Properties

Label 10.6.a.a.1.1
Level 10
Weight 6
Character 10.1
Self dual yes
Analytic conductor 1.604
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 10.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.60383819813\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 10.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -26.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +104.000 q^{6} -22.0000 q^{7} -64.0000 q^{8} +433.000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -26.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +104.000 q^{6} -22.0000 q^{7} -64.0000 q^{8} +433.000 q^{9} +100.000 q^{10} -768.000 q^{11} -416.000 q^{12} -46.0000 q^{13} +88.0000 q^{14} +650.000 q^{15} +256.000 q^{16} +378.000 q^{17} -1732.00 q^{18} +1100.00 q^{19} -400.000 q^{20} +572.000 q^{21} +3072.00 q^{22} -1986.00 q^{23} +1664.00 q^{24} +625.000 q^{25} +184.000 q^{26} -4940.00 q^{27} -352.000 q^{28} -5610.00 q^{29} -2600.00 q^{30} -3988.00 q^{31} -1024.00 q^{32} +19968.0 q^{33} -1512.00 q^{34} +550.000 q^{35} +6928.00 q^{36} -142.000 q^{37} -4400.00 q^{38} +1196.00 q^{39} +1600.00 q^{40} +1542.00 q^{41} -2288.00 q^{42} -5026.00 q^{43} -12288.0 q^{44} -10825.0 q^{45} +7944.00 q^{46} +24738.0 q^{47} -6656.00 q^{48} -16323.0 q^{49} -2500.00 q^{50} -9828.00 q^{51} -736.000 q^{52} -14166.0 q^{53} +19760.0 q^{54} +19200.0 q^{55} +1408.00 q^{56} -28600.0 q^{57} +22440.0 q^{58} +28380.0 q^{59} +10400.0 q^{60} +5522.00 q^{61} +15952.0 q^{62} -9526.00 q^{63} +4096.00 q^{64} +1150.00 q^{65} -79872.0 q^{66} -24742.0 q^{67} +6048.00 q^{68} +51636.0 q^{69} -2200.00 q^{70} +42372.0 q^{71} -27712.0 q^{72} -52126.0 q^{73} +568.000 q^{74} -16250.0 q^{75} +17600.0 q^{76} +16896.0 q^{77} -4784.00 q^{78} -39640.0 q^{79} -6400.00 q^{80} +23221.0 q^{81} -6168.00 q^{82} -59826.0 q^{83} +9152.00 q^{84} -9450.00 q^{85} +20104.0 q^{86} +145860. q^{87} +49152.0 q^{88} +57690.0 q^{89} +43300.0 q^{90} +1012.00 q^{91} -31776.0 q^{92} +103688. q^{93} -98952.0 q^{94} -27500.0 q^{95} +26624.0 q^{96} -144382. q^{97} +65292.0 q^{98} -332544. q^{99} +O(q^{100})\)

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 \(-0.813926\pi\)
−0.833950 + 0.551839i \(0.813926\pi\)
\(4\) 16.0000 0.500000
\(5\) −25.0000 −0.447214
\(6\) 104.000 1.17938
\(7\) −22.0000 −0.169698 −0.0848492 0.996394i \(-0.527041\pi\)
−0.0848492 + 0.996394i \(0.527041\pi\)
\(8\) −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 \(-0.512018\pi\)
−0.0377459 + 0.999287i \(0.512018\pi\)
\(14\) 88.0000 0.119995
\(15\) 650.000 0.745908
\(16\) 256.000 0.250000
\(17\) 378.000 0.317227 0.158613 0.987341i \(-0.449298\pi\)
0.158613 + 0.987341i \(0.449298\pi\)
\(18\) −1732.00 −1.25999
\(19\) 1100.00 0.699051 0.349525 0.936927i \(-0.386343\pi\)
0.349525 + 0.936927i \(0.386343\pi\)
\(20\) −400.000 −0.223607
\(21\) 572.000 0.283040
\(22\) 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
\(28\) −352.000 −0.0848492
\(29\) −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 \(-0.621557\pi\)
−0.372667 + 0.927965i \(0.621557\pi\)
\(32\) −1024.00 −0.176777
\(33\) 19968.0 3.19190
\(34\) −1512.00 −0.224313
\(35\) 550.000 0.0758914
\(36\) 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 \(-0.477180\pi\)
0.0716300 + 0.997431i \(0.477180\pi\)
\(42\) −2288.00 −0.200139
\(43\) −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 \(-0.195773\pi\)
0.816752 + 0.576990i \(0.195773\pi\)
\(48\) −6656.00 −0.416975
\(49\) −16323.0 −0.971202
\(50\) −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
