Properties

Label 5265.2.a.ba.1.8
Level $5265$
Weight $2$
Character 5265.1
Self dual yes
Analytic conductor $42.041$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5265.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.0412366642\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-2.58610\) of defining polynomial
Character \(\chi\) \(=\) 5265.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.58610 q^{2} +4.68793 q^{4} +1.00000 q^{5} -4.27489 q^{7} +6.95128 q^{8} +O(q^{10})\) \(q+2.58610 q^{2} +4.68793 q^{4} +1.00000 q^{5} -4.27489 q^{7} +6.95128 q^{8} +2.58610 q^{10} -4.38446 q^{11} -1.00000 q^{13} -11.0553 q^{14} +8.60086 q^{16} -0.619151 q^{17} -2.61288 q^{19} +4.68793 q^{20} -11.3387 q^{22} -5.42887 q^{23} +1.00000 q^{25} -2.58610 q^{26} -20.0404 q^{28} -6.95774 q^{29} -6.88609 q^{31} +8.34015 q^{32} -1.60119 q^{34} -4.27489 q^{35} -4.02164 q^{37} -6.75717 q^{38} +6.95128 q^{40} +4.07427 q^{41} -10.0369 q^{43} -20.5541 q^{44} -14.0396 q^{46} +0.405987 q^{47} +11.2747 q^{49} +2.58610 q^{50} -4.68793 q^{52} +8.71205 q^{53} -4.38446 q^{55} -29.7160 q^{56} -17.9934 q^{58} +10.7215 q^{59} +5.07217 q^{61} -17.8081 q^{62} +4.36679 q^{64} -1.00000 q^{65} +14.5579 q^{67} -2.90254 q^{68} -11.0553 q^{70} -6.57523 q^{71} +16.7313 q^{73} -10.4004 q^{74} -12.2490 q^{76} +18.7431 q^{77} +14.5458 q^{79} +8.60086 q^{80} +10.5365 q^{82} +3.04113 q^{83} -0.619151 q^{85} -25.9565 q^{86} -30.4776 q^{88} -7.27070 q^{89} +4.27489 q^{91} -25.4502 q^{92} +1.04992 q^{94} -2.61288 q^{95} -9.63475 q^{97} +29.1576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 8 q^{13} - 10 q^{14} + 11 q^{16} + 2 q^{17} - 10 q^{19} + 9 q^{20} + 3 q^{22} - 6 q^{23} + 8 q^{25} + 3 q^{26} - 34 q^{28} - 14 q^{29} - 31 q^{31} - q^{32} - 7 q^{34} - 11 q^{35} + q^{37} - 9 q^{38} + 6 q^{40} + 12 q^{41} + 15 q^{43} - 16 q^{44} - 32 q^{46} + 18 q^{47} + 17 q^{49} - 3 q^{50} - 9 q^{52} - 2 q^{53} - 6 q^{55} - 16 q^{56} - 42 q^{58} - 24 q^{59} - 9 q^{61} + 20 q^{62} - 30 q^{64} - 8 q^{65} - 18 q^{67} + 14 q^{68} - 10 q^{70} - 10 q^{71} + 6 q^{73} + 37 q^{74} - 53 q^{76} + 34 q^{77} - 3 q^{79} + 11 q^{80} - 34 q^{82} + 10 q^{83} + 2 q^{85} - 60 q^{86} - 14 q^{88} + 13 q^{89} + 11 q^{91} - 5 q^{92} + 17 q^{94} - 10 q^{95} - 34 q^{97} + 30 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58610 1.82865 0.914326 0.404979i \(-0.132721\pi\)
0.914326 + 0.404979i \(0.132721\pi\)
\(3\) 0 0
\(4\) 4.68793 2.34397
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.27489 −1.61576 −0.807879 0.589349i \(-0.799384\pi\)
−0.807879 + 0.589349i \(0.799384\pi\)
\(8\) 6.95128 2.45765
\(9\) 0 0
\(10\) 2.58610 0.817798
\(11\) −4.38446 −1.32197 −0.660983 0.750401i \(-0.729860\pi\)
−0.660983 + 0.750401i \(0.729860\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) −11.0553 −2.95466
\(15\) 0 0
\(16\) 8.60086 2.15021
\(17\) −0.619151 −0.150166 −0.0750831 0.997177i \(-0.523922\pi\)
−0.0750831 + 0.997177i \(0.523922\pi\)
\(18\) 0 0
\(19\) −2.61288 −0.599435 −0.299718 0.954028i \(-0.596892\pi\)
−0.299718 + 0.954028i \(0.596892\pi\)
\(20\) 4.68793 1.04825
\(21\) 0 0
\(22\) −11.3387 −2.41741
\(23\) −5.42887 −1.13200 −0.565998 0.824406i \(-0.691509\pi\)
−0.565998 + 0.824406i \(0.691509\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.58610 −0.507177
\(27\) 0 0
\(28\) −20.0404 −3.78728
\(29\) −6.95774 −1.29202 −0.646010 0.763329i \(-0.723564\pi\)
−0.646010 + 0.763329i \(0.723564\pi\)
\(30\) 0 0
\(31\) −6.88609 −1.23678 −0.618389 0.785872i \(-0.712214\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(32\) 8.34015 1.47434
\(33\) 0 0
\(34\) −1.60119 −0.274602
\(35\) −4.27489 −0.722589
\(36\) 0 0
\(37\) −4.02164 −0.661154 −0.330577 0.943779i \(-0.607243\pi\)
−0.330577 + 0.943779i \(0.607243\pi\)
\(38\) −6.75717 −1.09616
\(39\) 0 0
\(40\) 6.95128 1.09909
\(41\) 4.07427 0.636295 0.318147 0.948041i \(-0.396939\pi\)
0.318147 + 0.948041i \(0.396939\pi\)
\(42\) 0 0
\(43\) −10.0369 −1.53061 −0.765307 0.643666i \(-0.777413\pi\)
−0.765307 + 0.643666i \(0.777413\pi\)
\(44\) −20.5541 −3.09864
\(45\) 0 0
\(46\) −14.0396 −2.07003
\(47\) 0.405987 0.0592192 0.0296096 0.999562i \(-0.490574\pi\)
0.0296096 + 0.999562i \(0.490574\pi\)
\(48\) 0 0
\(49\) 11.2747 1.61067
\(50\) 2.58610 0.365730
\(51\) 0 0
\(52\) −4.68793 −0.650099
\(53\) 8.71205 1.19669 0.598346 0.801238i \(-0.295825\pi\)
0.598346 + 0.801238i \(0.295825\pi\)
\(54\) 0 0
\(55\) −4.38446 −0.591201
\(56\) −29.7160 −3.97096
\(57\) 0 0
\(58\) −17.9934 −2.36265
\(59\) 10.7215 1.39581 0.697907 0.716188i \(-0.254115\pi\)
