Properties

Label 43.6.a.b.1.1
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 1.1
Root \(11.5305\) 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

\(f(q)\) \(=\) \(q-10.5305 q^{2} +27.4953 q^{3} +78.8905 q^{4} +86.8464 q^{5} -289.538 q^{6} -19.8137 q^{7} -493.778 q^{8} +512.989 q^{9} +O(q^{10})\) \(q-10.5305 q^{2} +27.4953 q^{3} +78.8905 q^{4} +86.8464 q^{5} -289.538 q^{6} -19.8137 q^{7} -493.778 q^{8} +512.989 q^{9} -914.532 q^{10} -85.3712 q^{11} +2169.11 q^{12} -229.081 q^{13} +208.647 q^{14} +2387.86 q^{15} +2675.21 q^{16} +1356.51 q^{17} -5402.01 q^{18} -2795.35 q^{19} +6851.35 q^{20} -544.783 q^{21} +898.997 q^{22} -1856.11 q^{23} -13576.6 q^{24} +4417.29 q^{25} +2412.33 q^{26} +7423.41 q^{27} -1563.11 q^{28} +7312.96 q^{29} -25145.3 q^{30} -2937.36 q^{31} -12370.3 q^{32} -2347.30 q^{33} -14284.7 q^{34} -1720.75 q^{35} +40469.9 q^{36} +2577.36 q^{37} +29436.3 q^{38} -6298.65 q^{39} -42882.8 q^{40} -3532.54 q^{41} +5736.81 q^{42} +1849.00 q^{43} -6734.97 q^{44} +44551.2 q^{45} +19545.7 q^{46} -7065.73 q^{47} +73555.6 q^{48} -16414.4 q^{49} -46516.1 q^{50} +37297.6 q^{51} -18072.3 q^{52} -3852.63 q^{53} -78171.9 q^{54} -7414.18 q^{55} +9783.57 q^{56} -76858.8 q^{57} -77008.8 q^{58} +27996.1 q^{59} +188380. q^{60} -39244.4 q^{61} +30931.7 q^{62} -10164.2 q^{63} +44658.1 q^{64} -19894.9 q^{65} +24718.2 q^{66} -14809.1 q^{67} +107016. q^{68} -51034.2 q^{69} +18120.3 q^{70} +8956.13 q^{71} -253303. q^{72} +35168.6 q^{73} -27140.8 q^{74} +121455. q^{75} -220526. q^{76} +1691.52 q^{77} +66327.6 q^{78} -13263.6 q^{79} +232332. q^{80} +79452.3 q^{81} +37199.3 q^{82} -9812.47 q^{83} -42978.2 q^{84} +117808. q^{85} -19470.8 q^{86} +201072. q^{87} +42154.4 q^{88} -87124.9 q^{89} -469145. q^{90} +4538.95 q^{91} -146429. q^{92} -80763.5 q^{93} +74405.4 q^{94} -242766. q^{95} -340124. q^{96} +83982.4 q^{97} +172851. q^{98} -43794.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.5305 −1.86154 −0.930769 0.365607i \(-0.880862\pi\)
−0.930769 + 0.365607i \(0.880862\pi\)
\(3\) 27.4953 1.76382 0.881911 0.471417i \(-0.156257\pi\)
0.881911 + 0.471417i \(0.156257\pi\)
\(4\) 78.8905 2.46533
\(5\) 86.8464 1.55356 0.776778 0.629775i \(-0.216853\pi\)
0.776778 + 0.629775i \(0.216853\pi\)
\(6\) −289.538 −3.28342
\(7\) −19.8137 −0.152834 −0.0764171 0.997076i \(-0.524348\pi\)
−0.0764171 + 0.997076i \(0.524348\pi\)
\(8\) −493.778 −2.72776
\(9\) 512.989 2.11107
\(10\) −914.532 −2.89200
\(11\) −85.3712 −0.212730 −0.106365 0.994327i \(-0.533921\pi\)
−0.106365 + 0.994327i \(0.533921\pi\)
\(12\) 2169.11 4.34840
\(13\) −229.081 −0.375951 −0.187975 0.982174i \(-0.560193\pi\)
−0.187975 + 0.982174i \(0.560193\pi\)
\(14\) 208.647 0.284507
\(15\) 2387.86 2.74019
\(16\) 2675.21 2.61251
\(17\) 1356.51 1.13841 0.569207 0.822194i \(-0.307250\pi\)
0.569207 + 0.822194i \(0.307250\pi\)
\(18\) −5402.01 −3.92983
\(19\) −2795.35 −1.77645 −0.888223 0.459413i \(-0.848060\pi\)
−0.888223 + 0.459413i \(0.848060\pi\)
\(20\) 6851.35 3.83002
\(21\) −544.783 −0.269572
\(22\) 898.997 0.396006
\(23\) −1856.11 −0.731618 −0.365809 0.930690i \(-0.619208\pi\)
−0.365809 + 0.930690i \(0.619208\pi\)
\(24\) −13576.6 −4.81129
\(25\) 4417.29 1.41353
\(26\) 2412.33 0.699847
\(27\) 7423.41 1.95972
\(28\) −1563.11 −0.376786
\(29\) 7312.96 1.61472 0.807362 0.590057i \(-0.200895\pi\)
0.807362 + 0.590057i \(0.200895\pi\)
\(30\) −25145.3 −5.10098
\(31\) −2937.36 −0.548975 −0.274488 0.961591i \(-0.588508\pi\)
−0.274488 + 0.961591i \(0.588508\pi\)
\(32\) −12370.3 −2.13553
\(33\) −2347.30 −0.375218
\(34\) −14284.7 −2.11920
\(35\) −1720.75 −0.237436
\(36\) 40469.9 5.20447
\(37\) 2577.36 0.309507 0.154754 0.987953i \(-0.450542\pi\)
0.154754 + 0.987953i \(0.450542\pi\)
\(38\) 29436.3 3.30692
\(39\) −6298.65 −0.663110
\(40\) −42882.8 −4.23773
\(41\) −3532.54 −0.328192 −0.164096 0.986444i \(-0.552471\pi\)
−0.164096 + 0.986444i \(0.552471\pi\)
\(42\) 5736.81 0.501819
\(43\) 1849.00 0.152499
\(44\) −6734.97 −0.524450
\(45\) 44551.2 3.27966
\(46\) 19545.7 1.36194
\(47\) −7065.73 −0.466566 −0.233283 0.972409i \(-0.574947\pi\)
−0.233283 + 0.972409i \(0.574947\pi\)
\(48\) 73555.6 4.60800
\(49\) −16414.4 −0.976642
\(50\) −46516.1 −2.63135
\(51\) 37297.6 2.00796
\(52\) −18072.3 −0.926842
\(53\) −3852.63 −0.188394 −0.0941972 0.995554i \(-0.530028\pi\)
−0.0941972 + 0.995554i \(0.530028\pi\)
\(54\) −78171.9 −3.64810
\(55\) −7414.18 −0.330488
\(56\) 9783.57 0.416896
\(57\) −76858.8 −3.13333
\(58\) −77008.8 −3.00587
\(59\) 27996.1 1.04705 0.523524 0.852011i \(-0.324617\pi\)
0.523524 + 0.852011i \(0.324617\pi\)
\(60\) 188380. 6.75547
\(61\) −39244.4 −1.35037 −0.675186 0.737648i \(-0.735937\pi\)
−0.675186 + 0.737648i \(0.735937\pi\)
\(62\) 30931.7 1.02194
\(63\) −10164.2 −0.322643
\(64\) 44658.1 1.36286
\(65\) −19894.9 −0.584060
\(66\) 24718.2 0.698484
\(67\) −14809.1 −0.403034 −0.201517 0.979485i \(-0.564587\pi\)
−0.201517 + 0.979485i \(0.564587\pi\)
\(68\) 107016. 2.80656
\(69\) −51034.2 −1.29044
\(70\) 18120.3 0.441997
\(71\) 8956.13 0.210850 0.105425 0.994427i \(-0.466380\pi\)
0.105425 + 0.994427i \(0.466380\pi\)
\(72\) −253303. −5.75849
\(73\) 35168.6 0.772411 0.386205 0.922413i \(-0.373786\pi\)
0.386205 + 0.922413i \(0.373786\pi\)
\(74\) −27140.8 −0.576160
