Properties

Label 32.6.a.a.1.1
Level 32
Weight 6
Character 32.1
Self dual yes
Analytic conductor 5.132
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.13228223402\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 32.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.00000 q^{3} +14.0000 q^{5} -208.000 q^{7} -179.000 q^{9} +O(q^{10})\) \(q-8.00000 q^{3} +14.0000 q^{5} -208.000 q^{7} -179.000 q^{9} -536.000 q^{11} +694.000 q^{13} -112.000 q^{15} -1278.00 q^{17} +1112.00 q^{19} +1664.00 q^{21} +3216.00 q^{23} -2929.00 q^{25} +3376.00 q^{27} +2918.00 q^{29} -2624.00 q^{31} +4288.00 q^{33} -2912.00 q^{35} -9458.00 q^{37} -5552.00 q^{39} +170.000 q^{41} -19928.0 q^{43} -2506.00 q^{45} +32.0000 q^{47} +26457.0 q^{49} +10224.0 q^{51} -22178.0 q^{53} -7504.00 q^{55} -8896.00 q^{57} +41480.0 q^{59} +15462.0 q^{61} +37232.0 q^{63} +9716.00 q^{65} -20744.0 q^{67} -25728.0 q^{69} +28592.0 q^{71} -53670.0 q^{73} +23432.0 q^{75} +111488. q^{77} -69152.0 q^{79} +16489.0 q^{81} -37800.0 q^{83} -17892.0 q^{85} -23344.0 q^{87} -126806. q^{89} -144352. q^{91} +20992.0 q^{93} +15568.0 q^{95} +62290.0 q^{97} +95944.0 q^{99} +O(q^{100})\)

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
\(3\) −8.00000 −0.513200 −0.256600 0.966518i \(-0.582602\pi\)
−0.256600 + 0.966518i \(0.582602\pi\)
\(4\) 0 0
\(5\) 14.0000 0.250440 0.125220 0.992129i \(-0.460036\pi\)
0.125220 + 0.992129i \(0.460036\pi\)
\(6\) 0 0
\(7\) −208.000 −1.60442 −0.802210 0.597042i \(-0.796343\pi\)
−0.802210 + 0.597042i \(0.796343\pi\)
\(8\) 0 0
\(9\) −179.000 −0.736626
\(10\) 0 0
\(11\) −536.000 −1.33562 −0.667810 0.744332i \(-0.732768\pi\)
−0.667810 + 0.744332i \(0.732768\pi\)
\(12\) 0 0
\(13\) 694.000 1.13894 0.569470 0.822012i \(-0.307148\pi\)
0.569470 + 0.822012i \(0.307148\pi\)
\(14\) 0 0
\(15\) −112.000 −0.128526
\(16\) 0 0
\(17\) −1278.00 −1.07253 −0.536264 0.844050i \(-0.680165\pi\)
−0.536264 + 0.844050i \(0.680165\pi\)
\(18\) 0 0
\(19\) 1112.00 0.706677 0.353338 0.935496i \(-0.385046\pi\)
0.353338 + 0.935496i \(0.385046\pi\)
\(20\) 0 0
\(21\) 1664.00 0.823389
\(22\) 0 0
\(23\) 3216.00 1.26764 0.633821 0.773480i \(-0.281486\pi\)
0.633821 + 0.773480i \(0.281486\pi\)
\(24\) 0 0
\(25\) −2929.00 −0.937280
\(26\) 0 0
\(27\) 3376.00 0.891237
\(28\) 0 0
\(29\) 2918.00 0.644303 0.322152 0.946688i \(-0.395594\pi\)
0.322152 + 0.946688i \(0.395594\pi\)
\(30\) 0 0
\(31\) −2624.00 −0.490410 −0.245205 0.969471i \(-0.578855\pi\)
−0.245205 + 0.969471i \(0.578855\pi\)
\(32\) 0 0
\(33\) 4288.00 0.685441
\(34\) 0 0
\(35\) −2912.00 −0.401810
\(36\) 0 0
\(37\) −9458.00 −1.13578 −0.567891 0.823104i \(-0.692241\pi\)
−0.567891 + 0.823104i \(0.692241\pi\)
\(38\) 0 0
\(39\) −5552.00 −0.584505
\(40\) 0 0
\(41\) 170.000 0.0157939 0.00789695 0.999969i \(-0.497486\pi\)
0.00789695 + 0.999969i \(0.497486\pi\)
\(42\) 0 0
\(43\) −19928.0 −1.64359 −0.821793 0.569786i \(-0.807026\pi\)
−0.821793 + 0.569786i \(0.807026\pi\)
\(44\) 0 0
\(45\) −2506.00 −0.184480
\(46\) 0 0
\(47\) 32.0000 0.00211303 0.00105651 0.999999i \(-0.499664\pi\)
0.00105651 + 0.999999i \(0.499664\pi\)
\(48\) 0 0
\(49\) 26457.0 1.57417
\(50\) 0 0
\(51\) 10224.0 0.550422
\(52\) 0 0
\(53\) −22178.0 −1.08451 −0.542254 0.840215i \(-0.682429\pi\)
−0.542254 + 0.840215i \(0.682429\pi\)
\(54\) 0 0
\(55\) −7504.00 −0.334492
\(56\) 0 0
\(57\) −8896.00 −0.362667
\(58\) 0 0
\(59\) 41480.0 1.55135 0.775673 0.631135i \(-0.217411\pi\)
0.775673 + 0.631135i \(0.217411\pi\)
\(60\) 0 0
\(61\) 15462.0 0.532036 0.266018 0.963968i \(-0.414292\pi\)
0.266018 + 0.963968i \(0.414292\pi\)
\(62\) 0 0
\(63\) 37232.0 1.18186
\(64\) 0 0
\(65\) 9716.00 0.285236
\(66\) 0 0
\(67\) −20744.0 −0.564554 −0.282277 0.959333i \(-0.591090\pi\)
−0.282277 + 0.959333i \(0.591090\pi\)
\(68\) 0 0
\(69\) −25728.0 −0.650554
\(70\) 0 0
\(71\) 28592.0 0.673130 0.336565 0.941660i \(-0.390735\pi\)
0.336565 + 0.941660i \(0.390735\pi\)
\(72\) 0 0
\(73\) −53670.0 −1.17876 −0.589379 0.807857i \(-0.700627\pi\)
−0.589379 + 0.807857i \(0.700627\pi\)
\(74\) 0 0
\(75\) 23432.0 0.481012
\(76\) 0 0
\(77\) 111488. 2.14290
\(78\) 0 0
\(79\) −69152.0 −1.24663 −0.623314 0.781971i \(-0.714214\pi\)
−0.623314 + 0.781971i \(0.714214\pi\)
\(80\) 0 0
\(81\) 16489.0 0.279243
\(82\) 0 0
\(83\) −37800.0 −0.602277 −0.301139 0.953580i \(-0.597367\pi\)
