Properties

Label 8470.2.a.cn.1.3
Level $8470$
Weight $2$
Character 8470.1
Self dual yes
Analytic conductor $67.633$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8470.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(67.6332905120\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.81361\) of defining polynomial
Character \(\chi\) \(=\) 8470.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.10278 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.10278 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{10} +3.10278 q^{12} +1.00000 q^{14} +3.10278 q^{15} +1.00000 q^{16} +5.62721 q^{17} +6.62721 q^{18} -4.72999 q^{19} +1.00000 q^{20} +3.10278 q^{21} +4.52444 q^{23} +3.10278 q^{24} +1.00000 q^{25} +11.2544 q^{27} +1.00000 q^{28} -2.52444 q^{29} +3.10278 q^{30} -3.04888 q^{31} +1.00000 q^{32} +5.62721 q^{34} +1.00000 q^{35} +6.62721 q^{36} +4.52444 q^{37} -4.72999 q^{38} +1.00000 q^{40} -7.30833 q^{41} +3.10278 q^{42} +0.578337 q^{43} +6.62721 q^{45} +4.52444 q^{46} +11.8328 q^{47} +3.10278 q^{48} +1.00000 q^{49} +1.00000 q^{50} +17.4600 q^{51} -5.57331 q^{53} +11.2544 q^{54} +1.00000 q^{56} -14.6761 q^{57} -2.52444 q^{58} -7.62721 q^{59} +3.10278 q^{60} -9.83276 q^{61} -3.04888 q^{62} +6.62721 q^{63} +1.00000 q^{64} -13.2544 q^{67} +5.62721 q^{68} +14.0383 q^{69} +1.00000 q^{70} -8.41110 q^{71} +6.62721 q^{72} -4.57834 q^{73} +4.52444 q^{74} +3.10278 q^{75} -4.72999 q^{76} +9.77886 q^{79} +1.00000 q^{80} +15.0383 q^{81} -7.30833 q^{82} -7.25443 q^{83} +3.10278 q^{84} +5.62721 q^{85} +0.578337 q^{86} -7.83276 q^{87} +14.4111 q^{89} +6.62721 q^{90} +4.52444 q^{92} -9.45998 q^{93} +11.8328 q^{94} -4.72999 q^{95} +3.10278 q^{96} +16.5244 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 3q^{5} + 2q^{6} + 3q^{7} + 3q^{8} + 7q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 3q^{5} + 2q^{6} + 3q^{7} + 3q^{8} + 7q^{9} + 3q^{10} + 2q^{12} + 3q^{14} + 2q^{15} + 3q^{16} + 4q^{17} + 7q^{18} + 6q^{19} + 3q^{20} + 2q^{21} + 8q^{23} + 2q^{24} + 3q^{25} + 8q^{27} + 3q^{28} - 2q^{29} + 2q^{30} + 2q^{31} + 3q^{32} + 4q^{34} + 3q^{35} + 7q^{36} + 8q^{37} + 6q^{38} + 3q^{40} + 2q^{42} + 7q^{45} + 8q^{46} + 8q^{47} + 2q^{48} + 3q^{49} + 3q^{50} + 12q^{51} + 8q^{54} + 3q^{56} - 20q^{57} - 2q^{58} - 10q^{59} + 2q^{60} - 2q^{61} + 2q^{62} + 7q^{63} + 3q^{64} - 14q^{67} + 4q^{68} + 3q^{70} + 4q^{71} + 7q^{72} - 12q^{73} + 8q^{74} + 2q^{75} + 6q^{76} - 2q^{79} + 3q^{80} + 3q^{81} + 4q^{83} + 2q^{84} + 4q^{85} + 4q^{87} + 14q^{89} + 7q^{90} + 8q^{92} + 12q^{93} + 8q^{94} + 6q^{95} + 2q^{96} + 44q^{97} + 3q^{98} + O(q^{100}) \)

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
\(3\) 3.10278 1.79139 0.895694 0.444671i \(-0.146679\pi\)
0.895694 + 0.444671i \(0.146679\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 3.10278 1.26670
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 6.62721 2.20907
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) 3.10278 0.895694
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 1.00000 0.267261
\(15\) 3.10278 0.801133
\(16\) 1.00000 0.250000
\(17\) 5.62721 1.36480 0.682400 0.730979i \(-0.260936\pi\)
0.682400 + 0.730979i \(0.260936\pi\)
\(18\) 6.62721 1.56205
\(19\) −4.72999 −1.08513 −0.542567 0.840013i \(-0.682547\pi\)
−0.542567 + 0.840013i \(0.682547\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.10278 0.677081
\(22\) 0 0
\(23\) 4.52444 0.943411 0.471705 0.881756i \(-0.343639\pi\)
0.471705 + 0.881756i \(0.343639\pi\)
\(24\) 3.10278 0.633351
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 11.2544 2.16592
\(28\) 1.00000 0.188982
\(29\) −2.52444 −0.468776 −0.234388 0.972143i \(-0.575309\pi\)
−0.234388 + 0.972143i \(0.575309\pi\)
\(30\) 3.10278 0.566487
\(31\) −3.04888 −0.547594 −0.273797 0.961787i \(-0.588280\pi\)
−0.273797 + 0.961787i \(0.588280\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 5.62721 0.965059
\(35\) 1.00000 0.169031
\(36\) 6.62721 1.10454
\(37\) 4.52444 0.743813 0.371907 0.928270i \(-0.378704\pi\)
0.371907 + 0.928270i \(0.378704\pi\)
\(38\) −4.72999 −0.767305
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −7.30833 −1.14137 −0.570684 0.821170i \(-0.693322\pi\)
−0.570684 + 0.821170i \(0.693322\pi\)
\(42\) 3.10278 0.478769
\(43\) 0.578337 0.0881956 0.0440978 0.999027i \(-0.485959\pi\)
0.0440978 + 0.999027i \(0.485959\pi\)
\(44\) 0 0
\(45\) 6.62721 0.987927
\(46\) 4.52444 0.667092
\(47\) 11.8328 1.72599 0.862993 0.505216i \(-0.168587\pi\)
0.862993 + 0.505216i \(0.168587\pi\)
\(48\) 3.10278 0.447847
\(49\) 1.00000 0.142857
\(50\) 1.00000 0.141421
\(51\) 17.4600 2.44489
\(52\) 0 0
\(53\) −5.57331 −0.765554 −0.382777 0.923841i \(-0.625032\pi\)
−0.382777 + 0.923841i \(0.625032\pi\)
\(54\) 11.2544 1.53153
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −14.6761 −1.94390
\(58\) −2.52444 −0.331475
\(59\) −7.62721 −0.992979 −0.496489 0.868043i \(-0.665378\pi\)
