Properties

Label 7800.2.a.bi.1.2
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.940.1
Defining polynomial: \( x^{3} - 7x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.89511\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -2.40857 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -2.40857 q^{7} +1.00000 q^{9} +5.38164 q^{11} +1.00000 q^{13} +7.17185 q^{17} +7.79021 q^{19} +2.40857 q^{21} +2.40857 q^{23} -1.00000 q^{27} +4.97307 q^{29} -6.76328 q^{31} -5.38164 q^{33} -7.38164 q^{37} -1.00000 q^{39} +3.38164 q^{41} +11.5804 q^{43} +10.7633 q^{47} -1.19878 q^{49} -7.17185 q^{51} -1.43550 q^{53} -7.79021 q^{57} +5.94614 q^{59} -1.43550 q^{61} -2.40857 q^{63} -7.58043 q^{67} -2.40857 q^{69} -2.61836 q^{71} -7.02693 q^{73} -12.9621 q^{77} +2.61836 q^{79} +1.00000 q^{81} -1.94614 q^{83} -4.97307 q^{87} +0.618358 q^{89} -2.40857 q^{91} +6.76328 q^{93} -9.22571 q^{97} +5.38164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - q^{7} + 3 q^{9} + 5 q^{11} + 3 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} + q^{23} - 3 q^{27} + 10 q^{29} + 2 q^{31} - 5 q^{33} - 11 q^{37} - 3 q^{39} - q^{41} + 10 q^{47} + 20 q^{49} + 7 q^{51} - 3 q^{53} - 6 q^{57} + 8 q^{59} - 3 q^{61} - q^{63} + 12 q^{67} - q^{69} - 19 q^{71} - 26 q^{73} + 7 q^{77} + 19 q^{79} + 3 q^{81} + 4 q^{83} - 10 q^{87} + 13 q^{89} - q^{91} - 2 q^{93} - 9 q^{97} + 5 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.40857 −0.910354 −0.455177 0.890401i \(-0.650424\pi\)
−0.455177 + 0.890401i \(0.650424\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.38164 1.62263 0.811313 0.584612i \(-0.198753\pi\)
0.811313 + 0.584612i \(0.198753\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.17185 1.73943 0.869715 0.493554i \(-0.164302\pi\)
0.869715 + 0.493554i \(0.164302\pi\)
\(18\) 0 0
\(19\) 7.79021 1.78720 0.893599 0.448867i \(-0.148172\pi\)
0.893599 + 0.448867i \(0.148172\pi\)
\(20\) 0 0
\(21\) 2.40857 0.525593
\(22\) 0 0
\(23\) 2.40857 0.502222 0.251111 0.967958i \(-0.419204\pi\)
0.251111 + 0.967958i \(0.419204\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.97307 0.923476 0.461738 0.887016i \(-0.347226\pi\)
0.461738 + 0.887016i \(0.347226\pi\)
\(30\) 0 0
\(31\) −6.76328 −1.21472 −0.607361 0.794426i \(-0.707772\pi\)
−0.607361 + 0.794426i \(0.707772\pi\)
\(32\) 0 0
\(33\) −5.38164 −0.936824
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.38164 −1.21353 −0.606767 0.794880i \(-0.707534\pi\)
−0.606767 + 0.794880i \(0.707534\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 3.38164 0.528124 0.264062 0.964506i \(-0.414938\pi\)
0.264062 + 0.964506i \(0.414938\pi\)
\(42\) 0 0
\(43\) 11.5804 1.76600 0.882999 0.469374i \(-0.155521\pi\)
0.882999 + 0.469374i \(0.155521\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.7633 1.56999 0.784993 0.619504i \(-0.212666\pi\)
0.784993 + 0.619504i \(0.212666\pi\)
\(48\) 0 0
\(49\) −1.19878 −0.171255
\(50\) 0 0
\(51\) −7.17185 −1.00426
\(52\) 0 0
\(53\) −1.43550 −0.197181 −0.0985906 0.995128i \(-0.531433\pi\)
−0.0985906 + 0.995128i \(0.531433\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −7.79021 −1.03184
\(58\) 0 0
\(59\) 5.94614 0.774122 0.387061 0.922054i \(-0.373490\pi\)
0.387061 + 0.922054i \(0.373490\pi\)
\(60\) 0 0
\(61\) −1.43550 −0.183797 −0.0918985 0.995768i \(-0.529294\pi\)
−0.0918985 + 0.995768i \(0.529294\pi\)
\(62\) 0 0
\(63\) −2.40857 −0.303451
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.58043 −0.926096 −0.463048 0.886333i \(-0.653244\pi\)
−0.463048 + 0.886333i \(0.653244\pi\)
\(68\) 0 0
\(69\) −2.40857 −0.289958
\(70\) 0 0
\(71\) −2.61836 −0.310742 −0.155371 0.987856i \(-0.549657\pi\)
−0.155371 + 0.987856i \(0.549657\pi\)
\(72\) 0 0
\(73\) −7.02693 −0.822440 −0.411220 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −12.9621 −1.47716
\(78\) 0 0
\(79\) 2.61836 0.294588 0.147294 0.989093i \(-0.452944\pi\)
