Properties

Label 2001.2.a.b.1.1
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.9780654445\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -2.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -2.00000 q^{4} +4.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} +4.00000 q^{11} +2.00000 q^{12} -5.00000 q^{13} -4.00000 q^{15} +4.00000 q^{16} -5.00000 q^{17} +5.00000 q^{19} -8.00000 q^{20} +4.00000 q^{21} +1.00000 q^{23} +11.0000 q^{25} -1.00000 q^{27} +8.00000 q^{28} -1.00000 q^{29} -2.00000 q^{31} -4.00000 q^{33} -16.0000 q^{35} -2.00000 q^{36} +5.00000 q^{37} +5.00000 q^{39} -2.00000 q^{41} +1.00000 q^{43} -8.00000 q^{44} +4.00000 q^{45} +6.00000 q^{47} -4.00000 q^{48} +9.00000 q^{49} +5.00000 q^{51} +10.0000 q^{52} +2.00000 q^{53} +16.0000 q^{55} -5.00000 q^{57} +9.00000 q^{59} +8.00000 q^{60} -10.0000 q^{61} -4.00000 q^{63} -8.00000 q^{64} -20.0000 q^{65} +8.00000 q^{67} +10.0000 q^{68} -1.00000 q^{69} -3.00000 q^{71} +8.00000 q^{73} -11.0000 q^{75} -10.0000 q^{76} -16.0000 q^{77} +13.0000 q^{79} +16.0000 q^{80} +1.00000 q^{81} -6.00000 q^{83} -8.00000 q^{84} -20.0000 q^{85} +1.00000 q^{87} -9.00000 q^{89} +20.0000 q^{91} -2.00000 q^{92} +2.00000 q^{93} +20.0000 q^{95} -6.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) −1.00000 −0.577350
\(4\) −2.00000 −1.00000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) 2.00000 0.577350
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 4.00000 1.00000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) −8.00000 −1.78885
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 8.00000 1.51186
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) −16.0000 −2.70449
\(36\) −2.00000 −0.333333
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 0 0
\(39\) 5.00000 0.800641
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −8.00000 −1.20605
\(45\) 4.00000 0.596285
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −4.00000 −0.577350
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 5.00000 0.700140
\(52\) 10.0000 1.38675
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 16.0000 2.15744
\(56\) 0 0
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) 9.00000 1.17170 0.585850 0.810419i \(-0.300761\pi\)
0.585850 + 0.810419i \(0.300761\pi\)
\(60\) 8.00000 1.03280
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −4.00000 −0.503953
\(64\) −8.00000 −1.00000
\(65\) −20.0000 −2.48069
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 10.0000 1.21268
\(69\) −1.00000 −0.120386
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 0 0
\(75\) −11.0000 −1.27017
\(76\) −10.0000 −1.14708
\(77\) −16.0000 −1.82337
\(78\) 0 0
\(79\) 13.0000 1.46261 0.731307 0.682048i \(-0.238911\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 16.0000 1.78885
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −8.00000 −0.872872
\(85\) −20.0000 −2.16930
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 20.0000 2.09657
\(92\) −2.00000 −0.208514
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 20.0000 2.05196
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) −22.0000 −2.20000
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 16.0000 1.56144
\(106\) 0 0
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) 2.00000 0.192450
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) −5.00000 −0.474579
\(112\) −16.0000 −1.51186
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 2.00000 0.185695
\(117\) −5.00000 −0.462250
\(118\) 0 0
\(119\) 20.0000 1.83340
