Properties

Label 6037.2.a.b.1.1
Level 6037
Weight 2
Character 6037.1
Self dual yes
Analytic conductor 48.206
Analytic rank 0
Dimension 259
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} +O(q^{10})\) \(q-2.75717 q^{2} -1.09794 q^{3} +5.60201 q^{4} +2.84974 q^{5} +3.02722 q^{6} +3.79647 q^{7} -9.93137 q^{8} -1.79452 q^{9} -7.85722 q^{10} -0.397993 q^{11} -6.15069 q^{12} -2.48387 q^{13} -10.4675 q^{14} -3.12885 q^{15} +16.1785 q^{16} +2.84790 q^{17} +4.94781 q^{18} -2.45811 q^{19} +15.9642 q^{20} -4.16831 q^{21} +1.09734 q^{22} +3.57879 q^{23} +10.9041 q^{24} +3.12099 q^{25} +6.84846 q^{26} +5.26411 q^{27} +21.2679 q^{28} +1.79285 q^{29} +8.62677 q^{30} -0.342150 q^{31} -24.7442 q^{32} +0.436973 q^{33} -7.85216 q^{34} +10.8189 q^{35} -10.0529 q^{36} -6.20613 q^{37} +6.77745 q^{38} +2.72714 q^{39} -28.3018 q^{40} +1.27240 q^{41} +11.4928 q^{42} -3.33696 q^{43} -2.22956 q^{44} -5.11391 q^{45} -9.86734 q^{46} -0.761099 q^{47} -17.7631 q^{48} +7.41320 q^{49} -8.60512 q^{50} -3.12683 q^{51} -13.9147 q^{52} +3.51736 q^{53} -14.5141 q^{54} -1.13417 q^{55} -37.7042 q^{56} +2.69887 q^{57} -4.94320 q^{58} -0.993904 q^{59} -17.5278 q^{60} +6.36307 q^{61} +0.943366 q^{62} -6.81285 q^{63} +35.8671 q^{64} -7.07837 q^{65} -1.20481 q^{66} -4.46689 q^{67} +15.9540 q^{68} -3.92930 q^{69} -29.8297 q^{70} +4.45247 q^{71} +17.8221 q^{72} +0.508279 q^{73} +17.1114 q^{74} -3.42667 q^{75} -13.7704 q^{76} -1.51097 q^{77} -7.51921 q^{78} -12.9156 q^{79} +46.1045 q^{80} -0.396122 q^{81} -3.50822 q^{82} -2.24676 q^{83} -23.3509 q^{84} +8.11576 q^{85} +9.20057 q^{86} -1.96845 q^{87} +3.95262 q^{88} +5.76691 q^{89} +14.1000 q^{90} -9.42994 q^{91} +20.0484 q^{92} +0.375661 q^{93} +2.09848 q^{94} -7.00497 q^{95} +27.1677 q^{96} +0.292271 q^{97} -20.4395 q^{98} +0.714207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75717 −1.94962 −0.974808 0.223044i \(-0.928401\pi\)
−0.974808 + 0.223044i \(0.928401\pi\)
\(3\) −1.09794 −0.633897 −0.316949 0.948443i \(-0.602658\pi\)
−0.316949 + 0.948443i \(0.602658\pi\)
\(4\) 5.60201 2.80101
\(5\) 2.84974 1.27444 0.637220 0.770682i \(-0.280084\pi\)
0.637220 + 0.770682i \(0.280084\pi\)
\(6\) 3.02722 1.23586
\(7\) 3.79647 1.43493 0.717466 0.696594i \(-0.245302\pi\)
0.717466 + 0.696594i \(0.245302\pi\)
\(8\) −9.93137 −3.51127
\(9\) −1.79452 −0.598174
\(10\) −7.85722 −2.48467
\(11\) −0.397993 −0.119999 −0.0599997 0.998198i \(-0.519110\pi\)
−0.0599997 + 0.998198i \(0.519110\pi\)
\(12\) −6.15069 −1.77555
\(13\) −2.48387 −0.688901 −0.344451 0.938804i \(-0.611935\pi\)
−0.344451 + 0.938804i \(0.611935\pi\)
\(14\) −10.4675 −2.79757
\(15\) −3.12885 −0.807864
\(16\) 16.1785 4.04463
\(17\) 2.84790 0.690717 0.345359 0.938471i \(-0.387757\pi\)
0.345359 + 0.938471i \(0.387757\pi\)
\(18\) 4.94781 1.16621
\(19\) −2.45811 −0.563930 −0.281965 0.959425i \(-0.590986\pi\)
−0.281965 + 0.959425i \(0.590986\pi\)
\(20\) 15.9642 3.56971
\(21\) −4.16831 −0.909599
\(22\) 1.09734 0.233953
\(23\) 3.57879 0.746228 0.373114 0.927785i \(-0.378290\pi\)
0.373114 + 0.927785i \(0.378290\pi\)
\(24\) 10.9041 2.22579
\(25\) 3.12099 0.624198
\(26\) 6.84846 1.34309
\(27\) 5.26411 1.01308
\(28\) 21.2679 4.01925
\(29\) 1.79285 0.332924 0.166462 0.986048i \(-0.446766\pi\)
0.166462 + 0.986048i \(0.446766\pi\)
\(30\) 8.62677 1.57503
\(31\) −0.342150 −0.0614519 −0.0307259 0.999528i \(-0.509782\pi\)
−0.0307259 + 0.999528i \(0.509782\pi\)
\(32\) −24.7442 −4.37420
\(33\) 0.436973 0.0760673
\(34\) −7.85216 −1.34663
\(35\) 10.8189 1.82873
\(36\) −10.0529 −1.67549
\(37\) −6.20613 −1.02028 −0.510141 0.860091i \(-0.670407\pi\)
−0.510141 + 0.860091i \(0.670407\pi\)
\(38\) 6.77745 1.09945
\(39\) 2.72714 0.436693
\(40\) −28.3018 −4.47491
\(41\) 1.27240 0.198715 0.0993576 0.995052i \(-0.468321\pi\)
0.0993576 + 0.995052i \(0.468321\pi\)
\(42\) 11.4928 1.77337
\(43\) −3.33696 −0.508881 −0.254441 0.967088i \(-0.581891\pi\)
−0.254441 + 0.967088i \(0.581891\pi\)
\(44\) −2.22956 −0.336119
\(45\) −5.11391 −0.762337
\(46\) −9.86734 −1.45486
\(47\) −0.761099 −0.111018 −0.0555088 0.998458i \(-0.517678\pi\)
−0.0555088 + 0.998458i \(0.517678\pi\)
\(48\) −17.7631 −2.56388
\(49\) 7.41320 1.05903
\(50\) −8.60512 −1.21695
\(51\) −3.12683 −0.437844
\(52\) −13.9147 −1.92962
\(53\) 3.51736 0.483147 0.241573 0.970383i \(-0.422337\pi\)
0.241573 + 0.970383i \(0.422337\pi\)
\(54\) −14.5141 −1.97511
\(55\) −1.13417 −0.152932
\(56\) −37.7042 −5.03843
\(57\) 2.69887 0.357474
\(58\) −4.94320 −0.649075
\(59\) −0.993904 −0.129395 −0.0646976 0.997905i \(-0.520608\pi\)
−0.0646976 + 0.997905i \(0.520608\pi\)
\(60\) −17.5278 −2.26283
\(61\) 6.36307 0.814708 0.407354 0.913270i \(-0.366452\pi\)
0.407354 + 0.913270i \(0.366452\pi\)
\(62\) 0.943366 0.119808
\(63\) −6.81285 −0.858339
\(64\) 35.8671 4.48339
\(65\) −7.07837 −0.877964
\(66\) −1.20481 −0.148302
\(67\) −4.46689 −0.545717 −0.272859 0.962054i \(-0.587969\pi\)
−0.272859 + 0.962054i \(0.587969\pi\)
\(68\) 15.9540 1.93470
\(69\) −3.92930 −0.473032
\(70\) −29.8297 −3.56533
\(71\) 4.45247 0.528411 0.264206 0.964466i \(-0.414890\pi\)
