Properties

Label 4016.2.a.g.1.6
Level 4016
Weight 2
Character 4016.1
Self dual yes
Analytic conductor 32.068
Analytic rank 0
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4016 = 2^{4} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0679214517\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.29157\)
Character \(\chi\) = 4016.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.29157 q^{3} -1.78468 q^{5} -0.671050 q^{7} +2.25130 q^{9} +O(q^{10})\) \(q+2.29157 q^{3} -1.78468 q^{5} -0.671050 q^{7} +2.25130 q^{9} -2.23015 q^{11} +0.0525243 q^{13} -4.08972 q^{15} +5.52610 q^{17} -1.49944 q^{19} -1.53776 q^{21} +7.13437 q^{23} -1.81492 q^{25} -1.71570 q^{27} +2.08515 q^{29} +9.61596 q^{31} -5.11055 q^{33} +1.19761 q^{35} +5.33025 q^{37} +0.120363 q^{39} -11.8708 q^{41} +9.09066 q^{43} -4.01785 q^{45} -5.21388 q^{47} -6.54969 q^{49} +12.6635 q^{51} +4.27480 q^{53} +3.98011 q^{55} -3.43607 q^{57} +0.163804 q^{59} +11.4800 q^{61} -1.51073 q^{63} -0.0937391 q^{65} +10.6984 q^{67} +16.3489 q^{69} +8.24538 q^{71} -12.8635 q^{73} -4.15901 q^{75} +1.49654 q^{77} +7.86983 q^{79} -10.6855 q^{81} +5.22811 q^{83} -9.86233 q^{85} +4.77826 q^{87} -2.70075 q^{89} -0.0352465 q^{91} +22.0357 q^{93} +2.67602 q^{95} +16.2733 q^{97} -5.02074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + O(q^{10}) \) \( 7q + 3q^{3} - 2q^{5} + 6q^{7} + 5q^{11} - q^{13} + 6q^{15} - 8q^{17} + 15q^{19} - 3q^{21} + 5q^{23} - 9q^{25} + 9q^{27} + 21q^{31} + 7q^{35} - q^{37} + 23q^{39} - 10q^{41} + 23q^{43} - 4q^{45} + 10q^{47} - 13q^{49} + 20q^{51} - q^{53} + 23q^{55} - 6q^{57} + 4q^{59} + 3q^{61} + 4q^{63} + 4q^{65} + 28q^{67} + 18q^{69} + 18q^{71} - 7q^{73} - 11q^{75} + 6q^{77} + 30q^{79} - 5q^{81} - 13q^{83} + q^{85} + 7q^{87} + 18q^{91} + 36q^{93} - 2q^{97} + 10q^{99} + O(q^{100}) \)

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
\(3\) 2.29157 1.32304 0.661520 0.749928i \(-0.269912\pi\)
0.661520 + 0.749928i \(0.269912\pi\)
\(4\) 0 0
\(5\) −1.78468 −0.798133 −0.399067 0.916922i \(-0.630666\pi\)
−0.399067 + 0.916922i \(0.630666\pi\)
\(6\) 0 0
\(7\) −0.671050 −0.253633 −0.126817 0.991926i \(-0.540476\pi\)
−0.126817 + 0.991926i \(0.540476\pi\)
\(8\) 0 0
\(9\) 2.25130 0.750433
\(10\) 0 0
\(11\) −2.23015 −0.672416 −0.336208 0.941788i \(-0.609145\pi\)
−0.336208 + 0.941788i \(0.609145\pi\)
\(12\) 0 0
\(13\) 0.0525243 0.0145676 0.00728381 0.999973i \(-0.497681\pi\)
0.00728381 + 0.999973i \(0.497681\pi\)
\(14\) 0 0
\(15\) −4.08972 −1.05596
\(16\) 0 0
\(17\) 5.52610 1.34028 0.670138 0.742236i \(-0.266235\pi\)
0.670138 + 0.742236i \(0.266235\pi\)
\(18\) 0 0
\(19\) −1.49944 −0.343995 −0.171997 0.985097i \(-0.555022\pi\)
−0.171997 + 0.985097i \(0.555022\pi\)
\(20\) 0 0
\(21\) −1.53776 −0.335567
\(22\) 0 0
\(23\) 7.13437 1.48762 0.743810 0.668391i \(-0.233017\pi\)
0.743810 + 0.668391i \(0.233017\pi\)
\(24\) 0 0
\(25\) −1.81492 −0.362984
\(26\) 0 0
\(27\) −1.71570 −0.330187
\(28\) 0 0
\(29\) 2.08515 0.387202 0.193601 0.981080i \(-0.437983\pi\)
0.193601 + 0.981080i \(0.437983\pi\)
\(30\) 0 0
\(31\) 9.61596 1.72708 0.863539 0.504282i \(-0.168243\pi\)
0.863539 + 0.504282i \(0.168243\pi\)
\(32\) 0 0
\(33\) −5.11055 −0.889633
\(34\) 0 0
\(35\) 1.19761 0.202433
\(36\) 0 0
\(37\) 5.33025 0.876288 0.438144 0.898905i \(-0.355636\pi\)
0.438144 + 0.898905i \(0.355636\pi\)
\(38\) 0 0
\(39\) 0.120363 0.0192735
\(40\) 0 0
\(41\) −11.8708 −1.85391 −0.926956 0.375170i \(-0.877584\pi\)
−0.926956 + 0.375170i \(0.877584\pi\)
\(42\) 0 0
\(43\) 9.09066 1.38631 0.693157 0.720787i \(-0.256219\pi\)
0.693157 + 0.720787i \(0.256219\pi\)
\(44\) 0 0
\(45\) −4.01785 −0.598946
\(46\) 0 0
\(47\) −5.21388 −0.760523 −0.380261 0.924879i \(-0.624166\pi\)
−0.380261 + 0.924879i \(0.624166\pi\)
\(48\) 0 0
\(49\) −6.54969 −0.935670
\(50\) 0 0
\(51\) 12.6635 1.77324
\(52\) 0 0
\(53\) 4.27480 0.587189 0.293595 0.955930i \(-0.405148\pi\)
0.293595 + 0.955930i \(0.405148\pi\)
\(54\) 0 0
\(55\) 3.98011 0.536678
\(56\) 0 0
\(57\) −3.43607 −0.455118
\(58\) 0 0
\(59\) 0.163804 0.0213254 0.0106627 0.999943i \(-0.496606\pi\)
0.0106627 + 0.999943i \(0.496606\pi\)
\(60\) 0 0
\(61\) 11.4800 1.46987 0.734934 0.678138i \(-0.237213\pi\)
0.734934 + 0.678138i \(0.237213\pi\)
