Properties

Label 9200.2.a.ca.1.2
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \(x^{2} - x - 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.30278 q^{3} -0.302776 q^{7} +7.90833 q^{9} +O(q^{10})\) \(q+3.30278 q^{3} -0.302776 q^{7} +7.90833 q^{9} +5.30278 q^{11} +0.302776 q^{13} +3.90833 q^{17} +4.90833 q^{19} -1.00000 q^{21} -1.00000 q^{23} +16.2111 q^{27} +4.60555 q^{29} -2.90833 q^{31} +17.5139 q^{33} -8.00000 q^{37} +1.00000 q^{39} -9.90833 q^{41} +5.21110 q^{43} +4.60555 q^{47} -6.90833 q^{49} +12.9083 q^{51} -3.21110 q^{53} +16.2111 q^{57} +10.6056 q^{59} -6.51388 q^{61} -2.39445 q^{63} -4.00000 q^{67} -3.30278 q^{69} +12.6972 q^{71} -15.8167 q^{73} -1.60555 q^{77} -14.4222 q^{79} +29.8167 q^{81} -3.21110 q^{83} +15.2111 q^{87} -0.0916731 q^{91} -9.60555 q^{93} -2.69722 q^{97} +41.9361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + 3q^{7} + 5q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 3q^{7} + 5q^{9} + 7q^{11} - 3q^{13} - 3q^{17} - q^{19} - 2q^{21} - 2q^{23} + 18q^{27} + 2q^{29} + 5q^{31} + 17q^{33} - 16q^{37} + 2q^{39} - 9q^{41} - 4q^{43} + 2q^{47} - 3q^{49} + 15q^{51} + 8q^{53} + 18q^{57} + 14q^{59} + 5q^{61} - 12q^{63} - 8q^{67} - 3q^{69} + 29q^{71} - 10q^{73} + 4q^{77} + 38q^{81} + 8q^{83} + 16q^{87} - 11q^{91} - 12q^{93} - 9q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 3.30278 1.90686 0.953429 0.301617i \(-0.0975264\pi\)
0.953429 + 0.301617i \(0.0975264\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.302776 −0.114438 −0.0572192 0.998362i \(-0.518223\pi\)
−0.0572192 + 0.998362i \(0.518223\pi\)
\(8\) 0 0
\(9\) 7.90833 2.63611
\(10\) 0 0
\(11\) 5.30278 1.59885 0.799424 0.600768i \(-0.205138\pi\)
0.799424 + 0.600768i \(0.205138\pi\)
\(12\) 0 0
\(13\) 0.302776 0.0839749 0.0419874 0.999118i \(-0.486631\pi\)
0.0419874 + 0.999118i \(0.486631\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.90833 0.947909 0.473954 0.880549i \(-0.342826\pi\)
0.473954 + 0.880549i \(0.342826\pi\)
\(18\) 0 0
\(19\) 4.90833 1.12605 0.563024 0.826441i \(-0.309638\pi\)
0.563024 + 0.826441i \(0.309638\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 16.2111 3.11983
\(28\) 0 0
\(29\) 4.60555 0.855229 0.427615 0.903961i \(-0.359354\pi\)
0.427615 + 0.903961i \(0.359354\pi\)
\(30\) 0 0
\(31\) −2.90833 −0.522351 −0.261175 0.965291i \(-0.584110\pi\)
−0.261175 + 0.965291i \(0.584110\pi\)
\(32\) 0 0
\(33\) 17.5139 3.04877
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −9.90833 −1.54742 −0.773710 0.633540i \(-0.781601\pi\)
−0.773710 + 0.633540i \(0.781601\pi\)
\(42\) 0 0
\(43\) 5.21110 0.794686 0.397343 0.917670i \(-0.369932\pi\)
0.397343 + 0.917670i \(0.369932\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.60555 0.671789 0.335894 0.941900i \(-0.390961\pi\)
0.335894 + 0.941900i \(0.390961\pi\)
\(48\) 0 0
\(49\) −6.90833 −0.986904
\(50\) 0 0
\(51\) 12.9083 1.80753
\(52\) 0 0
\(53\) −3.21110 −0.441079 −0.220539 0.975378i \(-0.570782\pi\)
−0.220539 + 0.975378i \(0.570782\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 16.2111 2.14721
\(58\) 0 0
\(59\) 10.6056 1.38073 0.690363 0.723464i \(-0.257451\pi\)
0.690363 + 0.723464i \(0.257451\pi\)
\(60\) 0 0
\(61\) −6.51388 −0.834017 −0.417008 0.908903i \(-0.636921\pi\)
−0.417008 + 0.908903i \(0.636921\pi\)
\(62\) 0 0
\(63\) −2.39445 −0.301672
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) −3.30278 −0.397607
\(70\) 0 0
\(71\) 12.6972 1.50688 0.753442 0.657515i \(-0.228392\pi\)
0.753442 + 0.657515i \(0.228392\pi\)
\(72\) 0 0
\(73\) −15.8167 −1.85120 −0.925600 0.378504i \(-0.876439\pi\)
−0.925600 + 0.378504i \(0.876439\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.60555 −0.182970
\(78\) 0 0
\(79\) −14.4222 −1.62262 −0.811312 0.584613i \(-0.801246\pi\)
−0.811312 + 0.584613i \(0.801246\pi\)
\(80\) 0 0
\(81\) 29.8167 3.31296
\(82\) 0 0
\(83\) −3.21110 −0.352464 −0.176232 0.984349i \(-0.556391\pi\)
