Properties

Label 4730.2.a.w.1.3
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 8
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: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.843708\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.84371 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.84371 q^{6} +0.526782 q^{7} -1.00000 q^{8} +0.399257 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.84371 q^{12} +5.89041 q^{13} -0.526782 q^{14} -1.84371 q^{15} +1.00000 q^{16} -7.20596 q^{17} -0.399257 q^{18} -7.63854 q^{19} +1.00000 q^{20} -0.971232 q^{21} -1.00000 q^{22} +3.89041 q^{23} +1.84371 q^{24} +1.00000 q^{25} -5.89041 q^{26} +4.79501 q^{27} +0.526782 q^{28} +8.04808 q^{29} +1.84371 q^{30} +2.80935 q^{31} -1.00000 q^{32} -1.84371 q^{33} +7.20596 q^{34} +0.526782 q^{35} +0.399257 q^{36} -5.62837 q^{37} +7.63854 q^{38} -10.8602 q^{39} -1.00000 q^{40} -1.80726 q^{41} +0.971232 q^{42} -1.00000 q^{43} +1.00000 q^{44} +0.399257 q^{45} -3.89041 q^{46} -8.47301 q^{47} -1.84371 q^{48} -6.72250 q^{49} -1.00000 q^{50} +13.2857 q^{51} +5.89041 q^{52} -6.63743 q^{53} -4.79501 q^{54} +1.00000 q^{55} -0.526782 q^{56} +14.0832 q^{57} -8.04808 q^{58} -2.91366 q^{59} -1.84371 q^{60} -0.160654 q^{61} -2.80935 q^{62} +0.210322 q^{63} +1.00000 q^{64} +5.89041 q^{65} +1.84371 q^{66} -1.49655 q^{67} -7.20596 q^{68} -7.17278 q^{69} -0.526782 q^{70} +9.81253 q^{71} -0.399257 q^{72} -0.652307 q^{73} +5.62837 q^{74} -1.84371 q^{75} -7.63854 q^{76} +0.526782 q^{77} +10.8602 q^{78} -9.25084 q^{79} +1.00000 q^{80} -10.0384 q^{81} +1.80726 q^{82} +0.697543 q^{83} -0.971232 q^{84} -7.20596 q^{85} +1.00000 q^{86} -14.8383 q^{87} -1.00000 q^{88} +10.4841 q^{89} -0.399257 q^{90} +3.10296 q^{91} +3.89041 q^{92} -5.17962 q^{93} +8.47301 q^{94} -7.63854 q^{95} +1.84371 q^{96} -11.7126 q^{97} +6.72250 q^{98} +0.399257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 7q^{3} + 8q^{4} + 8q^{5} + 7q^{6} - 6q^{7} - 8q^{8} + 7q^{9} - 8q^{10} + 8q^{11} - 7q^{12} - 2q^{13} + 6q^{14} - 7q^{15} + 8q^{16} - 8q^{17} - 7q^{18} + 8q^{20} + 14q^{21} - 8q^{22} - 18q^{23} + 7q^{24} + 8q^{25} + 2q^{26} - 22q^{27} - 6q^{28} + 8q^{29} + 7q^{30} - 11q^{31} - 8q^{32} - 7q^{33} + 8q^{34} - 6q^{35} + 7q^{36} - 17q^{37} - 6q^{39} - 8q^{40} + 12q^{41} - 14q^{42} - 8q^{43} + 8q^{44} + 7q^{45} + 18q^{46} - 19q^{47} - 7q^{48} - 2q^{49} - 8q^{50} - q^{51} - 2q^{52} - 7q^{53} + 22q^{54} + 8q^{55} + 6q^{56} - 3q^{57} - 8q^{58} + q^{59} - 7q^{60} + 6q^{61} + 11q^{62} - 15q^{63} + 8q^{64} - 2q^{65} + 7q^{66} - 22q^{67} - 8q^{68} + 8q^{69} + 6q^{70} - 14q^{71} - 7q^{72} - 13q^{73} + 17q^{74} - 7q^{75} - 6q^{77} + 6q^{78} - 8q^{79} + 8q^{80} + 28q^{81} - 12q^{82} - 4q^{83} + 14q^{84} - 8q^{85} + 8q^{86} - 30q^{87} - 8q^{88} + 5q^{89} - 7q^{90} - 8q^{91} - 18q^{92} + q^{93} + 19q^{94} + 7q^{96} - 23q^{97} + 2q^{98} + 7q^{99} + O(q^{100}) \)

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
\(3\) −1.84371 −1.06447 −0.532233 0.846598i \(-0.678647\pi\)
−0.532233 + 0.846598i \(0.678647\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.84371 0.752690
\(7\) 0.526782 0.199105 0.0995525 0.995032i \(-0.468259\pi\)
0.0995525 + 0.995032i \(0.468259\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.399257 0.133086
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −1.84371 −0.532233
\(13\) 5.89041 1.63371 0.816853 0.576845i \(-0.195716\pi\)
0.816853 + 0.576845i \(0.195716\pi\)
\(14\) −0.526782 −0.140788
\(15\) −1.84371 −0.476043
\(16\) 1.00000 0.250000
\(17\) −7.20596 −1.74770 −0.873851 0.486194i \(-0.838385\pi\)
−0.873851 + 0.486194i \(0.838385\pi\)
\(18\) −0.399257 −0.0941059
\(19\) −7.63854 −1.75240 −0.876201 0.481947i \(-0.839930\pi\)
−0.876201 + 0.481947i \(0.839930\pi\)
\(20\) 1.00000 0.223607
\(21\) −0.971232 −0.211940
\(22\) −1.00000 −0.213201
\(23\) 3.89041 0.811207 0.405604 0.914049i \(-0.367061\pi\)
0.405604 + 0.914049i \(0.367061\pi\)
\(24\) 1.84371 0.376345
\(25\) 1.00000 0.200000
\(26\) −5.89041 −1.15521
\(27\) 4.79501 0.922800
\(28\) 0.526782 0.0995525
\(29\) 8.04808 1.49449 0.747245 0.664548i \(-0.231376\pi\)
0.747245 + 0.664548i \(0.231376\pi\)
\(30\) 1.84371 0.336613
\(31\) 2.80935 0.504574 0.252287 0.967652i \(-0.418817\pi\)
0.252287 + 0.967652i \(0.418817\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.84371 −0.320948
\(34\) 7.20596 1.23581
\(35\) 0.526782 0.0890424
\(36\) 0.399257 0.0665429
\(37\) −5.62837 −0.925299 −0.462649 0.886541i \(-0.653101\pi\)
−0.462649 + 0.886541i \(0.653101\pi\)
\(38\) 7.63854 1.23913
\(39\) −10.8602 −1.73902
\(40\) −1.00000 −0.158114
\(41\) −1.80726 −0.282246 −0.141123 0.989992i \(-0.545071\pi\)
−0.141123 + 0.989992i \(0.545071\pi\)
\(42\) 0.971232 0.149864
\(43\) −1.00000 −0.152499
\(44\) 1.00000 0.150756
\(45\) 0.399257 0.0595178
\(46\) −3.89041 −0.573610
\(47\) −8.47301 −1.23592 −0.617958 0.786211i \(-0.712040\pi\)
−0.617958 + 0.786211i \(0.712040\pi\)
\(48\) −1.84371 −0.266116
\(49\) −6.72250 −0.960357
\(50\) −1.00000 −0.141421
\(51\) 13.2857 1.86037
\(52\) 5.89041 0.816853
\(53\) −6.63743 −0.911721 −0.455860 0.890051i \(-0.650668\pi\)
−0.455860 + 0.890051i \(0.650668\pi\)
\(54\) −4.79501 −0.652518
\(55\) 1.00000 0.134840
\(56\) −0.526782 −0.0703942
