 0.132142i −0.00428784 0.00537678i
\(605\) 2.49662 1.20231i 0.101502 0.0488807i
\(606\) 0 0
\(607\) 30.0756 1.22073 0.610365 0.792120i \(-0.291023\pi\)
0.610365 + 0.792120i \(0.291023\pi\)
\(608\) 1.55110 0.746972i 0.0629055 0.0302937i
\(609\) 0 0
\(610\) 2.41753 + 1.16422i 0.0978831 + 0.0471380i
\(611\) 5.27511 + 2.54036i 0.213408 + 0.102772i
\(612\) 0 0
\(613\) 2.48999 + 10.9094i 0.100570 + 0.440625i 0.999994 + 0.00354752i \(0.00112921\pi\)
−0.899424 + 0.437077i \(0.856014\pi\)
\(614\) −0.997328 0.480288i −0.0402489 0.0193828i
\(615\) 0 0
\(616\) −2.65934 4.93642i −0.107148 0.198894i
\(617\) −29.4610 + 14.1877i −1.18606 + 0.571174i −0.919670 0.392692i \(-0.871544\pi\)
−0.266386 + 0.963866i \(0.585830\pi\)
\(618\) 0 0
\(619\) −18.1718 −0.730385 −0.365192 0.930932i \(-0.618997\pi\)
−0.365192 + 0.930932i \(0.618997\pi\)
\(620\) −0.719700 + 0.346589i −0.0289039 + 0.0139194i
\(621\) 0 0
\(622\) 0.453282 + 1.98596i 0.0181749 + 0.0796296i
\(623\) −2.22597 49.0592i −0.0891814 1.96552i
\(624\) 0 0
\(625\) −21.5911 + 10.3977i −0.863645 + 0.415910i
\(626\) −3.04904 + 13.3587i −0.121864 + 0.533922i
\(627\) 0 0
\(628\) −1.34271 5.88279i −0.0535799 0.234749i
\(629\) −7.57209 + 9.49510i −0.301919 + 0.378595i
\(630\) 0 0
\(631\) 5.79564 + 7.26750i 0.230721 + 0.289315i 0.883693 0.468067i \(-0.155050\pi\)
−0.652972 + 0.757382i \(0.726478\pi\)
\(632\) −30.2360 + 37.9148i −1.20272 + 1.50817i
\(633\) 0 0
\(634\) −9.68835 + 12.1488i −0.384773 + 0.482491i
\(635\) −1.26045 + 5.52237i −0.0500192 + 0.219149i
\(636\) 0 0
\(637\) −2.34103 + 3.55364i −0.0927548 + 0.140800i
\(638\) 1.76059 0.0697025
\(639\) 0 0
\(640\) 0.859831 1.07819i 0.0339878 0.0426193i
\(641\) 30.7638 + 14.8151i 1.21510 + 0.585160i 0.927942 0.372724i \(-0.121576\pi\)
0.287155 + 0.957884i \(0.407291\pi\)
\(642\) 0 0
\(643\) −7.68251 9.63356i −0.302968 0.379910i 0.606920 0.794763i \(-0.292405\pi\)
−0.909889 + 0.414852i \(0.863833\pi\)
\(644\) 4.07676 + 7.56751i 0.160647 + 0.298202i
\(645\) 0 0
\(646\) −0.640576 2.80655i −0.0252031 0.110422i
\(647\) −1.48480 1.86189i −0.0583737 0.0731983i 0.751788 0.659405i \(-0.229192\pi\)
−0.810161 + 0.586207i \(0.800620\pi\)
\(648\) 0 0
\(649\) −6.23513 + 3.00268i −0.244750 + 0.117866i
\(650\) 0.814674 3.56932i 0.0319542 0.140000i
\(651\) 0 0
\(652\) −1.16525 5.10527i −0.0456345 0.199938i
\(653\) 25.7182 + 32.2496i 1.00643 + 1.26202i 0.964826 + 0.262891i \(0.0846759\pi\)
0.0416056 + 0.999134i \(0.486753\pi\)
\(654\) 0 0
\(655\) −1.73850 −0.0679288
\(656\) 3.22723 0.126002
\(657\) 0 0
\(658\) 25.1879 + 18.2823i 0.981925 + 0.712718i
\(659\) 42.7495 + 20.5871i 1.66529 + 0.801959i 0.998385 + 0.0568128i \(0.0180938\pi\)
