Properties

Label 4003.2.a.c.1.4
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} +O(q^{10})\) \(q-2.64748 q^{2} +2.89261 q^{3} +5.00915 q^{4} +3.62616 q^{5} -7.65814 q^{6} +1.08314 q^{7} -7.96667 q^{8} +5.36721 q^{9} -9.60018 q^{10} -4.28161 q^{11} +14.4895 q^{12} +5.59638 q^{13} -2.86759 q^{14} +10.4891 q^{15} +11.0733 q^{16} +1.81985 q^{17} -14.2096 q^{18} -7.75770 q^{19} +18.1640 q^{20} +3.13311 q^{21} +11.3355 q^{22} +4.67094 q^{23} -23.0445 q^{24} +8.14901 q^{25} -14.8163 q^{26} +6.84743 q^{27} +5.42561 q^{28} +9.07311 q^{29} -27.7696 q^{30} +5.85538 q^{31} -13.3830 q^{32} -12.3850 q^{33} -4.81801 q^{34} +3.92764 q^{35} +26.8852 q^{36} -0.0758430 q^{37} +20.5383 q^{38} +16.1882 q^{39} -28.8884 q^{40} +8.62838 q^{41} -8.29483 q^{42} -5.57989 q^{43} -21.4472 q^{44} +19.4624 q^{45} -12.3662 q^{46} -10.9631 q^{47} +32.0308 q^{48} -5.82681 q^{49} -21.5744 q^{50} +5.26412 q^{51} +28.0331 q^{52} +4.13375 q^{53} -18.1284 q^{54} -15.5258 q^{55} -8.62902 q^{56} -22.4400 q^{57} -24.0209 q^{58} +14.6491 q^{59} +52.5414 q^{60} -11.0384 q^{61} -15.5020 q^{62} +5.81344 q^{63} +13.2846 q^{64} +20.2933 q^{65} +32.7891 q^{66} -6.78760 q^{67} +9.11589 q^{68} +13.5112 q^{69} -10.3983 q^{70} -5.11064 q^{71} -42.7588 q^{72} -13.7830 q^{73} +0.200793 q^{74} +23.5719 q^{75} -38.8595 q^{76} -4.63758 q^{77} -42.8578 q^{78} -5.34405 q^{79} +40.1535 q^{80} +3.70534 q^{81} -22.8435 q^{82} -10.2636 q^{83} +15.6942 q^{84} +6.59905 q^{85} +14.7727 q^{86} +26.2450 q^{87} +34.1101 q^{88} +0.730464 q^{89} -51.5262 q^{90} +6.06166 q^{91} +23.3975 q^{92} +16.9374 q^{93} +29.0247 q^{94} -28.1306 q^{95} -38.7119 q^{96} +9.43142 q^{97} +15.4264 q^{98} -22.9803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64748 −1.87205 −0.936026 0.351932i \(-0.885525\pi\)
−0.936026 + 0.351932i \(0.885525\pi\)
\(3\) 2.89261 1.67005 0.835026 0.550211i \(-0.185453\pi\)
0.835026 + 0.550211i \(0.185453\pi\)
\(4\) 5.00915 2.50458
\(5\) 3.62616 1.62167 0.810833 0.585277i \(-0.199014\pi\)
0.810833 + 0.585277i \(0.199014\pi\)
\(6\) −7.65814 −3.12642
\(7\) 1.08314 0.409388 0.204694 0.978826i \(-0.434380\pi\)
0.204694 + 0.978826i \(0.434380\pi\)
\(8\) −7.96667 −2.81664
\(9\) 5.36721 1.78907
\(10\) −9.60018 −3.03584
\(11\) −4.28161 −1.29095 −0.645476 0.763780i \(-0.723341\pi\)
−0.645476 + 0.763780i \(0.723341\pi\)
\(12\) 14.4895 4.18277
\(13\) 5.59638 1.55216 0.776078 0.630637i \(-0.217206\pi\)
0.776078 + 0.630637i \(0.217206\pi\)
\(14\) −2.86759 −0.766396
\(15\) 10.4891 2.70827
\(16\) 11.0733 2.76833
\(17\) 1.81985 0.441378 0.220689 0.975344i \(-0.429169\pi\)
0.220689 + 0.975344i \(0.429169\pi\)
\(18\) −14.2096 −3.34923
\(19\) −7.75770 −1.77974 −0.889869 0.456217i \(-0.849204\pi\)
−0.889869 + 0.456217i \(0.849204\pi\)
\(20\) 18.1640 4.06159
\(21\) 3.13311 0.683700
\(22\) 11.3355 2.41673
\(23\) 4.67094 0.973959 0.486979 0.873413i \(-0.338099\pi\)
0.486979 + 0.873413i \(0.338099\pi\)
\(24\) −23.0445 −4.70394
\(25\) 8.14901 1.62980
\(26\) −14.8163 −2.90571
\(27\) 6.84743 1.31779
\(28\) 5.42561 1.02534
\(29\) 9.07311 1.68483 0.842417 0.538826i \(-0.181132\pi\)
0.842417 + 0.538826i \(0.181132\pi\)
\(30\) −27.7696 −5.07001
\(31\) 5.85538 1.05166 0.525829 0.850590i \(-0.323755\pi\)
0.525829 + 0.850590i \(0.323755\pi\)
\(32\) −13.3830 −2.36580
\(33\) −12.3850 −2.15596
\(34\) −4.81801 −0.826282
\(35\) 3.92764 0.663892
\(36\) 26.8852 4.48087
\(37\) −0.0758430 −0.0124685 −0.00623425 0.999981i \(-0.501984\pi\)
−0.00623425 + 0.999981i \(0.501984\pi\)
\(38\) 20.5383 3.33176
\(39\) 16.1882 2.59218
\(40\) −28.8884 −4.56766
\(41\) 8.62838 1.34753 0.673764 0.738947i \(-0.264677\pi\)
0.673764 + 0.738947i \(0.264677\pi\)
\(42\) −8.29483 −1.27992
\(43\) −5.57989 −0.850925 −0.425463 0.904976i \(-0.639889\pi\)
−0.425463 + 0.904976i \(0.639889\pi\)
\(44\) −21.4472 −3.23329
\(45\) 19.4624 2.90128
\(46\) −12.3662 −1.82330
\(47\) −10.9631 −1.59914 −0.799569 0.600574i \(-0.794939\pi\)
−0.799569 + 0.600574i \(0.794939\pi\)
\(48\) 32.0308 4.62325
\(49\) −5.82681 −0.832401
\(50\) −21.5744 −3.05107
\(51\) 5.26412 0.737124
\(52\) 28.0331 3.88749
\(53\) 4.13375 0.567814 0.283907 0.958852i \(-0.408369\pi\)
0.283907 + 0.958852i \(0.408369\pi\)
\(54\) −18.1284 −2.46697
\(55\) −15.5258 −2.09349
\(56\) −8.62902 −1.15310
\(57\) −22.4400 −2.97225
\(58\) −24.0209 −3.15410
\(59\) 14.6491 1.90716 0.953578 0.301147i \(-0.0973694\pi\)
0.953578 + 0.301147i \(0.0973694\pi\)
\(60\) 52.5414 6.78306
\(61\) −11.0384 −1.41332 −0.706658 0.707555i \(-0.749798\pi\)
−0.706658 + 0.707555i \(0.749798\pi\)
\(62\) −15.5020 −1.96876
\(63\) 5.81344 0.732425
\(64\) 13.2846 1.66058
\(65\) 20.2933 2.51708
\(66\) 32.7891 4.03606
\(67\) −6.78760 −0.829237 −0.414618 0.909995i \(-0.636085\pi\)
−0.414618 + 0.909995i \(0.636085\pi\)
\(68\) 9.11589 1.10546
\(69\) 13.5112 1.62656
\(70\) −10.3983 −1.24284
\(71\) −5.11064 −0.606521 −0.303261 0.952908i \(-0.598075\pi\)
−0.303261 + 0.952908i \(0.598075\pi\)
\(72\) −42.7588 −5.03918
\(73\) −13.7830 −1.61317 −0.806587 0.591116i \(-0.798688\pi\)
