Properties

Label 4730.2.a.bb.1.2
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
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 1.2
Root \(2.78036\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.78036 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.78036 q^{6} -2.23633 q^{7} -1.00000 q^{8} +4.73038 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.78036 q^{12} +6.07518 q^{13} +2.23633 q^{14} +2.78036 q^{15} +1.00000 q^{16} -2.92626 q^{17} -4.73038 q^{18} +3.18904 q^{19} -1.00000 q^{20} +6.21781 q^{21} +1.00000 q^{22} +4.07518 q^{23} +2.78036 q^{24} +1.00000 q^{25} -6.07518 q^{26} -4.81108 q^{27} -2.23633 q^{28} -1.19176 q^{29} -2.78036 q^{30} +9.94427 q^{31} -1.00000 q^{32} +2.78036 q^{33} +2.92626 q^{34} +2.23633 q^{35} +4.73038 q^{36} -7.90048 q^{37} -3.18904 q^{38} -16.8912 q^{39} +1.00000 q^{40} +0.260470 q^{41} -6.21781 q^{42} +1.00000 q^{43} -1.00000 q^{44} -4.73038 q^{45} -4.07518 q^{46} +4.67376 q^{47} -2.78036 q^{48} -1.99881 q^{49} -1.00000 q^{50} +8.13606 q^{51} +6.07518 q^{52} -7.82089 q^{53} +4.81108 q^{54} +1.00000 q^{55} +2.23633 q^{56} -8.86666 q^{57} +1.19176 q^{58} -0.284247 q^{59} +2.78036 q^{60} +9.70548 q^{61} -9.94427 q^{62} -10.5787 q^{63} +1.00000 q^{64} -6.07518 q^{65} -2.78036 q^{66} +4.43505 q^{67} -2.92626 q^{68} -11.3304 q^{69} -2.23633 q^{70} +0.755828 q^{71} -4.73038 q^{72} -14.1030 q^{73} +7.90048 q^{74} -2.78036 q^{75} +3.18904 q^{76} +2.23633 q^{77} +16.8912 q^{78} -0.0896609 q^{79} -1.00000 q^{80} -0.814626 q^{81} -0.260470 q^{82} -1.36880 q^{83} +6.21781 q^{84} +2.92626 q^{85} -1.00000 q^{86} +3.31352 q^{87} +1.00000 q^{88} -0.566497 q^{89} +4.73038 q^{90} -13.5861 q^{91} +4.07518 q^{92} -27.6486 q^{93} -4.67376 q^{94} -3.18904 q^{95} +2.78036 q^{96} -9.83384 q^{97} +1.99881 q^{98} -4.73038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

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
\(3\) −2.78036 −1.60524 −0.802620 0.596491i \(-0.796561\pi\)
−0.802620 + 0.596491i \(0.796561\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 2.78036 1.13508
\(7\) −2.23633 −0.845255 −0.422628 0.906303i \(-0.638892\pi\)
−0.422628 + 0.906303i \(0.638892\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.73038 1.57679
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −2.78036 −0.802620
\(13\) 6.07518 1.68495 0.842475 0.538735i \(-0.181098\pi\)
0.842475 + 0.538735i \(0.181098\pi\)
\(14\) 2.23633 0.597686
\(15\) 2.78036 0.717885
\(16\) 1.00000 0.250000
\(17\) −2.92626 −0.709723 −0.354862 0.934919i \(-0.615472\pi\)
−0.354862 + 0.934919i \(0.615472\pi\)
\(18\) −4.73038 −1.11496
\(19\) 3.18904 0.731616 0.365808 0.930690i \(-0.380793\pi\)
0.365808 + 0.930690i \(0.380793\pi\)
\(20\) −1.00000 −0.223607
\(21\) 6.21781 1.35684
\(22\) 1.00000 0.213201
\(23\) 4.07518 0.849733 0.424866 0.905256i \(-0.360321\pi\)
0.424866 + 0.905256i \(0.360321\pi\)
\(24\) 2.78036 0.567538
\(25\) 1.00000 0.200000
\(26\) −6.07518 −1.19144
\(27\) −4.81108 −0.925893
\(28\) −2.23633 −0.422628
\(29\) −1.19176 −0.221304 −0.110652 0.993859i \(-0.535294\pi\)
−0.110652 + 0.993859i \(0.535294\pi\)
\(30\) −2.78036 −0.507621
\(31\) 9.94427 1.78604 0.893022 0.450013i \(-0.148581\pi\)
0.893022 + 0.450013i \(0.148581\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.78036 0.483998
\(34\) 2.92626 0.501850
\(35\) 2.23633 0.378010
\(36\) 4.73038 0.788397
\(37\) −7.90048 −1.29883 −0.649415 0.760434i \(-0.724986\pi\)
−0.649415 + 0.760434i \(0.724986\pi\)
\(38\) −3.18904 −0.517330
\(39\) −16.8912 −2.70475
\(40\) 1.00000 0.158114
\(41\) 0.260470 0.0406785 0.0203393 0.999793i \(-0.493525\pi\)
0.0203393 + 0.999793i \(0.493525\pi\)
\(42\) −6.21781 −0.959429
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) −4.73038 −0.705164
\(46\) −4.07518 −0.600852
\(47\) 4.67376 0.681738 0.340869 0.940111i \(-0.389279\pi\)
0.340869 + 0.940111i \(0.389279\pi\)
\(48\) −2.78036 −0.401310
\(49\) −1.99881 −0.285544
\(50\) −1.00000 −0.141421
\(51\) 8.13606 1.13928
\(52\) 6.07518 0.842475
\(53\) −7.82089 −1.07428 −0.537141 0.843493i \(-0.680496\pi\)
−0.537141 + 0.843493i \(0.680496\pi\)
\(54\) 4.81108 0.654705
\(55\) 1.00000 0.134840
\(56\) 2.23633 0.298843
\(57\) −8.86666 −1.17442
\(58\) 1.19176 0.156486
\(59\) −0.284247 −0.0370059 −0.0185029 0.999829i \(-0.505890\pi\)
−0.0185029 + 0.999829i \(0.505890\pi\)
\(60\) 2.78036 0.358942
\(61\) 9.70548 1.24266 0.621330 0.783549i \(-0.286593\pi\)
0.621330 + 0.783549i \(0.286593\pi\)
\(62\) −9.94427 −1.26292
\(63\) −10.5787 −1.33279
\(64\) 1.00000 0.125000
\(65\) −6.07518 −0.753533
\(66\) −2.78036 −0.342238
\(67\) 4.43505 0.541827 0.270914 0.962604i \(-0.412674\pi\)
0.270914 + 0.962604i \(0.412674\pi\)
\(68\) −2.92626 −0.354862
\(69\) −11.3304 −1.36402
\(70\) −2.23633 −0.267293
\(71\) 0.755828 0.0897003 0.0448501 0.998994i \(-0.485719\pi\)
0.0448501 + 0.998994i \(0.485719\pi\)
\(72\) −4.73038 −0.557481
\(73\) −14.1030 −1.65063 −0.825317 0.564670i \(-0.809004\pi\)
−0.825317 + 0.564670i \(0.809004\pi\)
\(74\) 7.90048 0.918412
\(75\) −2.78036 −0.321048
\(76\) 3.18904 0.365808
