Properties

Label 546.6.a.b.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

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +99.0000 q^{5} -36.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +99.0000 q^{5} -36.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} -396.000 q^{10} +783.000 q^{11} +144.000 q^{12} +169.000 q^{13} -196.000 q^{14} +891.000 q^{15} +256.000 q^{16} +33.0000 q^{17} -324.000 q^{18} +1433.00 q^{19} +1584.00 q^{20} +441.000 q^{21} -3132.00 q^{22} -3087.00 q^{23} -576.000 q^{24} +6676.00 q^{25} -676.000 q^{26} +729.000 q^{27} +784.000 q^{28} +1515.00 q^{29} -3564.00 q^{30} +2780.00 q^{31} -1024.00 q^{32} +7047.00 q^{33} -132.000 q^{34} +4851.00 q^{35} +1296.00 q^{36} -6595.00 q^{37} -5732.00 q^{38} +1521.00 q^{39} -6336.00 q^{40} +4380.00 q^{41} -1764.00 q^{42} +16043.0 q^{43} +12528.0 q^{44} +8019.00 q^{45} +12348.0 q^{46} +3480.00 q^{47} +2304.00 q^{48} +2401.00 q^{49} -26704.0 q^{50} +297.000 q^{51} +2704.00 q^{52} +618.000 q^{53} -2916.00 q^{54} +77517.0 q^{55} -3136.00 q^{56} +12897.0 q^{57} -6060.00 q^{58} -52116.0 q^{59} +14256.0 q^{60} +887.000 q^{61} -11120.0 q^{62} +3969.00 q^{63} +4096.00 q^{64} +16731.0 q^{65} -28188.0 q^{66} +854.000 q^{67} +528.000 q^{68} -27783.0 q^{69} -19404.0 q^{70} -47340.0 q^{71} -5184.00 q^{72} -64915.0 q^{73} +26380.0 q^{74} +60084.0 q^{75} +22928.0 q^{76} +38367.0 q^{77} -6084.00 q^{78} -73282.0 q^{79} +25344.0 q^{80} +6561.00 q^{81} -17520.0 q^{82} -97062.0 q^{83} +7056.00 q^{84} +3267.00 q^{85} -64172.0 q^{86} +13635.0 q^{87} -50112.0 q^{88} +118218. q^{89} -32076.0 q^{90} +8281.00 q^{91} -49392.0 q^{92} +25020.0 q^{93} -13920.0 q^{94} +141867. q^{95} -9216.00 q^{96} -184522. q^{97} -9604.00 q^{98} +63423.0 q^{99} +O(q^{100})\)

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
\(5\) 99.0000 1.77097 0.885483 0.464672i \(-0.153828\pi\)
0.885483 + 0.464672i \(0.153828\pi\)
\(6\) −36.0000 −0.408248
\(7\) 49.0000 0.377964
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −396.000 −1.25226
\(11\) 783.000 1.95110 0.975551 0.219772i \(-0.0705315\pi\)
0.975551 + 0.219772i \(0.0705315\pi\)
\(12\) 144.000 0.288675
\(13\) 169.000 0.277350
\(14\) −196.000 −0.267261
\(15\) 891.000 1.02247
\(16\) 256.000 0.250000
\(17\) 33.0000 0.0276944 0.0138472 0.999904i \(-0.495592\pi\)
0.0138472 + 0.999904i \(0.495592\pi\)
\(18\) −324.000 −0.235702
\(19\) 1433.00 0.910672 0.455336 0.890320i \(-0.349519\pi\)
0.455336 + 0.890320i \(0.349519\pi\)
\(20\) 1584.00 0.885483
\(21\) 441.000 0.218218
\(22\) −3132.00 −1.37964
\(23\) −3087.00 −1.21679 −0.608397 0.793633i \(-0.708187\pi\)
−0.608397 + 0.793633i \(0.708187\pi\)
\(24\) −576.000 −0.204124
\(25\) 6676.00 2.13632
\(26\) −676.000 −0.196116
\(27\) 729.000 0.192450
\(28\) 784.000 0.188982
\(29\) 1515.00 0.334517 0.167258 0.985913i \(-0.446509\pi\)
0.167258 + 0.985913i \(0.446509\pi\)
\(30\) −3564.00 −0.722994
\(31\) 2780.00 0.519566 0.259783 0.965667i \(-0.416349\pi\)
0.259783 + 0.965667i \(0.416349\pi\)
\(32\) −1024.00 −0.176777
\(33\) 7047.00 1.12647
\(34\) −132.000 −0.0195829
\(35\) 4851.00 0.669362
\(36\) 1296.00 0.166667
\(37\) −6595.00 −0.791973 −0.395987 0.918256i \(-0.629597\pi\)
−0.395987 + 0.918256i \(0.629597\pi\)
\(38\) −5732.00 −0.643943
\(39\) 1521.00 0.160128
\(40\) −6336.00 −0.626131
\(41\) 4380.00 0.406925 0.203463 0.979083i \(-0.434780\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(42\) −1764.00 −0.154303
\(43\) 16043.0 1.32317 0.661583 0.749872i \(-0.269885\pi\)
0.661583 + 0.749872i \(0.269885\pi\)
\(44\) 12528.0 0.975551
\(45\) 8019.00 0.590322
\(46\) 12348.0 0.860403
\(47\) 3480.00 0.229792 0.114896 0.993378i \(-0.463347\pi\)
0.114896 + 0.993378i \(0.463347\pi\)
\(48\) 2304.00 0.144338
\(49\) 2401.00 0.142857
\(50\) −26704.0 −1.51061
\(51\) 297.000 0.0159894
\(52\) 2704.00 0.138675
\(53\) 618.000 0.0302203 0.0151102 0.999886i \(-0.495190\pi\)
0.0151102 + 0.999886i \(0.495190\pi\)
\(54\) −2916.00 −0.136083
\(55\) 77517.0 3.45534
\(56\) −3136.00 −0.133631
\(57\) 12897.0 0.525777
\(58\) −6060.00 −0.236539
\(59\) −52116.0 −1.94913 −0.974566 0.224103i \(-0.928055\pi\)
−0.974566 + 0.224103i \(0.928055\pi\)
\(60\) 14256.0 0.511234
\(61\) 887.000 0.0305210 0.0152605 0.999884i \(-0.495142\pi\)
0.0152605 + 0.999884i \(0.495142\pi\)
\(62\) −11120.0 −0.367389
\(63\) 3969.00 0.125988
\(64\) 4096.00 0.125000
\(65\) 16731.0 0.491178
\(66\) −28188.0 −0.796534
\(67\) 854.000 0.0232419 0.0116209 0.999932i \(-0.496301\pi\)
0.0116209 + 0.999932i \(0.496301\pi\)
\(68\) 528.000 0.0138472
\(69\) −27783.0 −0.702516
\(70\) −19404.0 −0.473311
\(71\) −47340.0 −1.11451 −0.557253 0.830343i \(-0.688145\pi\)
−0.557253 + 0.830343i \(0.688145\pi\)
\(72\) −5184.00 −0.117851
\(73\) −64915.0 −1.42573 −0.712866 0.701300i \(-0.752603\pi\)
−0.712866 + 0.701300i \(0.752603\pi\)
\(74\) 26380.0 0.560010
\(75\) 60084.0 1.23340
\(76\) 22928.0 0.455336
\(77\) 38367.0 0.737447
\(78\) −6084.00 −0.113228
\(79\) −73282.0 −1.32108 −0.660541 0.750790i \(-0.729673\pi\)
−0.660541 + 0.750790i \(0.729673\pi\)
\(80\) 25344.0 0.442741
\(81\) 6561.00 0.111111
\(82\) −17520.0 −0.287739
\(83\) −97062.0 −1.54651 −0.773257 0.634092i \(-0.781374\pi\)