−0.806587 + 0.591116i \(0.798688\pi\)
\(74\) 0.200793 0.0233417
\(75\) 23.5719 2.72185
\(76\) −38.8595 −4.45749
\(77\) −4.63758 −0.528501
\(78\) −42.8578 −4.85269
\(79\) −5.34405 −0.601252 −0.300626 0.953742i \(-0.597196\pi\)
−0.300626 + 0.953742i \(0.597196\pi\)
\(80\) 40.1535 4.48930
\(81\) 3.70534 0.411704
\(82\) −22.8435 −2.52264
\(83\) −10.2636 −1.12658 −0.563288 0.826261i \(-0.690464\pi\)
−0.563288 + 0.826261i \(0.690464\pi\)
\(84\) 15.6942 1.71238
\(85\) 6.59905 0.715768
\(86\) 14.7727 1.59298
\(87\) 26.2450 2.81376
\(88\) 34.1101 3.63615
\(89\) 0.730464 0.0774290 0.0387145 0.999250i \(-0.487674\pi\)
0.0387145 + 0.999250i \(0.487674\pi\)
\(90\) −51.5262 −5.43134
\(91\) 6.06166 0.635434
\(92\) 23.3975 2.43935
\(93\) 16.9374 1.75632
\(94\) 29.0247 2.99367
\(95\) −28.1306 −2.88614
\(96\) −38.7119 −3.95101
\(97\) 9.43142 0.957616 0.478808 0.877920i \(-0.341069\pi\)
0.478808 + 0.877920i \(0.341069\pi\)
\(98\) 15.4264 1.55830
\(99\) −22.9803 −2.30961
\(100\) 40.8196 4.08196
\(101\) −6.89393 −0.685972 −0.342986 0.939341i \(-0.611438\pi\)
−0.342986 + 0.939341i \(0.611438\pi\)
\(102\) −13.9366 −1.37993
\(103\) 12.3202 1.21395 0.606974 0.794722i \(-0.292383\pi\)
0.606974 + 0.794722i \(0.292383\pi\)
\(104\) −44.5845 −4.37187
\(105\) 11.3611 1.10873
\(106\) −10.9440 −1.06298
\(107\) 10.0047 0.967190 0.483595 0.875292i \(-0.339331\pi\)
0.483595 + 0.875292i \(0.339331\pi\)
\(108\) 34.2998 3.30050
\(109\) −1.52346 −0.145921 −0.0729603 0.997335i \(-0.523245\pi\)
−0.0729603 + 0.997335i \(0.523245\pi\)
\(110\) 41.1042 3.91913
\(111\) −0.219384 −0.0208230
\(112\) 11.9939 1.13332
\(113\) 3.01613 0.283734 0.141867 0.989886i \(-0.454690\pi\)
0.141867 + 0.989886i \(0.454690\pi\)
\(114\) 59.4095 5.56421
\(115\) 16.9376 1.57944
\(116\) 45.4486 4.21980
\(117\) 30.0369 2.77692
\(118\) −38.7833 −3.57029
\(119\) 1.97115 0.180695
\(120\) −83.5630 −7.62822
\(121\) 7.33214 0.666559
\(122\) 29.2238 2.64580
\(123\) 24.9586 2.25044
\(124\) 29.3305 2.63396
\(125\) 11.4188 1.02133
\(126\) −15.3910 −1.37114
\(127\) −0.197600 −0.0175341 −0.00876707 0.999962i \(-0.502791\pi\)
−0.00876707 + 0.999962i \(0.502791\pi\)
\(128\) −8.40482 −0.742889
\(129\) −16.1405 −1.42109
\(130\) −53.7262 −4.71210
\(131\) 6.83446 0.597130 0.298565 0.954389i \(-0.403492\pi\)
0.298565 + 0.954389i \(0.403492\pi\)
\(132\) −62.0385 −5.39976
\(133\) −8.40267 −0.728604
\(134\) 17.9700 1.55237
\(135\) 24.8299 2.13701
\(136\) −14.4981 −1.24320
\(137\) 16.3806 1.39949 0.699744 0.714393i \(-0.253297\pi\)
0.699744 + 0.714393i \(0.253297\pi\)
\(138\) −35.7707 −3.04501
\(139\) −0.374348 −0.0317517 −0.0158759 0.999874i \(-0.505054\pi\)
−0.0158759 + 0.999874i \(0.505054\pi\)
\(140\) 19.6741 1.66277
\(141\) −31.7121 −2.67064
\(142\) 13.5303 1.13544
\(143\) −23.9615 −2.00376
\(144\) 59.4328 4.95273
\(145\) 32.9005 2.73224
\(146\) 36.4901 3.01994
\(147\) −16.8547 −1.39015
\(148\) −0.379909 −0.0312283
\(149\) 3.75611 0.307712 0.153856 0.988093i \(-0.450831\pi\)
0.153856 + 0.988093i \(0.450831\pi\)
\(150\) −62.4063 −5.09545
\(151\) −5.76659 −0.469278 −0.234639 0.972083i \(-0.575391\pi\)
−0.234639 + 0.972083i \(0.575391\pi\)
\(152\) 61.8030 5.01289
\(153\) 9.76751 0.789656
\(154\) 12.2779 0.989381
\(155\) 21.2325 1.70544
\(156\) 81.0889 6.49231
\(157\) −14.9576 −1.19375 −0.596873 0.802336i \(-0.703590\pi\)
−0.596873 + 0.802336i \(0.703590\pi\)
\(158\) 14.1483 1.12557
\(159\) 11.9573 0.948279
\(160\) −48.5289 −3.83655
\(161\) 5.05928 0.398727
\(162\) −9.80982 −0.770732
\(163\) −19.7624 −1.54791 −0.773957 0.633238i \(-0.781725\pi\)
−0.773957 + 0.633238i \(0.781725\pi\)
\(164\) 43.2209 3.37498
\(165\) −44.9101 −3.49624
\(166\) 27.1727 2.10901
\(167\) −13.0546 −1.01020 −0.505099 0.863061i \(-0.668544\pi\)
−0.505099 + 0.863061i \(0.668544\pi\)
\(168\) −24.9604 −1.92574
\(169\) 18.3194 1.40919
\(170\) −17.4709 −1.33995
\(171\) −41.6372 −3.18408
\(172\) −27.9505 −2.13121
\(173\) −22.4559 −1.70729 −0.853646 0.520854i \(-0.825614\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(174\) −69.4831 −5.26750
\(175\) 8.82652 0.667222
\(176\) −47.4115 −3.57378
\(177\) 42.3743 3.18505
\(178\) −1.93389 −0.144951
\(179\) 13.2450 0.989977 0.494988 0.868900i \(-0.335172\pi\)
0.494988 + 0.868900i \(0.335172\pi\)
\(180\) 97.4899 7.26647
\(181\) 14.1328 1.05048 0.525242 0.850953i \(-0.323975\pi\)
0.525242 + 0.850953i \(0.323975\pi\)
\(182\) −16.0481 −1.18957
\(183\) −31.9297 −2.36031
\(184\) −37.2119 −2.74330
\(185\) −0.275019 −0.0202198
\(186\) −44.8413 −3.28793
\(187\) −7.79187 −0.569798
\(188\) −54.9160 −4.00516
\(189\) 7.41673 0.539488
\(190\) 74.4753 5.40300
\(191\) −5.81177 −0.420525 −0.210263 0.977645i \(-0.567432\pi\)
−0.210263 + 0.977645i \(0.567432\pi\)
\(192\) 38.4273 2.77326
\(193\) 7.21340 0.519232 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(194\) −24.9695 −1.79271
\(195\) 58.7008 4.20365
\(196\) −29.1874 −2.08481
\(197\) −6.42877 −0.458031 −0.229015 0.973423i \(-0.573551\pi\)
−0.229015 + 0.973423i \(0.573551\pi\)