−0.301139 + 0.953580i \(0.597367\pi\)
\(84\) 0 0
\(85\) −17892.0 −0.268603
\(86\) 0 0
\(87\) −23344.0 −0.330657
\(88\) 0 0
\(89\) −126806. −1.69693 −0.848467 0.529249i \(-0.822474\pi\)
−0.848467 + 0.529249i \(0.822474\pi\)
\(90\) 0 0
\(91\) −144352. −1.82734
\(92\) 0 0
\(93\) 20992.0 0.251679
\(94\) 0 0
\(95\) 15568.0 0.176980
\(96\) 0 0
\(97\) 62290.0 0.672185 0.336093 0.941829i \(-0.390894\pi\)
0.336093 + 0.941829i \(0.390894\pi\)
\(98\) 0 0
\(99\) 95944.0 0.983852
\(100\) 0 0
\(101\) 6414.00 0.0625641 0.0312821 0.999511i \(-0.490041\pi\)
0.0312821 + 0.999511i \(0.490041\pi\)
\(102\) 0 0
\(103\) −108432. −1.00708 −0.503541 0.863972i \(-0.667970\pi\)
−0.503541 + 0.863972i \(0.667970\pi\)
\(104\) 0 0
\(105\) 23296.0 0.206209
\(106\) 0 0
\(107\) 103976. 0.877958 0.438979 0.898497i \(-0.355340\pi\)
0.438979 + 0.898497i \(0.355340\pi\)
\(108\) 0 0
\(109\) 2486.00 0.0200417 0.0100209 0.999950i \(-0.496810\pi\)
0.0100209 + 0.999950i \(0.496810\pi\)
\(110\) 0 0
\(111\) 75664.0 0.582884
\(112\) 0 0
\(113\) 15794.0 0.116358 0.0581790 0.998306i \(-0.481471\pi\)
0.0581790 + 0.998306i \(0.481471\pi\)
\(114\) 0 0
\(115\) 45024.0 0.317468
\(116\) 0 0
\(117\) −124226. −0.838973
\(118\) 0 0
\(119\) 265824. 1.72079
\(120\) 0 0
\(121\) 126245. 0.783882
\(122\) 0 0
\(123\) −1360.00 −0.00810543
\(124\) 0 0
\(125\) −84756.0 −0.485172
\(126\) 0 0
\(127\) 1024.00 0.00563366 0.00281683 0.999996i \(-0.499103\pi\)
0.00281683 + 0.999996i \(0.499103\pi\)
\(128\) 0 0
\(129\) 159424. 0.843489
\(130\) 0 0
\(131\) −22664.0 −0.115387 −0.0576937 0.998334i \(-0.518375\pi\)
−0.0576937 + 0.998334i \(0.518375\pi\)
\(132\) 0 0
\(133\) −231296. −1.13381
\(134\) 0 0
\(135\) 47264.0 0.223201
\(136\) 0 0
\(137\) −53238.0 −0.242337 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(138\) 0 0
\(139\) 19816.0 0.0869919 0.0434960 0.999054i \(-0.486150\pi\)
0.0434960 + 0.999054i \(0.486150\pi\)
\(140\) 0 0
\(141\) −256.000 −0.00108441
\(142\) 0 0
\(143\) −371984. −1.52119
\(144\) 0 0
\(145\) 40852.0 0.161359
\(146\) 0 0
\(147\) −211656. −0.807862
\(148\) 0 0
\(149\) 452190. 1.66861 0.834306 0.551302i \(-0.185869\pi\)
0.834306 + 0.551302i \(0.185869\pi\)
\(150\) 0 0
\(151\) −263280. −0.939670 −0.469835 0.882754i \(-0.655687\pi\)
−0.469835 + 0.882754i \(0.655687\pi\)
\(152\) 0 0
\(153\) 228762. 0.790051
\(154\) 0 0
\(155\) −36736.0 −0.122818
\(156\) 0 0
\(157\) −353530. −1.14466 −0.572331 0.820023i \(-0.693961\pi\)
−0.572331 + 0.820023i \(0.693961\pi\)
\(158\) 0 0
\(159\) 177424. 0.556570
\(160\) 0 0
\(161\) −668928. −2.03383
\(162\) 0 0
\(163\) −100936. −0.297562 −0.148781 0.988870i \(-0.547535\pi\)
−0.148781 + 0.988870i \(0.547535\pi\)
\(164\) 0 0
\(165\) 60032.0 0.171662
\(166\) 0 0
\(167\) −284944. −0.790621 −0.395310 0.918548i \(-0.629363\pi\)
−0.395310 + 0.918548i \(0.629363\pi\)
\(168\) 0 0
\(169\) 110343. 0.297186
\(170\) 0 0
\(171\) −199048. −0.520556
\(172\) 0 0
\(173\) 484374. 1.23045 0.615227 0.788350i \(-0.289064\pi\)
0.615227 + 0.788350i \(0.289064\pi\)
\(174\) 0 0
\(175\) 609232. 1.50379
\(176\) 0 0
\(177\) −331840. −0.796151
\(178\) 0 0
\(179\) 406680. 0.948681 0.474341 0.880341i \(-0.342687\pi\)
0.474341 + 0.880341i \(0.342687\pi\)
\(180\) 0 0
\(181\) 570302. 1.29392 0.646962 0.762523i \(-0.276039\pi\)
0.646962 + 0.762523i \(0.276039\pi\)
\(182\) 0 0
\(183\) −123696. −0.273041
\(184\) 0 0
\(185\) −132412. −0.284445
\(186\) 0 0
\(187\) 685008. 1.43249
\(188\) 0 0
\(189\) −702208. −1.42992
\(190\) 0 0
\(191\) 138624. 0.274951 0.137475 0.990505i \(-0.456101\pi\)
0.137475 + 0.990505i \(0.456101\pi\)
\(192\) 0 0
\(193\) 34482.0 0.0666345 0.0333173 0.999445i \(-0.489393\pi\)
0.0333173 + 0.999445i \(0.489393\pi\)
\(194\) 0 0
\(195\) −77728.0 −0.146383
\(196\) 0 0
\(197\) 643598. 1.18154 0.590771 0.806839i \(-0.298824\pi\)
0.590771 + 0.806839i \(0.298824\pi\)
\(198\) 0 0
\(199\) 1.10738e6 1.98227 0.991134 0.132865i \(-0.0424178\pi\)
0.991134 + 0.132865i \(0.0424178\pi\)
\(200\) 0 0
\(201\) 165952. 0.289729
\(202\) 0 0
\(203\) −606944. −1.03373
\(204\) 0 0
\(205\) 2380.00 0.00395542
\(206\) 0 0
\(207\) −575664. −0.933777
\(208\) 0 0
\(209\) −596032. −0.943852
\(210\) 0 0
\(211\) 229976. 0.355612 0.177806 0.984066i \(-0.443100\pi\)
0.177806 + 0.984066i \(0.443100\pi\)
\(212\) 0 0
\(213\) −228736. −0.345450
\(214\) 0 0
\(215\) −278992. −0.411619