−0.773257 + 0.634092i \(0.781374\pi\)
\(84\) 7056.00 0.109109
\(85\) 3267.00 0.0490458
\(86\) −64172.0 −0.935620
\(87\) 13635.0 0.193133
\(88\) −50112.0 −0.689819
\(89\) 118218. 1.58201 0.791004 0.611811i \(-0.209559\pi\)
0.791004 + 0.611811i \(0.209559\pi\)
\(90\) −32076.0 −0.417421
\(91\) 8281.00 0.104828
\(92\) −49392.0 −0.608397
\(93\) 25020.0 0.299971
\(94\) −13920.0 −0.162487
\(95\) 141867. 1.61277
\(96\) −9216.00 −0.102062
\(97\) −184522. −1.99122 −0.995609 0.0936092i \(-0.970160\pi\)
−0.995609 + 0.0936092i \(0.970160\pi\)
\(98\) −9604.00 −0.101015
\(99\) 63423.0 0.650367
\(100\) 106816. 1.06816
\(101\) −88452.0 −0.862788 −0.431394 0.902164i \(-0.641978\pi\)
−0.431394 + 0.902164i \(0.641978\pi\)
\(102\) −1188.00 −0.0113062
\(103\) 3311.00 0.0307515 0.0153757 0.999882i \(-0.495106\pi\)
0.0153757 + 0.999882i \(0.495106\pi\)
\(104\) −10816.0 −0.0980581
\(105\) 43659.0 0.386456
\(106\) −2472.00 −0.0213690
\(107\) −67902.0 −0.573354 −0.286677 0.958027i \(-0.592551\pi\)
−0.286677 + 0.958027i \(0.592551\pi\)
\(108\) 11664.0 0.0962250
\(109\) −4993.00 −0.0402527 −0.0201264 0.999797i \(-0.506407\pi\)
−0.0201264 + 0.999797i \(0.506407\pi\)
\(110\) −310068. −2.44329
\(111\) −59355.0 −0.457246
\(112\) 12544.0 0.0944911
\(113\) 152358. 1.12246 0.561228 0.827661i \(-0.310329\pi\)
0.561228 + 0.827661i \(0.310329\pi\)
\(114\) −51588.0 −0.371780
\(115\) −305613. −2.15490
\(116\) 24240.0 0.167258
\(117\) 13689.0 0.0924500
\(118\) 208464. 1.37824
\(119\) 1617.00 0.0104675
\(120\) −57024.0 −0.361497
\(121\) 452038. 2.80680
\(122\) −3548.00 −0.0215816
\(123\) 39420.0 0.234938
\(124\) 44480.0 0.259783
\(125\) 351549. 2.01238
\(126\) −15876.0 −0.0890871
\(127\) −203902. −1.12179 −0.560896 0.827886i \(-0.689543\pi\)
−0.560896 + 0.827886i \(0.689543\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 144387. 0.763930
\(130\) −66924.0 −0.347315
\(131\) 214857. 1.09388 0.546942 0.837171i \(-0.315792\pi\)
0.546942 + 0.837171i \(0.315792\pi\)
\(132\) 112752. 0.563235
\(133\) 70217.0 0.344202
\(134\) −3416.00 −0.0164345
\(135\) 72171.0 0.340823
\(136\) −2112.00 −0.00979144
\(137\) −207927. −0.946476 −0.473238 0.880935i \(-0.656915\pi\)
−0.473238 + 0.880935i \(0.656915\pi\)
\(138\) 111132. 0.496754
\(139\) −231364. −1.01568 −0.507842 0.861450i \(-0.669557\pi\)
−0.507842 + 0.861450i \(0.669557\pi\)
\(140\) 77616.0 0.334681
\(141\) 31320.0 0.132670
\(142\) 189360. 0.788075
\(143\) 132327. 0.541138
\(144\) 20736.0 0.0833333
\(145\) 149985. 0.592417
\(146\) 259660. 1.00814
\(147\) 21609.0 0.0824786
\(148\) −105520. −0.395987
\(149\) 242172. 0.893631 0.446816 0.894626i \(-0.352558\pi\)
0.446816 + 0.894626i \(0.352558\pi\)
\(150\) −240336. −0.872149
\(151\) 268241. 0.957377 0.478688 0.877985i \(-0.341112\pi\)
0.478688 + 0.877985i \(0.341112\pi\)
\(152\) −91712.0 −0.321971
\(153\) 2673.00 0.00923146
\(154\) −153468. −0.521454
\(155\) 275220. 0.920133
\(156\) 24336.0 0.0800641
\(157\) −340885. −1.10372 −0.551860 0.833937i \(-0.686082\pi\)
−0.551860 + 0.833937i \(0.686082\pi\)
\(158\) 293128. 0.934146
\(159\) 5562.00 0.0174477
\(160\) −101376. −0.313065
\(161\) −151263. −0.459905
\(162\) −26244.0 −0.0785674
\(163\) −10222.0 −0.0301347 −0.0150673 0.999886i \(-0.504796\pi\)
−0.0150673 + 0.999886i \(0.504796\pi\)
\(164\) 70080.0 0.203463
\(165\) 697653. 1.99494
\(166\) 388248. 1.09355
\(167\) 397815. 1.10380 0.551899 0.833911i \(-0.313903\pi\)
0.551899 + 0.833911i \(0.313903\pi\)
\(168\) −28224.0 −0.0771517
\(169\) 28561.0 0.0769231
\(170\) −13068.0 −0.0346806
\(171\) 116073. 0.303557
\(172\) 256688. 0.661583
\(173\) −368886. −0.937081 −0.468540 0.883442i \(-0.655220\pi\)
−0.468540 + 0.883442i \(0.655220\pi\)
\(174\) −54540.0 −0.136566
\(175\) 327124. 0.807453
\(176\) 200448. 0.487776
\(177\) −469044. −1.12533
\(178\) −472872. −1.11865
\(179\) −201864. −0.470897 −0.235449 0.971887i \(-0.575656\pi\)
−0.235449 + 0.971887i \(0.575656\pi\)
\(180\) 128304. 0.295161
\(181\) 548210. 1.24380 0.621900 0.783097i \(-0.286361\pi\)
0.621900 + 0.783097i \(0.286361\pi\)
\(182\) −33124.0 −0.0741249
\(183\) 7983.00 0.0176213
\(184\) 197568. 0.430202
\(185\) −652905. −1.40256
\(186\) −100080. −0.212112
\(187\) 25839.0 0.0540346
\(188\) 55680.0 0.114896
\(189\) 35721.0 0.0727393
\(190\) −567468. −1.14040
\(191\) 291201. 0.577576 0.288788 0.957393i \(-0.406748\pi\)
0.288788 + 0.957393i \(0.406748\pi\)
\(192\) 36864.0 0.0721688
\(193\) −793324. −1.53305 −0.766527 0.642212i \(-0.778017\pi\)
−0.766527 + 0.642212i \(0.778017\pi\)
\(194\) 738088. 1.40800
\(195\) 150579. 0.283581
\(196\) 38416.0 0.0714286
\(197\) 396180. 0.727322 0.363661 0.931531i \(-0.381527\pi\)
0.363661 + 0.931531i \(0.381527\pi\)
\(198\) −253692. −0.459879
\(199\) 624341. 1.11761 0.558804 0.829300i \(-0.311261\pi\)
0.558804 + 0.829300i \(0.311261\pi\)
\(200\) −427264. −0.755303
\(201\) 7686.00 0.0134187
\(202\) 353808. 0.610083
\(203\) 74235.0 0.126435
\(204\) 4752.00 0.00799468
\(205\) 433620. 0.720650
\(206\) −13244.0 −0.0217446
\(207\) −250047. −0.405598
\(208\) 43264.0 0.0693375
\(209\) 1.12204e6 1.77682
\(210\) −174636. −0.273266
\(211\) −212095. −0.327963 −0.163981 0.986463i \(-0.552434\pi\)
