Properties

Label 546.6.a.e.1.1
Level $546$
Weight $6$
Character 546.1
Self dual yes
Analytic conductor $87.570$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(87.5695656179\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 546.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +93.0000 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +93.0000 q^{5} -36.0000 q^{6} -49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +372.000 q^{10} -302.000 q^{11} -144.000 q^{12} -169.000 q^{13} -196.000 q^{14} -837.000 q^{15} +256.000 q^{16} -488.000 q^{17} +324.000 q^{18} +2053.00 q^{19} +1488.00 q^{20} +441.000 q^{21} -1208.00 q^{22} +59.0000 q^{23} -576.000 q^{24} +5524.00 q^{25} -676.000 q^{26} -729.000 q^{27} -784.000 q^{28} +5871.00 q^{29} -3348.00 q^{30} +3861.00 q^{31} +1024.00 q^{32} +2718.00 q^{33} -1952.00 q^{34} -4557.00 q^{35} +1296.00 q^{36} +12388.0 q^{37} +8212.00 q^{38} +1521.00 q^{39} +5952.00 q^{40} +2602.00 q^{41} +1764.00 q^{42} -14221.0 q^{43} -4832.00 q^{44} +7533.00 q^{45} +236.000 q^{46} -21645.0 q^{47} -2304.00 q^{48} +2401.00 q^{49} +22096.0 q^{50} +4392.00 q^{51} -2704.00 q^{52} -7781.00 q^{53} -2916.00 q^{54} -28086.0 q^{55} -3136.00 q^{56} -18477.0 q^{57} +23484.0 q^{58} +19072.0 q^{59} -13392.0 q^{60} +13954.0 q^{61} +15444.0 q^{62} -3969.00 q^{63} +4096.00 q^{64} -15717.0 q^{65} +10872.0 q^{66} +2694.00 q^{67} -7808.00 q^{68} -531.000 q^{69} -18228.0 q^{70} +82032.0 q^{71} +5184.00 q^{72} +6503.00 q^{73} +49552.0 q^{74} -49716.0 q^{75} +32848.0 q^{76} +14798.0 q^{77} +6084.00 q^{78} +28535.0 q^{79} +23808.0 q^{80} +6561.00 q^{81} +10408.0 q^{82} +15019.0 q^{83} +7056.00 q^{84} -45384.0 q^{85} -56884.0 q^{86} -52839.0 q^{87} -19328.0 q^{88} +41979.0 q^{89} +30132.0 q^{90} +8281.00 q^{91} +944.000 q^{92} -34749.0 q^{93} -86580.0 q^{94} +190929. q^{95} -9216.00 q^{96} -57405.0 q^{97} +9604.00 q^{98} -24462.0 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) −9.00000 −0.577350
\(4\) 16.0000 0.500000
\(5\) 93.0000 1.66363 0.831817 0.555050i \(-0.187301\pi\)
0.831817 + 0.555050i \(0.187301\pi\)
\(6\) −36.0000 −0.408248
\(7\) −49.0000 −0.377964
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 372.000 1.17637
\(11\) −302.000 −0.752532 −0.376266 0.926512i \(-0.622792\pi\)
−0.376266 + 0.926512i \(0.622792\pi\)
\(12\) −144.000 −0.288675
\(13\) −169.000 −0.277350
\(14\) −196.000 −0.267261
\(15\) −837.000 −0.960500
\(16\) 256.000 0.250000
\(17\) −488.000 −0.409541 −0.204771 0.978810i \(-0.565645\pi\)
−0.204771 + 0.978810i \(0.565645\pi\)
\(18\) 324.000 0.235702
\(19\) 2053.00 1.30468 0.652341 0.757925i \(-0.273787\pi\)
0.652341 + 0.757925i \(0.273787\pi\)
\(20\) 1488.00 0.831817
\(21\) 441.000 0.218218
\(22\) −1208.00 −0.532121
\(23\) 59.0000 0.0232559 0.0116279 0.999932i \(-0.496299\pi\)
0.0116279 + 0.999932i \(0.496299\pi\)
\(24\) −576.000 −0.204124
\(25\) 5524.00 1.76768
\(26\) −676.000 −0.196116
\(27\) −729.000 −0.192450
\(28\) −784.000 −0.188982
\(29\) 5871.00 1.29633 0.648167 0.761498i \(-0.275536\pi\)
0.648167 + 0.761498i \(0.275536\pi\)
\(30\) −3348.00 −0.679176
\(31\) 3861.00 0.721598 0.360799 0.932644i \(-0.382504\pi\)
0.360799 + 0.932644i \(0.382504\pi\)
\(32\) 1024.00 0.176777
\(33\) 2718.00 0.434475
\(34\) −1952.00 −0.289589
\(35\) −4557.00 −0.628795
\(36\) 1296.00 0.166667
\(37\) 12388.0 1.48764 0.743818 0.668382i \(-0.233013\pi\)
0.743818 + 0.668382i \(0.233013\pi\)
\(38\) 8212.00 0.922550
\(39\) 1521.00 0.160128
\(40\) 5952.00 0.588184
\(41\) 2602.00 0.241740 0.120870 0.992668i \(-0.461432\pi\)
0.120870 + 0.992668i \(0.461432\pi\)
\(42\) 1764.00 0.154303
\(43\) −14221.0 −1.17289 −0.586447 0.809987i \(-0.699474\pi\)
−0.586447 + 0.809987i \(0.699474\pi\)
\(44\) −4832.00 −0.376266
\(45\) 7533.00 0.554545
\(46\) 236.000 0.0164444
\(47\) −21645.0 −1.42927 −0.714633 0.699500i \(-0.753406\pi\)
−0.714633 + 0.699500i \(0.753406\pi\)
\(48\) −2304.00 −0.144338
\(49\) 2401.00 0.142857
\(50\) 22096.0 1.24994
\(51\) 4392.00 0.236449
\(52\) −2704.00 −0.138675
\(53\) −7781.00 −0.380492 −0.190246 0.981736i \(-0.560929\pi\)
−0.190246 + 0.981736i \(0.560929\pi\)
\(54\) −2916.00 −0.136083
\(55\) −28086.0 −1.25194
\(56\) −3136.00 −0.133631
\(57\) −18477.0 −0.753259
\(58\) 23484.0 0.916647
\(59\) 19072.0 0.713290 0.356645 0.934240i \(-0.383921\pi\)
0.356645 + 0.934240i \(0.383921\pi\)
\(60\) −13392.0 −0.480250
\(61\) 13954.0 0.480147 0.240073 0.970755i \(-0.422828\pi\)
0.240073 + 0.970755i \(0.422828\pi\)
\(62\) 15444.0 0.510247
\(63\) −3969.00 −0.125988
\(64\) 4096.00 0.125000
\(65\) −15717.0 −0.461409
\(66\) 10872.0 0.307220
\(67\) 2694.00 0.0733180 0.0366590 0.999328i \(-0.488328\pi\)
0.0366590 + 0.999328i \(0.488328\pi\)
\(68\) −7808.00 −0.204771
\(69\) −531.000 −0.0134268
\(70\) −18228.0 −0.444625
\(71\) 82032.0 1.93125 0.965623 0.259948i \(-0.0837054\pi\)
0.965623 + 0.259948i \(0.0837054\pi\)
\(72\) 5184.00 0.117851
\(73\) 6503.00 0.142826 0.0714129 0.997447i \(-0.477249\pi\)
0.0714129 + 0.997447i \(0.477249\pi\)
\(74\) 49552.0 1.05192
\(75\) −49716.0 −1.02057
\(76\) 32848.0 0.652341
\(77\) 14798.0 0.284431
\(78\) 6084.00 0.113228
\(79\) 28535.0 0.514411 0.257205 0.966357i \(-0.417198\pi\)
0.257205 + 0.966357i \(0.417198\pi\)
