Properties

Label 4026.2.a.x.1.2
Level $4026$
Weight $2$
Character 4026.1
Self dual yes
Analytic conductor $32.148$
Analytic rank $1$
Dimension $6$
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] = [4026,2,Mod(1,4026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.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: \(32.1477718538\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.46101901.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 5x^{4} + 12x^{3} + 6x^{2} - 5x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.90193\) of defining polynomial
Character \(\chi\) \(=\) 4026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.05628 q^{5} -1.00000 q^{6} -1.59539 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.05628 q^{5} -1.00000 q^{6} -1.59539 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.05628 q^{10} -1.00000 q^{11} -1.00000 q^{12} +3.49732 q^{13} -1.59539 q^{14} +4.05628 q^{15} +1.00000 q^{16} +7.31489 q^{17} +1.00000 q^{18} -1.76811 q^{19} -4.05628 q^{20} +1.59539 q^{21} -1.00000 q^{22} -6.99038 q^{23} -1.00000 q^{24} +11.4534 q^{25} +3.49732 q^{26} -1.00000 q^{27} -1.59539 q^{28} +0.0241165 q^{29} +4.05628 q^{30} +8.75593 q^{31} +1.00000 q^{32} +1.00000 q^{33} +7.31489 q^{34} +6.47134 q^{35} +1.00000 q^{36} -4.81967 q^{37} -1.76811 q^{38} -3.49732 q^{39} -4.05628 q^{40} -7.72352 q^{41} +1.59539 q^{42} +9.27497 q^{43} -1.00000 q^{44} -4.05628 q^{45} -6.99038 q^{46} -2.91348 q^{47} -1.00000 q^{48} -4.45474 q^{49} +11.4534 q^{50} -7.31489 q^{51} +3.49732 q^{52} -6.04474 q^{53} -1.00000 q^{54} +4.05628 q^{55} -1.59539 q^{56} +1.76811 q^{57} +0.0241165 q^{58} -1.28905 q^{59} +4.05628 q^{60} +1.00000 q^{61} +8.75593 q^{62} -1.59539 q^{63} +1.00000 q^{64} -14.1861 q^{65} +1.00000 q^{66} +7.70883 q^{67} +7.31489 q^{68} +6.99038 q^{69} +6.47134 q^{70} +5.90050 q^{71} +1.00000 q^{72} -13.4718 q^{73} -4.81967 q^{74} -11.4534 q^{75} -1.76811 q^{76} +1.59539 q^{77} -3.49732 q^{78} -12.4045 q^{79} -4.05628 q^{80} +1.00000 q^{81} -7.72352 q^{82} +17.4819 q^{83} +1.59539 q^{84} -29.6713 q^{85} +9.27497 q^{86} -0.0241165 q^{87} -1.00000 q^{88} -15.3912 q^{89} -4.05628 q^{90} -5.57958 q^{91} -6.99038 q^{92} -8.75593 q^{93} -2.91348 q^{94} +7.17196 q^{95} -1.00000 q^{96} -7.51149 q^{97} -4.45474 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −4.05628 −1.81402 −0.907012 0.421104i \(-0.861643\pi\)
−0.907012 + 0.421104i \(0.861643\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.59539 −0.603000 −0.301500 0.953466i \(-0.597487\pi\)
−0.301500 + 0.953466i \(0.597487\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −4.05628 −1.28271
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) 3.49732 0.969982 0.484991 0.874519i \(-0.338823\pi\)
0.484991 + 0.874519i \(0.338823\pi\)
\(14\) −1.59539 −0.426385
\(15\) 4.05628 1.04733
\(16\) 1.00000 0.250000
\(17\) 7.31489 1.77412 0.887061 0.461653i \(-0.152744\pi\)
0.887061 + 0.461653i \(0.152744\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.76811 −0.405632 −0.202816 0.979217i \(-0.565009\pi\)
−0.202816 + 0.979217i \(0.565009\pi\)
\(20\) −4.05628 −0.907012
\(21\) 1.59539 0.348142
\(22\) −1.00000 −0.213201
\(23\) −6.99038 −1.45760 −0.728798 0.684729i \(-0.759921\pi\)
−0.728798 + 0.684729i \(0.759921\pi\)
\(24\) −1.00000 −0.204124
\(25\) 11.4534 2.29069
\(26\) 3.49732 0.685881
\(27\) −1.00000 −0.192450
\(28\) −1.59539 −0.301500
\(29\) 0.0241165 0.00447832 0.00223916 0.999997i \(-0.499287\pi\)
0.00223916 + 0.999997i \(0.499287\pi\)
\(30\) 4.05628 0.740573
\(31\) 8.75593 1.57261 0.786305 0.617838i \(-0.211991\pi\)
0.786305 + 0.617838i \(0.211991\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 7.31489 1.25449
\(35\) 6.47134 1.09386
\(36\) 1.00000 0.166667
\(37\) −4.81967 −0.792349 −0.396175 0.918175i \(-0.629663\pi\)
−0.396175 + 0.918175i \(0.629663\pi\)
\(38\) −1.76811 −0.286825
\(39\) −3.49732 −0.560020
\(40\) −4.05628 −0.641355
\(41\) −7.72352 −1.20621 −0.603105 0.797662i \(-0.706070\pi\)
−0.603105 + 0.797662i \(0.706070\pi\)
\(42\) 1.59539 0.246174
\(43\) 9.27497 1.41442 0.707210 0.707004i \(-0.249954\pi\)
0.707210 + 0.707004i \(0.249954\pi\)
\(44\) −1.00000 −0.150756
\(45\) −4.05628 −0.604675
\(46\) −6.99038 −1.03068
\(47\) −2.91348 −0.424975 −0.212487 0.977164i \(-0.568156\pi\)
−0.212487 + 0.977164i \(0.568156\pi\)
\(48\) −1.00000 −0.144338
\(49\) −4.45474 −0.636391
\(50\) 11.4534 1.61976
\(51\) −7.31489 −1.02429
\(52\) 3.49732 0.484991
\(53\) −6.04474 −0.830308 −0.415154 0.909751i \(-0.636272\pi\)
−0.415154 + 0.909751i \(0.636272\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.05628 0.546949
\(56\) −1.59539 −0.213193
\(57\) 1.76811 0.234192
\(58\) 0.0241165 0.00316665
\(59\) −1.28905 −0.167820 −0.0839102 0.996473i \(-0.526741\pi\)
−0.0839102 + 0.996473i \(0.526741\pi\)
\(60\) 4.05628 0.523664
\(61\) 1.00000 0.128037
\(62\) 8.75593 1.11200
\(63\) −1.59539 −0.201000
\(64\) 1.00000 0.125000
\(65\) −14.1861 −1.75957
\(66\) 1.00000 0.123091
\(67\) 7.70883 0.941784 0.470892 0.882191i \(-0.343932\pi\)
0.470892 + 0.882191i \(0.343932\pi\)
\(68\) 7.31489 0.887061
\(69\) 6.99038 0.841543
\(70\) 6.47134 0.773473
