Properties

Label 43.6.a.b.1.9
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 1.9
Root \(-8.57770\) 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

\(f(q)\) \(=\) \(q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +O(q^{10})\) \(q+9.57770 q^{2} -7.84343 q^{3} +59.7324 q^{4} +28.1028 q^{5} -75.1221 q^{6} +195.604 q^{7} +265.613 q^{8} -181.481 q^{9} +269.160 q^{10} +72.8476 q^{11} -468.507 q^{12} +301.666 q^{13} +1873.44 q^{14} -220.422 q^{15} +632.525 q^{16} -1207.20 q^{17} -1738.17 q^{18} -2350.21 q^{19} +1678.65 q^{20} -1534.21 q^{21} +697.713 q^{22} +516.070 q^{23} -2083.32 q^{24} -2335.23 q^{25} +2889.27 q^{26} +3329.38 q^{27} +11683.9 q^{28} +1531.55 q^{29} -2111.14 q^{30} +1126.13 q^{31} -2441.48 q^{32} -571.375 q^{33} -11562.2 q^{34} +5497.02 q^{35} -10840.3 q^{36} -9339.18 q^{37} -22509.6 q^{38} -2366.10 q^{39} +7464.47 q^{40} +19704.2 q^{41} -14694.2 q^{42} +1849.00 q^{43} +4351.37 q^{44} -5100.11 q^{45} +4942.77 q^{46} -13797.6 q^{47} -4961.16 q^{48} +21453.9 q^{49} -22366.2 q^{50} +9468.56 q^{51} +18019.2 q^{52} -3351.03 q^{53} +31887.9 q^{54} +2047.22 q^{55} +51954.9 q^{56} +18433.7 q^{57} +14668.7 q^{58} +2511.18 q^{59} -13166.4 q^{60} +49249.3 q^{61} +10785.7 q^{62} -35498.3 q^{63} -43624.6 q^{64} +8477.66 q^{65} -5472.46 q^{66} +9116.54 q^{67} -72108.8 q^{68} -4047.76 q^{69} +52648.8 q^{70} +43397.3 q^{71} -48203.6 q^{72} +80067.4 q^{73} -89447.9 q^{74} +18316.2 q^{75} -140384. q^{76} +14249.3 q^{77} -22661.8 q^{78} -65991.7 q^{79} +17775.7 q^{80} +17986.0 q^{81} +188721. q^{82} -76880.9 q^{83} -91641.8 q^{84} -33925.6 q^{85} +17709.2 q^{86} -12012.6 q^{87} +19349.3 q^{88} -75722.6 q^{89} -48847.4 q^{90} +59007.1 q^{91} +30826.1 q^{92} -8832.73 q^{93} -132150. q^{94} -66047.5 q^{95} +19149.6 q^{96} -67921.7 q^{97} +205479. q^{98} -13220.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} + O(q^{10}) \) \( 10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + 294q^{8} + 1356q^{9} - 17q^{10} + 745q^{11} + 4627q^{12} + 1917q^{13} + 1936q^{14} + 1688q^{15} + 5354q^{16} + 4017q^{17} - 2725q^{18} - 2404q^{19} + 1311q^{20} - 228q^{21} - 5836q^{22} + 1733q^{23} - 10711q^{24} + 7120q^{25} - 1484q^{26} - 2324q^{27} - 15028q^{28} + 6996q^{29} - 48420q^{30} - 4899q^{31} - 7554q^{32} - 15734q^{33} - 27033q^{34} + 7084q^{35} + 4433q^{36} + 1466q^{37} + 13905q^{38} - 26542q^{39} - 93211q^{40} + 10297q^{41} - 37642q^{42} + 18490q^{43} - 36140q^{44} + 73822q^{45} + 17991q^{46} + 48592q^{47} + 83607q^{48} + 29458q^{49} + 983q^{50} + 92972q^{51} + 14232q^{52} + 127165q^{53} - 92002q^{54} + 106672q^{55} - 7780q^{56} + 34060q^{57} - 10305q^{58} + 99372q^{59} + 111372q^{60} + 17408q^{61} + 28265q^{62} + 2244q^{63} + 47202q^{64} + 54484q^{65} - 150292q^{66} - 2021q^{67} + 192151q^{68} + 1654q^{69} - 33194q^{70} + 11286q^{71} - 298365q^{72} + 49892q^{73} - 125431q^{74} - 44662q^{75} - 249803q^{76} + 98144q^{77} - 28494q^{78} - 91524q^{79} + 12251q^{80} - 26450q^{81} - 158909q^{82} - 105203q^{83} - 357682q^{84} - 87212q^{85} + 14792q^{86} + 181200q^{87} - 461824q^{88} - 62682q^{89} - 522670q^{90} - 295304q^{91} + 183783q^{92} - 238430q^{93} + 7259q^{94} - 305340q^{95} - 162399q^{96} + 108383q^{97} + 354656q^{98} - 270499q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.57770 1.69311 0.846557 0.532297i \(-0.178671\pi\)
0.846557 + 0.532297i \(0.178671\pi\)
\(3\) −7.84343 −0.503156 −0.251578 0.967837i \(-0.580950\pi\)
−0.251578 + 0.967837i \(0.580950\pi\)
\(4\) 59.7324 1.86664
\(5\) 28.1028 0.502718 0.251359 0.967894i \(-0.419122\pi\)
0.251359 + 0.967894i \(0.419122\pi\)
\(6\) −75.1221 −0.851901
\(7\) 195.604 1.50880 0.754401 0.656413i \(-0.227927\pi\)
0.754401 + 0.656413i \(0.227927\pi\)
\(8\) 265.613 1.46732
\(9\) −181.481 −0.746834
\(10\) 269.160 0.851160
\(11\) 72.8476 0.181524 0.0907619 0.995873i \(-0.471070\pi\)
0.0907619 + 0.995873i \(0.471070\pi\)
\(12\) −468.507 −0.939211
\(13\) 301.666 0.495072 0.247536 0.968879i \(-0.420379\pi\)
0.247536 + 0.968879i \(0.420379\pi\)
\(14\) 1873.44 2.55458
\(15\) −220.422 −0.252946
\(16\) 632.525 0.617700
\(17\) −1207.20 −1.01311 −0.506554 0.862208i \(-0.669081\pi\)
−0.506554 + 0.862208i \(0.669081\pi\)
\(18\) −1738.17 −1.26448
\(19\) −2350.21 −1.49356 −0.746780 0.665071i \(-0.768401\pi\)
−0.746780 + 0.665071i \(0.768401\pi\)
\(20\) 1678.65 0.938393
\(21\) −1534.21 −0.759164
\(22\) 697.713 0.307341
\(23\) 516.070 0.203418 0.101709 0.994814i \(-0.467569\pi\)
0.101709 + 0.994814i \(0.467569\pi\)
\(24\) −2083.32 −0.738290
\(25\) −2335.23 −0.747274
\(26\) 2889.27 0.838213
\(27\) 3329.38 0.878930
\(28\) 11683.9 2.81639
\(29\) 1531.55 0.338171 0.169085 0.985601i \(-0.445919\pi\)
0.169085 + 0.985601i \(0.445919\pi\)
\(30\) −2111.14 −0.428266
\(31\) 1126.13 0.210467 0.105234 0.994448i \(-0.466441\pi\)
0.105234 + 0.994448i \(0.466441\pi\)
\(32\) −2441.48 −0.421481
\(33\) −571.375 −0.0913349
\(34\) −11562.2 −1.71531
\(35\) 5497.02 0.758503
\(36\) −10840.3 −1.39407
\(37\) −9339.18 −1.12151 −0.560756 0.827981i \(-0.689490\pi\)
−0.560756 + 0.827981i \(0.689490\pi\)
\(38\) −22509.6 −2.52877
\(39\) −2366.10 −0.249098
\(40\) 7464.47 0.737647
\(41\) 19704.2 1.83062 0.915310 0.402750i \(-0.131946\pi\)
0.915310 + 0.402750i \(0.131946\pi\)
\(42\) −14694.2 −1.28535
\(43\) 1849.00 0.152499
\(44\) 4351.37 0.338839
\(45\) −5100.11 −0.375447
\(46\) 4942.77 0.344410
\(47\) −13797.6 −0.911088 −0.455544 0.890213i \(-0.650555\pi\)
