Properties

Label 1008.2.cz.h.607.7
Level $1008$
Weight $2$
Character 1008.607
Analytic conductor $8.049$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(367,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.367");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cz (of order \(6\), 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 607.7
Character \(\chi\) \(=\) 1008.607
Dual form 1008.2.cz.h.367.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.706216 - 1.58154i) q^{3} +(-1.27943 + 0.738680i) q^{5} +(-1.34028 + 2.28115i) q^{7} +(-2.00252 - 2.23381i) q^{9} +O(q^{10})\) \(q+(0.706216 - 1.58154i) q^{3} +(-1.27943 + 0.738680i) q^{5} +(-1.34028 + 2.28115i) q^{7} +(-2.00252 - 2.23381i) q^{9} +(-2.40250 - 1.38709i) q^{11} +(0.955418 + 0.551611i) q^{13} +(0.264694 + 2.54514i) q^{15} +(1.69424 - 0.978168i) q^{17} +(-3.46466 + 6.00097i) q^{19} +(2.66120 + 3.73068i) q^{21} +(-0.0279687 + 0.0161477i) q^{23} +(-1.40870 + 2.43994i) q^{25} +(-4.94707 + 1.58950i) q^{27} +(4.53801 + 7.86007i) q^{29} -0.704107 q^{31} +(-3.89041 + 2.82006i) q^{33} +(0.0297482 - 3.90862i) q^{35} +(-1.92560 + 3.33523i) q^{37} +(1.54713 - 1.12147i) q^{39} +(-2.23630 - 1.29113i) q^{41} +(-8.95705 + 5.17136i) q^{43} +(4.21216 + 1.37879i) q^{45} -4.28149 q^{47} +(-3.40732 - 6.11475i) q^{49} +(-0.350511 - 3.37030i) q^{51} +(3.49123 + 6.04699i) q^{53} +4.09845 q^{55} +(7.04395 + 9.71747i) q^{57} -1.13799 q^{59} +2.58999i q^{61} +(7.77960 - 1.57412i) q^{63} -1.62986 q^{65} -11.6636i q^{67} +(0.00578629 + 0.0556373i) q^{69} -15.6777i q^{71} +(-4.41573 + 2.54942i) q^{73} +(2.86401 + 3.95104i) q^{75} +(6.38417 - 3.62140i) q^{77} +8.38410i q^{79} +(-0.979853 + 8.94650i) q^{81} +(5.34759 + 9.26231i) q^{83} +(-1.44511 + 2.50300i) q^{85} +(15.6358 - 1.62613i) q^{87} +(8.83761 + 5.10240i) q^{89} +(-2.53883 + 1.44015i) q^{91} +(-0.497252 + 1.11357i) q^{93} -10.2371i q^{95} +(6.95620 - 4.01617i) q^{97} +(1.71256 + 8.14441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{3} - 3 q^{5} - 4 q^{7} + 17 q^{9} + 9 q^{11} - 3 q^{13} + 6 q^{15} - 3 q^{17} + 4 q^{19} + 13 q^{21} + 6 q^{23} + 15 q^{25} - 9 q^{27} + 18 q^{29} - 34 q^{31} - 21 q^{33} + 42 q^{35} - 3 q^{37} - 27 q^{39} + 36 q^{41} - 24 q^{43} + 21 q^{45} + 42 q^{47} + 30 q^{49} + 6 q^{51} - 12 q^{53} + 30 q^{55} - 13 q^{57} + 12 q^{59} + 3 q^{63} + 6 q^{69} + 48 q^{73} - 36 q^{75} - 48 q^{77} - 31 q^{81} + 48 q^{83} - 21 q^{85} - 15 q^{87} + 39 q^{89} - 9 q^{91} + 10 q^{93} + 3 q^{97} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.706216 1.58154i 0.407734 0.913101i
\(4\) 0 0
\(5\) −1.27943 + 0.738680i −0.572179 + 0.330348i −0.758019 0.652232i \(-0.773833\pi\)
0.185840 + 0.982580i \(0.440499\pi\)
\(6\) 0 0
\(7\) −1.34028 + 2.28115i −0.506577 + 0.862195i
\(8\) 0 0
\(9\) −2.00252 2.23381i −0.667506 0.744605i
\(10\) 0 0
\(11\) −2.40250 1.38709i −0.724382 0.418222i 0.0919816 0.995761i \(-0.470680\pi\)
−0.816363 + 0.577539i \(0.804013\pi\)
\(12\) 0 0
\(13\) 0.955418 + 0.551611i 0.264985 + 0.152989i 0.626607 0.779336i \(-0.284443\pi\)
−0.361621 + 0.932325i \(0.617777\pi\)
\(14\) 0 0
\(15\) 0.264694 + 2.54514i 0.0683438 + 0.657151i
\(16\) 0 0
\(17\) 1.69424 0.978168i 0.410913 0.237241i −0.280269 0.959921i \(-0.590424\pi\)
0.691182 + 0.722681i \(0.257090\pi\)
\(18\) 0 0
\(19\) −3.46466 + 6.00097i −0.794847 + 1.37672i 0.128089 + 0.991763i \(0.459116\pi\)
−0.922936 + 0.384953i \(0.874218\pi\)
\(20\) 0 0
\(21\) 2.66120 + 3.73068i 0.580722 + 0.814102i
\(22\) 0 0
\(23\) −0.0279687 + 0.0161477i −0.00583188 + 0.00336704i −0.502913 0.864337i \(-0.667738\pi\)
0.497081 + 0.867704i \(0.334405\pi\)
\(24\) 0 0
\(25\) −1.40870 + 2.43994i −0.281741 + 0.487989i
\(26\) 0 0
\(27\) −4.94707 + 1.58950i −0.952064 + 0.305899i
\(28\) 0 0
\(29\) 4.53801 + 7.86007i 0.842688 + 1.45958i 0.887614 + 0.460588i \(0.152361\pi\)
−0.0449259 + 0.998990i \(0.514305\pi\)
\(30\) 0 0
\(31\) −0.704107 −0.126461 −0.0632306 0.997999i \(-0.520140\pi\)
−0.0632306 + 0.997999i \(0.520140\pi\)
\(32\) 0 0
\(33\) −3.89041 + 2.82006i −0.677234 + 0.490910i
\(34\) 0 0
\(35\) 0.0297482 3.90862i 0.00502837 0.660677i
\(36\) 0 0
\(37\) −1.92560 + 3.33523i −0.316566 + 0.548309i −0.979769 0.200131i \(-0.935863\pi\)
0.663203 + 0.748440i \(0.269197\pi\)
\(38\) 0 0
\(39\) 1.54713 1.12147i 0.247738 0.179579i
\(40\) 0 0
\(41\) −2.23630 1.29113i −0.349252 0.201640i 0.315104 0.949057i \(-0.397961\pi\)
−0.664356 + 0.747417i \(0.731294\pi\)
\(42\) 0 0
\(43\) −8.95705 + 5.17136i −1.36594 + 0.788624i −0.990406 0.138185i \(-0.955873\pi\)
−0.375531 + 0.926810i \(0.622540\pi\)
\(44\) 0 0
\(45\) 4.21216 + 1.37879i 0.627912 + 0.205538i
\(46\) 0 0
\(47\) −4.28149 −0.624520 −0.312260 0.949997i \(-0.601086\pi\)
−0.312260 + 0.949997i \(0.601086\pi\)
\(48\) 0 0
\(49\) −3.40732 6.11475i −0.486760 0.873536i
\(50\) 0 0
\(51\) −0.350511 3.37030i −0.0490814 0.471936i
\(52\) 0 0
\(53\) 3.49123 + 6.04699i 0.479558 + 0.830618i 0.999725 0.0234462i \(-0.00746385\pi\)
−0.520168 + 0.854064i \(0.674131\pi\)
\(54\) 0 0
\(55\) 4.09845 0.552635
\(56\) 0 0
\(57\) 7.04395 + 9.71747i 0.932994 + 1.28711i
\(58\) 0 0
\(59\) −1.13799 −0.148154 −0.0740768 0.997253i \(-0.523601\pi\)
−0.0740768 + 0.997253i \(0.523601\pi\)
\(60\) 0 0
\(61\) 2.58999i 0.331614i 0.986158 + 0.165807i \(0.0530228\pi\)
−0.986158 + 0.165807i \(0.946977\pi\)
\(62\) 0 0
\(63\) 7.77960 1.57412i 0.980137 0.198321i
\(64\) 0 0
\(65\) −1.62986 −0.202159
\(66\) 0 0
\(67\) 11.6636i 1.42493i −0.701707 0.712466i \(-0.747578\pi\)
0.701707 0.712466i \(-0.252422\pi\)