0.697907 + 0.716188i \(0.254115\pi\)
\(60\) 0 0
\(61\) 5.07217 0.649425 0.324713 0.945813i \(-0.394732\pi\)
0.324713 + 0.945813i \(0.394732\pi\)
\(62\) −17.8081 −2.26164
\(63\) 0 0
\(64\) 4.36679 0.545849
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 14.5579 1.77853 0.889264 0.457395i \(-0.151217\pi\)
0.889264 + 0.457395i \(0.151217\pi\)
\(68\) −2.90254 −0.351985
\(69\) 0 0
\(70\) −11.0553 −1.32136
\(71\) −6.57523 −0.780336 −0.390168 0.920744i \(-0.627583\pi\)
−0.390168 + 0.920744i \(0.627583\pi\)
\(72\) 0 0
\(73\) 16.7313 1.95825 0.979125 0.203257i \(-0.0651527\pi\)
0.979125 + 0.203257i \(0.0651527\pi\)
\(74\) −10.4004 −1.20902
\(75\) 0 0
\(76\) −12.2490 −1.40506
\(77\) 18.7431 2.13598
\(78\) 0 0
\(79\) 14.5458 1.63653 0.818263 0.574844i \(-0.194937\pi\)
0.818263 + 0.574844i \(0.194937\pi\)
\(80\) 8.60086 0.961605
\(81\) 0 0
\(82\) 10.5365 1.16356
\(83\) 3.04113 0.333808 0.166904 0.985973i \(-0.446623\pi\)
0.166904 + 0.985973i \(0.446623\pi\)
\(84\) 0 0
\(85\) −0.619151 −0.0671564
\(86\) −25.9565 −2.79896
\(87\) 0 0
\(88\) −30.4776 −3.24893
\(89\) −7.27070 −0.770693 −0.385347 0.922772i \(-0.625918\pi\)
−0.385347 + 0.922772i \(0.625918\pi\)
\(90\) 0 0
\(91\) 4.27489 0.448131
\(92\) −25.4502 −2.65336
\(93\) 0 0
\(94\) 1.04992 0.108291
\(95\) −2.61288 −0.268076
\(96\) 0 0
\(97\) −9.63475 −0.978261 −0.489130 0.872211i \(-0.662686\pi\)
−0.489130 + 0.872211i \(0.662686\pi\)
\(98\) 29.1576 2.94536
\(99\) 0 0
\(100\) 4.68793 0.468793
\(101\) −7.79952 −0.776081 −0.388041 0.921642i \(-0.626848\pi\)
−0.388041 + 0.921642i \(0.626848\pi\)
\(102\) 0 0
\(103\) 0.993241 0.0978670 0.0489335 0.998802i \(-0.484418\pi\)
0.0489335 + 0.998802i \(0.484418\pi\)
\(104\) −6.95128 −0.681629
\(105\) 0 0
\(106\) 22.5303 2.18833
\(107\) −4.24171 −0.410062 −0.205031 0.978755i \(-0.565730\pi\)
−0.205031 + 0.978755i \(0.565730\pi\)
\(108\) 0 0
\(109\) 4.72247 0.452330 0.226165 0.974089i \(-0.427381\pi\)
0.226165 + 0.974089i \(0.427381\pi\)
\(110\) −11.3387 −1.08110
\(111\) 0 0
\(112\) −36.7677 −3.47422
\(113\) 3.55408 0.334339 0.167170 0.985928i \(-0.446537\pi\)
0.167170 + 0.985928i \(0.446537\pi\)
\(114\) 0 0
\(115\) −5.42887 −0.506244
\(116\) −32.6174 −3.02845
\(117\) 0 0
\(118\) 27.7268 2.55246
\(119\) 2.64681 0.242632
\(120\) 0 0
\(121\) 8.22353 0.747594
\(122\) 13.1172 1.18757
\(123\) 0 0
\(124\) −32.2815 −2.89897
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −13.6413 −1.21047 −0.605234 0.796048i \(-0.706920\pi\)
−0.605234 + 0.796048i \(0.706920\pi\)
\(128\) −5.38732 −0.476177
\(129\) 0 0
\(130\) −2.58610 −0.226816
\(131\) −8.36237 −0.730623 −0.365312 0.930885i \(-0.619038\pi\)
−0.365312 + 0.930885i \(0.619038\pi\)
\(132\) 0 0
\(133\) 11.1698 0.968542
\(134\) 37.6482 3.25231
\(135\) 0 0
\(136\) −4.30389 −0.369056
\(137\) 6.75088 0.576767 0.288383 0.957515i \(-0.406882\pi\)
0.288383 + 0.957515i \(0.406882\pi\)
\(138\) 0 0
\(139\) 3.50577 0.297355 0.148678 0.988886i \(-0.452498\pi\)
0.148678 + 0.988886i \(0.452498\pi\)
\(140\) −20.0404 −1.69372
\(141\) 0 0
\(142\) −17.0042 −1.42696
\(143\) 4.38446 0.366647
\(144\) 0 0
\(145\) −6.95774 −0.577809
\(146\) 43.2689 3.58096
\(147\) 0 0
\(148\) −18.8532 −1.54972
\(149\) −12.2790 −1.00594 −0.502968 0.864305i \(-0.667759\pi\)
−0.502968 + 0.864305i \(0.667759\pi\)
\(150\) 0 0
\(151\) −16.6964 −1.35873 −0.679367 0.733798i \(-0.737746\pi\)
−0.679367 + 0.733798i \(0.737746\pi\)
\(152\) −18.1628 −1.47320
\(153\) 0 0
\(154\) 48.4717 3.90596
\(155\) −6.88609 −0.553104
\(156\) 0 0
\(157\) 7.99688 0.638220 0.319110 0.947718i \(-0.396616\pi\)
0.319110 + 0.947718i \(0.396616\pi\)
\(158\) 37.6168 2.99264
\(159\) 0 0
\(160\) 8.34015 0.659347
\(161\) 23.2078 1.82903
\(162\) 0 0
\(163\) −17.3723 −1.36071 −0.680353 0.732885i \(-0.738173\pi\)
−0.680353 + 0.732885i \(0.738173\pi\)
\(164\) 19.0999 1.49145
\(165\) 0 0
\(166\) 7.86468 0.610418
\(167\) −4.27589 −0.330879 −0.165439 0.986220i \(-0.552904\pi\)
−0.165439 + 0.986220i \(0.552904\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −1.60119 −0.122806
\(171\) 0 0
\(172\) −47.0523 −3.58771
\(173\) −12.9559 −0.985016 −0.492508 0.870308i \(-0.663920\pi\)
−0.492508 + 0.870308i \(0.663920\pi\)
\(174\) 0 0
\(175\) −4.27489 −0.323152
\(176\) −37.7101 −2.84251
\(177\) 0 0
\(178\) −18.8028 −1.40933
\(179\) −18.8530 −1.40914 −0.704571 0.709633i \(-0.748861\pi\)
−0.704571 + 0.709633i \(0.748861\pi\)
\(180\) 0 0
\(181\) −21.2593 −1.58019 −0.790097 0.612982i \(-0.789970\pi\)
−0.790097 + 0.612982i \(0.789970\pi\)
\(182\) 11.0553 0.819475
\(183\) 0 0
\(184\) −37.7375 −2.78205
