Properties

Label 177.6.a.a.1.8
Level $177$
Weight $6$
Character 177.1
Self dual yes
Analytic conductor $28.388$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3879361069\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 5 x^{10} - 238 x^{9} + 1067 x^{8} + 20782 x^{7} - 79077 x^{6} - 813818 x^{5} + 2364885 x^{4} + 13849341 x^{3} - 23890558 x^{2} - 74443300 x - 14846072\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(5.75393\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.75393 q^{2} +9.00000 q^{3} -9.40015 q^{4} -8.06966 q^{5} +42.7854 q^{6} -28.8581 q^{7} -196.813 q^{8} +81.0000 q^{9} -38.3626 q^{10} +556.758 q^{11} -84.6013 q^{12} -1129.41 q^{13} -137.189 q^{14} -72.6270 q^{15} -634.832 q^{16} +447.456 q^{17} +385.068 q^{18} -1350.14 q^{19} +75.8560 q^{20} -259.723 q^{21} +2646.79 q^{22} -4466.66 q^{23} -1771.32 q^{24} -3059.88 q^{25} -5369.15 q^{26} +729.000 q^{27} +271.270 q^{28} -2943.74 q^{29} -345.264 q^{30} +1113.75 q^{31} +3280.08 q^{32} +5010.83 q^{33} +2127.18 q^{34} +232.875 q^{35} -761.412 q^{36} -5875.21 q^{37} -6418.45 q^{38} -10164.7 q^{39} +1588.22 q^{40} -638.732 q^{41} -1234.70 q^{42} -9932.25 q^{43} -5233.61 q^{44} -653.643 q^{45} -21234.2 q^{46} +25092.0 q^{47} -5713.49 q^{48} -15974.2 q^{49} -14546.5 q^{50} +4027.11 q^{51} +10616.6 q^{52} +19396.9 q^{53} +3465.62 q^{54} -4492.85 q^{55} +5679.66 q^{56} -12151.2 q^{57} -13994.3 q^{58} +3481.00 q^{59} +682.704 q^{60} +7814.71 q^{61} +5294.71 q^{62} -2337.51 q^{63} +35907.9 q^{64} +9113.98 q^{65} +23821.1 q^{66} +36824.7 q^{67} -4206.15 q^{68} -40199.9 q^{69} +1107.07 q^{70} +24174.9 q^{71} -15941.9 q^{72} -78229.0 q^{73} -27930.3 q^{74} -27538.9 q^{75} +12691.5 q^{76} -16067.0 q^{77} -48322.3 q^{78} +4205.35 q^{79} +5122.88 q^{80} +6561.00 q^{81} -3036.49 q^{82} -36905.9 q^{83} +2441.43 q^{84} -3610.82 q^{85} -47217.2 q^{86} -26493.7 q^{87} -109578. q^{88} +6625.63 q^{89} -3107.37 q^{90} +32592.7 q^{91} +41987.2 q^{92} +10023.8 q^{93} +119286. q^{94} +10895.1 q^{95} +29520.7 q^{96} +88314.2 q^{97} -75940.3 q^{98} +45097.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} + O(q^{10}) \) \( 11q - 6q^{2} + 99q^{3} + 150q^{4} - 192q^{5} - 54q^{6} - 371q^{7} - 621q^{8} + 891q^{9} - 399q^{10} - 698q^{11} + 1350q^{12} - 1556q^{13} - 1679q^{14} - 1728q^{15} - 2662q^{16} - 4793q^{17} - 486q^{18} - 3753q^{19} - 11023q^{20} - 3339q^{21} - 9534q^{22} - 7323q^{23} - 5589q^{24} + 7867q^{25} - 4844q^{26} + 8019q^{27} + 3650q^{28} - 15467q^{29} - 3591q^{30} - 5151q^{31} - 15368q^{32} - 6282q^{33} + 8452q^{34} - 23285q^{35} + 12150q^{36} + 8623q^{37} + 15205q^{38} - 14004q^{39} + 41530q^{40} - 6369q^{41} - 15111q^{42} - 20506q^{43} - 55632q^{44} - 15552q^{45} - 45191q^{46} - 47899q^{47} - 23958q^{48} - 10322q^{49} - 102147q^{50} - 43137q^{51} - 292q^{52} - 80048q^{53} - 4374q^{54} - 2114q^{55} - 108126q^{56} - 33777q^{57} - 58294q^{58} + 38291q^{59} - 99207q^{60} - 82527q^{61} - 67438q^{62} - 30051q^{63} - 51411q^{64} - 167646q^{65} - 85806q^{66} - 166976q^{67} - 136533q^{68} - 65907q^{69} + 76140q^{70} - 183560q^{71} - 50301q^{72} - 36809q^{73} - 116686q^{74} + 70803q^{75} + 55580q^{76} - 164885q^{77} - 43596q^{78} - 281518q^{79} - 32683q^{80} + 72171q^{81} + 178815q^{82} - 254691q^{83} + 32850q^{84} + 4763q^{85} + 349324q^{86} - 139203q^{87} + 251285q^{88} - 89687q^{89} - 32319q^{90} + 34897q^{91} - 20240q^{92} - 46359q^{93} + 96548q^{94} - 155113q^{95} - 138312q^{96} - 45828q^{97} + 465864q^{98} - 56538q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.75393 0.840384 0.420192 0.907435i \(-0.361963\pi\)
0.420192 + 0.907435i \(0.361963\pi\)
\(3\) 9.00000 0.577350
\(4\) −9.40015 −0.293755
\(5\) −8.06966 −0.144355 −0.0721773 0.997392i \(-0.522995\pi\)
−0.0721773 + 0.997392i \(0.522995\pi\)
\(6\) 42.7854 0.485196
\(7\) −28.8581 −0.222599 −0.111299 0.993787i \(-0.535501\pi\)
−0.111299 + 0.993787i \(0.535501\pi\)
\(8\) −196.813 −1.08725
\(9\) 81.0000 0.333333
\(10\) −38.3626 −0.121313
\(11\) 556.758 1.38735 0.693673 0.720290i \(-0.255991\pi\)
0.693673 + 0.720290i \(0.255991\pi\)
\(12\) −84.6013 −0.169599
\(13\) −1129.41 −1.85351 −0.926754 0.375670i \(-0.877413\pi\)
−0.926754 + 0.375670i \(0.877413\pi\)
\(14\) −137.189 −0.187068
\(15\) −72.6270 −0.0833431
\(16\) −634.832 −0.619954
\(17\) 447.456 0.375516 0.187758 0.982215i \(-0.439878\pi\)
0.187758 + 0.982215i \(0.439878\pi\)
\(18\) 385.068 0.280128
\(19\) −1350.14 −0.858012 −0.429006 0.903302i \(-0.641136\pi\)
−0.429006 + 0.903302i \(0.641136\pi\)
\(20\) 75.8560 0.0424048
\(21\) −259.723 −0.128517
\(22\) 2646.79 1.16590
\(23\) −4466.66 −1.76061 −0.880304 0.474409i \(-0.842662\pi\)
−0.880304 + 0.474409i \(0.842662\pi\)
\(24\) −1771.32 −0.627725
\(25\) −3059.88 −0.979162
\(26\) −5369.15 −1.55766
\(27\) 729.000 0.192450
\(28\) 271.270 0.0653894
\(29\) −2943.74 −0.649987 −0.324994 0.945716i \(-0.605362\pi\)
−0.324994 + 0.945716i \(0.605362\pi\)
\(30\) −345.264 −0.0700402
\(31\) 1113.75 0.208154 0.104077 0.994569i \(-0.466811\pi\)
0.104077 + 0.994569i \(0.466811\pi\)
\(32\) 3280.08 0.566252
\(33\) 5010.83 0.800985
\(34\) 2127.18 0.315578
\(35\) 232.875 0.0321331
\(36\) −761.412 −0.0979182
\(37\) −5875.21 −0.705536 −0.352768 0.935711i \(-0.614759\pi\)
−0.352768 + 0.935711i \(0.614759\pi\)
\(38\) −6418.45 −0.721060
\(39\) −10164.7 −1.07012
\(40\) 1588.22 0.156950
\(41\) −638.732 −0.0593415 −0.0296708 0.999560i \(-0.509446\pi\)
−0.0296708 + 0.999560i \(0.509446\pi\)
