Properties

Label 1075.6.a.b.1.9
Level 1075
Weight 6
Character 1075.1
Self dual yes
Analytic conductor 172.413
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(172.412606299\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(9.86547\) of defining polynomial
Character \(\chi\) \(=\) 1075.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.86547 q^{2} -1.50169 q^{3} +46.5966 q^{4} -13.3132 q^{6} +124.747 q^{7} +129.406 q^{8} -240.745 q^{9} +O(q^{10})\) \(q+8.86547 q^{2} -1.50169 q^{3} +46.5966 q^{4} -13.3132 q^{6} +124.747 q^{7} +129.406 q^{8} -240.745 q^{9} +590.079 q^{11} -69.9735 q^{12} -434.774 q^{13} +1105.94 q^{14} -343.849 q^{16} -1925.58 q^{17} -2134.32 q^{18} +654.129 q^{19} -187.332 q^{21} +5231.33 q^{22} -2805.03 q^{23} -194.327 q^{24} -3854.47 q^{26} +726.434 q^{27} +5812.80 q^{28} -1456.23 q^{29} +4419.85 q^{31} -7189.36 q^{32} -886.115 q^{33} -17071.2 q^{34} -11217.9 q^{36} -3753.09 q^{37} +5799.17 q^{38} +652.894 q^{39} +1972.85 q^{41} -1660.78 q^{42} -1849.00 q^{43} +27495.7 q^{44} -24867.9 q^{46} -2204.84 q^{47} +516.354 q^{48} -1245.12 q^{49} +2891.62 q^{51} -20259.0 q^{52} -24984.2 q^{53} +6440.18 q^{54} +16143.0 q^{56} -982.298 q^{57} -12910.1 q^{58} -42756.2 q^{59} -21022.8 q^{61} +39184.0 q^{62} -30032.3 q^{63} -52733.9 q^{64} -7855.83 q^{66} +25272.1 q^{67} -89725.4 q^{68} +4212.28 q^{69} +48082.8 q^{71} -31153.7 q^{72} -58801.2 q^{73} -33272.9 q^{74} +30480.2 q^{76} +73610.8 q^{77} +5788.22 q^{78} +92704.7 q^{79} +57410.1 q^{81} +17490.3 q^{82} +1849.64 q^{83} -8729.01 q^{84} -16392.3 q^{86} +2186.80 q^{87} +76359.5 q^{88} -70380.3 q^{89} -54236.8 q^{91} -130705. q^{92} -6637.23 q^{93} -19546.9 q^{94} +10796.2 q^{96} +88842.1 q^{97} -11038.6 q^{98} -142059. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 8q^{2} - 28q^{3} + 202q^{4} + 75q^{6} - 60q^{7} - 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q - 8q^{2} - 28q^{3} + 202q^{4} + 75q^{6} - 60q^{7} - 294q^{8} + 1356q^{9} + 745q^{11} - 4627q^{12} - 1917q^{13} + 1936q^{14} + 5354q^{16} - 4017q^{17} + 2725q^{18} - 2404q^{19} - 228q^{21} + 5836q^{22} - 1733q^{23} - 10711q^{24} - 1484q^{26} + 2324q^{27} + 15028q^{28} + 6996q^{29} - 4899q^{31} + 7554q^{32} + 15734q^{33} - 27033q^{34} + 4433q^{36} - 1466q^{37} - 13905q^{38} - 26542q^{39} + 10297q^{41} + 37642q^{42} - 18490q^{43} - 36140q^{44} + 17991q^{46} - 48592q^{47} - 83607q^{48} + 29458q^{49} + 92972q^{51} - 14232q^{52} - 127165q^{53} - 92002q^{54} - 7780q^{56} - 34060q^{57} + 10305q^{58} + 99372q^{59} + 17408q^{61} - 28265q^{62} - 2244q^{63} + 47202q^{64} - 150292q^{66} + 2021q^{67} - 192151q^{68} + 1654q^{69} + 11286q^{71} + 298365q^{72} - 49892q^{73} - 125431q^{74} - 249803q^{76} - 98144q^{77} + 28494q^{78} - 91524q^{79} - 26450q^{81} + 158909q^{82} + 105203q^{83} - 357682q^{84} + 14792q^{86} - 181200q^{87} + 461824q^{88} - 62682q^{89} - 295304q^{91} - 183783q^{92} + 238430q^{93} + 7259q^{94} - 162399q^{96} - 108383q^{97} - 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.86547 1.56721 0.783604 0.621260i \(-0.213379\pi\)
0.783604 + 0.621260i \(0.213379\pi\)
\(3\) −1.50169 −0.0963333 −0.0481667 0.998839i \(-0.515338\pi\)
−0.0481667 + 0.998839i \(0.515338\pi\)
\(4\) 46.5966 1.45614
\(5\) 0 0
\(6\) −13.3132 −0.150974
\(7\) 124.747 0.962246 0.481123 0.876653i \(-0.340229\pi\)
0.481123 + 0.876653i \(0.340229\pi\)
\(8\) 129.406 0.714872
\(9\) −240.745 −0.990720
\(10\) 0 0
\(11\) 590.079 1.47038 0.735188 0.677863i \(-0.237094\pi\)
0.735188 + 0.677863i \(0.237094\pi\)
\(12\) −69.9735 −0.140275
\(13\) −434.774 −0.713518 −0.356759 0.934196i \(-0.616118\pi\)
−0.356759 + 0.934196i \(0.616118\pi\)
\(14\) 1105.94 1.50804
\(15\) 0 0
\(16\) −343.849 −0.335790
\(17\) −1925.58 −1.61599 −0.807995 0.589189i \(-0.799447\pi\)
−0.807995 + 0.589189i \(0.799447\pi\)
\(18\) −2134.32 −1.55266
\(19\) 654.129 0.415700 0.207850 0.978161i \(-0.433353\pi\)
0.207850 + 0.978161i \(0.433353\pi\)
\(20\) 0 0
\(21\) −187.332 −0.0926963
\(22\) 5231.33 2.30439
\(23\) −2805.03 −1.10565 −0.552825 0.833297i \(-0.686450\pi\)
−0.552825 + 0.833297i \(0.686450\pi\)
\(24\) −194.327 −0.0688660
\(25\) 0 0
\(26\) −3854.47 −1.11823
\(27\) 726.434 0.191773
\(28\) 5812.80 1.40117
\(29\) −1456.23 −0.321540 −0.160770 0.986992i \(-0.551398\pi\)
−0.160770 + 0.986992i \(0.551398\pi\)
\(30\) 0 0
\(31\) 4419.85 0.826044 0.413022 0.910721i \(-0.364473\pi\)
0.413022 + 0.910721i \(0.364473\pi\)
\(32\) −7189.36 −1.24112
\(33\) −886.115 −0.141646
\(34\) −17071.2 −2.53259
\(35\) 0 0
\(36\) −11217.9 −1.44263
\(37\) −3753.09 −0.450697 −0.225348 0.974278i \(-0.572352\pi\)
−0.225348 + 0.974278i \(0.572352\pi\)
\(38\) 5799.17 0.651488
\(39\) 652.894 0.0687356
\(40\) 0 0
\(41\) 1972.85 0.183288 0.0916442 0.995792i \(-0.470788\pi\)
0.0916442 + 0.995792i \(0.470788\pi\)
\(42\) −1660.78 −0.145275
\(43\) −1849.00 −0.152499
\(44\) 27495.7 2.14108
\(45\) 0 0
\(46\) −24867.9 −1.73279
\(47\) −2204.84 −0.145590 −0.0727950 0.997347i \(-0.523192\pi\)
−0.0727950 + 0.997347i \(0.523192\pi\)
