Properties

Label 7800.2.a.bv.1.4
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $4$
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: \(4\)
Coefficient field: 4.4.10304.1
Defining polynomial: \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.69230\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +2.82843 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +2.82843 q^{7} +1.00000 q^{9} +0.393270 q^{11} +1.00000 q^{13} -6.21302 q^{17} -7.34271 q^{19} -2.82843 q^{21} -1.44383 q^{23} -1.00000 q^{27} -0.828427 q^{29} +1.65685 q^{31} -0.393270 q^{33} +6.78654 q^{37} -1.00000 q^{39} +3.77786 q^{41} -2.51428 q^{43} +3.00868 q^{47} +1.00000 q^{49} +6.21302 q^{51} -9.55573 q^{53} +7.34271 q^{57} +0.393270 q^{59} +11.0414 q^{61} +2.82843 q^{63} +15.5557 q^{67} +1.44383 q^{69} +6.56440 q^{71} +13.6150 q^{73} +1.11233 q^{77} -14.9403 q^{79} +1.00000 q^{81} +16.4633 q^{83} +0.828427 q^{87} -9.67674 q^{89} +2.82843 q^{91} -1.65685 q^{93} +0.0418875 q^{97} +0.393270 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 4 q^{9} - 8 q^{11} + 4 q^{13} - 4 q^{17} - 12 q^{19} - 4 q^{23} - 4 q^{27} + 8 q^{29} - 16 q^{31} + 8 q^{33} + 8 q^{37} - 4 q^{39} - 4 q^{41} - 4 q^{43} + 12 q^{47} + 4 q^{49} + 4 q^{51} + 12 q^{57} - 8 q^{59} + 12 q^{61} + 24 q^{67} + 4 q^{69} - 12 q^{71} + 24 q^{73} + 8 q^{77} - 12 q^{79} + 4 q^{81} + 12 q^{83} - 8 q^{87} - 4 q^{89} + 16 q^{93} + 8 q^{97} - 8 q^{99}+O(q^{100}) \) 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
\(7\) 2.82843 1.06904 0.534522 0.845154i \(-0.320491\pi\)
0.534522 + 0.845154i \(0.320491\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.393270 0.118575 0.0592877 0.998241i \(-0.481117\pi\)
0.0592877 + 0.998241i \(0.481117\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.21302 −1.50688 −0.753440 0.657517i \(-0.771607\pi\)
−0.753440 + 0.657517i \(0.771607\pi\)
\(18\) 0 0
\(19\) −7.34271 −1.68453 −0.842266 0.539062i \(-0.818779\pi\)
−0.842266 + 0.539062i \(0.818779\pi\)
\(20\) 0 0
\(21\) −2.82843 −0.617213
\(22\) 0 0
\(23\) −1.44383 −0.301060 −0.150530 0.988605i \(-0.548098\pi\)
−0.150530 + 0.988605i \(0.548098\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.828427 −0.153835 −0.0769175 0.997037i \(-0.524508\pi\)
−0.0769175 + 0.997037i \(0.524508\pi\)
\(30\) 0 0
\(31\) 1.65685 0.297580 0.148790 0.988869i \(-0.452462\pi\)
0.148790 + 0.988869i \(0.452462\pi\)
\(32\) 0 0
\(33\) −0.393270 −0.0684595
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.78654 1.11570 0.557850 0.829942i \(-0.311626\pi\)
0.557850 + 0.829942i \(0.311626\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 3.77786 0.590003 0.295002 0.955497i \(-0.404680\pi\)
0.295002 + 0.955497i \(0.404680\pi\)
\(42\) 0 0
\(43\) −2.51428 −0.383424 −0.191712 0.981451i \(-0.561404\pi\)
−0.191712 + 0.981451i \(0.561404\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00868 0.438860 0.219430 0.975628i \(-0.429580\pi\)
0.219430 + 0.975628i \(0.429580\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 6.21302 0.869997
\(52\) 0 0
\(53\) −9.55573 −1.31258 −0.656290 0.754509i \(-0.727875\pi\)
−0.656290 + 0.754509i \(0.727875\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.34271 0.972565
\(58\) 0 0
\(59\) 0.393270 0.0511994 0.0255997 0.999672i \(-0.491850\pi\)
0.0255997 + 0.999672i \(0.491850\pi\)
\(60\) 0 0
\(61\) 11.0414 1.41371 0.706856 0.707357i \(-0.250113\pi\)
0.706856 + 0.707357i \(0.250113\pi\)
\(62\) 0 0
\(63\) 2.82843 0.356348
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 15.5557 1.90043 0.950217 0.311588i \(-0.100861\pi\)
0.950217 + 0.311588i \(0.100861\pi\)
\(68\) 0 0
\(69\) 1.44383 0.173817
\(70\) 0 0
\(71\) 6.56440 0.779051 0.389526 0.921016i \(-0.372639\pi\)
0.389526 + 0.921016i \(0.372639\pi\)
\(72\) 0 0
\(73\) 13.6150 1.59351 0.796756 0.604302i \(-0.206548\pi\)
0.796756 + 0.604302i \(0.206548\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.11233 0.126762
\(78\) 0 0
\(79\) −14.9403 −1.68092 −0.840459 0.541875i \(-0.817714\pi\)
