Properties

Label 1900.2.a.i.1.2
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.321.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.46050\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.59358 q^{3} -4.51459 q^{7} -0.460505 q^{9} +O(q^{10})\) \(q+1.59358 q^{3} -4.51459 q^{7} -0.460505 q^{9} +0.593579 q^{11} +4.05408 q^{13} +5.32743 q^{17} +1.00000 q^{19} -7.19436 q^{21} +7.46050 q^{23} -5.51459 q^{27} -2.32743 q^{29} +6.97509 q^{31} +0.945916 q^{33} -3.40642 q^{37} +6.46050 q^{39} -7.38151 q^{41} +6.18716 q^{43} +12.7089 q^{47} +13.3815 q^{49} +8.48968 q^{51} -8.84202 q^{53} +1.59358 q^{57} +4.10817 q^{59} +9.89610 q^{61} +2.07899 q^{63} +12.0613 q^{67} +11.8889 q^{69} -7.10817 q^{71} +5.27335 q^{73} -2.67977 q^{77} -3.96790 q^{79} -7.40642 q^{81} +7.53950 q^{83} -3.70895 q^{87} +9.19436 q^{89} -18.3025 q^{91} +11.1154 q^{93} +6.42840 q^{97} -0.273346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 2 q^{7} + 5 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{3} + 2 q^{7} + 5 q^{9} - q^{11} + 3 q^{13} + 6 q^{17} + 3 q^{19} - 8 q^{21} + 16 q^{23} - q^{27} + 3 q^{29} - q^{31} + 12 q^{33} - 13 q^{37} + 13 q^{39} - 3 q^{41} + 13 q^{43} + 9 q^{47} + 21 q^{49} - 12 q^{51} - q^{53} + 2 q^{57} - 6 q^{59} - 5 q^{61} + 19 q^{63} + 19 q^{67} + 9 q^{69} - 3 q^{71} + 15 q^{73} - 10 q^{77} + 2 q^{79} - 25 q^{81} + 29 q^{83} + 18 q^{87} + 14 q^{89} - 23 q^{91} + 7 q^{93} - q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.59358 0.920053 0.460027 0.887905i \(-0.347840\pi\)
0.460027 + 0.887905i \(0.347840\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.51459 −1.70635 −0.853177 0.521621i \(-0.825327\pi\)
−0.853177 + 0.521621i \(0.825327\pi\)
\(8\) 0 0
\(9\) −0.460505 −0.153502
\(10\) 0 0
\(11\) 0.593579 0.178971 0.0894855 0.995988i \(-0.471478\pi\)
0.0894855 + 0.995988i \(0.471478\pi\)
\(12\) 0 0
\(13\) 4.05408 1.12440 0.562200 0.827001i \(-0.309955\pi\)
0.562200 + 0.827001i \(0.309955\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.32743 1.29209 0.646046 0.763299i \(-0.276421\pi\)
0.646046 + 0.763299i \(0.276421\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −7.19436 −1.56994
\(22\) 0 0
\(23\) 7.46050 1.55562 0.777811 0.628498i \(-0.216330\pi\)
0.777811 + 0.628498i \(0.216330\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.51459 −1.06128
\(28\) 0 0
\(29\) −2.32743 −0.432193 −0.216096 0.976372i \(-0.569333\pi\)
−0.216096 + 0.976372i \(0.569333\pi\)
\(30\) 0 0
\(31\) 6.97509 1.25276 0.626382 0.779516i \(-0.284535\pi\)
0.626382 + 0.779516i \(0.284535\pi\)
\(32\) 0 0
\(33\) 0.945916 0.164663
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.40642 −0.560012 −0.280006 0.959998i \(-0.590336\pi\)
−0.280006 + 0.959998i \(0.590336\pi\)
\(38\) 0 0
\(39\) 6.46050 1.03451
\(40\) 0 0
\(41\) −7.38151 −1.15280 −0.576399 0.817168i \(-0.695543\pi\)
−0.576399 + 0.817168i \(0.695543\pi\)
\(42\) 0 0
\(43\) 6.18716 0.943533 0.471766 0.881724i \(-0.343617\pi\)
0.471766 + 0.881724i \(0.343617\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.7089 1.85379 0.926895 0.375321i \(-0.122467\pi\)
0.926895 + 0.375321i \(0.122467\pi\)
\(48\) 0 0
\(49\) 13.3815 1.91164
\(50\) 0 0
\(51\) 8.48968 1.18879
\(52\) 0 0
\(53\) −8.84202 −1.21454 −0.607272 0.794494i \(-0.707736\pi\)
−0.607272 + 0.794494i \(0.707736\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.59358 0.211075
\(58\) 0 0
\(59\) 4.10817 0.534838 0.267419 0.963580i \(-0.413829\pi\)
0.267419 + 0.963580i \(0.413829\pi\)
\(60\) 0 0
\(61\) 9.89610 1.26707 0.633533 0.773716i \(-0.281604\pi\)
0.633533 + 0.773716i \(0.281604\pi\)
\(62\) 0 0
\(63\) 2.07899 0.261928
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.0613 1.47352 0.736760 0.676154i \(-0.236355\pi\)
0.736760 + 0.676154i \(0.236355\pi\)
\(68\) 0 0
\(69\) 11.8889 1.43126
\(70\) 0 0
\(71\) −7.10817 −0.843584 −0.421792 0.906693i \(-0.638599\pi\)
−0.421792 + 0.906693i \(0.638599\pi\)
\(72\) 0 0
\(73\) 5.27335 0.617198 0.308599 0.951192i \(-0.400140\pi\)
