Properties

Label 4033.2.a.f.1.17
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.88550 q^{2} +3.14155 q^{3} +1.55513 q^{4} -2.47668 q^{5} -5.92341 q^{6} +4.66231 q^{7} +0.838810 q^{8} +6.86935 q^{9} +O(q^{10})\) \(q-1.88550 q^{2} +3.14155 q^{3} +1.55513 q^{4} -2.47668 q^{5} -5.92341 q^{6} +4.66231 q^{7} +0.838810 q^{8} +6.86935 q^{9} +4.66980 q^{10} -0.962397 q^{11} +4.88551 q^{12} -3.22360 q^{13} -8.79081 q^{14} -7.78063 q^{15} -4.69183 q^{16} -0.966111 q^{17} -12.9522 q^{18} -7.38402 q^{19} -3.85156 q^{20} +14.6469 q^{21} +1.81460 q^{22} +8.81219 q^{23} +2.63517 q^{24} +1.13396 q^{25} +6.07810 q^{26} +12.1558 q^{27} +7.25049 q^{28} -7.87334 q^{29} +14.6704 q^{30} -6.88170 q^{31} +7.16885 q^{32} -3.02342 q^{33} +1.82161 q^{34} -11.5471 q^{35} +10.6827 q^{36} +1.00000 q^{37} +13.9226 q^{38} -10.1271 q^{39} -2.07747 q^{40} +10.1834 q^{41} -27.6168 q^{42} +12.1719 q^{43} -1.49665 q^{44} -17.0132 q^{45} -16.6154 q^{46} +9.31410 q^{47} -14.7396 q^{48} +14.7371 q^{49} -2.13809 q^{50} -3.03509 q^{51} -5.01310 q^{52} +7.66767 q^{53} -22.9198 q^{54} +2.38355 q^{55} +3.91079 q^{56} -23.1973 q^{57} +14.8452 q^{58} +9.29419 q^{59} -12.0999 q^{60} +6.99911 q^{61} +12.9755 q^{62} +32.0271 q^{63} -4.13324 q^{64} +7.98383 q^{65} +5.70068 q^{66} +2.99266 q^{67} -1.50243 q^{68} +27.6839 q^{69} +21.7721 q^{70} +9.33956 q^{71} +5.76208 q^{72} -3.36832 q^{73} -1.88550 q^{74} +3.56240 q^{75} -11.4831 q^{76} -4.48700 q^{77} +19.0947 q^{78} +4.28866 q^{79} +11.6202 q^{80} +17.5799 q^{81} -19.2008 q^{82} -13.4224 q^{83} +22.7778 q^{84} +2.39275 q^{85} -22.9502 q^{86} -24.7345 q^{87} -0.807269 q^{88} +17.4343 q^{89} +32.0785 q^{90} -15.0294 q^{91} +13.7041 q^{92} -21.6192 q^{93} -17.5618 q^{94} +18.2879 q^{95} +22.5213 q^{96} +3.21593 q^{97} -27.7870 q^{98} -6.61105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88550 −1.33325 −0.666626 0.745392i \(-0.732262\pi\)
−0.666626 + 0.745392i \(0.732262\pi\)
\(3\) 3.14155 1.81378 0.906888 0.421371i \(-0.138451\pi\)
0.906888 + 0.421371i \(0.138451\pi\)
\(4\) 1.55513 0.777563
\(5\) −2.47668 −1.10761 −0.553803 0.832648i \(-0.686824\pi\)
−0.553803 + 0.832648i \(0.686824\pi\)
\(6\) −5.92341 −2.41822
\(7\) 4.66231 1.76219 0.881094 0.472941i \(-0.156808\pi\)
0.881094 + 0.472941i \(0.156808\pi\)
\(8\) 0.838810 0.296564
\(9\) 6.86935 2.28978
\(10\) 4.66980 1.47672
\(11\) −0.962397 −0.290174 −0.145087 0.989419i \(-0.546346\pi\)
−0.145087 + 0.989419i \(0.546346\pi\)
\(12\) 4.88551 1.41033
\(13\) −3.22360 −0.894064 −0.447032 0.894518i \(-0.647519\pi\)
−0.447032 + 0.894518i \(0.647519\pi\)
\(14\) −8.79081 −2.34944
\(15\) −7.78063 −2.00895
\(16\) −4.69183 −1.17296
\(17\) −0.966111 −0.234316 −0.117158 0.993113i \(-0.537378\pi\)
−0.117158 + 0.993113i \(0.537378\pi\)
\(18\) −12.9522 −3.05286
\(19\) −7.38402 −1.69401 −0.847005 0.531585i \(-0.821597\pi\)
−0.847005 + 0.531585i \(0.821597\pi\)
\(20\) −3.85156 −0.861234
\(21\) 14.6469 3.19621
\(22\) 1.81460 0.386875
\(23\) 8.81219 1.83747 0.918734 0.394877i \(-0.129213\pi\)
0.918734 + 0.394877i \(0.129213\pi\)
\(24\) 2.63517 0.537901
\(25\) 1.13396 0.226792
\(26\) 6.07810 1.19201
\(27\) 12.1558 2.33938
\(28\) 7.25049 1.37021
\(29\) −7.87334 −1.46204 −0.731021 0.682355i \(-0.760956\pi\)
−0.731021 + 0.682355i \(0.760956\pi\)
\(30\) 14.6704 2.67844
\(31\) −6.88170 −1.23599 −0.617995 0.786182i \(-0.712055\pi\)
−0.617995 + 0.786182i \(0.712055\pi\)
\(32\) 7.16885 1.26729
\(33\) −3.02342 −0.526310
\(34\) 1.82161 0.312403
\(35\) −11.5471 −1.95181
\(36\) 10.6827 1.78045
\(37\) 1.00000 0.164399
\(38\) 13.9226 2.25854
\(39\) −10.1271 −1.62163
\(40\) −2.07747 −0.328476
\(41\) 10.1834 1.59037 0.795187 0.606364i \(-0.207372\pi\)
0.795187 + 0.606364i \(0.207372\pi\)
\(42\) −27.6168 −4.26136
\(43\) 12.1719 1.85620 0.928099 0.372334i \(-0.121442\pi\)
0.928099 + 0.372334i \(0.121442\pi\)
\(44\) −1.49665 −0.225628
\(45\) −17.0132 −2.53618
\(46\) −16.6154 −2.44981
\(47\) 9.31410 1.35860 0.679301 0.733860i \(-0.262283\pi\)
0.679301 + 0.733860i \(0.262283\pi\)
\(48\) −14.7396 −2.12748
\(49\) 14.7371 2.10531
\(50\) −2.13809 −0.302372
\(51\) −3.03509 −0.424997
\(52\) −5.01310 −0.695192
\(53\) 7.66767 1.05324 0.526618 0.850102i \(-0.323460\pi\)
0.526618 + 0.850102i \(0.323460\pi\)
\(54\) −22.9198 −3.11899
\(55\) 2.38355 0.321398
\(56\) 3.91079 0.522602
\(57\) −23.1973 −3.07255
\(58\) 14.8452 1.94927
\(59\) 9.29419 1.21000 0.605000 0.796225i \(-0.293173\pi\)
0.605000 + 0.796225i \(0.293173\pi\)
\(60\) −12.0999 −1.56209
\(61\) 6.99911 0.896145 0.448072 0.893997i \(-0.352111\pi\)
0.448072 + 0.893997i \(0.352111\pi\)
\(62\) 12.9755 1.64789
\(63\) 32.0271 4.03503
\(64\) −4.13324 −0.516655
\(65\) 7.98383 0.990272
\(66\) 5.70068 0.701705
\(67\) 2.99266 0.365612 0.182806 0.983149i \(-0.441482\pi\)
0.182806 + 0.983149i \(0.441482\pi\)
\(68\) −1.50243 −0.182196
\(69\) 27.6839 3.33276
\(70\) 21.7721 2.60226
\(71\) 9.33956 1.10840 0.554201 0.832383i \(-0.313024\pi\)
0.554201 + 0.832383i \(0.313024\pi\)
\(72\) 5.76208 0.679068