\(62\) 0 0
\(63\) −1.51073 −0.190335
\(64\) 0 0
\(65\) −0.0937391 −0.0116269
\(66\) 0 0
\(67\) 10.6984 1.30702 0.653509 0.756918i \(-0.273296\pi\)
0.653509 + 0.756918i \(0.273296\pi\)
\(68\) 0 0
\(69\) 16.3489 1.96818
\(70\) 0 0
\(71\) 8.24538 0.978546 0.489273 0.872131i \(-0.337262\pi\)
0.489273 + 0.872131i \(0.337262\pi\)
\(72\) 0 0
\(73\) −12.8635 −1.50556 −0.752779 0.658273i \(-0.771287\pi\)
−0.752779 + 0.658273i \(0.771287\pi\)
\(74\) 0 0
\(75\) −4.15901 −0.480241
\(76\) 0 0
\(77\) 1.49654 0.170547
\(78\) 0 0
\(79\) 7.86983 0.885425 0.442712 0.896664i \(-0.354016\pi\)
0.442712 + 0.896664i \(0.354016\pi\)
\(80\) 0 0
\(81\) −10.6855 −1.18728
\(82\) 0 0
\(83\) 5.22811 0.573860 0.286930 0.957952i \(-0.407365\pi\)
0.286930 + 0.957952i \(0.407365\pi\)
\(84\) 0 0
\(85\) −9.86233 −1.06972
\(86\) 0 0
\(87\) 4.77826 0.512283
\(88\) 0 0
\(89\) −2.70075 −0.286279 −0.143140 0.989703i \(-0.545720\pi\)
−0.143140 + 0.989703i \(0.545720\pi\)
\(90\) 0 0
\(91\) −0.0352465 −0.00369483
\(92\) 0 0
\(93\) 22.0357 2.28499
\(94\) 0 0
\(95\) 2.67602 0.274554
\(96\) 0 0
\(97\) 16.2733 1.65230 0.826150 0.563450i \(-0.190526\pi\)
0.826150 + 0.563450i \(0.190526\pi\)
\(98\) 0 0
\(99\) −5.02074 −0.504604
\(100\) 0 0
\(101\) 7.31471 0.727841 0.363920 0.931430i \(-0.381438\pi\)
0.363920 + 0.931430i \(0.381438\pi\)
\(102\) 0 0
\(103\) 8.43476 0.831102 0.415551 0.909570i \(-0.363589\pi\)
0.415551 + 0.909570i \(0.363589\pi\)
\(104\) 0 0
\(105\) 2.74441 0.267827
\(106\) 0 0
\(107\) 13.4235 1.29770 0.648851 0.760915i \(-0.275250\pi\)
0.648851 + 0.760915i \(0.275250\pi\)
\(108\) 0 0
\(109\) −10.8033 −1.03477 −0.517386 0.855752i \(-0.673095\pi\)
−0.517386 + 0.855752i \(0.673095\pi\)
\(110\) 0 0
\(111\) 12.2147 1.15936
\(112\) 0 0
\(113\) 6.62110 0.622861 0.311431 0.950269i \(-0.399192\pi\)
0.311431 + 0.950269i \(0.399192\pi\)
\(114\) 0 0
\(115\) −12.7326 −1.18732
\(116\) 0 0
\(117\) 0.118248 0.0109320
\(118\) 0 0
\(119\) −3.70829 −0.339939
\(120\) 0 0
\(121\) −6.02642 −0.547856
\(122\) 0 0
\(123\) −27.2029 −2.45280
\(124\) 0 0
\(125\) 12.1624 1.08784
\(126\) 0 0
\(127\) 1.34857 0.119666 0.0598329 0.998208i \(-0.480943\pi\)
0.0598329 + 0.998208i \(0.480943\pi\)
\(128\) 0 0
\(129\) 20.8319 1.83415
\(130\) 0 0
\(131\) −14.5213 −1.26873 −0.634365 0.773034i \(-0.718738\pi\)
−0.634365 + 0.773034i \(0.718738\pi\)
\(132\) 0 0
\(133\) 1.00620 0.0872484
\(134\) 0 0
\(135\) 3.06198 0.263533
\(136\) 0 0
\(137\) 4.81237 0.411148 0.205574 0.978642i \(-0.434094\pi\)
0.205574 + 0.978642i \(0.434094\pi\)
\(138\) 0 0
\(139\) 17.6736 1.49905 0.749527 0.661974i \(-0.230281\pi\)
0.749527 + 0.661974i \(0.230281\pi\)
\(140\) 0 0
\(141\) −11.9480 −1.00620
\(142\) 0 0
\(143\) −0.117137 −0.00979551
\(144\) 0 0
\(145\) −3.72132 −0.309039
\(146\) 0 0
\(147\) −15.0091 −1.23793
\(148\) 0 0
\(149\) 3.49560 0.286371 0.143185 0.989696i \(-0.454265\pi\)
0.143185 + 0.989696i \(0.454265\pi\)
\(150\) 0 0
\(151\) 3.05261 0.248418 0.124209 0.992256i \(-0.460361\pi\)
0.124209 + 0.992256i \(0.460361\pi\)
\(152\) 0 0
\(153\) 12.4409 1.00579
\(154\) 0 0
\(155\) −17.1614 −1.37844
\(156\) 0 0
\(157\) −2.92795 −0.233676 −0.116838 0.993151i \(-0.537276\pi\)
−0.116838 + 0.993151i \(0.537276\pi\)
\(158\) 0 0
\(159\) 9.79602 0.776875
\(160\) 0 0
\(161\) −4.78752 −0.377310
\(162\) 0 0
\(163\) −11.1100 −0.870200 −0.435100 0.900382i \(-0.643287\pi\)
−0.435100 + 0.900382i \(0.643287\pi\)
\(164\) 0 0
\(165\) 9.12070 0.710046
\(166\) 0 0
\(167\) −6.79223 −0.525599 −0.262799 0.964851i \(-0.584646\pi\)
−0.262799 + 0.964851i \(0.584646\pi\)
\(168\) 0 0
\(169\) −12.9972 −0.999788
\(170\) 0 0
\(171\) −3.37568 −0.258145
\(172\) 0 0
\(173\) 19.7703 1.50311 0.751553 0.659673i \(-0.229305\pi\)
0.751553 + 0.659673i \(0.229305\pi\)
\(174\) 0 0
\(175\) 1.21790 0.0920646
\(176\) 0 0
\(177\) 0.375368 0.0282144
\(178\) 0 0
\(179\) 17.5575 1.31231 0.656154 0.754627i \(-0.272182\pi\)
0.656154 + 0.754627i \(0.272182\pi\)
\(180\) 0 0
\(181\) −3.21551 −0.239007 −0.119503 0.992834i \(-0.538130\pi\)
−0.119503 + 0.992834i \(0.538130\pi\)
\(182\) 0 0
\(183\) 26.3073 1.94469
\(184\) 0 0
\(185\) −9.51280 −0.699395
\(186\) 0 0
\(187\) −12.3241 −0.901224
\(188\) 0 0
\(189\) 1.15132 0.0837463