0.308599 + 0.951192i \(0.400140\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.67977 −0.305388
\(78\) 0 0
\(79\) −3.96790 −0.446423 −0.223212 0.974770i \(-0.571654\pi\)
−0.223212 + 0.974770i \(0.571654\pi\)
\(80\) 0 0
\(81\) −7.40642 −0.822936
\(82\) 0 0
\(83\) 7.53950 0.827567 0.413784 0.910375i \(-0.364207\pi\)
0.413784 + 0.910375i \(0.364207\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.70895 −0.397641
\(88\) 0 0
\(89\) 9.19436 0.974600 0.487300 0.873235i \(-0.337982\pi\)
0.487300 + 0.873235i \(0.337982\pi\)
\(90\) 0 0
\(91\) −18.3025 −1.91863
\(92\) 0 0
\(93\) 11.1154 1.15261
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.42840 0.652705 0.326353 0.945248i \(-0.394180\pi\)
0.326353 + 0.945248i \(0.394180\pi\)
\(98\) 0 0
\(99\) −0.273346 −0.0274723
\(100\) 0 0
\(101\) −11.8099 −1.17513 −0.587565 0.809177i \(-0.699913\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(102\) 0 0
\(103\) 18.4648 1.81939 0.909694 0.415279i \(-0.136316\pi\)
0.909694 + 0.415279i \(0.136316\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.431327 0.0416979 0.0208490 0.999783i \(-0.493363\pi\)
0.0208490 + 0.999783i \(0.493363\pi\)
\(108\) 0 0
\(109\) −7.11537 −0.681528 −0.340764 0.940149i \(-0.610686\pi\)
−0.340764 + 0.940149i \(0.610686\pi\)
\(110\) 0 0
\(111\) −5.42840 −0.515241
\(112\) 0 0
\(113\) −3.16225 −0.297480 −0.148740 0.988876i \(-0.547522\pi\)
−0.148740 + 0.988876i \(0.547522\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.86693 −0.172597
\(118\) 0 0
\(119\) −24.0512 −2.20477
\(120\) 0 0
\(121\) −10.6477 −0.967969
\(122\) 0 0
\(123\) −11.7630 −1.06064
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.4107 −1.36748 −0.683739 0.729727i \(-0.739647\pi\)
−0.683739 + 0.729727i \(0.739647\pi\)
\(128\) 0 0
\(129\) 9.85973 0.868101
\(130\) 0 0
\(131\) 11.0072 0.961703 0.480852 0.876802i \(-0.340328\pi\)
0.480852 + 0.876802i \(0.340328\pi\)
\(132\) 0 0
\(133\) −4.51459 −0.391465
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.72665 0.745568 0.372784 0.927918i \(-0.378403\pi\)
0.372784 + 0.927918i \(0.378403\pi\)
\(138\) 0 0
\(139\) −7.64047 −0.648056 −0.324028 0.946048i \(-0.605037\pi\)
−0.324028 + 0.946048i \(0.605037\pi\)
\(140\) 0 0
\(141\) 20.2527 1.70559
\(142\) 0 0
\(143\) 2.40642 0.201235
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 21.3245 1.75882
\(148\) 0 0
\(149\) −6.67684 −0.546988 −0.273494 0.961874i \(-0.588179\pi\)
−0.273494 + 0.961874i \(0.588179\pi\)
\(150\) 0 0
\(151\) −19.1623 −1.55940 −0.779701 0.626152i \(-0.784629\pi\)
−0.779701 + 0.626152i \(0.784629\pi\)
\(152\) 0 0
\(153\) −2.45331 −0.198338
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −16.7558 −1.33726 −0.668630 0.743595i \(-0.733119\pi\)
−0.668630 + 0.743595i \(0.733119\pi\)
\(158\) 0 0
\(159\) −14.0905 −1.11745
\(160\) 0 0
\(161\) −33.6811 −2.65444
\(162\) 0 0
\(163\) 2.32023 0.181735 0.0908673 0.995863i \(-0.471036\pi\)
0.0908673 + 0.995863i \(0.471036\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.56867 0.663064 0.331532 0.943444i \(-0.392435\pi\)
0.331532 + 0.943444i \(0.392435\pi\)
\(168\) 0 0
\(169\) 3.43560 0.264277
\(170\) 0 0
\(171\) −0.460505 −0.0352157
\(172\) 0 0
\(173\) −9.04689 −0.687822 −0.343911 0.939002i \(-0.611752\pi\)
−0.343911 + 0.939002i \(0.611752\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.54669 0.492080
\(178\) 0 0
\(179\) 13.4969 1.00880 0.504402 0.863469i \(-0.331713\pi\)
0.504402 + 0.863469i \(0.331713\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 15.7702 1.16577
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.16225 0.231247
\(188\) 0 0
\(189\) 24.8961 1.81093
\(190\) 0 0
\(191\) −12.4356 −0.899808 −0.449904 0.893077i \(-0.648542\pi\)
−0.449904 + 0.893077i \(0.648542\pi\)
\(192\) 0 0
\(193\) 1.64766 0.118601 0.0593007 0.998240i \(-0.481113\pi\)
0.0593007 + 0.998240i \(0.481113\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.3566 1.52160 0.760798 0.648989i \(-0.224808\pi\)
0.760798 + 0.648989i \(0.224808\pi\)
\(198\) 0 0
\(199\) −12.2632 −0.869317 −0.434658 0.900595i \(-0.643131\pi\)
