Properties

Label 490.6.a.j.1.1
Level 490
Weight 6
Character 490.1
Self dual yes
Analytic conductor 78.588
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 490.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(78.5880717084\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 10)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 490.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +26.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -104.000 q^{6} -64.0000 q^{8} +433.000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +26.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -104.000 q^{6} -64.0000 q^{8} +433.000 q^{9} -100.000 q^{10} -768.000 q^{11} +416.000 q^{12} +46.0000 q^{13} +650.000 q^{15} +256.000 q^{16} -378.000 q^{17} -1732.00 q^{18} -1100.00 q^{19} +400.000 q^{20} +3072.00 q^{22} -1986.00 q^{23} -1664.00 q^{24} +625.000 q^{25} -184.000 q^{26} +4940.00 q^{27} -5610.00 q^{29} -2600.00 q^{30} +3988.00 q^{31} -1024.00 q^{32} -19968.0 q^{33} +1512.00 q^{34} +6928.00 q^{36} -142.000 q^{37} +4400.00 q^{38} +1196.00 q^{39} -1600.00 q^{40} -1542.00 q^{41} -5026.00 q^{43} -12288.0 q^{44} +10825.0 q^{45} +7944.00 q^{46} -24738.0 q^{47} +6656.00 q^{48} -2500.00 q^{50} -9828.00 q^{51} +736.000 q^{52} -14166.0 q^{53} -19760.0 q^{54} -19200.0 q^{55} -28600.0 q^{57} +22440.0 q^{58} -28380.0 q^{59} +10400.0 q^{60} -5522.00 q^{61} -15952.0 q^{62} +4096.00 q^{64} +1150.00 q^{65} +79872.0 q^{66} -24742.0 q^{67} -6048.00 q^{68} -51636.0 q^{69} +42372.0 q^{71} -27712.0 q^{72} +52126.0 q^{73} +568.000 q^{74} +16250.0 q^{75} -17600.0 q^{76} -4784.00 q^{78} -39640.0 q^{79} +6400.00 q^{80} +23221.0 q^{81} +6168.00 q^{82} +59826.0 q^{83} -9450.00 q^{85} +20104.0 q^{86} -145860. q^{87} +49152.0 q^{88} -57690.0 q^{89} -43300.0 q^{90} -31776.0 q^{92} +103688. q^{93} +98952.0 q^{94} -27500.0 q^{95} -26624.0 q^{96} +144382. q^{97} -332544. q^{99} +O(q^{100})\)

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
\(3\) 26.0000 1.66790 0.833950 0.551839i \(-0.186074\pi\)
0.833950 + 0.551839i \(0.186074\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −104.000 −1.17938
\(7\) 0 0
\(8\) −64.0000 −0.353553
\(9\) 433.000 1.78189
\(10\) −100.000 −0.316228
\(11\) −768.000 −1.91372 −0.956862 0.290541i \(-0.906165\pi\)
−0.956862 + 0.290541i \(0.906165\pi\)
\(12\) 416.000 0.833950
\(13\) 46.0000 0.0754917 0.0377459 0.999287i \(-0.487982\pi\)
0.0377459 + 0.999287i \(0.487982\pi\)
\(14\) 0 0
\(15\) 650.000 0.745908
\(16\) 256.000 0.250000
\(17\) −378.000 −0.317227 −0.158613 0.987341i \(-0.550702\pi\)
−0.158613 + 0.987341i \(0.550702\pi\)
\(18\) −1732.00 −1.25999
\(19\) −1100.00 −0.699051 −0.349525 0.936927i \(-0.613657\pi\)
−0.349525 + 0.936927i \(0.613657\pi\)
\(20\) 400.000 0.223607
\(21\) 0 0
\(22\) 3072.00 1.35321
\(23\) −1986.00 −0.782816 −0.391408 0.920217i \(-0.628012\pi\)
−0.391408 + 0.920217i \(0.628012\pi\)
\(24\) −1664.00 −0.589692
\(25\) 625.000 0.200000
\(26\) −184.000 −0.0533807
\(27\) 4940.00 1.30412
\(28\) 0 0
\(29\) −5610.00 −1.23870 −0.619352 0.785113i \(-0.712605\pi\)
−0.619352 + 0.785113i \(0.712605\pi\)
\(30\) −2600.00 −0.527437
\(31\) 3988.00 0.745334 0.372667 0.927965i \(-0.378443\pi\)
0.372667 + 0.927965i \(0.378443\pi\)
\(32\) −1024.00 −0.176777
\(33\) −19968.0 −3.19190
\(34\) 1512.00 0.224313
\(35\) 0 0
\(36\) 6928.00 0.890947
\(37\) −142.000 −0.0170523 −0.00852617 0.999964i \(-0.502714\pi\)
−0.00852617 + 0.999964i \(0.502714\pi\)
\(38\) 4400.00 0.494303
\(39\) 1196.00 0.125913
\(40\) −1600.00 −0.158114
\(41\) −1542.00 −0.143260 −0.0716300 0.997431i \(-0.522820\pi\)
−0.0716300 + 0.997431i \(0.522820\pi\)
\(42\) 0 0
\(43\) −5026.00 −0.414526 −0.207263 0.978285i \(-0.566456\pi\)
−0.207263 + 0.978285i \(0.566456\pi\)
\(44\) −12288.0 −0.956862
\(45\) 10825.0 0.796887
\(46\) 7944.00 0.553534
\(47\) −24738.0 −1.63350 −0.816752 0.576990i \(-0.804227\pi\)
−0.816752 + 0.576990i \(0.804227\pi\)
\(48\) 6656.00 0.416975
\(49\) 0 0
\(50\) −2500.00 −0.141421
\(51\) −9828.00 −0.529102
\(52\) 736.000 0.0377459
\(53\) −14166.0 −0.692720 −0.346360 0.938102i \(-0.612582\pi\)
−0.346360 + 0.938102i \(0.612582\pi\)
\(54\) −19760.0 −0.922152
\(55\) −19200.0 −0.855844
\(56\) 0 0
\(57\) −28600.0 −1.16595
\(58\) 22440.0 0.875897
\(59\) −28380.0 −1.06141 −0.530704 0.847557i \(-0.678072\pi\)
−0.530704 + 0.847557i \(0.678072\pi\)
\(60\) 10400.0 0.372954
\(61\) −5522.00 −0.190008 −0.0950040 0.995477i \(-0.530286\pi\)
−0.0950040 + 0.995477i \(0.530286\pi\)
\(62\) −15952.0 −0.527031
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 1150.00 0.0337609
\(66\) 79872.0 2.25702
\(67\) −24742.0 −0.673361 −0.336680 0.941619i \(-0.609304\pi\)
−0.336680 + 0.941619i \(0.609304\pi\)
\(68\) −6048.00 −0.158613
\(69\) −51636.0 −1.30566
\(70\) 0 0
\(71\) 42372.0 0.997546 0.498773 0.866733i \(-0.333784\pi\)
0.498773 + 0.866733i \(0.333784\pi\)
\(72\) −27712.0 −0.629994
\(73\) 52126.0 1.14485 0.572423 0.819958i \(-0.306003\pi\)
0.572423 + 0.819958i \(0.306003\pi\)
\(74\) 568.000 0.0120578
\(75\) 16250.0 0.333580
\(76\) −17600.0 −0.349525