−0.455544 + 0.890213i \(0.650555\pi\)
\(48\) −4961.16 −0.310800
\(49\) 21453.9 1.27649
\(50\) −22366.2 −1.26522
\(51\) 9468.56 0.509752
\(52\) 18019.2 0.924120
\(53\) −3351.03 −0.163866 −0.0819330 0.996638i \(-0.526109\pi\)
−0.0819330 + 0.996638i \(0.526109\pi\)
\(54\) 31887.9 1.48813
\(55\) 2047.22 0.0912554
\(56\) 51954.9 2.21389
\(57\) 18433.7 0.751494
\(58\) 14668.7 0.572562
\(59\) 2511.18 0.0939177 0.0469588 0.998897i \(-0.485047\pi\)
0.0469588 + 0.998897i \(0.485047\pi\)
\(60\) −13166.4 −0.472158
\(61\) 49249.3 1.69463 0.847316 0.531088i \(-0.178217\pi\)
0.847316 + 0.531088i \(0.178217\pi\)
\(62\) 10785.7 0.356345
\(63\) −35498.3 −1.12682
\(64\) −43624.6 −1.33132
\(65\) 8477.66 0.248882
\(66\) −5472.46 −0.154640
\(67\) 9116.54 0.248109 0.124055 0.992275i \(-0.460410\pi\)
0.124055 + 0.992275i \(0.460410\pi\)
\(68\) −72108.8 −1.89111
\(69\) −4047.76 −0.102351
\(70\) 52648.8 1.28423
\(71\) 43397.3 1.02168 0.510842 0.859675i \(-0.329334\pi\)
0.510842 + 0.859675i \(0.329334\pi\)
\(72\) −48203.6 −1.09584
\(73\) 80067.4 1.75852 0.879262 0.476338i \(-0.158036\pi\)
0.879262 + 0.476338i \(0.158036\pi\)
\(74\) −89447.9 −1.89885
\(75\) 18316.2 0.375996
\(76\) −140384. −2.78794
\(77\) 14249.3 0.273884
\(78\) −22661.8 −0.421752
\(79\) −65991.7 −1.18966 −0.594828 0.803853i \(-0.702780\pi\)
−0.594828 + 0.803853i \(0.702780\pi\)
\(80\) 17775.7 0.310529
\(81\) 17986.0 0.304594
\(82\) 188721. 3.09945
\(83\) −76880.9 −1.22496 −0.612482 0.790484i \(-0.709829\pi\)
−0.612482 + 0.790484i \(0.709829\pi\)
\(84\) −91641.8 −1.41708
\(85\) −33925.6 −0.509308
\(86\) 17709.2 0.258198
\(87\) −12012.6 −0.170153
\(88\) 19349.3 0.266353
\(89\) −75722.6 −1.01333 −0.506665 0.862143i \(-0.669122\pi\)
−0.506665 + 0.862143i \(0.669122\pi\)
\(90\) −48847.4 −0.635675
\(91\) 59007.1 0.746965
\(92\) 30826.1 0.379708
\(93\) −8832.73 −0.105898
\(94\) −132150. −1.54258
\(95\) −66047.5 −0.750840
\(96\) 19149.6 0.212071
\(97\) −67921.7 −0.732958 −0.366479 0.930426i \(-0.619437\pi\)
−0.366479 + 0.930426i \(0.619437\pi\)
\(98\) 205479. 2.16124
\(99\) −13220.4 −0.135568
\(100\) −139489. −1.39489
\(101\) 130824. 1.27610 0.638051 0.769994i \(-0.279741\pi\)
0.638051 + 0.769994i \(0.279741\pi\)
\(102\) 90687.1 0.863068
\(103\) 41945.9 0.389580 0.194790 0.980845i \(-0.437597\pi\)
0.194790 + 0.980845i \(0.437597\pi\)
\(104\) 80126.4 0.726428
\(105\) −43115.5 −0.381645
\(106\) −32095.2 −0.277444
\(107\) −5277.45 −0.0445620 −0.0222810 0.999752i \(-0.507093\pi\)
−0.0222810 + 0.999752i \(0.507093\pi\)
\(108\) 198872. 1.64064
\(109\) −138680. −1.11802 −0.559008 0.829163i \(-0.688818\pi\)
−0.559008 + 0.829163i \(0.688818\pi\)
\(110\) 19607.7 0.154506
\(111\) 73251.2 0.564296
\(112\) 123724. 0.931988
\(113\) 251325. 1.85157 0.925783 0.378055i \(-0.123407\pi\)
0.925783 + 0.378055i \(0.123407\pi\)
\(114\) 176553. 1.27237
\(115\) 14503.0 0.102262
\(116\) 91483.1 0.631242
\(117\) −54746.5 −0.369736
\(118\) 24051.3 0.159013
\(119\) −236132. −1.52858
\(120\) −58547.0 −0.371152
\(121\) −155744. −0.967049
\(122\) 471695. 2.86921
\(123\) −154548. −0.921088
\(124\) 67266.5 0.392866
\(125\) −153448. −0.878387
\(126\) −339992. −1.90784
\(127\) −175695. −0.966606 −0.483303 0.875453i \(-0.660563\pi\)
−0.483303 + 0.875453i \(0.660563\pi\)
\(128\) −339696. −1.83259
\(129\) −14502.5 −0.0767306
\(130\) 81196.5 0.421385
\(131\) 213758. 1.08829 0.544144 0.838992i \(-0.316854\pi\)
0.544144 + 0.838992i \(0.316854\pi\)
\(132\) −34129.6 −0.170489
\(133\) −459711. −2.25349
\(134\) 87315.5 0.420077
\(135\) 93565.0 0.441854
\(136\) −320647. −1.48655
\(137\) 126026. 0.573664 0.286832 0.957981i \(-0.407398\pi\)
0.286832 + 0.957981i \(0.407398\pi\)
\(138\) −38768.2 −0.173292
\(139\) 181105. 0.795049 0.397524 0.917592i \(-0.369869\pi\)
0.397524 + 0.917592i \(0.369869\pi\)
\(140\) 328350. 1.41585
\(141\) 108221. 0.458419
\(142\) 415646. 1.72983
\(143\) 21975.7 0.0898673
\(144\) −114791. −0.461319
\(145\) 43040.8 0.170004
\(146\) 766862. 2.97738
\(147\) −168272. −0.642272
\(148\) −557852. −2.09346
\(149\) 187084. 0.690354 0.345177 0.938538i \(-0.387819\pi\)
0.345177 + 0.938538i \(0.387819\pi\)
\(150\) 175427. 0.636604
\(151\) −396158. −1.41392 −0.706962 0.707252i \(-0.749935\pi\)
−0.706962 + 0.707252i \(0.749935\pi\)
\(152\) −624247. −2.19153
\(153\) 219083. 0.756623
\(154\) 136475. 0.463717
\(155\) 31647.4 0.105806
\(156\) −141333. −0.464977
\(157\) 504286. 1.63278 0.816390 0.577501i \(-0.195972\pi\)
0.816390 + 0.577501i \(0.195972\pi\)
\(158\) −632049. −2.01423
\(159\) 26283.6 0.0824502
\(160\) −68612.4 −0.211886
\(161\) 100945. 0.306917
\(162\) 172265. 0.515713
\(163\) −466039. −1.37389 −0.686946 0.726708i \(-0.741049\pi\)
−0.686946 + 0.726708i \(0.741049\pi\)
\(164\) 1.17698e6 3.41711
\(165\) −16057.2 −0.0459157
\(166\) −736343. −2.07401
\(167\) −142267. −0.394742 −0.197371 0.980329i \(-0.563240\pi\)
−0.197371 + 0.980329i \(0.563240\pi\)
\(168\) −407505. −1.11393
\(169\) −280291. −0.754904
\(170\) −324930. −0.862317
\(171\) 426518. 1.11544
\(172\) 110445. 0.284660
\(173\) 526184. 1.33666 0.668332 0.743863i \(-0.267009\pi\)
0.668332 + 0.743863i \(0.267009\pi\)
\(174\) −115053. −0.288088
\(175\) −456781. −1.12749
\(176\) 46077.9 0.112127
\(177\) −19696.2 −0.0472553
\(178\) −725249. −1.71568
\(179\) 692470. 1.61536 0.807678 0.589624i \(-0.200724\pi\)
0.807678 + 0.589624i \(0.200724\pi\)
\(180\) −304642. −0.700824
