Properties

Label 1232.4.a.i.1.1
Level $1232$
Weight $4$
Character 1232.1
Self dual yes
Analytic conductor $72.690$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1232.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.6903531271\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1232.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.0000 q^{3} -14.0000 q^{5} -7.00000 q^{7} +73.0000 q^{9} +O(q^{10})\) \(q+10.0000 q^{3} -14.0000 q^{5} -7.00000 q^{7} +73.0000 q^{9} +11.0000 q^{11} -16.0000 q^{13} -140.000 q^{15} +108.000 q^{17} -116.000 q^{19} -70.0000 q^{21} -68.0000 q^{23} +71.0000 q^{25} +460.000 q^{27} +122.000 q^{29} +262.000 q^{31} +110.000 q^{33} +98.0000 q^{35} +130.000 q^{37} -160.000 q^{39} +204.000 q^{41} +396.000 q^{43} -1022.00 q^{45} -166.000 q^{47} +49.0000 q^{49} +1080.00 q^{51} +442.000 q^{53} -154.000 q^{55} -1160.00 q^{57} -702.000 q^{59} +196.000 q^{61} -511.000 q^{63} +224.000 q^{65} +416.000 q^{67} -680.000 q^{69} -492.000 q^{71} +408.000 q^{73} +710.000 q^{75} -77.0000 q^{77} -600.000 q^{79} +2629.00 q^{81} +1212.00 q^{83} -1512.00 q^{85} +1220.00 q^{87} +1146.00 q^{89} +112.000 q^{91} +2620.00 q^{93} +1624.00 q^{95} -482.000 q^{97} +803.000 q^{99} +O(q^{100})\)

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
\(3\) 10.0000 1.92450 0.962250 0.272166i \(-0.0877398\pi\)
0.962250 + 0.272166i \(0.0877398\pi\)
\(4\) 0 0
\(5\) −14.0000 −1.25220 −0.626099 0.779744i \(-0.715349\pi\)
−0.626099 + 0.779744i \(0.715349\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 73.0000 2.70370
\(10\) 0 0
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −16.0000 −0.341354 −0.170677 0.985327i \(-0.554595\pi\)
−0.170677 + 0.985327i \(0.554595\pi\)
\(14\) 0 0
\(15\) −140.000 −2.40986
\(16\) 0 0
\(17\) 108.000 1.54081 0.770407 0.637552i \(-0.220053\pi\)
0.770407 + 0.637552i \(0.220053\pi\)
\(18\) 0 0
\(19\) −116.000 −1.40064 −0.700322 0.713827i \(-0.746960\pi\)
−0.700322 + 0.713827i \(0.746960\pi\)
\(20\) 0 0
\(21\) −70.0000 −0.727393
\(22\) 0 0
\(23\) −68.0000 −0.616477 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 0 0
\(27\) 460.000 3.27878
\(28\) 0 0
\(29\) 122.000 0.781201 0.390601 0.920560i \(-0.372267\pi\)
0.390601 + 0.920560i \(0.372267\pi\)
\(30\) 0 0
\(31\) 262.000 1.51795 0.758977 0.651117i \(-0.225699\pi\)
0.758977 + 0.651117i \(0.225699\pi\)
\(32\) 0 0
\(33\) 110.000 0.580259
\(34\) 0 0
\(35\) 98.0000 0.473286
\(36\) 0 0
\(37\) 130.000 0.577618 0.288809 0.957387i \(-0.406741\pi\)
0.288809 + 0.957387i \(0.406741\pi\)
\(38\) 0 0
\(39\) −160.000 −0.656936
\(40\) 0 0
\(41\) 204.000 0.777060 0.388530 0.921436i \(-0.372983\pi\)
0.388530 + 0.921436i \(0.372983\pi\)
\(42\) 0 0
\(43\) 396.000 1.40441 0.702203 0.711977i \(-0.252200\pi\)
0.702203 + 0.711977i \(0.252200\pi\)
\(44\) 0 0
\(45\) −1022.00 −3.38557
\(46\) 0 0
\(47\) −166.000 −0.515183 −0.257591 0.966254i \(-0.582929\pi\)
−0.257591 + 0.966254i \(0.582929\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 1080.00 2.96530
\(52\) 0 0
\(53\) 442.000 1.14554 0.572768 0.819718i \(-0.305870\pi\)
0.572768 + 0.819718i \(0.305870\pi\)
\(54\) 0 0
\(55\) −154.000 −0.377552
\(56\) 0 0
\(57\) −1160.00 −2.69554
\(58\) 0 0
\(59\) −702.000 −1.54903 −0.774514 0.632557i \(-0.782005\pi\)
−0.774514 + 0.632557i \(0.782005\pi\)
\(60\) 0 0
\(61\) 196.000 0.411397 0.205699 0.978615i \(-0.434053\pi\)
0.205699 + 0.978615i \(0.434053\pi\)
\(62\) 0 0
\(63\) −511.000 −1.02190
\(64\) 0 0
\(65\) 224.000 0.427443
\(66\) 0 0
\(67\) 416.000 0.758545 0.379272 0.925285i \(-0.376174\pi\)
0.379272 + 0.925285i \(0.376174\pi\)
\(68\) 0 0
\(69\) −680.000 −1.18641
\(70\) 0 0
\(71\) −492.000 −0.822390 −0.411195 0.911548i \(-0.634888\pi\)
−0.411195 + 0.911548i \(0.634888\pi\)
\(72\) 0 0
\(73\) 408.000 0.654148 0.327074 0.944999i \(-0.393937\pi\)
0.327074 + 0.944999i \(0.393937\pi\)
\(74\) 0 0
\(75\) 710.000 1.09312
\(76\) 0 0
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) −600.000 −0.854497 −0.427249 0.904134i \(-0.640517\pi\)
−0.427249 + 0.904134i \(0.640517\pi\)
\(80\) 0 0
\(81\) 2629.00 3.60631
\(82\) 0 0
\(83\) 1212.00 1.60282 0.801411 0.598114i \(-0.204083\pi\)