\(42\) −1234.70 −0.108004
\(43\) −9932.25 −0.819175 −0.409587 0.912271i \(-0.634327\pi\)
−0.409587 + 0.912271i \(0.634327\pi\)
\(44\) −5233.61 −0.407540
\(45\) −653.643 −0.0481182
\(46\) −21234.2 −1.47959
\(47\) 25092.0 1.65688 0.828440 0.560078i \(-0.189229\pi\)
0.828440 + 0.560078i \(0.189229\pi\)
\(48\) −5713.49 −0.357930
\(49\) −15974.2 −0.950450
\(50\) −14546.5 −0.822872
\(51\) 4027.11 0.216804
\(52\) 10616.6 0.544476
\(53\) 19396.9 0.948509 0.474255 0.880388i \(-0.342718\pi\)
0.474255 + 0.880388i \(0.342718\pi\)
\(54\) 3465.62 0.161732
\(55\) −4492.85 −0.200270
\(56\) 5679.66 0.242021
\(57\) −12151.2 −0.495374
\(58\) −13994.3 −0.546239
\(59\) 3481.00 0.130189
\(60\) 682.704 0.0244824
\(61\) 7814.71 0.268898 0.134449 0.990920i \(-0.457073\pi\)
0.134449 + 0.990920i \(0.457073\pi\)
\(62\) 5294.71 0.174929
\(63\) −2337.51 −0.0741996
\(64\) 35907.9 1.09582
\(65\) 9113.98 0.267562
\(66\) 23821.1 0.673135
\(67\) 36824.7 1.00220 0.501098 0.865391i \(-0.332930\pi\)
0.501098 + 0.865391i \(0.332930\pi\)
\(68\) −4206.15 −0.110310
\(69\) −40199.9 −1.01649
\(70\) 1107.07 0.0270042
\(71\) 24174.9 0.569141 0.284570 0.958655i \(-0.408149\pi\)
0.284570 + 0.958655i \(0.408149\pi\)
\(72\) −15941.9 −0.362417
\(73\) −78229.0 −1.71815 −0.859075 0.511850i \(-0.828960\pi\)
−0.859075 + 0.511850i \(0.828960\pi\)
\(74\) −27930.3 −0.592921
\(75\) −27538.9 −0.565319
\(76\) 12691.5 0.252045
\(77\) −16067.0 −0.308822
\(78\) −48322.3 −0.899314
\(79\) 4205.35 0.0758115 0.0379057 0.999281i \(-0.487931\pi\)
0.0379057 + 0.999281i \(0.487931\pi\)
\(80\) 5122.88 0.0894931
\(81\) 6561.00 0.111111
\(82\) −3036.49 −0.0498697
\(83\) −36905.9 −0.588032 −0.294016 0.955801i \(-0.594992\pi\)
−0.294016 + 0.955801i \(0.594992\pi\)
\(84\) 2441.43 0.0377526
\(85\) −3610.82 −0.0542074
\(86\) −47217.2 −0.688421
\(87\) −26493.7 −0.375270
\(88\) −109578. −1.50839
\(89\) 6625.63 0.0886650 0.0443325 0.999017i \(-0.485884\pi\)
0.0443325 + 0.999017i \(0.485884\pi\)
\(90\) −3107.37 −0.0404377
\(91\) 32592.7 0.412588
\(92\) 41987.2 0.517187
\(93\) 10023.8 0.120178
\(94\) 119286. 1.39242
\(95\) 10895.1 0.123858
\(96\) 29520.7 0.326926
\(97\) 88314.2 0.953018 0.476509 0.879170i \(-0.341902\pi\)
0.476509 + 0.879170i \(0.341902\pi\)
\(98\) −75940.3 −0.798743
\(99\) 45097.4 0.462449
\(100\) 28763.3 0.287633
\(101\) −123051. −1.20028 −0.600138 0.799896i \(-0.704888\pi\)
−0.600138 + 0.799896i \(0.704888\pi\)
\(102\) 19144.6 0.182199
\(103\) 87267.1 0.810509 0.405254 0.914204i \(-0.367183\pi\)
0.405254 + 0.914204i \(0.367183\pi\)
\(104\) 222284. 2.01523
\(105\) 2095.88 0.0185521
\(106\) 92211.3 0.797112
\(107\) −2531.40 −0.0213748 −0.0106874 0.999943i \(-0.503402\pi\)
−0.0106874 + 0.999943i \(0.503402\pi\)
\(108\) −6852.71 −0.0565331
\(109\) −158752. −1.27983 −0.639914 0.768446i \(-0.721030\pi\)
−0.639914 + 0.768446i \(0.721030\pi\)
\(110\) −21358.7 −0.168304
\(111\) −52876.9 −0.407341
\(112\) 18320.1 0.138001
\(113\) −45254.3 −0.333399 −0.166699 0.986008i \(-0.553311\pi\)
−0.166699 + 0.986008i \(0.553311\pi\)
\(114\) −57766.1 −0.416304
\(115\) 36044.4 0.254152
\(116\) 27671.6 0.190937
\(117\) −91482.4 −0.617836
\(118\) 16548.4 0.109409
\(119\) −12912.7 −0.0835893
\(120\) 14294.0 0.0906149
\(121\) 148929. 0.924731
\(122\) 37150.6 0.225978
\(123\) −5748.58 −0.0342608
\(124\) −10469.5 −0.0611463
\(125\) 49909.9 0.285701
\(126\) −11112.3 −0.0623561
\(127\) −60121.1 −0.330764 −0.165382 0.986230i \(-0.552886\pi\)
−0.165382 + 0.986230i \(0.552886\pi\)
\(128\) 65741.1 0.354660
\(129\) −89390.3 −0.472951
\(130\) 43327.2 0.224855
\(131\) 339921. 1.73061 0.865307 0.501243i \(-0.167124\pi\)
0.865307 + 0.501243i \(0.167124\pi\)
\(132\) −47102.5 −0.235293
\(133\) 38962.4 0.190992
\(134\) 175062. 0.842229
\(135\) −5882.78 −0.0277810
\(136\) −88065.4 −0.408280
\(137\) 67355.2 0.306598 0.153299 0.988180i \(-0.451010\pi\)
0.153299 + 0.988180i \(0.451010\pi\)
\(138\) −191108. −0.854240
\(139\) 308422. 1.35397 0.676983 0.735999i \(-0.263287\pi\)
0.676983 + 0.735999i \(0.263287\pi\)
\(140\) −2189.06 −0.00943926
\(141\) 225828. 0.956600
\(142\) 114926. 0.478297
\(143\) −628810. −2.57146
\(144\) −51421.4 −0.206651
\(145\) 23755.0 0.0938286
\(146\) −371895. −1.44391
\(147\) −143768. −0.548742
\(148\) 55227.8 0.207254
\(149\) 386065. 1.42460 0.712302 0.701873i \(-0.247653\pi\)
0.712302 + 0.701873i \(0.247653\pi\)
\(150\) −130918. −0.475085
\(151\) 361671. 1.29084 0.645418 0.763829i \(-0.276683\pi\)
0.645418 + 0.763829i \(0.276683\pi\)
\(152\) 265725. 0.932875
\(153\) 36244.0 0.125172
\(154\) −76381.3 −0.259529
\(155\) −8987.62 −0.0300480
\(156\) 95549.8 0.314354
\(157\) −125710. −0.407026 −0.203513 0.979072i \(-0.565236\pi\)
−0.203513 + 0.979072i \(0.565236\pi\)
\(158\) 19992.0 0.0637107
\(159\) 174572. 0.547622
\(160\) −26469.1 −0.0817410
\(161\) 128899. 0.391909
\(162\) 31190.5 0.0933760
\(163\) 312195. 0.920358 0.460179 0.887826i \(-0.347785\pi\)
0.460179 + 0.887826i \(0.347785\pi\)
\(164\) 6004.17 0.0174318
\(165\) −40435.7 −0.115626
\(166\) −175448. −0.494173
\(167\) −696281. −1.93194 −0.965969 0.258656i \(-0.916720\pi\)
−0.965969 + 0.258656i \(0.916720\pi\)
\(168\) 51117.0 0.139731
\(169\) 904280. 2.43549
\(170\) −17165.6 −0.0455550
\(171\) −109361. −0.286004
\(172\) 93364.6 0.240636
\(173\) −467449. −1.18746 −0.593730 0.804664i \(-0.702345\pi\)
−0.593730 + 0.804664i \(0.702345\pi\)
\(174\) −125949. −0.315371
\(175\) 88302.3 0.217960
