Properties

Label 8003.2.a.b.1.13
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 1.13
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +O(q^{10})\) \(q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +4.81810 q^{10} +3.56216 q^{11} -11.8605 q^{12} +1.09024 q^{13} +7.99655 q^{14} +5.82484 q^{15} +4.02322 q^{16} -5.29205 q^{17} -14.1504 q^{18} -3.97632 q^{19} -7.87299 q^{20} +9.66744 q^{21} -8.72828 q^{22} +0.162150 q^{23} +14.5448 q^{24} -1.13348 q^{25} -2.67140 q^{26} -8.22034 q^{27} -13.0667 q^{28} +6.56483 q^{29} -14.2725 q^{30} +3.12887 q^{31} -0.0379352 q^{32} -10.5521 q^{33} +12.9670 q^{34} +6.41723 q^{35} +23.1224 q^{36} +5.80524 q^{37} +9.74308 q^{38} -3.22959 q^{39} +9.65483 q^{40} -6.58031 q^{41} -23.6879 q^{42} +2.90103 q^{43} +14.2624 q^{44} -11.3557 q^{45} -0.397313 q^{46} -6.26327 q^{47} -11.9178 q^{48} +3.65061 q^{49} +2.77734 q^{50} +15.6765 q^{51} +4.36518 q^{52} -1.00000 q^{53} +20.1421 q^{54} -7.00444 q^{55} +16.0240 q^{56} +11.7789 q^{57} -16.0857 q^{58} +10.7020 q^{59} +23.3219 q^{60} +1.30768 q^{61} -7.66661 q^{62} -18.8469 q^{63} -7.95348 q^{64} -2.14379 q^{65} +25.8555 q^{66} -1.23584 q^{67} -21.1887 q^{68} -0.480332 q^{69} -15.7240 q^{70} -12.4187 q^{71} -28.3555 q^{72} -12.5572 q^{73} -14.2245 q^{74} +3.35767 q^{75} -15.9206 q^{76} -11.6252 q^{77} +7.91339 q^{78} -2.70892 q^{79} -7.91104 q^{80} +7.02579 q^{81} +16.1236 q^{82} -14.0500 q^{83} +38.7071 q^{84} +10.4060 q^{85} -7.10834 q^{86} -19.4468 q^{87} -17.4903 q^{88} +3.16585 q^{89} +27.8246 q^{90} -3.55803 q^{91} +0.649227 q^{92} -9.26855 q^{93} +15.3468 q^{94} +7.81881 q^{95} +0.112374 q^{96} -14.7322 q^{97} -8.94502 q^{98} +20.5715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45028 −1.73261 −0.866304 0.499516i \(-0.833511\pi\)
−0.866304 + 0.499516i \(0.833511\pi\)
\(3\) −2.96227 −1.71026 −0.855132 0.518410i \(-0.826524\pi\)
−0.855132 + 0.518410i \(0.826524\pi\)
\(4\) 4.00387 2.00193
\(5\) −1.96635 −0.879377 −0.439688 0.898150i \(-0.644911\pi\)
−0.439688 + 0.898150i \(0.644911\pi\)
\(6\) 7.25838 2.96322
\(7\) −3.26353 −1.23350 −0.616749 0.787160i \(-0.711551\pi\)
−0.616749 + 0.787160i \(0.711551\pi\)
\(8\) −4.91003 −1.73596
\(9\) 5.77502 1.92501
\(10\) 4.81810 1.52362
\(11\) 3.56216 1.07403 0.537015 0.843572i \(-0.319552\pi\)
0.537015 + 0.843572i \(0.319552\pi\)
\(12\) −11.8605 −3.42384
\(13\) 1.09024 0.302379 0.151189 0.988505i \(-0.451690\pi\)
0.151189 + 0.988505i \(0.451690\pi\)
\(14\) 7.99655 2.13717
\(15\) 5.82484 1.50397
\(16\) 4.02322 1.00580
\(17\) −5.29205 −1.28351 −0.641755 0.766910i \(-0.721793\pi\)
−0.641755 + 0.766910i \(0.721793\pi\)
\(18\) −14.1504 −3.33528
\(19\) −3.97632 −0.912229 −0.456115 0.889921i \(-0.650759\pi\)
−0.456115 + 0.889921i \(0.650759\pi\)
\(20\) −7.87299 −1.76045
\(21\) 9.66744 2.10961
\(22\) −8.72828 −1.86088
\(23\) 0.162150 0.0338106 0.0169053 0.999857i \(-0.494619\pi\)
0.0169053 + 0.999857i \(0.494619\pi\)
\(24\) 14.5448 2.96895
\(25\) −1.13348 −0.226696
\(26\) −2.67140 −0.523904
\(27\) −8.22034 −1.58201
\(28\) −13.0667 −2.46938
\(29\) 6.56483 1.21906 0.609529 0.792764i \(-0.291359\pi\)
0.609529 + 0.792764i \(0.291359\pi\)
\(30\) −14.2725 −2.60579
\(31\) 3.12887 0.561962 0.280981 0.959713i \(-0.409340\pi\)
0.280981 + 0.959713i \(0.409340\pi\)
\(32\) −0.0379352 −0.00670606
\(33\) −10.5521 −1.83688
\(34\) 12.9670 2.22382
\(35\) 6.41723 1.08471
\(36\) 23.1224 3.85373
\(37\) 5.80524 0.954375 0.477188 0.878801i \(-0.341656\pi\)
0.477188 + 0.878801i \(0.341656\pi\)
\(38\) 9.74308 1.58054
\(39\) −3.22959 −0.517148
\(40\) 9.65483 1.52656
\(41\) −6.58031 −1.02767 −0.513836 0.857889i \(-0.671776\pi\)
−0.513836 + 0.857889i \(0.671776\pi\)
\(42\) −23.6879 −3.65512
\(43\) 2.90103 0.442404 0.221202 0.975228i \(-0.429002\pi\)
0.221202 + 0.975228i \(0.429002\pi\)
\(44\) 14.2624 2.15014
\(45\) −11.3557 −1.69281
\(46\) −0.397313 −0.0585806
\(47\) −6.26327 −0.913592 −0.456796 0.889572i \(-0.651003\pi\)
−0.456796 + 0.889572i \(0.651003\pi\)
\(48\) −11.9178 −1.72019
\(49\) 3.65061 0.521516
\(50\) 2.77734 0.392776
\(51\) 15.6765 2.19514
\(52\) 4.36518 0.605342
\(53\) −1.00000 −0.137361
\(54\) 20.1421 2.74100
\(55\) −7.00444 −0.944478
\(56\) 16.0240 2.14130
\(57\) 11.7789 1.56015
\(58\) −16.0857 −2.11215
\(59\) 10.7020 1.39328 0.696639 0.717422i \(-0.254678\pi\)
0.696639 + 0.717422i \(0.254678\pi\)
\(60\) 23.3219 3.01084
\(61\) 1.30768 0.167432 0.0837159 0.996490i \(-0.473321\pi\)
0.0837159 + 0.996490i \(0.473321\pi\)
\(62\) −7.66661 −0.973660
\(63\) −18.8469 −2.37449
\(64\) −7.95348 −0.994185
\(65\) −2.14379 −0.265905
\(66\) 25.8555 3.18259
\(67\) −1.23584 −0.150981 −0.0754907 0.997147i \(-0.524052\pi\)
−0.0754907 + 0.997147i \(0.524052\pi\)
\(68\) −21.1887 −2.56950
\(69\) −0.480332 −0.0578251
\(70\) −15.7240 −1.87938
\(71\) −12.4187 −1.47383 −0.736914 0.675986i \(-0.763718\pi\)
−0.736914 + 0.675986i \(0.763718\pi\)
\(72\) −28.3555 −3.34173
\(73\) −12.5572 −1.46970 −0.734852 0.678227i \(-0.762748\pi\)
−0.734852 + 0.678227i \(0.762748\pi\)
