Properties

Label 4003.2.a.c.1.19
Level $4003$
Weight $2$
Character 4003.1
Self dual yes
Analytic conductor $31.964$
Analytic rank $0$
Dimension $179$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4003,2,Mod(1,4003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4003, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4003.a (trivial)

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: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 4003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.33012 q^{2} -0.602166 q^{3} +3.42946 q^{4} +1.32408 q^{5} +1.40312 q^{6} -1.36511 q^{7} -3.33081 q^{8} -2.63740 q^{9} +O(q^{10})\) \(q-2.33012 q^{2} -0.602166 q^{3} +3.42946 q^{4} +1.32408 q^{5} +1.40312 q^{6} -1.36511 q^{7} -3.33081 q^{8} -2.63740 q^{9} -3.08526 q^{10} -0.0777918 q^{11} -2.06510 q^{12} -4.41950 q^{13} +3.18086 q^{14} -0.797315 q^{15} +0.902278 q^{16} +1.21540 q^{17} +6.14545 q^{18} +0.960375 q^{19} +4.54088 q^{20} +0.822021 q^{21} +0.181264 q^{22} -8.67641 q^{23} +2.00570 q^{24} -3.24682 q^{25} +10.2980 q^{26} +3.39465 q^{27} -4.68158 q^{28} -7.04953 q^{29} +1.85784 q^{30} -1.89745 q^{31} +4.55921 q^{32} +0.0468436 q^{33} -2.83204 q^{34} -1.80751 q^{35} -9.04485 q^{36} +7.32980 q^{37} -2.23779 q^{38} +2.66127 q^{39} -4.41026 q^{40} -7.66124 q^{41} -1.91541 q^{42} +5.26894 q^{43} -0.266784 q^{44} -3.49212 q^{45} +20.2171 q^{46} -12.8976 q^{47} -0.543321 q^{48} -5.13648 q^{49} +7.56547 q^{50} -0.731874 q^{51} -15.1565 q^{52} +7.76041 q^{53} -7.90994 q^{54} -0.103002 q^{55} +4.54692 q^{56} -0.578305 q^{57} +16.4263 q^{58} +10.6714 q^{59} -2.73436 q^{60} -7.38442 q^{61} +4.42129 q^{62} +3.60033 q^{63} -12.4281 q^{64} -5.85177 q^{65} -0.109151 q^{66} -6.57719 q^{67} +4.16818 q^{68} +5.22464 q^{69} +4.21171 q^{70} +6.73510 q^{71} +8.78468 q^{72} +6.88195 q^{73} -17.0793 q^{74} +1.95512 q^{75} +3.29357 q^{76} +0.106194 q^{77} -6.20109 q^{78} +3.73122 q^{79} +1.19469 q^{80} +5.86805 q^{81} +17.8516 q^{82} +4.04725 q^{83} +2.81909 q^{84} +1.60929 q^{85} -12.2773 q^{86} +4.24499 q^{87} +0.259110 q^{88} +11.3044 q^{89} +8.13706 q^{90} +6.03309 q^{91} -29.7554 q^{92} +1.14258 q^{93} +30.0530 q^{94} +1.27161 q^{95} -2.74540 q^{96} -13.5334 q^{97} +11.9686 q^{98} +0.205168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33012 −1.64764 −0.823822 0.566849i \(-0.808162\pi\)
−0.823822 + 0.566849i \(0.808162\pi\)
\(3\) −0.602166 −0.347661 −0.173830 0.984776i \(-0.555614\pi\)
−0.173830 + 0.984776i \(0.555614\pi\)
\(4\) 3.42946 1.71473
\(5\) 1.32408 0.592146 0.296073 0.955165i \(-0.404323\pi\)
0.296073 + 0.955165i \(0.404323\pi\)
\(6\) 1.40312 0.572821
\(7\) −1.36511 −0.515962 −0.257981 0.966150i \(-0.583057\pi\)
−0.257981 + 0.966150i \(0.583057\pi\)
\(8\) −3.33081 −1.17762
\(9\) −2.63740 −0.879132
\(10\) −3.08526 −0.975646
\(11\) −0.0777918 −0.0234551 −0.0117276 0.999931i \(-0.503733\pi\)
−0.0117276 + 0.999931i \(0.503733\pi\)
\(12\) −2.06510 −0.596144
\(13\) −4.41950 −1.22575 −0.612875 0.790180i \(-0.709987\pi\)
−0.612875 + 0.790180i \(0.709987\pi\)
\(14\) 3.18086 0.850121
\(15\) −0.797315 −0.205866
\(16\) 0.902278 0.225569
\(17\) 1.21540 0.294779 0.147389 0.989079i \(-0.452913\pi\)
0.147389 + 0.989079i \(0.452913\pi\)
\(18\) 6.14545 1.44850
\(19\) 0.960375 0.220325 0.110163 0.993914i \(-0.464863\pi\)
0.110163 + 0.993914i \(0.464863\pi\)
\(20\) 4.54088 1.01537
\(21\) 0.822021 0.179380
\(22\) 0.181264 0.0386457
\(23\) −8.67641 −1.80916 −0.904578 0.426308i \(-0.859814\pi\)
−0.904578 + 0.426308i \(0.859814\pi\)
\(24\) 2.00570 0.409412
\(25\) −3.24682 −0.649363
\(26\) 10.2980 2.01960
\(27\) 3.39465 0.653300
\(28\) −4.68158 −0.884735
\(29\) −7.04953 −1.30906 −0.654532 0.756034i \(-0.727134\pi\)
−0.654532 + 0.756034i \(0.727134\pi\)
\(30\) 1.85784 0.339194
\(31\) −1.89745 −0.340792 −0.170396 0.985376i \(-0.554505\pi\)
−0.170396 + 0.985376i \(0.554505\pi\)
\(32\) 4.55921 0.805963
\(33\) 0.0468436 0.00815442
\(34\) −2.83204 −0.485690
\(35\) −1.80751 −0.305525
\(36\) −9.04485 −1.50747
\(37\) 7.32980 1.20501 0.602506 0.798114i \(-0.294169\pi\)
0.602506 + 0.798114i \(0.294169\pi\)
\(38\) −2.23779 −0.363017
\(39\) 2.66127 0.426145
\(40\) −4.41026 −0.697323
\(41\) −7.66124 −1.19649 −0.598243 0.801315i \(-0.704134\pi\)
−0.598243 + 0.801315i \(0.704134\pi\)
\(42\) −1.91541 −0.295554
\(43\) 5.26894 0.803505 0.401753 0.915748i \(-0.368401\pi\)
0.401753 + 0.915748i \(0.368401\pi\)
\(44\) −0.266784 −0.0402192
\(45\) −3.49212 −0.520575
\(46\) 20.2171 2.98085
\(47\) −12.8976 −1.88131 −0.940654 0.339367i \(-0.889787\pi\)
−0.940654 + 0.339367i \(0.889787\pi\)
\(48\) −0.543321 −0.0784216
\(49\) −5.13648 −0.733783
\(50\) 7.56547 1.06992
\(51\) −0.731874 −0.102483
\(52\) −15.1565 −2.10183
\(53\) 7.76041 1.06597 0.532987 0.846123i \(-0.321069\pi\)
0.532987 + 0.846123i \(0.321069\pi\)
\(54\) −7.90994 −1.07641
\(55\) −0.103002 −0.0138889
\(56\) 4.54692 0.607607
\(57\) −0.578305 −0.0765983
\(58\) 16.4263 2.15687
\(59\) 10.6714 1.38930 0.694650 0.719348i \(-0.255559\pi\)
0.694650 + 0.719348i \(0.255559\pi\)
\(60\) −2.73436 −0.353004
\(61\) −7.38442 −0.945478 −0.472739 0.881203i \(-0.656735\pi\)
−0.472739 + 0.881203i \(0.656735\pi\)
