Properties

Label 4730.2.a.w.1.5
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
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 1.5
Root \(0.484643\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.515357 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.515357 q^{6} -4.64210 q^{7} -1.00000 q^{8} -2.73441 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.515357 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.515357 q^{6} -4.64210 q^{7} -1.00000 q^{8} -2.73441 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.515357 q^{12} -0.108612 q^{13} +4.64210 q^{14} -0.515357 q^{15} +1.00000 q^{16} +4.19244 q^{17} +2.73441 q^{18} -3.02164 q^{19} +1.00000 q^{20} +2.39234 q^{21} -1.00000 q^{22} -2.10861 q^{23} +0.515357 q^{24} +1.00000 q^{25} +0.108612 q^{26} +2.95527 q^{27} -4.64210 q^{28} +8.06684 q^{29} +0.515357 q^{30} +3.88930 q^{31} -1.00000 q^{32} -0.515357 q^{33} -4.19244 q^{34} -4.64210 q^{35} -2.73441 q^{36} +6.82873 q^{37} +3.02164 q^{38} +0.0559741 q^{39} -1.00000 q^{40} +2.16893 q^{41} -2.39234 q^{42} -1.00000 q^{43} +1.00000 q^{44} -2.73441 q^{45} +2.10861 q^{46} -9.78816 q^{47} -0.515357 q^{48} +14.5491 q^{49} -1.00000 q^{50} -2.16060 q^{51} -0.108612 q^{52} +1.84597 q^{53} -2.95527 q^{54} +1.00000 q^{55} +4.64210 q^{56} +1.55722 q^{57} -8.06684 q^{58} +1.63626 q^{59} -0.515357 q^{60} +8.07848 q^{61} -3.88930 q^{62} +12.6934 q^{63} +1.00000 q^{64} -0.108612 q^{65} +0.515357 q^{66} -3.43337 q^{67} +4.19244 q^{68} +1.08669 q^{69} +4.64210 q^{70} -13.9385 q^{71} +2.73441 q^{72} +7.68332 q^{73} -6.82873 q^{74} -0.515357 q^{75} -3.02164 q^{76} -4.64210 q^{77} -0.0559741 q^{78} +6.50096 q^{79} +1.00000 q^{80} +6.68021 q^{81} -2.16893 q^{82} -6.38996 q^{83} +2.39234 q^{84} +4.19244 q^{85} +1.00000 q^{86} -4.15730 q^{87} -1.00000 q^{88} -10.4488 q^{89} +2.73441 q^{90} +0.504189 q^{91} -2.10861 q^{92} -2.00438 q^{93} +9.78816 q^{94} -3.02164 q^{95} +0.515357 q^{96} -13.7821 q^{97} -14.5491 q^{98} -2.73441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} - 8q^{10} + 8q^{11} - 7q^{12} - 2q^{13} + 6q^{14} - 7q^{15} + 8q^{16} - 8q^{17} - 7q^{18} + 8q^{20} + 14q^{21} - 8q^{22} - 18q^{23} + 7q^{24} + 8q^{25} + 2q^{26} - 22q^{27} - 6q^{28} + 8q^{29} + 7q^{30} - 11q^{31} - 8q^{32} - 7q^{33} + 8q^{34} - 6q^{35} + 7q^{36} - 17q^{37} - 6q^{39} - 8q^{40} + 12q^{41} - 14q^{42} - 8q^{43} + 8q^{44} + 7q^{45} + 18q^{46} - 19q^{47} - 7q^{48} - 2q^{49} - 8q^{50} - q^{51} - 2q^{52} - 7q^{53} + 22q^{54} + 8q^{55} + 6q^{56} - 3q^{57} - 8q^{58} + q^{59} - 7q^{60} + 6q^{61} + 11q^{62} - 15q^{63} + 8q^{64} - 2q^{65} + 7q^{66} - 22q^{67} - 8q^{68} + 8q^{69} + 6q^{70} - 14q^{71} - 7q^{72} - 13q^{73} + 17q^{74} - 7q^{75} - 6q^{77} + 6q^{78} - 8q^{79} + 8q^{80} + 28q^{81} - 12q^{82} - 4q^{83} + 14q^{84} - 8q^{85} + 8q^{86} - 30q^{87} - 8q^{88} + 5q^{89} - 7q^{90} - 8q^{91} - 18q^{92} + q^{93} + 19q^{94} + 7q^{96} - 23q^{97} + 2q^{98} + 7q^{99} + O(q^{100}) \)

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
\(3\) −0.515357 −0.297541 −0.148771 0.988872i \(-0.547532\pi\)
−0.148771 + 0.988872i \(0.547532\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.515357 0.210394
\(7\) −4.64210 −1.75455 −0.877275 0.479988i \(-0.840641\pi\)
−0.877275 + 0.479988i \(0.840641\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.73441 −0.911469
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −0.515357 −0.148771
\(13\) −0.108612 −0.0301236 −0.0150618 0.999887i \(-0.504795\pi\)
−0.0150618 + 0.999887i \(0.504795\pi\)
\(14\) 4.64210 1.24065
\(15\) −0.515357 −0.133065
\(16\) 1.00000 0.250000
\(17\) 4.19244 1.01682 0.508409 0.861116i \(-0.330234\pi\)
0.508409 + 0.861116i \(0.330234\pi\)
\(18\) 2.73441 0.644506
\(19\) −3.02164 −0.693212 −0.346606 0.938011i \(-0.612666\pi\)
−0.346606 + 0.938011i \(0.612666\pi\)
\(20\) 1.00000 0.223607
\(21\) 2.39234 0.522051
\(22\) −1.00000 −0.213201
\(23\) −2.10861 −0.439676 −0.219838 0.975536i \(-0.570553\pi\)
−0.219838 + 0.975536i \(0.570553\pi\)
\(24\) 0.515357 0.105197
\(25\) 1.00000 0.200000
\(26\) 0.108612 0.0213006
\(27\) 2.95527 0.568741
\(28\) −4.64210 −0.877275
\(29\) 8.06684 1.49798 0.748988 0.662584i \(-0.230540\pi\)
0.748988 + 0.662584i \(0.230540\pi\)
\(30\) 0.515357 0.0940908
\(31\) 3.88930 0.698538 0.349269 0.937022i \(-0.386430\pi\)
0.349269 + 0.937022i \(0.386430\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.515357 −0.0897121
\(34\) −4.19244 −0.718998
\(35\) −4.64210 −0.784659
\(36\) −2.73441 −0.455735
\(37\) 6.82873 1.12264 0.561318 0.827600i \(-0.310294\pi\)
0.561318 + 0.827600i \(0.310294\pi\)
\(38\) 3.02164 0.490175
\(39\) 0.0559741 0.00896302
\(40\) −1.00000 −0.158114
\(41\) 2.16893 0.338730 0.169365 0.985553i \(-0.445828\pi\)
0.169365 + 0.985553i \(0.445828\pi\)
\(42\) −2.39234 −0.369146
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) −2.73441 −0.407621
\(46\) 2.10861 0.310898
\(47\) −9.78816 −1.42775 −0.713875 0.700273i \(-0.753061\pi\)
−0.713875 + 0.700273i \(0.753061\pi\)
\(48\) −0.515357 −0.0743853
\(49\) 14.5491 2.07845
\(50\) −1.00000 −0.141421
\(51\) −2.16060 −0.302545
\(52\) −0.108612 −0.0150618
\(53\) 1.84597 0.253563 0.126781 0.991931i \(-0.459535\pi\)
0.126781 + 0.991931i \(0.459535\pi\)
\(54\) −2.95527 −0.402161
