Properties

Label 4010.2.a.i.1.6
Level 4010
Weight 2
Character 4010.1
Self dual yes
Analytic conductor 32.020
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.96171\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} -1.00000 q^{10} +6.17044 q^{11} +0.223737 q^{12} -4.22120 q^{13} +0.465545 q^{14} +0.223737 q^{15} +1.00000 q^{16} +1.20014 q^{17} +2.94994 q^{18} -2.12314 q^{19} +1.00000 q^{20} -0.104160 q^{21} -6.17044 q^{22} -0.690450 q^{23} -0.223737 q^{24} +1.00000 q^{25} +4.22120 q^{26} -1.33122 q^{27} -0.465545 q^{28} -9.84937 q^{29} -0.223737 q^{30} +1.38297 q^{31} -1.00000 q^{32} +1.38056 q^{33} -1.20014 q^{34} -0.465545 q^{35} -2.94994 q^{36} +6.67643 q^{37} +2.12314 q^{38} -0.944440 q^{39} -1.00000 q^{40} -7.06932 q^{41} +0.104160 q^{42} +4.32772 q^{43} +6.17044 q^{44} -2.94994 q^{45} +0.690450 q^{46} +2.50929 q^{47} +0.223737 q^{48} -6.78327 q^{49} -1.00000 q^{50} +0.268517 q^{51} -4.22120 q^{52} -3.84117 q^{53} +1.33122 q^{54} +6.17044 q^{55} +0.465545 q^{56} -0.475026 q^{57} +9.84937 q^{58} -9.21300 q^{59} +0.223737 q^{60} -6.81367 q^{61} -1.38297 q^{62} +1.37333 q^{63} +1.00000 q^{64} -4.22120 q^{65} -1.38056 q^{66} +5.63972 q^{67} +1.20014 q^{68} -0.154479 q^{69} +0.465545 q^{70} -3.71289 q^{71} +2.94994 q^{72} +2.89694 q^{73} -6.67643 q^{74} +0.223737 q^{75} -2.12314 q^{76} -2.87261 q^{77} +0.944440 q^{78} -0.949571 q^{79} +1.00000 q^{80} +8.55198 q^{81} +7.06932 q^{82} +14.2879 q^{83} -0.104160 q^{84} +1.20014 q^{85} -4.32772 q^{86} -2.20367 q^{87} -6.17044 q^{88} -13.0690 q^{89} +2.94994 q^{90} +1.96516 q^{91} -0.690450 q^{92} +0.309423 q^{93} -2.50929 q^{94} -2.12314 q^{95} -0.223737 q^{96} -7.25226 q^{97} +6.78327 q^{98} -18.2024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} + O(q^{10}) \) \( 10q - 10q^{2} - 4q^{3} + 10q^{4} + 10q^{5} + 4q^{6} - 3q^{7} - 10q^{8} + 6q^{9} - 10q^{10} - 11q^{11} - 4q^{12} + 6q^{13} + 3q^{14} - 4q^{15} + 10q^{16} + 9q^{17} - 6q^{18} - 13q^{19} + 10q^{20} - 24q^{21} + 11q^{22} - 3q^{23} + 4q^{24} + 10q^{25} - 6q^{26} - 10q^{27} - 3q^{28} - 4q^{29} + 4q^{30} - 17q^{31} - 10q^{32} - 2q^{33} - 9q^{34} - 3q^{35} + 6q^{36} - 15q^{37} + 13q^{38} - 6q^{39} - 10q^{40} - 11q^{41} + 24q^{42} - 11q^{43} - 11q^{44} + 6q^{45} + 3q^{46} + 3q^{47} - 4q^{48} - 5q^{49} - 10q^{50} - 21q^{51} + 6q^{52} + 25q^{53} + 10q^{54} - 11q^{55} + 3q^{56} + 31q^{57} + 4q^{58} - 46q^{59} - 4q^{60} - 54q^{61} + 17q^{62} - 6q^{63} + 10q^{64} + 6q^{65} + 2q^{66} - 26q^{67} + 9q^{68} - 9q^{69} + 3q^{70} - 16q^{71} - 6q^{72} + 4q^{73} + 15q^{74} - 4q^{75} - 13q^{76} + 11q^{77} + 6q^{78} - 19q^{79} + 10q^{80} - 6q^{81} + 11q^{82} + 19q^{83} - 24q^{84} + 9q^{85} + 11q^{86} + 28q^{87} + 11q^{88} - 30q^{89} - 6q^{90} - 38q^{91} - 3q^{92} - 18q^{93} - 3q^{94} - 13q^{95} + 4q^{96} - 16q^{97} + 5q^{98} - 59q^{99} + O(q^{100}) \)

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
\(3\) 0.223737 0.129175 0.0645874 0.997912i \(-0.479427\pi\)
0.0645874 + 0.997912i \(0.479427\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.223737 −0.0913404
\(7\) −0.465545 −0.175959 −0.0879797 0.996122i \(-0.528041\pi\)
−0.0879797 + 0.996122i \(0.528041\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.94994 −0.983314
\(10\) −1.00000 −0.316228
\(11\) 6.17044 1.86046 0.930228 0.366982i \(-0.119609\pi\)
0.930228 + 0.366982i \(0.119609\pi\)
\(12\) 0.223737 0.0645874
\(13\) −4.22120 −1.17075 −0.585375 0.810763i \(-0.699053\pi\)
−0.585375 + 0.810763i \(0.699053\pi\)
\(14\) 0.465545 0.124422
\(15\) 0.223737 0.0577687
\(16\) 1.00000 0.250000
\(17\) 1.20014 0.291078 0.145539 0.989353i \(-0.453508\pi\)
0.145539 + 0.989353i \(0.453508\pi\)
\(18\) 2.94994 0.695308
\(19\) −2.12314 −0.487082 −0.243541 0.969891i \(-0.578309\pi\)
−0.243541 + 0.969891i \(0.578309\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.104160 −0.0227295
\(22\) −6.17044 −1.31554
\(23\) −0.690450 −0.143969 −0.0719844 0.997406i \(-0.522933\pi\)
−0.0719844 + 0.997406i \(0.522933\pi\)
\(24\) −0.223737 −0.0456702
\(25\) 1.00000 0.200000
\(26\) 4.22120 0.827846
\(27\) −1.33122 −0.256194
\(28\) −0.465545 −0.0879797
\(29\) −9.84937 −1.82898 −0.914491 0.404607i \(-0.867408\pi\)
−0.914491 + 0.404607i \(0.867408\pi\)
\(30\) −0.223737 −0.0408487
\(31\) 1.38297 0.248389 0.124195 0.992258i \(-0.460365\pi\)
0.124195 + 0.992258i \(0.460365\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.38056 0.240324
\(34\) −1.20014 −0.205823
\(35\) −0.465545 −0.0786914
\(36\) −2.94994 −0.491657
\(37\) 6.67643 1.09760 0.548799 0.835954i \(-0.315085\pi\)
0.548799 + 0.835954i \(0.315085\pi\)
\(38\) 2.12314 0.344419
\(39\) −0.944440 −0.151231
\(40\) −1.00000 −0.158114
\(41\) −7.06932 −1.10404 −0.552021 0.833830i \(-0.686143\pi\)
−0.552021 + 0.833830i \(0.686143\pi\)
\(42\) 0.104160 0.0160722
\(43\) 4.32772 0.659971 0.329985 0.943986i \(-0.392956\pi\)
0.329985 + 0.943986i \(0.392956\pi\)
\(44\) 6.17044 0.930228
\(45\) −2.94994 −0.439751
\(46\) 0.690450 0.101801
\(47\) 2.50929 0.366017 0.183008 0.983111i \(-0.441416\pi\)
0.183008 + 0.983111i \(0.441416\pi\)
\(48\) 0.223737 0.0322937
\(49\) −6.78327 −0.969038
\(50\) −1.00000 −0.141421
\(51\) 0.268517 0.0375999
\(52\) −4.22120 −0.585375
\(53\) −3.84117 −0.527625 −0.263812 0.964574i \(-0.584980\pi\)