0.264206 + 0.964466i \(0.414890\pi\)
\(72\) 17.8221 2.10035
\(73\) 0.508279 0.0594896 0.0297448 0.999558i \(-0.490531\pi\)
0.0297448 + 0.999558i \(0.490531\pi\)
\(74\) 17.1114 1.98916
\(75\) −3.42667 −0.395678
\(76\) −13.7704 −1.57957
\(77\) −1.51097 −0.172191
\(78\) −7.51921 −0.851383
\(79\) −12.9156 −1.45311 −0.726557 0.687106i \(-0.758881\pi\)
−0.726557 + 0.687106i \(0.758881\pi\)
\(80\) 46.1045 5.15464
\(81\) −0.396122 −0.0440136
\(82\) −3.50822 −0.387418
\(83\) −2.24676 −0.246614 −0.123307 0.992369i \(-0.539350\pi\)
−0.123307 + 0.992369i \(0.539350\pi\)
\(84\) −23.3509 −2.54779
\(85\) 8.11576 0.880278
\(86\) 9.20057 0.992123
\(87\) −1.96845 −0.211040
\(88\) 3.95262 0.421350
\(89\) 5.76691 0.611291 0.305645 0.952145i \(-0.401128\pi\)
0.305645 + 0.952145i \(0.401128\pi\)
\(90\) 14.1000 1.48627
\(91\) −9.42994 −0.988526
\(92\) 20.0484 2.09019
\(93\) 0.375661 0.0389542
\(94\) 2.09848 0.216442
\(95\) −7.00497 −0.718695
\(96\) 27.1677 2.77279
\(97\) 0.292271 0.0296756 0.0148378 0.999890i \(-0.495277\pi\)
0.0148378 + 0.999890i \(0.495277\pi\)
\(98\) −20.4395 −2.06470
\(99\) 0.714207 0.0717805
\(100\) 17.4838 1.74838
\(101\) 13.2075 1.31420 0.657100 0.753804i \(-0.271783\pi\)
0.657100 + 0.753804i \(0.271783\pi\)
\(102\) 8.62121 0.853627
\(103\) 15.9673 1.57330 0.786650 0.617399i \(-0.211814\pi\)
0.786650 + 0.617399i \(0.211814\pi\)
\(104\) 24.6682 2.41892
\(105\) −11.8786 −1.15923
\(106\) −9.69798 −0.941951
\(107\) 3.08392 0.298134 0.149067 0.988827i \(-0.452373\pi\)
0.149067 + 0.988827i \(0.452373\pi\)
\(108\) 29.4896 2.83764
\(109\) −0.323117 −0.0309490 −0.0154745 0.999880i \(-0.504926\pi\)
−0.0154745 + 0.999880i \(0.504926\pi\)
\(110\) 3.12712 0.298159
\(111\) 6.81398 0.646754
\(112\) 61.4212 5.80376
\(113\) 10.6173 0.998791 0.499396 0.866374i \(-0.333555\pi\)
0.499396 + 0.866374i \(0.333555\pi\)
\(114\) −7.44125 −0.696937
\(115\) 10.1986 0.951023
\(116\) 10.0436 0.932523
\(117\) 4.45736 0.412083
\(118\) 2.74037 0.252271
\(119\) 10.8120 0.991132
\(120\) 31.0737 2.83663
\(121\) −10.8416 −0.985600
\(122\) −17.5441 −1.58837
\(123\) −1.39702 −0.125965
\(124\) −1.91673 −0.172127
\(125\) −5.35468 −0.478937
\(126\) 18.7842 1.67343
\(127\) 5.19412 0.460904 0.230452 0.973084i \(-0.425980\pi\)
0.230452 + 0.973084i \(0.425980\pi\)
\(128\) −49.4035 −4.36669
\(129\) 3.66379 0.322578
\(130\) 19.5163 1.71169
\(131\) 9.78458 0.854883 0.427442 0.904043i \(-0.359415\pi\)
0.427442 + 0.904043i \(0.359415\pi\)
\(132\) 2.44793 0.213065
\(133\) −9.33216 −0.809201
\(134\) 12.3160 1.06394
\(135\) 15.0013 1.29111
\(136\) −28.2836 −2.42529
\(137\) 2.57721 0.220186 0.110093 0.993921i \(-0.464885\pi\)
0.110093 + 0.993921i \(0.464885\pi\)
\(138\) 10.8338 0.922231
\(139\) 14.6138 1.23952 0.619762 0.784789i \(-0.287229\pi\)
0.619762 + 0.784789i \(0.287229\pi\)
\(140\) 60.6078 5.12230
\(141\) 0.835642 0.0703738
\(142\) −12.2762 −1.03020
\(143\) 0.988562 0.0826677
\(144\) −29.0327 −2.41939
\(145\) 5.10915 0.424292
\(146\) −1.40141 −0.115982
\(147\) −8.13927 −0.671315
\(148\) −34.7668 −2.85782
\(149\) 17.1846 1.40782 0.703909 0.710290i \(-0.251436\pi\)
0.703909 + 0.710290i \(0.251436\pi\)
\(150\) 9.44792 0.771420
\(151\) 6.87461 0.559448 0.279724 0.960080i \(-0.409757\pi\)
0.279724 + 0.960080i \(0.409757\pi\)
\(152\) 24.4125 1.98011
\(153\) −5.11062 −0.413169
\(154\) 4.16600 0.335706
\(155\) −0.975036 −0.0783167
\(156\) 15.2775 1.22318
\(157\) 1.63569 0.130542 0.0652712 0.997868i \(-0.479209\pi\)
0.0652712 + 0.997868i \(0.479209\pi\)
\(158\) 35.6104 2.83301
\(159\) −3.86186 −0.306266
\(160\) −70.5145 −5.57466
\(161\) 13.5868 1.07079
\(162\) 1.09218 0.0858096
\(163\) 12.7857 1.00145 0.500725 0.865607i \(-0.333067\pi\)
0.500725 + 0.865607i \(0.333067\pi\)
\(164\) 7.12799 0.556602
\(165\) 1.24526 0.0969432
\(166\) 6.19471 0.480803
\(167\) 15.5911 1.20647 0.603237 0.797562i \(-0.293877\pi\)
0.603237 + 0.797562i \(0.293877\pi\)
\(168\) 41.3970 3.19385
\(169\) −6.83040 −0.525415
\(170\) −22.3766 −1.71620
\(171\) 4.41114 0.337328
\(172\) −18.6937 −1.42538
\(173\) −1.16595 −0.0886456 −0.0443228 0.999017i \(-0.514113\pi\)
−0.0443228 + 0.999017i \(0.514113\pi\)
\(174\) 5.42735 0.411447
\(175\) 11.8488 0.895682
\(176\) −6.43893 −0.485353
\(177\) 1.09125 0.0820233
\(178\) −15.9004 −1.19178
\(179\) 3.99398 0.298524 0.149262 0.988798i \(-0.452310\pi\)
0.149262 + 0.988798i \(0.452310\pi\)
\(180\) −28.6482 −2.13531
\(181\) −15.5804 −1.15809 −0.579043 0.815297i \(-0.696574\pi\)
−0.579043 + 0.815297i \(0.696574\pi\)
\(182\) 26.0000 1.92725
\(183\) −6.98629 −0.516441
\(184\) −35.5423 −2.62021
\(185\) −17.6858 −1.30029
\(186\) −1.03576 −0.0759457
\(187\) −1.13344 −0.0828856
\(188\) −4.26368 −0.310961
\(189\) 19.9850 1.45370
\(190\) 19.3139 1.40118
\(191\) −20.8941 −1.51184 −0.755922 0.654662i \(-0.772811\pi\)
−0.755922 + 0.654662i \(0.772811\pi\)
\(192\) −39.3800 −2.84201
\(193\) −15.0447 −1.08294 −0.541469 0.840721i \(-0.682132\pi\)
−0.541469 + 0.840721i \(0.682132\pi\)
\(194\) −0.805841 −0.0578560
\(195\) 7.77164 0.556539
\(196\) 41.5288 2.96634
