Properties

Label 1150.2.a.m.1.1
Level $1150$
Weight $2$
Character 1150.1
Self dual yes
Analytic conductor $9.183$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.18279623245\)
Analytic rank: \(1\)
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 1.1
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.30278 q^{3} +1.00000 q^{4} -3.30278 q^{6} +0.302776 q^{7} +1.00000 q^{8} +7.90833 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.30278 q^{3} +1.00000 q^{4} -3.30278 q^{6} +0.302776 q^{7} +1.00000 q^{8} +7.90833 q^{9} -5.30278 q^{11} -3.30278 q^{12} +0.302776 q^{13} +0.302776 q^{14} +1.00000 q^{16} +3.90833 q^{17} +7.90833 q^{18} -4.90833 q^{19} -1.00000 q^{21} -5.30278 q^{22} +1.00000 q^{23} -3.30278 q^{24} +0.302776 q^{26} -16.2111 q^{27} +0.302776 q^{28} +4.60555 q^{29} +2.90833 q^{31} +1.00000 q^{32} +17.5139 q^{33} +3.90833 q^{34} +7.90833 q^{36} -8.00000 q^{37} -4.90833 q^{38} -1.00000 q^{39} -9.90833 q^{41} -1.00000 q^{42} -5.21110 q^{43} -5.30278 q^{44} +1.00000 q^{46} -4.60555 q^{47} -3.30278 q^{48} -6.90833 q^{49} -12.9083 q^{51} +0.302776 q^{52} -3.21110 q^{53} -16.2111 q^{54} +0.302776 q^{56} +16.2111 q^{57} +4.60555 q^{58} -10.6056 q^{59} -6.51388 q^{61} +2.90833 q^{62} +2.39445 q^{63} +1.00000 q^{64} +17.5139 q^{66} +4.00000 q^{67} +3.90833 q^{68} -3.30278 q^{69} -12.6972 q^{71} +7.90833 q^{72} -15.8167 q^{73} -8.00000 q^{74} -4.90833 q^{76} -1.60555 q^{77} -1.00000 q^{78} +14.4222 q^{79} +29.8167 q^{81} -9.90833 q^{82} +3.21110 q^{83} -1.00000 q^{84} -5.21110 q^{86} -15.2111 q^{87} -5.30278 q^{88} +0.0916731 q^{91} +1.00000 q^{92} -9.60555 q^{93} -4.60555 q^{94} -3.30278 q^{96} -2.69722 q^{97} -6.90833 q^{98} -41.9361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 3q^{6} - 3q^{7} + 2q^{8} + 5q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 3q^{3} + 2q^{4} - 3q^{6} - 3q^{7} + 2q^{8} + 5q^{9} - 7q^{11} - 3q^{12} - 3q^{13} - 3q^{14} + 2q^{16} - 3q^{17} + 5q^{18} + q^{19} - 2q^{21} - 7q^{22} + 2q^{23} - 3q^{24} - 3q^{26} - 18q^{27} - 3q^{28} + 2q^{29} - 5q^{31} + 2q^{32} + 17q^{33} - 3q^{34} + 5q^{36} - 16q^{37} + q^{38} - 2q^{39} - 9q^{41} - 2q^{42} + 4q^{43} - 7q^{44} + 2q^{46} - 2q^{47} - 3q^{48} - 3q^{49} - 15q^{51} - 3q^{52} + 8q^{53} - 18q^{54} - 3q^{56} + 18q^{57} + 2q^{58} - 14q^{59} + 5q^{61} - 5q^{62} + 12q^{63} + 2q^{64} + 17q^{66} + 8q^{67} - 3q^{68} - 3q^{69} - 29q^{71} + 5q^{72} - 10q^{73} - 16q^{74} + q^{76} + 4q^{77} - 2q^{78} + 38q^{81} - 9q^{82} - 8q^{83} - 2q^{84} + 4q^{86} - 16q^{87} - 7q^{88} + 11q^{91} + 2q^{92} - 12q^{93} - 2q^{94} - 3q^{96} - 9q^{97} - 3q^{98} - 37q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.30278 −1.90686 −0.953429 0.301617i \(-0.902474\pi\)
−0.953429 + 0.301617i \(0.902474\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −3.30278 −1.34835
\(7\) 0.302776 0.114438 0.0572192 0.998362i \(-0.481777\pi\)
0.0572192 + 0.998362i \(0.481777\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.90833 2.63611
\(10\) 0 0
\(11\) −5.30278 −1.59885 −0.799424 0.600768i \(-0.794862\pi\)
−0.799424 + 0.600768i \(0.794862\pi\)
\(12\) −3.30278 −0.953429
\(13\) 0.302776 0.0839749 0.0419874 0.999118i \(-0.486631\pi\)
0.0419874 + 0.999118i \(0.486631\pi\)
\(14\) 0.302776 0.0809202
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.90833 0.947909 0.473954 0.880549i \(-0.342826\pi\)
0.473954 + 0.880549i \(0.342826\pi\)
\(18\) 7.90833 1.86401
\(19\) −4.90833 −1.12605 −0.563024 0.826441i \(-0.690362\pi\)
−0.563024 + 0.826441i \(0.690362\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) −5.30278 −1.13056
\(23\) 1.00000 0.208514
\(24\) −3.30278 −0.674176
\(25\) 0 0
\(26\) 0.302776 0.0593792
\(27\) −16.2111 −3.11983
\(28\) 0.302776 0.0572192
\(29\) 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 \(-0.415890\pi\)
0.261175 + 0.965291i \(0.415890\pi\)
\(32\) 1.00000 0.176777
\(33\) 17.5139 3.04877
\(34\) 3.90833 0.670273
\(35\) 0 0
\(36\) 7.90833 1.31805
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) −4.90833 −0.796236
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −9.90833 −1.54742 −0.773710 0.633540i \(-0.781601\pi\)
−0.773710 + 0.633540i \(0.781601\pi\)
\(42\) −1.00000 −0.154303
\(43\) −5.21110 −0.794686 −0.397343 0.917670i \(-0.630068\pi\)
−0.397343 + 0.917670i \(0.630068\pi\)
\(44\) −5.30278 −0.799424
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −4.60555 −0.671789 −0.335894 0.941900i \(-0.609039\pi\)
−0.335894 + 0.941900i \(0.609039\pi\)
\(48\) −3.30278 −0.476715
\(49\) −6.90833 −0.986904
\(50\) 0 0
\(51\) −12.9083 −1.80753
\(52\) 0.302776 0.0419874
\(53\) −3.21110 −0.441079 −0.220539 0.975378i \(-0.570782\pi\)