\(55\) 1.00000 0.134840
\(56\) 4.64210 0.620327
\(57\) 1.55722 0.206259
\(58\) −8.06684 −1.05923
\(59\) 1.63626 0.213023 0.106512 0.994311i \(-0.466032\pi\)
0.106512 + 0.994311i \(0.466032\pi\)
\(60\) −0.515357 −0.0665323
\(61\) 8.07848 1.03434 0.517172 0.855882i \(-0.326985\pi\)
0.517172 + 0.855882i \(0.326985\pi\)
\(62\) −3.88930 −0.493941
\(63\) 12.6934 1.59922
\(64\) 1.00000 0.125000
\(65\) −0.108612 −0.0134717
\(66\) 0.515357 0.0634360
\(67\) −3.43337 −0.419453 −0.209726 0.977760i \(-0.567257\pi\)
−0.209726 + 0.977760i \(0.567257\pi\)
\(68\) 4.19244 0.508409
\(69\) 1.08669 0.130822
\(70\) 4.64210 0.554838
\(71\) −13.9385 −1.65420 −0.827098 0.562058i \(-0.810010\pi\)
−0.827098 + 0.562058i \(0.810010\pi\)
\(72\) 2.73441 0.322253
\(73\) 7.68332 0.899265 0.449633 0.893214i \(-0.351555\pi\)
0.449633 + 0.893214i \(0.351555\pi\)
\(74\) −6.82873 −0.793823
\(75\) −0.515357 −0.0595083
\(76\) −3.02164 −0.346606
\(77\) −4.64210 −0.529017
\(78\) −0.0559741 −0.00633782
\(79\) 6.50096 0.731415 0.365707 0.930730i \(-0.380827\pi\)
0.365707 + 0.930730i \(0.380827\pi\)
\(80\) 1.00000 0.111803
\(81\) 6.68021 0.742245
\(82\) −2.16893 −0.239518
\(83\) −6.38996 −0.701389 −0.350695 0.936490i \(-0.614054\pi\)
−0.350695 + 0.936490i \(0.614054\pi\)
\(84\) 2.39234 0.261026
\(85\) 4.19244 0.454734
\(86\) 1.00000 0.107833
\(87\) −4.15730 −0.445710
\(88\) −1.00000 −0.106600
\(89\) −10.4488 −1.10757 −0.553783 0.832661i \(-0.686816\pi\)
−0.553783 + 0.832661i \(0.686816\pi\)
\(90\) 2.73441 0.288232
\(91\) 0.504189 0.0528534
\(92\) −2.10861 −0.219838
\(93\) −2.00438 −0.207844
\(94\) 9.78816 1.00957
\(95\) −3.02164 −0.310014
\(96\) 0.515357 0.0525984
\(97\) −13.7821 −1.39936 −0.699680 0.714456i \(-0.746674\pi\)
−0.699680 + 0.714456i \(0.746674\pi\)
\(98\) −14.5491 −1.46968
\(99\) −2.73441 −0.274818
\(100\) 1.00000 0.100000
\(101\) −8.50862 −0.846640 −0.423320 0.905980i \(-0.639135\pi\)
−0.423320 + 0.905980i \(0.639135\pi\)
\(102\) 2.16060 0.213932
\(103\) −7.21580 −0.710994 −0.355497 0.934677i \(-0.615688\pi\)
−0.355497 + 0.934677i \(0.615688\pi\)
\(104\) 0.108612 0.0106503
\(105\) 2.39234 0.233468
\(106\) −1.84597 −0.179296
\(107\) 1.17431 0.113525 0.0567623 0.998388i \(-0.481922\pi\)
0.0567623 + 0.998388i \(0.481922\pi\)
\(108\) 2.95527 0.284371
\(109\) −2.34821 −0.224918 −0.112459 0.993656i \(-0.535873\pi\)
−0.112459 + 0.993656i \(0.535873\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −3.51923 −0.334031
\(112\) −4.64210 −0.438638
\(113\) −9.55477 −0.898837 −0.449419 0.893321i \(-0.648369\pi\)
−0.449419 + 0.893321i \(0.648369\pi\)
\(114\) −1.55722 −0.145847
\(115\) −2.10861 −0.196629
\(116\) 8.06684 0.748988
\(117\) 0.296990 0.0274568
\(118\) −1.63626 −0.150630
\(119\) −19.4618 −1.78406
\(120\) 0.515357 0.0470454
\(121\) 1.00000 0.0909091
\(122\) −8.07848 −0.731392
\(123\) −1.11777 −0.100786
\(124\) 3.88930 0.349269
\(125\) 1.00000 0.0894427
\(126\) −12.6934 −1.13082
\(127\) 4.23775 0.376039 0.188020 0.982165i \(-0.439793\pi\)
0.188020 + 0.982165i \(0.439793\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.515357 0.0453746
\(130\) 0.108612 0.00952593
\(131\) 12.4238 1.08547 0.542736 0.839903i \(-0.317388\pi\)
0.542736 + 0.839903i \(0.317388\pi\)
\(132\) −0.515357 −0.0448560
\(133\) 14.0268 1.21628
\(134\) 3.43337 0.296598
\(135\) 2.95527 0.254349
\(136\) −4.19244 −0.359499
\(137\) −19.5669 −1.67172 −0.835859 0.548945i \(-0.815030\pi\)
−0.835859 + 0.548945i \(0.815030\pi\)
\(138\) −1.08669 −0.0925050
\(139\) −3.28946 −0.279009 −0.139504 0.990221i \(-0.544551\pi\)
−0.139504 + 0.990221i \(0.544551\pi\)
\(140\) −4.64210 −0.392329
\(141\) 5.04439 0.424815
\(142\) 13.9385 1.16969
\(143\) −0.108612 −0.00908261
\(144\) −2.73441 −0.227867
\(145\) 8.06684 0.669915
\(146\) −7.68332 −0.635876
\(147\) −7.49799 −0.618424
\(148\) 6.82873 0.561318
\(149\) −11.9446 −0.978542 −0.489271 0.872132i \(-0.662737\pi\)
−0.489271 + 0.872132i \(0.662737\pi\)
\(150\) 0.515357 0.0420787
\(151\) −5.74924 −0.467866 −0.233933 0.972253i \(-0.575160\pi\)
−0.233933 + 0.972253i \(0.575160\pi\)
\(152\) 3.02164 0.245088
\(153\) −11.4639 −0.926797
\(154\) 4.64210 0.374071
\(155\) 3.88930 0.312396
\(156\) 0.0559741 0.00448151
\(157\) −20.9392 −1.67113 −0.835565 0.549392i \(-0.814859\pi\)
−0.835565 + 0.549392i \(0.814859\pi\)
\(158\) −6.50096 −0.517188
\(159\) −0.951331 −0.0754454
\(160\) −1.00000 −0.0790569
\(161\) 9.78840 0.771434
\(162\) −6.68021 −0.524847
\(163\) −2.46138 −0.192790 −0.0963949 0.995343i \(-0.530731\pi\)
−0.0963949 + 0.995343i \(0.530731\pi\)
\(164\) 2.16893 0.169365
\(165\) −0.515357 −0.0401205
\(166\) 6.38996 0.495957
\(167\) −15.9201 −1.23193 −0.615967 0.787772i \(-0.711235\pi\)
−0.615967 + 0.787772i \(0.711235\pi\)
\(168\) −2.39234 −0.184573
\(169\) −12.9882 −0.999093
\(170\) −4.19244 −0.321546
\(171\) 8.26240 0.631842
\(172\) −1.00000 −0.0762493
\(173\) 23.1251 1.75817 0.879083 0.476669i \(-0.158156\pi\)
0.879083 + 0.476669i \(0.158156\pi\)
\(174\) 4.15730 0.315164
\(175\) −4.64210 −0.350910
\(176\) 1.00000 0.0753778
\(177\) −0.843259 −0.0633832
\(178\) 10.4488 0.783168
\(179\) 7.74932 0.579212 0.289606 0.957146i \(-0.406476\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(180\) −2.73441 −0.203811
