Properties

Label 177.10.a.a.1.4
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-31.8892 q^{2} +81.0000 q^{3} +504.921 q^{4} -1889.12 q^{5} -2583.03 q^{6} +12272.3 q^{7} +225.735 q^{8} +6561.00 q^{9} +60242.4 q^{10} -17051.0 q^{11} +40898.6 q^{12} +2771.93 q^{13} -391354. q^{14} -153018. q^{15} -265718. q^{16} -307419. q^{17} -209225. q^{18} +334845. q^{19} -953854. q^{20} +994057. q^{21} +543743. q^{22} -829855. q^{23} +18284.6 q^{24} +1.61563e6 q^{25} -88394.6 q^{26} +531441. q^{27} +6.19655e6 q^{28} -1.06708e6 q^{29} +4.87963e6 q^{30} -806611. q^{31} +8.35797e6 q^{32} -1.38113e6 q^{33} +9.80336e6 q^{34} -2.31838e7 q^{35} +3.31279e6 q^{36} -298636. q^{37} -1.06780e7 q^{38} +224526. q^{39} -426440. q^{40} +957358. q^{41} -3.16997e7 q^{42} -1.34324e7 q^{43} -8.60942e6 q^{44} -1.23945e7 q^{45} +2.64634e7 q^{46} +2.47451e6 q^{47} -2.15232e7 q^{48} +1.10256e8 q^{49} -5.15212e7 q^{50} -2.49010e7 q^{51} +1.39961e6 q^{52} -1.59804e7 q^{53} -1.69472e7 q^{54} +3.22113e7 q^{55} +2.77029e6 q^{56} +2.71225e7 q^{57} +3.40285e7 q^{58} +1.21174e7 q^{59} -7.72622e7 q^{60} +4.27262e7 q^{61} +2.57222e7 q^{62} +8.05186e7 q^{63} -1.30481e8 q^{64} -5.23649e6 q^{65} +4.40432e7 q^{66} -1.05151e8 q^{67} -1.55223e8 q^{68} -6.72183e7 q^{69} +7.39313e8 q^{70} -2.00930e6 q^{71} +1.48105e6 q^{72} +4.31697e8 q^{73} +9.52327e6 q^{74} +1.30866e8 q^{75} +1.69071e8 q^{76} -2.09255e8 q^{77} -7.15996e6 q^{78} -3.46731e8 q^{79} +5.01972e8 q^{80} +4.30467e7 q^{81} -3.05294e7 q^{82} +2.37127e8 q^{83} +5.01920e8 q^{84} +5.80750e8 q^{85} +4.28349e8 q^{86} -8.64338e7 q^{87} -3.84902e6 q^{88} +5.27887e8 q^{89} +3.95250e8 q^{90} +3.40180e7 q^{91} -4.19012e8 q^{92} -6.53355e7 q^{93} -7.89103e7 q^{94} -6.32561e8 q^{95} +6.76995e8 q^{96} +9.13439e8 q^{97} -3.51597e9 q^{98} -1.11872e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.8892 −1.40932 −0.704658 0.709547i \(-0.748900\pi\)
−0.704658 + 0.709547i \(0.748900\pi\)
\(3\) 81.0000 0.577350
\(4\) 504.921 0.986174
\(5\) −1889.12 −1.35174 −0.675870 0.737021i \(-0.736232\pi\)
−0.675870 + 0.737021i \(0.736232\pi\)
\(6\) −2583.03 −0.813670
\(7\) 12272.3 1.93190 0.965951 0.258726i \(-0.0833027\pi\)
0.965951 + 0.258726i \(0.0833027\pi\)
\(8\) 225.735 0.0194847
\(9\) 6561.00 0.333333
\(10\) 60242.4 1.90503
\(11\) −17051.0 −0.351142 −0.175571 0.984467i \(-0.556177\pi\)
−0.175571 + 0.984467i \(0.556177\pi\)
\(12\) 40898.6 0.569368
\(13\) 2771.93 0.0269176 0.0134588 0.999909i \(-0.495716\pi\)
0.0134588 + 0.999909i \(0.495716\pi\)
\(14\) −391354. −2.72266
\(15\) −153018. −0.780428
\(16\) −265718. −1.01363
\(17\) −307419. −0.892711 −0.446356 0.894856i \(-0.647278\pi\)
−0.446356 + 0.894856i \(0.647278\pi\)
\(18\) −209225. −0.469772
