Properties

Label 1950.2.a.bc.1.1
Level $1950$
Weight $2$
Character 1950.1
Self dual yes
Analytic conductor $15.571$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \(x^{2} - x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.70156\) of defining polynomial
Character \(\chi\) \(=\) 1950.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -4.70156 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.70156 q^{11} -1.00000 q^{12} +1.00000 q^{13} +4.70156 q^{14} +1.00000 q^{16} +0.701562 q^{17} -1.00000 q^{18} -1.70156 q^{19} +4.70156 q^{21} -4.70156 q^{22} +1.00000 q^{24} -1.00000 q^{26} -1.00000 q^{27} -4.70156 q^{28} -6.40312 q^{29} -10.1047 q^{31} -1.00000 q^{32} -4.70156 q^{33} -0.701562 q^{34} +1.00000 q^{36} +1.70156 q^{37} +1.70156 q^{38} -1.00000 q^{39} -3.70156 q^{41} -4.70156 q^{42} +11.4031 q^{43} +4.70156 q^{44} -7.00000 q^{47} -1.00000 q^{48} +15.1047 q^{49} -0.701562 q^{51} +1.00000 q^{52} -2.40312 q^{53} +1.00000 q^{54} +4.70156 q^{56} +1.70156 q^{57} +6.40312 q^{58} +2.70156 q^{59} +14.1047 q^{61} +10.1047 q^{62} -4.70156 q^{63} +1.00000 q^{64} +4.70156 q^{66} +6.40312 q^{67} +0.701562 q^{68} -1.70156 q^{71} -1.00000 q^{72} +12.0000 q^{73} -1.70156 q^{74} -1.70156 q^{76} -22.1047 q^{77} +1.00000 q^{78} -5.70156 q^{79} +1.00000 q^{81} +3.70156 q^{82} +10.7016 q^{83} +4.70156 q^{84} -11.4031 q^{86} +6.40312 q^{87} -4.70156 q^{88} +11.4031 q^{89} -4.70156 q^{91} +10.1047 q^{93} +7.00000 q^{94} +1.00000 q^{96} +2.59688 q^{97} -15.1047 q^{98} +4.70156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 3 q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 2 q^{16} - 5 q^{17} - 2 q^{18} + 3 q^{19} + 3 q^{21} - 3 q^{22} + 2 q^{24} - 2 q^{26} - 2 q^{27} - 3 q^{28} - q^{31} - 2 q^{32} - 3 q^{33} + 5 q^{34} + 2 q^{36} - 3 q^{37} - 3 q^{38} - 2 q^{39} - q^{41} - 3 q^{42} + 10 q^{43} + 3 q^{44} - 14 q^{47} - 2 q^{48} + 11 q^{49} + 5 q^{51} + 2 q^{52} + 8 q^{53} + 2 q^{54} + 3 q^{56} - 3 q^{57} - q^{59} + 9 q^{61} + q^{62} - 3 q^{63} + 2 q^{64} + 3 q^{66} - 5 q^{68} + 3 q^{71} - 2 q^{72} + 24 q^{73} + 3 q^{74} + 3 q^{76} - 25 q^{77} + 2 q^{78} - 5 q^{79} + 2 q^{81} + q^{82} + 15 q^{83} + 3 q^{84} - 10 q^{86} - 3 q^{88} + 10 q^{89} - 3 q^{91} + q^{93} + 14 q^{94} + 2 q^{96} + 18 q^{97} - 11 q^{98} + 3 q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) −4.70156 −1.77702 −0.888512 0.458854i \(-0.848260\pi\)
−0.888512 + 0.458854i \(0.848260\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.70156 1.41757 0.708787 0.705422i \(-0.249243\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 4.70156 1.25655
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.701562 0.170154 0.0850769 0.996374i \(-0.472886\pi\)
0.0850769 + 0.996374i \(0.472886\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.70156 −0.390365 −0.195183 0.980767i \(-0.562530\pi\)
−0.195183 + 0.980767i \(0.562530\pi\)
\(20\) 0 0
\(21\) 4.70156 1.02596
\(22\) −4.70156 −1.00238
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −4.70156 −0.888512
\(29\) −6.40312 −1.18903 −0.594515 0.804084i \(-0.702656\pi\)
−0.594515 + 0.804084i \(0.702656\pi\)
\(30\) 0 0
\(31\) −10.1047 −1.81486 −0.907428 0.420208i \(-0.861957\pi\)
−0.907428 + 0.420208i \(0.861957\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.70156 −0.818437
\(34\) −0.701562 −0.120317
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 1.70156 0.279735 0.139868 0.990170i \(-0.455332\pi\)
0.139868 + 0.990170i \(0.455332\pi\)
\(38\) 1.70156 0.276030
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −3.70156 −0.578087 −0.289043 0.957316i \(-0.593337\pi\)
−0.289043 + 0.957316i \(0.593337\pi\)
\(42\) −4.70156 −0.725467
\(43\) 11.4031 1.73896 0.869480 0.493968i \(-0.164454\pi\)
0.869480 + 0.493968i \(0.164454\pi\)
\(44\) 4.70156 0.708787
\(45\) 0 0
\(46\) 0 0
\(47\) −7.00000 −1.02105 −0.510527 0.859861i \(-0.670550\pi\)
−0.510527 + 0.859861i \(0.670550\pi\)
\(48\) −1.00000 −0.144338
\(49\) 15.1047 2.15781
\(50\) 0 0
\(51\) −0.701562 −0.0982383
\(52\) 1.00000 0.138675
\(53\) −2.40312 −0.330095 −0.165047 0.986286i \(-0.552778\pi\)
−0.165047 + 0.986286i \(0.552778\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 4.70156 0.628273
\(57\) 1.70156 0.225377
\(58\) 6.40312 0.840771
\(59\) 2.70156 0.351713 0.175857 0.984416i \(-0.443730\pi\)
0.175857 + 0.984416i \(0.443730\pi\)
\(60\) 0 0
\(61\) 14.1047 1.80592 0.902960 0.429725i \(-0.141389\pi\)
0.902960 + 0.429725i \(0.141389\pi\)
\(62\) 10.1047 1.28330
\(63\) −4.70156 −0.592341
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.70156 0.578722
\(67\) 6.40312 0.782266 0.391133 0.920334i \(-0.372083\pi\)
0.391133 + 0.920334i \(0.372083\pi\)
\(68\) 0.701562 0.0850769