\(77\) 2.23633 0.254854
\(78\) 16.8912 1.91255
\(79\) −0.0896609 −0.0100876 −0.00504382 0.999987i \(-0.501606\pi\)
−0.00504382 + 0.999987i \(0.501606\pi\)
\(80\) −1.00000 −0.111803
\(81\) −0.814626 −0.0905140
\(82\) −0.260470 −0.0287641
\(83\) −1.36880 −0.150245 −0.0751227 0.997174i \(-0.523935\pi\)
−0.0751227 + 0.997174i \(0.523935\pi\)
\(84\) 6.21781 0.678419
\(85\) 2.92626 0.317398
\(86\) −1.00000 −0.107833
\(87\) 3.31352 0.355247
\(88\) 1.00000 0.106600
\(89\) −0.566497 −0.0600486 −0.0300243 0.999549i \(-0.509558\pi\)
−0.0300243 + 0.999549i \(0.509558\pi\)
\(90\) 4.73038 0.498626
\(91\) −13.5861 −1.42421
\(92\) 4.07518 0.424866
\(93\) −27.6486 −2.86703
\(94\) −4.67376 −0.482062
\(95\) −3.18904 −0.327188
\(96\) 2.78036 0.283769
\(97\) −9.83384 −0.998475 −0.499237 0.866465i \(-0.666386\pi\)
−0.499237 + 0.866465i \(0.666386\pi\)
\(98\) 1.99881 0.201910
\(99\) −4.73038 −0.475421
\(100\) 1.00000 0.100000
\(101\) 5.70831 0.567998 0.283999 0.958825i \(-0.408339\pi\)
0.283999 + 0.958825i \(0.408339\pi\)
\(102\) −8.13606 −0.805590
\(103\) 13.7977 1.35953 0.679765 0.733430i \(-0.262082\pi\)
0.679765 + 0.733430i \(0.262082\pi\)
\(104\) −6.07518 −0.595720
\(105\) −6.21781 −0.606796
\(106\) 7.82089 0.759632
\(107\) −13.2977 −1.28554 −0.642768 0.766061i \(-0.722214\pi\)
−0.642768 + 0.766061i \(0.722214\pi\)
\(108\) −4.81108 −0.462947
\(109\) 19.6096 1.87826 0.939131 0.343560i \(-0.111633\pi\)
0.939131 + 0.343560i \(0.111633\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 21.9661 2.08493
\(112\) −2.23633 −0.211314
\(113\) −15.7306 −1.47981 −0.739906 0.672711i \(-0.765130\pi\)
−0.739906 + 0.672711i \(0.765130\pi\)
\(114\) 8.86666 0.830439
\(115\) −4.07518 −0.380012
\(116\) −1.19176 −0.110652
\(117\) 28.7379 2.65682
\(118\) 0.284247 0.0261671
\(119\) 6.54411 0.599897
\(120\) −2.78036 −0.253811
\(121\) 1.00000 0.0909091
\(122\) −9.70548 −0.878693
\(123\) −0.724198 −0.0652988
\(124\) 9.94427 0.893022
\(125\) −1.00000 −0.0894427
\(126\) 10.5787 0.942427
\(127\) 11.5520 1.02507 0.512536 0.858666i \(-0.328706\pi\)
0.512536 + 0.858666i \(0.328706\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.78036 −0.244797
\(130\) 6.07518 0.532828
\(131\) 10.5776 0.924169 0.462085 0.886836i \(-0.347102\pi\)
0.462085 + 0.886836i \(0.347102\pi\)
\(132\) 2.78036 0.241999
\(133\) −7.13176 −0.618402
\(134\) −4.43505 −0.383130
\(135\) 4.81108 0.414072
\(136\) 2.92626 0.250925
\(137\) −13.7741 −1.17680 −0.588398 0.808571i \(-0.700241\pi\)
−0.588398 + 0.808571i \(0.700241\pi\)
\(138\) 11.3304 0.964511
\(139\) −20.5287 −1.74122 −0.870612 0.491971i \(-0.836277\pi\)
−0.870612 + 0.491971i \(0.836277\pi\)
\(140\) 2.23633 0.189005
\(141\) −12.9947 −1.09435
\(142\) −0.755828 −0.0634277
\(143\) −6.07518 −0.508032
\(144\) 4.73038 0.394199
\(145\) 1.19176 0.0989704
\(146\) 14.1030 1.16717
\(147\) 5.55739 0.458366
\(148\) −7.90048 −0.649415
\(149\) −15.6368 −1.28101 −0.640507 0.767953i \(-0.721276\pi\)
−0.640507 + 0.767953i \(0.721276\pi\)
\(150\) 2.78036 0.227015
\(151\) −2.68616 −0.218596 −0.109298 0.994009i \(-0.534860\pi\)
−0.109298 + 0.994009i \(0.534860\pi\)
\(152\) −3.18904 −0.258665
\(153\) −13.8423 −1.11909
\(154\) −2.23633 −0.180209
\(155\) −9.94427 −0.798743
\(156\) −16.8912 −1.35237
\(157\) −8.69120 −0.693633 −0.346817 0.937933i \(-0.612737\pi\)
−0.346817 + 0.937933i \(0.612737\pi\)
\(158\) 0.0896609 0.00713304
\(159\) 21.7449 1.72448
\(160\) 1.00000 0.0790569
\(161\) −9.11346 −0.718241
\(162\) 0.814626 0.0640031
\(163\) 17.9395 1.40513 0.702566 0.711618i \(-0.252037\pi\)
0.702566 + 0.711618i \(0.252037\pi\)
\(164\) 0.260470 0.0203393
\(165\) −2.78036 −0.216450
\(166\) 1.36880 0.106240
\(167\) 2.55987 0.198089 0.0990444 0.995083i \(-0.468421\pi\)
0.0990444 + 0.995083i \(0.468421\pi\)
\(168\) −6.21781 −0.479714
\(169\) 23.9078 1.83906
\(170\) −2.92626 −0.224434
\(171\) 15.0854 1.15361
\(172\) 1.00000 0.0762493
\(173\) −5.95162 −0.452493 −0.226247 0.974070i \(-0.572645\pi\)
−0.226247 + 0.974070i \(0.572645\pi\)
\(174\) −3.31352 −0.251197
\(175\) −2.23633 −0.169051
\(176\) −1.00000 −0.0753778
\(177\) 0.790309 0.0594033
\(178\) 0.566497 0.0424608
\(179\) 13.1577 0.983450 0.491725 0.870750i \(-0.336366\pi\)
0.491725 + 0.870750i \(0.336366\pi\)
\(180\) −4.73038 −0.352582
\(181\) −4.22391 −0.313961 −0.156980 0.987602i \(-0.550176\pi\)
−0.156980 + 0.987602i \(0.550176\pi\)
\(182\) 13.5861 1.00707
\(183\) −26.9847 −1.99477
\(184\) −4.07518 −0.300426
\(185\) 7.90048 0.580855
\(186\) 27.6486 2.02730
\(187\) 2.92626 0.213990
\(188\) 4.67376 0.340869
\(189\) 10.7592 0.782616
\(190\) 3.18904 0.231357
\(191\) 5.16411 0.373662 0.186831 0.982392i \(-0.440178\pi\)
0.186831 + 0.982392i \(0.440178\pi\)
\(192\) −2.78036 −0.200655
\(193\) −6.27237 −0.451495 −0.225747 0.974186i \(-0.572482\pi\)
−0.225747 + 0.974186i \(0.572482\pi\)
\(194\) 9.83384 0.706028
\(195\) 16.8912 1.20960
\(196\) −1.99881 −0.142772
\(197\) −3.22621 −0.229858 −0.114929 0.993374i \(-0.536664\pi\)
−0.114929 + 0.993374i \(0.536664\pi\)
\(198\) 4.73038 0.336174
\(199\) −10.4621 −0.741639 −0.370820 0.928705i \(-0.620923\pi\)
