Properties

Label 7800.2.a.bt.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
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: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.30056.1
Defining polynomial: \(x^{4} - 11 x^{2} + 26\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
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 1.3
Root \(-2.74983\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -0.633776 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -0.633776 q^{7} +1.00000 q^{9} -0.177949 q^{11} +1.00000 q^{13} +4.48933 q^{17} +0.633776 q^{21} -6.48933 q^{23} -1.00000 q^{27} -3.49966 q^{29} +0.177949 q^{33} +1.75688 q^{37} -1.00000 q^{39} +7.67760 q^{41} -7.49966 q^{43} -3.18827 q^{47} -6.59833 q^{49} -4.48933 q^{51} -1.75688 q^{53} +3.93483 q^{59} +3.01033 q^{61} -0.633776 q^{63} -1.62345 q^{67} +6.48933 q^{69} -4.41005 q^{71} -3.85555 q^{73} +0.112780 q^{77} +9.63309 q^{79} +1.00000 q^{81} -1.72338 q^{83} +3.49966 q^{87} -0.589258 q^{89} -0.633776 q^{91} -4.45457 q^{97} -0.177949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 7 q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{3} - 7 q^{7} + 4 q^{9} + q^{11} + 4 q^{13} - 3 q^{17} + 7 q^{21} - 5 q^{23} - 4 q^{27} + 8 q^{29} - q^{33} - 5 q^{37} - 4 q^{39} + 7 q^{41} - 8 q^{43} - 10 q^{47} + 9 q^{49} + 3 q^{51} + 5 q^{53} + 2 q^{59} + 11 q^{61} - 7 q^{63} - 12 q^{67} + 5 q^{69} + 15 q^{71} + 10 q^{73} - 15 q^{77} - q^{79} + 4 q^{81} - 22 q^{83} - 8 q^{87} + 9 q^{89} - 7 q^{91} - q^{97} + q^{99} + O(q^{100}) \)

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
\(7\) −0.633776 −0.239545 −0.119772 0.992801i \(-0.538216\pi\)
−0.119772 + 0.992801i \(0.538216\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.177949 −0.0536537 −0.0268269 0.999640i \(-0.508540\pi\)
−0.0268269 + 0.999640i \(0.508540\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.48933 1.08882 0.544411 0.838818i \(-0.316753\pi\)
0.544411 + 0.838818i \(0.316753\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0.633776 0.138301
\(22\) 0 0
\(23\) −6.48933 −1.35312 −0.676559 0.736388i \(-0.736530\pi\)
−0.676559 + 0.736388i \(0.736530\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.49966 −0.649870 −0.324935 0.945736i \(-0.605342\pi\)
−0.324935 + 0.945736i \(0.605342\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0.177949 0.0309770
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.75688 0.288830 0.144415 0.989517i \(-0.453870\pi\)
0.144415 + 0.989517i \(0.453870\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 7.67760 1.19904 0.599520 0.800360i \(-0.295358\pi\)
0.599520 + 0.800360i \(0.295358\pi\)
\(42\) 0 0
\(43\) −7.49966 −1.14369 −0.571843 0.820363i \(-0.693772\pi\)
−0.571843 + 0.820363i \(0.693772\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.18827 −0.465058 −0.232529 0.972589i \(-0.574700\pi\)
−0.232529 + 0.972589i \(0.574700\pi\)
\(48\) 0 0
\(49\) −6.59833 −0.942618
\(50\) 0 0
\(51\) −4.48933 −0.628632
\(52\) 0 0
\(53\) −1.75688 −0.241326 −0.120663 0.992694i \(-0.538502\pi\)
−0.120663 + 0.992694i \(0.538502\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.93483 0.512271 0.256136 0.966641i \(-0.417551\pi\)
0.256136 + 0.966641i \(0.417551\pi\)
\(60\) 0 0
\(61\) 3.01033 0.385433 0.192716 0.981255i \(-0.438270\pi\)
0.192716 + 0.981255i \(0.438270\pi\)
\(62\) 0 0
\(63\) −0.633776 −0.0798482
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.62345 −0.198336 −0.0991680 0.995071i \(-0.531618\pi\)
−0.0991680 + 0.995071i \(0.531618\pi\)
\(68\) 0 0
\(69\) 6.48933 0.781224
\(70\) 0 0
\(71\) −4.41005 −0.523377 −0.261689 0.965152i \(-0.584279\pi\)
−0.261689 + 0.965152i \(0.584279\pi\)
\(72\) 0 0
\(73\) −3.85555 −0.451258 −0.225629 0.974213i \(-0.572444\pi\)
−0.225629 + 0.974213i \(0.572444\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.112780 0.0128525
\(78\) 0 0
\(79\) 9.63309 1.08381 0.541903 0.840441i \(-0.317704\pi\)
