Properties

Label 43.6.a.b.1.2
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: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
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: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(9.86547\) of defining polynomial
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.86547 q^{2} +1.50169 q^{3} +46.5966 q^{4} -37.8251 q^{5} -13.3132 q^{6} -124.747 q^{7} -129.406 q^{8} -240.745 q^{9} +O(q^{10})\) \(q-8.86547 q^{2} +1.50169 q^{3} +46.5966 q^{4} -37.8251 q^{5} -13.3132 q^{6} -124.747 q^{7} -129.406 q^{8} -240.745 q^{9} +335.337 q^{10} +590.079 q^{11} +69.9735 q^{12} +434.774 q^{13} +1105.94 q^{14} -56.8015 q^{15} -343.849 q^{16} +1925.58 q^{17} +2134.32 q^{18} +654.129 q^{19} -1762.52 q^{20} -187.332 q^{21} -5231.33 q^{22} +2805.03 q^{23} -194.327 q^{24} -1694.26 q^{25} -3854.47 q^{26} -726.434 q^{27} -5812.80 q^{28} -1456.23 q^{29} +503.572 q^{30} +4419.85 q^{31} +7189.36 q^{32} +886.115 q^{33} -17071.2 q^{34} +4718.58 q^{35} -11217.9 q^{36} +3753.09 q^{37} -5799.17 q^{38} +652.894 q^{39} +4894.78 q^{40} +1972.85 q^{41} +1660.78 q^{42} +1849.00 q^{43} +27495.7 q^{44} +9106.20 q^{45} -24867.9 q^{46} +2204.84 q^{47} -516.354 q^{48} -1245.12 q^{49} +15020.4 q^{50} +2891.62 q^{51} +20259.0 q^{52} +24984.2 q^{53} +6440.18 q^{54} -22319.8 q^{55} +16143.0 q^{56} +982.298 q^{57} +12910.1 q^{58} -42756.2 q^{59} -2646.76 q^{60} -21022.8 q^{61} -39184.0 q^{62} +30032.3 q^{63} -52733.9 q^{64} -16445.4 q^{65} -7855.83 q^{66} -25272.1 q^{67} +89725.4 q^{68} +4212.28 q^{69} -41832.4 q^{70} +48082.8 q^{71} +31153.7 q^{72} +58801.2 q^{73} -33272.9 q^{74} -2544.25 q^{75} +30480.2 q^{76} -73610.8 q^{77} -5788.22 q^{78} +92704.7 q^{79} +13006.1 q^{80} +57410.1 q^{81} -17490.3 q^{82} -1849.64 q^{83} -8729.01 q^{84} -72835.2 q^{85} -16392.3 q^{86} -2186.80 q^{87} -76359.5 q^{88} -70380.3 q^{89} -80730.8 q^{90} -54236.8 q^{91} +130705. q^{92} +6637.23 q^{93} -19546.9 q^{94} -24742.5 q^{95} +10796.2 q^{96} -88842.1 q^{97} +11038.6 q^{98} -142059. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.86547 −1.56721 −0.783604 0.621260i \(-0.786621\pi\)
−0.783604 + 0.621260i \(0.786621\pi\)
\(3\) 1.50169 0.0963333 0.0481667 0.998839i \(-0.484662\pi\)
0.0481667 + 0.998839i \(0.484662\pi\)
\(4\) 46.5966 1.45614
\(5\) −37.8251 −0.676636 −0.338318 0.941032i \(-0.609858\pi\)
−0.338318 + 0.941032i \(0.609858\pi\)
\(6\) −13.3132 −0.150974
\(7\) −124.747 −0.962246 −0.481123 0.876653i \(-0.659771\pi\)
−0.481123 + 0.876653i \(0.659771\pi\)
\(8\) −129.406 −0.714872
\(9\) −240.745 −0.990720
\(10\) 335.337 1.06043
\(11\) 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 \(-0.383882\pi\)
0.356759 + 0.934196i \(0.383882\pi\)
\(14\) 1105.94 1.50804
\(15\) −56.8015 −0.0651826
\(16\) −343.849 −0.335790
\(17\) 1925.58 1.61599 0.807995 0.589189i \(-0.200553\pi\)
0.807995 + 0.589189i \(0.200553\pi\)
\(18\) 2134.32 1.55266
\(19\) 654.129 0.415700 0.207850 0.978161i \(-0.433353\pi\)
0.207850 + 0.978161i \(0.433353\pi\)
\(20\) −1762.52 −0.985279
\(21\) −187.332 −0.0926963
\(22\) −5231.33 −2.30439
\(23\) 2805.03 1.10565 0.552825 0.833297i \(-0.313550\pi\)
0.552825 + 0.833297i \(0.313550\pi\)
\(24\) −194.327 −0.0688660
\(25\) −1694.26 −0.542163
\(26\) −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 \(0.551398\pi\)
\(30\) 503.572 0.102155
\(31\) 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
\(35\) 4718.58 0.651090
\(36\) −11217.9 −1.44263
\(37\) 3753.09 0.450697 0.225348 0.974278i \(-0.427648\pi\)
0.225348 + 0.974278i \(0.427648\pi\)
\(38\) −5799.17 −0.651488
\(39\) 652.894 0.0687356
\(40\) 4894.78 0.483708
\(41\) 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
\(45\) 9106.20 0.670357
\(46\) −24867.9 −1.73279
\(47\) 2204.84 0.145590 0.0727950 0.997347i \(-0.476808\pi\)
0.0727950 + 0.997347i \(0.476808\pi\)
\(48\) −516.354 −0.0323478
\(49\) −1245.12 −0.0740834
\(50\) 15020.4 0.849683
\(51\) 2891.62 0.155674
\(52\) 20259.0 1.03898
\(53\) 24984.2 1.22173 0.610865 0.791735i \(-0.290822\pi\)
0.610865 + 0.791735i \(0.290822\pi\)
\(54\) 6440.18 0.300548
\(55\) −22319.8 −0.994910
\(56\) 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 \(0.794922\pi\)
\(60\) −2646.76 −0.0949152
\(61\) −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