\(190\) 0 0
\(191\) 12.1389 0.878342 0.439171 0.898404i \(-0.355272\pi\)
0.439171 + 0.898404i \(0.355272\pi\)
\(192\) 0 0
\(193\) 11.5502 0.831399 0.415700 0.909502i \(-0.363537\pi\)
0.415700 + 0.909502i \(0.363537\pi\)
\(194\) 0 0
\(195\) −0.214810 −0.0153829
\(196\) 0 0
\(197\) −0.556439 −0.0396447 −0.0198223 0.999804i \(-0.506310\pi\)
−0.0198223 + 0.999804i \(0.506310\pi\)
\(198\) 0 0
\(199\) −15.8849 −1.12605 −0.563025 0.826440i \(-0.690363\pi\)
−0.563025 + 0.826440i \(0.690363\pi\)
\(200\) 0 0
\(201\) 24.5162 1.72924
\(202\) 0 0
\(203\) −1.39924 −0.0982072
\(204\) 0 0
\(205\) 21.1856 1.47967
\(206\) 0 0
\(207\) 16.0616 1.11636
\(208\) 0 0
\(209\) 3.34398 0.231308
\(210\) 0 0
\(211\) 23.8560 1.64231 0.821156 0.570703i \(-0.193329\pi\)
0.821156 + 0.570703i \(0.193329\pi\)
\(212\) 0 0
\(213\) 18.8949 1.29466
\(214\) 0 0
\(215\) −16.2239 −1.10646
\(216\) 0 0
\(217\) −6.45279 −0.438044
\(218\) 0 0
\(219\) −29.4776 −1.99191
\(220\) 0 0
\(221\) 0.290255 0.0195247
\(222\) 0 0
\(223\) −6.27008 −0.419876 −0.209938 0.977715i \(-0.567326\pi\)
−0.209938 + 0.977715i \(0.567326\pi\)
\(224\) 0 0
\(225\) −4.08592 −0.272395
\(226\) 0 0
\(227\) −5.69103 −0.377727 −0.188863 0.982003i \(-0.560480\pi\)
−0.188863 + 0.982003i \(0.560480\pi\)
\(228\) 0 0
\(229\) −21.9135 −1.44808 −0.724042 0.689756i \(-0.757718\pi\)
−0.724042 + 0.689756i \(0.757718\pi\)
\(230\) 0 0
\(231\) 3.42944 0.225640
\(232\) 0 0
\(233\) 11.6290 0.761841 0.380921 0.924608i \(-0.375607\pi\)
0.380921 + 0.924608i \(0.375607\pi\)
\(234\) 0 0
\(235\) 9.30511 0.606999
\(236\) 0 0
\(237\) 18.0343 1.17145
\(238\) 0 0
\(239\) −17.3971 −1.12533 −0.562664 0.826686i \(-0.690223\pi\)
−0.562664 + 0.826686i \(0.690223\pi\)
\(240\) 0 0
\(241\) −2.35929 −0.151975 −0.0759875 0.997109i \(-0.524211\pi\)
−0.0759875 + 0.997109i \(0.524211\pi\)
\(242\) 0 0
\(243\) −19.3396 −1.24064
\(244\) 0 0
\(245\) 11.6891 0.746789
\(246\) 0 0
\(247\) −0.0787570 −0.00501119
\(248\) 0 0
\(249\) 11.9806 0.759239
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) −15.9107 −1.00030
\(254\) 0 0
\(255\) −22.6002 −1.41528
\(256\) 0 0
\(257\) −18.2850 −1.14059 −0.570293 0.821442i \(-0.693170\pi\)
−0.570293 + 0.821442i \(0.693170\pi\)
\(258\) 0 0
\(259\) −3.57687 −0.222256
\(260\) 0 0
\(261\) 4.69429 0.290569
\(262\) 0 0
\(263\) 1.62067 0.0999350 0.0499675 0.998751i \(-0.484088\pi\)
0.0499675 + 0.998751i \(0.484088\pi\)
\(264\) 0 0
\(265\) −7.62916 −0.468655
\(266\) 0 0
\(267\) −6.18896 −0.378758
\(268\) 0 0
\(269\) −26.9395 −1.64253 −0.821265 0.570547i \(-0.806731\pi\)
−0.821265 + 0.570547i \(0.806731\pi\)
\(270\) 0 0
\(271\) −1.70433 −0.103531 −0.0517653 0.998659i \(-0.516485\pi\)
−0.0517653 + 0.998659i \(0.516485\pi\)
\(272\) 0 0
\(273\) −0.0807698 −0.00488841
\(274\) 0 0
\(275\) 4.04754 0.244076
\(276\) 0 0
\(277\) 0.720069 0.0432648 0.0216324 0.999766i \(-0.493114\pi\)
0.0216324 + 0.999766i \(0.493114\pi\)
\(278\) 0 0
\(279\) 21.6484 1.29606
\(280\) 0 0
\(281\) −9.07112 −0.541138 −0.270569 0.962701i \(-0.587212\pi\)
−0.270569 + 0.962701i \(0.587212\pi\)
\(282\) 0 0
\(283\) 10.0455 0.597140 0.298570 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(284\) 0 0
\(285\) 6.13228 0.363245
\(286\) 0 0
\(287\) 7.96592 0.470213
\(288\) 0 0
\(289\) 13.5378 0.796342
\(290\) 0 0
\(291\) 37.2914 2.18606
\(292\) 0 0
\(293\) −9.10277 −0.531790 −0.265895 0.964002i \(-0.585667\pi\)
−0.265895 + 0.964002i \(0.585667\pi\)
\(294\) 0 0
\(295\) −0.292337 −0.0170205
\(296\) 0 0
\(297\) 3.82628 0.222023
\(298\) 0 0
\(299\) 0.374728 0.0216711
\(300\) 0 0
\(301\) −6.10029 −0.351615
\(302\) 0 0
\(303\) 16.7622 0.962962
\(304\) 0 0
\(305\) −20.4882 −1.17315
\(306\) 0 0
\(307\) 9.11554 0.520251 0.260126 0.965575i \(-0.416236\pi\)
0.260126 + 0.965575i \(0.416236\pi\)
\(308\) 0 0
\(309\) 19.3289 1.09958
\(310\) 0 0
\(311\) −29.5389 −1.67500 −0.837498 0.546440i \(-0.815982\pi\)
−0.837498 + 0.546440i \(0.815982\pi\)
\(312\) 0 0
\(313\) −1.02555 −0.0579676 −0.0289838 0.999580i \(-0.509227\pi\)
−0.0289838 + 0.999580i \(0.509227\pi\)
\(314\) 0 0
\(315\) 2.69618 0.151912
\(316\) 0 0
\(317\) −3.25854 −0.183018 −0.0915089 0.995804i \(-0.529169\pi\)
−0.0915089 + 0.995804i \(0.529169\pi\)
\(318\) 0 0