\(74\) −14.2245 −1.65356
\(75\) 3.35767 0.387711
\(76\) −15.9206 −1.82622
\(77\) −11.6252 −1.32481
\(78\) 7.91339 0.896015
\(79\) −2.70892 −0.304777 −0.152388 0.988321i \(-0.548696\pi\)
−0.152388 + 0.988321i \(0.548696\pi\)
\(80\) −7.91104 −0.884481
\(81\) 7.02579 0.780643
\(82\) 16.1236 1.78055
\(83\) −14.0500 −1.54219 −0.771093 0.636723i \(-0.780290\pi\)
−0.771093 + 0.636723i \(0.780290\pi\)
\(84\) 38.7071 4.22329
\(85\) 10.4060 1.12869
\(86\) −7.10834 −0.766512
\(87\) −19.4468 −2.08491
\(88\) −17.4903 −1.86447
\(89\) 3.16585 0.335579 0.167789 0.985823i \(-0.446337\pi\)
0.167789 + 0.985823i \(0.446337\pi\)
\(90\) 27.8246 2.93297
\(91\) −3.55803 −0.372983
\(92\) 0.649227 0.0676866
\(93\) −9.26855 −0.961104
\(94\) 15.3468 1.58290
\(95\) 7.81881 0.802193
\(96\) 0.112374 0.0114691
\(97\) −14.7322 −1.49583 −0.747914 0.663795i \(-0.768945\pi\)
−0.747914 + 0.663795i \(0.768945\pi\)
\(98\) −8.94502 −0.903584
\(99\) 20.5715 2.06752
\(100\) −4.53831 −0.453831
\(101\) −8.49672 −0.845456 −0.422728 0.906257i \(-0.638927\pi\)
−0.422728 + 0.906257i \(0.638927\pi\)
\(102\) −38.4117 −3.80332
\(103\) 17.2789 1.70254 0.851272 0.524725i \(-0.175832\pi\)
0.851272 + 0.524725i \(0.175832\pi\)
\(104\) −5.35312 −0.524917
\(105\) −19.0095 −1.85514
\(106\) 2.45028 0.237992
\(107\) 2.26294 0.218766 0.109383 0.994000i \(-0.465112\pi\)
0.109383 + 0.994000i \(0.465112\pi\)
\(108\) −32.9132 −3.16707
\(109\) 0.443095 0.0424408 0.0212204 0.999775i \(-0.493245\pi\)
0.0212204 + 0.999775i \(0.493245\pi\)
\(110\) 17.1628 1.63641
\(111\) −17.1967 −1.63223
\(112\) −13.1299 −1.24066
\(113\) 6.68196 0.628586 0.314293 0.949326i \(-0.398233\pi\)
0.314293 + 0.949326i \(0.398233\pi\)
\(114\) −28.8616 −2.70314
\(115\) −0.318843 −0.0297323
\(116\) 26.2847 2.44047
\(117\) 6.29617 0.582081
\(118\) −26.2228 −2.41401
\(119\) 17.2707 1.58321
\(120\) −28.6002 −2.61083
\(121\) 1.68897 0.153542
\(122\) −3.20419 −0.290094
\(123\) 19.4926 1.75759
\(124\) 12.5276 1.12501
\(125\) 12.0605 1.07873
\(126\) 46.1802 4.11406
\(127\) −1.65972 −0.147277 −0.0736383 0.997285i \(-0.523461\pi\)
−0.0736383 + 0.997285i \(0.523461\pi\)
\(128\) 19.5641 1.72924
\(129\) −8.59363 −0.756627
\(130\) 5.25289 0.460709
\(131\) 12.4205 1.08518 0.542590 0.839998i \(-0.317444\pi\)
0.542590 + 0.839998i \(0.317444\pi\)
\(132\) −42.2490 −3.67731
\(133\) 12.9768 1.12523
\(134\) 3.02814 0.261592
\(135\) 16.1640 1.39118
\(136\) 25.9841 2.22812
\(137\) −1.71680 −0.146676 −0.0733382 0.997307i \(-0.523365\pi\)
−0.0733382 + 0.997307i \(0.523365\pi\)
\(138\) 1.17695 0.100188
\(139\) 10.4177 0.883617 0.441808 0.897109i \(-0.354337\pi\)
0.441808 + 0.897109i \(0.354337\pi\)
\(140\) 25.6937 2.17152
\(141\) 18.5535 1.56248
\(142\) 30.4293 2.55357
\(143\) 3.88361 0.324764
\(144\) 23.2341 1.93618
\(145\) −12.9087 −1.07201
\(146\) 30.7685 2.54642
\(147\) −10.8141 −0.891931
\(148\) 23.2434 1.91060
\(149\) 16.6667 1.36539 0.682697 0.730702i \(-0.260807\pi\)
0.682697 + 0.730702i \(0.260807\pi\)
\(150\) −8.22723 −0.671751
\(151\) −1.00000 −0.0813788
\(152\) 19.5238 1.58359
\(153\) −30.5617 −2.47077
\(154\) 28.4850 2.29539
\(155\) −6.15245 −0.494177
\(156\) −12.9308 −1.03530
\(157\) 4.32729 0.345355 0.172678 0.984978i \(-0.444758\pi\)
0.172678 + 0.984978i \(0.444758\pi\)
\(158\) 6.63760 0.528059
\(159\) 2.96227 0.234923
\(160\) 0.0745938 0.00589716
\(161\) −0.529181 −0.0417053
\(162\) −17.2151 −1.35255
\(163\) −19.2665 −1.50907 −0.754534 0.656261i \(-0.772137\pi\)
−0.754534 + 0.656261i \(0.772137\pi\)
\(164\) −26.3467 −2.05733
\(165\) 20.7490 1.61531
\(166\) 34.4264 2.67200
\(167\) 5.22062 0.403984 0.201992 0.979387i \(-0.435259\pi\)
0.201992 + 0.979387i \(0.435259\pi\)
\(168\) −47.4674 −3.66219
\(169\) −11.8114 −0.908567
\(170\) −25.4976 −1.95558
\(171\) −22.9633 −1.75605
\(172\) 11.6154 0.885662
\(173\) −3.55070 −0.269955 −0.134978 0.990849i \(-0.543096\pi\)
−0.134978 + 0.990849i \(0.543096\pi\)
\(174\) 47.6500 3.61234
\(175\) 3.69915 0.279629
\(176\) 14.3313 1.08026
\(177\) −31.7021 −2.38287
\(178\) −7.75720 −0.581427
\(179\) 4.39686 0.328637 0.164318 0.986407i \(-0.447458\pi\)
0.164318 + 0.986407i \(0.447458\pi\)
\(180\) −45.4667 −3.38889
\(181\) 4.21653 0.313412 0.156706 0.987645i \(-0.449912\pi\)
0.156706 + 0.987645i \(0.449912\pi\)
\(182\) 8.71818 0.646234
\(183\) −3.87371 −0.286353
\(184\) −0.796162 −0.0586939
\(185\) −11.4151 −0.839255
\(186\) 22.7105 1.66522
\(187\) −18.8511 −1.37853
\(188\) −25.0773 −1.82895
\(189\) 26.8273 1.95140
\(190\) −19.1583 −1.38989
\(191\) 8.23548 0.595898 0.297949 0.954582i \(-0.403697\pi\)
0.297949 + 0.954582i \(0.403697\pi\)
\(192\) 23.5603 1.70032
\(193\) −1.42050 −0.102250 −0.0511250 0.998692i \(-0.516281\pi\)
−0.0511250 + 0.998692i \(0.516281\pi\)
\(194\) 36.0980 2.59169
\(195\) 6.35049 0.454768
\(196\) 14.6166 1.04404
\(197\) 5.98355 0.426310 0.213155 0.977018i \(-0.431626\pi\)
0.213155 + 0.977018i \(0.431626\pi\)
\(198\) −50.4060 −3.58220
\(199\) 1.19685 0.0848427 0.0424214 0.999100i \(-0.486493\pi\)
0.0424214 + 0.999100i \(0.486493\pi\)