\(75\) 121455. 2.49322
\(76\) −220526. −4.37952
\(77\) 1691.52 0.0325125
\(78\) 66327.6 1.23441
\(79\) −13263.6 −0.239108 −0.119554 0.992828i \(-0.538146\pi\)
−0.119554 + 0.992828i \(0.538146\pi\)
\(80\) 232332. 4.05868
\(81\) 79452.3 1.34553
\(82\) 37199.3 0.610942
\(83\) −9812.47 −0.156345 −0.0781724 0.996940i \(-0.524908\pi\)
−0.0781724 + 0.996940i \(0.524908\pi\)
\(84\) −42978.2 −0.664584
\(85\) 117808. 1.76859
\(86\) −19470.8 −0.283882
\(87\) 201072. 2.84808
\(88\) 42154.4 0.580278
\(89\) −87124.9 −1.16592 −0.582958 0.812502i \(-0.698105\pi\)
−0.582958 + 0.812502i \(0.698105\pi\)
\(90\) −469145. −6.10521
\(91\) 4538.95 0.0574581
\(92\) −146429. −1.80368
\(93\) −80763.5 −0.968295
\(94\) 74405.4 0.868530
\(95\) −242766. −2.75981
\(96\) −340124. −3.76669
\(97\) 83982.4 0.906272 0.453136 0.891441i \(-0.350305\pi\)
0.453136 + 0.891441i \(0.350305\pi\)
\(98\) 172851. 1.81806
\(99\) −43794.5 −0.449088
\(100\) 348482. 3.48482
\(101\) 74775.4 0.729382 0.364691 0.931129i \(-0.381175\pi\)
0.364691 + 0.931129i \(0.381175\pi\)
\(102\) −392760. −3.73789
\(103\) 29400.7 0.273064 0.136532 0.990636i \(-0.456404\pi\)
0.136532 + 0.990636i \(0.456404\pi\)
\(104\) 113115. 1.02551
\(105\) −47312.4 −0.418795
\(106\) 40570.0 0.350704
\(107\) −199822. −1.68727 −0.843635 0.536917i \(-0.819589\pi\)
−0.843635 + 0.536917i \(0.819589\pi\)
\(108\) 585637. 4.83135
\(109\) −39465.7 −0.318166 −0.159083 0.987265i \(-0.550854\pi\)
−0.159083 + 0.987265i \(0.550854\pi\)
\(110\) 78074.7 0.615217
\(111\) 70865.2 0.545915
\(112\) −53005.8 −0.399281
\(113\) 41487.8 0.305650 0.152825 0.988253i \(-0.451163\pi\)
0.152825 + 0.988253i \(0.451163\pi\)
\(114\) 809358. 5.83282
\(115\) −161196. −1.13661
\(116\) 576923. 3.98082
\(117\) −117516. −0.793657
\(118\) −294811. −1.94912
\(119\) −26877.5 −0.173989
\(120\) −1.17907e6 −7.47460
\(121\) −153763. −0.954746
\(122\) 413262. 2.51377
\(123\) −97128.1 −0.578871
\(124\) −231730. −1.35340
\(125\) 112231. 0.642448
\(126\) 107034. 0.600612
\(127\) 357769. 1.96831 0.984156 0.177305i \(-0.0567379\pi\)
0.984156 + 0.177305i \(0.0567379\pi\)
\(128\) −74420.5 −0.401483
\(129\) 50838.7 0.268980
\(130\) 209502. 1.08725
\(131\) −61207.9 −0.311623 −0.155811 0.987787i \(-0.549799\pi\)
−0.155811 + 0.987787i \(0.549799\pi\)
\(132\) −185180. −0.925036
\(133\) 55386.2 0.271502
\(134\) 155946. 0.750263
\(135\) 644697. 3.04453
\(136\) −669814. −3.10533
\(137\) −309777. −1.41009 −0.705047 0.709161i \(-0.749074\pi\)
−0.705047 + 0.709161i \(0.749074\pi\)
\(138\) 537414. 2.40221
\(139\) −193740. −0.850517 −0.425259 0.905072i \(-0.639817\pi\)
−0.425259 + 0.905072i \(0.639817\pi\)
\(140\) −135751. −0.585358
\(141\) −194274. −0.822938
\(142\) −94312.1 −0.392506
\(143\) 19556.9 0.0799762
\(144\) 1.37235e6 5.51518
\(145\) 635104. 2.50856
\(146\) −370342. −1.43787
\(147\) −451319. −1.72262
\(148\) 203329. 0.763037
\(149\) −455017. −1.67904 −0.839521 0.543327i \(-0.817164\pi\)
−0.839521 + 0.543327i \(0.817164\pi\)
\(150\) −1.27897e6 −4.64123
\(151\) −505868. −1.80549 −0.902744 0.430179i \(-0.858451\pi\)
−0.902744 + 0.430179i \(0.858451\pi\)
\(152\) 1.38028e6 4.84572
\(153\) 695874. 2.40327
\(154\) −17812.5 −0.0605232
\(155\) −255099. −0.852864
\(156\) −496903. −1.63478
\(157\) 348495. 1.12836 0.564179 0.825652i \(-0.309193\pi\)
0.564179 + 0.825652i \(0.309193\pi\)
\(158\) 139672. 0.445108
\(159\) −105929. −0.332294
\(160\) −1.07432e6 −3.31766
\(161\) 36776.4 0.111816
\(162\) −836669. −2.50476
\(163\) 104915. 0.309291 0.154645 0.987970i \(-0.450576\pi\)
0.154645 + 0.987970i \(0.450576\pi\)
\(164\) −278684. −0.809100
\(165\) −203855. −0.582923
\(166\) 103330. 0.291042
\(167\) 186982. 0.518809 0.259405 0.965769i \(-0.416474\pi\)
0.259405 + 0.965769i \(0.416474\pi\)
\(168\) 269002. 0.735329
\(169\) −318815. −0.858661
\(170\) −1.24057e6 −3.29230
\(171\) −1.43398e6 −3.75019
\(172\) 145868. 0.375959
\(173\) 491718. 1.24911 0.624555 0.780981i \(-0.285280\pi\)
0.624555 + 0.780981i \(0.285280\pi\)
\(174\) −2.11738e6 −5.30182
\(175\) −87522.9 −0.216036
\(176\) −228386. −0.555761
\(177\) 769758. 1.84681
\(178\) 917464. 2.17040
\(179\) 374509. 0.873634 0.436817 0.899550i \(-0.356106\pi\)
0.436817 + 0.899550i \(0.356106\pi\)
\(180\) 3.51467e6 8.08543
\(181\) 460794. 1.04547 0.522733 0.852496i \(-0.324912\pi\)
0.522733 + 0.852496i \(0.324912\pi\)
\(182\) −47797.2 −0.106961
\(183\) −1.07904e6 −2.38181
\(184\) 916507. 1.99568
\(185\) 223834. 0.480837
\(186\) 850476. 1.80252
\(187\) −115807. −0.242175
\(188\) −557419. −1.15024
\(189\) −147085. −0.299512
\(190\) 2.55643e6 5.13749
\(191\) −22464.4 −0.0445565 −0.0222783 0.999752i \(-0.507092\pi\)
−0.0222783 + 0.999752i \(0.507092\pi\)
\(192\) 1.22789e6 2.40384
\(193\) 830124. 1.60417 0.802083 0.597212i \(-0.203725\pi\)
0.802083 + 0.597212i \(0.203725\pi\)
\(194\) −884372. −1.68706
\(195\) −547015. −1.03018
\(196\) −1.29494e6 −2.40774
\(197\) 802058. 1.47245 0.736224 0.676738i \(-0.236607\pi\)
0.736224 + 0.676738i \(0.236607\pi\)
\(198\) 461176. 0.835995
\(199\) −187945. −0.336432 −0.168216 0.985750i \(-0.553801\pi\)
−0.168216 + 0.985750i \(0.553801\pi\)
\(200\) −2.18116e6 −3.85579
\(201\) −407180. −0.710879
\(202\) −787419. −1.35777
\(203\) −144897. −0.246785