0.801411 + 0.598114i \(0.204083\pi\)
\(84\) 0 0
\(85\) −1512.00 −1.92941
\(86\) 0 0
\(87\) 1220.00 1.50342
\(88\) 0 0
\(89\) 1146.00 1.36490 0.682448 0.730934i \(-0.260915\pi\)
0.682448 + 0.730934i \(0.260915\pi\)
\(90\) 0 0
\(91\) 112.000 0.129020
\(92\) 0 0
\(93\) 2620.00 2.92130
\(94\) 0 0
\(95\) 1624.00 1.75388
\(96\) 0 0
\(97\) −482.000 −0.504533 −0.252266 0.967658i \(-0.581176\pi\)
−0.252266 + 0.967658i \(0.581176\pi\)
\(98\) 0 0
\(99\) 803.000 0.815197
\(100\) 0 0
\(101\) 1216.00 1.19799 0.598993 0.800754i \(-0.295568\pi\)
0.598993 + 0.800754i \(0.295568\pi\)
\(102\) 0 0
\(103\) −1406.00 −1.34502 −0.672511 0.740087i \(-0.734784\pi\)
−0.672511 + 0.740087i \(0.734784\pi\)
\(104\) 0 0
\(105\) 980.000 0.910840
\(106\) 0 0
\(107\) 588.000 0.531253 0.265627 0.964076i \(-0.414421\pi\)
0.265627 + 0.964076i \(0.414421\pi\)
\(108\) 0 0
\(109\) 154.000 0.135326 0.0676630 0.997708i \(-0.478446\pi\)
0.0676630 + 0.997708i \(0.478446\pi\)
\(110\) 0 0
\(111\) 1300.00 1.11163
\(112\) 0 0
\(113\) −1902.00 −1.58341 −0.791704 0.610905i \(-0.790806\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(114\) 0 0
\(115\) 952.000 0.771952
\(116\) 0 0
\(117\) −1168.00 −0.922920
\(118\) 0 0
\(119\) −756.000 −0.582373
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 2040.00 1.49545
\(124\) 0 0
\(125\) 756.000 0.540950
\(126\) 0 0
\(127\) −64.0000 −0.0447172 −0.0223586 0.999750i \(-0.507118\pi\)
−0.0223586 + 0.999750i \(0.507118\pi\)
\(128\) 0 0
\(129\) 3960.00 2.70278
\(130\) 0 0
\(131\) 1584.00 1.05645 0.528224 0.849105i \(-0.322858\pi\)
0.528224 + 0.849105i \(0.322858\pi\)
\(132\) 0 0
\(133\) 812.000 0.529393
\(134\) 0 0
\(135\) −6440.00 −4.10568
\(136\) 0 0
\(137\) 998.000 0.622371 0.311186 0.950349i \(-0.399274\pi\)
0.311186 + 0.950349i \(0.399274\pi\)
\(138\) 0 0
\(139\) −276.000 −0.168417 −0.0842087 0.996448i \(-0.526836\pi\)
−0.0842087 + 0.996448i \(0.526836\pi\)
\(140\) 0 0
\(141\) −1660.00 −0.991470
\(142\) 0 0
\(143\) −176.000 −0.102922
\(144\) 0 0
\(145\) −1708.00 −0.978218
\(146\) 0 0
\(147\) 490.000 0.274929
\(148\) 0 0
\(149\) 1318.00 0.724663 0.362331 0.932049i \(-0.381981\pi\)
0.362331 + 0.932049i \(0.381981\pi\)
\(150\) 0 0
\(151\) 984.000 0.530310 0.265155 0.964206i \(-0.414577\pi\)
0.265155 + 0.964206i \(0.414577\pi\)
\(152\) 0 0
\(153\) 7884.00 4.16591
\(154\) 0 0
\(155\) −3668.00 −1.90078
\(156\) 0 0
\(157\) 1706.00 0.867221 0.433610 0.901101i \(-0.357239\pi\)
0.433610 + 0.901101i \(0.357239\pi\)
\(158\) 0 0
\(159\) 4420.00 2.20458
\(160\) 0 0
\(161\) 476.000 0.233007
\(162\) 0 0
\(163\) −1168.00 −0.561257 −0.280628 0.959817i \(-0.590543\pi\)
−0.280628 + 0.959817i \(0.590543\pi\)
\(164\) 0 0
\(165\) −1540.00 −0.726599
\(166\) 0 0
\(167\) −72.0000 −0.0333624 −0.0166812 0.999861i \(-0.505310\pi\)
−0.0166812 + 0.999861i \(0.505310\pi\)
\(168\) 0 0
\(169\) −1941.00 −0.883477
\(170\) 0 0
\(171\) −8468.00 −3.78692
\(172\) 0 0
\(173\) −4328.00 −1.90203 −0.951017 0.309140i \(-0.899959\pi\)
−0.951017 + 0.309140i \(0.899959\pi\)
\(174\) 0 0
\(175\) −497.000 −0.214684
\(176\) 0 0
\(177\) −7020.00 −2.98110
\(178\) 0 0
\(179\) 1924.00 0.803388 0.401694 0.915774i \(-0.368421\pi\)
0.401694 + 0.915774i \(0.368421\pi\)
\(180\) 0 0
\(181\) 2230.00 0.915771 0.457886 0.889011i \(-0.348607\pi\)
0.457886 + 0.889011i \(0.348607\pi\)
\(182\) 0 0
\(183\) 1960.00 0.791734
\(184\) 0 0
\(185\) −1820.00 −0.723292
\(186\) 0 0
\(187\) 1188.00 0.464573
\(188\) 0 0
\(189\) −3220.00 −1.23926
\(190\) 0 0
\(191\) −2176.00 −0.824345 −0.412172 0.911106i \(-0.635230\pi\)
−0.412172 + 0.911106i \(0.635230\pi\)
\(192\) 0 0
\(193\) −3126.00 −1.16588 −0.582939 0.812516i \(-0.698097\pi\)
−0.582939 + 0.812516i \(0.698097\pi\)
\(194\) 0 0
\(195\) 2240.00 0.822614
\(196\) 0 0
\(197\) −1122.00 −0.405783 −0.202891 0.979201i \(-0.565034\pi\)
−0.202891 + 0.979201i \(0.565034\pi\)
\(198\) 0 0
\(199\) 5586.00 1.98985 0.994927 0.100597i \(-0.0320753\pi\)
0.994927 + 0.100597i \(0.0320753\pi\)
\(200\) 0 0
\(201\) 4160.00 1.45982
\(202\) 0 0
\(203\) −854.000 −0.295266
\(204\) 0 0
\(205\) −2856.00 −0.973033
\(206\) 0 0