\(200\) 5.56543 0.393535
\(201\) 3.66088 0.258218
\(202\) 20.8193 1.46484
\(203\) −21.4245 −1.50370
\(204\) 62.7664 4.39453
\(205\) 12.9392 0.903711
\(206\) −42.3382 −2.94984
\(207\) 0.936420 0.0650857
\(208\) 4.38628 0.304134
\(209\) −14.1643 −0.979763
\(210\) 46.5787 3.21423
\(211\) 17.7688 1.22326 0.611628 0.791145i \(-0.290515\pi\)
0.611628 + 0.791145i \(0.290515\pi\)
\(212\) −4.00387 −0.274987
\(213\) 36.7875 2.52064
\(214\) −5.54482 −0.379036
\(215\) −5.70444 −0.389039
\(216\) 40.3622 2.74630
\(217\) −10.2112 −0.693179
\(218\) −1.08571 −0.0735333
\(219\) 37.1976 2.51358
\(220\) −28.0448 −1.89078
\(221\) −5.76961 −0.388106
\(222\) 42.1366 2.82802
\(223\) 13.6375 0.913232 0.456616 0.889664i \(-0.349061\pi\)
0.456616 + 0.889664i \(0.349061\pi\)
\(224\) 0.123803 0.00827191
\(225\) −6.54587 −0.436392
\(226\) −16.3727 −1.08909
\(227\) 14.6922 0.975153 0.487576 0.873080i \(-0.337881\pi\)
0.487576 + 0.873080i \(0.337881\pi\)
\(228\) 47.1612 3.12332
\(229\) −7.23368 −0.478015 −0.239008 0.971018i \(-0.576822\pi\)
−0.239008 + 0.971018i \(0.576822\pi\)
\(230\) 0.781255 0.0515144
\(231\) 34.4369 2.26578
\(232\) −32.2335 −2.11623
\(233\) 26.8164 1.75680 0.878401 0.477924i \(-0.158611\pi\)
0.878401 + 0.477924i \(0.158611\pi\)
\(234\) −15.4274 −1.00852
\(235\) 12.3158 0.803392
\(236\) 42.8493 2.78925
\(237\) 8.02453 0.521249
\(238\) −42.3182 −2.74308
\(239\) −2.46332 −0.159339 −0.0796695 0.996821i \(-0.525387\pi\)
−0.0796695 + 0.996821i \(0.525387\pi\)
\(240\) 23.4346 1.51270
\(241\) −22.1624 −1.42760 −0.713802 0.700348i \(-0.753028\pi\)
−0.713802 + 0.700348i \(0.753028\pi\)
\(242\) −4.13844 −0.266029
\(243\) 3.84879 0.246900
\(244\) 5.23579 0.335187
\(245\) −7.17837 −0.458609
\(246\) −47.7624 −3.04522
\(247\) −4.33515 −0.275839
\(248\) −15.3629 −0.975543
\(249\) 41.6198 2.63755
\(250\) −29.5517 −1.86901
\(251\) 1.19272 0.0752840 0.0376420 0.999291i \(-0.488015\pi\)
0.0376420 + 0.999291i \(0.488015\pi\)
\(252\) −75.4606 −4.75357
\(253\) 0.577604 0.0363137
\(254\) 4.06678 0.255173
\(255\) −30.8253 −1.93036
\(256\) −32.0306 −2.00191
\(257\) 17.6728 1.10240 0.551198 0.834374i \(-0.314171\pi\)
0.551198 + 0.834374i \(0.314171\pi\)
\(258\) 21.0568 1.31094
\(259\) −18.9456 −1.17722
\(260\) −8.58346 −0.532324
\(261\) 37.9120 2.34669
\(262\) −30.4336 −1.88019
\(263\) 24.1349 1.48822 0.744112 0.668055i \(-0.232873\pi\)
0.744112 + 0.668055i \(0.232873\pi\)
\(264\) 51.8109 3.18874
\(265\) 1.96635 0.120792
\(266\) −31.7968 −1.94959
\(267\) −9.37808 −0.573929
\(268\) −4.94812 −0.302255
\(269\) 1.07322 0.0654355 0.0327178 0.999465i \(-0.489584\pi\)
0.0327178 + 0.999465i \(0.489584\pi\)
\(270\) −39.6064 −2.41037
\(271\) 2.30668 0.140121 0.0700604 0.997543i \(-0.477681\pi\)
0.0700604 + 0.997543i \(0.477681\pi\)
\(272\) −21.2911 −1.29096
\(273\) 10.5398 0.637900
\(274\) 4.20665 0.254133
\(275\) −4.03764 −0.243479
\(276\) −1.92318 −0.115762
\(277\) −16.4807 −0.990228 −0.495114 0.868828i \(-0.664874\pi\)
−0.495114 + 0.868828i \(0.664874\pi\)
\(278\) −25.5262 −1.53096
\(279\) 18.0693 1.08178
\(280\) −31.5088 −1.88301
\(281\) 16.6634 0.994056 0.497028 0.867735i \(-0.334425\pi\)
0.497028 + 0.867735i \(0.334425\pi\)
\(282\) −45.4612 −2.70717
\(283\) −13.2183 −0.785745 −0.392872 0.919593i \(-0.628519\pi\)
−0.392872 + 0.919593i \(0.628519\pi\)
\(284\) −49.7228 −2.95051
\(285\) −23.1614 −1.37196
\(286\) −9.51594 −0.562689
\(287\) 21.4750 1.26763
\(288\) −0.219077 −0.0129092
\(289\) 11.0058 0.647399
\(290\) 31.6300 1.85738
\(291\) 43.6407 2.55826
\(292\) −50.2772 −2.94225
\(293\) 23.9230 1.39760 0.698798 0.715319i \(-0.253719\pi\)
0.698798 + 0.715319i \(0.253719\pi\)
\(294\) 26.4975 1.54537
\(295\) −21.0438 −1.22522
\(296\) −28.5039 −1.65676
\(297\) −29.2822 −1.69912
\(298\) −40.8382 −2.36569
\(299\) 0.176783 0.0102236
\(300\) 13.4437 0.776171
\(301\) −9.46760 −0.545704
\(302\) 2.45028 0.140998
\(303\) 25.1696 1.44595
\(304\) −15.9976 −0.917524
\(305\) −2.57136 −0.147236
\(306\) 74.8846 4.28087
\(307\) 25.1651 1.43625 0.718125 0.695914i \(-0.245001\pi\)
0.718125 + 0.695914i \(0.245001\pi\)
\(308\) −46.5458 −2.65219
\(309\) −51.1848 −2.91180
\(310\) 15.0752 0.856215
\(311\) 17.9741 1.01922 0.509608 0.860407i \(-0.329790\pi\)
0.509608 + 0.860407i \(0.329790\pi\)
\(312\) 15.8574 0.897747
\(313\) −4.05388 −0.229139 −0.114570 0.993415i \(-0.536549\pi\)
−0.114570 + 0.993415i \(0.536549\pi\)
\(314\) −10.6031 −0.598366
\(315\) 37.0596 2.08807
\(316\) −10.8461 −0.610143
\(317\) 17.6752 0.992740 0.496370 0.868111i \(-0.334666\pi\)
0.496370 + 0.868111i \(0.334666\pi\)
\(318\) −7.25838 −0.407030
\(319\) 23.3849 1.30931
\(320\) 15.6393 0.874263
\(321\) −6.70342 −0.374148
\(322\) 1.29664 0.0722590
\(323\) 21.0429 1.17086
\(324\) 28.1303 1.56279
\(325\) −1.23577 −0.0685481
\(326\) 47.2083 2.61463
\(327\) −1.31256 −0.0725850
\(328\) 32.3095 1.78400
\(329\) 20.4404 1.12691
\(330\) −50.8408 −2.79870
\(331\) −18.9977 −1.04421 −0.522105 0.852881i \(-0.674853\pi\)
−0.522105 + 0.852881i \(0.674853\pi\)
\(332\) −56.2542 −3.08735