\(204\) 2.94242e6 4.95028
\(205\) −306788. −0.509864
\(206\) −309602. −0.508319
\(207\) −952164. −1.54449
\(208\) −612841. −0.982176
\(209\) 238642. 0.377904
\(210\) 498221. 0.779604
\(211\) 327613. 0.506589 0.253294 0.967389i \(-0.418486\pi\)
0.253294 + 0.967389i \(0.418486\pi\)
\(212\) −303936. −0.464454
\(213\) 246251. 0.371902
\(214\) 2.10422e6 3.14092
\(215\) 160579. 0.236915
\(216\) −3.66552e6 −5.34566
\(217\) 58200.0 0.0839022
\(218\) 415592. 0.592278
\(219\) 966970. 1.36239
\(220\) −584908. −0.814762
\(221\) −310751. −0.427988
\(222\) −746243. −1.01624
\(223\) −166692. −0.224467 −0.112234 0.993682i \(-0.535801\pi\)
−0.112234 + 0.993682i \(0.535801\pi\)
\(224\) 245101. 0.326382
\(225\) 2.26602e6 2.98406
\(226\) −436886. −0.568980
\(227\) −155259. −0.199982 −0.0999912 0.994988i \(-0.531881\pi\)
−0.0999912 + 0.994988i \(0.531881\pi\)
\(228\) −6.06343e6 −7.72469
\(229\) −1.01590e6 −1.28016 −0.640079 0.768309i \(-0.721098\pi\)
−0.640079 + 0.768309i \(0.721098\pi\)
\(230\) 1.69747e6 2.11584
\(231\) 46508.7 0.0573462
\(232\) −3.61098e6 −4.40458
\(233\) 23299.8 0.0281166 0.0140583 0.999901i \(-0.495525\pi\)
0.0140583 + 0.999901i \(0.495525\pi\)
\(234\) 1.23750e6 1.47742
\(235\) −613633. −0.724835
\(236\) 2.20862e6 2.58132
\(237\) −364686. −0.421743
\(238\) 283032. 0.323887
\(239\) 4871.64 0.00551671 0.00275836 0.999996i \(-0.499122\pi\)
0.00275836 + 0.999996i \(0.499122\pi\)
\(240\) 6.38804e6 7.15879
\(241\) 918873. 1.01909 0.509545 0.860444i \(-0.329814\pi\)
0.509545 + 0.860444i \(0.329814\pi\)
\(242\) 1.61919e6 1.77730
\(243\) 380672. 0.413557
\(244\) −3.09601e6 −3.32911
\(245\) −1.42553e6 −1.51727
\(246\) 1.02280e6 1.07759
\(247\) 640362. 0.667856
\(248\) 1.45040e6 1.49748
\(249\) −269796. −0.275764
\(250\) −1.18184e6 −1.19594
\(251\) 1.47118e6 1.47395 0.736973 0.675922i \(-0.236254\pi\)
0.736973 + 0.675922i \(0.236254\pi\)
\(252\) −801859. −0.795421
\(253\) 158458. 0.155637
\(254\) −3.76747e6 −3.66409
\(255\) 3.23916e6 3.11948
\(256\) −645377. −0.615480
\(257\) −813506. −0.768295 −0.384147 0.923272i \(-0.625505\pi\)
−0.384147 + 0.923272i \(0.625505\pi\)
\(258\) −535355. −0.500717
\(259\) −51067.0 −0.0473033
\(260\) −1.56952e6 −1.43990
\(261\) 3.75147e6 3.40879
\(262\) 644546. 0.580098
\(263\) 691865. 0.616782 0.308391 0.951260i \(-0.400209\pi\)
0.308391 + 0.951260i \(0.400209\pi\)
\(264\) 1.15905e6 1.02351
\(265\) −334587. −0.292681
\(266\) −583242. −0.505411
\(267\) −2.39552e6 −2.05647
\(268\) −1.16830e6 −0.993610
\(269\) −759828. −0.640228 −0.320114 0.947379i \(-0.603721\pi\)
−0.320114 + 0.947379i \(0.603721\pi\)
\(270\) −6.78895e6 −5.66752
\(271\) 954020. 0.789104 0.394552 0.918874i \(-0.370900\pi\)
0.394552 + 0.918874i \(0.370900\pi\)
\(272\) 3.62895e6 2.97412
\(273\) 124799. 0.101346
\(274\) 3.26209e6 2.62494
\(275\) −377110. −0.300702
\(276\) −4.02611e6 −3.18136
\(277\) 1.03398e6 0.809680 0.404840 0.914387i \(-0.367327\pi\)
0.404840 + 0.914387i \(0.367327\pi\)
\(278\) 2.04017e6 1.58327
\(279\) −1.50683e6 −1.15892
\(280\) 849668. 0.647670
\(281\) 2.05117e6 1.54966 0.774829 0.632171i \(-0.217836\pi\)
0.774829 + 0.632171i \(0.217836\pi\)
\(282\) 2.04580e6 1.53193
\(283\) −2.37044e6 −1.75940 −0.879698 0.475533i \(-0.842255\pi\)
−0.879698 + 0.475533i \(0.842255\pi\)
\(284\) 706553. 0.519815
\(285\) −6.67491e6 −4.86780
\(286\) −205943. −0.148879
\(287\) 69992.7 0.0501589
\(288\) −6.34583e6 −4.50824
\(289\) 420259. 0.295987
\(290\) −6.68793e6 −4.66979
\(291\) 2.30912e6 1.59850
\(292\) 2.77447e6 1.90425
\(293\) 1.48623e6 1.01138 0.505692 0.862714i \(-0.331237\pi\)
0.505692 + 0.862714i \(0.331237\pi\)
\(294\) 4.75259e6 3.20673
\(295\) 2.43136e6 1.62665
\(296\) −1.27264e6 −0.844263
\(297\) −633746. −0.416892
\(298\) 4.79153e6 3.12560
\(299\) 425200. 0.275052
\(300\) 9.58161e6 6.14661
\(301\) −36635.5 −0.0233070
\(302\) 5.32702e6 3.36099
\(303\) 2.05597e6 1.28650
\(304\) −7.47815e6 −4.64098
\(305\) −3.40824e6 −2.09788
\(306\) −7.32787e6 −4.47378
\(307\) −1.62571e6 −0.984456 −0.492228 0.870466i \(-0.663817\pi\)
−0.492228 + 0.870466i \(0.663817\pi\)
\(308\) 133445. 0.0801539
\(309\) 808378. 0.481636
\(310\) 2.68631e6 1.58764
\(311\) 2.07269e6 1.21516 0.607581 0.794258i \(-0.292140\pi\)
0.607581 + 0.794258i \(0.292140\pi\)
\(312\) 3.11013e6 1.80881
\(313\) −345918. −0.199578 −0.0997889 0.995009i \(-0.531817\pi\)
−0.0997889 + 0.995009i \(0.531817\pi\)
\(314\) −3.66981e6 −2.10048
\(315\) −882725. −0.501244
\(316\) −1.04637e6 −0.589479
\(317\) 574435. 0.321065 0.160532 0.987031i \(-0.448679\pi\)
0.160532 + 0.987031i \(0.448679\pi\)
\(318\) 1.11548e6 0.618579
\(319\) −624316. −0.343501
\(320\) 3.87839e6 2.11727
\(321\) −5.49417e6 −2.97604
\(322\) −387272. −0.208150
\(323\) −3.79191e6 −2.02233
\(324\) 6.26803e6 3.31718
\(325\) −1.01192e6 −0.531419
\(326\) −1.10480e6 −0.575757
\(327\) −1.08512e6 −0.561187
\(328\) 1.74429e6 0.895229
\(329\) 139998. 0.0713072
\(330\) 2.14668e6 1.08513
\(331\) −1.12898e6 −0.566393 −0.283196 0.959062i \(-0.591395\pi\)
−0.283196 + 0.959062i \(0.591395\pi\)
\(332\) −774111. −0.385441
\(333\) 1.32216e6 0.653390
\(334\) −1.96900e6 −0.965784
\(335\) −1.28612e6 −0.626135
\(336\) −1.45741e6 −0.704260
\(337\) −370207. −0.177570 −0.0887850 0.996051i \(-0.528298\pi\)
