Properties

Label 475.2.e.g.201.4
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(26,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(-1.05958 + 1.83525i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.235942 - 0.408663i) q^{2} +(-0.520111 + 0.900858i) q^{3} +(0.888663 + 1.53921i) q^{4} +(0.245432 + 0.425100i) q^{6} +1.17540 q^{7} +1.78246 q^{8} +(0.958970 + 1.66098i) q^{9} +O(q^{10})\) \(q+(0.235942 - 0.408663i) q^{2} +(-0.520111 + 0.900858i) q^{3} +(0.888663 + 1.53921i) q^{4} +(0.245432 + 0.425100i) q^{6} +1.17540 q^{7} +1.78246 q^{8} +(0.958970 + 1.66098i) q^{9} +0.713538 q^{11} -1.84881 q^{12} +(-2.05158 - 3.55344i) q^{13} +(0.277326 - 0.480342i) q^{14} +(-1.35677 + 2.34999i) q^{16} +(-1.27616 + 2.21038i) q^{17} +0.905045 q^{18} +(1.57031 + 4.06622i) q^{19} +(-0.611337 + 1.05887i) q^{21} +(0.168353 - 0.291597i) q^{22} +(0.303530 + 0.525730i) q^{23} +(-0.927076 + 1.60574i) q^{24} -1.93621 q^{26} -5.11575 q^{27} +(1.04453 + 1.80918i) q^{28} +(0.429693 + 0.744250i) q^{29} +2.50914 q^{31} +(2.42270 + 4.19623i) q^{32} +(-0.371119 + 0.642796i) q^{33} +(0.602201 + 1.04304i) q^{34} +(-1.70440 + 2.95211i) q^{36} +9.38171 q^{37} +(2.03222 + 0.317665i) q^{38} +4.26819 q^{39} +(2.06117 - 3.57005i) q^{41} +(0.288480 + 0.499662i) q^{42} +(-5.06197 + 8.76759i) q^{43} +(0.634095 + 1.09828i) q^{44} +0.286462 q^{46} +(-5.25919 - 9.10919i) q^{47} +(-1.41134 - 2.44451i) q^{48} -5.61844 q^{49} +(-1.32749 - 2.29928i) q^{51} +(3.64632 - 6.31561i) q^{52} +(-2.49028 - 4.31330i) q^{53} +(-1.20702 + 2.09062i) q^{54} +2.09510 q^{56} +(-4.47982 - 0.700260i) q^{57} +0.405530 q^{58} +(3.12496 - 5.41259i) q^{59} +(2.27733 + 3.94444i) q^{61} +(0.592010 - 1.02539i) q^{62} +(1.12717 + 1.95232i) q^{63} -3.14061 q^{64} +(0.175125 + 0.303325i) q^{66} +(2.59105 + 4.48783i) q^{67} -4.53632 q^{68} -0.631477 q^{69} +(6.58393 - 11.4037i) q^{71} +(1.70932 + 2.96064i) q^{72} +(6.18914 - 10.7199i) q^{73} +(2.21354 - 3.83396i) q^{74} +(-4.86329 + 6.03053i) q^{76} +0.838691 q^{77} +(1.00704 - 1.74425i) q^{78} +(2.98173 - 5.16450i) q^{79} +(-0.216155 + 0.374392i) q^{81} +(-0.972633 - 1.68465i) q^{82} +13.8603 q^{83} -2.17309 q^{84} +(2.38866 + 4.13729i) q^{86} -0.893952 q^{87} +1.27185 q^{88} +(-7.98173 - 13.8248i) q^{89} +(-2.41142 - 4.17670i) q^{91} +(-0.539472 + 0.934393i) q^{92} +(-1.30503 + 2.26038i) q^{93} -4.96345 q^{94} -5.04028 q^{96} +(-8.35099 + 14.4643i) q^{97} +(-1.32563 + 2.29605i) q^{98} +(0.684261 + 1.18518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.235942 0.408663i 0.166836 0.288969i −0.770470 0.637477i \(-0.779978\pi\)
0.937306 + 0.348508i \(0.113312\pi\)
\(3\) −0.520111 + 0.900858i −0.300286 + 0.520111i −0.976201 0.216869i \(-0.930415\pi\)
0.675915 + 0.736980i \(0.263749\pi\)
\(4\) 0.888663 + 1.53921i 0.444331 + 0.769605i
\(5\) 0 0
\(6\) 0.245432 + 0.425100i 0.100197 + 0.173546i
\(7\) 1.17540 0.444259 0.222129 0.975017i \(-0.428699\pi\)
0.222129 + 0.975017i \(0.428699\pi\)
\(8\) 1.78246 0.630194
\(9\) 0.958970 + 1.66098i 0.319657 + 0.553661i
\(10\) 0 0
\(11\) 0.713538 0.215140 0.107570 0.994198i \(-0.465693\pi\)
0.107570 + 0.994198i \(0.465693\pi\)
\(12\) −1.84881 −0.533706
\(13\) −2.05158 3.55344i −0.569005 0.985546i −0.996665 0.0816060i \(-0.973995\pi\)
0.427659 0.903940i \(-0.359338\pi\)
\(14\) 0.277326 0.480342i 0.0741184 0.128377i
\(15\) 0 0
\(16\) −1.35677 + 2.34999i −0.339192 + 0.587498i
\(17\) −1.27616 + 2.21038i −0.309515 + 0.536096i −0.978256 0.207399i \(-0.933500\pi\)
0.668741 + 0.743495i \(0.266833\pi\)
\(18\) 0.905045 0.213321
\(19\) 1.57031 + 4.06622i 0.360253 + 0.932855i
\(20\) 0 0
\(21\) −0.611337 + 1.05887i −0.133405 + 0.231064i
\(22\) 0.168353 0.291597i 0.0358931 0.0621686i
\(23\) 0.303530 + 0.525730i 0.0632904 + 0.109622i 0.895934 0.444186i \(-0.146507\pi\)
−0.832644 + 0.553809i \(0.813174\pi\)
\(24\) −0.927076 + 1.60574i −0.189239 + 0.327771i
\(25\) 0 0
\(26\) −1.93621 −0.379722
\(27\) −5.11575 −0.984526
\(28\) 1.04453 + 1.80918i 0.197398 + 0.341904i
\(29\) 0.429693 + 0.744250i 0.0797920 + 0.138204i 0.903160 0.429304i \(-0.141241\pi\)
−0.823368 + 0.567508i \(0.807908\pi\)
\(30\) 0 0
\(31\) 2.50914 0.450654 0.225327 0.974283i \(-0.427655\pi\)
0.225327 + 0.974283i \(0.427655\pi\)
\(32\) 2.42270 + 4.19623i 0.428276 + 0.741796i
\(33\) −0.371119 + 0.642796i −0.0646035 + 0.111897i
\(34\) 0.602201 + 1.04304i 0.103277 + 0.178880i
\(35\) 0 0
\(36\) −1.70440 + 2.95211i −0.284067 + 0.492018i
\(37\) 9.38171 1.54234 0.771172 0.636627i \(-0.219671\pi\)
0.771172 + 0.636627i \(0.219671\pi\)
\(38\) 2.03222 + 0.317665i 0.329669 + 0.0515320i
\(39\) 4.26819 0.683457
\(40\) 0 0
\(41\) 2.06117 3.57005i 0.321901 0.557548i −0.658979 0.752161i \(-0.729012\pi\)
0.980880 + 0.194612i \(0.0623449\pi\)
\(42\) 0.288480 + 0.499662i 0.0445134 + 0.0770996i
\(43\) −5.06197 + 8.76759i −0.771944 + 1.33705i 0.164553 + 0.986368i \(0.447382\pi\)
−0.936496 + 0.350677i \(0.885951\pi\)
\(44\) 0.634095 + 1.09828i 0.0955934 + 0.165573i
\(45\) 0 0
\(46\) 0.286462 0.0422365
\(47\) −5.25919 9.10919i −0.767132 1.32871i −0.939112 0.343611i \(-0.888350\pi\)
0.171980 0.985100i \(-0.444984\pi\)
\(48\) −1.41134 2.44451i −0.203709 0.352835i
\(49\) −5.61844 −0.802634
\(50\) 0 0
\(51\) −1.32749 2.29928i −0.185886 0.321964i
\(52\) 3.64632 6.31561i 0.505654 0.875818i
\(53\) −2.49028 4.31330i −0.342067 0.592477i 0.642750 0.766076i \(-0.277794\pi\)
−0.984816 + 0.173599i \(0.944460\pi\)
\(54\) −1.20702 + 2.09062i −0.164254 + 0.284497i
\(55\) 0 0
\(56\) 2.09510 0.279969
\(57\) −4.47982 0.700260i −0.593367 0.0927517i
\(58\) 0.405530 0.0532488
\(59\) 3.12496 5.41259i 0.406835 0.704659i −0.587698 0.809080i \(-0.699966\pi\)
0.994533 + 0.104421i \(0.0332991\pi\)
\(60\) 0 0
\(61\) 2.27733 + 3.94444i 0.291582 + 0.505034i 0.974184 0.225756i \(-0.0724852\pi\)
−0.682602 + 0.730790i \(0.739152\pi\)
\(62\) 0.592010 1.02539i 0.0751854 0.130225i
\(63\) 1.12717 + 1.95232i 0.142010 + 0.245969i
\(64\) −3.14061 −0.392577
\(65\) 0 0
\(66\) 0.175125 + 0.303325i 0.0215564 + 0.0373368i
\(67\) 2.59105 + 4.48783i 0.316547 + 0.548276i 0.979765 0.200151i \(-0.0641431\pi\)
−0.663218 + 0.748426i \(0.730810\pi\)
\(68\) −4.53632 −0.550109
\(69\) −0.631477 −0.0760209
\(70\) 0 0
\(71\) 6.58393 11.4037i 0.781368 1.35337i −0.149776 0.988720i \(-0.547855\pi\)
0.931145 0.364650i \(-0.118811\pi\)
\(72\) 1.70932 + 2.96064i 0.201446 + 0.348914i
\(73\) 6.18914 10.7199i 0.724384 1.25467i −0.234842 0.972033i \(-0.575457\pi\)
0.959227 0.282637i \(-0.0912093\pi\)