−0.176232 + 0.984349i \(0.556391\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 15.2111 1.63080
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −0.0916731 −0.00960995
\(92\) 0 0
\(93\) −9.60555 −0.996049
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.69722 −0.273862 −0.136931 0.990581i \(-0.543724\pi\)
−0.136931 + 0.990581i \(0.543724\pi\)
\(98\) 0 0
\(99\) 41.9361 4.21473
\(100\) 0 0
\(101\) −4.60555 −0.458269 −0.229135 0.973395i \(-0.573590\pi\)
−0.229135 + 0.973395i \(0.573590\pi\)
\(102\) 0 0
\(103\) −17.1194 −1.68683 −0.843414 0.537265i \(-0.819458\pi\)
−0.843414 + 0.537265i \(0.819458\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.60555 0.445235 0.222618 0.974906i \(-0.428540\pi\)
0.222618 + 0.974906i \(0.428540\pi\)
\(108\) 0 0
\(109\) 19.5139 1.86909 0.934545 0.355844i \(-0.115807\pi\)
0.934545 + 0.355844i \(0.115807\pi\)
\(110\) 0 0
\(111\) −26.4222 −2.50788
\(112\) 0 0
\(113\) −12.4222 −1.16858 −0.584291 0.811544i \(-0.698627\pi\)
−0.584291 + 0.811544i \(0.698627\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.39445 0.221367
\(118\) 0 0
\(119\) −1.18335 −0.108477
\(120\) 0 0
\(121\) 17.1194 1.55631
\(122\) 0 0
\(123\) −32.7250 −2.95071
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.8167 −1.04856 −0.524279 0.851546i \(-0.675665\pi\)
−0.524279 + 0.851546i \(0.675665\pi\)
\(128\) 0 0
\(129\) 17.2111 1.51535
\(130\) 0 0
\(131\) −3.21110 −0.280555 −0.140278 0.990112i \(-0.544800\pi\)
−0.140278 + 0.990112i \(0.544800\pi\)
\(132\) 0 0
\(133\) −1.48612 −0.128863
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.90833 0.590218 0.295109 0.955464i \(-0.404644\pi\)
0.295109 + 0.955464i \(0.404644\pi\)
\(138\) 0 0
\(139\) 5.39445 0.457551 0.228776 0.973479i \(-0.426528\pi\)
0.228776 + 0.973479i \(0.426528\pi\)
\(140\) 0 0
\(141\) 15.2111 1.28101
\(142\) 0 0
\(143\) 1.60555 0.134263
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −22.8167 −1.88189
\(148\) 0 0
\(149\) 9.69722 0.794428 0.397214 0.917726i \(-0.369977\pi\)
0.397214 + 0.917726i \(0.369977\pi\)
\(150\) 0 0
\(151\) 1.90833 0.155297 0.0776487 0.996981i \(-0.475259\pi\)
0.0776487 + 0.996981i \(0.475259\pi\)
\(152\) 0 0
\(153\) 30.9083 2.49879
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.3944 0.909376 0.454688 0.890651i \(-0.349751\pi\)
0.454688 + 0.890651i \(0.349751\pi\)
\(158\) 0 0
\(159\) −10.6056 −0.841075
\(160\) 0 0
\(161\) 0.302776 0.0238621
\(162\) 0 0
\(163\) 5.69722 0.446241 0.223121 0.974791i \(-0.428376\pi\)
0.223121 + 0.974791i \(0.428376\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.2111 1.64136 0.820682 0.571385i \(-0.193594\pi\)
0.820682 + 0.571385i \(0.193594\pi\)
\(168\) 0 0
\(169\) −12.9083 −0.992948
\(170\) 0 0
\(171\) 38.8167 2.96838
\(172\) 0 0
\(173\) −23.3028 −1.77168 −0.885839 0.463993i \(-0.846416\pi\)
−0.885839 + 0.463993i \(0.846416\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 35.0278 2.63285
\(178\) 0 0
\(179\) −16.6056 −1.24116 −0.620579 0.784144i \(-0.713102\pi\)
−0.620579 + 0.784144i \(0.713102\pi\)
\(180\) 0 0
\(181\) −8.11943 −0.603512 −0.301756 0.953385i \(-0.597573\pi\)
−0.301756 + 0.953385i \(0.597573\pi\)
\(182\) 0 0
\(183\) −21.5139 −1.59035
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 20.7250 1.51556
\(188\) 0 0
\(189\) −4.90833 −0.357028
\(190\) 0 0
\(191\) 1.39445 0.100899 0.0504494 0.998727i \(-0.483935\pi\)
0.0504494 + 0.998727i \(0.483935\pi\)
\(192\) 0 0
\(193\) −3.81665 −0.274729 −0.137364 0.990521i \(-0.543863\pi\)
−0.137364 + 0.990521i \(0.543863\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.697224 −0.0496752 −0.0248376 0.999691i \(-0.507907\pi\)
−0.0248376 + 0.999691i \(0.507907\pi\)
\(198\) 0 0
\(199\) −8.42221 −0.597034 −0.298517 0.954404i \(-0.596492\pi\)
−0.298517 + 0.954404i \(0.596492\pi\)
\(200\) 0 0
\(201\) −13.2111 −0.931839
\(202\) 0 0
\(203\) −1.39445 −0.0978711