−0.0887850 + 0.996051i \(0.528298\pi\)
\(338\) 3.35726e6 1.59843
\(339\) 1.14072e6 0.539112
\(340\) 9.29392e6 4.36015
\(341\) 250766. 0.116784
\(342\) 1.51005e7 6.98113
\(343\) 658239. 0.302098
\(344\) −912996. −0.415980
\(345\) −4.43214e6 −2.00477
\(346\) −5.17801e6 −2.32527
\(347\) 372676. 0.166153 0.0830764 0.996543i \(-0.473525\pi\)
0.0830764 + 0.996543i \(0.473525\pi\)
\(348\) 1.58626e7 7.02146
\(349\) −2.14587e6 −0.943060 −0.471530 0.881850i \(-0.656298\pi\)
−0.471530 + 0.881850i \(0.656298\pi\)
\(350\) 921656. 0.402160
\(351\) −1.70056e6 −0.736759
\(352\) 1.05607e6 0.454292
\(353\) −2.87740e6 −1.22903 −0.614517 0.788904i \(-0.710649\pi\)
−0.614517 + 0.788904i \(0.710649\pi\)
\(354\) −8.10591e6 −3.43790
\(355\) 777807. 0.327568
\(356\) −6.87332e6 −2.87436
\(357\) −739003. −0.306885
\(358\) −3.94375e6 −1.62630
\(359\) 647359. 0.265100 0.132550 0.991176i \(-0.457684\pi\)
0.132550 + 0.991176i \(0.457684\pi\)
\(360\) −2.19984e7 −8.94613
\(361\) 5.33787e6 2.15576
\(362\) −4.85237e6 −1.94618
\(363\) −4.22775e6 −1.68400
\(364\) 358080. 0.141653
\(365\) 3.05427e6 1.19998
\(366\) 1.13627e7 4.43384
\(367\) 3.06021e6 1.18600 0.593001 0.805202i \(-0.297943\pi\)
0.593001 + 0.805202i \(0.297943\pi\)
\(368\) −4.96549e6 −1.91136
\(369\) −1.81215e6 −0.692834
\(370\) −2.35708e6 −0.895096
\(371\) 76335.0 0.0287931
\(372\) −6.37147e6 −2.38716
\(373\) 3.54156e6 1.31802 0.659010 0.752134i \(-0.270975\pi\)
0.659010 + 0.752134i \(0.270975\pi\)
\(374\) 1.21950e6 0.450819
\(375\) 3.08582e6 1.13316
\(376\) 3.48890e6 1.27268
\(377\) −1.67526e6 −0.607057
\(378\) 1.54888e6 0.557554
\(379\) −3.92757e6 −1.40451 −0.702257 0.711923i \(-0.747824\pi\)
−0.702257 + 0.711923i \(0.747824\pi\)
\(380\) −1.91519e7 −6.80383
\(381\) 9.83696e6 3.47175
\(382\) 236560. 0.0829437
\(383\) −1.29688e6 −0.451754 −0.225877 0.974156i \(-0.572525\pi\)
−0.225877 + 0.974156i \(0.572525\pi\)
\(384\) −2.04621e6 −0.708145
\(385\) 146902. 0.0505099
\(386\) −8.74158e6 −2.98622
\(387\) 948517. 0.321934
\(388\) 6.62541e6 2.23426
\(389\) −100541. −0.0336874 −0.0168437 0.999858i \(-0.505362\pi\)
−0.0168437 + 0.999858i \(0.505362\pi\)
\(390\) 5.76031e6 1.91772
\(391\) −2.51783e6 −0.832884
\(392\) 8.10508e6 2.66405
\(393\) −1.68293e6 −0.549647
\(394\) −8.44603e6 −2.74102
\(395\) −1.15190e6 −0.371467
\(396\) −3.45497e6 −1.10715
\(397\) 3.36979e6 1.07307 0.536533 0.843879i \(-0.319734\pi\)
0.536533 + 0.843879i \(0.319734\pi\)
\(398\) 1.97914e6 0.626281
\(399\) 1.52286e6 0.478880
\(400\) 1.18172e7 3.69287
\(401\) 4.73407e6 1.47019 0.735095 0.677964i \(-0.237138\pi\)
0.735095 + 0.677964i \(0.237138\pi\)
\(402\) 4.28779e6 1.32333
\(403\) 672894. 0.206388
\(404\) 5.89906e6 1.79817
\(405\) 6.90015e6 2.09036
\(406\) 1.52583e6 0.459400
\(407\) −220032. −0.0658416
\(408\) −1.84167e7 −5.47724
\(409\) −84169.8 −0.0248799 −0.0124399 0.999923i \(-0.503960\pi\)
−0.0124399 + 0.999923i \(0.503960\pi\)
\(410\) 3.23062e6 0.949131
\(411\) −8.51740e6 −2.48715
\(412\) 2.31943e6 0.673191
\(413\) −554705. −0.160025
\(414\) 1.00267e7 2.87513
\(415\) −852178. −0.242890
\(416\) 2.83380e6 0.802854
\(417\) −5.32694e6 −1.50016
\(418\) −2.51301e6 −0.703483
\(419\) −1.45191e6 −0.404022 −0.202011 0.979383i \(-0.564748\pi\)
−0.202011 + 0.979383i \(0.564748\pi\)
\(420\) −3.73250e6 −1.03247
\(421\) 4.69910e6 1.29214 0.646070 0.763278i \(-0.276411\pi\)
0.646070 + 0.763278i \(0.276411\pi\)
\(422\) −3.44992e6 −0.943034
\(423\) −3.62464e6 −0.984950
\(424\) 1.90235e6 0.513896
\(425\) 5.99210e6 1.60919
\(426\) −2.59314e6 −0.692311
\(427\) 777577. 0.206383
\(428\) −1.57641e7 −4.15967
\(429\) 537723. 0.141064
\(430\) −1.69097e6 −0.441026
\(431\) 3.34282e6 0.866803 0.433401 0.901201i \(-0.357313\pi\)
0.433401 + 0.901201i \(0.357313\pi\)
\(432\) 1.98592e7 5.11979
\(433\) 629642. 0.161389 0.0806945 0.996739i \(-0.474286\pi\)
0.0806945 + 0.996739i \(0.474286\pi\)
\(434\) −612872. −0.156187
\(435\) 1.74623e7 4.42465
\(436\) −3.11347e6 −0.784383
\(437\) 5.18847e6 1.29968
\(438\) −1.01826e7 −2.53615
\(439\) 6.24963e6 1.54772 0.773861 0.633355i \(-0.218323\pi\)
0.773861 + 0.633355i \(0.218323\pi\)
\(440\) 3.66096e6 0.901494
\(441\) −8.42041e6 −2.06175
\(442\) 3.27235e6 0.796716
\(443\) 6.58305e6 1.59374 0.796871 0.604149i \(-0.206487\pi\)
0.796871 + 0.604149i \(0.206487\pi\)
\(444\) 5.59059e6 1.34586
\(445\) −7.56648e6 −1.81131
\(446\) 1.75534e6 0.417855
\(447\) −1.25108e7 −2.96153
\(448\) −884842. −0.208291
\(449\) 1.62106e6 0.379476 0.189738 0.981835i \(-0.439236\pi\)
0.189738 + 0.981835i \(0.439236\pi\)
\(450\) −2.38622e7 −5.55495
\(451\) 301577. 0.0698163
\(452\) 3.27300e6 0.753528
\(453\) −1.39090e7 −3.18456
\(454\) 1.63495e6 0.372275
\(455\) 394191. 0.0892644
\(456\) 3.79512e7 8.54699
\(457\) −6.01194e6 −1.34656 −0.673278 0.739390i \(-0.735114\pi\)
−0.673278 + 0.739390i \(0.735114\pi\)
\(458\) 1.06979e7 2.38306
\(459\) 1.00699e7 2.23097
\(460\) −1.27169e7 −2.80211
\(461\) −1.97072e6 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(462\) −489758. −0.106752
\(463\) −925538. −0.200651 −0.100326 0.994955i \(-0.531988\pi\)
−0.100326 + 0.994955i \(0.531988\pi\)
\(464\) 1.95637e7 4.21848
\(465\) −7.01401e6 −1.50430
\(466\) −245357. −0.0523401
\(467\) 1.87994e6 0.398890 0.199445 0.979909i \(-0.436086\pi\)