\(57\) 14.0832 1.86537
\(58\) −8.04808 −1.05676
\(59\) −2.91366 −0.379326 −0.189663 0.981849i \(-0.560740\pi\)
−0.189663 + 0.981849i \(0.560740\pi\)
\(60\) −1.84371 −0.238022
\(61\) −0.160654 −0.0205697 −0.0102848 0.999947i \(-0.503274\pi\)
−0.0102848 + 0.999947i \(0.503274\pi\)
\(62\) −2.80935 −0.356788
\(63\) 0.210322 0.0264980
\(64\) 1.00000 0.125000
\(65\) 5.89041 0.730616
\(66\) 1.84371 0.226945
\(67\) −1.49655 −0.182833 −0.0914164 0.995813i \(-0.529139\pi\)
−0.0914164 + 0.995813i \(0.529139\pi\)
\(68\) −7.20596 −0.873851
\(69\) −7.17278 −0.863502
\(70\) −0.526782 −0.0629625
\(71\) 9.81253 1.16453 0.582267 0.812998i \(-0.302166\pi\)
0.582267 + 0.812998i \(0.302166\pi\)
\(72\) −0.399257 −0.0470529
\(73\) −0.652307 −0.0763468 −0.0381734 0.999271i \(-0.512154\pi\)
−0.0381734 + 0.999271i \(0.512154\pi\)
\(74\) 5.62837 0.654285
\(75\) −1.84371 −0.212893
\(76\) −7.63854 −0.876201
\(77\) 0.526782 0.0600324
\(78\) 10.8602 1.22968
\(79\) −9.25084 −1.04080 −0.520400 0.853922i \(-0.674217\pi\)
−0.520400 + 0.853922i \(0.674217\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.0384 −1.11537
\(82\) 1.80726 0.199578
\(83\) 0.697543 0.0765653 0.0382826 0.999267i \(-0.487811\pi\)
0.0382826 + 0.999267i \(0.487811\pi\)
\(84\) −0.971232 −0.105970
\(85\) −7.20596 −0.781596
\(86\) 1.00000 0.107833
\(87\) −14.8383 −1.59083
\(88\) −1.00000 −0.106600
\(89\) 10.4841 1.11131 0.555654 0.831414i \(-0.312468\pi\)
0.555654 + 0.831414i \(0.312468\pi\)
\(90\) −0.399257 −0.0420854
\(91\) 3.10296 0.325279
\(92\) 3.89041 0.405604
\(93\) −5.17962 −0.537102
\(94\) 8.47301 0.873924
\(95\) −7.63854 −0.783698
\(96\) 1.84371 0.188173
\(97\) −11.7126 −1.18924 −0.594619 0.804008i \(-0.702697\pi\)
−0.594619 + 0.804008i \(0.702697\pi\)
\(98\) 6.72250 0.679075
\(99\) 0.399257 0.0401269
\(100\) 1.00000 0.100000
\(101\) 19.6520 1.95545 0.977723 0.209901i \(-0.0673142\pi\)
0.977723 + 0.209901i \(0.0673142\pi\)
\(102\) −13.2857 −1.31548
\(103\) −0.603792 −0.0594934 −0.0297467 0.999557i \(-0.509470\pi\)
−0.0297467 + 0.999557i \(0.509470\pi\)
\(104\) −5.89041 −0.577603
\(105\) −0.971232 −0.0947826
\(106\) 6.63743 0.644684
\(107\) −10.0918 −0.975612 −0.487806 0.872952i \(-0.662203\pi\)
−0.487806 + 0.872952i \(0.662203\pi\)
\(108\) 4.79501 0.461400
\(109\) 16.5979 1.58979 0.794894 0.606748i \(-0.207526\pi\)
0.794894 + 0.606748i \(0.207526\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 10.3771 0.984948
\(112\) 0.526782 0.0497762
\(113\) 1.71905 0.161715 0.0808573 0.996726i \(-0.474234\pi\)
0.0808573 + 0.996726i \(0.474234\pi\)
\(114\) −14.0832 −1.31902
\(115\) 3.89041 0.362783
\(116\) 8.04808 0.747245
\(117\) 2.35179 0.217423
\(118\) 2.91366 0.268224
\(119\) −3.79597 −0.347976
\(120\) 1.84371 0.168307
\(121\) 1.00000 0.0909091
\(122\) 0.160654 0.0145450
\(123\) 3.33206 0.300441
\(124\) 2.80935 0.252287
\(125\) 1.00000 0.0894427
\(126\) −0.210322 −0.0187369
\(127\) −10.9238 −0.969329 −0.484665 0.874700i \(-0.661058\pi\)
−0.484665 + 0.874700i \(0.661058\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.84371 0.162329
\(130\) −5.89041 −0.516623
\(131\) −4.31446 −0.376956 −0.188478 0.982077i \(-0.560355\pi\)
−0.188478 + 0.982077i \(0.560355\pi\)
\(132\) −1.84371 −0.160474
\(133\) −4.02385 −0.348912
\(134\) 1.49655 0.129282
\(135\) 4.79501 0.412689
\(136\) 7.20596 0.617906
\(137\) −2.68562 −0.229448 −0.114724 0.993397i \(-0.536598\pi\)
−0.114724 + 0.993397i \(0.536598\pi\)
\(138\) 7.17278 0.610588
\(139\) 8.08386 0.685664 0.342832 0.939397i \(-0.388614\pi\)
0.342832 + 0.939397i \(0.388614\pi\)
\(140\) 0.526782 0.0445212
\(141\) 15.6218 1.31559
\(142\) −9.81253 −0.823449
\(143\) 5.89041 0.492581
\(144\) 0.399257 0.0332715
\(145\) 8.04808 0.668357
\(146\) 0.652307 0.0539854
\(147\) 12.3943 1.02227
\(148\) −5.62837 −0.462649
\(149\) 20.8051 1.70442 0.852210 0.523200i \(-0.175262\pi\)
0.852210 + 0.523200i \(0.175262\pi\)
\(150\) 1.84371 0.150538
\(151\) −13.5775 −1.10492 −0.552462 0.833538i \(-0.686312\pi\)
−0.552462 + 0.833538i \(0.686312\pi\)
\(152\) 7.63854 0.619567
\(153\) −2.87703 −0.232594
\(154\) −0.526782 −0.0424493
\(155\) 2.80935 0.225652
\(156\) −10.8602 −0.869512
\(157\) −13.5103 −1.07824 −0.539120 0.842229i \(-0.681243\pi\)
−0.539120 + 0.842229i \(0.681243\pi\)
\(158\) 9.25084 0.735957
\(159\) 12.2375 0.970495
\(160\) −1.00000 −0.0790569
\(161\) 2.04940 0.161515
\(162\) 10.0384 0.788689
\(163\) −7.39647 −0.579336 −0.289668 0.957127i \(-0.593545\pi\)
−0.289668 + 0.957127i \(0.593545\pi\)
\(164\) −1.80726 −0.141123
\(165\) −1.84371 −0.143532
\(166\) −0.697543 −0.0541398
\(167\) 11.9003 0.920876 0.460438 0.887692i \(-0.347692\pi\)
0.460438 + 0.887692i \(0.347692\pi\)
\(168\) 0.971232 0.0749322
\(169\) 21.6970 1.66900
\(170\) 7.20596 0.552672
\(171\) −3.04974 −0.233220
\(172\) −1.00000 −0.0762493
\(173\) 5.09205 0.387142 0.193571 0.981086i \(-0.437993\pi\)
0.193571 + 0.981086i \(0.437993\pi\)
\(174\) 14.8383 1.12489
\(175\) 0.526782 0.0398210
\(176\) 1.00000 0.0753778
\(177\) 5.37193 0.403779
\(178\) −10.4841 −0.785813
\(179\) −24.0445 −1.79717 −0.898585 0.438799i \(-0.855404\pi\)
−0.898585 + 0.438799i \(0.855404\pi\)
\(180\) 0.399257 0.0297589
\(181\) −1.85958 −0.138222 −0.0691108 0.997609i \(-0.522016\pi\)