0.147294 + 0.989093i \(0.452944\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.94614 −0.213617 −0.106808 0.994280i \(-0.534063\pi\)
−0.106808 + 0.994280i \(0.534063\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.97307 −0.533169
\(88\) 0 0
\(89\) 0.618358 0.0655458 0.0327729 0.999463i \(-0.489566\pi\)
0.0327729 + 0.999463i \(0.489566\pi\)
\(90\) 0 0
\(91\) −2.40857 −0.252487
\(92\) 0 0
\(93\) 6.76328 0.701320
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.22571 −0.936729 −0.468365 0.883535i \(-0.655157\pi\)
−0.468365 + 0.883535i \(0.655157\pi\)
\(98\) 0 0
\(99\) 5.38164 0.540875
\(100\) 0 0
\(101\) −19.7364 −1.96384 −0.981920 0.189295i \(-0.939380\pi\)
−0.981920 + 0.189295i \(0.939380\pi\)
\(102\) 0 0
\(103\) −3.58043 −0.352790 −0.176395 0.984319i \(-0.556444\pi\)
−0.176395 + 0.984319i \(0.556444\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.9621 1.63978 0.819892 0.572518i \(-0.194033\pi\)
0.819892 + 0.572518i \(0.194033\pi\)
\(108\) 0 0
\(109\) 13.7902 1.32086 0.660431 0.750886i \(-0.270373\pi\)
0.660431 + 0.750886i \(0.270373\pi\)
\(110\) 0 0
\(111\) 7.38164 0.700634
\(112\) 0 0
\(113\) −0.973070 −0.0915388 −0.0457694 0.998952i \(-0.514574\pi\)
−0.0457694 + 0.998952i \(0.514574\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −17.2739 −1.58350
\(120\) 0 0
\(121\) 17.9621 1.63292
\(122\) 0 0
\(123\) −3.38164 −0.304912
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −14.3437 −1.27280 −0.636399 0.771360i \(-0.719577\pi\)
−0.636399 + 0.771360i \(0.719577\pi\)
\(128\) 0 0
\(129\) −11.5804 −1.01960
\(130\) 0 0
\(131\) 1.84407 0.161117 0.0805587 0.996750i \(-0.474330\pi\)
0.0805587 + 0.996750i \(0.474330\pi\)
\(132\) 0 0
\(133\) −18.7633 −1.62698
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) −4.14493 −0.351568 −0.175784 0.984429i \(-0.556246\pi\)
−0.175784 + 0.984429i \(0.556246\pi\)
\(140\) 0 0
\(141\) −10.7633 −0.906432
\(142\) 0 0
\(143\) 5.38164 0.450035
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 1.19878 0.0988741
\(148\) 0 0
\(149\) 0.618358 0.0506579 0.0253289 0.999679i \(-0.491937\pi\)
0.0253289 + 0.999679i \(0.491937\pi\)
\(150\) 0 0
\(151\) −13.6343 −1.10954 −0.554771 0.832003i \(-0.687194\pi\)
−0.554771 + 0.832003i \(0.687194\pi\)
\(152\) 0 0
\(153\) 7.17185 0.579810
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.5266 0.919920 0.459960 0.887940i \(-0.347864\pi\)
0.459960 + 0.887940i \(0.347864\pi\)
\(158\) 0 0
\(159\) 1.43550 0.113843
\(160\) 0 0
\(161\) −5.80122 −0.457200
\(162\) 0 0
\(163\) 10.1988 0.798830 0.399415 0.916770i \(-0.369213\pi\)
0.399415 + 0.916770i \(0.369213\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.419574 0.0324676 0.0162338 0.999868i \(-0.494832\pi\)
0.0162338 + 0.999868i \(0.494832\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 7.79021 0.595732
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.94614 −0.446939
\(178\) 0 0
\(179\) −9.84407 −0.735780 −0.367890 0.929869i \(-0.619920\pi\)
−0.367890 + 0.929869i \(0.619920\pi\)
\(180\) 0 0
\(181\) −9.01593 −0.670149 −0.335074 0.942192i \(-0.608761\pi\)
−0.335074 + 0.942192i \(0.608761\pi\)
\(182\) 0 0
\(183\) 1.43550 0.106115
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 38.5964 2.82244
\(188\) 0 0
\(189\) 2.40857 0.175198
\(190\) 0 0
\(191\) −9.63429 −0.697112 −0.348556 0.937288i \(-0.613328\pi\)
−0.348556 + 0.937288i \(0.613328\pi\)
\(192\) 0 0
\(193\) −25.9351 −1.86685 −0.933426 0.358770i \(-0.883196\pi\)
−0.933426 + 0.358770i \(0.883196\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.871002 0.0620563 0.0310282 0.999519i \(-0.490122\pi\)
0.0310282 + 0.999519i \(0.490122\pi\)
\(198\) 0 0
\(199\) 23.5804 1.67157 0.835786 0.549055i \(-0.185012\pi\)
0.835786 + 0.549055i \(0.185012\pi\)
\(200\) 0 0
\(201\) 7.58043 0.534682
\(202\) 0 0
\(203\) −11.9780 −0.840690
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.40857 0.167407
\(208\) 0 0
\(209\) 41.9241 2.89995
\(210\) 0 0
\(211\) 19.1609 1.31909 0.659544 0.751666i \(-0.270750\pi\)