\(197\) 27.4853 1.95824 0.979122 0.203271i \(-0.0651574\pi\)
0.979122 + 0.203271i \(0.0651574\pi\)
\(198\) −1.96919 −0.139945
\(199\) −13.3027 −0.943000 −0.471500 0.881866i \(-0.656287\pi\)
−0.471500 + 0.881866i \(0.656287\pi\)
\(200\) −30.9957 −2.19173
\(201\) 4.90439 0.345929
\(202\) −36.4155 −2.56219
\(203\) 6.80651 0.477723
\(204\) −17.5165 −1.22640
\(205\) 3.62600 0.253251
\(206\) −44.0245 −3.06733
\(207\) −6.42221 −0.446374
\(208\) −40.1853 −2.78635
\(209\) 0.978312 0.0676713
\(210\) 32.7513 2.26005
\(211\) 3.75289 0.258359 0.129180 0.991621i \(-0.458766\pi\)
0.129180 + 0.991621i \(0.458766\pi\)
\(212\) 19.7043 1.35330
\(213\) −4.88856 −0.334958
\(214\) −8.50290 −0.581247
\(215\) −9.50944 −0.648539
\(216\) −52.2798 −3.55719
\(217\) −1.29896 −0.0881792
\(218\) 0.890890 0.0603387
\(219\) −0.558061 −0.0377103
\(220\) −6.35366 −0.428364
\(221\) −7.07381 −0.475836
\(222\) −18.7873 −1.26092
\(223\) 7.52079 0.503630 0.251815 0.967775i \(-0.418973\pi\)
0.251815 + 0.967775i \(0.418973\pi\)
\(224\) −93.9407 −6.27668
\(225\) −5.60069 −0.373379
\(226\) −29.2737 −1.94726
\(227\) 16.2101 1.07590 0.537952 0.842975i \(-0.319198\pi\)
0.537952 + 0.842975i \(0.319198\pi\)
\(228\) 15.1191 1.00129
\(229\) 10.8728 0.718493 0.359247 0.933243i \(-0.383034\pi\)
0.359247 + 0.933243i \(0.383034\pi\)
\(230\) −28.1193 −1.85413
\(231\) 1.65896 0.109151
\(232\) −17.8055 −1.16899
\(233\) 4.63581 0.303702 0.151851 0.988403i \(-0.451477\pi\)
0.151851 + 0.988403i \(0.451477\pi\)
\(234\) −12.2897 −0.803404
\(235\) −2.16893 −0.141485
\(236\) −5.56786 −0.362437
\(237\) 14.1805 0.921125
\(238\) −29.8105 −1.93233
\(239\) −13.2645 −0.858006 −0.429003 0.903303i \(-0.641135\pi\)
−0.429003 + 0.903303i \(0.641135\pi\)
\(240\) −50.6200 −3.26751
\(241\) 19.1691 1.23479 0.617395 0.786653i \(-0.288188\pi\)
0.617395 + 0.786653i \(0.288188\pi\)
\(242\) 29.8922 1.92154
\(243\) −15.3574 −0.985178
\(244\) 35.6460 2.28200
\(245\) 21.1257 1.34967
\(246\) 3.85183 0.245584
\(247\) 6.10563 0.388492
\(248\) 3.39802 0.215774
\(249\) 2.46681 0.156328
\(250\) 14.7638 0.933744
\(251\) 2.62057 0.165409 0.0827046 0.996574i \(-0.473644\pi\)
0.0827046 + 0.996574i \(0.473644\pi\)
\(252\) −38.1657 −2.40421
\(253\) −1.42433 −0.0895469
\(254\) −14.3211 −0.898585
\(255\) −8.91064 −0.558006
\(256\) 64.4797 4.02998
\(257\) −6.26214 −0.390622 −0.195311 0.980741i \(-0.562572\pi\)
−0.195311 + 0.980741i \(0.562572\pi\)
\(258\) −10.1017 −0.628904
\(259\) −23.5614 −1.46403
\(260\) −39.6531 −2.45918
\(261\) −3.21731 −0.199147
\(262\) −26.9778 −1.66669
\(263\) 5.31092 0.327485 0.163743 0.986503i \(-0.447643\pi\)
0.163743 + 0.986503i \(0.447643\pi\)
\(264\) −4.33975 −0.267093
\(265\) 10.0236 0.615742
\(266\) 25.7304 1.57763
\(267\) −6.33173 −0.387496
\(268\) −25.0236 −1.52856
\(269\) −22.9417 −1.39878 −0.699390 0.714741i \(-0.746545\pi\)
−0.699390 + 0.714741i \(0.746545\pi\)
\(270\) −41.3613 −2.51717
\(271\) 14.2725 0.866995 0.433498 0.901155i \(-0.357279\pi\)
0.433498 + 0.901155i \(0.357279\pi\)
\(272\) 46.0748 2.79369
\(273\) 10.3535 0.626624
\(274\) −7.10582 −0.429278
\(275\) −1.24213 −0.0749034
\(276\) −22.0120 −1.32497
\(277\) 9.13943 0.549135 0.274568 0.961568i \(-0.411465\pi\)
0.274568 + 0.961568i \(0.411465\pi\)
\(278\) −40.2927 −2.41660
\(279\) 0.613995 0.0367589
\(280\) −107.447 −6.42118
\(281\) 9.55233 0.569844 0.284922 0.958551i \(-0.408032\pi\)
0.284922 + 0.958551i \(0.408032\pi\)
\(282\) −2.30401 −0.137202
\(283\) 11.6925 0.695046 0.347523 0.937671i \(-0.387023\pi\)
0.347523 + 0.937671i \(0.387023\pi\)
\(284\) 24.9428 1.48008
\(285\) 7.69106 0.455579
\(286\) −2.72564 −0.161170
\(287\) 4.83062 0.285143
\(288\) 44.4041 2.61653
\(289\) −8.88947 −0.522910
\(290\) −14.0868 −0.827207
\(291\) −0.320896 −0.0188113
\(292\) 2.84739 0.166631
\(293\) 0.562309 0.0328504 0.0164252 0.999865i \(-0.494771\pi\)
0.0164252 + 0.999865i \(0.494771\pi\)
\(294\) 22.4414 1.30881
\(295\) −2.83236 −0.164907
\(296\) 61.6354 3.58249
\(297\) −2.09508 −0.121569
\(298\) −47.3810 −2.74471
\(299\) −8.88923 −0.514078
\(300\) −19.1962 −1.10830
\(301\) −12.6687 −0.730209
\(302\) −18.9545 −1.09071
\(303\) −14.5011 −0.833067
\(304\) −39.7686 −2.28089
\(305\) 18.1331 1.03830
\(306\) 14.0909 0.805521
\(307\) 28.4774 1.62529 0.812645 0.582759i \(-0.198027\pi\)
0.812645 + 0.582759i \(0.198027\pi\)
\(308\) −8.46446 −0.482308
\(309\) −17.5311 −0.997311
\(310\) 2.68834 0.152688
\(311\) 4.99213 0.283078 0.141539 0.989933i \(-0.454795\pi\)
0.141539 + 0.989933i \(0.454795\pi\)
\(312\) −27.0843 −1.53335
\(313\) 29.7665 1.68250 0.841252 0.540643i \(-0.181819\pi\)
0.841252 + 0.540643i \(0.181819\pi\)
\(314\) −4.50988 −0.254508
\(315\) −19.4148 −1.09390
\(316\) −72.3531 −4.07018
\(317\) 7.55931 0.424573 0.212287 0.977207i \(-0.431909\pi\)
0.212287 + 0.977207i \(0.431909\pi\)
\(318\) 10.6478 0.597101
\(319\) −0.713542 −0.0399507
\(320\) 102.212 5.71381
\(321\) −3.38597 −0.188986
\(322\) −37.4611 −2.08762
\(323\) −7.00046 −0.389516
\(324\) −2.21908 −0.123282
\(325\) −7.75213 −0.430011
\(326\) −35.2523 −1.95244
\(327\) 0.354764 0.0196185
