Properties

Label 4001.2.a.b.1.109
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, 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("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.109
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.635075 q^{2} +2.40773 q^{3} -1.59668 q^{4} -0.176134 q^{5} +1.52909 q^{6} +0.607658 q^{7} -2.28416 q^{8} +2.79716 q^{9} +O(q^{10})\) \(q+0.635075 q^{2} +2.40773 q^{3} -1.59668 q^{4} -0.176134 q^{5} +1.52909 q^{6} +0.607658 q^{7} -2.28416 q^{8} +2.79716 q^{9} -0.111858 q^{10} +0.724171 q^{11} -3.84437 q^{12} -3.12375 q^{13} +0.385908 q^{14} -0.424082 q^{15} +1.74275 q^{16} -1.81722 q^{17} +1.77640 q^{18} +3.76611 q^{19} +0.281229 q^{20} +1.46307 q^{21} +0.459903 q^{22} +4.76589 q^{23} -5.49964 q^{24} -4.96898 q^{25} -1.98381 q^{26} -0.488393 q^{27} -0.970235 q^{28} +9.17023 q^{29} -0.269324 q^{30} +10.3551 q^{31} +5.67510 q^{32} +1.74361 q^{33} -1.15407 q^{34} -0.107029 q^{35} -4.46616 q^{36} -4.97256 q^{37} +2.39176 q^{38} -7.52113 q^{39} +0.402318 q^{40} +6.40622 q^{41} +0.929162 q^{42} +12.8602 q^{43} -1.15627 q^{44} -0.492674 q^{45} +3.02670 q^{46} -8.43691 q^{47} +4.19607 q^{48} -6.63075 q^{49} -3.15567 q^{50} -4.37538 q^{51} +4.98762 q^{52} -1.37242 q^{53} -0.310166 q^{54} -0.127551 q^{55} -1.38799 q^{56} +9.06778 q^{57} +5.82378 q^{58} -3.41084 q^{59} +0.677124 q^{60} +12.6507 q^{61} +6.57626 q^{62} +1.69971 q^{63} +0.118612 q^{64} +0.550197 q^{65} +1.10732 q^{66} +3.00526 q^{67} +2.90153 q^{68} +11.4750 q^{69} -0.0679714 q^{70} +14.7122 q^{71} -6.38915 q^{72} +7.69266 q^{73} -3.15795 q^{74} -11.9639 q^{75} -6.01328 q^{76} +0.440048 q^{77} -4.77648 q^{78} -6.27366 q^{79} -0.306957 q^{80} -9.56739 q^{81} +4.06843 q^{82} +13.4465 q^{83} -2.33606 q^{84} +0.320075 q^{85} +8.16721 q^{86} +22.0794 q^{87} -1.65412 q^{88} -0.176694 q^{89} -0.312885 q^{90} -1.89817 q^{91} -7.60960 q^{92} +24.9323 q^{93} -5.35806 q^{94} -0.663340 q^{95} +13.6641 q^{96} +8.88739 q^{97} -4.21102 q^{98} +2.02562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.635075 0.449066 0.224533 0.974467i \(-0.427914\pi\)
0.224533 + 0.974467i \(0.427914\pi\)
\(3\) 2.40773 1.39010 0.695051 0.718960i \(-0.255382\pi\)
0.695051 + 0.718960i \(0.255382\pi\)
\(4\) −1.59668 −0.798340
\(5\) −0.176134 −0.0787695 −0.0393847 0.999224i \(-0.512540\pi\)
−0.0393847 + 0.999224i \(0.512540\pi\)
\(6\) 1.52909 0.624247
\(7\) 0.607658 0.229673 0.114837 0.993384i \(-0.463366\pi\)
0.114837 + 0.993384i \(0.463366\pi\)
\(8\) −2.28416 −0.807573
\(9\) 2.79716 0.932385
\(10\) −0.111858 −0.0353726
\(11\) 0.724171 0.218346 0.109173 0.994023i \(-0.465180\pi\)
0.109173 + 0.994023i \(0.465180\pi\)
\(12\) −3.84437 −1.10977
\(13\) −3.12375 −0.866371 −0.433186 0.901305i \(-0.642611\pi\)
−0.433186 + 0.901305i \(0.642611\pi\)
\(14\) 0.385908 0.103138
\(15\) −0.424082 −0.109498
\(16\) 1.74275 0.435687
\(17\) −1.81722 −0.440742 −0.220371 0.975416i \(-0.570727\pi\)
−0.220371 + 0.975416i \(0.570727\pi\)
\(18\) 1.77640 0.418702
\(19\) 3.76611 0.864006 0.432003 0.901872i \(-0.357807\pi\)
0.432003 + 0.901872i \(0.357807\pi\)
\(20\) 0.281229 0.0628848
\(21\) 1.46307 0.319269
\(22\) 0.459903 0.0980516
\(23\) 4.76589 0.993757 0.496879 0.867820i \(-0.334479\pi\)
0.496879 + 0.867820i \(0.334479\pi\)
\(24\) −5.49964 −1.12261
\(25\) −4.96898 −0.993795
\(26\) −1.98381 −0.389057
\(27\) −0.488393 −0.0939912
\(28\) −0.970235 −0.183357
\(29\) 9.17023 1.70287 0.851434 0.524462i \(-0.175733\pi\)
0.851434 + 0.524462i \(0.175733\pi\)
\(30\) −0.269324 −0.0491716
\(31\) 10.3551 1.85983 0.929916 0.367773i \(-0.119880\pi\)
0.929916 + 0.367773i \(0.119880\pi\)
\(32\) 5.67510 1.00322
\(33\) 1.74361 0.303523
\(34\) −1.15407 −0.197922
\(35\) −0.107029 −0.0180912
\(36\) −4.46616 −0.744361
\(37\) −4.97256 −0.817484 −0.408742 0.912650i \(-0.634032\pi\)
−0.408742 + 0.912650i \(0.634032\pi\)
\(38\) 2.39176 0.387995
\(39\) −7.52113 −1.20434
\(40\) 0.402318 0.0636120
\(41\) 6.40622 1.00048 0.500241 0.865886i \(-0.333245\pi\)
0.500241 + 0.865886i \(0.333245\pi\)
\(42\) 0.929162 0.143373
\(43\) 12.8602 1.96117 0.980584 0.196098i \(-0.0628271\pi\)
0.980584 + 0.196098i \(0.0628271\pi\)
\(44\) −1.15627 −0.174314
\(45\) −0.492674 −0.0734435
\(46\) 3.02670 0.446262
\(47\) −8.43691 −1.23065 −0.615325 0.788274i \(-0.710975\pi\)
−0.615325 + 0.788274i \(0.710975\pi\)
\(48\) 4.19607 0.605650
\(49\) −6.63075 −0.947250
\(50\) −3.15567 −0.446279
\(51\) −4.37538 −0.612676
\(52\) 4.98762 0.691659
\(53\) −1.37242 −0.188517 −0.0942583 0.995548i \(-0.530048\pi\)
−0.0942583 + 0.995548i \(0.530048\pi\)
\(54\) −0.310166 −0.0422082
\(55\) −0.127551 −0.0171990
\(56\) −1.38799 −0.185478
\(57\) 9.06778 1.20106
\(58\) 5.82378 0.764699
\(59\) −3.41084 −0.444053 −0.222027 0.975041i \(-0.571267\pi\)
−0.222027 + 0.975041i \(0.571267\pi\)
\(60\) 0.677124 0.0874163
\(61\) 12.6507 1.61976 0.809881 0.586594i \(-0.199532\pi\)
0.809881 + 0.586594i \(0.199532\pi\)
\(62\) 6.57626 0.835186
\(63\) 1.69971 0.214144
\(64\) 0.118612 0.0148264
\(65\) 0.550197 0.0682436
\(66\) 1.10732 0.136302
\(67\) 3.00526 0.367151 0.183576 0.983006i \(-0.441233\pi\)
0.183576 + 0.983006i \(0.441233\pi\)