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 2.00000 0.180334
\(124\) 4.00000 0.359211
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 0 0
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) 8.00000 0.696311
\(133\) −20.0000 −1.73422
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 32.0000 2.70449
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −20.0000 −1.67248
\(144\) 4.00000 0.333333
\(145\) −4.00000 −0.332182
\(146\) 0 0
\(147\) −9.00000 −0.742307
\(148\) −10.0000 −0.821995
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 0 0
\(153\) −5.00000 −0.404226
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) −10.0000 −0.800641
\(157\) −23.0000 −1.83560 −0.917800 0.397043i \(-0.870036\pi\)
−0.917800 + 0.397043i \(0.870036\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 4.00000 0.312348
\(165\) −16.0000 −1.24560
\(166\) 0 0
\(167\) −21.0000 −1.62503 −0.812514 0.582941i \(-0.801902\pi\)
−0.812514 + 0.582941i \(0.801902\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 5.00000 0.382360
\(172\) −2.00000 −0.152499
\(173\) 5.00000 0.380143 0.190071 0.981770i \(-0.439128\pi\)
0.190071 + 0.981770i \(0.439128\pi\)
\(174\) 0 0
\(175\) −44.0000 −3.32609
\(176\) 16.0000 1.20605
\(177\) −9.00000 −0.676481
\(178\) 0 0
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) −8.00000 −0.596285
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 20.0000 1.47043
\(186\) 0 0
\(187\) −20.0000 −1.46254
\(188\) −12.0000 −0.875190
\(189\) 4.00000 0.290957
\(190\) 0 0
\(191\) 21.0000 1.51951 0.759753 0.650211i \(-0.225320\pi\)
0.759753 + 0.650211i \(0.225320\pi\)
\(192\) 8.00000 0.577350
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 20.0000 1.43223
\(196\) −18.0000 −1.28571
\(197\) 9.00000 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) −8.00000 −0.564276
\(202\) 0 0
\(203\) 4.00000 0.280745
\(204\) −10.0000 −0.700140
\(205\) −8.00000 −0.558744
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) −20.0000 −1.38675
\(209\) 20.0000 1.38343
\(210\) 0 0
\(211\) 18.0000 1.23917 0.619586 0.784929i \(-0.287301\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(212\) −4.00000 −0.274721
\(213\) 3.00000 0.205557
\(214\) 0 0
\(215\) 4.00000 0.272798
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) 0 0
\(219\) −8.00000 −0.540590
\(220\) −32.0000 −2.15744
\(221\) 25.0000 1.68168
\(222\) 0 0
\(223\) 17.0000 1.13840 0.569202 0.822198i \(-0.307252\pi\)
0.569202 + 0.822198i \(0.307252\pi\)
\(224\) 0 0
\(225\) 11.0000 0.733333
\(226\) 0 0
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 10.0000 0.662266
\(229\) 19.0000 1.25556 0.627778 0.778393i \(-0.283965\pi\)
0.627778 + 0.778393i \(0.283965\pi\)
\(230\) 0 0
\(231\) 16.0000 1.05272
\(232\) 0 0
\(233\) −9.00000 −0.589610 −0.294805 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(234\) 0 0
\(235\) 24.0000 1.56559
\(236\) −18.0000 −1.17170
\(237\) −13.0000 −0.844441
\(238\) 0 0
\(239\) −29.0000 −1.87585 −0.937927 0.346833i \(-0.887257\pi\)
−0.937927 + 0.346833i \(0.887257\pi\)
\(240\) −16.0000 −1.03280
\(241\) −26.0000 −1.67481 −0.837404 0.546585i \(-0.815928\pi\)
−0.837404 + 0.546585i \(0.815928\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 20.0000 1.28037
\(245\) 36.0000 2.29996
\(246\) 0 0
\(247\) −25.0000 −1.59071
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 8.00000 0.503953
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) 20.0000 1.25245
\(256\) 16.0000 1.00000
\(257\) −27.0000 −1.68421 −0.842107 0.539311i \(-0.818685\pi\)