\(80\) 23808.0 0.415909
\(81\) 6561.00 0.111111
\(82\) 10408.0 0.170936
\(83\) 15019.0 0.239302 0.119651 0.992816i \(-0.461822\pi\)
0.119651 + 0.992816i \(0.461822\pi\)
\(84\) 7056.00 0.109109
\(85\) −45384.0 −0.681327
\(86\) −56884.0 −0.829362
\(87\) −52839.0 −0.748439
\(88\) −19328.0 −0.266060
\(89\) 41979.0 0.561768 0.280884 0.959742i \(-0.409372\pi\)
0.280884 + 0.959742i \(0.409372\pi\)
\(90\) 30132.0 0.392122
\(91\) 8281.00 0.104828
\(92\) 944.000 0.0116279
\(93\) −34749.0 −0.416615
\(94\) −86580.0 −1.01064
\(95\) 190929. 2.17052
\(96\) −9216.00 −0.102062
\(97\) −57405.0 −0.619470 −0.309735 0.950823i \(-0.600240\pi\)
−0.309735 + 0.950823i \(0.600240\pi\)
\(98\) 9604.00 0.101015
\(99\) −24462.0 −0.250844
\(100\) 88384.0 0.883840
\(101\) 49902.0 0.486760 0.243380 0.969931i \(-0.421744\pi\)
0.243380 + 0.969931i \(0.421744\pi\)
\(102\) 17568.0 0.167194
\(103\) −44608.0 −0.414305 −0.207152 0.978309i \(-0.566420\pi\)
−0.207152 + 0.978309i \(0.566420\pi\)
\(104\) −10816.0 −0.0980581
\(105\) 41013.0 0.363035
\(106\) −31124.0 −0.269049
\(107\) −92556.0 −0.781529 −0.390765 0.920491i \(-0.627789\pi\)
−0.390765 + 0.920491i \(0.627789\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 71606.0 0.577276 0.288638 0.957438i \(-0.406798\pi\)
0.288638 + 0.957438i \(0.406798\pi\)
\(110\) −112344. −0.885255
\(111\) −111492. −0.858887
\(112\) −12544.0 −0.0944911
\(113\) 99577.0 0.733606 0.366803 0.930299i \(-0.380452\pi\)
0.366803 + 0.930299i \(0.380452\pi\)
\(114\) −73908.0 −0.532635
\(115\) 5487.00 0.0386893
\(116\) 93936.0 0.648167
\(117\) −13689.0 −0.0924500
\(118\) 76288.0 0.504372
\(119\) 23912.0 0.154792
\(120\) −53568.0 −0.339588
\(121\) −69847.0 −0.433695
\(122\) 55816.0 0.339515
\(123\) −23418.0 −0.139568
\(124\) 61776.0 0.360799
\(125\) 223107. 1.27714
\(126\) −15876.0 −0.0890871
\(127\) 81172.0 0.446578 0.223289 0.974752i \(-0.428321\pi\)
0.223289 + 0.974752i \(0.428321\pi\)
\(128\) 16384.0 0.0883883
\(129\) 127989. 0.677171
\(130\) −62868.0 −0.326266
\(131\) 145320. 0.739856 0.369928 0.929060i \(-0.379382\pi\)
0.369928 + 0.929060i \(0.379382\pi\)
\(132\) 43488.0 0.217237
\(133\) −100597. −0.493124
\(134\) 10776.0 0.0518437
\(135\) −67797.0 −0.320167
\(136\) −31232.0 −0.144795
\(137\) 405024. 1.84365 0.921827 0.387602i \(-0.126696\pi\)
0.921827 + 0.387602i \(0.126696\pi\)
\(138\) −2124.00 −0.00949417
\(139\) −22634.0 −0.0993629 −0.0496815 0.998765i \(-0.515821\pi\)
−0.0496815 + 0.998765i \(0.515821\pi\)
\(140\) −72912.0 −0.314397
\(141\) 194805. 0.825187
\(142\) 328128. 1.36560
\(143\) 51038.0 0.208715
\(144\) 20736.0 0.0833333
\(145\) 546003. 2.15663
\(146\) 26012.0 0.100993
\(147\) −21609.0 −0.0824786
\(148\) 198208. 0.743818
\(149\) 121558. 0.448557 0.224279 0.974525i \(-0.427997\pi\)
0.224279 + 0.974525i \(0.427997\pi\)
\(150\) −198864. −0.721652
\(151\) 386992. 1.38121 0.690605 0.723232i \(-0.257344\pi\)
0.690605 + 0.723232i \(0.257344\pi\)
\(152\) 131392. 0.461275
\(153\) −39528.0 −0.136514
\(154\) 59192.0 0.201123
\(155\) 359073. 1.20048
\(156\) 24336.0 0.0800641
\(157\) −11008.0 −0.0356418 −0.0178209 0.999841i \(-0.505673\pi\)
−0.0178209 + 0.999841i \(0.505673\pi\)
\(158\) 114140. 0.363743
\(159\) 70029.0 0.219677
\(160\) 95232.0 0.294092
\(161\) −2891.00 −0.00878989
\(162\) 26244.0 0.0785674
\(163\) −395468. −1.16585 −0.582925 0.812526i \(-0.698092\pi\)
−0.582925 + 0.812526i \(0.698092\pi\)
\(164\) 41632.0 0.120870
\(165\) 252774. 0.722807
\(166\) 60076.0 0.169212
\(167\) −177287. −0.491910 −0.245955 0.969281i \(-0.579102\pi\)
−0.245955 + 0.969281i \(0.579102\pi\)
\(168\) 28224.0 0.0771517
\(169\) 28561.0 0.0769231
\(170\) −181536. −0.481771
\(171\) 166293. 0.434894
\(172\) −227536. −0.586447
\(173\) 466064. 1.18394 0.591971 0.805959i \(-0.298350\pi\)
0.591971 + 0.805959i \(0.298350\pi\)
\(174\) −211356. −0.529226
\(175\) −270676. −0.668120
\(176\) −77312.0 −0.188133
\(177\) −171648. −0.411818
\(178\) 167916. 0.397230
\(179\) −708985. −1.65388 −0.826941 0.562289i \(-0.809921\pi\)
−0.826941 + 0.562289i \(0.809921\pi\)
\(180\) 120528. 0.277272
\(181\) 321862. 0.730253 0.365126 0.930958i \(-0.381026\pi\)
0.365126 + 0.930958i \(0.381026\pi\)
\(182\) 33124.0 0.0741249
\(183\) −125586. −0.277213
\(184\) 3776.00 0.00822219
\(185\) 1.15208e6 2.47488
\(186\) −138996. −0.294591
\(187\) 147376. 0.308193
\(188\) −346320. −0.714633
\(189\) 35721.0 0.0727393
\(190\) 763716. 1.53479
\(191\) −386880. −0.767349 −0.383674 0.923468i \(-0.625342\pi\)
−0.383674 + 0.923468i \(0.625342\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −264854. −0.511815 −0.255908 0.966701i \(-0.582374\pi\)
−0.255908 + 0.966701i \(0.582374\pi\)
\(194\) −229620. −0.438032
\(195\) 141453. 0.266395
\(196\) 38416.0 0.0714286
\(197\) −282062. −0.517820 −0.258910 0.965901i \(-0.583363\pi\)
−0.258910 + 0.965901i \(0.583363\pi\)
\(198\) −97848.0 −0.177374
\(199\) 872688. 1.56216 0.781081 0.624429i \(-0.214668\pi\)
0.781081 + 0.624429i \(0.214668\pi\)
\(200\) 353536. 0.624969
\(201\) −24246.0 −0.0423302
\(202\) 199608. 0.344191
\(203\) −287679. −0.489968
\(204\) 70272.0 0.118224
\(205\) 241986. 0.402166
\(206\) −178432. −0.292958
\(207\) 4779.00 0.00775195
\(208\) −43264.0 −0.0693375
