Properties

Label 8003.2.a.b.1.15
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} +O(q^{10})\) \(q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} -3.79414 q^{10} +2.83952 q^{11} +9.15010 q^{12} +2.38822 q^{13} +9.01688 q^{14} +3.82326 q^{15} +2.71562 q^{16} -1.20694 q^{17} -6.89073 q^{18} -2.50380 q^{19} +5.96298 q^{20} -9.08609 q^{21} -6.82532 q^{22} -6.40600 q^{23} -10.3499 q^{24} -2.50844 q^{25} -5.74053 q^{26} -0.322786 q^{27} -14.1712 q^{28} +5.21159 q^{29} -9.18992 q^{30} +6.95630 q^{31} +2.01856 q^{32} +6.87771 q^{33} +2.90109 q^{34} -5.92127 q^{35} +10.8297 q^{36} -2.27675 q^{37} +6.01834 q^{38} +5.78460 q^{39} -6.74485 q^{40} -3.13902 q^{41} +21.8401 q^{42} -1.85137 q^{43} +10.7269 q^{44} +4.52505 q^{45} +15.3980 q^{46} -5.28542 q^{47} +6.57760 q^{48} +7.07207 q^{49} +6.02950 q^{50} -2.92336 q^{51} +9.02199 q^{52} -1.00000 q^{53} +0.775876 q^{54} +4.48210 q^{55} +16.0293 q^{56} -6.06454 q^{57} -12.5270 q^{58} -10.9540 q^{59} +14.4431 q^{60} -4.26030 q^{61} -16.7207 q^{62} -10.7539 q^{63} -10.2832 q^{64} +3.76973 q^{65} -16.5318 q^{66} +7.32529 q^{67} -4.55944 q^{68} -15.5162 q^{69} +14.2329 q^{70} +2.39880 q^{71} -12.2497 q^{72} +12.3298 q^{73} +5.47260 q^{74} -6.07578 q^{75} -9.45860 q^{76} -10.6518 q^{77} -13.9043 q^{78} -14.0130 q^{79} +4.28652 q^{80} -9.38204 q^{81} +7.54523 q^{82} -6.98219 q^{83} -34.3245 q^{84} -1.90511 q^{85} +4.45010 q^{86} +12.6232 q^{87} -12.1334 q^{88} -16.4636 q^{89} -10.8768 q^{90} -8.95888 q^{91} -24.1999 q^{92} +16.8491 q^{93} +12.7045 q^{94} -3.95217 q^{95} +4.88923 q^{96} -8.99278 q^{97} -16.9990 q^{98} +8.14016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40368 −1.69966 −0.849831 0.527055i \(-0.823296\pi\)
−0.849831 + 0.527055i \(0.823296\pi\)
\(3\) 2.42213 1.39842 0.699210 0.714916i \(-0.253535\pi\)
0.699210 + 0.714916i \(0.253535\pi\)
\(4\) 3.77770 1.88885
\(5\) 1.57847 0.705912 0.352956 0.935640i \(-0.385176\pi\)
0.352956 + 0.935640i \(0.385176\pi\)
\(6\) −5.82205 −2.37684
\(7\) −3.75128 −1.41785 −0.708924 0.705284i \(-0.750819\pi\)
−0.708924 + 0.705284i \(0.750819\pi\)
\(8\) −4.27303 −1.51075
\(9\) 2.86673 0.955578
\(10\) −3.79414 −1.19981
\(11\) 2.83952 0.856148 0.428074 0.903744i \(-0.359192\pi\)
0.428074 + 0.903744i \(0.359192\pi\)
\(12\) 9.15010 2.64141
\(13\) 2.38822 0.662374 0.331187 0.943565i \(-0.392551\pi\)
0.331187 + 0.943565i \(0.392551\pi\)
\(14\) 9.01688 2.40986
\(15\) 3.82326 0.987162
\(16\) 2.71562 0.678906
\(17\) −1.20694 −0.292725 −0.146363 0.989231i \(-0.546757\pi\)
−0.146363 + 0.989231i \(0.546757\pi\)
\(18\) −6.89073 −1.62416
\(19\) −2.50380 −0.574411 −0.287205 0.957869i \(-0.592726\pi\)
−0.287205 + 0.957869i \(0.592726\pi\)
\(20\) 5.96298 1.33336
\(21\) −9.08609 −1.98275
\(22\) −6.82532 −1.45516
\(23\) −6.40600 −1.33574 −0.667872 0.744277i \(-0.732794\pi\)
−0.667872 + 0.744277i \(0.732794\pi\)
\(24\) −10.3499 −2.11266
\(25\) −2.50844 −0.501688
\(26\) −5.74053 −1.12581
\(27\) −0.322786 −0.0621202
\(28\) −14.1712 −2.67810
\(29\) 5.21159 0.967767 0.483884 0.875132i \(-0.339226\pi\)
0.483884 + 0.875132i \(0.339226\pi\)
\(30\) −9.18992 −1.67784
\(31\) 6.95630 1.24939 0.624694 0.780870i \(-0.285224\pi\)
0.624694 + 0.780870i \(0.285224\pi\)
\(32\) 2.01856 0.356835
\(33\) 6.87771 1.19726
\(34\) 2.90109 0.497534
\(35\) −5.92127 −1.00088
\(36\) 10.8297 1.80494
\(37\) −2.27675 −0.374296 −0.187148 0.982332i \(-0.559924\pi\)
−0.187148 + 0.982332i \(0.559924\pi\)
\(38\) 6.01834 0.976304
\(39\) 5.78460 0.926277
\(40\) −6.74485 −1.06645
\(41\) −3.13902 −0.490233 −0.245117 0.969494i \(-0.578826\pi\)
−0.245117 + 0.969494i \(0.578826\pi\)
\(42\) 21.8401 3.37000
\(43\) −1.85137 −0.282331 −0.141165 0.989986i \(-0.545085\pi\)
−0.141165 + 0.989986i \(0.545085\pi\)
\(44\) 10.7269 1.61714
\(45\) 4.52505 0.674554
\(46\) 15.3980 2.27031
\(47\) −5.28542 −0.770958 −0.385479 0.922717i \(-0.625964\pi\)
−0.385479 + 0.922717i \(0.625964\pi\)
\(48\) 6.57760 0.949395
\(49\) 7.07207 1.01030
\(50\) 6.02950 0.852700
\(51\) −2.92336 −0.409353
\(52\) 9.02199 1.25113
\(53\) −1.00000 −0.137361
\(54\) 0.775876 0.105583
\(55\) 4.48210 0.604366
\(56\) 16.0293 2.14201
\(57\) −6.06454 −0.803267
\(58\) −12.5270 −1.64488
\(59\) −10.9540 −1.42609 −0.713043 0.701121i \(-0.752683\pi\)
−0.713043 + 0.701121i \(0.752683\pi\)
\(60\) 14.4431 1.86460
\(61\) −4.26030 −0.545475 −0.272738 0.962088i \(-0.587929\pi\)
−0.272738 + 0.962088i \(0.587929\pi\)
\(62\) −16.7207 −2.12354
\(63\) −10.7539 −1.35487
\(64\) −10.2832 −1.28540
\(65\) 3.76973 0.467578
\(66\) −16.5318 −2.03493
\(67\) 7.32529 0.894927 0.447464 0.894302i \(-0.352327\pi\)
0.447464 + 0.894302i \(0.352327\pi\)
\(68\) −4.55944 −0.552914
\(69\) −15.5162 −1.86793
\(70\) 14.2329 1.70115
\(71\) 2.39880 0.284685 0.142342 0.989817i \(-0.454537\pi\)
0.142342 + 0.989817i \(0.454537\pi\)
\(72\) −12.2497 −1.44364
\(73\) 12.3298 1.44310 0.721549 0.692363i \(-0.243430\pi\)
0.721549 + 0.692363i \(0.243430\pi\)
\(74\) 5.47260 0.636176
\(75\) −6.07578 −0.701570
\(76\) −9.45860 −1.08498