\(207\) −4964.00 −1.66677
\(208\) 0 0
\(209\) −1276.00 −0.422310
\(210\) 0 0
\(211\) −3372.00 −1.10018 −0.550090 0.835105i \(-0.685407\pi\)
−0.550090 + 0.835105i \(0.685407\pi\)
\(212\) 0 0
\(213\) −4920.00 −1.58269
\(214\) 0 0
\(215\) −5544.00 −1.75859
\(216\) 0 0
\(217\) −1834.00 −0.573733
\(218\) 0 0
\(219\) 4080.00 1.25891
\(220\) 0 0
\(221\) −1728.00 −0.525963
\(222\) 0 0
\(223\) −606.000 −0.181977 −0.0909883 0.995852i \(-0.529003\pi\)
−0.0909883 + 0.995852i \(0.529003\pi\)
\(224\) 0 0
\(225\) 5183.00 1.53570
\(226\) 0 0
\(227\) −144.000 −0.0421040 −0.0210520 0.999778i \(-0.506702\pi\)
−0.0210520 + 0.999778i \(0.506702\pi\)
\(228\) 0 0
\(229\) −1010.00 −0.291453 −0.145726 0.989325i \(-0.546552\pi\)
−0.145726 + 0.989325i \(0.546552\pi\)
\(230\) 0 0
\(231\) −770.000 −0.219317
\(232\) 0 0
\(233\) 3790.00 1.06563 0.532814 0.846233i \(-0.321135\pi\)
0.532814 + 0.846233i \(0.321135\pi\)
\(234\) 0 0
\(235\) 2324.00 0.645111
\(236\) 0 0
\(237\) −6000.00 −1.64448
\(238\) 0 0
\(239\) −2184.00 −0.591093 −0.295546 0.955328i \(-0.595502\pi\)
−0.295546 + 0.955328i \(0.595502\pi\)
\(240\) 0 0
\(241\) −4268.00 −1.14077 −0.570386 0.821377i \(-0.693206\pi\)
−0.570386 + 0.821377i \(0.693206\pi\)
\(242\) 0 0
\(243\) 13870.0 3.66157
\(244\) 0 0
\(245\) −686.000 −0.178885
\(246\) 0 0
\(247\) 1856.00 0.478115
\(248\) 0 0
\(249\) 12120.0 3.08463
\(250\) 0 0
\(251\) −7922.00 −1.99216 −0.996080 0.0884559i \(-0.971807\pi\)
−0.996080 + 0.0884559i \(0.971807\pi\)
\(252\) 0 0
\(253\) −748.000 −0.185875
\(254\) 0 0
\(255\) −15120.0 −3.71314
\(256\) 0 0
\(257\) 4002.00 0.971354 0.485677 0.874138i \(-0.338573\pi\)
0.485677 + 0.874138i \(0.338573\pi\)
\(258\) 0 0
\(259\) −910.000 −0.218319
\(260\) 0 0
\(261\) 8906.00 2.11214
\(262\) 0 0
\(263\) 3960.00 0.928457 0.464228 0.885716i \(-0.346332\pi\)
0.464228 + 0.885716i \(0.346332\pi\)
\(264\) 0 0
\(265\) −6188.00 −1.43444
\(266\) 0 0
\(267\) 11460.0 2.62674
\(268\) 0 0
\(269\) 1878.00 0.425664 0.212832 0.977089i \(-0.431731\pi\)
0.212832 + 0.977089i \(0.431731\pi\)
\(270\) 0 0
\(271\) 4740.00 1.06249 0.531244 0.847219i \(-0.321725\pi\)
0.531244 + 0.847219i \(0.321725\pi\)
\(272\) 0 0
\(273\) 1120.00 0.248298
\(274\) 0 0
\(275\) 781.000 0.171258
\(276\) 0 0
\(277\) 710.000 0.154006 0.0770032 0.997031i \(-0.475465\pi\)
0.0770032 + 0.997031i \(0.475465\pi\)
\(278\) 0 0
\(279\) 19126.0 4.10410
\(280\) 0 0
\(281\) −90.0000 −0.0191066 −0.00955329 0.999954i \(-0.503041\pi\)
−0.00955329 + 0.999954i \(0.503041\pi\)
\(282\) 0 0
\(283\) 3448.00 0.724248 0.362124 0.932130i \(-0.382052\pi\)
0.362124 + 0.932130i \(0.382052\pi\)
\(284\) 0 0
\(285\) 16240.0 3.37535
\(286\) 0 0
\(287\) −1428.00 −0.293701
\(288\) 0 0
\(289\) 6751.00 1.37411
\(290\) 0 0
\(291\) −4820.00 −0.970974
\(292\) 0 0
\(293\) −2804.00 −0.559083 −0.279542 0.960134i \(-0.590183\pi\)
−0.279542 + 0.960134i \(0.590183\pi\)
\(294\) 0 0
\(295\) 9828.00 1.93969
\(296\) 0 0
\(297\) 5060.00 0.988589
\(298\) 0 0
\(299\) 1088.00 0.210437
\(300\) 0 0
\(301\) −2772.00 −0.530815
\(302\) 0 0
\(303\) 12160.0 2.30552
\(304\) 0 0
\(305\) −2744.00 −0.515151
\(306\) 0 0
\(307\) −1320.00 −0.245395 −0.122698 0.992444i \(-0.539155\pi\)
−0.122698 + 0.992444i \(0.539155\pi\)
\(308\) 0 0
\(309\) −14060.0 −2.58850
\(310\) 0 0
\(311\) 1066.00 0.194364 0.0971822 0.995267i \(-0.469017\pi\)
0.0971822 + 0.995267i \(0.469017\pi\)
\(312\) 0 0
\(313\) −9254.00 −1.67114 −0.835570 0.549384i \(-0.814863\pi\)
−0.835570 + 0.549384i \(0.814863\pi\)
\(314\) 0 0
\(315\) 7154.00 1.27963
\(316\) 0 0
\(317\) −9722.00 −1.72253 −0.861265 0.508156i \(-0.830327\pi\)
−0.861265 + 0.508156i \(0.830327\pi\)
\(318\) 0 0
\(319\) 1342.00 0.235541
\(320\) 0 0
\(321\) 5880.00 1.02240
\(322\) 0 0
\(323\) −12528.0 −2.15813
\(324\) 0 0
\(325\) −1136.00 −0.193889
\(326\) 0 0
\(327\) 1540.00 0.260435
\(328\) 0 0
\(329\) 1162.00 0.194721
\(330\) 0 0
\(331\) −2620.00 −0.435070 −0.217535 0.976053i \(-0.569802\pi\)
−0.217535 + 0.976053i \(0.569802\pi\)
\(332\) 0 0
\(333\) 9490.00 1.56171
\(334\) 0 0
\(335\) −5824.00 −0.949848
\(336\) 0 0
\(337\) 2806.00 0.453568 0.226784 0.973945i \(-0.427179\pi\)