\(181\) 0.948206 0.0704796 0.0352398 0.999379i \(-0.488780\pi\)
0.0352398 + 0.999379i \(0.488780\pi\)
\(182\) −0.504189 −0.0373730
\(183\) −4.16330 −0.307760
\(184\) 2.10861 0.155449
\(185\) 6.82873 0.502058
\(186\) 2.00438 0.146968
\(187\) 4.19244 0.306582
\(188\) −9.78816 −0.713875
\(189\) −13.7186 −0.997885
\(190\) 3.02164 0.219213
\(191\) 13.9647 1.01045 0.505224 0.862988i \(-0.331410\pi\)
0.505224 + 0.862988i \(0.331410\pi\)
\(192\) −0.515357 −0.0371927
\(193\) −17.6616 −1.27131 −0.635655 0.771974i \(-0.719270\pi\)
−0.635655 + 0.771974i \(0.719270\pi\)
\(194\) 13.7821 0.989497
\(195\) 0.0559741 0.00400839
\(196\) 14.5491 1.03922
\(197\) −20.8737 −1.48719 −0.743594 0.668632i \(-0.766880\pi\)
−0.743594 + 0.668632i \(0.766880\pi\)
\(198\) 2.73441 0.194326
\(199\) −24.9553 −1.76903 −0.884516 0.466510i \(-0.845511\pi\)
−0.884516 + 0.466510i \(0.845511\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.76941 0.124805
\(202\) 8.50862 0.598665
\(203\) −37.4471 −2.62827
\(204\) −2.16060 −0.151273
\(205\) 2.16893 0.151485
\(206\) 7.21580 0.502749
\(207\) 5.76581 0.400751
\(208\) −0.108612 −0.00753091
\(209\) −3.02164 −0.209011
\(210\) −2.39234 −0.165087
\(211\) 0.968285 0.0666595 0.0333297 0.999444i \(-0.489389\pi\)
0.0333297 + 0.999444i \(0.489389\pi\)
\(212\) 1.84597 0.126781
\(213\) 7.18330 0.492192
\(214\) −1.17431 −0.0802740
\(215\) −1.00000 −0.0681994
\(216\) −2.95527 −0.201080
\(217\) −18.0545 −1.22562
\(218\) 2.34821 0.159041
\(219\) −3.95965 −0.267569
\(220\) 1.00000 0.0674200
\(221\) −0.455351 −0.0306302
\(222\) 3.51923 0.236195
\(223\) 19.7291 1.32116 0.660579 0.750757i \(-0.270311\pi\)
0.660579 + 0.750757i \(0.270311\pi\)
\(224\) 4.64210 0.310164
\(225\) −2.73441 −0.182294
\(226\) 9.55477 0.635574
\(227\) −13.8242 −0.917543 −0.458772 0.888554i \(-0.651710\pi\)
−0.458772 + 0.888554i \(0.651710\pi\)
\(228\) 1.55722 0.103130
\(229\) 24.4201 1.61372 0.806862 0.590740i \(-0.201164\pi\)
0.806862 + 0.590740i \(0.201164\pi\)
\(230\) 2.10861 0.139038
\(231\) 2.39234 0.157404
\(232\) −8.06684 −0.529614
\(233\) 17.3137 1.13426 0.567130 0.823629i \(-0.308054\pi\)
0.567130 + 0.823629i \(0.308054\pi\)
\(234\) −0.296990 −0.0194149
\(235\) −9.78816 −0.638509
\(236\) 1.63626 0.106512
\(237\) −3.35031 −0.217626
\(238\) 19.4618 1.26152
\(239\) 15.6399 1.01166 0.505831 0.862632i \(-0.331186\pi\)
0.505831 + 0.862632i \(0.331186\pi\)
\(240\) −0.515357 −0.0332661
\(241\) −4.82493 −0.310801 −0.155401 0.987852i \(-0.549667\pi\)
−0.155401 + 0.987852i \(0.549667\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −12.3085 −0.789590
\(244\) 8.07848 0.517172
\(245\) 14.5491 0.929510
\(246\) 1.11777 0.0712666
\(247\) 0.328187 0.0208821
\(248\) −3.88930 −0.246971
\(249\) 3.29311 0.208692
\(250\) −1.00000 −0.0632456
\(251\) 29.3009 1.84946 0.924729 0.380625i \(-0.124291\pi\)
0.924729 + 0.380625i \(0.124291\pi\)
\(252\) 12.6934 0.799609
\(253\) −2.10861 −0.132567
\(254\) −4.23775 −0.265900
\(255\) −2.16060 −0.135302
\(256\) 1.00000 0.0625000
\(257\) 16.6058 1.03584 0.517921 0.855428i \(-0.326706\pi\)
0.517921 + 0.855428i \(0.326706\pi\)
\(258\) −0.515357 −0.0320847
\(259\) −31.6997 −1.96972
\(260\) −0.108612 −0.00673585
\(261\) −22.0580 −1.36536
\(262\) −12.4238 −0.767545
\(263\) −7.44987 −0.459379 −0.229689 0.973264i \(-0.573771\pi\)
−0.229689 + 0.973264i \(0.573771\pi\)
\(264\) 0.515357 0.0317180
\(265\) 1.84597 0.113397
\(266\) −14.0268 −0.860037
\(267\) 5.38484 0.329547
\(268\) −3.43337 −0.209726
\(269\) −20.2166 −1.23263 −0.616314 0.787500i \(-0.711375\pi\)
−0.616314 + 0.787500i \(0.711375\pi\)
\(270\) −2.95527 −0.179852
\(271\) 13.9835 0.849436 0.424718 0.905326i \(-0.360373\pi\)
0.424718 + 0.905326i \(0.360373\pi\)
\(272\) 4.19244 0.254204
\(273\) −0.259837 −0.0157261
\(274\) 19.5669 1.18208
\(275\) 1.00000 0.0603023
\(276\) 1.08669 0.0654109
\(277\) −31.3576 −1.88410 −0.942048 0.335477i \(-0.891102\pi\)
−0.942048 + 0.335477i \(0.891102\pi\)
\(278\) 3.28946 0.197289
\(279\) −10.6349 −0.636696
\(280\) 4.64210 0.277419
\(281\) 22.2132 1.32513 0.662563 0.749006i \(-0.269468\pi\)
0.662563 + 0.749006i \(0.269468\pi\)
\(282\) −5.04439 −0.300389
\(283\) 8.84763 0.525937 0.262968 0.964804i \(-0.415299\pi\)
0.262968 + 0.964804i \(0.415299\pi\)
\(284\) −13.9385 −0.827098
\(285\) 1.55722 0.0922420
\(286\) 0.108612 0.00642238
\(287\) −10.0684 −0.594319
\(288\) 2.73441 0.161127
\(289\) 0.576587 0.0339169
\(290\) −8.06684 −0.473701
\(291\) 7.10270 0.416368
\(292\) 7.68332 0.449633
\(293\) 10.6467 0.621984 0.310992 0.950413i \(-0.399339\pi\)
0.310992 + 0.950413i \(0.399339\pi\)
\(294\) 7.49799 0.437292
\(295\) 1.63626 0.0952669
\(296\) −6.82873 −0.396912
\(297\) 2.95527 0.171482
\(298\) 11.9446 0.691934
\(299\) 0.229021 0.0132446
\(300\) −0.515357 −0.0297541
\(301\) 4.64210 0.267566
\(302\) 5.74924 0.330832
\(303\) 4.38498 0.251910
\(304\) −3.02164 −0.173303
\(305\) 8.07848 0.462573
\(306\) 11.4639 0.655345
\(307\) 5.80506 0.331312 0.165656 0.986184i \(-0.447026\pi\)
0.165656 + 0.986184i \(0.447026\pi\)
\(308\) −4.64210 −0.264508
\(309\) 3.71871 0.211550
\(310\) −3.88930 −0.220897
\(311\) 23.6920 1.34345 0.671724 0.740801i \(-0.265554\pi\)
0.671724 + 0.740801i \(0.265554\pi\)
\(312\) −0.0559741 −0.00316891
