Properties

Label 5290.2.a.j.1.2
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
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 \(\chi\) \(=\) 5290.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +7.90833 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.30278 q^{6} +0.302776 q^{7} -1.00000 q^{8} +7.90833 q^{9} +1.00000 q^{10} +5.30278 q^{11} +3.30278 q^{12} -0.302776 q^{13} -0.302776 q^{14} -3.30278 q^{15} +1.00000 q^{16} +3.90833 q^{17} -7.90833 q^{18} +4.90833 q^{19} -1.00000 q^{20} +1.00000 q^{21} -5.30278 q^{22} -3.30278 q^{24} +1.00000 q^{25} +0.302776 q^{26} +16.2111 q^{27} +0.302776 q^{28} +4.60555 q^{29} +3.30278 q^{30} +2.90833 q^{31} -1.00000 q^{32} +17.5139 q^{33} -3.90833 q^{34} -0.302776 q^{35} +7.90833 q^{36} -8.00000 q^{37} -4.90833 q^{38} -1.00000 q^{39} +1.00000 q^{40} -9.90833 q^{41} -1.00000 q^{42} -5.21110 q^{43} +5.30278 q^{44} -7.90833 q^{45} +4.60555 q^{47} +3.30278 q^{48} -6.90833 q^{49} -1.00000 q^{50} +12.9083 q^{51} -0.302776 q^{52} -3.21110 q^{53} -16.2111 q^{54} -5.30278 q^{55} -0.302776 q^{56} +16.2111 q^{57} -4.60555 q^{58} -10.6056 q^{59} -3.30278 q^{60} +6.51388 q^{61} -2.90833 q^{62} +2.39445 q^{63} +1.00000 q^{64} +0.302776 q^{65} -17.5139 q^{66} +4.00000 q^{67} +3.90833 q^{68} +0.302776 q^{70} -12.6972 q^{71} -7.90833 q^{72} +15.8167 q^{73} +8.00000 q^{74} +3.30278 q^{75} +4.90833 q^{76} +1.60555 q^{77} +1.00000 q^{78} -14.4222 q^{79} -1.00000 q^{80} +29.8167 q^{81} +9.90833 q^{82} +3.21110 q^{83} +1.00000 q^{84} -3.90833 q^{85} +5.21110 q^{86} +15.2111 q^{87} -5.30278 q^{88} +7.90833 q^{90} -0.0916731 q^{91} +9.60555 q^{93} -4.60555 q^{94} -4.90833 q^{95} -3.30278 q^{96} -2.69722 q^{97} +6.90833 q^{98} +41.9361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + 3q^{3} + 2q^{4} - 2q^{5} - 3q^{6} - 3q^{7} - 2q^{8} + 5q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + 3q^{3} + 2q^{4} - 2q^{5} - 3q^{6} - 3q^{7} - 2q^{8} + 5q^{9} + 2q^{10} + 7q^{11} + 3q^{12} + 3q^{13} + 3q^{14} - 3q^{15} + 2q^{16} - 3q^{17} - 5q^{18} - q^{19} - 2q^{20} + 2q^{21} - 7q^{22} - 3q^{24} + 2q^{25} - 3q^{26} + 18q^{27} - 3q^{28} + 2q^{29} + 3q^{30} - 5q^{31} - 2q^{32} + 17q^{33} + 3q^{34} + 3q^{35} + 5q^{36} - 16q^{37} + q^{38} - 2q^{39} + 2q^{40} - 9q^{41} - 2q^{42} + 4q^{43} + 7q^{44} - 5q^{45} + 2q^{47} + 3q^{48} - 3q^{49} - 2q^{50} + 15q^{51} + 3q^{52} + 8q^{53} - 18q^{54} - 7q^{55} + 3q^{56} + 18q^{57} - 2q^{58} - 14q^{59} - 3q^{60} - 5q^{61} + 5q^{62} + 12q^{63} + 2q^{64} - 3q^{65} - 17q^{66} + 8q^{67} - 3q^{68} - 3q^{70} - 29q^{71} - 5q^{72} + 10q^{73} + 16q^{74} + 3q^{75} - q^{76} - 4q^{77} + 2q^{78} - 2q^{80} + 38q^{81} + 9q^{82} - 8q^{83} + 2q^{84} + 3q^{85} - 4q^{86} + 16q^{87} - 7q^{88} + 5q^{90} - 11q^{91} + 12q^{93} - 2q^{94} + q^{95} - 3q^{96} - 9q^{97} + 3q^{98} + 37q^{99} + O(q^{100}) \)

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 \(-0.0975264\pi\)
0.953429 + 0.301617i \(0.0975264\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −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
\(10\) 1.00000 0.316228
\(11\) 5.30278 1.59885 0.799424 0.600768i \(-0.205138\pi\)
0.799424 + 0.600768i \(0.205138\pi\)
\(12\) 3.30278 0.953429
\(13\) −0.302776 −0.0839749 −0.0419874 0.999118i \(-0.513369\pi\)
−0.0419874 + 0.999118i \(0.513369\pi\)
\(14\) −0.302776 −0.0809202
\(15\) −3.30278 −0.852773
\(16\) 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 \(-0.309638\pi\)
0.563024 + 0.826441i \(0.309638\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) −5.30278 −1.13056
\(23\) 0 0
\(24\) −3.30278 −0.674176
\(25\) 1.00000 0.200000
\(26\) 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 \(0.359354\pi\)
\(30\) 3.30278 0.603002
\(31\) 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
\(35\) −0.302776 −0.0511784
\(36\) 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
\(40\) 1.00000 0.158114
\(41\) −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
\(45\) −7.90833 −1.17890
\(46\) 0 0
\(47\) 4.60555 0.671789 0.335894 0.941900i \(-0.390961\pi\)