\(69\) 0 0
\(70\) 0 0
\(71\) −1.70156 −0.201938 −0.100969 0.994890i \(-0.532194\pi\)
−0.100969 + 0.994890i \(0.532194\pi\)
\(72\) −1.00000 −0.117851
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) −1.70156 −0.197803
\(75\) 0 0
\(76\) −1.70156 −0.195183
\(77\) −22.1047 −2.51906
\(78\) 1.00000 0.113228
\(79\) −5.70156 −0.641476 −0.320738 0.947168i \(-0.603931\pi\)
−0.320738 + 0.947168i \(0.603931\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 3.70156 0.408769
\(83\) 10.7016 1.17465 0.587325 0.809352i \(-0.300181\pi\)
0.587325 + 0.809352i \(0.300181\pi\)
\(84\) 4.70156 0.512982
\(85\) 0 0
\(86\) −11.4031 −1.22963
\(87\) 6.40312 0.686487
\(88\) −4.70156 −0.501188
\(89\) 11.4031 1.20873 0.604364 0.796708i \(-0.293427\pi\)
0.604364 + 0.796708i \(0.293427\pi\)
\(90\) 0 0
\(91\) −4.70156 −0.492858
\(92\) 0 0
\(93\) 10.1047 1.04781
\(94\) 7.00000 0.721995
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 2.59688 0.263673 0.131836 0.991271i \(-0.457913\pi\)
0.131836 + 0.991271i \(0.457913\pi\)
\(98\) −15.1047 −1.52580
\(99\) 4.70156 0.472525
\(100\) 0 0
\(101\) 6.70156 0.666830 0.333415 0.942780i \(-0.391799\pi\)
0.333415 + 0.942780i \(0.391799\pi\)
\(102\) 0.701562 0.0694650
\(103\) −1.40312 −0.138254 −0.0691270 0.997608i \(-0.522021\pi\)
−0.0691270 + 0.997608i \(0.522021\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 2.40312 0.233412
\(107\) −19.1047 −1.84692 −0.923460 0.383695i \(-0.874651\pi\)
−0.923460 + 0.383695i \(0.874651\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 4.29844 0.411716 0.205858 0.978582i \(-0.434002\pi\)
0.205858 + 0.978582i \(0.434002\pi\)
\(110\) 0 0
\(111\) −1.70156 −0.161505
\(112\) −4.70156 −0.444256
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) −1.70156 −0.159366
\(115\) 0 0
\(116\) −6.40312 −0.594515
\(117\) 1.00000 0.0924500
\(118\) −2.70156 −0.248699
\(119\) −3.29844 −0.302367
\(120\) 0 0
\(121\) 11.1047 1.00952
\(122\) −14.1047 −1.27698
\(123\) 3.70156 0.333759
\(124\) −10.1047 −0.907428
\(125\) 0 0
\(126\) 4.70156 0.418848
\(127\) 6.29844 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.4031 −1.00399
\(130\) 0 0
\(131\) 22.5078 1.96652 0.983258 0.182217i \(-0.0583275\pi\)
0.983258 + 0.182217i \(0.0583275\pi\)
\(132\) −4.70156 −0.409218
\(133\) 8.00000 0.693688
\(134\) −6.40312 −0.553146
\(135\) 0 0
\(136\) −0.701562 −0.0601585
\(137\) −13.7016 −1.17060 −0.585302 0.810816i \(-0.699024\pi\)
−0.585302 + 0.810816i \(0.699024\pi\)
\(138\) 0 0
\(139\) 9.40312 0.797563 0.398781 0.917046i \(-0.369433\pi\)
0.398781 + 0.917046i \(0.369433\pi\)
\(140\) 0 0
\(141\) 7.00000 0.589506
\(142\) 1.70156 0.142792
\(143\) 4.70156 0.393164
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −12.0000 −0.993127
\(147\) −15.1047 −1.24581
\(148\) 1.70156 0.139868
\(149\) 6.59688 0.540437 0.270219 0.962799i \(-0.412904\pi\)
0.270219 + 0.962799i \(0.412904\pi\)
\(150\) 0 0
\(151\) −14.1047 −1.14782 −0.573912 0.818917i \(-0.694575\pi\)
−0.573912 + 0.818917i \(0.694575\pi\)
\(152\) 1.70156 0.138015
\(153\) 0.701562 0.0567179
\(154\) 22.1047 1.78125
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 22.7016 1.81178 0.905891 0.423511i \(-0.139203\pi\)
0.905891 + 0.423511i \(0.139203\pi\)
\(158\) 5.70156 0.453592
\(159\) 2.40312 0.190580
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 18.8062 1.47302 0.736510 0.676427i \(-0.236473\pi\)
0.736510 + 0.676427i \(0.236473\pi\)
\(164\) −3.70156 −0.289043
\(165\) 0 0
\(166\) −10.7016 −0.830602
\(167\) 1.10469 0.0854832 0.0427416 0.999086i \(-0.486391\pi\)
0.0427416 + 0.999086i \(0.486391\pi\)
\(168\) −4.70156 −0.362733
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −1.70156 −0.130122
\(172\) 11.4031 0.869480
\(173\) 0.193752 0.0147307 0.00736533 0.999973i \(-0.497656\pi\)
0.00736533 + 0.999973i \(0.497656\pi\)
\(174\) −6.40312 −0.485420
\(175\) 0 0
\(176\) 4.70156 0.354394
\(177\) −2.70156 −0.203062
\(178\) −11.4031 −0.854700
\(179\) −24.2094 −1.80949 −0.904747 0.425950i \(-0.859940\pi\)
−0.904747 + 0.425950i \(0.859940\pi\)
\(180\) 0 0
\(181\) 11.2984 0.839806 0.419903 0.907569i \(-0.362064\pi\)
0.419903 + 0.907569i \(0.362064\pi\)
\(182\) 4.70156 0.348503
\(183\) −14.1047 −1.04265
\(184\) 0 0
\(185\) 0 0
\(186\) −10.1047 −0.740912
\(187\) 3.29844 0.241206
\(188\) −7.00000 −0.510527
\(189\) 4.70156 0.341988
\(190\) 0 0
\(191\) −12.8062 −0.926628 −0.463314 0.886194i \(-0.653340\pi\)
−0.463314 + 0.886194i \(0.653340\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −16.2094 −1.16678 −0.583388 0.812194i \(-0.698273\pi\)
−0.583388 + 0.812194i \(0.698273\pi\)
\(194\) −2.59688 −0.186445
\(195\) 0 0
\(196\) 15.1047 1.07891