\(56\) 1408.00 0.0599974
\(57\) −28600.0 −1.16595
\(58\) 22440.0 0.875897
\(59\) 28380.0 1.06141 0.530704 0.847557i \(-0.321928\pi\)
0.530704 + 0.847557i \(0.321928\pi\)
\(60\) 10400.0 0.372954
\(61\) 5522.00 0.190008 0.0950040 0.995477i \(-0.469714\pi\)
0.0950040 + 0.995477i \(0.469714\pi\)
\(62\) 15952.0 0.527031
\(63\) −9526.00 −0.302384
\(64\) 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
\(70\) −2200.00 −0.0536633
\(71\) 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 \(-0.693997\pi\)
−0.572423 + 0.819958i \(0.693997\pi\)
\(74\) 568.000 0.0120578
\(75\) −16250.0 −0.333580
\(76\) 17600.0 0.349525
\(77\) 16896.0 0.324756
\(78\) −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 \(-0.658135\pi\)
−0.476612 + 0.879114i \(0.658135\pi\)
\(84\) 9152.00 0.141520
\(85\) −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 \(-0.373854\pi\)
0.386007 + 0.922496i \(0.373854\pi\)
\(90\) 43300.0 0.563484
\(91\) 1012.00 0.0128108
\(92\) −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 \(-0.784288\pi\)
−0.779029 + 0.626988i \(0.784288\pi\)
\(98\) 65292.0 0.686744
\(99\) −332544. −3.41005
\(100\) 10000.0 0.100000
\(101\) −141258. −1.37787 −0.688937 0.724821i \(-0.741922\pi\)
−0.688937 + 0.724821i \(0.741922\pi\)
\(102\) 39312.0 0.374132
\(103\) 139814. 1.29855 0.649273 0.760555i \(-0.275073\pi\)
0.649273 + 0.760555i \(0.275073\pi\)
\(104\) 2944.00 0.0266904
\(105\) −14300.0 −0.126579
\(106\) 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
\(112\) −5632.00 −0.0424246
\(113\) −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
\(119\) −8316.00 −0.0538328
\(120\) −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
\(126\) 38104.0 0.213818
\(127\) −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 \(-0.713955\pi\)
−0.622676 + 0.782479i \(0.713955\pi\)
\(132\) 319488. 1.59595
\(133\) −24200.0 −0.118628
\(134\) 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 \(-0.478422\pi\)
0.0677375 + 0.997703i \(0.478422\pi\)
\(140\) 8800.00 0.0379457
\(141\) −643188. −2.72452
\(142\) −169488. −0.705372
\(143\) 35328.0 0.144470
\(144\) 110848. 0.445473
\(145\) 140250. 0.553966
\(146\) 208504. 0.809529
\(147\) 424398. 1.61987
\(148\) −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
\(154\) −67584.0 −0.229637
\(155\) 99700.0 0.333323
\(156\) 19136.0 0.0629564
\(157\) −6022.00 −0.0194981 −0.00974903 0.999952i \(-0.503103\pi\)
−0.00974903 + 0.999952i \(0.503103\pi\)
\(158\) 158560. 0.505302
\(159\) 368316. 1.15539
\(160\) 25600.0 0.0790569
\(161\) 43692.0 0.132843
\(162\) −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 \(-0.220094\pi\)
0.770324 + 0.637652i \(0.220094\pi\)
\(168\) −36608.0 −0.100070
\(169\) −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 \(-0.322154\pi\)
0.530102 + 0.847934i \(0.322154\pi\)
\(174\) −583440. −1.46091
\(175\) −13750.0 −0.0339397
\(176\) −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 \(-0.287074\pi\)
0.620144 + 0.784488i \(0.287074\pi\)
\(182\) −4048.00 −0.00905862
\(183\) −143572. −0.316914
\(184\) 127104. 0.276767
\(185\) 3550.00 0.00762604
\(186\) −414752. −0.879035
\(187\) −290304. −0.607084
\(188\) 395808. 0.816752
\(189\) 108680. 0.221307
\(190\) 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
\(196\) −261168. −0.485601
\(197\) 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 \(-0.757174\pi\)
−0.722862 + 0.690993i \(0.757174\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 643292. 1.12310
\(202\) 565032. 0.974304
\(203\) 123420. 0.210206