\(185\) −4.02164 −0.295677
\(186\) 0 0
\(187\) 2.71465 0.198515
\(188\) 1.90324 0.138808
\(189\) 0 0
\(190\) −6.75717 −0.490217
\(191\) 15.4170 1.11553 0.557767 0.829998i \(-0.311658\pi\)
0.557767 + 0.829998i \(0.311658\pi\)
\(192\) 0 0
\(193\) 1.88802 0.135902 0.0679512 0.997689i \(-0.478354\pi\)
0.0679512 + 0.997689i \(0.478354\pi\)
\(194\) −24.9165 −1.78890
\(195\) 0 0
\(196\) 52.8551 3.77536
\(197\) 10.8597 0.773723 0.386862 0.922138i \(-0.373559\pi\)
0.386862 + 0.922138i \(0.373559\pi\)
\(198\) 0 0
\(199\) −1.20110 −0.0851436 −0.0425718 0.999093i \(-0.513555\pi\)
−0.0425718 + 0.999093i \(0.513555\pi\)
\(200\) 6.95128 0.491529
\(201\) 0 0
\(202\) −20.1704 −1.41918
\(203\) 29.7436 2.08759
\(204\) 0 0
\(205\) 4.07427 0.284560
\(206\) 2.56863 0.178965
\(207\) 0 0
\(208\) −8.60086 −0.596362
\(209\) 11.4561 0.792433
\(210\) 0 0
\(211\) −0.235212 −0.0161926 −0.00809632 0.999967i \(-0.502577\pi\)
−0.00809632 + 0.999967i \(0.502577\pi\)
\(212\) 40.8415 2.80501
\(213\) 0 0
\(214\) −10.9695 −0.749861
\(215\) −10.0369 −0.684511
\(216\) 0 0
\(217\) 29.4373 1.99833
\(218\) 12.2128 0.827154
\(219\) 0 0
\(220\) −20.5541 −1.38576
\(221\) 0.619151 0.0416486
\(222\) 0 0
\(223\) −16.7549 −1.12199 −0.560997 0.827818i \(-0.689582\pi\)
−0.560997 + 0.827818i \(0.689582\pi\)
\(224\) −35.6533 −2.38218
\(225\) 0 0
\(226\) 9.19121 0.611390
\(227\) −22.8003 −1.51331 −0.756656 0.653813i \(-0.773168\pi\)
−0.756656 + 0.653813i \(0.773168\pi\)
\(228\) 0 0
\(229\) −6.97478 −0.460906 −0.230453 0.973083i \(-0.574021\pi\)
−0.230453 + 0.973083i \(0.574021\pi\)
\(230\) −14.0396 −0.925745
\(231\) 0 0
\(232\) −48.3652 −3.17533
\(233\) 8.63201 0.565502 0.282751 0.959193i \(-0.408753\pi\)
0.282751 + 0.959193i \(0.408753\pi\)
\(234\) 0 0
\(235\) 0.405987 0.0264836
\(236\) 50.2615 3.27174
\(237\) 0 0
\(238\) 6.84491 0.443690
\(239\) 3.07101 0.198647 0.0993235 0.995055i \(-0.468332\pi\)
0.0993235 + 0.995055i \(0.468332\pi\)
\(240\) 0 0
\(241\) 5.83268 0.375716 0.187858 0.982196i \(-0.439846\pi\)
0.187858 + 0.982196i \(0.439846\pi\)
\(242\) 21.2669 1.36709
\(243\) 0 0
\(244\) 23.7780 1.52223
\(245\) 11.2747 0.720315
\(246\) 0 0
\(247\) 2.61288 0.166253
\(248\) −47.8671 −3.03956
\(249\) 0 0
\(250\) 2.58610 0.163560
\(251\) 23.7101 1.49657 0.748285 0.663378i \(-0.230878\pi\)
0.748285 + 0.663378i \(0.230878\pi\)
\(252\) 0 0
\(253\) 23.8027 1.49646
\(254\) −35.2777 −2.21352
\(255\) 0 0
\(256\) −22.6658 −1.41661
\(257\) −19.3077 −1.20438 −0.602190 0.798353i \(-0.705705\pi\)
−0.602190 + 0.798353i \(0.705705\pi\)
\(258\) 0 0
\(259\) 17.1921 1.06826
\(260\) −4.68793 −0.290733
\(261\) 0 0
\(262\) −21.6260 −1.33606
\(263\) 11.7197 0.722667 0.361334 0.932437i \(-0.382322\pi\)
0.361334 + 0.932437i \(0.382322\pi\)
\(264\) 0 0
\(265\) 8.71205 0.535177
\(266\) 28.8862 1.77113
\(267\) 0 0
\(268\) 68.2464 4.16881
\(269\) 17.0088 1.03705 0.518524 0.855063i \(-0.326482\pi\)
0.518524 + 0.855063i \(0.326482\pi\)
\(270\) 0 0
\(271\) −12.4840 −0.758348 −0.379174 0.925325i \(-0.623792\pi\)
−0.379174 + 0.925325i \(0.623792\pi\)
\(272\) −5.32523 −0.322890
\(273\) 0 0
\(274\) 17.4585 1.05471
\(275\) −4.38446 −0.264393
\(276\) 0 0
\(277\) 20.2887 1.21903 0.609516 0.792774i \(-0.291364\pi\)
0.609516 + 0.792774i \(0.291364\pi\)
\(278\) 9.06628 0.543759
\(279\) 0 0
\(280\) −29.7160 −1.77587
\(281\) 8.37449 0.499580 0.249790 0.968300i \(-0.419638\pi\)
0.249790 + 0.968300i \(0.419638\pi\)
\(282\) 0 0
\(283\) −2.22562 −0.132300 −0.0661498 0.997810i \(-0.521072\pi\)
−0.0661498 + 0.997810i \(0.521072\pi\)
\(284\) −30.8242 −1.82908
\(285\) 0 0
\(286\) 11.3387 0.670470
\(287\) −17.4171 −1.02810
\(288\) 0 0
\(289\) −16.6167 −0.977450
\(290\) −17.9934 −1.05661
\(291\) 0 0
\(292\) 78.4352 4.59008
\(293\) 2.53887 0.148323 0.0741613 0.997246i \(-0.476372\pi\)
0.0741613 + 0.997246i \(0.476372\pi\)
\(294\) 0 0
\(295\) 10.7215 0.624227
\(296\) −27.9555 −1.62488
\(297\) 0 0
\(298\) −31.7548 −1.83951
\(299\) 5.42887 0.313959
\(300\) 0 0
\(301\) 42.9067 2.47310
\(302\) −43.1787 −2.48465
\(303\) 0 0
\(304\) −22.4730 −1.28891
\(305\) 5.07217 0.290432
\(306\) 0 0
\(307\) 19.2343 1.09776 0.548881 0.835901i \(-0.315054\pi\)
0.548881 + 0.835901i \(0.315054\pi\)
\(308\) 87.8665 5.00666
\(309\) 0 0
\(310\) −17.8081 −1.01143
\(311\) −8.76042 −0.496758 −0.248379 0.968663i \(-0.579898\pi\)
−0.248379 + 0.968663i \(0.579898\pi\)
\(312\) 0 0
\(313\) −12.1782 −0.688353 −0.344176 0.938905i \(-0.611842\pi\)
−0.344176 + 0.938905i \(0.611842\pi\)
\(314\) 20.6808 1.16708
\(315\) 0 0
\(316\) 68.1896 3.83596