0.541903 + 0.840441i \(0.317704\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.72338 −0.189165 −0.0945827 0.995517i \(-0.530152\pi\)
−0.0945827 + 0.995517i \(0.530152\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.49966 0.375202
\(88\) 0 0
\(89\) −0.589258 −0.0624612 −0.0312306 0.999512i \(-0.509943\pi\)
−0.0312306 + 0.999512i \(0.509943\pi\)
\(90\) 0 0
\(91\) −0.633776 −0.0664378
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −4.45457 −0.452293 −0.226147 0.974093i \(-0.572613\pi\)
−0.226147 + 0.974093i \(0.572613\pi\)
\(98\) 0 0
\(99\) −0.177949 −0.0178846
\(100\) 0 0
\(101\) 16.4783 1.63965 0.819827 0.572612i \(-0.194070\pi\)
0.819827 + 0.572612i \(0.194070\pi\)
\(102\) 0 0
\(103\) 5.86966 0.578355 0.289177 0.957276i \(-0.406618\pi\)
0.289177 + 0.957276i \(0.406618\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.509981 0.0493017 0.0246509 0.999696i \(-0.492153\pi\)
0.0246509 + 0.999696i \(0.492153\pi\)
\(108\) 0 0
\(109\) 6.35590 0.608785 0.304392 0.952547i \(-0.401547\pi\)
0.304392 + 0.952547i \(0.401547\pi\)
\(110\) 0 0
\(111\) −1.75688 −0.166756
\(112\) 0 0
\(113\) −9.71111 −0.913544 −0.456772 0.889584i \(-0.650995\pi\)
−0.456772 + 0.889584i \(0.650995\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −2.84523 −0.260822
\(120\) 0 0
\(121\) −10.9683 −0.997121
\(122\) 0 0
\(123\) −7.67760 −0.692266
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.1231 −0.987016 −0.493508 0.869741i \(-0.664286\pi\)
−0.493508 + 0.869741i \(0.664286\pi\)
\(128\) 0 0
\(129\) 7.49966 0.660308
\(130\) 0 0
\(131\) 12.9439 1.13091 0.565457 0.824778i \(-0.308700\pi\)
0.565457 + 0.824778i \(0.308700\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.7904 −1.00732 −0.503660 0.863902i \(-0.668014\pi\)
−0.503660 + 0.863902i \(0.668014\pi\)
\(138\) 0 0
\(139\) 0.112780 0.00956587 0.00478293 0.999989i \(-0.498478\pi\)
0.00478293 + 0.999989i \(0.498478\pi\)
\(140\) 0 0
\(141\) 3.18827 0.268501
\(142\) 0 0
\(143\) −0.177949 −0.0148809
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.59833 0.544221
\(148\) 0 0
\(149\) 2.30829 0.189102 0.0945512 0.995520i \(-0.469858\pi\)
0.0945512 + 0.995520i \(0.469858\pi\)
\(150\) 0 0
\(151\) −17.7318 −1.44299 −0.721495 0.692420i \(-0.756545\pi\)
−0.721495 + 0.692420i \(0.756545\pi\)
\(152\) 0 0
\(153\) 4.48933 0.362941
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.8549 1.02593 0.512965 0.858410i \(-0.328547\pi\)
0.512965 + 0.858410i \(0.328547\pi\)
\(158\) 0 0
\(159\) 1.75688 0.139330
\(160\) 0 0
\(161\) 4.11278 0.324132
\(162\) 0 0
\(163\) −14.3308 −1.12247 −0.561237 0.827655i \(-0.689674\pi\)
−0.561237 + 0.827655i \(0.689674\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.43449 0.111004 0.0555019 0.998459i \(-0.482324\pi\)
0.0555019 + 0.998459i \(0.482324\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.24690 −0.0948001 −0.0474000 0.998876i \(-0.515094\pi\)
−0.0474000 + 0.998876i \(0.515094\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.93483 −0.295760
\(178\) 0 0
\(179\) −7.87621 −0.588695 −0.294348 0.955698i \(-0.595102\pi\)
−0.294348 + 0.955698i \(0.595102\pi\)
\(180\) 0 0
\(181\) 10.3796 0.771513 0.385756 0.922601i \(-0.373941\pi\)
0.385756 + 0.922601i \(0.373941\pi\)
\(182\) 0 0
\(183\) −3.01033 −0.222530
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.798873 −0.0584194
\(188\) 0 0
\(189\) 0.633776 0.0461004
\(190\) 0 0
\(191\) 13.7318 0.993595 0.496798 0.867866i \(-0.334509\pi\)
0.496798 + 0.867866i \(0.334509\pi\)
\(192\) 0 0
\(193\) −6.34488 −0.456715 −0.228357 0.973577i \(-0.573335\pi\)
−0.228357 + 0.973577i \(0.573335\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.2966 −1.51732 −0.758659 0.651487i \(-0.774145\pi\)
−0.758659 + 0.651487i \(0.774145\pi\)
\(198\) 0 0
\(199\) 11.2108 0.794710 0.397355 0.917665i \(-0.369928\pi\)
0.397355 + 0.917665i \(0.369928\pi\)
\(200\) 0 0
\(201\) 1.62345 0.114509
\(202\) 0 0
\(203\) 2.21800 0.155673
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −6.48933 −0.451040
