Properties

Label 950.2.a.l.1.3
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.993.1
Defining polynomial: \(x^{3} - x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.25342\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +3.25342 q^{3} +1.00000 q^{4} +3.25342 q^{6} -0.0778929 q^{7} +1.00000 q^{8} +7.58473 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +3.25342 q^{3} +1.00000 q^{4} +3.25342 q^{6} -0.0778929 q^{7} +1.00000 q^{8} +7.58473 q^{9} -4.50684 q^{11} +3.25342 q^{12} -5.33131 q^{13} -0.0778929 q^{14} +1.00000 q^{16} +7.33131 q^{17} +7.58473 q^{18} +1.00000 q^{19} -0.253418 q^{21} -4.50684 q^{22} +3.40920 q^{23} +3.25342 q^{24} -5.33131 q^{26} +14.9160 q^{27} -0.0778929 q^{28} -1.33131 q^{29} -2.50684 q^{31} +1.00000 q^{32} -14.6626 q^{33} +7.33131 q^{34} +7.58473 q^{36} -5.50684 q^{37} +1.00000 q^{38} -17.3450 q^{39} -0.253418 q^{42} +0.506836 q^{43} -4.50684 q^{44} +3.40920 q^{46} -5.66262 q^{47} +3.25342 q^{48} -6.99393 q^{49} +23.8518 q^{51} -5.33131 q^{52} -12.9358 q^{53} +14.9160 q^{54} -0.0778929 q^{56} +3.25342 q^{57} -1.33131 q^{58} +7.56499 q^{59} -2.15579 q^{61} -2.50684 q^{62} -0.590796 q^{63} +1.00000 q^{64} -14.6626 q^{66} -4.58473 q^{67} +7.33131 q^{68} +11.0916 q^{69} -10.8579 q^{71} +7.58473 q^{72} -5.09763 q^{73} -5.50684 q^{74} +1.00000 q^{76} +0.351050 q^{77} -17.3450 q^{78} +17.0137 q^{79} +25.7739 q^{81} -13.1695 q^{83} -0.253418 q^{84} +0.506836 q^{86} -4.33131 q^{87} -4.50684 q^{88} +15.0137 q^{89} +0.415271 q^{91} +3.40920 q^{92} -8.15579 q^{93} -5.66262 q^{94} +3.25342 q^{96} +7.67629 q^{97} -6.99393 q^{98} -34.1831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + 2q^{3} + 3q^{4} + 2q^{6} + 2q^{7} + 3q^{8} + 5q^{9} + 2q^{11} + 2q^{12} - 6q^{13} + 2q^{14} + 3q^{16} + 12q^{17} + 5q^{18} + 3q^{19} + 7q^{21} + 2q^{22} - 2q^{23} + 2q^{24} - 6q^{26} + 17q^{27} + 2q^{28} + 6q^{29} + 8q^{31} + 3q^{32} - 24q^{33} + 12q^{34} + 5q^{36} - q^{37} + 3q^{38} - 11q^{39} + 7q^{42} - 14q^{43} + 2q^{44} - 2q^{46} + 3q^{47} + 2q^{48} + 9q^{49} + 15q^{51} - 6q^{52} - 10q^{53} + 17q^{54} + 2q^{56} + 2q^{57} + 6q^{58} + 6q^{59} - 2q^{61} + 8q^{62} - 14q^{63} + 3q^{64} - 24q^{66} + 4q^{67} + 12q^{68} - 6q^{71} + 5q^{72} - 12q^{73} - q^{74} + 3q^{76} - 10q^{77} - 11q^{78} + 20q^{79} + 23q^{81} - 4q^{83} + 7q^{84} - 14q^{86} - 3q^{87} + 2q^{88} + 14q^{89} + 19q^{91} - 2q^{92} - 20q^{93} + 3q^{94} + 2q^{96} - 28q^{97} + 9q^{98} - 36q^{99} + O(q^{100}) \)

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
\(3\) 3.25342 1.87836 0.939181 0.343423i \(-0.111586\pi\)
0.939181 + 0.343423i \(0.111586\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 3.25342 1.32820
\(7\) −0.0778929 −0.0294407 −0.0147204 0.999892i \(-0.504686\pi\)
−0.0147204 + 0.999892i \(0.504686\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.58473 2.52824
\(10\) 0 0
\(11\) −4.50684 −1.35886 −0.679431 0.733739i \(-0.737773\pi\)
−0.679431 + 0.733739i \(0.737773\pi\)
\(12\) 3.25342 0.939181
\(13\) −5.33131 −1.47864 −0.739320 0.673354i \(-0.764853\pi\)
−0.739320 + 0.673354i \(0.764853\pi\)
\(14\) −0.0778929 −0.0208177
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.33131 1.77810 0.889052 0.457806i \(-0.151365\pi\)
0.889052 + 0.457806i \(0.151365\pi\)
\(18\) 7.58473 1.78774
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −0.253418 −0.0553003
\(22\) −4.50684 −0.960861
\(23\) 3.40920 0.710868 0.355434 0.934701i \(-0.384333\pi\)
0.355434 + 0.934701i \(0.384333\pi\)
\(24\) 3.25342 0.664101
\(25\) 0 0
\(26\) −5.33131 −1.04556
\(27\) 14.9160 2.87059
\(28\) −0.0778929 −0.0147204
\(29\) −1.33131 −0.247218 −0.123609 0.992331i \(-0.539447\pi\)
−0.123609 + 0.992331i \(0.539447\pi\)
\(30\) 0 0
\(31\) −2.50684 −0.450241 −0.225121 0.974331i \(-0.572278\pi\)
−0.225121 + 0.974331i \(0.572278\pi\)
\(32\) 1.00000 0.176777
\(33\) −14.6626 −2.55243
\(34\) 7.33131 1.25731
\(35\) 0 0
\(36\) 7.58473 1.26412
\(37\) −5.50684 −0.905318 −0.452659 0.891684i \(-0.649525\pi\)
−0.452659 + 0.891684i \(0.649525\pi\)
\(38\) 1.00000 0.162221
\(39\) −17.3450 −2.77742
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −0.253418 −0.0391033
\(43\) 0.506836 0.0772918 0.0386459 0.999253i \(-0.487696\pi\)
0.0386459 + 0.999253i \(0.487696\pi\)
\(44\) −4.50684 −0.679431
\(45\) 0 0
\(46\) 3.40920 0.502660
\(47\) −5.66262 −0.825978 −0.412989 0.910736i \(-0.635515\pi\)
−0.412989 + 0.910736i \(0.635515\pi\)
\(48\) 3.25342 0.469590
\(49\) −6.99393 −0.999133
\(50\) 0 0
\(51\) 23.8518 3.33992
\(52\) −5.33131 −0.739320
\(53\) −12.9358 −1.77687 −0.888433 0.459006i \(-0.848206\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(54\) 14.9160 2.02982
\(55\) 0 0
\(56\) −0.0778929 −0.0104089
\(57\) 3.25342 0.430926
\(58\) −1.33131 −0.174810
\(59\) 7.56499 0.984878 0.492439 0.870347i \(-0.336106\pi\)
0.492439 + 0.870347i \(0.336106\pi\)