0.335894 + 0.941900i \(0.390961\pi\)
\(48\) 3.30278 0.476715
\(49\) −6.90833 −0.986904
\(50\) −1.00000 −0.141421
\(51\) 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
\(55\) −5.30278 −0.715026
\(56\) −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 \(0.742549\pi\)
\(60\) −3.30278 −0.426387
\(61\) 6.51388 0.834017 0.417008 0.908903i \(-0.363079\pi\)
0.417008 + 0.908903i \(0.363079\pi\)
\(62\) −2.90833 −0.369358
\(63\) 2.39445 0.301672
\(64\) 1.00000 0.125000
\(65\) 0.302776 0.0375547
\(66\) −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
\(69\) 0 0
\(70\) 0.302776 0.0361886
\(71\) −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 \(-0.123561\pi\)
0.925600 + 0.378504i \(0.123561\pi\)
\(74\) 8.00000 0.929981
\(75\) 3.30278 0.381372
\(76\) 4.90833 0.563024
\(77\) 1.60555 0.182970
\(78\) 1.00000 0.113228
\(79\) −14.4222 −1.62262 −0.811312 0.584613i \(-0.801246\pi\)
−0.811312 + 0.584613i \(0.801246\pi\)
\(80\) −1.00000 −0.111803
\(81\) 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
\(85\) −3.90833 −0.423918
\(86\) 5.21110 0.561928
\(87\) 15.2111 1.63080
\(88\) −5.30278 −0.565278
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 7.90833 0.833611
\(91\) −0.0916731 −0.00960995
\(92\) 0 0
\(93\) 9.60555 0.996049
\(94\) −4.60555 −0.475026
\(95\) −4.90833 −0.503584
\(96\) −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
\(100\) 1.00000 0.100000
\(101\) −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
\(105\) −1.00000 −0.0975900
\(106\) 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 \(-0.884193\pi\)
−0.934545 + 0.355844i \(0.884193\pi\)
\(110\) 5.30278 0.505600
\(111\) −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
\(120\) 3.30278 0.301501
\(121\) 17.1194 1.55631
\(122\) −6.51388 −0.589739
\(123\) −32.7250 −2.95071
\(124\) 2.90833 0.261175
\(125\) −1.00000 −0.0894427
\(126\) −2.39445 −0.213314
\(127\) −11.8167 −1.04856 −0.524279 0.851546i \(-0.675665\pi\)
−0.524279 + 0.851546i \(0.675665\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −17.2111 −1.51535
\(130\) −0.302776 −0.0265552
\(131\) 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
\(135\) −16.2111 −1.39523
\(136\) −3.90833 −0.335136
\(137\) 6.90833 0.590218 0.295109 0.955464i \(-0.404644\pi\)
0.295109 + 0.955464i \(0.404644\pi\)
\(138\) 0 0
\(139\) −5.39445 −0.457551 −0.228776 0.973479i \(-0.573472\pi\)
−0.228776 + 0.973479i \(0.573472\pi\)
\(140\) −0.302776 −0.0255892
\(141\) 15.2111 1.28101
\(142\) 12.6972 1.06553
\(143\) −1.60555 −0.134263
\(144\) 7.90833 0.659027
\(145\) −4.60555 −0.382470
\(146\) −15.8167 −1.30900
\(147\) −22.8167 −1.88189
\(148\) −8.00000 −0.657596
\(149\) −9.69722 −0.794428 −0.397214 0.917726i \(-0.630023\pi\)
−0.397214 + 0.917726i \(0.630023\pi\)
\(150\) −3.30278 −0.269671
\(151\) −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
\(155\) −2.90833 −0.233602
\(156\) −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
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −29.8167 −2.34262
\(163\) 5.69722 0.446241 0.223121 0.974791i \(-0.428376\pi\)
0.223121 + 0.974791i \(0.428376\pi\)
\(164\) −9.90833 −0.773710
\(165\) −17.5139 −1.36345
\(166\) −3.21110 −0.249230
\(167\) 21.2111 1.64136 0.820682 0.571385i \(-0.193594\pi\)
0.820682 + 0.571385i \(0.193594\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.9083 −0.992948
\(170\) 3.90833 0.299755
\(171\) 38.8167 2.96838
\(172\) −5.21110 −0.397343
\(173\) 23.3028 1.77168 0.885839 0.463993i \(-0.153584\pi\)
0.885839 + 0.463993i \(0.153584\pi\)
\(174\) −15.2111 −1.15315
\(175\) 0.302776 0.0228877
\(176\) 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 \(0.286898\pi\)
\(180\) −7.90833 −0.589452
\(181\) 8.11943 0.603512 0.301756 0.953385i \(-0.402427\pi\)
0.301756 + 0.953385i \(0.402427\pi\)
\(182\) 0.0916731 0.00679526
\(183\) 21.5139 1.59035
\(184\) 0 0
\(185\) 8.00000 0.588172
\(186\) −9.60555 −0.704313
\(187\) 20.7250 1.51556
\(188\) 4.60555 0.335894
\(189\) 4.90833 0.357028