−0.163981 + 0.986463i \(0.552434\pi\)
\(212\) 9888.00 0.0151102
\(213\) −426060. −0.643460
\(214\) 271608. 0.405423
\(215\) 1.58826e6 2.34328
\(216\) −46656.0 −0.0680414
\(217\) 136220. 0.196377
\(218\) 19972.0 0.0284630
\(219\) −584235. −0.823147
\(220\) 1.24027e6 1.72767
\(221\) 5577.00 0.00768104
\(222\) 237420. 0.323322
\(223\) 945554. 1.27328 0.636640 0.771161i \(-0.280324\pi\)
0.636640 + 0.771161i \(0.280324\pi\)
\(224\) −50176.0 −0.0668153
\(225\) 540756. 0.712107
\(226\) −609432. −0.793696
\(227\) 462726. 0.596018 0.298009 0.954563i \(-0.403677\pi\)
0.298009 + 0.954563i \(0.403677\pi\)
\(228\) 206352. 0.262888
\(229\) 752606. 0.948373 0.474186 0.880425i \(-0.342742\pi\)
0.474186 + 0.880425i \(0.342742\pi\)
\(230\) 1.22245e6 1.52374
\(231\) 345303. 0.425765
\(232\) −96960.0 −0.118269
\(233\) −739032. −0.891812 −0.445906 0.895080i \(-0.647118\pi\)
−0.445906 + 0.895080i \(0.647118\pi\)
\(234\) −54756.0 −0.0653720
\(235\) 344520. 0.406953
\(236\) −833856. −0.974566
\(237\) −659538. −0.762727
\(238\) −6468.00 −0.00740163
\(239\) −97752.0 −0.110696 −0.0553479 0.998467i \(-0.517627\pi\)
−0.0553479 + 0.998467i \(0.517627\pi\)
\(240\) 228096. 0.255617
\(241\) −1.23313e6 −1.36762 −0.683811 0.729659i \(-0.739679\pi\)
−0.683811 + 0.729659i \(0.739679\pi\)
\(242\) −1.80815e6 −1.98471
\(243\) 59049.0 0.0641500
\(244\) 14192.0 0.0152605
\(245\) 237699. 0.252995
\(246\) −157680. −0.166126
\(247\) 242177. 0.252575
\(248\) −177920. −0.183694
\(249\) −873558. −0.892881
\(250\) −1.40620e6 −1.42297
\(251\) 198117. 0.198489 0.0992447 0.995063i \(-0.468357\pi\)
0.0992447 + 0.995063i \(0.468357\pi\)
\(252\) 63504.0 0.0629941
\(253\) −2.41712e6 −2.37409
\(254\) 815608. 0.793226
\(255\) 29403.0 0.0283166
\(256\) 65536.0 0.0625000
\(257\) −277362. −0.261947 −0.130974 0.991386i \(-0.541810\pi\)
−0.130974 + 0.991386i \(0.541810\pi\)
\(258\) −577548. −0.540180
\(259\) −323155. −0.299338
\(260\) 267696. 0.245589
\(261\) 122715. 0.111506
\(262\) −859428. −0.773493
\(263\) 1.25996e6 1.12323 0.561615 0.827399i \(-0.310180\pi\)
0.561615 + 0.827399i \(0.310180\pi\)
\(264\) −451008. −0.398267
\(265\) 61182.0 0.0535191
\(266\) −280868. −0.243387
\(267\) 1.06396e6 0.913373
\(268\) 13664.0 0.0116209
\(269\) 1.77437e6 1.49508 0.747540 0.664217i \(-0.231235\pi\)
0.747540 + 0.664217i \(0.231235\pi\)
\(270\) −288684. −0.240998
\(271\) 509330. 0.421285 0.210643 0.977563i \(-0.432444\pi\)
0.210643 + 0.977563i \(0.432444\pi\)
\(272\) 8448.00 0.00692359
\(273\) 74529.0 0.0605228
\(274\) 831708. 0.669259
\(275\) 5.22731e6 4.16818
\(276\) −444528. −0.351258
\(277\) −418198. −0.327478 −0.163739 0.986504i \(-0.552356\pi\)
−0.163739 + 0.986504i \(0.552356\pi\)
\(278\) 925456. 0.718197
\(279\) 225180. 0.173189
\(280\) −310464. −0.236655
\(281\) −1.09383e6 −0.826388 −0.413194 0.910643i \(-0.635587\pi\)
−0.413194 + 0.910643i \(0.635587\pi\)
\(282\) −125280. −0.0938121
\(283\) 2.48145e6 1.84179 0.920894 0.389812i \(-0.127460\pi\)
0.920894 + 0.389812i \(0.127460\pi\)
\(284\) −757440. −0.557253
\(285\) 1.27680e6 0.931133
\(286\) −529308. −0.382643
\(287\) 214620. 0.153803
\(288\) −82944.0 −0.0589256
\(289\) −1.41877e6 −0.999233
\(290\) −599940. −0.418902
\(291\) −1.66070e6 −1.14963
\(292\) −1.03864e6 −0.712866
\(293\) 2.36297e6 1.60801 0.804007 0.594620i \(-0.202697\pi\)
0.804007 + 0.594620i \(0.202697\pi\)
\(294\) −86436.0 −0.0583212
\(295\) −5.15948e6 −3.45184
\(296\) 422080. 0.280005
\(297\) 570807. 0.375490
\(298\) −968688. −0.631893
\(299\) −521703. −0.337478
\(300\) 961344. 0.616702
\(301\) 786107. 0.500110
\(302\) −1.07296e6 −0.676967
\(303\) −796068. −0.498131
\(304\) 366848. 0.227668
\(305\) 87813.0 0.0540517
\(306\) −10692.0 −0.00652763
\(307\) −720880. −0.436533 −0.218266 0.975889i \(-0.570040\pi\)
−0.218266 + 0.975889i \(0.570040\pi\)
\(308\) 613872. 0.368724
\(309\) 29799.0 0.0177544
\(310\) −1.10088e6 −0.650632
\(311\) 691194. 0.405228 0.202614 0.979259i \(-0.435056\pi\)
0.202614 + 0.979259i \(0.435056\pi\)
\(312\) −97344.0 −0.0566139
\(313\) −2.26912e6 −1.30917 −0.654586 0.755988i \(-0.727157\pi\)
−0.654586 + 0.755988i \(0.727157\pi\)
\(314\) 1.36354e6 0.780448
\(315\) 392931. 0.223121
\(316\) −1.17251e6 −0.660541
\(317\) 2.29798e6 1.28439 0.642196 0.766541i \(-0.278024\pi\)
0.642196 + 0.766541i \(0.278024\pi\)
\(318\) −22248.0 −0.0123374
\(319\) 1.18624e6 0.652676
\(320\) 405504. 0.221371
\(321\) −611118. −0.331026
\(322\) 605052. 0.325202
\(323\) 47289.0 0.0252205
\(324\) 104976. 0.0555556
\(325\) 1.12824e6 0.592509
\(326\) 40888.0 0.0213085
\(327\) −44937.0 −0.0232399
\(328\) −280320. −0.143870
\(329\) 170520. 0.0868532
\(330\) −2.79061e6 −1.41063
\(331\) −2.47614e6 −1.24224 −0.621119 0.783716i \(-0.713322\pi\)
−0.621119 + 0.783716i \(0.713322\pi\)
\(332\) −1.55299e6 −0.773257
\(333\) −534195. −0.263991
\(334\) −1.59126e6 −0.780504
\(335\) 84546.0 0.0411605
\(336\) 112896. 0.0545545
\(337\) 2.35926e6 1.13162 0.565810 0.824535i \(-0.308563\pi\)
0.565810 + 0.824535i \(0.308563\pi\)
\(338\) −114244. −0.0543928
\(339\) 1.37122e6 0.648050
\(340\) 52272.0 0.0245229
\(341\) 2.17674e6 1.01373
\(342\) −464292. −0.214648
\(343\) 117649. 0.0539949
\(344\) −1.02675e6 −0.467810
