Properties

Label 950.2.b.h.799.1
Level $950$
Weight $2$
Character 950.799
Analytic conductor $7.586$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.63107136.1
Defining polynomial: \(x^{6} + 13 x^{4} + 42 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 799.1
Root \(-2.77339i\) of defining polynomial
Character \(\chi\) \(=\) 950.799
Dual form 950.2.b.h.799.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.77339i q^{3} -1.00000 q^{4} -1.77339 q^{6} +2.69168i q^{7} +1.00000i q^{8} -0.144903 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.77339i q^{3} -1.00000 q^{4} -1.77339 q^{6} +2.69168i q^{7} +1.00000i q^{8} -0.144903 q^{9} +5.54677 q^{11} +1.77339i q^{12} -2.91829i q^{13} +2.69168 q^{14} +1.00000 q^{16} -4.91829i q^{17} +0.144903i q^{18} -1.00000 q^{19} +4.77339 q^{21} -5.54677i q^{22} +3.60997i q^{23} +1.77339 q^{24} -2.91829 q^{26} -5.06319i q^{27} -2.69168i q^{28} -1.08171 q^{29} +7.54677 q^{31} -1.00000i q^{32} -9.83658i q^{33} -4.91829 q^{34} +0.144903 q^{36} -4.54677i q^{37} +1.00000i q^{38} -5.17526 q^{39} -4.77339i q^{42} -9.54677i q^{43} -5.54677 q^{44} +3.60997 q^{46} +0.836581i q^{47} -1.77339i q^{48} -0.245129 q^{49} -8.72203 q^{51} +2.91829i q^{52} +9.78523i q^{53} -5.06319 q^{54} -2.69168 q^{56} +1.77339i q^{57} +1.08171i q^{58} -12.9933 q^{59} -7.38336 q^{61} -7.54677i q^{62} -0.390032i q^{63} -1.00000 q^{64} -9.83658 q^{66} -2.85510i q^{67} +4.91829i q^{68} +6.40187 q^{69} +14.4769 q^{71} -0.144903i q^{72} +5.15674i q^{73} -4.54677 q^{74} +1.00000 q^{76} +14.9301i q^{77} +5.17526i q^{78} +3.09355 q^{79} -9.41371 q^{81} +1.71019i q^{83} -4.77339 q^{84} -9.54677 q^{86} +1.91829i q^{87} +5.54677i q^{88} +5.09355 q^{89} +7.85510 q^{91} -3.60997i q^{92} -13.3834i q^{93} +0.836581 q^{94} -1.77339 q^{96} +17.2570i q^{97} +0.245129i q^{98} -0.803744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} + 4q^{6} - 10q^{9} + O(q^{10}) \) \( 6q - 6q^{4} + 4q^{6} - 10q^{9} + 4q^{11} - 4q^{14} + 6q^{16} - 6q^{19} + 14q^{21} - 4q^{24} - 12q^{26} - 12q^{29} + 16q^{31} - 24q^{34} + 10q^{36} + 22q^{39} - 4q^{44} - 4q^{46} - 18q^{49} + 30q^{51} - 34q^{54} + 4q^{56} - 12q^{59} - 4q^{61} - 6q^{64} - 48q^{66} - 12q^{71} + 2q^{74} + 6q^{76} - 40q^{79} + 46q^{81} - 14q^{84} - 28q^{86} - 28q^{89} + 38q^{91} - 6q^{94} + 4q^{96} + 72q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 1.00000i − 0.707107i
\(3\) − 1.77339i − 1.02387i −0.859025 0.511933i \(-0.828930\pi\)
0.859025 0.511933i \(-0.171070\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) −1.77339 −0.723982
\(7\) 2.69168i 1.01736i 0.860956 + 0.508679i \(0.169866\pi\)
−0.860956 + 0.508679i \(0.830134\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.144903 −0.0483010
\(10\) 0 0
\(11\) 5.54677 1.67242 0.836208 0.548413i \(-0.184768\pi\)
0.836208 + 0.548413i \(0.184768\pi\)
\(12\) 1.77339i 0.511933i
\(13\) − 2.91829i − 0.809388i −0.914452 0.404694i \(-0.867378\pi\)
0.914452 0.404694i \(-0.132622\pi\)
\(14\) 2.69168 0.719381
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) − 4.91829i − 1.19286i −0.802665 0.596430i \(-0.796585\pi\)
0.802665 0.596430i \(-0.203415\pi\)
\(18\) 0.144903i 0.0341539i
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 4.77339 1.04164
\(22\) − 5.54677i − 1.18258i
\(23\) 3.60997i 0.752730i 0.926471 + 0.376365i \(0.122826\pi\)
−0.926471 + 0.376365i \(0.877174\pi\)
\(24\) 1.77339 0.361991
\(25\) 0 0
\(26\) −2.91829 −0.572324
\(27\) − 5.06319i − 0.974412i
\(28\) − 2.69168i − 0.508679i
\(29\) −1.08171 −0.200868 −0.100434 0.994944i \(-0.532023\pi\)
−0.100434 + 0.994944i \(0.532023\pi\)
\(30\) 0 0
\(31\) 7.54677 1.35544 0.677720 0.735320i \(-0.262968\pi\)
0.677720 + 0.735320i \(0.262968\pi\)
\(32\) − 1.00000i − 0.176777i
\(33\) − 9.83658i − 1.71233i
\(34\) −4.91829 −0.843480
\(35\) 0 0
\(36\) 0.144903 0.0241505
\(37\) − 4.54677i − 0.747485i −0.927532 0.373743i \(-0.878074\pi\)
0.927532 0.373743i \(-0.121926\pi\)
\(38\) 1.00000i 0.162221i
\(39\) −5.17526 −0.828705
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) − 4.77339i − 0.736550i
\(43\) − 9.54677i − 1.45587i −0.685646 0.727935i \(-0.740480\pi\)
0.685646 0.727935i \(-0.259520\pi\)
\(44\) −5.54677 −0.836208
\(45\) 0 0
\(46\) 3.60997 0.532261
\(47\) 0.836581i 0.122028i 0.998137 + 0.0610139i \(0.0194334\pi\)
−0.998137 + 0.0610139i \(0.980567\pi\)
\(48\) − 1.77339i − 0.255966i
\(49\) −0.245129 −0.0350184
\(50\) 0 0
\(51\) −8.72203 −1.22133
\(52\) 2.91829i 0.404694i
\(53\) 9.78523i 1.34410i 0.740504 + 0.672052i \(0.234587\pi\)
−0.740504 + 0.672052i \(0.765413\pi\)
\(54\) −5.06319 −0.689013
\(55\) 0 0
\(56\) −2.69168 −0.359691
\(57\) 1.77339i 0.234891i
\(58\) 1.08171i 0.142035i
\(59\) −12.9933 −1.69159 −0.845793 0.533511i \(-0.820872\pi\)
−0.845793 + 0.533511i \(0.820872\pi\)
\(60\) 0 0
\(61\) −7.38336 −0.945342 −0.472671 0.881239i \(-0.656710\pi\)
−0.472671 + 0.881239i \(0.656710\pi\)
\(62\) − 7.54677i − 0.958441i