\(77\) 0 0
\(78\) −4784.00 −0.0890337
\(79\) −39640.0 −0.714605 −0.357302 0.933989i \(-0.616303\pi\)
−0.357302 + 0.933989i \(0.616303\pi\)
\(80\) 6400.00 0.111803
\(81\) 23221.0 0.393250
\(82\) 6168.00 0.101300
\(83\) 59826.0 0.953223 0.476612 0.879114i \(-0.341865\pi\)
0.476612 + 0.879114i \(0.341865\pi\)
\(84\) 0 0
\(85\) −9450.00 −0.141868
\(86\) 20104.0 0.293114
\(87\) −145860. −2.06604
\(88\) 49152.0 0.676604
\(89\) −57690.0 −0.772015 −0.386007 0.922496i \(-0.626146\pi\)
−0.386007 + 0.922496i \(0.626146\pi\)
\(90\) −43300.0 −0.563484
\(91\) 0 0
\(92\) −31776.0 −0.391408
\(93\) 103688. 1.24314
\(94\) 98952.0 1.15506
\(95\) −27500.0 −0.312625
\(96\) −26624.0 −0.294846
\(97\) 144382. 1.55806 0.779029 0.626988i \(-0.215712\pi\)
0.779029 + 0.626988i \(0.215712\pi\)
\(98\) 0 0
\(99\) −332544. −3.41005
\(100\) 10000.0 0.100000
\(101\) 141258. 1.37787 0.688937 0.724821i \(-0.258078\pi\)
0.688937 + 0.724821i \(0.258078\pi\)
\(102\) 39312.0 0.374132
\(103\) −139814. −1.29855 −0.649273 0.760555i \(-0.724927\pi\)
−0.649273 + 0.760555i \(0.724927\pi\)
\(104\) −2944.00 −0.0266904
\(105\) 0 0
\(106\) 56664.0 0.489827
\(107\) 86418.0 0.729701 0.364850 0.931066i \(-0.381120\pi\)
0.364850 + 0.931066i \(0.381120\pi\)
\(108\) 79040.0 0.652060
\(109\) 218450. 1.76111 0.880554 0.473947i \(-0.157171\pi\)
0.880554 + 0.473947i \(0.157171\pi\)
\(110\) 76800.0 0.605173
\(111\) −3692.00 −0.0284416
\(112\) 0 0
\(113\) −28806.0 −0.212220 −0.106110 0.994354i \(-0.533840\pi\)
−0.106110 + 0.994354i \(0.533840\pi\)
\(114\) 114400. 0.824449
\(115\) −49650.0 −0.350086
\(116\) −89760.0 −0.619352
\(117\) 19918.0 0.134518
\(118\) 113520. 0.750529
\(119\) 0 0
\(120\) −41600.0 −0.263718
\(121\) 428773. 2.66234
\(122\) 22088.0 0.134356
\(123\) −40092.0 −0.238943
\(124\) 63808.0 0.372667
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −216502. −1.19111 −0.595556 0.803314i \(-0.703068\pi\)
−0.595556 + 0.803314i \(0.703068\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −130676. −0.691388
\(130\) −4600.00 −0.0238726
\(131\) 244608. 1.24535 0.622676 0.782479i \(-0.286045\pi\)
0.622676 + 0.782479i \(0.286045\pi\)
\(132\) −319488. −1.59595
\(133\) 0 0
\(134\) 98968.0 0.476138
\(135\) 123500. 0.583220
\(136\) 24192.0 0.112157
\(137\) −239502. −1.09020 −0.545102 0.838370i \(-0.683509\pi\)
−0.545102 + 0.838370i \(0.683509\pi\)
\(138\) 206544. 0.923241
\(139\) −30860.0 −0.135475 −0.0677375 0.997703i \(-0.521578\pi\)
−0.0677375 + 0.997703i \(0.521578\pi\)
\(140\) 0 0
\(141\) −643188. −2.72452
\(142\) −169488. −0.705372
\(143\) −35328.0 −0.144470
\(144\) 110848. 0.445473
\(145\) −140250. −0.553966
\(146\) −208504. −0.809529
\(147\) 0 0
\(148\) −2272.00 −0.00852617
\(149\) −100950. −0.372512 −0.186256 0.982501i \(-0.559635\pi\)
−0.186256 + 0.982501i \(0.559635\pi\)
\(150\) −65000.0 −0.235877
\(151\) 12452.0 0.0444423 0.0222212 0.999753i \(-0.492926\pi\)
0.0222212 + 0.999753i \(0.492926\pi\)
\(152\) 70400.0 0.247152
\(153\) −163674. −0.565264
\(154\) 0 0
\(155\) 99700.0 0.333323
\(156\) 19136.0 0.0629564
\(157\) 6022.00 0.0194981 0.00974903 0.999952i \(-0.496897\pi\)
0.00974903 + 0.999952i \(0.496897\pi\)
\(158\) 158560. 0.505302
\(159\) −368316. −1.15539
\(160\) −25600.0 −0.0790569
\(161\) 0 0
\(162\) −92884.0 −0.278070
\(163\) −500866. −1.47656 −0.738282 0.674492i \(-0.764363\pi\)
−0.738282 + 0.674492i \(0.764363\pi\)
\(164\) −24672.0 −0.0716300
\(165\) −499200. −1.42746
\(166\) −239304. −0.674031
\(167\) −555258. −1.54065 −0.770324 0.637652i \(-0.779906\pi\)
−0.770324 + 0.637652i \(0.779906\pi\)
\(168\) 0 0
\(169\) −369177. −0.994301
\(170\) 37800.0 0.100316
\(171\) −476300. −1.24563
\(172\) −80416.0 −0.207263
\(173\) −417354. −1.06020 −0.530102 0.847934i \(-0.677846\pi\)
−0.530102 + 0.847934i \(0.677846\pi\)
\(174\) 583440. 1.46091
\(175\) 0 0
\(176\) −196608. −0.478431
\(177\) −737880. −1.77032
\(178\) 230760. 0.545897
\(179\) −52380.0 −0.122189 −0.0610946 0.998132i \(-0.519459\pi\)
−0.0610946 + 0.998132i \(0.519459\pi\)
\(180\) 173200. 0.398443
\(181\) −546662. −1.24029 −0.620144 0.784488i \(-0.712926\pi\)
−0.620144 + 0.784488i \(0.712926\pi\)
\(182\) 0 0
\(183\) −143572. −0.316914
\(184\) 127104. 0.276767
\(185\) −3550.00 −0.00762604
\(186\) −414752. −0.879035
\(187\) 290304. 0.607084
\(188\) −395808. −0.816752
\(189\) 0 0
\(190\) 110000. 0.221059
\(191\) −452028. −0.896565 −0.448283 0.893892i \(-0.647964\pi\)
−0.448283 + 0.893892i \(0.647964\pi\)
\(192\) 106496. 0.208488
\(193\) 485594. 0.938383 0.469191 0.883097i \(-0.344545\pi\)
0.469191 + 0.883097i \(0.344545\pi\)
\(194\) −577528. −1.10171
\(195\) 29900.0 0.0563099
\(196\) 0 0
\(197\) 1.01018e6 1.85452 0.927262 0.374414i \(-0.122156\pi\)
0.927262 + 0.374414i \(0.122156\pi\)
\(198\) 1.33018e6 2.41127
\(199\) 807640. 1.44572 0.722862 0.690993i \(-0.242826\pi\)
0.722862 + 0.690993i \(0.242826\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −643292. −1.12310
\(202\) −565032. −0.974304
\(203\) 0 0
\(204\) −157248. −0.264551
\(205\) −38550.0 −0.0640678
\(206\) 559256. 0.918211
\(207\) −859938. −1.39489