\(73\) −3.36832 −0.394232 −0.197116 0.980380i \(-0.563158\pi\)
−0.197116 + 0.980380i \(0.563158\pi\)
\(74\) −1.88550 −0.219185
\(75\) 3.56240 0.411351
\(76\) −11.4831 −1.31720
\(77\) −4.48700 −0.511341
\(78\) 19.0947 2.16205
\(79\) 4.28866 0.482512 0.241256 0.970462i \(-0.422441\pi\)
0.241256 + 0.970462i \(0.422441\pi\)
\(80\) 11.6202 1.29918
\(81\) 17.5799 1.95333
\(82\) −19.2008 −2.12037
\(83\) −13.4224 −1.47330 −0.736650 0.676274i \(-0.763593\pi\)
−0.736650 + 0.676274i \(0.763593\pi\)
\(84\) 22.7778 2.48526
\(85\) 2.39275 0.259530
\(86\) −22.9502 −2.47478
\(87\) −24.7345 −2.65182
\(88\) −0.807269 −0.0860551
\(89\) 17.4343 1.84803 0.924015 0.382356i \(-0.124887\pi\)
0.924015 + 0.382356i \(0.124887\pi\)
\(90\) 32.0785 3.38137
\(91\) −15.0294 −1.57551
\(92\) 13.7041 1.42875
\(93\) −21.6192 −2.24181
\(94\) −17.5618 −1.81136
\(95\) 18.2879 1.87630
\(96\) 22.5213 2.29857
\(97\) 3.21593 0.326528 0.163264 0.986582i \(-0.447798\pi\)
0.163264 + 0.986582i \(0.447798\pi\)
\(98\) −27.7870 −2.80691
\(99\) −6.61105 −0.664435
\(100\) 1.76345 0.176345
\(101\) −1.54359 −0.153593 −0.0767965 0.997047i \(-0.524469\pi\)
−0.0767965 + 0.997047i \(0.524469\pi\)
\(102\) 5.72267 0.566629
\(103\) 11.8362 1.16626 0.583130 0.812379i \(-0.301828\pi\)
0.583130 + 0.812379i \(0.301828\pi\)
\(104\) −2.70398 −0.265147
\(105\) −36.2757 −3.54015
\(106\) −14.4574 −1.40423
\(107\) 4.99090 0.482489 0.241244 0.970464i \(-0.422444\pi\)
0.241244 + 0.970464i \(0.422444\pi\)
\(108\) 18.9038 1.81902
\(109\) −1.00000 −0.0957826
\(110\) −4.49420 −0.428505
\(111\) 3.14155 0.298183
\(112\) −21.8748 −2.06697
\(113\) −10.2072 −0.960211 −0.480105 0.877211i \(-0.659402\pi\)
−0.480105 + 0.877211i \(0.659402\pi\)
\(114\) 43.7386 4.09649
\(115\) −21.8250 −2.03519
\(116\) −12.2440 −1.13683
\(117\) −22.1440 −2.04721
\(118\) −17.5242 −1.61324
\(119\) −4.50431 −0.412909
\(120\) −6.52647 −0.595783
\(121\) −10.0738 −0.915799
\(122\) −13.1969 −1.19479
\(123\) 31.9916 2.88458
\(124\) −10.7019 −0.961061
\(125\) 9.57495 0.856410
\(126\) −60.3872 −5.37972
\(127\) −3.55746 −0.315673 −0.157837 0.987465i \(-0.550452\pi\)
−0.157837 + 0.987465i \(0.550452\pi\)
\(128\) −6.54447 −0.578455
\(129\) 38.2387 3.36673
\(130\) −15.0535 −1.32028
\(131\) −1.35242 −0.118162 −0.0590808 0.998253i \(-0.518817\pi\)
−0.0590808 + 0.998253i \(0.518817\pi\)
\(132\) −4.70180 −0.409240
\(133\) −34.4266 −2.98516
\(134\) −5.64268 −0.487453
\(135\) −30.1060 −2.59111
\(136\) −0.810384 −0.0694898
\(137\) −4.97282 −0.424857 −0.212428 0.977177i \(-0.568137\pi\)
−0.212428 + 0.977177i \(0.568137\pi\)
\(138\) −52.1982 −4.44341
\(139\) 5.83934 0.495287 0.247643 0.968851i \(-0.420344\pi\)
0.247643 + 0.968851i \(0.420344\pi\)
\(140\) −17.9572 −1.51766
\(141\) 29.2607 2.46420
\(142\) −17.6098 −1.47778
\(143\) 3.10238 0.259434
\(144\) −32.2299 −2.68582
\(145\) 19.4998 1.61937
\(146\) 6.35099 0.525612
\(147\) 46.2975 3.81855
\(148\) 1.55513 0.127831
\(149\) −19.3627 −1.58625 −0.793126 0.609058i \(-0.791548\pi\)
−0.793126 + 0.609058i \(0.791548\pi\)
\(150\) −6.71692 −0.548434
\(151\) 3.83050 0.311722 0.155861 0.987779i \(-0.450185\pi\)
0.155861 + 0.987779i \(0.450185\pi\)
\(152\) −6.19379 −0.502383
\(153\) −6.63656 −0.536534
\(154\) 8.46025 0.681746
\(155\) 17.0438 1.36899
\(156\) −15.7489 −1.26092
\(157\) −0.535485 −0.0427364 −0.0213682 0.999772i \(-0.506802\pi\)
−0.0213682 + 0.999772i \(0.506802\pi\)
\(158\) −8.08629 −0.643310
\(159\) 24.0884 1.91033
\(160\) −17.7550 −1.40365
\(161\) 41.0852 3.23796
\(162\) −33.1471 −2.60428
\(163\) −12.5476 −0.982805 −0.491403 0.870933i \(-0.663516\pi\)
−0.491403 + 0.870933i \(0.663516\pi\)
\(164\) 15.8364 1.23662
\(165\) 7.48806 0.582945
\(166\) 25.3080 1.96428
\(167\) 3.36955 0.260744 0.130372 0.991465i \(-0.458383\pi\)
0.130372 + 0.991465i \(0.458383\pi\)
\(168\) 12.2860 0.947883
\(169\) −2.60843 −0.200649
\(170\) −4.51154 −0.346020
\(171\) −50.7234 −3.87892
\(172\) 18.9289 1.44331
\(173\) 6.39975 0.486564 0.243282 0.969956i \(-0.421776\pi\)
0.243282 + 0.969956i \(0.421776\pi\)
\(174\) 46.6370 3.53554
\(175\) 5.28688 0.399651
\(176\) 4.51541 0.340362
\(177\) 29.1982 2.19467
\(178\) −32.8724 −2.46389
\(179\) 16.6011 1.24083 0.620413 0.784275i \(-0.286965\pi\)
0.620413 + 0.784275i \(0.286965\pi\)
\(180\) −26.4577 −1.97204
\(181\) −7.44531 −0.553405 −0.276703 0.960956i \(-0.589242\pi\)
−0.276703 + 0.960956i \(0.589242\pi\)
\(182\) 28.3380 2.10055
\(183\) 21.9881 1.62541
\(184\) 7.39175 0.544927
\(185\) −2.47668 −0.182089
\(186\) 40.7632 2.98890
\(187\) 0.929783 0.0679924
\(188\) 14.4846 1.05640
\(189\) 56.6740 4.12243
\(190\) −34.4819 −2.50158
\(191\) 4.04583 0.292746 0.146373 0.989229i \(-0.453240\pi\)
0.146373 + 0.989229i \(0.453240\pi\)
\(192\) −12.9848 −0.937096
\(193\) 15.0082 1.08031 0.540156 0.841565i \(-0.318365\pi\)
0.540156 + 0.841565i \(0.318365\pi\)
\(194\) −6.06365 −0.435345
\(195\) 25.0816 1.79613
\(196\) 22.9181 1.63701
\(197\) 12.7603 0.909136 0.454568 0.890712i \(-0.349794\pi\)
0.454568 + 0.890712i \(0.349794\pi\)
\(198\) 12.4652 0.885860