−0.0691108 + 0.997609i \(0.522016\pi\)
\(182\) −3.10296 −0.230007
\(183\) 0.296200 0.0218957
\(184\) −3.89041 −0.286805
\(185\) −5.62837 −0.413806
\(186\) 5.17962 0.379788
\(187\) −7.20596 −0.526952
\(188\) −8.47301 −0.617958
\(189\) 2.52593 0.183734
\(190\) 7.63854 0.554158
\(191\) −15.8411 −1.14622 −0.573111 0.819478i \(-0.694263\pi\)
−0.573111 + 0.819478i \(0.694263\pi\)
\(192\) −1.84371 −0.133058
\(193\) −2.34648 −0.168904 −0.0844518 0.996428i \(-0.526914\pi\)
−0.0844518 + 0.996428i \(0.526914\pi\)
\(194\) 11.7126 0.840918
\(195\) −10.8602 −0.777715
\(196\) −6.72250 −0.480179
\(197\) 21.5343 1.53426 0.767128 0.641495i \(-0.221685\pi\)
0.767128 + 0.641495i \(0.221685\pi\)
\(198\) −0.399257 −0.0283740
\(199\) 8.62734 0.611576 0.305788 0.952100i \(-0.401080\pi\)
0.305788 + 0.952100i \(0.401080\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.75920 0.194619
\(202\) −19.6520 −1.38271
\(203\) 4.23958 0.297561
\(204\) 13.2857 0.930184
\(205\) −1.80726 −0.126224
\(206\) 0.603792 0.0420682
\(207\) 1.55328 0.107960
\(208\) 5.89041 0.408427
\(209\) −7.63854 −0.528369
\(210\) 0.971232 0.0670214
\(211\) −10.9150 −0.751423 −0.375711 0.926737i \(-0.622602\pi\)
−0.375711 + 0.926737i \(0.622602\pi\)
\(212\) −6.63743 −0.455860
\(213\) −18.0914 −1.23961
\(214\) 10.0918 0.689862
\(215\) −1.00000 −0.0681994
\(216\) −4.79501 −0.326259
\(217\) 1.47992 0.100463
\(218\) −16.5979 −1.12415
\(219\) 1.20266 0.0812685
\(220\) 1.00000 0.0674200
\(221\) −42.4461 −2.85523
\(222\) −10.3771 −0.696464
\(223\) −18.3010 −1.22553 −0.612763 0.790267i \(-0.709942\pi\)
−0.612763 + 0.790267i \(0.709942\pi\)
\(224\) −0.526782 −0.0351971
\(225\) 0.399257 0.0266172
\(226\) −1.71905 −0.114349
\(227\) −13.0373 −0.865316 −0.432658 0.901558i \(-0.642424\pi\)
−0.432658 + 0.901558i \(0.642424\pi\)
\(228\) 14.0832 0.932685
\(229\) 26.1503 1.72806 0.864031 0.503439i \(-0.167932\pi\)
0.864031 + 0.503439i \(0.167932\pi\)
\(230\) −3.89041 −0.256526
\(231\) −0.971232 −0.0639024
\(232\) −8.04808 −0.528382
\(233\) −27.7381 −1.81719 −0.908593 0.417683i \(-0.862842\pi\)
−0.908593 + 0.417683i \(0.862842\pi\)
\(234\) −2.35179 −0.153741
\(235\) −8.47301 −0.552718
\(236\) −2.91366 −0.189663
\(237\) 17.0558 1.10790
\(238\) 3.79597 0.246056
\(239\) −11.8971 −0.769562 −0.384781 0.923008i \(-0.625723\pi\)
−0.384781 + 0.923008i \(0.625723\pi\)
\(240\) −1.84371 −0.119011
\(241\) −24.6656 −1.58885 −0.794425 0.607362i \(-0.792228\pi\)
−0.794425 + 0.607362i \(0.792228\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 4.12278 0.264477
\(244\) −0.160654 −0.0102848
\(245\) −6.72250 −0.429485
\(246\) −3.33206 −0.212444
\(247\) −44.9942 −2.86291
\(248\) −2.80935 −0.178394
\(249\) −1.28606 −0.0815011
\(250\) −1.00000 −0.0632456
\(251\) 17.8753 1.12828 0.564141 0.825679i \(-0.309207\pi\)
0.564141 + 0.825679i \(0.309207\pi\)
\(252\) 0.210322 0.0132490
\(253\) 3.89041 0.244588
\(254\) 10.9238 0.685419
\(255\) 13.2857 0.831981
\(256\) 1.00000 0.0625000
\(257\) 17.4938 1.09123 0.545617 0.838035i \(-0.316295\pi\)
0.545617 + 0.838035i \(0.316295\pi\)
\(258\) −1.84371 −0.114784
\(259\) −2.96493 −0.184232
\(260\) 5.89041 0.365308
\(261\) 3.21326 0.198896
\(262\) 4.31446 0.266548
\(263\) 12.1394 0.748546 0.374273 0.927319i \(-0.377892\pi\)
0.374273 + 0.927319i \(0.377892\pi\)
\(264\) 1.84371 0.113472
\(265\) −6.63743 −0.407734
\(266\) 4.02385 0.246718
\(267\) −19.3295 −1.18295
\(268\) −1.49655 −0.0914164
\(269\) −23.0397 −1.40476 −0.702379 0.711803i \(-0.747879\pi\)
−0.702379 + 0.711803i \(0.747879\pi\)
\(270\) −4.79501 −0.291815
\(271\) −3.48956 −0.211976 −0.105988 0.994367i \(-0.533800\pi\)
−0.105988 + 0.994367i \(0.533800\pi\)
\(272\) −7.20596 −0.436925
\(273\) −5.72096 −0.346248
\(274\) 2.68562 0.162244
\(275\) 1.00000 0.0603023
\(276\) −7.17278 −0.431751
\(277\) −20.5513 −1.23481 −0.617404 0.786646i \(-0.711816\pi\)
−0.617404 + 0.786646i \(0.711816\pi\)
\(278\) −8.08386 −0.484838
\(279\) 1.12165 0.0671517
\(280\) −0.526782 −0.0314813
\(281\) 1.52433 0.0909339 0.0454670 0.998966i \(-0.485522\pi\)
0.0454670 + 0.998966i \(0.485522\pi\)
\(282\) −15.6218 −0.930262
\(283\) −14.4127 −0.856745 −0.428372 0.903602i \(-0.640913\pi\)
−0.428372 + 0.903602i \(0.640913\pi\)
\(284\) 9.81253 0.582267
\(285\) 14.0832 0.834219
\(286\) −5.89041 −0.348307
\(287\) −0.952031 −0.0561966
\(288\) −0.399257 −0.0235265
\(289\) 34.9258 2.05446
\(290\) −8.04808 −0.472600
\(291\) 21.5947 1.26590
\(292\) −0.652307 −0.0381734
\(293\) 15.6013 0.911440 0.455720 0.890123i \(-0.349382\pi\)
0.455720 + 0.890123i \(0.349382\pi\)
\(294\) −12.3943 −0.722852
\(295\) −2.91366 −0.169640
\(296\) 5.62837 0.327143
\(297\) 4.79501 0.278235
\(298\) −20.8051 −1.20521
\(299\) 22.9161 1.32527
\(300\) −1.84371 −0.106447
\(301\) −0.526782 −0.0303632
\(302\) 13.5775 0.781299
\(303\) −36.2325 −2.08150
\(304\) −7.63854 −0.438100
\(305\) −0.160654 −0.00919904
\(306\) 2.87703 0.164469
\(307\) 8.90251 0.508093 0.254047 0.967192i \(-0.418238\pi\)
0.254047 + 0.967192i \(0.418238\pi\)
\(308\) 0.526782 0.0300162
\(309\) 1.11322 0.0633287
\(310\) −2.80935 −0.159560
\(311\) −2.14844 −0.121827 −0.0609135 0.998143i \(-0.519401\pi\)
−0.0609135 + 0.998143i \(0.519401\pi\)
\(312\) 10.8602 0.614838