−0.370820 + 0.928705i \(0.620923\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −12.3310 −0.869763
\(202\) −5.70831 −0.401635
\(203\) 2.66518 0.187059
\(204\) 8.13606 0.569638
\(205\) −0.260470 −0.0181920
\(206\) −13.7977 −0.961333
\(207\) 19.2771 1.33985
\(208\) 6.07518 0.421238
\(209\) −3.18904 −0.220590
\(210\) 6.21781 0.429070
\(211\) 5.79975 0.399271 0.199636 0.979870i \(-0.436024\pi\)
0.199636 + 0.979870i \(0.436024\pi\)
\(212\) −7.82089 −0.537141
\(213\) −2.10147 −0.143990
\(214\) 13.2977 0.909012
\(215\) −1.00000 −0.0681994
\(216\) 4.81108 0.327353
\(217\) −22.2387 −1.50966
\(218\) −19.6096 −1.32813
\(219\) 39.2114 2.64966
\(220\) 1.00000 0.0674200
\(221\) −17.7776 −1.19585
\(222\) −21.9661 −1.47427
\(223\) 5.90132 0.395182 0.197591 0.980285i \(-0.436688\pi\)
0.197591 + 0.980285i \(0.436688\pi\)
\(224\) 2.23633 0.149421
\(225\) 4.73038 0.315359
\(226\) 15.7306 1.04638
\(227\) 4.86985 0.323224 0.161612 0.986854i \(-0.448331\pi\)
0.161612 + 0.986854i \(0.448331\pi\)
\(228\) −8.86666 −0.587209
\(229\) 7.27039 0.480441 0.240221 0.970718i \(-0.422780\pi\)
0.240221 + 0.970718i \(0.422780\pi\)
\(230\) 4.07518 0.268709
\(231\) −6.21781 −0.409102
\(232\) 1.19176 0.0782430
\(233\) 20.2797 1.32856 0.664282 0.747482i \(-0.268737\pi\)
0.664282 + 0.747482i \(0.268737\pi\)
\(234\) −28.7379 −1.87866
\(235\) −4.67376 −0.304883
\(236\) −0.284247 −0.0185029
\(237\) 0.249289 0.0161931
\(238\) −6.54411 −0.424191
\(239\) −4.03204 −0.260811 −0.130405 0.991461i \(-0.541628\pi\)
−0.130405 + 0.991461i \(0.541628\pi\)
\(240\) 2.78036 0.179471
\(241\) 17.7984 1.14650 0.573248 0.819382i \(-0.305683\pi\)
0.573248 + 0.819382i \(0.305683\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 16.6982 1.07119
\(244\) 9.70548 0.621330
\(245\) 1.99881 0.127699
\(246\) 0.724198 0.0461732
\(247\) 19.3740 1.23274
\(248\) −9.94427 −0.631462
\(249\) 3.80576 0.241180
\(250\) 1.00000 0.0632456
\(251\) −12.9233 −0.815714 −0.407857 0.913046i \(-0.633724\pi\)
−0.407857 + 0.913046i \(0.633724\pi\)
\(252\) −10.5787 −0.666397
\(253\) −4.07518 −0.256204
\(254\) −11.5520 −0.724836
\(255\) −8.13606 −0.509500
\(256\) 1.00000 0.0625000
\(257\) −4.64010 −0.289442 −0.144721 0.989473i \(-0.546228\pi\)
−0.144721 + 0.989473i \(0.546228\pi\)
\(258\) 2.78036 0.173097
\(259\) 17.6681 1.09784
\(260\) −6.07518 −0.376766
\(261\) −5.63749 −0.348952
\(262\) −10.5776 −0.653486
\(263\) 23.3570 1.44025 0.720126 0.693843i \(-0.244084\pi\)
0.720126 + 0.693843i \(0.244084\pi\)
\(264\) −2.78036 −0.171119
\(265\) 7.82089 0.480433
\(266\) 7.13176 0.437276
\(267\) 1.57506 0.0963924
\(268\) 4.43505 0.270914
\(269\) 25.6357 1.56304 0.781518 0.623882i \(-0.214446\pi\)
0.781518 + 0.623882i \(0.214446\pi\)
\(270\) −4.81108 −0.292793
\(271\) −22.9503 −1.39413 −0.697065 0.717008i \(-0.745511\pi\)
−0.697065 + 0.717008i \(0.745511\pi\)
\(272\) −2.92626 −0.177431
\(273\) 37.7743 2.28620
\(274\) 13.7741 0.832121
\(275\) −1.00000 −0.0603023
\(276\) −11.3304 −0.682012
\(277\) −6.32737 −0.380175 −0.190088 0.981767i \(-0.560877\pi\)
−0.190088 + 0.981767i \(0.560877\pi\)
\(278\) 20.5287 1.23123
\(279\) 47.0402 2.81622
\(280\) −2.23633 −0.133647
\(281\) 3.92493 0.234142 0.117071 0.993124i \(-0.462650\pi\)
0.117071 + 0.993124i \(0.462650\pi\)
\(282\) 12.9947 0.773825
\(283\) 24.3865 1.44963 0.724814 0.688945i \(-0.241926\pi\)
0.724814 + 0.688945i \(0.241926\pi\)
\(284\) 0.755828 0.0448501
\(285\) 8.86666 0.525216
\(286\) 6.07518 0.359233
\(287\) −0.582497 −0.0343837
\(288\) −4.73038 −0.278740
\(289\) −8.43698 −0.496293
\(290\) −1.19176 −0.0699826
\(291\) 27.3416 1.60279
\(292\) −14.1030 −0.825317
\(293\) −7.85186 −0.458711 −0.229355 0.973343i \(-0.573662\pi\)
−0.229355 + 0.973343i \(0.573662\pi\)
\(294\) −5.55739 −0.324114
\(295\) 0.284247 0.0165495
\(296\) 7.90048 0.459206
\(297\) 4.81108 0.279167
\(298\) 15.6368 0.905813
\(299\) 24.7574 1.43176
\(300\) −2.78036 −0.160524
\(301\) −2.23633 −0.128900
\(302\) 2.68616 0.154571
\(303\) −15.8711 −0.911773
\(304\) 3.18904 0.182904
\(305\) −9.70548 −0.555734
\(306\) 13.8423 0.791314
\(307\) −17.5404 −1.00109 −0.500543 0.865712i \(-0.666866\pi\)
−0.500543 + 0.865712i \(0.666866\pi\)
\(308\) 2.23633 0.127427
\(309\) −38.3626 −2.18237
\(310\) 9.94427 0.564797
\(311\) 4.70078 0.266557 0.133278 0.991079i \(-0.457450\pi\)
0.133278 + 0.991079i \(0.457450\pi\)
\(312\) 16.8912 0.956273
\(313\) 5.93044 0.335208 0.167604 0.985854i \(-0.446397\pi\)
0.167604 + 0.985854i \(0.446397\pi\)
\(314\) 8.69120 0.490473
\(315\) 10.5787 0.596043
\(316\) −0.0896609 −0.00504382
\(317\) 30.5059 1.71338 0.856690 0.515832i \(-0.172517\pi\)
0.856690 + 0.515832i \(0.172517\pi\)
\(318\) −21.7449 −1.21939
\(319\) 1.19176 0.0667258
\(320\) −1.00000 −0.0559017
\(321\) 36.9723 2.06359
\(322\) 9.11346 0.507873
\(323\) −9.33197 −0.519245
\(324\) −0.814626 −0.0452570
\(325\) 6.07518 0.336990
\(326\) −17.9395 −0.993579
\(327\) −54.5218 −3.01506
\(328\) −0.260470 −0.0143820
\(329\) −10.4521 −0.576243
\(330\) 2.78036 0.153054
\(331\) −33.8704 −1.86169 −0.930844 0.365418i \(-0.880926\pi\)