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −20.2810 −1.39620 −0.698100 0.716000i \(-0.745971\pi\)
−0.698100 + 0.716000i \(0.745971\pi\)
\(212\) 0 0
\(213\) 4.41005 0.302172
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 3.85555 0.260534
\(220\) 0 0
\(221\) 4.48933 0.301985
\(222\) 0 0
\(223\) 11.3900 0.762729 0.381364 0.924425i \(-0.375454\pi\)
0.381364 + 0.924425i \(0.375454\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.7020 −0.975809 −0.487904 0.872897i \(-0.662238\pi\)
−0.487904 + 0.872897i \(0.662238\pi\)
\(228\) 0 0
\(229\) 9.84145 0.650341 0.325171 0.945655i \(-0.394578\pi\)
0.325171 + 0.945655i \(0.394578\pi\)
\(230\) 0 0
\(231\) −0.112780 −0.00742038
\(232\) 0 0
\(233\) 22.8439 1.49655 0.748275 0.663388i \(-0.230882\pi\)
0.748275 + 0.663388i \(0.230882\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −9.63309 −0.625736
\(238\) 0 0
\(239\) −24.1907 −1.56476 −0.782382 0.622798i \(-0.785996\pi\)
−0.782382 + 0.622798i \(0.785996\pi\)
\(240\) 0 0
\(241\) −22.8896 −1.47445 −0.737225 0.675647i \(-0.763864\pi\)
−0.737225 + 0.675647i \(0.763864\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 1.72338 0.109215
\(250\) 0 0
\(251\) −11.6763 −0.737005 −0.368502 0.929627i \(-0.620129\pi\)
−0.368502 + 0.929627i \(0.620129\pi\)
\(252\) 0 0
\(253\) 1.15477 0.0725999
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.9993 −1.55941 −0.779707 0.626144i \(-0.784632\pi\)
−0.779707 + 0.626144i \(0.784632\pi\)
\(258\) 0 0
\(259\) −1.11347 −0.0691876
\(260\) 0 0
\(261\) −3.49966 −0.216623
\(262\) 0 0
\(263\) −7.12965 −0.439633 −0.219817 0.975541i \(-0.570546\pi\)
−0.219817 + 0.975541i \(0.570546\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.589258 0.0360620
\(268\) 0 0
\(269\) −8.47832 −0.516932 −0.258466 0.966020i \(-0.583217\pi\)
−0.258466 + 0.966020i \(0.583217\pi\)
\(270\) 0 0
\(271\) 5.60142 0.340262 0.170131 0.985421i \(-0.445581\pi\)
0.170131 + 0.985421i \(0.445581\pi\)
\(272\) 0 0
\(273\) 0.633776 0.0383579
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −24.2991 −1.45999 −0.729996 0.683451i \(-0.760478\pi\)
−0.729996 + 0.683451i \(0.760478\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.6318 0.693897 0.346948 0.937884i \(-0.387218\pi\)
0.346948 + 0.937884i \(0.387218\pi\)
\(282\) 0 0
\(283\) 0.197345 0.0117310 0.00586549 0.999983i \(-0.498133\pi\)
0.00586549 + 0.999983i \(0.498133\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.86588 −0.287224
\(288\) 0 0
\(289\) 3.15408 0.185534
\(290\) 0 0
\(291\) 4.45457 0.261132
\(292\) 0 0
\(293\) 29.3918 1.71709 0.858544 0.512740i \(-0.171370\pi\)
0.858544 + 0.512740i \(0.171370\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0.177949 0.0103257
\(298\) 0 0
\(299\) −6.48933 −0.375288
\(300\) 0 0
\(301\) 4.75310 0.273964
\(302\) 0 0
\(303\) −16.4783 −0.946654
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −29.1997 −1.66652 −0.833259 0.552883i \(-0.813528\pi\)
−0.833259 + 0.552883i \(0.813528\pi\)
\(308\) 0 0
\(309\) −5.86966 −0.333913
\(310\) 0 0
\(311\) −13.3346 −0.756133 −0.378067 0.925778i \(-0.623411\pi\)
−0.378067 + 0.925778i \(0.623411\pi\)
\(312\) 0 0
\(313\) −5.16441 −0.291910 −0.145955 0.989291i \(-0.546625\pi\)
−0.145955 + 0.989291i \(0.546625\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −28.3461 −1.59208 −0.796039 0.605245i \(-0.793075\pi\)
−0.796039 + 0.605245i \(0.793075\pi\)
\(318\) 0 0
\(319\) 0.622761 0.0348679
\(320\) 0 0
\(321\) −0.509981 −0.0284644
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.35590 −0.351482
\(328\) 0 0
\(329\) 2.02065 0.111402
\(330\) 0 0
\(331\) −11.1296 −0.611741 −0.305870 0.952073i \(-0.598947\pi\)
−0.305870 + 0.952073i \(0.598947\pi\)
\(332\) 0 0
\(333\) 1.75688 0.0962765
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 12.0529 0.656563 0.328282 0.944580i \(-0.393530\pi\)
0.328282 + 0.944580i \(0.393530\pi\)
\(338\) 0 0
\(339\) 9.71111 0.527435