\(74\) 2.21354 3.83396i 0.257319 0.445689i
\(75\) 0 0
\(76\) −4.86329 + 6.03053i −0.557857 + 0.691749i
\(77\) 0.838691 0.0955777
\(78\) 1.00704 1.74425i 0.114025 0.197498i
\(79\) 2.98173 5.16450i 0.335471 0.581052i −0.648105 0.761551i \(-0.724438\pi\)
0.983575 + 0.180499i \(0.0577714\pi\)
\(80\) 0 0
\(81\) −0.216155 + 0.374392i −0.0240172 + 0.0415991i
\(82\) −0.972633 1.68465i −0.107409 0.186038i
\(83\) 13.8603 1.52136 0.760682 0.649124i \(-0.224864\pi\)
0.760682 + 0.649124i \(0.224864\pi\)
\(84\) −2.17309 −0.237104
\(85\) 0 0
\(86\) 2.38866 + 4.13729i 0.257576 + 0.446135i
\(87\) −0.893952 −0.0958417
\(88\) 1.27185 0.135580
\(89\) −7.98173 13.8248i −0.846061 1.46542i −0.884696 0.466168i \(-0.845634\pi\)
0.0386349 0.999253i \(-0.487699\pi\)
\(90\) 0 0
\(91\) −2.41142 4.17670i −0.252786 0.437837i
\(92\) −0.539472 + 0.934393i −0.0562439 + 0.0974172i
\(93\) −1.30503 + 2.26038i −0.135325 + 0.234390i
\(94\) −4.96345 −0.511941
\(95\) 0 0
\(96\) −5.04028 −0.514421
\(97\) −8.35099 + 14.4643i −0.847915 + 1.46863i 0.0351512 + 0.999382i \(0.488809\pi\)
−0.883066 + 0.469249i \(0.844525\pi\)
\(98\) −1.32563 + 2.29605i −0.133908 + 0.231936i
\(99\) 0.684261 + 1.18518i 0.0687708 + 0.119115i
\(100\) 0 0
\(101\) −7.01362 12.1479i −0.697881 1.20877i −0.969200 0.246276i \(-0.920793\pi\)
0.271318 0.962490i \(-0.412540\pi\)
\(102\) −1.25284 −0.124050
\(103\) 3.55382 0.350169 0.175084 0.984553i \(-0.443980\pi\)
0.175084 + 0.984553i \(0.443980\pi\)
\(104\) −3.65685 6.33385i −0.358584 0.621085i
\(105\) 0 0
\(106\) −2.35025 −0.228276
\(107\) 3.63127 0.351048 0.175524 0.984475i \(-0.443838\pi\)
0.175524 + 0.984475i \(0.443838\pi\)
\(108\) −4.54617 7.87420i −0.437456 0.757696i
\(109\) 3.11134 5.38899i 0.298012 0.516172i −0.677669 0.735367i \(-0.737010\pi\)
0.975681 + 0.219195i \(0.0703431\pi\)
\(110\) 0 0
\(111\) −4.87953 + 8.45159i −0.463144 + 0.802189i
\(112\) −1.59474 + 2.76218i −0.150689 + 0.261001i
\(113\) −12.2707 −1.15433 −0.577167 0.816626i \(-0.695842\pi\)
−0.577167 + 0.816626i \(0.695842\pi\)
\(114\) −1.34315 + 1.66552i −0.125797 + 0.155990i
\(115\) 0 0
\(116\) −0.763705 + 1.32278i −0.0709082 + 0.122817i
\(117\) 3.93480 6.81528i 0.363773 0.630072i
\(118\) −1.47462 2.55411i −0.135750 0.235125i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) −10.4909 −0.953715
\(122\) 2.14927 0.194585
\(123\) 2.14407 + 3.71364i 0.193325 + 0.334848i
\(124\) 2.22978 + 3.86209i 0.200240 + 0.346826i
\(125\) 0 0
\(126\) 1.06379 0.0947697
\(127\) −1.07894 1.86879i −0.0957408 0.165828i 0.814177 0.580617i \(-0.197189\pi\)
−0.909918 + 0.414789i \(0.863855\pi\)
\(128\) −5.58639 + 9.67592i −0.493772 + 0.855239i
\(129\) −5.26557 9.12024i −0.463608 0.802992i
\(130\) 0 0
\(131\) 8.77471 15.1982i 0.766650 1.32788i −0.172720 0.984971i \(-0.555256\pi\)
0.939370 0.342906i \(-0.111411\pi\)
\(132\) −1.31920 −0.114821
\(133\) 1.84574 + 4.77943i 0.160046 + 0.414429i
\(134\) 2.44535 0.211246
\(135\) 0 0
\(136\) −2.27471 + 3.93991i −0.195055 + 0.337845i
\(137\) −2.53728 4.39469i −0.216774 0.375464i 0.737046 0.675843i \(-0.236220\pi\)
−0.953820 + 0.300379i \(0.902887\pi\)
\(138\) −0.148992 + 0.258062i −0.0126830 + 0.0219677i
\(139\) −2.99086 5.18033i −0.253682 0.439390i 0.710855 0.703339i \(-0.248308\pi\)
−0.964537 + 0.263949i \(0.914975\pi\)
\(140\) 0 0
\(141\) 10.9414 0.921436
\(142\) −3.10685 5.38122i −0.260721 0.451582i
\(143\) −1.46388 2.53551i −0.122416 0.212030i
\(144\) −5.20440 −0.433700
\(145\) 0 0
\(146\) −2.92056 5.05855i −0.241707 0.418649i
\(147\) 2.92221 5.06142i 0.241020 0.417459i
\(148\) 8.33718 + 14.4404i 0.685312 + 1.18699i
\(149\) −4.80008 + 8.31399i −0.393238 + 0.681108i −0.992875 0.119164i \(-0.961979\pi\)
0.599636 + 0.800273i \(0.295312\pi\)
\(150\) 0 0
\(151\) 7.53638 0.613302 0.306651 0.951822i \(-0.400792\pi\)
0.306651 + 0.951822i \(0.400792\pi\)
\(152\) 2.79901 + 7.24787i 0.227029 + 0.587880i
\(153\) −4.89521 −0.395754
\(154\) 0.197882 0.342742i 0.0159458 0.0276190i
\(155\) 0 0
\(156\) 3.79298 + 6.56964i 0.303682 + 0.525992i
\(157\) 4.92803 8.53560i 0.393300 0.681215i −0.599583 0.800313i \(-0.704667\pi\)
0.992883 + 0.119098i \(0.0380002\pi\)
\(158\) −1.40703 2.43705i −0.111937 0.193881i
\(159\) 5.18089 0.410872
\(160\) 0 0
\(161\) 0.356769 + 0.617942i 0.0281173 + 0.0487007i
\(162\) 0.102000 + 0.176669i 0.00801389 + 0.0138805i
\(163\) −0.0688234 −0.00539067 −0.00269533 0.999996i \(-0.500858\pi\)
−0.00269533 + 0.999996i \(0.500858\pi\)
\(164\) 7.32674 0.572122
\(165\) 0 0
\(166\) 3.27022 5.66419i 0.253819 0.439627i
\(167\) 8.32212 + 14.4143i 0.643985 + 1.11542i 0.984535 + 0.175189i \(0.0560536\pi\)
−0.340550 + 0.940227i \(0.610613\pi\)
\(168\) −1.08968 + 1.88739i −0.0840709 + 0.145615i
\(169\) −1.91794 + 3.32197i −0.147534 + 0.255536i
\(170\) 0 0
\(171\) −5.24805 + 6.50764i −0.401328 + 0.497651i
\(172\) −17.9935 −1.37200
\(173\) −6.06778 + 10.5097i −0.461325 + 0.799038i −0.999027 0.0440965i \(-0.985959\pi\)
0.537702 + 0.843135i \(0.319292\pi\)
\(174\) −0.210921 + 0.365325i −0.0159899 + 0.0276952i
\(175\) 0 0
\(176\) −0.968106 + 1.67681i −0.0729737 + 0.126394i
\(177\) 3.25065 + 5.63029i 0.244334 + 0.423198i
\(178\) −7.53290 −0.564614
\(179\) 11.7538 0.878522 0.439261 0.898360i \(-0.355240\pi\)
0.439261 + 0.898360i \(0.355240\pi\)
\(180\) 0 0
\(181\) 4.41794 + 7.65210i 0.328383 + 0.568776i 0.982191 0.187884i \(-0.0601631\pi\)
−0.653808 + 0.756660i \(0.726830\pi\)
\(182\) −2.27582 −0.168695
\(183\) −4.73785 −0.350232
\(184\) 0.541030 + 0.937092i 0.0398853 + 0.0690833i
\(185\) 0 0
\(186\) 0.615822 + 1.06663i 0.0451543 + 0.0782095i
\(187\) −0.910591 + 1.57719i −0.0665890 + 0.115336i
\(188\) 9.34730 16.1900i 0.681722 1.18078i
\(189\) −6.01304 −0.437384
\(190\) 0 0
\(191\) 14.2447 1.03071 0.515355 0.856977i \(-0.327660\pi\)
0.515355 + 0.856977i \(0.327660\pi\)
\(192\) 1.63347 2.82925i 0.117885 0.204183i
\(193\) 9.75283 16.8924i 0.702024 1.21594i −0.265731 0.964047i \(-0.585613\pi\)
0.967755 0.251894i \(-0.0810533\pi\)
\(194\) 3.94070 + 6.82549i 0.282926 + 0.490041i
\(195\) 0 0
\(196\) −4.99290 8.64795i −0.356636 0.617711i
\(197\) 4.33232 0.308665 0.154332 0.988019i \(-0.450677\pi\)
0.154332 + 0.988019i \(0.450677\pi\)
\(198\) 0.645784 0.0458938
\(199\) 6.31574 + 10.9392i 0.447711 + 0.775458i 0.998237 0.0593602i \(-0.0189061\pi\)
−0.550526 + 0.834818i \(0.685573\pi\)
\(200\) 0 0
\(201\) −5.39053 −0.380219
\(202\) −6.61923 −0.465727
\(203\) 0.505060 + 0.874790i 0.0354483 + 0.0613983i
\(204\) 2.35939 4.08658i 0.165190 0.286118i