\(62\) 4.42129 0.561504
\(63\) 3.60033 0.453599
\(64\) −12.4281 −1.55351
\(65\) −5.85177 −0.725823
\(66\) −0.109151 −0.0134356
\(67\) −6.57719 −0.803531 −0.401766 0.915743i \(-0.631603\pi\)
−0.401766 + 0.915743i \(0.631603\pi\)
\(68\) 4.16818 0.505466
\(69\) 5.22464 0.628972
\(70\) 4.21171 0.503396
\(71\) 6.73510 0.799309 0.399655 0.916666i \(-0.369130\pi\)
0.399655 + 0.916666i \(0.369130\pi\)
\(72\) 8.78468 1.03528
\(73\) 6.88195 0.805471 0.402736 0.915316i \(-0.368059\pi\)
0.402736 + 0.915316i \(0.368059\pi\)
\(74\) −17.0793 −1.98543
\(75\) 1.95512 0.225758
\(76\) 3.29357 0.377798
\(77\) 0.106194 0.0121019
\(78\) −6.20109 −0.702135
\(79\) 3.73122 0.419795 0.209897 0.977723i \(-0.432687\pi\)
0.209897 + 0.977723i \(0.432687\pi\)
\(80\) 1.19469 0.133570
\(81\) 5.86805 0.652005
\(82\) 17.8516 1.97138
\(83\) 4.04725 0.444243 0.222122 0.975019i \(-0.428702\pi\)
0.222122 + 0.975019i \(0.428702\pi\)
\(84\) 2.81909 0.307588
\(85\) 1.60929 0.174552
\(86\) −12.2773 −1.32389
\(87\) 4.24499 0.455110
\(88\) 0.259110 0.0276212
\(89\) 11.3044 1.19826 0.599132 0.800650i \(-0.295512\pi\)
0.599132 + 0.800650i \(0.295512\pi\)
\(90\) 8.13706 0.857721
\(91\) 6.03309 0.632440
\(92\) −29.7554 −3.10222
\(93\) 1.14258 0.118480
\(94\) 30.0530 3.09973
\(95\) 1.27161 0.130465
\(96\) −2.74540 −0.280201
\(97\) −13.5334 −1.37411 −0.687054 0.726607i \(-0.741096\pi\)
−0.687054 + 0.726607i \(0.741096\pi\)
\(98\) 11.9686 1.20901
\(99\) 0.205168 0.0206201
\(100\) −11.1348 −1.11348
\(101\) −6.21352 −0.618268 −0.309134 0.951018i \(-0.600039\pi\)
−0.309134 + 0.951018i \(0.600039\pi\)
\(102\) 1.70536 0.168855
\(103\) 13.9862 1.37810 0.689050 0.724714i \(-0.258028\pi\)
0.689050 + 0.724714i \(0.258028\pi\)
\(104\) 14.7205 1.44347
\(105\) 1.08842 0.106219
\(106\) −18.0827 −1.75635
\(107\) 3.52256 0.340539 0.170269 0.985398i \(-0.445536\pi\)
0.170269 + 0.985398i \(0.445536\pi\)
\(108\) 11.6418 1.12023
\(109\) 12.7414 1.22041 0.610204 0.792244i \(-0.291087\pi\)
0.610204 + 0.792244i \(0.291087\pi\)
\(110\) 0.240008 0.0228839
\(111\) −4.41376 −0.418935
\(112\) −1.23171 −0.116385
\(113\) 15.9631 1.50168 0.750840 0.660484i \(-0.229649\pi\)
0.750840 + 0.660484i \(0.229649\pi\)
\(114\) 1.34752 0.126207
\(115\) −11.4882 −1.07128
\(116\) −24.1761 −2.24469
\(117\) 11.6560 1.07760
\(118\) −24.8657 −2.28907
\(119\) −1.65915 −0.152094
\(120\) 2.65571 0.242432
\(121\) −10.9939 −0.999450
\(122\) 17.2066 1.55781
\(123\) 4.61334 0.415971
\(124\) −6.50723 −0.584366
\(125\) −10.9194 −0.976664
\(126\) −8.38920 −0.747369
\(127\) 9.26656 0.822275 0.411137 0.911573i \(-0.365132\pi\)
0.411137 + 0.911573i \(0.365132\pi\)
\(128\) 19.8405 1.75367
\(129\) −3.17277 −0.279347
\(130\) 13.6353 1.19590
\(131\) 3.55953 0.310997 0.155499 0.987836i \(-0.450302\pi\)
0.155499 + 0.987836i \(0.450302\pi\)
\(132\) 0.160648 0.0139826
\(133\) −1.31101 −0.113679
\(134\) 15.3256 1.32393
\(135\) 4.49478 0.386849
\(136\) −4.04828 −0.347137
\(137\) 21.2859 1.81858 0.909288 0.416167i \(-0.136627\pi\)
0.909288 + 0.416167i \(0.136627\pi\)
\(138\) −12.1740 −1.03632
\(139\) −13.2048 −1.12001 −0.560006 0.828488i \(-0.689201\pi\)
−0.560006 + 0.828488i \(0.689201\pi\)
\(140\) −6.19878 −0.523892
\(141\) 7.76649 0.654057
\(142\) −15.6936 −1.31698
\(143\) 0.343801 0.0287501
\(144\) −2.37966 −0.198305
\(145\) −9.33413 −0.775157
\(146\) −16.0358 −1.32713
\(147\) 3.09302 0.255108
\(148\) 25.1373 2.06627
\(149\) −9.52196 −0.780069 −0.390035 0.920800i \(-0.627537\pi\)
−0.390035 + 0.920800i \(0.627537\pi\)
\(150\) −4.55567 −0.371969
\(151\) −5.51607 −0.448892 −0.224446 0.974487i \(-0.572057\pi\)
−0.224446 + 0.974487i \(0.572057\pi\)
\(152\) −3.19883 −0.259459
\(153\) −3.20550 −0.259149
\(154\) −0.247445 −0.0199397
\(155\) −2.51237 −0.201799
\(156\) 9.12673 0.730723
\(157\) 18.4394 1.47162 0.735812 0.677186i \(-0.236801\pi\)
0.735812 + 0.677186i \(0.236801\pi\)
\(158\) −8.69418 −0.691672
\(159\) −4.67305 −0.370597
\(160\) 6.03676 0.477248
\(161\) 11.8442 0.933456
\(162\) −13.6733 −1.07427
\(163\) −15.0090 −1.17560 −0.587799 0.809007i \(-0.700005\pi\)
−0.587799 + 0.809007i \(0.700005\pi\)
\(164\) −26.2739 −2.05165
\(165\) 0.0620246 0.00482861
\(166\) −9.43057 −0.731954
\(167\) 1.40736 0.108905 0.0544524 0.998516i \(-0.482659\pi\)
0.0544524 + 0.998516i \(0.482659\pi\)
\(168\) −2.73800 −0.211241
\(169\) 6.53201 0.502462
\(170\) −3.74984 −0.287599
\(171\) −2.53289 −0.193695
\(172\) 18.0696 1.37779
\(173\) −18.1572 −1.38047 −0.690234 0.723586i \(-0.742492\pi\)
−0.690234 + 0.723586i \(0.742492\pi\)
\(174\) −9.89133 −0.749860
\(175\) 4.43225 0.335047
\(176\) −0.0701898 −0.00529076
\(177\) −6.42596 −0.483005
\(178\) −26.3406 −1.97431
\(179\) −12.0069 −0.897435 −0.448717 0.893674i \(-0.648119\pi\)
−0.448717 + 0.893674i \(0.648119\pi\)
\(180\) −11.9761 −0.892645
\(181\) −6.56194 −0.487745 −0.243873 0.969807i \(-0.578418\pi\)
−0.243873 + 0.969807i \(0.578418\pi\)
\(182\) −14.0578 −1.04204
\(183\) 4.44664 0.328705
\(184\) 28.8995 2.13050
\(185\) 9.70524 0.713543
\(186\) −2.66235 −0.195213
\(187\) −0.0945484 −0.00691407
\(188\) −44.2318 −3.22594
\(189\) −4.63406 −0.337078
\(190\) −2.96301 −0.214959