−0.930844 + 0.365418i \(0.880926\pi\)
\(332\) −1.36880 −0.0751227
\(333\) −37.3723 −2.04799
\(334\) −2.55987 −0.140070
\(335\) −4.43505 −0.242313
\(336\) 6.21781 0.339209
\(337\) −14.4868 −0.789146 −0.394573 0.918865i \(-0.629107\pi\)
−0.394573 + 0.918865i \(0.629107\pi\)
\(338\) −23.9078 −1.30041
\(339\) 43.7367 2.37545
\(340\) 2.92626 0.158699
\(341\) −9.94427 −0.538512
\(342\) −15.0854 −0.815724
\(343\) 20.1243 1.08661
\(344\) −1.00000 −0.0539164
\(345\) 11.3304 0.610010
\(346\) 5.95162 0.319961
\(347\) −22.2669 −1.19535 −0.597676 0.801738i \(-0.703909\pi\)
−0.597676 + 0.801738i \(0.703909\pi\)
\(348\) 3.31352 0.177623
\(349\) 15.9685 0.854772 0.427386 0.904069i \(-0.359434\pi\)
0.427386 + 0.904069i \(0.359434\pi\)
\(350\) 2.23633 0.119537
\(351\) −29.2282 −1.56008
\(352\) 1.00000 0.0533002
\(353\) −3.31107 −0.176230 −0.0881152 0.996110i \(-0.528084\pi\)
−0.0881152 + 0.996110i \(0.528084\pi\)
\(354\) −0.790309 −0.0420045
\(355\) −0.755828 −0.0401152
\(356\) −0.566497 −0.0300243
\(357\) −18.1949 −0.962979
\(358\) −13.1577 −0.695404
\(359\) 26.7424 1.41141 0.705706 0.708505i \(-0.250630\pi\)
0.705706 + 0.708505i \(0.250630\pi\)
\(360\) 4.73038 0.249313
\(361\) −8.83003 −0.464739
\(362\) 4.22391 0.222004
\(363\) −2.78036 −0.145931
\(364\) −13.5861 −0.712107
\(365\) 14.1030 0.738186
\(366\) 26.9847 1.41051
\(367\) 16.9938 0.887067 0.443534 0.896258i \(-0.353725\pi\)
0.443534 + 0.896258i \(0.353725\pi\)
\(368\) 4.07518 0.212433
\(369\) 1.23212 0.0641417
\(370\) −7.90048 −0.410726
\(371\) 17.4901 0.908042
\(372\) −27.6486 −1.43351
\(373\) 37.3692 1.93490 0.967451 0.253060i \(-0.0814369\pi\)
0.967451 + 0.253060i \(0.0814369\pi\)
\(374\) −2.92626 −0.151313
\(375\) 2.78036 0.143577
\(376\) −4.67376 −0.241031
\(377\) −7.24016 −0.372887
\(378\) −10.7592 −0.553393
\(379\) 1.03658 0.0532455 0.0266227 0.999646i \(-0.491525\pi\)
0.0266227 + 0.999646i \(0.491525\pi\)
\(380\) −3.18904 −0.163594
\(381\) −32.1186 −1.64549
\(382\) −5.16411 −0.264219
\(383\) 27.6980 1.41530 0.707650 0.706563i \(-0.249755\pi\)
0.707650 + 0.706563i \(0.249755\pi\)
\(384\) 2.78036 0.141884
\(385\) −2.23633 −0.113974
\(386\) 6.27237 0.319255
\(387\) 4.73038 0.240459
\(388\) −9.83384 −0.499237
\(389\) 17.5667 0.890667 0.445333 0.895365i \(-0.353085\pi\)
0.445333 + 0.895365i \(0.353085\pi\)
\(390\) −16.8912 −0.855317
\(391\) −11.9250 −0.603075
\(392\) 1.99881 0.100955
\(393\) −29.4095 −1.48351
\(394\) 3.22621 0.162534
\(395\) 0.0896609 0.00451133
\(396\) −4.73038 −0.237711
\(397\) −6.40764 −0.321590 −0.160795 0.986988i \(-0.551406\pi\)
−0.160795 + 0.986988i \(0.551406\pi\)
\(398\) 10.4621 0.524418
\(399\) 19.8288 0.992683
\(400\) 1.00000 0.0500000
\(401\) 10.7565 0.537153 0.268576 0.963258i \(-0.413447\pi\)
0.268576 + 0.963258i \(0.413447\pi\)
\(402\) 12.3310 0.615015
\(403\) 60.4132 3.00940
\(404\) 5.70831 0.283999
\(405\) 0.814626 0.0404791
\(406\) −2.66518 −0.132271
\(407\) 7.90048 0.391612
\(408\) −8.13606 −0.402795
\(409\) 1.88588 0.0932510 0.0466255 0.998912i \(-0.485153\pi\)
0.0466255 + 0.998912i \(0.485153\pi\)
\(410\) 0.260470 0.0128637
\(411\) 38.2968 1.88904
\(412\) 13.7977 0.679765
\(413\) 0.635673 0.0312794
\(414\) −19.2771 −0.947420
\(415\) 1.36880 0.0671918
\(416\) −6.07518 −0.297860
\(417\) 57.0772 2.79508
\(418\) 3.18904 0.155981
\(419\) −17.9288 −0.875877 −0.437938 0.899005i \(-0.644291\pi\)
−0.437938 + 0.899005i \(0.644291\pi\)
\(420\) −6.21781 −0.303398
\(421\) 16.8657 0.821982 0.410991 0.911639i \(-0.365183\pi\)
0.410991 + 0.911639i \(0.365183\pi\)
\(422\) −5.79975 −0.282327
\(423\) 22.1087 1.07496
\(424\) 7.82089 0.379816
\(425\) −2.92626 −0.141945
\(426\) 2.10147 0.101817
\(427\) −21.7047 −1.05036
\(428\) −13.2977 −0.642768
\(429\) 16.8912 0.815513
\(430\) 1.00000 0.0482243
\(431\) −17.1282 −0.825034 −0.412517 0.910950i \(-0.635350\pi\)
−0.412517 + 0.910950i \(0.635350\pi\)
\(432\) −4.81108 −0.231473
\(433\) 21.8387 1.04950 0.524750 0.851257i \(-0.324159\pi\)
0.524750 + 0.851257i \(0.324159\pi\)
\(434\) 22.2387 1.06749
\(435\) −3.31352 −0.158871
\(436\) 19.6096 0.939131
\(437\) 12.9959 0.621678
\(438\) −39.2114 −1.87359
\(439\) −19.9372 −0.951549 −0.475775 0.879567i \(-0.657832\pi\)
−0.475775 + 0.879567i \(0.657832\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −9.45512 −0.450244
\(442\) 17.7776 0.845593
\(443\) −0.843192 −0.0400612 −0.0200306 0.999799i \(-0.506376\pi\)
−0.0200306 + 0.999799i \(0.506376\pi\)
\(444\) 21.9661 1.04247
\(445\) 0.566497 0.0268546
\(446\) −5.90132 −0.279436
\(447\) 43.4758 2.05633
\(448\) −2.23633 −0.105657
\(449\) 7.31208 0.345079 0.172539 0.985003i \(-0.444803\pi\)
0.172539 + 0.985003i \(0.444803\pi\)
\(450\) −4.73038 −0.222992
\(451\) −0.260470 −0.0122650
\(452\) −15.7306 −0.739906
\(453\) 7.46848 0.350900
\(454\) −4.86985 −0.228554
\(455\) 13.5861 0.636928
\(456\) 8.86666 0.415220
\(457\) 38.6073 1.80597 0.902986 0.429670i \(-0.141370\pi\)
0.902986 + 0.429670i \(0.141370\pi\)
\(458\) −7.27039 −0.339723
\(459\) 14.0785 0.657128
\(460\) −4.07518 −0.190006
\(461\) 23.3428 1.08718 0.543590 0.839351i \(-0.317064\pi\)