\(71\) 5.90050 0.700260 0.350130 0.936701i \(-0.386137\pi\)
0.350130 + 0.936701i \(0.386137\pi\)
\(72\) 1.00000 0.117851
\(73\) −13.4718 −1.57676 −0.788378 0.615191i \(-0.789079\pi\)
−0.788378 + 0.615191i \(0.789079\pi\)
\(74\) −4.81967 −0.560276
\(75\) −11.4534 −1.32253
\(76\) −1.76811 −0.202816
\(77\) 1.59539 0.181811
\(78\) −3.49732 −0.395994
\(79\) −12.4045 −1.39562 −0.697810 0.716283i \(-0.745842\pi\)
−0.697810 + 0.716283i \(0.745842\pi\)
\(80\) −4.05628 −0.453506
\(81\) 1.00000 0.111111
\(82\) −7.72352 −0.852920
\(83\) 17.4819 1.91889 0.959445 0.281896i \(-0.0909633\pi\)
0.959445 + 0.281896i \(0.0909633\pi\)
\(84\) 1.59539 0.174071
\(85\) −29.6713 −3.21830
\(86\) 9.27497 1.00015
\(87\) −0.0241165 −0.00258556
\(88\) −1.00000 −0.106600
\(89\) −15.3912 −1.63147 −0.815734 0.578427i \(-0.803667\pi\)
−0.815734 + 0.578427i \(0.803667\pi\)
\(90\) −4.05628 −0.427570
\(91\) −5.57958 −0.584899
\(92\) −6.99038 −0.728798
\(93\) −8.75593 −0.907947
\(94\) −2.91348 −0.300503
\(95\) 7.17196 0.735827
\(96\) −1.00000 −0.102062
\(97\) −7.51149 −0.762676 −0.381338 0.924436i \(-0.624537\pi\)
−0.381338 + 0.924436i \(0.624537\pi\)
\(98\) −4.45474 −0.449997
\(99\) −1.00000 −0.100504
\(100\) 11.4534 1.14534
\(101\) −8.79915 −0.875548 −0.437774 0.899085i \(-0.644233\pi\)
−0.437774 + 0.899085i \(0.644233\pi\)
\(102\) −7.31489 −0.724282
\(103\) −9.36709 −0.922967 −0.461483 0.887149i \(-0.652683\pi\)
−0.461483 + 0.887149i \(0.652683\pi\)
\(104\) 3.49732 0.342941
\(105\) −6.47134 −0.631538
\(106\) −6.04474 −0.587117
\(107\) −15.5823 −1.50640 −0.753200 0.657792i \(-0.771491\pi\)
−0.753200 + 0.657792i \(0.771491\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 15.1906 1.45499 0.727497 0.686110i \(-0.240683\pi\)
0.727497 + 0.686110i \(0.240683\pi\)
\(110\) 4.05628 0.386751
\(111\) 4.81967 0.457463
\(112\) −1.59539 −0.150750
\(113\) −10.1615 −0.955915 −0.477957 0.878383i \(-0.658623\pi\)
−0.477957 + 0.878383i \(0.658623\pi\)
\(114\) 1.76811 0.165599
\(115\) 28.3550 2.64411
\(116\) 0.0241165 0.00223916
\(117\) 3.49732 0.323327
\(118\) −1.28905 −0.118667
\(119\) −11.6701 −1.06979
\(120\) 4.05628 0.370286
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 7.72352 0.696406
\(124\) 8.75593 0.786305
\(125\) −26.1769 −2.34134
\(126\) −1.59539 −0.142128
\(127\) −2.08914 −0.185381 −0.0926904 0.995695i \(-0.529547\pi\)
−0.0926904 + 0.995695i \(0.529547\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.27497 −0.816615
\(130\) −14.1861 −1.24421
\(131\) 18.2582 1.59523 0.797614 0.603169i \(-0.206095\pi\)
0.797614 + 0.603169i \(0.206095\pi\)
\(132\) 1.00000 0.0870388
\(133\) 2.82082 0.244596
\(134\) 7.70883 0.665942
\(135\) 4.05628 0.349109
\(136\) 7.31489 0.627247
\(137\) −8.18386 −0.699194 −0.349597 0.936900i \(-0.613682\pi\)
−0.349597 + 0.936900i \(0.613682\pi\)
\(138\) 6.99038 0.595061
\(139\) −21.3918 −1.81443 −0.907215 0.420668i \(-0.861796\pi\)
−0.907215 + 0.420668i \(0.861796\pi\)
\(140\) 6.47134 0.546928
\(141\) 2.91348 0.245359
\(142\) 5.90050 0.495159
\(143\) −3.49732 −0.292461
\(144\) 1.00000 0.0833333
\(145\) −0.0978233 −0.00812378
\(146\) −13.4718 −1.11493
\(147\) 4.45474 0.367421
\(148\) −4.81967 −0.396175
\(149\) 15.9486 1.30656 0.653282 0.757115i \(-0.273392\pi\)
0.653282 + 0.757115i \(0.273392\pi\)
\(150\) −11.4534 −0.935169
\(151\) 7.33832 0.597184 0.298592 0.954381i \(-0.403483\pi\)
0.298592 + 0.954381i \(0.403483\pi\)
\(152\) −1.76811 −0.143413
\(153\) 7.31489 0.591374
\(154\) 1.59539 0.128560
\(155\) −35.5165 −2.85276
\(156\) −3.49732 −0.280010
\(157\) −10.6194 −0.847518 −0.423759 0.905775i \(-0.639290\pi\)
−0.423759 + 0.905775i \(0.639290\pi\)
\(158\) −12.4045 −0.986852
\(159\) 6.04474 0.479379
\(160\) −4.05628 −0.320677
\(161\) 11.1524 0.878930
\(162\) 1.00000 0.0785674
\(163\) −3.56996 −0.279621 −0.139811 0.990178i \(-0.544649\pi\)
−0.139811 + 0.990178i \(0.544649\pi\)
\(164\) −7.72352 −0.603105
\(165\) −4.05628 −0.315781
\(166\) 17.4819 1.35686
\(167\) −7.41687 −0.573934 −0.286967 0.957940i \(-0.592647\pi\)
−0.286967 + 0.957940i \(0.592647\pi\)
\(168\) 1.59539 0.123087
\(169\) −0.768748 −0.0591345
\(170\) −29.6713 −2.27568
\(171\) −1.76811 −0.135211
\(172\) 9.27497 0.707210
\(173\) −14.3532 −1.09126 −0.545628 0.838028i \(-0.683709\pi\)
−0.545628 + 0.838028i \(0.683709\pi\)
\(174\) −0.0241165 −0.00182827
\(175\) −18.2727 −1.38128
\(176\) −1.00000 −0.0753778
\(177\) 1.28905 0.0968911
\(178\) −15.3912 −1.15362
\(179\) 3.34343 0.249899 0.124950 0.992163i \(-0.460123\pi\)
0.124950 + 0.992163i \(0.460123\pi\)
\(180\) −4.05628 −0.302337
\(181\) −18.1342 −1.34791 −0.673953 0.738774i \(-0.735405\pi\)
−0.673953 + 0.738774i \(0.735405\pi\)
\(182\) −5.57958 −0.413586
\(183\) −1.00000 −0.0739221
\(184\) −6.99038 −0.515338
\(185\) 19.5500 1.43734
\(186\) −8.75593 −0.642016
\(187\) −7.31489 −0.534918
\(188\) −2.91348 −0.212487
\(189\) 1.59539 0.116047
\(190\) 7.17196 0.520309
\(191\) −15.6458 −1.13209 −0.566045 0.824374i \(-0.691527\pi\)
−0.566045 + 0.824374i \(0.691527\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 18.9924 1.36710 0.683551 0.729903i \(-0.260435\pi\)
0.683551 + 0.729903i \(0.260435\pi\)