\(216\) 0 0
\(217\) 545792. 0.786824
\(218\) 0 0
\(219\) 429360. 0.604939
\(220\) 0 0
\(221\) −886932. −1.22155
\(222\) 0 0
\(223\) −1.08947e6 −1.46708 −0.733540 0.679646i \(-0.762133\pi\)
−0.733540 + 0.679646i \(0.762133\pi\)
\(224\) 0 0
\(225\) 524291. 0.690424
\(226\) 0 0
\(227\) −687048. −0.884958 −0.442479 0.896779i \(-0.645901\pi\)
−0.442479 + 0.896779i \(0.645901\pi\)
\(228\) 0 0
\(229\) −699730. −0.881743 −0.440871 0.897570i \(-0.645330\pi\)
−0.440871 + 0.897570i \(0.645330\pi\)
\(230\) 0 0
\(231\) −891904. −1.09974
\(232\) 0 0
\(233\) 937722. 1.13158 0.565789 0.824550i \(-0.308572\pi\)
0.565789 + 0.824550i \(0.308572\pi\)
\(234\) 0 0
\(235\) 448.000 0.000529186 0
\(236\) 0 0
\(237\) 553216. 0.639770
\(238\) 0 0
\(239\) 643488. 0.728695 0.364347 0.931263i \(-0.381292\pi\)
0.364347 + 0.931263i \(0.381292\pi\)
\(240\) 0 0
\(241\) 157282. 0.174436 0.0872181 0.996189i \(-0.472202\pi\)
0.0872181 + 0.996189i \(0.472202\pi\)
\(242\) 0 0
\(243\) −952280. −1.03454
\(244\) 0 0
\(245\) 370398. 0.394233
\(246\) 0 0
\(247\) 771728. 0.804863
\(248\) 0 0
\(249\) 302400. 0.309089
\(250\) 0 0
\(251\) −1.58604e6 −1.58902 −0.794511 0.607250i \(-0.792273\pi\)
−0.794511 + 0.607250i \(0.792273\pi\)
\(252\) 0 0
\(253\) −1.72378e6 −1.69309
\(254\) 0 0
\(255\) 143136. 0.137847
\(256\) 0 0
\(257\) −654334. −0.617969 −0.308984 0.951067i \(-0.599989\pi\)
−0.308984 + 0.951067i \(0.599989\pi\)
\(258\) 0 0
\(259\) 1.96726e6 1.82227
\(260\) 0 0
\(261\) −522322. −0.474610
\(262\) 0 0
\(263\) −330192. −0.294359 −0.147179 0.989110i \(-0.547019\pi\)
−0.147179 + 0.989110i \(0.547019\pi\)
\(264\) 0 0
\(265\) −310492. −0.271604
\(266\) 0 0
\(267\) 1.01445e6 0.870867
\(268\) 0 0
\(269\) 1.56956e6 1.32250 0.661252 0.750164i \(-0.270026\pi\)
0.661252 + 0.750164i \(0.270026\pi\)
\(270\) 0 0
\(271\) 957792. 0.792224 0.396112 0.918202i \(-0.370359\pi\)
0.396112 + 0.918202i \(0.370359\pi\)
\(272\) 0 0
\(273\) 1.15482e6 0.937791
\(274\) 0 0
\(275\) 1.56994e6 1.25185
\(276\) 0 0
\(277\) 565438. 0.442778 0.221389 0.975186i \(-0.428941\pi\)
0.221389 + 0.975186i \(0.428941\pi\)
\(278\) 0 0
\(279\) 469696. 0.361249
\(280\) 0 0
\(281\) −1.34127e6 −1.01333 −0.506664 0.862143i \(-0.669122\pi\)
−0.506664 + 0.862143i \(0.669122\pi\)
\(282\) 0 0
\(283\) −734264. −0.544987 −0.272494 0.962158i \(-0.587848\pi\)
−0.272494 + 0.962158i \(0.587848\pi\)
\(284\) 0 0
\(285\) −124544. −0.0908261
\(286\) 0 0
\(287\) −35360.0 −0.0253401
\(288\) 0 0
\(289\) 213427. 0.150316
\(290\) 0 0
\(291\) −498320. −0.344966
\(292\) 0 0
\(293\) −1.13320e6 −0.771149 −0.385574 0.922677i \(-0.625997\pi\)
−0.385574 + 0.922677i \(0.625997\pi\)
\(294\) 0 0
\(295\) 580720. 0.388519
\(296\) 0 0
\(297\) −1.80954e6 −1.19035
\(298\) 0 0
\(299\) 2.23190e6 1.44377
\(300\) 0 0
\(301\) 4.14502e6 2.63700
\(302\) 0 0
\(303\) −51312.0 −0.0321079
\(304\) 0 0
\(305\) 216468. 0.133243
\(306\) 0 0
\(307\) −2.91377e6 −1.76445 −0.882224 0.470829i \(-0.843955\pi\)
−0.882224 + 0.470829i \(0.843955\pi\)
\(308\) 0 0
\(309\) 867456. 0.516834
\(310\) 0 0
\(311\) −1.43813e6 −0.843134 −0.421567 0.906797i \(-0.638520\pi\)
−0.421567 + 0.906797i \(0.638520\pi\)
\(312\) 0 0
\(313\) −1.37601e6 −0.793888 −0.396944 0.917843i \(-0.629929\pi\)
−0.396944 + 0.917843i \(0.629929\pi\)
\(314\) 0 0
\(315\) 521248. 0.295984
\(316\) 0 0
\(317\) −1.23494e6 −0.690235 −0.345118 0.938559i \(-0.612161\pi\)
−0.345118 + 0.938559i \(0.612161\pi\)
\(318\) 0 0
\(319\) −1.56405e6 −0.860545
\(320\) 0 0
\(321\) −831808. −0.450568
\(322\) 0 0
\(323\) −1.42114e6 −0.757930
\(324\) 0 0
\(325\) −2.03273e6 −1.06751
\(326\) 0 0
\(327\) −19888.0 −0.0102854
\(328\) 0 0
\(329\) −6656.00 −0.00339019
\(330\) 0 0
\(331\) −1.48930e6 −0.747160 −0.373580 0.927598i \(-0.621870\pi\)
−0.373580 + 0.927598i \(0.621870\pi\)
\(332\) 0 0
\(333\) 1.69298e6 0.836646
\(334\) 0 0
\(335\) −290416. −0.141387
\(336\) 0 0
\(337\) 838226. 0.402056 0.201028 0.979586i \(-0.435572\pi\)
0.201028 + 0.979586i \(0.435572\pi\)
\(338\) 0 0
\(339\) −126352. −0.0597149
\(340\) 0 0
\(341\) 1.40646e6 0.655002
\(342\) 0 0
\(343\) −2.00720e6 −0.921203
\(344\) 0 0
\(345\) −360192. −0.162924
\(346\) 0 0
\(347\) −350008. −0.156047 −0.0780233 0.996952i \(-0.524861\pi\)
−0.0780233 + 0.996952i \(0.524861\pi\)
\(348\) 0 0
\(349\) −383642. −0.168602 −0.0843010 0.996440i \(-0.526866\pi\)