\(345\) −2.75052e6 −1.24413
\(346\) 1.47554e6 0.662616
\(347\) −2.54144e6 −1.13307 −0.566535 0.824038i \(-0.691716\pi\)
−0.566535 + 0.824038i \(0.691716\pi\)
\(348\) 218160. 0.0965666
\(349\) −2.86368e6 −1.25852 −0.629261 0.777194i \(-0.716642\pi\)
−0.629261 + 0.777194i \(0.716642\pi\)
\(350\) −1.30850e6 −0.570956
\(351\) 123201. 0.0533761
\(352\) −801792. −0.344909
\(353\) 3.01156e6 1.28634 0.643169 0.765724i \(-0.277619\pi\)
0.643169 + 0.765724i \(0.277619\pi\)
\(354\) 1.87618e6 0.795729
\(355\) −4.68666e6 −1.97375
\(356\) 1.89149e6 0.791004
\(357\) 14553.0 0.00604341
\(358\) 807456. 0.332975
\(359\) 986448. 0.403960 0.201980 0.979390i \(-0.435262\pi\)
0.201980 + 0.979390i \(0.435262\pi\)
\(360\) −513216. −0.208710
\(361\) −422610. −0.170676
\(362\) −2.19284e6 −0.879499
\(363\) 4.06834e6 1.62051
\(364\) 132496. 0.0524142
\(365\) −6.42658e6 −2.52492
\(366\) −31932.0 −0.0124602
\(367\) 225392. 0.0873521 0.0436760 0.999046i \(-0.486093\pi\)
0.0436760 + 0.999046i \(0.486093\pi\)
\(368\) −790272. −0.304198
\(369\) 354780. 0.135642
\(370\) 2.61162e6 0.991758
\(371\) 30282.0 0.0114222
\(372\) 400320. 0.149986
\(373\) −286876. −0.106763 −0.0533817 0.998574i \(-0.517000\pi\)
−0.0533817 + 0.998574i \(0.517000\pi\)
\(374\) −103356. −0.0382082
\(375\) 3.16394e6 1.16185
\(376\) −222720. −0.0812437
\(377\) 256035. 0.0927782
\(378\) −142884. −0.0514344
\(379\) 4.67343e6 1.67124 0.835618 0.549311i \(-0.185110\pi\)
0.835618 + 0.549311i \(0.185110\pi\)
\(380\) 2.26987e6 0.806385
\(381\) −1.83512e6 −0.647667
\(382\) −1.16480e6 −0.408408
\(383\) −3.52635e6 −1.22837 −0.614185 0.789162i \(-0.710515\pi\)
−0.614185 + 0.789162i \(0.710515\pi\)
\(384\) −147456. −0.0510310
\(385\) 3.79833e6 1.30599
\(386\) 3.17330e6 1.08403
\(387\) 1.29948e6 0.441055
\(388\) −2.95235e6 −0.995609
\(389\) −2.84427e6 −0.953009 −0.476504 0.879172i \(-0.658096\pi\)
−0.476504 + 0.879172i \(0.658096\pi\)
\(390\) −602316. −0.200522
\(391\) −101871. −0.0336984
\(392\) −153664. −0.0505076
\(393\) 1.93371e6 0.631554
\(394\) −1.58472e6 −0.514295
\(395\) −7.25492e6 −2.33959
\(396\) 1.01477e6 0.325184
\(397\) −2.74727e6 −0.874832 −0.437416 0.899259i \(-0.644106\pi\)
−0.437416 + 0.899259i \(0.644106\pi\)
\(398\) −2.49736e6 −0.790268
\(399\) 631953. 0.198725
\(400\) 1.70906e6 0.534080
\(401\) −4.63621e6 −1.43980 −0.719899 0.694078i \(-0.755812\pi\)
−0.719899 + 0.694078i \(0.755812\pi\)
\(402\) −30744.0 −0.00948845
\(403\) 469820. 0.144102
\(404\) −1.41523e6 −0.431394
\(405\) 649539. 0.196774
\(406\) −296940. −0.0894033
\(407\) −5.16388e6 −1.54522
\(408\) −19008.0 −0.00565309
\(409\) −4.55465e6 −1.34631 −0.673157 0.739499i \(-0.735062\pi\)
−0.673157 + 0.739499i \(0.735062\pi\)
\(410\) −1.73448e6 −0.509577
\(411\) −1.87134e6 −0.546448
\(412\) 52976.0 0.0153757
\(413\) −2.55368e6 −0.736702
\(414\) 1.00019e6 0.286801
\(415\) −9.60914e6 −2.73882
\(416\) −173056. −0.0490290
\(417\) −2.08228e6 −0.586406
\(418\) −4.48816e6 −1.25640
\(419\) −2.01681e6 −0.561217 −0.280608 0.959822i \(-0.590536\pi\)
−0.280608 + 0.959822i \(0.590536\pi\)
\(420\) 698544. 0.193228
\(421\) 2.01148e6 0.553108 0.276554 0.960998i \(-0.410808\pi\)
0.276554 + 0.960998i \(0.410808\pi\)
\(422\) 848380. 0.231905
\(423\) 281880. 0.0765973
\(424\) −39552.0 −0.0106845
\(425\) 220308. 0.0591641
\(426\) 1.70424e6 0.454995
\(427\) 43463.0 0.0115359
\(428\) −1.08643e6 −0.286677
\(429\) 1.19094e6 0.312426
\(430\) −6.35303e6 −1.65695
\(431\) −3.13520e6 −0.812965 −0.406482 0.913659i \(-0.633245\pi\)
−0.406482 + 0.913659i \(0.633245\pi\)
\(432\) 186624. 0.0481125
\(433\) −3.90933e6 −1.00203 −0.501017 0.865438i \(-0.667041\pi\)
−0.501017 + 0.865438i \(0.667041\pi\)
\(434\) −544880. −0.138860
\(435\) 1.34986e6 0.342032
\(436\) −79888.0 −0.0201264
\(437\) −4.42367e6 −1.10810
\(438\) 2.33694e6 0.582053
\(439\) −3.44543e6 −0.853261 −0.426631 0.904426i \(-0.640300\pi\)
−0.426631 + 0.904426i \(0.640300\pi\)
\(440\) −4.96109e6 −1.22165
\(441\) 194481. 0.0476190
\(442\) −22308.0 −0.00543131
\(443\) −535350. −0.129607 −0.0648035 0.997898i \(-0.520642\pi\)
−0.0648035 + 0.997898i \(0.520642\pi\)
\(444\) −949680. −0.228623
\(445\) 1.17036e7 2.80168
\(446\) −3.78222e6 −0.900345
\(447\) 2.17955e6 0.515938
\(448\) 200704. 0.0472456
\(449\) 5.00800e6 1.17233 0.586164 0.810193i \(-0.300638\pi\)
0.586164 + 0.810193i \(0.300638\pi\)
\(450\) −2.16302e6 −0.503535
\(451\) 3.42954e6 0.793952
\(452\) 2.43773e6 0.561228
\(453\) 2.41417e6 0.552742
\(454\) −1.85090e6 −0.421448
\(455\) 819819. 0.185648
\(456\) −825408. −0.185890
\(457\) 938516. 0.210209 0.105104 0.994461i \(-0.466482\pi\)
0.105104 + 0.994461i \(0.466482\pi\)
\(458\) −3.01042e6 −0.670601
\(459\) 24057.0 0.00532979
\(460\) −4.88981e6 −1.07745
\(461\) −2.07095e6 −0.453855 −0.226928 0.973912i \(-0.572868\pi\)
−0.226928 + 0.973912i \(0.572868\pi\)
\(462\) −1.38121e6 −0.301062
\(463\) −4.38025e6 −0.949612 −0.474806 0.880091i \(-0.657482\pi\)
−0.474806 + 0.880091i \(0.657482\pi\)
\(464\) 387840. 0.0836291
\(465\) 2.47698e6 0.531239
\(466\) 2.95613e6 0.630607
\(467\) −1.66822e6 −0.353965 −0.176983 0.984214i \(-0.556634\pi\)
−0.176983 + 0.984214i \(0.556634\pi\)
\(468\) 219024. 0.0462250
\(469\) 41846.0 0.00878460