−0.263812 + 0.964574i \(0.584980\pi\)
\(54\) 1.33122 0.181157
\(55\) 6.17044 0.832021
\(56\) 0.465545 0.0622110
\(57\) −0.475026 −0.0629188
\(58\) 9.84937 1.29329
\(59\) −9.21300 −1.19943 −0.599715 0.800214i \(-0.704719\pi\)
−0.599715 + 0.800214i \(0.704719\pi\)
\(60\) 0.223737 0.0288844
\(61\) −6.81367 −0.872401 −0.436200 0.899850i \(-0.643676\pi\)
−0.436200 + 0.899850i \(0.643676\pi\)
\(62\) −1.38297 −0.175638
\(63\) 1.37333 0.173023
\(64\) 1.00000 0.125000
\(65\) −4.22120 −0.523575
\(66\) −1.38056 −0.169935
\(67\) 5.63972 0.689001 0.344501 0.938786i \(-0.388048\pi\)
0.344501 + 0.938786i \(0.388048\pi\)
\(68\) 1.20014 0.145539
\(69\) −0.154479 −0.0185971
\(70\) 0.465545 0.0556432
\(71\) −3.71289 −0.440638 −0.220319 0.975428i \(-0.570710\pi\)
−0.220319 + 0.975428i \(0.570710\pi\)
\(72\) 2.94994 0.347654
\(73\) 2.89694 0.339061 0.169531 0.985525i \(-0.445775\pi\)
0.169531 + 0.985525i \(0.445775\pi\)
\(74\) −6.67643 −0.776119
\(75\) 0.223737 0.0258350
\(76\) −2.12314 −0.243541
\(77\) −2.87261 −0.327365
\(78\) 0.944440 0.106937
\(79\) −0.949571 −0.106835 −0.0534175 0.998572i \(-0.517011\pi\)
−0.0534175 + 0.998572i \(0.517011\pi\)
\(80\) 1.00000 0.111803
\(81\) 8.55198 0.950220
\(82\) 7.06932 0.780676
\(83\) 14.2879 1.56830 0.784151 0.620570i \(-0.213099\pi\)
0.784151 + 0.620570i \(0.213099\pi\)
\(84\) −0.104160 −0.0113648
\(85\) 1.20014 0.130174
\(86\) −4.32772 −0.466670
\(87\) −2.20367 −0.236258
\(88\) −6.17044 −0.657771
\(89\) −13.0690 −1.38531 −0.692656 0.721268i \(-0.743559\pi\)
−0.692656 + 0.721268i \(0.743559\pi\)
\(90\) 2.94994 0.310951
\(91\) 1.96516 0.206004
\(92\) −0.690450 −0.0719844
\(93\) 0.309423 0.0320856
\(94\) −2.50929 −0.258813
\(95\) −2.12314 −0.217830
\(96\) −0.223737 −0.0228351
\(97\) −7.25226 −0.736355 −0.368178 0.929756i \(-0.620018\pi\)
−0.368178 + 0.929756i \(0.620018\pi\)
\(98\) 6.78327 0.685214
\(99\) −18.2024 −1.82941
\(100\) 1.00000 0.100000
\(101\) 3.41556 0.339861 0.169930 0.985456i \(-0.445646\pi\)
0.169930 + 0.985456i \(0.445646\pi\)
\(102\) −0.268517 −0.0265872
\(103\) 4.07066 0.401094 0.200547 0.979684i \(-0.435728\pi\)
0.200547 + 0.979684i \(0.435728\pi\)
\(104\) 4.22120 0.413923
\(105\) −0.104160 −0.0101650
\(106\) 3.84117 0.373087
\(107\) −12.7930 −1.23675 −0.618374 0.785884i \(-0.712208\pi\)
−0.618374 + 0.785884i \(0.712208\pi\)
\(108\) −1.33122 −0.128097
\(109\) −15.7644 −1.50995 −0.754977 0.655751i \(-0.772352\pi\)
−0.754977 + 0.655751i \(0.772352\pi\)
\(110\) −6.17044 −0.588328
\(111\) 1.49377 0.141782
\(112\) −0.465545 −0.0439898
\(113\) −4.94582 −0.465264 −0.232632 0.972565i \(-0.574734\pi\)
−0.232632 + 0.972565i \(0.574734\pi\)
\(114\) 0.475026 0.0444903
\(115\) −0.690450 −0.0643848
\(116\) −9.84937 −0.914491
\(117\) 12.4523 1.15122
\(118\) 9.21300 0.848125
\(119\) −0.558721 −0.0512178
\(120\) −0.223737 −0.0204243
\(121\) 27.0743 2.46130
\(122\) 6.81367 0.616881
\(123\) −1.58167 −0.142615
\(124\) 1.38297 0.124195
\(125\) 1.00000 0.0894427
\(126\) −1.37333 −0.122346
\(127\) 7.48068 0.663803 0.331902 0.943314i \(-0.392310\pi\)
0.331902 + 0.943314i \(0.392310\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.968273 0.0852516
\(130\) 4.22120 0.370224
\(131\) −12.8152 −1.11967 −0.559836 0.828603i \(-0.689136\pi\)
−0.559836 + 0.828603i \(0.689136\pi\)
\(132\) 1.38056 0.120162
\(133\) 0.988418 0.0857067
\(134\) −5.63972 −0.487197
\(135\) −1.33122 −0.114574
\(136\) −1.20014 −0.102912
\(137\) −15.4820 −1.32272 −0.661358 0.750070i \(-0.730020\pi\)
−0.661358 + 0.750070i \(0.730020\pi\)
\(138\) 0.154479 0.0131502
\(139\) 7.12322 0.604184 0.302092 0.953279i \(-0.402315\pi\)
0.302092 + 0.953279i \(0.402315\pi\)
\(140\) −0.465545 −0.0393457
\(141\) 0.561421 0.0472802
\(142\) 3.71289 0.311578
\(143\) −26.0466 −2.17813
\(144\) −2.94994 −0.245828
\(145\) −9.84937 −0.817945
\(146\) −2.89694 −0.239753
\(147\) −1.51767 −0.125175
\(148\) 6.67643 0.548799
\(149\) 12.8092 1.04937 0.524687 0.851295i \(-0.324182\pi\)
0.524687 + 0.851295i \(0.324182\pi\)
\(150\) −0.223737 −0.0182681
\(151\) −18.7986 −1.52981 −0.764905 0.644143i \(-0.777214\pi\)
−0.764905 + 0.644143i \(0.777214\pi\)
\(152\) 2.12314 0.172210
\(153\) −3.54035 −0.286221
\(154\) 2.87261 0.231482
\(155\) 1.38297 0.111083
\(156\) −0.944440 −0.0756157
\(157\) −17.4414 −1.39198 −0.695988 0.718054i \(-0.745033\pi\)
−0.695988 + 0.718054i \(0.745033\pi\)
\(158\) 0.949571 0.0755438
\(159\) −0.859413 −0.0681559
\(160\) −1.00000 −0.0790569
\(161\) 0.321435 0.0253327
\(162\) −8.55198 −0.671907
\(163\) −20.5938 −1.61303 −0.806514 0.591215i \(-0.798649\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(164\) −7.06932 −0.552021
\(165\) 1.38056 0.107476
\(166\) −14.2879 −1.10896
\(167\) 24.2024 1.87284 0.936419 0.350883i \(-0.114118\pi\)
0.936419 + 0.350883i \(0.114118\pi\)
\(168\) 0.104160 0.00803610
\(169\) 4.81853 0.370656
\(170\) −1.20014 −0.0920468
\(171\) 6.26315 0.478955
\(172\) 4.32772 0.329985
\(173\) 5.58475 0.424601 0.212300 0.977204i \(-0.431904\pi\)
0.212300 + 0.977204i \(0.431904\pi\)
\(174\) 2.20367 0.167060
\(175\) −0.465545 −0.0351919
\(176\) 6.17044 0.465114
\(177\) −2.06129 −0.154936
\(178\) 13.0690 0.979563
\(179\) −12.7410 −0.952306 −0.476153 0.879362i \(-0.657969\pi\)
−0.476153 + 0.879362i \(0.657969\pi\)