0.666901 + 0.745147i \(0.267620\pi\)
\(660\) 0 0
\(661\) −5.88583 25.7875i −0.228932 1.00302i −0.950512 0.310687i \(-0.899441\pi\)
0.721580 0.692331i \(-0.243416\pi\)
\(662\) −0.771849 3.38169i −0.0299988 0.131433i
\(663\) 0 0
\(664\) −22.8006 10.9802i −0.884837 0.426115i
\(665\) −0.322747 + 0.282239i −0.0125156 + 0.0109448i
\(666\) 0 0
\(667\) −13.3219 −0.515827
\(668\) −1.44464 −0.0558947
\(669\) 0 0
\(670\) −2.15579 2.70328i −0.0832855 0.104437i
\(671\) 1.28405 + 5.62578i 0.0495701 + 0.217181i
\(672\) 0 0
\(673\) 10.3952 45.5443i 0.400705 1.75560i −0.223852 0.974623i \(-0.571863\pi\)
0.624557 0.780980i \(-0.285280\pi\)
\(674\) −20.9058 + 10.0677i −0.805263 + 0.387794i
\(675\) 0 0
\(676\) 4.00159 + 5.01783i 0.153907 + 0.192993i
\(677\) 6.62975 + 29.0468i 0.254802 + 1.11636i 0.926725 + 0.375740i \(0.122611\pi\)
−0.671923 + 0.740621i \(0.734532\pi\)
\(678\) 0 0
\(679\) 31.6071 + 5.72077i 1.21297 + 0.219543i
\(680\) 1.92692 + 2.41628i 0.0738941 + 0.0926603i
\(681\) 0 0
\(682\) 4.54404 + 2.18829i 0.174000 + 0.0837941i
\(683\) −25.5870 + 32.0851i −0.979059 + 1.22770i −0.00533178 + 0.999986i \(0.501697\pi\)
−0.973728 + 0.227716i \(0.926874\pi\)
\(684\) 0 0
\(685\) 0.377640 0.0144289
\(686\) −15.6098 + 16.3720i −0.595986 + 0.625084i
\(687\) 0 0
\(688\) −5.02873 + 22.0323i −0.191718 + 0.839973i
\(689\) 0.585035 0.733611i 0.0222881 0.0279484i
\(690\) 0 0
\(691\) 1.90528 2.38915i 0.0724804 0.0908875i −0.744269 0.667879i \(-0.767202\pi\)
0.816750 + 0.576992i \(0.195774\pi\)
\(692\) 2.92458 + 3.66731i 0.111176 + 0.139410i
\(693\) 0 0
\(694\) 6.59532 8.27028i 0.250355 0.313935i
\(695\) −0.680791 2.98274i −0.0258239 0.113142i
\(696\) 0 0
\(697\) −1.00926 + 4.42187i −0.0382285 + 0.167490i
\(698\) −21.6338 + 10.4183i −0.818850 + 0.394338i
\(699\) 0 0
\(700\) −2.60248 + 6.09659i −0.0983644 + 0.230429i
\(701\) −2.19633 9.62277i −0.0829544 0.363447i 0.916365 0.400345i \(-0.131110\pi\)
−0.999319 + 0.0368977i \(0.988252\pi\)
\(702\) 0 0
\(703\) 1.75764 0.846435i 0.0662907 0.0319239i
\(704\) 6.13523 0.231230
\(705\) 0 0
\(706\) 8.63805 4.15987i 0.325097 0.156559i
\(707\) 2.61030 2.28268i 0.0981704 0.0858489i
\(708\) 0 0
\(709\) 18.9376 + 9.11985i 0.711215 + 0.342503i 0.754265 0.656570i \(-0.227993\pi\)
−0.0430500 + 0.999073i \(0.513707\pi\)
\(710\) −0.371037 1.62562i −0.0139248 0.0610085i
\(711\) 0 0
\(712\) 51.2323 + 24.6722i 1.92001 + 0.924629i
\(713\) −34.3835 16.5582i −1.28767 0.620111i
\(714\) 0 0
\(715\) −0.0997937 + 0.0480581i −0.00373207 + 0.00179727i
\(716\) −8.68531 −0.324585
\(717\) 0 0
\(718\) −9.38810 + 4.52107i −0.350361 + 0.168725i