\(63\) − 0.390032i − 0.0491394i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −9.83658 −1.21080
\(67\) − 2.85510i − 0.348806i −0.984674 0.174403i \(-0.944201\pi\)
0.984674 0.174403i \(-0.0557995\pi\)
\(68\) 4.91829i 0.596430i
\(69\) 6.40187 0.770695
\(70\) 0 0
\(71\) 14.4769 1.71809 0.859046 0.511898i \(-0.171057\pi\)
0.859046 + 0.511898i \(0.171057\pi\)
\(72\) − 0.144903i − 0.0170770i
\(73\) 5.15674i 0.603551i 0.953379 + 0.301776i \(0.0975793\pi\)
−0.953379 + 0.301776i \(0.902421\pi\)
\(74\) −4.54677 −0.528552
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 14.9301i 1.70145i
\(78\) 5.17526i 0.585983i
\(79\) 3.09355 0.348052 0.174026 0.984741i \(-0.444322\pi\)
0.174026 + 0.984741i \(0.444322\pi\)
\(80\) 0 0
\(81\) −9.41371 −1.04597
\(82\) 0 0
\(83\) 1.71019i 0.187718i 0.995585 + 0.0938591i \(0.0299203\pi\)
−0.995585 + 0.0938591i \(0.970080\pi\)
\(84\) −4.77339 −0.520819
\(85\) 0 0
\(86\) −9.54677 −1.02946
\(87\) 1.91829i 0.205662i
\(88\) 5.54677i 0.591288i
\(89\) 5.09355 0.539915 0.269958 0.962872i \(-0.412990\pi\)
0.269958 + 0.962872i \(0.412990\pi\)
\(90\) 0 0
\(91\) 7.85510 0.823438
\(92\) − 3.60997i − 0.376365i
\(93\) − 13.3834i − 1.38779i
\(94\) 0.836581 0.0862867
\(95\) 0 0
\(96\) −1.77339 −0.180996
\(97\) 17.2570i 1.75218i 0.482148 + 0.876090i \(0.339857\pi\)
−0.482148 + 0.876090i \(0.660143\pi\)
\(98\) 0.245129i 0.0247618i
\(99\) −0.803744 −0.0807793
\(100\) 0 0
\(101\) −9.38336 −0.933679 −0.466839 0.884342i \(-0.654607\pi\)
−0.466839 + 0.884342i \(0.654607\pi\)
\(102\) 8.72203i 0.863610i
\(103\) − 12.9301i − 1.27404i −0.770846 0.637022i \(-0.780166\pi\)
0.770846 0.637022i \(-0.219834\pi\)
\(104\) 2.91829 0.286162
\(105\) 0 0
\(106\) 9.78523 0.950425
\(107\) − 18.9420i − 1.83119i −0.402102 0.915595i \(-0.631720\pi\)
0.402102 0.915595i \(-0.368280\pi\)
\(108\) 5.06319i 0.487206i
\(109\) 2.69168 0.257816 0.128908 0.991657i \(-0.458853\pi\)
0.128908 + 0.991657i \(0.458853\pi\)
\(110\) 0 0
\(111\) −8.06319 −0.765324
\(112\) 2.69168i 0.254340i
\(113\) − 6.00000i − 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 1.77339 0.166093
\(115\) 0 0
\(116\) 1.08171 0.100434
\(117\) 0.422869i 0.0390942i
\(118\) 12.9933i 1.19613i
\(119\) 13.2385 1.21357
\(120\) 0 0
\(121\) 19.7667 1.79697
\(122\) 7.38336i 0.668458i
\(123\) 0 0
\(124\) −7.54677 −0.677720
\(125\) 0 0
\(126\) −0.390032 −0.0347468
\(127\) 1.87361i 0.166256i 0.996539 + 0.0831282i \(0.0264911\pi\)
−0.996539 + 0.0831282i \(0.973509\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −16.9301 −1.49061
\(130\) 0 0
\(131\) −11.5468 −1.00885 −0.504423 0.863457i \(-0.668295\pi\)
−0.504423 + 0.863457i \(0.668295\pi\)
\(132\) 9.83658i 0.856164i
\(133\) − 2.69168i − 0.233398i
\(134\) −2.85510 −0.246643
\(135\) 0 0
\(136\) 4.91829 0.421740
\(137\) − 4.23845i − 0.362115i −0.983472 0.181058i \(-0.942048\pi\)
0.983472 0.181058i \(-0.0579521\pi\)
\(138\) − 6.40187i − 0.544964i
\(139\) −9.21994 −0.782025 −0.391012 0.920385i \(-0.627875\pi\)
−0.391012 + 0.920385i \(0.627875\pi\)
\(140\) 0 0
\(141\) 1.48358 0.124940
\(142\) − 14.4769i − 1.21487i
\(143\) − 16.1871i − 1.35363i
\(144\) −0.144903 −0.0120752
\(145\) 0 0
\(146\) 5.15674 0.426775
\(147\) 0.434709i 0.0358542i
\(148\) 4.54677i 0.373743i
\(149\) 7.25697 0.594514 0.297257 0.954797i \(-0.403928\pi\)
0.297257 + 0.954797i \(0.403928\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) − 1.00000i − 0.0811107i
\(153\) 0.712675i 0.0576163i
\(154\) 14.9301 1.20310
\(155\) 0 0
\(156\) 5.17526 0.414352
\(157\) 9.54677i 0.761916i 0.924592 + 0.380958i \(0.124406\pi\)
−0.924592 + 0.380958i \(0.875594\pi\)
\(158\) − 3.09355i − 0.246110i
\(159\) 17.3530 1.37618
\(160\) 0 0
\(161\) −9.71687 −0.765797
\(162\) 9.41371i 0.739611i
\(163\) 15.7102i 1.23052i 0.788325 + 0.615259i \(0.210948\pi\)
−0.788325 + 0.615259i \(0.789052\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.71019 0.132737
\(167\) − 6.45323i − 0.499366i −0.968328 0.249683i \(-0.919674\pi\)
0.968328 0.249683i \(-0.0803263\pi\)
\(168\) 4.77339i 0.368275i
\(169\) 4.48358 0.344891
\(170\) 0 0
\(171\) 0.144903 0.0110810
\(172\) 9.54677i 0.727935i
\(173\) − 0.873614i − 0.0664196i −0.999448 0.0332098i \(-0.989427\pi\)
0.999448 0.0332098i \(-0.0105730\pi\)
\(174\) 1.91829 0.145425
\(175\) 0 0
\(176\) 5.54677 0.418104
\(177\) 23.0422i 1.73196i
\(178\) − 5.09355i − 0.381778i
\(179\) 12.3834 0.925575 0.462788 0.886469i \(-0.346849\pi\)
0.462788 + 0.886469i \(0.346849\pi\)
\(180\) 0 0
\(181\) −17.6403 −1.31119 −0.655597 0.755111i \(-0.727583\pi\)
−0.655597 + 0.755111i \(0.727583\pi\)
\(182\) − 7.85510i − 0.582259i
\(183\) 13.0935i 0.967903i
\(184\) −3.60997 −0.266130
\(185\) 0 0
\(186\) −13.3834 −0.981315
\(187\) − 27.2806i − 1.99496i
\(188\) − 0.836581i − 0.0610139i
\(189\) 13.6285 0.991326
\(190\) 0 0
\(191\) −15.1567 −1.09670 −0.548352 0.836248i \(-0.684744\pi\)
−0.548352 + 0.836248i \(0.684744\pi\)
\(192\) 1.77339i 0.127983i
\(193\) 23.3834i 1.68317i 0.540124 + 0.841585i \(0.318377\pi\)