\(191\) −2.35110 −0.170119 −0.0850597 0.996376i \(-0.527108\pi\)
−0.0850597 + 0.996376i \(0.527108\pi\)
\(192\) 7.48376 0.540094
\(193\) −5.42724 −0.390662 −0.195331 0.980737i \(-0.562578\pi\)
−0.195331 + 0.980737i \(0.562578\pi\)
\(194\) 31.5344 2.26404
\(195\) 3.52374 0.252340
\(196\) −17.6154 −1.25824
\(197\) −0.545520 −0.0388667 −0.0194334 0.999811i \(-0.506186\pi\)
−0.0194334 + 0.999811i \(0.506186\pi\)
\(198\) −0.478066 −0.0339747
\(199\) −12.7766 −0.905709 −0.452855 0.891584i \(-0.649594\pi\)
−0.452855 + 0.891584i \(0.649594\pi\)
\(200\) 10.8145 0.764704
\(201\) 3.96056 0.279356
\(202\) 14.4782 1.01869
\(203\) 9.62336 0.675427
\(204\) −2.50993 −0.175731
\(205\) −10.1441 −0.708494
\(206\) −32.5895 −2.27062
\(207\) 22.8831 1.59049
\(208\) −3.98762 −0.276492
\(209\) −0.0747093 −0.00516775
\(210\) −2.53615 −0.175011
\(211\) −12.0368 −0.828645 −0.414322 0.910130i \(-0.635981\pi\)
−0.414322 + 0.910130i \(0.635981\pi\)
\(212\) 26.6140 1.82786
\(213\) −4.05565 −0.277888
\(214\) −8.20799 −0.561087
\(215\) 6.97649 0.475792
\(216\) −11.3069 −0.769340
\(217\) 2.59022 0.175836
\(218\) −29.6891 −2.01080
\(219\) −4.14407 −0.280031
\(220\) −0.353243 −0.0238156
\(221\) −5.37148 −0.361325
\(222\) 10.2846 0.690256
\(223\) 8.10464 0.542727 0.271363 0.962477i \(-0.412525\pi\)
0.271363 + 0.962477i \(0.412525\pi\)
\(224\) −6.22381 −0.415846
\(225\) 8.56314 0.570876
\(226\) −37.1959 −2.47423
\(227\) −17.0681 −1.13285 −0.566423 0.824115i \(-0.691673\pi\)
−0.566423 + 0.824115i \(0.691673\pi\)
\(228\) −1.98327 −0.131345
\(229\) 1.22546 0.0809808 0.0404904 0.999180i \(-0.487108\pi\)
0.0404904 + 0.999180i \(0.487108\pi\)
\(230\) 26.7690 1.76510
\(231\) −0.0639465 −0.00420737
\(232\) 23.4807 1.54158
\(233\) −4.88188 −0.319822 −0.159911 0.987131i \(-0.551121\pi\)
−0.159911 + 0.987131i \(0.551121\pi\)
\(234\) −27.1598 −1.77549
\(235\) −17.0774 −1.11401
\(236\) 36.5972 2.38227
\(237\) −2.24681 −0.145946
\(238\) 3.86603 0.250598
\(239\) 11.8024 0.763436 0.381718 0.924279i \(-0.375332\pi\)
0.381718 + 0.924279i \(0.375332\pi\)
\(240\) −0.719400 −0.0464370
\(241\) 23.0757 1.48644 0.743219 0.669048i \(-0.233298\pi\)
0.743219 + 0.669048i \(0.233298\pi\)
\(242\) 25.6172 1.64674
\(243\) −13.7175 −0.879977
\(244\) −25.3246 −1.62124
\(245\) −6.80111 −0.434507
\(246\) −10.7496 −0.685372
\(247\) −4.24438 −0.270063
\(248\) 6.32005 0.401324
\(249\) −2.43711 −0.154446
\(250\) 25.4436 1.60919
\(251\) −11.6615 −0.736065 −0.368033 0.929813i \(-0.619969\pi\)
−0.368033 + 0.929813i \(0.619969\pi\)
\(252\) 12.3472 0.777799
\(253\) 0.674954 0.0424340
\(254\) −21.5922 −1.35482
\(255\) −0.969059 −0.0606848
\(256\) −21.3745 −1.33591
\(257\) 16.3711 1.02120 0.510600 0.859818i \(-0.329423\pi\)
0.510600 + 0.859818i \(0.329423\pi\)
\(258\) 7.39294 0.460265
\(259\) −10.0060 −0.621740
\(260\) −20.0684 −1.24459
\(261\) 18.5924 1.15084
\(262\) −8.29412 −0.512413
\(263\) 22.4755 1.38590 0.692950 0.720986i \(-0.256311\pi\)
0.692950 + 0.720986i \(0.256311\pi\)
\(264\) −0.156027 −0.00960281
\(265\) 10.2754 0.631212
\(266\) 3.05482 0.187303
\(267\) −6.80712 −0.416589
\(268\) −22.5562 −1.37784
\(269\) 2.19773 0.133998 0.0669989 0.997753i \(-0.478658\pi\)
0.0669989 + 0.997753i \(0.478658\pi\)
\(270\) −10.4734 −0.637390
\(271\) 1.07274 0.0651642 0.0325821 0.999469i \(-0.489627\pi\)
0.0325821 + 0.999469i \(0.489627\pi\)
\(272\) 1.09663 0.0664930
\(273\) −3.63292 −0.219874
\(274\) −49.5987 −2.99637
\(275\) 0.252576 0.0152309
\(276\) 17.9177 1.07852
\(277\) 4.69125 0.281870 0.140935 0.990019i \(-0.454989\pi\)
0.140935 + 0.990019i \(0.454989\pi\)
\(278\) 30.7687 1.84538
\(279\) 5.00433 0.299601
\(280\) 6.02048 0.359792
\(281\) 33.3377 1.98876 0.994379 0.105875i \(-0.0337643\pi\)
0.994379 + 0.105875i \(0.0337643\pi\)
\(282\) −18.0969 −1.07765
\(283\) −26.4146 −1.57019 −0.785093 0.619377i \(-0.787385\pi\)
−0.785093 + 0.619377i \(0.787385\pi\)
\(284\) 23.0978 1.37060
\(285\) −0.765721 −0.0453574
\(286\) −0.801098 −0.0473699
\(287\) 10.4584 0.617341
\(288\) −12.0245 −0.708548
\(289\) −15.5228 −0.913106
\(290\) 21.7496 1.27718
\(291\) 8.14934 0.477723
\(292\) 23.6014 1.38117
\(293\) 9.68309 0.565692 0.282846 0.959165i \(-0.408721\pi\)
0.282846 + 0.959165i \(0.408721\pi\)
\(294\) −7.20710 −0.420326
\(295\) 14.1298 0.822668
\(296\) −24.4142 −1.41905
\(297\) −0.264076 −0.0153232
\(298\) 22.1873 1.28528
\(299\) 38.3454 2.21757
\(300\) 6.70501 0.387114
\(301\) −7.19266 −0.414578
\(302\) 12.8531 0.739614
\(303\) 3.74157 0.214948
\(304\) 0.866525 0.0496986
\(305\) −9.77755 −0.559861
\(306\) 7.46920 0.426986
\(307\) 13.7834 0.786658 0.393329 0.919398i \(-0.371323\pi\)
0.393329 + 0.919398i \(0.371323\pi\)
\(308\) 0.364189 0.0207516
\(309\) −8.42200 −0.479111
\(310\) 5.85413 0.332492
\(311\) 17.3375 0.983117 0.491558 0.870845i \(-0.336427\pi\)
0.491558 + 0.870845i \(0.336427\pi\)
\(312\) −8.86421 −0.501837
\(313\) −6.82737 −0.385906 −0.192953 0.981208i \(-0.561806\pi\)
−0.192953 + 0.981208i \(0.561806\pi\)
\(314\) −42.9660 −2.42471
\(315\) 4.76712 0.268597
\(316\) 12.7961 0.719834
\(317\) 25.7736 1.44759 0.723794 0.690016i \(-0.242396\pi\)
0.723794 + 0.690016i \(0.242396\pi\)
\(318\) 10.8888 0.610612
