Properties

Label 43.6.a.b.1.7
Level 43
Weight 6
Character 43.1
Self dual yes
Analytic conductor 6.897
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.89650425196\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-4.38824\) of \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} +O(q^{10})\) \(q+5.38824 q^{2} +25.0462 q^{3} -2.96684 q^{4} -0.456695 q^{5} +134.955 q^{6} +166.517 q^{7} -188.410 q^{8} +384.312 q^{9} -2.46078 q^{10} -65.6764 q^{11} -74.3080 q^{12} -689.371 q^{13} +897.236 q^{14} -11.4385 q^{15} -920.259 q^{16} +737.385 q^{17} +2070.77 q^{18} -609.887 q^{19} +1.35494 q^{20} +4170.63 q^{21} -353.880 q^{22} +1312.45 q^{23} -4718.95 q^{24} -3124.79 q^{25} -3714.50 q^{26} +3539.34 q^{27} -494.030 q^{28} -8969.74 q^{29} -61.6333 q^{30} +5858.93 q^{31} +1070.53 q^{32} -1644.94 q^{33} +3973.21 q^{34} -76.0477 q^{35} -1140.19 q^{36} -55.9069 q^{37} -3286.22 q^{38} -17266.1 q^{39} +86.0458 q^{40} -10450.3 q^{41} +22472.4 q^{42} +1849.00 q^{43} +194.851 q^{44} -175.514 q^{45} +7071.82 q^{46} +1942.82 q^{47} -23049.0 q^{48} +10921.1 q^{49} -16837.1 q^{50} +18468.7 q^{51} +2045.25 q^{52} +30129.2 q^{53} +19070.8 q^{54} +29.9941 q^{55} -31373.5 q^{56} -15275.3 q^{57} -48331.2 q^{58} +52167.4 q^{59} +33.9361 q^{60} -14040.1 q^{61} +31569.4 q^{62} +63994.7 q^{63} +35216.6 q^{64} +314.832 q^{65} -8863.36 q^{66} +51437.7 q^{67} -2187.70 q^{68} +32872.0 q^{69} -409.764 q^{70} +11268.6 q^{71} -72408.2 q^{72} -61124.5 q^{73} -301.240 q^{74} -78264.2 q^{75} +1809.44 q^{76} -10936.3 q^{77} -93034.1 q^{78} +96018.3 q^{79} +420.278 q^{80} -4740.91 q^{81} -56308.8 q^{82} +30378.0 q^{83} -12373.6 q^{84} -336.760 q^{85} +9962.86 q^{86} -224658. q^{87} +12374.1 q^{88} -65040.4 q^{89} -945.710 q^{90} -114792. q^{91} -3893.84 q^{92} +146744. q^{93} +10468.4 q^{94} +278.532 q^{95} +26812.8 q^{96} +12067.6 q^{97} +58845.3 q^{98} -25240.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.38824 0.952516 0.476258 0.879306i \(-0.341993\pi\)
0.476258 + 0.879306i \(0.341993\pi\)
\(3\) 25.0462 1.60671 0.803357 0.595497i \(-0.203045\pi\)
0.803357 + 0.595497i \(0.203045\pi\)
\(4\) −2.96684 −0.0927137
\(5\) −0.456695 −0.00816961 −0.00408481 0.999992i \(-0.501300\pi\)
−0.00408481 + 0.999992i \(0.501300\pi\)
\(6\) 134.955 1.53042
\(7\) 166.517 1.28444 0.642221 0.766519i \(-0.278013\pi\)
0.642221 + 0.766519i \(0.278013\pi\)
\(8\) −188.410 −1.04083
\(9\) 384.312 1.58153
\(10\) −2.46078 −0.00778168
\(11\) −65.6764 −0.163654 −0.0818272 0.996647i \(-0.526076\pi\)
−0.0818272 + 0.996647i \(0.526076\pi\)
\(12\) −74.3080 −0.148964
\(13\) −689.371 −1.13134 −0.565672 0.824630i \(-0.691383\pi\)
−0.565672 + 0.824630i \(0.691383\pi\)
\(14\) 897.236 1.22345
\(15\) −11.4385 −0.0131262
\(16\) −920.259 −0.898690
\(17\) 737.385 0.618831 0.309415 0.950927i \(-0.399867\pi\)
0.309415 + 0.950927i \(0.399867\pi\)
\(18\) 2070.77 1.50643
\(19\) −609.887 −0.387583 −0.193792 0.981043i \(-0.562079\pi\)
−0.193792 + 0.981043i \(0.562079\pi\)
\(20\) 1.35494 0.000757435 0
\(21\) 4170.63 2.06373
\(22\) −353.880 −0.155883
\(23\) 1312.45 0.517326 0.258663 0.965968i \(-0.416718\pi\)
0.258663 + 0.965968i \(0.416718\pi\)
\(24\) −4718.95 −1.67231
\(25\) −3124.79 −0.999933
\(26\) −3714.50 −1.07762
\(27\) 3539.34 0.934357
\(28\) −494.030 −0.119085
\(29\) −8969.74 −1.98055 −0.990273 0.139137i \(-0.955567\pi\)
−0.990273 + 0.139137i \(0.955567\pi\)
\(30\) −61.6333 −0.0125029
\(31\) 5858.93 1.09500 0.547500 0.836806i \(-0.315580\pi\)
0.547500 + 0.836806i \(0.315580\pi\)
\(32\) 1070.53 0.184810
\(33\) −1644.94 −0.262946
\(34\) 3973.21 0.589446
\(35\) −76.0477 −0.0104934
\(36\) −1140.19 −0.146630
\(37\) −55.9069 −0.00671369 −0.00335685 0.999994i \(-0.501069\pi\)
−0.00335685 + 0.999994i \(0.501069\pi\)
\(38\) −3286.22 −0.369179
\(39\) −17266.1 −1.81775
\(40\) 86.0458 0.00850315
\(41\) −10450.3 −0.970889 −0.485445 0.874267i \(-0.661342\pi\)
−0.485445 + 0.874267i \(0.661342\pi\)
\(42\) 22472.4 1.96574
\(43\) 1849.00 0.152499
\(44\) 194.851 0.0151730
\(45\) −175.514 −0.0129205
\(46\) 7071.82 0.492762
\(47\) 1942.82 0.128288 0.0641442 0.997941i \(-0.479568\pi\)
0.0641442 + 0.997941i \(0.479568\pi\)
\(48\) −23049.0 −1.44394
\(49\) 10921.1 0.649792
\(50\) −16837.1 −0.952452
\(51\) 18468.7 0.994284
\(52\) 2045.25 0.104891
\(53\) 30129.2 1.47332 0.736661 0.676262i \(-0.236401\pi\)
0.736661 + 0.676262i \(0.236401\pi\)
\(54\) 19070.8 0.889989
\(55\) 29.9941 0.00133699
\(56\) −31373.5 −1.33688
\(57\) −15275.3 −0.622736
\(58\) −48331.2 −1.88650
\(59\) 52167.4 1.95106 0.975528 0.219877i \(-0.0705657\pi\)
0.975528 + 0.219877i \(0.0705657\pi\)
\(60\) 33.9361 0.00121698
\(61\) −14040.1 −0.483108 −0.241554 0.970387i \(-0.577657\pi\)
−0.241554 + 0.970387i \(0.577657\pi\)
\(62\) 31569.4 1.04301
\(63\) 63994.7 2.03139
\(64\) 35216.6 1.07473
\(65\) 314.832 0.00924264
\(66\) −8863.36 −0.250460
\(67\) 51437.7 1.39989 0.699946 0.714196i \(-0.253208\pi\)
0.699946 + 0.714196i \(0.253208\pi\)
\(68\) −2187.70 −0.0573741
\(69\) 32872.0 0.831196
\(70\) −409.764 −0.00999512
\(71\) 11268.6 0.265292 0.132646 0.991163i \(-0.457653\pi\)
0.132646 + 0.991163i \(0.457653\pi\)
\(72\) −72408.2 −1.64610
\(73\) −61124.5 −1.34248 −0.671241 0.741239i \(-0.734238\pi\)
−0.671241 + 0.741239i \(0.734238\pi\)