\(60\) 0 0
\(61\) −2.15579 −0.276020 −0.138010 0.990431i \(-0.544071\pi\)
−0.138010 + 0.990431i \(0.544071\pi\)
\(62\) −2.50684 −0.318369
\(63\) −0.590796 −0.0744333
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −14.6626 −1.80484
\(67\) −4.58473 −0.560114 −0.280057 0.959983i \(-0.590353\pi\)
−0.280057 + 0.959983i \(0.590353\pi\)
\(68\) 7.33131 0.889052
\(69\) 11.0916 1.33527
\(70\) 0 0
\(71\) −10.8579 −1.28859 −0.644297 0.764775i \(-0.722850\pi\)
−0.644297 + 0.764775i \(0.722850\pi\)
\(72\) 7.58473 0.893869
\(73\) −5.09763 −0.596633 −0.298316 0.954467i \(-0.596425\pi\)
−0.298316 + 0.954467i \(0.596425\pi\)
\(74\) −5.50684 −0.640157
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 0.351050 0.0400059
\(78\) −17.3450 −1.96393
\(79\) 17.0137 1.91419 0.957094 0.289778i \(-0.0935815\pi\)
0.957094 + 0.289778i \(0.0935815\pi\)
\(80\) 0 0
\(81\) 25.7739 2.86377
\(82\) 0 0
\(83\) −13.1695 −1.44554 −0.722768 0.691091i \(-0.757130\pi\)
−0.722768 + 0.691091i \(0.757130\pi\)
\(84\) −0.253418 −0.0276502
\(85\) 0 0
\(86\) 0.506836 0.0546535
\(87\) −4.33131 −0.464365
\(88\) −4.50684 −0.480430
\(89\) 15.0137 1.59145 0.795723 0.605661i \(-0.207091\pi\)
0.795723 + 0.605661i \(0.207091\pi\)
\(90\) 0 0
\(91\) 0.415271 0.0435322
\(92\) 3.40920 0.355434
\(93\) −8.15579 −0.845716
\(94\) −5.66262 −0.584055
\(95\) 0 0
\(96\) 3.25342 0.332051
\(97\) 7.67629 0.779410 0.389705 0.920940i \(-0.372577\pi\)
0.389705 + 0.920940i \(0.372577\pi\)
\(98\) −6.99393 −0.706494
\(99\) −34.1831 −3.43553
\(100\) 0 0
\(101\) −4.15579 −0.413516 −0.206758 0.978392i \(-0.566291\pi\)
−0.206758 + 0.978392i \(0.566291\pi\)
\(102\) 23.8518 2.36168
\(103\) 2.35105 0.231656 0.115828 0.993269i \(-0.463048\pi\)
0.115828 + 0.993269i \(0.463048\pi\)
\(104\) −5.33131 −0.522778
\(105\) 0 0
\(106\) −12.9358 −1.25643
\(107\) −14.0334 −1.35666 −0.678331 0.734757i \(-0.737296\pi\)
−0.678331 + 0.734757i \(0.737296\pi\)
\(108\) 14.9160 1.43530
\(109\) −0.0778929 −0.00746078 −0.00373039 0.999993i \(-0.501187\pi\)
−0.00373039 + 0.999993i \(0.501187\pi\)
\(110\) 0 0
\(111\) −17.9160 −1.70052
\(112\) −0.0778929 −0.00736018
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 3.25342 0.304711
\(115\) 0 0
\(116\) −1.33131 −0.123609
\(117\) −40.4365 −3.73836
\(118\) 7.56499 0.696414
\(119\) −0.571057 −0.0523487
\(120\) 0 0
\(121\) 9.31157 0.846506
\(122\) −2.15579 −0.195176
\(123\) 0 0
\(124\) −2.50684 −0.225121
\(125\) 0 0
\(126\) −0.590796 −0.0526323
\(127\) 17.8321 1.58234 0.791171 0.611596i \(-0.209472\pi\)
0.791171 + 0.611596i \(0.209472\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.64895 0.145182
\(130\) 0 0
\(131\) −1.49316 −0.130458 −0.0652292 0.997870i \(-0.520778\pi\)
−0.0652292 + 0.997870i \(0.520778\pi\)
\(132\) −14.6626 −1.27622
\(133\) −0.0778929 −0.00675417
\(134\) −4.58473 −0.396060
\(135\) 0 0
\(136\) 7.33131 0.628655
\(137\) −8.42894 −0.720133 −0.360067 0.932927i \(-0.617246\pi\)
−0.360067 + 0.932927i \(0.617246\pi\)
\(138\) 11.0916 0.944177
\(139\) 8.81841 0.747968 0.373984 0.927435i \(-0.377992\pi\)
0.373984 + 0.927435i \(0.377992\pi\)
\(140\) 0 0
\(141\) −18.4229 −1.55149
\(142\) −10.8579 −0.911174
\(143\) 24.0273 2.00927
\(144\) 7.58473 0.632061
\(145\) 0 0
\(146\) −5.09763 −0.421883
\(147\) −22.7542 −1.87673
\(148\) −5.50684 −0.452659
\(149\) 17.6763 1.44810 0.724049 0.689748i \(-0.242279\pi\)
0.724049 + 0.689748i \(0.242279\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 1.00000 0.0811107
\(153\) 55.6060 4.49548
\(154\) 0.351050 0.0282884
\(155\) 0 0
\(156\) −17.3450 −1.38871
\(157\) 0.506836 0.0404499 0.0202250 0.999795i \(-0.493562\pi\)
0.0202250 + 0.999795i \(0.493562\pi\)
\(158\) 17.0137 1.35354
\(159\) −42.0855 −3.33760
\(160\) 0 0
\(161\) −0.265553 −0.0209285
\(162\) 25.7739 2.02499
\(163\) 0.830542 0.0650531 0.0325265 0.999471i \(-0.489645\pi\)
0.0325265 + 0.999471i \(0.489645\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −13.1695 −1.02215
\(167\) 16.5068 1.27734 0.638669 0.769482i \(-0.279485\pi\)
0.638669 + 0.769482i \(0.279485\pi\)
\(168\) −0.253418 −0.0195516
\(169\) 15.4229 1.18638
\(170\) 0 0
\(171\) 7.58473 0.580019
\(172\) 0.506836 0.0386459
\(173\) 18.8321 1.43178 0.715888 0.698215i \(-0.246022\pi\)
0.715888 + 0.698215i \(0.246022\pi\)
\(174\) −4.33131 −0.328356
\(175\) 0 0
\(176\) −4.50684 −0.339716
\(177\) 24.6121 1.84996
\(178\) 15.0137 1.12532
\(179\) −7.15579 −0.534849 −0.267424 0.963579i \(-0.586173\pi\)
−0.267424 + 0.963579i \(0.586173\pi\)
\(180\) 0 0
\(181\) 12.5205 0.930642 0.465321 0.885142i \(-0.345939\pi\)
0.465321 + 0.885142i \(0.345939\pi\)
\(182\) 0.415271 0.0307819
\(183\) −7.01367 −0.518466
\(184\) 3.40920 0.251330
\(185\) 0 0
\(186\) −8.15579 −0.598011
\(187\) −33.0410 −2.41620
\(188\) −5.66262 −0.412989
\(189\) −1.16185 −0.0845124
\(190\) 0 0
