Properties

Label 4730.2.a.z.1.10
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-2.42851\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.42851 q^{12} -1.86739 q^{13} +0.184466 q^{14} +3.42851 q^{15} +1.00000 q^{16} +1.38300 q^{17} -8.75468 q^{18} +2.95225 q^{19} +1.00000 q^{20} -0.632445 q^{21} -1.00000 q^{22} +4.77865 q^{23} -3.42851 q^{24} +1.00000 q^{25} +1.86739 q^{26} +19.7300 q^{27} -0.184466 q^{28} -2.99075 q^{29} -3.42851 q^{30} +10.5154 q^{31} -1.00000 q^{32} +3.42851 q^{33} -1.38300 q^{34} -0.184466 q^{35} +8.75468 q^{36} -8.37690 q^{37} -2.95225 q^{38} -6.40237 q^{39} -1.00000 q^{40} -4.20340 q^{41} +0.632445 q^{42} +1.00000 q^{43} +1.00000 q^{44} +8.75468 q^{45} -4.77865 q^{46} -8.11982 q^{47} +3.42851 q^{48} -6.96597 q^{49} -1.00000 q^{50} +4.74164 q^{51} -1.86739 q^{52} +8.47957 q^{53} -19.7300 q^{54} +1.00000 q^{55} +0.184466 q^{56} +10.1218 q^{57} +2.99075 q^{58} +0.668546 q^{59} +3.42851 q^{60} -1.18222 q^{61} -10.5154 q^{62} -1.61495 q^{63} +1.00000 q^{64} -1.86739 q^{65} -3.42851 q^{66} -7.72801 q^{67} +1.38300 q^{68} +16.3837 q^{69} +0.184466 q^{70} -13.0883 q^{71} -8.75468 q^{72} +13.7339 q^{73} +8.37690 q^{74} +3.42851 q^{75} +2.95225 q^{76} -0.184466 q^{77} +6.40237 q^{78} -17.0422 q^{79} +1.00000 q^{80} +41.3804 q^{81} +4.20340 q^{82} +9.61476 q^{83} -0.632445 q^{84} +1.38300 q^{85} -1.00000 q^{86} -10.2538 q^{87} -1.00000 q^{88} +9.80120 q^{89} -8.75468 q^{90} +0.344471 q^{91} +4.77865 q^{92} +36.0520 q^{93} +8.11982 q^{94} +2.95225 q^{95} -3.42851 q^{96} +10.6985 q^{97} +6.96597 q^{98} +8.75468 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 3.42851 1.97945 0.989726 0.142979i \(-0.0456681\pi\)
0.989726 + 0.142979i \(0.0456681\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −3.42851 −1.39968
\(7\) −0.184466 −0.0697218 −0.0348609 0.999392i \(-0.511099\pi\)
−0.0348609 + 0.999392i \(0.511099\pi\)
\(8\) −1.00000 −0.353553
\(9\) 8.75468 2.91823
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 3.42851 0.989726
\(13\) −1.86739 −0.517921 −0.258960 0.965888i \(-0.583380\pi\)
−0.258960 + 0.965888i \(0.583380\pi\)
\(14\) 0.184466 0.0493007
\(15\) 3.42851 0.885238
\(16\) 1.00000 0.250000
\(17\) 1.38300 0.335427 0.167714 0.985836i \(-0.446362\pi\)
0.167714 + 0.985836i \(0.446362\pi\)
\(18\) −8.75468 −2.06350
\(19\) 2.95225 0.677293 0.338647 0.940914i \(-0.390031\pi\)
0.338647 + 0.940914i \(0.390031\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.632445 −0.138011
\(22\) −1.00000 −0.213201
\(23\) 4.77865 0.996418 0.498209 0.867057i \(-0.333991\pi\)
0.498209 + 0.867057i \(0.333991\pi\)
\(24\) −3.42851 −0.699842
\(25\) 1.00000 0.200000
\(26\) 1.86739 0.366225
\(27\) 19.7300 3.79704
\(28\) −0.184466 −0.0348609
\(29\) −2.99075 −0.555369 −0.277684 0.960672i \(-0.589567\pi\)
−0.277684 + 0.960672i \(0.589567\pi\)
\(30\) −3.42851 −0.625958
\(31\) 10.5154 1.88861 0.944307 0.329065i \(-0.106734\pi\)
0.944307 + 0.329065i \(0.106734\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.42851 0.596827
\(34\) −1.38300 −0.237183
\(35\) −0.184466 −0.0311805
\(36\) 8.75468 1.45911
\(37\) −8.37690 −1.37715 −0.688577 0.725163i \(-0.741764\pi\)
−0.688577 + 0.725163i \(0.741764\pi\)
\(38\) −2.95225 −0.478919
\(39\) −6.40237 −1.02520
\(40\) −1.00000 −0.158114
\(41\) −4.20340 −0.656461 −0.328231 0.944598i \(-0.606452\pi\)
−0.328231 + 0.944598i \(0.606452\pi\)
\(42\) 0.632445 0.0975884
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 8.75468 1.30507
\(46\) −4.77865 −0.704574
\(47\) −8.11982 −1.18440 −0.592198 0.805792i \(-0.701740\pi\)
−0.592198 + 0.805792i \(0.701740\pi\)
\(48\) 3.42851 0.494863
\(49\) −6.96597 −0.995139
\(50\) −1.00000 −0.141421
\(51\) 4.74164 0.663962
\(52\) −1.86739 −0.258960
\(53\) 8.47957 1.16476 0.582380 0.812917i \(-0.302122\pi\)
0.582380 + 0.812917i \(0.302122\pi\)
\(54\) −19.7300 −2.68491
\(55\) 1.00000 0.134840
\(56\) 0.184466 0.0246504
\(57\) 10.1218 1.34067
\(58\) 2.99075 0.392705
\(59\) 0.668546 0.0870373 0.0435187 0.999053i \(-0.486143\pi\)
0.0435187 + 0.999053i \(0.486143\pi\)
\(60\) 3.42851 0.442619
\(61\) −1.18222 −0.151368 −0.0756840 0.997132i \(-0.524114\pi\)
−0.0756840 + 0.997132i \(0.524114\pi\)
\(62\) −10.5154 −1.33545
\(63\) −1.61495 −0.203464
\(64\) 1.00000 0.125000
\(65\) −1.86739 −0.231621
\(66\) −3.42851 −0.422020
\(67\) −7.72801 −0.944127 −0.472063 0.881565i \(-0.656491\pi\)
−0.472063 + 0.881565i \(0.656491\pi\)
\(68\) 1.38300 0.167714
\(69\) 16.3837 1.97236
\(70\) 0.184466 0.0220480
\(71\) −13.0883 −1.55329 −0.776646 0.629937i \(-0.783081\pi\)
−0.776646 + 0.629937i \(0.783081\pi\)
\(72\) −8.75468 −1.03175
\(73\) 13.7339 1.60743 0.803713 0.595017i \(-0.202855\pi\)
0.803713 + 0.595017i \(0.202855\pi\)
\(74\) 8.37690 0.973795
\(75\) 3.42851 0.395890
\(76\) 2.95225 0.338647
\(77\) −0.184466 −0.0210219
\(78\) 6.40237 0.724925
\(79\) −17.0422 −1.91740 −0.958698 0.284425i \(-0.908197\pi\)
−0.958698 + 0.284425i \(0.908197\pi\)
\(80\) 1.00000 0.111803
\(81\) 41.3804 4.59783
\(82\) 4.20340 0.464188
\(83\) 9.61476 1.05536 0.527679 0.849444i \(-0.323063\pi\)
