Properties

Label 950.2.a.h.1.1
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.56155\) of defining polynomial
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -1.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} -1.56155 q^{6} -1.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +4.00000 q^{11} -1.56155 q^{12} +6.68466 q^{13} -1.56155 q^{14} +1.00000 q^{16} -7.56155 q^{17} -0.561553 q^{18} -1.00000 q^{19} +2.43845 q^{21} +4.00000 q^{22} +4.68466 q^{23} -1.56155 q^{24} +6.68466 q^{26} +5.56155 q^{27} -1.56155 q^{28} +6.68466 q^{29} +3.12311 q^{31} +1.00000 q^{32} -6.24621 q^{33} -7.56155 q^{34} -0.561553 q^{36} +6.00000 q^{37} -1.00000 q^{38} -10.4384 q^{39} -4.24621 q^{41} +2.43845 q^{42} +11.1231 q^{43} +4.00000 q^{44} +4.68466 q^{46} +10.2462 q^{47} -1.56155 q^{48} -4.56155 q^{49} +11.8078 q^{51} +6.68466 q^{52} +0.438447 q^{53} +5.56155 q^{54} -1.56155 q^{56} +1.56155 q^{57} +6.68466 q^{58} -1.56155 q^{59} +2.87689 q^{61} +3.12311 q^{62} +0.876894 q^{63} +1.00000 q^{64} -6.24621 q^{66} -1.56155 q^{67} -7.56155 q^{68} -7.31534 q^{69} -6.24621 q^{71} -0.561553 q^{72} -10.6847 q^{73} +6.00000 q^{74} -1.00000 q^{76} -6.24621 q^{77} -10.4384 q^{78} +3.12311 q^{79} -7.00000 q^{81} -4.24621 q^{82} -11.1231 q^{83} +2.43845 q^{84} +11.1231 q^{86} -10.4384 q^{87} +4.00000 q^{88} +2.00000 q^{89} -10.4384 q^{91} +4.68466 q^{92} -4.87689 q^{93} +10.2462 q^{94} -1.56155 q^{96} -6.00000 q^{97} -4.56155 q^{98} -2.24621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + q^{3} + 2q^{4} + q^{6} + q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + 2q^{2} + q^{3} + 2q^{4} + q^{6} + q^{7} + 2q^{8} + 3q^{9} + 8q^{11} + q^{12} + q^{13} + q^{14} + 2q^{16} - 11q^{17} + 3q^{18} - 2q^{19} + 9q^{21} + 8q^{22} - 3q^{23} + q^{24} + q^{26} + 7q^{27} + q^{28} + q^{29} - 2q^{31} + 2q^{32} + 4q^{33} - 11q^{34} + 3q^{36} + 12q^{37} - 2q^{38} - 25q^{39} + 8q^{41} + 9q^{42} + 14q^{43} + 8q^{44} - 3q^{46} + 4q^{47} + q^{48} - 5q^{49} + 3q^{51} + q^{52} + 5q^{53} + 7q^{54} + q^{56} - q^{57} + q^{58} + q^{59} + 14q^{61} - 2q^{62} + 10q^{63} + 2q^{64} + 4q^{66} + q^{67} - 11q^{68} - 27q^{69} + 4q^{71} + 3q^{72} - 9q^{73} + 12q^{74} - 2q^{76} + 4q^{77} - 25q^{78} - 2q^{79} - 14q^{81} + 8q^{82} - 14q^{83} + 9q^{84} + 14q^{86} - 25q^{87} + 8q^{88} + 4q^{89} - 25q^{91} - 3q^{92} - 18q^{93} + 4q^{94} + q^{96} - 12q^{97} - 5q^{98} + 12q^{99} + O(q^{100}) \)

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
\(3\) −1.56155 −0.901563 −0.450781 0.892634i \(-0.648855\pi\)
−0.450781 + 0.892634i \(0.648855\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.56155 −0.637501
\(7\) −1.56155 −0.590211 −0.295106 0.955465i \(-0.595355\pi\)
−0.295106 + 0.955465i \(0.595355\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.561553 −0.187184
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) −1.56155 −0.450781
\(13\) 6.68466 1.85399 0.926995 0.375073i \(-0.122382\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) −1.56155 −0.417343
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −7.56155 −1.83395 −0.916973 0.398949i \(-0.869375\pi\)
−0.916973 + 0.398949i \(0.869375\pi\)
\(18\) −0.561553 −0.132359
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.43845 0.532113
\(22\) 4.00000 0.852803
\(23\) 4.68466 0.976819 0.488409 0.872615i \(-0.337577\pi\)
0.488409 + 0.872615i \(0.337577\pi\)
\(24\) −1.56155 −0.318751
\(25\) 0 0
\(26\) 6.68466 1.31097
\(27\) 5.56155 1.07032
\(28\) −1.56155 −0.295106
\(29\) 6.68466 1.24131 0.620655 0.784084i \(-0.286867\pi\)
0.620655 + 0.784084i \(0.286867\pi\)
\(30\) 0 0
\(31\) 3.12311 0.560926 0.280463 0.959865i \(-0.409512\pi\)
0.280463 + 0.959865i \(0.409512\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.24621 −1.08733
\(34\) −7.56155 −1.29680
\(35\) 0 0
\(36\) −0.561553 −0.0935921
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) −1.00000 −0.162221
\(39\) −10.4384 −1.67149
\(40\) 0 0
\(41\) −4.24621 −0.663147 −0.331573 0.943429i \(-0.607579\pi\)
−0.331573 + 0.943429i \(0.607579\pi\)
\(42\) 2.43845 0.376261
\(43\) 11.1231 1.69626 0.848129 0.529790i \(-0.177729\pi\)
0.848129 + 0.529790i \(0.177729\pi\)
\(44\) 4.00000 0.603023
\(45\) 0 0
\(46\) 4.68466 0.690715
\(47\) 10.2462 1.49456 0.747282 0.664507i \(-0.231359\pi\)
0.747282 + 0.664507i \(0.231359\pi\)
\(48\) −1.56155 −0.225391
\(49\) −4.56155 −0.651650
\(50\) 0 0
\(51\) 11.8078 1.65342
\(52\) 6.68466 0.926995
\(53\) 0.438447 0.0602254 0.0301127 0.999547i \(-0.490413\pi\)
0.0301127 + 0.999547i \(0.490413\pi\)
\(54\) 5.56155 0.756831
\(55\) 0 0
\(56\) −1.56155 −0.208671
\(57\) 1.56155 0.206833
\(58\) 6.68466 0.877739
\(59\) −1.56155 −0.203297 −0.101648 0.994820i \(-0.532412\pi\)
−0.101648 + 0.994820i \(0.532412\pi\)
\(60\) 0 0
\(61\) 2.87689 0.368349 0.184174 0.982894i \(-0.441039\pi\)