−0.840459 + 0.541875i \(0.817714\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.4633 1.80708 0.903540 0.428504i \(-0.140959\pi\)
0.903540 + 0.428504i \(0.140959\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.828427 0.0888167
\(88\) 0 0
\(89\) −9.67674 −1.02573 −0.512866 0.858469i \(-0.671416\pi\)
−0.512866 + 0.858469i \(0.671416\pi\)
\(90\) 0 0
\(91\) 2.82843 0.296500
\(92\) 0 0
\(93\) −1.65685 −0.171808
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.0418875 0.00425303 0.00212652 0.999998i \(-0.499323\pi\)
0.00212652 + 0.999998i \(0.499323\pi\)
\(98\) 0 0
\(99\) 0.393270 0.0395251
\(100\) 0 0
\(101\) 12.1421 1.20819 0.604094 0.796913i \(-0.293535\pi\)
0.604094 + 0.796913i \(0.293535\pi\)
\(102\) 0 0
\(103\) −0.0173504 −0.00170958 −0.000854792 1.00000i \(-0.500272\pi\)
−0.000854792 1.00000i \(0.500272\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.10113 0.203123 0.101562 0.994829i \(-0.467616\pi\)
0.101562 + 0.994829i \(0.467616\pi\)
\(108\) 0 0
\(109\) 6.21302 0.595100 0.297550 0.954706i \(-0.403831\pi\)
0.297550 + 0.954706i \(0.403831\pi\)
\(110\) 0 0
\(111\) −6.78654 −0.644150
\(112\) 0 0
\(113\) 1.42648 0.134192 0.0670961 0.997747i \(-0.478627\pi\)
0.0670961 + 0.997747i \(0.478627\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −17.5731 −1.61092
\(120\) 0 0
\(121\) −10.8453 −0.985940
\(122\) 0 0
\(123\) −3.77786 −0.340639
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.50307 0.133376 0.0666880 0.997774i \(-0.478757\pi\)
0.0666880 + 0.997774i \(0.478757\pi\)
\(128\) 0 0
\(129\) 2.51428 0.221370
\(130\) 0 0
\(131\) 3.85699 0.336987 0.168493 0.985703i \(-0.446110\pi\)
0.168493 + 0.985703i \(0.446110\pi\)
\(132\) 0 0
\(133\) −20.7683 −1.80084
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.5644 1.41519 0.707596 0.706617i \(-0.249780\pi\)
0.707596 + 0.706617i \(0.249780\pi\)
\(138\) 0 0
\(139\) 10.6854 0.906325 0.453163 0.891428i \(-0.350296\pi\)
0.453163 + 0.891428i \(0.350296\pi\)
\(140\) 0 0
\(141\) −3.00868 −0.253376
\(142\) 0 0
\(143\) 0.393270 0.0328869
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.00000 −0.0824786
\(148\) 0 0
\(149\) 4.05012 0.331799 0.165900 0.986143i \(-0.446947\pi\)
0.165900 + 0.986143i \(0.446947\pi\)
\(150\) 0 0
\(151\) 5.02856 0.409218 0.204609 0.978844i \(-0.434408\pi\)
0.204609 + 0.978844i \(0.434408\pi\)
\(152\) 0 0
\(153\) −6.21302 −0.502293
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 24.4961 1.95500 0.977499 0.210940i \(-0.0676526\pi\)
0.977499 + 0.210940i \(0.0676526\pi\)
\(158\) 0 0
\(159\) 9.55573 0.757819
\(160\) 0 0
\(161\) −4.08378 −0.321847
\(162\) 0 0
\(163\) 15.3137 1.19946 0.599731 0.800202i \(-0.295274\pi\)
0.599731 + 0.800202i \(0.295274\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.7770 −1.22086 −0.610430 0.792070i \(-0.709003\pi\)
−0.610430 + 0.792070i \(0.709003\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −7.34271 −0.561511
\(172\) 0 0
\(173\) −14.9706 −1.13819 −0.569095 0.822272i \(-0.692706\pi\)
−0.569095 + 0.822272i \(0.692706\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.393270 −0.0295600
\(178\) 0 0
\(179\) −4.84578 −0.362190 −0.181095 0.983466i \(-0.557964\pi\)
−0.181095 + 0.983466i \(0.557964\pi\)
\(180\) 0 0
\(181\) −7.99912 −0.594570 −0.297285 0.954789i \(-0.596081\pi\)
−0.297285 + 0.954789i \(0.596081\pi\)
\(182\) 0 0
\(183\) −11.0414 −0.816207
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.44339 −0.178679
\(188\) 0 0
\(189\) −2.82843 −0.205738
\(190\) 0 0
\(191\) −20.4260 −1.47798 −0.738988 0.673718i \(-0.764696\pi\)
−0.738988 + 0.673718i \(0.764696\pi\)
\(192\) 0 0
\(193\) 24.0237 1.72926 0.864630 0.502408i \(-0.167553\pi\)
0.864630 + 0.502408i \(0.167553\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.80642 −0.342444 −0.171222 0.985233i \(-0.554771\pi\)
−0.171222 + 0.985233i \(0.554771\pi\)
\(198\) 0 0
\(199\) −14.9403 −1.05909 −0.529546 0.848281i \(-0.677638\pi\)
−0.529546 + 0.848281i \(0.677638\pi\)
\(200\) 0 0
\(201\) −15.5557 −1.09722
\(202\) 0 0
\(203\) −2.34315 −0.164457
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.44383 −0.100353
