Properties

Label 8003.2.a.b.1.17
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 1.17
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} +O(q^{10})\) \(q-2.35186 q^{2} +2.82673 q^{3} +3.53125 q^{4} +2.18646 q^{5} -6.64808 q^{6} +0.649269 q^{7} -3.60130 q^{8} +4.99041 q^{9} -5.14224 q^{10} -5.34465 q^{11} +9.98190 q^{12} -0.189937 q^{13} -1.52699 q^{14} +6.18053 q^{15} +1.40724 q^{16} -3.29894 q^{17} -11.7368 q^{18} +1.35877 q^{19} +7.72093 q^{20} +1.83531 q^{21} +12.5699 q^{22} -5.91189 q^{23} -10.1799 q^{24} -0.219405 q^{25} +0.446705 q^{26} +5.62636 q^{27} +2.29273 q^{28} -2.86131 q^{29} -14.5357 q^{30} -0.767405 q^{31} +3.89295 q^{32} -15.1079 q^{33} +7.75866 q^{34} +1.41960 q^{35} +17.6224 q^{36} -7.04121 q^{37} -3.19564 q^{38} -0.536900 q^{39} -7.87408 q^{40} +3.71273 q^{41} -4.31639 q^{42} -0.473048 q^{43} -18.8733 q^{44} +10.9113 q^{45} +13.9040 q^{46} +9.61595 q^{47} +3.97790 q^{48} -6.57845 q^{49} +0.516010 q^{50} -9.32523 q^{51} -0.670715 q^{52} -1.00000 q^{53} -13.2324 q^{54} -11.6859 q^{55} -2.33821 q^{56} +3.84088 q^{57} +6.72941 q^{58} -2.59554 q^{59} +21.8250 q^{60} -3.99537 q^{61} +1.80483 q^{62} +3.24012 q^{63} -11.9702 q^{64} -0.415289 q^{65} +35.5317 q^{66} -3.61822 q^{67} -11.6494 q^{68} -16.7113 q^{69} -3.33870 q^{70} +13.0451 q^{71} -17.9719 q^{72} -9.39429 q^{73} +16.5599 q^{74} -0.620199 q^{75} +4.79817 q^{76} -3.47012 q^{77} +1.26272 q^{78} -2.10091 q^{79} +3.07688 q^{80} +0.932969 q^{81} -8.73183 q^{82} -4.63441 q^{83} +6.48094 q^{84} -7.21300 q^{85} +1.11254 q^{86} -8.08816 q^{87} +19.2477 q^{88} +16.4581 q^{89} -25.6619 q^{90} -0.123320 q^{91} -20.8764 q^{92} -2.16925 q^{93} -22.6154 q^{94} +2.97090 q^{95} +11.0043 q^{96} -10.8351 q^{97} +15.4716 q^{98} -26.6720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35186 −1.66302 −0.831509 0.555512i \(-0.812522\pi\)
−0.831509 + 0.555512i \(0.812522\pi\)
\(3\) 2.82673 1.63201 0.816007 0.578042i \(-0.196183\pi\)
0.816007 + 0.578042i \(0.196183\pi\)
\(4\) 3.53125 1.76563
\(5\) 2.18646 0.977813 0.488907 0.872336i \(-0.337396\pi\)
0.488907 + 0.872336i \(0.337396\pi\)
\(6\) −6.64808 −2.71407
\(7\) 0.649269 0.245401 0.122700 0.992444i \(-0.460845\pi\)
0.122700 + 0.992444i \(0.460845\pi\)
\(8\) −3.60130 −1.27325
\(9\) 4.99041 1.66347
\(10\) −5.14224 −1.62612
\(11\) −5.34465 −1.61147 −0.805736 0.592274i \(-0.798230\pi\)
−0.805736 + 0.592274i \(0.798230\pi\)
\(12\) 9.98190 2.88153
\(13\) −0.189937 −0.0526790 −0.0263395 0.999653i \(-0.508385\pi\)
−0.0263395 + 0.999653i \(0.508385\pi\)
\(14\) −1.52699 −0.408105
\(15\) 6.18053 1.59581
\(16\) 1.40724 0.351811
\(17\) −3.29894 −0.800112 −0.400056 0.916491i \(-0.631009\pi\)
−0.400056 + 0.916491i \(0.631009\pi\)
\(18\) −11.7368 −2.76638
\(19\) 1.35877 0.311724 0.155862 0.987779i \(-0.450185\pi\)
0.155862 + 0.987779i \(0.450185\pi\)
\(20\) 7.72093 1.72645
\(21\) 1.83531 0.400497
\(22\) 12.5699 2.67991
\(23\) −5.91189 −1.23271 −0.616357 0.787467i \(-0.711392\pi\)
−0.616357 + 0.787467i \(0.711392\pi\)
\(24\) −10.1799 −2.07796
\(25\) −0.219405 −0.0438810
\(26\) 0.446705 0.0876061
\(27\) 5.62636 1.08279
\(28\) 2.29273 0.433286
\(29\) −2.86131 −0.531332 −0.265666 0.964065i \(-0.585592\pi\)
−0.265666 + 0.964065i \(0.585592\pi\)
\(30\) −14.5357 −2.65385
\(31\) −0.767405 −0.137830 −0.0689150 0.997623i \(-0.521954\pi\)
−0.0689150 + 0.997623i \(0.521954\pi\)
\(32\) 3.89295 0.688183
\(33\) −15.1079 −2.62995
\(34\) 7.75866 1.33060
\(35\) 1.41960 0.239956
\(36\) 17.6224 2.93707
\(37\) −7.04121 −1.15757 −0.578784 0.815481i \(-0.696472\pi\)
−0.578784 + 0.815481i \(0.696472\pi\)
\(38\) −3.19564 −0.518402
\(39\) −0.536900 −0.0859729
\(40\) −7.87408 −1.24500
\(41\) 3.71273 0.579831 0.289916 0.957052i \(-0.406373\pi\)
0.289916 + 0.957052i \(0.406373\pi\)
\(42\) −4.31639 −0.666034
\(43\) −0.473048 −0.0721391 −0.0360696 0.999349i \(-0.511484\pi\)
−0.0360696 + 0.999349i \(0.511484\pi\)
\(44\) −18.8733 −2.84526
\(45\) 10.9113 1.62656
\(46\) 13.9040 2.05003
\(47\) 9.61595 1.40263 0.701315 0.712852i \(-0.252597\pi\)
0.701315 + 0.712852i \(0.252597\pi\)
\(48\) 3.97790 0.574160
\(49\) −6.57845 −0.939779
\(50\) 0.516010 0.0729748
\(51\) −9.32523 −1.30579
\(52\) −0.670715 −0.0930115
\(53\) −1.00000 −0.137361
\(54\) −13.2324 −1.80070
\(55\) −11.6859 −1.57572
\(56\) −2.33821 −0.312456
\(57\) 3.84088 0.508737
\(58\) 6.72941 0.883614
\(59\) −2.59554 −0.337911 −0.168956 0.985624i \(-0.554039\pi\)
−0.168956 + 0.985624i \(0.554039\pi\)
\(60\) 21.8250 2.81760
\(61\) −3.99537 −0.511555 −0.255778 0.966736i \(-0.582332\pi\)
−0.255778 + 0.966736i \(0.582332\pi\)
\(62\) 1.80483 0.229214
\(63\) 3.24012 0.408217
\(64\) −11.9702 −1.49627
\(65\) −0.415289 −0.0515102
\(66\) 35.5317 4.37365
\(67\) −3.61822 −0.442036 −0.221018 0.975270i \(-0.570938\pi\)
−0.221018 + 0.975270i \(0.570938\pi\)
\(68\) −11.6494 −1.41270
\(69\) −16.7113 −2.01181
\(70\) −3.33870 −0.399051
\(71\) 13.0451 1.54816 0.774082 0.633085i \(-0.218212\pi\)
0.774082 + 0.633085i \(0.218212\pi\)
\(72\) −17.9719 −2.11801
\(73\) −9.39429 −1.09952 −0.549759 0.835323i \(-0.685281\pi\)