0.659544 + 0.751666i \(0.270750\pi\)
\(212\) 0 0
\(213\) 2.61836 0.179407
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.2899 1.10583
\(218\) 0 0
\(219\) 7.02693 0.474836
\(220\) 0 0
\(221\) 7.17185 0.482431
\(222\) 0 0
\(223\) 18.9731 1.27053 0.635265 0.772294i \(-0.280891\pi\)
0.635265 + 0.772294i \(0.280891\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.76328 0.448895 0.224447 0.974486i \(-0.427942\pi\)
0.224447 + 0.974486i \(0.427942\pi\)
\(228\) 0 0
\(229\) 3.02693 0.200025 0.100013 0.994986i \(-0.468112\pi\)
0.100013 + 0.994986i \(0.468112\pi\)
\(230\) 0 0
\(231\) 12.9621 0.852841
\(232\) 0 0
\(233\) 17.9351 1.17497 0.587485 0.809235i \(-0.300118\pi\)
0.587485 + 0.809235i \(0.300118\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.61836 −0.170081
\(238\) 0 0
\(239\) 3.32778 0.215256 0.107628 0.994191i \(-0.465674\pi\)
0.107628 + 0.994191i \(0.465674\pi\)
\(240\) 0 0
\(241\) −21.1609 −1.36309 −0.681545 0.731776i \(-0.738692\pi\)
−0.681545 + 0.731776i \(0.738692\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 7.79021 0.495679
\(248\) 0 0
\(249\) 1.94614 0.123332
\(250\) 0 0
\(251\) 28.1878 1.77920 0.889599 0.456743i \(-0.150984\pi\)
0.889599 + 0.456743i \(0.150984\pi\)
\(252\) 0 0
\(253\) 12.9621 0.814918
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.1878 1.88306 0.941531 0.336926i \(-0.109387\pi\)
0.941531 + 0.336926i \(0.109387\pi\)
\(258\) 0 0
\(259\) 17.7792 1.10475
\(260\) 0 0
\(261\) 4.97307 0.307825
\(262\) 0 0
\(263\) 13.0269 0.803275 0.401637 0.915799i \(-0.368441\pi\)
0.401637 + 0.915799i \(0.368441\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.618358 −0.0378429
\(268\) 0 0
\(269\) −6.20979 −0.378617 −0.189309 0.981918i \(-0.560625\pi\)
−0.189309 + 0.981918i \(0.560625\pi\)
\(270\) 0 0
\(271\) −29.9241 −1.81776 −0.908881 0.417056i \(-0.863062\pi\)
−0.908881 + 0.417056i \(0.863062\pi\)
\(272\) 0 0
\(273\) 2.40857 0.145773
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −5.89228 −0.354033 −0.177016 0.984208i \(-0.556645\pi\)
−0.177016 + 0.984208i \(0.556645\pi\)
\(278\) 0 0
\(279\) −6.76328 −0.404907
\(280\) 0 0
\(281\) −15.9461 −0.951267 −0.475634 0.879644i \(-0.657781\pi\)
−0.475634 + 0.879644i \(0.657781\pi\)
\(282\) 0 0
\(283\) 17.9461 1.06679 0.533394 0.845867i \(-0.320916\pi\)
0.533394 + 0.845867i \(0.320916\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.14493 −0.480780
\(288\) 0 0
\(289\) 34.4355 2.02562
\(290\) 0 0
\(291\) 9.22571 0.540821
\(292\) 0 0
\(293\) −0.763283 −0.0445915 −0.0222957 0.999751i \(-0.507098\pi\)
−0.0222957 + 0.999751i \(0.507098\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.38164 −0.312275
\(298\) 0 0
\(299\) 2.40857 0.139291
\(300\) 0 0
\(301\) −27.8923 −1.60768
\(302\) 0 0
\(303\) 19.7364 1.13382
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.1449 0.921440 0.460720 0.887546i \(-0.347591\pi\)
0.460720 + 0.887546i \(0.347591\pi\)
\(308\) 0 0
\(309\) 3.58043 0.203683
\(310\) 0 0
\(311\) −29.5266 −1.67430 −0.837149 0.546975i \(-0.815779\pi\)
−0.837149 + 0.546975i \(0.815779\pi\)
\(312\) 0 0
\(313\) −33.5804 −1.89808 −0.949039 0.315159i \(-0.897942\pi\)
−0.949039 + 0.315159i \(0.897942\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.23672 0.406454 0.203227 0.979132i \(-0.434857\pi\)
0.203227 + 0.979132i \(0.434857\pi\)
\(318\) 0 0
\(319\) 26.7633 1.49846
\(320\) 0 0
\(321\) −16.9621 −0.946730
\(322\) 0 0
\(323\) 55.8703 3.10871
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.7902 −0.762601
\(328\) 0 0
\(329\) −25.9241 −1.42924
\(330\) 0 0
\(331\) 2.55350 0.140353 0.0701764 0.997535i \(-0.477644\pi\)
0.0701764 + 0.997535i \(0.477644\pi\)
\(332\) 0 0
\(333\) −7.38164 −0.404511
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4.34371 −0.236617 −0.118308 0.992977i \(-0.537747\pi\)
−0.118308 + 0.992977i \(0.537747\pi\)
\(338\) 0 0
\(339\) 0.973070 0.0528499
\(340\) 0 0
\(341\) −36.3976 −1.97104