\(328\) −12.6367 −0.697743
\(329\) −2.88949 −0.159303
\(330\) −3.43339 −0.189002
\(331\) −17.3871 −0.955680 −0.477840 0.878447i \(-0.658580\pi\)
−0.477840 + 0.878447i \(0.658580\pi\)
\(332\) −12.5864 −0.690768
\(333\) 11.1370 0.610306
\(334\) −42.9874 −2.35216
\(335\) −12.7295 −0.695484
\(336\) −67.4370 −3.67899
\(337\) −4.32376 −0.235530 −0.117765 0.993041i \(-0.537573\pi\)
−0.117765 + 0.993041i \(0.537573\pi\)
\(338\) 18.8326 1.02436
\(339\) −11.6572 −0.633131
\(340\) 45.4646 2.46566
\(341\) 0.136173 0.00737419
\(342\) −12.1623 −0.657661
\(343\) 1.56870 0.0847016
\(344\) 33.1406 1.78682
\(345\) −11.1975 −0.602851
\(346\) 3.21473 0.172825
\(347\) −6.10499 −0.327733 −0.163867 0.986483i \(-0.552397\pi\)
−0.163867 + 0.986483i \(0.552397\pi\)
\(348\) −11.0273 −0.591124
\(349\) −30.8775 −1.65283 −0.826417 0.563058i \(-0.809625\pi\)
−0.826417 + 0.563058i \(0.809625\pi\)
\(350\) −32.6691 −1.74624
\(351\) −13.0754 −0.697911
\(352\) 9.84803 0.524901
\(353\) 30.2230 1.60861 0.804304 0.594218i \(-0.202538\pi\)
0.804304 + 0.594218i \(0.202538\pi\)
\(354\) −3.00876 −0.159914
\(355\) 12.6884 0.673429
\(356\) 32.3063 1.71223
\(357\) −11.8709 −0.628276
\(358\) −11.0121 −0.582007
\(359\) −2.32282 −0.122594 −0.0612968 0.998120i \(-0.519524\pi\)
−0.0612968 + 0.998120i \(0.519524\pi\)
\(360\) 50.7882 2.67677
\(361\) −12.9577 −0.681983
\(362\) 42.9580 2.25782
\(363\) 11.9035 0.624769
\(364\) −52.8266 −2.76887
\(365\) 1.44846 0.0758159
\(366\) 19.2624 1.00686
\(367\) −15.0709 −0.786693 −0.393347 0.919390i \(-0.628683\pi\)
−0.393347 + 0.919390i \(0.628683\pi\)
\(368\) 57.8994 3.01822
\(369\) −2.28335 −0.118866
\(370\) 48.7629 2.53506
\(371\) 13.3536 0.693283
\(372\) 2.10445 0.109111
\(373\) −20.9214 −1.08327 −0.541634 0.840614i \(-0.682194\pi\)
−0.541634 + 0.840614i \(0.682194\pi\)
\(374\) 3.12510 0.161595
\(375\) 5.87913 0.303597
\(376\) 7.55875 0.389813
\(377\) −4.45321 −0.229352
\(378\) −55.1023 −2.83415
\(379\) −25.8409 −1.32736 −0.663680 0.748016i \(-0.731006\pi\)
−0.663680 + 0.748016i \(0.731006\pi\)
\(380\) −39.2419 −2.01307
\(381\) −5.70284 −0.292166
\(382\) 57.6087 2.94752
\(383\) 6.88938 0.352031 0.176015 0.984387i \(-0.443679\pi\)
0.176015 + 0.984387i \(0.443679\pi\)
\(384\) 54.2422 2.76803
\(385\) −4.30586 −0.219447
\(386\) 41.4807 2.11131
\(387\) 5.98824 0.304399
\(388\) 1.63730 0.0831215
\(389\) 12.9194 0.655038 0.327519 0.944845i \(-0.393787\pi\)
0.327519 + 0.944845i \(0.393787\pi\)
\(390\) −21.4278 −1.08504
\(391\) 10.1920 0.515433
\(392\) −73.6232 −3.71854
\(393\) −10.7429 −0.541908
\(394\) −75.7817 −3.81783
\(395\) −36.8059 −1.85191
\(396\) 4.00100 0.201058
\(397\) 34.6691 1.73999 0.869997 0.493058i \(-0.164121\pi\)
0.869997 + 0.493058i \(0.164121\pi\)
\(398\) 36.6777 1.83849
\(399\) 10.2462 0.512950
\(400\) 50.4930 2.52465
\(401\) 32.8690 1.64140 0.820699 0.571361i \(-0.193585\pi\)
0.820699 + 0.571361i \(0.193585\pi\)
\(402\) −13.5223 −0.674429
\(403\) 0.849855 0.0423343
\(404\) 73.9888 3.68108
\(405\) −1.12884 −0.0560927
\(406\) −18.7667 −0.931378
\(407\) 2.47000 0.122433
\(408\) 31.0537 1.53739
\(409\) 3.74382 0.185120 0.0925601 0.995707i \(-0.470495\pi\)
0.0925601 + 0.995707i \(0.470495\pi\)
\(410\) −9.99751 −0.493742
\(411\) −2.82963 −0.139575
\(412\) 89.4487 4.40682
\(413\) −3.77333 −0.185673
\(414\) 17.7072 0.870259
\(415\) −6.40268 −0.314295
\(416\) 61.4614 3.01339
\(417\) −16.0451 −0.785732
\(418\) −2.69738 −0.131933
\(419\) −1.40691 −0.0687320 −0.0343660 0.999409i \(-0.510941\pi\)
−0.0343660 + 0.999409i \(0.510941\pi\)
\(420\) −66.5439 −3.24701
\(421\) 10.9790 0.535081 0.267541 0.963547i \(-0.413789\pi\)
0.267541 + 0.963547i \(0.413789\pi\)
\(422\) −10.3474 −0.503702
\(423\) 1.36581 0.0664079
\(424\) −34.9322 −1.69646
\(425\) 8.88827 0.431144
\(426\) 13.4786 0.653041
\(427\) 24.1572 1.16905
\(428\) 17.2762 0.835074
\(429\) −1.08538 −0.0524029
\(430\) 26.2192 1.26440
\(431\) 2.49114 0.119994 0.0599969 0.998199i \(-0.480891\pi\)
0.0599969 + 0.998199i \(0.480891\pi\)
\(432\) 85.1654 4.09752
\(433\) −1.54120 −0.0740655 −0.0370327 0.999314i \(-0.511791\pi\)
−0.0370327 + 0.999314i \(0.511791\pi\)
\(434\) 3.58146 0.171916
\(435\) −5.60956 −0.268958
\(436\) −1.81011 −0.0866884
\(437\) −8.79706 −0.420821
\(438\) 1.53867 0.0735206
\(439\) −4.05491 −0.193530 −0.0967652 0.995307i \(-0.530850\pi\)
−0.0967652 + 0.995307i \(0.530850\pi\)
\(440\) 11.2639 0.536986
\(441\) −13.3032 −0.633483
\(442\) 19.5037 0.927698
\(443\) 33.2327 1.57893 0.789466 0.613794i \(-0.210357\pi\)
0.789466 + 0.613794i \(0.210357\pi\)
\(444\) 38.1720 1.81156
\(445\) 16.4342 0.779054
\(446\) −20.7361 −0.981885
\(447\) −18.8677 −0.892412
\(448\) 136.169 6.43336
\(449\) −37.1219 −1.75189 −0.875946 0.482409i \(-0.839762\pi\)
−0.875946 + 0.482409i \(0.839762\pi\)
\(450\) 15.4421 0.727946
\(451\) −0.506405 −0.0238457
\(452\) 59.4782 2.79762
\(453\) −7.54793 −0.354633
\(454\) −44.6942 −2.09760
\(455\) −26.8728 −1.25982
\(456\) −26.8035 −1.25519
\(457\) 22.7120 1.06242 0.531211 0.847239i \(-0.321737\pi\)
0.531211 + 0.847239i \(0.321737\pi\)
\(458\) −29.9781 −1.40079