\(65\) −16445.4 −0.482792
\(66\) −7855.83 −0.221989
\(67\) −25272.1 −0.687788 −0.343894 0.939008i \(-0.611746\pi\)
−0.343894 + 0.939008i \(0.611746\pi\)
\(68\) 89725.4 2.35311
\(69\) 4212.28 0.106511
\(70\) −41832.4 −1.02039
\(71\) 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 \(-0.276554\pi\)
0.645727 + 0.763568i \(0.276554\pi\)
\(74\) −33272.9 −0.706336
\(75\) −2544.25 −0.0522284
\(76\) 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 \(0.185114\pi\)
\(80\) 13006.1 0.227208
\(81\) 57410.1 0.972246
\(82\) −17490.3 −0.287251
\(83\) −1849.64 −0.0294708 −0.0147354 0.999891i \(-0.504691\pi\)
−0.0147354 + 0.999891i \(0.504691\pi\)
\(84\) −8729.01 −0.134979
\(85\) −72835.2 −1.09344
\(86\) −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 \(0.656078\pi\)
\(90\) −80730.8 −1.05059
\(91\) −54236.8 −0.686579
\(92\) 130705. 1.60999
\(93\) 6637.23 0.0795756
\(94\) −19546.9 −0.228170
\(95\) −24742.5 −0.281277
\(96\) 10796.2 0.119562
\(97\) −88842.1 −0.958714 −0.479357 0.877620i \(-0.659130\pi\)
−0.479357 + 0.877620i \(0.659130\pi\)
\(98\) 11038.6 0.116104
\(99\) −142059. −1.45673
\(100\) −78946.8 −0.789468
\(101\) 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 \(-0.305683\pi\)
0.573248 + 0.819382i \(0.305683\pi\)
\(104\) −56262.1 −0.510074
\(105\) 7085.84 0.0627217
\(106\) −221496. −1.91471
\(107\) 98991.7 0.835871 0.417936 0.908477i \(-0.362754\pi\)
0.417936 + 0.908477i \(0.362754\pi\)
\(108\) −33849.3 −0.279249
\(109\) 46356.0 0.373715 0.186857 0.982387i \(-0.440170\pi\)
0.186857 + 0.982387i \(0.440170\pi\)
\(110\) 197876. 1.55923
\(111\) 5635.97 0.0434171
\(112\) 42894.2 0.323113
\(113\) 185076. 1.36350 0.681750 0.731586i \(-0.261219\pi\)
0.681750 + 0.731586i \(0.261219\pi\)
\(114\) −8708.54 −0.0627600
\(115\) −106101. −0.748123
\(116\) −67855.3 −0.468208
\(117\) −104670. −0.706896
\(118\) 379054. 2.50608
\(119\) −240211. −1.55498
\(120\) 7350.43 0.0465972
\(121\) 187142. 1.16201
\(122\) 186377. 1.13369
\(123\) 2962.61 0.0176568
\(124\) 205950. 1.20284
\(125\) 182289. 1.04348
\(126\) −266250. −1.49404
\(127\) −237332. −1.30571 −0.652856 0.757482i \(-0.726429\pi\)
−0.652856 + 0.757482i \(0.726429\pi\)
\(128\) 237451. 1.28100
\(129\) 2776.62 0.0146907
\(130\) 145796. 0.756636
\(131\) −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
\(135\) 27477.5 0.129760
\(136\) −249181. −1.15523
\(137\) 330992. 1.50666 0.753331 0.657642i \(-0.228446\pi\)
0.753331 + 0.657642i \(0.228446\pi\)
\(138\) −37343.9 −0.166925
\(139\) 105975. 0.465230 0.232615 0.972569i \(-0.425272\pi\)
0.232615 + 0.972569i \(0.425272\pi\)
\(140\) 219870. 0.948081
\(141\) 3310.98 0.0140252
\(142\) −426277. −1.77407
\(143\) 256551. 1.04914
\(144\) 82780.0 0.332674
\(145\) 55082.0 0.217565
\(146\) −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 \(0.618220\pi\)
\(150\) 22556.0 0.0818528
\(151\) −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
\(155\) −167181. −0.558931
\(156\) 30422.7 0.100089
\(157\) 410971. 1.33064 0.665322 0.746557i \(-0.268294\pi\)
0.665322 + 0.746557i \(0.268294\pi\)
\(158\) −821871. −2.61915
\(159\) 37518.4 0.117693
\(160\) −271938. −0.839790
\(161\) −349920. −1.06391
\(162\) −508968. −1.52371
\(163\) −82488.7 −0.243179 −0.121589 0.992580i \(-0.538799\pi\)
−0.121589 + 0.992580i \(0.538799\pi\)
\(164\) 91928.2 0.266894
\(165\) −33517.4 −0.0958430
\(166\) 16397.9 0.0461868
\(167\) −380336. −1.05530 −0.527650 0.849462i \(-0.676927\pi\)
−0.527650 + 0.849462i \(0.676927\pi\)
\(168\) 24241.7 0.0662660
\(169\) −182265. −0.490892
\(170\) 645718. 1.71365
\(171\) −157478. −0.411842
\(172\) 86157.1 0.222060
\(173\) 91482.2 0.232392 0.116196 0.993226i \(-0.462930\pi\)
0.116196 + 0.993226i \(0.462930\pi\)
\(174\) 19387.0 0.0485443
\(175\) 211354. 0.521694
\(176\) −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 \(0.750698\pi\)
\(180\) 424318. 0.976136
\(181\) 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
\(185\) −141961. −0.304958
\(186\) −58842.2 −0.124712
\(187\) 1.13624e6 2.37611
\(188\) 102738. 0.212000
\(189\) 90620.7 0.184532
\(190\) 219354. 0.440820
\(191\) −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 \(-0.550491\pi\)
−0.157959 + 0.987446i \(0.550491\pi\)
\(194\) 787627. 1.50251
\(195\) −24695.8 −0.0465090