−0.0843010 + 0.996440i \(0.526866\pi\)
\(350\) 0 0
\(351\) 2.34294e6 1.01507
\(352\) 0 0
\(353\) 4.09309e6 1.74829 0.874147 0.485661i \(-0.161421\pi\)
0.874147 + 0.485661i \(0.161421\pi\)
\(354\) 0 0
\(355\) 400288. 0.168578
\(356\) 0 0
\(357\) −2.12659e6 −0.883108
\(358\) 0 0
\(359\) 3.14430e6 1.28762 0.643811 0.765185i \(-0.277352\pi\)
0.643811 + 0.765185i \(0.277352\pi\)
\(360\) 0 0
\(361\) −1.23955e6 −0.500608
\(362\) 0 0
\(363\) −1.00996e6 −0.402288
\(364\) 0 0
\(365\) −751380. −0.295208
\(366\) 0 0
\(367\) −1.47619e6 −0.572108 −0.286054 0.958214i \(-0.592344\pi\)
−0.286054 + 0.958214i \(0.592344\pi\)
\(368\) 0 0
\(369\) −30430.0 −0.0116342
\(370\) 0 0
\(371\) 4.61302e6 1.74001
\(372\) 0 0
\(373\) −3.73981e6 −1.39180 −0.695901 0.718138i \(-0.744995\pi\)
−0.695901 + 0.718138i \(0.744995\pi\)
\(374\) 0 0
\(375\) 678048. 0.248990
\(376\) 0 0
\(377\) 2.02509e6 0.733823
\(378\) 0 0
\(379\) 1.89966e6 0.679324 0.339662 0.940548i \(-0.389687\pi\)
0.339662 + 0.940548i \(0.389687\pi\)
\(380\) 0 0
\(381\) −8192.00 −0.00289120
\(382\) 0 0
\(383\) 1.74310e6 0.607192 0.303596 0.952801i \(-0.401813\pi\)
0.303596 + 0.952801i \(0.401813\pi\)
\(384\) 0 0
\(385\) 1.56083e6 0.536666
\(386\) 0 0
\(387\) 3.56711e6 1.21071
\(388\) 0 0
\(389\) −2.69147e6 −0.901812 −0.450906 0.892571i \(-0.648899\pi\)
−0.450906 + 0.892571i \(0.648899\pi\)
\(390\) 0 0
\(391\) −4.11005e6 −1.35958
\(392\) 0 0
\(393\) 181312. 0.0592168
\(394\) 0 0
\(395\) −968128. −0.312205
\(396\) 0 0
\(397\) 5.37353e6 1.71113 0.855565 0.517695i \(-0.173210\pi\)
0.855565 + 0.517695i \(0.173210\pi\)
\(398\) 0 0
\(399\) 1.85037e6 0.581870
\(400\) 0 0
\(401\) 156418. 0.0485765 0.0242882 0.999705i \(-0.492268\pi\)
0.0242882 + 0.999705i \(0.492268\pi\)
\(402\) 0 0
\(403\) −1.82106e6 −0.558548
\(404\) 0 0
\(405\) 230846. 0.0699334
\(406\) 0 0
\(407\) 5.06949e6 1.51697
\(408\) 0 0
\(409\) −306086. −0.0904764 −0.0452382 0.998976i \(-0.514405\pi\)
−0.0452382 + 0.998976i \(0.514405\pi\)
\(410\) 0 0
\(411\) 425904. 0.124368
\(412\) 0 0
\(413\) −8.62784e6 −2.48901
\(414\) 0 0
\(415\) −529200. −0.150834
\(416\) 0 0
\(417\) −158528. −0.0446443
\(418\) 0 0
\(419\) −6.70868e6 −1.86682 −0.933409 0.358814i \(-0.883181\pi\)
−0.933409 + 0.358814i \(0.883181\pi\)
\(420\) 0 0
\(421\) 4.02347e6 1.10636 0.553179 0.833063i \(-0.313415\pi\)
0.553179 + 0.833063i \(0.313415\pi\)
\(422\) 0 0
\(423\) −5728.00 −0.00155651
\(424\) 0 0
\(425\) 3.74326e6 1.00526
\(426\) 0 0
\(427\) −3.21610e6 −0.853610
\(428\) 0 0
\(429\) 2.97587e6 0.780676
\(430\) 0 0
\(431\) −7.04304e6 −1.82628 −0.913139 0.407648i \(-0.866349\pi\)
−0.913139 + 0.407648i \(0.866349\pi\)
\(432\) 0 0
\(433\) −1.25142e6 −0.320763 −0.160381 0.987055i \(-0.551272\pi\)
−0.160381 + 0.987055i \(0.551272\pi\)
\(434\) 0 0
\(435\) −326816. −0.0828095
\(436\) 0 0
\(437\) 3.57619e6 0.895813
\(438\) 0 0
\(439\) −1.25406e6 −0.310569 −0.155285 0.987870i \(-0.549629\pi\)
−0.155285 + 0.987870i \(0.549629\pi\)
\(440\) 0 0
\(441\) −4.73580e6 −1.15957
\(442\) 0 0
\(443\) 5.18081e6 1.25426 0.627131 0.778914i \(-0.284229\pi\)
0.627131 + 0.778914i \(0.284229\pi\)
\(444\) 0 0
\(445\) −1.77528e6 −0.424979
\(446\) 0 0
\(447\) −3.61752e6 −0.856332
\(448\) 0 0
\(449\) −5.73064e6 −1.34149 −0.670745 0.741688i \(-0.734025\pi\)
−0.670745 + 0.741688i \(0.734025\pi\)
\(450\) 0 0
\(451\) −91120.0 −0.0210947
\(452\) 0 0
\(453\) 2.10624e6 0.482239
\(454\) 0 0
\(455\) −2.02093e6 −0.457638
\(456\) 0 0
\(457\) −5.24153e6 −1.17400 −0.586999 0.809588i \(-0.699691\pi\)
−0.586999 + 0.809588i \(0.699691\pi\)
\(458\) 0 0
\(459\) −4.31453e6 −0.955876
\(460\) 0 0
\(461\) −173994. −0.0381313 −0.0190657 0.999818i \(-0.506069\pi\)
−0.0190657 + 0.999818i \(0.506069\pi\)
\(462\) 0 0
\(463\) 4.01277e6 0.869945 0.434972 0.900444i \(-0.356758\pi\)
0.434972 + 0.900444i \(0.356758\pi\)
\(464\) 0 0
\(465\) 293888. 0.0630303
\(466\) 0 0
\(467\) 774616. 0.164359 0.0821796 0.996618i \(-0.473812\pi\)
0.0821796 + 0.996618i \(0.473812\pi\)
\(468\) 0 0
\(469\) 4.31475e6 0.905782
\(470\) 0 0
\(471\) 2.82824e6 0.587441
\(472\) 0 0
\(473\) 1.06814e7 2.19521
\(474\) 0 0
\(475\) −3.25705e6 −0.662354
\(476\) 0 0
\(477\) 3.96986e6 0.798876
\(478\) 0 0
\(479\) 2.33530e6 0.465054 0.232527 0.972590i \(-0.425301\pi\)
0.232527 + 0.972590i \(0.425301\pi\)
\(480\) 0 0