\(204\) −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
\(210\) 57200.0 0.0895051
\(211\) 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
\(217\) 87736.0 0.126482
\(218\) −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 \(-0.596524\pi\)
−0.298612 + 0.954375i \(0.596524\pi\)
\(224\) 22528.0 0.0299987
\(225\) 270625. 0.356379
\(226\) 115224. 0.150062
\(227\) 420018. 0.541007 0.270504 0.962719i \(-0.412810\pi\)
0.270504 + 0.962719i \(0.412810\pi\)
\(228\) −457600. −0.582974
\(229\) 1.05875e6 1.33415 0.667075 0.744990i \(-0.267546\pi\)
0.667075 + 0.744990i \(0.267546\pi\)
\(230\) −198600. −0.247548
\(231\) −439296. −0.541661
\(232\) 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
\(238\) 33264.0 0.0380655
\(239\) −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 \(-0.600750\pi\)
−0.311258 + 0.950325i \(0.600750\pi\)
\(242\) −1.71509e6 −1.88256
\(243\) 596674. 0.648219
\(244\) 88352.0 0.0950040
\(245\) 408075. 0.434335
\(246\) 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 \(-0.406638\pi\)
0.289119 + 0.957293i \(0.406638\pi\)
\(252\) −152416. −0.151192
\(253\) 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 \(-0.599535\pi\)
−0.307628 + 0.951507i \(0.599535\pi\)
\(258\) −522704. −0.488885
\(259\) 3124.00 0.00289375
\(260\) 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
\(266\) 96800.0 0.0838825
\(267\) −1.49994e6 −1.28764
\(268\) −395872. −0.336680
\(269\) −735390. −0.619637 −0.309818 0.950796i \(-0.600268\pi\)
−0.309818 + 0.950796i \(0.600268\pi\)
\(270\) −494000. −0.412399
\(271\) −1.12131e6 −0.927474 −0.463737 0.885973i \(-0.653492\pi\)
−0.463737 + 0.885973i \(0.653492\pi\)
\(272\) 96768.0 0.0793066
\(273\) −26312.0 −0.0213672
\(274\) 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
\(280\) −35200.0 −0.0268317
\(281\) 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 \(-0.463416\pi\)
0.114679 + 0.993403i \(0.463416\pi\)
\(284\) 677952. 0.498773
\(285\) 715000. 0.521427
\(286\) −141312. −0.102156
\(287\) −33924.0 −0.0243110
\(288\) −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 \(-0.682342\pi\)
−0.542024 + 0.840363i \(0.682342\pi\)
\(294\) −1.69759e6 −1.14542
\(295\) −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
\(301\) 110572. 0.0703443
\(302\) −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 \(-0.376735\pi\)
0.377642 + 0.925952i \(0.376735\pi\)
\(308\) 270336. 0.162378
\(309\) −3.63516e6 −2.16585
\(310\) −398800. −0.235695
\(311\) −665988. −0.390450 −0.195225 0.980758i \(-0.562544\pi\)
−0.195225 + 0.980758i \(0.562544\pi\)
\(312\) −76544.0 −0.0445169
\(313\) −591286. −0.341143 −0.170572 0.985345i \(-0.554561\pi\)
−0.170572 + 0.985345i \(0.554561\pi\)
\(314\) 24088.0 0.0137872
\(315\) 238150. 0.135230
\(316\) −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
\(322\) −174768. −0.0939339
\(323\) 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
\(329\) −544236. −0.277203
\(330\) 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
\(336\) 146432. 0.0707600
\(337\) 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
\(343\) 728860. 0.334510
\(344\) 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 \(-0.314268\pi\)
0.550944 + 0.834542i \(0.314268\pi\)
\(350\) 55000.0 0.0239990
\(351\) 227240. 0.0984503
\(352\) 786432. 0.338302
\(353\) −413166. −0.176477 −0.0882384 0.996099i \(-0.528124\pi\)
−0.0882384 + 0.996099i \(0.528124\pi\)
\(354\) 2.95152e6 1.25181
\(355\) −1.05930e6 −0.446116
\(356\) 923040. 0.386007
\(357\) 216216. 0.0897878