0.527679 + 0.849444i \(0.323063\pi\)
\(84\) −0.632445 −0.0690054
\(85\) 1.38300 0.150008
\(86\) −1.00000 −0.107833
\(87\) −10.2538 −1.09933
\(88\) −1.00000 −0.106600
\(89\) 9.80120 1.03892 0.519462 0.854493i \(-0.326132\pi\)
0.519462 + 0.854493i \(0.326132\pi\)
\(90\) −8.75468 −0.922825
\(91\) 0.344471 0.0361104
\(92\) 4.77865 0.498209
\(93\) 36.0520 3.73842
\(94\) 8.11982 0.837495
\(95\) 2.95225 0.302895
\(96\) −3.42851 −0.349921
\(97\) 10.6985 1.08627 0.543137 0.839644i \(-0.317237\pi\)
0.543137 + 0.839644i \(0.317237\pi\)
\(98\) 6.96597 0.703669
\(99\) 8.75468 0.879879
\(100\) 1.00000 0.100000
\(101\) −11.2581 −1.12022 −0.560109 0.828419i \(-0.689241\pi\)
−0.560109 + 0.828419i \(0.689241\pi\)
\(102\) −4.74164 −0.469492
\(103\) −10.9672 −1.08063 −0.540313 0.841464i \(-0.681694\pi\)
−0.540313 + 0.841464i \(0.681694\pi\)
\(104\) 1.86739 0.183113
\(105\) −0.632445 −0.0617203
\(106\) −8.47957 −0.823609
\(107\) −13.3494 −1.29053 −0.645267 0.763958i \(-0.723254\pi\)
−0.645267 + 0.763958i \(0.723254\pi\)
\(108\) 19.7300 1.89852
\(109\) −11.5308 −1.10445 −0.552226 0.833694i \(-0.686222\pi\)
−0.552226 + 0.833694i \(0.686222\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −28.7203 −2.72601
\(112\) −0.184466 −0.0174304
\(113\) 2.29281 0.215689 0.107845 0.994168i \(-0.465605\pi\)
0.107845 + 0.994168i \(0.465605\pi\)
\(114\) −10.1218 −0.947996
\(115\) 4.77865 0.445612
\(116\) −2.99075 −0.277684
\(117\) −16.3484 −1.51141
\(118\) −0.668546 −0.0615447
\(119\) −0.255117 −0.0233866
\(120\) −3.42851 −0.312979
\(121\) 1.00000 0.0909091
\(122\) 1.18222 0.107033
\(123\) −14.4114 −1.29943
\(124\) 10.5154 0.944307
\(125\) 1.00000 0.0894427
\(126\) 1.61495 0.143871
\(127\) 10.6919 0.948752 0.474376 0.880322i \(-0.342674\pi\)
0.474376 + 0.880322i \(0.342674\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.42851 0.301864
\(130\) 1.86739 0.163781
\(131\) −17.2083 −1.50349 −0.751746 0.659453i \(-0.770788\pi\)
−0.751746 + 0.659453i \(0.770788\pi\)
\(132\) 3.42851 0.298414
\(133\) −0.544592 −0.0472221
\(134\) 7.72801 0.667598
\(135\) 19.7300 1.69809
\(136\) −1.38300 −0.118591
\(137\) 3.49548 0.298639 0.149320 0.988789i \(-0.452292\pi\)
0.149320 + 0.988789i \(0.452292\pi\)
\(138\) −16.3837 −1.39467
\(139\) 4.60638 0.390708 0.195354 0.980733i \(-0.437414\pi\)
0.195354 + 0.980733i \(0.437414\pi\)
\(140\) −0.184466 −0.0155903
\(141\) −27.8389 −2.34446
\(142\) 13.0883 1.09834
\(143\) −1.86739 −0.156159
\(144\) 8.75468 0.729557
\(145\) −2.99075 −0.248368
\(146\) −13.7339 −1.13662
\(147\) −23.8829 −1.96983
\(148\) −8.37690 −0.688577
\(149\) 11.1739 0.915405 0.457702 0.889105i \(-0.348673\pi\)
0.457702 + 0.889105i \(0.348673\pi\)
\(150\) −3.42851 −0.279937
\(151\) 21.3949 1.74109 0.870546 0.492087i \(-0.163766\pi\)
0.870546 + 0.492087i \(0.163766\pi\)
\(152\) −2.95225 −0.239459
\(153\) 12.1077 0.978853
\(154\) 0.184466 0.0148647
\(155\) 10.5154 0.844614
\(156\) −6.40237 −0.512600
\(157\) 1.88759 0.150646 0.0753232 0.997159i \(-0.476001\pi\)
0.0753232 + 0.997159i \(0.476001\pi\)
\(158\) 17.0422 1.35580
\(159\) 29.0723 2.30558
\(160\) −1.00000 −0.0790569
\(161\) −0.881502 −0.0694721
\(162\) −41.3804 −3.25115
\(163\) 8.28406 0.648858 0.324429 0.945910i \(-0.394828\pi\)
0.324429 + 0.945910i \(0.394828\pi\)
\(164\) −4.20340 −0.328231
\(165\) 3.42851 0.266909
\(166\) −9.61476 −0.746250
\(167\) 14.6096 1.13052 0.565261 0.824912i \(-0.308776\pi\)
0.565261 + 0.824912i \(0.308776\pi\)
\(168\) 0.632445 0.0487942
\(169\) −9.51285 −0.731758
\(170\) −1.38300 −0.106071
\(171\) 25.8460 1.97650
\(172\) 1.00000 0.0762493
\(173\) 17.7273 1.34779 0.673893 0.738829i \(-0.264621\pi\)
0.673893 + 0.738829i \(0.264621\pi\)
\(174\) 10.2538 0.777340
\(175\) −0.184466 −0.0139444
\(176\) 1.00000 0.0753778
\(177\) 2.29212 0.172286
\(178\) −9.80120 −0.734631
\(179\) 8.47601 0.633526 0.316763 0.948505i \(-0.397404\pi\)
0.316763 + 0.948505i \(0.397404\pi\)
\(180\) 8.75468 0.652536
\(181\) 13.9575 1.03746 0.518728 0.854940i \(-0.326406\pi\)
0.518728 + 0.854940i \(0.326406\pi\)
\(182\) −0.344471 −0.0255339
\(183\) −4.05326 −0.299626
\(184\) −4.77865 −0.352287
\(185\) −8.37690 −0.615882
\(186\) −36.0520 −2.64346
\(187\) 1.38300 0.101135
\(188\) −8.11982 −0.592198
\(189\) −3.63952 −0.264736
\(190\) −2.95225 −0.214179
\(191\) −4.20514 −0.304273 −0.152137 0.988359i \(-0.548615\pi\)
−0.152137 + 0.988359i \(0.548615\pi\)
\(192\) 3.42851 0.247431
\(193\) 4.54871 0.327423 0.163711 0.986508i \(-0.447653\pi\)
0.163711 + 0.986508i \(0.447653\pi\)
\(194\) −10.6985 −0.768111
\(195\) −6.40237 −0.458483
\(196\) −6.96597 −0.497569
\(197\) 6.70590 0.477776 0.238888 0.971047i \(-0.423217\pi\)
0.238888 + 0.971047i \(0.423217\pi\)
\(198\) −8.75468 −0.622168
\(199\) −4.34710 −0.308158 −0.154079 0.988059i \(-0.549241\pi\)
−0.154079 + 0.988059i \(0.549241\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −26.4956 −1.86885
\(202\) 11.2581 0.792114
\(203\) 0.551693 0.0387213
\(204\) 4.74164 0.331981
\(205\) −4.20340 −0.293578
\(206\) 10.9672 0.764118