\(198\) 60.8399 4.32370
\(199\) 26.7237 1.89439 0.947197 0.320651i \(-0.103902\pi\)
0.947197 + 0.320651i \(0.103902\pi\)
\(200\) −64.9205 −4.59057
\(201\) −19.6339 −1.38487
\(202\) 18.2515 1.28417
\(203\) 9.82745 0.689752
\(204\) 26.3688 1.84618
\(205\) 31.2879 2.18524
\(206\) −32.6176 −2.27257
\(207\) 25.0699 1.74248
\(208\) 61.9704 4.29687
\(209\) 33.2154 2.29756
\(210\) −30.0784 −2.07560
\(211\) −8.88244 −0.611493 −0.305746 0.952113i \(-0.598906\pi\)
−0.305746 + 0.952113i \(0.598906\pi\)
\(212\) 20.7066 1.42213
\(213\) −14.7831 −1.01292
\(214\) −26.4872 −1.81063
\(215\) −20.2336 −1.37992
\(216\) −54.5513 −3.71174
\(217\) 6.34220 0.430537
\(218\) 4.03332 0.273171
\(219\) −39.8688 −2.69408
\(220\) −77.7710 −5.24332
\(221\) 10.1846 0.685087
\(222\) 0.580816 0.0389818
\(223\) −3.25366 −0.217881 −0.108941 0.994048i \(-0.534746\pi\)
−0.108941 + 0.994048i \(0.534746\pi\)
\(224\) −14.4957 −0.968533
\(225\) 43.7375 2.91583
\(226\) −7.98515 −0.531164
\(227\) 15.1823 1.00768 0.503842 0.863796i \(-0.331919\pi\)
0.503842 + 0.863796i \(0.331919\pi\)
\(228\) −112.405 −7.44423
\(229\) −2.33262 −0.154144 −0.0770719 0.997026i \(-0.524557\pi\)
−0.0770719 + 0.997026i \(0.524557\pi\)
\(230\) −44.8419 −2.95679
\(231\) −13.4147 −0.882624
\(232\) −72.2825 −4.74558
\(233\) −9.45867 −0.619658 −0.309829 0.950792i \(-0.600272\pi\)
−0.309829 + 0.950792i \(0.600272\pi\)
\(234\) −79.5222 −5.19853
\(235\) −39.7541 −2.59327
\(236\) 73.3798 4.77662
\(237\) −15.4583 −1.00412
\(238\) −5.21858 −0.338270
\(239\) −26.7926 −1.73307 −0.866533 0.499119i \(-0.833657\pi\)
−0.866533 + 0.499119i \(0.833657\pi\)
\(240\) 116.149 7.49736
\(241\) −13.6719 −0.880686 −0.440343 0.897830i \(-0.645143\pi\)
−0.440343 + 0.897830i \(0.645143\pi\)
\(242\) −19.4117 −1.24783
\(243\) −9.82418 −0.630222
\(244\) −55.2928 −3.53976
\(245\) −21.1289 −1.34988
\(246\) −66.0774 −4.21294
\(247\) −43.4150 −2.76243
\(248\) −46.6479 −2.96215
\(249\) −29.6886 −1.88144
\(250\) −30.2311 −1.91198
\(251\) −5.25740 −0.331844 −0.165922 0.986139i \(-0.553060\pi\)
−0.165922 + 0.986139i \(0.553060\pi\)
\(252\) 29.1204 1.83441
\(253\) −19.9991 −1.25733
\(254\) 0.523141 0.0328248
\(255\) 19.0885 1.19537
\(256\) −4.31769 −0.269855
\(257\) 2.72408 0.169923 0.0849616 0.996384i \(-0.472923\pi\)
0.0849616 + 0.996384i \(0.472923\pi\)
\(258\) 42.7316 2.66035
\(259\) −0.0821486 −0.00510446
\(260\) 101.652 6.30422
\(261\) 48.6973 3.01429
\(262\) −18.0941 −1.11786
\(263\) 9.87419 0.608869 0.304434 0.952533i \(-0.401533\pi\)
0.304434 + 0.952533i \(0.401533\pi\)
\(264\) 98.6675 6.07256
\(265\) 14.9896 0.920805
\(266\) 22.2459 1.36398
\(267\) 2.11295 0.129310
\(268\) −34.0001 −2.07689
\(269\) −1.39306 −0.0849364 −0.0424682 0.999098i \(-0.513522\pi\)
−0.0424682 + 0.999098i \(0.513522\pi\)
\(270\) −65.7366 −4.00060
\(271\) 22.6658 1.37685 0.688425 0.725307i \(-0.258302\pi\)
0.688425 + 0.725307i \(0.258302\pi\)
\(272\) 20.1517 1.22188
\(273\) 17.5340 1.06121
\(274\) −43.3673 −2.61991
\(275\) −34.8909 −2.10400
\(276\) 67.6798 4.07385
\(277\) 21.4396 1.28818 0.644090 0.764949i \(-0.277236\pi\)
0.644090 + 0.764949i \(0.277236\pi\)
\(278\) 0.991078 0.0594409
\(279\) 31.4271 1.88149
\(280\) −31.2902 −1.86995
\(281\) 24.5703 1.46574 0.732870 0.680368i \(-0.238180\pi\)
0.732870 + 0.680368i \(0.238180\pi\)
\(282\) 83.9572 4.99958
\(283\) 9.30052 0.552859 0.276429 0.961034i \(-0.410849\pi\)
0.276429 + 0.961034i \(0.410849\pi\)
\(284\) −25.6000 −1.51908
\(285\) −81.3710 −4.82000
\(286\) 63.4375 3.75114
\(287\) 9.34575 0.551662
\(288\) −71.8295 −4.23259
\(289\) −13.6882 −0.805186
\(290\) −87.1035 −5.11489
\(291\) 27.2815 1.59927
\(292\) −69.0410 −4.04032
\(293\) 15.8700 0.927137 0.463569 0.886061i \(-0.346569\pi\)
0.463569 + 0.886061i \(0.346569\pi\)
\(294\) 44.6225 2.60244
\(295\) 53.1201 3.09277
\(296\) 0.604216 0.0351193
\(297\) −29.3180 −1.70120
\(298\) −9.94421 −0.576053
\(299\) 26.1404 1.51174
\(300\) 118.075 6.81709
\(301\) −6.04380 −0.348359
\(302\) 15.2669 0.878513
\(303\) −19.9415 −1.14561
\(304\) −85.9033 −4.92689
\(305\) −40.0268 −2.29193
\(306\) −25.8593 −1.47828
\(307\) −8.17943 −0.466825 −0.233412 0.972378i \(-0.574989\pi\)
−0.233412 + 0.972378i \(0.574989\pi\)
\(308\) −23.2303 −1.32367
\(309\) 35.6377 2.02736
\(310\) −56.2127 −3.19267
\(311\) 9.29348 0.526985 0.263492 0.964661i \(-0.415126\pi\)
0.263492 + 0.964661i \(0.415126\pi\)
\(312\) −128.966 −7.30125
\(313\) 25.2307 1.42612 0.713062 0.701101i \(-0.247308\pi\)
0.713062 + 0.701101i \(0.247308\pi\)
\(314\) 39.5999 2.23475
\(315\) 21.0805 1.18775
\(316\) −26.7691 −1.50588
\(317\) −12.3336 −0.692726 −0.346363 0.938101i \(-0.612583\pi\)
−0.346363 + 0.938101i \(0.612583\pi\)
\(318\) −31.6568 −1.77523
\(319\) −38.8475 −2.17504
\(320\) 48.1722 2.69291
\(321\) 28.9397 1.61526
\(322\) −13.3944 −0.746438
\(323\) −14.1178 −0.785537
\(324\) 18.5606 1.03115
\(325\) 45.6049 2.52971
\(326\) 52.3207 2.89777
\(327\) −4.40677 −0.243695
\(328\) −68.7395 −3.79550
\(329\) −11.8746 −0.654669
\(330\) 118.899 6.54515