0.184174 + 0.982894i \(0.441039\pi\)
\(62\) 3.12311 0.396635
\(63\) 0.876894 0.110478
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.24621 −0.768855
\(67\) −1.56155 −0.190774 −0.0953870 0.995440i \(-0.530409\pi\)
−0.0953870 + 0.995440i \(0.530409\pi\)
\(68\) −7.56155 −0.916973
\(69\) −7.31534 −0.880664
\(70\) 0 0
\(71\) −6.24621 −0.741289 −0.370644 0.928775i \(-0.620863\pi\)
−0.370644 + 0.928775i \(0.620863\pi\)
\(72\) −0.561553 −0.0661796
\(73\) −10.6847 −1.25054 −0.625272 0.780407i \(-0.715012\pi\)
−0.625272 + 0.780407i \(0.715012\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) −6.24621 −0.711822
\(78\) −10.4384 −1.18192
\(79\) 3.12311 0.351377 0.175688 0.984446i \(-0.443785\pi\)
0.175688 + 0.984446i \(0.443785\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) −4.24621 −0.468916
\(83\) −11.1231 −1.22092 −0.610460 0.792047i \(-0.709015\pi\)
−0.610460 + 0.792047i \(0.709015\pi\)
\(84\) 2.43845 0.266056
\(85\) 0 0
\(86\) 11.1231 1.19944
\(87\) −10.4384 −1.11912
\(88\) 4.00000 0.426401
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) −10.4384 −1.09425
\(92\) 4.68466 0.488409
\(93\) −4.87689 −0.505710
\(94\) 10.2462 1.05682
\(95\) 0 0
\(96\) −1.56155 −0.159375
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) −4.56155 −0.460786
\(99\) −2.24621 −0.225753
\(100\) 0 0
\(101\) 7.36932 0.733274 0.366637 0.930364i \(-0.380509\pi\)
0.366637 + 0.930364i \(0.380509\pi\)
\(102\) 11.8078 1.16914
\(103\) 14.2462 1.40372 0.701860 0.712314i \(-0.252353\pi\)
0.701860 + 0.712314i \(0.252353\pi\)
\(104\) 6.68466 0.655485
\(105\) 0 0
\(106\) 0.438447 0.0425858
\(107\) 9.56155 0.924350 0.462175 0.886789i \(-0.347069\pi\)
0.462175 + 0.886789i \(0.347069\pi\)
\(108\) 5.56155 0.535161
\(109\) 3.56155 0.341135 0.170567 0.985346i \(-0.445440\pi\)
0.170567 + 0.985346i \(0.445440\pi\)
\(110\) 0 0
\(111\) −9.36932 −0.889296
\(112\) −1.56155 −0.147553
\(113\) −17.1231 −1.61081 −0.805403 0.592727i \(-0.798051\pi\)
−0.805403 + 0.592727i \(0.798051\pi\)
\(114\) 1.56155 0.146253
\(115\) 0 0
\(116\) 6.68466 0.620655
\(117\) −3.75379 −0.347038
\(118\) −1.56155 −0.143753
\(119\) 11.8078 1.08242
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 2.87689 0.260462
\(123\) 6.63068 0.597869
\(124\) 3.12311 0.280463
\(125\) 0 0
\(126\) 0.876894 0.0781200
\(127\) −4.87689 −0.432754 −0.216377 0.976310i \(-0.569424\pi\)
−0.216377 + 0.976310i \(0.569424\pi\)
\(128\) 1.00000 0.0883883
\(129\) −17.3693 −1.52928
\(130\) 0 0
\(131\) 16.4924 1.44095 0.720475 0.693481i \(-0.243924\pi\)
0.720475 + 0.693481i \(0.243924\pi\)
\(132\) −6.24621 −0.543663
\(133\) 1.56155 0.135404
\(134\) −1.56155 −0.134898
\(135\) 0 0
\(136\) −7.56155 −0.648398
\(137\) −5.80776 −0.496191 −0.248095 0.968736i \(-0.579805\pi\)
−0.248095 + 0.968736i \(0.579805\pi\)
\(138\) −7.31534 −0.622723
\(139\) −16.4924 −1.39887 −0.699435 0.714697i \(-0.746565\pi\)
−0.699435 + 0.714697i \(0.746565\pi\)
\(140\) 0 0
\(141\) −16.0000 −1.34744
\(142\) −6.24621 −0.524170
\(143\) 26.7386 2.23600
\(144\) −0.561553 −0.0467961
\(145\) 0 0
\(146\) −10.6847 −0.884269
\(147\) 7.12311 0.587504
\(148\) 6.00000 0.493197
\(149\) −11.3693 −0.931411 −0.465705 0.884940i \(-0.654199\pi\)
−0.465705 + 0.884940i \(0.654199\pi\)
\(150\) 0 0
\(151\) −3.12311 −0.254155 −0.127077 0.991893i \(-0.540560\pi\)
−0.127077 + 0.991893i \(0.540560\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 4.24621 0.343286
\(154\) −6.24621 −0.503334
\(155\) 0 0
\(156\) −10.4384 −0.835745
\(157\) 3.75379 0.299585 0.149792 0.988717i \(-0.452139\pi\)
0.149792 + 0.988717i \(0.452139\pi\)
\(158\) 3.12311 0.248461
\(159\) −0.684658 −0.0542969
\(160\) 0 0
\(161\) −7.31534 −0.576530
\(162\) −7.00000 −0.549972
\(163\) −9.36932 −0.733862 −0.366931 0.930248i \(-0.619591\pi\)
−0.366931 + 0.930248i \(0.619591\pi\)
\(164\) −4.24621 −0.331573
\(165\) 0 0
\(166\) −11.1231 −0.863320
\(167\) −17.3693 −1.34408 −0.672039 0.740516i \(-0.734581\pi\)
−0.672039 + 0.740516i \(0.734581\pi\)
\(168\) 2.43845 0.188130
\(169\) 31.6847 2.43728
\(170\) 0 0
\(171\) 0.561553 0.0429430
\(172\) 11.1231 0.848129
\(173\) −3.75379 −0.285395 −0.142698 0.989766i \(-0.545578\pi\)
−0.142698 + 0.989766i \(0.545578\pi\)
\(174\) −10.4384 −0.791337
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 2.43845 0.183285
\(178\) 2.00000 0.149906
\(179\) −5.75379 −0.430058 −0.215029 0.976608i \(-0.568985\pi\)
−0.215029 + 0.976608i \(0.568985\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) −10.4384 −0.773749
\(183\) −4.49242 −0.332089
\(184\) 4.68466 0.345358
\(185\) 0 0
\(186\) −4.87689 −0.357591
\(187\) −30.2462 −2.21182
\(188\) 10.2462 0.747282
\(189\) −8.68466 −0.631716
\(190\) 0 0
\(191\) 8.68466 0.628400 0.314200 0.949357i \(-0.398264\pi\)
0.314200 + 0.949357i \(0.398264\pi\)