\(77\) −10.6518 −1.21389
\(78\) −13.9043 −1.57436
\(79\) −14.0130 −1.57658 −0.788290 0.615304i \(-0.789033\pi\)
−0.788290 + 0.615304i \(0.789033\pi\)
\(80\) 4.28652 0.479248
\(81\) −9.38204 −1.04245
\(82\) 7.54523 0.833231
\(83\) −6.98219 −0.766395 −0.383197 0.923666i \(-0.625177\pi\)
−0.383197 + 0.923666i \(0.625177\pi\)
\(84\) −34.3245 −3.74511
\(85\) −1.90511 −0.206638
\(86\) 4.45010 0.479867
\(87\) 12.6232 1.35334
\(88\) −12.1334 −1.29342
\(89\) −16.4636 −1.74514 −0.872568 0.488492i \(-0.837547\pi\)
−0.872568 + 0.488492i \(0.837547\pi\)
\(90\) −10.8768 −1.14651
\(91\) −8.95888 −0.939146
\(92\) −24.1999 −2.52302
\(93\) 16.8491 1.74717
\(94\) 12.7045 1.31037
\(95\) −3.95217 −0.405484
\(96\) 4.88923 0.499005
\(97\) −8.99278 −0.913079 −0.456539 0.889703i \(-0.650911\pi\)
−0.456539 + 0.889703i \(0.650911\pi\)
\(98\) −16.9990 −1.71716
\(99\) 8.14016 0.818117
\(100\) −9.47613 −0.947613
\(101\) 6.90734 0.687306 0.343653 0.939097i \(-0.388336\pi\)
0.343653 + 0.939097i \(0.388336\pi\)
\(102\) 7.02684 0.695761
\(103\) 5.39416 0.531502 0.265751 0.964042i \(-0.414380\pi\)
0.265751 + 0.964042i \(0.414380\pi\)
\(104\) −10.2050 −1.00068
\(105\) −14.3421 −1.39965
\(106\) 2.40368 0.233467
\(107\) 4.17172 0.403296 0.201648 0.979458i \(-0.435370\pi\)
0.201648 + 0.979458i \(0.435370\pi\)
\(108\) −1.21939 −0.117336
\(109\) 4.86152 0.465650 0.232825 0.972519i \(-0.425203\pi\)
0.232825 + 0.972519i \(0.425203\pi\)
\(110\) −10.7735 −1.02722
\(111\) −5.51460 −0.523423
\(112\) −10.1871 −0.962586
\(113\) 3.21602 0.302538 0.151269 0.988493i \(-0.451664\pi\)
0.151269 + 0.988493i \(0.451664\pi\)
\(114\) 14.5772 1.36528
\(115\) −10.1117 −0.942918
\(116\) 19.6878 1.82797
\(117\) 6.84640 0.632950
\(118\) 26.3299 2.42386
\(119\) 4.52755 0.415040
\(120\) −16.3369 −1.49135
\(121\) −2.93711 −0.267010
\(122\) 10.2404 0.927123
\(123\) −7.60314 −0.685552
\(124\) 26.2788 2.35991
\(125\) −11.8518 −1.06006
\(126\) 25.8490 2.30281
\(127\) 2.30053 0.204139 0.102069 0.994777i \(-0.467454\pi\)
0.102069 + 0.994777i \(0.467454\pi\)
\(128\) 20.6805 1.82792
\(129\) −4.48426 −0.394817
\(130\) −9.06125 −0.794724
\(131\) 0.986426 0.0861844 0.0430922 0.999071i \(-0.486279\pi\)
0.0430922 + 0.999071i \(0.486279\pi\)
\(132\) 25.9819 2.26144
\(133\) 9.39244 0.814428
\(134\) −17.6077 −1.52107
\(135\) −0.509508 −0.0438514
\(136\) 5.15728 0.442233
\(137\) −10.9831 −0.938353 −0.469177 0.883104i \(-0.655449\pi\)
−0.469177 + 0.883104i \(0.655449\pi\)
\(138\) 37.2960 3.17485
\(139\) 20.2952 1.72142 0.860710 0.509096i \(-0.170020\pi\)
0.860710 + 0.509096i \(0.170020\pi\)
\(140\) −22.3688 −1.89051
\(141\) −12.8020 −1.07812
\(142\) −5.76595 −0.483868
\(143\) 6.78141 0.567090
\(144\) 7.78497 0.648748
\(145\) 8.22632 0.683159
\(146\) −29.6370 −2.45278
\(147\) 17.1295 1.41282
\(148\) −8.60089 −0.706989
\(149\) −3.46818 −0.284124 −0.142062 0.989858i \(-0.545373\pi\)
−0.142062 + 0.989858i \(0.545373\pi\)
\(150\) 14.6043 1.19243
\(151\) −1.00000 −0.0813788
\(152\) 10.6988 0.867788
\(153\) −3.45997 −0.279722
\(154\) 25.6037 2.06320
\(155\) 10.9803 0.881958
\(156\) 21.8525 1.74960
\(157\) −18.5966 −1.48417 −0.742085 0.670306i \(-0.766163\pi\)
−0.742085 + 0.670306i \(0.766163\pi\)
\(158\) 33.6827 2.67965
\(159\) −2.42213 −0.192088
\(160\) 3.18624 0.251894
\(161\) 24.0307 1.89388
\(162\) 22.5515 1.77181
\(163\) 9.32753 0.730589 0.365294 0.930892i \(-0.380968\pi\)
0.365294 + 0.930892i \(0.380968\pi\)
\(164\) −11.8583 −0.925977
\(165\) 10.8562 0.845157
\(166\) 16.7830 1.30261
\(167\) −12.8931 −0.997697 −0.498849 0.866689i \(-0.666244\pi\)
−0.498849 + 0.866689i \(0.666244\pi\)
\(168\) 38.8252 2.99543
\(169\) −7.29639 −0.561261
\(170\) 4.57928 0.351215
\(171\) −7.17773 −0.548894
\(172\) −6.99391 −0.533281
\(173\) −5.87716 −0.446832 −0.223416 0.974723i \(-0.571721\pi\)
−0.223416 + 0.974723i \(0.571721\pi\)
\(174\) −30.3421 −2.30023
\(175\) 9.40985 0.711317
\(176\) 7.71108 0.581244
\(177\) −26.5320 −1.99427
\(178\) 39.5733 2.96614
\(179\) 20.8473 1.55820 0.779099 0.626901i \(-0.215677\pi\)
0.779099 + 0.626901i \(0.215677\pi\)
\(180\) 17.0943 1.27413
\(181\) −10.4849 −0.779333 −0.389667 0.920956i \(-0.627410\pi\)
−0.389667 + 0.920956i \(0.627410\pi\)
\(182\) 21.5343 1.59623
\(183\) −10.3190 −0.762803
\(184\) 27.3730 2.01797
\(185\) −3.59378 −0.264220
\(186\) −40.4999 −2.96960
\(187\) −3.42712 −0.250616
\(188\) −19.9668 −1.45623
\(189\) 1.21086 0.0880771
\(190\) 9.49976 0.689185
\(191\) 10.1470 0.734213 0.367106 0.930179i \(-0.380348\pi\)
0.367106 + 0.930179i \(0.380348\pi\)
\(192\) −24.9074 −1.79754
\(193\) −6.77082 −0.487375 −0.243687 0.969854i \(-0.578357\pi\)
−0.243687 + 0.969854i \(0.578357\pi\)
\(194\) 21.6158 1.55193
\(195\) 9.13080 0.653870
\(196\) 26.7162 1.90830
\(197\) 7.38688 0.526293 0.263147 0.964756i \(-0.415240\pi\)
0.263147 + 0.964756i \(0.415240\pi\)
\(198\) −19.5664 −1.39052
\(199\) −14.8010 −1.04921 −0.524606 0.851345i \(-0.675787\pi\)
−0.524606 + 0.851345i \(0.675787\pi\)
\(200\) 10.7186 0.757923
\(201\) 17.7428 1.25148