\(331\) −9.53761 −0.524234 −0.262117 0.965036i \(-0.584421\pi\)
−0.262117 + 0.965036i \(0.584421\pi\)
\(332\) −51.4119 −2.82159
\(333\) −0.407065 −0.0223070
\(334\) 34.5619 1.89114
\(335\) −24.6129 −1.34475
\(336\) 34.6938 1.89270
\(337\) 15.3667 0.837076 0.418538 0.908199i \(-0.362543\pi\)
0.418538 + 0.908199i \(0.362543\pi\)
\(338\) −48.5003 −2.63807
\(339\) 8.72450 0.473850
\(340\) 33.0557 1.79269
\(341\) −25.0704 −1.35764
\(342\) 110.234 5.96076
\(343\) −13.8932 −0.750164
\(344\) 44.4532 2.39675
\(345\) 48.9938 2.63774
\(346\) 59.4516 3.19614
\(347\) −7.15827 −0.384276 −0.192138 0.981368i \(-0.561542\pi\)
−0.192138 + 0.981368i \(0.561542\pi\)
\(348\) 131.465 7.04728
\(349\) −15.6055 −0.835343 −0.417671 0.908598i \(-0.637154\pi\)
−0.417671 + 0.908598i \(0.637154\pi\)
\(350\) −23.3680 −1.24907
\(351\) 38.3208 2.04541
\(352\) 57.3008 3.05414
\(353\) −35.1808 −1.87248 −0.936242 0.351356i \(-0.885721\pi\)
−0.936242 + 0.351356i \(0.885721\pi\)
\(354\) −112.185 −5.96257
\(355\) −18.5320 −0.983576
\(356\) 3.65900 0.193927
\(357\) 5.70177 0.301770
\(358\) −35.0658 −1.85329
\(359\) 12.9142 0.681583 0.340792 0.940139i \(-0.389305\pi\)
0.340792 + 0.940139i \(0.389305\pi\)
\(360\) −155.050 −8.17186
\(361\) 41.1818 2.16747
\(362\) −37.4163 −1.96656
\(363\) 21.2091 1.11319
\(364\) 30.3638 1.59149
\(365\) −49.9792 −2.61603
\(366\) 84.5332 4.41862
\(367\) −22.6161 −1.18055 −0.590275 0.807202i \(-0.700981\pi\)
−0.590275 + 0.807202i \(0.700981\pi\)
\(368\) 51.7228 2.69624
\(369\) 46.3104 2.41082
\(370\) 0.728106 0.0378524
\(371\) 4.47743 0.232457
\(372\) 84.8418 4.39884
\(373\) −17.6455 −0.913650 −0.456825 0.889557i \(-0.651013\pi\)
−0.456825 + 0.889557i \(0.651013\pi\)
\(374\) 20.6288 1.06669
\(375\) 33.0302 1.70567
\(376\) 87.3397 4.50420
\(377\) 50.7765 2.61513
\(378\) −19.6356 −1.00995
\(379\) −19.0429 −0.978167 −0.489083 0.872237i \(-0.662669\pi\)
−0.489083 + 0.872237i \(0.662669\pi\)
\(380\) −140.911 −7.22856
\(381\) −0.571580 −0.0292829
\(382\) 15.3866 0.787245
\(383\) −12.9167 −0.660010 −0.330005 0.943979i \(-0.607051\pi\)
−0.330005 + 0.943979i \(0.607051\pi\)
\(384\) −24.3119 −1.24066
\(385\) −16.8166 −0.857052
\(386\) −19.0973 −0.972028
\(387\) −29.9485 −1.52237
\(388\) 47.2434 2.39842
\(389\) 29.7573 1.50875 0.754376 0.656442i \(-0.227939\pi\)
0.754376 + 0.656442i \(0.227939\pi\)
\(390\) −155.409 −7.86945
\(391\) 8.50040 0.429884
\(392\) 46.4203 2.34458
\(393\) 19.7695 0.997237
\(394\) 17.0200 0.857458
\(395\) −19.3783 −0.975030
\(396\) −115.112 −5.78458
\(397\) 22.3698 1.12271 0.561355 0.827575i \(-0.310280\pi\)
0.561355 + 0.827575i \(0.310280\pi\)
\(398\) −70.7505 −3.54640
\(399\) −24.3057 −1.21681
\(400\) 90.2365 4.51182
\(401\) −11.6158 −0.580066 −0.290033 0.957017i \(-0.593666\pi\)
−0.290033 + 0.957017i \(0.593666\pi\)
\(402\) 51.9803 2.59254
\(403\) 32.7689 1.63234
\(404\) −34.5328 −1.71807
\(405\) 13.4361 0.667647
\(406\) −26.0180 −1.29125
\(407\) 0.324730 0.0160963
\(408\) −41.9375 −2.07621
\(409\) 12.9847 0.642051 0.321025 0.947071i \(-0.395973\pi\)
0.321025 + 0.947071i \(0.395973\pi\)
\(410\) −82.8340 −4.09088
\(411\) 47.3827 2.33722
\(412\) 61.7139 3.04042
\(413\) 15.8671 0.780767
\(414\) −66.3722 −3.26202
\(415\) −37.2174 −1.82693
\(416\) −74.8964 −3.67210
\(417\) −1.08284 −0.0530270
\(418\) −87.9371 −4.30114
\(419\) −3.17947 −0.155327 −0.0776635 0.996980i \(-0.524746\pi\)
−0.0776635 + 0.996980i \(0.524746\pi\)
\(420\) 56.9096 2.77691
\(421\) 6.80322 0.331569 0.165784 0.986162i \(-0.446984\pi\)
0.165784 + 0.986162i \(0.446984\pi\)
\(422\) 23.5161 1.14475
\(423\) −58.8415 −2.86097
\(424\) −32.9322 −1.59933
\(425\) 14.8300 0.719359
\(426\) 39.1380 1.89624
\(427\) −11.9561 −0.578595
\(428\) 50.1150 2.42240
\(429\) −69.3113 −3.34638
\(430\) 53.5679 2.58328
\(431\) −3.44615 −0.165995 −0.0829975 0.996550i \(-0.526449\pi\)
−0.0829975 + 0.996550i \(0.526449\pi\)
\(432\) 75.8237 3.64807
\(433\) −8.31846 −0.399760 −0.199880 0.979820i \(-0.564055\pi\)
−0.199880 + 0.979820i \(0.564055\pi\)
\(434\) −16.7908 −0.805987
\(435\) 95.1685 4.56298
\(436\) −7.63122 −0.365469
\(437\) −36.2358 −1.73339
\(438\) 105.552 5.04346
\(439\) −12.8921 −0.615306 −0.307653 0.951499i \(-0.599544\pi\)
−0.307653 + 0.951499i \(0.599544\pi\)
\(440\) 123.689 5.89663
\(441\) −31.2737 −1.48922
\(442\) −26.9634 −1.28252
\(443\) 7.60334 0.361245 0.180623 0.983552i \(-0.442189\pi\)
0.180623 + 0.983552i \(0.442189\pi\)
\(444\) −1.09893 −0.0521529
\(445\) 2.64878 0.125564
\(446\) 8.61400 0.407885
\(447\) 10.8650 0.513895
\(448\) 14.3891 0.679823
\(449\) −33.5784 −1.58466 −0.792331 0.610091i \(-0.791133\pi\)
−0.792331 + 0.610091i \(0.791133\pi\)
\(450\) −115.794 −5.45859
\(451\) −36.9433 −1.73959
\(452\) 15.1083 0.710633
\(453\) −16.6805 −0.783719
\(454\) −40.1948 −1.88644
\(455\) 21.9805 1.03046
\(456\) 178.772 8.37178
\(457\) 21.3349 0.998004 0.499002 0.866601i \(-0.333700\pi\)
0.499002 + 0.866601i \(0.333700\pi\)
\(458\) 6.17557 0.288565
\(459\) 12.4613 0.581643
\(460\) 84.8429 3.95582