\(205\) 0 0
\(206\) 0.838496 1.45232i 0.0584208 0.101188i
\(207\) −0.582153 + 1.00832i −0.0404624 + 0.0700830i
\(208\) 11.1341 0.772009
\(209\) 1.12047 + 2.90140i 0.0775048 + 0.200694i
\(210\) 0 0
\(211\) −11.1223 + 19.2645i −0.765694 + 1.32622i 0.174186 + 0.984713i \(0.444271\pi\)
−0.939879 + 0.341507i \(0.889063\pi\)
\(212\) 4.42605 7.66614i 0.303982 0.526512i
\(213\) 6.84874 + 11.8624i 0.469268 + 0.812796i
\(214\) 0.856769 1.48397i 0.0585675 0.101442i
\(215\) 0 0
\(216\) −9.11861 −0.620443
\(217\) 2.94923 0.200207
\(218\) −1.46819 2.54298i −0.0994383 0.172232i
\(219\) 6.43808 + 11.1511i 0.435045 + 0.753520i
\(220\) 0 0
\(221\) 10.4726 0.704463
\(222\) 2.30257 + 3.98817i 0.154538 + 0.267668i
\(223\) 6.81125 11.7974i 0.456115 0.790015i −0.542636 0.839968i \(-0.682574\pi\)
0.998752 + 0.0499529i \(0.0159071\pi\)
\(224\) 2.84763 + 4.93224i 0.190265 + 0.329549i
\(225\) 0 0
\(226\) −2.89518 + 5.01460i −0.192585 + 0.333566i
\(227\) −6.58913 −0.437336 −0.218668 0.975799i \(-0.570171\pi\)
−0.218668 + 0.975799i \(0.570171\pi\)
\(228\) −2.90320 7.51768i −0.192269 0.497870i
\(229\) −0.585962 −0.0387215 −0.0193607 0.999813i \(-0.506163\pi\)
−0.0193607 + 0.999813i \(0.506163\pi\)
\(230\) 0 0
\(231\) −0.436212 + 0.755542i −0.0287007 + 0.0497110i
\(232\) 0.765910 + 1.32660i 0.0502845 + 0.0870953i
\(233\) 3.57873 6.19855i 0.234451 0.406080i −0.724662 0.689104i \(-0.758004\pi\)
0.959113 + 0.283024i \(0.0913376\pi\)
\(234\) −1.85677 3.21602i −0.121381 0.210238i
\(235\) 0 0
\(236\) 11.1081 0.723078
\(237\) 3.10166 + 5.37223i 0.201474 + 0.348964i
\(238\) 0.707826 + 1.22599i 0.0458815 + 0.0794691i
\(239\) 3.65498 0.236421 0.118211 0.992989i \(-0.462284\pi\)
0.118211 + 0.992989i \(0.462284\pi\)
\(240\) 0 0
\(241\) −8.63148 14.9502i −0.556002 0.963024i −0.997825 0.0659218i \(-0.979001\pi\)
0.441822 0.897103i \(-0.354332\pi\)
\(242\) −2.47523 + 4.28723i −0.159114 + 0.275594i
\(243\) −7.89847 13.6805i −0.506687 0.877608i
\(244\) −4.04755 + 7.01056i −0.259118 + 0.448805i
\(245\) 0 0
\(246\) 2.02351 0.129014
\(247\) 11.2274 13.9221i 0.714385 0.885845i
\(248\) 4.47243 0.284000
\(249\) −7.20889 + 12.4862i −0.456845 + 0.791278i
\(250\) 0 0
\(251\) 9.70702 + 16.8130i 0.612702 + 1.06123i 0.990783 + 0.135458i \(0.0432506\pi\)
−0.378082 + 0.925772i \(0.623416\pi\)
\(252\) −2.00335 + 3.46990i −0.126199 + 0.218583i
\(253\) 0.216580 + 0.375128i 0.0136163 + 0.0235841i
\(254\) −1.01827 −0.0638921
\(255\) 0 0
\(256\) −0.504485 0.873793i −0.0315303 0.0546121i
\(257\) −6.94643 12.0316i −0.433306 0.750509i 0.563849 0.825878i \(-0.309320\pi\)
−0.997156 + 0.0753689i \(0.975987\pi\)
\(258\) −4.96948 −0.309386
\(259\) 11.0272 0.685199
\(260\) 0 0
\(261\) −0.824125 + 1.42743i −0.0510121 + 0.0883555i
\(262\) −4.14064 7.17180i −0.255810 0.443076i
\(263\) −7.49417 + 12.9803i −0.462110 + 0.800399i −0.999066 0.0432118i \(-0.986241\pi\)
0.536955 + 0.843611i \(0.319574\pi\)
\(264\) −0.661504 + 1.14576i −0.0407127 + 0.0705165i
\(265\) 0 0
\(266\) 2.38866 + 0.373382i 0.146458 + 0.0228935i
\(267\) 16.6055 1.01624
\(268\) −4.60514 + 7.97633i −0.281304 + 0.487232i
\(269\) −9.68613 + 16.7769i −0.590574 + 1.02290i 0.403582 + 0.914944i \(0.367765\pi\)
−0.994155 + 0.107960i \(0.965568\pi\)
\(270\) 0 0
\(271\) −5.95897 + 10.3212i −0.361982 + 0.626971i −0.988287 0.152607i \(-0.951233\pi\)
0.626305 + 0.779578i \(0.284566\pi\)
\(272\) −3.46292 5.99795i −0.209970 0.363679i
\(273\) 5.01682 0.303632
\(274\) −2.39460 −0.144663
\(275\) 0 0
\(276\) −0.561171 0.971976i −0.0337785 0.0585061i
\(277\) −10.9824 −0.659866 −0.329933 0.944004i \(-0.607026\pi\)
−0.329933 + 0.944004i \(0.607026\pi\)
\(278\) −2.82268 −0.169293
\(279\) 2.40619 + 4.16764i 0.144055 + 0.249510i
\(280\) 0 0
\(281\) −7.32488 12.6871i −0.436965 0.756846i 0.560488 0.828162i \(-0.310613\pi\)
−0.997454 + 0.0713160i \(0.977280\pi\)
\(282\) 2.58155 4.47137i 0.153729 0.266266i
\(283\) −9.46435 + 16.3927i −0.562597 + 0.974447i 0.434672 + 0.900589i \(0.356864\pi\)
−0.997269 + 0.0738576i \(0.976469\pi\)
\(284\) 23.4036 1.38875
\(285\) 0 0
\(286\) −1.38156 −0.0816934
\(287\) 2.42270 4.19623i 0.143007 0.247696i
\(288\) −4.64658 + 8.04812i −0.273803 + 0.474240i
\(289\) 5.24281 + 9.08082i 0.308401 + 0.534166i
\(290\) 0 0
\(291\) −8.68688 15.0461i −0.509234 0.882019i
\(292\) 22.0002 1.28747
\(293\) −5.59625 −0.326937 −0.163468 0.986549i \(-0.552268\pi\)
−0.163468 + 0.986549i \(0.552268\pi\)
\(294\) −1.37894 2.38840i −0.0804216 0.139294i
\(295\) 0 0
\(296\) 16.7225 0.971976
\(297\) −3.65028 −0.211811
\(298\) 2.26508 + 3.92324i 0.131213 + 0.227267i
\(299\) 1.24543 2.15715i 0.0720252 0.124751i
\(300\) 0 0
\(301\) −5.94983 + 10.3054i −0.342943 + 0.593994i
\(302\) 1.77815 3.07984i 0.102321 0.177225i
\(303\) 14.5914 0.838256
\(304\) −11.6861 1.82671i −0.670245 0.104769i
\(305\) 0 0
\(306\) −1.15498 + 2.00049i −0.0660261 + 0.114361i
\(307\) −10.3160 + 17.8678i −0.588764 + 1.01977i 0.405631 + 0.914037i \(0.367052\pi\)
−0.994395 + 0.105732i \(0.966282\pi\)
\(308\) 0.745314 + 1.29092i 0.0424682 + 0.0735571i
\(309\) −1.84838 + 3.20149i −0.105151 + 0.182127i
\(310\) 0 0
\(311\) −24.6587 −1.39827 −0.699134 0.714991i \(-0.746431\pi\)
−0.699134 + 0.714991i \(0.746431\pi\)
\(312\) 7.60787 0.430711
\(313\) −1.74928 3.02985i −0.0988753 0.171257i 0.812344 0.583178i \(-0.198191\pi\)
−0.911219 + 0.411921i \(0.864858\pi\)
\(314\) −2.32546 4.02781i −0.131233 0.227303i
\(315\) 0 0
\(316\) 10.5990 0.596240
\(317\) −15.6854 27.1680i −0.880982 1.52590i −0.850251 0.526377i \(-0.823550\pi\)
−0.0307305 0.999528i \(-0.509783\pi\)
\(318\) 1.22239 2.11724i 0.0685482 0.118729i
\(319\) 0.306602 + 0.531051i 0.0171664 + 0.0297331i
\(320\) 0 0
\(321\) −1.88866 + 3.27126i −0.105415 + 0.182584i
\(322\) 0.336707 0.0187639
\(323\) −10.9919 1.71818i −0.611603 0.0956024i
\(324\) −0.768356 −0.0426865
\(325\) 0 0
\(326\) −0.0162383 + 0.0281256i −0.000899358 + 0.00155773i
\(327\) 3.23648 + 5.60575i 0.178978 + 0.309999i
\(328\) 3.67395 6.36347i 0.202860 0.351364i
\(329\) −6.18164 10.7069i −0.340805 0.590292i
\(330\) 0 0
\(331\) 35.7497 1.96498 0.982492 0.186305i \(-0.0596512\pi\)
0.982492 + 0.186305i \(0.0596512\pi\)
\(332\) 12.3171 + 21.3339i 0.675990 + 1.17085i
\(333\) 8.99677 + 15.5829i 0.493020 + 0.853936i
\(334\) 7.85415 0.429760
\(335\) 0 0
\(336\) −1.65889 2.87328i −0.0904997 0.156750i
\(337\) −13.2446 + 22.9403i −0.721480 + 1.24964i 0.238927 + 0.971038i \(0.423204\pi\)
−0.960407 + 0.278602i \(0.910129\pi\)
\(338\) 0.905045 + 1.56758i 0.0492279 + 0.0852653i