\(208\) 0 0
\(209\) −2.88767 −0.199744
\(210\) 0 0
\(211\) −1.82799 −0.125844 −0.0629220 0.998018i \(-0.520042\pi\)
−0.0629220 + 0.998018i \(0.520042\pi\)
\(212\) 0 0
\(213\) −6.56440 −0.449786
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.68629 0.318126
\(218\) 0 0
\(219\) −13.6150 −0.920014
\(220\) 0 0
\(221\) −6.21302 −0.417933
\(222\) 0 0
\(223\) −7.07045 −0.473472 −0.236736 0.971574i \(-0.576078\pi\)
−0.236736 + 0.971574i \(0.576078\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.43560 0.360773 0.180387 0.983596i \(-0.442265\pi\)
0.180387 + 0.983596i \(0.442265\pi\)
\(228\) 0 0
\(229\) 24.8147 1.63980 0.819899 0.572508i \(-0.194029\pi\)
0.819899 + 0.572508i \(0.194029\pi\)
\(230\) 0 0
\(231\) −1.11233 −0.0731863
\(232\) 0 0
\(233\) 23.4256 1.53466 0.767331 0.641251i \(-0.221584\pi\)
0.767331 + 0.641251i \(0.221584\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 14.9403 0.970478
\(238\) 0 0
\(239\) −21.7779 −1.40869 −0.704346 0.709856i \(-0.748760\pi\)
−0.704346 + 0.709856i \(0.748760\pi\)
\(240\) 0 0
\(241\) −15.2126 −0.979929 −0.489964 0.871742i \(-0.662990\pi\)
−0.489964 + 0.871742i \(0.662990\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.34271 −0.467205
\(248\) 0 0
\(249\) −16.4633 −1.04332
\(250\) 0 0
\(251\) −17.9399 −1.13236 −0.566178 0.824283i \(-0.691578\pi\)
−0.566178 + 0.824283i \(0.691578\pi\)
\(252\) 0 0
\(253\) −0.567816 −0.0356983
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.88810 0.242533 0.121267 0.992620i \(-0.461304\pi\)
0.121267 + 0.992620i \(0.461304\pi\)
\(258\) 0 0
\(259\) 19.1952 1.19273
\(260\) 0 0
\(261\) −0.828427 −0.0512784
\(262\) 0 0
\(263\) −0.296797 −0.0183013 −0.00915064 0.999958i \(-0.502913\pi\)
−0.00915064 + 0.999958i \(0.502913\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.67674 0.592207
\(268\) 0 0
\(269\) −1.25447 −0.0764864 −0.0382432 0.999268i \(-0.512176\pi\)
−0.0382432 + 0.999268i \(0.512176\pi\)
\(270\) 0 0
\(271\) 9.81510 0.596225 0.298112 0.954531i \(-0.403643\pi\)
0.298112 + 0.954531i \(0.403643\pi\)
\(272\) 0 0
\(273\) −2.82843 −0.171184
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4.35603 −0.261729 −0.130864 0.991400i \(-0.541775\pi\)
−0.130864 + 0.991400i \(0.541775\pi\)
\(278\) 0 0
\(279\) 1.65685 0.0991933
\(280\) 0 0
\(281\) 3.45207 0.205933 0.102967 0.994685i \(-0.467167\pi\)
0.102967 + 0.994685i \(0.467167\pi\)
\(282\) 0 0
\(283\) 2.25937 0.134306 0.0671528 0.997743i \(-0.478608\pi\)
0.0671528 + 0.997743i \(0.478608\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.6854 0.630740
\(288\) 0 0
\(289\) 21.6016 1.27068
\(290\) 0 0
\(291\) −0.0418875 −0.00245549
\(292\) 0 0
\(293\) 19.5358 1.14130 0.570648 0.821195i \(-0.306692\pi\)
0.570648 + 0.821195i \(0.306692\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −0.393270 −0.0228198
\(298\) 0 0
\(299\) −1.44383 −0.0834990
\(300\) 0 0
\(301\) −7.11146 −0.409898
\(302\) 0 0
\(303\) −12.1421 −0.697547
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −27.8142 −1.58744 −0.793721 0.608282i \(-0.791859\pi\)
−0.793721 + 0.608282i \(0.791859\pi\)
\(308\) 0 0
\(309\) 0.0173504 0.000987028 0
\(310\) 0 0
\(311\) 2.10113 0.119144 0.0595719 0.998224i \(-0.481026\pi\)
0.0595719 + 0.998224i \(0.481026\pi\)
\(312\) 0 0
\(313\) 9.64397 0.545109 0.272555 0.962140i \(-0.412131\pi\)
0.272555 + 0.962140i \(0.412131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.1201 −0.905397 −0.452698 0.891664i \(-0.649539\pi\)
−0.452698 + 0.891664i \(0.649539\pi\)
\(318\) 0 0
\(319\) −0.325795 −0.0182410
\(320\) 0 0
\(321\) −2.10113 −0.117273
\(322\) 0 0
\(323\) 45.6204 2.53839
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.21302 −0.343581
\(328\) 0 0
\(329\) 8.50982 0.469161
\(330\) 0 0
\(331\) 13.9537 0.766962 0.383481 0.923549i \(-0.374725\pi\)
0.383481 + 0.923549i \(0.374725\pi\)
\(332\) 0 0
\(333\) 6.78654 0.371900
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 9.66974 0.526744 0.263372 0.964694i \(-0.415165\pi\)
0.263372 + 0.964694i \(0.415165\pi\)