\(48\) 516.354 0.0323478
\(49\) −1245.12 −0.0740834
\(50\) 0 0
\(51\) 2891.62 0.155674
\(52\) −20259.0 −1.03898
\(53\) −24984.2 −1.22173 −0.610865 0.791735i \(-0.709178\pi\)
−0.610865 + 0.791735i \(0.709178\pi\)
\(54\) 6440.18 0.300548
\(55\) 0 0
\(56\) 16143.0 0.687882
\(57\) −982.298 −0.0400457
\(58\) −12910.1 −0.503920
\(59\) −42756.2 −1.59907 −0.799537 0.600616i \(-0.794922\pi\)
−0.799537 + 0.600616i \(0.794922\pi\)
\(60\) 0 0
\(61\) −21022.8 −0.723379 −0.361689 0.932299i \(-0.617800\pi\)
−0.361689 + 0.932299i \(0.617800\pi\)
\(62\) 39184.0 1.29458
\(63\) −30032.3 −0.953316
\(64\) −52733.9 −1.60931
\(65\) 0 0
\(66\) −7855.83 −0.221989
\(67\) 25272.1 0.687788 0.343894 0.939008i \(-0.388254\pi\)
0.343894 + 0.939008i \(0.388254\pi\)
\(68\) −89725.4 −2.35311
\(69\) 4212.28 0.106511
\(70\) 0 0
\(71\) 48082.8 1.13199 0.565997 0.824407i \(-0.308491\pi\)
0.565997 + 0.824407i \(0.308491\pi\)
\(72\) −31153.7 −0.708237
\(73\) −58801.2 −1.29145 −0.645727 0.763568i \(-0.723446\pi\)
−0.645727 + 0.763568i \(0.723446\pi\)
\(74\) −33272.9 −0.706336
\(75\) 0 0
\(76\) 30480.2 0.605318
\(77\) 73610.8 1.41486
\(78\) 5788.22 0.107723
\(79\) 92704.7 1.67122 0.835611 0.549322i \(-0.185114\pi\)
0.835611 + 0.549322i \(0.185114\pi\)
\(80\) 0 0
\(81\) 57410.1 0.972246
\(82\) 17490.3 0.287251
\(83\) 1849.64 0.0294708 0.0147354 0.999891i \(-0.495309\pi\)
0.0147354 + 0.999891i \(0.495309\pi\)
\(84\) −8729.01 −0.134979
\(85\) 0 0
\(86\) −16392.3 −0.238997
\(87\) 2186.80 0.0309750
\(88\) 76359.5 1.05113
\(89\) −70380.3 −0.941838 −0.470919 0.882176i \(-0.656078\pi\)
−0.470919 + 0.882176i \(0.656078\pi\)
\(90\) 0 0
\(91\) −54236.8 −0.686579
\(92\) −130705. −1.60999
\(93\) −6637.23 −0.0795756
\(94\) −19546.9 −0.228170
\(95\) 0 0
\(96\) 10796.2 0.119562
\(97\) 88842.1 0.958714 0.479357 0.877620i \(-0.340870\pi\)
0.479357 + 0.877620i \(0.340870\pi\)
\(98\) −11038.6 −0.116104
\(99\) −142059. −1.45673
\(100\) 0 0
\(101\) 179221. 1.74818 0.874090 0.485763i \(-0.161458\pi\)
0.874090 + 0.485763i \(0.161458\pi\)
\(102\) 25635.6 0.243973
\(103\) −123443. −1.14650 −0.573248 0.819382i \(-0.694317\pi\)
−0.573248 + 0.819382i \(0.694317\pi\)
\(104\) −56262.1 −0.510074
\(105\) 0 0
\(106\) −221496. −1.91471
\(107\) −98991.7 −0.835871 −0.417936 0.908477i \(-0.637246\pi\)
−0.417936 + 0.908477i \(0.637246\pi\)
\(108\) 33849.3 0.279249
\(109\) 46356.0 0.373715 0.186857 0.982387i \(-0.440170\pi\)
0.186857 + 0.982387i \(0.440170\pi\)
\(110\) 0 0
\(111\) 5635.97 0.0434171
\(112\) −42894.2 −0.323113
\(113\) −185076. −1.36350 −0.681750 0.731586i \(-0.738781\pi\)
−0.681750 + 0.731586i \(0.738781\pi\)
\(114\) −8708.54 −0.0627600
\(115\) 0 0
\(116\) −67855.3 −0.468208
\(117\) 104670. 0.706896
\(118\) −379054. −2.50608
\(119\) −240211. −1.55498
\(120\) 0 0
\(121\) 187142. 1.16201
\(122\) −186377. −1.13369
\(123\) −2962.61 −0.0176568
\(124\) 205950. 1.20284
\(125\) 0 0
\(126\) −266250. −1.49404
\(127\) 237332. 1.30571 0.652856 0.757482i \(-0.273571\pi\)
0.652856 + 0.757482i \(0.273571\pi\)
\(128\) −237451. −1.28100
\(129\) 2776.62 0.0146907
\(130\) 0 0
\(131\) −283496. −1.44334 −0.721671 0.692236i \(-0.756626\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(132\) −41289.9 −0.206257
\(133\) 81600.9 0.400005
\(134\) 224049. 1.07791
\(135\) 0 0
\(136\) −249181. −1.15523
\(137\) −330992. −1.50666 −0.753331 0.657642i \(-0.771554\pi\)
−0.753331 + 0.657642i \(0.771554\pi\)
\(138\) 37343.9 0.166925
\(139\) 105975. 0.465230 0.232615 0.972569i \(-0.425272\pi\)
0.232615 + 0.972569i \(0.425272\pi\)
\(140\) 0 0
\(141\) 3310.98 0.0140252
\(142\) 426277. 1.77407
\(143\) −256551. −1.04914
\(144\) 82780.0 0.332674
\(145\) 0 0
\(146\) −521300. −2.02398
\(147\) 1869.78 0.00713670
\(148\) −174881. −0.656279
\(149\) −196700. −0.725836 −0.362918 0.931821i \(-0.618220\pi\)
−0.362918 + 0.931821i \(0.618220\pi\)
\(150\) 0 0
\(151\) −412513. −1.47230 −0.736148 0.676820i \(-0.763357\pi\)
−0.736148 + 0.676820i \(0.763357\pi\)
\(152\) 84648.0 0.297172
\(153\) 463573. 1.60099
\(154\) 652594. 2.21739
\(155\) 0 0
\(156\) 30422.7 0.100089
\(157\) −410971. −1.33064 −0.665322 0.746557i \(-0.731706\pi\)
−0.665322 + 0.746557i \(0.731706\pi\)
\(158\) 821871. 2.61915
\(159\) 37518.4 0.117693
\(160\) 0 0
\(161\) −349920. −1.06391
\(162\) 508968. 1.52371
\(163\) 82488.7 0.243179 0.121589 0.992580i \(-0.461201\pi\)
0.121589 + 0.992580i \(0.461201\pi\)
\(164\) 91928.2 0.266894
\(165\) 0 0
\(166\) 16397.9 0.0461868
\(167\) 380336. 1.05530 0.527650 0.849462i \(-0.323073\pi\)
0.527650 + 0.849462i \(0.323073\pi\)
\(168\) −24241.7 −0.0662660
\(169\) −182265. −0.490892
\(170\) 0 0
\(171\) −157478. −0.411842
\(172\) −86157.1 −0.222060
\(173\) −91482.2 −0.232392 −0.116196 0.993226i \(-0.537070\pi\)
−0.116196 + 0.993226i \(0.537070\pi\)
\(174\) 19387.0 0.0485443
\(175\) 0 0
\(176\) −202898. −0.493738
\(177\) 64206.4 0.154044
\(178\) −623955. −1.47606
\(179\) −607572. −1.41731 −0.708656 0.705554i \(-0.750698\pi\)