\(339\) 6.38214 11.0542i 0.346630 0.600382i
\(340\) 0 0
\(341\) 1.79036 0.0969536
\(342\) 1.42120 + 3.68011i 0.0768496 + 0.198998i
\(343\) −14.8317 −0.800836
\(344\) −9.02276 + 15.6279i −0.486474 + 0.842599i
\(345\) 0 0
\(346\) 2.86329 + 4.95936i 0.153931 + 0.266617i
\(347\) −17.1699 + 29.7392i −0.921729 + 1.59648i −0.124990 + 0.992158i \(0.539890\pi\)
−0.796739 + 0.604323i \(0.793444\pi\)
\(348\) −0.794422 1.37598i −0.0425855 0.0737602i
\(349\) −21.4308 −1.14717 −0.573583 0.819148i \(-0.694447\pi\)
−0.573583 + 0.819148i \(0.694447\pi\)
\(350\) 0 0
\(351\) 10.4953 + 18.1785i 0.560200 + 0.970295i
\(352\) 1.72869 + 2.99417i 0.0921393 + 0.159590i
\(353\) 19.5659 1.04139 0.520693 0.853744i \(-0.325674\pi\)
0.520693 + 0.853744i \(0.325674\pi\)
\(354\) 3.06786 0.163055
\(355\) 0 0
\(356\) 14.1861 24.5711i 0.751863 1.30227i
\(357\) −1.56033 2.70257i −0.0825815 0.143035i
\(358\) 2.77322 4.80335i 0.146569 0.253865i
\(359\) 8.23630 14.2657i 0.434695 0.752914i −0.562576 0.826746i \(-0.690189\pi\)
0.997271 + 0.0738319i \(0.0235228\pi\)
\(360\) 0 0
\(361\) −14.0683 + 12.7704i −0.740435 + 0.672128i
\(362\) 4.16951 0.219144
\(363\) 5.45641 9.45078i 0.286387 0.496037i
\(364\) 4.28588 7.42336i 0.224641 0.389090i
\(365\) 0 0
\(366\) −1.11786 + 1.93618i −0.0584313 + 0.101206i
\(367\) −6.36735 11.0286i −0.332373 0.575687i 0.650603 0.759418i \(-0.274516\pi\)
−0.982977 + 0.183730i \(0.941183\pi\)
\(368\) −1.64728 −0.0858705
\(369\) 7.90640 0.411591
\(370\) 0 0
\(371\) −2.92708 5.06984i −0.151966 0.263213i
\(372\) −4.63892 −0.240517
\(373\) −19.3342 −1.00109 −0.500544 0.865711i \(-0.666867\pi\)
−0.500544 + 0.865711i \(0.666867\pi\)
\(374\) 0.429693 + 0.744250i 0.0222189 + 0.0384843i
\(375\) 0 0
\(376\) −9.37429 16.2368i −0.483442 0.837346i
\(377\) 1.76310 3.05377i 0.0908041 0.157277i
\(378\) −1.41873 + 2.45731i −0.0729715 + 0.126390i
\(379\) 9.85789 0.506366 0.253183 0.967418i \(-0.418523\pi\)
0.253183 + 0.967418i \(0.418523\pi\)
\(380\) 0 0
\(381\) 2.24468 0.114999
\(382\) 3.36092 5.82128i 0.171959 0.297843i
\(383\) 10.1666 17.6091i 0.519490 0.899784i −0.480253 0.877130i \(-0.659455\pi\)
0.999743 0.0226536i \(-0.00721149\pi\)
\(384\) −5.81109 10.0651i −0.296546 0.513632i
\(385\) 0 0
\(386\) −4.60220 7.97125i −0.234246 0.405726i
\(387\) −19.4171 −0.987027
\(388\) −29.6849 −1.50702
\(389\) 0.502617 + 0.870559i 0.0254837 + 0.0441391i 0.878486 0.477768i \(-0.158554\pi\)
−0.853002 + 0.521907i \(0.825221\pi\)
\(390\) 0 0
\(391\) −1.54942 −0.0783574
\(392\) −10.0146 −0.505816
\(393\) 9.12764 + 15.8095i 0.460428 + 0.797486i
\(394\) 1.02217 1.77046i 0.0514964 0.0891944i
\(395\) 0 0
\(396\) −1.21616 + 2.10644i −0.0611141 + 0.105853i
\(397\) 4.93111 8.54093i 0.247485 0.428657i −0.715342 0.698774i \(-0.753729\pi\)
0.962827 + 0.270117i \(0.0870625\pi\)
\(398\) 5.96059 0.298777
\(399\) −5.26557 0.823085i −0.263608 0.0412058i
\(400\) 0 0
\(401\) −14.9159 + 25.8351i −0.744865 + 1.29014i 0.205393 + 0.978680i \(0.434153\pi\)
−0.950258 + 0.311464i \(0.899181\pi\)
\(402\) −1.27185 + 2.20291i −0.0634342 + 0.109871i
\(403\) −5.14769 8.91606i −0.256425 0.444140i
\(404\) 12.4655 21.5909i 0.620181 1.07419i
\(405\) 0 0
\(406\) 0.476660 0.0236562
\(407\) 6.69420 0.331819
\(408\) −2.36620 4.09838i −0.117144 0.202900i
\(409\) −13.8221 23.9406i −0.683458 1.18378i −0.973919 0.226898i \(-0.927142\pi\)
0.290460 0.956887i \(-0.406192\pi\)
\(410\) 0 0
\(411\) 5.27866 0.260377
\(412\) 3.15815 + 5.47008i 0.155591 + 0.269491i
\(413\) 3.67307 6.36194i 0.180740 0.313051i
\(414\) 0.274708 + 0.475809i 0.0135012 + 0.0233847i
\(415\) 0 0
\(416\) 9.94070 17.2178i 0.487383 0.844172i
\(417\) 6.22232 0.304708
\(418\) 1.45006 + 0.226666i 0.0709249 + 0.0110866i
\(419\) −11.2902 −0.551562 −0.275781 0.961220i \(-0.588936\pi\)
−0.275781 + 0.961220i \(0.588936\pi\)
\(420\) 0 0
\(421\) −2.27471 + 3.93991i −0.110863 + 0.192019i −0.916118 0.400908i \(-0.868695\pi\)
0.805256 + 0.592928i \(0.202028\pi\)
\(422\) 5.24845 + 9.09059i 0.255491 + 0.442523i
\(423\) 10.0868 17.4709i 0.490438 0.849463i
\(424\) −4.43883 7.68828i −0.215569 0.373376i
\(425\) 0 0
\(426\) 6.46362 0.313163
\(427\) 2.67676 + 4.63629i 0.129538 + 0.224366i
\(428\) 3.22698 + 5.58929i 0.155982 + 0.270168i
\(429\) 3.04551 0.147039
\(430\) 0 0
\(431\) −16.4517 28.4952i −0.792451 1.37256i −0.924445 0.381314i \(-0.875472\pi\)
0.131995 0.991250i \(-0.457862\pi\)
\(432\) 6.94089 12.0220i 0.333943 0.578407i
\(433\) 11.1547 + 19.3204i 0.536059 + 0.928481i 0.999111 + 0.0421503i \(0.0134208\pi\)
−0.463052 + 0.886331i \(0.653246\pi\)
\(434\) 0.695848 1.20524i 0.0334018 0.0578536i
\(435\) 0 0
\(436\) 11.0597 0.529664
\(437\) −1.66110 + 2.05978i −0.0794611 + 0.0985325i
\(438\) 6.07605 0.290325
\(439\) −2.85287 + 4.94131i −0.136160 + 0.235836i −0.926040 0.377425i \(-0.876809\pi\)
0.789880 + 0.613261i \(0.210143\pi\)
\(440\) 0 0
\(441\) −5.38791 9.33214i −0.256567 0.444388i
\(442\) 2.47092 4.27976i 0.117530 0.203568i
\(443\) 5.78881 + 10.0265i 0.275034 + 0.476374i 0.970144 0.242530i \(-0.0779774\pi\)
−0.695109 + 0.718904i \(0.744644\pi\)
\(444\) −17.3450 −0.823158
\(445\) 0 0
\(446\) −3.21412 5.56702i −0.152193 0.263606i
\(447\) −4.99315 8.64839i −0.236168 0.409055i
\(448\) −3.69147 −0.174406
\(449\) −25.4726 −1.20213 −0.601063 0.799202i \(-0.705256\pi\)
−0.601063 + 0.799202i \(0.705256\pi\)
\(450\) 0 0
\(451\) 1.47072 2.54737i 0.0692537 0.119951i
\(452\) −10.9046 18.8872i −0.512907 0.888381i
\(453\) −3.91975 + 6.78921i −0.184166 + 0.318985i
\(454\) −1.55465 + 2.69274i −0.0729634 + 0.126376i
\(455\) 0 0
\(456\) −7.98509 1.24818i −0.373936 0.0584516i
\(457\) 6.92830 0.324092 0.162046 0.986783i \(-0.448191\pi\)
0.162046 + 0.986783i \(0.448191\pi\)
\(458\) −0.138253 + 0.239461i −0.00646014 + 0.0111893i
\(459\) 6.52853 11.3077i 0.304726 0.527800i
\(460\) 0 0
\(461\) −16.2473 + 28.1411i −0.756712 + 1.31066i 0.187806 + 0.982206i \(0.439862\pi\)
−0.944519 + 0.328458i \(0.893471\pi\)
\(462\) 0.205841 + 0.356528i 0.00957661 + 0.0165872i
\(463\) −21.5062 −0.999477 −0.499738 0.866176i \(-0.666571\pi\)
−0.499738 + 0.866176i \(0.666571\pi\)
\(464\) −2.33198 −0.108259
\(465\) 0 0
\(466\) −1.68875 2.92499i −0.0782296 0.135498i
\(467\) 16.9509 0.784392 0.392196 0.919882i \(-0.371715\pi\)
0.392196 + 0.919882i \(0.371715\pi\)
\(468\) 13.9868 0.646542
\(469\) 3.04551 + 5.27499i 0.140629 + 0.243576i
\(470\) 0 0
\(471\) 5.12624 + 8.87891i 0.236205 + 0.409119i
\(472\) 5.57011 9.64771i 0.256385 0.444072i