−0.434658 + 0.900595i \(0.643131\pi\)
\(200\) 0 0
\(201\) 19.2206 1.35572
\(202\) 0 0
\(203\) 10.5074 0.737474
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.43560 −0.238791
\(208\) 0 0
\(209\) 0.593579 0.0410587
\(210\) 0 0
\(211\) 19.3743 1.33378 0.666892 0.745155i \(-0.267624\pi\)
0.666892 + 0.745155i \(0.267624\pi\)
\(212\) 0 0
\(213\) −11.3274 −0.776143
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −31.4897 −2.13766
\(218\) 0 0
\(219\) 8.40350 0.567856
\(220\) 0 0
\(221\) 21.5979 1.45283
\(222\) 0 0
\(223\) −20.5117 −1.37356 −0.686781 0.726864i \(-0.740977\pi\)
−0.686781 + 0.726864i \(0.740977\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.91381 −0.259769 −0.129884 0.991529i \(-0.541461\pi\)
−0.129884 + 0.991529i \(0.541461\pi\)
\(228\) 0 0
\(229\) 3.58638 0.236995 0.118497 0.992954i \(-0.462192\pi\)
0.118497 + 0.992954i \(0.462192\pi\)
\(230\) 0 0
\(231\) −4.27042 −0.280973
\(232\) 0 0
\(233\) 12.5294 0.820827 0.410413 0.911900i \(-0.365384\pi\)
0.410413 + 0.911900i \(0.365384\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −6.32316 −0.410733
\(238\) 0 0
\(239\) −23.5218 −1.52150 −0.760749 0.649046i \(-0.775168\pi\)
−0.760749 + 0.649046i \(0.775168\pi\)
\(240\) 0 0
\(241\) 9.22353 0.594140 0.297070 0.954856i \(-0.403991\pi\)
0.297070 + 0.954856i \(0.403991\pi\)
\(242\) 0 0
\(243\) 4.74105 0.304138
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.05408 0.257955
\(248\) 0 0
\(249\) 12.0148 0.761406
\(250\) 0 0
\(251\) 18.7237 1.18183 0.590916 0.806733i \(-0.298767\pi\)
0.590916 + 0.806733i \(0.298767\pi\)
\(252\) 0 0
\(253\) 4.42840 0.278411
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −27.1196 −1.69168 −0.845838 0.533439i \(-0.820899\pi\)
−0.845838 + 0.533439i \(0.820899\pi\)
\(258\) 0 0
\(259\) 15.3786 0.955579
\(260\) 0 0
\(261\) 1.07179 0.0663423
\(262\) 0 0
\(263\) −18.5510 −1.14390 −0.571951 0.820288i \(-0.693813\pi\)
−0.571951 + 0.820288i \(0.693813\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 14.6519 0.896684
\(268\) 0 0
\(269\) −26.1331 −1.59336 −0.796681 0.604400i \(-0.793413\pi\)
−0.796681 + 0.604400i \(0.793413\pi\)
\(270\) 0 0
\(271\) 1.95311 0.118643 0.0593216 0.998239i \(-0.481106\pi\)
0.0593216 + 0.998239i \(0.481106\pi\)
\(272\) 0 0
\(273\) −29.1665 −1.76524
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.46770 0.148270 0.0741349 0.997248i \(-0.476380\pi\)
0.0741349 + 0.997248i \(0.476380\pi\)
\(278\) 0 0
\(279\) −3.21206 −0.192301
\(280\) 0 0
\(281\) 24.8712 1.48369 0.741846 0.670571i \(-0.233951\pi\)
0.741846 + 0.670571i \(0.233951\pi\)
\(282\) 0 0
\(283\) −9.55389 −0.567920 −0.283960 0.958836i \(-0.591648\pi\)
−0.283960 + 0.958836i \(0.591648\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 33.3245 1.96708
\(288\) 0 0
\(289\) 11.3815 0.669501
\(290\) 0 0
\(291\) 10.2442 0.600524
\(292\) 0 0
\(293\) 11.2527 0.657390 0.328695 0.944436i \(-0.393391\pi\)
0.328695 + 0.944436i \(0.393391\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.27335 −0.189939
\(298\) 0 0
\(299\) 30.2455 1.74914
\(300\) 0 0
\(301\) −27.9325 −1.61000
\(302\) 0 0
\(303\) −18.8200 −1.08118
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.2877 0.701298 0.350649 0.936507i \(-0.385961\pi\)
0.350649 + 0.936507i \(0.385961\pi\)
\(308\) 0 0
\(309\) 29.4251 1.67393
\(310\) 0 0
\(311\) 17.1331 0.971528 0.485764 0.874090i \(-0.338542\pi\)
0.485764 + 0.874090i \(0.338542\pi\)
\(312\) 0 0
\(313\) −4.98229 −0.281616 −0.140808 0.990037i \(-0.544970\pi\)
−0.140808 + 0.990037i \(0.544970\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −22.3963 −1.25790 −0.628951 0.777445i \(-0.716515\pi\)
−0.628951 + 0.777445i \(0.716515\pi\)
\(318\) 0 0
\(319\) −1.38151 −0.0773500
\(320\) 0 0
\(321\) 0.687353 0.0383643
\(322\) 0 0
\(323\) 5.32743 0.296426
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −11.3389 −0.627043
\(328\) 0 0
\(329\) −57.3757 −3.16322
\(330\) 0 0
\(331\) 4.06887 0.223645 0.111823 0.993728i \(-0.464331\pi\)
0.111823 + 0.993728i \(0.464331\pi\)
\(332\) 0 0
\(333\) 1.56867 0.0859628
