Properties

Label 8003.2.a.b.1.5
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 1.5
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} +O(q^{10})\) \(q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} -7.58334 q^{10} -5.07692 q^{11} +9.47160 q^{12} -1.58864 q^{13} -2.28672 q^{14} +5.46820 q^{15} +10.7922 q^{16} +4.06347 q^{17} -1.65354 q^{18} -2.49635 q^{19} +14.2831 q^{20} +1.64891 q^{21} +13.4073 q^{22} +3.25725 q^{23} -14.9553 q^{24} +3.24599 q^{25} +4.19532 q^{26} -4.52040 q^{27} +4.30700 q^{28} +4.81083 q^{29} -14.4405 q^{30} -7.75030 q^{31} -12.7930 q^{32} -9.66770 q^{33} -10.7309 q^{34} +2.48654 q^{35} +3.11442 q^{36} +2.59888 q^{37} +6.59241 q^{38} -3.02516 q^{39} -22.5524 q^{40} -8.69377 q^{41} -4.35447 q^{42} +8.52505 q^{43} -25.2523 q^{44} +1.79803 q^{45} -8.60181 q^{46} -4.47985 q^{47} +20.5510 q^{48} -6.25020 q^{49} -8.57208 q^{50} +7.73783 q^{51} -7.90182 q^{52} -1.00000 q^{53} +11.9376 q^{54} -14.5788 q^{55} -6.80057 q^{56} -4.75366 q^{57} -12.7046 q^{58} -7.84810 q^{59} +27.1985 q^{60} -5.71184 q^{61} +20.4672 q^{62} +0.542187 q^{63} +12.1997 q^{64} -4.56192 q^{65} +25.5307 q^{66} -2.28294 q^{67} +20.2114 q^{68} +6.20260 q^{69} -6.56650 q^{70} -10.9402 q^{71} -4.91754 q^{72} -5.06707 q^{73} -6.86317 q^{74} +6.18116 q^{75} -12.4167 q^{76} -4.39617 q^{77} +7.98892 q^{78} -7.96414 q^{79} +30.9908 q^{80} -10.4864 q^{81} +22.9587 q^{82} +3.51804 q^{83} +8.20157 q^{84} +11.6686 q^{85} -22.5131 q^{86} +9.16100 q^{87} +39.8724 q^{88} +3.47330 q^{89} -4.74828 q^{90} -1.37562 q^{91} +16.2014 q^{92} -14.7585 q^{93} +11.8305 q^{94} -7.16847 q^{95} -24.3610 q^{96} +10.2628 q^{97} +16.5057 q^{98} -3.17890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64082 −1.86734 −0.933672 0.358130i \(-0.883414\pi\)
−0.933672 + 0.358130i \(0.883414\pi\)
\(3\) 1.90424 1.09942 0.549708 0.835357i \(-0.314739\pi\)
0.549708 + 0.835357i \(0.314739\pi\)
\(4\) 4.97394 2.48697
\(5\) 2.87158 1.28421 0.642105 0.766616i \(-0.278061\pi\)
0.642105 + 0.766616i \(0.278061\pi\)
\(6\) −5.02877 −2.05299
\(7\) 0.865912 0.327284 0.163642 0.986520i \(-0.447676\pi\)
0.163642 + 0.986520i \(0.447676\pi\)
\(8\) −7.85365 −2.77669
\(9\) 0.626146 0.208715
\(10\) −7.58334 −2.39806
\(11\) −5.07692 −1.53075 −0.765375 0.643584i \(-0.777447\pi\)
−0.765375 + 0.643584i \(0.777447\pi\)
\(12\) 9.47160 2.73422
\(13\) −1.58864 −0.440610 −0.220305 0.975431i \(-0.570705\pi\)
−0.220305 + 0.975431i \(0.570705\pi\)
\(14\) −2.28672 −0.611151
\(15\) 5.46820 1.41188
\(16\) 10.7922 2.69805
\(17\) 4.06347 0.985535 0.492768 0.870161i \(-0.335985\pi\)
0.492768 + 0.870161i \(0.335985\pi\)
\(18\) −1.65354 −0.389743
\(19\) −2.49635 −0.572702 −0.286351 0.958125i \(-0.592442\pi\)
−0.286351 + 0.958125i \(0.592442\pi\)
\(20\) 14.2831 3.19380
\(21\) 1.64891 0.359821
\(22\) 13.4073 2.85844
\(23\) 3.25725 0.679183 0.339592 0.940573i \(-0.389711\pi\)
0.339592 + 0.940573i \(0.389711\pi\)
\(24\) −14.9553 −3.05273
\(25\) 3.24599 0.649198
\(26\) 4.19532 0.822770
\(27\) −4.52040 −0.869951
\(28\) 4.30700 0.813946
\(29\) 4.81083 0.893349 0.446675 0.894696i \(-0.352608\pi\)
0.446675 + 0.894696i \(0.352608\pi\)
\(30\) −14.4405 −2.63647
\(31\) −7.75030 −1.39199 −0.695997 0.718044i \(-0.745038\pi\)
−0.695997 + 0.718044i \(0.745038\pi\)
\(32\) −12.7930 −2.26151
\(33\) −9.66770 −1.68293
\(34\) −10.7309 −1.84033
\(35\) 2.48654 0.420302
\(36\) 3.11442 0.519069
\(37\) 2.59888 0.427253 0.213626 0.976915i \(-0.431472\pi\)
0.213626 + 0.976915i \(0.431472\pi\)
\(38\) 6.59241 1.06943
\(39\) −3.02516 −0.484414
\(40\) −22.5524 −3.56585
\(41\) −8.69377 −1.35774 −0.678869 0.734259i \(-0.737530\pi\)
−0.678869 + 0.734259i \(0.737530\pi\)
\(42\) −4.35447 −0.671910
\(43\) 8.52505 1.30006 0.650029 0.759909i \(-0.274757\pi\)
0.650029 + 0.759909i \(0.274757\pi\)
\(44\) −25.2523 −3.80693
\(45\) 1.79803 0.268035
\(46\) −8.60181 −1.26827
\(47\) −4.47985 −0.653453 −0.326726 0.945119i \(-0.605946\pi\)
−0.326726 + 0.945119i \(0.605946\pi\)
\(48\) 20.5510 2.96628
\(49\) −6.25020 −0.892885
\(50\) −8.57208 −1.21228
\(51\) 7.73783 1.08351
\(52\) −7.90182 −1.09578
\(53\) −1.00000 −0.137361
\(54\) 11.9376 1.62450
\(55\) −14.5788 −1.96581
\(56\) −6.80057 −0.908765
\(57\) −4.75366 −0.629637
\(58\) −12.7046 −1.66819
\(59\) −7.84810 −1.02174 −0.510868 0.859659i \(-0.670676\pi\)
−0.510868 + 0.859659i \(0.670676\pi\)
\(60\) 27.1985 3.51131
\(61\) −5.71184 −0.731326 −0.365663 0.930747i \(-0.619158\pi\)
−0.365663 + 0.930747i \(0.619158\pi\)
\(62\) 20.4672 2.59933
\(63\) 0.542187 0.0683092
\(64\) 12.1997 1.52496
\(65\) −4.56192 −0.565836
\(66\) 25.5307 3.14261
\(67\) −2.28294 −0.278906 −0.139453 0.990229i \(-0.544534\pi\)
−0.139453 + 0.990229i \(0.544534\pi\)
\(68\) 20.2114 2.45100
\(69\) 6.20260 0.746705
\(70\) −6.56650 −0.784847
\(71\) −10.9402 −1.29836 −0.649179 0.760636i \(-0.724887\pi\)
−0.649179 + 0.760636i \(0.724887\pi\)
\(72\) −4.91754 −0.579537
\(73\) −5.06707 −0.593056 −0.296528 0.955024i \(-0.595829\pi\)
−0.296528 + 0.955024i \(0.595829\pi\)