\(470\) −1.37808e6 −0.287760
\(471\) −3.06796e6 −0.637233
\(472\) 3.33542e6 0.689122
\(473\) 1.25617e7 2.58163
\(474\) 2.63815e6 0.539329
\(475\) 9.56671e6 1.94549
\(476\) 25872.0 0.00523375
\(477\) 50058.0 0.0100734
\(478\) 391008. 0.0782737
\(479\) 8.40532e6 1.67385 0.836923 0.547320i \(-0.184352\pi\)
0.836923 + 0.547320i \(0.184352\pi\)
\(480\) −912384. −0.180748
\(481\) −1.11456e6 −0.219654
\(482\) 4.93252e6 0.967055
\(483\) −1.36137e6 −0.265526
\(484\) 7.23261e6 1.40340
\(485\) −1.82677e7 −3.52638
\(486\) −236196. −0.0453609
\(487\) 5.45499e6 1.04225 0.521125 0.853481i \(-0.325513\pi\)
0.521125 + 0.853481i \(0.325513\pi\)
\(488\) −56768.0 −0.0107908
\(489\) −91998.0 −0.0173983
\(490\) −950796. −0.178895
\(491\) 9.07107e6 1.69807 0.849033 0.528339i \(-0.177185\pi\)
0.849033 + 0.528339i \(0.177185\pi\)
\(492\) 630720. 0.117469
\(493\) 49995.0 0.00926423
\(494\) −968708. −0.178598
\(495\) 6.27888e6 1.15178
\(496\) 711680. 0.129891
\(497\) −2.31966e6 −0.421244
\(498\) 3.49423e6 0.631362
\(499\) −4.62902e6 −0.832218 −0.416109 0.909315i \(-0.636607\pi\)
−0.416109 + 0.909315i \(0.636607\pi\)
\(500\) 5.62478e6 1.00619
\(501\) 3.58034e6 0.637279
\(502\) −792468. −0.140353
\(503\) 5.00935e6 0.882797 0.441399 0.897311i \(-0.354482\pi\)
0.441399 + 0.897311i \(0.354482\pi\)
\(504\) −254016. −0.0445435
\(505\) −8.75675e6 −1.52797
\(506\) 9.66848e6 1.67873
\(507\) 257049. 0.0444116
\(508\) −3.26243e6 −0.560896
\(509\) 7.66606e6 1.31153 0.655765 0.754965i \(-0.272346\pi\)
0.655765 + 0.754965i \(0.272346\pi\)
\(510\) −117612. −0.0200229
\(511\) −3.18084e6 −0.538876
\(512\) −262144. −0.0441942
\(513\) 1.04466e6 0.175259
\(514\) 1.10945e6 0.185225
\(515\) 327789. 0.0544598
\(516\) 2.31019e6 0.381965
\(517\) 2.72484e6 0.448347
\(518\) 1.29262e6 0.211664
\(519\) −3.31997e6 −0.541024
\(520\) −1.07078e6 −0.173657
\(521\) 5.43684e6 0.877511 0.438755 0.898607i \(-0.355419\pi\)
0.438755 + 0.898607i \(0.355419\pi\)
\(522\) −490860. −0.0788463
\(523\) 7.35759e6 1.17620 0.588100 0.808788i \(-0.299876\pi\)
0.588100 + 0.808788i \(0.299876\pi\)
\(524\) 3.43771e6 0.546942
\(525\) 2.94412e6 0.466183
\(526\) −5.03986e6 −0.794244
\(527\) 91740.0 0.0143891
\(528\) 1.80403e6 0.281617
\(529\) 3.09323e6 0.480588
\(530\) −244728. −0.0378437
\(531\) −4.22140e6 −0.649710
\(532\) 1.12347e6 0.172101
\(533\) 740220. 0.112861
\(534\) −4.25585e6 −0.645852
\(535\) −6.72230e6 −1.01539
\(536\) −54656.0 −0.00821724
\(537\) −1.81678e6 −0.271873
\(538\) −7.09750e6 −1.05718
\(539\) 1.87998e6 0.278729
\(540\) 1.15474e6 0.170411
\(541\) −4.05946e6 −0.596314 −0.298157 0.954517i \(-0.596372\pi\)
−0.298157 + 0.954517i \(0.596372\pi\)
\(542\) −2.03732e6 −0.297894
\(543\) 4.93389e6 0.718108
\(544\) −33792.0 −0.00489572
\(545\) −494307. −0.0712862
\(546\) −298116. −0.0427960
\(547\) 8.30563e6 1.18687 0.593436 0.804881i \(-0.297771\pi\)
0.593436 + 0.804881i \(0.297771\pi\)
\(548\) −3.32683e6 −0.473238
\(549\) 71847.0 0.0101737
\(550\) −2.09092e7 −2.94735
\(551\) 2.17100e6 0.304635
\(552\) 1.77811e6 0.248377
\(553\) −3.59082e6 −0.499322
\(554\) 1.67279e6 0.231562
\(555\) −5.87614e6 −0.809767
\(556\) −3.70182e6 −0.507842
\(557\) −7.21366e6 −0.985184 −0.492592 0.870260i \(-0.663951\pi\)
−0.492592 + 0.870260i \(0.663951\pi\)
\(558\) −900720. −0.122463
\(559\) 2.71127e6 0.366980
\(560\) 1.24186e6 0.167341
\(561\) 232551. 0.0311969
\(562\) 4.37532e6 0.584345
\(563\) 1.11052e7 1.47657 0.738287 0.674487i \(-0.235635\pi\)
0.738287 + 0.674487i \(0.235635\pi\)
\(564\) 501120. 0.0663352
\(565\) 1.50834e7 1.98783
\(566\) −9.92581e6 −1.30234
\(567\) 321489. 0.0419961
\(568\) 3.02976e6 0.394037
\(569\) 5.82358e6 0.754066 0.377033 0.926200i \(-0.376944\pi\)
0.377033 + 0.926200i \(0.376944\pi\)
\(570\) −5.10721e6 −0.658410
\(571\) 7.76146e6 0.996216 0.498108 0.867115i \(-0.334028\pi\)
0.498108 + 0.867115i \(0.334028\pi\)
\(572\) 2.11723e6 0.270569
\(573\) 2.62081e6 0.333464
\(574\) −858480. −0.108755
\(575\) −2.06088e7 −2.59946
\(576\) 331776. 0.0416667
\(577\) −5.02239e6 −0.628017 −0.314008 0.949420i \(-0.601672\pi\)
−0.314008 + 0.949420i \(0.601672\pi\)
\(578\) 5.67507e6 0.706564
\(579\) −7.13992e6 −0.885109
\(580\) 2.39976e6 0.296209
\(581\) −4.75604e6 −0.584528
\(582\) 6.64279e6 0.812911
\(583\) 483894. 0.0589629
\(584\) 4.15456e6 0.504072
\(585\) 1.35521e6 0.163726
\(586\) −9.45190e6 −1.13704
\(587\) −1.80400e6 −0.216094 −0.108047 0.994146i \(-0.534460\pi\)
−0.108047 + 0.994146i \(0.534460\pi\)
\(588\) 345744. 0.0412393
\(589\) 3.98374e6 0.473154
\(590\) 2.06379e7 2.44082
\(591\) 3.56562e6 0.419920
\(592\) −1.68832e6 −0.197993
\(593\) 167646. 0.0195775 0.00978873 0.999952i \(-0.496884\pi\)
0.00978873 + 0.999952i \(0.496884\pi\)
\(594\) −2.28323e6 −0.265511
\(595\) 160083. 0.0185376
\(596\) 3.87475e6 0.446816
\(597\) 5.61907e6 0.645251
\(598\) 2.08681e6 0.238633
\(599\) −1.46631e7 −1.66978 −0.834890 0.550417i \(-0.814469\pi\)
−0.834890 + 0.550417i \(0.814469\pi\)
\(600\) −3.84538e6 −0.436074
\(601\) 3.50773e6 0.396132 0.198066 0.980189i \(-0.436534\pi\)
0.198066 + 0.980189i \(0.436534\pi\)
\(602\) −3.14443e6 −0.353631
\(603\) 69174.0 0.00774729
\(604\) 4.29186e6 0.478688
\(605\) 4.47518e7 4.97075