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9.52179 −0.518685 −0.259342 0.965785i \(-0.583506\pi\)
−0.259342 + 0.965785i \(0.583506\pi\)
\(338\) 0 0
\(339\) −5.03930 −0.273697
\(340\) 0 0
\(341\) 4.14027 0.224208
\(342\) 0 0
\(343\) −28.8099 −1.55559
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.1052 −0.757209 −0.378605 0.925559i \(-0.623596\pi\)
−0.378605 + 0.925559i \(0.623596\pi\)
\(348\) 0 0
\(349\) 15.2704 0.817407 0.408703 0.912667i \(-0.365981\pi\)
0.408703 + 0.912667i \(0.365981\pi\)
\(350\) 0 0
\(351\) −22.3566 −1.19331
\(352\) 0 0
\(353\) 31.6591 1.68505 0.842523 0.538661i \(-0.181070\pi\)
0.842523 + 0.538661i \(0.181070\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −38.3274 −2.02850
\(358\) 0 0
\(359\) −26.5366 −1.40055 −0.700273 0.713875i \(-0.746939\pi\)
−0.700273 + 0.713875i \(0.746939\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −16.9679 −0.890584
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 31.2379 1.63061 0.815303 0.579034i \(-0.196570\pi\)
0.815303 + 0.579034i \(0.196570\pi\)
\(368\) 0 0
\(369\) 3.39922 0.176957
\(370\) 0 0
\(371\) 39.9181 2.07244
\(372\) 0 0
\(373\) −29.8961 −1.54796 −0.773981 0.633209i \(-0.781737\pi\)
−0.773981 + 0.633209i \(0.781737\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.43560 −0.485958
\(378\) 0 0
\(379\) −36.6093 −1.88049 −0.940247 0.340492i \(-0.889406\pi\)
−0.940247 + 0.340492i \(0.889406\pi\)
\(380\) 0 0
\(381\) −24.5582 −1.25815
\(382\) 0 0
\(383\) 22.9751 1.17397 0.586986 0.809597i \(-0.300314\pi\)
0.586986 + 0.809597i \(0.300314\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.84922 −0.144834
\(388\) 0 0
\(389\) −27.4183 −1.39016 −0.695081 0.718931i \(-0.744631\pi\)
−0.695081 + 0.718931i \(0.744631\pi\)
\(390\) 0 0
\(391\) 39.7453 2.01001
\(392\) 0 0
\(393\) 17.5408 0.884818
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.05408 −0.454411 −0.227206 0.973847i \(-0.572959\pi\)
−0.227206 + 0.973847i \(0.572959\pi\)
\(398\) 0 0
\(399\) −7.19436 −0.360168
\(400\) 0 0
\(401\) 7.21926 0.360513 0.180256 0.983620i \(-0.442307\pi\)
0.180256 + 0.983620i \(0.442307\pi\)
\(402\) 0 0
\(403\) 28.2776 1.40861
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.02198 −0.100226
\(408\) 0 0
\(409\) 1.08619 0.0537085 0.0268543 0.999639i \(-0.491451\pi\)
0.0268543 + 0.999639i \(0.491451\pi\)
\(410\) 0 0
\(411\) 13.9066 0.685963
\(412\) 0 0
\(413\) −18.5467 −0.912623
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −12.1757 −0.596246
\(418\) 0 0
\(419\) 10.9899 0.536891 0.268445 0.963295i \(-0.413490\pi\)
0.268445 + 0.963295i \(0.413490\pi\)
\(420\) 0 0
\(421\) 5.30545 0.258572 0.129286 0.991607i \(-0.458732\pi\)
0.129286 + 0.991607i \(0.458732\pi\)
\(422\) 0 0
\(423\) −5.85253 −0.284560
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −44.6768 −2.16206
\(428\) 0 0
\(429\) 3.83482 0.185147
\(430\) 0 0
\(431\) 11.0905 0.534209 0.267104 0.963668i \(-0.413933\pi\)
0.267104 + 0.963668i \(0.413933\pi\)
\(432\) 0 0
\(433\) −12.1652 −0.584621 −0.292311 0.956323i \(-0.594424\pi\)
−0.292311 + 0.956323i \(0.594424\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.46050 0.356884
\(438\) 0 0
\(439\) 27.5586 1.31530 0.657649 0.753325i \(-0.271551\pi\)
0.657649 + 0.753325i \(0.271551\pi\)
\(440\) 0 0
\(441\) −6.16225 −0.293441
\(442\) 0 0
\(443\) 14.1800 0.673710 0.336855 0.941556i \(-0.390637\pi\)
0.336855 + 0.941556i \(0.390637\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −10.6401 −0.503258
\(448\) 0 0
\(449\) −14.9895 −0.707398 −0.353699 0.935359i \(-0.615076\pi\)
−0.353699 + 0.935359i \(0.615076\pi\)
\(450\) 0 0
\(451\) −4.38151 −0.206317
\(452\) 0 0
\(453\) −30.5366 −1.43473
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −21.1331 −0.988564 −0.494282 0.869302i \(-0.664569\pi\)
−0.494282 + 0.869302i \(0.664569\pi\)
\(458\) 0 0
\(459\) −29.3786 −1.37128
\(460\) 0 0
\(461\) 40.5801 1.89001 0.945003 0.327062i \(-0.106059\pi\)
0.945003 + 0.327062i \(0.106059\pi\)
\(462\) 0 0
\(463\) 12.7381 0.591991 0.295995 0.955189i \(-0.404349\pi\)