0.543590 + 0.839351i \(0.317064\pi\)
\(462\) 6.21781 0.289279
\(463\) −8.38418 −0.389646 −0.194823 0.980838i \(-0.562413\pi\)
−0.194823 + 0.980838i \(0.562413\pi\)
\(464\) −1.19176 −0.0553261
\(465\) 27.6486 1.28217
\(466\) −20.2797 −0.939437
\(467\) −11.1461 −0.515779 −0.257889 0.966174i \(-0.583027\pi\)
−0.257889 + 0.966174i \(0.583027\pi\)
\(468\) 28.7379 1.32841
\(469\) −9.91825 −0.457982
\(470\) 4.67376 0.215585
\(471\) 24.1646 1.11345
\(472\) 0.284247 0.0130836
\(473\) −1.00000 −0.0459800
\(474\) −0.249289 −0.0114502
\(475\) 3.18904 0.146323
\(476\) 6.54411 0.299949
\(477\) −36.9958 −1.69392
\(478\) 4.03204 0.184421
\(479\) 2.37394 0.108468 0.0542342 0.998528i \(-0.482728\pi\)
0.0542342 + 0.998528i \(0.482728\pi\)
\(480\) −2.78036 −0.126905
\(481\) −47.9968 −2.18847
\(482\) −17.7984 −0.810695
\(483\) 25.3387 1.15295
\(484\) 1.00000 0.0454545
\(485\) 9.83384 0.446532
\(486\) −16.6982 −0.757446
\(487\) −19.6638 −0.891051 −0.445526 0.895269i \(-0.646983\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(488\) −9.70548 −0.439346
\(489\) −49.8783 −2.25557
\(490\) −1.99881 −0.0902969
\(491\) 25.7939 1.16406 0.582031 0.813167i \(-0.302258\pi\)
0.582031 + 0.813167i \(0.302258\pi\)
\(492\) −0.724198 −0.0326494
\(493\) 3.48741 0.157065
\(494\) −19.3740 −0.871676
\(495\) 4.73038 0.212615
\(496\) 9.94427 0.446511
\(497\) −1.69028 −0.0758196
\(498\) −3.80576 −0.170540
\(499\) 27.9568 1.25152 0.625759 0.780017i \(-0.284790\pi\)
0.625759 + 0.780017i \(0.284790\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −7.11735 −0.317980
\(502\) 12.9233 0.576797
\(503\) −17.4342 −0.777352 −0.388676 0.921374i \(-0.627068\pi\)
−0.388676 + 0.921374i \(0.627068\pi\)
\(504\) 10.5787 0.471214
\(505\) −5.70831 −0.254016
\(506\) 4.07518 0.181164
\(507\) −66.4721 −2.95213
\(508\) 11.5520 0.512536
\(509\) −9.04819 −0.401054 −0.200527 0.979688i \(-0.564265\pi\)
−0.200527 + 0.979688i \(0.564265\pi\)
\(510\) 8.13606 0.360271
\(511\) 31.5391 1.39521
\(512\) −1.00000 −0.0441942
\(513\) −15.3427 −0.677398
\(514\) 4.64010 0.204666
\(515\) −13.7977 −0.608000
\(516\) −2.78036 −0.122398
\(517\) −4.67376 −0.205552
\(518\) −17.6681 −0.776292
\(519\) 16.5476 0.726360
\(520\) 6.07518 0.266414
\(521\) −23.4949 −1.02933 −0.514665 0.857391i \(-0.672084\pi\)
−0.514665 + 0.857391i \(0.672084\pi\)
\(522\) 5.63749 0.246746
\(523\) 19.5821 0.856266 0.428133 0.903716i \(-0.359172\pi\)
0.428133 + 0.903716i \(0.359172\pi\)
\(524\) 10.5776 0.462085
\(525\) 6.21781 0.271367
\(526\) −23.3570 −1.01841
\(527\) −29.0996 −1.26760
\(528\) 2.78036 0.120999
\(529\) −6.39294 −0.277954
\(530\) −7.82089 −0.339718
\(531\) −1.34460 −0.0583506
\(532\) −7.13176 −0.309201
\(533\) 1.58240 0.0685413
\(534\) −1.57506 −0.0681597
\(535\) 13.2977 0.574909
\(536\) −4.43505 −0.191565
\(537\) −36.5830 −1.57867
\(538\) −25.6357 −1.10523
\(539\) 1.99881 0.0860947
\(540\) 4.81108 0.207036
\(541\) 32.6334 1.40302 0.701510 0.712659i \(-0.252509\pi\)
0.701510 + 0.712659i \(0.252509\pi\)
\(542\) 22.9503 0.985799
\(543\) 11.7440 0.503982
\(544\) 2.92626 0.125463
\(545\) −19.6096 −0.839984
\(546\) −37.7743 −1.61659
\(547\) 16.9552 0.724953 0.362476 0.931993i \(-0.381931\pi\)
0.362476 + 0.931993i \(0.381931\pi\)
\(548\) −13.7741 −0.588398
\(549\) 45.9106 1.95942
\(550\) 1.00000 0.0426401
\(551\) −3.80057 −0.161910
\(552\) 11.3304 0.482256
\(553\) 0.200512 0.00852663
\(554\) 6.32737 0.268824
\(555\) −21.9661 −0.932411
\(556\) −20.5287 −0.870612
\(557\) 7.68137 0.325470 0.162735 0.986670i \(-0.447968\pi\)
0.162735 + 0.986670i \(0.447968\pi\)
\(558\) −47.0402 −1.99137
\(559\) 6.07518 0.256953
\(560\) 2.23633 0.0945024
\(561\) −8.13606 −0.343505
\(562\) −3.92493 −0.165563
\(563\) −4.33255 −0.182595 −0.0912977 0.995824i \(-0.529101\pi\)
−0.0912977 + 0.995824i \(0.529101\pi\)
\(564\) −12.9947 −0.547177
\(565\) 15.7306 0.661792
\(566\) −24.3865 −1.02504
\(567\) 1.82178 0.0765074
\(568\) −0.755828 −0.0317138
\(569\) 42.1183 1.76569 0.882845 0.469664i \(-0.155625\pi\)
0.882845 + 0.469664i \(0.155625\pi\)
\(570\) −8.86666 −0.371384
\(571\) −27.8033 −1.16353 −0.581765 0.813357i \(-0.697638\pi\)
−0.581765 + 0.813357i \(0.697638\pi\)
\(572\) −6.07518 −0.254016
\(573\) −14.3581 −0.599816
\(574\) 0.582497 0.0243130
\(575\) 4.07518 0.169947
\(576\) 4.73038 0.197099
\(577\) 9.66392 0.402314 0.201157 0.979559i \(-0.435530\pi\)
0.201157 + 0.979559i \(0.435530\pi\)
\(578\) 8.43698 0.350932
\(579\) 17.4394 0.724757
\(580\) 1.19176 0.0494852
\(581\) 3.06110 0.126996
\(582\) −27.3416 −1.13334
\(583\) 7.82089 0.323908
\(584\) 14.1030 0.583587
\(585\) −28.7379 −1.18817
\(586\) 7.85186 0.324358
\(587\) 14.6392 0.604225 0.302113 0.953272i \(-0.402308\pi\)
0.302113 + 0.953272i \(0.402308\pi\)
\(588\) 5.55739 0.229183
\(589\) 31.7127 1.30670
\(590\) −0.284247 −0.0117023
\(591\) 8.97002 0.368977
\(592\) −7.90048 −0.324708
\(593\) −41.5135 −1.70475 −0.852377 0.522928i \(-0.824840\pi\)
−0.852377 + 0.522928i \(0.824840\pi\)
\(594\) −4.81108 −0.197401
\(595\) −6.54411 −0.268282
\(596\) −15.6368 −0.640507
\(597\) 29.0884 1.19051
\(598\) −24.7574 −1.01241