\(180\) −2.94994 −0.219876
\(181\) −4.11942 −0.306194 −0.153097 0.988211i \(-0.548925\pi\)
−0.153097 + 0.988211i \(0.548925\pi\)
\(182\) −1.96516 −0.145667
\(183\) −1.52447 −0.112692
\(184\) 0.690450 0.0509007
\(185\) 6.67643 0.490861
\(186\) −0.309423 −0.0226880
\(187\) 7.40541 0.541537
\(188\) 2.50929 0.183008
\(189\) 0.619744 0.0450798
\(190\) 2.12314 0.154029
\(191\) 9.89876 0.716249 0.358125 0.933674i \(-0.383416\pi\)
0.358125 + 0.933674i \(0.383416\pi\)
\(192\) 0.223737 0.0161469
\(193\) −8.42443 −0.606404 −0.303202 0.952926i \(-0.598056\pi\)
−0.303202 + 0.952926i \(0.598056\pi\)
\(194\) 7.25226 0.520682
\(195\) −0.944440 −0.0676328
\(196\) −6.78327 −0.484519
\(197\) 13.6917 0.975493 0.487747 0.872985i \(-0.337819\pi\)
0.487747 + 0.872985i \(0.337819\pi\)
\(198\) 18.2024 1.29359
\(199\) 24.5276 1.73871 0.869357 0.494184i \(-0.164533\pi\)
0.869357 + 0.494184i \(0.164533\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.26182 0.0890016
\(202\) −3.41556 −0.240318
\(203\) 4.58532 0.321826
\(204\) 0.268517 0.0188000
\(205\) −7.06932 −0.493743
\(206\) −4.07066 −0.283616
\(207\) 2.03679 0.141567
\(208\) −4.22120 −0.292688
\(209\) −13.1007 −0.906195
\(210\) 0.104160 0.00718771
\(211\) −12.7980 −0.881053 −0.440527 0.897739i \(-0.645208\pi\)
−0.440527 + 0.897739i \(0.645208\pi\)
\(212\) −3.84117 −0.263812
\(213\) −0.830711 −0.0569194
\(214\) 12.7930 0.874513
\(215\) 4.32772 0.295148
\(216\) 1.33122 0.0905783
\(217\) −0.643836 −0.0437064
\(218\) 15.7644 1.06770
\(219\) 0.648154 0.0437982
\(220\) 6.17044 0.416011
\(221\) −5.06605 −0.340779
\(222\) −1.49377 −0.100255
\(223\) −15.4771 −1.03642 −0.518212 0.855252i \(-0.673402\pi\)
−0.518212 + 0.855252i \(0.673402\pi\)
\(224\) 0.465545 0.0311055
\(225\) −2.94994 −0.196663
\(226\) 4.94582 0.328991
\(227\) 22.3520 1.48355 0.741776 0.670648i \(-0.233984\pi\)
0.741776 + 0.670648i \(0.233984\pi\)
\(228\) −0.475026 −0.0314594
\(229\) −5.95136 −0.393277 −0.196639 0.980476i \(-0.563003\pi\)
−0.196639 + 0.980476i \(0.563003\pi\)
\(230\) 0.690450 0.0455269
\(231\) −0.642711 −0.0422873
\(232\) 9.84937 0.646643
\(233\) 5.81744 0.381113 0.190557 0.981676i \(-0.438971\pi\)
0.190557 + 0.981676i \(0.438971\pi\)
\(234\) −12.4523 −0.814032
\(235\) 2.50929 0.163688
\(236\) −9.21300 −0.599715
\(237\) −0.212454 −0.0138004
\(238\) 0.558721 0.0362165
\(239\) 23.3866 1.51275 0.756376 0.654137i \(-0.226968\pi\)
0.756376 + 0.654137i \(0.226968\pi\)
\(240\) 0.223737 0.0144422
\(241\) −21.2691 −1.37007 −0.685033 0.728512i \(-0.740212\pi\)
−0.685033 + 0.728512i \(0.740212\pi\)
\(242\) −27.0743 −1.74040
\(243\) 5.90707 0.378939
\(244\) −6.81367 −0.436200
\(245\) −6.78327 −0.433367
\(246\) 1.58167 0.100844
\(247\) 8.96221 0.570252
\(248\) −1.38297 −0.0878189
\(249\) 3.19674 0.202585
\(250\) −1.00000 −0.0632456
\(251\) −13.8455 −0.873922 −0.436961 0.899481i \(-0.643945\pi\)
−0.436961 + 0.899481i \(0.643945\pi\)
\(252\) 1.37333 0.0865116
\(253\) −4.26038 −0.267848
\(254\) −7.48068 −0.469380
\(255\) 0.268517 0.0168152
\(256\) 1.00000 0.0625000
\(257\) −29.3052 −1.82801 −0.914005 0.405702i \(-0.867027\pi\)
−0.914005 + 0.405702i \(0.867027\pi\)
\(258\) −0.968273 −0.0602820
\(259\) −3.10818 −0.193133
\(260\) −4.22120 −0.261788
\(261\) 29.0551 1.79846
\(262\) 12.8152 0.791728
\(263\) −19.1480 −1.18072 −0.590358 0.807141i \(-0.701013\pi\)
−0.590358 + 0.807141i \(0.701013\pi\)
\(264\) −1.38056 −0.0849674
\(265\) −3.84117 −0.235961
\(266\) −0.988418 −0.0606038
\(267\) −2.92402 −0.178947
\(268\) 5.63972 0.344501
\(269\) −0.785668 −0.0479030 −0.0239515 0.999713i \(-0.507625\pi\)
−0.0239515 + 0.999713i \(0.507625\pi\)
\(270\) 1.33122 0.0810157
\(271\) 3.61875 0.219823 0.109912 0.993941i \(-0.464943\pi\)
0.109912 + 0.993941i \(0.464943\pi\)
\(272\) 1.20014 0.0727694
\(273\) 0.439679 0.0266106
\(274\) 15.4820 0.935302
\(275\) 6.17044 0.372091
\(276\) −0.154479 −0.00929857
\(277\) 27.3303 1.64212 0.821059 0.570844i \(-0.193384\pi\)
0.821059 + 0.570844i \(0.193384\pi\)
\(278\) −7.12322 −0.427222
\(279\) −4.07969 −0.244245
\(280\) 0.465545 0.0278216
\(281\) 29.1906 1.74136 0.870682 0.491847i \(-0.163678\pi\)
0.870682 + 0.491847i \(0.163678\pi\)
\(282\) −0.561421 −0.0334321
\(283\) −5.48019 −0.325764 −0.162882 0.986646i \(-0.552079\pi\)
−0.162882 + 0.986646i \(0.552079\pi\)
\(284\) −3.71289 −0.220319
\(285\) −0.475026 −0.0281381
\(286\) 26.0466 1.54017
\(287\) 3.29108 0.194267
\(288\) 2.94994 0.173827
\(289\) −15.5597 −0.915274
\(290\) 9.84937 0.578375
\(291\) −1.62260 −0.0951185
\(292\) 2.89694 0.169531
\(293\) −15.3116 −0.894515 −0.447258 0.894405i \(-0.647599\pi\)
−0.447258 + 0.894405i \(0.647599\pi\)
\(294\) 1.51767 0.0885124
\(295\) −9.21300 −0.536401
\(296\) −6.67643 −0.388060
\(297\) −8.21423 −0.476638
\(298\) −12.8092 −0.742020
\(299\) 2.91453 0.168552
\(300\) 0.223737 0.0129175
\(301\) −2.01475 −0.116128
\(302\) 18.7986 1.08174
\(303\) 0.764188 0.0439014
\(304\) −2.12314 −0.121771
\(305\) −6.81367 −0.390150
\(306\) 3.54035 0.202389
\(307\) 15.2082 0.867975 0.433988 0.900919i \(-0.357106\pi\)
0.433988 + 0.900919i \(0.357106\pi\)
\(308\) −2.87261 −0.163682
\(309\) 0.910759 0.0518113
\(310\) −1.38297 −0.0785476
\(311\) −26.2950 −1.49105 −0.745527 0.666475i \(-0.767802\pi\)
