Properties

Label 912.6.a.y.1.2
Level $912$
Weight $6$
Character 912.1
Self dual yes
Analytic conductor $146.270$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 912.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(146.270043669\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 2x^{5} - 4725x^{4} + 92430x^{3} + 1610577x^{2} - 16081740x - 24661341 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: no (minimal twist has level 456)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(34.8797\) of defining polynomial
Character \(\chi\) \(=\) 912.1

$q$-expansion

\(f(q)\) \(=\) \(q+9.00000 q^{3} -80.1366 q^{5} +221.037 q^{7} +81.0000 q^{9} +O(q^{10})\) \(q+9.00000 q^{3} -80.1366 q^{5} +221.037 q^{7} +81.0000 q^{9} -6.83714 q^{11} +1037.03 q^{13} -721.230 q^{15} +89.8390 q^{17} -361.000 q^{19} +1989.33 q^{21} -1939.48 q^{23} +3296.88 q^{25} +729.000 q^{27} +8952.03 q^{29} +152.627 q^{31} -61.5342 q^{33} -17713.1 q^{35} -2971.83 q^{37} +9333.27 q^{39} -13839.3 q^{41} +12954.7 q^{43} -6491.07 q^{45} +23530.5 q^{47} +32050.2 q^{49} +808.551 q^{51} +5834.26 q^{53} +547.905 q^{55} -3249.00 q^{57} +5031.13 q^{59} -56361.1 q^{61} +17904.0 q^{63} -83104.1 q^{65} -48315.2 q^{67} -17455.3 q^{69} -73547.4 q^{71} +59881.4 q^{73} +29671.9 q^{75} -1511.26 q^{77} +34028.2 q^{79} +6561.00 q^{81} -76249.7 q^{83} -7199.39 q^{85} +80568.3 q^{87} -18300.9 q^{89} +229222. q^{91} +1373.64 q^{93} +28929.3 q^{95} +55155.8 q^{97} -553.808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 54 q^{3} - 65 q^{5} + 149 q^{7} + 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 54 q^{3} - 65 q^{5} + 149 q^{7} + 486 q^{9} + 203 q^{11} - 298 q^{13} - 585 q^{15} + 1319 q^{17} - 2166 q^{19} + 1341 q^{21} - 1234 q^{23} + 4589 q^{25} + 4374 q^{27} + 7356 q^{29} - 1632 q^{31} + 1827 q^{33} - 4383 q^{35} + 14204 q^{37} - 2682 q^{39} + 14734 q^{41} + 4693 q^{43} - 5265 q^{45} + 10955 q^{47} + 38561 q^{49} + 11871 q^{51} + 47500 q^{53} - 769 q^{55} - 19494 q^{57} + 61744 q^{59} - 81581 q^{61} + 12069 q^{63} - 59686 q^{65} + 45756 q^{67} - 11106 q^{69} + 10416 q^{71} - 54615 q^{73} + 41301 q^{75} - 29515 q^{77} + 145594 q^{79} + 39366 q^{81} + 160548 q^{83} - 53947 q^{85} + 66204 q^{87} - 97728 q^{89} + 418294 q^{91} - 14688 q^{93} + 23465 q^{95} - 760 q^{97} + 16443 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 9.00000 0.577350
\(4\) 0 0
\(5\) −80.1366 −1.43353 −0.716764 0.697316i \(-0.754377\pi\)
−0.716764 + 0.697316i \(0.754377\pi\)
\(6\) 0 0
\(7\) 221.037 1.70498 0.852490 0.522744i \(-0.175092\pi\)
0.852490 + 0.522744i \(0.175092\pi\)
\(8\) 0 0
\(9\) 81.0000 0.333333
\(10\) 0 0
\(11\) −6.83714 −0.0170370 −0.00851849 0.999964i \(-0.502712\pi\)
−0.00851849 + 0.999964i \(0.502712\pi\)
\(12\) 0 0
\(13\) 1037.03 1.70190 0.850948 0.525251i \(-0.176028\pi\)
0.850948 + 0.525251i \(0.176028\pi\)
\(14\) 0 0
\(15\) −721.230 −0.827647
\(16\) 0 0
\(17\) 89.8390 0.0753950 0.0376975 0.999289i \(-0.487998\pi\)
0.0376975 + 0.999289i \(0.487998\pi\)
\(18\) 0 0
\(19\) −361.000 −0.229416
\(20\) 0 0
\(21\) 1989.33 0.984370
\(22\) 0 0
\(23\) −1939.48 −0.764480 −0.382240 0.924063i \(-0.624847\pi\)
−0.382240 + 0.924063i \(0.624847\pi\)
\(24\) 0 0
\(25\) 3296.88 1.05500
\(26\) 0 0
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 8952.03 1.97664 0.988318 0.152407i \(-0.0487024\pi\)
0.988318 + 0.152407i \(0.0487024\pi\)
\(30\) 0 0
\(31\) 152.627 0.0285251 0.0142626 0.999898i \(-0.495460\pi\)
0.0142626 + 0.999898i \(0.495460\pi\)
\(32\) 0 0
\(33\) −61.5342 −0.00983631
\(34\) 0 0
\(35\) −17713.1 −2.44413
\(36\) 0 0
\(37\) −2971.83 −0.356878 −0.178439 0.983951i \(-0.557105\pi\)
−0.178439 + 0.983951i \(0.557105\pi\)
\(38\) 0 0
\(39\) 9333.27 0.982590
\(40\) 0 0
\(41\) −13839.3 −1.28574 −0.642870 0.765975i \(-0.722257\pi\)
−0.642870 + 0.765975i \(0.722257\pi\)
\(42\) 0 0
\(43\) 12954.7 1.06846 0.534229 0.845339i \(-0.320602\pi\)
0.534229 + 0.845339i \(0.320602\pi\)
\(44\) 0 0
\(45\) −6491.07 −0.477842
\(46\) 0 0
\(47\) 23530.5 1.55377 0.776883 0.629645i \(-0.216799\pi\)
0.776883 + 0.629645i \(0.216799\pi\)
\(48\) 0 0
\(49\) 32050.2 1.90695
\(50\) 0 0
\(51\) 808.551 0.0435293
\(52\) 0 0
\(53\) 5834.26 0.285296 0.142648 0.989773i \(-0.454438\pi\)
0.142648 + 0.989773i \(0.454438\pi\)
\(54\) 0 0
\(55\) 547.905 0.0244230
\(56\) 0 0