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.90833 −0.549667
\(208\) 0 0
\(209\) 26.0278 1.80038
\(210\) 0 0
\(211\) 7.21110 0.496433 0.248216 0.968705i \(-0.420156\pi\)
0.248216 + 0.968705i \(0.420156\pi\)
\(212\) 0 0
\(213\) 41.9361 2.87341
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.880571 0.0597770
\(218\) 0 0
\(219\) −52.2389 −3.52997
\(220\) 0 0
\(221\) 1.18335 0.0796005
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.39445 −0.490787 −0.245393 0.969424i \(-0.578917\pi\)
−0.245393 + 0.969424i \(0.578917\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) −5.30278 −0.348897
\(232\) 0 0
\(233\) −4.18335 −0.274060 −0.137030 0.990567i \(-0.543756\pi\)
−0.137030 + 0.990567i \(0.543756\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −47.6333 −3.09412
\(238\) 0 0
\(239\) 9.21110 0.595817 0.297908 0.954594i \(-0.403711\pi\)
0.297908 + 0.954594i \(0.403711\pi\)
\(240\) 0 0
\(241\) 14.4222 0.929016 0.464508 0.885569i \(-0.346231\pi\)
0.464508 + 0.885569i \(0.346231\pi\)
\(242\) 0 0
\(243\) 49.8444 3.19752
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.48612 0.0945597
\(248\) 0 0
\(249\) −10.6056 −0.672100
\(250\) 0 0
\(251\) 5.51388 0.348033 0.174016 0.984743i \(-0.444325\pi\)
0.174016 + 0.984743i \(0.444325\pi\)
\(252\) 0 0
\(253\) −5.30278 −0.333383
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −19.8167 −1.23613 −0.618064 0.786127i \(-0.712083\pi\)
−0.618064 + 0.786127i \(0.712083\pi\)
\(258\) 0 0
\(259\) 2.42221 0.150509
\(260\) 0 0
\(261\) 36.4222 2.25448
\(262\) 0 0
\(263\) −14.5139 −0.894964 −0.447482 0.894293i \(-0.647679\pi\)
−0.447482 + 0.894293i \(0.647679\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 25.8167 1.57407 0.787035 0.616909i \(-0.211615\pi\)
0.787035 + 0.616909i \(0.211615\pi\)
\(270\) 0 0
\(271\) 6.30278 0.382866 0.191433 0.981506i \(-0.438686\pi\)
0.191433 + 0.981506i \(0.438686\pi\)
\(272\) 0 0
\(273\) −0.302776 −0.0183248
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.7889 0.768410 0.384205 0.923248i \(-0.374476\pi\)
0.384205 + 0.923248i \(0.374476\pi\)
\(278\) 0 0
\(279\) −23.0000 −1.37697
\(280\) 0 0
\(281\) −19.3944 −1.15698 −0.578488 0.815691i \(-0.696357\pi\)
−0.578488 + 0.815691i \(0.696357\pi\)
\(282\) 0 0
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) −1.72498 −0.101469
\(290\) 0 0
\(291\) −8.90833 −0.522215
\(292\) 0 0
\(293\) −8.78890 −0.513453 −0.256726 0.966484i \(-0.582644\pi\)
−0.256726 + 0.966484i \(0.582644\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 85.9638 4.98813
\(298\) 0 0
\(299\) −0.302776 −0.0175100
\(300\) 0 0
\(301\) −1.57779 −0.0909426
\(302\) 0 0
\(303\) −15.2111 −0.873855
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −15.3028 −0.873376 −0.436688 0.899613i \(-0.643849\pi\)
−0.436688 + 0.899613i \(0.643849\pi\)
\(308\) 0 0
\(309\) −56.5416 −3.21654
\(310\) 0 0
\(311\) 6.42221 0.364170 0.182085 0.983283i \(-0.441715\pi\)
0.182085 + 0.983283i \(0.441715\pi\)
\(312\) 0 0
\(313\) 12.7250 0.719258 0.359629 0.933095i \(-0.382903\pi\)
0.359629 + 0.933095i \(0.382903\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.7250 0.827037 0.413519 0.910496i \(-0.364300\pi\)
0.413519 + 0.910496i \(0.364300\pi\)
\(318\) 0 0
\(319\) 24.4222 1.36738
\(320\) 0 0
\(321\) 15.2111 0.849001
\(322\) 0 0
\(323\) 19.1833 1.06739
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 64.4500 3.56409
\(328\) 0 0
\(329\) −1.39445 −0.0768784
\(330\) 0 0
\(331\) −9.39445 −0.516366 −0.258183 0.966096i \(-0.583124\pi\)
−0.258183 + 0.966096i \(0.583124\pi\)
\(332\) 0 0
\(333\) −63.2666 −3.46699
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 4.48612 0.244375 0.122187 0.992507i \(-0.461009\pi\)
0.122187 + 0.992507i \(0.461009\pi\)
\(338\) 0 0
\(339\) −41.0278 −2.22832
\(340\) 0 0
\(341\) −15.4222 −0.835159
\(342\) 0 0
\(343\) 4.21110 0.227378