0.199445 + 0.979909i \(0.436086\pi\)
\(468\) −9.27090e6 −1.95662
\(469\) 293423. 0.0615973
\(470\) 6.46184e6 1.34931
\(471\) 9.58195e6 1.99022
\(472\) −1.38238e7 −2.85610
\(473\) −157851. −0.0324411
\(474\) 3.84031e6 0.785091
\(475\) −1.23479e7 −2.51107
\(476\) −2.12038e6 −0.428939
\(477\) −1.97636e6 −0.397713
\(478\) −51300.6 −0.0102696
\(479\) 8.18229e6 1.62943 0.814716 0.579860i \(-0.196893\pi\)
0.814716 + 0.579860i \(0.196893\pi\)
\(480\) −2.95386e7 −5.85176
\(481\) −590425. −0.116360
\(482\) −9.67615e6 −1.89708
\(483\) 1.01118e6 0.197224
\(484\) −1.21304e7 −2.35376
\(485\) 7.29356e6 1.40794
\(486\) −4.00865e6 −0.769853
\(487\) −1.84424e6 −0.352367 −0.176184 0.984357i \(-0.556375\pi\)
−0.176184 + 0.984357i \(0.556375\pi\)
\(488\) 1.93780e7 3.68350
\(489\) 2.88465e6 0.545534
\(490\) 1.50115e7 2.82445
\(491\) −4.29014e6 −0.803096 −0.401548 0.915838i \(-0.631528\pi\)
−0.401548 + 0.915838i \(0.631528\pi\)
\(492\) −7.66248e6 −1.42711
\(493\) 9.92009e6 1.83822
\(494\) −6.74330e6 −1.24324
\(495\) −3.80339e6 −0.697683
\(496\) −7.85806e6 −1.43420
\(497\) −177454. −0.0322252
\(498\) 2.84108e6 0.513346
\(499\) −7.80338e6 −1.40291 −0.701457 0.712711i \(-0.747467\pi\)
−0.701457 + 0.712711i \(0.747467\pi\)
\(500\) 8.85396e6 1.58384
\(501\) 5.14111e6 0.915087
\(502\) −1.54922e7 −2.74381
\(503\) 673490. 0.118689 0.0593446 0.998238i \(-0.481099\pi\)
0.0593446 + 0.998238i \(0.481099\pi\)
\(504\) 5.01886e6 0.880094
\(505\) 6.49397e6 1.13314
\(506\) −1.66864e6 −0.289725
\(507\) −8.76589e6 −1.51452
\(508\) 2.82246e7 4.85253
\(509\) 9.44081e6 1.61516 0.807579 0.589760i \(-0.200778\pi\)
0.807579 + 0.589760i \(0.200778\pi\)
\(510\) −3.41098e7 −5.80703
\(511\) −696821. −0.118051
\(512\) 9.17757e6 1.54722
\(513\) −2.07510e7 −3.48134
\(514\) 8.56659e6 1.43021
\(515\) 2.55334e6 0.424220
\(516\) 4.01069e6 0.663124
\(517\) 603210. 0.0992527
\(518\) 537759. 0.0880569
\(519\) 1.35199e7 2.20321
\(520\) 9.82365e6 1.59318
\(521\) −1.01037e7 −1.63074 −0.815369 0.578941i \(-0.803466\pi\)
−0.815369 + 0.578941i \(0.803466\pi\)
\(522\) −3.95046e7 −6.34559
\(523\) 1.22441e6 0.195737 0.0978687 0.995199i \(-0.468797\pi\)
0.0978687 + 0.995199i \(0.468797\pi\)
\(524\) −4.82872e6 −0.768252
\(525\) −2.40647e6 −0.381049
\(526\) −7.28565e6 −1.14816
\(527\) −3.98455e6 −0.624961
\(528\) −6.27953e6 −0.980262
\(529\) −2.99120e6 −0.464735
\(530\) 3.52336e6 0.544838
\(531\) 1.43617e7 2.21039
\(532\) 4.36944e6 0.669340
\(533\) 809239. 0.123384
\(534\) 2.52259e7 3.82819
\(535\) −1.73539e7 −2.62127
\(536\) 7.31240e6 1.09938
\(537\) 1.02972e7 1.54093
\(538\) 8.00133e6 1.19181
\(539\) 1.40132e6 0.207761
\(540\) 5.08604e7 7.50577
\(541\) −2.66077e6 −0.390853 −0.195426 0.980718i \(-0.562609\pi\)
−0.195426 + 0.980718i \(0.562609\pi\)
\(542\) −1.00463e7 −1.46895
\(543\) 1.26696e7 1.84402
\(544\) −1.67804e7 −2.43112
\(545\) −3.42745e6 −0.494288
\(546\) −1.31420e6 −0.188659
\(547\) 7.44368e6 1.06370 0.531850 0.846839i \(-0.321497\pi\)
0.531850 + 0.846839i \(0.321497\pi\)
\(548\) −2.44385e7 −3.47634
\(549\) −2.01320e7 −2.85072
\(550\) 3.97114e6 0.559768
\(551\) −2.04423e7 −2.86847
\(552\) 2.51996e7 3.52002
\(553\) 262801. 0.0365438
\(554\) −1.08883e7 −1.50725
\(555\) 6.15438e6 0.848110
\(556\) −1.52843e7 −2.09680
\(557\) 5.55246e6 0.758311 0.379155 0.925333i \(-0.376215\pi\)
0.379155 + 0.925333i \(0.376215\pi\)
\(558\) 1.58676e7 2.15738
\(559\) −423571. −0.0573320
\(560\) −4.60337e6 −0.620305
\(561\) −3.18414e6 −0.427154
\(562\) −2.15998e7 −2.88475
\(563\) −2.05400e6 −0.273105 −0.136552 0.990633i \(-0.543602\pi\)
−0.136552 + 0.990633i \(0.543602\pi\)
\(564\) −1.53264e7 −2.02881
\(565\) 3.60307e6 0.474845
\(566\) 2.49618e7 3.27518
\(567\) −1.57424e6 −0.205643
\(568\) −4.42234e6 −0.575150
\(569\) 5.13151e6 0.664453 0.332227 0.943200i \(-0.392200\pi\)
0.332227 + 0.943200i \(0.392200\pi\)
\(570\) 7.02898e7 9.06161
\(571\) −1.13394e7 −1.45546 −0.727730 0.685863i \(-0.759425\pi\)
−0.727730 + 0.685863i \(0.759425\pi\)
\(572\) 1.54286e6 0.197167
\(573\) −617664. −0.0785898
\(574\) −737055. −0.0933728
\(575\) −8.19899e6 −1.03417
\(576\) 2.29091e7 2.87708
\(577\) −9.19195e6 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(578\) −4.42552e6 −0.550992
\(579\) 2.28245e7 2.82946
\(580\) 5.01037e7 6.18443
\(581\) 194421. 0.0238948
\(582\) −2.43160e7 −2.97567
\(583\) 328904. 0.0400772
\(584\) −1.73655e7 −2.10695
\(585\) −1.02058e7 −1.23299
\(586\) −1.56506e7 −1.88273
\(587\) 7.32138e6 0.876997 0.438498 0.898732i \(-0.355510\pi\)
0.438498 + 0.898732i \(0.355510\pi\)
\(588\) −3.56047e7 −4.24683
\(589\) 8.21094e6 0.975225
\(590\) −2.56033e7 −3.02807
\(591\) 2.20528e7 2.59714
\(592\) 6.89498e6 0.808591
\(593\) 8.89330e6 1.03855 0.519274 0.854608i \(-0.326203\pi\)
0.519274 + 0.854608i \(0.326203\pi\)
\(594\) 6.67363e6 0.776061
\(595\) −2.33421e6 −0.270301
\(596\) −3.58965e7 −4.13939
\(597\) −5.16758e6 −0.593406
\(598\) −4.47755e6 −0.512021
\(599\) 7.52622e6 0.857057 0.428529 0.903528i \(-0.359032\pi\)
0.428529 + 0.903528i \(0.359032\pi\)
\(600\) −5.99716e7 −6.80092
\(601\) 1.53849e7 1.73743 0.868716 0.495311i \(-0.164946\pi\)
0.868716 + 0.495311i \(0.164946\pi\)
\(602\) 385789. 0.0433869
\(603\) −7.59690e6 −0.850830
\(604\) −3.99081e7 −4.45112