\(333\) 33.5254 1.83718
\(334\) −12.7920 −0.699945
\(335\) 2.43008 0.132770
\(336\) 38.8942 2.12185
\(337\) 15.8202 0.861783 0.430891 0.902404i \(-0.358199\pi\)
0.430891 + 0.902404i \(0.358199\pi\)
\(338\) 28.9412 1.57419
\(339\) −19.7938 −1.07505
\(340\) 41.6642 2.25956
\(341\) 11.1455 0.603565
\(342\) 56.2665 3.04254
\(343\) 10.9308 0.590209
\(344\) −14.2442 −0.767994
\(345\) 0.944499 0.0508501
\(346\) 8.70022 0.467727
\(347\) −8.06703 −0.433061 −0.216530 0.976276i \(-0.569474\pi\)
−0.216530 + 0.976276i \(0.569474\pi\)
\(348\) −77.8622 −4.17385
\(349\) −16.5903 −0.888057 −0.444028 0.896013i \(-0.646451\pi\)
−0.444028 + 0.896013i \(0.646451\pi\)
\(350\) −9.06394 −0.484488
\(351\) −8.96216 −0.478365
\(352\) −0.135131 −0.00720252
\(353\) −32.6584 −1.73823 −0.869115 0.494611i \(-0.835311\pi\)
−0.869115 + 0.494611i \(0.835311\pi\)
\(354\) 77.6789 4.12859
\(355\) 24.4195 1.29605
\(356\) 12.6756 0.671807
\(357\) −51.1605 −2.70770
\(358\) −10.7735 −0.569399
\(359\) 15.2901 0.806980 0.403490 0.914984i \(-0.367797\pi\)
0.403490 + 0.914984i \(0.367797\pi\)
\(360\) 55.7568 2.93864
\(361\) −3.18891 −0.167838
\(362\) −10.3317 −0.543021
\(363\) −5.00317 −0.262598
\(364\) −14.2459 −0.746688
\(365\) 24.6917 1.29242
\(366\) 9.49166 0.496137
\(367\) 18.1862 0.949312 0.474656 0.880171i \(-0.342572\pi\)
0.474656 + 0.880171i \(0.342572\pi\)
\(368\) 0.652365 0.0340069
\(369\) −38.0014 −1.97827
\(370\) 27.9702 1.45410
\(371\) 3.26353 0.169434
\(372\) −37.1100 −1.92407
\(373\) −9.10499 −0.471438 −0.235719 0.971821i \(-0.575745\pi\)
−0.235719 + 0.971821i \(0.575745\pi\)
\(374\) 46.1905 2.38845
\(375\) −35.7266 −1.84491
\(376\) 30.7529 1.58596
\(377\) 7.15725 0.368617
\(378\) −65.7344 −3.38101
\(379\) 9.51955 0.488987 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(380\) 31.3055 1.60594
\(381\) 4.91654 0.251882
\(382\) −20.1792 −1.03246
\(383\) −22.8947 −1.16986 −0.584932 0.811083i \(-0.698879\pi\)
−0.584932 + 0.811083i \(0.698879\pi\)
\(384\) −57.9541 −2.95746
\(385\) 22.8592 1.16501
\(386\) 3.48063 0.177159
\(387\) 16.7535 0.851630
\(388\) −58.9858 −2.99455
\(389\) 4.86002 0.246413 0.123206 0.992381i \(-0.460682\pi\)
0.123206 + 0.992381i \(0.460682\pi\)
\(390\) −15.5605 −0.787935
\(391\) −0.858106 −0.0433963
\(392\) −17.9246 −0.905331
\(393\) −36.7927 −1.85594
\(394\) −14.6614 −0.738629
\(395\) 5.32667 0.268014
\(396\) 82.3657 4.13903
\(397\) 25.6001 1.28483 0.642417 0.766355i \(-0.277932\pi\)
0.642417 + 0.766355i \(0.277932\pi\)
\(398\) −2.93263 −0.146999
\(399\) −38.4408 −1.92445
\(400\) −4.56024 −0.228012
\(401\) −26.1927 −1.30800 −0.654000 0.756495i \(-0.726910\pi\)
−0.654000 + 0.756495i \(0.726910\pi\)
\(402\) −8.97017 −0.447391
\(403\) 3.41123 0.169925
\(404\) −34.0198 −1.69255
\(405\) −13.8151 −0.686479
\(406\) 52.4960 2.60533
\(407\) 20.6792 1.02503
\(408\) −76.9719 −3.81068
\(409\) −8.40417 −0.415560 −0.207780 0.978176i \(-0.566624\pi\)
−0.207780 + 0.978176i \(0.566624\pi\)
\(410\) −31.7046 −1.56578
\(411\) 5.08563 0.250855
\(412\) 69.1825 3.40838
\(413\) −34.9262 −1.71860
\(414\) −2.29449 −0.112768
\(415\) 27.6271 1.35616
\(416\) −0.0413586 −0.00202777
\(417\) −30.8600 −1.51122
\(418\) 34.7064 1.69755
\(419\) −7.78340 −0.380244 −0.190122 0.981760i \(-0.560888\pi\)
−0.190122 + 0.981760i \(0.560888\pi\)
\(420\) −76.1116 −3.71387
\(421\) 5.51175 0.268626 0.134313 0.990939i \(-0.457117\pi\)
0.134313 + 0.990939i \(0.457117\pi\)
\(422\) −43.5386 −2.11942
\(423\) −36.1705 −1.75867
\(424\) 4.91003 0.238452
\(425\) 5.99844 0.290967
\(426\) −90.1396 −4.36728
\(427\) −4.26766 −0.206527
\(428\) 9.06049 0.437955
\(429\) −11.5043 −0.555433
\(430\) 13.9775 0.674053
\(431\) 32.0908 1.54576 0.772879 0.634553i \(-0.218816\pi\)
0.772879 + 0.634553i \(0.218816\pi\)
\(432\) −33.0722 −1.59119
\(433\) −8.75824 −0.420894 −0.210447 0.977605i \(-0.567492\pi\)
−0.210447 + 0.977605i \(0.567492\pi\)
\(434\) 25.0202 1.20101
\(435\) 38.2391 1.83342
\(436\) 1.77409 0.0849636
\(437\) −0.644760 −0.0308431
\(438\) −91.1446 −4.35506
\(439\) −37.3328 −1.78180 −0.890898 0.454203i \(-0.849924\pi\)
−0.890898 + 0.454203i \(0.849924\pi\)
\(440\) 34.3920 1.63957
\(441\) 21.0824 1.00392
\(442\) 14.1372 0.672436
\(443\) 7.55558 0.358976 0.179488 0.983760i \(-0.442556\pi\)
0.179488 + 0.983760i \(0.442556\pi\)
\(444\) −68.8531 −3.26762
\(445\) −6.22515 −0.295100
\(446\) −33.4156 −1.58227
\(447\) −49.3713 −2.33518
\(448\) 25.9564 1.22632
\(449\) 28.7793 1.35818 0.679089 0.734056i \(-0.262375\pi\)
0.679089 + 0.734056i \(0.262375\pi\)
\(450\) 16.0392 0.756096
\(451\) −23.4401 −1.10375
\(452\) 26.7537 1.25839
\(453\) 2.96227 0.139179
\(454\) −35.9999 −1.68956
\(455\) 6.99633 0.327993
\(456\) −57.8348 −2.70836
\(457\) 16.0985 0.753058 0.376529 0.926405i \(-0.377118\pi\)
0.376529 + 0.926405i \(0.377118\pi\)
\(458\) 17.7245 0.828213
\(459\) 43.5025 2.03052
\(460\) −1.27661 −0.0595221
\(461\) 10.9706 0.510950 0.255475 0.966816i \(-0.417768\pi\)
0.255475 + 0.966816i \(0.417768\pi\)
\(462\) −84.3801 −3.92572