\(181\) 286664. 0.650393 0.325197 0.945646i \(-0.394569\pi\)
0.325197 + 0.945646i \(0.394569\pi\)
\(182\) 565152. 1.26470
\(183\) −386284. −0.852665
\(184\) 137075. 0.298479
\(185\) −262457. −0.563805
\(186\) −84597.3 −0.179297
\(187\) −87941.4 −0.183903
\(188\) −824167. −1.70067
\(189\) 651241. 1.32613
\(190\) −632584. −1.27126
\(191\) −692472. −1.37347 −0.686734 0.726909i \(-0.740956\pi\)
−0.686734 + 0.726909i \(0.740956\pi\)
\(192\) 342166. 0.669860
\(193\) 855425. 1.65306 0.826530 0.562893i \(-0.190312\pi\)
0.826530 + 0.562893i \(0.190312\pi\)
\(194\) −650534. −1.24098
\(195\) −66493.9 −0.125226
\(196\) 1.28149e6 2.38274
\(197\) −749649. −1.37623 −0.688117 0.725600i \(-0.741562\pi\)
−0.688117 + 0.725600i \(0.741562\pi\)
\(198\) −126621. −0.229532
\(199\) 990082. 1.77230 0.886152 0.463394i \(-0.153369\pi\)
0.886152 + 0.463394i \(0.153369\pi\)
\(200\) −620268. −1.09649
\(201\) −71504.9 −0.124838
\(202\) 1.25300e6 2.16059
\(203\) 299577. 0.510233
\(204\) 565580. 0.951522
\(205\) 553742. 0.920286
\(206\) 401746. 0.659604
\(207\) −93656.7 −0.151919
\(208\) 190811. 0.305806
\(209\) −171207. −0.271117
\(210\) −412947. −0.646169
\(211\) −274555. −0.424545 −0.212272 0.977211i \(-0.568086\pi\)
−0.212272 + 0.977211i \(0.568086\pi\)
\(212\) −200165. −0.305879
\(213\) −340384. −0.514067
\(214\) −50545.8 −0.0754486
\(215\) 51962.1 0.0766638
\(216\) 884327. 1.28967
\(217\) 220276. 0.317554
\(218\) −1.32824e6 −1.89293
\(219\) −628003. −0.884813
\(220\) 122286. 0.170341
\(221\) −364170. −0.501561
\(222\) 701578. 0.955418
\(223\) −568751. −0.765878 −0.382939 0.923774i \(-0.625088\pi\)
−0.382939 + 0.923774i \(0.625088\pi\)
\(224\) −477563. −0.635932
\(225\) 423799. 0.558090
\(226\) 2.40712e6 3.13492
\(227\) 607473. 0.782461 0.391230 0.920293i \(-0.372050\pi\)
0.391230 + 0.920293i \(0.372050\pi\)
\(228\) 1.10109e6 1.40277
\(229\) 104213. 0.131320 0.0656600 0.997842i \(-0.479085\pi\)
0.0656600 + 0.997842i \(0.479085\pi\)
\(230\) 138906. 0.173141
\(231\) −111763. −0.137806
\(232\) 406799. 0.496204
\(233\) 1.28050e6 1.54521 0.772606 0.634885i \(-0.218953\pi\)
0.772606 + 0.634885i \(0.218953\pi\)
\(234\) −524346. −0.626006
\(235\) −387752. −0.458020
\(236\) 149999. 0.175310
\(237\) 517601. 0.598583
\(238\) −2.26161e6 −2.58806
\(239\) 221000. 0.250264 0.125132 0.992140i \(-0.460065\pi\)
0.125132 + 0.992140i \(0.460065\pi\)
\(240\) −139423. −0.156245
\(241\) −480522. −0.532931 −0.266465 0.963845i \(-0.585856\pi\)
−0.266465 + 0.963845i \(0.585856\pi\)
\(242\) −1.49167e6 −1.63733
\(243\) −950112. −1.03219
\(244\) 2.94178e6 3.16327
\(245\) 602915. 0.641713
\(246\) −1.48022e6 −1.55951
\(247\) −708979. −0.739420
\(248\) 299115. 0.308822
\(249\) 603010. 0.616348
\(250\) −1.46968e6 −1.48721
\(251\) 722732. 0.724091 0.362045 0.932161i \(-0.382079\pi\)
0.362045 + 0.932161i \(0.382079\pi\)
\(252\) −2.12040e6 −2.10337
\(253\) 37594.5 0.0369252
\(254\) −1.68275e6 −1.63657
\(255\) 266093. 0.256261
\(256\) −1.85752e6 −1.77147
\(257\) −1.34492e6 −1.27018 −0.635089 0.772439i \(-0.719037\pi\)
−0.635089 + 0.772439i \(0.719037\pi\)
\(258\) −138901. −0.129914
\(259\) −1.82678e6 −1.69214
\(260\) 506391. 0.464572
\(261\) −277946. −0.252557
\(262\) 2.04731e6 1.84260
\(263\) −18066.1 −0.0161055 −0.00805275 0.999968i \(-0.502563\pi\)
−0.00805275 + 0.999968i \(0.502563\pi\)
\(264\) −151765. −0.134017
\(265\) −94173.4 −0.0823784
\(266\) −4.40297e6 −3.81542
\(267\) 593925. 0.509863
\(268\) 544553. 0.463130
\(269\) −549502. −0.463008 −0.231504 0.972834i \(-0.574365\pi\)
−0.231504 + 0.972834i \(0.574365\pi\)
\(270\) 896138. 0.748110
\(271\) 13732.4 0.0113586 0.00567929 0.999984i \(-0.498192\pi\)
0.00567929 + 0.999984i \(0.498192\pi\)
\(272\) −763582. −0.625797
\(273\) −462818. −0.375840
\(274\) 1.20704e6 0.971278
\(275\) −170116. −0.135648
\(276\) −241782. −0.191052
\(277\) −501657. −0.392833 −0.196416 0.980521i \(-0.562930\pi\)
−0.196416 + 0.980521i \(0.562930\pi\)
\(278\) 1.73457e6 1.34611
\(279\) −204371. −0.157184
\(280\) 1.46008e6 1.11296
\(281\) 605657. 0.457574 0.228787 0.973477i \(-0.426524\pi\)
0.228787 + 0.973477i \(0.426524\pi\)
\(282\) 1.03651e6 0.776157
\(283\) −1.85484e6 −1.37671 −0.688353 0.725376i \(-0.741666\pi\)
−0.688353 + 0.725376i \(0.741666\pi\)
\(284\) 2.59223e6 1.90711
\(285\) 518039. 0.377790
\(286\) 210476. 0.152156
\(287\) 3.85421e6 2.76204
\(288\) 443081. 0.314776
\(289\) 37467.4 0.0263882
\(290\) 412232. 0.287837
\(291\) 532739. 0.368792
\(292\) 4.78262e6 3.28253
\(293\) 950968. 0.647138 0.323569 0.946205i \(-0.395117\pi\)
0.323569 + 0.946205i \(0.395117\pi\)
\(294\) −1.61166e6 −1.08744
\(295\) 70571.1 0.0472141
\(296\) −2.48061e6 −1.64562
\(297\) 242538. 0.159547
\(298\) 1.79184e6 1.16885
\(299\) 155681. 0.100706
\(300\) 1.09407e6 0.701848
\(301\) 361672. 0.230090
\(302\) −3.79428e6 −2.39393
\(303\) −1.02611e6 −0.642079
\(304\) −1.48657e6 −0.922572
\(305\) 1.38404e6 0.851923
\(306\) 2.09831e6 1.28105
\(307\) −736219. −0.445822 −0.222911 0.974839i \(-0.571556\pi\)
−0.222911 + 0.974839i \(0.571556\pi\)
\(308\) 851144. 0.511242
\(309\) −329000. −0.196020
\(310\) 303110. 0.179141
\(311\) −1.02220e6 −0.599286 −0.299643 0.954051i \(-0.596867\pi\)
−0.299643 + 0.954051i \(0.596867\pi\)
\(312\) −628466. −0.365507
\(313\) −60474.7 −0.0348909 −0.0174455 0.999848i \(-0.505553\pi\)
−0.0174455 + 0.999848i \(0.505553\pi\)
\(314\) 4.82990e6 2.76448
\(315\) −997602. −0.566475
\(316\) −3.94184e6 −2.22066