\(196\) −58018.3 −0.107876
\(197\) 581124. 1.06685 0.533425 0.845848i \(-0.320905\pi\)
0.533425 + 0.845848i \(0.320905\pi\)
\(198\) 1.25942e6 2.28300
\(199\) 351526. 0.629253 0.314627 0.949216i \(-0.398121\pi\)
0.314627 + 0.949216i \(0.398121\pi\)
\(200\) 219247. 0.387577
\(201\) −37950.9 −0.0662570
\(202\) −1.58888e6 −2.73976
\(203\) 181660. 0.309400
\(204\) 134740. 0.226683
\(205\) −74623.4 −0.124020
\(206\) −1.09438e6 −1.79680
\(207\) −675297. −1.09539
\(208\) −149497. −0.239592
\(209\) 385988. 0.611235
\(210\) −62819.3 −0.0982980
\(211\) 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
\(215\) −69938.6 −0.103186
\(216\) 94004.6 0.137093
\(217\) −551364. −0.794857
\(218\) −410968. −0.585689
\(219\) 88301.0 0.124410
\(220\) −1.04003e6 −1.44873
\(221\) 837191. 1.15304
\(222\) −49965.5 −0.0680437
\(223\) 619602. 0.834355 0.417177 0.908825i \(-0.363019\pi\)
0.417177 + 0.908825i \(0.363019\pi\)
\(224\) −896853. −1.19427
\(225\) 407885. 0.537132
\(226\) −1.64079e6 −2.13689
\(227\) −757446. −0.975635 −0.487817 0.872946i \(-0.662207\pi\)
−0.487817 + 0.872946i \(0.662207\pi\)
\(228\) 45771.8 0.0583123
\(229\) 1.21739e6 1.53405 0.767025 0.641617i \(-0.221736\pi\)
0.767025 + 0.641617i \(0.221736\pi\)
\(230\) 940632. 1.17247
\(231\) −110540. −0.136299
\(232\) 188444. 0.229860
\(233\) 379715. 0.458213 0.229107 0.973401i \(-0.426420\pi\)
0.229107 + 0.973401i \(0.426420\pi\)
\(234\) 927945. 1.10785
\(235\) −83398.2 −0.0985115
\(236\) −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 \(0.449001\pi\)
\(240\) 19531.2 0.0218877
\(241\) −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
\(245\) 47096.8 0.0501275
\(246\) −26264.9 −0.0276719
\(247\) 284398. 0.296609
\(248\) −571953. −0.590515
\(249\) −2777.58 −0.00283902
\(250\) −1.61608e6 −1.63536
\(251\) −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
\(255\) −109376. −0.105335
\(256\) −417633. −0.398286
\(257\) 1.85623e6 1.75306 0.876532 0.481343i \(-0.159851\pi\)
0.876532 + 0.481343i \(0.159851\pi\)
\(258\) −24616.1 −0.0230234
\(259\) −468188. −0.433681
\(260\) −766298. −0.703014
\(261\) 350580. 0.318556
\(262\) 2.51333e6 2.26202
\(263\) −1.54160e6 −1.37430 −0.687149 0.726516i \(-0.741138\pi\)
−0.687149 + 0.726516i \(0.741138\pi\)
\(264\) −114668. −0.101259
\(265\) −945029. −0.826667
\(266\) 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 \(0.336276\pi\)
\(270\) −243601. −0.203362
\(271\) −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
\(275\) −999748. −0.797184
\(276\) 196278. 0.155095
\(277\) −504463. −0.395030 −0.197515 0.980300i \(-0.563287\pi\)
−0.197515 + 0.980300i \(0.563287\pi\)
\(278\) −939521. −0.729112
\(279\) −1.06406e6 −0.818378
\(280\) −610610. −0.465446
\(281\) 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 \(-0.264096\pi\)
0.675110 + 0.737717i \(0.264096\pi\)
\(284\) 2.24049e6 1.64834
\(285\) −37155.5 −0.0270964
\(286\) −2.27444e6 −1.64422
\(287\) −246108. −0.176369
\(288\) −1.73080e6 −1.22961
\(289\) 2.28799e6 1.61143
\(290\) −488328. −0.340970
\(291\) −133413. −0.0923562
\(292\) 2.73993e6 1.88054
\(293\) −2.35975e6 −1.60582 −0.802911 0.596099i \(-0.796717\pi\)
−0.802911 + 0.596099i \(0.796717\pi\)
\(294\) 16576.5 0.0111847
\(295\) 1.61726e6 1.08199
\(296\) −485671. −0.322190
\(297\) −428654. −0.281978
\(298\) 1.74384e6 1.13754
\(299\) 1.21955e6 0.788901
\(300\) −118553. −0.0760521
\(301\) −230658. −0.146741
\(302\) 3.65712e6 2.30740
\(303\) 269135. 0.168408
\(304\) −224922. −0.139588
\(305\) 795189. 0.489464
\(306\) 4.10979e6 2.50909
\(307\) −2.59790e6 −1.57317 −0.786587 0.617480i \(-0.788154\pi\)
−0.786587 + 0.617480i \(0.788154\pi\)
\(308\) −3.43001e6 −2.06024
\(309\) 185373. 0.110446
\(310\) 1.48214e6 0.875962
\(311\) −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 \(-0.748073\pi\)
−0.702813 + 0.711374i \(0.748073\pi\)
\(314\) −3.64345e6 −2.08540
\(315\) −1.13597e6 −0.645048
\(316\) 4.31972e6 2.43354
\(317\) −2.59108e6 −1.44821 −0.724106 0.689689i \(-0.757747\pi\)
−0.724106 + 0.689689i \(0.757747\pi\)
\(318\) −332619. −0.184450
\(319\) −859290. −0.472784
\(320\) 1.99467e6 1.08892
\(321\) 148655. 0.0805223
\(322\) 3.10220e6 1.66737
\(323\) 1.25958e6 0.671767
\(324\) 2.67512e6 1.41573
\(325\) −736620. −0.386843
\(326\) 731301. 0.381112
\(327\) 69612.3 0.0360012