\(19\) 334845. 0.589458 0.294729 0.955581i \(-0.404771\pi\)
0.294729 + 0.955581i \(0.404771\pi\)
\(20\) −953854. −1.33305
\(21\) 994057. 1.11538
\(22\) 543743. 0.494871
\(23\) −829855. −0.618340 −0.309170 0.951007i \(-0.600051\pi\)
−0.309170 + 0.951007i \(0.600051\pi\)
\(24\) 18284.6 0.0112495
\(25\) 1.61563e6 0.827203
\(26\) −88394.6 −0.0379355
\(27\) 531441. 0.192450
\(28\) 6.19655e6 1.90519
\(29\) −1.06708e6 −0.280161 −0.140081 0.990140i \(-0.544736\pi\)
−0.140081 + 0.990140i \(0.544736\pi\)
\(30\) 4.87963e6 1.09987
\(31\) −806611. −0.156869 −0.0784344 0.996919i \(-0.524992\pi\)
−0.0784344 + 0.996919i \(0.524992\pi\)
\(32\) 8.35797e6 1.40905
\(33\) −1.38113e6 −0.202732
\(34\) 9.80336e6 1.25811
\(35\) −2.31838e7 −2.61143
\(36\) 3.31279e6 0.328725
\(37\) −298636. −0.0261960 −0.0130980 0.999914i \(-0.504169\pi\)
−0.0130980 + 0.999914i \(0.504169\pi\)
\(38\) −1.06780e7 −0.830733
\(39\) 224526. 0.0155409
\(40\) −426440. −0.0263383
\(41\) 957358. 0.0529111 0.0264556 0.999650i \(-0.491578\pi\)
0.0264556 + 0.999650i \(0.491578\pi\)
\(42\) −3.16997e7 −1.57193
\(43\) −1.34324e7 −0.599164 −0.299582 0.954071i \(-0.596847\pi\)
−0.299582 + 0.954071i \(0.596847\pi\)
\(44\) −8.60942e6 −0.346288
\(45\) −1.23945e7 −0.450580
\(46\) 2.64634e7 0.871437
\(47\) 2.47451e6 0.0739690 0.0369845 0.999316i \(-0.488225\pi\)
0.0369845 + 0.999316i \(0.488225\pi\)
\(48\) −2.15232e7 −0.585222
\(49\) 1.10256e8 2.73224
\(50\) −5.15212e7 −1.16579
\(51\) −2.49010e7 −0.515407
\(52\) 1.39961e6 0.0265455
\(53\) −1.59804e7 −0.278193 −0.139097 0.990279i \(-0.544420\pi\)
−0.139097 + 0.990279i \(0.544420\pi\)
\(54\) −1.69472e7 −0.271223
\(55\) 3.22113e7 0.474653
\(56\) 2.77029e6 0.0376426
\(57\) 2.71225e7 0.340324
\(58\) 3.40285e7 0.394836
\(59\) 1.21174e7 0.130189
\(60\) −7.72622e7 −0.769638
\(61\) 4.27262e7 0.395102 0.197551 0.980293i \(-0.436701\pi\)
0.197551 + 0.980293i \(0.436701\pi\)
\(62\) 2.57222e7 0.221078
\(63\) 8.05186e7 0.643967
\(64\) −1.30481e8 −0.972160
\(65\) −5.23649e6 −0.0363857
\(66\) 4.40432e7 0.285714
\(67\) −1.05151e8 −0.637498 −0.318749 0.947839i \(-0.603263\pi\)
−0.318749 + 0.947839i \(0.603263\pi\)
\(68\) −1.55223e8 −0.880369
\(69\) −6.72183e7 −0.356999
\(70\) 7.39313e8 3.68033
\(71\) −2.00930e6 −0.00938386 −0.00469193 0.999989i \(-0.501493\pi\)
−0.00469193 + 0.999989i \(0.501493\pi\)
\(72\) 1.48105e6 0.00649491
\(73\) 4.31697e8 1.77921 0.889603 0.456734i \(-0.150981\pi\)
0.889603 + 0.456734i \(0.150981\pi\)
\(74\) 9.52327e6 0.0369185
\(75\) 1.30866e8 0.477586
\(76\) 1.69071e8 0.581309
\(77\) −2.09255e8 −0.678372
\(78\) −7.15996e6 −0.0219021
\(79\) −3.46731e8 −1.00154 −0.500772 0.865579i \(-0.666951\pi\)
−0.500772 + 0.865579i \(0.666951\pi\)