\(338\) 0 0
\(339\) −1.42648 −0.0774759
\(340\) 0 0
\(341\) 0.651591 0.0352856
\(342\) 0 0
\(343\) −16.9706 −0.916324
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.2014 0.547638 0.273819 0.961781i \(-0.411713\pi\)
0.273819 + 0.961781i \(0.411713\pi\)
\(348\) 0 0
\(349\) 28.7402 1.53843 0.769214 0.638992i \(-0.220648\pi\)
0.769214 + 0.638992i \(0.220648\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 20.9067 1.11275 0.556375 0.830931i \(-0.312192\pi\)
0.556375 + 0.830931i \(0.312192\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 17.5731 0.930066
\(358\) 0 0
\(359\) 19.3162 1.01947 0.509736 0.860331i \(-0.329743\pi\)
0.509736 + 0.860331i \(0.329743\pi\)
\(360\) 0 0
\(361\) 34.9153 1.83765
\(362\) 0 0
\(363\) 10.8453 0.569233
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 37.6957 1.96770 0.983851 0.178990i \(-0.0572828\pi\)
0.983851 + 0.178990i \(0.0572828\pi\)
\(368\) 0 0
\(369\) 3.77786 0.196668
\(370\) 0 0
\(371\) −27.0277 −1.40321
\(372\) 0 0
\(373\) 22.4607 1.16297 0.581487 0.813556i \(-0.302471\pi\)
0.581487 + 0.813556i \(0.302471\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.828427 −0.0426662
\(378\) 0 0
\(379\) −24.3133 −1.24889 −0.624444 0.781069i \(-0.714675\pi\)
−0.624444 + 0.781069i \(0.714675\pi\)
\(380\) 0 0
\(381\) −1.50307 −0.0770046
\(382\) 0 0
\(383\) 37.2498 1.90338 0.951688 0.307065i \(-0.0993471\pi\)
0.951688 + 0.307065i \(0.0993471\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.51428 −0.127808
\(388\) 0 0
\(389\) −0.467931 −0.0237250 −0.0118625 0.999930i \(-0.503776\pi\)
−0.0118625 + 0.999930i \(0.503776\pi\)
\(390\) 0 0
\(391\) 8.97056 0.453661
\(392\) 0 0
\(393\) −3.85699 −0.194559
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 34.5263 1.73282 0.866412 0.499329i \(-0.166420\pi\)
0.866412 + 0.499329i \(0.166420\pi\)
\(398\) 0 0
\(399\) 20.7683 1.03972
\(400\) 0 0
\(401\) 31.8781 1.59192 0.795958 0.605351i \(-0.206967\pi\)
0.795958 + 0.605351i \(0.206967\pi\)
\(402\) 0 0
\(403\) 1.65685 0.0825338
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.66894 0.132294
\(408\) 0 0
\(409\) −8.01735 −0.396432 −0.198216 0.980158i \(-0.563515\pi\)
−0.198216 + 0.980158i \(0.563515\pi\)
\(410\) 0 0
\(411\) −16.5644 −0.817062
\(412\) 0 0
\(413\) 1.11233 0.0547344
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.6854 −0.523267
\(418\) 0 0
\(419\) 8.40151 0.410440 0.205220 0.978716i \(-0.434209\pi\)
0.205220 + 0.978716i \(0.434209\pi\)
\(420\) 0 0
\(421\) −11.7514 −0.572728 −0.286364 0.958121i \(-0.592447\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(422\) 0 0
\(423\) 3.00868 0.146287
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 31.2299 1.51132
\(428\) 0 0
\(429\) −0.393270 −0.0189872
\(430\) 0 0
\(431\) −20.5818 −0.991388 −0.495694 0.868497i \(-0.665086\pi\)
−0.495694 + 0.868497i \(0.665086\pi\)
\(432\) 0 0
\(433\) −5.12522 −0.246303 −0.123151 0.992388i \(-0.539300\pi\)
−0.123151 + 0.992388i \(0.539300\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.6016 0.507145
\(438\) 0 0
\(439\) −12.8868 −0.615053 −0.307526 0.951540i \(-0.599501\pi\)
−0.307526 + 0.951540i \(0.599501\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −35.1279 −1.66898 −0.834489 0.551024i \(-0.814237\pi\)
−0.834489 + 0.551024i \(0.814237\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.05012 −0.191564
\(448\) 0 0
\(449\) 18.2213 0.859914 0.429957 0.902849i \(-0.358529\pi\)
0.429957 + 0.902849i \(0.358529\pi\)
\(450\) 0 0
\(451\) 1.48572 0.0699598
\(452\) 0 0
\(453\) −5.02856 −0.236262
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −23.4118 −1.09516 −0.547580 0.836753i \(-0.684451\pi\)
−0.547580 + 0.836753i \(0.684451\pi\)
\(458\) 0 0
\(459\) 6.21302 0.289999
\(460\) 0 0
\(461\) −14.2913 −0.665611 −0.332805 0.942996i \(-0.607995\pi\)
−0.332805 + 0.942996i \(0.607995\pi\)
\(462\) 0 0
\(463\) −23.7152 −1.10214 −0.551070 0.834459i \(-0.685780\pi\)
−0.551070 + 0.834459i \(0.685780\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.8989 1.01336 0.506680 0.862134i \(-0.330873\pi\)