\(473\) −3.61191 + 6.25601i −0.166076 + 0.287652i
\(474\) 2.92724 0.134453
\(475\) 0 0
\(476\) −5.33198 −0.244391
\(477\) 4.77621 8.27265i 0.218688 0.378778i
\(478\) 0.862364 1.49366i 0.0394436 0.0683183i
\(479\) −4.42894 7.67115i −0.202364 0.350504i 0.746926 0.664907i \(-0.231529\pi\)
−0.949290 + 0.314403i \(0.898196\pi\)
\(480\) 0 0
\(481\) −19.2473 33.3373i −0.877601 1.52005i
\(482\) −8.14611 −0.371045
\(483\) −0.742237 −0.0337730
\(484\) −9.32284 16.1476i −0.423765 0.733983i
\(485\) 0 0
\(486\) −7.45432 −0.338135
\(487\) 30.0628 1.36227 0.681137 0.732156i \(-0.261486\pi\)
0.681137 + 0.732156i \(0.261486\pi\)
\(488\) 4.05924 + 7.03081i 0.183753 + 0.318270i
\(489\) 0.0357958 0.0620001i 0.00161874 0.00280374i
\(490\) 0 0
\(491\) −1.55017 + 2.68497i −0.0699580 + 0.121171i −0.898883 0.438190i \(-0.855620\pi\)
0.828925 + 0.559360i \(0.188953\pi\)
\(492\) −3.81072 + 6.60036i −0.171800 + 0.297567i
\(493\) −2.19343 −0.0987873
\(494\) −3.04045 7.87306i −0.136796 0.354226i
\(495\) 0 0
\(496\) −3.40432 + 5.89645i −0.152858 + 0.264759i
\(497\) 7.73874 13.4039i 0.347130 0.601246i
\(498\) 3.40176 + 5.89202i 0.152436 + 0.264028i
\(499\) −16.0696 + 27.8333i −0.719372 + 1.24599i 0.241877 + 0.970307i \(0.422237\pi\)
−0.961249 + 0.275682i \(0.911096\pi\)
\(500\) 0 0
\(501\) −17.3137 −0.773519
\(502\) 9.16117 0.408883
\(503\) −4.20911 7.29040i −0.187675 0.325063i 0.756800 0.653647i \(-0.226762\pi\)
−0.944475 + 0.328584i \(0.893429\pi\)
\(504\) 2.00914 + 3.47993i 0.0894940 + 0.155008i
\(505\) 0 0
\(506\) 0.204402 0.00908676
\(507\) −1.99508 3.45558i −0.0886047 0.153468i
\(508\) 1.91764 3.32144i 0.0850813 0.147365i
\(509\) −10.1725 17.6193i −0.450888 0.780962i 0.547553 0.836771i \(-0.315559\pi\)
−0.998441 + 0.0558093i \(0.982226\pi\)
\(510\) 0 0
\(511\) 7.27471 12.6002i 0.321814 0.557398i
\(512\) −22.8217 −1.00859
\(513\) −8.03329 20.8017i −0.354678 0.918419i
\(514\) −6.55582 −0.289165
\(515\) 0 0
\(516\) 9.35864 16.2096i 0.411991 0.713589i
\(517\) −3.75263 6.49975i −0.165041 0.285859i
\(518\) 2.60179 4.50643i 0.114316 0.198001i
\(519\) −6.31184 10.9324i −0.277059 0.479880i
\(520\) 0 0
\(521\) 15.3502 0.672507 0.336253 0.941772i \(-0.390840\pi\)
0.336253 + 0.941772i \(0.390840\pi\)
\(522\) 0.388891 + 0.673580i 0.0170213 + 0.0294818i
\(523\) −6.61835 11.4633i −0.289400 0.501256i 0.684267 0.729232i \(-0.260122\pi\)
−0.973667 + 0.227976i \(0.926789\pi\)
\(524\) 31.1910 1.36259
\(525\) 0 0
\(526\) 3.53638 + 6.12519i 0.154193 + 0.267071i
\(527\) −3.20207 + 5.54614i −0.139484 + 0.241594i
\(528\) −1.00704 1.74425i −0.0438260 0.0759088i
\(529\) 11.3157 19.5994i 0.491989 0.852149i
\(530\) 0 0
\(531\) 11.9870 0.520190
\(532\) −5.71630 + 7.08827i −0.247833 + 0.307316i
\(533\) −16.9146 −0.732653
\(534\) 3.91794 6.78607i 0.169546 0.293662i
\(535\) 0 0
\(536\) 4.61844 + 7.99937i 0.199486 + 0.345520i
\(537\) −6.11329 + 10.5885i −0.263808 + 0.456928i
\(538\) 4.57073 + 7.91673i 0.197058 + 0.341315i
\(539\) −4.00897 −0.172679
\(540\) 0 0
\(541\) 13.8704 + 24.0242i 0.596335 + 1.03288i 0.993357 + 0.115073i \(0.0367102\pi\)
−0.397022 + 0.917809i \(0.629956\pi\)
\(542\) 2.81194 + 4.87043i 0.120783 + 0.209203i
\(543\) −9.19127 −0.394435
\(544\) −12.3670 −0.530232
\(545\) 0 0
\(546\) 1.18368 2.05019i 0.0506568 0.0877401i
\(547\) −8.53008 14.7745i −0.364720 0.631714i 0.624011 0.781415i \(-0.285502\pi\)
−0.988731 + 0.149702i \(0.952169\pi\)
\(548\) 4.50957 7.81080i 0.192639 0.333661i
\(549\) −4.36777 + 7.56520i −0.186412 + 0.322875i
\(550\) 0 0
\(551\) −2.35153 + 2.91593i −0.100179 + 0.124223i
\(552\) −1.12558 −0.0479080
\(553\) 3.50472 6.07035i 0.149036 0.258137i
\(554\) −2.59120 + 4.48808i −0.110089 + 0.190680i
\(555\) 0 0
\(556\) 5.31574 9.20713i 0.225438 0.390469i
\(557\) 13.2708 + 22.9856i 0.562300 + 0.973932i 0.997295 + 0.0734992i \(0.0234166\pi\)
−0.434995 + 0.900433i \(0.643250\pi\)
\(558\) 2.27088 0.0961340
\(559\) 41.5401 1.75696
\(560\) 0 0
\(561\) −0.947216 1.64063i −0.0399915 0.0692673i
\(562\) −6.91298 −0.291606
\(563\) 35.5594 1.49865 0.749325 0.662203i \(-0.230378\pi\)
0.749325 + 0.662203i \(0.230378\pi\)
\(564\) 9.72326 + 16.8412i 0.409423 + 0.709141i
\(565\) 0 0
\(566\) 4.46607 + 7.73546i 0.187723 + 0.325146i
\(567\) −0.254068 + 0.440059i −0.0106699 + 0.0184808i
\(568\) 11.7356 20.3266i 0.492414 0.852886i
\(569\) −14.9713 −0.627628 −0.313814 0.949485i \(-0.601607\pi\)
−0.313814 + 0.949485i \(0.601607\pi\)
\(570\) 0 0
\(571\) 5.92724 0.248047 0.124024 0.992279i \(-0.460420\pi\)
0.124024 + 0.992279i \(0.460420\pi\)
\(572\) 2.60179 4.50643i 0.108786 0.188423i
\(573\) −7.40881 + 12.8324i −0.309508 + 0.536083i
\(574\) −1.14323 1.98013i −0.0477175 0.0826492i
\(575\) 0 0
\(576\) −3.01175 5.21651i −0.125490 0.217355i
\(577\) 14.5559 0.605970 0.302985 0.952995i \(-0.402017\pi\)
0.302985 + 0.952995i \(0.402017\pi\)
\(578\) 4.94800 0.205810
\(579\) 10.1451 + 17.5718i 0.421616 + 0.730260i
\(580\) 0 0
\(581\) 16.2914 0.675880
\(582\) −8.19839 −0.339834
\(583\) −1.77691 3.07770i −0.0735922 0.127465i
\(584\) 11.0319 19.1078i 0.456503 0.790686i
\(585\) 0 0
\(586\) −1.32039 + 2.28698i −0.0545448 + 0.0944744i
\(587\) 10.2919 17.8262i 0.424794 0.735765i −0.571607 0.820527i \(-0.693680\pi\)
0.996401 + 0.0847626i \(0.0270132\pi\)
\(588\) 10.3874 0.428371
\(589\) 3.94011 + 10.2027i 0.162350 + 0.420395i
\(590\) 0 0
\(591\) −2.25328 + 3.90280i −0.0926877 + 0.160540i
\(592\) −12.7288 + 22.0469i −0.523151 + 0.906124i
\(593\) 7.16609 + 12.4120i 0.294276 + 0.509701i 0.974816 0.223010i \(-0.0715882\pi\)
−0.680540 + 0.732711i \(0.738255\pi\)
\(594\) −0.861254 + 1.49174i −0.0353377 + 0.0612066i
\(595\) 0 0
\(596\) −17.0626 −0.698912
\(597\) −13.1395 −0.537765
\(598\) −0.587699 1.01792i −0.0240328 0.0416260i
\(599\) −1.25008 2.16521i −0.0510770 0.0884680i 0.839356 0.543581i \(-0.182932\pi\)
−0.890434 + 0.455113i \(0.849599\pi\)
\(600\) 0 0
\(601\) 14.5259 0.592524 0.296262 0.955107i \(-0.404260\pi\)
0.296262 + 0.955107i \(0.404260\pi\)
\(602\) 2.80763 + 4.86296i 0.114430 + 0.198199i
\(603\) −4.96948 + 8.60739i −0.202373 + 0.350520i
\(604\) 6.69730 + 11.6001i 0.272509 + 0.472000i
\(605\) 0 0
\(606\) 3.44273 5.96299i 0.139851 0.242230i
\(607\) −31.8704 −1.29358 −0.646789 0.762669i \(-0.723889\pi\)
−0.646789 + 0.762669i \(0.723889\pi\)
\(608\) −13.2584 + 16.4406i −0.537700 + 0.666754i
\(609\) −1.05075 −0.0425785
\(610\) 0 0
\(611\) −21.5793 + 37.3764i −0.873004 + 1.51209i
\(612\) −4.35019 7.53475i −0.175846 0.304574i