\(197\) 5.40312 0.384957 0.192478 0.981301i \(-0.438347\pi\)
0.192478 + 0.981301i \(0.438347\pi\)
\(198\) −4.70156 −0.334125
\(199\) 8.29844 0.588261 0.294130 0.955765i \(-0.404970\pi\)
0.294130 + 0.955765i \(0.404970\pi\)
\(200\) 0 0
\(201\) −6.40312 −0.451642
\(202\) −6.70156 −0.471520
\(203\) 30.1047 2.11293
\(204\) −0.701562 −0.0491192
\(205\) 0 0
\(206\) 1.40312 0.0977603
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) 6.80625 0.468561 0.234281 0.972169i \(-0.424727\pi\)
0.234281 + 0.972169i \(0.424727\pi\)
\(212\) −2.40312 −0.165047
\(213\) 1.70156 0.116589
\(214\) 19.1047 1.30597
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 47.5078 3.22504
\(218\) −4.29844 −0.291127
\(219\) −12.0000 −0.810885
\(220\) 0 0
\(221\) 0.701562 0.0471922
\(222\) 1.70156 0.114201
\(223\) −11.4031 −0.763610 −0.381805 0.924243i \(-0.624697\pi\)
−0.381805 + 0.924243i \(0.624697\pi\)
\(224\) 4.70156 0.314136
\(225\) 0 0
\(226\) −14.0000 −0.931266
\(227\) 16.1047 1.06891 0.534453 0.845198i \(-0.320518\pi\)
0.534453 + 0.845198i \(0.320518\pi\)
\(228\) 1.70156 0.112689
\(229\) 15.7016 1.03759 0.518794 0.854899i \(-0.326381\pi\)
0.518794 + 0.854899i \(0.326381\pi\)
\(230\) 0 0
\(231\) 22.1047 1.45438
\(232\) 6.40312 0.420386
\(233\) 20.2094 1.32396 0.661980 0.749521i \(-0.269716\pi\)
0.661980 + 0.749521i \(0.269716\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 0 0
\(236\) 2.70156 0.175857
\(237\) 5.70156 0.370356
\(238\) 3.29844 0.213806
\(239\) 6.10469 0.394879 0.197440 0.980315i \(-0.436737\pi\)
0.197440 + 0.980315i \(0.436737\pi\)
\(240\) 0 0
\(241\) −2.59688 −0.167279 −0.0836397 0.996496i \(-0.526654\pi\)
−0.0836397 + 0.996496i \(0.526654\pi\)
\(242\) −11.1047 −0.713836
\(243\) −1.00000 −0.0641500
\(244\) 14.1047 0.902960
\(245\) 0 0
\(246\) −3.70156 −0.236003
\(247\) −1.70156 −0.108268
\(248\) 10.1047 0.641648
\(249\) −10.7016 −0.678184
\(250\) 0 0
\(251\) 0.298438 0.0188372 0.00941862 0.999956i \(-0.497002\pi\)
0.00941862 + 0.999956i \(0.497002\pi\)
\(252\) −4.70156 −0.296171
\(253\) 0 0
\(254\) −6.29844 −0.395199
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.2984 0.954290 0.477145 0.878824i \(-0.341672\pi\)
0.477145 + 0.878824i \(0.341672\pi\)
\(258\) 11.4031 0.709928
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) −6.40312 −0.396343
\(262\) −22.5078 −1.39054
\(263\) −2.00000 −0.123325 −0.0616626 0.998097i \(-0.519640\pi\)
−0.0616626 + 0.998097i \(0.519640\pi\)
\(264\) 4.70156 0.289361
\(265\) 0 0
\(266\) −8.00000 −0.490511
\(267\) −11.4031 −0.697860
\(268\) 6.40312 0.391133
\(269\) 31.2094 1.90287 0.951435 0.307851i \(-0.0996099\pi\)
0.951435 + 0.307851i \(0.0996099\pi\)
\(270\) 0 0
\(271\) 19.5078 1.18502 0.592508 0.805565i \(-0.298138\pi\)
0.592508 + 0.805565i \(0.298138\pi\)
\(272\) 0.701562 0.0425385
\(273\) 4.70156 0.284551
\(274\) 13.7016 0.827742
\(275\) 0 0
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) −9.40312 −0.563962
\(279\) −10.1047 −0.604952
\(280\) 0 0
\(281\) −21.9109 −1.30710 −0.653548 0.756885i \(-0.726720\pi\)
−0.653548 + 0.756885i \(0.726720\pi\)
\(282\) −7.00000 −0.416844
\(283\) −21.4031 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(284\) −1.70156 −0.100969
\(285\) 0 0
\(286\) −4.70156 −0.278009
\(287\) 17.4031 1.02727
\(288\) −1.00000 −0.0589256
\(289\) −16.5078 −0.971048
\(290\) 0 0
\(291\) −2.59688 −0.152232
\(292\) 12.0000 0.702247
\(293\) −21.4031 −1.25038 −0.625192 0.780471i \(-0.714979\pi\)
−0.625192 + 0.780471i \(0.714979\pi\)
\(294\) 15.1047 0.880923
\(295\) 0 0
\(296\) −1.70156 −0.0989013
\(297\) −4.70156 −0.272812
\(298\) −6.59688 −0.382147
\(299\) 0 0
\(300\) 0 0
\(301\) −53.6125 −3.09017
\(302\) 14.1047 0.811633
\(303\) −6.70156 −0.384995
\(304\) −1.70156 −0.0975913
\(305\) 0 0
\(306\) −0.701562 −0.0401056
\(307\) 5.70156 0.325405 0.162703 0.986675i \(-0.447979\pi\)
0.162703 + 0.986675i \(0.447979\pi\)
\(308\) −22.1047 −1.25953
\(309\) 1.40312 0.0798209
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 1.00000 0.0566139
\(313\) 21.2094 1.19882 0.599412 0.800440i \(-0.295401\pi\)
0.599412 + 0.800440i \(0.295401\pi\)
\(314\) −22.7016 −1.28112
\(315\) 0 0
\(316\) −5.70156 −0.320738
\(317\) −1.19375 −0.0670478 −0.0335239 0.999438i \(-0.510673\pi\)
−0.0335239 + 0.999438i \(0.510673\pi\)
\(318\) −2.40312 −0.134761
\(319\) −30.1047 −1.68554
\(320\) 0 0
\(321\) 19.1047 1.06632
\(322\) 0 0
\(323\) −1.19375 −0.0664221
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −18.8062 −1.04158
\(327\) −4.29844 −0.237704
\(328\) 3.70156 0.204385
\(329\) 32.9109 1.81444
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 10.7016 0.587325
\(333\) 1.70156 0.0932450
\(334\) −1.10469 −0.0604457