\(319\) −4.65019 −0.260361
\(320\) 0 0
\(321\) 30.7610 1.71691
\(322\) 0 0
\(323\) −8.28605 −0.461048
\(324\) 0 0
\(325\) −0.0953273 −0.00528781
\(326\) 0 0
\(327\) −24.7566 −1.36904
\(328\) 0 0
\(329\) 3.49878 0.192894
\(330\) 0 0
\(331\) −1.22129 −0.0671281 −0.0335640 0.999437i \(-0.510686\pi\)
−0.0335640 + 0.999437i \(0.510686\pi\)
\(332\) 0 0
\(333\) 12.0000 0.657596
\(334\) 0 0
\(335\) −19.0932 −1.04318
\(336\) 0 0
\(337\) 28.7954 1.56859 0.784293 0.620391i \(-0.213026\pi\)
0.784293 + 0.620391i \(0.213026\pi\)
\(338\) 0 0
\(339\) 15.1727 0.824070
\(340\) 0 0
\(341\) −21.4451 −1.16132
\(342\) 0 0
\(343\) 9.09252 0.490950
\(344\) 0 0
\(345\) −29.1776 −1.57087
\(346\) 0 0
\(347\) 13.0949 0.702970 0.351485 0.936194i \(-0.385677\pi\)
0.351485 + 0.936194i \(0.385677\pi\)
\(348\) 0 0
\(349\) −14.8887 −0.796974 −0.398487 0.917174i \(-0.630465\pi\)
−0.398487 + 0.917174i \(0.630465\pi\)
\(350\) 0 0
\(351\) −0.0901160 −0.00481004
\(352\) 0 0
\(353\) −29.2068 −1.55452 −0.777260 0.629179i \(-0.783391\pi\)
−0.777260 + 0.629179i \(0.783391\pi\)
\(354\) 0 0
\(355\) −14.7154 −0.781010
\(356\) 0 0
\(357\) −8.49782 −0.449752
\(358\) 0 0
\(359\) −27.4180 −1.44707 −0.723534 0.690288i \(-0.757484\pi\)
−0.723534 + 0.690288i \(0.757484\pi\)
\(360\) 0 0
\(361\) −16.7517 −0.881668
\(362\) 0 0
\(363\) −13.8100 −0.724835
\(364\) 0 0
\(365\) 22.9572 1.20164
\(366\) 0 0
\(367\) 31.9200 1.66621 0.833105 0.553115i \(-0.186561\pi\)
0.833105 + 0.553115i \(0.186561\pi\)
\(368\) 0 0
\(369\) −26.7248 −1.39124
\(370\) 0 0
\(371\) −2.86861 −0.148931
\(372\) 0 0
\(373\) 16.2376 0.840753 0.420376 0.907350i \(-0.361898\pi\)
0.420376 + 0.907350i \(0.361898\pi\)
\(374\) 0 0
\(375\) 27.8711 1.43926
\(376\) 0 0
\(377\) 0.109521 0.00564061
\(378\) 0 0
\(379\) −21.8277 −1.12121 −0.560607 0.828082i \(-0.689432\pi\)
−0.560607 + 0.828082i \(0.689432\pi\)
\(380\) 0 0
\(381\) 3.09033 0.158323
\(382\) 0 0
\(383\) −5.38270 −0.275043 −0.137521 0.990499i \(-0.543914\pi\)
−0.137521 + 0.990499i \(0.543914\pi\)
\(384\) 0 0
\(385\) −2.67085 −0.136119
\(386\) 0 0
\(387\) 20.4658 1.04034
\(388\) 0 0
\(389\) −30.3894 −1.54080 −0.770401 0.637560i \(-0.779944\pi\)
−0.770401 + 0.637560i \(0.779944\pi\)
\(390\) 0 0
\(391\) 39.4253 1.99382
\(392\) 0 0
\(393\) −33.2766 −1.67858
\(394\) 0 0
\(395\) −14.0451 −0.706687
\(396\) 0 0
\(397\) 13.3900 0.672023 0.336011 0.941858i \(-0.390922\pi\)
0.336011 + 0.941858i \(0.390922\pi\)
\(398\) 0 0
\(399\) 2.30577 0.115433
\(400\) 0 0
\(401\) −34.2511 −1.71042 −0.855209 0.518284i \(-0.826571\pi\)
−0.855209 + 0.518284i \(0.826571\pi\)
\(402\) 0 0
\(403\) 0.505072 0.0251594
\(404\) 0 0
\(405\) 19.0703 0.947610
\(406\) 0 0
\(407\) −11.8873 −0.589231
\(408\) 0 0
\(409\) 13.3152 0.658394 0.329197 0.944261i \(-0.393222\pi\)
0.329197 + 0.944261i \(0.393222\pi\)
\(410\) 0 0
\(411\) 11.0279 0.543965
\(412\) 0 0
\(413\) −0.109920 −0.00540883
\(414\) 0 0
\(415\) −9.33050 −0.458016
\(416\) 0 0
\(417\) 40.5003 1.98331
\(418\) 0 0
\(419\) −3.62652 −0.177167 −0.0885836 0.996069i \(-0.528234\pi\)
−0.0885836 + 0.996069i \(0.528234\pi\)
\(420\) 0 0
\(421\) −9.05916 −0.441516 −0.220758 0.975329i \(-0.570853\pi\)
−0.220758 + 0.975329i \(0.570853\pi\)
\(422\) 0 0
\(423\) −11.7380 −0.570722
\(424\) 0 0
\(425\) −10.0294 −0.486498
\(426\) 0 0
\(427\) −7.70368 −0.372807
\(428\) 0 0
\(429\) −0.268428 −0.0129598
\(430\) 0 0
\(431\) −1.80929 −0.0871506 −0.0435753 0.999050i \(-0.513875\pi\)
−0.0435753 + 0.999050i \(0.513875\pi\)
\(432\) 0 0
\(433\) 6.34504 0.304923 0.152462 0.988309i \(-0.451280\pi\)
0.152462 + 0.988309i \(0.451280\pi\)
\(434\) 0 0
\(435\) −8.52766 −0.408870
\(436\) 0 0
\(437\) −10.6975 −0.511733
\(438\) 0 0
\(439\) −30.1384 −1.43843 −0.719214 0.694788i \(-0.755498\pi\)
−0.719214 + 0.694788i \(0.755498\pi\)
\(440\) 0 0
\(441\) −14.7453 −0.702158
\(442\) 0 0
\(443\) 11.1274 0.528679 0.264339 0.964430i \(-0.414846\pi\)
0.264339 + 0.964430i \(0.414846\pi\)
\(444\) 0 0
\(445\) 4.81998 0.228489
\(446\) 0 0
\(447\) 8.01042 0.378880
\(448\) 0 0
\(449\) 35.6616 1.68297 0.841487 0.540277i \(-0.181680\pi\)
0.841487 + 0.540277i \(0.181680\pi\)
\(450\) 0 0
\(451\) 26.4738 1.24660
\(452\) 0 0
\(453\) 6.99527 0.328666
\(454\) 0 0