\(68\) 2.90153 0.351862
\(69\) 11.4750 1.38142
\(70\) −0.0679714 −0.00812414
\(71\) 14.7122 1.74602 0.873008 0.487706i \(-0.162166\pi\)
0.873008 + 0.487706i \(0.162166\pi\)
\(72\) −6.38915 −0.752969
\(73\) 7.69266 0.900358 0.450179 0.892938i \(-0.351360\pi\)
0.450179 + 0.892938i \(0.351360\pi\)
\(74\) −3.15795 −0.367104
\(75\) −11.9639 −1.38148
\(76\) −6.01328 −0.689770
\(77\) 0.440048 0.0501481
\(78\) −4.77648 −0.540830
\(79\) −6.27366 −0.705842 −0.352921 0.935653i \(-0.614812\pi\)
−0.352921 + 0.935653i \(0.614812\pi\)
\(80\) −0.306957 −0.0343188
\(81\) −9.56739 −1.06304
\(82\) 4.06843 0.449282
\(83\) 13.4465 1.47595 0.737975 0.674828i \(-0.235782\pi\)
0.737975 + 0.674828i \(0.235782\pi\)
\(84\) −2.33606 −0.254885
\(85\) 0.320075 0.0347170
\(86\) 8.16721 0.880693
\(87\) 22.0794 2.36716
\(88\) −1.65412 −0.176330
\(89\) −0.176694 −0.0187295 −0.00936477 0.999956i \(-0.502981\pi\)
−0.00936477 + 0.999956i \(0.502981\pi\)
\(90\) −0.312885 −0.0329809
\(91\) −1.89817 −0.198982
\(92\) −7.60960 −0.793356
\(93\) 24.9323 2.58536
\(94\) −5.35806 −0.552642
\(95\) −0.663340 −0.0680572
\(96\) 13.6641 1.39459
\(97\) 8.88739 0.902378 0.451189 0.892428i \(-0.351000\pi\)
0.451189 + 0.892428i \(0.351000\pi\)
\(98\) −4.21102 −0.425377
\(99\) 2.02562 0.203582
\(100\) 7.93387 0.793387
\(101\) −12.9674 −1.29031 −0.645154 0.764053i \(-0.723207\pi\)
−0.645154 + 0.764053i \(0.723207\pi\)
\(102\) −2.77869 −0.275132
\(103\) −19.8336 −1.95427 −0.977133 0.212629i \(-0.931798\pi\)
−0.977133 + 0.212629i \(0.931798\pi\)
\(104\) 7.13513 0.699658
\(105\) −0.257697 −0.0251486
\(106\) −0.871590 −0.0846563
\(107\) 7.83410 0.757351 0.378676 0.925529i \(-0.376380\pi\)
0.378676 + 0.925529i \(0.376380\pi\)
\(108\) 0.779807 0.0750370
\(109\) 14.6274 1.40105 0.700525 0.713627i \(-0.252949\pi\)
0.700525 + 0.713627i \(0.252949\pi\)
\(110\) −0.0810044 −0.00772347
\(111\) −11.9726 −1.13639
\(112\) 1.05899 0.100066
\(113\) 9.61490 0.904493 0.452247 0.891893i \(-0.350623\pi\)
0.452247 + 0.891893i \(0.350623\pi\)
\(114\) 5.75871 0.539353
\(115\) −0.839435 −0.0782777
\(116\) −14.6419 −1.35947
\(117\) −8.73760 −0.807792
\(118\) −2.16614 −0.199409
\(119\) −1.10425 −0.101226
\(120\) 0.968672 0.0884273
\(121\) −10.4756 −0.952325
\(122\) 8.03417 0.727379
\(123\) 15.4244 1.39077
\(124\) −16.5338 −1.48478
\(125\) 1.75587 0.157050
\(126\) 1.07944 0.0961646
\(127\) −18.8576 −1.67334 −0.836672 0.547704i \(-0.815502\pi\)
−0.836672 + 0.547704i \(0.815502\pi\)
\(128\) −11.2749 −0.996567
\(129\) 30.9640 2.72623
\(130\) 0.349416 0.0306458
\(131\) −2.73047 −0.238563 −0.119281 0.992860i \(-0.538059\pi\)
−0.119281 + 0.992860i \(0.538059\pi\)
\(132\) −2.78398 −0.242315
\(133\) 2.28851 0.198439
\(134\) 1.90857 0.164875
\(135\) 0.0860225 0.00740364
\(136\) 4.15083 0.355931
\(137\) 7.27473 0.621522 0.310761 0.950488i \(-0.399416\pi\)
0.310761 + 0.950488i \(0.399416\pi\)
\(138\) 7.28746 0.620350
\(139\) 0.817790 0.0693640 0.0346820 0.999398i \(-0.488958\pi\)
0.0346820 + 0.999398i \(0.488958\pi\)
\(140\) 0.170891 0.0144429
\(141\) −20.3138 −1.71073
\(142\) 9.34334 0.784075
\(143\) −2.26213 −0.189168
\(144\) 4.87474 0.406228
\(145\) −1.61519 −0.134134
\(146\) 4.88541 0.404320
\(147\) −15.9651 −1.31678
\(148\) 7.93959 0.652630
\(149\) 14.2722 1.16923 0.584613 0.811312i \(-0.301246\pi\)
0.584613 + 0.811312i \(0.301246\pi\)
\(150\) −7.59800 −0.620374
\(151\) 17.4665 1.42140 0.710700 0.703495i \(-0.248378\pi\)
0.710700 + 0.703495i \(0.248378\pi\)
\(152\) −8.60240 −0.697747
\(153\) −5.08306 −0.410941
\(154\) 0.279463 0.0225198
\(155\) −1.82388 −0.146498
\(156\) 12.0088 0.961477
\(157\) −5.24052 −0.418239 −0.209119 0.977890i \(-0.567060\pi\)
−0.209119 + 0.977890i \(0.567060\pi\)
\(158\) −3.98424 −0.316969
\(159\) −3.30442 −0.262057
\(160\) −0.999576 −0.0790235
\(161\) 2.89603 0.228239
\(162\) −6.07600 −0.477376
\(163\) −2.26445 −0.177366 −0.0886828 0.996060i \(-0.528266\pi\)
−0.0886828 + 0.996060i \(0.528266\pi\)
\(164\) −10.2287 −0.798726
\(165\) −0.307108 −0.0239083
\(166\) 8.53956 0.662799
\(167\) −0.734105 −0.0568068 −0.0284034 0.999597i \(-0.509042\pi\)
−0.0284034 + 0.999597i \(0.509042\pi\)
\(168\) −3.34190 −0.257833
\(169\) −3.24221 −0.249401
\(170\) 0.203271 0.0155902
\(171\) 10.5344 0.805586
\(172\) −20.5337 −1.56568
\(173\) 0.151447 0.0115143 0.00575716 0.999983i \(-0.498167\pi\)
0.00575716 + 0.999983i \(0.498167\pi\)
\(174\) 14.0221 1.06301
\(175\) −3.01944 −0.228248
\(176\) 1.26205 0.0951304
\(177\) −8.21237 −0.617280
\(178\) −0.112214 −0.00841079
\(179\) −16.2761 −1.21653 −0.608267 0.793733i \(-0.708135\pi\)
−0.608267 + 0.793733i \(0.708135\pi\)
\(180\) 0.786643 0.0586329
\(181\) 0.272612 0.0202631 0.0101315 0.999949i \(-0.496775\pi\)
0.0101315 + 0.999949i \(0.496775\pi\)
\(182\) −1.20548 −0.0893560
\(183\) 30.4596 2.25164
\(184\) −10.8861 −0.802531
\(185\) 0.875836 0.0643928
\(186\) 15.8339 1.16099
\(187\) −1.31598 −0.0962341
\(188\) 13.4710 0.982477
\(189\) −0.296776 −0.0215873
\(190\) −0.421270 −0.0305622
\(191\) −20.1278 −1.45640 −0.728199 0.685366i \(-0.759642\pi\)
−0.728199 + 0.685366i \(0.759642\pi\)
\(192\) 0.285584 0.0206103
\(193\) −5.05542 −0.363897 −0.181949 0.983308i \(-0.558240\pi\)