\(202\) −16.6031 −1.16819
\(203\) −19.5501 −1.37215
\(204\) −11.0436 −0.773206
\(205\) −4.95485 −0.346062
\(206\) −12.9659 −0.903374
\(207\) −18.3643 −1.27641
\(208\) 6.48551 0.449689
\(209\) −7.10959 −0.491781
\(210\) 34.4739 2.37893
\(211\) −7.94259 −0.546791 −0.273395 0.961902i \(-0.588147\pi\)
−0.273395 + 0.961902i \(0.588147\pi\)
\(212\) −3.77770 −0.259454
\(213\) 5.81021 0.398109
\(214\) −10.0275 −0.685467
\(215\) −2.92232 −0.199301
\(216\) 1.37928 0.0938478
\(217\) −26.0950 −1.77144
\(218\) −11.6856 −0.791447
\(219\) 29.8645 2.01806
\(220\) 16.9320 1.14156
\(221\) −2.88243 −0.193893
\(222\) 13.2554 0.889642
\(223\) −25.9156 −1.73544 −0.867718 0.497056i \(-0.834414\pi\)
−0.867718 + 0.497056i \(0.834414\pi\)
\(224\) −7.57219 −0.505938
\(225\) −7.19103 −0.479402
\(226\) −7.73030 −0.514212
\(227\) −7.83570 −0.520073 −0.260037 0.965599i \(-0.583735\pi\)
−0.260037 + 0.965599i \(0.583735\pi\)
\(228\) −22.9100 −1.51725
\(229\) 12.4189 0.820661 0.410330 0.911937i \(-0.365413\pi\)
0.410330 + 0.911937i \(0.365413\pi\)
\(230\) 24.3053 1.60264
\(231\) −25.8002 −1.69753
\(232\) −22.2693 −1.46205
\(233\) 8.64607 0.566423 0.283211 0.959057i \(-0.408600\pi\)
0.283211 + 0.959057i \(0.408600\pi\)
\(234\) −16.4566 −1.07580
\(235\) −8.34287 −0.544229
\(236\) −41.3808 −2.69366
\(237\) −33.9413 −2.20472
\(238\) −10.8828 −0.705427
\(239\) 30.0760 1.94545 0.972726 0.231956i \(-0.0745124\pi\)
0.972726 + 0.231956i \(0.0745124\pi\)
\(240\) 10.3825 0.670190
\(241\) 19.5405 1.25871 0.629357 0.777117i \(-0.283319\pi\)
0.629357 + 0.777117i \(0.283319\pi\)
\(242\) 7.05988 0.453826
\(243\) −21.7562 −1.39566
\(244\) −16.0941 −1.03032
\(245\) 11.1630 0.713180
\(246\) 18.2756 1.16521
\(247\) −5.97963 −0.380475
\(248\) −29.7245 −1.88751
\(249\) −16.9118 −1.07174
\(250\) 28.4881 1.80174
\(251\) 2.74701 0.173390 0.0866948 0.996235i \(-0.472370\pi\)
0.0866948 + 0.996235i \(0.472370\pi\)
\(252\) −40.6251 −2.55914
\(253\) −18.1900 −1.14359
\(254\) −5.52974 −0.346967
\(255\) −4.61443 −0.288967
\(256\) −29.1430 −1.82144
\(257\) −29.2490 −1.82450 −0.912250 0.409634i \(-0.865656\pi\)
−0.912250 + 0.409634i \(0.865656\pi\)
\(258\) 10.7787 0.671056
\(259\) 8.54072 0.530695
\(260\) 14.2409 0.883185
\(261\) 14.9402 0.924777
\(262\) −2.37106 −0.146484
\(263\) −10.6878 −0.659040 −0.329520 0.944149i \(-0.606887\pi\)
−0.329520 + 0.944149i \(0.606887\pi\)
\(264\) −29.3887 −1.80875
\(265\) −1.57847 −0.0969645
\(266\) −22.5765 −1.38425
\(267\) −39.8770 −2.44043
\(268\) 27.6728 1.69038
\(269\) 3.93504 0.239924 0.119962 0.992778i \(-0.461723\pi\)
0.119962 + 0.992778i \(0.461723\pi\)
\(270\) 1.22470 0.0745326
\(271\) −12.4841 −0.758353 −0.379176 0.925324i \(-0.623793\pi\)
−0.379176 + 0.925324i \(0.623793\pi\)
\(272\) −3.27758 −0.198733
\(273\) −21.6996 −1.31332
\(274\) 26.4000 1.59488
\(275\) −7.12277 −0.429519
\(276\) −58.6155 −3.52824
\(277\) −2.10637 −0.126560 −0.0632799 0.997996i \(-0.520156\pi\)
−0.0632799 + 0.997996i \(0.520156\pi\)
\(278\) −48.7834 −2.92583
\(279\) 19.9419 1.19389
\(280\) 25.3018 1.51207
\(281\) 6.64271 0.396271 0.198135 0.980175i \(-0.436511\pi\)
0.198135 + 0.980175i \(0.436511\pi\)
\(282\) 30.7720 1.83245
\(283\) −11.9042 −0.707629 −0.353814 0.935316i \(-0.615116\pi\)
−0.353814 + 0.935316i \(0.615116\pi\)
\(284\) 9.06193 0.537727
\(285\) −9.57267 −0.567036
\(286\) −16.3004 −0.963862
\(287\) 11.7753 0.695077
\(288\) 5.78669 0.340984
\(289\) −15.5433 −0.914312
\(290\) −19.7735 −1.16114
\(291\) −21.7817 −1.27687
\(292\) 46.5784 2.72580
\(293\) −14.2875 −0.834687 −0.417343 0.908749i \(-0.637039\pi\)
−0.417343 + 0.908749i \(0.637039\pi\)
\(294\) −41.1739 −2.40131
\(295\) −17.2905 −1.00669
\(296\) 9.72864 0.565466
\(297\) −0.916559 −0.0531841
\(298\) 8.33641 0.482915
\(299\) −15.2990 −0.884761
\(300\) −22.9525 −1.32516
\(301\) 6.94499 0.400303
\(302\) 2.40368 0.138317
\(303\) 16.7305 0.961142
\(304\) −6.79937 −0.389971
\(305\) −6.72474 −0.385058
\(306\) 8.31667 0.475432
\(307\) −12.9623 −0.739797 −0.369898 0.929072i \(-0.620608\pi\)
−0.369898 + 0.929072i \(0.620608\pi\)
\(308\) −40.2394 −2.29286
\(309\) 13.0654 0.743263
\(310\) −26.3932 −1.49903
\(311\) 31.9300 1.81059 0.905293 0.424788i \(-0.139651\pi\)
0.905293 + 0.424788i \(0.139651\pi\)
\(312\) −24.7178 −1.39937
\(313\) −4.03535 −0.228091 −0.114046 0.993475i \(-0.536381\pi\)
−0.114046 + 0.993475i \(0.536381\pi\)
\(314\) 44.7003 2.52259
\(315\) −16.9747 −0.956416
\(316\) −52.9368 −2.97792
\(317\) −20.2195 −1.13564 −0.567820 0.823153i \(-0.692213\pi\)
−0.567820 + 0.823153i \(0.692213\pi\)
\(318\) 5.82205 0.326484
\(319\) 14.7984 0.828552
\(320\) −16.2318 −0.907383
\(321\) 10.1045 0.563977
\(322\) −57.7622 −3.21896
\(323\) 3.02193 0.168144
\(324\) −35.4425 −1.96903
\(325\) −5.99071 −0.332305
\(326\) −22.4205 −1.24175
\(327\) 11.7753 0.651174
\(328\) 13.4132 0.740618
\(329\) 19.8271 1.09310
\(330\) −26.0950 −1.43648
\(331\) −11.4199 −0.627696 −0.313848 0.949473i \(-0.601618\pi\)
−0.313848 + 0.949473i \(0.601618\pi\)
\(332\) −26.3766 −1.44761