\(335\) 0 0
\(336\) 4.70156 0.256491
\(337\) −8.10469 −0.441490 −0.220745 0.975332i \(-0.570849\pi\)
−0.220745 + 0.975332i \(0.570849\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −14.0000 −0.760376
\(340\) 0 0
\(341\) −47.5078 −2.57269
\(342\) 1.70156 0.0920099
\(343\) −38.1047 −2.05746
\(344\) −11.4031 −0.614815
\(345\) 0 0
\(346\) −0.193752 −0.0104161
\(347\) −10.5078 −0.564089 −0.282044 0.959401i \(-0.591013\pi\)
−0.282044 + 0.959401i \(0.591013\pi\)
\(348\) 6.40312 0.343243
\(349\) −11.4031 −0.610395 −0.305198 0.952289i \(-0.598723\pi\)
−0.305198 + 0.952289i \(0.598723\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −4.70156 −0.250594
\(353\) −14.5078 −0.772173 −0.386086 0.922463i \(-0.626173\pi\)
−0.386086 + 0.922463i \(0.626173\pi\)
\(354\) 2.70156 0.143586
\(355\) 0 0
\(356\) 11.4031 0.604364
\(357\) 3.29844 0.174572
\(358\) 24.2094 1.27951
\(359\) −34.6125 −1.82678 −0.913389 0.407088i \(-0.866544\pi\)
−0.913389 + 0.407088i \(0.866544\pi\)
\(360\) 0 0
\(361\) −16.1047 −0.847615
\(362\) −11.2984 −0.593833
\(363\) −11.1047 −0.582845
\(364\) −4.70156 −0.246429
\(365\) 0 0
\(366\) 14.1047 0.737264
\(367\) 2.29844 0.119977 0.0599887 0.998199i \(-0.480894\pi\)
0.0599887 + 0.998199i \(0.480894\pi\)
\(368\) 0 0
\(369\) −3.70156 −0.192696
\(370\) 0 0
\(371\) 11.2984 0.586586
\(372\) 10.1047 0.523904
\(373\) −5.29844 −0.274343 −0.137171 0.990547i \(-0.543801\pi\)
−0.137171 + 0.990547i \(0.543801\pi\)
\(374\) −3.29844 −0.170558
\(375\) 0 0
\(376\) 7.00000 0.360997
\(377\) −6.40312 −0.329778
\(378\) −4.70156 −0.241822
\(379\) −13.8953 −0.713754 −0.356877 0.934151i \(-0.616159\pi\)
−0.356877 + 0.934151i \(0.616159\pi\)
\(380\) 0 0
\(381\) −6.29844 −0.322679
\(382\) 12.8062 0.655225
\(383\) −32.5078 −1.66107 −0.830536 0.556965i \(-0.811966\pi\)
−0.830536 + 0.556965i \(0.811966\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 16.2094 0.825035
\(387\) 11.4031 0.579653
\(388\) 2.59688 0.131836
\(389\) −27.1047 −1.37426 −0.687131 0.726533i \(-0.741130\pi\)
−0.687131 + 0.726533i \(0.741130\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −15.1047 −0.762902
\(393\) −22.5078 −1.13537
\(394\) −5.40312 −0.272205
\(395\) 0 0
\(396\) 4.70156 0.236262
\(397\) 21.9109 1.09968 0.549839 0.835271i \(-0.314689\pi\)
0.549839 + 0.835271i \(0.314689\pi\)
\(398\) −8.29844 −0.415963
\(399\) −8.00000 −0.400501
\(400\) 0 0
\(401\) 18.2094 0.909333 0.454666 0.890662i \(-0.349759\pi\)
0.454666 + 0.890662i \(0.349759\pi\)
\(402\) 6.40312 0.319359
\(403\) −10.1047 −0.503350
\(404\) 6.70156 0.333415
\(405\) 0 0
\(406\) −30.1047 −1.49407
\(407\) 8.00000 0.396545
\(408\) 0.701562 0.0347325
\(409\) 29.4031 1.45389 0.726945 0.686695i \(-0.240939\pi\)
0.726945 + 0.686695i \(0.240939\pi\)
\(410\) 0 0
\(411\) 13.7016 0.675848
\(412\) −1.40312 −0.0691270
\(413\) −12.7016 −0.625003
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 −0.0490290
\(417\) −9.40312 −0.460473
\(418\) 8.00000 0.391293
\(419\) 9.91093 0.484181 0.242090 0.970254i \(-0.422167\pi\)
0.242090 + 0.970254i \(0.422167\pi\)
\(420\) 0 0
\(421\) −0.596876 −0.0290899 −0.0145450 0.999894i \(-0.504630\pi\)
−0.0145450 + 0.999894i \(0.504630\pi\)
\(422\) −6.80625 −0.331323
\(423\) −7.00000 −0.340352
\(424\) 2.40312 0.116706
\(425\) 0 0
\(426\) −1.70156 −0.0824410
\(427\) −66.3141 −3.20916
\(428\) −19.1047 −0.923460
\(429\) −4.70156 −0.226994
\(430\) 0 0
\(431\) 35.3141 1.70102 0.850509 0.525960i \(-0.176294\pi\)
0.850509 + 0.525960i \(0.176294\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 11.1047 0.533657 0.266829 0.963744i \(-0.414024\pi\)
0.266829 + 0.963744i \(0.414024\pi\)
\(434\) −47.5078 −2.28045
\(435\) 0 0
\(436\) 4.29844 0.205858
\(437\) 0 0
\(438\) 12.0000 0.573382
\(439\) −10.2984 −0.491518 −0.245759 0.969331i \(-0.579037\pi\)
−0.245759 + 0.969331i \(0.579037\pi\)
\(440\) 0 0
\(441\) 15.1047 0.719271
\(442\) −0.701562 −0.0333699
\(443\) −32.5078 −1.54449 −0.772246 0.635323i \(-0.780867\pi\)
−0.772246 + 0.635323i \(0.780867\pi\)
\(444\) −1.70156 −0.0807526
\(445\) 0 0
\(446\) 11.4031 0.539954
\(447\) −6.59688 −0.312022
\(448\) −4.70156 −0.222128
\(449\) 2.29844 0.108470 0.0542350 0.998528i \(-0.482728\pi\)
0.0542350 + 0.998528i \(0.482728\pi\)
\(450\) 0 0
\(451\) −17.4031 −0.819481
\(452\) 14.0000 0.658505
\(453\) 14.1047 0.662696
\(454\) −16.1047 −0.755830
\(455\) 0 0
\(456\) −1.70156 −0.0796829
\(457\) 2.59688 0.121477 0.0607384 0.998154i \(-0.480654\pi\)
0.0607384 + 0.998154i \(0.480654\pi\)
\(458\) −15.7016 −0.733686
\(459\) −0.701562 −0.0327461
\(460\) 0 0
\(461\) 36.2094 1.68644 0.843219 0.537570i \(-0.180658\pi\)
0.843219 + 0.537570i \(0.180658\pi\)
\(462\) −22.1047 −1.02840