−0.496489 + 0.868043i \(0.665378\pi\)
\(60\) 3.10278 0.400567
\(61\) −9.83276 −1.25896 −0.629478 0.777018i \(-0.716731\pi\)
−0.629478 + 0.777018i \(0.716731\pi\)
\(62\) −3.04888 −0.387208
\(63\) 6.62721 0.834950
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −13.2544 −1.61929 −0.809643 0.586923i \(-0.800339\pi\)
−0.809643 + 0.586923i \(0.800339\pi\)
\(68\) 5.62721 0.682400
\(69\) 14.0383 1.69001
\(70\) 1.00000 0.119523
\(71\) −8.41110 −0.998214 −0.499107 0.866540i \(-0.666339\pi\)
−0.499107 + 0.866540i \(0.666339\pi\)
\(72\) 6.62721 0.781025
\(73\) −4.57834 −0.535854 −0.267927 0.963439i \(-0.586339\pi\)
−0.267927 + 0.963439i \(0.586339\pi\)
\(74\) 4.52444 0.525955
\(75\) 3.10278 0.358278
\(76\) −4.72999 −0.542567
\(77\) 0 0
\(78\) 0 0
\(79\) 9.77886 1.10021 0.550104 0.835096i \(-0.314588\pi\)
0.550104 + 0.835096i \(0.314588\pi\)
\(80\) 1.00000 0.111803
\(81\) 15.0383 1.67092
\(82\) −7.30833 −0.807069
\(83\) −7.25443 −0.796277 −0.398138 0.917325i \(-0.630344\pi\)
−0.398138 + 0.917325i \(0.630344\pi\)
\(84\) 3.10278 0.338541
\(85\) 5.62721 0.610357
\(86\) 0.578337 0.0623637
\(87\) −7.83276 −0.839760
\(88\) 0 0
\(89\) 14.4111 1.52757 0.763787 0.645469i \(-0.223338\pi\)
0.763787 + 0.645469i \(0.223338\pi\)
\(90\) 6.62721 0.698570
\(91\) 0 0
\(92\) 4.52444 0.471705
\(93\) −9.45998 −0.980954
\(94\) 11.8328 1.22046
\(95\) −4.72999 −0.485287
\(96\) 3.10278 0.316676
\(97\) 16.5244 1.67780 0.838901 0.544284i \(-0.183198\pi\)
0.838901 + 0.544284i \(0.183198\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −5.42166 −0.539476 −0.269738 0.962934i \(-0.586937\pi\)
−0.269738 + 0.962934i \(0.586937\pi\)
\(102\) 17.4600 1.72880
\(103\) −5.62721 −0.554466 −0.277233 0.960803i \(-0.589417\pi\)
−0.277233 + 0.960803i \(0.589417\pi\)
\(104\) 0 0
\(105\) 3.10278 0.302800
\(106\) −5.57331 −0.541328
\(107\) −11.8328 −1.14392 −0.571958 0.820283i \(-0.693816\pi\)
−0.571958 + 0.820283i \(0.693816\pi\)
\(108\) 11.2544 1.08296
\(109\) 5.88666 0.563840 0.281920 0.959438i \(-0.409029\pi\)
0.281920 + 0.959438i \(0.409029\pi\)
\(110\) 0 0
\(111\) 14.0383 1.33246
\(112\) 1.00000 0.0944911
\(113\) −5.25443 −0.494295 −0.247147 0.968978i \(-0.579493\pi\)
−0.247147 + 0.968978i \(0.579493\pi\)
\(114\) −14.6761 −1.37454
\(115\) 4.52444 0.421906
\(116\) −2.52444 −0.234388
\(117\) 0 0
\(118\) −7.62721 −0.702142
\(119\) 5.62721 0.515846
\(120\) 3.10278 0.283243
\(121\) 0 0
\(122\) −9.83276 −0.890217
\(123\) −22.6761 −2.04463
\(124\) −3.04888 −0.273797
\(125\) 1.00000 0.0894427
\(126\) 6.62721 0.590399
\(127\) −20.7144 −1.83811 −0.919053 0.394134i \(-0.871045\pi\)
−0.919053 + 0.394134i \(0.871045\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.79445 0.157993
\(130\) 0 0
\(131\) 17.7789 1.55335 0.776673 0.629904i \(-0.216906\pi\)
0.776673 + 0.629904i \(0.216906\pi\)
\(132\) 0 0
\(133\) −4.72999 −0.410142
\(134\) −13.2544 −1.14501
\(135\) 11.2544 0.968627
\(136\) 5.62721 0.482530
\(137\) −6.41110 −0.547737 −0.273869 0.961767i \(-0.588303\pi\)
−0.273869 + 0.961767i \(0.588303\pi\)
\(138\) 14.0383 1.19502
\(139\) 9.77886 0.829432 0.414716 0.909951i \(-0.363881\pi\)
0.414716 + 0.909951i \(0.363881\pi\)
\(140\) 1.00000 0.0845154
\(141\) 36.7144 3.09191
\(142\) −8.41110 −0.705844
\(143\) 0 0
\(144\) 6.62721 0.552268
\(145\) −2.52444 −0.209643
\(146\) −4.57834 −0.378906
\(147\) 3.10278 0.255913
\(148\) 4.52444 0.371907
\(149\) −1.88666 −0.154561 −0.0772807 0.997009i \(-0.524624\pi\)
−0.0772807 + 0.997009i \(0.524624\pi\)
\(150\) 3.10278 0.253341
\(151\) 19.9844 1.62631 0.813154 0.582048i \(-0.197749\pi\)
0.813154 + 0.582048i \(0.197749\pi\)
\(152\) −4.72999 −0.383653
\(153\) 37.2927 3.01494
\(154\) 0 0
\(155\) −3.04888 −0.244892
\(156\) 0 0
\(157\) 9.36222 0.747187 0.373593 0.927593i \(-0.378126\pi\)
0.373593 + 0.927593i \(0.378126\pi\)
\(158\) 9.77886 0.777965
\(159\) −17.2927 −1.37140
\(160\) 1.00000 0.0790569
\(161\) 4.52444 0.356576
\(162\) 15.0383 1.18152
\(163\) 17.2544 1.35147 0.675735 0.737144i \(-0.263826\pi\)
0.675735 + 0.737144i \(0.263826\pi\)
\(164\) −7.30833 −0.570684
\(165\) 0 0
\(166\) −7.25443 −0.563053
\(167\) −17.5678 −1.35944 −0.679718 0.733474i \(-0.737898\pi\)
−0.679718 + 0.733474i \(0.737898\pi\)
\(168\) 3.10278 0.239384
\(169\) −13.0000 −1.00000
\(170\) 5.62721 0.431588
\(171\) −31.3466 −2.39714
\(172\) 0.578337 0.0440978
\(173\) −10.6761 −0.811688 −0.405844 0.913942i \(-0.633022\pi\)
−0.405844 + 0.913942i \(0.633022\pi\)
\(174\) −7.83276 −0.593800
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −23.6655 −1.77881
\(178\) 14.4111 1.08016
\(179\) −4.47054 −0.334144 −0.167072 0.985945i \(-0.553431\pi\)
−0.167072 + 0.985945i \(0.553431\pi\)
\(180\) 6.62721 0.493963
\(181\) −10.4111 −0.773851 −0.386925 0.922111i \(-0.626463\pi\)
−0.386925 + 0.922111i \(0.626463\pi\)
\(182\) 0 0
\(183\) −30.5089 −2.25528
\(184\) 4.52444 0.333546