\(68\) 0 0
\(69\) 0.00578629 + 0.0556373i 0.000696587 + 0.00669795i
\(70\) 0 0
\(71\) 15.6777i 1.86060i −0.366799 0.930300i \(-0.619546\pi\)
0.366799 0.930300i \(-0.380454\pi\)
\(72\) 0 0
\(73\) −4.41573 + 2.54942i −0.516822 + 0.298388i −0.735634 0.677380i \(-0.763115\pi\)
0.218811 + 0.975767i \(0.429782\pi\)
\(74\) 0 0
\(75\) 2.86401 + 3.95104i 0.330708 + 0.456227i
\(76\) 0 0
\(77\) 6.38417 3.62140i 0.727544 0.412697i
\(78\) 0 0
\(79\) 8.38410i 0.943285i 0.881790 + 0.471643i \(0.156339\pi\)
−0.881790 + 0.471643i \(0.843661\pi\)
\(80\) 0 0
\(81\) −0.979853 + 8.94650i −0.108873 + 0.994056i
\(82\) 0 0
\(83\) 5.34759 + 9.26231i 0.586975 + 1.01667i 0.994626 + 0.103532i \(0.0330146\pi\)
−0.407651 + 0.913138i \(0.633652\pi\)
\(84\) 0 0
\(85\) −1.44511 + 2.50300i −0.156744 + 0.271488i
\(86\) 0 0
\(87\) 15.6358 1.62613i 1.67633 0.174339i
\(88\) 0 0
\(89\) 8.83761 + 5.10240i 0.936785 + 0.540853i 0.888951 0.458002i \(-0.151435\pi\)
0.0478337 + 0.998855i \(0.484768\pi\)
\(90\) 0 0
\(91\) −2.53883 + 1.44015i −0.266142 + 0.150968i
\(92\) 0 0
\(93\) −0.497252 + 1.11357i −0.0515626 + 0.115472i
\(94\) 0 0
\(95\) 10.2371i 1.05030i
\(96\) 0 0
\(97\) 6.95620 4.01617i 0.706296 0.407780i −0.103392 0.994641i \(-0.532970\pi\)
0.809688 + 0.586861i \(0.199636\pi\)
\(98\) 0 0
\(99\) 1.71256 + 8.14441i 0.172119 + 0.818544i
\(100\) 0 0
\(101\) −0.762717 0.440355i −0.0758932 0.0438169i 0.461573 0.887102i \(-0.347285\pi\)
−0.537466 + 0.843285i \(0.680618\pi\)
\(102\) 0 0
\(103\) 0.535717 + 0.927889i 0.0527858 + 0.0914276i 0.891211 0.453589i \(-0.149857\pi\)
−0.838425 + 0.545017i \(0.816523\pi\)
\(104\) 0 0
\(105\) −6.16061 2.80738i −0.601214 0.273972i
\(106\) 0 0
\(107\) −16.4651 9.50613i −1.59174 0.918993i −0.993008 0.118045i \(-0.962337\pi\)
−0.598734 0.800948i \(-0.704329\pi\)
\(108\) 0 0
\(109\) 1.39943 + 2.42389i 0.134041 + 0.232166i 0.925231 0.379405i \(-0.123871\pi\)
−0.791190 + 0.611571i \(0.790538\pi\)
\(110\) 0 0
\(111\) 3.91491 + 5.40080i 0.371586 + 0.512621i
\(112\) 0 0
\(113\) 4.66742 8.08421i 0.439074 0.760499i −0.558544 0.829475i \(-0.688640\pi\)
0.997618 + 0.0689759i \(0.0219732\pi\)
\(114\) 0 0
\(115\) 0.0238560 0.0413199i 0.00222459 0.00385310i
\(116\) 0 0
\(117\) −0.681045 3.23884i −0.0629626 0.299431i
\(118\) 0 0
\(119\) −0.0393929 + 5.17583i −0.00361114 + 0.474468i
\(120\) 0 0
\(121\) −1.65199 2.86133i −0.150181 0.260121i
\(122\) 0 0
\(123\) −3.62128 + 2.62498i −0.326520 + 0.236686i
\(124\) 0 0
\(125\) 11.5491i 1.03299i
\(126\) 0 0
\(127\) 6.43956i 0.571419i 0.958316 + 0.285709i \(0.0922292\pi\)
−0.958316 + 0.285709i \(0.907771\pi\)
\(128\) 0 0
\(129\) 1.85307 + 17.8180i 0.163154 + 1.56879i
\(130\) 0 0
\(131\) 1.76490 + 3.05690i 0.154200 + 0.267083i 0.932768 0.360478i \(-0.117387\pi\)
−0.778567 + 0.627561i \(0.784053\pi\)
\(132\) 0 0
\(133\) −9.04553 15.9464i −0.784347 1.38273i
\(134\) 0 0
\(135\) 5.15531 5.68796i 0.443698 0.489541i
\(136\) 0 0
\(137\) 9.60299 16.6329i 0.820439 1.42104i −0.0849170 0.996388i \(-0.527063\pi\)
0.905356 0.424654i \(-0.139604\pi\)
\(138\) 0 0
\(139\) −8.42275 + 14.5886i −0.714408 + 1.23739i 0.248779 + 0.968560i \(0.419971\pi\)
−0.963187 + 0.268831i \(0.913363\pi\)
\(140\) 0 0
\(141\) −3.02366 + 6.77134i −0.254638 + 0.570250i
\(142\) 0 0
\(143\) −1.53026 2.65049i −0.127967 0.221645i
\(144\) 0 0
\(145\) −11.6122 6.70428i −0.964337 0.556760i
\(146\) 0 0
\(147\) −12.0770 + 1.07047i −0.996095 + 0.0882908i
\(148\) 0 0
\(149\) −10.6203 18.3949i −0.870050 1.50697i −0.861944 0.507003i \(-0.830753\pi\)
−0.00810521 0.999967i \(-0.502580\pi\)
\(150\) 0 0
\(151\) −12.4787 7.20460i −1.01551 0.586302i −0.102706 0.994712i \(-0.532750\pi\)
−0.912799 + 0.408410i \(0.866084\pi\)
\(152\) 0 0
\(153\) −5.57778 1.82581i −0.450937 0.147608i
\(154\) 0 0
\(155\) 0.900856 0.520110i 0.0723585 0.0417762i
\(156\) 0 0
\(157\) 5.69801i 0.454751i 0.973807 + 0.227375i \(0.0730144\pi\)
−0.973807 + 0.227375i \(0.926986\pi\)
\(158\) 0 0
\(159\) 12.0291 1.25103i 0.953970 0.0992129i
\(160\) 0 0
\(161\) 0.000650304 0.0854433i 5.12511e−5 0.00673388i
\(162\) 0 0
\(163\) −4.25007 2.45378i −0.332891 0.192195i 0.324233 0.945977i \(-0.394894\pi\)
−0.657124 + 0.753783i \(0.728227\pi\)
\(164\) 0 0
\(165\) 2.89439 6.48185i 0.225328 0.504611i
\(166\) 0 0
\(167\) −0.958089 + 1.65946i −0.0741392 + 0.128413i −0.900712 0.434418i \(-0.856954\pi\)
0.826572 + 0.562830i \(0.190288\pi\)
\(168\) 0 0
\(169\) −5.89145 10.2043i −0.453188 0.784945i
\(170\) 0 0
\(171\) 20.3431 4.27763i 1.55567 0.327119i
\(172\) 0 0
\(173\) 23.8613i 1.81414i 0.420978 + 0.907071i \(0.361687\pi\)
−0.420978 + 0.907071i \(0.638313\pi\)
\(174\) 0 0
\(175\) −3.67784 6.48367i −0.278018 0.490119i
\(176\) 0 0
\(177\) −0.803667 + 1.79977i −0.0604073 + 0.135279i
\(178\) 0 0
\(179\) 8.43765 4.87148i 0.630659 0.364111i −0.150348 0.988633i \(-0.548039\pi\)
0.781007 + 0.624522i \(0.214706\pi\)
\(180\) 0 0
\(181\) 1.54520i 0.114854i 0.998350 + 0.0574269i \(0.0182896\pi\)
−0.998350 + 0.0574269i \(0.981710\pi\)
\(182\) 0 0
\(183\) 4.09616 + 1.82909i 0.302797 + 0.135210i
\(184\) 0 0
\(185\) 5.68961i 0.418308i
\(186\) 0 0
\(187\) −5.42721 −0.396877
\(188\) 0 0
\(189\) 3.00455 13.4154i 0.218549 0.975826i
\(190\) 0 0
\(191\) 1.83767i 0.132969i −0.997787 0.0664845i \(-0.978822\pi\)
0.997787 0.0664845i \(-0.0211783\pi\)
\(192\) 0 0
\(193\) 1.87378 0.134878 0.0674389 0.997723i \(-0.478517\pi\)
0.0674389 + 0.997723i \(0.478517\pi\)
\(194\) 0 0
\(195\) −1.15103 + 2.57768i −0.0824271 + 0.184591i
\(196\) 0 0
\(197\) −21.3079 −1.51812 −0.759061 0.651019i \(-0.774342\pi\)