\(333\) −6.52685 −0.357669
\(334\) 30.9909 1.69575
\(335\) 11.5627 0.631740
\(336\) −24.6744 −1.34610
\(337\) −15.8766 −0.864854 −0.432427 0.901669i \(-0.642343\pi\)
−0.432427 + 0.901669i \(0.642343\pi\)
\(338\) 17.5382 0.953954
\(339\) 7.78963 0.423075
\(340\) −7.19694 −0.390309
\(341\) 19.7526 1.06966
\(342\) 17.2530 0.932935
\(343\) −0.270344 −0.0145972
\(344\) 7.91095 0.426530
\(345\) −24.4918 −1.31859
\(346\) 14.1268 0.759464
\(347\) 0.826373 0.0443620 0.0221810 0.999754i \(-0.492939\pi\)
0.0221810 + 0.999754i \(0.492939\pi\)
\(348\) 47.6865 2.55627
\(349\) −23.3241 −1.24851 −0.624256 0.781220i \(-0.714598\pi\)
−0.624256 + 0.781220i \(0.714598\pi\)
\(350\) −22.6183 −1.20900
\(351\) −0.770885 −0.0411468
\(352\) 5.73176 0.305504
\(353\) −11.3747 −0.605412 −0.302706 0.953084i \(-0.597890\pi\)
−0.302706 + 0.953084i \(0.597890\pi\)
\(354\) 63.7745 3.38958
\(355\) 3.78642 0.200962
\(356\) −62.1945 −3.29630
\(357\) 10.9663 0.580400
\(358\) −50.1102 −2.64841
\(359\) 14.1037 0.744367 0.372184 0.928159i \(-0.378609\pi\)
0.372184 + 0.928159i \(0.378609\pi\)
\(360\) −19.3357 −1.01908
\(361\) −12.7310 −0.670052
\(362\) 25.2023 1.32460
\(363\) −7.11407 −0.373392
\(364\) −33.8440 −1.77391
\(365\) 19.4622 1.01870
\(366\) 24.8037 1.29651
\(367\) 0.449979 0.0234887 0.0117443 0.999931i \(-0.496262\pi\)
0.0117443 + 0.999931i \(0.496262\pi\)
\(368\) −17.3963 −0.906844
\(369\) −8.99875 −0.468456
\(370\) 8.63832 0.449085
\(371\) 3.75128 0.194757
\(372\) 63.6508 3.30014
\(373\) 7.96094 0.412202 0.206101 0.978531i \(-0.433922\pi\)
0.206101 + 0.978531i \(0.433922\pi\)
\(374\) 8.23773 0.425963
\(375\) −28.7067 −1.48241
\(376\) 22.5848 1.16472
\(377\) 12.4464 0.641024
\(378\) −2.91053 −0.149701
\(379\) 15.7089 0.806914 0.403457 0.914999i \(-0.367808\pi\)
0.403457 + 0.914999i \(0.367808\pi\)
\(380\) −14.9301 −0.765898
\(381\) 5.57219 0.285472
\(382\) −24.3903 −1.24791
\(383\) 30.5471 1.56088 0.780441 0.625229i \(-0.214994\pi\)
0.780441 + 0.625229i \(0.214994\pi\)
\(384\) 50.0910 2.55620
\(385\) −16.8136 −0.856899
\(386\) 16.2749 0.828372
\(387\) −5.30738 −0.269789
\(388\) −33.9720 −1.72467
\(389\) −13.3576 −0.677257 −0.338628 0.940920i \(-0.609963\pi\)
−0.338628 + 0.940920i \(0.609963\pi\)
\(390\) −21.9476 −1.11136
\(391\) 7.73163 0.391005
\(392\) −30.2192 −1.52630
\(393\) 2.38926 0.120522
\(394\) −17.7557 −0.894521
\(395\) −22.1190 −1.11293
\(396\) 30.7511 1.54530
\(397\) −35.2040 −1.76684 −0.883419 0.468585i \(-0.844764\pi\)
−0.883419 + 0.468585i \(0.844764\pi\)
\(398\) 35.5769 1.78331
\(399\) 22.7497 1.13891
\(400\) −6.81198 −0.340599
\(401\) −17.5374 −0.875775 −0.437887 0.899030i \(-0.644273\pi\)
−0.437887 + 0.899030i \(0.644273\pi\)
\(402\) −42.6482 −2.12710
\(403\) 16.6132 0.827562
\(404\) 26.0938 1.29822
\(405\) −14.8092 −0.735877
\(406\) 46.9923 2.33219
\(407\) −6.46489 −0.320453
\(408\) 12.4916 0.618428
\(409\) 20.6312 1.02015 0.510073 0.860131i \(-0.329618\pi\)
0.510073 + 0.860131i \(0.329618\pi\)
\(410\) 11.9099 0.588188
\(411\) −26.6027 −1.31221
\(412\) 20.3775 1.00393
\(413\) 41.0914 2.02197
\(414\) 44.1420 2.16946
\(415\) −11.0212 −0.541008
\(416\) 4.82078 0.236358
\(417\) 49.1578 2.40727
\(418\) 17.0892 0.835861
\(419\) 22.2186 1.08545 0.542726 0.839910i \(-0.317392\pi\)
0.542726 + 0.839910i \(0.317392\pi\)
\(420\) −54.1802 −2.64372
\(421\) −3.81156 −0.185764 −0.0928821 0.995677i \(-0.529608\pi\)
−0.0928821 + 0.995677i \(0.529608\pi\)
\(422\) 19.0915 0.929359
\(423\) −15.1519 −0.736711
\(424\) 4.27303 0.207517
\(425\) 3.02753 0.146857
\(426\) −13.9659 −0.676650
\(427\) 15.9815 0.773401
\(428\) 15.7595 0.761766
\(429\) 16.4255 0.793030
\(430\) 7.02435 0.338744
\(431\) −6.84137 −0.329537 −0.164769 0.986332i \(-0.552688\pi\)
−0.164769 + 0.986332i \(0.552688\pi\)
\(432\) −0.876566 −0.0421738
\(433\) 16.3119 0.783900 0.391950 0.919987i \(-0.371801\pi\)
0.391950 + 0.919987i \(0.371801\pi\)
\(434\) 62.7241 3.01085
\(435\) 19.9253 0.955343
\(436\) 18.3654 0.879542
\(437\) 16.0393 0.767265
\(438\) −71.7849 −3.43001
\(439\) 5.83894 0.278678 0.139339 0.990245i \(-0.455502\pi\)
0.139339 + 0.990245i \(0.455502\pi\)
\(440\) −19.1521 −0.913043
\(441\) 20.2737 0.965416
\(442\) 6.92846 0.329553
\(443\) 35.0640 1.66594 0.832972 0.553316i \(-0.186638\pi\)
0.832972 + 0.553316i \(0.186638\pi\)
\(444\) −20.8325 −0.988667
\(445\) −25.9872 −1.23191
\(446\) 62.2929 2.94966
\(447\) −8.40040 −0.397325
\(448\) 38.5753 1.82251
\(449\) 18.1293 0.855574 0.427787 0.903880i \(-0.359293\pi\)
0.427787 + 0.903880i \(0.359293\pi\)
\(450\) 17.2850 0.814821
\(451\) −8.91333 −0.419712
\(452\) 12.1492 0.571449
\(453\) −2.42213 −0.113802
\(454\) 18.8345 0.883949
\(455\) −14.1413 −0.662955
\(456\) 25.9140 1.21353
\(457\) 20.3238 0.950708 0.475354 0.879795i \(-0.342320\pi\)
0.475354 + 0.879795i \(0.342320\pi\)
\(458\) −29.8510 −1.39485
\(459\) 0.389582 0.0181841
\(460\) −38.1988 −1.78103
\(461\) 4.90690 0.228537 0.114268 0.993450i \(-0.463548\pi\)
0.114268 + 0.993450i \(0.463548\pi\)
\(462\) 62.0155 2.88522