\(185\) 4.52444 0.332643
\(186\) −9.45998 −0.693639
\(187\) 0 0
\(188\) 11.8328 0.862993
\(189\) 11.2544 0.818639
\(190\) −4.72999 −0.343149
\(191\) 14.6167 1.05762 0.528812 0.848739i \(-0.322638\pi\)
0.528812 + 0.848739i \(0.322638\pi\)
\(192\) 3.10278 0.223924
\(193\) 25.4983 1.83541 0.917704 0.397266i \(-0.130041\pi\)
0.917704 + 0.397266i \(0.130041\pi\)
\(194\) 16.5244 1.18639
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −5.89220 −0.419802 −0.209901 0.977723i \(-0.567314\pi\)
−0.209901 + 0.977723i \(0.567314\pi\)
\(198\) 0 0
\(199\) 15.9305 1.12928 0.564642 0.825336i \(-0.309014\pi\)
0.564642 + 0.825336i \(0.309014\pi\)
\(200\) 1.00000 0.0707107
\(201\) −41.1255 −2.90077
\(202\) −5.42166 −0.381467
\(203\) −2.52444 −0.177181
\(204\) 17.4600 1.22244
\(205\) −7.30833 −0.510436
\(206\) −5.62721 −0.392067
\(207\) 29.9844 2.08406
\(208\) 0 0
\(209\) 0 0
\(210\) 3.10278 0.214112
\(211\) −17.5678 −1.20942 −0.604708 0.796447i \(-0.706710\pi\)
−0.604708 + 0.796447i \(0.706710\pi\)
\(212\) −5.57331 −0.382777
\(213\) −26.0978 −1.78819
\(214\) −11.8328 −0.808871
\(215\) 0.578337 0.0394423
\(216\) 11.2544 0.765767
\(217\) −3.04888 −0.206971
\(218\) 5.88666 0.398695
\(219\) −14.2056 −0.959922
\(220\) 0 0
\(221\) 0 0
\(222\) 14.0383 0.942190
\(223\) 9.62721 0.644686 0.322343 0.946623i \(-0.395530\pi\)
0.322343 + 0.946623i \(0.395530\pi\)
\(224\) 1.00000 0.0668153
\(225\) 6.62721 0.441814
\(226\) −5.25443 −0.349519
\(227\) −18.6167 −1.23563 −0.617815 0.786323i \(-0.711982\pi\)
−0.617815 + 0.786323i \(0.711982\pi\)
\(228\) −14.6761 −0.971948
\(229\) −10.8816 −0.719079 −0.359539 0.933130i \(-0.617066\pi\)
−0.359539 + 0.933130i \(0.617066\pi\)
\(230\) 4.52444 0.298333
\(231\) 0 0
\(232\) −2.52444 −0.165737
\(233\) −12.8433 −0.841394 −0.420697 0.907201i \(-0.638214\pi\)
−0.420697 + 0.907201i \(0.638214\pi\)
\(234\) 0 0
\(235\) 11.8328 0.771884
\(236\) −7.62721 −0.496489
\(237\) 30.3416 1.97090
\(238\) 5.62721 0.364758
\(239\) 25.8867 1.67447 0.837234 0.546844i \(-0.184171\pi\)
0.837234 + 0.546844i \(0.184171\pi\)
\(240\) 3.10278 0.200283
\(241\) −13.5139 −0.870505 −0.435253 0.900308i \(-0.643341\pi\)
−0.435253 + 0.900308i \(0.643341\pi\)
\(242\) 0 0
\(243\) 12.8972 0.827357
\(244\) −9.83276 −0.629478
\(245\) 1.00000 0.0638877
\(246\) −22.6761 −1.44577
\(247\) 0 0
\(248\) −3.04888 −0.193604
\(249\) −22.5089 −1.42644
\(250\) 1.00000 0.0632456
\(251\) 26.9894 1.70356 0.851779 0.523901i \(-0.175524\pi\)
0.851779 + 0.523901i \(0.175524\pi\)
\(252\) 6.62721 0.417475
\(253\) 0 0
\(254\) −20.7144 −1.29974
\(255\) 17.4600 1.09339
\(256\) 1.00000 0.0625000
\(257\) −2.83779 −0.177016 −0.0885081 0.996075i \(-0.528210\pi\)
−0.0885081 + 0.996075i \(0.528210\pi\)
\(258\) 1.79445 0.111718
\(259\) 4.52444 0.281135
\(260\) 0 0
\(261\) −16.7300 −1.03556
\(262\) 17.7789 1.09838
\(263\) 2.95112 0.181974 0.0909871 0.995852i \(-0.470998\pi\)
0.0909871 + 0.995852i \(0.470998\pi\)
\(264\) 0 0
\(265\) −5.57331 −0.342366
\(266\) −4.72999 −0.290014
\(267\) 44.7144 2.73648
\(268\) −13.2544 −0.809643
\(269\) −2.88164 −0.175697 −0.0878483 0.996134i \(-0.527999\pi\)
−0.0878483 + 0.996134i \(0.527999\pi\)
\(270\) 11.2544 0.684923
\(271\) 16.3033 0.990355 0.495178 0.868792i \(-0.335103\pi\)
0.495178 + 0.868792i \(0.335103\pi\)
\(272\) 5.62721 0.341200
\(273\) 0 0
\(274\) −6.41110 −0.387309
\(275\) 0 0
\(276\) 14.0383 0.845007
\(277\) −13.3622 −0.802858 −0.401429 0.915890i \(-0.631486\pi\)
−0.401429 + 0.915890i \(0.631486\pi\)
\(278\) 9.77886 0.586497
\(279\) −20.2056 −1.20967
\(280\) 1.00000 0.0597614
\(281\) 27.5577 1.64396 0.821978 0.569519i \(-0.192871\pi\)
0.821978 + 0.569519i \(0.192871\pi\)
\(282\) 36.7144 2.18631
\(283\) 11.8922 0.706918 0.353459 0.935450i \(-0.385005\pi\)
0.353459 + 0.935450i \(0.385005\pi\)
\(284\) −8.41110 −0.499107
\(285\) −14.6761 −0.869336
\(286\) 0 0
\(287\) −7.30833 −0.431397
\(288\) 6.62721 0.390512
\(289\) 14.6655 0.862678
\(290\) −2.52444 −0.148240
\(291\) 51.2716 3.00560
\(292\) −4.57834 −0.267927
\(293\) −14.3133 −0.836195 −0.418097 0.908402i \(-0.637303\pi\)
−0.418097 + 0.908402i \(0.637303\pi\)
\(294\) 3.10278 0.180958
\(295\) −7.62721 −0.444074
\(296\) 4.52444 0.262978
\(297\) 0 0
\(298\) −1.88666 −0.109291
\(299\) 0 0
\(300\) 3.10278 0.179139
\(301\) 0.578337 0.0333348
\(302\) 19.9844 1.14997
\(303\) −16.8222 −0.966410
\(304\) −4.72999 −0.271283
\(305\) −9.83276 −0.563022
\(306\) 37.2927 2.13188
\(307\) 20.3033 1.15877 0.579385 0.815054i \(-0.303293\pi\)
0.579385 + 0.815054i \(0.303293\pi\)
\(308\) 0 0
\(309\) −17.4600 −0.993263
\(310\) −3.04888 −0.173165
\(311\) −0.951124 −0.0539333 −0.0269666 0.999636i \(-0.508585\pi\)
−0.0269666 + 0.999636i \(0.508585\pi\)
\(312\) 0 0
\(313\) −10.0922 −0.570446 −0.285223 0.958461i \(-0.592068\pi\)
−0.285223 + 0.958461i \(0.592068\pi\)
\(314\) 9.36222 0.528341
\(315\) 6.62721 0.373401