\(459\) 14.9917 0.699750
\(460\) 57.1326 2.66382
\(461\) −2.52455 −0.117580 −0.0587899 0.998270i \(-0.518724\pi\)
−0.0587899 + 0.998270i \(0.518724\pi\)
\(462\) −4.57403 −0.212803
\(463\) −10.6338 −0.494196 −0.247098 0.968991i \(-0.579477\pi\)
−0.247098 + 0.968991i \(0.579477\pi\)
\(464\) 29.0057 1.34655
\(465\) 1.07053 0.0496448
\(466\) −12.7817 −0.592103
\(467\) 17.7635 0.821995 0.410998 0.911636i \(-0.365180\pi\)
0.410998 + 0.911636i \(0.365180\pi\)
\(468\) 24.9702 1.15425
\(469\) −16.9584 −0.783067
\(470\) 5.98012 0.275842
\(471\) −1.79589 −0.0827504
\(472\) 9.87083 0.454342
\(473\) 1.32808 0.0610654
\(474\) −39.0982 −1.79584
\(475\) −7.67175 −0.352004
\(476\) 60.5688 2.77617
\(477\) −6.31199 −0.289006
\(478\) 36.5724 1.67278
\(479\) −22.4781 −1.02705 −0.513525 0.858075i \(-0.671660\pi\)
−0.513525 + 0.858075i \(0.671660\pi\)
\(480\) 77.4208 3.53376
\(481\) 15.4152 0.702873
\(482\) −52.8526 −2.40737
\(483\) −14.9175 −0.678769
\(484\) −60.7348 −2.76067
\(485\) 0.832894 0.0378198
\(486\) 42.3431 1.92072
\(487\) −12.2676 −0.555898 −0.277949 0.960596i \(-0.589655\pi\)
−0.277949 + 0.960596i \(0.589655\pi\)
\(488\) −63.1940 −2.86066
\(489\) −14.0379 −0.634816
\(490\) −58.2471 −2.63134
\(491\) −32.6946 −1.47549 −0.737743 0.675082i \(-0.764108\pi\)
−0.737743 + 0.675082i \(0.764108\pi\)
\(492\) −7.82612 −0.352829
\(493\) 5.10586 0.229956
\(494\) −16.8343 −0.757411
\(495\) 2.03530 0.0914800
\(496\) −5.53547 −0.248550
\(497\) 16.9037 0.758234
\(498\) −6.80144 −0.304780
\(499\) −17.9868 −0.805199 −0.402599 0.915376i \(-0.631893\pi\)
−0.402599 + 0.915376i \(0.631893\pi\)
\(500\) −29.9970 −1.34151
\(501\) −17.1181 −0.764781
\(502\) −7.22538 −0.322484
\(503\) −14.6166 −0.651722 −0.325861 0.945418i \(-0.605654\pi\)
−0.325861 + 0.945418i \(0.605654\pi\)
\(504\) 67.6610 3.01386
\(505\) 37.6380 1.67487
\(506\) 3.92713 0.174582
\(507\) 7.49938 0.333059
\(508\) 29.0975 1.29099
\(509\) −15.1314 −0.670688 −0.335344 0.942096i \(-0.608853\pi\)
−0.335344 + 0.942096i \(0.608853\pi\)
\(510\) 24.5682 1.08790
\(511\) 1.92967 0.0853635
\(512\) −78.9750 −3.49023
\(513\) −12.9398 −0.571305
\(514\) 17.2658 0.761562
\(515\) 45.5024 2.00508
\(516\) 20.5246 0.903544
\(517\) 0.302912 0.0133220
\(518\) 64.9629 2.85431
\(519\) 1.28015 0.0561922
\(520\) 70.2979 3.08277
\(521\) −15.5065 −0.679352 −0.339676 0.940543i \(-0.610317\pi\)
−0.339676 + 0.940543i \(0.610317\pi\)
\(522\) 8.87069 0.388260
\(523\) 14.3989 0.629618 0.314809 0.949155i \(-0.398060\pi\)
0.314809 + 0.949155i \(0.398060\pi\)
\(524\) 54.8134 2.39453
\(525\) −13.0092 −0.567770
\(526\) −14.6431 −0.638471
\(527\) −0.974407 −0.0424459
\(528\) 7.06958 0.307664
\(529\) −10.1923 −0.443143
\(530\) −27.6367 −1.20046
\(531\) 1.78358 0.0774009
\(532\) −52.2789 −2.26658
\(533\) −3.16047 −0.136895
\(534\) 17.4577 0.755468
\(535\) 8.78835 0.379954
\(536\) 44.3623 1.91616
\(537\) −4.38516 −0.189233
\(538\) 63.2542 2.72708
\(539\) −2.95040 −0.127083
\(540\) 84.0376 3.61640
\(541\) 23.3071 1.00205 0.501026 0.865432i \(-0.332956\pi\)
0.501026 + 0.865432i \(0.332956\pi\)
\(542\) −39.3519 −1.69031
\(543\) 17.1064 0.734107
\(544\) −70.4691 −3.02134
\(545\) −0.920798 −0.0394427
\(546\) −28.5465 −1.22168
\(547\) 6.49767 0.277820 0.138910 0.990305i \(-0.455640\pi\)
0.138910 + 0.990305i \(0.455640\pi\)
\(548\) 14.4376 0.616742
\(549\) −11.4187 −0.487337
\(550\) 3.42478 0.146033
\(551\) −4.40703 −0.187746
\(552\) 39.0233 1.66094
\(553\) −49.0335 −2.08512
\(554\) −25.1990 −1.07060
\(555\) 19.4180 0.824249
\(556\) 81.8666 3.47192
\(557\) 1.60081 0.0678284 0.0339142 0.999425i \(-0.489203\pi\)
0.0339142 + 0.999425i \(0.489203\pi\)
\(558\) −1.69289 −0.0716658
\(559\) 8.28856 0.350569
\(560\) 175.034 7.39655
\(561\) 1.24446 0.0525410
\(562\) −26.3374 −1.11098
\(563\) 12.7006 0.535267 0.267634 0.963521i \(-0.413758\pi\)
0.267634 + 0.963521i \(0.413758\pi\)
\(564\) 4.68128 0.197117
\(565\) 30.2565 1.27290
\(566\) −32.2382 −1.35507
\(567\) −1.50387 −0.0631564
\(568\) −44.2192 −1.85539
\(569\) −25.0756 −1.05123 −0.525613 0.850724i \(-0.676164\pi\)
−0.525613 + 0.850724i \(0.676164\pi\)
\(570\) −21.2056 −0.888204
\(571\) 41.6074 1.74121 0.870607 0.491979i \(-0.163726\pi\)
0.870607 + 0.491979i \(0.163726\pi\)
\(572\) 5.53794 0.231553
\(573\) 22.9405 0.958354
\(574\) −13.3189 −0.555919
\(575\) 11.1694 0.465794
\(576\) −64.3644 −2.68185
\(577\) −35.3494 −1.47162 −0.735808 0.677190i \(-0.763197\pi\)
−0.735808 + 0.677190i \(0.763197\pi\)
\(578\) 24.5098 1.01947
\(579\) 16.5182 0.686471
\(580\) 28.6215 1.18844
\(581\) −8.52977 −0.353874
\(582\) 0.884767 0.0366748
\(583\) −1.39989 −0.0579773
\(584\) −5.04791 −0.208884
\(585\) 12.7023 0.525175
\(586\) −1.55038 −0.0640458
\(587\) 39.4334 1.62759 0.813795 0.581152i \(-0.197398\pi\)
0.813795 + 0.581152i \(0.197398\pi\)
\(588\) −45.5963 −1.88036
\(589\) 0.841043 0.0346546
\(590\) 7.80932 0.321505
\(591\) −30.1773 −1.24133
\(592\) −100.406 −4.12666
\(593\) −7.35315 −0.301958 −0.150979 0.988537i \(-0.548243\pi\)
−0.150979 + 0.988537i \(0.548243\pi\)
\(594\) 5.77650 0.237013