\(57\) −3249.00 −0.132453
\(58\) 0 0
\(59\) 5031.13 0.188164 0.0940818 0.995564i \(-0.470008\pi\)
0.0940818 + 0.995564i \(0.470008\pi\)
\(60\) 0 0
\(61\) −56361.1 −1.93934 −0.969672 0.244408i \(-0.921406\pi\)
−0.969672 + 0.244408i \(0.921406\pi\)
\(62\) 0 0
\(63\) 17904.0 0.568326
\(64\) 0 0
\(65\) −83104.1 −2.43971
\(66\) 0 0
\(67\) −48315.2 −1.31491 −0.657456 0.753493i \(-0.728368\pi\)
−0.657456 + 0.753493i \(0.728368\pi\)
\(68\) 0 0
\(69\) −17455.3 −0.441373
\(70\) 0 0
\(71\) −73547.4 −1.73150 −0.865748 0.500480i \(-0.833157\pi\)
−0.865748 + 0.500480i \(0.833157\pi\)
\(72\) 0 0
\(73\) 59881.4 1.31518 0.657589 0.753377i \(-0.271576\pi\)
0.657589 + 0.753377i \(0.271576\pi\)
\(74\) 0 0
\(75\) 29671.9 0.609105
\(76\) 0 0
\(77\) −1511.26 −0.0290477
\(78\) 0 0
\(79\) 34028.2 0.613439 0.306720 0.951800i \(-0.400769\pi\)
0.306720 + 0.951800i \(0.400769\pi\)
\(80\) 0 0
\(81\) 6561.00 0.111111
\(82\) 0 0
\(83\) −76249.7 −1.21491 −0.607453 0.794356i \(-0.707809\pi\)
−0.607453 + 0.794356i \(0.707809\pi\)
\(84\) 0 0
\(85\) −7199.39 −0.108081
\(86\) 0 0
\(87\) 80568.3 1.14121
\(88\) 0 0
\(89\) −18300.9 −0.244905 −0.122453 0.992474i \(-0.539076\pi\)
−0.122453 + 0.992474i \(0.539076\pi\)
\(90\) 0 0
\(91\) 229222. 2.90170
\(92\) 0 0
\(93\) 1373.64 0.0164690
\(94\) 0 0
\(95\) 28929.3 0.328874
\(96\) 0 0
\(97\) 55155.8 0.595199 0.297599 0.954691i \(-0.403814\pi\)
0.297599 + 0.954691i \(0.403814\pi\)
\(98\) 0 0
\(99\) −553.808 −0.00567899
\(100\) 0 0
\(101\) −2327.63 −0.0227045 −0.0113522 0.999936i \(-0.503614\pi\)
−0.0113522 + 0.999936i \(0.503614\pi\)
\(102\) 0 0
\(103\) −39962.2 −0.371156 −0.185578 0.982630i \(-0.559416\pi\)
−0.185578 + 0.982630i \(0.559416\pi\)
\(104\) 0 0
\(105\) −159418. −1.41112
\(106\) 0 0
\(107\) −27485.4 −0.232083 −0.116041 0.993244i \(-0.537021\pi\)
−0.116041 + 0.993244i \(0.537021\pi\)
\(108\) 0 0
\(109\) 141384. 1.13982 0.569908 0.821709i \(-0.306979\pi\)
0.569908 + 0.821709i \(0.306979\pi\)
\(110\) 0 0
\(111\) −26746.5 −0.206044
\(112\) 0 0
\(113\) −89708.4 −0.660902 −0.330451 0.943823i \(-0.607201\pi\)
−0.330451 + 0.943823i \(0.607201\pi\)
\(114\) 0 0
\(115\) 155424. 1.09590
\(116\) 0 0
\(117\) 83999.4 0.567298
\(118\) 0 0
\(119\) 19857.7 0.128547
\(120\) 0 0
\(121\) −161004. −0.999710
\(122\) 0 0
\(123\) −124553. −0.742323
\(124\) 0 0
\(125\) −13773.8 −0.0788456
\(126\) 0 0
\(127\) 264999. 1.45792 0.728962 0.684554i \(-0.240003\pi\)
0.728962 + 0.684554i \(0.240003\pi\)
\(128\) 0 0
\(129\) 116593. 0.616875
\(130\) 0 0
\(131\) 143573. 0.730961 0.365480 0.930819i \(-0.380905\pi\)
0.365480 + 0.930819i \(0.380905\pi\)
\(132\) 0 0
\(133\) −79794.2 −0.391149
\(134\) 0 0
\(135\) −58419.6 −0.275882
\(136\) 0 0
\(137\) 201383. 0.916690 0.458345 0.888774i \(-0.348442\pi\)
0.458345 + 0.888774i \(0.348442\pi\)
\(138\) 0 0
\(139\) 449847. 1.97482 0.987411 0.158174i \(-0.0505608\pi\)
0.987411 + 0.158174i \(0.0505608\pi\)
\(140\) 0 0
\(141\) 211774. 0.897068
\(142\) 0 0
\(143\) −7090.31 −0.0289952
\(144\) 0 0
\(145\) −717386. −2.83356
\(146\) 0 0
\(147\) 288452. 1.10098
\(148\) 0 0
\(149\) 262602. 0.969021 0.484510 0.874786i \(-0.338998\pi\)
0.484510 + 0.874786i \(0.338998\pi\)
\(150\) 0 0
\(151\) 318671. 1.13737 0.568683 0.822557i \(-0.307453\pi\)
0.568683 + 0.822557i \(0.307453\pi\)
\(152\) 0 0
\(153\) 7276.96 0.0251317
\(154\) 0 0
\(155\) −12231.0 −0.0408916
\(156\) 0 0
\(157\) 435520. 1.41013 0.705065 0.709143i \(-0.250918\pi\)
0.705065 + 0.709143i \(0.250918\pi\)
\(158\) 0 0
\(159\) 52508.3 0.164716
\(160\) 0 0
\(161\) −428697. −1.30342
\(162\) 0 0
\(163\) 341902. 1.00794 0.503968 0.863722i \(-0.331873\pi\)
0.503968 + 0.863722i \(0.331873\pi\)
\(164\) 0 0
\(165\) 4931.15 0.0141006
\(166\) 0 0
\(167\) 105364. 0.292348 0.146174 0.989259i \(-0.453304\pi\)
0.146174 + 0.989259i \(0.453304\pi\)
\(168\) 0 0
\(169\) 704138. 1.89645
\(170\) 0 0
\(171\) −29241.0 −0.0764719
\(172\) 0 0
\(173\) −487341. −1.23799 −0.618996 0.785394i \(-0.712460\pi\)
−0.618996 + 0.785394i \(0.712460\pi\)
\(174\) 0 0
\(175\) 728731. 1.79876
\(176\) 0 0
\(177\) 45280.2 0.108636
\(178\) 0 0
\(179\) 586070. 1.36715 0.683576 0.729879i \(-0.260424\pi\)
0.683576 + 0.729879i \(0.260424\pi\)
\(180\) 0 0
\(181\) −143643. −0.325903 −0.162951 0.986634i \(-0.552101\pi\)
−0.162951 + 0.986634i \(0.552101\pi\)
\(182\) 0 0
\(183\) −507250. −1.11968