\(208\) 11776.0 0.0188729
\(209\) 844800. 1.33779
\(210\) 0 0
\(211\) 149552. 0.231252 0.115626 0.993293i \(-0.463113\pi\)
0.115626 + 0.993293i \(0.463113\pi\)
\(212\) −226656. −0.346360
\(213\) 1.10167e6 1.66381
\(214\) −345672. −0.515976
\(215\) −125650. −0.185381
\(216\) −316160. −0.461076
\(217\) 0 0
\(218\) −873800. −1.24529
\(219\) 1.35528e6 1.90949
\(220\) −307200. −0.427922
\(221\) −17388.0 −0.0239480
\(222\) 14768.0 0.0201113
\(223\) 443506. 0.597224 0.298612 0.954375i \(-0.403476\pi\)
0.298612 + 0.954375i \(0.403476\pi\)
\(224\) 0 0
\(225\) 270625. 0.356379
\(226\) 115224. 0.150062
\(227\) −420018. −0.541007 −0.270504 0.962719i \(-0.587190\pi\)
−0.270504 + 0.962719i \(0.587190\pi\)
\(228\) −457600. −0.582974
\(229\) −1.05875e6 −1.33415 −0.667075 0.744990i \(-0.732454\pi\)
−0.667075 + 0.744990i \(0.732454\pi\)
\(230\) 198600. 0.247548
\(231\) 0 0
\(232\) 359040. 0.437948
\(233\) −1.27345e6 −1.53671 −0.768353 0.640026i \(-0.778923\pi\)
−0.768353 + 0.640026i \(0.778923\pi\)
\(234\) −79672.0 −0.0951187
\(235\) −618450. −0.730525
\(236\) −454080. −0.530704
\(237\) −1.03064e6 −1.19189
\(238\) 0 0
\(239\) −370680. −0.419763 −0.209882 0.977727i \(-0.567308\pi\)
−0.209882 + 0.977727i \(0.567308\pi\)
\(240\) 166400. 0.186477
\(241\) 561298. 0.622517 0.311258 0.950325i \(-0.399250\pi\)
0.311258 + 0.950325i \(0.399250\pi\)
\(242\) −1.71509e6 −1.88256
\(243\) −596674. −0.648219
\(244\) −88352.0 −0.0950040
\(245\) 0 0
\(246\) 160368. 0.168958
\(247\) −50600.0 −0.0527726
\(248\) −255232. −0.263515
\(249\) 1.55548e6 1.58988
\(250\) −62500.0 −0.0632456
\(251\) −577152. −0.578237 −0.289119 0.957293i \(-0.593362\pi\)
−0.289119 + 0.957293i \(0.593362\pi\)
\(252\) 0 0
\(253\) 1.52525e6 1.49809
\(254\) 866008. 0.842243
\(255\) −245700. −0.236622
\(256\) 65536.0 0.0625000
\(257\) 651462. 0.615257 0.307628 0.951507i \(-0.400465\pi\)
0.307628 + 0.951507i \(0.400465\pi\)
\(258\) 522704. 0.488885
\(259\) 0 0
\(260\) 18400.0 0.0168805
\(261\) −2.42913e6 −2.20724
\(262\) −978432. −0.880597
\(263\) 917574. 0.817997 0.408999 0.912535i \(-0.365878\pi\)
0.408999 + 0.912535i \(0.365878\pi\)
\(264\) 1.27795e6 1.12851
\(265\) −354150. −0.309794
\(266\) 0 0
\(267\) −1.49994e6 −1.28764
\(268\) −395872. −0.336680
\(269\) 735390. 0.619637 0.309818 0.950796i \(-0.399732\pi\)
0.309818 + 0.950796i \(0.399732\pi\)
\(270\) −494000. −0.412399
\(271\) 1.12131e6 0.927474 0.463737 0.885973i \(-0.346508\pi\)
0.463737 + 0.885973i \(0.346508\pi\)
\(272\) −96768.0 −0.0793066
\(273\) 0 0
\(274\) 958008. 0.770891
\(275\) −480000. −0.382745
\(276\) −826176. −0.652830
\(277\) −1.66034e6 −1.30016 −0.650082 0.759864i \(-0.725265\pi\)
−0.650082 + 0.759864i \(0.725265\pi\)
\(278\) 123440. 0.0957952
\(279\) 1.72680e6 1.32811
\(280\) 0 0
\(281\) 1.45210e6 1.09706 0.548531 0.836130i \(-0.315187\pi\)
0.548531 + 0.836130i \(0.315187\pi\)
\(282\) 2.57275e6 1.92653
\(283\) −309014. −0.229357 −0.114679 0.993403i \(-0.536584\pi\)
−0.114679 + 0.993403i \(0.536584\pi\)
\(284\) 677952. 0.498773
\(285\) −715000. −0.521427
\(286\) 141312. 0.102156
\(287\) 0 0
\(288\) −443392. −0.314997
\(289\) −1.27697e6 −0.899367
\(290\) 561000. 0.391713
\(291\) 3.75393e6 2.59869
\(292\) 834016. 0.572423
\(293\) 1.59301e6 1.08405 0.542024 0.840363i \(-0.317658\pi\)
0.542024 + 0.840363i \(0.317658\pi\)
\(294\) 0 0
\(295\) −709500. −0.474676
\(296\) 9088.00 0.00602891
\(297\) −3.79392e6 −2.49573
\(298\) 403800. 0.263406
\(299\) −91356.0 −0.0590961
\(300\) 260000. 0.166790
\(301\) 0 0
\(302\) −49808.0 −0.0314255
\(303\) 3.67271e6 2.29816
\(304\) −281600. −0.174763
\(305\) −138050. −0.0849741
\(306\) 654696. 0.399702
\(307\) −1.24726e6 −0.755284 −0.377642 0.925952i \(-0.623265\pi\)
−0.377642 + 0.925952i \(0.623265\pi\)
\(308\) 0 0
\(309\) −3.63516e6 −2.16585
\(310\) −398800. −0.235695
\(311\) 665988. 0.390450 0.195225 0.980758i \(-0.437456\pi\)
0.195225 + 0.980758i \(0.437456\pi\)
\(312\) −76544.0 −0.0445169
\(313\) 591286. 0.341143 0.170572 0.985345i \(-0.445439\pi\)
0.170572 + 0.985345i \(0.445439\pi\)
\(314\) −24088.0 −0.0137872
\(315\) 0 0
\(316\) −634240. −0.357302
\(317\) −516342. −0.288595 −0.144298 0.989534i \(-0.546092\pi\)
−0.144298 + 0.989534i \(0.546092\pi\)
\(318\) 1.47326e6 0.816983
\(319\) 4.30848e6 2.37054
\(320\) 102400. 0.0559017
\(321\) 2.24687e6 1.21707
\(322\) 0 0
\(323\) 415800. 0.221757
\(324\) 371536. 0.196625
\(325\) 28750.0 0.0150983
\(326\) 2.00346e6 1.04409
\(327\) 5.67970e6 2.93735
\(328\) 98688.0 0.0506500
\(329\) 0 0
\(330\) 1.99680e6 1.00937
\(331\) −3.29577e6 −1.65343 −0.826717 0.562619i \(-0.809794\pi\)
−0.826717 + 0.562619i \(0.809794\pi\)
\(332\) 957216. 0.476612
\(333\) −61486.0 −0.0303854
\(334\) 2.22103e6 1.08940
\(335\) −618550. −0.301136
\(336\) 0 0
\(337\) 1.91098e6 0.916602 0.458301 0.888797i \(-0.348458\pi\)
0.458301 + 0.888797i \(0.348458\pi\)
\(338\) 1.47671e6 0.703077
\(339\) −748956. −0.353962
\(340\) −151200. −0.0709340
\(341\) −3.06278e6 −1.42636
\(342\) 1.90520e6 0.880796
\(343\) 0 0
\(344\) 321664. 0.146557
\(345\) −1.29090e6 −0.583909