−0.842107 + 0.539311i \(0.818685\pi\)
\(258\) 0 0
\(259\) −20.0000 −1.24274
\(260\) 40.0000 2.48069
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) 9.00000 0.550791
\(268\) −16.0000 −0.977356
\(269\) −16.0000 −0.975537 −0.487769 0.872973i \(-0.662189\pi\)
−0.487769 + 0.872973i \(0.662189\pi\)
\(270\) 0 0
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) −20.0000 −1.21268
\(273\) −20.0000 −1.21046
\(274\) 0 0
\(275\) 44.0000 2.65330
\(276\) 2.00000 0.120386
\(277\) 3.00000 0.180253 0.0901263 0.995930i \(-0.471273\pi\)
0.0901263 + 0.995930i \(0.471273\pi\)
\(278\) 0 0
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) −16.0000 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(282\) 0 0
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 6.00000 0.356034
\(285\) −20.0000 −1.18470
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 6.00000 0.351726
\(292\) −16.0000 −0.936329
\(293\) 1.00000 0.0584206 0.0292103 0.999573i \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) 0 0
\(295\) 36.0000 2.09600
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) −5.00000 −0.289157
\(300\) 22.0000 1.27017
\(301\) −4.00000 −0.230556
\(302\) 0 0
\(303\) −12.0000 −0.689382
\(304\) 20.0000 1.14708
\(305\) −40.0000 −2.29039
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 32.0000 1.82337
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 0 0
\(315\) −16.0000 −0.901498
\(316\) −26.0000 −1.46261
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) −4.00000 −0.223957
\(320\) −32.0000 −1.78885
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) −25.0000 −1.39104
\(324\) −2.00000 −0.111111
\(325\) −55.0000 −3.05085
\(326\) 0 0
\(327\) −14.0000 −0.774202
\(328\) 0 0
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) −10.0000 −0.549650 −0.274825 0.961494i \(-0.588620\pi\)
−0.274825 + 0.961494i \(0.588620\pi\)
\(332\) 12.0000 0.658586
\(333\) 5.00000 0.273998
\(334\) 0 0
\(335\) 32.0000 1.74835
\(336\) 16.0000 0.872872
\(337\) −27.0000 −1.47078 −0.735392 0.677642i \(-0.763002\pi\)
−0.735392 + 0.677642i \(0.763002\pi\)
\(338\) 0 0
\(339\) −10.0000 −0.543125
\(340\) 40.0000 2.16930
\(341\) −8.00000 −0.433224
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) −4.00000 −0.215353
\(346\) 0 0
\(347\) −27.0000 −1.44944 −0.724718 0.689046i \(-0.758030\pi\)
−0.724718 + 0.689046i \(0.758030\pi\)
\(348\) −2.00000 −0.107211
\(349\) 27.0000 1.44528 0.722638 0.691226i \(-0.242929\pi\)
0.722638 + 0.691226i \(0.242929\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 18.0000 0.953998
\(357\) −20.0000 −1.05851
\(358\) 0 0
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) −5.00000 −0.262432
\(364\) −40.0000 −2.09657
\(365\) 32.0000 1.67496
\(366\) 0 0
\(367\) 4.00000 0.208798 0.104399 0.994535i \(-0.466708\pi\)
0.104399 + 0.994535i \(0.466708\pi\)
\(368\) 4.00000 0.208514
\(369\) −2.00000 −0.104116
\(370\) 0 0
\(371\) −8.00000 −0.415339
\(372\) −4.00000 −0.207390
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0 0
\(377\) 5.00000 0.257513
\(378\) 0 0
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) −40.0000 −2.05196
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) 10.0000 0.510976 0.255488 0.966812i \(-0.417764\pi\)
0.255488 + 0.966812i \(0.417764\pi\)
\(384\) 0 0
\(385\) −64.0000 −3.26174
\(386\) 0 0
\(387\) 1.00000 0.0508329
\(388\) 12.0000 0.609208
\(389\) 25.0000 1.26755 0.633775 0.773517i \(-0.281504\pi\)
0.633775 + 0.773517i \(0.281504\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) −8.00000 −0.403547