\(313\) −8.81800 −0.498423 −0.249212 0.968449i \(-0.580171\pi\)
−0.249212 + 0.968449i \(0.580171\pi\)
\(314\) 20.9392 1.18167
\(315\) 12.6934 0.715192
\(316\) 6.50096 0.365707
\(317\) 8.44230 0.474167 0.237083 0.971489i \(-0.423809\pi\)
0.237083 + 0.971489i \(0.423809\pi\)
\(318\) 0.951331 0.0533480
\(319\) 8.06684 0.451657
\(320\) 1.00000 0.0559017
\(321\) −0.605187 −0.0337783
\(322\) −9.78840 −0.545486
\(323\) −12.6681 −0.704870
\(324\) 6.68021 0.371123
\(325\) −0.108612 −0.00602473
\(326\) 2.46138 0.136323
\(327\) 1.21017 0.0669224
\(328\) −2.16893 −0.119759
\(329\) 45.4376 2.50506
\(330\) 0.515357 0.0283695
\(331\) −29.9604 −1.64677 −0.823387 0.567481i \(-0.807918\pi\)
−0.823387 + 0.567481i \(0.807918\pi\)
\(332\) −6.38996 −0.350695
\(333\) −18.6725 −1.02325
\(334\) 15.9201 0.871109
\(335\) −3.43337 −0.187585
\(336\) 2.39234 0.130513
\(337\) 23.5427 1.28245 0.641226 0.767352i \(-0.278426\pi\)
0.641226 + 0.767352i \(0.278426\pi\)
\(338\) 12.9882 0.706465
\(339\) 4.92412 0.267441
\(340\) 4.19244 0.227367
\(341\) 3.88930 0.210617
\(342\) −8.26240 −0.446779
\(343\) −35.0438 −1.89219
\(344\) 1.00000 0.0539164
\(345\) 1.08669 0.0585053
\(346\) −23.1251 −1.24321
\(347\) −7.25581 −0.389512 −0.194756 0.980852i \(-0.562392\pi\)
−0.194756 + 0.980852i \(0.562392\pi\)
\(348\) −4.15730 −0.222855
\(349\) 21.1451 1.13187 0.565936 0.824449i \(-0.308515\pi\)
0.565936 + 0.824449i \(0.308515\pi\)
\(350\) 4.64210 0.248131
\(351\) −0.320978 −0.0171325
\(352\) −1.00000 −0.0533002
\(353\) −23.2194 −1.23584 −0.617922 0.786239i \(-0.712025\pi\)
−0.617922 + 0.786239i \(0.712025\pi\)
\(354\) 0.843259 0.0448187
\(355\) −13.9385 −0.739779
\(356\) −10.4488 −0.553783
\(357\) 10.0297 0.530831
\(358\) −7.74932 −0.409564
\(359\) −9.60819 −0.507101 −0.253550 0.967322i \(-0.581598\pi\)
−0.253550 + 0.967322i \(0.581598\pi\)
\(360\) 2.73441 0.144116
\(361\) −9.86968 −0.519457
\(362\) −0.948206 −0.0498366
\(363\) −0.515357 −0.0270492
\(364\) 0.504189 0.0264267
\(365\) 7.68332 0.402164
\(366\) 4.16330 0.217619
\(367\) −10.2861 −0.536929 −0.268464 0.963290i \(-0.586516\pi\)
−0.268464 + 0.963290i \(0.586516\pi\)
\(368\) −2.10861 −0.109919
\(369\) −5.93074 −0.308742
\(370\) −6.82873 −0.355009
\(371\) −8.56916 −0.444889
\(372\) −2.00438 −0.103922
\(373\) 16.3654 0.847368 0.423684 0.905810i \(-0.360737\pi\)
0.423684 + 0.905810i \(0.360737\pi\)
\(374\) −4.19244 −0.216786
\(375\) −0.515357 −0.0266129
\(376\) 9.78816 0.504786
\(377\) −0.876158 −0.0451245
\(378\) 13.7186 0.705611
\(379\) 16.9114 0.868680 0.434340 0.900749i \(-0.356982\pi\)
0.434340 + 0.900749i \(0.356982\pi\)
\(380\) −3.02164 −0.155007
\(381\) −2.18395 −0.111887
\(382\) −13.9647 −0.714495
\(383\) −30.1347 −1.53981 −0.769907 0.638156i \(-0.779697\pi\)
−0.769907 + 0.638156i \(0.779697\pi\)
\(384\) 0.515357 0.0262992
\(385\) −4.64210 −0.236584
\(386\) 17.6616 0.898951
\(387\) 2.73441 0.138998
\(388\) −13.7821 −0.699680
\(389\) 2.46692 0.125078 0.0625390 0.998043i \(-0.480080\pi\)
0.0625390 + 0.998043i \(0.480080\pi\)
\(390\) −0.0559741 −0.00283436
\(391\) −8.84024 −0.447070
\(392\) −14.5491 −0.734842
\(393\) −6.40269 −0.322973
\(394\) 20.8737 1.05160
\(395\) 6.50096 0.327099
\(396\) −2.73441 −0.137409
\(397\) −16.0944 −0.807756 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(398\) 24.9553 1.25089
\(399\) −7.22879 −0.361892
\(400\) 1.00000 0.0500000
\(401\) −14.3654 −0.717373 −0.358687 0.933458i \(-0.616775\pi\)
−0.358687 + 0.933458i \(0.616775\pi\)
\(402\) −1.76941 −0.0882502
\(403\) −0.422425 −0.0210425
\(404\) −8.50862 −0.423320
\(405\) 6.68021 0.331942
\(406\) 37.4471 1.85847
\(407\) 6.82873 0.338487
\(408\) 2.16060 0.106966
\(409\) −34.1092 −1.68659 −0.843295 0.537452i \(-0.819387\pi\)
−0.843295 + 0.537452i \(0.819387\pi\)
\(410\) −2.16893 −0.107116
\(411\) 10.0840 0.497405
\(412\) −7.21580 −0.355497
\(413\) −7.59570 −0.373760
\(414\) −5.76581 −0.283374
\(415\) −6.38996 −0.313671
\(416\) 0.108612 0.00532515
\(417\) 1.69525 0.0830166
\(418\) 3.02164 0.147793
\(419\) −9.23855 −0.451333 −0.225666 0.974205i \(-0.572456\pi\)
−0.225666 + 0.974205i \(0.572456\pi\)
\(420\) 2.39234 0.116734
\(421\) −19.8056 −0.965265 −0.482633 0.875823i \(-0.660319\pi\)
−0.482633 + 0.875823i \(0.660319\pi\)
\(422\) −0.968285 −0.0471354
\(423\) 26.7648 1.30135
\(424\) −1.84597 −0.0896480
\(425\) 4.19244 0.203363
\(426\) −7.18330 −0.348032
\(427\) −37.5012 −1.81481
\(428\) 1.17431 0.0567623
\(429\) 0.0559741 0.00270245
\(430\) 1.00000 0.0482243
\(431\) 14.1192 0.680099 0.340050 0.940407i \(-0.389556\pi\)
0.340050 + 0.940407i \(0.389556\pi\)
\(432\) 2.95527 0.142185
\(433\) 20.3340 0.977191 0.488596 0.872510i \(-0.337509\pi\)
0.488596 + 0.872510i \(0.337509\pi\)
\(434\) 18.0545 0.866645
\(435\) −4.15730 −0.199327
\(436\) −2.34821 −0.112459
\(437\) 6.37147 0.304789
\(438\) 3.95965 0.189200
\(439\) −34.3522 −1.63954 −0.819772 0.572691i \(-0.805900\pi\)
−0.819772 + 0.572691i \(0.805900\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −39.7832 −1.89444
\(442\) 0.455351 0.0216588
\(443\) 14.2974 0.679290 0.339645 0.940554i \(-0.389693\pi\)
0.339645 + 0.940554i \(0.389693\pi\)
\(444\) −3.51923 −0.167015
\(445\) −10.4488 −0.495319
\(446\) −19.7291 −0.934199
\(447\) 6.15575 0.291157
\(448\) −4.64210 −0.219319