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −25.5416 −1.37115 −0.685573 0.728004i \(-0.740448\pi\)
−0.685573 + 0.728004i \(0.740448\pi\)
\(348\) 0 0
\(349\) −12.7889 −0.684574 −0.342287 0.939595i \(-0.611202\pi\)
−0.342287 + 0.939595i \(0.611202\pi\)
\(350\) 0 0
\(351\) 4.90833 0.261987
\(352\) 0 0
\(353\) −18.4222 −0.980515 −0.490258 0.871578i \(-0.663097\pi\)
−0.490258 + 0.871578i \(0.663097\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.90833 −0.206851
\(358\) 0 0
\(359\) 3.21110 0.169476 0.0847378 0.996403i \(-0.472995\pi\)
0.0847378 + 0.996403i \(0.472995\pi\)
\(360\) 0 0
\(361\) 5.09167 0.267983
\(362\) 0 0
\(363\) 56.5416 2.96767
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 29.2111 1.52481 0.762404 0.647102i \(-0.224019\pi\)
0.762404 + 0.647102i \(0.224019\pi\)
\(368\) 0 0
\(369\) −78.3583 −4.07917
\(370\) 0 0
\(371\) 0.972244 0.0504764
\(372\) 0 0
\(373\) 2.60555 0.134910 0.0674552 0.997722i \(-0.478512\pi\)
0.0674552 + 0.997722i \(0.478512\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.39445 0.0718178
\(378\) 0 0
\(379\) −4.09167 −0.210175 −0.105088 0.994463i \(-0.533512\pi\)
−0.105088 + 0.994463i \(0.533512\pi\)
\(380\) 0 0
\(381\) −39.0278 −1.99945
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 41.2111 2.09488
\(388\) 0 0
\(389\) 20.9361 1.06150 0.530751 0.847528i \(-0.321910\pi\)
0.530751 + 0.847528i \(0.321910\pi\)
\(390\) 0 0
\(391\) −3.90833 −0.197653
\(392\) 0 0
\(393\) −10.6056 −0.534979
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 21.7250 1.09035 0.545173 0.838324i \(-0.316464\pi\)
0.545173 + 0.838324i \(0.316464\pi\)
\(398\) 0 0
\(399\) −4.90833 −0.245724
\(400\) 0 0
\(401\) −1.39445 −0.0696354 −0.0348177 0.999394i \(-0.511085\pi\)
−0.0348177 + 0.999394i \(0.511085\pi\)
\(402\) 0 0
\(403\) −0.880571 −0.0438643
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −42.4222 −2.10279
\(408\) 0 0
\(409\) −15.0917 −0.746235 −0.373118 0.927784i \(-0.621711\pi\)
−0.373118 + 0.927784i \(0.621711\pi\)
\(410\) 0 0
\(411\) 22.8167 1.12546
\(412\) 0 0
\(413\) −3.21110 −0.158008
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 17.8167 0.872485
\(418\) 0 0
\(419\) 39.6333 1.93621 0.968107 0.250538i \(-0.0806073\pi\)
0.968107 + 0.250538i \(0.0806073\pi\)
\(420\) 0 0
\(421\) 34.3028 1.67181 0.835907 0.548870i \(-0.184942\pi\)
0.835907 + 0.548870i \(0.184942\pi\)
\(422\) 0 0
\(423\) 36.4222 1.77091
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.97224 0.0954436
\(428\) 0 0
\(429\) 5.30278 0.256020
\(430\) 0 0
\(431\) −20.2389 −0.974872 −0.487436 0.873159i \(-0.662068\pi\)
−0.487436 + 0.873159i \(0.662068\pi\)
\(432\) 0 0
\(433\) 34.9083 1.67759 0.838794 0.544450i \(-0.183261\pi\)
0.838794 + 0.544450i \(0.183261\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.90833 −0.234797
\(438\) 0 0
\(439\) 18.3028 0.873544 0.436772 0.899572i \(-0.356122\pi\)
0.436772 + 0.899572i \(0.356122\pi\)
\(440\) 0 0
\(441\) −54.6333 −2.60159
\(442\) 0 0
\(443\) 35.5139 1.68732 0.843658 0.536882i \(-0.180398\pi\)
0.843658 + 0.536882i \(0.180398\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 32.0278 1.51486
\(448\) 0 0
\(449\) −12.9083 −0.609182 −0.304591 0.952483i \(-0.598520\pi\)
−0.304591 + 0.952483i \(0.598520\pi\)
\(450\) 0 0
\(451\) −52.5416 −2.47409
\(452\) 0 0
\(453\) 6.30278 0.296130
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.57779 0.167362 0.0836811 0.996493i \(-0.473332\pi\)
0.0836811 + 0.996493i \(0.473332\pi\)
\(458\) 0 0
\(459\) 63.3583 2.95731
\(460\) 0 0
\(461\) 31.8167 1.48185 0.740925 0.671588i \(-0.234388\pi\)
0.740925 + 0.671588i \(0.234388\pi\)
\(462\) 0 0
\(463\) −25.6333 −1.19128 −0.595640 0.803251i \(-0.703102\pi\)
−0.595640 + 0.803251i \(0.703102\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.8167 0.917005 0.458503 0.888693i \(-0.348386\pi\)
0.458503 + 0.888693i \(0.348386\pi\)
\(468\) 0 0
\(469\) 1.21110 0.0559235