−0.549759 + 0.835323i \(0.685281\pi\)
\(74\) 16.5599 1.92505
\(75\) −0.620199 −0.0716144
\(76\) 4.79817 0.550387
\(77\) −3.47012 −0.395456
\(78\) 1.26272 0.142974
\(79\) −2.10091 −0.236371 −0.118186 0.992992i \(-0.537708\pi\)
−0.118186 + 0.992992i \(0.537708\pi\)
\(80\) 3.07688 0.344005
\(81\) 0.932969 0.103663
\(82\) −8.73183 −0.964269
\(83\) −4.63441 −0.508692 −0.254346 0.967113i \(-0.581860\pi\)
−0.254346 + 0.967113i \(0.581860\pi\)
\(84\) 6.48094 0.707129
\(85\) −7.21300 −0.782360
\(86\) 1.11254 0.119969
\(87\) −8.08816 −0.867141
\(88\) 19.2477 2.05181
\(89\) 16.4581 1.74456 0.872278 0.489010i \(-0.162642\pi\)
0.872278 + 0.489010i \(0.162642\pi\)
\(90\) −25.6619 −2.70500
\(91\) −0.123320 −0.0129275
\(92\) −20.8764 −2.17651
\(93\) −2.16925 −0.224941
\(94\) −22.6154 −2.33260
\(95\) 2.97090 0.304807
\(96\) 11.0043 1.12312
\(97\) −10.8351 −1.10014 −0.550069 0.835119i \(-0.685399\pi\)
−0.550069 + 0.835119i \(0.685399\pi\)
\(98\) 15.4716 1.56287
\(99\) −26.6720 −2.68064
\(100\) −0.774774 −0.0774774
\(101\) 18.9357 1.88417 0.942087 0.335369i \(-0.108861\pi\)
0.942087 + 0.335369i \(0.108861\pi\)
\(102\) 21.9317 2.17156
\(103\) −5.41593 −0.533647 −0.266823 0.963745i \(-0.585974\pi\)
−0.266823 + 0.963745i \(0.585974\pi\)
\(104\) 0.684019 0.0670736
\(105\) 4.01283 0.391612
\(106\) 2.35186 0.228433
\(107\) 14.2897 1.38144 0.690718 0.723124i \(-0.257295\pi\)
0.690718 + 0.723124i \(0.257295\pi\)
\(108\) 19.8681 1.91181
\(109\) 6.58682 0.630903 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(110\) 27.4835 2.62045
\(111\) −19.9036 −1.88917
\(112\) 0.913679 0.0863346
\(113\) −4.67125 −0.439434 −0.219717 0.975564i \(-0.570513\pi\)
−0.219717 + 0.975564i \(0.570513\pi\)
\(114\) −9.03322 −0.846039
\(115\) −12.9261 −1.20536
\(116\) −10.1040 −0.938134
\(117\) −0.947863 −0.0876300
\(118\) 6.10436 0.561952
\(119\) −2.14190 −0.196348
\(120\) −22.2579 −2.03186
\(121\) 17.5653 1.59684
\(122\) 9.39657 0.850725
\(123\) 10.4949 0.946293
\(124\) −2.70990 −0.243356
\(125\) −11.4120 −1.02072
\(126\) −7.62031 −0.678871
\(127\) −11.4958 −1.02009 −0.510043 0.860149i \(-0.670371\pi\)
−0.510043 + 0.860149i \(0.670371\pi\)
\(128\) 20.3663 1.80014
\(129\) −1.33718 −0.117732
\(130\) 0.976702 0.0856624
\(131\) −7.13561 −0.623441 −0.311720 0.950174i \(-0.600905\pi\)
−0.311720 + 0.950174i \(0.600905\pi\)
\(132\) −53.3498 −4.64350
\(133\) 0.882208 0.0764971
\(134\) 8.50955 0.735113
\(135\) 12.3018 1.05877
\(136\) 11.8805 1.01874
\(137\) −22.0498 −1.88384 −0.941919 0.335841i \(-0.890980\pi\)
−0.941919 + 0.335841i \(0.890980\pi\)
\(138\) 39.3027 3.34567
\(139\) −9.02924 −0.765850 −0.382925 0.923779i \(-0.625083\pi\)
−0.382925 + 0.923779i \(0.625083\pi\)
\(140\) 5.01296 0.423673
\(141\) 27.1817 2.28911
\(142\) −30.6802 −2.57463
\(143\) 1.01515 0.0848908
\(144\) 7.02272 0.585227
\(145\) −6.25613 −0.519544
\(146\) 22.0941 1.82852
\(147\) −18.5955 −1.53373
\(148\) −24.8643 −2.04383
\(149\) −5.37609 −0.440426 −0.220213 0.975452i \(-0.570675\pi\)
−0.220213 + 0.975452i \(0.570675\pi\)
\(150\) 1.45862 0.119096
\(151\) −1.00000 −0.0813788
\(152\) −4.89334 −0.396902
\(153\) −16.4631 −1.33096
\(154\) 8.16123 0.657651
\(155\) −1.67790 −0.134772
\(156\) −1.89593 −0.151796
\(157\) 17.0154 1.35798 0.678990 0.734147i \(-0.262418\pi\)
0.678990 + 0.734147i \(0.262418\pi\)
\(158\) 4.94106 0.393089
\(159\) −2.82673 −0.224174
\(160\) 8.51177 0.672915
\(161\) −3.83841 −0.302509
\(162\) −2.19421 −0.172394
\(163\) −0.789089 −0.0618062 −0.0309031 0.999522i \(-0.509838\pi\)
−0.0309031 + 0.999522i \(0.509838\pi\)
\(164\) 13.1106 1.02377
\(165\) −33.0328 −2.57160
\(166\) 10.8995 0.845964
\(167\) 10.1582 0.786063 0.393032 0.919525i \(-0.371426\pi\)
0.393032 + 0.919525i \(0.371426\pi\)
\(168\) −6.60949 −0.509933
\(169\) −12.9639 −0.997225
\(170\) 16.9640 1.30108
\(171\) 6.78083 0.518543
\(172\) −1.67045 −0.127371
\(173\) 4.78049 0.363454 0.181727 0.983349i \(-0.441831\pi\)
0.181727 + 0.983349i \(0.441831\pi\)
\(174\) 19.0222 1.44207
\(175\) −0.142453 −0.0107684
\(176\) −7.52122 −0.566933
\(177\) −7.33691 −0.551476
\(178\) −38.7072 −2.90123
\(179\) −13.6695 −1.02171 −0.510853 0.859668i \(-0.670670\pi\)
−0.510853 + 0.859668i \(0.670670\pi\)
\(180\) 38.5306 2.87190
\(181\) −1.97701 −0.146950 −0.0734751 0.997297i \(-0.523409\pi\)
−0.0734751 + 0.997297i \(0.523409\pi\)
\(182\) 0.290032 0.0214986
\(183\) −11.2939 −0.834866
\(184\) 21.2905 1.56955
\(185\) −15.3953 −1.13188
\(186\) 5.10177 0.374080
\(187\) 17.6317 1.28936
\(188\) 33.9563 2.47652
\(189\) 3.65302 0.265718
\(190\) −6.98713 −0.506900
\(191\) −13.2396 −0.957984 −0.478992 0.877819i \(-0.658998\pi\)
−0.478992 + 0.877819i \(0.658998\pi\)
\(192\) −33.8365 −2.44194
\(193\) −9.58195 −0.689724 −0.344862 0.938653i \(-0.612074\pi\)
−0.344862 + 0.938653i \(0.612074\pi\)
\(194\) 25.4827 1.82955
\(195\) −1.17391 −0.0840654
\(196\) −23.2302 −1.65930
\(197\) −8.71250 −0.620740 −0.310370 0.950616i \(-0.600453\pi\)
−0.310370 + 0.950616i \(0.600453\pi\)
\(198\) 62.7289 4.45795
\(199\) −8.14936 −0.577693 −0.288846 0.957375i \(-0.593272\pi\)