\(192\) −1.56155 −0.112695
\(193\) −18.4924 −1.33111 −0.665557 0.746347i \(-0.731806\pi\)
−0.665557 + 0.746347i \(0.731806\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −4.56155 −0.325825
\(197\) 3.75379 0.267446 0.133723 0.991019i \(-0.457307\pi\)
0.133723 + 0.991019i \(0.457307\pi\)
\(198\) −2.24621 −0.159631
\(199\) −3.80776 −0.269925 −0.134963 0.990851i \(-0.543091\pi\)
−0.134963 + 0.990851i \(0.543091\pi\)
\(200\) 0 0
\(201\) 2.43845 0.171995
\(202\) 7.36932 0.518503
\(203\) −10.4384 −0.732635
\(204\) 11.8078 0.826709
\(205\) 0 0
\(206\) 14.2462 0.992581
\(207\) −2.63068 −0.182845
\(208\) 6.68466 0.463498
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 20.6847 1.42399 0.711995 0.702184i \(-0.247792\pi\)
0.711995 + 0.702184i \(0.247792\pi\)
\(212\) 0.438447 0.0301127
\(213\) 9.75379 0.668319
\(214\) 9.56155 0.653614
\(215\) 0 0
\(216\) 5.56155 0.378416
\(217\) −4.87689 −0.331065
\(218\) 3.56155 0.241219
\(219\) 16.6847 1.12744
\(220\) 0 0
\(221\) −50.5464 −3.40012
\(222\) −9.36932 −0.628827
\(223\) −1.36932 −0.0916962 −0.0458481 0.998948i \(-0.514599\pi\)
−0.0458481 + 0.998948i \(0.514599\pi\)
\(224\) −1.56155 −0.104336
\(225\) 0 0
\(226\) −17.1231 −1.13901
\(227\) 2.93087 0.194529 0.0972643 0.995259i \(-0.468991\pi\)
0.0972643 + 0.995259i \(0.468991\pi\)
\(228\) 1.56155 0.103416
\(229\) 18.4924 1.22201 0.611007 0.791625i \(-0.290765\pi\)
0.611007 + 0.791625i \(0.290765\pi\)
\(230\) 0 0
\(231\) 9.75379 0.641752
\(232\) 6.68466 0.438869
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) −3.75379 −0.245393
\(235\) 0 0
\(236\) −1.56155 −0.101648
\(237\) −4.87689 −0.316788
\(238\) 11.8078 0.765384
\(239\) −5.56155 −0.359747 −0.179873 0.983690i \(-0.557569\pi\)
−0.179873 + 0.983690i \(0.557569\pi\)
\(240\) 0 0
\(241\) 14.8769 0.958305 0.479153 0.877732i \(-0.340944\pi\)
0.479153 + 0.877732i \(0.340944\pi\)
\(242\) 5.00000 0.321412
\(243\) −5.75379 −0.369106
\(244\) 2.87689 0.184174
\(245\) 0 0
\(246\) 6.63068 0.422757
\(247\) −6.68466 −0.425335
\(248\) 3.12311 0.198317
\(249\) 17.3693 1.10074
\(250\) 0 0
\(251\) −10.2462 −0.646735 −0.323368 0.946273i \(-0.604815\pi\)
−0.323368 + 0.946273i \(0.604815\pi\)
\(252\) 0.876894 0.0552392
\(253\) 18.7386 1.17809
\(254\) −4.87689 −0.306004
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.0000 −0.873296 −0.436648 0.899632i \(-0.643834\pi\)
−0.436648 + 0.899632i \(0.643834\pi\)
\(258\) −17.3693 −1.08137
\(259\) −9.36932 −0.582181
\(260\) 0 0
\(261\) −3.75379 −0.232354
\(262\) 16.4924 1.01891
\(263\) 5.75379 0.354794 0.177397 0.984139i \(-0.443232\pi\)
0.177397 + 0.984139i \(0.443232\pi\)
\(264\) −6.24621 −0.384428
\(265\) 0 0
\(266\) 1.56155 0.0957449
\(267\) −3.12311 −0.191131
\(268\) −1.56155 −0.0953870
\(269\) −26.0000 −1.58525 −0.792624 0.609711i \(-0.791286\pi\)
−0.792624 + 0.609711i \(0.791286\pi\)
\(270\) 0 0
\(271\) 6.93087 0.421020 0.210510 0.977592i \(-0.432487\pi\)
0.210510 + 0.977592i \(0.432487\pi\)
\(272\) −7.56155 −0.458486
\(273\) 16.3002 0.986532
\(274\) −5.80776 −0.350860
\(275\) 0 0
\(276\) −7.31534 −0.440332
\(277\) −9.12311 −0.548154 −0.274077 0.961708i \(-0.588372\pi\)
−0.274077 + 0.961708i \(0.588372\pi\)
\(278\) −16.4924 −0.989150
\(279\) −1.75379 −0.104997
\(280\) 0 0
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) −16.0000 −0.952786
\(283\) 12.8769 0.765452 0.382726 0.923862i \(-0.374985\pi\)
0.382726 + 0.923862i \(0.374985\pi\)
\(284\) −6.24621 −0.370644
\(285\) 0 0
\(286\) 26.7386 1.58109
\(287\) 6.63068 0.391397
\(288\) −0.561553 −0.0330898
\(289\) 40.1771 2.36336
\(290\) 0 0
\(291\) 9.36932 0.549239
\(292\) −10.6847 −0.625272
\(293\) −23.1771 −1.35402 −0.677010 0.735974i \(-0.736725\pi\)
−0.677010 + 0.735974i \(0.736725\pi\)
\(294\) 7.12311 0.415428
\(295\) 0 0
\(296\) 6.00000 0.348743
\(297\) 22.2462 1.29086
\(298\) −11.3693 −0.658607
\(299\) 31.3153 1.81101
\(300\) 0 0
\(301\) −17.3693 −1.00115
\(302\) −3.12311 −0.179715
\(303\) −11.5076 −0.661093
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 4.24621 0.242740
\(307\) 0.492423 0.0281040 0.0140520 0.999901i \(-0.495527\pi\)
0.0140520 + 0.999901i \(0.495527\pi\)
\(308\) −6.24621 −0.355911
\(309\) −22.2462 −1.26554
\(310\) 0 0
\(311\) 8.68466 0.492462 0.246231 0.969211i \(-0.420808\pi\)
0.246231 + 0.969211i \(0.420808\pi\)
\(312\) −10.4384 −0.590961
\(313\) 32.0540 1.81180 0.905899 0.423494i \(-0.139197\pi\)
0.905899 + 0.423494i \(0.139197\pi\)
\(314\) 3.75379 0.211839
\(315\) 0 0
\(316\) 3.12311 0.175688
\(317\) 24.0540 1.35101 0.675503 0.737357i \(-0.263927\pi\)
0.675503 + 0.737357i \(0.263927\pi\)
\(318\) −0.684658 −0.0383937
\(319\) 26.7386 1.49708
\(320\) 0 0
\(321\) −14.9309 −0.833360
\(322\) −7.31534 −0.407668
\(323\) 7.56155 0.420736
\(324\) −7.00000 −0.388889
\(325\) 0 0