\(176\) −353448. −0.860091
\(177\) 31329.0 0.0751646
\(178\) 31497.8 0.0745127
\(179\) −205080. −0.478400 −0.239200 0.970970i \(-0.576885\pi\)
−0.239200 + 0.970970i \(0.576885\pi\)
\(180\) 6144.34 0.0141349
\(181\) 184862. 0.419421 0.209711 0.977763i \(-0.432748\pi\)
0.209711 + 0.977763i \(0.432748\pi\)
\(182\) 154943. 0.346733
\(183\) 70332.4 0.155249
\(184\) 879098. 1.91422
\(185\) 47411.0 0.101847
\(186\) 47652.4 0.100996
\(187\) 249125. 0.520971
\(188\) −235869. −0.486716
\(189\) −21037.6 −0.0428391
\(190\) 51794.7 0.104088
\(191\) −272484. −0.540453 −0.270226 0.962797i \(-0.587099\pi\)
−0.270226 + 0.962797i \(0.587099\pi\)
\(192\) 323171. 0.632673
\(193\) −270438. −0.522606 −0.261303 0.965257i \(-0.584152\pi\)
−0.261303 + 0.965257i \(0.584152\pi\)
\(194\) 419840. 0.800901
\(195\) 82025.8 0.154477
\(196\) 150160. 0.279199
\(197\) −707478. −1.29882 −0.649408 0.760440i \(-0.724983\pi\)
−0.649408 + 0.760440i \(0.724983\pi\)
\(198\) 214390. 0.388635
\(199\) −1.02712e6 −1.83861 −0.919303 0.393550i \(-0.871247\pi\)
−0.919303 + 0.393550i \(0.871247\pi\)
\(200\) 602226. 1.06459
\(201\) 331423. 0.578618
\(202\) −584975. −1.00869
\(203\) 84950.8 0.144686
\(204\) −37855.4 −0.0636872
\(205\) 5154.35 0.00856622
\(206\) 414862. 0.681138
\(207\) −361799. −0.586870
\(208\) 716988. 1.14909
\(209\) −751699. −1.19036
\(210\) 9963.65 0.0155909
\(211\) −806769. −1.24751 −0.623753 0.781621i \(-0.714393\pi\)
−0.623753 + 0.781621i \(0.714393\pi\)
\(212\) −182333. −0.278629
\(213\) 217575. 0.328594
\(214\) −12034.1 −0.0179630
\(215\) 80149.9 0.118252
\(216\) −143477. −0.209242
\(217\) −32140.8 −0.0463349
\(218\) −754694. −1.07555
\(219\) −704061. −0.991974
\(220\) 42233.5 0.0588302
\(221\) −505363. −0.696021
\(222\) −251373. −0.342323
\(223\) −337189. −0.454058 −0.227029 0.973888i \(-0.572901\pi\)
−0.227029 + 0.973888i \(0.572901\pi\)
\(224\) −94656.9 −0.126047
\(225\) −247850. −0.326387
\(226\) −215136. −0.280183
\(227\) −259818. −0.334661 −0.167331 0.985901i \(-0.553515\pi\)
−0.167331 + 0.985901i \(0.553515\pi\)
\(228\) 114223. 0.145518
\(229\) 227371. 0.286515 0.143257 0.989685i \(-0.454242\pi\)
0.143257 + 0.989685i \(0.454242\pi\)
\(230\) 171353. 0.213585
\(231\) −144603. −0.178298
\(232\) 579368. 0.706699
\(233\) 265219. 0.320048 0.160024 0.987113i \(-0.448843\pi\)
0.160024 + 0.987113i \(0.448843\pi\)
\(234\) −434901. −0.519219
\(235\) −202484. −0.239178
\(236\) −32721.9 −0.0382436
\(237\) 37848.2 0.0437698
\(238\) −61386.2 −0.0702471
\(239\) −245730. −0.278268 −0.139134 0.990274i \(-0.544432\pi\)
−0.139134 + 0.990274i \(0.544432\pi\)
\(240\) 46106.0 0.0516689
\(241\) 1.23701e6 1.37193 0.685963 0.727636i \(-0.259381\pi\)
0.685963 + 0.727636i \(0.259381\pi\)
\(242\) 707997. 0.777129
\(243\) 59049.0 0.0641500
\(244\) −73459.4 −0.0789902
\(245\) 128906. 0.137202
\(246\) −27328.4 −0.0287923
\(247\) 1.52486e6 1.59033
\(248\) −219202. −0.226316
\(249\) −332153. −0.339500
\(250\) 237268. 0.240099
\(251\) −412168. −0.412943 −0.206472 0.978453i \(-0.566198\pi\)
−0.206472 + 0.978453i \(0.566198\pi\)
\(252\) 21972.9 0.0217965
\(253\) −2.48685e6 −2.44258
\(254\) −285812. −0.277969
\(255\) −32497.4 −0.0312967
\(256\) −836524. −0.797772
\(257\) −1.57045e6 −1.48317 −0.741585 0.670859i \(-0.765926\pi\)
−0.741585 + 0.670859i \(0.765926\pi\)
\(258\) −424955. −0.397460
\(259\) 169547. 0.157051
\(260\) −85672.7 −0.0785976
\(261\) −238443. −0.216662
\(262\) 1.61596e6 1.45438
\(263\) 1.39983e6 1.24792 0.623959 0.781457i \(-0.285523\pi\)
0.623959 + 0.781457i \(0.285523\pi\)
\(264\) −986198. −0.870872
\(265\) −156526. −0.136922
\(266\) 185224. 0.160507
\(267\) 59630.7 0.0511908
\(268\) −346158. −0.294400
\(269\) −1.66101e6 −1.39956 −0.699780 0.714358i \(-0.746719\pi\)
−0.699780 + 0.714358i \(0.746719\pi\)
\(270\) −27966.3 −0.0233467
\(271\) −2.02912e6 −1.67836 −0.839178 0.543856i \(-0.816964\pi\)
−0.839178 + 0.543856i \(0.816964\pi\)
\(272\) −284060. −0.232802
\(273\) 293334. 0.238208
\(274\) 320202. 0.257660
\(275\) −1.70361e6 −1.35844
\(276\) 377885. 0.298598
\(277\) −1.82153e6 −1.42638 −0.713191 0.700970i \(-0.752751\pi\)
−0.713191 + 0.700970i \(0.752751\pi\)
\(278\) 1.46621e6 1.13785
\(279\) 90214.1 0.0693847
\(280\) −45833.0 −0.0349368
\(281\) −1.98485e6 −1.49955 −0.749777 0.661691i \(-0.769839\pi\)
−0.749777 + 0.661691i \(0.769839\pi\)
\(282\) 1.07357e6 0.803912
\(283\) 2.17263e6 1.61258 0.806289 0.591522i \(-0.201473\pi\)
0.806289 + 0.591522i \(0.201473\pi\)
\(284\) −227248. −0.167188
\(285\) 98056.3 0.0715094
\(286\) −2.98932e6 −2.16101
\(287\) 18432.6 0.0132093
\(288\) 265686. 0.188751
\(289\) −1.21964e6 −0.858988
\(290\) 112930. 0.0788521
\(291\) 794828. 0.550225
\(292\) 735365. 0.504714
\(293\) −1.73848e6 −1.18305 −0.591523 0.806288i \(-0.701473\pi\)
−0.591523 + 0.806288i \(0.701473\pi\)
\(294\) −683463. −0.461154
\(295\) −28090.5 −0.0187934
\(296\) 1.15632e6 0.767094
\(297\) 405877. 0.266995
\(298\) 1.83532e6 1.19721
\(299\) 5.04470e6 3.26330
\(300\) 258870. 0.166065
\(301\) 286626. 0.182347
\(302\) 1.71936e6 1.08480
\(303\) −1.10746e6 −0.692980
\(304\) 857110. 0.531928
\(305\) −63062.1 −0.0388167
\(306\) 172301. 0.105193
\(307\) 1.20069e6 0.727082 0.363541 0.931578i \(-0.381568\pi\)
0.363541 + 0.931578i \(0.381568\pi\)
\(308\) 151032. 0.0907178
\(309\) 785404. 0.467947
\(310\) −42726.5 −0.0252519
\(311\) 1.20148e6 0.704395 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(312\) 2.00055e6 1.16349