\(74\) −6.86317 −0.797828
\(75\) 6.18116 0.713738
\(76\) −12.4167 −1.42429
\(77\) −4.39617 −0.500990
\(78\) 7.98892 0.904567
\(79\) −7.96414 −0.896035 −0.448018 0.894025i \(-0.647870\pi\)
−0.448018 + 0.894025i \(0.647870\pi\)
\(80\) 30.9908 3.46487
\(81\) −10.4864 −1.16515
\(82\) 22.9587 2.53536
\(83\) 3.51804 0.386155 0.193077 0.981184i \(-0.438153\pi\)
0.193077 + 0.981184i \(0.438153\pi\)
\(84\) 8.20157 0.894865
\(85\) 11.6686 1.26564
\(86\) −22.5131 −2.42765
\(87\) 9.16100 0.982162
\(88\) 39.8724 4.25041
\(89\) 3.47330 0.368169 0.184084 0.982910i \(-0.441068\pi\)
0.184084 + 0.982910i \(0.441068\pi\)
\(90\) −4.74828 −0.500513
\(91\) −1.37562 −0.144205
\(92\) 16.2014 1.68911
\(93\) −14.7585 −1.53038
\(94\) 11.8305 1.22022
\(95\) −7.16847 −0.735470
\(96\) −24.3610 −2.48634
\(97\) 10.2628 1.04203 0.521015 0.853548i \(-0.325554\pi\)
0.521015 + 0.853548i \(0.325554\pi\)
\(98\) 16.5057 1.66732
\(99\) −3.17890 −0.319491
\(100\) 16.1454 1.61454
\(101\) −6.44317 −0.641119 −0.320560 0.947228i \(-0.603871\pi\)
−0.320560 + 0.947228i \(0.603871\pi\)
\(102\) −20.4342 −2.02329
\(103\) 18.9566 1.86785 0.933923 0.357474i \(-0.116362\pi\)
0.933923 + 0.357474i \(0.116362\pi\)
\(104\) 12.4766 1.22344
\(105\) 4.73497 0.462086
\(106\) 2.64082 0.256499
\(107\) 7.46514 0.721682 0.360841 0.932627i \(-0.382490\pi\)
0.360841 + 0.932627i \(0.382490\pi\)
\(108\) −22.4842 −2.16354
\(109\) −15.2660 −1.46222 −0.731111 0.682259i \(-0.760998\pi\)
−0.731111 + 0.682259i \(0.760998\pi\)
\(110\) 38.5000 3.67084
\(111\) 4.94890 0.469729
\(112\) 9.34511 0.883030
\(113\) −7.09890 −0.667809 −0.333904 0.942607i \(-0.608366\pi\)
−0.333904 + 0.942607i \(0.608366\pi\)
\(114\) 12.5536 1.17575
\(115\) 9.35346 0.872215
\(116\) 23.9288 2.22173
\(117\) −0.994723 −0.0919622
\(118\) 20.7254 1.90793
\(119\) 3.51860 0.322550
\(120\) −42.9453 −3.92035
\(121\) 14.7752 1.34320
\(122\) 15.0840 1.36564
\(123\) −16.5551 −1.49272
\(124\) −38.5495 −3.46185
\(125\) −5.03679 −0.450504
\(126\) −1.43182 −0.127557
\(127\) 4.37883 0.388559 0.194279 0.980946i \(-0.437763\pi\)
0.194279 + 0.980946i \(0.437763\pi\)
\(128\) −6.63111 −0.586113
\(129\) 16.2338 1.42930
\(130\) 12.0472 1.05661
\(131\) 10.4704 0.914806 0.457403 0.889260i \(-0.348780\pi\)
0.457403 + 0.889260i \(0.348780\pi\)
\(132\) −48.0866 −4.18540
\(133\) −2.16162 −0.187436
\(134\) 6.02884 0.520812
\(135\) −12.9807 −1.11720
\(136\) −31.9131 −2.73652
\(137\) 2.51642 0.214992 0.107496 0.994206i \(-0.465717\pi\)
0.107496 + 0.994206i \(0.465717\pi\)
\(138\) −16.3800 −1.39435
\(139\) −13.4906 −1.14426 −0.572129 0.820164i \(-0.693882\pi\)
−0.572129 + 0.820164i \(0.693882\pi\)
\(140\) 12.3679 1.04528
\(141\) −8.53072 −0.718416
\(142\) 28.8910 2.42448
\(143\) 8.06542 0.674464
\(144\) 6.75751 0.563126
\(145\) 13.8147 1.14725
\(146\) 13.3812 1.10744
\(147\) −11.9019 −0.981652
\(148\) 12.9267 1.06257
\(149\) 2.61309 0.214073 0.107036 0.994255i \(-0.465864\pi\)
0.107036 + 0.994255i \(0.465864\pi\)
\(150\) −16.3233 −1.33279
\(151\) −1.00000 −0.0813788
\(152\) 19.6055 1.59021
\(153\) 2.54432 0.205696
\(154\) 11.6095 0.935520
\(155\) −22.2556 −1.78762
\(156\) −15.0470 −1.20472
\(157\) −18.2827 −1.45912 −0.729559 0.683918i \(-0.760275\pi\)
−0.729559 + 0.683918i \(0.760275\pi\)
\(158\) 21.0319 1.67321
\(159\) −1.90424 −0.151016
\(160\) −36.7362 −2.90425
\(161\) 2.82049 0.222286
\(162\) 27.6927 2.17574
\(163\) −4.77495 −0.374003 −0.187002 0.982360i \(-0.559877\pi\)
−0.187002 + 0.982360i \(0.559877\pi\)
\(164\) −43.2423 −3.37666
\(165\) −27.7616 −2.16124
\(166\) −9.29051 −0.721083
\(167\) −7.01823 −0.543087 −0.271543 0.962426i \(-0.587534\pi\)
−0.271543 + 0.962426i \(0.587534\pi\)
\(168\) −12.9499 −0.999110
\(169\) −10.4762 −0.805863
\(170\) −30.8146 −2.36338
\(171\) −1.56308 −0.119532
\(172\) 42.4031 3.23321
\(173\) 19.9581 1.51739 0.758695 0.651446i \(-0.225837\pi\)
0.758695 + 0.651446i \(0.225837\pi\)
\(174\) −24.1926 −1.83403
\(175\) 2.81074 0.212472
\(176\) −54.7913 −4.13005
\(177\) −14.9447 −1.12331
\(178\) −9.17236 −0.687498
\(179\) 0.783302 0.0585467 0.0292734 0.999571i \(-0.490681\pi\)
0.0292734 + 0.999571i \(0.490681\pi\)
\(180\) 8.94330 0.666595
\(181\) −11.8315 −0.879425 −0.439713 0.898139i \(-0.644920\pi\)
−0.439713 + 0.898139i \(0.644920\pi\)
\(182\) 3.63278 0.269280
\(183\) −10.8767 −0.804031
\(184\) −25.5813 −1.88588
\(185\) 7.46289 0.548683
\(186\) 38.9745 2.85775
\(187\) −20.6299 −1.50861
\(188\) −22.2825 −1.62512
\(189\) −3.91426 −0.284721
\(190\) 18.9307 1.37337
\(191\) 4.27886 0.309607 0.154804 0.987945i \(-0.450526\pi\)
0.154804 + 0.987945i \(0.450526\pi\)
\(192\) 23.2312 1.67656
\(193\) −19.3397 −1.39210 −0.696052 0.717991i \(-0.745062\pi\)
−0.696052 + 0.717991i \(0.745062\pi\)
\(194\) −27.1022 −1.94583
\(195\) −8.68701 −0.622090
\(196\) −31.0881 −2.22058
\(197\) 8.32141 0.592876 0.296438 0.955052i \(-0.404201\pi\)
0.296438 + 0.955052i \(0.404201\pi\)
\(198\) 8.39490 0.596600
\(199\) −4.18541 −0.296696 −0.148348 0.988935i \(-0.547396\pi\)
−0.148348 + 0.988935i \(0.547396\pi\)