\(326\) −9.36932 −0.518918
\(327\) −5.56155 −0.307555
\(328\) −4.24621 −0.234458
\(329\) −16.0000 −0.882109
\(330\) 0 0
\(331\) 1.56155 0.0858307 0.0429154 0.999079i \(-0.486335\pi\)
0.0429154 + 0.999079i \(0.486335\pi\)
\(332\) −11.1231 −0.610460
\(333\) −3.36932 −0.184637
\(334\) −17.3693 −0.950407
\(335\) 0 0
\(336\) 2.43845 0.133028
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 31.6847 1.72342
\(339\) 26.7386 1.45224
\(340\) 0 0
\(341\) 12.4924 0.676503
\(342\) 0.561553 0.0303653
\(343\) 18.0540 0.974823
\(344\) 11.1231 0.599718
\(345\) 0 0
\(346\) −3.75379 −0.201805
\(347\) 33.3693 1.79136 0.895679 0.444700i \(-0.146690\pi\)
0.895679 + 0.444700i \(0.146690\pi\)
\(348\) −10.4384 −0.559560
\(349\) 20.2462 1.08375 0.541877 0.840458i \(-0.317714\pi\)
0.541877 + 0.840458i \(0.317714\pi\)
\(350\) 0 0
\(351\) 37.1771 1.98437
\(352\) 4.00000 0.213201
\(353\) −24.9309 −1.32694 −0.663468 0.748205i \(-0.730916\pi\)
−0.663468 + 0.748205i \(0.730916\pi\)
\(354\) 2.43845 0.129602
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) −18.4384 −0.975866
\(358\) −5.75379 −0.304097
\(359\) 5.56155 0.293528 0.146764 0.989172i \(-0.453114\pi\)
0.146764 + 0.989172i \(0.453114\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −18.0000 −0.946059
\(363\) −7.80776 −0.409801
\(364\) −10.4384 −0.547123
\(365\) 0 0
\(366\) −4.49242 −0.234823
\(367\) 10.2462 0.534848 0.267424 0.963579i \(-0.413828\pi\)
0.267424 + 0.963579i \(0.413828\pi\)
\(368\) 4.68466 0.244205
\(369\) 2.38447 0.124131
\(370\) 0 0
\(371\) −0.684658 −0.0355457
\(372\) −4.87689 −0.252855
\(373\) 27.5616 1.42708 0.713542 0.700613i \(-0.247090\pi\)
0.713542 + 0.700613i \(0.247090\pi\)
\(374\) −30.2462 −1.56399
\(375\) 0 0
\(376\) 10.2462 0.528408
\(377\) 44.6847 2.30138
\(378\) −8.68466 −0.446691
\(379\) 6.43845 0.330721 0.165360 0.986233i \(-0.447121\pi\)
0.165360 + 0.986233i \(0.447121\pi\)
\(380\) 0 0
\(381\) 7.61553 0.390155
\(382\) 8.68466 0.444346
\(383\) −30.2462 −1.54551 −0.772755 0.634705i \(-0.781122\pi\)
−0.772755 + 0.634705i \(0.781122\pi\)
\(384\) −1.56155 −0.0796877
\(385\) 0 0
\(386\) −18.4924 −0.941240
\(387\) −6.24621 −0.317513
\(388\) −6.00000 −0.304604
\(389\) 1.12311 0.0569437 0.0284719 0.999595i \(-0.490936\pi\)
0.0284719 + 0.999595i \(0.490936\pi\)
\(390\) 0 0
\(391\) −35.4233 −1.79143
\(392\) −4.56155 −0.230393
\(393\) −25.7538 −1.29911
\(394\) 3.75379 0.189113
\(395\) 0 0
\(396\) −2.24621 −0.112876
\(397\) −1.12311 −0.0563671 −0.0281835 0.999603i \(-0.508972\pi\)
−0.0281835 + 0.999603i \(0.508972\pi\)
\(398\) −3.80776 −0.190866
\(399\) −2.43845 −0.122075
\(400\) 0 0
\(401\) −20.2462 −1.01105 −0.505524 0.862813i \(-0.668701\pi\)
−0.505524 + 0.862813i \(0.668701\pi\)
\(402\) 2.43845 0.121619
\(403\) 20.8769 1.03995
\(404\) 7.36932 0.366637
\(405\) 0 0
\(406\) −10.4384 −0.518051
\(407\) 24.0000 1.18964
\(408\) 11.8078 0.584571
\(409\) −24.7386 −1.22325 −0.611623 0.791149i \(-0.709483\pi\)
−0.611623 + 0.791149i \(0.709483\pi\)
\(410\) 0 0
\(411\) 9.06913 0.447347
\(412\) 14.2462 0.701860
\(413\) 2.43845 0.119988
\(414\) −2.63068 −0.129291
\(415\) 0 0
\(416\) 6.68466 0.327742
\(417\) 25.7538 1.26117
\(418\) −4.00000 −0.195646
\(419\) −33.8617 −1.65425 −0.827127 0.562015i \(-0.810026\pi\)
−0.827127 + 0.562015i \(0.810026\pi\)
\(420\) 0 0
\(421\) 4.93087 0.240316 0.120158 0.992755i \(-0.461660\pi\)
0.120158 + 0.992755i \(0.461660\pi\)
\(422\) 20.6847 1.00691
\(423\) −5.75379 −0.279759
\(424\) 0.438447 0.0212929
\(425\) 0 0
\(426\) 9.75379 0.472573
\(427\) −4.49242 −0.217404
\(428\) 9.56155 0.462175
\(429\) −41.7538 −2.01589
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 5.56155 0.267580
\(433\) −39.3693 −1.89197 −0.945984 0.324212i \(-0.894901\pi\)
−0.945984 + 0.324212i \(0.894901\pi\)
\(434\) −4.87689 −0.234098
\(435\) 0 0
\(436\) 3.56155 0.170567
\(437\) −4.68466 −0.224098
\(438\) 16.6847 0.797224
\(439\) −4.87689 −0.232761 −0.116381 0.993205i \(-0.537129\pi\)
−0.116381 + 0.993205i \(0.537129\pi\)
\(440\) 0 0
\(441\) 2.56155 0.121979
\(442\) −50.5464 −2.40425
\(443\) 14.2462 0.676858 0.338429 0.940992i \(-0.390105\pi\)
0.338429 + 0.940992i \(0.390105\pi\)
\(444\) −9.36932 −0.444648
\(445\) 0 0
\(446\) −1.36932 −0.0648390
\(447\) 17.7538 0.839725
\(448\) −1.56155 −0.0737764
\(449\) 20.7386 0.978717 0.489358 0.872083i \(-0.337231\pi\)
0.489358 + 0.872083i \(0.337231\pi\)
\(450\) 0 0
\(451\) −16.9848 −0.799785
\(452\) −17.1231 −0.805403
\(453\) 4.87689 0.229136
\(454\) 2.93087 0.137553
\(455\) 0 0
\(456\) 1.56155 0.0731264
\(457\) −18.6847 −0.874031 −0.437016 0.899454i \(-0.643965\pi\)
−0.437016 + 0.899454i \(0.643965\pi\)
\(458\) 18.4924 0.864094
\(459\) −42.0540 −1.96291
\(460\) 0 0
\(461\) 20.2462 0.942960 0.471480 0.881877i \(-0.343720\pi\)
0.471480 + 0.881877i \(0.343720\pi\)