\(719\) 15.5889 + 19.5478i 0.581367 + 0.729011i 0.982345 0.187076i \(-0.0599012\pi\)
−0.400978 + 0.916087i \(0.631330\pi\)
\(720\) 0 0
\(721\) 18.9004 16.5282i 0.703886 0.615541i
\(722\) 5.06113 22.1742i 0.188356 0.825240i
\(723\) 0 0
\(724\) 0.422421 1.85075i 0.0156992 0.0687825i
\(725\) −6.40543 8.03216i −0.237892 0.298307i
\(726\) 0 0
\(727\) −27.5324 + 34.5246i −1.02112 + 1.28044i −0.0618114 + 0.998088i \(0.519688\pi\)
−0.959309 + 0.282357i \(0.908884\pi\)
\(728\) −2.33691 4.33790i −0.0866116 0.160773i
\(729\) 0 0
\(730\) 2.25853 2.83210i 0.0835918 0.104821i
\(731\) −28.6154 13.7805i −1.05838 0.509689i
\(732\) 0 0
\(733\) 9.62999 42.1918i 0.355692 1.55839i −0.408107 0.912934i \(-0.633811\pi\)
0.763799 0.645454i \(-0.223332\pi\)
\(734\) 28.8876 1.06626
\(735\) 0 0
\(736\) −17.8895 −0.659414
\(737\) 1.65461 7.24932i 0.0609484 0.267032i
\(738\) 0 0
\(739\) 19.7573 + 9.51464i 0.726786 + 0.350002i 0.760419 0.649433i \(-0.224994\pi\)
−0.0336333 + 0.999434i \(0.510708\pi\)
\(740\) −0.264556 + 0.331742i −0.00972526 + 0.0121951i
\(741\) 0 0
\(742\) 3.75474 3.28348i 0.137841 0.120540i
\(743\) 3.29353 4.12996i 0.120828 0.151514i −0.717739 0.696313i \(-0.754823\pi\)
0.838567 + 0.544799i \(0.183394\pi\)
\(744\) 0 0
\(745\) −1.77233 2.22243i −0.0649332 0.0814237i
\(746\) 1.36953 6.00031i 0.0501421 0.219687i
\(747\) 0 0
\(748\) −0.299630 + 1.31277i −0.0109556 + 0.0479995i
\(749\) −1.49013 32.8418i −0.0544483 1.20001i
\(750\) 0 0
\(751\) 12.0682 + 15.1330i 0.440374 + 0.552212i 0.951642 0.307210i \(-0.0993953\pi\)
−0.511268 + 0.859422i \(0.670824\pi\)
\(752\) −23.6501 + 11.3893i −0.862430 + 0.415324i
\(753\) 0 0
\(754\) 1.54713 0.0563431
\(755\) −0.0789261 + 0.0380088i −0.00287242 + 0.00138328i
\(756\) 0 0
\(757\) −14.9351 7.19235i −0.542825 0.261411i 0.142316 0.989821i \(-0.454545\pi\)
−0.685141 + 0.728411i \(0.740259\pi\)
\(758\) 16.3084 + 7.85372i 0.592348 + 0.285260i
\(759\) 0 0
\(760\) −0.110469 0.483995i −0.00400712 0.0175564i
\(761\) −1.09688 0.528229i −0.0397618 0.0191483i 0.413897 0.910324i \(-0.364167\pi\)
−0.453659 + 0.891175i \(0.649882\pi\)
\(762\) 0 0
\(763\) −1.46857 + 3.44029i −0.0531659 + 0.124547i
\(764\) −11.2148 + 5.40075i −0.405736 + 0.195392i
\(765\) 0 0
\(766\) 26.8435 0.969896
\(767\) −5.47915 + 2.63862i −0.197841 + 0.0952750i
\(768\) 0 0
\(769\) −2.22490 9.74790i −0.0802318 0.351518i 0.918838 0.394634i \(-0.129129\pi\)
−0.999070 + 0.0431158i \(0.986272\pi\)
\(770\) −0.567499 + 0.156902i −0.0204512 + 0.00565435i
\(771\) 0 0
\(772\) −1.04557 + 0.503518i −0.0376308 + 0.0181220i
\(773\) 8.74191 38.3008i 0.314425 1.37758i −0.532752 0.846272i \(-0.678842\pi\)