−0.181949 + 0.983308i \(0.558240\pi\)
\(194\) 5.64416 0.405227
\(195\) 1.32473 0.0948656
\(196\) 10.5872 0.756228
\(197\) 2.29838 0.163753 0.0818765 0.996642i \(-0.473909\pi\)
0.0818765 + 0.996642i \(0.473909\pi\)
\(198\) 1.28642 0.0914218
\(199\) 18.0824 1.28183 0.640913 0.767614i \(-0.278556\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(200\) 11.3499 0.802562
\(201\) 7.23586 0.510378
\(202\) −8.23528 −0.579432
\(203\) 5.57236 0.391103
\(204\) 6.98609 0.489124
\(205\) −1.12835 −0.0788075
\(206\) −12.5958 −0.877594
\(207\) 13.3309 0.926565
\(208\) −5.44390 −0.377467
\(209\) 2.72731 0.188652
\(210\) −0.163657 −0.0112934
\(211\) −14.4216 −0.992824 −0.496412 0.868087i \(-0.665350\pi\)
−0.496412 + 0.868087i \(0.665350\pi\)
\(212\) 2.19132 0.150500
\(213\) 35.4230 2.42714
\(214\) 4.97524 0.340100
\(215\) −2.26512 −0.154480
\(216\) 1.11557 0.0759048
\(217\) 6.29236 0.427153
\(218\) 9.28949 0.629164
\(219\) 18.5218 1.25159
\(220\) 0.203658 0.0137306
\(221\) 5.67655 0.381846
\(222\) −7.60348 −0.510312
\(223\) −24.4696 −1.63861 −0.819303 0.573361i \(-0.805639\pi\)
−0.819303 + 0.573361i \(0.805639\pi\)
\(224\) 3.44852 0.230414
\(225\) −13.8990 −0.926600
\(226\) 6.10618 0.406177
\(227\) −10.9184 −0.724681 −0.362340 0.932046i \(-0.618022\pi\)
−0.362340 + 0.932046i \(0.618022\pi\)
\(228\) −14.4783 −0.958852
\(229\) 19.7809 1.30716 0.653579 0.756858i \(-0.273267\pi\)
0.653579 + 0.756858i \(0.273267\pi\)
\(230\) −0.533104 −0.0351518
\(231\) 1.05952 0.0697111
\(232\) −20.9463 −1.37519
\(233\) −13.7176 −0.898671 −0.449335 0.893363i \(-0.648339\pi\)
−0.449335 + 0.893363i \(0.648339\pi\)
\(234\) −5.54903 −0.362751
\(235\) 1.48602 0.0969376
\(236\) 5.44602 0.354506
\(237\) −15.1053 −0.981193
\(238\) −0.701281 −0.0454573
\(239\) −5.54277 −0.358532 −0.179266 0.983801i \(-0.557372\pi\)
−0.179266 + 0.983801i \(0.557372\pi\)
\(240\) −0.739069 −0.0477067
\(241\) 8.06605 0.519580 0.259790 0.965665i \(-0.416347\pi\)
0.259790 + 0.965665i \(0.416347\pi\)
\(242\) −6.65277 −0.427656
\(243\) −21.5705 −1.38375
\(244\) −20.1992 −1.29312
\(245\) 1.16790 0.0746144
\(246\) 9.79566 0.624549
\(247\) −11.7644 −0.748549
\(248\) −23.6527 −1.50195
\(249\) 32.3756 2.05172
\(250\) 1.11511 0.0705258
\(251\) 5.73783 0.362168 0.181084 0.983468i \(-0.442039\pi\)
0.181084 + 0.983468i \(0.442039\pi\)
\(252\) −2.71390 −0.170960
\(253\) 3.45132 0.216983
\(254\) −11.9760 −0.751441
\(255\) 0.770653 0.0482602
\(256\) −7.39760 −0.462350
\(257\) −24.2566 −1.51308 −0.756541 0.653946i \(-0.773112\pi\)
−0.756541 + 0.653946i \(0.773112\pi\)
\(258\) 19.6644 1.22425
\(259\) −3.02161 −0.187754
\(260\) −0.878489 −0.0544816
\(261\) 25.6506 1.58773
\(262\) −1.73405 −0.107130
\(263\) 2.32155 0.143153 0.0715764 0.997435i \(-0.477197\pi\)
0.0715764 + 0.997435i \(0.477197\pi\)
\(264\) −3.98268 −0.245117
\(265\) 0.241730 0.0148494
\(266\) 1.45337 0.0891120
\(267\) −0.425431 −0.0260360
\(268\) −4.79844 −0.293112
\(269\) −4.95698 −0.302232 −0.151116 0.988516i \(-0.548287\pi\)
−0.151116 + 0.988516i \(0.548287\pi\)
\(270\) 0.0546307 0.00332472
\(271\) −20.5983 −1.25126 −0.625630 0.780120i \(-0.715158\pi\)
−0.625630 + 0.780120i \(0.715158\pi\)
\(272\) −3.16697 −0.192025
\(273\) −4.57027 −0.276606
\(274\) 4.61999 0.279104
\(275\) −3.59839 −0.216991
\(276\) −18.3219 −1.10285
\(277\) 32.4420 1.94925 0.974625 0.223846i \(-0.0718612\pi\)
0.974625 + 0.223846i \(0.0718612\pi\)
\(278\) 0.519357 0.0311490
\(279\) 28.9648 1.73408
\(280\) 0.244472 0.0146100
\(281\) 26.8662 1.60270 0.801352 0.598193i \(-0.204114\pi\)
0.801352 + 0.598193i \(0.204114\pi\)
\(282\) −12.9008 −0.768229
\(283\) 19.4549 1.15647 0.578237 0.815869i \(-0.303741\pi\)
0.578237 + 0.815869i \(0.303741\pi\)
\(284\) −23.4907 −1.39391
\(285\) −1.59714 −0.0946066
\(286\) −1.43662 −0.0849490
\(287\) 3.89279 0.229784
\(288\) 15.8741 0.935392
\(289\) −13.6977 −0.805747
\(290\) −1.02576 −0.0602349
\(291\) 21.3984 1.25440
\(292\) −12.2827 −0.718792
\(293\) −6.12616 −0.357894 −0.178947 0.983859i \(-0.557269\pi\)
−0.178947 + 0.983859i \(0.557269\pi\)
\(294\) −10.1390 −0.591318
\(295\) 0.600764 0.0349778
\(296\) 11.3581 0.660178
\(297\) −0.353680 −0.0205226
\(298\) 9.06393 0.525059
\(299\) −14.8874 −0.860962
\(300\) 19.1026 1.10289
\(301\) 7.81462 0.450427
\(302\) 11.0925 0.638302
\(303\) −31.2220 −1.79366
\(304\) 6.56339 0.376436
\(305\) −2.22822 −0.127588
\(306\) −3.22812 −0.184539
\(307\) 3.75293 0.214191 0.107095 0.994249i \(-0.465845\pi\)
0.107095 + 0.994249i \(0.465845\pi\)
\(308\) −0.702616 −0.0400353
\(309\) −47.7540 −2.71663
\(310\) −1.15830 −0.0657871
\(311\) 26.5046 1.50294 0.751470 0.659767i \(-0.229345\pi\)
0.751470 + 0.659767i \(0.229345\pi\)
\(312\) 17.1795 0.972596
\(313\) 12.0658 0.682000 0.341000 0.940063i \(-0.389234\pi\)
0.341000 + 0.940063i \(0.389234\pi\)
\(314\) −3.32812 −0.187817
\(315\) −0.299377 −0.0168680
\(316\) 10.0170 0.563502
\(317\) 13.5511 0.761107 0.380554 0.924759i \(-0.375733\pi\)
0.380554 + 0.924759i \(0.375733\pi\)
\(318\) −2.09855 −0.117681
\(319\) 6.64081 0.371814
\(320\) −0.0208915 −0.00116787
\(321\) 18.8624 1.05280
\(322\) 1.83920 0.102494
\(323\) −6.84387 −0.380803