−0.708656 + 0.705554i \(0.750698\pi\)
\(180\) 0 0
\(181\) 351519. 0.797540 0.398770 0.917051i \(-0.369437\pi\)
0.398770 + 0.917051i \(0.369437\pi\)
\(182\) −480835. −1.07601
\(183\) 31569.7 0.0696855
\(184\) −362987. −0.790398
\(185\) 0 0
\(186\) −58842.2 −0.124712
\(187\) −1.13624e6 −2.37611
\(188\) −102738. −0.212000
\(189\) 90620.7 0.184532
\(190\) 0 0
\(191\) −123308. −0.244573 −0.122286 0.992495i \(-0.539023\pi\)
−0.122286 + 0.992495i \(0.539023\pi\)
\(192\) 79189.9 0.155030
\(193\) 163481. 0.315917 0.157959 0.987446i \(-0.449509\pi\)
0.157959 + 0.987446i \(0.449509\pi\)
\(194\) 787627. 1.50251
\(195\) 0 0
\(196\) −58018.3 −0.107876
\(197\) −581124. −1.06685 −0.533425 0.845848i \(-0.679095\pi\)
−0.533425 + 0.845848i \(0.679095\pi\)
\(198\) −1.25942e6 −2.28300
\(199\) 351526. 0.629253 0.314627 0.949216i \(-0.398121\pi\)
0.314627 + 0.949216i \(0.398121\pi\)
\(200\) 0 0
\(201\) −37950.9 −0.0662570
\(202\) 1.58888e6 2.73976
\(203\) −181660. −0.309400
\(204\) 134740. 0.226683
\(205\) 0 0
\(206\) −1.09438e6 −1.79680
\(207\) 675297. 1.09539
\(208\) 149497. 0.239592
\(209\) 385988. 0.611235
\(210\) 0 0
\(211\) 327480. 0.506383 0.253192 0.967416i \(-0.418520\pi\)
0.253192 + 0.967416i \(0.418520\pi\)
\(212\) −1.16418e6 −1.77901
\(213\) −72205.4 −0.109049
\(214\) −877608. −1.30998
\(215\) 0 0
\(216\) 94004.6 0.137093
\(217\) 551364. 0.794857
\(218\) 410968. 0.585689
\(219\) 88301.0 0.124410
\(220\) 0 0
\(221\) 837191. 1.15304
\(222\) 49965.5 0.0680437
\(223\) −619602. −0.834355 −0.417177 0.908825i \(-0.636981\pi\)
−0.417177 + 0.908825i \(0.636981\pi\)
\(224\) −896853. −1.19427
\(225\) 0 0
\(226\) −1.64079e6 −2.13689
\(227\) 757446. 0.975635 0.487817 0.872946i \(-0.337793\pi\)
0.487817 + 0.872946i \(0.337793\pi\)
\(228\) −45771.8 −0.0583123
\(229\) 1.21739e6 1.53405 0.767025 0.641617i \(-0.221736\pi\)
0.767025 + 0.641617i \(0.221736\pi\)
\(230\) 0 0
\(231\) −110540. −0.136299
\(232\) −188444. −0.229860
\(233\) −379715. −0.458213 −0.229107 0.973401i \(-0.573580\pi\)
−0.229107 + 0.973401i \(0.573580\pi\)
\(234\) 927945. 1.10785
\(235\) 0 0
\(236\) −1.99229e6 −2.32848
\(237\) −139214. −0.160994
\(238\) −2.12958e6 −2.43698
\(239\) 281756. 0.319064 0.159532 0.987193i \(-0.449001\pi\)
0.159532 + 0.987193i \(0.449001\pi\)
\(240\) 0 0
\(241\) −1.12524e6 −1.24796 −0.623981 0.781439i \(-0.714486\pi\)
−0.623981 + 0.781439i \(0.714486\pi\)
\(242\) 1.65911e6 1.82111
\(243\) −262736. −0.285432
\(244\) −979590. −1.05334
\(245\) 0 0
\(246\) −26264.9 −0.0276719
\(247\) −284398. −0.296609
\(248\) 571953. 0.590515
\(249\) −2777.58 −0.00283902
\(250\) 0 0
\(251\) −675567. −0.676837 −0.338419 0.940996i \(-0.609892\pi\)
−0.338419 + 0.940996i \(0.609892\pi\)
\(252\) −1.39940e6 −1.38816
\(253\) −1.65519e6 −1.62572
\(254\) 2.10406e6 2.04632
\(255\) 0 0
\(256\) −417633. −0.398286
\(257\) −1.85623e6 −1.75306 −0.876532 0.481343i \(-0.840149\pi\)
−0.876532 + 0.481343i \(0.840149\pi\)
\(258\) 24616.1 0.0230234
\(259\) −468188. −0.433681
\(260\) 0 0
\(261\) 350580. 0.318556
\(262\) −2.51333e6 −2.26202
\(263\) 1.54160e6 1.37430 0.687149 0.726516i \(-0.258862\pi\)
0.687149 + 0.726516i \(0.258862\pi\)
\(264\) −114668. −0.101259
\(265\) 0 0
\(266\) 723430. 0.626892
\(267\) 105689. 0.0907304
\(268\) 1.17759e6 1.00152
\(269\) 1.16775e6 0.983945 0.491973 0.870611i \(-0.336276\pi\)
0.491973 + 0.870611i \(0.336276\pi\)
\(270\) 0 0
\(271\) −1.20256e6 −0.994684 −0.497342 0.867555i \(-0.665691\pi\)
−0.497342 + 0.867555i \(0.665691\pi\)
\(272\) 662109. 0.542634
\(273\) 81446.8 0.0661405
\(274\) −2.93440e6 −2.36125
\(275\) 0 0
\(276\) 196278. 0.155095
\(277\) 504463. 0.395030 0.197515 0.980300i \(-0.436713\pi\)
0.197515 + 0.980300i \(0.436713\pi\)
\(278\) 939521. 0.729112
\(279\) −1.06406e6 −0.818378
\(280\) 0 0
\(281\) 1.52712e6 1.15374 0.576870 0.816836i \(-0.304274\pi\)
0.576870 + 0.816836i \(0.304274\pi\)
\(282\) 29353.4 0.0219804
\(283\) −1.81916e6 −1.35022 −0.675110 0.737717i \(-0.735904\pi\)
−0.675110 + 0.737717i \(0.735904\pi\)
\(284\) 2.24049e6 1.64834
\(285\) 0 0
\(286\) −2.27444e6 −1.64422
\(287\) 246108. 0.176369
\(288\) 1.73080e6 1.22961
\(289\) 2.28799e6 1.61143
\(290\) 0 0
\(291\) −133413. −0.0923562
\(292\) −2.73993e6 −1.88054
\(293\) 2.35975e6 1.60582 0.802911 0.596099i \(-0.203283\pi\)
0.802911 + 0.596099i \(0.203283\pi\)
\(294\) 16576.5 0.0111847
\(295\) 0 0
\(296\) −485671. −0.322190
\(297\) 428654. 0.281978
\(298\) −1.74384e6 −1.13754
\(299\) 1.21955e6 0.788901
\(300\) 0 0
\(301\) −230658. −0.146741
\(302\) −3.65712e6 −2.30740
\(303\) −269135. −0.168408
\(304\) −224922. −0.139588
\(305\) 0 0
\(306\) 4.10979e6 2.50909
\(307\) 2.59790e6 1.57317 0.786587 0.617480i \(-0.211846\pi\)
0.786587 + 0.617480i \(0.211846\pi\)
\(308\) 3.43001e6 2.06024
\(309\) 185373. 0.110446
\(310\) 0 0
\(311\) −2.21471e6 −1.29842 −0.649212 0.760607i \(-0.724901\pi\)
−0.649212 + 0.760607i \(0.724901\pi\)
\(312\) 84488.2 0.0491371
\(313\) 2.43630e6 1.40563 0.702813 0.711374i \(-0.251927\pi\)
0.702813 + 0.711374i \(0.251927\pi\)