\(313\) 4.21362 0.238168 0.119084 0.992884i \(-0.462004\pi\)
0.119084 + 0.992884i \(0.462004\pi\)
\(314\) 13.5103 0.762431
\(315\) 0.210322 0.0118503
\(316\) −9.25084 −0.520400
\(317\) −4.99993 −0.280824 −0.140412 0.990093i \(-0.544843\pi\)
−0.140412 + 0.990093i \(0.544843\pi\)
\(318\) −12.2375 −0.686244
\(319\) 8.04808 0.450606
\(320\) 1.00000 0.0559017
\(321\) 18.6063 1.03850
\(322\) −2.04940 −0.114209
\(323\) 55.0430 3.06267
\(324\) −10.0384 −0.557687
\(325\) 5.89041 0.326741
\(326\) 7.39647 0.409652
\(327\) −30.6016 −1.69227
\(328\) 1.80726 0.0997891
\(329\) −4.46343 −0.246077
\(330\) 1.84371 0.101493
\(331\) −25.0935 −1.37926 −0.689632 0.724160i \(-0.742228\pi\)
−0.689632 + 0.724160i \(0.742228\pi\)
\(332\) 0.697543 0.0382826
\(333\) −2.24717 −0.123144
\(334\) −11.9003 −0.651158
\(335\) −1.49655 −0.0817653
\(336\) −0.971232 −0.0529851
\(337\) −20.7616 −1.13095 −0.565477 0.824764i \(-0.691308\pi\)
−0.565477 + 0.824764i \(0.691308\pi\)
\(338\) −21.6970 −1.18016
\(339\) −3.16942 −0.172139
\(340\) −7.20596 −0.390798
\(341\) 2.80935 0.152135
\(342\) 3.04974 0.164911
\(343\) −7.22877 −0.390317
\(344\) 1.00000 0.0539164
\(345\) −7.17278 −0.386170
\(346\) −5.09205 −0.273751
\(347\) −34.1269 −1.83203 −0.916015 0.401145i \(-0.868612\pi\)
−0.916015 + 0.401145i \(0.868612\pi\)
\(348\) −14.8383 −0.795417
\(349\) 17.4117 0.932025 0.466013 0.884778i \(-0.345690\pi\)
0.466013 + 0.884778i \(0.345690\pi\)
\(350\) −0.526782 −0.0281577
\(351\) 28.2446 1.50758
\(352\) −1.00000 −0.0533002
\(353\) −13.6768 −0.727943 −0.363972 0.931410i \(-0.618579\pi\)
−0.363972 + 0.931410i \(0.618579\pi\)
\(354\) −5.37193 −0.285515
\(355\) 9.81253 0.520795
\(356\) 10.4841 0.555654
\(357\) 6.99866 0.370408
\(358\) 24.0445 1.27079
\(359\) −9.14780 −0.482803 −0.241401 0.970425i \(-0.577607\pi\)
−0.241401 + 0.970425i \(0.577607\pi\)
\(360\) −0.399257 −0.0210427
\(361\) 39.3473 2.07091
\(362\) 1.85958 0.0977374
\(363\) −1.84371 −0.0967695
\(364\) 3.10296 0.162640
\(365\) −0.652307 −0.0341433
\(366\) −0.296200 −0.0154826
\(367\) 28.3962 1.48227 0.741135 0.671356i \(-0.234288\pi\)
0.741135 + 0.671356i \(0.234288\pi\)
\(368\) 3.89041 0.202802
\(369\) −0.721561 −0.0375630
\(370\) 5.62837 0.292605
\(371\) −3.49648 −0.181528
\(372\) −5.17962 −0.268551
\(373\) −26.1185 −1.35237 −0.676183 0.736734i \(-0.736367\pi\)
−0.676183 + 0.736734i \(0.736367\pi\)
\(374\) 7.20596 0.372611
\(375\) −1.84371 −0.0952086
\(376\) 8.47301 0.436962
\(377\) 47.4065 2.44156
\(378\) −2.52593 −0.129920
\(379\) 23.3670 1.20028 0.600140 0.799895i \(-0.295111\pi\)
0.600140 + 0.799895i \(0.295111\pi\)
\(380\) −7.63854 −0.391849
\(381\) 20.1403 1.03182
\(382\) 15.8411 0.810501
\(383\) −29.8275 −1.52412 −0.762058 0.647509i \(-0.775811\pi\)
−0.762058 + 0.647509i \(0.775811\pi\)
\(384\) 1.84371 0.0940863
\(385\) 0.526782 0.0268473
\(386\) 2.34648 0.119433
\(387\) −0.399257 −0.0202954
\(388\) −11.7126 −0.594619
\(389\) −23.9197 −1.21278 −0.606390 0.795168i \(-0.707383\pi\)
−0.606390 + 0.795168i \(0.707383\pi\)
\(390\) 10.8602 0.549928
\(391\) −28.0342 −1.41775
\(392\) 6.72250 0.339538
\(393\) 7.95460 0.401256
\(394\) −21.5343 −1.08488
\(395\) −9.25084 −0.465460
\(396\) 0.399257 0.0200634
\(397\) −34.4620 −1.72960 −0.864799 0.502118i \(-0.832554\pi\)
−0.864799 + 0.502118i \(0.832554\pi\)
\(398\) −8.62734 −0.432449
\(399\) 7.41880 0.371404
\(400\) 1.00000 0.0500000
\(401\) 7.52593 0.375827 0.187914 0.982186i \(-0.439828\pi\)
0.187914 + 0.982186i \(0.439828\pi\)
\(402\) −2.75920 −0.137616
\(403\) 16.5482 0.824326
\(404\) 19.6520 0.977723
\(405\) −10.0384 −0.498810
\(406\) −4.23958 −0.210407
\(407\) −5.62837 −0.278988
\(408\) −13.2857 −0.657739
\(409\) 9.24746 0.457257 0.228629 0.973514i \(-0.426576\pi\)
0.228629 + 0.973514i \(0.426576\pi\)
\(410\) 1.80726 0.0892541
\(411\) 4.95149 0.244239
\(412\) −0.603792 −0.0297467
\(413\) −1.53486 −0.0755257
\(414\) −1.55328 −0.0763394
\(415\) 0.697543 0.0342410
\(416\) −5.89041 −0.288801
\(417\) −14.9043 −0.729866
\(418\) 7.63854 0.373613
\(419\) −6.74591 −0.329559 −0.164780 0.986330i \(-0.552691\pi\)
−0.164780 + 0.986330i \(0.552691\pi\)
\(420\) −0.971232 −0.0473913
\(421\) −37.6196 −1.83347 −0.916735 0.399497i \(-0.869185\pi\)
−0.916735 + 0.399497i \(0.869185\pi\)
\(422\) 10.9150 0.531336
\(423\) −3.38291 −0.164483
\(424\) 6.63743 0.322342
\(425\) −7.20596 −0.349540
\(426\) 18.0914 0.876533
\(427\) −0.0846298 −0.00409552
\(428\) −10.0918 −0.487806
\(429\) −10.8602 −0.524335
\(430\) 1.00000 0.0482243
\(431\) −21.3741 −1.02955 −0.514776 0.857325i \(-0.672125\pi\)
−0.514776 + 0.857325i \(0.672125\pi\)
\(432\) 4.79501 0.230700
\(433\) −29.9923 −1.44134 −0.720668 0.693280i \(-0.756165\pi\)
−0.720668 + 0.693280i \(0.756165\pi\)
\(434\) −1.47992 −0.0710382
\(435\) −14.8383 −0.711442
\(436\) 16.5979 0.794894
\(437\) −29.7171 −1.42156
\(438\) −1.20266 −0.0574655
\(439\) −26.1904 −1.25000 −0.624999 0.780625i \(-0.714901\pi\)
−0.624999 + 0.780625i \(0.714901\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −2.68401 −0.127810
\(442\) 42.4461 2.01895
\(443\) −12.9088 −0.613317 −0.306658 0.951820i \(-0.599211\pi\)
−0.306658 + 0.951820i \(0.599211\pi\)
\(444\) 10.3771 0.492474
\(445\) 10.4841 0.496992
\(446\) 18.3010 0.866577
\(447\) −38.3585 −1.81430