\(190\) 4.90833 0.356087
\(191\) 1.39445 0.100899 0.0504494 0.998727i \(-0.483935\pi\)
0.0504494 + 0.998727i \(0.483935\pi\)
\(192\) 3.30278 0.238357
\(193\) 3.81665 0.274729 0.137364 0.990521i \(-0.456137\pi\)
0.137364 + 0.990521i \(0.456137\pi\)
\(194\) 2.69722 0.193649
\(195\) 1.00000 0.0716115
\(196\) −6.90833 −0.493452
\(197\) 0.697224 0.0496752 0.0248376 0.999691i \(-0.492093\pi\)
0.0248376 + 0.999691i \(0.492093\pi\)
\(198\) −41.9361 −2.98027
\(199\) −8.42221 −0.597034 −0.298517 0.954404i \(-0.596492\pi\)
−0.298517 + 0.954404i \(0.596492\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 13.2111 0.931839
\(202\) 4.60555 0.324045
\(203\) 1.39445 0.0978711
\(204\) 12.9083 0.903764
\(205\) 9.90833 0.692028
\(206\) −17.1194 −1.19277
\(207\) 0 0
\(208\) −0.302776 −0.0209937
\(209\) 26.0278 1.80038
\(210\) 1.00000 0.0690066
\(211\) −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
\(215\) 5.21110 0.355394
\(216\) −16.2111 −1.10303
\(217\) 0.880571 0.0597770
\(218\) 19.5139 1.32165
\(219\) 52.2389 3.52997
\(220\) −5.30278 −0.357513
\(221\) −1.18335 −0.0796005
\(222\) 26.4222 1.77334
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) −0.302776 −0.0202300
\(225\) 7.90833 0.527222
\(226\) 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 \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 5.30278 0.348897
\(232\) −4.60555 −0.302369
\(233\) 4.18335 0.274060 0.137030 0.990567i \(-0.456244\pi\)
0.137030 + 0.990567i \(0.456244\pi\)
\(234\) 2.39445 0.156530
\(235\) −4.60555 −0.300433
\(236\) −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 \(0.596289\pi\)
\(240\) −3.30278 −0.213193
\(241\) −14.4222 −0.929016 −0.464508 0.885569i \(-0.653769\pi\)
−0.464508 + 0.885569i \(0.653769\pi\)
\(242\) −17.1194 −1.10048
\(243\) 49.8444 3.19752
\(244\) 6.51388 0.417008
\(245\) 6.90833 0.441357
\(246\) 32.7250 2.08647
\(247\) −1.48612 −0.0945597
\(248\) −2.90833 −0.184679
\(249\) 10.6056 0.672100
\(250\) 1.00000 0.0632456
\(251\) 5.51388 0.348033 0.174016 0.984743i \(-0.444325\pi\)
0.174016 + 0.984743i \(0.444325\pi\)
\(252\) 2.39445 0.150836
\(253\) 0 0
\(254\) 11.8167 0.741443
\(255\) −12.9083 −0.808351
\(256\) 1.00000 0.0625000
\(257\) 19.8167 1.23613 0.618064 0.786127i \(-0.287917\pi\)
0.618064 + 0.786127i \(0.287917\pi\)
\(258\) 17.2111 1.07152
\(259\) −2.42221 −0.150509
\(260\) 0.302776 0.0187773
\(261\) 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
\(265\) 3.21110 0.197256
\(266\) −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 \(0.211615\pi\)
\(270\) 16.2111 0.986576
\(271\) −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
\(275\) 5.30278 0.319769
\(276\) 0 0
\(277\) −12.7889 −0.768410 −0.384205 0.923248i \(-0.625524\pi\)
−0.384205 + 0.923248i \(0.625524\pi\)
\(278\) 5.39445 0.323538
\(279\) 23.0000 1.37697
\(280\) 0.302776 0.0180943
\(281\) 19.3944 1.15698 0.578488 0.815691i \(-0.303643\pi\)
0.578488 + 0.815691i \(0.303643\pi\)
\(282\) −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
\(285\) −16.2111 −0.960263
\(286\) 1.60555 0.0949382
\(287\) −3.00000 −0.177084
\(288\) −7.90833 −0.466003
\(289\) −1.72498 −0.101469
\(290\) 4.60555 0.270447
\(291\) −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
\(295\) 10.6056 0.617479
\(296\) 8.00000 0.464991
\(297\) 85.9638 4.98813
\(298\) 9.69722 0.561745
\(299\) 0 0
\(300\) 3.30278 0.190686
\(301\) −1.57779 −0.0909426
\(302\) 1.90833 0.109812
\(303\) −15.2111 −0.873855
\(304\) 4.90833 0.281512
\(305\) −6.51388 −0.372984
\(306\) −30.9083 −1.76691
\(307\) −15.3028 −0.873376 −0.436688 0.899613i \(-0.643849\pi\)
−0.436688 + 0.899613i \(0.643849\pi\)
\(308\) 1.60555 0.0914848
\(309\) 56.5416 3.21654
\(310\) 2.90833 0.165182
\(311\) −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
\(315\) −2.39445 −0.134912
\(316\) −14.4222 −0.811312
\(317\) −14.7250 −0.827037 −0.413519 0.910496i \(-0.635700\pi\)
−0.413519 + 0.910496i \(0.635700\pi\)
\(318\) 10.6056 0.594730
\(319\) 24.4222 1.36738
\(320\) −1.00000 −0.0559017