\(358\) 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
\(364\) 16192.0 0.00640541
\(365\) 1.30315e6 0.511991
\(366\) 574288. 0.224092
\(367\) 1.16098e6 0.449944 0.224972 0.974365i \(-0.427771\pi\)
0.224972 + 0.974365i \(0.427771\pi\)
\(368\) −508416. −0.195704
\(369\) 667686. 0.255274
\(370\) −14200.0 −0.00539242
\(371\) 311652. 0.117553
\(372\) 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
\(378\) −434720. −0.156488
\(379\) 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 \(-0.667293\pi\)
−0.501704 + 0.865039i \(0.667293\pi\)
\(384\) 425984. 0.147423
\(385\) −422400. −0.145235
\(386\) −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
\(392\) 1.04467e6 0.343372
\(393\) 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 \(-0.454974\pi\)
0.140981 + 0.990012i \(0.454974\pi\)
\(398\) 3.23056e6 1.02228
\(399\) 629200. 0.197859
\(400\) 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
\(406\) −493680. −0.148638
\(407\) 109056. 0.0326335
\(408\) 628992. 0.187066
\(409\) −1.94653e6 −0.575377 −0.287689 0.957724i \(-0.592887\pi\)
−0.287689 + 0.957724i \(0.592887\pi\)
\(410\) 154200. 0.0453028
\(411\) 6.22705e6 1.81835
\(412\) 2.23702e6 0.649273
\(413\) −624360. −0.180119
\(414\) 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 \(-0.636654\pi\)
−0.416243 + 0.909253i \(0.636654\pi\)
\(420\) −228800. −0.0632897
\(421\) 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
\(427\) −121484. −0.0322440
\(428\) 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 \(-0.697410\pi\)
−0.581183 + 0.813773i \(0.697410\pi\)
\(434\) −350944. −0.0894362
\(435\) −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 \(-0.542783\pi\)
−0.134004 + 0.990981i \(0.542783\pi\)
\(440\) −1.22880e6 −0.302586
\(441\) −7.06786e6 −1.73058
\(442\) 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
\(448\) −90112.0 −0.0212123
\(449\) 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
\(455\) −25300.0 −0.00572917
\(456\) 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 \(-0.345617\pi\)
0.466216 + 0.884671i \(0.345617\pi\)
\(462\) 1.75718e6 0.383012
\(463\) 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 \(-0.520328\pi\)
−0.0638181 + 0.997962i \(0.520328\pi\)
\(468\) −318688. −0.0672591
\(469\) 544324. 0.114268
\(470\) 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
\(476\) −133056. −0.0269164
\(477\) −6.13388e6 −1.23435
\(478\) 1.48272e6 0.296817
\(479\) −4.57932e6 −0.911931 −0.455966 0.889997i \(-0.650706\pi\)
−0.455966 + 0.889997i \(0.650706\pi\)
\(480\) −665600. −0.131859
\(481\) 6532.00 0.00128731
\(482\) 2.24519e6 0.440186
\(483\) −1.13599e6 −0.221568
\(484\) 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
\(490\) −1.63230e6 −0.307121
\(491\) −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
\(497\) −932184. −0.169282
\(498\) −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 \(-0.201194\pi\)
0.806807 + 0.590815i \(0.201194\pi\)
\(504\) 609664. 0.106909
\(505\) 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 \(-0.286660\pi\)
0.621165 + 0.783679i \(0.286660\pi\)
\(510\) −982800. −0.167317
\(511\) 1.14677e6 0.194279
\(512\) −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
\(518\) −12496.0 −0.00204619
\(519\) −1.08512e7 −1.76831
\(520\) −73600.0 −0.0119363
\(521\) 5.81020e6 0.937771 0.468886 0.883259i \(-0.344656\pi\)
0.468886 + 0.883259i \(0.344656\pi\)
\(522\) 9.71652e6 1.56075
\(523\) −8.17067e6 −1.30618 −0.653090 0.757280i \(-0.726528\pi\)
−0.653090 + 0.757280i \(0.726528\pi\)
\(524\) −3.91373e6 −0.622676