\(319\) 0.548396 0.0307043
\(320\) −16.4557 −0.919904
\(321\) −2.12117 −0.118392
\(322\) −27.5985 −1.53800
\(323\) 1.16724 0.0649471
\(324\) 20.1242 1.11801
\(325\) 14.3493 0.795957
\(326\) 34.9728 1.93697
\(327\) −7.67246 −0.424288
\(328\) 25.5182 1.40901
\(329\) 17.6066 0.970683
\(330\) −0.144525 −0.00795582
\(331\) −12.7055 −0.698355 −0.349178 0.937057i \(-0.613539\pi\)
−0.349178 + 0.937057i \(0.613539\pi\)
\(332\) 13.8799 0.761757
\(333\) −19.3316 −1.05937
\(334\) −3.27932 −0.179436
\(335\) −8.70871 −0.475808
\(336\) 0.741691 0.0404626
\(337\) −13.8969 −0.757014 −0.378507 0.925599i \(-0.623562\pi\)
−0.378507 + 0.925599i \(0.623562\pi\)
\(338\) −15.2204 −0.827878
\(339\) −9.61242 −0.522075
\(340\) 5.51899 0.299309
\(341\) 0.147606 0.00799332
\(342\) 5.90193 0.319140
\(343\) 16.5676 0.894566
\(344\) −17.5498 −0.946224
\(345\) 6.91783 0.372444
\(346\) 42.3085 2.27452
\(347\) 13.6074 0.730483 0.365242 0.930913i \(-0.380986\pi\)
0.365242 + 0.930913i \(0.380986\pi\)
\(348\) 14.5580 0.780391
\(349\) −10.3719 −0.555197 −0.277599 0.960697i \(-0.589539\pi\)
−0.277599 + 0.960697i \(0.589539\pi\)
\(350\) −10.3277 −0.552037
\(351\) −15.0027 −0.800782
\(352\) −0.354670 −0.0189039
\(353\) 2.15599 0.114752 0.0573760 0.998353i \(-0.481727\pi\)
0.0573760 + 0.998353i \(0.481727\pi\)
\(354\) 14.9733 0.795820
\(355\) 8.91780 0.473308
\(356\) 38.7680 2.05470
\(357\) 0.999086 0.0528773
\(358\) 27.9774 1.47865
\(359\) 35.7983 1.88936 0.944680 0.327993i \(-0.106372\pi\)
0.944680 + 0.327993i \(0.106372\pi\)
\(360\) 11.6316 0.613039
\(361\) −18.0777 −0.951457
\(362\) 15.2901 0.803630
\(363\) 6.62018 0.347469
\(364\) 20.6903 1.08446
\(365\) 9.11224 0.476956
\(366\) −10.3612 −0.541589
\(367\) −22.5101 −1.17502 −0.587509 0.809218i \(-0.699891\pi\)
−0.587509 + 0.809218i \(0.699891\pi\)
\(368\) −7.82853 −0.408090
\(369\) 20.2057 1.05187
\(370\) −22.6144 −1.17567
\(371\) −10.5938 −0.550002
\(372\) 3.91843 0.203161
\(373\) −4.74914 −0.245901 −0.122951 0.992413i \(-0.539236\pi\)
−0.122951 + 0.992413i \(0.539236\pi\)
\(374\) 0.220309 0.0113919
\(375\) 6.57531 0.339548
\(376\) 42.9595 2.21547
\(377\) 31.1554 1.60459
\(378\) 10.7979 0.555384
\(379\) 7.76279 0.398748 0.199374 0.979923i \(-0.436109\pi\)
0.199374 + 0.979923i \(0.436109\pi\)
\(380\) 4.36094 0.223712
\(381\) −5.58001 −0.285872
\(382\) 5.47834 0.280296
\(383\) 5.15905 0.263615 0.131808 0.991275i \(-0.457922\pi\)
0.131808 + 0.991275i \(0.457922\pi\)
\(384\) −11.9473 −0.609681
\(385\) 0.140609 0.00716612
\(386\) 12.6461 0.643671
\(387\) −13.8963 −0.706387
\(388\) −46.4122 −2.35622
\(389\) 21.9624 1.11354 0.556768 0.830668i \(-0.312041\pi\)
0.556768 + 0.830668i \(0.312041\pi\)
\(390\) −8.21073 −0.415766
\(391\) −10.5453 −0.533301
\(392\) 17.1087 0.864119
\(393\) −2.14342 −0.108121
\(394\) 1.27113 0.0640385
\(395\) 4.94042 0.248580
\(396\) 0.703615 0.0353580
\(397\) 35.4778 1.78058 0.890291 0.455392i \(-0.150501\pi\)
0.890291 + 0.455392i \(0.150501\pi\)
\(398\) 29.7710 1.49229
\(399\) 0.789448 0.0395218
\(400\) −2.92953 −0.146476
\(401\) 10.8155 0.540099 0.270049 0.962846i \(-0.412960\pi\)
0.270049 + 0.962846i \(0.412960\pi\)
\(402\) −9.22857 −0.460279
\(403\) 8.38579 0.417726
\(404\) −21.3090 −1.06016
\(405\) 7.76976 0.386082
\(406\) −22.4236 −1.11286
\(407\) −0.570199 −0.0282637
\(408\) 2.43774 0.120686
\(409\) −0.103382 −0.00511192 −0.00255596 0.999997i \(-0.500814\pi\)
−0.00255596 + 0.999997i \(0.500814\pi\)
\(410\) 23.6369 1.16735
\(411\) −12.8176 −0.632247
\(412\) 47.9651 2.36307
\(413\) −14.5676 −0.716826
\(414\) −53.3205 −2.62056
\(415\) 5.35887 0.263057
\(416\) −20.1495 −0.987908
\(417\) 7.95145 0.389384
\(418\) 0.174082 0.00851461
\(419\) −13.3064 −0.650062 −0.325031 0.945703i \(-0.605375\pi\)
−0.325031 + 0.945703i \(0.605375\pi\)
\(420\) 3.73269 0.182137
\(421\) 20.6781 1.00779 0.503894 0.863765i \(-0.331900\pi\)
0.503894 + 0.863765i \(0.331900\pi\)
\(422\) 28.0471 1.36531
\(423\) 34.0161 1.65392
\(424\) −25.8485 −1.25531
\(425\) −3.94619 −0.191418
\(426\) 9.45014 0.457861
\(427\) 10.0805 0.487831
\(428\) 12.0805 0.583932
\(429\) −0.207025 −0.00999528
\(430\) −16.2561 −0.783936
\(431\) 12.7856 0.615860 0.307930 0.951409i \(-0.400364\pi\)
0.307930 + 0.951409i \(0.400364\pi\)
\(432\) 3.06291 0.147365
\(433\) 38.3209 1.84158 0.920792 0.390053i \(-0.127543\pi\)
0.920792 + 0.390053i \(0.127543\pi\)
\(434\) −6.03553 −0.289715
\(435\) 5.62069 0.269492
\(436\) 43.6963 2.09267
\(437\) −8.33260 −0.398603
\(438\) 9.65619 0.461391
\(439\) −40.3093 −1.92386 −0.961930 0.273297i \(-0.911886\pi\)
−0.961930 + 0.273297i \(0.911886\pi\)
\(440\) 0.343082 0.0163558
\(441\) 13.5469 0.645093
\(442\) 12.5162 0.595334
\(443\) −7.67688 −0.364740 −0.182370 0.983230i \(-0.558377\pi\)
−0.182370 + 0.983230i \(0.558377\pi\)
\(444\) −15.1368 −0.718361
\(445\) 14.9679 0.709547
\(446\) −18.8848 −0.894221
\(447\) 5.73380 0.271199
\(448\) 16.9656 0.801551
\(449\) −28.6328 −1.35126 −0.675632 0.737239i \(-0.736129\pi\)
−0.675632 + 0.737239i \(0.736129\pi\)
\(450\) −19.9531 −0.940600
\(451\) 0.595982 0.0280637
\(452\) 54.7448 2.57498
\(453\) 3.32159 0.156062
\(454\) 39.7706 1.86653
\(455\) 7.98829 0.374497