\(463\) 21.2984 0.989822 0.494911 0.868944i \(-0.335201\pi\)
0.494911 + 0.868944i \(0.335201\pi\)
\(464\) −6.40312 −0.297258
\(465\) 0 0
\(466\) −20.2094 −0.936181
\(467\) −30.2984 −1.40204 −0.701022 0.713139i \(-0.747273\pi\)
−0.701022 + 0.713139i \(0.747273\pi\)
\(468\) 1.00000 0.0462250
\(469\) −30.1047 −1.39011
\(470\) 0 0
\(471\) −22.7016 −1.04603
\(472\) −2.70156 −0.124349
\(473\) 53.6125 2.46511
\(474\) −5.70156 −0.261881
\(475\) 0 0
\(476\) −3.29844 −0.151184
\(477\) −2.40312 −0.110032
\(478\) −6.10469 −0.279222
\(479\) −40.6125 −1.85563 −0.927816 0.373038i \(-0.878316\pi\)
−0.927816 + 0.373038i \(0.878316\pi\)
\(480\) 0 0
\(481\) 1.70156 0.0775846
\(482\) 2.59688 0.118284
\(483\) 0 0
\(484\) 11.1047 0.504758
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 7.89531 0.357771 0.178885 0.983870i \(-0.442751\pi\)
0.178885 + 0.983870i \(0.442751\pi\)
\(488\) −14.1047 −0.638489
\(489\) −18.8062 −0.850448
\(490\) 0 0
\(491\) 33.4031 1.50746 0.753731 0.657183i \(-0.228252\pi\)
0.753731 + 0.657183i \(0.228252\pi\)
\(492\) 3.70156 0.166879
\(493\) −4.49219 −0.202318
\(494\) 1.70156 0.0765569
\(495\) 0 0
\(496\) −10.1047 −0.453714
\(497\) 8.00000 0.358849
\(498\) 10.7016 0.479548
\(499\) 17.2094 0.770397 0.385199 0.922834i \(-0.374133\pi\)
0.385199 + 0.922834i \(0.374133\pi\)
\(500\) 0 0
\(501\) −1.10469 −0.0493537
\(502\) −0.298438 −0.0133199
\(503\) 12.2094 0.544389 0.272195 0.962242i \(-0.412251\pi\)
0.272195 + 0.962242i \(0.412251\pi\)
\(504\) 4.70156 0.209424
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 6.29844 0.279448
\(509\) −5.40312 −0.239489 −0.119745 0.992805i \(-0.538208\pi\)
−0.119745 + 0.992805i \(0.538208\pi\)
\(510\) 0 0
\(511\) −56.4187 −2.49582
\(512\) −1.00000 −0.0441942
\(513\) 1.70156 0.0751258
\(514\) −15.2984 −0.674785
\(515\) 0 0
\(516\) −11.4031 −0.501995
\(517\) −32.9109 −1.44742
\(518\) 8.00000 0.351500
\(519\) −0.193752 −0.00850475
\(520\) 0 0
\(521\) −36.2094 −1.58636 −0.793181 0.608986i \(-0.791576\pi\)
−0.793181 + 0.608986i \(0.791576\pi\)
\(522\) 6.40312 0.280257
\(523\) 24.8062 1.08470 0.542351 0.840152i \(-0.317534\pi\)
0.542351 + 0.840152i \(0.317534\pi\)
\(524\) 22.5078 0.983258
\(525\) 0 0
\(526\) 2.00000 0.0872041
\(527\) −7.08907 −0.308805
\(528\) −4.70156 −0.204609
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 2.70156 0.117238
\(532\) 8.00000 0.346844
\(533\) −3.70156 −0.160332
\(534\) 11.4031 0.493461
\(535\) 0 0
\(536\) −6.40312 −0.276573
\(537\) 24.2094 1.04471
\(538\) −31.2094 −1.34553
\(539\) 71.0156 3.05886
\(540\) 0 0
\(541\) −1.79063 −0.0769851 −0.0384925 0.999259i \(-0.512256\pi\)
−0.0384925 + 0.999259i \(0.512256\pi\)
\(542\) −19.5078 −0.837932
\(543\) −11.2984 −0.484862
\(544\) −0.701562 −0.0300792
\(545\) 0 0
\(546\) −4.70156 −0.201208
\(547\) 31.6125 1.35165 0.675826 0.737061i \(-0.263787\pi\)
0.675826 + 0.737061i \(0.263787\pi\)
\(548\) −13.7016 −0.585302
\(549\) 14.1047 0.601973
\(550\) 0 0
\(551\) 10.8953 0.464156
\(552\) 0 0
\(553\) 26.8062 1.13992
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) 9.40312 0.398781
\(557\) −16.8062 −0.712104 −0.356052 0.934466i \(-0.615877\pi\)
−0.356052 + 0.934466i \(0.615877\pi\)
\(558\) 10.1047 0.427765
\(559\) 11.4031 0.482301
\(560\) 0 0
\(561\) −3.29844 −0.139260
\(562\) 21.9109 0.924257
\(563\) 32.5078 1.37004 0.685020 0.728524i \(-0.259793\pi\)
0.685020 + 0.728524i \(0.259793\pi\)
\(564\) 7.00000 0.294753
\(565\) 0 0
\(566\) 21.4031 0.899640
\(567\) −4.70156 −0.197447
\(568\) 1.70156 0.0713960
\(569\) −11.2984 −0.473655 −0.236828 0.971552i \(-0.576108\pi\)
−0.236828 + 0.971552i \(0.576108\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 4.70156 0.196582
\(573\) 12.8062 0.534989
\(574\) −17.4031 −0.726392
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) −24.2094 −1.00785 −0.503925 0.863748i \(-0.668111\pi\)
−0.503925 + 0.863748i \(0.668111\pi\)
\(578\) 16.5078 0.686634
\(579\) 16.2094 0.673639
\(580\) 0 0
\(581\) −50.3141 −2.08738
\(582\) 2.59688 0.107644
\(583\) −11.2984 −0.467933
\(584\) −12.0000 −0.496564
\(585\) 0 0
\(586\) 21.4031 0.884155
\(587\) 7.50781 0.309881 0.154940 0.987924i \(-0.450481\pi\)
0.154940 + 0.987924i \(0.450481\pi\)
\(588\) −15.1047 −0.622907
\(589\) 17.1938 0.708456
\(590\) 0 0
\(591\) −5.40312 −0.222255
\(592\) 1.70156 0.0699338
\(593\) −17.9109 −0.735514 −0.367757 0.929922i \(-0.619874\pi\)
−0.367757 + 0.929922i \(0.619874\pi\)
\(594\) 4.70156 0.192907
\(595\) 0 0
\(596\) 6.59688 0.270219
\(597\) −8.29844 −0.339632
\(598\) 0 0
\(599\) 8.20937 0.335426 0.167713 0.985836i \(-0.446362\pi\)
0.167713 + 0.985836i \(0.446362\pi\)
\(600\) 0 0
\(601\) 10.6125 0.432893 0.216446 0.976295i \(-0.430553\pi\)