\(448\) 0.526782 0.0248881
\(449\) −14.6849 −0.693021 −0.346511 0.938046i \(-0.612634\pi\)
−0.346511 + 0.938046i \(0.612634\pi\)
\(450\) −0.399257 −0.0188212
\(451\) −1.80726 −0.0851005
\(452\) 1.71905 0.0808573
\(453\) 25.0330 1.17615
\(454\) 13.0373 0.611871
\(455\) 3.10296 0.145469
\(456\) −14.0832 −0.659508
\(457\) 8.15480 0.381465 0.190733 0.981642i \(-0.438914\pi\)
0.190733 + 0.981642i \(0.438914\pi\)
\(458\) −26.1503 −1.22192
\(459\) −34.5526 −1.61278
\(460\) 3.89041 0.181391
\(461\) −7.35296 −0.342462 −0.171231 0.985231i \(-0.554774\pi\)
−0.171231 + 0.985231i \(0.554774\pi\)
\(462\) 0.971232 0.0451858
\(463\) −25.7336 −1.19594 −0.597971 0.801518i \(-0.704026\pi\)
−0.597971 + 0.801518i \(0.704026\pi\)
\(464\) 8.04808 0.373623
\(465\) −5.17962 −0.240199
\(466\) 27.7381 1.28494
\(467\) 35.0874 1.62365 0.811826 0.583899i \(-0.198474\pi\)
0.811826 + 0.583899i \(0.198474\pi\)
\(468\) 2.35179 0.108712
\(469\) −0.788356 −0.0364029
\(470\) 8.47301 0.390831
\(471\) 24.9091 1.14775
\(472\) 2.91366 0.134112
\(473\) −1.00000 −0.0459800
\(474\) −17.0558 −0.783401
\(475\) −7.63854 −0.350480
\(476\) −3.79597 −0.173988
\(477\) −2.65004 −0.121337
\(478\) 11.8971 0.544162
\(479\) −15.2906 −0.698647 −0.349323 0.937002i \(-0.613589\pi\)
−0.349323 + 0.937002i \(0.613589\pi\)
\(480\) 1.84371 0.0841534
\(481\) −33.1534 −1.51167
\(482\) 24.6656 1.12349
\(483\) −3.77849 −0.171927
\(484\) 1.00000 0.0454545
\(485\) −11.7126 −0.531843
\(486\) −4.12278 −0.187013
\(487\) −23.6677 −1.07248 −0.536242 0.844064i \(-0.680157\pi\)
−0.536242 + 0.844064i \(0.680157\pi\)
\(488\) 0.160654 0.00727248
\(489\) 13.6369 0.616683
\(490\) 6.72250 0.303692
\(491\) −36.7951 −1.66054 −0.830269 0.557362i \(-0.811813\pi\)
−0.830269 + 0.557362i \(0.811813\pi\)
\(492\) 3.33206 0.150221
\(493\) −57.9941 −2.61192
\(494\) 44.9942 2.02438
\(495\) 0.399257 0.0179453
\(496\) 2.80935 0.126144
\(497\) 5.16907 0.231864
\(498\) 1.28606 0.0576299
\(499\) −31.2771 −1.40016 −0.700078 0.714066i \(-0.746851\pi\)
−0.700078 + 0.714066i \(0.746851\pi\)
\(500\) 1.00000 0.0447214
\(501\) −21.9407 −0.980240
\(502\) −17.8753 −0.797816
\(503\) 15.9981 0.713318 0.356659 0.934235i \(-0.383916\pi\)
0.356659 + 0.934235i \(0.383916\pi\)
\(504\) −0.210322 −0.00936847
\(505\) 19.6520 0.874502
\(506\) −3.89041 −0.172950
\(507\) −40.0029 −1.77659
\(508\) −10.9238 −0.484665
\(509\) 7.65897 0.339478 0.169739 0.985489i \(-0.445708\pi\)
0.169739 + 0.985489i \(0.445708\pi\)
\(510\) −13.2857 −0.588300
\(511\) −0.343624 −0.0152010
\(512\) −1.00000 −0.0441942
\(513\) −36.6269 −1.61712
\(514\) −17.4938 −0.771619
\(515\) −0.603792 −0.0266063
\(516\) 1.84371 0.0811647
\(517\) −8.47301 −0.372643
\(518\) 2.96493 0.130271
\(519\) −9.38826 −0.412099
\(520\) −5.89041 −0.258312
\(521\) 36.9212 1.61755 0.808773 0.588121i \(-0.200132\pi\)
0.808773 + 0.588121i \(0.200132\pi\)
\(522\) −3.21326 −0.140640
\(523\) 41.9065 1.83244 0.916221 0.400672i \(-0.131223\pi\)
0.916221 + 0.400672i \(0.131223\pi\)
\(524\) −4.31446 −0.188478
\(525\) −0.971232 −0.0423881
\(526\) −12.1394 −0.529302
\(527\) −20.2441 −0.881845
\(528\) −1.84371 −0.0802371
\(529\) −7.86468 −0.341943
\(530\) 6.63743 0.288311
\(531\) −1.16330 −0.0504829
\(532\) −4.02385 −0.174456
\(533\) −10.6455 −0.461108
\(534\) 19.3295 0.836470
\(535\) −10.0918 −0.436307
\(536\) 1.49655 0.0646412
\(537\) 44.3310 1.91303
\(538\) 23.0397 0.993314
\(539\) −6.72250 −0.289559
\(540\) 4.79501 0.206344
\(541\) −36.0689 −1.55072 −0.775362 0.631517i \(-0.782432\pi\)
−0.775362 + 0.631517i \(0.782432\pi\)
\(542\) 3.48956 0.149889
\(543\) 3.42852 0.147132
\(544\) 7.20596 0.308953
\(545\) 16.5979 0.710975
\(546\) 5.72096 0.244834
\(547\) −12.2130 −0.522191 −0.261096 0.965313i \(-0.584084\pi\)
−0.261096 + 0.965313i \(0.584084\pi\)
\(548\) −2.68562 −0.114724
\(549\) −0.0641424 −0.00273753
\(550\) −1.00000 −0.0426401
\(551\) −61.4756 −2.61895
\(552\) 7.17278 0.305294
\(553\) −4.87318 −0.207229
\(554\) 20.5513 0.873142
\(555\) 10.3771 0.440482
\(556\) 8.08386 0.342832
\(557\) 21.2962 0.902351 0.451175 0.892435i \(-0.351005\pi\)
0.451175 + 0.892435i \(0.351005\pi\)
\(558\) −1.12165 −0.0474834
\(559\) −5.89041 −0.249138
\(560\) 0.526782 0.0222606
\(561\) 13.2857 0.560922
\(562\) −1.52433 −0.0643000
\(563\) 31.7347 1.33746 0.668729 0.743506i \(-0.266839\pi\)
0.668729 + 0.743506i \(0.266839\pi\)
\(564\) 15.6218 0.657794
\(565\) 1.71905 0.0723209
\(566\) 14.4127 0.605810
\(567\) −5.28803 −0.222076
\(568\) −9.81253 −0.411725
\(569\) 19.2618 0.807496 0.403748 0.914870i \(-0.367707\pi\)
0.403748 + 0.914870i \(0.367707\pi\)
\(570\) −14.0832 −0.589882
\(571\) 16.8798 0.706397 0.353199 0.935548i \(-0.385094\pi\)
0.353199 + 0.935548i \(0.385094\pi\)
\(572\) 5.89041 0.246291
\(573\) 29.2063 1.22011
\(574\) 0.952031 0.0397370
\(575\) 3.89041 0.162241
\(576\) 0.399257 0.0166357
\(577\) −44.7277 −1.86204 −0.931018 0.364973i \(-0.881078\pi\)
−0.931018 + 0.364973i \(0.881078\pi\)
\(578\) −34.9258 −1.45272
\(579\) 4.32623 0.179792
\(580\) 8.04808 0.334178
\(581\) 0.367453 0.0152445
\(582\) −21.5947 −0.895128
\(583\) −6.63743 −0.274894
\(584\) 0.652307 0.0269927
\(585\) 2.35179 0.0972346
\(586\) −15.6013 −0.644485
\(587\) −16.5631 −0.683634 −0.341817 0.939767i \(-0.611042\pi\)