\(184\) 0 0
\(185\) 238153. 0.511595
\(186\) 0 0
\(187\) −614.241 −0.00128450
\(188\) 0 0
\(189\) 161136. 0.328123
\(190\) 0 0
\(191\) −912988. −1.81085 −0.905424 0.424509i \(-0.860447\pi\)
−0.905424 + 0.424509i \(0.860447\pi\)
\(192\) 0 0
\(193\) 160240. 0.309654 0.154827 0.987942i \(-0.450518\pi\)
0.154827 + 0.987942i \(0.450518\pi\)
\(194\) 0 0
\(195\) −747937. −1.40857
\(196\) 0 0
\(197\) 47620.7 0.0874240 0.0437120 0.999044i \(-0.486082\pi\)
0.0437120 + 0.999044i \(0.486082\pi\)
\(198\) 0 0
\(199\) −647040. −1.15824 −0.579120 0.815242i \(-0.696604\pi\)
−0.579120 + 0.815242i \(0.696604\pi\)
\(200\) 0 0
\(201\) −434837. −0.759165
\(202\) 0 0
\(203\) 1.97873e6 3.37012
\(204\) 0 0
\(205\) 1.10903e6 1.84314
\(206\) 0 0
\(207\) −157098. −0.254827
\(208\) 0 0
\(209\) 2468.21 0.00390855
\(210\) 0 0
\(211\) 797079. 1.23252 0.616261 0.787542i \(-0.288646\pi\)
0.616261 + 0.787542i \(0.288646\pi\)
\(212\) 0 0
\(213\) −661927. −0.999680
\(214\) 0 0
\(215\) −1.03815e6 −1.53167
\(216\) 0 0
\(217\) 33736.2 0.0486348
\(218\) 0 0
\(219\) 538933. 0.759319
\(220\) 0 0
\(221\) 93165.7 0.128314
\(222\) 0 0
\(223\) 698425. 0.940497 0.470249 0.882534i \(-0.344164\pi\)
0.470249 + 0.882534i \(0.344164\pi\)
\(224\) 0 0
\(225\) 267047. 0.351667
\(226\) 0 0
\(227\) 809651. 1.04288 0.521438 0.853289i \(-0.325396\pi\)
0.521438 + 0.853289i \(0.325396\pi\)
\(228\) 0 0
\(229\) 244499. 0.308098 0.154049 0.988063i \(-0.450769\pi\)
0.154049 + 0.988063i \(0.450769\pi\)
\(230\) 0 0
\(231\) −13601.3 −0.0167707
\(232\) 0 0
\(233\) 263509. 0.317984 0.158992 0.987280i \(-0.449176\pi\)
0.158992 + 0.987280i \(0.449176\pi\)
\(234\) 0 0
\(235\) −1.88565e6 −2.22737
\(236\) 0 0
\(237\) 306254. 0.354169
\(238\) 0 0
\(239\) −181693. −0.205752 −0.102876 0.994694i \(-0.532804\pi\)
−0.102876 + 0.994694i \(0.532804\pi\)
\(240\) 0 0
\(241\) −1.00530e6 −1.11495 −0.557474 0.830194i \(-0.688229\pi\)
−0.557474 + 0.830194i \(0.688229\pi\)
\(242\) 0 0
\(243\) 59049.0 0.0641500
\(244\) 0 0
\(245\) −2.56839e6 −2.73367
\(246\) 0 0
\(247\) −374368. −0.390442
\(248\) 0 0
\(249\) −686247. −0.701426
\(250\) 0 0
\(251\) −151883. −0.152168 −0.0760841 0.997101i \(-0.524242\pi\)
−0.0760841 + 0.997101i \(0.524242\pi\)
\(252\) 0 0
\(253\) 13260.5 0.0130244
\(254\) 0 0
\(255\) −64794.5 −0.0624005
\(256\) 0 0
\(257\) 1.47290e6 1.39104 0.695522 0.718505i \(-0.255173\pi\)
0.695522 + 0.718505i \(0.255173\pi\)
\(258\) 0 0
\(259\) −656884. −0.608470
\(260\) 0 0
\(261\) 725115. 0.658879
\(262\) 0 0
\(263\) −602508. −0.537123 −0.268561 0.963263i \(-0.586548\pi\)
−0.268561 + 0.963263i \(0.586548\pi\)
\(264\) 0 0
\(265\) −467538. −0.408980
\(266\) 0 0
\(267\) −164708. −0.141396
\(268\) 0 0
\(269\) 1.17808e6 0.992643 0.496321 0.868139i \(-0.334684\pi\)
0.496321 + 0.868139i \(0.334684\pi\)
\(270\) 0 0
\(271\) −476163. −0.393851 −0.196926 0.980418i \(-0.563096\pi\)
−0.196926 + 0.980418i \(0.563096\pi\)
\(272\) 0 0
\(273\) 2.06299e6 1.67530
\(274\) 0 0
\(275\) −22541.2 −0.0179740
\(276\) 0 0
\(277\) −1.95601e6 −1.53170 −0.765848 0.643022i \(-0.777680\pi\)
−0.765848 + 0.643022i \(0.777680\pi\)
\(278\) 0 0
\(279\) 12362.8 0.00950837
\(280\) 0 0
\(281\) −2.46010e6 −1.85861 −0.929304 0.369316i \(-0.879592\pi\)
−0.929304 + 0.369316i \(0.879592\pi\)
\(282\) 0 0
\(283\) 954640. 0.708555 0.354277 0.935140i \(-0.384727\pi\)
0.354277 + 0.935140i \(0.384727\pi\)
\(284\) 0 0
\(285\) 260364. 0.189875
\(286\) 0 0
\(287\) −3.05898e6 −2.19216
\(288\) 0 0
\(289\) −1.41179e6 −0.994316
\(290\) 0 0
\(291\) 496402. 0.343638
\(292\) 0 0
\(293\) 425873. 0.289808 0.144904 0.989446i \(-0.453713\pi\)
0.144904 + 0.989446i \(0.453713\pi\)
\(294\) 0 0
\(295\) −403178. −0.269738
\(296\) 0 0
\(297\) −4984.27 −0.00327877
\(298\) 0 0
\(299\) −2.01130e6 −1.30106
\(300\) 0 0
\(301\) 2.86347e6 1.82170
\(302\) 0 0
\(303\) −20948.7 −0.0131084
\(304\) 0 0
\(305\) 4.51659e6 2.78010
\(306\) 0 0
\(307\) 2.25152e6 1.36342 0.681711 0.731622i \(-0.261236\pi\)
0.681711 + 0.731622i \(0.261236\pi\)
\(308\) 0 0
\(309\) −359660. −0.214287
\(310\) 0 0
\(311\) 2.97390e6 1.74352 0.871758 0.489937i \(-0.162980\pi\)
0.871758 + 0.489937i \(0.162980\pi\)
\(312\) 0 0
\(313\) 1.38952e6 0.801683 0.400842 0.916147i \(-0.368718\pi\)
0.400842 + 0.916147i \(0.368718\pi\)
\(314\) 0 0
\(315\) −1.43476e6 −0.814712
\(316\) 0 0