\(342\) 0 0
\(343\) 19.7474 1.06626
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −29.7792 −1.59863 −0.799316 0.600911i \(-0.794805\pi\)
−0.799316 + 0.600911i \(0.794805\pi\)
\(348\) 0 0
\(349\) 15.4245 0.825654 0.412827 0.910809i \(-0.364541\pi\)
0.412827 + 0.910809i \(0.364541\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 17.2739 0.914233
\(358\) 0 0
\(359\) −10.0539 −0.530622 −0.265311 0.964163i \(-0.585475\pi\)
−0.265311 + 0.964163i \(0.585475\pi\)
\(360\) 0 0
\(361\) 41.6874 2.19407
\(362\) 0 0
\(363\) −17.9621 −0.942764
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 11.5804 0.604493 0.302247 0.953230i \(-0.402263\pi\)
0.302247 + 0.953230i \(0.402263\pi\)
\(368\) 0 0
\(369\) 3.38164 0.176041
\(370\) 0 0
\(371\) 3.45751 0.179505
\(372\) 0 0
\(373\) −6.39757 −0.331254 −0.165627 0.986189i \(-0.552965\pi\)
−0.165627 + 0.986189i \(0.552965\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.97307 0.256126
\(378\) 0 0
\(379\) −17.4245 −0.895036 −0.447518 0.894275i \(-0.647692\pi\)
−0.447518 + 0.894275i \(0.647692\pi\)
\(380\) 0 0
\(381\) 14.3437 0.734851
\(382\) 0 0
\(383\) 20.8171 1.06371 0.531853 0.846837i \(-0.321496\pi\)
0.531853 + 0.846837i \(0.321496\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11.5804 0.588666
\(388\) 0 0
\(389\) −19.7364 −1.00067 −0.500336 0.865831i \(-0.666790\pi\)
−0.500336 + 0.865831i \(0.666790\pi\)
\(390\) 0 0
\(391\) 17.2739 0.873580
\(392\) 0 0
\(393\) −1.84407 −0.0930211
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −14.5425 −0.729867 −0.364933 0.931034i \(-0.618908\pi\)
−0.364933 + 0.931034i \(0.618908\pi\)
\(398\) 0 0
\(399\) 18.7633 0.939339
\(400\) 0 0
\(401\) −27.2147 −1.35904 −0.679519 0.733658i \(-0.737811\pi\)
−0.679519 + 0.733658i \(0.737811\pi\)
\(402\) 0 0
\(403\) −6.76328 −0.336903
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −39.7254 −1.96911
\(408\) 0 0
\(409\) 2.41957 0.119640 0.0598201 0.998209i \(-0.480947\pi\)
0.0598201 + 0.998209i \(0.480947\pi\)
\(410\) 0 0
\(411\) 2.00000 0.0986527
\(412\) 0 0
\(413\) −14.3217 −0.704725
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.14493 0.202978
\(418\) 0 0
\(419\) −13.3168 −0.650567 −0.325284 0.945616i \(-0.605460\pi\)
−0.325284 + 0.945616i \(0.605460\pi\)
\(420\) 0 0
\(421\) −29.6825 −1.44664 −0.723318 0.690515i \(-0.757384\pi\)
−0.723318 + 0.690515i \(0.757384\pi\)
\(422\) 0 0
\(423\) 10.7633 0.523329
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.45751 0.167320
\(428\) 0 0
\(429\) −5.38164 −0.259828
\(430\) 0 0
\(431\) 11.8923 0.572831 0.286416 0.958105i \(-0.407536\pi\)
0.286416 + 0.958105i \(0.407536\pi\)
\(432\) 0 0
\(433\) −5.18286 −0.249072 −0.124536 0.992215i \(-0.539744\pi\)
−0.124536 + 0.992215i \(0.539744\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.7633 0.897570
\(438\) 0 0
\(439\) −25.3596 −1.21035 −0.605175 0.796093i \(-0.706897\pi\)
−0.605175 + 0.796093i \(0.706897\pi\)
\(440\) 0 0
\(441\) −1.19878 −0.0570850
\(442\) 0 0
\(443\) 3.01593 0.143291 0.0716455 0.997430i \(-0.477175\pi\)
0.0716455 + 0.997430i \(0.477175\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.618358 −0.0292473
\(448\) 0 0
\(449\) 38.6502 1.82402 0.912008 0.410172i \(-0.134531\pi\)
0.912008 + 0.410172i \(0.134531\pi\)
\(450\) 0 0
\(451\) 18.1988 0.856947
\(452\) 0 0
\(453\) 13.6343 0.640595
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −22.7523 −1.06431 −0.532153 0.846648i \(-0.678617\pi\)
−0.532153 + 0.846648i \(0.678617\pi\)
\(458\) 0 0
\(459\) −7.17185 −0.334754
\(460\) 0 0
\(461\) −29.8331 −1.38946 −0.694732 0.719268i \(-0.744477\pi\)
−0.694732 + 0.719268i \(0.744477\pi\)
\(462\) 0 0
\(463\) 22.8061 1.05989 0.529946 0.848032i \(-0.322212\pi\)
0.529946 + 0.848032i \(0.322212\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −41.2519 −1.90891 −0.954456 0.298353i \(-0.903563\pi\)
−0.954456 + 0.298353i \(0.903563\pi\)
\(468\) 0 0
\(469\) 18.2580 0.843076
\(470\) 0 0