\(191\) −4.90237 −0.354723 −0.177361 0.984146i \(-0.556756\pi\)
−0.177361 + 0.984146i \(0.556756\pi\)
\(192\) 3.25342 0.234795
\(193\) 18.1558 1.30688 0.653441 0.756977i \(-0.273325\pi\)
0.653441 + 0.756977i \(0.273325\pi\)
\(194\) 7.67629 0.551126
\(195\) 0 0
\(196\) −6.99393 −0.499567
\(197\) −2.98633 −0.212767 −0.106384 0.994325i \(-0.533927\pi\)
−0.106384 + 0.994325i \(0.533927\pi\)
\(198\) −34.1831 −2.42929
\(199\) −3.06422 −0.217217 −0.108608 0.994085i \(-0.534639\pi\)
−0.108608 + 0.994085i \(0.534639\pi\)
\(200\) 0 0
\(201\) −14.9160 −1.05210
\(202\) −4.15579 −0.292400
\(203\) 0.103700 0.00727829
\(204\) 23.8518 1.66996
\(205\) 0 0
\(206\) 2.35105 0.163805
\(207\) 25.8579 1.79725
\(208\) −5.33131 −0.369660
\(209\) −4.50684 −0.311744
\(210\) 0 0
\(211\) 19.2534 1.32546 0.662730 0.748858i \(-0.269398\pi\)
0.662730 + 0.748858i \(0.269398\pi\)
\(212\) −12.9358 −0.888433
\(213\) −35.3252 −2.42045
\(214\) −14.0334 −0.959304
\(215\) 0 0
\(216\) 14.9160 1.01491
\(217\) 0.195265 0.0132554
\(218\) −0.0778929 −0.00527557
\(219\) −16.5847 −1.12069
\(220\) 0 0
\(221\) −39.0855 −2.62918
\(222\) −17.9160 −1.20245
\(223\) −14.5068 −0.971450 −0.485725 0.874112i \(-0.661444\pi\)
−0.485725 + 0.874112i \(0.661444\pi\)
\(224\) −0.0778929 −0.00520444
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −21.5984 −1.43354 −0.716768 0.697312i \(-0.754379\pi\)
−0.716768 + 0.697312i \(0.754379\pi\)
\(228\) 3.25342 0.215463
\(229\) −19.0137 −1.25646 −0.628229 0.778028i \(-0.716220\pi\)
−0.628229 + 0.778028i \(0.716220\pi\)
\(230\) 0 0
\(231\) 1.14211 0.0751456
\(232\) −1.33131 −0.0874048
\(233\) −6.01367 −0.393969 −0.196984 0.980407i \(-0.563115\pi\)
−0.196984 + 0.980407i \(0.563115\pi\)
\(234\) −40.4365 −2.64342
\(235\) 0 0
\(236\) 7.56499 0.492439
\(237\) 55.3526 3.59554
\(238\) −0.571057 −0.0370161
\(239\) 15.4092 0.996739 0.498369 0.866965i \(-0.333932\pi\)
0.498369 + 0.866965i \(0.333932\pi\)
\(240\) 0 0
\(241\) −4.81841 −0.310381 −0.155190 0.987885i \(-0.549599\pi\)
−0.155190 + 0.987885i \(0.549599\pi\)
\(242\) 9.31157 0.598570
\(243\) 39.1052 2.50860
\(244\) −2.15579 −0.138010
\(245\) 0 0
\(246\) 0 0
\(247\) −5.33131 −0.339223
\(248\) −2.50684 −0.159184
\(249\) −42.8458 −2.71524
\(250\) 0 0
\(251\) 1.52051 0.0959736 0.0479868 0.998848i \(-0.484719\pi\)
0.0479868 + 0.998848i \(0.484719\pi\)
\(252\) −0.590796 −0.0372167
\(253\) −15.3647 −0.965972
\(254\) 17.8321 1.11888
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 16.5068 1.02967 0.514834 0.857290i \(-0.327854\pi\)
0.514834 + 0.857290i \(0.327854\pi\)
\(258\) 1.64895 0.102659
\(259\) 0.428943 0.0266532
\(260\) 0 0
\(261\) −10.0976 −0.625028
\(262\) −1.49316 −0.0922480
\(263\) −18.0273 −1.11161 −0.555807 0.831311i \(-0.687591\pi\)
−0.555807 + 0.831311i \(0.687591\pi\)
\(264\) −14.6626 −0.902422
\(265\) 0 0
\(266\) −0.0778929 −0.00477592
\(267\) 48.8458 2.98931
\(268\) −4.58473 −0.280057
\(269\) 20.2089 1.23216 0.616080 0.787683i \(-0.288720\pi\)
0.616080 + 0.787683i \(0.288720\pi\)
\(270\) 0 0
\(271\) 6.08396 0.369574 0.184787 0.982779i \(-0.440840\pi\)
0.184787 + 0.982779i \(0.440840\pi\)
\(272\) 7.33131 0.444526
\(273\) 1.35105 0.0817693
\(274\) −8.42894 −0.509211
\(275\) 0 0
\(276\) 11.0916 0.667634
\(277\) −31.3647 −1.88452 −0.942262 0.334877i \(-0.891305\pi\)
−0.942262 + 0.334877i \(0.891305\pi\)
\(278\) 8.81841 0.528893
\(279\) −19.0137 −1.13832
\(280\) 0 0
\(281\) 11.3252 0.675607 0.337804 0.941217i \(-0.390316\pi\)
0.337804 + 0.941217i \(0.390316\pi\)
\(282\) −18.4229 −1.09707
\(283\) 26.1437 1.55408 0.777039 0.629452i \(-0.216721\pi\)
0.777039 + 0.629452i \(0.216721\pi\)
\(284\) −10.8579 −0.644297
\(285\) 0 0
\(286\) 24.0273 1.42077
\(287\) 0 0
\(288\) 7.58473 0.446934
\(289\) 36.7481 2.16165
\(290\) 0 0
\(291\) 24.9742 1.46401
\(292\) −5.09763 −0.298316
\(293\) 1.33131 0.0777760 0.0388880 0.999244i \(-0.487618\pi\)
0.0388880 + 0.999244i \(0.487618\pi\)
\(294\) −22.7542 −1.32705
\(295\) 0 0
\(296\) −5.50684 −0.320078
\(297\) −67.2241 −3.90074
\(298\) 17.6763 1.02396
\(299\) −18.1755 −1.05112
\(300\) 0 0
\(301\) −0.0394789 −0.00227553
\(302\) 20.0000 1.15087
\(303\) −13.5205 −0.776733
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 55.6060 3.17878
\(307\) −2.84421 −0.162328 −0.0811639 0.996701i \(-0.525864\pi\)
−0.0811639 + 0.996701i \(0.525864\pi\)
\(308\) 0.351050 0.0200030
\(309\) 7.64895 0.435134
\(310\) 0 0
\(311\) −16.3895 −0.929361 −0.464681 0.885478i \(-0.653831\pi\)
−0.464681 + 0.885478i \(0.653831\pi\)
\(312\) −17.3450 −0.981966
\(313\) −21.0471 −1.18965 −0.594826 0.803855i \(-0.702779\pi\)
−0.594826 + 0.803855i \(0.702779\pi\)
\(314\) 0.506836 0.0286024
\(315\) 0 0
\(316\) 17.0137 0.957094
\(317\) −30.8902 −1.73497 −0.867484 0.497465i \(-0.834264\pi\)
−0.867484 + 0.497465i \(0.834264\pi\)
\(318\) −42.0855 −2.36004