\(321\) −15.2111 −0.849001
\(322\) 0 0
\(323\) 19.1833 1.06739
\(324\) 29.8167 1.65648
\(325\) −0.302776 −0.0167950
\(326\) −5.69722 −0.315540
\(327\) −64.4500 −3.56409
\(328\) 9.90833 0.547096
\(329\) 1.39445 0.0768784
\(330\) 17.5139 0.964107
\(331\) 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
\(335\) −4.00000 −0.218543
\(336\) 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
\(340\) −3.90833 −0.211959
\(341\) 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 \(-0.740448\pi\)
−0.685573 + 0.728004i \(0.740448\pi\)
\(348\) 15.2111 0.815401
\(349\) −12.7889 −0.684574 −0.342287 0.939595i \(-0.611202\pi\)
−0.342287 + 0.939595i \(0.611202\pi\)
\(350\) −0.302776 −0.0161840
\(351\) −4.90833 −0.261987
\(352\) −5.30278 −0.282639
\(353\) 18.4222 0.980515 0.490258 0.871578i \(-0.336903\pi\)
0.490258 + 0.871578i \(0.336903\pi\)
\(354\) 35.0278 1.86170
\(355\) 12.6972 0.673899
\(356\) 0 0
\(357\) 3.90833 0.206851
\(358\) −16.6056 −0.877631
\(359\) 3.21110 0.169476 0.0847378 0.996403i \(-0.472995\pi\)
0.0847378 + 0.996403i \(0.472995\pi\)
\(360\) 7.90833 0.416805
\(361\) 5.09167 0.267983
\(362\) −8.11943 −0.426748
\(363\) 56.5416 2.96767
\(364\) −0.0916731 −0.00480498
\(365\) −15.8167 −0.827881
\(366\) −21.5139 −1.12455
\(367\) −29.2111 −1.52481 −0.762404 0.647102i \(-0.775981\pi\)
−0.762404 + 0.647102i \(0.775981\pi\)
\(368\) 0 0
\(369\) −78.3583 −4.07917
\(370\) −8.00000 −0.415900
\(371\) −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
\(375\) −3.30278 −0.170555
\(376\) −4.60555 −0.237513
\(377\) −1.39445 −0.0718178
\(378\) −4.90833 −0.252457
\(379\) −4.09167 −0.210175 −0.105088 0.994463i \(-0.533512\pi\)
−0.105088 + 0.994463i \(0.533512\pi\)
\(380\) −4.90833 −0.251792
\(381\) −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
\(385\) −1.60555 −0.0818265
\(386\) −3.81665 −0.194263
\(387\) −41.2111 −2.09488
\(388\) −2.69722 −0.136931
\(389\) −20.9361 −1.06150 −0.530751 0.847528i \(-0.678090\pi\)
−0.530751 + 0.847528i \(0.678090\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 0 0
\(392\) 6.90833 0.348923
\(393\) 10.6056 0.534979
\(394\) −0.697224 −0.0351257
\(395\) 14.4222 0.725660
\(396\) 41.9361 2.10737
\(397\) −21.7250 −1.09035 −0.545173 0.838324i \(-0.683536\pi\)
−0.545173 + 0.838324i \(0.683536\pi\)
\(398\) 8.42221 0.422167
\(399\) 4.90833 0.245724
\(400\) 1.00000 0.0500000
\(401\) 1.39445 0.0696354 0.0348177 0.999394i \(-0.488915\pi\)
0.0348177 + 0.999394i \(0.488915\pi\)
\(402\) −13.2111 −0.658910
\(403\) −0.880571 −0.0438643
\(404\) −4.60555 −0.229135
\(405\) −29.8167 −1.48160
\(406\) −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 \(0.621711\pi\)
\(410\) −9.90833 −0.489337
\(411\) 22.8167 1.12546
\(412\) 17.1194 0.843414
\(413\) −3.21110 −0.158008
\(414\) 0 0
\(415\) −3.21110 −0.157627
\(416\) 0.302776 0.0148448
\(417\) −17.8167 −0.872485
\(418\) −26.0278 −1.27306
\(419\) 39.6333 1.93621 0.968107 0.250538i \(-0.0806073\pi\)
0.968107 + 0.250538i \(0.0806073\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −34.3028 −1.67181 −0.835907 0.548870i \(-0.815058\pi\)
−0.835907 + 0.548870i \(0.815058\pi\)
\(422\) 7.21110 0.351031
\(423\) 36.4222 1.77091
\(424\) 3.21110 0.155945
\(425\) 3.90833 0.189582
\(426\) 41.9361 2.03181
\(427\) 1.97224 0.0954436
\(428\) −4.60555 −0.222618
\(429\) −5.30278 −0.256020
\(430\) −5.21110 −0.251302
\(431\) −20.2389 −0.974872 −0.487436 0.873159i \(-0.662068\pi\)
−0.487436 + 0.873159i \(0.662068\pi\)
\(432\) 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
\(435\) −15.2111 −0.729317
\(436\) −19.5139 −0.934545
\(437\) 0 0
\(438\) −52.2389 −2.49607
\(439\) −18.3028 −0.873544 −0.436772 0.899572i \(-0.643878\pi\)
−0.436772 + 0.899572i \(0.643878\pi\)
\(440\) 5.30278 0.252800
\(441\) −54.6333 −2.60159
\(442\) 1.18335 0.0562860
\(443\) 35.5139 1.68732 0.843658 0.536882i \(-0.180398\pi\)
0.843658 + 0.536882i \(0.180398\pi\)
\(444\) −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 \(0.598520\pi\)
\(450\) −7.90833 −0.372802