−0.220539 + 0.975378i \(0.570782\pi\)
\(54\) −16.2111 −2.20605
\(55\) 0 0
\(56\) 0.302776 0.0404601
\(57\) 16.2111 2.14721
\(58\) 4.60555 0.604739
\(59\) −10.6056 −1.38073 −0.690363 0.723464i \(-0.742549\pi\)
−0.690363 + 0.723464i \(0.742549\pi\)
\(60\) 0 0
\(61\) −6.51388 −0.834017 −0.417008 0.908903i \(-0.636921\pi\)
−0.417008 + 0.908903i \(0.636921\pi\)
\(62\) 2.90833 0.369358
\(63\) 2.39445 0.301672
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 17.5139 2.15581
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 3.90833 0.473954
\(69\) −3.30278 −0.397607
\(70\) 0 0
\(71\) −12.6972 −1.50688 −0.753442 0.657515i \(-0.771608\pi\)
−0.753442 + 0.657515i \(0.771608\pi\)
\(72\) 7.90833 0.932005
\(73\) −15.8167 −1.85120 −0.925600 0.378504i \(-0.876439\pi\)
−0.925600 + 0.378504i \(0.876439\pi\)
\(74\) −8.00000 −0.929981
\(75\) 0 0
\(76\) −4.90833 −0.563024
\(77\) −1.60555 −0.182970
\(78\) −1.00000 −0.113228
\(79\) 14.4222 1.62262 0.811312 0.584613i \(-0.198754\pi\)
0.811312 + 0.584613i \(0.198754\pi\)
\(80\) 0 0
\(81\) 29.8167 3.31296
\(82\) −9.90833 −1.09419
\(83\) 3.21110 0.352464 0.176232 0.984349i \(-0.443609\pi\)
0.176232 + 0.984349i \(0.443609\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −5.21110 −0.561928
\(87\) −15.2111 −1.63080
\(88\) −5.30278 −0.565278
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0.0916731 0.00960995
\(92\) 1.00000 0.104257
\(93\) −9.60555 −0.996049
\(94\) −4.60555 −0.475026
\(95\) 0 0
\(96\) −3.30278 −0.337088
\(97\) −2.69722 −0.273862 −0.136931 0.990581i \(-0.543724\pi\)
−0.136931 + 0.990581i \(0.543724\pi\)
\(98\) −6.90833 −0.697846
\(99\) −41.9361 −4.21473
\(100\) 0 0
\(101\) −4.60555 −0.458269 −0.229135 0.973395i \(-0.573590\pi\)
−0.229135 + 0.973395i \(0.573590\pi\)
\(102\) −12.9083 −1.27811
\(103\) 17.1194 1.68683 0.843414 0.537265i \(-0.180542\pi\)
0.843414 + 0.537265i \(0.180542\pi\)
\(104\) 0.302776 0.0296896
\(105\) 0 0
\(106\) −3.21110 −0.311890
\(107\) −4.60555 −0.445235 −0.222618 0.974906i \(-0.571460\pi\)
−0.222618 + 0.974906i \(0.571460\pi\)
\(108\) −16.2111 −1.55991
\(109\) 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
\(112\) 0.302776 0.0286096
\(113\) −12.4222 −1.16858 −0.584291 0.811544i \(-0.698627\pi\)
−0.584291 + 0.811544i \(0.698627\pi\)
\(114\) 16.2111 1.51831
\(115\) 0 0
\(116\) 4.60555 0.427615
\(117\) 2.39445 0.221367
\(118\) −10.6056 −0.976320
\(119\) 1.18335 0.108477
\(120\) 0 0
\(121\) 17.1194 1.55631
\(122\) −6.51388 −0.589739
\(123\) 32.7250 2.95071
\(124\) 2.90833 0.261175
\(125\) 0 0
\(126\) 2.39445 0.213314
\(127\) 11.8167 1.04856 0.524279 0.851546i \(-0.324335\pi\)
0.524279 + 0.851546i \(0.324335\pi\)
\(128\) 1.00000 0.0883883
\(129\) 17.2111 1.51535
\(130\) 0 0
\(131\) 3.21110 0.280555 0.140278 0.990112i \(-0.455200\pi\)
0.140278 + 0.990112i \(0.455200\pi\)
\(132\) 17.5139 1.52439
\(133\) −1.48612 −0.128863
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 3.90833 0.335136
\(137\) 6.90833 0.590218 0.295109 0.955464i \(-0.404644\pi\)
0.295109 + 0.955464i \(0.404644\pi\)
\(138\) −3.30278 −0.281151
\(139\) −5.39445 −0.457551 −0.228776 0.973479i \(-0.573472\pi\)
−0.228776 + 0.973479i \(0.573472\pi\)
\(140\) 0 0
\(141\) 15.2111 1.28101
\(142\) −12.6972 −1.06553
\(143\) −1.60555 −0.134263
\(144\) 7.90833 0.659027
\(145\) 0 0
\(146\) −15.8167 −1.30900
\(147\) 22.8167 1.88189
\(148\) −8.00000 −0.657596
\(149\) 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 \(-0.524741\pi\)
−0.0776487 + 0.996981i \(0.524741\pi\)
\(152\) −4.90833 −0.398118
\(153\) 30.9083 2.49879
\(154\) −1.60555 −0.129379
\(155\) 0 0
\(156\) −1.00000 −0.0800641
\(157\) 11.3944 0.909376 0.454688 0.890651i \(-0.349751\pi\)
0.454688 + 0.890651i \(0.349751\pi\)
\(158\) 14.4222 1.14737
\(159\) 10.6056 0.841075
\(160\) 0 0
\(161\) 0.302776 0.0238621
\(162\) 29.8167 2.34262
\(163\) −5.69722 −0.446241 −0.223121 0.974791i \(-0.571624\pi\)
−0.223121 + 0.974791i \(0.571624\pi\)
\(164\) −9.90833 −0.773710
\(165\) 0 0
\(166\) 3.21110 0.249230
\(167\) −21.2111 −1.64136 −0.820682 0.571385i \(-0.806406\pi\)
−0.820682 + 0.571385i \(0.806406\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.9083 −0.992948
\(170\) 0 0
\(171\) −38.8167 −2.96838
\(172\) −5.21110 −0.397343
\(173\) −23.3028 −1.77168 −0.885839 0.463993i \(-0.846416\pi\)
−0.885839 + 0.463993i \(0.846416\pi\)
\(174\) −15.2111 −1.15315
\(175\) 0 0
\(176\) −5.30278 −0.399712
\(177\) 35.0278 2.63285
\(178\) 0 0
\(179\) 16.6056 1.24116 0.620579 0.784144i \(-0.286898\pi\)
0.620579 + 0.784144i \(0.286898\pi\)
\(180\) 0 0
\(181\) −8.11943 −0.603512 −0.301756 0.953385i \(-0.597573\pi\)