0.847176 0.531312i \(-0.178301\pi\)
\(774\) 0 0
\(775\) −6.54882 28.6923i −0.235241 1.03066i
\(776\) −23.1889 + 29.0780i −0.832434 + 1.04384i
\(777\) 0 0
\(778\) 22.5239 + 28.2440i 0.807520 + 1.01260i
\(779\) 0.454251 0.569613i 0.0162752 0.0204085i
\(780\) 0 0
\(781\) 2.23575 2.80354i 0.0800015 0.100319i
\(782\) −6.65636 + 29.1634i −0.238031 + 1.04288i
\(783\) 0 0
\(784\) −5.91237 18.1393i −0.211156 0.647834i
\(785\) −3.12748 −0.111624
\(786\) 0 0
\(787\) −14.6664 + 18.3910i −0.522799 + 0.655570i −0.971201 0.238263i \(-0.923422\pi\)
0.448401 + 0.893832i \(0.351994\pi\)
\(788\) −7.27635 3.50411i −0.259209 0.124829i
\(789\) 0 0
\(790\) 3.17498 + 3.98130i 0.112961 + 0.141648i
\(791\) −1.65581 36.4932i −0.0588737 1.29755i
\(792\) 0 0
\(793\) 1.12836 + 4.94368i 0.0400693 + 0.175555i
\(794\) 3.52503 + 4.42025i 0.125099 + 0.156869i
\(795\) 0 0
\(796\) −4.89080 + 2.35528i −0.173350 + 0.0834808i
\(797\) 3.34689 14.6637i 0.118553 0.519414i −0.880424 0.474187i \(-0.842742\pi\)
0.998977 0.0452265i \(-0.0144010\pi\)
\(798\) 0 0
\(799\) −8.20913 35.9666i −0.290418 1.27241i
\(800\) −8.60158 10.7860i −0.304112 0.381344i
\(801\) 0 0
\(802\) 30.7998 1.08758
\(803\) 7.79010 0.274907
\(804\) 0 0
\(805\) 4.29411 1.18723i 0.151347 0.0418445i
\(806\) 3.99309 + 1.92297i 0.140651 + 0.0677338i
\(807\) 0 0
\(808\) 0.893444 + 3.91443i 0.0314312 + 0.137709i
\(809\) 1.34541 + 5.89464i 0.0473022 + 0.207245i 0.993057 0.117638i \(-0.0375323\pi\)
−0.945754 + 0.324883i \(0.894675\pi\)
\(810\) 0 0
\(811\) −46.3147 22.3040i −1.62633 0.783199i −0.999993 0.00364568i \(-0.998840\pi\)
−0.626336 0.779553i \(-0.715446\pi\)
\(812\) −2.75645 0.498906i −0.0967324 0.0175082i
\(813\) 0 0
\(814\) 2.67903 0.0939001
\(815\) −2.71413 −0.0950717
\(816\) 0 0
\(817\) 3.18093 + 3.98876i 0.111287 + 0.139549i
\(818\) 1.38196 + 6.05478i 0.0483193 + 0.211701i
\(819\) 0 0
\(820\) −0.0352619 + 0.154492i −0.00123140 + 0.00539511i
\(821\) −14.3255 + 6.89880i −0.499964 + 0.240770i −0.666830 0.745210i \(-0.732349\pi\)
0.166866 + 0.985980i \(0.446635\pi\)
\(822\) 0 0
\(823\) −1.26170 1.58212i −0.0439802 0.0551494i 0.759355 0.650677i \(-0.225515\pi\)
−0.803335 + 0.595527i \(0.796943\pi\)
\(824\) 6.46915 + 28.3432i 0.225363 + 0.987382i
\(825\) 0 0
\(826\) −31.1583 + 8.61465i −1.08414 + 0.299742i
\(827\) −9.55215 11.9780i −0.332161 0.416516i 0.587504 0.809221i \(-0.300111\pi\)
−0.919664 + 0.392705i \(0.871539\pi\)
\(828\) 0 0
\(829\) 2.33036 + 1.12224i 0.0809367 + 0.0389770i 0.473914 0.880571i \(-0.342841\pi\)
−0.392978 + 0.919548i \(0.628555\pi\)
\(830\) −1.65685 + 2.07762i −0.0575100 + 0.0721153i
\(831\) 0 0
\(832\) 5.39136 0.186912