\(317\) 1.09173e6 0.610193 0.305096 0.952321i \(-0.401311\pi\)
0.305096 + 0.952321i \(0.401311\pi\)
\(318\) 0 0
\(319\) −61206.3 −0.0336759
\(320\) 0 0
\(321\) −247369. −0.133993
\(322\) 0 0
\(323\) −32431.9 −0.0172968
\(324\) 0 0
\(325\) 3.41896e6 1.79550
\(326\) 0 0
\(327\) 1.27246e6 0.658073
\(328\) 0 0
\(329\) 5.20109e6 2.64914
\(330\) 0 0
\(331\) 2.67033e6 1.33966 0.669830 0.742514i \(-0.266367\pi\)
0.669830 + 0.742514i \(0.266367\pi\)
\(332\) 0 0
\(333\) −240719. −0.118959
\(334\) 0 0
\(335\) 3.87182e6 1.88496
\(336\) 0 0
\(337\) −599879. −0.287732 −0.143866 0.989597i \(-0.545953\pi\)
−0.143866 + 0.989597i \(0.545953\pi\)
\(338\) 0 0
\(339\) −807376. −0.381572
\(340\) 0 0
\(341\) −1043.53 −0.000485982 0
\(342\) 0 0
\(343\) 3.36930e6 1.54634
\(344\) 0 0
\(345\) 1.39881e6 0.632720
\(346\) 0 0
\(347\) 369338. 0.164665 0.0823324 0.996605i \(-0.473763\pi\)
0.0823324 + 0.996605i \(0.473763\pi\)
\(348\) 0 0
\(349\) −3.23931e6 −1.42360 −0.711802 0.702380i \(-0.752121\pi\)
−0.711802 + 0.702380i \(0.752121\pi\)
\(350\) 0 0
\(351\) 755995. 0.327530
\(352\) 0 0
\(353\) 2.91385e6 1.24460 0.622300 0.782779i \(-0.286198\pi\)
0.622300 + 0.782779i \(0.286198\pi\)
\(354\) 0 0
\(355\) 5.89384e6 2.48215
\(356\) 0 0
\(357\) 178719. 0.0742166
\(358\) 0 0
\(359\) −3.00994e6 −1.23260 −0.616299 0.787512i \(-0.711369\pi\)
−0.616299 + 0.787512i \(0.711369\pi\)
\(360\) 0 0
\(361\) 130321. 0.0526316
\(362\) 0 0
\(363\) −1.44904e6 −0.577183
\(364\) 0 0
\(365\) −4.79869e6 −1.88534
\(366\) 0 0
\(367\) −144945. −0.0561744 −0.0280872 0.999605i \(-0.508942\pi\)
−0.0280872 + 0.999605i \(0.508942\pi\)
\(368\) 0 0
\(369\) −1.12098e6 −0.428580
\(370\) 0 0
\(371\) 1.28958e6 0.486424
\(372\) 0 0
\(373\) −1.07459e6 −0.399917 −0.199959 0.979804i \(-0.564081\pi\)
−0.199959 + 0.979804i \(0.564081\pi\)
\(374\) 0 0
\(375\) −123964. −0.0455215
\(376\) 0 0
\(377\) 9.28352e6 3.36403
\(378\) 0 0
\(379\) −348280. −0.124546 −0.0622732 0.998059i \(-0.519835\pi\)
−0.0622732 + 0.998059i \(0.519835\pi\)
\(380\) 0 0
\(381\) 2.38499e6 0.841733
\(382\) 0 0
\(383\) −923631. −0.321737 −0.160869 0.986976i \(-0.551430\pi\)
−0.160869 + 0.986976i \(0.551430\pi\)
\(384\) 0 0
\(385\) 121107. 0.0416407
\(386\) 0 0
\(387\) 1.04933e6 0.356153
\(388\) 0 0
\(389\) 3.16205e6 1.05948 0.529742 0.848159i \(-0.322289\pi\)
0.529742 + 0.848159i \(0.322289\pi\)
\(390\) 0 0
\(391\) −174241. −0.0576380
\(392\) 0 0
\(393\) 1.29216e6 0.422021
\(394\) 0 0
\(395\) −2.72691e6 −0.879382
\(396\) 0 0
\(397\) −4.50866e6 −1.43572 −0.717862 0.696186i \(-0.754879\pi\)
−0.717862 + 0.696186i \(0.754879\pi\)
\(398\) 0 0
\(399\) −718148. −0.225830
\(400\) 0 0
\(401\) −72297.9 −0.0224525 −0.0112262 0.999937i \(-0.503573\pi\)
−0.0112262 + 0.999937i \(0.503573\pi\)
\(402\) 0 0
\(403\) 158279. 0.0485468
\(404\) 0 0
\(405\) −525776. −0.159281
\(406\) 0 0
\(407\) 20318.8 0.00608013
\(408\) 0 0
\(409\) 4.86659e6 1.43852 0.719261 0.694740i \(-0.244481\pi\)
0.719261 + 0.694740i \(0.244481\pi\)
\(410\) 0 0
\(411\) 1.81245e6 0.529251
\(412\) 0 0
\(413\) 1.11206e6 0.320815
\(414\) 0 0
\(415\) 6.11039e6 1.74160
\(416\) 0 0
\(417\) 4.04863e6 1.14016
\(418\) 0 0
\(419\) 2.24133e6 0.623692 0.311846 0.950133i \(-0.399053\pi\)
0.311846 + 0.950133i \(0.399053\pi\)
\(420\) 0 0
\(421\) 244516. 0.0672361 0.0336180 0.999435i \(-0.489297\pi\)
0.0336180 + 0.999435i \(0.489297\pi\)
\(422\) 0 0
\(423\) 1.90597e6 0.517922
\(424\) 0 0
\(425\) 296188. 0.0795418
\(426\) 0 0
\(427\) −1.24579e7 −3.30654
\(428\) 0 0
\(429\) −63812.8 −0.0167404
\(430\) 0 0
\(431\) 91916.4 0.0238342 0.0119171 0.999929i \(-0.496207\pi\)
0.0119171 + 0.999929i \(0.496207\pi\)
\(432\) 0 0
\(433\) −7.21065e6 −1.84823 −0.924113 0.382120i \(-0.875194\pi\)
−0.924113 + 0.382120i \(0.875194\pi\)
\(434\) 0 0
\(435\) −6.45647e6 −1.63596
\(436\) 0 0
\(437\) 700153. 0.175384
\(438\) 0 0
\(439\) −818398. −0.202677 −0.101338 0.994852i \(-0.532312\pi\)
−0.101338 + 0.994852i \(0.532312\pi\)
\(440\) 0 0
\(441\) 2.59607e6 0.635652
\(442\) 0 0
\(443\) 1.01390e6 0.245464 0.122732 0.992440i \(-0.460834\pi\)
0.122732 + 0.992440i \(0.460834\pi\)
\(444\) 0 0
\(445\) 1.46657e6 0.351078
\(446\) 0 0
\(447\) 2.36342e6 0.559464
\(448\) 0 0
\(449\) 4.25379e6 0.995773 0.497887 0.867242i \(-0.334110\pi\)
0.497887 + 0.867242i \(0.334110\pi\)
\(450\) 0 0
\(451\) 94621.0 0.0219051