\(328\) −255298. −0.131028
\(329\) −275047. −0.140093
\(330\) 297148. 0.150206
\(331\) −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
\(335\) 955921. 0.465383
\(336\) 64413.8 0.0311265
\(337\) −159199. −0.0763600 −0.0381800 0.999271i \(-0.512156\pi\)
−0.0381800 + 0.999271i \(0.512156\pi\)
\(338\) 1.61586e6 0.769331
\(339\) 277927. 0.131350
\(340\) −3.39387e6 −1.59220
\(341\) 2.60806e6 1.21460
\(342\) 1.39612e6 0.645442
\(343\) 2.25195e6 1.03353
\(344\) −239271. −0.109017
\(345\) −159330. −0.0720692
\(346\) −811033. −0.364207
\(347\) 4.35264e6 1.94057 0.970285 0.241966i \(-0.0777923\pi\)
0.970285 + 0.241966i \(0.0777923\pi\)
\(348\) −101897. −0.0451040
\(349\) −502730. −0.220938 −0.110469 0.993880i \(-0.535235\pi\)
−0.110469 + 0.993880i \(0.535235\pi\)
\(350\) −1.87376e6 −0.817604
\(351\) −315834. −0.136833
\(352\) 4.24229e6 1.82492
\(353\) −990932. −0.423260 −0.211630 0.977350i \(-0.567877\pi\)
−0.211630 + 0.977350i \(0.567877\pi\)
\(354\) 569220. 0.241419
\(355\) −1.81874e6 −0.765948
\(356\) −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 \(0.619311\pi\)
\(360\) −1.17839e6 −0.479219
\(361\) −2.04821e6 −0.827194
\(362\) −3.11638e6 −1.24991
\(363\) 281029. 0.111940
\(364\) −2.52725e6 −0.999758
\(365\) −2.22416e6 −0.873844
\(366\) 279880. 0.109212
\(367\) −68021.3 −0.0263621 −0.0131810 0.999913i \(-0.504196\pi\)
−0.0131810 + 0.999913i \(0.504196\pi\)
\(368\) −964507. −0.371267
\(369\) −474954. −0.181588
\(370\) 1.25855e6 0.477933
\(371\) −3.11671e6 −1.17560
\(372\) 309272. 0.115873
\(373\) −949477. −0.353356 −0.176678 0.984269i \(-0.556535\pi\)
−0.176678 + 0.984269i \(0.556535\pi\)
\(374\) −1.00733e7 −3.72387
\(375\) 273741. 0.100522
\(376\) −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 \(0.350535\pi\)
\(380\) −1.15292e6 −0.409580
\(381\) −356399. −0.125784
\(382\) 1.09318e6 0.383297
\(383\) 500631. 0.174390 0.0871948 0.996191i \(-0.472210\pi\)
0.0871948 + 0.996191i \(0.472210\pi\)
\(384\) 356578. 0.123403
\(385\) 2.78434e6 0.957348
\(386\) 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 \(0.739955\pi\)
\(390\) 218940. 0.0728893
\(391\) 5.40130e6 1.78672
\(392\) 161125. 0.0529601
\(393\) −425723. −0.139042
\(394\) −5.15194e6 −1.67198
\(395\) −3.50657e6 −1.13081
\(396\) −6.61944e6 −2.12121
\(397\) 953651. 0.303678 0.151839 0.988405i \(-0.451480\pi\)
0.151839 + 0.988405i \(0.451480\pi\)
\(398\) −3.11645e6 −0.986171
\(399\) −122539. −0.0385338
\(400\) 582570. 0.182053
\(401\) 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
\(405\) −2.17155e6 −0.657857
\(406\) −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 \(0.567569\pi\)
\(410\) 661572. 0.194365
\(411\) 497046. 0.145142
\(412\) 5.75201e6 1.66946
\(413\) 5.33372e6 1.53870
\(414\) 5.98682e6 1.71670
\(415\) 69962.7 0.0199410
\(416\) 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 \(0.367007\pi\)
\(420\) 330176. 0.0913318
\(421\) 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
\(425\) −3.26243e6 −0.876131
\(426\) −640135. −0.170902
\(427\) 2.62254e6 0.696068
\(428\) 4.61268e6 1.21715
\(429\) 385259. 0.101067
\(430\) 620039. 0.161714
\(431\) 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 \(-0.657815\pi\)
−0.475727 + 0.879593i \(0.657815\pi\)
\(434\) 4.88810e6 1.24571
\(435\) 82716.0 0.0209588
\(436\) 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 \(0.516395\pi\)
\(440\) 2.88831e6 0.711233
\(441\) 299756. 0.0733959
\(442\) −7.42209e6 −1.80705
\(443\) −602736. −0.145921 −0.0729605 0.997335i \(-0.523245\pi\)
−0.0729605 + 0.997335i \(0.523245\pi\)
\(444\) 262617. 0.0632216
\(445\) 2.66214e6 0.637282
\(446\) −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 \(0.430560\pi\)
\(450\) −3.61609e6 −0.841798
\(451\) 1.16414e6 0.269503
\(452\) 8.62393e6 1.98545
\(453\) −619466. −0.141831
\(454\) 6.71512e6 1.52902
\(455\) 2.05151e6 0.464564
\(456\) −127115. −0.0286276
\(457\) −7.35472e6 −1.64731 −0.823655 0.567091i \(-0.808069\pi\)
−0.823655 + 0.567091i \(0.808069\pi\)
\(458\) −1.07927e7 −2.40418
\(459\) −1.39881e6 −0.309903
\(460\) −4.94392e6 −1.08937
\(461\) −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 \(-0.767199\pi\)
−0.744262 + 0.667888i \(0.767199\pi\)
\(464\) 500723. 0.107970
\(465\) −251054. −0.0538437
\(466\) −3.36635e6 −0.718116
