Properties

Label 7800.2.a.bn.1.3
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: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +2.12489 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +2.12489 q^{7} +1.00000 q^{9} +3.15516 q^{11} -1.00000 q^{13} -0.515138 q^{17} +6.73463 q^{19} +2.12489 q^{21} +4.24977 q^{23} +1.00000 q^{27} +0.0302761 q^{29} +7.15516 q^{31} +3.15516 q^{33} -5.76491 q^{37} -1.00000 q^{39} -3.76491 q^{41} +3.28005 q^{43} +4.60975 q^{47} -2.48486 q^{49} -0.515138 q^{51} -0.280047 q^{53} +6.73463 q^{57} +11.3444 q^{59} -5.01468 q^{61} +2.12489 q^{63} -15.1093 q^{67} +4.24977 q^{69} +2.23509 q^{71} +2.96972 q^{73} +6.70436 q^{77} -8.98440 q^{79} +1.00000 q^{81} -5.40493 q^{83} +0.0302761 q^{87} -15.5298 q^{89} -2.12489 q^{91} +7.15516 q^{93} -0.909172 q^{97} +3.15516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{3} - 2q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{3} - 2q^{7} + 3q^{9} + 2q^{11} - 3q^{13} - 2q^{17} + 3q^{19} - 2q^{21} - 4q^{23} + 3q^{27} + q^{29} + 14q^{31} + 2q^{33} - q^{37} - 3q^{39} + 5q^{41} - 6q^{43} + 5q^{47} - 7q^{49} - 2q^{51} + 15q^{53} + 3q^{57} + 8q^{59} + 18q^{61} - 2q^{63} - 3q^{67} - 4q^{69} + 23q^{71} + 8q^{73} + 2q^{77} + 7q^{79} + 3q^{81} + 8q^{83} + q^{87} - 14q^{89} + 2q^{91} + 14q^{93} + 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.12489 0.803131 0.401566 0.915830i \(-0.368466\pi\)
0.401566 + 0.915830i \(0.368466\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.15516 0.951317 0.475658 0.879630i \(-0.342210\pi\)
0.475658 + 0.879630i \(0.342210\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.515138 −0.124939 −0.0624697 0.998047i \(-0.519898\pi\)
−0.0624697 + 0.998047i \(0.519898\pi\)
\(18\) 0 0
\(19\) 6.73463 1.54503 0.772515 0.634996i \(-0.218998\pi\)
0.772515 + 0.634996i \(0.218998\pi\)
\(20\) 0 0
\(21\) 2.12489 0.463688
\(22\) 0 0
\(23\) 4.24977 0.886138 0.443069 0.896487i \(-0.353890\pi\)
0.443069 + 0.896487i \(0.353890\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.0302761 0.00562213 0.00281106 0.999996i \(-0.499105\pi\)
0.00281106 + 0.999996i \(0.499105\pi\)
\(30\) 0 0
\(31\) 7.15516 1.28510 0.642552 0.766242i \(-0.277875\pi\)
0.642552 + 0.766242i \(0.277875\pi\)
\(32\) 0 0
\(33\) 3.15516 0.549243
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.76491 −0.947745 −0.473873 0.880593i \(-0.657144\pi\)
−0.473873 + 0.880593i \(0.657144\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −3.76491 −0.587980 −0.293990 0.955808i \(-0.594983\pi\)
−0.293990 + 0.955808i \(0.594983\pi\)
\(42\) 0 0
\(43\) 3.28005 0.500202 0.250101 0.968220i \(-0.419536\pi\)
0.250101 + 0.968220i \(0.419536\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.60975 0.672401 0.336200 0.941790i \(-0.390858\pi\)
0.336200 + 0.941790i \(0.390858\pi\)
\(48\) 0 0
\(49\) −2.48486 −0.354980
\(50\) 0 0
\(51\) −0.515138 −0.0721338
\(52\) 0 0
\(53\) −0.280047 −0.0384674 −0.0192337 0.999815i \(-0.506123\pi\)
−0.0192337 + 0.999815i \(0.506123\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.73463 0.892024
\(58\) 0 0
\(59\) 11.3444 1.47691 0.738456 0.674301i \(-0.235555\pi\)
0.738456 + 0.674301i \(0.235555\pi\)
\(60\) 0 0
\(61\) −5.01468 −0.642064 −0.321032 0.947068i \(-0.604030\pi\)
−0.321032 + 0.947068i \(0.604030\pi\)
\(62\) 0 0
\(63\) 2.12489 0.267710
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −15.1093 −1.84589 −0.922947 0.384928i \(-0.874226\pi\)
−0.922947 + 0.384928i \(0.874226\pi\)
\(68\) 0 0
\(69\) 4.24977 0.511612
\(70\) 0 0
\(71\) 2.23509 0.265257 0.132628 0.991166i \(-0.457658\pi\)
0.132628 + 0.991166i \(0.457658\pi\)
\(72\) 0 0
\(73\) 2.96972 0.347580 0.173790 0.984783i \(-0.444399\pi\)
0.173790 + 0.984783i \(0.444399\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.70436 0.764032
\(78\) 0 0
\(79\) −8.98440 −1.01082 −0.505412 0.862878i \(-0.668660\pi\)
−0.505412 + 0.862878i \(0.668660\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.40493 −0.593268 −0.296634 0.954991i \(-0.595864\pi\)