\(314\) −3.64345e6 −2.08540
\(315\) 0 0
\(316\) 4.31972e6 2.43354
\(317\) 2.59108e6 1.44821 0.724106 0.689689i \(-0.242253\pi\)
0.724106 + 0.689689i \(0.242253\pi\)
\(318\) 332619. 0.184450
\(319\) −859290. −0.472784
\(320\) 0 0
\(321\) 148655. 0.0805223
\(322\) −3.10220e6 −1.66737
\(323\) −1.25958e6 −0.671767
\(324\) 2.67512e6 1.41573
\(325\) 0 0
\(326\) 731301. 0.381112
\(327\) −69612.3 −0.0360012
\(328\) 255298. 0.131028
\(329\) −275047. −0.140093
\(330\) 0 0
\(331\) −2.49362e6 −1.25101 −0.625503 0.780221i \(-0.715106\pi\)
−0.625503 + 0.780221i \(0.715106\pi\)
\(332\) 86186.7 0.0429136
\(333\) 903537. 0.446514
\(334\) 3.37186e6 1.65388
\(335\) 0 0
\(336\) 64413.8 0.0311265
\(337\) 159199. 0.0763600 0.0381800 0.999271i \(-0.487844\pi\)
0.0381800 + 0.999271i \(0.487844\pi\)
\(338\) −1.61586e6 −0.769331
\(339\) 277927. 0.131350
\(340\) 0 0
\(341\) 2.60806e6 1.21460
\(342\) −1.39612e6 −0.645442
\(343\) −2.25195e6 −1.03353
\(344\) −239271. −0.109017
\(345\) 0 0
\(346\) −811033. −0.364207
\(347\) −4.35264e6 −1.94057 −0.970285 0.241966i \(-0.922208\pi\)
−0.970285 + 0.241966i \(0.922208\pi\)
\(348\) 101897. 0.0451040
\(349\) −502730. −0.220938 −0.110469 0.993880i \(-0.535235\pi\)
−0.110469 + 0.993880i \(0.535235\pi\)
\(350\) 0 0
\(351\) −315834. −0.136833
\(352\) −4.24229e6 −1.82492
\(353\) 990932. 0.423260 0.211630 0.977350i \(-0.432123\pi\)
0.211630 + 0.977350i \(0.432123\pi\)
\(354\) 569220. 0.241419
\(355\) 0 0
\(356\) −3.27948e6 −1.37145
\(357\) 360721. 0.149796
\(358\) −5.38641e6 −2.22122
\(359\) −1.78805e6 −0.732223 −0.366112 0.930571i \(-0.619311\pi\)
−0.366112 + 0.930571i \(0.619311\pi\)
\(360\) 0 0
\(361\) −2.04821e6 −0.827194
\(362\) 3.11638e6 1.24991
\(363\) −281029. −0.111940
\(364\) −2.52725e6 −0.999758
\(365\) 0 0
\(366\) 279880. 0.109212
\(367\) 68021.3 0.0263621 0.0131810 0.999913i \(-0.495804\pi\)
0.0131810 + 0.999913i \(0.495804\pi\)
\(368\) 964507. 0.371267
\(369\) −474954. −0.181588
\(370\) 0 0
\(371\) −3.11671e6 −1.17560
\(372\) −309272. −0.115873
\(373\) 949477. 0.353356 0.176678 0.984269i \(-0.443465\pi\)
0.176678 + 0.984269i \(0.443465\pi\)
\(374\) −1.00733e7 −3.72387
\(375\) 0 0
\(376\) −285318. −0.104078
\(377\) 633130. 0.229424
\(378\) 803395. 0.289201
\(379\) 2.53069e6 0.904982 0.452491 0.891769i \(-0.350535\pi\)
0.452491 + 0.891769i \(0.350535\pi\)
\(380\) 0 0
\(381\) −356399. −0.125784
\(382\) −1.09318e6 −0.383297
\(383\) −500631. −0.174390 −0.0871948 0.996191i \(-0.527790\pi\)
−0.0871948 + 0.996191i \(0.527790\pi\)
\(384\) 356578. 0.123403
\(385\) 0 0
\(386\) 1.44933e6 0.495108
\(387\) 445137. 0.151083
\(388\) 4.13974e6 1.39603
\(389\) −4.08546e6 −1.36889 −0.684443 0.729066i \(-0.739955\pi\)
−0.684443 + 0.729066i \(0.739955\pi\)
\(390\) 0 0
\(391\) 5.40130e6 1.78672
\(392\) −161125. −0.0529601
\(393\) 425723. 0.139042
\(394\) −5.15194e6 −1.67198
\(395\) 0 0
\(396\) −6.61944e6 −2.12121
\(397\) −953651. −0.303678 −0.151839 0.988405i \(-0.548520\pi\)
−0.151839 + 0.988405i \(0.548520\pi\)
\(398\) 3.11645e6 0.986171
\(399\) −122539. −0.0385338
\(400\) 0 0
\(401\) 4.81115e6 1.49413 0.747064 0.664752i \(-0.231463\pi\)
0.747064 + 0.664752i \(0.231463\pi\)
\(402\) −336452. −0.103838
\(403\) −1.92163e6 −0.589397
\(404\) 8.35110e6 2.54560
\(405\) 0 0
\(406\) −1.61051e6 −0.484894
\(407\) −2.21462e6 −0.662694
\(408\) 374192. 0.111287
\(409\) −1.42551e6 −0.421370 −0.210685 0.977554i \(-0.567569\pi\)
−0.210685 + 0.977554i \(0.567569\pi\)
\(410\) 0 0
\(411\) 497046. 0.145142
\(412\) −5.75201e6 −1.66946
\(413\) −5.33372e6 −1.53870
\(414\) 5.98682e6 1.71670
\(415\) 0 0
\(416\) 3.12575e6 0.885565
\(417\) −159142. −0.0448171
\(418\) 3.42197e6 0.957933
\(419\) 2.91631e6 0.811520 0.405760 0.913980i \(-0.367007\pi\)
0.405760 + 0.913980i \(0.367007\pi\)
\(420\) 0 0
\(421\) 6.91223e6 1.90070 0.950349 0.311186i \(-0.100726\pi\)
0.950349 + 0.311186i \(0.100726\pi\)
\(422\) 2.90327e6 0.793608
\(423\) 530803. 0.144239
\(424\) −3.23309e6 −0.873380
\(425\) 0 0
\(426\) −640135. −0.170902
\(427\) −2.62254e6 −0.696068
\(428\) −4.61268e6 −1.21715
\(429\) 385259. 0.101067
\(430\) 0 0
\(431\) 2.58575e6 0.670493 0.335246 0.942131i \(-0.391180\pi\)
0.335246 + 0.942131i \(0.391180\pi\)
\(432\) −249784. −0.0643954
\(433\) 3.71200e6 0.951455 0.475727 0.879593i \(-0.342185\pi\)
0.475727 + 0.879593i \(0.342185\pi\)
\(434\) 4.88810e6 1.24571
\(435\) 0 0
\(436\) 2.16003e6 0.544182
\(437\) −1.83485e6 −0.459619
\(438\) 782830. 0.194977
\(439\) −415772. −0.102966 −0.0514830 0.998674i \(-0.516395\pi\)
−0.0514830 + 0.998674i \(0.516395\pi\)
\(440\) 0 0
\(441\) 299756. 0.0733959
\(442\) 7.42209e6 1.80705
\(443\) 602736. 0.145921 0.0729605 0.997335i \(-0.476755\pi\)
0.0729605 + 0.997335i \(0.476755\pi\)
\(444\) 262617. 0.0632216
\(445\) 0 0
\(446\) −5.49307e6 −1.30761
\(447\) 295382. 0.0699223
\(448\) −6.57841e6 −1.54855
\(449\) 1.84907e6 0.432849 0.216424 0.976299i \(-0.430560\pi\)
0.216424 + 0.976299i \(0.430560\pi\)
\(450\) 0 0
\(451\) 1.16414e6 0.269503