\(200\) −25.4929 −1.80262
\(201\) −4.34728 −0.306633
\(202\) 17.0153 1.19719
\(203\) 4.16576 0.292379
\(204\) 38.4875 2.69467
\(205\) −24.9649 −1.74362
\(206\) −50.0609 −3.48791
\(207\) 2.03951 0.141756
\(208\) −17.1450 −1.18879
\(209\) 12.6738 0.876663
\(210\) −12.5042 −0.862874
\(211\) 26.5581 1.82834 0.914168 0.405335i \(-0.132845\pi\)
0.914168 + 0.405335i \(0.132845\pi\)
\(212\) −4.97394 −0.341612
\(213\) −20.8327 −1.42744
\(214\) −19.7141 −1.34763
\(215\) 24.4804 1.66955
\(216\) 35.5016 2.41558
\(217\) −6.71108 −0.455577
\(218\) 40.3149 2.73047
\(219\) −9.64894 −0.652015
\(220\) −72.5142 −4.88890
\(221\) −6.45539 −0.434237
\(222\) −13.0692 −0.877145
\(223\) −20.0528 −1.34283 −0.671417 0.741080i \(-0.734314\pi\)
−0.671417 + 0.741080i \(0.734314\pi\)
\(224\) −11.0776 −0.740155
\(225\) 2.03246 0.135498
\(226\) 18.7469 1.24703
\(227\) 8.96692 0.595155 0.297578 0.954698i \(-0.403821\pi\)
0.297578 + 0.954698i \(0.403821\pi\)
\(228\) −23.6444 −1.56589
\(229\) 1.31289 0.0867579 0.0433790 0.999059i \(-0.486188\pi\)
0.0433790 + 0.999059i \(0.486188\pi\)
\(230\) −24.7008 −1.62872
\(231\) −8.37138 −0.550796
\(232\) −37.7826 −2.48055
\(233\) −28.7788 −1.88536 −0.942681 0.333694i \(-0.891705\pi\)
−0.942681 + 0.333694i \(0.891705\pi\)
\(234\) 2.62689 0.171725
\(235\) −12.8642 −0.839171
\(236\) −39.0360 −2.54103
\(237\) −15.1657 −0.985115
\(238\) −9.29200 −0.602311
\(239\) −6.14669 −0.397596 −0.198798 0.980040i \(-0.563704\pi\)
−0.198798 + 0.980040i \(0.563704\pi\)
\(240\) 59.0140 3.80934
\(241\) 2.46131 0.158547 0.0792734 0.996853i \(-0.474740\pi\)
0.0792734 + 0.996853i \(0.474740\pi\)
\(242\) −39.0186 −2.50821
\(243\) −6.40744 −0.411037
\(244\) −28.4104 −1.81879
\(245\) −17.9480 −1.14665
\(246\) 43.7190 2.78742
\(247\) 3.96581 0.252338
\(248\) 60.8682 3.86513
\(249\) 6.69920 0.424545
\(250\) 13.3013 0.841246
\(251\) 19.3759 1.22299 0.611497 0.791247i \(-0.290568\pi\)
0.611497 + 0.791247i \(0.290568\pi\)
\(252\) 2.69681 0.169883
\(253\) −16.5368 −1.03966
\(254\) −11.5637 −0.725572
\(255\) 22.2198 1.39146
\(256\) −6.88775 −0.430485
\(257\) −26.2452 −1.63713 −0.818566 0.574412i \(-0.805231\pi\)
−0.818566 + 0.574412i \(0.805231\pi\)
\(258\) −42.8705 −2.66900
\(259\) 2.25040 0.139833
\(260\) −22.6907 −1.40722
\(261\) 3.01229 0.186456
\(262\) −27.6505 −1.70826
\(263\) 24.3298 1.50024 0.750120 0.661301i \(-0.229996\pi\)
0.750120 + 0.661301i \(0.229996\pi\)
\(264\) 75.9268 4.67297
\(265\) −2.87158 −0.176400
\(266\) 5.70845 0.350007
\(267\) 6.61401 0.404771
\(268\) −11.3552 −0.693630
\(269\) 19.3453 1.17950 0.589751 0.807585i \(-0.299226\pi\)
0.589751 + 0.807585i \(0.299226\pi\)
\(270\) 34.2797 2.08620
\(271\) 2.17924 0.132379 0.0661897 0.997807i \(-0.478916\pi\)
0.0661897 + 0.997807i \(0.478916\pi\)
\(272\) 43.8538 2.65903
\(273\) −2.61952 −0.158541
\(274\) −6.64541 −0.401464
\(275\) −16.4796 −0.993760
\(276\) 30.8514 1.85703
\(277\) −18.5180 −1.11264 −0.556319 0.830969i \(-0.687787\pi\)
−0.556319 + 0.830969i \(0.687787\pi\)
\(278\) 35.6263 2.13672
\(279\) −4.85282 −0.290531
\(280\) −19.5284 −1.16705
\(281\) 26.5933 1.58642 0.793212 0.608945i \(-0.208407\pi\)
0.793212 + 0.608945i \(0.208407\pi\)
\(282\) 22.5281 1.34153
\(283\) 8.82135 0.524375 0.262188 0.965017i \(-0.415556\pi\)
0.262188 + 0.965017i \(0.415556\pi\)
\(284\) −54.4157 −3.22898
\(285\) −13.6505 −0.808587
\(286\) −21.2993 −1.25946
\(287\) −7.52803 −0.444366
\(288\) −8.01031 −0.472012
\(289\) −0.488247 −0.0287204
\(290\) −36.4822 −2.14231
\(291\) 19.5429 1.14562
\(292\) −25.2033 −1.47491
\(293\) 19.4358 1.13545 0.567726 0.823218i \(-0.307823\pi\)
0.567726 + 0.823218i \(0.307823\pi\)
\(294\) 31.4308 1.83308
\(295\) −22.5365 −1.31212
\(296\) −20.4107 −1.18635
\(297\) 22.9497 1.33168
\(298\) −6.90071 −0.399747
\(299\) −5.17460 −0.299255
\(300\) 30.7447 1.77505
\(301\) 7.38194 0.425488
\(302\) 2.64082 0.151962
\(303\) −12.2694 −0.704857
\(304\) −26.9411 −1.54518
\(305\) −16.4020 −0.939177
\(306\) −6.71911 −0.384106
\(307\) −6.14086 −0.350478 −0.175239 0.984526i \(-0.556070\pi\)
−0.175239 + 0.984526i \(0.556070\pi\)
\(308\) −21.8663 −1.24595
\(309\) 36.0979 2.05354
\(310\) 58.7732 3.33809
\(311\) 2.20631 0.125108 0.0625541 0.998042i \(-0.480075\pi\)
0.0625541 + 0.998042i \(0.480075\pi\)
\(312\) 23.7586 1.34507
\(313\) −15.8019 −0.893177 −0.446588 0.894739i \(-0.647361\pi\)
−0.446588 + 0.894739i \(0.647361\pi\)
\(314\) 48.2814 2.72468
\(315\) 1.55694 0.0877234
\(316\) −39.6132 −2.22841
\(317\) −10.0983 −0.567176 −0.283588 0.958946i \(-0.591525\pi\)
−0.283588 + 0.958946i \(0.591525\pi\)
\(318\) 5.02877 0.281999
\(319\) −24.4242 −1.36749
\(320\) 35.0324 1.95837
\(321\) 14.2154 0.793429
\(322\) −7.44841 −0.415084
\(323\) −10.1438 −0.564418
\(324\) −52.1587 −2.89770
\(325\) −5.15672 −0.286043
\(326\) 12.6098 0.698393
\(327\) −29.0703 −1.60759
\(328\) 68.2778 3.77001
\(329\) −3.87915 −0.213865
\(330\) 73.3135 4.03577
\(331\) −1.86507 −0.102514 −0.0512568 0.998686i \(-0.516323\pi\)
−0.0512568 + 0.998686i \(0.516323\pi\)