−0.301756 + 0.953385i \(0.597573\pi\)
\(182\) 0.0916731 0.00679526
\(183\) 21.5139 1.59035
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) −9.60555 −0.704313
\(187\) −20.7250 −1.51556
\(188\) −4.60555 −0.335894
\(189\) −4.90833 −0.357028
\(190\) 0 0
\(191\) −1.39445 −0.100899 −0.0504494 0.998727i \(-0.516065\pi\)
−0.0504494 + 0.998727i \(0.516065\pi\)
\(192\) −3.30278 −0.238357
\(193\) −3.81665 −0.274729 −0.137364 0.990521i \(-0.543863\pi\)
−0.137364 + 0.990521i \(0.543863\pi\)
\(194\) −2.69722 −0.193649
\(195\) 0 0
\(196\) −6.90833 −0.493452
\(197\) −0.697224 −0.0496752 −0.0248376 0.999691i \(-0.507907\pi\)
−0.0248376 + 0.999691i \(0.507907\pi\)
\(198\) −41.9361 −2.98027
\(199\) 8.42221 0.597034 0.298517 0.954404i \(-0.403508\pi\)
0.298517 + 0.954404i \(0.403508\pi\)
\(200\) 0 0
\(201\) −13.2111 −0.931839
\(202\) −4.60555 −0.324045
\(203\) 1.39445 0.0978711
\(204\) −12.9083 −0.903764
\(205\) 0 0
\(206\) 17.1194 1.19277
\(207\) 7.90833 0.549667
\(208\) 0.302776 0.0209937
\(209\) 26.0278 1.80038
\(210\) 0 0
\(211\) −7.21110 −0.496433 −0.248216 0.968705i \(-0.579844\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(212\) −3.21110 −0.220539
\(213\) 41.9361 2.87341
\(214\) −4.60555 −0.314829
\(215\) 0 0
\(216\) −16.2111 −1.10303
\(217\) 0.880571 0.0597770
\(218\) 19.5139 1.32165
\(219\) 52.2389 3.52997
\(220\) 0 0
\(221\) 1.18335 0.0796005
\(222\) 26.4222 1.77334
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0.302776 0.0202300
\(225\) 0 0
\(226\) −12.4222 −0.826313
\(227\) 7.39445 0.490787 0.245393 0.969424i \(-0.421083\pi\)
0.245393 + 0.969424i \(0.421083\pi\)
\(228\) 16.2111 1.07361
\(229\) 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
\(232\) 4.60555 0.302369
\(233\) −4.18335 −0.274060 −0.137030 0.990567i \(-0.543756\pi\)
−0.137030 + 0.990567i \(0.543756\pi\)
\(234\) 2.39445 0.156530
\(235\) 0 0
\(236\) −10.6056 −0.690363
\(237\) −47.6333 −3.09412
\(238\) 1.18335 0.0767049
\(239\) −9.21110 −0.595817 −0.297908 0.954594i \(-0.596289\pi\)
−0.297908 + 0.954594i \(0.596289\pi\)
\(240\) 0 0
\(241\) 14.4222 0.929016 0.464508 0.885569i \(-0.346231\pi\)
0.464508 + 0.885569i \(0.346231\pi\)
\(242\) 17.1194 1.10048
\(243\) −49.8444 −3.19752
\(244\) −6.51388 −0.417008
\(245\) 0 0
\(246\) 32.7250 2.08647
\(247\) −1.48612 −0.0945597
\(248\) 2.90833 0.184679
\(249\) −10.6056 −0.672100
\(250\) 0 0
\(251\) −5.51388 −0.348033 −0.174016 0.984743i \(-0.555675\pi\)
−0.174016 + 0.984743i \(0.555675\pi\)
\(252\) 2.39445 0.150836
\(253\) −5.30278 −0.333383
\(254\) 11.8167 0.741443
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −19.8167 −1.23613 −0.618064 0.786127i \(-0.712083\pi\)
−0.618064 + 0.786127i \(0.712083\pi\)
\(258\) 17.2111 1.07152
\(259\) −2.42221 −0.150509
\(260\) 0 0
\(261\) 36.4222 2.25448
\(262\) 3.21110 0.198383
\(263\) 14.5139 0.894964 0.447482 0.894293i \(-0.352321\pi\)
0.447482 + 0.894293i \(0.352321\pi\)
\(264\) 17.5139 1.07790
\(265\) 0 0
\(266\) −1.48612 −0.0911200
\(267\) 0 0
\(268\) 4.00000 0.244339
\(269\) 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 \(-0.561314\pi\)
−0.191433 + 0.981506i \(0.561314\pi\)
\(272\) 3.90833 0.236977
\(273\) −0.302776 −0.0183248
\(274\) 6.90833 0.417347
\(275\) 0 0
\(276\) −3.30278 −0.198804
\(277\) 12.7889 0.768410 0.384205 0.923248i \(-0.374476\pi\)
0.384205 + 0.923248i \(0.374476\pi\)
\(278\) −5.39445 −0.323538
\(279\) 23.0000 1.37697
\(280\) 0 0
\(281\) −19.3944 −1.15698 −0.578488 0.815691i \(-0.696357\pi\)
−0.578488 + 0.815691i \(0.696357\pi\)
\(282\) 15.2111 0.905808
\(283\) −2.00000 −0.118888 −0.0594438 0.998232i \(-0.518933\pi\)
−0.0594438 + 0.998232i \(0.518933\pi\)
\(284\) −12.6972 −0.753442
\(285\) 0 0
\(286\) −1.60555 −0.0949382
\(287\) −3.00000 −0.177084
\(288\) 7.90833 0.466003
\(289\) −1.72498 −0.101469
\(290\) 0 0
\(291\) 8.90833 0.522215
\(292\) −15.8167 −0.925600
\(293\) −8.78890 −0.513453 −0.256726 0.966484i \(-0.582644\pi\)
−0.256726 + 0.966484i \(0.582644\pi\)
\(294\) 22.8167 1.33069
\(295\) 0 0
\(296\) −8.00000 −0.464991
\(297\) 85.9638 4.98813
\(298\) 9.69722 0.561745
\(299\) 0.302776 0.0175100
\(300\) 0 0
\(301\) −1.57779 −0.0909426
\(302\) −1.90833 −0.109812
\(303\) 15.2111 0.873855
\(304\) −4.90833 −0.281512
\(305\) 0 0
\(306\) 30.9083 1.76691
\(307\) 15.3028 0.873376 0.436688 0.899613i \(-0.356151\pi\)
0.436688 + 0.899613i \(0.356151\pi\)
\(308\) −1.60555 −0.0914848
\(309\) −56.5416 −3.21654
\(310\) 0 0
\(311\) −6.42221 −0.364170 −0.182085 0.983283i \(-0.558285\pi\)
−0.182085 + 0.983283i \(0.558285\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 12.7250 0.719258 0.359629 0.933095i \(-0.382903\pi\)