−0.288846 + 0.957375i \(0.593272\pi\)
\(200\) 0.790142 0.0558715
\(201\) −10.2277 −0.721408
\(202\) −44.5342 −3.13341
\(203\) −1.85776 −0.130389
\(204\) −32.9298 −2.30554
\(205\) 8.11773 0.566967
\(206\) 12.7375 0.887464
\(207\) −29.5028 −2.05058
\(208\) −0.267287 −0.0185330
\(209\) −7.26216 −0.502334
\(210\) −9.43761 −0.651257
\(211\) 6.77458 0.466382 0.233191 0.972431i \(-0.425083\pi\)
0.233191 + 0.972431i \(0.425083\pi\)
\(212\) −3.53125 −0.242527
\(213\) 36.8749 2.52663
\(214\) −33.6074 −2.29735
\(215\) −1.03430 −0.0705386
\(216\) −20.2622 −1.37867
\(217\) −0.498253 −0.0338236
\(218\) −15.4913 −1.04920
\(219\) −26.5551 −1.79443
\(220\) −41.2657 −2.78213
\(221\) 0.626591 0.0421491
\(222\) 46.8105 3.14172
\(223\) −9.25211 −0.619567 −0.309783 0.950807i \(-0.600257\pi\)
−0.309783 + 0.950807i \(0.600257\pi\)
\(224\) 2.52757 0.168881
\(225\) −1.09492 −0.0729947
\(226\) 10.9861 0.730787
\(227\) −16.9130 −1.12255 −0.561277 0.827628i \(-0.689690\pi\)
−0.561277 + 0.827628i \(0.689690\pi\)
\(228\) 13.5631 0.898240
\(229\) −15.9422 −1.05349 −0.526744 0.850024i \(-0.676587\pi\)
−0.526744 + 0.850024i \(0.676587\pi\)
\(230\) 30.4004 2.00454
\(231\) −9.80909 −0.645391
\(232\) 10.3044 0.676519
\(233\) 23.2135 1.52076 0.760382 0.649476i \(-0.225012\pi\)
0.760382 + 0.649476i \(0.225012\pi\)
\(234\) 2.22924 0.145730
\(235\) 21.0249 1.37151
\(236\) −9.16553 −0.596625
\(237\) −5.93872 −0.385761
\(238\) 5.03746 0.326530
\(239\) −9.16593 −0.592894 −0.296447 0.955049i \(-0.595802\pi\)
−0.296447 + 0.955049i \(0.595802\pi\)
\(240\) 8.69750 0.561421
\(241\) −3.09850 −0.199592 −0.0997958 0.995008i \(-0.531819\pi\)
−0.0997958 + 0.995008i \(0.531819\pi\)
\(242\) −41.3111 −2.65558
\(243\) −14.2418 −0.913613
\(244\) −14.1087 −0.903216
\(245\) −14.3835 −0.918928
\(246\) −24.6825 −1.57370
\(247\) −0.258081 −0.0164213
\(248\) 2.76365 0.175492
\(249\) −13.1002 −0.830193
\(250\) 26.8395 1.69748
\(251\) −19.6078 −1.23764 −0.618818 0.785534i \(-0.712388\pi\)
−0.618818 + 0.785534i \(0.712388\pi\)
\(252\) 11.4417 0.720758
\(253\) 31.5970 1.98649
\(254\) 27.0365 1.69642
\(255\) −20.3892 −1.27682
\(256\) −23.9583 −1.49740
\(257\) 7.29879 0.455286 0.227643 0.973745i \(-0.426898\pi\)
0.227643 + 0.973745i \(0.426898\pi\)
\(258\) 3.14486 0.195790
\(259\) −4.57164 −0.284068
\(260\) −1.46649 −0.0909478
\(261\) −14.2791 −0.883855
\(262\) 16.7820 1.03679
\(263\) 4.30882 0.265693 0.132847 0.991137i \(-0.457588\pi\)
0.132847 + 0.991137i \(0.457588\pi\)
\(264\) 54.4080 3.34858
\(265\) −2.18646 −0.134313
\(266\) −2.07483 −0.127216
\(267\) 46.5227 2.84714
\(268\) −12.7768 −0.780470
\(269\) 8.30770 0.506530 0.253265 0.967397i \(-0.418496\pi\)
0.253265 + 0.967397i \(0.418496\pi\)
\(270\) −28.9321 −1.76075
\(271\) −16.6422 −1.01094 −0.505472 0.862843i \(-0.668682\pi\)
−0.505472 + 0.862843i \(0.668682\pi\)
\(272\) −4.64242 −0.281488
\(273\) −0.348593 −0.0210978
\(274\) 51.8580 3.13285
\(275\) 1.17264 0.0707130
\(276\) −59.0119 −3.55210
\(277\) −0.350159 −0.0210390 −0.0105195 0.999945i \(-0.503349\pi\)
−0.0105195 + 0.999945i \(0.503349\pi\)
\(278\) 21.2355 1.27362
\(279\) −3.82967 −0.229276
\(280\) −5.11240 −0.305524
\(281\) 17.1334 1.02209 0.511047 0.859553i \(-0.329258\pi\)
0.511047 + 0.859553i \(0.329258\pi\)
\(282\) −63.9276 −3.80683
\(283\) −6.53218 −0.388298 −0.194149 0.980972i \(-0.562194\pi\)
−0.194149 + 0.980972i \(0.562194\pi\)
\(284\) 46.0654 2.73348
\(285\) 8.39792 0.497450
\(286\) −2.38748 −0.141175
\(287\) 2.41056 0.142291
\(288\) 19.4274 1.14477
\(289\) −6.11696 −0.359821
\(290\) 14.7136 0.864010
\(291\) −30.6279 −1.79544
\(292\) −33.1736 −1.94134
\(293\) −34.1937 −1.99762 −0.998809 0.0488000i \(-0.984460\pi\)
−0.998809 + 0.0488000i \(0.984460\pi\)
\(294\) 43.7341 2.55062
\(295\) −5.67505 −0.330414
\(296\) 25.3575 1.47387
\(297\) −30.0709 −1.74489
\(298\) 12.6438 0.732437
\(299\) 1.12289 0.0649382
\(300\) −2.19008 −0.126444
\(301\) −0.307135 −0.0177030
\(302\) 2.35186 0.135334
\(303\) 53.5262 3.07500
\(304\) 1.91212 0.109668
\(305\) −8.73572 −0.500206
\(306\) 38.7189 2.21341
\(307\) 27.4336 1.56572 0.782859 0.622199i \(-0.213760\pi\)
0.782859 + 0.622199i \(0.213760\pi\)
\(308\) −12.2539 −0.698228
\(309\) −15.3094 −0.870919
\(310\) 3.94619 0.224128
\(311\) −29.2038 −1.65600 −0.827998 0.560731i \(-0.810520\pi\)
−0.827998 + 0.560731i \(0.810520\pi\)
\(312\) 1.93354 0.109465
\(313\) 0.0328369 0.00185605 0.000928026 1.00000i \(-0.499705\pi\)
0.000928026 1.00000i \(0.499705\pi\)
\(314\) −40.0180 −2.25835
\(315\) 7.08438 0.399160
\(316\) −7.41885 −0.417343
\(317\) −8.77824 −0.493035 −0.246517 0.969138i \(-0.579286\pi\)
−0.246517 + 0.969138i \(0.579286\pi\)
\(318\) 6.64808 0.372806
\(319\) 15.2927 0.856227
\(320\) −26.1723 −1.46307
\(321\) 40.3931 2.25452
\(322\) 9.02740 0.503078
\(323\) −4.48251 −0.249414
\(324\) 3.29455 0.183030
\(325\) 0.0416731 0.00231161
\(326\) 1.85583 0.102785
\(327\) 18.6192 1.02964
\(328\) −13.3706 −0.738270
\(329\) 6.24334 0.344206
\(330\) 77.6885 4.27661
\(331\) −32.5836 −1.79096 −0.895479 0.445104i \(-0.853167\pi\)