\(209\) −620006. −0.981816
\(210\) 164052. 0.256704
\(211\) 117895. 0.182301 0.0911505 0.995837i \(-0.470946\pi\)
0.0911505 + 0.995837i \(0.470946\pi\)
\(212\) −124496. −0.190246
\(213\) −738288. −1.11500
\(214\) −370224. −0.552625
\(215\) −1.32255e6 −1.95127
\(216\) −46656.0 −0.0680414
\(217\) −189189. −0.272739
\(218\) 286424. 0.408195
\(219\) −58527.0 −0.0824605
\(220\) −449376. −0.625969
\(221\) 82472.0 0.113586
\(222\) −445968. −0.607325
\(223\) −752569. −1.01341 −0.506704 0.862120i \(-0.669136\pi\)
−0.506704 + 0.862120i \(0.669136\pi\)
\(224\) −50176.0 −0.0668153
\(225\) 447444. 0.589227
\(226\) 398308. 0.518738
\(227\) 484812. 0.624466 0.312233 0.950006i \(-0.398923\pi\)
0.312233 + 0.950006i \(0.398923\pi\)
\(228\) −295632. −0.376629
\(229\) −397746. −0.501207 −0.250603 0.968090i \(-0.580629\pi\)
−0.250603 + 0.968090i \(0.580629\pi\)
\(230\) 21948.0 0.0273574
\(231\) −133182. −0.164216
\(232\) 375744. 0.458323
\(233\) −272541. −0.328883 −0.164442 0.986387i \(-0.552582\pi\)
−0.164442 + 0.986387i \(0.552582\pi\)
\(234\) −54756.0 −0.0653720
\(235\) −2.01299e6 −2.37778
\(236\) 305152. 0.356645
\(237\) −256815. −0.296995
\(238\) 95648.0 0.109454
\(239\) −818896. −0.927329 −0.463665 0.886011i \(-0.653466\pi\)
−0.463665 + 0.886011i \(0.653466\pi\)
\(240\) −214272. −0.240125
\(241\) 1.34780e6 1.49479 0.747397 0.664378i \(-0.231303\pi\)
0.747397 + 0.664378i \(0.231303\pi\)
\(242\) −279388. −0.306669
\(243\) −59049.0 −0.0641500
\(244\) 223264. 0.240073
\(245\) 223293. 0.237662
\(246\) −93672.0 −0.0986897
\(247\) −346957. −0.361854
\(248\) 247104. 0.255124
\(249\) −135171. −0.138161
\(250\) 892428. 0.903074
\(251\) 423426. 0.424222 0.212111 0.977246i \(-0.431966\pi\)
0.212111 + 0.977246i \(0.431966\pi\)
\(252\) −63504.0 −0.0629941
\(253\) −17818.0 −0.0175008
\(254\) 324688. 0.315778
\(255\) 408456. 0.393364
\(256\) 65536.0 0.0625000
\(257\) −2.11090e6 −1.99358 −0.996792 0.0800385i \(-0.974496\pi\)
−0.996792 + 0.0800385i \(0.974496\pi\)
\(258\) 511956. 0.478832
\(259\) −607012. −0.562274
\(260\) −251472. −0.230705
\(261\) 475551. 0.432112
\(262\) 581280. 0.523157
\(263\) −675943. −0.602588 −0.301294 0.953531i \(-0.597419\pi\)
−0.301294 + 0.953531i \(0.597419\pi\)
\(264\) 173952. 0.153610
\(265\) −723633. −0.633000
\(266\) −402388. −0.348691
\(267\) −377811. −0.324337
\(268\) 43104.0 0.0366590
\(269\) 897716. 0.756412 0.378206 0.925722i \(-0.376541\pi\)
0.378206 + 0.925722i \(0.376541\pi\)
\(270\) −271188. −0.226392
\(271\) −2.16653e6 −1.79201 −0.896006 0.444041i \(-0.853544\pi\)
−0.896006 + 0.444041i \(0.853544\pi\)
\(272\) −124928. −0.102385
\(273\) −74529.0 −0.0605228
\(274\) 1.62010e6 1.30366
\(275\) −1.66825e6 −1.33024
\(276\) −8496.00 −0.00671339
\(277\) 1.30656e6 1.02313 0.511564 0.859245i \(-0.329066\pi\)
0.511564 + 0.859245i \(0.329066\pi\)
\(278\) −90536.0 −0.0702602
\(279\) 312741. 0.240533
\(280\) −291648. −0.222313
\(281\) 1.64837e6 1.24535 0.622673 0.782482i \(-0.286047\pi\)
0.622673 + 0.782482i \(0.286047\pi\)
\(282\) 779220. 0.583495
\(283\) 834116. 0.619099 0.309550 0.950883i \(-0.399822\pi\)
0.309550 + 0.950883i \(0.399822\pi\)
\(284\) 1.31251e6 0.965623
\(285\) −1.71836e6 −1.25315
\(286\) 204152. 0.147584
\(287\) −127498. −0.0913689
\(288\) 82944.0 0.0589256
\(289\) −1.18171e6 −0.832276
\(290\) 2.18401e6 1.52497
\(291\) 516645. 0.357651
\(292\) 104048. 0.0714129
\(293\) 241437. 0.164299 0.0821495 0.996620i \(-0.473822\pi\)
0.0821495 + 0.996620i \(0.473822\pi\)
\(294\) −86436.0 −0.0583212
\(295\) 1.77370e6 1.18665
\(296\) 792832. 0.525959
\(297\) 220158. 0.144825
\(298\) 486232. 0.317178
\(299\) −9971.00 −0.00645002
\(300\) −795456. −0.510285
\(301\) 696829. 0.443313
\(302\) 1.54797e6 0.976663
\(303\) −449118. −0.281031
\(304\) 525568. 0.326171
\(305\) 1.29772e6 0.798789
\(306\) −158112. −0.0965298
\(307\) 1.67540e6 1.01455 0.507274 0.861785i \(-0.330653\pi\)
0.507274 + 0.861785i \(0.330653\pi\)
\(308\) 236768. 0.142215
\(309\) 401472. 0.239199
\(310\) 1.43629e6 0.848865
\(311\) 1.63906e6 0.960934 0.480467 0.877013i \(-0.340467\pi\)
0.480467 + 0.877013i \(0.340467\pi\)
\(312\) 97344.0 0.0566139
\(313\) −1.96954e6 −1.13633 −0.568165 0.822915i \(-0.692346\pi\)
−0.568165 + 0.822915i \(0.692346\pi\)
\(314\) −44032.0 −0.0252025
\(315\) −369117. −0.209598
\(316\) 456560. 0.257205
\(317\) −1.22674e6 −0.685653 −0.342826 0.939399i \(-0.611384\pi\)
−0.342826 + 0.939399i \(0.611384\pi\)
\(318\) 280116. 0.155335
\(319\) −1.77304e6 −0.975534
\(320\) 380928. 0.207954
\(321\) 833004. 0.451216
\(322\) −11564.0 −0.00621539
\(323\) −1.00186e6 −0.534321
\(324\) 104976. 0.0555556
\(325\) −933556. −0.490266
\(326\) −1.58187e6 −0.824380
\(327\) −644454. −0.333290
\(328\) 166528. 0.0854678
\(329\) 1.06060e6 0.540212
\(330\) 1.01110e6 0.511102
\(331\) −2.41427e6 −1.21120 −0.605600 0.795769i \(-0.707067\pi\)
−0.605600 + 0.795769i \(0.707067\pi\)
\(332\) 240304. 0.119651
\(333\) 1.00343e6 0.495879
\(334\) −709148. −0.347833
\(335\) 250542. 0.121974
\(336\) 112896. 0.0545545
\(337\) 617817. 0.296336 0.148168 0.988962i \(-0.452662\pi\)
0.148168 + 0.988962i \(0.452662\pi\)
\(338\) 114244. 0.0543928
\(339\) −896193. −0.423548
\(340\) −726144. −0.340663
\(341\) −1.16602e6 −0.543026