0.359629 + 0.933095i \(0.382903\pi\)
\(314\) 11.3944 0.643026
\(315\) 0 0
\(316\) 14.4222 0.811312
\(317\) 14.7250 0.827037 0.413519 0.910496i \(-0.364300\pi\)
0.413519 + 0.910496i \(0.364300\pi\)
\(318\) 10.6056 0.594730
\(319\) −24.4222 −1.36738
\(320\) 0 0
\(321\) 15.2111 0.849001
\(322\) 0.302776 0.0168730
\(323\) −19.1833 −1.06739
\(324\) 29.8167 1.65648
\(325\) 0 0
\(326\) −5.69722 −0.315540
\(327\) −64.4500 −3.56409
\(328\) −9.90833 −0.547096
\(329\) −1.39445 −0.0768784
\(330\) 0 0
\(331\) 9.39445 0.516366 0.258183 0.966096i \(-0.416876\pi\)
0.258183 + 0.966096i \(0.416876\pi\)
\(332\) 3.21110 0.176232
\(333\) −63.2666 −3.46699
\(334\) −21.2111 −1.16062
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) 4.48612 0.244375 0.122187 0.992507i \(-0.461009\pi\)
0.122187 + 0.992507i \(0.461009\pi\)
\(338\) −12.9083 −0.702120
\(339\) 41.0278 2.22832
\(340\) 0 0
\(341\) −15.4222 −0.835159
\(342\) −38.8167 −2.09896
\(343\) −4.21110 −0.227378
\(344\) −5.21110 −0.280964
\(345\) 0 0
\(346\) −23.3028 −1.25276
\(347\) 25.5416 1.37115 0.685573 0.728004i \(-0.259552\pi\)
0.685573 + 0.728004i \(0.259552\pi\)
\(348\) −15.2111 −0.815401
\(349\) −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
\(352\) −5.30278 −0.282639
\(353\) −18.4222 −0.980515 −0.490258 0.871578i \(-0.663097\pi\)
−0.490258 + 0.871578i \(0.663097\pi\)
\(354\) 35.0278 1.86170
\(355\) 0 0
\(356\) 0 0
\(357\) −3.90833 −0.206851
\(358\) 16.6056 0.877631
\(359\) −3.21110 −0.169476 −0.0847378 0.996403i \(-0.527005\pi\)
−0.0847378 + 0.996403i \(0.527005\pi\)
\(360\) 0 0
\(361\) 5.09167 0.267983
\(362\) −8.11943 −0.426748
\(363\) −56.5416 −2.96767
\(364\) 0.0916731 0.00480498
\(365\) 0 0
\(366\) 21.5139 1.12455
\(367\) −29.2111 −1.52481 −0.762404 0.647102i \(-0.775981\pi\)
−0.762404 + 0.647102i \(0.775981\pi\)
\(368\) 1.00000 0.0521286
\(369\) −78.3583 −4.07917
\(370\) 0 0
\(371\) −0.972244 −0.0504764
\(372\) −9.60555 −0.498025
\(373\) 2.60555 0.134910 0.0674552 0.997722i \(-0.478512\pi\)
0.0674552 + 0.997722i \(0.478512\pi\)
\(374\) −20.7250 −1.07166
\(375\) 0 0
\(376\) −4.60555 −0.237513
\(377\) 1.39445 0.0718178
\(378\) −4.90833 −0.252457
\(379\) 4.09167 0.210175 0.105088 0.994463i \(-0.466488\pi\)
0.105088 + 0.994463i \(0.466488\pi\)
\(380\) 0 0
\(381\) −39.0278 −1.99945
\(382\) −1.39445 −0.0713462
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −3.30278 −0.168544
\(385\) 0 0
\(386\) −3.81665 −0.194263
\(387\) −41.2111 −2.09488
\(388\) −2.69722 −0.136931
\(389\) 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
\(392\) −6.90833 −0.348923
\(393\) −10.6056 −0.534979
\(394\) −0.697224 −0.0351257
\(395\) 0 0
\(396\) −41.9361 −2.10737
\(397\) 21.7250 1.09035 0.545173 0.838324i \(-0.316464\pi\)
0.545173 + 0.838324i \(0.316464\pi\)
\(398\) 8.42221 0.422167
\(399\) 4.90833 0.245724
\(400\) 0 0
\(401\) −1.39445 −0.0696354 −0.0348177 0.999394i \(-0.511085\pi\)
−0.0348177 + 0.999394i \(0.511085\pi\)
\(402\) −13.2111 −0.658910
\(403\) 0.880571 0.0438643
\(404\) −4.60555 −0.229135
\(405\) 0 0
\(406\) 1.39445 0.0692053
\(407\) 42.4222 2.10279
\(408\) −12.9083 −0.639057
\(409\) −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
\(412\) 17.1194 0.843414
\(413\) −3.21110 −0.158008
\(414\) 7.90833 0.388673
\(415\) 0 0
\(416\) 0.302776 0.0148448
\(417\) 17.8167 0.872485
\(418\) 26.0278 1.27306
\(419\) −39.6333 −1.93621 −0.968107 0.250538i \(-0.919393\pi\)
−0.968107 + 0.250538i \(0.919393\pi\)
\(420\) 0 0
\(421\) 34.3028 1.67181 0.835907 0.548870i \(-0.184942\pi\)
0.835907 + 0.548870i \(0.184942\pi\)
\(422\) −7.21110 −0.351031
\(423\) −36.4222 −1.77091
\(424\) −3.21110 −0.155945
\(425\) 0 0
\(426\) 41.9361 2.03181
\(427\) −1.97224 −0.0954436
\(428\) −4.60555 −0.222618
\(429\) 5.30278 0.256020
\(430\) 0 0
\(431\) 20.2389 0.974872 0.487436 0.873159i \(-0.337932\pi\)
0.487436 + 0.873159i \(0.337932\pi\)
\(432\) −16.2111 −0.779957
\(433\) 34.9083 1.67759 0.838794 0.544450i \(-0.183261\pi\)
0.838794 + 0.544450i \(0.183261\pi\)
\(434\) 0.880571 0.0422687
\(435\) 0 0
\(436\) 19.5139 0.934545
\(437\) −4.90833 −0.234797
\(438\) 52.2389 2.49607
\(439\) −18.3028 −0.873544 −0.436772 0.899572i \(-0.643878\pi\)
−0.436772 + 0.899572i \(0.643878\pi\)
\(440\) 0 0
\(441\) −54.6333 −2.60159
\(442\) 1.18335 0.0562860
\(443\) −35.5139 −1.68732 −0.843658 0.536882i \(-0.819602\pi\)
−0.843658 + 0.536882i \(0.819602\pi\)
\(444\) 26.4222 1.25394
\(445\) 0 0
\(446\) 4.00000 0.189405
\(447\) −32.0278 −1.51486
\(448\) 0.302776 0.0143048
\(449\) −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
\(452\) −12.4222 −0.584291
\(453\) 6.30278 0.296130