\(470\) 0 0
\(471\) 37.6333 1.73405
\(472\) 0 0
\(473\) 27.6333 1.27058
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −25.3944 −1.16273
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) −2.42221 −0.110443
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −11.8167 −0.535464 −0.267732 0.963493i \(-0.586274\pi\)
−0.267732 + 0.963493i \(0.586274\pi\)
\(488\) 0 0
\(489\) 18.8167 0.850918
\(490\) 0 0
\(491\) 25.8167 1.16509 0.582545 0.812799i \(-0.302057\pi\)
0.582545 + 0.812799i \(0.302057\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.84441 −0.172445
\(498\) 0 0
\(499\) −11.6333 −0.520778 −0.260389 0.965504i \(-0.583851\pi\)
−0.260389 + 0.965504i \(0.583851\pi\)
\(500\) 0 0
\(501\) 70.0555 3.12985
\(502\) 0 0
\(503\) −2.72498 −0.121501 −0.0607504 0.998153i \(-0.519349\pi\)
−0.0607504 + 0.998153i \(0.519349\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −42.6333 −1.89341
\(508\) 0 0
\(509\) 29.4500 1.30535 0.652673 0.757639i \(-0.273647\pi\)
0.652673 + 0.757639i \(0.273647\pi\)
\(510\) 0 0
\(511\) 4.78890 0.211848
\(512\) 0 0
\(513\) 79.5694 3.51307
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 24.4222 1.07409
\(518\) 0 0
\(519\) −76.9638 −3.37834
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 8.42221 0.368277 0.184139 0.982900i \(-0.441050\pi\)
0.184139 + 0.982900i \(0.441050\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.3667 −0.495141
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 83.8722 3.63974
\(532\) 0 0
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −54.8444 −2.36671
\(538\) 0 0
\(539\) −36.6333 −1.57791
\(540\) 0 0
\(541\) −28.8444 −1.24012 −0.620059 0.784555i \(-0.712891\pi\)
−0.620059 + 0.784555i \(0.712891\pi\)
\(542\) 0 0
\(543\) −26.8167 −1.15081
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.51388 0.321270 0.160635 0.987014i \(-0.448646\pi\)
0.160635 + 0.987014i \(0.448646\pi\)
\(548\) 0 0
\(549\) −51.5139 −2.19856
\(550\) 0 0
\(551\) 22.6056 0.963029
\(552\) 0 0
\(553\) 4.36669 0.185691
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.42221 0.272118 0.136059 0.990701i \(-0.456556\pi\)
0.136059 + 0.990701i \(0.456556\pi\)
\(558\) 0 0
\(559\) 1.57779 0.0667336
\(560\) 0 0
\(561\) 68.4500 2.88996
\(562\) 0 0
\(563\) 39.6333 1.67034 0.835172 0.549988i \(-0.185368\pi\)
0.835172 + 0.549988i \(0.185368\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −9.02776 −0.379130
\(568\) 0 0
\(569\) −0.422205 −0.0176998 −0.00884988 0.999961i \(-0.502817\pi\)
−0.00884988 + 0.999961i \(0.502817\pi\)
\(570\) 0 0
\(571\) −9.11943 −0.381636 −0.190818 0.981625i \(-0.561114\pi\)
−0.190818 + 0.981625i \(0.561114\pi\)
\(572\) 0 0
\(573\) 4.60555 0.192400
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 0 0
\(579\) −12.6056 −0.523869
\(580\) 0 0
\(581\) 0.972244 0.0403355
\(582\) 0 0
\(583\) −17.0278 −0.705218
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −37.5416 −1.54951 −0.774755 0.632262i \(-0.782127\pi\)
−0.774755 + 0.632262i \(0.782127\pi\)
\(588\) 0 0
\(589\) −14.2750 −0.588192
\(590\) 0 0
\(591\) −2.30278 −0.0947235
\(592\) 0 0
\(593\) −19.8167 −0.813772 −0.406886 0.913479i \(-0.633385\pi\)
−0.406886 + 0.913479i \(0.633385\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −27.8167 −1.13846
\(598\) 0 0
\(599\) −4.33053 −0.176941 −0.0884704 0.996079i \(-0.528198\pi\)
−0.0884704 + 0.996079i \(0.528198\pi\)
\(600\) 0 0
\(601\) −3.93608 −0.160556 −0.0802781 0.996773i \(-0.525581\pi\)
−0.0802781 + 0.996773i \(0.525581\pi\)
\(602\) 0 0
\(603\) −31.6333 −1.28821
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −26.0555 −1.05756 −0.528780 0.848759i \(-0.677350\pi\)
−0.528780 + 0.848759i \(0.677350\pi\)
\(608\) 0 0
\(609\) −4.60555 −0.186626
\(610\) 0 0
\(611\) 1.39445 0.0564134
\(612\) 0 0
\(613\) −32.4222 −1.30952 −0.654760 0.755837i \(-0.727230\pi\)