\(463\) 4.83514 0.224708 0.112354 0.993668i \(-0.464161\pi\)
0.112354 + 0.993668i \(0.464161\pi\)
\(464\) 14.1527 0.657023
\(465\) 26.5957 1.23335
\(466\) −20.7824 −0.962727
\(467\) −15.4888 −0.716735 −0.358367 0.933581i \(-0.616666\pi\)
−0.358367 + 0.933581i \(0.616666\pi\)
\(468\) 25.8637 1.19555
\(469\) −27.4792 −1.26887
\(470\) 20.0536 0.925005
\(471\) −45.0434 −2.07549
\(472\) 46.8067 2.15445
\(473\) −5.25700 −0.241717
\(474\) 81.5841 3.74728
\(475\) 6.28063 0.288175
\(476\) 17.1037 0.783948
\(477\) −2.86673 −0.131259
\(478\) −72.2932 −3.30661
\(479\) −32.1674 −1.46976 −0.734882 0.678195i \(-0.762763\pi\)
−0.734882 + 0.678195i \(0.762763\pi\)
\(480\) 7.71750 0.352254
\(481\) −5.43739 −0.247924
\(482\) −46.9692 −2.13939
\(483\) 58.2055 2.64844
\(484\) −11.0955 −0.504342
\(485\) −14.1948 −0.644554
\(486\) 52.2950 2.37215
\(487\) −0.814366 −0.0369025 −0.0184512 0.999830i \(-0.505874\pi\)
−0.0184512 + 0.999830i \(0.505874\pi\)
\(488\) 18.2044 0.824074
\(489\) 22.5925 1.02167
\(490\) −26.8324 −1.21216
\(491\) 26.0192 1.17423 0.587116 0.809503i \(-0.300263\pi\)
0.587116 + 0.809503i \(0.300263\pi\)
\(492\) −28.7224 −1.29491
\(493\) −6.29005 −0.283290
\(494\) 14.3731 0.646678
\(495\) 12.8490 0.577519
\(496\) 18.8907 0.848217
\(497\) −8.99854 −0.403640
\(498\) 40.6506 1.82160
\(499\) −15.5272 −0.695095 −0.347548 0.937662i \(-0.612985\pi\)
−0.347548 + 0.937662i \(0.612985\pi\)
\(500\) −44.7727 −2.00229
\(501\) −31.2288 −1.39520
\(502\) −6.60294 −0.294704
\(503\) −37.5124 −1.67259 −0.836297 0.548277i \(-0.815284\pi\)
−0.836297 + 0.548277i \(0.815284\pi\)
\(504\) 45.9518 2.04686
\(505\) 10.9030 0.485177
\(506\) 43.7230 1.94372
\(507\) −17.6728 −0.784879
\(508\) 8.69071 0.385588
\(509\) −34.1133 −1.51204 −0.756022 0.654546i \(-0.772860\pi\)
−0.756022 + 0.654546i \(0.772860\pi\)
\(510\) 11.0916 0.491146
\(511\) −46.2526 −2.04609
\(512\) 28.6896 1.26791
\(513\) 0.808191 0.0356825
\(514\) 70.3053 3.10103
\(515\) 8.51451 0.375194
\(516\) −16.9402 −0.745751
\(517\) −15.0081 −0.660055
\(518\) −20.5292 −0.902002
\(519\) −14.2353 −0.624859
\(520\) −16.1082 −0.706391
\(521\) 14.6023 0.639736 0.319868 0.947462i \(-0.396361\pi\)
0.319868 + 0.947462i \(0.396361\pi\)
\(522\) −35.9116 −1.57181
\(523\) 3.72926 0.163069 0.0815347 0.996671i \(-0.474018\pi\)
0.0815347 + 0.996671i \(0.474018\pi\)
\(524\) 3.72642 0.162790
\(525\) 22.7919 0.994721
\(526\) 25.6902 1.12015
\(527\) −8.39581 −0.365727
\(528\) 18.6773 0.812823
\(529\) 18.0368 0.784210
\(530\) 3.79414 0.164807
\(531\) −31.4021 −1.36274
\(532\) 35.4818 1.53833
\(533\) −7.49669 −0.324718
\(534\) 95.8518 4.14791
\(535\) 6.58493 0.284691
\(536\) −31.3012 −1.35201
\(537\) 50.4949 2.17901
\(538\) −9.45860 −0.407789
\(539\) 20.0813 0.864963
\(540\) −1.92477 −0.0828288
\(541\) −26.2522 −1.12867 −0.564335 0.825546i \(-0.690867\pi\)
−0.564335 + 0.825546i \(0.690867\pi\)
\(542\) 30.0077 1.28894
\(543\) −25.3957 −1.08983
\(544\) −2.43628 −0.104455
\(545\) 7.67376 0.328708
\(546\) 52.1590 2.23220
\(547\) −13.2251 −0.565463 −0.282731 0.959199i \(-0.591240\pi\)
−0.282731 + 0.959199i \(0.591240\pi\)
\(548\) −41.4910 −1.77241
\(549\) −12.2131 −0.521244
\(550\) 17.1209 0.730037
\(551\) −13.0488 −0.555896
\(552\) 66.3012 2.82197
\(553\) 52.5664 2.23535
\(554\) 5.06306 0.215109
\(555\) −8.70462 −0.369490
\(556\) 76.6693 3.25150
\(557\) 41.0420 1.73900 0.869502 0.493930i \(-0.164440\pi\)
0.869502 + 0.493930i \(0.164440\pi\)
\(558\) −47.9339 −2.02921
\(559\) −4.42148 −0.187009
\(560\) −16.0799 −0.679501
\(561\) −8.30095 −0.350467
\(562\) −15.9670 −0.673526
\(563\) −38.6381 −1.62840 −0.814200 0.580584i \(-0.802824\pi\)
−0.814200 + 0.580584i \(0.802824\pi\)
\(564\) −48.3622 −2.03641
\(565\) 5.07639 0.213565
\(566\) 28.6139 1.20273
\(567\) 35.1946 1.47803
\(568\) −10.2501 −0.430086
\(569\) 16.5901 0.695493 0.347746 0.937589i \(-0.386947\pi\)
0.347746 + 0.937589i \(0.386947\pi\)
\(570\) 23.0097 0.963770
\(571\) 31.7119 1.32710 0.663550 0.748132i \(-0.269049\pi\)
0.663550 + 0.748132i \(0.269049\pi\)
\(572\) 25.6182 1.07115
\(573\) 24.5775 1.02674
\(574\) −28.3042 −1.18140
\(575\) 16.0691 0.670126
\(576\) −29.4793 −1.22830
\(577\) −8.67383 −0.361096 −0.180548 0.983566i \(-0.557787\pi\)
−0.180548 + 0.983566i \(0.557787\pi\)
\(578\) 37.3612 1.55402
\(579\) −16.3998 −0.681554
\(580\) 31.0766 1.29038
\(581\) 26.1921 1.08663
\(582\) 52.3564 2.17024
\(583\) −2.83952 −0.117601
\(584\) −52.6858 −2.18015
\(585\) 10.8068 0.446807
\(586\) 34.3427 1.41869
\(587\) −35.9896 −1.48545 −0.742726 0.669596i \(-0.766467\pi\)
−0.742726 + 0.669596i \(0.766467\pi\)
\(588\) 64.7101 2.66860
\(589\) −17.4172 −0.717662
\(590\) 41.5609 1.71103
\(591\) 17.8920 0.735979
\(592\) −6.18280 −0.254112
\(593\) 1.41898 0.0582704 0.0291352 0.999575i \(-0.490725\pi\)
0.0291352 + 0.999575i \(0.490725\pi\)
\(594\) 2.20312 0.0903950
\(595\) 7.14659 0.292982
\(596\) −13.1017 −0.536668
\(597\) −35.8499 −1.46724
\(598\) 36.7739 1.50379
\(599\) 38.5688 1.57588 0.787940 0.615752i \(-0.211148\pi\)