\(199\) 9.39122 0.665726 0.332863 0.942975i \(-0.391985\pi\)
0.332863 + 0.942975i \(0.391985\pi\)
\(200\) 0.951179 0.0672585
\(201\) 9.40161 0.663138
\(202\) 2.91045 0.204778
\(203\) −36.7079 −2.57639
\(204\) −4.71995 −0.330462
\(205\) −25.2210 −1.76151
\(206\) −22.3173 −1.55492
\(207\) 60.5340 4.20741
\(208\) 15.1246 1.04870
\(209\) 7.10636 0.491557
\(210\) 68.3980 4.71991
\(211\) −1.81639 −0.125045 −0.0625227 0.998044i \(-0.519915\pi\)
−0.0625227 + 0.998044i \(0.519915\pi\)
\(212\) 11.9242 0.818957
\(213\) 29.3407 2.01039
\(214\) −9.41037 −0.643280
\(215\) −30.1460 −2.05594
\(216\) 10.1964 0.693776
\(217\) −32.0846 −2.17805
\(218\) 1.88550 0.127702
\(219\) −10.5818 −0.715050
\(220\) 3.70673 0.249908
\(221\) 3.11435 0.209494
\(222\) −5.92341 −0.397553
\(223\) 3.18174 0.213065 0.106532 0.994309i \(-0.466025\pi\)
0.106532 + 0.994309i \(0.466025\pi\)
\(224\) 33.4234 2.23320
\(225\) 7.78958 0.519306
\(226\) 19.2457 1.28020
\(227\) −2.08476 −0.138370 −0.0691852 0.997604i \(-0.522040\pi\)
−0.0691852 + 0.997604i \(0.522040\pi\)
\(228\) −36.0747 −2.38911
\(229\) −26.9614 −1.78166 −0.890831 0.454335i \(-0.849877\pi\)
−0.890831 + 0.454335i \(0.849877\pi\)
\(230\) 41.1511 2.71343
\(231\) −14.0961 −0.927457
\(232\) −6.60423 −0.433589
\(233\) −15.1250 −0.990870 −0.495435 0.868645i \(-0.664991\pi\)
−0.495435 + 0.868645i \(0.664991\pi\)
\(234\) 41.7526 2.72946
\(235\) −23.0681 −1.50480
\(236\) 14.4536 0.940852
\(237\) 13.4731 0.875169
\(238\) 8.49290 0.550513
\(239\) −11.0264 −0.713239 −0.356620 0.934250i \(-0.616071\pi\)
−0.356620 + 0.934250i \(0.616071\pi\)
\(240\) 36.5054 2.35642
\(241\) −8.84780 −0.569937 −0.284969 0.958537i \(-0.591983\pi\)
−0.284969 + 0.958537i \(0.591983\pi\)
\(242\) 18.9942 1.22099
\(243\) 18.7610 1.20352
\(244\) 10.8845 0.696809
\(245\) −36.4992 −2.33185
\(246\) −60.3203 −3.84588
\(247\) 23.8031 1.51455
\(248\) −5.77244 −0.366551
\(249\) −42.1672 −2.67224
\(250\) −18.0536 −1.14181
\(251\) 30.9323 1.95243 0.976215 0.216804i \(-0.0695632\pi\)
0.976215 + 0.216804i \(0.0695632\pi\)
\(252\) 49.8061 3.13749
\(253\) −8.48083 −0.533185
\(254\) 6.70760 0.420872
\(255\) 7.51695 0.470730
\(256\) 20.6061 1.28788
\(257\) 3.76602 0.234918 0.117459 0.993078i \(-0.462525\pi\)
0.117459 + 0.993078i \(0.462525\pi\)
\(258\) −72.0992 −4.48870
\(259\) 4.66231 0.289702
\(260\) 12.4159 0.769999
\(261\) −54.0847 −3.34776
\(262\) 2.54999 0.157539
\(263\) 21.7434 1.34075 0.670377 0.742021i \(-0.266132\pi\)
0.670377 + 0.742021i \(0.266132\pi\)
\(264\) −2.53608 −0.156085
\(265\) −18.9904 −1.16657
\(266\) 64.9115 3.97998
\(267\) 54.7707 3.35191
\(268\) 4.65397 0.284287
\(269\) 21.9524 1.33846 0.669231 0.743054i \(-0.266624\pi\)
0.669231 + 0.743054i \(0.266624\pi\)
\(270\) 56.7650 3.45461
\(271\) 25.0407 1.52112 0.760558 0.649270i \(-0.224925\pi\)
0.760558 + 0.649270i \(0.224925\pi\)
\(272\) 4.53283 0.274843
\(273\) −47.2157 −2.85762
\(274\) 9.37627 0.566441
\(275\) −1.09132 −0.0658092
\(276\) 43.0521 2.59143
\(277\) −1.11436 −0.0669556 −0.0334778 0.999439i \(-0.510658\pi\)
−0.0334778 + 0.999439i \(0.510658\pi\)
\(278\) −11.0101 −0.660343
\(279\) −47.2729 −2.83015
\(280\) −9.68580 −0.578837
\(281\) 6.28813 0.375119 0.187559 0.982253i \(-0.439942\pi\)
0.187559 + 0.982253i \(0.439942\pi\)
\(282\) −55.1713 −3.28540
\(283\) −19.4081 −1.15369 −0.576845 0.816854i \(-0.695716\pi\)
−0.576845 + 0.816854i \(0.695716\pi\)
\(284\) 14.5242 0.861853
\(285\) 57.4523 3.40318
\(286\) −5.84955 −0.345891
\(287\) 47.4780 2.80254
\(288\) 49.2454 2.90181
\(289\) −16.0666 −0.945096
\(290\) −36.7669 −2.15903
\(291\) 10.1030 0.592249
\(292\) −5.23817 −0.306541
\(293\) 4.23655 0.247502 0.123751 0.992313i \(-0.460508\pi\)
0.123751 + 0.992313i \(0.460508\pi\)
\(294\) −87.2942 −5.09110
\(295\) −23.0188 −1.34020
\(296\) 0.838810 0.0487549
\(297\) −11.6987 −0.678827
\(298\) 36.5084 2.11488
\(299\) −28.4069 −1.64281
\(300\) 5.53999 0.319851
\(301\) 56.7492 3.27097
\(302\) −7.22243 −0.415604
\(303\) −4.84927 −0.278583
\(304\) 34.6446 1.98700
\(305\) −17.3346 −0.992576
\(306\) 12.5133 0.715335
\(307\) −23.3781 −1.33426 −0.667130 0.744941i \(-0.732478\pi\)
−0.667130 + 0.744941i \(0.732478\pi\)
\(308\) −6.97785 −0.397600
\(309\) 37.1842 2.11533
\(310\) −32.1362 −1.82521
\(311\) 16.6144 0.942119 0.471059 0.882101i \(-0.343872\pi\)
0.471059 + 0.882101i \(0.343872\pi\)
\(312\) −8.49471 −0.480918
\(313\) 6.00130 0.339214 0.169607 0.985512i \(-0.445750\pi\)
0.169607 + 0.985512i \(0.445750\pi\)
\(314\) 1.00966 0.0569784
\(315\) −79.3209 −4.46923
\(316\) 6.66941 0.375184
\(317\) −16.3912 −0.920622 −0.460311 0.887758i \(-0.652262\pi\)
−0.460311 + 0.887758i \(0.652262\pi\)
\(318\) −45.4188 −2.54696
\(319\) 7.57728 0.424246
\(320\) 10.2367 0.572250
\(321\) 15.6792 0.875127
\(322\) −77.4662 −4.31703
\(323\) 7.13378 0.396934
\(324\) 27.3391 1.51884
\(325\) −3.65543 −0.202767
\(326\) 23.6586 1.31033
\(327\) −3.14155 −0.173728
\(328\) 8.54191 0.471648
\(329\) 43.4252 2.39411
\(330\) −14.1188 −0.777213
\(331\) −16.2096 −0.890961 −0.445480 0.895292i \(-0.646967\pi\)