\(346\) 1.66942e6 0.749677
\(347\) 2.42006e6 1.07895 0.539476 0.842001i \(-0.318622\pi\)
0.539476 + 0.842001i \(0.318622\pi\)
\(348\) −2.33376e6 −1.03302
\(349\) −2.50727e6 −1.10189 −0.550944 0.834542i \(-0.685732\pi\)
−0.550944 + 0.834542i \(0.685732\pi\)
\(350\) 0 0
\(351\) 227240. 0.0984503
\(352\) 786432. 0.338302
\(353\) 413166. 0.176477 0.0882384 0.996099i \(-0.471876\pi\)
0.0882384 + 0.996099i \(0.471876\pi\)
\(354\) 2.95152e6 1.25181
\(355\) 1.05930e6 0.446116
\(356\) −923040. −0.386007
\(357\) 0 0
\(358\) 209520. 0.0864008
\(359\) 1.73772e6 0.711613 0.355806 0.934560i \(-0.384206\pi\)
0.355806 + 0.934560i \(0.384206\pi\)
\(360\) −692800. −0.281742
\(361\) −1.26610e6 −0.511328
\(362\) 2.18665e6 0.877016
\(363\) 1.11481e7 4.44052
\(364\) 0 0
\(365\) 1.30315e6 0.511991
\(366\) 574288. 0.224092
\(367\) −1.16098e6 −0.449944 −0.224972 0.974365i \(-0.572229\pi\)
−0.224972 + 0.974365i \(0.572229\pi\)
\(368\) −508416. −0.195704
\(369\) −667686. −0.255274
\(370\) 14200.0 0.00539242
\(371\) 0 0
\(372\) 1.65901e6 0.621572
\(373\) 343754. 0.127931 0.0639655 0.997952i \(-0.479625\pi\)
0.0639655 + 0.997952i \(0.479625\pi\)
\(374\) −1.16122e6 −0.429273
\(375\) 406250. 0.149182
\(376\) 1.58323e6 0.577531
\(377\) −258060. −0.0935120
\(378\) 0 0
\(379\) 573140. 0.204957 0.102478 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(380\) −440000. −0.156312
\(381\) −5.62905e6 −1.98666
\(382\) 1.80811e6 0.633967
\(383\) 2.88055e6 1.00341 0.501704 0.865039i \(-0.332707\pi\)
0.501704 + 0.865039i \(0.332707\pi\)
\(384\) −425984. −0.147423
\(385\) 0 0
\(386\) −1.94238e6 −0.663537
\(387\) −2.17626e6 −0.738640
\(388\) 2.31011e6 0.779029
\(389\) −3.08559e6 −1.03387 −0.516933 0.856026i \(-0.672926\pi\)
−0.516933 + 0.856026i \(0.672926\pi\)
\(390\) −119600. −0.0398171
\(391\) 750708. 0.248330
\(392\) 0 0
\(393\) 6.35981e6 2.07712
\(394\) −4.04071e6 −1.31135
\(395\) −991000. −0.319581
\(396\) −5.32070e6 −1.70503
\(397\) −885458. −0.281963 −0.140981 0.990012i \(-0.545026\pi\)
−0.140981 + 0.990012i \(0.545026\pi\)
\(398\) −3.23056e6 −1.02228
\(399\) 0 0
\(400\) 160000. 0.0500000
\(401\) −3.75344e6 −1.16565 −0.582825 0.812598i \(-0.698053\pi\)
−0.582825 + 0.812598i \(0.698053\pi\)
\(402\) 2.57317e6 0.794151
\(403\) 183448. 0.0562666
\(404\) 2.26013e6 0.688937
\(405\) 580525. 0.175867
\(406\) 0 0
\(407\) 109056. 0.0326335
\(408\) 628992. 0.187066
\(409\) 1.94653e6 0.575377 0.287689 0.957724i \(-0.407113\pi\)
0.287689 + 0.957724i \(0.407113\pi\)
\(410\) 154200. 0.0453028
\(411\) −6.22705e6 −1.81835
\(412\) −2.23702e6 −0.649273
\(413\) 0 0
\(414\) 3.43975e6 0.986339
\(415\) 1.49565e6 0.426295
\(416\) −47104.0 −0.0133452
\(417\) −802360. −0.225959
\(418\) −3.37920e6 −0.945961
\(419\) 2.99166e6 0.832486 0.416243 0.909253i \(-0.363346\pi\)
0.416243 + 0.909253i \(0.363346\pi\)
\(420\) 0 0
\(421\) 3.96660e6 1.09072 0.545360 0.838202i \(-0.316393\pi\)
0.545360 + 0.838202i \(0.316393\pi\)
\(422\) −598208. −0.163520
\(423\) −1.07116e7 −2.91073
\(424\) 906624. 0.244913
\(425\) −236250. −0.0634453
\(426\) −4.40669e6 −1.17649
\(427\) 0 0
\(428\) 1.38269e6 0.364850
\(429\) −918528. −0.240962
\(430\) 502600. 0.131085
\(431\) −5.17115e6 −1.34089 −0.670446 0.741958i \(-0.733897\pi\)
−0.670446 + 0.741958i \(0.733897\pi\)
\(432\) 1.26464e6 0.326030
\(433\) 4.53485e6 1.16237 0.581183 0.813773i \(-0.302590\pi\)
0.581183 + 0.813773i \(0.302590\pi\)
\(434\) 0 0
\(435\) −3.64650e6 −0.923960
\(436\) 3.49520e6 0.880554
\(437\) 2.18460e6 0.547228
\(438\) −5.42110e6 −1.35021
\(439\) 1.08220e6 0.268007 0.134004 0.990981i \(-0.457217\pi\)
0.134004 + 0.990981i \(0.457217\pi\)
\(440\) 1.22880e6 0.302586
\(441\) 0 0
\(442\) 69552.0 0.0169338
\(443\) −1.08079e6 −0.261656 −0.130828 0.991405i \(-0.541764\pi\)
−0.130828 + 0.991405i \(0.541764\pi\)
\(444\) −59072.0 −0.0142208
\(445\) −1.44225e6 −0.345255
\(446\) −1.77402e6 −0.422301
\(447\) −2.62470e6 −0.621314
\(448\) 0 0
\(449\) 2.61783e6 0.612810 0.306405 0.951901i \(-0.400874\pi\)
0.306405 + 0.951901i \(0.400874\pi\)
\(450\) −1.08250e6 −0.251998
\(451\) 1.18426e6 0.274160
\(452\) −460896. −0.106110
\(453\) 323752. 0.0741254
\(454\) 1.68007e6 0.382550
\(455\) 0 0
\(456\) 1.83040e6 0.412225
\(457\) 1.59046e6 0.356231 0.178115 0.984010i \(-0.443000\pi\)
0.178115 + 0.984010i \(0.443000\pi\)
\(458\) 4.23500e6 0.943387
\(459\) −1.86732e6 −0.413701
\(460\) −794400. −0.175043
\(461\) −4.25470e6 −0.932431 −0.466216 0.884671i \(-0.654383\pi\)
−0.466216 + 0.884671i \(0.654383\pi\)
\(462\) 0 0
\(463\) 3.26605e6 0.708061 0.354031 0.935234i \(-0.384811\pi\)
0.354031 + 0.935234i \(0.384811\pi\)
\(464\) −1.43616e6 −0.309676
\(465\) 2.59220e6 0.555950
\(466\) 5.09378e6 1.08662
\(467\) 601542. 0.127636 0.0638181 0.997962i \(-0.479672\pi\)
0.0638181 + 0.997962i \(0.479672\pi\)
\(468\) 318688. 0.0672591
\(469\) 0 0
\(470\) 2.47380e6 0.516559
\(471\) 156572. 0.0325208
\(472\) 1.81632e6 0.375264
\(473\) 3.85997e6 0.793288
\(474\) 4.12256e6 0.842793
\(475\) −687500. −0.139810
\(476\) 0 0
\(477\) −6.13388e6 −1.23435
\(478\) 1.48272e6 0.296817