−0.759061 + 0.651019i \(0.774342\pi\)
\(198\) 0 0
\(199\) 10.4408 + 18.0840i 0.740129 + 1.28194i 0.952436 + 0.304738i \(0.0985690\pi\)
−0.212307 + 0.977203i \(0.568098\pi\)
\(200\) 0 0
\(201\) −18.4464 8.23700i −1.30111 0.580993i
\(202\) 0 0
\(203\) −24.0122 0.182756i −1.68533 0.0128269i
\(204\) 0 0
\(205\) 3.81493 0.266446
\(206\) 0 0
\(207\) 0.0920789 + 0.0301408i 0.00639992 + 0.00209493i
\(208\) 0 0
\(209\) 16.6477 9.61156i 1.15155 0.664845i
\(210\) 0 0
\(211\) 12.5460 + 7.24345i 0.863704 + 0.498660i 0.865251 0.501339i \(-0.167159\pi\)
−0.00154663 + 0.999999i \(0.500492\pi\)
\(212\) 0 0
\(213\) −24.7949 11.0718i −1.69892 0.758631i
\(214\) 0 0
\(215\) 7.63996 13.2328i 0.521041 0.902469i
\(216\) 0 0
\(217\) 0.943697 1.60617i 0.0640623 0.109034i
\(218\) 0 0
\(219\) 0.913545 + 8.78409i 0.0617317 + 0.593574i
\(220\) 0 0
\(221\) 2.15827 0.145181
\(222\) 0 0
\(223\) 7.93256 + 13.7396i 0.531204 + 0.920072i 0.999337 + 0.0364138i \(0.0115934\pi\)
−0.468133 + 0.883658i \(0.655073\pi\)
\(224\) 0 0
\(225\) 8.27133 1.73925i 0.551422 0.115950i
\(226\) 0 0
\(227\) 9.68469 16.7744i 0.642795 1.11335i −0.342011 0.939696i \(-0.611108\pi\)
0.984806 0.173658i \(-0.0555587\pi\)
\(228\) 0 0
\(229\) 17.6120 10.1683i 1.16384 0.671941i 0.211616 0.977353i \(-0.432127\pi\)
0.952220 + 0.305411i \(0.0987940\pi\)
\(230\) 0 0
\(231\) −1.21877 12.6543i −0.0801892 0.832591i
\(232\) 0 0
\(233\) −13.2043 + 22.8706i −0.865046 + 1.49830i 0.00195620 + 0.999998i \(0.499377\pi\)
−0.867002 + 0.498305i \(0.833956\pi\)
\(234\) 0 0
\(235\) 5.47788 3.16266i 0.357338 0.206309i
\(236\) 0 0
\(237\) 13.2598 + 5.92099i 0.861314 + 0.384610i
\(238\) 0 0
\(239\) −5.27359 3.04471i −0.341120 0.196946i 0.319647 0.947537i \(-0.396436\pi\)
−0.660767 + 0.750591i \(0.729769\pi\)
\(240\) 0 0
\(241\) 0.519055 + 0.299676i 0.0334353 + 0.0193039i 0.516624 0.856212i \(-0.327188\pi\)
−0.483189 + 0.875516i \(0.660522\pi\)
\(242\) 0 0
\(243\) 13.4572 + 7.86784i 0.863282 + 0.504722i
\(244\) 0 0
\(245\) 8.87628 + 5.30648i 0.567085 + 0.339019i
\(246\) 0 0
\(247\) −6.62040 + 3.82229i −0.421246 + 0.243206i
\(248\) 0 0
\(249\) 18.4252 1.91623i 1.16765 0.121436i
\(250\) 0 0
\(251\) −14.7398 −0.930366 −0.465183 0.885215i \(-0.654011\pi\)
−0.465183 + 0.885215i \(0.654011\pi\)
\(252\) 0 0
\(253\) 0.0895932 0.00563268
\(254\) 0 0
\(255\) 2.93803 + 4.05315i 0.183986 + 0.253818i
\(256\) 0 0
\(257\) 14.1894 8.19227i 0.885112 0.511020i 0.0127718 0.999918i \(-0.495934\pi\)
0.872341 + 0.488898i \(0.162601\pi\)
\(258\) 0 0
\(259\) −5.02735 8.86272i −0.312384 0.550703i
\(260\) 0 0
\(261\) 8.47049 25.8770i 0.524310 1.60175i
\(262\) 0 0
\(263\) 5.12161 + 2.95696i 0.315812 + 0.182334i 0.649524 0.760341i \(-0.274968\pi\)
−0.333712 + 0.942675i \(0.608301\pi\)
\(264\) 0 0
\(265\) −8.93359 5.15781i −0.548786 0.316842i
\(266\) 0 0
\(267\) 14.3109 10.3736i 0.875812 0.634854i
\(268\) 0 0
\(269\) −9.08351 + 5.24436i −0.553831 + 0.319755i −0.750666 0.660682i \(-0.770267\pi\)
0.196835 + 0.980437i \(0.436934\pi\)
\(270\) 0 0
\(271\) 3.68306 6.37925i 0.223730 0.387512i −0.732208 0.681081i \(-0.761510\pi\)
0.955938 + 0.293570i \(0.0948433\pi\)
\(272\) 0 0
\(273\) 0.484677 + 5.03231i 0.0293340 + 0.304569i
\(274\) 0 0
\(275\) 6.76882 3.90798i 0.408175 0.235660i
\(276\) 0 0
\(277\) 0.887744 1.53762i 0.0533394 0.0923865i −0.838123 0.545481i \(-0.816347\pi\)
0.891462 + 0.453095i \(0.149680\pi\)
\(278\) 0 0
\(279\) 1.40999 + 1.57284i 0.0844136 + 0.0941637i
\(280\) 0 0
\(281\) −2.08260 3.60717i −0.124237 0.215185i 0.797197 0.603719i \(-0.206315\pi\)
−0.921435 + 0.388534i \(0.872982\pi\)
\(282\) 0 0
\(283\) −3.40760 −0.202561 −0.101280 0.994858i \(-0.532294\pi\)
−0.101280 + 0.994858i \(0.532294\pi\)
\(284\) 0 0
\(285\) −16.1904 7.22961i −0.959034 0.428245i
\(286\) 0 0
\(287\) 5.94252 3.37088i 0.350776 0.198977i
\(288\) 0 0
\(289\) −6.58637 + 11.4079i −0.387434 + 0.671055i
\(290\) 0 0
\(291\) −1.43913 13.8378i −0.0843632 0.811185i
\(292\) 0 0
\(293\) −16.1931 9.34911i −0.946013 0.546181i −0.0541729 0.998532i \(-0.517252\pi\)
−0.891840 + 0.452351i \(0.850586\pi\)
\(294\) 0 0
\(295\) 1.45598 0.840610i 0.0847704 0.0489422i
\(296\) 0 0
\(297\) 14.0901 + 3.04324i 0.817591 + 0.176586i
\(298\) 0 0
\(299\) −0.0356291 −0.00206048
\(300\) 0 0
\(301\) 0.208262 27.3635i 0.0120040 1.57720i
\(302\) 0 0
\(303\) −1.23508 + 0.895279i −0.0709535 + 0.0514324i
\(304\) 0 0
\(305\) −1.91317 3.31371i −0.109548 0.189742i
\(306\) 0 0
\(307\) −13.0627 −0.745528 −0.372764 0.927926i \(-0.621590\pi\)
−0.372764 + 0.927926i \(0.621590\pi\)
\(308\) 0 0
\(309\) 1.84582 0.191966i 0.105005 0.0109205i
\(310\) 0 0
\(311\) 30.8740 1.75070 0.875352 0.483487i \(-0.160630\pi\)
0.875352 + 0.483487i \(0.160630\pi\)
\(312\) 0 0
\(313\) 15.9800i 0.903244i −0.892209 0.451622i \(-0.850846\pi\)
0.892209 0.451622i \(-0.149154\pi\)
\(314\) 0 0
\(315\) −8.79069 + 7.76062i −0.495299 + 0.437261i
\(316\) 0 0
\(317\) 3.70957 0.208350 0.104175 0.994559i \(-0.466780\pi\)
0.104175 + 0.994559i \(0.466780\pi\)
\(318\) 0 0
\(319\) 25.1784i 1.40972i
\(320\) 0 0
\(321\) −26.6622 + 19.3268i −1.48814 + 1.07872i
\(322\) 0 0
\(323\) 13.5561i 0.754280i
\(324\) 0 0
\(325\) −2.69180 + 1.55411i −0.149314 + 0.0862066i
\(326\) 0 0
\(327\) 4.82177 0.501464i 0.266644 0.0277310i
\(328\) 0 0
\(329\) 5.73838 9.76675i 0.316367 0.538458i
\(330\) 0 0
\(331\) 27.8487i 1.53070i 0.643612 + 0.765352i \(0.277435\pi\)
−0.643612 + 0.765352i \(0.722565\pi\)
\(332\) 0 0
\(333\) 11.3063 2.37743i 0.619583 0.130283i
\(334\) 0 0