\(455\) 0.0629036 0.00294897
\(456\) 0 0
\(457\) −31.2226 −1.46053 −0.730266 0.683163i \(-0.760604\pi\)
−0.730266 + 0.683163i \(0.760604\pi\)
\(458\) 0 0
\(459\) −9.48114 −0.442542
\(460\) 0 0
\(461\) 10.3296 0.481097 0.240549 0.970637i \(-0.422673\pi\)
0.240549 + 0.970637i \(0.422673\pi\)
\(462\) 0 0
\(463\) 24.1578 1.12271 0.561355 0.827575i \(-0.310280\pi\)
0.561355 + 0.827575i \(0.310280\pi\)
\(464\) 0 0
\(465\) −39.3266 −1.82373
\(466\) 0 0
\(467\) −35.6761 −1.65089 −0.825447 0.564479i \(-0.809077\pi\)
−0.825447 + 0.564479i \(0.809077\pi\)
\(468\) 0 0
\(469\) −7.17917 −0.331503
\(470\) 0 0
\(471\) −6.70960 −0.309162
\(472\) 0 0
\(473\) −20.2736 −0.932180
\(474\) 0 0
\(475\) 2.72136 0.124864
\(476\) 0 0
\(477\) 9.62386 0.440646
\(478\) 0 0
\(479\) 4.37843 0.200055 0.100028 0.994985i \(-0.468107\pi\)
0.100028 + 0.994985i \(0.468107\pi\)
\(480\) 0 0
\(481\) 0.279968 0.0127654
\(482\) 0 0
\(483\) −10.9709 −0.499195
\(484\) 0 0
\(485\) −29.0426 −1.31876
\(486\) 0 0
\(487\) 32.4930 1.47240 0.736198 0.676766i \(-0.236619\pi\)
0.736198 + 0.676766i \(0.236619\pi\)
\(488\) 0 0
\(489\) −25.4593 −1.15131
\(490\) 0 0
\(491\) −12.9926 −0.586348 −0.293174 0.956059i \(-0.594711\pi\)
−0.293174 + 0.956059i \(0.594711\pi\)
\(492\) 0 0
\(493\) 11.5227 0.518958
\(494\) 0 0
\(495\) 8.96042 0.402741
\(496\) 0 0
\(497\) −5.53306 −0.248192
\(498\) 0 0
\(499\) −2.12523 −0.0951383 −0.0475691 0.998868i \(-0.515147\pi\)
−0.0475691 + 0.998868i \(0.515147\pi\)
\(500\) 0 0
\(501\) −15.5649 −0.695388
\(502\) 0 0
\(503\) −28.1675 −1.25593 −0.627964 0.778243i \(-0.716111\pi\)
−0.627964 + 0.778243i \(0.716111\pi\)
\(504\) 0 0
\(505\) −13.0544 −0.580914
\(506\) 0 0
\(507\) −29.7841 −1.32276
\(508\) 0 0
\(509\) −3.65358 −0.161942 −0.0809710 0.996716i \(-0.525802\pi\)
−0.0809710 + 0.996716i \(0.525802\pi\)
\(510\) 0 0
\(511\) 8.63205 0.381859
\(512\) 0 0
\(513\) 2.57259 0.113582
\(514\) 0 0
\(515\) −15.0533 −0.663330
\(516\) 0 0
\(517\) 11.6278 0.511388
\(518\) 0 0
\(519\) 45.3050 1.98867
\(520\) 0 0
\(521\) −30.7443 −1.34693 −0.673465 0.739219i \(-0.735195\pi\)
−0.673465 + 0.739219i \(0.735195\pi\)
\(522\) 0 0
\(523\) −25.0146 −1.09381 −0.546906 0.837194i \(-0.684194\pi\)
−0.546906 + 0.837194i \(0.684194\pi\)
\(524\) 0 0
\(525\) 2.79091 0.121805
\(526\) 0 0
\(527\) 53.1388 2.31476
\(528\) 0 0
\(529\) 27.8993 1.21301
\(530\) 0 0
\(531\) 0.368771 0.0160033
\(532\) 0 0
\(533\) −0.623507 −0.0270071
\(534\) 0 0
\(535\) −23.9567 −1.03574
\(536\) 0 0
\(537\) 40.2342 1.73623
\(538\) 0 0
\(539\) 14.6068 0.629160
\(540\) 0 0
\(541\) 19.3510 0.831964 0.415982 0.909373i \(-0.363438\pi\)
0.415982 + 0.909373i \(0.363438\pi\)
\(542\) 0 0
\(543\) −7.36856 −0.316215
\(544\) 0 0
\(545\) 19.2805 0.825886
\(546\) 0 0
\(547\) 2.14537 0.0917294 0.0458647 0.998948i \(-0.485396\pi\)
0.0458647 + 0.998948i \(0.485396\pi\)
\(548\) 0 0
\(549\) 25.8450 1.10304
\(550\) 0 0
\(551\) −3.12655 −0.133195
\(552\) 0 0
\(553\) −5.28105 −0.224573
\(554\) 0 0
\(555\) −21.7993 −0.925327
\(556\) 0 0
\(557\) 42.7554 1.81160 0.905802 0.423702i \(-0.139270\pi\)
0.905802 + 0.423702i \(0.139270\pi\)
\(558\) 0 0
\(559\) 0.477481 0.0201953
\(560\) 0 0
\(561\) −28.2415 −1.19236
\(562\) 0 0
\(563\) −17.4443 −0.735191 −0.367596 0.929986i \(-0.619819\pi\)
−0.367596 + 0.929986i \(0.619819\pi\)
\(564\) 0 0
\(565\) −11.8166 −0.497126
\(566\) 0 0
\(567\) 7.17054 0.301134
\(568\) 0 0
\(569\) −36.4900 −1.52974 −0.764871 0.644184i \(-0.777197\pi\)
−0.764871 + 0.644184i \(0.777197\pi\)
\(570\) 0 0
\(571\) 41.9707 1.75642 0.878210 0.478275i \(-0.158738\pi\)
0.878210 + 0.478275i \(0.158738\pi\)
\(572\) 0 0
\(573\) 27.8172 1.16208
\(574\) 0 0
\(575\) −12.9483 −0.539981
\(576\) 0 0
\(577\) 12.3140 0.512639 0.256320 0.966592i \(-0.417490\pi\)
0.256320 + 0.966592i \(0.417490\pi\)
\(578\) 0 0
\(579\) 26.4680 1.09997
\(580\) 0 0
\(581\) −3.50832 −0.145550
\(582\) 0 0
\(583\) −9.53347 −0.394836
\(584\) 0 0
\(585\) −0.211035 −0.00872522
\(586\) 0 0
\(587\) −13.8231 −0.570540 −0.285270 0.958447i \(-0.592083\pi\)
−0.285270 + 0.958447i \(0.592083\pi\)
\(588\) 0 0
\(589\) −14.4185 −0.594105
\(590\) 0 0
\(591\) −1.27512 −0.0524515
\(592\) 0 0
\(593\) 15.5625 0.639075 0.319538 0.947574i \(-0.396472\pi\)