−0.296634 + 0.954991i \(0.595864\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.0302761 0.00324594
\(88\) 0 0
\(89\) −15.5298 −1.64616 −0.823079 0.567927i \(-0.807745\pi\)
−0.823079 + 0.567927i \(0.807745\pi\)
\(90\) 0 0
\(91\) −2.12489 −0.222749
\(92\) 0 0
\(93\) 7.15516 0.741956
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.909172 −0.0923124 −0.0461562 0.998934i \(-0.514697\pi\)
−0.0461562 + 0.998934i \(0.514697\pi\)
\(98\) 0 0
\(99\) 3.15516 0.317106
\(100\) 0 0
\(101\) 16.0450 1.59653 0.798266 0.602305i \(-0.205751\pi\)
0.798266 + 0.602305i \(0.205751\pi\)
\(102\) 0 0
\(103\) 10.5601 1.04052 0.520258 0.854009i \(-0.325836\pi\)
0.520258 + 0.854009i \(0.325836\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0450 1.06776 0.533878 0.845561i \(-0.320734\pi\)
0.533878 + 0.845561i \(0.320734\pi\)
\(108\) 0 0
\(109\) 0.734633 0.0703651 0.0351825 0.999381i \(-0.488799\pi\)
0.0351825 + 0.999381i \(0.488799\pi\)
\(110\) 0 0
\(111\) −5.76491 −0.547181
\(112\) 0 0
\(113\) 7.93945 0.746880 0.373440 0.927654i \(-0.378178\pi\)
0.373440 + 0.927654i \(0.378178\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −1.09461 −0.100343
\(120\) 0 0
\(121\) −1.04496 −0.0949960
\(122\) 0 0
\(123\) −3.76491 −0.339470
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.51514 −0.311918 −0.155959 0.987764i \(-0.549847\pi\)
−0.155959 + 0.987764i \(0.549847\pi\)
\(128\) 0 0
\(129\) 3.28005 0.288792
\(130\) 0 0
\(131\) 7.76491 0.678423 0.339212 0.940710i \(-0.389840\pi\)
0.339212 + 0.940710i \(0.389840\pi\)
\(132\) 0 0
\(133\) 14.3103 1.24086
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.2039 −1.55526 −0.777632 0.628720i \(-0.783579\pi\)
−0.777632 + 0.628720i \(0.783579\pi\)
\(138\) 0 0
\(139\) −12.7493 −1.08138 −0.540691 0.841221i \(-0.681837\pi\)
−0.540691 + 0.841221i \(0.681837\pi\)
\(140\) 0 0
\(141\) 4.60975 0.388211
\(142\) 0 0
\(143\) −3.15516 −0.263848
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −2.48486 −0.204948
\(148\) 0 0
\(149\) −9.52982 −0.780713 −0.390357 0.920664i \(-0.627648\pi\)
−0.390357 + 0.920664i \(0.627648\pi\)
\(150\) 0 0
\(151\) 18.6244 1.51563 0.757817 0.652467i \(-0.226266\pi\)
0.757817 + 0.652467i \(0.226266\pi\)
\(152\) 0 0
\(153\) −0.515138 −0.0416464
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.6741 0.931693 0.465847 0.884866i \(-0.345750\pi\)
0.465847 + 0.884866i \(0.345750\pi\)
\(158\) 0 0
\(159\) −0.280047 −0.0222092
\(160\) 0 0
\(161\) 9.03028 0.711685
\(162\) 0 0
\(163\) −1.03028 −0.0806975 −0.0403487 0.999186i \(-0.512847\pi\)
−0.0403487 + 0.999186i \(0.512847\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.7346 −0.830671 −0.415335 0.909668i \(-0.636336\pi\)
−0.415335 + 0.909668i \(0.636336\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 6.73463 0.515010
\(172\) 0 0
\(173\) −3.74931 −0.285055 −0.142527 0.989791i \(-0.545523\pi\)
−0.142527 + 0.989791i \(0.545523\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 11.3444 0.852696
\(178\) 0 0
\(179\) 10.4390 0.780247 0.390123 0.920763i \(-0.372432\pi\)
0.390123 + 0.920763i \(0.372432\pi\)
\(180\) 0 0
\(181\) 5.17454 0.384620 0.192310 0.981334i \(-0.438402\pi\)
0.192310 + 0.981334i \(0.438402\pi\)
\(182\) 0 0
\(183\) −5.01468 −0.370696
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.62534 −0.118857
\(188\) 0 0
\(189\) 2.12489 0.154563
\(190\) 0 0
\(191\) 7.15894 0.518003 0.259001 0.965877i \(-0.416607\pi\)
0.259001 + 0.965877i \(0.416607\pi\)
\(192\) 0 0
\(193\) −14.5601 −1.04806 −0.524029 0.851700i \(-0.675572\pi\)
−0.524029 + 0.851700i \(0.675572\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.5601 1.03736 0.518682 0.854967i \(-0.326423\pi\)
0.518682 + 0.854967i \(0.326423\pi\)
\(198\) 0 0
\(199\) 17.1055 1.21258 0.606289 0.795245i \(-0.292658\pi\)
0.606289 + 0.795245i \(0.292658\pi\)
\(200\) 0 0
\(201\) −15.1093 −1.06573
\(202\) 0 0
\(203\) 0.0643332 0.00451531
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.24977 0.295379