\(449\) −18.5194 −0.873984 −0.436992 0.899465i \(-0.643956\pi\)
−0.436992 + 0.899465i \(0.643956\pi\)
\(450\) 2.73441 0.128901
\(451\) 2.16893 0.102131
\(452\) −9.55477 −0.449419
\(453\) 2.96291 0.139210
\(454\) 13.8242 0.648801
\(455\) 0.504189 0.0236368
\(456\) −1.55722 −0.0729237
\(457\) −30.4296 −1.42343 −0.711717 0.702466i \(-0.752082\pi\)
−0.711717 + 0.702466i \(0.752082\pi\)
\(458\) −24.4201 −1.14108
\(459\) 12.3898 0.578306
\(460\) −2.10861 −0.0983146
\(461\) 5.19765 0.242079 0.121039 0.992648i \(-0.461377\pi\)
0.121039 + 0.992648i \(0.461377\pi\)
\(462\) −2.39234 −0.111302
\(463\) −33.4985 −1.55681 −0.778405 0.627763i \(-0.783971\pi\)
−0.778405 + 0.627763i \(0.783971\pi\)
\(464\) 8.06684 0.374494
\(465\) −2.00438 −0.0929507
\(466\) −17.3137 −0.802042
\(467\) 6.88311 0.318512 0.159256 0.987237i \(-0.449090\pi\)
0.159256 + 0.987237i \(0.449090\pi\)
\(468\) 0.296990 0.0137284
\(469\) 15.9381 0.735951
\(470\) 9.78816 0.451494
\(471\) 10.7912 0.497230
\(472\) −1.63626 −0.0753151
\(473\) −1.00000 −0.0459800
\(474\) 3.35031 0.153885
\(475\) −3.02164 −0.138642
\(476\) −19.4618 −0.892028
\(477\) −5.04762 −0.231115
\(478\) −15.6399 −0.715354
\(479\) −41.7556 −1.90786 −0.953931 0.300026i \(-0.903005\pi\)
−0.953931 + 0.300026i \(0.903005\pi\)
\(480\) 0.515357 0.0235227
\(481\) −0.741684 −0.0338179
\(482\) 4.82493 0.219770
\(483\) −5.04452 −0.229533
\(484\) 1.00000 0.0454545
\(485\) −13.7821 −0.625813
\(486\) 12.3085 0.558324
\(487\) −17.2846 −0.783239 −0.391619 0.920127i \(-0.628085\pi\)
−0.391619 + 0.920127i \(0.628085\pi\)
\(488\) −8.07848 −0.365696
\(489\) 1.26849 0.0573629
\(490\) −14.5491 −0.657263
\(491\) 1.38700 0.0625944 0.0312972 0.999510i \(-0.490036\pi\)
0.0312972 + 0.999510i \(0.490036\pi\)
\(492\) −1.11777 −0.0503931
\(493\) 33.8198 1.52317
\(494\) −0.328187 −0.0147658
\(495\) −2.73441 −0.122902
\(496\) 3.88930 0.174635
\(497\) 64.7040 2.90237
\(498\) −3.29311 −0.147568
\(499\) 8.42570 0.377186 0.188593 0.982055i \(-0.439607\pi\)
0.188593 + 0.982055i \(0.439607\pi\)
\(500\) 1.00000 0.0447214
\(501\) 8.20453 0.366551
\(502\) −29.3009 −1.30776
\(503\) −39.0067 −1.73922 −0.869612 0.493735i \(-0.835631\pi\)
−0.869612 + 0.493735i \(0.835631\pi\)
\(504\) −12.6934 −0.565409
\(505\) −8.50862 −0.378629
\(506\) 2.10861 0.0937392
\(507\) 6.69356 0.297271
\(508\) 4.23775 0.188020
\(509\) −7.93266 −0.351609 −0.175804 0.984425i \(-0.556253\pi\)
−0.175804 + 0.984425i \(0.556253\pi\)
\(510\) 2.16060 0.0956732
\(511\) −35.6668 −1.57781
\(512\) −1.00000 −0.0441942
\(513\) −8.92975 −0.394258
\(514\) −16.6058 −0.732452
\(515\) −7.21580 −0.317966
\(516\) 0.515357 0.0226873
\(517\) −9.78816 −0.430483
\(518\) 31.6997 1.39280
\(519\) −11.9177 −0.523127
\(520\) 0.108612 0.00476296
\(521\) −12.4595 −0.545862 −0.272931 0.962034i \(-0.587993\pi\)
−0.272931 + 0.962034i \(0.587993\pi\)
\(522\) 22.0580 0.965454
\(523\) −27.6000 −1.20686 −0.603431 0.797415i \(-0.706200\pi\)
−0.603431 + 0.797415i \(0.706200\pi\)
\(524\) 12.4238 0.542736
\(525\) 2.39234 0.104410
\(526\) 7.44987 0.324830
\(527\) 16.3057 0.710286
\(528\) −0.515357 −0.0224280
\(529\) −18.5538 −0.806685
\(530\) −1.84597 −0.0801836
\(531\) −4.47421 −0.194164
\(532\) 14.0268 0.608138
\(533\) −0.235573 −0.0102038
\(534\) −5.38484 −0.233025
\(535\) 1.17431 0.0507697
\(536\) 3.43337 0.148299
\(537\) −3.99367 −0.172339
\(538\) 20.2166 0.871600
\(539\) 14.5491 0.626675
\(540\) 2.95527 0.127174
\(541\) 43.0961 1.85285 0.926423 0.376485i \(-0.122867\pi\)
0.926423 + 0.376485i \(0.122867\pi\)
\(542\) −13.9835 −0.600642
\(543\) −0.488665 −0.0209706
\(544\) −4.19244 −0.179750
\(545\) −2.34821 −0.100586
\(546\) 0.259837 0.0111200
\(547\) −9.47881 −0.405285 −0.202642 0.979253i \(-0.564953\pi\)
−0.202642 + 0.979253i \(0.564953\pi\)
\(548\) −19.5669 −0.835859
\(549\) −22.0899 −0.942773
\(550\) −1.00000 −0.0426401
\(551\) −24.3751 −1.03841
\(552\) −1.08669 −0.0462525
\(553\) −30.1781 −1.28330
\(554\) 31.3576 1.33226
\(555\) −3.51923 −0.149383
\(556\) −3.28946 −0.139504
\(557\) 6.96985 0.295322 0.147661 0.989038i \(-0.452826\pi\)
0.147661 + 0.989038i \(0.452826\pi\)
\(558\) 10.6349 0.450212
\(559\) 0.108612 0.00459381
\(560\) −4.64210 −0.196165
\(561\) −2.16060 −0.0912208
\(562\) −22.2132 −0.937006
\(563\) 9.30571 0.392189 0.196094 0.980585i \(-0.437174\pi\)
0.196094 + 0.980585i \(0.437174\pi\)
\(564\) 5.04439 0.212407
\(565\) −9.55477 −0.401972
\(566\) −8.84763 −0.371893
\(567\) −31.0102 −1.30231
\(568\) 13.9385 0.584846
\(569\) −6.44699 −0.270272 −0.135136 0.990827i \(-0.543147\pi\)
−0.135136 + 0.990827i \(0.543147\pi\)
\(570\) −1.55722 −0.0652249
\(571\) −11.1962 −0.468545 −0.234273 0.972171i \(-0.575271\pi\)
−0.234273 + 0.972171i \(0.575271\pi\)
\(572\) −0.108612 −0.00454131
\(573\) −7.19679 −0.300650
\(574\) 10.0684 0.420247
\(575\) −2.10861 −0.0879352
\(576\) −2.73441 −0.113934
\(577\) 3.83486 0.159647 0.0798236 0.996809i \(-0.474564\pi\)
0.0798236 + 0.996809i \(0.474564\pi\)
\(578\) −0.576587 −0.0239829
\(579\) 9.10202 0.378267
\(580\) 8.06684 0.334957
\(581\) 29.6628 1.23062
\(582\) −7.10270 −0.294416
\(583\) 1.84597 0.0764521
\(584\) −7.68332 −0.317938
\(585\) 0.296990 0.0122790
\(586\) −10.6467 −0.439809
\(587\) −29.6034 −1.22186 −0.610932 0.791683i \(-0.709205\pi\)