\(456\) 1.92623 0.0902038
\(457\) −9.94190 −0.465062 −0.232531 0.972589i \(-0.574701\pi\)
−0.232531 + 0.972589i \(0.574701\pi\)
\(458\) −2.85547 −0.133427
\(459\) 4.12587 0.192579
\(460\) −39.3985 −1.83696
\(461\) −10.3989 −0.484327 −0.242163 0.970235i \(-0.577857\pi\)
−0.242163 + 0.970235i \(0.577857\pi\)
\(462\) 0.149003 0.00693225
\(463\) 7.32945 0.340628 0.170314 0.985390i \(-0.445522\pi\)
0.170314 + 0.985390i \(0.445522\pi\)
\(464\) −6.36063 −0.295285
\(465\) 1.51287 0.0701574
\(466\) 11.3754 0.526953
\(467\) −5.35459 −0.247781 −0.123890 0.992296i \(-0.539537\pi\)
−0.123890 + 0.992296i \(0.539537\pi\)
\(468\) 39.9737 1.84779
\(469\) 8.97856 0.414591
\(470\) 39.7925 1.83549
\(471\) −11.1036 −0.511625
\(472\) −35.5445 −1.63607
\(473\) −0.409880 −0.0188463
\(474\) 5.23534 0.240467
\(475\) −3.11816 −0.143071
\(476\) −5.69001 −0.260801
\(477\) −20.4673 −0.937132
\(478\) −27.5011 −1.25787
\(479\) 31.7796 1.45205 0.726023 0.687671i \(-0.241367\pi\)
0.726023 + 0.687671i \(0.241367\pi\)
\(480\) −3.63513 −0.165920
\(481\) −32.3941 −1.47704
\(482\) −53.7692 −2.44912
\(483\) −7.13219 −0.324526
\(484\) −37.7033 −1.71379
\(485\) −17.9193 −0.813672
\(486\) 31.9634 1.44989
\(487\) 3.14020 0.142296 0.0711481 0.997466i \(-0.477334\pi\)
0.0711481 + 0.997466i \(0.477334\pi\)
\(488\) 24.5961 1.11341
\(489\) 9.03792 0.408709
\(490\) 15.8474 0.715913
\(491\) 23.5419 1.06243 0.531215 0.847237i \(-0.321736\pi\)
0.531215 + 0.847237i \(0.321736\pi\)
\(492\) 15.8213 0.713278
\(493\) −8.56802 −0.385884
\(494\) 9.88991 0.444968
\(495\) 0.271658 0.0122101
\(496\) −1.71203 −0.0768723
\(497\) −9.19413 −0.412413
\(498\) 5.67877 0.254472
\(499\) −5.86590 −0.262594 −0.131297 0.991343i \(-0.541914\pi\)
−0.131297 + 0.991343i \(0.541914\pi\)
\(500\) −37.4478 −1.67471
\(501\) −0.847464 −0.0378619
\(502\) 27.1726 1.21277
\(503\) 28.3501 1.26407 0.632034 0.774941i \(-0.282220\pi\)
0.632034 + 0.774941i \(0.282220\pi\)
\(504\) −11.9920 −0.534167
\(505\) −8.22719 −0.366105
\(506\) −1.57272 −0.0699161
\(507\) −3.93335 −0.174686
\(508\) 31.7793 1.40998
\(509\) −21.0958 −0.935054 −0.467527 0.883979i \(-0.654855\pi\)
−0.467527 + 0.883979i \(0.654855\pi\)
\(510\) 2.25802 0.0999870
\(511\) −9.39459 −0.415592
\(512\) 10.1243 0.447436
\(513\) 3.26013 0.143938
\(514\) −38.1466 −1.68257
\(515\) 18.5188 0.816036
\(516\) −10.8809 −0.479005
\(517\) 1.00333 0.0441263
\(518\) 23.3151 1.02441
\(519\) 10.9337 0.479934
\(520\) 19.4912 0.854744
\(521\) −14.4116 −0.631384 −0.315692 0.948862i \(-0.602237\pi\)
−0.315692 + 0.948862i \(0.602237\pi\)
\(522\) −43.3225 −1.89618
\(523\) 26.7550 1.16991 0.584956 0.811065i \(-0.301112\pi\)
0.584956 + 0.811065i \(0.301112\pi\)
\(524\) 12.2073 0.533276
\(525\) −2.66895 −0.116483
\(526\) −52.3707 −2.28347
\(527\) −2.30617 −0.100458
\(528\) 0.0422659 0.00183939
\(529\) 52.2801 2.27305
\(530\) −23.9429 −1.04001
\(531\) −28.1447 −1.22138
\(532\) −4.49607 −0.194929
\(533\) 33.8589 1.46659
\(534\) 15.8614 0.686391
\(535\) 4.66415 0.201649
\(536\) 21.9074 0.946255
\(537\) 7.23012 0.312003
\(538\) −5.12097 −0.220781
\(539\) 0.399576 0.0172110
\(540\) 15.4147 0.663342
\(541\) 17.0096 0.731300 0.365650 0.930752i \(-0.380847\pi\)
0.365650 + 0.930752i \(0.380847\pi\)
\(542\) −2.49961 −0.107367
\(543\) 3.95138 0.169570
\(544\) 5.54128 0.237581
\(545\) 16.8707 0.722660
\(546\) 8.46515 0.362275
\(547\) −27.9256 −1.19401 −0.597005 0.802237i \(-0.703643\pi\)
−0.597005 + 0.802237i \(0.703643\pi\)
\(548\) 72.9991 3.11837
\(549\) 19.4756 0.831200
\(550\) −0.588532 −0.0250951
\(551\) −6.77019 −0.288420
\(552\) −17.4023 −0.740691
\(553\) −5.09351 −0.216598
\(554\) −10.9312 −0.464421
\(555\) −5.84416 −0.248071
\(556\) −45.2852 −1.92052
\(557\) 30.8316 1.30638 0.653189 0.757195i \(-0.273431\pi\)
0.653189 + 0.757195i \(0.273431\pi\)
\(558\) −11.6607 −0.493636
\(559\) −23.2861 −0.984896
\(560\) −1.63087 −0.0689170
\(561\) 0.0569338 0.00240375
\(562\) −77.6808 −3.27677
\(563\) 12.2705 0.517139 0.258569 0.965993i \(-0.416749\pi\)
0.258569 + 0.965993i \(0.416749\pi\)
\(564\) 26.6349 1.12153
\(565\) 21.1364 0.889214
\(566\) 61.5493 2.58711
\(567\) −8.01051 −0.336410
\(568\) −22.4334 −0.941283
\(569\) 31.8746 1.33625 0.668127 0.744047i \(-0.267096\pi\)
0.668127 + 0.744047i \(0.267096\pi\)
\(570\) 1.78422 0.0747328
\(571\) −41.8752 −1.75242 −0.876212 0.481927i \(-0.839937\pi\)
−0.876212 + 0.481927i \(0.839937\pi\)
\(572\) 1.17905 0.0492987
\(573\) 1.41575 0.0591438
\(574\) −24.3694 −1.01716
\(575\) 28.1707 1.17480
\(576\) 32.7777 1.36574
\(577\) −33.2442 −1.38398 −0.691988 0.721909i \(-0.743265\pi\)
−0.691988 + 0.721909i \(0.743265\pi\)
\(578\) 36.1700 1.50447
\(579\) 3.26810 0.135818
\(580\) −32.0110 −1.32919
\(581\) −5.52492 −0.229212
\(582\) −18.9889 −0.787117
\(583\) −0.603696 −0.0250026
\(584\) −22.9225 −0.948539
\(585\) 15.4334 0.638094
\(586\) −22.5628 −0.932059
\(587\) −37.7145 −1.55664 −0.778322 0.627865i \(-0.783929\pi\)
−0.778322 + 0.627865i \(0.783929\pi\)
\(588\) 10.6074 0.437441
\(589\) −1.82226 −0.0750850
\(590\) −32.9241 −1.35546
\(591\) 0.328494 0.0135124
\(592\) 6.61352 0.271814
\(593\) 32.4179 1.33124 0.665621 0.746290i \(-0.268167\pi\)