\(833\) 26.7031 2.42819i 0.925206 0.0841320i
\(834\) 0 0
\(835\) −0.166615 + 0.729986i −0.00576594 + 0.0252622i
\(836\) 0.134858 0.169107i 0.00466417 0.00584869i
\(837\) 0 0
\(838\) 20.6841 25.9370i 0.714520 0.895980i
\(839\) 17.0802 + 21.4179i 0.589674 + 0.739428i 0.983729 0.179659i \(-0.0574994\pi\)
−0.394055 + 0.919087i \(0.628928\pi\)
\(840\) 0 0
\(841\) −15.3744 + 19.2789i −0.530151 + 0.664788i
\(842\) −3.18640 13.9605i −0.109811 0.481112i
\(843\) 0 0
\(844\) −1.67845 + 7.35376i −0.0577746 + 0.253127i
\(845\) 2.99706 1.44331i 0.103102 0.0496514i
\(846\) 0 0
\(847\) 22.5282 + 16.3518i 0.774078 + 0.561855i
\(848\) 0.936106 + 4.10135i 0.0321460 + 0.140841i
\(849\) 0 0
\(850\) −20.7839 + 10.0090i −0.712883 + 0.343306i
\(851\) −20.2715 −0.694899
\(852\) 0 0
\(853\) −49.6552 + 23.9127i −1.70016 + 0.818755i −0.706327 + 0.707885i \(0.749649\pi\)
−0.993835 + 0.110870i \(0.964636\pi\)
\(854\) 1.22179 + 26.9276i 0.0418086 + 0.921443i
\(855\) 0 0
\(856\) 34.2966 + 16.5164i 1.17223 + 0.564518i
\(857\) −7.86298 34.4500i −0.268594 1.17679i −0.911650 0.410968i \(-0.865191\pi\)
0.643055 0.765820i \(-0.277666\pi\)
\(858\) 0 0
\(859\) −41.1045 19.7949i −1.40247 0.675393i −0.428808 0.903396i \(-0.641066\pi\)
−0.973660 + 0.228003i \(0.926780\pi\)
\(860\) −0.999773 0.481466i −0.0340920 0.0164178i
\(861\) 0 0
\(862\) −26.5798 + 12.8002i −0.905311 + 0.435975i
\(863\) 53.9681 1.83709 0.918547 0.395311i \(-0.129363\pi\)
0.918547 + 0.395311i \(0.129363\pi\)
\(864\) 0 0
\(865\) 2.19042 1.05485i 0.0744766 0.0358660i
\(866\) −7.54105 9.45618i −0.256255 0.321334i
\(867\) 0 0
\(868\) −6.49421 4.71374i −0.220428 0.159995i
\(869\) −2.43685 + 10.6766i −0.0826646 + 0.362177i
\(870\) 0 0
\(871\) 1.45400 6.37037i 0.0492668 0.215852i
\(872\) −2.70048 3.38630i −0.0914498 0.114674i
\(873\) 0 0
\(874\) 2.99591 3.75676i 0.101338 0.127074i
\(875\) 5.60012 + 4.06477i 0.189319 + 0.137414i
\(876\) 0 0
\(877\) −29.7449 + 37.2989i −1.00441 + 1.25949i −0.0388718 + 0.999244i \(0.512376\pi\)
−0.965541 + 0.260250i \(0.916195\pi\)
\(878\) −27.8234 13.3990i −0.938993 0.452195i
\(879\) 0 0
\(880\) 0.110501 0.484136i 0.00372498 0.0163202i
\(881\) 19.2658 0.649081 0.324540 0.945872i \(-0.394790\pi\)
0.324540 + 0.945872i \(0.394790\pi\)
\(882\) 0 0
\(883\) −6.72757 −0.226401 −0.113200 0.993572i \(-0.536110\pi\)
−0.113200 + 0.993572i \(0.536110\pi\)
\(884\) −0.263301 + 1.15360i −0.00885578 + 0.0387997i
\(885\) 0 0
\(886\) −41.4473 19.9600i −1.39245 0.670569i
\(887\) 31.6120 39.6402i 1.06143 1.33099i 0.120376 0.992728i \(-0.461590\pi\)
0.941052 0.338261i \(-0.109839\pi\)
\(888\) 0 0
\(889\) −54.8453 + 15.1636i −1.83945 + 0.508571i