0.319538 + 0.947574i \(0.396472\pi\)
\(594\) 0 0
\(595\) 6.61811 0.271316
\(596\) 0 0
\(597\) −36.4014 −1.48981
\(598\) 0 0
\(599\) −6.86070 −0.280321 −0.140160 0.990129i \(-0.544762\pi\)
−0.140160 + 0.990129i \(0.544762\pi\)
\(600\) 0 0
\(601\) 3.73347 0.152292 0.0761458 0.997097i \(-0.475739\pi\)
0.0761458 + 0.997097i \(0.475739\pi\)
\(602\) 0 0
\(603\) 24.0853 0.980830
\(604\) 0 0
\(605\) 10.7552 0.437262
\(606\) 0 0
\(607\) −40.4537 −1.64197 −0.820983 0.570953i \(-0.806574\pi\)
−0.820983 + 0.570953i \(0.806574\pi\)
\(608\) 0 0
\(609\) −3.20645 −0.129932
\(610\) 0 0
\(611\) −0.273856 −0.0110790
\(612\) 0 0
\(613\) −18.2453 −0.736921 −0.368460 0.929643i \(-0.620115\pi\)
−0.368460 + 0.929643i \(0.620115\pi\)
\(614\) 0 0
\(615\) 48.5484 1.95766
\(616\) 0 0
\(617\) 20.5886 0.828864 0.414432 0.910080i \(-0.363980\pi\)
0.414432 + 0.910080i \(0.363980\pi\)
\(618\) 0 0
\(619\) 11.8400 0.475890 0.237945 0.971279i \(-0.423526\pi\)
0.237945 + 0.971279i \(0.423526\pi\)
\(620\) 0 0
\(621\) −12.2404 −0.491192
\(622\) 0 0
\(623\) 1.81234 0.0726098
\(624\) 0 0
\(625\) −12.6315 −0.505259
\(626\) 0 0
\(627\) 7.66296 0.306029
\(628\) 0 0
\(629\) 29.4555 1.17447
\(630\) 0 0
\(631\) 24.3224 0.968258 0.484129 0.874997i \(-0.339137\pi\)
0.484129 + 0.874997i \(0.339137\pi\)
\(632\) 0 0
\(633\) 54.6677 2.17284
\(634\) 0 0
\(635\) −2.40676 −0.0955093
\(636\) 0 0
\(637\) −0.344018 −0.0136305
\(638\) 0 0
\(639\) 18.5628 0.734333
\(640\) 0 0
\(641\) 14.8821 0.587808 0.293904 0.955835i \(-0.405045\pi\)
0.293904 + 0.955835i \(0.405045\pi\)
\(642\) 0 0
\(643\) 9.38851 0.370247 0.185123 0.982715i \(-0.440732\pi\)
0.185123 + 0.982715i \(0.440732\pi\)
\(644\) 0 0
\(645\) −37.1783 −1.46389
\(646\) 0 0
\(647\) 24.9638 0.981430 0.490715 0.871320i \(-0.336736\pi\)
0.490715 + 0.871320i \(0.336736\pi\)
\(648\) 0 0
\(649\) −0.365307 −0.0143396
\(650\) 0 0
\(651\) −14.7870 −0.579550
\(652\) 0 0
\(653\) 34.0819 1.33373 0.666865 0.745179i \(-0.267636\pi\)
0.666865 + 0.745179i \(0.267636\pi\)
\(654\) 0 0
\(655\) 25.9158 1.01262
\(656\) 0 0
\(657\) −28.9596 −1.12982
\(658\) 0 0
\(659\) −19.7009 −0.767440 −0.383720 0.923450i \(-0.625357\pi\)
−0.383720 + 0.923450i \(0.625357\pi\)
\(660\) 0 0
\(661\) 17.9804 0.699358 0.349679 0.936870i \(-0.386291\pi\)
0.349679 + 0.936870i \(0.386291\pi\)
\(662\) 0 0
\(663\) 0.665140 0.0258319
\(664\) 0 0
\(665\) −1.79574 −0.0696359
\(666\) 0 0
\(667\) 14.8762 0.576009
\(668\) 0 0
\(669\) −14.3683 −0.555512
\(670\) 0 0
\(671\) −25.6022 −0.988364
\(672\) 0 0
\(673\) −10.6371 −0.410029 −0.205015 0.978759i \(-0.565724\pi\)
−0.205015 + 0.978759i \(0.565724\pi\)
\(674\) 0 0
\(675\) 3.11386 0.119852
\(676\) 0 0
\(677\) −11.0551 −0.424883 −0.212441 0.977174i \(-0.568141\pi\)
−0.212441 + 0.977174i \(0.568141\pi\)
\(678\) 0 0
\(679\) −10.9202 −0.419078
\(680\) 0 0
\(681\) −13.0414 −0.499748
\(682\) 0 0
\(683\) 26.2786 1.00552 0.502762 0.864425i \(-0.332317\pi\)
0.502762 + 0.864425i \(0.332317\pi\)
\(684\) 0 0
\(685\) −8.58853 −0.328151
\(686\) 0 0
\(687\) −50.2163 −1.91587
\(688\) 0 0
\(689\) 0.224531 0.00855396
\(690\) 0 0
\(691\) 29.0629 1.10561 0.552803 0.833312i \(-0.313558\pi\)
0.552803 + 0.833312i \(0.313558\pi\)
\(692\) 0 0
\(693\) 3.36917 0.127984
\(694\) 0 0
\(695\) −31.5417 −1.19644
\(696\) 0 0
\(697\) −65.5994 −2.48476
\(698\) 0 0
\(699\) 26.6487 1.00795
\(700\) 0 0
\(701\) −29.7473 −1.12354 −0.561771 0.827293i \(-0.689880\pi\)
−0.561771 + 0.827293i \(0.689880\pi\)
\(702\) 0 0
\(703\) −7.99238 −0.301438
\(704\) 0 0
\(705\) 21.3233 0.803083
\(706\) 0 0
\(707\) −4.90854 −0.184605
\(708\) 0 0
\(709\) 30.8047 1.15689 0.578447 0.815720i \(-0.303659\pi\)
0.578447 + 0.815720i \(0.303659\pi\)
\(710\) 0 0
\(711\) 17.7173 0.664452
\(712\) 0 0
\(713\) 68.6038 2.56923
\(714\) 0 0
\(715\) 0.209053 0.00781812
\(716\) 0 0
\(717\) −39.8668 −1.48885
\(718\) 0 0
\(719\) −29.2904 −1.09235 −0.546175 0.837671i \(-0.683917\pi\)
−0.546175 + 0.837671i \(0.683917\pi\)
\(720\) 0 0
\(721\) −5.66015 −0.210795
\(722\) 0 0
\(723\) −5.40647 −0.201069
\(724\) 0 0
\(725\) −3.78437 −0.140548
\(726\) 0 0
\(727\) 37.9357 1.40696 0.703479 0.710716i \(-0.251629\pi\)
0.703479 + 0.710716i \(0.251629\pi\)
\(728\) 0 0