\(394\) 0 0
\(395\) 52.0000 2.61640
\(396\) −8.00000 −0.402015
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 20.0000 1.00125
\(400\) 44.0000 2.20000
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 0 0
\(403\) 10.0000 0.498135
\(404\) −24.0000 −1.19404
\(405\) 4.00000 0.198762
\(406\) 0 0
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) −36.0000 −1.78009 −0.890043 0.455877i \(-0.849326\pi\)
−0.890043 + 0.455877i \(0.849326\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −32.0000 −1.57653
\(413\) −36.0000 −1.77144
\(414\) 0 0
\(415\) −24.0000 −1.17811
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) −32.0000 −1.56144
\(421\) 13.0000 0.633581 0.316791 0.948495i \(-0.397395\pi\)
0.316791 + 0.948495i \(0.397395\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) −55.0000 −2.66789
\(426\) 0 0
\(427\) 40.0000 1.93574
\(428\) −36.0000 −1.74013
\(429\) 20.0000 0.965609
\(430\) 0 0
\(431\) −2.00000 −0.0963366 −0.0481683 0.998839i \(-0.515338\pi\)
−0.0481683 + 0.998839i \(0.515338\pi\)
\(432\) −4.00000 −0.192450
\(433\) −30.0000 −1.44171 −0.720854 0.693087i \(-0.756250\pi\)
−0.720854 + 0.693087i \(0.756250\pi\)
\(434\) 0 0
\(435\) 4.00000 0.191785
\(436\) −28.0000 −1.34096
\(437\) 5.00000 0.239182
\(438\) 0 0
\(439\) −27.0000 −1.28864 −0.644320 0.764756i \(-0.722859\pi\)
−0.644320 + 0.764756i \(0.722859\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) −18.0000 −0.855206 −0.427603 0.903967i \(-0.640642\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(444\) 10.0000 0.474579
\(445\) −36.0000 −1.70656
\(446\) 0 0
\(447\) −20.0000 −0.945968
\(448\) 32.0000 1.51186
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) −8.00000 −0.376705
\(452\) −20.0000 −0.940721
\(453\) −19.0000 −0.892698
\(454\) 0 0
\(455\) 80.0000 3.75046
\(456\) 0 0
\(457\) −16.0000 −0.748448 −0.374224 0.927338i \(-0.622091\pi\)
−0.374224 + 0.927338i \(0.622091\pi\)
\(458\) 0 0
\(459\) 5.00000 0.233380
\(460\) −8.00000 −0.373002
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) −39.0000 −1.81248 −0.906242 0.422760i \(-0.861061\pi\)
−0.906242 + 0.422760i \(0.861061\pi\)
\(464\) −4.00000 −0.185695
\(465\) 8.00000 0.370991
\(466\) 0 0
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 10.0000 0.462250
\(469\) −32.0000 −1.47762
\(470\) 0 0
\(471\) 23.0000 1.05978
\(472\) 0 0
\(473\) 4.00000 0.183920
\(474\) 0 0
\(475\) 55.0000 2.52357
\(476\) −40.0000 −1.83340
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −25.0000 −1.13990
\(482\) 0 0
\(483\) 4.00000 0.182006
\(484\) −10.0000 −0.454545
\(485\) −24.0000 −1.08978
\(486\) 0 0
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) −4.00000 −0.180334
\(493\) 5.00000 0.225189
\(494\) 0 0
\(495\) 16.0000 0.719147
\(496\) −8.00000 −0.359211
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) 15.0000 0.671492 0.335746 0.941953i \(-0.391012\pi\)
0.335746 + 0.941953i \(0.391012\pi\)
\(500\) −48.0000 −2.14663
\(501\) 21.0000 0.938211
\(502\) 0 0
\(503\) 37.0000 1.64975 0.824874 0.565316i \(-0.191246\pi\)
0.824874 + 0.565316i \(0.191246\pi\)
\(504\) 0 0
\(505\) 48.0000 2.13597
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 8.00000 0.354943
\(509\) 43.0000 1.90594 0.952971 0.303062i \(-0.0980090\pi\)
0.952971 + 0.303062i \(0.0980090\pi\)
\(510\) 0 0
\(511\) −32.0000 −1.41560
\(512\) 0 0
\(513\) −5.00000 −0.220755
\(514\) 0 0
\(515\) 64.0000 2.82018
\(516\) 2.00000 0.0880451
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) −5.00000 −0.219476
\(520\) 0 0