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) −45.6566 −2.54830
\(322\) −0.265553 −0.0147987
\(323\) 7.33131 0.407925
\(324\) 25.7739 1.43188
\(325\) 0 0
\(326\) 0.830542 0.0459995
\(327\) −0.253418 −0.0140140
\(328\) 0 0
\(329\) 0.441078 0.0243174
\(330\) 0 0
\(331\) 28.3845 1.56015 0.780076 0.625685i \(-0.215181\pi\)
0.780076 + 0.625685i \(0.215181\pi\)
\(332\) −13.1695 −0.722768
\(333\) −41.7679 −2.28886
\(334\) 16.5068 0.903214
\(335\) 0 0
\(336\) −0.253418 −0.0138251
\(337\) −17.8716 −0.973526 −0.486763 0.873534i \(-0.661822\pi\)
−0.486763 + 0.873534i \(0.661822\pi\)
\(338\) 15.4229 0.838894
\(339\) −19.5205 −1.06021
\(340\) 0 0
\(341\) 11.2979 0.611816
\(342\) 7.58473 0.410135
\(343\) 1.09003 0.0588560
\(344\) 0.506836 0.0273268
\(345\) 0 0
\(346\) 18.8321 1.01242
\(347\) 33.0410 1.77373 0.886867 0.462024i \(-0.152877\pi\)
0.886867 + 0.462024i \(0.152877\pi\)
\(348\) −4.33131 −0.232183
\(349\) −19.7158 −1.05536 −0.527681 0.849443i \(-0.676938\pi\)
−0.527681 + 0.849443i \(0.676938\pi\)
\(350\) 0 0
\(351\) −79.5220 −4.24457
\(352\) −4.50684 −0.240215
\(353\) −5.90997 −0.314556 −0.157278 0.987554i \(-0.550272\pi\)
−0.157278 + 0.987554i \(0.550272\pi\)
\(354\) 24.6121 1.30812
\(355\) 0 0
\(356\) 15.0137 0.795723
\(357\) −1.85789 −0.0983298
\(358\) −7.15579 −0.378195
\(359\) −7.00760 −0.369847 −0.184924 0.982753i \(-0.559204\pi\)
−0.184924 + 0.982753i \(0.559204\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 12.5205 0.658063
\(363\) 30.2944 1.59005
\(364\) 0.415271 0.0217661
\(365\) 0 0
\(366\) −7.01367 −0.366611
\(367\) 17.7158 0.924756 0.462378 0.886683i \(-0.346996\pi\)
0.462378 + 0.886683i \(0.346996\pi\)
\(368\) 3.40920 0.177717
\(369\) 0 0
\(370\) 0 0
\(371\) 1.00760 0.0523122
\(372\) −8.15579 −0.422858
\(373\) 15.4487 0.799902 0.399951 0.916536i \(-0.369027\pi\)
0.399951 + 0.916536i \(0.369027\pi\)
\(374\) −33.0410 −1.70851
\(375\) 0 0
\(376\) −5.66262 −0.292027
\(377\) 7.09763 0.365547
\(378\) −1.16185 −0.0597593
\(379\) 34.4563 1.76990 0.884950 0.465685i \(-0.154192\pi\)
0.884950 + 0.465685i \(0.154192\pi\)
\(380\) 0 0
\(381\) 58.0152 2.97221
\(382\) −4.90237 −0.250827
\(383\) −12.0273 −0.614569 −0.307284 0.951618i \(-0.599420\pi\)
−0.307284 + 0.951618i \(0.599420\pi\)
\(384\) 3.25342 0.166025
\(385\) 0 0
\(386\) 18.1558 0.924105
\(387\) 3.84421 0.195412
\(388\) 7.67629 0.389705
\(389\) −15.3647 −0.779022 −0.389511 0.921022i \(-0.627356\pi\)
−0.389511 + 0.921022i \(0.627356\pi\)
\(390\) 0 0
\(391\) 24.9939 1.26400
\(392\) −6.99393 −0.353247
\(393\) −4.85789 −0.245048
\(394\) −2.98633 −0.150449
\(395\) 0 0
\(396\) −34.1831 −1.71777
\(397\) 1.32524 0.0665121 0.0332560 0.999447i \(-0.489412\pi\)
0.0332560 + 0.999447i \(0.489412\pi\)
\(398\) −3.06422 −0.153596
\(399\) −0.253418 −0.0126868
\(400\) 0 0
\(401\) −6.46736 −0.322964 −0.161482 0.986876i \(-0.551627\pi\)
−0.161482 + 0.986876i \(0.551627\pi\)
\(402\) −14.9160 −0.743944
\(403\) 13.3647 0.665744
\(404\) −4.15579 −0.206758
\(405\) 0 0
\(406\) 0.103700 0.00514653
\(407\) 24.8184 1.23020
\(408\) 23.8518 1.18084
\(409\) −1.36472 −0.0674812 −0.0337406 0.999431i \(-0.510742\pi\)
−0.0337406 + 0.999431i \(0.510742\pi\)
\(410\) 0 0
\(411\) −27.4229 −1.35267
\(412\) 2.35105 0.115828
\(413\) −0.589259 −0.0289955
\(414\) 25.8579 1.27085
\(415\) 0 0
\(416\) −5.33131 −0.261389
\(417\) 28.6900 1.40495
\(418\) −4.50684 −0.220437
\(419\) 16.6231 0.812094 0.406047 0.913852i \(-0.366907\pi\)
0.406047 + 0.913852i \(0.366907\pi\)
\(420\) 0 0
\(421\) −31.1128 −1.51635 −0.758174 0.652053i \(-0.773908\pi\)
−0.758174 + 0.652053i \(0.773908\pi\)
\(422\) 19.2534 0.937242
\(423\) −42.9495 −2.08827
\(424\) −12.9358 −0.628217
\(425\) 0 0
\(426\) −35.3252 −1.71151
\(427\) 0.167920 0.00812623
\(428\) −14.0334 −0.678331
\(429\) 78.1710 3.77413
\(430\) 0 0
\(431\) −10.1831 −0.490504 −0.245252 0.969459i \(-0.578871\pi\)
−0.245252 + 0.969459i \(0.578871\pi\)
\(432\) 14.9160 0.717648
\(433\) 22.1953 1.06664 0.533318 0.845915i \(-0.320945\pi\)
0.533318 + 0.845915i \(0.320945\pi\)
\(434\) 0.195265 0.00937300
\(435\) 0 0
\(436\) −0.0778929 −0.00373039
\(437\) 3.40920 0.163084
\(438\) −16.5847 −0.792449
\(439\) −9.32524 −0.445070 −0.222535 0.974925i \(-0.571433\pi\)
−0.222535 + 0.974925i \(0.571433\pi\)
\(440\) 0 0
\(441\) −53.0471 −2.52605
\(442\) −39.0855 −1.85911
\(443\) −13.9879 −0.664584 −0.332292 0.943177i \(-0.607822\pi\)
−0.332292 + 0.943177i \(0.607822\pi\)
\(444\) −17.9160 −0.850258
\(445\) 0 0
\(446\) −14.5068 −0.686919
\(447\) 57.5084 2.72005
\(448\) −0.0778929 −0.00368009
\(449\) 13.4932 0.636782 0.318391 0.947960i \(-0.396858\pi\)
0.318391 + 0.947960i \(0.396858\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 65.0684 3.05718
\(454\) −21.5984 −1.01366
\(455\) 0 0
\(456\) 3.25342 0.152355
\(457\) 9.68236 0.452922 0.226461 0.974020i \(-0.427284\pi\)