\(479\) 4.57932e6 0.911931 0.455966 0.889997i \(-0.349294\pi\)
0.455966 + 0.889997i \(0.349294\pi\)
\(480\) −665600. −0.131859
\(481\) −6532.00 −0.00128731
\(482\) −2.24519e6 −0.440186
\(483\) 0 0
\(484\) 6.86037e6 1.33117
\(485\) 3.60955e6 0.696785
\(486\) 2.38670e6 0.458360
\(487\) 7.05226e6 1.34743 0.673714 0.738992i \(-0.264698\pi\)
0.673714 + 0.738992i \(0.264698\pi\)
\(488\) 353408. 0.0671780
\(489\) −1.30225e7 −2.46276
\(490\) 0 0
\(491\) −2.62349e6 −0.491106 −0.245553 0.969383i \(-0.578970\pi\)
−0.245553 + 0.969383i \(0.578970\pi\)
\(492\) −641472. −0.119472
\(493\) 2.12058e6 0.392950
\(494\) 202400. 0.0373158
\(495\) −8.31360e6 −1.52502
\(496\) 1.02093e6 0.186333
\(497\) 0 0
\(498\) −6.22190e6 −1.12422
\(499\) −3.61234e6 −0.649437 −0.324719 0.945811i \(-0.605270\pi\)
−0.324719 + 0.945811i \(0.605270\pi\)
\(500\) 250000. 0.0447214
\(501\) −1.44367e7 −2.56965
\(502\) 2.30861e6 0.408875
\(503\) −9.15629e6 −1.61361 −0.806807 0.590815i \(-0.798806\pi\)
−0.806807 + 0.590815i \(0.798806\pi\)
\(504\) 0 0
\(505\) 3.53145e6 0.616204
\(506\) −6.10099e6 −1.05931
\(507\) −9.59860e6 −1.65840
\(508\) −3.46403e6 −0.595556
\(509\) −7.26159e6 −1.24233 −0.621165 0.783679i \(-0.713340\pi\)
−0.621165 + 0.783679i \(0.713340\pi\)
\(510\) 982800. 0.167317
\(511\) 0 0
\(512\) −262144. −0.0441942
\(513\) −5.43400e6 −0.911646
\(514\) −2.60585e6 −0.435052
\(515\) −3.49535e6 −0.580728
\(516\) −2.09082e6 −0.345694
\(517\) 1.89988e7 3.12608
\(518\) 0 0
\(519\) −1.08512e7 −1.76831
\(520\) −73600.0 −0.0119363
\(521\) −5.81020e6 −0.937771 −0.468886 0.883259i \(-0.655344\pi\)
−0.468886 + 0.883259i \(0.655344\pi\)
\(522\) 9.71652e6 1.56075
\(523\) 8.17067e6 1.30618 0.653090 0.757280i \(-0.273472\pi\)
0.653090 + 0.757280i \(0.273472\pi\)
\(524\) 3.91373e6 0.622676
\(525\) 0 0
\(526\) −3.67030e6 −0.578411
\(527\) −1.50746e6 −0.236440
\(528\) −5.11181e6 −0.797976
\(529\) −2.49215e6 −0.387199
\(530\) 1.41660e6 0.219057
\(531\) −1.22885e7 −1.89132
\(532\) 0 0
\(533\) −70932.0 −0.0108149
\(534\) 5.99976e6 0.910502
\(535\) 2.16045e6 0.326332
\(536\) 1.58349e6 0.238069
\(537\) −1.36188e6 −0.203800
\(538\) −2.94156e6 −0.438149
\(539\) 0 0
\(540\) 1.97600e6 0.291610
\(541\) −817378. −0.120069 −0.0600343 0.998196i \(-0.519121\pi\)
−0.0600343 + 0.998196i \(0.519121\pi\)
\(542\) −4.48523e6 −0.655823
\(543\) −1.42132e7 −2.06868
\(544\) 387072. 0.0560783
\(545\) 5.46125e6 0.787591
\(546\) 0 0
\(547\) −3.50750e6 −0.501221 −0.250611 0.968088i \(-0.580631\pi\)
−0.250611 + 0.968088i \(0.580631\pi\)
\(548\) −3.83203e6 −0.545102
\(549\) −2.39103e6 −0.338574
\(550\) 1.92000e6 0.270642
\(551\) 6.17100e6 0.865918
\(552\) 3.30470e6 0.461620
\(553\) 0 0
\(554\) 6.64137e6 0.919355
\(555\) −92300.0 −0.0127195
\(556\) −493760. −0.0677375
\(557\) 9.61490e6 1.31313 0.656563 0.754271i \(-0.272009\pi\)
0.656563 + 0.754271i \(0.272009\pi\)
\(558\) −6.90722e6 −0.939112
\(559\) −231196. −0.0312933
\(560\) 0 0
\(561\) 7.54790e6 1.01256
\(562\) −5.80841e6 −0.775740
\(563\) −2.01941e6 −0.268506 −0.134253 0.990947i \(-0.542864\pi\)
−0.134253 + 0.990947i \(0.542864\pi\)
\(564\) −1.02910e7 −1.36226
\(565\) −720150. −0.0949078
\(566\) 1.23606e6 0.162180
\(567\) 0 0
\(568\) −2.71181e6 −0.352686
\(569\) 1.37859e6 0.178507 0.0892533 0.996009i \(-0.471552\pi\)
0.0892533 + 0.996009i \(0.471552\pi\)
\(570\) 2.86000e6 0.368705
\(571\) 8.54295e6 1.09652 0.548261 0.836307i \(-0.315290\pi\)
0.548261 + 0.836307i \(0.315290\pi\)
\(572\) −565248. −0.0722352
\(573\) −1.17527e7 −1.49538
\(574\) 0 0
\(575\) −1.24125e6 −0.156563
\(576\) 1.77357e6 0.222737
\(577\) 2.31458e6 0.289423 0.144711 0.989474i \(-0.453775\pi\)
0.144711 + 0.989474i \(0.453775\pi\)
\(578\) 5.10789e6 0.635949
\(579\) 1.26254e7 1.56513
\(580\) −2.24400e6 −0.276983
\(581\) 0 0
\(582\) −1.50157e7 −1.83755
\(583\) 1.08795e7 1.32568
\(584\) −3.33606e6 −0.404764
\(585\) 497950. 0.0601584
\(586\) −6.37202e6 −0.766537
\(587\) −928338. −0.111202 −0.0556008 0.998453i \(-0.517707\pi\)
−0.0556008 + 0.998453i \(0.517707\pi\)
\(588\) 0 0
\(589\) −4.38680e6 −0.521026
\(590\) 2.83800e6 0.335647
\(591\) 2.62646e7 3.09316
\(592\) −36352.0 −0.00426309
\(593\) 909486. 0.106209 0.0531043 0.998589i \(-0.483088\pi\)
0.0531043 + 0.998589i \(0.483088\pi\)
\(594\) 1.51757e7 1.76475
\(595\) 0 0
\(596\) −1.61520e6 −0.186256
\(597\) 2.09986e7 2.41132
\(598\) 365424. 0.0417873
\(599\) −8.51136e6 −0.969241 −0.484621 0.874724i \(-0.661042\pi\)
−0.484621 + 0.874724i \(0.661042\pi\)
\(600\) −1.04000e6 −0.117938
\(601\) −6.12498e6 −0.691701 −0.345851 0.938290i \(-0.612410\pi\)
−0.345851 + 0.938290i \(0.612410\pi\)
\(602\) 0 0
\(603\) −1.07133e7 −1.19986
\(604\) 199232. 0.0222212
\(605\) 1.07193e7 1.19064
\(606\) −1.46908e7 −1.62504
\(607\) 4.51646e6 0.497538 0.248769 0.968563i \(-0.419974\pi\)
0.248769 + 0.968563i \(0.419974\pi\)
\(608\) 1.12640e6 0.123576
\(609\) 0 0
\(610\) 552200. 0.0600858
\(611\) −1.13795e6 −0.123316
\(612\) −2.61878e6 −0.282632
\(613\) 9.63979e6 1.03614 0.518068 0.855340i \(-0.326651\pi\)
0.518068 + 0.855340i \(0.326651\pi\)
\(614\) 4.98903e6 0.534067