\(74\) −301.240 −0.00639490
\(75\) −78264.2 −1.60661
\(76\) 1809.44 0.0359343
\(77\) −10936.3 −0.210205
\(78\) −93034.1 −1.73143
\(79\) 96018.3 1.73096 0.865478 0.500947i \(-0.167015\pi\)
0.865478 + 0.500947i \(0.167015\pi\)
\(80\) 420.278 0.00734195
\(81\) −4740.91 −0.0802878
\(82\) −56308.8 −0.924787
\(83\) 30378.0 0.484021 0.242010 0.970274i \(-0.422193\pi\)
0.242010 + 0.970274i \(0.422193\pi\)
\(84\) −12373.6 −0.191336
\(85\) −336.760 −0.00505561
\(86\) 9962.86 0.145257
\(87\) −224658. −3.18217
\(88\) 12374.1 0.170336
\(89\) −65040.4 −0.870378 −0.435189 0.900339i \(-0.643319\pi\)
−0.435189 + 0.900339i \(0.643319\pi\)
\(90\) −945.710 −0.0123070
\(91\) −114792. −1.45315
\(92\) −3893.84 −0.0479632
\(93\) 146744. 1.75935
\(94\) 10468.4 0.122197
\(95\) 278.532 0.00316641
\(96\) 26812.8 0.296937
\(97\) 12067.6 0.130224 0.0651119 0.997878i \(-0.479260\pi\)
0.0651119 + 0.997878i \(0.479260\pi\)
\(98\) 58845.3 0.618938
\(99\) −25240.2 −0.258825
\(100\) 9270.75 0.0927075
\(101\) 107046. 1.04416 0.522079 0.852897i \(-0.325157\pi\)
0.522079 + 0.852897i \(0.325157\pi\)
\(102\) 99513.8 0.947072
\(103\) −86209.7 −0.800688 −0.400344 0.916365i \(-0.631109\pi\)
−0.400344 + 0.916365i \(0.631109\pi\)
\(104\) 129884. 1.17753
\(105\) −1904.71 −0.0168599
\(106\) 162343. 1.40336
\(107\) 197153. 1.66473 0.832365 0.554227i \(-0.186986\pi\)
0.832365 + 0.554227i \(0.186986\pi\)
\(108\) −10500.6 −0.0866276
\(109\) 165311. 1.33271 0.666355 0.745634i \(-0.267853\pi\)
0.666355 + 0.745634i \(0.267853\pi\)
\(110\) 161.615 0.00127351
\(111\) −1400.26 −0.0107870
\(112\) −153239. −1.15432
\(113\) −179790. −1.32455 −0.662275 0.749260i \(-0.730409\pi\)
−0.662275 + 0.749260i \(0.730409\pi\)
\(114\) −82307.3 −0.593166
\(115\) −599.391 −0.00422635
\(116\) 26611.8 0.183624
\(117\) −264934. −1.78926
\(118\) 281091. 1.85841
\(119\) 122787. 0.794852
\(120\) 2155.12 0.0136621
\(121\) −156738. −0.973217
\(122\) −75651.3 −0.460168
\(123\) −261741. −1.55994
\(124\) −17382.5 −0.101522
\(125\) 2854.25 0.0163387
\(126\) 344819. 1.93493
\(127\) −286585. −1.57668 −0.788341 0.615238i \(-0.789060\pi\)
−0.788341 + 0.615238i \(0.789060\pi\)
\(128\) 155498. 0.838882
\(129\) 46310.4 0.245022
\(130\) 1696.39 0.00880376
\(131\) 67619.1 0.344263 0.172132 0.985074i \(-0.444935\pi\)
0.172132 + 0.985074i \(0.444935\pi\)
\(132\) 4880.28 0.0243787
\(133\) −101557. −0.497829
\(134\) 277159. 1.33342
\(135\) −1616.40 −0.00763333
\(136\) −138931. −0.644096
\(137\) 133580. 0.608050 0.304025 0.952664i \(-0.401669\pi\)
0.304025 + 0.952664i \(0.401669\pi\)
\(138\) 177122. 0.791727
\(139\) −262195. −1.15103 −0.575516 0.817790i \(-0.695199\pi\)
−0.575516 + 0.817790i \(0.695199\pi\)
\(140\) 225.621 0.000972881 0
\(141\) 48660.2 0.206123
\(142\) 60718.0 0.252695
\(143\) 45275.4 0.185149
\(144\) −353667. −1.42131
\(145\) 4096.44 0.0161803
\(146\) −329354. −1.27873
\(147\) 273531. 1.04403
\(148\) 165.867 0.000622451 0
\(149\) 187414. 0.691569 0.345785 0.938314i \(-0.387613\pi\)
0.345785 + 0.938314i \(0.387613\pi\)
\(150\) −421706. −1.53032
\(151\) −131632. −0.469807 −0.234904 0.972019i \(-0.575477\pi\)
−0.234904 + 0.972019i \(0.575477\pi\)
\(152\) 114909. 0.403407
\(153\) 283386. 0.978701
\(154\) −58927.3 −0.200223
\(155\) −2675.75 −0.00894573
\(156\) 51225.8 0.168530
\(157\) −252270. −0.816800 −0.408400 0.912803i \(-0.633913\pi\)
−0.408400 + 0.912803i \(0.633913\pi\)
\(158\) 517370. 1.64876
\(159\) 754622. 2.36721
\(160\) −488.908 −0.00150983
\(161\) 218547. 0.664476
\(162\) −25545.2 −0.0764754
\(163\) −518121. −1.52743 −0.763717 0.645552i \(-0.776627\pi\)
−0.763717 + 0.645552i \(0.776627\pi\)
\(164\) 31004.4 0.0900147
\(165\) 751.238 0.00214817
\(166\) 163684. 0.461038
\(167\) −681328. −1.89045 −0.945224 0.326422i \(-0.894157\pi\)
−0.945224 + 0.326422i \(0.894157\pi\)
\(168\) −785788. −2.14799
\(169\) 103939. 0.279939
\(170\) −1814.54 −0.00481554
\(171\) −234387. −0.612976
\(172\) −5485.68 −0.0141387
\(173\) −148596. −0.377478 −0.188739 0.982027i \(-0.560440\pi\)
−0.188739 + 0.982027i \(0.560440\pi\)
\(174\) −1.21051e6 −3.03107
\(175\) −520332. −1.28436
\(176\) 60439.3 0.147075
\(177\) 1.30660e6 3.13479
\(178\) −350453. −0.829049
\(179\) 103068. 0.240432 0.120216 0.992748i \(-0.461641\pi\)
0.120216 + 0.992748i \(0.461641\pi\)
\(180\) 520.720 0.00119791
\(181\) 309316. 0.701789 0.350894 0.936415i \(-0.385878\pi\)
0.350894 + 0.936415i \(0.385878\pi\)
\(182\) −618529. −1.38414
\(183\) −351650. −0.776217
\(184\) −247279. −0.538447
\(185\) 25.5324 5.48483e−5 0
\(186\) 790693. 1.67581
\(187\) −48428.8 −0.101274
\(188\) −5764.02 −0.0118941
\(189\) 589362. 1.20013
\(190\) 1500.80 0.00301605
\(191\) 373258. 0.740330 0.370165 0.928966i \(-0.379301\pi\)
0.370165 + 0.928966i \(0.379301\pi\)
\(192\) 882042. 1.72678
\(193\) 85782.8 0.165770 0.0828852 0.996559i \(-0.473587\pi\)
0.0828852 + 0.996559i \(0.473587\pi\)
\(194\) 65023.0 0.124040
\(195\) 7885.36 0.0148503
\(196\) −32401.0 −0.0602446
\(197\) −178146. −0.327047 −0.163523 0.986539i \(-0.552286\pi\)
−0.163523 + 0.986539i \(0.552286\pi\)
\(198\) −136001. −0.246535
\(199\) 154725. 0.276967 0.138484 0.990365i \(-0.455777\pi\)
0.138484 + 0.990365i \(0.455777\pi\)
\(200\) 588741. 1.04076
\(201\) 1.28832e6 2.24923
\(202\) 576789. 0.994577
\(203\) −1.49362e6 −2.54390