\(317\) −17.3245 −0.973043 −0.486521 0.873669i \(-0.661734\pi\)
−0.486521 + 0.873669i \(0.661734\pi\)
\(318\) 0 0
\(319\) 30.5060 1.70801
\(320\) 4.36679 0.244111
\(321\) 0 0
\(322\) 60.0178 3.34466
\(323\) 1.61777 0.0900149
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) −44.9266 −2.48826
\(327\) 0 0
\(328\) 28.3214 1.56379
\(329\) −1.73555 −0.0956839
\(330\) 0 0
\(331\) 2.46074 0.135254 0.0676272 0.997711i \(-0.478457\pi\)
0.0676272 + 0.997711i \(0.478457\pi\)
\(332\) 14.2566 0.782434
\(333\) 0 0
\(334\) −11.0579 −0.605062
\(335\) 14.5579 0.795382
\(336\) 0 0
\(337\) 20.7486 1.13025 0.565123 0.825007i \(-0.308829\pi\)
0.565123 + 0.825007i \(0.308829\pi\)
\(338\) 2.58610 0.140666
\(339\) 0 0
\(340\) −2.90254 −0.157412
\(341\) 30.1918 1.63498
\(342\) 0 0
\(343\) −18.2739 −0.986700
\(344\) −69.7693 −3.76171
\(345\) 0 0
\(346\) −33.5052 −1.80125
\(347\) 12.5877 0.675741 0.337871 0.941193i \(-0.390293\pi\)
0.337871 + 0.941193i \(0.390293\pi\)
\(348\) 0 0
\(349\) −19.9728 −1.06912 −0.534561 0.845130i \(-0.679523\pi\)
−0.534561 + 0.845130i \(0.679523\pi\)
\(350\) −11.0553 −0.590932
\(351\) 0 0
\(352\) −36.5671 −1.94903
\(353\) −5.88934 −0.313458 −0.156729 0.987642i \(-0.550095\pi\)
−0.156729 + 0.987642i \(0.550095\pi\)
\(354\) 0 0
\(355\) −6.57523 −0.348977
\(356\) −34.0846 −1.80648
\(357\) 0 0
\(358\) −48.7559 −2.57683
\(359\) −17.8334 −0.941209 −0.470605 0.882344i \(-0.655964\pi\)
−0.470605 + 0.882344i \(0.655964\pi\)
\(360\) 0 0
\(361\) −12.1729 −0.640677
\(362\) −54.9788 −2.88962
\(363\) 0 0
\(364\) 20.0404 1.05040
\(365\) 16.7313 0.875756
\(366\) 0 0
\(367\) −29.8329 −1.55727 −0.778633 0.627480i \(-0.784086\pi\)
−0.778633 + 0.627480i \(0.784086\pi\)
\(368\) −46.6929 −2.43404
\(369\) 0 0
\(370\) −10.4004 −0.540690
\(371\) −37.2431 −1.93357
\(372\) 0 0
\(373\) −14.5794 −0.754892 −0.377446 0.926032i \(-0.623198\pi\)
−0.377446 + 0.926032i \(0.623198\pi\)
\(374\) 7.02036 0.363014
\(375\) 0 0
\(376\) 2.82212 0.145540
\(377\) 6.95774 0.358342
\(378\) 0 0
\(379\) 20.7048 1.06353 0.531766 0.846891i \(-0.321529\pi\)
0.531766 + 0.846891i \(0.321529\pi\)
\(380\) −12.2490 −0.628360
\(381\) 0 0
\(382\) 39.8699 2.03992
\(383\) 25.5665 1.30639 0.653193 0.757191i \(-0.273429\pi\)
0.653193 + 0.757191i \(0.273429\pi\)
\(384\) 0 0
\(385\) 18.7431 0.955238
\(386\) 4.88260 0.248518
\(387\) 0 0
\(388\) −45.1671 −2.29301
\(389\) 17.1304 0.868546 0.434273 0.900781i \(-0.357005\pi\)
0.434273 + 0.900781i \(0.357005\pi\)
\(390\) 0 0
\(391\) 3.36129 0.169988
\(392\) 78.3736 3.95847
\(393\) 0 0
\(394\) 28.0844 1.41487
\(395\) 14.5458 0.731877
\(396\) 0 0
\(397\) −15.8337 −0.794669 −0.397334 0.917674i \(-0.630065\pi\)
−0.397334 + 0.917674i \(0.630065\pi\)
\(398\) −3.10617 −0.155698
\(399\) 0 0
\(400\) 8.60086 0.430043
\(401\) 34.1108 1.70341 0.851706 0.524021i \(-0.175569\pi\)
0.851706 + 0.524021i \(0.175569\pi\)
\(402\) 0 0
\(403\) 6.88609 0.343021
\(404\) −36.5636 −1.81911
\(405\) 0 0
\(406\) 76.9200 3.81748
\(407\) 17.6327 0.874023
\(408\) 0 0
\(409\) −19.1453 −0.946673 −0.473336 0.880882i \(-0.656950\pi\)
−0.473336 + 0.880882i \(0.656950\pi\)
\(410\) 10.5365 0.520360
\(411\) 0 0
\(412\) 4.65625 0.229397
\(413\) −45.8331 −2.25530
\(414\) 0 0
\(415\) 3.04113 0.149283
\(416\) −8.34015 −0.408910
\(417\) 0 0
\(418\) 29.6266 1.44908
\(419\) −7.13499 −0.348567 −0.174284 0.984696i \(-0.555761\pi\)
−0.174284 + 0.984696i \(0.555761\pi\)
\(420\) 0 0
\(421\) −26.1618 −1.27505 −0.637524 0.770431i \(-0.720041\pi\)
−0.637524 + 0.770431i \(0.720041\pi\)
\(422\) −0.608282 −0.0296107
\(423\) 0 0
\(424\) 60.5599 2.94105
\(425\) −0.619151 −0.0300332
\(426\) 0 0
\(427\) −21.6830 −1.04931
\(428\) −19.8849 −0.961172
\(429\) 0 0
\(430\) −25.9565 −1.25173
\(431\) 12.4211 0.598302 0.299151 0.954206i \(-0.403297\pi\)
0.299151 + 0.954206i \(0.403297\pi\)
\(432\) 0 0
\(433\) −6.04541 −0.290524 −0.145262 0.989393i \(-0.546402\pi\)
−0.145262 + 0.989393i \(0.546402\pi\)
\(434\) 76.1279 3.65426
\(435\) 0 0
\(436\) 22.1386 1.06025
\(437\) 14.1850 0.678559
\(438\) 0 0
\(439\) −28.6764 −1.36865 −0.684326 0.729177i \(-0.739903\pi\)
−0.684326 + 0.729177i \(0.739903\pi\)
\(440\) −30.4776 −1.45296
\(441\) 0 0
\(442\) 1.60119 0.0761608
\(443\) 9.14996 0.434728 0.217364 0.976091i \(-0.430254\pi\)
0.217364 + 0.976091i \(0.430254\pi\)
\(444\) 0 0
\(445\) −7.27070 −0.344664
\(446\) −43.3300 −2.05174
\(447\) 0 0
\(448\) −18.6676 −0.881960
\(449\) −35.4645 −1.67367 −0.836837 0.547452i \(-0.815598\pi\)
−0.836837 + 0.547452i \(0.815598\pi\)
\(450\) 0 0
\(451\) −17.8635 −0.841160