\(332\) 17.4985 0.960356
\(333\) 1.62728 0.0891743
\(334\) 18.5339 1.01413
\(335\) −6.55565 −0.358174
\(336\) 17.7954 0.970817
\(337\) −3.39581 −0.184981 −0.0924907 0.995714i \(-0.529483\pi\)
−0.0924907 + 0.995714i \(0.529483\pi\)
\(338\) 27.6658 1.50482
\(339\) −13.5180 −0.734200
\(340\) 58.0388 3.14760
\(341\) 39.3477 2.13080
\(342\) 4.12782 0.223207
\(343\) −11.4735 −0.619511
\(344\) −66.9528 −3.60985
\(345\) 17.8113 0.958927
\(346\) −52.7059 −2.83349
\(347\) 6.18277 0.331908 0.165954 0.986133i \(-0.446930\pi\)
0.165954 + 0.986133i \(0.446930\pi\)
\(348\) 45.5663 2.44261
\(349\) −17.1937 −0.920357 −0.460179 0.887826i \(-0.652215\pi\)
−0.460179 + 0.887826i \(0.652215\pi\)
\(350\) −7.42266 −0.396758
\(351\) 7.18130 0.383309
\(352\) 64.9492 3.46181
\(353\) −20.6151 −1.09723 −0.548615 0.836075i \(-0.684845\pi\)
−0.548615 + 0.836075i \(0.684845\pi\)
\(354\) 39.4663 2.09761
\(355\) −31.4156 −1.66737
\(356\) 17.2760 0.915625
\(357\) 6.70028 0.354616
\(358\) −2.06856 −0.109327
\(359\) 36.4022 1.92123 0.960617 0.277877i \(-0.0896309\pi\)
0.960617 + 0.277877i \(0.0896309\pi\)
\(360\) −14.1211 −0.744248
\(361\) −12.7682 −0.672013
\(362\) 31.2448 1.64219
\(363\) 28.1355 1.47673
\(364\) −6.84228 −0.358633
\(365\) −14.5505 −0.761609
\(366\) 28.7235 1.50140
\(367\) −4.84571 −0.252944 −0.126472 0.991970i \(-0.540365\pi\)
−0.126472 + 0.991970i \(0.540365\pi\)
\(368\) 35.1529 1.83247
\(369\) −5.44357 −0.283381
\(370\) −19.7082 −1.02458
\(371\) −0.865912 −0.0449559
\(372\) −73.4078 −3.80601
\(373\) 24.2899 1.25768 0.628842 0.777533i \(-0.283529\pi\)
0.628842 + 0.777533i \(0.283529\pi\)
\(374\) 54.4799 2.81709
\(375\) −9.59128 −0.495291
\(376\) 35.1832 1.81443
\(377\) −7.64269 −0.393619
\(378\) 10.3369 0.531672
\(379\) −12.1224 −0.622685 −0.311343 0.950298i \(-0.600779\pi\)
−0.311343 + 0.950298i \(0.600779\pi\)
\(380\) −35.6556 −1.82909
\(381\) 8.33837 0.427188
\(382\) −11.2997 −0.578143
\(383\) −0.255363 −0.0130484 −0.00652422 0.999979i \(-0.502077\pi\)
−0.00652422 + 0.999979i \(0.502077\pi\)
\(384\) −12.6273 −0.644382
\(385\) −12.6240 −0.643377
\(386\) 51.0728 2.59954
\(387\) 5.33793 0.271342
\(388\) 51.0466 2.59150
\(389\) −17.5238 −0.888494 −0.444247 0.895904i \(-0.646529\pi\)
−0.444247 + 0.895904i \(0.646529\pi\)
\(390\) 22.9408 1.16165
\(391\) 13.2357 0.669359
\(392\) 49.0869 2.47926
\(393\) 19.9383 1.00575
\(394\) −21.9754 −1.10710
\(395\) −22.8697 −1.15070
\(396\) −15.8117 −0.794566
\(397\) 15.1018 0.757936 0.378968 0.925410i \(-0.376279\pi\)
0.378968 + 0.925410i \(0.376279\pi\)
\(398\) 11.0529 0.554034
\(399\) −4.11625 −0.206070
\(400\) 35.0314 1.75157
\(401\) −37.5996 −1.87764 −0.938818 0.344413i \(-0.888078\pi\)
−0.938818 + 0.344413i \(0.888078\pi\)
\(402\) 11.4804 0.572589
\(403\) 12.3125 0.613327
\(404\) −32.0480 −1.59445
\(405\) −30.1125 −1.49630
\(406\) −11.0010 −0.545972
\(407\) −13.1943 −0.654017
\(408\) −60.7703 −3.00858
\(409\) −12.6670 −0.626345 −0.313172 0.949696i \(-0.601392\pi\)
−0.313172 + 0.949696i \(0.601392\pi\)
\(410\) 65.9278 3.25594
\(411\) 4.79187 0.236366
\(412\) 94.2889 4.64528
\(413\) −6.79576 −0.334397
\(414\) −5.38599 −0.264707
\(415\) 10.1023 0.495904
\(416\) 20.3235 0.996444
\(417\) −25.6894 −1.25802
\(418\) −33.4692 −1.63703
\(419\) 26.9680 1.31747 0.658735 0.752375i \(-0.271092\pi\)
0.658735 + 0.752375i \(0.271092\pi\)
\(420\) 23.5515 1.14920
\(421\) −34.3404 −1.67365 −0.836824 0.547472i \(-0.815590\pi\)
−0.836824 + 0.547472i \(0.815590\pi\)
\(422\) −70.1353 −3.41413
\(423\) −2.80504 −0.136386
\(424\) 7.85365 0.381407
\(425\) 13.1900 0.639807
\(426\) 55.0155 2.66551
\(427\) −4.94595 −0.239351
\(428\) 37.1312 1.79480
\(429\) 15.3585 0.741517
\(430\) −64.6484 −3.11762
\(431\) −40.8154 −1.96601 −0.983005 0.183580i \(-0.941231\pi\)
−0.983005 + 0.183580i \(0.941231\pi\)
\(432\) −48.7851 −2.34718
\(433\) 15.6625 0.752694 0.376347 0.926479i \(-0.377180\pi\)
0.376347 + 0.926479i \(0.377180\pi\)
\(434\) 17.7228 0.850720
\(435\) 26.3066 1.26130
\(436\) −75.9324 −3.63650
\(437\) −8.13123 −0.388969
\(438\) 25.4811 1.21754
\(439\) −29.5994 −1.41270 −0.706351 0.707862i \(-0.749660\pi\)
−0.706351 + 0.707862i \(0.749660\pi\)
\(440\) 114.497 5.45843
\(441\) −3.91354 −0.186359
\(442\) 17.0475 0.810869
\(443\) −4.78264 −0.227230 −0.113615 0.993525i \(-0.536243\pi\)
−0.113615 + 0.993525i \(0.536243\pi\)
\(444\) 24.6155 1.16820
\(445\) 9.97386 0.472806
\(446\) 52.9558 2.50753
\(447\) 4.97596 0.235355
\(448\) 10.5638 0.499094
\(449\) 0.156761 0.00739800 0.00369900 0.999993i \(-0.498823\pi\)
0.00369900 + 0.999993i \(0.498823\pi\)
\(450\) −5.36738 −0.253021
\(451\) 44.1376 2.07836
\(452\) −35.3095 −1.66082
\(453\) −1.90424 −0.0894692
\(454\) −23.6800 −1.11136
\(455\) −3.95022 −0.185189
\(456\) 37.3336 1.74831
\(457\) −10.5875 −0.495263 −0.247632 0.968854i \(-0.579652\pi\)
−0.247632 + 0.968854i \(0.579652\pi\)
\(458\) −3.46710 −0.162007
\(459\) −18.3685 −0.857367
\(460\) 46.5236 2.16917
\(461\) 24.7311 1.15184 0.575921 0.817505i \(-0.304643\pi\)