−0.745527 + 0.666475i \(0.767802\pi\)
\(312\) 0.944440 0.0534684
\(313\) 5.62420 0.317898 0.158949 0.987287i \(-0.449189\pi\)
0.158949 + 0.987287i \(0.449189\pi\)
\(314\) 17.4414 0.984275
\(315\) 1.37333 0.0773784
\(316\) −0.949571 −0.0534175
\(317\) −5.47504 −0.307509 −0.153754 0.988109i \(-0.549136\pi\)
−0.153754 + 0.988109i \(0.549136\pi\)
\(318\) 0.859413 0.0481935
\(319\) −60.7749 −3.40274
\(320\) 1.00000 0.0559017
\(321\) −2.86228 −0.159757
\(322\) −0.321435 −0.0179129
\(323\) −2.54808 −0.141779
\(324\) 8.55198 0.475110
\(325\) −4.22120 −0.234150
\(326\) 20.5938 1.14058
\(327\) −3.52708 −0.195048
\(328\) 7.06932 0.390338
\(329\) −1.16818 −0.0644041
\(330\) −1.38056 −0.0759972
\(331\) 5.77869 0.317626 0.158813 0.987309i \(-0.449233\pi\)
0.158813 + 0.987309i \(0.449233\pi\)
\(332\) 14.2879 0.784151
\(333\) −19.6951 −1.07928
\(334\) −24.2024 −1.32430
\(335\) 5.63972 0.308131
\(336\) −0.104160 −0.00568238
\(337\) −29.5860 −1.61165 −0.805826 0.592153i \(-0.798278\pi\)
−0.805826 + 0.592153i \(0.798278\pi\)
\(338\) −4.81853 −0.262094
\(339\) −1.10656 −0.0601004
\(340\) 1.20014 0.0650870
\(341\) 8.53355 0.462117
\(342\) −6.26315 −0.338672
\(343\) 6.41673 0.346471
\(344\) −4.32772 −0.233335
\(345\) −0.154479 −0.00831690
\(346\) −5.58475 −0.300238
\(347\) −23.8256 −1.27902 −0.639511 0.768782i \(-0.720863\pi\)
−0.639511 + 0.768782i \(0.720863\pi\)
\(348\) −2.20367 −0.118129
\(349\) 27.2318 1.45769 0.728843 0.684681i \(-0.240058\pi\)
0.728843 + 0.684681i \(0.240058\pi\)
\(350\) 0.465545 0.0248844
\(351\) 5.61936 0.299940
\(352\) −6.17044 −0.328885
\(353\) 16.6058 0.883837 0.441919 0.897055i \(-0.354298\pi\)
0.441919 + 0.897055i \(0.354298\pi\)
\(354\) 2.06129 0.109556
\(355\) −3.71289 −0.197059
\(356\) −13.0690 −0.692656
\(357\) −0.125007 −0.00661606
\(358\) 12.7410 0.673382
\(359\) −10.1818 −0.537375 −0.268687 0.963227i \(-0.586590\pi\)
−0.268687 + 0.963227i \(0.586590\pi\)
\(360\) 2.94994 0.155476
\(361\) −14.4923 −0.762751
\(362\) 4.11942 0.216512
\(363\) 6.05753 0.317938
\(364\) 1.96516 0.103002
\(365\) 2.89694 0.151633
\(366\) 1.52447 0.0796855
\(367\) −14.6483 −0.764635 −0.382318 0.924031i \(-0.624874\pi\)
−0.382318 + 0.924031i \(0.624874\pi\)
\(368\) −0.690450 −0.0359922
\(369\) 20.8541 1.08562
\(370\) −6.67643 −0.347091
\(371\) 1.78823 0.0928405
\(372\) 0.309423 0.0160428
\(373\) −34.3658 −1.77939 −0.889697 0.456551i \(-0.849085\pi\)
−0.889697 + 0.456551i \(0.849085\pi\)
\(374\) −7.40541 −0.382925
\(375\) 0.223737 0.0115537
\(376\) −2.50929 −0.129407
\(377\) 41.5761 2.14128
\(378\) −0.619744 −0.0318762
\(379\) −24.3264 −1.24956 −0.624782 0.780800i \(-0.714812\pi\)
−0.624782 + 0.780800i \(0.714812\pi\)
\(380\) −2.12314 −0.108915
\(381\) 1.67371 0.0857467
\(382\) −9.89876 −0.506465
\(383\) 18.2216 0.931080 0.465540 0.885027i \(-0.345860\pi\)
0.465540 + 0.885027i \(0.345860\pi\)
\(384\) −0.223737 −0.0114176
\(385\) −2.87261 −0.146402
\(386\) 8.42443 0.428792
\(387\) −12.7665 −0.648959
\(388\) −7.25226 −0.368178
\(389\) −14.8767 −0.754281 −0.377140 0.926156i \(-0.623093\pi\)
−0.377140 + 0.926156i \(0.623093\pi\)
\(390\) 0.944440 0.0478236
\(391\) −0.828640 −0.0419061
\(392\) 6.78327 0.342607
\(393\) −2.86725 −0.144634
\(394\) −13.6917 −0.689778
\(395\) −0.949571 −0.0477781
\(396\) −18.2024 −0.914706
\(397\) 15.8903 0.797510 0.398755 0.917057i \(-0.369442\pi\)
0.398755 + 0.917057i \(0.369442\pi\)
\(398\) −24.5276 −1.22946
\(399\) 0.221146 0.0110711
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) −1.26182 −0.0629336
\(403\) −5.83781 −0.290802
\(404\) 3.41556 0.169930
\(405\) 8.55198 0.424951
\(406\) −4.58532 −0.227566
\(407\) 41.1965 2.04203
\(408\) −0.268517 −0.0132936
\(409\) 2.81572 0.139229 0.0696143 0.997574i \(-0.477823\pi\)
0.0696143 + 0.997574i \(0.477823\pi\)
\(410\) 7.06932 0.349129
\(411\) −3.46390 −0.170862
\(412\) 4.07066 0.200547
\(413\) 4.28906 0.211051
\(414\) −2.03679 −0.100103
\(415\) 14.2879 0.701366
\(416\) 4.22120 0.206961
\(417\) 1.59373 0.0780453
\(418\) 13.1007 0.640777
\(419\) −7.95481 −0.388618 −0.194309 0.980940i \(-0.562246\pi\)
−0.194309 + 0.980940i \(0.562246\pi\)
\(420\) −0.104160 −0.00508248
\(421\) −20.6725 −1.00752 −0.503758 0.863845i \(-0.668050\pi\)
−0.503758 + 0.863845i \(0.668050\pi\)
\(422\) 12.7980 0.622999
\(423\) −7.40225 −0.359910
\(424\) 3.84117 0.186544
\(425\) 1.20014 0.0582155
\(426\) 0.830711 0.0402481
\(427\) 3.17207 0.153507
\(428\) −12.7930 −0.618374
\(429\) −5.82761 −0.281360
\(430\) −4.32772 −0.208701
\(431\) 8.65440 0.416868 0.208434 0.978036i \(-0.433163\pi\)
0.208434 + 0.978036i \(0.433163\pi\)
\(432\) −1.33122 −0.0640486
\(433\) −26.3018 −1.26398 −0.631992 0.774975i \(-0.717763\pi\)
−0.631992 + 0.774975i \(0.717763\pi\)
\(434\) 0.643836 0.0309051
\(435\) −2.20367 −0.105658
\(436\) −15.7644 −0.754977
\(437\) 1.46592 0.0701246
\(438\) −0.648154 −0.0309700
\(439\) 7.91844 0.377926 0.188963 0.981984i \(-0.439487\pi\)
0.188963 + 0.981984i \(0.439487\pi\)
\(440\) −6.17044 −0.294164
\(441\) 20.0102 0.952869
\(442\) 5.06605 0.240967
\(443\) −2.52617 −0.120022 −0.0600109 0.998198i \(-0.519114\pi\)
−0.0600109 + 0.998198i \(0.519114\pi\)
\(444\) 1.49377 0.0708911
\(445\) −13.0690 −0.619530
\(446\) 15.4771 0.732863
\(447\) 2.86591 0.135553