\(595\) 30.8113 1.26314
\(596\) 96.2684 3.94331
\(597\) 14.6055 0.597765
\(598\) 24.5092 1.00225
\(599\) 29.6448 1.21125 0.605627 0.795749i \(-0.292922\pi\)
0.605627 + 0.795749i \(0.292922\pi\)
\(600\) 34.0315 1.38933
\(601\) 15.6617 0.638854 0.319427 0.947611i \(-0.396510\pi\)
0.319427 + 0.947611i \(0.396510\pi\)
\(602\) 34.9297 1.42363
\(603\) 8.01593 0.326434
\(604\) 38.5116 1.56702
\(605\) −30.8957 −1.25609
\(606\) 39.9821 1.62416
\(607\) −25.5109 −1.03546 −0.517728 0.855545i \(-0.673222\pi\)
−0.517728 + 0.855545i \(0.673222\pi\)
\(608\) 60.8241 2.46674
\(609\) −7.47316 −0.302828
\(610\) −49.9960 −2.02428
\(611\) 1.89047 0.0764802
\(612\) −28.6297 −1.15729
\(613\) 48.4431 1.95660 0.978300 0.207195i \(-0.0664333\pi\)
0.978300 + 0.207195i \(0.0664333\pi\)
\(614\) −78.5171 −3.16869
\(615\) −3.98114 −0.160535
\(616\) 15.0060 0.604609
\(617\) −43.0885 −1.73468 −0.867339 0.497718i \(-0.834171\pi\)
−0.867339 + 0.497718i \(0.834171\pi\)
\(618\) 48.3364 1.94437
\(619\) 15.1169 0.607600 0.303800 0.952736i \(-0.401745\pi\)
0.303800 + 0.952736i \(0.401745\pi\)
\(620\) −5.46216 −0.219366
\(621\) 18.8391 0.755988
\(622\) −13.7642 −0.551893
\(623\) 21.8939 0.877160
\(624\) 44.1211 1.76626
\(625\) −30.8644 −1.23457
\(626\) −82.0715 −3.28024
\(627\) −1.07413 −0.0428966
\(628\) 9.16316 0.365650
\(629\) −17.6744 −0.704726
\(630\) 53.5301 2.13269
\(631\) −21.2247 −0.844941 −0.422470 0.906377i \(-0.638837\pi\)
−0.422470 + 0.906377i \(0.638837\pi\)
\(632\) 128.269 5.10228
\(633\) −4.12045 −0.163773
\(634\) −20.8423 −0.827755
\(635\) 14.8019 0.587394
\(636\) −21.6342 −0.857852
\(637\) −18.4134 −0.729566
\(638\) 1.96736 0.0778885
\(639\) −7.99006 −0.316082
\(640\) −140.787 −5.56509
\(641\) 4.84075 0.191198 0.0955990 0.995420i \(-0.469523\pi\)
0.0955990 + 0.995420i \(0.469523\pi\)
\(642\) 9.33570 0.368451
\(643\) 42.6346 1.68134 0.840671 0.541546i \(-0.182161\pi\)
0.840671 + 0.541546i \(0.182161\pi\)
\(644\) 76.1132 2.99928
\(645\) 10.4408 0.411107
\(646\) 19.3015 0.759407
\(647\) 41.8377 1.64481 0.822405 0.568902i \(-0.192632\pi\)
0.822405 + 0.568902i \(0.192632\pi\)
\(648\) 3.93404 0.154544
\(649\) 0.395567 0.0155274
\(650\) 21.3740 0.838356
\(651\) 1.42618 0.0558966
\(652\) 71.6254 2.80507
\(653\) 10.4646 0.409513 0.204757 0.978813i \(-0.434360\pi\)
0.204757 + 0.978813i \(0.434360\pi\)
\(654\) −0.978146 −0.0382486
\(655\) 27.8835 1.08950
\(656\) 20.5855 0.803729
\(657\) −0.912118 −0.0355851
\(658\) 7.96683 0.310579
\(659\) 41.0338 1.59845 0.799226 0.601031i \(-0.205243\pi\)
0.799226 + 0.601031i \(0.205243\pi\)
\(660\) 6.97595 0.271539
\(661\) −22.4413 −0.872865 −0.436433 0.899737i \(-0.643758\pi\)
−0.436433 + 0.899737i \(0.643758\pi\)
\(662\) 47.9392 1.86321
\(663\) 7.76663 0.301631
\(664\) 22.3134 0.865929
\(665\) −26.5942 −1.03128
\(666\) −30.7068 −1.18986
\(667\) 6.41623 0.248437
\(668\) 87.3415 3.37934
\(669\) −8.25740 −0.319249
\(670\) 35.0973 1.35593
\(671\) −2.53246 −0.0977644
\(672\) 103.142 3.97877
\(673\) −25.0608 −0.966022 −0.483011 0.875614i \(-0.660457\pi\)
−0.483011 + 0.875614i \(0.660457\pi\)
\(674\) 11.9214 0.459193
\(675\) 16.4292 0.632362
\(676\) −38.2640 −1.47169
\(677\) −7.81351 −0.300297 −0.150149 0.988663i \(-0.547975\pi\)
−0.150149 + 0.988663i \(0.547975\pi\)
\(678\) 32.1409 1.23436
\(679\) 1.10960 0.0425824
\(680\) −80.6006 −3.09089
\(681\) −17.7978 −0.682013
\(682\) −0.375453 −0.0143768
\(683\) 16.6413 0.636763 0.318381 0.947963i \(-0.396861\pi\)
0.318381 + 0.947963i \(0.396861\pi\)
\(684\) 24.7113 0.944859
\(685\) 7.34436 0.280614
\(686\) −4.32517 −0.165136
\(687\) −11.9377 −0.455451
\(688\) −53.9870 −2.05823
\(689\) −8.73667 −0.332841
\(690\) 30.8734 1.17533
\(691\) −2.33468 −0.0888154 −0.0444077 0.999013i \(-0.514140\pi\)
−0.0444077 + 0.999013i \(0.514140\pi\)
\(692\) −6.53167 −0.248297
\(693\) 2.71147 0.103000
\(694\) 16.8325 0.638954
\(695\) 41.6454 1.57970
\(696\) 19.5494 0.741018
\(697\) 3.62366 0.137256
\(698\) 85.1347 3.22239
\(699\) −5.08986 −0.192516
\(700\) 66.3768 2.50881
\(701\) −20.1316 −0.760359 −0.380180 0.924913i \(-0.624138\pi\)
−0.380180 + 0.924913i \(0.624138\pi\)
\(702\) 36.0510 1.36066
\(703\) 15.2554 0.575368
\(704\) −14.2749 −0.538004
\(705\) 2.38136 0.0896872
\(706\) −83.3301 −3.13617
\(707\) 50.1421 1.88579
\(708\) 6.11319 0.229748
\(709\) −12.0459 −0.452394 −0.226197 0.974082i \(-0.572629\pi\)
−0.226197 + 0.974082i \(0.572629\pi\)
\(710\) −34.9840 −1.31293
\(711\) 23.1773 0.869215
\(712\) −57.2733 −2.14641
\(713\) −1.22448 −0.0458571
\(714\) 32.7302 1.22490
\(715\) 2.81714 0.105355
\(716\) 22.3743 0.836167
\(717\) 14.5636 0.543888
\(718\) 6.40442 0.239011
\(719\) −44.5043 −1.65973 −0.829865 0.557965i \(-0.811582\pi\)
−0.829865 + 0.557965i \(0.811582\pi\)
\(720\) −82.7355 −3.08337
\(721\) 60.6192 2.25758
\(722\) 35.7266 1.32961
\(723\) −21.0466 −0.782730
\(724\) −87.2818 −3.24380
\(725\) 5.59547 0.207811
\(726\) −32.8199 −1.21806
\(727\) −25.3119 −0.938768 −0.469384 0.882994i \(-0.655524\pi\)
−0.469384 + 0.882994i \(0.655524\pi\)
\(728\) 93.6522 3.47098
\(729\) 18.0499 0.668515