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 8.61829 0.465344
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.62654 0.409414 0.204707 0.978823i \(-0.434376\pi\)
0.204707 + 0.978823i \(0.434376\pi\)
\(348\) 0 0
\(349\) −15.2455 −0.816074 −0.408037 0.912965i \(-0.633787\pi\)
−0.408037 + 0.912965i \(0.633787\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −4.83238 −0.257201 −0.128601 0.991696i \(-0.541049\pi\)
−0.128601 + 0.991696i \(0.541049\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.84523 0.150585
\(358\) 0 0
\(359\) 7.25528 0.382919 0.191460 0.981501i \(-0.438678\pi\)
0.191460 + 0.981501i \(0.438678\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 10.9683 0.575688
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −33.5808 −1.75290 −0.876451 0.481491i \(-0.840095\pi\)
−0.876451 + 0.481491i \(0.840095\pi\)
\(368\) 0 0
\(369\) 7.67760 0.399680
\(370\) 0 0
\(371\) 1.11347 0.0578084
\(372\) 0 0
\(373\) 2.78131 0.144011 0.0720055 0.997404i \(-0.477060\pi\)
0.0720055 + 0.997404i \(0.477060\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.49966 −0.180241
\(378\) 0 0
\(379\) −34.0268 −1.74784 −0.873921 0.486069i \(-0.838430\pi\)
−0.873921 + 0.486069i \(0.838430\pi\)
\(380\) 0 0
\(381\) 11.1231 0.569854
\(382\) 0 0
\(383\) −8.45332 −0.431944 −0.215972 0.976400i \(-0.569292\pi\)
−0.215972 + 0.976400i \(0.569292\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −7.49966 −0.381229
\(388\) 0 0
\(389\) −14.2991 −0.724994 −0.362497 0.931985i \(-0.618076\pi\)
−0.362497 + 0.931985i \(0.618076\pi\)
\(390\) 0 0
\(391\) −29.1327 −1.47331
\(392\) 0 0
\(393\) −12.9439 −0.652933
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3.97488 0.199493 0.0997467 0.995013i \(-0.468197\pi\)
0.0997467 + 0.995013i \(0.468197\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10.2560 −0.512159 −0.256079 0.966656i \(-0.582431\pi\)
−0.256079 + 0.966656i \(0.582431\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.312636 −0.0154968
\(408\) 0 0
\(409\) 19.6296 0.970623 0.485311 0.874341i \(-0.338706\pi\)
0.485311 + 0.874341i \(0.338706\pi\)
\(410\) 0 0
\(411\) 11.7904 0.581577
\(412\) 0 0
\(413\) −2.49380 −0.122712
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.112780 −0.00552286
\(418\) 0 0
\(419\) 23.7238 1.15899 0.579493 0.814977i \(-0.303251\pi\)
0.579493 + 0.814977i \(0.303251\pi\)
\(420\) 0 0
\(421\) 17.8697 0.870914 0.435457 0.900210i \(-0.356587\pi\)
0.435457 + 0.900210i \(0.356587\pi\)
\(422\) 0 0
\(423\) −3.18827 −0.155019
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.90787 −0.0923284
\(428\) 0 0
\(429\) 0.177949 0.00859147
\(430\) 0 0
\(431\) 35.9476 1.73153 0.865767 0.500448i \(-0.166831\pi\)
0.865767 + 0.500448i \(0.166831\pi\)
\(432\) 0 0
\(433\) −8.21396 −0.394738 −0.197369 0.980329i \(-0.563240\pi\)
−0.197369 + 0.980329i \(0.563240\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −25.0914 −1.19755 −0.598775 0.800918i \(-0.704345\pi\)
−0.598775 + 0.800918i \(0.704345\pi\)
\(440\) 0 0
\(441\) −6.59833 −0.314206
\(442\) 0 0
\(443\) 2.75619 0.130951 0.0654753 0.997854i \(-0.479144\pi\)
0.0654753 + 0.997854i \(0.479144\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.30829 −0.109178
\(448\) 0 0
\(449\) 39.7639 1.87657 0.938287 0.345858i \(-0.112412\pi\)
0.938287 + 0.345858i \(0.112412\pi\)
\(450\) 0 0
\(451\) −1.36622 −0.0643330
\(452\) 0 0
\(453\) 17.7318 0.833111
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 8.72143 0.407971 0.203986 0.978974i \(-0.434610\pi\)
0.203986 + 0.978974i \(0.434610\pi\)
\(458\) 0 0
\(459\) −4.48933 −0.209544
\(460\) 0 0
\(461\) 17.5332 0.816601 0.408300 0.912848i \(-0.366122\pi\)
0.408300 + 0.912848i \(0.366122\pi\)
\(462\) 0 0
\(463\) 18.1049 0.841404 0.420702 0.907199i \(-0.361784\pi\)
0.420702 + 0.907199i \(0.361784\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.0451 0.511106 0.255553 0.966795i \(-0.417743\pi\)
0.255553 + 0.966795i \(0.417743\pi\)