−0.540124 + 0.841585i \(0.681623\pi\)
\(194\) 17.2570 1.23898
\(195\) 0 0
\(196\) 0.245129 0.0175092
\(197\) 23.0935i 1.64535i 0.568514 + 0.822674i \(0.307519\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(198\) 0.803744i 0.0571196i
\(199\) 25.7852 1.82787 0.913933 0.405865i \(-0.133030\pi\)
0.913933 + 0.405865i \(0.133030\pi\)
\(200\) 0 0
\(201\) −5.06319 −0.357130
\(202\) 9.38336i 0.660211i
\(203\) − 2.91161i − 0.204355i
\(204\) 8.72203 0.610665
\(205\) 0 0
\(206\) −12.9301 −0.900885
\(207\) − 0.523095i − 0.0363576i
\(208\) − 2.91829i − 0.202347i
\(209\) −5.54677 −0.383678
\(210\) 0 0
\(211\) 14.2266 0.979400 0.489700 0.871891i \(-0.337106\pi\)
0.489700 + 0.871891i \(0.337106\pi\)
\(212\) − 9.78523i − 0.672052i
\(213\) − 25.6732i − 1.75910i
\(214\) −18.9420 −1.29485
\(215\) 0 0
\(216\) 5.06319 0.344507
\(217\) 20.3135i 1.37897i
\(218\) − 2.69168i − 0.182303i
\(219\) 9.14490 0.617955
\(220\) 0 0
\(221\) −14.3530 −0.965487
\(222\) 8.06319i 0.541166i
\(223\) − 4.45323i − 0.298210i −0.988821 0.149105i \(-0.952361\pi\)
0.988821 0.149105i \(-0.0476392\pi\)
\(224\) 2.69168 0.179845
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) − 5.94865i − 0.394826i −0.980320 0.197413i \(-0.936746\pi\)
0.980320 0.197413i \(-0.0632539\pi\)
\(228\) − 1.77339i − 0.117445i
\(229\) −1.09355 −0.0722638 −0.0361319 0.999347i \(-0.511504\pi\)
−0.0361319 + 0.999347i \(0.511504\pi\)
\(230\) 0 0
\(231\) 26.4769 1.74205
\(232\) − 1.08171i − 0.0710177i
\(233\) 14.0935i 0.923299i 0.887062 + 0.461650i \(0.152742\pi\)
−0.887062 + 0.461650i \(0.847258\pi\)
\(234\) 0.422869 0.0276438
\(235\) 0 0
\(236\) 12.9933 0.845793
\(237\) − 5.48606i − 0.356358i
\(238\) − 13.2385i − 0.858121i
\(239\) −15.6100 −1.00972 −0.504862 0.863200i \(-0.668457\pi\)
−0.504862 + 0.863200i \(0.668457\pi\)
\(240\) 0 0
\(241\) −5.21994 −0.336246 −0.168123 0.985766i \(-0.553771\pi\)
−0.168123 + 0.985766i \(0.553771\pi\)
\(242\) − 19.7667i − 1.27065i
\(243\) 1.50458i 0.0965188i
\(244\) 7.38336 0.472671
\(245\) 0 0
\(246\) 0 0
\(247\) 2.91829i 0.185686i
\(248\) 7.54677i 0.479221i
\(249\) 3.03284 0.192198
\(250\) 0 0
\(251\) −28.6403 −1.80776 −0.903881 0.427785i \(-0.859294\pi\)
−0.903881 + 0.427785i \(0.859294\pi\)
\(252\) 0.390032i 0.0245697i
\(253\) 20.0237i 1.25888i
\(254\) 1.87361 0.117561
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) − 6.45323i − 0.402541i −0.979536 0.201271i \(-0.935493\pi\)
0.979536 0.201271i \(-0.0645070\pi\)
\(258\) 16.9301i 1.05402i
\(259\) 12.2385 0.760460
\(260\) 0 0
\(261\) 0.156743 0.00970214
\(262\) 11.5468i 0.713362i
\(263\) 22.1871i 1.36812i 0.729428 + 0.684058i \(0.239786\pi\)
−0.729428 + 0.684058i \(0.760214\pi\)
\(264\) 9.83658 0.605400
\(265\) 0 0
\(266\) −2.69168 −0.165037
\(267\) − 9.03284i − 0.552801i
\(268\) 2.85510i 0.174403i
\(269\) 20.4070 1.24424 0.622119 0.782922i \(-0.286272\pi\)
0.622119 + 0.782922i \(0.286272\pi\)
\(270\) 0 0
\(271\) 15.9368 0.968092 0.484046 0.875043i \(-0.339167\pi\)
0.484046 + 0.875043i \(0.339167\pi\)
\(272\) − 4.91829i − 0.298215i
\(273\) − 13.9301i − 0.843090i
\(274\) −4.23845 −0.256054
\(275\) 0 0
\(276\) −6.40187 −0.385347
\(277\) − 4.02368i − 0.241759i −0.992667 0.120880i \(-0.961428\pi\)
0.992667 0.120880i \(-0.0385715\pi\)
\(278\) 9.21994i 0.552975i
\(279\) −1.09355 −0.0654691
\(280\) 0 0
\(281\) 1.67316 0.0998124 0.0499062 0.998754i \(-0.484108\pi\)
0.0499062 + 0.998754i \(0.484108\pi\)
\(282\) − 1.48358i − 0.0883460i
\(283\) 16.8931i 1.00419i 0.864812 + 0.502095i \(0.167437\pi\)
−0.864812 + 0.502095i \(0.832563\pi\)
\(284\) −14.4769 −0.859046
\(285\) 0 0
\(286\) −16.1871 −0.957163
\(287\) 0 0
\(288\) 0.144903i 0.00853849i
\(289\) −7.18958 −0.422916
\(290\) 0 0
\(291\) 30.6033 1.79400
\(292\) − 5.15674i − 0.301776i
\(293\) − 1.08171i − 0.0631942i −0.999501 0.0315971i \(-0.989941\pi\)
0.999501 0.0315971i \(-0.0100593\pi\)
\(294\) 0.434709 0.0253527
\(295\) 0 0
\(296\) 4.54677 0.264276
\(297\) − 28.0844i − 1.62962i
\(298\) − 7.25697i − 0.420385i
\(299\) 10.5349 0.609251
\(300\) 0 0
\(301\) 25.6968 1.48114
\(302\) − 20.0000i − 1.15087i
\(303\) 16.6403i 0.955962i
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 0.712675 0.0407409
\(307\) − 2.38336i − 0.136025i −0.997684 0.0680126i \(-0.978334\pi\)
0.997684 0.0680126i \(-0.0216658\pi\)
\(308\) − 14.9301i − 0.850723i
\(309\) −22.9301 −1.30445
\(310\) 0 0
\(311\) −29.4584 −1.67043 −0.835216 0.549922i \(-0.814657\pi\)
−0.835216 + 0.549922i \(0.814657\pi\)
\(312\) − 5.17526i − 0.292991i
\(313\) 32.0355i 1.81075i 0.424608 + 0.905377i \(0.360412\pi\)
−0.424608 + 0.905377i \(0.639588\pi\)
\(314\) 9.54677 0.538756
\(315\) 0 0
\(316\) −3.09355 −0.174026
\(317\) 26.6665i 1.49774i 0.662717 + 0.748870i \(0.269403\pi\)
−0.662717 + 0.748870i \(0.730597\pi\)
\(318\) − 17.3530i − 0.973108i
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −33.5915 −1.87489
\(322\) 9.71687i 0.541500i
\(323\) 4.91829i 0.273661i
\(324\) 9.41371 0.522984