−0.654760 + 0.755837i \(0.727230\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.09167 −0.325758 −0.162879 0.986646i \(-0.552078\pi\)
−0.162879 + 0.986646i \(0.552078\pi\)
\(618\) 0 0
\(619\) −27.3305 −1.09851 −0.549253 0.835656i \(-0.685088\pi\)
−0.549253 + 0.835656i \(0.685088\pi\)
\(620\) 0 0
\(621\) −16.2111 −0.650529
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 85.9638 3.43307
\(628\) 0 0
\(629\) −31.2666 −1.24668
\(630\) 0 0
\(631\) −30.6056 −1.21839 −0.609194 0.793021i \(-0.708507\pi\)
−0.609194 + 0.793021i \(0.708507\pi\)
\(632\) 0 0
\(633\) 23.8167 0.946627
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −2.09167 −0.0828751
\(638\) 0 0
\(639\) 100.414 3.97231
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) 0 0
\(643\) 16.2389 0.640398 0.320199 0.947350i \(-0.396250\pi\)
0.320199 + 0.947350i \(0.396250\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.8444 −1.21262 −0.606309 0.795229i \(-0.707351\pi\)
−0.606309 + 0.795229i \(0.707351\pi\)
\(648\) 0 0
\(649\) 56.2389 2.20757
\(650\) 0 0
\(651\) 2.90833 0.113986
\(652\) 0 0
\(653\) −9.27502 −0.362960 −0.181480 0.983395i \(-0.558089\pi\)
−0.181480 + 0.983395i \(0.558089\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −125.083 −4.87996
\(658\) 0 0
\(659\) 27.6333 1.07644 0.538220 0.842804i \(-0.319097\pi\)
0.538220 + 0.842804i \(0.319097\pi\)
\(660\) 0 0
\(661\) −24.0917 −0.937057 −0.468529 0.883448i \(-0.655216\pi\)
−0.468529 + 0.883448i \(0.655216\pi\)
\(662\) 0 0
\(663\) 3.90833 0.151787
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.60555 −0.178328
\(668\) 0 0
\(669\) −13.2111 −0.510771
\(670\) 0 0
\(671\) −34.5416 −1.33347
\(672\) 0 0
\(673\) −5.63331 −0.217148 −0.108574 0.994088i \(-0.534628\pi\)
−0.108574 + 0.994088i \(0.534628\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.4222 0.477424 0.238712 0.971090i \(-0.423275\pi\)
0.238712 + 0.971090i \(0.423275\pi\)
\(678\) 0 0
\(679\) 0.816654 0.0313403
\(680\) 0 0
\(681\) −24.4222 −0.935861
\(682\) 0 0
\(683\) −32.7250 −1.25219 −0.626093 0.779748i \(-0.715347\pi\)
−0.626093 + 0.779748i \(0.715347\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 6.60555 0.252018
\(688\) 0 0
\(689\) −0.972244 −0.0370395
\(690\) 0 0
\(691\) −30.1833 −1.14823 −0.574114 0.818775i \(-0.694653\pi\)
−0.574114 + 0.818775i \(0.694653\pi\)
\(692\) 0 0
\(693\) −12.6972 −0.482328
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −38.7250 −1.46681
\(698\) 0 0
\(699\) −13.8167 −0.522594
\(700\) 0 0
\(701\) 42.9083 1.62063 0.810313 0.585998i \(-0.199297\pi\)
0.810313 + 0.585998i \(0.199297\pi\)
\(702\) 0 0
\(703\) −39.2666 −1.48097
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.39445 0.0524436
\(708\) 0 0
\(709\) −41.1194 −1.54427 −0.772136 0.635457i \(-0.780812\pi\)
−0.772136 + 0.635457i \(0.780812\pi\)
\(710\) 0 0
\(711\) −114.056 −4.27742
\(712\) 0 0
\(713\) 2.90833 0.108918
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 30.4222 1.13614
\(718\) 0 0
\(719\) −14.3028 −0.533404 −0.266702 0.963779i \(-0.585934\pi\)
−0.266702 + 0.963779i \(0.585934\pi\)
\(720\) 0 0
\(721\) 5.18335 0.193038
\(722\) 0 0
\(723\) 47.6333 1.77150
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −7.90833 −0.293304 −0.146652 0.989188i \(-0.546850\pi\)
−0.146652 + 0.989188i \(0.546850\pi\)
\(728\) 0 0
\(729\) 75.1749 2.78426
\(730\) 0 0
\(731\) 20.3667 0.753289
\(732\) 0 0
\(733\) 13.6333 0.503558 0.251779 0.967785i \(-0.418984\pi\)
0.251779 + 0.967785i \(0.418984\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.2111 −0.781321
\(738\) 0 0
\(739\) 7.63331 0.280796 0.140398 0.990095i \(-0.455162\pi\)
0.140398 + 0.990095i \(0.455162\pi\)
\(740\) 0 0
\(741\) 4.90833 0.180312
\(742\) 0 0
\(743\) 7.33053 0.268931 0.134466 0.990918i \(-0.457068\pi\)
0.134466 + 0.990918i \(0.457068\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −25.3944 −0.929134
\(748\) 0 0
\(749\) −1.39445 −0.0509520
\(750\) 0 0