0.295995 + 0.955189i \(0.404349\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.95739 −0.414498 −0.207249 0.978288i \(-0.566451\pi\)
−0.207249 + 0.978288i \(0.566451\pi\)
\(468\) 0 0
\(469\) −54.4517 −2.51435
\(470\) 0 0
\(471\) −26.7017 −1.23035
\(472\) 0 0
\(473\) 3.67257 0.168865
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 4.07179 0.186435
\(478\) 0 0
\(479\) 6.32451 0.288974 0.144487 0.989507i \(-0.453847\pi\)
0.144487 + 0.989507i \(0.453847\pi\)
\(480\) 0 0
\(481\) −13.8099 −0.629678
\(482\) 0 0
\(483\) −53.6735 −2.44223
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 14.4461 0.654616 0.327308 0.944918i \(-0.393859\pi\)
0.327308 + 0.944918i \(0.393859\pi\)
\(488\) 0 0
\(489\) 3.69748 0.167206
\(490\) 0 0
\(491\) 6.28813 0.283779 0.141890 0.989882i \(-0.454682\pi\)
0.141890 + 0.989882i \(0.454682\pi\)
\(492\) 0 0
\(493\) −12.3992 −0.558433
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 32.0905 1.43945
\(498\) 0 0
\(499\) −31.9181 −1.42885 −0.714425 0.699712i \(-0.753312\pi\)
−0.714425 + 0.699712i \(0.753312\pi\)
\(500\) 0 0
\(501\) 13.6549 0.610054
\(502\) 0 0
\(503\) 15.7601 0.702708 0.351354 0.936243i \(-0.385721\pi\)
0.351354 + 0.936243i \(0.385721\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 5.47490 0.243149
\(508\) 0 0
\(509\) 26.1885 1.16079 0.580393 0.814337i \(-0.302899\pi\)
0.580393 + 0.814337i \(0.302899\pi\)
\(510\) 0 0
\(511\) −23.8070 −1.05316
\(512\) 0 0
\(513\) −5.51459 −0.243475
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.54377 0.331775
\(518\) 0 0
\(519\) −14.4169 −0.632833
\(520\) 0 0
\(521\) −42.3245 −1.85427 −0.927135 0.374727i \(-0.877736\pi\)
−0.927135 + 0.374727i \(0.877736\pi\)
\(522\) 0 0
\(523\) −19.3714 −0.847052 −0.423526 0.905884i \(-0.639208\pi\)
−0.423526 + 0.905884i \(0.639208\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 37.1593 1.61869
\(528\) 0 0
\(529\) 32.6591 1.41996
\(530\) 0 0
\(531\) −1.89183 −0.0820985
\(532\) 0 0
\(533\) −29.9253 −1.29621
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.5083 0.928154
\(538\) 0 0
\(539\) 7.94299 0.342129
\(540\) 0 0
\(541\) −5.87451 −0.252565 −0.126282 0.991994i \(-0.540305\pi\)
−0.126282 + 0.991994i \(0.540305\pi\)
\(542\) 0 0
\(543\) −11.1551 −0.478709
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.2556 −0.866069 −0.433034 0.901377i \(-0.642557\pi\)
−0.433034 + 0.901377i \(0.642557\pi\)
\(548\) 0 0
\(549\) −4.55720 −0.194497
\(550\) 0 0
\(551\) −2.32743 −0.0991519
\(552\) 0 0
\(553\) 17.9134 0.761756
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.76010 −0.159321 −0.0796604 0.996822i \(-0.525384\pi\)
−0.0796604 + 0.996822i \(0.525384\pi\)
\(558\) 0 0
\(559\) 25.0833 1.06091
\(560\) 0 0
\(561\) 5.03930 0.212759
\(562\) 0 0
\(563\) 11.2484 0.474065 0.237033 0.971502i \(-0.423825\pi\)
0.237033 + 0.971502i \(0.423825\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 33.4369 1.40422
\(568\) 0 0
\(569\) 12.2949 0.515431 0.257715 0.966221i \(-0.417030\pi\)
0.257715 + 0.966221i \(0.417030\pi\)
\(570\) 0 0
\(571\) 13.8784 0.580793 0.290396 0.956906i \(-0.406213\pi\)
0.290396 + 0.956906i \(0.406213\pi\)
\(572\) 0 0
\(573\) −19.8171 −0.827872
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 31.1052 1.29493 0.647464 0.762096i \(-0.275830\pi\)
0.647464 + 0.762096i \(0.275830\pi\)
\(578\) 0 0
\(579\) 2.62568 0.109120
\(580\) 0 0
\(581\) −34.0377 −1.41212
\(582\) 0 0
\(583\) −5.24844 −0.217368
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 37.7807 1.55938 0.779689 0.626167i \(-0.215377\pi\)
0.779689 + 0.626167i \(0.215377\pi\)
\(588\) 0 0
\(589\) 6.97509 0.287404
\(590\) 0 0
\(591\) 34.0335 1.39995
\(592\) 0 0
\(593\) −40.5949 −1.66703 −0.833517 0.552494i \(-0.813676\pi\)
−0.833517 + 0.552494i \(0.813676\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −19.5424 −0.799818
\(598\) 0 0
\(599\) 18.2776 0.746803 0.373402 0.927670i \(-0.378191\pi\)
0.373402 + 0.927670i \(0.378191\pi\)
\(600\) 0 0
\(601\) −13.4313 −0.547875 −0.273938 0.961747i \(-0.588326\pi\)