\(452\) 16.6613 0.783680
\(453\) 0 0
\(454\) −58.9641 −2.76732
\(455\) 4.27489 0.200410
\(456\) 0 0
\(457\) 9.41261 0.440303 0.220152 0.975466i \(-0.429345\pi\)
0.220152 + 0.975466i \(0.429345\pi\)
\(458\) −18.0375 −0.842837
\(459\) 0 0
\(460\) −25.4502 −1.18662
\(461\) 20.5026 0.954899 0.477450 0.878659i \(-0.341561\pi\)
0.477450 + 0.878659i \(0.341561\pi\)
\(462\) 0 0
\(463\) −37.7831 −1.75593 −0.877965 0.478724i \(-0.841099\pi\)
−0.877965 + 0.478724i \(0.841099\pi\)
\(464\) −59.8425 −2.77812
\(465\) 0 0
\(466\) 22.3233 1.03411
\(467\) 12.8882 0.596394 0.298197 0.954504i \(-0.403615\pi\)
0.298197 + 0.954504i \(0.403615\pi\)
\(468\) 0 0
\(469\) −62.2334 −2.87367
\(470\) 1.04992 0.0484294
\(471\) 0 0
\(472\) 74.5278 3.43042
\(473\) 44.0064 2.02342
\(474\) 0 0
\(475\) −2.61288 −0.119887
\(476\) 12.4080 0.568722
\(477\) 0 0
\(478\) 7.94194 0.363256
\(479\) −20.1880 −0.922415 −0.461207 0.887292i \(-0.652584\pi\)
−0.461207 + 0.887292i \(0.652584\pi\)
\(480\) 0 0
\(481\) 4.02164 0.183371
\(482\) 15.0839 0.687053
\(483\) 0 0
\(484\) 38.5514 1.75233
\(485\) −9.63475 −0.437492
\(486\) 0 0
\(487\) 15.1480 0.686423 0.343212 0.939258i \(-0.388485\pi\)
0.343212 + 0.939258i \(0.388485\pi\)
\(488\) 35.2581 1.59606
\(489\) 0 0
\(490\) 29.1576 1.31721
\(491\) 11.4875 0.518423 0.259211 0.965821i \(-0.416537\pi\)
0.259211 + 0.965821i \(0.416537\pi\)
\(492\) 0 0
\(493\) 4.30789 0.194018
\(494\) 6.75717 0.304020
\(495\) 0 0
\(496\) −59.2263 −2.65934
\(497\) 28.1084 1.26083
\(498\) 0 0
\(499\) −13.1201 −0.587336 −0.293668 0.955907i \(-0.594876\pi\)
−0.293668 + 0.955907i \(0.594876\pi\)
\(500\) 4.68793 0.209651
\(501\) 0 0
\(502\) 61.3168 2.73670
\(503\) −7.80396 −0.347961 −0.173981 0.984749i \(-0.555663\pi\)
−0.173981 + 0.984749i \(0.555663\pi\)
\(504\) 0 0
\(505\) −7.79952 −0.347074
\(506\) 61.5562 2.73651
\(507\) 0 0
\(508\) −63.9494 −2.83729
\(509\) −21.9837 −0.974411 −0.487205 0.873287i \(-0.661984\pi\)
−0.487205 + 0.873287i \(0.661984\pi\)
\(510\) 0 0
\(511\) −71.5245 −3.16406
\(512\) −47.8414 −2.11431
\(513\) 0 0
\(514\) −49.9316 −2.20239
\(515\) 0.993241 0.0437674
\(516\) 0 0
\(517\) −1.78003 −0.0782858
\(518\) 44.4605 1.95348
\(519\) 0 0
\(520\) −6.95128 −0.304834
\(521\) −12.1706 −0.533205 −0.266603 0.963807i \(-0.585901\pi\)
−0.266603 + 0.963807i \(0.585901\pi\)
\(522\) 0 0
\(523\) 32.5468 1.42317 0.711587 0.702598i \(-0.247977\pi\)
0.711587 + 0.702598i \(0.247977\pi\)
\(524\) −39.2022 −1.71256
\(525\) 0 0
\(526\) 30.3083 1.32151
\(527\) 4.26353 0.185722
\(528\) 0 0
\(529\) 6.47259 0.281417
\(530\) 22.5303 0.978653
\(531\) 0 0
\(532\) 52.3632 2.27023
\(533\) −4.07427 −0.176476
\(534\) 0 0
\(535\) −4.24171 −0.183385
\(536\) 101.196 4.37099
\(537\) 0 0
\(538\) 43.9866 1.89640
\(539\) −49.4336 −2.12925
\(540\) 0 0
\(541\) −16.3865 −0.704511 −0.352256 0.935904i \(-0.614585\pi\)
−0.352256 + 0.935904i \(0.614585\pi\)
\(542\) −32.2849 −1.38676
\(543\) 0 0
\(544\) −5.16382 −0.221397
\(545\) 4.72247 0.202288
\(546\) 0 0
\(547\) 19.0667 0.815233 0.407616 0.913153i \(-0.366360\pi\)
0.407616 + 0.913153i \(0.366360\pi\)
\(548\) 31.6477 1.35192
\(549\) 0 0
\(550\) −11.3387 −0.483483
\(551\) 18.1797 0.774482
\(552\) 0 0
\(553\) −62.1816 −2.64423
\(554\) 52.4687 2.22918
\(555\) 0 0
\(556\) 16.4348 0.696991
\(557\) 38.2913 1.62245 0.811227 0.584732i \(-0.198800\pi\)
0.811227 + 0.584732i \(0.198800\pi\)
\(558\) 0 0
\(559\) 10.0369 0.424516
\(560\) −36.7677 −1.55372
\(561\) 0 0
\(562\) 21.6573 0.913559
\(563\) −10.3408 −0.435813 −0.217906 0.975970i \(-0.569923\pi\)
−0.217906 + 0.975970i \(0.569923\pi\)
\(564\) 0 0
\(565\) 3.55408 0.149521
\(566\) −5.75569 −0.241930
\(567\) 0 0
\(568\) −45.7062 −1.91779
\(569\) 26.0267 1.09110 0.545548 0.838080i \(-0.316322\pi\)
0.545548 + 0.838080i \(0.316322\pi\)
\(570\) 0 0
\(571\) −32.3239 −1.35271 −0.676357 0.736574i \(-0.736442\pi\)
−0.676357 + 0.736574i \(0.736442\pi\)
\(572\) 20.5541 0.859409
\(573\) 0 0
\(574\) −45.0424 −1.88003
\(575\) −5.42887 −0.226399
\(576\) 0 0
\(577\) 12.4808 0.519581 0.259790 0.965665i \(-0.416347\pi\)
0.259790 + 0.965665i \(0.416347\pi\)
\(578\) −42.9724 −1.78742
\(579\) 0 0
\(580\) −32.6174 −1.35436
\(581\) −13.0005 −0.539352
\(582\) 0 0
\(583\) −38.1977 −1.58199
\(584\) 116.304 4.81269
\(585\) 0 0
\(586\) 6.56579 0.271230
\(587\) 25.1950 1.03991 0.519955 0.854194i \(-0.325949\pi\)
0.519955 + 0.854194i \(0.325949\pi\)
\(588\) 0 0
\(589\) 17.9925 0.741368
\(590\) 27.7268 1.14149
\(591\) 0 0
\(592\) −34.5896 −1.42162
\(593\) 38.4456 1.57877 0.789385 0.613898i \(-0.210399\pi\)