\(325\) 0 0
\(326\) 15.7102 0.870107
\(327\) − 4.77339i − 0.263969i
\(328\) 0 0
\(329\) −2.25181 −0.124146
\(330\) 0 0
\(331\) −19.8721 −1.09227 −0.546135 0.837697i \(-0.683901\pi\)
−0.546135 + 0.837697i \(0.683901\pi\)
\(332\) − 1.71019i − 0.0938591i
\(333\) 0.658841i 0.0361043i
\(334\) −6.45323 −0.353105
\(335\) 0 0
\(336\) 4.77339 0.260410
\(337\) − 27.5705i − 1.50186i −0.660383 0.750929i \(-0.729606\pi\)
0.660383 0.750929i \(-0.270394\pi\)
\(338\) − 4.48358i − 0.243875i
\(339\) −10.6403 −0.577903
\(340\) 0 0
\(341\) 41.8603 2.26686
\(342\) − 0.144903i − 0.00783545i
\(343\) 18.1819i 0.981732i
\(344\) 9.54677 0.514728
\(345\) 0 0
\(346\) −0.873614 −0.0469658
\(347\) 27.2806i 1.46450i 0.681035 + 0.732251i \(0.261530\pi\)
−0.681035 + 0.732251i \(0.738470\pi\)
\(348\) − 1.91829i − 0.102831i
\(349\) −30.9538 −1.65692 −0.828460 0.560049i \(-0.810782\pi\)
−0.828460 + 0.560049i \(0.810782\pi\)
\(350\) 0 0
\(351\) −14.7759 −0.788677
\(352\) − 5.54677i − 0.295644i
\(353\) 11.1819i 0.595154i 0.954698 + 0.297577i \(0.0961786\pi\)
−0.954698 + 0.297577i \(0.903821\pi\)
\(354\) 23.0422 1.22468
\(355\) 0 0
\(356\) −5.09355 −0.269958
\(357\) − 23.4769i − 1.24253i
\(358\) − 12.3834i − 0.654481i
\(359\) −20.3387 −1.07343 −0.536717 0.843762i \(-0.680336\pi\)
−0.536717 + 0.843762i \(0.680336\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 17.6403i 0.927155i
\(363\) − 35.0540i − 1.83986i
\(364\) −7.85510 −0.411719
\(365\) 0 0
\(366\) 13.0935 0.684411
\(367\) 32.9538i 1.72017i 0.510147 + 0.860087i \(0.329591\pi\)
−0.510147 + 0.860087i \(0.670409\pi\)
\(368\) 3.60997i 0.188183i
\(369\) 0 0
\(370\) 0 0
\(371\) −26.3387 −1.36744
\(372\) 13.3834i 0.693895i
\(373\) − 10.0869i − 0.522278i −0.965301 0.261139i \(-0.915902\pi\)
0.965301 0.261139i \(-0.0840982\pi\)
\(374\) −27.2806 −1.41065
\(375\) 0 0
\(376\) −0.836581 −0.0431434
\(377\) 3.15674i 0.162581i
\(378\) − 13.6285i − 0.700974i
\(379\) 18.4256 0.946457 0.473229 0.880940i \(-0.343088\pi\)
0.473229 + 0.880940i \(0.343088\pi\)
\(380\) 0 0
\(381\) 3.32264 0.170224
\(382\) 15.1567i 0.775486i
\(383\) 28.1871i 1.44029i 0.693822 + 0.720147i \(0.255926\pi\)
−0.693822 + 0.720147i \(0.744074\pi\)
\(384\) 1.77339 0.0904978
\(385\) 0 0
\(386\) 23.3834 1.19018
\(387\) 1.38336i 0.0703199i
\(388\) − 17.2570i − 0.876090i
\(389\) −20.0237 −1.01524 −0.507620 0.861581i \(-0.669475\pi\)
−0.507620 + 0.861581i \(0.669475\pi\)
\(390\) 0 0
\(391\) 17.7549 0.897902
\(392\) − 0.245129i − 0.0123809i
\(393\) 20.4769i 1.03292i
\(394\) 23.0935 1.16344
\(395\) 0 0
\(396\) 0.803744 0.0403896
\(397\) 8.32684i 0.417912i 0.977925 + 0.208956i \(0.0670066\pi\)
−0.977925 + 0.208956i \(0.932993\pi\)
\(398\) − 25.7852i − 1.29250i
\(399\) −4.77339 −0.238968
\(400\) 0 0
\(401\) −22.1501 −1.10612 −0.553061 0.833141i \(-0.686540\pi\)
−0.553061 + 0.833141i \(0.686540\pi\)
\(402\) 5.06319i 0.252529i
\(403\) − 22.0237i − 1.09708i
\(404\) 9.38336 0.466839
\(405\) 0 0
\(406\) −2.91161 −0.144501
\(407\) − 25.2199i − 1.25011i
\(408\) − 8.72203i − 0.431805i
\(409\) −34.0237 −1.68236 −0.841181 0.540753i \(-0.818139\pi\)
−0.841181 + 0.540753i \(0.818139\pi\)
\(410\) 0 0
\(411\) −7.51642 −0.370758
\(412\) 12.9301i 0.637022i
\(413\) − 34.9738i − 1.72095i
\(414\) −0.523095 −0.0257087
\(415\) 0 0
\(416\) −2.91829 −0.143081
\(417\) 16.3505i 0.800688i
\(418\) 5.54677i 0.271302i
\(419\) −37.5334 −1.83363 −0.916814 0.399315i \(-0.869248\pi\)
−0.916814 + 0.399315i \(0.869248\pi\)
\(420\) 0 0
\(421\) 33.8341 1.64897 0.824487 0.565882i \(-0.191464\pi\)
0.824487 + 0.565882i \(0.191464\pi\)
\(422\) − 14.2266i − 0.692541i
\(423\) − 0.121223i − 0.00589406i
\(424\) −9.78523 −0.475213
\(425\) 0 0
\(426\) −25.6732 −1.24387
\(427\) − 19.8736i − 0.961752i
\(428\) 18.9420i 0.915595i
\(429\) −28.7060 −1.38594
\(430\) 0 0
\(431\) 24.8037 1.19475 0.597377 0.801960i \(-0.296210\pi\)
0.597377 + 0.801960i \(0.296210\pi\)
\(432\) − 5.06319i − 0.243603i
\(433\) 1.68651i 0.0810487i 0.999179 + 0.0405244i \(0.0129028\pi\)
−0.999179 + 0.0405244i \(0.987097\pi\)
\(434\) 20.3135 0.975079
\(435\) 0 0
\(436\) −2.69168 −0.128908
\(437\) − 3.60997i − 0.172688i
\(438\) − 9.14490i − 0.436960i
\(439\) −0.326839 −0.0155992 −0.00779958 0.999970i \(-0.502483\pi\)
−0.00779958 + 0.999970i \(0.502483\pi\)
\(440\) 0 0
\(441\) 0.0355199 0.00169142
\(442\) 14.3530i 0.682703i
\(443\) 0.490258i 0.0232929i 0.999932 + 0.0116464i \(0.00370726\pi\)
−0.999932 + 0.0116464i \(0.996293\pi\)
\(444\) 8.06319 0.382662
\(445\) 0 0
\(446\) −4.45323 −0.210866
\(447\) − 12.8694i − 0.608703i
\(448\) − 2.69168i − 0.127170i
\(449\) −23.5468 −1.11124 −0.555621 0.831436i \(-0.687519\pi\)
−0.555621 + 0.831436i \(0.687519\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000i 0.282216i
\(453\) − 35.4677i − 1.66642i
\(454\) −5.94865 −0.279184
\(455\) 0 0
\(456\) −1.77339 −0.0830465
\(457\) 8.01184i 0.374778i 0.982286 + 0.187389i \(0.0600025\pi\)
−0.982286 + 0.187389i \(0.939997\pi\)
\(458\) 1.09355i 0.0510982i