\(324\) 15.2761 0.848670
\(325\) 15.5218 0.860996
\(326\) −1.43810 −0.0796487
\(327\) 35.2188 1.94760
\(328\) −14.6328 −0.807963
\(329\) −5.12675 −0.282647
\(330\) −0.195037 −0.0107364
\(331\) 28.6918 1.57705 0.788523 0.615005i \(-0.210846\pi\)
0.788523 + 0.615005i \(0.210846\pi\)
\(332\) −21.4698 −1.17831
\(333\) −13.9090 −0.762210
\(334\) −0.466211 −0.0255100
\(335\) −0.529328 −0.0289203
\(336\) 2.54977 0.139101
\(337\) 8.58771 0.467803 0.233901 0.972260i \(-0.424851\pi\)
0.233901 + 0.972260i \(0.424851\pi\)
\(338\) −2.05905 −0.111997
\(339\) 23.1501 1.25734
\(340\) −0.511057 −0.0277160
\(341\) 7.49886 0.406086
\(342\) 6.69013 0.361761
\(343\) −8.28283 −0.447231
\(344\) −29.3749 −1.58379
\(345\) −2.02113 −0.108814
\(346\) 0.0961802 0.00517068
\(347\) −15.2240 −0.817265 −0.408633 0.912699i \(-0.633994\pi\)
−0.408633 + 0.912699i \(0.633994\pi\)
\(348\) −35.2538 −1.88980
\(349\) 17.8082 0.953252 0.476626 0.879106i \(-0.341860\pi\)
0.476626 + 0.879106i \(0.341860\pi\)
\(350\) −1.91757 −0.102498
\(351\) 1.52561 0.0814313
\(352\) 4.10974 0.219050
\(353\) 16.6349 0.885387 0.442693 0.896673i \(-0.354023\pi\)
0.442693 + 0.896673i \(0.354023\pi\)
\(354\) −5.21547 −0.277199
\(355\) −2.59131 −0.137533
\(356\) 0.282124 0.0149525
\(357\) −2.65874 −0.140715
\(358\) −10.3365 −0.546303
\(359\) 16.4374 0.867535 0.433767 0.901025i \(-0.357184\pi\)
0.433767 + 0.901025i \(0.357184\pi\)
\(360\) 1.12535 0.0593109
\(361\) −4.81639 −0.253494
\(362\) 0.173129 0.00909945
\(363\) −25.2223 −1.32383
\(364\) 3.03077 0.158855
\(365\) −1.35494 −0.0709207
\(366\) 19.3441 1.01113
\(367\) −7.72221 −0.403096 −0.201548 0.979479i \(-0.564597\pi\)
−0.201548 + 0.979479i \(0.564597\pi\)
\(368\) 8.30575 0.432967
\(369\) 17.9192 0.932836
\(370\) 0.556221 0.0289166
\(371\) −0.833963 −0.0432972
\(372\) −39.8089 −2.06399
\(373\) 1.70082 0.0880650 0.0440325 0.999030i \(-0.485979\pi\)
0.0440325 + 0.999030i \(0.485979\pi\)
\(374\) −0.835746 −0.0432154
\(375\) 4.22767 0.218316
\(376\) 19.2712 0.993838
\(377\) −28.6454 −1.47532
\(378\) −0.188475 −0.00969409
\(379\) 15.6176 0.802224 0.401112 0.916029i \(-0.368624\pi\)
0.401112 + 0.916029i \(0.368624\pi\)
\(380\) 1.05914 0.0543328
\(381\) −45.4041 −2.32612
\(382\) −12.7827 −0.654018
\(383\) −4.30563 −0.220008 −0.110004 0.993931i \(-0.535086\pi\)
−0.110004 + 0.993931i \(0.535086\pi\)
\(384\) −27.1468 −1.38533
\(385\) −0.0775074 −0.00395014
\(386\) −3.21057 −0.163414
\(387\) 35.9721 1.82856
\(388\) −14.1903 −0.720404
\(389\) −34.1729 −1.73264 −0.866318 0.499492i \(-0.833520\pi\)
−0.866318 + 0.499492i \(0.833520\pi\)
\(390\) 0.841300 0.0426009
\(391\) −8.66069 −0.437990
\(392\) 15.1457 0.764973
\(393\) −6.57424 −0.331627
\(394\) 1.45965 0.0735359
\(395\) 1.10500 0.0555988
\(396\) −3.23427 −0.162528
\(397\) 12.3301 0.618829 0.309414 0.950927i \(-0.399867\pi\)
0.309414 + 0.950927i \(0.399867\pi\)
\(398\) 11.4837 0.575624
\(399\) 5.51010 0.275850
\(400\) −8.65968 −0.432984
\(401\) −35.2145 −1.75853 −0.879265 0.476333i \(-0.841966\pi\)
−0.879265 + 0.476333i \(0.841966\pi\)
\(402\) 4.59531 0.229193
\(403\) −32.3467 −1.61130
\(404\) 20.7048 1.03010
\(405\) 1.68514 0.0837353
\(406\) 3.53886 0.175631
\(407\) −3.60098 −0.178494
\(408\) 9.99408 0.494780
\(409\) −7.35670 −0.363766 −0.181883 0.983320i \(-0.558219\pi\)
−0.181883 + 0.983320i \(0.558219\pi\)
\(410\) −0.716587 −0.0353897
\(411\) 17.5156 0.863979
\(412\) 31.6680 1.56017
\(413\) −2.07262 −0.101987
\(414\) 8.46614 0.416088
\(415\) −2.36839 −0.116260
\(416\) −17.7276 −0.869165
\(417\) 1.96902 0.0964231
\(418\) 1.73204 0.0847171
\(419\) 17.0403 0.832471 0.416236 0.909257i \(-0.363349\pi\)
0.416236 + 0.909257i \(0.363349\pi\)
\(420\) 0.411460 0.0200772
\(421\) −18.9374 −0.922951 −0.461476 0.887153i \(-0.652680\pi\)
−0.461476 + 0.887153i \(0.652680\pi\)
\(422\) −9.15880 −0.445843
\(423\) −23.5993 −1.14744
\(424\) 3.13483 0.152241
\(425\) 9.02975 0.438007
\(426\) 22.4962 1.08995
\(427\) 7.68732 0.372016
\(428\) −12.5086 −0.604624
\(429\) −5.44658 −0.262964
\(430\) −1.43852 −0.0693717
\(431\) −20.6409 −0.994238 −0.497119 0.867682i \(-0.665609\pi\)
−0.497119 + 0.867682i \(0.665609\pi\)
\(432\) −0.851146 −0.0409508
\(433\) −30.0335 −1.44332 −0.721660 0.692248i \(-0.756620\pi\)
−0.721660 + 0.692248i \(0.756620\pi\)
\(434\) 3.99612 0.191820
\(435\) −3.88893 −0.186460
\(436\) −23.3553 −1.11852
\(437\) 17.9489 0.858612
\(438\) 11.7628 0.562046
\(439\) −7.91987 −0.377995 −0.188997 0.981978i \(-0.560524\pi\)
−0.188997 + 0.981978i \(0.560524\pi\)
\(440\) 0.291347 0.0138894
\(441\) −18.5472 −0.883202
\(442\) 3.60503 0.171474
\(443\) −31.6434 −1.50342 −0.751712 0.659491i \(-0.770772\pi\)
−0.751712 + 0.659491i \(0.770772\pi\)
\(444\) 19.1164 0.907223
\(445\) 0.0311218 0.00147531
\(446\) −15.5400 −0.735841
\(447\) 34.3637 1.62535
\(448\) 0.0720752 0.00340523
\(449\) 17.3272 0.817720 0.408860 0.912597i \(-0.365926\pi\)
0.408860 + 0.912597i \(0.365926\pi\)
\(450\) −8.82690 −0.416104
\(451\) 4.63920 0.218451
\(452\) −15.3519 −0.722093
\(453\) 42.0545 1.97589
\(454\) −6.93401 −0.325429
\(455\) 0.334332 0.0156737
\(456\) −20.7123 −0.969940
\(457\) −14.1405 −0.661467 −0.330733 0.943724i \(-0.607296\pi\)