\(468\) 0 0
\(469\) 1.02890 0.0475103
\(470\) 0 0
\(471\) −12.8549 −0.592321
\(472\) 0 0
\(473\) 1.33456 0.0613631
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.75688 −0.0804421
\(478\) 0 0
\(479\) −33.3887 −1.52557 −0.762785 0.646653i \(-0.776168\pi\)
−0.762785 + 0.646653i \(0.776168\pi\)
\(480\) 0 0
\(481\) 1.75688 0.0801069
\(482\) 0 0
\(483\) −4.11278 −0.187138
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −35.7414 −1.61960 −0.809799 0.586708i \(-0.800424\pi\)
−0.809799 + 0.586708i \(0.800424\pi\)
\(488\) 0 0
\(489\) 14.3308 0.648060
\(490\) 0 0
\(491\) 36.9914 1.66940 0.834699 0.550706i \(-0.185642\pi\)
0.834699 + 0.550706i \(0.185642\pi\)
\(492\) 0 0
\(493\) −15.7111 −0.707593
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.79498 0.125372
\(498\) 0 0
\(499\) −20.0670 −0.898323 −0.449161 0.893451i \(-0.648277\pi\)
−0.449161 + 0.893451i \(0.648277\pi\)
\(500\) 0 0
\(501\) −1.43449 −0.0640881
\(502\) 0 0
\(503\) −15.3332 −0.683673 −0.341836 0.939759i \(-0.611049\pi\)
−0.341836 + 0.939759i \(0.611049\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 30.0476 1.33184 0.665918 0.746025i \(-0.268040\pi\)
0.665918 + 0.746025i \(0.268040\pi\)
\(510\) 0 0
\(511\) 2.44356 0.108097
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.567351 0.0249521
\(518\) 0 0
\(519\) 1.24690 0.0547328
\(520\) 0 0
\(521\) −30.8263 −1.35052 −0.675262 0.737578i \(-0.735970\pi\)
−0.675262 + 0.737578i \(0.735970\pi\)
\(522\) 0 0
\(523\) −12.0141 −0.525340 −0.262670 0.964886i \(-0.584603\pi\)
−0.262670 + 0.964886i \(0.584603\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 19.1114 0.830931
\(530\) 0 0
\(531\) 3.93483 0.170757
\(532\) 0 0
\(533\) 7.67760 0.332554
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 7.87621 0.339883
\(538\) 0 0
\(539\) 1.17417 0.0505750
\(540\) 0 0
\(541\) 16.3132 0.701360 0.350680 0.936495i \(-0.385950\pi\)
0.350680 + 0.936495i \(0.385950\pi\)
\(542\) 0 0
\(543\) −10.3796 −0.445433
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.239667 −0.0102474 −0.00512371 0.999987i \(-0.501631\pi\)
−0.00512371 + 0.999987i \(0.501631\pi\)
\(548\) 0 0
\(549\) 3.01033 0.128478
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −6.10522 −0.259620
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.0304 −0.425002 −0.212501 0.977161i \(-0.568161\pi\)
−0.212501 + 0.977161i \(0.568161\pi\)
\(558\) 0 0
\(559\) −7.49966 −0.317202
\(560\) 0 0
\(561\) 0.798873 0.0337284
\(562\) 0 0
\(563\) 0.310125 0.0130702 0.00653511 0.999979i \(-0.497920\pi\)
0.00653511 + 0.999979i \(0.497920\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.633776 −0.0266161
\(568\) 0 0
\(569\) 12.2850 0.515014 0.257507 0.966276i \(-0.417099\pi\)
0.257507 + 0.966276i \(0.417099\pi\)
\(570\) 0 0
\(571\) −31.6124 −1.32294 −0.661470 0.749972i \(-0.730067\pi\)
−0.661470 + 0.749972i \(0.730067\pi\)
\(572\) 0 0
\(573\) −13.7318 −0.573652
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −6.36691 −0.265058 −0.132529 0.991179i \(-0.542310\pi\)
−0.132529 + 0.991179i \(0.542310\pi\)
\(578\) 0 0
\(579\) 6.34488 0.263684
\(580\) 0 0
\(581\) 1.09224 0.0453136
\(582\) 0 0
\(583\) 0.312636 0.0129481
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.8103 −0.611288 −0.305644 0.952146i \(-0.598872\pi\)
−0.305644 + 0.952146i \(0.598872\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 21.2966 0.876024
\(592\) 0 0
\(593\) −33.9864 −1.39565 −0.697826 0.716267i \(-0.745849\pi\)
−0.697826 + 0.716267i \(0.745849\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.2108 −0.458826
\(598\) 0 0
\(599\) −1.10900 −0.0453124 −0.0226562 0.999743i \(-0.507212\pi\)
−0.0226562 + 0.999743i \(0.507212\pi\)
\(600\) 0 0
\(601\) −47.9670 −1.95661 −0.978306 0.207163i \(-0.933577\pi\)
−0.978306 + 0.207163i \(0.933577\pi\)
\(602\) 0 0
\(603\) −1.62345 −0.0661120
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −35.5319 −1.44220 −0.721098 0.692833i \(-0.756362\pi\)