\(204\) −54793.6 −0.0921838
\(205\) 4772.61 0.00793179
\(206\) −464519. −0.762668
\(207\) 504392. 0.818168
\(208\) 634400. 1.01673
\(209\) 40055.2 0.0634297
\(210\) −10263.0 −0.0160593
\(211\) −682180. −1.05485 −0.527427 0.849600i \(-0.676843\pi\)
−0.527427 + 0.849600i \(0.676843\pi\)
\(212\) −89388.4 −0.136597
\(213\) 282236. 0.426249
\(214\) 1.06231e6 1.58568
\(215\) −844.429 −0.00124585
\(216\) −666846. −0.972504
\(217\) 975615. 1.40647
\(218\) 890736. 1.26943
\(219\) −1.53094e6 −2.15698
\(220\) −88.9876 −0.000123957 0
\(221\) −508332. −0.700110
\(222\) −7544.92 −0.0102748
\(223\) −464004. −0.624827 −0.312413 0.949946i \(-0.601137\pi\)
−0.312413 + 0.949946i \(0.601137\pi\)
\(224\) 178263. 0.237378
\(225\) −1.20090e6 −1.58143
\(226\) −968750. −1.26166
\(227\) 1.13876e6 1.46679 0.733396 0.679801i \(-0.237934\pi\)
0.733396 + 0.679801i \(0.237934\pi\)
\(228\) 45319.5 0.0577361
\(229\) 648718. 0.817462 0.408731 0.912655i \(-0.365971\pi\)
0.408731 + 0.912655i \(0.365971\pi\)
\(230\) −3229.67 −0.00402567
\(231\) −273912. −0.337739
\(232\) 1.68999e6 2.06141
\(233\) −588684. −0.710383 −0.355191 0.934794i \(-0.615584\pi\)
−0.355191 + 0.934794i \(0.615584\pi\)
\(234\) −1.42753e6 −1.70430
\(235\) −887.275 −0.00104807
\(236\) −154772. −0.180889
\(237\) 2.40489e6 2.78115
\(238\) 661608. 0.757109
\(239\) 739129. 0.837000 0.418500 0.908217i \(-0.362556\pi\)
0.418500 + 0.908217i \(0.362556\pi\)
\(240\) 10526.4 0.0117964
\(241\) −1.57360e6 −1.74523 −0.872615 0.488409i \(-0.837577\pi\)
−0.872615 + 0.488409i \(0.837577\pi\)
\(242\) −844540. −0.927005
\(243\) −978801. −1.06336
\(244\) 41654.6 0.0447908
\(245\) −4987.60 −0.00530855
\(246\) −1.41032e6 −1.48587
\(247\) 420438. 0.438490
\(248\) −1.10388e6 −1.13971
\(249\) 760854. 0.777684
\(250\) 15379.4 0.0155628
\(251\) 456789. 0.457648 0.228824 0.973468i \(-0.426512\pi\)
0.228824 + 0.973468i \(0.426512\pi\)
\(252\) −189862. −0.188337
\(253\) −86197.3 −0.0846627
\(254\) −1.54419e6 −1.50181
\(255\) −8434.56 −0.00812292
\(256\) −289068. −0.275676
\(257\) 1.12132e6 1.05900 0.529499 0.848310i \(-0.322380\pi\)
0.529499 + 0.848310i \(0.322380\pi\)
\(258\) 249532. 0.233387
\(259\) −9309.48 −0.00862335
\(260\) −934.057 −0.000856919 0
\(261\) −3.44718e6 −3.13230
\(262\) 364348. 0.327916
\(263\) 1.75620e6 1.56562 0.782808 0.622263i \(-0.213786\pi\)
0.782808 + 0.622263i \(0.213786\pi\)
\(264\) 309924. 0.273681
\(265\) −13759.9 −0.0120365
\(266\) −547213. −0.474190
\(267\) −1.62901e6 −1.39845
\(268\) −152607. −0.129789
\(269\) 1.22933e6 1.03583 0.517915 0.855432i \(-0.326708\pi\)
0.517915 + 0.855432i \(0.326708\pi\)
\(270\) −8709.55 −0.00727087
\(271\) 1.32305e6 1.09435 0.547173 0.837020i \(-0.315704\pi\)
0.547173 + 0.837020i \(0.315704\pi\)
\(272\) −678585. −0.556137
\(273\) −2.87511e6 −2.33479
\(274\) 719760. 0.579177
\(275\) 205225. 0.163643
\(276\) −97525.9 −0.0770632
\(277\) 1.96854e6 1.54151 0.770754 0.637133i \(-0.219880\pi\)
0.770754 + 0.637133i \(0.219880\pi\)
\(278\) −1.41277e6 −1.09638
\(279\) 2.25166e6 1.73178
\(280\) 14328.1 0.0109218
\(281\) −1.11820e6 −0.844801 −0.422400 0.906409i \(-0.638812\pi\)
−0.422400 + 0.906409i \(0.638812\pi\)
\(282\) 262193. 0.196335
\(283\) 1.25727e6 0.933174 0.466587 0.884475i \(-0.345483\pi\)
0.466587 + 0.884475i \(0.345483\pi\)
\(284\) −33432.2 −0.0245962
\(285\) 6976.18 0.00508751
\(286\) 243955. 0.176358
\(287\) −1.74016e6 −1.24705
\(288\) 411420. 0.292283
\(289\) −876121. −0.617049
\(290\) 22072.6 0.0154120
\(291\) 302247. 0.209233
\(292\) 181347. 0.124466
\(293\) −260406. −0.177207 −0.0886037 0.996067i \(-0.528240\pi\)
−0.0886037 + 0.996067i \(0.528240\pi\)
\(294\) 1.47385e6 0.994456
\(295\) −23824.6 −0.0159394
\(296\) 10533.4 0.00698779
\(297\) −232451. −0.152912
\(298\) 1.00983e6 0.658731
\(299\) −904768. −0.585274
\(300\) 232197. 0.148954
\(301\) 307891. 0.195876
\(302\) −709266. −0.447499
\(303\) 2.68109e6 1.67766
\(304\) 561254. 0.348318
\(305\) 6412.03 0.00394681
\(306\) 1.52695e6 0.932228
\(307\) −1.56144e6 −0.945536 −0.472768 0.881187i \(-0.656745\pi\)
−0.472768 + 0.881187i \(0.656745\pi\)
\(308\) 32446.1 0.0194888
\(309\) −2.15923e6 −1.28648
\(310\) −14417.6 −0.00852095
\(311\) 655137. 0.384088 0.192044 0.981386i \(-0.438488\pi\)
0.192044 + 0.981386i \(0.438488\pi\)
\(312\) 3.25311e6 1.89196
\(313\) −212890. −0.122827 −0.0614136 0.998112i \(-0.519561\pi\)
−0.0614136 + 0.998112i \(0.519561\pi\)
\(314\) −1.35929e6 −0.778015
\(315\) −29226.1 −0.0165956
\(316\) −284871. −0.160483
\(317\) −385858. −0.215665 −0.107832 0.994169i \(-0.534391\pi\)
−0.107832 + 0.994169i \(0.534391\pi\)
\(318\) 4.06608e6 2.25480
\(319\) 589100. 0.324125
\(320\) −16083.2 −0.00878009
\(321\) 4.93794e6 2.67475
\(322\) 1.17758e6 0.632924
\(323\) −449721. −0.239849
\(324\) 14065.5 0.00744378
\(325\) 2.15414e6 1.13127
\(326\) −2.79176e6 −1.45490
\(327\) 4.14042e6 2.14129
\(328\) 1.96894e6 1.01053
\(329\) 323513. 0.164779
\(330\) 4047.85 0.00204616
\(331\) −1.62905e6 −0.817269 −0.408634 0.912698i \(-0.633995\pi\)
−0.408634 + 0.912698i \(0.633995\pi\)
\(332\) −90126.6 −0.0448754
\(333\) −21485.7 −0.0106179
\(334\) −3.67116e6 −1.80068
\(335\) −23491.3 −0.0114366
\(336\) −3.83806e6 −1.85466
\(337\) −2.32344e6 −1.11444 −0.557220 0.830365i \(-0.688132\pi\)