\(316\) 9.77886 0.550104
\(317\) −5.98441 −0.336118 −0.168059 0.985777i \(-0.553750\pi\)
−0.168059 + 0.985777i \(0.553750\pi\)
\(318\) −17.2927 −0.969729
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) −36.7144 −2.04920
\(322\) 4.52444 0.252137
\(323\) −26.6167 −1.48099
\(324\) 15.0383 0.835462
\(325\) 0 0
\(326\) 17.2544 0.955634
\(327\) 18.2650 1.01006
\(328\) −7.30833 −0.403535
\(329\) 11.8328 0.652361
\(330\) 0 0
\(331\) 17.2927 0.950495 0.475247 0.879852i \(-0.342359\pi\)
0.475247 + 0.879852i \(0.342359\pi\)
\(332\) −7.25443 −0.398138
\(333\) 29.9844 1.64314
\(334\) −17.5678 −0.961266
\(335\) −13.2544 −0.724167
\(336\) 3.10278 0.169270
\(337\) −27.1567 −1.47932 −0.739659 0.672982i \(-0.765013\pi\)
−0.739659 + 0.672982i \(0.765013\pi\)
\(338\) −13.0000 −0.707107
\(339\) −16.3033 −0.885474
\(340\) 5.62721 0.305178
\(341\) 0 0
\(342\) −31.3466 −1.69503
\(343\) 1.00000 0.0539949
\(344\) 0.578337 0.0311818
\(345\) 14.0383 0.755797
\(346\) −10.6761 −0.573950
\(347\) −31.0872 −1.66885 −0.834424 0.551123i \(-0.814199\pi\)
−0.834424 + 0.551123i \(0.814199\pi\)
\(348\) −7.83276 −0.419880
\(349\) −21.7250 −1.16291 −0.581455 0.813578i \(-0.697516\pi\)
−0.581455 + 0.813578i \(0.697516\pi\)
\(350\) 1.00000 0.0534522
\(351\) 0 0
\(352\) 0 0
\(353\) 8.22114 0.437567 0.218783 0.975773i \(-0.429791\pi\)
0.218783 + 0.975773i \(0.429791\pi\)
\(354\) −23.6655 −1.25781
\(355\) −8.41110 −0.446415
\(356\) 14.4111 0.763787
\(357\) 17.4600 0.924080
\(358\) −4.47054 −0.236275
\(359\) −14.8277 −0.782578 −0.391289 0.920268i \(-0.627971\pi\)
−0.391289 + 0.920268i \(0.627971\pi\)
\(360\) 6.62721 0.349285
\(361\) 3.37279 0.177515
\(362\) −10.4111 −0.547195
\(363\) 0 0
\(364\) 0 0
\(365\) −4.57834 −0.239641
\(366\) −30.5089 −1.59472
\(367\) −23.9406 −1.24969 −0.624844 0.780750i \(-0.714837\pi\)
−0.624844 + 0.780750i \(0.714837\pi\)
\(368\) 4.52444 0.235853
\(369\) −48.4338 −2.52136
\(370\) 4.52444 0.235214
\(371\) −5.57331 −0.289352
\(372\) −9.45998 −0.490477
\(373\) 3.04888 0.157865 0.0789324 0.996880i \(-0.474849\pi\)
0.0789324 + 0.996880i \(0.474849\pi\)
\(374\) 0 0
\(375\) 3.10278 0.160227
\(376\) 11.8328 0.610228
\(377\) 0 0
\(378\) 11.2544 0.578865
\(379\) −27.6655 −1.42108 −0.710541 0.703655i \(-0.751550\pi\)
−0.710541 + 0.703655i \(0.751550\pi\)
\(380\) −4.72999 −0.242643
\(381\) −64.2721 −3.29276
\(382\) 14.6167 0.747853
\(383\) −7.52946 −0.384737 −0.192369 0.981323i \(-0.561617\pi\)
−0.192369 + 0.981323i \(0.561617\pi\)
\(384\) 3.10278 0.158338
\(385\) 0 0
\(386\) 25.4983 1.29783
\(387\) 3.83276 0.194830
\(388\) 16.5244 0.838901
\(389\) −27.4600 −1.39228 −0.696138 0.717908i \(-0.745100\pi\)
−0.696138 + 0.717908i \(0.745100\pi\)
\(390\) 0 0
\(391\) 25.4600 1.28757
\(392\) 1.00000 0.0505076
\(393\) 55.1638 2.78265
\(394\) −5.89220 −0.296845
\(395\) 9.77886 0.492028
\(396\) 0 0
\(397\) 27.4600 1.37818 0.689088 0.724677i \(-0.258011\pi\)
0.689088 + 0.724677i \(0.258011\pi\)
\(398\) 15.9305 0.798525
\(399\) −14.6761 −0.734723
\(400\) 1.00000 0.0500000
\(401\) 1.52946 0.0763776 0.0381888 0.999271i \(-0.487841\pi\)
0.0381888 + 0.999271i \(0.487841\pi\)
\(402\) −41.1255 −2.05115
\(403\) 0 0
\(404\) −5.42166 −0.269738
\(405\) 15.0383 0.747260
\(406\) −2.52444 −0.125286
\(407\) 0 0
\(408\) 17.4600 0.864398
\(409\) 34.6705 1.71435 0.857174 0.515027i \(-0.172218\pi\)
0.857174 + 0.515027i \(0.172218\pi\)
\(410\) −7.30833 −0.360932
\(411\) −19.8922 −0.981210
\(412\) −5.62721 −0.277233
\(413\) −7.62721 −0.375311
\(414\) 29.9844 1.47365
\(415\) −7.25443 −0.356106
\(416\) 0 0
\(417\) 30.3416 1.48584
\(418\) 0 0
\(419\) 25.4217 1.24193 0.620965 0.783838i \(-0.286741\pi\)
0.620965 + 0.783838i \(0.286741\pi\)
\(420\) 3.10278 0.151400
\(421\) −13.7733 −0.671271 −0.335635 0.941992i \(-0.608951\pi\)
−0.335635 + 0.941992i \(0.608951\pi\)
\(422\) −17.5678 −0.855186
\(423\) 78.4182 3.81283
\(424\) −5.57331 −0.270664
\(425\) 5.62721 0.272960
\(426\) −26.0978 −1.26444
\(427\) −9.83276 −0.475841
\(428\) −11.8328 −0.571958
\(429\) 0 0
\(430\) 0.578337 0.0278899
\(431\) −29.2489 −1.40887 −0.704435 0.709769i \(-0.748799\pi\)
−0.704435 + 0.709769i \(0.748799\pi\)
\(432\) 11.2544 0.541479
\(433\) −9.04334 −0.434595 −0.217298 0.976105i \(-0.569724\pi\)
−0.217298 + 0.976105i \(0.569724\pi\)
\(434\) −3.04888 −0.146351
\(435\) −7.83276 −0.375552
\(436\) 5.88666 0.281920
\(437\) −21.4005 −1.02373
\(438\) −14.2056 −0.678767
\(439\) −36.7144 −1.75228 −0.876141 0.482054i \(-0.839891\pi\)
−0.876141 + 0.482054i \(0.839891\pi\)
\(440\) 0 0
\(441\) 6.62721 0.315582
\(442\) 0 0
\(443\) −13.6655 −0.649269 −0.324634 0.945840i \(-0.605241\pi\)
−0.324634 + 0.945840i \(0.605241\pi\)
\(444\) 14.0383 0.666229
\(445\) 14.4111 0.683152
\(446\) 9.62721 0.455862
\(447\) −5.85389 −0.276879
\(448\) 1.00000 0.0472456
\(449\) −18.3517 −0.866068 −0.433034 0.901377i \(-0.642557\pi\)
−0.433034 + 0.901377i \(0.642557\pi\)