\(599\) 16.8623 0.688974 0.344487 0.938791i \(-0.388053\pi\)
0.344487 + 0.938791i \(0.388053\pi\)
\(600\) 2.78036 0.113508
\(601\) 42.7351 1.74320 0.871600 0.490218i \(-0.163083\pi\)
0.871600 + 0.490218i \(0.163083\pi\)
\(602\) 2.23633 0.0911462
\(603\) 20.9795 0.854350
\(604\) −2.68616 −0.109298
\(605\) −1.00000 −0.0406558
\(606\) 15.8711 0.644721
\(607\) 3.01569 0.122403 0.0612015 0.998125i \(-0.480507\pi\)
0.0612015 + 0.998125i \(0.480507\pi\)
\(608\) −3.18904 −0.129333
\(609\) −7.41014 −0.300274
\(610\) 9.70548 0.392963
\(611\) 28.3939 1.14870
\(612\) −13.8423 −0.559544
\(613\) 38.9176 1.57187 0.785934 0.618311i \(-0.212183\pi\)
0.785934 + 0.618311i \(0.212183\pi\)
\(614\) 17.5404 0.707874
\(615\) 0.724198 0.0292025
\(616\) −2.23633 −0.0901045
\(617\) 0.0901936 0.00363106 0.00181553 0.999998i \(-0.499422\pi\)
0.00181553 + 0.999998i \(0.499422\pi\)
\(618\) 38.3626 1.54317
\(619\) 2.45207 0.0985570 0.0492785 0.998785i \(-0.484308\pi\)
0.0492785 + 0.998785i \(0.484308\pi\)
\(620\) −9.94427 −0.399372
\(621\) −19.6060 −0.786762
\(622\) −4.70078 −0.188484
\(623\) 1.26688 0.0507564
\(624\) −16.8912 −0.676187
\(625\) 1.00000 0.0400000
\(626\) −5.93044 −0.237028
\(627\) 8.86666 0.354100
\(628\) −8.69120 −0.346817
\(629\) 23.1189 0.921810
\(630\) −10.5787 −0.421466
\(631\) −26.5739 −1.05789 −0.528946 0.848656i \(-0.677413\pi\)
−0.528946 + 0.848656i \(0.677413\pi\)
\(632\) 0.0896609 0.00356652
\(633\) −16.1254 −0.640926
\(634\) −30.5059 −1.21154
\(635\) −11.5520 −0.458426
\(636\) 21.7449 0.862240
\(637\) −12.1431 −0.481127
\(638\) −1.19176 −0.0471823
\(639\) 3.57536 0.141439
\(640\) 1.00000 0.0395285
\(641\) 19.5523 0.772269 0.386134 0.922443i \(-0.373810\pi\)
0.386134 + 0.922443i \(0.373810\pi\)
\(642\) −36.9723 −1.45918
\(643\) 4.33884 0.171107 0.0855536 0.996334i \(-0.472734\pi\)
0.0855536 + 0.996334i \(0.472734\pi\)
\(644\) −9.11346 −0.359121
\(645\) 2.78036 0.109476
\(646\) 9.33197 0.367161
\(647\) 16.2937 0.640571 0.320285 0.947321i \(-0.396221\pi\)
0.320285 + 0.947321i \(0.396221\pi\)
\(648\) 0.814626 0.0320015
\(649\) 0.284247 0.0111577
\(650\) −6.07518 −0.238288
\(651\) 61.8316 2.42337
\(652\) 17.9395 0.702566
\(653\) −0.332094 −0.0129959 −0.00649793 0.999979i \(-0.502068\pi\)
−0.00649793 + 0.999979i \(0.502068\pi\)
\(654\) 54.5218 2.13197
\(655\) −10.5776 −0.413301
\(656\) 0.260470 0.0101696
\(657\) −66.7127 −2.60271
\(658\) 10.4521 0.407465
\(659\) −33.0075 −1.28579 −0.642894 0.765955i \(-0.722267\pi\)
−0.642894 + 0.765955i \(0.722267\pi\)
\(660\) −2.78036 −0.108225
\(661\) −20.2264 −0.786717 −0.393359 0.919385i \(-0.628687\pi\)
−0.393359 + 0.919385i \(0.628687\pi\)
\(662\) 33.8704 1.31641
\(663\) 49.4280 1.91962
\(664\) 1.36880 0.0531198
\(665\) 7.13176 0.276558
\(666\) 37.3723 1.44815
\(667\) −4.85664 −0.188050
\(668\) 2.55987 0.0990444
\(669\) −16.4078 −0.634362
\(670\) 4.43505 0.171341
\(671\) −9.70548 −0.374676
\(672\) −6.21781 −0.239857
\(673\) −39.1340 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(674\) 14.4868 0.558010
\(675\) −4.81108 −0.185179
\(676\) 23.9078 0.919529
\(677\) 37.5404 1.44279 0.721397 0.692522i \(-0.243500\pi\)
0.721397 + 0.692522i \(0.243500\pi\)
\(678\) −43.7367 −1.67970
\(679\) 21.9918 0.843966
\(680\) −2.92626 −0.112217
\(681\) −13.5399 −0.518851
\(682\) 9.94427 0.380786
\(683\) 25.0783 0.959593 0.479797 0.877380i \(-0.340710\pi\)
0.479797 + 0.877380i \(0.340710\pi\)
\(684\) 15.0854 0.576804
\(685\) 13.7741 0.526280
\(686\) −20.1243 −0.768351
\(687\) −20.2143 −0.771223
\(688\) 1.00000 0.0381246
\(689\) −47.5133 −1.81011
\(690\) −11.3304 −0.431343
\(691\) 12.3002 0.467923 0.233962 0.972246i \(-0.424831\pi\)
0.233962 + 0.972246i \(0.424831\pi\)
\(692\) −5.95162 −0.226247
\(693\) 10.5787 0.401852
\(694\) 22.2669 0.845241
\(695\) 20.5287 0.778699
\(696\) −3.31352 −0.125599
\(697\) −0.762203 −0.0288705
\(698\) −15.9685 −0.604415
\(699\) −56.3847 −2.13266
\(700\) −2.23633 −0.0845255
\(701\) −21.2307 −0.801873 −0.400937 0.916106i \(-0.631315\pi\)
−0.400937 + 0.916106i \(0.631315\pi\)
\(702\) 29.2282 1.10315
\(703\) −25.1949 −0.950245
\(704\) −1.00000 −0.0376889
\(705\) 12.9947 0.489410
\(706\) 3.31107 0.124614
\(707\) −12.7657 −0.480103
\(708\) 0.790309 0.0297016
\(709\) −6.08228 −0.228425 −0.114212 0.993456i \(-0.536434\pi\)
−0.114212 + 0.993456i \(0.536434\pi\)
\(710\) 0.755828 0.0283657
\(711\) −0.424131 −0.0159061
\(712\) 0.566497 0.0212304
\(713\) 40.5247 1.51766
\(714\) 18.1949 0.680929
\(715\) 6.07518 0.227199
\(716\) 13.1577 0.491725
\(717\) 11.2105 0.418664
\(718\) −26.7424 −0.998019
\(719\) 1.07483 0.0400845 0.0200422 0.999799i \(-0.493620\pi\)
0.0200422 + 0.999799i \(0.493620\pi\)
\(720\) −4.73038 −0.176291
\(721\) −30.8563 −1.14915
\(722\) 8.83003 0.328620
\(723\) −49.4859 −1.84040
\(724\) −4.22391 −0.156980
\(725\) −1.19176 −0.0442609
\(726\) 2.78036 0.103189
\(727\) −17.9217 −0.664681 −0.332340 0.943160i \(-0.607838\pi\)
−0.332340 + 0.943160i \(0.607838\pi\)
\(728\) 13.5861 0.503535
\(729\) −43.9831 −1.62900
\(730\) −14.1030 −0.521976
\(731\) −2.92626 −0.108232