−0.330733 + 0.943724i \(0.607296\pi\)
\(458\) 12.5623 0.587000
\(459\) 0.887519 0.0414259
\(460\) 1.34031 0.0624922
\(461\) 1.42940 0.0665736 0.0332868 0.999446i \(-0.489403\pi\)
0.0332868 + 0.999446i \(0.489403\pi\)
\(462\) 0.672872 0.0313048
\(463\) 0.337105 0.0156666 0.00783330 0.999969i \(-0.497507\pi\)
0.00783330 + 0.999969i \(0.497507\pi\)
\(464\) 15.9814 0.741918
\(465\) −4.39142 −0.203647
\(466\) −8.71171 −0.403562
\(467\) −20.7741 −0.961308 −0.480654 0.876910i \(-0.659601\pi\)
−0.480654 + 0.876910i \(0.659601\pi\)
\(468\) 13.9512 0.644893
\(469\) 1.82617 0.0843247
\(470\) 0.943736 0.0435313
\(471\) −12.6177 −0.581395
\(472\) 7.79090 0.358605
\(473\) 9.31301 0.428213
\(474\) −9.59297 −0.440620
\(475\) −18.7137 −0.858645
\(476\) 1.76313 0.0808132
\(477\) −3.83888 −0.175770
\(478\) −3.52007 −0.161004
\(479\) 6.13427 0.280282 0.140141 0.990132i \(-0.455244\pi\)
0.140141 + 0.990132i \(0.455244\pi\)
\(480\) −2.40671 −0.109851
\(481\) 15.5330 0.708244
\(482\) 5.12254 0.233325
\(483\) 6.97286 0.317276
\(484\) 16.7261 0.760279
\(485\) −1.56537 −0.0710798
\(486\) −13.6989 −0.621393
\(487\) −29.9065 −1.35519 −0.677596 0.735434i \(-0.736978\pi\)
−0.677596 + 0.735434i \(0.736978\pi\)
\(488\) −28.8963 −1.30808
\(489\) −5.45218 −0.246556
\(490\) 0.741703 0.0335067
\(491\) 6.47968 0.292424 0.146212 0.989253i \(-0.453292\pi\)
0.146212 + 0.989253i \(0.453292\pi\)
\(492\) −24.6279 −1.11031
\(493\) −16.6644 −0.750525
\(494\) −7.47126 −0.336148
\(495\) −0.356780 −0.0160361
\(496\) 18.0463 0.810305
\(497\) 8.93998 0.401013
\(498\) 20.5609 0.921358
\(499\) −31.0634 −1.39059 −0.695294 0.718726i \(-0.744726\pi\)
−0.695294 + 0.718726i \(0.744726\pi\)
\(500\) −2.80357 −0.125379
\(501\) −1.76753 −0.0789672
\(502\) 3.64395 0.162637
\(503\) −5.69577 −0.253962 −0.126981 0.991905i \(-0.540529\pi\)
−0.126981 + 0.991905i \(0.540529\pi\)
\(504\) −3.88242 −0.172937
\(505\) 2.28400 0.101637
\(506\) 2.19185 0.0974394
\(507\) −7.80637 −0.346693
\(508\) 30.1096 1.33590
\(509\) −12.1525 −0.538649 −0.269325 0.963049i \(-0.586800\pi\)
−0.269325 + 0.963049i \(0.586800\pi\)
\(510\) 0.489422 0.0216720
\(511\) 4.67451 0.206788
\(512\) 17.8517 0.788941
\(513\) −1.83934 −0.0812090
\(514\) −15.4047 −0.679473
\(515\) 3.49337 0.153936
\(516\) −49.4396 −2.17646
\(517\) −6.10976 −0.268707
\(518\) −1.91895 −0.0843138
\(519\) 0.364644 0.0160061
\(520\) −1.25674 −0.0551116
\(521\) −1.56247 −0.0684529 −0.0342264 0.999414i \(-0.510897\pi\)
−0.0342264 + 0.999414i \(0.510897\pi\)
\(522\) 16.2900 0.712995
\(523\) −3.02707 −0.132365 −0.0661823 0.997808i \(-0.521082\pi\)
−0.0661823 + 0.997808i \(0.521082\pi\)
\(524\) 4.35970 0.190454
\(525\) −7.26998 −0.317288
\(526\) 1.47436 0.0642850
\(527\) −18.8175 −0.819705
\(528\) 3.03867 0.132241
\(529\) −0.286279 −0.0124469
\(530\) 0.153517 0.00666833
\(531\) −9.54065 −0.414029
\(532\) −3.65401 −0.158422
\(533\) −20.0114 −0.866790
\(534\) −0.270181 −0.0116919
\(535\) −1.37985 −0.0596562
\(536\) −6.86450 −0.296501
\(537\) −39.1884 −1.69111
\(538\) −3.14805 −0.135722
\(539\) −4.80180 −0.206828
\(540\) −0.137350 −0.00591062
\(541\) −26.5451 −1.14126 −0.570631 0.821207i \(-0.693301\pi\)
−0.570631 + 0.821207i \(0.693301\pi\)
\(542\) −13.0815 −0.561897
\(543\) 0.656375 0.0281678
\(544\) −10.3129 −0.442163
\(545\) −2.57638 −0.110360
\(546\) −2.90246 −0.124214
\(547\) −34.7992 −1.48790 −0.743952 0.668233i \(-0.767051\pi\)
−0.743952 + 0.668233i \(0.767051\pi\)
\(548\) −11.6154 −0.496186
\(549\) 35.3861 1.51024
\(550\) −2.28525 −0.0974432
\(551\) 34.5361 1.47129
\(552\) −26.2107 −1.11560
\(553\) −3.81224 −0.162113
\(554\) 20.6031 0.875341
\(555\) 2.10878 0.0895125
\(556\) −1.30575 −0.0553761
\(557\) −41.3801 −1.75333 −0.876665 0.481102i \(-0.840237\pi\)
−0.876665 + 0.481102i \(0.840237\pi\)
\(558\) 18.3948 0.778715
\(559\) −40.1721 −1.69910
\(560\) −0.186525 −0.00788211
\(561\) −3.16853 −0.133775
\(562\) 17.0621 0.719719
\(563\) 24.8102 1.04562 0.522812 0.852448i \(-0.324883\pi\)
0.522812 + 0.852448i \(0.324883\pi\)
\(564\) 32.4346 1.36574
\(565\) −1.69351 −0.0712464
\(566\) 12.3553 0.519332
\(567\) −5.81370 −0.244152
\(568\) −33.6050 −1.41003
\(569\) 23.5407 0.986876 0.493438 0.869781i \(-0.335740\pi\)
0.493438 + 0.869781i \(0.335740\pi\)
\(570\) −1.01430 −0.0424845
\(571\) 11.2932 0.472608 0.236304 0.971679i \(-0.424064\pi\)
0.236304 + 0.971679i \(0.424064\pi\)
\(572\) 3.61189 0.151021
\(573\) −48.4623 −2.02454
\(574\) 2.47221 0.103188
\(575\) −23.6816 −0.987591
\(576\) 0.331775 0.0138240
\(577\) −14.3977 −0.599384 −0.299692 0.954036i \(-0.596884\pi\)
−0.299692 + 0.954036i \(0.596884\pi\)
\(578\) −8.69906 −0.361833
\(579\) −12.1721 −0.505855
\(580\) 2.57894 0.107085
\(581\) 8.17090 0.338986
\(582\) 13.5896 0.563307
\(583\) −0.993868 −0.0411618
\(584\) −17.5713 −0.727104
\(585\) 1.53899 0.0636293
\(586\) −3.89057 −0.160718
\(587\) 27.9863 1.15512 0.577560 0.816348i \(-0.304005\pi\)
0.577560 + 0.816348i \(0.304005\pi\)
\(588\) 25.4911 1.05123
\(589\) 38.9985 1.60690
\(590\) 0.381530 0.0157073
\(591\) 5.53388 0.227634
\(592\) −8.66592 −0.356167
\(593\) 15.3065 0.628561 0.314281 0.949330i \(-0.398237\pi\)