\(450\) 6.62721 0.312410
\(451\) 0 0
\(452\) −5.25443 −0.247147
\(453\) 62.0071 2.91335
\(454\) −18.6167 −0.873723
\(455\) 0 0
\(456\) −14.6761 −0.687271
\(457\) 15.1567 0.708999 0.354500 0.935056i \(-0.384651\pi\)
0.354500 + 0.935056i \(0.384651\pi\)
\(458\) −10.8816 −0.508466
\(459\) 63.3311 2.95604
\(460\) 4.52444 0.210953
\(461\) 9.52946 0.443831 0.221916 0.975066i \(-0.428769\pi\)
0.221916 + 0.975066i \(0.428769\pi\)
\(462\) 0 0
\(463\) 16.9355 0.787061 0.393531 0.919312i \(-0.371254\pi\)
0.393531 + 0.919312i \(0.371254\pi\)
\(464\) −2.52444 −0.117194
\(465\) −9.45998 −0.438696
\(466\) −12.8433 −0.594956
\(467\) 16.0439 0.742421 0.371210 0.928549i \(-0.378943\pi\)
0.371210 + 0.928549i \(0.378943\pi\)
\(468\) 0 0
\(469\) −13.2544 −0.612033
\(470\) 11.8328 0.545805
\(471\) 29.0489 1.33850
\(472\) −7.62721 −0.351071
\(473\) 0 0
\(474\) 30.3416 1.39364
\(475\) −4.72999 −0.217027
\(476\) 5.62721 0.257923
\(477\) −36.9355 −1.69116
\(478\) 25.8867 1.18403
\(479\) −12.4111 −0.567078 −0.283539 0.958961i \(-0.591508\pi\)
−0.283539 + 0.958961i \(0.591508\pi\)
\(480\) 3.10278 0.141622
\(481\) 0 0
\(482\) −13.5139 −0.615540
\(483\) 14.0383 0.638765
\(484\) 0 0
\(485\) 16.5244 0.750336
\(486\) 12.8972 0.585030
\(487\) 1.37781 0.0624345 0.0312173 0.999513i \(-0.490062\pi\)
0.0312173 + 0.999513i \(0.490062\pi\)
\(488\) −9.83276 −0.445108
\(489\) 53.5366 2.42101
\(490\) 1.00000 0.0451754
\(491\) 6.31335 0.284917 0.142459 0.989801i \(-0.454499\pi\)
0.142459 + 0.989801i \(0.454499\pi\)
\(492\) −22.6761 −1.02232
\(493\) −14.2056 −0.639786
\(494\) 0 0
\(495\) 0 0
\(496\) −3.04888 −0.136899
\(497\) −8.41110 −0.377289
\(498\) −22.5089 −1.00865
\(499\) 10.9794 0.491505 0.245753 0.969333i \(-0.420965\pi\)
0.245753 + 0.969333i \(0.420965\pi\)
\(500\) 1.00000 0.0447214
\(501\) −54.5089 −2.43528
\(502\) 26.9894 1.20460
\(503\) 34.1744 1.52376 0.761880 0.647718i \(-0.224277\pi\)
0.761880 + 0.647718i \(0.224277\pi\)
\(504\) 6.62721 0.295200
\(505\) −5.42166 −0.241261
\(506\) 0 0
\(507\) −40.3361 −1.79139
\(508\) −20.7144 −0.919053
\(509\) −19.5678 −0.867326 −0.433663 0.901075i \(-0.642779\pi\)
−0.433663 + 0.901075i \(0.642779\pi\)
\(510\) 17.4600 0.773141
\(511\) −4.57834 −0.202534
\(512\) 1.00000 0.0441942
\(513\) −53.2333 −2.35031
\(514\) −2.83779 −0.125169
\(515\) −5.62721 −0.247965
\(516\) 1.79445 0.0789963
\(517\) 0 0
\(518\) 4.52444 0.198792
\(519\) −33.1255 −1.45405
\(520\) 0 0
\(521\) 13.0278 0.570756 0.285378 0.958415i \(-0.407881\pi\)
0.285378 + 0.958415i \(0.407881\pi\)
\(522\) −16.7300 −0.732252
\(523\) 33.6555 1.47165 0.735826 0.677171i \(-0.236794\pi\)
0.735826 + 0.677171i \(0.236794\pi\)
\(524\) 17.7789 0.776673
\(525\) 3.10278 0.135416
\(526\) 2.95112 0.128675
\(527\) −17.1567 −0.747356
\(528\) 0 0
\(529\) −2.52946 −0.109977
\(530\) −5.57331 −0.242089
\(531\) −50.5472 −2.19356
\(532\) −4.72999 −0.205071
\(533\) 0 0
\(534\) 44.7144 1.93498
\(535\) −11.8328 −0.511575
\(536\) −13.2544 −0.572504
\(537\) −13.8711 −0.598581
\(538\) −2.88164 −0.124236
\(539\) 0 0
\(540\) 11.2544 0.484313
\(541\) 6.29776 0.270762 0.135381 0.990794i \(-0.456774\pi\)
0.135381 + 0.990794i \(0.456774\pi\)
\(542\) 16.3033 0.700287
\(543\) −32.3033 −1.38627
\(544\) 5.62721 0.241265
\(545\) 5.88666 0.252157
\(546\) 0 0
\(547\) 17.6867 0.756227 0.378113 0.925759i \(-0.376573\pi\)
0.378113 + 0.925759i \(0.376573\pi\)
\(548\) −6.41110 −0.273869
\(549\) −65.1638 −2.78112
\(550\) 0 0
\(551\) 11.9406 0.508685
\(552\) 14.0383 0.597510
\(553\) 9.77886 0.415840
\(554\) −13.3622 −0.567707
\(555\) 14.0383 0.595893
\(556\) 9.77886 0.414716
\(557\) 6.94108 0.294103 0.147051 0.989129i \(-0.453022\pi\)
0.147051 + 0.989129i \(0.453022\pi\)
\(558\) −20.2056 −0.855369
\(559\) 0 0
\(560\) 1.00000 0.0422577
\(561\) 0 0
\(562\) 27.5577 1.16245
\(563\) 27.1355 1.14363 0.571814 0.820384i \(-0.306240\pi\)
0.571814 + 0.820384i \(0.306240\pi\)
\(564\) 36.7144 1.54596
\(565\) −5.25443 −0.221055
\(566\) 11.8922 0.499867
\(567\) 15.0383 0.631550
\(568\) −8.41110 −0.352922
\(569\) −6.31335 −0.264669 −0.132335 0.991205i \(-0.542247\pi\)
−0.132335 + 0.991205i \(0.542247\pi\)
\(570\) −14.6761 −0.614714
\(571\) 37.5366 1.57086 0.785429 0.618952i \(-0.212442\pi\)
0.785429 + 0.618952i \(0.212442\pi\)
\(572\) 0 0
\(573\) 45.3522 1.89461
\(574\) −7.30833 −0.305044
\(575\) 4.52444 0.188682
\(576\) 6.62721 0.276134
\(577\) −8.11334 −0.337763 −0.168881 0.985636i \(-0.554015\pi\)
−0.168881 + 0.985636i \(0.554015\pi\)
\(578\) 14.6655 0.610005
\(579\) 79.1155 3.28793
\(580\) −2.52444 −0.104822
\(581\) −7.25443 −0.300964
\(582\) 51.2716 2.12528
\(583\) 0 0
\(584\) −4.57834 −0.189453
\(585\) 0 0
\(586\) −14.3133 −0.591279
\(587\) −45.7961 −1.89021 −0.945103 0.326774i \(-0.894039\pi\)
−0.945103 + 0.326774i \(0.894039\pi\)
\(588\) 3.10278 0.127956
\(589\) 14.4211 0.594213
\(590\) −7.62721 −0.314007