\(342\) 665172. 0.307517
\(343\) −117649. −0.0539949
\(344\) −910144. −0.414681
\(345\) −49383.0 −0.0223373
\(346\) 1.86426e6 0.837173
\(347\) −1.87077e6 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(348\) −845424. −0.374220
\(349\) −3.75833e6 −1.65170 −0.825850 0.563890i \(-0.809304\pi\)
−0.825850 + 0.563890i \(0.809304\pi\)
\(350\) −1.08270e6 −0.472432
\(351\) 123201. 0.0533761
\(352\) −309248. −0.133030
\(353\) 140774. 0.0601292 0.0300646 0.999548i \(-0.490429\pi\)
0.0300646 + 0.999548i \(0.490429\pi\)
\(354\) −686592. −0.291199
\(355\) 7.62898e6 3.21289
\(356\) 671664. 0.280884
\(357\) −215208. −0.0893692
\(358\) −2.83594e6 −1.16947
\(359\) −1.78318e6 −0.730227 −0.365114 0.930963i \(-0.618970\pi\)
−0.365114 + 0.930963i \(0.618970\pi\)
\(360\) 482112. 0.196061
\(361\) 1.73871e6 0.702197
\(362\) 1.28745e6 0.516367
\(363\) 628623. 0.250394
\(364\) 132496. 0.0524142
\(365\) 604779. 0.237610
\(366\) −502344. −0.196019
\(367\) −3.07850e6 −1.19309 −0.596546 0.802579i \(-0.703461\pi\)
−0.596546 + 0.802579i \(0.703461\pi\)
\(368\) 15104.0 0.00581397
\(369\) 210762. 0.0805798
\(370\) 4.60834e6 1.75001
\(371\) 381269. 0.143813
\(372\) −555984. −0.208308
\(373\) −3.45143e6 −1.28448 −0.642240 0.766503i \(-0.721995\pi\)
−0.642240 + 0.766503i \(0.721995\pi\)
\(374\) 589504. 0.217925
\(375\) −2.00796e6 −0.737357
\(376\) −1.38528e6 −0.505322
\(377\) −992199. −0.359539
\(378\) 142884. 0.0514344
\(379\) −2.49923e6 −0.893732 −0.446866 0.894601i \(-0.647460\pi\)
−0.446866 + 0.894601i \(0.647460\pi\)
\(380\) 3.05486e6 1.08526
\(381\) −730548. −0.257832
\(382\) −1.54752e6 −0.542598
\(383\) 3.94648e6 1.37472 0.687359 0.726318i \(-0.258770\pi\)
0.687359 + 0.726318i \(0.258770\pi\)
\(384\) −147456. −0.0510310
\(385\) 1.37621e6 0.473188
\(386\) −1.05942e6 −0.361908
\(387\) −1.15190e6 −0.390965
\(388\) −918480. −0.309735
\(389\) −4.05665e6 −1.35923 −0.679616 0.733568i \(-0.737854\pi\)
−0.679616 + 0.733568i \(0.737854\pi\)
\(390\) 565812. 0.188370
\(391\) −28792.0 −0.00952423
\(392\) 153664. 0.0505076
\(393\) −1.30788e6 −0.427156
\(394\) −1.12825e6 −0.366154
\(395\) 2.65376e6 0.855792
\(396\) −391392. −0.125422
\(397\) 3.34947e6 1.06660 0.533298 0.845927i \(-0.320952\pi\)
0.533298 + 0.845927i \(0.320952\pi\)
\(398\) 3.49075e6 1.10462
\(399\) 905373. 0.284705
\(400\) 1.41414e6 0.441920
\(401\) 6.00207e6 1.86397 0.931987 0.362491i \(-0.118074\pi\)
0.931987 + 0.362491i \(0.118074\pi\)
\(402\) −96984.0 −0.0299319
\(403\) −652509. −0.200135
\(404\) 798432. 0.243380
\(405\) 610173. 0.184848
\(406\) −1.15072e6 −0.346460
\(407\) −3.74118e6 −1.11949
\(408\) 281088. 0.0835972
\(409\) 2.16245e6 0.639201 0.319600 0.947552i \(-0.396451\pi\)
0.319600 + 0.947552i \(0.396451\pi\)
\(410\) 967944. 0.284374
\(411\) −3.64522e6 −1.06443
\(412\) −713728. −0.207152
\(413\) −934528. −0.269598
\(414\) 19116.0 0.00548146
\(415\) 1.39677e6 0.398111
\(416\) −173056. −0.0490290
\(417\) 203706. 0.0573672
\(418\) −2.48002e6 −0.694249
\(419\) −4.99448e6 −1.38981 −0.694905 0.719102i \(-0.744554\pi\)
−0.694905 + 0.719102i \(0.744554\pi\)
\(420\) 656208. 0.181517
\(421\) 46040.0 0.0126599 0.00632995 0.999980i \(-0.497985\pi\)
0.00632995 + 0.999980i \(0.497985\pi\)
\(422\) 471580. 0.128906
\(423\) −1.75324e6 −0.476422
\(424\) −497984. −0.134524
\(425\) −2.69571e6 −0.723938
\(426\) −2.95315e6 −0.788428
\(427\) −683746. −0.181478
\(428\) −1.48090e6 −0.390765
\(429\) −459342. −0.120502
\(430\) −5.29021e6 −1.37975
\(431\) −6.96428e6 −1.80586 −0.902928 0.429792i \(-0.858587\pi\)
−0.902928 + 0.429792i \(0.858587\pi\)
\(432\) −186624. −0.0481125
\(433\) 5.61426e6 1.43904 0.719520 0.694471i \(-0.244362\pi\)
0.719520 + 0.694471i \(0.244362\pi\)
\(434\) −756756. −0.192855
\(435\) −4.91403e6 −1.24513
\(436\) 1.14570e6 0.288638
\(437\) 121127. 0.0303415
\(438\) −234108. −0.0583084
\(439\) 1.88335e6 0.466413 0.233207 0.972427i \(-0.425078\pi\)
0.233207 + 0.972427i \(0.425078\pi\)
\(440\) −1.79750e6 −0.442627
\(441\) 194481. 0.0476190
\(442\) 329888. 0.0803176
\(443\) −6.97660e6 −1.68902 −0.844509 0.535541i \(-0.820108\pi\)
−0.844509 + 0.535541i \(0.820108\pi\)
\(444\) −1.78387e6 −0.429444
\(445\) 3.90405e6 0.934577
\(446\) −3.01028e6 −0.716587
\(447\) −1.09402e6 −0.258975
\(448\) −200704. −0.0472456
\(449\) 1.42088e6 0.332614 0.166307 0.986074i \(-0.446816\pi\)
0.166307 + 0.986074i \(0.446816\pi\)
\(450\) 1.78978e6 0.416646
\(451\) −785804. −0.181917
\(452\) 1.59323e6 0.366803
\(453\) −3.48293e6 −0.797442
\(454\) 1.93925e6 0.441564
\(455\) 770133. 0.174396
\(456\) −1.18253e6 −0.266317
\(457\) 180272. 0.0403773 0.0201887 0.999796i \(-0.493573\pi\)
0.0201887 + 0.999796i \(0.493573\pi\)
\(458\) −1.59098e6 −0.354407
\(459\) 355752. 0.0788162
\(460\) 87792.0 0.0193446
\(461\) −3.59082e6 −0.786940 −0.393470 0.919337i \(-0.628725\pi\)
−0.393470 + 0.919337i \(0.628725\pi\)
\(462\) −532728. −0.116118
\(463\) 5.31597e6 1.15247 0.576235 0.817284i \(-0.304521\pi\)
0.576235 + 0.817284i \(0.304521\pi\)
\(464\) 1.50298e6 0.324084
\(465\) −3.23166e6 −0.693095
\(466\) −1.09016e6 −0.232556
\(467\) −2.77316e6 −0.588413 −0.294207 0.955742i \(-0.595055\pi\)
−0.294207 + 0.955742i \(0.595055\pi\)
\(468\) −219024. −0.0462250