\(890\) 3.72288 4.66835i 0.124791 0.156483i
\(891\) 0 0
\(892\) −6.03433 7.56681i −0.202044 0.253356i
\(893\) −1.31865 + 5.77740i −0.0441271 + 0.193333i
\(894\) 0 0
\(895\) −1.00170 + 4.38875i −0.0334833 + 0.146700i
\(896\) 13.6322 + 2.46737i 0.455419 + 0.0824290i
\(897\) 0 0
\(898\) −10.0014 12.5414i −0.333752 0.418512i
\(899\) 11.2051 5.39609i 0.373711 0.179970i
\(900\) 0 0
\(901\) −5.91231 −0.196968
\(902\) 0.901436 0.434109i 0.0300145 0.0144542i
\(903\) 0 0
\(904\) 38.1097 + 18.3527i 1.26751 + 0.610401i
\(905\) −0.886478 0.426905i −0.0294675 0.0141908i
\(906\) 0 0
\(907\) −2.74124 12.0101i −0.0910213 0.398790i 0.908809 0.417212i \(-0.136993\pi\)
−0.999830 + 0.0184220i \(0.994136\pi\)
\(908\) −12.3076 5.92703i −0.408442 0.196695i
\(909\) 0 0
\(910\) −0.498692 + 0.137878i −0.0165315 + 0.00457062i
\(911\) 31.7245 15.2777i 1.05108 0.506173i 0.173116 0.984901i \(-0.444616\pi\)
0.877963 + 0.478728i \(0.158902\pi\)
\(912\) 0 0
\(913\) −5.71479 −0.189132
\(914\) 27.2908 13.1426i 0.902701 0.434718i
\(915\) 0 0
\(916\) −1.57464 6.89894i −0.0520275 0.227947i
\(917\) −8.28297 15.3753i −0.273528 0.507738i
\(918\) 0 0
\(919\) 26.5726 12.7967i 0.876549 0.422124i 0.0591863 0.998247i \(-0.481149\pi\)
0.817363 + 0.576123i \(0.195435\pi\)
\(920\) −1.14790 + 5.02930i −0.0378453 + 0.165811i
\(921\) 0 0
\(922\) −10.4030 45.5785i −0.342605 1.50105i
\(923\) 1.96468 2.46363i 0.0646681 0.0810912i
\(924\) 0 0
\(925\) −9.74692 12.2223i −0.320477 0.401865i
\(926\) −13.5011 + 16.9298i −0.443674 + 0.556349i
\(927\) 0 0
\(928\) 3.63489 4.55801i 0.119321 0.149624i
\(929\) −6.49583 + 28.4601i −0.213121 + 0.933745i 0.749310 + 0.662219i \(0.230385\pi\)
−0.962431 + 0.271526i \(0.912472\pi\)
\(930\) 0 0
\(931\) −4.03384 1.50967i −0.132204 0.0494775i
\(932\) 8.14181 0.266694
\(933\) 0 0
\(934\) 31.3441 39.3043i 1.02561 1.28608i
\(935\) 0.628793 + 0.302811i 0.0205637 + 0.00990298i
\(936\) 0 0
\(937\) 5.75823 + 7.22060i 0.188113 + 0.235887i 0.866941 0.498411i \(-0.166083\pi\)
−0.678827 + 0.734298i \(0.737512\pi\)
\(938\) 13.6367 31.9455i 0.445254 1.04306i
\(939\) 0 0
\(940\) −0.286813 1.25661i −0.00935480 0.0409861i
\(941\) −4.24973 5.32899i −0.138537 0.173720i 0.707723 0.706490i \(-0.249723\pi\)
−0.846260 + 0.532770i \(0.821151\pi\)
\(942\) 0 0
\(943\) −6.82092 + 3.28478i −0.222120 + 0.106967i
\(944\) 6.06702 26.5813i 0.197465 0.865149i
\(945\) 0 0
\(946\) 1.55903 + 6.83054i 0.0506883 + 0.222080i
\(947\) −14.8014 18.5603i −0.480980 0.603130i 0.480842 0.876807i \(-0.340331\pi\)
−0.961821 + 0.273678i \(0.911760\pi\)
\(948\) 0 0
\(949\) 6.84558 0.222217
\(950\) 3.70554 0.120224
\(951\) 0 0