\(194\) −7.51149 −0.539293
\(195\) 14.1861 1.01589
\(196\) −4.45474 −0.318196
\(197\) −22.8297 −1.62655 −0.813276 0.581878i \(-0.802318\pi\)
−0.813276 + 0.581878i \(0.802318\pi\)
\(198\) −1.00000 −0.0710669
\(199\) −19.4535 −1.37902 −0.689510 0.724276i \(-0.742174\pi\)
−0.689510 + 0.724276i \(0.742174\pi\)
\(200\) 11.4534 0.809880
\(201\) −7.70883 −0.543739
\(202\) −8.79915 −0.619106
\(203\) −0.0384751 −0.00270043
\(204\) −7.31489 −0.512145
\(205\) 31.3288 2.18810
\(206\) −9.36709 −0.652636
\(207\) −6.99038 −0.485865
\(208\) 3.49732 0.242496
\(209\) 1.76811 0.122303
\(210\) −6.47134 −0.446565
\(211\) 11.3970 0.784603 0.392302 0.919837i \(-0.371679\pi\)
0.392302 + 0.919837i \(0.371679\pi\)
\(212\) −6.04474 −0.415154
\(213\) −5.90050 −0.404295
\(214\) −15.5823 −1.06519
\(215\) −37.6219 −2.56579
\(216\) −1.00000 −0.0680414
\(217\) −13.9691 −0.948284
\(218\) 15.1906 1.02884
\(219\) 13.4718 0.910340
\(220\) 4.05628 0.273475
\(221\) 25.5825 1.72087
\(222\) 4.81967 0.323475
\(223\) 21.5423 1.44258 0.721288 0.692635i \(-0.243550\pi\)
0.721288 + 0.692635i \(0.243550\pi\)
\(224\) −1.59539 −0.106596
\(225\) 11.4534 0.763562
\(226\) −10.1615 −0.675934
\(227\) 19.6763 1.30596 0.652980 0.757375i \(-0.273518\pi\)
0.652980 + 0.757375i \(0.273518\pi\)
\(228\) 1.76811 0.117096
\(229\) −6.12424 −0.404701 −0.202351 0.979313i \(-0.564858\pi\)
−0.202351 + 0.979313i \(0.564858\pi\)
\(230\) 28.3550 1.86967
\(231\) −1.59539 −0.104969
\(232\) 0.0241165 0.00158332
\(233\) −16.9596 −1.11106 −0.555530 0.831497i \(-0.687485\pi\)
−0.555530 + 0.831497i \(0.687485\pi\)
\(234\) 3.49732 0.228627
\(235\) 11.8179 0.770915
\(236\) −1.28905 −0.0839102
\(237\) 12.4045 0.805761
\(238\) −11.6701 −0.756459
\(239\) 9.48939 0.613818 0.306909 0.951739i \(-0.400705\pi\)
0.306909 + 0.951739i \(0.400705\pi\)
\(240\) 4.05628 0.261832
\(241\) −6.07417 −0.391272 −0.195636 0.980677i \(-0.562677\pi\)
−0.195636 + 0.980677i \(0.562677\pi\)
\(242\) 1.00000 0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 1.00000 0.0640184
\(245\) 18.0697 1.15443
\(246\) 7.72352 0.492433
\(247\) −6.18365 −0.393456
\(248\) 8.75593 0.556002
\(249\) −17.4819 −1.10787
\(250\) −26.1769 −1.65558
\(251\) −1.76315 −0.111289 −0.0556447 0.998451i \(-0.517721\pi\)
−0.0556447 + 0.998451i \(0.517721\pi\)
\(252\) −1.59539 −0.100500
\(253\) 6.99038 0.439482
\(254\) −2.08914 −0.131084
\(255\) 29.6713 1.85809
\(256\) 1.00000 0.0625000
\(257\) −24.0061 −1.49746 −0.748731 0.662874i \(-0.769337\pi\)
−0.748731 + 0.662874i \(0.769337\pi\)
\(258\) −9.27497 −0.577434
\(259\) 7.68924 0.477786
\(260\) −14.1861 −0.879786
\(261\) 0.0241165 0.00149277
\(262\) 18.2582 1.12800
\(263\) −3.36152 −0.207280 −0.103640 0.994615i \(-0.533049\pi\)
−0.103640 + 0.994615i \(0.533049\pi\)
\(264\) 1.00000 0.0615457
\(265\) 24.5192 1.50620
\(266\) 2.82082 0.172956
\(267\) 15.3912 0.941928
\(268\) 7.70883 0.470892
\(269\) 18.7805 1.14507 0.572535 0.819881i \(-0.305960\pi\)
0.572535 + 0.819881i \(0.305960\pi\)
\(270\) 4.05628 0.246858
\(271\) 2.15131 0.130683 0.0653413 0.997863i \(-0.479186\pi\)
0.0653413 + 0.997863i \(0.479186\pi\)
\(272\) 7.31489 0.443530
\(273\) 5.57958 0.337692
\(274\) −8.18386 −0.494405
\(275\) −11.4534 −0.690668
\(276\) 6.99038 0.420772
\(277\) 19.4266 1.16723 0.583614 0.812031i \(-0.301638\pi\)
0.583614 + 0.812031i \(0.301638\pi\)
\(278\) −21.3918 −1.28300
\(279\) 8.75593 0.524204
\(280\) 6.47134 0.386737
\(281\) −6.42452 −0.383255 −0.191627 0.981468i \(-0.561376\pi\)
−0.191627 + 0.981468i \(0.561376\pi\)
\(282\) 2.91348 0.173495
\(283\) −11.1655 −0.663719 −0.331860 0.943329i \(-0.607676\pi\)
−0.331860 + 0.943329i \(0.607676\pi\)
\(284\) 5.90050 0.350130
\(285\) −7.17196 −0.424830
\(286\) −3.49732 −0.206801
\(287\) 12.3220 0.727345
\(288\) 1.00000 0.0589256
\(289\) 36.5076 2.14751
\(290\) −0.0978233 −0.00574438
\(291\) 7.51149 0.440331
\(292\) −13.4718 −0.788378
\(293\) −13.7647 −0.804140 −0.402070 0.915609i \(-0.631709\pi\)
−0.402070 + 0.915609i \(0.631709\pi\)
\(294\) 4.45474 0.259806
\(295\) 5.22876 0.304430
\(296\) −4.81967 −0.280138
\(297\) 1.00000 0.0580259
\(298\) 15.9486 0.923880
\(299\) −24.4476 −1.41384
\(300\) −11.4534 −0.661264
\(301\) −14.7972 −0.852894
\(302\) 7.33832 0.422273
\(303\) 8.79915 0.505498
\(304\) −1.76811 −0.101408
\(305\) −4.05628 −0.232262
\(306\) 7.31489 0.418164
\(307\) 20.1444 1.14970 0.574851 0.818258i \(-0.305060\pi\)
0.574851 + 0.818258i \(0.305060\pi\)
\(308\) 1.59539 0.0909056
\(309\) 9.36709 0.532875
\(310\) −35.5165 −2.01720
\(311\) −7.95965 −0.451350 −0.225675 0.974203i \(-0.572459\pi\)
−0.225675 + 0.974203i \(0.572459\pi\)
\(312\) −3.49732 −0.197997
\(313\) 19.6501 1.11069 0.555345 0.831620i \(-0.312586\pi\)
0.555345 + 0.831620i \(0.312586\pi\)
\(314\) −10.6194 −0.599286
\(315\) 6.47134 0.364619
\(316\) −12.4045 −0.697810
\(317\) −10.4525 −0.587072 −0.293536 0.955948i \(-0.594832\pi\)
−0.293536 + 0.955948i \(0.594832\pi\)
\(318\) 6.04474 0.338972
\(319\) −0.0241165 −0.00135026
\(320\) −4.05628 −0.226753
\(321\) 15.5823 0.869720
\(322\) 11.1524 0.621497
\(323\) −12.9335 −0.719641
\(324\) 1.00000 0.0555556
\(325\) 40.0563 2.22193