−0.557220 + 0.830365i \(0.688132\pi\)
\(338\) 560050. 0.266646
\(339\) −4.50305e6 −2.12818
\(340\) 999.112 0.000468724 0
\(341\) −384794. −0.179202
\(342\) −1.26293e6 −0.583869
\(343\) −980112. −0.449822
\(344\) −348370. −0.158725
\(345\) −15012.5 −0.00679055
\(346\) −800670. −0.359553
\(347\) −2.45789e6 −1.09582 −0.547910 0.836537i \(-0.684576\pi\)
−0.547910 + 0.836537i \(0.684576\pi\)
\(348\) 666524. 0.295031
\(349\) −4.36489e6 −1.91827 −0.959135 0.282950i \(-0.908687\pi\)
−0.959135 + 0.282950i \(0.908687\pi\)
\(350\) −2.80368e6 −1.22337
\(351\) −2.43992e6 −1.05708
\(352\) −70308.9 −0.0302450
\(353\) 898354. 0.383717 0.191858 0.981423i \(-0.438549\pi\)
0.191858 + 0.981423i \(0.438549\pi\)
\(354\) 7.04026e6 2.98594
\(355\) −5146.32 −0.00216734
\(356\) 192964. 0.0806960
\(357\) 3.07536e6 1.27710
\(358\) 555357. 0.229015
\(359\) 1.81866e6 0.744759 0.372379 0.928081i \(-0.378542\pi\)
0.372379 + 0.928081i \(0.378542\pi\)
\(360\) 33068.5 0.0134480
\(361\) −2.10414e6 −0.849779
\(362\) 1.66667e6 0.668465
\(363\) −3.92568e6 −1.56368
\(364\) 340570. 0.134727
\(365\) 27915.3 0.0109675
\(366\) −1.89478e6 −0.739359
\(367\) −2.34762e6 −0.909836 −0.454918 0.890533i \(-0.650331\pi\)
−0.454918 + 0.890533i \(0.650331\pi\)
\(368\) −1.20780e6 −0.464916
\(369\) −4.01619e6 −1.53549
\(370\) 137.575 5.22438e−5 0
\(371\) 5.01703e6 1.89240
\(372\) −435366. −0.163116
\(373\) 2.97881e6 1.10859 0.554295 0.832321i \(-0.312988\pi\)
0.554295 + 0.832321i \(0.312988\pi\)
\(374\) −260946. −0.0964654
\(375\) 71488.1 0.0262516
\(376\) −366046. −0.133526
\(377\) 6.18348e6 2.24068
\(378\) 3.17562e6 1.14314
\(379\) 1.77718e6 0.635527 0.317764 0.948170i \(-0.397068\pi\)
0.317764 + 0.948170i \(0.397068\pi\)
\(380\) −826.360 −0.000293569 0
\(381\) −7.17787e6 −2.53328
\(382\) 2.01120e6 0.705176
\(383\) −2.08193e6 −0.725220 −0.362610 0.931941i \(-0.618114\pi\)
−0.362610 + 0.931941i \(0.618114\pi\)
\(384\) 3.89465e6 1.34784
\(385\) 4994.54 0.00171729
\(386\) 462219. 0.157899
\(387\) 710594. 0.241181
\(388\) −35802.5 −0.0120735
\(389\) −1.81080e6 −0.606730 −0.303365 0.952874i \(-0.598110\pi\)
−0.303365 + 0.952874i \(0.598110\pi\)
\(390\) 42488.2 0.0141451
\(391\) 967784. 0.320137
\(392\) −2.05764e6 −0.676321
\(393\) 1.69360e6 0.553133
\(394\) −959892. −0.311517
\(395\) −43851.1 −0.0141412
\(396\) 74883.7 0.0239966
\(397\) 185900. 0.0591975 0.0295988 0.999562i \(-0.490577\pi\)
0.0295988 + 0.999562i \(0.490577\pi\)
\(398\) 833697. 0.263816
\(399\) −2.54361e6 −0.799869
\(400\) 2.87562e6 0.898631
\(401\) −3.41892e6 −1.06176 −0.530882 0.847446i \(-0.678139\pi\)
−0.530882 + 0.847446i \(0.678139\pi\)
\(402\) 6.94177e6 2.14242
\(403\) −4.03898e6 −1.23882
\(404\) −317587. −0.0968077
\(405\) 2165.15 0.000655920 0
\(406\) −8.04798e6 −2.42310
\(407\) 3671.77 0.00109873
\(408\) −3.47968e6 −1.03488
\(409\) −428179. −0.126566 −0.0632830 0.997996i \(-0.520157\pi\)
−0.0632830 + 0.997996i \(0.520157\pi\)
\(410\) 25716.0 0.00755515
\(411\) 3.34567e6 0.976963
\(412\) 255770. 0.0742347
\(413\) 8.68679e6 2.50602
\(414\) 2.71779e6 0.779318
\(415\) −13873.5 −0.00395426
\(416\) −737996. −0.209084
\(417\) −6.56699e6 −1.84938
\(418\) 215827. 0.0604178
\(419\) 3.84011e6 1.06858 0.534292 0.845300i \(-0.320578\pi\)
0.534292 + 0.845300i \(0.320578\pi\)
\(420\) 5650.95 0.00156314
\(421\) 7.05884e6 1.94101 0.970506 0.241078i \(-0.0775010\pi\)
0.970506 + 0.241078i \(0.0775010\pi\)
\(422\) −3.67575e6 −1.00477
\(423\) 746649. 0.202892
\(424\) −5.67663e6 −1.53347
\(425\) −2.30417e6 −0.618789
\(426\) 1.52076e6 0.406009
\(427\) −2.33792e6 −0.620525
\(428\) −584921. −0.154343
\(429\) 1.13398e6 0.297482
\(430\) −4549.99 −0.00118670
\(431\) −2.11813e6 −0.549237 −0.274619 0.961553i \(-0.588552\pi\)
−0.274619 + 0.961553i \(0.588552\pi\)
\(432\) −3.25711e6 −0.839697
\(433\) −1.58858e6 −0.407182 −0.203591 0.979056i \(-0.565261\pi\)
−0.203591 + 0.979056i \(0.565261\pi\)
\(434\) 5.25685e6 1.33968
\(435\) 102600. 0.0259971
\(436\) −490451. −0.123560
\(437\) −800448. −0.200507
\(438\) −8.24906e6 −2.05456
\(439\) 7.11302e6 1.76154 0.880771 0.473543i \(-0.157025\pi\)
0.880771 + 0.473543i \(0.157025\pi\)
\(440\) −5651.18 −0.00139158
\(441\) 4.19710e6 1.02767
\(442\) −2.73901e6 −0.666866
\(443\) 2.52423e6 0.611110 0.305555 0.952174i \(-0.401158\pi\)
0.305555 + 0.952174i \(0.401158\pi\)
\(444\) 4154.33 0.00100010
\(445\) 29703.6 0.00711065
\(446\) −2.50017e6 −0.595157
\(447\) 4.69400e6 1.11115
\(448\) 5.86418e6 1.38042
\(449\) −471868. −0.110460 −0.0552300 0.998474i \(-0.517589\pi\)
−0.0552300 + 0.998474i \(0.517589\pi\)
\(450\) −6.47072e6 −1.50633
\(451\) 686339. 0.158890
\(452\) 533407. 0.122804
\(453\) −3.29689e6 −0.754846
\(454\) 6.13593e6 1.39714
\(455\) 52425.1 0.0118716
\(456\) 2.87803e6 0.648160
\(457\) −6.11039e6 −1.36861 −0.684303 0.729198i \(-0.739893\pi\)
−0.684303 + 0.729198i \(0.739893\pi\)
\(458\) 3.49545e6 0.778645
\(459\) 2.60985e6 0.578209
\(460\) 1778.30 0.000391841 0
\(461\) 7.47383e6 1.63791 0.818957 0.573855i \(-0.194553\pi\)
0.818957 + 0.573855i \(0.194553\pi\)
\(462\) −1.47590e6 −0.321702
\(463\) −4.14981e6 −0.899654 −0.449827 0.893116i \(-0.648514\pi\)
−0.449827 + 0.893116i \(0.648514\pi\)
\(464\) 8.25449e6 1.77990
\(465\) −67017.3 −0.0143732
\(466\) −3.17197e6 −0.676651