\(605\) −1.33537e7 −1.48325
\(606\) −2.16503e7 −2.39487
\(607\) −1.10155e7 −1.21348 −0.606740 0.794900i \(-0.707523\pi\)
−0.606740 + 0.794900i \(0.707523\pi\)
\(608\) 3.45793e7 3.79365
\(609\) −3.98397e6 −0.435285
\(610\) 3.58903e7 3.90528
\(611\) 1.61863e6 0.175406
\(612\) 5.48978e7 5.92484
\(613\) −8.89814e6 −0.956419 −0.478209 0.878246i \(-0.658714\pi\)
−0.478209 + 0.878246i \(0.658714\pi\)
\(614\) 1.71194e7 1.83260
\(615\) −8.43522e6 −0.899309
\(616\) −835235. −0.0886864
\(617\) 7.40581e6 0.783177 0.391588 0.920140i \(-0.371926\pi\)
0.391588 + 0.920140i \(0.371926\pi\)
\(618\) −8.51259e6 −0.896583
\(619\) 1.41475e7 1.48406 0.742032 0.670364i \(-0.233862\pi\)
0.742032 + 0.670364i \(0.233862\pi\)
\(620\) −2.01249e7 −2.10259
\(621\) −1.37787e7 −1.43377
\(622\) −2.18264e7 −2.26207
\(623\) 1.72627e6 0.178192
\(624\) −1.68502e7 −1.73238
\(625\) −4.05719e6 −0.415456
\(626\) 3.64267e6 0.371522
\(627\) 6.56153e6 0.666555
\(628\) 2.74929e7 2.78177
\(629\) 3.49621e6 0.352347
\(630\) 9.29549e6 0.933085
\(631\) 9.57148e6 0.956986 0.478493 0.878091i \(-0.341183\pi\)
0.478493 + 0.878091i \(0.341183\pi\)
\(632\) 6.54927e6 0.652229
\(633\) 9.00781e6 0.893532
\(634\) −6.04906e6 −0.597675
\(635\) 3.10710e7 3.05788
\(636\) −8.35680e6 −0.819214
\(637\) 3.76023e6 0.367169
\(638\) 6.57433e6 0.639440
\(639\) 4.59440e6 0.445119
\(640\) −6.46315e6 −0.623727
\(641\) −637566. −0.0612887 −0.0306443 0.999530i \(-0.509756\pi\)
−0.0306443 + 0.999530i \(0.509756\pi\)
\(642\) 5.78561e7 5.54002
\(643\) −1.89702e7 −1.80944 −0.904718 0.426010i \(-0.859919\pi\)
−0.904718 + 0.426010i \(0.859919\pi\)
\(644\) 2.90131e6 0.275664
\(645\) 4.41516e6 0.417876
\(646\) 3.99306e7 3.76465
\(647\) 2.02807e7 1.90468 0.952338 0.305044i \(-0.0986713\pi\)
0.952338 + 0.305044i \(0.0986713\pi\)
\(648\) −3.92318e7 −3.67029
\(649\) −2.39006e6 −0.222739
\(650\) 1.06560e7 0.989258
\(651\) 1.60022e6 0.147989
\(652\) 8.27676e6 0.762503
\(653\) −3.76628e6 −0.345645 −0.172822 0.984953i \(-0.555289\pi\)
−0.172822 + 0.984953i \(0.555289\pi\)
\(654\) 1.14268e7 1.04467
\(655\) −5.31568e6 −0.484123
\(656\) −9.45029e6 −0.857404
\(657\) 1.80411e7 1.63061
\(658\) −1.47425e6 −0.132741
\(659\) −1.70994e7 −1.53379 −0.766897 0.641770i \(-0.778200\pi\)
−0.766897 + 0.641770i \(0.778200\pi\)
\(660\) −1.60822e7 −1.43709
\(661\) 875240. 0.0779154 0.0389577 0.999241i \(-0.487596\pi\)
0.0389577 + 0.999241i \(0.487596\pi\)
\(662\) 1.18887e7 1.05436
\(663\) −8.54417e6 −0.754894
\(664\) 4.84518e6 0.426472
\(665\) 4.81009e6 0.421793
\(666\) −1.39229e7 −1.21631
\(667\) −1.35737e7 −1.18136
\(668\) 1.47511e7 1.27904
\(669\) −4.58324e6 −0.395920
\(670\) 1.35434e7 1.16557
\(671\) 3.35034e6 0.287265
\(672\) 6.73913e6 0.575679
\(673\) −1.59835e7 −1.36030 −0.680149 0.733074i \(-0.738085\pi\)
−0.680149 + 0.733074i \(0.738085\pi\)
\(674\) 3.89844e6 0.330553
\(675\) 3.27914e7 2.77013
\(676\) −2.51515e7 −2.11688
\(677\) −2.27744e7 −1.90974 −0.954871 0.297020i \(-0.904007\pi\)
−0.954871 + 0.297020i \(0.904007\pi\)
\(678\) −1.20123e7 −1.00358
\(679\) −1.66400e6 −0.138509
\(680\) −5.81709e7 −4.82429
\(681\) −4.26888e6 −0.352733
\(682\) −2.64068e6 −0.217398
\(683\) −1.16349e7 −0.954354 −0.477177 0.878807i \(-0.658340\pi\)
−0.477177 + 0.878807i \(0.658340\pi\)
\(684\) −1.13128e8 −9.24545
\(685\) −2.69030e7 −2.19066
\(686\) −6.93156e6 −0.562368
\(687\) −2.79325e7 −2.25797
\(688\) 4.94647e6 0.398404
\(689\) 882566. 0.0708271
\(690\) 4.66724e7 3.73197
\(691\) −5.50626e6 −0.438694 −0.219347 0.975647i \(-0.570393\pi\)
−0.219347 + 0.975647i \(0.570393\pi\)
\(692\) 3.87918e7 3.07946
\(693\) 867731. 0.0686360
\(694\) −3.92444e6 −0.309300
\(695\) −1.68257e7 −1.32133
\(696\) −9.92848e7 −7.76890
\(697\) −4.79192e6 −0.373618
\(698\) 2.25970e7 1.75554
\(699\) 640633. 0.0495926
\(700\) −6.90473e6 −0.532600
\(701\) −1.26842e7 −0.974916 −0.487458 0.873146i \(-0.662076\pi\)
−0.487458 + 0.873146i \(0.662076\pi\)
\(702\) 1.79077e7 1.37151
\(703\) −7.20462e6 −0.549823
\(704\) −3.81251e6 −0.289921
\(705\) −1.68720e7 −1.27848
\(706\) 3.03004e7 2.28789
\(707\) −1.48158e6 −0.111475
\(708\) 6.07266e7 4.55298
\(709\) 919145. 0.0686702 0.0343351 0.999410i \(-0.489069\pi\)
0.0343351 + 0.999410i \(0.489069\pi\)
\(710\) −8.19067e6 −0.609780
\(711\) −6.80408e6 −0.504772
\(712\) 4.30203e7 3.18034
\(713\) 5.45207e6 0.401640
\(714\) 7.78203e6 0.571278
\(715\) 1.69845e6 0.124247
\(716\) 2.95452e7 2.15379
\(717\) 133947. 0.00973049
\(718\) −6.81699e6 −0.493493
\(719\) 7.21135e6 0.520228 0.260114 0.965578i \(-0.416240\pi\)
0.260114 + 0.965578i \(0.416240\pi\)
\(720\) 1.19184e8 8.56814
\(721\) −582536. −0.0417335
\(722\) −5.62102e7 −4.01303
\(723\) 2.52646e7 1.79749
\(724\) 3.63522e7 2.57742
\(725\) 3.23035e7 2.28247
\(726\) 4.45201e7 3.13483
\(727\) −4.15671e6 −0.291685 −0.145842 0.989308i \(-0.546589\pi\)
−0.145842 + 0.989308i \(0.546589\pi\)
\(728\) −2.24123e6 −0.156732
\(729\) −8.84023e6 −0.616091
\(730\) −3.21628e7 −2.23381
\(731\) 2.50818e6 0.173607
\(732\) −8.51256e7 −5.87195
\(733\) 4.05351e6 0.278658 0.139329 0.990246i \(-0.455505\pi\)
0.139329 + 0.990246i \(0.455505\pi\)
\(734\) −3.22254e7 −2.20779
\(735\) −3.91954e7 −2.67619
\(736\) 2.29606e7 1.56239
\(737\) 1.26427e6 0.0857375