\(326\) −3.56996 −0.197722
\(327\) −15.1906 −0.840042
\(328\) −7.72352 −0.426460
\(329\) 4.64813 0.256260
\(330\) −4.05628 −0.223291
\(331\) 16.3350 0.897855 0.448927 0.893568i \(-0.351806\pi\)
0.448927 + 0.893568i \(0.351806\pi\)
\(332\) 17.4819 0.959445
\(333\) −4.81967 −0.264116
\(334\) −7.41687 −0.405833
\(335\) −31.2692 −1.70842
\(336\) 1.59539 0.0870355
\(337\) 16.2029 0.882627 0.441314 0.897353i \(-0.354513\pi\)
0.441314 + 0.897353i \(0.354513\pi\)
\(338\) −0.768748 −0.0418144
\(339\) 10.1615 0.551898
\(340\) −29.6713 −1.60915
\(341\) −8.75593 −0.474160
\(342\) −1.76811 −0.0956085
\(343\) 18.2747 0.986744
\(344\) 9.27497 0.500073
\(345\) −28.3550 −1.52658
\(346\) −14.3532 −0.771634
\(347\) 34.3941 1.84637 0.923186 0.384353i \(-0.125575\pi\)
0.923186 + 0.384353i \(0.125575\pi\)
\(348\) −0.0241165 −0.00129278
\(349\) 5.63869 0.301832 0.150916 0.988547i \(-0.451778\pi\)
0.150916 + 0.988547i \(0.451778\pi\)
\(350\) −18.2727 −0.976715
\(351\) −3.49732 −0.186673
\(352\) −1.00000 −0.0533002
\(353\) −1.44339 −0.0768241 −0.0384121 0.999262i \(-0.512230\pi\)
−0.0384121 + 0.999262i \(0.512230\pi\)
\(354\) 1.28905 0.0685124
\(355\) −23.9341 −1.27029
\(356\) −15.3912 −0.815734
\(357\) 11.6701 0.617646
\(358\) 3.34343 0.176706
\(359\) −17.9121 −0.945366 −0.472683 0.881233i \(-0.656714\pi\)
−0.472683 + 0.881233i \(0.656714\pi\)
\(360\) −4.05628 −0.213785
\(361\) −15.8738 −0.835462
\(362\) −18.1342 −0.953114
\(363\) −1.00000 −0.0524864
\(364\) −5.57958 −0.292450
\(365\) 54.6455 2.86027
\(366\) −1.00000 −0.0522708
\(367\) −2.10345 −0.109799 −0.0548997 0.998492i \(-0.517484\pi\)
−0.0548997 + 0.998492i \(0.517484\pi\)
\(368\) −6.99038 −0.364399
\(369\) −7.72352 −0.402070
\(370\) 19.5500 1.01635
\(371\) 9.64370 0.500676
\(372\) −8.75593 −0.453974
\(373\) 35.0349 1.81404 0.907018 0.421092i \(-0.138353\pi\)
0.907018 + 0.421092i \(0.138353\pi\)
\(374\) −7.31489 −0.378244
\(375\) 26.1769 1.35177
\(376\) −2.91348 −0.150251
\(377\) 0.0843431 0.00434389
\(378\) 1.59539 0.0820579
\(379\) −19.6090 −1.00725 −0.503624 0.863923i \(-0.668000\pi\)
−0.503624 + 0.863923i \(0.668000\pi\)
\(380\) 7.17196 0.367914
\(381\) 2.08914 0.107030
\(382\) −15.6458 −0.800508
\(383\) −24.4725 −1.25049 −0.625244 0.780430i \(-0.715000\pi\)
−0.625244 + 0.780430i \(0.715000\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −6.47134 −0.329810
\(386\) 18.9924 0.966687
\(387\) 9.27497 0.471473
\(388\) −7.51149 −0.381338
\(389\) −35.5397 −1.80193 −0.900967 0.433887i \(-0.857142\pi\)
−0.900967 + 0.433887i \(0.857142\pi\)
\(390\) 14.1861 0.718342
\(391\) −51.1339 −2.58595
\(392\) −4.45474 −0.224998
\(393\) −18.2582 −0.921005
\(394\) −22.8297 −1.15015
\(395\) 50.3163 2.53169
\(396\) −1.00000 −0.0502519
\(397\) −28.1055 −1.41058 −0.705288 0.708920i \(-0.749182\pi\)
−0.705288 + 0.708920i \(0.749182\pi\)
\(398\) −19.4535 −0.975115
\(399\) −2.82082 −0.141218
\(400\) 11.4534 0.572672
\(401\) 1.97149 0.0984517 0.0492258 0.998788i \(-0.484325\pi\)
0.0492258 + 0.998788i \(0.484325\pi\)
\(402\) −7.70883 −0.384482
\(403\) 30.6223 1.52540
\(404\) −8.79915 −0.437774
\(405\) −4.05628 −0.201558
\(406\) −0.0384751 −0.00190949
\(407\) 4.81967 0.238902
\(408\) −7.31489 −0.362141
\(409\) 17.5750 0.869027 0.434513 0.900665i \(-0.356920\pi\)
0.434513 + 0.900665i \(0.356920\pi\)
\(410\) 31.3288 1.54722
\(411\) 8.18386 0.403680
\(412\) −9.36709 −0.461483
\(413\) 2.05654 0.101196
\(414\) −6.99038 −0.343559
\(415\) −70.9116 −3.48091
\(416\) 3.49732 0.171470
\(417\) 21.3918 1.04756
\(418\) 1.76811 0.0864811
\(419\) 20.9628 1.02410 0.512051 0.858955i \(-0.328886\pi\)
0.512051 + 0.858955i \(0.328886\pi\)
\(420\) −6.47134 −0.315769
\(421\) 2.69583 0.131387 0.0656934 0.997840i \(-0.479074\pi\)
0.0656934 + 0.997840i \(0.479074\pi\)
\(422\) 11.3970 0.554798
\(423\) −2.91348 −0.141658
\(424\) −6.04474 −0.293558
\(425\) 83.7806 4.06396
\(426\) −5.90050 −0.285880
\(427\) −1.59539 −0.0772062
\(428\) −15.5823 −0.753200
\(429\) 3.49732 0.168852
\(430\) −37.6219 −1.81429
\(431\) −26.5387 −1.27832 −0.639162 0.769072i \(-0.720719\pi\)
−0.639162 + 0.769072i \(0.720719\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −1.34440 −0.0646076 −0.0323038 0.999478i \(-0.510284\pi\)
−0.0323038 + 0.999478i \(0.510284\pi\)
\(434\) −13.9691 −0.670538
\(435\) 0.0978233 0.00469027
\(436\) 15.1906 0.727497
\(437\) 12.3598 0.591248
\(438\) 13.4718 0.643708
\(439\) −30.0973 −1.43646 −0.718232 0.695804i \(-0.755048\pi\)
−0.718232 + 0.695804i \(0.755048\pi\)
\(440\) 4.05628 0.193376
\(441\) −4.45474 −0.212130
\(442\) 25.5825 1.21684
\(443\) 15.3679 0.730149 0.365074 0.930978i \(-0.381044\pi\)
0.365074 + 0.930978i \(0.381044\pi\)
\(444\) 4.81967 0.228732
\(445\) 62.4312 2.95952
\(446\) 21.5423 1.02006
\(447\) −15.9486 −0.754345
\(448\) −1.59539 −0.0753750
\(449\) 10.2979 0.485988 0.242994 0.970028i \(-0.421870\pi\)
0.242994 + 0.970028i \(0.421870\pi\)
\(450\) 11.4534 0.539920
\(451\) 7.72352 0.363686
\(452\) −10.1615 −0.477957
\(453\) −7.33832 −0.344784
\(454\) 19.6763 0.923454
\(455\) 22.6324 1.06102
\(456\) 1.76811 0.0827994
\(457\) −21.1684 −0.990217 −0.495109 0.868831i \(-0.664872\pi\)