\(463\) −9.21276 −0.428153 −0.214077 0.976817i \(-0.568674\pi\)
−0.214077 + 0.976817i \(0.568674\pi\)
\(464\) 26.4117 1.22613
\(465\) 18.2252 0.845173
\(466\) −65.7077 −3.04385
\(467\) 39.4780 1.82682 0.913411 0.407038i \(-0.133438\pi\)
0.913411 + 0.407038i \(0.133438\pi\)
\(468\) 25.2090 1.16529
\(469\) 4.03319 0.186235
\(470\) −30.1770 −1.39196
\(471\) −12.8186 −0.590649
\(472\) −52.5470 −2.41867
\(473\) 10.3339 0.475155
\(474\) −19.6623 −0.903121
\(475\) 4.50708 0.206799
\(476\) 69.1498 3.16947
\(477\) −5.77502 −0.264420
\(478\) 6.03583 0.276072
\(479\) 6.77108 0.309379 0.154689 0.987963i \(-0.450562\pi\)
0.154689 + 0.987963i \(0.450562\pi\)
\(480\) −0.220967 −0.0100857
\(481\) 6.32911 0.288583
\(482\) 54.3040 2.47348
\(483\) 1.56758 0.0713272
\(484\) 6.76240 0.307382
\(485\) 28.9686 1.31540
\(486\) −9.43060 −0.427781
\(487\) −25.4186 −1.15182 −0.575912 0.817511i \(-0.695353\pi\)
−0.575912 + 0.817511i \(0.695353\pi\)
\(488\) −6.42077 −0.290655
\(489\) 57.0725 2.58091
\(490\) 17.5890 0.794591
\(491\) −24.3051 −1.09687 −0.548437 0.836192i \(-0.684777\pi\)
−0.548437 + 0.836192i \(0.684777\pi\)
\(492\) 78.0459 3.51858
\(493\) −34.7414 −1.56467
\(494\) 10.6223 0.477921
\(495\) −40.4508 −1.81813
\(496\) 12.5881 0.565224
\(497\) 40.5288 1.81796
\(498\) −101.980 −4.56984
\(499\) 24.7739 1.10903 0.554516 0.832173i \(-0.312903\pi\)
0.554516 + 0.832173i \(0.312903\pi\)
\(500\) 48.2888 2.15954
\(501\) −15.4649 −0.690919
\(502\) −2.92250 −0.130438
\(503\) −18.0043 −0.802771 −0.401385 0.915909i \(-0.631471\pi\)
−0.401385 + 0.915909i \(0.631471\pi\)
\(504\) 92.5391 4.12202
\(505\) 16.7075 0.743474
\(506\) −1.41529 −0.0629174
\(507\) 34.9884 1.55389
\(508\) −6.64531 −0.294838
\(509\) 24.5310 1.08732 0.543659 0.839306i \(-0.317039\pi\)
0.543659 + 0.839306i \(0.317039\pi\)
\(510\) 75.5307 3.34456
\(511\) 40.9806 1.81288
\(512\) 39.3556 1.73929
\(513\) 32.6867 1.44315
\(514\) −43.3032 −1.91002
\(515\) −33.9764 −1.49718
\(516\) −34.4078 −1.51472
\(517\) −22.3108 −0.981226
\(518\) 46.4219 2.03966
\(519\) 10.5181 0.461695
\(520\) 10.5261 0.461600
\(521\) −27.9598 −1.22494 −0.612471 0.790493i \(-0.709824\pi\)
−0.612471 + 0.790493i \(0.709824\pi\)
\(522\) −92.8949 −4.06590
\(523\) 30.0613 1.31449 0.657244 0.753678i \(-0.271722\pi\)
0.657244 + 0.753678i \(0.271722\pi\)
\(524\) 49.7298 2.17246
\(525\) −10.9579 −0.478240
\(526\) −59.1373 −2.57851
\(527\) −16.5581 −0.721284
\(528\) −42.4532 −1.84754
\(529\) −22.9737 −0.998857
\(530\) −4.81810 −0.209285
\(531\) 61.8041 2.68207
\(532\) 51.9574 2.25264
\(533\) −7.17413 −0.310746
\(534\) 22.9789 0.994394
\(535\) −4.44972 −0.192378
\(536\) 6.06800 0.262098
\(537\) −13.0247 −0.562056
\(538\) −2.62969 −0.113374
\(539\) 13.0041 0.560125
\(540\) 64.7187 2.78505
\(541\) −10.9625 −0.471314 −0.235657 0.971836i \(-0.575724\pi\)
−0.235657 + 0.971836i \(0.575724\pi\)
\(542\) −5.65201 −0.242775
\(543\) −12.4905 −0.536018
\(544\) 0.200755 0.00860730
\(545\) −0.871278 −0.0373214
\(546\) −25.8256 −1.10523
\(547\) 43.4615 1.85828 0.929140 0.369728i \(-0.120549\pi\)
0.929140 + 0.369728i \(0.120549\pi\)
\(548\) −6.87385 −0.293636
\(549\) 7.55190 0.322307
\(550\) 9.89334 0.421853
\(551\) −26.1038 −1.11206
\(552\) 2.35844 0.100382
\(553\) 8.84062 0.375942
\(554\) 40.3822 1.71568
\(555\) 33.8146 1.43535
\(556\) 41.7110 1.76894
\(557\) −11.3213 −0.479699 −0.239850 0.970810i \(-0.577098\pi\)
−0.239850 + 0.970810i \(0.577098\pi\)
\(558\) −44.2748 −1.87430
\(559\) 3.16283 0.133773
\(560\) 25.8179 1.09100
\(561\) 55.8420 2.35765
\(562\) −40.8300 −1.72231
\(563\) −23.7475 −1.00084 −0.500418 0.865784i \(-0.666820\pi\)
−0.500418 + 0.865784i \(0.666820\pi\)
\(564\) 74.2856 3.12799
\(565\) −13.1391 −0.552764
\(566\) 32.3884 1.36139
\(567\) −22.9288 −0.962921
\(568\) 60.9762 2.55850
\(569\) 21.5985 0.905454 0.452727 0.891649i \(-0.350451\pi\)
0.452727 + 0.891649i \(0.350451\pi\)
\(570\) 56.7519 2.37708
\(571\) 5.94116 0.248630 0.124315 0.992243i \(-0.460327\pi\)
0.124315 + 0.992243i \(0.460327\pi\)
\(572\) 15.5495 0.650156
\(573\) −24.3957 −1.01914
\(574\) −52.6198 −2.19631
\(575\) −0.183794 −0.00766474
\(576\) −45.9315 −1.91381
\(577\) −18.8625 −0.785255 −0.392628 0.919698i \(-0.628434\pi\)
−0.392628 + 0.919698i \(0.628434\pi\)
\(578\) −26.9672 −1.12169
\(579\) 4.20791 0.174875
\(580\) −51.6848 −2.14609
\(581\) 45.8525 1.90228
\(582\) −106.932 −4.43247
\(583\) −3.56216 −0.147529
\(584\) 61.6561 2.55135
\(585\) −12.3804 −0.511869
\(586\) −58.6180 −2.42149
\(587\) −17.4219 −0.719077 −0.359538 0.933130i \(-0.617066\pi\)
−0.359538 + 0.933130i \(0.617066\pi\)
\(588\) −43.2982 −1.78559
\(589\) −12.4414 −0.512638
\(590\) 51.5631 2.12282
\(591\) −17.7249 −0.729103
\(592\) 23.3557 0.959914
\(593\) 43.8395 1.80027 0.900136 0.435609i \(-0.143467\pi\)
0.900136 + 0.435609i \(0.143467\pi\)
\(594\) 71.7495 2.94392
\(595\) −33.9603 −1.39224
\(596\) 66.7314 2.73343
\(597\) −3.54540 −0.145104
\(598\) −0.433167 −0.0177135
\(599\) 35.0789 1.43328 0.716642 0.697441i \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(600\) −16.4863 −0.673049