\(452\) 0 0
\(453\) 2.86804e6 0.656659
\(454\) 0 0
\(455\) −1.83690e7 −4.15966
\(456\) 0 0
\(457\) 858691. 0.192330 0.0961648 0.995365i \(-0.469342\pi\)
0.0961648 + 0.995365i \(0.469342\pi\)
\(458\) 0 0
\(459\) 65492.6 0.0145098
\(460\) 0 0
\(461\) 3.19905e6 0.701083 0.350541 0.936547i \(-0.385998\pi\)
0.350541 + 0.936547i \(0.385998\pi\)
\(462\) 0 0
\(463\) −4.68844e6 −1.01643 −0.508213 0.861231i \(-0.669694\pi\)
−0.508213 + 0.861231i \(0.669694\pi\)
\(464\) 0 0
\(465\) −110079. −0.0236087
\(466\) 0 0
\(467\) 1.89088e6 0.401210 0.200605 0.979672i \(-0.435709\pi\)
0.200605 + 0.979672i \(0.435709\pi\)
\(468\) 0 0
\(469\) −1.06794e7 −2.24190
\(470\) 0 0
\(471\) 3.91968e6 0.814139
\(472\) 0 0
\(473\) −88573.4 −0.0182033
\(474\) 0 0
\(475\) −1.19017e6 −0.242034
\(476\) 0 0
\(477\) 472575. 0.0950987
\(478\) 0 0
\(479\) 4.39562e6 0.875350 0.437675 0.899133i \(-0.355802\pi\)
0.437675 + 0.899133i \(0.355802\pi\)
\(480\) 0 0
\(481\) −3.08188e6 −0.607369
\(482\) 0 0
\(483\) −3.85827e6 −0.752531
\(484\) 0 0
\(485\) −4.42000e6 −0.853234
\(486\) 0 0
\(487\) −4.71164e6 −0.900222 −0.450111 0.892973i \(-0.648616\pi\)
−0.450111 + 0.892973i \(0.648616\pi\)
\(488\) 0 0
\(489\) 3.07712e6 0.581933
\(490\) 0 0
\(491\) 817691. 0.153068 0.0765342 0.997067i \(-0.475615\pi\)
0.0765342 + 0.997067i \(0.475615\pi\)
\(492\) 0 0
\(493\) 804241. 0.149028
\(494\) 0 0
\(495\) 44380.3 0.00814099
\(496\) 0 0
\(497\) −1.62567e7 −2.95217
\(498\) 0 0
\(499\) 6.57253e6 1.18163 0.590815 0.806807i \(-0.298806\pi\)
0.590815 + 0.806807i \(0.298806\pi\)
\(500\) 0 0
\(501\) 948274. 0.168787
\(502\) 0 0
\(503\) −6.81301e6 −1.20066 −0.600329 0.799753i \(-0.704964\pi\)
−0.600329 + 0.799753i \(0.704964\pi\)
\(504\) 0 0
\(505\) 186529. 0.0325475
\(506\) 0 0
\(507\) 6.33724e6 1.09491
\(508\) 0 0
\(509\) −384616. −0.0658011 −0.0329006 0.999459i \(-0.510474\pi\)
−0.0329006 + 0.999459i \(0.510474\pi\)
\(510\) 0 0
\(511\) 1.32360e7 2.24235
\(512\) 0 0
\(513\) −263169. −0.0441511
\(514\) 0 0
\(515\) 3.20244e6 0.532063
\(516\) 0 0
\(517\) −160881. −0.0264715
\(518\) 0 0
\(519\) −4.38607e6 −0.714755
\(520\) 0 0
\(521\) −8.55777e6 −1.38123 −0.690615 0.723222i \(-0.742660\pi\)
−0.690615 + 0.723222i \(0.742660\pi\)
\(522\) 0 0
\(523\) 1.00968e6 0.161410 0.0807051 0.996738i \(-0.474283\pi\)
0.0807051 + 0.996738i \(0.474283\pi\)
\(524\) 0 0
\(525\) 6.55858e6 1.03851
\(526\) 0 0
\(527\) 13711.9 0.00215065
\(528\) 0 0
\(529\) −2.67475e6 −0.415570
\(530\) 0 0
\(531\) 407522. 0.0627212
\(532\) 0 0
\(533\) −1.43517e7 −2.18820
\(534\) 0 0
\(535\) 2.20259e6 0.332697
\(536\) 0 0
\(537\) 5.27463e6 0.789326
\(538\) 0 0
\(539\) −219132. −0.0324888
\(540\) 0 0
\(541\) 631611. 0.0927805 0.0463902 0.998923i \(-0.485228\pi\)
0.0463902 + 0.998923i \(0.485228\pi\)
\(542\) 0 0
\(543\) −1.29279e6 −0.188160
\(544\) 0 0
\(545\) −1.13300e7 −1.63396
\(546\) 0 0
\(547\) 3.90704e6 0.558316 0.279158 0.960245i \(-0.409945\pi\)
0.279158 + 0.960245i \(0.409945\pi\)
\(548\) 0 0
\(549\) −4.56525e6 −0.646448
\(550\) 0 0
\(551\) −3.23168e6 −0.453471
\(552\) 0 0
\(553\) 7.52148e6 1.04590
\(554\) 0 0
\(555\) 2.14337e6 0.295369
\(556\) 0 0
\(557\) −3.44118e6 −0.469969 −0.234985 0.971999i \(-0.575504\pi\)
−0.234985 + 0.971999i \(0.575504\pi\)
\(558\) 0 0
\(559\) 1.34345e7 1.81841
\(560\) 0 0
\(561\) −5528.17 −0.000741608 0
\(562\) 0 0
\(563\) −1.40711e7 −1.87093 −0.935464 0.353421i \(-0.885018\pi\)
−0.935464 + 0.353421i \(0.885018\pi\)
\(564\) 0 0
\(565\) 7.18893e6 0.947421
\(566\) 0 0
\(567\) 1.45022e6 0.189442
\(568\) 0 0
\(569\) −1.29191e7 −1.67283 −0.836413 0.548100i \(-0.815351\pi\)
−0.836413 + 0.548100i \(0.815351\pi\)
\(570\) 0 0
\(571\) 3.35324e6 0.430401 0.215201 0.976570i \(-0.430959\pi\)
0.215201 + 0.976570i \(0.430959\pi\)
\(572\) 0 0
\(573\) −8.21689e6 −1.04549
\(574\) 0 0
\(575\) −6.39424e6 −0.806527
\(576\) 0 0
\(577\) −9.54867e6 −1.19400 −0.596999 0.802242i \(-0.703640\pi\)
−0.596999 + 0.802242i \(0.703640\pi\)
\(578\) 0 0
\(579\) 1.44216e6 0.178779
\(580\) 0 0
\(581\) −1.68540e7 −2.07139
\(582\) 0 0
\(583\) −39889.6 −0.00486059
\(584\) 0 0
\(585\) −6.73143e6 −0.813238
\(586\) 0 0
\(587\) 74106.0 0.00887683 0.00443842 0.999990i \(-0.498587\pi\)
0.00443842 + 0.999990i \(0.498587\pi\)
\(588\) 0 0
\(589\) −55098.4 −0.00654411
\(590\) 0 0
\(591\) 428587. 0.0504743
\(592\) 0 0