\(208\) 0 0
\(209\) 21.2489 1.46981
\(210\) 0 0
\(211\) 14.1892 0.976826 0.488413 0.872613i \(-0.337576\pi\)
0.488413 + 0.872613i \(0.337576\pi\)
\(212\) 0 0
\(213\) 2.23509 0.153146
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 15.2039 1.03211
\(218\) 0 0
\(219\) 2.96972 0.200675
\(220\) 0 0
\(221\) 0.515138 0.0346519
\(222\) 0 0
\(223\) 4.06055 0.271915 0.135957 0.990715i \(-0.456589\pi\)
0.135957 + 0.990715i \(0.456589\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.6850 −0.974676 −0.487338 0.873213i \(-0.662032\pi\)
−0.487338 + 0.873213i \(0.662032\pi\)
\(228\) 0 0
\(229\) −24.3250 −1.60744 −0.803721 0.595007i \(-0.797149\pi\)
−0.803721 + 0.595007i \(0.797149\pi\)
\(230\) 0 0
\(231\) 6.70436 0.441114
\(232\) 0 0
\(233\) 13.6509 0.894302 0.447151 0.894459i \(-0.352439\pi\)
0.447151 + 0.894459i \(0.352439\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −8.98440 −0.583600
\(238\) 0 0
\(239\) 15.0341 0.972472 0.486236 0.873827i \(-0.338369\pi\)
0.486236 + 0.873827i \(0.338369\pi\)
\(240\) 0 0
\(241\) 14.5601 0.937898 0.468949 0.883225i \(-0.344633\pi\)
0.468949 + 0.883225i \(0.344633\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.73463 −0.428514
\(248\) 0 0
\(249\) −5.40493 −0.342524
\(250\) 0 0
\(251\) −9.20482 −0.581003 −0.290501 0.956875i \(-0.593822\pi\)
−0.290501 + 0.956875i \(0.593822\pi\)
\(252\) 0 0
\(253\) 13.4087 0.842999
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.7952 −0.860520 −0.430260 0.902705i \(-0.641578\pi\)
−0.430260 + 0.902705i \(0.641578\pi\)
\(258\) 0 0
\(259\) −12.2498 −0.761164
\(260\) 0 0
\(261\) 0.0302761 0.00187404
\(262\) 0 0
\(263\) 3.03028 0.186855 0.0934274 0.995626i \(-0.470218\pi\)
0.0934274 + 0.995626i \(0.470218\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −15.5298 −0.950409
\(268\) 0 0
\(269\) −0.469266 −0.0286116 −0.0143058 0.999898i \(-0.504554\pi\)
−0.0143058 + 0.999898i \(0.504554\pi\)
\(270\) 0 0
\(271\) −2.87420 −0.174595 −0.0872975 0.996182i \(-0.527823\pi\)
−0.0872975 + 0.996182i \(0.527823\pi\)
\(272\) 0 0
\(273\) −2.12489 −0.128604
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.87890 −0.112892 −0.0564459 0.998406i \(-0.517977\pi\)
−0.0564459 + 0.998406i \(0.517977\pi\)
\(278\) 0 0
\(279\) 7.15516 0.428368
\(280\) 0 0
\(281\) 23.2342 1.38603 0.693017 0.720921i \(-0.256281\pi\)
0.693017 + 0.720921i \(0.256281\pi\)
\(282\) 0 0
\(283\) −26.8099 −1.59368 −0.796841 0.604190i \(-0.793497\pi\)
−0.796841 + 0.604190i \(0.793497\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) −16.7346 −0.984390
\(290\) 0 0
\(291\) −0.909172 −0.0532966
\(292\) 0 0
\(293\) 10.4702 0.611675 0.305837 0.952084i \(-0.401064\pi\)
0.305837 + 0.952084i \(0.401064\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.15516 0.183081
\(298\) 0 0
\(299\) −4.24977 −0.245771
\(300\) 0 0
\(301\) 6.96972 0.401728
\(302\) 0 0
\(303\) 16.0450 0.921759
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −26.3856 −1.50590 −0.752952 0.658076i \(-0.771371\pi\)
−0.752952 + 0.658076i \(0.771371\pi\)
\(308\) 0 0
\(309\) 10.5601 0.600743
\(310\) 0 0
\(311\) −24.2791 −1.37674 −0.688372 0.725358i \(-0.741674\pi\)
−0.688372 + 0.725358i \(0.741674\pi\)
\(312\) 0 0
\(313\) −14.2800 −0.807156 −0.403578 0.914945i \(-0.632234\pi\)
−0.403578 + 0.914945i \(0.632234\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.5298 −1.20924 −0.604618 0.796516i \(-0.706674\pi\)
−0.604618 + 0.796516i \(0.706674\pi\)
\(318\) 0 0
\(319\) 0.0955260 0.00534843
\(320\) 0 0
\(321\) 11.0450 0.616469
\(322\) 0 0
\(323\) −3.46927 −0.193035
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.734633 0.0406253
\(328\) 0 0
\(329\) 9.79518 0.540026
\(330\) 0 0
\(331\) 31.5904 1.73636 0.868182 0.496246i \(-0.165289\pi\)
0.868182 + 0.496246i \(0.165289\pi\)
\(332\) 0 0
\(333\) −5.76491 −0.315915
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −7.42431 −0.404428 −0.202214 0.979341i \(-0.564814\pi\)
−0.202214 + 0.979341i \(0.564814\pi\)