\(462\) 9.75379 0.453787
\(463\) 13.7538 0.639193 0.319596 0.947554i \(-0.396453\pi\)
0.319596 + 0.947554i \(0.396453\pi\)
\(464\) 6.68466 0.310327
\(465\) 0 0
\(466\) −10.0000 −0.463241
\(467\) −1.75379 −0.0811557 −0.0405778 0.999176i \(-0.512920\pi\)
−0.0405778 + 0.999176i \(0.512920\pi\)
\(468\) −3.75379 −0.173519
\(469\) 2.43845 0.112597
\(470\) 0 0
\(471\) −5.86174 −0.270095
\(472\) −1.56155 −0.0718763
\(473\) 44.4924 2.04576
\(474\) −4.87689 −0.224003
\(475\) 0 0
\(476\) 11.8078 0.541208
\(477\) −0.246211 −0.0112732
\(478\) −5.56155 −0.254380
\(479\) 32.0000 1.46212 0.731059 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 0 0
\(481\) 40.1080 1.82877
\(482\) 14.8769 0.677624
\(483\) 11.4233 0.519778
\(484\) 5.00000 0.227273
\(485\) 0 0
\(486\) −5.75379 −0.260997
\(487\) −23.6155 −1.07012 −0.535061 0.844814i \(-0.679711\pi\)
−0.535061 + 0.844814i \(0.679711\pi\)
\(488\) 2.87689 0.130231
\(489\) 14.6307 0.661622
\(490\) 0 0
\(491\) 7.12311 0.321461 0.160731 0.986998i \(-0.448615\pi\)
0.160731 + 0.986998i \(0.448615\pi\)
\(492\) 6.63068 0.298934
\(493\) −50.5464 −2.27650
\(494\) −6.68466 −0.300757
\(495\) 0 0
\(496\) 3.12311 0.140232
\(497\) 9.75379 0.437517
\(498\) 17.3693 0.778338
\(499\) −32.1080 −1.43735 −0.718675 0.695347i \(-0.755251\pi\)
−0.718675 + 0.695347i \(0.755251\pi\)
\(500\) 0 0
\(501\) 27.1231 1.21177
\(502\) −10.2462 −0.457311
\(503\) −30.0540 −1.34004 −0.670020 0.742343i \(-0.733715\pi\)
−0.670020 + 0.742343i \(0.733715\pi\)
\(504\) 0.876894 0.0390600
\(505\) 0 0
\(506\) 18.7386 0.833034
\(507\) −49.4773 −2.19736
\(508\) −4.87689 −0.216377
\(509\) −30.4924 −1.35155 −0.675776 0.737107i \(-0.736192\pi\)
−0.675776 + 0.737107i \(0.736192\pi\)
\(510\) 0 0
\(511\) 16.6847 0.738086
\(512\) 1.00000 0.0441942
\(513\) −5.56155 −0.245549
\(514\) −14.0000 −0.617514
\(515\) 0 0
\(516\) −17.3693 −0.764642
\(517\) 40.9848 1.80251
\(518\) −9.36932 −0.411664
\(519\) 5.86174 0.257302
\(520\) 0 0
\(521\) 5.12311 0.224447 0.112224 0.993683i \(-0.464203\pi\)
0.112224 + 0.993683i \(0.464203\pi\)
\(522\) −3.75379 −0.164299
\(523\) 19.3153 0.844601 0.422300 0.906456i \(-0.361223\pi\)
0.422300 + 0.906456i \(0.361223\pi\)
\(524\) 16.4924 0.720475
\(525\) 0 0
\(526\) 5.75379 0.250877
\(527\) −23.6155 −1.02871
\(528\) −6.24621 −0.271831
\(529\) −1.05398 −0.0458250
\(530\) 0 0
\(531\) 0.876894 0.0380540
\(532\) 1.56155 0.0677019
\(533\) −28.3845 −1.22947
\(534\) −3.12311 −0.135150
\(535\) 0 0
\(536\) −1.56155 −0.0674488
\(537\) 8.98485 0.387725
\(538\) −26.0000 −1.12094
\(539\) −18.2462 −0.785920
\(540\) 0 0
\(541\) −41.6155 −1.78919 −0.894596 0.446877i \(-0.852536\pi\)
−0.894596 + 0.446877i \(0.852536\pi\)
\(542\) 6.93087 0.297706
\(543\) 28.1080 1.20623
\(544\) −7.56155 −0.324199
\(545\) 0 0
\(546\) 16.3002 0.697584
\(547\) 16.4924 0.705165 0.352583 0.935781i \(-0.385304\pi\)
0.352583 + 0.935781i \(0.385304\pi\)
\(548\) −5.80776 −0.248095
\(549\) −1.61553 −0.0689491
\(550\) 0 0
\(551\) −6.68466 −0.284776
\(552\) −7.31534 −0.311362
\(553\) −4.87689 −0.207387
\(554\) −9.12311 −0.387604
\(555\) 0 0
\(556\) −16.4924 −0.699435
\(557\) 1.61553 0.0684521 0.0342261 0.999414i \(-0.489103\pi\)
0.0342261 + 0.999414i \(0.489103\pi\)
\(558\) −1.75379 −0.0742438
\(559\) 74.3542 3.14485
\(560\) 0 0
\(561\) 47.2311 1.99410
\(562\) 2.00000 0.0843649
\(563\) −24.4924 −1.03223 −0.516116 0.856519i \(-0.672623\pi\)
−0.516116 + 0.856519i \(0.672623\pi\)
\(564\) −16.0000 −0.673722
\(565\) 0 0
\(566\) 12.8769 0.541256
\(567\) 10.9309 0.459053
\(568\) −6.24621 −0.262085
\(569\) 5.12311 0.214772 0.107386 0.994217i \(-0.465752\pi\)
0.107386 + 0.994217i \(0.465752\pi\)
\(570\) 0 0
\(571\) −19.6155 −0.820884 −0.410442 0.911887i \(-0.634626\pi\)
−0.410442 + 0.911887i \(0.634626\pi\)
\(572\) 26.7386 1.11800
\(573\) −13.5616 −0.566542
\(574\) 6.63068 0.276759
\(575\) 0 0
\(576\) −0.561553 −0.0233980
\(577\) 22.6847 0.944375 0.472187 0.881498i \(-0.343465\pi\)
0.472187 + 0.881498i \(0.343465\pi\)
\(578\) 40.1771 1.67115
\(579\) 28.8769 1.20008
\(580\) 0 0
\(581\) 17.3693 0.720601
\(582\) 9.36932 0.388371
\(583\) 1.75379 0.0726345
\(584\) −10.6847 −0.442134
\(585\) 0 0
\(586\) −23.1771 −0.957436
\(587\) −17.3693 −0.716908 −0.358454 0.933547i \(-0.616696\pi\)
−0.358454 + 0.933547i \(0.616696\pi\)
\(588\) 7.12311 0.293752
\(589\) −3.12311 −0.128685
\(590\) 0 0
\(591\) −5.86174 −0.241120
\(592\) 6.00000 0.246598
\(593\) −24.2462 −0.995673 −0.497836 0.867271i \(-0.665872\pi\)
−0.497836 + 0.867271i \(0.665872\pi\)
\(594\) 22.2462 0.912773
\(595\) 0 0
\(596\) −11.3693 −0.465705
\(597\) 5.94602 0.243355
\(598\) 31.3153 1.28058
\(599\) 45.8617 1.87386 0.936930 0.349517i \(-0.113654\pi\)
0.936930 + 0.349517i \(0.113654\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) −17.3693 −0.707921