0.226784 + 0.973945i \(0.427179\pi\)
\(338\) 0 0
\(339\) −19020.0 −3.04727
\(340\) 0 0
\(341\) 2882.00 0.457680
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 9520.00 1.48562
\(346\) 0 0
\(347\) −5564.00 −0.860781 −0.430391 0.902643i \(-0.641624\pi\)
−0.430391 + 0.902643i \(0.641624\pi\)
\(348\) 0 0
\(349\) 10060.0 1.54298 0.771489 0.636242i \(-0.219512\pi\)
0.771489 + 0.636242i \(0.219512\pi\)
\(350\) 0 0
\(351\) −7360.00 −1.11922
\(352\) 0 0
\(353\) −5102.00 −0.769269 −0.384635 0.923069i \(-0.625673\pi\)
−0.384635 + 0.923069i \(0.625673\pi\)
\(354\) 0 0
\(355\) 6888.00 1.02979
\(356\) 0 0
\(357\) −7560.00 −1.12078
\(358\) 0 0
\(359\) −7976.00 −1.17258 −0.586291 0.810100i \(-0.699413\pi\)
−0.586291 + 0.810100i \(0.699413\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) 0 0
\(363\) 1210.00 0.174955
\(364\) 0 0
\(365\) −5712.00 −0.819123
\(366\) 0 0
\(367\) 1234.00 0.175516 0.0877579 0.996142i \(-0.472030\pi\)
0.0877579 + 0.996142i \(0.472030\pi\)
\(368\) 0 0
\(369\) 14892.0 2.10094
\(370\) 0 0
\(371\) −3094.00 −0.432972
\(372\) 0 0
\(373\) 8030.00 1.11469 0.557343 0.830283i \(-0.311821\pi\)
0.557343 + 0.830283i \(0.311821\pi\)
\(374\) 0 0
\(375\) 7560.00 1.04106
\(376\) 0 0
\(377\) −1952.00 −0.266666
\(378\) 0 0
\(379\) 5184.00 0.702597 0.351298 0.936264i \(-0.385740\pi\)
0.351298 + 0.936264i \(0.385740\pi\)
\(380\) 0 0
\(381\) −640.000 −0.0860583
\(382\) 0 0
\(383\) −7570.00 −1.00994 −0.504972 0.863135i \(-0.668497\pi\)
−0.504972 + 0.863135i \(0.668497\pi\)
\(384\) 0 0
\(385\) 1078.00 0.142701
\(386\) 0 0
\(387\) 28908.0 3.79710
\(388\) 0 0
\(389\) −5370.00 −0.699922 −0.349961 0.936764i \(-0.613805\pi\)
−0.349961 + 0.936764i \(0.613805\pi\)
\(390\) 0 0
\(391\) −7344.00 −0.949877
\(392\) 0 0
\(393\) 15840.0 2.03314
\(394\) 0 0
\(395\) 8400.00 1.07000
\(396\) 0 0
\(397\) 11442.0 1.44649 0.723246 0.690590i \(-0.242649\pi\)
0.723246 + 0.690590i \(0.242649\pi\)
\(398\) 0 0
\(399\) 8120.00 1.01882
\(400\) 0 0
\(401\) 2362.00 0.294146 0.147073 0.989126i \(-0.453015\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(402\) 0 0
\(403\) −4192.00 −0.518160
\(404\) 0 0
\(405\) −36806.0 −4.51581
\(406\) 0 0
\(407\) 1430.00 0.174158
\(408\) 0 0
\(409\) −16.0000 −0.00193435 −0.000967175 1.00000i \(-0.500308\pi\)
−0.000967175 1.00000i \(0.500308\pi\)
\(410\) 0 0
\(411\) 9980.00 1.19775
\(412\) 0 0
\(413\) 4914.00 0.585477
\(414\) 0 0
\(415\) −16968.0 −2.00705
\(416\) 0 0
\(417\) −2760.00 −0.324119
\(418\) 0 0
\(419\) −9462.00 −1.10322 −0.551610 0.834102i \(-0.685986\pi\)
−0.551610 + 0.834102i \(0.685986\pi\)
\(420\) 0 0
\(421\) −6302.00 −0.729550 −0.364775 0.931096i \(-0.618854\pi\)
−0.364775 + 0.931096i \(0.618854\pi\)
\(422\) 0 0
\(423\) −12118.0 −1.39290
\(424\) 0 0
\(425\) 7668.00 0.875183
\(426\) 0 0
\(427\) −1372.00 −0.155494
\(428\) 0 0
\(429\) −1760.00 −0.198074
\(430\) 0 0
\(431\) −7816.00 −0.873512 −0.436756 0.899580i \(-0.643873\pi\)
−0.436756 + 0.899580i \(0.643873\pi\)
\(432\) 0 0
\(433\) −9506.00 −1.05503 −0.527516 0.849545i \(-0.676877\pi\)
−0.527516 + 0.849545i \(0.676877\pi\)
\(434\) 0 0
\(435\) −17080.0 −1.88258
\(436\) 0 0
\(437\) 7888.00 0.863465
\(438\) 0 0
\(439\) 8228.00 0.894535 0.447268 0.894400i \(-0.352397\pi\)
0.447268 + 0.894400i \(0.352397\pi\)
\(440\) 0 0
\(441\) 3577.00 0.386243
\(442\) 0 0
\(443\) −7668.00 −0.822388 −0.411194 0.911548i \(-0.634888\pi\)
−0.411194 + 0.911548i \(0.634888\pi\)
\(444\) 0 0
\(445\) −16044.0 −1.70912
\(446\) 0 0
\(447\) 13180.0 1.39461
\(448\) 0 0
\(449\) −922.000 −0.0969084 −0.0484542 0.998825i \(-0.515429\pi\)
−0.0484542 + 0.998825i \(0.515429\pi\)
\(450\) 0 0
\(451\) 2244.00 0.234292
\(452\) 0 0
\(453\) 9840.00 1.02058
\(454\) 0 0
\(455\) −1568.00 −0.161558
\(456\) 0 0
\(457\) 3386.00 0.346587 0.173294 0.984870i \(-0.444559\pi\)
0.173294 + 0.984870i \(0.444559\pi\)
\(458\) 0 0
\(459\) 49680.0 5.05199
\(460\) 0 0
\(461\) −3300.00 −0.333398 −0.166699 0.986008i \(-0.553311\pi\)
−0.166699 + 0.986008i \(0.553311\pi\)
\(462\) 0 0
\(463\) −14236.0 −1.42895 −0.714474 0.699662i \(-0.753334\pi\)
−0.714474 + 0.699662i \(0.753334\pi\)