\(313\) −1.09781e6 −0.633385 −0.316693 0.948528i \(-0.602572\pi\)
−0.316693 + 0.948528i \(0.602572\pi\)
\(314\) −597619. −0.342058
\(315\) 18862.9 0.0107110
\(316\) −39531.0 −0.0222700
\(317\) 36761.0 0.0205466 0.0102733 0.999947i \(-0.496730\pi\)
0.0102733 + 0.999947i \(0.496730\pi\)
\(318\) 829902. 0.460213
\(319\) −1.63895e6 −0.901758
\(320\) −289765. −0.158187
\(321\) −22782.6 −0.0123407
\(322\) 612778. 0.329354
\(323\) −604127. −0.322197
\(324\) −61674.4 −0.0326394
\(325\) 3.45587e6 1.81488
\(326\) 1.48415e6 0.773454
\(327\) −1.42876e6 −0.738910
\(328\) 125711. 0.0645191
\(329\) −724108. −0.368819
\(330\) −192228. −0.0971701
\(331\) 2.44095e6 1.22459 0.612293 0.790631i \(-0.290247\pi\)
0.612293 + 0.790631i \(0.290247\pi\)
\(332\) 346921. 0.172737
\(333\) −475892. −0.235179
\(334\) −3.31007e6 −1.62357
\(335\) −297163. −0.144671
\(336\) 164881. 0.0796748
\(337\) −532207. −0.255274 −0.127637 0.991821i \(-0.540739\pi\)
−0.127637 + 0.991821i \(0.540739\pi\)
\(338\) 4.29888e6 2.04675
\(339\) −407289. −0.192488
\(340\) 33942.3 0.0159237
\(341\) 620092. 0.288782
\(342\) −519895. −0.240353
\(343\) 946003. 0.434168
\(344\) 1.95480e6 0.890648
\(345\) 324400. 0.146735
\(346\) −2.22222e6 −0.997923
\(347\) −3.36260e6 −1.49917 −0.749587 0.661906i \(-0.769748\pi\)
−0.749587 + 0.661906i \(0.769748\pi\)
\(348\) 249045. 0.110237
\(349\) 3.19465e6 1.40398 0.701989 0.712188i \(-0.252296\pi\)
0.701989 + 0.712188i \(0.252296\pi\)
\(350\) 419783. 0.183170
\(351\) −823342. −0.356708
\(352\) 1.82621e6 0.785587
\(353\) 3.86212e6 1.64964 0.824821 0.565394i \(-0.191276\pi\)
0.824821 + 0.565394i \(0.191276\pi\)
\(354\) 148936. 0.0631671
\(355\) −195084. −0.0821580
\(356\) −62281.9 −0.0260458
\(357\) −116215. −0.0482603
\(358\) −974936. −0.402039
\(359\) 3.20790e6 1.31367 0.656833 0.754036i \(-0.271896\pi\)
0.656833 + 0.754036i \(0.271896\pi\)
\(360\) 128646. 0.0523165
\(361\) −653232. −0.263815
\(362\) 878819. 0.352475
\(363\) 1.34036e6 0.533894
\(364\) −306376. −0.121200
\(365\) 631282. 0.248023
\(366\) 334355. 0.130468
\(367\) −3.71516e6 −1.43983 −0.719917 0.694060i \(-0.755820\pi\)
−0.719917 + 0.694060i \(0.755820\pi\)
\(368\) 2.83558e6 1.09150
\(369\) −51737.3 −0.0197805
\(370\) 225388. 0.0855908
\(371\) −559756. −0.211137
\(372\) −94225.1 −0.0353028
\(373\) −106590. −0.0396684 −0.0198342 0.999803i \(-0.506314\pi\)
−0.0198342 + 0.999803i \(0.506314\pi\)
\(374\) 1.18432e6 0.437815
\(375\) 449189. 0.164950
\(376\) −4.93845e6 −1.80144
\(377\) 3.32470e6 1.20476
\(378\) −100011. −0.0360013
\(379\) 2.90777e6 1.03983 0.519914 0.854219i \(-0.325964\pi\)
0.519914 + 0.854219i \(0.325964\pi\)
\(380\) −102416. −0.0363838
\(381\) −541090. −0.190966
\(382\) −1.29537e6 −0.454188
\(383\) 4.43725e6 1.54567 0.772835 0.634608i \(-0.218838\pi\)
0.772835 + 0.634608i \(0.218838\pi\)
\(384\) 591670. 0.204763
\(385\) 129655. 0.0445798
\(386\) −1.28564e6 −0.439190
\(387\) −804512. −0.273058
\(388\) −830167. −0.279954
\(389\) −2.41971e6 −0.810755 −0.405378 0.914149i \(-0.632860\pi\)
−0.405378 + 0.914149i \(0.632860\pi\)
\(390\) 389945. 0.129820
\(391\) −1.99863e6 −0.661137
\(392\) 3.14394e6 1.03338
\(393\) 3.05929e6 0.999170
\(394\) −3.36330e6 −1.09150
\(395\) −33935.8 −0.0109437
\(396\) −423922. −0.135847
\(397\) −435661. −0.138731 −0.0693654 0.997591i \(-0.522097\pi\)
−0.0693654 + 0.997591i \(0.522097\pi\)
\(398\) −4.88286e6 −1.54514
\(399\) 350661. 0.110270
\(400\) 1.94251e6 0.607035
\(401\) 2.31919e6 0.720237 0.360119 0.932906i \(-0.382736\pi\)
0.360119 + 0.932906i \(0.382736\pi\)
\(402\) 1.57556e6 0.486261
\(403\) −1.25789e6 −0.385815
\(404\) 1.15670e6 0.352587
\(405\) −52945.1 −0.0160394
\(406\) 403850. 0.121592
\(407\) −3.27107e6 −0.978823
\(408\) −792588. −0.235720
\(409\) −293179. −0.0866612 −0.0433306 0.999061i \(-0.513797\pi\)
−0.0433306 + 0.999061i \(0.513797\pi\)
\(410\) 24503.4 0.00719891
\(411\) 606197. 0.177015
\(412\) −820324. −0.238091
\(413\) −100455. −0.0289799
\(414\) −1.71997e6 −0.493196
\(415\) 297818. 0.0848851
\(416\) −3.70456e6 −1.04955
\(417\) 2.77579e6 0.781713
\(418\) −3.57353e6 −1.00036
\(419\) 989556. 0.275363 0.137681 0.990477i \(-0.456035\pi\)
0.137681 + 0.990477i \(0.456035\pi\)
\(420\) −19701.5 −0.00544976
\(421\) −1.03799e6 −0.285421 −0.142711 0.989764i \(-0.545582\pi\)
−0.142711 + 0.989764i \(0.545582\pi\)
\(422\) −3.83532e6 −1.04838
\(423\) 2.03245e6 0.552293
\(424\) −3.81756e6 −1.03127
\(425\) −1.36916e6 −0.367691
\(426\) 1.03433e6 0.276145
\(427\) −225518. −0.0598564
\(428\) 23795.6 0.00627895
\(429\) −5.65929e6 −1.48463
\(430\) 381027. 0.0993767
\(431\) −6.08956e6 −1.57904 −0.789519 0.613726i \(-0.789670\pi\)
−0.789519 + 0.613726i \(0.789670\pi\)
\(432\) −462793. −0.119310
\(433\) 679052. 0.174054 0.0870269 0.996206i \(-0.472263\pi\)
0.0870269 + 0.996206i \(0.472263\pi\)
\(434\) −152795. −0.0389391
\(435\) 213795. 0.0541720
\(436\) 1.49229e6 0.375956
\(437\) 6.03059e6 1.51062
\(438\) −3.34706e6 −0.833639
\(439\) −6.18297e6 −1.53121 −0.765606 0.643309i \(-0.777561\pi\)
−0.765606 + 0.643309i \(0.777561\pi\)
\(440\) 884254. 0.217743
\(441\) −1.29391e6 −0.316817
\(442\) −2.40246e6 −0.584925
\(443\) 226949. 0.0549437 0.0274719 0.999623i \(-0.491254\pi\)
0.0274719 + 0.999623i \(0.491254\pi\)
\(444\) 497051. 0.119658
\(445\) −53466.6 −0.0127992
\(446\) −1.60297e6 −0.381583
\(447\) 3.47458e6 0.822496
\(448\) −1.03623e6 −0.243929
\(449\) −418434. −0.0979515 −0.0489758 0.998800i \(-0.515596\pi\)