−0.895479 + 0.445104i \(0.853167\pi\)
\(332\) −16.3653 −0.898161
\(333\) −35.1385 −1.92558
\(334\) −23.8906 −1.30724
\(335\) −7.91108 −0.432228
\(336\) 2.58273 0.140899
\(337\) 15.7606 0.858536 0.429268 0.903177i \(-0.358772\pi\)
0.429268 + 0.903177i \(0.358772\pi\)
\(338\) 30.4894 1.65840
\(339\) −13.2044 −0.717163
\(340\) −25.4709 −1.38136
\(341\) 4.10151 0.222109
\(342\) −15.9476 −0.862346
\(343\) −8.81607 −0.476023
\(344\) 1.70358 0.0918511
\(345\) −36.5386 −1.96717
\(346\) −11.2431 −0.604431
\(347\) −25.3683 −1.36184 −0.680920 0.732358i \(-0.738420\pi\)
−0.680920 + 0.732358i \(0.738420\pi\)
\(348\) −28.5613 −1.53105
\(349\) −5.99131 −0.320708 −0.160354 0.987060i \(-0.551264\pi\)
−0.160354 + 0.987060i \(0.551264\pi\)
\(350\) 0.335029 0.0179081
\(351\) −1.06865 −0.0570405
\(352\) −20.8065 −1.10899
\(353\) 21.1371 1.12502 0.562508 0.826792i \(-0.309837\pi\)
0.562508 + 0.826792i \(0.309837\pi\)
\(354\) 17.2554 0.917114
\(355\) 28.5225 1.51382
\(356\) 58.1177 3.08023
\(357\) −6.05458 −0.320443
\(358\) 32.1488 1.69912
\(359\) −23.4806 −1.23926 −0.619629 0.784895i \(-0.712717\pi\)
−0.619629 + 0.784895i \(0.712717\pi\)
\(360\) −39.2949 −2.07102
\(361\) −17.1537 −0.902828
\(362\) 4.64966 0.244381
\(363\) 49.6524 2.60607
\(364\) −0.435475 −0.0228251
\(365\) −20.5402 −1.07512
\(366\) 26.5616 1.38840
\(367\) −21.7027 −1.13287 −0.566437 0.824105i \(-0.691679\pi\)
−0.566437 + 0.824105i \(0.691679\pi\)
\(368\) −8.31947 −0.433682
\(369\) 18.5281 0.964532
\(370\) 36.2076 1.88234
\(371\) −0.649269 −0.0337084
\(372\) −7.66017 −0.397161
\(373\) −7.78919 −0.403309 −0.201655 0.979457i \(-0.564632\pi\)
−0.201655 + 0.979457i \(0.564632\pi\)
\(374\) −41.4673 −2.14422
\(375\) −32.2587 −1.66583
\(376\) −34.6299 −1.78590
\(377\) 0.543468 0.0279900
\(378\) −8.59140 −0.441894
\(379\) 3.56636 0.183192 0.0915958 0.995796i \(-0.470803\pi\)
0.0915958 + 0.995796i \(0.470803\pi\)
\(380\) 10.4910 0.538176
\(381\) −32.4955 −1.66479
\(382\) 31.1377 1.59314
\(383\) 16.5281 0.844547 0.422274 0.906468i \(-0.361232\pi\)
0.422274 + 0.906468i \(0.361232\pi\)
\(384\) 57.5700 2.93786
\(385\) −7.58726 −0.386683
\(386\) 22.5354 1.14702
\(387\) −2.36070 −0.120001
\(388\) −38.2615 −1.94243
\(389\) 31.0412 1.57385 0.786925 0.617048i \(-0.211672\pi\)
0.786925 + 0.617048i \(0.211672\pi\)
\(390\) 2.76087 0.139802
\(391\) 19.5030 0.986309
\(392\) 23.6909 1.19657
\(393\) −20.1704 −1.01746
\(394\) 20.4906 1.03230
\(395\) −4.59356 −0.231127
\(396\) −94.1856 −4.73300
\(397\) −11.7455 −0.589488 −0.294744 0.955576i \(-0.595234\pi\)
−0.294744 + 0.955576i \(0.595234\pi\)
\(398\) 19.1662 0.960713
\(399\) 2.49377 0.124844
\(400\) −0.308756 −0.0154378
\(401\) 8.07233 0.403113 0.201557 0.979477i \(-0.435400\pi\)
0.201557 + 0.979477i \(0.435400\pi\)
\(402\) 24.0542 1.19971
\(403\) 0.145759 0.00726075
\(404\) 66.8668 3.32675
\(405\) 2.03990 0.101363
\(406\) 4.36919 0.216839
\(407\) 37.6328 1.86539
\(408\) 33.5829 1.66260
\(409\) 20.7926 1.02813 0.514065 0.857752i \(-0.328139\pi\)
0.514065 + 0.857752i \(0.328139\pi\)
\(410\) −19.0918 −0.942875
\(411\) −62.3287 −3.07445
\(412\) −19.1250 −0.942221
\(413\) −1.68521 −0.0829236
\(414\) 69.3864 3.41016
\(415\) −10.1329 −0.497406
\(416\) −0.739415 −0.0362528
\(417\) −25.5232 −1.24988
\(418\) 17.0796 0.835390
\(419\) 23.9526 1.17016 0.585081 0.810975i \(-0.301063\pi\)
0.585081 + 0.810975i \(0.301063\pi\)
\(420\) 14.1703 0.691440
\(421\) 32.4255 1.58032 0.790162 0.612898i \(-0.209996\pi\)
0.790162 + 0.612898i \(0.209996\pi\)
\(422\) −15.9329 −0.775601
\(423\) 47.9875 2.33323
\(424\) 3.60130 0.174894
\(425\) 0.723804 0.0351097
\(426\) −86.7247 −4.20182
\(427\) −2.59407 −0.125536
\(428\) 50.4605 2.43910
\(429\) 2.86955 0.138543
\(430\) 2.43253 0.117307
\(431\) −1.92059 −0.0925117 −0.0462558 0.998930i \(-0.514729\pi\)
−0.0462558 + 0.998930i \(0.514729\pi\)
\(432\) 7.91765 0.380938
\(433\) −15.8278 −0.760635 −0.380317 0.924856i \(-0.624185\pi\)
−0.380317 + 0.924856i \(0.624185\pi\)
\(434\) 1.17182 0.0562492
\(435\) −17.6844 −0.847902
\(436\) 23.2597 1.11394
\(437\) −8.03291 −0.384266
\(438\) 62.4540 2.98417
\(439\) 20.8129 0.993344 0.496672 0.867938i \(-0.334555\pi\)
0.496672 + 0.867938i \(0.334555\pi\)
\(440\) 42.0842 2.00629
\(441\) −32.8292 −1.56329
\(442\) −1.47366 −0.0700947
\(443\) −34.4274 −1.63570 −0.817849 0.575433i \(-0.804833\pi\)
−0.817849 + 0.575433i \(0.804833\pi\)
\(444\) −70.2847 −3.33556
\(445\) 35.9849 1.70585
\(446\) 21.7597 1.03035
\(447\) −15.1968 −0.718782
\(448\) −7.77186 −0.367186
\(449\) −16.4141 −0.774629 −0.387314 0.921948i \(-0.626597\pi\)
−0.387314 + 0.921948i \(0.626597\pi\)
\(450\) 2.57510 0.121391
\(451\) −19.8432 −0.934382
\(452\) −16.4954 −0.775877
\(453\) −2.82673 −0.132811
\(454\) 39.7770 1.86683
\(455\) −0.269634 −0.0126406
\(456\) −13.8322 −0.647750
\(457\) 17.1914 0.804179 0.402089 0.915600i \(-0.368284\pi\)
0.402089 + 0.915600i \(0.368284\pi\)
\(458\) 37.4938 1.75197
\(459\) −18.5610 −0.866355
\(460\) −45.6453 −2.12822
\(461\) 11.6355 0.541918 0.270959 0.962591i \(-0.412659\pi\)