\(601\) 24.3495 0.993238 0.496619 0.867969i \(-0.334575\pi\)
0.496619 + 0.867969i \(0.334575\pi\)
\(602\) 23.1983 0.945491
\(603\) −7.13698 −0.290640
\(604\) −4.00387 −0.162915
\(605\) −3.32109 −0.135022
\(606\) −61.6724 −2.50527
\(607\) −11.5199 −0.467579 −0.233790 0.972287i \(-0.575113\pi\)
−0.233790 + 0.972287i \(0.575113\pi\)
\(608\) 0.150842 0.00611747
\(609\) 63.4650 2.57173
\(610\) 6.30055 0.255102
\(611\) −6.82848 −0.276251
\(612\) −122.365 −4.94631
\(613\) −25.8075 −1.04235 −0.521177 0.853449i \(-0.674507\pi\)
−0.521177 + 0.853449i \(0.674507\pi\)
\(614\) −61.6616 −2.48846
\(615\) −38.3293 −1.54558
\(616\) 57.0801 2.29982
\(617\) 0.852748 0.0343303 0.0171652 0.999853i \(-0.494536\pi\)
0.0171652 + 0.999853i \(0.494536\pi\)
\(618\) 125.417 5.04501
\(619\) −34.9995 −1.40675 −0.703375 0.710819i \(-0.748324\pi\)
−0.703375 + 0.710819i \(0.748324\pi\)
\(620\) −24.6336 −0.989308
\(621\) −1.33293 −0.0534886
\(622\) −44.0415 −1.76590
\(623\) −10.3318 −0.413936
\(624\) −12.9933 −0.520149
\(625\) −18.0478 −0.721913
\(626\) 9.93314 0.397008
\(627\) 41.9583 1.67565
\(628\) 17.3259 0.691378
\(629\) −30.7216 −1.22495
\(630\) −90.8064 −3.61781
\(631\) −6.30963 −0.251183 −0.125591 0.992082i \(-0.540083\pi\)
−0.125591 + 0.992082i \(0.540083\pi\)
\(632\) 13.3009 0.529080
\(633\) −52.6360 −2.09209
\(634\) −43.3093 −1.72003
\(635\) 3.26359 0.129512
\(636\) 11.8605 0.470300
\(637\) 3.98005 0.157695
\(638\) −57.2996 −2.26851
\(639\) −71.7182 −2.83713
\(640\) −38.4698 −1.52065
\(641\) 18.8798 0.745705 0.372853 0.927891i \(-0.378380\pi\)
0.372853 + 0.927891i \(0.378380\pi\)
\(642\) 16.4252 0.648253
\(643\) 3.98211 0.157039 0.0785196 0.996913i \(-0.474981\pi\)
0.0785196 + 0.996913i \(0.474981\pi\)
\(644\) −2.11877 −0.0834913
\(645\) 16.8981 0.665361
\(646\) −51.5609 −2.02864
\(647\) −11.7687 −0.462676 −0.231338 0.972873i \(-0.574310\pi\)
−0.231338 + 0.972873i \(0.574310\pi\)
\(648\) −34.4968 −1.35516
\(649\) 38.1221 1.49642
\(650\) 3.02798 0.118767
\(651\) 30.2482 1.18552
\(652\) −77.1405 −3.02105
\(653\) −11.8183 −0.462485 −0.231242 0.972896i \(-0.574279\pi\)
−0.231242 + 0.972896i \(0.574279\pi\)
\(654\) 3.21615 0.125761
\(655\) −24.4229 −0.954282
\(656\) −26.4740 −1.03364
\(657\) −72.5178 −2.82919
\(658\) −50.0846 −1.95250
\(659\) −0.414096 −0.0161309 −0.00806545 0.999967i \(-0.502567\pi\)
−0.00806545 + 0.999967i \(0.502567\pi\)
\(660\) 83.0762 3.23374
\(661\) 5.01480 0.195053 0.0975266 0.995233i \(-0.468907\pi\)
0.0975266 + 0.995233i \(0.468907\pi\)
\(662\) 46.5498 1.80921
\(663\) 17.0911 0.663764
\(664\) 68.9859 2.67717
\(665\) −25.5169 −0.989504
\(666\) −82.1465 −3.18311
\(667\) 1.06449 0.0412171
\(668\) 20.9027 0.808748
\(669\) −40.3978 −1.56187
\(670\) −5.95438 −0.230038
\(671\) 4.65818 0.179827
\(672\) −0.366736 −0.0141472
\(673\) −36.5076 −1.40727 −0.703633 0.710563i \(-0.748440\pi\)
−0.703633 + 0.710563i \(0.748440\pi\)
\(674\) −38.7640 −1.49313
\(675\) 9.31760 0.358635
\(676\) −47.2912 −1.81889
\(677\) −21.3313 −0.819829 −0.409915 0.912124i \(-0.634441\pi\)
−0.409915 + 0.912124i \(0.634441\pi\)
\(678\) 48.5002 1.86264
\(679\) 48.0790 1.84510
\(680\) −51.0938 −1.95936
\(681\) −43.5221 −1.66777
\(682\) −27.3097 −1.04574
\(683\) 14.6046 0.558831 0.279415 0.960170i \(-0.409859\pi\)
0.279415 + 0.960170i \(0.409859\pi\)
\(684\) −91.9420 −3.51549
\(685\) 3.37583 0.128984
\(686\) −26.7835 −1.02260
\(687\) 21.4281 0.817533
\(688\) 11.6715 0.444971
\(689\) −1.09024 −0.0415349
\(690\) −2.31429 −0.0881033
\(691\) −24.8921 −0.946942 −0.473471 0.880810i \(-0.656999\pi\)
−0.473471 + 0.880810i \(0.656999\pi\)
\(692\) −14.2165 −0.540432
\(693\) −67.1357 −2.55028
\(694\) 19.7665 0.750325
\(695\) −20.4848 −0.777032
\(696\) 95.4842 3.61932
\(697\) 34.8233 1.31903
\(698\) 40.6508 1.53865
\(699\) −79.4374 −3.00460
\(700\) 14.8109 0.559799
\(701\) 31.2330 1.17965 0.589827 0.807529i \(-0.299196\pi\)
0.589827 + 0.807529i \(0.299196\pi\)
\(702\) 21.9598 0.828819
\(703\) −23.0835 −0.870609
\(704\) −28.3315 −1.06779
\(705\) −36.4826 −1.37401
\(706\) 80.0221 3.01167
\(707\) 27.7293 1.04287
\(708\) −126.931 −4.77035
\(709\) −33.5776 −1.26103 −0.630517 0.776176i \(-0.717157\pi\)
−0.630517 + 0.776176i \(0.717157\pi\)
\(710\) −59.8345 −2.24555
\(711\) −15.6440 −0.586697
\(712\) −15.5444 −0.582551
\(713\) 0.507347 0.0190003
\(714\) 125.358 4.69139
\(715\) −7.63653 −0.285590
\(716\) 17.6044 0.657909
\(717\) 7.29701 0.272512
\(718\) −37.4650 −1.39818
\(719\) −29.8743 −1.11412 −0.557062 0.830471i \(-0.688071\pi\)
−0.557062 + 0.830471i \(0.688071\pi\)
\(720\) −45.6864 −1.70263
\(721\) −56.3903 −2.10008
\(722\) 7.81373 0.290797
\(723\) 65.6508 2.44158
\(724\) 16.8824 0.627431
\(725\) −7.44110 −0.276356
\(726\) 12.2592 0.454980
\(727\) −5.35827 −0.198727 −0.0993636 0.995051i \(-0.531681\pi\)
−0.0993636 + 0.995051i \(0.531681\pi\)
\(728\) 17.4701 0.647484
\(729\) −32.4785 −1.20291
\(730\) −60.5016 −2.23927
\(731\) −15.3524 −0.567830
\(732\) −15.5098 −0.573259