\(452\) −8.62393e6 −1.98545
\(453\) 619466. 0.141831
\(454\) 6.71512e6 1.52902
\(455\) 0 0
\(456\) −127115. −0.0286276
\(457\) 7.35472e6 1.64731 0.823655 0.567091i \(-0.191931\pi\)
0.823655 + 0.567091i \(0.191931\pi\)
\(458\) 1.07927e7 2.40418
\(459\) −1.39881e6 −0.309903
\(460\) 0 0
\(461\) −3.51032e6 −0.769298 −0.384649 0.923063i \(-0.625678\pi\)
−0.384649 + 0.923063i \(0.625678\pi\)
\(462\) −979993. −0.213608
\(463\) 6.86607e6 1.48852 0.744262 0.667888i \(-0.232801\pi\)
0.744262 + 0.667888i \(0.232801\pi\)
\(464\) 500723. 0.107970
\(465\) 0 0
\(466\) −3.36635e6 −0.718116
\(467\) −5.66490e6 −1.20199 −0.600993 0.799254i \(-0.705228\pi\)
−0.600993 + 0.799254i \(0.705228\pi\)
\(468\) 4.87724e6 1.02934
\(469\) 3.15263e6 0.661821
\(470\) 0 0
\(471\) 617150. 0.128185
\(472\) −5.53289e6 −1.14313
\(473\) −1.09106e6 −0.224230
\(474\) −1.23419e6 −0.252312
\(475\) 0 0
\(476\) −1.11930e7 −2.26427
\(477\) 6.01481e6 1.21039
\(478\) 2.49790e6 0.500041
\(479\) 4.55961e6 0.908006 0.454003 0.891000i \(-0.349996\pi\)
0.454003 + 0.891000i \(0.349996\pi\)
\(480\) 0 0
\(481\) 1.63174e6 0.321580
\(482\) −9.97576e6 −1.95582
\(483\) 525470. 0.102490
\(484\) 8.72019e6 1.69205
\(485\) 0 0
\(486\) −2.32928e6 −0.447332
\(487\) 9.17550e6 1.75310 0.876552 0.481308i \(-0.159838\pi\)
0.876552 + 0.481308i \(0.159838\pi\)
\(488\) −2.72047e6 −0.517123
\(489\) −123872. −0.0234262
\(490\) 0 0
\(491\) 3.41449e6 0.639179 0.319589 0.947556i \(-0.396455\pi\)
0.319589 + 0.947556i \(0.396455\pi\)
\(492\) −138048. −0.0257108
\(493\) 2.80408e6 0.519605
\(494\) −2.52132e6 −0.464848
\(495\) 0 0
\(496\) −1.51976e6 −0.277377
\(497\) 5.99820e6 1.08926
\(498\) −24624.5 −0.00444933
\(499\) −1.99364e6 −0.358423 −0.179211 0.983811i \(-0.557355\pi\)
−0.179211 + 0.983811i \(0.557355\pi\)
\(500\) 0 0
\(501\) −571146. −0.101661
\(502\) −5.98922e6 −1.06074
\(503\) −9.15685e6 −1.61371 −0.806856 0.590748i \(-0.798833\pi\)
−0.806856 + 0.590748i \(0.798833\pi\)
\(504\) −3.88634e6 −0.681498
\(505\) 0 0
\(506\) −1.46740e7 −2.54785
\(507\) 273705. 0.0472893
\(508\) 1.10589e7 1.90130
\(509\) 6.56697e6 1.12349 0.561746 0.827309i \(-0.310130\pi\)
0.561746 + 0.827309i \(0.310130\pi\)
\(510\) 0 0
\(511\) −7.33529e6 −1.24270
\(512\) 3.89593e6 0.656805
\(513\) 475182. 0.0797199
\(514\) −1.64563e7 −2.74742
\(515\) 0 0
\(516\) 129381. 0.0213918
\(517\) −1.30103e6 −0.214072
\(518\) −4.15070e6 −0.679669
\(519\) 137378. 0.0223871
\(520\) 0 0
\(521\) 6.45805e6 1.04234 0.521168 0.853454i \(-0.325497\pi\)
0.521168 + 0.853454i \(0.325497\pi\)
\(522\) 3.10805e6 0.499243
\(523\) −184405. −0.0294794 −0.0147397 0.999891i \(-0.504692\pi\)
−0.0147397 + 0.999891i \(0.504692\pi\)
\(524\) −1.32100e7 −2.10171
\(525\) 0 0
\(526\) 1.36670e7 2.15381
\(527\) −8.51076e6 −1.33488
\(528\) 304690. 0.0475634
\(529\) 1.43185e6 0.222463
\(530\) 0 0
\(531\) 1.02933e7 1.58424
\(532\) 3.80232e6 0.582465
\(533\) −857745. −0.130780
\(534\) 936986. 0.142194
\(535\) 0 0
\(536\) 3.27035e6 0.491680
\(537\) 912384. 0.136534
\(538\) 1.03527e7 1.54205
\(539\) −734719. −0.108931
\(540\) 0 0
\(541\) −7.10369e6 −1.04350 −0.521748 0.853100i \(-0.674720\pi\)
−0.521748 + 0.853100i \(0.674720\pi\)
\(542\) −1.06613e7 −1.55888
\(543\) −527872. −0.0768297
\(544\) 1.38437e7 2.00565
\(545\) 0 0
\(546\) 722064. 0.103656
\(547\) 9.75210e6 1.39357 0.696787 0.717279i \(-0.254612\pi\)
0.696787 + 0.717279i \(0.254612\pi\)
\(548\) −1.54231e7 −2.19392
\(549\) 5.06113e6 0.716666
\(550\) 0 0
\(551\) −952562. −0.133664
\(552\) 545093. 0.0761417
\(553\) 1.15647e7 1.60813
\(554\) 4.47230e6 0.619094
\(555\) 0 0
\(556\) 4.93809e6 0.677441
\(557\) 2.28586e6 0.312185 0.156092 0.987742i \(-0.450110\pi\)
0.156092 + 0.987742i \(0.450110\pi\)
\(558\) −9.43336e6 −1.28257
\(559\) 803896. 0.108810
\(560\) 0 0
\(561\) 1.70628e6 0.228899
\(562\) 1.35386e7 1.80815
\(563\) −2.31099e6 −0.307275 −0.153638 0.988127i \(-0.549099\pi\)
−0.153638 + 0.988127i \(0.549099\pi\)
\(564\) 154280. 0.0204227
\(565\) 0 0
\(566\) −1.61277e7 −2.11608
\(567\) 7.16176e6 0.935539
\(568\) 6.22218e6 0.809230
\(569\) 1.17226e7 1.51790 0.758949 0.651151i \(-0.225713\pi\)
0.758949 + 0.651151i \(0.225713\pi\)
\(570\) 0 0
\(571\) −5.10057e6 −0.654679 −0.327340 0.944907i \(-0.606152\pi\)
−0.327340 + 0.944907i \(0.606152\pi\)
\(572\) −1.19544e7 −1.52770
\(573\) 185170. 0.0235605
\(574\) 2.18186e6 0.276406
\(575\) 0 0
\(576\) 1.26954e7 1.59438
\(577\) −599429. −0.0749546 −0.0374773 0.999297i \(-0.511932\pi\)
−0.0374773 + 0.999297i \(0.511932\pi\)
\(578\) 2.02841e7 2.52544
\(579\) −245497. −0.0304334
\(580\) 0 0
\(581\) 230737. 0.0283581
\(582\) −1.18277e6 −0.144741
\(583\) −1.47426e7 −1.79640
\(584\) −7.60920e6 −0.923224
\(585\) 0 0
\(586\) 2.09203e7 2.51666
\(587\) −4.32755e6 −0.518379 −0.259189 0.965826i \(-0.583455\pi\)
−0.259189 + 0.965826i \(0.583455\pi\)
\(588\) 87125.5 0.0103921
\(589\) 2.89115e6 0.343386
\(590\) 0 0
\(591\) 872667. 0.102773
\(592\) 1.29050e6 0.151340
\(593\) 1.59099e7 1.85794 0.928968 0.370160i \(-0.120697\pi\)