\(317\) 842265. 0.470761 0.235381 0.971903i \(-0.424366\pi\)
0.235381 + 0.971903i \(0.424366\pi\)
\(318\) 251736. 0.139598
\(319\) 111570. 0.0613860
\(320\) −1.22597e6 −0.669277
\(321\) 41393.3 0.0224216
\(322\) 966825. 0.519646
\(323\) 2.83717e6 1.51314
\(324\) 1.07435e6 0.568568
\(325\) −704460. −0.369954
\(326\) −4.46358e6 −2.32616
\(327\) 1.08773e6 0.562536
\(328\) 5.23368e6 2.68610
\(329\) −2.69887e6 −1.37465
\(330\) −153792. −0.0777406
\(331\) −3.50942e6 −1.76062 −0.880308 0.474402i \(-0.842664\pi\)
−0.880308 + 0.474402i \(0.842664\pi\)
\(332\) −4.59228e6 −2.28657
\(333\) 1.69488e6 0.837584
\(334\) −1.36259e6 −0.668344
\(335\) 256200. 0.124729
\(336\) −970423. −0.468935
\(337\) −1.49987e6 −0.719414 −0.359707 0.933065i \(-0.617123\pi\)
−0.359707 + 0.933065i \(0.617123\pi\)
\(338\) −2.68454e6 −1.27814
\(339\) −1.97125e6 −0.931627
\(340\) −2.02646e6 −0.950694
\(341\) 82036.0 0.0382048
\(342\) 4.08506e6 1.88857
\(343\) 908952. 0.417163
\(344\) 491118. 0.223764
\(345\) −113753. −0.0514537
\(346\) 5.03963e6 2.26313
\(347\) 2.16958e6 0.967280 0.483640 0.875267i \(-0.339314\pi\)
0.483640 + 0.875267i \(0.339314\pi\)
\(348\) −717541. −0.317613
\(349\) 393576. 0.172968 0.0864838 0.996253i \(-0.472437\pi\)
0.0864838 + 0.996253i \(0.472437\pi\)
\(350\) −4.37491e6 −1.90897
\(351\) 1.00436e6 0.435133
\(352\) −177856. −0.0765089
\(353\) 272744. 0.116498 0.0582491 0.998302i \(-0.481448\pi\)
0.0582491 + 0.998302i \(0.481448\pi\)
\(354\) −188645. −0.0800086
\(355\) 1.21959e6 0.513619
\(356\) −4.52309e6 −1.89152
\(357\) 1.85209e6 0.769115
\(358\) 6.63227e6 2.73498
\(359\) −3.96827e6 −1.62504 −0.812521 0.582932i \(-0.801906\pi\)
−0.812521 + 0.582932i \(0.801906\pi\)
\(360\) −1.35466e6 −0.550900
\(361\) 3.04739e6 1.23072
\(362\) 2.74558e6 1.10119
\(363\) 1.22157e6 0.486577
\(364\) 3.52464e6 1.39431
\(365\) 2.25012e6 0.884042
\(366\) −3.69971e6 −1.44366
\(367\) −4.90395e6 −1.90056 −0.950278 0.311404i \(-0.899201\pi\)
−0.950278 + 0.311404i \(0.899201\pi\)
\(368\) 326427. 0.125651
\(369\) −3.57592e6 −1.36717
\(370\) −2.51374e6 −0.954587
\(371\) −655475. −0.247242
\(372\) −527600. −0.197673
\(373\) 2.52633e6 0.940196 0.470098 0.882614i \(-0.344219\pi\)
0.470098 + 0.882614i \(0.344219\pi\)
\(374\) −842277. −0.311369
\(375\) 1.20356e6 0.441966
\(376\) −3.66483e6 −1.33686
\(377\) 462016. 0.167419
\(378\) 6.23739e6 2.24529
\(379\) −607631. −0.217291 −0.108646 0.994081i \(-0.534651\pi\)
−0.108646 + 0.994081i \(0.534651\pi\)
\(380\) −3.94518e6 −1.40155
\(381\) 1.37805e6 0.486354
\(382\) −6.63229e6 −2.32544
\(383\) −3.94370e6 −1.37375 −0.686874 0.726777i \(-0.741018\pi\)
−0.686874 + 0.726777i \(0.741018\pi\)
\(384\) 2.66438e6 0.922079
\(385\) 400445. 0.137686
\(386\) 8.19301e6 2.79882
\(387\) −335558. −0.113891
\(388\) −4.05713e6 −1.36817
\(389\) −2.42464e6 −0.812405 −0.406203 0.913783i \(-0.633147\pi\)
−0.406203 + 0.913783i \(0.633147\pi\)
\(390\) −636859. −0.212023
\(391\) −622998. −0.206084
\(392\) 5.69843e6 1.87301
\(393\) −1.67660e6 −0.547579
\(394\) −7.17991e6 −2.33012
\(395\) −1.85455e6 −0.598062
\(396\) −789689. −0.253057
\(397\) −2.94322e6 −0.937232 −0.468616 0.883402i \(-0.655247\pi\)
−0.468616 + 0.883402i \(0.655247\pi\)
\(398\) 9.48271e6 3.00072
\(399\) 3.60571e6 1.13386
\(400\) −1.47709e6 −0.461591
\(401\) −5.82714e6 −1.80965 −0.904824 0.425785i \(-0.859998\pi\)
−0.904824 + 0.425785i \(0.859998\pi\)
\(402\) −684853. −0.211365
\(403\) 339715. 0.104196
\(404\) 7.81446e6 2.38202
\(405\) 505457. 0.153125
\(406\) 2.86926e6 0.863883
\(407\) −680337. −0.203581
\(408\) 2.51497e6 0.747968
\(409\) 1.22650e6 0.362542 0.181271 0.983433i \(-0.441979\pi\)
0.181271 + 0.983433i \(0.441979\pi\)
\(410\) 5.30358e6 1.55815
\(411\) −988473. −0.288642
\(412\) 2.50553e6 0.727205
\(413\) 491196. 0.141703
\(414\) −897016. −0.257217
\(415\) −2.16057e6 −0.615812
\(416\) −736511. −0.208663
\(417\) −1.42049e6 −0.400034
\(418\) −1.63977e6 −0.459032
\(419\) 1.13490e6 0.315809 0.157904 0.987454i \(-0.449526\pi\)
0.157904 + 0.987454i \(0.449526\pi\)
\(420\) −2.57539e6 −0.712394
\(421\) −5.21555e6 −1.43415 −0.717075 0.696996i \(-0.754520\pi\)
−0.717075 + 0.696996i \(0.754520\pi\)
\(422\) −2.62961e6 −0.718803
\(423\) 2.50400e6 0.680431
\(424\) −890078. −0.240444
\(425\) 2.81909e6 0.757070
\(426\) −3.26009e6 −0.870374
\(427\) 9.63336e6 2.55687
\(428\) −315235. −0.0831811
\(429\) −172365. −0.0452173
\(430\) 497677. 0.129801
\(431\) 4.94938e6 1.28339 0.641693 0.766961i \(-0.278232\pi\)
0.641693 + 0.766961i \(0.278232\pi\)
\(432\) 2.10592e6 0.542915
\(433\) −2.02994e6 −0.520311 −0.260156 0.965567i \(-0.583774\pi\)
−0.260156 + 0.965567i \(0.583774\pi\)
\(434\) 2.10973e6 0.537655
\(435\) −337588. −0.0855388
\(436\) −8.28369e6 −2.08693
\(437\) −1.21287e6 −0.303817
\(438\) −6.01482e6 −1.49809
\(439\) −4.05767e6 −1.00488 −0.502442 0.864611i \(-0.667565\pi\)
−0.502442 + 0.864611i \(0.667565\pi\)
\(440\) 543769. 0.133901
\(441\) −3.89347e6 −0.953323
\(442\) −3.48792e6 −0.849201
\(443\) 3.73717e6 0.904761 0.452380 0.891825i \(-0.350575\pi\)
0.452380 + 0.891825i \(0.350575\pi\)
\(444\) 4.37547e6 1.05334
\(445\) −2.12802e6 −0.509419
\(446\) −5.44733e6 −1.29672
\(447\) −1.46738e6 −0.347356
\(448\) −8.53313e6 −2.00869
\(449\) −2.08643e6 −0.488414 −0.244207 0.969723i \(-0.578528\pi\)
−0.244207 + 0.969723i \(0.578528\pi\)
\(450\) 4.05903e6 0.944910
\(451\) 1.43540e6 0.332301
\(452\) 1.50122e7 3.45620