\(593\) −2.81239e6 −0.328427 −0.164214 0.986425i \(-0.552509\pi\)
−0.164214 + 0.986425i \(0.552509\pi\)
\(594\) 0 0
\(595\) −1.59133e6 −0.184276
\(596\) 0 0
\(597\) −5.82336e6 −0.668710
\(598\) 0 0
\(599\) 8.13698e6 0.926608 0.463304 0.886199i \(-0.346664\pi\)
0.463304 + 0.886199i \(0.346664\pi\)
\(600\) 0 0
\(601\) −8.80255e6 −0.994082 −0.497041 0.867727i \(-0.665580\pi\)
−0.497041 + 0.867727i \(0.665580\pi\)
\(602\) 0 0
\(603\) −3.91353e6 −0.438304
\(604\) 0 0
\(605\) 1.29023e7 1.43311
\(606\) 0 0
\(607\) −6.04706e6 −0.666150 −0.333075 0.942900i \(-0.608086\pi\)
−0.333075 + 0.942900i \(0.608086\pi\)
\(608\) 0 0
\(609\) 1.78085e7 1.94574
\(610\) 0 0
\(611\) 2.44018e7 2.64435
\(612\) 0 0
\(613\) −4.60257e6 −0.494708 −0.247354 0.968925i \(-0.579561\pi\)
−0.247354 + 0.968925i \(0.579561\pi\)
\(614\) 0 0
\(615\) 9.98129e6 1.06414
\(616\) 0 0
\(617\) −1.17504e7 −1.24263 −0.621314 0.783562i \(-0.713401\pi\)
−0.621314 + 0.783562i \(0.713401\pi\)
\(618\) 0 0
\(619\) −2.99190e6 −0.313849 −0.156924 0.987611i \(-0.550158\pi\)
−0.156924 + 0.987611i \(0.550158\pi\)
\(620\) 0 0
\(621\) −1.41388e6 −0.147124
\(622\) 0 0
\(623\) −4.04517e6 −0.417558
\(624\) 0 0
\(625\) −9.19896e6 −0.941974
\(626\) 0 0
\(627\) 22213.9 0.00225660
\(628\) 0 0
\(629\) −266986. −0.0269068
\(630\) 0 0
\(631\) 5.95172e6 0.595072 0.297536 0.954711i \(-0.403835\pi\)
0.297536 + 0.954711i \(0.403835\pi\)
\(632\) 0 0
\(633\) 7.17371e6 0.711597
\(634\) 0 0
\(635\) −2.12361e7 −2.08997
\(636\) 0 0
\(637\) 3.32370e7 3.24544
\(638\) 0 0
\(639\) −5.95734e6 −0.577165
\(640\) 0 0
\(641\) −1.94545e6 −0.187015 −0.0935073 0.995619i \(-0.529808\pi\)
−0.0935073 + 0.995619i \(0.529808\pi\)
\(642\) 0 0
\(643\) 8.98422e6 0.856945 0.428472 0.903555i \(-0.359052\pi\)
0.428472 + 0.903555i \(0.359052\pi\)
\(644\) 0 0
\(645\) −9.34335e6 −0.884307
\(646\) 0 0
\(647\) −1.64265e7 −1.54271 −0.771356 0.636404i \(-0.780421\pi\)
−0.771356 + 0.636404i \(0.780421\pi\)
\(648\) 0 0
\(649\) −34398.6 −0.00320574
\(650\) 0 0
\(651\) 303626. 0.0280793
\(652\) 0 0
\(653\) −3.64800e6 −0.334789 −0.167395 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(654\) 0 0
\(655\) −1.15054e7 −1.04785
\(656\) 0 0
\(657\) 4.85039e6 0.438393
\(658\) 0 0
\(659\) 4.42986e6 0.397353 0.198677 0.980065i \(-0.436336\pi\)
0.198677 + 0.980065i \(0.436336\pi\)
\(660\) 0 0
\(661\) −1.30589e6 −0.116252 −0.0581262 0.998309i \(-0.518513\pi\)
−0.0581262 + 0.998309i \(0.518513\pi\)
\(662\) 0 0
\(663\) 838491. 0.0740823
\(664\) 0 0
\(665\) 6.39444e6 0.560723
\(666\) 0 0
\(667\) −1.73623e7 −1.51110
\(668\) 0 0
\(669\) 6.28582e6 0.542996
\(670\) 0 0
\(671\) 385349. 0.0330406
\(672\) 0 0
\(673\) 1.74209e7 1.48263 0.741316 0.671157i \(-0.234202\pi\)
0.741316 + 0.671157i \(0.234202\pi\)
\(674\) 0 0
\(675\) 2.40342e6 0.203035
\(676\) 0 0
\(677\) −6.47484e6 −0.542947 −0.271473 0.962446i \(-0.587511\pi\)
−0.271473 + 0.962446i \(0.587511\pi\)
\(678\) 0 0
\(679\) 1.21915e7 1.01480
\(680\) 0 0
\(681\) 7.28686e6 0.602105
\(682\) 0 0
\(683\) 1.44202e7 1.18282 0.591411 0.806371i \(-0.298571\pi\)
0.591411 + 0.806371i \(0.298571\pi\)
\(684\) 0 0
\(685\) −1.61382e7 −1.31410
\(686\) 0 0
\(687\) 2.20050e6 0.177881
\(688\) 0 0
\(689\) 6.05030e6 0.485544
\(690\) 0 0
\(691\) 1.80165e6 0.143541 0.0717703 0.997421i \(-0.477135\pi\)
0.0717703 + 0.997421i \(0.477135\pi\)
\(692\) 0 0
\(693\) −122412. −0.00968257
\(694\) 0 0
\(695\) −3.60492e7 −2.83096
\(696\) 0 0
\(697\) −1.24331e6 −0.0969384
\(698\) 0 0
\(699\) 2.37158e6 0.183588
\(700\) 0 0
\(701\) 1.09790e7 0.843857 0.421928 0.906629i \(-0.361353\pi\)
0.421928 + 0.906629i \(0.361353\pi\)
\(702\) 0 0
\(703\) 1.07283e6 0.0818735
\(704\) 0 0
\(705\) −1.69709e7 −1.28597
\(706\) 0 0
\(707\) −514492. −0.0387106
\(708\) 0 0
\(709\) −1.53321e7 −1.14548 −0.572738 0.819739i \(-0.694119\pi\)
−0.572738 + 0.819739i \(0.694119\pi\)
\(710\) 0 0
\(711\) 2.75629e6 0.204480
\(712\) 0 0
\(713\) −296018. −0.0218069
\(714\) 0 0
\(715\) 568194. 0.0415654
\(716\) 0 0
\(717\) −1.63524e6 −0.118791
\(718\) 0 0
\(719\) 1.63305e7 1.17808 0.589042 0.808103i \(-0.299505\pi\)
0.589042 + 0.808103i \(0.299505\pi\)
\(720\) 0 0
\(721\) −8.83312e6 −0.632814
\(722\) 0 0
\(723\) −9.04773e6 −0.643715
\(724\) 0 0
\(725\) 2.95138e7 2.08535
\(726\) 0 0
\(727\) 79286.1 0.00556367 0.00278183 0.999996i \(-0.499115\pi\)