\(338\) 0 0
\(339\) 7.93945 0.431212
\(340\) 0 0
\(341\) 22.5757 1.22254
\(342\) 0 0
\(343\) −20.1542 −1.08823
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.9541 0.749097 0.374548 0.927207i \(-0.377798\pi\)
0.374548 + 0.927207i \(0.377798\pi\)
\(348\) 0 0
\(349\) −4.06055 −0.217356 −0.108678 0.994077i \(-0.534662\pi\)
−0.108678 + 0.994077i \(0.534662\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 24.3856 1.29791 0.648956 0.760826i \(-0.275206\pi\)
0.648956 + 0.760826i \(0.275206\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.09461 −0.0579329
\(358\) 0 0
\(359\) −3.76869 −0.198904 −0.0994519 0.995042i \(-0.531709\pi\)
−0.0994519 + 0.995042i \(0.531709\pi\)
\(360\) 0 0
\(361\) 26.3553 1.38712
\(362\) 0 0
\(363\) −1.04496 −0.0548460
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −19.2654 −1.00564 −0.502822 0.864390i \(-0.667705\pi\)
−0.502822 + 0.864390i \(0.667705\pi\)
\(368\) 0 0
\(369\) −3.76491 −0.195993
\(370\) 0 0
\(371\) −0.595068 −0.0308944
\(372\) 0 0
\(373\) 14.3553 0.743288 0.371644 0.928375i \(-0.378794\pi\)
0.371644 + 0.928375i \(0.378794\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.0302761 −0.00155930
\(378\) 0 0
\(379\) 33.1845 1.70457 0.852287 0.523074i \(-0.175215\pi\)
0.852287 + 0.523074i \(0.175215\pi\)
\(380\) 0 0
\(381\) −3.51514 −0.180086
\(382\) 0 0
\(383\) 30.8851 1.57815 0.789077 0.614294i \(-0.210559\pi\)
0.789077 + 0.614294i \(0.210559\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.28005 0.166734
\(388\) 0 0
\(389\) 0.295643 0.0149897 0.00749486 0.999972i \(-0.497614\pi\)
0.00749486 + 0.999972i \(0.497614\pi\)
\(390\) 0 0
\(391\) −2.18922 −0.110714
\(392\) 0 0
\(393\) 7.76491 0.391688
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.3250 −0.819328 −0.409664 0.912236i \(-0.634354\pi\)
−0.409664 + 0.912236i \(0.634354\pi\)
\(398\) 0 0
\(399\) 14.3103 0.716412
\(400\) 0 0
\(401\) 28.4390 1.42018 0.710088 0.704113i \(-0.248655\pi\)
0.710088 + 0.704113i \(0.248655\pi\)
\(402\) 0 0
\(403\) −7.15516 −0.356424
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −18.1892 −0.901606
\(408\) 0 0
\(409\) −16.3784 −0.809862 −0.404931 0.914347i \(-0.632704\pi\)
−0.404931 + 0.914347i \(0.632704\pi\)
\(410\) 0 0
\(411\) −18.2039 −0.897932
\(412\) 0 0
\(413\) 24.1055 1.18615
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −12.7493 −0.624337
\(418\) 0 0
\(419\) 31.4158 1.53476 0.767382 0.641190i \(-0.221559\pi\)
0.767382 + 0.641190i \(0.221559\pi\)
\(420\) 0 0
\(421\) 23.5298 1.14677 0.573387 0.819285i \(-0.305629\pi\)
0.573387 + 0.819285i \(0.305629\pi\)
\(422\) 0 0
\(423\) 4.60975 0.224134
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −10.6556 −0.515662
\(428\) 0 0
\(429\) −3.15516 −0.152333
\(430\) 0 0
\(431\) −19.3553 −0.932311 −0.466155 0.884703i \(-0.654361\pi\)
−0.466155 + 0.884703i \(0.654361\pi\)
\(432\) 0 0
\(433\) −19.7044 −0.946931 −0.473465 0.880812i \(-0.656997\pi\)
−0.473465 + 0.880812i \(0.656997\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 28.6206 1.36911
\(438\) 0 0
\(439\) 8.98440 0.428802 0.214401 0.976746i \(-0.431220\pi\)
0.214401 + 0.976746i \(0.431220\pi\)
\(440\) 0 0
\(441\) −2.48486 −0.118327
\(442\) 0 0
\(443\) 2.92385 0.138916 0.0694582 0.997585i \(-0.477873\pi\)
0.0694582 + 0.997585i \(0.477873\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −9.52982 −0.450745
\(448\) 0 0
\(449\) −17.3553 −0.819046 −0.409523 0.912300i \(-0.634305\pi\)
−0.409523 + 0.912300i \(0.634305\pi\)
\(450\) 0 0
\(451\) −11.8789 −0.559355
\(452\) 0 0
\(453\) 18.6244 0.875052
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.05964 −0.330236 −0.165118 0.986274i \(-0.552800\pi\)
−0.165118 + 0.986274i \(0.552800\pi\)
\(458\) 0 0
\(459\) −0.515138 −0.0240446
\(460\) 0 0
\(461\) −1.52982 −0.0712507 −0.0356254 0.999365i \(-0.511342\pi\)
−0.0356254 + 0.999365i \(0.511342\pi\)
\(462\) 0 0
\(463\) 27.3132 1.26935 0.634676 0.772779i \(-0.281134\pi\)