\(733\) −17.5986 −0.650020 −0.325010 0.945711i \(-0.605368\pi\)
−0.325010 + 0.945711i \(0.605368\pi\)
\(734\) −44.5613 −1.64479
\(735\) 21.2642 0.784343
\(736\) −0.00615120 −0.000226736 0
\(737\) −4.40224 −0.162159
\(738\) 93.1140 3.42758
\(739\) 0.486686 0.0179030 0.00895152 0.999960i \(-0.497151\pi\)
0.00895152 + 0.999960i \(0.497151\pi\)
\(740\) −45.7046 −1.68013
\(741\) 12.8419 0.471757
\(742\) −7.99655 −0.293563
\(743\) 0.801487 0.0294037 0.0147019 0.999892i \(-0.495320\pi\)
0.0147019 + 0.999892i \(0.495320\pi\)
\(744\) 45.5089 1.66844
\(745\) −32.7726 −1.20070
\(746\) 22.3098 0.816818
\(747\) −81.1389 −2.96872
\(748\) −75.4773 −2.75972
\(749\) −7.38515 −0.269848
\(750\) 87.5400 3.19651
\(751\) 46.2840 1.68893 0.844464 0.535613i \(-0.179919\pi\)
0.844464 + 0.535613i \(0.179919\pi\)
\(752\) −25.1985 −0.918894
\(753\) −3.53316 −0.128756
\(754\) −17.5373 −0.638669
\(755\) 1.96635 0.0715627
\(756\) 107.413 3.90657
\(757\) −28.4996 −1.03583 −0.517917 0.855431i \(-0.673292\pi\)
−0.517917 + 0.855431i \(0.673292\pi\)
\(758\) −23.3256 −0.847223
\(759\) −1.71102 −0.0621060
\(760\) −38.3906 −1.39257
\(761\) 17.7227 0.642446 0.321223 0.947004i \(-0.395906\pi\)
0.321223 + 0.947004i \(0.395906\pi\)
\(762\) −12.0469 −0.436413
\(763\) −1.44605 −0.0523506
\(764\) 32.9737 1.19295
\(765\) 60.0949 2.17273
\(766\) 56.0983 2.02692
\(767\) 11.6677 0.421297
\(768\) 94.8831 3.42380
\(769\) −11.2835 −0.406893 −0.203446 0.979086i \(-0.565214\pi\)
−0.203446 + 0.979086i \(0.565214\pi\)
\(770\) −56.0114 −2.01851
\(771\) −52.3514 −1.88539
\(772\) −5.68750 −0.204698
\(773\) 1.62369 0.0584002 0.0292001 0.999574i \(-0.490704\pi\)
0.0292001 + 0.999574i \(0.490704\pi\)
\(774\) −41.0508 −1.47554
\(775\) −3.54652 −0.127395
\(776\) 72.3356 2.59670
\(777\) 56.1218 2.01336
\(778\) −11.9084 −0.426937
\(779\) 26.1654 0.937472
\(780\) 25.4265 0.910415
\(781\) −44.2374 −1.58294
\(782\) 2.10260 0.0751888
\(783\) −53.9651 −1.92856
\(784\) 14.6872 0.524543
\(785\) −8.50895 −0.303697
\(786\) 90.1523 3.21563
\(787\) 31.0802 1.10789 0.553944 0.832554i \(-0.313122\pi\)
0.553944 + 0.832554i \(0.313122\pi\)
\(788\) 23.9573 0.853444
\(789\) −71.4941 −2.54526
\(790\) −13.0518 −0.464363
\(791\) −21.8068 −0.775360
\(792\) −101.007 −3.58912
\(793\) 1.42569 0.0506278
\(794\) −62.7275 −2.22611
\(795\) −5.82484 −0.206586
\(796\) 4.79204 0.169849
\(797\) −36.5664 −1.29525 −0.647624 0.761960i \(-0.724237\pi\)
−0.647624 + 0.761960i \(0.724237\pi\)
\(798\) 94.1906 3.33431
\(799\) 33.1455 1.17260
\(800\) 0.0429988 0.00152024
\(801\) 18.2828 0.645992
\(802\) 64.1794 2.26625
\(803\) −44.7306 −1.57851
\(804\) 14.6577 0.516936
\(805\) 1.04055 0.0366747
\(806\) −8.35846 −0.294414
\(807\) −3.17917 −0.111912
\(808\) 41.7192 1.46768
\(809\) −24.4929 −0.861126 −0.430563 0.902561i \(-0.641685\pi\)
−0.430563 + 0.902561i \(0.641685\pi\)
\(810\) 33.8509 1.18940
\(811\) 43.8376 1.53935 0.769673 0.638438i \(-0.220419\pi\)
0.769673 + 0.638438i \(0.220419\pi\)
\(812\) −85.7808 −3.01032
\(813\) −6.83300 −0.239644
\(814\) −50.6697 −1.77597
\(815\) 37.8846 1.32704
\(816\) 63.0698 2.20788
\(817\) −11.5354 −0.403573
\(818\) 20.5926 0.720002
\(819\) −20.5477 −0.717995
\(820\) 51.8067 1.80917
\(821\) 2.06908 0.0722113 0.0361056 0.999348i \(-0.488505\pi\)
0.0361056 + 0.999348i \(0.488505\pi\)
\(822\) −12.4612 −0.434634
\(823\) −33.1957 −1.15713 −0.578565 0.815637i \(-0.696387\pi\)
−0.578565 + 0.815637i \(0.696387\pi\)
\(824\) −84.8401 −2.95554
\(825\) 11.9606 0.416413
\(826\) 85.5789 2.97767
\(827\) −37.6137 −1.30796 −0.653979 0.756513i \(-0.726901\pi\)
−0.653979 + 0.756513i \(0.726901\pi\)
\(828\) 3.74930 0.130297
\(829\) 13.8814 0.482119 0.241060 0.970510i \(-0.422505\pi\)
0.241060 + 0.970510i \(0.422505\pi\)
\(830\) −67.6942 −2.34970
\(831\) 48.8201 1.69355
\(832\) −8.67122 −0.300620
\(833\) −19.3192 −0.669371
\(834\) 75.6155 2.61835
\(835\) −10.2655 −0.355254
\(836\) −56.7118 −1.96142
\(837\) −25.7204 −0.889027
\(838\) 19.0715 0.658814
\(839\) 33.9640 1.17257 0.586283 0.810106i \(-0.300591\pi\)
0.586283 + 0.810106i \(0.300591\pi\)
\(840\) 93.3374 3.22045
\(841\) 14.0969 0.486101
\(842\) −13.5053 −0.465425
\(843\) −49.3615 −1.70010
\(844\) 71.1440 2.44888
\(845\) 23.2253 0.798973
\(846\) 88.6278 3.04709
\(847\) −5.51199 −0.189394
\(848\) −4.02322 −0.138158
\(849\) 39.1560 1.34383
\(850\) −14.6978 −0.504132
\(851\) 0.941320 0.0322680
\(852\) 147.292 5.04615
\(853\) −29.8424 −1.02178 −0.510892 0.859645i \(-0.670685\pi\)
−0.510892 + 0.859645i \(0.670685\pi\)
\(854\) 10.4570 0.357830
\(855\) 45.1538 1.54423
\(856\) −11.1111 −0.379769
\(857\) −36.7877 −1.25665 −0.628323 0.777953i \(-0.716258\pi\)
−0.628323 + 0.777953i \(0.716258\pi\)
\(858\) 28.1887 0.962348
\(859\) 50.3098 1.71655 0.858275 0.513190i \(-0.171536\pi\)
0.858275 + 0.513190i \(0.171536\pi\)
\(860\) −22.8398 −0.778831
\(861\) −63.6147 −2.16798
\(862\) −78.6314 −2.67819
\(863\) 33.9217 1.15471 0.577355 0.816493i \(-0.304085\pi\)
0.577355 + 0.816493i \(0.304085\pi\)
\(864\) 0.311840 0.0106090