\(751\) −0.183346 −0.00669040 −0.00334520 0.999994i \(-0.501065\pi\)
−0.00334520 + 0.999994i \(0.501065\pi\)
\(752\) 0 0
\(753\) 18.2111 0.663649
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.21110 0.0440183 0.0220091 0.999758i \(-0.492994\pi\)
0.0220091 + 0.999758i \(0.492994\pi\)
\(758\) 0 0
\(759\) −17.5139 −0.635714
\(760\) 0 0
\(761\) 4.54163 0.164634 0.0823171 0.996606i \(-0.473768\pi\)
0.0823171 + 0.996606i \(0.473768\pi\)
\(762\) 0 0
\(763\) −5.90833 −0.213896
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.21110 0.115946
\(768\) 0 0
\(769\) −41.2666 −1.48811 −0.744056 0.668117i \(-0.767100\pi\)
−0.744056 + 0.668117i \(0.767100\pi\)
\(770\) 0 0
\(771\) −65.4500 −2.35712
\(772\) 0 0
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 8.00000 0.286998
\(778\) 0 0
\(779\) −48.6333 −1.74247
\(780\) 0 0
\(781\) 67.3305 2.40928
\(782\) 0 0
\(783\) 74.6611 2.66817
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −27.4500 −0.978485 −0.489243 0.872148i \(-0.662727\pi\)
−0.489243 + 0.872148i \(0.662727\pi\)
\(788\) 0 0
\(789\) −47.9361 −1.70657
\(790\) 0 0
\(791\) 3.76114 0.133731
\(792\) 0 0
\(793\) −1.97224 −0.0700364
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 19.8167 0.701942 0.350971 0.936386i \(-0.385852\pi\)
0.350971 + 0.936386i \(0.385852\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −83.8722 −2.95978
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 85.2666 3.00153
\(808\) 0 0
\(809\) 18.2750 0.642515 0.321258 0.946992i \(-0.395894\pi\)
0.321258 + 0.946992i \(0.395894\pi\)
\(810\) 0 0
\(811\) 4.97224 0.174599 0.0872995 0.996182i \(-0.472176\pi\)
0.0872995 + 0.996182i \(0.472176\pi\)
\(812\) 0 0
\(813\) 20.8167 0.730072
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 25.5778 0.894854
\(818\) 0 0
\(819\) −0.724981 −0.0253329
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) −0.788897 −0.0274992 −0.0137496 0.999905i \(-0.504377\pi\)
−0.0137496 + 0.999905i \(0.504377\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 35.4500 1.23272 0.616358 0.787466i \(-0.288607\pi\)
0.616358 + 0.787466i \(0.288607\pi\)
\(828\) 0 0
\(829\) 16.7889 0.583103 0.291551 0.956555i \(-0.405829\pi\)
0.291551 + 0.956555i \(0.405829\pi\)
\(830\) 0 0
\(831\) 42.2389 1.46525
\(832\) 0 0
\(833\) −27.0000 −0.935495
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −47.1472 −1.62965
\(838\) 0 0
\(839\) 22.1833 0.765854 0.382927 0.923779i \(-0.374916\pi\)
0.382927 + 0.923779i \(0.374916\pi\)
\(840\) 0 0
\(841\) −7.78890 −0.268583
\(842\) 0 0
\(843\) −64.0555 −2.20619
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −5.18335 −0.178102
\(848\) 0 0
\(849\) 6.60555 0.226702
\(850\) 0 0
\(851\) 8.00000 0.274236
\(852\) 0 0
\(853\) −10.7250 −0.367216 −0.183608 0.983000i \(-0.558778\pi\)
−0.183608 + 0.983000i \(0.558778\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 33.6333 1.14889 0.574446 0.818543i \(-0.305218\pi\)
0.574446 + 0.818543i \(0.305218\pi\)
\(858\) 0 0
\(859\) 14.1833 0.483930 0.241965 0.970285i \(-0.422208\pi\)
0.241965 + 0.970285i \(0.422208\pi\)
\(860\) 0 0
\(861\) 9.90833 0.337675
\(862\) 0 0
\(863\) 23.4500 0.798246 0.399123 0.916897i \(-0.369315\pi\)
0.399123 + 0.916897i \(0.369315\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −5.69722 −0.193488
\(868\) 0 0
\(869\) −76.4777 −2.59433
\(870\) 0 0
\(871\) −1.21110 −0.0410366
\(872\) 0 0
\(873\) −21.3305 −0.721929
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −49.1749 −1.66052 −0.830260 0.557376i \(-0.811808\pi\)
−0.830260 + 0.557376i \(0.811808\pi\)
\(878\) 0 0
\(879\) −29.0278 −0.979082
\(880\) 0 0
\(881\) −31.2666 −1.05340 −0.526700 0.850052i \(-0.676571\pi\)
−0.526700 + 0.850052i \(0.676571\pi\)
\(882\) 0 0
\(883\) 40.7250 1.37050 0.685252 0.728306i \(-0.259692\pi\)
0.685252 + 0.728306i \(0.259692\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −15.6333 −0.524915 −0.262458 0.964944i \(-0.584533\pi\)