\(521\) −16.0000 −0.700973 −0.350486 0.936568i \(-0.613984\pi\)
−0.350486 + 0.936568i \(0.613984\pi\)
\(522\) 0 0
\(523\) −24.0000 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(524\) −16.0000 −0.698963
\(525\) 44.0000 1.92032
\(526\) 0 0
\(527\) 10.0000 0.435607
\(528\) −16.0000 −0.696311
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 9.00000 0.390567
\(532\) 40.0000 1.73422
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) 72.0000 3.11283
\(536\) 0 0
\(537\) −7.00000 −0.302072
\(538\) 0 0
\(539\) 36.0000 1.55063
\(540\) 8.00000 0.344265
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 0 0
\(543\) −6.00000 −0.257485
\(544\) 0 0
\(545\) 56.0000 2.39878
\(546\) 0 0
\(547\) −17.0000 −0.726868 −0.363434 0.931620i \(-0.618396\pi\)
−0.363434 + 0.931620i \(0.618396\pi\)
\(548\) 18.0000 0.768922
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) −52.0000 −2.21126
\(554\) 0 0
\(555\) −20.0000 −0.848953
\(556\) 0 0
\(557\) 14.0000 0.593199 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) −64.0000 −2.70449
\(561\) 20.0000 0.844401
\(562\) 0 0
\(563\) 1.00000 0.0421450 0.0210725 0.999778i \(-0.493292\pi\)
0.0210725 + 0.999778i \(0.493292\pi\)
\(564\) 12.0000 0.505291
\(565\) 40.0000 1.68281
\(566\) 0 0
\(567\) −4.00000 −0.167984
\(568\) 0 0
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) 18.0000 0.753277 0.376638 0.926360i \(-0.377080\pi\)
0.376638 + 0.926360i \(0.377080\pi\)
\(572\) 40.0000 1.67248
\(573\) −21.0000 −0.877288
\(574\) 0 0
\(575\) 11.0000 0.458732
\(576\) −8.00000 −0.333333
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 0 0
\(579\) −14.0000 −0.581820
\(580\) 8.00000 0.332182
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 8.00000 0.331326
\(584\) 0 0
\(585\) −20.0000 −0.826898
\(586\) 0 0
\(587\) −27.0000 −1.11441 −0.557205 0.830375i \(-0.688126\pi\)
−0.557205 + 0.830375i \(0.688126\pi\)
\(588\) 18.0000 0.742307
\(589\) −10.0000 −0.412043
\(590\) 0 0
\(591\) −9.00000 −0.370211
\(592\) 20.0000 0.821995
\(593\) −21.0000 −0.862367 −0.431183 0.902264i \(-0.641904\pi\)
−0.431183 + 0.902264i \(0.641904\pi\)
\(594\) 0 0
\(595\) 80.0000 3.27968
\(596\) −40.0000 −1.63846
\(597\) 2.00000 0.0818546
\(598\) 0 0
\(599\) −2.00000 −0.0817178 −0.0408589 0.999165i \(-0.513009\pi\)
−0.0408589 + 0.999165i \(0.513009\pi\)
\(600\) 0 0
\(601\) 40.0000 1.63163 0.815817 0.578310i \(-0.196288\pi\)
0.815817 + 0.578310i \(0.196288\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) −38.0000 −1.54620
\(605\) 20.0000 0.813116
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) −4.00000 −0.162088
\(610\) 0 0
\(611\) −30.0000 −1.21367
\(612\) 10.0000 0.404226
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 41.0000 1.64793 0.823965 0.566641i \(-0.191757\pi\)
0.823965 + 0.566641i \(0.191757\pi\)
\(620\) 16.0000 0.642575
\(621\) −1.00000 −0.0401286
\(622\) 0 0
\(623\) 36.0000 1.44231
\(624\) 20.0000 0.800641
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) −20.0000 −0.798723
\(628\) 46.0000 1.83560
\(629\) −25.0000 −0.996815
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 0 0
\(633\) −18.0000 −0.715436
\(634\) 0 0
\(635\) −16.0000 −0.634941
\(636\) 4.00000 0.158610
\(637\) −45.0000 −1.78296
\(638\) 0 0
\(639\) −3.00000 −0.118678
\(640\) 0 0
\(641\) −39.0000 −1.54041 −0.770204 0.637798i \(-0.779845\pi\)
−0.770204 + 0.637798i \(0.779845\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 8.00000 0.315244
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −3.00000 −0.117942 −0.0589711 0.998260i \(-0.518782\pi\)