\(453\) 3.10724e6 0.711424
\(454\) 5.81820e6 1.32480
\(455\) 1.65826e6 0.375513
\(456\) 4.89623e6 1.10268
\(457\) 383012. 0.0857871 0.0428936 0.999080i \(-0.486342\pi\)
0.0428936 + 0.999080i \(0.486342\pi\)
\(458\) 998117. 0.222340
\(459\) −4.01922e6 −0.890452
\(460\) 866300. 0.190886
\(461\) −767599. −0.168222 −0.0841109 0.996456i \(-0.526805\pi\)
−0.0841109 + 0.996456i \(0.526805\pi\)
\(462\) −1.07044e6 −0.233322
\(463\) 2.87956e6 0.624272 0.312136 0.950037i \(-0.398955\pi\)
0.312136 + 0.950037i \(0.398955\pi\)
\(464\) 968743. 0.208888
\(465\) −248224. −0.0532368
\(466\) 1.22642e7 2.61622
\(467\) 4.73971e6 1.00568 0.502840 0.864379i \(-0.332288\pi\)
0.502840 + 0.864379i \(0.332288\pi\)
\(468\) −3.27014e6 −0.690164
\(469\) 1.78323e6 0.374348
\(470\) −3.71378e6 −0.775481
\(471\) −3.95533e6 −0.821543
\(472\) 667001. 0.137807
\(473\) 134695. 0.0276821
\(474\) 4.95743e6 1.01347
\(475\) 5.48829e6 1.11610
\(476\) −1.41048e7 −2.85331
\(477\) 608147. 0.122381
\(478\) 2.11668e6 0.423726
\(479\) 5.41230e6 1.07781 0.538906 0.842366i \(-0.318838\pi\)
0.538906 + 0.842366i \(0.318838\pi\)
\(480\) 538156. 0.106612
\(481\) −2.81731e6 −0.555229
\(482\) −4.60230e6 −0.902313
\(483\) −791758. −0.154427
\(484\) −9.30298e6 −1.80513
\(485\) −1.90879e6 −0.368471
\(486\) −9.09989e6 −1.74761
\(487\) 5.16701e6 0.987227 0.493614 0.869681i \(-0.335676\pi\)
0.493614 + 0.869681i \(0.335676\pi\)
\(488\) 1.30813e7 2.48657
\(489\) 3.65534e6 0.691283
\(490\) 5.77454e6 1.08649
\(491\) 1.68112e6 0.314698 0.157349 0.987543i \(-0.449705\pi\)
0.157349 + 0.987543i \(0.449705\pi\)
\(492\) −9.23154e6 −1.71934
\(493\) −1.84888e6 −0.342603
\(494\) −6.79039e6 −1.25192
\(495\) −371531. −0.0681526
\(496\) 712306. 0.130006
\(497\) 8.48868e6 1.54152
\(498\) 5.77545e6 1.04355
\(499\) 3.57956e6 0.643545 0.321772 0.946817i \(-0.395721\pi\)
0.321772 + 0.946817i \(0.395721\pi\)
\(500\) −9.16581e6 −1.63963
\(501\) 1.11586e6 0.198617
\(502\) 6.92211e6 1.22597
\(503\) −1.07972e6 −0.190279 −0.0951397 0.995464i \(-0.530330\pi\)
−0.0951397 + 0.995464i \(0.530330\pi\)
\(504\) −9.42881e6 −1.65341
\(505\) 3.67653e6 0.641520
\(506\) 360069. 0.0625186
\(507\) 2.19844e6 0.379835
\(508\) −1.04947e7 −1.80430
\(509\) 1.11760e6 0.191202 0.0956012 0.995420i \(-0.469523\pi\)
0.0956012 + 0.995420i \(0.469523\pi\)
\(510\) 2.54856e6 0.433880
\(511\) 1.56615e7 2.65327
\(512\) −6.92051e6 −1.16671
\(513\) −7.82475e6 −1.31274
\(514\) −1.28813e7 −2.15056
\(515\) 1.17880e6 0.195849
\(516\) −866270. −0.143228
\(517\) −1.00513e6 −0.165384
\(518\) −1.74964e7 −2.86499
\(519\) −4.12709e6 −0.672551
\(520\) 2.25178e6 0.365188
\(521\) −6.50399e6 −1.04975 −0.524874 0.851180i \(-0.675888\pi\)
−0.524874 + 0.851180i \(0.675888\pi\)
\(522\) −2.66209e6 −0.427608
\(523\) 437675. 0.0699677 0.0349838 0.999388i \(-0.488862\pi\)
0.0349838 + 0.999388i \(0.488862\pi\)
\(524\) 1.27683e7 2.03144
\(525\) 3.58273e6 0.567304
\(526\) −173031. −0.0272685
\(527\) −1.35946e6 −0.213226
\(528\) −361409. −0.0564176
\(529\) −6.17001e6 −0.958621
\(530\) −901965. −0.139476
\(531\) −455730. −0.0701409
\(532\) −2.74596e7 −4.20645
\(533\) 5.94407e6 0.906288
\(534\) 5.68844e6 0.863256
\(535\) −148311. −0.0224021
\(536\) 2.42147e6 0.364055
\(537\) −5.43134e6 −0.812777
\(538\) −5.26297e6 −0.783926
\(539\) 1.56287e6 0.231713
\(540\) 5.58886e6 0.824782
\(541\) 6.56956e6 0.965035 0.482518 0.875886i \(-0.339722\pi\)
0.482518 + 0.875886i \(0.339722\pi\)
\(542\) 131525. 0.0192314
\(543\) −2.24843e6 −0.327249
\(544\) 2.94735e6 0.427006
\(545\) −3.89730e6 −0.562047
\(546\) −4.43273e6 −0.636341
\(547\) −2.84947e6 −0.407189 −0.203595 0.979055i \(-0.565262\pi\)
−0.203595 + 0.979055i \(0.565262\pi\)
\(548\) 7.52781e6 1.07082
\(549\) −8.93780e6 −1.26561
\(550\) −1.62932e6 −0.229668
\(551\) −3.59946e6 −0.505078
\(552\) −1.07514e6 −0.150181
\(553\) −1.29082e7 −1.79496
\(554\) −4.80472e6 −0.665111
\(555\) 2.05856e6 0.283682
\(556\) 1.08178e7 1.48407
\(557\) 1.14478e7 1.56344 0.781722 0.623627i \(-0.214342\pi\)
0.781722 + 0.623627i \(0.214342\pi\)
\(558\) −1.95740e6 −0.266131
\(559\) 557781. 0.0754977
\(560\) 3.47700e6 0.468527
\(561\) 689763. 0.0925321
\(562\) 5.80080e6 0.774725
\(563\) 3.98082e6 0.529300 0.264650 0.964345i \(-0.414744\pi\)
0.264650 + 0.964345i \(0.414744\pi\)
\(564\) 6.46429e6 0.855703
\(565\) 7.06293e6 0.930816
\(566\) −1.77652e7 −2.33092
\(567\) 3.51813e6 0.459573
\(568\) 1.15269e7 1.49914
\(569\) 8.49999e6 1.10062 0.550311 0.834960i \(-0.314509\pi\)
0.550311 + 0.834960i \(0.314509\pi\)
\(570\) 4.96162e6 0.639642
\(571\) 5.24847e6 0.673663 0.336831 0.941565i \(-0.390645\pi\)
0.336831 + 0.941565i \(0.390645\pi\)
\(572\) 1.31266e6 0.167750
\(573\) 5.43135e6 0.691069
\(574\) 3.69145e7 4.67646
\(575\) −1.20514e6 −0.152009
\(576\) 7.91701e6 0.994272
\(577\) 1.94309e6 0.242970 0.121485 0.992593i \(-0.461234\pi\)
0.121485 + 0.992593i \(0.461234\pi\)
\(578\) 358852. 0.0446782
\(579\) −6.70946e6 −0.831747
\(580\) 2.57093e6 0.317337
\(581\) −1.50382e7 −1.84823
\(582\) 5.10242e6 0.624408
\(583\) −244115. −0.0297456
\(584\) 2.12669e7 2.58031
\(585\) −1.53853e6 −0.185873
\(586\) 9.10809e6 1.09568
\(587\) 924441. 0.110735 0.0553674 0.998466i \(-0.482367\pi\)
0.0553674 + 0.998466i \(0.482367\pi\)
\(588\) −1.00513e7 −1.19889
\(589\) −2.64665e6 −0.314346
\(590\) 675909. 0.0799389
\(591\) 5.87982e6 0.692461
\(592\) −5.90726e6 −0.692759
\(593\) −1.09140e7 −1.27453 −0.637263 0.770646i \(-0.719934\pi\)