−0.445480 + 0.895292i \(0.646967\pi\)
\(332\) −20.8735 −1.14558
\(333\) 6.86935 0.376438
\(334\) −6.35330 −0.347637
\(335\) −7.41188 −0.404954
\(336\) −68.7208 −3.74903
\(337\) −22.1472 −1.20643 −0.603216 0.797578i \(-0.706114\pi\)
−0.603216 + 0.797578i \(0.706114\pi\)
\(338\) 4.91821 0.267516
\(339\) −32.0664 −1.74161
\(340\) 3.72103 0.201801
\(341\) 6.62293 0.358652
\(342\) 95.6392 5.17158
\(343\) 36.0730 1.94776
\(344\) 10.2099 0.550482
\(345\) −68.5644 −3.69138
\(346\) −12.0668 −0.648713
\(347\) −3.61850 −0.194251 −0.0971256 0.995272i \(-0.530965\pi\)
−0.0971256 + 0.995272i \(0.530965\pi\)
\(348\) −38.4653 −2.06196
\(349\) −1.51397 −0.0810408 −0.0405204 0.999179i \(-0.512902\pi\)
−0.0405204 + 0.999179i \(0.512902\pi\)
\(350\) −9.96844 −0.532836
\(351\) −39.1853 −2.09156
\(352\) −6.89929 −0.367733
\(353\) −12.0128 −0.639374 −0.319687 0.947523i \(-0.603578\pi\)
−0.319687 + 0.947523i \(0.603578\pi\)
\(354\) −55.0533 −2.92605
\(355\) −23.1311 −1.22767
\(356\) 27.1125 1.43696
\(357\) −14.1505 −0.748925
\(358\) −31.3015 −1.65434
\(359\) −34.6875 −1.83074 −0.915368 0.402619i \(-0.868100\pi\)
−0.915368 + 0.402619i \(0.868100\pi\)
\(360\) −14.2709 −0.752140
\(361\) 35.5237 1.86967
\(362\) 14.0382 0.737829
\(363\) −31.6473 −1.66105
\(364\) −23.3726 −1.22506
\(365\) 8.34227 0.436654
\(366\) −41.4586 −2.16708
\(367\) −22.2414 −1.16099 −0.580497 0.814262i \(-0.697142\pi\)
−0.580497 + 0.814262i \(0.697142\pi\)
\(368\) −41.3453 −2.15527
\(369\) 69.9531 3.64161
\(370\) 4.66980 0.242771
\(371\) 35.7491 1.85600
\(372\) −33.6207 −1.74315
\(373\) 3.86313 0.200025 0.100013 0.994986i \(-0.468112\pi\)
0.100013 + 0.994986i \(0.468112\pi\)
\(374\) −1.75311 −0.0906511
\(375\) 30.0802 1.55334
\(376\) 7.81276 0.402913
\(377\) 25.3804 1.30716
\(378\) −106.859 −5.49624
\(379\) −26.8479 −1.37908 −0.689542 0.724245i \(-0.742188\pi\)
−0.689542 + 0.724245i \(0.742188\pi\)
\(380\) 28.4400 1.45894
\(381\) −11.1759 −0.572560
\(382\) −7.62844 −0.390305
\(383\) −8.62786 −0.440863 −0.220432 0.975402i \(-0.570747\pi\)
−0.220432 + 0.975402i \(0.570747\pi\)
\(384\) −20.5598 −1.04919
\(385\) 11.1129 0.566364
\(386\) −28.2980 −1.44033
\(387\) 83.6131 4.25029
\(388\) 5.00118 0.253896
\(389\) 10.6546 0.540209 0.270104 0.962831i \(-0.412942\pi\)
0.270104 + 0.962831i \(0.412942\pi\)
\(390\) −47.2915 −2.39470
\(391\) −8.51355 −0.430549
\(392\) 12.3617 0.624358
\(393\) −4.24870 −0.214319
\(394\) −24.0597 −1.21211
\(395\) −10.6217 −0.534433
\(396\) −10.2810 −0.516641
\(397\) 3.77458 0.189441 0.0947205 0.995504i \(-0.469804\pi\)
0.0947205 + 0.995504i \(0.469804\pi\)
\(398\) −17.7072 −0.887581
\(399\) −108.153 −5.41442
\(400\) −5.32036 −0.266018
\(401\) −5.88149 −0.293708 −0.146854 0.989158i \(-0.546915\pi\)
−0.146854 + 0.989158i \(0.546915\pi\)
\(402\) −17.7268 −0.884131
\(403\) 22.1838 1.10506
\(404\) −2.40048 −0.119428
\(405\) −43.5400 −2.16352
\(406\) 69.2130 3.43498
\(407\) −0.962397 −0.0477043
\(408\) −2.54586 −0.126039
\(409\) −24.8526 −1.22888 −0.614442 0.788962i \(-0.710619\pi\)
−0.614442 + 0.788962i \(0.710619\pi\)
\(410\) 47.5543 2.34854
\(411\) −15.6224 −0.770595
\(412\) 18.4069 0.906841
\(413\) 43.3324 2.13225
\(414\) −114.137 −5.60954
\(415\) 33.2430 1.63184
\(416\) −23.1095 −1.13304
\(417\) 18.3446 0.898339
\(418\) −13.3991 −0.655370
\(419\) 26.6992 1.30434 0.652171 0.758072i \(-0.273858\pi\)
0.652171 + 0.758072i \(0.273858\pi\)
\(420\) −56.4134 −2.75269
\(421\) −15.8071 −0.770389 −0.385195 0.922835i \(-0.625866\pi\)
−0.385195 + 0.922835i \(0.625866\pi\)
\(422\) 3.42481 0.166717
\(423\) 63.9819 3.11090
\(424\) 6.43172 0.312352
\(425\) −1.09553 −0.0531411
\(426\) −55.3221 −2.68036
\(427\) 32.6321 1.57918
\(428\) 7.76149 0.375166
\(429\) 9.74629 0.470555
\(430\) 56.8403 2.74108
\(431\) −13.6763 −0.658766 −0.329383 0.944196i \(-0.606841\pi\)
−0.329383 + 0.944196i \(0.606841\pi\)
\(432\) −57.0329 −2.74400
\(433\) 1.31622 0.0632534 0.0316267 0.999500i \(-0.489931\pi\)
0.0316267 + 0.999500i \(0.489931\pi\)
\(434\) 60.4957 2.90389
\(435\) 61.2595 2.93717
\(436\) −1.55513 −0.0744771
\(437\) −65.0693 −3.11269
\(438\) 19.9520 0.953342
\(439\) −29.2462 −1.39585 −0.697923 0.716173i \(-0.745892\pi\)
−0.697923 + 0.716173i \(0.745892\pi\)
\(440\) 1.99935 0.0953152
\(441\) 101.235 4.82070
\(442\) −5.87212 −0.279308
\(443\) −34.6794 −1.64767 −0.823833 0.566832i \(-0.808169\pi\)
−0.823833 + 0.566832i \(0.808169\pi\)
\(444\) 4.88551 0.231856
\(445\) −43.1792 −2.04689
\(446\) −5.99918 −0.284069
\(447\) −60.8289 −2.87711
\(448\) −19.2704 −0.910443
\(449\) 7.40171 0.349308 0.174654 0.984630i \(-0.444119\pi\)
0.174654 + 0.984630i \(0.444119\pi\)
\(450\) −14.6873 −0.692366
\(451\) −9.80044 −0.461485
\(452\) −15.8735 −0.746625
\(453\) 12.0337 0.565394
\(454\) 3.93082 0.184483
\(455\) 37.2231 1.74504
\(456\) −19.4581 −0.911210
\(457\) 26.1181 1.22175 0.610876 0.791726i \(-0.290817\pi\)
0.610876 + 0.791726i \(0.290817\pi\)
\(458\) 50.8359 2.37541
\(459\) −11.7438 −0.548155
\(460\) −33.9406 −1.58249
\(461\) 2.67482 0.124579 0.0622893 0.998058i \(-0.480160\pi\)