\(459\) −24.9023 −1.16234
\(460\) 0 0
\(461\) 3.83658 0.178687 0.0893437 0.996001i \(-0.471523\pi\)
0.0893437 + 0.996001i \(0.471523\pi\)
\(462\) − 26.4769i − 1.23182i
\(463\) − 6.58381i − 0.305975i −0.988228 0.152988i \(-0.951110\pi\)
0.988228 0.152988i \(-0.0488895\pi\)
\(464\) −1.08171 −0.0502171
\(465\) 0 0
\(466\) 14.0935 0.652871
\(467\) − 22.6033i − 1.04596i −0.852346 0.522978i \(-0.824821\pi\)
0.852346 0.522978i \(-0.175179\pi\)
\(468\) − 0.422869i − 0.0195471i
\(469\) 7.68500 0.354860
\(470\) 0 0
\(471\) 16.9301 0.780099
\(472\) − 12.9933i − 0.598066i
\(473\) − 52.9538i − 2.43482i
\(474\) −5.48606 −0.251983
\(475\) 0 0
\(476\) −13.2385 −0.606783
\(477\) − 1.41791i − 0.0649215i
\(478\) 15.6100i 0.713983i
\(479\) 35.7904 1.63530 0.817652 0.575712i \(-0.195275\pi\)
0.817652 + 0.575712i \(0.195275\pi\)
\(480\) 0 0
\(481\) −13.2688 −0.605006
\(482\) 5.21994i 0.237762i
\(483\) 17.2318i 0.784073i
\(484\) −19.7667 −0.898487
\(485\) 0 0
\(486\) 1.50458 0.0682491
\(487\) 21.4070i 0.970045i 0.874502 + 0.485023i \(0.161189\pi\)
−0.874502 + 0.485023i \(0.838811\pi\)
\(488\) − 7.38336i − 0.334229i
\(489\) 27.8603 1.25988
\(490\) 0 0
\(491\) −4.32684 −0.195267 −0.0976337 0.995222i \(-0.531127\pi\)
−0.0976337 + 0.995222i \(0.531127\pi\)
\(492\) 0 0
\(493\) 5.32016i 0.239608i
\(494\) 2.91829 0.131300
\(495\) 0 0
\(496\) 7.54677 0.338860
\(497\) 38.9672i 1.74792i
\(498\) − 3.03284i − 0.135905i
\(499\) 37.6968 1.68754 0.843771 0.536703i \(-0.180330\pi\)
0.843771 + 0.536703i \(0.180330\pi\)
\(500\) 0 0
\(501\) −11.4441 −0.511283
\(502\) 28.6403i 1.27828i
\(503\) − 16.9183i − 0.754349i −0.926142 0.377175i \(-0.876896\pi\)
0.926142 0.377175i \(-0.123104\pi\)
\(504\) 0.390032 0.0173734
\(505\) 0 0
\(506\) 20.0237 0.890161
\(507\) − 7.95113i − 0.353122i
\(508\) − 1.87361i − 0.0831282i
\(509\) 6.79955 0.301385 0.150692 0.988581i \(-0.451850\pi\)
0.150692 + 0.988581i \(0.451850\pi\)
\(510\) 0 0
\(511\) −13.8803 −0.614028
\(512\) − 1.00000i − 0.0441942i
\(513\) 5.06319i 0.223545i
\(514\) −6.45323 −0.284640
\(515\) 0 0
\(516\) 16.9301 0.745307
\(517\) 4.64032i 0.204081i
\(518\) − 12.2385i − 0.537727i
\(519\) −1.54926 −0.0680048
\(520\) 0 0
\(521\) −1.35968 −0.0595685 −0.0297842 0.999556i \(-0.509482\pi\)
−0.0297842 + 0.999556i \(0.509482\pi\)
\(522\) − 0.156743i − 0.00686045i
\(523\) − 21.9486i − 0.959747i −0.877338 0.479874i \(-0.840682\pi\)
0.877338 0.479874i \(-0.159318\pi\)
\(524\) 11.5468 0.504423
\(525\) 0 0
\(526\) 22.1871 0.967404
\(527\) − 37.1172i − 1.61685i
\(528\) − 9.83658i − 0.428082i
\(529\) 9.96813 0.433397
\(530\) 0 0
\(531\) 1.88277 0.0817053
\(532\) 2.69168i 0.116699i
\(533\) 0 0
\(534\) −9.03284 −0.390889
\(535\) 0 0
\(536\) 2.85510 0.123321
\(537\) − 21.9605i − 0.947665i
\(538\) − 20.4070i − 0.879810i
\(539\) −1.35968 −0.0585654
\(540\) 0 0
\(541\) −39.8973 −1.71532 −0.857659 0.514218i \(-0.828082\pi\)
−0.857659 + 0.514218i \(0.828082\pi\)
\(542\) − 15.9368i − 0.684544i
\(543\) 31.2831i 1.34249i
\(544\) −4.91829 −0.210870
\(545\) 0 0
\(546\) −13.9301 −0.596155
\(547\) 7.34632i 0.314106i 0.987590 + 0.157053i \(0.0501994\pi\)
−0.987590 + 0.157053i \(0.949801\pi\)
\(548\) 4.23845i 0.181058i
\(549\) 1.06987 0.0456609
\(550\) 0 0
\(551\) 1.08171 0.0460824
\(552\) 6.40187i 0.272482i
\(553\) 8.32684i 0.354093i
\(554\) −4.02368 −0.170950
\(555\) 0 0
\(556\) 9.21994 0.391012
\(557\) 26.9672i 1.14264i 0.820729 + 0.571318i \(0.193568\pi\)
−0.820729 + 0.571318i \(0.806432\pi\)
\(558\) 1.09355i 0.0462936i
\(559\) −27.8603 −1.17836
\(560\) 0 0
\(561\) −48.3792 −2.04257
\(562\) − 1.67316i − 0.0705780i
\(563\) − 44.8973i − 1.89220i −0.323881 0.946098i \(-0.604988\pi\)
0.323881 0.946098i \(-0.395012\pi\)
\(564\) −1.48358 −0.0624701
\(565\) 0 0
\(566\) 16.8931 0.710070
\(567\) − 25.3387i − 1.06412i
\(568\) 14.4769i 0.607437i
\(569\) −31.1172 −1.30450 −0.652251 0.758003i \(-0.726175\pi\)
−0.652251 + 0.758003i \(0.726175\pi\)
\(570\) 0 0
\(571\) 33.2570 1.39176 0.695880 0.718158i \(-0.255014\pi\)
0.695880 + 0.718158i \(0.255014\pi\)
\(572\) 16.1871i 0.676817i
\(573\) 26.8788i 1.12288i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.144903 0.00603762
\(577\) − 23.4702i − 0.977078i −0.872542 0.488539i \(-0.837530\pi\)
0.872542 0.488539i \(-0.162470\pi\)
\(578\) 7.18958i 0.299047i
\(579\) 41.4677 1.72334
\(580\) 0 0
\(581\) −4.60329 −0.190977
\(582\) − 30.6033i − 1.26855i
\(583\) 54.2765i 2.24790i
\(584\) −5.15674 −0.213388
\(585\) 0 0
\(586\) −1.08171 −0.0446850
\(587\) 10.1501i 0.418938i 0.977815 + 0.209469i \(0.0671735\pi\)
−0.977815 + 0.209469i \(0.932826\pi\)
\(588\) − 0.434709i − 0.0179271i
\(589\) −7.54677 −0.310959
\(590\) 0 0
\(591\) 40.9538 1.68461
\(592\) − 4.54677i − 0.186871i
\(593\) − 16.6732i − 0.684685i −0.939575 0.342342i \(-0.888780\pi\)
0.939575 0.342342i \(-0.111220\pi\)
\(594\) −28.0844 −1.15232
\(595\) 0 0
\(596\) −7.25697 −0.297257
\(597\) − 45.7272i − 1.87149i
\(598\) − 10.5349i − 0.430806i