\(464\) 0 0
\(465\) −36680.0 −3.65805
\(466\) 0 0
\(467\) −3770.00 −0.373565 −0.186782 0.982401i \(-0.559806\pi\)
−0.186782 + 0.982401i \(0.559806\pi\)
\(468\) 0 0
\(469\) −2912.00 −0.286703
\(470\) 0 0
\(471\) 17060.0 1.66897
\(472\) 0 0
\(473\) 4356.00 0.423444
\(474\) 0 0
\(475\) −8236.00 −0.795565
\(476\) 0 0
\(477\) 32266.0 3.09719
\(478\) 0 0
\(479\) −17796.0 −1.69754 −0.848768 0.528765i \(-0.822655\pi\)
−0.848768 + 0.528765i \(0.822655\pi\)
\(480\) 0 0
\(481\) −2080.00 −0.197172
\(482\) 0 0
\(483\) 4760.00 0.448421
\(484\) 0 0
\(485\) 6748.00 0.631775
\(486\) 0 0
\(487\) 3684.00 0.342788 0.171394 0.985203i \(-0.445173\pi\)
0.171394 + 0.985203i \(0.445173\pi\)
\(488\) 0 0
\(489\) −11680.0 −1.08014
\(490\) 0 0
\(491\) 17236.0 1.58422 0.792108 0.610381i \(-0.208984\pi\)
0.792108 + 0.610381i \(0.208984\pi\)
\(492\) 0 0
\(493\) 13176.0 1.20369
\(494\) 0 0
\(495\) −11242.0 −1.02079
\(496\) 0 0
\(497\) 3444.00 0.310834
\(498\) 0 0
\(499\) −13176.0 −1.18204 −0.591021 0.806656i \(-0.701275\pi\)
−0.591021 + 0.806656i \(0.701275\pi\)
\(500\) 0 0
\(501\) −720.000 −0.0642060
\(502\) 0 0
\(503\) −15428.0 −1.36760 −0.683798 0.729672i \(-0.739673\pi\)
−0.683798 + 0.729672i \(0.739673\pi\)
\(504\) 0 0
\(505\) −17024.0 −1.50011
\(506\) 0 0
\(507\) −19410.0 −1.70025
\(508\) 0 0
\(509\) −7842.00 −0.682889 −0.341445 0.939902i \(-0.610916\pi\)
−0.341445 + 0.939902i \(0.610916\pi\)
\(510\) 0 0
\(511\) −2856.00 −0.247245
\(512\) 0 0
\(513\) −53360.0 −4.59240
\(514\) 0 0
\(515\) 19684.0 1.68423
\(516\) 0 0
\(517\) −1826.00 −0.155333
\(518\) 0 0
\(519\) −43280.0 −3.66046
\(520\) 0 0
\(521\) −17250.0 −1.45055 −0.725275 0.688460i \(-0.758287\pi\)
−0.725275 + 0.688460i \(0.758287\pi\)
\(522\) 0 0
\(523\) −1032.00 −0.0862834 −0.0431417 0.999069i \(-0.513737\pi\)
−0.0431417 + 0.999069i \(0.513737\pi\)
\(524\) 0 0
\(525\) −4970.00 −0.413159
\(526\) 0 0
\(527\) 28296.0 2.33889
\(528\) 0 0
\(529\) −7543.00 −0.619956
\(530\) 0 0
\(531\) −51246.0 −4.18811
\(532\) 0 0
\(533\) −3264.00 −0.265252
\(534\) 0 0
\(535\) −8232.00 −0.665234
\(536\) 0 0
\(537\) 19240.0 1.54612
\(538\) 0 0
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 94.0000 0.00747020 0.00373510 0.999993i \(-0.498811\pi\)
0.00373510 + 0.999993i \(0.498811\pi\)
\(542\) 0 0
\(543\) 22300.0 1.76240
\(544\) 0 0
\(545\) −2156.00 −0.169455
\(546\) 0 0
\(547\) 11676.0 0.912669 0.456334 0.889808i \(-0.349162\pi\)
0.456334 + 0.889808i \(0.349162\pi\)
\(548\) 0 0
\(549\) 14308.0 1.11230
\(550\) 0 0
\(551\) −14152.0 −1.09418
\(552\) 0 0
\(553\) 4200.00 0.322970
\(554\) 0 0
\(555\) −18200.0 −1.39198
\(556\) 0 0
\(557\) −1858.00 −0.141339 −0.0706696 0.997500i \(-0.522514\pi\)
−0.0706696 + 0.997500i \(0.522514\pi\)
\(558\) 0 0
\(559\) −6336.00 −0.479399
\(560\) 0 0
\(561\) 11880.0 0.894071
\(562\) 0 0
\(563\) 23028.0 1.72383 0.861913 0.507056i \(-0.169266\pi\)
0.861913 + 0.507056i \(0.169266\pi\)
\(564\) 0 0
\(565\) 26628.0 1.98274
\(566\) 0 0
\(567\) −18403.0 −1.36306
\(568\) 0 0
\(569\) −17066.0 −1.25737 −0.628685 0.777660i \(-0.716407\pi\)
−0.628685 + 0.777660i \(0.716407\pi\)
\(570\) 0 0
\(571\) 10252.0 0.751371 0.375686 0.926747i \(-0.377407\pi\)
0.375686 + 0.926747i \(0.377407\pi\)
\(572\) 0 0
\(573\) −21760.0 −1.58645
\(574\) 0 0
\(575\) −4828.00 −0.350159
\(576\) 0 0
\(577\) 2142.00 0.154545 0.0772726 0.997010i \(-0.475379\pi\)
0.0772726 + 0.997010i \(0.475379\pi\)
\(578\) 0 0
\(579\) −31260.0 −2.24373
\(580\) 0 0
\(581\) −8484.00 −0.605810
\(582\) 0 0
\(583\) 4862.00 0.345392
\(584\) 0 0
\(585\) 16352.0 1.15568
\(586\) 0 0
\(587\) −3474.00 −0.244271 −0.122136 0.992513i \(-0.538974\pi\)
−0.122136 + 0.992513i \(0.538974\pi\)
\(588\) 0 0
\(589\) −30392.0 −2.12611
\(590\) 0 0
\(591\) −11220.0 −0.780929
\(592\) 0 0
\(593\) −17424.0 −1.20661 −0.603303 0.797512i \(-0.706149\pi\)
−0.603303 + 0.797512i \(0.706149\pi\)
\(594\) 0 0
\(595\) 10584.0 0.729247
\(596\) 0 0
\(597\) 55860.0 3.82948
\(598\) 0 0
\(599\) −6916.00 −0.471753 −0.235877 0.971783i \(-0.575796\pi\)
−0.235877 + 0.971783i \(0.575796\pi\)
\(600\) 0 0
\(601\) 16468.0 1.11771 0.558855 0.829265i \(-0.311241\pi\)