0.226461 + 0.974020i \(0.427284\pi\)
\(458\) −19.0137 −0.888451
\(459\) 109.354 5.10421
\(460\) 0 0
\(461\) 8.66262 0.403459 0.201729 0.979441i \(-0.435344\pi\)
0.201729 + 0.979441i \(0.435344\pi\)
\(462\) 1.14211 0.0531359
\(463\) 28.0015 1.30134 0.650671 0.759360i \(-0.274488\pi\)
0.650671 + 0.759360i \(0.274488\pi\)
\(464\) −1.33131 −0.0618046
\(465\) 0 0
\(466\) −6.01367 −0.278578
\(467\) 16.9742 0.785472 0.392736 0.919651i \(-0.371529\pi\)
0.392736 + 0.919651i \(0.371529\pi\)
\(468\) −40.4365 −1.86918
\(469\) 0.357118 0.0164902
\(470\) 0 0
\(471\) 1.64895 0.0759796
\(472\) 7.56499 0.348207
\(473\) −2.28423 −0.105029
\(474\) 55.3526 2.54243
\(475\) 0 0
\(476\) −0.571057 −0.0261743
\(477\) −98.1144 −4.49235
\(478\) 15.4092 0.704801
\(479\) 10.0532 0.459340 0.229670 0.973269i \(-0.426235\pi\)
0.229670 + 0.973269i \(0.426235\pi\)
\(480\) 0 0
\(481\) 29.3587 1.33864
\(482\) −4.81841 −0.219472
\(483\) −0.863954 −0.0393113
\(484\) 9.31157 0.423253
\(485\) 0 0
\(486\) 39.1052 1.77385
\(487\) 19.2089 0.870440 0.435220 0.900324i \(-0.356671\pi\)
0.435220 + 0.900324i \(0.356671\pi\)
\(488\) −2.15579 −0.0975878
\(489\) 2.70210 0.122193
\(490\) 0 0
\(491\) 5.32524 0.240325 0.120162 0.992754i \(-0.461658\pi\)
0.120162 + 0.992754i \(0.461658\pi\)
\(492\) 0 0
\(493\) −9.76025 −0.439580
\(494\) −5.33131 −0.239867
\(495\) 0 0
\(496\) −2.50684 −0.112560
\(497\) 0.845752 0.0379372
\(498\) −42.8458 −1.91996
\(499\) −11.9605 −0.535426 −0.267713 0.963499i \(-0.586268\pi\)
−0.267713 + 0.963499i \(0.586268\pi\)
\(500\) 0 0
\(501\) 53.7036 2.39930
\(502\) 1.52051 0.0678636
\(503\) −19.3313 −0.861941 −0.430970 0.902366i \(-0.641829\pi\)
−0.430970 + 0.902366i \(0.641829\pi\)
\(504\) −0.590796 −0.0263162
\(505\) 0 0
\(506\) −15.3647 −0.683045
\(507\) 50.1771 2.22844
\(508\) 17.8321 0.791171
\(509\) −36.1573 −1.60265 −0.801323 0.598232i \(-0.795870\pi\)
−0.801323 + 0.598232i \(0.795870\pi\)
\(510\) 0 0
\(511\) 0.397069 0.0175653
\(512\) 1.00000 0.0441942
\(513\) 14.9160 0.658559
\(514\) 16.5068 0.728085
\(515\) 0 0
\(516\) 1.64895 0.0725910
\(517\) 25.5205 1.12239
\(518\) 0.428943 0.0188467
\(519\) 61.2686 2.68939
\(520\) 0 0
\(521\) −31.5205 −1.38094 −0.690469 0.723362i \(-0.742596\pi\)
−0.690469 + 0.723362i \(0.742596\pi\)
\(522\) −10.0976 −0.441961
\(523\) 5.59840 0.244801 0.122400 0.992481i \(-0.460941\pi\)
0.122400 + 0.992481i \(0.460941\pi\)
\(524\) −1.49316 −0.0652292
\(525\) 0 0
\(526\) −18.0273 −0.786030
\(527\) −18.3784 −0.800575
\(528\) −14.6626 −0.638109
\(529\) −11.3773 −0.494667
\(530\) 0 0
\(531\) 57.3784 2.49001
\(532\) −0.0778929 −0.00337708
\(533\) 0 0
\(534\) 48.8458 2.11376
\(535\) 0 0
\(536\) −4.58473 −0.198030
\(537\) −23.2808 −1.00464
\(538\) 20.2089 0.871269
\(539\) 31.5205 1.35768
\(540\) 0 0
\(541\) 15.1968 0.653362 0.326681 0.945135i \(-0.394070\pi\)
0.326681 + 0.945135i \(0.394070\pi\)
\(542\) 6.08396 0.261328
\(543\) 40.7344 1.74808
\(544\) 7.33131 0.314327
\(545\) 0 0
\(546\) 1.35105 0.0578196
\(547\) −26.6505 −1.13949 −0.569746 0.821821i \(-0.692959\pi\)
−0.569746 + 0.821821i \(0.692959\pi\)
\(548\) −8.42894 −0.360067
\(549\) −16.3511 −0.697846
\(550\) 0 0
\(551\) −1.33131 −0.0567158
\(552\) 11.0916 0.472088
\(553\) −1.32524 −0.0563551
\(554\) −31.3647 −1.33256
\(555\) 0 0
\(556\) 8.81841 0.373984
\(557\) 12.8458 0.544292 0.272146 0.962256i \(-0.412267\pi\)
0.272146 + 0.962256i \(0.412267\pi\)
\(558\) −19.0137 −0.804913
\(559\) −2.70210 −0.114287
\(560\) 0 0
\(561\) −107.496 −4.53849
\(562\) 11.3252 0.477727
\(563\) 10.1968 0.429744 0.214872 0.976642i \(-0.431067\pi\)
0.214872 + 0.976642i \(0.431067\pi\)
\(564\) −18.4229 −0.775743
\(565\) 0 0
\(566\) 26.1437 1.09890
\(567\) −2.00760 −0.0843115
\(568\) −10.8579 −0.455587
\(569\) −24.3784 −1.02200 −0.510998 0.859582i \(-0.670724\pi\)
−0.510998 + 0.859582i \(0.670724\pi\)
\(570\) 0 0
\(571\) 8.32371 0.348336 0.174168 0.984716i \(-0.444276\pi\)
0.174168 + 0.984716i \(0.444276\pi\)
\(572\) 24.0273 1.00463
\(573\) −15.9495 −0.666298
\(574\) 0 0
\(575\) 0 0
\(576\) 7.58473 0.316030
\(577\) −7.29290 −0.303607 −0.151804 0.988411i \(-0.548508\pi\)
−0.151804 + 0.988411i \(0.548508\pi\)
\(578\) 36.7481 1.52852
\(579\) 59.0684 2.45480
\(580\) 0 0
\(581\) 1.02581 0.0425576
\(582\) 24.9742 1.03521
\(583\) 58.2994 2.41452
\(584\) −5.09763 −0.210942
\(585\) 0 0
\(586\) 1.33131 0.0549959
\(587\) 5.53264 0.228357 0.114178 0.993460i \(-0.463576\pi\)
0.114178 + 0.993460i \(0.463576\pi\)
\(588\) −22.7542 −0.938367
\(589\) −2.50684 −0.103292
\(590\) 0 0
\(591\) −9.71577 −0.399653
\(592\) −5.50684 −0.226330
\(593\) −26.3252 −1.08105 −0.540524 0.841329i \(-0.681774\pi\)
−0.540524 + 0.841329i \(0.681774\pi\)
\(594\) −67.2241 −2.75824
\(595\) 0 0
\(596\) 17.6763 0.724049
\(597\) −9.96919 −0.408012
\(598\) −18.1755 −0.743252