\(467\) −1.18789e6 −0.252048 −0.126024 0.992027i \(-0.540222\pi\)
−0.126024 + 0.992027i \(0.540222\pi\)
\(468\) 786016. 0.165889
\(469\) 8.56527e6 1.79808
\(470\) −4780.86 −0.000998300 0
\(471\) −6.31840e6 −1.31237
\(472\) −9.82886e6 −2.03071
\(473\) −121436. −0.0249571
\(474\) 1.29581e7 2.64909
\(475\) 1.90577e6 0.387558
\(476\) −364290. −0.0736937
\(477\) 1.15790e7 2.33011
\(478\) 3.98260e6 0.797255
\(479\) 3.74102e6 0.744992 0.372496 0.928034i \(-0.378502\pi\)
0.372496 + 0.928034i \(0.378502\pi\)
\(480\) −12245.3 −0.00242586
\(481\) 38540.6 0.00759549
\(482\) −8.47896e6 −1.66236
\(483\) 5.47376e6 1.06762
\(484\) 465015. 0.0902306
\(485\) −5511.20 −0.00106388
\(486\) −5.27402e6 −1.01286
\(487\) 7.18109e6 1.37204 0.686021 0.727581i \(-0.259356\pi\)
0.686021 + 0.727581i \(0.259356\pi\)
\(488\) 2.64529e6 0.502832
\(489\) −1.29770e7 −2.45415
\(490\) −26874.4 −0.00505648
\(491\) −7.37443e6 −1.38046 −0.690231 0.723589i \(-0.742491\pi\)
−0.690231 + 0.723589i \(0.742491\pi\)
\(492\) 776542. 0.144628
\(493\) −6.61415e6 −1.22562
\(494\) 2.26542e6 0.417669
\(495\) 11527.1 0.00211450
\(496\) −5.39174e6 −0.984067
\(497\) 1.87642e6 0.340753
\(498\) 4.09967e6 0.740756
\(499\) 2.61086e6 0.469388 0.234694 0.972069i \(-0.424591\pi\)
0.234694 + 0.972069i \(0.424591\pi\)
\(500\) −8468.09 −0.00151482
\(501\) −1.70647e7 −3.03741
\(502\) 2.46129e6 0.435917
\(503\) −398438. −0.0702167 −0.0351084 0.999384i \(-0.511178\pi\)
−0.0351084 + 0.999384i \(0.511178\pi\)
\(504\) −1.20572e7 −2.11432
\(505\) −48887.3 −0.00853036
\(506\) −464452. −0.0806426
\(507\) 2.60329e6 0.449782
\(508\) 850251. 0.146180
\(509\) 556201. 0.0951563 0.0475781 0.998868i \(-0.484850\pi\)
0.0475781 + 0.998868i \(0.484850\pi\)
\(510\) −45447.5 −0.00773721
\(511\) −1.01783e7 −1.72434
\(512\) −6.53352e6 −1.10147
\(513\) −2.15860e6 −0.362141
\(514\) 6.04193e6 1.00871
\(515\) 39371.6 0.00654131
\(516\) −137396. −0.0227169
\(517\) −127597. −0.0209950
\(518\) −50161.8 −0.00821388
\(519\) −3.72176e6 −0.606499
\(520\) −59317.5 −0.00961999
\(521\) 3.39465e6 0.547898 0.273949 0.961744i \(-0.411670\pi\)
0.273949 + 0.961744i \(0.411670\pi\)
\(522\) −1.85743e7 −2.98356
\(523\) −9.40326e6 −1.50323 −0.751613 0.659605i \(-0.770724\pi\)
−0.751613 + 0.659605i \(0.770724\pi\)
\(524\) −200615. −0.0319179
\(525\) −1.30323e7 −2.06359
\(526\) 9.46285e6 1.49127
\(527\) 4.32029e6 0.677620
\(528\) 1.51377e6 0.236307
\(529\) −4.71381e6 −0.732373
\(530\) −74141.4 −0.0114649
\(531\) 2.00486e7 3.08566
\(532\) 301303. 0.0461555
\(533\) 7.20414e6 1.09841
\(534\) −8.77753e6 −1.33205
\(535\) −90038.8 −0.0136002
\(536\) −9.69136e6 −1.45704
\(537\) 2.58147e6 0.386306
\(538\) 6.62393e6 0.986644
\(539\) −717256. −0.106341
\(540\) 4795.59 0.000707714 0
\(541\) 4.76159e6 0.699453 0.349727 0.936852i \(-0.386274\pi\)
0.349727 + 0.936852i \(0.386274\pi\)
\(542\) 7.12894e6 1.04238
\(543\) 7.74720e6 1.12757
\(544\) 789396. 0.114366
\(545\) −75496.8 −0.0108877
\(546\) −1.54918e7 −2.22393
\(547\) 4.68380e6 0.669314 0.334657 0.942340i \(-0.391379\pi\)
0.334657 + 0.942340i \(0.391379\pi\)
\(548\) −396309. −0.0563745
\(549\) −5.39577e6 −0.764051
\(550\) 1.10580e6 0.155873
\(551\) 5.47053e6 0.767627
\(552\) −6.19341e6 −0.865131
\(553\) 1.59887e7 2.22331
\(554\) 1.06070e7 1.46831
\(555\) 639.490 8.81255e−5 0
\(556\) 777890. 0.106716
\(557\) 4.37082e6 0.596931 0.298466 0.954420i \(-0.403525\pi\)
0.298466 + 0.954420i \(0.403525\pi\)
\(558\) 1.21325e7 1.64955
\(559\) −1.27465e6 −0.172528
\(560\) 69983.6 0.00943031
\(561\) −1.21296e6 −0.162719
\(562\) −6.02514e6 −0.804686
\(563\) −9.98439e6 −1.32755 −0.663774 0.747933i \(-0.731046\pi\)
−0.663774 + 0.747933i \(0.731046\pi\)
\(564\) −144367. −0.0191104
\(565\) 82109.1 0.0108211
\(566\) 6.77448e6 0.888863
\(567\) −789445. −0.103125
\(568\) −2.12312e6 −0.276123
\(569\) −3.03616e6 −0.393137 −0.196568 0.980490i \(-0.562980\pi\)
−0.196568 + 0.980490i \(0.562980\pi\)
\(570\) 37589.3 0.00484593
\(571\) −4.66426e6 −0.598677 −0.299339 0.954147i \(-0.596766\pi\)
−0.299339 + 0.954147i \(0.596766\pi\)
\(572\) −134325. −0.0171659
\(573\) 9.34869e6 1.18950
\(574\) −9.37640e6 −1.18784
\(575\) −4.10115e6 −0.517292
\(576\) 1.35342e7 1.69971
\(577\) 2.53940e6 0.317536 0.158768 0.987316i \(-0.449248\pi\)
0.158768 + 0.987316i \(0.449248\pi\)
\(578\) −4.72075e6 −0.587749
\(579\) 2.14853e6 0.266346
\(580\) −12153.5 −0.00150013
\(581\) 5.05847e6 0.621697
\(582\) 1.62858e6 0.199297
\(583\) −1.97878e6 −0.241116
\(584\) 1.15165e7 1.39729
\(585\) 120994. 0.0146175
\(586\) −1.40313e6 −0.168793
\(587\) 1.18921e7 1.42450 0.712248 0.701927i \(-0.247677\pi\)
0.712248 + 0.701927i \(0.247677\pi\)
\(588\) −811522. −0.0967960
\(589\) −3.57329e6 −0.424404
\(590\) −128373. −0.0151825
\(591\) −4.46187e6 −0.525471
\(592\) 51448.9 0.00603353
\(593\) 1.49053e6 0.174062 0.0870311 0.996206i \(-0.472262\pi\)
0.0870311 + 0.996206i \(0.472262\pi\)
\(594\) −1.25250e6 −0.145651
\(595\) −56076.4 −0.00649363
\(596\) −556026. −0.0641179
\(597\) 3.87528e6 0.445008
\(598\) −4.87511e6 −0.557483
\(599\) −1.13339e7 −1.29066 −0.645328 0.763905i \(-0.723279\pi\)
−0.645328 + 0.763905i \(0.723279\pi\)
\(600\) 1.47457e7 1.67220
\(601\) 1.07157e7 1.21014 0.605069 0.796173i \(-0.293145\pi\)
0.605069 + 0.796173i \(0.293145\pi\)
\(602\) 1.65899e6 0.186575