\(207\) 41.8356 2.90778
\(208\) −1.86739 −0.129480
\(209\) 2.95225 0.204212
\(210\) 0.632445 0.0436429
\(211\) −17.4496 −1.20128 −0.600639 0.799520i \(-0.705087\pi\)
−0.600639 + 0.799520i \(0.705087\pi\)
\(212\) 8.47957 0.582380
\(213\) −44.8733 −3.07467
\(214\) 13.3494 0.912545
\(215\) 1.00000 0.0681994
\(216\) −19.7300 −1.34246
\(217\) −1.93973 −0.131678
\(218\) 11.5308 0.780966
\(219\) 47.0867 3.18182
\(220\) 1.00000 0.0674200
\(221\) −2.58260 −0.173725
\(222\) 28.7203 1.92758
\(223\) 9.03133 0.604783 0.302391 0.953184i \(-0.402215\pi\)
0.302391 + 0.953184i \(0.402215\pi\)
\(224\) 0.184466 0.0123252
\(225\) 8.75468 0.583646
\(226\) −2.29281 −0.152515
\(227\) 6.69594 0.444425 0.222213 0.974998i \(-0.428672\pi\)
0.222213 + 0.974998i \(0.428672\pi\)
\(228\) 10.1218 0.670335
\(229\) 14.1110 0.932483 0.466242 0.884657i \(-0.345608\pi\)
0.466242 + 0.884657i \(0.345608\pi\)
\(230\) −4.77865 −0.315095
\(231\) −0.632445 −0.0416118
\(232\) 2.99075 0.196352
\(233\) −10.6897 −0.700303 −0.350152 0.936693i \(-0.613870\pi\)
−0.350152 + 0.936693i \(0.613870\pi\)
\(234\) 16.3484 1.06873
\(235\) −8.11982 −0.529678
\(236\) 0.668546 0.0435187
\(237\) −58.4293 −3.79539
\(238\) 0.255117 0.0165368
\(239\) −18.7181 −1.21077 −0.605387 0.795931i \(-0.706982\pi\)
−0.605387 + 0.795931i \(0.706982\pi\)
\(240\) 3.42851 0.221309
\(241\) 13.0392 0.839929 0.419965 0.907540i \(-0.362042\pi\)
0.419965 + 0.907540i \(0.362042\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 82.6833 5.30414
\(244\) −1.18222 −0.0756840
\(245\) −6.96597 −0.445040
\(246\) 14.4114 0.918838
\(247\) −5.51301 −0.350784
\(248\) −10.5154 −0.667726
\(249\) 32.9643 2.08903
\(250\) −1.00000 −0.0632456
\(251\) −3.25282 −0.205316 −0.102658 0.994717i \(-0.532735\pi\)
−0.102658 + 0.994717i \(0.532735\pi\)
\(252\) −1.61495 −0.101732
\(253\) 4.77865 0.300431
\(254\) −10.6919 −0.670869
\(255\) 4.74164 0.296933
\(256\) 1.00000 0.0625000
\(257\) −2.88382 −0.179888 −0.0899439 0.995947i \(-0.528669\pi\)
−0.0899439 + 0.995947i \(0.528669\pi\)
\(258\) −3.42851 −0.213450
\(259\) 1.54526 0.0960176
\(260\) −1.86739 −0.115811
\(261\) −26.1831 −1.62069
\(262\) 17.2083 1.06313
\(263\) −27.2673 −1.68138 −0.840688 0.541520i \(-0.817849\pi\)
−0.840688 + 0.541520i \(0.817849\pi\)
\(264\) −3.42851 −0.211010
\(265\) 8.47957 0.520896
\(266\) 0.544592 0.0333911
\(267\) 33.6035 2.05650
\(268\) −7.72801 −0.472063
\(269\) −24.3978 −1.48756 −0.743779 0.668426i \(-0.766968\pi\)
−0.743779 + 0.668426i \(0.766968\pi\)
\(270\) −19.7300 −1.20073
\(271\) −5.30420 −0.322207 −0.161104 0.986937i \(-0.551505\pi\)
−0.161104 + 0.986937i \(0.551505\pi\)
\(272\) 1.38300 0.0838568
\(273\) 1.18102 0.0714787
\(274\) −3.49548 −0.211170
\(275\) 1.00000 0.0603023
\(276\) 16.3837 0.986181
\(277\) −11.8561 −0.712364 −0.356182 0.934417i \(-0.615922\pi\)
−0.356182 + 0.934417i \(0.615922\pi\)
\(278\) −4.60638 −0.276272
\(279\) 92.0586 5.51141
\(280\) 0.184466 0.0110240
\(281\) 17.2792 1.03079 0.515396 0.856952i \(-0.327645\pi\)
0.515396 + 0.856952i \(0.327645\pi\)
\(282\) 27.8389 1.65778
\(283\) −6.28973 −0.373886 −0.186943 0.982371i \(-0.559858\pi\)
−0.186943 + 0.982371i \(0.559858\pi\)
\(284\) −13.0883 −0.776646
\(285\) 10.1218 0.599566
\(286\) 1.86739 0.110421
\(287\) 0.775387 0.0457696
\(288\) −8.75468 −0.515875
\(289\) −15.0873 −0.887489
\(290\) 2.99075 0.175623
\(291\) 36.6801 2.15022
\(292\) 13.7339 0.803713
\(293\) 12.3915 0.723916 0.361958 0.932194i \(-0.382108\pi\)
0.361958 + 0.932194i \(0.382108\pi\)
\(294\) 23.8829 1.39288
\(295\) 0.668546 0.0389243
\(296\) 8.37690 0.486897
\(297\) 19.7300 1.14485
\(298\) −11.1739 −0.647289
\(299\) −8.92361 −0.516066
\(300\) 3.42851 0.197945
\(301\) −0.184466 −0.0106325
\(302\) −21.3949 −1.23114
\(303\) −38.5984 −2.21742
\(304\) 2.95225 0.169323
\(305\) −1.18222 −0.0676938
\(306\) −12.1077 −0.692154
\(307\) −20.3927 −1.16387 −0.581936 0.813234i \(-0.697705\pi\)
−0.581936 + 0.813234i \(0.697705\pi\)
\(308\) −0.184466 −0.0105110
\(309\) −37.6010 −2.13905
\(310\) −10.5154 −0.597232
\(311\) −7.49923 −0.425243 −0.212621 0.977135i \(-0.568200\pi\)
−0.212621 + 0.977135i \(0.568200\pi\)
\(312\) 6.40237 0.362463
\(313\) 7.80151 0.440967 0.220484 0.975391i \(-0.429236\pi\)
0.220484 + 0.975391i \(0.429236\pi\)
\(314\) −1.88759 −0.106523
\(315\) −1.61495 −0.0909919
\(316\) −17.0422 −0.958698
\(317\) 7.28303 0.409056 0.204528 0.978861i \(-0.434434\pi\)
0.204528 + 0.978861i \(0.434434\pi\)
\(318\) −29.0723 −1.63029
\(319\) −2.99075 −0.167450
\(320\) 1.00000 0.0559017
\(321\) −45.7685 −2.55455
\(322\) 0.881502 0.0491242
\(323\) 4.08297 0.227183
\(324\) 41.3804 2.29891
\(325\) −1.86739 −0.103584
\(326\) −8.28406 −0.458812
\(327\) −39.5336 −2.18621
\(328\) 4.20340 0.232094
\(329\) 1.49783 0.0825782
\(330\) −3.42851 −0.188733
\(331\) 6.13299 0.337100 0.168550 0.985693i \(-0.446092\pi\)
0.168550 + 0.985693i \(0.446092\pi\)
\(332\) 9.61476 0.527679
\(333\) −73.3371 −4.01885
\(334\) −14.6096 −0.799399
\(335\) −7.72801 −0.422226
\(336\) −0.632445 −0.0345027