\(481\) −6.56385e6 −1.29359
\(482\) 0 0
\(483\) 5.35142e6 1.04376
\(484\) 0 0
\(485\) 872060. 0.168342
\(486\) 0 0
\(487\) 1.03947e6 0.198605 0.0993025 0.995057i \(-0.468339\pi\)
0.0993025 + 0.995057i \(0.468339\pi\)
\(488\) 0 0
\(489\) 807488. 0.152709
\(490\) 0 0
\(491\) 7.85092e6 1.46966 0.734830 0.678251i \(-0.237262\pi\)
0.734830 + 0.678251i \(0.237262\pi\)
\(492\) 0 0
\(493\) −3.72920e6 −0.691033
\(494\) 0 0
\(495\) 1.34322e6 0.246396
\(496\) 0 0
\(497\) −5.94714e6 −1.07998
\(498\) 0 0
\(499\) 2.71644e6 0.488370 0.244185 0.969729i \(-0.421480\pi\)
0.244185 + 0.969729i \(0.421480\pi\)
\(500\) 0 0
\(501\) 2.27955e6 0.405747
\(502\) 0 0
\(503\) −4.62034e6 −0.814242 −0.407121 0.913374i \(-0.633467\pi\)
−0.407121 + 0.913374i \(0.633467\pi\)
\(504\) 0 0
\(505\) 89796.0 0.0156685
\(506\) 0 0
\(507\) −882744. −0.152516
\(508\) 0 0
\(509\) −4.46198e6 −0.763366 −0.381683 0.924293i \(-0.624655\pi\)
−0.381683 + 0.924293i \(0.624655\pi\)
\(510\) 0 0
\(511\) 1.11634e7 1.89122
\(512\) 0 0
\(513\) 3.75411e6 0.629816
\(514\) 0 0
\(515\) −1.51805e6 −0.252213
\(516\) 0 0
\(517\) −17152.0 −0.00282220
\(518\) 0 0
\(519\) −3.87499e6 −0.631470
\(520\) 0 0
\(521\) 3.74375e6 0.604245 0.302122 0.953269i \(-0.402305\pi\)
0.302122 + 0.953269i \(0.402305\pi\)
\(522\) 0 0
\(523\) 9.28433e6 1.48421 0.742107 0.670282i \(-0.233827\pi\)
0.742107 + 0.670282i \(0.233827\pi\)
\(524\) 0 0
\(525\) −4.87386e6 −0.771746
\(526\) 0 0
\(527\) 3.35347e6 0.525979
\(528\) 0 0
\(529\) 3.90631e6 0.606915
\(530\) 0 0
\(531\) −7.42492e6 −1.14276
\(532\) 0 0
\(533\) 117980. 0.0179883
\(534\) 0 0
\(535\) 1.45566e6 0.219875
\(536\) 0 0
\(537\) −3.25344e6 −0.486863
\(538\) 0 0
\(539\) −1.41810e7 −2.10249
\(540\) 0 0
\(541\) 862150. 0.126645 0.0633227 0.997993i \(-0.479830\pi\)
0.0633227 + 0.997993i \(0.479830\pi\)
\(542\) 0 0
\(543\) −4.56242e6 −0.664042
\(544\) 0 0
\(545\) 34804.0 0.00501924
\(546\) 0 0
\(547\) 1.75442e6 0.250707 0.125353 0.992112i \(-0.459994\pi\)
0.125353 + 0.992112i \(0.459994\pi\)
\(548\) 0 0
\(549\) −2.76770e6 −0.391911
\(550\) 0 0
\(551\) 3.24482e6 0.455314
\(552\) 0 0
\(553\) 1.43836e7 2.00012
\(554\) 0 0
\(555\) 1.05930e6 0.145977
\(556\) 0 0
\(557\) −1.00292e7 −1.36971 −0.684856 0.728678i \(-0.740135\pi\)
−0.684856 + 0.728678i \(0.740135\pi\)
\(558\) 0 0
\(559\) −1.38300e7 −1.87195
\(560\) 0 0
\(561\) −5.48006e6 −0.735154
\(562\) 0 0
\(563\) −5.27460e6 −0.701324 −0.350662 0.936502i \(-0.614043\pi\)
−0.350662 + 0.936502i \(0.614043\pi\)
\(564\) 0 0
\(565\) 221116. 0.0291406
\(566\) 0 0
\(567\) −3.42971e6 −0.448023
\(568\) 0 0
\(569\) 8.36940e6 1.08371 0.541856 0.840471i \(-0.317722\pi\)
0.541856 + 0.840471i \(0.317722\pi\)
\(570\) 0 0
\(571\) 4.02702e6 0.516884 0.258442 0.966027i \(-0.416791\pi\)
0.258442 + 0.966027i \(0.416791\pi\)
\(572\) 0 0
\(573\) −1.10899e6 −0.141105
\(574\) 0 0
\(575\) −9.41966e6 −1.18814
\(576\) 0 0
\(577\) 2.37568e6 0.297063 0.148532 0.988908i \(-0.452545\pi\)
0.148532 + 0.988908i \(0.452545\pi\)
\(578\) 0 0
\(579\) −275856. −0.0341968
\(580\) 0 0
\(581\) 7.86240e6 0.966306
\(582\) 0 0
\(583\) 1.18874e7 1.44849
\(584\) 0 0
\(585\) −1.73916e6 −0.210112
\(586\) 0 0
\(587\) −3.44028e6 −0.412096 −0.206048 0.978542i \(-0.566060\pi\)
−0.206048 + 0.978542i \(0.566060\pi\)
\(588\) 0 0
\(589\) −2.91789e6 −0.346562
\(590\) 0 0
\(591\) −5.14878e6 −0.606368
\(592\) 0 0
\(593\) −3.22942e6 −0.377127 −0.188564 0.982061i \(-0.560383\pi\)
−0.188564 + 0.982061i \(0.560383\pi\)
\(594\) 0 0
\(595\) 3.72154e6 0.430953
\(596\) 0 0
\(597\) −8.85901e6 −1.01730
\(598\) 0 0
\(599\) −9.29714e6 −1.05872 −0.529361 0.848397i \(-0.677568\pi\)
−0.529361 + 0.848397i \(0.677568\pi\)
\(600\) 0 0
\(601\) −1.12782e7 −1.27366 −0.636828 0.771006i \(-0.719754\pi\)
−0.636828 + 0.771006i \(0.719754\pi\)
\(602\) 0 0
\(603\) 3.71318e6 0.415865
\(604\) 0 0
\(605\) 1.76743e6 0.196315
\(606\) 0 0
\(607\) 7.00115e6 0.771255 0.385627 0.922655i \(-0.373985\pi\)
0.385627 + 0.922655i \(0.373985\pi\)
\(608\) 0 0
\(609\) 4.85555e6 0.530512
\(610\) 0 0
\(611\) 22208.0 0.00240661
\(612\) 0 0
\(613\) −6.19432e6 −0.665798 −0.332899 0.942962i \(-0.608027\pi\)
−0.332899 + 0.942962i \(0.608027\pi\)
\(614\) 0 0
\(615\) −19040.0 −0.00202992
\(616\) 0 0
\(617\) −2.62407e6 −0.277500 −0.138750 0.990327i \(-0.544308\pi\)
−0.138750 + 0.990327i \(0.544308\pi\)