\(335\) 8.61565 + 14.9227i 0.470723 + 0.815316i
\(336\) 0 0
\(337\) −5.14339 + 8.90861i −0.280178 + 0.485283i −0.971428 0.237333i \(-0.923727\pi\)
0.691250 + 0.722615i \(0.257060\pi\)
\(338\) 0 0
\(339\) −9.48927 13.0909i −0.515386 0.711000i
\(340\) 0 0
\(341\) 1.69162 + 0.976656i 0.0916062 + 0.0528889i
\(342\) 0 0
\(343\) 18.5154 + 0.422825i 0.999739 + 0.0228304i
\(344\) 0 0
\(345\) −0.0485014 0.0669100i −0.00261123 0.00360231i
\(346\) 0 0
\(347\) 13.5568i 0.727767i −0.931445 0.363883i \(-0.881451\pi\)
0.931445 0.363883i \(-0.118549\pi\)
\(348\) 0 0
\(349\) −28.9208 + 16.6974i −1.54809 + 0.893792i −0.549805 + 0.835293i \(0.685298\pi\)
−0.998287 + 0.0584989i \(0.981369\pi\)
\(350\) 0 0
\(351\) −5.60331 1.21022i −0.299082 0.0645969i
\(352\) 0 0
\(353\) 24.4575 + 14.1205i 1.30174 + 0.751560i 0.980703 0.195506i \(-0.0626348\pi\)
0.321038 + 0.947066i \(0.395968\pi\)
\(354\) 0 0
\(355\) 11.5808 + 20.0585i 0.614646 + 1.06460i
\(356\) 0 0
\(357\) 8.15795 + 3.71756i 0.431764 + 0.196754i
\(358\) 0 0
\(359\) 4.95868 + 2.86289i 0.261709 + 0.151098i 0.625114 0.780534i \(-0.285053\pi\)
−0.363405 + 0.931631i \(0.618386\pi\)
\(360\) 0 0
\(361\) −14.5077 25.1281i −0.763565 1.32253i
\(362\) 0 0
\(363\) −5.69196 + 0.591964i −0.298750 + 0.0310700i
\(364\) 0 0
\(365\) 3.76642 6.52363i 0.197143 0.341462i
\(366\) 0 0
\(367\) 10.8969 18.8740i 0.568813 0.985213i −0.427871 0.903840i \(-0.640736\pi\)
0.996684 0.0813728i \(-0.0259304\pi\)
\(368\) 0 0
\(369\) 1.59409 + 7.58099i 0.0829849 + 0.394650i
\(370\) 0 0
\(371\) −18.4733 0.140599i −0.959087 0.00729955i
\(372\) 0 0
\(373\) 19.0200 + 32.9436i 0.984817 + 1.70575i 0.642745 + 0.766080i \(0.277796\pi\)
0.342073 + 0.939674i \(0.388871\pi\)
\(374\) 0 0
\(375\) −18.2654 8.15618i −0.943220 0.421183i
\(376\) 0 0
\(377\) 10.0129i 0.515689i
\(378\) 0 0
\(379\) 11.6200i 0.596878i −0.954429 0.298439i \(-0.903534\pi\)
0.954429 0.298439i \(-0.0964660\pi\)
\(380\) 0 0
\(381\) 10.1844 + 4.54773i 0.521763 + 0.232987i
\(382\) 0 0
\(383\) 11.6806 + 20.2313i 0.596849 + 1.03377i 0.993283 + 0.115710i \(0.0369142\pi\)
−0.396434 + 0.918063i \(0.629752\pi\)
\(384\) 0 0
\(385\) −5.49305 + 9.34919i −0.279952 + 0.476479i
\(386\) 0 0
\(387\) 29.4885 + 9.65266i 1.49898 + 0.490672i
\(388\) 0 0
\(389\) 3.31559 5.74277i 0.168107 0.291170i −0.769647 0.638469i \(-0.779568\pi\)
0.937754 + 0.347299i \(0.112901\pi\)
\(390\) 0 0
\(391\) −0.0315904 + 0.0547162i −0.00159760 + 0.00276712i
\(392\) 0 0
\(393\) 6.08101 0.632425i 0.306746 0.0319016i
\(394\) 0 0
\(395\) −6.19317 10.7269i −0.311612 0.539728i
\(396\) 0 0
\(397\) 21.0152 + 12.1331i 1.05472 + 0.608943i 0.923967 0.382472i \(-0.124927\pi\)
0.130753 + 0.991415i \(0.458260\pi\)
\(398\) 0 0
\(399\) −31.6079 + 3.04424i −1.58237 + 0.152403i
\(400\) 0 0
\(401\) −5.84669 10.1268i −0.291970 0.505706i 0.682306 0.731067i \(-0.260977\pi\)
−0.974275 + 0.225361i \(0.927644\pi\)
\(402\) 0 0
\(403\) −0.672716 0.388393i −0.0335104 0.0193472i
\(404\) 0 0
\(405\) −5.35495 12.1702i −0.266090 0.604744i
\(406\) 0 0
\(407\) 9.25251 5.34194i 0.458630 0.264790i
\(408\) 0 0
\(409\) 30.2767i 1.49708i 0.663087 + 0.748542i \(0.269246\pi\)
−0.663087 + 0.748542i \(0.730754\pi\)
\(410\) 0 0
\(411\) −19.5237 26.9339i −0.963033 1.32855i
\(412\) 0 0
\(413\) 1.52522 2.59593i 0.0750512 0.127737i
\(414\) 0 0
\(415\) −13.6838 7.90033i −0.671710 0.387812i
\(416\) 0 0
\(417\) 17.1242 + 23.6236i 0.838574 + 1.15685i
\(418\) 0 0
\(419\) 4.44019 7.69063i 0.216917 0.375712i −0.736947 0.675951i \(-0.763733\pi\)
0.953864 + 0.300239i \(0.0970664\pi\)
\(420\) 0 0
\(421\) 7.59052 + 13.1472i 0.369939 + 0.640753i 0.989556 0.144151i \(-0.0460452\pi\)
−0.619617 + 0.784905i \(0.712712\pi\)
\(422\) 0 0
\(423\) 8.57376 + 9.56406i 0.416871 + 0.465021i
\(424\) 0 0
\(425\) 5.51179i 0.267361i
\(426\) 0 0
\(427\) −5.90815 3.47129i −0.285916 0.167988i
\(428\) 0 0
\(429\) −5.27255 + 0.548345i −0.254561 + 0.0264744i
\(430\) 0 0
\(431\) 3.60242 2.07986i 0.173523 0.100183i −0.410723 0.911760i \(-0.634724\pi\)
0.584246 + 0.811577i \(0.301390\pi\)
\(432\) 0 0
\(433\) 31.2165i 1.50017i −0.661343 0.750084i \(-0.730013\pi\)
0.661343 0.750084i \(-0.269987\pi\)
\(434\) 0 0
\(435\) −18.8038 + 13.6304i −0.901572 + 0.653527i
\(436\) 0 0
\(437\) 0.223786i 0.0107051i
\(438\) 0 0
\(439\) 15.5826 0.743717 0.371858 0.928289i \(-0.378721\pi\)
0.371858 + 0.928289i \(0.378721\pi\)
\(440\) 0 0
\(441\) −6.83599 + 19.8562i −0.325524 + 0.945534i
\(442\) 0 0
\(443\) 12.4016i 0.589218i 0.955618 + 0.294609i \(0.0951893\pi\)
−0.955618 + 0.294609i \(0.904811\pi\)
\(444\) 0 0
\(445\) −15.0762 −0.714678
\(446\) 0 0
\(447\) −36.5925 + 3.80562i −1.73076 + 0.180000i
\(448\) 0 0
\(449\) −22.8280 −1.07732 −0.538660 0.842524i \(-0.681069\pi\)
−0.538660 + 0.842524i \(0.681069\pi\)
\(450\) 0 0
\(451\) 3.58181 + 6.20388i 0.168661 + 0.292129i
\(452\) 0 0
\(453\) −20.2070 + 14.6476i −0.949409 + 0.688203i
\(454\) 0 0
\(455\) 2.18446 3.71795i 0.102409 0.174300i
\(456\) 0 0
\(457\) 22.0978 1.03369 0.516846 0.856078i \(-0.327106\pi\)
0.516846 + 0.856078i \(0.327106\pi\)
\(458\) 0 0
\(459\) −6.82671 + 7.53205i −0.318644 + 0.351566i
\(460\) 0 0
\(461\) −20.2378 + 11.6843i −0.942568 + 0.544192i −0.890764 0.454465i \(-0.849830\pi\)
−0.0518038 + 0.998657i \(0.516497\pi\)
\(462\) 0 0
\(463\) −21.5837 12.4613i −1.00308 0.579127i −0.0939203 0.995580i \(-0.529940\pi\)
−0.909157 + 0.416452i \(0.863273\pi\)
\(464\) 0 0
\(465\) −0.186373 1.79205i −0.00864284 0.0831042i
\(466\) 0 0