\(615\) −1.00230e6 −0.106859
\(616\) 0 0
\(617\) −9.92650e6 −1.04974 −0.524872 0.851181i \(-0.675887\pi\)
−0.524872 + 0.851181i \(0.675887\pi\)
\(618\) 1.45407e7 1.53149
\(619\) −7.63322e6 −0.800721 −0.400360 0.916358i \(-0.631115\pi\)
−0.400360 + 0.916358i \(0.631115\pi\)
\(620\) 1.59520e6 0.166662
\(621\) −9.81084e6 −1.02089
\(622\) −2.66395e6 −0.276090
\(623\) 0 0
\(624\) 306176. 0.0314782
\(625\) 390625. 0.0400000
\(626\) −2.36514e6 −0.241225
\(627\) 2.19648e7 2.23130
\(628\) 96352.0 0.00974903
\(629\) 53676.0 0.00540946
\(630\) 0 0
\(631\) 1.80314e7 1.80284 0.901418 0.432949i \(-0.142527\pi\)
0.901418 + 0.432949i \(0.142527\pi\)
\(632\) 2.53696e6 0.252651
\(633\) 3.88835e6 0.385706
\(634\) 2.06537e6 0.204068
\(635\) −5.41255e6 −0.532681
\(636\) −5.89306e6 −0.577694
\(637\) 0 0
\(638\) −1.72339e7 −1.67623
\(639\) 1.83471e7 1.77752
\(640\) −409600. −0.0395285
\(641\) 9.30190e6 0.894184 0.447092 0.894488i \(-0.352460\pi\)
0.447092 + 0.894488i \(0.352460\pi\)
\(642\) −8.98747e6 −0.860597
\(643\) 1.38332e7 1.31946 0.659730 0.751503i \(-0.270671\pi\)
0.659730 + 0.751503i \(0.270671\pi\)
\(644\) 0 0
\(645\) −3.26690e6 −0.309198
\(646\) −1.66320e6 −0.156806
\(647\) 1.48997e7 1.39932 0.699658 0.714478i \(-0.253336\pi\)
0.699658 + 0.714478i \(0.253336\pi\)
\(648\) −1.48614e6 −0.139035
\(649\) 2.17958e7 2.03124
\(650\) −115000. −0.0106761
\(651\) 0 0
\(652\) −8.01386e6 −0.738282
\(653\) −1.93306e7 −1.77403 −0.887016 0.461738i \(-0.847226\pi\)
−0.887016 + 0.461738i \(0.847226\pi\)
\(654\) −2.27188e7 −2.07702
\(655\) 6.11520e6 0.556939
\(656\) −394752. −0.0358150
\(657\) 2.25706e7 2.03999
\(658\) 0 0
\(659\) −4.06110e6 −0.364276 −0.182138 0.983273i \(-0.558302\pi\)
−0.182138 + 0.983273i \(0.558302\pi\)
\(660\) −7.98720e6 −0.713731
\(661\) 1.35152e7 1.20315 0.601575 0.798816i \(-0.294540\pi\)
0.601575 + 0.798816i \(0.294540\pi\)
\(662\) 1.31831e7 1.16915
\(663\) −452088. −0.0399429
\(664\) −3.82886e6 −0.337015
\(665\) 0 0
\(666\) 245944. 0.0214858
\(667\) 1.11415e7 0.969678
\(668\) −8.88413e6 −0.770324
\(669\) 1.15312e7 0.996111
\(670\) 2.47420e6 0.212935
\(671\) 4.24090e6 0.363623
\(672\) 0 0
\(673\) 1.43520e7 1.22144 0.610722 0.791845i \(-0.290879\pi\)
0.610722 + 0.791845i \(0.290879\pi\)
\(674\) −7.64391e6 −0.648136
\(675\) 3.08750e6 0.260824
\(676\) −5.90683e6 −0.497150
\(677\) −1.89530e6 −0.158930 −0.0794650 0.996838i \(-0.525321\pi\)
−0.0794650 + 0.996838i \(0.525321\pi\)
\(678\) 2.99582e6 0.250289
\(679\) 0 0
\(680\) 604800. 0.0501579
\(681\) −1.09205e7 −0.902347
\(682\) 1.22511e7 1.00859
\(683\) 2.91641e6 0.239220 0.119610 0.992821i \(-0.461836\pi\)
0.119610 + 0.992821i \(0.461836\pi\)
\(684\) −7.62080e6 −0.622817
\(685\) −5.98755e6 −0.487554
\(686\) 0 0
\(687\) −2.75275e7 −2.22523
\(688\) −1.28666e6 −0.103631
\(689\) −651636. −0.0522946
\(690\) 5.16360e6 0.412886
\(691\) −1.44278e7 −1.14949 −0.574743 0.818334i \(-0.694898\pi\)
−0.574743 + 0.818334i \(0.694898\pi\)
\(692\) −6.67766e6 −0.530102
\(693\) 0 0
\(694\) −9.68023e6 −0.762934
\(695\) −771500. −0.0605862
\(696\) 9.33504e6 0.730454
\(697\) 582876. 0.0454458
\(698\) 1.00291e7 0.779153
\(699\) −3.31096e7 −2.56307
\(700\) 0 0
\(701\) −1.58679e7 −1.21962 −0.609811 0.792547i \(-0.708754\pi\)
−0.609811 + 0.792547i \(0.708754\pi\)
\(702\) −908960. −0.0696149
\(703\) 156200. 0.0119205
\(704\) −3.14573e6 −0.239216
\(705\) −1.60797e7 −1.21844
\(706\) −1.65266e6 −0.124788
\(707\) 0 0
\(708\) −1.18061e7 −0.885162
\(709\) −301810. −0.0225485 −0.0112743 0.999936i \(-0.503589\pi\)
−0.0112743 + 0.999936i \(0.503589\pi\)
\(710\) −4.23720e6 −0.315452
\(711\) −1.71641e7 −1.27335
\(712\) 3.69216e6 0.272948
\(713\) −7.92017e6 −0.583459
\(714\) 0 0
\(715\) −883200. −0.0646091
\(716\) −838080. −0.0610946
\(717\) −9.63768e6 −0.700123
\(718\) −6.95088e6 −0.503186
\(719\) −2.12677e7 −1.53426 −0.767130 0.641492i \(-0.778316\pi\)
−0.767130 + 0.641492i \(0.778316\pi\)
\(720\) 2.77120e6 0.199222
\(721\) 0 0
\(722\) 5.06440e6 0.361564
\(723\) 1.45937e7 1.03830
\(724\) −8.74659e6 −0.620144
\(725\) −3.50625e6 −0.247741
\(726\) −4.45924e7 −3.13992
\(727\) −1.55009e7 −1.08773 −0.543863 0.839174i \(-0.683039\pi\)
−0.543863 + 0.839174i \(0.683039\pi\)
\(728\) 0 0
\(729\) −2.11562e7 −1.47441
\(730\) −5.21260e6 −0.362032
\(731\) 1.89983e6 0.131499
\(732\) −2.29715e6 −0.158457
\(733\) 1.21850e7 0.837653 0.418827 0.908066i \(-0.362441\pi\)
0.418827 + 0.908066i \(0.362441\pi\)
\(734\) 4.64391e6 0.318159
\(735\) 0 0
\(736\) 2.03366e6 0.138384
\(737\) 1.90019e7 1.28863
\(738\) 2.67074e6 0.180506
\(739\) −2.90282e7 −1.95528 −0.977641 0.210282i \(-0.932562\pi\)
−0.977641 + 0.210282i \(0.932562\pi\)
\(740\) −56800.0 −0.00381302
\(741\) −1.31560e6 −0.0880194
\(742\) 0 0
\(743\) 1.61145e7 1.07089 0.535445 0.844570i \(-0.320144\pi\)
0.535445 + 0.844570i \(0.320144\pi\)
\(744\) −6.63603e6 −0.439517
\(745\) −2.52375e6 −0.166593
\(746\) −1.37502e6 −0.0904609
\(747\) 2.59047e7 1.69854
\(748\) 4.64486e6 0.303542
\(749\) 0 0
\(750\) −1.62500e6 −0.105487
\(751\) −2.92431e6 −0.189201 −0.0946005 0.995515i \(-0.530157\pi\)