\(337\) −18.2108 −0.992004 −0.496002 0.868321i \(-0.665199\pi\)
−0.496002 + 0.868321i \(0.665199\pi\)
\(338\) 9.51285 0.517431
\(339\) 7.86092 0.426947
\(340\) 1.38300 0.0750038
\(341\) 10.5154 0.569439
\(342\) −25.8460 −1.39759
\(343\) 2.57625 0.139105
\(344\) −1.00000 −0.0539164
\(345\) 16.3837 0.882067
\(346\) −17.7273 −0.953028
\(347\) −5.17920 −0.278034 −0.139017 0.990290i \(-0.544394\pi\)
−0.139017 + 0.990290i \(0.544394\pi\)
\(348\) −10.2538 −0.549663
\(349\) 9.30012 0.497824 0.248912 0.968526i \(-0.419927\pi\)
0.248912 + 0.968526i \(0.419927\pi\)
\(350\) 0.184466 0.00986015
\(351\) −36.8436 −1.96657
\(352\) −1.00000 −0.0533002
\(353\) −0.645416 −0.0343520 −0.0171760 0.999852i \(-0.505468\pi\)
−0.0171760 + 0.999852i \(0.505468\pi\)
\(354\) −2.29212 −0.121825
\(355\) −13.0883 −0.694654
\(356\) 9.80120 0.519462
\(357\) −0.874673 −0.0462926
\(358\) −8.47601 −0.447971
\(359\) 26.5913 1.40344 0.701718 0.712455i \(-0.252417\pi\)
0.701718 + 0.712455i \(0.252417\pi\)
\(360\) −8.75468 −0.461412
\(361\) −10.2842 −0.541274
\(362\) −13.9575 −0.733592
\(363\) 3.42851 0.179950
\(364\) 0.344471 0.0180552
\(365\) 13.7339 0.718863
\(366\) 4.05326 0.211867
\(367\) −14.7740 −0.771196 −0.385598 0.922667i \(-0.626005\pi\)
−0.385598 + 0.922667i \(0.626005\pi\)
\(368\) 4.77865 0.249105
\(369\) −36.7995 −1.91570
\(370\) 8.37690 0.435494
\(371\) −1.56420 −0.0812091
\(372\) 36.0520 1.86921
\(373\) −15.2156 −0.787833 −0.393916 0.919146i \(-0.628880\pi\)
−0.393916 + 0.919146i \(0.628880\pi\)
\(374\) −1.38300 −0.0715133
\(375\) 3.42851 0.177048
\(376\) 8.11982 0.418747
\(377\) 5.58490 0.287637
\(378\) 3.63952 0.187197
\(379\) 28.3159 1.45449 0.727244 0.686379i \(-0.240801\pi\)
0.727244 + 0.686379i \(0.240801\pi\)
\(380\) 2.95225 0.151447
\(381\) 36.6573 1.87801
\(382\) 4.20514 0.215154
\(383\) −32.8852 −1.68035 −0.840177 0.542313i \(-0.817549\pi\)
−0.840177 + 0.542313i \(0.817549\pi\)
\(384\) −3.42851 −0.174960
\(385\) −0.184466 −0.00940128
\(386\) −4.54871 −0.231523
\(387\) 8.75468 0.445026
\(388\) 10.6985 0.543137
\(389\) −14.7176 −0.746212 −0.373106 0.927789i \(-0.621707\pi\)
−0.373106 + 0.927789i \(0.621707\pi\)
\(390\) 6.40237 0.324196
\(391\) 6.60889 0.334226
\(392\) 6.96597 0.351835
\(393\) −58.9987 −2.97609
\(394\) −6.70590 −0.337839
\(395\) −17.0422 −0.857486
\(396\) 8.75468 0.439939
\(397\) 24.4872 1.22898 0.614489 0.788925i \(-0.289362\pi\)
0.614489 + 0.788925i \(0.289362\pi\)
\(398\) 4.34710 0.217900
\(399\) −1.86714 −0.0934739
\(400\) 1.00000 0.0500000
\(401\) −28.2812 −1.41229 −0.706147 0.708065i \(-0.749568\pi\)
−0.706147 + 0.708065i \(0.749568\pi\)
\(402\) 26.4956 1.32148
\(403\) −19.6363 −0.978153
\(404\) −11.2581 −0.560109
\(405\) 41.3804 2.05621
\(406\) −0.551693 −0.0273801
\(407\) −8.37690 −0.415228
\(408\) −4.74164 −0.234746
\(409\) 4.72448 0.233610 0.116805 0.993155i \(-0.462735\pi\)
0.116805 + 0.993155i \(0.462735\pi\)
\(410\) 4.20340 0.207591
\(411\) 11.9843 0.591142
\(412\) −10.9672 −0.540313
\(413\) −0.123324 −0.00606840
\(414\) −41.8356 −2.05611
\(415\) 9.61476 0.471970
\(416\) 1.86739 0.0915563
\(417\) 15.7930 0.773388
\(418\) −2.95225 −0.144399
\(419\) −16.7677 −0.819156 −0.409578 0.912275i \(-0.634324\pi\)
−0.409578 + 0.912275i \(0.634324\pi\)
\(420\) −0.632445 −0.0308602
\(421\) −38.1148 −1.85760 −0.928800 0.370581i \(-0.879159\pi\)
−0.928800 + 0.370581i \(0.879159\pi\)
\(422\) 17.4496 0.849432
\(423\) −71.0864 −3.45634
\(424\) −8.47957 −0.411805
\(425\) 1.38300 0.0670854
\(426\) 44.8733 2.17412
\(427\) 0.218080 0.0105536
\(428\) −13.3494 −0.645267
\(429\) −6.40237 −0.309109
\(430\) −1.00000 −0.0482243
\(431\) −1.60385 −0.0772547 −0.0386274 0.999254i \(-0.512299\pi\)
−0.0386274 + 0.999254i \(0.512299\pi\)
\(432\) 19.7300 0.949260
\(433\) 27.9656 1.34394 0.671971 0.740577i \(-0.265448\pi\)
0.671971 + 0.740577i \(0.265448\pi\)
\(434\) 1.93973 0.0931101
\(435\) −10.2538 −0.491633
\(436\) −11.5308 −0.552226
\(437\) 14.1078 0.674868
\(438\) −47.0867 −2.24989
\(439\) 32.6484 1.55822 0.779111 0.626886i \(-0.215671\pi\)
0.779111 + 0.626886i \(0.215671\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −60.9849 −2.90404
\(442\) 2.58260 0.122842
\(443\) −26.0337 −1.23690 −0.618450 0.785824i \(-0.712239\pi\)
−0.618450 + 0.785824i \(0.712239\pi\)
\(444\) −28.7203 −1.36300
\(445\) 9.80120 0.464621
\(446\) −9.03133 −0.427646
\(447\) 38.3100 1.81200
\(448\) −0.184466 −0.00871522
\(449\) −15.2249 −0.718509 −0.359254 0.933240i \(-0.616969\pi\)
−0.359254 + 0.933240i \(0.616969\pi\)
\(450\) −8.75468 −0.412700
\(451\) −4.20340 −0.197931
\(452\) 2.29281 0.107845
\(453\) 73.3526 3.44641
\(454\) −6.69594 −0.314256
\(455\) 0.344471 0.0161490
\(456\) −10.1218 −0.473998
\(457\) −31.6495 −1.48050 −0.740251 0.672331i \(-0.765293\pi\)
−0.740251 + 0.672331i \(0.765293\pi\)
\(458\) −14.1110 −0.659365
\(459\) 27.2866 1.27363
\(460\) 4.77865 0.222806
\(461\) −3.73982 −0.174181 −0.0870905 0.996200i \(-0.527757\pi\)
−0.0870905 + 0.996200i \(0.527757\pi\)
\(462\) 0.632445 0.0294240
\(463\) −17.8767 −0.830800 −0.415400 0.909639i \(-0.636358\pi\)