\(471\) −11.5266 −0.531116
\(472\) 0 0
\(473\) 62.3217 2.86556
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.43550 −0.0657271
\(478\) 0 0
\(479\) 30.0911 1.37490 0.687448 0.726234i \(-0.258731\pi\)
0.687448 + 0.726234i \(0.258731\pi\)
\(480\) 0 0
\(481\) −7.38164 −0.336574
\(482\) 0 0
\(483\) 5.80122 0.263964
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 37.8813 1.71656 0.858282 0.513178i \(-0.171532\pi\)
0.858282 + 0.513178i \(0.171532\pi\)
\(488\) 0 0
\(489\) −10.1988 −0.461205
\(490\) 0 0
\(491\) −24.0801 −1.08672 −0.543359 0.839500i \(-0.682848\pi\)
−0.543359 + 0.839500i \(0.682848\pi\)
\(492\) 0 0
\(493\) 35.6661 1.60632
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.30650 0.282885
\(498\) 0 0
\(499\) 15.3706 0.688084 0.344042 0.938954i \(-0.388204\pi\)
0.344042 + 0.938954i \(0.388204\pi\)
\(500\) 0 0
\(501\) −0.419574 −0.0187452
\(502\) 0 0
\(503\) 26.5535 1.18396 0.591981 0.805952i \(-0.298346\pi\)
0.591981 + 0.805952i \(0.298346\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −7.80122 −0.345783 −0.172891 0.984941i \(-0.555311\pi\)
−0.172891 + 0.984941i \(0.555311\pi\)
\(510\) 0 0
\(511\) 16.9249 0.748712
\(512\) 0 0
\(513\) −7.79021 −0.343946
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 57.9241 2.54750
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 35.2147 1.54278 0.771392 0.636360i \(-0.219561\pi\)
0.771392 + 0.636360i \(0.219561\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −48.5053 −2.11292
\(528\) 0 0
\(529\) −17.1988 −0.747773
\(530\) 0 0
\(531\) 5.94614 0.258041
\(532\) 0 0
\(533\) 3.38164 0.146475
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.84407 0.424803
\(538\) 0 0
\(539\) −6.45143 −0.277883
\(540\) 0 0
\(541\) 14.4996 0.623388 0.311694 0.950183i \(-0.399104\pi\)
0.311694 + 0.950183i \(0.399104\pi\)
\(542\) 0 0
\(543\) 9.01593 0.386910
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 13.6343 0.582960 0.291480 0.956577i \(-0.405852\pi\)
0.291480 + 0.956577i \(0.405852\pi\)
\(548\) 0 0
\(549\) −1.43550 −0.0612657
\(550\) 0 0
\(551\) 38.7413 1.65043
\(552\) 0 0
\(553\) −6.30650 −0.268180
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.89228 0.249664 0.124832 0.992178i \(-0.460161\pi\)
0.124832 + 0.992178i \(0.460161\pi\)
\(558\) 0 0
\(559\) 11.5804 0.489800
\(560\) 0 0
\(561\) −38.5964 −1.62954
\(562\) 0 0
\(563\) −14.6184 −0.616090 −0.308045 0.951372i \(-0.599675\pi\)
−0.308045 + 0.951372i \(0.599675\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.40857 −0.101150
\(568\) 0 0
\(569\) 45.9780 1.92750 0.963749 0.266811i \(-0.0859699\pi\)
0.963749 + 0.266811i \(0.0859699\pi\)
\(570\) 0 0
\(571\) 8.25264 0.345362 0.172681 0.984978i \(-0.444757\pi\)
0.172681 + 0.984978i \(0.444757\pi\)
\(572\) 0 0
\(573\) 9.63429 0.402478
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 14.3547 0.597594 0.298797 0.954317i \(-0.403415\pi\)
0.298797 + 0.954317i \(0.403415\pi\)
\(578\) 0 0
\(579\) 25.9351 1.07783
\(580\) 0 0
\(581\) 4.68742 0.194467
\(582\) 0 0
\(583\) −7.72535 −0.319951
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.2367 −0.711435 −0.355718 0.934593i \(-0.615764\pi\)
−0.355718 + 0.934593i \(0.615764\pi\)
\(588\) 0 0
\(589\) −52.6874 −2.17095
\(590\) 0 0
\(591\) −0.871002 −0.0358282
\(592\) 0 0
\(593\) −33.8703 −1.39089 −0.695443 0.718581i \(-0.744792\pi\)
−0.695443 + 0.718581i \(0.744792\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −23.5804 −0.965083
\(598\) 0 0
\(599\) −35.0531 −1.43223 −0.716116 0.697981i \(-0.754082\pi\)
−0.716116 + 0.697981i \(0.754082\pi\)
\(600\) 0 0
\(601\) 3.90893 0.159449 0.0797244 0.996817i \(-0.474596\pi\)
0.0797244 + 0.996817i \(0.474596\pi\)
\(602\) 0 0
\(603\) −7.58043 −0.308699
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.05386 −0.245719 −0.122859 0.992424i \(-0.539206\pi\)
−0.122859 + 0.992424i \(0.539206\pi\)
\(608\) 0 0
\(609\) 11.9780 0.485373
\(610\) 0 0
\(611\) 10.7633 0.435436