−0.495109 + 0.868831i \(0.664872\pi\)
\(458\) −6.12424 −0.286167
\(459\) −7.31489 −0.341430
\(460\) 28.3550 1.32206
\(461\) −24.9393 −1.16154 −0.580770 0.814067i \(-0.697249\pi\)
−0.580770 + 0.814067i \(0.697249\pi\)
\(462\) −1.59539 −0.0742241
\(463\) −15.8084 −0.734677 −0.367339 0.930087i \(-0.619731\pi\)
−0.367339 + 0.930087i \(0.619731\pi\)
\(464\) 0.0241165 0.00111958
\(465\) 35.5165 1.64704
\(466\) −16.9596 −0.785638
\(467\) −25.4798 −1.17907 −0.589533 0.807744i \(-0.700688\pi\)
−0.589533 + 0.807744i \(0.700688\pi\)
\(468\) 3.49732 0.161664
\(469\) −12.2986 −0.567896
\(470\) 11.8179 0.545119
\(471\) 10.6194 0.489315
\(472\) −1.28905 −0.0593335
\(473\) −9.27497 −0.426463
\(474\) 12.4045 0.569759
\(475\) −20.2509 −0.929177
\(476\) −11.6701 −0.534897
\(477\) −6.04474 −0.276769
\(478\) 9.48939 0.434035
\(479\) −5.99410 −0.273878 −0.136939 0.990580i \(-0.543726\pi\)
−0.136939 + 0.990580i \(0.543726\pi\)
\(480\) 4.05628 0.185143
\(481\) −16.8559 −0.768565
\(482\) −6.07417 −0.276671
\(483\) −11.1524 −0.507450
\(484\) 1.00000 0.0454545
\(485\) 30.4687 1.38351
\(486\) −1.00000 −0.0453609
\(487\) −18.9550 −0.858934 −0.429467 0.903082i \(-0.641299\pi\)
−0.429467 + 0.903082i \(0.641299\pi\)
\(488\) 1.00000 0.0452679
\(489\) 3.56996 0.161439
\(490\) 18.0697 0.816305
\(491\) 37.8774 1.70938 0.854692 0.519135i \(-0.173746\pi\)
0.854692 + 0.519135i \(0.173746\pi\)
\(492\) 7.72352 0.348203
\(493\) 0.176409 0.00794508
\(494\) −6.18365 −0.278216
\(495\) 4.05628 0.182316
\(496\) 8.75593 0.393153
\(497\) −9.41358 −0.422257
\(498\) −17.4819 −0.783384
\(499\) 29.3414 1.31350 0.656751 0.754108i \(-0.271930\pi\)
0.656751 + 0.754108i \(0.271930\pi\)
\(500\) −26.1769 −1.17067
\(501\) 7.41687 0.331361
\(502\) −1.76315 −0.0786934
\(503\) 11.6830 0.520921 0.260460 0.965485i \(-0.416126\pi\)
0.260460 + 0.965485i \(0.416126\pi\)
\(504\) −1.59539 −0.0710642
\(505\) 35.6918 1.58827
\(506\) 6.99038 0.310760
\(507\) 0.768748 0.0341413
\(508\) −2.08914 −0.0926904
\(509\) −30.6045 −1.35652 −0.678261 0.734822i \(-0.737266\pi\)
−0.678261 + 0.734822i \(0.737266\pi\)
\(510\) 29.6713 1.31387
\(511\) 21.4927 0.950783
\(512\) 1.00000 0.0441942
\(513\) 1.76811 0.0780640
\(514\) −24.0061 −1.05887
\(515\) 37.9956 1.67428
\(516\) −9.27497 −0.408308
\(517\) 2.91348 0.128135
\(518\) 7.68924 0.337846
\(519\) 14.3532 0.630037
\(520\) −14.1861 −0.622103
\(521\) −2.24959 −0.0985563 −0.0492782 0.998785i \(-0.515692\pi\)
−0.0492782 + 0.998785i \(0.515692\pi\)
\(522\) 0.0241165 0.00105555
\(523\) −19.7086 −0.861797 −0.430899 0.902400i \(-0.641803\pi\)
−0.430899 + 0.902400i \(0.641803\pi\)
\(524\) 18.2582 0.797614
\(525\) 18.2727 0.797484
\(526\) −3.36152 −0.146569
\(527\) 64.0486 2.79000
\(528\) 1.00000 0.0435194
\(529\) 25.8655 1.12458
\(530\) 24.5192 1.06504
\(531\) −1.28905 −0.0559401
\(532\) 2.82082 0.122298
\(533\) −27.0116 −1.17000
\(534\) 15.3912 0.666044
\(535\) 63.2063 2.73265
\(536\) 7.70883 0.332971
\(537\) −3.34343 −0.144279
\(538\) 18.7805 0.809686
\(539\) 4.45474 0.191879
\(540\) 4.05628 0.174555
\(541\) −16.5311 −0.710726 −0.355363 0.934728i \(-0.615643\pi\)
−0.355363 + 0.934728i \(0.615643\pi\)
\(542\) 2.15131 0.0924065
\(543\) 18.1342 0.778214
\(544\) 7.31489 0.313623
\(545\) −61.6173 −2.63940
\(546\) 5.57958 0.238784
\(547\) −6.57762 −0.281239 −0.140619 0.990064i \(-0.544909\pi\)
−0.140619 + 0.990064i \(0.544909\pi\)
\(548\) −8.18386 −0.349597
\(549\) 1.00000 0.0426790
\(550\) −11.4534 −0.488376
\(551\) −0.0426406 −0.00181655
\(552\) 6.99038 0.297530
\(553\) 19.7900 0.841558
\(554\) 19.4266 0.825356
\(555\) −19.5500 −0.829849
\(556\) −21.3918 −0.907215
\(557\) 17.6540 0.748022 0.374011 0.927424i \(-0.377982\pi\)
0.374011 + 0.927424i \(0.377982\pi\)
\(558\) 8.75593 0.370668
\(559\) 32.4375 1.37196
\(560\) 6.47134 0.273464
\(561\) 7.31489 0.308835
\(562\) −6.42452 −0.271002
\(563\) −23.5153 −0.991051 −0.495525 0.868594i \(-0.665024\pi\)
−0.495525 + 0.868594i \(0.665024\pi\)
\(564\) 2.91348 0.122680
\(565\) 41.2180 1.73405
\(566\) −11.1655 −0.469320
\(567\) −1.59539 −0.0670000
\(568\) 5.90050 0.247579
\(569\) −21.6465 −0.907469 −0.453735 0.891137i \(-0.649909\pi\)
−0.453735 + 0.891137i \(0.649909\pi\)
\(570\) −7.17196 −0.300400
\(571\) 38.7224 1.62048 0.810241 0.586097i \(-0.199336\pi\)
0.810241 + 0.586097i \(0.199336\pi\)
\(572\) −3.49732 −0.146230
\(573\) 15.6458 0.653612
\(574\) 12.3220 0.514310
\(575\) −80.0639 −3.33889
\(576\) 1.00000 0.0416667
\(577\) −29.4016 −1.22400 −0.612002 0.790856i \(-0.709636\pi\)
−0.612002 + 0.790856i \(0.709636\pi\)
\(578\) 36.5076 1.51852
\(579\) −18.9924 −0.789296
\(580\) −0.0978233 −0.00406189
\(581\) −27.8904 −1.15709
\(582\) 7.51149 0.311361
\(583\) 6.04474 0.250347
\(584\) −13.4718 −0.557467
\(585\) −14.1861 −0.586524
\(586\) −13.7647 −0.568613
\(587\) 19.3932 0.800445 0.400222 0.916418i \(-0.368933\pi\)
0.400222 + 0.916418i \(0.368933\pi\)
\(588\) 4.45474 0.183710
\(589\) −15.4814 −0.637902
\(590\) 5.22876 0.215265
\(591\) 22.8297 0.939090
\(592\) −4.81967 −0.198087
\(593\) 29.1440 1.19680 0.598401 0.801197i \(-0.295803\pi\)
0.598401 + 0.801197i \(0.295803\pi\)
\(594\) 1.00000 0.0410305