\(448\) −0.465545 −0.0219949
\(449\) 18.4140 0.869008 0.434504 0.900670i \(-0.356924\pi\)
0.434504 + 0.900670i \(0.356924\pi\)
\(450\) 2.94994 0.139062
\(451\) −43.6208 −2.05402
\(452\) −4.94582 −0.232632
\(453\) −4.20595 −0.197613
\(454\) −22.3520 −1.04903
\(455\) 1.96516 0.0921280
\(456\) 0.475026 0.0222451
\(457\) −31.4150 −1.46953 −0.734765 0.678322i \(-0.762708\pi\)
−0.734765 + 0.678322i \(0.762708\pi\)
\(458\) 5.95136 0.278089
\(459\) −1.59766 −0.0745724
\(460\) −0.690450 −0.0321924
\(461\) 39.3309 1.83182 0.915912 0.401378i \(-0.131469\pi\)
0.915912 + 0.401378i \(0.131469\pi\)
\(462\) 0.642711 0.0299016
\(463\) −23.1919 −1.07782 −0.538909 0.842364i \(-0.681163\pi\)
−0.538909 + 0.842364i \(0.681163\pi\)
\(464\) −9.84937 −0.457245
\(465\) 0.309423 0.0143491
\(466\) −5.81744 −0.269488
\(467\) −14.8344 −0.686452 −0.343226 0.939253i \(-0.611520\pi\)
−0.343226 + 0.939253i \(0.611520\pi\)
\(468\) 12.4523 0.575608
\(469\) −2.62554 −0.121236
\(470\) −2.50929 −0.115745
\(471\) −3.90229 −0.179808
\(472\) 9.21300 0.424063
\(473\) 26.7039 1.22785
\(474\) 0.212454 0.00975836
\(475\) −2.12314 −0.0974165
\(476\) −0.558721 −0.0256089
\(477\) 11.3312 0.518821
\(478\) −23.3866 −1.06968
\(479\) −25.2619 −1.15425 −0.577123 0.816657i \(-0.695825\pi\)
−0.577123 + 0.816657i \(0.695825\pi\)
\(480\) −0.223737 −0.0102122
\(481\) −28.1826 −1.28501
\(482\) 21.2691 0.968782
\(483\) 0.0719171 0.00327234
\(484\) 27.0743 1.23065
\(485\) −7.25226 −0.329308
\(486\) −5.90707 −0.267950
\(487\) −26.5813 −1.20452 −0.602258 0.798302i \(-0.705732\pi\)
−0.602258 + 0.798302i \(0.705732\pi\)
\(488\) 6.81367 0.308440
\(489\) −4.60760 −0.208363
\(490\) 6.78327 0.306437
\(491\) −14.8140 −0.668547 −0.334273 0.942476i \(-0.608491\pi\)
−0.334273 + 0.942476i \(0.608491\pi\)
\(492\) −1.58167 −0.0713073
\(493\) −11.8207 −0.532376
\(494\) −8.96221 −0.403229
\(495\) −18.2024 −0.818138
\(496\) 1.38297 0.0620973
\(497\) 1.72851 0.0775344
\(498\) −3.19674 −0.143249
\(499\) −16.0747 −0.719603 −0.359801 0.933029i \(-0.617156\pi\)
−0.359801 + 0.933029i \(0.617156\pi\)
\(500\) 1.00000 0.0447214
\(501\) 5.41498 0.241924
\(502\) 13.8455 0.617956
\(503\) 17.4153 0.776512 0.388256 0.921552i \(-0.373078\pi\)
0.388256 + 0.921552i \(0.373078\pi\)
\(504\) −1.37333 −0.0611730
\(505\) 3.41556 0.151990
\(506\) 4.26038 0.189397
\(507\) 1.07809 0.0478795
\(508\) 7.48068 0.331902
\(509\) −22.7315 −1.00756 −0.503778 0.863833i \(-0.668057\pi\)
−0.503778 + 0.863833i \(0.668057\pi\)
\(510\) −0.268517 −0.0118901
\(511\) −1.34866 −0.0596610
\(512\) −1.00000 −0.0441942
\(513\) 2.82638 0.124788
\(514\) 29.3052 1.29260
\(515\) 4.07066 0.179375
\(516\) 0.968273 0.0426258
\(517\) 15.4834 0.680959
\(518\) 3.10818 0.136565
\(519\) 1.24952 0.0548478
\(520\) 4.22120 0.185112
\(521\) 4.37519 0.191680 0.0958402 0.995397i \(-0.469446\pi\)
0.0958402 + 0.995397i \(0.469446\pi\)
\(522\) −29.0551 −1.27171
\(523\) 5.79741 0.253503 0.126752 0.991934i \(-0.459545\pi\)
0.126752 + 0.991934i \(0.459545\pi\)
\(524\) −12.8152 −0.559836
\(525\) −0.104160 −0.00454590
\(526\) 19.1480 0.834892
\(527\) 1.65977 0.0723006
\(528\) 1.38056 0.0600810
\(529\) −22.5233 −0.979273
\(530\) 3.84117 0.166850
\(531\) 27.1778 1.17942
\(532\) 0.988418 0.0428533
\(533\) 29.8410 1.29256
\(534\) 2.92402 0.126535
\(535\) −12.7930 −0.553091
\(536\) −5.63972 −0.243599
\(537\) −2.85063 −0.123014
\(538\) 0.785668 0.0338725
\(539\) −41.8557 −1.80285
\(540\) −1.33122 −0.0572868
\(541\) −3.62022 −0.155646 −0.0778228 0.996967i \(-0.524797\pi\)
−0.0778228 + 0.996967i \(0.524797\pi\)
\(542\) −3.61875 −0.155439
\(543\) −0.921668 −0.0395526
\(544\) −1.20014 −0.0514558
\(545\) −15.7644 −0.675272
\(546\) −0.439679 −0.0188165
\(547\) 38.7497 1.65682 0.828408 0.560125i \(-0.189247\pi\)
0.828408 + 0.560125i \(0.189247\pi\)
\(548\) −15.4820 −0.661358
\(549\) 20.0999 0.857844
\(550\) −6.17044 −0.263108
\(551\) 20.9116 0.890864
\(552\) 0.154479 0.00657508
\(553\) 0.442068 0.0187986
\(554\) −27.3303 −1.16115
\(555\) 1.49377 0.0634069
\(556\) 7.12322 0.302092
\(557\) 32.7860 1.38919 0.694594 0.719402i \(-0.255584\pi\)
0.694594 + 0.719402i \(0.255584\pi\)
\(558\) 4.07969 0.172707
\(559\) −18.2682 −0.772661
\(560\) −0.465545 −0.0196729
\(561\) 1.65687 0.0699530
\(562\) −29.1906 −1.23133
\(563\) −11.7215 −0.494003 −0.247001 0.969015i \(-0.579445\pi\)
−0.247001 + 0.969015i \(0.579445\pi\)
\(564\) 0.561421 0.0236401
\(565\) −4.94582 −0.208072
\(566\) 5.48019 0.230350
\(567\) −3.98133 −0.167200
\(568\) 3.71289 0.155789
\(569\) 17.1213 0.717760 0.358880 0.933384i \(-0.383159\pi\)
0.358880 + 0.933384i \(0.383159\pi\)
\(570\) 0.475026 0.0198967
\(571\) −40.2838 −1.68582 −0.842912 0.538051i \(-0.819161\pi\)
−0.842912 + 0.538051i \(0.819161\pi\)
\(572\) −26.0466 −1.08907
\(573\) 2.21472 0.0925214
\(574\) −3.29108 −0.137367
\(575\) −0.690450 −0.0287938
\(576\) −2.94994 −0.122914
\(577\) 15.8660 0.660510 0.330255 0.943892i \(-0.392865\pi\)
0.330255 + 0.943892i \(0.392865\pi\)
\(578\) 15.5597 0.647196
\(579\) −1.88486 −0.0783321
\(580\) −9.84937 −0.408973
\(581\) −6.65166 −0.275958
\(582\) 1.62260 0.0672590
\(583\) −23.7017 −0.981623
\(584\) −2.89694 −0.119876
\(585\) 12.4523 0.514839
\(586\) 15.3116 0.632518
\(587\) −2.62424 −0.108314 −0.0541569 0.998532i \(-0.517247\pi\)