0.506680 + 0.862134i \(0.330873\pi\)
\(468\) 0 0
\(469\) 43.9982 2.03165
\(470\) 0 0
\(471\) −24.4961 −1.12872
\(472\) 0 0
\(473\) −0.988790 −0.0454646
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.55573 −0.437527
\(478\) 0 0
\(479\) −17.0916 −0.780934 −0.390467 0.920617i \(-0.627686\pi\)
−0.390467 + 0.920617i \(0.627686\pi\)
\(480\) 0 0
\(481\) 6.78654 0.309440
\(482\) 0 0
\(483\) 4.08378 0.185818
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.87434 0.0849343 0.0424672 0.999098i \(-0.486478\pi\)
0.0424672 + 0.999098i \(0.486478\pi\)
\(488\) 0 0
\(489\) −15.3137 −0.692510
\(490\) 0 0
\(491\) −10.7704 −0.486063 −0.243031 0.970018i \(-0.578142\pi\)
−0.243031 + 0.970018i \(0.578142\pi\)
\(492\) 0 0
\(493\) 5.14704 0.231811
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 18.5669 0.832841
\(498\) 0 0
\(499\) 33.5259 1.50082 0.750412 0.660971i \(-0.229855\pi\)
0.750412 + 0.660971i \(0.229855\pi\)
\(500\) 0 0
\(501\) 15.7770 0.704864
\(502\) 0 0
\(503\) −7.58473 −0.338186 −0.169093 0.985600i \(-0.554084\pi\)
−0.169093 + 0.985600i \(0.554084\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 38.0145 1.68497 0.842483 0.538724i \(-0.181093\pi\)
0.842483 + 0.538724i \(0.181093\pi\)
\(510\) 0 0
\(511\) 38.5089 1.70354
\(512\) 0 0
\(513\) 7.34271 0.324188
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.18322 0.0520380
\(518\) 0 0
\(519\) 14.9706 0.657135
\(520\) 0 0
\(521\) −18.2420 −0.799197 −0.399599 0.916690i \(-0.630851\pi\)
−0.399599 + 0.916690i \(0.630851\pi\)
\(522\) 0 0
\(523\) 10.1720 0.444791 0.222396 0.974957i \(-0.428612\pi\)
0.222396 + 0.974957i \(0.428612\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.2941 −0.448417
\(528\) 0 0
\(529\) −20.9153 −0.909363
\(530\) 0 0
\(531\) 0.393270 0.0170665
\(532\) 0 0
\(533\) 3.77786 0.163637
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.84578 0.209111
\(538\) 0 0
\(539\) 0.393270 0.0169393
\(540\) 0 0
\(541\) 1.98923 0.0855236 0.0427618 0.999085i \(-0.486384\pi\)
0.0427618 + 0.999085i \(0.486384\pi\)
\(542\) 0 0
\(543\) 7.99912 0.343275
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.31817 0.0563609 0.0281804 0.999603i \(-0.491029\pi\)
0.0281804 + 0.999603i \(0.491029\pi\)
\(548\) 0 0
\(549\) 11.0414 0.471238
\(550\) 0 0
\(551\) 6.08290 0.259140
\(552\) 0 0
\(553\) −42.2576 −1.79698
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.0804 0.511861 0.255931 0.966695i \(-0.417618\pi\)
0.255931 + 0.966695i \(0.417618\pi\)
\(558\) 0 0
\(559\) −2.51428 −0.106343
\(560\) 0 0
\(561\) 2.44339 0.103160
\(562\) 0 0
\(563\) −22.9930 −0.969039 −0.484519 0.874781i \(-0.661005\pi\)
−0.484519 + 0.874781i \(0.661005\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.82843 0.118783
\(568\) 0 0
\(569\) 29.0370 1.21729 0.608647 0.793441i \(-0.291713\pi\)
0.608647 + 0.793441i \(0.291713\pi\)
\(570\) 0 0
\(571\) 5.56950 0.233076 0.116538 0.993186i \(-0.462820\pi\)
0.116538 + 0.993186i \(0.462820\pi\)
\(572\) 0 0
\(573\) 20.4260 0.853310
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −20.2822 −0.844357 −0.422179 0.906513i \(-0.638734\pi\)
−0.422179 + 0.906513i \(0.638734\pi\)
\(578\) 0 0
\(579\) −24.0237 −0.998389
\(580\) 0 0
\(581\) 46.5652 1.93185
\(582\) 0 0
\(583\) −3.75798 −0.155640
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.82377 0.364196 0.182098 0.983280i \(-0.441711\pi\)
0.182098 + 0.983280i \(0.441711\pi\)
\(588\) 0 0
\(589\) −12.1658 −0.501283
\(590\) 0 0
\(591\) 4.80642 0.197710
\(592\) 0 0
\(593\) 10.2213 0.419737 0.209868 0.977730i \(-0.432696\pi\)
0.209868 + 0.977730i \(0.432696\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.9403 0.611467
\(598\) 0 0
\(599\) −18.4925 −0.755582 −0.377791 0.925891i \(-0.623316\pi\)
−0.377791 + 0.925891i \(0.623316\pi\)
\(600\) 0 0
\(601\) 26.0129 1.06109 0.530544 0.847657i \(-0.321988\pi\)
0.530544 + 0.847657i \(0.321988\pi\)
\(602\) 0 0
\(603\) 15.5557 0.633478
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 24.1227 0.979109 0.489554 0.871973i \(-0.337159\pi\)