\(618\) 0 0
\(619\) −2.83721e6 −0.297622 −0.148811 0.988866i \(-0.547545\pi\)
−0.148811 + 0.988866i \(0.547545\pi\)
\(620\) 0 0
\(621\) 1.08572e7 1.12977
\(622\) 0 0
\(623\) 2.63756e7 2.72259
\(624\) 0 0
\(625\) 7.96654e6 0.815774
\(626\) 0 0
\(627\) 4.76826e6 0.484385
\(628\) 0 0
\(629\) 1.20873e7 1.21816
\(630\) 0 0
\(631\) 1.29656e7 1.29634 0.648170 0.761496i \(-0.275535\pi\)
0.648170 + 0.761496i \(0.275535\pi\)
\(632\) 0 0
\(633\) −1.83981e6 −0.182500
\(634\) 0 0
\(635\) 14336.0 0.00141089
\(636\) 0 0
\(637\) 1.83612e7 1.79288
\(638\) 0 0
\(639\) −5.11797e6 −0.495844
\(640\) 0 0
\(641\) −1.16798e7 −1.12276 −0.561382 0.827557i \(-0.689730\pi\)
−0.561382 + 0.827557i \(0.689730\pi\)
\(642\) 0 0
\(643\) 7.02732e6 0.670289 0.335145 0.942167i \(-0.391215\pi\)
0.335145 + 0.942167i \(0.391215\pi\)
\(644\) 0 0
\(645\) 2.23194e6 0.211243
\(646\) 0 0
\(647\) −9.72821e6 −0.913634 −0.456817 0.889561i \(-0.651011\pi\)
−0.456817 + 0.889561i \(0.651011\pi\)
\(648\) 0 0
\(649\) −2.22333e7 −2.07201
\(650\) 0 0
\(651\) −4.36634e6 −0.403798
\(652\) 0 0
\(653\) −9.81425e6 −0.900688 −0.450344 0.892855i \(-0.648699\pi\)
−0.450344 + 0.892855i \(0.648699\pi\)
\(654\) 0 0
\(655\) −317296. −0.0288976
\(656\) 0 0
\(657\) 9.60693e6 0.868303
\(658\) 0 0
\(659\) 1.46652e7 1.31545 0.657724 0.753259i \(-0.271519\pi\)
0.657724 + 0.753259i \(0.271519\pi\)
\(660\) 0 0
\(661\) −1.41837e7 −1.26265 −0.631327 0.775517i \(-0.717489\pi\)
−0.631327 + 0.775517i \(0.717489\pi\)
\(662\) 0 0
\(663\) 7.09546e6 0.626897
\(664\) 0 0
\(665\) −3.23814e6 −0.283950
\(666\) 0 0
\(667\) 9.38429e6 0.816745
\(668\) 0 0
\(669\) 8.71578e6 0.752906
\(670\) 0 0
\(671\) −8.28763e6 −0.710598
\(672\) 0 0
\(673\) 5.49941e6 0.468035 0.234018 0.972232i \(-0.424813\pi\)
0.234018 + 0.972232i \(0.424813\pi\)
\(674\) 0 0
\(675\) −9.88830e6 −0.835338
\(676\) 0 0
\(677\) 1.77375e7 1.48737 0.743687 0.668528i \(-0.233075\pi\)
0.743687 + 0.668528i \(0.233075\pi\)
\(678\) 0 0
\(679\) −1.29563e7 −1.07847
\(680\) 0 0
\(681\) 5.49638e6 0.454160
\(682\) 0 0
\(683\) −9.39670e6 −0.770768 −0.385384 0.922756i \(-0.625931\pi\)
−0.385384 + 0.922756i \(0.625931\pi\)
\(684\) 0 0
\(685\) −745332. −0.0606909
\(686\) 0 0
\(687\) 5.59784e6 0.452510
\(688\) 0 0
\(689\) −1.53915e7 −1.23519
\(690\) 0 0
\(691\) −1.34767e7 −1.07371 −0.536857 0.843673i \(-0.680389\pi\)
−0.536857 + 0.843673i \(0.680389\pi\)
\(692\) 0 0
\(693\) −1.99564e7 −1.57851
\(694\) 0 0
\(695\) 277424. 0.0217862
\(696\) 0 0
\(697\) −217260. −0.0169394
\(698\) 0 0
\(699\) −7.50178e6 −0.580726
\(700\) 0 0
\(701\) 2.15594e7 1.65707 0.828536 0.559935i \(-0.189174\pi\)
0.828536 + 0.559935i \(0.189174\pi\)
\(702\) 0 0
\(703\) −1.05173e7 −0.802631
\(704\) 0 0
\(705\) −3584.00 −0.000271578 0
\(706\) 0 0
\(707\) −1.33411e6 −0.100379
\(708\) 0 0
\(709\) −6.38165e6 −0.476779 −0.238390 0.971170i \(-0.576620\pi\)
−0.238390 + 0.971170i \(0.576620\pi\)
\(710\) 0 0
\(711\) 1.23782e7 0.918298
\(712\) 0 0
\(713\) −8.43878e6 −0.621664
\(714\) 0 0
\(715\) −5.20778e6 −0.380967
\(716\) 0 0
\(717\) −5.14790e6 −0.373966
\(718\) 0 0
\(719\) −1.63566e7 −1.17997 −0.589986 0.807413i \(-0.700867\pi\)
−0.589986 + 0.807413i \(0.700867\pi\)
\(720\) 0 0
\(721\) 2.25539e7 1.61578
\(722\) 0 0
\(723\) −1.25826e6 −0.0895207
\(724\) 0 0
\(725\) −8.54682e6 −0.603893
\(726\) 0 0
\(727\) −2.13130e7 −1.49558 −0.747788 0.663937i \(-0.768884\pi\)
−0.747788 + 0.663937i \(0.768884\pi\)
\(728\) 0 0
\(729\) 3.61141e6 0.251686
\(730\) 0 0
\(731\) 2.54680e7 1.76279
\(732\) 0 0
\(733\) 1.21571e7 0.835737 0.417869 0.908507i \(-0.362777\pi\)
0.417869 + 0.908507i \(0.362777\pi\)
\(734\) 0 0
\(735\) −2.96318e6 −0.202321
\(736\) 0 0
\(737\) 1.11188e7 0.754030
\(738\) 0 0
\(739\) −1.92337e7 −1.29555 −0.647773 0.761834i \(-0.724299\pi\)
−0.647773 + 0.761834i \(0.724299\pi\)
\(740\) 0 0
\(741\) −6.17382e6 −0.413056
\(742\) 0 0
\(743\) 1.66565e6 0.110691 0.0553454 0.998467i \(-0.482374\pi\)
0.0553454 + 0.998467i \(0.482374\pi\)
\(744\) 0 0
\(745\) 6.33066e6 0.417886
\(746\) 0 0
\(747\) 6.76620e6 0.443653
\(748\) 0 0
\(749\) −2.16270e7 −1.40861
\(750\) 0 0
\(751\) 9.81290e6 0.634888 0.317444 0.948277i \(-0.397175\pi\)
0.317444 + 0.948277i \(0.397175\pi\)
\(752\) 0 0
\(753\) 1.26883e7 0.815486
\(754\) 0 0
\(755\) −3.68592e6 −0.235331
\(756\) 0 0