−0.0589711 + 0.998260i \(0.518782\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) −8.00000 −0.313304
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 32.0000 1.25034
\(656\) −8.00000 −0.312348
\(657\) 8.00000 0.312110
\(658\) 0 0
\(659\) 29.0000 1.12968 0.564840 0.825201i \(-0.308938\pi\)
0.564840 + 0.825201i \(0.308938\pi\)
\(660\) 32.0000 1.24560
\(661\) −6.00000 −0.233373 −0.116686 0.993169i \(-0.537227\pi\)
−0.116686 + 0.993169i \(0.537227\pi\)
\(662\) 0 0
\(663\) −25.0000 −0.970920
\(664\) 0 0
\(665\) −80.0000 −3.10227
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 42.0000 1.62503
\(669\) −17.0000 −0.657258
\(670\) 0 0
\(671\) −40.0000 −1.54418
\(672\) 0 0
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 0 0
\(675\) −11.0000 −0.423390
\(676\) −24.0000 −0.923077
\(677\) 10.0000 0.384331 0.192166 0.981363i \(-0.438449\pi\)
0.192166 + 0.981363i \(0.438449\pi\)
\(678\) 0 0
\(679\) 24.0000 0.921035
\(680\) 0 0
\(681\) 18.0000 0.689761
\(682\) 0 0
\(683\) 20.0000 0.765279 0.382639 0.923898i \(-0.375015\pi\)
0.382639 + 0.923898i \(0.375015\pi\)
\(684\) −10.0000 −0.382360
\(685\) −36.0000 −1.37549
\(686\) 0 0
\(687\) −19.0000 −0.724895
\(688\) 4.00000 0.152499
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) 52.0000 1.97817 0.989087 0.147335i \(-0.0470696\pi\)
0.989087 + 0.147335i \(0.0470696\pi\)
\(692\) −10.0000 −0.380143
\(693\) −16.0000 −0.607790
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 10.0000 0.378777
\(698\) 0 0
\(699\) 9.00000 0.340411
\(700\) 88.0000 3.32609
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 25.0000 0.942893
\(704\) −32.0000 −1.20605
\(705\) −24.0000 −0.903892
\(706\) 0 0
\(707\) −48.0000 −1.80523
\(708\) 18.0000 0.676481
\(709\) 34.0000 1.27690 0.638448 0.769665i \(-0.279577\pi\)
0.638448 + 0.769665i \(0.279577\pi\)
\(710\) 0 0
\(711\) 13.0000 0.487538
\(712\) 0 0
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) −80.0000 −2.99183
\(716\) −14.0000 −0.523205
\(717\) 29.0000 1.08302
\(718\) 0 0
\(719\) −21.0000 −0.783168 −0.391584 0.920142i \(-0.628073\pi\)
−0.391584 + 0.920142i \(0.628073\pi\)
\(720\) 16.0000 0.596285
\(721\) −64.0000 −2.38348
\(722\) 0 0
\(723\) 26.0000 0.966950
\(724\) −12.0000 −0.445976
\(725\) −11.0000 −0.408530
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.00000 −0.184932
\(732\) −20.0000 −0.739221
\(733\) 42.0000 1.55131 0.775653 0.631160i \(-0.217421\pi\)
0.775653 + 0.631160i \(0.217421\pi\)
\(734\) 0 0
\(735\) −36.0000 −1.32788
\(736\) 0 0
\(737\) 32.0000 1.17874
\(738\) 0 0
\(739\) −50.0000 −1.83928 −0.919640 0.392763i \(-0.871519\pi\)
−0.919640 + 0.392763i \(0.871519\pi\)
\(740\) −40.0000 −1.47043
\(741\) 25.0000 0.918398
\(742\) 0 0
\(743\) 13.0000 0.476924 0.238462 0.971152i \(-0.423357\pi\)
0.238462 + 0.971152i \(0.423357\pi\)
\(744\) 0 0
\(745\) 80.0000 2.93097
\(746\) 0 0
\(747\) −6.00000 −0.219529
\(748\) 40.0000 1.46254
\(749\) −72.0000 −2.63082
\(750\) 0 0
\(751\) 41.0000 1.49611 0.748056 0.663636i \(-0.230988\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) 24.0000 0.875190
\(753\) −9.00000 −0.327978
\(754\) 0 0
\(755\) 76.0000 2.76592
\(756\) −8.00000 −0.290957
\(757\) 7.00000 0.254419 0.127210 0.991876i \(-0.459398\pi\)
0.127210 + 0.991876i \(0.459398\pi\)
\(758\) 0 0
\(759\) −4.00000 −0.145191
\(760\) 0 0
\(761\) −25.0000 −0.906249 −0.453125 0.891447i \(-0.649691\pi\)
−0.453125 + 0.891447i \(0.649691\pi\)
\(762\) 0 0
\(763\) −56.0000 −2.02734
\(764\) −42.0000 −1.51951
\(765\) −20.0000 −0.723102
\(766\) 0 0