\(595\) 47.3372 1.94063
\(596\) 15.9486 0.653282
\(597\) 19.4535 0.796178
\(598\) −24.4476 −0.999737
\(599\) −14.7904 −0.604318 −0.302159 0.953258i \(-0.597707\pi\)
−0.302159 + 0.953258i \(0.597707\pi\)
\(600\) −11.4534 −0.467584
\(601\) −0.0209419 −0.000854238 0 −0.000427119 1.00000i \(-0.500136\pi\)
−0.000427119 1.00000i \(0.500136\pi\)
\(602\) −14.7972 −0.603087
\(603\) 7.70883 0.313928
\(604\) 7.33832 0.298592
\(605\) −4.05628 −0.164911
\(606\) 8.79915 0.357441
\(607\) −2.15688 −0.0875449 −0.0437725 0.999042i \(-0.513938\pi\)
−0.0437725 + 0.999042i \(0.513938\pi\)
\(608\) −1.76811 −0.0717064
\(609\) 0.0384751 0.00155909
\(610\) −4.05628 −0.164234
\(611\) −10.1894 −0.412218
\(612\) 7.31489 0.295687
\(613\) 10.0404 0.405528 0.202764 0.979228i \(-0.435008\pi\)
0.202764 + 0.979228i \(0.435008\pi\)
\(614\) 20.1444 0.812962
\(615\) −31.3288 −1.26330
\(616\) 1.59539 0.0642800
\(617\) 12.0455 0.484932 0.242466 0.970160i \(-0.422044\pi\)
0.242466 + 0.970160i \(0.422044\pi\)
\(618\) 9.36709 0.376800
\(619\) −48.0060 −1.92952 −0.964762 0.263124i \(-0.915247\pi\)
−0.964762 + 0.263124i \(0.915247\pi\)
\(620\) −35.5165 −1.42638
\(621\) 6.99038 0.280514
\(622\) −7.95965 −0.319153
\(623\) 24.5550 0.983775
\(624\) −3.49732 −0.140005
\(625\) 48.9140 1.95656
\(626\) 19.6501 0.785377
\(627\) −1.76811 −0.0706115
\(628\) −10.6194 −0.423759
\(629\) −35.2554 −1.40572
\(630\) 6.47134 0.257824
\(631\) 8.69115 0.345989 0.172995 0.984923i \(-0.444656\pi\)
0.172995 + 0.984923i \(0.444656\pi\)
\(632\) −12.4045 −0.493426
\(633\) −11.3970 −0.452991
\(634\) −10.4525 −0.415122
\(635\) 8.47413 0.336285
\(636\) 6.04474 0.239689
\(637\) −15.5797 −0.617288
\(638\) −0.0241165 −0.000954781 0
\(639\) 5.90050 0.233420
\(640\) −4.05628 −0.160339
\(641\) −44.0722 −1.74075 −0.870373 0.492393i \(-0.836122\pi\)
−0.870373 + 0.492393i \(0.836122\pi\)
\(642\) 15.5823 0.614985
\(643\) 3.08542 0.121677 0.0608384 0.998148i \(-0.480623\pi\)
0.0608384 + 0.998148i \(0.480623\pi\)
\(644\) 11.1524 0.439465
\(645\) 37.6219 1.48136
\(646\) −12.9335 −0.508863
\(647\) 0.220969 0.00868720 0.00434360 0.999991i \(-0.498617\pi\)
0.00434360 + 0.999991i \(0.498617\pi\)
\(648\) 1.00000 0.0392837
\(649\) 1.28905 0.0505997
\(650\) 40.0563 1.57114
\(651\) 13.9691 0.547492
\(652\) −3.56996 −0.139811
\(653\) −6.11922 −0.239464 −0.119732 0.992806i \(-0.538203\pi\)
−0.119732 + 0.992806i \(0.538203\pi\)
\(654\) −15.1906 −0.593999
\(655\) −74.0605 −2.89378
\(656\) −7.72352 −0.301553
\(657\) −13.4718 −0.525585
\(658\) 4.64813 0.181203
\(659\) −3.97739 −0.154937 −0.0774685 0.996995i \(-0.524684\pi\)
−0.0774685 + 0.996995i \(0.524684\pi\)
\(660\) −4.05628 −0.157891
\(661\) −43.0060 −1.67274 −0.836371 0.548165i \(-0.815327\pi\)
−0.836371 + 0.548165i \(0.815327\pi\)
\(662\) 16.3350 0.634879
\(663\) −25.5825 −0.993542
\(664\) 17.4819 0.678430
\(665\) −11.4421 −0.443704
\(666\) −4.81967 −0.186759
\(667\) −0.168583 −0.00652758
\(668\) −7.41687 −0.286967
\(669\) −21.5423 −0.832872
\(670\) −31.2692 −1.20804
\(671\) −1.00000 −0.0386046
\(672\) 1.59539 0.0615434
\(673\) −0.890377 −0.0343215 −0.0171608 0.999853i \(-0.505463\pi\)
−0.0171608 + 0.999853i \(0.505463\pi\)
\(674\) 16.2029 0.624112
\(675\) −11.4534 −0.440843
\(676\) −0.768748 −0.0295672
\(677\) 30.9340 1.18889 0.594445 0.804136i \(-0.297372\pi\)
0.594445 + 0.804136i \(0.297372\pi\)
\(678\) 10.1615 0.390250
\(679\) 11.9837 0.459893
\(680\) −29.6713 −1.13784
\(681\) −19.6763 −0.753997
\(682\) −8.75593 −0.335282
\(683\) 31.7892 1.21638 0.608189 0.793792i \(-0.291896\pi\)
0.608189 + 0.793792i \(0.291896\pi\)
\(684\) −1.76811 −0.0676054
\(685\) 33.1960 1.26836
\(686\) 18.2747 0.697733
\(687\) 6.12424 0.233654
\(688\) 9.27497 0.353605
\(689\) −21.1404 −0.805384
\(690\) −28.3550 −1.07946
\(691\) −42.3625 −1.61154 −0.805772 0.592226i \(-0.798249\pi\)
−0.805772 + 0.592226i \(0.798249\pi\)
\(692\) −14.3532 −0.545628
\(693\) 1.59539 0.0606038
\(694\) 34.3941 1.30558
\(695\) 86.7712 3.29142
\(696\) −0.0241165 −0.000914133 0
\(697\) −56.4967 −2.13996
\(698\) 5.63869 0.213427
\(699\) 16.9596 0.641471
\(700\) −18.2727 −0.690642
\(701\) 42.1024 1.59019 0.795093 0.606488i \(-0.207422\pi\)
0.795093 + 0.606488i \(0.207422\pi\)
\(702\) −3.49732 −0.131998
\(703\) 8.52172 0.321403
\(704\) −1.00000 −0.0376889
\(705\) −11.8179 −0.445088
\(706\) −1.44339 −0.0543229
\(707\) 14.0380 0.527955
\(708\) 1.28905 0.0484456
\(709\) 30.6239 1.15010 0.575052 0.818117i \(-0.304982\pi\)
0.575052 + 0.818117i \(0.304982\pi\)
\(710\) −23.9341 −0.898230
\(711\) −12.4045 −0.465206
\(712\) −15.3912 −0.576811
\(713\) −61.2073 −2.29223
\(714\) 11.6701 0.436742
\(715\) 14.1861 0.530531
\(716\) 3.34343 0.124950
\(717\) −9.48939 −0.354388
\(718\) −17.9121 −0.668475
\(719\) 18.3754 0.685288 0.342644 0.939465i \(-0.388678\pi\)
0.342644 + 0.939465i \(0.388678\pi\)
\(720\) −4.05628 −0.151169
\(721\) 14.9441 0.556549
\(722\) −15.8738 −0.590761
\(723\) 6.07417 0.225901
\(724\) −18.1342 −0.673953
\(725\) 0.276217 0.0102584
\(726\) −1.00000 −0.0371135
\(727\) 37.1060 1.37618 0.688092 0.725623i \(-0.258449\pi\)
0.688092 + 0.725623i \(0.258449\pi\)
\(728\) −5.57958 −0.206793