\(757\) −1.92753e7 −1.22254 −0.611269 0.791423i \(-0.709341\pi\)
−0.611269 + 0.791423i \(0.709341\pi\)
\(758\) 0 0
\(759\) 1.37902e7 0.868893
\(760\) 0 0
\(761\) −1.17863e7 −0.737762 −0.368881 0.929477i \(-0.620259\pi\)
−0.368881 + 0.929477i \(0.620259\pi\)
\(762\) 0 0
\(763\) −517088. −0.0321553
\(764\) 0 0
\(765\) 3.20267e6 0.197860
\(766\) 0 0
\(767\) 2.87871e7 1.76689
\(768\) 0 0
\(769\) 1.22941e7 0.749690 0.374845 0.927087i \(-0.377696\pi\)
0.374845 + 0.927087i \(0.377696\pi\)
\(770\) 0 0
\(771\) 5.23467e6 0.317142
\(772\) 0 0
\(773\) 2.57086e6 0.154750 0.0773749 0.997002i \(-0.475346\pi\)
0.0773749 + 0.997002i \(0.475346\pi\)
\(774\) 0 0
\(775\) 7.68570e6 0.459652
\(776\) 0 0
\(777\) −1.57381e7 −0.935190
\(778\) 0 0
\(779\) 189040. 0.0111612
\(780\) 0 0
\(781\) −1.53253e7 −0.899046
\(782\) 0 0
\(783\) 9.85117e6 0.574227
\(784\) 0 0
\(785\) −4.94942e6 −0.286669
\(786\) 0 0
\(787\) 5.54594e6 0.319182 0.159591 0.987183i \(-0.448982\pi\)
0.159591 + 0.987183i \(0.448982\pi\)
\(788\) 0 0
\(789\) 2.64154e6 0.151065
\(790\) 0 0
\(791\) −3.28515e6 −0.186687
\(792\) 0 0
\(793\) 1.07306e7 0.605958
\(794\) 0 0
\(795\) 2.48394e6 0.139387
\(796\) 0 0
\(797\) 2.09610e7 1.16887 0.584436 0.811440i \(-0.301316\pi\)
0.584436 + 0.811440i \(0.301316\pi\)
\(798\) 0 0
\(799\) −40896.0 −0.00226628
\(800\) 0 0
\(801\) 2.26983e7 1.25000
\(802\) 0 0
\(803\) 2.87671e7 1.57437
\(804\) 0 0
\(805\) −9.36499e6 −0.509352
\(806\) 0 0
\(807\) −1.25565e7 −0.678709
\(808\) 0 0
\(809\) 2.70297e7 1.45201 0.726005 0.687690i \(-0.241375\pi\)
0.726005 + 0.687690i \(0.241375\pi\)
\(810\) 0 0
\(811\) −2.13052e6 −0.113745 −0.0568727 0.998381i \(-0.518113\pi\)
−0.0568727 + 0.998381i \(0.518113\pi\)
\(812\) 0 0
\(813\) −7.66234e6 −0.406570
\(814\) 0 0
\(815\) −1.41310e6 −0.0745212
\(816\) 0 0
\(817\) −2.21599e7 −1.16148
\(818\) 0 0
\(819\) 2.58390e7 1.34607
\(820\) 0 0
\(821\) 1.58060e7 0.818396 0.409198 0.912446i \(-0.365809\pi\)
0.409198 + 0.912446i \(0.365809\pi\)
\(822\) 0 0
\(823\) −2.28848e7 −1.17773 −0.588867 0.808230i \(-0.700426\pi\)
−0.588867 + 0.808230i \(0.700426\pi\)
\(824\) 0 0
\(825\) −1.25596e7 −0.642450
\(826\) 0 0
\(827\) −2.55336e7 −1.29822 −0.649109 0.760695i \(-0.724858\pi\)
−0.649109 + 0.760695i \(0.724858\pi\)
\(828\) 0 0
\(829\) 8.31786e6 0.420364 0.210182 0.977662i \(-0.432594\pi\)
0.210182 + 0.977662i \(0.432594\pi\)
\(830\) 0 0
\(831\) −4.52350e6 −0.227234
\(832\) 0 0
\(833\) −3.38120e7 −1.68834
\(834\) 0 0
\(835\) −3.98922e6 −0.198003
\(836\) 0 0
\(837\) −8.85862e6 −0.437072
\(838\) 0 0
\(839\) 3.66261e7 1.79633 0.898164 0.439660i \(-0.144901\pi\)
0.898164 + 0.439660i \(0.144901\pi\)
\(840\) 0 0
\(841\) −1.19964e7 −0.584873
\(842\) 0 0
\(843\) 1.07302e7 0.520041
\(844\) 0 0
\(845\) 1.54480e6 0.0744271
\(846\) 0 0
\(847\) −2.62590e7 −1.25768
\(848\) 0 0
\(849\) 5.87411e6 0.279687
\(850\) 0 0
\(851\) −3.04169e7 −1.43976
\(852\) 0 0
\(853\) 1.74802e7 0.822571 0.411286 0.911507i \(-0.365080\pi\)
0.411286 + 0.911507i \(0.365080\pi\)
\(854\) 0 0
\(855\) −2.78667e6 −0.130368
\(856\) 0 0
\(857\) 9.31062e6 0.433038 0.216519 0.976278i \(-0.430530\pi\)
0.216519 + 0.976278i \(0.430530\pi\)
\(858\) 0 0
\(859\) −3.49525e7 −1.61620 −0.808101 0.589045i \(-0.799504\pi\)
−0.808101 + 0.589045i \(0.799504\pi\)
\(860\) 0 0
\(861\) 282880. 0.0130045
\(862\) 0 0
\(863\) −2.02349e7 −0.924858 −0.462429 0.886656i \(-0.653022\pi\)
−0.462429 + 0.886656i \(0.653022\pi\)
\(864\) 0 0
\(865\) 6.78124e6 0.308155
\(866\) 0 0
\(867\) −1.70742e6 −0.0771421
\(868\) 0 0
\(869\) 3.70655e7 1.66502
\(870\) 0 0
\(871\) −1.43963e7 −0.642994
\(872\) 0 0
\(873\) −1.11499e7 −0.495149
\(874\) 0 0
\(875\) 1.76292e7 0.778419
\(876\) 0 0
\(877\) −1.98343e7 −0.870797 −0.435398 0.900238i \(-0.643392\pi\)
−0.435398 + 0.900238i \(0.643392\pi\)
\(878\) 0 0
\(879\) 9.06562e6 0.395754
\(880\) 0 0
\(881\) −3.81023e7 −1.65391 −0.826954 0.562270i \(-0.809928\pi\)
−0.826954 + 0.562270i \(0.809928\pi\)
\(882\) 0 0
\(883\) −2.41560e7 −1.04261 −0.521307 0.853369i \(-0.674555\pi\)
−0.521307 + 0.853369i \(0.674555\pi\)
\(884\) 0 0
\(885\) −4.64576e6 −0.199388
\(886\) 0 0
\(887\) 2.02368e7 0.863638 0.431819 0.901960i \(-0.357872\pi\)
0.431819 + 0.901960i \(0.357872\pi\)
\(888\) 0 0
\(889\) −212992. −0.00903876
\(890\) 0 0
\(891\) −8.83810e6 −0.372962
\(892\) 0 0