\(451\) −52.5416 −2.47409
\(452\) −12.4222 −0.584291
\(453\) −6.30278 −0.296130
\(454\) −7.39445 −0.347039
\(455\) 0.0916731 0.00429770
\(456\) −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 \(-0.703102\pi\)
−0.595640 + 0.803251i \(0.703102\pi\)
\(464\) 4.60555 0.213807
\(465\) −9.60555 −0.445447
\(466\) −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
\(470\) 4.60555 0.212438
\(471\) 37.6333 1.73405
\(472\) 10.6056 0.488160
\(473\) −27.6333 −1.27058
\(474\) 47.6333 2.18787
\(475\) 4.90833 0.225209
\(476\) 1.18335 0.0542386
\(477\) −25.3944 −1.16273
\(478\) 9.21110 0.421306
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 3.30278 0.150750
\(481\) 2.42221 0.110443
\(482\) 14.4222 0.656913
\(483\) 0 0
\(484\) 17.1194 0.778156
\(485\) 2.69722 0.122475
\(486\) −49.8444 −2.26099
\(487\) −11.8167 −0.535464 −0.267732 0.963493i \(-0.586274\pi\)
−0.267732 + 0.963493i \(0.586274\pi\)
\(488\) −6.51388 −0.294869
\(489\) 18.8167 0.850918
\(490\) −6.90833 −0.312086
\(491\) −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
\(495\) −41.9361 −1.88489
\(496\) 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 \(0.416149\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 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
\(505\) 4.60555 0.204944
\(506\) 0 0
\(507\) −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 \(0.273647\pi\)
\(510\) 12.9083 0.571590
\(511\) 4.78890 0.211848
\(512\) −1.00000 −0.0441942
\(513\) 79.5694 3.51307
\(514\) −19.8167 −0.874075
\(515\) −17.1194 −0.754372
\(516\) −17.2111 −0.757677
\(517\) 24.4222 1.07409
\(518\) 2.42221 0.106426
\(519\) 76.9638 3.37834
\(520\) −0.302776 −0.0132776
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −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
\(525\) 1.00000 0.0436436
\(526\) −14.5139 −0.632835
\(527\) 11.3667 0.495141
\(528\) 17.5139 0.762194
\(529\) 0 0
\(530\) −3.21110 −0.139481
\(531\) −83.8722 −3.63974
\(532\) 1.48612 0.0644316
\(533\) 3.00000 0.129944
\(534\) 0 0
\(535\) 4.60555 0.199115
\(536\) −4.00000 −0.172774
\(537\) 54.8444 2.36671
\(538\) −25.8167 −1.11303
\(539\) −36.6333 −1.57791
\(540\) −16.2111 −0.697615
\(541\) −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
\(545\) 19.5139 0.835883
\(546\) 0.302776 0.0129576
\(547\) 7.51388 0.321270 0.160635 0.987014i \(-0.448646\pi\)
0.160635 + 0.987014i \(0.448646\pi\)
\(548\) 6.90833 0.295109
\(549\) 51.5139 2.19856
\(550\) −5.30278 −0.226111
\(551\) 22.6056 0.963029
\(552\) 0 0
\(553\) −4.36669 −0.185691
\(554\) 12.7889 0.543348
\(555\) 26.4222 1.12156
\(556\) −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
\(560\) −0.302776 −0.0127946
\(561\) 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
\(565\) 12.4222 0.522606
\(566\) 2.00000 0.0840663
\(567\) 9.02776 0.379130
\(568\) 12.6972 0.532764
\(569\) 0.422205 0.0176998 0.00884988 0.999961i \(-0.497183\pi\)
0.00884988 + 0.999961i \(0.497183\pi\)
\(570\) 16.2111 0.679008
\(571\) −9.11943 −0.381636 −0.190818 0.981625i \(-0.561114\pi\)
−0.190818 + 0.981625i \(0.561114\pi\)
\(572\) −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 \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 1.72498 0.0717497
\(579\) 12.6056 0.523869
\(580\) −4.60555 −0.191235
\(581\) 0.972244 0.0403355
\(582\) 8.90833 0.369262
\(583\) −17.0278 −0.705218
\(584\) −15.8167 −0.654498
\(585\) 2.39445 0.0989983
\(586\) 8.78890 0.363066
\(587\) −37.5416 −1.54951 −0.774755 0.632262i \(-0.782127\pi\)
−0.774755 + 0.632262i \(0.782127\pi\)
\(588\) −22.8167 −0.940943
\(589\) 14.2750 0.588192
\(590\) −10.6056 −0.436624
\(591\) 2.30278 0.0947235
\(592\) −8.00000 −0.328798
\(593\) 19.8167 0.813772 0.406886 0.913479i \(-0.366615\pi\)
0.406886 + 0.913479i \(0.366615\pi\)
\(594\) −85.9638 −3.52714
\(595\) −1.18335 −0.0485125
\(596\) −9.69722 −0.397214
\(597\) −27.8167 −1.13846
\(598\) 0 0
\(599\) 4.33053 0.176941 0.0884704 0.996079i \(-0.471802\pi\)
0.0884704 + 0.996079i \(0.471802\pi\)
\(600\) −3.30278 −0.134835