\(80\) 5.01972e8 1.37017
\(81\) 4.30467e7 0.111111
\(82\) −3.05294e7 −0.0745686
\(83\) 2.37127e8 0.548440 0.274220 0.961667i \(-0.411580\pi\)
0.274220 + 0.961667i \(0.411580\pi\)
\(84\) 5.01920e8 1.09996
\(85\) 5.80750e8 1.20671
\(86\) 4.28349e8 0.844412
\(87\) −8.64338e7 −0.161751
\(88\) −3.84902e6 −0.00684192
\(89\) 5.27887e8 0.891837 0.445919 0.895073i \(-0.352877\pi\)
0.445919 + 0.895073i \(0.352877\pi\)
\(90\) 3.95250e8 0.635010
\(91\) 3.40180e7 0.0520022
\(92\) −4.19012e8 −0.609791
\(93\) −6.53355e7 −0.0905683
\(94\) −7.89103e7 −0.104246
\(95\) −6.32561e8 −0.796795
\(96\) 6.76995e8 0.813514
\(97\) 9.13439e8 1.04763 0.523814 0.851833i \(-0.324509\pi\)
0.523814 + 0.851833i \(0.324509\pi\)
\(98\) −3.51597e9 −3.85060
\(99\) −1.11872e8 −0.117047
\(100\) 8.15766e8 0.815766
\(101\) −1.51441e9 −1.44810 −0.724050 0.689748i \(-0.757721\pi\)
−0.724050 + 0.689748i \(0.757721\pi\)
\(102\) 7.94072e8 0.726372
\(103\) −1.02106e9 −0.893892 −0.446946 0.894561i \(-0.647488\pi\)
−0.446946 + 0.894561i \(0.647488\pi\)
\(104\) 625722. 0.000524483 0
\(105\) −1.87789e9 −1.50771
\(106\) 5.09602e8 0.392062
\(107\) 8.43566e8 0.622146 0.311073 0.950386i \(-0.399312\pi\)
0.311073 + 0.950386i \(0.399312\pi\)
\(108\) 2.68336e8 0.189789
\(109\) −2.50291e9 −1.69834 −0.849172 0.528117i \(-0.822898\pi\)
−0.849172 + 0.528117i \(0.822898\pi\)
\(110\) −1.02719e9 −0.668937
\(111\) −2.41895e7 −0.0151243
\(112\) −3.26097e9 −1.95824
\(113\) −1.87981e9 −1.08458 −0.542288 0.840192i \(-0.682442\pi\)
−0.542288 + 0.840192i \(0.682442\pi\)
\(114\) −8.64914e8 −0.479624
\(115\) 1.56769e9 0.835835
\(116\) −5.38794e8 −0.276288
\(117\) 1.81866e7 0.00897255
\(118\) −3.86413e8 −0.183477
\(119\) −3.77274e9 −1.72463
\(120\) −3.45416e7 −0.0152064
\(121\) −2.06721e9 −0.876699
\(122\) −1.36250e9 −0.556824
\(123\) 7.75460e7 0.0305483
\(124\) −4.07275e8 −0.154700
\(125\) 6.37566e8 0.233577
\(126\) −2.56767e9 −0.907554
\(127\) −3.26424e9 −1.11343 −0.556717 0.830702i \(-0.687939\pi\)
−0.556717 + 0.830702i \(0.687939\pi\)
\(128\) −1.18339e8 −0.0389658
\(129\) −1.08803e9 −0.345928
\(130\) 1.66988e8 0.0512789
\(131\) 1.77758e9 0.527363 0.263681 0.964610i \(-0.415063\pi\)
0.263681 + 0.964610i \(0.415063\pi\)
\(132\) −6.97363e8 −0.199929
\(133\) 4.10932e9 1.13878
\(134\) 3.35319e9 0.898436
\(135\) −1.00395e9 −0.260143
\(136\) −6.93954e7 −0.0173942
\(137\) −9.42311e8 −0.228535 −0.114267 0.993450i \(-0.536452\pi\)
−0.114267 + 0.993450i \(0.536452\pi\)
\(138\) 2.14354e9 0.503124
\(139\) −3.94122e9 −0.895496 −0.447748 0.894160i \(-0.647774\pi\)
−0.447748 + 0.894160i \(0.647774\pi\)
\(140\) −1.17060e10 −2.57533
\(141\) 2.00436e8 0.0427060
\(142\) 6.40749e7 0.0132248
\(143\) −4.72642e7 −0.00945192