0.928968 + 0.370160i \(0.120697\pi\)
\(594\) 3.80022e6 0.441918
\(595\) 0 0
\(596\) −9.16555e6 −1.05692
\(597\) −527883. −0.0606181
\(598\) 1.08119e7 1.23637
\(599\) 73202.1 0.00833598 0.00416799 0.999991i \(-0.498673\pi\)
0.00416799 + 0.999991i \(0.498673\pi\)
\(600\) 0 0
\(601\) −3.77328e6 −0.426121 −0.213060 0.977039i \(-0.568343\pi\)
−0.213060 + 0.977039i \(0.568343\pi\)
\(602\) −2.04489e6 −0.229974
\(603\) −6.08414e6 −0.681406
\(604\) −1.92217e7 −2.14387
\(605\) 0 0
\(606\) −2.38601e6 −0.263931
\(607\) −3.39314e6 −0.373792 −0.186896 0.982380i \(-0.559843\pi\)
−0.186896 + 0.982380i \(0.559843\pi\)
\(608\) −4.70277e6 −0.515935
\(609\) 272797. 0.0298055
\(610\) 0 0
\(611\) 958605. 0.103881
\(612\) 2.16009e7 2.33128
\(613\) −5.93491e6 −0.637915 −0.318957 0.947769i \(-0.603333\pi\)
−0.318957 + 0.947769i \(0.603333\pi\)
\(614\) 2.30316e7 2.46549
\(615\) 0 0
\(616\) 9.52564e6 1.01145
\(617\) 1.07871e7 1.14076 0.570379 0.821382i \(-0.306796\pi\)
0.570379 + 0.821382i \(0.306796\pi\)
\(618\) 1.64341e6 0.173092
\(619\) 9.97743e6 1.04663 0.523313 0.852140i \(-0.324696\pi\)
0.523313 + 0.852140i \(0.324696\pi\)
\(620\) 0 0
\(621\) −2.03767e6 −0.212034
\(622\) −1.96345e7 −2.03490
\(623\) −8.77976e6 −0.906280
\(624\) −224497. −0.0230807
\(625\) 0 0
\(626\) 2.15990e7 2.20291
\(627\) −579634. −0.0588823
\(628\) −1.91498e7 −1.93761
\(629\) 7.22687e6 0.728322
\(630\) 0 0
\(631\) −3.42994e6 −0.342936 −0.171468 0.985190i \(-0.554851\pi\)
−0.171468 + 0.985190i \(0.554851\pi\)
\(632\) 1.19965e7 1.19471
\(633\) −491774. −0.0487816
\(634\) 2.29711e7 2.26965
\(635\) 0 0
\(636\) 1.74823e6 0.171378
\(637\) 541345. 0.0528598
\(638\) −7.61801e6 −0.740952
\(639\) −1.15757e7 −1.12149
\(640\) 0 0
\(641\) −1.41725e7 −1.36239 −0.681193 0.732104i \(-0.738538\pi\)
−0.681193 + 0.732104i \(0.738538\pi\)
\(642\) 1.31789e6 0.126195
\(643\) −4.26802e6 −0.407098 −0.203549 0.979065i \(-0.565248\pi\)
−0.203549 + 0.979065i \(0.565248\pi\)
\(644\) −1.63051e7 −1.54920
\(645\) 0 0
\(646\) −1.11667e7 −1.05280
\(647\) −1.26038e7 −1.18370 −0.591849 0.806049i \(-0.701602\pi\)
−0.591849 + 0.806049i \(0.701602\pi\)
\(648\) 7.42919e6 0.695031
\(649\) −2.52295e7 −2.35124
\(650\) 0 0
\(651\) −827977. −0.0765712
\(652\) 3.84369e6 0.354103
\(653\) −1.67724e7 −1.53926 −0.769631 0.638489i \(-0.779560\pi\)
−0.769631 + 0.638489i \(0.779560\pi\)
\(654\) −617146. −0.0564214
\(655\) 0 0
\(656\) −678364. −0.0615465
\(657\) 1.41561e7 1.27947
\(658\) −2.43842e6 −0.219556
\(659\) −1.72113e7 −1.54383 −0.771915 0.635725i \(-0.780701\pi\)
−0.771915 + 0.635725i \(0.780701\pi\)
\(660\) 0 0
\(661\) 5.67723e6 0.505397 0.252699 0.967545i \(-0.418682\pi\)
0.252699 + 0.967545i \(0.418682\pi\)
\(662\) −2.21071e7 −1.96059
\(663\) −1.25720e6 −0.111076
\(664\) 239353. 0.0210678
\(665\) 0 0
\(666\) 8.01028e6 0.699781
\(667\) 4.08476e6 0.355510
\(668\) 1.77223e7 1.53667
\(669\) 930449. 0.0803762
\(670\) 0 0
\(671\) −1.24051e7 −1.06364
\(672\) 1.34679e6 0.115048
\(673\) −4.92989e6 −0.419565 −0.209783 0.977748i \(-0.567276\pi\)
−0.209783 + 0.977748i \(0.567276\pi\)
\(674\) 1.41137e6 0.119672
\(675\) 0 0
\(676\) −8.49292e6 −0.714809
\(677\) 1.25498e7 1.05236 0.526180 0.850373i \(-0.323624\pi\)
0.526180 + 0.850373i \(0.323624\pi\)
\(678\) 2.46395e6 0.205854
\(679\) 1.10828e7 0.922519
\(680\) 0 0
\(681\) −1.13745e6 −0.0939861
\(682\) 2.31217e7 1.90352
\(683\) 7.08503e6 0.581152 0.290576 0.956852i \(-0.406153\pi\)
0.290576 + 0.956852i \(0.406153\pi\)
\(684\) −7.33795e6 −0.599701
\(685\) 0 0
\(686\) −1.99646e7 −1.61976
\(687\) −1.82813e6 −0.147780
\(688\) 635777. 0.0512075
\(689\) 1.08625e7 0.871726
\(690\) 0 0
\(691\) −9.40053e6 −0.748958 −0.374479 0.927235i \(-0.622178\pi\)
−0.374479 + 0.927235i \(0.622178\pi\)
\(692\) −4.26276e6 −0.338396
\(693\) −1.77214e7 −1.40173
\(694\) −3.85882e7 −3.04128
\(695\) 0 0
\(696\) 282984. 0.0221431
\(697\) −3.79888e6 −0.296192
\(698\) −4.45694e6 −0.346256
\(699\) 570213. 0.0441412
\(700\) 0 0
\(701\) 2.14131e7 1.64583 0.822914 0.568167i \(-0.192347\pi\)
0.822914 + 0.568167i \(0.192347\pi\)
\(702\) −2.80002e6 −0.214446
\(703\) −2.45501e6 −0.187355
\(704\) −3.11172e7 −2.36629
\(705\) 0 0
\(706\) 8.78508e6 0.663337
\(707\) 2.23574e7 1.68218
\(708\) 2.99180e6 0.224310
\(709\) 1.70494e7 1.27377 0.636887 0.770957i \(-0.280222\pi\)
0.636887 + 0.770957i \(0.280222\pi\)
\(710\) 0 0
\(711\) −2.23182e7 −1.65571
\(712\) −9.10761e6 −0.673293
\(713\) −1.23978e7 −0.913316
\(714\) 3.19797e6 0.234762
\(715\) 0 0
\(716\) −2.83108e7 −2.06381
\(717\) −423110. −0.0307365
\(718\) −1.58519e7 −1.14755
\(719\) −1.59376e7 −1.14974 −0.574872 0.818243i \(-0.694948\pi\)
−0.574872 + 0.818243i \(0.694948\pi\)
\(720\) 0 0
\(721\) −1.53991e7 −1.10321
\(722\) −1.81584e7 −1.29639
\(723\) 1.68976e6 0.120220
\(724\) 1.63796e7 1.16133
\(725\) 0 0
\(726\) −2.49146e6 −0.175433
\(727\) −8.26202e6 −0.579763 −0.289881 0.957063i \(-0.593616\pi\)
−0.289881 + 0.957063i \(0.593616\pi\)
\(728\) −7.01855e6 −0.490816