\(467\) −20.1004 + 34.8149i −0.930137 + 1.61104i −0.147052 + 0.989129i \(0.546978\pi\)
−0.783085 + 0.621915i \(0.786355\pi\)
\(468\) 0 0
\(469\) 26.6064 + 15.6324i 1.22857 + 0.721837i
\(470\) 0 0
\(471\) 9.01161 + 4.02403i 0.415233 + 0.185417i
\(472\) 0 0
\(473\) 28.6924 1.31928
\(474\) 0 0
\(475\) −9.76135 16.9072i −0.447881 0.775753i
\(476\) 0 0
\(477\) 6.51660 19.9080i 0.298375 0.911523i
\(478\) 0 0
\(479\) −16.4450 + 28.4835i −0.751390 + 1.30145i 0.195759 + 0.980652i \(0.437283\pi\)
−0.947149 + 0.320794i \(0.896050\pi\)
\(480\) 0 0
\(481\) −3.67950 + 2.12436i −0.167771 + 0.0968626i
\(482\) 0 0
\(483\) −0.134673 0.0613700i −0.00612781 0.00279243i
\(484\) 0 0
\(485\) −5.93333 + 10.2768i −0.269418 + 0.466646i
\(486\) 0 0
\(487\) −15.3672 + 8.87224i −0.696353 + 0.402040i −0.805988 0.591932i \(-0.798365\pi\)
0.109634 + 0.993972i \(0.465032\pi\)
\(488\) 0 0
\(489\) −6.88221 + 4.98874i −0.311224 + 0.225599i
\(490\) 0 0
\(491\) 13.0636 + 7.54226i 0.589551 + 0.340377i 0.764920 0.644126i \(-0.222779\pi\)
−0.175369 + 0.984503i \(0.556112\pi\)
\(492\) 0 0
\(493\) 15.3769 + 8.87788i 0.692543 + 0.399840i
\(494\) 0 0
\(495\) −8.20722 9.15518i −0.368887 0.411495i
\(496\) 0 0
\(497\) 35.7632 + 21.0124i 1.60420 + 0.942537i
\(498\) 0 0
\(499\) −11.7257 + 6.76985i −0.524915 + 0.303060i −0.738943 0.673768i \(-0.764675\pi\)
0.214028 + 0.976827i \(0.431342\pi\)
\(500\) 0 0
\(501\) 1.94788 + 2.68719i 0.0870247 + 0.120055i
\(502\) 0 0
\(503\) −19.0537 −0.849563 −0.424782 0.905296i \(-0.639649\pi\)
−0.424782 + 0.905296i \(0.639649\pi\)
\(504\) 0 0
\(505\) 1.30113 0.0578993
\(506\) 0 0
\(507\) −20.2991 + 2.11111i −0.901515 + 0.0937576i
\(508\) 0 0
\(509\) −36.3115 + 20.9644i −1.60948 + 0.929233i −0.619992 + 0.784608i \(0.712864\pi\)
−0.989487 + 0.144624i \(0.953803\pi\)
\(510\) 0 0
\(511\) 0.102671 13.4899i 0.00454189 0.596758i
\(512\) 0 0
\(513\) 7.60139 35.1943i 0.335610 1.55386i
\(514\) 0 0
\(515\) −1.37083 0.791447i −0.0604058 0.0348753i
\(516\) 0 0
\(517\) 10.2863 + 5.93880i 0.452391 + 0.261188i
\(518\) 0 0
\(519\) 37.7375 + 16.8513i 1.65649 + 0.739688i
\(520\) 0 0
\(521\) −16.8365 + 9.72055i −0.737620 + 0.425865i −0.821203 0.570636i \(-0.806697\pi\)
0.0835832 + 0.996501i \(0.473364\pi\)
\(522\) 0 0
\(523\) 3.84616 6.66175i 0.168181 0.291298i −0.769599 0.638527i \(-0.779544\pi\)
0.937780 + 0.347229i \(0.112877\pi\)
\(524\) 0 0
\(525\) −12.8515 + 1.23777i −0.560886 + 0.0540205i
\(526\) 0 0
\(527\) −1.19292 + 0.688735i −0.0519646 + 0.0300018i
\(528\) 0 0
\(529\) −11.4995 + 19.9177i −0.499977 + 0.865986i
\(530\) 0 0
\(531\) 2.27884 + 2.54206i 0.0988934 + 0.110316i
\(532\) 0 0
\(533\) −1.42440 2.46714i −0.0616977 0.106864i
\(534\) 0 0
\(535\) 28.0880 1.21435
\(536\) 0 0
\(537\) −1.74562 16.7848i −0.0753289 0.724316i
\(538\) 0 0
\(539\) −0.295579 + 19.4169i −0.0127315 + 0.836347i
\(540\) 0 0
\(541\) 11.0310 19.1062i 0.474258 0.821439i −0.525307 0.850913i \(-0.676050\pi\)
0.999566 + 0.0294732i \(0.00938296\pi\)
\(542\) 0 0
\(543\) 2.44379 + 1.09125i 0.104873 + 0.0468298i
\(544\) 0 0
\(545\) −3.58095 2.06746i −0.153391 0.0885605i
\(546\) 0 0
\(547\) 19.5580 11.2918i 0.836240 0.482803i −0.0197443 0.999805i \(-0.506285\pi\)
0.855984 + 0.517002i \(0.172952\pi\)
\(548\) 0 0
\(549\) 5.78555 5.18649i 0.246921 0.221354i
\(550\) 0 0
\(551\) −62.8907 −2.67923
\(552\) 0 0
\(553\) −19.1254 11.2370i −0.813296 0.477846i
\(554\) 0 0
\(555\) −8.99832 4.01809i −0.381957 0.170559i
\(556\) 0 0
\(557\) −9.21343 15.9581i −0.390386 0.676168i 0.602115 0.798410i \(-0.294325\pi\)
−0.992500 + 0.122242i \(0.960992\pi\)
\(558\) 0 0
\(559\) −11.4103 −0.482605
\(560\) 0 0
\(561\) −3.83279 + 8.58333i −0.161820 + 0.362389i
\(562\) 0 0
\(563\) 37.5803 1.58382 0.791910 0.610637i \(-0.209087\pi\)
0.791910 + 0.610637i \(0.209087\pi\)
\(564\) 0 0
\(565\) 13.7909i 0.580189i
\(566\) 0 0
\(567\) −19.0951 14.2260i −0.801918 0.597435i
\(568\) 0 0
\(569\) −31.4967 −1.32041 −0.660204 0.751086i \(-0.729530\pi\)
−0.660204 + 0.751086i \(0.729530\pi\)
\(570\) 0 0
\(571\) 9.97991i 0.417646i −0.977953 0.208823i \(-0.933037\pi\)
0.977953 0.208823i \(-0.0669633\pi\)
\(572\) 0 0
\(573\) −2.90634 1.29779i −0.121414 0.0542160i
\(574\) 0 0
\(575\) 0.0909895i 0.00379452i
\(576\) 0 0
\(577\) 16.2027 9.35463i 0.674527 0.389438i −0.123263 0.992374i \(-0.539336\pi\)
0.797790 + 0.602936i \(0.206003\pi\)
\(578\) 0 0
\(579\) 1.32330 2.96346i 0.0549943 0.123157i
\(580\) 0 0
\(581\) −28.2960 0.215359i −1.17392 0.00893460i
\(582\) 0 0
\(583\) 19.3705i 0.802246i
\(584\) 0 0
\(585\) 3.26382 + 3.64080i 0.134942 + 0.150528i
\(586\) 0 0
\(587\) 16.4635 + 28.5156i 0.679521 + 1.17697i 0.975125 + 0.221655i \(0.0711458\pi\)
−0.295604 + 0.955311i \(0.595521\pi\)
\(588\) 0 0
\(589\) 2.43949 4.22532i 0.100517 0.174101i
\(590\) 0 0
\(591\) −15.0480 + 33.6992i −0.618991 + 1.38620i
\(592\) 0 0
\(593\) 15.3537 + 8.86447i 0.630502 + 0.364020i 0.780946 0.624598i \(-0.214737\pi\)
−0.150445 + 0.988618i \(0.548071\pi\)
\(594\) 0 0
\(595\) −3.77288 6.65122i −0.154673 0.272673i
\(596\) 0 0
\(597\) 35.9740 3.74130i 1.47232 0.153121i
\(598\) 0 0
\(599\) 29.8516i 1.21970i 0.792516 + 0.609852i \(0.208771\pi\)
−0.792516 + 0.609852i \(0.791229\pi\)
\(600\) 0 0
\(601\) −15.3153 + 8.84232i −0.624726 + 0.360686i −0.778707 0.627388i \(-0.784124\pi\)
0.153981 + 0.988074i \(0.450791\pi\)
\(602\) 0 0
\(603\) −26.0542 + 23.3565i −1.06101 + 0.951150i
\(604\) 0 0
\(605\) 4.22721 + 2.44058i 0.171861 + 0.0992238i
\(606\) 0 0
\(607\) 21.9556 + 38.0282i 0.891149 + 1.54352i 0.838500 + 0.544902i \(0.183433\pi\)