\(732\) −26.9847 −0.997383
\(733\) −8.14994 −0.301025 −0.150512 0.988608i \(-0.548092\pi\)
−0.150512 + 0.988608i \(0.548092\pi\)
\(734\) −16.9938 −0.627251
\(735\) −5.55739 −0.204988
\(736\) −4.07518 −0.150213
\(737\) −4.43505 −0.163367
\(738\) −1.23212 −0.0453550
\(739\) −7.03166 −0.258664 −0.129332 0.991601i \(-0.541283\pi\)
−0.129332 + 0.991601i \(0.541283\pi\)
\(740\) 7.90048 0.290427
\(741\) −53.8665 −1.97884
\(742\) −17.4901 −0.642083
\(743\) −30.6577 −1.12472 −0.562362 0.826891i \(-0.690107\pi\)
−0.562362 + 0.826891i \(0.690107\pi\)
\(744\) 27.6486 1.01365
\(745\) 15.6368 0.572887
\(746\) −37.3692 −1.36818
\(747\) −6.47496 −0.236906
\(748\) 2.92626 0.106995
\(749\) 29.7381 1.08661
\(750\) −2.78036 −0.101524
\(751\) −16.3040 −0.594942 −0.297471 0.954731i \(-0.596143\pi\)
−0.297471 + 0.954731i \(0.596143\pi\)
\(752\) 4.67376 0.170435
\(753\) 35.9315 1.30942
\(754\) 7.24016 0.263671
\(755\) 2.68616 0.0977593
\(756\) 10.7592 0.391308
\(757\) 9.87049 0.358749 0.179375 0.983781i \(-0.442593\pi\)
0.179375 + 0.983781i \(0.442593\pi\)
\(758\) −1.03658 −0.0376502
\(759\) 11.3304 0.411269
\(760\) 3.18904 0.115679
\(761\) −11.4904 −0.416528 −0.208264 0.978073i \(-0.566781\pi\)
−0.208264 + 0.978073i \(0.566781\pi\)
\(762\) 32.1186 1.16353
\(763\) −43.8537 −1.58761
\(764\) 5.16411 0.186831
\(765\) 13.8423 0.500471
\(766\) −27.6980 −1.00077
\(767\) −1.72685 −0.0623531
\(768\) −2.78036 −0.100327
\(769\) 28.1250 1.01421 0.507107 0.861883i \(-0.330715\pi\)
0.507107 + 0.861883i \(0.330715\pi\)
\(770\) 2.23633 0.0805919
\(771\) 12.9011 0.464623
\(772\) −6.27237 −0.225747
\(773\) 23.9790 0.862464 0.431232 0.902241i \(-0.358079\pi\)
0.431232 + 0.902241i \(0.358079\pi\)
\(774\) −4.73038 −0.170030
\(775\) 9.94427 0.357209
\(776\) 9.83384 0.353014
\(777\) −49.1237 −1.76230
\(778\) −17.5667 −0.629796
\(779\) 0.830648 0.0297610
\(780\) 16.8912 0.604800
\(781\) −0.755828 −0.0270457
\(782\) 11.9250 0.426439
\(783\) 5.73366 0.204904
\(784\) −1.99881 −0.0713859
\(785\) 8.69120 0.310202
\(786\) 29.4095 1.04900
\(787\) 26.1714 0.932908 0.466454 0.884545i \(-0.345531\pi\)
0.466454 + 0.884545i \(0.345531\pi\)
\(788\) −3.22621 −0.114929
\(789\) −64.9407 −2.31195
\(790\) −0.0896609 −0.00318999
\(791\) 35.1789 1.25082
\(792\) 4.73038 0.168087
\(793\) 58.9625 2.09382
\(794\) 6.40764 0.227398
\(795\) −21.7449 −0.771211
\(796\) −10.4621 −0.370820
\(797\) 37.7124 1.33584 0.667921 0.744232i \(-0.267184\pi\)
0.667921 + 0.744232i \(0.267184\pi\)
\(798\) −19.8288 −0.701933
\(799\) −13.6767 −0.483846
\(800\) −1.00000 −0.0353553
\(801\) −2.67975 −0.0946843
\(802\) −10.7565 −0.379824
\(803\) 14.1030 0.497685
\(804\) −12.3310 −0.434881
\(805\) 9.11346 0.321207
\(806\) −60.4132 −2.12796
\(807\) −71.2764 −2.50905
\(808\) −5.70831 −0.200818
\(809\) −42.1131 −1.48062 −0.740309 0.672267i \(-0.765321\pi\)
−0.740309 + 0.672267i \(0.765321\pi\)
\(810\) −0.814626 −0.0286230
\(811\) −46.4013 −1.62937 −0.814684 0.579905i \(-0.803090\pi\)
−0.814684 + 0.579905i \(0.803090\pi\)
\(812\) 2.66518 0.0935294
\(813\) 63.8100 2.23791
\(814\) −7.90048 −0.276912
\(815\) −17.9395 −0.628394
\(816\) 8.13606 0.284819
\(817\) 3.18904 0.111570
\(818\) −1.88588 −0.0659384
\(819\) −64.2676 −2.24569
\(820\) −0.260470 −0.00909599
\(821\) −24.1105 −0.841463 −0.420731 0.907185i \(-0.638226\pi\)
−0.420731 + 0.907185i \(0.638226\pi\)
\(822\) −38.2968 −1.33575
\(823\) 9.31660 0.324756 0.162378 0.986729i \(-0.448084\pi\)
0.162378 + 0.986729i \(0.448084\pi\)
\(824\) −13.7977 −0.480666
\(825\) 2.78036 0.0967996
\(826\) −0.635673 −0.0221179
\(827\) 12.6945 0.441431 0.220715 0.975338i \(-0.429161\pi\)
0.220715 + 0.975338i \(0.429161\pi\)
\(828\) 19.2771 0.669927
\(829\) 41.3858 1.43739 0.718695 0.695326i \(-0.244740\pi\)
0.718695 + 0.695326i \(0.244740\pi\)
\(830\) −1.36880 −0.0475118
\(831\) 17.5924 0.610272
\(832\) 6.07518 0.210619
\(833\) 5.84903 0.202657
\(834\) −57.0772 −1.97642
\(835\) −2.55987 −0.0885880
\(836\) −3.18904 −0.110295
\(837\) −47.8427 −1.65369
\(838\) 17.9288 0.619339
\(839\) 3.92581 0.135534 0.0677671 0.997701i \(-0.478413\pi\)
0.0677671 + 0.997701i \(0.478413\pi\)
\(840\) 6.21781 0.214535
\(841\) −27.5797 −0.951024
\(842\) −16.8657 −0.581229
\(843\) −10.9127 −0.375853
\(844\) 5.79975 0.199636
\(845\) −23.9078 −0.822452
\(846\) −22.1087 −0.760112
\(847\) −2.23633 −0.0768414
\(848\) −7.82089 −0.268570
\(849\) −67.8032 −2.32700
\(850\) 2.92626 0.100370
\(851\) −32.1958 −1.10366
\(852\) −2.10147 −0.0719952
\(853\) −31.4017 −1.07517 −0.537587 0.843208i \(-0.680664\pi\)
−0.537587 + 0.843208i \(0.680664\pi\)
\(854\) 21.7047 0.742720
\(855\) −15.0854 −0.515909
\(856\) 13.2977 0.454506
\(857\) −43.8245 −1.49701 −0.748507 0.663126i \(-0.769229\pi\)
−0.748507 + 0.663126i \(0.769229\pi\)
\(858\) −16.8912 −0.576655
\(859\) −40.9094 −1.39581 −0.697905 0.716191i \(-0.745884\pi\)
−0.697905 + 0.716191i \(0.745884\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 1.61955 0.0551941
\(862\) 17.1282 0.583387
\(863\) 16.9259 0.576165 0.288082 0.957606i \(-0.406982\pi\)
0.288082 + 0.957606i \(0.406982\pi\)