\(467\) 5.66490e6 1.20199 0.600993 0.799254i \(-0.294772\pi\)
0.600993 + 0.799254i \(0.294772\pi\)
\(468\) −4.87724e6 −1.02934
\(469\) 3.15263e6 0.661821
\(470\) 739364. 0.154388
\(471\) 617150. 0.128185
\(472\) 5.53289e6 1.14313
\(473\) 1.09106e6 0.224230
\(474\) −1.23419e6 −0.252312
\(475\) −1.10827e6 −0.225377
\(476\) −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 \(0.349996\pi\)
\(480\) −408367. −0.0808998
\(481\) 1.63174e6 0.321580
\(482\) 9.97576e6 1.95582
\(483\) −525470. −0.102490
\(484\) 8.72019e6 1.69205
\(485\) 3.36046e6 0.648701
\(486\) −2.32928e6 −0.447332
\(487\) −9.17550e6 −1.75310 −0.876552 0.481308i \(-0.840162\pi\)
−0.876552 + 0.481308i \(0.840162\pi\)
\(488\) 2.72047e6 0.517123
\(489\) −123872. −0.0234262
\(490\) −417535. −0.0785603
\(491\) 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
\(495\) 5.37338e6 0.985677
\(496\) −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 \(0.557355\pi\)
\(500\) 8.49405e6 1.51946
\(501\) −571146. −0.101661
\(502\) 5.98922e6 1.06074
\(503\) 9.15685e6 1.61371 0.806856 0.590748i \(-0.201167\pi\)
0.806856 + 0.590748i \(0.201167\pi\)
\(504\) −3.88634e6 −0.681498
\(505\) −6.77907e6 −1.18288
\(506\) −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 \(0.310130\pi\)
\(510\) 969668. 0.165081
\(511\) −7.33529e6 −1.24270
\(512\) −3.89593e6 −0.656805
\(513\) −475182. −0.0797199
\(514\) −1.64563e7 −2.74742
\(515\) −4.66924e6 −0.775761
\(516\) 129381. 0.0213918
\(517\) 1.30103e6 0.214072
\(518\) 4.15070e6 0.679669
\(519\) 137378. 0.0223871
\(520\) 2.12812e6 0.345134
\(521\) 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 \(-0.495308\pi\)
0.0147397 + 0.999891i \(0.495308\pi\)
\(524\) −1.32100e7 −2.10171
\(525\) 317388. 0.0502566
\(526\) 1.36670e7 2.15381
\(527\) 8.51076e6 1.33488
\(528\) −304690. −0.0475634
\(529\) 1.43185e6 0.222463
\(530\) 8.37813e6 1.29556
\(531\) 1.02933e7 1.58424
\(532\) −3.80232e6 −0.582465
\(533\) 857745. 0.130780
\(534\) 936986. 0.142194
\(535\) −3.74437e6 −0.565581
\(536\) 3.27035e6 0.491680
\(537\) −912384. −0.136534
\(538\) −1.03527e7 −1.54205
\(539\) −734719. −0.108931
\(540\) 1.28036e6 0.188950
\(541\) −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
\(545\) −1.75342e6 −0.252869
\(546\) 722064. 0.103656
\(547\) −9.75210e6 −1.39357 −0.696787 0.717279i \(-0.745388\pi\)
−0.696787 + 0.717279i \(0.745388\pi\)
\(548\) 1.54231e7 2.19392
\(549\) 5.06113e6 0.716666
\(550\) 8.86324e6 1.24935
\(551\) −952562. −0.133664
\(552\) −545093. −0.0761417
\(553\) −1.15647e7 −1.60813
\(554\) 4.47230e6 0.619094
\(555\) −213181. −0.0293776
\(556\) 4.93809e6 0.677441
\(557\) −2.28586e6 −0.312185 −0.156092 0.987742i \(-0.549890\pi\)
−0.156092 + 0.987742i \(0.549890\pi\)
\(558\) 9.43336e6 1.28257
\(559\) 803896. 0.108810
\(560\) −1.62248e6 −0.218630
\(561\) 1.70628e6 0.228899
\(562\) −1.35386e7 −1.80815
\(563\) 2.31099e6 0.307275 0.153638 0.988127i \(-0.450901\pi\)
0.153638 + 0.988127i \(0.450901\pi\)
\(564\) 154280. 0.0204227
\(565\) −7.00054e6 −0.922593
\(566\) −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 \(0.225713\pi\)
\(570\) 329401. 0.0424657
\(571\) −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
\(575\) −4.75245e6 −0.599443
\(576\) 1.26954e7 1.59438
\(577\) 599429. 0.0749546 0.0374773 0.999297i \(-0.488068\pi\)
0.0374773 + 0.999297i \(0.488068\pi\)
\(578\) −2.02841e7 −2.52544
\(579\) −245497. −0.0304334
\(580\) 2.56663e6 0.316806
\(581\) 230737. 0.0283581
\(582\) 1.18277e6 0.144741
\(583\) 1.47426e7 1.79640
\(584\) −7.60920e6 −0.923224
\(585\) 3.95914e6 0.478312
\(586\) 2.09203e7 2.51666
\(587\) 4.32755e6 0.518379 0.259189 0.965826i \(-0.416545\pi\)
0.259189 + 0.965826i \(0.416545\pi\)
\(588\) −87125.5 −0.0103921
\(589\) 2.89115e6 0.343386
\(590\) −1.43377e7 −1.69571
\(591\) 872667. 0.102773
\(592\) −1.29050e6 −0.151340
\(593\) −1.59099e7 −1.85794 −0.928968 0.370160i \(-0.879303\pi\)
−0.928968 + 0.370160i \(0.879303\pi\)
\(594\) 3.80022e6 0.441918
\(595\) 9.08599e6 1.05216
\(596\) −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 \(0.498673\pi\)
\(600\) 329240. 0.0373366
\(601\) −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
\(605\) −7.07868e6 −0.786256
\(606\) −2.38601e6 −0.263931
\(607\) 3.39314e6 0.373792 0.186896 0.982380i \(-0.440157\pi\)
0.186896 + 0.982380i \(0.440157\pi\)