\(603\) 0.876894 0.0357099
\(604\) −3.12311 −0.127077
\(605\) 0 0
\(606\) −11.5076 −0.467463
\(607\) 12.8769 0.522657 0.261329 0.965250i \(-0.415839\pi\)
0.261329 + 0.965250i \(0.415839\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 16.3002 0.660517
\(610\) 0 0
\(611\) 68.4924 2.77091
\(612\) 4.24621 0.171643
\(613\) 19.3693 0.782319 0.391160 0.920323i \(-0.372074\pi\)
0.391160 + 0.920323i \(0.372074\pi\)
\(614\) 0.492423 0.0198726
\(615\) 0 0
\(616\) −6.24621 −0.251667
\(617\) 4.24621 0.170946 0.0854730 0.996340i \(-0.472760\pi\)
0.0854730 + 0.996340i \(0.472760\pi\)
\(618\) −22.2462 −0.894874
\(619\) −36.0000 −1.44696 −0.723481 0.690344i \(-0.757459\pi\)
−0.723481 + 0.690344i \(0.757459\pi\)
\(620\) 0 0
\(621\) 26.0540 1.04551
\(622\) 8.68466 0.348223
\(623\) −3.12311 −0.125125
\(624\) −10.4384 −0.417872
\(625\) 0 0
\(626\) 32.0540 1.28113
\(627\) 6.24621 0.249450
\(628\) 3.75379 0.149792
\(629\) −45.3693 −1.80899
\(630\) 0 0
\(631\) 12.4924 0.497315 0.248658 0.968591i \(-0.420011\pi\)
0.248658 + 0.968591i \(0.420011\pi\)
\(632\) 3.12311 0.124230
\(633\) −32.3002 −1.28382
\(634\) 24.0540 0.955305
\(635\) 0 0
\(636\) −0.684658 −0.0271485
\(637\) −30.4924 −1.20815
\(638\) 26.7386 1.05859
\(639\) 3.50758 0.138758
\(640\) 0 0
\(641\) −35.8617 −1.41645 −0.708227 0.705985i \(-0.750505\pi\)
−0.708227 + 0.705985i \(0.750505\pi\)
\(642\) −14.9309 −0.589274
\(643\) −7.61553 −0.300327 −0.150164 0.988661i \(-0.547980\pi\)
−0.150164 + 0.988661i \(0.547980\pi\)
\(644\) −7.31534 −0.288265
\(645\) 0 0
\(646\) 7.56155 0.297505
\(647\) −9.56155 −0.375903 −0.187952 0.982178i \(-0.560185\pi\)
−0.187952 + 0.982178i \(0.560185\pi\)
\(648\) −7.00000 −0.274986
\(649\) −6.24621 −0.245185
\(650\) 0 0
\(651\) 7.61553 0.298476
\(652\) −9.36932 −0.366931
\(653\) −1.12311 −0.0439505 −0.0219753 0.999759i \(-0.506996\pi\)
−0.0219753 + 0.999759i \(0.506996\pi\)
\(654\) −5.56155 −0.217474
\(655\) 0 0
\(656\) −4.24621 −0.165787
\(657\) 6.00000 0.234082
\(658\) −16.0000 −0.623745
\(659\) −42.9309 −1.67235 −0.836175 0.548463i \(-0.815213\pi\)
−0.836175 + 0.548463i \(0.815213\pi\)
\(660\) 0 0
\(661\) 9.80776 0.381478 0.190739 0.981641i \(-0.438912\pi\)
0.190739 + 0.981641i \(0.438912\pi\)
\(662\) 1.56155 0.0606915
\(663\) 78.9309 3.06542
\(664\) −11.1231 −0.431660
\(665\) 0 0
\(666\) −3.36932 −0.130558
\(667\) 31.3153 1.21253
\(668\) −17.3693 −0.672039
\(669\) 2.13826 0.0826699
\(670\) 0 0
\(671\) 11.5076 0.444245
\(672\) 2.43845 0.0940651
\(673\) 3.36932 0.129878 0.0649388 0.997889i \(-0.479315\pi\)
0.0649388 + 0.997889i \(0.479315\pi\)
\(674\) 26.0000 1.00148
\(675\) 0 0
\(676\) 31.6847 1.21864
\(677\) −36.4384 −1.40044 −0.700222 0.713926i \(-0.746915\pi\)
−0.700222 + 0.713926i \(0.746915\pi\)
\(678\) 26.7386 1.02689
\(679\) 9.36932 0.359561
\(680\) 0 0
\(681\) −4.57671 −0.175380
\(682\) 12.4924 0.478360
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0.561553 0.0214715
\(685\) 0 0
\(686\) 18.0540 0.689304
\(687\) −28.8769 −1.10172
\(688\) 11.1231 0.424064
\(689\) 2.93087 0.111657
\(690\) 0 0
\(691\) −8.87689 −0.337693 −0.168846 0.985642i \(-0.554004\pi\)
−0.168846 + 0.985642i \(0.554004\pi\)
\(692\) −3.75379 −0.142698
\(693\) 3.50758 0.133242
\(694\) 33.3693 1.26668
\(695\) 0 0
\(696\) −10.4384 −0.395668
\(697\) 32.1080 1.21618
\(698\) 20.2462 0.766330
\(699\) 15.6155 0.590634
\(700\) 0 0
\(701\) −29.1231 −1.09996 −0.549982 0.835176i \(-0.685366\pi\)
−0.549982 + 0.835176i \(0.685366\pi\)
\(702\) 37.1771 1.40316
\(703\) −6.00000 −0.226294
\(704\) 4.00000 0.150756
\(705\) 0 0
\(706\) −24.9309 −0.938286
\(707\) −11.5076 −0.432787
\(708\) 2.43845 0.0916425
\(709\) 38.0000 1.42712 0.713560 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) 0 0
\(711\) −1.75379 −0.0657722
\(712\) 2.00000 0.0749532
\(713\) 14.6307 0.547923
\(714\) −18.4384 −0.690042
\(715\) 0 0
\(716\) −5.75379 −0.215029
\(717\) 8.68466 0.324335
\(718\) 5.56155 0.207555
\(719\) −29.5616 −1.10246 −0.551230 0.834353i \(-0.685841\pi\)
−0.551230 + 0.834353i \(0.685841\pi\)
\(720\) 0 0
\(721\) −22.2462 −0.828492
\(722\) 1.00000 0.0372161
\(723\) −23.2311 −0.863972
\(724\) −18.0000 −0.668965
\(725\) 0 0
\(726\) −7.80776 −0.289773
\(727\) 36.6847 1.36056 0.680279 0.732953i \(-0.261858\pi\)
0.680279 + 0.732953i \(0.261858\pi\)
\(728\) −10.4384 −0.386875
\(729\) 29.9848 1.11055
\(730\) 0 0
\(731\) −84.1080 −3.11084
\(732\) −4.49242 −0.166045
\(733\) 45.1231 1.66666 0.833330 0.552776i \(-0.186431\pi\)
0.833330 + 0.552776i \(0.186431\pi\)
\(734\) 10.2462 0.378195
\(735\) 0 0
\(736\) 4.68466 0.172679
\(737\) −6.24621 −0.230082
\(738\) 2.38447 0.0877736
\(739\) 16.8769 0.620827 0.310413 0.950602i \(-0.399533\pi\)
0.310413 + 0.950602i \(0.399533\pi\)
\(740\) 0 0
\(741\) 10.4384 0.383466