\(454\) 7.39445 0.347039
\(455\) 0 0
\(456\) 16.2111 0.759154
\(457\) 3.57779 0.167362 0.0836811 0.996493i \(-0.473332\pi\)
0.0836811 + 0.996493i \(0.473332\pi\)
\(458\) 2.00000 0.0934539
\(459\) −63.3583 −2.95731
\(460\) 0 0
\(461\) 31.8167 1.48185 0.740925 0.671588i \(-0.234388\pi\)
0.740925 + 0.671588i \(0.234388\pi\)
\(462\) 5.30278 0.246707
\(463\) 25.6333 1.19128 0.595640 0.803251i \(-0.296898\pi\)
0.595640 + 0.803251i \(0.296898\pi\)
\(464\) 4.60555 0.213807
\(465\) 0 0
\(466\) −4.18335 −0.193790
\(467\) −19.8167 −0.917005 −0.458503 0.888693i \(-0.651614\pi\)
−0.458503 + 0.888693i \(0.651614\pi\)
\(468\) 2.39445 0.110683
\(469\) 1.21110 0.0559235
\(470\) 0 0
\(471\) −37.6333 −1.73405
\(472\) −10.6056 −0.488160
\(473\) 27.6333 1.27058
\(474\) −47.6333 −2.18787
\(475\) 0 0
\(476\) 1.18335 0.0542386
\(477\) −25.3944 −1.16273
\(478\) −9.21110 −0.421306
\(479\) −30.0000 −1.37073 −0.685367 0.728197i \(-0.740358\pi\)
−0.685367 + 0.728197i \(0.740358\pi\)
\(480\) 0 0
\(481\) −2.42221 −0.110443
\(482\) 14.4222 0.656913
\(483\) −1.00000 −0.0455016
\(484\) 17.1194 0.778156
\(485\) 0 0
\(486\) −49.8444 −2.26099
\(487\) 11.8167 0.535464 0.267732 0.963493i \(-0.413726\pi\)
0.267732 + 0.963493i \(0.413726\pi\)
\(488\) −6.51388 −0.294869
\(489\) 18.8167 0.850918
\(490\) 0 0
\(491\) −25.8167 −1.16509 −0.582545 0.812799i \(-0.697943\pi\)
−0.582545 + 0.812799i \(0.697943\pi\)
\(492\) 32.7250 1.47536
\(493\) 18.0000 0.810679
\(494\) −1.48612 −0.0668638
\(495\) 0 0
\(496\) 2.90833 0.130588
\(497\) −3.84441 −0.172445
\(498\) −10.6056 −0.475246
\(499\) 11.6333 0.520778 0.260389 0.965504i \(-0.416149\pi\)
0.260389 + 0.965504i \(0.416149\pi\)
\(500\) 0 0
\(501\) 70.0555 3.12985
\(502\) −5.51388 −0.246096
\(503\) 2.72498 0.121501 0.0607504 0.998153i \(-0.480651\pi\)
0.0607504 + 0.998153i \(0.480651\pi\)
\(504\) 2.39445 0.106657
\(505\) 0 0
\(506\) −5.30278 −0.235737
\(507\) 42.6333 1.89341
\(508\) 11.8167 0.524279
\(509\) 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
\(512\) 1.00000 0.0441942
\(513\) 79.5694 3.51307
\(514\) −19.8167 −0.874075
\(515\) 0 0
\(516\) 17.2111 0.757677
\(517\) 24.4222 1.07409
\(518\) −2.42221 −0.106426
\(519\) 76.9638 3.37834
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 36.4222 1.59416
\(523\) −8.42221 −0.368277 −0.184139 0.982900i \(-0.558950\pi\)
−0.184139 + 0.982900i \(0.558950\pi\)
\(524\) 3.21110 0.140278
\(525\) 0 0
\(526\) 14.5139 0.632835
\(527\) 11.3667 0.495141
\(528\) 17.5139 0.762194
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −83.8722 −3.63974
\(532\) −1.48612 −0.0644316
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) 0 0
\(536\) 4.00000 0.172774
\(537\) −54.8444 −2.36671
\(538\) 25.8167 1.11303
\(539\) 36.6333 1.57791
\(540\) 0 0
\(541\) −28.8444 −1.24012 −0.620059 0.784555i \(-0.712891\pi\)
−0.620059 + 0.784555i \(0.712891\pi\)
\(542\) −6.30278 −0.270727
\(543\) 26.8167 1.15081
\(544\) 3.90833 0.167568
\(545\) 0 0
\(546\) −0.302776 −0.0129576
\(547\) −7.51388 −0.321270 −0.160635 0.987014i \(-0.551354\pi\)
−0.160635 + 0.987014i \(0.551354\pi\)
\(548\) 6.90833 0.295109
\(549\) −51.5139 −2.19856
\(550\) 0 0
\(551\) −22.6056 −0.963029
\(552\) −3.30278 −0.140575
\(553\) 4.36669 0.185691
\(554\) 12.7889 0.543348
\(555\) 0 0
\(556\) −5.39445 −0.228776
\(557\) 6.42221 0.272118 0.136059 0.990701i \(-0.456556\pi\)
0.136059 + 0.990701i \(0.456556\pi\)
\(558\) 23.0000 0.973668
\(559\) −1.57779 −0.0667336
\(560\) 0 0
\(561\) 68.4500 2.88996
\(562\) −19.3944 −0.818105
\(563\) −39.6333 −1.67034 −0.835172 0.549988i \(-0.814632\pi\)
−0.835172 + 0.549988i \(0.814632\pi\)
\(564\) 15.2111 0.640503
\(565\) 0 0
\(566\) −2.00000 −0.0840663
\(567\) 9.02776 0.379130
\(568\) −12.6972 −0.532764
\(569\) −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 \(-0.438886\pi\)
0.190818 + 0.981625i \(0.438886\pi\)
\(572\) −1.60555 −0.0671315
\(573\) 4.60555 0.192400
\(574\) −3.00000 −0.125218
\(575\) 0 0
\(576\) 7.90833 0.329514
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −1.72498 −0.0717497
\(579\) 12.6056 0.523869
\(580\) 0 0
\(581\) 0.972244 0.0403355
\(582\) 8.90833 0.369262
\(583\) 17.0278 0.705218
\(584\) −15.8167 −0.654498
\(585\) 0 0
\(586\) −8.78890 −0.363066
\(587\) 37.5416 1.54951 0.774755 0.632262i \(-0.217873\pi\)
0.774755 + 0.632262i \(0.217873\pi\)
\(588\) 22.8167 0.940943
\(589\) −14.2750 −0.588192
\(590\) 0 0
\(591\) 2.30278 0.0947235
\(592\) −8.00000 −0.328798
\(593\) −19.8167 −0.813772 −0.406886 0.913479i \(-0.633385\pi\)
−0.406886 + 0.913479i \(0.633385\pi\)
\(594\) 85.9638 3.52714
\(595\) 0 0
\(596\) 9.69722 0.397214
\(597\) −27.8167 −1.13846