0.665621 + 0.746290i \(0.268167\pi\)
\(594\) 0.615328 0.0252472
\(595\) −2.19685 −0.0900621
\(596\) −32.6552 −1.33761
\(597\) 7.69363 0.314879
\(598\) −89.3494 −3.65377
\(599\) −18.3584 −0.750105 −0.375052 0.927004i \(-0.622375\pi\)
−0.375052 + 0.927004i \(0.622375\pi\)
\(600\) −6.51215 −0.265857
\(601\) −37.7899 −1.54148 −0.770741 0.637149i \(-0.780114\pi\)
−0.770741 + 0.637149i \(0.780114\pi\)
\(602\) 16.7598 0.683077
\(603\) 17.3466 0.706410
\(604\) −18.9172 −0.769728
\(605\) −14.5569 −0.591820
\(606\) −8.71830 −0.354157
\(607\) 24.8244 1.00759 0.503795 0.863823i \(-0.331937\pi\)
0.503795 + 0.863823i \(0.331937\pi\)
\(608\) 4.37855 0.177574
\(609\) −5.79486 −0.234820
\(610\) 22.7829 0.922451
\(611\) 57.0010 2.30601
\(612\) −10.9931 −0.444371
\(613\) −31.0163 −1.25274 −0.626368 0.779527i \(-0.715459\pi\)
−0.626368 + 0.779527i \(0.715459\pi\)
\(614\) −32.1169 −1.29613
\(615\) 6.10842 0.246315
\(616\) −0.353713 −0.0142515
\(617\) 35.0353 1.41047 0.705234 0.708975i \(-0.250842\pi\)
0.705234 + 0.708975i \(0.250842\pi\)
\(618\) 19.6243 0.789404
\(619\) 10.8811 0.437348 0.218674 0.975798i \(-0.429827\pi\)
0.218674 + 0.975798i \(0.429827\pi\)
\(620\) −8.61608 −0.346030
\(621\) −29.4534 −1.18192
\(622\) −40.3983 −1.61983
\(623\) −15.4317 −0.618258
\(624\) 2.40121 0.0961253
\(625\) 1.77589 0.0710357
\(626\) 15.9086 0.635835
\(627\) 0.0449874 0.00179662
\(628\) 63.2371 2.52344
\(629\) 8.90867 0.355212
\(630\) −11.1080 −0.442552
\(631\) 5.71731 0.227603 0.113801 0.993504i \(-0.463697\pi\)
0.113801 + 0.993504i \(0.463697\pi\)
\(632\) −12.4280 −0.494359
\(633\) 7.24812 0.288087
\(634\) −60.0556 −2.38511
\(635\) 12.2697 0.486907
\(636\) −16.0261 −0.635474
\(637\) 22.7007 0.899435
\(638\) −1.27783 −0.0505897
\(639\) −17.7631 −0.702698
\(640\) 26.2703 1.03843
\(641\) −4.21327 −0.166414 −0.0832072 0.996532i \(-0.526516\pi\)
−0.0832072 + 0.996532i \(0.526516\pi\)
\(642\) 4.94257 0.195068
\(643\) −29.4539 −1.16155 −0.580774 0.814065i \(-0.697250\pi\)
−0.580774 + 0.814065i \(0.697250\pi\)
\(644\) 40.6193 1.60062
\(645\) −4.20100 −0.165414
\(646\) −2.71981 −0.107010
\(647\) 11.1428 0.438067 0.219034 0.975717i \(-0.429710\pi\)
0.219034 + 0.975717i \(0.429710\pi\)
\(648\) −19.5454 −0.767815
\(649\) −0.830149 −0.0325862
\(650\) −33.4356 −1.31145
\(651\) −1.55974 −0.0611311
\(652\) −51.4728 −2.01583
\(653\) 5.72977 0.224223 0.112112 0.993696i \(-0.464239\pi\)
0.112112 + 0.993696i \(0.464239\pi\)
\(654\) 17.8778 0.699075
\(655\) 4.71309 0.184156
\(656\) −6.91257 −0.269890
\(657\) −18.1504 −0.708115
\(658\) −41.0255 −1.59934
\(659\) −12.3162 −0.479771 −0.239886 0.970801i \(-0.577110\pi\)
−0.239886 + 0.970801i \(0.577110\pi\)
\(660\) 0.212711 0.00827976
\(661\) 34.8939 1.35721 0.678607 0.734502i \(-0.262584\pi\)
0.678607 + 0.734502i \(0.262584\pi\)
\(662\) 29.6053 1.15064
\(663\) 3.23452 0.125618
\(664\) −13.4806 −0.523150
\(665\) −1.73589 −0.0673147
\(666\) 45.0450 1.74546
\(667\) 61.1646 2.36830
\(668\) 4.82648 0.186742
\(669\) −4.88034 −0.188685
\(670\) 20.2923 0.783962
\(671\) 0.574447 0.0221763
\(672\) 3.74777 0.144573
\(673\) 0.911582 0.0351389 0.0175694 0.999846i \(-0.494407\pi\)
0.0175694 + 0.999846i \(0.494407\pi\)
\(674\) 32.3815 1.24729
\(675\) −11.0218 −0.424229
\(676\) 22.4013 0.861587
\(677\) 20.8095 0.799774 0.399887 0.916564i \(-0.369049\pi\)
0.399887 + 0.916564i \(0.369049\pi\)
\(678\) 22.3981 0.860194
\(679\) 18.4745 0.708987
\(680\) −5.36024 −0.205556
\(681\) 10.2778 0.393846
\(682\) −0.343940 −0.0131701
\(683\) 23.1134 0.884410 0.442205 0.896914i \(-0.354196\pi\)
0.442205 + 0.896914i \(0.354196\pi\)
\(684\) −8.68644 −0.332134
\(685\) 28.1842 1.07686
\(686\) −38.6045 −1.47393
\(687\) −0.737931 −0.0281538
\(688\) 4.75404 0.181246
\(689\) −34.2972 −1.30662
\(690\) −16.1194 −0.613654
\(691\) 23.7898 0.905005 0.452503 0.891763i \(-0.350531\pi\)
0.452503 + 0.891763i \(0.350531\pi\)
\(692\) −62.2695 −2.36713
\(693\) −0.280076 −0.0106392
\(694\) −31.7069 −1.20358
\(695\) −17.4841 −0.663211
\(696\) −14.1393 −0.535947
\(697\) −9.31150 −0.352698
\(698\) 24.1679 0.914767
\(699\) 2.93970 0.111190
\(700\) 15.2002 0.574515
\(701\) 10.7114 0.404565 0.202283 0.979327i \(-0.435164\pi\)
0.202283 + 0.979327i \(0.435164\pi\)
\(702\) 34.9580 1.31940
\(703\) 7.03936 0.265494
\(704\) 0.966802 0.0364377
\(705\) 10.2834 0.387297
\(706\) −5.02372 −0.189070
\(707\) 8.48212 0.319003
\(708\) −22.0376 −0.828223
\(709\) 22.3840 0.840648 0.420324 0.907374i \(-0.361916\pi\)
0.420324 + 0.907374i \(0.361916\pi\)
\(710\) −20.7795 −0.779842
\(711\) −9.84069 −0.369055
\(712\) −37.6529 −1.41110
\(713\) 16.4631 0.616546
\(714\) −2.32799 −0.0871229
\(715\) 0.455220 0.0170243
\(716\) −41.1770 −1.53886
\(717\) −7.10703 −0.265417
\(718\) −83.4143 −3.11299
\(719\) −12.4489 −0.464267 −0.232134 0.972684i \(-0.574571\pi\)
−0.232134 + 0.972684i \(0.574571\pi\)
\(720\) −3.15086 −0.117426
\(721\) −19.0926 −0.711047
\(722\) 42.1232 1.56766
\(723\) −13.8954 −0.516776
\(724\) −22.5039 −0.836351
\(725\) 22.8885 0.850058
\(726\) −15.4258 −0.572506
\(727\) 42.6429 1.58154 0.790768 0.612116i \(-0.209681\pi\)
0.790768 + 0.612116i \(0.209681\pi\)