0.489554 + 0.871973i \(0.337159\pi\)
\(608\) 0 0
\(609\) 2.34315 0.0949491
\(610\) 0 0
\(611\) 3.00868 0.121718
\(612\) 0 0
\(613\) 34.2056 1.38155 0.690775 0.723070i \(-0.257270\pi\)
0.690775 + 0.723070i \(0.257270\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.3622 −0.497682 −0.248841 0.968544i \(-0.580050\pi\)
−0.248841 + 0.968544i \(0.580050\pi\)
\(618\) 0 0
\(619\) −11.6685 −0.468997 −0.234498 0.972117i \(-0.575345\pi\)
−0.234498 + 0.972117i \(0.575345\pi\)
\(620\) 0 0
\(621\) 1.44383 0.0579390
\(622\) 0 0
\(623\) −27.3700 −1.09655
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 2.88767 0.115322
\(628\) 0 0
\(629\) −42.1649 −1.68123
\(630\) 0 0
\(631\) 3.79775 0.151186 0.0755930 0.997139i \(-0.475915\pi\)
0.0755930 + 0.997139i \(0.475915\pi\)
\(632\) 0 0
\(633\) 1.82799 0.0726560
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) 6.56440 0.259684
\(640\) 0 0
\(641\) −6.91008 −0.272932 −0.136466 0.990645i \(-0.543574\pi\)
−0.136466 + 0.990645i \(0.543574\pi\)
\(642\) 0 0
\(643\) −2.50139 −0.0986452 −0.0493226 0.998783i \(-0.515706\pi\)
−0.0493226 + 0.998783i \(0.515706\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.3124 −1.19170 −0.595852 0.803095i \(-0.703185\pi\)
−0.595852 + 0.803095i \(0.703185\pi\)
\(648\) 0 0
\(649\) 0.154661 0.00607098
\(650\) 0 0
\(651\) −4.68629 −0.183670
\(652\) 0 0
\(653\) −33.4537 −1.30915 −0.654573 0.755999i \(-0.727151\pi\)
−0.654573 + 0.755999i \(0.727151\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 13.6150 0.531170
\(658\) 0 0
\(659\) −31.2942 −1.21905 −0.609525 0.792767i \(-0.708640\pi\)
−0.609525 + 0.792767i \(0.708640\pi\)
\(660\) 0 0
\(661\) 40.1119 1.56017 0.780086 0.625672i \(-0.215175\pi\)
0.780086 + 0.625672i \(0.215175\pi\)
\(662\) 0 0
\(663\) 6.21302 0.241294
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1.19611 0.0463136
\(668\) 0 0
\(669\) 7.07045 0.273359
\(670\) 0 0
\(671\) 4.34227 0.167631
\(672\) 0 0
\(673\) 4.99386 0.192499 0.0962496 0.995357i \(-0.469315\pi\)
0.0962496 + 0.995357i \(0.469315\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.0174 −0.615597 −0.307798 0.951452i \(-0.599592\pi\)
−0.307798 + 0.951452i \(0.599592\pi\)
\(678\) 0 0
\(679\) 0.118476 0.00454668
\(680\) 0 0
\(681\) −5.43560 −0.208292
\(682\) 0 0
\(683\) −35.5400 −1.35990 −0.679951 0.733258i \(-0.737999\pi\)
−0.679951 + 0.733258i \(0.737999\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −24.8147 −0.946738
\(688\) 0 0
\(689\) −9.55573 −0.364044
\(690\) 0 0
\(691\) 13.0393 0.496040 0.248020 0.968755i \(-0.420220\pi\)
0.248020 + 0.968755i \(0.420220\pi\)
\(692\) 0 0
\(693\) 1.11233 0.0422541
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −23.4720 −0.889064
\(698\) 0 0
\(699\) −23.4256 −0.886038
\(700\) 0 0
\(701\) −0.502632 −0.0189841 −0.00949207 0.999955i \(-0.503021\pi\)
−0.00949207 + 0.999955i \(0.503021\pi\)
\(702\) 0 0
\(703\) −49.8316 −1.87943
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 34.3431 1.29161
\(708\) 0 0
\(709\) 42.0712 1.58002 0.790009 0.613095i \(-0.210076\pi\)
0.790009 + 0.613095i \(0.210076\pi\)
\(710\) 0 0
\(711\) −14.9403 −0.560306
\(712\) 0 0
\(713\) −2.39222 −0.0895893
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 21.7779 0.813309
\(718\) 0 0
\(719\) 32.7848 1.22267 0.611333 0.791373i \(-0.290634\pi\)
0.611333 + 0.791373i \(0.290634\pi\)
\(720\) 0 0
\(721\) −0.0490743 −0.00182762
\(722\) 0 0
\(723\) 15.2126 0.565762
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −49.5246 −1.83677 −0.918383 0.395692i \(-0.870505\pi\)
−0.918383 + 0.395692i \(0.870505\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.6213 0.577774
\(732\) 0 0
\(733\) −2.11848 −0.0782477 −0.0391238 0.999234i \(-0.512457\pi\)
−0.0391238 + 0.999234i \(0.512457\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.11760 0.225345
\(738\) 0 0
\(739\) −47.7014 −1.75473 −0.877363 0.479827i \(-0.840699\pi\)
−0.877363 + 0.479827i \(0.840699\pi\)
\(740\) 0 0
\(741\) 7.34271 0.269741
\(742\) 0 0
\(743\) 32.8055 1.20352 0.601759 0.798677i \(-0.294467\pi\)