0.0526491 + 0.998613i \(0.483234\pi\)
\(608\) 0 0
\(609\) −17.2469 + 37.8471i −0.698878 + 1.53364i
\(610\) 0 0
\(611\) −4.09062 2.36172i −0.165489 0.0955450i
\(612\) 0 0
\(613\) 15.8984 + 27.5368i 0.642129 + 1.11220i 0.984957 + 0.172801i \(0.0552818\pi\)
−0.342828 + 0.939398i \(0.611385\pi\)
\(614\) 0 0
\(615\) 2.69416 6.03345i 0.108639 0.243292i
\(616\) 0 0
\(617\) 4.52841 7.84343i 0.182307 0.315765i −0.760359 0.649503i \(-0.774977\pi\)
0.942666 + 0.333738i \(0.108310\pi\)
\(618\) 0 0
\(619\) 7.17201 12.4223i 0.288267 0.499294i −0.685129 0.728422i \(-0.740254\pi\)
0.973396 + 0.229128i \(0.0735875\pi\)
\(620\) 0 0
\(621\) 0.112696 0.124340i 0.00452235 0.00498960i
\(622\) 0 0
\(623\) −23.4842 + 13.3213i −0.940874 + 0.533708i
\(624\) 0 0
\(625\) 1.48760 + 2.57660i 0.0595040 + 0.103064i
\(626\) 0 0
\(627\) −3.44415 33.1168i −0.137546 1.32256i
\(628\) 0 0
\(629\) 7.53424i 0.300410i
\(630\) 0 0
\(631\) 22.0848i 0.879182i −0.898198 0.439591i \(-0.855123\pi\)
0.898198 0.439591i \(-0.144877\pi\)
\(632\) 0 0
\(633\) 20.3160 14.7266i 0.807489 0.585328i
\(634\) 0 0
\(635\) −4.75678 8.23898i −0.188767 0.326954i
\(636\) 0 0
\(637\) 0.117545 7.72166i 0.00465730 0.305943i
\(638\) 0 0
\(639\) −35.0211 + 31.3949i −1.38541 + 1.24196i
\(640\) 0 0
\(641\) 16.0436 27.7883i 0.633683 1.09757i −0.353110 0.935582i \(-0.614876\pi\)
0.986793 0.161989i \(-0.0517909\pi\)
\(642\) 0 0
\(643\) 20.7215 35.8906i 0.817175 1.41539i −0.0905805 0.995889i \(-0.528872\pi\)
0.907756 0.419500i \(-0.137794\pi\)
\(644\) 0 0
\(645\) −15.5327 21.4281i −0.611599 0.843730i
\(646\) 0 0
\(647\) 2.08629 + 3.61356i 0.0820205 + 0.142064i 0.904118 0.427284i \(-0.140529\pi\)
−0.822097 + 0.569347i \(0.807196\pi\)
\(648\) 0 0
\(649\) 2.73402 + 1.57849i 0.107320 + 0.0619611i
\(650\) 0 0
\(651\) −1.87377 2.62680i −0.0734389 0.102952i
\(652\) 0 0
\(653\) 3.11613 + 5.39730i 0.121944 + 0.211213i 0.920534 0.390662i \(-0.127754\pi\)
−0.798590 + 0.601875i \(0.794421\pi\)
\(654\) 0 0
\(655\) −4.51615 2.60740i −0.176460 0.101879i
\(656\) 0 0
\(657\) 14.5375 + 4.75866i 0.567163 + 0.185653i
\(658\) 0 0
\(659\) 12.0701 6.96869i 0.470186 0.271462i −0.246132 0.969236i \(-0.579160\pi\)
0.716317 + 0.697775i \(0.245826\pi\)
\(660\) 0 0
\(661\) 8.94427i 0.347892i −0.984755 0.173946i \(-0.944348\pi\)
0.984755 0.173946i \(-0.0556518\pi\)
\(662\) 0 0
\(663\) 1.52421 3.41339i 0.0591954 0.132565i
\(664\) 0 0
\(665\) 23.3524 + 13.7205i 0.905567 + 0.532060i
\(666\) 0 0
\(667\) −0.253845 0.146557i −0.00982891 0.00567472i
\(668\) 0 0
\(669\) 27.3318 2.84251i 1.05671 0.109898i
\(670\) 0 0
\(671\) 3.59253 6.22245i 0.138688 0.240215i
\(672\) 0 0
\(673\) 10.5409 + 18.2573i 0.406321 + 0.703769i 0.994474 0.104981i \(-0.0334782\pi\)
−0.588153 + 0.808749i \(0.700145\pi\)
\(674\) 0 0
\(675\) 3.09066 14.3097i 0.118960 0.550781i
\(676\) 0 0
\(677\) 42.2089i 1.62222i 0.584894 + 0.811110i \(0.301136\pi\)
−0.584894 + 0.811110i \(0.698864\pi\)
\(678\) 0 0
\(679\) −0.161740 + 21.2509i −0.00620700 + 0.815536i
\(680\) 0 0
\(681\) −19.6898 27.1630i −0.754515 1.04089i
\(682\) 0 0
\(683\) 25.4778 14.7096i 0.974880 0.562847i 0.0741597 0.997246i \(-0.476373\pi\)
0.900721 + 0.434399i \(0.143039\pi\)
\(684\) 0 0
\(685\) 28.3742i 1.08412i
\(686\) 0 0
\(687\) −3.64365 35.0351i −0.139014 1.33667i
\(688\) 0 0
\(689\) 7.70321i 0.293469i
\(690\) 0 0
\(691\) 35.2505 1.34099 0.670496 0.741913i \(-0.266081\pi\)
0.670496 + 0.741913i \(0.266081\pi\)
\(692\) 0 0
\(693\) −20.8739 7.00914i −0.792935 0.266255i
\(694\) 0 0
\(695\) 24.8869i 0.944013i
\(696\) 0 0
\(697\) −5.05177 −0.191349
\(698\) 0 0
\(699\) 26.8456 + 37.0348i 1.01539 + 1.40078i
\(700\) 0 0
\(701\) −21.2983 −0.804426 −0.402213 0.915546i \(-0.631759\pi\)
−0.402213 + 0.915546i \(0.631759\pi\)
\(702\) 0 0
\(703\) −13.3431 23.1109i −0.503244 0.871644i
\(704\) 0 0
\(705\) −1.13329 10.8970i −0.0426821 0.410404i
\(706\) 0 0
\(707\) 2.02677 1.14968i 0.0762244 0.0432381i
\(708\) 0 0
\(709\) 52.3922 1.96763 0.983815 0.179185i \(-0.0573462\pi\)
0.983815 + 0.179185i \(0.0573462\pi\)
\(710\) 0 0
\(711\) 18.7285 16.7893i 0.702375 0.629648i
\(712\) 0 0
\(713\) 0.0196930 0.0113697i 0.000737507 0.000425800i
\(714\) 0 0
\(715\) 3.91574 + 2.26075i 0.146440 + 0.0845473i
\(716\) 0 0
\(717\) −8.53962 + 6.19016i −0.318918 + 0.231176i
\(718\) 0 0
\(719\) 2.03467 3.52415i 0.0758802 0.131428i −0.825588 0.564273i \(-0.809157\pi\)
0.901469 + 0.432844i \(0.142490\pi\)
\(720\) 0 0
\(721\) −2.83467 0.0215745i −0.105568 0.000803475i
\(722\) 0 0
\(723\) 0.840514 0.609268i 0.0312591 0.0226589i
\(724\) 0 0
\(725\) −25.5709 −0.949678
\(726\) 0 0
\(727\) 6.63112 + 11.4854i 0.245935 + 0.425971i 0.962394 0.271658i \(-0.0875718\pi\)
−0.716459 + 0.697629i \(0.754238\pi\)
\(728\) 0 0
\(729\) 21.9470 15.7267i 0.812852 0.582471i
\(730\) 0 0
\(731\) −10.1169 + 17.5230i −0.374188 + 0.648112i
\(732\) 0 0
\(733\) 39.4414 22.7715i 1.45680 0.841084i 0.457948 0.888979i \(-0.348585\pi\)
0.998852 + 0.0478949i \(0.0152513\pi\)
\(734\) 0 0
\(735\) 14.6610 10.2906i 0.540778 0.379576i
\(736\) 0 0
\(737\) −16.1784 + 28.0217i −0.595938 + 1.03219i
\(738\) 0 0
\(739\) 32.1653 18.5707i 1.18322 0.683133i 0.226464 0.974020i \(-0.427284\pi\)
0.956758 + 0.290886i \(0.0939502\pi\)
\(740\) 0 0
\(741\) 1.36966 + 13.1698i 0.0503156 + 0.483804i
\(742\) 0 0
\(743\) 15.9963 + 9.23546i 0.586847 + 0.338816i 0.763850 0.645394i \(-0.223307\pi\)
−0.177003 + 0.984210i \(0.556640\pi\)
\(744\) 0 0
\(745\) 27.1759 + 15.6900i 0.995649 + 0.574838i
\(746\) 0 0
\(747\) 9.98162 30.4935i 0.365208 1.11570i