−0.341817 + 0.939767i \(0.611042\pi\)
\(588\) 12.3943 0.511133
\(589\) −21.4593 −0.884217
\(590\) 2.91366 0.119953
\(591\) −39.7029 −1.63316
\(592\) −5.62837 −0.231325
\(593\) −13.8365 −0.568199 −0.284099 0.958795i \(-0.591695\pi\)
−0.284099 + 0.958795i \(0.591695\pi\)
\(594\) −4.79501 −0.196742
\(595\) −3.79597 −0.155620
\(596\) 20.8051 0.852210
\(597\) −15.9063 −0.651001
\(598\) −22.9161 −0.937111
\(599\) 17.2368 0.704278 0.352139 0.935948i \(-0.385454\pi\)
0.352139 + 0.935948i \(0.385454\pi\)
\(600\) 1.84371 0.0752690
\(601\) 4.81572 0.196437 0.0982186 0.995165i \(-0.468686\pi\)
0.0982186 + 0.995165i \(0.468686\pi\)
\(602\) 0.526782 0.0214700
\(603\) −0.597509 −0.0243325
\(604\) −13.5775 −0.552462
\(605\) 1.00000 0.0406558
\(606\) 36.2325 1.47184
\(607\) −20.5621 −0.834591 −0.417295 0.908771i \(-0.637022\pi\)
−0.417295 + 0.908771i \(0.637022\pi\)
\(608\) 7.63854 0.309784
\(609\) −7.81655 −0.316743
\(610\) 0.160654 0.00650470
\(611\) −49.9095 −2.01912
\(612\) −2.87703 −0.116297
\(613\) 34.0893 1.37685 0.688427 0.725306i \(-0.258302\pi\)
0.688427 + 0.725306i \(0.258302\pi\)
\(614\) −8.90251 −0.359276
\(615\) 3.33206 0.134361
\(616\) −0.526782 −0.0212247
\(617\) 10.0658 0.405233 0.202617 0.979258i \(-0.435055\pi\)
0.202617 + 0.979258i \(0.435055\pi\)
\(618\) −1.11322 −0.0447801
\(619\) 30.0395 1.20739 0.603694 0.797216i \(-0.293695\pi\)
0.603694 + 0.797216i \(0.293695\pi\)
\(620\) 2.80935 0.112826
\(621\) 18.6546 0.748582
\(622\) 2.14844 0.0861447
\(623\) 5.52281 0.221267
\(624\) −10.8602 −0.434756
\(625\) 1.00000 0.0400000
\(626\) −4.21362 −0.168410
\(627\) 14.0832 0.562430
\(628\) −13.5103 −0.539120
\(629\) 40.5578 1.61715
\(630\) −0.210322 −0.00837942
\(631\) −2.41275 −0.0960502 −0.0480251 0.998846i \(-0.515293\pi\)
−0.0480251 + 0.998846i \(0.515293\pi\)
\(632\) 9.25084 0.367979
\(633\) 20.1242 0.799863
\(634\) 4.99993 0.198573
\(635\) −10.9238 −0.433497
\(636\) 12.2375 0.485248
\(637\) −39.5983 −1.56894
\(638\) −8.04808 −0.318627
\(639\) 3.91773 0.154983
\(640\) −1.00000 −0.0395285
\(641\) 32.7454 1.29337 0.646683 0.762759i \(-0.276156\pi\)
0.646683 + 0.762759i \(0.276156\pi\)
\(642\) −18.6063 −0.734334
\(643\) 35.2464 1.38998 0.694991 0.719018i \(-0.255408\pi\)
0.694991 + 0.719018i \(0.255408\pi\)
\(644\) 2.04940 0.0807577
\(645\) 1.84371 0.0725959
\(646\) −55.0430 −2.16564
\(647\) −34.0720 −1.33951 −0.669754 0.742583i \(-0.733600\pi\)
−0.669754 + 0.742583i \(0.733600\pi\)
\(648\) 10.0384 0.394344
\(649\) −2.91366 −0.114371
\(650\) −5.89041 −0.231041
\(651\) −2.72853 −0.106940
\(652\) −7.39647 −0.289668
\(653\) −18.7291 −0.732928 −0.366464 0.930432i \(-0.619432\pi\)
−0.366464 + 0.930432i \(0.619432\pi\)
\(654\) 30.6016 1.19662
\(655\) −4.31446 −0.168580
\(656\) −1.80726 −0.0705616
\(657\) −0.260439 −0.0101607
\(658\) 4.46343 0.174003
\(659\) −26.9154 −1.04848 −0.524238 0.851572i \(-0.675650\pi\)
−0.524238 + 0.851572i \(0.675650\pi\)
\(660\) −1.84371 −0.0717662
\(661\) −27.3557 −1.06401 −0.532007 0.846740i \(-0.678562\pi\)
−0.532007 + 0.846740i \(0.678562\pi\)
\(662\) 25.0935 0.975287
\(663\) 78.2581 3.03929
\(664\) −0.697543 −0.0270699
\(665\) −4.02385 −0.156038
\(666\) 2.24717 0.0870761
\(667\) 31.3104 1.21234
\(668\) 11.9003 0.460438
\(669\) 33.7417 1.30453
\(670\) 1.49655 0.0578168
\(671\) −0.160654 −0.00620199
\(672\) 0.971232 0.0374661
\(673\) 5.68801 0.219257 0.109628 0.993973i \(-0.465034\pi\)
0.109628 + 0.993973i \(0.465034\pi\)
\(674\) 20.7616 0.799706
\(675\) 4.79501 0.184560
\(676\) 21.6970 0.834499
\(677\) −46.1017 −1.77183 −0.885915 0.463847i \(-0.846469\pi\)
−0.885915 + 0.463847i \(0.846469\pi\)
\(678\) 3.16942 0.121721
\(679\) −6.17001 −0.236783
\(680\) 7.20596 0.276336
\(681\) 24.0370 0.921099
\(682\) −2.80935 −0.107576
\(683\) −6.90132 −0.264072 −0.132036 0.991245i \(-0.542151\pi\)
−0.132036 + 0.991245i \(0.542151\pi\)
\(684\) −3.04974 −0.116610
\(685\) −2.68562 −0.102612
\(686\) 7.22877 0.275996
\(687\) −48.2135 −1.83946
\(688\) −1.00000 −0.0381246
\(689\) −39.0972 −1.48948
\(690\) 7.17278 0.273063
\(691\) −22.7919 −0.867045 −0.433522 0.901143i \(-0.642729\pi\)
−0.433522 + 0.901143i \(0.642729\pi\)
\(692\) 5.09205 0.193571
\(693\) 0.210322 0.00798946
\(694\) 34.1269 1.29544
\(695\) 8.08386 0.306638
\(696\) 14.8383 0.562445
\(697\) 13.0230 0.493282
\(698\) −17.4117 −0.659041
\(699\) 51.1410 1.93433
\(700\) 0.526782 0.0199105
\(701\) 21.5915 0.815498 0.407749 0.913094i \(-0.366314\pi\)
0.407749 + 0.913094i \(0.366314\pi\)
\(702\) −28.2446 −1.06602
\(703\) 42.9925 1.62149
\(704\) 1.00000 0.0376889
\(705\) 15.6218 0.588349
\(706\) 13.6768 0.514734
\(707\) 10.3523 0.389339
\(708\) 5.37193 0.201890
\(709\) −3.13688 −0.117808 −0.0589040 0.998264i \(-0.518761\pi\)
−0.0589040 + 0.998264i \(0.518761\pi\)
\(710\) −9.81253 −0.368258
\(711\) −3.69347 −0.138516
\(712\) −10.4841 −0.392906
\(713\) 10.9295 0.409314
\(714\) −6.99866 −0.261918
\(715\) 5.89041 0.220289
\(716\) −24.0445 −0.898585
\(717\) 21.9348 0.819171
\(718\) 9.14780 0.341393
\(719\) −11.6082 −0.432913 −0.216456 0.976292i \(-0.569450\pi\)
−0.216456 + 0.976292i \(0.569450\pi\)
\(720\) 0.399257 0.0148794
\(721\) −0.318067 −0.0118454
\(722\) −39.3473 −1.46435
\(723\) 45.4762 1.69128