−0.0489758 + 0.998800i \(0.515596\pi\)
\(450\) −1.17826e6 −0.274291
\(451\) −355619. −0.0823273
\(452\) 425397. 0.0979374
\(453\) 3.25504e6 0.745265
\(454\) −1.23516e6 −0.281244
\(455\) −263012. −0.0595590
\(456\) 2.39152e6 0.538595
\(457\) 6.90035e6 1.54554 0.772770 0.634686i \(-0.218871\pi\)
0.772770 + 0.634686i \(0.218871\pi\)
\(458\) 1.08091e6 0.240782
\(459\) 326196. 0.0722681
\(460\) −338823. −0.0746583
\(461\) 373717. 0.0819013 0.0409507 0.999161i \(-0.486961\pi\)
0.0409507 + 0.999161i \(0.486961\pi\)
\(462\) −687432. −0.149839
\(463\) −5.19758e6 −1.12680 −0.563402 0.826183i \(-0.690508\pi\)
−0.563402 + 0.826183i \(0.690508\pi\)
\(464\) 1.86878e6 0.402962
\(465\) −80888.6 −0.0173482
\(466\) 1.26083e6 0.268963
\(467\) −6.54913e6 −1.38961 −0.694803 0.719200i \(-0.744508\pi\)
−0.694803 + 0.719200i \(0.744508\pi\)
\(468\) 859948. 0.181492
\(469\) −1.06269e6 −0.223087
\(470\) −962596. −0.201001
\(471\) −1.13139e6 −0.234997
\(472\) −685107. −0.141548
\(473\) −5.52986e6 −1.13648
\(474\) 179928. 0.0367834
\(475\) 4.13125e6 0.840133
\(476\) 121382. 0.0245548
\(477\) 1.57115e6 0.316170
\(478\) −1.16818e6 −0.233852
\(479\) −2.70999e6 −0.539671 −0.269836 0.962906i \(-0.586969\pi\)
−0.269836 + 0.962906i \(0.586969\pi\)
\(480\) −238222. −0.0471932
\(481\) 6.63554e6 1.30772
\(482\) 5.88066e6 1.15294
\(483\) 1.16009e6 0.226269
\(484\) −1.39995e6 −0.271644
\(485\) −712666. −0.137572
\(486\) 280715. 0.0539107
\(487\) −3.13993e6 −0.599925 −0.299963 0.953951i \(-0.596974\pi\)
−0.299963 + 0.953951i \(0.596974\pi\)
\(488\) −1.53804e6 −0.292360
\(489\) 2.80975e6 0.531369
\(490\) 612812. 0.115302
\(491\) −51374.3 −0.00961705 −0.00480853 0.999988i \(-0.501531\pi\)
−0.00480853 + 0.999988i \(0.501531\pi\)
\(492\) 54037.5 0.0100643
\(493\) −1.31720e6 −0.244081
\(494\) 7.24908e6 1.33649
\(495\) −363921. −0.0667566
\(496\) −707048. −0.129046
\(497\) −697643. −0.126690
\(498\) −1.57903e6 −0.285311
\(499\) 4.49962e6 0.808955 0.404477 0.914548i \(-0.367453\pi\)
0.404477 + 0.914548i \(0.367453\pi\)
\(500\) −469160. −0.0839260
\(501\) −6.26653e6 −1.11541
\(502\) −1.95942e6 −0.347031
\(503\) 1.70528e6 0.300521 0.150260 0.988646i \(-0.451989\pi\)
0.150260 + 0.988646i \(0.451989\pi\)
\(504\) 460053. 0.0806735
\(505\) 992979. 0.173265
\(506\) −1.18223e7 −2.05270
\(507\) 8.13852e6 1.40613
\(508\) 565147. 0.0971634
\(509\) 616751. 0.105515 0.0527576 0.998607i \(-0.483199\pi\)
0.0527576 + 0.998607i \(0.483199\pi\)
\(510\) −154490. −0.0263012
\(511\) 2.25754e6 0.382458
\(512\) −6.08049e6 −1.02509
\(513\) −984249. −0.165125
\(514\) −7.46580e6 −1.24643
\(515\) −704216. −0.117001
\(516\) 840282. 0.138931
\(517\) 1.39702e7 2.29867
\(518\) 806017. 0.131983
\(519\) −4.20704e6 −0.685581
\(520\) −1.79375e6 −0.290907
\(521\) 1.06106e7 1.71255 0.856277 0.516517i \(-0.172772\pi\)
0.856277 + 0.516517i \(0.172772\pi\)
\(522\) −1.13354e6 −0.182080
\(523\) −8.38687e6 −1.34074 −0.670371 0.742026i \(-0.733865\pi\)
−0.670371 + 0.742026i \(0.733865\pi\)
\(524\) −3.19531e6 −0.508376
\(525\) 794721. 0.125839
\(526\) 6.65470e6 1.04873
\(527\) 498356. 0.0781652
\(528\) −3.18103e6 −0.496574
\(529\) 1.35147e7 2.09974
\(530\) −744114. −0.115067
\(531\) 281961. 0.0433963
\(532\) −366252. −0.0561049
\(533\) 721391. 0.109990
\(534\) 283480. 0.0430199
\(535\) 20427.6 0.00308555
\(536\) −7.24760e6 −1.08964
\(537\) −1.84572e6 −0.276204
\(538\) −7.89633e6 −1.17617
\(539\) −8.89377e6 −1.31860
\(540\) 55299.0 0.00816081
\(541\) −3.78138e6 −0.555465 −0.277733 0.960658i \(-0.589583\pi\)
−0.277733 + 0.960658i \(0.589583\pi\)
\(542\) −9.64629e6 −1.41046
\(543\) 1.66376e6 0.242153
\(544\) 1.46769e6 0.212636
\(545\) 1.28107e6 0.184749
\(546\) 1.39449e6 0.200186
\(547\) −3.06265e6 −0.437652 −0.218826 0.975764i \(-0.570223\pi\)
−0.218826 + 0.975764i \(0.570223\pi\)
\(548\) −633149. −0.0900647
\(549\) 632992. 0.0896328
\(550\) −8.09886e6 −1.14161
\(551\) 3.97445e6 0.557697
\(552\) 7.91188e6 1.10518
\(553\) −121359. −0.0168755
\(554\) −8.65941e6 −1.19871
\(555\) 426699. 0.0588016
\(556\) −2.89921e6 −0.397734
\(557\) 2.10567e6 0.287576 0.143788 0.989608i \(-0.454072\pi\)
0.143788 + 0.989608i \(0.454072\pi\)
\(558\) 428872. 0.0583098
\(559\) 1.12176e7 1.51835
\(560\) −147837. −0.0199210
\(561\) 2.24212e6 0.300783
\(562\) −9.43584e6 −1.26020
\(563\) −3.85100e6 −0.512039 −0.256019 0.966672i \(-0.582411\pi\)
−0.256019 + 0.966672i \(0.582411\pi\)
\(564\) −2.12282e6 −0.281006
\(565\) 365187. 0.0481276
\(566\) 1.03286e7 1.35518
\(567\) −189338. −0.0247332
\(568\) −4.75795e6 −0.618799
\(569\) 7.28749e6 0.943621 0.471810 0.881700i \(-0.343601\pi\)
0.471810 + 0.881700i \(0.343601\pi\)
\(570\) 466153. 0.0600954
\(571\) 9.75125e6 1.25161 0.625807 0.779978i \(-0.284770\pi\)
0.625807 + 0.779978i \(0.284770\pi\)
\(572\) 5.91091e6 0.755377
\(573\) −2.45236e6 −0.312031
\(574\) 87627.2 0.0111009
\(575\) 1.36674e7 1.72392
\(576\) 2.90854e6 0.365274
\(577\) −3.33348e6 −0.416829 −0.208415 0.978041i \(-0.566830\pi\)
−0.208415 + 0.978041i \(0.566830\pi\)
\(578\) −5.79808e6 −0.721880
\(579\) −2.43394e6 −0.301727
\(580\) −223301. −0.0275626
\(581\) 1.06504e6 0.130895
\(582\) 3.77856e6 0.462401
\(583\) 1.07994e7 1.31591
\(584\) 1.53965e7 1.86806
\(585\) 738232. 0.0891874
\(586\) −8.26464e6 −0.994214
\(587\) 1.65752e6 0.198548 0.0992738 0.995060i \(-0.468348\pi\)
0.0992738 + 0.995060i \(0.468348\pi\)
\(588\) 1.35144e6 0.161196
\(589\) −1.50372e6 −0.178599
\(590\) −133540. −0.0157936