\(729\) −1.35561e7 −0.944749
\(730\) 0 0
\(731\) 3.56039e6 0.246436
\(732\) 1.47104e6 0.101472
\(733\) −6.20168e6 −0.426334 −0.213167 0.977016i \(-0.568378\pi\)
−0.213167 + 0.977016i \(0.568378\pi\)
\(734\) 603041. 0.0413149
\(735\) 0 0
\(736\) 2.01664e7 1.37225
\(737\) 1.49126e7 1.01131
\(738\) −4.21069e6 −0.284586
\(739\) −1.19003e7 −0.801578 −0.400789 0.916170i \(-0.631264\pi\)
−0.400789 + 0.916170i \(0.631264\pi\)
\(740\) 0 0
\(741\) 427077. 0.0285734
\(742\) −2.76311e7 −1.84242
\(743\) −7.41722e6 −0.492912 −0.246456 0.969154i \(-0.579266\pi\)
−0.246456 + 0.969154i \(0.579266\pi\)
\(744\) −858895. −0.0568863
\(745\) 0 0
\(746\) 8.41756e6 0.553782
\(747\) −445291. −0.0291973
\(748\) −5.29451e7 −3.45996
\(749\) −1.23489e7 −0.804314
\(750\) 0 0
\(751\) 1.46691e7 0.949084 0.474542 0.880233i \(-0.342614\pi\)
0.474542 + 0.880233i \(0.342614\pi\)
\(752\) 758131. 0.0488877
\(753\) 1.01449e6 0.0652020
\(754\) 5.61299e6 0.359556
\(755\) 0 0
\(756\) 4.22261e6 0.268706
\(757\) −2.41775e6 −0.153346 −0.0766729 0.997056i \(-0.524430\pi\)
−0.0766729 + 0.997056i \(0.524430\pi\)
\(758\) 2.24357e7 1.41830
\(759\) 2.48558e6 0.156611
\(760\) 0 0
\(761\) 2.32422e7 1.45484 0.727422 0.686191i \(-0.240718\pi\)
0.727422 + 0.686191i \(0.240718\pi\)
\(762\) −3.15964e6 −0.197129
\(763\) 5.78279e6 0.359605
\(764\) −5.74574e6 −0.356133
\(765\) 0 0
\(766\) −4.43833e6 −0.273305
\(767\) 1.85893e7 1.14097
\(768\) 627155. 0.0383682
\(769\) −2.55432e7 −1.55761 −0.778806 0.627265i \(-0.784174\pi\)
−0.778806 + 0.627265i \(0.784174\pi\)
\(770\) 0 0
\(771\) 2.78747e6 0.168879
\(772\) 7.61765e6 0.460021
\(773\) −1.72159e7 −1.03629 −0.518146 0.855292i \(-0.673378\pi\)
−0.518146 + 0.855292i \(0.673378\pi\)
\(774\) 3.94635e6 0.236779
\(775\) 0 0
\(776\) 1.14967e7 0.685358
\(777\) 703072. 0.0417780
\(778\) −3.62196e7 −2.14533
\(779\) 1.29050e6 0.0761930
\(780\) 0 0
\(781\) 2.83727e7 1.66446
\(782\) 4.78851e7 2.80016
\(783\) −1.05785e6 −0.0616625
\(784\) 428134. 0.0248765
\(785\) 0 0
\(786\) 3.77424e6 0.217908
\(787\) 1.48812e7 0.856449 0.428225 0.903672i \(-0.359139\pi\)
0.428225 + 0.903672i \(0.359139\pi\)
\(788\) −2.70784e7 −1.55349
\(789\) −2.31500e6 −0.132391
\(790\) 0 0
\(791\) −2.30878e7 −1.31202
\(792\) −1.83832e7 −1.04138
\(793\) 9.14016e6 0.516144
\(794\) −8.45456e6 −0.475927
\(795\) 0 0
\(796\) 1.63799e7 0.916283
\(797\) −5.81135e6 −0.324064 −0.162032 0.986785i \(-0.551805\pi\)
−0.162032 + 0.986785i \(0.551805\pi\)
\(798\) −1.08637e6 −0.0603906
\(799\) 4.24559e6 0.235272
\(800\) 0 0
\(801\) 1.69437e7 0.933098
\(802\) 4.26531e7 2.34161
\(803\) −3.46973e7 −1.89892
\(804\) −1.76838e6 −0.0964796
\(805\) 0 0
\(806\) −1.70362e7 −0.923708
\(807\) −1.75360e6 −0.0947867
\(808\) 2.31922e7 1.24972
\(809\) −2.41530e7 −1.29748 −0.648740 0.761010i \(-0.724704\pi\)
−0.648740 + 0.761010i \(0.724704\pi\)
\(810\) 0 0
\(811\) 2.14467e7 1.14501 0.572505 0.819901i \(-0.305972\pi\)
0.572505 + 0.819901i \(0.305972\pi\)
\(812\) −8.46476e6 −0.450531
\(813\) 1.80588e6 0.0958212
\(814\) −1.96336e7 −1.03858
\(815\) 0 0
\(816\) −994281. −0.0522737
\(817\) −1.20949e6 −0.0633936
\(818\) −1.26379e7 −0.660375
\(819\) 1.30572e7 0.680208
\(820\) 0 0
\(821\) −1.06313e7 −0.550465 −0.275232 0.961378i \(-0.588755\pi\)
−0.275232 + 0.961378i \(0.588755\pi\)
\(822\) 4.40655e6 0.227467
\(823\) 871518. 0.0448515 0.0224257 0.999749i \(-0.492861\pi\)
0.0224257 + 0.999749i \(0.492861\pi\)
\(824\) −1.59742e7 −0.819597
\(825\) 0 0
\(826\) −4.72859e7 −2.41147
\(827\) 1.70354e7 0.866141 0.433071 0.901360i \(-0.357430\pi\)
0.433071 + 0.901360i \(0.357430\pi\)
\(828\) 3.14665e7 1.59504
\(829\) 5.65731e6 0.285906 0.142953 0.989729i \(-0.454340\pi\)
0.142953 + 0.989729i \(0.454340\pi\)
\(830\) 0 0
\(831\) −757546. −0.0380546
\(832\) 2.29273e7 1.14827
\(833\) 2.39758e6 0.119718
\(834\) −1.41087e6 −0.0702378
\(835\) 0 0
\(836\) 1.79857e7 0.890046
\(837\) 3.21073e6 0.158413
\(838\) 2.58545e7 1.27182
\(839\) 3.42452e7 1.67956 0.839779 0.542929i \(-0.182685\pi\)
0.839779 + 0.542929i \(0.182685\pi\)
\(840\) 0 0
\(841\) −1.83905e7 −0.896612
\(842\) 6.12802e7 2.97879
\(843\) −2.29326e6 −0.111144
\(844\) 1.52595e7 0.737366
\(845\) 0 0
\(846\) 4.70582e6 0.226053
\(847\) 2.33455e7 1.11814
\(848\) 8.59078e6 0.410245
\(849\) 2.73181e6 0.130071
\(850\) 0 0
\(851\) 1.05275e7 0.498313
\(852\) −3.36452e6 −0.158791
\(853\) 2.21968e7 1.04452 0.522261 0.852785i \(-0.325089\pi\)
0.522261 + 0.852785i \(0.325089\pi\)
\(854\) −2.32500e7 −1.09088
\(855\) 0 0
\(856\) −1.28101e7 −0.597541
\(857\) −3.15803e7 −1.46881 −0.734403 0.678714i \(-0.762538\pi\)
−0.734403 + 0.678714i \(0.762538\pi\)
\(858\) 3.41551e6 0.158393
\(859\) −1.22037e6 −0.0564297 −0.0282148 0.999602i \(-0.508982\pi\)
−0.0282148 + 0.999602i \(0.508982\pi\)
\(860\) 0 0
\(861\) −369578. −0.0169902
\(862\) 2.29239e7 1.05080
\(863\) 2.43543e7 1.11314 0.556570 0.830801i \(-0.312117\pi\)
0.556570 + 0.830801i \(0.312117\pi\)
\(864\) −5.22260e6 −0.238014
\(865\) 0 0
\(866\) 3.29086e7 1.49113