\(469\) −132006. −0.0277116
\(470\) −8.05194e6 −1.68134
\(471\) 99072.0 0.0205778
\(472\) 1.22061e6 0.252186
\(473\) 4.29474e6 0.882641
\(474\) −1.02726e6 −0.210007
\(475\) 1.13408e7 2.30626
\(476\) 382592. 0.0773960
\(477\) −630261. −0.126831
\(478\) −3.27558e6 −0.655721
\(479\) 3.72434e6 0.741671 0.370835 0.928699i \(-0.379071\pi\)
0.370835 + 0.928699i \(0.379071\pi\)
\(480\) −857088. −0.169794
\(481\) −2.09357e6 −0.412596
\(482\) 5.39118e6 1.05698
\(483\) 26019.0 0.00507484
\(484\) −1.11755e6 −0.216847
\(485\) −5.33866e6 −1.03057
\(486\) −236196. −0.0453609
\(487\) 9.57663e6 1.82974 0.914872 0.403743i \(-0.132291\pi\)
0.914872 + 0.403743i \(0.132291\pi\)
\(488\) 893056. 0.169758
\(489\) 3.55921e6 0.673103
\(490\) 893172. 0.168052
\(491\) −8.71582e6 −1.63157 −0.815783 0.578358i \(-0.803694\pi\)
−0.815783 + 0.578358i \(0.803694\pi\)
\(492\) −374688. −0.0697842
\(493\) −2.86505e6 −0.530902
\(494\) −1.38783e6 −0.255869
\(495\) −2.27497e6 −0.417313
\(496\) 988416. 0.180400
\(497\) −4.01957e6 −0.729942
\(498\) −540684. −0.0976945
\(499\) −808088. −0.145280 −0.0726402 0.997358i \(-0.523142\pi\)
−0.0726402 + 0.997358i \(0.523142\pi\)
\(500\) 3.56971e6 0.638569
\(501\) 1.59558e6 0.284004
\(502\) 1.69370e6 0.299970
\(503\) −9.61039e6 −1.69364 −0.846820 0.531880i \(-0.821486\pi\)
−0.846820 + 0.531880i \(0.821486\pi\)
\(504\) −254016. −0.0445435
\(505\) 4.64089e6 0.809790
\(506\) −71272.0 −0.0123749
\(507\) −257049. −0.0444116
\(508\) 1.29875e6 0.223289
\(509\) 4.29919e6 0.735516 0.367758 0.929922i \(-0.380125\pi\)
0.367758 + 0.929922i \(0.380125\pi\)
\(510\) 1.63382e6 0.278150
\(511\) −318647. −0.0539831
\(512\) 262144. 0.0441942
\(513\) −1.49664e6 −0.251086
\(514\) −8.44359e6 −1.40968
\(515\) −4.14854e6 −0.689251
\(516\) 2.04782e6 0.338586
\(517\) 6.53679e6 1.07557
\(518\) −2.42805e6 −0.397588
\(519\) −4.19458e6 −0.683549
\(520\) −1.00589e6 −0.163133
\(521\) −1.03603e6 −0.167216 −0.0836079 0.996499i \(-0.526644\pi\)
−0.0836079 + 0.996499i \(0.526644\pi\)
\(522\) 1.90220e6 0.305549
\(523\) −732526. −0.117103 −0.0585516 0.998284i \(-0.518648\pi\)
−0.0585516 + 0.998284i \(0.518648\pi\)
\(524\) 2.32512e6 0.369928
\(525\) 2.43608e6 0.385739
\(526\) −2.70377e6 −0.426094
\(527\) −1.88417e6 −0.295524
\(528\) 695808. 0.108619
\(529\) −6.43286e6 −0.999459
\(530\) −2.89453e6 −0.447599
\(531\) 1.54483e6 0.237763
\(532\) −1.60955e6 −0.246562
\(533\) −439738. −0.0670465
\(534\) −1.51124e6 −0.229341
\(535\) −8.60771e6 −1.30018
\(536\) 172416. 0.0259218
\(537\) 6.38086e6 0.954869
\(538\) 3.59086e6 0.534864
\(539\) −725102. −0.107505
\(540\) −1.08475e6 −0.160083
\(541\) −669764. −0.0983849 −0.0491925 0.998789i \(-0.515665\pi\)
−0.0491925 + 0.998789i \(0.515665\pi\)
\(542\) −8.66611e6 −1.26714
\(543\) −2.89676e6 −0.421612
\(544\) −499712. −0.0723973
\(545\) 6.65936e6 0.960376
\(546\) −298116. −0.0427960
\(547\) 482197. 0.0689059 0.0344529 0.999406i \(-0.489031\pi\)
0.0344529 + 0.999406i \(0.489031\pi\)
\(548\) 6.48038e6 0.921827
\(549\) 1.13027e6 0.160049
\(550\) −6.67299e6 −0.940619
\(551\) 1.20532e7 1.69131
\(552\) −33984.0 −0.00474708
\(553\) −1.39821e6 −0.194429
\(554\) 5.22624e6 0.723461
\(555\) −1.03688e7 −1.42887
\(556\) −362144. −0.0496815
\(557\) −328440. −0.0448557 −0.0224279 0.999748i \(-0.507140\pi\)
−0.0224279 + 0.999748i \(0.507140\pi\)
\(558\) 1.25096e6 0.170082
\(559\) 2.40335e6 0.325302
\(560\) −1.16659e6 −0.157199
\(561\) −1.32638e6 −0.177935
\(562\) 6.59350e6 0.880592
\(563\) 9.51348e6 1.26494 0.632468 0.774587i \(-0.282042\pi\)
0.632468 + 0.774587i \(0.282042\pi\)
\(564\) 3.11688e6 0.412593
\(565\) 9.26066e6 1.22045
\(566\) 3.33646e6 0.437769
\(567\) −321489. −0.0419961
\(568\) 5.25005e6 0.682798
\(569\) −1.43629e7 −1.85978 −0.929890 0.367837i \(-0.880099\pi\)
−0.929890 + 0.367837i \(0.880099\pi\)
\(570\) −6.87344e6 −0.886109
\(571\) −1.86893e6 −0.239885 −0.119943 0.992781i \(-0.538271\pi\)
−0.119943 + 0.992781i \(0.538271\pi\)
\(572\) 816608. 0.104357
\(573\) 3.48192e6 0.443029
\(574\) −509992. −0.0646076
\(575\) 325916. 0.0411089
\(576\) 331776. 0.0416667
\(577\) −7.96326e6 −0.995753 −0.497876 0.867248i \(-0.665887\pi\)
−0.497876 + 0.867248i \(0.665887\pi\)
\(578\) −4.72685e6 −0.588508
\(579\) 2.38369e6 0.295497
\(580\) 8.73605e6 1.07831
\(581\) −735931. −0.0904475
\(582\) 2.06658e6 0.252898
\(583\) 2.34986e6 0.286333
\(584\) 416192. 0.0504965
\(585\) −1.27308e6 −0.153803
\(586\) 965748. 0.116177
\(587\) −1.78965e6 −0.214375 −0.107187 0.994239i \(-0.534184\pi\)
−0.107187 + 0.994239i \(0.534184\pi\)
\(588\) −345744. −0.0412393
\(589\) 7.92663e6 0.941457
\(590\) 7.09478e6 0.839091
\(591\) 2.53856e6 0.298964
\(592\) 3.17133e6 0.371909
\(593\) −4.82506e6 −0.563464 −0.281732 0.959493i \(-0.590909\pi\)
−0.281732 + 0.959493i \(0.590909\pi\)
\(594\) 880632. 0.102407
\(595\) 2.22382e6 0.257517
\(596\) 1.94493e6 0.224279
\(597\) −7.85419e6 −0.901915
\(598\) −39884.0 −0.00456085
\(599\) −1.18825e7 −1.35313 −0.676567 0.736381i \(-0.736533\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(600\) −3.18182e6 −0.360826
\(601\) −1.04865e7 −1.18425 −0.592126 0.805845i \(-0.701711\pi\)
−0.592126 + 0.805845i \(0.701711\pi\)
\(602\) 2.78732e6 0.313469
\(603\) 218214. 0.0244393