\(598\) 0.302776 0.0123814
\(599\) 4.33053 0.176941 0.0884704 0.996079i \(-0.471802\pi\)
0.0884704 + 0.996079i \(0.471802\pi\)
\(600\) 0 0
\(601\) −3.93608 −0.160556 −0.0802781 0.996773i \(-0.525581\pi\)
−0.0802781 + 0.996773i \(0.525581\pi\)
\(602\) −1.57779 −0.0643061
\(603\) 31.6333 1.28821
\(604\) −1.90833 −0.0776487
\(605\) 0 0
\(606\) 15.2111 0.617909
\(607\) 26.0555 1.05756 0.528780 0.848759i \(-0.322650\pi\)
0.528780 + 0.848759i \(0.322650\pi\)
\(608\) −4.90833 −0.199059
\(609\) −4.60555 −0.186626
\(610\) 0 0
\(611\) −1.39445 −0.0564134
\(612\) 30.9083 1.24940
\(613\) −32.4222 −1.30952 −0.654760 0.755837i \(-0.727230\pi\)
−0.654760 + 0.755837i \(0.727230\pi\)
\(614\) 15.3028 0.617570
\(615\) 0 0
\(616\) −1.60555 −0.0646895
\(617\) −8.09167 −0.325758 −0.162879 0.986646i \(-0.552078\pi\)
−0.162879 + 0.986646i \(0.552078\pi\)
\(618\) −56.5416 −2.27444
\(619\) 27.3305 1.09851 0.549253 0.835656i \(-0.314912\pi\)
0.549253 + 0.835656i \(0.314912\pi\)
\(620\) 0 0
\(621\) −16.2111 −0.650529
\(622\) −6.42221 −0.257507
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) 0 0
\(626\) 12.7250 0.508593
\(627\) −85.9638 −3.43307
\(628\) 11.3944 0.454688
\(629\) −31.2666 −1.24668
\(630\) 0 0
\(631\) 30.6056 1.21839 0.609194 0.793021i \(-0.291493\pi\)
0.609194 + 0.793021i \(0.291493\pi\)
\(632\) 14.4222 0.573685
\(633\) 23.8167 0.946627
\(634\) 14.7250 0.584804
\(635\) 0 0
\(636\) 10.6056 0.420537
\(637\) −2.09167 −0.0828751
\(638\) −24.4222 −0.966884
\(639\) −100.414 −3.97231
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) 15.2111 0.600334
\(643\) −16.2389 −0.640398 −0.320199 0.947350i \(-0.603750\pi\)
−0.320199 + 0.947350i \(0.603750\pi\)
\(644\) 0.302776 0.0119310
\(645\) 0 0
\(646\) −19.1833 −0.754759
\(647\) 30.8444 1.21262 0.606309 0.795229i \(-0.292649\pi\)
0.606309 + 0.795229i \(0.292649\pi\)
\(648\) 29.8167 1.17131
\(649\) 56.2389 2.20757
\(650\) 0 0
\(651\) −2.90833 −0.113986
\(652\) −5.69722 −0.223121
\(653\) −9.27502 −0.362960 −0.181480 0.983395i \(-0.558089\pi\)
−0.181480 + 0.983395i \(0.558089\pi\)
\(654\) −64.4500 −2.52019
\(655\) 0 0
\(656\) −9.90833 −0.386855
\(657\) −125.083 −4.87996
\(658\) −1.39445 −0.0543613
\(659\) −27.6333 −1.07644 −0.538220 0.842804i \(-0.680903\pi\)
−0.538220 + 0.842804i \(0.680903\pi\)
\(660\) 0 0
\(661\) −24.0917 −0.937057 −0.468529 0.883448i \(-0.655216\pi\)
−0.468529 + 0.883448i \(0.655216\pi\)
\(662\) 9.39445 0.365126
\(663\) −3.90833 −0.151787
\(664\) 3.21110 0.124615
\(665\) 0 0
\(666\) −63.2666 −2.45153
\(667\) 4.60555 0.178328
\(668\) −21.2111 −0.820682
\(669\) −13.2111 −0.510771
\(670\) 0 0
\(671\) 34.5416 1.33347
\(672\) −1.00000 −0.0385758
\(673\) −5.63331 −0.217148 −0.108574 0.994088i \(-0.534628\pi\)
−0.108574 + 0.994088i \(0.534628\pi\)
\(674\) 4.48612 0.172799
\(675\) 0 0
\(676\) −12.9083 −0.496474
\(677\) 12.4222 0.477424 0.238712 0.971090i \(-0.423275\pi\)
0.238712 + 0.971090i \(0.423275\pi\)
\(678\) 41.0278 1.57566
\(679\) −0.816654 −0.0313403
\(680\) 0 0
\(681\) −24.4222 −0.935861
\(682\) −15.4222 −0.590547
\(683\) 32.7250 1.25219 0.626093 0.779748i \(-0.284653\pi\)
0.626093 + 0.779748i \(0.284653\pi\)
\(684\) −38.8167 −1.48419
\(685\) 0 0
\(686\) −4.21110 −0.160781
\(687\) −6.60555 −0.252018
\(688\) −5.21110 −0.198671
\(689\) −0.972244 −0.0370395
\(690\) 0 0
\(691\) 30.1833 1.14823 0.574114 0.818775i \(-0.305347\pi\)
0.574114 + 0.818775i \(0.305347\pi\)
\(692\) −23.3028 −0.885839
\(693\) −12.6972 −0.482328
\(694\) 25.5416 0.969547
\(695\) 0 0
\(696\) −15.2111 −0.576575
\(697\) −38.7250 −1.46681
\(698\) −12.7889 −0.484067
\(699\) 13.8167 0.522594
\(700\) 0 0
\(701\) 42.9083 1.62063 0.810313 0.585998i \(-0.199297\pi\)
0.810313 + 0.585998i \(0.199297\pi\)
\(702\) −4.90833 −0.185253
\(703\) 39.2666 1.48097
\(704\) −5.30278 −0.199856
\(705\) 0 0
\(706\) −18.4222 −0.693329
\(707\) −1.39445 −0.0524436
\(708\) 35.0278 1.31642
\(709\) −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
\(714\) −3.90833 −0.146265
\(715\) 0 0
\(716\) 16.6056 0.620579
\(717\) 30.4222 1.13614
\(718\) −3.21110 −0.119837
\(719\) 14.3028 0.533404 0.266702 0.963779i \(-0.414066\pi\)
0.266702 + 0.963779i \(0.414066\pi\)
\(720\) 0 0
\(721\) 5.18335 0.193038
\(722\) 5.09167 0.189492
\(723\) −47.6333 −1.77150
\(724\) −8.11943 −0.301756
\(725\) 0 0
\(726\) −56.5416 −2.09846
\(727\) 7.90833 0.293304 0.146652 0.989188i \(-0.453150\pi\)
0.146652 + 0.989188i \(0.453150\pi\)
\(728\) 0.0916731 0.00339763
\(729\) 75.1749 2.78426
\(730\) 0 0
\(731\) −20.3667 −0.753289
\(732\) 21.5139 0.795176
\(733\) 13.6333 0.503558 0.251779 0.967785i \(-0.418984\pi\)
0.251779 + 0.967785i \(0.418984\pi\)