−0.415400 + 0.909639i \(0.636358\pi\)
\(464\) −2.99075 −0.138842
\(465\) 36.0520 1.67187
\(466\) 10.6897 0.495189
\(467\) −5.29123 −0.244849 −0.122424 0.992478i \(-0.539067\pi\)
−0.122424 + 0.992478i \(0.539067\pi\)
\(468\) −16.3484 −0.755706
\(469\) 1.42556 0.0658262
\(470\) 8.11982 0.374539
\(471\) 6.47163 0.298197
\(472\) −0.668546 −0.0307723
\(473\) 1.00000 0.0459800
\(474\) 58.4293 2.68375
\(475\) 2.95225 0.135459
\(476\) −0.255117 −0.0116933
\(477\) 74.2360 3.39903
\(478\) 18.7181 0.856146
\(479\) −27.4380 −1.25367 −0.626837 0.779150i \(-0.715651\pi\)
−0.626837 + 0.779150i \(0.715651\pi\)
\(480\) −3.42851 −0.156489
\(481\) 15.6429 0.713257
\(482\) −13.0392 −0.593920
\(483\) −3.02224 −0.137517
\(484\) 1.00000 0.0454545
\(485\) 10.6985 0.485796
\(486\) −82.6833 −3.75059
\(487\) −3.14932 −0.142710 −0.0713548 0.997451i \(-0.522732\pi\)
−0.0713548 + 0.997451i \(0.522732\pi\)
\(488\) 1.18222 0.0535167
\(489\) 28.4020 1.28438
\(490\) 6.96597 0.314691
\(491\) −18.2086 −0.821741 −0.410871 0.911694i \(-0.634775\pi\)
−0.410871 + 0.911694i \(0.634775\pi\)
\(492\) −14.4114 −0.649717
\(493\) −4.13621 −0.186286
\(494\) 5.51301 0.248042
\(495\) 8.75468 0.393494
\(496\) 10.5154 0.472154
\(497\) 2.41435 0.108298
\(498\) −32.9643 −1.47717
\(499\) 7.55692 0.338294 0.169147 0.985591i \(-0.445899\pi\)
0.169147 + 0.985591i \(0.445899\pi\)
\(500\) 1.00000 0.0447214
\(501\) 50.0890 2.23781
\(502\) 3.25282 0.145181
\(503\) −35.2791 −1.57302 −0.786508 0.617580i \(-0.788113\pi\)
−0.786508 + 0.617580i \(0.788113\pi\)
\(504\) 1.61495 0.0719354
\(505\) −11.2581 −0.500977
\(506\) −4.77865 −0.212437
\(507\) −32.6149 −1.44848
\(508\) 10.6919 0.474376
\(509\) −30.6656 −1.35923 −0.679614 0.733570i \(-0.737853\pi\)
−0.679614 + 0.733570i \(0.737853\pi\)
\(510\) −4.74164 −0.209963
\(511\) −2.53344 −0.112073
\(512\) −1.00000 −0.0441942
\(513\) 58.2480 2.57171
\(514\) 2.88382 0.127200
\(515\) −10.9672 −0.483270
\(516\) 3.42851 0.150932
\(517\) −8.11982 −0.357109
\(518\) −1.54526 −0.0678947
\(519\) 60.7784 2.66788
\(520\) 1.86739 0.0818905
\(521\) 10.2281 0.448101 0.224051 0.974578i \(-0.428072\pi\)
0.224051 + 0.974578i \(0.428072\pi\)
\(522\) 26.1831 1.14600
\(523\) 33.9426 1.48421 0.742104 0.670285i \(-0.233828\pi\)
0.742104 + 0.670285i \(0.233828\pi\)
\(524\) −17.2083 −0.751746
\(525\) −0.632445 −0.0276022
\(526\) 27.2673 1.18891
\(527\) 14.5428 0.633492
\(528\) 3.42851 0.149207
\(529\) −0.164461 −0.00715046
\(530\) −8.47957 −0.368329
\(531\) 5.85291 0.253995
\(532\) −0.544592 −0.0236111
\(533\) 7.84939 0.339995
\(534\) −33.6035 −1.45417
\(535\) −13.3494 −0.577144
\(536\) 7.72801 0.333799
\(537\) 29.0601 1.25403
\(538\) 24.3978 1.05186
\(539\) −6.96597 −0.300046
\(540\) 19.7300 0.849044
\(541\) 38.7747 1.66706 0.833528 0.552477i \(-0.186317\pi\)
0.833528 + 0.552477i \(0.186317\pi\)
\(542\) 5.30420 0.227835
\(543\) 47.8535 2.05359
\(544\) −1.38300 −0.0592957
\(545\) −11.5308 −0.493926
\(546\) −1.18102 −0.0505431
\(547\) 14.9174 0.637822 0.318911 0.947785i \(-0.396683\pi\)
0.318911 + 0.947785i \(0.396683\pi\)
\(548\) 3.49548 0.149320
\(549\) −10.3500 −0.441726
\(550\) −1.00000 −0.0426401
\(551\) −8.82946 −0.376147
\(552\) −16.3837 −0.697335
\(553\) 3.14371 0.133684
\(554\) 11.8561 0.503717
\(555\) −28.7203 −1.21911
\(556\) 4.60638 0.195354
\(557\) −20.8782 −0.884639 −0.442320 0.896858i \(-0.645844\pi\)
−0.442320 + 0.896858i \(0.645844\pi\)
\(558\) −92.0586 −3.89715
\(559\) −1.86739 −0.0789822
\(560\) −0.184466 −0.00779513
\(561\) 4.74164 0.200192
\(562\) −17.2792 −0.728881
\(563\) 35.6253 1.50143 0.750713 0.660629i \(-0.229710\pi\)
0.750713 + 0.660629i \(0.229710\pi\)
\(564\) −27.8389 −1.17223
\(565\) 2.29281 0.0964592
\(566\) 6.28973 0.264377
\(567\) −7.63331 −0.320569
\(568\) 13.0883 0.549172
\(569\) −19.0655 −0.799267 −0.399633 0.916675i \(-0.630863\pi\)
−0.399633 + 0.916675i \(0.630863\pi\)
\(570\) −10.1218 −0.423957
\(571\) −4.86908 −0.203765 −0.101882 0.994796i \(-0.532487\pi\)
−0.101882 + 0.994796i \(0.532487\pi\)
\(572\) −1.86739 −0.0780795
\(573\) −14.4174 −0.602294
\(574\) −0.775387 −0.0323640
\(575\) 4.77865 0.199284
\(576\) 8.75468 0.364779
\(577\) −16.2337 −0.675816 −0.337908 0.941179i \(-0.609719\pi\)
−0.337908 + 0.941179i \(0.609719\pi\)
\(578\) 15.0873 0.627549
\(579\) 15.5953 0.648118
\(580\) −2.99075 −0.124184
\(581\) −1.77360 −0.0735814
\(582\) −36.6801 −1.52044
\(583\) 8.47957 0.351188
\(584\) −13.7339 −0.568311
\(585\) −16.3484 −0.675924
\(586\) −12.3915 −0.511886
\(587\) 22.9307 0.946452 0.473226 0.880941i \(-0.343089\pi\)
0.473226 + 0.880941i \(0.343089\pi\)
\(588\) −23.8829 −0.984915
\(589\) 31.0440 1.27915
\(590\) −0.668546 −0.0275236
\(591\) 22.9913 0.945734
\(592\) −8.37690 −0.344289
\(593\) 37.6810 1.54737 0.773686 0.633569i \(-0.218411\pi\)
0.773686 + 0.633569i \(0.218411\pi\)
\(594\) −19.7300 −0.809532
\(595\) −0.255117 −0.0104588
\(596\) 11.1739 0.457702
\(597\) −14.9041 −0.609983
\(598\) 8.92361 0.364914
\(599\) 16.5054 0.674390 0.337195 0.941435i \(-0.390522\pi\)
0.337195 + 0.941435i \(0.390522\pi\)