0.789385 + 0.613898i \(0.210399\pi\)
\(594\) 0 0
\(595\) 2.64681 0.108508
\(596\) −57.5632 −2.35788
\(597\) 0 0
\(598\) 14.0396 0.574122
\(599\) 47.3236 1.93359 0.966795 0.255553i \(-0.0822574\pi\)
0.966795 + 0.255553i \(0.0822574\pi\)
\(600\) 0 0
\(601\) 40.0656 1.63431 0.817156 0.576417i \(-0.195550\pi\)
0.817156 + 0.576417i \(0.195550\pi\)
\(602\) 110.961 4.52244
\(603\) 0 0
\(604\) −78.2717 −3.18483
\(605\) 8.22353 0.334334
\(606\) 0 0
\(607\) 20.6119 0.836612 0.418306 0.908306i \(-0.362624\pi\)
0.418306 + 0.908306i \(0.362624\pi\)
\(608\) −21.7918 −0.883774
\(609\) 0 0
\(610\) 13.1172 0.531098
\(611\) −0.405987 −0.0164245
\(612\) 0 0
\(613\) −4.02465 −0.162554 −0.0812770 0.996692i \(-0.525900\pi\)
−0.0812770 + 0.996692i \(0.525900\pi\)
\(614\) 49.7420 2.00742
\(615\) 0 0
\(616\) 130.289 5.24948
\(617\) −29.8240 −1.20067 −0.600334 0.799749i \(-0.704966\pi\)
−0.600334 + 0.799749i \(0.704966\pi\)
\(618\) 0 0
\(619\) −47.5386 −1.91074 −0.955368 0.295419i \(-0.904541\pi\)
−0.955368 + 0.295419i \(0.904541\pi\)
\(620\) −32.2815 −1.29646
\(621\) 0 0
\(622\) −22.6554 −0.908397
\(623\) 31.0815 1.24525
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −31.4941 −1.25876
\(627\) 0 0
\(628\) 37.4888 1.49597
\(629\) 2.49000 0.0992830
\(630\) 0 0
\(631\) 32.2213 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(632\) 101.112 4.02200
\(633\) 0 0
\(634\) −44.8030 −1.77936
\(635\) −13.6413 −0.541337
\(636\) 0 0
\(637\) −11.2747 −0.446720
\(638\) 78.8916 3.12335
\(639\) 0 0
\(640\) −5.38732 −0.212953
\(641\) −3.50215 −0.138326 −0.0691632 0.997605i \(-0.522033\pi\)
−0.0691632 + 0.997605i \(0.522033\pi\)
\(642\) 0 0
\(643\) 0.0231395 0.000912533 0 0.000456266 1.00000i \(-0.499855\pi\)
0.000456266 1.00000i \(0.499855\pi\)
\(644\) 108.797 4.28719
\(645\) 0 0
\(646\) 4.18371 0.164606
\(647\) 20.8611 0.820136 0.410068 0.912055i \(-0.365505\pi\)
0.410068 + 0.912055i \(0.365505\pi\)
\(648\) 0 0
\(649\) −47.0078 −1.84522
\(650\) −2.58610 −0.101435
\(651\) 0 0
\(652\) −81.4403 −3.18945
\(653\) −10.9565 −0.428760 −0.214380 0.976750i \(-0.568773\pi\)
−0.214380 + 0.976750i \(0.568773\pi\)
\(654\) 0 0
\(655\) −8.36237 −0.326745
\(656\) 35.0422 1.36817
\(657\) 0 0
\(658\) −4.48831 −0.174973
\(659\) 34.1093 1.32871 0.664354 0.747418i \(-0.268707\pi\)
0.664354 + 0.747418i \(0.268707\pi\)
\(660\) 0 0
\(661\) −24.1801 −0.940498 −0.470249 0.882534i \(-0.655836\pi\)
−0.470249 + 0.882534i \(0.655836\pi\)
\(662\) 6.36373 0.247333
\(663\) 0 0
\(664\) 21.1397 0.820381
\(665\) 11.1698 0.433145
\(666\) 0 0
\(667\) 37.7726 1.46256
\(668\) −20.0451 −0.775569
\(669\) 0 0
\(670\) 37.6482 1.45448
\(671\) −22.2388 −0.858518
\(672\) 0 0
\(673\) 19.3215 0.744788 0.372394 0.928075i \(-0.378537\pi\)
0.372394 + 0.928075i \(0.378537\pi\)
\(674\) 53.6579 2.06683
\(675\) 0 0
\(676\) 4.68793 0.180305
\(677\) 38.2734 1.47097 0.735483 0.677543i \(-0.236955\pi\)
0.735483 + 0.677543i \(0.236955\pi\)
\(678\) 0 0
\(679\) 41.1875 1.58063
\(680\) −4.30389 −0.165047
\(681\) 0 0
\(682\) 78.0792 2.98981
\(683\) −0.692198 −0.0264862 −0.0132431 0.999912i \(-0.504216\pi\)
−0.0132431 + 0.999912i \(0.504216\pi\)
\(684\) 0 0
\(685\) 6.75088 0.257938
\(686\) −47.2583 −1.80433
\(687\) 0 0
\(688\) −86.3260 −3.29115
\(689\) −8.71205 −0.331903
\(690\) 0 0
\(691\) −32.9911 −1.25504 −0.627520 0.778600i \(-0.715930\pi\)
−0.627520 + 0.778600i \(0.715930\pi\)
\(692\) −60.7363 −2.30885
\(693\) 0 0
\(694\) 32.5530 1.23569
\(695\) 3.50577 0.132981
\(696\) 0 0
\(697\) −2.52259 −0.0955500
\(698\) −51.6518 −1.95505
\(699\) 0 0
\(700\) −20.0404 −0.757457
\(701\) 18.7776 0.709219 0.354610 0.935014i \(-0.384614\pi\)
0.354610 + 0.935014i \(0.384614\pi\)
\(702\) 0 0
\(703\) 10.5081 0.396319
\(704\) −19.1461 −0.721594
\(705\) 0 0
\(706\) −15.2304 −0.573205
\(707\) 33.3421 1.25396
\(708\) 0 0
\(709\) 8.09442 0.303992 0.151996 0.988381i \(-0.451430\pi\)
0.151996 + 0.988381i \(0.451430\pi\)
\(710\) −17.0042 −0.638157
\(711\) 0 0
\(712\) −50.5407 −1.89409
\(713\) 37.3837 1.40003
\(714\) 0 0
\(715\) 4.38446 0.163970
\(716\) −88.3818 −3.30298
\(717\) 0 0
\(718\) −46.1190 −1.72114
\(719\) −31.8467 −1.18768 −0.593840 0.804583i \(-0.702389\pi\)
−0.593840 + 0.804583i \(0.702389\pi\)
\(720\) 0 0
\(721\) −4.24600 −0.158129
\(722\) −31.4803 −1.17158
\(723\) 0 0
\(724\) −99.6623 −3.70392
\(725\) −6.95774 −0.258404
\(726\) 0 0
\(727\) −20.3092 −0.753227 −0.376613 0.926371i \(-0.622911\pi\)
−0.376613 + 0.926371i \(0.622911\pi\)
\(728\) 29.7160 1.10135
\(729\) 0 0
\(730\) 43.2689 1.60145
\(731\) 6.21436 0.229846
\(732\) 0 0