\(606\) 3.18427e6 0.352232
\(607\) −1.63805e7 −1.80449 −0.902245 0.431223i \(-0.858082\pi\)
−0.902245 + 0.431223i \(0.858082\pi\)
\(608\) −1.46739e6 −0.160986
\(609\) 668115. 0.0729975
\(610\) −351252. −0.0382203
\(611\) 588120. 0.0637328
\(612\) 42768.0 0.00461573
\(613\) −1.75848e6 −0.189011 −0.0945054 0.995524i \(-0.530127\pi\)
−0.0945054 + 0.995524i \(0.530127\pi\)
\(614\) 2.88352e6 0.308675
\(615\) 3.90258e6 0.416068
\(616\) −2.45549e6 −0.260727
\(617\) 9.99581e6 1.05707 0.528537 0.848910i \(-0.322741\pi\)
0.528537 + 0.848910i \(0.322741\pi\)
\(618\) −119196. −0.0125542
\(619\) −9.36392e6 −0.982270 −0.491135 0.871083i \(-0.663418\pi\)
−0.491135 + 0.871083i \(0.663418\pi\)
\(620\) 4.40352e6 0.460067
\(621\) −2.25042e6 −0.234172
\(622\) −2.76478e6 −0.286539
\(623\) 5.79268e6 0.597943
\(624\) 389376. 0.0400320
\(625\) 1.39409e7 1.42754
\(626\) 9.07648e6 0.925724
\(627\) 1.00984e7 1.02584
\(628\) −5.45416e6 −0.551860
\(629\) −217635. −0.0219332
\(630\) −1.57172e6 −0.157770
\(631\) −1.26052e7 −1.26031 −0.630155 0.776469i \(-0.717009\pi\)
−0.630155 + 0.776469i \(0.717009\pi\)
\(632\) 4.69005e6 0.467073
\(633\) −1.90886e6 −0.189349
\(634\) −9.19190e6 −0.908202
\(635\) −2.01863e7 −1.98665
\(636\) 88992.0 0.00872385
\(637\) 405769. 0.0396214
\(638\) −4.74498e6 −0.461512
\(639\) −3.83454e6 −0.371502
\(640\) −1.62202e6 −0.156533
\(641\) −1.56405e7 −1.50351 −0.751756 0.659442i \(-0.770793\pi\)
−0.751756 + 0.659442i \(0.770793\pi\)
\(642\) 2.44447e6 0.234071
\(643\) −1.45253e6 −0.138547 −0.0692735 0.997598i \(-0.522068\pi\)
−0.0692735 + 0.997598i \(0.522068\pi\)
\(644\) −2.42021e6 −0.229952
\(645\) 1.42943e7 1.35289
\(646\) −189156. −0.0178336
\(647\) 1.28264e7 1.20460 0.602301 0.798269i \(-0.294251\pi\)
0.602301 + 0.798269i \(0.294251\pi\)
\(648\) −419904. −0.0392837
\(649\) −4.08068e7 −3.80295
\(650\) −4.51298e6 −0.418967
\(651\) 1.22598e6 0.113379
\(652\) −163552. −0.0150673
\(653\) −3.88644e6 −0.356672 −0.178336 0.983970i \(-0.557071\pi\)
−0.178336 + 0.983970i \(0.557071\pi\)
\(654\) 179748. 0.0164331
\(655\) 2.12708e7 1.93723
\(656\) 1.12128e6 0.101731
\(657\) −5.25812e6 −0.475244
\(658\) −682080. −0.0614145
\(659\) −6.80296e6 −0.610217 −0.305109 0.952318i \(-0.598693\pi\)
−0.305109 + 0.952318i \(0.598693\pi\)
\(660\) 1.11624e7 0.997469
\(661\) 1.36404e7 1.21429 0.607146 0.794590i \(-0.292314\pi\)
0.607146 + 0.794590i \(0.292314\pi\)
\(662\) 9.90455e6 0.878395
\(663\) 50193.0 0.00443465
\(664\) 6.21197e6 0.546775
\(665\) 6.95148e6 0.609570
\(666\) 2.13678e6 0.186670
\(667\) −4.67680e6 −0.407038
\(668\) 6.36504e6 0.551899
\(669\) 8.50999e6 0.735129
\(670\) −338184. −0.0291049
\(671\) 694521. 0.0595496
\(672\) −451584. −0.0385758
\(673\) −1.86150e7 −1.58426 −0.792128 0.610355i \(-0.791027\pi\)
−0.792128 + 0.610355i \(0.791027\pi\)
\(674\) −9.43704e6 −0.800177
\(675\) 4.86680e6 0.411135
\(676\) 456976. 0.0384615
\(677\) −7.31919e6 −0.613750 −0.306875 0.951750i \(-0.599283\pi\)
−0.306875 + 0.951750i \(0.599283\pi\)
\(678\) −5.48489e6 −0.458241
\(679\) −9.04158e6 −0.752610
\(680\) −209088. −0.0173403
\(681\) 4.16453e6 0.344111
\(682\) −8.70696e6 −0.716813
\(683\) 4.87742e6 0.400072 0.200036 0.979789i \(-0.435894\pi\)
0.200036 + 0.979789i \(0.435894\pi\)
\(684\) 1.85717e6 0.151779
\(685\) −2.05848e7 −1.67618
\(686\) −470596. −0.0381802
\(687\) 6.77345e6 0.547543
\(688\) 4.10701e6 0.330792
\(689\) 104442. 0.00838160
\(690\) 1.10021e7 0.879734
\(691\) 9.38815e6 0.747971 0.373986 0.927435i \(-0.377991\pi\)
0.373986 + 0.927435i \(0.377991\pi\)
\(692\) −5.90218e6 −0.468540
\(693\) 3.10773e6 0.245816
\(694\) 1.01658e7 0.801202
\(695\) −2.29050e7 −1.79874
\(696\) −872640. −0.0682829
\(697\) 144540. 0.0112695
\(698\) 1.14547e7 0.889909
\(699\) −6.65129e6 −0.514888
\(700\) 5.23398e6 0.403727
\(701\) −3.88816e6 −0.298847 −0.149424 0.988773i \(-0.547742\pi\)
−0.149424 + 0.988773i \(0.547742\pi\)
\(702\) −492804. −0.0377426
\(703\) −9.45064e6 −0.721228
\(704\) 3.20717e6 0.243888
\(705\) 3.10068e6 0.234955
\(706\) −1.20462e7 −0.909578
\(707\) −4.33415e6 −0.326103
\(708\) −7.50470e6 −0.562666
\(709\) 2.00356e6 0.149688 0.0748439 0.997195i \(-0.476154\pi\)
0.0748439 + 0.997195i \(0.476154\pi\)
\(710\) 1.87466e7 1.39565
\(711\) −5.93584e6 −0.440360
\(712\) −7.56595e6 −0.559324
\(713\) −8.58186e6 −0.632205
\(714\) −58212.0 −0.00427334
\(715\) 1.31004e7 0.958338
\(716\) −3.22982e6 −0.235449
\(717\) −879768. −0.0639102
\(718\) −3.94579e6 −0.285643
\(719\) 1.27107e7 0.916950 0.458475 0.888707i \(-0.348396\pi\)
0.458475 + 0.888707i \(0.348396\pi\)
\(720\) 2.05286e6 0.147580
\(721\) 162239. 0.0116230
\(722\) 1.69044e6 0.120686
\(723\) −1.10982e7 −0.789597
\(724\) 8.77136e6 0.621900
\(725\) 1.01141e7 0.714634
\(726\) −1.62734e7 −1.14587
\(727\) 1.38863e7 0.974432 0.487216 0.873281i \(-0.338012\pi\)
0.487216 + 0.873281i \(0.338012\pi\)
\(728\) −529984. −0.0370625
\(729\) 531441. 0.0370370
\(730\) 2.57063e7 1.78539
\(731\) 529419. 0.0366443
\(732\) 127728. 0.00881066
\(733\) −2.87911e7 −1.97924 −0.989621 0.143703i \(-0.954099\pi\)
−0.989621 + 0.143703i \(0.954099\pi\)
\(734\) −901568. −0.0617673
\(735\) 2.13929e6 0.146067
\(736\) 3.16109e6 0.215101