−0.0541569 + 0.998532i \(0.517247\pi\)
\(588\) −1.51767 −0.0625877
\(589\) −2.93625 −0.120986
\(590\) 9.21300 0.379293
\(591\) 3.06334 0.126009
\(592\) 6.67643 0.274400
\(593\) −12.7863 −0.525072 −0.262536 0.964922i \(-0.584559\pi\)
−0.262536 + 0.964922i \(0.584559\pi\)
\(594\) 8.21423 0.337034
\(595\) −0.558721 −0.0229053
\(596\) 12.8092 0.524687
\(597\) 5.48774 0.224598
\(598\) −2.91453 −0.119184
\(599\) −22.3214 −0.912028 −0.456014 0.889973i \(-0.650723\pi\)
−0.456014 + 0.889973i \(0.650723\pi\)
\(600\) −0.223737 −0.00913404
\(601\) 8.57834 0.349918 0.174959 0.984576i \(-0.444021\pi\)
0.174959 + 0.984576i \(0.444021\pi\)
\(602\) 2.01475 0.0821149
\(603\) −16.6368 −0.677504
\(604\) −18.7986 −0.764905
\(605\) 27.0743 1.10073
\(606\) −0.764188 −0.0310430
\(607\) 36.3319 1.47467 0.737333 0.675530i \(-0.236085\pi\)
0.737333 + 0.675530i \(0.236085\pi\)
\(608\) 2.12314 0.0861048
\(609\) 1.02591 0.0415719
\(610\) 6.81367 0.275877
\(611\) −10.5922 −0.428514
\(612\) −3.54035 −0.143110
\(613\) 10.0621 0.406405 0.203203 0.979137i \(-0.434865\pi\)
0.203203 + 0.979137i \(0.434865\pi\)
\(614\) −15.2082 −0.613751
\(615\) −1.58167 −0.0637791
\(616\) 2.87261 0.115741
\(617\) 44.2627 1.78195 0.890974 0.454054i \(-0.150023\pi\)
0.890974 + 0.454054i \(0.150023\pi\)
\(618\) −0.910759 −0.0366361
\(619\) 36.4444 1.46482 0.732412 0.680862i \(-0.238395\pi\)
0.732412 + 0.680862i \(0.238395\pi\)
\(620\) 1.38297 0.0555415
\(621\) 0.919144 0.0368840
\(622\) 26.2950 1.05433
\(623\) 6.08420 0.243758
\(624\) −0.944440 −0.0378079
\(625\) 1.00000 0.0400000
\(626\) −5.62420 −0.224788
\(627\) −2.93112 −0.117058
\(628\) −17.4414 −0.695988
\(629\) 8.01268 0.319486
\(630\) −1.37333 −0.0547148
\(631\) −15.5830 −0.620350 −0.310175 0.950679i \(-0.600388\pi\)
−0.310175 + 0.950679i \(0.600388\pi\)
\(632\) 0.949571 0.0377719
\(633\) −2.86340 −0.113810
\(634\) 5.47504 0.217442
\(635\) 7.48068 0.296862
\(636\) −0.859413 −0.0340779
\(637\) 28.6335 1.13450
\(638\) 60.7749 2.40610
\(639\) 10.9528 0.433286
\(640\) −1.00000 −0.0395285
\(641\) −8.89075 −0.351164 −0.175582 0.984465i \(-0.556181\pi\)
−0.175582 + 0.984465i \(0.556181\pi\)
\(642\) 2.86228 0.112965
\(643\) −5.39515 −0.212764 −0.106382 0.994325i \(-0.533927\pi\)
−0.106382 + 0.994325i \(0.533927\pi\)
\(644\) 0.321435 0.0126663
\(645\) 0.968273 0.0381257
\(646\) 2.54808 0.100253
\(647\) −9.98088 −0.392389 −0.196195 0.980565i \(-0.562858\pi\)
−0.196195 + 0.980565i \(0.562858\pi\)
\(648\) −8.55198 −0.335954
\(649\) −56.8482 −2.23149
\(650\) 4.22120 0.165569
\(651\) −0.144050 −0.00564577
\(652\) −20.5938 −0.806514
\(653\) 41.7998 1.63575 0.817877 0.575393i \(-0.195151\pi\)
0.817877 + 0.575393i \(0.195151\pi\)
\(654\) 3.52708 0.137920
\(655\) −12.8152 −0.500733
\(656\) −7.06932 −0.276011
\(657\) −8.54581 −0.333404
\(658\) 1.16818 0.0455406
\(659\) 2.65148 0.103287 0.0516434 0.998666i \(-0.483554\pi\)
0.0516434 + 0.998666i \(0.483554\pi\)
\(660\) 1.38056 0.0537381
\(661\) 9.20619 0.358079 0.179040 0.983842i \(-0.442701\pi\)
0.179040 + 0.983842i \(0.442701\pi\)
\(662\) −5.77869 −0.224595
\(663\) −1.13346 −0.0440201
\(664\) −14.2879 −0.554479
\(665\) 0.988418 0.0383292
\(666\) 19.6951 0.763169
\(667\) 6.80050 0.263316
\(668\) 24.2024 0.936419
\(669\) −3.46281 −0.133880
\(670\) −5.63972 −0.217881
\(671\) −42.0433 −1.62306
\(672\) 0.104160 0.00401805
\(673\) 2.53826 0.0978428 0.0489214 0.998803i \(-0.484422\pi\)
0.0489214 + 0.998803i \(0.484422\pi\)
\(674\) 29.5860 1.13961
\(675\) −1.33122 −0.0512388
\(676\) 4.81853 0.185328
\(677\) −19.8646 −0.763458 −0.381729 0.924274i \(-0.624671\pi\)
−0.381729 + 0.924274i \(0.624671\pi\)
\(678\) 1.10656 0.0424974
\(679\) 3.37625 0.129569
\(680\) −1.20014 −0.0460234
\(681\) 5.00097 0.191637
\(682\) −8.53355 −0.326766
\(683\) 0.359755 0.0137656 0.00688282 0.999976i \(-0.497809\pi\)
0.00688282 + 0.999976i \(0.497809\pi\)
\(684\) 6.26315 0.239477
\(685\) −15.4820 −0.591537
\(686\) −6.41673 −0.244992
\(687\) −1.33154 −0.0508015
\(688\) 4.32772 0.164993
\(689\) 16.2143 0.617717
\(690\) 0.154479 0.00588093
\(691\) 25.4382 0.967714 0.483857 0.875147i \(-0.339235\pi\)
0.483857 + 0.875147i \(0.339235\pi\)
\(692\) 5.58475 0.212300
\(693\) 8.47404 0.321902
\(694\) 23.8256 0.904406
\(695\) 7.12322 0.270199
\(696\) 2.20367 0.0835300
\(697\) −8.48420 −0.321362
\(698\) −27.2318 −1.03074
\(699\) 1.30158 0.0492303
\(700\) −0.465545 −0.0175959
\(701\) 39.4988 1.49185 0.745924 0.666031i \(-0.232008\pi\)
0.745924 + 0.666031i \(0.232008\pi\)
\(702\) −5.61936 −0.212089
\(703\) −14.1750 −0.534621
\(704\) 6.17044 0.232557
\(705\) 0.561421 0.0211443
\(706\) −16.6058 −0.624967
\(707\) −1.59009 −0.0598017
\(708\) −2.06129 −0.0774681
\(709\) 38.0028 1.42723 0.713613 0.700540i \(-0.247058\pi\)
0.713613 + 0.700540i \(0.247058\pi\)
\(710\) 3.71289 0.139342
\(711\) 2.80118 0.105052
\(712\) 13.0690 0.489782
\(713\) −0.954874 −0.0357603
\(714\) 0.125007 0.00467826
\(715\) −26.0466 −0.974089
\(716\) −12.7410 −0.476153
\(717\) 5.23245 0.195410
\(718\) 10.1818 0.379981
\(719\) 28.8205 1.07482 0.537412 0.843320i \(-0.319402\pi\)
0.537412 + 0.843320i \(0.319402\pi\)
\(720\) −2.94994 −0.109938
\(721\) −1.89507 −0.0705762
\(722\) 14.4923 0.539346
\(723\) −4.75870 −0.176978