0.00278183 + 0.999996i \(0.499115\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 0 0
\(731\) 1.16384e6 0.0805565
\(732\) 0 0
\(733\) 1.68148e7 1.15593 0.577965 0.816062i \(-0.303847\pi\)
0.577965 + 0.816062i \(0.303847\pi\)
\(734\) 0 0
\(735\) −2.31155e7 −1.57829
\(736\) 0 0
\(737\) 330338. 0.0224021
\(738\) 0 0
\(739\) 2.23677e7 1.50664 0.753322 0.657652i \(-0.228450\pi\)
0.753322 + 0.657652i \(0.228450\pi\)
\(740\) 0 0
\(741\) −3.36931e6 −0.225422
\(742\) 0 0
\(743\) −1.54060e7 −1.02380 −0.511902 0.859044i \(-0.671059\pi\)
−0.511902 + 0.859044i \(0.671059\pi\)
\(744\) 0 0
\(745\) −2.10441e7 −1.38912
\(746\) 0 0
\(747\) −6.17622e6 −0.404969
\(748\) 0 0
\(749\) −6.07528e6 −0.395696
\(750\) 0 0
\(751\) 1.22337e7 0.791512 0.395756 0.918356i \(-0.370483\pi\)
0.395756 + 0.918356i \(0.370483\pi\)
\(752\) 0 0
\(753\) −1.36694e6 −0.0878543
\(754\) 0 0
\(755\) −2.55372e7 −1.63045
\(756\) 0 0
\(757\) 1.12366e7 0.712683 0.356341 0.934356i \(-0.384024\pi\)
0.356341 + 0.934356i \(0.384024\pi\)
\(758\) 0 0
\(759\) 119345. 0.00751966
\(760\) 0 0
\(761\) 2.50972e7 1.57095 0.785477 0.618890i \(-0.212417\pi\)
0.785477 + 0.618890i \(0.212417\pi\)
\(762\) 0 0
\(763\) 3.12511e7 1.94336
\(764\) 0 0
\(765\) −583151. −0.0360269
\(766\) 0 0
\(767\) 5.21743e6 0.320235
\(768\) 0 0
\(769\) −2.70225e7 −1.64782 −0.823910 0.566720i \(-0.808212\pi\)
−0.823910 + 0.566720i \(0.808212\pi\)
\(770\) 0 0
\(771\) 1.32561e7 0.803119
\(772\) 0 0
\(773\) 5.42992e6 0.326847 0.163424 0.986556i \(-0.447746\pi\)
0.163424 + 0.986556i \(0.447746\pi\)
\(774\) 0 0
\(775\) 503193. 0.0300940
\(776\) 0 0
\(777\) −5.91196e6 −0.351300
\(778\) 0 0
\(779\) 4.99598e6 0.294969
\(780\) 0 0
\(781\) 502854. 0.0294995
\(782\) 0 0
\(783\) 6.52603e6 0.380404
\(784\) 0 0
\(785\) −3.49011e7 −2.02146
\(786\) 0 0
\(787\) −3.63648e6 −0.209288 −0.104644 0.994510i \(-0.533370\pi\)
−0.104644 + 0.994510i \(0.533370\pi\)
\(788\) 0 0
\(789\) −5.42257e6 −0.310108
\(790\) 0 0
\(791\) −1.98289e7 −1.12682
\(792\) 0 0
\(793\) −5.84482e7 −3.30056
\(794\) 0 0
\(795\) −4.20784e6 −0.236125
\(796\) 0 0
\(797\) −5.06851e6 −0.282641 −0.141320 0.989964i \(-0.545135\pi\)
−0.141320 + 0.989964i \(0.545135\pi\)
\(798\) 0 0
\(799\) 2.11395e6 0.117146
\(800\) 0 0
\(801\) −1.48237e6 −0.0816350
\(802\) 0 0
\(803\) −409417. −0.0224067
\(804\) 0 0
\(805\) 3.43543e7 1.86849
\(806\) 0 0
\(807\) 1.06027e7 0.573102
\(808\) 0 0
\(809\) −1.93485e7 −1.03938 −0.519691 0.854354i \(-0.673953\pi\)
−0.519691 + 0.854354i \(0.673953\pi\)
\(810\) 0 0
\(811\) −1.75853e7 −0.938854 −0.469427 0.882971i \(-0.655539\pi\)
−0.469427 + 0.882971i \(0.655539\pi\)
\(812\) 0 0
\(813\) −4.28546e6 −0.227390
\(814\) 0 0
\(815\) −2.73989e7 −1.44490
\(816\) 0 0
\(817\) −4.67666e6 −0.245121
\(818\) 0 0
\(819\) 1.85669e7 0.967232
\(820\) 0 0
\(821\) −1.24199e6 −0.0643074 −0.0321537 0.999483i \(-0.510237\pi\)
−0.0321537 + 0.999483i \(0.510237\pi\)
\(822\) 0 0
\(823\) 1.79887e6 0.0925761 0.0462881 0.998928i \(-0.485261\pi\)
0.0462881 + 0.998928i \(0.485261\pi\)
\(824\) 0 0
\(825\) −202871. −0.0103773
\(826\) 0 0
\(827\) −6.43748e6 −0.327304 −0.163652 0.986518i \(-0.552327\pi\)
−0.163652 + 0.986518i \(0.552327\pi\)
\(828\) 0 0
\(829\) 1.46989e7 0.742843 0.371422 0.928464i \(-0.378870\pi\)
0.371422 + 0.928464i \(0.378870\pi\)
\(830\) 0 0
\(831\) −1.76041e7 −0.884325
\(832\) 0 0
\(833\) 2.87936e6 0.143775
\(834\) 0 0
\(835\) −8.44350e6 −0.419089
\(836\) 0 0
\(837\) 111265. 0.00548966
\(838\) 0 0
\(839\) 1.92855e7 0.945859 0.472929 0.881100i \(-0.343197\pi\)
0.472929 + 0.881100i \(0.343197\pi\)
\(840\) 0 0
\(841\) 5.96277e7 2.90709
\(842\) 0 0
\(843\) −2.21409e7 −1.07307
\(844\) 0 0
\(845\) −5.64272e7 −2.71861
\(846\) 0 0
\(847\) −3.55878e7 −1.70448
\(848\) 0 0
\(849\) 8.59176e6 0.409084
\(850\) 0 0
\(851\) 5.76382e6 0.272826
\(852\) 0 0
\(853\) −3.26519e7 −1.53651 −0.768256 0.640143i \(-0.778875\pi\)
−0.768256 + 0.640143i \(0.778875\pi\)
\(854\) 0 0
\(855\) 2.34328e6 0.109625
\(856\) 0 0
\(857\) −2.78009e7 −1.29303 −0.646513 0.762903i \(-0.723773\pi\)
−0.646513 + 0.762903i \(0.723773\pi\)
\(858\) 0 0
\(859\) −2.12121e7 −0.980844 −0.490422 0.871485i \(-0.663157\pi\)
−0.490422 + 0.871485i \(0.663157\pi\)
\(860\) 0 0
\(861\) −2.75309e7 −1.26565
\(862\) 0 0
\(863\) −2.36175e7 −1.07946 −0.539730 0.841838i \(-0.681474\pi\)