\(612\) 0 0
\(613\) 28.1768 1.13805 0.569025 0.822320i \(-0.307321\pi\)
0.569025 + 0.822320i \(0.307321\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −46.6874 −1.87956 −0.939782 0.341773i \(-0.888972\pi\)
−0.939782 + 0.341773i \(0.888972\pi\)
\(618\) 0 0
\(619\) 35.2629 1.41734 0.708668 0.705542i \(-0.249296\pi\)
0.708668 + 0.705542i \(0.249296\pi\)
\(620\) 0 0
\(621\) −2.40857 −0.0966526
\(622\) 0 0
\(623\) −1.48936 −0.0596699
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −41.9241 −1.67429
\(628\) 0 0
\(629\) −52.9401 −2.11086
\(630\) 0 0
\(631\) 35.5804 1.41643 0.708217 0.705995i \(-0.249500\pi\)
0.708217 + 0.705995i \(0.249500\pi\)
\(632\) 0 0
\(633\) −19.1609 −0.761575
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.19878 −0.0474976
\(638\) 0 0
\(639\) −2.61836 −0.103581
\(640\) 0 0
\(641\) 6.39757 0.252689 0.126344 0.991986i \(-0.459676\pi\)
0.126344 + 0.991986i \(0.459676\pi\)
\(642\) 0 0
\(643\) 26.6184 1.04973 0.524863 0.851187i \(-0.324117\pi\)
0.524863 + 0.851187i \(0.324117\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.11800 0.122581 0.0612905 0.998120i \(-0.480478\pi\)
0.0612905 + 0.998120i \(0.480478\pi\)
\(648\) 0 0
\(649\) 32.0000 1.25611
\(650\) 0 0
\(651\) −16.2899 −0.638450
\(652\) 0 0
\(653\) 17.4727 0.683760 0.341880 0.939744i \(-0.388936\pi\)
0.341880 + 0.939744i \(0.388936\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −7.02693 −0.274147
\(658\) 0 0
\(659\) −7.28493 −0.283780 −0.141890 0.989882i \(-0.545318\pi\)
−0.141890 + 0.989882i \(0.545318\pi\)
\(660\) 0 0
\(661\) 18.8972 0.735016 0.367508 0.930020i \(-0.380211\pi\)
0.367508 + 0.930020i \(0.380211\pi\)
\(662\) 0 0
\(663\) −7.17185 −0.278532
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 11.9780 0.463790
\(668\) 0 0
\(669\) −18.9731 −0.733541
\(670\) 0 0
\(671\) −7.72535 −0.298234
\(672\) 0 0
\(673\) 30.7951 1.18707 0.593533 0.804810i \(-0.297733\pi\)
0.593533 + 0.804810i \(0.297733\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.8323 1.33872 0.669358 0.742940i \(-0.266569\pi\)
0.669358 + 0.742940i \(0.266569\pi\)
\(678\) 0 0
\(679\) 22.2208 0.852756
\(680\) 0 0
\(681\) −6.76328 −0.259170
\(682\) 0 0
\(683\) −49.1070 −1.87903 −0.939513 0.342512i \(-0.888722\pi\)
−0.939513 + 0.342512i \(0.888722\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −3.02693 −0.115485
\(688\) 0 0
\(689\) −1.43550 −0.0546882
\(690\) 0 0
\(691\) −43.2629 −1.64580 −0.822900 0.568187i \(-0.807645\pi\)
−0.822900 + 0.568187i \(0.807645\pi\)
\(692\) 0 0
\(693\) −12.9621 −0.492388
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 24.2526 0.918634
\(698\) 0 0
\(699\) −17.9351 −0.678369
\(700\) 0 0
\(701\) 1.79021 0.0676154 0.0338077 0.999428i \(-0.489237\pi\)
0.0338077 + 0.999428i \(0.489237\pi\)
\(702\) 0 0
\(703\) −57.5046 −2.16883
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 47.5364 1.78779
\(708\) 0 0
\(709\) 19.3168 0.725457 0.362728 0.931895i \(-0.381845\pi\)
0.362728 + 0.931895i \(0.381845\pi\)
\(710\) 0 0
\(711\) 2.61836 0.0981961
\(712\) 0 0
\(713\) −16.2899 −0.610060
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.32778 −0.124278
\(718\) 0 0
\(719\) 13.9461 0.520103 0.260052 0.965595i \(-0.416260\pi\)
0.260052 + 0.965595i \(0.416260\pi\)
\(720\) 0 0
\(721\) 8.62371 0.321164
\(722\) 0 0
\(723\) 21.1609 0.786981
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 37.9241 1.40653 0.703264 0.710929i \(-0.251725\pi\)
0.703264 + 0.710929i \(0.251725\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 83.0531 3.07183
\(732\) 0 0
\(733\) −28.0691 −1.03675 −0.518377 0.855152i \(-0.673464\pi\)
−0.518377 + 0.855152i \(0.673464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −40.7951 −1.50271
\(738\) 0 0
\(739\) −22.9511 −0.844269 −0.422134 0.906533i \(-0.638719\pi\)
−0.422134 + 0.906533i \(0.638719\pi\)
\(740\) 0 0
\(741\) −7.79021 −0.286181
\(742\) 0 0
\(743\) −35.9780 −1.31990 −0.659952 0.751307i \(-0.729424\pi\)