0.634676 + 0.772779i \(0.281134\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.29564 −0.291328 −0.145664 0.989334i \(-0.546532\pi\)
−0.145664 + 0.989334i \(0.546532\pi\)
\(468\) 0 0
\(469\) −32.1055 −1.48249
\(470\) 0 0
\(471\) 11.6741 0.537913
\(472\) 0 0
\(473\) 10.3491 0.475851
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.280047 −0.0128225
\(478\) 0 0
\(479\) 26.9806 1.23278 0.616388 0.787443i \(-0.288595\pi\)
0.616388 + 0.787443i \(0.288595\pi\)
\(480\) 0 0
\(481\) 5.76491 0.262857
\(482\) 0 0
\(483\) 9.03028 0.410892
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −11.8751 −0.538113 −0.269056 0.963124i \(-0.586712\pi\)
−0.269056 + 0.963124i \(0.586712\pi\)
\(488\) 0 0
\(489\) −1.03028 −0.0465907
\(490\) 0 0
\(491\) −41.8695 −1.88954 −0.944772 0.327728i \(-0.893717\pi\)
−0.944772 + 0.327728i \(0.893717\pi\)
\(492\) 0 0
\(493\) −0.0155964 −0.000702425 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.74931 0.213036
\(498\) 0 0
\(499\) 30.5786 1.36888 0.684442 0.729067i \(-0.260046\pi\)
0.684442 + 0.729067i \(0.260046\pi\)
\(500\) 0 0
\(501\) −10.7346 −0.479588
\(502\) 0 0
\(503\) 32.9991 1.47136 0.735678 0.677331i \(-0.236864\pi\)
0.735678 + 0.677331i \(0.236864\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) 41.6197 1.84476 0.922381 0.386281i \(-0.126241\pi\)
0.922381 + 0.386281i \(0.126241\pi\)
\(510\) 0 0
\(511\) 6.31032 0.279152
\(512\) 0 0
\(513\) 6.73463 0.297341
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 14.5445 0.639666
\(518\) 0 0
\(519\) −3.74931 −0.164577
\(520\) 0 0
\(521\) 6.47018 0.283464 0.141732 0.989905i \(-0.454733\pi\)
0.141732 + 0.989905i \(0.454733\pi\)
\(522\) 0 0
\(523\) −37.8401 −1.65463 −0.827317 0.561735i \(-0.810134\pi\)
−0.827317 + 0.561735i \(0.810134\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.68590 −0.160560
\(528\) 0 0
\(529\) −4.93945 −0.214759
\(530\) 0 0
\(531\) 11.3444 0.492304
\(532\) 0 0
\(533\) 3.76491 0.163076
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.4390 0.450476
\(538\) 0 0
\(539\) −7.84014 −0.337699
\(540\) 0 0
\(541\) 6.37844 0.274230 0.137115 0.990555i \(-0.456217\pi\)
0.137115 + 0.990555i \(0.456217\pi\)
\(542\) 0 0
\(543\) 5.17454 0.222061
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 10.0899 0.431413 0.215707 0.976458i \(-0.430794\pi\)
0.215707 + 0.976458i \(0.430794\pi\)
\(548\) 0 0
\(549\) −5.01468 −0.214021
\(550\) 0 0
\(551\) 0.203898 0.00868636
\(552\) 0 0
\(553\) −19.0908 −0.811825
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.96972 0.210574 0.105287 0.994442i \(-0.466424\pi\)
0.105287 + 0.994442i \(0.466424\pi\)
\(558\) 0 0
\(559\) −3.28005 −0.138731
\(560\) 0 0
\(561\) −1.62534 −0.0686221
\(562\) 0 0
\(563\) −14.8027 −0.623861 −0.311931 0.950105i \(-0.600976\pi\)
−0.311931 + 0.950105i \(0.600976\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.12489 0.0892368
\(568\) 0 0
\(569\) −3.85574 −0.161641 −0.0808205 0.996729i \(-0.525754\pi\)
−0.0808205 + 0.996729i \(0.525754\pi\)
\(570\) 0 0
\(571\) 24.6282 1.03066 0.515329 0.856992i \(-0.327670\pi\)
0.515329 + 0.856992i \(0.327670\pi\)
\(572\) 0 0
\(573\) 7.15894 0.299069
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.02936 0.251006 0.125503 0.992093i \(-0.459946\pi\)
0.125503 + 0.992093i \(0.459946\pi\)
\(578\) 0 0
\(579\) −14.5601 −0.605097
\(580\) 0 0
\(581\) −11.4849 −0.476472
\(582\) 0 0
\(583\) −0.883593 −0.0365947
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.0861 0.581397 0.290698 0.956815i \(-0.406112\pi\)
0.290698 + 0.956815i \(0.406112\pi\)
\(588\) 0 0
\(589\) 48.1874 1.98553
\(590\) 0 0
\(591\) 14.5601 0.598922
\(592\) 0 0
\(593\) −28.2333 −1.15940 −0.579700 0.814830i \(-0.696830\pi\)
−0.579700 + 0.814830i \(0.696830\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.1055 0.700082
\(598\) 0 0
\(599\) −23.0596 −0.942191 −0.471096 0.882082i \(-0.656141\pi\)
−0.471096 + 0.882082i \(0.656141\pi\)
\(600\) 0 0
\(601\) 14.1901 0.578828 0.289414 0.957204i \(-0.406540\pi\)
0.289414 + 0.957204i \(0.406540\pi\)