0.314281 + 0.949330i \(0.398237\pi\)
\(594\) −0.224613 −0.00921599
\(595\) 0.194496 0.00797355
\(596\) −22.7882 −0.933441
\(597\) 43.5374 1.78187
\(598\) −9.45463 −0.386629
\(599\) −17.5465 −0.716930 −0.358465 0.933543i \(-0.616700\pi\)
−0.358465 + 0.933543i \(0.616700\pi\)
\(600\) 27.3276 1.11564
\(601\) 39.5400 1.61287 0.806434 0.591324i \(-0.201394\pi\)
0.806434 + 0.591324i \(0.201394\pi\)
\(602\) 4.96287 0.202271
\(603\) 8.40619 0.342326
\(604\) −27.8884 −1.13476
\(605\) 1.84510 0.0750141
\(606\) −19.8283 −0.805471
\(607\) 25.8799 1.05043 0.525216 0.850969i \(-0.323985\pi\)
0.525216 + 0.850969i \(0.323985\pi\)
\(608\) 21.3731 0.866792
\(609\) 13.4167 0.543673
\(610\) −1.41509 −0.0572953
\(611\) 26.3547 1.06620
\(612\) 8.11602 0.328071
\(613\) 11.3209 0.457246 0.228623 0.973515i \(-0.426578\pi\)
0.228623 + 0.973515i \(0.426578\pi\)
\(614\) 2.38339 0.0961857
\(615\) −2.71676 −0.109551
\(616\) −1.00514 −0.0404983
\(617\) −32.2416 −1.29800 −0.648999 0.760789i \(-0.724812\pi\)
−0.648999 + 0.760789i \(0.724812\pi\)
\(618\) −30.3274 −1.21995
\(619\) −10.9416 −0.439778 −0.219889 0.975525i \(-0.570570\pi\)
−0.219889 + 0.975525i \(0.570570\pi\)
\(620\) 2.91216 0.116955
\(621\) −2.32763 −0.0934045
\(622\) 16.8324 0.674919
\(623\) −0.107369 −0.00430167
\(624\) −13.1074 −0.524718
\(625\) 24.5356 0.981425
\(626\) 7.66269 0.306263
\(627\) 6.56662 0.262246
\(628\) 8.36743 0.333897
\(629\) 9.03626 0.360299
\(630\) −0.190127 −0.00757483
\(631\) −0.302984 −0.0120616 −0.00603081 0.999982i \(-0.501920\pi\)
−0.00603081 + 0.999982i \(0.501920\pi\)
\(632\) 14.3300 0.570018
\(633\) −34.7233 −1.38013
\(634\) 8.60598 0.341787
\(635\) 3.32147 0.131808
\(636\) 5.27610 0.209211
\(637\) 20.7128 0.820670
\(638\) 4.21741 0.166969
\(639\) 41.1523 1.62796
\(640\) 1.98589 0.0784990
\(641\) 44.3485 1.75166 0.875831 0.482619i \(-0.160314\pi\)
0.875831 + 0.482619i \(0.160314\pi\)
\(642\) 11.9790 0.472775
\(643\) −24.9513 −0.983982 −0.491991 0.870600i \(-0.663731\pi\)
−0.491991 + 0.870600i \(0.663731\pi\)
\(644\) −4.62404 −0.182213
\(645\) −5.45380 −0.214743
\(646\) −4.34637 −0.171006
\(647\) 35.1007 1.37995 0.689976 0.723832i \(-0.257621\pi\)
0.689976 + 0.723832i \(0.257621\pi\)
\(648\) 21.8534 0.858484
\(649\) −2.47003 −0.0969571
\(650\) 9.85751 0.386643
\(651\) 15.1503 0.593787
\(652\) 3.61560 0.141598
\(653\) 40.8715 1.59943 0.799713 0.600383i \(-0.204985\pi\)
0.799713 + 0.600383i \(0.204985\pi\)
\(654\) 22.3666 0.874602
\(655\) 0.480929 0.0187915
\(656\) 11.1644 0.435898
\(657\) 21.5176 0.839481
\(658\) −3.25587 −0.126927
\(659\) 34.1506 1.33032 0.665159 0.746702i \(-0.268364\pi\)
0.665159 + 0.746702i \(0.268364\pi\)
\(660\) 0.490354 0.0190870
\(661\) −3.68626 −0.143379 −0.0716895 0.997427i \(-0.522839\pi\)
−0.0716895 + 0.997427i \(0.522839\pi\)
\(662\) 18.2215 0.708197
\(663\) 13.6676 0.530805
\(664\) −30.7141 −1.19194
\(665\) −0.403084 −0.0156309
\(666\) −8.83327 −0.342282
\(667\) 43.7043 1.69224
\(668\) 1.17213 0.0453511
\(669\) −58.9161 −2.27783
\(670\) −0.336163 −0.0129871
\(671\) 9.16130 0.353668
\(672\) 8.30309 0.320299
\(673\) −19.1692 −0.738919 −0.369460 0.929247i \(-0.620457\pi\)
−0.369460 + 0.929247i \(0.620457\pi\)
\(674\) 5.45384 0.210074
\(675\) 2.42681 0.0934081
\(676\) 5.17678 0.199107
\(677\) −28.1525 −1.08199 −0.540994 0.841026i \(-0.681952\pi\)
−0.540994 + 0.841026i \(0.681952\pi\)
\(678\) 14.7020 0.564627
\(679\) 5.40049 0.207252
\(680\) −0.731102 −0.0280365
\(681\) −26.2886 −1.00738
\(682\) 4.76234 0.182359
\(683\) −35.9956 −1.37734 −0.688668 0.725077i \(-0.741804\pi\)
−0.688668 + 0.725077i \(0.741804\pi\)
\(684\) −16.8201 −0.643132
\(685\) −1.28133 −0.0489569
\(686\) −5.26022 −0.200836
\(687\) 47.6270 1.81708
\(688\) 22.4122 0.854456
\(689\) 4.28710 0.163325
\(690\) −1.28357 −0.0488646
\(691\) 7.55169 0.287280 0.143640 0.989630i \(-0.454119\pi\)
0.143640 + 0.989630i \(0.454119\pi\)
\(692\) −0.241813 −0.00919234
\(693\) 1.23088 0.0467574
\(694\) −9.66835 −0.367006
\(695\) −0.144040 −0.00546377
\(696\) −50.4329 −1.91165
\(697\) −11.6415 −0.440955
\(698\) 11.3095 0.428072
\(699\) −33.0283 −1.24924
\(700\) 4.82108 0.182220
\(701\) −6.15196 −0.232356 −0.116178 0.993228i \(-0.537064\pi\)
−0.116178 + 0.993228i \(0.537064\pi\)
\(702\) 0.968879 0.0365680
\(703\) −18.7272 −0.706311
\(704\) 0.0858950 0.00323729
\(705\) 3.57794 0.134753
\(706\) 10.5644 0.397597
\(707\) −7.87976 −0.296349
\(708\) 13.1125 0.492799
\(709\) 48.5620 1.82378 0.911892 0.410430i \(-0.134621\pi\)
0.911892 + 0.410430i \(0.134621\pi\)
\(710\) −1.64568 −0.0617612
\(711\) −17.5484 −0.658117
\(712\) 0.403597 0.0151255
\(713\) 49.3513 1.84822
\(714\) −1.68850 −0.0631903
\(715\) 0.398437 0.0149007
\(716\) 25.9877 0.971207
\(717\) −13.3455 −0.498396
\(718\) 10.4390 0.389580
\(719\) 28.8372 1.07545 0.537724 0.843121i \(-0.319284\pi\)
0.537724 + 0.843121i \(0.319284\pi\)
\(720\) −0.858607 −0.0319984
\(721\) −12.0521 −0.448842
\(722\) −3.05877 −0.113836
\(723\) 19.4209 0.722269
\(724\) −0.435274 −0.0161768
\(725\) −45.5666 −1.69230
\(726\) −16.0181 −0.594486
\(727\) −13.8642 −0.514194 −0.257097 0.966386i \(-0.582766\pi\)
−0.257097 + 0.966386i \(0.582766\pi\)