\(729\) 1.00000 0.0370370
\(730\) 54.6455 2.02252
\(731\) 67.8453 2.50935
\(732\) −1.00000 −0.0369611
\(733\) −1.08534 −0.0400878 −0.0200439 0.999799i \(-0.506381\pi\)
−0.0200439 + 0.999799i \(0.506381\pi\)
\(734\) −2.10345 −0.0776399
\(735\) −18.0697 −0.666510
\(736\) −6.99038 −0.257669
\(737\) −7.70883 −0.283959
\(738\) −7.72352 −0.284307
\(739\) 5.10783 0.187894 0.0939472 0.995577i \(-0.470052\pi\)
0.0939472 + 0.995577i \(0.470052\pi\)
\(740\) 19.5500 0.718671
\(741\) 6.18365 0.227162
\(742\) 9.64370 0.354031
\(743\) −42.9820 −1.57686 −0.788428 0.615127i \(-0.789105\pi\)
−0.788428 + 0.615127i \(0.789105\pi\)
\(744\) −8.75593 −0.321008
\(745\) −64.6922 −2.37014
\(746\) 35.0349 1.28272
\(747\) 17.4819 0.639630
\(748\) −7.31489 −0.267459
\(749\) 24.8598 0.908358
\(750\) 26.1769 0.955847
\(751\) 2.12348 0.0774868 0.0387434 0.999249i \(-0.487665\pi\)
0.0387434 + 0.999249i \(0.487665\pi\)
\(752\) −2.91348 −0.106244
\(753\) 1.76315 0.0642529
\(754\) 0.0843431 0.00307159
\(755\) −29.7663 −1.08331
\(756\) 1.59539 0.0580237
\(757\) −5.59093 −0.203206 −0.101603 0.994825i \(-0.532397\pi\)
−0.101603 + 0.994825i \(0.532397\pi\)
\(758\) −19.6090 −0.712231
\(759\) −6.99038 −0.253735
\(760\) 7.17196 0.260154
\(761\) −13.0742 −0.473939 −0.236969 0.971517i \(-0.576154\pi\)
−0.236969 + 0.971517i \(0.576154\pi\)
\(762\) 2.08914 0.0756814
\(763\) −24.2349 −0.877362
\(764\) −15.6458 −0.566045
\(765\) −29.6713 −1.07277
\(766\) −24.4725 −0.884228
\(767\) −4.50823 −0.162783
\(768\) −1.00000 −0.0360844
\(769\) −0.481859 −0.0173763 −0.00868814 0.999962i \(-0.502766\pi\)
−0.00868814 + 0.999962i \(0.502766\pi\)
\(770\) −6.47134 −0.233211
\(771\) 24.0061 0.864560
\(772\) 18.9924 0.683551
\(773\) −37.0758 −1.33352 −0.666762 0.745271i \(-0.732320\pi\)
−0.666762 + 0.745271i \(0.732320\pi\)
\(774\) 9.27497 0.333382
\(775\) 100.285 3.60236
\(776\) −7.51149 −0.269647
\(777\) −7.68924 −0.275850
\(778\) −35.5397 −1.27416
\(779\) 13.6560 0.489278
\(780\) 14.1861 0.507945
\(781\) −5.90050 −0.211136
\(782\) −51.1339 −1.82854
\(783\) −0.0241165 −0.000861853 0
\(784\) −4.45474 −0.159098
\(785\) 43.0752 1.53742
\(786\) −18.2582 −0.651249
\(787\) −5.67271 −0.202210 −0.101105 0.994876i \(-0.532238\pi\)
−0.101105 + 0.994876i \(0.532238\pi\)
\(788\) −22.8297 −0.813276
\(789\) 3.36152 0.119673
\(790\) 50.3163 1.79017
\(791\) 16.2115 0.576416
\(792\) −1.00000 −0.0355335
\(793\) 3.49732 0.124193
\(794\) −28.1055 −0.997428
\(795\) −24.5192 −0.869605
\(796\) −19.4535 −0.689510
\(797\) −47.0014 −1.66488 −0.832438 0.554119i \(-0.813055\pi\)
−0.832438 + 0.554119i \(0.813055\pi\)
\(798\) −2.82082 −0.0998560
\(799\) −21.3118 −0.753957
\(800\) 11.4534 0.404940
\(801\) −15.3912 −0.543823
\(802\) 1.97149 0.0696158
\(803\) 13.4718 0.475410
\(804\) −7.70883 −0.271870
\(805\) −45.2372 −1.59440
\(806\) 30.6223 1.07862
\(807\) −18.7805 −0.661106
\(808\) −8.79915 −0.309553
\(809\) 3.27711 0.115217 0.0576086 0.998339i \(-0.481652\pi\)
0.0576086 + 0.998339i \(0.481652\pi\)
\(810\) −4.05628 −0.142523
\(811\) −14.9746 −0.525828 −0.262914 0.964819i \(-0.584684\pi\)
−0.262914 + 0.964819i \(0.584684\pi\)
\(812\) −0.0384751 −0.00135021
\(813\) −2.15131 −0.0754496
\(814\) 4.81967 0.168929
\(815\) 14.4808 0.507240
\(816\) −7.31489 −0.256072
\(817\) −16.3992 −0.573734
\(818\) 17.5750 0.614495
\(819\) −5.57958 −0.194966
\(820\) 31.3288 1.09405
\(821\) −31.3319 −1.09349 −0.546745 0.837299i \(-0.684133\pi\)
−0.546745 + 0.837299i \(0.684133\pi\)
\(822\) 8.18386 0.285445
\(823\) 28.8828 1.00679 0.503395 0.864056i \(-0.332084\pi\)
0.503395 + 0.864056i \(0.332084\pi\)
\(824\) −9.36709 −0.326318
\(825\) 11.4534 0.398757
\(826\) 2.05654 0.0715561
\(827\) −19.2429 −0.669142 −0.334571 0.942371i \(-0.608591\pi\)
−0.334571 + 0.942371i \(0.608591\pi\)
\(828\) −6.99038 −0.242933
\(829\) 4.23675 0.147149 0.0735743 0.997290i \(-0.476559\pi\)
0.0735743 + 0.997290i \(0.476559\pi\)
\(830\) −70.9116 −2.46138
\(831\) −19.4266 −0.673900
\(832\) 3.49732 0.121248
\(833\) −32.5859 −1.12904
\(834\) 21.3918 0.740738
\(835\) 30.0849 1.04113
\(836\) 1.76811 0.0611514
\(837\) −8.75593 −0.302649
\(838\) 20.9628 0.724150
\(839\) 11.4086 0.393870 0.196935 0.980417i \(-0.436901\pi\)
0.196935 + 0.980417i \(0.436901\pi\)
\(840\) −6.47134 −0.223283
\(841\) −28.9994 −0.999980
\(842\) 2.69583 0.0929045
\(843\) 6.42452 0.221272
\(844\) 11.3970 0.392302
\(845\) 3.11826 0.107271
\(846\) −2.91348 −0.100168
\(847\) −1.59539 −0.0548182
\(848\) −6.04474 −0.207577
\(849\) 11.1655 0.383198
\(850\) 83.7806 2.87365
\(851\) 33.6914 1.15492
\(852\) −5.90050 −0.202148
\(853\) 17.1149 0.586001 0.293001 0.956112i \(-0.405346\pi\)
0.293001 + 0.956112i \(0.405346\pi\)
\(854\) −1.59539 −0.0545930
\(855\) 7.17196 0.245276
\(856\) −15.5823 −0.532593
\(857\) −4.10315 −0.140161 −0.0700805 0.997541i \(-0.522326\pi\)
−0.0700805 + 0.997541i \(0.522326\pi\)
\(858\) 3.49732 0.119397
\(859\) 11.5004 0.392390 0.196195 0.980565i \(-0.437142\pi\)
0.196195 + 0.980565i \(0.437142\pi\)
\(860\) −37.6219 −1.28290
\(861\) −12.3220 −0.419933
\(862\) −26.5387 −0.903912
\(863\) −21.6785 −0.737944 −0.368972 0.929440i \(-0.620290\pi\)