\(733\) −14.3193 −0.528896 −0.264448 0.964400i \(-0.585190\pi\)
−0.264448 + 0.964400i \(0.585190\pi\)
\(734\) −77.1510 −2.84770
\(735\) 0 0
\(736\) −45.2776 −1.66895
\(737\) −63.8285 −2.35115
\(738\) 0 0
\(739\) −32.7316 −1.20405 −0.602025 0.798477i \(-0.705639\pi\)
−0.602025 + 0.798477i \(0.705639\pi\)
\(740\) −18.8532 −0.693057
\(741\) 0 0
\(742\) −96.3145 −3.53582
\(743\) −38.9507 −1.42896 −0.714481 0.699655i \(-0.753337\pi\)
−0.714481 + 0.699655i \(0.753337\pi\)
\(744\) 0 0
\(745\) −12.2790 −0.449868
\(746\) −37.7038 −1.38044
\(747\) 0 0
\(748\) 12.7261 0.465312
\(749\) 18.1329 0.662561
\(750\) 0 0
\(751\) −23.0151 −0.839832 −0.419916 0.907563i \(-0.637940\pi\)
−0.419916 + 0.907563i \(0.637940\pi\)
\(752\) 3.49183 0.127334
\(753\) 0 0
\(754\) 17.9934 0.655282
\(755\) −16.6964 −0.607645
\(756\) 0 0
\(757\) 41.6474 1.51370 0.756850 0.653588i \(-0.226737\pi\)
0.756850 + 0.653588i \(0.226737\pi\)
\(758\) 53.5447 1.94483
\(759\) 0 0
\(760\) −18.1628 −0.658835
\(761\) −6.88861 −0.249712 −0.124856 0.992175i \(-0.539847\pi\)
−0.124856 + 0.992175i \(0.539847\pi\)
\(762\) 0 0
\(763\) −20.1880 −0.730856
\(764\) 72.2738 2.61477
\(765\) 0 0
\(766\) 66.1176 2.38893
\(767\) −10.7215 −0.387129
\(768\) 0 0
\(769\) −9.56774 −0.345021 −0.172511 0.985008i \(-0.555188\pi\)
−0.172511 + 0.985008i \(0.555188\pi\)
\(770\) 48.4717 1.74680
\(771\) 0 0
\(772\) 8.85089 0.318551
\(773\) 10.5131 0.378131 0.189066 0.981964i \(-0.439454\pi\)
0.189066 + 0.981964i \(0.439454\pi\)
\(774\) 0 0
\(775\) −6.88609 −0.247356
\(776\) −66.9738 −2.40422
\(777\) 0 0
\(778\) 44.3010 1.58827
\(779\) −10.6456 −0.381417
\(780\) 0 0
\(781\) 28.8289 1.03158
\(782\) 8.69264 0.310848
\(783\) 0 0
\(784\) 96.9722 3.46329
\(785\) 7.99688 0.285421
\(786\) 0 0
\(787\) −36.1200 −1.28754 −0.643769 0.765220i \(-0.722630\pi\)
−0.643769 + 0.765220i \(0.722630\pi\)
\(788\) 50.9097 1.81358
\(789\) 0 0
\(790\) 37.6168 1.33835
\(791\) −15.1933 −0.540211
\(792\) 0 0
\(793\) −5.07217 −0.180118
\(794\) −40.9475 −1.45317
\(795\) 0 0
\(796\) −5.63067 −0.199574
\(797\) 14.7492 0.522445 0.261223 0.965279i \(-0.415874\pi\)
0.261223 + 0.965279i \(0.415874\pi\)
\(798\) 0 0
\(799\) −0.251367 −0.00889273
\(800\) 8.34015 0.294869
\(801\) 0 0
\(802\) 88.2140 3.11495
\(803\) −73.3578 −2.58874
\(804\) 0 0
\(805\) 23.2078 0.817968
\(806\) 17.8081 0.627265
\(807\) 0 0
\(808\) −54.2166 −1.90733
\(809\) −1.81657 −0.0638672 −0.0319336 0.999490i \(-0.510167\pi\)
−0.0319336 + 0.999490i \(0.510167\pi\)
\(810\) 0 0
\(811\) −33.3279 −1.17030 −0.585151 0.810924i \(-0.698965\pi\)
−0.585151 + 0.810924i \(0.698965\pi\)
\(812\) 139.436 4.89324
\(813\) 0 0
\(814\) 45.6001 1.59828
\(815\) −17.3723 −0.608526
\(816\) 0 0
\(817\) 26.2252 0.917504
\(818\) −49.5117 −1.73113
\(819\) 0 0
\(820\) 19.0999 0.666998
\(821\) −35.4878 −1.23853 −0.619266 0.785181i \(-0.712570\pi\)
−0.619266 + 0.785181i \(0.712570\pi\)
\(822\) 0 0
\(823\) −16.5800 −0.577941 −0.288971 0.957338i \(-0.593313\pi\)
−0.288971 + 0.957338i \(0.593313\pi\)
\(824\) 6.90429 0.240523
\(825\) 0 0
\(826\) −118.529 −4.12415
\(827\) −8.93071 −0.310551 −0.155276 0.987871i \(-0.549627\pi\)
−0.155276 + 0.987871i \(0.549627\pi\)
\(828\) 0 0
\(829\) 12.9059 0.448240 0.224120 0.974562i \(-0.428049\pi\)
0.224120 + 0.974562i \(0.428049\pi\)
\(830\) 7.86468 0.272987
\(831\) 0 0
\(832\) −4.36679 −0.151391
\(833\) −6.98075 −0.241869
\(834\) 0 0
\(835\) −4.27589 −0.147973
\(836\) 53.7053 1.85744
\(837\) 0 0
\(838\) −18.4518 −0.637408
\(839\) −34.9919 −1.20805 −0.604027 0.796964i \(-0.706438\pi\)
−0.604027 + 0.796964i \(0.706438\pi\)
\(840\) 0 0
\(841\) 19.4101 0.669315
\(842\) −67.6571 −2.33162
\(843\) 0 0
\(844\) −1.10266 −0.0379550
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −35.1547 −1.20793
\(848\) 74.9311 2.57314
\(849\) 0 0
\(850\) −1.60119 −0.0549204
\(851\) 21.8330 0.748424
\(852\) 0 0
\(853\) −21.1568 −0.724395 −0.362198 0.932101i \(-0.617973\pi\)
−0.362198 + 0.932101i \(0.617973\pi\)
\(854\) −56.0745 −1.91883
\(855\) 0 0
\(856\) −29.4853 −1.00779
\(857\) 11.6305 0.397290 0.198645 0.980072i \(-0.436346\pi\)
0.198645 + 0.980072i \(0.436346\pi\)
\(858\) 0 0
\(859\) 1.78067 0.0607557 0.0303778 0.999538i \(-0.490329\pi\)
0.0303778 + 0.999538i \(0.490329\pi\)
\(860\) −47.0523 −1.60447
\(861\) 0 0
\(862\) 32.1222 1.09409
\(863\) 7.65256 0.260496 0.130248 0.991481i \(-0.458423\pi\)
0.130248 + 0.991481i \(0.458423\pi\)
\(864\) 0 0
\(865\) −12.9559 −0.440513
\(866\) −15.6341 −0.531267
\(867\) 0 0
\(868\) 138.000 4.68403
\(869\) −63.7754 −2.16343
\(870\) 0 0