\(591\) −6.36730e6 −0.749872
\(592\) 3.72977e6 0.437400
\(593\) −1.21542e7 −1.41935 −0.709677 0.704527i \(-0.751159\pi\)
−0.709677 + 0.704527i \(0.751159\pi\)
\(594\) 1.92951e6 0.224378
\(595\) 104201. 0.0120665
\(596\) −3.62906e6 −0.418484
\(597\) −9.24409e6 −1.06152
\(598\) 2.39821e7 2.74243
\(599\) 6.59980e6 0.751560 0.375780 0.926709i \(-0.377375\pi\)
0.375780 + 0.926709i \(0.377375\pi\)
\(600\) 5.42003e6 0.614644
\(601\) −2.88369e6 −0.325658 −0.162829 0.986654i \(-0.552062\pi\)
−0.162829 + 0.986654i \(0.552062\pi\)
\(602\) 1.36260e6 0.153242
\(603\) 2.98280e6 0.334065
\(604\) −3.39976e6 −0.379189
\(605\) −1.20181e6 −0.133489
\(606\) −5.26478e6 −0.582369
\(607\) −1.26616e7 −1.39482 −0.697410 0.716673i \(-0.745664\pi\)
−0.697410 + 0.716673i \(0.745664\pi\)
\(608\) −4.42855e6 −0.485851
\(609\) 764557. 0.0835347
\(610\) −299793. −0.0326209
\(611\) −2.83393e7 −3.07104
\(612\) −340699. −0.0367698
\(613\) 2.13203e6 0.229162 0.114581 0.993414i \(-0.463447\pi\)
0.114581 + 0.993414i \(0.463447\pi\)
\(614\) 5.70798e6 0.611028
\(615\) 46389.1 0.00494571
\(616\) 3.16220e6 0.335767
\(617\) 1.12243e7 1.18698 0.593492 0.804840i \(-0.297749\pi\)
0.593492 + 0.804840i \(0.297749\pi\)
\(618\) 3.73376e6 0.393255
\(619\) −1.62425e7 −1.70383 −0.851916 0.523679i \(-0.824559\pi\)
−0.851916 + 0.523679i \(0.824559\pi\)
\(620\) 84485.0 0.00882674
\(621\) −3.25619e6 −0.338829
\(622\) 5.71176e6 0.591962
\(623\) −191203. −0.0197367
\(624\) 6.45289e6 0.663426
\(625\) 9.15937e6 0.937920
\(626\) −5.21893e6 −0.532287
\(627\) −6.76530e6 −0.687255
\(628\) 1.18170e6 0.119566
\(629\) −2.62890e6 −0.264940
\(630\) 89672.8 0.00900139
\(631\) 1.11288e7 1.11270 0.556348 0.830950i \(-0.312202\pi\)
0.556348 + 0.830950i \(0.312202\pi\)
\(632\) −827670. −0.0824261
\(633\) −7.26092e6 −0.720248
\(634\) 174759. 0.0172670
\(635\) 485157. 0.0477472
\(636\) −1.64100e6 −0.160867
\(637\) 1.80415e7 1.76167
\(638\) −7.79147e6 −0.757823
\(639\) 1.95817e6 0.189714
\(640\) −530509. −0.0511968
\(641\) 2.41239e6 0.231901 0.115950 0.993255i \(-0.463009\pi\)
0.115950 + 0.993255i \(0.463009\pi\)
\(642\) −108307. −0.0103710
\(643\) 7.10405e6 0.677608 0.338804 0.940857i \(-0.389978\pi\)
0.338804 + 0.940857i \(0.389978\pi\)
\(644\) −1.21167e6 −0.115125
\(645\) 721349. 0.0682726
\(646\) −2.87198e6 −0.270769
\(647\) −4.34524e6 −0.408088 −0.204044 0.978962i \(-0.565409\pi\)
−0.204044 + 0.978962i \(0.565409\pi\)
\(648\) −1.29129e6 −0.120806
\(649\) 1.93808e6 0.180617
\(650\) 1.64290e7 1.52520
\(651\) −289268. −0.0267514
\(652\) −2.93468e6 −0.270359
\(653\) −1.74836e7 −1.60453 −0.802263 0.596971i \(-0.796371\pi\)
−0.802263 + 0.596971i \(0.796371\pi\)
\(654\) −6.79225e6 −0.620968
\(655\) −2.74305e6 −0.249822
\(656\) 405488. 0.0367890
\(657\) −6.33655e6 −0.572716
\(658\) −3.44236e6 −0.309950
\(659\) −1.73557e7 −1.55678 −0.778392 0.627779i \(-0.783964\pi\)
−0.778392 + 0.627779i \(0.783964\pi\)
\(660\) 380101. 0.0339656
\(661\) 5.32811e6 0.474318 0.237159 0.971471i \(-0.423784\pi\)
0.237159 + 0.971471i \(0.423784\pi\)
\(662\) 1.16041e7 1.02912
\(663\) −4.54826e6 −0.401848
\(664\) 7.26358e6 0.639338
\(665\) −314413. −0.0275706
\(666\) −2.26236e6 −0.197640
\(667\) 1.31487e7 1.14437
\(668\) 6.54514e6 0.567516
\(669\) −3.03470e6 −0.262150
\(670\) −1.41269e6 −0.121580
\(671\) 4.35091e6 0.373055
\(672\) −851912. −0.0727732
\(673\) 9.87967e6 0.840823 0.420412 0.907333i \(-0.361886\pi\)
0.420412 + 0.907333i \(0.361886\pi\)
\(674\) −2.53008e6 −0.214528
\(675\) −2.23065e6 −0.188440
\(676\) −8.50036e6 −0.715436
\(677\) 1.67635e7 1.40570 0.702849 0.711339i \(-0.251911\pi\)
0.702849 + 0.711339i \(0.251911\pi\)
\(678\) −1.93622e6 −0.161764
\(679\) −2.54858e6 −0.212141
\(680\) 710658. 0.0589370
\(681\) −2.33837e6 −0.193217
\(682\) 2.94787e6 0.242688
\(683\) 4.71929e6 0.387102 0.193551 0.981090i \(-0.438000\pi\)
0.193551 + 0.981090i \(0.438000\pi\)
\(684\) 1.02801e6 0.0840150
\(685\) −543534. −0.0442589
\(686\) 4.49723e6 0.364868
\(687\) 2.04634e6 0.165419
\(688\) 6.30532e6 0.507850
\(689\) −2.19071e7 −1.75807
\(690\) 1.54217e6 0.123313
\(691\) −1.44431e7 −1.15071 −0.575353 0.817905i \(-0.695135\pi\)
−0.575353 + 0.817905i \(0.695135\pi\)
\(692\) 4.39409e6 0.348822
\(693\) −1.30143e6 −0.102941
\(694\) −1.59856e7 −1.25988
\(695\) −2.48886e6 −0.195451
\(696\) 5.21431e6 0.408013
\(697\) −285804. −0.0222837
\(698\) 1.51872e7 1.17988
\(699\) 2.38697e6 0.184780
\(700\) −830055. −0.0640268
\(701\) −40301.8 −0.00309763 −0.00154881 0.999999i \(-0.500493\pi\)
−0.00154881 + 0.999999i \(0.500493\pi\)
\(702\) −3.91411e6 −0.299771
\(703\) 7.93233e6 0.605358
\(704\) 1.99920e7 1.52029
\(705\) −1.82236e6 −0.138090
\(706\) 1.83603e7 1.38633
\(707\) 3.55102e6 0.267180
\(708\) −294497. −0.0220800
\(709\) 2.32913e7 1.74011 0.870056 0.492953i \(-0.164082\pi\)
0.870056 + 0.492953i \(0.164082\pi\)
\(710\) −927414. −0.0690443
\(711\) 340634. 0.0252705
\(712\) −1.30401e6 −0.0964011
\(713\) −4.97476e6 −0.366478
\(714\) −552476. −0.0405572
\(715\) 5.07428e6 0.371201
\(716\) 1.92778e6 0.140532
\(717\) −2.21157e6 −0.160658
\(718\) 1.52501e7 1.10398
\(719\) 2.22695e7 1.60653 0.803265 0.595622i \(-0.203094\pi\)
0.803265 + 0.595622i \(0.203094\pi\)
\(720\) 414954. 0.0298310
\(721\) −2.51836e6 −0.180418
\(722\) −3.10542e6 −0.221706
\(723\) 1.11331e7 0.792082
\(724\) −1.73773e6 −0.123207
\(725\) 9.00750e6 0.636443
\(726\) 6.37198e6 0.448676
\(727\) −2.97421e6 −0.208706 −0.104353 0.994540i \(-0.533277\pi\)