−0.0946005 + 0.995515i \(0.530157\pi\)
\(752\) −6.33293e6 −0.408376
\(753\) −1.50060e7 −0.964442
\(754\) 1.03224e6 0.0661230
\(755\) 311300. 0.0198752
\(756\) 0 0
\(757\) 2.60325e7 1.65111 0.825557 0.564319i \(-0.190861\pi\)
0.825557 + 0.564319i \(0.190861\pi\)
\(758\) −2.29256e6 −0.144926
\(759\) 3.96564e7 2.49867
\(760\) 1.76000e6 0.110530
\(761\) −1.63263e7 −1.02194 −0.510970 0.859598i \(-0.670714\pi\)
−0.510970 + 0.859598i \(0.670714\pi\)
\(762\) 2.25162e7 1.40478
\(763\) 0 0
\(764\) −7.23245e6 −0.448283
\(765\) −4.09185e6 −0.252794
\(766\) −1.15222e7 −0.709517
\(767\) −1.30548e6 −0.0801275
\(768\) 1.70394e6 0.104244
\(769\) −2.58132e7 −1.57408 −0.787040 0.616902i \(-0.788388\pi\)
−0.787040 + 0.616902i \(0.788388\pi\)
\(770\) 0 0
\(771\) 1.69380e7 1.02619
\(772\) 7.76950e6 0.469191
\(773\) 1.90592e7 1.14725 0.573624 0.819119i \(-0.305537\pi\)
0.573624 + 0.819119i \(0.305537\pi\)
\(774\) 8.70503e6 0.522298
\(775\) 2.49250e6 0.149067
\(776\) −9.24045e6 −0.550857
\(777\) 0 0
\(778\) 1.23424e7 0.731054
\(779\) 1.69620e6 0.100146
\(780\) 478400. 0.0281549
\(781\) −3.25417e7 −1.90903
\(782\) −3.00283e6 −0.175596
\(783\) −2.77134e7 −1.61542
\(784\) 0 0
\(785\) 150550. 0.00871980
\(786\) −2.54392e7 −1.46875
\(787\) 1.73411e7 0.998021 0.499011 0.866596i \(-0.333697\pi\)
0.499011 + 0.866596i \(0.333697\pi\)
\(788\) 1.61628e7 0.927262
\(789\) 2.38569e7 1.36434
\(790\) 3.96400e6 0.225978
\(791\) 0 0
\(792\) 2.12828e7 1.20564
\(793\) −254012. −0.0143440
\(794\) 3.54183e6 0.199378
\(795\) −9.20790e6 −0.516705
\(796\) 1.29222e7 0.722862
\(797\) 2.58169e7 1.43965 0.719827 0.694153i \(-0.244221\pi\)
0.719827 + 0.694153i \(0.244221\pi\)
\(798\) 0 0
\(799\) 9.35096e6 0.518190
\(800\) −640000. −0.0353553
\(801\) −2.49798e7 −1.37565
\(802\) 1.50138e7 0.824239
\(803\) −4.00328e7 −2.19092
\(804\) −1.02927e7 −0.561549
\(805\) 0 0
\(806\) −733792. −0.0397865
\(807\) 1.91201e7 1.03349
\(808\) −9.04051e6 −0.487152
\(809\) 8.88489e6 0.477288 0.238644 0.971107i \(-0.423297\pi\)
0.238644 + 0.971107i \(0.423297\pi\)
\(810\) −2.32210e6 −0.124356
\(811\) 2.46396e7 1.31547 0.657735 0.753249i \(-0.271515\pi\)
0.657735 + 0.753249i \(0.271515\pi\)
\(812\) 0 0
\(813\) 2.91540e7 1.54693
\(814\) −436224. −0.0230754
\(815\) −1.25216e7 −0.660340
\(816\) −2.51597e6 −0.132276
\(817\) 5.52860e6 0.289774
\(818\) −7.78612e6 −0.406853
\(819\) 0 0
\(820\) −616800. −0.0320339
\(821\) 1.13768e7 0.589062 0.294531 0.955642i \(-0.404837\pi\)
0.294531 + 0.955642i \(0.404837\pi\)
\(822\) 2.49082e7 1.28577
\(823\) −1.30783e7 −0.673057 −0.336529 0.941673i \(-0.609253\pi\)
−0.336529 + 0.941673i \(0.609253\pi\)
\(824\) 8.94810e6 0.459106
\(825\) −1.24800e7 −0.638381
\(826\) 0 0
\(827\) −3.57188e7 −1.81607 −0.908037 0.418891i \(-0.862419\pi\)
−0.908037 + 0.418891i \(0.862419\pi\)
\(828\) −1.37590e7 −0.697447
\(829\) −1.61880e7 −0.818103 −0.409052 0.912511i \(-0.634140\pi\)
−0.409052 + 0.912511i \(0.634140\pi\)
\(830\) −5.98260e6 −0.301436
\(831\) −4.31689e7 −2.16854
\(832\) 188416. 0.00943647
\(833\) 0 0
\(834\) 3.20944e6 0.159777
\(835\) −1.38814e7 −0.688999
\(836\) 1.35168e7 0.668895
\(837\) 1.97007e7 0.972005
\(838\) −1.19666e7 −0.588657
\(839\) 2.55497e7 1.25309 0.626543 0.779387i \(-0.284469\pi\)
0.626543 + 0.779387i \(0.284469\pi\)
\(840\) 0 0
\(841\) 1.09610e7 0.534390
\(842\) −1.58664e7 −0.771256
\(843\) 3.77547e7 1.82979
\(844\) 2.39283e6 0.115626
\(845\) −9.22943e6 −0.444665
\(846\) 4.28462e7 2.05820
\(847\) 0 0
\(848\) −3.62650e6 −0.173180
\(849\) −8.03436e6 −0.382545
\(850\) 945000. 0.0448626
\(851\) 282012. 0.0133488
\(852\) 1.76268e7 0.831904
\(853\) 2.22953e7 1.04916 0.524579 0.851362i \(-0.324223\pi\)
0.524579 + 0.851362i \(0.324223\pi\)
\(854\) 0 0
\(855\) −1.19075e7 −0.557064
\(856\) −5.53075e6 −0.257988
\(857\) −1.96872e7 −0.915656 −0.457828 0.889041i \(-0.651372\pi\)
−0.457828 + 0.889041i \(0.651372\pi\)
\(858\) 3.67411e6 0.170386
\(859\) −6.77582e6 −0.313313 −0.156657 0.987653i \(-0.550072\pi\)
−0.156657 + 0.987653i \(0.550072\pi\)
\(860\) −2.01040e6 −0.0926907
\(861\) 0 0
\(862\) 2.06846e7 0.948154
\(863\) −2.63804e7 −1.20574 −0.602871 0.797839i \(-0.705977\pi\)
−0.602871 + 0.797839i \(0.705977\pi\)
\(864\) −5.05856e6 −0.230538
\(865\) −1.04338e7 −0.474138
\(866\) −1.81394e7 −0.821917
\(867\) −3.32013e7 −1.50006
\(868\) 0 0
\(869\) 3.04435e7 1.36756
\(870\) 1.45860e7 0.653338
\(871\) −1.13813e6 −0.0508332
\(872\) −1.39808e7 −0.622645
\(873\) 6.25174e7 2.77629
\(874\) −8.73840e6 −0.386949
\(875\) 0 0
\(876\) 2.16844e7 0.954745
\(877\) 2.95161e7 1.29587 0.647934 0.761697i \(-0.275633\pi\)
0.647934 + 0.761697i \(0.275633\pi\)
\(878\) −4.32880e6 −0.189510
\(879\) 4.14182e7 1.80808
\(880\) −4.91520e6 −0.213961
\(881\) 1.48565e7 0.644877 0.322438 0.946590i \(-0.395498\pi\)
0.322438 + 0.946590i \(0.395498\pi\)
\(882\) 0 0
\(883\) −1.45340e7 −0.627313 −0.313656 0.949537i \(-0.601554\pi\)
−0.313656 + 0.949537i \(0.601554\pi\)
\(884\) −278208. −0.0119740
\(885\) −1.84470e7 −0.791713
\(886\) 4.32314e6 0.185019