\(724\) −1.85958 −0.0691108
\(725\) 8.04808 0.298898
\(726\) 1.84371 0.0684264
\(727\) −15.5092 −0.575203 −0.287601 0.957750i \(-0.592858\pi\)
−0.287601 + 0.957750i \(0.592858\pi\)
\(728\) −3.10296 −0.115004
\(729\) 22.5139 0.833848
\(730\) 0.652307 0.0241430
\(731\) 7.20596 0.266522
\(732\) 0.296200 0.0109478
\(733\) 31.2579 1.15454 0.577268 0.816555i \(-0.304119\pi\)
0.577268 + 0.816555i \(0.304119\pi\)
\(734\) −28.3962 −1.04812
\(735\) 12.3943 0.457172
\(736\) −3.89041 −0.143403
\(737\) −1.49655 −0.0551262
\(738\) 0.721561 0.0265610
\(739\) 18.9309 0.696386 0.348193 0.937423i \(-0.386795\pi\)
0.348193 + 0.937423i \(0.386795\pi\)
\(740\) −5.62837 −0.206903
\(741\) 82.9561 3.04747
\(742\) 3.49648 0.128360
\(743\) −4.58551 −0.168226 −0.0841130 0.996456i \(-0.526806\pi\)
−0.0841130 + 0.996456i \(0.526806\pi\)
\(744\) 5.17962 0.189894
\(745\) 20.8051 0.762240
\(746\) 26.1185 0.956267
\(747\) 0.278499 0.0101898
\(748\) −7.20596 −0.263476
\(749\) −5.31618 −0.194249
\(750\) 1.84371 0.0673227
\(751\) −20.7377 −0.756731 −0.378365 0.925656i \(-0.623514\pi\)
−0.378365 + 0.925656i \(0.623514\pi\)
\(752\) −8.47301 −0.308979
\(753\) −32.9569 −1.20102
\(754\) −47.4065 −1.72644
\(755\) −13.5775 −0.494137
\(756\) 2.52593 0.0918670
\(757\) 45.9361 1.66958 0.834789 0.550570i \(-0.185590\pi\)
0.834789 + 0.550570i \(0.185590\pi\)
\(758\) −23.3670 −0.848727
\(759\) −7.17278 −0.260356
\(760\) 7.63854 0.277079
\(761\) 52.4758 1.90224 0.951122 0.308814i \(-0.0999322\pi\)
0.951122 + 0.308814i \(0.0999322\pi\)
\(762\) −20.1403 −0.729605
\(763\) 8.74347 0.316535
\(764\) −15.8411 −0.573111
\(765\) −2.87703 −0.104019
\(766\) 29.8275 1.07771
\(767\) −17.1626 −0.619707
\(768\) −1.84371 −0.0665291
\(769\) −30.8563 −1.11271 −0.556353 0.830946i \(-0.687800\pi\)
−0.556353 + 0.830946i \(0.687800\pi\)
\(770\) −0.526782 −0.0189839
\(771\) −32.2535 −1.16158
\(772\) −2.34648 −0.0844518
\(773\) 15.1562 0.545131 0.272565 0.962137i \(-0.412128\pi\)
0.272565 + 0.962137i \(0.412128\pi\)
\(774\) 0.399257 0.0143510
\(775\) 2.80935 0.100915
\(776\) 11.7126 0.420459
\(777\) 5.46646 0.196108
\(778\) 23.9197 0.857564
\(779\) 13.8048 0.494609
\(780\) −10.8602 −0.388858
\(781\) 9.81253 0.351120
\(782\) 28.0342 1.00250
\(783\) 38.5906 1.37912
\(784\) −6.72250 −0.240089
\(785\) −13.5103 −0.482204
\(786\) −7.95460 −0.283731
\(787\) 42.9607 1.53139 0.765693 0.643207i \(-0.222396\pi\)
0.765693 + 0.643207i \(0.222396\pi\)
\(788\) 21.5343 0.767128
\(789\) −22.3815 −0.796801
\(790\) 9.25084 0.329130
\(791\) 0.905564 0.0321982
\(792\) −0.399257 −0.0141870
\(793\) −0.946320 −0.0336048
\(794\) 34.4620 1.22301
\(795\) 12.2375 0.434019
\(796\) 8.62734 0.305788
\(797\) −32.0526 −1.13536 −0.567680 0.823249i \(-0.692159\pi\)
−0.567680 + 0.823249i \(0.692159\pi\)
\(798\) −7.41880 −0.262623
\(799\) 61.0561 2.16001
\(800\) −1.00000 −0.0353553
\(801\) 4.18584 0.147899
\(802\) −7.52593 −0.265750
\(803\) −0.652307 −0.0230194
\(804\) 2.75920 0.0973096
\(805\) 2.04940 0.0722319
\(806\) −16.5482 −0.582887
\(807\) 42.4785 1.49532
\(808\) −19.6520 −0.691354
\(809\) −17.7819 −0.625177 −0.312589 0.949889i \(-0.601196\pi\)
−0.312589 + 0.949889i \(0.601196\pi\)
\(810\) 10.0384 0.352712
\(811\) 47.1429 1.65541 0.827705 0.561163i \(-0.189646\pi\)
0.827705 + 0.561163i \(0.189646\pi\)
\(812\) 4.23958 0.148780
\(813\) 6.43372 0.225641
\(814\) 5.62837 0.197274
\(815\) −7.39647 −0.259087
\(816\) 13.2857 0.465092
\(817\) 7.63854 0.267239
\(818\) −9.24746 −0.323330
\(819\) 1.23888 0.0432900
\(820\) −1.80726 −0.0631122
\(821\) 40.2195 1.40367 0.701835 0.712339i \(-0.252364\pi\)
0.701835 + 0.712339i \(0.252364\pi\)
\(822\) −4.95149 −0.172703
\(823\) 53.6556 1.87032 0.935158 0.354230i \(-0.115257\pi\)
0.935158 + 0.354230i \(0.115257\pi\)
\(824\) 0.603792 0.0210341
\(825\) −1.84371 −0.0641897
\(826\) 1.53486 0.0534047
\(827\) 30.9452 1.07607 0.538035 0.842923i \(-0.319167\pi\)
0.538035 + 0.842923i \(0.319167\pi\)
\(828\) 1.55328 0.0539801
\(829\) −28.1206 −0.976670 −0.488335 0.872656i \(-0.662396\pi\)
−0.488335 + 0.872656i \(0.662396\pi\)
\(830\) −0.697543 −0.0242121
\(831\) 37.8906 1.31441
\(832\) 5.89041 0.204213
\(833\) 48.4421 1.67842
\(834\) 14.9043 0.516093
\(835\) 11.9003 0.411828
\(836\) −7.63854 −0.264184
\(837\) 13.4709 0.465621
\(838\) 6.74591 0.233034
\(839\) −18.9715 −0.654968 −0.327484 0.944857i \(-0.606201\pi\)
−0.327484 + 0.944857i \(0.606201\pi\)
\(840\) 0.971232 0.0335107
\(841\) 35.7716 1.23350
\(842\) 37.6196 1.29646
\(843\) −2.81042 −0.0967960
\(844\) −10.9150 −0.375711
\(845\) 21.6970 0.746398
\(846\) 3.38291 0.116307
\(847\) 0.526782 0.0181004
\(848\) −6.63743 −0.227930
\(849\) 26.5728 0.911975
\(850\) 7.20596 0.247162
\(851\) −21.8967 −0.750609
\(852\) −18.0914 −0.619803
\(853\) −55.9063 −1.91419 −0.957097 0.289768i \(-0.906422\pi\)
−0.957097 + 0.289768i \(0.906422\pi\)
\(854\) 0.0846298 0.00289597
\(855\) −3.04974 −0.104299
\(856\) 10.0918 0.344931
\(857\) 29.6040 1.01125 0.505626 0.862753i \(-0.331262\pi\)
0.505626 + 0.862753i \(0.331262\pi\)
\(858\) 10.8602 0.370761
\(859\) 4.31461 0.147213 0.0736063 0.997287i \(-0.476549\pi\)
0.0736063 + 0.997287i \(0.476549\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 1.75527 0.0598194
\(862\) 21.3741 0.728003