−0.273938 + 0.961747i \(0.588326\pi\)
\(602\) 0 0
\(603\) −5.55428 −0.226188
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −47.2235 −1.91674 −0.958372 0.285522i \(-0.907833\pi\)
−0.958372 + 0.285522i \(0.907833\pi\)
\(608\) 0 0
\(609\) 16.7444 0.678516
\(610\) 0 0
\(611\) 51.5231 2.08440
\(612\) 0 0
\(613\) 10.2268 0.413059 0.206529 0.978440i \(-0.433783\pi\)
0.206529 + 0.978440i \(0.433783\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −32.3829 −1.30368 −0.651842 0.758354i \(-0.726004\pi\)
−0.651842 + 0.758354i \(0.726004\pi\)
\(618\) 0 0
\(619\) 19.8784 0.798980 0.399490 0.916738i \(-0.369187\pi\)
0.399490 + 0.916738i \(0.369187\pi\)
\(620\) 0 0
\(621\) −41.1416 −1.65096
\(622\) 0 0
\(623\) −41.5087 −1.66301
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0.945916 0.0377762
\(628\) 0 0
\(629\) −18.1475 −0.723587
\(630\) 0 0
\(631\) 14.5103 0.577647 0.288823 0.957382i \(-0.406736\pi\)
0.288823 + 0.957382i \(0.406736\pi\)
\(632\) 0 0
\(633\) 30.8745 1.22715
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 54.2498 2.14945
\(638\) 0 0
\(639\) 3.27335 0.129492
\(640\) 0 0
\(641\) 3.15798 0.124733 0.0623664 0.998053i \(-0.480135\pi\)
0.0623664 + 0.998053i \(0.480135\pi\)
\(642\) 0 0
\(643\) −22.0000 −0.867595 −0.433798 0.901010i \(-0.642827\pi\)
−0.433798 + 0.901010i \(0.642827\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.36673 −0.0537317 −0.0268659 0.999639i \(-0.508553\pi\)
−0.0268659 + 0.999639i \(0.508553\pi\)
\(648\) 0 0
\(649\) 2.43852 0.0957204
\(650\) 0 0
\(651\) −50.1813 −1.96676
\(652\) 0 0
\(653\) −17.0220 −0.666122 −0.333061 0.942905i \(-0.608081\pi\)
−0.333061 + 0.942905i \(0.608081\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.42840 −0.0947410
\(658\) 0 0
\(659\) 14.6883 0.572175 0.286088 0.958203i \(-0.407645\pi\)
0.286088 + 0.958203i \(0.407645\pi\)
\(660\) 0 0
\(661\) −1.86693 −0.0726150 −0.0363075 0.999341i \(-0.511560\pi\)
−0.0363075 + 0.999341i \(0.511560\pi\)
\(662\) 0 0
\(663\) 34.4179 1.33668
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −17.3638 −0.672329
\(668\) 0 0
\(669\) −32.6870 −1.26375
\(670\) 0 0
\(671\) 5.87412 0.226768
\(672\) 0 0
\(673\) −15.3465 −0.591564 −0.295782 0.955256i \(-0.595580\pi\)
−0.295782 + 0.955256i \(0.595580\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.3422 0.666515 0.333258 0.942836i \(-0.391852\pi\)
0.333258 + 0.942836i \(0.391852\pi\)
\(678\) 0 0
\(679\) −29.0216 −1.11375
\(680\) 0 0
\(681\) −6.23697 −0.239001
\(682\) 0 0
\(683\) 40.9473 1.56680 0.783402 0.621516i \(-0.213483\pi\)
0.783402 + 0.621516i \(0.213483\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.71518 0.218048
\(688\) 0 0
\(689\) −35.8463 −1.36563
\(690\) 0 0
\(691\) 5.65525 0.215136 0.107568 0.994198i \(-0.465694\pi\)
0.107568 + 0.994198i \(0.465694\pi\)
\(692\) 0 0
\(693\) 1.23405 0.0468775
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −39.3245 −1.48952
\(698\) 0 0
\(699\) 19.9665 0.755204
\(700\) 0 0
\(701\) 35.3786 1.33623 0.668115 0.744058i \(-0.267101\pi\)
0.668115 + 0.744058i \(0.267101\pi\)
\(702\) 0 0
\(703\) −3.40642 −0.128476
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 53.3169 2.00519
\(708\) 0 0
\(709\) −41.2852 −1.55050 −0.775249 0.631655i \(-0.782376\pi\)
−0.775249 + 0.631655i \(0.782376\pi\)
\(710\) 0 0
\(711\) 1.82724 0.0685267
\(712\) 0 0
\(713\) 52.0377 1.94883
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −37.4838 −1.39986
\(718\) 0 0
\(719\) 17.0689 0.636561 0.318281 0.947997i \(-0.396895\pi\)
0.318281 + 0.947997i \(0.396895\pi\)
\(720\) 0 0
\(721\) −83.3609 −3.10452
\(722\) 0 0
\(723\) 14.6984 0.546641
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −27.8741 −1.03379 −0.516897 0.856048i \(-0.672913\pi\)
−0.516897 + 0.856048i \(0.672913\pi\)
\(728\) 0 0
\(729\) 29.7745 1.10276
\(730\) 0 0
\(731\) 32.9617 1.21913
\(732\) 0 0
\(733\) −34.7922 −1.28508 −0.642540 0.766252i \(-0.722119\pi\)
−0.642540 + 0.766252i \(0.722119\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.15933 0.263717
\(738\) 0 0