\(613\) −10.0244 + 17.3628i −0.404882 + 0.701277i −0.994308 0.106546i \(-0.966021\pi\)
0.589425 + 0.807823i \(0.299354\pi\)
\(614\) 4.86794 + 8.43152i 0.196454 + 0.340268i
\(615\) 0 0
\(616\) 1.49493 0.0602325
\(617\) 10.0410 + 17.3914i 0.404234 + 0.700153i 0.994232 0.107251i \(-0.0342050\pi\)
−0.589998 + 0.807404i \(0.700872\pi\)
\(618\) 0.872222 + 1.51073i 0.0350859 + 0.0607706i
\(619\) 5.62217 0.225974 0.112987 0.993596i \(-0.463958\pi\)
0.112987 + 0.993596i \(0.463958\pi\)
\(620\) 0 0
\(621\) −1.55278 2.68950i −0.0623111 0.107926i
\(622\) −5.81803 + 10.0771i −0.233282 + 0.404056i
\(623\) −9.38171 16.2496i −0.375870 0.651026i
\(624\) −5.79095 + 10.0302i −0.231823 + 0.401530i
\(625\) 0 0
\(626\) −1.65092 −0.0659839
\(627\) −3.19652 0.499662i −0.127657 0.0199546i
\(628\) 17.5174 0.699022
\(629\) −11.9726 + 20.7371i −0.477378 + 0.826844i
\(630\) 0 0
\(631\) 2.42184 + 4.19475i 0.0964120 + 0.166990i 0.910197 0.414176i \(-0.135930\pi\)
−0.813785 + 0.581166i \(0.802597\pi\)
\(632\) 5.31481 9.20551i 0.211412 0.366176i
\(633\) −11.5697 20.0393i −0.459854 0.796491i
\(634\) −14.8034 −0.587918
\(635\) 0 0
\(636\) 4.60407 + 7.97448i 0.182563 + 0.316209i
\(637\) 11.5267 + 19.9648i 0.456703 + 0.791033i
\(638\) 0.289361 0.0114559
\(639\) 25.2552 0.999078
\(640\) 0 0
\(641\) 12.6503 21.9110i 0.499658 0.865433i −0.500342 0.865828i \(-0.666792\pi\)
1.00000 0.000394734i \(0.000125648\pi\)
\(642\) 0.891229 + 1.54365i 0.0351740 + 0.0609232i
\(643\) −6.97283 + 12.0773i −0.274981 + 0.476282i −0.970130 0.242584i \(-0.922005\pi\)
0.695149 + 0.718866i \(0.255338\pi\)
\(644\) −0.634095 + 1.09828i −0.0249868 + 0.0432785i
\(645\) 0 0
\(646\) −3.29560 + 4.08658i −0.129664 + 0.160784i
\(647\) −2.51360 −0.0988200 −0.0494100 0.998779i \(-0.515734\pi\)
−0.0494100 + 0.998779i \(0.515734\pi\)
\(648\) −0.385288 + 0.667338i −0.0151355 + 0.0262155i
\(649\) 2.22978 3.86209i 0.0875264 0.151600i
\(650\) 0 0
\(651\) −1.53393 + 2.65684i −0.0601194 + 0.104130i
\(652\) −0.0611608 0.105934i −0.00239524 0.00414868i
\(653\) 1.92873 0.0754770 0.0377385 0.999288i \(-0.487985\pi\)
0.0377385 + 0.999288i \(0.487985\pi\)
\(654\) 3.05448 0.119440
\(655\) 0 0
\(656\) 5.59306 + 9.68747i 0.218372 + 0.378232i
\(657\) 23.7408 0.926217
\(658\) −5.83404 −0.227434
\(659\) −7.90042 13.6839i −0.307757 0.533050i 0.670115 0.742258i \(-0.266245\pi\)
−0.977871 + 0.209208i \(0.932912\pi\)
\(660\) 0 0
\(661\) −8.20178 14.2059i −0.319012 0.552546i 0.661270 0.750148i \(-0.270018\pi\)
−0.980282 + 0.197602i \(0.936685\pi\)
\(662\) 8.43486 14.6096i 0.327830 0.567819i
\(663\) −5.44691 + 9.43432i −0.211540 + 0.366399i
\(664\) 24.7054 0.958755
\(665\) 0 0
\(666\) 8.49086 0.329014
\(667\) −0.260850 + 0.451805i −0.0101001 + 0.0174940i
\(668\) −14.7911 + 25.6190i −0.572286 + 0.991228i
\(669\) 7.08521 + 12.2719i 0.273930 + 0.474461i
\(670\) 0 0
\(671\) 1.62496 + 2.81451i 0.0627308 + 0.108653i
\(672\) −5.92434 −0.228536
\(673\) 17.0878 0.658686 0.329343 0.944210i \(-0.393173\pi\)
0.329343 + 0.944210i \(0.393173\pi\)
\(674\) 6.24992 + 10.8252i 0.240738 + 0.416970i
\(675\) 0 0
\(676\) −6.81761 −0.262216
\(677\) −4.57680 −0.175901 −0.0879504 0.996125i \(-0.528032\pi\)
−0.0879504 + 0.996125i \(0.528032\pi\)
\(678\) −3.01163 5.21630i −0.115661 0.200331i
\(679\) −9.81574 + 17.0014i −0.376693 + 0.652452i
\(680\) 0 0
\(681\) 3.42708 5.93587i 0.131326 0.227463i
\(682\) 0.422422 0.731656i 0.0161754 0.0280166i
\(683\) −29.0692 −1.11230 −0.556151 0.831082i \(-0.687722\pi\)
−0.556151 + 0.831082i \(0.687722\pi\)
\(684\) −14.6804 2.29475i −0.561318 0.0877420i
\(685\) 0 0
\(686\) −3.49942 + 6.06117i −0.133608 + 0.231416i
\(687\) 0.304765 0.527869i 0.0116275 0.0201395i
\(688\) −13.7359 23.7912i −0.523675 0.907031i
\(689\) −10.2180 + 17.6981i −0.389276 + 0.674245i
\(690\) 0 0
\(691\) −6.07833 −0.231230 −0.115615 0.993294i \(-0.536884\pi\)
−0.115615 + 0.993294i \(0.536884\pi\)
\(692\) −21.5689 −0.819925
\(693\) 0.804279 + 1.39305i 0.0305521 + 0.0529177i
\(694\) 8.10220 + 14.0334i 0.307555 + 0.532701i
\(695\) 0 0
\(696\) −1.59343 −0.0603989
\(697\) 5.26078 + 9.11194i 0.199266 + 0.345139i
\(698\) −5.05643 + 8.75799i −0.191389 + 0.331495i
\(699\) 3.72267 + 6.44786i 0.140804 + 0.243881i
\(700\) 0 0
\(701\) −5.20569 + 9.01651i −0.196616 + 0.340549i −0.947429 0.319966i \(-0.896329\pi\)
0.750813 + 0.660515i \(0.229662\pi\)
\(702\) 9.90517 0.373847
\(703\) 14.7322 + 38.1481i 0.555634 + 1.43878i
\(704\) −2.24095 −0.0844589
\(705\) 0 0
\(706\) 4.61640 7.99585i 0.173741 0.300928i
\(707\) −8.24380 14.2787i −0.310040 0.537005i
\(708\) −5.77746 + 10.0069i −0.217130 + 0.376081i
\(709\) 0.265572 + 0.459984i 0.00997377 + 0.0172751i 0.870969 0.491338i \(-0.163492\pi\)
−0.860995 + 0.508613i \(0.830159\pi\)
\(710\) 0 0
\(711\) 11.4375 0.428941
\(712\) −14.2271 24.6421i −0.533183 0.923500i
\(713\) 0.761599 + 1.31913i 0.0285221 + 0.0494017i
\(714\) −1.47259 −0.0551103
\(715\) 0 0
\(716\) 10.4452 + 18.0916i 0.390355 + 0.676114i
\(717\) −1.90100 + 3.29262i −0.0709940 + 0.122965i
\(718\) −3.88657 6.73174i −0.145046 0.251226i
\(719\) −11.2135 + 19.4224i −0.418194 + 0.724334i −0.995758 0.0920118i \(-0.970670\pi\)
0.577564 + 0.816346i \(0.304004\pi\)
\(720\) 0 0
\(721\) 4.17716 0.155566
\(722\) 1.89951 + 8.76227i 0.0706924 + 0.326098i
\(723\) 17.9573 0.667839
\(724\) −7.85212 + 13.6003i −0.291822 + 0.505450i
\(725\) 0 0
\(726\) −2.57479 4.45967i −0.0955595 0.165514i
\(727\) 22.9867 39.8141i 0.852529 1.47662i −0.0263888 0.999652i \(-0.508401\pi\)
0.878918 0.476972i \(-0.158266\pi\)
\(728\) −4.29826 7.44480i −0.159304 0.275923i
\(729\) 15.1354 0.560570
\(730\) 0 0
\(731\) −12.9198 22.3778i −0.477856 0.827671i
\(732\) −4.21035 7.29254i −0.155619 0.269540i
\(733\) 42.5178 1.57043 0.785215 0.619223i \(-0.212552\pi\)
0.785215 + 0.619223i \(0.212552\pi\)
\(734\) −6.00930 −0.221807
\(735\) 0 0
\(736\) −1.47072 + 2.54737i −0.0542116 + 0.0938972i
\(737\) 1.84881 + 3.20224i 0.0681019 + 0.117956i
\(738\) 1.86545 3.23106i 0.0686682 0.118937i
\(739\) 1.70889 2.95988i 0.0628624 0.108881i −0.832881 0.553452i \(-0.813310\pi\)
0.895744 + 0.444571i \(0.146644\pi\)
\(740\) 0 0
\(741\) 6.70237 + 17.3554i 0.246218 + 0.637566i
\(742\) −2.76248 −0.101414
\(743\) 4.86044 8.41853i 0.178312 0.308846i −0.762990 0.646410i \(-0.776270\pi\)
0.941303 + 0.337564i \(0.109603\pi\)
\(744\) −2.32616 + 4.02903i −0.0852812 + 0.147711i
\(745\) 0 0
\(746\) −4.56175 + 7.90119i −0.167018 + 0.289283i
\(747\) 13.2916 + 23.0217i 0.486314 + 0.842321i
\(748\) −3.23683 −0.118350
\(749\) 4.26819 0.155956