\(604\) 6.19187e6 0.690605
\(605\) −6.49577e6 −0.721510
\(606\) −1.79647e6 −0.198719
\(607\) 2.11548e6 0.233043 0.116522 0.993188i \(-0.462826\pi\)
0.116522 + 0.993188i \(0.462826\pi\)
\(608\) 2.10227e6 0.230638
\(609\) 2.58911e6 0.282883
\(610\) 5.19089e6 0.564829
\(611\) 3.65800e6 0.396407
\(612\) −632448. −0.0682569
\(613\) −1.09830e6 −0.118051 −0.0590257 0.998256i \(-0.518799\pi\)
−0.0590257 + 0.998256i \(0.518799\pi\)
\(614\) 6.70160e6 0.717393
\(615\) −2.17787e6 −0.232191
\(616\) 947072. 0.100561
\(617\) −1.45577e7 −1.53950 −0.769750 0.638345i \(-0.779619\pi\)
−0.769750 + 0.638345i \(0.779619\pi\)
\(618\) 1.60589e6 0.169139
\(619\) −108428. −0.0113740 −0.00568702 0.999984i \(-0.501810\pi\)
−0.00568702 + 0.999984i \(0.501810\pi\)
\(620\) 5.74517e6 0.600238
\(621\) −43011.0 −0.00447559
\(622\) 6.55623e6 0.679483
\(623\) −2.05697e6 −0.212328
\(624\) 389376. 0.0400320
\(625\) 3.48645e6 0.357013
\(626\) −7.87817e6 −0.803507
\(627\) 5.58005e6 0.566852
\(628\) −176128. −0.0178209
\(629\) −6.04534e6 −0.609248
\(630\) −1.47647e6 −0.148208
\(631\) 8.40559e6 0.840417 0.420209 0.907428i \(-0.361957\pi\)
0.420209 + 0.907428i \(0.361957\pi\)
\(632\) 1.82624e6 0.181872
\(633\) −1.06106e6 −0.105252
\(634\) −4.90696e6 −0.484830
\(635\) 7.54900e6 0.742942
\(636\) 1.12046e6 0.109839
\(637\) −405769. −0.0396214
\(638\) −7.09217e6 −0.689807
\(639\) 6.64459e6 0.643748
\(640\) 1.52371e6 0.147046
\(641\) 5.45817e6 0.524689 0.262345 0.964974i \(-0.415504\pi\)
0.262345 + 0.964974i \(0.415504\pi\)
\(642\) 3.33202e6 0.319058
\(643\) 1.36889e7 1.30569 0.652844 0.757492i \(-0.273576\pi\)
0.652844 + 0.757492i \(0.273576\pi\)
\(644\) −46256.0 −0.00439494
\(645\) 1.19030e7 1.12657
\(646\) −4.00746e6 −0.377822
\(647\) 6.58287e6 0.618236 0.309118 0.951024i \(-0.399966\pi\)
0.309118 + 0.951024i \(0.399966\pi\)
\(648\) 419904. 0.0392837
\(649\) −5.75974e6 −0.536774
\(650\) −3.73422e6 −0.346671
\(651\) 1.70270e6 0.157466
\(652\) −6.32749e6 −0.582925
\(653\) −1.66239e7 −1.52563 −0.762816 0.646616i \(-0.776184\pi\)
−0.762816 + 0.646616i \(0.776184\pi\)
\(654\) −2.57782e6 −0.235672
\(655\) 1.35148e7 1.23085
\(656\) 666112. 0.0604349
\(657\) 526743. 0.0476086
\(658\) 4.24242e6 0.381987
\(659\) −2.17810e7 −1.95373 −0.976864 0.213860i \(-0.931396\pi\)
−0.976864 + 0.213860i \(0.931396\pi\)
\(660\) 4.04438e6 0.361404
\(661\) 4.49538e6 0.400187 0.200093 0.979777i \(-0.435875\pi\)
0.200093 + 0.979777i \(0.435875\pi\)
\(662\) −9.65708e6 −0.856448
\(663\) −742248. −0.0655791
\(664\) 961216. 0.0846059
\(665\) −9.35552e6 −0.820378
\(666\) 4.01371e6 0.350639
\(667\) 346389. 0.0301474
\(668\) −2.83659e6 −0.245955
\(669\) 6.77312e6 0.585091
\(670\) 1.00217e6 0.0862489
\(671\) −4.21411e6 −0.361326
\(672\) 451584. 0.0385758
\(673\) −1.50204e7 −1.27833 −0.639164 0.769070i \(-0.720720\pi\)
−0.639164 + 0.769070i \(0.720720\pi\)
\(674\) 2.47127e6 0.209542
\(675\) −4.02700e6 −0.340190
\(676\) 456976. 0.0384615
\(677\) −3.20280e6 −0.268571 −0.134285 0.990943i \(-0.542874\pi\)
−0.134285 + 0.990943i \(0.542874\pi\)
\(678\) −3.58477e6 −0.299493
\(679\) 2.81284e6 0.234138
\(680\) −2.90458e6 −0.240885
\(681\) −4.36331e6 −0.360536
\(682\) −4.66409e6 −0.383978
\(683\) −1.43886e7 −1.18023 −0.590115 0.807319i \(-0.700918\pi\)
−0.590115 + 0.807319i \(0.700918\pi\)
\(684\) 2.66069e6 0.217447
\(685\) 3.76672e7 3.06717
\(686\) −470596. −0.0381802
\(687\) 3.57971e6 0.289372
\(688\) −3.64058e6 −0.293224
\(689\) 1.31499e6 0.105530
\(690\) −197532. −0.0157948
\(691\) 2.87339e6 0.228928 0.114464 0.993427i \(-0.463485\pi\)
0.114464 + 0.993427i \(0.463485\pi\)
\(692\) 7.45702e6 0.591971
\(693\) 1.19864e6 0.0948102
\(694\) −7.48307e6 −0.589768
\(695\) −2.10496e6 −0.165304
\(696\) −3.38170e6 −0.264613
\(697\) −1.26978e6 −0.0990023
\(698\) −1.50333e7 −1.16793
\(699\) 2.45287e6 0.189881
\(700\) −4.33082e6 −0.334060
\(701\) 4.93926e6 0.379635 0.189818 0.981819i \(-0.439210\pi\)
0.189818 + 0.981819i \(0.439210\pi\)
\(702\) 492804. 0.0377426
\(703\) 2.54326e7 1.94089
\(704\) −1.23699e6 −0.0940666
\(705\) 1.81169e7 1.37281
\(706\) 563096. 0.0425178
\(707\) −2.44520e6 −0.183978
\(708\) −2.74637e6 −0.205909
\(709\) 6.77459e6 0.506136 0.253068 0.967448i \(-0.418560\pi\)
0.253068 + 0.967448i \(0.418560\pi\)
\(710\) 3.05159e7 2.27185
\(711\) 2.31134e6 0.171470
\(712\) 2.68666e6 0.198615
\(713\) 227799. 0.0167814
\(714\) −860832. −0.0631936
\(715\) 4.74653e6 0.347225
\(716\) −1.13438e7 −0.826941
\(717\) 7.37006e6 0.535394
\(718\) −7.13270e6 −0.516349
\(719\) 5.84618e6 0.421745 0.210872 0.977514i \(-0.432370\pi\)
0.210872 + 0.977514i \(0.432370\pi\)
\(720\) 1.92845e6 0.138636
\(721\) 2.18579e6 0.156592
\(722\) 6.95484e6 0.496528
\(723\) −1.21302e7 −0.863019
\(724\) 5.14979e6 0.365126
\(725\) 3.24314e7 2.29150
\(726\) 2.51449e6 0.177055
\(727\) 2.15115e7 1.50951 0.754754 0.656008i \(-0.227756\pi\)
0.754754 + 0.656008i \(0.227756\pi\)
\(728\) 529984. 0.0370625
\(729\) 531441. 0.0370370
\(730\) 2.41912e6 0.168016
\(731\) 6.93985e6 0.480349
\(732\) −2.00938e6 −0.138606
\(733\) 1.45662e7 1.00135 0.500677 0.865634i \(-0.333084\pi\)
0.500677 + 0.865634i \(0.333084\pi\)
\(734\) −1.23140e7 −0.843644
\(735\) −2.00964e6 −0.137214
\(736\) 60416.0 0.00411109