\(600\) −3.42851 −0.139968
\(601\) 22.7227 0.926877 0.463439 0.886129i \(-0.346615\pi\)
0.463439 + 0.886129i \(0.346615\pi\)
\(602\) 0.184466 0.00751829
\(603\) −67.6563 −2.75518
\(604\) 21.3949 0.870546
\(605\) 1.00000 0.0406558
\(606\) 38.5984 1.56795
\(607\) −4.59208 −0.186387 −0.0931935 0.995648i \(-0.529708\pi\)
−0.0931935 + 0.995648i \(0.529708\pi\)
\(608\) −2.95225 −0.119730
\(609\) 1.89149 0.0766469
\(610\) 1.18222 0.0478668
\(611\) 15.1629 0.613424
\(612\) 12.1077 0.489426
\(613\) −44.7721 −1.80833 −0.904164 0.427186i \(-0.859505\pi\)
−0.904164 + 0.427186i \(0.859505\pi\)
\(614\) 20.3927 0.822982
\(615\) −14.4114 −0.581124
\(616\) 0.184466 0.00743237
\(617\) −37.9235 −1.52674 −0.763372 0.645959i \(-0.776458\pi\)
−0.763372 + 0.645959i \(0.776458\pi\)
\(618\) 37.6010 1.51253
\(619\) 28.5741 1.14849 0.574245 0.818684i \(-0.305296\pi\)
0.574245 + 0.818684i \(0.305296\pi\)
\(620\) 10.5154 0.422307
\(621\) 94.2828 3.78344
\(622\) 7.49923 0.300692
\(623\) −1.80799 −0.0724357
\(624\) −6.40237 −0.256300
\(625\) 1.00000 0.0400000
\(626\) −7.80151 −0.311811
\(627\) 10.1218 0.404227
\(628\) 1.88759 0.0753232
\(629\) −11.5853 −0.461935
\(630\) 1.61495 0.0643410
\(631\) 39.1470 1.55842 0.779209 0.626764i \(-0.215621\pi\)
0.779209 + 0.626764i \(0.215621\pi\)
\(632\) 17.0422 0.677902
\(633\) −59.8260 −2.37787
\(634\) −7.28303 −0.289246
\(635\) 10.6919 0.424295
\(636\) 29.0723 1.15279
\(637\) 13.0082 0.515403
\(638\) 2.99075 0.118405
\(639\) −114.584 −4.53286
\(640\) −1.00000 −0.0395285
\(641\) −49.5520 −1.95719 −0.978594 0.205802i \(-0.934020\pi\)
−0.978594 + 0.205802i \(0.934020\pi\)
\(642\) 45.7685 1.80634
\(643\) 28.1755 1.11113 0.555567 0.831472i \(-0.312501\pi\)
0.555567 + 0.831472i \(0.312501\pi\)
\(644\) −0.881502 −0.0347360
\(645\) 3.42851 0.134997
\(646\) −4.08297 −0.160642
\(647\) −25.7087 −1.01071 −0.505356 0.862911i \(-0.668639\pi\)
−0.505356 + 0.862911i \(0.668639\pi\)
\(648\) −41.3804 −1.62558
\(649\) 0.668546 0.0262427
\(650\) 1.86739 0.0732451
\(651\) −6.65039 −0.260649
\(652\) 8.28406 0.324429
\(653\) 14.8029 0.579284 0.289642 0.957135i \(-0.406464\pi\)
0.289642 + 0.957135i \(0.406464\pi\)
\(654\) 39.5336 1.54588
\(655\) −17.2083 −0.672382
\(656\) −4.20340 −0.164115
\(657\) 120.236 4.69084
\(658\) −1.49783 −0.0583916
\(659\) 43.8772 1.70921 0.854607 0.519275i \(-0.173798\pi\)
0.854607 + 0.519275i \(0.173798\pi\)
\(660\) 3.42851 0.133455
\(661\) −42.2923 −1.64498 −0.822490 0.568779i \(-0.807416\pi\)
−0.822490 + 0.568779i \(0.807416\pi\)
\(662\) −6.13299 −0.238366
\(663\) −8.85448 −0.343880
\(664\) −9.61476 −0.373125
\(665\) −0.544592 −0.0211184
\(666\) 73.3371 2.84176
\(667\) −14.2918 −0.553379
\(668\) 14.6096 0.565261
\(669\) 30.9640 1.19714
\(670\) 7.72801 0.298559
\(671\) −1.18222 −0.0456392
\(672\) 0.632445 0.0243971
\(673\) −24.1133 −0.929500 −0.464750 0.885442i \(-0.653856\pi\)
−0.464750 + 0.885442i \(0.653856\pi\)
\(674\) 18.2108 0.701452
\(675\) 19.7300 0.759408
\(676\) −9.51285 −0.365879
\(677\) 22.3245 0.858001 0.429000 0.903304i \(-0.358866\pi\)
0.429000 + 0.903304i \(0.358866\pi\)
\(678\) −7.86092 −0.301897
\(679\) −1.97352 −0.0757369
\(680\) −1.38300 −0.0530357
\(681\) 22.9571 0.879718
\(682\) −10.5154 −0.402654
\(683\) −20.8228 −0.796763 −0.398382 0.917220i \(-0.630428\pi\)
−0.398382 + 0.917220i \(0.630428\pi\)
\(684\) 25.8460 0.988248
\(685\) 3.49548 0.133556
\(686\) −2.57625 −0.0983618
\(687\) 48.3798 1.84581
\(688\) 1.00000 0.0381246
\(689\) −15.8347 −0.603253
\(690\) −16.3837 −0.623716
\(691\) −39.3969 −1.49873 −0.749365 0.662157i \(-0.769641\pi\)
−0.749365 + 0.662157i \(0.769641\pi\)
\(692\) 17.7273 0.673893
\(693\) −1.61495 −0.0613467
\(694\) 5.17920 0.196600
\(695\) 4.60638 0.174730
\(696\) 10.2538 0.388670
\(697\) −5.81331 −0.220195
\(698\) −9.30012 −0.352015
\(699\) −36.6496 −1.38622
\(700\) −0.184466 −0.00697218
\(701\) −43.8307 −1.65546 −0.827731 0.561125i \(-0.810369\pi\)
−0.827731 + 0.561125i \(0.810369\pi\)
\(702\) 36.8436 1.39057
\(703\) −24.7307 −0.932737
\(704\) 1.00000 0.0376889
\(705\) −27.8389 −1.04847
\(706\) 0.645416 0.0242906
\(707\) 2.07673 0.0781036
\(708\) 2.29212 0.0861431
\(709\) 17.7070 0.665000 0.332500 0.943103i \(-0.392108\pi\)
0.332500 + 0.943103i \(0.392108\pi\)
\(710\) 13.0883 0.491194
\(711\) −149.199 −5.59540
\(712\) −9.80120 −0.367315
\(713\) 50.2493 1.88185
\(714\) 0.874673 0.0327338
\(715\) −1.86739 −0.0698364
\(716\) 8.47601 0.316763
\(717\) −64.1752 −2.39667
\(718\) −26.5913 −0.992379
\(719\) −8.39883 −0.313224 −0.156612 0.987660i \(-0.550057\pi\)
−0.156612 + 0.987660i \(0.550057\pi\)
\(720\) 8.75468 0.326268
\(721\) 2.02307 0.0753431
\(722\) 10.2842 0.382738
\(723\) 44.7051 1.66260
\(724\) 13.9575 0.518728
\(725\) −2.99075 −0.111074
\(726\) −3.42851 −0.127244
\(727\) 48.1774 1.78680 0.893401 0.449261i \(-0.148313\pi\)
0.893401 + 0.449261i \(0.148313\pi\)
\(728\) −0.344471 −0.0127669
\(729\) 159.339 5.90145
\(730\) −13.7339 −0.508313
\(731\) 1.38300 0.0511522
\(732\) −4.05326 −0.149813