\(750\) 0 0
\(751\) 5.69265 + 9.85996i 0.207728 + 0.359795i 0.950998 0.309196i \(-0.100060\pi\)
−0.743271 + 0.668991i \(0.766727\pi\)
\(752\) 28.5420 1.04082
\(753\) −20.1949 −0.735943
\(754\) −0.831977 1.44103i −0.0302988 0.0524791i
\(755\) 0 0
\(756\) −5.34356 9.25532i −0.194344 0.336613i
\(757\) −11.3921 + 19.7317i −0.414053 + 0.717160i −0.995328 0.0965464i \(-0.969220\pi\)
0.581276 + 0.813707i \(0.302554\pi\)
\(758\) 2.32589 4.02856i 0.0844801 0.146324i
\(759\) −0.450583 −0.0163551
\(760\) 0 0
\(761\) −36.7665 −1.33279 −0.666393 0.745601i \(-0.732163\pi\)
−0.666393 + 0.745601i \(0.732163\pi\)
\(762\) 0.529615 0.917319i 0.0191859 0.0332310i
\(763\) 3.65706 6.33421i 0.132394 0.229314i
\(764\) 12.6587 + 21.9255i 0.457976 + 0.793238i
\(765\) 0 0
\(766\) −4.79747 8.30945i −0.173339 0.300233i
\(767\) −25.6444 −0.925965
\(768\) 1.04955 0.0378724
\(769\) 10.4004 + 18.0140i 0.375049 + 0.649603i 0.990334 0.138701i \(-0.0442927\pi\)
−0.615286 + 0.788304i \(0.710959\pi\)
\(770\) 0 0
\(771\) 14.4517 0.520464
\(772\) 34.6679 1.24772
\(773\) −10.5046 18.1944i −0.377823 0.654409i 0.612922 0.790143i \(-0.289994\pi\)
−0.990745 + 0.135735i \(0.956661\pi\)
\(774\) −4.58131 + 7.93506i −0.164672 + 0.285220i
\(775\) 0 0
\(776\) −14.8853 + 25.7821i −0.534351 + 0.925523i
\(777\) −5.73539 + 9.93398i −0.205756 + 0.356380i
\(778\) 0.474354 0.0170064
\(779\) 17.7533 + 2.77509i 0.636077 + 0.0994280i
\(780\) 0 0
\(781\) 4.69788 8.13697i 0.168103 0.291164i
\(782\) −0.365572 + 0.633190i −0.0130728 + 0.0226428i
\(783\) −2.19820 3.80740i −0.0785573 0.136065i
\(784\) 7.62292 13.2033i 0.272247 0.471546i
\(785\) 0 0
\(786\) 8.61437 0.307264
\(787\) −18.0606 −0.643791 −0.321896 0.946775i \(-0.604320\pi\)
−0.321896 + 0.946775i \(0.604320\pi\)
\(788\) 3.84997 + 6.66834i 0.137149 + 0.237550i
\(789\) −7.79560 13.5024i −0.277531 0.480697i
\(790\) 0 0
\(791\) −14.4230 −0.512823
\(792\) 1.21967 + 2.11253i 0.0433390 + 0.0750653i
\(793\) 9.34422 16.1847i 0.331823 0.574734i
\(794\) −2.32691 4.03033i −0.0825789 0.143031i
\(795\) 0 0
\(796\) −11.2251 + 19.4425i −0.397864 + 0.689121i
\(797\) 24.2571 0.859229 0.429615 0.903012i \(-0.358649\pi\)
0.429615 + 0.903012i \(0.358649\pi\)
\(798\) −1.57873 + 1.95765i −0.0558866 + 0.0692999i
\(799\) 26.8463 0.949756
\(800\) 0 0
\(801\) 15.3085 26.5150i 0.540898 0.936863i
\(802\) 7.03857 + 12.1912i 0.248541 + 0.430485i
\(803\) 4.41619 7.64906i 0.155844 0.269930i
\(804\) −4.79036 8.29715i −0.168943 0.292618i
\(805\) 0 0
\(806\) −4.85822 −0.171124
\(807\) −10.0757 17.4517i −0.354682 0.614327i
\(808\) −12.5015 21.6532i −0.439801 0.761758i
\(809\) −4.27192 −0.150193 −0.0750964 0.997176i \(-0.523926\pi\)
−0.0750964 + 0.997176i \(0.523926\pi\)
\(810\) 0 0
\(811\) −5.09120 8.81821i −0.178776 0.309649i 0.762685 0.646770i \(-0.223880\pi\)
−0.941462 + 0.337120i \(0.890547\pi\)
\(812\) −0.897657 + 1.55479i −0.0315016 + 0.0545623i
\(813\) −6.19865 10.7364i −0.217396 0.376541i
\(814\) 1.57944 2.73568i 0.0553595 0.0958854i
\(815\) 0 0
\(816\) 7.20440 0.252205
\(817\) −43.5998 6.81528i −1.52536 0.238436i
\(818\) −13.0448 −0.456102
\(819\) 4.62496 8.01066i 0.161609 0.279915i
\(820\) 0 0
\(821\) 28.0108 + 48.5162i 0.977585 + 1.69323i 0.671127 + 0.741343i \(0.265811\pi\)
0.306458 + 0.951884i \(0.400856\pi\)
\(822\) 1.24546 2.15719i 0.0434403 0.0752408i
\(823\) 16.7708 + 29.0479i 0.584593 + 1.01255i 0.994926 + 0.100610i \(0.0320793\pi\)
−0.410333 + 0.911936i \(0.634587\pi\)
\(824\) 6.33455 0.220674
\(825\) 0 0
\(826\) −1.73326 3.00210i −0.0603079 0.104456i
\(827\) −0.0181265 0.0313960i −0.000630320 0.00109175i 0.865710 0.500546i \(-0.166867\pi\)
−0.866340 + 0.499454i \(0.833534\pi\)
\(828\) −2.06935 −0.0719149
\(829\) 39.5662 1.37419 0.687095 0.726567i \(-0.258885\pi\)
0.687095 + 0.726567i \(0.258885\pi\)
\(830\) 0 0
\(831\) 5.71204 9.89354i 0.198148 0.343203i
\(832\) 6.44321 + 11.1600i 0.223378 + 0.386902i
\(833\) 7.17005 12.4189i 0.248427 0.430289i
\(834\) 1.46811 2.54283i 0.0508364 0.0880512i
\(835\) 0 0
\(836\) −3.47014 + 4.30301i −0.120017 + 0.148823i
\(837\) −12.8361 −0.443681
\(838\) −2.66383 + 4.61389i −0.0920205 + 0.159384i
\(839\) −20.0811 + 34.7816i −0.693278 + 1.20079i 0.277480 + 0.960732i \(0.410501\pi\)
−0.970758 + 0.240061i \(0.922832\pi\)
\(840\) 0 0
\(841\) 14.1307 24.4751i 0.487266 0.843970i
\(842\) 1.07340 + 1.85918i 0.0369917 + 0.0640716i
\(843\) 15.2390 0.524858
\(844\) −39.5360 −1.36089
\(845\) 0 0
\(846\) −4.75980 8.24422i −0.163645 0.283442i
\(847\) −12.3309 −0.423696
\(848\) 13.5150 0.464106
\(849\) −9.84502 17.0521i −0.337880 0.585225i
\(850\) 0 0
\(851\) 2.84763 + 4.93224i 0.0976156 + 0.169075i
\(852\) −12.1724 + 21.0833i −0.417021 + 0.722302i
\(853\) 8.23086 14.2563i 0.281819 0.488126i −0.690014 0.723796i \(-0.742395\pi\)
0.971833 + 0.235671i \(0.0757288\pi\)
\(854\) 2.52624 0.0864463
\(855\) 0 0
\(856\) 6.47259 0.221229
\(857\) 2.80332 4.85549i 0.0957595 0.165860i −0.814166 0.580632i \(-0.802805\pi\)
0.909925 + 0.414772i \(0.136139\pi\)
\(858\) 0.718565 1.24459i 0.0245314 0.0424896i
\(859\) −12.5149 21.6765i −0.427003 0.739591i 0.569602 0.821921i \(-0.307097\pi\)
−0.996605 + 0.0823296i \(0.973764\pi\)
\(860\) 0 0
\(861\) 2.52014 + 4.36501i 0.0858862 + 0.148759i
\(862\) −15.5266 −0.528837
\(863\) 42.4307 1.44436 0.722178 0.691707i \(-0.243141\pi\)
0.722178 + 0.691707i \(0.243141\pi\)
\(864\) −12.3939 21.4669i −0.421649 0.730317i
\(865\) 0 0
\(866\) 10.5274 0.357736
\(867\) −10.9074 −0.370434
\(868\) 2.62087 + 4.53949i 0.0889583 + 0.154080i
\(869\) 2.12758 3.68507i 0.0721731 0.125007i
\(870\) 0 0
\(871\) 10.6315 18.4143i 0.360234 0.623943i
\(872\) 5.54583 9.60566i 0.187806 0.325289i
\(873\) −32.0334 −1.08417
\(874\) 0.449833 + 1.16482i 0.0152158 + 0.0394005i
\(875\) 0 0
\(876\) −11.4426 + 19.8191i −0.386608 + 0.669625i
\(877\) 0.278622 0.482588i 0.00940841 0.0162958i −0.861283 0.508126i \(-0.830338\pi\)
0.870691 + 0.491830i \(0.163672\pi\)
\(878\) 1.34622 + 2.33172i 0.0454328 + 0.0786919i
\(879\) 2.91067 5.04143i 0.0981745 0.170043i
\(880\) 0 0
\(881\) 8.35432 0.281464 0.140732 0.990048i \(-0.455054\pi\)
0.140732 + 0.990048i \(0.455054\pi\)
\(882\) −5.08494 −0.171219
\(883\) 9.74209 + 16.8738i 0.327847 + 0.567848i 0.982084 0.188441i \(-0.0603435\pi\)
−0.654237 + 0.756289i \(0.727010\pi\)
\(884\) 9.30660 + 16.1195i 0.313015 + 0.542158i
\(885\) 0 0
\(886\) 5.46329 0.183543
\(887\) 17.9686 + 31.1226i 0.603328 + 1.04499i 0.992313 + 0.123751i \(0.0394923\pi\)
−0.388985 + 0.921244i \(0.627174\pi\)