\(864\) 4.81108 0.163676
\(865\) 5.95162 0.202361
\(866\) −21.8387 −0.742108
\(867\) 23.4578 0.796669
\(868\) −22.2387 −0.754831
\(869\) 0.0896609 0.00304154
\(870\) 3.31352 0.112339
\(871\) 26.9437 0.912952
\(872\) −19.6096 −0.664066
\(873\) −46.5178 −1.57439
\(874\) −12.9959 −0.439593
\(875\) 2.23633 0.0756019
\(876\) 39.2114 1.32483
\(877\) 28.5771 0.964979 0.482489 0.875902i \(-0.339733\pi\)
0.482489 + 0.875902i \(0.339733\pi\)
\(878\) 19.9372 0.672847
\(879\) 21.8310 0.736341
\(880\) 1.00000 0.0337100
\(881\) −22.4892 −0.757681 −0.378840 0.925462i \(-0.623677\pi\)
−0.378840 + 0.925462i \(0.623677\pi\)
\(882\) 9.45512 0.318370
\(883\) 37.3828 1.25803 0.629015 0.777393i \(-0.283458\pi\)
0.629015 + 0.777393i \(0.283458\pi\)
\(884\) −17.7776 −0.597924
\(885\) −0.790309 −0.0265660
\(886\) 0.843192 0.0283276
\(887\) −30.7267 −1.03170 −0.515852 0.856678i \(-0.672524\pi\)
−0.515852 + 0.856678i \(0.672524\pi\)
\(888\) −21.9661 −0.737136
\(889\) −25.8341 −0.866448
\(890\) −0.566497 −0.0189890
\(891\) 0.814626 0.0272910
\(892\) 5.90132 0.197591
\(893\) 14.9048 0.498771
\(894\) −43.4758 −1.45405
\(895\) −13.1577 −0.439812
\(896\) 2.23633 0.0747107
\(897\) −68.8344 −2.29831
\(898\) −7.31208 −0.244007
\(899\) −11.8512 −0.395260
\(900\) 4.73038 0.157679
\(901\) 22.8860 0.762443
\(902\) 0.260470 0.00867269
\(903\) 6.21781 0.206916
\(904\) 15.7306 0.523192
\(905\) 4.22391 0.140407
\(906\) −7.46848 −0.248124
\(907\) 44.2721 1.47003 0.735015 0.678051i \(-0.237175\pi\)
0.735015 + 0.678051i \(0.237175\pi\)
\(908\) 4.86985 0.161612
\(909\) 27.0025 0.895616
\(910\) −13.5861 −0.450376
\(911\) −35.5107 −1.17652 −0.588261 0.808671i \(-0.700187\pi\)
−0.588261 + 0.808671i \(0.700187\pi\)
\(912\) −8.86666 −0.293605
\(913\) 1.36880 0.0453007
\(914\) −38.6073 −1.27701
\(915\) 26.9847 0.892087
\(916\) 7.27039 0.240221
\(917\) −23.6551 −0.781159
\(918\) −14.0785 −0.464660
\(919\) −20.4651 −0.675080 −0.337540 0.941311i \(-0.609595\pi\)
−0.337540 + 0.941311i \(0.609595\pi\)
\(920\) 4.07518 0.134355
\(921\) 48.7686 1.60698
\(922\) −23.3428 −0.768753
\(923\) 4.59179 0.151141
\(924\) −6.21781 −0.204551
\(925\) −7.90048 −0.259766
\(926\) 8.38418 0.275521
\(927\) 65.2685 2.14370
\(928\) 1.19176 0.0391215
\(929\) −14.6723 −0.481382 −0.240691 0.970602i \(-0.577374\pi\)
−0.240691 + 0.970602i \(0.577374\pi\)
\(930\) −27.6486 −0.906634
\(931\) −6.37427 −0.208908
\(932\) 20.2797 0.664282
\(933\) −13.0698 −0.427887
\(934\) 11.1461 0.364711
\(935\) −2.92626 −0.0956991
\(936\) −28.7379 −0.939328
\(937\) −28.0827 −0.917422 −0.458711 0.888586i \(-0.651689\pi\)
−0.458711 + 0.888586i \(0.651689\pi\)
\(938\) 9.91825 0.323842
\(939\) −16.4887 −0.538089
\(940\) −4.67376 −0.152441
\(941\) −50.3679 −1.64195 −0.820974 0.570966i \(-0.806569\pi\)
−0.820974 + 0.570966i \(0.806569\pi\)
\(942\) −24.1646 −0.787326
\(943\) 1.06146 0.0345659
\(944\) −0.284247 −0.00925147
\(945\) −10.7592 −0.349996
\(946\) 1.00000 0.0325128
\(947\) −55.6353 −1.80790 −0.903951 0.427635i \(-0.859347\pi\)
−0.903951 + 0.427635i \(0.859347\pi\)
\(948\) 0.249289 0.00809654
\(949\) −85.6783 −2.78124
\(950\) −3.18904 −0.103466
\(951\) −84.8172 −2.75038
\(952\) −6.54411 −0.212096
\(953\) −40.6791 −1.31772 −0.658862 0.752264i \(-0.728962\pi\)
−0.658862 + 0.752264i \(0.728962\pi\)
\(954\) 36.9958 1.19778
\(955\) −5.16411 −0.167107
\(956\) −4.03204 −0.130405
\(957\) −3.31352 −0.107111
\(958\) −2.37394 −0.0766987
\(959\) 30.8034 0.994694
\(960\) 2.78036 0.0897356
\(961\) 67.8885 2.18995
\(962\) 47.9968 1.54748
\(963\) −62.9032 −2.02703
\(964\) 17.7984 0.573248
\(965\) 6.27237 0.201915
\(966\) −25.3387 −0.815258
\(967\) 61.0806 1.96422 0.982110 0.188310i \(-0.0603010\pi\)
0.982110 + 0.188310i \(0.0603010\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 25.9462 0.833512
\(970\) −9.83384 −0.315745
\(971\) −18.0646 −0.579719 −0.289860 0.957069i \(-0.593609\pi\)
−0.289860 + 0.957069i \(0.593609\pi\)
\(972\) 16.6982 0.535595
\(973\) 45.9091 1.47178
\(974\) 19.6638 0.630068
\(975\) −16.8912 −0.540950
\(976\) 9.70548 0.310665
\(977\) 24.8109 0.793771 0.396885 0.917868i \(-0.370091\pi\)
0.396885 + 0.917868i \(0.370091\pi\)
\(978\) 49.8783 1.59493
\(979\) 0.566497 0.0181053
\(980\) 1.99881 0.0638495
\(981\) 92.7611 2.96163
\(982\) −25.7939 −0.823116
\(983\) −43.9925 −1.40314 −0.701571 0.712599i \(-0.747518\pi\)
−0.701571 + 0.712599i \(0.747518\pi\)
\(984\) 0.724198 0.0230866
\(985\) 3.22621 0.102796
\(986\) −3.48741 −0.111062
\(987\) 29.0606 0.925008
\(988\) 19.3740 0.616368
\(989\) 4.07518 0.129583
\(990\) −4.73038 −0.150341
\(991\) −60.1570 −1.91095 −0.955476 0.295070i \(-0.904657\pi\)
−0.955476 + 0.295070i \(0.904657\pi\)
\(992\) −9.94427 −0.315731
\(993\) 94.1719 2.98845
\(994\) 1.69028 0.0536126
\(995\) 10.4621 0.331671
\(996\) 3.80576 0.120590
\(997\) −23.9534 −0.758612 −0.379306 0.925271i \(-0.623837\pi\)
−0.379306 + 0.925271i \(0.623837\pi\)
\(998\) −27.9568 −0.884956
\(999\) 38.0098 1.20258
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.bb.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.2 11 1.1 even 1 trivial