0.270959 + 0.962591i \(0.412659\pi\)
\(462\) 23.0696 1.07330
\(463\) 17.2073 0.799692 0.399846 0.916582i \(-0.369064\pi\)
0.399846 + 0.916582i \(0.369064\pi\)
\(464\) −4.02656 −0.186928
\(465\) −4.74297 −0.219950
\(466\) −54.5949 −2.52906
\(467\) 2.87758 0.133159 0.0665793 0.997781i \(-0.478791\pi\)
0.0665793 + 0.997781i \(0.478791\pi\)
\(468\) −3.34714 −0.154722
\(469\) −2.34920 −0.108476
\(470\) −49.4475 −2.28085
\(471\) 48.0981 2.21624
\(472\) 9.34732 0.430245
\(473\) 2.52828 0.116250
\(474\) 13.9670 0.641527
\(475\) −0.298121 −0.0136787
\(476\) −7.56360 −0.346677
\(477\) −4.99041 −0.228495
\(478\) 21.5570 0.985994
\(479\) 18.2131 0.832176 0.416088 0.909324i \(-0.363401\pi\)
0.416088 + 0.909324i \(0.363401\pi\)
\(480\) 24.0605 1.09821
\(481\) 1.33738 0.0609795
\(482\) 7.28723 0.331924
\(483\) −10.8501 −0.493699
\(484\) 62.0275 2.81943
\(485\) −23.6905 −1.07573
\(486\) 33.4948 1.51935
\(487\) 16.8696 0.764432 0.382216 0.924073i \(-0.375161\pi\)
0.382216 + 0.924073i \(0.375161\pi\)
\(488\) 14.3885 0.651338
\(489\) −2.23054 −0.100869
\(490\) 33.8280 1.52819
\(491\) 28.5819 1.28988 0.644942 0.764232i \(-0.276882\pi\)
0.644942 + 0.764232i \(0.276882\pi\)
\(492\) 37.0601 1.67080
\(493\) 9.43930 0.425125
\(494\) 0.606970 0.0273089
\(495\) −58.3172 −2.62116
\(496\) −1.07993 −0.0484901
\(497\) 8.46976 0.379921
\(498\) 30.8099 1.38063
\(499\) 30.3202 1.35732 0.678660 0.734453i \(-0.262561\pi\)
0.678660 + 0.734453i \(0.262561\pi\)
\(500\) −40.2987 −1.80221
\(501\) 28.7144 1.28287
\(502\) 46.1149 2.05821
\(503\) 12.9292 0.576486 0.288243 0.957557i \(-0.406929\pi\)
0.288243 + 0.957557i \(0.406929\pi\)
\(504\) −11.6686 −0.519762
\(505\) 41.4021 1.84237
\(506\) −74.3118 −3.30356
\(507\) −36.6455 −1.62749
\(508\) −40.5945 −1.80109
\(509\) 10.7872 0.478136 0.239068 0.971003i \(-0.423158\pi\)
0.239068 + 0.971003i \(0.423158\pi\)
\(510\) 47.9526 2.12338
\(511\) −6.09942 −0.269823
\(512\) 15.6141 0.690053
\(513\) 7.64493 0.337532
\(514\) −17.1657 −0.757149
\(515\) −11.8417 −0.521807
\(516\) −4.72192 −0.207871
\(517\) −51.3939 −2.26030
\(518\) 10.7519 0.472410
\(519\) 13.5132 0.593162
\(520\) 1.49558 0.0655854
\(521\) −27.3887 −1.19992 −0.599961 0.800029i \(-0.704817\pi\)
−0.599961 + 0.800029i \(0.704817\pi\)
\(522\) 33.5825 1.46987
\(523\) 0.115821 0.00506451 0.00253226 0.999997i \(-0.499194\pi\)
0.00253226 + 0.999997i \(0.499194\pi\)
\(524\) −25.1976 −1.10076
\(525\) −0.402676 −0.0175742
\(526\) −10.1337 −0.441852
\(527\) 2.53163 0.110279
\(528\) −21.2605 −0.925243
\(529\) 11.9505 0.519585
\(530\) 5.14224 0.223365
\(531\) −12.9528 −0.562105
\(532\) 3.11530 0.135065
\(533\) −0.705184 −0.0305449
\(534\) −109.415 −4.73484
\(535\) 31.2438 1.35079
\(536\) 13.0303 0.562822
\(537\) −38.6400 −1.66744
\(538\) −19.5386 −0.842368
\(539\) 35.1595 1.51443
\(540\) 43.4407 1.86939
\(541\) 31.6286 1.35982 0.679909 0.733296i \(-0.262019\pi\)
0.679909 + 0.733296i \(0.262019\pi\)
\(542\) 39.1402 1.68122
\(543\) −5.58849 −0.239825
\(544\) −12.8426 −0.550623
\(545\) 14.4018 0.616905
\(546\) 0.819842 0.0350860
\(547\) 16.7267 0.715180 0.357590 0.933879i \(-0.383599\pi\)
0.357590 + 0.933879i \(0.383599\pi\)
\(548\) −77.8633 −3.32615
\(549\) −19.9386 −0.850957
\(550\) −2.75789 −0.117597
\(551\) −3.88787 −0.165629
\(552\) 60.1824 2.56153
\(553\) −1.36406 −0.0580056
\(554\) 0.823526 0.0349883
\(555\) −43.5184 −1.84725
\(556\) −31.8845 −1.35221
\(557\) 12.6953 0.537919 0.268960 0.963151i \(-0.413320\pi\)
0.268960 + 0.963151i \(0.413320\pi\)
\(558\) 9.00685 0.381290
\(559\) 0.0898492 0.00380022
\(560\) 1.99772 0.0844191
\(561\) 49.8401 2.10425
\(562\) −40.2954 −1.69976
\(563\) 29.1361 1.22794 0.613971 0.789329i \(-0.289571\pi\)
0.613971 + 0.789329i \(0.289571\pi\)
\(564\) 95.9855 4.04172
\(565\) −10.2135 −0.429685
\(566\) 15.3628 0.645746
\(567\) 0.605748 0.0254390
\(568\) −46.9792 −1.97120
\(569\) −24.4091 −1.02328 −0.511642 0.859199i \(-0.670963\pi\)
−0.511642 + 0.859199i \(0.670963\pi\)
\(570\) −19.7508 −0.827268
\(571\) 22.8812 0.957547 0.478773 0.877939i \(-0.341082\pi\)
0.478773 + 0.877939i \(0.341082\pi\)
\(572\) 3.58474 0.149885
\(573\) −37.4248 −1.56344
\(574\) −5.66931 −0.236632
\(575\) 1.29710 0.0540927
\(576\) −59.7361 −2.48900
\(577\) −25.9784 −1.08150 −0.540748 0.841184i \(-0.681859\pi\)
−0.540748 + 0.841184i \(0.681859\pi\)
\(578\) 14.3863 0.598389
\(579\) −27.0856 −1.12564
\(580\) −22.0920 −0.917320
\(581\) −3.00898 −0.124833
\(582\) 72.0326 2.98585
\(583\) 5.34465 0.221353
\(584\) 33.8316 1.39996
\(585\) −2.07246 −0.0856858
\(586\) 80.4188 3.32207
\(587\) −15.6146 −0.644485 −0.322243 0.946657i \(-0.604437\pi\)
−0.322243 + 0.946657i \(0.604437\pi\)
\(588\) −65.6655 −2.70800
\(589\) −1.04273 −0.0429649
\(590\) 13.3469 0.549484
\(591\) −24.6279 −1.01306
\(592\) −9.90869 −0.407245
\(593\) 14.6430 0.601315 0.300658 0.953732i \(-0.402794\pi\)
0.300658 + 0.953732i \(0.402794\pi\)
\(594\) 70.7226 2.90178
\(595\) −4.68318 −0.191992
\(596\) −18.9843 −0.777629
\(597\) −23.0361 −0.942803
\(598\) −2.64087 −0.107993