−0.262458 + 0.964944i \(0.584533\pi\)
\(888\) 0 0
\(889\) 3.57779 0.119995
\(890\) 0 0
\(891\) 158.111 5.29692
\(892\) 0 0
\(893\) 22.6056 0.756466
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.00000 −0.0333890
\(898\) 0 0
\(899\) −13.3944 −0.446730
\(900\) 0 0
\(901\) −12.5500 −0.418102
\(902\) 0 0
\(903\) −5.21110 −0.173415
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −30.6611 −1.01808 −0.509042 0.860742i \(-0.670000\pi\)
−0.509042 + 0.860742i \(0.670000\pi\)
\(908\) 0 0
\(909\) −36.4222 −1.20805
\(910\) 0 0
\(911\) 25.8167 0.855344 0.427672 0.903934i \(-0.359334\pi\)
0.427672 + 0.903934i \(0.359334\pi\)
\(912\) 0 0
\(913\) −17.0278 −0.563536
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.972244 0.0321063
\(918\) 0 0
\(919\) −44.0000 −1.45143 −0.725713 0.687998i \(-0.758490\pi\)
−0.725713 + 0.687998i \(0.758490\pi\)
\(920\) 0 0
\(921\) −50.5416 −1.66540
\(922\) 0 0
\(923\) 3.84441 0.126540
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −135.386 −4.44666
\(928\) 0 0
\(929\) −57.6333 −1.89089 −0.945444 0.325785i \(-0.894371\pi\)
−0.945444 + 0.325785i \(0.894371\pi\)
\(930\) 0 0
\(931\) −33.9083 −1.11130
\(932\) 0 0
\(933\) 21.2111 0.694420
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 44.9638 1.46890 0.734452 0.678660i \(-0.237439\pi\)
0.734452 + 0.678660i \(0.237439\pi\)
\(938\) 0 0
\(939\) 42.0278 1.37152
\(940\) 0 0
\(941\) −20.9361 −0.682497 −0.341248 0.939973i \(-0.610850\pi\)
−0.341248 + 0.939973i \(0.610850\pi\)
\(942\) 0 0
\(943\) 9.90833 0.322660
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 41.9361 1.36274 0.681370 0.731939i \(-0.261385\pi\)
0.681370 + 0.731939i \(0.261385\pi\)
\(948\) 0 0
\(949\) −4.78890 −0.155454
\(950\) 0 0
\(951\) 48.6333 1.57704
\(952\) 0 0
\(953\) 1.66947 0.0540794 0.0270397 0.999634i \(-0.491392\pi\)
0.0270397 + 0.999634i \(0.491392\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 80.6611 2.60740
\(958\) 0 0
\(959\) −2.09167 −0.0675436
\(960\) 0 0
\(961\) −22.5416 −0.727150
\(962\) 0 0
\(963\) 36.4222 1.17369
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.39445 −0.173474 −0.0867369 0.996231i \(-0.527644\pi\)
−0.0867369 + 0.996231i \(0.527644\pi\)
\(968\) 0 0
\(969\) 63.3583 2.03536
\(970\) 0 0
\(971\) 27.9083 0.895621 0.447810 0.894129i \(-0.352204\pi\)
0.447810 + 0.894129i \(0.352204\pi\)
\(972\) 0 0
\(973\) −1.63331 −0.0523614
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 11.5139 0.368362 0.184181 0.982892i \(-0.441037\pi\)
0.184181 + 0.982892i \(0.441037\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 154.322 4.92713
\(982\) 0 0
\(983\) −19.5416 −0.623281 −0.311641 0.950200i \(-0.600879\pi\)
−0.311641 + 0.950200i \(0.600879\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −4.60555 −0.146596
\(988\) 0 0
\(989\) −5.21110 −0.165703
\(990\) 0 0
\(991\) −24.3305 −0.772885 −0.386442 0.922314i \(-0.626296\pi\)
−0.386442 + 0.922314i \(0.626296\pi\)
\(992\) 0 0
\(993\) −31.0278 −0.984636
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 31.2111 0.988466 0.494233 0.869330i \(-0.335449\pi\)
0.494233 + 0.869330i \(0.335449\pi\)
\(998\) 0 0
\(999\) −129.689 −4.10317
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 9200.2.a.ca.1.2 2
4.3 odd 2 1150.2.a.m.1.1 2
5.4 even 2 1840.2.a.j.1.1 2
20.3 even 4 1150.2.b.f.599.1 4
20.7 even 4 1150.2.b.f.599.4 4
20.19 odd 2 230.2.a.b.1.2 2
40.19 odd 2 7360.2.a.bc.1.1 2
40.29 even 2 7360.2.a.bu.1.2 2
60.59 even 2 2070.2.a.w.1.1 2
460.459 even 2 5290.2.a.j.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.b.1.2 2 20.19 odd 2
1150.2.a.m.1.1 2 4.3 odd 2
1150.2.b.f.599.1 4 20.3 even 4
1150.2.b.f.599.4 4 20.7 even 4
1840.2.a.j.1.1 2 5.4 even 2
2070.2.a.w.1.1 2 60.59 even 2
5290.2.a.j.1.2 2 460.459 even 2
7360.2.a.bc.1.1 2 40.19 odd 2
7360.2.a.bu.1.2 2 40.29 even 2
9200.2.a.ca.1.2 2 1.1 even 1 trivial