\(734\) −29.2111 −1.07820
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −21.2111 −0.781321
\(738\) −78.3583 −2.88441
\(739\) −7.63331 −0.280796 −0.140398 0.990095i \(-0.544838\pi\)
−0.140398 + 0.990095i \(0.544838\pi\)
\(740\) 0 0
\(741\) 4.90833 0.180312
\(742\) −0.972244 −0.0356922
\(743\) −7.33053 −0.268931 −0.134466 0.990918i \(-0.542932\pi\)
−0.134466 + 0.990918i \(0.542932\pi\)
\(744\) −9.60555 −0.352157
\(745\) 0 0
\(746\) 2.60555 0.0953960
\(747\) 25.3944 0.929134
\(748\) −20.7250 −0.757780
\(749\) −1.39445 −0.0509520
\(750\) 0 0
\(751\) 0.183346 0.00669040 0.00334520 0.999994i \(-0.498935\pi\)
0.00334520 + 0.999994i \(0.498935\pi\)
\(752\) −4.60555 −0.167947
\(753\) 18.2111 0.663649
\(754\) 1.39445 0.0507828
\(755\) 0 0
\(756\) −4.90833 −0.178514
\(757\) 1.21110 0.0440183 0.0220091 0.999758i \(-0.492994\pi\)
0.0220091 + 0.999758i \(0.492994\pi\)
\(758\) 4.09167 0.148616
\(759\) 17.5139 0.635714
\(760\) 0 0
\(761\) 4.54163 0.164634 0.0823171 0.996606i \(-0.473768\pi\)
0.0823171 + 0.996606i \(0.473768\pi\)
\(762\) −39.0278 −1.41383
\(763\) 5.90833 0.213896
\(764\) −1.39445 −0.0504494
\(765\) 0 0
\(766\) 0 0
\(767\) −3.21110 −0.115946
\(768\) −3.30278 −0.119179
\(769\) −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
\(772\) −3.81665 −0.137364
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) −41.2111 −1.48130
\(775\) 0 0
\(776\) −2.69722 −0.0968247
\(777\) 8.00000 0.286998
\(778\) 20.9361 0.750595
\(779\) 48.6333 1.74247
\(780\) 0 0
\(781\) 67.3305 2.40928
\(782\) 3.90833 0.139761
\(783\) −74.6611 −2.66817
\(784\) −6.90833 −0.246726
\(785\) 0 0
\(786\) −10.6056 −0.378287
\(787\) 27.4500 0.978485 0.489243 0.872148i \(-0.337273\pi\)
0.489243 + 0.872148i \(0.337273\pi\)
\(788\) −0.697224 −0.0248376
\(789\) −47.9361 −1.70657
\(790\) 0 0
\(791\) −3.76114 −0.133731
\(792\) −41.9361 −1.49013
\(793\) −1.97224 −0.0700364
\(794\) 21.7250 0.770991
\(795\) 0 0
\(796\) 8.42221 0.298517
\(797\) 19.8167 0.701942 0.350971 0.936386i \(-0.385852\pi\)
0.350971 + 0.936386i \(0.385852\pi\)
\(798\) 4.90833 0.173753
\(799\) −18.0000 −0.636794
\(800\) 0 0
\(801\) 0 0
\(802\) −1.39445 −0.0492397
\(803\) 83.8722 2.95978
\(804\) −13.2111 −0.465920
\(805\) 0 0
\(806\) 0.880571 0.0310168
\(807\) −85.2666 −3.00153
\(808\) −4.60555 −0.162023
\(809\) 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 \(-0.527824\pi\)
−0.0872995 + 0.996182i \(0.527824\pi\)
\(812\) 1.39445 0.0489356
\(813\) 20.8167 0.730072
\(814\) 42.4222 1.48690
\(815\) 0 0
\(816\) −12.9083 −0.451882
\(817\) 25.5778 0.894854
\(818\) −15.0917 −0.527668
\(819\) 0.724981 0.0253329
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) −22.8167 −0.795822
\(823\) 0.788897 0.0274992 0.0137496 0.999905i \(-0.495623\pi\)
0.0137496 + 0.999905i \(0.495623\pi\)
\(824\) 17.1194 0.596384
\(825\) 0 0
\(826\) −3.21110 −0.111729
\(827\) −35.4500 −1.23272 −0.616358 0.787466i \(-0.711393\pi\)
−0.616358 + 0.787466i \(0.711393\pi\)
\(828\) 7.90833 0.274833
\(829\) 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
\(832\) 0.302776 0.0104969
\(833\) −27.0000 −0.935495
\(834\) 17.8167 0.616940
\(835\) 0 0
\(836\) 26.0278 0.900189
\(837\) −47.1472 −1.62965
\(838\) −39.6333 −1.36911
\(839\) −22.1833 −0.765854 −0.382927 0.923779i \(-0.625084\pi\)
−0.382927 + 0.923779i \(0.625084\pi\)
\(840\) 0 0
\(841\) −7.78890 −0.268583
\(842\) 34.3028 1.18215
\(843\) 64.0555 2.20619
\(844\) −7.21110 −0.248216
\(845\) 0 0
\(846\) −36.4222 −1.25222
\(847\) 5.18335 0.178102
\(848\) −3.21110 −0.110270
\(849\) 6.60555 0.226702
\(850\) 0 0
\(851\) −8.00000 −0.274236
\(852\) 41.9361 1.43671
\(853\) −10.7250 −0.367216 −0.183608 0.983000i \(-0.558778\pi\)
−0.183608 + 0.983000i \(0.558778\pi\)
\(854\) −1.97224 −0.0674888
\(855\) 0 0
\(856\) −4.60555 −0.157415
\(857\) 33.6333 1.14889 0.574446 0.818543i \(-0.305218\pi\)
0.574446 + 0.818543i \(0.305218\pi\)
\(858\) 5.30278 0.181034
\(859\) −14.1833 −0.483930 −0.241965 0.970285i \(-0.577792\pi\)
−0.241965 + 0.970285i \(0.577792\pi\)
\(860\) 0 0
\(861\) 9.90833 0.337675
\(862\) 20.2389 0.689338
\(863\) −23.4500 −0.798246 −0.399123 0.916897i \(-0.630685\pi\)
−0.399123 + 0.916897i \(0.630685\pi\)
\(864\) −16.2111 −0.551513
\(865\) 0 0
\(866\) 34.9083 1.18623
\(867\) 5.69722 0.193488
\(868\) 0.880571 0.0298885
\(869\) −76.4777 −2.59433
\(870\) 0 0
\(871\) 1.21110 0.0410366
\(872\) 19.5139 0.660823
\(873\) −21.3305 −0.721929
\(874\) −4.90833 −0.166027
\(875\) 0 0
\(876\) 52.2389 1.76499
\(877\) −49.1749 −1.66052 −0.830260 0.557376i \(-0.811808\pi\)
−0.830260 + 0.557376i \(0.811808\pi\)
\(878\) −18.3028 −0.617689
\(879\) 29.0278 0.979082