\(737\) −813588. −0.0551742
\(738\) 843048. 0.0569786
\(739\) −5.48841e6 −0.369688 −0.184844 0.982768i \(-0.559178\pi\)
−0.184844 + 0.982768i \(0.559178\pi\)
\(740\) 1.84333e7 1.23744
\(741\) 3.12261e6 0.208916
\(742\) 1.52508e6 0.101691
\(743\) 7.56646e6 0.502829 0.251415 0.967879i \(-0.419104\pi\)
0.251415 + 0.967879i \(0.419104\pi\)
\(744\) −2.22394e6 −0.147296
\(745\) 1.13049e7 0.746235
\(746\) −1.38057e7 −0.908265
\(747\) 1.21654e6 0.0797672
\(748\) 2.35802e6 0.154096
\(749\) 4.53524e6 0.295390
\(750\) −8.03185e6 −0.521390
\(751\) 1.63386e7 1.05710 0.528549 0.848903i \(-0.322736\pi\)
0.528549 + 0.848903i \(0.322736\pi\)
\(752\) −5.54112e6 −0.357316
\(753\) −3.81083e6 −0.244925
\(754\) −3.96880e6 −0.254232
\(755\) 3.59903e7 2.29783
\(756\) 571536. 0.0363696
\(757\) 5.90963e6 0.374818 0.187409 0.982282i \(-0.439991\pi\)
0.187409 + 0.982282i \(0.439991\pi\)
\(758\) −9.99690e6 −0.631964
\(759\) 160362. 0.0101041
\(760\) 1.22195e7 0.767393
\(761\) 2.58402e7 1.61746 0.808730 0.588180i \(-0.200155\pi\)
0.808730 + 0.588180i \(0.200155\pi\)
\(762\) −2.92219e6 −0.182315
\(763\) −3.50869e6 −0.218190
\(764\) −6.19008e6 −0.383674
\(765\) −3.67610e6 −0.227109
\(766\) 1.57859e7 0.972072
\(767\) −3.22317e6 −0.197831
\(768\) −589824. −0.0360844
\(769\) 6.11750e6 0.373042 0.186521 0.982451i \(-0.440279\pi\)
0.186521 + 0.982451i \(0.440279\pi\)
\(770\) 5.50486e6 0.334595
\(771\) 1.89981e7 1.15100
\(772\) −4.23766e6 −0.255908
\(773\) −1.45256e6 −0.0874351 −0.0437176 0.999044i \(-0.513920\pi\)
−0.0437176 + 0.999044i \(0.513920\pi\)
\(774\) −4.60760e6 −0.276454
\(775\) 2.13282e7 1.27556
\(776\) −3.67392e6 −0.219016
\(777\) 5.46311e6 0.324629
\(778\) −1.62266e7 −0.961122
\(779\) 5.34191e6 0.315393
\(780\) 2.26325e6 0.133197
\(781\) −2.47737e7 −1.45332
\(782\) −115168. −0.00673465
\(783\) −4.27996e6 −0.249480
\(784\) 614656. 0.0357143
\(785\) −1.02374e6 −0.0592949
\(786\) −5.23152e6 −0.302045
\(787\) −2.84829e7 −1.63926 −0.819630 0.572893i \(-0.805821\pi\)
−0.819630 + 0.572893i \(0.805821\pi\)
\(788\) −4.51299e6 −0.258910
\(789\) 6.08349e6 0.347905
\(790\) 1.06150e7 0.605136
\(791\) −4.87927e6 −0.277277
\(792\) −1.56557e6 −0.0886868
\(793\) −2.35823e6 −0.133169
\(794\) 1.33979e7 0.754197
\(795\) 6.51270e6 0.365463
\(796\) 1.39630e7 0.781081
\(797\) 3.29521e6 0.183754 0.0918770 0.995770i \(-0.470713\pi\)
0.0918770 + 0.995770i \(0.470713\pi\)
\(798\) 3.62149e6 0.201317
\(799\) 1.05628e7 0.585343
\(800\) 5.65658e6 0.312485
\(801\) 3.40030e6 0.187256
\(802\) 2.40083e7 1.31803
\(803\) −1.96391e6 −0.107481
\(804\) −387936. −0.0211651
\(805\) −268863. −0.0146232
\(806\) −2.61004e6 −0.141517
\(807\) −8.07944e6 −0.436715
\(808\) 3.19373e6 0.172096
\(809\) −1.02681e7 −0.551590 −0.275795 0.961216i \(-0.588941\pi\)
−0.275795 + 0.961216i \(0.588941\pi\)
\(810\) 2.44069e6 0.130707
\(811\) −3.00578e7 −1.60474 −0.802371 0.596825i \(-0.796429\pi\)
−0.802371 + 0.596825i \(0.796429\pi\)
\(812\) −4.60286e6 −0.244984
\(813\) 1.94988e7 1.03462
\(814\) −1.49647e7 −0.791602
\(815\) −3.67785e7 −1.93955
\(816\) 1.12435e6 0.0591122
\(817\) −2.91957e7 −1.53026
\(818\) 8.64979e6 0.451983
\(819\) 670761. 0.0349428
\(820\) 3.87178e6 0.201083
\(821\) 3.43710e7 1.77965 0.889825 0.456302i \(-0.150826\pi\)
0.889825 + 0.456302i \(0.150826\pi\)
\(822\) −1.45809e7 −0.752668
\(823\) 2.95480e7 1.52065 0.760324 0.649544i \(-0.225040\pi\)
0.760324 + 0.649544i \(0.225040\pi\)
\(824\) −2.85491e6 −0.146479
\(825\) 1.50142e7 0.768012
\(826\) −3.73811e6 −0.190635
\(827\) 1.04233e7 0.529960 0.264980 0.964254i \(-0.414635\pi\)
0.264980 + 0.964254i \(0.414635\pi\)
\(828\) 76464.0 0.00387598
\(829\) 7.34305e6 0.371099 0.185550 0.982635i \(-0.440593\pi\)
0.185550 + 0.982635i \(0.440593\pi\)
\(830\) 5.58707e6 0.281507
\(831\) −1.17590e7 −0.590704
\(832\) −692224. −0.0346688
\(833\) −1.17169e6 −0.0585059
\(834\) 814824. 0.0405647
\(835\) −1.64877e7 −0.818359
\(836\) −9.92010e6 −0.490908
\(837\) −2.81467e6 −0.138872
\(838\) −1.99779e7 −0.982744
\(839\) 1.74785e7 0.857233 0.428617 0.903486i \(-0.359001\pi\)
0.428617 + 0.903486i \(0.359001\pi\)
\(840\) 2.62483e6 0.128352
\(841\) 1.39575e7 0.680483
\(842\) 184160. 0.00895190
\(843\) −1.48354e7 −0.719001
\(844\) 1.88632e6 0.0911505
\(845\) 2.65617e6 0.127972
\(846\) −7.01298e6 −0.336881
\(847\) 3.42250e6 0.163921
\(848\) −1.99194e6 −0.0951230
\(849\) −7.50704e6 −0.357437
\(850\) −1.07828e7 −0.511901
\(851\) 730892. 0.0345963
\(852\) −1.18126e7 −0.557502
\(853\) −3.15389e7 −1.48414 −0.742069 0.670324i \(-0.766155\pi\)
−0.742069 + 0.670324i \(0.766155\pi\)
\(854\) −2.73498e6 −0.128325
\(855\) 1.54652e7 0.723505
\(856\) −5.92358e6 −0.276312
\(857\) 1.09861e7 0.510965 0.255482 0.966814i \(-0.417766\pi\)
0.255482 + 0.966814i \(0.417766\pi\)
\(858\) −1.83737e6 −0.0852075
\(859\) 3.42347e6 0.158301 0.0791504 0.996863i \(-0.474779\pi\)
0.0791504 + 0.996863i \(0.474779\pi\)
\(860\) −2.11608e7 −0.975634
\(861\) 1.14748e6 0.0527519
\(862\) −2.78571e7 −1.27693
\(863\) −1.85496e7 −0.847826 −0.423913 0.905703i \(-0.639344\pi\)
−0.423913 + 0.905703i \(0.639344\pi\)
\(864\) −746496. −0.0340207
\(865\) 4.33440e7 1.96965
\(866\) 2.24571e7 1.01756
\(867\) 1.06354e7 0.480515
\(868\) −3.02702e6 −0.136369