\(602\) 0 0
\(603\) −15.1093 −0.615298
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −43.9229 −1.78278 −0.891388 0.453240i \(-0.850268\pi\)
−0.891388 + 0.453240i \(0.850268\pi\)
\(608\) 0 0
\(609\) 0.0643332 0.00260691
\(610\) 0 0
\(611\) −4.60975 −0.186490
\(612\) 0 0
\(613\) 1.62156 0.0654943 0.0327472 0.999464i \(-0.489574\pi\)
0.0327472 + 0.999464i \(0.489574\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.3250 −0.496186 −0.248093 0.968736i \(-0.579804\pi\)
−0.248093 + 0.968736i \(0.579804\pi\)
\(618\) 0 0
\(619\) −5.15138 −0.207051 −0.103526 0.994627i \(-0.533012\pi\)
−0.103526 + 0.994627i \(0.533012\pi\)
\(620\) 0 0
\(621\) 4.24977 0.170537
\(622\) 0 0
\(623\) −32.9991 −1.32208
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 21.2489 0.848597
\(628\) 0 0
\(629\) 2.96972 0.118411
\(630\) 0 0
\(631\) 1.97064 0.0784500 0.0392250 0.999230i \(-0.487511\pi\)
0.0392250 + 0.999230i \(0.487511\pi\)
\(632\) 0 0
\(633\) 14.1892 0.563971
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.48486 0.0984538
\(638\) 0 0
\(639\) 2.23509 0.0884188
\(640\) 0 0
\(641\) 4.33348 0.171162 0.0855811 0.996331i \(-0.472725\pi\)
0.0855811 + 0.996331i \(0.472725\pi\)
\(642\) 0 0
\(643\) −6.85574 −0.270364 −0.135182 0.990821i \(-0.543162\pi\)
−0.135182 + 0.990821i \(0.543162\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.93945 −0.233504 −0.116752 0.993161i \(-0.537248\pi\)
−0.116752 + 0.993161i \(0.537248\pi\)
\(648\) 0 0
\(649\) 35.7934 1.40501
\(650\) 0 0
\(651\) 15.2039 0.595888
\(652\) 0 0
\(653\) 9.61353 0.376206 0.188103 0.982149i \(-0.439766\pi\)
0.188103 + 0.982149i \(0.439766\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.96972 0.115860
\(658\) 0 0
\(659\) 0.455503 0.0177439 0.00887193 0.999961i \(-0.497176\pi\)
0.00887193 + 0.999961i \(0.497176\pi\)
\(660\) 0 0
\(661\) −29.2635 −1.13822 −0.569110 0.822262i \(-0.692712\pi\)
−0.569110 + 0.822262i \(0.692712\pi\)
\(662\) 0 0
\(663\) 0.515138 0.0200063
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.128666 0.00498199
\(668\) 0 0
\(669\) 4.06055 0.156990
\(670\) 0 0
\(671\) −15.8221 −0.610806
\(672\) 0 0
\(673\) −24.7796 −0.955183 −0.477591 0.878582i \(-0.658490\pi\)
−0.477591 + 0.878582i \(0.658490\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.93945 0.305138 0.152569 0.988293i \(-0.451245\pi\)
0.152569 + 0.988293i \(0.451245\pi\)
\(678\) 0 0
\(679\) −1.93189 −0.0741390
\(680\) 0 0
\(681\) −14.6850 −0.562730
\(682\) 0 0
\(683\) 7.53360 0.288265 0.144133 0.989558i \(-0.453961\pi\)
0.144133 + 0.989558i \(0.453961\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −24.3250 −0.928057
\(688\) 0 0
\(689\) 0.280047 0.0106689
\(690\) 0 0
\(691\) −51.4490 −1.95721 −0.978606 0.205745i \(-0.934038\pi\)
−0.978606 + 0.205745i \(0.934038\pi\)
\(692\) 0 0
\(693\) 6.70436 0.254677
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.93945 0.0734618
\(698\) 0 0
\(699\) 13.6509 0.516325
\(700\) 0 0
\(701\) −5.35620 −0.202301 −0.101150 0.994871i \(-0.532252\pi\)
−0.101150 + 0.994871i \(0.532252\pi\)
\(702\) 0 0
\(703\) −38.8245 −1.46430
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 34.0937 1.28223
\(708\) 0 0
\(709\) 0.969724 0.0364187 0.0182094 0.999834i \(-0.494203\pi\)
0.0182094 + 0.999834i \(0.494203\pi\)
\(710\) 0 0
\(711\) −8.98440 −0.336941
\(712\) 0 0
\(713\) 30.4078 1.13878
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.0341 0.561457
\(718\) 0 0
\(719\) 23.5592 0.878609 0.439305 0.898338i \(-0.355225\pi\)
0.439305 + 0.898338i \(0.355225\pi\)
\(720\) 0 0
\(721\) 22.4390 0.835672
\(722\) 0 0
\(723\) 14.5601 0.541496
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −22.3179 −0.827725 −0.413862 0.910340i \(-0.635820\pi\)
−0.413862 + 0.910340i \(0.635820\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.68968 −0.0624950
\(732\) 0 0
\(733\) 46.7034 1.72503 0.862515 0.506031i \(-0.168888\pi\)
0.862515 + 0.506031i \(0.168888\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −47.6722 −1.75603