\(603\) 1.97681e7 2.21397
\(604\) 390531. 0.0435576
\(605\) 71581.3 0.00795081
\(606\) 1.44464e7 1.59800
\(607\) −871321. −0.0959857 −0.0479929 0.998848i \(-0.515282\pi\)
−0.0479929 + 0.998848i \(0.515282\pi\)
\(608\) −652905. −0.0716293
\(609\) −3.74095e7 −4.08732
\(610\) 34549.6 0.00375940
\(611\) −1.33932e6 −0.145138
\(612\) −840760. −0.0907389
\(613\) −1.62264e7 −1.74410 −0.872051 0.489415i \(-0.837210\pi\)
−0.872051 + 0.489415i \(0.837210\pi\)
\(614\) −8.41339e6 −0.900638
\(615\) 119536. 0.0127441
\(616\) 2.06050e6 0.218787
\(617\) 1.18192e6 0.124990 0.0624950 0.998045i \(-0.480094\pi\)
0.0624950 + 0.998045i \(0.480094\pi\)
\(618\) −1.16344e7 −1.22539
\(619\) 1.78346e7 1.87084 0.935418 0.353544i \(-0.115023\pi\)
0.935418 + 0.353544i \(0.115023\pi\)
\(620\) 7938.50 0.000829391 0
\(621\) 4.64522e6 0.483367
\(622\) 3.53004e6 0.365850
\(623\) −1.08304e7 −1.11795
\(624\) 1.58893e7 1.63359
\(625\) 9.76367e6 0.999800
\(626\) −1.14710e6 −0.116995
\(627\) 1.00323e6 0.101913
\(628\) 748443. 0.0757286
\(629\) −41224.9 −0.00415464
\(630\) −157477. −0.0158076
\(631\) −1.56569e7 −1.56543 −0.782715 0.622381i \(-0.786166\pi\)
−0.782715 + 0.622381i \(0.786166\pi\)
\(632\) −1.80908e7 −1.80163
\(633\) −1.70860e7 −1.69485
\(634\) −2.07910e6 −0.205424
\(635\) 130882. 0.0128809
\(636\) −2.23884e6 −0.219473
\(637\) −7.52866e6 −0.735139
\(638\) 3.17422e6 0.308734
\(639\) 4.33067e6 0.419568
\(640\) −71015.4 −0.00685334
\(641\) −9.56677e6 −0.919645 −0.459822 0.888011i \(-0.652087\pi\)
−0.459822 + 0.888011i \(0.652087\pi\)
\(642\) 2.66068e7 2.54774
\(643\) 6.58449e6 0.628050 0.314025 0.949415i \(-0.398322\pi\)
0.314025 + 0.949415i \(0.398322\pi\)
\(644\) −648392. −0.0616060
\(645\) −21149.7 −0.00200173
\(646\) −2.42321e6 −0.228459
\(647\) −5.77942e6 −0.542779 −0.271390 0.962470i \(-0.587483\pi\)
−0.271390 + 0.962470i \(0.587483\pi\)
\(648\) 893235. 0.0835657
\(649\) −3.42617e6 −0.319299
\(650\) 1.16070e7 1.07755
\(651\) 2.44354e7 2.25979
\(652\) 1.53718e6 0.141614
\(653\) −1.76847e7 −1.62298 −0.811492 0.584364i \(-0.801344\pi\)
−0.811492 + 0.584364i \(0.801344\pi\)
\(654\) 2.23096e7 2.03961
\(655\) −30881.3 −0.00281250
\(656\) 9.61700e6 0.872529
\(657\) −2.34909e7 −2.12318
\(658\) 1.74317e6 0.156955
\(659\) 1.07891e7 0.967769 0.483884 0.875132i \(-0.339226\pi\)
0.483884 + 0.875132i \(0.339226\pi\)
\(660\) −2228.80 −0.000199164 0
\(661\) −1.27678e7 −1.13662 −0.568308 0.822816i \(-0.692402\pi\)
−0.568308 + 0.822816i \(0.692402\pi\)
\(662\) −8.77773e6 −0.778461
\(663\) −1.27318e7 −1.12488
\(664\) −5.72352e6 −0.503782
\(665\) 46380.5 0.00406707
\(666\) −115770. −0.0101137
\(667\) −1.17724e7 −1.02459
\(668\) 2.02139e6 0.175270
\(669\) −1.16215e7 −1.00392
\(670\) −126577. −0.0108935
\(671\) 922101. 0.0790628
\(672\) 4.46480e6 0.381399
\(673\) 5.05831e6 0.430495 0.215247 0.976560i \(-0.430944\pi\)
0.215247 + 0.976560i \(0.430944\pi\)
\(674\) −1.25193e7 −1.06152
\(675\) −1.10597e7 −0.934294
\(676\) −308371. −0.0259542
\(677\) 1.48127e7 1.24211 0.621057 0.783766i \(-0.286704\pi\)
0.621057 + 0.783766i \(0.286704\pi\)
\(678\) −2.42635e7 −2.02712
\(679\) 2.00946e6 0.167265
\(680\) 63448.9 0.00526201
\(681\) 2.85217e7 2.35672
\(682\) −2.07336e6 −0.170692
\(683\) −9.52658e6 −0.781421 −0.390711 0.920514i \(-0.627771\pi\)
−0.390711 + 0.920514i \(0.627771\pi\)
\(684\) 695388. 0.0568312
\(685\) −61005.2 −0.00496753
\(686\) −5.28108e6 −0.428462
\(687\) 1.62479e7 1.31343
\(688\) −1.70156e6 −0.137049
\(689\) −2.07702e7 −1.66683
\(690\) −80890.9 −0.00646810
\(691\) −4.04497e6 −0.322270 −0.161135 0.986932i \(-0.551516\pi\)
−0.161135 + 0.986932i \(0.551516\pi\)
\(692\) 440860. 0.0349973
\(693\) −4.20294e6 −0.332445
\(694\) −1.32437e7 −1.04379
\(695\) 119743. 0.00940349
\(696\) 4.23278e7 3.31209
\(697\) −7.70590e6 −0.600816
\(698\) −2.35191e7 −1.82718
\(699\) −1.47443e7 −1.14138
\(700\) 1.54374e6 0.119077
\(701\) 1.78401e6 0.137120 0.0685602 0.997647i \(-0.478159\pi\)
0.0685602 + 0.997647i \(0.478159\pi\)
\(702\) −1.31469e7 −1.00688
\(703\) 34096.9 0.00260212
\(704\) −2.31290e6 −0.175883
\(705\) −22222.9 −0.00168394
\(706\) 4.84055e6 0.365496
\(707\) 1.78250e7 1.34116
\(708\) −3.87646e6 −0.290638
\(709\) −1.22322e7 −0.913878 −0.456939 0.889498i \(-0.651054\pi\)
−0.456939 + 0.889498i \(0.651054\pi\)
\(710\) −27729.6 −0.00206442
\(711\) 3.69010e7 2.73756
\(712\) 1.22542e7 0.905913
\(713\) 7.68958e6 0.566473
\(714\) 1.65708e7 1.21646
\(715\) −20677.1 −0.00151260
\(716\) −305787. −0.0222913
\(717\) 1.85124e7 1.34482
\(718\) 9.79938e6 0.709394
\(719\) 8.42924e6 0.608088 0.304044 0.952658i \(-0.401663\pi\)
0.304044 + 0.952658i \(0.401663\pi\)
\(720\) 161518. 0.0116115
\(721\) −1.43554e7 −1.02844
\(722\) −1.13376e7 −0.809428
\(723\) −3.94128e7 −2.80409
\(724\) −917691. −0.0650654
\(725\) 2.80286e7 1.98041
\(726\) −2.11525e7 −1.48943
\(727\) 1.10329e7 0.774201 0.387101 0.922037i \(-0.373477\pi\)
0.387101 + 0.922037i \(0.373477\pi\)
\(728\) 2.16280e7 1.51247
\(729\) −2.33632e7 −1.62822
\(730\) 150414. 0.0104468
\(731\) 1.36342e6 0.0943708
\(732\) 1.04329e6 0.0719660
\(733\) −5.02000e6 −0.345099 −0.172550 0.985001i \(-0.555201\pi\)
−0.172550 + 0.985001i \(0.555201\pi\)
\(734\) −1.26496e7 −0.866633
\(735\) −124920. −0.00852933
\(736\) 1.40503e6 0.0956072