\(601\) −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
\(605\) −17.1194 −0.696004
\(606\) 15.2111 0.617909
\(607\) −26.0555 −1.05756 −0.528780 0.848759i \(-0.677350\pi\)
−0.528780 + 0.848759i \(0.677350\pi\)
\(608\) −4.90833 −0.199059
\(609\) 4.60555 0.186626
\(610\) 6.51388 0.263739
\(611\) −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
\(615\) 32.7250 1.31960
\(616\) −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 \(-0.685088\pi\)
−0.549253 + 0.835656i \(0.685088\pi\)
\(620\) −2.90833 −0.116801
\(621\) 0 0
\(622\) 6.42221 0.257507
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) 1.00000 0.0400000
\(626\) −12.7250 −0.508593
\(627\) 85.9638 3.43307
\(628\) 11.3944 0.454688
\(629\) −31.2666 −1.24668
\(630\) 2.39445 0.0953971
\(631\) −30.6056 −1.21839 −0.609194 0.793021i \(-0.708507\pi\)
−0.609194 + 0.793021i \(0.708507\pi\)
\(632\) 14.4222 0.573685
\(633\) −23.8167 −0.946627
\(634\) 14.7250 0.584804
\(635\) 11.8167 0.468930
\(636\) −10.6056 −0.420537
\(637\) 2.09167 0.0828751
\(638\) −24.4222 −0.966884
\(639\) −100.414 −3.97231
\(640\) 1.00000 0.0395285
\(641\) 36.0000 1.42191 0.710957 0.703235i \(-0.248262\pi\)
0.710957 + 0.703235i \(0.248262\pi\)
\(642\) 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 0
\(645\) 17.2111 0.677687
\(646\) −19.1833 −0.754759
\(647\) −30.8444 −1.21262 −0.606309 0.795229i \(-0.707351\pi\)
−0.606309 + 0.795229i \(0.707351\pi\)
\(648\) −29.8167 −1.17131
\(649\) −56.2389 −2.20757
\(650\) 0.302776 0.0118758
\(651\) 2.90833 0.113986
\(652\) 5.69722 0.223121
\(653\) 9.27502 0.362960 0.181480 0.983395i \(-0.441911\pi\)
0.181480 + 0.983395i \(0.441911\pi\)
\(654\) 64.4500 2.52019
\(655\) −3.21110 −0.125468
\(656\) −9.90833 −0.386855
\(657\) 125.083 4.87996
\(658\) −1.39445 −0.0543613
\(659\) 27.6333 1.07644 0.538220 0.842804i \(-0.319097\pi\)
0.538220 + 0.842804i \(0.319097\pi\)
\(660\) −17.5139 −0.681727
\(661\) 24.0917 0.937057 0.468529 0.883448i \(-0.344784\pi\)
0.468529 + 0.883448i \(0.344784\pi\)
\(662\) −9.39445 −0.365126
\(663\) −3.90833 −0.151787
\(664\) −3.21110 −0.124615
\(665\) −1.48612 −0.0576293
\(666\) 63.2666 2.45153
\(667\) 0 0
\(668\) 21.2111 0.820682
\(669\) −13.2111 −0.510771
\(670\) 4.00000 0.154533
\(671\) 34.5416 1.33347
\(672\) −1.00000 −0.0385758
\(673\) 5.63331 0.217148 0.108574 0.994088i \(-0.465372\pi\)
0.108574 + 0.994088i \(0.465372\pi\)
\(674\) −4.48612 −0.172799
\(675\) 16.2111 0.623966
\(676\) −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
\(680\) 3.90833 0.149877
\(681\) 24.4222 0.935861
\(682\) −15.4222 −0.590547
\(683\) −32.7250 −1.25219 −0.626093 0.779748i \(-0.715347\pi\)
−0.626093 + 0.779748i \(0.715347\pi\)
\(684\) 38.8167 1.48419
\(685\) −6.90833 −0.263954
\(686\) 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
\(695\) 5.39445 0.204623
\(696\) −15.2111 −0.576575
\(697\) −38.7250 −1.46681
\(698\) 12.7889 0.484067
\(699\) 13.8167 0.522594
\(700\) 0.302776 0.0114438
\(701\) −42.9083 −1.62063 −0.810313 0.585998i \(-0.800703\pi\)
−0.810313 + 0.585998i \(0.800703\pi\)
\(702\) 4.90833 0.185253
\(703\) −39.2666 −1.48097
\(704\) 5.30278 0.199856
\(705\) −15.2111 −0.572883
\(706\) −18.4222 −0.693329
\(707\) −1.39445 −0.0524436
\(708\) −35.0278 −1.31642
\(709\) 41.1194 1.54427 0.772136 0.635457i \(-0.219188\pi\)
0.772136 + 0.635457i \(0.219188\pi\)
\(710\) −12.6972 −0.476518
\(711\) −114.056 −4.27742
\(712\) 0 0
\(713\) 0 0
\(714\) −3.90833 −0.146265
\(715\) 1.60555 0.0600442
\(716\) 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 \(0.414066\pi\)
\(720\) −7.90833 −0.294726
\(721\) 5.18335 0.193038
\(722\) −5.09167 −0.189492
\(723\) −47.6333 −1.77150
\(724\) 8.11943 0.301756
\(725\) 4.60555 0.171046
\(726\) −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
\(730\) 15.8167 0.585401
\(731\) −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
\(735\) 22.8167 0.841605
\(736\) 0 0
\(737\) 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 \(0.544838\pi\)
\(740\) 8.00000 0.294086