\(893\) 35584.0 0.00149323
\(894\) 0 0
\(895\) 5.69352e6 0.237587
\(896\) 0 0
\(897\) −1.78552e7 −0.740942
\(898\) 0 0
\(899\) −7.65683e6 −0.315973
\(900\) 0 0
\(901\) 2.83435e7 1.16316
\(902\) 0 0
\(903\) −3.31602e7 −1.35331
\(904\) 0 0
\(905\) 7.98423e6 0.324050
\(906\) 0 0
\(907\) 1.97976e7 0.799088 0.399544 0.916714i \(-0.369169\pi\)
0.399544 + 0.916714i \(0.369169\pi\)
\(908\) 0 0
\(909\) −1.14811e6 −0.0460863
\(910\) 0 0
\(911\) −2.13242e7 −0.851288 −0.425644 0.904891i \(-0.639952\pi\)
−0.425644 + 0.904891i \(0.639952\pi\)
\(912\) 0 0
\(913\) 2.02608e7 0.804414
\(914\) 0 0
\(915\) −1.73174e6 −0.0683803
\(916\) 0 0
\(917\) 4.71411e6 0.185130
\(918\) 0 0
\(919\) 3.49941e7 1.36680 0.683401 0.730043i \(-0.260500\pi\)
0.683401 + 0.730043i \(0.260500\pi\)
\(920\) 0 0
\(921\) 2.33101e7 0.905515
\(922\) 0 0
\(923\) 1.98428e7 0.766655
\(924\) 0 0
\(925\) 2.77025e7 1.06455
\(926\) 0 0
\(927\) 1.94093e7 0.741842
\(928\) 0 0
\(929\) −2.88107e7 −1.09525 −0.547627 0.836722i \(-0.684469\pi\)
−0.547627 + 0.836722i \(0.684469\pi\)
\(930\) 0 0
\(931\) 2.94202e7 1.11243
\(932\) 0 0
\(933\) 1.15050e7 0.432697
\(934\) 0 0
\(935\) 9.59011e6 0.358752
\(936\) 0 0
\(937\) 1.28854e7 0.479457 0.239729 0.970840i \(-0.422941\pi\)
0.239729 + 0.970840i \(0.422941\pi\)
\(938\) 0 0
\(939\) 1.10080e7 0.407424
\(940\) 0 0
\(941\) −5.27615e7 −1.94242 −0.971210 0.238227i \(-0.923434\pi\)
−0.971210 + 0.238227i \(0.923434\pi\)
\(942\) 0 0
\(943\) 546720. 0.0200210
\(944\) 0 0
\(945\) −9.83091e6 −0.358108
\(946\) 0 0
\(947\) 5.53961e6 0.200726 0.100363 0.994951i \(-0.468000\pi\)
0.100363 + 0.994951i \(0.468000\pi\)
\(948\) 0 0
\(949\) −3.72470e7 −1.34253
\(950\) 0 0
\(951\) 9.87950e6 0.354229
\(952\) 0 0
\(953\) −228102. −0.00813574 −0.00406787 0.999992i \(-0.501295\pi\)
−0.00406787 + 0.999992i \(0.501295\pi\)
\(954\) 0 0
\(955\) 1.94074e6 0.0688586
\(956\) 0 0
\(957\) 1.25124e7 0.441632
\(958\) 0 0
\(959\) 1.10735e7 0.388811
\(960\) 0 0
\(961\) −2.17438e7 −0.759498
\(962\) 0 0
\(963\) −1.86117e7 −0.646726
\(964\) 0 0
\(965\) 482748. 0.0166879
\(966\) 0 0
\(967\) 7.36709e6 0.253355 0.126678 0.991944i \(-0.459569\pi\)
0.126678 + 0.991944i \(0.459569\pi\)
\(968\) 0 0
\(969\) 1.13691e7 0.388970
\(970\) 0 0
\(971\) −1.91161e7 −0.650654 −0.325327 0.945602i \(-0.605474\pi\)
−0.325327 + 0.945602i \(0.605474\pi\)
\(972\) 0 0
\(973\) −4.12173e6 −0.139572
\(974\) 0 0
\(975\) 1.62618e7 0.547844
\(976\) 0 0
\(977\) 5.57040e7 1.86702 0.933512 0.358546i \(-0.116727\pi\)
0.933512 + 0.358546i \(0.116727\pi\)
\(978\) 0 0
\(979\) 6.79680e7 2.26646
\(980\) 0 0
\(981\) −444994. −0.0147632
\(982\) 0 0
\(983\) −1.55469e7 −0.513167 −0.256584 0.966522i \(-0.582597\pi\)
−0.256584 + 0.966522i \(0.582597\pi\)
\(984\) 0 0
\(985\) 9.01037e6 0.295905
\(986\) 0 0
\(987\) 53248.0 0.00173984
\(988\) 0 0
\(989\) −6.40884e7 −2.08348
\(990\) 0 0
\(991\) 2.36890e7 0.766237 0.383118 0.923699i \(-0.374850\pi\)
0.383118 + 0.923699i \(0.374850\pi\)
\(992\) 0 0
\(993\) 1.19144e7 0.383442
\(994\) 0 0
\(995\) 1.55033e7 0.496438
\(996\) 0 0
\(997\) 3.71720e6 0.118434 0.0592172 0.998245i \(-0.481140\pi\)
0.0592172 + 0.998245i \(0.481140\pi\)
\(998\) 0 0
\(999\) −3.19302e7 −1.01225
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 32.6.a.a.1.1 1
3.2 odd 2 288.6.a.d.1.1 1
4.3 odd 2 32.6.a.c.1.1 yes 1
5.2 odd 4 800.6.c.a.449.2 2
5.3 odd 4 800.6.c.a.449.1 2
5.4 even 2 800.6.a.e.1.1 1
8.3 odd 2 64.6.a.c.1.1 1
8.5 even 2 64.6.a.e.1.1 1
12.11 even 2 288.6.a.e.1.1 1
16.3 odd 4 256.6.b.b.129.2 2
16.5 even 4 256.6.b.h.129.2 2
16.11 odd 4 256.6.b.b.129.1 2
16.13 even 4 256.6.b.h.129.1 2
20.3 even 4 800.6.c.b.449.2 2
20.7 even 4 800.6.c.b.449.1 2
20.19 odd 2 800.6.a.a.1.1 1
24.5 odd 2 576.6.a.u.1.1 1
24.11 even 2 576.6.a.v.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.6.a.a.1.1 1 1.1 even 1 trivial
32.6.a.c.1.1 yes 1 4.3 odd 2
64.6.a.c.1.1 1 8.3 odd 2
64.6.a.e.1.1 1 8.5 even 2
256.6.b.b.129.1 2 16.11 odd 4
256.6.b.b.129.2 2 16.3 odd 4
256.6.b.h.129.1 2 16.13 even 4
256.6.b.h.129.2 2 16.5 even 4
288.6.a.d.1.1 1 3.2 odd 2
288.6.a.e.1.1 1 12.11 even 2
576.6.a.u.1.1 1 24.5 odd 2
576.6.a.v.1.1 1 24.11 even 2
800.6.a.a.1.1 1 20.19 odd 2
800.6.a.e.1.1 1 5.4 even 2
800.6.c.a.449.1 2 5.3 odd 4
800.6.c.a.449.2 2 5.2 odd 4
800.6.c.b.449.1 2 20.7 even 4
800.6.c.b.449.2 2 20.3 even 4