\(525\) 357500. 0.0566080
\(526\) −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
\(532\) −387200. −0.0593139
\(533\) −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
\(539\) 1.25361e7 1.85861
\(540\) 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
\(546\) 105248. 0.0151089
\(547\) −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
\(553\) 872080. 0.121267
\(554\) 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
\(560\) 140800. 0.0189729
\(561\) 7.54790e6 1.01256
\(562\) −5.80841e6 −0.775740
\(563\) 2.01941e6 0.268506 0.134253 0.990947i \(-0.457136\pi\)
0.134253 + 0.990947i \(0.457136\pi\)
\(564\) −1.02910e7 −1.36226
\(565\) 720150. 0.0949078
\(566\) −1.23606e6 −0.162180
\(567\) −510862. −0.0667338
\(568\) −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
\(574\) 135696. 0.0171905
\(575\) −1.24125e6 −0.156563
\(576\) 1.77357e6 0.222737
\(577\) −2.31458e6 −0.289423 −0.144711 0.989474i \(-0.546225\pi\)
−0.144711 + 0.989474i \(0.546225\pi\)
\(578\) 5.10789e6 0.635949
\(579\) −1.26254e7 −1.56513
\(580\) 2.24400e6 0.276983
\(581\) 1.31617e6 0.161760
\(582\) −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 \(-0.482293\pi\)
0.0556008 + 0.998453i \(0.482293\pi\)
\(588\) 6.79037e6 0.809935
\(589\) −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 \(-0.516912\pi\)
−0.0531043 + 0.998589i \(0.516912\pi\)
\(594\) −1.51757e7 −1.76475
\(595\) 207900. 0.0240748
\(596\) −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 \(-0.387590\pi\)
0.345851 + 0.938290i \(0.387590\pi\)
\(602\) −442288. −0.0497409
\(603\) −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 \(-0.580026\pi\)
−0.248769 + 0.968563i \(0.580026\pi\)
\(608\) −1.12640e6 −0.123576
\(609\) −3.20892e6 −0.350603
\(610\) 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
\(616\) −1.08134e6 −0.114819
\(617\) −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 \(-0.368885\pi\)
0.400360 + 0.916358i \(0.368885\pi\)
\(620\) 1.59520e6 0.166662
\(621\) 9.81084e6 1.02089
\(622\) 2.66395e6 0.276090
\(623\) −1.26918e6 −0.131010
\(624\) 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
\(630\) −952600. −0.0956223
\(631\) 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
\(637\) 750858. 0.0733178
\(638\) −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 \(-0.729329\pi\)
−0.659730 + 0.751503i \(0.729329\pi\)
\(644\) 699072. 0.0664213
\(645\) −3.26690e6 −0.309198
\(646\) −1.66320e6 −0.156806
\(647\) −1.48997e7 −1.39932 −0.699658 0.714478i \(-0.746664\pi\)
−0.699658 + 0.714478i \(0.746664\pi\)
\(648\) −1.48614e6 −0.139035
\(649\) −2.17958e7 −2.03124
\(650\) 115000. 0.0106761
\(651\) −2.28114e6 −0.210959
\(652\) −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
\(658\) 2.17694e6 0.196012
\(659\) −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 \(-0.705460\pi\)
−0.601575 + 0.798816i \(0.705460\pi\)
\(662\) 1.31831e7 1.16915
\(663\) 452088. 0.0399429
\(664\) 3.82886e6 0.337015
\(665\) 605000. 0.0530519
\(666\) 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
\(672\) −585728. −0.0500349
\(673\) 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 \(-0.474679\pi\)
0.0794650 + 0.996838i \(0.474679\pi\)
\(678\) −2.99582e6 −0.250289
\(679\) 3.17640e6 0.264400
\(680\) 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
\(686\) −2.91544e6 −0.236534
\(687\) −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 \(-0.305102\pi\)
0.574743 + 0.818334i \(0.305102\pi\)
\(692\) 6.67766e6 0.530102
\(693\) 7.31597e6 0.578680