\(729\) −12.2614 −0.454127
\(730\) 0 0
\(731\) 50.2359 1.85804
\(732\) 0 0
\(733\) 15.8326 0.584792 0.292396 0.956297i \(-0.405547\pi\)
0.292396 + 0.956297i \(0.405547\pi\)
\(734\) 0 0
\(735\) 26.7864 0.988032
\(736\) 0 0
\(737\) −23.8591 −0.878861
\(738\) 0 0
\(739\) −9.06045 −0.333294 −0.166647 0.986017i \(-0.553294\pi\)
−0.166647 + 0.986017i \(0.553294\pi\)
\(740\) 0 0
\(741\) −0.180477 −0.00663000
\(742\) 0 0
\(743\) 8.42135 0.308949 0.154475 0.987997i \(-0.450631\pi\)
0.154475 + 0.987997i \(0.450631\pi\)
\(744\) 0 0
\(745\) −6.23853 −0.228562
\(746\) 0 0
\(747\) 11.7700 0.430643
\(748\) 0 0
\(749\) −9.00787 −0.329140
\(750\) 0 0
\(751\) 19.2016 0.700677 0.350338 0.936623i \(-0.386067\pi\)
0.350338 + 0.936623i \(0.386067\pi\)
\(752\) 0 0
\(753\) −2.29157 −0.0835095
\(754\) 0 0
\(755\) −5.44793 −0.198270
\(756\) 0 0
\(757\) −9.32193 −0.338811 −0.169406 0.985546i \(-0.554185\pi\)
−0.169406 + 0.985546i \(0.554185\pi\)
\(758\) 0 0
\(759\) −36.4606 −1.32344
\(760\) 0 0
\(761\) 51.3651 1.86198 0.930992 0.365041i \(-0.118945\pi\)
0.930992 + 0.365041i \(0.118945\pi\)
\(762\) 0 0
\(763\) 7.24958 0.262452
\(764\) 0 0
\(765\) −22.2030 −0.802753
\(766\) 0 0
\(767\) 0.00860367 0.000310661 0
\(768\) 0 0
\(769\) 43.2738 1.56049 0.780246 0.625473i \(-0.215094\pi\)
0.780246 + 0.625473i \(0.215094\pi\)
\(770\) 0 0
\(771\) −41.9013 −1.50904
\(772\) 0 0
\(773\) −6.59292 −0.237131 −0.118565 0.992946i \(-0.537830\pi\)
−0.118565 + 0.992946i \(0.537830\pi\)
\(774\) 0 0
\(775\) −17.4522 −0.626901
\(776\) 0 0
\(777\) −8.19665 −0.294053
\(778\) 0 0
\(779\) 17.7996 0.637736
\(780\) 0 0
\(781\) −18.3885 −0.657991
\(782\) 0 0
\(783\) −3.57749 −0.127849
\(784\) 0 0
\(785\) 5.22545 0.186504
\(786\) 0 0
\(787\) 51.1075 1.82179 0.910893 0.412642i \(-0.135394\pi\)
0.910893 + 0.412642i \(0.135394\pi\)
\(788\) 0 0
\(789\) 3.71389 0.132218
\(790\) 0 0
\(791\) −4.44309 −0.157978
\(792\) 0 0
\(793\) 0.602981 0.0214125
\(794\) 0 0
\(795\) −17.4828 −0.620049
\(796\) 0 0
\(797\) 37.6794 1.33467 0.667337 0.744756i \(-0.267434\pi\)
0.667337 + 0.744756i \(0.267434\pi\)
\(798\) 0 0
\(799\) −28.8125 −1.01931
\(800\) 0 0
\(801\) −6.08020 −0.214833
\(802\) 0 0
\(803\) 28.6876 1.01236
\(804\) 0 0
\(805\) 8.54419 0.301143
\(806\) 0 0
\(807\) −61.7338 −2.17313
\(808\) 0 0
\(809\) −38.0342 −1.33721 −0.668605 0.743618i \(-0.733108\pi\)
−0.668605 + 0.743618i \(0.733108\pi\)
\(810\) 0 0
\(811\) −13.6164 −0.478138 −0.239069 0.971003i \(-0.576842\pi\)
−0.239069 + 0.971003i \(0.576842\pi\)
\(812\) 0 0
\(813\) −3.90559 −0.136975
\(814\) 0 0
\(815\) 19.8277 0.694535
\(816\) 0 0
\(817\) −13.6309 −0.476884
\(818\) 0 0
\(819\) −0.0793503 −0.00277272
\(820\) 0 0
\(821\) 30.5818 1.06731 0.533656 0.845702i \(-0.320818\pi\)
0.533656 + 0.845702i \(0.320818\pi\)
\(822\) 0 0
\(823\) 18.4303 0.642439 0.321220 0.947005i \(-0.395907\pi\)
0.321220 + 0.947005i \(0.395907\pi\)
\(824\) 0 0
\(825\) 9.27524 0.322922
\(826\) 0 0
\(827\) 2.06070 0.0716577 0.0358288 0.999358i \(-0.488593\pi\)
0.0358288 + 0.999358i \(0.488593\pi\)
\(828\) 0 0
\(829\) 53.5915 1.86131 0.930655 0.365897i \(-0.119238\pi\)
0.930655 + 0.365897i \(0.119238\pi\)
\(830\) 0 0
\(831\) 1.65009 0.0572410
\(832\) 0 0
\(833\) −36.1943 −1.25406
\(834\) 0 0
\(835\) 12.1220 0.419498
\(836\) 0 0
\(837\) −16.4981 −0.570258
\(838\) 0 0
\(839\) 9.37280 0.323585 0.161792 0.986825i \(-0.448272\pi\)
0.161792 + 0.986825i \(0.448272\pi\)
\(840\) 0 0
\(841\) −24.6522 −0.850075
\(842\) 0 0
\(843\) −20.7871 −0.715946
\(844\) 0 0
\(845\) 23.1959 0.797964
\(846\) 0 0
\(847\) 4.04403 0.138954
\(848\) 0 0
\(849\) 23.0199 0.790040
\(850\) 0 0
\(851\) 38.0280 1.30358
\(852\) 0 0
\(853\) −8.69000 −0.297540 −0.148770 0.988872i \(-0.547531\pi\)
−0.148770 + 0.988872i \(0.547531\pi\)
\(854\) 0 0
\(855\) 6.02451 0.206034
\(856\) 0 0
\(857\) −17.4197 −0.595045 −0.297522 0.954715i \(-0.596160\pi\)
−0.297522 + 0.954715i \(0.596160\pi\)
\(858\) 0 0
\(859\) −38.0839 −1.29941 −0.649703 0.760188i \(-0.725107\pi\)
−0.649703 + 0.760188i \(0.725107\pi\)
\(860\) 0 0
\(861\) 18.2545 0.622111
\(862\) 0 0
\(863\) −1.47779 −0.0503046 −0.0251523 0.999684i \(-0.508007\pi\)
−0.0251523 + 0.999684i \(0.508007\pi\)
\(864\) 0 0
\(865\) −35.2836 −1.19968