\(748\) 0 0
\(749\) 43.7527 24.8186i 1.59869 0.906852i
\(750\) 0 0
\(751\) −16.6822 + 9.63147i −0.608742 + 0.351457i −0.772473 0.635048i \(-0.780980\pi\)
0.163731 + 0.986505i \(0.447647\pi\)
\(752\) 0 0
\(753\) −10.4095 + 23.3115i −0.379342 + 0.849517i
\(754\) 0 0
\(755\) 21.2876 0.774735
\(756\) 0 0
\(757\) 8.29756 0.301580 0.150790 0.988566i \(-0.451818\pi\)
0.150790 + 0.988566i \(0.451818\pi\)
\(758\) 0 0
\(759\) 0.0632722 0.141695i 0.00229663 0.00514320i
\(760\) 0 0
\(761\) −13.2960 + 7.67646i −0.481980 + 0.278272i −0.721241 0.692684i \(-0.756428\pi\)
0.239261 + 0.970955i \(0.423095\pi\)
\(762\) 0 0
\(763\) −7.40488 0.0563581i −0.268075 0.00204030i
\(764\) 0 0
\(765\) 8.48509 1.78420i 0.306779 0.0645078i
\(766\) 0 0
\(767\) −1.08726 0.627728i −0.0392585 0.0226659i
\(768\) 0 0
\(769\) −32.4625 18.7422i −1.17063 0.675862i −0.216800 0.976216i \(-0.569562\pi\)
−0.953828 + 0.300354i \(0.902895\pi\)
\(770\) 0 0
\(771\) −2.93557 28.2266i −0.105722 1.01656i
\(772\) 0 0
\(773\) −36.9329 + 21.3232i −1.32838 + 0.766942i −0.985050 0.172271i \(-0.944889\pi\)
−0.343334 + 0.939214i \(0.611556\pi\)
\(774\) 0 0
\(775\) 0.991877 1.71798i 0.0356293 0.0617117i
\(776\) 0 0
\(777\) −17.5671 + 1.69194i −0.630217 + 0.0606980i
\(778\) 0 0
\(779\) 15.4960 8.94664i 0.555203 0.320547i
\(780\) 0 0
\(781\) −21.7463 + 37.6657i −0.778144 + 1.34779i
\(782\) 0 0
\(783\) −34.9434 31.6712i −1.24878 1.13183i
\(784\) 0 0
\(785\) −4.20901 7.29021i −0.150226 0.260199i
\(786\) 0 0
\(787\) −18.1499 −0.646972 −0.323486 0.946233i \(-0.604855\pi\)
−0.323486 + 0.946233i \(0.604855\pi\)
\(788\) 0 0
\(789\) 8.29350 6.01175i 0.295257 0.214024i
\(790\) 0 0
\(791\) 12.1857 + 21.4822i 0.433274 + 0.763819i
\(792\) 0 0
\(793\) −1.42866 + 2.47452i −0.0507334 + 0.0878728i
\(794\) 0 0
\(795\) −14.4663 + 10.4863i −0.513067 + 0.371909i
\(796\) 0 0
\(797\) 30.3572 + 17.5268i 1.07531 + 0.620830i 0.929627 0.368502i \(-0.120129\pi\)
0.145681 + 0.989332i \(0.453463\pi\)
\(798\) 0 0
\(799\) −7.25387 + 4.18802i −0.256623 + 0.148162i
\(800\) 0 0
\(801\) −6.29966 29.9592i −0.222587 1.05856i
\(802\) 0 0
\(803\) 14.1451 0.499169
\(804\) 0 0
\(805\) 0.0622833 + 0.109799i 0.00219520 + 0.00386992i
\(806\) 0 0
\(807\) 1.87923 + 18.0696i 0.0661522 + 0.636078i
\(808\) 0 0
\(809\) −18.5834 32.1874i −0.653358 1.13165i −0.982303 0.187300i \(-0.940026\pi\)
0.328945 0.944349i \(-0.393307\pi\)
\(810\) 0 0
\(811\) 13.3687 0.469439 0.234720 0.972063i \(-0.424583\pi\)
0.234720 + 0.972063i \(0.424583\pi\)
\(812\) 0 0
\(813\) −7.48798 10.3300i −0.262615 0.362290i
\(814\) 0 0
\(815\) 7.25023 0.253964
\(816\) 0 0
\(817\) 71.6679i 2.50734i
\(818\) 0 0
\(819\) 8.30107 + 2.78737i 0.290063 + 0.0973985i
\(820\) 0 0
\(821\) −21.7944 −0.760629 −0.380315 0.924857i \(-0.624184\pi\)
−0.380315 + 0.924857i \(0.624184\pi\)
\(822\) 0 0
\(823\) 13.5246i 0.471439i −0.971821 0.235719i \(-0.924255\pi\)
0.971821 0.235719i \(-0.0757446\pi\)
\(824\) 0 0
\(825\) −1.40036 13.4650i −0.0487544 0.468792i
\(826\) 0 0
\(827\) 45.6866i 1.58868i 0.607474 + 0.794339i \(0.292183\pi\)
−0.607474 + 0.794339i \(0.707817\pi\)
\(828\) 0 0
\(829\) −30.2094 + 17.4414i −1.04922 + 0.605766i −0.922430 0.386164i \(-0.873800\pi\)
−0.126787 + 0.991930i \(0.540466\pi\)
\(830\) 0 0
\(831\) −1.80486 2.48989i −0.0626099 0.0863733i
\(832\) 0 0
\(833\) −11.7541 7.02690i −0.407254 0.243468i
\(834\) 0 0
\(835\) 2.83089i 0.0979669i
\(836\) 0 0
\(837\) 3.48326 1.11918i 0.120399 0.0386844i
\(838\) 0 0
\(839\) −6.74592 11.6843i −0.232895 0.403386i 0.725764 0.687944i \(-0.241487\pi\)
−0.958659 + 0.284558i \(0.908153\pi\)
\(840\) 0 0
\(841\) −26.6871 + 46.2235i −0.920246 + 1.59391i
\(842\) 0 0
\(843\) −7.17563 + 0.746266i −0.247142 + 0.0257028i
\(844\) 0 0
\(845\) 15.0754 + 8.70380i 0.518610 + 0.299420i
\(846\) 0 0
\(847\) 8.74125 + 0.0665291i 0.300353 + 0.00228597i
\(848\) 0 0
\(849\) −2.40650 + 5.38925i −0.0825910 + 0.184958i
\(850\) 0 0
\(851\) 0.124376i 0.00426356i
\(852\) 0 0
\(853\) 25.7099 14.8436i 0.880291 0.508236i 0.00953667 0.999955i \(-0.496964\pi\)
0.870754 + 0.491718i \(0.163631\pi\)
\(854\) 0 0
\(855\) −22.8678 + 20.5000i −0.782062 + 0.701084i
\(856\) 0 0
\(857\) −22.0886 12.7529i −0.754534 0.435630i 0.0727959 0.997347i \(-0.476808\pi\)
−0.827330 + 0.561717i \(0.810141\pi\)
\(858\) 0 0
\(859\) 1.31398 + 2.27588i 0.0448324 + 0.0776521i 0.887571 0.460671i \(-0.152391\pi\)
−0.842738 + 0.538323i \(0.819058\pi\)
\(860\) 0 0
\(861\) −1.13446 11.7789i −0.0386622 0.401423i
\(862\) 0 0
\(863\) −29.6590 17.1237i −1.00961 0.582896i −0.0985294 0.995134i \(-0.531414\pi\)
−0.911076 + 0.412238i \(0.864747\pi\)
\(864\) 0 0
\(865\) −17.6259 30.5289i −0.599298 1.03801i
\(866\) 0 0
\(867\) 13.3907 + 18.4731i 0.454771 + 0.627378i
\(868\) 0 0
\(869\) 11.6295 20.1428i 0.394503 0.683299i
\(870\) 0 0
\(871\) 6.43375 11.1436i 0.217999 0.377586i
\(872\) 0 0
\(873\) −22.9013 7.49643i −0.775091 0.253716i
\(874\) 0 0
\(875\) 26.3453 + 15.4790i 0.890635 + 0.523286i
\(876\) 0 0
\(877\) 17.7909 + 30.8147i 0.600754 + 1.04054i 0.992707 + 0.120552i \(0.0384664\pi\)
−0.391953 + 0.919985i \(0.628200\pi\)
\(878\) 0 0
\(879\) −26.2218 + 19.0075i −0.884440 + 0.641109i
\(880\) 0 0
\(881\) 40.8828i 1.37738i −0.725058 0.688688i \(-0.758187\pi\)
0.725058 0.688688i \(-0.241813\pi\)
\(882\) 0 0
\(883\) 13.9504i 0.469468i −0.972060 0.234734i \(-0.924578\pi\)
0.972060 0.234734i \(-0.0754219\pi\)
\(884\) 0 0
\(885\) −0.301219 2.89634i −0.0101254 0.0973594i
\(886\) 0 0
\(887\) 14.9999 + 25.9805i 0.503646 + 0.872340i 0.999991 + 0.00421500i \(0.00134168\pi\)