0.0622893 + 0.998058i \(0.480160\pi\)
\(462\) 26.5783 1.23654
\(463\) −10.6459 −0.494759 −0.247380 0.968919i \(-0.579569\pi\)
−0.247380 + 0.968919i \(0.579569\pi\)
\(464\) 36.9404 1.71491
\(465\) 53.5440 2.48304
\(466\) 28.5182 1.32108
\(467\) −15.2321 −0.704859 −0.352430 0.935838i \(-0.614644\pi\)
−0.352430 + 0.935838i \(0.614644\pi\)
\(468\) −34.4367 −1.59184
\(469\) 13.9527 0.644277
\(470\) 43.4950 2.00627
\(471\) −1.68226 −0.0775142
\(472\) 7.79606 0.358843
\(473\) −11.7142 −0.538620
\(474\) −25.4035 −1.16682
\(475\) −8.37319 −0.384188
\(476\) −7.00477 −0.321063
\(477\) 52.6719 2.41168
\(478\) 20.7903 0.950928
\(479\) 21.8413 0.997956 0.498978 0.866615i \(-0.333709\pi\)
0.498978 + 0.866615i \(0.333709\pi\)
\(480\) −55.7782 −2.54592
\(481\) −3.22360 −0.146983
\(482\) 16.6826 0.759870
\(483\) 129.071 5.87294
\(484\) −15.6660 −0.712092
\(485\) −7.96484 −0.361665
\(486\) −35.3740 −1.60460
\(487\) 2.58327 0.117059 0.0585296 0.998286i \(-0.481359\pi\)
0.0585296 + 0.998286i \(0.481359\pi\)
\(488\) 5.87093 0.265764
\(489\) −39.4190 −1.78259
\(490\) 68.8195 3.10895
\(491\) 21.0707 0.950909 0.475454 0.879740i \(-0.342284\pi\)
0.475454 + 0.879740i \(0.342284\pi\)
\(492\) 49.7510 2.24295
\(493\) 7.60652 0.342580
\(494\) −44.8808 −2.01928
\(495\) 16.3735 0.735933
\(496\) 32.2878 1.44977
\(497\) 43.5439 1.95321
\(498\) 79.5064 3.56277
\(499\) −11.9247 −0.533823 −0.266912 0.963721i \(-0.586003\pi\)
−0.266912 + 0.963721i \(0.586003\pi\)
\(500\) 14.8903 0.665913
\(501\) 10.5856 0.472931
\(502\) −58.3230 −2.60308
\(503\) −8.05541 −0.359173 −0.179586 0.983742i \(-0.557476\pi\)
−0.179586 + 0.983742i \(0.557476\pi\)
\(504\) 26.8646 1.19665
\(505\) 3.82298 0.170121
\(506\) 15.9906 0.710870
\(507\) −8.19453 −0.363932
\(508\) −5.53230 −0.245456
\(509\) −27.2131 −1.20620 −0.603099 0.797666i \(-0.706068\pi\)
−0.603099 + 0.797666i \(0.706068\pi\)
\(510\) −14.1732 −0.627602
\(511\) −15.7042 −0.694712
\(512\) −25.7640 −1.13862
\(513\) −89.7584 −3.96293
\(514\) −7.10085 −0.313205
\(515\) −29.3146 −1.29176
\(516\) 59.4660 2.61784
\(517\) −8.96387 −0.394230
\(518\) −8.79081 −0.386246
\(519\) 20.1051 0.882518
\(520\) 6.69691 0.293679
\(521\) −27.2910 −1.19564 −0.597821 0.801630i \(-0.703966\pi\)
−0.597821 + 0.801630i \(0.703966\pi\)
\(522\) 101.977 4.46341
\(523\) −12.4316 −0.543597 −0.271798 0.962354i \(-0.587618\pi\)
−0.271798 + 0.962354i \(0.587618\pi\)
\(524\) −2.10319 −0.0918781
\(525\) 16.6090 0.724877
\(526\) −40.9972 −1.78756
\(527\) 6.64849 0.289613
\(528\) 14.1854 0.617340
\(529\) 54.6546 2.37629
\(530\) 35.8065 1.55533
\(531\) 63.8451 2.77064
\(532\) −53.5377 −2.32115
\(533\) −32.8271 −1.42190
\(534\) −103.270 −4.46895
\(535\) −12.3609 −0.534408
\(536\) 2.51028 0.108427
\(537\) 52.1533 2.25058
\(538\) −41.3914 −1.78451
\(539\) −14.1830 −0.610905
\(540\) −46.8187 −2.01475
\(541\) 43.7701 1.88182 0.940911 0.338654i \(-0.109972\pi\)
0.940911 + 0.338654i \(0.109972\pi\)
\(542\) −47.2144 −2.02803
\(543\) −23.3898 −1.00375
\(544\) −6.92591 −0.296946
\(545\) 2.47668 0.106089
\(546\) 89.0253 3.80993
\(547\) 4.55584 0.194794 0.0973968 0.995246i \(-0.468948\pi\)
0.0973968 + 0.995246i \(0.468948\pi\)
\(548\) −7.73337 −0.330353
\(549\) 48.0794 2.05198
\(550\) 2.05769 0.0877403
\(551\) 58.1368 2.47671
\(552\) 23.2216 0.988376
\(553\) 19.9951 0.850277
\(554\) 2.10114 0.0892687
\(555\) −7.78063 −0.330269
\(556\) 9.08092 0.385117
\(557\) −39.6417 −1.67967 −0.839836 0.542840i \(-0.817349\pi\)
−0.839836 + 0.542840i \(0.817349\pi\)
\(558\) 89.1332 3.77331
\(559\) −39.2373 −1.65956
\(560\) 54.1769 2.28939
\(561\) 2.92096 0.123323
\(562\) −11.8563 −0.500128
\(563\) 7.45319 0.314114 0.157057 0.987590i \(-0.449799\pi\)
0.157057 + 0.987590i \(0.449799\pi\)
\(564\) 45.5042 1.91607
\(565\) 25.2800 1.06354
\(566\) 36.5940 1.53816
\(567\) 81.9632 3.44213
\(568\) 7.83412 0.328712
\(569\) −9.77723 −0.409883 −0.204941 0.978774i \(-0.565700\pi\)
−0.204941 + 0.978774i \(0.565700\pi\)
\(570\) −108.327 −4.53730
\(571\) −29.2452 −1.22387 −0.611936 0.790907i \(-0.709609\pi\)
−0.611936 + 0.790907i \(0.709609\pi\)
\(572\) 4.82459 0.201726
\(573\) 12.7102 0.530976
\(574\) −89.5200 −3.73649
\(575\) 9.99268 0.416724
\(576\) −28.3927 −1.18303
\(577\) 18.4699 0.768913 0.384457 0.923143i \(-0.374389\pi\)
0.384457 + 0.923143i \(0.374389\pi\)
\(578\) 30.2937 1.26005
\(579\) 47.1490 1.95944
\(580\) 30.3246 1.25916
\(581\) −62.5794 −2.59623
\(582\) −19.0493 −0.789618
\(583\) −7.37935 −0.305621
\(584\) −2.82538 −0.116915
\(585\) 54.8437 2.26751
\(586\) −7.98804 −0.329983
\(587\) 31.7415 1.31011 0.655056 0.755580i \(-0.272645\pi\)
0.655056 + 0.755580i \(0.272645\pi\)
\(588\) 71.9985 2.96917
\(589\) 50.8146 2.09378
\(590\) 43.4020 1.78683
\(591\) 40.0872 1.64897
\(592\) −4.69183 −0.192833
\(593\) −23.5019 −0.965107 −0.482553 0.875867i \(-0.660291\pi\)
−0.482553 + 0.875867i \(0.660291\pi\)
\(594\) 22.0579 0.905048
\(595\) 11.1557 0.457341
\(596\) −30.1114 −1.23341
\(597\) 29.5030 1.20748
\(598\) 53.5614 2.19029