\(767\) −45.0000 −1.62486
\(768\) −16.0000 −0.577350
\(769\) −25.0000 −0.901523 −0.450762 0.892644i \(-0.648848\pi\)
−0.450762 + 0.892644i \(0.648848\pi\)
\(770\) 0 0
\(771\) 27.0000 0.972381
\(772\) −28.0000 −1.00774
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) −22.0000 −0.790263
\(776\) 0 0
\(777\) 20.0000 0.717496
\(778\) 0 0
\(779\) −10.0000 −0.358287
\(780\) −40.0000 −1.43223
\(781\) −12.0000 −0.429394
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 36.0000 1.28571
\(785\) −92.0000 −3.28362
\(786\) 0 0
\(787\) −22.0000 −0.784215 −0.392108 0.919919i \(-0.628254\pi\)
−0.392108 + 0.919919i \(0.628254\pi\)
\(788\) −18.0000 −0.641223
\(789\) −12.0000 −0.427211
\(790\) 0 0
\(791\) −40.0000 −1.42224
\(792\) 0 0
\(793\) 50.0000 1.77555
\(794\) 0 0
\(795\) −8.00000 −0.283731
\(796\) 4.00000 0.141776
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −30.0000 −1.06132
\(800\) 0 0
\(801\) −9.00000 −0.317999
\(802\) 0 0
\(803\) 32.0000 1.12926
\(804\) 16.0000 0.564276
\(805\) −16.0000 −0.563926
\(806\) 0 0
\(807\) 16.0000 0.563227
\(808\) 0 0
\(809\) 18.0000 0.632846 0.316423 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −8.00000 −0.280745
\(813\) 12.0000 0.420858
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) 20.0000 0.700140
\(817\) 5.00000 0.174928
\(818\) 0 0
\(819\) 20.0000 0.698857
\(820\) 16.0000 0.558744
\(821\) 15.0000 0.523504 0.261752 0.965135i \(-0.415700\pi\)
0.261752 + 0.965135i \(0.415700\pi\)
\(822\) 0 0
\(823\) −20.0000 −0.697156 −0.348578 0.937280i \(-0.613335\pi\)
−0.348578 + 0.937280i \(0.613335\pi\)
\(824\) 0 0
\(825\) −44.0000 −1.53188
\(826\) 0 0
\(827\) −3.00000 −0.104320 −0.0521601 0.998639i \(-0.516611\pi\)
−0.0521601 + 0.998639i \(0.516611\pi\)
\(828\) −2.00000 −0.0695048
\(829\) 28.0000 0.972480 0.486240 0.873825i \(-0.338368\pi\)
0.486240 + 0.873825i \(0.338368\pi\)
\(830\) 0 0
\(831\) −3.00000 −0.104069
\(832\) 40.0000 1.38675
\(833\) −45.0000 −1.55916
\(834\) 0 0
\(835\) −84.0000 −2.90694
\(836\) −40.0000 −1.38343
\(837\) 2.00000 0.0691301
\(838\) 0 0
\(839\) 44.0000 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 16.0000 0.551069
\(844\) −36.0000 −1.23917
\(845\) 48.0000 1.65125
\(846\) 0 0
\(847\) −20.0000 −0.687208
\(848\) 8.00000 0.274721
\(849\) 6.00000 0.205919
\(850\) 0 0
\(851\) 5.00000 0.171398
\(852\) −6.00000 −0.205557
\(853\) −18.0000 −0.616308 −0.308154 0.951336i \(-0.599711\pi\)
−0.308154 + 0.951336i \(0.599711\pi\)
\(854\) 0 0
\(855\) 20.0000 0.683986
\(856\) 0 0
\(857\) 26.0000 0.888143 0.444072 0.895991i \(-0.353534\pi\)
0.444072 + 0.895991i \(0.353534\pi\)
\(858\) 0 0
\(859\) −26.0000 −0.887109 −0.443554 0.896248i \(-0.646283\pi\)
−0.443554 + 0.896248i \(0.646283\pi\)
\(860\) −8.00000 −0.272798
\(861\) −8.00000 −0.272639
\(862\) 0 0
\(863\) −4.00000 −0.136162 −0.0680808 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 0 0
\(865\) 20.0000 0.680020
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) −16.0000 −0.543075
\(869\) 52.0000 1.76398
\(870\) 0 0
\(871\) −40.0000 −1.35535
\(872\) 0 0
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) −96.0000 −3.24539
\(876\) 16.0000 0.540590
\(877\) −33.0000 −1.11433 −0.557165 0.830402i \(-0.688111\pi\)
−0.557165 + 0.830402i \(0.688111\pi\)
\(878\) 0 0
\(879\) −1.00000 −0.0337292
\(880\) 64.0000 2.15744
\(881\) 43.0000 1.44871 0.724353 0.689429i \(-0.242138\pi\)
0.724353 + 0.689429i \(0.242138\pi\)
\(882\) 0 0
\(883\) 51.0000 1.71629 0.858143 0.513410i \(-0.171618\pi\)
0.858143 + 0.513410i \(0.171618\pi\)