\(737\) 668682. 0.0453472
\(738\) −1.41912e6 −0.0959132
\(739\) 2.79137e7 1.88021 0.940106 0.340884i \(-0.110726\pi\)
0.940106 + 0.340884i \(0.110726\pi\)
\(740\) −1.04465e7 −0.701279
\(741\) 2.17959e6 0.145824
\(742\) −121128. −0.00807672
\(743\) −1.77697e7 −1.18089 −0.590444 0.807078i \(-0.701047\pi\)
−0.590444 + 0.807078i \(0.701047\pi\)
\(744\) −1.60128e6 −0.106056
\(745\) 2.39750e7 1.58259
\(746\) 1.14750e6 0.0754931
\(747\) −7.86202e6 −0.515505
\(748\) 413424. 0.0270173
\(749\) −3.32720e6 −0.216708
\(750\) −1.26558e7 −0.821552
\(751\) 1.74520e7 1.12913 0.564566 0.825388i \(-0.309043\pi\)
0.564566 + 0.825388i \(0.309043\pi\)
\(752\) 890880. 0.0574480
\(753\) 1.78305e6 0.114598
\(754\) −1.02414e6 −0.0656041
\(755\) 2.65559e7 1.69548
\(756\) 571536. 0.0363696
\(757\) 1.27070e7 0.805938 0.402969 0.915214i \(-0.367978\pi\)
0.402969 + 0.915214i \(0.367978\pi\)
\(758\) −1.86937e7 −1.18174
\(759\) −2.17541e7 −1.37068
\(760\) −9.07949e6 −0.570200
\(761\) 9.75769e6 0.610781 0.305390 0.952227i \(-0.401213\pi\)
0.305390 + 0.952227i \(0.401213\pi\)
\(762\) 7.34047e6 0.457970
\(763\) −244657. −0.0152141
\(764\) 4.65922e6 0.288788
\(765\) 264627. 0.0163486
\(766\) 1.41054e7 0.868588
\(767\) −8.80760e6 −0.540592
\(768\) 589824. 0.0360844
\(769\) 2.53703e7 1.54707 0.773534 0.633755i \(-0.218487\pi\)
0.773534 + 0.633755i \(0.218487\pi\)
\(770\) −1.51933e7 −0.923477
\(771\) −2.49626e6 −0.151235
\(772\) −1.26932e7 −0.766527
\(773\) 4.54316e6 0.273470 0.136735 0.990608i \(-0.456339\pi\)
0.136735 + 0.990608i \(0.456339\pi\)
\(774\) −5.19793e6 −0.311873
\(775\) 1.85593e7 1.10996
\(776\) 1.18094e7 0.704002
\(777\) −2.90840e6 −0.172823
\(778\) 1.13771e7 0.673879
\(779\) 6.27654e6 0.370575
\(780\) 2.40926e6 0.141791
\(781\) −3.70672e7 −2.17452
\(782\) 407484. 0.0238283
\(783\) 1.10444e6 0.0643777
\(784\) 614656. 0.0357143
\(785\) −3.37476e7 −1.95465
\(786\) −7.73485e6 −0.446576
\(787\) −2.17187e7 −1.24996 −0.624982 0.780639i \(-0.714894\pi\)
−0.624982 + 0.780639i \(0.714894\pi\)
\(788\) 6.33888e6 0.363661
\(789\) 1.13397e7 0.648497
\(790\) 2.90197e7 1.65434
\(791\) 7.46554e6 0.424248
\(792\) −4.05907e6 −0.229940
\(793\) 149903. 0.00846501
\(794\) 1.09891e7 0.618599
\(795\) 550638. 0.0308993
\(796\) 9.98946e6 0.558804
\(797\) −1.12329e7 −0.626395 −0.313197 0.949688i \(-0.601400\pi\)
−0.313197 + 0.949688i \(0.601400\pi\)
\(798\) −2.52781e6 −0.140520
\(799\) 114840. 0.00636394
\(800\) −6.83622e6 −0.377652
\(801\) 9.57566e6 0.527336
\(802\) 1.85448e7 1.01809
\(803\) −5.08284e7 −2.78175
\(804\) 122976. 0.00670935
\(805\) −1.49750e7 −0.814476
\(806\) −1.87928e6 −0.101895
\(807\) 1.59694e7 0.863185
\(808\) 5.66093e6 0.305042
\(809\) −3.51542e7 −1.88845 −0.944226 0.329298i \(-0.893188\pi\)
−0.944226 + 0.329298i \(0.893188\pi\)
\(810\) −2.59816e6 −0.139140
\(811\) −3.15188e7 −1.68274 −0.841372 0.540457i \(-0.818252\pi\)
−0.841372 + 0.540457i \(0.818252\pi\)
\(812\) 1.18776e6 0.0632177
\(813\) 4.58397e6 0.243229
\(814\) 2.06555e7 1.09264
\(815\) −1.01198e6 −0.0533675
\(816\) 76032.0 0.00399734
\(817\) 2.29896e7 1.20497
\(818\) 1.82186e7 0.951988
\(819\) 670761. 0.0349428
\(820\) 6.93792e6 0.360325
\(821\) 1.58199e7 0.819115 0.409557 0.912284i \(-0.365683\pi\)
0.409557 + 0.912284i \(0.365683\pi\)
\(822\) 7.48537e6 0.386397
\(823\) 1.51130e7 0.777771 0.388886 0.921286i \(-0.372860\pi\)
0.388886 + 0.921286i \(0.372860\pi\)
\(824\) −211904. −0.0108723
\(825\) 4.70458e7 2.40650
\(826\) 1.02147e7 0.520927
\(827\) 4.27161e6 0.217184 0.108592 0.994086i \(-0.465366\pi\)
0.108592 + 0.994086i \(0.465366\pi\)
\(828\) −4.00075e6 −0.202799
\(829\) −2.64597e7 −1.33721 −0.668603 0.743620i \(-0.733107\pi\)
−0.668603 + 0.743620i \(0.733107\pi\)
\(830\) 3.84366e7 1.93664
\(831\) −3.76378e6 −0.189070
\(832\) 692224. 0.0346688
\(833\) 79233.0 0.00395634
\(834\) 8.32910e6 0.414651
\(835\) 3.93837e7 1.95479
\(836\) 1.79526e7 0.888408
\(837\) 2.02662e6 0.0999905
\(838\) 8.06725e6 0.396840
\(839\) −2.49933e7 −1.22580 −0.612900 0.790161i \(-0.709997\pi\)
−0.612900 + 0.790161i \(0.709997\pi\)
\(840\) −2.79418e6 −0.136633
\(841\) −1.82159e7 −0.888099
\(842\) −8.04591e6 −0.391107
\(843\) −9.84447e6 −0.477115
\(844\) −3.39352e6 −0.163981
\(845\) 2.82754e6 0.136228
\(846\) −1.12752e6 −0.0541625
\(847\) 2.21499e7 1.06087
\(848\) 158208. 0.00755508
\(849\) 2.23331e7 1.06336
\(850\) −881232. −0.0418353
\(851\) 2.03588e7 0.963668
\(852\) −6.81696e6 −0.321730
\(853\) 1.10142e7 0.518299 0.259149 0.965837i \(-0.416558\pi\)
0.259149 + 0.965837i \(0.416558\pi\)
\(854\) −173852. −0.00815709
\(855\) 1.14912e7 0.537590
\(856\) 4.34573e6 0.202711
\(857\) 1.63028e7 0.758244 0.379122 0.925347i \(-0.376226\pi\)
0.379122 + 0.925347i \(0.376226\pi\)
\(858\) −4.76377e6 −0.220919
\(859\) 934172. 0.0431960 0.0215980 0.999767i \(-0.493125\pi\)
0.0215980 + 0.999767i \(0.493125\pi\)
\(860\) 2.54121e7 1.17164
\(861\) 1.93158e6 0.0887983
\(862\) 1.25408e7 0.574853
\(863\) 3.36625e6 0.153858 0.0769288 0.997037i \(-0.475489\pi\)
0.0769288 + 0.997037i \(0.475489\pi\)
\(864\) −746496. −0.0340207
\(865\) −3.65197e7 −1.65954
\(866\) 1.56373e7 0.708545
\(867\) −1.27689e7 −0.576907
\(868\) 2.17952e6 0.0981887