\(728\) 4.33572 0.160692
\(729\) −23.2337 −0.860508
\(730\) −0.860487 −0.0318480
\(731\) −23.3699 −0.864369
\(732\) −48.6342 −1.79757
\(733\) 36.1980 1.33700 0.668501 0.743711i \(-0.266936\pi\)
0.668501 + 0.743711i \(0.266936\pi\)
\(734\) −4.90418 −0.181016
\(735\) 2.81199 0.103722
\(736\) 27.0469 0.996962
\(737\) 2.17632 0.0801659
\(738\) 11.3800 0.418904
\(739\) 12.6074 0.463769 0.231885 0.972743i \(-0.425511\pi\)
0.231885 + 0.972743i \(0.425511\pi\)
\(740\) −1.39843 −0.0514073
\(741\) −28.3254 −1.04056
\(742\) −0.529628 −0.0194433
\(743\) −1.17912 −0.0432577 −0.0216288 0.999766i \(-0.506885\pi\)
−0.0216288 + 0.999766i \(0.506885\pi\)
\(744\) −56.9493 −2.08786
\(745\) −2.51382 −0.0920993
\(746\) 1.08015 0.0395470
\(747\) 37.6121 1.37615
\(748\) 2.10120 0.0768275
\(749\) 4.76045 0.173943
\(750\) 2.68488 0.0980381
\(751\) 40.8675 1.49128 0.745638 0.666351i \(-0.232145\pi\)
0.745638 + 0.666351i \(0.232145\pi\)
\(752\) −14.7034 −0.536178
\(753\) 13.8151 0.503451
\(754\) −18.1920 −0.662513
\(755\) −3.07643 −0.111963
\(756\) 0.473856 0.0172340
\(757\) −37.7187 −1.37091 −0.685455 0.728115i \(-0.740397\pi\)
−0.685455 + 0.728115i \(0.740397\pi\)
\(758\) 9.91836 0.360251
\(759\) 8.30984 0.301628
\(760\) 1.51517 0.0549612
\(761\) −37.0936 −1.34464 −0.672320 0.740260i \(-0.734702\pi\)
−0.672320 + 0.740260i \(0.734702\pi\)
\(762\) −28.8350 −1.04458
\(763\) 8.88845 0.321784
\(764\) 32.1377 1.16270
\(765\) 0.895299 0.0323696
\(766\) −2.73440 −0.0987978
\(767\) 10.6546 0.384715
\(768\) −17.8114 −0.642714
\(769\) −42.7296 −1.54087 −0.770434 0.637519i \(-0.779961\pi\)
−0.770434 + 0.637519i \(0.779961\pi\)
\(770\) −0.0492230 −0.00177387
\(771\) −58.4032 −2.10334
\(772\) 8.07189 0.290514
\(773\) 47.5229 1.70928 0.854640 0.519220i \(-0.173778\pi\)
0.854640 + 0.519220i \(0.173778\pi\)
\(774\) 22.8450 0.821145
\(775\) −51.4543 −1.84829
\(776\) −20.3002 −0.728736
\(777\) −7.27523 −0.260997
\(778\) −21.7024 −0.778067
\(779\) 24.1265 0.864423
\(780\) −2.11516 −0.0757350
\(781\) 10.6541 0.381235
\(782\) −5.50019 −0.196686
\(783\) −4.47867 −0.160055
\(784\) −11.5557 −0.412705
\(785\) 0.923033 0.0329445
\(786\) −4.17513 −0.148922
\(787\) 25.3634 0.904106 0.452053 0.891991i \(-0.350692\pi\)
0.452053 + 0.891991i \(0.350692\pi\)
\(788\) −3.66978 −0.130731
\(789\) 5.58966 0.198997
\(790\) 0.701760 0.0249675
\(791\) 5.84257 0.207738
\(792\) −4.62684 −0.164408
\(793\) −39.5177 −1.40331
\(794\) 7.83052 0.277895
\(795\) 0.582020 0.0206421
\(796\) −28.8718 −1.02333
\(797\) −12.4440 −0.440791 −0.220395 0.975411i \(-0.570735\pi\)
−0.220395 + 0.975411i \(0.570735\pi\)
\(798\) 3.49933 0.123875
\(799\) 15.3318 0.542398
\(800\) −28.1994 −0.997000
\(801\) −0.494241 −0.0174631
\(802\) −22.3639 −0.789695
\(803\) 5.57080 0.196589
\(804\) −11.5533 −0.407455
\(805\) −0.510089 −0.0179783
\(806\) −20.5426 −0.723581
\(807\) −11.9351 −0.420134
\(808\) 29.6197 1.04202
\(809\) −37.2615 −1.31004 −0.655022 0.755610i \(-0.727341\pi\)
−0.655022 + 0.755610i \(0.727341\pi\)
\(810\) 1.07019 0.0376026
\(811\) −32.5136 −1.14171 −0.570853 0.821052i \(-0.693387\pi\)
−0.570853 + 0.821052i \(0.693387\pi\)
\(812\) −8.89727 −0.312233
\(813\) −49.5952 −1.73938
\(814\) −2.28689 −0.0801556
\(815\) 0.398846 0.0139710
\(816\) −7.62519 −0.266935
\(817\) 48.4331 1.69446
\(818\) −4.67206 −0.163355
\(819\) −5.30947 −0.185528
\(820\) 1.80162 0.0629152
\(821\) 26.9597 0.940899 0.470449 0.882427i \(-0.344092\pi\)
0.470449 + 0.882427i \(0.344092\pi\)
\(822\) 11.1237 0.387983
\(823\) −34.6716 −1.20858 −0.604288 0.796766i \(-0.706542\pi\)
−0.604288 + 0.796766i \(0.706542\pi\)
\(824\) 45.3032 1.57821
\(825\) −8.66394 −0.301640
\(826\) −1.31627 −0.0457989
\(827\) −10.3523 −0.359983 −0.179992 0.983668i \(-0.557607\pi\)
−0.179992 + 0.983668i \(0.557607\pi\)
\(828\) −21.2853 −0.739714
\(829\) 37.8331 1.31400 0.656998 0.753892i \(-0.271826\pi\)
0.656998 + 0.753892i \(0.271826\pi\)
\(830\) −1.50411 −0.0522083
\(831\) 78.1115 2.70966
\(832\) −0.370512 −0.0128452
\(833\) 12.0496 0.417493
\(834\) 1.25047 0.0433003
\(835\) 0.129301 0.00447464
\(836\) −4.35464 −0.150608
\(837\) −5.05736 −0.174808
\(838\) 10.8218 0.373834
\(839\) 34.8243 1.20227 0.601134 0.799148i \(-0.294716\pi\)
0.601134 + 0.799148i \(0.294716\pi\)
\(840\) 0.588621 0.0203094
\(841\) 55.0930 1.89976
\(842\) −12.0266 −0.414466
\(843\) 64.6866 2.22792
\(844\) 23.0267 0.792612
\(845\) 0.571064 0.0196452
\(846\) −14.9873 −0.515275
\(847\) −6.36556 −0.218723
\(848\) −2.39179 −0.0821343
\(849\) 46.8421 1.60762
\(850\) 5.73456 0.196694
\(851\) −23.6987 −0.812380
\(852\) −56.5591 −1.93768
\(853\) −39.5421 −1.35389 −0.676947 0.736032i \(-0.736697\pi\)
−0.676947 + 0.736032i \(0.736697\pi\)
\(854\) 4.88202 0.167059
\(855\) −1.85547 −0.0634556
\(856\) −17.8943 −0.611616
\(857\) −31.8063 −1.08648 −0.543242 0.839576i \(-0.682803\pi\)
−0.543242 + 0.839576i \(0.682803\pi\)
\(858\) −3.45899 −0.118088
\(859\) −46.6429 −1.59144 −0.795718 0.605668i \(-0.792906\pi\)
−0.795718 + 0.605668i \(0.792906\pi\)
\(860\) 3.61668 0.123328
\(861\) 9.37277 0.319423
\(862\) −13.1085 −0.446478
\(863\) 1.38859 0.0472681 0.0236341 0.999721i \(-0.492476\pi\)