−0.104353 + 0.994540i \(0.533277\pi\)
\(728\) −6.41468e6 −0.448587
\(729\) 531441. 0.0370370
\(730\) 3.00107e6 0.208434
\(731\) −4.44425e6 −0.307613
\(732\) −661135. −0.0456050
\(733\) 6.38381e6 0.438854 0.219427 0.975629i \(-0.429581\pi\)
0.219427 + 0.975629i \(0.429581\pi\)
\(734\) −1.76616e7 −1.21001
\(735\) 1.16016e6 0.0792135
\(736\) −1.46510e7 −0.996948
\(737\) 2.05025e7 1.39039
\(738\) −245955. −0.0166232
\(739\) −2.18800e7 −1.47379 −0.736897 0.676005i \(-0.763710\pi\)
−0.736897 + 0.676005i \(0.763710\pi\)
\(740\) −445670. −0.0299181
\(741\) 1.37237e7 0.918178
\(742\) −2.66104e6 −0.177436
\(743\) −1.15290e7 −0.766157 −0.383079 0.923716i \(-0.625136\pi\)
−0.383079 + 0.923716i \(0.625136\pi\)
\(744\) −1.97282e6 −0.130664
\(745\) −3.11541e6 −0.205648
\(746\) −506722. −0.0333367
\(747\) −2.98938e6 −0.196011
\(748\) −2.34181e6 −0.153038
\(749\) 73051.5 0.00475800
\(750\) 2.13541e6 0.138621
\(751\) −1.87579e6 −0.121363 −0.0606813 0.998157i \(-0.519327\pi\)
−0.0606813 + 0.998157i \(0.519327\pi\)
\(752\) −1.59292e7 −1.02719
\(753\) −3.70951e6 −0.238413
\(754\) 1.58054e7 1.01246
\(755\) −2.91856e6 −0.186338
\(756\) 197756. 0.0125842
\(757\) −1.76953e7 −1.12232 −0.561161 0.827707i \(-0.689645\pi\)
−0.561161 + 0.827707i \(0.689645\pi\)
\(758\) 1.38233e7 0.873855
\(759\) −2.23816e7 −1.41022
\(760\) −2.14431e6 −0.134665
\(761\) 8.98396e6 0.562349 0.281175 0.959657i \(-0.409276\pi\)
0.281175 + 0.959657i \(0.409276\pi\)
\(762\) −2.57230e6 −0.160485
\(763\) 4.58127e6 0.284888
\(764\) 2.56139e6 0.158760
\(765\) −292476. −0.0180691
\(766\) 2.10944e7 1.29896
\(767\) −3.93149e6 −0.241306
\(768\) −7.52872e6 −0.460594
\(769\) −1.93851e7 −1.18210 −0.591049 0.806636i \(-0.701286\pi\)
−0.591049 + 0.806636i \(0.701286\pi\)
\(770\) 616372. 0.0374641
\(771\) −1.41340e7 −0.856309
\(772\) 2.54216e6 0.153518
\(773\) 1.11176e7 0.669207 0.334604 0.942359i \(-0.391398\pi\)
0.334604 + 0.942359i \(0.391398\pi\)
\(774\) −3.82460e6 −0.229474
\(775\) −3.40796e6 −0.203817
\(776\) −1.73814e7 −1.03617
\(777\) 1.52593e6 0.0906737
\(778\) −1.15031e7 −0.681346
\(779\) 862374. 0.0509158
\(780\) −771055. −0.0453784
\(781\) 1.34596e7 0.789596
\(782\) −9.50136e6 −0.555609
\(783\) −2.14599e6 −0.125090
\(784\) 1.01409e7 0.589235
\(785\) 1.01444e6 0.0587560
\(786\) 1.45437e7 0.839686
\(787\) 3.09807e7 1.78302 0.891508 0.453006i \(-0.149648\pi\)
0.891508 + 0.453006i \(0.149648\pi\)
\(788\) 6.65040e6 0.381533
\(789\) 1.25985e7 0.720486
\(790\) −161328. −0.00919693
\(791\) 1.30595e6 0.0742141
\(792\) −8.87578e6 −0.502798
\(793\) −8.82603e6 −0.498405
\(794\) −2.07110e6 −0.116587
\(795\) −1.40873e6 −0.0790517
\(796\) 9.65509e6 0.540099
\(797\) 1.87042e6 0.104302 0.0521511 0.998639i \(-0.483392\pi\)
0.0521511 + 0.998639i \(0.483392\pi\)
\(798\) 1.66702e6 0.0926688
\(799\) 1.12276e7 0.622185
\(800\) −1.00367e7 −0.554452
\(801\) 536676. 0.0295550
\(802\) 1.10253e7 0.605276
\(803\) −4.35547e7 −2.38367
\(804\) −3.11542e6 −0.169972
\(805\) −1.04017e6 −0.0565739
\(806\) −5.97991e6 −0.324233
\(807\) −1.49491e7 −0.808037
\(808\) 2.42181e7 1.30500
\(809\) 2.51924e7 1.35331 0.676656 0.736299i \(-0.263428\pi\)
0.676656 + 0.736299i \(0.263428\pi\)
\(810\) −251697. −0.0134792
\(811\) −4.70372e6 −0.251125 −0.125562 0.992086i \(-0.540073\pi\)
−0.125562 + 0.992086i \(0.540073\pi\)
\(812\) −798550. −0.0425023
\(813\) −1.82621e7 −0.969000
\(814\) −1.55504e7 −0.822587
\(815\) −2.51931e6 −0.132858
\(816\) −2.55654e6 −0.134409
\(817\) 1.34099e7 0.702862
\(818\) −1.39375e6 −0.0728287
\(819\) 2.64001e6 0.137529
\(820\) −48451.6 −0.00251637
\(821\) −2.56227e6 −0.132668 −0.0663341 0.997797i \(-0.521130\pi\)
−0.0663341 + 0.997797i \(0.521130\pi\)
\(822\) 2.88182e6 0.148760
\(823\) −1.26515e7 −0.651092 −0.325546 0.945526i \(-0.605548\pi\)
−0.325546 + 0.945526i \(0.605548\pi\)
\(824\) −1.71753e7 −0.881226
\(825\) −1.53325e7 −0.784294
\(826\) −477556. −0.0243542
\(827\) 2.53615e7 1.28947 0.644735 0.764406i \(-0.276968\pi\)
0.644735 + 0.764406i \(0.276968\pi\)
\(828\) 3.40097e6 0.172396
\(829\) −3.29273e7 −1.66406 −0.832032 0.554728i \(-0.812822\pi\)
−0.832032 + 0.554728i \(0.812822\pi\)
\(830\) 1.41581e6 0.0713361
\(831\) −1.63937e7 −0.823522
\(832\) −4.05548e7 −2.03111
\(833\) −7.14776e6 −0.356909
\(834\) 1.31959e7 0.656939
\(835\) 5.61875e6 0.278884
\(836\) 7.06609e6 0.349674
\(837\) 811927. 0.0400593
\(838\) 4.70428e6 0.231411
\(839\) 7.45341e6 0.365553 0.182776 0.983155i \(-0.441492\pi\)
0.182776 + 0.983155i \(0.441492\pi\)
\(840\) −412497. −0.0201708
\(841\) −1.18455e7 −0.577516
\(842\) −4.93451e6 −0.239863
\(843\) −1.78637e7 −0.865768
\(844\) 7.58375e6 0.366461
\(845\) −7.29723e6 −0.351574
\(846\) 9.66214e6 0.464139
\(847\) −4.29780e6 −0.205844
\(848\) −1.23138e7 −0.588032
\(849\) 1.95537e7 0.931022
\(850\) −6.50890e6 −0.309001
\(851\) 2.62425e7 1.24217
\(852\) −2.04523e6 −0.0965259
\(853\) 8.47401e6 0.398764 0.199382 0.979922i \(-0.436106\pi\)
0.199382 + 0.979922i \(0.436106\pi\)
\(854\) −1.07210e6 −0.0503024
\(855\) 882506. 0.0412860
\(856\) 498214. 0.0232398
\(857\) 400864. 0.0186443 0.00932213 0.999957i \(-0.497033\pi\)
0.00932213 + 0.999957i \(0.497033\pi\)
\(858\) −2.69039e7 −1.24766
\(859\) −3.38025e7 −1.56302 −0.781512 0.623890i \(-0.785551\pi\)
−0.781512 + 0.623890i \(0.785551\pi\)
\(860\) −753421. −0.0347369
\(861\) 165893. 0.00762642
\(862\) −2.89493e7 −1.32700
\(863\) −1.70141e7 −0.777648 −0.388824 0.921312i \(-0.627119\pi\)