\(739\) −49.0128 −1.80297 −0.901483 0.432815i \(-0.857520\pi\)
−0.901483 + 0.432815i \(0.857520\pi\)
\(740\) 0 0
\(741\) 6.46050 0.237333
\(742\) 0 0
\(743\) −20.8142 −0.763599 −0.381799 0.924245i \(-0.624695\pi\)
−0.381799 + 0.924245i \(0.624695\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.47197 −0.127033
\(748\) 0 0
\(749\) −1.94726 −0.0711514
\(750\) 0 0
\(751\) −14.4457 −0.527132 −0.263566 0.964641i \(-0.584899\pi\)
−0.263566 + 0.964641i \(0.584899\pi\)
\(752\) 0 0
\(753\) 29.8377 1.08735
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 8.11537 0.294958 0.147479 0.989065i \(-0.452884\pi\)
0.147479 + 0.989065i \(0.452884\pi\)
\(758\) 0 0
\(759\) 7.05701 0.256153
\(760\) 0 0
\(761\) 30.2967 1.09825 0.549127 0.835739i \(-0.314960\pi\)
0.549127 + 0.835739i \(0.314960\pi\)
\(762\) 0 0
\(763\) 32.1230 1.16293
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.6549 0.601372
\(768\) 0 0
\(769\) 40.4471 1.45856 0.729279 0.684216i \(-0.239856\pi\)
0.729279 + 0.684216i \(0.239856\pi\)
\(770\) 0 0
\(771\) −43.2173 −1.55643
\(772\) 0 0
\(773\) −2.16518 −0.0778760 −0.0389380 0.999242i \(-0.512397\pi\)
−0.0389380 + 0.999242i \(0.512397\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 24.5070 0.879184
\(778\) 0 0
\(779\) −7.38151 −0.264470
\(780\) 0 0
\(781\) −4.21926 −0.150977
\(782\) 0 0
\(783\) 12.8348 0.458679
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −26.4284 −0.942071 −0.471035 0.882114i \(-0.656120\pi\)
−0.471035 + 0.882114i \(0.656120\pi\)
\(788\) 0 0
\(789\) −29.5624 −1.05245
\(790\) 0 0
\(791\) 14.2763 0.507606
\(792\) 0 0
\(793\) 40.1196 1.42469
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −39.5041 −1.39931 −0.699653 0.714483i \(-0.746662\pi\)
−0.699653 + 0.714483i \(0.746662\pi\)
\(798\) 0 0
\(799\) 67.7060 2.39527
\(800\) 0 0
\(801\) −4.23405 −0.149603
\(802\) 0 0
\(803\) 3.13015 0.110461
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −41.6451 −1.46598
\(808\) 0 0
\(809\) −27.4078 −0.963606 −0.481803 0.876280i \(-0.660018\pi\)
−0.481803 + 0.876280i \(0.660018\pi\)
\(810\) 0 0
\(811\) −50.7467 −1.78196 −0.890978 0.454046i \(-0.849980\pi\)
−0.890978 + 0.454046i \(0.849980\pi\)
\(812\) 0 0
\(813\) 3.11244 0.109158
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.18716 0.216461
\(818\) 0 0
\(819\) 8.42840 0.294512
\(820\) 0 0
\(821\) 12.7410 0.444666 0.222333 0.974971i \(-0.428633\pi\)
0.222333 + 0.974971i \(0.428633\pi\)
\(822\) 0 0
\(823\) 17.1623 0.598239 0.299119 0.954216i \(-0.403307\pi\)
0.299119 + 0.954216i \(0.403307\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 53.6735 1.86641 0.933206 0.359343i \(-0.116999\pi\)
0.933206 + 0.359343i \(0.116999\pi\)
\(828\) 0 0
\(829\) 7.45331 0.258864 0.129432 0.991588i \(-0.458685\pi\)
0.129432 + 0.991588i \(0.458685\pi\)
\(830\) 0 0
\(831\) 3.93248 0.136416
\(832\) 0 0
\(833\) 71.2891 2.47002
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −38.4648 −1.32954
\(838\) 0 0
\(839\) 52.8257 1.82374 0.911872 0.410474i \(-0.134637\pi\)
0.911872 + 0.410474i \(0.134637\pi\)
\(840\) 0 0
\(841\) −23.5831 −0.813209
\(842\) 0 0
\(843\) 39.6342 1.36508
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 48.0698 1.65170
\(848\) 0 0
\(849\) −15.2249 −0.522517
\(850\) 0 0
\(851\) −25.4136 −0.871168
\(852\) 0 0
\(853\) −16.6663 −0.570644 −0.285322 0.958432i \(-0.592101\pi\)
−0.285322 + 0.958432i \(0.592101\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 16.6654 0.569278 0.284639 0.958635i \(-0.408126\pi\)
0.284639 + 0.958635i \(0.408126\pi\)
\(858\) 0 0
\(859\) −30.0010 −1.02362 −0.511810 0.859099i \(-0.671025\pi\)
−0.511810 + 0.859099i \(0.671025\pi\)
\(860\) 0 0
\(861\) 53.1052 1.80982
\(862\) 0 0
\(863\) 23.0498 0.784625 0.392312 0.919832i \(-0.371675\pi\)
0.392312 + 0.919832i \(0.371675\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 18.1373 0.615977
\(868\) 0 0
\(869\) −2.35526 −0.0798968
\(870\) 0 0
\(871\) 48.8975 1.65683
\(872\) 0 0
\(873\) −2.96031 −0.100191
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −24.9938 −0.843979 −0.421990 0.906601i \(-0.638668\pi\)