\(461\) 14.1583 0.659419 0.329709 0.944082i \(-0.393049\pi\)
0.329709 + 0.944082i \(0.393049\pi\)
\(462\) 35.5152 1.65232
\(463\) −36.8277 −1.71153 −0.855764 0.517367i \(-0.826912\pi\)
−0.855764 + 0.517367i \(0.826912\pi\)
\(464\) 100.469 4.66417
\(465\) 61.4175 2.84817
\(466\) 25.0416 1.16003
\(467\) 24.9682 1.15539 0.577696 0.816252i \(-0.303952\pi\)
0.577696 + 0.816252i \(0.303952\pi\)
\(468\) 150.460 6.95500
\(469\) −7.35192 −0.339480
\(470\) 105.248 4.85473
\(471\) −43.2665 −1.99362
\(472\) −116.705 −5.37178
\(473\) 23.8909 1.09850
\(474\) 40.9254 1.87977
\(475\) −63.2176 −2.90062
\(476\) 9.87379 0.452564
\(477\) 22.1867 1.01586
\(478\) 70.9328 3.24439
\(479\) −18.6823 −0.853618 −0.426809 0.904342i \(-0.640362\pi\)
−0.426809 + 0.904342i \(0.640362\pi\)
\(480\) −140.375 −6.40723
\(481\) −0.424446 −0.0193531
\(482\) 36.1962 1.64869
\(483\) 14.6346 0.665895
\(484\) 36.7278 1.66945
\(485\) 34.1998 1.55293
\(486\) 26.0093 1.17981
\(487\) 12.4357 0.563515 0.281757 0.959486i \(-0.409083\pi\)
0.281757 + 0.959486i \(0.409083\pi\)
\(488\) 87.9389 3.98081
\(489\) −57.1651 −2.58510
\(490\) 55.9384 2.52704
\(491\) 4.15707 0.187606 0.0938031 0.995591i \(-0.470098\pi\)
0.0938031 + 0.995591i \(0.470098\pi\)
\(492\) 125.021 5.63640
\(493\) 16.5117 0.743649
\(494\) 114.940 5.17141
\(495\) −83.3301 −3.74541
\(496\) 64.8384 2.91133
\(497\) −5.53554 −0.248303
\(498\) 78.6000 3.52215
\(499\) −6.33437 −0.283566 −0.141783 0.989898i \(-0.545283\pi\)
−0.141783 + 0.989898i \(0.545283\pi\)
\(500\) 57.1986 2.55800
\(501\) −37.7620 −1.68708
\(502\) 13.9189 0.621230
\(503\) −10.4867 −0.467579 −0.233789 0.972287i \(-0.575113\pi\)
−0.233789 + 0.972287i \(0.575113\pi\)
\(504\) −46.3138 −2.06298
\(505\) −24.9985 −1.11242
\(506\) 52.9473 2.35380
\(507\) 52.9910 2.35341
\(508\) −0.989807 −0.0439156
\(509\) −33.5799 −1.48840 −0.744202 0.667954i \(-0.767170\pi\)
−0.744202 + 0.667954i \(0.767170\pi\)
\(510\) −50.5365 −2.23779
\(511\) −14.9289 −0.660415
\(512\) 28.2406 1.24807
\(513\) −53.1203 −2.34532
\(514\) −7.21194 −0.318105
\(515\) 44.6751 1.96862
\(516\) −80.8501 −3.55923
\(517\) 46.9398 2.06441
\(518\) 0.217487 0.00955582
\(519\) −64.9563 −2.85127
\(520\) −161.670 −7.08971
\(521\) 39.4913 1.73014 0.865072 0.501649i \(-0.167273\pi\)
0.865072 + 0.501649i \(0.167273\pi\)
\(522\) −128.925 −5.64290
\(523\) 40.4774 1.76995 0.884976 0.465636i \(-0.154174\pi\)
0.884976 + 0.465636i \(0.154174\pi\)
\(524\) 34.2349 1.49556
\(525\) 25.5317 1.11430
\(526\) −26.1417 −1.13983
\(527\) 10.6559 0.464178
\(528\) −137.143 −5.96839
\(529\) −1.18229 −0.0514041
\(530\) −39.6847 −1.72379
\(531\) 78.6251 3.41204
\(532\) −42.0903 −1.82484
\(533\) 48.2877 2.09157
\(534\) −5.59399 −0.242076
\(535\) 36.2786 1.56846
\(536\) 54.0745 2.33566
\(537\) 38.3126 1.65331
\(538\) 3.68810 0.159005
\(539\) 24.9481 1.07459
\(540\) 124.377 5.35232
\(541\) 37.5916 1.61619 0.808094 0.589054i \(-0.200499\pi\)
0.808094 + 0.589054i \(0.200499\pi\)
\(542\) −60.0073 −2.57753
\(543\) 40.8808 1.75436
\(544\) −24.3550 −1.04421
\(545\) −5.52429 −0.236635
\(546\) −46.4210 −1.98664
\(547\) −16.7892 −0.717855 −0.358927 0.933366i \(-0.616857\pi\)
−0.358927 + 0.933366i \(0.616857\pi\)
\(548\) 82.0529 3.50513
\(549\) −59.2452 −2.52852
\(550\) 92.3729 3.93879
\(551\) −70.3864 −2.99856
\(552\) −107.640 −4.58144
\(553\) −5.78835 −0.246146
\(554\) −56.7609 −2.41154
\(555\) −0.795522 −0.0337680
\(556\) −1.87516 −0.0795247
\(557\) 5.76993 0.244480 0.122240 0.992501i \(-0.460992\pi\)
0.122240 + 0.992501i \(0.460992\pi\)
\(558\) −83.2026 −3.52225
\(559\) −31.2272 −1.32077
\(560\) 43.4919 1.83787
\(561\) −22.5389 −0.951592
\(562\) −65.0494 −2.74394
\(563\) −12.1989 −0.514124 −0.257062 0.966395i \(-0.582754\pi\)
−0.257062 + 0.966395i \(0.582754\pi\)
\(564\) −158.851 −6.68883
\(565\) 10.9370 0.460121
\(566\) −24.6230 −1.03498
\(567\) 4.01340 0.168547
\(568\) 40.7148 1.70836
\(569\) 31.9559 1.33966 0.669830 0.742515i \(-0.266367\pi\)
0.669830 + 0.742515i \(0.266367\pi\)
\(570\) 215.428 9.02329
\(571\) −35.2509 −1.47521 −0.737603 0.675234i \(-0.764042\pi\)
−0.737603 + 0.675234i \(0.764042\pi\)
\(572\) −120.027 −5.01857
\(573\) −16.8112 −0.702298
\(574\) −24.7427 −1.03274
\(575\) 38.0636 1.58736
\(576\) 71.3015 2.97090
\(577\) −17.7779 −0.740103 −0.370051 0.929011i \(-0.620660\pi\)
−0.370051 + 0.929011i \(0.620660\pi\)
\(578\) 36.2391 1.50735
\(579\) 20.8656 0.867144
\(580\) 164.804 6.84310
\(581\) −11.1169 −0.461207
\(582\) −72.2271 −2.99391
\(583\) −17.6991 −0.733021
\(584\) 109.804 4.54374
\(585\) 108.919 4.50323
\(586\) −42.0156 −1.73565
\(587\) 40.2878 1.66285 0.831427 0.555634i \(-0.187524\pi\)
0.831427 + 0.555634i \(0.187524\pi\)
\(588\) −84.4278 −3.48174
\(589\) −45.4243 −1.87167
\(590\) −140.634 −5.78983
\(591\) −18.5960 −0.764935
\(592\) −0.839832 −0.0345169
\(593\) 15.8728 0.651817 0.325908 0.945401i \(-0.394330\pi\)
0.325908 + 0.945401i \(0.394330\pi\)
\(594\) 77.6189 3.18474
\(595\) 7.14770 0.293027
\(596\) 18.8149 0.770688
\(597\) 77.3014 3.16374
\(598\) −69.2061 −2.83005