\(694\) −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
\(700\) −220000. −0.0169698
\(701\) −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
\(707\) 3.10768e6 0.233823
\(708\) −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
\(714\) −864864. −0.0634896
\(715\) −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 \(-0.221684\pi\)
0.767130 + 0.641492i \(0.221684\pi\)
\(720\) −2.77120e6 −0.199222
\(721\) −3.07591e6 −0.220361
\(722\) 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 \(-0.316961\pi\)
0.543863 + 0.839174i \(0.316961\pi\)
\(728\) −64768.0 −0.00452931
\(729\) −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 \(-0.637559\pi\)
−0.418827 + 0.908066i \(0.637559\pi\)
\(734\) −4.64391e6 −0.318159
\(735\) −1.06100e7 −0.724428
\(736\) 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
\(742\) −1.24661e6 −0.0831228
\(743\) 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
\(749\) −1.90120e6 −0.123829
\(750\) −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
\(756\) 1.73888e6 0.110653
\(757\) 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 \(-0.329286\pi\)
0.510970 + 0.859598i \(0.329286\pi\)
\(762\) −2.25162e7 −1.40478
\(763\) −4.80590e6 −0.298857
\(764\) −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 \(-0.211612\pi\)
0.787040 + 0.616902i \(0.211612\pi\)
\(770\) 1.68960e6 0.102697
\(771\) 1.69380e7 1.02619
\(772\) 7.76950e6 0.469191
\(773\) −1.90592e7 −1.14725 −0.573624 0.819119i \(-0.694463\pi\)
−0.573624 + 0.819119i \(0.694463\pi\)
\(774\) 8.70503e6 0.522298
\(775\) −2.49250e6 −0.149067
\(776\) 9.24045e6 0.550857
\(777\) −81224.0 −0.00482649
\(778\) 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
\(784\) −4.17869e6 −0.242801
\(785\) 150550. 0.00871980
\(786\) −2.54392e7 −1.46875
\(787\) −1.73411e7 −0.998021 −0.499011 0.866596i \(-0.666303\pi\)
−0.499011 + 0.866596i \(0.666303\pi\)
\(788\) 1.61628e7 0.927262
\(789\) −2.38569e7 −1.36434
\(790\) −3.96400e6 −0.225978
\(791\) 633732. 0.0360134
\(792\) 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 \(-0.755779\pi\)
−0.719827 + 0.694153i \(0.755779\pi\)
\(798\) −2.51680e6 −0.139908
\(799\) 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
\(805\) −1.09230e6 −0.0594090
\(806\) −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 \(-0.728485\pi\)
−0.657735 + 0.753249i \(0.728485\pi\)
\(812\) 1.97472e6 0.105103
\(813\) 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
\(819\) 438196. 0.0228275
\(820\) −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
\(826\) 2.49744e6 0.127363
\(827\) −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 \(-0.365860\pi\)
0.409052 + 0.912511i \(0.365860\pi\)
\(830\) −5.98260e6 −0.301436
\(831\) 4.31689e7 2.16854
\(832\) −188416. −0.00943647
\(833\) −6.17009e6 −0.308091
\(834\) 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 \(-0.715531\pi\)
−0.626543 + 0.779387i \(0.715531\pi\)
\(840\) 915200. 0.0447526
\(841\) 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
\(847\) −9.43301e6 −0.451795
\(848\) −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 \(-0.675777\pi\)
−0.524579 + 0.851362i \(0.675777\pi\)
\(854\) 485936. 0.0228000
\(855\) −1.19075e7 −0.557064
\(856\) −5.53075e6 −0.257988
\(857\) 1.96872e7 0.915656 0.457828 0.889041i \(-0.348628\pi\)
0.457828 + 0.889041i \(0.348628\pi\)
\(858\) 3.67411e6 0.170386
\(859\) 6.77582e6 0.313313 0.156657 0.987653i \(-0.449928\pi\)
0.156657 + 0.987653i \(0.449928\pi\)
\(860\) 2.01040e6 0.0926907
\(861\) 882024. 0.0405483