\(599\) 41.3504 1.68953 0.844766 0.535135i \(-0.179739\pi\)
0.844766 + 0.535135i \(0.179739\pi\)
\(600\) 2.23352 0.0911830
\(601\) −9.15808 −0.373566 −0.186783 0.982401i \(-0.559806\pi\)
−0.186783 + 0.982401i \(0.559806\pi\)
\(602\) 0.722340 0.0294404
\(603\) −18.0564 −0.735313
\(604\) −3.53125 −0.143685
\(605\) 38.4058 1.56142
\(606\) −125.886 −5.11378
\(607\) 30.0754 1.22072 0.610362 0.792122i \(-0.291024\pi\)
0.610362 + 0.792122i \(0.291024\pi\)
\(608\) 5.28963 0.214523
\(609\) −5.25139 −0.212797
\(610\) 20.5452 0.831851
\(611\) −1.82642 −0.0738891
\(612\) −58.1353 −2.34998
\(613\) 4.05911 0.163946 0.0819731 0.996635i \(-0.473878\pi\)
0.0819731 + 0.996635i \(0.473878\pi\)
\(614\) −64.5201 −2.60382
\(615\) 22.9466 0.925298
\(616\) 12.4969 0.503515
\(617\) 4.68419 0.188578 0.0942892 0.995545i \(-0.469942\pi\)
0.0942892 + 0.995545i \(0.469942\pi\)
\(618\) 36.0055 1.44835
\(619\) −13.5790 −0.545786 −0.272893 0.962044i \(-0.587981\pi\)
−0.272893 + 0.962044i \(0.587981\pi\)
\(620\) −5.92509 −0.237957
\(621\) −33.2624 −1.33477
\(622\) 68.6833 2.75395
\(623\) 10.6857 0.428115
\(624\) −0.755549 −0.0302462
\(625\) −23.8548 −0.954193
\(626\) −0.0772279 −0.00308665
\(627\) −20.5282 −0.819816
\(628\) 60.0859 2.39769
\(629\) 23.2285 0.926183
\(630\) −16.6615 −0.663810
\(631\) −24.0659 −0.958048 −0.479024 0.877802i \(-0.659009\pi\)
−0.479024 + 0.877802i \(0.659009\pi\)
\(632\) 7.56601 0.300960
\(633\) 19.1499 0.761141
\(634\) 20.6452 0.819926
\(635\) −25.1350 −0.997454
\(636\) −9.98190 −0.395808
\(637\) 1.24949 0.0495066
\(638\) −35.9663 −1.42392
\(639\) 65.1003 2.57533
\(640\) 44.5300 1.76020
\(641\) 25.8986 1.02293 0.511467 0.859303i \(-0.329102\pi\)
0.511467 + 0.859303i \(0.329102\pi\)
\(642\) −94.9990 −3.74931
\(643\) 22.7745 0.898137 0.449069 0.893497i \(-0.351756\pi\)
0.449069 + 0.893497i \(0.351756\pi\)
\(644\) −13.5544 −0.534118
\(645\) −2.92368 −0.115120
\(646\) 10.5422 0.414779
\(647\) −15.6913 −0.616890 −0.308445 0.951242i \(-0.599809\pi\)
−0.308445 + 0.951242i \(0.599809\pi\)
\(648\) −3.35990 −0.131989
\(649\) 13.8723 0.544535
\(650\) −0.0980093 −0.00384424
\(651\) −1.40843 −0.0552006
\(652\) −2.78647 −0.109127
\(653\) 45.0422 1.76264 0.881319 0.472523i \(-0.156657\pi\)
0.881319 + 0.472523i \(0.156657\pi\)
\(654\) −43.7897 −1.71231
\(655\) −15.6017 −0.609609
\(656\) 5.22471 0.203991
\(657\) −46.8814 −1.82902
\(658\) −14.6835 −0.572421
\(659\) 35.2831 1.37444 0.687218 0.726451i \(-0.258832\pi\)
0.687218 + 0.726451i \(0.258832\pi\)
\(660\) −116.647 −4.54048
\(661\) −1.57733 −0.0613510 −0.0306755 0.999529i \(-0.509766\pi\)
−0.0306755 + 0.999529i \(0.509766\pi\)
\(662\) 76.6322 2.97839
\(663\) 1.77120 0.0687879
\(664\) 16.6899 0.647693
\(665\) 1.92891 0.0747999
\(666\) 82.6409 3.20227
\(667\) 16.9158 0.654981
\(668\) 35.8711 1.38789
\(669\) −26.1532 −1.01114
\(670\) 18.6058 0.718803
\(671\) 21.3539 0.824358
\(672\) 7.14477 0.275615
\(673\) 34.5383 1.33135 0.665677 0.746240i \(-0.268143\pi\)
0.665677 + 0.746240i \(0.268143\pi\)
\(674\) −37.0668 −1.42776
\(675\) −1.23445 −0.0475140
\(676\) −45.7789 −1.76073
\(677\) 4.81359 0.185001 0.0925006 0.995713i \(-0.470514\pi\)
0.0925006 + 0.995713i \(0.470514\pi\)
\(678\) 31.0548 1.19265
\(679\) −7.03489 −0.269974
\(680\) 25.9761 0.996140
\(681\) −47.8084 −1.83202
\(682\) −9.64619 −0.369372
\(683\) 32.8625 1.25745 0.628724 0.777628i \(-0.283577\pi\)
0.628724 + 0.777628i \(0.283577\pi\)
\(684\) 23.9448 0.915553
\(685\) −48.2108 −1.84204
\(686\) 20.7342 0.791634
\(687\) −45.0642 −1.71931
\(688\) −0.665693 −0.0253793
\(689\) 0.189937 0.00723602
\(690\) 85.9338 3.27144
\(691\) 18.4093 0.700323 0.350161 0.936689i \(-0.386127\pi\)
0.350161 + 0.936689i \(0.386127\pi\)
\(692\) 16.8811 0.641724
\(693\) −17.3173 −0.657830
\(694\) 59.6626 2.26476
\(695\) −19.7420 −0.748858
\(696\) 29.1278 1.10409
\(697\) −12.2481 −0.463930
\(698\) 14.0907 0.533342
\(699\) 65.6182 2.48191
\(700\) −0.503037 −0.0190130
\(701\) 32.5235 1.22840 0.614199 0.789151i \(-0.289479\pi\)
0.614199 + 0.789151i \(0.289479\pi\)
\(702\) 2.51332 0.0948593
\(703\) −9.56739 −0.360841
\(704\) 63.9764 2.41120
\(705\) 59.4316 2.23832
\(706\) −49.7116 −1.87092
\(707\) 12.2944 0.462377
\(708\) −25.9085 −0.973700
\(709\) −20.2299 −0.759748 −0.379874 0.925038i \(-0.624033\pi\)
−0.379874 + 0.925038i \(0.624033\pi\)
\(710\) −67.0809 −2.51750
\(711\) −10.4844 −0.393196
\(712\) −59.2705 −2.22126
\(713\) 4.53682 0.169905
\(714\) 14.2395 0.532901
\(715\) 2.21957 0.0830074
\(716\) −48.2705 −1.80395
\(717\) −25.9096 −0.967612
\(718\) 55.2231 2.06091
\(719\) 5.26701 0.196426 0.0982131 0.995165i \(-0.468687\pi\)
0.0982131 + 0.995165i \(0.468687\pi\)
\(720\) 15.3549 0.572242
\(721\) −3.51639 −0.130957
\(722\) 40.3432 1.50142
\(723\) −8.75862 −0.325736
\(724\) −6.98134 −0.259459
\(725\) 0.627785 0.0233154
\(726\) −116.776 −4.33395
\(727\) 32.8962 1.22005 0.610027 0.792381i \(-0.291159\pi\)
0.610027 + 0.792381i \(0.291159\pi\)
\(728\) 0.444112 0.0164599
\(729\) −43.0567 −1.59469
\(730\) 48.3078 1.78795
\(731\) 1.56056 0.0577193