\(724\) −4.11942 −0.153097
\(725\) −9.84937 −0.365796
\(726\) −6.05753 −0.224816
\(727\) −49.4658 −1.83458 −0.917292 0.398216i \(-0.869630\pi\)
−0.917292 + 0.398216i \(0.869630\pi\)
\(728\) −1.96516 −0.0728336
\(729\) −24.3343 −0.901271
\(730\) −2.89694 −0.107221
\(731\) 5.19389 0.192103
\(732\) −1.52447 −0.0563461
\(733\) 43.1912 1.59530 0.797652 0.603118i \(-0.206075\pi\)
0.797652 + 0.603118i \(0.206075\pi\)
\(734\) 14.6483 0.540679
\(735\) −1.51767 −0.0559801
\(736\) 0.690450 0.0254503
\(737\) 34.7995 1.28186
\(738\) −20.8541 −0.767649
\(739\) −14.6073 −0.537339 −0.268670 0.963232i \(-0.586584\pi\)
−0.268670 + 0.963232i \(0.586584\pi\)
\(740\) 6.67643 0.245430
\(741\) 2.00518 0.0736622
\(742\) −1.78823 −0.0656482
\(743\) 41.4080 1.51911 0.759556 0.650442i \(-0.225416\pi\)
0.759556 + 0.650442i \(0.225416\pi\)
\(744\) −0.309423 −0.0113440
\(745\) 12.8092 0.469294
\(746\) 34.3658 1.25822
\(747\) −42.1485 −1.54213
\(748\) 7.40541 0.270769
\(749\) 5.95573 0.217617
\(750\) −0.223737 −0.00816973
\(751\) −31.3070 −1.14241 −0.571205 0.820807i \(-0.693524\pi\)
−0.571205 + 0.820807i \(0.693524\pi\)
\(752\) 2.50929 0.0915042
\(753\) −3.09776 −0.112889
\(754\) −41.5761 −1.51411
\(755\) −18.7986 −0.684152
\(756\) 0.619744 0.0225399
\(757\) 13.2452 0.481406 0.240703 0.970599i \(-0.422622\pi\)
0.240703 + 0.970599i \(0.422622\pi\)
\(758\) 24.3264 0.883574
\(759\) −0.953206 −0.0345992
\(760\) 2.12314 0.0770145
\(761\) −27.7894 −1.00737 −0.503683 0.863889i \(-0.668022\pi\)
−0.503683 + 0.863889i \(0.668022\pi\)
\(762\) −1.67371 −0.0606320
\(763\) 7.33902 0.265691
\(764\) 9.89876 0.358125
\(765\) −3.54035 −0.128002
\(766\) −18.2216 −0.658373
\(767\) 38.8899 1.40423
\(768\) 0.223737 0.00807343
\(769\) −1.50117 −0.0541335 −0.0270668 0.999634i \(-0.508617\pi\)
−0.0270668 + 0.999634i \(0.508617\pi\)
\(770\) 2.87261 0.103522
\(771\) −6.55668 −0.236133
\(772\) −8.42443 −0.303202
\(773\) 39.0725 1.40534 0.702670 0.711516i \(-0.251991\pi\)
0.702670 + 0.711516i \(0.251991\pi\)
\(774\) 12.7665 0.458883
\(775\) 1.38297 0.0496779
\(776\) 7.25226 0.260341
\(777\) −0.695415 −0.0249479
\(778\) 14.8767 0.533357
\(779\) 15.0092 0.537760
\(780\) −0.944440 −0.0338164
\(781\) −22.9101 −0.819789
\(782\) 0.828640 0.0296321
\(783\) 13.1117 0.468575
\(784\) −6.78327 −0.242260
\(785\) −17.4414 −0.622510
\(786\) 2.86725 0.102271
\(787\) 40.2946 1.43635 0.718174 0.695864i \(-0.244978\pi\)
0.718174 + 0.695864i \(0.244978\pi\)
\(788\) 13.6917 0.487747
\(789\) −4.28412 −0.152519
\(790\) 0.949571 0.0337842
\(791\) 2.30250 0.0818675
\(792\) 18.2024 0.646795
\(793\) 28.7619 1.02136
\(794\) −15.8903 −0.563925
\(795\) −0.859413 −0.0304802
\(796\) 24.5276 0.869357
\(797\) 18.1418 0.642614 0.321307 0.946975i \(-0.395878\pi\)
0.321307 + 0.946975i \(0.395878\pi\)
\(798\) −0.221146 −0.00782848
\(799\) 3.01150 0.106539
\(800\) −1.00000 −0.0353553
\(801\) 38.5528 1.36220
\(802\) −1.00000 −0.0353112
\(803\) 17.8754 0.630809
\(804\) 1.26182 0.0445008
\(805\) 0.321435 0.0113291
\(806\) 5.83781 0.205628
\(807\) −0.175783 −0.00618786
\(808\) −3.41556 −0.120159
\(809\) 45.7120 1.60715 0.803574 0.595205i \(-0.202929\pi\)
0.803574 + 0.595205i \(0.202929\pi\)
\(810\) −8.55198 −0.300486
\(811\) 46.4323 1.63046 0.815230 0.579137i \(-0.196611\pi\)
0.815230 + 0.579137i \(0.196611\pi\)
\(812\) 4.58532 0.160913
\(813\) 0.809650 0.0283957
\(814\) −41.1965 −1.44394
\(815\) −20.5938 −0.721368
\(816\) 0.268517 0.00939998
\(817\) −9.18836 −0.321460
\(818\) −2.81572 −0.0984494
\(819\) −5.79710 −0.202567
\(820\) −7.06932 −0.246871
\(821\) 40.5631 1.41566 0.707831 0.706382i \(-0.249674\pi\)
0.707831 + 0.706382i \(0.249674\pi\)
\(822\) 3.46390 0.120817
\(823\) 17.9067 0.624189 0.312094 0.950051i \(-0.398969\pi\)
0.312094 + 0.950051i \(0.398969\pi\)
\(824\) −4.07066 −0.141808
\(825\) 1.38056 0.0480648
\(826\) −4.28906 −0.149236
\(827\) −37.7630 −1.31315 −0.656574 0.754262i \(-0.727995\pi\)
−0.656574 + 0.754262i \(0.727995\pi\)
\(828\) 2.03679 0.0707833
\(829\) −3.76049 −0.130607 −0.0653036 0.997865i \(-0.520802\pi\)
−0.0653036 + 0.997865i \(0.520802\pi\)
\(830\) −14.2879 −0.495941
\(831\) 6.11481 0.212120
\(832\) −4.22120 −0.146344
\(833\) −8.14090 −0.282065
\(834\) −1.59373 −0.0551864
\(835\) 24.2024 0.837559
\(836\) −13.1007 −0.453098
\(837\) −1.84105 −0.0636359
\(838\) 7.95481 0.274794
\(839\) 54.0314 1.86537 0.932686 0.360689i \(-0.117458\pi\)
0.932686 + 0.360689i \(0.117458\pi\)
\(840\) 0.104160 0.00359385
\(841\) 68.0100 2.34517
\(842\) 20.6725 0.712422
\(843\) 6.53102 0.224940
\(844\) −12.7980 −0.440527
\(845\) 4.81853 0.165763
\(846\) 7.40225 0.254494
\(847\) −12.6043 −0.433088
\(848\) −3.84117 −0.131906
\(849\) −1.22612 −0.0420805
\(850\) −1.20014 −0.0411646
\(851\) −4.60974 −0.158020
\(852\) −0.830711 −0.0284597
\(853\) 6.08028 0.208185 0.104092 0.994568i \(-0.466806\pi\)
0.104092 + 0.994568i \(0.466806\pi\)
\(854\) −3.17207 −0.108546
\(855\) 6.26315 0.214195
\(856\) 12.7930 0.437257
\(857\) 18.9392 0.646950 0.323475 0.946237i \(-0.395149\pi\)
0.323475 + 0.946237i \(0.395149\pi\)
\(858\) 5.82761 0.198951
\(859\) 20.8115 0.710078 0.355039 0.934852i \(-0.384468\pi\)
0.355039 + 0.934852i \(0.384468\pi\)
\(860\) 4.32772 0.147574
\(861\) 0.736339 0.0250944