\(599\) −18.2765 −0.746756 −0.373378 0.927679i \(-0.621800\pi\)
−0.373378 + 0.927679i \(0.621800\pi\)
\(600\) 0 0
\(601\) 7.96297 0.324816 0.162408 0.986724i \(-0.448074\pi\)
0.162408 + 0.986724i \(0.448074\pi\)
\(602\) − 25.6968i − 1.04733i
\(603\) 0.413712i 0.0168477i
\(604\) −20.0000 −0.813788
\(605\) 0 0
\(606\) 16.6403 0.675967
\(607\) 6.93013i 0.281285i 0.990060 + 0.140643i \(0.0449169\pi\)
−0.990060 + 0.140643i \(0.955083\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) −5.16342 −0.209232
\(610\) 0 0
\(611\) 2.44139 0.0987679
\(612\) − 0.712675i − 0.0288082i
\(613\) − 34.2765i − 1.38441i −0.721700 0.692206i \(-0.756639\pi\)
0.721700 0.692206i \(-0.243361\pi\)
\(614\) −2.38336 −0.0961844
\(615\) 0 0
\(616\) −14.9301 −0.601552
\(617\) − 35.5139i − 1.42974i −0.699259 0.714869i \(-0.746486\pi\)
0.699259 0.714869i \(-0.253514\pi\)
\(618\) 22.9301i 0.922385i
\(619\) 29.5334 1.18705 0.593524 0.804816i \(-0.297736\pi\)
0.593524 + 0.804816i \(0.297736\pi\)
\(620\) 0 0
\(621\) 18.2780 0.733470
\(622\) 29.4584i 1.18117i
\(623\) 13.7102i 0.549287i
\(624\) −5.17526 −0.207176
\(625\) 0 0
\(626\) 32.0355 1.28040
\(627\) 9.83658i 0.392835i
\(628\) − 9.54677i − 0.380958i
\(629\) −22.3624 −0.891646
\(630\) 0 0
\(631\) −15.1634 −0.603646 −0.301823 0.953364i \(-0.597595\pi\)
−0.301823 + 0.953364i \(0.597595\pi\)
\(632\) 3.09355i 0.123055i
\(633\) − 25.2293i − 1.00277i
\(634\) 26.6665 1.05906
\(635\) 0 0
\(636\) −17.3530 −0.688091
\(637\) 0.715358i 0.0283435i
\(638\) 6.00000i 0.237542i
\(639\) −2.09775 −0.0829855
\(640\) 0 0
\(641\) −25.0802 −0.990608 −0.495304 0.868720i \(-0.664943\pi\)
−0.495304 + 0.868720i \(0.664943\pi\)
\(642\) 33.5915i 1.32575i
\(643\) 19.1306i 0.754437i 0.926124 + 0.377218i \(0.123119\pi\)
−0.926124 + 0.377218i \(0.876881\pi\)
\(644\) 9.71687 0.382898
\(645\) 0 0
\(646\) 4.91829 0.193508
\(647\) − 12.4019i − 0.487568i −0.969830 0.243784i \(-0.921611\pi\)
0.969830 0.243784i \(-0.0783888\pi\)
\(648\) − 9.41371i − 0.369806i
\(649\) −72.0710 −2.82904
\(650\) 0 0
\(651\) 36.0237 1.41188
\(652\) − 15.7102i − 0.615259i
\(653\) − 10.7801i − 0.421856i −0.977502 0.210928i \(-0.932351\pi\)
0.977502 0.210928i \(-0.0676486\pi\)
\(654\) −4.77339 −0.186654
\(655\) 0 0
\(656\) 0 0
\(657\) − 0.747227i − 0.0291521i
\(658\) 2.25181i 0.0877845i
\(659\) −8.56529 −0.333656 −0.166828 0.985986i \(-0.553353\pi\)
−0.166828 + 0.985986i \(0.553353\pi\)
\(660\) 0 0
\(661\) −26.2883 −1.02250 −0.511248 0.859433i \(-0.670817\pi\)
−0.511248 + 0.859433i \(0.670817\pi\)
\(662\) 19.8721i 0.772351i
\(663\) 25.4534i 0.988529i
\(664\) −1.71019 −0.0663684
\(665\) 0 0
\(666\) 0.658841 0.0255296
\(667\) − 3.90494i − 0.151200i
\(668\) 6.45323i 0.249683i
\(669\) −7.89729 −0.305327
\(670\) 0 0
\(671\) −40.9538 −1.58100
\(672\) − 4.77339i − 0.184137i
\(673\) − 12.9301i − 0.498420i −0.968449 0.249210i \(-0.919829\pi\)
0.968449 0.249210i \(-0.0801709\pi\)
\(674\) −27.5705 −1.06197
\(675\) 0 0
\(676\) −4.48358 −0.172445
\(677\) 15.9250i 0.612046i 0.952024 + 0.306023i \(0.0989985\pi\)
−0.952024 + 0.306023i \(0.901002\pi\)
\(678\) 10.6403i 0.408639i
\(679\) −46.4502 −1.78260
\(680\) 0 0
\(681\) −10.5493 −0.404248
\(682\) − 41.8603i − 1.60291i
\(683\) 13.2898i 0.508520i 0.967136 + 0.254260i \(0.0818319\pi\)
−0.967136 + 0.254260i \(0.918168\pi\)
\(684\) −0.144903 −0.00554050
\(685\) 0 0
\(686\) 18.1819 0.694190
\(687\) 1.93929i 0.0739884i
\(688\) − 9.54677i − 0.363967i
\(689\) 28.5561 1.08790
\(690\) 0 0
\(691\) 27.2570 1.03690 0.518452 0.855107i \(-0.326508\pi\)
0.518452 + 0.855107i \(0.326508\pi\)
\(692\) 0.873614i 0.0332098i
\(693\) − 2.16342i − 0.0821815i
\(694\) 27.2806 1.03556
\(695\) 0 0
\(696\) −1.91829 −0.0727126
\(697\) 0 0
\(698\) 30.9538i 1.17162i
\(699\) 24.9933 0.945334
\(700\) 0 0
\(701\) −41.4441 −1.56532 −0.782660 0.622449i \(-0.786138\pi\)
−0.782660 + 0.622449i \(0.786138\pi\)
\(702\) 14.7759i 0.557679i
\(703\) 4.54677i 0.171485i
\(704\) −5.54677 −0.209052
\(705\) 0 0
\(706\) 11.1819 0.420838
\(707\) − 25.2570i − 0.949886i
\(708\) − 23.0422i − 0.865979i
\(709\) 36.7904 1.38169 0.690846 0.723002i \(-0.257238\pi\)
0.690846 + 0.723002i \(0.257238\pi\)
\(710\) 0 0
\(711\) −0.448264 −0.0168112
\(712\) 5.09355i 0.190889i
\(713\) 27.2436i 1.02028i
\(714\) −23.4769 −0.878601
\(715\) 0 0
\(716\) −12.3834 −0.462788
\(717\) 27.6825i 1.03382i
\(718\) 20.3387i 0.759033i
\(719\) 4.13726 0.154294 0.0771469 0.997020i \(-0.475419\pi\)
0.0771469 + 0.997020i \(0.475419\pi\)
\(720\) 0 0
\(721\) 34.8037 1.29616
\(722\) − 1.00000i − 0.0372161i
\(723\) 9.25697i 0.344270i
\(724\) 17.6403 0.655597
\(725\) 0 0
\(726\) −35.0540 −1.30098
\(727\) 40.4374i 1.49974i 0.661585 + 0.749870i \(0.269884\pi\)
−0.661585 + 0.749870i \(0.730116\pi\)
\(728\) 7.85510i 0.291129i
\(729\) −25.5729 −0.947146
\(730\) 0 0
\(731\) −46.9538 −1.73665
\(732\) − 13.0935i − 0.483952i
\(733\) 28.1264i 1.03887i 0.854509 + 0.519436i \(0.173858\pi\)
−0.854509 + 0.519436i \(0.826142\pi\)