\(742\) −0.684658 −0.0251346
\(743\) −27.1231 −0.995050 −0.497525 0.867450i \(-0.665758\pi\)
−0.497525 + 0.867450i \(0.665758\pi\)
\(744\) −4.87689 −0.178796
\(745\) 0 0
\(746\) 27.5616 1.00910
\(747\) 6.24621 0.228537
\(748\) −30.2462 −1.10591
\(749\) −14.9309 −0.545562
\(750\) 0 0
\(751\) −43.1231 −1.57358 −0.786792 0.617218i \(-0.788260\pi\)
−0.786792 + 0.617218i \(0.788260\pi\)
\(752\) 10.2462 0.373641
\(753\) 16.0000 0.583072
\(754\) 44.6847 1.62732
\(755\) 0 0
\(756\) −8.68466 −0.315858
\(757\) −9.50758 −0.345559 −0.172779 0.984961i \(-0.555275\pi\)
−0.172779 + 0.984961i \(0.555275\pi\)
\(758\) 6.43845 0.233855
\(759\) −29.2614 −1.06212
\(760\) 0 0
\(761\) −28.5464 −1.03481 −0.517403 0.855742i \(-0.673101\pi\)
−0.517403 + 0.855742i \(0.673101\pi\)
\(762\) 7.61553 0.275881
\(763\) −5.56155 −0.201342
\(764\) 8.68466 0.314200
\(765\) 0 0
\(766\) −30.2462 −1.09284
\(767\) −10.4384 −0.376910
\(768\) −1.56155 −0.0563477
\(769\) 31.5616 1.13814 0.569069 0.822290i \(-0.307304\pi\)
0.569069 + 0.822290i \(0.307304\pi\)
\(770\) 0 0
\(771\) 21.8617 0.787331
\(772\) −18.4924 −0.665557
\(773\) 9.80776 0.352761 0.176380 0.984322i \(-0.443561\pi\)
0.176380 + 0.984322i \(0.443561\pi\)
\(774\) −6.24621 −0.224515
\(775\) 0 0
\(776\) −6.00000 −0.215387
\(777\) 14.6307 0.524873
\(778\) 1.12311 0.0402653
\(779\) 4.24621 0.152136
\(780\) 0 0
\(781\) −24.9848 −0.894028
\(782\) −35.4233 −1.26673
\(783\) 37.1771 1.32860
\(784\) −4.56155 −0.162913
\(785\) 0 0
\(786\) −25.7538 −0.918607
\(787\) −31.8078 −1.13382 −0.566912 0.823778i \(-0.691862\pi\)
−0.566912 + 0.823778i \(0.691862\pi\)
\(788\) 3.75379 0.133723
\(789\) −8.98485 −0.319869
\(790\) 0 0
\(791\) 26.7386 0.950716
\(792\) −2.24621 −0.0798156
\(793\) 19.2311 0.682915
\(794\) −1.12311 −0.0398575
\(795\) 0 0
\(796\) −3.80776 −0.134963
\(797\) −42.3002 −1.49835 −0.749175 0.662372i \(-0.769550\pi\)
−0.749175 + 0.662372i \(0.769550\pi\)
\(798\) −2.43845 −0.0863201
\(799\) −77.4773 −2.74095
\(800\) 0 0
\(801\) −1.12311 −0.0396830
\(802\) −20.2462 −0.714919
\(803\) −42.7386 −1.50821
\(804\) 2.43845 0.0859974
\(805\) 0 0
\(806\) 20.8769 0.735357
\(807\) 40.6004 1.42920
\(808\) 7.36932 0.259252
\(809\) −8.43845 −0.296680 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(810\) 0 0
\(811\) −0.192236 −0.00675032 −0.00337516 0.999994i \(-0.501074\pi\)
−0.00337516 + 0.999994i \(0.501074\pi\)
\(812\) −10.4384 −0.366318
\(813\) −10.8229 −0.379576
\(814\) 24.0000 0.841200
\(815\) 0 0
\(816\) 11.8078 0.413354
\(817\) −11.1231 −0.389148
\(818\) −24.7386 −0.864966
\(819\) 5.86174 0.204826
\(820\) 0 0
\(821\) 7.36932 0.257191 0.128595 0.991697i \(-0.458953\pi\)
0.128595 + 0.991697i \(0.458953\pi\)
\(822\) 9.06913 0.316322
\(823\) 33.5616 1.16988 0.584941 0.811076i \(-0.301118\pi\)
0.584941 + 0.811076i \(0.301118\pi\)
\(824\) 14.2462 0.496290
\(825\) 0 0
\(826\) 2.43845 0.0848444
\(827\) 6.43845 0.223887 0.111943 0.993715i \(-0.464292\pi\)
0.111943 + 0.993715i \(0.464292\pi\)
\(828\) −2.63068 −0.0914226
\(829\) 16.0540 0.557578 0.278789 0.960352i \(-0.410067\pi\)
0.278789 + 0.960352i \(0.410067\pi\)
\(830\) 0 0
\(831\) 14.2462 0.494196
\(832\) 6.68466 0.231749
\(833\) 34.4924 1.19509
\(834\) 25.7538 0.891781
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) 17.3693 0.600371
\(838\) −33.8617 −1.16973
\(839\) −12.4924 −0.431286 −0.215643 0.976472i \(-0.569185\pi\)
−0.215643 + 0.976472i \(0.569185\pi\)
\(840\) 0 0
\(841\) 15.6847 0.540850
\(842\) 4.93087 0.169929
\(843\) −3.12311 −0.107565
\(844\) 20.6847 0.711995
\(845\) 0 0
\(846\) −5.75379 −0.197819
\(847\) −7.80776 −0.268278
\(848\) 0.438447 0.0150563
\(849\) −20.1080 −0.690103
\(850\) 0 0
\(851\) 28.1080 0.963528
\(852\) 9.75379 0.334159
\(853\) −24.7386 −0.847035 −0.423517 0.905888i \(-0.639205\pi\)
−0.423517 + 0.905888i \(0.639205\pi\)
\(854\) −4.49242 −0.153728
\(855\) 0 0
\(856\) 9.56155 0.326807
\(857\) −39.3693 −1.34483 −0.672415 0.740174i \(-0.734743\pi\)
−0.672415 + 0.740174i \(0.734743\pi\)
\(858\) −41.7538 −1.42545
\(859\) 12.9848 0.443037 0.221519 0.975156i \(-0.428899\pi\)
0.221519 + 0.975156i \(0.428899\pi\)
\(860\) 0 0
\(861\) −10.3542 −0.352869
\(862\) −16.0000 −0.544962
\(863\) 14.2462 0.484947 0.242473 0.970158i \(-0.422041\pi\)
0.242473 + 0.970158i \(0.422041\pi\)
\(864\) 5.56155 0.189208
\(865\) 0 0
\(866\) −39.3693 −1.33782
\(867\) −62.7386 −2.13072
\(868\) −4.87689 −0.165533
\(869\) 12.4924 0.423776
\(870\) 0 0
\(871\) −10.4384 −0.353693
\(872\) 3.56155 0.120609
\(873\) 3.36932 0.114034
\(874\) −4.68466 −0.158461
\(875\) 0 0
\(876\) 16.6847 0.563722
\(877\) −24.9309 −0.841856 −0.420928 0.907094i \(-0.638295\pi\)
−0.420928 + 0.907094i \(0.638295\pi\)
\(878\) −4.87689 −0.164587
\(879\) 36.1922 1.22073
\(880\) 0 0
\(881\) −22.9848 −0.774379 −0.387190 0.922000i \(-0.626554\pi\)