0.787940 + 0.615752i \(0.211148\pi\)
\(600\) 25.9620 1.05989
\(601\) −11.0190 −0.449475 −0.224738 0.974419i \(-0.572152\pi\)
−0.224738 + 0.974419i \(0.572152\pi\)
\(602\) −16.6936 −0.680379
\(603\) 20.9997 0.855173
\(604\) −3.77770 −0.153712
\(605\) −4.63613 −0.188486
\(606\) −40.2148 −1.63362
\(607\) −8.78187 −0.356445 −0.178223 0.983990i \(-0.557035\pi\)
−0.178223 + 0.983990i \(0.557035\pi\)
\(608\) −5.05408 −0.204970
\(609\) −47.3530 −1.91884
\(610\) 16.1642 0.654468
\(611\) −12.6228 −0.510663
\(612\) −13.0707 −0.528353
\(613\) −35.1540 −1.41986 −0.709929 0.704273i \(-0.751273\pi\)
−0.709929 + 0.704273i \(0.751273\pi\)
\(614\) 31.1573 1.25740
\(615\) −12.0013 −0.483940
\(616\) 45.5156 1.83388
\(617\) 39.7995 1.60227 0.801135 0.598484i \(-0.204230\pi\)
0.801135 + 0.598484i \(0.204230\pi\)
\(618\) −31.4050 −1.26330
\(619\) 18.0851 0.726901 0.363450 0.931614i \(-0.381599\pi\)
0.363450 + 0.931614i \(0.381599\pi\)
\(620\) 41.4803 1.66589
\(621\) 2.06777 0.0829767
\(622\) −76.7497 −3.07738
\(623\) 61.7594 2.47434
\(624\) 15.7088 0.628855
\(625\) −6.16554 −0.246622
\(626\) 9.69971 0.387678
\(627\) −17.2204 −0.687716
\(628\) −70.2524 −2.80337
\(629\) 2.74790 0.109566
\(630\) 40.8018 1.62558
\(631\) −0.895242 −0.0356390 −0.0178195 0.999841i \(-0.505672\pi\)
−0.0178195 + 0.999841i \(0.505672\pi\)
\(632\) 59.8778 2.38181
\(633\) −19.2380 −0.764643
\(634\) 48.6013 1.93020
\(635\) 3.63131 0.144104
\(636\) −9.15010 −0.362825
\(637\) 16.8897 0.669193
\(638\) −35.5707 −1.40826
\(639\) 6.87671 0.272039
\(640\) 32.6436 1.29035
\(641\) −8.58602 −0.339127 −0.169564 0.985519i \(-0.554236\pi\)
−0.169564 + 0.985519i \(0.554236\pi\)
\(642\) −24.2880 −0.958570
\(643\) 9.72406 0.383479 0.191740 0.981446i \(-0.438587\pi\)
0.191740 + 0.981446i \(0.438587\pi\)
\(644\) 90.7807 3.57726
\(645\) −7.07826 −0.278706
\(646\) −7.26376 −0.285789
\(647\) −13.9584 −0.548763 −0.274381 0.961621i \(-0.588473\pi\)
−0.274381 + 0.961621i \(0.588473\pi\)
\(648\) 40.0898 1.57487
\(649\) −31.1041 −1.22094
\(650\) 14.3998 0.564806
\(651\) −63.2056 −2.47722
\(652\) 35.2366 1.37997
\(653\) −36.2427 −1.41829 −0.709143 0.705065i \(-0.750918\pi\)
−0.709143 + 0.705065i \(0.750918\pi\)
\(654\) −28.3040 −1.10677
\(655\) 1.55704 0.0608387
\(656\) −8.52441 −0.332822
\(657\) 35.3464 1.37899
\(658\) −47.6581 −1.85790
\(659\) 16.1040 0.627324 0.313662 0.949535i \(-0.398444\pi\)
0.313662 + 0.949535i \(0.398444\pi\)
\(660\) 41.0116 1.59638
\(661\) −3.65684 −0.142234 −0.0711172 0.997468i \(-0.522656\pi\)
−0.0711172 + 0.997468i \(0.522656\pi\)
\(662\) 27.4499 1.06687
\(663\) −6.98164 −0.271144
\(664\) 29.8351 1.15783
\(665\) 14.8257 0.574914
\(666\) 15.6885 0.607916
\(667\) −33.3854 −1.29269
\(668\) −48.7062 −1.88450
\(669\) −62.7711 −2.42687
\(670\) −27.7932 −1.07374
\(671\) −12.0972 −0.467008
\(672\) −18.3409 −0.707514
\(673\) 11.8992 0.458679 0.229339 0.973347i \(-0.426343\pi\)
0.229339 + 0.973347i \(0.426343\pi\)
\(674\) 38.1624 1.46996
\(675\) 0.809689 0.0311650
\(676\) −27.5636 −1.06014
\(677\) 32.4936 1.24883 0.624415 0.781093i \(-0.285338\pi\)
0.624415 + 0.781093i \(0.285338\pi\)
\(678\) −18.7238 −0.719084
\(679\) 33.7344 1.29461
\(680\) 8.14060 0.312178
\(681\) −18.9791 −0.727281
\(682\) −47.4789 −1.81806
\(683\) 3.62747 0.138801 0.0694005 0.997589i \(-0.477891\pi\)
0.0694005 + 0.997589i \(0.477891\pi\)
\(684\) −27.1153 −1.03678
\(685\) −17.3365 −0.662395
\(686\) 0.649822 0.0248103
\(687\) 30.0801 1.14763
\(688\) −5.02762 −0.191676
\(689\) −2.38822 −0.0909840
\(690\) 58.8706 2.24117
\(691\) −36.0676 −1.37207 −0.686037 0.727566i \(-0.740651\pi\)
−0.686037 + 0.727566i \(0.740651\pi\)
\(692\) −22.2022 −0.844000
\(693\) −30.5360 −1.15997
\(694\) −1.98634 −0.0754004
\(695\) 32.0354 1.21517
\(696\) −53.9392 −2.04456
\(697\) 3.78860 0.143504
\(698\) 56.0639 2.12205
\(699\) 20.9419 0.792097
\(700\) 35.5476 1.34357
\(701\) 15.2388 0.575561 0.287780 0.957696i \(-0.407083\pi\)
0.287780 + 0.957696i \(0.407083\pi\)
\(702\) 1.85296 0.0699357
\(703\) 5.70053 0.214999
\(704\) −29.1995 −1.10050
\(705\) −20.2076 −0.761061
\(706\) 27.3411 1.02899
\(707\) −25.9113 −0.974495
\(708\) −100.230 −3.76687
\(709\) 4.20490 0.157918 0.0789592 0.996878i \(-0.474840\pi\)
0.0789592 + 0.996878i \(0.474840\pi\)
\(710\) −9.10137 −0.341568
\(711\) −40.1714 −1.50655
\(712\) 70.3494 2.63646
\(713\) −44.5620 −1.66886
\(714\) −26.3596 −0.986484
\(715\) 10.7042 0.400316
\(716\) 78.7547 2.94320
\(717\) 72.8480 2.72056
\(718\) −33.9010 −1.26517
\(719\) 7.06419 0.263450 0.131725 0.991286i \(-0.457948\pi\)
0.131725 + 0.991286i \(0.457948\pi\)
\(720\) 12.2883 0.457959
\(721\) −20.2350 −0.753590
\(722\) 30.6013 1.13886
\(723\) 47.3297 1.76021
\(724\) −39.6086 −1.47204
\(725\) −13.0729 −0.485517
\(726\) 17.1000 0.634640
\(727\) −42.0260 −1.55866 −0.779329 0.626615i \(-0.784440\pi\)
−0.779329 + 0.626615i \(0.784440\pi\)
\(728\) 38.2816 1.41881
\(729\) −24.5503 −0.909271
\(730\) −46.7811 −1.73145
\(731\) 2.23448 0.0826453
\(732\) −38.9821 −1.44082