0.575921 + 0.817505i \(0.304643\pi\)
\(462\) 22.1073 1.02853
\(463\) 34.1252 1.58593 0.792967 0.609264i \(-0.208535\pi\)
0.792967 + 0.609264i \(0.208535\pi\)
\(464\) 51.9196 2.41031
\(465\) −42.3802 −1.96533
\(466\) 75.9997 3.52062
\(467\) 2.51842 0.116539 0.0582693 0.998301i \(-0.481442\pi\)
0.0582693 + 0.998301i \(0.481442\pi\)
\(468\) −4.94769 −0.228707
\(469\) −1.97682 −0.0912813
\(470\) 33.9722 1.56702
\(471\) −34.8147 −1.60418
\(472\) 61.6362 2.83704
\(473\) −43.2810 −1.99006
\(474\) 40.0498 1.83955
\(475\) −8.10312 −0.371797
\(476\) 17.5013 0.802172
\(477\) −0.626146 −0.0286693
\(478\) 16.2323 0.742449
\(479\) 24.7135 1.12919 0.564595 0.825368i \(-0.309032\pi\)
0.564595 + 0.825368i \(0.309032\pi\)
\(480\) −69.9548 −3.19298
\(481\) −4.12869 −0.188252
\(482\) −6.49988 −0.296061
\(483\) 5.37090 0.244384
\(484\) 73.4908 3.34049
\(485\) 29.4705 1.33819
\(486\) 16.9209 0.767548
\(487\) 26.2202 1.18815 0.594076 0.804409i \(-0.297518\pi\)
0.594076 + 0.804409i \(0.297518\pi\)
\(488\) 44.8588 2.03066
\(489\) −9.09268 −0.411185
\(490\) 47.3974 2.14119
\(491\) 16.1862 0.730475 0.365237 0.930914i \(-0.380988\pi\)
0.365237 + 0.930914i \(0.380988\pi\)
\(492\) −82.3439 −3.71235
\(493\) 19.5487 0.880427
\(494\) −10.4730 −0.471202
\(495\) −9.12847 −0.410294
\(496\) −83.6429 −3.75568
\(497\) −9.47321 −0.424932
\(498\) −17.6914 −0.792771
\(499\) −23.0880 −1.03356 −0.516781 0.856118i \(-0.672870\pi\)
−0.516781 + 0.856118i \(0.672870\pi\)
\(500\) −25.0527 −1.12039
\(501\) −13.3644 −0.597078
\(502\) −51.1682 −2.28375
\(503\) 31.4981 1.40443 0.702216 0.711964i \(-0.252194\pi\)
0.702216 + 0.711964i \(0.252194\pi\)
\(504\) −4.25815 −0.189673
\(505\) −18.5021 −0.823333
\(506\) 43.6708 1.94140
\(507\) −19.9493 −0.885978
\(508\) 21.7801 0.966334
\(509\) 37.2875 1.65274 0.826371 0.563127i \(-0.190402\pi\)
0.826371 + 0.563127i \(0.190402\pi\)
\(510\) −58.6786 −2.59833
\(511\) −4.38764 −0.194098
\(512\) 31.4516 1.38998
\(513\) 11.2845 0.498222
\(514\) 69.3090 3.05709
\(515\) 54.4354 2.39871
\(516\) 80.7459 3.55464
\(517\) 22.7438 1.00027
\(518\) −5.94290 −0.261116
\(519\) 38.0052 1.66824
\(520\) 35.8277 1.57115
\(521\) 6.58312 0.288412 0.144206 0.989548i \(-0.453937\pi\)
0.144206 + 0.989548i \(0.453937\pi\)
\(522\) −7.95491 −0.348177
\(523\) −7.06556 −0.308956 −0.154478 0.987996i \(-0.549370\pi\)
−0.154478 + 0.987996i \(0.549370\pi\)
\(524\) 52.0793 2.27510
\(525\) 5.35233 0.233595
\(526\) −64.2507 −2.80146
\(527\) −31.4931 −1.37186
\(528\) −104.336 −4.54064
\(529\) −12.3903 −0.538710
\(530\) 7.58334 0.329399
\(531\) −4.91406 −0.213252
\(532\) −10.7518 −0.466148
\(533\) 13.8113 0.598233
\(534\) −17.4664 −0.755846
\(535\) 21.4368 0.926792
\(536\) 17.9294 0.774433
\(537\) 1.49160 0.0643672
\(538\) −51.0874 −2.20253
\(539\) 31.7318 1.36678
\(540\) −64.5652 −2.77845
\(541\) −12.9548 −0.556969 −0.278485 0.960441i \(-0.589832\pi\)
−0.278485 + 0.960441i \(0.589832\pi\)
\(542\) −5.75499 −0.247198
\(543\) −22.5300 −0.966854
\(544\) −51.9840 −2.22880
\(545\) −43.8377 −1.87780
\(546\) 6.91770 0.296050
\(547\) −21.6112 −0.924028 −0.462014 0.886873i \(-0.652873\pi\)
−0.462014 + 0.886873i \(0.652873\pi\)
\(548\) 12.5165 0.534679
\(549\) −3.57645 −0.152639
\(550\) 43.5198 1.85569
\(551\) −12.0095 −0.511623
\(552\) −48.7130 −2.07337
\(553\) −6.89624 −0.293258
\(554\) 48.9027 2.07768
\(555\) 14.2112 0.603231
\(556\) −67.1015 −2.84574
\(557\) −39.4774 −1.67271 −0.836356 0.548187i \(-0.815318\pi\)
−0.836356 + 0.548187i \(0.815318\pi\)
\(558\) 12.8154 0.542521
\(559\) −13.5433 −0.572819
\(560\) 26.8353 1.13400
\(561\) −39.2844 −1.65859
\(562\) −70.2282 −2.96240
\(563\) 1.94790 0.0820944 0.0410472 0.999157i \(-0.486931\pi\)
0.0410472 + 0.999157i \(0.486931\pi\)
\(564\) −42.4313 −1.78668
\(565\) −20.3851 −0.857607
\(566\) −23.2956 −0.979188
\(567\) −9.08028 −0.381336
\(568\) 85.9202 3.60513
\(569\) −27.5057 −1.15310 −0.576549 0.817062i \(-0.695601\pi\)
−0.576549 + 0.817062i \(0.695601\pi\)
\(570\) 36.0486 1.50991
\(571\) 15.5208 0.649525 0.324762 0.945796i \(-0.394716\pi\)
0.324762 + 0.945796i \(0.394716\pi\)
\(572\) 40.1169 1.67737
\(573\) 8.14799 0.340387
\(574\) 19.8802 0.829783
\(575\) 10.5730 0.440924
\(576\) 7.63878 0.318283
\(577\) −23.1851 −0.965210 −0.482605 0.875838i \(-0.660309\pi\)
−0.482605 + 0.875838i \(0.660309\pi\)
\(578\) 1.28937 0.0536309
\(579\) −36.8276 −1.53050
\(580\) 68.7136 2.85317
\(581\) 3.04631 0.126382
\(582\) −51.6093 −2.13927
\(583\) 5.07692 0.210265
\(584\) 39.7950 1.64673
\(585\) −2.85643 −0.118099
\(586\) −51.3265 −2.12028
\(587\) −11.1928 −0.461976 −0.230988 0.972957i \(-0.574196\pi\)
−0.230988 + 0.972957i \(0.574196\pi\)
\(588\) −59.1994 −2.44134
\(589\) 19.3474 0.797198
\(590\) 59.5148 2.45019
\(591\) 15.8460 0.651817
\(592\) 28.0477 1.15275
\(593\) 6.05389 0.248603 0.124302 0.992244i \(-0.460331\pi\)
0.124302 + 0.992244i \(0.460331\pi\)
\(594\) −60.6061 −2.48670
\(595\) 10.1040 0.414222
\(596\) 12.9974 0.532393
\(597\) −7.97005 −0.326193
\(598\) 13.6652 0.558812