\(591\) −18.2822 −0.752028
\(592\) 4.52444 0.185953
\(593\) 46.3416 1.90302 0.951511 0.307615i \(-0.0995308\pi\)
0.951511 + 0.307615i \(0.0995308\pi\)
\(594\) 0 0
\(595\) 5.62721 0.230693
\(596\) −1.88666 −0.0772807
\(597\) 49.4288 2.02299
\(598\) 0 0
\(599\) 15.5889 0.636945 0.318473 0.947932i \(-0.396830\pi\)
0.318473 + 0.947932i \(0.396830\pi\)
\(600\) 3.10278 0.126670
\(601\) −23.9461 −0.976782 −0.488391 0.872625i \(-0.662416\pi\)
−0.488391 + 0.872625i \(0.662416\pi\)
\(602\) 0.578337 0.0235713
\(603\) −87.8399 −3.57712
\(604\) 19.9844 0.813154
\(605\) 0 0
\(606\) −16.8222 −0.683355
\(607\) −8.24386 −0.334608 −0.167304 0.985905i \(-0.553506\pi\)
−0.167304 + 0.985905i \(0.553506\pi\)
\(608\) −4.72999 −0.191826
\(609\) −7.83276 −0.317400
\(610\) −9.83276 −0.398117
\(611\) 0 0
\(612\) 37.2927 1.50747
\(613\) −27.0177 −1.09123 −0.545617 0.838034i \(-0.683705\pi\)
−0.545617 + 0.838034i \(0.683705\pi\)
\(614\) 20.3033 0.819375
\(615\) −22.6761 −0.914388
\(616\) 0 0
\(617\) 16.4011 0.660282 0.330141 0.943932i \(-0.392904\pi\)
0.330141 + 0.943932i \(0.392904\pi\)
\(618\) −17.4600 −0.702343
\(619\) −0.146111 −0.00587272 −0.00293636 0.999996i \(-0.500935\pi\)
−0.00293636 + 0.999996i \(0.500935\pi\)
\(620\) −3.04888 −0.122446
\(621\) 50.9200 2.04335
\(622\) −0.951124 −0.0381366
\(623\) 14.4111 0.577369
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −10.0922 −0.403366
\(627\) 0 0
\(628\) 9.36222 0.373593
\(629\) 25.4600 1.01516
\(630\) 6.62721 0.264034
\(631\) 44.6832 1.77881 0.889406 0.457119i \(-0.151119\pi\)
0.889406 + 0.457119i \(0.151119\pi\)
\(632\) 9.77886 0.388982
\(633\) −54.5089 −2.16653
\(634\) −5.98441 −0.237671
\(635\) −20.7144 −0.822026
\(636\) −17.2927 −0.685702
\(637\) 0 0
\(638\) 0 0
\(639\) −55.7422 −2.20513
\(640\) 1.00000 0.0395285
\(641\) −37.1355 −1.46677 −0.733383 0.679816i \(-0.762060\pi\)
−0.733383 + 0.679816i \(0.762060\pi\)
\(642\) −36.7144 −1.44900
\(643\) −28.1205 −1.10896 −0.554482 0.832196i \(-0.687083\pi\)
−0.554482 + 0.832196i \(0.687083\pi\)
\(644\) 4.52444 0.178288
\(645\) 1.79445 0.0706564
\(646\) −26.6167 −1.04722
\(647\) −30.4494 −1.19709 −0.598545 0.801089i \(-0.704254\pi\)
−0.598545 + 0.801089i \(0.704254\pi\)
\(648\) 15.0383 0.590761
\(649\) 0 0
\(650\) 0 0
\(651\) −9.45998 −0.370766
\(652\) 17.2544 0.675735
\(653\) 32.9355 1.28887 0.644434 0.764660i \(-0.277093\pi\)
0.644434 + 0.764660i \(0.277093\pi\)
\(654\) 18.2650 0.714218
\(655\) 17.7789 0.694678
\(656\) −7.30833 −0.285342
\(657\) −30.3416 −1.18374
\(658\) 11.8328 0.461289
\(659\) −27.8922 −1.08653 −0.543263 0.839563i \(-0.682811\pi\)
−0.543263 + 0.839563i \(0.682811\pi\)
\(660\) 0 0
\(661\) −29.0388 −1.12948 −0.564740 0.825269i \(-0.691023\pi\)
−0.564740 + 0.825269i \(0.691023\pi\)
\(662\) 17.2927 0.672101
\(663\) 0 0
\(664\) −7.25443 −0.281526
\(665\) −4.72999 −0.183421
\(666\) 29.9844 1.16187
\(667\) −11.4217 −0.442249
\(668\) −17.5678 −0.679718
\(669\) 29.8711 1.15488
\(670\) −13.2544 −0.512063
\(671\) 0 0
\(672\) 3.10278 0.119692
\(673\) 11.6867 0.450487 0.225244 0.974302i \(-0.427682\pi\)
0.225244 + 0.974302i \(0.427682\pi\)
\(674\) −27.1567 −1.04604
\(675\) 11.2544 0.433183
\(676\) −13.0000 −0.500000
\(677\) 31.1638 1.19772 0.598861 0.800853i \(-0.295620\pi\)
0.598861 + 0.800853i \(0.295620\pi\)
\(678\) −16.3033 −0.626125
\(679\) 16.5244 0.634150
\(680\) 5.62721 0.215794
\(681\) −57.7633 −2.21349
\(682\) 0 0
\(683\) 12.5400 0.479831 0.239915 0.970794i \(-0.422880\pi\)
0.239915 + 0.970794i \(0.422880\pi\)
\(684\) −31.3466 −1.19857
\(685\) −6.41110 −0.244956
\(686\) 1.00000 0.0381802
\(687\) −33.7633 −1.28815
\(688\) 0.578337 0.0220489
\(689\) 0 0
\(690\) 14.0383 0.534429
\(691\) −25.1638 −0.957277 −0.478638 0.878012i \(-0.658869\pi\)
−0.478638 + 0.878012i \(0.658869\pi\)
\(692\) −10.6761 −0.405844
\(693\) 0 0
\(694\) −31.0872 −1.18005
\(695\) 9.77886 0.370933
\(696\) −7.83276 −0.296900
\(697\) −41.1255 −1.55774
\(698\) −21.7250 −0.822302
\(699\) −39.8500 −1.50726
\(700\) 1.00000 0.0377964
\(701\) 13.1411 0.496332 0.248166 0.968718i \(-0.420172\pi\)
0.248166 + 0.968718i \(0.420172\pi\)
\(702\) 0 0
\(703\) −21.4005 −0.807137
\(704\) 0 0
\(705\) 36.7144 1.38274
\(706\) 8.22114 0.309407
\(707\) −5.42166 −0.203903
\(708\) −23.6655 −0.889405
\(709\) 25.3311 0.951328 0.475664 0.879627i \(-0.342208\pi\)
0.475664 + 0.879627i \(0.342208\pi\)
\(710\) −8.41110 −0.315663
\(711\) 64.8066 2.43044
\(712\) 14.4111 0.540079
\(713\) −13.7944 −0.516606
\(714\) 17.4600 0.653423
\(715\) 0 0
\(716\) −4.47054 −0.167072
\(717\) 80.3205 2.99962
\(718\) −14.8277 −0.553366
\(719\) −43.2616 −1.61338 −0.806692 0.590972i \(-0.798744\pi\)
−0.806692 + 0.590972i \(0.798744\pi\)
\(720\) 6.62721 0.246982
\(721\) −5.62721 −0.209568
\(722\) 3.37279 0.125522
\(723\) −41.9305 −1.55941
\(724\) −10.4111 −0.386925
\(725\) −2.52444 −0.0937553
\(726\) 0 0