\(888\) −8.69755 + 15.0646i −0.291871 + 0.505535i
\(889\) −1.26819 2.19657i −0.0425337 0.0736705i
\(890\) 0 0
\(891\) −0.154235 + 0.267143i −0.00516706 + 0.00894962i
\(892\) 24.2116 0.810666
\(893\) 28.7814 35.6892i 0.963133 1.19429i
\(894\) −4.71237 −0.157605
\(895\) 0 0
\(896\) −6.56624 + 11.3731i −0.219363 + 0.379947i
\(897\) 1.29552 + 2.24391i 0.0432563 + 0.0749221i
\(898\) −6.01005 + 10.4097i −0.200558 + 0.347377i
\(899\) 1.07816 + 1.86743i 0.0359586 + 0.0622821i
\(900\) 0 0
\(901\) 12.7120 0.423499
\(902\) −0.694011 1.20206i −0.0231080 0.0400243i
\(903\) −6.18914 10.7199i −0.205962 0.356736i
\(904\) −21.8721 −0.727455
\(905\) 0 0
\(906\) 1.84967 + 3.20372i 0.0614511 + 0.106436i
\(907\) 24.4751 42.3922i 0.812683 1.40761i −0.0982962 0.995157i \(-0.531339\pi\)
0.910980 0.412452i \(-0.135327\pi\)
\(908\) −5.85551 10.1420i −0.194322 0.336576i
\(909\) 13.4517 23.2990i 0.446165 0.772780i
\(910\) 0 0
\(911\) −19.7811 −0.655376 −0.327688 0.944786i \(-0.606269\pi\)
−0.327688 + 0.944786i \(0.606269\pi\)
\(912\) 7.72369 9.57745i 0.255757 0.317141i
\(913\) 9.88984 0.327306
\(914\) 1.63468 2.83134i 0.0540703 0.0936525i
\(915\) 0 0
\(916\) −0.520723 0.901919i −0.0172052 0.0298002i
\(917\) 10.3138 17.8640i 0.340591 0.589921i
\(918\) −3.08071 5.33594i −0.101678 0.176112i
\(919\) 26.0582 0.859581 0.429791 0.902929i \(-0.358587\pi\)
0.429791 + 0.902929i \(0.358587\pi\)
\(920\) 0 0
\(921\) −10.7309 18.5865i −0.353595 0.612444i
\(922\) 7.66684 + 13.2794i 0.252494 + 0.437332i
\(923\) −54.0298 −1.77841
\(924\) −1.55058 −0.0510104
\(925\) 0 0
\(926\) −5.07421 + 8.78879i −0.166749 + 0.288817i
\(927\) 3.40801 + 5.90285i 0.111934 + 0.193875i
\(928\) −2.08203 + 3.60618i −0.0683460 + 0.118379i
\(929\) 3.98900 6.90914i 0.130875 0.226682i −0.793139 0.609040i \(-0.791555\pi\)
0.924014 + 0.382359i \(0.124888\pi\)
\(930\) 0 0
\(931\) −8.82267 22.8458i −0.289151 0.748741i
\(932\) 12.7211 0.416695
\(933\) 12.8253 22.2140i 0.419880 0.727254i
\(934\) 3.99942 6.92719i 0.130865 0.226665i
\(935\) 0 0
\(936\) 7.01362 12.1479i 0.229247 0.397068i
\(937\) −23.3271 40.4037i −0.762063 1.31993i −0.941785 0.336215i \(-0.890853\pi\)
0.179722 0.983717i \(-0.442480\pi\)
\(938\) 2.87426 0.0938479
\(939\) 3.63928 0.118763
\(940\) 0 0
\(941\) 0.700500 + 1.21330i 0.0228356 + 0.0395525i 0.877217 0.480093i \(-0.159397\pi\)
−0.854382 + 0.519646i \(0.826064\pi\)
\(942\) 4.83798 0.157630
\(943\) 2.50251 0.0814930
\(944\) 8.47969 + 14.6873i 0.275990 + 0.478030i
\(945\) 0 0
\(946\) 1.70440 + 2.95211i 0.0554149 + 0.0959814i
\(947\) −19.1250 + 33.1255i −0.621480 + 1.07643i 0.367730 + 0.929932i \(0.380135\pi\)
−0.989210 + 0.146502i \(0.953198\pi\)
\(948\) −5.51265 + 9.54820i −0.179043 + 0.310111i
\(949\) −50.7900 −1.64871
\(950\) 0 0
\(951\) 32.6326 1.05819
\(952\) −2.67369 + 4.63096i −0.0866547 + 0.150090i
\(953\) −27.2195 + 47.1455i −0.881726 + 1.52719i −0.0323042 + 0.999478i \(0.510285\pi\)
−0.849421 + 0.527715i \(0.823049\pi\)
\(954\) −2.25382 3.90373i −0.0729701 0.126388i
\(955\) 0 0
\(956\) 3.24805 + 5.62579i 0.105049 + 0.181951i
\(957\) −0.637869 −0.0206194
\(958\) −4.17989 −0.135046
\(959\) −2.98231 5.16551i −0.0963038 0.166803i
\(960\) 0 0
\(961\) −24.7042 −0.796911
\(962\) −18.1650 −0.585662
\(963\) 3.48228 + 6.03148i 0.112215 + 0.194362i
\(964\) 15.3409 26.5713i 0.494099 0.855804i
\(965\) 0 0
\(966\) −0.175125 + 0.303325i −0.00563455 + 0.00975933i
\(967\) −2.49460 + 4.32077i −0.0802208 + 0.138946i −0.903345 0.428915i \(-0.858896\pi\)
0.823124 + 0.567862i \(0.192229\pi\)
\(968\) −18.6995 −0.601026
\(969\) 7.26482 9.00846i 0.233380 0.289393i
\(970\) 0 0
\(971\) 7.27006 12.5921i 0.233307 0.404100i −0.725472 0.688252i \(-0.758379\pi\)
0.958779 + 0.284152i \(0.0917119\pi\)
\(972\) 14.0381 24.3148i 0.450274 0.779897i
\(973\) −3.51546 6.08895i −0.112700 0.195203i
\(974\) 7.09306 12.2855i 0.227276 0.393654i
\(975\) 0 0
\(976\) −12.3592 −0.395609
\(977\) 26.1353 0.836141 0.418071 0.908415i \(-0.362706\pi\)
0.418071 + 0.908415i \(0.362706\pi\)
\(978\) −0.0168915 0.0292569i −0.000540129 0.000935531i
\(979\) −5.69527 9.86449i −0.182021 0.315270i
\(980\) 0 0
\(981\) 11.9347 0.381046
\(982\) 0.731499 + 1.26699i 0.0233431 + 0.0404314i
\(983\) −23.0580 + 39.9376i −0.735436 + 1.27381i 0.219096 + 0.975703i \(0.429689\pi\)
−0.954532 + 0.298109i \(0.903644\pi\)
\(984\) 3.82172 + 6.61942i 0.121832 + 0.211019i
\(985\) 0 0
\(986\) −0.517523 + 0.896376i −0.0164813 + 0.0285464i
\(987\) 12.8606 0.409356
\(988\) 31.4065 + 4.90929i 0.999174 + 0.156185i
\(989\) −6.14585 −0.195427
\(990\) 0 0
\(991\) 15.6640 27.1308i 0.497582 0.861837i −0.502414 0.864627i \(-0.667555\pi\)
0.999996 + 0.00278993i \(0.000888065\pi\)
\(992\) 6.07887 + 10.5289i 0.193004 + 0.334294i
\(993\) −18.5938 + 32.2055i −0.590057 + 1.02201i
\(994\) −3.65178 6.32508i −0.115828 0.200619i
\(995\) 0 0
\(996\) −25.6251 −0.811962
\(997\) 10.8072 + 18.7186i 0.342268 + 0.592826i 0.984854 0.173388i \(-0.0554716\pi\)
−0.642586 + 0.766214i \(0.722138\pi\)
\(998\) 7.58296 + 13.1341i 0.240035 + 0.415752i
\(999\) −47.9944 −1.51848
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 475.2.e.g.201.4 12
5.2 odd 4 95.2.i.b.49.4 yes 12
5.3 odd 4 95.2.i.b.49.3 12
5.4 even 2 inner 475.2.e.g.201.3 12
15.2 even 4 855.2.be.d.334.3 12
15.8 even 4 855.2.be.d.334.4 12
19.7 even 3 inner 475.2.e.g.26.4 12
19.8 odd 6 9025.2.a.bt.1.4 6
19.11 even 3 9025.2.a.bu.1.3 6
95.7 odd 12 95.2.i.b.64.3 yes 12
95.8 even 12 1805.2.b.g.1084.3 6
95.27 even 12 1805.2.b.g.1084.4 6
95.49 even 6 9025.2.a.bu.1.4 6
95.64 even 6 inner 475.2.e.g.26.3 12
95.68 odd 12 1805.2.b.f.1084.4 6
95.83 odd 12 95.2.i.b.64.4 yes 12
95.84 odd 6 9025.2.a.bt.1.3 6
95.87 odd 12 1805.2.b.f.1084.3 6
285.83 even 12 855.2.be.d.64.3 12
285.197 even 12 855.2.be.d.64.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.3 12 5.3 odd 4
95.2.i.b.49.4 yes 12 5.2 odd 4
95.2.i.b.64.3 yes 12 95.7 odd 12
95.2.i.b.64.4 yes 12 95.83 odd 12
475.2.e.g.26.3 12 95.64 even 6 inner
475.2.e.g.26.4 12 19.7 even 3 inner
475.2.e.g.201.3 12 5.4 even 2 inner
475.2.e.g.201.4 12 1.1 even 1 trivial
855.2.be.d.64.3 12 285.83 even 12
855.2.be.d.64.4 12 285.197 even 12
855.2.be.d.334.3 12 15.2 even 4
855.2.be.d.334.4 12 15.8 even 4
1805.2.b.f.1084.3 6 95.87 odd 12
1805.2.b.f.1084.4 6 95.68 odd 12
1805.2.b.g.1084.3 6 95.8 even 12
1805.2.b.g.1084.4 6 95.27 even 12
9025.2.a.bt.1.3 6 95.84 odd 6
9025.2.a.bt.1.4 6 19.8 odd 6
9025.2.a.bu.1.3 6 19.11 even 3
9025.2.a.bu.1.4 6 95.49 even 6