−0.721098 + 0.692833i \(0.756362\pi\)
\(608\) 0 0
\(609\) −2.21800 −0.0898778
\(610\) 0 0
\(611\) −3.18827 −0.128984
\(612\) 0 0
\(613\) −20.4955 −0.827806 −0.413903 0.910321i \(-0.635835\pi\)
−0.413903 + 0.910321i \(0.635835\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −10.6119 −0.427218 −0.213609 0.976919i \(-0.568522\pi\)
−0.213609 + 0.976919i \(0.568522\pi\)
\(618\) 0 0
\(619\) −28.5312 −1.14677 −0.573383 0.819287i \(-0.694369\pi\)
−0.573383 + 0.819287i \(0.694369\pi\)
\(620\) 0 0
\(621\) 6.48933 0.260408
\(622\) 0 0
\(623\) 0.373457 0.0149623
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.88722 0.314484
\(630\) 0 0
\(631\) −7.71111 −0.306974 −0.153487 0.988151i \(-0.549050\pi\)
−0.153487 + 0.988151i \(0.549050\pi\)
\(632\) 0 0
\(633\) 20.2810 0.806096
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.59833 −0.261435
\(638\) 0 0
\(639\) −4.41005 −0.174459
\(640\) 0 0
\(641\) −27.5124 −1.08667 −0.543337 0.839515i \(-0.682839\pi\)
−0.543337 + 0.839515i \(0.682839\pi\)
\(642\) 0 0
\(643\) 24.1798 0.953558 0.476779 0.879023i \(-0.341804\pi\)
0.476779 + 0.879023i \(0.341804\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 27.9347 1.09823 0.549113 0.835748i \(-0.314966\pi\)
0.549113 + 0.835748i \(0.314966\pi\)
\(648\) 0 0
\(649\) −0.700200 −0.0274853
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −27.2868 −1.06782 −0.533908 0.845543i \(-0.679277\pi\)
−0.533908 + 0.845543i \(0.679277\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.85555 −0.150419
\(658\) 0 0
\(659\) −30.3198 −1.18109 −0.590545 0.807005i \(-0.701087\pi\)
−0.590545 + 0.807005i \(0.701087\pi\)
\(660\) 0 0
\(661\) 16.7104 0.649960 0.324980 0.945721i \(-0.394642\pi\)
0.324980 + 0.945721i \(0.394642\pi\)
\(662\) 0 0
\(663\) −4.48933 −0.174351
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 22.7104 0.879351
\(668\) 0 0
\(669\) −11.3900 −0.440362
\(670\) 0 0
\(671\) −0.535685 −0.0206799
\(672\) 0 0
\(673\) 0.950445 0.0366370 0.0183185 0.999832i \(-0.494169\pi\)
0.0183185 + 0.999832i \(0.494169\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.1991 1.31438 0.657188 0.753726i \(-0.271746\pi\)
0.657188 + 0.753726i \(0.271746\pi\)
\(678\) 0 0
\(679\) 2.82320 0.108344
\(680\) 0 0
\(681\) 14.7020 0.563383
\(682\) 0 0
\(683\) 5.68208 0.217419 0.108709 0.994074i \(-0.465328\pi\)
0.108709 + 0.994074i \(0.465328\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −9.84145 −0.375475
\(688\) 0 0
\(689\) −1.75688 −0.0669319
\(690\) 0 0
\(691\) −13.7795 −0.524197 −0.262098 0.965041i \(-0.584414\pi\)
−0.262098 + 0.965041i \(0.584414\pi\)
\(692\) 0 0
\(693\) 0.112780 0.00428416
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 34.4673 1.30554
\(698\) 0 0
\(699\) −22.8439 −0.864034
\(700\) 0 0
\(701\) 20.4113 0.770924 0.385462 0.922724i \(-0.374042\pi\)
0.385462 + 0.922724i \(0.374042\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.4436 −0.392770
\(708\) 0 0
\(709\) 3.17852 0.119372 0.0596858 0.998217i \(-0.480990\pi\)
0.0596858 + 0.998217i \(0.480990\pi\)
\(710\) 0 0
\(711\) 9.63309 0.361269
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 24.1907 0.903417
\(718\) 0 0
\(719\) −40.5312 −1.51156 −0.755780 0.654826i \(-0.772742\pi\)
−0.755780 + 0.654826i \(0.772742\pi\)
\(720\) 0 0
\(721\) −3.72005 −0.138542
\(722\) 0 0
\(723\) 22.8896 0.851274
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −4.39066 −0.162840 −0.0814202 0.996680i \(-0.525946\pi\)
−0.0814202 + 0.996680i \(0.525946\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −33.6684 −1.24527
\(732\) 0 0
\(733\) −30.1823 −1.11481 −0.557404 0.830241i \(-0.688203\pi\)
−0.557404 + 0.830241i \(0.688203\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.288892 0.0106415
\(738\) 0 0
\(739\) −49.1565 −1.80825 −0.904125 0.427267i \(-0.859476\pi\)
−0.904125 + 0.427267i \(0.859476\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.8317 0.800927 0.400463 0.916313i \(-0.368849\pi\)