\(727\) −47.6938 −1.76886 −0.884432 0.466668i \(-0.845454\pi\)
−0.884432 + 0.466668i \(0.845454\pi\)
\(728\) 0 0
\(729\) −5.09775 −0.188806
\(730\) −4.57834 −0.169452
\(731\) 3.25443 0.120369
\(732\) −30.5089 −1.12764
\(733\) −32.7738 −1.21053 −0.605265 0.796024i \(-0.706933\pi\)
−0.605265 + 0.796024i \(0.706933\pi\)
\(734\) −23.9406 −0.883662
\(735\) 3.10278 0.114448
\(736\) 4.52444 0.166773
\(737\) 0 0
\(738\) −48.4338 −1.78287
\(739\) 34.5089 1.26943 0.634714 0.772747i \(-0.281118\pi\)
0.634714 + 0.772747i \(0.281118\pi\)
\(740\) 4.52444 0.166322
\(741\) 0 0
\(742\) −5.57331 −0.204603
\(743\) 34.2822 1.25769 0.628846 0.777530i \(-0.283528\pi\)
0.628846 + 0.777530i \(0.283528\pi\)
\(744\) −9.45998 −0.346820
\(745\) −1.88666 −0.0691220
\(746\) 3.04888 0.111627
\(747\) −48.0766 −1.75903
\(748\) 0 0
\(749\) −11.8328 −0.432360
\(750\) 3.10278 0.113297
\(751\) −39.1355 −1.42808 −0.714038 0.700107i \(-0.753136\pi\)
−0.714038 + 0.700107i \(0.753136\pi\)
\(752\) 11.8328 0.431496
\(753\) 83.7422 3.05173
\(754\) 0 0
\(755\) 19.9844 0.727307
\(756\) 11.2544 0.409320
\(757\) −25.7577 −0.936181 −0.468090 0.883681i \(-0.655058\pi\)
−0.468090 + 0.883681i \(0.655058\pi\)
\(758\) −27.6655 −1.00486
\(759\) 0 0
\(760\) −4.72999 −0.171575
\(761\) −1.74055 −0.0630949 −0.0315475 0.999502i \(-0.510044\pi\)
−0.0315475 + 0.999502i \(0.510044\pi\)
\(762\) −64.2721 −2.32833
\(763\) 5.88666 0.213111
\(764\) 14.6167 0.528812
\(765\) 37.2927 1.34832
\(766\) −7.52946 −0.272050
\(767\) 0 0
\(768\) 3.10278 0.111962
\(769\) 36.8449 1.32866 0.664331 0.747438i \(-0.268717\pi\)
0.664331 + 0.747438i \(0.268717\pi\)
\(770\) 0 0
\(771\) −8.80501 −0.317105
\(772\) 25.4983 0.917704
\(773\) −33.4499 −1.20311 −0.601555 0.798831i \(-0.705452\pi\)
−0.601555 + 0.798831i \(0.705452\pi\)
\(774\) 3.83276 0.137766
\(775\) −3.04888 −0.109519
\(776\) 16.5244 0.593193
\(777\) 14.0383 0.503622
\(778\) −27.4600 −0.984488
\(779\) 34.5683 1.23854
\(780\) 0 0
\(781\) 0 0
\(782\) 25.4600 0.910447
\(783\) −28.4111 −1.01533
\(784\) 1.00000 0.0357143
\(785\) 9.36222 0.334152
\(786\) 55.1638 1.96763
\(787\) −6.72445 −0.239701 −0.119850 0.992792i \(-0.538241\pi\)
−0.119850 + 0.992792i \(0.538241\pi\)
\(788\) −5.89220 −0.209901
\(789\) 9.15667 0.325986
\(790\) 9.77886 0.347916
\(791\) −5.25443 −0.186826
\(792\) 0 0
\(793\) 0 0
\(794\) 27.4600 0.974518
\(795\) −17.2927 −0.613310
\(796\) 15.9305 0.564642
\(797\) −31.2444 −1.10673 −0.553366 0.832938i \(-0.686657\pi\)
−0.553366 + 0.832938i \(0.686657\pi\)
\(798\) −14.6761 −0.519528
\(799\) 66.5855 2.35562
\(800\) 1.00000 0.0353553
\(801\) 95.5054 3.37452
\(802\) 1.52946 0.0540072
\(803\) 0 0
\(804\) −41.1255 −1.45038
\(805\) 4.52444 0.159465
\(806\) 0 0
\(807\) −8.94108 −0.314741
\(808\) −5.42166 −0.190733
\(809\) 44.7910 1.57477 0.787384 0.616462i \(-0.211435\pi\)
0.787384 + 0.616462i \(0.211435\pi\)
\(810\) 15.0383 0.528392
\(811\) 15.3466 0.538893 0.269447 0.963015i \(-0.413159\pi\)
0.269447 + 0.963015i \(0.413159\pi\)
\(812\) −2.52444 −0.0885904
\(813\) 50.5855 1.77411
\(814\) 0 0
\(815\) 17.2544 0.604396
\(816\) 17.4600 0.611221
\(817\) −2.73553 −0.0957040
\(818\) 34.6705 1.21223
\(819\) 0 0
\(820\) −7.30833 −0.255218
\(821\) 10.0822 0.351870 0.175935 0.984402i \(-0.443705\pi\)
0.175935 + 0.984402i \(0.443705\pi\)
\(822\) −19.8922 −0.693820
\(823\) 17.2388 0.600908 0.300454 0.953796i \(-0.402862\pi\)
0.300454 + 0.953796i \(0.402862\pi\)
\(824\) −5.62721 −0.196033
\(825\) 0 0
\(826\) −7.62721 −0.265385
\(827\) −55.7422 −1.93834 −0.969172 0.246384i \(-0.920758\pi\)
−0.969172 + 0.246384i \(0.920758\pi\)
\(828\) 29.9844 1.04203
\(829\) −32.8605 −1.14129 −0.570646 0.821196i \(-0.693307\pi\)
−0.570646 + 0.821196i \(0.693307\pi\)
\(830\) −7.25443 −0.251805
\(831\) −41.4600 −1.43823
\(832\) 0 0
\(833\) 5.62721 0.194971
\(834\) 30.3416 1.05064
\(835\) −17.5678 −0.607958
\(836\) 0 0
\(837\) −34.3133 −1.18604
\(838\) 25.4217 0.878177
\(839\) 6.71440 0.231807 0.115903 0.993260i \(-0.463024\pi\)
0.115903 + 0.993260i \(0.463024\pi\)
\(840\) 3.10278 0.107056
\(841\) −22.6272 −0.780249
\(842\) −13.7733 −0.474660
\(843\) 85.5054 2.94496
\(844\) −17.5678 −0.604708
\(845\) −13.0000 −0.447214
\(846\) 78.4182 2.69607
\(847\) 0 0
\(848\) −5.57331 −0.191388
\(849\) 36.8988 1.26636
\(850\) 5.62721 0.193012
\(851\) 20.4705 0.701721
\(852\) −26.0978 −0.894094
\(853\) −3.01056 −0.103080 −0.0515399 0.998671i \(-0.516413\pi\)
−0.0515399 + 0.998671i \(0.516413\pi\)
\(854\) −9.83276 −0.336470
\(855\) −31.3466 −1.07203
\(856\) −11.8328 −0.404436
\(857\) −17.8116 −0.608434 −0.304217 0.952603i \(-0.598395\pi\)
−0.304217 + 0.952603i \(0.598395\pi\)
\(858\) 0 0
\(859\) −44.3416 −1.51292 −0.756458 0.654042i \(-0.773072\pi\)
−0.756458 + 0.654042i \(0.773072\pi\)
\(860\) 0.578337 0.0197211
\(861\) −22.6761 −0.772799
\(862\) −29.2489 −0.996221
\(863\) −27.1099 −0.922832 −0.461416 0.887184i \(-0.652658\pi\)