\(608\) 4.70277e6 0.515935
\(609\) 272797. 0.0298055
\(610\) −7.04973e6 −0.767093
\(611\) 958605. 0.103881
\(612\) −2.16009e7 −2.33128
\(613\) 5.93491e6 0.637915 0.318957 0.947769i \(-0.396667\pi\)
0.318957 + 0.947769i \(0.396667\pi\)
\(614\) 2.30316e7 2.46549
\(615\) −112061. −0.0119472
\(616\) 9.52564e6 1.01145
\(617\) −1.07871e7 −1.14076 −0.570379 0.821382i \(-0.693204\pi\)
−0.570379 + 0.821382i \(0.693204\pi\)
\(618\) −1.64341e6 −0.173092
\(619\) 9.97743e6 1.04663 0.523313 0.852140i \(-0.324696\pi\)
0.523313 + 0.852140i \(0.324696\pi\)
\(620\) −7.79008e6 −0.813884
\(621\) −2.03767e6 −0.212034
\(622\) 1.96345e7 2.03490
\(623\) 8.77976e6 0.906280
\(624\) −224497. −0.0230807
\(625\) −1.60054e6 −0.163895
\(626\) 2.15990e7 2.20291
\(627\) 579634. 0.0588823
\(628\) 1.91498e7 1.93761
\(629\) 7.22687e6 0.728322
\(630\) 1.00709e7 1.01092
\(631\) −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
\(635\) 8.97711e6 0.883492
\(636\) 1.74823e6 0.171378
\(637\) −541345. −0.0528598
\(638\) 7.61801e6 0.740952
\(639\) −1.15757e7 −1.12149
\(640\) −8.98163e6 −0.866772
\(641\) −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 \(-0.434752\pi\)
0.203549 + 0.979065i \(0.434752\pi\)
\(644\) −1.63051e7 −1.54920
\(645\) −105026. −0.00994026
\(646\) −1.11667e7 −1.05280
\(647\) 1.26038e7 1.18370 0.591849 0.806049i \(-0.298398\pi\)
0.591849 + 0.806049i \(0.298398\pi\)
\(648\) −7.42919e6 −0.695031
\(649\) −2.52295e7 −2.35124
\(650\) 6.53048e6 0.606264
\(651\) −827977. −0.0765712
\(652\) −3.84369e6 −0.354103
\(653\) 1.67724e7 1.53926 0.769631 0.638489i \(-0.220440\pi\)
0.769631 + 0.638489i \(0.220440\pi\)
\(654\) −617146. −0.0564214
\(655\) 1.07233e7 0.976618
\(656\) −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 \(0.780701\pi\)
\(660\) −1.56180e6 −0.139561
\(661\) 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
\(665\) 3.08656e6 0.270658
\(666\) 8.01028e6 0.699781
\(667\) −4.08476e6 −0.355510
\(668\) −1.77223e7 −1.53667
\(669\) 930449. 0.0803762
\(670\) −8.47469e6 −0.729352
\(671\) −1.24051e7 −1.06364
\(672\) −1.34679e6 −0.115048
\(673\) 4.92989e6 0.419565 0.209783 0.977748i \(-0.432724\pi\)
0.209783 + 0.977748i \(0.432724\pi\)
\(674\) 1.41137e6 0.119672
\(675\) 1.23077e6 0.103972
\(676\) −8.49292e6 −0.714809
\(677\) −1.25498e7 −1.05236 −0.526180 0.850373i \(-0.676376\pi\)
−0.526180 + 0.850373i \(0.676376\pi\)
\(678\) −2.46395e6 −0.205854
\(679\) 1.10828e7 0.922519
\(680\) 9.42528e6 0.781668
\(681\) −1.13745e6 −0.0939861
\(682\) −2.31217e7 −1.90352
\(683\) −7.08503e6 −0.581152 −0.290576 0.956852i \(-0.593847\pi\)
−0.290576 + 0.956852i \(0.593847\pi\)
\(684\) −7.33795e6 −0.599701
\(685\) −1.25198e7 −1.01946
\(686\) −1.99646e7 −1.61976
\(687\) 1.82813e6 0.147780
\(688\) −635777. −0.0512075
\(689\) 1.08625e7 0.871726
\(690\) 1.41254e6 0.112947
\(691\) −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
\(695\) −4.00853e6 −0.314791
\(696\) 282984. 0.0221431
\(697\) 3.79888e6 0.296192
\(698\) 4.45694e6 0.346256
\(699\) 570213. 0.0441412
\(700\) 9.84839e6 0.759662
\(701\) 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
\(705\) −125238. −0.00948995
\(706\) 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 \(0.280222\pi\)
\(710\) 1.61240e7 1.20040
\(711\) −2.23182e7 −1.65571
\(712\) 9.10761e6 0.673293
\(713\) 1.23978e7 0.913316
\(714\) 3.19797e6 0.234762
\(715\) −9.70406e6 −0.709886
\(716\) −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 \(0.694948\pi\)
\(720\) −3.13116e6 −0.225099
\(721\) −1.53991e7 −1.10321
\(722\) 1.81584e7 1.29639
\(723\) −1.68976e6 −0.120220
\(724\) 1.63796e7 1.16133
\(725\) 2.46723e6 0.174327
\(726\) −2.49146e6 −0.175433
\(727\) 8.26202e6 0.579763 0.289881 0.957063i \(-0.406384\pi\)
0.289881 + 0.957063i \(0.406384\pi\)
\(728\) 7.01855e6 0.490816
\(729\) −1.35561e7 −0.944749
\(730\) 1.97182e7 1.36950
\(731\) 3.56039e6 0.246436
\(732\) −1.47104e6 −0.101472
\(733\) 6.20168e6 0.426334 0.213167 0.977016i \(-0.431622\pi\)
0.213167 + 0.977016i \(0.431622\pi\)
\(734\) 603041. 0.0413149
\(735\) 70724.7 0.00482895
\(736\) 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 \(0.631264\pi\)
\(740\) −6.61490e6 −0.444062
\(741\) 427077. 0.0285734
\(742\) 2.76311e7 1.84242
\(743\) 7.41722e6 0.492912 0.246456 0.969154i \(-0.420734\pi\)