0.400463 + 0.916313i \(0.368849\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.72338 −0.0630551
\(748\) 0 0
\(749\) −0.323214 −0.0118100
\(750\) 0 0
\(751\) −22.8170 −0.832605 −0.416302 0.909226i \(-0.636674\pi\)
−0.416302 + 0.909226i \(0.636674\pi\)
\(752\) 0 0
\(753\) 11.6763 0.425510
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −11.4649 −0.416699 −0.208349 0.978054i \(-0.566809\pi\)
−0.208349 + 0.978054i \(0.566809\pi\)
\(758\) 0 0
\(759\) −1.15477 −0.0419156
\(760\) 0 0
\(761\) −26.9005 −0.975143 −0.487571 0.873083i \(-0.662117\pi\)
−0.487571 + 0.873083i \(0.662117\pi\)
\(762\) 0 0
\(763\) −4.02821 −0.145831
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.93483 0.142079
\(768\) 0 0
\(769\) 12.9298 0.466260 0.233130 0.972446i \(-0.425103\pi\)
0.233130 + 0.972446i \(0.425103\pi\)
\(770\) 0 0
\(771\) 24.9993 0.900328
\(772\) 0 0
\(773\) −7.56231 −0.271998 −0.135999 0.990709i \(-0.543424\pi\)
−0.135999 + 0.990709i \(0.543424\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.11347 0.0399455
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0.784766 0.0280811
\(782\) 0 0
\(783\) 3.49966 0.125067
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 53.3318 1.90107 0.950537 0.310612i \(-0.100534\pi\)
0.950537 + 0.310612i \(0.100534\pi\)
\(788\) 0 0
\(789\) 7.12965 0.253822
\(790\) 0 0
\(791\) 6.15466 0.218835
\(792\) 0 0
\(793\) 3.01033 0.106900
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.9391 −1.66267 −0.831334 0.555774i \(-0.812422\pi\)
−0.831334 + 0.555774i \(0.812422\pi\)
\(798\) 0 0
\(799\) −14.3132 −0.506365
\(800\) 0 0
\(801\) −0.589258 −0.0208204
\(802\) 0 0
\(803\) 0.686093 0.0242117
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 8.47832 0.298451
\(808\) 0 0
\(809\) 18.1365 0.637646 0.318823 0.947814i \(-0.396712\pi\)
0.318823 + 0.947814i \(0.396712\pi\)
\(810\) 0 0
\(811\) 50.6664 1.77914 0.889568 0.456802i \(-0.151005\pi\)
0.889568 + 0.456802i \(0.151005\pi\)
\(812\) 0 0
\(813\) −5.60142 −0.196450
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −0.633776 −0.0221459
\(820\) 0 0
\(821\) 36.1986 1.26334 0.631670 0.775237i \(-0.282370\pi\)
0.631670 + 0.775237i \(0.282370\pi\)
\(822\) 0 0
\(823\) 0.307033 0.0107025 0.00535124 0.999986i \(-0.498297\pi\)
0.00535124 + 0.999986i \(0.498297\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 55.9733 1.94638 0.973191 0.230000i \(-0.0738727\pi\)
0.973191 + 0.230000i \(0.0738727\pi\)
\(828\) 0 0
\(829\) −37.1912 −1.29171 −0.645853 0.763462i \(-0.723498\pi\)
−0.645853 + 0.763462i \(0.723498\pi\)
\(830\) 0 0
\(831\) 24.2991 0.842927
\(832\) 0 0
\(833\) −29.6221 −1.02634
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 31.2570 1.07911 0.539556 0.841950i \(-0.318592\pi\)
0.539556 + 0.841950i \(0.318592\pi\)
\(840\) 0 0
\(841\) −16.7524 −0.577669
\(842\) 0 0
\(843\) −11.6318 −0.400622
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 6.95146 0.238855
\(848\) 0 0
\(849\) −0.197345 −0.00677288
\(850\) 0 0
\(851\) −11.4010 −0.390821
\(852\) 0 0
\(853\) 37.7066 1.29105 0.645525 0.763739i \(-0.276638\pi\)
0.645525 + 0.763739i \(0.276638\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −19.5364 −0.667350 −0.333675 0.942688i \(-0.608289\pi\)
−0.333675 + 0.942688i \(0.608289\pi\)
\(858\) 0 0
\(859\) 34.0340 1.16122 0.580612 0.814180i \(-0.302813\pi\)
0.580612 + 0.814180i \(0.302813\pi\)
\(860\) 0 0
\(861\) 4.86588 0.165829
\(862\) 0 0
\(863\) −16.9482 −0.576925 −0.288463 0.957491i \(-0.593144\pi\)
−0.288463 + 0.957491i \(0.593144\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −3.15408 −0.107118
\(868\) 0 0
\(869\) −1.71420 −0.0581503
\(870\) 0 0
\(871\) −1.62345 −0.0550085
\(872\) 0 0
\(873\) −4.45457 −0.150764
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30.3339 1.02430 0.512151 0.858895i \(-0.328849\pi\)
0.512151 + 0.858895i \(0.328849\pi\)
\(878\) 0 0
\(879\) −29.3918 −0.991361
\(880\) 0 0
\(881\) −8.66544 −0.291946 −0.145973 0.989289i \(-0.546631\pi\)