−0.637263 + 0.770646i \(0.719934\pi\)
\(594\) 2.32296e6 0.270131
\(595\) −6.63598e6 −0.768445
\(596\) 1.11750e7 1.28864
\(597\) −7.76564e6 −0.891746
\(598\) 1.49106e6 0.170508
\(599\) −6.47200e6 −0.737006 −0.368503 0.929626i \(-0.620130\pi\)
−0.368503 + 0.929626i \(0.620130\pi\)
\(600\) 4.86503e6 0.551705
\(601\) −9.66608e6 −1.09160 −0.545801 0.837915i \(-0.683775\pi\)
−0.545801 + 0.837915i \(0.683775\pi\)
\(602\) 3.46398e6 0.389569
\(603\) −1.65447e6 −0.185296
\(604\) −2.36635e7 −2.63928
\(605\) −4.37685e6 −0.486153
\(606\) −9.82780e6 −1.08711
\(607\) 1.50825e7 1.66151 0.830753 0.556641i \(-0.187910\pi\)
0.830753 + 0.556641i \(0.187910\pi\)
\(608\) 5.73799e6 0.629507
\(609\) −2.34971e6 −0.256727
\(610\) 1.32560e7 1.44240
\(611\) −4.16228e6 −0.451054
\(612\) 1.30863e7 1.41234
\(613\) −2.07592e6 −0.223131 −0.111565 0.993757i \(-0.535586\pi\)
−0.111565 + 0.993757i \(0.535586\pi\)
\(614\) −7.05129e6 −0.754827
\(615\) −4.34324e6 −0.463048
\(616\) 3.78479e6 0.401875
\(617\) 1.05100e7 1.11145 0.555727 0.831365i \(-0.312440\pi\)
0.555727 + 0.831365i \(0.312440\pi\)
\(618\) −3.15106e6 −0.331884
\(619\) −6.33902e6 −0.664960 −0.332480 0.943110i \(-0.607885\pi\)
−0.332480 + 0.943110i \(0.607885\pi\)
\(620\) 1.89038e6 0.197501
\(621\) 1.71820e6 0.178790
\(622\) −9.79030e6 −1.01466
\(623\) −1.48116e7 −1.52891
\(624\) −1.49661e6 −0.153868
\(625\) 2.98529e6 0.305694
\(626\) −579208. −0.0590744
\(627\) 1.34285e6 0.136414
\(628\) 3.01222e7 3.04781
\(629\) 1.12742e7 1.13621
\(630\) −9.55474e6 −0.959108
\(631\) −1.15541e7 −1.15521 −0.577606 0.816316i \(-0.696013\pi\)
−0.577606 + 0.816316i \(0.696013\pi\)
\(632\) −1.75283e7 −1.74560
\(633\) 2.15345e6 0.213612
\(634\) 8.06697e6 0.797053
\(635\) −4.93751e6 −0.485930
\(636\) 1.56998e6 0.153905
\(637\) 6.47191e6 0.631952
\(638\) 1.06858e6 0.103934
\(639\) −7.87577e6 −0.763028
\(640\) −9.54640e6 −0.921276
\(641\) −3.92627e6 −0.377429 −0.188714 0.982032i \(-0.560432\pi\)
−0.188714 + 0.982032i \(0.560432\pi\)
\(642\) 396453. 0.0379624
\(643\) −1.87570e7 −1.78911 −0.894553 0.446961i \(-0.852506\pi\)
−0.894553 + 0.446961i \(0.852506\pi\)
\(644\) 6.02971e6 0.572904
\(645\) −407561. −0.0385739
\(646\) 2.71736e7 2.56192
\(647\) −9.03463e6 −0.848496 −0.424248 0.905546i \(-0.639462\pi\)
−0.424248 + 0.905546i \(0.639462\pi\)
\(648\) 4.77731e6 0.446937
\(649\) 182933. 0.0170483
\(650\) −6.74711e6 −0.626375
\(651\) −1.72772e6 −0.159779
\(652\) −2.78376e7 −2.56456
\(653\) 1.74423e7 1.60074 0.800371 0.599505i \(-0.204636\pi\)
0.800371 + 0.599505i \(0.204636\pi\)
\(654\) 1.04179e7 0.952439
\(655\) 6.00720e6 0.547103
\(656\) 1.24634e7 1.13077
\(657\) −1.45307e7 −1.31333
\(658\) −2.58490e7 −2.32744
\(659\) 1.74636e7 1.56646 0.783230 0.621732i \(-0.213571\pi\)
0.783230 + 0.621732i \(0.213571\pi\)
\(660\) −959138. −0.0857080
\(661\) 5.12626e6 0.456348 0.228174 0.973620i \(-0.426724\pi\)
0.228174 + 0.973620i \(0.426724\pi\)
\(662\) −3.36121e7 −2.98093
\(663\) 2.85634e6 0.252364
\(664\) −2.04206e7 −1.79741
\(665\) −1.29192e7 −1.13287
\(666\) 1.62331e7 1.41813
\(667\) 790386. 0.0687899
\(668\) −8.49796e6 −0.736841
\(669\) 4.46096e6 0.385356
\(670\) 2.45381e6 0.211181
\(671\) 3.58770e6 0.307616
\(672\) 3.74573e6 0.319973
\(673\) 4.98529e6 0.424280 0.212140 0.977239i \(-0.431957\pi\)
0.212140 + 0.977239i \(0.431957\pi\)
\(674\) −1.43653e7 −1.21805
\(675\) −7.77489e6 −0.656802
\(676\) −1.67424e7 −1.40913
\(677\) 8.15170e6 0.683560 0.341780 0.939780i \(-0.388970\pi\)
0.341780 + 0.939780i \(0.388970\pi\)
\(678\) −1.88800e7 −1.57735
\(679\) −1.32857e7 −1.10589
\(680\) −9.01108e6 −0.747317
\(681\) −4.76467e6 −0.393700
\(682\) 785716. 0.0646852
\(683\) −3.28051e6 −0.269085 −0.134543 0.990908i \(-0.542957\pi\)
−0.134543 + 0.990908i \(0.542957\pi\)
\(684\) 2.54769e7 2.08213
\(685\) 3.54167e6 0.288391
\(686\) 8.70567e6 0.706305
\(687\) −817384. −0.0660745
\(688\) 1.16954e6 0.0941984
\(689\) −1.01089e6 −0.0811254
\(690\) −1.08950e6 −0.0871170
\(691\) 1.54825e7 1.23352 0.616758 0.787153i \(-0.288446\pi\)
0.616758 + 0.787153i \(0.288446\pi\)
\(692\) 3.14302e7 2.49507
\(693\) −2.58597e6 −0.204546
\(694\) 2.07796e7 1.63772
\(695\) 5.08956e6 0.399685
\(696\) −3.19070e6 −0.249668
\(697\) −2.37868e7 −1.85462
\(698\) 3.76955e6 0.292854
\(699\) −1.00435e7 −0.777483
\(700\) −2.72846e7 −2.10462
\(701\) −4.91809e6 −0.378008 −0.189004 0.981976i \(-0.560526\pi\)
−0.189004 + 0.981976i \(0.560526\pi\)
\(702\) 9.61948e6 0.736731
\(703\) 2.19490e7 1.67505
\(704\) −3.17795e6 −0.241666
\(705\) 3.04131e6 0.230456
\(706\) 2.61227e6 0.197245
\(707\) 2.55898e7 1.92539
\(708\) −1.17650e6 −0.0882085
\(709\) −8.69925e6 −0.649930 −0.324965 0.945726i \(-0.605352\pi\)
−0.324965 + 0.945726i \(0.605352\pi\)
\(710\) 1.16808e7 0.869616
\(711\) 1.19762e7 0.888476
\(712\) −2.01129e7 −1.48688
\(713\) 581162. 0.0428128
\(714\) 1.77388e7 1.30220
\(715\) 617578. 0.0451779
\(716\) 4.13629e7 3.01529
\(717\) −1.73340e6 −0.125922
\(718\) −3.80069e7 −2.75138
\(719\) −8.92512e6 −0.643861 −0.321930 0.946763i \(-0.604332\pi\)
−0.321930 + 0.946763i \(0.604332\pi\)
\(720\) −3.22595e6 −0.231914
\(721\) 8.20479e6 0.587799
\(722\) 2.91870e7 2.08376
\(723\) 3.76894e6 0.268147
\(724\) 1.71231e7 1.21405
\(725\) −3.57652e6 −0.252706
\(726\) 1.16998e7 0.823830
\(727\) 1.33205e7 0.934729 0.467365 0.884065i \(-0.345204\pi\)
0.467365 + 0.884065i \(0.345204\pi\)
\(728\) 1.56730e7 1.09604
\(729\) 3.08154e6 0.214758