\(741\) −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
\(745\) 9.69722 0.355279
\(746\) −2.60555 −0.0953960
\(747\) 25.3944 0.929134
\(748\) 20.7250 0.757780
\(749\) −1.39445 −0.0509520
\(750\) 3.30278 0.120600
\(751\) −0.183346 −0.00669040 −0.00334520 0.999994i \(-0.501065\pi\)
−0.00334520 + 0.999994i \(0.501065\pi\)
\(752\) 4.60555 0.167947
\(753\) 18.2111 0.663649
\(754\) 1.39445 0.0507828
\(755\) 1.90833 0.0694511
\(756\) 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
\(759\) 0 0
\(760\) 4.90833 0.178044
\(761\) 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
\(765\) −30.9083 −1.11749
\(766\) 0 0
\(767\) 3.21110 0.115946
\(768\) 3.30278 0.119179
\(769\) 41.2666 1.48811 0.744056 0.668117i \(-0.232900\pi\)
0.744056 + 0.668117i \(0.232900\pi\)
\(770\) 1.60555 0.0578601
\(771\) 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
\(775\) 2.90833 0.104470
\(776\) 2.69722 0.0968247
\(777\) −8.00000 −0.286998
\(778\) 20.9361 0.750595
\(779\) −48.6333 −1.74247
\(780\) 1.00000 0.0358057
\(781\) −67.3305 −2.40928
\(782\) 0 0
\(783\) 74.6611 2.66817
\(784\) −6.90833 −0.246726
\(785\) −11.3944 −0.406685
\(786\) −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
\(790\) −14.4222 −0.513119
\(791\) −3.76114 −0.133731
\(792\) −41.9361 −1.49013
\(793\) −1.97224 −0.0700364
\(794\) 21.7250 0.770991
\(795\) 10.6056 0.376140
\(796\) −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
\(800\) −1.00000 −0.0353553
\(801\) 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 \(0.395894\pi\)
\(810\) 29.8167 1.04765
\(811\) −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
\(815\) −5.69722 −0.199565
\(816\) 12.9083 0.451882
\(817\) −25.5778 −0.894854
\(818\) 15.0917 0.527668
\(819\) −0.724981 −0.0253329
\(820\) 9.90833 0.346014
\(821\) −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 \(-0.504377\pi\)
−0.0137496 + 0.999905i \(0.504377\pi\)
\(824\) −17.1194 −0.596384
\(825\) 17.5139 0.609755
\(826\) 3.21110 0.111729
\(827\) −35.4500 −1.23272 −0.616358 0.787466i \(-0.711393\pi\)
−0.616358 + 0.787466i \(0.711393\pi\)
\(828\) 0 0
\(829\) 16.7889 0.583103 0.291551 0.956555i \(-0.405829\pi\)
0.291551 + 0.956555i \(0.405829\pi\)
\(830\) 3.21110 0.111459
\(831\) −42.2389 −1.46525
\(832\) −0.302776 −0.0104969
\(833\) −27.0000 −0.935495
\(834\) 17.8167 0.616940
\(835\) −21.2111 −0.734040
\(836\) 26.0278 0.900189
\(837\) 47.1472 1.62965
\(838\) −39.6333 −1.36911
\(839\) 22.1833 0.765854 0.382927 0.923779i \(-0.374916\pi\)
0.382927 + 0.923779i \(0.374916\pi\)
\(840\) 1.00000 0.0345033
\(841\) −7.78890 −0.268583
\(842\) 34.3028 1.18215
\(843\) 64.0555 2.20619
\(844\) −7.21110 −0.248216
\(845\) 12.9083 0.444060
\(846\) −36.4222 −1.25222
\(847\) 5.18335 0.178102
\(848\) −3.21110 −0.110270
\(849\) −6.60555 −0.226702
\(850\) −3.90833 −0.134055
\(851\) 0 0
\(852\) −41.9361 −1.43671
\(853\) 10.7250 0.367216 0.183608 0.983000i \(-0.441222\pi\)
0.183608 + 0.983000i \(0.441222\pi\)
\(854\) −1.97224 −0.0674888
\(855\) −38.8167 −1.32750
\(856\) 4.60555 0.157415
\(857\) −33.6333 −1.14889 −0.574446 0.818543i \(-0.694782\pi\)
−0.574446 + 0.818543i \(0.694782\pi\)
\(858\) 5.30278 0.181034
\(859\) −14.1833 −0.483930 −0.241965 0.970285i \(-0.577792\pi\)
−0.241965 + 0.970285i \(0.577792\pi\)
\(860\) 5.21110 0.177697
\(861\) −9.90833 −0.337675
\(862\) 20.2389 0.689338
\(863\) 23.4500 0.798246 0.399123 0.916897i \(-0.369315\pi\)
0.399123 + 0.916897i \(0.369315\pi\)
\(864\) −16.2111 −0.551513
\(865\) −23.3028 −0.792318
\(866\) −34.9083 −1.18623
\(867\) −5.69722 −0.193488
\(868\) 0.880571 0.0298885
\(869\) −76.4777 −2.59433
\(870\) 15.2111 0.515705
\(871\) −1.21110 −0.0410366
\(872\) 19.5139 0.660823
\(873\) −21.3305 −0.721929
\(874\) 0 0
\(875\) −0.302776 −0.0102357
\(876\) 52.2389 1.76499
\(877\) 49.1749 1.66052 0.830260 0.557376i \(-0.188192\pi\)
0.830260 + 0.557376i \(0.188192\pi\)
\(878\) 18.3028 0.617689
\(879\) −29.0278 −0.979082
\(880\) −5.30278 −0.178757
\(881\) 31.2666 1.05340 0.526700 0.850052i \(-0.323429\pi\)