0.246456 + 0.969154i \(0.420734\pi\)
\(744\) −858895. −0.0568863
\(745\) 7.44020e6 0.491127
\(746\) 8.41756e6 0.553782
\(747\) 445291. 0.0291973
\(748\) 5.29451e7 3.45996
\(749\) −1.23489e7 −0.804314
\(750\) −2.42685e6 −0.157539
\(751\) 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
\(755\) 1.56033e7 0.996209
\(756\) 4.22261e6 0.268706
\(757\) 2.41775e6 0.153346 0.0766729 0.997056i \(-0.475570\pi\)
0.0766729 + 0.997056i \(0.475570\pi\)
\(758\) −2.24357e7 −1.41830
\(759\) 2.48558e6 0.156611
\(760\) 3.20182e6 0.201077
\(761\) 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
\(765\) 1.75347e7 1.08329
\(766\) −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 \(0.784174\pi\)
\(770\) −2.46844e7 −1.50036
\(771\) 2.78747e6 0.168879
\(772\) −7.61765e6 −0.460021
\(773\) 1.72159e7 1.03629 0.518146 0.855292i \(-0.326622\pi\)
0.518146 + 0.855292i \(0.326622\pi\)
\(774\) 3.94635e6 0.236779
\(775\) −7.48838e6 −0.447851
\(776\) 1.14967e7 0.685358
\(777\) −703072. −0.0417780
\(778\) 3.62196e7 2.14533
\(779\) 1.29050e6 0.0761930
\(780\) −1.15074e6 −0.0677237
\(781\) 2.83727e7 1.66446
\(782\) −4.78851e7 −2.80016
\(783\) 1.05785e6 0.0616625
\(784\) 428134. 0.0248765
\(785\) −1.55450e7 −0.900362
\(786\) 3.77424e6 0.217908
\(787\) −1.48812e7 −0.856449 −0.428225 0.903672i \(-0.640861\pi\)
−0.428225 + 0.903672i \(0.640861\pi\)
\(788\) 2.70784e7 1.55349
\(789\) −2.31500e6 −0.132391
\(790\) 3.10874e7 1.77221
\(791\) −2.30878e7 −1.31202
\(792\) 1.83832e7 1.04138
\(793\) −9.14016e6 −0.516144
\(794\) −8.45456e6 −0.475927
\(795\) −1.41914e6 −0.0796356
\(796\) 1.63799e7 0.916283
\(797\) 5.81135e6 0.324064 0.162032 0.986785i \(-0.448195\pi\)
0.162032 + 0.986785i \(0.448195\pi\)
\(798\) 1.08637e6 0.0603906
\(799\) 4.24559e6 0.235272
\(800\) −1.21807e7 −0.672893
\(801\) 1.69437e7 0.933098
\(802\) −4.26531e7 −2.34161
\(803\) 3.46973e7 1.89892
\(804\) −1.76838e6 −0.0964796
\(805\) 1.32358e7 0.719878
\(806\) −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 \(0.724704\pi\)
\(810\) 1.92518e7 1.03100
\(811\) 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
\(815\) 3.12014e6 0.164543
\(816\) −994281. −0.0522737
\(817\) 1.20949e6 0.0633936
\(818\) 1.26379e7 0.660375
\(819\) 1.30572e7 0.680208
\(820\) −3.47720e6 −0.180590
\(821\) −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 \(-0.507139\pi\)
−0.0224257 + 0.999749i \(0.507139\pi\)
\(824\) −1.59742e7 −0.819597
\(825\) −1.50131e6 −0.0767954
\(826\) −4.72859e7 −2.41147
\(827\) −1.70354e7 −0.866141 −0.433071 0.901360i \(-0.642570\pi\)
−0.433071 + 0.901360i \(0.642570\pi\)
\(828\) −3.14665e7 −1.59504
\(829\) 5.65731e6 0.285906 0.142953 0.989729i \(-0.454340\pi\)
0.142953 + 0.989729i \(0.454340\pi\)
\(830\) −620252. −0.0312517
\(831\) −757546. −0.0380546
\(832\) −2.29273e7 −1.14827
\(833\) −2.39758e6 −0.119718
\(834\) −1.41087e6 −0.0702378
\(835\) 1.43862e7 0.714054
\(836\) 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 \(0.182685\pi\)
\(840\) −916947. −0.0448380
\(841\) −1.83905e7 −0.896612
\(842\) −6.12802e7 −2.97879
\(843\) 2.29326e6 0.111144
\(844\) 1.52595e7 0.737366
\(845\) 6.89419e6 0.332155
\(846\) 4.70582e6 0.226053
\(847\) −2.33455e7 −1.11814
\(848\) −8.59078e6 −0.410245
\(849\) 2.73181e6 0.130071
\(850\) 2.89230e7 1.37308
\(851\) 1.05275e7 0.498313
\(852\) 3.36452e6 0.158791
\(853\) −2.21968e7 −1.04452 −0.522261 0.852785i \(-0.674911\pi\)
−0.522261 + 0.852785i \(0.674911\pi\)
\(854\) −2.32500e7 −1.09088
\(855\) 5.95664e6 0.278667
\(856\) −1.28101e7 −0.597541
\(857\) 3.15803e7 1.46881 0.734403 0.678714i \(-0.237462\pi\)
0.734403 + 0.678714i \(0.237462\pi\)
\(858\) −3.41551e6 −0.158393
\(859\) −1.22037e6 −0.0564297 −0.0282148 0.999602i \(-0.508982\pi\)
−0.0282148 + 0.999602i \(0.508982\pi\)
\(860\) −3.25890e6 −0.150254
\(861\) −369578. −0.0169902
\(862\) −2.29239e7 −1.05080
\(863\) −2.43543e7 −1.11314 −0.556570 0.830801i \(-0.687883\pi\)
−0.556570 + 0.830801i \(0.687883\pi\)
\(864\) −5.22260e6 −0.238014
\(865\) −3.46032e6 −0.157245
\(866\) 3.29086e7 1.49113
\(867\) 3.43585e6 0.155234
\(868\) −2.56917e7 −1.15743
\(869\) 5.47031e7 2.45732
\(870\) −733316. −0.0328468
\(871\) −1.09877e7 −0.490749
\(872\) −5.99873e6 −0.267158
\(873\) 2.13883e7 0.949817
\(874\) −1.62668e7 −0.720318
\(875\) −2.27401e7 −1.00409