−0.387190 + 0.922000i \(0.626554\pi\)
\(882\) 2.56155 0.0862520
\(883\) 47.6155 1.60239 0.801195 0.598403i \(-0.204198\pi\)
0.801195 + 0.598403i \(0.204198\pi\)
\(884\) −50.5464 −1.70006
\(885\) 0 0
\(886\) 14.2462 0.478611
\(887\) 4.49242 0.150841 0.0754204 0.997152i \(-0.475970\pi\)
0.0754204 + 0.997152i \(0.475970\pi\)
\(888\) −9.36932 −0.314414
\(889\) 7.61553 0.255417
\(890\) 0 0
\(891\) −28.0000 −0.938035
\(892\) −1.36932 −0.0458481
\(893\) −10.2462 −0.342876
\(894\) 17.7538 0.593776
\(895\) 0 0
\(896\) −1.56155 −0.0521678
\(897\) −48.9006 −1.63274
\(898\) 20.7386 0.692057
\(899\) 20.8769 0.696283
\(900\) 0 0
\(901\) −3.31534 −0.110450
\(902\) −16.9848 −0.565533
\(903\) 27.1231 0.902600
\(904\) −17.1231 −0.569506
\(905\) 0 0
\(906\) 4.87689 0.162024
\(907\) −25.1771 −0.835991 −0.417996 0.908449i \(-0.637267\pi\)
−0.417996 + 0.908449i \(0.637267\pi\)
\(908\) 2.93087 0.0972643
\(909\) −4.13826 −0.137257
\(910\) 0 0
\(911\) −28.4924 −0.943996 −0.471998 0.881600i \(-0.656467\pi\)
−0.471998 + 0.881600i \(0.656467\pi\)
\(912\) 1.56155 0.0517082
\(913\) −44.4924 −1.47248
\(914\) −18.6847 −0.618034
\(915\) 0 0
\(916\) 18.4924 0.611007
\(917\) −25.7538 −0.850465
\(918\) −42.0540 −1.38799
\(919\) −30.9309 −1.02032 −0.510158 0.860081i \(-0.670413\pi\)
−0.510158 + 0.860081i \(0.670413\pi\)
\(920\) 0 0
\(921\) −0.768944 −0.0253376
\(922\) 20.2462 0.666773
\(923\) −41.7538 −1.37434
\(924\) 9.75379 0.320876
\(925\) 0 0
\(926\) 13.7538 0.451978
\(927\) −8.00000 −0.262754
\(928\) 6.68466 0.219435
\(929\) 34.3002 1.12535 0.562676 0.826677i \(-0.309772\pi\)
0.562676 + 0.826677i \(0.309772\pi\)
\(930\) 0 0
\(931\) 4.56155 0.149499
\(932\) −10.0000 −0.327561
\(933\) −13.5616 −0.443985
\(934\) −1.75379 −0.0573857
\(935\) 0 0
\(936\) −3.75379 −0.122696
\(937\) −36.4384 −1.19039 −0.595196 0.803580i \(-0.702926\pi\)
−0.595196 + 0.803580i \(0.702926\pi\)
\(938\) 2.43845 0.0796181
\(939\) −50.0540 −1.63345
\(940\) 0 0
\(941\) 34.1922 1.11464 0.557318 0.830299i \(-0.311831\pi\)
0.557318 + 0.830299i \(0.311831\pi\)
\(942\) −5.86174 −0.190986
\(943\) −19.8920 −0.647774
\(944\) −1.56155 −0.0508242
\(945\) 0 0
\(946\) 44.4924 1.44657
\(947\) 17.7538 0.576921 0.288460 0.957492i \(-0.406857\pi\)
0.288460 + 0.957492i \(0.406857\pi\)
\(948\) −4.87689 −0.158394
\(949\) −71.4233 −2.31850
\(950\) 0 0
\(951\) −37.5616 −1.21802
\(952\) 11.8078 0.382692
\(953\) 30.1080 0.975292 0.487646 0.873041i \(-0.337856\pi\)
0.487646 + 0.873041i \(0.337856\pi\)
\(954\) −0.246211 −0.00797138
\(955\) 0 0
\(956\) −5.56155 −0.179873
\(957\) −41.7538 −1.34971
\(958\) 32.0000 1.03387
\(959\) 9.06913 0.292857
\(960\) 0 0
\(961\) −21.2462 −0.685362
\(962\) 40.1080 1.29313
\(963\) −5.36932 −0.173024
\(964\) 14.8769 0.479153
\(965\) 0 0
\(966\) 11.4233 0.367538
\(967\) 48.4924 1.55941 0.779706 0.626146i \(-0.215369\pi\)
0.779706 + 0.626146i \(0.215369\pi\)
\(968\) 5.00000 0.160706
\(969\) −11.8078 −0.379320
\(970\) 0 0
\(971\) −23.5076 −0.754394 −0.377197 0.926133i \(-0.623112\pi\)
−0.377197 + 0.926133i \(0.623112\pi\)
\(972\) −5.75379 −0.184553
\(973\) 25.7538 0.825629
\(974\) −23.6155 −0.756690
\(975\) 0 0
\(976\) 2.87689 0.0920871
\(977\) 20.7386 0.663488 0.331744 0.943370i \(-0.392363\pi\)
0.331744 + 0.943370i \(0.392363\pi\)
\(978\) 14.6307 0.467838
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) 7.12311 0.227307
\(983\) −27.1231 −0.865093 −0.432546 0.901612i \(-0.642385\pi\)
−0.432546 + 0.901612i \(0.642385\pi\)
\(984\) 6.63068 0.211378
\(985\) 0 0
\(986\) −50.5464 −1.60973
\(987\) 24.9848 0.795276
\(988\) −6.68466 −0.212667
\(989\) 52.1080 1.65694
\(990\) 0 0
\(991\) 11.1231 0.353337 0.176669 0.984270i \(-0.443468\pi\)
0.176669 + 0.984270i \(0.443468\pi\)
\(992\) 3.12311 0.0991587
\(993\) −2.43845 −0.0773818
\(994\) 9.75379 0.309371
\(995\) 0 0
\(996\) 17.3693 0.550368
\(997\) −32.7386 −1.03684 −0.518421 0.855125i \(-0.673480\pi\)
−0.518421 + 0.855125i \(0.673480\pi\)
\(998\) −32.1080 −1.01636
\(999\) 33.3693 1.05576
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.h.1.1 2
3.2 odd 2 8550.2.a.br.1.1 2
4.3 odd 2 7600.2.a.y.1.2 2
5.2 odd 4 950.2.b.f.799.4 4
5.3 odd 4 950.2.b.f.799.1 4
5.4 even 2 190.2.a.d.1.2 2
15.14 odd 2 1710.2.a.w.1.2 2
20.19 odd 2 1520.2.a.n.1.1 2
35.34 odd 2 9310.2.a.bc.1.1 2
40.19 odd 2 6080.2.a.bb.1.2 2
40.29 even 2 6080.2.a.bh.1.1 2
95.94 odd 2 3610.2.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.d.1.2 2 5.4 even 2
950.2.a.h.1.1 2 1.1 even 1 trivial
950.2.b.f.799.1 4 5.3 odd 4
950.2.b.f.799.4 4 5.2 odd 4
1520.2.a.n.1.1 2 20.19 odd 2
1710.2.a.w.1.2 2 15.14 odd 2
3610.2.a.t.1.1 2 95.94 odd 2
6080.2.a.bb.1.2 2 40.19 odd 2
6080.2.a.bh.1.1 2 40.29 even 2
7600.2.a.y.1.2 2 4.3 odd 2
8550.2.a.br.1.1 2 3.2 odd 2
9310.2.a.bc.1.1 2 35.34 odd 2