\(599\) 34.0434 1.39097 0.695487 0.718539i \(-0.255189\pi\)
0.695487 + 0.718539i \(0.255189\pi\)
\(600\) −48.5447 −1.98183
\(601\) 7.09683 0.289486 0.144743 0.989469i \(-0.453764\pi\)
0.144743 + 0.989469i \(0.453764\pi\)
\(602\) −19.4944 −0.794532
\(603\) −1.42945 −0.0582119
\(604\) −4.97394 −0.202387
\(605\) 42.4281 1.72495
\(606\) 32.4012 1.31621
\(607\) 35.9856 1.46061 0.730305 0.683121i \(-0.239378\pi\)
0.730305 + 0.683121i \(0.239378\pi\)
\(608\) 31.9359 1.29517
\(609\) 7.93262 0.321446
\(610\) 43.3148 1.75377
\(611\) 7.11687 0.287918
\(612\) 12.6553 0.511561
\(613\) −12.8668 −0.519687 −0.259843 0.965651i \(-0.583671\pi\)
−0.259843 + 0.965651i \(0.583671\pi\)
\(614\) 16.2169 0.654462
\(615\) −47.5392 −1.91697
\(616\) 34.5260 1.39109
\(617\) −13.5505 −0.545524 −0.272762 0.962081i \(-0.587937\pi\)
−0.272762 + 0.962081i \(0.587937\pi\)
\(618\) −95.3282 −3.83466
\(619\) −10.5374 −0.423534 −0.211767 0.977320i \(-0.567922\pi\)
−0.211767 + 0.977320i \(0.567922\pi\)
\(620\) −110.698 −4.44575
\(621\) −14.7241 −0.590856
\(622\) −5.82647 −0.233620
\(623\) 3.00757 0.120496
\(624\) −32.6482 −1.30698
\(625\) −30.6935 −1.22774
\(626\) 41.7300 1.66787
\(627\) 24.1340 0.963817
\(628\) −90.9371 −3.62879
\(629\) 10.5604 0.421073
\(630\) −4.11159 −0.163810
\(631\) 12.4768 0.496694 0.248347 0.968671i \(-0.420113\pi\)
0.248347 + 0.968671i \(0.420113\pi\)
\(632\) 62.5476 2.48801
\(633\) 50.5731 2.01010
\(634\) 26.6678 1.05911
\(635\) 12.5742 0.498991
\(636\) −9.47160 −0.375573
\(637\) 9.92933 0.393414
\(638\) 64.5001 2.55358
\(639\) −6.85014 −0.270987
\(640\) −19.0418 −0.752693
\(641\) −34.4431 −1.36042 −0.680210 0.733017i \(-0.738112\pi\)
−0.680210 + 0.733017i \(0.738112\pi\)
\(642\) −37.5405 −1.48160
\(643\) 41.7518 1.64653 0.823265 0.567657i \(-0.192150\pi\)
0.823265 + 0.567657i \(0.192150\pi\)
\(644\) 14.0290 0.552818
\(645\) 46.6166 1.83553
\(646\) 26.7880 1.05396
\(647\) 0.0702995 0.00276376 0.00138188 0.999999i \(-0.499560\pi\)
0.00138188 + 0.999999i \(0.499560\pi\)
\(648\) 82.3564 3.23526
\(649\) 39.8442 1.56402
\(650\) 13.6180 0.534141
\(651\) −12.7795 −0.500869
\(652\) −23.7504 −0.930135
\(653\) −0.441920 −0.0172936 −0.00864682 0.999963i \(-0.502752\pi\)
−0.00864682 + 0.999963i \(0.502752\pi\)
\(654\) 76.7694 3.00192
\(655\) 30.0667 1.17480
\(656\) −93.8250 −3.66325
\(657\) −3.17273 −0.123780
\(658\) 10.2441 0.399358
\(659\) −50.9099 −1.98317 −0.991585 0.129459i \(-0.958676\pi\)
−0.991585 + 0.129459i \(0.958676\pi\)
\(660\) −138.085 −5.37494
\(661\) −33.8203 −1.31546 −0.657728 0.753256i \(-0.728482\pi\)
−0.657728 + 0.753256i \(0.728482\pi\)
\(662\) 4.92533 0.191428
\(663\) −12.2926 −0.477407
\(664\) −27.6294 −1.07223
\(665\) −6.20726 −0.240707
\(666\) −4.29735 −0.166519
\(667\) 15.6701 0.606748
\(668\) −34.9083 −1.35064
\(669\) −38.1854 −1.47633
\(670\) 17.3123 0.668833
\(671\) 28.9986 1.11948
\(672\) −21.0945 −0.813739
\(673\) 42.6052 1.64231 0.821155 0.570705i \(-0.193330\pi\)
0.821155 + 0.570705i \(0.193330\pi\)
\(674\) 8.96772 0.345424
\(675\) −14.6732 −0.564770
\(676\) −52.1081 −2.00416
\(677\) −35.8751 −1.37879 −0.689395 0.724385i \(-0.742124\pi\)
−0.689395 + 0.724385i \(0.742124\pi\)
\(678\) 35.6988 1.37100
\(679\) 8.88668 0.341039
\(680\) −91.6410 −3.51427
\(681\) 17.0752 0.654323
\(682\) −103.910 −3.97893
\(683\) −36.2126 −1.38563 −0.692817 0.721113i \(-0.743631\pi\)
−0.692817 + 0.721113i \(0.743631\pi\)
\(684\) −7.77467 −0.297272
\(685\) 7.22610 0.276095
\(686\) 30.2995 1.15684
\(687\) 2.50006 0.0953831
\(688\) 92.0042 3.50763
\(689\) 1.58864 0.0605225
\(690\) −47.0364 −1.79065
\(691\) 37.1473 1.41315 0.706575 0.707638i \(-0.250239\pi\)
0.706575 + 0.707638i \(0.250239\pi\)
\(692\) 99.2707 3.77370
\(693\) −2.75264 −0.104564
\(694\) −16.3276 −0.619787
\(695\) −38.7394 −1.46947
\(696\) −71.9473 −2.72716
\(697\) −35.3268 −1.33810
\(698\) 45.4055 1.71862
\(699\) −54.8019 −2.07280
\(700\) 13.9805 0.528412
\(701\) 14.7737 0.557996 0.278998 0.960292i \(-0.409998\pi\)
0.278998 + 0.960292i \(0.409998\pi\)
\(702\) −18.9645 −0.715770
\(703\) −6.48770 −0.244688
\(704\) −61.9368 −2.33433
\(705\) −24.4967 −0.922598
\(706\) 54.4408 2.04891
\(707\) −5.57922 −0.209828
\(708\) −74.3341 −2.79364
\(709\) 14.7950 0.555637 0.277818 0.960634i \(-0.410389\pi\)
0.277818 + 0.960634i \(0.410389\pi\)
\(710\) 82.9629 3.11354
\(711\) −4.98671 −0.187016
\(712\) −27.2781 −1.02229
\(713\) −25.2447 −0.945420
\(714\) −17.6942 −0.662191
\(715\) 23.1605 0.866154
\(716\) 3.89610 0.145604
\(717\) −11.7048 −0.437124
\(718\) −96.1317 −3.58760
\(719\) −11.5355 −0.430200 −0.215100 0.976592i \(-0.569008\pi\)
−0.215100 + 0.976592i \(0.569008\pi\)
\(720\) 19.4047 0.723172
\(721\) 16.4147 0.611316
\(722\) 33.7187 1.25488
\(723\) 4.68693 0.174309
\(724\) −58.8490 −2.18710
\(725\) 15.6159 0.579960
\(726\) −74.3009 −2.75756
\(727\) −9.23117 −0.342365 −0.171183 0.985239i \(-0.554759\pi\)
−0.171183 + 0.985239i \(0.554759\pi\)
\(728\) 10.8037 0.400411
\(729\) 19.2578 0.713252
\(730\) 38.4253 1.42219
\(731\) 34.6413 1.28125