\(599\) −8.67101 −0.354288 −0.177144 0.984185i \(-0.556686\pi\)
−0.177144 + 0.984185i \(0.556686\pi\)
\(600\) −187.790 −7.66649
\(601\) −26.3945 −1.07665 −0.538327 0.842736i \(-0.680943\pi\)
−0.538327 + 0.842736i \(0.680943\pi\)
\(602\) 16.0008 0.652146
\(603\) −36.4305 −1.48356
\(604\) −28.8857 −1.17534
\(605\) 26.5875 1.08094
\(606\) 52.7947 2.14464
\(607\) −4.02326 −0.163299 −0.0816496 0.996661i \(-0.526019\pi\)
−0.0816496 + 0.996661i \(0.526019\pi\)
\(608\) 103.821 4.21051
\(609\) 28.4270 1.15192
\(610\) 105.970 4.29061
\(611\) −61.3539 −2.48211
\(612\) 48.9269 1.97775
\(613\) 5.25999 0.212449 0.106224 0.994342i \(-0.466124\pi\)
0.106224 + 0.994342i \(0.466124\pi\)
\(614\) 21.6549 0.873920
\(615\) 90.5037 3.64946
\(616\) 36.9461 1.48860
\(617\) −11.6549 −0.469209 −0.234604 0.972091i \(-0.575379\pi\)
−0.234604 + 0.972091i \(0.575379\pi\)
\(618\) −94.3500 −3.79531
\(619\) −9.86867 −0.396656 −0.198328 0.980136i \(-0.563551\pi\)
−0.198328 + 0.980136i \(0.563551\pi\)
\(620\) 106.357 4.27140
\(621\) 31.9840 1.28347
\(622\) −24.6043 −0.986542
\(623\) 0.791194 0.0316985
\(624\) 179.256 7.17600
\(625\) 0.661348 0.0264539
\(626\) −66.7978 −2.66978
\(627\) 96.0793 3.83704
\(628\) −74.9249 −2.98983
\(629\) −0.138023 −0.00550332
\(630\) −55.8101 −2.22353
\(631\) 4.02347 0.160172 0.0800859 0.996788i \(-0.474481\pi\)
0.0800859 + 0.996788i \(0.474481\pi\)
\(632\) 42.5743 1.69351
\(633\) −25.6935 −1.02122
\(634\) 32.6530 1.29682
\(635\) −0.716528 −0.0284345
\(636\) 59.8961 2.37504
\(637\) −32.6090 −1.29202
\(638\) 102.848 4.07179
\(639\) −27.4299 −1.08511
\(640\) −30.4772 −1.20472
\(641\) 17.7703 0.701885 0.350942 0.936397i \(-0.385861\pi\)
0.350942 + 0.936397i \(0.385861\pi\)
\(642\) −76.6173 −3.02384
\(643\) 14.3452 0.565719 0.282860 0.959161i \(-0.408717\pi\)
0.282860 + 0.959161i \(0.408717\pi\)
\(644\) 25.3427 0.998643
\(645\) −58.5279 −2.30453
\(646\) 37.3767 1.47056
\(647\) −25.3910 −0.998224 −0.499112 0.866537i \(-0.666340\pi\)
−0.499112 + 0.866537i \(0.666340\pi\)
\(648\) −29.5192 −1.15962
\(649\) −62.7218 −2.46205
\(650\) −120.738 −4.73574
\(651\) 18.3455 0.719018
\(652\) −98.9931 −3.87687
\(653\) 15.8088 0.618646 0.309323 0.950957i \(-0.399898\pi\)
0.309323 + 0.950957i \(0.399898\pi\)
\(654\) 11.6668 0.456209
\(655\) 24.7828 0.968345
\(656\) 95.5447 3.73039
\(657\) −73.9761 −2.88608
\(658\) 31.4378 1.22557
\(659\) 3.07014 0.119596 0.0597979 0.998211i \(-0.480954\pi\)
0.0597979 + 0.998211i \(0.480954\pi\)
\(660\) −224.961 −8.75661
\(661\) −19.9291 −0.775151 −0.387575 0.921838i \(-0.626687\pi\)
−0.387575 + 0.921838i \(0.626687\pi\)
\(662\) 25.2506 0.981394
\(663\) 29.4600 1.14413
\(664\) 81.7667 3.17316
\(665\) −30.4694 −1.18155
\(666\) 1.07770 0.0417599
\(667\) 42.3800 1.64096
\(668\) −65.3927 −2.53012
\(669\) −9.41158 −0.363873
\(670\) 65.1621 2.51743
\(671\) 47.2619 1.82452
\(672\) −41.9304 −1.61750
\(673\) −28.4756 −1.09765 −0.548826 0.835937i \(-0.684925\pi\)
−0.548826 + 0.835937i \(0.684925\pi\)
\(674\) −40.6830 −1.56705
\(675\) 55.7998 2.14774
\(676\) 91.7648 3.52942
\(677\) −14.6200 −0.561893 −0.280946 0.959723i \(-0.590648\pi\)
−0.280946 + 0.959723i \(0.590648\pi\)
\(678\) −23.0979 −0.887071
\(679\) 10.2156 0.392037
\(680\) −52.5725 −2.01606
\(681\) 43.9165 1.68288
\(682\) 66.3735 2.54157
\(683\) 30.3090 1.15974 0.579870 0.814709i \(-0.303103\pi\)
0.579870 + 0.814709i \(0.303103\pi\)
\(684\) −208.567 −7.97476
\(685\) 59.3986 2.26950
\(686\) 36.7820 1.40435
\(687\) −6.74737 −0.257428
\(688\) −61.7878 −2.35564
\(689\) 23.1340 0.881336
\(690\) −129.710 −4.93798
\(691\) −20.4529 −0.778064 −0.389032 0.921224i \(-0.627190\pi\)
−0.389032 + 0.921224i \(0.627190\pi\)
\(692\) −112.485 −4.27604
\(693\) −24.8909 −0.945526
\(694\) 18.9514 0.719385
\(695\) −1.35744 −0.0514907
\(696\) −209.085 −7.92536
\(697\) 15.7023 0.594769
\(698\) 41.3152 1.56380
\(699\) −27.3603 −1.03486
\(700\) 44.2134 1.67111
\(701\) 7.05619 0.266509 0.133254 0.991082i \(-0.457457\pi\)
0.133254 + 0.991082i \(0.457457\pi\)
\(702\) −101.454 −3.82912
\(703\) 0.588367 0.0221907
\(704\) −56.8796 −2.14373
\(705\) −114.993 −4.33089
\(706\) 93.1404 3.50539
\(707\) −7.46709 −0.280829
\(708\) 212.259 7.97719
\(709\) −45.7817 −1.71937 −0.859683 0.510827i \(-0.829339\pi\)
−0.859683 + 0.510827i \(0.829339\pi\)
\(710\) 49.0631 1.84130
\(711\) −28.6826 −1.07568
\(712\) −5.81936 −0.218090
\(713\) 27.3502 1.02427
\(714\) −15.0953 −0.564929
\(715\) −86.8881 −3.24943
\(716\) 66.3462 2.47947
\(717\) −77.5005 −2.89431
\(718\) −34.1900 −1.27596
\(719\) −10.4873 −0.391110 −0.195555 0.980693i \(-0.562651\pi\)
−0.195555 + 0.980693i \(0.562651\pi\)
\(720\) 215.513 8.03168
\(721\) 13.3445 0.496976
\(722\) −109.028 −4.05761
\(723\) −39.5476 −1.47079
\(724\) 70.7934 2.63102
\(725\) 73.9369 2.74595
\(726\) −56.1506 −2.08394
\(727\) 15.8430 0.587585 0.293792 0.955869i \(-0.405083\pi\)
0.293792 + 0.955869i \(0.405083\pi\)
\(728\) −48.2912 −1.78979
\(729\) −39.5336 −1.46421
\(730\) 132.319 4.89734
\(731\) −10.1545 −0.375580