−0.496345 + 0.868125i \(0.665325\pi\)
\(888\) 0 0
\(889\) −14.6896 8.63079i −0.492675 0.289467i
\(890\) 0 0
\(891\) 14.7637 20.1349i 0.494601 0.674543i
\(892\) 0 0
\(893\) 14.8339 25.6931i 0.496398 0.859787i
\(894\) 0 0
\(895\) −7.19693 + 12.4655i −0.240567 + 0.416674i
\(896\) 0 0
\(897\) −0.0251619 + 0.0563487i −0.000840130 + 0.00188143i
\(898\) 0 0
\(899\) −3.19525 5.53433i −0.106567 0.184580i
\(900\) 0 0
\(901\) 11.8299 + 6.83002i 0.394113 + 0.227541i
\(902\) 0 0
\(903\) −43.1292 19.6539i −1.43525 0.654041i
\(904\) 0 0
\(905\) −1.14141 1.97698i −0.0379417 0.0657170i
\(906\) 0 0
\(907\) 34.8441 + 20.1173i 1.15698 + 0.667983i 0.950578 0.310485i \(-0.100491\pi\)
0.206401 + 0.978467i \(0.433825\pi\)
\(908\) 0 0
\(909\) 0.543683 + 2.58559i 0.0180328 + 0.0857585i
\(910\) 0 0
\(911\) 16.1689 9.33513i 0.535700 0.309287i −0.207634 0.978206i \(-0.566576\pi\)
0.743334 + 0.668920i \(0.233243\pi\)
\(912\) 0 0
\(913\) 29.6703i 0.981943i
\(914\) 0 0
\(915\) −6.59187 + 0.685555i −0.217920 + 0.0226637i
\(916\) 0 0
\(917\) −9.33872 0.0710764i −0.308392 0.00234715i
\(918\) 0 0
\(919\) −16.6056 9.58726i −0.547769 0.316254i 0.200453 0.979703i \(-0.435759\pi\)
−0.748222 + 0.663449i \(0.769092\pi\)
\(920\) 0 0
\(921\) −9.22509 + 20.6591i −0.303977 + 0.680742i
\(922\) 0 0
\(923\) 8.64799 14.9788i 0.284652 0.493032i
\(924\) 0 0
\(925\) −5.42519 9.39671i −0.178379 0.308962i
\(926\) 0 0
\(927\) 0.999949 3.05480i 0.0328426 0.100333i
\(928\) 0 0
\(929\) 32.8222i 1.07686i −0.842669 0.538431i \(-0.819017\pi\)
0.842669 0.538431i \(-0.180983\pi\)
\(930\) 0 0
\(931\) 48.4996 + 0.738298i 1.58951 + 0.0241967i
\(932\) 0 0
\(933\) 21.8037 48.8283i 0.713822 1.59857i
\(934\) 0 0
\(935\) 6.94375 4.00897i 0.227085 0.131107i
\(936\) 0 0
\(937\) 5.98141i 0.195404i 0.995216 + 0.0977020i \(0.0311492\pi\)
−0.995216 + 0.0977020i \(0.968851\pi\)
\(938\) 0 0
\(939\) −25.2730 11.2854i −0.824753 0.368283i
\(940\) 0 0
\(941\) 25.2347i 0.822629i −0.911494 0.411314i \(-0.865070\pi\)
0.911494 0.411314i \(-0.134930\pi\)
\(942\) 0 0
\(943\) 0.0833953 0.00271572
\(944\) 0 0
\(945\) 6.06557 + 19.3835i 0.197313 + 0.630545i
\(946\) 0 0
\(947\) 8.61244i 0.279867i −0.990161 0.139933i \(-0.955311\pi\)
0.990161 0.139933i \(-0.0446888\pi\)
\(948\) 0 0
\(949\) −5.62516 −0.182601
\(950\) 0 0
\(951\) 2.61976 5.86681i 0.0849514 0.190244i
\(952\) 0 0
\(953\) 12.1465 0.393463 0.196731 0.980457i \(-0.436967\pi\)
0.196731 + 0.980457i \(0.436967\pi\)
\(954\) 0 0
\(955\) 1.35745 + 2.35117i 0.0439260 + 0.0760821i
\(956\) 0 0
\(957\) −39.8206 17.7814i −1.28722 0.574792i
\(958\) 0 0
\(959\) 25.0715 + 44.1985i 0.809600 + 1.42724i
\(960\) 0 0
\(961\) −30.5042 −0.984008
\(962\) 0 0
\(963\) 11.7367 + 55.8162i 0.378210 + 1.79865i
\(964\) 0 0
\(965\) −2.39738 + 1.38413i −0.0771743 + 0.0445566i
\(966\) 0 0
\(967\) 10.8574 + 6.26853i 0.349151 + 0.201582i 0.664311 0.747456i \(-0.268725\pi\)
−0.315160 + 0.949038i \(0.602058\pi\)
\(968\) 0 0
\(969\) 21.4394 + 9.57353i 0.688734 + 0.307546i
\(970\) 0 0
\(971\) −1.23493 + 2.13896i −0.0396308 + 0.0686426i −0.885160 0.465286i \(-0.845952\pi\)
0.845530 + 0.533929i \(0.179285\pi\)
\(972\) 0 0
\(973\) −21.9901 38.7664i −0.704970 1.24279i
\(974\) 0 0
\(975\) 0.556891 + 5.35472i 0.0178348 + 0.171488i
\(976\) 0 0
\(977\) 41.3188 1.32191 0.660953 0.750428i \(-0.270152\pi\)
0.660953 + 0.750428i \(0.270152\pi\)
\(978\) 0 0
\(979\) −14.1549 24.5170i −0.452393 0.783568i
\(980\) 0 0
\(981\) 2.61213 7.97994i 0.0833988 0.254780i
\(982\) 0 0
\(983\) 4.40445 7.62872i 0.140480 0.243319i −0.787197 0.616701i \(-0.788469\pi\)
0.927677 + 0.373382i \(0.121802\pi\)
\(984\) 0 0
\(985\) 27.2620 15.7397i 0.868639 0.501509i
\(986\) 0 0
\(987\) −11.3939 15.9729i −0.362673 0.508423i
\(988\) 0 0
\(989\) 0.167011 0.289272i 0.00531065 0.00919832i
\(990\) 0 0
\(991\) −23.1527 + 13.3672i −0.735470 + 0.424624i −0.820420 0.571761i \(-0.806260\pi\)
0.0849498 + 0.996385i \(0.472927\pi\)
\(992\) 0 0
\(993\) 44.0438 + 19.6672i 1.39769 + 0.624120i
\(994\) 0 0
\(995\) −26.7166 15.4248i −0.846973 0.489000i
\(996\) 0 0
\(997\) −26.4192 15.2531i −0.836705 0.483072i 0.0194379 0.999811i \(-0.493812\pi\)
−0.856143 + 0.516739i \(0.827146\pi\)
\(998\) 0 0
\(999\) 4.22472 19.5604i 0.133664 0.618863i
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 1008.2.cz.h.607.7 yes 24
3.2 odd 2 3024.2.cz.g.1279.8 24
4.3 odd 2 1008.2.cz.g.607.6 yes 24
7.3 odd 6 1008.2.bf.h.31.12 yes 24
9.2 odd 6 3024.2.bf.h.2287.8 24
9.7 even 3 1008.2.bf.g.943.1 yes 24
12.11 even 2 3024.2.cz.h.1279.8 24
21.17 even 6 3024.2.bf.g.1711.5 24
28.3 even 6 1008.2.bf.g.31.1 24
36.7 odd 6 1008.2.bf.h.943.12 yes 24
36.11 even 6 3024.2.bf.g.2287.8 24
63.38 even 6 3024.2.cz.h.2719.8 24
63.52 odd 6 1008.2.cz.g.367.6 yes 24
84.59 odd 6 3024.2.bf.h.1711.5 24
252.115 even 6 inner 1008.2.cz.h.367.7 yes 24
252.227 odd 6 3024.2.cz.g.2719.8 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1008.2.bf.g.31.1 24 28.3 even 6
1008.2.bf.g.943.1 yes 24 9.7 even 3
1008.2.bf.h.31.12 yes 24 7.3 odd 6
1008.2.bf.h.943.12 yes 24 36.7 odd 6
1008.2.cz.g.367.6 yes 24 63.52 odd 6
1008.2.cz.g.607.6 yes 24 4.3 odd 2
1008.2.cz.h.367.7 yes 24 252.115 even 6 inner
1008.2.cz.h.607.7 yes 24 1.1 even 1 trivial
3024.2.bf.g.1711.5 24 21.17 even 6
3024.2.bf.g.2287.8 24 36.11 even 6
3024.2.bf.h.1711.5 24 84.59 odd 6
3024.2.bf.h.2287.8 24 9.2 odd 6
3024.2.cz.g.1279.8 24 3.2 odd 2
3024.2.cz.g.2719.8 24 252.227 odd 6
3024.2.cz.h.1279.8 24 12.11 even 2
3024.2.cz.h.2719.8 24 63.38 even 6