−0.610932 + 0.791683i \(0.709205\pi\)
\(588\) −7.49799 −0.309212
\(589\) −11.7521 −0.484235
\(590\) −1.63626 −0.0673639
\(591\) 10.7574 0.442500
\(592\) 6.82873 0.280659
\(593\) 7.69040 0.315807 0.157904 0.987455i \(-0.449526\pi\)
0.157904 + 0.987455i \(0.449526\pi\)
\(594\) −2.95527 −0.121256
\(595\) −19.4618 −0.797854
\(596\) −11.9446 −0.489271
\(597\) 12.8609 0.526360
\(598\) −0.229021 −0.00936537
\(599\) 14.3870 0.587837 0.293918 0.955831i \(-0.405041\pi\)
0.293918 + 0.955831i \(0.405041\pi\)
\(600\) 0.515357 0.0210394
\(601\) −38.4395 −1.56798 −0.783989 0.620775i \(-0.786818\pi\)
−0.783989 + 0.620775i \(0.786818\pi\)
\(602\) −4.64210 −0.189198
\(603\) 9.38823 0.382318
\(604\) −5.74924 −0.233933
\(605\) 1.00000 0.0406558
\(606\) −4.38498 −0.178128
\(607\) 0.771069 0.0312967 0.0156484 0.999878i \(-0.495019\pi\)
0.0156484 + 0.999878i \(0.495019\pi\)
\(608\) 3.02164 0.122544
\(609\) 19.2986 0.782020
\(610\) −8.07848 −0.327088
\(611\) 1.06311 0.0430090
\(612\) −11.4639 −0.463399
\(613\) 39.7389 1.60504 0.802519 0.596627i \(-0.203493\pi\)
0.802519 + 0.596627i \(0.203493\pi\)
\(614\) −5.80506 −0.234273
\(615\) −1.11777 −0.0450730
\(616\) 4.64210 0.187036
\(617\) −12.5833 −0.506585 −0.253292 0.967390i \(-0.581513\pi\)
−0.253292 + 0.967390i \(0.581513\pi\)
\(618\) −3.71871 −0.149588
\(619\) 1.55022 0.0623088 0.0311544 0.999515i \(-0.490082\pi\)
0.0311544 + 0.999515i \(0.490082\pi\)
\(620\) 3.88930 0.156198
\(621\) −6.23151 −0.250062
\(622\) −23.6920 −0.949962
\(623\) 48.5042 1.94328
\(624\) 0.0559741 0.00224076
\(625\) 1.00000 0.0400000
\(626\) 8.81800 0.352438
\(627\) 1.55722 0.0621895
\(628\) −20.9392 −0.835565
\(629\) 28.6291 1.14152
\(630\) −12.6934 −0.505717
\(631\) −29.4029 −1.17051 −0.585255 0.810850i \(-0.699005\pi\)
−0.585255 + 0.810850i \(0.699005\pi\)
\(632\) −6.50096 −0.258594
\(633\) −0.499012 −0.0198340
\(634\) −8.44230 −0.335286
\(635\) 4.23775 0.168170
\(636\) −0.951331 −0.0377227
\(637\) −1.58021 −0.0626103
\(638\) −8.06684 −0.319369
\(639\) 38.1135 1.50775
\(640\) −1.00000 −0.0395285
\(641\) −29.5181 −1.16589 −0.582947 0.812510i \(-0.698101\pi\)
−0.582947 + 0.812510i \(0.698101\pi\)
\(642\) 0.605187 0.0238848
\(643\) 42.6204 1.68079 0.840393 0.541978i \(-0.182324\pi\)
0.840393 + 0.541978i \(0.182324\pi\)
\(644\) 9.78840 0.385717
\(645\) 0.515357 0.0202922
\(646\) 12.6681 0.498418
\(647\) 14.4992 0.570023 0.285012 0.958524i \(-0.408003\pi\)
0.285012 + 0.958524i \(0.408003\pi\)
\(648\) −6.68021 −0.262423
\(649\) 1.63626 0.0642289
\(650\) 0.108612 0.00426012
\(651\) 9.30452 0.364673
\(652\) −2.46138 −0.0963949
\(653\) 22.6007 0.884434 0.442217 0.896908i \(-0.354192\pi\)
0.442217 + 0.896908i \(0.354192\pi\)
\(654\) −1.21017 −0.0473213
\(655\) 12.4238 0.485438
\(656\) 2.16893 0.0846826
\(657\) −21.0093 −0.819652
\(658\) −45.4376 −1.77134
\(659\) 12.6779 0.493862 0.246931 0.969033i \(-0.420578\pi\)
0.246931 + 0.969033i \(0.420578\pi\)
\(660\) −0.515357 −0.0200602
\(661\) −0.952140 −0.0370340 −0.0185170 0.999829i \(-0.505894\pi\)
−0.0185170 + 0.999829i \(0.505894\pi\)
\(662\) 29.9604 1.16444
\(663\) 0.234668 0.00911376
\(664\) 6.38996 0.247978
\(665\) 14.0268 0.543935
\(666\) 18.6725 0.723546
\(667\) −17.0098 −0.658624
\(668\) −15.9201 −0.615967
\(669\) −10.1675 −0.393099
\(670\) 3.43337 0.132643
\(671\) 8.07848 0.311866
\(672\) −2.39234 −0.0922865
\(673\) 14.3018 0.551295 0.275648 0.961259i \(-0.411108\pi\)
0.275648 + 0.961259i \(0.411108\pi\)
\(674\) −23.5427 −0.906830
\(675\) 2.95527 0.113748
\(676\) −12.9882 −0.499546
\(677\) 29.2082 1.12256 0.561281 0.827625i \(-0.310309\pi\)
0.561281 + 0.827625i \(0.310309\pi\)
\(678\) −4.92412 −0.189110
\(679\) 63.9779 2.45525
\(680\) −4.19244 −0.160773
\(681\) 7.12439 0.273007
\(682\) −3.88930 −0.148929
\(683\) −24.3572 −0.932001 −0.466001 0.884784i \(-0.654306\pi\)
−0.466001 + 0.884784i \(0.654306\pi\)
\(684\) 8.26240 0.315921
\(685\) −19.5669 −0.747615
\(686\) 35.0438 1.33798
\(687\) −12.5851 −0.480150
\(688\) −1.00000 −0.0381246
\(689\) −0.200494 −0.00763823
\(690\) −1.08669 −0.0413695
\(691\) 41.0692 1.56234 0.781172 0.624316i \(-0.214622\pi\)
0.781172 + 0.624316i \(0.214622\pi\)
\(692\) 23.1251 0.879083
\(693\) 12.6934 0.482182
\(694\) 7.25581 0.275427
\(695\) −3.28946 −0.124776
\(696\) 4.15730 0.157582
\(697\) 9.09312 0.344427
\(698\) −21.1451 −0.800354
\(699\) −8.92274 −0.337489
\(700\) −4.64210 −0.175455
\(701\) −21.1868 −0.800214 −0.400107 0.916468i \(-0.631027\pi\)
−0.400107 + 0.916468i \(0.631027\pi\)
\(702\) 0.320978 0.0121145
\(703\) −20.6340 −0.778225
\(704\) 1.00000 0.0376889
\(705\) 5.04439 0.189983
\(706\) 23.2194 0.873874
\(707\) 39.4979 1.48547
\(708\) −0.843259 −0.0316916
\(709\) 39.7164 1.49158 0.745791 0.666180i \(-0.232072\pi\)
0.745791 + 0.666180i \(0.232072\pi\)
\(710\) 13.9385 0.523103
\(711\) −17.7763 −0.666662
\(712\) 10.4488 0.391584
\(713\) −8.20102 −0.307131
\(714\) −10.0297 −0.375354
\(715\) −0.108612 −0.00406187
\(716\) 7.74932 0.289606
\(717\) −8.06014 −0.301012
\(718\) 9.60819 0.358574
\(719\) −22.2000 −0.827921 −0.413961 0.910295i \(-0.635855\pi\)
−0.413961 + 0.910295i \(0.635855\pi\)
\(720\) −2.73441 −0.101905
\(721\) 33.4965 1.24747
\(722\) 9.86968 0.367311
\(723\) 2.48656 0.0924762
\(724\) 0.948206 0.0352398