\(869\) −5.73798e7 −2.57757
\(870\) −5.39946e6 −0.241853
\(871\) 144326. 0.00644613
\(872\) 319552. 0.0142315
\(873\) −1.49463e7 −0.663739
\(874\) 1.76947e7 0.783546
\(875\) 1.72259e7 0.760610
\(876\) −9.34776e6 −0.411573
\(877\) −2.78648e7 −1.22337 −0.611684 0.791102i \(-0.709508\pi\)
−0.611684 + 0.791102i \(0.709508\pi\)
\(878\) 1.37817e7 0.603347
\(879\) 2.12668e7 0.928387
\(880\) 1.98444e7 0.863834
\(881\) 1.76751e7 0.767223 0.383611 0.923495i \(-0.374680\pi\)
0.383611 + 0.923495i \(0.374680\pi\)
\(882\) −777924. −0.0336718
\(883\) 1.80758e7 0.780183 0.390091 0.920776i \(-0.372443\pi\)
0.390091 + 0.920776i \(0.372443\pi\)
\(884\) 89232.0 0.00384052
\(885\) −4.64354e7 −1.99292
\(886\) 2.14140e6 0.0916460
\(887\) −2.04628e7 −0.873285 −0.436642 0.899635i \(-0.643833\pi\)
−0.436642 + 0.899635i \(0.643833\pi\)
\(888\) 3.79872e6 0.161661
\(889\) −9.99120e6 −0.423997
\(890\) −4.68143e7 −1.98109
\(891\) 5.13726e6 0.216789
\(892\) 1.51289e7 0.636640
\(893\) 4.98684e6 0.209265
\(894\) −8.71819e6 −0.364823
\(895\) −1.99845e7 −0.833943
\(896\) −802816. −0.0334077
\(897\) −4.69533e6 −0.194843
\(898\) −2.00320e7 −0.828961
\(899\) 4.21170e6 0.173803
\(900\) 8.65210e6 0.356053
\(901\) 20394.0 0.000836933 0
\(902\) −1.37182e7 −0.561409
\(903\) 7.07496e6 0.288739
\(904\) −9.75091e6 −0.396848
\(905\) 5.42728e7 2.20273
\(906\) −9.65668e6 −0.390847
\(907\) 3.60854e7 1.45651 0.728254 0.685307i \(-0.240332\pi\)
0.728254 + 0.685307i \(0.240332\pi\)
\(908\) 7.40362e6 0.298009
\(909\) −7.16461e6 −0.287596
\(910\) −3.27928e6 −0.131273
\(911\) −155841. −0.00622137 −0.00311068 0.999995i \(-0.500990\pi\)
−0.00311068 + 0.999995i \(0.500990\pi\)
\(912\) 3.30163e6 0.131444
\(913\) −7.59995e7 −3.01741
\(914\) −3.75406e6 −0.148640
\(915\) 790317. 0.0312068
\(916\) 1.20417e7 0.474186
\(917\) 1.05280e7 0.413449
\(918\) −96228.0 −0.00376873
\(919\) −4.09049e7 −1.59767 −0.798834 0.601552i \(-0.794549\pi\)
−0.798834 + 0.601552i \(0.794549\pi\)
\(920\) 1.95592e7 0.761872
\(921\) −6.48792e6 −0.252032
\(922\) 8.28380e6 0.320924
\(923\) −8.00046e6 −0.309108
\(924\) 5.52485e6 0.212883
\(925\) −4.40282e7 −1.69191
\(926\) 1.75210e7 0.671477
\(927\) 268191. 0.0102505
\(928\) −1.55136e6 −0.0591347
\(929\) 1.22573e7 0.465969 0.232984 0.972480i \(-0.425151\pi\)
0.232984 + 0.972480i \(0.425151\pi\)
\(930\) −9.90792e6 −0.375643
\(931\) 3.44063e6 0.130096
\(932\) −1.18245e7 −0.445906
\(933\) 6.22075e6 0.233958
\(934\) 6.67288e6 0.250291
\(935\) 2.55806e6 0.0956934
\(936\) −876096. −0.0326860
\(937\) −3.08207e7 −1.14682 −0.573408 0.819270i \(-0.694379\pi\)
−0.573408 + 0.819270i \(0.694379\pi\)
\(938\) −167384. −0.00621165
\(939\) −2.04221e7 −0.755851
\(940\) 5.51232e6 0.203477
\(941\) 2.11450e7 0.778456 0.389228 0.921141i \(-0.372742\pi\)
0.389228 + 0.921141i \(0.372742\pi\)
\(942\) 1.22719e7 0.450592
\(943\) −1.35211e7 −0.495144
\(944\) −1.33417e7 −0.487283
\(945\) 3.53638e6 0.128819
\(946\) −5.02467e7 −1.82549
\(947\) 1.97293e7 0.714888 0.357444 0.933935i \(-0.383648\pi\)
0.357444 + 0.933935i \(0.383648\pi\)
\(948\) −1.05526e7 −0.381363
\(949\) −1.09706e7 −0.395427
\(950\) −3.82668e7 −1.37567
\(951\) 2.06818e7 0.741544
\(952\) −103488. −0.00370082
\(953\) −2.94280e7 −1.04961 −0.524805 0.851222i \(-0.675862\pi\)
−0.524805 + 0.851222i \(0.675862\pi\)
\(954\) −200232. −0.00712299
\(955\) 2.88289e7 1.02287
\(956\) −1.56403e6 −0.0553479
\(957\) 1.06762e7 0.376823
\(958\) −3.36213e7 −1.18359
\(959\) −1.01884e7 −0.357734
\(960\) 3.64954e6 0.127808
\(961\) −2.09008e7 −0.730051
\(962\) 4.45822e6 0.155319
\(963\) −5.50006e6 −0.191118
\(964\) −1.97301e7 −0.683811
\(965\) −7.85391e7 −2.71499
\(966\) 5.44547e6 0.187755
\(967\) 7.79389e6 0.268033 0.134016 0.990979i \(-0.457212\pi\)
0.134016 + 0.990979i \(0.457212\pi\)
\(968\) −2.89304e7 −0.992354
\(969\) 425601. 0.0145611
\(970\) 7.30707e7 2.49353
\(971\) −2.24472e7 −0.764038 −0.382019 0.924154i \(-0.624771\pi\)
−0.382019 + 0.924154i \(0.624771\pi\)
\(972\) 944784. 0.0320750
\(973\) −1.13368e7 −0.383893
\(974\) −2.18200e7 −0.736982
\(975\) 1.01542e7 0.342085
\(976\) 227072. 0.00763025
\(977\) −5.22839e6 −0.175239 −0.0876196 0.996154i \(-0.527926\pi\)
−0.0876196 + 0.996154i \(0.527926\pi\)
\(978\) 367992. 0.0123024
\(979\) 9.25647e7 3.08666
\(980\) 3.80318e6 0.126498
\(981\) −404433. −0.0134176
\(982\) −3.62843e7 −1.20071
\(983\) −4.36835e7 −1.44190 −0.720948 0.692990i \(-0.756293\pi\)
−0.720948 + 0.692990i \(0.756293\pi\)
\(984\) −2.52288e6 −0.0830632
\(985\) 3.92218e7 1.28806
\(986\) −199980. −0.00655080
\(987\) 1.53468e6 0.0501447
\(988\) 3.87483e6 0.126288
\(989\) −4.95247e7 −1.61002
\(990\) −2.51155e7 −0.814430
\(991\) 1.79892e7 0.581874 0.290937 0.956742i \(-0.406033\pi\)
0.290937 + 0.956742i \(0.406033\pi\)
\(992\) −2.84672e6 −0.0918471
\(993\) −2.22852e7 −0.717207
\(994\) 9.27864e6 0.297864
\(995\) 6.18098e7 1.97924
\(996\) −1.39769e7 −0.446440
\(997\) 1.70256e7 0.542456 0.271228 0.962515i \(-0.412570\pi\)
0.271228 + 0.962515i \(0.412570\pi\)
\(998\) 1.85161e7 0.588467
\(999\) −4.80776e6 −0.152415
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.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.6.a.b.1.1 1 1.1 even 1 trivial