\(730\) 2.15510e7 1.49678
\(731\) −2.23211e6 −0.154498
\(732\) −2.30737e7 −1.59162
\(733\) 1.41244e7 0.970981 0.485490 0.874242i \(-0.338641\pi\)
0.485490 + 0.874242i \(0.338641\pi\)
\(734\) −4.69685e7 −3.21786
\(735\) −4.72892e6 −0.322882
\(736\) −1.25997e6 −0.0857368
\(737\) 664118. 0.0450377
\(738\) −3.42491e7 −2.31477
\(739\) −1.65506e7 −1.11482 −0.557408 0.830239i \(-0.688204\pi\)
−0.557408 + 0.830239i \(0.688204\pi\)
\(740\) −1.56772e7 −1.05242
\(741\) 5.56083e6 0.372044
\(742\) −6.27795e6 −0.418608
\(743\) 1.32085e7 0.877771 0.438885 0.898543i \(-0.355373\pi\)
0.438885 + 0.898543i \(0.355373\pi\)
\(744\) −2.34609e6 −0.155386
\(745\) 5.25759e6 0.347054
\(746\) 2.41965e7 1.59186
\(747\) 1.39524e7 0.914845
\(748\) −5.25296e6 −0.343281
\(749\) −1.03229e6 −0.0672353
\(750\) 1.15273e7 0.748299
\(751\) 1.62740e6 0.105291 0.0526457 0.998613i \(-0.483235\pi\)
0.0526457 + 0.998613i \(0.483235\pi\)
\(752\) −8.72735e6 −0.562779
\(753\) −5.66870e6 −0.364331
\(754\) 4.42506e6 0.283459
\(755\) −1.11331e7 −0.710805
\(756\) 3.89002e7 2.47541
\(757\) −1.41817e7 −0.899472 −0.449736 0.893162i \(-0.648482\pi\)
−0.449736 + 0.893162i \(0.648482\pi\)
\(758\) −5.81971e6 −0.367899
\(759\) −294870. −0.0185791
\(760\) −1.75431e7 −1.10172
\(761\) −631434. −0.0395245 −0.0197622 0.999805i \(-0.506291\pi\)
−0.0197622 + 0.999805i \(0.506291\pi\)
\(762\) 1.31985e7 0.823453
\(763\) −2.71264e7 −1.68686
\(764\) −4.13630e7 −2.56377
\(765\) 6.15684e6 0.380368
\(766\) −3.77716e7 −2.32591
\(767\) 757537. 0.0464960
\(768\) 1.45693e7 0.891326
\(769\) 2920.58 0.000178096 0 8.90480e−5 1.00000i \(-0.499972\pi\)
8.90480e−5 1.00000i \(0.499972\pi\)
\(770\) 3.83534e6 0.233119
\(771\) 1.05488e7 0.639098
\(772\) 5.10966e7 3.08566
\(773\) −8.64224e6 −0.520209 −0.260104 0.965580i \(-0.583757\pi\)
−0.260104 + 0.965580i \(0.583757\pi\)
\(774\) −3.21387e6 −0.192831
\(775\) −2.62978e6 −0.157277
\(776\) −1.80409e7 −1.07548
\(777\) 1.43282e7 0.851412
\(778\) −2.32225e7 −1.37550
\(779\) −4.63089e7 −2.73414
\(780\) −3.97184e6 −0.233752
\(781\) 3.16139e6 0.185460
\(782\) −5.96689e6 −0.348924
\(783\) 5.09911e6 0.297228
\(784\) 1.35701e7 0.788485
\(785\) 1.41718e7 0.820828
\(786\) −1.60579e7 −0.927115
\(787\) 6.88838e6 0.396443 0.198221 0.980157i \(-0.436484\pi\)
0.198221 + 0.980157i \(0.436484\pi\)
\(788\) −4.47783e7 −2.56893
\(789\) 141700. 0.00810358
\(790\) −1.77623e7 −1.01259
\(791\) 4.91601e7 2.79365
\(792\) −3.51152e6 −0.198922
\(793\) 1.48568e7 0.838965
\(794\) −2.81893e7 −1.58684
\(795\) 738642. 0.0414492
\(796\) 5.91400e7 3.30825
\(797\) 2.93617e7 1.63733 0.818664 0.574273i \(-0.194715\pi\)
0.818664 + 0.574273i \(0.194715\pi\)
\(798\) 3.45344e7 1.91975
\(799\) 1.66565e7 0.923030
\(800\) 5.70142e6 0.314962
\(801\) 1.37422e7 0.756788
\(802\) −5.58106e7 −3.06394
\(803\) 5.83272e6 0.319214
\(804\) −4.27116e6 −0.233027
\(805\) 2.83685e6 0.154293
\(806\) 3.25369e6 0.176416
\(807\) 4.30998e6 0.232965
\(808\) 3.47487e7 1.87245
\(809\) −2.84195e6 −0.152667 −0.0763334 0.997082i \(-0.524321\pi\)
−0.0763334 + 0.997082i \(0.524321\pi\)
\(810\) 4.84112e6 0.259259
\(811\) 1.67390e6 0.0893670 0.0446835 0.999001i \(-0.485772\pi\)
0.0446835 + 0.999001i \(0.485772\pi\)
\(812\) 1.78945e7 0.952420
\(813\) −107709. −0.00571515
\(814\) −6.51607e6 −0.344687
\(815\) −1.30970e7 −0.690681
\(816\) 5.98910e6 0.314874
\(817\) −4.34554e6 −0.227766
\(818\) 1.17470e7 0.613825
\(819\) −1.07086e7 −0.557859
\(820\) 3.30763e7 1.71784
\(821\) 3.75970e7 1.94668 0.973340 0.229365i \(-0.0736650\pi\)
0.973340 + 0.229365i \(0.0736650\pi\)
\(822\) −9.46730e6 −0.488705
\(823\) 1.67263e7 0.860797 0.430398 0.902639i \(-0.358373\pi\)
0.430398 + 0.902639i \(0.358373\pi\)
\(824\) 1.11414e7 0.571638
\(825\) 1.33429e6 0.0682522
\(826\) 4.70453e6 0.239920
\(827\) −2.69145e7 −1.36843 −0.684216 0.729279i \(-0.739856\pi\)
−0.684216 + 0.729279i \(0.739856\pi\)
\(828\) −5.59434e6 −0.283578
\(829\) −7.34223e6 −0.371058 −0.185529 0.982639i \(-0.559400\pi\)
−0.185529 + 0.982639i \(0.559400\pi\)
\(830\) −2.06933e7 −1.04264
\(831\) 3.93471e6 0.197656
\(832\) −1.31600e7 −0.659097
\(833\) −2.58991e7 −1.29322
\(834\) −1.36050e7 −0.677303
\(835\) −3.99811e6 −0.198444
\(836\) −1.02266e7 −0.506077
\(837\) 3.74932e6 0.184986
\(838\) 1.08698e7 0.534701
\(839\) −1.44619e7 −0.709284 −0.354642 0.935002i \(-0.615397\pi\)
−0.354642 + 0.935002i \(0.615397\pi\)
\(840\) −1.14520e7 −0.559995
\(841\) −1.81655e7 −0.885641
\(842\) −4.99530e7 −2.42818
\(843\) −4.75043e6 −0.230231
\(844\) −1.63998e7 −0.792471
\(845\) −7.87695e6 −0.379504
\(846\) 2.39826e7 1.15205
\(847\) −3.04642e7 −1.45909
\(848\) −2.11961e6 −0.101220
\(849\) 1.45483e7 0.692699
\(850\) 2.70004e7 1.28181
\(851\) −4.81967e6 −0.228136
\(852\) −2.03319e7 −0.959577
\(853\) −3.00835e6 −0.141565 −0.0707825 0.997492i \(-0.522550\pi\)
−0.0707825 + 0.997492i \(0.522550\pi\)
\(854\) 9.22655e7 4.32907
\(855\) 1.19863e7 0.560753
\(856\) −1.40176e6 −0.0653866
\(857\) 5.35883e6 0.249240 0.124620 0.992205i \(-0.460229\pi\)
0.124620 + 0.992205i \(0.460229\pi\)
\(858\) −1.65086e6 −0.0765581
\(859\) 2.59898e7 1.20176 0.600882 0.799338i \(-0.294816\pi\)
0.600882 + 0.799338i \(0.294816\pi\)
\(860\) 3.10382e6 0.143104
\(861\) −3.02302e7 −1.38974
\(862\) 4.74037e7 2.17292
\(863\) −4.32743e7 −1.97789 −0.988947 0.148266i \(-0.952631\pi\)
−0.988947 + 0.148266i \(0.952631\pi\)
\(864\) −8.12862e6 −0.370452
\(865\) 1.47872e7 0.671965