\(730\) −3.99366 −0.147812
\(731\) −9.50332 −0.351493
\(732\) −39.1373 −1.44655
\(733\) 36.5932 1.35160 0.675800 0.737085i \(-0.263798\pi\)
0.675800 + 0.737085i \(0.263798\pi\)
\(734\) 41.5530 1.53375
\(735\) −23.1947 −0.855551
\(736\) −88.5543 −3.26415
\(737\) 1.77779 0.0654858
\(738\) 6.29559 0.231744
\(739\) 0.195944 0.00720792 0.00360396 0.999994i \(-0.498853\pi\)
0.00360396 + 0.999994i \(0.498853\pi\)
\(740\) −99.0762 −3.64212
\(741\) −6.70363 −0.246264
\(742\) −36.8181 −1.35164
\(743\) −26.9426 −0.988429 −0.494215 0.869340i \(-0.664544\pi\)
−0.494215 + 0.869340i \(0.664544\pi\)
\(744\) −3.73082 −0.136779
\(745\) 48.9716 1.79418
\(746\) 57.6839 2.11196
\(747\) 4.03186 0.147518
\(748\) −6.34956 −0.232163
\(749\) 11.7080 0.427802
\(750\) −16.2098 −0.591898
\(751\) −6.28468 −0.229331 −0.114666 0.993404i \(-0.536580\pi\)
−0.114666 + 0.993404i \(0.536580\pi\)
\(752\) −12.3134 −0.449025
\(753\) −2.87724 −0.104852
\(754\) 12.2783 0.447148
\(755\) 19.5908 0.712983
\(756\) 111.956 4.07182
\(757\) −41.4628 −1.50699 −0.753496 0.657452i \(-0.771634\pi\)
−0.753496 + 0.657452i \(0.771634\pi\)
\(758\) 71.2480 2.58784
\(759\) 1.56383 0.0567636
\(760\) 69.5690 2.52353
\(761\) −1.08106 −0.0391883 −0.0195942 0.999808i \(-0.506237\pi\)
−0.0195942 + 0.999808i \(0.506237\pi\)
\(762\) 15.7237 0.569611
\(763\) −1.22671 −0.0444097
\(764\) −117.049 −4.23468
\(765\) −14.5639 −0.526559
\(766\) −18.9952 −0.686325
\(767\) 2.46873 0.0891406
\(768\) −70.7951 −2.55460
\(769\) 27.5592 0.993811 0.496905 0.867805i \(-0.334470\pi\)
0.496905 + 0.867805i \(0.334470\pi\)
\(770\) 11.8720 0.427838
\(771\) 6.87547 0.247614
\(772\) −84.2803 −3.03332
\(773\) 17.9752 0.646523 0.323262 0.946310i \(-0.395221\pi\)
0.323262 + 0.946310i \(0.395221\pi\)
\(774\) −16.5106 −0.593462
\(775\) −1.06785 −0.0383581
\(776\) −2.90265 −0.104199
\(777\) 25.8691 0.928048
\(778\) −35.6209 −1.27707
\(779\) −3.12770 −0.112061
\(780\) 43.5368 1.55887
\(781\) −1.77205 −0.0634090
\(782\) −28.1012 −1.00490
\(783\) 9.43777 0.337278
\(784\) 119.934 4.28337
\(785\) 4.66129 0.166368
\(786\) 29.6201 1.05651
\(787\) 2.59217 0.0924007 0.0462004 0.998932i \(-0.485289\pi\)
0.0462004 + 0.998932i \(0.485289\pi\)
\(788\) 153.973 5.48505
\(789\) −5.83108 −0.207592
\(790\) 101.480 3.61051
\(791\) 40.3083 1.43320
\(792\) −7.09306 −0.252041
\(793\) −15.8050 −0.561253
\(794\) −95.5888 −3.39232
\(795\) −11.0053 −0.390317
\(796\) −74.5216 −2.64135
\(797\) −27.2886 −0.966611 −0.483305 0.875452i \(-0.660564\pi\)
−0.483305 + 0.875452i \(0.660564\pi\)
\(798\) −28.2505 −1.00006
\(799\) −2.16753 −0.0766818
\(800\) −77.2265 −2.73037
\(801\) −10.3488 −0.365658
\(802\) −90.6254 −3.20010
\(803\) −0.202292 −0.00713871
\(804\) 27.4744 0.968949
\(805\) 38.7187 1.36465
\(806\) −2.34320 −0.0825356
\(807\) 25.1886 0.886682
\(808\) −131.169 −4.61451
\(809\) −49.9218 −1.75516 −0.877578 0.479434i \(-0.840842\pi\)
−0.877578 + 0.479434i \(0.840842\pi\)
\(810\) 3.11242 0.109359
\(811\) −26.9446 −0.946152 −0.473076 0.881022i \(-0.656856\pi\)
−0.473076 + 0.881022i \(0.656856\pi\)
\(812\) 38.1301 1.33811
\(813\) −15.6704 −0.549586
\(814\) −6.81021 −0.238698
\(815\) 36.4357 1.27629
\(816\) −50.5874 −1.77091
\(817\) 8.20262 0.286973
\(818\) −10.3224 −0.360913
\(819\) 16.9222 0.591311
\(820\) 20.3129 0.709356
\(821\) 24.2129 0.845035 0.422517 0.906355i \(-0.361147\pi\)
0.422517 + 0.906355i \(0.361147\pi\)
\(822\) 7.80178 0.272118
\(823\) 19.1779 0.668498 0.334249 0.942485i \(-0.391517\pi\)
0.334249 + 0.942485i \(0.391517\pi\)
\(824\) −158.577 −5.52428
\(825\) 1.36379 0.0474811
\(826\) 10.4037 0.361992
\(827\) −42.1158 −1.46451 −0.732256 0.681030i \(-0.761532\pi\)
−0.732256 + 0.681030i \(0.761532\pi\)
\(828\) −35.9773 −1.25030
\(829\) −28.6024 −0.993404 −0.496702 0.867921i \(-0.665456\pi\)
−0.496702 + 0.867921i \(0.665456\pi\)
\(830\) 17.6533 0.612755
\(831\) −10.0346 −0.348095
\(832\) −89.0892 −3.08861
\(833\) 21.1120 0.731489
\(834\) 44.2391 1.53188
\(835\) 44.4305 1.53758
\(836\) 5.48051 0.189548
\(837\) −1.80111 −0.0622556
\(838\) 3.87909 0.134001
\(839\) 3.92016 0.135339 0.0676694 0.997708i \(-0.478444\pi\)
0.0676694 + 0.997708i \(0.478444\pi\)
\(840\) 117.971 4.07037
\(841\) −25.7857 −0.889161
\(842\) −30.2709 −1.04320
\(843\) −10.4879 −0.361223
\(844\) 21.0237 0.723666
\(845\) −19.4648 −0.669610
\(846\) −3.76577 −0.129470
\(847\) −41.1598 −1.41427
\(848\) 56.9057 1.95415
\(849\) −12.8377 −0.440588
\(850\) −24.5065 −0.840566
\(851\) −22.2104 −0.761363
\(852\) −27.3858 −0.938221
\(853\) 18.2311 0.624221 0.312110 0.950046i \(-0.398964\pi\)
0.312110 + 0.950046i \(0.398964\pi\)
\(854\) −66.6057 −2.27920
\(855\) 12.5706 0.429905
\(856\) −30.6276 −1.04683
\(857\) −40.5325 −1.38456 −0.692282 0.721627i \(-0.743395\pi\)
−0.692282 + 0.721627i \(0.743395\pi\)
\(858\) 2.99259 0.102165
\(859\) −4.23798 −0.144598 −0.0722989 0.997383i \(-0.523034\pi\)
−0.0722989 + 0.997383i \(0.523034\pi\)
\(860\) −53.2720 −1.81656
\(861\) −5.30375 −0.180751
\(862\) −6.86850 −0.233942
\(863\) −16.6849 −0.567960 −0.283980 0.958830i \(-0.591655\pi\)