\(599\) 22.2994 0.911130 0.455565 0.890202i \(-0.349437\pi\)
0.455565 + 0.890202i \(0.349437\pi\)
\(600\) 0 0
\(601\) 32.4947 1.32549 0.662743 0.748847i \(-0.269392\pi\)
0.662743 + 0.748847i \(0.269392\pi\)
\(602\) −0.0394789 −0.00160904
\(603\) −34.7739 −1.41610
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) −13.5205 −0.549233
\(607\) 8.35105 0.338959 0.169479 0.985534i \(-0.445791\pi\)
0.169479 + 0.985534i \(0.445791\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0.337378 0.0136713
\(610\) 0 0
\(611\) 30.1892 1.22132
\(612\) 55.6060 2.24774
\(613\) −38.2994 −1.54690 −0.773450 0.633858i \(-0.781471\pi\)
−0.773450 + 0.633858i \(0.781471\pi\)
\(614\) −2.84421 −0.114783
\(615\) 0 0
\(616\) 0.351050 0.0141442
\(617\) −14.3526 −0.577813 −0.288907 0.957357i \(-0.593292\pi\)
−0.288907 + 0.957357i \(0.593292\pi\)
\(618\) 7.64895 0.307686
\(619\) −8.62314 −0.346593 −0.173297 0.984870i \(-0.555442\pi\)
−0.173297 + 0.984870i \(0.555442\pi\)
\(620\) 0 0
\(621\) 50.8518 2.04061
\(622\) −16.3895 −0.657158
\(623\) −1.16946 −0.0468533
\(624\) −17.3450 −0.694355
\(625\) 0 0
\(626\) −21.0471 −0.841211
\(627\) −14.6626 −0.585569
\(628\) 0.506836 0.0202250
\(629\) −40.3723 −1.60975
\(630\) 0 0
\(631\) −10.3374 −0.411525 −0.205762 0.978602i \(-0.565967\pi\)
−0.205762 + 0.978602i \(0.565967\pi\)
\(632\) 17.0137 0.676768
\(633\) 62.6394 2.48969
\(634\) −30.8902 −1.22681
\(635\) 0 0
\(636\) −42.0855 −1.66880
\(637\) 37.2868 1.47736
\(638\) 6.00000 0.237542
\(639\) −82.3541 −3.25788
\(640\) 0 0
\(641\) 5.88369 0.232392 0.116196 0.993226i \(-0.462930\pi\)
0.116196 + 0.993226i \(0.462930\pi\)
\(642\) −45.6566 −1.80192
\(643\) −25.5084 −1.00595 −0.502976 0.864300i \(-0.667762\pi\)
−0.502976 + 0.864300i \(0.667762\pi\)
\(644\) −0.265553 −0.0104642
\(645\) 0 0
\(646\) 7.33131 0.288447
\(647\) −5.09157 −0.200170 −0.100085 0.994979i \(-0.531911\pi\)
−0.100085 + 0.994979i \(0.531911\pi\)
\(648\) 25.7739 1.01250
\(649\) −34.0942 −1.33831
\(650\) 0 0
\(651\) 0.635277 0.0248985
\(652\) 0.830542 0.0325265
\(653\) −11.1816 −0.437570 −0.218785 0.975773i \(-0.570209\pi\)
−0.218785 + 0.975773i \(0.570209\pi\)
\(654\) −0.253418 −0.00990943
\(655\) 0 0
\(656\) 0 0
\(657\) −38.6642 −1.50843
\(658\) 0.441078 0.0171950
\(659\) −13.7542 −0.535787 −0.267894 0.963449i \(-0.586328\pi\)
−0.267894 + 0.963449i \(0.586328\pi\)
\(660\) 0 0
\(661\) −12.6171 −0.490747 −0.245374 0.969429i \(-0.578911\pi\)
−0.245374 + 0.969429i \(0.578911\pi\)
\(662\) 28.3845 1.10319
\(663\) −127.161 −4.93854
\(664\) −13.1695 −0.511074
\(665\) 0 0
\(666\) −41.7679 −1.61847
\(667\) −4.53871 −0.175740
\(668\) 16.5068 0.638669
\(669\) −47.1968 −1.82473
\(670\) 0 0
\(671\) 9.71577 0.375073
\(672\) −0.253418 −0.00977581
\(673\) 2.35105 0.0906263 0.0453132 0.998973i \(-0.485571\pi\)
0.0453132 + 0.998973i \(0.485571\pi\)
\(674\) −17.8716 −0.688387
\(675\) 0 0
\(676\) 15.4229 0.593188
\(677\) −23.7663 −0.913414 −0.456707 0.889617i \(-0.650971\pi\)
−0.456707 + 0.889617i \(0.650971\pi\)
\(678\) −19.5205 −0.749681
\(679\) −0.597928 −0.0229464
\(680\) 0 0
\(681\) −70.2686 −2.69270
\(682\) 11.2979 0.432619
\(683\) 28.1695 1.07787 0.538937 0.842346i \(-0.318826\pi\)
0.538937 + 0.842346i \(0.318826\pi\)
\(684\) 7.58473 0.290009
\(685\) 0 0
\(686\) 1.09003 0.0416174
\(687\) −61.8594 −2.36008
\(688\) 0.506836 0.0193229
\(689\) 68.9647 2.62734
\(690\) 0 0
\(691\) 2.32371 0.0883979 0.0441990 0.999023i \(-0.485926\pi\)
0.0441990 + 0.999023i \(0.485926\pi\)
\(692\) 18.8321 0.715888
\(693\) 2.66262 0.101145
\(694\) 33.0410 1.25422
\(695\) 0 0
\(696\) −4.33131 −0.164178
\(697\) 0 0
\(698\) −19.7158 −0.746253
\(699\) −19.5650 −0.740016
\(700\) 0 0
\(701\) 23.7036 0.895274 0.447637 0.894215i \(-0.352266\pi\)
0.447637 + 0.894215i \(0.352266\pi\)
\(702\) −79.5220 −3.00137
\(703\) −5.50684 −0.207694
\(704\) −4.50684 −0.169858
\(705\) 0 0
\(706\) −5.90997 −0.222425
\(707\) 0.323706 0.0121742
\(708\) 24.6121 0.924978
\(709\) 9.05315 0.339998 0.169999 0.985444i \(-0.445624\pi\)
0.169999 + 0.985444i \(0.445624\pi\)
\(710\) 0 0
\(711\) 129.044 4.83953
\(712\) 15.0137 0.562661
\(713\) −8.54631 −0.320062
\(714\) −1.85789 −0.0695297
\(715\) 0 0
\(716\) −7.15579 −0.267424
\(717\) 50.1326 1.87224
\(718\) −7.00760 −0.261521
\(719\) 35.0734 1.30802 0.654008 0.756488i \(-0.273086\pi\)
0.654008 + 0.756488i \(0.273086\pi\)
\(720\) 0 0
\(721\) −0.183130 −0.00682012
\(722\) 1.00000 0.0372161
\(723\) −15.6763 −0.583008
\(724\) 12.5205 0.465321
\(725\) 0 0
\(726\) 30.2944 1.12433
\(727\) 30.1386 1.11778 0.558890 0.829242i \(-0.311227\pi\)
0.558890 + 0.829242i \(0.311227\pi\)
\(728\) 0.415271 0.0153910
\(729\) 49.9039 1.84829
\(730\) 0 0
\(731\) 3.71577 0.137433
\(732\) −7.01367 −0.259233
\(733\) 47.8321 1.76672 0.883359 0.468697i \(-0.155276\pi\)
0.883359 + 0.468697i \(0.155276\pi\)