\(733\) 9.45432 0.349203 0.174602 0.984639i \(-0.444136\pi\)
0.174602 + 0.984639i \(0.444136\pi\)
\(734\) 14.7740 0.545318
\(735\) −23.8829 −0.880934
\(736\) −4.77865 −0.176144
\(737\) −7.72801 −0.284665
\(738\) 36.7995 1.35461
\(739\) 28.3743 1.04376 0.521882 0.853018i \(-0.325230\pi\)
0.521882 + 0.853018i \(0.325230\pi\)
\(740\) −8.37690 −0.307941
\(741\) −18.9014 −0.694361
\(742\) 1.56420 0.0574235
\(743\) −24.0323 −0.881659 −0.440829 0.897591i \(-0.645316\pi\)
−0.440829 + 0.897591i \(0.645316\pi\)
\(744\) −36.0520 −1.32173
\(745\) 11.1739 0.409381
\(746\) 15.2156 0.557082
\(747\) 84.1742 3.07977
\(748\) 1.38300 0.0505675
\(749\) 2.46251 0.0899783
\(750\) −3.42851 −0.125192
\(751\) −4.35455 −0.158900 −0.0794499 0.996839i \(-0.525316\pi\)
−0.0794499 + 0.996839i \(0.525316\pi\)
\(752\) −8.11982 −0.296099
\(753\) −11.1523 −0.406414
\(754\) −5.58490 −0.203390
\(755\) 21.3949 0.778640
\(756\) −3.63952 −0.132368
\(757\) 44.4631 1.61604 0.808020 0.589155i \(-0.200539\pi\)
0.808020 + 0.589155i \(0.200539\pi\)
\(758\) −28.3159 −1.02848
\(759\) 16.3837 0.594689
\(760\) −2.95225 −0.107089
\(761\) −48.0020 −1.74007 −0.870036 0.492988i \(-0.835904\pi\)
−0.870036 + 0.492988i \(0.835904\pi\)
\(762\) −36.6573 −1.32795
\(763\) 2.12705 0.0770044
\(764\) −4.20514 −0.152137
\(765\) 12.1077 0.437756
\(766\) 32.8852 1.18819
\(767\) −1.24844 −0.0450784
\(768\) 3.42851 0.123716
\(769\) 28.8769 1.04133 0.520665 0.853761i \(-0.325684\pi\)
0.520665 + 0.853761i \(0.325684\pi\)
\(770\) 0.184466 0.00664771
\(771\) −9.88721 −0.356079
\(772\) 4.54871 0.163711
\(773\) −28.1242 −1.01156 −0.505779 0.862663i \(-0.668795\pi\)
−0.505779 + 0.862663i \(0.668795\pi\)
\(774\) −8.75468 −0.314681
\(775\) 10.5154 0.377723
\(776\) −10.6985 −0.384056
\(777\) 5.29793 0.190062
\(778\) 14.7176 0.527652
\(779\) −12.4095 −0.444617
\(780\) −6.40237 −0.229242
\(781\) −13.0883 −0.468335
\(782\) −6.60889 −0.236333
\(783\) −59.0075 −2.10876
\(784\) −6.96597 −0.248785
\(785\) 1.88759 0.0673711
\(786\) 58.9987 2.10441
\(787\) 2.47731 0.0883065 0.0441532 0.999025i \(-0.485941\pi\)
0.0441532 + 0.999025i \(0.485941\pi\)
\(788\) 6.70590 0.238888
\(789\) −93.4863 −3.32820
\(790\) 17.0422 0.606334
\(791\) −0.422947 −0.0150382
\(792\) −8.75468 −0.311084
\(793\) 2.20767 0.0783967
\(794\) −24.4872 −0.869019
\(795\) 29.0723 1.03109
\(796\) −4.34710 −0.154079
\(797\) 38.3325 1.35781 0.678903 0.734228i \(-0.262456\pi\)
0.678903 + 0.734228i \(0.262456\pi\)
\(798\) 1.86714 0.0660960
\(799\) −11.2297 −0.397279
\(800\) −1.00000 −0.0353553
\(801\) 85.8064 3.03182
\(802\) 28.2812 0.998643
\(803\) 13.7339 0.484657
\(804\) −26.4956 −0.934427
\(805\) −0.881502 −0.0310688
\(806\) 19.6363 0.691658
\(807\) −83.6480 −2.94455
\(808\) 11.2581 0.396057
\(809\) −38.7940 −1.36392 −0.681962 0.731387i \(-0.738873\pi\)
−0.681962 + 0.731387i \(0.738873\pi\)
\(810\) −41.3804 −1.45396
\(811\) 8.02415 0.281766 0.140883 0.990026i \(-0.455006\pi\)
0.140883 + 0.990026i \(0.455006\pi\)
\(812\) 0.551693 0.0193606
\(813\) −18.1855 −0.637794
\(814\) 8.37690 0.293610
\(815\) 8.28406 0.290178
\(816\) 4.74164 0.165990
\(817\) 2.95225 0.103286
\(818\) −4.72448 −0.165188
\(819\) 3.01573 0.105378
\(820\) −4.20340 −0.146789
\(821\) 19.8993 0.694490 0.347245 0.937775i \(-0.387117\pi\)
0.347245 + 0.937775i \(0.387117\pi\)
\(822\) −11.9843 −0.418001
\(823\) 10.1533 0.353923 0.176961 0.984218i \(-0.443373\pi\)
0.176961 + 0.984218i \(0.443373\pi\)
\(824\) 10.9672 0.382059
\(825\) 3.42851 0.119365
\(826\) 0.123324 0.00429100
\(827\) 26.6730 0.927510 0.463755 0.885963i \(-0.346502\pi\)
0.463755 + 0.885963i \(0.346502\pi\)
\(828\) 41.8356 1.45389
\(829\) −45.8403 −1.59210 −0.796050 0.605231i \(-0.793081\pi\)
−0.796050 + 0.605231i \(0.793081\pi\)
\(830\) −9.61476 −0.333733
\(831\) −40.6488 −1.41009
\(832\) −1.86739 −0.0647401
\(833\) −9.63395 −0.333797
\(834\) −15.7930 −0.546868
\(835\) 14.6096 0.505584
\(836\) 2.95225 0.102106
\(837\) 207.468 7.17114
\(838\) 16.7677 0.579231
\(839\) −10.9506 −0.378055 −0.189028 0.981972i \(-0.560534\pi\)
−0.189028 + 0.981972i \(0.560534\pi\)
\(840\) 0.632445 0.0218214
\(841\) −20.0554 −0.691566
\(842\) 38.1148 1.31352
\(843\) 59.2420 2.04040
\(844\) −17.4496 −0.600639
\(845\) −9.51285 −0.327252
\(846\) 71.0864 2.44400
\(847\) −0.184466 −0.00633834
\(848\) 8.47957 0.291190
\(849\) −21.5644 −0.740088
\(850\) −1.38300 −0.0474366
\(851\) −40.0303 −1.37222
\(852\) −44.8733 −1.53733
\(853\) 46.6945 1.59879 0.799394 0.600807i \(-0.205154\pi\)
0.799394 + 0.600807i \(0.205154\pi\)
\(854\) −0.218080 −0.00746256
\(855\) 25.8460 0.883916
\(856\) 13.3494 0.456272
\(857\) 30.4220 1.03920 0.519598 0.854411i \(-0.326082\pi\)
0.519598 + 0.854411i \(0.326082\pi\)
\(858\) 6.40237 0.218573
\(859\) 13.6881 0.467031 0.233515 0.972353i \(-0.424977\pi\)
0.233515 + 0.972353i \(0.424977\pi\)
\(860\) 1.00000 0.0340997
\(861\) 2.65842 0.0905988
\(862\) 1.60385 0.0546274
\(863\) −19.0802 −0.649498 −0.324749 0.945800i \(-0.605280\pi\)
−0.324749 + 0.945800i \(0.605280\pi\)
\(864\) −19.7300 −0.671228
\(865\) 17.7273 0.602748