\(862\) 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
\(868\) 1.40378e6 0.0632410
\(869\) 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
\(875\) 343750. 0.0151783
\(876\) 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 \(-0.604502\pi\)
−0.322438 + 0.946590i \(0.604502\pi\)
\(882\) 2.82714e7 1.22370
\(883\) −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 \(-0.619642\pi\)
−0.367080 + 0.930189i \(0.619642\pi\)
\(888\) −236288. −0.0100556
\(889\) 4.76304e6 0.202130
\(890\) 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
\(896\) 360448. 0.0149994
\(897\) −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
\(903\) −2.87487e6 −0.117327
\(904\) 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
\(910\) 101200. 0.00405114
\(911\) −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
\(917\) 5.38138e6 0.211334
\(918\) 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
\(924\) −7.02874e6 −0.270830
\(925\) −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 \(-0.708794\pi\)
−0.609909 + 0.792472i \(0.708794\pi\)
\(930\) 1.03688e7 0.393116
\(931\) −1.79553e7 −0.678920
\(932\) −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 \(-0.408419\pi\)
0.283757 + 0.958896i \(0.408419\pi\)
\(938\) −2.17730e6 −0.0807998
\(939\) 1.53734e7 0.568993
\(940\) −9.89520e6 −0.365262
\(941\) 3.48166e6 0.128178 0.0640889 0.997944i \(-0.479586\pi\)
0.0640889 + 0.997944i \(0.479586\pi\)
\(942\) −626288. −0.0229957
\(943\) −3.06241e6 −0.112146
\(944\) 7.26528e6 0.265352
\(945\) −2.71700e6 −0.0989715
\(946\) −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
\(952\) 532224. 0.0190328
\(953\) −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
\(959\) 5.26904e6 0.185006
\(960\) 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
\(966\) 4.54397e6 0.156672
\(967\) 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 \(-0.316779\pi\)
0.544344 + 0.838862i \(0.316779\pi\)
\(972\) 9.54678e6 0.324109
\(973\) −678920. −0.0229899
\(974\) −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
\(980\) 6.52920e6 0.217167
\(981\) 9.45888e7 3.13810
\(982\) 1.04940e7 0.347264
\(983\) 3.49621e7 1.15402 0.577010 0.816737i \(-0.304219\pi\)
0.577010 + 0.816737i \(0.304219\pi\)
\(984\) 2.56589e6 0.0844792
\(985\) −2.52544e7 −0.829368
\(986\) 8.48232e6 0.277858
\(987\) 1.41501e7 0.462347
\(988\) −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
\(994\) 3.72874e6 0.119700
\(995\) 2.01910e7 0.646547
\(996\) 2.48876e7 0.794941
\(997\) 3.20789e7 1.02207 0.511035 0.859560i \(-0.329262\pi\)
0.511035 + 0.859560i \(0.329262\pi\)
\(998\) 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 10.6.a.a.1.1 1
3.2 odd 2 90.6.a.f.1.1 1
4.3 odd 2 80.6.a.h.1.1 1
5.2 odd 4 50.6.b.d.49.1 2
5.3 odd 4 50.6.b.d.49.2 2
5.4 even 2 50.6.a.g.1.1 1
7.6 odd 2 490.6.a.j.1.1 1
8.3 odd 2 320.6.a.a.1.1 1
8.5 even 2 320.6.a.p.1.1 1
12.11 even 2 720.6.a.r.1.1 1
15.2 even 4 450.6.c.o.199.2 2
15.8 even 4 450.6.c.o.199.1 2
15.14 odd 2 450.6.a.h.1.1 1
20.3 even 4 400.6.c.a.49.2 2
20.7 even 4 400.6.c.a.49.1 2
20.19 odd 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 1.1 even 1 trivial
50.6.a.g.1.1 1 5.4 even 2
50.6.b.d.49.1 2 5.2 odd 4
50.6.b.d.49.2 2 5.3 odd 4
80.6.a.h.1.1 1 4.3 odd 2
90.6.a.f.1.1 1 3.2 odd 2
320.6.a.a.1.1 1 8.3 odd 2
320.6.a.p.1.1 1 8.5 even 2
400.6.a.a.1.1 1 20.19 odd 2
400.6.c.a.49.1 2 20.7 even 4
400.6.c.a.49.2 2 20.3 even 4
450.6.a.h.1.1 1 15.14 odd 2
450.6.c.o.199.1 2 15.8 even 4
450.6.c.o.199.2 2 15.2 even 4
490.6.a.j.1.1 1 7.6 odd 2
720.6.a.r.1.1 1 12.11 even 2