\(599\) −17.5921 −0.718793 −0.359396 0.933185i \(-0.617017\pi\)
−0.359396 + 0.933185i \(0.617017\pi\)
\(600\) 2.98818 0.121992
\(601\) 39.9434 1.62932 0.814662 0.579936i \(-0.196922\pi\)
0.814662 + 0.579936i \(0.196922\pi\)
\(602\) −107.001 −4.36103
\(603\) 20.5577 0.837173
\(604\) 5.95692 0.242384
\(605\) 24.9496 1.01435
\(606\) 9.14332 0.371422
\(607\) −17.4151 −0.706855 −0.353428 0.935462i \(-0.614984\pi\)
−0.353428 + 0.935462i \(0.614984\pi\)
\(608\) −52.9349 −2.14680
\(609\) −115.320 −4.67300
\(610\) 32.6845 1.32335
\(611\) −30.0249 −1.21468
\(612\) −10.3207 −0.417189
\(613\) 23.6579 0.955533 0.477767 0.878487i \(-0.341446\pi\)
0.477767 + 0.878487i \(0.341446\pi\)
\(614\) 44.0796 1.77891
\(615\) −79.2330 −3.19498
\(616\) −3.76374 −0.151645
\(617\) −15.5629 −0.626537 −0.313269 0.949665i \(-0.601424\pi\)
−0.313269 + 0.949665i \(0.601424\pi\)
\(618\) −70.1109 −2.82027
\(619\) 31.0690 1.24877 0.624385 0.781117i \(-0.285350\pi\)
0.624385 + 0.781117i \(0.285350\pi\)
\(620\) 26.5053 1.06448
\(621\) 107.119 4.29854
\(622\) −31.3266 −1.25608
\(623\) 81.2840 3.25658
\(624\) 47.5146 1.90211
\(625\) −29.3839 −1.17536
\(626\) −11.3155 −0.452257
\(627\) 22.3250 0.891575
\(628\) −0.832748 −0.0332302
\(629\) −0.966111 −0.0385214
\(630\) 149.560 5.95861
\(631\) −7.19600 −0.286468 −0.143234 0.989689i \(-0.545750\pi\)
−0.143234 + 0.989689i \(0.545750\pi\)
\(632\) 3.59737 0.143096
\(633\) −5.70628 −0.226804
\(634\) 30.9057 1.22742
\(635\) 8.81069 0.349642
\(636\) 37.4605 1.48541
\(637\) −47.5066 −1.88228
\(638\) −14.2870 −0.565627
\(639\) 64.1567 2.53800
\(640\) 16.2086 0.640701
\(641\) 4.86319 0.192085 0.0960423 0.995377i \(-0.469382\pi\)
0.0960423 + 0.995377i \(0.469382\pi\)
\(642\) −29.5632 −1.16677
\(643\) −11.6229 −0.458363 −0.229182 0.973384i \(-0.573605\pi\)
−0.229182 + 0.973384i \(0.573605\pi\)
\(644\) 63.8926 2.51772
\(645\) −94.7051 −3.72901
\(646\) −13.4508 −0.529214
\(647\) −19.8855 −0.781781 −0.390890 0.920437i \(-0.627833\pi\)
−0.390890 + 0.920437i \(0.627833\pi\)
\(648\) 14.7462 0.579287
\(649\) −8.94471 −0.351110
\(650\) 6.89234 0.270340
\(651\) −100.796 −3.95049
\(652\) −19.5131 −0.764194
\(653\) 7.28945 0.285258 0.142629 0.989776i \(-0.454444\pi\)
0.142629 + 0.989776i \(0.454444\pi\)
\(654\) 5.92341 0.231624
\(655\) 3.34952 0.130876
\(656\) −47.7787 −1.86544
\(657\) −23.1382 −0.902707
\(658\) −81.8785 −3.19196
\(659\) −22.5229 −0.877368 −0.438684 0.898641i \(-0.644555\pi\)
−0.438684 + 0.898641i \(0.644555\pi\)
\(660\) 11.6449 0.453276
\(661\) −4.84123 −0.188302 −0.0941510 0.995558i \(-0.530014\pi\)
−0.0941510 + 0.995558i \(0.530014\pi\)
\(662\) 30.5633 1.18788
\(663\) 9.78390 0.379975
\(664\) −11.2588 −0.436928
\(665\) 85.2638 3.30639
\(666\) −12.9522 −0.501887
\(667\) −69.3813 −2.68646
\(668\) 5.24008 0.202745
\(669\) 9.99559 0.386452
\(670\) 13.9751 0.539906
\(671\) −6.73593 −0.260038
\(672\) 105.001 4.05052
\(673\) 11.9610 0.461062 0.230531 0.973065i \(-0.425954\pi\)
0.230531 + 0.973065i \(0.425954\pi\)
\(674\) 41.7586 1.60848
\(675\) 13.7842 0.530554
\(676\) −4.05645 −0.156017
\(677\) 46.9617 1.80489 0.902443 0.430809i \(-0.141772\pi\)
0.902443 + 0.430809i \(0.141772\pi\)
\(678\) 60.4613 2.32200
\(679\) 14.9937 0.575404
\(680\) 2.00706 0.0769674
\(681\) −6.54938 −0.250973
\(682\) −12.4876 −0.478174
\(683\) −25.5505 −0.977663 −0.488832 0.872378i \(-0.662577\pi\)
−0.488832 + 0.872378i \(0.662577\pi\)
\(684\) −78.8813 −3.01610
\(685\) 12.3161 0.470574
\(686\) −68.0158 −2.59685
\(687\) −84.7008 −3.23154
\(688\) −57.1086 −2.17724
\(689\) −24.7175 −0.941660
\(690\) 129.278 4.92155
\(691\) −26.3063 −1.00074 −0.500370 0.865812i \(-0.666803\pi\)
−0.500370 + 0.865812i \(0.666803\pi\)
\(692\) 9.95242 0.378334
\(693\) −30.8228 −1.17086
\(694\) 6.82270 0.258986
\(695\) −14.4622 −0.548583
\(696\) −20.7476 −0.786434
\(697\) −9.83826 −0.372651
\(698\) 2.85459 0.108048
\(699\) −47.5159 −1.79722
\(700\) 8.22177 0.310754
\(701\) −1.94129 −0.0733214 −0.0366607 0.999328i \(-0.511672\pi\)
−0.0366607 + 0.999328i \(0.511672\pi\)
\(702\) 73.8841 2.78857
\(703\) −7.38402 −0.278493
\(704\) 3.97782 0.149920
\(705\) −72.4696 −2.72936
\(706\) 22.6501 0.852448
\(707\) −7.19670 −0.270660
\(708\) 45.4069 1.70650
\(709\) −11.6460 −0.437374 −0.218687 0.975795i \(-0.570177\pi\)
−0.218687 + 0.975795i \(0.570177\pi\)
\(710\) 43.6139 1.63680
\(711\) 29.4603 1.10485
\(712\) 14.6241 0.548060
\(713\) −60.6429 −2.27109
\(714\) 26.6809 0.998507
\(715\) −7.68361 −0.287351
\(716\) 25.8169 0.964821
\(717\) −34.6400 −1.29366
\(718\) 65.4034 2.44083
\(719\) −43.2884 −1.61439 −0.807193 0.590288i \(-0.799014\pi\)
−0.807193 + 0.590288i \(0.799014\pi\)
\(720\) 79.8232 2.97483
\(721\) 55.1842 2.05517
\(722\) −66.9801 −2.49274
\(723\) −27.7958 −1.03374
\(724\) −11.5784 −0.430308
\(725\) −8.92806 −0.331580
\(726\) 59.6712 2.21461
\(727\) −5.14695 −0.190890 −0.0954450 0.995435i \(-0.530427\pi\)
−0.0954450 + 0.995435i \(0.530427\pi\)
\(728\) −12.6068 −0.467240
\(729\) 6.19885 0.229587
\(730\) −15.7294 −0.582171
\(731\) −11.7594 −0.434937