−0.659952 + 0.751307i \(0.729424\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.94614 −0.0712056
\(748\) 0 0
\(749\) −40.8543 −1.49279
\(750\) 0 0
\(751\) 30.5964 1.11648 0.558238 0.829681i \(-0.311477\pi\)
0.558238 + 0.829681i \(0.311477\pi\)
\(752\) 0 0
\(753\) −28.1878 −1.02722
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −53.5584 −1.94661 −0.973307 0.229507i \(-0.926289\pi\)
−0.973307 + 0.229507i \(0.926289\pi\)
\(758\) 0 0
\(759\) −12.9621 −0.470493
\(760\) 0 0
\(761\) 10.3119 0.373804 0.186902 0.982379i \(-0.440155\pi\)
0.186902 + 0.982379i \(0.440155\pi\)
\(762\) 0 0
\(763\) −33.2147 −1.20245
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.94614 0.214703
\(768\) 0 0
\(769\) 0.871002 0.0314091 0.0157046 0.999877i \(-0.495001\pi\)
0.0157046 + 0.999877i \(0.495001\pi\)
\(770\) 0 0
\(771\) −30.1878 −1.08719
\(772\) 0 0
\(773\) −26.3976 −0.949455 −0.474727 0.880133i \(-0.657453\pi\)
−0.474727 + 0.880133i \(0.657453\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −17.7792 −0.637826
\(778\) 0 0
\(779\) 26.3437 0.943861
\(780\) 0 0
\(781\) −14.0911 −0.504218
\(782\) 0 0
\(783\) −4.97307 −0.177723
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −21.5266 −0.767339 −0.383670 0.923470i \(-0.625340\pi\)
−0.383670 + 0.923470i \(0.625340\pi\)
\(788\) 0 0
\(789\) −13.0269 −0.463771
\(790\) 0 0
\(791\) 2.34371 0.0833327
\(792\) 0 0
\(793\) −1.43550 −0.0509761
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.6722 −0.519717 −0.259858 0.965647i \(-0.583676\pi\)
−0.259858 + 0.965647i \(0.583676\pi\)
\(798\) 0 0
\(799\) 77.1927 2.73088
\(800\) 0 0
\(801\) 0.618358 0.0218486
\(802\) 0 0
\(803\) −37.8164 −1.33451
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 6.20979 0.218595
\(808\) 0 0
\(809\) 24.3657 0.856653 0.428326 0.903624i \(-0.359103\pi\)
0.428326 + 0.903624i \(0.359103\pi\)
\(810\) 0 0
\(811\) 40.0801 1.40740 0.703701 0.710497i \(-0.251530\pi\)
0.703701 + 0.710497i \(0.251530\pi\)
\(812\) 0 0
\(813\) 29.9241 1.04949
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 90.2140 3.15619
\(818\) 0 0
\(819\) −2.40857 −0.0841623
\(820\) 0 0
\(821\) 9.74736 0.340185 0.170093 0.985428i \(-0.445593\pi\)
0.170093 + 0.985428i \(0.445593\pi\)
\(822\) 0 0
\(823\) −1.94614 −0.0678382 −0.0339191 0.999425i \(-0.510799\pi\)
−0.0339191 + 0.999425i \(0.510799\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −18.4514 −0.641619 −0.320810 0.947144i \(-0.603955\pi\)
−0.320810 + 0.947144i \(0.603955\pi\)
\(828\) 0 0
\(829\) 5.16085 0.179244 0.0896219 0.995976i \(-0.471434\pi\)
0.0896219 + 0.995976i \(0.471434\pi\)
\(830\) 0 0
\(831\) 5.89228 0.204401
\(832\) 0 0
\(833\) −8.59751 −0.297886
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 6.76328 0.233773
\(838\) 0 0
\(839\) 8.27465 0.285673 0.142836 0.989746i \(-0.454378\pi\)
0.142836 + 0.989746i \(0.454378\pi\)
\(840\) 0 0
\(841\) −4.26857 −0.147192
\(842\) 0 0
\(843\) 15.9461 0.549214
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −43.2629 −1.48653
\(848\) 0 0
\(849\) −17.9461 −0.615910
\(850\) 0 0
\(851\) −17.7792 −0.609463
\(852\) 0 0
\(853\) −7.09179 −0.242818 −0.121409 0.992603i \(-0.538741\pi\)
−0.121409 + 0.992603i \(0.538741\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.17185 −0.108348 −0.0541742 0.998531i \(-0.517253\pi\)
−0.0541742 + 0.998531i \(0.517253\pi\)
\(858\) 0 0
\(859\) −27.7254 −0.945977 −0.472988 0.881069i \(-0.656825\pi\)
−0.472988 + 0.881069i \(0.656825\pi\)
\(860\) 0 0
\(861\) 8.14493 0.277578
\(862\) 0 0
\(863\) −3.18286 −0.108346 −0.0541729 0.998532i \(-0.517252\pi\)
−0.0541729 + 0.998532i \(0.517252\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −34.4355 −1.16949
\(868\) 0 0
\(869\) 14.0911 0.478007
\(870\) 0 0
\(871\) −7.58043 −0.256853
\(872\) 0 0
\(873\) −9.22571 −0.312243
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −17.7846 −0.600542 −0.300271 0.953854i \(-0.597077\pi\)