\(952\) −12.1890 + 28.5540i −0.395046 + 0.925440i
\(953\) −28.4093 13.6812i −0.920269 0.443178i −0.0871017 0.996199i \(-0.527761\pi\)
−0.833167 + 0.553021i \(0.813475\pi\)
\(954\) 0 0
\(955\) 1.43560 + 6.28979i 0.0464551 + 0.203533i
\(956\) 1.01892 + 4.46418i 0.0329542 + 0.144382i
\(957\) 0 0
\(958\) −3.24521 1.56281i −0.104848 0.0504922i
\(959\) 1.79924 + 3.33985i 0.0581006 + 0.107849i
\(960\) 0 0
\(961\) 4.62698 0.149258
\(962\) 2.35421 0.0759028
\(963\) 0 0
\(964\) 4.97171 + 6.23433i 0.160128 + 0.200794i
\(965\) 0.133843 + 0.586405i 0.00430857 + 0.0188771i
\(966\) 0 0
\(967\) −0.832164 + 3.64595i −0.0267606 + 0.117246i −0.986544 0.163495i \(-0.947723\pi\)
0.959784 + 0.280741i \(0.0905803\pi\)
\(968\) −29.0402 + 13.9850i −0.933388 + 0.449496i
\(969\) 0 0
\(970\) 2.43499 + 3.05338i 0.0781827 + 0.0980381i
\(971\) −11.5725 50.7023i −0.371378 1.62711i −0.722913 0.690939i \(-0.757197\pi\)
0.351534 0.936175i \(-0.385660\pi\)
\(972\) 0 0
\(973\) 23.1358 20.2320i 0.741700 0.648608i
\(974\) 1.70127 + 2.13333i 0.0545123 + 0.0683562i
\(975\) 0 0
\(976\) −20.4828 9.86398i −0.655637 0.315738i
\(977\) 7.08169 8.88016i 0.226563 0.284102i −0.655537 0.755163i \(-0.727558\pi\)
0.882100 + 0.471062i \(0.156129\pi\)
\(978\) 0 0
\(979\) 12.8410 0.410399
\(980\) 0.932959 0.0848369i 0.0298023 0.00271002i
\(981\) 0 0
\(982\) −3.19370 + 13.9925i −0.101915 + 0.446519i
\(983\) −7.22506 + 9.05994i −0.230444 + 0.288967i −0.883587 0.468267i \(-0.844879\pi\)
0.653143 + 0.757234i \(0.273450\pi\)
\(984\) 0 0
\(985\) −2.60986 + 3.27266i −0.0831570 + 0.104276i
\(986\) −6.07800 7.62157i −0.193563 0.242720i
\(987\) 0 0
\(988\) 0.118507 0.148604i 0.00377022 0.00472771i
\(989\) −11.7967 51.6848i −0.375114 1.64348i
\(990\) 0 0
\(991\) 4.77334 20.9134i 0.151630 0.664335i −0.840781 0.541375i \(-0.817904\pi\)
0.992412 0.122961i \(-0.0392389\pi\)
\(992\) 15.0468 7.24617i 0.477738 0.230066i
\(993\) 0 0
\(994\) 12.6092 11.0266i 0.399941 0.349744i
\(995\) 0.626072 + 2.74300i 0.0198478 + 0.0869589i
\(996\) 0 0
\(997\) 37.4176 18.0194i 1.18503 0.570679i 0.265655 0.964068i \(-0.414412\pi\)
0.919372 + 0.393389i \(0.128697\pi\)
\(998\) −28.7094 −0.908780
\(999\) 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 441.2.u.c.64.2 24
3.2 odd 2 147.2.i.a.64.3 24
49.36 even 7 inner 441.2.u.c.379.2 24
147.92 odd 14 7203.2.a.a.1.5 12
147.104 even 14 7203.2.a.b.1.5 12
147.134 odd 14 147.2.i.a.85.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.i.a.64.3 24 3.2 odd 2
147.2.i.a.85.3 yes 24 147.134 odd 14
441.2.u.c.64.2 24 1.1 even 1 trivial
441.2.u.c.379.2 24 49.36 even 7 inner
7203.2.a.a.1.5 12 147.92 odd 14
7203.2.a.b.1.5 12 147.104 even 14