\(732\) −159.941 −5.91158
\(733\) −5.74382 −0.212153 −0.106076 0.994358i \(-0.533829\pi\)
−0.106076 + 0.994358i \(0.533829\pi\)
\(734\) 59.8757 2.21005
\(735\) −61.1178 −2.25436
\(736\) −62.5113 −2.30420
\(737\) 29.0618 1.07051
\(738\) −122.606 −4.51318
\(739\) 14.4032 0.529830 0.264915 0.964272i \(-0.414656\pi\)
0.264915 + 0.964272i \(0.414656\pi\)
\(740\) −1.37761 −0.0506419
\(741\) −125.583 −4.61340
\(742\) −11.8539 −0.435171
\(743\) −37.1271 −1.36206 −0.681031 0.732255i \(-0.738468\pi\)
−0.681031 + 0.732255i \(0.738468\pi\)
\(744\) −134.934 −4.94694
\(745\) 13.6202 0.499006
\(746\) 46.7161 1.71040
\(747\) −55.0869 −2.01552
\(748\) −39.0307 −1.42710
\(749\) 10.8365 0.395956
\(750\) −87.4469 −3.19311
\(751\) 15.6616 0.571501 0.285751 0.958304i \(-0.407757\pi\)
0.285751 + 0.958304i \(0.407757\pi\)
\(752\) −121.398 −4.42694
\(753\) −15.2076 −0.554197
\(754\) −134.430 −4.89565
\(755\) −20.9106 −0.761013
\(756\) 37.1515 1.35119
\(757\) 44.9984 1.63549 0.817747 0.575578i \(-0.195223\pi\)
0.817747 + 0.575578i \(0.195223\pi\)
\(758\) 50.4156 1.83118
\(759\) −57.8498 −2.09981
\(760\) 224.107 8.12923
\(761\) −18.7194 −0.678579 −0.339290 0.940682i \(-0.610187\pi\)
−0.339290 + 0.940682i \(0.610187\pi\)
\(762\) 1.51325 0.0548191
\(763\) −1.65012 −0.0597382
\(764\) −29.1121 −1.05324
\(765\) 35.4185 1.28056
\(766\) 34.1966 1.23557
\(767\) 81.9821 2.96020
\(768\) −12.4894 −0.450672
\(769\) −11.2397 −0.405314 −0.202657 0.979250i \(-0.564958\pi\)
−0.202657 + 0.979250i \(0.564958\pi\)
\(770\) 44.5216 1.60445
\(771\) 7.87970 0.283780
\(772\) 36.1330 1.30046
\(773\) 16.3028 0.586371 0.293185 0.956056i \(-0.405285\pi\)
0.293185 + 0.956056i \(0.405285\pi\)
\(774\) 79.2880 2.84995
\(775\) 47.7156 1.71399
\(776\) −75.1371 −2.69726
\(777\) −0.237624 −0.00852471
\(778\) −78.7817 −2.82446
\(779\) −66.9364 −2.39824
\(780\) 294.041 10.5284
\(781\) 21.8817 0.782991
\(782\) −22.5047 −0.804765
\(783\) 62.1275 2.22026
\(784\) −64.5220 −2.30436
\(785\) −54.2386 −1.93586
\(786\) −52.3392 −1.86688
\(787\) 22.1732 0.790389 0.395194 0.918598i \(-0.370677\pi\)
0.395194 + 0.918598i \(0.370677\pi\)
\(788\) −32.2027 −1.14717
\(789\) 28.5622 1.01684
\(790\) 51.3038 1.82531
\(791\) 3.26689 0.116157
\(792\) 183.076 6.50534
\(793\) −61.7748 −2.19369
\(794\) −59.2237 −2.10177
\(795\) 43.3592 1.53779
\(796\) 133.863 4.74466
\(797\) −19.8872 −0.704442 −0.352221 0.935917i \(-0.614573\pi\)
−0.352221 + 0.935917i \(0.614573\pi\)
\(798\) 64.3488 2.27792
\(799\) −19.9512 −0.705824
\(800\) −109.058 −3.85579
\(801\) 3.92055 0.138526
\(802\) 30.7526 1.08591
\(803\) 59.0132 2.08253
\(804\) −98.3492 −3.46851
\(805\) 18.3458 0.646603
\(806\) −86.7551 −3.05582
\(807\) −4.02959 −0.141848
\(808\) 54.9217 1.93214
\(809\) −15.0672 −0.529733 −0.264867 0.964285i \(-0.585328\pi\)
−0.264867 + 0.964285i \(0.585328\pi\)
\(810\) −35.5719 −1.24987
\(811\) −36.2069 −1.27139 −0.635697 0.771938i \(-0.719287\pi\)
−0.635697 + 0.771938i \(0.719287\pi\)
\(812\) 49.2272 1.72754
\(813\) 65.5634 2.29941
\(814\) −0.859715 −0.0301330
\(815\) −71.6617 −2.51020
\(816\) 58.2911 2.04060
\(817\) 43.2871 1.51442
\(818\) −34.3767 −1.20195
\(819\) 32.5342 1.13684
\(820\) 156.726 5.47310
\(821\) 33.9167 1.18370 0.591851 0.806047i \(-0.298397\pi\)
0.591851 + 0.806047i \(0.298397\pi\)
\(822\) −125.445 −4.37539
\(823\) −26.3234 −0.917575 −0.458788 0.888546i \(-0.651716\pi\)
−0.458788 + 0.888546i \(0.651716\pi\)
\(824\) −98.1512 −3.41926
\(825\) −100.926 −3.51378
\(826\) −42.0078 −1.46164
\(827\) 15.3608 0.534149 0.267074 0.963676i \(-0.413943\pi\)
0.267074 + 0.963676i \(0.413943\pi\)
\(828\) 125.579 4.36418
\(829\) −23.3827 −0.812115 −0.406057 0.913848i \(-0.633097\pi\)
−0.406057 + 0.913848i \(0.633097\pi\)
\(830\) 98.5323 3.42011
\(831\) 62.0165 2.15133
\(832\) 74.3459 2.57748
\(833\) −10.6039 −0.367403
\(834\) 2.86681 0.0992693
\(835\) −47.3382 −1.63820
\(836\) 166.381 5.75441
\(837\) 40.0944 1.38586
\(838\) 8.41757 0.290780
\(839\) 44.4168 1.53344 0.766719 0.641982i \(-0.221888\pi\)
0.766719 + 0.641982i \(0.221888\pi\)
\(840\) −90.5104 −3.12291
\(841\) 53.3213 1.83867
\(842\) −18.0114 −0.620713
\(843\) 71.0724 2.44786
\(844\) −44.4935 −1.53153
\(845\) 66.4291 2.28523
\(846\) 155.782 5.35589
\(847\) 7.94174 0.272881
\(848\) 45.7743 1.57189
\(849\) 26.9028 0.923303
\(850\) −39.2620 −1.34668
\(851\) −0.354258 −0.0121438
\(852\) −74.0508 −2.53694
\(853\) −41.4600 −1.41956 −0.709782 0.704421i \(-0.751207\pi\)
−0.709782 + 0.704421i \(0.751207\pi\)
\(854\) 31.6535 1.08316
\(855\) −150.983 −5.16351
\(856\) −79.7041 −2.72423
\(857\) −9.23705 −0.315531 −0.157766 0.987477i \(-0.550429\pi\)
−0.157766 + 0.987477i \(0.550429\pi\)
\(858\) 183.500 6.26460
\(859\) −28.2804 −0.964915 −0.482458 0.875919i \(-0.660256\pi\)
−0.482458 + 0.875919i \(0.660256\pi\)
\(860\) −101.353 −3.45611
\(861\) 27.0336 0.921304
\(862\) 9.12360 0.310751
\(863\) −3.49136 −0.118847 −0.0594237 0.998233i \(-0.518926\pi\)
−0.0594237 + 0.998233i \(0.518926\pi\)
\(864\) −91.6393 −3.11763