−0.145973 + 0.989289i \(0.546631\pi\)
\(882\) 0 0
\(883\) −12.6898 −0.427045 −0.213522 0.976938i \(-0.568494\pi\)
−0.213522 + 0.976938i \(0.568494\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 41.8638 1.40565 0.702825 0.711363i \(-0.251922\pi\)
0.702825 + 0.711363i \(0.251922\pi\)
\(888\) 0 0
\(889\) 7.04955 0.236434
\(890\) 0 0
\(891\) −0.177949 −0.00596153
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.48933 0.216672
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −7.88722 −0.262761
\(902\) 0 0
\(903\) −4.75310 −0.158173
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 19.2531 0.639288 0.319644 0.947538i \(-0.396437\pi\)
0.319644 + 0.947538i \(0.396437\pi\)
\(908\) 0 0
\(909\) 16.4783 0.546551
\(910\) 0 0
\(911\) −9.30885 −0.308416 −0.154208 0.988038i \(-0.549283\pi\)
−0.154208 + 0.988038i \(0.549283\pi\)
\(912\) 0 0
\(913\) 0.306674 0.0101494
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −8.20353 −0.270904
\(918\) 0 0
\(919\) −13.9282 −0.459448 −0.229724 0.973256i \(-0.573782\pi\)
−0.229724 + 0.973256i \(0.573782\pi\)
\(920\) 0 0
\(921\) 29.1997 0.962164
\(922\) 0 0
\(923\) −4.41005 −0.145159
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 5.86966 0.192785
\(928\) 0 0
\(929\) −10.4734 −0.343621 −0.171810 0.985130i \(-0.554962\pi\)
−0.171810 + 0.985130i \(0.554962\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 13.3346 0.436554
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 6.63825 0.216862 0.108431 0.994104i \(-0.465417\pi\)
0.108431 + 0.994104i \(0.465417\pi\)
\(938\) 0 0
\(939\) 5.16441 0.168534
\(940\) 0 0
\(941\) 43.5538 1.41981 0.709907 0.704296i \(-0.248737\pi\)
0.709907 + 0.704296i \(0.248737\pi\)
\(942\) 0 0
\(943\) −49.8225 −1.62244
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −29.8379 −0.969601 −0.484800 0.874625i \(-0.661108\pi\)
−0.484800 + 0.874625i \(0.661108\pi\)
\(948\) 0 0
\(949\) −3.85555 −0.125157
\(950\) 0 0
\(951\) 28.3461 0.919187
\(952\) 0 0
\(953\) 16.4285 0.532172 0.266086 0.963949i \(-0.414270\pi\)
0.266086 + 0.963949i \(0.414270\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −0.622761 −0.0201310
\(958\) 0 0
\(959\) 7.47246 0.241298
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0.509981 0.0164339
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −39.1011 −1.25741 −0.628703 0.777646i \(-0.716414\pi\)
−0.628703 + 0.777646i \(0.716414\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 45.0240 1.44489 0.722444 0.691429i \(-0.243019\pi\)
0.722444 + 0.691429i \(0.243019\pi\)
\(972\) 0 0
\(973\) −0.0714772 −0.00229145
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 26.5616 0.849782 0.424891 0.905245i \(-0.360312\pi\)
0.424891 + 0.905245i \(0.360312\pi\)
\(978\) 0 0
\(979\) 0.104858 0.00335128
\(980\) 0 0
\(981\) 6.35590 0.202928
\(982\) 0 0
\(983\) −12.7420 −0.406405 −0.203203 0.979137i \(-0.565135\pi\)
−0.203203 + 0.979137i \(0.565135\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2.02065 −0.0643180
\(988\) 0 0
\(989\) 48.6677 1.54754
\(990\) 0 0
\(991\) −34.0639 −1.08208 −0.541038 0.840998i \(-0.681968\pi\)
−0.541038 + 0.840998i \(0.681968\pi\)
\(992\) 0 0
\(993\) 11.1296 0.353189
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 17.5887 0.557039 0.278520 0.960431i \(-0.410156\pi\)
0.278520 + 0.960431i \(0.410156\pi\)
\(998\) 0 0
\(999\) −1.75688 −0.0555853
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.bt.1.3 4
5.2 odd 4 1560.2.l.d.1249.8 yes 8
5.3 odd 4 1560.2.l.d.1249.4 8
5.4 even 2 7800.2.a.by.1.2 4
15.2 even 4 4680.2.l.g.2809.1 8
15.8 even 4 4680.2.l.g.2809.2 8
20.3 even 4 3120.2.l.n.1249.8 8
20.7 even 4 3120.2.l.n.1249.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.d.1249.4 8 5.3 odd 4
1560.2.l.d.1249.8 yes 8 5.2 odd 4
3120.2.l.n.1249.4 8 20.7 even 4
3120.2.l.n.1249.8 8 20.3 even 4
4680.2.l.g.2809.1 8 15.2 even 4
4680.2.l.g.2809.2 8 15.8 even 4
7800.2.a.bt.1.3 4 1.1 even 1 trivial
7800.2.a.by.1.2 4 5.4 even 2