−0.539730 + 0.841838i \(0.681474\pi\)
\(864\) 0 0
\(865\) 3.90539e7 1.77470
\(866\) 0 0
\(867\) −1.27061e7 −0.574068
\(868\) 0 0
\(869\) −232656. −0.0104512
\(870\) 0 0
\(871\) −5.01043e7 −2.23784
\(872\) 0 0
\(873\) 4.46762e6 0.198400
\(874\) 0 0
\(875\) −3.04450e6 −0.134430
\(876\) 0 0
\(877\) 4.13618e7 1.81594 0.907968 0.419040i \(-0.137633\pi\)
0.907968 + 0.419040i \(0.137633\pi\)
\(878\) 0 0
\(879\) 3.83286e6 0.167321
\(880\) 0 0
\(881\) 1.56620e7 0.679843 0.339921 0.940454i \(-0.389600\pi\)
0.339921 + 0.940454i \(0.389600\pi\)
\(882\) 0 0
\(883\) −3.53491e6 −0.152572 −0.0762862 0.997086i \(-0.524306\pi\)
−0.0762862 + 0.997086i \(0.524306\pi\)
\(884\) 0 0
\(885\) −3.62860e6 −0.155733
\(886\) 0 0
\(887\) 4.43493e7 1.89268 0.946341 0.323170i \(-0.104749\pi\)
0.946341 + 0.323170i \(0.104749\pi\)
\(888\) 0 0
\(889\) 5.85745e7 2.48573
\(890\) 0 0
\(891\) −44858.5 −0.00189300
\(892\) 0 0
\(893\) −8.49450e6 −0.356458
\(894\) 0 0
\(895\) −4.69657e7 −1.95985
\(896\) 0 0
\(897\) −1.81017e7 −0.751170
\(898\) 0 0
\(899\) 1.36632e6 0.0563838
\(900\) 0 0
\(901\) 524144. 0.0215099
\(902\) 0 0
\(903\) 2.57713e7 1.05176
\(904\) 0 0
\(905\) 1.15111e7 0.467190
\(906\) 0 0
\(907\) 9.76359e6 0.394086 0.197043 0.980395i \(-0.436866\pi\)
0.197043 + 0.980395i \(0.436866\pi\)
\(908\) 0 0
\(909\) −188538. −0.00756815
\(910\) 0 0
\(911\) −3.16139e7 −1.26207 −0.631033 0.775756i \(-0.717369\pi\)
−0.631033 + 0.775756i \(0.717369\pi\)
\(912\) 0 0
\(913\) 521330. 0.0206983
\(914\) 0 0
\(915\) 4.06493e7 1.60509
\(916\) 0 0
\(917\) 3.17349e7 1.24627
\(918\) 0 0
\(919\) −8.93593e6 −0.349020 −0.174510 0.984655i \(-0.555834\pi\)
−0.174510 + 0.984655i \(0.555834\pi\)
\(920\) 0 0
\(921\) 2.02637e7 0.787172
\(922\) 0 0
\(923\) −7.62708e7 −2.94682
\(924\) 0 0
\(925\) −9.79777e6 −0.376507
\(926\) 0 0
\(927\) −3.23694e6 −0.123719
\(928\) 0 0
\(929\) 3.99767e7 1.51973 0.759866 0.650079i \(-0.225264\pi\)
0.759866 + 0.650079i \(0.225264\pi\)
\(930\) 0 0
\(931\) −1.15701e7 −0.437485
\(932\) 0 0
\(933\) 2.67651e7 1.00662
\(934\) 0 0
\(935\) 49223.2 0.00184137
\(936\) 0 0
\(937\) −2.81200e7 −1.04633 −0.523163 0.852233i \(-0.675248\pi\)
−0.523163 + 0.852233i \(0.675248\pi\)
\(938\) 0 0
\(939\) 1.25056e7 0.462852
\(940\) 0 0
\(941\) −2.50473e6 −0.0922120 −0.0461060 0.998937i \(-0.514681\pi\)
−0.0461060 + 0.998937i \(0.514681\pi\)
\(942\) 0 0
\(943\) 2.68410e7 0.982923
\(944\) 0 0
\(945\) −1.29129e7 −0.470374
\(946\) 0 0
\(947\) 8.47836e6 0.307211 0.153606 0.988132i \(-0.450912\pi\)
0.153606 + 0.988132i \(0.450912\pi\)
\(948\) 0 0
\(949\) 6.20988e7 2.23830
\(950\) 0 0
\(951\) 9.82557e6 0.352295
\(952\) 0 0
\(953\) −3.34630e6 −0.119353 −0.0596765 0.998218i \(-0.519007\pi\)
−0.0596765 + 0.998218i \(0.519007\pi\)
\(954\) 0 0
\(955\) 7.31638e7 2.59590
\(956\) 0 0
\(957\) −550856. −0.0194428
\(958\) 0 0
\(959\) 4.45131e7 1.56294
\(960\) 0 0
\(961\) −2.86059e7 −0.999186
\(962\) 0 0
\(963\) −2.22632e6 −0.0773609
\(964\) 0 0
\(965\) −1.28411e7 −0.443897
\(966\) 0 0
\(967\) −4.23247e6 −0.145555 −0.0727776 0.997348i \(-0.523186\pi\)
−0.0727776 + 0.997348i \(0.523186\pi\)
\(968\) 0 0
\(969\) −291887. −0.00998631
\(970\) 0 0
\(971\) 4.58111e7 1.55927 0.779637 0.626231i \(-0.215403\pi\)
0.779637 + 0.626231i \(0.215403\pi\)
\(972\) 0 0
\(973\) 9.94327e7 3.36703
\(974\) 0 0
\(975\) 3.07706e7 1.03663
\(976\) 0 0
\(977\) 1.45408e7 0.487361 0.243681 0.969856i \(-0.421645\pi\)
0.243681 + 0.969856i \(0.421645\pi\)
\(978\) 0 0
\(979\) 125126. 0.00417244
\(980\) 0 0
\(981\) 1.14521e7 0.379938
\(982\) 0 0
\(983\) −2.36787e7 −0.781580 −0.390790 0.920480i \(-0.627798\pi\)
−0.390790 + 0.920480i \(0.627798\pi\)
\(984\) 0 0
\(985\) −3.81616e6 −0.125325
\(986\) 0 0
\(987\) 4.68098e7 1.52948
\(988\) 0 0
\(989\) −2.51255e7 −0.816815
\(990\) 0 0
\(991\) −4.16060e7 −1.34577 −0.672887 0.739745i \(-0.734946\pi\)
−0.672887 + 0.739745i \(0.734946\pi\)
\(992\) 0 0
\(993\) 2.40330e7 0.773453
\(994\) 0 0
\(995\) 5.18516e7 1.66037
\(996\) 0 0
\(997\) −2.76770e6 −0.0881823 −0.0440912 0.999028i \(-0.514039\pi\)
−0.0440912 + 0.999028i \(0.514039\pi\)
\(998\) 0 0
\(999\) −2.16647e6 −0.0686813
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 912.6.a.y.1.2 6
4.3 odd 2 456.6.a.f.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.6.a.f.1.2 6 4.3 odd 2
912.6.a.y.1.2 6 1.1 even 1 trivial