0.558855 + 0.829265i \(0.311241\pi\)
\(602\) 0 0
\(603\) 30368.0 2.05088
\(604\) 0 0
\(605\) −1694.00 −0.113836
\(606\) 0 0
\(607\) 17176.0 1.14852 0.574261 0.818673i \(-0.305290\pi\)
0.574261 + 0.818673i \(0.305290\pi\)
\(608\) 0 0
\(609\) −8540.00 −0.568240
\(610\) 0 0
\(611\) 2656.00 0.175860
\(612\) 0 0
\(613\) 11402.0 0.751260 0.375630 0.926770i \(-0.377426\pi\)
0.375630 + 0.926770i \(0.377426\pi\)
\(614\) 0 0
\(615\) −28560.0 −1.87260
\(616\) 0 0
\(617\) 3654.00 0.238419 0.119209 0.992869i \(-0.461964\pi\)
0.119209 + 0.992869i \(0.461964\pi\)
\(618\) 0 0
\(619\) 11318.0 0.734909 0.367455 0.930041i \(-0.380229\pi\)
0.367455 + 0.930041i \(0.380229\pi\)
\(620\) 0 0
\(621\) −31280.0 −2.02129
\(622\) 0 0
\(623\) −8022.00 −0.515882
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 0 0
\(627\) −12760.0 −0.812736
\(628\) 0 0
\(629\) 14040.0 0.890002
\(630\) 0 0
\(631\) 23872.0 1.50607 0.753034 0.657981i \(-0.228589\pi\)
0.753034 + 0.657981i \(0.228589\pi\)
\(632\) 0 0
\(633\) −33720.0 −2.11730
\(634\) 0 0
\(635\) 896.000 0.0559948
\(636\) 0 0
\(637\) −784.000 −0.0487649
\(638\) 0 0
\(639\) −35916.0 −2.22350
\(640\) 0 0
\(641\) −27026.0 −1.66531 −0.832654 0.553793i \(-0.813180\pi\)
−0.832654 + 0.553793i \(0.813180\pi\)
\(642\) 0 0
\(643\) −6498.00 −0.398532 −0.199266 0.979945i \(-0.563856\pi\)
−0.199266 + 0.979945i \(0.563856\pi\)
\(644\) 0 0
\(645\) −55440.0 −3.38442
\(646\) 0 0
\(647\) 6422.00 0.390224 0.195112 0.980781i \(-0.437493\pi\)
0.195112 + 0.980781i \(0.437493\pi\)
\(648\) 0 0
\(649\) −7722.00 −0.467049
\(650\) 0 0
\(651\) −18340.0 −1.10415
\(652\) 0 0
\(653\) 23670.0 1.41850 0.709249 0.704958i \(-0.249034\pi\)
0.709249 + 0.704958i \(0.249034\pi\)
\(654\) 0 0
\(655\) −22176.0 −1.32288
\(656\) 0 0
\(657\) 29784.0 1.76862
\(658\) 0 0
\(659\) 9812.00 0.580002 0.290001 0.957026i \(-0.406344\pi\)
0.290001 + 0.957026i \(0.406344\pi\)
\(660\) 0 0
\(661\) −5190.00 −0.305397 −0.152699 0.988273i \(-0.548796\pi\)
−0.152699 + 0.988273i \(0.548796\pi\)
\(662\) 0 0
\(663\) −17280.0 −1.01222
\(664\) 0 0
\(665\) −11368.0 −0.662905
\(666\) 0 0
\(667\) −8296.00 −0.481593
\(668\) 0 0
\(669\) −6060.00 −0.350214
\(670\) 0 0
\(671\) 2156.00 0.124041
\(672\) 0 0
\(673\) 94.0000 0.00538400 0.00269200 0.999996i \(-0.499143\pi\)
0.00269200 + 0.999996i \(0.499143\pi\)
\(674\) 0 0
\(675\) 32660.0 1.86235
\(676\) 0 0
\(677\) −12432.0 −0.705762 −0.352881 0.935668i \(-0.614798\pi\)
−0.352881 + 0.935668i \(0.614798\pi\)
\(678\) 0 0
\(679\) 3374.00 0.190695
\(680\) 0 0
\(681\) −1440.00 −0.0810293
\(682\) 0 0
\(683\) 2308.00 0.129302 0.0646509 0.997908i \(-0.479407\pi\)
0.0646509 + 0.997908i \(0.479407\pi\)
\(684\) 0 0
\(685\) −13972.0 −0.779332
\(686\) 0 0
\(687\) −10100.0 −0.560901
\(688\) 0 0
\(689\) −7072.00 −0.391033
\(690\) 0 0
\(691\) −26446.0 −1.45594 −0.727969 0.685610i \(-0.759536\pi\)
−0.727969 + 0.685610i \(0.759536\pi\)
\(692\) 0 0
\(693\) −5621.00 −0.308116
\(694\) 0 0
\(695\) 3864.00 0.210892
\(696\) 0 0
\(697\) 22032.0 1.19730
\(698\) 0 0
\(699\) 37900.0 2.05080
\(700\) 0 0
\(701\) 26450.0 1.42511 0.712555 0.701616i \(-0.247538\pi\)
0.712555 + 0.701616i \(0.247538\pi\)
\(702\) 0 0
\(703\) −15080.0 −0.809037
\(704\) 0 0
\(705\) 23240.0 1.24152
\(706\) 0 0
\(707\) −8512.00 −0.452796
\(708\) 0 0
\(709\) 17102.0 0.905894 0.452947 0.891537i \(-0.350373\pi\)
0.452947 + 0.891537i \(0.350373\pi\)
\(710\) 0 0
\(711\) −43800.0 −2.31031
\(712\) 0 0
\(713\) −17816.0 −0.935785
\(714\) 0 0
\(715\) 2464.00 0.128879
\(716\) 0 0
\(717\) −21840.0 −1.13756
\(718\) 0 0
\(719\) 16854.0 0.874198 0.437099 0.899413i \(-0.356006\pi\)
0.437099 + 0.899413i \(0.356006\pi\)
\(720\) 0 0
\(721\) 9842.00 0.508371
\(722\) 0 0
\(723\) −42680.0 −2.19542
\(724\) 0 0
\(725\) 8662.00 0.443722
\(726\) 0 0
\(727\) 34670.0 1.76869 0.884346 0.466832i \(-0.154605\pi\)
0.884346 + 0.466832i \(0.154605\pi\)
\(728\) 0 0
\(729\) 67717.0 3.44038
\(730\) 0 0
\(731\) 42768.0 2.16393
\(732\) 0 0
\(733\) 11716.0 0.590369 0.295184 0.955440i \(-0.404619\pi\)
0.295184 + 0.955440i \(0.404619\pi\)
\(734\) 0 0
\(735\) −6860.00 −0.344265
\(736\) 0 0
\(737\) 4576.00 0.228710