−0.368972 + 0.929440i \(0.620290\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 58.2207 1.97956
\(866\) −1.34440 −0.0456845
\(867\) −36.5076 −1.23986
\(868\) −13.9691 −0.474142
\(869\) 12.4045 0.420795
\(870\) 0.0978233 0.00331652
\(871\) 26.9603 0.913514
\(872\) 15.1906 0.514418
\(873\) −7.51149 −0.254225
\(874\) 12.3598 0.418076
\(875\) 41.7624 1.41183
\(876\) 13.4718 0.455170
\(877\) 2.32846 0.0786264 0.0393132 0.999227i \(-0.487483\pi\)
0.0393132 + 0.999227i \(0.487483\pi\)
\(878\) −30.0973 −1.01573
\(879\) 13.7647 0.464270
\(880\) 4.05628 0.136737
\(881\) 28.4074 0.957068 0.478534 0.878069i \(-0.341168\pi\)
0.478534 + 0.878069i \(0.341168\pi\)
\(882\) −4.45474 −0.149999
\(883\) −26.2079 −0.881967 −0.440983 0.897515i \(-0.645370\pi\)
−0.440983 + 0.897515i \(0.645370\pi\)
\(884\) 25.5825 0.860433
\(885\) −5.22876 −0.175763
\(886\) 15.3679 0.516293
\(887\) 1.65184 0.0554632 0.0277316 0.999615i \(-0.491172\pi\)
0.0277316 + 0.999615i \(0.491172\pi\)
\(888\) 4.81967 0.161738
\(889\) 3.33298 0.111785
\(890\) 62.4312 2.09270
\(891\) −1.00000 −0.0335013
\(892\) 21.5423 0.721288
\(893\) 5.15136 0.172384
\(894\) −15.9486 −0.533403
\(895\) −13.5619 −0.453324
\(896\) −1.59539 −0.0532982
\(897\) 24.4476 0.816282
\(898\) 10.2979 0.343646
\(899\) 0.211162 0.00704265
\(900\) 11.4534 0.381781
\(901\) −44.2166 −1.47307
\(902\) 7.72352 0.257165
\(903\) 14.7972 0.492419
\(904\) −10.1615 −0.337967
\(905\) 73.5576 2.44514
\(906\) −7.33832 −0.243799
\(907\) −52.6512 −1.74825 −0.874127 0.485698i \(-0.838566\pi\)
−0.874127 + 0.485698i \(0.838566\pi\)
\(908\) 19.6763 0.652980
\(909\) −8.79915 −0.291849
\(910\) 22.6324 0.750255
\(911\) −12.9737 −0.429836 −0.214918 0.976632i \(-0.568948\pi\)
−0.214918 + 0.976632i \(0.568948\pi\)
\(912\) 1.76811 0.0585480
\(913\) −17.4819 −0.578567
\(914\) −21.1684 −0.700189
\(915\) 4.05628 0.134097
\(916\) −6.12424 −0.202351
\(917\) −29.1289 −0.961922
\(918\) −7.31489 −0.241427
\(919\) 8.12884 0.268146 0.134073 0.990971i \(-0.457194\pi\)
0.134073 + 0.990971i \(0.457194\pi\)
\(920\) 28.3550 0.934836
\(921\) −20.1444 −0.663781
\(922\) −24.9393 −0.821333
\(923\) 20.6359 0.679240
\(924\) −1.59539 −0.0524844
\(925\) −55.2018 −1.81502
\(926\) −15.8084 −0.519495
\(927\) −9.36709 −0.307656
\(928\) 0.0241165 0.000791662 0
\(929\) −22.8797 −0.750657 −0.375329 0.926892i \(-0.622470\pi\)
−0.375329 + 0.926892i \(0.622470\pi\)
\(930\) 35.5165 1.16463
\(931\) 7.87647 0.258141
\(932\) −16.9596 −0.555530
\(933\) 7.95965 0.260587
\(934\) −25.4798 −0.833726
\(935\) 29.6713 0.970354
\(936\) 3.49732 0.114314
\(937\) −49.7726 −1.62600 −0.813000 0.582264i \(-0.802167\pi\)
−0.813000 + 0.582264i \(0.802167\pi\)
\(938\) −12.2986 −0.401563
\(939\) −19.6501 −0.641258
\(940\) 11.8179 0.385457
\(941\) 24.2116 0.789276 0.394638 0.918837i \(-0.370870\pi\)
0.394638 + 0.918837i \(0.370870\pi\)
\(942\) 10.6194 0.345998
\(943\) 53.9903 1.75817
\(944\) −1.28905 −0.0419551
\(945\) −6.47134 −0.210513
\(946\) −9.27497 −0.301555
\(947\) −2.48161 −0.0806415 −0.0403207 0.999187i \(-0.512838\pi\)
−0.0403207 + 0.999187i \(0.512838\pi\)
\(948\) 12.4045 0.402881
\(949\) −47.1152 −1.52942
\(950\) −20.2509 −0.657027
\(951\) 10.4525 0.338946
\(952\) −11.6701 −0.378230
\(953\) 49.4472 1.60175 0.800876 0.598830i \(-0.204367\pi\)
0.800876 + 0.598830i \(0.204367\pi\)
\(954\) −6.04474 −0.195706
\(955\) 63.4638 2.05364
\(956\) 9.48939 0.306909
\(957\) 0.0241165 0.000779575 0
\(958\) −5.99410 −0.193661
\(959\) 13.0564 0.421614
\(960\) 4.05628 0.130916
\(961\) 45.6662 1.47310
\(962\) −16.8559 −0.543457
\(963\) −15.5823 −0.502133
\(964\) −6.07417 −0.195636
\(965\) −77.0385 −2.47996
\(966\) −11.1524 −0.358822
\(967\) 37.9534 1.22050 0.610250 0.792209i \(-0.291069\pi\)
0.610250 + 0.792209i \(0.291069\pi\)
\(968\) 1.00000 0.0321412
\(969\) 12.9335 0.415485
\(970\) 30.4687 0.978291
\(971\) 40.1816 1.28949 0.644744 0.764398i \(-0.276964\pi\)
0.644744 + 0.764398i \(0.276964\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 34.1282 1.09410
\(974\) −18.9550 −0.607358
\(975\) −40.0563 −1.28283
\(976\) 1.00000 0.0320092
\(977\) −13.1013 −0.419148 −0.209574 0.977793i \(-0.567208\pi\)
−0.209574 + 0.977793i \(0.567208\pi\)
\(978\) 3.56996 0.114155
\(979\) 15.3912 0.491906
\(980\) 18.0697 0.577215
\(981\) 15.1906 0.484998
\(982\) 37.8774 1.20872
\(983\) 54.8375 1.74905 0.874523 0.484984i \(-0.161175\pi\)
0.874523 + 0.484984i \(0.161175\pi\)
\(984\) 7.72352 0.246217
\(985\) 92.6039 2.95061
\(986\) 0.176409 0.00561802
\(987\) −4.64813 −0.147952
\(988\) −6.18365 −0.196728
\(989\) −64.8356 −2.06165
\(990\) 4.05628 0.128917
\(991\) −47.5971 −1.51197 −0.755987 0.654587i \(-0.772842\pi\)
−0.755987 + 0.654587i \(0.772842\pi\)
\(992\) 8.75593 0.278001
\(993\) −16.3350 −0.518377
\(994\) −9.41358 −0.298581
\(995\) 78.9088 2.50158
\(996\) −17.4819 −0.553936
\(997\) 10.4773 0.331819 0.165910 0.986141i \(-0.446944\pi\)
0.165910 + 0.986141i \(0.446944\pi\)
\(998\) 29.3414 0.928786
\(999\) 4.81967 0.152488
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 4026.2.a.x.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.x.1.2 6 1.1 even 1 trivial