\(733\) −12.6726 −0.468072 −0.234036 0.972228i \(-0.575193\pi\)
−0.234036 + 0.972228i \(0.575193\pi\)
\(734\) −1.08161 −0.0399228
\(735\) 27.0384 0.997325
\(736\) −12.9309 −0.476640
\(737\) 20.8003 0.766191
\(738\) 21.6302 0.796217
\(739\) −38.9112 −1.43137 −0.715685 0.698423i \(-0.753886\pi\)
−0.715685 + 0.698423i \(0.753886\pi\)
\(740\) −13.5762 −0.499072
\(741\) −14.4835 −0.532063
\(742\) −9.01688 −0.331020
\(743\) 15.8388 0.581071 0.290535 0.956864i \(-0.406167\pi\)
0.290535 + 0.956864i \(0.406167\pi\)
\(744\) −71.9967 −2.63953
\(745\) −5.47441 −0.200567
\(746\) −19.1356 −0.700604
\(747\) −20.0161 −0.732350
\(748\) −12.9466 −0.473376
\(749\) −15.6493 −0.571813
\(750\) 69.0019 2.51959
\(751\) 44.2746 1.61560 0.807802 0.589454i \(-0.200657\pi\)
0.807802 + 0.589454i \(0.200657\pi\)
\(752\) −14.3532 −0.523408
\(753\) 6.65362 0.242471
\(754\) −29.9173 −1.08952
\(755\) −1.57847 −0.0574463
\(756\) 4.57427 0.166364
\(757\) −15.0084 −0.545490 −0.272745 0.962086i \(-0.587932\pi\)
−0.272745 + 0.962086i \(0.587932\pi\)
\(758\) −37.7593 −1.37148
\(759\) −44.0586 −1.59923
\(760\) 16.8877 0.612582
\(761\) −50.5056 −1.83083 −0.915413 0.402517i \(-0.868135\pi\)
−0.915413 + 0.402517i \(0.868135\pi\)
\(762\) −13.3938 −0.485206
\(763\) −18.2369 −0.660221
\(764\) 38.3324 1.38682
\(765\) −5.46145 −0.197459
\(766\) −73.4256 −2.65297
\(767\) −26.1605 −0.944602
\(768\) −70.5883 −2.54714
\(769\) −4.11073 −0.148237 −0.0741183 0.997249i \(-0.523614\pi\)
−0.0741183 + 0.997249i \(0.523614\pi\)
\(770\) 40.4145 1.45644
\(771\) −70.8449 −2.55142
\(772\) −25.5781 −0.920578
\(773\) 8.21353 0.295420 0.147710 0.989031i \(-0.452810\pi\)
0.147710 + 0.989031i \(0.452810\pi\)
\(774\) 12.7573 0.458551
\(775\) −17.4494 −0.626803
\(776\) 38.4265 1.37943
\(777\) 20.6868 0.742134
\(778\) 32.1074 1.15111
\(779\) 7.85948 0.281595
\(780\) 34.4934 1.23506
\(781\) 6.81144 0.243732
\(782\) −18.5844 −0.664577
\(783\) −1.68223 −0.0601179
\(784\) 19.2051 0.685895
\(785\) −29.3541 −1.04769
\(786\) −5.74302 −0.204847
\(787\) 40.4303 1.44119 0.720593 0.693359i \(-0.243870\pi\)
0.720593 + 0.693359i \(0.243870\pi\)
\(788\) 27.9054 0.994089
\(789\) −25.8874 −0.921615
\(790\) 53.1671 1.89160
\(791\) −12.0642 −0.428953
\(792\) −34.7832 −1.23597
\(793\) −10.1745 −0.361308
\(794\) 84.6193 3.00303
\(795\) −3.82326 −0.135597
\(796\) −55.9136 −1.98181
\(797\) −18.7392 −0.663775 −0.331888 0.943319i \(-0.607686\pi\)
−0.331888 + 0.943319i \(0.607686\pi\)
\(798\) −54.6832 −1.93576
\(799\) 6.37917 0.225679
\(800\) −5.06344 −0.179020
\(801\) −47.1967 −1.66761
\(802\) 42.1543 1.48852
\(803\) 35.0109 1.23551
\(804\) 67.0272 2.36387
\(805\) 37.9316 1.33691
\(806\) −39.9329 −1.40657
\(807\) 9.53120 0.335514
\(808\) −29.5153 −1.03834
\(809\) 16.3720 0.575610 0.287805 0.957689i \(-0.407074\pi\)
0.287805 + 0.957689i \(0.407074\pi\)
\(810\) 35.5968 1.25074
\(811\) 18.7958 0.660008 0.330004 0.943979i \(-0.392950\pi\)
0.330004 + 0.943979i \(0.392950\pi\)
\(812\) −73.8544 −2.59178
\(813\) −30.2381 −1.06050
\(814\) 15.5396 0.544661
\(815\) 14.7232 0.515732
\(816\) −7.93875 −0.277912
\(817\) 4.63545 0.162174
\(818\) −49.5909 −1.73390
\(819\) −25.6827 −0.897427
\(820\) −18.7179 −0.653659
\(821\) −20.6437 −0.720468 −0.360234 0.932862i \(-0.617303\pi\)
−0.360234 + 0.932862i \(0.617303\pi\)
\(822\) 63.9444 2.23032
\(823\) 5.59875 0.195160 0.0975801 0.995228i \(-0.468890\pi\)
0.0975801 + 0.995228i \(0.468890\pi\)
\(824\) −23.0494 −0.802965
\(825\) −17.2523 −0.600648
\(826\) −98.7707 −3.43667
\(827\) −36.5470 −1.27086 −0.635431 0.772157i \(-0.719178\pi\)
−0.635431 + 0.772157i \(0.719178\pi\)
\(828\) −69.3748 −2.41094
\(829\) 35.0523 1.21742 0.608708 0.793394i \(-0.291688\pi\)
0.608708 + 0.793394i \(0.291688\pi\)
\(830\) 26.4914 0.919530
\(831\) −5.10192 −0.176984
\(832\) −24.5587 −0.851418
\(833\) −8.53554 −0.295739
\(834\) −118.160 −4.09154
\(835\) −20.3513 −0.704287
\(836\) −26.8579 −0.928900
\(837\) −2.24540 −0.0776122
\(838\) −53.4066 −1.84490
\(839\) 24.8153 0.856719 0.428360 0.903608i \(-0.359092\pi\)
0.428360 + 0.903608i \(0.359092\pi\)
\(840\) 61.2843 2.11451
\(841\) −1.83938 −0.0634268
\(842\) 9.16179 0.315736
\(843\) 16.0895 0.554153
\(844\) −30.0047 −1.03281
\(845\) −11.5171 −0.396201
\(846\) 36.4204 1.25216
\(847\) 11.0179 0.378580
\(848\) −2.71562 −0.0932549
\(849\) −28.8335 −0.989562
\(850\) −7.27722 −0.249607
\(851\) 14.5849 0.499963
\(852\) 21.9492 0.751968
\(853\) −21.5019 −0.736212 −0.368106 0.929784i \(-0.619994\pi\)
−0.368106 + 0.929784i \(0.619994\pi\)
\(854\) −38.4146 −1.31452
\(855\) −11.3298 −0.387471
\(856\) −17.8259 −0.609277
\(857\) 46.8424 1.60010 0.800052 0.599930i \(-0.204805\pi\)
0.800052 + 0.599930i \(0.204805\pi\)
\(858\) −39.4817 −1.34788
\(859\) −12.4843 −0.425959 −0.212980 0.977057i \(-0.568317\pi\)
−0.212980 + 0.977057i \(0.568317\pi\)
\(860\) −11.0397 −0.376450
\(861\) 28.5215 0.972009
\(862\) 16.4445 0.560102
\(863\) 38.6416 1.31538 0.657688 0.753291i \(-0.271535\pi\)
0.657688 + 0.753291i \(0.271535\pi\)
\(864\) −0.651564 −0.0221667