\(732\) −39.8815 −1.47406
\(733\) −50.0303 −1.84791 −0.923956 0.382498i \(-0.875064\pi\)
−0.923956 + 0.382498i \(0.875064\pi\)
\(734\) 51.0419 1.88399
\(735\) −40.6583 −1.49970
\(736\) −23.0147 −0.848333
\(737\) 19.3381 0.712328
\(738\) −43.5754 −1.60403
\(739\) −3.31631 −0.121993 −0.0609963 0.998138i \(-0.519428\pi\)
−0.0609963 + 0.998138i \(0.519428\pi\)
\(740\) −54.3647 −1.99849
\(741\) −0.729525 −0.0267998
\(742\) 1.52699 0.0560576
\(743\) 28.8675 1.05905 0.529523 0.848296i \(-0.322371\pi\)
0.529523 + 0.848296i \(0.322371\pi\)
\(744\) 7.81211 0.286406
\(745\) −11.7546 −0.430655
\(746\) 18.3191 0.670710
\(747\) −23.1276 −0.846195
\(748\) 62.2620 2.27653
\(749\) 9.27785 0.339005
\(750\) 75.8679 2.77031
\(751\) 3.02544 0.110400 0.0551999 0.998475i \(-0.482420\pi\)
0.0551999 + 0.998475i \(0.482420\pi\)
\(752\) 13.5320 0.493460
\(753\) −55.4261 −2.01984
\(754\) −1.27816 −0.0465479
\(755\) −2.18646 −0.0795733
\(756\) 12.8997 0.469159
\(757\) 0.405510 0.0147385 0.00736926 0.999973i \(-0.497654\pi\)
0.00736926 + 0.999973i \(0.497654\pi\)
\(758\) −8.38758 −0.304651
\(759\) 89.3162 3.24197
\(760\) −10.6991 −0.388096
\(761\) −46.7594 −1.69503 −0.847513 0.530774i \(-0.821901\pi\)
−0.847513 + 0.530774i \(0.821901\pi\)
\(762\) 76.4249 2.76858
\(763\) 4.27662 0.154824
\(764\) −46.7524 −1.69144
\(765\) −35.9958 −1.30143
\(766\) −38.8718 −1.40450
\(767\) 0.492990 0.0178008
\(768\) −67.7238 −2.44377
\(769\) 41.0181 1.47915 0.739575 0.673075i \(-0.235027\pi\)
0.739575 + 0.673075i \(0.235027\pi\)
\(770\) 17.8442 0.643060
\(771\) 20.6317 0.743033
\(772\) −33.8363 −1.21779
\(773\) −30.9734 −1.11403 −0.557017 0.830501i \(-0.688054\pi\)
−0.557017 + 0.830501i \(0.688054\pi\)
\(774\) 5.55205 0.199564
\(775\) 0.168372 0.00604812
\(776\) 39.0204 1.40075
\(777\) −12.9228 −0.463603
\(778\) −73.0046 −2.61734
\(779\) 5.04475 0.180747
\(780\) −4.14537 −0.148428
\(781\) −69.7213 −2.49483
\(782\) −45.8684 −1.64025
\(783\) −16.0988 −0.575323
\(784\) −9.25748 −0.330624
\(785\) 37.2035 1.32785
\(786\) 47.4381 1.69206
\(787\) −9.16751 −0.326787 −0.163393 0.986561i \(-0.552244\pi\)
−0.163393 + 0.986561i \(0.552244\pi\)
\(788\) −30.7660 −1.09599
\(789\) 12.1799 0.433615
\(790\) 10.8034 0.384368
\(791\) −3.03290 −0.107837
\(792\) 96.0538 3.41312
\(793\) 0.758869 0.0269482
\(794\) 27.6237 0.980329
\(795\) −6.18053 −0.219201
\(796\) −28.7775 −1.01999
\(797\) 28.2935 1.00221 0.501103 0.865388i \(-0.332928\pi\)
0.501103 + 0.865388i \(0.332928\pi\)
\(798\) −5.86499 −0.207618
\(799\) −31.7225 −1.12226
\(800\) −0.854132 −0.0301981
\(801\) 82.1327 2.90202
\(802\) −18.9850 −0.670384
\(803\) 50.2092 1.77184
\(804\) −36.1167 −1.27374
\(805\) −8.39252 −0.295797
\(806\) −0.342804 −0.0120748
\(807\) 23.4837 0.826664
\(808\) −68.1931 −2.39902
\(809\) −29.1140 −1.02359 −0.511797 0.859107i \(-0.671020\pi\)
−0.511797 + 0.859107i \(0.671020\pi\)
\(810\) −4.79755 −0.168569
\(811\) −4.21551 −0.148027 −0.0740133 0.997257i \(-0.523581\pi\)
−0.0740133 + 0.997257i \(0.523581\pi\)
\(812\) −6.56022 −0.230219
\(813\) −47.0431 −1.64987
\(814\) −88.5071 −3.10217
\(815\) −1.72531 −0.0604350
\(816\) −13.1229 −0.459392
\(817\) −0.642764 −0.0224875
\(818\) −48.9014 −1.70980
\(819\) −0.615418 −0.0215044
\(820\) 28.6657 1.00105
\(821\) −11.1721 −0.389909 −0.194954 0.980812i \(-0.562456\pi\)
−0.194954 + 0.980812i \(0.562456\pi\)
\(822\) 146.589 5.11286
\(823\) −7.66442 −0.267165 −0.133582 0.991038i \(-0.542648\pi\)
−0.133582 + 0.991038i \(0.542648\pi\)
\(824\) 19.5043 0.679466
\(825\) 3.31474 0.115405
\(826\) 3.96337 0.137903
\(827\) −37.4183 −1.30116 −0.650581 0.759437i \(-0.725475\pi\)
−0.650581 + 0.759437i \(0.725475\pi\)
\(828\) −104.182 −3.62057
\(829\) 21.2962 0.739648 0.369824 0.929102i \(-0.379418\pi\)
0.369824 + 0.929102i \(0.379418\pi\)
\(830\) 23.8313 0.827195
\(831\) −0.989806 −0.0343360
\(832\) 2.27358 0.0788221
\(833\) 21.7019 0.751928
\(834\) 60.0271 2.07857
\(835\) 22.2104 0.768623
\(836\) −25.6445 −0.886934
\(837\) −4.31770 −0.149241
\(838\) −56.3333 −1.94600
\(839\) 39.7046 1.37076 0.685378 0.728188i \(-0.259637\pi\)
0.685378 + 0.728188i \(0.259637\pi\)
\(840\) −14.4514 −0.498620
\(841\) −20.8129 −0.717686
\(842\) −76.2604 −2.62811
\(843\) 48.4316 1.66807
\(844\) 23.9228 0.823456
\(845\) −28.3451 −0.975100
\(846\) −112.860 −3.88021
\(847\) 11.4046 0.391867
\(848\) −1.40724 −0.0483249
\(849\) −18.4647 −0.633707
\(850\) −1.70229 −0.0583880
\(851\) 41.6268 1.42695
\(852\) 130.215 4.46108
\(853\) 39.6051 1.35605 0.678027 0.735037i \(-0.262835\pi\)
0.678027 + 0.735037i \(0.262835\pi\)
\(854\) 6.10090 0.208769
\(855\) 14.8260 0.507038
\(856\) −51.4614 −1.75891
\(857\) −31.1748 −1.06491 −0.532455 0.846458i \(-0.678730\pi\)
−0.532455 + 0.846458i \(0.678730\pi\)
\(858\) −6.74877 −0.230399
\(859\) −11.6880 −0.398790 −0.199395 0.979919i \(-0.563898\pi\)
−0.199395 + 0.979919i \(0.563898\pi\)
\(860\) −3.65237 −0.124545
\(861\) 6.81401 0.232221
\(862\) 4.51697 0.153849
\(863\) −49.8343 −1.69638 −0.848189 0.529693i \(-0.822307\pi\)
−0.848189 + 0.529693i \(0.822307\pi\)