−0.461416 + 0.887184i \(0.652658\pi\)
\(864\) 11.2544 0.382883
\(865\) −10.6761 −0.362998
\(866\) −9.04334 −0.307305
\(867\) 45.5038 1.54539
\(868\) −3.04888 −0.103486
\(869\) 0 0
\(870\) −7.83276 −0.265556
\(871\) 0 0
\(872\) 5.88666 0.199348
\(873\) 109.511 3.70638
\(874\) −21.4005 −0.723884
\(875\) 1.00000 0.0338062
\(876\) −14.2056 −0.479961
\(877\) −40.9511 −1.38282 −0.691411 0.722462i \(-0.743010\pi\)
−0.691411 + 0.722462i \(0.743010\pi\)
\(878\) −36.7144 −1.23905
\(879\) −44.4111 −1.49795
\(880\) 0 0
\(881\) 53.3311 1.79677 0.898384 0.439210i \(-0.144742\pi\)
0.898384 + 0.439210i \(0.144742\pi\)
\(882\) 6.62721 0.223150
\(883\) 27.7944 0.935358 0.467679 0.883898i \(-0.345090\pi\)
0.467679 + 0.883898i \(0.345090\pi\)
\(884\) 0 0
\(885\) −23.6655 −0.795508
\(886\) −13.6655 −0.459102
\(887\) −30.2933 −1.01715 −0.508574 0.861018i \(-0.669827\pi\)
−0.508574 + 0.861018i \(0.669827\pi\)
\(888\) 14.0383 0.471095
\(889\) −20.7144 −0.694739
\(890\) 14.4111 0.483061
\(891\) 0 0
\(892\) 9.62721 0.322343
\(893\) −55.9688 −1.87293
\(894\) −5.85389 −0.195783
\(895\) −4.47054 −0.149434
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −18.3517 −0.612403
\(899\) 7.69670 0.256699
\(900\) 6.62721 0.220907
\(901\) −31.3622 −1.04483
\(902\) 0 0
\(903\) 1.79445 0.0597156
\(904\) −5.25443 −0.174760
\(905\) −10.4111 −0.346077
\(906\) 62.0071 2.06005
\(907\) −39.8711 −1.32390 −0.661949 0.749549i \(-0.730270\pi\)
−0.661949 + 0.749549i \(0.730270\pi\)
\(908\) −18.6167 −0.617815
\(909\) −35.9305 −1.19174
\(910\) 0 0
\(911\) 19.7733 0.655119 0.327560 0.944830i \(-0.393774\pi\)
0.327560 + 0.944830i \(0.393774\pi\)
\(912\) −14.6761 −0.485974
\(913\) 0 0
\(914\) 15.1567 0.501338
\(915\) −30.5089 −1.00859
\(916\) −10.8816 −0.359539
\(917\) 17.7789 0.587110
\(918\) 63.3311 2.09024
\(919\) 17.8100 0.587499 0.293749 0.955882i \(-0.405097\pi\)
0.293749 + 0.955882i \(0.405097\pi\)
\(920\) 4.52444 0.149166
\(921\) 62.9966 2.07581
\(922\) 9.52946 0.313836
\(923\) 0 0
\(924\) 0 0
\(925\) 4.52444 0.148763
\(926\) 16.9355 0.556536
\(927\) −37.2927 −1.22485
\(928\) −2.52444 −0.0828687
\(929\) 24.7355 0.811546 0.405773 0.913974i \(-0.367002\pi\)
0.405773 + 0.913974i \(0.367002\pi\)
\(930\) −9.45998 −0.310205
\(931\) −4.72999 −0.155019
\(932\) −12.8433 −0.420697
\(933\) −2.95112 −0.0966155
\(934\) 16.0439 0.524971
\(935\) 0 0
\(936\) 0 0
\(937\) 3.52946 0.115302 0.0576512 0.998337i \(-0.481639\pi\)
0.0576512 + 0.998337i \(0.481639\pi\)
\(938\) −13.2544 −0.432772
\(939\) −31.3139 −1.02189
\(940\) 11.8328 0.385942
\(941\) −49.4217 −1.61110 −0.805550 0.592528i \(-0.798130\pi\)
−0.805550 + 0.592528i \(0.798130\pi\)
\(942\) 29.0489 0.946464
\(943\) −33.0661 −1.07678
\(944\) −7.62721 −0.248245
\(945\) 11.2544 0.366107
\(946\) 0 0
\(947\) 30.7144 0.998084 0.499042 0.866578i \(-0.333685\pi\)
0.499042 + 0.866578i \(0.333685\pi\)
\(948\) 30.3416 0.985450
\(949\) 0 0
\(950\) −4.72999 −0.153461
\(951\) −18.5683 −0.602118
\(952\) 5.62721 0.182379
\(953\) 24.7527 0.801819 0.400910 0.916118i \(-0.368694\pi\)
0.400910 + 0.916118i \(0.368694\pi\)
\(954\) −36.9355 −1.19583
\(955\) 14.6167 0.472984
\(956\) 25.8867 0.837234
\(957\) 0 0
\(958\) −12.4111 −0.400984
\(959\) −6.41110 −0.207025
\(960\) 3.10278 0.100142
\(961\) −21.7044 −0.700141
\(962\) 0 0
\(963\) −78.4182 −2.52699
\(964\) −13.5139 −0.435253
\(965\) 25.4983 0.820819
\(966\) 14.0383 0.451675
\(967\) 34.2822 1.10244 0.551220 0.834360i \(-0.314162\pi\)
0.551220 + 0.834360i \(0.314162\pi\)
\(968\) 0 0
\(969\) −82.5855 −2.65303
\(970\) 16.5244 0.530568
\(971\) −48.0383 −1.54162 −0.770811 0.637063i \(-0.780149\pi\)
−0.770811 + 0.637063i \(0.780149\pi\)
\(972\) 12.8972 0.413679
\(973\) 9.77886 0.313496
\(974\) 1.37781 0.0441479
\(975\) 0 0
\(976\) −9.83276 −0.314739
\(977\) 27.5678 0.881971 0.440986 0.897514i \(-0.354629\pi\)
0.440986 + 0.897514i \(0.354629\pi\)
\(978\) 53.5366 1.71191
\(979\) 0 0
\(980\) 1.00000 0.0319438
\(981\) 39.0122 1.24556
\(982\) 6.31335 0.201467
\(983\) 56.3316 1.79670 0.898349 0.439282i \(-0.144767\pi\)
0.898349 + 0.439282i \(0.144767\pi\)
\(984\) −22.6761 −0.722887
\(985\) −5.89220 −0.187741
\(986\) −14.2056 −0.452397
\(987\) 36.7144 1.16863
\(988\) 0 0
\(989\) 2.61665 0.0832046
\(990\) 0 0
\(991\) 4.37993 0.139133 0.0695665 0.997577i \(-0.477838\pi\)
0.0695665 + 0.997577i \(0.477838\pi\)
\(992\) −3.04888 −0.0968019
\(993\) 53.6555 1.70271
\(994\) −8.41110 −0.266784
\(995\) 15.9305 0.505031
\(996\) −22.5089 −0.713220
\(997\) −27.7139 −0.877708 −0.438854 0.898558i \(-0.644615\pi\)
−0.438854 + 0.898558i \(0.644615\pi\)
\(998\) 10.9794 0.347547
\(999\) 50.9200 1.61104
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 8470.2.a.cn.1.3 yes 3
11.10 odd 2 8470.2.a.ch.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8470.2.a.ch.1.3 3 11.10 odd 2
8470.2.a.cn.1.3 yes 3 1.1 even 1 trivial