−0.283980 + 0.958830i \(0.591655\pi\)
\(864\) −130.256 −4.43141
\(865\) −3.32265 −0.112974
\(866\) 4.24936 0.144399
\(867\) 9.76013 0.331471
\(868\) −7.27679 −0.246991
\(869\) 5.14030 0.174373
\(870\) 15.4665 0.524364
\(871\) 11.0952 0.375945
\(872\) 3.20900 0.108670
\(873\) −0.524486 −0.0177512
\(874\) 24.2550 0.820439
\(875\) −20.3289 −0.687242
\(876\) −3.12627 −0.105627
\(877\) −55.7717 −1.88328 −0.941638 0.336626i \(-0.890714\pi\)
−0.941638 + 0.336626i \(0.890714\pi\)
\(878\) 11.1801 0.377310
\(879\) −0.617383 −0.0208238
\(880\) −18.3492 −0.618553
\(881\) 51.5797 1.73777 0.868883 0.495018i \(-0.164838\pi\)
0.868883 + 0.495018i \(0.164838\pi\)
\(882\) 36.6791 1.23505
\(883\) 34.4573 1.15958 0.579790 0.814766i \(-0.303135\pi\)
0.579790 + 0.814766i \(0.303135\pi\)
\(884\) −39.6276 −1.33282
\(885\) 3.10977 0.104534
\(886\) −91.6283 −3.07831
\(887\) −28.2620 −0.948946 −0.474473 0.880270i \(-0.657361\pi\)
−0.474473 + 0.880270i \(0.657361\pi\)
\(888\) −67.6721 −2.27093
\(889\) 19.7193 0.661365
\(890\) −45.3118 −1.51886
\(891\) 0.157654 0.00528160
\(892\) 42.1316 1.41067
\(893\) 1.87087 0.0626062
\(894\) 52.0216 1.73986
\(895\) 11.3818 0.380451
\(896\) −187.559 −6.26590
\(897\) 9.75987 0.325872
\(898\) 102.352 3.41552
\(899\) −0.613423 −0.0204588
\(900\) −31.3751 −1.04584
\(901\) 10.0171 0.333718
\(902\) 1.39625 0.0464900
\(903\) 13.9095 0.462878
\(904\) −105.444 −3.50703
\(905\) −44.4001 −1.47591
\(906\) 20.8110 0.691398
\(907\) 56.6617 1.88142 0.940710 0.339211i \(-0.110160\pi\)
0.940710 + 0.339211i \(0.110160\pi\)
\(908\) 90.8093 3.01361
\(909\) −23.7012 −0.786120
\(910\) 74.0931 2.45616
\(911\) 55.3263 1.83304 0.916520 0.399988i \(-0.130986\pi\)
0.916520 + 0.399988i \(0.130986\pi\)
\(912\) 43.6637 1.44585
\(913\) 0.894195 0.0295935
\(914\) −62.6209 −2.07132
\(915\) −19.9091 −0.658173
\(916\) 60.9094 2.01250
\(917\) 37.1469 1.22670
\(918\) −41.3346 −1.36425
\(919\) 47.7811 1.57615 0.788077 0.615577i \(-0.211077\pi\)
0.788077 + 0.615577i \(0.211077\pi\)
\(920\) −101.286 −3.33930
\(921\) −31.2665 −1.03027
\(922\) 6.96062 0.229236
\(923\) −11.0594 −0.364023
\(924\) 9.29349 0.305734
\(925\) −19.3693 −0.636858
\(926\) 29.3193 0.963492
\(927\) −28.6536 −0.941107
\(928\) −44.3627 −1.45628
\(929\) 7.69006 0.252303 0.126151 0.992011i \(-0.459737\pi\)
0.126151 + 0.992011i \(0.459737\pi\)
\(930\) −2.95165 −0.0967883
\(931\) −18.2225 −0.597218
\(932\) 25.9699 0.850672
\(933\) −5.48107 −0.179442
\(934\) −48.9770 −1.60258
\(935\) −3.23001 −0.105633
\(936\) −44.2677 −1.44693
\(937\) 56.5139 1.84623 0.923115 0.384524i \(-0.125635\pi\)
0.923115 + 0.384524i \(0.125635\pi\)
\(938\) 46.7573 1.52668
\(939\) −32.6819 −1.06653
\(940\) −12.1504 −0.396301
\(941\) 11.3043 0.368509 0.184254 0.982879i \(-0.441013\pi\)
0.184254 + 0.982879i \(0.441013\pi\)
\(942\) 4.95159 0.161332
\(943\) 4.55364 0.148287
\(944\) −16.0799 −0.523356
\(945\) 56.9521 1.85265
\(946\) −3.66176 −0.119054
\(947\) 1.51932 0.0493712 0.0246856 0.999695i \(-0.492142\pi\)
0.0246856 + 0.999695i \(0.492142\pi\)
\(948\) 79.4395 2.58008
\(949\) −1.26250 −0.0409824
\(950\) 21.1524 0.686273
\(951\) −8.29969 −0.269136
\(952\) −107.378 −3.48013
\(953\) −28.5691 −0.925444 −0.462722 0.886504i \(-0.653127\pi\)
−0.462722 + 0.886504i \(0.653127\pi\)
\(954\) 17.4032 0.563451
\(955\) −59.5426 −1.92675
\(956\) −74.3076 −2.40328
\(957\) 0.783428 0.0253246
\(958\) 61.9760 2.00235
\(959\) 9.78430 0.315952
\(960\) −112.223 −3.62197
\(961\) −30.8829 −0.996224
\(962\) −42.5024 −1.37033
\(963\) −5.53416 −0.178336
\(964\) 107.386 3.45865
\(965\) −42.8733 −1.38014
\(966\) 41.1301 1.32334
\(967\) 11.7892 0.379115 0.189558 0.981870i \(-0.439295\pi\)
0.189558 + 0.981870i \(0.439295\pi\)
\(968\) 107.672 3.46071
\(969\) 7.68610 0.246913
\(970\) −2.29643 −0.0737340
\(971\) 32.0269 1.02779 0.513896 0.857853i \(-0.328202\pi\)
0.513896 + 0.857853i \(0.328202\pi\)
\(972\) −86.0324 −2.75949
\(973\) 55.4808 1.77863
\(974\) 33.8239 1.08379
\(975\) 8.51139 0.272583
\(976\) 102.945 3.29519
\(977\) 11.7665 0.376445 0.188222 0.982126i \(-0.439727\pi\)
0.188222 + 0.982126i \(0.439727\pi\)
\(978\) 38.7050 1.23765
\(979\) −2.29519 −0.0733545
\(980\) 118.346 3.78043
\(981\) 0.579841 0.0185129
\(982\) 90.1447 2.87663
\(983\) −9.19434 −0.293254 −0.146627 0.989192i \(-0.546842\pi\)
−0.146627 + 0.989192i \(0.546842\pi\)
\(984\) 13.8743 0.442297
\(985\) 78.3258 2.49567
\(986\) −14.0777 −0.448327
\(987\) 3.17249 0.100982
\(988\) 34.2038 1.08817
\(989\) −11.9423 −0.379741
\(990\) −5.61168 −0.178351
\(991\) −15.3089 −0.486303 −0.243151 0.969988i \(-0.578181\pi\)
−0.243151 + 0.969988i \(0.578181\pi\)
\(992\) 8.46622 0.268803
\(993\) 19.0900 0.605803
\(994\) −46.6064 −1.47827
\(995\) −37.9090 −1.20180
\(996\) 13.8191 0.437876
\(997\) −43.8493 −1.38872 −0.694361 0.719627i \(-0.744313\pi\)
−0.694361 + 0.719627i \(0.744313\pi\)
\(998\) 49.5927 1.56983
\(999\) −32.6698 −1.03363
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 6037.2.a.b.1.1 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.1 259 1.1 even 1 trivial