−0.300271 + 0.953854i \(0.597077\pi\)
\(878\) 0 0
\(879\) 0.763283 0.0257449
\(880\) 0 0
\(881\) −37.3650 −1.25886 −0.629429 0.777058i \(-0.716711\pi\)
−0.629429 + 0.777058i \(0.716711\pi\)
\(882\) 0 0
\(883\) 32.6874 1.10002 0.550010 0.835158i \(-0.314624\pi\)
0.550010 + 0.835158i \(0.314624\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.5156 −0.789575 −0.394788 0.918772i \(-0.629182\pi\)
−0.394788 + 0.918772i \(0.629182\pi\)
\(888\) 0 0
\(889\) 34.5478 1.15870
\(890\) 0 0
\(891\) 5.38164 0.180292
\(892\) 0 0
\(893\) 83.8483 2.80588
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2.40857 −0.0804199
\(898\) 0 0
\(899\) −33.6343 −1.12177
\(900\) 0 0
\(901\) −10.2952 −0.342983
\(902\) 0 0
\(903\) 27.8923 0.928197
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 9.65629 0.320632 0.160316 0.987066i \(-0.448749\pi\)
0.160316 + 0.987066i \(0.448749\pi\)
\(908\) 0 0
\(909\) −19.7364 −0.654614
\(910\) 0 0
\(911\) 13.9461 0.462056 0.231028 0.972947i \(-0.425791\pi\)
0.231028 + 0.972947i \(0.425791\pi\)
\(912\) 0 0
\(913\) −10.4734 −0.346620
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.44158 −0.146674
\(918\) 0 0
\(919\) 55.7254 1.83821 0.919105 0.394013i \(-0.128914\pi\)
0.919105 + 0.394013i \(0.128914\pi\)
\(920\) 0 0
\(921\) −16.1449 −0.531993
\(922\) 0 0
\(923\) −2.61836 −0.0861843
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −3.58043 −0.117597
\(928\) 0 0
\(929\) 47.7792 1.56759 0.783793 0.621023i \(-0.213283\pi\)
0.783793 + 0.621023i \(0.213283\pi\)
\(930\) 0 0
\(931\) −9.33879 −0.306066
\(932\) 0 0
\(933\) 29.5266 0.966656
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −17.7846 −0.580996 −0.290498 0.956876i \(-0.593821\pi\)
−0.290498 + 0.956876i \(0.593821\pi\)
\(938\) 0 0
\(939\) 33.5804 1.09586
\(940\) 0 0
\(941\) 7.77921 0.253595 0.126798 0.991929i \(-0.459530\pi\)
0.126798 + 0.991929i \(0.459530\pi\)
\(942\) 0 0
\(943\) 8.14493 0.265235
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 38.6336 1.25542 0.627711 0.778446i \(-0.283992\pi\)
0.627711 + 0.778446i \(0.283992\pi\)
\(948\) 0 0
\(949\) −7.02693 −0.228104
\(950\) 0 0
\(951\) −7.23672 −0.234667
\(952\) 0 0
\(953\) −31.9890 −1.03623 −0.518113 0.855312i \(-0.673365\pi\)
−0.518113 + 0.855312i \(0.673365\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −26.7633 −0.865134
\(958\) 0 0
\(959\) 4.81714 0.155554
\(960\) 0 0
\(961\) 14.7420 0.475548
\(962\) 0 0
\(963\) 16.9621 0.546595
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −6.86535 −0.220775 −0.110387 0.993889i \(-0.535209\pi\)
−0.110387 + 0.993889i \(0.535209\pi\)
\(968\) 0 0
\(969\) −55.8703 −1.79481
\(970\) 0 0
\(971\) −49.2948 −1.58194 −0.790972 0.611852i \(-0.790425\pi\)
−0.790972 + 0.611852i \(0.790425\pi\)
\(972\) 0 0
\(973\) 9.98335 0.320051
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 12.2360 0.391464 0.195732 0.980657i \(-0.437292\pi\)
0.195732 + 0.980657i \(0.437292\pi\)
\(978\) 0 0
\(979\) 3.32778 0.106356
\(980\) 0 0
\(981\) 13.7902 0.440288
\(982\) 0 0
\(983\) 50.8490 1.62183 0.810916 0.585163i \(-0.198970\pi\)
0.810916 + 0.585163i \(0.198970\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 25.9241 0.825174
\(988\) 0 0
\(989\) 27.8923 0.886923
\(990\) 0 0
\(991\) 19.7474 0.627295 0.313648 0.949539i \(-0.398449\pi\)
0.313648 + 0.949539i \(0.398449\pi\)
\(992\) 0 0
\(993\) −2.55350 −0.0810328
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −27.9241 −0.884366 −0.442183 0.896925i \(-0.645796\pi\)
−0.442183 + 0.896925i \(0.645796\pi\)
\(998\) 0 0
\(999\) 7.38164 0.233545
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 7800.2.a.bi.1.2 3
5.4 even 2 1560.2.a.q.1.2 3
15.14 odd 2 4680.2.a.bh.1.2 3
20.19 odd 2 3120.2.a.bi.1.2 3
60.59 even 2 9360.2.a.cy.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.a.q.1.2 3 5.4 even 2
3120.2.a.bi.1.2 3 20.19 odd 2
4680.2.a.bh.1.2 3 15.14 odd 2
7800.2.a.bi.1.2 3 1.1 even 1 trivial
9360.2.a.cy.1.2 3 60.59 even 2