\(725\) 8.06684 0.299595
\(726\) 0.515357 0.0191267
\(727\) −30.3674 −1.12627 −0.563133 0.826367i \(-0.690404\pi\)
−0.563133 + 0.826367i \(0.690404\pi\)
\(728\) −0.504189 −0.0186865
\(729\) −13.6974 −0.507310
\(730\) −7.68332 −0.284373
\(731\) −4.19244 −0.155063
\(732\) −4.16330 −0.153880
\(733\) 9.20083 0.339841 0.169920 0.985458i \(-0.445649\pi\)
0.169920 + 0.985458i \(0.445649\pi\)
\(734\) 10.2861 0.379666
\(735\) −7.49799 −0.276568
\(736\) 2.10861 0.0777245
\(737\) −3.43337 −0.126470
\(738\) 5.93074 0.218314
\(739\) −8.70249 −0.320126 −0.160063 0.987107i \(-0.551170\pi\)
−0.160063 + 0.987107i \(0.551170\pi\)
\(740\) 6.82873 0.251029
\(741\) −0.169134 −0.00621328
\(742\) 8.56916 0.314584
\(743\) −14.4927 −0.531684 −0.265842 0.964017i \(-0.585650\pi\)
−0.265842 + 0.964017i \(0.585650\pi\)
\(744\) 2.00438 0.0734840
\(745\) −11.9446 −0.437617
\(746\) −16.3654 −0.599180
\(747\) 17.4727 0.639294
\(748\) 4.19244 0.153291
\(749\) −5.45126 −0.199185
\(750\) 0.515357 0.0188182
\(751\) 7.81010 0.284995 0.142497 0.989795i \(-0.454487\pi\)
0.142497 + 0.989795i \(0.454487\pi\)
\(752\) −9.78816 −0.356937
\(753\) −15.1004 −0.550291
\(754\) 0.876158 0.0319078
\(755\) −5.74924 −0.209236
\(756\) −13.7186 −0.498942
\(757\) −10.1738 −0.369772 −0.184886 0.982760i \(-0.559192\pi\)
−0.184886 + 0.982760i \(0.559192\pi\)
\(758\) −16.9114 −0.614250
\(759\) 1.08669 0.0394443
\(760\) 3.02164 0.109606
\(761\) 15.3951 0.558072 0.279036 0.960281i \(-0.409985\pi\)
0.279036 + 0.960281i \(0.409985\pi\)
\(762\) 2.18395 0.0791162
\(763\) 10.9006 0.394630
\(764\) 13.9647 0.505224
\(765\) −11.4639 −0.414476
\(766\) 30.1347 1.08881
\(767\) −0.177718 −0.00641703
\(768\) −0.515357 −0.0185963
\(769\) −7.01853 −0.253095 −0.126547 0.991961i \(-0.540390\pi\)
−0.126547 + 0.991961i \(0.540390\pi\)
\(770\) 4.64210 0.167290
\(771\) −8.55792 −0.308206
\(772\) −17.6616 −0.635655
\(773\) 14.4099 0.518288 0.259144 0.965839i \(-0.416560\pi\)
0.259144 + 0.965839i \(0.416560\pi\)
\(774\) −2.73441 −0.0982862
\(775\) 3.88930 0.139708
\(776\) 13.7821 0.494749
\(777\) 16.3366 0.586074
\(778\) −2.46692 −0.0884435
\(779\) −6.55373 −0.234812
\(780\) 0.0559741 0.00200419
\(781\) −13.9385 −0.498759
\(782\) 8.84024 0.316126
\(783\) 23.8397 0.851960
\(784\) 14.5491 0.519612
\(785\) −20.9392 −0.747352
\(786\) 6.40269 0.228376
\(787\) −42.3946 −1.51120 −0.755602 0.655031i \(-0.772655\pi\)
−0.755602 + 0.655031i \(0.772655\pi\)
\(788\) −20.8737 −0.743594
\(789\) 3.83934 0.136684
\(790\) −6.50096 −0.231294
\(791\) 44.3542 1.57705
\(792\) 2.73441 0.0971629
\(793\) −0.877423 −0.0311582
\(794\) 16.0944 0.571170
\(795\) −0.951331 −0.0337402
\(796\) −24.9553 −0.884516
\(797\) 36.7130 1.30044 0.650220 0.759746i \(-0.274677\pi\)
0.650220 + 0.759746i \(0.274677\pi\)
\(798\) 7.22879 0.255897
\(799\) −41.0363 −1.45176
\(800\) −1.00000 −0.0353553
\(801\) 28.5712 1.00951
\(802\) 14.3654 0.507260
\(803\) 7.68332 0.271139
\(804\) 1.76941 0.0624023
\(805\) 9.78840 0.344996
\(806\) 0.422425 0.0148793
\(807\) 10.4188 0.366758
\(808\) 8.50862 0.299332
\(809\) 48.9521 1.72107 0.860533 0.509395i \(-0.170131\pi\)
0.860533 + 0.509395i \(0.170131\pi\)
\(810\) −6.68021 −0.234719
\(811\) −15.0448 −0.528293 −0.264147 0.964483i \(-0.585090\pi\)
−0.264147 + 0.964483i \(0.585090\pi\)
\(812\) −37.4471 −1.31414
\(813\) −7.20648 −0.252742
\(814\) −6.82873 −0.239347
\(815\) −2.46138 −0.0862182
\(816\) −2.16060 −0.0756363
\(817\) 3.02164 0.105714
\(818\) 34.1092 1.19260
\(819\) −1.37866 −0.0481743
\(820\) 2.16893 0.0757424
\(821\) −4.58575 −0.160044 −0.0800219 0.996793i \(-0.525499\pi\)
−0.0800219 + 0.996793i \(0.525499\pi\)
\(822\) −10.0840 −0.351718
\(823\) −54.9163 −1.91426 −0.957131 0.289656i \(-0.906459\pi\)
−0.957131 + 0.289656i \(0.906459\pi\)
\(824\) 7.21580 0.251374
\(825\) −0.515357 −0.0179424
\(826\) 7.59570 0.264288
\(827\) −12.9128 −0.449021 −0.224510 0.974472i \(-0.572078\pi\)
−0.224510 + 0.974472i \(0.572078\pi\)
\(828\) 5.76581 0.200376
\(829\) −0.368814 −0.0128094 −0.00640472 0.999979i \(-0.502039\pi\)
−0.00640472 + 0.999979i \(0.502039\pi\)
\(830\) 6.38996 0.221799
\(831\) 16.1604 0.560597
\(832\) −0.108612 −0.00376545
\(833\) 60.9964 2.11340
\(834\) −1.69525 −0.0587016
\(835\) −15.9201 −0.550938
\(836\) −3.02164 −0.104506
\(837\) 11.4939 0.397288
\(838\) 9.23855 0.319141
\(839\) 27.9683 0.965573 0.482786 0.875738i \(-0.339625\pi\)
0.482786 + 0.875738i \(0.339625\pi\)
\(840\) −2.39234 −0.0825436
\(841\) 36.0740 1.24393
\(842\) 19.8056 0.682546
\(843\) −11.4477 −0.394280
\(844\) 0.968285 0.0333297
\(845\) −12.9882 −0.446808
\(846\) −26.7648 −0.920193
\(847\) −4.64210 −0.159505
\(848\) 1.84597 0.0633907
\(849\) −4.55968 −0.156488
\(850\) −4.19244 −0.143800
\(851\) −14.3991 −0.493596
\(852\) 7.18330 0.246096
\(853\) 23.8544 0.816757 0.408379 0.912813i \(-0.366094\pi\)
0.408379 + 0.912813i \(0.366094\pi\)
\(854\) 37.5012 1.28326
\(855\) 8.26240 0.282568
\(856\) −1.17431 −0.0401370
\(857\) −39.4611 −1.34797 −0.673983 0.738747i \(-0.735418\pi\)
−0.673983 + 0.738747i \(0.735418\pi\)
\(858\) −0.0559741 −0.00191092
\(859\) −51.4843 −1.75662 −0.878311 0.478090i \(-0.841329\pi\)
−0.878311 + 0.478090i \(0.841329\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 5.18882 0.176835