\(865\) 6.98192 0.237392
\(866\) 21.4601 0.729245
\(867\) −32.6021 −1.10722
\(868\) −40.8841 −1.38770
\(869\) −9.64959 −0.327340
\(870\) −93.6964 −3.17660
\(871\) −1.34736 −0.0456536
\(872\) −2.17561 −0.0736754
\(873\) −85.0788 −2.87948
\(874\) 1.57984 0.0534390
\(875\) −39.3599 −1.33061
\(876\) 148.934 5.03203
\(877\) 50.8266 1.71629 0.858147 0.513404i \(-0.171616\pi\)
0.858147 + 0.513404i \(0.171616\pi\)
\(878\) 91.4758 3.08716
\(879\) −70.8662 −2.39026
\(880\) −28.1804 −0.949960
\(881\) −4.30083 −0.144899 −0.0724493 0.997372i \(-0.523082\pi\)
−0.0724493 + 0.997372i \(0.523082\pi\)
\(882\) −51.6577 −1.73940
\(883\) −42.9355 −1.44489 −0.722447 0.691426i \(-0.756983\pi\)
−0.722447 + 0.691426i \(0.756983\pi\)
\(884\) −23.1008 −0.776963
\(885\) 62.3373 2.09544
\(886\) −18.5133 −0.621966
\(887\) −12.4257 −0.417214 −0.208607 0.978000i \(-0.566893\pi\)
−0.208607 + 0.978000i \(0.566893\pi\)
\(888\) 84.4361 2.83349
\(889\) 5.41655 0.181665
\(890\) 15.2534 0.511294
\(891\) 25.0270 0.838434
\(892\) 54.6026 1.82823
\(893\) 24.9047 0.833405
\(894\) 120.974 4.04596
\(895\) −8.64575 −0.288996
\(896\) −63.8480 −2.13301
\(897\) −0.523678 −0.0174851
\(898\) −70.5173 −2.35319
\(899\) 20.5405 0.685064
\(900\) −26.2088 −0.873627
\(901\) 5.29205 0.176304
\(902\) 57.4348 1.91237
\(903\) 28.0456 0.933298
\(904\) −32.8087 −1.09120
\(905\) −8.29117 −0.275608
\(906\) −7.25838 −0.241143
\(907\) −52.3413 −1.73796 −0.868982 0.494843i \(-0.835225\pi\)
−0.868982 + 0.494843i \(0.835225\pi\)
\(908\) 58.8255 1.95219
\(909\) −49.0687 −1.62751
\(910\) −17.1430 −0.568284
\(911\) 50.2606 1.66521 0.832604 0.553869i \(-0.186849\pi\)
0.832604 + 0.553869i \(0.186849\pi\)
\(912\) 47.3891 1.56921
\(913\) −50.0482 −1.65636
\(914\) −39.4459 −1.30475
\(915\) 7.61705 0.251812
\(916\) −28.9627 −0.956955
\(917\) −40.5345 −1.33857
\(918\) −106.593 −3.51810
\(919\) 31.1967 1.02908 0.514542 0.857465i \(-0.327962\pi\)
0.514542 + 0.857465i \(0.327962\pi\)
\(920\) 1.56553 0.0516140
\(921\) −74.5458 −2.45637
\(922\) −26.8810 −0.885277
\(923\) −13.5394 −0.445654
\(924\) 137.881 4.53595
\(925\) −6.58013 −0.216353
\(926\) 22.5738 0.741822
\(927\) 99.7861 3.27741
\(928\) −0.249038 −0.00817507
\(929\) −5.95097 −0.195245 −0.0976225 0.995224i \(-0.531124\pi\)
−0.0976225 + 0.995224i \(0.531124\pi\)
\(930\) −44.6568 −1.46435
\(931\) −14.5160 −0.475742
\(932\) 107.369 3.51700
\(933\) −53.2440 −1.74313
\(934\) −96.7320 −3.16517
\(935\) 37.0678 1.21225
\(936\) −30.9144 −1.01047
\(937\) 33.5806 1.09703 0.548515 0.836141i \(-0.315193\pi\)
0.548515 + 0.836141i \(0.315193\pi\)
\(938\) −9.88243 −0.322673
\(939\) 12.0087 0.391888
\(940\) 49.3107 1.60834
\(941\) −18.0817 −0.589448 −0.294724 0.955582i \(-0.595228\pi\)
−0.294724 + 0.955582i \(0.595228\pi\)
\(942\) 31.4091 1.02336
\(943\) −1.06700 −0.0347462
\(944\) 43.0563 1.40136
\(945\) −52.7518 −1.71602
\(946\) −25.3210 −0.823258
\(947\) 10.7948 0.350783 0.175391 0.984499i \(-0.443881\pi\)
0.175391 + 0.984499i \(0.443881\pi\)
\(948\) 32.1291 1.04351
\(949\) −13.6903 −0.444407
\(950\) −11.0436 −0.358302
\(951\) −52.3588 −1.69785
\(952\) −84.7999 −2.74838
\(953\) −33.1558 −1.07402 −0.537010 0.843576i \(-0.680446\pi\)
−0.537010 + 0.843576i \(0.680446\pi\)
\(954\) 14.1504 0.458136
\(955\) −16.1938 −0.524019
\(956\) −9.86281 −0.318986
\(957\) −69.2724 −2.23926
\(958\) −16.5910 −0.536032
\(959\) 5.60283 0.180925
\(960\) −46.3278 −1.49522
\(961\) −21.2102 −0.684199
\(962\) −15.5081 −0.500001
\(963\) 13.0685 0.421126
\(964\) −88.7352 −2.85797
\(965\) 2.79320 0.0899163
\(966\) −3.84100 −0.123582
\(967\) −8.92640 −0.287054 −0.143527 0.989646i \(-0.545844\pi\)
−0.143527 + 0.989646i \(0.545844\pi\)
\(968\) −8.29288 −0.266543
\(969\) −62.3345 −2.00247
\(970\) −70.9812 −2.27907
\(971\) −56.0548 −1.79889 −0.899443 0.437039i \(-0.856027\pi\)
−0.899443 + 0.437039i \(0.856027\pi\)
\(972\) 15.4100 0.494277
\(973\) −33.9984 −1.08994
\(974\) 62.2826 1.99566
\(975\) 3.66067 0.117235
\(976\) 5.26109 0.168404
\(977\) 19.0003 0.607875 0.303937 0.952692i \(-0.401699\pi\)
0.303937 + 0.952692i \(0.401699\pi\)
\(978\) −139.843 −4.47170
\(979\) 11.2772 0.360422
\(980\) −28.7412 −0.918105
\(981\) 2.55888 0.0816987
\(982\) 59.5542 1.90045
\(983\) −46.5060 −1.48331 −0.741655 0.670781i \(-0.765959\pi\)
−0.741655 + 0.670781i \(0.765959\pi\)
\(984\) −95.7094 −3.05110
\(985\) −11.7657 −0.374887
\(986\) 85.1261 2.71097
\(987\) −60.5498 −1.92732
\(988\) −17.3573 −0.552211
\(989\) 0.470403 0.0149579
\(990\) 99.1156 3.15010
\(991\) 27.8489 0.884650 0.442325 0.896855i \(-0.354154\pi\)
0.442325 + 0.896855i \(0.354154\pi\)
\(992\) −0.118694 −0.00376855
\(993\) 56.2763 1.78588
\(994\) −99.3068 −3.14982
\(995\) −2.35343 −0.0746087
\(996\) 166.640 5.28019
\(997\) 35.2711 1.11705 0.558523 0.829489i \(-0.311368\pi\)
0.558523 + 0.829489i \(0.311368\pi\)
\(998\) −60.7030 −1.92152
\(999\) −47.7210 −1.50983
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.1.13 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.13 153 1.1 even 1 trivial