\(734\) 17.7158 0.653901
\(735\) 0 0
\(736\) 3.40920 0.125665
\(737\) 20.6626 0.761117
\(738\) 0 0
\(739\) −22.4674 −0.826475 −0.413238 0.910623i \(-0.635602\pi\)
−0.413238 + 0.910623i \(0.635602\pi\)
\(740\) 0 0
\(741\) −17.3450 −0.637184
\(742\) 1.00760 0.0369903
\(743\) −11.7926 −0.432629 −0.216314 0.976324i \(-0.569404\pi\)
−0.216314 + 0.976324i \(0.569404\pi\)
\(744\) −8.15579 −0.299006
\(745\) 0 0
\(746\) 15.4487 0.565616
\(747\) −99.8868 −3.65467
\(748\) −33.0410 −1.20810
\(749\) 1.09310 0.0399411
\(750\) 0 0
\(751\) −2.03948 −0.0744216 −0.0372108 0.999307i \(-0.511847\pi\)
−0.0372108 + 0.999307i \(0.511847\pi\)
\(752\) −5.66262 −0.206495
\(753\) 4.94685 0.180273
\(754\) 7.09763 0.258481
\(755\) 0 0
\(756\) −1.16185 −0.0422562
\(757\) 43.3526 1.57568 0.787838 0.615882i \(-0.211200\pi\)
0.787838 + 0.615882i \(0.211200\pi\)
\(758\) 34.4563 1.25151
\(759\) −49.9879 −1.81444
\(760\) 0 0
\(761\) 6.62921 0.240309 0.120154 0.992755i \(-0.461661\pi\)
0.120154 + 0.992755i \(0.461661\pi\)
\(762\) 58.0152 2.10167
\(763\) 0.00606730 0.000219651 0
\(764\) −4.90237 −0.177361
\(765\) 0 0
\(766\) −12.0273 −0.434566
\(767\) −40.3313 −1.45628
\(768\) 3.25342 0.117398
\(769\) −19.6429 −0.708340 −0.354170 0.935181i \(-0.615237\pi\)
−0.354170 + 0.935181i \(0.615237\pi\)
\(770\) 0 0
\(771\) 53.7036 1.93409
\(772\) 18.1558 0.653441
\(773\) 14.4107 0.518318 0.259159 0.965835i \(-0.416555\pi\)
0.259159 + 0.965835i \(0.416555\pi\)
\(774\) 3.84421 0.138177
\(775\) 0 0
\(776\) 7.67629 0.275563
\(777\) 1.39553 0.0500644
\(778\) −15.3647 −0.550852
\(779\) 0 0
\(780\) 0 0
\(781\) 48.9347 1.75102
\(782\) 24.9939 0.893781
\(783\) −19.8579 −0.709663
\(784\) −6.99393 −0.249783
\(785\) 0 0
\(786\) −4.85789 −0.173275
\(787\) 24.3176 0.866830 0.433415 0.901194i \(-0.357308\pi\)
0.433415 + 0.901194i \(0.357308\pi\)
\(788\) −2.98633 −0.106384
\(789\) −58.6505 −2.08801
\(790\) 0 0
\(791\) 0.467357 0.0166173
\(792\) −34.1831 −1.21464
\(793\) 11.4932 0.408134
\(794\) 1.32524 0.0470311
\(795\) 0 0
\(796\) −3.06422 −0.108608
\(797\) −7.30397 −0.258720 −0.129360 0.991598i \(-0.541292\pi\)
−0.129360 + 0.991598i \(0.541292\pi\)
\(798\) −0.253418 −0.00897090
\(799\) −41.5144 −1.46868
\(800\) 0 0
\(801\) 113.875 4.02356
\(802\) −6.46736 −0.228370
\(803\) 22.9742 0.810742
\(804\) −14.9160 −0.526048
\(805\) 0 0
\(806\) 13.3647 0.470752
\(807\) 65.7481 2.31444
\(808\) −4.15579 −0.146200
\(809\) −0.584729 −0.0205580 −0.0102790 0.999947i \(-0.503272\pi\)
−0.0102790 + 0.999947i \(0.503272\pi\)
\(810\) 0 0
\(811\) 1.90997 0.0670682 0.0335341 0.999438i \(-0.489324\pi\)
0.0335341 + 0.999438i \(0.489324\pi\)
\(812\) 0.103700 0.00363914
\(813\) 19.7937 0.694194
\(814\) 24.8184 0.869885
\(815\) 0 0
\(816\) 23.8518 0.834981
\(817\) 0.506836 0.0177319
\(818\) −1.36472 −0.0477164
\(819\) 3.14972 0.110060
\(820\) 0 0
\(821\) −38.2226 −1.33398 −0.666989 0.745067i \(-0.732417\pi\)
−0.666989 + 0.745067i \(0.732417\pi\)
\(822\) −27.4229 −0.956483
\(823\) −45.7481 −1.59468 −0.797340 0.603531i \(-0.793760\pi\)
−0.797340 + 0.603531i \(0.793760\pi\)
\(824\) 2.35105 0.0819027
\(825\) 0 0
\(826\) −0.589259 −0.0205029
\(827\) −22.6687 −0.788268 −0.394134 0.919053i \(-0.628955\pi\)
−0.394134 + 0.919053i \(0.628955\pi\)
\(828\) 25.8579 0.898624
\(829\) −4.63028 −0.160816 −0.0804081 0.996762i \(-0.525622\pi\)
−0.0804081 + 0.996762i \(0.525622\pi\)
\(830\) 0 0
\(831\) −102.043 −3.53982
\(832\) −5.33131 −0.184830
\(833\) −51.2747 −1.77656
\(834\) 28.6900 0.993452
\(835\) 0 0
\(836\) −4.50684 −0.155872
\(837\) −37.3921 −1.29246
\(838\) 16.6231 0.574237
\(839\) −50.4826 −1.74285 −0.871426 0.490527i \(-0.836804\pi\)
−0.871426 + 0.490527i \(0.836804\pi\)
\(840\) 0 0
\(841\) −27.2276 −0.938883
\(842\) −31.1128 −1.07222
\(843\) 36.8458 1.26904
\(844\) 19.2534 0.662730
\(845\) 0 0
\(846\) −42.9495 −1.47663
\(847\) −0.725305 −0.0249218
\(848\) −12.9358 −0.444216
\(849\) 85.0562 2.91912
\(850\) 0 0
\(851\) −18.7739 −0.643562
\(852\) −35.3252 −1.21022
\(853\) 36.2105 1.23982 0.619912 0.784672i \(-0.287168\pi\)
0.619912 + 0.784672i \(0.287168\pi\)
\(854\) 0.167920 0.00574611
\(855\) 0 0
\(856\) −14.0334 −0.479652
\(857\) 25.1968 0.860706 0.430353 0.902661i \(-0.358389\pi\)
0.430353 + 0.902661i \(0.358389\pi\)
\(858\) 78.1710 2.66871
\(859\) 18.8579 0.643423 0.321711 0.946838i \(-0.395742\pi\)
0.321711 + 0.946838i \(0.395742\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −10.1831 −0.346839
\(863\) 15.0137 0.511071 0.255536 0.966800i \(-0.417748\pi\)
0.255536 + 0.966800i \(0.417748\pi\)
\(864\) 14.9160 0.507454
\(865\) 0 0
\(866\) 22.1953 0.754226
\(867\) 119.557 4.06037
\(868\) 0.195265 0.00662771
\(869\) −76.6778 −2.60112
\(870\) 0 0
\(871\) 24.4426 0.828206
\(872\) −0.0778929 −0.00263779
\(873\) 58.2226 1.97054
\(874\) 3.40920 0.115318
\(875\) 0 0