\(738\) 1.90828e7 1.28974
\(739\) 1.27176e7 0.856629 0.428315 0.903630i \(-0.359108\pi\)
0.428315 + 0.903630i \(0.359108\pi\)
\(740\) 1.76584e7 1.18542
\(741\) 1.76069e7 1.17798
\(742\) −803842. −0.0535995
\(743\) −1.86660e6 −0.124045 −0.0620224 0.998075i \(-0.519755\pi\)
−0.0620224 + 0.998075i \(0.519755\pi\)
\(744\) 3.98792e7 2.64128
\(745\) −3.95165e7 −2.60848
\(746\) −3.72942e7 −2.45355
\(747\) −5.03369e6 −0.330054
\(748\) −9.13605e6 −0.597041
\(749\) 3.95922e6 0.257873
\(750\) −3.24951e7 −2.10943
\(751\) 2.61334e7 1.69081 0.845407 0.534122i \(-0.179358\pi\)
0.845407 + 0.534122i \(0.179358\pi\)
\(752\) −1.89023e7 −1.21891
\(753\) 4.04505e7 2.59978
\(754\) 1.76413e7 1.13006
\(755\) −4.39328e7 −2.80492
\(756\) −1.16036e7 −0.738396
\(757\) 1.20591e6 0.0764846 0.0382423 0.999268i \(-0.487824\pi\)
0.0382423 + 0.999268i \(0.487824\pi\)
\(758\) 4.13591e7 2.61456
\(759\) 4.35685e6 0.274516
\(760\) 1.19872e8 7.52810
\(761\) −1.63050e6 −0.102061 −0.0510303 0.998697i \(-0.516251\pi\)
−0.0510303 + 0.998697i \(0.516251\pi\)
\(762\) −1.03588e8 −6.46280
\(763\) 781961. 0.0486266
\(764\) −1.77223e6 −0.109846
\(765\) 6.04341e7 3.73361
\(766\) 1.36567e7 0.840958
\(767\) −6.41337e6 −0.393639
\(768\) −1.77448e7 −1.08560
\(769\) −3.03077e6 −0.184815 −0.0924074 0.995721i \(-0.529456\pi\)
−0.0924074 + 0.995721i \(0.529456\pi\)
\(770\) −1.54695e6 −0.0940262
\(771\) −2.23676e7 −1.35513
\(772\) 6.54888e7 3.95480
\(773\) 1.56440e7 0.941669 0.470834 0.882222i \(-0.343953\pi\)
0.470834 + 0.882222i \(0.343953\pi\)
\(774\) −9.98831e6 −0.599294
\(775\) −1.29752e7 −0.775995
\(776\) −4.14686e7 −2.47210
\(777\) −1.40410e6 −0.0834346
\(778\) 1.05874e6 0.0627104
\(779\) 9.87468e6 0.583015
\(780\) −4.31542e7 −2.53973
\(781\) −764595. −0.0448543
\(782\) 2.65139e7 1.55045
\(783\) 5.42871e7 3.16441
\(784\) −4.39120e7 −2.55149
\(785\) 3.02655e7 1.75297
\(786\) 1.77220e7 1.02319
\(787\) 2.77750e7 1.59852 0.799260 0.600986i \(-0.205225\pi\)
0.799260 + 0.600986i \(0.205225\pi\)
\(788\) 6.32747e7 3.63007
\(789\) 1.90230e7 1.08789
\(790\) 1.21300e7 0.691500
\(791\) −822028. −0.0467138
\(792\) 2.16247e7 1.22501
\(793\) 8.99016e6 0.507673
\(794\) −3.54854e7 −1.99756
\(795\) −9.19957e6 −0.516237
\(796\) −1.48270e7 −0.829414
\(797\) −646020. −0.0360247 −0.0180123 0.999838i \(-0.505734\pi\)
−0.0180123 + 0.999838i \(0.505734\pi\)
\(798\) −1.60364e7 −0.891454
\(799\) −9.58473e6 −0.531145
\(800\) −5.46432e7 −3.01864
\(801\) −4.46941e7 −2.46132
\(802\) −4.98519e7 −2.73682
\(803\) −3.00239e6 −0.164315
\(804\) −3.21226e7 −1.75255
\(805\) 3.19390e6 0.173713
\(806\) −7.08588e6 −0.384199
\(807\) −2.08917e7 −1.12925
\(808\) −3.69224e7 −1.98958
\(809\) −1.67691e6 −0.0900823 −0.0450412 0.998985i \(-0.514342\pi\)
−0.0450412 + 0.998985i \(0.514342\pi\)
\(810\) −7.26617e7 −3.89128
\(811\) 1.09231e7 0.583169 0.291585 0.956545i \(-0.405817\pi\)
0.291585 + 0.956545i \(0.405817\pi\)
\(812\) −1.14310e7 −0.608406
\(813\) 2.62310e7 1.39184
\(814\) 2.31704e6 0.122567
\(815\) 9.11145e6 0.480500
\(816\) 9.97789e7 5.24582
\(817\) −5.16860e6 −0.270905
\(818\) 886346. 0.0463148
\(819\) 2.32843e6 0.121298
\(820\) −2.42027e7 −1.25698
\(821\) 1.94364e7 1.00637 0.503186 0.864178i \(-0.332161\pi\)
0.503186 + 0.864178i \(0.332161\pi\)
\(822\) 8.96921e7 4.62993
\(823\) −3.08462e7 −1.58746 −0.793730 0.608271i \(-0.791864\pi\)
−0.793730 + 0.608271i \(0.791864\pi\)
\(824\) −1.45174e7 −0.744853
\(825\) −1.03687e7 −0.530384
\(826\) 5.84130e6 0.297892
\(827\) −1.97925e7 −1.00632 −0.503161 0.864193i \(-0.667830\pi\)
−0.503161 + 0.864193i \(0.667830\pi\)
\(828\) −7.51167e7 −3.80768
\(829\) −1.75755e7 −0.888223 −0.444111 0.895972i \(-0.646481\pi\)
−0.444111 + 0.895972i \(0.646481\pi\)
\(830\) 8.97382e6 0.452150
\(831\) 2.84296e7 1.42813
\(832\) −1.02303e7 −0.512367
\(833\) −2.22663e7 −1.11182
\(834\) 5.60951e7 2.79261
\(835\) 1.62387e7 0.805999
\(836\) 1.88266e7 0.931657
\(837\) −2.18052e7 −1.07584
\(838\) 1.52893e7 0.752103
\(839\) −1.50238e7 −0.736842 −0.368421 0.929659i \(-0.620101\pi\)
−0.368421 + 0.929659i \(0.620101\pi\)
\(840\) 2.33618e7 1.14237
\(841\) 3.29682e7 1.60733
\(842\) −4.94837e7 −2.40537
\(843\) 5.63974e7 2.73332
\(844\) 2.58456e7 1.24891
\(845\) −2.76879e7 −1.33398
\(846\) 3.81691e7 1.83352
\(847\) 3.04661e6 0.145918
\(848\) −1.03066e7 −0.492183
\(849\) −6.51759e7 −3.10326
\(850\) −6.30995e7 −2.99556
\(851\) −4.78387e6 −0.226441
\(852\) 1.94269e7 0.916861
\(853\) 3.88390e7 1.82766 0.913829 0.406099i \(-0.133111\pi\)
0.913829 + 0.406099i \(0.133111\pi\)
\(854\) −8.18824e6 −0.384190
\(855\) −1.24536e8 −5.82613
\(856\) 9.86679e7 4.60248
\(857\) −3.57330e6 −0.166195 −0.0830975 0.996541i \(-0.526481\pi\)
−0.0830975 + 0.996541i \(0.526481\pi\)
\(858\) −5.66247e6 −0.262596
\(859\) 3.27850e6 0.151598 0.0757988 0.997123i \(-0.475849\pi\)
0.0757988 + 0.997123i \(0.475849\pi\)
\(860\) 1.26681e7 0.584073
\(861\) 1.92447e6 0.0884713
\(862\) −3.52014e7 −1.61359
\(863\) 1.93441e7 0.884139 0.442070 0.896981i \(-0.354244\pi\)
0.442070 + 0.896981i \(0.354244\pi\)
\(864\) −9.18298e7 −4.18504
\(865\) 4.27039e7 1.94056
\(866\) −6.63042e6 −0.300432
\(867\) 1.15551e7 0.522068
\(868\) 4.59142e6 0.206846
\(869\) 1.13233e6 0.0508655
\(870\) −1.83886e8 −8.23667
\(871\) 3.39248e6 0.151521