0.216446 + 0.976295i \(0.430553\pi\)
\(602\) 53.6125 2.18508
\(603\) 6.40312 0.260755
\(604\) −14.1047 −0.573912
\(605\) 0 0
\(606\) 6.70156 0.272232
\(607\) 35.1047 1.42486 0.712428 0.701746i \(-0.247596\pi\)
0.712428 + 0.701746i \(0.247596\pi\)
\(608\) 1.70156 0.0690075
\(609\) −30.1047 −1.21990
\(610\) 0 0
\(611\) −7.00000 −0.283190
\(612\) 0.701562 0.0283590
\(613\) 12.8062 0.517240 0.258620 0.965979i \(-0.416732\pi\)
0.258620 + 0.965979i \(0.416732\pi\)
\(614\) −5.70156 −0.230096
\(615\) 0 0
\(616\) 22.1047 0.890623
\(617\) 27.1047 1.09119 0.545597 0.838048i \(-0.316303\pi\)
0.545597 + 0.838048i \(0.316303\pi\)
\(618\) −1.40312 −0.0564419
\(619\) −13.1938 −0.530302 −0.265151 0.964207i \(-0.585422\pi\)
−0.265151 + 0.964207i \(0.585422\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −30.0000 −1.20289
\(623\) −53.6125 −2.14794
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) −21.2094 −0.847697
\(627\) 8.00000 0.319489
\(628\) 22.7016 0.905891
\(629\) 1.19375 0.0475980
\(630\) 0 0
\(631\) 33.6125 1.33809 0.669046 0.743221i \(-0.266703\pi\)
0.669046 + 0.743221i \(0.266703\pi\)
\(632\) 5.70156 0.226796
\(633\) −6.80625 −0.270524
\(634\) 1.19375 0.0474099
\(635\) 0 0
\(636\) 2.40312 0.0952901
\(637\) 15.1047 0.598469
\(638\) 30.1047 1.19186
\(639\) −1.70156 −0.0673128
\(640\) 0 0
\(641\) 5.50781 0.217545 0.108773 0.994067i \(-0.465308\pi\)
0.108773 + 0.994067i \(0.465308\pi\)
\(642\) −19.1047 −0.754002
\(643\) 10.2984 0.406131 0.203065 0.979165i \(-0.434910\pi\)
0.203065 + 0.979165i \(0.434910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.19375 0.0469675
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 12.7016 0.498580
\(650\) 0 0
\(651\) −47.5078 −1.86198
\(652\) 18.8062 0.736510
\(653\) 21.2984 0.833472 0.416736 0.909027i \(-0.363174\pi\)
0.416736 + 0.909027i \(0.363174\pi\)
\(654\) 4.29844 0.168082
\(655\) 0 0
\(656\) −3.70156 −0.144522
\(657\) 12.0000 0.468165
\(658\) −32.9109 −1.28300
\(659\) −19.3141 −0.752369 −0.376184 0.926545i \(-0.622764\pi\)
−0.376184 + 0.926545i \(0.622764\pi\)
\(660\) 0 0
\(661\) −40.1203 −1.56050 −0.780250 0.625468i \(-0.784908\pi\)
−0.780250 + 0.625468i \(0.784908\pi\)
\(662\) 12.0000 0.466393
\(663\) −0.701562 −0.0272464
\(664\) −10.7016 −0.415301
\(665\) 0 0
\(666\) −1.70156 −0.0659342
\(667\) 0 0
\(668\) 1.10469 0.0427416
\(669\) 11.4031 0.440870
\(670\) 0 0
\(671\) 66.3141 2.56003
\(672\) −4.70156 −0.181367
\(673\) −36.0156 −1.38830 −0.694150 0.719830i \(-0.744220\pi\)
−0.694150 + 0.719830i \(0.744220\pi\)
\(674\) 8.10469 0.312181
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) −31.6125 −1.21497 −0.607483 0.794332i \(-0.707821\pi\)
−0.607483 + 0.794332i \(0.707821\pi\)
\(678\) 14.0000 0.537667
\(679\) −12.2094 −0.468553
\(680\) 0 0
\(681\) −16.1047 −0.617133
\(682\) 47.5078 1.81917
\(683\) −44.7016 −1.71046 −0.855229 0.518251i \(-0.826583\pi\)
−0.855229 + 0.518251i \(0.826583\pi\)
\(684\) −1.70156 −0.0650609
\(685\) 0 0
\(686\) 38.1047 1.45484
\(687\) −15.7016 −0.599052
\(688\) 11.4031 0.434740
\(689\) −2.40312 −0.0915517
\(690\) 0 0
\(691\) −22.1938 −0.844290 −0.422145 0.906528i \(-0.638723\pi\)
−0.422145 + 0.906528i \(0.638723\pi\)
\(692\) 0.193752 0.00736533
\(693\) −22.1047 −0.839688
\(694\) 10.5078 0.398871
\(695\) 0 0
\(696\) −6.40312 −0.242710
\(697\) −2.59688 −0.0983637
\(698\) 11.4031 0.431615
\(699\) −20.2094 −0.764389
\(700\) 0 0
\(701\) 30.9109 1.16749 0.583745 0.811937i \(-0.301587\pi\)
0.583745 + 0.811937i \(0.301587\pi\)
\(702\) 1.00000 0.0377426
\(703\) −2.89531 −0.109199
\(704\) 4.70156 0.177197
\(705\) 0 0
\(706\) 14.5078 0.546009
\(707\) −31.5078 −1.18497
\(708\) −2.70156 −0.101531
\(709\) 15.6125 0.586340 0.293170 0.956060i \(-0.405290\pi\)
0.293170 + 0.956060i \(0.405290\pi\)
\(710\) 0 0
\(711\) −5.70156 −0.213825
\(712\) −11.4031 −0.427350
\(713\) 0 0
\(714\) −3.29844 −0.123441
\(715\) 0 0
\(716\) −24.2094 −0.904747
\(717\) −6.10469 −0.227984
\(718\) 34.6125 1.29173
\(719\) −11.0156 −0.410813 −0.205407 0.978677i \(-0.565852\pi\)
−0.205407 + 0.978677i \(0.565852\pi\)
\(720\) 0 0
\(721\) 6.59688 0.245680
\(722\) 16.1047 0.599354
\(723\) 2.59688 0.0965788
\(724\) 11.2984 0.419903
\(725\) 0 0
\(726\) 11.1047 0.412134
\(727\) −7.79063 −0.288938 −0.144469 0.989509i \(-0.546147\pi\)
−0.144469 + 0.989509i \(0.546147\pi\)
\(728\) 4.70156 0.174251
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) −14.1047 −0.521324
\(733\) −47.9109 −1.76963 −0.884815 0.465942i \(-0.845716\pi\)
−0.884815 + 0.465942i \(0.845716\pi\)
\(734\) −2.29844 −0.0848369
\(735\) 0 0
\(736\) 0 0
\(737\) 30.1047 1.10892
\(738\) 3.70156 0.136256
\(739\) 4.61250 0.169673 0.0848367 0.996395i \(-0.472963\pi\)