\(738\) 0 0
\(739\) −29.2985 −1.07776 −0.538882 0.842382i \(-0.681153\pi\)
−0.538882 + 0.842382i \(0.681153\pi\)
\(740\) 0 0
\(741\) −6.73463 −0.247403
\(742\) 0 0
\(743\) 51.0175 1.87165 0.935826 0.352462i \(-0.114655\pi\)
0.935826 + 0.352462i \(0.114655\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.40493 −0.197756
\(748\) 0 0
\(749\) 23.4693 0.857548
\(750\) 0 0
\(751\) 4.36376 0.159236 0.0796179 0.996825i \(-0.474630\pi\)
0.0796179 + 0.996825i \(0.474630\pi\)
\(752\) 0 0
\(753\) −9.20482 −0.335442
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −42.6344 −1.54957 −0.774787 0.632222i \(-0.782143\pi\)
−0.774787 + 0.632222i \(0.782143\pi\)
\(758\) 0 0
\(759\) 13.4087 0.486705
\(760\) 0 0
\(761\) −3.73372 −0.135347 −0.0676736 0.997708i \(-0.521558\pi\)
−0.0676736 + 0.997708i \(0.521558\pi\)
\(762\) 0 0
\(763\) 1.56101 0.0565124
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.3444 −0.409622
\(768\) 0 0
\(769\) −20.3784 −0.734865 −0.367433 0.930050i \(-0.619763\pi\)
−0.367433 + 0.930050i \(0.619763\pi\)
\(770\) 0 0
\(771\) −13.7952 −0.496821
\(772\) 0 0
\(773\) −14.5289 −0.522568 −0.261284 0.965262i \(-0.584146\pi\)
−0.261284 + 0.965262i \(0.584146\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −12.2498 −0.439458
\(778\) 0 0
\(779\) −25.3553 −0.908447
\(780\) 0 0
\(781\) 7.05207 0.252343
\(782\) 0 0
\(783\) 0.0302761 0.00108198
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −5.00470 −0.178398 −0.0891991 0.996014i \(-0.528431\pi\)
−0.0891991 + 0.996014i \(0.528431\pi\)
\(788\) 0 0
\(789\) 3.03028 0.107881
\(790\) 0 0
\(791\) 16.8704 0.599843
\(792\) 0 0
\(793\) 5.01468 0.178076
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.3846 1.71387 0.856936 0.515423i \(-0.172365\pi\)
0.856936 + 0.515423i \(0.172365\pi\)
\(798\) 0 0
\(799\) −2.37466 −0.0840093
\(800\) 0 0
\(801\) −15.5298 −0.548719
\(802\) 0 0
\(803\) 9.36996 0.330659
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −0.469266 −0.0165189
\(808\) 0 0
\(809\) 9.18074 0.322778 0.161389 0.986891i \(-0.448403\pi\)
0.161389 + 0.986891i \(0.448403\pi\)
\(810\) 0 0
\(811\) 30.2224 1.06125 0.530625 0.847607i \(-0.321957\pi\)
0.530625 + 0.847607i \(0.321957\pi\)
\(812\) 0 0
\(813\) −2.87420 −0.100803
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 22.0899 0.772828
\(818\) 0 0
\(819\) −2.12489 −0.0742495
\(820\) 0 0
\(821\) 31.6197 1.10354 0.551768 0.833998i \(-0.313953\pi\)
0.551768 + 0.833998i \(0.313953\pi\)
\(822\) 0 0
\(823\) −31.4158 −1.09509 −0.547544 0.836777i \(-0.684437\pi\)
−0.547544 + 0.836777i \(0.684437\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11.2838 −0.392377 −0.196189 0.980566i \(-0.562856\pi\)
−0.196189 + 0.980566i \(0.562856\pi\)
\(828\) 0 0
\(829\) −4.83302 −0.167858 −0.0839289 0.996472i \(-0.526747\pi\)
−0.0839289 + 0.996472i \(0.526747\pi\)
\(830\) 0 0
\(831\) −1.87890 −0.0651782
\(832\) 0 0
\(833\) 1.28005 0.0443510
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 7.15516 0.247319
\(838\) 0 0
\(839\) −15.4693 −0.534058 −0.267029 0.963688i \(-0.586042\pi\)
−0.267029 + 0.963688i \(0.586042\pi\)
\(840\) 0 0
\(841\) −28.9991 −0.999968
\(842\) 0 0
\(843\) 23.2342 0.800227
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.22041 −0.0762942
\(848\) 0 0
\(849\) −26.8099 −0.920112
\(850\) 0 0
\(851\) −24.4995 −0.839833
\(852\) 0 0
\(853\) −41.2635 −1.41284 −0.706418 0.707795i \(-0.749690\pi\)
−0.706418 + 0.707795i \(0.749690\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 9.87890 0.337457 0.168728 0.985663i \(-0.446034\pi\)
0.168728 + 0.985663i \(0.446034\pi\)
\(858\) 0 0
\(859\) −20.7200 −0.706956 −0.353478 0.935443i \(-0.615001\pi\)
−0.353478 + 0.935443i \(0.615001\pi\)
\(860\) 0 0
\(861\) −8.00000 −0.272639
\(862\) 0 0
\(863\) −1.91915 −0.0653288 −0.0326644 0.999466i \(-0.510399\pi\)
−0.0326644 + 0.999466i \(0.510399\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −16.7346 −0.568338
\(868\) 0 0
\(869\) −28.3472 −0.961614