\(884\) −50.0000 −1.68168
\(885\) −36.0000 −1.21013
\(886\) 0 0
\(887\) −20.0000 −0.671534 −0.335767 0.941945i \(-0.608996\pi\)
−0.335767 + 0.941945i \(0.608996\pi\)
\(888\) 0 0
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 4.00000 0.134005
\(892\) −34.0000 −1.13840
\(893\) 30.0000 1.00391
\(894\) 0 0
\(895\) 28.0000 0.935937
\(896\) 0 0
\(897\) 5.00000 0.166945
\(898\) 0 0
\(899\) 2.00000 0.0667037
\(900\) −22.0000 −0.733333
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) 4.00000 0.133112
\(904\) 0 0
\(905\) 24.0000 0.797787
\(906\) 0 0
\(907\) −1.00000 −0.0332045 −0.0166022 0.999862i \(-0.505285\pi\)
−0.0166022 + 0.999862i \(0.505285\pi\)
\(908\) 36.0000 1.19470
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 9.00000 0.298183 0.149092 0.988823i \(-0.452365\pi\)
0.149092 + 0.988823i \(0.452365\pi\)
\(912\) −20.0000 −0.662266
\(913\) −24.0000 −0.794284
\(914\) 0 0
\(915\) 40.0000 1.32236
\(916\) −38.0000 −1.25556
\(917\) −32.0000 −1.05673
\(918\) 0 0
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 0 0
\(921\) 2.00000 0.0659022
\(922\) 0 0
\(923\) 15.0000 0.493731
\(924\) −32.0000 −1.05272
\(925\) 55.0000 1.80839
\(926\) 0 0
\(927\) 16.0000 0.525509
\(928\) 0 0
\(929\) −7.00000 −0.229663 −0.114831 0.993385i \(-0.536633\pi\)
−0.114831 + 0.993385i \(0.536633\pi\)
\(930\) 0 0
\(931\) 45.0000 1.47482
\(932\) 18.0000 0.589610
\(933\) 24.0000 0.785725
\(934\) 0 0
\(935\) −80.0000 −2.61628
\(936\) 0 0
\(937\) −26.0000 −0.849383 −0.424691 0.905338i \(-0.639617\pi\)
−0.424691 + 0.905338i \(0.639617\pi\)
\(938\) 0 0
\(939\) −14.0000 −0.456873
\(940\) −48.0000 −1.56559
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) 0 0
\(943\) −2.00000 −0.0651290
\(944\) 36.0000 1.17170
\(945\) 16.0000 0.520480
\(946\) 0 0
\(947\) −8.00000 −0.259965 −0.129983 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(948\) 26.0000 0.844441
\(949\) −40.0000 −1.29845
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) −22.0000 −0.712650 −0.356325 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) 0 0
\(955\) 84.0000 2.71818
\(956\) 58.0000 1.87585
\(957\) 4.00000 0.129302
\(958\) 0 0
\(959\) 36.0000 1.16250
\(960\) 32.0000 1.03280
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 18.0000 0.580042
\(964\) 52.0000 1.67481
\(965\) 56.0000 1.80270
\(966\) 0 0
\(967\) −30.0000 −0.964735 −0.482367 0.875969i \(-0.660223\pi\)
−0.482367 + 0.875969i \(0.660223\pi\)
\(968\) 0 0
\(969\) 25.0000 0.803116
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 2.00000 0.0641500
\(973\) 0 0
\(974\) 0 0
\(975\) 55.0000 1.76141
\(976\) −40.0000 −1.28037
\(977\) −8.00000 −0.255943 −0.127971 0.991778i \(-0.540847\pi\)
−0.127971 + 0.991778i \(0.540847\pi\)
\(978\) 0 0
\(979\) −36.0000 −1.15056
\(980\) −72.0000 −2.29996
\(981\) 14.0000 0.446986
\(982\) 0 0
\(983\) 21.0000 0.669796 0.334898 0.942254i \(-0.391298\pi\)
0.334898 + 0.942254i \(0.391298\pi\)
\(984\) 0 0
\(985\) 36.0000 1.14706
\(986\) 0 0
\(987\) 24.0000 0.763928
\(988\) 50.0000 1.59071
\(989\) 1.00000 0.0317982
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0 0
\(993\) 10.0000 0.317340
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) −12.0000 −0.380235
\(997\) 60.0000 1.90022 0.950110 0.311916i \(-0.100971\pi\)
0.950110 + 0.311916i \(0.100971\pi\)
\(998\) 0 0
\(999\) −5.00000 −0.158193
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 2001.2.a.b.1.1 1
3.2 odd 2 6003.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.b.1.1 1 1.1 even 1 trivial
6003.2.a.a.1.1 1 3.2 odd 2