0.0848367 + 0.996395i \(0.472963\pi\)
\(740\) 0 0
\(741\) 1.70156 0.0625084
\(742\) −11.2984 −0.414779
\(743\) 30.6125 1.12306 0.561532 0.827455i \(-0.310212\pi\)
0.561532 + 0.827455i \(0.310212\pi\)
\(744\) −10.1047 −0.370456
\(745\) 0 0
\(746\) 5.29844 0.193990
\(747\) 10.7016 0.391550
\(748\) 3.29844 0.120603
\(749\) 89.8219 3.28202
\(750\) 0 0
\(751\) 8.50781 0.310454 0.155227 0.987879i \(-0.450389\pi\)
0.155227 + 0.987879i \(0.450389\pi\)
\(752\) −7.00000 −0.255264
\(753\) −0.298438 −0.0108757
\(754\) 6.40312 0.233188
\(755\) 0 0
\(756\) 4.70156 0.170994
\(757\) 17.8953 0.650416 0.325208 0.945642i \(-0.394566\pi\)
0.325208 + 0.945642i \(0.394566\pi\)
\(758\) 13.8953 0.504701
\(759\) 0 0
\(760\) 0 0
\(761\) −26.7172 −0.968497 −0.484249 0.874930i \(-0.660907\pi\)
−0.484249 + 0.874930i \(0.660907\pi\)
\(762\) 6.29844 0.228168
\(763\) −20.2094 −0.731628
\(764\) −12.8062 −0.463314
\(765\) 0 0
\(766\) 32.5078 1.17455
\(767\) 2.70156 0.0975478
\(768\) −1.00000 −0.0360844
\(769\) −8.00000 −0.288487 −0.144244 0.989542i \(-0.546075\pi\)
−0.144244 + 0.989542i \(0.546075\pi\)
\(770\) 0 0
\(771\) −15.2984 −0.550960
\(772\) −16.2094 −0.583388
\(773\) −26.5969 −0.956623 −0.478312 0.878190i \(-0.658751\pi\)
−0.478312 + 0.878190i \(0.658751\pi\)
\(774\) −11.4031 −0.409877
\(775\) 0 0
\(776\) −2.59688 −0.0932224
\(777\) 8.00000 0.286998
\(778\) 27.1047 0.971750
\(779\) 6.29844 0.225665
\(780\) 0 0
\(781\) −8.00000 −0.286263
\(782\) 0 0
\(783\) 6.40312 0.228829
\(784\) 15.1047 0.539453
\(785\) 0 0
\(786\) 22.5078 0.802827
\(787\) −33.8953 −1.20824 −0.604119 0.796894i \(-0.706475\pi\)
−0.604119 + 0.796894i \(0.706475\pi\)
\(788\) 5.40312 0.192478
\(789\) 2.00000 0.0712019
\(790\) 0 0
\(791\) −65.8219 −2.34036
\(792\) −4.70156 −0.167063
\(793\) 14.1047 0.500872
\(794\) −21.9109 −0.777590
\(795\) 0 0
\(796\) 8.29844 0.294130
\(797\) −2.91093 −0.103111 −0.0515553 0.998670i \(-0.516418\pi\)
−0.0515553 + 0.998670i \(0.516418\pi\)
\(798\) 8.00000 0.283197
\(799\) −4.91093 −0.173736
\(800\) 0 0
\(801\) 11.4031 0.402910
\(802\) −18.2094 −0.642995
\(803\) 56.4187 1.99097
\(804\) −6.40312 −0.225821
\(805\) 0 0
\(806\) 10.1047 0.355922
\(807\) −31.2094 −1.09862
\(808\) −6.70156 −0.235760
\(809\) 7.19375 0.252919 0.126459 0.991972i \(-0.459639\pi\)
0.126459 + 0.991972i \(0.459639\pi\)
\(810\) 0 0
\(811\) 48.7016 1.71014 0.855072 0.518510i \(-0.173513\pi\)
0.855072 + 0.518510i \(0.173513\pi\)
\(812\) 30.1047 1.05647
\(813\) −19.5078 −0.684169
\(814\) −8.00000 −0.280400
\(815\) 0 0
\(816\) −0.701562 −0.0245596
\(817\) −19.4031 −0.678829
\(818\) −29.4031 −1.02806
\(819\) −4.70156 −0.164286
\(820\) 0 0
\(821\) −20.5969 −0.718836 −0.359418 0.933177i \(-0.617025\pi\)
−0.359418 + 0.933177i \(0.617025\pi\)
\(822\) −13.7016 −0.477897
\(823\) −17.1047 −0.596232 −0.298116 0.954530i \(-0.596358\pi\)
−0.298116 + 0.954530i \(0.596358\pi\)
\(824\) 1.40312 0.0488801
\(825\) 0 0
\(826\) 12.7016 0.441944
\(827\) −20.7016 −0.719864 −0.359932 0.932979i \(-0.617200\pi\)
−0.359932 + 0.932979i \(0.617200\pi\)
\(828\) 0 0
\(829\) −5.50781 −0.191294 −0.0956471 0.995415i \(-0.530492\pi\)
−0.0956471 + 0.995415i \(0.530492\pi\)
\(830\) 0 0
\(831\) −22.0000 −0.763172
\(832\) 1.00000 0.0346688
\(833\) 10.5969 0.367160
\(834\) 9.40312 0.325604
\(835\) 0 0
\(836\) −8.00000 −0.276686
\(837\) 10.1047 0.349269
\(838\) −9.91093 −0.342368
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 12.0000 0.413793
\(842\) 0.596876 0.0205697
\(843\) 21.9109 0.754653
\(844\) 6.80625 0.234281
\(845\) 0 0
\(846\) 7.00000 0.240665
\(847\) −52.2094 −1.79394
\(848\) −2.40312 −0.0825236
\(849\) 21.4031 0.734553
\(850\) 0 0
\(851\) 0 0
\(852\) 1.70156 0.0582946
\(853\) −0.507811 −0.0173871 −0.00869355 0.999962i \(-0.502767\pi\)
−0.00869355 + 0.999962i \(0.502767\pi\)
\(854\) 66.3141 2.26922
\(855\) 0 0
\(856\) 19.1047 0.652985
\(857\) 7.61250 0.260038 0.130019 0.991512i \(-0.458496\pi\)
0.130019 + 0.991512i \(0.458496\pi\)
\(858\) 4.70156 0.160509
\(859\) −6.20937 −0.211861 −0.105931 0.994374i \(-0.533782\pi\)
−0.105931 + 0.994374i \(0.533782\pi\)
\(860\) 0 0
\(861\) −17.4031 −0.593097
\(862\) −35.3141 −1.20280
\(863\) −54.2250 −1.84584 −0.922920 0.384991i \(-0.874204\pi\)
−0.922920 + 0.384991i \(0.874204\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0 0
\(866\) −11.1047 −0.377353
\(867\) 16.5078 0.560635
\(868\) 47.5078 1.61252
\(869\) −26.8062 −0.909340
\(870\) 0 0
\(871\) 6.40312 0.216962
\(872\) −4.29844 −0.145563
\(873\) 2.59688 0.0878909
\(874\) 0 0
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) 42.7172 1.44246 0.721228 0.692697i \(-0.243578\pi\)
0.721228 + 0.692697i \(0.243578\pi\)