\(871\) −14.5579 −0.493275
\(872\) 32.8272 1.11167
\(873\) 0 0
\(874\) 36.6838 1.24085
\(875\) −4.27489 −0.144518
\(876\) 0 0
\(877\) 6.79223 0.229357 0.114679 0.993403i \(-0.463416\pi\)
0.114679 + 0.993403i \(0.463416\pi\)
\(878\) −74.1602 −2.50279
\(879\) 0 0
\(880\) −37.7101 −1.27121
\(881\) −8.06104 −0.271583 −0.135792 0.990737i \(-0.543358\pi\)
−0.135792 + 0.990737i \(0.543358\pi\)
\(882\) 0 0
\(883\) 15.7753 0.530882 0.265441 0.964127i \(-0.414482\pi\)
0.265441 + 0.964127i \(0.414482\pi\)
\(884\) 2.90254 0.0976230
\(885\) 0 0
\(886\) 23.6627 0.794965
\(887\) 17.7631 0.596428 0.298214 0.954499i \(-0.403609\pi\)
0.298214 + 0.954499i \(0.403609\pi\)
\(888\) 0 0
\(889\) 58.3150 1.95582
\(890\) −18.8028 −0.630271
\(891\) 0 0
\(892\) −78.5461 −2.62992
\(893\) −1.06079 −0.0354981
\(894\) 0 0
\(895\) −18.8530 −0.630188
\(896\) 23.0302 0.769386
\(897\) 0 0
\(898\) −91.7149 −3.06057
\(899\) 47.9116 1.59794
\(900\) 0 0
\(901\) −5.39408 −0.179703
\(902\) −46.1969 −1.53819
\(903\) 0 0
\(904\) 24.7054 0.821688
\(905\) −21.2593 −0.706684
\(906\) 0 0
\(907\) 48.6359 1.61493 0.807464 0.589916i \(-0.200839\pi\)
0.807464 + 0.589916i \(0.200839\pi\)
\(908\) −106.887 −3.54715
\(909\) 0 0
\(910\) 11.0553 0.366480
\(911\) −18.6599 −0.618229 −0.309115 0.951025i \(-0.600033\pi\)
−0.309115 + 0.951025i \(0.600033\pi\)
\(912\) 0 0
\(913\) −13.3337 −0.441282
\(914\) 24.3420 0.805162
\(915\) 0 0
\(916\) −32.6973 −1.08035
\(917\) 35.7482 1.18051
\(918\) 0 0
\(919\) −13.8812 −0.457898 −0.228949 0.973438i \(-0.573529\pi\)
−0.228949 + 0.973438i \(0.573529\pi\)
\(920\) −37.7375 −1.24417
\(921\) 0 0
\(922\) 53.0217 1.74618
\(923\) 6.57523 0.216426
\(924\) 0 0
\(925\) −4.02164 −0.132231
\(926\) −97.7111 −3.21099
\(927\) 0 0
\(928\) −58.0286 −1.90488
\(929\) −17.6717 −0.579791 −0.289895 0.957058i \(-0.593621\pi\)
−0.289895 + 0.957058i \(0.593621\pi\)
\(930\) 0 0
\(931\) −29.4594 −0.965494
\(932\) 40.4663 1.32552
\(933\) 0 0
\(934\) 33.3302 1.09060
\(935\) 2.71465 0.0887784
\(936\) 0 0
\(937\) 33.4041 1.09126 0.545632 0.838025i \(-0.316290\pi\)
0.545632 + 0.838025i \(0.316290\pi\)
\(938\) −160.942 −5.25494
\(939\) 0 0
\(940\) 1.90324 0.0620768
\(941\) 57.8947 1.88731 0.943656 0.330928i \(-0.107362\pi\)
0.943656 + 0.330928i \(0.107362\pi\)
\(942\) 0 0
\(943\) −22.1187 −0.720283
\(944\) 92.2136 3.00130
\(945\) 0 0
\(946\) 113.805 3.70013
\(947\) 54.6285 1.77519 0.887593 0.460628i \(-0.152376\pi\)
0.887593 + 0.460628i \(0.152376\pi\)
\(948\) 0 0
\(949\) −16.7313 −0.543121
\(950\) −6.75717 −0.219232
\(951\) 0 0
\(952\) 18.3987 0.596305
\(953\) −19.7207 −0.638815 −0.319407 0.947618i \(-0.603484\pi\)
−0.319407 + 0.947618i \(0.603484\pi\)
\(954\) 0 0
\(955\) 15.4170 0.498882
\(956\) 14.3967 0.465622
\(957\) 0 0
\(958\) −52.2083 −1.68678
\(959\) −28.8593 −0.931915
\(960\) 0 0
\(961\) 16.4182 0.529620
\(962\) 10.4004 0.335322
\(963\) 0 0
\(964\) 27.3432 0.880665
\(965\) 1.88802 0.0607774
\(966\) 0 0
\(967\) −35.2175 −1.13252 −0.566259 0.824227i \(-0.691610\pi\)
−0.566259 + 0.824227i \(0.691610\pi\)
\(968\) 57.1640 1.83732
\(969\) 0 0
\(970\) −24.9165 −0.800020
\(971\) 13.9711 0.448354 0.224177 0.974548i \(-0.428031\pi\)
0.224177 + 0.974548i \(0.428031\pi\)
\(972\) 0 0
\(973\) −14.9868 −0.480454
\(974\) 39.1744 1.25523
\(975\) 0 0
\(976\) 43.6250 1.39640
\(977\) −36.4905 −1.16744 −0.583718 0.811957i \(-0.698403\pi\)
−0.583718 + 0.811957i \(0.698403\pi\)
\(978\) 0 0
\(979\) 31.8781 1.01883
\(980\) 52.8551 1.68839
\(981\) 0 0
\(982\) 29.7078 0.948015
\(983\) 17.5005 0.558180 0.279090 0.960265i \(-0.409967\pi\)
0.279090 + 0.960265i \(0.409967\pi\)
\(984\) 0 0
\(985\) 10.8597 0.346020
\(986\) 11.1407 0.354791
\(987\) 0 0
\(988\) 12.2490 0.389693
\(989\) 54.4890 1.73265
\(990\) 0 0
\(991\) 18.8114 0.597565 0.298783 0.954321i \(-0.403419\pi\)
0.298783 + 0.954321i \(0.403419\pi\)
\(992\) −57.4310 −1.82344
\(993\) 0 0
\(994\) 72.6912 2.30563
\(995\) −1.20110 −0.0380774
\(996\) 0 0
\(997\) 3.53423 0.111930 0.0559651 0.998433i \(-0.482176\pi\)
0.0559651 + 0.998433i \(0.482176\pi\)
\(998\) −33.9299 −1.07403
\(999\) 0 0
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 5265.2.a.ba.1.8 8
3.2 odd 2 5265.2.a.bf.1.1 8
9.2 odd 6 585.2.i.e.391.8 yes 16
9.4 even 3 1755.2.i.f.586.1 16
9.5 odd 6 585.2.i.e.196.8 16
9.7 even 3 1755.2.i.f.1171.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.e.196.8 16 9.5 odd 6
585.2.i.e.391.8 yes 16 9.2 odd 6
1755.2.i.f.586.1 16 9.4 even 3
1755.2.i.f.1171.1 16 9.7 even 3
5265.2.a.ba.1.8 8 1.1 even 1 trivial
5265.2.a.bf.1.1 8 3.2 odd 2