\(880\) 0 0
\(881\) −31.2666 −1.05340 −0.526700 0.850052i \(-0.676571\pi\)
−0.526700 + 0.850052i \(0.676571\pi\)
\(882\) −54.6333 −1.83960
\(883\) −40.7250 −1.37050 −0.685252 0.728306i \(-0.740308\pi\)
−0.685252 + 0.728306i \(0.740308\pi\)
\(884\) 1.18335 0.0398002
\(885\) 0 0
\(886\) −35.5139 −1.19311
\(887\) 15.6333 0.524915 0.262458 0.964944i \(-0.415467\pi\)
0.262458 + 0.964944i \(0.415467\pi\)
\(888\) 26.4222 0.886671
\(889\) 3.57779 0.119995
\(890\) 0 0
\(891\) −158.111 −5.29692
\(892\) 4.00000 0.133930
\(893\) 22.6056 0.756466
\(894\) −32.0278 −1.07117
\(895\) 0 0
\(896\) 0.302776 0.0101150
\(897\) −1.00000 −0.0333890
\(898\) −12.9083 −0.430756
\(899\) 13.3944 0.446730
\(900\) 0 0
\(901\) −12.5500 −0.418102
\(902\) 52.5416 1.74945
\(903\) 5.21110 0.173415
\(904\) −12.4222 −0.413156
\(905\) 0 0
\(906\) 6.30278 0.209396
\(907\) 30.6611 1.01808 0.509042 0.860742i \(-0.330000\pi\)
0.509042 + 0.860742i \(0.330000\pi\)
\(908\) 7.39445 0.245393
\(909\) −36.4222 −1.20805
\(910\) 0 0
\(911\) −25.8167 −0.855344 −0.427672 0.903934i \(-0.640666\pi\)
−0.427672 + 0.903934i \(0.640666\pi\)
\(912\) 16.2111 0.536803
\(913\) −17.0278 −0.563536
\(914\) 3.57779 0.118343
\(915\) 0 0
\(916\) 2.00000 0.0660819
\(917\) 0.972244 0.0321063
\(918\) −63.3583 −2.09114
\(919\) 44.0000 1.45143 0.725713 0.687998i \(-0.241510\pi\)
0.725713 + 0.687998i \(0.241510\pi\)
\(920\) 0 0
\(921\) −50.5416 −1.66540
\(922\) 31.8167 1.04783
\(923\) −3.84441 −0.126540
\(924\) 5.30278 0.174449
\(925\) 0 0
\(926\) 25.6333 0.842363
\(927\) 135.386 4.44666
\(928\) 4.60555 0.151185
\(929\) −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
\(932\) −4.18335 −0.137030
\(933\) 21.2111 0.694420
\(934\) −19.8167 −0.648421
\(935\) 0 0
\(936\) 2.39445 0.0782650
\(937\) 44.9638 1.46890 0.734452 0.678660i \(-0.237439\pi\)
0.734452 + 0.678660i \(0.237439\pi\)
\(938\) 1.21110 0.0395439
\(939\) −42.0278 −1.37152
\(940\) 0 0
\(941\) −20.9361 −0.682497 −0.341248 0.939973i \(-0.610850\pi\)
−0.341248 + 0.939973i \(0.610850\pi\)
\(942\) −37.6333 −1.22616
\(943\) −9.90833 −0.322660
\(944\) −10.6056 −0.345181
\(945\) 0 0
\(946\) 27.6333 0.898436
\(947\) −41.9361 −1.36274 −0.681370 0.731939i \(-0.738615\pi\)
−0.681370 + 0.731939i \(0.738615\pi\)
\(948\) −47.6333 −1.54706
\(949\) −4.78890 −0.155454
\(950\) 0 0
\(951\) −48.6333 −1.57704
\(952\) 1.18335 0.0383525
\(953\) 1.66947 0.0540794 0.0270397 0.999634i \(-0.491392\pi\)
0.0270397 + 0.999634i \(0.491392\pi\)
\(954\) −25.3944 −0.822176
\(955\) 0 0
\(956\) −9.21110 −0.297908
\(957\) 80.6611 2.60740
\(958\) −30.0000 −0.969256
\(959\) 2.09167 0.0675436
\(960\) 0 0
\(961\) −22.5416 −0.727150
\(962\) −2.42221 −0.0780950
\(963\) −36.4222 −1.17369
\(964\) 14.4222 0.464508
\(965\) 0 0
\(966\) −1.00000 −0.0321745
\(967\) 5.39445 0.173474 0.0867369 0.996231i \(-0.472356\pi\)
0.0867369 + 0.996231i \(0.472356\pi\)
\(968\) 17.1194 0.550239
\(969\) 63.3583 2.03536
\(970\) 0 0
\(971\) −27.9083 −0.895621 −0.447810 0.894129i \(-0.647796\pi\)
−0.447810 + 0.894129i \(0.647796\pi\)
\(972\) −49.8444 −1.59876
\(973\) −1.63331 −0.0523614
\(974\) 11.8167 0.378630
\(975\) 0 0
\(976\) −6.51388 −0.208504
\(977\) 11.5139 0.368362 0.184181 0.982892i \(-0.441037\pi\)
0.184181 + 0.982892i \(0.441037\pi\)
\(978\) 18.8167 0.601690
\(979\) 0 0
\(980\) 0 0
\(981\) 154.322 4.92713
\(982\) −25.8167 −0.823843
\(983\) 19.5416 0.623281 0.311641 0.950200i \(-0.399121\pi\)
0.311641 + 0.950200i \(0.399121\pi\)
\(984\) 32.7250 1.04323
\(985\) 0 0
\(986\) 18.0000 0.573237
\(987\) 4.60555 0.146596
\(988\) −1.48612 −0.0472798
\(989\) −5.21110 −0.165703
\(990\) 0 0
\(991\) 24.3305 0.772885 0.386442 0.922314i \(-0.373704\pi\)
0.386442 + 0.922314i \(0.373704\pi\)
\(992\) 2.90833 0.0923395
\(993\) −31.0278 −0.984636
\(994\) −3.84441 −0.121937
\(995\) 0 0
\(996\) −10.6056 −0.336050
\(997\) 31.2111 0.988466 0.494233 0.869330i \(-0.335449\pi\)
0.494233 + 0.869330i \(0.335449\pi\)
\(998\) 11.6333 0.368246
\(999\) 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 1150.2.a.m.1.1 2
4.3 odd 2 9200.2.a.ca.1.2 2
5.2 odd 4 1150.2.b.f.599.4 4
5.3 odd 4 1150.2.b.f.599.1 4
5.4 even 2 230.2.a.b.1.2 2
15.14 odd 2 2070.2.a.w.1.1 2
20.19 odd 2 1840.2.a.j.1.1 2
40.19 odd 2 7360.2.a.bu.1.2 2
40.29 even 2 7360.2.a.bc.1.1 2
115.114 odd 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 5.4 even 2
1150.2.a.m.1.1 2 1.1 even 1 trivial
1150.2.b.f.599.1 4 5.3 odd 4
1150.2.b.f.599.4 4 5.2 odd 4
1840.2.a.j.1.1 2 20.19 odd 2
2070.2.a.w.1.1 2 15.14 odd 2
5290.2.a.j.1.2 2 115.114 odd 2
7360.2.a.bc.1.1 2 40.29 even 2
7360.2.a.bu.1.2 2 40.19 odd 2
9200.2.a.ca.1.2 2 4.3 odd 2