\(866\) −27.9656 −0.950311
\(867\) −51.7270 −1.75674
\(868\) −1.93973 −0.0658388
\(869\) −17.0422 −0.578117
\(870\) 10.2538 0.347637
\(871\) 14.4312 0.488983
\(872\) 11.5308 0.390483
\(873\) 93.6624 3.16999
\(874\) −14.1078 −0.477203
\(875\) −0.184466 −0.00623611
\(876\) 47.0867 1.59091
\(877\) 1.98680 0.0670895 0.0335448 0.999437i \(-0.489320\pi\)
0.0335448 + 0.999437i \(0.489320\pi\)
\(878\) −32.6484 −1.10183
\(879\) 42.4842 1.43296
\(880\) 1.00000 0.0337100
\(881\) −33.5881 −1.13161 −0.565805 0.824539i \(-0.691435\pi\)
−0.565805 + 0.824539i \(0.691435\pi\)
\(882\) 60.9849 2.05347
\(883\) 4.62390 0.155607 0.0778033 0.996969i \(-0.475209\pi\)
0.0778033 + 0.996969i \(0.475209\pi\)
\(884\) −2.58260 −0.0868624
\(885\) 2.29212 0.0770487
\(886\) 26.0337 0.874620
\(887\) −48.6666 −1.63406 −0.817032 0.576593i \(-0.804382\pi\)
−0.817032 + 0.576593i \(0.804382\pi\)
\(888\) 28.7203 0.963790
\(889\) −1.97230 −0.0661487
\(890\) −9.80120 −0.328537
\(891\) 41.3804 1.38630
\(892\) 9.03133 0.302391
\(893\) −23.9718 −0.802184
\(894\) −38.3100 −1.28128
\(895\) 8.47601 0.283322
\(896\) 0.184466 0.00616259
\(897\) −30.5947 −1.02153
\(898\) 15.2249 0.508062
\(899\) −31.4488 −1.04888
\(900\) 8.75468 0.291823
\(901\) 11.7273 0.390692
\(902\) 4.20340 0.139958
\(903\) −0.632445 −0.0210465
\(904\) −2.29281 −0.0762577
\(905\) 13.9575 0.463964
\(906\) −73.3526 −2.43698
\(907\) −13.6309 −0.452605 −0.226303 0.974057i \(-0.572664\pi\)
−0.226303 + 0.974057i \(0.572664\pi\)
\(908\) 6.69594 0.222213
\(909\) −98.5608 −3.26905
\(910\) −0.344471 −0.0114191
\(911\) −31.0975 −1.03031 −0.515154 0.857098i \(-0.672265\pi\)
−0.515154 + 0.857098i \(0.672265\pi\)
\(912\) 10.1218 0.335167
\(913\) 9.61476 0.318202
\(914\) 31.6495 1.04687
\(915\) −4.05326 −0.133997
\(916\) 14.1110 0.466242
\(917\) 3.17435 0.104826
\(918\) −27.2866 −0.900592
\(919\) −37.5417 −1.23839 −0.619194 0.785238i \(-0.712541\pi\)
−0.619194 + 0.785238i \(0.712541\pi\)
\(920\) −4.77865 −0.157548
\(921\) −69.9166 −2.30383
\(922\) 3.73982 0.123165
\(923\) 24.4409 0.804483
\(924\) −0.632445 −0.0208059
\(925\) −8.37690 −0.275431
\(926\) 17.8767 0.587464
\(927\) −96.0140 −3.15351
\(928\) 2.99075 0.0981762
\(929\) 39.9446 1.31054 0.655269 0.755395i \(-0.272555\pi\)
0.655269 + 0.755395i \(0.272555\pi\)
\(930\) −36.0520 −1.18219
\(931\) −20.5653 −0.674001
\(932\) −10.6897 −0.350152
\(933\) −25.7112 −0.841747
\(934\) 5.29123 0.173134
\(935\) 1.38300 0.0452290
\(936\) 16.3484 0.534365
\(937\) 39.5559 1.29224 0.646118 0.763238i \(-0.276392\pi\)
0.646118 + 0.763238i \(0.276392\pi\)
\(938\) −1.42556 −0.0465461
\(939\) 26.7476 0.872873
\(940\) −8.11982 −0.264839
\(941\) −24.8616 −0.810467 −0.405233 0.914213i \(-0.632810\pi\)
−0.405233 + 0.914213i \(0.632810\pi\)
\(942\) −6.47163 −0.210857
\(943\) −20.0866 −0.654110
\(944\) 0.668546 0.0217593
\(945\) −3.63952 −0.118394
\(946\) −1.00000 −0.0325128
\(947\) 40.0629 1.30187 0.650935 0.759133i \(-0.274377\pi\)
0.650935 + 0.759133i \(0.274377\pi\)
\(948\) −58.4293 −1.89770
\(949\) −25.6465 −0.832520
\(950\) −2.95225 −0.0957838
\(951\) 24.9699 0.809706
\(952\) 0.255117 0.00826840
\(953\) 3.50313 0.113478 0.0567388 0.998389i \(-0.481930\pi\)
0.0567388 + 0.998389i \(0.481930\pi\)
\(954\) −74.2360 −2.40348
\(955\) −4.20514 −0.136075
\(956\) −18.7181 −0.605387
\(957\) −10.2538 −0.331459
\(958\) 27.4380 0.886482
\(959\) −0.644800 −0.0208217
\(960\) 3.42851 0.110655
\(961\) 79.5728 2.56686
\(962\) −15.6429 −0.504349
\(963\) −116.870 −3.76607
\(964\) 13.0392 0.419965
\(965\) 4.54871 0.146428
\(966\) 3.02224 0.0972389
\(967\) 37.3781 1.20200 0.600999 0.799250i \(-0.294769\pi\)
0.600999 + 0.799250i \(0.294769\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 13.9985 0.449697
\(970\) −10.6985 −0.343510
\(971\) −15.7634 −0.505872 −0.252936 0.967483i \(-0.581396\pi\)
−0.252936 + 0.967483i \(0.581396\pi\)
\(972\) 82.6833 2.65207
\(973\) −0.849723 −0.0272409
\(974\) 3.14932 0.100911
\(975\) −6.40237 −0.205040
\(976\) −1.18222 −0.0378420
\(977\) 39.0346 1.24883 0.624414 0.781094i \(-0.285338\pi\)
0.624414 + 0.781094i \(0.285338\pi\)
\(978\) −28.4020 −0.908195
\(979\) 9.80120 0.313248
\(980\) −6.96597 −0.222520
\(981\) −100.949 −3.22304
\(982\) 18.2086 0.581059
\(983\) 31.9350 1.01857 0.509284 0.860598i \(-0.329910\pi\)
0.509284 + 0.860598i \(0.329910\pi\)
\(984\) 14.4114 0.459419
\(985\) 6.70590 0.213668
\(986\) 4.13621 0.131724
\(987\) 5.13534 0.163460
\(988\) −5.51301 −0.175392
\(989\) 4.77865 0.151952
\(990\) −8.75468 −0.278242
\(991\) −31.5856 −1.00335 −0.501674 0.865057i \(-0.667282\pi\)
−0.501674 + 0.865057i \(0.667282\pi\)
\(992\) −10.5154 −0.333863
\(993\) 21.0270 0.667273
\(994\) −2.41435 −0.0765785
\(995\) −4.34710 −0.137812
\(996\) 32.9643 1.04451
\(997\) −0.395014 −0.0125102 −0.00625511 0.999980i \(-0.501991\pi\)
−0.00625511 + 0.999980i \(0.501991\pi\)
\(998\) −7.55692 −0.239210
\(999\) −165.276 −5.22911
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 4730.2.a.z.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.10 10 1.1 even 1 trivial