\(737\) −3.37824e6 −0.229098
\(738\) −2.16402e7 −1.46258
\(739\) 2.49061e6 0.167762 0.0838810 0.996476i \(-0.473268\pi\)
0.0838810 + 0.996476i \(0.473268\pi\)
\(740\) −75.7506 −5.08518e−6 0
\(741\) 1.05304e7 0.704529
\(742\) 2.70330e7 1.80254
\(743\) −1.21111e7 −0.804847 −0.402423 0.915454i \(-0.631832\pi\)
−0.402423 + 0.915454i \(0.631832\pi\)
\(744\) −2.76480e7 −1.83118
\(745\) −85590.9 −0.00564985
\(746\) 1.60506e7 1.05595
\(747\) 1.16746e7 0.765495
\(748\) 143680. 0.00938952
\(749\) 3.28294e7 2.13825
\(750\) 385195. 0.0250051
\(751\) 2.21669e7 1.43418 0.717092 0.696978i \(-0.245472\pi\)
0.717092 + 0.696978i \(0.245472\pi\)
\(752\) −1.78790e6 −0.115292
\(753\) 1.14408e7 0.735310
\(754\) 3.33181e7 2.13428
\(755\) 60115.8 0.00383814
\(756\) −1.74854e6 −0.111268
\(757\) 1.03112e7 0.653986 0.326993 0.945027i \(-0.393965\pi\)
0.326993 + 0.945027i \(0.393965\pi\)
\(758\) 9.57590e6 0.605350
\(759\) −2.15891e6 −0.136029
\(760\) −52478.2 −0.00329568
\(761\) 5.23003e6 0.327373 0.163686 0.986512i \(-0.447661\pi\)
0.163686 + 0.986512i \(0.447661\pi\)
\(762\) −3.86761e7 −2.41299
\(763\) 2.75272e7 1.71179
\(764\) −1.10740e6 −0.0686387
\(765\) −129421. −0.00799560
\(766\) −1.12180e7 −0.690783
\(767\) −3.59627e7 −2.20731
\(768\) −7.24005e6 −0.442933
\(769\) 1.16812e7 0.712315 0.356157 0.934426i \(-0.384087\pi\)
0.356157 + 0.934426i \(0.384087\pi\)
\(770\) 26911.8 0.00163575
\(771\) 2.80847e7 1.70151
\(772\) −254504. −0.0153692
\(773\) 1.35127e7 0.813379 0.406690 0.913566i \(-0.366683\pi\)
0.406690 + 0.913566i \(0.366683\pi\)
\(774\) 3.82885e6 0.229729
\(775\) −1.83079e7 −1.09493
\(776\) −2.27365e6 −0.135540
\(777\) −233167. −0.0138553
\(778\) −9.75702e6 −0.577920
\(779\) 6.37351e6 0.376301
\(780\) −23394.6 −0.00137682
\(781\) −740082. −0.0434162
\(782\) 5.21465e6 0.304936
\(783\) −3.17470e7 −1.85054
\(784\) −1.00502e7 −0.583962
\(785\) 115210. 0.00667294
\(786\) 9.12553e6 0.526868
\(787\) −2.08780e7 −1.20158 −0.600789 0.799407i \(-0.705147\pi\)
−0.600789 + 0.799407i \(0.705147\pi\)
\(788\) 528529. 0.0303217
\(789\) 4.39862e7 2.51550
\(790\) −236280. −0.0134698
\(791\) −2.99381e7 −1.70131
\(792\) 4.75551e6 0.269392
\(793\) 9.67881e6 0.546562
\(794\) 1.00167e6 0.0563866
\(795\) −344632. −0.0193392
\(796\) −459045. −0.0256787
\(797\) −1.17024e7 −0.652573 −0.326286 0.945271i \(-0.605797\pi\)
−0.326286 + 0.945271i \(0.605797\pi\)
\(798\) −1.37056e7 −0.761887
\(799\) 1.43260e6 0.0793888
\(800\) −3.34520e6 −0.184798
\(801\) −2.49958e7 −1.37653
\(802\) −1.84220e7 −1.01135
\(803\) 4.01444e6 0.219703
\(804\) −3.82223e6 −0.208534
\(805\) −99809.1 −0.00542851
\(806\) −2.17630e7 −1.18000
\(807\) 3.07901e7 1.66428
\(808\) −2.01685e7 −1.08679
\(809\) −2.76467e7 −1.48516 −0.742578 0.669760i \(-0.766397\pi\)
−0.742578 + 0.669760i \(0.766397\pi\)
\(810\) 11666.4 0.000624774 0
\(811\) −8.32113e6 −0.444253 −0.222126 0.975018i \(-0.571300\pi\)
−0.222126 + 0.975018i \(0.571300\pi\)
\(812\) 4.43132e6 0.235854
\(813\) 3.31375e7 1.75830
\(814\) 19784.4 0.00104655
\(815\) 236623. 0.0124785
\(816\) −1.69960e7 −0.893554
\(817\) −1.12768e6 −0.0591059
\(818\) −2.30713e6 −0.120556
\(819\) −4.41161e7 −2.29820
\(820\) −14159.6 −0.000735385 0
\(821\) 8.01626e6 0.415063 0.207531 0.978228i \(-0.433457\pi\)
0.207531 + 0.978228i \(0.433457\pi\)
\(822\) 1.80273e7 0.930573
\(823\) 4.63830e6 0.238704 0.119352 0.992852i \(-0.461918\pi\)
0.119352 + 0.992852i \(0.461918\pi\)
\(824\) 1.62428e7 0.833378
\(825\) 5.14011e6 0.262928
\(826\) 4.68065e7 2.38702
\(827\) 5.55667e6 0.282521 0.141261 0.989972i \(-0.454884\pi\)
0.141261 + 0.989972i \(0.454884\pi\)
\(828\) −1.49645e6 −0.0758554
\(829\) 2.47536e7 1.25098 0.625491 0.780231i \(-0.284899\pi\)
0.625491 + 0.780231i \(0.284899\pi\)
\(830\) −74753.7 −0.00376650
\(831\) 4.93046e7 2.47676
\(832\) −2.42773e7 −1.21588
\(833\) 8.05302e6 0.402111
\(834\) −3.53846e7 −1.76156
\(835\) 311159. 0.0154442
\(836\) −118837. −0.00588080
\(837\) 2.07367e7 1.02312
\(838\) 2.06914e7 1.01784
\(839\) −3.24512e7 −1.59157 −0.795785 0.605579i \(-0.792942\pi\)
−0.795785 + 0.605579i \(0.792942\pi\)
\(840\) 358865. 0.0175482
\(841\) 5.99451e7 2.92256
\(842\) 3.80347e7 1.84884
\(843\) −2.80067e7 −1.35735
\(844\) 2.02392e6 0.0977994
\(845\) −47468.6 −0.00228699
\(846\) 4.02313e6 0.193258
\(847\) −2.60995e7 −1.25004
\(848\) −2.77267e7 −1.32406
\(849\) 3.14899e7 1.49935
\(850\) −1.24154e7 −0.589407
\(851\) −73375.3 −0.00347317
\(852\) −837349. −0.0395191
\(853\) 2.47564e7 1.16497 0.582485 0.812841i \(-0.302080\pi\)
0.582485 + 0.812841i \(0.302080\pi\)
\(854\) −1.25973e7 −0.591060
\(855\) 107043. 0.00500777
\(856\) −3.71456e7 −1.73270
\(857\) 1.28652e7 0.598363 0.299182 0.954196i \(-0.403286\pi\)
0.299182 + 0.954196i \(0.403286\pi\)
\(858\) 6.11014e6 0.283356
\(859\) 1.98227e6 0.0916601 0.0458300 0.998949i \(-0.485407\pi\)
0.0458300 + 0.998949i \(0.485407\pi\)
\(860\) 2505.28 0.000115508 0
\(861\) −4.35844e7 −2.00366
\(862\) −1.14130e7 −0.523157
\(863\) −3.11840e6 −0.142529 −0.0712647 0.997457i \(-0.522704\pi\)
−0.0712647 + 0.997457i \(0.522704\pi\)
\(864\) 3.78898e6 0.172679
\(865\) 67863.0 0.00308384
\(866\) −8.55964e6 −0.387847
\(867\) −2.19435e7 −0.991421
\(868\) −2.89449e6 −0.130399
\(869\) −6.30613e6 −0.283279
\(870\) 552835. 0.0247627