\(864\) 21.9031 0.745160
\(865\) 10.4523 0.355390
\(866\) 37.2248 1.26495
\(867\) −17.2910 −0.587234
\(868\) −1.75946 −0.0597198
\(869\) 11.2286 0.380906
\(870\) 41.5913 1.41008
\(871\) 0.687233 0.0232860
\(872\) −23.7211 −0.803298
\(873\) −54.0716 −1.83005
\(874\) 18.8923 0.639041
\(875\) −7.40946 −0.250486
\(876\) −93.7729 −3.16829
\(877\) −37.3205 −1.26022 −0.630111 0.776505i \(-0.716991\pi\)
−0.630111 + 0.776505i \(0.716991\pi\)
\(878\) −48.9490 −1.65195
\(879\) −96.6564 −3.26014
\(880\) −16.4448 −0.554355
\(881\) 25.0086 0.842560 0.421280 0.906931i \(-0.361581\pi\)
0.421280 + 0.906931i \(0.361581\pi\)
\(882\) 77.2097 2.59978
\(883\) −37.7411 −1.27009 −0.635045 0.772475i \(-0.719019\pi\)
−0.635045 + 0.772475i \(0.719019\pi\)
\(884\) 2.21265 0.0744195
\(885\) −16.0418 −0.539240
\(886\) 80.9686 2.72019
\(887\) 16.8898 0.567102 0.283551 0.958957i \(-0.408487\pi\)
0.283551 + 0.958957i \(0.408487\pi\)
\(888\) 71.6787 2.40538
\(889\) −7.46386 −0.250330
\(890\) −84.6316 −2.83686
\(891\) −4.98639 −0.167050
\(892\) −32.6715 −1.09392
\(893\) 13.0659 0.437233
\(894\) 35.7407 1.19535
\(895\) −29.8878 −0.999038
\(896\) 13.2232 0.441756
\(897\) 3.17410 0.105980
\(898\) 38.6037 1.28822
\(899\) 2.19578 0.0732335
\(900\) −3.86644 −0.128881
\(901\) 3.29894 0.109904
\(902\) 46.6686 1.55389
\(903\) −0.868189 −0.0288915
\(904\) 16.8226 0.559510
\(905\) −4.32266 −0.143690
\(906\) 6.64808 0.220868
\(907\) 18.6504 0.619278 0.309639 0.950854i \(-0.399792\pi\)
0.309639 + 0.950854i \(0.399792\pi\)
\(908\) −59.7240 −1.98201
\(909\) 94.4970 3.13427
\(910\) 0.634142 0.0210216
\(911\) 9.09311 0.301268 0.150634 0.988590i \(-0.451868\pi\)
0.150634 + 0.988590i \(0.451868\pi\)
\(912\) 5.40505 0.178979
\(913\) 24.7693 0.819744
\(914\) −40.4318 −1.33736
\(915\) −24.6935 −0.816343
\(916\) −56.2958 −1.86007
\(917\) −4.63293 −0.152993
\(918\) 43.6530 1.44076
\(919\) 18.3980 0.606896 0.303448 0.952848i \(-0.401862\pi\)
0.303448 + 0.952848i \(0.401862\pi\)
\(920\) 46.5507 1.53473
\(921\) 77.5474 2.55528
\(922\) −27.3650 −0.901219
\(923\) −2.47774 −0.0815558
\(924\) −34.6384 −1.13952
\(925\) 1.54487 0.0507952
\(926\) −40.4692 −1.32990
\(927\) −27.0277 −0.887706
\(928\) −11.1389 −0.365654
\(929\) −11.4362 −0.375210 −0.187605 0.982245i \(-0.560072\pi\)
−0.187605 + 0.982245i \(0.560072\pi\)
\(930\) 11.1548 0.365781
\(931\) −8.93861 −0.292951
\(932\) 81.9726 2.68510
\(933\) −82.5513 −2.70261
\(934\) −6.76767 −0.221445
\(935\) 38.5510 1.26075
\(936\) 3.41353 0.111575
\(937\) −31.2796 −1.02186 −0.510929 0.859623i \(-0.670699\pi\)
−0.510929 + 0.859623i \(0.670699\pi\)
\(938\) 5.52498 0.180397
\(939\) 0.0928212 0.00302910
\(940\) 74.2441 2.42157
\(941\) 25.2041 0.821629 0.410814 0.911719i \(-0.365244\pi\)
0.410814 + 0.911719i \(0.365244\pi\)
\(942\) −113.120 −3.68565
\(943\) −21.9493 −0.714766
\(944\) −3.65256 −0.118881
\(945\) 7.98717 0.259823
\(946\) −5.94615 −0.193326
\(947\) −11.3899 −0.370123 −0.185061 0.982727i \(-0.559248\pi\)
−0.185061 + 0.982727i \(0.559248\pi\)
\(948\) −20.9711 −0.681110
\(949\) 1.78432 0.0579216
\(950\) 0.701139 0.0227480
\(951\) −24.8137 −0.804640
\(952\) 7.71362 0.250000
\(953\) −7.75782 −0.251300 −0.125650 0.992075i \(-0.540102\pi\)
−0.125650 + 0.992075i \(0.540102\pi\)
\(954\) 11.7368 0.379992
\(955\) −28.9478 −0.936730
\(956\) −32.3672 −1.04683
\(957\) 43.2284 1.39737
\(958\) −42.8346 −1.38392
\(959\) −14.3162 −0.462295
\(960\) −73.9820 −2.38776
\(961\) −30.4111 −0.981003
\(962\) −3.14534 −0.101410
\(963\) 71.3114 2.29798
\(964\) −10.9416 −0.352404
\(965\) −20.9505 −0.674421
\(966\) 25.5180 0.821030
\(967\) 18.8604 0.606510 0.303255 0.952909i \(-0.401927\pi\)
0.303255 + 0.952909i \(0.401927\pi\)
\(968\) −63.2578 −2.03318
\(969\) −12.6709 −0.407047
\(970\) 55.7167 1.78896
\(971\) −3.56158 −0.114296 −0.0571482 0.998366i \(-0.518201\pi\)
−0.0571482 + 0.998366i \(0.518201\pi\)
\(972\) −50.2915 −1.61310
\(973\) −5.86240 −0.187940
\(974\) −39.6748 −1.27126
\(975\) 0.117799 0.00377257
\(976\) −5.62246 −0.179971
\(977\) −10.0827 −0.322573 −0.161287 0.986908i \(-0.551564\pi\)
−0.161287 + 0.986908i \(0.551564\pi\)
\(978\) 5.24593 0.167746
\(979\) −87.9628 −2.81130
\(980\) −50.7918 −1.62248
\(981\) 32.8709 1.04949
\(982\) −67.2207 −2.14510
\(983\) 15.1214 0.482298 0.241149 0.970488i \(-0.422476\pi\)
0.241149 + 0.970488i \(0.422476\pi\)
\(984\) −37.7952 −1.20487
\(985\) −19.0495 −0.606968
\(986\) −22.1999 −0.706990
\(987\) 17.6482 0.561749
\(988\) −0.911348 −0.0289939
\(989\) 2.79661 0.0889269
\(990\) 137.154 4.35904
\(991\) −40.3158 −1.28067 −0.640337 0.768094i \(-0.721205\pi\)
−0.640337 + 0.768094i \(0.721205\pi\)
\(992\) −2.98747 −0.0948523
\(993\) −92.1051 −2.92287
\(994\) −19.9197 −0.631815
\(995\) −17.8182 −0.564876
\(996\) −46.2602 −1.46581
\(997\) −45.7915 −1.45023 −0.725116 0.688627i \(-0.758214\pi\)
−0.725116 + 0.688627i \(0.758214\pi\)
\(998\) −71.3090 −2.25725
\(999\) −39.6163 −1.25341
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.1.17 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.17 153 1.1 even 1 trivial