\(867\) −3.43585e6 −0.155234
\(868\) 2.56917e7 1.15743
\(869\) 5.47031e7 2.45732
\(870\) 0 0
\(871\) −1.09877e7 −0.490749
\(872\) 5.99873e6 0.267158
\(873\) −2.13883e7 −0.949817
\(874\) −1.62668e7 −0.720318
\(875\) 0 0
\(876\) 4.11453e6 0.181159
\(877\) −2.52016e6 −0.110644 −0.0553222 0.998469i \(-0.517619\pi\)
−0.0553222 + 0.998469i \(0.517619\pi\)
\(878\) −3.68601e6 −0.161369
\(879\) −3.54361e6 −0.154694
\(880\) 0 0
\(881\) 1.04311e6 0.0452785 0.0226393 0.999744i \(-0.492793\pi\)
0.0226393 + 0.999744i \(0.492793\pi\)
\(882\) 2.65748e6 0.115027
\(883\) 3.57753e7 1.54412 0.772061 0.635548i \(-0.219226\pi\)
0.772061 + 0.635548i \(0.219226\pi\)
\(884\) 3.90102e7 1.67899
\(885\) 0 0
\(886\) 5.34354e6 0.228689
\(887\) 1.66616e7 0.711061 0.355531 0.934665i \(-0.384300\pi\)
0.355531 + 0.934665i \(0.384300\pi\)
\(888\) 729326. 0.0310377
\(889\) 2.96065e7 1.25642
\(890\) 0 0
\(891\) 3.38765e7 1.42957
\(892\) −2.88713e7 −1.21494
\(893\) −1.44225e6 −0.0605218
\(894\) 2.61870e6 0.109583
\(895\) 0 0
\(896\) −2.96214e7 −1.23264
\(897\) −1.83139e6 −0.0759975
\(898\) 1.63928e7 0.678365
\(899\) −6.43631e6 −0.265606
\(900\) 0 0
\(901\) 4.81090e7 1.97430
\(902\) 1.03206e7 0.422368
\(903\) 346376. 0.0141361
\(904\) −2.39499e7 −0.974727
\(905\) 0 0
\(906\) 5.49186e6 0.222279
\(907\) −3.59470e7 −1.45092 −0.725462 0.688262i \(-0.758374\pi\)
−0.725462 + 0.688262i \(0.758374\pi\)
\(908\) 3.52944e7 1.42066
\(909\) −4.31466e7 −1.73196
\(910\) 0 0
\(911\) 7.56404e6 0.301966 0.150983 0.988536i \(-0.451756\pi\)
0.150983 + 0.988536i \(0.451756\pi\)
\(912\) 337763. 0.0134470
\(913\) 1.09143e6 0.0433331
\(914\) 6.52030e7 2.58168
\(915\) 0 0
\(916\) 5.67260e7 2.23380
\(917\) −3.53654e7 −1.38885
\(918\) −1.24011e7 −0.485683
\(919\) −2.22167e7 −0.867741 −0.433870 0.900975i \(-0.642852\pi\)
−0.433870 + 0.900975i \(0.642852\pi\)
\(920\) 0 0
\(921\) −3.90124e6 −0.151549
\(922\) −3.11207e7 −1.20565
\(923\) −2.09051e7 −0.807698
\(924\) −5.15081e6 −0.198470
\(925\) 0 0
\(926\) 6.08709e7 2.33283
\(927\) 2.97182e7 1.13586
\(928\) 1.04694e7 0.399071
\(929\) 9.18809e6 0.349290 0.174645 0.984631i \(-0.444122\pi\)
0.174645 + 0.984631i \(0.444122\pi\)
\(930\) 0 0
\(931\) −814470. −0.0307965
\(932\) −1.76934e7 −0.667224
\(933\) 3.32581e6 0.125082
\(934\) −5.02220e7 −1.88376
\(935\) 0 0
\(936\) 1.35448e7 0.505340
\(937\) −4.06654e7 −1.51313 −0.756565 0.653919i \(-0.773124\pi\)
−0.756565 + 0.653919i \(0.773124\pi\)
\(938\) 2.79495e7 1.03721
\(939\) −3.65856e6 −0.135409
\(940\) 0 0
\(941\) −2.60105e7 −0.957580 −0.478790 0.877930i \(-0.658924\pi\)
−0.478790 + 0.877930i \(0.658924\pi\)
\(942\) 5.47132e6 0.200893
\(943\) −5.53391e6 −0.202653
\(944\) 1.47017e7 0.536954
\(945\) 0 0
\(946\) −9.67273e6 −0.351416
\(947\) 2.03967e7 0.739067 0.369534 0.929217i \(-0.379517\pi\)
0.369534 + 0.929217i \(0.379517\pi\)
\(948\) −6.48688e6 −0.234431
\(949\) 2.55652e7 0.921475
\(950\) 0 0
\(951\) −3.89099e6 −0.139511
\(952\) −3.10846e7 −1.11161
\(953\) 4.87462e6 0.173864 0.0869318 0.996214i \(-0.472294\pi\)
0.0869318 + 0.996214i \(0.472294\pi\)
\(954\) 5.33241e7 1.89694
\(955\) 0 0
\(956\) 1.31289e7 0.464603
\(957\) 1.29039e6 0.0455449
\(958\) 4.04231e7 1.42304
\(959\) −4.12903e7 −1.44978
\(960\) 0 0
\(961\) −9.09409e6 −0.317651
\(962\) 1.44662e7 0.503984
\(963\) 2.38318e7 0.828114
\(964\) −5.24322e7 −1.81721
\(965\) 0 0
\(966\) 4.65854e6 0.160623
\(967\) 1.26016e7 0.433371 0.216686 0.976241i \(-0.430475\pi\)
0.216686 + 0.976241i \(0.430475\pi\)
\(968\) 2.42173e7 0.830686
\(969\) 1.89149e6 0.0647135
\(970\) 0 0
\(971\) −1.39978e6 −0.0476443 −0.0238221 0.999716i \(-0.507584\pi\)
−0.0238221 + 0.999716i \(0.507584\pi\)
\(972\) −1.22426e7 −0.415630
\(973\) 1.32201e7 0.447665
\(974\) 8.13452e7 2.74748
\(975\) 0 0
\(976\) 7.22867e6 0.242904
\(977\) −1.43010e6 −0.0479325 −0.0239662 0.999713i \(-0.507629\pi\)
−0.0239662 + 0.999713i \(0.507629\pi\)
\(978\) −1.09819e6 −0.0367138
\(979\) −4.15300e7 −1.38486
\(980\) 0 0
\(981\) −1.11600e7 −0.370247
\(982\) 3.02711e7 1.00173
\(983\) −4.26255e7 −1.40697 −0.703487 0.710708i \(-0.748375\pi\)
−0.703487 + 0.710708i \(0.748375\pi\)
\(984\) −383378. −0.0126223
\(985\) 0 0
\(986\) 2.48595e7 0.814329
\(987\) 413035. 0.0134957
\(988\) −1.32520e7 −0.431905
\(989\) 5.18650e6 0.168610
\(990\) 0 0
\(991\) 1.88273e7 0.608980 0.304490 0.952516i \(-0.401514\pi\)
0.304490 + 0.952516i \(0.401514\pi\)
\(992\) −3.17759e7 −1.02522
\(993\) 3.74463e6 0.120514
\(994\) 5.31769e7 1.70709
\(995\) 0 0
\(996\) −129426. −0.00413401
\(997\) −2.10574e7 −0.670915 −0.335458 0.942055i \(-0.608891\pi\)
−0.335458 + 0.942055i \(0.608891\pi\)
\(998\) −1.76746e7 −0.561724
\(999\) −2.72637e6 −0.0864314
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 1075.6.a.b.1.9 10
5.4 even 2 43.6.a.b.1.2 10
15.14 odd 2 387.6.a.e.1.9 10
20.19 odd 2 688.6.a.h.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.2 10 5.4 even 2
387.6.a.e.1.9 10 15.14 odd 2
688.6.a.h.1.6 10 20.19 odd 2
1075.6.a.b.1.9 10 1.1 even 1 trivial