\(870\) 0 0
\(871\) 15.1093 0.511959
\(872\) 0 0
\(873\) −0.909172 −0.0307708
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −18.3250 −0.618791 −0.309396 0.950933i \(-0.600127\pi\)
−0.309396 + 0.950933i \(0.600127\pi\)
\(878\) 0 0
\(879\) 10.4702 0.353150
\(880\) 0 0
\(881\) 12.7649 0.430061 0.215030 0.976607i \(-0.431015\pi\)
0.215030 + 0.976607i \(0.431015\pi\)
\(882\) 0 0
\(883\) −11.8789 −0.399757 −0.199878 0.979821i \(-0.564055\pi\)
−0.199878 + 0.979821i \(0.564055\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −40.7493 −1.36823 −0.684114 0.729375i \(-0.739811\pi\)
−0.684114 + 0.729375i \(0.739811\pi\)
\(888\) 0 0
\(889\) −7.46927 −0.250511
\(890\) 0 0
\(891\) 3.15516 0.105702
\(892\) 0 0
\(893\) 31.0450 1.03888
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −4.24977 −0.141896
\(898\) 0 0
\(899\) 0.216630 0.00722503
\(900\) 0 0
\(901\) 0.144263 0.00480609
\(902\) 0 0
\(903\) 6.96972 0.231938
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 32.5289 1.08010 0.540052 0.841632i \(-0.318404\pi\)
0.540052 + 0.841632i \(0.318404\pi\)
\(908\) 0 0
\(909\) 16.0450 0.532178
\(910\) 0 0
\(911\) −22.2810 −0.738201 −0.369101 0.929389i \(-0.620334\pi\)
−0.369101 + 0.929389i \(0.620334\pi\)
\(912\) 0 0
\(913\) −17.0534 −0.564386
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 16.4995 0.544863
\(918\) 0 0
\(919\) 26.9239 0.888136 0.444068 0.895993i \(-0.353535\pi\)
0.444068 + 0.895993i \(0.353535\pi\)
\(920\) 0 0
\(921\) −26.3856 −0.869434
\(922\) 0 0
\(923\) −2.23509 −0.0735689
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 10.5601 0.346839
\(928\) 0 0
\(929\) −36.4755 −1.19672 −0.598361 0.801227i \(-0.704181\pi\)
−0.598361 + 0.801227i \(0.704181\pi\)
\(930\) 0 0
\(931\) −16.7346 −0.548455
\(932\) 0 0
\(933\) −24.2791 −0.794863
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 7.26445 0.237319 0.118660 0.992935i \(-0.462140\pi\)
0.118660 + 0.992935i \(0.462140\pi\)
\(938\) 0 0
\(939\) −14.2800 −0.466012
\(940\) 0 0
\(941\) −8.08991 −0.263724 −0.131862 0.991268i \(-0.542096\pi\)
−0.131862 + 0.991268i \(0.542096\pi\)
\(942\) 0 0
\(943\) −16.0000 −0.521032
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −48.9036 −1.58915 −0.794576 0.607165i \(-0.792307\pi\)
−0.794576 + 0.607165i \(0.792307\pi\)
\(948\) 0 0
\(949\) −2.96972 −0.0964013
\(950\) 0 0
\(951\) −21.5298 −0.698152
\(952\) 0 0
\(953\) 6.58325 0.213252 0.106626 0.994299i \(-0.465995\pi\)
0.106626 + 0.994299i \(0.465995\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0.0955260 0.00308792
\(958\) 0 0
\(959\) −38.6812 −1.24908
\(960\) 0 0
\(961\) 20.1963 0.651495
\(962\) 0 0
\(963\) 11.0450 0.355919
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −9.58659 −0.308284 −0.154142 0.988049i \(-0.549261\pi\)
−0.154142 + 0.988049i \(0.549261\pi\)
\(968\) 0 0
\(969\) −3.46927 −0.111449
\(970\) 0 0
\(971\) −36.1358 −1.15965 −0.579826 0.814740i \(-0.696880\pi\)
−0.579826 + 0.814740i \(0.696880\pi\)
\(972\) 0 0
\(973\) −27.0908 −0.868492
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 27.0303 0.864775 0.432388 0.901688i \(-0.357671\pi\)
0.432388 + 0.901688i \(0.357671\pi\)
\(978\) 0 0
\(979\) −48.9991 −1.56602
\(980\) 0 0
\(981\) 0.734633 0.0234550
\(982\) 0 0
\(983\) −49.9338 −1.59264 −0.796321 0.604874i \(-0.793223\pi\)
−0.796321 + 0.604874i \(0.793223\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 9.79518 0.311784
\(988\) 0 0
\(989\) 13.9394 0.443249
\(990\) 0 0
\(991\) 20.4849 0.650723 0.325362 0.945590i \(-0.394514\pi\)
0.325362 + 0.945590i \(0.394514\pi\)
\(992\) 0 0
\(993\) 31.5904 1.00249
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 40.9541 1.29703 0.648515 0.761202i \(-0.275390\pi\)
0.648515 + 0.761202i \(0.275390\pi\)
\(998\) 0 0
\(999\) −5.76491 −0.182394
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.bn.1.3 yes 3
5.4 even 2 7800.2.a.bm.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bm.1.1 3 5.4 even 2
7800.2.a.bn.1.3 yes 3 1.1 even 1 trivial