\(887\) 1.72028e7 0.734160 0.367080 0.930189i \(-0.380358\pi\)
0.367080 + 0.930189i \(0.380358\pi\)
\(888\) 236288. 0.0100556
\(889\) 0 0
\(890\) 5.76900e6 0.244132
\(891\) −1.78337e7 −0.752572
\(892\) 7.09610e6 0.298612
\(893\) 2.72118e7 1.14190
\(894\) 1.04988e7 0.439335
\(895\) −1.30950e6 −0.0546447
\(896\) 0 0
\(897\) −2.37526e6 −0.0985665
\(898\) −1.04713e7 −0.433322
\(899\) −2.23727e7 −0.923249
\(900\) 4.33000e6 0.178189
\(901\) 5.35475e6 0.219749
\(902\) −4.73702e6 −0.193860
\(903\) 0 0
\(904\) 1.84358e6 0.0750312
\(905\) −1.36665e7 −0.554674
\(906\) −1.29501e6 −0.0524146
\(907\) −3.44434e7 −1.39023 −0.695116 0.718897i \(-0.744647\pi\)
−0.695116 + 0.718897i \(0.744647\pi\)
\(908\) −6.72029e6 −0.270504
\(909\) 6.11647e7 2.45522
\(910\) 0 0
\(911\) −983748. −0.0392724 −0.0196362 0.999807i \(-0.506251\pi\)
−0.0196362 + 0.999807i \(0.506251\pi\)
\(912\) −7.32160e6 −0.291487
\(913\) −4.59464e7 −1.82421
\(914\) −6.36183e6 −0.251893
\(915\) −3.58930e6 −0.141728
\(916\) −1.69400e7 −0.667075
\(917\) 0 0
\(918\) 7.46928e6 0.292531
\(919\) 3.08857e7 1.20634 0.603168 0.797614i \(-0.293905\pi\)
0.603168 + 0.797614i \(0.293905\pi\)
\(920\) 3.17760e6 0.123774
\(921\) −3.24287e7 −1.25974
\(922\) 1.70188e7 0.659328
\(923\) 1.94911e6 0.0753065
\(924\) 0 0
\(925\) −88750.0 −0.00341047
\(926\) −1.30642e7 −0.500675
\(927\) −6.05395e7 −2.31387
\(928\) 5.74464e6 0.218974
\(929\) 3.20874e7 1.21982 0.609909 0.792472i \(-0.291206\pi\)
0.609909 + 0.792472i \(0.291206\pi\)
\(930\) −1.03688e7 −0.393116
\(931\) 0 0
\(932\) −2.03751e7 −0.768353
\(933\) 1.73157e7 0.651232
\(934\) −2.40617e6 −0.0902524
\(935\) 7.25760e6 0.271496
\(936\) −1.27475e6 −0.0475594
\(937\) −1.52520e7 −0.567515 −0.283757 0.958896i \(-0.591581\pi\)
−0.283757 + 0.958896i \(0.591581\pi\)
\(938\) 0 0
\(939\) 1.53734e7 0.568993
\(940\) −9.89520e6 −0.365262
\(941\) −3.48166e6 −0.128178 −0.0640889 0.997944i \(-0.520414\pi\)
−0.0640889 + 0.997944i \(0.520414\pi\)
\(942\) −626288. −0.0229957
\(943\) 3.06241e6 0.112146
\(944\) −7.26528e6 −0.265352
\(945\) 0 0
\(946\) −1.54399e7 −0.560939
\(947\) −2.54010e7 −0.920398 −0.460199 0.887816i \(-0.652222\pi\)
−0.460199 + 0.887816i \(0.652222\pi\)
\(948\) −1.64902e7 −0.595945
\(949\) 2.39780e6 0.0864265
\(950\) 2.75000e6 0.0988607
\(951\) −1.34249e7 −0.481348
\(952\) 0 0
\(953\) −4.97352e7 −1.77391 −0.886955 0.461856i \(-0.847184\pi\)
−0.886955 + 0.461856i \(0.847184\pi\)
\(954\) 2.45355e7 0.872819
\(955\) −1.13007e7 −0.400956
\(956\) −5.93088e6 −0.209882
\(957\) 1.12020e8 3.95383
\(958\) −1.83173e7 −0.644833
\(959\) 0 0
\(960\) 2.66240e6 0.0932385
\(961\) −1.27250e7 −0.444477
\(962\) 26128.0 0.000910266 0
\(963\) 3.74190e7 1.30025
\(964\) 8.98077e6 0.311258
\(965\) 1.21399e7 0.419658
\(966\) 0 0
\(967\) 3.05173e7 1.04949 0.524747 0.851258i \(-0.324160\pi\)
0.524747 + 0.851258i \(0.324160\pi\)
\(968\) −2.74415e7 −0.941280
\(969\) 1.08108e7 0.369869
\(970\) −1.44382e7 −0.492701
\(971\) −3.19854e7 −1.08869 −0.544344 0.838862i \(-0.683221\pi\)
−0.544344 + 0.838862i \(0.683221\pi\)
\(972\) −9.54678e6 −0.324109
\(973\) 0 0
\(974\) −2.82090e7 −0.952776
\(975\) 747500. 0.0251825
\(976\) −1.41363e6 −0.0475020
\(977\) 2.90786e6 0.0974623 0.0487312 0.998812i \(-0.484482\pi\)
0.0487312 + 0.998812i \(0.484482\pi\)
\(978\) 5.20901e7 1.74144
\(979\) 4.43059e7 1.47742
\(980\) 0 0
\(981\) 9.45888e7 3.13810
\(982\) 1.04940e7 0.347264
\(983\) −3.49621e7 −1.15402 −0.577010 0.816737i \(-0.695781\pi\)
−0.577010 + 0.816737i \(0.695781\pi\)
\(984\) 2.56589e6 0.0844792
\(985\) 2.52544e7 0.829368
\(986\) −8.48232e6 −0.277858
\(987\) 0 0
\(988\) −809600. −0.0263863
\(989\) 9.98164e6 0.324497
\(990\) 3.32544e7 1.07835
\(991\) 3.00465e6 0.0971874 0.0485937 0.998819i \(-0.484526\pi\)
0.0485937 + 0.998819i \(0.484526\pi\)
\(992\) −4.08371e6 −0.131758
\(993\) −8.56900e7 −2.75776
\(994\) 0 0
\(995\) 2.01910e7 0.646547
\(996\) 2.48876e7 0.794941
\(997\) −3.20789e7 −1.02207 −0.511035 0.859560i \(-0.670738\pi\)
−0.511035 + 0.859560i \(0.670738\pi\)
\(998\) 1.44494e7 0.459222
\(999\) −701480. −0.0222383
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 490.6.a.j.1.1 1
7.6 odd 2 10.6.a.a.1.1 1
21.20 even 2 90.6.a.f.1.1 1
28.27 even 2 80.6.a.h.1.1 1
35.13 even 4 50.6.b.d.49.2 2
35.27 even 4 50.6.b.d.49.1 2
35.34 odd 2 50.6.a.g.1.1 1
56.13 odd 2 320.6.a.p.1.1 1
56.27 even 2 320.6.a.a.1.1 1
84.83 odd 2 720.6.a.r.1.1 1
105.62 odd 4 450.6.c.o.199.2 2
105.83 odd 4 450.6.c.o.199.1 2
105.104 even 2 450.6.a.h.1.1 1
140.27 odd 4 400.6.c.a.49.1 2
140.83 odd 4 400.6.c.a.49.2 2
140.139 even 2 400.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.6.a.a.1.1 1 7.6 odd 2
50.6.a.g.1.1 1 35.34 odd 2
50.6.b.d.49.1 2 35.27 even 4
50.6.b.d.49.2 2 35.13 even 4
80.6.a.h.1.1 1 28.27 even 2
90.6.a.f.1.1 1 21.20 even 2
320.6.a.a.1.1 1 56.27 even 2
320.6.a.p.1.1 1 56.13 odd 2
400.6.a.a.1.1 1 140.139 even 2
400.6.c.a.49.1 2 140.27 odd 4
400.6.c.a.49.2 2 140.83 odd 4
450.6.a.h.1.1 1 105.104 even 2
450.6.c.o.199.1 2 105.83 odd 4
450.6.c.o.199.2 2 105.62 odd 4
490.6.a.j.1.1 1 1.1 even 1 trivial
720.6.a.r.1.1 1 84.83 odd 2