0.526700 + 0.850052i \(0.323429\pi\)
\(882\) 54.6333 1.83960
\(883\) 40.7250 1.37050 0.685252 0.728306i \(-0.259692\pi\)
0.685252 + 0.728306i \(0.259692\pi\)
\(884\) −1.18335 −0.0398002
\(885\) 35.0278 1.17745
\(886\) −35.5139 −1.19311
\(887\) −15.6333 −0.524915 −0.262458 0.964944i \(-0.584533\pi\)
−0.262458 + 0.964944i \(0.584533\pi\)
\(888\) 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
\(895\) −16.6056 −0.555062
\(896\) −0.302776 −0.0101150
\(897\) 0 0
\(898\) 12.9083 0.430756
\(899\) 13.3944 0.446730
\(900\) 7.90833 0.263611
\(901\) −12.5500 −0.418102
\(902\) 52.5416 1.74945
\(903\) −5.21110 −0.173415
\(904\) 12.4222 0.413156
\(905\) −8.11943 −0.269899
\(906\) 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
\(910\) −0.0916731 −0.00303893
\(911\) 25.8167 0.855344 0.427672 0.903934i \(-0.359334\pi\)
0.427672 + 0.903934i \(0.359334\pi\)
\(912\) 16.2111 0.536803
\(913\) 17.0278 0.563536
\(914\) −3.57779 −0.118343
\(915\) −21.5139 −0.711227
\(916\) −2.00000 −0.0660819
\(917\) 0.972244 0.0321063
\(918\) −63.3583 −2.09114
\(919\) −44.0000 −1.45143 −0.725713 0.687998i \(-0.758490\pi\)
−0.725713 + 0.687998i \(0.758490\pi\)
\(920\) 0 0
\(921\) −50.5416 −1.66540
\(922\) −31.8167 −1.04783
\(923\) 3.84441 0.126540
\(924\) 5.30278 0.174449
\(925\) −8.00000 −0.263038
\(926\) 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 \(0.894371\pi\)
\(930\) 9.60555 0.314978
\(931\) −33.9083 −1.11130
\(932\) 4.18335 0.137030
\(933\) −21.2111 −0.694420
\(934\) 19.8167 0.648421
\(935\) −20.7250 −0.677779
\(936\) 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
\(940\) −4.60555 −0.150217
\(941\) 20.9361 0.682497 0.341248 0.939973i \(-0.389150\pi\)
0.341248 + 0.939973i \(0.389150\pi\)
\(942\) −37.6333 −1.22616
\(943\) 0 0
\(944\) −10.6056 −0.345181
\(945\) −4.90833 −0.159668
\(946\) 27.6333 0.898436
\(947\) 41.9361 1.36274 0.681370 0.731939i \(-0.261385\pi\)
0.681370 + 0.731939i \(0.261385\pi\)
\(948\) −47.6333 −1.54706
\(949\) −4.78890 −0.155454
\(950\) −4.90833 −0.159247
\(951\) −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
\(955\) −1.39445 −0.0451233
\(956\) −9.21110 −0.297908
\(957\) 80.6611 2.60740
\(958\) −30.0000 −0.969256
\(959\) 2.09167 0.0675436
\(960\) −3.30278 −0.106597
\(961\) −22.5416 −0.727150
\(962\) −2.42221 −0.0780950
\(963\) −36.4222 −1.17369
\(964\) −14.4222 −0.464508
\(965\) −3.81665 −0.122862
\(966\) 0 0
\(967\) −5.39445 −0.173474 −0.0867369 0.996231i \(-0.527644\pi\)
−0.0867369 + 0.996231i \(0.527644\pi\)
\(968\) −17.1194 −0.550239
\(969\) 63.3583 2.03536
\(970\) −2.69722 −0.0866027
\(971\) 27.9083 0.895621 0.447810 0.894129i \(-0.352204\pi\)
0.447810 + 0.894129i \(0.352204\pi\)
\(972\) 49.8444 1.59876
\(973\) −1.63331 −0.0523614
\(974\) 11.8167 0.378630
\(975\) −1.00000 −0.0320256
\(976\) 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
\(980\) 6.90833 0.220678
\(981\) −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
\(985\) −0.697224 −0.0222154
\(986\) −18.0000 −0.573237
\(987\) 4.60555 0.146596
\(988\) −1.48612 −0.0472798
\(989\) 0 0
\(990\) 41.9361 1.33282
\(991\) 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
\(995\) 8.42221 0.267002
\(996\) 10.6056 0.336050
\(997\) −31.2111 −0.988466 −0.494233 0.869330i \(-0.664551\pi\)
−0.494233 + 0.869330i \(0.664551\pi\)
\(998\) −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 5290.2.a.j.1.2 2
23.22 odd 2 230.2.a.b.1.2 2
69.68 even 2 2070.2.a.w.1.1 2
92.91 even 2 1840.2.a.j.1.1 2
115.22 even 4 1150.2.b.f.599.1 4
115.68 even 4 1150.2.b.f.599.4 4
115.114 odd 2 1150.2.a.m.1.1 2
184.45 odd 2 7360.2.a.bc.1.1 2
184.91 even 2 7360.2.a.bu.1.2 2
460.459 even 2 9200.2.a.ca.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.b.1.2 2 23.22 odd 2
1150.2.a.m.1.1 2 115.114 odd 2
1150.2.b.f.599.1 4 115.22 even 4
1150.2.b.f.599.4 4 115.68 even 4
1840.2.a.j.1.1 2 92.91 even 2
2070.2.a.w.1.1 2 69.68 even 2
5290.2.a.j.1.2 2 1.1 even 1 trivial
7360.2.a.bc.1.1 2 184.45 odd 2
7360.2.a.bu.1.2 2 184.91 even 2
9200.2.a.ca.1.2 2 460.459 even 2