\(732\) −54.1003 −1.99960
\(733\) 19.9165 0.735635 0.367817 0.929898i \(-0.380105\pi\)
0.367817 + 0.929898i \(0.380105\pi\)
\(734\) 12.7967 0.472333
\(735\) −34.1773 −1.26065
\(736\) −41.6701 −1.53598
\(737\) 11.5903 0.426935
\(738\) 14.3755 0.529170
\(739\) 48.2890 1.77634 0.888170 0.459515i \(-0.151977\pi\)
0.888170 + 0.459515i \(0.151977\pi\)
\(740\) 37.1200 1.36456
\(741\) 7.55186 0.277425
\(742\) 2.28672 0.0839481
\(743\) 6.43494 0.236075 0.118038 0.993009i \(-0.462340\pi\)
0.118038 + 0.993009i \(0.462340\pi\)
\(744\) 115.908 4.24939
\(745\) 7.50370 0.274914
\(746\) −64.1453 −2.34853
\(747\) 2.20281 0.0805965
\(748\) −102.612 −3.75187
\(749\) 6.46415 0.236195
\(750\) 25.3289 0.924879
\(751\) −12.7479 −0.465176 −0.232588 0.972575i \(-0.574719\pi\)
−0.232588 + 0.972575i \(0.574719\pi\)
\(752\) −48.3475 −1.76305
\(753\) 36.8964 1.34458
\(754\) 20.1830 0.735021
\(755\) −2.87158 −0.104508
\(756\) −19.4693 −0.708093
\(757\) 19.0511 0.692422 0.346211 0.938157i \(-0.387468\pi\)
0.346211 + 0.938157i \(0.387468\pi\)
\(758\) 32.0131 1.16277
\(759\) −31.4901 −1.14302
\(760\) 56.2987 2.04217
\(761\) −18.3824 −0.666361 −0.333181 0.942863i \(-0.608122\pi\)
−0.333181 + 0.942863i \(0.608122\pi\)
\(762\) −22.0201 −0.797706
\(763\) −13.2190 −0.478561
\(764\) 21.2828 0.769984
\(765\) 7.30624 0.264158
\(766\) 0.674368 0.0243659
\(767\) 12.4678 0.450187
\(768\) −13.1160 −0.473282
\(769\) −6.83555 −0.246496 −0.123248 0.992376i \(-0.539331\pi\)
−0.123248 + 0.992376i \(0.539331\pi\)
\(770\) 33.3376 1.20141
\(771\) −49.9773 −1.79989
\(772\) −96.1947 −3.46212
\(773\) 30.1651 1.08496 0.542482 0.840067i \(-0.317485\pi\)
0.542482 + 0.840067i \(0.317485\pi\)
\(774\) −14.0965 −0.506689
\(775\) −25.1574 −0.903680
\(776\) −80.6005 −2.89339
\(777\) 4.28531 0.153735
\(778\) 46.2773 1.65912
\(779\) 21.7027 0.777579
\(780\) −43.2087 −1.54712
\(781\) 55.5423 1.98746
\(782\) −34.9532 −1.24992
\(783\) −21.7469 −0.777170
\(784\) −67.4535 −2.40905
\(785\) −52.5003 −1.87382
\(786\) −52.6534 −1.87808
\(787\) 21.4998 0.766385 0.383193 0.923668i \(-0.374825\pi\)
0.383193 + 0.923668i \(0.374825\pi\)
\(788\) 41.3902 1.47447
\(789\) 46.3299 1.64939
\(790\) 60.3948 2.14875
\(791\) −6.14702 −0.218563
\(792\) 24.9660 0.887127
\(793\) 9.07407 0.322230
\(794\) −39.8811 −1.41533
\(795\) −5.46820 −0.193937
\(796\) −20.8180 −0.737875
\(797\) 33.4073 1.18335 0.591673 0.806178i \(-0.298468\pi\)
0.591673 + 0.806178i \(0.298468\pi\)
\(798\) 10.8703 0.384804
\(799\) −18.2037 −0.644001
\(800\) −41.5260 −1.46817
\(801\) 2.17479 0.0768425
\(802\) 99.2940 3.50619
\(803\) 25.7251 0.907820
\(804\) −21.6231 −0.762588
\(805\) 8.09927 0.285462
\(806\) −32.5150 −1.14529
\(807\) 36.8381 1.29676
\(808\) 50.6024 1.78019
\(809\) −33.2202 −1.16796 −0.583980 0.811768i \(-0.698506\pi\)
−0.583980 + 0.811768i \(0.698506\pi\)
\(810\) 79.5218 2.79411
\(811\) −29.0169 −1.01892 −0.509460 0.860494i \(-0.670155\pi\)
−0.509460 + 0.860494i \(0.670155\pi\)
\(812\) 20.7202 0.727138
\(813\) 4.14981 0.145540
\(814\) 34.8438 1.22128
\(815\) −13.7117 −0.480299
\(816\) 83.5084 2.92338
\(817\) −21.2815 −0.744545
\(818\) 33.4514 1.16960
\(819\) −0.861342 −0.0300977
\(820\) −124.174 −4.33634
\(821\) 0.0910732 0.00317848 0.00158924 0.999999i \(-0.499494\pi\)
0.00158924 + 0.999999i \(0.499494\pi\)
\(822\) −12.6545 −0.441376
\(823\) −39.6351 −1.38159 −0.690796 0.723049i \(-0.742740\pi\)
−0.690796 + 0.723049i \(0.742740\pi\)
\(824\) −148.878 −5.18642
\(825\) −31.3813 −1.09256
\(826\) 17.9464 0.624435
\(827\) −21.9167 −0.762120 −0.381060 0.924550i \(-0.624441\pi\)
−0.381060 + 0.924550i \(0.624441\pi\)
\(828\) 10.1444 0.352543
\(829\) −33.6380 −1.16830 −0.584149 0.811647i \(-0.698572\pi\)
−0.584149 + 0.811647i \(0.698572\pi\)
\(830\) −26.6785 −0.926023
\(831\) −35.2628 −1.22325
\(832\) −19.3809 −0.671912
\(833\) −25.3975 −0.879970
\(834\) 67.8412 2.34915
\(835\) −20.1534 −0.697438
\(836\) 63.0386 2.18024
\(837\) 35.0344 1.21097
\(838\) −71.2176 −2.46017
\(839\) −52.2442 −1.80367 −0.901836 0.432079i \(-0.857780\pi\)
−0.901836 + 0.432079i \(0.857780\pi\)
\(840\) −37.1869 −1.28307
\(841\) −5.85589 −0.201927
\(842\) 90.6868 3.12527
\(843\) 50.6402 1.74414
\(844\) 132.099 4.54702
\(845\) −30.0833 −1.03490
\(846\) 7.40761 0.254679
\(847\) 12.7940 0.439606
\(848\) −10.7922 −0.370606
\(849\) 16.7980 0.576506
\(850\) −34.8323 −1.19474
\(851\) 8.46519 0.290183
\(852\) −103.621 −3.54999
\(853\) 29.4792 1.00935 0.504675 0.863310i \(-0.331612\pi\)
0.504675 + 0.863310i \(0.331612\pi\)
\(854\) 13.0614 0.446951
\(855\) −4.48851 −0.153504
\(856\) −58.6286 −2.00388
\(857\) 2.93122 0.100129 0.0500643 0.998746i \(-0.484057\pi\)
0.0500643 + 0.998746i \(0.484057\pi\)
\(858\) −40.5591 −1.38467
\(859\) −25.5101 −0.870395 −0.435197 0.900335i \(-0.643321\pi\)
−0.435197 + 0.900335i \(0.643321\pi\)
\(860\) 121.764 4.15212
\(861\) −14.3352 −0.488543
\(862\) 107.786 3.67122
\(863\) 46.1314 1.57033 0.785165 0.619286i \(-0.212578\pi\)
0.785165 + 0.619286i \(0.212578\pi\)
\(864\) 57.8296 1.96740