\(738\) 0 0
\(739\) −29772.0 −1.48198 −0.740988 0.671518i \(-0.765643\pi\)
−0.740988 + 0.671518i \(0.765643\pi\)
\(740\) 0 0
\(741\) 18560.0 0.920133
\(742\) 0 0
\(743\) 24928.0 1.23085 0.615424 0.788196i \(-0.288985\pi\)
0.615424 + 0.788196i \(0.288985\pi\)
\(744\) 0 0
\(745\) −18452.0 −0.907421
\(746\) 0 0
\(747\) 88476.0 4.33356
\(748\) 0 0
\(749\) −4116.00 −0.200795
\(750\) 0 0
\(751\) 4652.00 0.226037 0.113019 0.993593i \(-0.463948\pi\)
0.113019 + 0.993593i \(0.463948\pi\)
\(752\) 0 0
\(753\) −79220.0 −3.83391
\(754\) 0 0
\(755\) −13776.0 −0.664053
\(756\) 0 0
\(757\) −1802.00 −0.0865189 −0.0432594 0.999064i \(-0.513774\pi\)
−0.0432594 + 0.999064i \(0.513774\pi\)
\(758\) 0 0
\(759\) −7480.00 −0.357716
\(760\) 0 0
\(761\) −808.000 −0.0384888 −0.0192444 0.999815i \(-0.506126\pi\)
−0.0192444 + 0.999815i \(0.506126\pi\)
\(762\) 0 0
\(763\) −1078.00 −0.0511484
\(764\) 0 0
\(765\) −110376. −5.21654
\(766\) 0 0
\(767\) 11232.0 0.528767
\(768\) 0 0
\(769\) 23144.0 1.08530 0.542649 0.839960i \(-0.317421\pi\)
0.542649 + 0.839960i \(0.317421\pi\)
\(770\) 0 0
\(771\) 40020.0 1.86937
\(772\) 0 0
\(773\) −27466.0 −1.27799 −0.638993 0.769212i \(-0.720649\pi\)
−0.638993 + 0.769212i \(0.720649\pi\)
\(774\) 0 0
\(775\) 18602.0 0.862198
\(776\) 0 0
\(777\) −9100.00 −0.420155
\(778\) 0 0
\(779\) −23664.0 −1.08838
\(780\) 0 0
\(781\) −5412.00 −0.247960
\(782\) 0 0
\(783\) 56120.0 2.56139
\(784\) 0 0
\(785\) −23884.0 −1.08593
\(786\) 0 0
\(787\) −23604.0 −1.06911 −0.534556 0.845133i \(-0.679521\pi\)
−0.534556 + 0.845133i \(0.679521\pi\)
\(788\) 0 0
\(789\) 39600.0 1.78682
\(790\) 0 0
\(791\) 13314.0 0.598472
\(792\) 0 0
\(793\) −3136.00 −0.140432
\(794\) 0 0
\(795\) −61880.0 −2.76058
\(796\) 0 0
\(797\) 4122.00 0.183198 0.0915990 0.995796i \(-0.470802\pi\)
0.0915990 + 0.995796i \(0.470802\pi\)
\(798\) 0 0
\(799\) −17928.0 −0.793801
\(800\) 0 0
\(801\) 83658.0 3.69027
\(802\) 0 0
\(803\) 4488.00 0.197233
\(804\) 0 0
\(805\) −6664.00 −0.291770
\(806\) 0 0
\(807\) 18780.0 0.819191
\(808\) 0 0
\(809\) −9110.00 −0.395909 −0.197955 0.980211i \(-0.563430\pi\)
−0.197955 + 0.980211i \(0.563430\pi\)
\(810\) 0 0
\(811\) 28352.0 1.22759 0.613794 0.789466i \(-0.289643\pi\)
0.613794 + 0.789466i \(0.289643\pi\)
\(812\) 0 0
\(813\) 47400.0 2.04476
\(814\) 0 0
\(815\) 16352.0 0.702804
\(816\) 0 0
\(817\) −45936.0 −1.96707
\(818\) 0 0
\(819\) 8176.00 0.348831
\(820\) 0 0
\(821\) −14002.0 −0.595217 −0.297609 0.954688i \(-0.596189\pi\)
−0.297609 + 0.954688i \(0.596189\pi\)
\(822\) 0 0
\(823\) 14848.0 0.628881 0.314440 0.949277i \(-0.398183\pi\)
0.314440 + 0.949277i \(0.398183\pi\)
\(824\) 0 0
\(825\) 7810.00 0.329587
\(826\) 0 0
\(827\) −10500.0 −0.441500 −0.220750 0.975330i \(-0.570851\pi\)
−0.220750 + 0.975330i \(0.570851\pi\)
\(828\) 0 0
\(829\) 23890.0 1.00089 0.500443 0.865770i \(-0.333171\pi\)
0.500443 + 0.865770i \(0.333171\pi\)
\(830\) 0 0
\(831\) 7100.00 0.296385
\(832\) 0 0
\(833\) 5292.00 0.220116
\(834\) 0 0
\(835\) 1008.00 0.0417764
\(836\) 0 0
\(837\) 120520. 4.97704
\(838\) 0 0
\(839\) 670.000 0.0275697 0.0137848 0.999905i \(-0.495612\pi\)
0.0137848 + 0.999905i \(0.495612\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) 0 0
\(843\) −900.000 −0.0367706
\(844\) 0 0
\(845\) 27174.0 1.10629
\(846\) 0 0
\(847\) −847.000 −0.0343604
\(848\) 0 0
\(849\) 34480.0 1.39382
\(850\) 0 0
\(851\) −8840.00 −0.356088
\(852\) 0 0
\(853\) −4776.00 −0.191708 −0.0958541 0.995395i \(-0.530558\pi\)
−0.0958541 + 0.995395i \(0.530558\pi\)
\(854\) 0 0
\(855\) 118552. 4.74198
\(856\) 0 0
\(857\) −13024.0 −0.519126 −0.259563 0.965726i \(-0.583579\pi\)
−0.259563 + 0.965726i \(0.583579\pi\)
\(858\) 0 0
\(859\) 32998.0 1.31068 0.655342 0.755332i \(-0.272525\pi\)
0.655342 + 0.755332i \(0.272525\pi\)
\(860\) 0 0
\(861\) −14280.0 −0.565228
\(862\) 0 0
\(863\) −22272.0 −0.878503 −0.439251 0.898364i \(-0.644756\pi\)
−0.439251 + 0.898364i \(0.644756\pi\)
\(864\) 0 0
\(865\) 60592.0 2.38172
\(866\) 0 0
\(867\) 67510.0 2.64447
\(868\) 0 0
\(869\) −6600.00 −0.257641
\(870\) 0 0
\(871\) −6656.00 −0.258932
\(872\) 0 0
\(873\) −35186.0 −1.36411