\(734\) 32.9538 1.21635
\(735\) 0 0
\(736\) 3.60997 0.133065
\(737\) − 15.8366i − 0.583348i
\(738\) 0 0
\(739\) 38.1501 1.40337 0.701686 0.712486i \(-0.252431\pi\)
0.701686 + 0.712486i \(0.252431\pi\)
\(740\) 0 0
\(741\) 5.17526 0.190118
\(742\) 26.3387i 0.966923i
\(743\) − 17.8232i − 0.653871i −0.945047 0.326935i \(-0.893984\pi\)
0.945047 0.326935i \(-0.106016\pi\)
\(744\) 13.3834 0.490658
\(745\) 0 0
\(746\) −10.0869 −0.369307
\(747\) − 0.247812i − 0.00906697i
\(748\) 27.2806i 0.997479i
\(749\) 50.9857 1.86298
\(750\) 0 0
\(751\) 23.6968 0.864710 0.432355 0.901703i \(-0.357683\pi\)
0.432355 + 0.901703i \(0.357683\pi\)
\(752\) 0.836581i 0.0305070i
\(753\) 50.7904i 1.85090i
\(754\) 3.15674 0.114962
\(755\) 0 0
\(756\) −13.6285 −0.495663
\(757\) 6.51394i 0.236753i 0.992969 + 0.118377i \(0.0377690\pi\)
−0.992969 + 0.118377i \(0.962231\pi\)
\(758\) − 18.4256i − 0.669246i
\(759\) 35.5097 1.28892
\(760\) 0 0
\(761\) 34.7786 1.26072 0.630361 0.776302i \(-0.282907\pi\)
0.630361 + 0.776302i \(0.282907\pi\)
\(762\) − 3.32264i − 0.120367i
\(763\) 7.24513i 0.262291i
\(764\) 15.1567 0.548352
\(765\) 0 0
\(766\) 28.1871 1.01844
\(767\) 37.9183i 1.36915i
\(768\) − 1.77339i − 0.0639916i
\(769\) 27.6850 0.998347 0.499173 0.866502i \(-0.333637\pi\)
0.499173 + 0.866502i \(0.333637\pi\)
\(770\) 0 0
\(771\) −11.4441 −0.412148
\(772\) − 23.3834i − 0.841585i
\(773\) − 19.9738i − 0.718409i −0.933259 0.359205i \(-0.883048\pi\)
0.933259 0.359205i \(-0.116952\pi\)
\(774\) 1.38336 0.0497237
\(775\) 0 0
\(776\) −17.2570 −0.619489
\(777\) − 21.7035i − 0.778609i
\(778\) 20.0237i 0.717884i
\(779\) 0 0
\(780\) 0 0
\(781\) 80.3001 2.87336
\(782\) − 17.7549i − 0.634913i
\(783\) 5.47691i 0.195729i
\(784\) −0.245129 −0.00875461
\(785\) 0 0
\(786\) 20.4769 0.730387
\(787\) − 42.0118i − 1.49756i −0.662818 0.748780i \(-0.730640\pi\)
0.662818 0.748780i \(-0.269360\pi\)
\(788\) − 23.0935i − 0.822674i
\(789\) 39.3463 1.40077
\(790\) 0 0
\(791\) 16.1501 0.574230
\(792\) − 0.803744i − 0.0285598i
\(793\) 21.5468i 0.765148i
\(794\) 8.32684 0.295508
\(795\) 0 0
\(796\) −25.7852 −0.913933
\(797\) 45.1054i 1.59771i 0.601520 + 0.798857i \(0.294562\pi\)
−0.601520 + 0.798857i \(0.705438\pi\)
\(798\) 4.77339i 0.168976i
\(799\) 4.11455 0.145562
\(800\) 0 0
\(801\) −0.738070 −0.0260784
\(802\) 22.1501i 0.782146i
\(803\) 28.6033i 1.00939i
\(804\) 5.06319 0.178565
\(805\) 0 0
\(806\) −22.0237 −0.775751
\(807\) − 36.1896i − 1.27393i
\(808\) − 9.38336i − 0.330105i
\(809\) −6.85510 −0.241012 −0.120506 0.992713i \(-0.538452\pi\)
−0.120506 + 0.992713i \(0.538452\pi\)
\(810\) 0 0
\(811\) −15.1819 −0.533110 −0.266555 0.963820i \(-0.585885\pi\)
−0.266555 + 0.963820i \(0.585885\pi\)
\(812\) 2.91161i 0.102178i
\(813\) − 28.2621i − 0.991196i
\(814\) −25.2199 −0.883958
\(815\) 0 0
\(816\) −8.72203 −0.305332
\(817\) 9.54677i 0.333999i
\(818\) 34.0237i 1.18961i
\(819\) −1.13823 −0.0397729
\(820\) 0 0
\(821\) 22.5006 0.785276 0.392638 0.919693i \(-0.371563\pi\)
0.392638 + 0.919693i \(0.371563\pi\)
\(822\) 7.51642i 0.262165i
\(823\) − 16.1896i − 0.564333i −0.959365 0.282167i \(-0.908947\pi\)
0.959365 0.282167i \(-0.0910531\pi\)
\(824\) 12.9301 0.450442
\(825\) 0 0
\(826\) −34.9738 −1.21690
\(827\) 25.0817i 0.872177i 0.899904 + 0.436088i \(0.143636\pi\)
−0.899904 + 0.436088i \(0.856364\pi\)
\(828\) 0.523095i 0.0181788i
\(829\) −21.3068 −0.740016 −0.370008 0.929029i \(-0.620645\pi\)
−0.370008 + 0.929029i \(0.620645\pi\)
\(830\) 0 0
\(831\) −7.13554 −0.247529
\(832\) 2.91829i 0.101174i
\(833\) 1.20562i 0.0417721i
\(834\) 16.3505 0.566172
\(835\) 0 0
\(836\) 5.54677 0.191839
\(837\) − 38.2108i − 1.32076i
\(838\) 37.5334i 1.29657i
\(839\) 11.4727 0.396082 0.198041 0.980194i \(-0.436542\pi\)
0.198041 + 0.980194i \(0.436542\pi\)
\(840\) 0 0
\(841\) −27.8299 −0.959652
\(842\) − 33.8341i − 1.16600i
\(843\) − 2.96716i − 0.102195i
\(844\) −14.2266 −0.489700
\(845\) 0 0
\(846\) −0.121223 −0.00416773
\(847\) 53.2056i 1.82817i
\(848\) 9.78523i 0.336026i
\(849\) 29.9580 1.02816
\(850\) 0 0
\(851\) 16.4137 0.562655
\(852\) 25.6732i 0.879548i
\(853\) − 38.9908i − 1.33502i −0.744600 0.667511i \(-0.767360\pi\)
0.744600 0.667511i \(-0.232640\pi\)
\(854\) −19.8736 −0.680061
\(855\) 0 0
\(856\) 18.9420 0.647423
\(857\) 29.8973i 1.02127i 0.859797 + 0.510636i \(0.170590\pi\)
−0.859797 + 0.510636i \(0.829410\pi\)
\(858\) 28.7060i 0.980007i
\(859\) 6.47691 0.220989 0.110495 0.993877i \(-0.464757\pi\)
0.110495 + 0.993877i \(0.464757\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) − 24.8037i − 0.844819i
\(863\) − 5.09355i − 0.173386i −0.996235 0.0866932i \(-0.972370\pi\)
0.996235 0.0866932i \(-0.0276300\pi\)
\(864\) −5.06319 −0.172253
\(865\) 0 0
\(866\) 1.68651 0.0573101
\(867\) 12.7499i 0.433010i
\(868\) − 20.3135i − 0.689485i
\(869\) 17.1592 0.582087
\(870\) 0 0
\(871\) −8.33200 −0.282319
\(872\) 2.69168i 0.0911517i
\(873\) − 2.50059i − 0.0846320i
\(874\) −3.60997 −0.122109
\(875\) 0 0