\(871\) −3.54596e7 −1.58376
\(872\) −3.11462e7 −1.38712
\(873\) 4.63772e6 0.205953
\(874\) −4.31301e6 −0.190986
\(875\) 475282. 0.0209861
\(876\) 4.54204e6 0.199982
\(877\) −2.15790e7 −0.947398 −0.473699 0.880687i \(-0.657082\pi\)
−0.473699 + 0.880687i \(0.657082\pi\)
\(878\) 3.83267e7 1.67790
\(879\) −6.52218e6 −0.284722
\(880\) −27602.3 −0.00120154
\(881\) −1.27720e7 −0.554393 −0.277196 0.960813i \(-0.589405\pi\)
−0.277196 + 0.960813i \(0.589405\pi\)
\(882\) 2.26150e7 0.978870
\(883\) 8.80113e6 0.379871 0.189936 0.981797i \(-0.439172\pi\)
0.189936 + 0.981797i \(0.439172\pi\)
\(884\) 1.50814e6 0.0649098
\(885\) −596716. −0.0256100
\(886\) 1.36012e7 0.582092
\(887\) −3.47818e7 −1.48437 −0.742187 0.670192i \(-0.766212\pi\)
−0.742187 + 0.670192i \(0.766212\pi\)
\(888\) 263822. 0.0112274
\(889\) −4.77214e7 −2.02516
\(890\) 160050. 0.00677301
\(891\) 311366. 0.0131394
\(892\) 1.37662e6 0.0579300
\(893\) −1.18490e6 −0.0497225
\(894\) 2.52924e7 1.05839
\(895\) −47070.8 −0.00196424
\(896\) 2.58932e7 1.07750
\(897\) −2.26610e7 −0.940368
\(898\) −2.54254e6 −0.105215
\(899\) −5.25531e7 −2.16870
\(900\) 3.56286e6 0.146620
\(901\) 2.22168e7 0.911737
\(902\) 3.69816e6 0.151345
\(903\) 7.71150e6 0.314716
\(904\) 3.38741e7 1.37863
\(905\) −141263. −0.00573334
\(906\) −1.77644e7 −0.719003
\(907\) 1.91865e7 0.774420 0.387210 0.921992i \(-0.373439\pi\)
0.387210 + 0.921992i \(0.373439\pi\)
\(908\) −3.37853e6 −0.135992
\(909\) 4.11390e7 1.65137
\(910\) 282479. 0.0113079
\(911\) 834307. 0.0333066 0.0166533 0.999861i \(-0.494699\pi\)
0.0166533 + 0.999861i \(0.494699\pi\)
\(912\) 1.40573e7 0.559647
\(913\) −1.99512e6 −0.0792121
\(914\) −3.29242e7 −1.30362
\(915\) 160597. 0.00634139
\(916\) −1.92464e6 −0.0757899
\(917\) 1.12598e7 0.442187
\(918\) 1.40625e7 0.550753
\(919\) 1.11037e7 0.433690 0.216845 0.976206i \(-0.430423\pi\)
0.216845 + 0.976206i \(0.430423\pi\)
\(920\) 112931. 0.00439890
\(921\) −3.91080e7 −1.51921
\(922\) 4.02708e7 1.56014
\(923\) −7.76826e6 −0.300137
\(924\) 812652. 0.0313130
\(925\) 174698. 0.00671324
\(926\) −2.23602e7 −0.856935
\(927\) −3.31315e7 −1.26631
\(928\) −9.60242e6 −0.366025
\(929\) −1.03857e7 −0.394816 −0.197408 0.980321i \(-0.563252\pi\)
−0.197408 + 0.980321i \(0.563252\pi\)
\(930\) −361105. −0.0136907
\(931\) −6.66061e6 −0.251849
\(932\) 1.74653e6 0.0658622
\(933\) 1.64087e7 0.617120
\(934\) −6.40063e6 −0.240080
\(935\) 22117.2 0.000827372 0
\(936\) 4.99161e7 1.86231
\(937\) −2.10627e7 −0.783729 −0.391865 0.920023i \(-0.628170\pi\)
−0.391865 + 0.920023i \(0.628170\pi\)
\(938\) 4.61518e7 1.71270
\(939\) −5.33209e6 −0.197348
\(940\) 2632.40 9.71701e−5 0
\(941\) −3.67199e7 −1.35185 −0.675924 0.736971i \(-0.736255\pi\)
−0.675924 + 0.736971i \(0.736255\pi\)
\(942\) −3.40451e7 −1.25005
\(943\) −1.37156e7 −0.502267
\(944\) −4.80076e7 −1.75339
\(945\) −269159. −0.00980457
\(946\) −654325. −0.0237720
\(947\) 1.07332e7 0.388914 0.194457 0.980911i \(-0.437706\pi\)
0.194457 + 0.980911i \(0.437706\pi\)
\(948\) −7.13493e6 −0.257851
\(949\) 4.21375e7 1.51881
\(950\) 1.02687e7 0.369155
\(951\) −9.66428e6 −0.346512
\(952\) −2.31344e7 −0.827304
\(953\) 4.10240e7 1.46321 0.731603 0.681731i \(-0.238772\pi\)
0.731603 + 0.681731i \(0.238772\pi\)
\(954\) 6.23906e7 2.21946
\(955\) −170465. −0.00604821
\(956\) −2.19287e6 −0.0776013
\(957\) 1.47547e7 0.520776
\(958\) 2.01575e7 0.709617
\(959\) 2.22434e7 0.781005
\(960\) −402824. −0.0141071
\(961\) 5.69795e6 0.199026
\(962\) 207666. 0.00723483
\(963\) 7.57683e7 2.63283
\(964\) 4.66862e6 0.161807
\(965\) −39176.6 −0.00135428
\(966\) 2.94940e7 1.01693
\(967\) 2.93253e7 1.00850 0.504251 0.863557i \(-0.331769\pi\)
0.504251 + 0.863557i \(0.331769\pi\)
\(968\) 2.95309e7 1.01295
\(969\) −1.12638e7 −0.385368
\(970\) −29695.7 −0.00101336
\(971\) 3.44554e6 0.117276 0.0586381 0.998279i \(-0.481324\pi\)
0.0586381 + 0.998279i \(0.481324\pi\)
\(972\) 2.90394e6 0.0985877
\(973\) −4.36601e7 −1.47843
\(974\) 3.86934e7 1.30689
\(975\) 5.39530e7 1.81763
\(976\) 1.29205e7 0.434165
\(977\) 3.77647e7 1.26576 0.632878 0.774252i \(-0.281874\pi\)
0.632878 + 0.774252i \(0.281874\pi\)
\(978\) −6.99230e7 −2.33762
\(979\) 4.27162e6 0.142441
\(980\) 14797.4 0.000492175 0
\(981\) 6.35311e7 2.10772
\(982\) −3.97352e7 −1.31491
\(983\) 1.69058e7 0.558024 0.279012 0.960288i \(-0.409993\pi\)
0.279012 + 0.960288i \(0.409993\pi\)
\(984\) 4.93145e7 1.62363
\(985\) 81358.2 0.00267184
\(986\) −3.56387e7 −1.16743
\(987\) 8.10277e6 0.264753
\(988\) −1.24737e6 −0.0406540
\(989\) 2.42673e6 0.0788915
\(990\) 62110.8 0.00201409
\(991\) 1.83818e7 0.594570 0.297285 0.954789i \(-0.403919\pi\)
0.297285 + 0.954789i \(0.403919\pi\)
\(992\) 6.27219e6 0.202367
\(993\) −4.08016e7 −1.31312
\(994\) 1.01106e7 0.324572
\(995\) −70662.3 −0.00226272
\(996\) −2.25733e6 −0.0721019
\(997\) −2.05937e7 −0.656139 −0.328069 0.944654i \(-0.606398\pi\)
−0.328069 + 0.944654i \(0.606398\pi\)
\(998\) 1.40679e7 0.447099
\(999\) −197874. −0.00627298
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 43.6.a.b.1.7 10
3.2 odd 2 387.6.a.e.1.4 10
4.3 odd 2 688.6.a.h.1.2 10
5.4 even 2 1075.6.a.b.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.7 10 1.1 even 1 trivial
387.6.a.e.1.4 10 3.2 odd 2
688.6.a.h.1.2 10 4.3 odd 2
1075.6.a.b.1.4 10 5.4 even 2