\(732\) 34.1943 1.26386
\(733\) 17.4741 0.645419 0.322710 0.946498i \(-0.395406\pi\)
0.322710 + 0.946498i \(0.395406\pi\)
\(734\) 41.9363 1.54790
\(735\) −114.664 −4.22946
\(736\) 63.1733 2.32860
\(737\) −2.88013 −0.106091
\(738\) −131.897 −4.85519
\(739\) −6.52220 −0.239923 −0.119962 0.992779i \(-0.538277\pi\)
−0.119962 + 0.992779i \(0.538277\pi\)
\(740\) −3.85156 −0.141586
\(741\) 74.7786 2.74706
\(742\) −67.4050 −2.47452
\(743\) −2.65513 −0.0974072 −0.0487036 0.998813i \(-0.515509\pi\)
−0.0487036 + 0.998813i \(0.515509\pi\)
\(744\) −18.1344 −0.664841
\(745\) 47.9552 1.75694
\(746\) −7.28396 −0.266685
\(747\) −92.2032 −3.37354
\(748\) 1.44593 0.0528684
\(749\) 23.2691 0.850236
\(750\) −56.7164 −2.07099
\(751\) −0.572086 −0.0208757 −0.0104379 0.999946i \(-0.503323\pi\)
−0.0104379 + 0.999946i \(0.503323\pi\)
\(752\) −43.7002 −1.59358
\(753\) 97.1755 3.54127
\(754\) −47.8549 −1.74277
\(755\) −9.48695 −0.345265
\(756\) 88.1353 3.20545
\(757\) 40.1993 1.46107 0.730535 0.682875i \(-0.239271\pi\)
0.730535 + 0.682875i \(0.239271\pi\)
\(758\) 50.6219 1.83867
\(759\) −26.6430 −0.967078
\(760\) 15.3401 0.556442
\(761\) 24.4453 0.886141 0.443070 0.896487i \(-0.353889\pi\)
0.443070 + 0.896487i \(0.353889\pi\)
\(762\) 21.0723 0.763368
\(763\) −4.66231 −0.168787
\(764\) 6.29179 0.227629
\(765\) 16.4367 0.594268
\(766\) 16.2679 0.587782
\(767\) −29.9607 −1.08182
\(768\) 64.7352 2.33593
\(769\) −12.5550 −0.452745 −0.226373 0.974041i \(-0.572687\pi\)
−0.226373 + 0.974041i \(0.572687\pi\)
\(770\) −20.9534 −0.755107
\(771\) 11.8312 0.426089
\(772\) 23.3396 0.840011
\(773\) −3.94708 −0.141967 −0.0709833 0.997478i \(-0.522614\pi\)
−0.0709833 + 0.997478i \(0.522614\pi\)
\(774\) −157.653 −5.66672
\(775\) −7.80359 −0.280313
\(776\) 2.69755 0.0968366
\(777\) 14.6469 0.525454
\(778\) −20.0893 −0.720235
\(779\) −75.1941 −2.69411
\(780\) 39.0051 1.39661
\(781\) −8.98837 −0.321629
\(782\) 16.0523 0.574030
\(783\) −95.7065 −3.42027
\(784\) −69.1442 −2.46944
\(785\) 1.32623 0.0473351
\(786\) 8.01094 0.285741
\(787\) 24.0639 0.857785 0.428892 0.903356i \(-0.358904\pi\)
0.428892 + 0.903356i \(0.358904\pi\)
\(788\) 19.8439 0.706911
\(789\) 68.3080 2.43183
\(790\) 20.0272 0.712535
\(791\) −47.5891 −1.69207
\(792\) −5.54541 −0.197048
\(793\) −22.5623 −0.801211
\(794\) −7.11700 −0.252573
\(795\) −59.6593 −2.11590
\(796\) 14.6045 0.517644
\(797\) −33.6271 −1.19113 −0.595566 0.803307i \(-0.703072\pi\)
−0.595566 + 0.803307i \(0.703072\pi\)
\(798\) 203.923 7.21879
\(799\) −8.99846 −0.318343
\(800\) 8.12921 0.287411
\(801\) 119.762 4.23159
\(802\) 11.0896 0.391586
\(803\) 3.24167 0.114396
\(804\) 14.6207 0.515632
\(805\) −101.755 −3.58639
\(806\) −41.8277 −1.47332
\(807\) 68.9647 2.42767
\(808\) −1.29478 −0.0455502
\(809\) 37.7478 1.32714 0.663572 0.748113i \(-0.269040\pi\)
0.663572 + 0.748113i \(0.269040\pi\)
\(810\) 82.0948 2.88452
\(811\) −25.2396 −0.886284 −0.443142 0.896451i \(-0.646136\pi\)
−0.443142 + 0.896451i \(0.646136\pi\)
\(812\) −57.0855 −2.00331
\(813\) 78.6668 2.75896
\(814\) 1.81460 0.0636019
\(815\) 31.0765 1.08856
\(816\) 14.2401 0.498504
\(817\) −89.8775 −3.14442
\(818\) 46.8598 1.63841
\(819\) −103.242 −3.60758
\(820\) −39.2218 −1.36969
\(821\) 46.7434 1.63136 0.815678 0.578507i \(-0.196364\pi\)
0.815678 + 0.578507i \(0.196364\pi\)
\(822\) 29.4561 1.02740
\(823\) 26.2895 0.916393 0.458197 0.888851i \(-0.348496\pi\)
0.458197 + 0.888851i \(0.348496\pi\)
\(824\) 9.92836 0.345871
\(825\) −3.42844 −0.119363
\(826\) −81.7035 −2.84283
\(827\) −7.00302 −0.243519 −0.121759 0.992560i \(-0.538854\pi\)
−0.121759 + 0.992560i \(0.538854\pi\)
\(828\) 94.1381 3.27152
\(829\) −2.22179 −0.0771659 −0.0385829 0.999255i \(-0.512284\pi\)
−0.0385829 + 0.999255i \(0.512284\pi\)
\(830\) −62.6799 −2.17565
\(831\) −3.50083 −0.121442
\(832\) 13.3239 0.461923
\(833\) −14.2377 −0.493308
\(834\) −34.5888 −1.19771
\(835\) −8.34531 −0.288801
\(836\) 11.0513 0.382217
\(837\) −83.6525 −2.89145
\(838\) −50.3415 −1.73902
\(839\) 6.64832 0.229525 0.114763 0.993393i \(-0.463389\pi\)
0.114763 + 0.993393i \(0.463389\pi\)
\(840\) −30.4284 −1.04988
\(841\) 32.9894 1.13757
\(842\) 29.8043 1.02712
\(843\) 19.7545 0.680381
\(844\) −2.82472 −0.0972308
\(845\) 6.46027 0.222240
\(846\) −120.638 −4.14762
\(847\) −46.9671 −1.61381
\(848\) −35.9754 −1.23540
\(849\) −60.9715 −2.09254
\(850\) 2.06563 0.0708506
\(851\) 8.81219 0.302078
\(852\) 45.6286 1.56321
\(853\) 2.71839 0.0930760 0.0465380 0.998917i \(-0.485181\pi\)
0.0465380 + 0.998917i \(0.485181\pi\)
\(854\) −61.5279 −2.10544
\(855\) 125.626 4.29631
\(856\) 4.18642 0.143089
\(857\) −3.14670 −0.107489 −0.0537445 0.998555i \(-0.517116\pi\)
−0.0537445 + 0.998555i \(0.517116\pi\)
\(858\) −18.3767 −0.627369
\(859\) 42.8976 1.46365 0.731824 0.681493i \(-0.238669\pi\)
0.731824 + 0.681493i \(0.238669\pi\)
\(860\) −46.8808 −1.59862
\(861\) 149.155 5.08318
\(862\) 25.7868 0.878301
\(863\) 14.5518 0.495349 0.247674 0.968843i \(-0.420334\pi\)
0.247674 + 0.968843i \(0.420334\pi\)
\(864\) 87.1430 2.96466