\(728\) −20.0951 −0.744774
\(729\) −9.34395 −0.346072
\(730\) −21.2326 −0.785854
\(731\) 6.40388 0.236856
\(732\) 15.2496 0.563641
\(733\) 33.0759 1.22169 0.610843 0.791751i \(-0.290830\pi\)
0.610843 + 0.791751i \(0.290830\pi\)
\(734\) 52.4512 1.93601
\(735\) 4.09540 0.151061
\(736\) −39.5576 −1.45811
\(737\) 0.511651 0.0188469
\(738\) −47.0818 −1.73310
\(739\) 4.68863 0.172474 0.0862371 0.996275i \(-0.472516\pi\)
0.0862371 + 0.996275i \(0.472516\pi\)
\(740\) 33.2837 1.22353
\(741\) 2.55582 0.0938904
\(742\) 24.6848 0.906207
\(743\) −16.3647 −0.600362 −0.300181 0.953882i \(-0.597047\pi\)
−0.300181 + 0.953882i \(0.597047\pi\)
\(744\) −3.80572 −0.139524
\(745\) −12.6078 −0.461915
\(746\) 11.0661 0.405158
\(747\) −10.6742 −0.390548
\(748\) −0.324250 −0.0118558
\(749\) −4.80867 −0.175705
\(750\) −15.3213 −0.559453
\(751\) −38.3167 −1.39820 −0.699098 0.715026i \(-0.746415\pi\)
−0.699098 + 0.715026i \(0.746415\pi\)
\(752\) −11.6372 −0.424366
\(753\) 7.02214 0.255901
\(754\) −72.5959 −2.64379
\(755\) −7.30371 −0.265809
\(756\) −15.8923 −0.577998
\(757\) 11.8814 0.431836 0.215918 0.976411i \(-0.430726\pi\)
0.215918 + 0.976411i \(0.430726\pi\)
\(758\) −18.0882 −0.656994
\(759\) −0.406434 −0.0147526
\(760\) −4.23550 −0.153638
\(761\) −32.5677 −1.18058 −0.590289 0.807192i \(-0.700986\pi\)
−0.590289 + 0.807192i \(0.700986\pi\)
\(762\) 13.0021 0.471016
\(763\) −17.3934 −0.629684
\(764\) −8.06299 −0.291709
\(765\) −4.24433 −0.153454
\(766\) −12.0212 −0.434344
\(767\) −47.1623 −1.70293
\(768\) 12.8710 0.464443
\(769\) 10.4032 0.375150 0.187575 0.982250i \(-0.439937\pi\)
0.187575 + 0.982250i \(0.439937\pi\)
\(770\) −0.327637 −0.0118072
\(771\) −9.85811 −0.355031
\(772\) −18.6125 −0.669879
\(773\) 6.61323 0.237861 0.118931 0.992903i \(-0.462053\pi\)
0.118931 + 0.992903i \(0.462053\pi\)
\(774\) 32.3800 1.16387
\(775\) 6.16067 0.221298
\(776\) 45.0772 1.61818
\(777\) 6.02525 0.216155
\(778\) −51.1750 −1.83471
\(779\) −7.35766 −0.263616
\(780\) 12.0845 0.432695
\(781\) −0.523936 −0.0187479
\(782\) 24.5719 0.878689
\(783\) −23.9307 −0.855212
\(784\) −4.63454 −0.165519
\(785\) 24.4152 0.871416
\(786\) 4.99444 0.178146
\(787\) −17.2256 −0.614025 −0.307013 0.951705i \(-0.599329\pi\)
−0.307013 + 0.951705i \(0.599329\pi\)
\(788\) −1.87084 −0.0666459
\(789\) −13.5340 −0.481823
\(790\) −11.5118 −0.409571
\(791\) −21.7913 −0.774810
\(792\) −0.683376 −0.0242827
\(793\) 32.6355 1.15892
\(794\) −82.6676 −2.93376
\(795\) −6.18749 −0.219448
\(796\) −43.8168 −1.55305
\(797\) −1.88961 −0.0669334 −0.0334667 0.999440i \(-0.510655\pi\)
−0.0334667 + 0.999440i \(0.510655\pi\)
\(798\) −1.83951 −0.0651179
\(799\) −15.6758 −0.554569
\(800\) −14.8029 −0.523362
\(801\) −29.8142 −1.05343
\(802\) −25.2013 −0.889891
\(803\) −0.535359 −0.0188924
\(804\) 13.5826 0.479020
\(805\) 15.6827 0.552742
\(806\) −19.5399 −0.688263
\(807\) −1.32340 −0.0465858
\(808\) 20.6961 0.728086
\(809\) 10.6848 0.375656 0.187828 0.982202i \(-0.439855\pi\)
0.187828 + 0.982202i \(0.439855\pi\)
\(810\) −18.1045 −0.636126
\(811\) −28.0525 −0.985056 −0.492528 0.870297i \(-0.663927\pi\)
−0.492528 + 0.870297i \(0.663927\pi\)
\(812\) 33.0029 1.15818
\(813\) −0.645967 −0.0226550
\(814\) 1.32863 0.0465685
\(815\) −19.8731 −0.696125
\(816\) −0.660354 −0.0231170
\(817\) 5.06015 0.177032
\(818\) 0.240893 0.00842262
\(819\) −15.9117 −0.555998
\(820\) −34.7887 −1.21488
\(821\) −35.8701 −1.25188 −0.625938 0.779873i \(-0.715284\pi\)
−0.625938 + 0.779873i \(0.715284\pi\)
\(822\) 29.8666 1.04172
\(823\) 9.41093 0.328044 0.164022 0.986457i \(-0.447553\pi\)
0.164022 + 0.986457i \(0.447553\pi\)
\(824\) −46.5854 −1.62288
\(825\) −0.152092 −0.00529518
\(826\) 33.9443 1.18107
\(827\) −20.2417 −0.703873 −0.351936 0.936024i \(-0.614477\pi\)
−0.351936 + 0.936024i \(0.614477\pi\)
\(828\) 78.4768 2.72726
\(829\) 33.2249 1.15395 0.576975 0.816762i \(-0.304233\pi\)
0.576975 + 0.816762i \(0.304233\pi\)
\(830\) −12.4868 −0.433424
\(831\) −2.82491 −0.0979951
\(832\) 54.9259 1.90421
\(833\) −6.24290 −0.216304
\(834\) −18.5278 −0.641567
\(835\) 1.86346 0.0644875
\(836\) −0.256213 −0.00886130
\(837\) −6.44117 −0.222640
\(838\) 31.0056 1.07107
\(839\) 0.321810 0.0111101 0.00555506 0.999985i \(-0.498232\pi\)
0.00555506 + 0.999985i \(0.498232\pi\)
\(840\) −3.62532 −0.125086
\(841\) 20.6959 0.713650
\(842\) −48.1824 −1.66048
\(843\) −20.0748 −0.691413
\(844\) −41.2796 −1.42090
\(845\) 8.64889 0.297531
\(846\) −79.2615 −2.72507
\(847\) 15.0079 0.515678
\(848\) 7.00205 0.240451
\(849\) 15.9060 0.545892
\(850\) 9.19510 0.315389
\(851\) −63.5964 −2.18006
\(852\) −13.9087 −0.476503
\(853\) 52.4751 1.79671 0.898356 0.439269i \(-0.144762\pi\)
0.898356 + 0.439269i \(0.144762\pi\)
\(854\) −23.4888 −0.803771
\(855\) −3.35374 −0.114696
\(856\) −11.7330 −0.401026
\(857\) −23.3983 −0.799271 −0.399635 0.916674i \(-0.630863\pi\)
−0.399635 + 0.916674i \(0.630863\pi\)
\(858\) 0.482394 0.0164687
\(859\) 8.59949 0.293411 0.146705 0.989180i \(-0.453133\pi\)
0.146705 + 0.989180i \(0.453133\pi\)
\(860\) 23.9256 0.815856
\(861\) −6.29770 −0.214625
\(862\) −29.7919 −1.01472
\(863\) 5.71337 0.194485 0.0972427 0.995261i \(-0.468998\pi\)