\(865\) 57.3115 1.94865
\(866\) −41.3620 −1.40554
\(867\) −0.929742 −0.0315757
\(868\) −33.3805 −1.13301
\(869\) 40.4333 1.37161
\(870\) −69.4710 −2.35529
\(871\) 3.62678 0.122889
\(872\) 119.894 4.06013
\(873\) 6.42601 0.217488
\(874\) 21.4731 0.726339
\(875\) −4.36141 −0.147443
\(876\) −47.9933 −1.62154
\(877\) −13.9464 −0.470935 −0.235467 0.971882i \(-0.575662\pi\)
−0.235467 + 0.971882i \(0.575662\pi\)
\(878\) 78.1667 2.63800
\(879\) 37.0105 1.24833
\(880\) −157.338 −5.30385
\(881\) 5.63138 0.189726 0.0948630 0.995490i \(-0.469759\pi\)
0.0948630 + 0.995490i \(0.469759\pi\)
\(882\) 10.3350 0.347996
\(883\) 16.9208 0.569432 0.284716 0.958612i \(-0.408101\pi\)
0.284716 + 0.958612i \(0.408101\pi\)
\(884\) −32.1088 −1.07993
\(885\) −42.9149 −1.44257
\(886\) 12.6301 0.424317
\(887\) 22.3014 0.748806 0.374403 0.927266i \(-0.377848\pi\)
0.374403 + 0.927266i \(0.377848\pi\)
\(888\) −38.8669 −1.30429
\(889\) 3.79168 0.127169
\(890\) −26.3392 −0.882892
\(891\) 53.2386 1.78356
\(892\) −99.7413 −3.33959
\(893\) 11.1833 0.374233
\(894\) −13.1406 −0.439488
\(895\) 2.24932 0.0751864
\(896\) −5.74196 −0.191825
\(897\) −9.85371 −0.329006
\(898\) −0.413977 −0.0138146
\(899\) −37.2854 −1.24354
\(900\) 10.1094 0.336979
\(901\) −4.06347 −0.135374
\(902\) −116.560 −3.88101
\(903\) 14.0570 0.467788
\(904\) 55.7523 1.85430
\(905\) −33.9750 −1.12937
\(906\) 5.02877 0.167070
\(907\) −15.7894 −0.524280 −0.262140 0.965030i \(-0.584428\pi\)
−0.262140 + 0.965030i \(0.584428\pi\)
\(908\) 44.6009 1.48013
\(909\) −4.03437 −0.133812
\(910\) 10.4318 0.345812
\(911\) −33.0048 −1.09350 −0.546748 0.837297i \(-0.684135\pi\)
−0.546748 + 0.837297i \(0.684135\pi\)
\(912\) −51.3025 −1.69880
\(913\) −17.8608 −0.591106
\(914\) 27.9597 0.924826
\(915\) −31.2335 −1.03255
\(916\) 6.53022 0.215765
\(917\) 9.06647 0.299401
\(918\) 48.5079 1.60100
\(919\) 1.18009 0.0389274 0.0194637 0.999811i \(-0.493804\pi\)
0.0194637 + 0.999811i \(0.493804\pi\)
\(920\) −73.4588 −2.42187
\(921\) −11.6937 −0.385321
\(922\) −65.3105 −2.15089
\(923\) 17.3800 0.572070
\(924\) −41.6388 −1.36981
\(925\) 8.43593 0.277372
\(926\) −90.1187 −2.96148
\(927\) 11.8696 0.389848
\(928\) −61.5451 −2.02032
\(929\) 12.1282 0.397913 0.198957 0.980008i \(-0.436245\pi\)
0.198957 + 0.980008i \(0.436245\pi\)
\(930\) 111.918 3.66995
\(931\) 15.6027 0.511357
\(932\) −143.144 −4.68884
\(933\) 4.20135 0.137546
\(934\) −6.65070 −0.217617
\(935\) −59.2405 −1.93737
\(936\) 7.81221 0.255350
\(937\) −36.9376 −1.20670 −0.603349 0.797477i \(-0.706167\pi\)
−0.603349 + 0.797477i \(0.706167\pi\)
\(938\) 5.22044 0.170453
\(939\) −30.0907 −0.981973
\(940\) −63.9860 −2.08699
\(941\) −1.04523 −0.0340737 −0.0170368 0.999855i \(-0.505423\pi\)
−0.0170368 + 0.999855i \(0.505423\pi\)
\(942\) 91.9395 2.99555
\(943\) −28.3178 −0.922153
\(944\) −84.6984 −2.75670
\(945\) −11.2401 −0.365642
\(946\) 114.298 3.71613
\(947\) 17.9855 0.584449 0.292224 0.956350i \(-0.405605\pi\)
0.292224 + 0.956350i \(0.405605\pi\)
\(948\) −75.4331 −2.44995
\(949\) 8.04977 0.261306
\(950\) 21.3989 0.694272
\(951\) −19.2296 −0.623562
\(952\) −27.6339 −0.895619
\(953\) 36.4369 1.18031 0.590154 0.807291i \(-0.299067\pi\)
0.590154 + 0.807291i \(0.299067\pi\)
\(954\) 1.65354 0.0535354
\(955\) 12.2871 0.397601
\(956\) −30.5733 −0.988810
\(957\) −46.5097 −1.50345
\(958\) −65.2641 −2.10859
\(959\) 2.17900 0.0703634
\(960\) 66.7102 2.15306
\(961\) 29.0671 0.937650
\(962\) 10.9031 0.351531
\(963\) 4.67427 0.150626
\(964\) 12.2424 0.394301
\(965\) −55.5357 −1.78776
\(966\) −14.1836 −0.456350
\(967\) −7.14967 −0.229918 −0.114959 0.993370i \(-0.536674\pi\)
−0.114959 + 0.993370i \(0.536674\pi\)
\(968\) −116.039 −3.72963
\(969\) −19.3163 −0.620530
\(970\) −77.8263 −2.49885
\(971\) −35.5840 −1.14195 −0.570973 0.820969i \(-0.693434\pi\)
−0.570973 + 0.820969i \(0.693434\pi\)
\(972\) −31.8702 −1.02224
\(973\) −11.6817 −0.374497
\(974\) −69.2430 −2.21869
\(975\) −9.81965 −0.314480
\(976\) −61.6434 −1.97316
\(977\) 1.93879 0.0620275 0.0310138 0.999519i \(-0.490126\pi\)
0.0310138 + 0.999519i \(0.490126\pi\)
\(978\) 24.0122 0.767824
\(979\) −17.6337 −0.563575
\(980\) −89.2721 −2.85169
\(981\) −9.55878 −0.305188
\(982\) −42.7450 −1.36405
\(983\) −25.1485 −0.802112 −0.401056 0.916054i \(-0.631357\pi\)
−0.401056 + 0.916054i \(0.631357\pi\)
\(984\) 130.018 4.14481
\(985\) 23.8956 0.761378
\(986\) −51.6245 −1.64406
\(987\) −7.38685 −0.235126
\(988\) 19.7257 0.627558
\(989\) 27.7682 0.882978
\(990\) 24.1067 0.766160
\(991\) −12.8438 −0.407997 −0.203998 0.978971i \(-0.565394\pi\)
−0.203998 + 0.978971i \(0.565394\pi\)
\(992\) 99.1498 3.14801
\(993\) −3.55155 −0.112705
\(994\) 25.0171 0.793493
\(995\) −12.0188 −0.381021
\(996\) 33.3214 1.05583
\(997\) −15.5568 −0.492689 −0.246344 0.969182i \(-0.579229\pi\)
−0.246344 + 0.969182i \(0.579229\pi\)
\(998\) 60.9714 1.93002
\(999\) −11.7480 −0.371689
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.1.5 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.5 153 1.1 even 1 trivial