\(865\) −15.8502 −0.538921
\(866\) −2.48173 −0.0843327
\(867\) −50.4742 −1.71419
\(868\) −49.8957 −1.69357
\(869\) −4.12740 −0.140012
\(870\) −115.505 −3.91599
\(871\) −9.64713 −0.326881
\(872\) −0.838810 −0.0284057
\(873\) 22.0914 0.747679
\(874\) 122.689 4.15000
\(875\) 44.6414 1.50916
\(876\) −16.4560 −0.555996
\(877\) 36.1123 1.21942 0.609712 0.792623i \(-0.291285\pi\)
0.609712 + 0.792623i \(0.291285\pi\)
\(878\) 55.1439 1.86102
\(879\) 13.3093 0.448913
\(880\) −11.1832 −0.376987
\(881\) −10.0254 −0.337765 −0.168883 0.985636i \(-0.554016\pi\)
−0.168883 + 0.985636i \(0.554016\pi\)
\(882\) −190.878 −6.42721
\(883\) −22.5904 −0.760229 −0.380114 0.924939i \(-0.624115\pi\)
−0.380114 + 0.924939i \(0.624115\pi\)
\(884\) 4.84321 0.162895
\(885\) −72.3147 −2.43083
\(886\) 65.3881 2.19676
\(887\) −13.7256 −0.460861 −0.230430 0.973089i \(-0.574013\pi\)
−0.230430 + 0.973089i \(0.574013\pi\)
\(888\) 2.63517 0.0884304
\(889\) −16.5860 −0.556275
\(890\) 81.4146 2.72902
\(891\) −16.9189 −0.566804
\(892\) 4.94800 0.165671
\(893\) −68.7755 −2.30148
\(894\) 114.693 3.83591
\(895\) −41.1157 −1.37435
\(896\) −30.5124 −1.01935
\(897\) −89.2418 −2.97970
\(898\) −13.9559 −0.465716
\(899\) 54.1820 1.80707
\(900\) 12.1138 0.403793
\(901\) −7.40782 −0.246790
\(902\) 18.4788 0.615276
\(903\) 178.281 5.93281
\(904\) −8.56189 −0.284764
\(905\) 18.4397 0.612955
\(906\) −22.6896 −0.753813
\(907\) 6.39168 0.212232 0.106116 0.994354i \(-0.466158\pi\)
0.106116 + 0.994354i \(0.466158\pi\)
\(908\) −3.24207 −0.107592
\(909\) −10.6035 −0.351695
\(910\) −70.1843 −2.32659
\(911\) −0.258998 −0.00858098 −0.00429049 0.999991i \(-0.501366\pi\)
−0.00429049 + 0.999991i \(0.501366\pi\)
\(912\) 108.838 3.60398
\(913\) 12.9177 0.427513
\(914\) −49.2457 −1.62890
\(915\) −54.4575 −1.80031
\(916\) −41.9285 −1.38536
\(917\) −6.30541 −0.208223
\(918\) 22.1430 0.730829
\(919\) 26.3692 0.869838 0.434919 0.900470i \(-0.356777\pi\)
0.434919 + 0.900470i \(0.356777\pi\)
\(920\) −18.3070 −0.603565
\(921\) −73.4436 −2.42005
\(922\) −5.04338 −0.166095
\(923\) −30.1070 −0.990983
\(924\) −21.9213 −0.721157
\(925\) 1.13396 0.0372844
\(926\) 20.0730 0.659639
\(927\) 81.3073 2.67048
\(928\) −56.4428 −1.85283
\(929\) 44.7404 1.46788 0.733942 0.679212i \(-0.237678\pi\)
0.733942 + 0.679212i \(0.237678\pi\)
\(930\) −100.957 −3.31053
\(931\) −108.819 −3.56641
\(932\) −23.5212 −0.770464
\(933\) 52.1952 1.70879
\(934\) 28.7203 0.939756
\(935\) −2.30278 −0.0753089
\(936\) −18.5746 −0.607131
\(937\) −28.1796 −0.920588 −0.460294 0.887766i \(-0.652256\pi\)
−0.460294 + 0.887766i \(0.652256\pi\)
\(938\) −26.3079 −0.858984
\(939\) 18.8534 0.615257
\(940\) −35.8738 −1.17007
\(941\) −21.5781 −0.703427 −0.351713 0.936108i \(-0.614401\pi\)
−0.351713 + 0.936108i \(0.614401\pi\)
\(942\) 3.17190 0.103346
\(943\) 89.7377 2.92226
\(944\) −43.6068 −1.41928
\(945\) −140.364 −4.56603
\(946\) 22.0872 0.718117
\(947\) −52.6534 −1.71101 −0.855503 0.517798i \(-0.826752\pi\)
−0.855503 + 0.517798i \(0.826752\pi\)
\(948\) 20.9523 0.680499
\(949\) 10.8581 0.352469
\(950\) 15.7877 0.512220
\(951\) −51.4938 −1.66980
\(952\) −3.77826 −0.122454
\(953\) 19.6542 0.636662 0.318331 0.947980i \(-0.396878\pi\)
0.318331 + 0.947980i \(0.396878\pi\)
\(954\) −99.3132 −3.21538
\(955\) −10.0203 −0.324248
\(956\) −17.1475 −0.554589
\(957\) 23.8044 0.769488
\(958\) −41.1819 −1.33053
\(959\) −23.1848 −0.748677
\(960\) 32.1592 1.03793
\(961\) 16.3579 0.527673
\(962\) 6.07810 0.195966
\(963\) 34.2843 1.10480
\(964\) −13.7595 −0.443162
\(965\) −37.1705 −1.19656
\(966\) −243.364 −7.83012
\(967\) 0.886849 0.0285192 0.0142596 0.999898i \(-0.495461\pi\)
0.0142596 + 0.999898i \(0.495461\pi\)
\(968\) −8.45000 −0.271593
\(969\) 22.4111 0.719950
\(970\) 15.0177 0.482191
\(971\) −15.1111 −0.484939 −0.242470 0.970159i \(-0.577957\pi\)
−0.242470 + 0.970159i \(0.577957\pi\)
\(972\) 29.1757 0.935813
\(973\) 27.2248 0.872788
\(974\) −4.87077 −0.156070
\(975\) −11.4837 −0.367774
\(976\) −32.8387 −1.05114
\(977\) −30.6129 −0.979392 −0.489696 0.871893i \(-0.662892\pi\)
−0.489696 + 0.871893i \(0.662892\pi\)
\(978\) 74.3247 2.37664
\(979\) −16.7787 −0.536250
\(980\) −56.7610 −1.81316
\(981\) −6.86935 −0.219322
\(982\) −39.7290 −1.26780
\(983\) −15.6440 −0.498967 −0.249484 0.968379i \(-0.580261\pi\)
−0.249484 + 0.968379i \(0.580261\pi\)
\(984\) 26.8349 0.855464
\(985\) −31.6033 −1.00696
\(986\) −14.3421 −0.456746
\(987\) 136.423 4.34238
\(988\) 37.0168 1.17766
\(989\) 107.261 3.41070
\(990\) −30.8723 −0.981185
\(991\) 32.6209 1.03624 0.518119 0.855309i \(-0.326632\pi\)
0.518119 + 0.855309i \(0.326632\pi\)
\(992\) −49.3339 −1.56635
\(993\) −50.9233 −1.61600
\(994\) −82.1023 −2.60413
\(995\) −23.2591 −0.737363
\(996\) −65.5753 −2.07783
\(997\) −7.69707 −0.243769 −0.121884 0.992544i \(-0.538894\pi\)
−0.121884 + 0.992544i \(0.538894\pi\)
\(998\) 22.4841 0.711721
\(999\) 12.1558 0.384592
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 4033.2.a.f.1.17 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.17 85 1.1 even 1 trivial