\(863\) 23.9154 0.814088 0.407044 0.913409i \(-0.366560\pi\)
0.407044 + 0.913409i \(0.366560\pi\)
\(864\) −4.79501 −0.163130
\(865\) 5.09205 0.173135
\(866\) 29.9923 1.01918
\(867\) −64.3930 −2.18690
\(868\) 1.47992 0.0502316
\(869\) −9.25084 −0.313813
\(870\) 14.8383 0.503066
\(871\) −8.81530 −0.298695
\(872\) −16.5979 −0.562075
\(873\) −4.67636 −0.158271
\(874\) 29.7171 1.00520
\(875\) 0.526782 0.0178085
\(876\) 1.20266 0.0406343
\(877\) −31.1655 −1.05238 −0.526192 0.850366i \(-0.676381\pi\)
−0.526192 + 0.850366i \(0.676381\pi\)
\(878\) 26.1904 0.883883
\(879\) −28.7643 −0.970196
\(880\) 1.00000 0.0337100
\(881\) −23.7527 −0.800247 −0.400124 0.916461i \(-0.631033\pi\)
−0.400124 + 0.916461i \(0.631033\pi\)
\(882\) 2.68401 0.0903753
\(883\) −33.6169 −1.13130 −0.565650 0.824646i \(-0.691375\pi\)
−0.565650 + 0.824646i \(0.691375\pi\)
\(884\) −42.4461 −1.42762
\(885\) 5.37193 0.180576
\(886\) 12.9088 0.433680
\(887\) −7.64450 −0.256677 −0.128339 0.991730i \(-0.540964\pi\)
−0.128339 + 0.991730i \(0.540964\pi\)
\(888\) −10.3771 −0.348232
\(889\) −5.75446 −0.192998
\(890\) −10.4841 −0.351426
\(891\) −10.0384 −0.336298
\(892\) −18.3010 −0.612763
\(893\) 64.7214 2.16582
\(894\) 38.3585 1.28290
\(895\) −24.0445 −0.803719
\(896\) −0.526782 −0.0175986
\(897\) −42.2507 −1.41071
\(898\) 14.6849 0.490040
\(899\) 22.6099 0.754082
\(900\) 0.399257 0.0133086
\(901\) 47.8290 1.59342
\(902\) 1.80726 0.0601751
\(903\) 0.971232 0.0323206
\(904\) −1.71905 −0.0571747
\(905\) −1.85958 −0.0618146
\(906\) −25.0330 −0.831666
\(907\) −30.1758 −1.00197 −0.500986 0.865455i \(-0.667029\pi\)
−0.500986 + 0.865455i \(0.667029\pi\)
\(908\) −13.0373 −0.432658
\(909\) 7.84620 0.260242
\(910\) −3.10296 −0.102862
\(911\) −50.5305 −1.67415 −0.837075 0.547089i \(-0.815736\pi\)
−0.837075 + 0.547089i \(0.815736\pi\)
\(912\) 14.0832 0.466342
\(913\) 0.697543 0.0230853
\(914\) −8.15480 −0.269737
\(915\) 0.296200 0.00979205
\(916\) 26.1503 0.864031
\(917\) −2.27278 −0.0750538
\(918\) 34.5526 1.14041
\(919\) 18.5373 0.611490 0.305745 0.952113i \(-0.401094\pi\)
0.305745 + 0.952113i \(0.401094\pi\)
\(920\) −3.89041 −0.128263
\(921\) −16.4136 −0.540847
\(922\) 7.35296 0.242157
\(923\) 57.7999 1.90251
\(924\) −0.971232 −0.0319512
\(925\) −5.62837 −0.185060
\(926\) 25.7336 0.845658
\(927\) −0.241069 −0.00791773
\(928\) −8.04808 −0.264191
\(929\) 17.3909 0.570578 0.285289 0.958442i \(-0.407910\pi\)
0.285289 + 0.958442i \(0.407910\pi\)
\(930\) 5.17962 0.169846
\(931\) 51.3501 1.68293
\(932\) −27.7381 −0.908593
\(933\) 3.96110 0.129681
\(934\) −35.0874 −1.14810
\(935\) −7.20596 −0.235660
\(936\) −2.35179 −0.0768707
\(937\) 29.9119 0.977180 0.488590 0.872513i \(-0.337511\pi\)
0.488590 + 0.872513i \(0.337511\pi\)
\(938\) 0.788356 0.0257407
\(939\) −7.76868 −0.253521
\(940\) −8.47301 −0.276359
\(941\) −24.3246 −0.792960 −0.396480 0.918043i \(-0.629768\pi\)
−0.396480 + 0.918043i \(0.629768\pi\)
\(942\) −24.9091 −0.811582
\(943\) −7.03098 −0.228960
\(944\) −2.91366 −0.0948315
\(945\) 2.52593 0.0821683
\(946\) 1.00000 0.0325128
\(947\) −52.5982 −1.70921 −0.854606 0.519277i \(-0.826201\pi\)
−0.854606 + 0.519277i \(0.826201\pi\)
\(948\) 17.0558 0.553948
\(949\) −3.84236 −0.124728
\(950\) 7.63854 0.247827
\(951\) 9.21842 0.298928
\(952\) 3.79597 0.123028
\(953\) 59.6850 1.93339 0.966694 0.255935i \(-0.0823834\pi\)
0.966694 + 0.255935i \(0.0823834\pi\)
\(954\) 2.65004 0.0857983
\(955\) −15.8411 −0.512606
\(956\) −11.8971 −0.384781
\(957\) −14.8383 −0.479654
\(958\) 15.2906 0.494018
\(959\) −1.41474 −0.0456842
\(960\) −1.84371 −0.0595054
\(961\) −23.1075 −0.745405
\(962\) 33.1534 1.06891
\(963\) −4.02923 −0.129840
\(964\) −24.6656 −0.794425
\(965\) −2.34648 −0.0755360
\(966\) 3.77849 0.121571
\(967\) −14.9537 −0.480879 −0.240439 0.970664i \(-0.577292\pi\)
−0.240439 + 0.970664i \(0.577292\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −101.483 −3.26011
\(970\) 11.7126 0.376070
\(971\) −9.04987 −0.290424 −0.145212 0.989401i \(-0.546386\pi\)
−0.145212 + 0.989401i \(0.546386\pi\)
\(972\) 4.12278 0.132238
\(973\) 4.25843 0.136519
\(974\) 23.6677 0.758361
\(975\) −10.8602 −0.347805
\(976\) −0.160654 −0.00514242
\(977\) 42.7717 1.36839 0.684193 0.729301i \(-0.260154\pi\)
0.684193 + 0.729301i \(0.260154\pi\)
\(978\) −13.6369 −0.436061
\(979\) 10.4841 0.335072
\(980\) −6.72250 −0.214742
\(981\) 6.62683 0.211578
\(982\) 36.7951 1.17418
\(983\) 1.78248 0.0568523 0.0284261 0.999596i \(-0.490950\pi\)
0.0284261 + 0.999596i \(0.490950\pi\)
\(984\) −3.33206 −0.106222
\(985\) 21.5343 0.686140
\(986\) 57.9941 1.84691
\(987\) 8.22926 0.261940
\(988\) −44.9942 −1.43145
\(989\) −3.89041 −0.123708
\(990\) −0.399257 −0.0126892
\(991\) −0.178225 −0.00566150 −0.00283075 0.999996i \(-0.500901\pi\)
−0.00283075 + 0.999996i \(0.500901\pi\)
\(992\) −2.80935 −0.0891970
\(993\) 46.2651 1.46818
\(994\) −5.16907 −0.163953
\(995\) 8.62734 0.273505
\(996\) −1.28606 −0.0407505
\(997\) −42.2595 −1.33837 −0.669186 0.743095i \(-0.733357\pi\)
−0.669186 + 0.743095i \(0.733357\pi\)
\(998\) 31.2771 0.990060
\(999\) −26.9881 −0.853866
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.w.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.w.1.3 8 1.1 even 1 trivial