\(876\) 4.11453e6 0.181159
\(877\) 2.52016e6 0.110644 0.0553222 0.998469i \(-0.482381\pi\)
0.0553222 + 0.998469i \(0.482381\pi\)
\(878\) 3.68601e6 0.161369
\(879\) −3.54361e6 −0.154694
\(880\) 7.67465e6 0.334081
\(881\) 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 \(-0.780774\pi\)
−0.772061 + 0.635548i \(0.780774\pi\)
\(884\) 3.90102e7 1.67899
\(885\) 2.42862e6 0.104232
\(886\) 5.34354e6 0.228689
\(887\) −1.66616e7 −0.711061 −0.355531 0.934665i \(-0.615700\pi\)
−0.355531 + 0.934665i \(0.615700\pi\)
\(888\) −729326. −0.0310377
\(889\) 2.96065e7 1.25642
\(890\) −2.36012e7 −0.998754
\(891\) 3.38765e7 1.42957
\(892\) 2.88713e7 1.21494
\(893\) 1.44225e6 0.0605218
\(894\) 2.61870e6 0.109583
\(895\) 2.29815e7 0.959004
\(896\) −2.96214e7 −1.23264
\(897\) 1.83139e6 0.0759975
\(898\) −1.63928e7 −0.678365
\(899\) −6.43631e6 −0.265606
\(900\) 1.90060e7 0.782141
\(901\) 4.81090e7 1.97430
\(902\) −1.03206e7 −0.422368
\(903\) −346376. −0.0141361
\(904\) −2.39499e7 −0.974727
\(905\) −1.32963e7 −0.539645
\(906\) 5.49186e6 0.222279
\(907\) 3.59470e7 1.45092 0.725462 0.688262i \(-0.241626\pi\)
0.725462 + 0.688262i \(0.241626\pi\)
\(908\) −3.52944e7 −1.42066
\(909\) −4.31466e7 −1.73196
\(910\) −1.81876e7 −0.728069
\(911\) 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
\(915\) 1.19413e6 0.0471517
\(916\) 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 \(0.642852\pi\)
\(920\) 1.37300e7 0.534812
\(921\) −3.90124e6 −0.151549
\(922\) 3.11207e7 1.20565
\(923\) 2.09051e7 0.807698
\(924\) −5.15081e6 −0.198470
\(925\) −6.35871e6 −0.244351
\(926\) 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 \(0.444122\pi\)
\(930\) 2.22571e6 0.0843843
\(931\) −814470. −0.0307965
\(932\) 1.76934e7 0.667224
\(933\) −3.32581e6 −0.125082
\(934\) −5.02220e7 −1.88376
\(935\) −4.29785e7 −1.60777
\(936\) 1.35448e7 0.505340
\(937\) 4.06654e7 1.51313 0.756565 0.653919i \(-0.226876\pi\)
0.756565 + 0.653919i \(0.226876\pi\)
\(938\) −2.79495e7 −1.03721
\(939\) −3.65856e6 −0.135409
\(940\) −3.88607e6 −0.143447
\(941\) −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
\(945\) −3.42774e6 −0.124861
\(946\) −9.67273e6 −0.351416
\(947\) −2.03967e7 −0.739067 −0.369534 0.929217i \(-0.620483\pi\)
−0.369534 + 0.929217i \(0.620483\pi\)
\(948\) 6.48688e6 0.234431
\(949\) 2.55652e7 0.921475
\(950\) 9.82530e6 0.353213
\(951\) −3.89099e6 −0.139511
\(952\) 3.10846e7 1.11161
\(953\) −4.87462e6 −0.173864 −0.0869318 0.996214i \(-0.527706\pi\)
−0.0869318 + 0.996214i \(0.527706\pi\)
\(954\) 5.33241e7 1.89694
\(955\) 4.66414e6 0.165487
\(956\) 1.31289e7 0.464603
\(957\) −1.29039e6 −0.0455449
\(958\) −4.04231e7 −1.42304
\(959\) −4.12903e7 −1.44978
\(960\) 2.99537e6 0.104899
\(961\) −9.09409e6 −0.317651
\(962\) −1.44662e7 −0.503984
\(963\) −2.38318e7 −0.828114
\(964\) −5.24322e7 −1.81721
\(965\) 6.18368e6 0.213761
\(966\) 4.65854e6 0.160623
\(967\) −1.26016e7 −0.433371 −0.216686 0.976241i \(-0.569525\pi\)
−0.216686 + 0.976241i \(0.569525\pi\)
\(968\) −2.42173e7 −0.830686
\(969\) 1.89149e6 0.0647135
\(970\) −2.97921e7 −1.01665
\(971\) −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
\(975\) −1.10617e6 −0.0372659
\(976\) 7.22867e6 0.242904
\(977\) 1.43010e6 0.0479325 0.0239662 0.999713i \(-0.492371\pi\)
0.0239662 + 0.999713i \(0.492371\pi\)
\(978\) 1.09819e6 0.0367138
\(979\) −4.15300e7 −1.38486
\(980\) 2.19455e6 0.0729928
\(981\) −1.11600e7 −0.370247
\(982\) −3.02711e7 −1.00173
\(983\) 4.26255e7 1.40697 0.703487 0.710708i \(-0.251625\pi\)
0.703487 + 0.710708i \(0.251625\pi\)
\(984\) −383378. −0.0126223
\(985\) −2.19811e7 −0.721869
\(986\) 2.48595e7 0.814329
\(987\) −413035. −0.0134957
\(988\) 1.32520e7 0.431905
\(989\) 5.18650e6 0.168610
\(990\) −4.76376e7 −1.54476
\(991\) 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
\(995\) −1.32965e7 −0.425775
\(996\) −129426. −0.00413401
\(997\) 2.10574e7 0.670915 0.335458 0.942055i \(-0.391109\pi\)
0.335458 + 0.942055i \(0.391109\pi\)
\(998\) 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 43.6.a.b.1.2 10
3.2 odd 2 387.6.a.e.1.9 10
4.3 odd 2 688.6.a.h.1.6 10
5.4 even 2 1075.6.a.b.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.2 10 1.1 even 1 trivial
387.6.a.e.1.9 10 3.2 odd 2
688.6.a.h.1.6 10 4.3 odd 2
1075.6.a.b.1.9 10 5.4 even 2