0.601759 + 0.798677i \(0.294467\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 16.4633 0.602360
\(748\) 0 0
\(749\) 5.94288 0.217148
\(750\) 0 0
\(751\) −0.852087 −0.0310931 −0.0155465 0.999879i \(-0.504949\pi\)
−0.0155465 + 0.999879i \(0.504949\pi\)
\(752\) 0 0
\(753\) 17.9399 0.653766
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −6.68454 −0.242954 −0.121477 0.992594i \(-0.538763\pi\)
−0.121477 + 0.992594i \(0.538763\pi\)
\(758\) 0 0
\(759\) 0.567816 0.0206104
\(760\) 0 0
\(761\) −2.92578 −0.106059 −0.0530297 0.998593i \(-0.516888\pi\)
−0.0530297 + 0.998593i \(0.516888\pi\)
\(762\) 0 0
\(763\) 17.5731 0.636188
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.393270 0.0142001
\(768\) 0 0
\(769\) −12.6274 −0.455356 −0.227678 0.973736i \(-0.573113\pi\)
−0.227678 + 0.973736i \(0.573113\pi\)
\(770\) 0 0
\(771\) −3.88810 −0.140027
\(772\) 0 0
\(773\) 15.9454 0.573517 0.286758 0.958003i \(-0.407422\pi\)
0.286758 + 0.958003i \(0.407422\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −19.1952 −0.688625
\(778\) 0 0
\(779\) −27.7398 −0.993880
\(780\) 0 0
\(781\) 2.58158 0.0923763
\(782\) 0 0
\(783\) 0.828427 0.0296056
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 48.5825 1.73178 0.865890 0.500234i \(-0.166753\pi\)
0.865890 + 0.500234i \(0.166753\pi\)
\(788\) 0 0
\(789\) 0.296797 0.0105662
\(790\) 0 0
\(791\) 4.03470 0.143457
\(792\) 0 0
\(793\) 11.0414 0.392093
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 19.8971 0.704792 0.352396 0.935851i \(-0.385367\pi\)
0.352396 + 0.935851i \(0.385367\pi\)
\(798\) 0 0
\(799\) −18.6930 −0.661310
\(800\) 0 0
\(801\) −9.67674 −0.341911
\(802\) 0 0
\(803\) 5.35436 0.188951
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.25447 0.0441595
\(808\) 0 0
\(809\) −12.5487 −0.441189 −0.220595 0.975366i \(-0.570800\pi\)
−0.220595 + 0.975366i \(0.570800\pi\)
\(810\) 0 0
\(811\) 30.9149 1.08557 0.542785 0.839872i \(-0.317370\pi\)
0.542785 + 0.839872i \(0.317370\pi\)
\(812\) 0 0
\(813\) −9.81510 −0.344231
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 18.4616 0.645890
\(818\) 0 0
\(819\) 2.82843 0.0988332
\(820\) 0 0
\(821\) −29.9308 −1.04459 −0.522296 0.852765i \(-0.674924\pi\)
−0.522296 + 0.852765i \(0.674924\pi\)
\(822\) 0 0
\(823\) −16.1831 −0.564109 −0.282055 0.959398i \(-0.591016\pi\)
−0.282055 + 0.959398i \(0.591016\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 54.2022 1.88479 0.942397 0.334497i \(-0.108566\pi\)
0.942397 + 0.334497i \(0.108566\pi\)
\(828\) 0 0
\(829\) −42.2929 −1.46889 −0.734447 0.678666i \(-0.762558\pi\)
−0.734447 + 0.678666i \(0.762558\pi\)
\(830\) 0 0
\(831\) 4.35603 0.151109
\(832\) 0 0
\(833\) −6.21302 −0.215268
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.65685 −0.0572693
\(838\) 0 0
\(839\) 36.7873 1.27004 0.635020 0.772496i \(-0.280992\pi\)
0.635020 + 0.772496i \(0.280992\pi\)
\(840\) 0 0
\(841\) −28.3137 −0.976335
\(842\) 0 0
\(843\) −3.45207 −0.118896
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −30.6753 −1.05401
\(848\) 0 0
\(849\) −2.25937 −0.0775414
\(850\) 0 0
\(851\) −9.79863 −0.335893
\(852\) 0 0
\(853\) −15.4148 −0.527794 −0.263897 0.964551i \(-0.585008\pi\)
−0.263897 + 0.964551i \(0.585008\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.0628221 0.00214596 0.00107298 0.999999i \(-0.499658\pi\)
0.00107298 + 0.999999i \(0.499658\pi\)
\(858\) 0 0
\(859\) 28.6577 0.977787 0.488893 0.872344i \(-0.337401\pi\)
0.488893 + 0.872344i \(0.337401\pi\)
\(860\) 0 0
\(861\) −10.6854 −0.364158
\(862\) 0 0
\(863\) −5.96189 −0.202945 −0.101473 0.994838i \(-0.532355\pi\)
−0.101473 + 0.994838i \(0.532355\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −21.6016 −0.733630
\(868\) 0 0
\(869\) −5.87558 −0.199315
\(870\) 0 0
\(871\) 15.5557 0.527086
\(872\) 0 0
\(873\) 0.0418875 0.00141768
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.70276 −0.226336 −0.113168 0.993576i \(-0.536100\pi\)
−0.113168 + 0.993576i \(0.536100\pi\)
\(878\) 0 0
\(879\) −19.5358 −0.658928
\(880\) 0 0
\(881\) 39.8624 1.34300 0.671500 0.741005i \(-0.265651\pi\)