\(862\) −8.65440 −0.294770
\(863\) −9.26376 −0.315342 −0.157671 0.987492i \(-0.550399\pi\)
−0.157671 + 0.987492i \(0.550399\pi\)
\(864\) 1.33122 0.0452892
\(865\) 5.58475 0.189887
\(866\) 26.3018 0.893772
\(867\) −3.48128 −0.118230
\(868\) −0.643836 −0.0218532
\(869\) −5.85926 −0.198762
\(870\) 2.20367 0.0747115
\(871\) −23.8064 −0.806648
\(872\) 15.7644 0.533849
\(873\) 21.3937 0.724068
\(874\) −1.46592 −0.0495856
\(875\) −0.465545 −0.0157383
\(876\) 0.648154 0.0218991
\(877\) −44.2706 −1.49491 −0.747456 0.664312i \(-0.768725\pi\)
−0.747456 + 0.664312i \(0.768725\pi\)
\(878\) −7.91844 −0.267234
\(879\) −3.42578 −0.115549
\(880\) 6.17044 0.208005
\(881\) −29.7098 −1.00095 −0.500474 0.865752i \(-0.666841\pi\)
−0.500474 + 0.865752i \(0.666841\pi\)
\(882\) −20.0102 −0.673780
\(883\) −7.15526 −0.240794 −0.120397 0.992726i \(-0.538417\pi\)
−0.120397 + 0.992726i \(0.538417\pi\)
\(884\) −5.06605 −0.170390
\(885\) −2.06129 −0.0692896
\(886\) 2.52617 0.0848683
\(887\) −34.3751 −1.15420 −0.577101 0.816673i \(-0.695816\pi\)
−0.577101 + 0.816673i \(0.695816\pi\)
\(888\) −1.49377 −0.0501275
\(889\) −3.48259 −0.116802
\(890\) 13.0690 0.438074
\(891\) 52.7694 1.76784
\(892\) −15.4771 −0.518212
\(893\) −5.32757 −0.178280
\(894\) −2.86591 −0.0958503
\(895\) −12.7410 −0.425884
\(896\) 0.465545 0.0155528
\(897\) 0.652089 0.0217726
\(898\) −18.4140 −0.614482
\(899\) −13.6214 −0.454299
\(900\) −2.94994 −0.0983314
\(901\) −4.60995 −0.153580
\(902\) 43.6208 1.45241
\(903\) −0.450774 −0.0150008
\(904\) 4.94582 0.164496
\(905\) −4.11942 −0.136934
\(906\) 4.20595 0.139733
\(907\) −46.9550 −1.55911 −0.779557 0.626331i \(-0.784556\pi\)
−0.779557 + 0.626331i \(0.784556\pi\)
\(908\) 22.3520 0.741776
\(909\) −10.0757 −0.334190
\(910\) −1.96516 −0.0651443
\(911\) −31.4013 −1.04037 −0.520185 0.854054i \(-0.674137\pi\)
−0.520185 + 0.854054i \(0.674137\pi\)
\(912\) −0.475026 −0.0157297
\(913\) 88.1627 2.91776
\(914\) 31.4150 1.03911
\(915\) −1.52447 −0.0503975
\(916\) −5.95136 −0.196639
\(917\) 5.96607 0.197017
\(918\) 1.59766 0.0527307
\(919\) 2.25524 0.0743934 0.0371967 0.999308i \(-0.488157\pi\)
0.0371967 + 0.999308i \(0.488157\pi\)
\(920\) 0.690450 0.0227635
\(921\) 3.40263 0.112121
\(922\) −39.3309 −1.29530
\(923\) 15.6728 0.515878
\(924\) −0.642711 −0.0211436
\(925\) 6.67643 0.219520
\(926\) 23.1919 0.762132
\(927\) −12.0082 −0.394401
\(928\) 9.84937 0.323321
\(929\) −4.19376 −0.137593 −0.0687965 0.997631i \(-0.521916\pi\)
−0.0687965 + 0.997631i \(0.521916\pi\)
\(930\) −0.309423 −0.0101464
\(931\) 14.4018 0.472001
\(932\) 5.81744 0.190557
\(933\) −5.88318 −0.192607
\(934\) 14.8344 0.485395
\(935\) 7.40541 0.242183
\(936\) −12.4523 −0.407016
\(937\) −17.2328 −0.562970 −0.281485 0.959566i \(-0.590827\pi\)
−0.281485 + 0.959566i \(0.590827\pi\)
\(938\) 2.62554 0.0857269
\(939\) 1.25834 0.0410645
\(940\) 2.50929 0.0818439
\(941\) 39.4974 1.28758 0.643789 0.765203i \(-0.277361\pi\)
0.643789 + 0.765203i \(0.277361\pi\)
\(942\) 3.90229 0.127144
\(943\) 4.88101 0.158948
\(944\) −9.21300 −0.299858
\(945\) 0.619744 0.0201603
\(946\) −26.7039 −0.868219
\(947\) 5.95315 0.193451 0.0967257 0.995311i \(-0.469163\pi\)
0.0967257 + 0.995311i \(0.469163\pi\)
\(948\) −0.212454 −0.00690020
\(949\) −12.2286 −0.396956
\(950\) 2.12314 0.0688838
\(951\) −1.22497 −0.0397224
\(952\) 0.558721 0.0181082
\(953\) 16.5723 0.536830 0.268415 0.963303i \(-0.413500\pi\)
0.268415 + 0.963303i \(0.413500\pi\)
\(954\) −11.3312 −0.366862
\(955\) 9.89876 0.320316
\(956\) 23.3866 0.756376
\(957\) −13.5976 −0.439548
\(958\) 25.2619 0.816176
\(959\) 7.20756 0.232744
\(960\) 0.223737 0.00722109
\(961\) −29.0874 −0.938303
\(962\) 28.1826 0.908642
\(963\) 37.7387 1.21611
\(964\) −21.2691 −0.685033
\(965\) −8.42443 −0.271192
\(966\) −0.0719171 −0.00231389
\(967\) 56.4282 1.81461 0.907304 0.420475i \(-0.138137\pi\)
0.907304 + 0.420475i \(0.138137\pi\)
\(968\) −27.0743 −0.870200
\(969\) −0.570100 −0.0183143
\(970\) 7.25226 0.232856
\(971\) 58.0871 1.86410 0.932052 0.362324i \(-0.118017\pi\)
0.932052 + 0.362324i \(0.118017\pi\)
\(972\) 5.90707 0.189469
\(973\) −3.31618 −0.106312
\(974\) 26.5813 0.851721
\(975\) −0.944440 −0.0302463
\(976\) −6.81367 −0.218100
\(977\) 30.6485 0.980531 0.490266 0.871573i \(-0.336900\pi\)
0.490266 + 0.871573i \(0.336900\pi\)
\(978\) 4.60760 0.147335
\(979\) −80.6414 −2.57731
\(980\) −6.78327 −0.216684
\(981\) 46.5040 1.48476
\(982\) 14.8140 0.472734
\(983\) 36.9101 1.17725 0.588624 0.808407i \(-0.299670\pi\)
0.588624 + 0.808407i \(0.299670\pi\)
\(984\) 1.58167 0.0504218
\(985\) 13.6917 0.436254
\(986\) 11.8207 0.376446
\(987\) −0.261367 −0.00831939
\(988\) 8.96221 0.285126
\(989\) −2.98807 −0.0950152
\(990\) 18.2024 0.578511
\(991\) 2.49442 0.0792380 0.0396190 0.999215i \(-0.487386\pi\)
0.0396190 + 0.999215i \(0.487386\pi\)
\(992\) −1.38297 −0.0439094
\(993\) 1.29291 0.0410292
\(994\) −1.72851 −0.0548251
\(995\) 24.5276 0.777577
\(996\) 3.19674 0.101293
\(997\) 40.2257 1.27396 0.636980 0.770881i \(-0.280184\pi\)
0.636980 + 0.770881i \(0.280184\pi\)
\(998\) 16.0747 0.508836
\(999\) −8.88783 −0.281198
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 4010.2.a.i.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.i.1.6 10 1.1 even 1 trivial