\(872\) 1.94873e7 0.867881
\(873\) 4.30820e7 1.91320
\(874\) −5.46370e7 −2.41940
\(875\) −2.22371e6 −0.0981880
\(876\) 7.62847e7 3.35875
\(877\) −2.57531e7 −1.13066 −0.565329 0.824866i \(-0.691251\pi\)
−0.565329 + 0.824866i \(0.691251\pi\)
\(878\) −6.58114e7 −2.88115
\(879\) 4.08642e7 1.78390
\(880\) −1.98345e7 −0.863405
\(881\) 4.39384e6 0.190724 0.0953618 0.995443i \(-0.469599\pi\)
0.0953618 + 0.995443i \(0.469599\pi\)
\(882\) 8.86708e7 3.83804
\(883\) 2.21529e7 0.956156 0.478078 0.878317i \(-0.341334\pi\)
0.478078 + 0.878317i \(0.341334\pi\)
\(884\) −2.45153e7 −1.05513
\(885\) 6.68507e7 2.86912
\(886\) −6.93226e7 −2.96681
\(887\) −4.36187e7 −1.86150 −0.930750 0.365655i \(-0.880845\pi\)
−0.930750 + 0.365655i \(0.880845\pi\)
\(888\) −3.49917e7 −1.48913
\(889\) −7.08874e6 −0.300825
\(890\) 7.96785e7 3.37183
\(891\) −6.78294e6 −0.286236
\(892\) −1.31504e7 −0.553385
\(893\) 1.97512e7 0.828828
\(894\) 1.31744e8 5.51300
\(895\) 3.25247e7 1.35724
\(896\) 1.47455e6 0.0613604
\(897\) 1.16910e7 0.485143
\(898\) −1.70705e7 −0.706409
\(899\) −2.14808e7 −0.886443
\(900\) 1.78768e8 7.35669
\(901\) −5.22613e6 −0.214471
\(902\) −3.17574e6 −0.129966
\(903\) −1.00730e6 −0.0411094
\(904\) −2.04858e7 −0.833742
\(905\) 4.00183e7 1.62419
\(906\) 1.46468e8 5.92818
\(907\) 1.38621e7 0.559515 0.279758 0.960071i \(-0.409746\pi\)
0.279758 + 0.960071i \(0.409746\pi\)
\(908\) −1.22484e7 −0.493022
\(909\) 3.83589e7 1.53977
\(910\) −4.15101e6 −0.166169
\(911\) −2.31037e7 −0.922329 −0.461164 0.887315i \(-0.652568\pi\)
−0.461164 + 0.887315i \(0.652568\pi\)
\(912\) −2.05614e8 −8.18587
\(913\) 837702. 0.0332593
\(914\) 6.33085e7 2.50666
\(915\) −9.37103e7 −3.70028
\(916\) −8.01451e7 −3.15601
\(917\) 1.21275e6 0.0476266
\(918\) −1.06041e8 −4.15305
\(919\) −2.27313e7 −0.887842 −0.443921 0.896066i \(-0.646413\pi\)
−0.443921 + 0.896066i \(0.646413\pi\)
\(920\) 7.95953e7 3.10040
\(921\) −4.46992e7 −1.73640
\(922\) 2.07526e7 0.803978
\(923\) −2.05168e6 −0.0792694
\(924\) 3.66910e6 0.141377
\(925\) 1.13850e7 0.437499
\(926\) 9.74634e6 0.373520
\(927\) 1.50822e7 0.576455
\(928\) −9.04635e7 −3.44829
\(929\) −3.32467e7 −1.26389 −0.631945 0.775013i \(-0.717743\pi\)
−0.631945 + 0.775013i \(0.717743\pi\)
\(930\) 7.38607e7 2.80031
\(931\) 4.58840e7 1.73495
\(932\) 1.83813e6 0.0693165
\(933\) 5.69892e7 2.14333
\(934\) −1.97967e7 −0.742548
\(935\) −1.00574e7 −0.376233
\(936\) 5.80269e7 2.16491
\(937\) 1.72533e7 0.641981 0.320991 0.947082i \(-0.395984\pi\)
0.320991 + 0.947082i \(0.395984\pi\)
\(938\) −3.08988e6 −0.114666
\(939\) −9.51110e6 −0.352019
\(940\) −4.84098e7 −1.78696
\(941\) 1.12167e6 0.0412945 0.0206473 0.999787i \(-0.493427\pi\)
0.0206473 + 0.999787i \(0.493427\pi\)
\(942\) −1.00902e8 −3.70488
\(943\) 6.55679e6 0.240111
\(944\) 7.48954e7 2.73543
\(945\) −1.27738e7 −0.465309
\(946\) 1.66225e6 0.0603903
\(947\) 3.89113e7 1.40994 0.704970 0.709237i \(-0.250960\pi\)
0.704970 + 0.709237i \(0.250960\pi\)
\(948\) −2.87702e7 −1.03973
\(949\) −8.05647e6 −0.290388
\(950\) 1.30029e8 4.67445
\(951\) 1.57942e7 0.566301
\(952\) 1.32715e7 0.474600
\(953\) −1.79943e7 −0.641803 −0.320902 0.947113i \(-0.603986\pi\)
−0.320902 + 0.947113i \(0.603986\pi\)
\(954\) 2.08120e7 0.740358
\(955\) −1.95095e6 −0.0692210
\(956\) 384326. 0.0136005
\(957\) −1.71657e7 −0.605874
\(958\) −8.61632e7 −3.03325
\(959\) 6.13783e6 0.215510
\(960\) 1.06637e8 3.73449
\(961\) −2.00011e7 −0.698626
\(962\) 6.21744e6 0.216608
\(963\) −1.02507e8 −3.56194
\(964\) 7.24903e7 2.51239
\(965\) 7.20932e7 2.49216
\(966\) −1.06482e7 −0.367140
\(967\) 2.31110e7 0.794791 0.397395 0.917648i \(-0.369914\pi\)
0.397395 + 0.917648i \(0.369914\pi\)
\(968\) 7.59247e7 2.60432
\(969\) −1.04260e8 −3.56703
\(970\) −7.68045e7 −2.62094
\(971\) −3.50927e7 −1.19445 −0.597226 0.802073i \(-0.703730\pi\)
−0.597226 + 0.802073i \(0.703730\pi\)
\(972\) 3.00314e7 1.01955
\(973\) 3.83871e6 0.129988
\(974\) 1.94207e7 0.655945
\(975\) −2.78230e7 −0.937329
\(976\) −1.04987e8 −3.52786
\(977\) 7.20029e6 0.241331 0.120666 0.992693i \(-0.461497\pi\)
0.120666 + 0.992693i \(0.461497\pi\)
\(978\) −3.03767e7 −1.01553
\(979\) 7.43795e6 0.248026
\(980\) −1.12461e8 −3.74056
\(981\) −2.02455e7 −0.671669
\(982\) 4.51771e7 1.49499
\(983\) −3.28324e7 −1.08373 −0.541863 0.840467i \(-0.682281\pi\)
−0.541863 + 0.840467i \(0.682281\pi\)
\(984\) 4.79597e7 1.57902
\(985\) 6.96558e7 2.28753
\(986\) −1.04463e8 −3.42193
\(987\) 3.84929e6 0.125773
\(988\) 5.05184e7 1.64648
\(989\) −3.43195e6 −0.111571
\(990\) 4.00514e7 1.29876
\(991\) 5.19670e7 1.68090 0.840452 0.541885i \(-0.182289\pi\)
0.840452 + 0.541885i \(0.182289\pi\)
\(992\) 3.63360e7 1.17235
\(993\) −3.10417e7 −0.999015
\(994\) 1.86867e6 0.0599884
\(995\) −1.63223e7 −0.522665
\(996\) −2.12844e7 −0.679849
\(997\) −5.30582e6 −0.169050 −0.0845249 0.996421i \(-0.526937\pi\)
−0.0845249 + 0.996421i \(0.526937\pi\)
\(998\) 8.21731e7 2.61158
\(999\) 1.91328e7 0.606548
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.1.1 10
3.2 odd 2 387.6.a.e.1.10 10
4.3 odd 2 688.6.a.h.1.1 10
5.4 even 2 1075.6.a.b.1.10 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.1 10 1.1 even 1 trivial
387.6.a.e.1.10 10 3.2 odd 2
688.6.a.h.1.1 10 4.3 odd 2
1075.6.a.b.1.10 10 5.4 even 2