0.0236341 + 0.999721i \(0.492476\pi\)
\(864\) −2.77168 −0.0942943
\(865\) −0.0266750 −0.000906976 0
\(866\) −19.0735 −0.648145
\(867\) −32.9803 −1.12007
\(868\) −10.0469 −0.341013
\(869\) −4.54320 −0.154118
\(870\) −2.46976 −0.0837328
\(871\) −9.38768 −0.318089
\(872\) −33.4113 −1.13145
\(873\) 24.8594 0.841364
\(874\) 11.3989 0.385573
\(875\) 1.06697 0.0360702
\(876\) −29.5735 −0.999195
\(877\) −16.7394 −0.565249 −0.282624 0.959231i \(-0.591205\pi\)
−0.282624 + 0.959231i \(0.591205\pi\)
\(878\) −5.02971 −0.169744
\(879\) −14.7501 −0.497510
\(880\) −0.222289 −0.00749337
\(881\) −35.2674 −1.18819 −0.594095 0.804395i \(-0.702490\pi\)
−0.594095 + 0.804395i \(0.702490\pi\)
\(882\) −11.7789 −0.396616
\(883\) −12.2091 −0.410870 −0.205435 0.978671i \(-0.565861\pi\)
−0.205435 + 0.978671i \(0.565861\pi\)
\(884\) −9.06363 −0.304843
\(885\) 1.44648 0.0486228
\(886\) −20.0959 −0.675136
\(887\) −54.0998 −1.81649 −0.908247 0.418435i \(-0.862579\pi\)
−0.908247 + 0.418435i \(0.862579\pi\)
\(888\) 27.3473 0.917715
\(889\) −11.4590 −0.384322
\(890\) 0.0197647 0.000662513 0
\(891\) −6.92842 −0.232111
\(892\) 39.0701 1.30816
\(893\) −31.7743 −1.06329
\(894\) 21.8235 0.729887
\(895\) 2.86677 0.0958257
\(896\) −6.85126 −0.228884
\(897\) −35.8449 −1.19683
\(898\) 11.0040 0.367210
\(899\) 94.9586 3.16705
\(900\) 22.1923 0.739742
\(901\) 2.49400 0.0830871
\(902\) 2.94624 0.0980989
\(903\) 18.8155 0.626140
\(904\) −21.9620 −0.730444
\(905\) −0.0480162 −0.00159611
\(906\) 26.7077 0.887305
\(907\) 10.3854 0.344842 0.172421 0.985023i \(-0.444841\pi\)
0.172421 + 0.985023i \(0.444841\pi\)
\(908\) 17.4332 0.578542
\(909\) −36.2719 −1.20306
\(910\) 0.212326 0.00703852
\(911\) 38.4824 1.27498 0.637490 0.770459i \(-0.279973\pi\)
0.637490 + 0.770459i \(0.279973\pi\)
\(912\) 15.8029 0.523285
\(913\) 9.73760 0.322268
\(914\) −8.98030 −0.297042
\(915\) −5.36496 −0.177360
\(916\) −31.5838 −1.04356
\(917\) −1.65919 −0.0547914
\(918\) 0.563641 0.0186029
\(919\) 13.5106 0.445675 0.222837 0.974856i \(-0.428468\pi\)
0.222837 + 0.974856i \(0.428468\pi\)
\(920\) 1.91740 0.0632149
\(921\) 9.03603 0.297747
\(922\) 0.907773 0.0298959
\(923\) −45.9571 −1.51270
\(924\) −1.69171 −0.0556531
\(925\) 24.7085 0.812412
\(926\) 0.214087 0.00703533
\(927\) −55.4778 −1.82213
\(928\) 52.0419 1.70836
\(929\) −6.58540 −0.216060 −0.108030 0.994148i \(-0.534454\pi\)
−0.108030 + 0.994148i \(0.534454\pi\)
\(930\) −2.78888 −0.0914509
\(931\) −24.9722 −0.818430
\(932\) 21.9026 0.717445
\(933\) 63.8160 2.08924
\(934\) −13.1931 −0.431690
\(935\) 0.231789 0.00758031
\(936\) 19.9581 0.652350
\(937\) −33.4636 −1.09321 −0.546604 0.837391i \(-0.684080\pi\)
−0.546604 + 0.837391i \(0.684080\pi\)
\(938\) 1.15975 0.0378673
\(939\) 29.0512 0.948050
\(940\) −2.37271 −0.0773891
\(941\) 29.6727 0.967303 0.483651 0.875261i \(-0.339310\pi\)
0.483651 + 0.875261i \(0.339310\pi\)
\(942\) −8.01321 −0.261085
\(943\) 30.5313 0.994237
\(944\) −5.94423 −0.193468
\(945\) 0.0522722 0.00170042
\(946\) 5.91446 0.192296
\(947\) −38.4749 −1.25027 −0.625133 0.780518i \(-0.714955\pi\)
−0.625133 + 0.780518i \(0.714955\pi\)
\(948\) 24.1183 0.783325
\(949\) −24.0299 −0.780044
\(950\) −11.8846 −0.385588
\(951\) 32.6274 1.05802
\(952\) 2.52228 0.0817477
\(953\) 20.7040 0.670669 0.335335 0.942099i \(-0.391151\pi\)
0.335335 + 0.942099i \(0.391151\pi\)
\(954\) −2.43797 −0.0789323
\(955\) 3.54519 0.114720
\(956\) 8.85003 0.286230
\(957\) 15.9893 0.516860
\(958\) 3.89572 0.125865
\(959\) 4.42054 0.142747
\(960\) −0.0503011 −0.00162346
\(961\) 76.2281 2.45897
\(962\) 9.86462 0.318048
\(963\) 21.9132 0.706143
\(964\) −12.8789 −0.414801
\(965\) 0.890431 0.0286640
\(966\) 4.42828 0.142478
\(967\) 6.81229 0.219069 0.109534 0.993983i \(-0.465064\pi\)
0.109534 + 0.993983i \(0.465064\pi\)
\(968\) 23.9279 0.769072
\(969\) −16.4782 −0.529356
\(970\) −0.994127 −0.0319195
\(971\) −43.2325 −1.38740 −0.693698 0.720266i \(-0.744020\pi\)
−0.693698 + 0.720266i \(0.744020\pi\)
\(972\) 34.4412 1.10470
\(973\) 0.496936 0.0159310
\(974\) −18.9929 −0.608570
\(975\) 37.3723 1.19687
\(976\) 22.0471 0.705709
\(977\) −45.3628 −1.45128 −0.725642 0.688073i \(-0.758457\pi\)
−0.725642 + 0.688073i \(0.758457\pi\)
\(978\) −3.46254 −0.110720
\(979\) −0.127957 −0.00408951
\(980\) −1.86476 −0.0595677
\(981\) 40.9151 1.30632
\(982\) 4.11508 0.131317
\(983\) −1.32516 −0.0422661 −0.0211331 0.999777i \(-0.506727\pi\)
−0.0211331 + 0.999777i \(0.506727\pi\)
\(984\) −35.2319 −1.12315
\(985\) −0.404823 −0.0128987
\(986\) −10.5831 −0.337035
\(987\) −12.3438 −0.392908
\(988\) 18.7840 0.597597
\(989\) 61.2905 1.94893
\(990\) −0.226582 −0.00720125
\(991\) 0.415651 0.0132036 0.00660180 0.999978i \(-0.497899\pi\)
0.00660180 + 0.999978i \(0.497899\pi\)
\(992\) 58.7662 1.86583
\(993\) 69.0822 2.19226
\(994\) 5.67755 0.180081
\(995\) −3.18492 −0.100969
\(996\) −51.6935 −1.63797
\(997\) 54.8267 1.73638 0.868190 0.496232i \(-0.165283\pi\)
0.868190 + 0.496232i \(0.165283\pi\)
\(998\) −19.7276 −0.624465
\(999\) 2.42856 0.0768363
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 4001.2.a.b.1.109 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.109 184 1.1 even 1 trivial