\(876\) −16.5847 −0.560346
\(877\) 35.1128 1.18568 0.592838 0.805322i \(-0.298007\pi\)
0.592838 + 0.805322i \(0.298007\pi\)
\(878\) −9.32524 −0.314712
\(879\) 4.33131 0.146091
\(880\) 0 0
\(881\) −41.3389 −1.39274 −0.696372 0.717681i \(-0.745203\pi\)
−0.696372 + 0.717681i \(0.745203\pi\)
\(882\) −53.0471 −1.78619
\(883\) −12.6353 −0.425211 −0.212605 0.977138i \(-0.568195\pi\)
−0.212605 + 0.977138i \(0.568195\pi\)
\(884\) −39.0855 −1.31459
\(885\) 0 0
\(886\) −13.9879 −0.469932
\(887\) 4.15579 0.139538 0.0697688 0.997563i \(-0.477774\pi\)
0.0697688 + 0.997563i \(0.477774\pi\)
\(888\) −17.9160 −0.601223
\(889\) −1.38899 −0.0465853
\(890\) 0 0
\(891\) −116.159 −3.89147
\(892\) −14.5068 −0.485725
\(893\) −5.66262 −0.189492
\(894\) 57.5084 1.92337
\(895\) 0 0
\(896\) −0.0778929 −0.00260222
\(897\) −59.1326 −1.97438
\(898\) 13.4932 0.450273
\(899\) 3.33738 0.111308
\(900\) 0 0
\(901\) −94.8362 −3.15945
\(902\) 0 0
\(903\) −0.128441 −0.00427426
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 65.0684 2.16175
\(907\) −41.7542 −1.38643 −0.693213 0.720733i \(-0.743805\pi\)
−0.693213 + 0.720733i \(0.743805\pi\)
\(908\) −21.5984 −0.716768
\(909\) −31.5205 −1.04547
\(910\) 0 0
\(911\) −9.12998 −0.302490 −0.151245 0.988496i \(-0.548328\pi\)
−0.151245 + 0.988496i \(0.548328\pi\)
\(912\) 3.25342 0.107731
\(913\) 59.3526 1.96428
\(914\) 9.68236 0.320264
\(915\) 0 0
\(916\) −19.0137 −0.628229
\(917\) 0.116307 0.00384079
\(918\) 109.354 3.60922
\(919\) 19.0197 0.627403 0.313702 0.949522i \(-0.398431\pi\)
0.313702 + 0.949522i \(0.398431\pi\)
\(920\) 0 0
\(921\) −9.25342 −0.304910
\(922\) 8.66262 0.285288
\(923\) 57.8868 1.90537
\(924\) 1.14211 0.0375728
\(925\) 0 0
\(926\) 28.0015 0.920188
\(927\) 17.8321 0.585682
\(928\) −1.33131 −0.0437024
\(929\) −7.77239 −0.255004 −0.127502 0.991838i \(-0.540696\pi\)
−0.127502 + 0.991838i \(0.540696\pi\)
\(930\) 0 0
\(931\) −6.99393 −0.229217
\(932\) −6.01367 −0.196984
\(933\) −53.3218 −1.74568
\(934\) 16.9742 0.555413
\(935\) 0 0
\(936\) −40.4365 −1.32171
\(937\) −45.9818 −1.50216 −0.751080 0.660211i \(-0.770467\pi\)
−0.751080 + 0.660211i \(0.770467\pi\)
\(938\) 0.357118 0.0116603
\(939\) −68.4750 −2.23460
\(940\) 0 0
\(941\) −40.6242 −1.32431 −0.662156 0.749366i \(-0.730358\pi\)
−0.662156 + 0.749366i \(0.730358\pi\)
\(942\) 1.64895 0.0537257
\(943\) 0 0
\(944\) 7.56499 0.246219
\(945\) 0 0
\(946\) −2.28423 −0.0742666
\(947\) −2.28423 −0.0742274 −0.0371137 0.999311i \(-0.511816\pi\)
−0.0371137 + 0.999311i \(0.511816\pi\)
\(948\) 55.3526 1.79777
\(949\) 27.1771 0.882205
\(950\) 0 0
\(951\) −100.499 −3.25890
\(952\) −0.571057 −0.0185081
\(953\) −57.5084 −1.86288 −0.931439 0.363896i \(-0.881446\pi\)
−0.931439 + 0.363896i \(0.881446\pi\)
\(954\) −98.1144 −3.17657
\(955\) 0 0
\(956\) 15.4092 0.498369
\(957\) 19.5205 0.631008
\(958\) 10.0532 0.324803
\(959\) 0.656555 0.0212013
\(960\) 0 0
\(961\) −24.7158 −0.797283
\(962\) 29.3587 0.946561
\(963\) −106.440 −3.42997
\(964\) −4.81841 −0.155190
\(965\) 0 0
\(966\) −0.863954 −0.0277973
\(967\) −4.70210 −0.151209 −0.0756047 0.997138i \(-0.524089\pi\)
−0.0756047 + 0.997138i \(0.524089\pi\)
\(968\) 9.31157 0.299285
\(969\) 23.8518 0.766231
\(970\) 0 0
\(971\) 14.9863 0.480934 0.240467 0.970657i \(-0.422699\pi\)
0.240467 + 0.970657i \(0.422699\pi\)
\(972\) 39.1052 1.25430
\(973\) −0.686891 −0.0220207
\(974\) 19.2089 0.615494
\(975\) 0 0
\(976\) −2.15579 −0.0690050
\(977\) 8.89737 0.284652 0.142326 0.989820i \(-0.454542\pi\)
0.142326 + 0.989820i \(0.454542\pi\)
\(978\) 2.70210 0.0864037
\(979\) −67.6642 −2.16256
\(980\) 0 0
\(981\) −0.590796 −0.0188627
\(982\) 5.32524 0.169935
\(983\) −1.60947 −0.0513341 −0.0256671 0.999671i \(-0.508171\pi\)
−0.0256671 + 0.999671i \(0.508171\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −9.76025 −0.310830
\(987\) 1.43501 0.0456769
\(988\) −5.33131 −0.169612
\(989\) 1.72791 0.0549443
\(990\) 0 0
\(991\) 16.8974 0.536763 0.268381 0.963313i \(-0.413511\pi\)
0.268381 + 0.963313i \(0.413511\pi\)
\(992\) −2.50684 −0.0795921
\(993\) 92.3465 2.93053
\(994\) 0.845752 0.0268256
\(995\) 0 0
\(996\) −42.8458 −1.35762
\(997\) 24.1558 0.765021 0.382511 0.923951i \(-0.375060\pi\)
0.382511 + 0.923951i \(0.375060\pi\)
\(998\) −11.9605 −0.378604
\(999\) −82.1402 −2.59880
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 950.2.a.l.1.3 yes 3
3.2 odd 2 8550.2.a.ci.1.2 3
4.3 odd 2 7600.2.a.bk.1.1 3
5.2 odd 4 950.2.b.h.799.4 6
5.3 odd 4 950.2.b.h.799.3 6
5.4 even 2 950.2.a.j.1.1 3
15.14 odd 2 8550.2.a.cp.1.2 3
20.19 odd 2 7600.2.a.bz.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.1 3 5.4 even 2
950.2.a.l.1.3 yes 3 1.1 even 1 trivial
950.2.b.h.799.3 6 5.3 odd 4
950.2.b.h.799.4 6 5.2 odd 4
7600.2.a.bk.1.1 3 4.3 odd 2
7600.2.a.bz.1.3 3 20.19 odd 2
8550.2.a.ci.1.2 3 3.2 odd 2
8550.2.a.cp.1.2 3 15.14 odd 2