\(865\) −9.27691 −0.315425
\(866\) −39.2087 −1.33236
\(867\) −37.6480 −1.27859
\(868\) −98.5790 −3.34599
\(869\) −39.7901 −1.34979
\(870\) −47.8940 −1.62376
\(871\) 17.4944 0.592776
\(872\) −20.7735 −0.703478
\(873\) −25.7799 −0.872518
\(874\) −38.5535 −1.30409
\(875\) 44.4595 1.50300
\(876\) 112.819 3.81181
\(877\) 3.62945 0.122558 0.0612789 0.998121i \(-0.480482\pi\)
0.0612789 + 0.998121i \(0.480482\pi\)
\(878\) −14.0350 −0.473658
\(879\) −34.6063 −1.16724
\(880\) 12.1717 0.410307
\(881\) 9.54126 0.321453 0.160727 0.986999i \(-0.448616\pi\)
0.160727 + 0.986999i \(0.448616\pi\)
\(882\) −48.7317 −1.64088
\(883\) 26.1741 0.880828 0.440414 0.897795i \(-0.354832\pi\)
0.440414 + 0.897795i \(0.354832\pi\)
\(884\) −10.8890 −0.366236
\(885\) −41.8799 −1.40778
\(886\) −84.2829 −2.83154
\(887\) 7.84727 0.263486 0.131743 0.991284i \(-0.457943\pi\)
0.131743 + 0.991284i \(0.457943\pi\)
\(888\) 23.5641 0.790758
\(889\) −8.62991 −0.289438
\(890\) 62.4651 2.09384
\(891\) −26.6405 −0.892491
\(892\) −97.9014 −3.27798
\(893\) 13.2336 0.442847
\(894\) 20.1919 0.675318
\(895\) 32.9067 1.09995
\(896\) −77.5784 −2.59171
\(897\) −37.0561 −1.23727
\(898\) −43.5771 −1.45419
\(899\) 36.2533 1.20912
\(900\) −27.1656 −0.905519
\(901\) 1.20694 0.0402089
\(902\) 21.4248 0.713369
\(903\) 16.8217 0.559791
\(904\) −13.7422 −0.457058
\(905\) −16.5500 −0.550141
\(906\) 5.82205 0.193425
\(907\) 29.1445 0.967729 0.483864 0.875143i \(-0.339233\pi\)
0.483864 + 0.875143i \(0.339233\pi\)
\(908\) −29.6009 −0.982341
\(909\) 19.8015 0.656774
\(910\) 33.9912 1.12680
\(911\) −10.1576 −0.336535 −0.168267 0.985741i \(-0.553817\pi\)
−0.168267 + 0.985741i \(0.553817\pi\)
\(912\) −16.4690 −0.545343
\(913\) −19.8261 −0.656148
\(914\) −48.8521 −1.61588
\(915\) −16.2882 −0.538472
\(916\) 46.9147 1.55011
\(917\) −3.70036 −0.122197
\(918\) −0.936433 −0.0309069
\(919\) 20.8141 0.686593 0.343296 0.939227i \(-0.388457\pi\)
0.343296 + 0.939227i \(0.388457\pi\)
\(920\) 43.2075 1.42451
\(921\) −31.3964 −1.03455
\(922\) −11.7946 −0.388436
\(923\) 5.72886 0.188568
\(924\) −97.4653 −3.20637
\(925\) 5.71109 0.187780
\(926\) −11.6222 −0.381928
\(927\) 15.4636 0.507892
\(928\) 10.5199 0.345333
\(929\) −33.8827 −1.11166 −0.555828 0.831297i \(-0.687599\pi\)
−0.555828 + 0.831297i \(0.687599\pi\)
\(930\) −63.9278 −2.09627
\(931\) −17.7070 −0.580324
\(932\) 32.6623 1.06989
\(933\) 77.3388 2.53196
\(934\) 37.2301 1.21821
\(935\) −5.40960 −0.176913
\(936\) −29.2549 −0.956226
\(937\) −33.6988 −1.10089 −0.550446 0.834871i \(-0.685542\pi\)
−0.550446 + 0.834871i \(0.685542\pi\)
\(938\) 66.0513 2.15665
\(939\) −9.77416 −0.318968
\(940\) −31.5169 −1.02797
\(941\) −11.6528 −0.379869 −0.189935 0.981797i \(-0.560828\pi\)
−0.189935 + 0.981797i \(0.560828\pi\)
\(942\) 108.270 3.52764
\(943\) 20.1086 0.654826
\(944\) −29.7469 −0.968178
\(945\) 1.91130 0.0621747
\(946\) 12.6362 0.410837
\(947\) −13.7648 −0.447296 −0.223648 0.974670i \(-0.571797\pi\)
−0.223648 + 0.974670i \(0.571797\pi\)
\(948\) −128.220 −4.16439
\(949\) 29.4464 0.955870
\(950\) −15.0966 −0.489800
\(951\) −48.9743 −1.58810
\(952\) −19.3464 −0.627020
\(953\) 29.2856 0.948654 0.474327 0.880349i \(-0.342691\pi\)
0.474327 + 0.880349i \(0.342691\pi\)
\(954\) 6.89073 0.223096
\(955\) 16.0168 0.518290
\(956\) 113.618 3.67467
\(957\) 35.8438 1.15866
\(958\) 77.3202 2.49810
\(959\) 41.2008 1.33044
\(960\) −39.3155 −1.26890
\(961\) 17.3901 0.560970
\(962\) 13.0698 0.421386
\(963\) 11.9592 0.385381
\(964\) 73.8181 2.37752
\(965\) −10.6875 −0.344044
\(966\) −139.908 −4.50146
\(967\) 6.37922 0.205142 0.102571 0.994726i \(-0.467293\pi\)
0.102571 + 0.994726i \(0.467293\pi\)
\(968\) 12.5504 0.403384
\(969\) 7.31951 0.235136
\(970\) 34.1199 1.09552
\(971\) 26.2942 0.843821 0.421911 0.906637i \(-0.361360\pi\)
0.421911 + 0.906637i \(0.361360\pi\)
\(972\) −82.1884 −2.63619
\(973\) −76.1330 −2.44071
\(974\) 1.95748 0.0627217
\(975\) −14.5103 −0.464702
\(976\) −11.5694 −0.370326
\(977\) 13.2902 0.425192 0.212596 0.977140i \(-0.431808\pi\)
0.212596 + 0.977140i \(0.431808\pi\)
\(978\) −54.3053 −1.73649
\(979\) −46.7487 −1.49410
\(980\) 42.1706 1.34709
\(981\) 13.9367 0.444965
\(982\) −62.5420 −1.99580
\(983\) −31.3255 −0.999129 −0.499565 0.866277i \(-0.666507\pi\)
−0.499565 + 0.866277i \(0.666507\pi\)
\(984\) 32.4885 1.03569
\(985\) 11.6600 0.371517
\(986\) 15.1193 0.481497
\(987\) 48.0239 1.52862
\(988\) −22.5892 −0.718660
\(989\) 11.8599 0.377122
\(990\) −30.8849 −0.981587
\(991\) −61.0554 −1.93949 −0.969744 0.244125i \(-0.921499\pi\)
−0.969744 + 0.244125i \(0.921499\pi\)
\(992\) 14.0417 0.445825
\(993\) −27.6606 −0.877782
\(994\) 21.6297 0.686051
\(995\) −23.3628 −0.740652
\(996\) −63.8877 −2.02436
\(997\) 29.2574 0.926591 0.463295 0.886204i \(-0.346667\pi\)
0.463295 + 0.886204i \(0.346667\pi\)
\(998\) 37.3226 1.18143
\(999\) 0.734904 0.0232513
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 8003.2.a.b.1.15 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.15 153 1.1 even 1 trivial