\(876\) −9.14490 −0.308978
\(877\) 29.8341i 1.00743i 0.863871 + 0.503713i \(0.168033\pi\)
−0.863871 + 0.503713i \(0.831967\pi\)
\(878\) 0.326839i 0.0110303i
\(879\) −1.91829 −0.0647023
\(880\) 0 0
\(881\) −11.5796 −0.390127 −0.195064 0.980791i \(-0.562491\pi\)
−0.195064 + 0.980791i \(0.562491\pi\)
\(882\) − 0.0355199i − 0.00119602i
\(883\) − 48.0237i − 1.61613i −0.589096 0.808063i \(-0.700516\pi\)
0.589096 0.808063i \(-0.299484\pi\)
\(884\) 14.3530 0.482744
\(885\) 0 0
\(886\) 0.490258 0.0164705
\(887\) − 9.38336i − 0.315062i −0.987514 0.157531i \(-0.949647\pi\)
0.987514 0.157531i \(-0.0503535\pi\)
\(888\) − 8.06319i − 0.270583i
\(889\) −5.04316 −0.169142
\(890\) 0 0
\(891\) −52.2157 −1.74929
\(892\) 4.45323i 0.149105i
\(893\) − 0.836581i − 0.0279951i
\(894\) −12.8694 −0.430418
\(895\) 0 0
\(896\) −2.69168 −0.0899226
\(897\) − 18.6825i − 0.623791i
\(898\) 23.5468i 0.785766i
\(899\) −8.16342 −0.272265
\(900\) 0 0
\(901\) 48.1266 1.60333
\(902\) 0 0
\(903\) − 45.5705i − 1.51649i
\(904\) 6.00000 0.199557
\(905\) 0 0
\(906\) −35.4677 −1.17834
\(907\) 19.4347i 0.645319i 0.946515 + 0.322659i \(0.104577\pi\)
−0.946515 + 0.322659i \(0.895423\pi\)
\(908\) 5.94865i 0.197413i
\(909\) 1.35968 0.0450976
\(910\) 0 0
\(911\) −19.9866 −0.662187 −0.331094 0.943598i \(-0.607418\pi\)
−0.331094 + 0.943598i \(0.607418\pi\)
\(912\) 1.77339i 0.0587227i
\(913\) 9.48606i 0.313943i
\(914\) 8.01184 0.265008
\(915\) 0 0
\(916\) 1.09355 0.0361319
\(917\) − 31.0802i − 1.02636i
\(918\) 24.9023i 0.821897i
\(919\) −6.15158 −0.202922 −0.101461 0.994840i \(-0.532352\pi\)
−0.101461 + 0.994840i \(0.532352\pi\)
\(920\) 0 0
\(921\) −4.22661 −0.139272
\(922\) − 3.83658i − 0.126351i
\(923\) − 42.2478i − 1.39060i
\(924\) −26.4769 −0.871026
\(925\) 0 0
\(926\) −6.58381 −0.216357
\(927\) 1.87361i 0.0615375i
\(928\) 1.08171i 0.0355089i
\(929\) 7.17010 0.235243 0.117622 0.993058i \(-0.462473\pi\)
0.117622 + 0.993058i \(0.462473\pi\)
\(930\) 0 0
\(931\) 0.245129 0.00803378
\(932\) − 14.0935i − 0.461650i
\(933\) 52.2411i 1.71030i
\(934\) −22.6033 −0.739602
\(935\) 0 0
\(936\) −0.422869 −0.0138219
\(937\) 24.2646i 0.792690i 0.918102 + 0.396345i \(0.129722\pi\)
−0.918102 + 0.396345i \(0.870278\pi\)
\(938\) − 7.68500i − 0.250924i
\(939\) 56.8114 1.85397
\(940\) 0 0
\(941\) −7.44806 −0.242800 −0.121400 0.992604i \(-0.538738\pi\)
−0.121400 + 0.992604i \(0.538738\pi\)
\(942\) − 16.9301i − 0.551613i
\(943\) 0 0
\(944\) −12.9933 −0.422897
\(945\) 0 0
\(946\) −52.9538 −1.72168
\(947\) 52.9538i 1.72077i 0.509647 + 0.860384i \(0.329776\pi\)
−0.509647 + 0.860384i \(0.670224\pi\)
\(948\) 5.48606i 0.178179i
\(949\) 15.0489 0.488507
\(950\) 0 0
\(951\) 47.2900 1.53348
\(952\) 13.2385i 0.429061i
\(953\) − 12.8694i − 0.416881i −0.978035 0.208441i \(-0.933161\pi\)
0.978035 0.208441i \(-0.0668388\pi\)
\(954\) −1.41791 −0.0459065
\(955\) 0 0
\(956\) 15.6100 0.504862
\(957\) 10.6403i 0.343953i
\(958\) − 35.7904i − 1.15634i
\(959\) 11.4085 0.368401
\(960\) 0 0
\(961\) 25.9538 0.837220
\(962\) 13.2688i 0.427804i
\(963\) 2.74475i 0.0884482i
\(964\) 5.21994 0.168123
\(965\) 0 0
\(966\) 17.2318 0.554423
\(967\) − 25.8603i − 0.831610i −0.909454 0.415805i \(-0.863500\pi\)
0.909454 0.415805i \(-0.136500\pi\)
\(968\) 19.7667i 0.635326i
\(969\) 8.72203 0.280192
\(970\) 0 0
\(971\) 35.0935 1.12621 0.563103 0.826387i \(-0.309608\pi\)
0.563103 + 0.826387i \(0.309608\pi\)
\(972\) − 1.50458i − 0.0482594i
\(973\) − 24.8171i − 0.795600i
\(974\) 21.4070 0.685926
\(975\) 0 0
\(976\) −7.38336 −0.236335
\(977\) 42.1737i 1.34926i 0.738157 + 0.674629i \(0.235696\pi\)
−0.738157 + 0.674629i \(0.764304\pi\)
\(978\) − 27.8603i − 0.890873i
\(979\) 28.2528 0.902963
\(980\) 0 0
\(981\) −0.390032 −0.0124528
\(982\) 4.32684i 0.138075i
\(983\) − 42.6270i − 1.35959i −0.733403 0.679795i \(-0.762069\pi\)
0.733403 0.679795i \(-0.237931\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 5.32016 0.169428
\(987\) 3.99332i 0.127109i
\(988\) − 2.91829i − 0.0928432i
\(989\) 34.4636 1.09588
\(990\) 0 0
\(991\) −34.1737 −1.08556 −0.542782 0.839873i \(-0.682629\pi\)
−0.542782 + 0.839873i \(0.682629\pi\)
\(992\) − 7.54677i − 0.239610i
\(993\) 35.2409i 1.11834i
\(994\) 38.9672 1.23596
\(995\) 0 0
\(996\) −3.03284 −0.0960991
\(997\) − 29.3834i − 0.930580i −0.885158 0.465290i \(-0.845950\pi\)
0.885158 0.465290i \(-0.154050\pi\)
\(998\) − 37.6968i − 1.19327i
\(999\) −23.0212 −0.728359
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.b.h.799.1 6
5.2 odd 4 950.2.a.l.1.1 yes 3
5.3 odd 4 950.2.a.j.1.3 3
5.4 even 2 inner 950.2.b.h.799.6 6
15.2 even 4 8550.2.a.ci.1.1 3
15.8 even 4 8550.2.a.cp.1.3 3
20.3 even 4 7600.2.a.bz.1.1 3
20.7 even 4 7600.2.a.bk.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.3 3 5.3 odd 4
950.2.a.l.1.1 yes 3 5.2 odd 4
950.2.b.h.799.1 6 1.1 even 1 trivial
950.2.b.h.799.6 6 5.4 even 2 inner
7600.2.a.bk.1.3 3 20.7 even 4
7600.2.a.bz.1.1 3 20.3 even 4
8550.2.a.ci.1.1 3 15.2 even 4
8550.2.a.cp.1.3 3 15.8 even 4