\(878\) 10.2984 0.347555
\(879\) 21.4031 0.721909
\(880\) 0 0
\(881\) −39.7172 −1.33811 −0.669053 0.743215i \(-0.733300\pi\)
−0.669053 + 0.743215i \(0.733300\pi\)
\(882\) −15.1047 −0.508601
\(883\) −45.6125 −1.53498 −0.767491 0.641059i \(-0.778495\pi\)
−0.767491 + 0.641059i \(0.778495\pi\)
\(884\) 0.701562 0.0235961
\(885\) 0 0
\(886\) 32.5078 1.09212
\(887\) 20.0000 0.671534 0.335767 0.941945i \(-0.391004\pi\)
0.335767 + 0.941945i \(0.391004\pi\)
\(888\) 1.70156 0.0571007
\(889\) −29.6125 −0.993171
\(890\) 0 0
\(891\) 4.70156 0.157508
\(892\) −11.4031 −0.381805
\(893\) 11.9109 0.398584
\(894\) 6.59688 0.220633
\(895\) 0 0
\(896\) 4.70156 0.157068
\(897\) 0 0
\(898\) −2.29844 −0.0766999
\(899\) 64.7016 2.15792
\(900\) 0 0
\(901\) −1.68594 −0.0561668
\(902\) 17.4031 0.579461
\(903\) 53.6125 1.78411
\(904\) −14.0000 −0.465633
\(905\) 0 0
\(906\) −14.1047 −0.468597
\(907\) 25.0156 0.830630 0.415315 0.909678i \(-0.363671\pi\)
0.415315 + 0.909678i \(0.363671\pi\)
\(908\) 16.1047 0.534453
\(909\) 6.70156 0.222277
\(910\) 0 0
\(911\) 42.2094 1.39846 0.699229 0.714897i \(-0.253527\pi\)
0.699229 + 0.714897i \(0.253527\pi\)
\(912\) 1.70156 0.0563444
\(913\) 50.3141 1.66515
\(914\) −2.59688 −0.0858970
\(915\) 0 0
\(916\) 15.7016 0.518794
\(917\) −105.822 −3.49455
\(918\) 0.701562 0.0231550
\(919\) −4.89531 −0.161481 −0.0807407 0.996735i \(-0.525729\pi\)
−0.0807407 + 0.996735i \(0.525729\pi\)
\(920\) 0 0
\(921\) −5.70156 −0.187873
\(922\) −36.2094 −1.19249
\(923\) −1.70156 −0.0560076
\(924\) 22.1047 0.727191
\(925\) 0 0
\(926\) −21.2984 −0.699910
\(927\) −1.40312 −0.0460846
\(928\) 6.40312 0.210193
\(929\) 52.2984 1.71586 0.857928 0.513770i \(-0.171751\pi\)
0.857928 + 0.513770i \(0.171751\pi\)
\(930\) 0 0
\(931\) −25.7016 −0.842335
\(932\) 20.2094 0.661980
\(933\) −30.0000 −0.982156
\(934\) 30.2984 0.991395
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) −14.9109 −0.487119 −0.243560 0.969886i \(-0.578315\pi\)
−0.243560 + 0.969886i \(0.578315\pi\)
\(938\) 30.1047 0.982953
\(939\) −21.2094 −0.692142
\(940\) 0 0
\(941\) 28.4187 0.926425 0.463212 0.886247i \(-0.346697\pi\)
0.463212 + 0.886247i \(0.346697\pi\)
\(942\) 22.7016 0.739657
\(943\) 0 0
\(944\) 2.70156 0.0879284
\(945\) 0 0
\(946\) −53.6125 −1.74309
\(947\) −47.5078 −1.54380 −0.771898 0.635746i \(-0.780693\pi\)
−0.771898 + 0.635746i \(0.780693\pi\)
\(948\) 5.70156 0.185178
\(949\) 12.0000 0.389536
\(950\) 0 0
\(951\) 1.19375 0.0387100
\(952\) 3.29844 0.106903
\(953\) 31.2984 1.01386 0.506928 0.861988i \(-0.330781\pi\)
0.506928 + 0.861988i \(0.330781\pi\)
\(954\) 2.40312 0.0778040
\(955\) 0 0
\(956\) 6.10469 0.197440
\(957\) 30.1047 0.973146
\(958\) 40.6125 1.31213
\(959\) 64.4187 2.08019
\(960\) 0 0
\(961\) 71.1047 2.29370
\(962\) −1.70156 −0.0548606
\(963\) −19.1047 −0.615640
\(964\) −2.59688 −0.0836397
\(965\) 0 0
\(966\) 0 0
\(967\) −29.8953 −0.961368 −0.480684 0.876894i \(-0.659612\pi\)
−0.480684 + 0.876894i \(0.659612\pi\)
\(968\) −11.1047 −0.356918
\(969\) 1.19375 0.0383488
\(970\) 0 0
\(971\) −36.8953 −1.18403 −0.592013 0.805928i \(-0.701667\pi\)
−0.592013 + 0.805928i \(0.701667\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −44.2094 −1.41729
\(974\) −7.89531 −0.252982
\(975\) 0 0
\(976\) 14.1047 0.451480
\(977\) 23.4031 0.748732 0.374366 0.927281i \(-0.377860\pi\)
0.374366 + 0.927281i \(0.377860\pi\)
\(978\) 18.8062 0.601358
\(979\) 53.6125 1.71346
\(980\) 0 0
\(981\) 4.29844 0.137239
\(982\) −33.4031 −1.06594
\(983\) 7.50781 0.239462 0.119731 0.992806i \(-0.461797\pi\)
0.119731 + 0.992806i \(0.461797\pi\)
\(984\) −3.70156 −0.118001
\(985\) 0 0
\(986\) 4.49219 0.143060
\(987\) −32.9109 −1.04757
\(988\) −1.70156 −0.0541339
\(989\) 0 0
\(990\) 0 0
\(991\) −9.10469 −0.289220 −0.144610 0.989489i \(-0.546193\pi\)
−0.144610 + 0.989489i \(0.546193\pi\)
\(992\) 10.1047 0.320824
\(993\) 12.0000 0.380808
\(994\) −8.00000 −0.253745
\(995\) 0 0
\(996\) −10.7016 −0.339092
\(997\) 10.4922 0.332291 0.166145 0.986101i \(-0.446868\pi\)
0.166145 + 0.986101i \(0.446868\pi\)
\(998\) −17.2094 −0.544753
\(999\) −1.70156 −0.0538350
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 1950.2.a.bc.1.1 2
3.2 odd 2 5850.2.a.cj.1.1 2
5.2 odd 4 1950.2.e.p.1249.1 4
5.3 odd 4 1950.2.e.p.1249.4 4
5.4 even 2 1950.2.a.bg.1.2 yes 2
15.2 even 4 5850.2.e.bi.5149.3 4
15.8 even 4 5850.2.e.bi.5149.2 4
15.14 odd 2 5850.2.a.cg.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.a.bc.1.1 2 1.1 even 1 trivial
1950.2.a.bg.1.2 yes 2 5.4 even 2
1950.2.e.p.1249.1 4 5.2 odd 4
1950.2.e.p.1249.4 4 5.3 odd 4
5850.2.a.cg.1.2 2 15.14 odd 2
5850.2.a.cj.1.1 2 3.2 odd 2
5850.2.e.bi.5149.2 4 15.8 even 4
5850.2.e.bi.5149.3 4 15.2 even 4