\(862\) −14.1192 −0.480903
\(863\) 16.9377 0.576567 0.288284 0.957545i \(-0.406915\pi\)
0.288284 + 0.957545i \(0.406915\pi\)
\(864\) −2.95527 −0.100540
\(865\) 23.1251 0.786275
\(866\) −20.3340 −0.690979
\(867\) −0.297148 −0.0100917
\(868\) −18.0545 −0.612810
\(869\) 6.50096 0.220530
\(870\) 4.15730 0.140946
\(871\) 0.372906 0.0126354
\(872\) 2.34821 0.0795205
\(873\) 37.6859 1.27547
\(874\) −6.37147 −0.215518
\(875\) −4.64210 −0.156932
\(876\) −3.95965 −0.133784
\(877\) 10.4830 0.353986 0.176993 0.984212i \(-0.443363\pi\)
0.176993 + 0.984212i \(0.443363\pi\)
\(878\) 34.3522 1.15933
\(879\) −5.48682 −0.185066
\(880\) 1.00000 0.0337100
\(881\) −28.0986 −0.946667 −0.473334 0.880883i \(-0.656950\pi\)
−0.473334 + 0.880883i \(0.656950\pi\)
\(882\) 39.7832 1.33957
\(883\) 46.9823 1.58108 0.790541 0.612410i \(-0.209800\pi\)
0.790541 + 0.612410i \(0.209800\pi\)
\(884\) −0.455351 −0.0153151
\(885\) −0.843259 −0.0283458
\(886\) −14.2974 −0.480330
\(887\) 9.00177 0.302250 0.151125 0.988515i \(-0.451710\pi\)
0.151125 + 0.988515i \(0.451710\pi\)
\(888\) 3.51923 0.118098
\(889\) −19.6721 −0.659780
\(890\) 10.4488 0.350243
\(891\) 6.68021 0.223795
\(892\) 19.7291 0.660579
\(893\) 29.5763 0.989733
\(894\) −6.15575 −0.205879
\(895\) 7.74932 0.259031
\(896\) 4.64210 0.155082
\(897\) −0.118028 −0.00394083
\(898\) 18.5194 0.618000
\(899\) 31.3744 1.04639
\(900\) −2.73441 −0.0911469
\(901\) 7.73911 0.257827
\(902\) −2.16893 −0.0722175
\(903\) −2.39234 −0.0796121
\(904\) 9.55477 0.317787
\(905\) 0.948206 0.0315194
\(906\) −2.96291 −0.0984361
\(907\) 47.9218 1.59122 0.795608 0.605811i \(-0.207151\pi\)
0.795608 + 0.605811i \(0.207151\pi\)
\(908\) −13.8242 −0.458772
\(909\) 23.2660 0.771686
\(910\) −0.504189 −0.0167137
\(911\) −10.4414 −0.345939 −0.172969 0.984927i \(-0.555336\pi\)
−0.172969 + 0.984927i \(0.555336\pi\)
\(912\) 1.55722 0.0515648
\(913\) −6.38996 −0.211477
\(914\) 30.4296 1.00652
\(915\) −4.16330 −0.137635
\(916\) 24.4201 0.806862
\(917\) −57.6725 −1.90452
\(918\) −12.3898 −0.408924
\(919\) 21.8478 0.720693 0.360346 0.932819i \(-0.382659\pi\)
0.360346 + 0.932819i \(0.382659\pi\)
\(920\) 2.10861 0.0695189
\(921\) −2.99168 −0.0985792
\(922\) −5.19765 −0.171176
\(923\) 1.51389 0.0498304
\(924\) 2.39234 0.0787022
\(925\) 6.82873 0.224527
\(926\) 33.4985 1.10083
\(927\) 19.7309 0.648049
\(928\) −8.06684 −0.264807
\(929\) −49.9346 −1.63830 −0.819151 0.573578i \(-0.805555\pi\)
−0.819151 + 0.573578i \(0.805555\pi\)
\(930\) 2.00438 0.0657261
\(931\) −43.9622 −1.44080
\(932\) 17.3137 0.567130
\(933\) −12.2098 −0.399732
\(934\) −6.88311 −0.225222
\(935\) 4.19244 0.137108
\(936\) −0.296990 −0.00970743
\(937\) 0.289219 0.00944838 0.00472419 0.999989i \(-0.498496\pi\)
0.00472419 + 0.999989i \(0.498496\pi\)
\(938\) −15.9381 −0.520396
\(939\) 4.54442 0.148301
\(940\) −9.78816 −0.319255
\(941\) 24.3719 0.794502 0.397251 0.917710i \(-0.369964\pi\)
0.397251 + 0.917710i \(0.369964\pi\)
\(942\) −10.7912 −0.351595
\(943\) −4.57344 −0.148932
\(944\) 1.63626 0.0532558
\(945\) −13.7186 −0.446268
\(946\) 1.00000 0.0325128
\(947\) 28.6203 0.930033 0.465017 0.885302i \(-0.346048\pi\)
0.465017 + 0.885302i \(0.346048\pi\)
\(948\) −3.35031 −0.108813
\(949\) −0.834503 −0.0270891
\(950\) 3.02164 0.0980350
\(951\) −4.35079 −0.141084
\(952\) 19.4618 0.630759
\(953\) 38.7967 1.25675 0.628374 0.777911i \(-0.283721\pi\)
0.628374 + 0.777911i \(0.283721\pi\)
\(954\) 5.04762 0.163423
\(955\) 13.9647 0.451886
\(956\) 15.6399 0.505831
\(957\) −4.15730 −0.134387
\(958\) 41.7556 1.34906
\(959\) 90.8318 2.93311
\(960\) −0.515357 −0.0166331
\(961\) −15.8734 −0.512044
\(962\) 0.741684 0.0239128
\(963\) −3.21103 −0.103474
\(964\) −4.82493 −0.155401
\(965\) −17.6616 −0.568547
\(966\) 5.04452 0.162305
\(967\) 33.3917 1.07381 0.536903 0.843644i \(-0.319594\pi\)
0.536903 + 0.843644i \(0.319594\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 6.52857 0.209728
\(970\) 13.7821 0.442517
\(971\) −38.3504 −1.23072 −0.615361 0.788245i \(-0.710990\pi\)
−0.615361 + 0.788245i \(0.710990\pi\)
\(972\) −12.3085 −0.394795
\(973\) 15.2700 0.489535
\(974\) 17.2846 0.553833
\(975\) 0.0559741 0.00179260
\(976\) 8.07848 0.258586
\(977\) 32.1864 1.02973 0.514867 0.857270i \(-0.327841\pi\)
0.514867 + 0.857270i \(0.327841\pi\)
\(978\) −1.26849 −0.0405617
\(979\) −10.4488 −0.333944
\(980\) 14.5491 0.464755
\(981\) 6.42097 0.205006
\(982\) −1.38700 −0.0442609
\(983\) −26.1017 −0.832516 −0.416258 0.909247i \(-0.636659\pi\)
−0.416258 + 0.909247i \(0.636659\pi\)
\(984\) 1.11777 0.0356333
\(985\) −20.8737 −0.665090
\(986\) −33.8198 −1.07704
\(987\) −23.4166 −0.745359
\(988\) 0.328187 0.0104410
\(989\) 2.10861 0.0670500
\(990\) 2.73441 0.0869052
\(991\) 2.66903 0.0847844 0.0423922 0.999101i \(-0.486502\pi\)
0.0423922 + 0.999101i \(0.486502\pi\)
\(992\) −3.88930 −0.123485
\(993\) 15.4403 0.489983
\(994\) −64.7040 −2.05228
\(995\) −24.9553 −0.791135
\(996\) 3.29311 0.104346
\(997\) −15.0638 −0.477076 −0.238538 0.971133i \(-0.576668\pi\)
−0.238538 + 0.971133i \(0.576668\pi\)
\(998\) −8.42570 −0.266711
\(999\) 20.1807 0.638489
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 4730.2.a.w.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.w.1.5 8 1.1 even 1 trivial