−0.421990 + 0.906601i \(0.638668\pi\)
\(878\) 0 0
\(879\) 17.9321 0.604834
\(880\) 0 0
\(881\) 14.2590 0.480396 0.240198 0.970724i \(-0.422788\pi\)
0.240198 + 0.970724i \(0.422788\pi\)
\(882\) 0 0
\(883\) 47.6021 1.60194 0.800970 0.598705i \(-0.204318\pi\)
0.800970 + 0.598705i \(0.204318\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 33.6959 1.13140 0.565699 0.824612i \(-0.308607\pi\)
0.565699 + 0.824612i \(0.308607\pi\)
\(888\) 0 0
\(889\) 69.5729 2.33340
\(890\) 0 0
\(891\) −4.39630 −0.147282
\(892\) 0 0
\(893\) 12.7089 0.425289
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 48.1986 1.60931
\(898\) 0 0
\(899\) −16.2340 −0.541436
\(900\) 0 0
\(901\) −47.1052 −1.56930
\(902\) 0 0
\(903\) −44.5126 −1.48129
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −8.05701 −0.267529 −0.133764 0.991013i \(-0.542707\pi\)
−0.133764 + 0.991013i \(0.542707\pi\)
\(908\) 0 0
\(909\) 5.43852 0.180384
\(910\) 0 0
\(911\) −21.6942 −0.718760 −0.359380 0.933191i \(-0.617012\pi\)
−0.359380 + 0.933191i \(0.617012\pi\)
\(912\) 0 0
\(913\) 4.47529 0.148110
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −49.6930 −1.64101
\(918\) 0 0
\(919\) −42.7525 −1.41028 −0.705138 0.709070i \(-0.749115\pi\)
−0.705138 + 0.709070i \(0.749115\pi\)
\(920\) 0 0
\(921\) 19.5815 0.645232
\(922\) 0 0
\(923\) −28.8171 −0.948527
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −8.50312 −0.279279
\(928\) 0 0
\(929\) 32.8290 1.07708 0.538542 0.842599i \(-0.318975\pi\)
0.538542 + 0.842599i \(0.318975\pi\)
\(930\) 0 0
\(931\) 13.3815 0.438561
\(932\) 0 0
\(933\) 27.3029 0.893857
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −20.6313 −0.673995 −0.336998 0.941505i \(-0.609411\pi\)
−0.336998 + 0.941505i \(0.609411\pi\)
\(938\) 0 0
\(939\) −7.93968 −0.259102
\(940\) 0 0
\(941\) −2.25271 −0.0734363 −0.0367182 0.999326i \(-0.511690\pi\)
−0.0367182 + 0.999326i \(0.511690\pi\)
\(942\) 0 0
\(943\) −55.0698 −1.79332
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −51.1387 −1.66178 −0.830892 0.556434i \(-0.812169\pi\)
−0.830892 + 0.556434i \(0.812169\pi\)
\(948\) 0 0
\(949\) 21.3786 0.693978
\(950\) 0 0
\(951\) −35.6903 −1.15734
\(952\) 0 0
\(953\) −4.14454 −0.134255 −0.0671275 0.997744i \(-0.521383\pi\)
−0.0671275 + 0.997744i \(0.521383\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −2.20155 −0.0711661
\(958\) 0 0
\(959\) −39.3973 −1.27220
\(960\) 0 0
\(961\) 17.6519 0.569417
\(962\) 0 0
\(963\) −0.198628 −0.00640070
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 29.3202 0.942875 0.471438 0.881899i \(-0.343735\pi\)
0.471438 + 0.881899i \(0.343735\pi\)
\(968\) 0 0
\(969\) 8.48968 0.272728
\(970\) 0 0
\(971\) −10.0144 −0.321377 −0.160689 0.987005i \(-0.551371\pi\)
−0.160689 + 0.987005i \(0.551371\pi\)
\(972\) 0 0
\(973\) 34.4936 1.10581
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32.2206 1.03083 0.515414 0.856941i \(-0.327638\pi\)
0.515414 + 0.856941i \(0.327638\pi\)
\(978\) 0 0
\(979\) 5.45758 0.174425
\(980\) 0 0
\(981\) 3.27666 0.104616
\(982\) 0 0
\(983\) 12.7837 0.407736 0.203868 0.978998i \(-0.434649\pi\)
0.203868 + 0.978998i \(0.434649\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −91.4327 −2.91033
\(988\) 0 0
\(989\) 46.1593 1.46778
\(990\) 0 0
\(991\) −28.4893 −0.904992 −0.452496 0.891766i \(-0.649466\pi\)
−0.452496 + 0.891766i \(0.649466\pi\)
\(992\) 0 0
\(993\) 6.48406 0.205766
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 42.6122 1.34954 0.674772 0.738027i \(-0.264242\pi\)
0.674772 + 0.738027i \(0.264242\pi\)
\(998\) 0 0
\(999\) 18.7850 0.594331
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 1900.2.a.i.1.2 yes 3
4.3 odd 2 7600.2.a.bl.1.2 3
5.2 odd 4 1900.2.c.f.1749.3 6
5.3 odd 4 1900.2.c.f.1749.4 6
5.4 even 2 1900.2.a.g.1.2 3
20.19 odd 2 7600.2.a.ca.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1900.2.a.g.1.2 3 5.4 even 2
1900.2.a.i.1.2 yes 3 1.1 even 1 trivial
1900.2.c.f.1749.3 6 5.2 odd 4
1900.2.c.f.1749.4 6 5.3 odd 4
7600.2.a.bl.1.2 3 4.3 odd 2
7600.2.a.ca.1.2 3 20.19 odd 2