\(874\) 0 0
\(875\) −5292.00 −0.204460
\(876\) 0 0
\(877\) −30398.0 −1.17043 −0.585215 0.810878i \(-0.698990\pi\)
−0.585215 + 0.810878i \(0.698990\pi\)
\(878\) 0 0
\(879\) −28040.0 −1.07596
\(880\) 0 0
\(881\) 1630.00 0.0623338 0.0311669 0.999514i \(-0.490078\pi\)
0.0311669 + 0.999514i \(0.490078\pi\)
\(882\) 0 0
\(883\) 20228.0 0.770925 0.385462 0.922724i \(-0.374042\pi\)
0.385462 + 0.922724i \(0.374042\pi\)
\(884\) 0 0
\(885\) 98280.0 3.73293
\(886\) 0 0
\(887\) −38908.0 −1.47283 −0.736416 0.676528i \(-0.763484\pi\)
−0.736416 + 0.676528i \(0.763484\pi\)
\(888\) 0 0
\(889\) 448.000 0.0169015
\(890\) 0 0
\(891\) 28919.0 1.08734
\(892\) 0 0
\(893\) 19256.0 0.721587
\(894\) 0 0
\(895\) −26936.0 −1.00600
\(896\) 0 0
\(897\) 10880.0 0.404986
\(898\) 0 0
\(899\) 31964.0 1.18583
\(900\) 0 0
\(901\) 47736.0 1.76506
\(902\) 0 0
\(903\) −27720.0 −1.02155
\(904\) 0 0
\(905\) −31220.0 −1.14673
\(906\) 0 0
\(907\) 20936.0 0.766448 0.383224 0.923655i \(-0.374814\pi\)
0.383224 + 0.923655i \(0.374814\pi\)
\(908\) 0 0
\(909\) 88768.0 3.23900
\(910\) 0 0
\(911\) −48204.0 −1.75310 −0.876548 0.481315i \(-0.840159\pi\)
−0.876548 + 0.481315i \(0.840159\pi\)
\(912\) 0 0
\(913\) 13332.0 0.483269
\(914\) 0 0
\(915\) −27440.0 −0.991408
\(916\) 0 0
\(917\) −11088.0 −0.399300
\(918\) 0 0
\(919\) 27304.0 0.980061 0.490030 0.871705i \(-0.336986\pi\)
0.490030 + 0.871705i \(0.336986\pi\)
\(920\) 0 0
\(921\) −13200.0 −0.472264
\(922\) 0 0
\(923\) 7872.00 0.280726
\(924\) 0 0
\(925\) 9230.00 0.328087
\(926\) 0 0
\(927\) −102638. −3.63654
\(928\) 0 0
\(929\) 30.0000 0.00105949 0.000529746 1.00000i \(-0.499831\pi\)
0.000529746 1.00000i \(0.499831\pi\)
\(930\) 0 0
\(931\) −5684.00 −0.200092
\(932\) 0 0
\(933\) 10660.0 0.374054
\(934\) 0 0
\(935\) −16632.0 −0.581737
\(936\) 0 0
\(937\) 4736.00 0.165121 0.0825605 0.996586i \(-0.473690\pi\)
0.0825605 + 0.996586i \(0.473690\pi\)
\(938\) 0 0
\(939\) −92540.0 −3.21611
\(940\) 0 0
\(941\) 19996.0 0.692722 0.346361 0.938101i \(-0.387417\pi\)
0.346361 + 0.938101i \(0.387417\pi\)
\(942\) 0 0
\(943\) −13872.0 −0.479040
\(944\) 0 0
\(945\) 45080.0 1.55180
\(946\) 0 0
\(947\) 1252.00 0.0429615 0.0214807 0.999769i \(-0.493162\pi\)
0.0214807 + 0.999769i \(0.493162\pi\)
\(948\) 0 0
\(949\) −6528.00 −0.223296
\(950\) 0 0
\(951\) −97220.0 −3.31501
\(952\) 0 0
\(953\) 17986.0 0.611357 0.305679 0.952135i \(-0.401117\pi\)
0.305679 + 0.952135i \(0.401117\pi\)
\(954\) 0 0
\(955\) 30464.0 1.03224
\(956\) 0 0
\(957\) 13420.0 0.453299
\(958\) 0 0
\(959\) −6986.00 −0.235234
\(960\) 0 0
\(961\) 38853.0 1.30419
\(962\) 0 0
\(963\) 42924.0 1.43635
\(964\) 0 0
\(965\) 43764.0 1.45991
\(966\) 0 0
\(967\) −14256.0 −0.474087 −0.237043 0.971499i \(-0.576178\pi\)
−0.237043 + 0.971499i \(0.576178\pi\)
\(968\) 0 0
\(969\) −125280. −4.15333
\(970\) 0 0
\(971\) 50214.0 1.65957 0.829786 0.558082i \(-0.188463\pi\)
0.829786 + 0.558082i \(0.188463\pi\)
\(972\) 0 0
\(973\) 1932.00 0.0636558
\(974\) 0 0
\(975\) −11360.0 −0.373140
\(976\) 0 0
\(977\) −35814.0 −1.17276 −0.586382 0.810034i \(-0.699448\pi\)
−0.586382 + 0.810034i \(0.699448\pi\)
\(978\) 0 0
\(979\) 12606.0 0.411532
\(980\) 0 0
\(981\) 11242.0 0.365881
\(982\) 0 0
\(983\) 19274.0 0.625377 0.312688 0.949856i \(-0.398770\pi\)
0.312688 + 0.949856i \(0.398770\pi\)
\(984\) 0 0
\(985\) 15708.0 0.508120
\(986\) 0 0
\(987\) 11620.0 0.374740
\(988\) 0 0
\(989\) −26928.0 −0.865784
\(990\) 0 0
\(991\) −59996.0 −1.92314 −0.961572 0.274553i \(-0.911470\pi\)
−0.961572 + 0.274553i \(0.911470\pi\)
\(992\) 0 0
\(993\) −26200.0 −0.837293
\(994\) 0 0
\(995\) −78204.0 −2.49169
\(996\) 0 0
\(997\) 24344.0 0.773302 0.386651 0.922226i \(-0.373632\pi\)
0.386651 + 0.922226i \(0.373632\pi\)
\(998\) 0 0
\(999\) 59800.0 1.89388
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 1232.4.a.i.1.1 1
4.3 odd 2 154.4.a.c.1.1 1
12.11 even 2 1386.4.a.g.1.1 1
28.27 even 2 1078.4.a.h.1.1 1
44.43 even 2 1694.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.c.1.1 1 4.3 odd 2
1078.4.a.h.1.1 1 28.27 even 2
1232.4.a.i.1.1 1 1.1 even 1 trivial
1386.4.a.g.1.1 1 12.11 even 2
1694.4.a.a.1.1 1 44.43 even 2