\(866\) −1.94421e7 −0.880947
\(867\) −293873. −0.0132774
\(868\) 1.31576e7 0.592758
\(869\) −4.80734e6 −0.215951
\(870\) −3.23331e6 −0.144827
\(871\) 2.75015e6 0.122832
\(872\) −3.68352e7 −1.64048
\(873\) 1.23265e7 0.547398
\(874\) −1.16165e7 −0.514397
\(875\) −3.00150e7 −1.32531
\(876\) −3.75121e7 −1.65162
\(877\) 1.03640e7 0.455017 0.227508 0.973776i \(-0.426942\pi\)
0.227508 + 0.973776i \(0.426942\pi\)
\(878\) −3.88632e7 −1.70138
\(879\) −7.45885e6 −0.325611
\(880\) 1.29492e6 0.0563684
\(881\) −2.43175e7 −1.05555 −0.527776 0.849384i \(-0.676974\pi\)
−0.527776 + 0.849384i \(0.676974\pi\)
\(882\) −3.72905e7 −1.61409
\(883\) 1.78896e7 0.772147 0.386073 0.922468i \(-0.373831\pi\)
0.386073 + 0.922468i \(0.373831\pi\)
\(884\) −2.17528e7 −0.936233
\(885\) −553520. −0.0237561
\(886\) 3.57935e7 1.53186
\(887\) −2.17492e7 −0.928185 −0.464092 0.885787i \(-0.653619\pi\)
−0.464092 + 0.885787i \(0.653619\pi\)
\(888\) 1.94565e7 0.828002
\(889\) −3.43666e7 −1.45842
\(890\) −2.03815e7 −0.862505
\(891\) 1.31024e6 0.0552912
\(892\) −3.39729e7 −1.42962
\(893\) 3.24274e7 1.36076
\(894\) −1.40542e7 −0.588114
\(895\) 1.94603e7 0.812069
\(896\) −6.64458e7 −2.76502
\(897\) −1.22107e6 −0.0506711
\(898\) −1.99832e7 −0.826941
\(899\) 1.72472e6 0.0711738
\(900\) 2.53146e7 1.04175
\(901\) 4.04536e6 0.166014
\(902\) 1.37478e7 0.562624
\(903\) −2.83675e6 −0.115771
\(904\) 6.67551e7 2.71684
\(905\) 8.05605e6 0.326965
\(906\) 2.97602e7 1.20452
\(907\) 2.98499e7 1.20483 0.602414 0.798184i \(-0.294206\pi\)
0.602414 + 0.798184i \(0.294206\pi\)
\(908\) 3.62859e7 1.46057
\(909\) −2.37421e7 −0.953036
\(910\) 1.58824e7 0.635787
\(911\) −1.09193e7 −0.435912 −0.217956 0.975959i \(-0.569939\pi\)
−0.217956 + 0.975959i \(0.569939\pi\)
\(912\) 1.16598e7 0.464198
\(913\) −5.60060e6 −0.222360
\(914\) 3.66838e6 0.145247
\(915\) −1.08557e7 −0.428650
\(916\) 6.22487e6 0.245127
\(917\) 4.18119e7 1.64201
\(918\) −3.84949e7 −1.50764
\(919\) 9.16828e6 0.358096 0.179048 0.983840i \(-0.442698\pi\)
0.179048 + 0.983840i \(0.442698\pi\)
\(920\) 3.85219e6 0.150051
\(921\) 5.77448e6 0.224318
\(922\) −7.35184e6 −0.284819
\(923\) 1.30915e7 0.505807
\(924\) −6.67589e6 −0.257235
\(925\) 2.18091e7 0.838078
\(926\) 2.75796e7 1.05697
\(927\) −7.61237e6 −0.290952
\(928\) −3.73924e6 −0.142532
\(929\) −1.38913e6 −0.0528083 −0.0264041 0.999651i \(-0.508406\pi\)
−0.0264041 + 0.999651i \(0.508406\pi\)
\(930\) −2.37742e6 −0.0901361
\(931\) −5.04212e7 −1.90651
\(932\) 7.64871e7 2.88435
\(933\) 8.01753e6 0.301534
\(934\) 4.53956e7 1.70273
\(935\) −2.47140e6 −0.0924515
\(936\) −1.45414e7 −0.542521
\(937\) −2.52918e7 −0.941090 −0.470545 0.882376i \(-0.655943\pi\)
−0.470545 + 0.882376i \(0.655943\pi\)
\(938\) 1.70793e7 0.633814
\(939\) 474329. 0.0175556
\(940\) −2.31614e7 −0.854958
\(941\) 2.69608e7 0.992563 0.496282 0.868162i \(-0.334698\pi\)
0.496282 + 0.868162i \(0.334698\pi\)
\(942\) −3.78830e7 −1.39097
\(943\) 1.01687e7 0.372381
\(944\) 1.58838e6 0.0580129
\(945\) 1.83017e7 0.666671
\(946\) 1.29007e6 0.0468690
\(947\) −3.19275e6 −0.115689 −0.0578443 0.998326i \(-0.518423\pi\)
−0.0578443 + 0.998326i \(0.518423\pi\)
\(948\) 3.09176e7 1.11734
\(949\) 2.41536e7 0.870596
\(950\) 5.25652e7 1.88969
\(951\) −6.60625e6 −0.236866
\(952\) −6.27198e7 −2.24291
\(953\) −3.59618e7 −1.28265 −0.641327 0.767268i \(-0.721616\pi\)
−0.641327 + 0.767268i \(0.721616\pi\)
\(954\) 5.82466e6 0.207205
\(955\) −1.94604e7 −0.690468
\(956\) 1.32009e7 0.467152
\(957\) −875089. −0.0308868
\(958\) 5.18374e7 1.82486
\(959\) 2.46511e7 0.865545
\(960\) 9.61583e6 0.336751
\(961\) −2.73610e7 −0.955704
\(962\) −2.69834e7 −0.940067
\(963\) 957755. 0.0332804
\(964\) −2.87027e7 −0.994789
\(965\) 2.40398e7 0.831023
\(966\) −7.58322e6 −0.261463
\(967\) −1.05454e7 −0.362659 −0.181330 0.983422i \(-0.558040\pi\)
−0.181330 + 0.983422i \(0.558040\pi\)
\(968\) −4.13677e7 −1.41897
\(969\) −2.22531e7 −0.761345
\(970\) −1.82818e7 −0.623864
\(971\) −1.47340e7 −0.501500 −0.250750 0.968052i \(-0.580677\pi\)
−0.250750 + 0.968052i \(0.580677\pi\)
\(972\) −5.67525e7 −1.92672
\(973\) 3.54249e7 1.19957
\(974\) 4.94881e7 1.67149
\(975\) 5.52539e6 0.186145
\(976\) 3.11514e7 1.04677
\(977\) 4.83492e7 1.62051 0.810257 0.586075i \(-0.199327\pi\)
0.810257 + 0.586075i \(0.199327\pi\)
\(978\) 3.50098e7 1.17042
\(979\) −5.51621e6 −0.183943
\(980\) 3.60136e7 1.19785
\(981\) 2.51677e7 0.834971
\(982\) 1.61012e7 0.532820
\(983\) −1.25654e7 −0.414754 −0.207377 0.978261i \(-0.566493\pi\)
−0.207377 + 0.978261i \(0.566493\pi\)
\(984\) −4.10500e7 −1.35153
\(985\) −2.10672e7 −0.691858
\(986\) −1.77080e7 −0.580067
\(987\) 2.11684e7 0.691665
\(988\) −4.23490e7 −1.38023
\(989\) 954214. 0.0310209
\(990\) −3.55842e6 −0.115390
\(991\) −4.25363e7 −1.37586 −0.687932 0.725776i \(-0.741481\pi\)
−0.687932 + 0.725776i \(0.741481\pi\)
\(992\) −2.74942e6 −0.0887080
\(993\) 2.75259e7 0.885865
\(994\) 8.13021e7 2.60997
\(995\) 2.78241e7 0.890970
\(996\) 3.60193e7 1.15050
\(997\) −3.70772e7 −1.18132 −0.590662 0.806919i \(-0.701133\pi\)
−0.590662 + 0.806919i \(0.701133\pi\)
\(998\) 3.42840e7 1.08960
\(999\) −3.10937e7 −0.985732
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.1.9 10
3.2 odd 2 387.6.a.e.1.2 10
4.3 odd 2 688.6.a.h.1.7 10
5.4 even 2 1075.6.a.b.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.9 10 1.1 even 1 trivial
387.6.a.e.1.2 10 3.2 odd 2
688.6.a.h.1.7 10 4.3 odd 2
1075.6.a.b.1.2 10 5.4 even 2