−0.388824 + 0.921312i \(0.627119\pi\)
\(864\) 2.39118e6 0.108975
\(865\) 3.77216e6 0.171415
\(866\) 3.22817e6 0.146272
\(867\) −1.09768e7 −0.495937
\(868\) 302129. 0.0136111
\(869\) 2.34137e6 0.105177
\(870\) 1.01637e6 0.0455253
\(871\) −4.15903e7 −1.85758
\(872\) 3.12444e7 1.39149
\(873\) 7.15345e6 0.317673
\(874\) 2.86690e7 1.26950
\(875\) −1.44030e6 −0.0635967
\(876\) 6.61828e6 0.291397
\(877\) 2.44197e7 1.07212 0.536058 0.844181i \(-0.319913\pi\)
0.536058 + 0.844181i \(0.319913\pi\)
\(878\) −2.93934e7 −1.28681
\(879\) −1.56464e7 −0.683032
\(880\) 2.85221e6 0.124158
\(881\) 2.05768e7 0.893180 0.446590 0.894739i \(-0.352638\pi\)
0.446590 + 0.894739i \(0.352638\pi\)
\(882\) −6.15116e6 −0.266248
\(883\) −1.69532e7 −0.731727 −0.365864 0.930668i \(-0.619226\pi\)
−0.365864 + 0.930668i \(0.619226\pi\)
\(884\) 4.75048e6 0.204459
\(885\) −252814. −0.0108503
\(886\) 1.07890e6 0.0461738
\(887\) −2.25912e7 −0.964118 −0.482059 0.876139i \(-0.660111\pi\)
−0.482059 + 0.876139i \(0.660111\pi\)
\(888\) 1.04069e7 0.442882
\(889\) 1.73498e6 0.0736276
\(890\) −254177. −0.0107562
\(891\) 3.65289e6 0.154150
\(892\) 3.16962e6 0.133381
\(893\) −3.38776e7 −1.42162
\(894\) 1.65179e7 0.691212
\(895\) 1.65493e6 0.0690592
\(896\) −1.89716e6 −0.0789469
\(897\) 4.54023e7 1.88407
\(898\) −1.98921e6 −0.0823169
\(899\) −3.27861e6 −0.135298
\(900\) 2.32983e6 0.0958778
\(901\) 8.67924e6 0.356180
\(902\) −1.69059e6 −0.0691865
\(903\) 2.57963e6 0.105278
\(904\) 8.90665e6 0.362488
\(905\) −1.49177e6 −0.0605454
\(906\) 1.54742e7 0.626309
\(907\) −3.60866e6 −0.145656 −0.0728279 0.997345i \(-0.523202\pi\)
−0.0728279 + 0.997345i \(0.523202\pi\)
\(908\) 2.44233e6 0.0983082
\(909\) −9.96712e6 −0.400092
\(910\) −1.25034e6 −0.0500524
\(911\) −3.83128e7 −1.52950 −0.764748 0.644329i \(-0.777137\pi\)
−0.764748 + 0.644329i \(0.777137\pi\)
\(912\) 7.71399e6 0.307109
\(913\) −2.05477e7 −0.815804
\(914\) 3.28038e7 1.29885
\(915\) −567559. −0.0224108
\(916\) −2.13732e6 −0.0841650
\(917\) −9.80948e6 −0.385232
\(918\) 1.55071e6 0.0607329
\(919\) −4.24918e7 −1.65965 −0.829824 0.558026i \(-0.811559\pi\)
−0.829824 + 0.558026i \(0.811559\pi\)
\(920\) −7.09402e6 −0.276327
\(921\) 1.08062e7 0.419781
\(922\) 1.77663e6 0.0688286
\(923\) −2.73035e7 −1.05491
\(924\) 1.35929e6 0.0523759
\(925\) 1.79774e7 0.690834
\(926\) −2.47089e7 −0.946948
\(927\) 7.06864e6 0.270170
\(928\) −9.65571e6 −0.368056
\(929\) −2.93992e7 −1.11762 −0.558812 0.829294i \(-0.688743\pi\)
−0.558812 + 0.829294i \(0.688743\pi\)
\(930\) −384539. −0.0145792
\(931\) 2.15674e7 0.815498
\(932\) −2.49310e6 −0.0940156
\(933\) 1.08133e7 0.406682
\(934\) −3.11341e7 −1.16780
\(935\) −2.01035e6 −0.0752045
\(936\) 1.80050e7 0.671742
\(937\) −8.24040e6 −0.306619 −0.153310 0.988178i \(-0.548993\pi\)
−0.153310 + 0.988178i \(0.548993\pi\)
\(938\) −5.05196e6 −0.187479
\(939\) −9.88032e6 −0.365685
\(940\) 1.90338e6 0.0702597
\(941\) 1.23397e7 0.454286 0.227143 0.973861i \(-0.427062\pi\)
0.227143 + 0.973861i \(0.427062\pi\)
\(942\) −5.37857e6 −0.197487
\(943\) 2.85299e6 0.104477
\(944\) −2.20985e6 −0.0807111
\(945\) 169766. 0.00618402
\(946\) −2.62886e7 −0.955079
\(947\) 2.68109e7 0.971485 0.485743 0.874102i \(-0.338549\pi\)
0.485743 + 0.874102i \(0.338549\pi\)
\(948\) −355779. −0.0128576
\(949\) 8.83529e7 3.18460
\(950\) 1.96397e7 0.706034
\(951\) 330849. 0.0118626
\(952\) 2.54140e6 0.0908826
\(953\) 2.06693e6 0.0737214 0.0368607 0.999320i \(-0.488264\pi\)
0.0368607 + 0.999320i \(0.488264\pi\)
\(954\) 7.46911e6 0.265704
\(955\) 2.19885e6 0.0780168
\(956\) 2.30990e6 0.0817424
\(957\) −1.47506e7 −0.520630
\(958\) −1.28831e7 −0.453531
\(959\) −1.94374e6 −0.0682484
\(960\) −2.60788e6 −0.0913293
\(961\) −2.73887e7 −0.956672
\(962\) 3.15449e7 1.09898
\(963\) −205044. −0.00712493
\(964\) −1.16281e7 −0.403010
\(965\) 2.18234e6 0.0754406
\(966\) 5.51500e6 0.190153
\(967\) 1.24136e6 0.0426904 0.0213452 0.999772i \(-0.493205\pi\)
0.0213452 + 0.999772i \(0.493205\pi\)
\(968\) −2.93112e7 −1.00541
\(969\) −5.43714e6 −0.186021
\(970\) −3.38796e6 −0.115614
\(971\) 2.08971e7 0.711277 0.355639 0.934624i \(-0.384263\pi\)
0.355639 + 0.934624i \(0.384263\pi\)
\(972\) −555069. −0.0188444
\(973\) −8.90046e6 −0.301391
\(974\) −1.49270e7 −0.504167
\(975\) 3.11028e7 1.04782
\(976\) −4.96103e6 −0.166705
\(977\) 4.79889e7 1.60844 0.804220 0.594332i \(-0.202584\pi\)
0.804220 + 0.594332i \(0.202584\pi\)
\(978\) 1.33574e7 0.446554
\(979\) 3.68888e6 0.123009
\(980\) −1.21174e6 −0.0403036
\(981\) −1.28589e7 −0.426610
\(982\) −244230. −0.00808202
\(983\) −5.71930e7 −1.88781 −0.943907 0.330212i \(-0.892880\pi\)
−0.943907 + 0.330212i \(0.892880\pi\)
\(984\) 1.13140e6 0.0372501
\(985\) 5.70911e6 0.187490
\(986\) −6.26186e6 −0.205121
\(987\) −6.51697e6 −0.212938
\(988\) −1.43339e7 −0.467167
\(989\) 4.43639e7 1.44225
\(990\) −1.73006e6 −0.0561012
\(991\) 5.03427e7 1.62837 0.814184 0.580607i \(-0.197185\pi\)
0.814184 + 0.580607i \(0.197185\pi\)
\(992\) 3.65320e6 0.117868
\(993\) 2.19686e7 0.707015
\(994\) −3.31655e6 −0.106468
\(995\) 8.28852e6 0.265411
\(996\) 3.12229e6 0.0997298
\(997\) −2.10591e7 −0.670968 −0.335484 0.942046i \(-0.608900\pi\)
−0.335484 + 0.942046i \(0.608900\pi\)
\(998\) 2.13909e7 0.679833
\(999\) −4.28303e6 −0.135780
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 177.6.a.a.1.8 11
3.2 odd 2 531.6.a.b.1.4 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.6.a.a.1.8 11 1.1 even 1 trivial
531.6.a.b.1.4 11 3.2 odd 2