\(866\) 0 0
\(867\) 31.0229 1.05359
\(868\) 0 0
\(869\) −17.5509 −0.595374
\(870\) 0 0
\(871\) 0.561927 0.0190402
\(872\) 0 0
\(873\) 36.6360 1.23994
\(874\) 0 0
\(875\) −8.16161 −0.275913
\(876\) 0 0
\(877\) 16.1183 0.544278 0.272139 0.962258i \(-0.412269\pi\)
0.272139 + 0.962258i \(0.412269\pi\)
\(878\) 0 0
\(879\) −20.8597 −0.703579
\(880\) 0 0
\(881\) −25.7458 −0.867399 −0.433699 0.901058i \(-0.642792\pi\)
−0.433699 + 0.901058i \(0.642792\pi\)
\(882\) 0 0
\(883\) −51.3112 −1.72676 −0.863380 0.504554i \(-0.831657\pi\)
−0.863380 + 0.504554i \(0.831657\pi\)
\(884\) 0 0
\(885\) −0.669911 −0.0225188
\(886\) 0 0
\(887\) −26.4272 −0.887339 −0.443670 0.896190i \(-0.646324\pi\)
−0.443670 + 0.896190i \(0.646324\pi\)
\(888\) 0 0
\(889\) −0.904955 −0.0303512
\(890\) 0 0
\(891\) 23.8304 0.798349
\(892\) 0 0
\(893\) 7.81789 0.261616
\(894\) 0 0
\(895\) −31.3345 −1.04740
\(896\) 0 0
\(897\) 0.858716 0.0286717
\(898\) 0 0
\(899\) 20.0507 0.668727
\(900\) 0 0
\(901\) 23.6230 0.786996
\(902\) 0 0
\(903\) −13.9793 −0.465200
\(904\) 0 0
\(905\) 5.73865 0.190759
\(906\) 0 0
\(907\) −41.6133 −1.38175 −0.690873 0.722976i \(-0.742774\pi\)
−0.690873 + 0.722976i \(0.742774\pi\)
\(908\) 0 0
\(909\) 16.4676 0.546196
\(910\) 0 0
\(911\) −48.6569 −1.61208 −0.806038 0.591864i \(-0.798392\pi\)
−0.806038 + 0.591864i \(0.798392\pi\)
\(912\) 0 0
\(913\) −11.6595 −0.385873
\(914\) 0 0
\(915\) −46.9502 −1.55212
\(916\) 0 0
\(917\) 9.74451 0.321792
\(918\) 0 0
\(919\) −32.6597 −1.07734 −0.538672 0.842515i \(-0.681074\pi\)
−0.538672 + 0.842515i \(0.681074\pi\)
\(920\) 0 0
\(921\) 20.8889 0.688313
\(922\) 0 0
\(923\) 0.433083 0.0142551
\(924\) 0 0
\(925\) −9.67397 −0.318078
\(926\) 0 0
\(927\) 18.9892 0.623686
\(928\) 0 0
\(929\) −29.0898 −0.954406 −0.477203 0.878793i \(-0.658349\pi\)
−0.477203 + 0.878793i \(0.658349\pi\)
\(930\) 0 0
\(931\) 9.82086 0.321866
\(932\) 0 0
\(933\) −67.6904 −2.21609
\(934\) 0 0
\(935\) 21.9945 0.719297
\(936\) 0 0
\(937\) 39.3014 1.28392 0.641960 0.766738i \(-0.278122\pi\)
0.641960 + 0.766738i \(0.278122\pi\)
\(938\) 0 0
\(939\) −2.35013 −0.0766934
\(940\) 0 0
\(941\) 17.7356 0.578163 0.289082 0.957304i \(-0.406650\pi\)
0.289082 + 0.957304i \(0.406650\pi\)
\(942\) 0 0
\(943\) −84.6909 −2.75792
\(944\) 0 0
\(945\) −2.05474 −0.0668407
\(946\) 0 0
\(947\) −41.3091 −1.34237 −0.671183 0.741292i \(-0.734213\pi\)
−0.671183 + 0.741292i \(0.734213\pi\)
\(948\) 0 0
\(949\) −0.675646 −0.0219324
\(950\) 0 0
\(951\) −7.46717 −0.242140
\(952\) 0 0
\(953\) 19.6289 0.635842 0.317921 0.948117i \(-0.397015\pi\)
0.317921 + 0.948117i \(0.397015\pi\)
\(954\) 0 0
\(955\) −21.6641 −0.701033
\(956\) 0 0
\(957\) −10.6562 −0.344468
\(958\) 0 0
\(959\) −3.22934 −0.104281
\(960\) 0 0
\(961\) 61.4667 1.98280
\(962\) 0 0
\(963\) 30.2204 0.973839
\(964\) 0 0
\(965\) −20.6134 −0.663567
\(966\) 0 0
\(967\) −44.3193 −1.42521 −0.712606 0.701565i \(-0.752485\pi\)
−0.712606 + 0.701565i \(0.752485\pi\)
\(968\) 0 0
\(969\) −18.9881 −0.609985
\(970\) 0 0
\(971\) 4.22052 0.135443 0.0677214 0.997704i \(-0.478427\pi\)
0.0677214 + 0.997704i \(0.478427\pi\)
\(972\) 0 0
\(973\) −11.8599 −0.380210
\(974\) 0 0
\(975\) −0.218449 −0.00699598
\(976\) 0 0
\(977\) −29.3344 −0.938492 −0.469246 0.883068i \(-0.655474\pi\)
−0.469246 + 0.883068i \(0.655474\pi\)
\(978\) 0 0
\(979\) 6.02309 0.192499
\(980\) 0 0
\(981\) −24.3215 −0.776527
\(982\) 0 0
\(983\) −55.0110 −1.75458 −0.877290 0.479961i \(-0.840651\pi\)
−0.877290 + 0.479961i \(0.840651\pi\)
\(984\) 0 0
\(985\) 0.993066 0.0316417
\(986\) 0 0
\(987\) 8.01770 0.255206
\(988\) 0 0
\(989\) 64.8562 2.06231
\(990\) 0 0
\(991\) 8.39630 0.266717 0.133359 0.991068i \(-0.457424\pi\)
0.133359 + 0.991068i \(0.457424\pi\)
\(992\) 0 0
\(993\) −2.79867 −0.0888131
\(994\) 0 0
\(995\) 28.3495 0.898738
\(996\) 0 0
\(997\) 15.7423 0.498564 0.249282 0.968431i \(-0.419805\pi\)
0.249282 + 0.968431i \(0.419805\pi\)
\(998\) 0 0
\(999\) −9.14512 −0.289339
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 4016.2.a.g.1.6 7
4.3 odd 2 1004.2.a.a.1.2 7
12.11 even 2 9036.2.a.i.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.2 7 4.3 odd 2
4016.2.a.g.1.6 7 1.1 even 1 trivial
9036.2.a.i.1.6 7 12.11 even 2