0.0972427 + 0.995261i \(0.468998\pi\)
\(864\) 15.4769 0.526536
\(865\) −24.0416 −0.817438
\(866\) −89.2923 −3.03428
\(867\) 9.34730 0.317451
\(868\) 8.88306 0.301511
\(869\) −0.290258 −0.00984633
\(870\) −13.0969 −0.444026
\(871\) 29.0679 0.984928
\(872\) −42.4394 −1.43718
\(873\) 35.6929 1.20802
\(874\) 19.4160 0.656755
\(875\) 14.9062 0.503921
\(876\) −14.2119 −0.480177
\(877\) −46.9371 −1.58495 −0.792477 0.609902i \(-0.791209\pi\)
−0.792477 + 0.609902i \(0.791209\pi\)
\(878\) 93.9256 3.16984
\(879\) −5.83083 −0.196669
\(880\) −0.0929369 −0.00313290
\(881\) 4.32732 0.145791 0.0728955 0.997340i \(-0.476776\pi\)
0.0728955 + 0.997340i \(0.476776\pi\)
\(882\) −31.5660 −1.06288
\(883\) −33.9603 −1.14285 −0.571427 0.820653i \(-0.693610\pi\)
−0.571427 + 0.820653i \(0.693610\pi\)
\(884\) −18.4213 −0.619574
\(885\) −8.50848 −0.286009
\(886\) 17.8881 0.600961
\(887\) −45.0169 −1.51152 −0.755759 0.654850i \(-0.772732\pi\)
−0.755759 + 0.654850i \(0.772732\pi\)
\(888\) 14.7014 0.493347
\(889\) −12.6498 −0.424262
\(890\) −34.8770 −1.16908
\(891\) −0.456486 −0.0152929
\(892\) 27.7945 0.930630
\(893\) −12.3865 −0.414499
\(894\) −13.3604 −0.446840
\(895\) −15.8980 −0.531412
\(896\) −27.0844 −0.904825
\(897\) −23.0903 −0.770963
\(898\) 66.7178 2.22640
\(899\) 13.3761 0.446119
\(900\) 29.3669 0.978898
\(901\) 9.43203 0.314226
\(902\) −1.38871 −0.0462390
\(903\) 4.33117 0.144132
\(904\) −53.1701 −1.76841
\(905\) −8.68852 −0.288816
\(906\) −7.73971 −0.257135
\(907\) −12.5106 −0.415409 −0.207705 0.978192i \(-0.566599\pi\)
−0.207705 + 0.978192i \(0.566599\pi\)
\(908\) −58.5342 −1.94253
\(909\) 16.3875 0.543539
\(910\) −18.6137 −0.617037
\(911\) −45.6519 −1.51251 −0.756257 0.654275i \(-0.772974\pi\)
−0.756257 + 0.654275i \(0.772974\pi\)
\(912\) −0.521792 −0.0172782
\(913\) −0.314843 −0.0104198
\(914\) 23.1658 0.766257
\(915\) 5.88771 0.194642
\(916\) 4.20267 0.138860
\(917\) −4.85913 −0.160463
\(918\) −9.61376 −0.317301
\(919\) 19.9639 0.658547 0.329274 0.944235i \(-0.393196\pi\)
0.329274 + 0.944235i \(0.393196\pi\)
\(920\) 38.2652 1.26157
\(921\) −8.29987 −0.273490
\(922\) 24.2308 0.797998
\(923\) −29.7658 −0.979753
\(924\) −0.219302 −0.00721450
\(925\) −23.7985 −0.782491
\(926\) −17.0785 −0.561234
\(927\) −36.8871 −1.21153
\(928\) −32.1403 −1.05506
\(929\) 1.14632 0.0376096 0.0188048 0.999823i \(-0.494014\pi\)
0.0188048 + 0.999823i \(0.494014\pi\)
\(930\) −3.52516 −0.115594
\(931\) −4.93295 −0.161671
\(932\) −16.7422 −0.548409
\(933\) −10.4400 −0.341791
\(934\) 12.4768 0.408255
\(935\) −0.125190 −0.00409414
\(936\) −38.8239 −1.26900
\(937\) −31.0541 −1.01449 −0.507246 0.861801i \(-0.669336\pi\)
−0.507246 + 0.861801i \(0.669336\pi\)
\(938\) −20.9211 −0.683099
\(939\) 4.11121 0.134164
\(940\) −58.5664 −1.91022
\(941\) −15.5178 −0.505865 −0.252932 0.967484i \(-0.581395\pi\)
−0.252932 + 0.967484i \(0.581395\pi\)
\(942\) 25.8726 0.842976
\(943\) 66.4721 2.16463
\(944\) 9.62858 0.313384
\(945\) −6.13585 −0.199599
\(946\) 0.955070 0.0310520
\(947\) 51.2678 1.66598 0.832990 0.553288i \(-0.186627\pi\)
0.832990 + 0.553288i \(0.186627\pi\)
\(948\) −7.70535 −0.250258
\(949\) −30.4148 −0.987306
\(950\) 7.26569 0.235730
\(951\) −15.5200 −0.503270
\(952\) 5.52634 0.179110
\(953\) −41.7626 −1.35282 −0.676411 0.736524i \(-0.736466\pi\)
−0.676411 + 0.736524i \(0.736466\pi\)
\(954\) 47.6912 1.54406
\(955\) −3.11304 −0.100736
\(956\) 40.4760 1.30909
\(957\) −0.330225 −0.0106747
\(958\) −74.0502 −2.39245
\(959\) −29.0575 −0.938316
\(960\) 9.90909 0.319814
\(961\) −27.3997 −0.883861
\(962\) 75.4821 2.43364
\(963\) −9.29039 −0.299379
\(964\) 79.1373 2.54884
\(965\) −7.18610 −0.231329
\(966\) 16.6189 0.534703
\(967\) 38.4958 1.23794 0.618971 0.785414i \(-0.287550\pi\)
0.618971 + 0.785414i \(0.287550\pi\)
\(968\) 36.6188 1.17697
\(969\) −0.702873 −0.0225795
\(970\) 41.7540 1.34064
\(971\) 58.0340 1.86240 0.931200 0.364509i \(-0.118763\pi\)
0.931200 + 0.364509i \(0.118763\pi\)
\(972\) −47.0436 −1.50892
\(973\) 18.0259 0.577884
\(974\) −7.31705 −0.234453
\(975\) −8.64067 −0.276723
\(976\) −6.66280 −0.213271
\(977\) −18.3580 −0.587324 −0.293662 0.955909i \(-0.594874\pi\)
−0.293662 + 0.955909i \(0.594874\pi\)
\(978\) −21.0594 −0.673407
\(979\) −0.879390 −0.0281054
\(980\) −23.3241 −0.745062
\(981\) −33.6042 −1.07290
\(982\) −54.8554 −1.75051
\(983\) 62.4558 1.99203 0.996015 0.0891866i \(-0.0284267\pi\)
0.996015 + 0.0891866i \(0.0284267\pi\)
\(984\) −15.3662 −0.489856
\(985\) −0.722312 −0.0230148
\(986\) 19.9645 0.635800
\(987\) −10.6021 −0.337468
\(988\) −14.5559 −0.463086
\(989\) −45.7155 −1.45367
\(990\) −0.632997 −0.0201180
\(991\) 5.20461 0.165330 0.0826649 0.996577i \(-0.473657\pi\)
0.0826649 + 0.996577i \(0.473657\pi\)
\(992\) −8.65088 −0.274666
\(993\) 7.65080 0.242791
\(994\) 21.4234 0.679510
\(995\) −16.9172 −0.536312
\(996\) −8.35799 −0.264833
\(997\) −7.56919 −0.239719 −0.119859 0.992791i \(-0.538244\pi\)
−0.119859 + 0.992791i \(0.538244\pi\)
\(998\) 13.6682 0.432661
\(999\) 24.8821 0.787235
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 4003.2.a.c.1.19 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.19 179 1.1 even 1 trivial