0.671500 + 0.741005i \(0.265651\pi\)
\(882\) 0 0
\(883\) 21.7131 0.730704 0.365352 0.930869i \(-0.380949\pi\)
0.365352 + 0.930869i \(0.380949\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 51.3757 1.72503 0.862513 0.506035i \(-0.168889\pi\)
0.862513 + 0.506035i \(0.168889\pi\)
\(888\) 0 0
\(889\) 4.25133 0.142585
\(890\) 0 0
\(891\) 0.393270 0.0131750
\(892\) 0 0
\(893\) −22.0918 −0.739275
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 1.44383 0.0482082
\(898\) 0 0
\(899\) −1.37258 −0.0457782
\(900\) 0 0
\(901\) 59.3700 1.97790
\(902\) 0 0
\(903\) 7.11146 0.236654
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −21.3966 −0.710463 −0.355231 0.934778i \(-0.615598\pi\)
−0.355231 + 0.934778i \(0.615598\pi\)
\(908\) 0 0
\(909\) 12.1421 0.402729
\(910\) 0 0
\(911\) −51.0044 −1.68985 −0.844925 0.534884i \(-0.820355\pi\)
−0.844925 + 0.534884i \(0.820355\pi\)
\(912\) 0 0
\(913\) 6.47451 0.214275
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 10.9092 0.360254
\(918\) 0 0
\(919\) 11.3664 0.374942 0.187471 0.982270i \(-0.439971\pi\)
0.187471 + 0.982270i \(0.439971\pi\)
\(920\) 0 0
\(921\) 27.8142 0.916510
\(922\) 0 0
\(923\) 6.56440 0.216070
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −0.0173504 −0.000569861 0
\(928\) 0 0
\(929\) 47.9344 1.57268 0.786338 0.617797i \(-0.211975\pi\)
0.786338 + 0.617797i \(0.211975\pi\)
\(930\) 0 0
\(931\) −7.34271 −0.240648
\(932\) 0 0
\(933\) −2.10113 −0.0687878
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −23.3266 −0.762047 −0.381023 0.924565i \(-0.624428\pi\)
−0.381023 + 0.924565i \(0.624428\pi\)
\(938\) 0 0
\(939\) −9.64397 −0.314719
\(940\) 0 0
\(941\) −39.6316 −1.29195 −0.645977 0.763357i \(-0.723550\pi\)
−0.645977 + 0.763357i \(0.723550\pi\)
\(942\) 0 0
\(943\) −5.45460 −0.177626
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −19.7770 −0.642666 −0.321333 0.946966i \(-0.604131\pi\)
−0.321333 + 0.946966i \(0.604131\pi\)
\(948\) 0 0
\(949\) 13.6150 0.441961
\(950\) 0 0
\(951\) 16.1201 0.522731
\(952\) 0 0
\(953\) −45.2847 −1.46692 −0.733458 0.679735i \(-0.762095\pi\)
−0.733458 + 0.679735i \(0.762095\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0.325795 0.0105315
\(958\) 0 0
\(959\) 46.8512 1.51290
\(960\) 0 0
\(961\) −28.2548 −0.911446
\(962\) 0 0
\(963\) 2.10113 0.0677078
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 13.3903 0.430603 0.215301 0.976548i \(-0.430927\pi\)
0.215301 + 0.976548i \(0.430927\pi\)
\(968\) 0 0
\(969\) −45.6204 −1.46554
\(970\) 0 0
\(971\) −39.6150 −1.27130 −0.635652 0.771975i \(-0.719269\pi\)
−0.635652 + 0.771975i \(0.719269\pi\)
\(972\) 0 0
\(973\) 30.2229 0.968902
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19.2100 −0.614584 −0.307292 0.951615i \(-0.599423\pi\)
−0.307292 + 0.951615i \(0.599423\pi\)
\(978\) 0 0
\(979\) −3.80557 −0.121627
\(980\) 0 0
\(981\) 6.21302 0.198367
\(982\) 0 0
\(983\) −32.3960 −1.03327 −0.516636 0.856205i \(-0.672816\pi\)
−0.516636 + 0.856205i \(0.672816\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −8.50982 −0.270871
\(988\) 0 0
\(989\) 3.63020 0.115434
\(990\) 0 0
\(991\) 10.5107 0.333883 0.166942 0.985967i \(-0.446611\pi\)
0.166942 + 0.985967i \(0.446611\pi\)
\(992\) 0 0
\(993\) −13.9537 −0.442806
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 41.0753 1.30087 0.650433 0.759563i \(-0.274587\pi\)
0.650433 + 0.759563i \(0.274587\pi\)
\(998\) 0 0
\(999\) −6.78654 −0.214717
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.bv.1.4 4
5.2 odd 4 1560.2.l.e.1249.6 yes 8
5.3 odd 4 1560.2.l.e.1249.2 8
5.4 even 2 7800.2.a.bw.1.2 4
15.2 even 4 4680.2.l.f.2809.6 8
15.8 even 4 4680.2.l.f.2809.5 8
20.3 even 4 3120.2.l.o.1249.6 8
20.7 even 4 3120.2.l.o.1249.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.e.1249.2 8 5.3 odd 4
1560.2.l.e.1249.6 yes 8 5.2 odd 4
3120.2.l.o.1249.2 8 20.7 even 4
3120.2.l.o.1249.6 8 20.3 even 4
4680.2.l.f.2809.5 8 15.8 even 4
4680.2.l.f.2809.6 8 15.2 even 4
7800.2.a.bv.1.4 4 1.1 even 1 trivial
7800.2.a.bw.1.2 4 5.4 even 2