\(869\) −8.61757e6 −0.387111
\(870\) −1.96561e7 −0.880439
\(871\) −455286. −0.0203348
\(872\) 4.58278e6 0.204098
\(873\) −4.64980e6 −0.206490
\(874\) 484508. 0.0214547
\(875\) −1.09322e7 −0.482713
\(876\) −936432. −0.0412303
\(877\) 1.97177e7 0.865680 0.432840 0.901471i \(-0.357512\pi\)
0.432840 + 0.901471i \(0.357512\pi\)
\(878\) 7.53342e6 0.329804
\(879\) −2.17293e6 −0.0948580
\(880\) −7.19002e6 −0.312985
\(881\) 3.30056e7 1.43268 0.716338 0.697754i \(-0.245817\pi\)
0.716338 + 0.697754i \(0.245817\pi\)
\(882\) 777924. 0.0336718
\(883\) 1.31820e7 0.568958 0.284479 0.958682i \(-0.408179\pi\)
0.284479 + 0.958682i \(0.408179\pi\)
\(884\) 1.31955e6 0.0567931
\(885\) −1.59633e7 −0.685115
\(886\) −2.79064e7 −1.19432
\(887\) 2.56309e7 1.09384 0.546921 0.837184i \(-0.315800\pi\)
0.546921 + 0.837184i \(0.315800\pi\)
\(888\) −7.13549e6 −0.303663
\(889\) −3.97743e6 −0.168790
\(890\) 1.56162e7 0.660846
\(891\) −1.98142e6 −0.0836147
\(892\) −1.20411e7 −0.506704
\(893\) −4.44372e7 −1.86474
\(894\) −4.37609e6 −0.183123
\(895\) −6.59356e7 −2.75145
\(896\) −802816. −0.0334077
\(897\) 89739.0 0.00372392
\(898\) 5.68350e6 0.235194
\(899\) 2.26679e7 0.935433
\(900\) 7.15910e6 0.294613
\(901\) 3.79713e6 0.155827
\(902\) −3.14322e6 −0.128635
\(903\) −6.27146e6 −0.255947
\(904\) 6.37293e6 0.259369
\(905\) 2.99332e7 1.21487
\(906\) −1.39317e7 −0.563876
\(907\) 3.17787e6 0.128268 0.0641339 0.997941i \(-0.479572\pi\)
0.0641339 + 0.997941i \(0.479572\pi\)
\(908\) 7.75699e6 0.312233
\(909\) 4.04206e6 0.162253
\(910\) 3.08053e6 0.123317
\(911\) −1.99453e7 −0.796240 −0.398120 0.917333i \(-0.630337\pi\)
−0.398120 + 0.917333i \(0.630337\pi\)
\(912\) −4.73011e6 −0.188315
\(913\) −4.53574e6 −0.180082
\(914\) 721088. 0.0285511
\(915\) −1.16795e7 −0.461181
\(916\) −6.36394e6 −0.250603
\(917\) −7.12068e6 −0.279639
\(918\) 1.42301e6 0.0557315
\(919\) −4.09094e7 −1.59784 −0.798922 0.601434i \(-0.794596\pi\)
−0.798922 + 0.601434i \(0.794596\pi\)
\(920\) 351168. 0.0136787
\(921\) −1.50786e7 −0.585749
\(922\) −1.43633e7 −0.556451
\(923\) −1.38634e7 −0.535631
\(924\) −2.13091e6 −0.0821080
\(925\) 6.84313e7 2.62967
\(926\) 2.12639e7 0.814920
\(927\) −3.61325e6 −0.138102
\(928\) 6.01190e6 0.229162
\(929\) 1.07776e7 0.409714 0.204857 0.978792i \(-0.434327\pi\)
0.204857 + 0.978792i \(0.434327\pi\)
\(930\) −1.29266e7 −0.490092
\(931\) 4.92925e6 0.186383
\(932\) −4.36066e6 −0.164442
\(933\) −1.47515e7 −0.554795
\(934\) −1.10926e7 −0.416071
\(935\) 1.37060e7 0.512721
\(936\) −876096. −0.0326860
\(937\) −4.00147e7 −1.48892 −0.744459 0.667668i \(-0.767293\pi\)
−0.744459 + 0.667668i \(0.767293\pi\)
\(938\) −528024. −0.0195951
\(939\) 1.77259e7 0.656060
\(940\) −3.22078e7 −1.18889
\(941\) −2.44799e7 −0.901230 −0.450615 0.892718i \(-0.648795\pi\)
−0.450615 + 0.892718i \(0.648795\pi\)
\(942\) 396288. 0.0145507
\(943\) 153518. 0.00562186
\(944\) 4.88243e6 0.178323
\(945\) 3.32205e6 0.121012
\(946\) 1.71790e7 0.624122
\(947\) −4.00398e7 −1.45083 −0.725416 0.688311i \(-0.758352\pi\)
−0.725416 + 0.688311i \(0.758352\pi\)
\(948\) −4.10904e6 −0.148498
\(949\) −1.09901e6 −0.0396127
\(950\) 4.53631e7 1.63077
\(951\) 1.10407e7 0.395862
\(952\) 1.53037e6 0.0547272
\(953\) −2.17862e7 −0.777051 −0.388526 0.921438i \(-0.627015\pi\)
−0.388526 + 0.921438i \(0.627015\pi\)
\(954\) −2.52104e6 −0.0896829
\(955\) −3.59798e7 −1.27659
\(956\) −1.31023e7 −0.463665
\(957\) 1.59574e7 0.563225
\(958\) 1.48974e7 0.524440
\(959\) −1.98462e7 −0.696836
\(960\) −3.42835e6 −0.120062
\(961\) −1.37218e7 −0.479296
\(962\) −8.37429e6 −0.291750
\(963\) −7.49704e6 −0.260510
\(964\) 2.15647e7 0.747397
\(965\) −2.46314e7 −0.851474
\(966\) 104076. 0.00358846
\(967\) 3.66362e7 1.25992 0.629962 0.776626i \(-0.283071\pi\)
0.629962 + 0.776626i \(0.283071\pi\)
\(968\) −4.47021e6 −0.153334
\(969\) 9.01678e6 0.308491
\(970\) −2.13547e7 −0.728724
\(971\) −4.65132e7 −1.58317 −0.791587 0.611057i \(-0.790745\pi\)
−0.791587 + 0.611057i \(0.790745\pi\)
\(972\) −944784. −0.0320750
\(973\) 1.10907e6 0.0375557
\(974\) 3.83065e7 1.29382
\(975\) 8.40200e6 0.283055
\(976\) 3.57222e6 0.120037
\(977\) 5.12581e7 1.71801 0.859006 0.511966i \(-0.171082\pi\)
0.859006 + 0.511966i \(0.171082\pi\)
\(978\) 1.42368e7 0.475956
\(979\) −1.26777e7 −0.422749
\(980\) 3.57269e6 0.118831
\(981\) 5.80009e6 0.192425
\(982\) −3.48633e7 −1.15369
\(983\) 7.49074e6 0.247253 0.123626 0.992329i \(-0.460548\pi\)
0.123626 + 0.992329i \(0.460548\pi\)
\(984\) −1.49875e6 −0.0493449
\(985\) −2.62318e7 −0.861464
\(986\) −1.14602e7 −0.375405
\(987\) −9.54544e6 −0.311891
\(988\) −5.55131e6 −0.180927
\(989\) −839039. −0.0272767
\(990\) −9.09986e6 −0.295085
\(991\) −1.00629e6 −0.0325492 −0.0162746 0.999868i \(-0.505181\pi\)
−0.0162746 + 0.999868i \(0.505181\pi\)
\(992\) 3.95366e6 0.127562
\(993\) 2.17284e7 0.699287
\(994\) −1.60783e7 −0.516147
\(995\) 8.11600e7 2.59887
\(996\) −2.16274e6 −0.0690805
\(997\) −5.15011e7 −1.64089 −0.820443 0.571728i \(-0.806273\pi\)
−0.820443 + 0.571728i \(0.806273\pi\)
\(998\) −3.23235e6 −0.102729
\(999\) −9.03085e6 −0.286296
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 546.6.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.6.a.e.1.1 1 1.1 even 1 trivial