\(865\) −81.4287 −2.76866
\(866\) 22.0230 0.748370
\(867\) −39.5945 −1.34470
\(868\) 31.7690 1.07831
\(869\) 22.8811 0.776188
\(870\) −251.957 −8.54213
\(871\) −37.9859 −1.28710
\(872\) 12.1369 0.411006
\(873\) 50.6205 1.71324
\(874\) 95.9334 3.24500
\(875\) 12.3682 0.418121
\(876\) −199.709 −6.74754
\(877\) −18.9583 −0.640175 −0.320088 0.947388i \(-0.603712\pi\)
−0.320088 + 0.947388i \(0.603712\pi\)
\(878\) 34.1316 1.15188
\(879\) 45.9059 1.54837
\(880\) −171.922 −5.79548
\(881\) −40.7163 −1.37177 −0.685883 0.727712i \(-0.740584\pi\)
−0.685883 + 0.727712i \(0.740584\pi\)
\(882\) 82.7966 2.78791
\(883\) −8.94377 −0.300982 −0.150491 0.988611i \(-0.548085\pi\)
−0.150491 + 0.988611i \(0.548085\pi\)
\(884\) 51.0160 1.71585
\(885\) 153.656 5.16509
\(886\) −20.1297 −0.676270
\(887\) −15.5298 −0.521439 −0.260719 0.965415i \(-0.583960\pi\)
−0.260719 + 0.965415i \(0.583960\pi\)
\(888\) 1.74776 0.0586511
\(889\) −0.214028 −0.00717828
\(890\) −7.01258 −0.235062
\(891\) −15.8648 −0.531491
\(892\) −16.2981 −0.545700
\(893\) 85.0487 2.84605
\(894\) −28.7648 −0.962038
\(895\) 48.0284 1.60541
\(896\) −9.10360 −0.304130
\(897\) 75.6139 2.52468
\(898\) 88.8981 2.96657
\(899\) 53.1265 1.77187
\(900\) 219.088 7.30293
\(901\) 7.52279 0.250621
\(902\) 97.8068 3.25661
\(903\) −17.4824 −0.581777
\(904\) −24.0285 −0.799177
\(905\) 51.2478 1.70353
\(906\) 44.1613 1.46716
\(907\) 22.0161 0.731031 0.365516 0.930805i \(-0.380893\pi\)
0.365516 + 0.930805i \(0.380893\pi\)
\(908\) 76.0504 2.52382
\(909\) −37.0012 −1.22725
\(910\) −58.1930 −1.92908
\(911\) 0.623853 0.0206692 0.0103346 0.999947i \(-0.496710\pi\)
0.0103346 + 0.999947i \(0.496710\pi\)
\(912\) −248.485 −8.22816
\(913\) 43.9447 1.45436
\(914\) −56.4837 −1.86831
\(915\) −115.782 −3.82764
\(916\) −11.6845 −0.386065
\(917\) 7.40268 0.244458
\(918\) −32.9910 −1.08887
\(919\) −14.9507 −0.493179 −0.246589 0.969120i \(-0.579310\pi\)
−0.246589 + 0.969120i \(0.579310\pi\)
\(920\) −134.936 −4.44871
\(921\) −23.6599 −0.779622
\(922\) −37.4839 −1.23447
\(923\) −28.6011 −0.941416
\(924\) −67.1964 −2.21060
\(925\) −0.618045 −0.0203212
\(926\) 97.5006 3.20407
\(927\) 66.1253 2.17184
\(928\) −121.426 −3.98599
\(929\) −48.5592 −1.59318 −0.796588 0.604523i \(-0.793364\pi\)
−0.796588 + 0.604523i \(0.793364\pi\)
\(930\) −162.602 −5.33192
\(931\) 45.2026 1.48146
\(932\) −47.3799 −1.55198
\(933\) 26.8824 0.880091
\(934\) −66.1029 −2.16295
\(935\) −28.2545 −0.924022
\(936\) −239.294 −7.82159
\(937\) −44.0875 −1.44028 −0.720138 0.693831i \(-0.755922\pi\)
−0.720138 + 0.693831i \(0.755922\pi\)
\(938\) 19.4641 0.635524
\(939\) 72.9827 2.38170
\(940\) −199.134 −6.49504
\(941\) −20.5729 −0.670657 −0.335328 0.942101i \(-0.608847\pi\)
−0.335328 + 0.942101i \(0.608847\pi\)
\(942\) 114.547 3.73215
\(943\) 40.3027 1.31244
\(944\) 162.214 5.27963
\(945\) 26.8942 0.874869
\(946\) −63.2507 −2.05646
\(947\) −2.11136 −0.0686101 −0.0343050 0.999411i \(-0.510922\pi\)
−0.0343050 + 0.999411i \(0.510922\pi\)
\(948\) −77.4328 −2.51490
\(949\) −77.1346 −2.50390
\(950\) 167.367 5.43011
\(951\) −35.6764 −1.15689
\(952\) −15.7035 −0.508953
\(953\) 9.19987 0.298013 0.149007 0.988836i \(-0.452392\pi\)
0.149007 + 0.988836i \(0.452392\pi\)
\(954\) −58.7389 −1.90174
\(955\) −21.0744 −0.681952
\(956\) −134.208 −4.34060
\(957\) −112.371 −3.63243
\(958\) 49.4611 1.59802
\(959\) 17.7425 0.572934
\(960\) 139.344 4.49730
\(961\) 3.28551 0.105984
\(962\) 1.12371 0.0362299
\(963\) 53.6973 1.73037
\(964\) −68.4848 −2.20575
\(965\) 26.1569 0.842021
\(966\) −38.7447 −1.24659
\(967\) 41.8641 1.34626 0.673129 0.739525i \(-0.264950\pi\)
0.673129 + 0.739525i \(0.264950\pi\)
\(968\) −58.4128 −1.87746
\(969\) −40.8374 −1.31189
\(970\) −90.5433 −2.90717
\(971\) −39.8545 −1.27899 −0.639495 0.768795i \(-0.720857\pi\)
−0.639495 + 0.768795i \(0.720857\pi\)
\(972\) −49.2108 −1.57844
\(973\) −0.405471 −0.0129988
\(974\) −32.9232 −1.05493
\(975\) 131.917 4.22474
\(976\) −122.231 −3.91252
\(977\) 56.8097 1.81750 0.908752 0.417337i \(-0.137036\pi\)
0.908752 + 0.417337i \(0.137036\pi\)
\(978\) 151.344 4.83943
\(979\) −3.12756 −0.0999572
\(980\) −105.838 −3.38087
\(981\) −8.17671 −0.261062
\(982\) −11.0058 −0.351208
\(983\) −13.8591 −0.442036 −0.221018 0.975270i \(-0.570938\pi\)
−0.221018 + 0.975270i \(0.570938\pi\)
\(984\) −198.837 −6.33869
\(985\) −23.3117 −0.742774
\(986\) −43.7143 −1.39215
\(987\) −34.3487 −1.09333
\(988\) −217.472 −6.91871
\(989\) −26.0633 −0.828766
\(990\) 220.615 7.01160
\(991\) −13.7035 −0.435305 −0.217653 0.976026i \(-0.569840\pi\)
−0.217653 + 0.976026i \(0.569840\pi\)
\(992\) −78.3626 −2.48802
\(993\) −27.5886 −0.875498
\(994\) 14.6552 0.464836
\(995\) 96.9044 3.07208
\(996\) −148.715 −4.71221
\(997\) 23.8106 0.754088 0.377044 0.926195i \(-0.376940\pi\)
0.377044 + 0.926195i \(0.376940\pi\)
\(998\) 16.7701 0.530849
\(999\) −0.519330 −0.0164309
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 4003.2.a.c.1.4 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.4 179 1.1 even 1 trivial