\(144\) −1.74338e9 −0.337878
\(145\) 2.01585e9 0.378705
\(146\) −1.37665e10 −2.50747
\(147\) 8.93073e9 1.57746
\(148\) −1.50788e8 −0.0258338
\(149\) 8.74194e9 1.45301 0.726507 0.687159i \(-0.241143\pi\)
0.726507 + 0.687159i \(0.241143\pi\)
\(150\) −4.17321e9 −0.673070
\(151\) −6.56954e9 −1.02835 −0.514173 0.857687i \(-0.671901\pi\)
−0.514173 + 0.857687i \(0.671901\pi\)
\(152\) 7.55864e7 0.0114854
\(153\) −2.01698e9 −0.297570
\(154\) 6.67298e9 0.956042
\(155\) 1.52378e9 0.212046
\(156\) 1.13368e8 0.0153260
\(157\) 1.03687e10 1.36200 0.681001 0.732282i \(-0.261545\pi\)
0.681001 + 0.732282i \(0.261545\pi\)
\(158\) 1.10570e10 1.41149
\(159\) −1.29441e9 −0.160615
\(160\) −1.57892e10 −1.90467
\(161\) −1.01842e10 −1.19457
\(162\) −1.37273e9 −0.156591
\(163\) 6.31177e9 0.700337 0.350168 0.936687i \(-0.386124\pi\)
0.350168 + 0.936687i \(0.386124\pi\)
\(164\) 4.83390e8 0.0521796
\(165\) 2.60912e9 0.274041
\(166\) −7.56179e9 −0.772926
\(167\) 7.50187e8 0.0746355 0.0373177 0.999303i \(-0.488119\pi\)
0.0373177 + 0.999303i \(0.488119\pi\)
\(168\) 2.24394e8 0.0217330
\(169\) −1.05968e10 −0.999275
\(170\) −1.85197e10 −1.70064
\(171\) 2.19692e9 0.196486
\(172\) −6.78231e9 −0.590880
\(173\) −1.26990e10 −1.07786 −0.538929 0.842351i \(-0.681171\pi\)
−0.538929 + 0.842351i \(0.681171\pi\)
\(174\) 2.75631e9 0.227959
\(175\) 1.98275e10 1.59807
\(176\) 4.53077e9 0.355930
\(177\) 9.81506e8 0.0751646
\(178\) −1.68339e10 −1.25688
\(179\) −1.79316e10 −1.30551 −0.652754 0.757570i \(-0.726387\pi\)
−0.652754 + 0.757570i \(0.726387\pi\)
\(180\) −6.25824e9 −0.444351
\(181\) −1.71696e10 −1.18907 −0.594534 0.804070i \(-0.702664\pi\)
−0.594534 + 0.804070i \(0.702664\pi\)
\(182\) −1.08481e9 −0.0732876
\(183\) 3.46082e9 0.228112
\(184\) −1.87328e8 −0.0120482
\(185\) 5.64158e8 0.0354102
\(186\) 2.08350e9 0.127639
\(187\) 5.24181e9 0.313469
\(188\) 1.24943e9 0.0729463
\(189\) 6.52201e9 0.371795
\(190\) 2.01719e10 1.12294
\(191\) −2.64175e10 −1.43629 −0.718143 0.695895i \(-0.755008\pi\)
−0.718143 + 0.695895i \(0.755008\pi\)
\(192\) −1.05690e10 −0.561277
\(193\) −2.24534e10 −1.16486 −0.582431 0.812880i \(-0.697898\pi\)
−0.582431 + 0.812880i \(0.697898\pi\)
\(194\) −2.91288e10 −1.47644
\(195\) −4.24156e8 −0.0210073
\(196\) 5.56705e10 2.69447
\(197\) 2.52454e10 1.19422 0.597110 0.802160i \(-0.296316\pi\)
0.597110 + 0.802160i \(0.296316\pi\)
\(198\) 3.56750e9 0.164957
\(199\) 1.59249e10 0.719843 0.359922 0.932983i \(-0.382803\pi\)
0.359922 + 0.932983i \(0.382803\pi\)
\(200\) 3.64705e8 0.0161178
\(201\) −8.51727e9 −0.368059
\(202\) 4.82934e10 2.04083
\(203\) −1.30956e10 −0.541244
\(204\) −1.25730e10 −0.508281
\(205\) −1.80856e9 −0.0715221
\(206\) 3.25609e10 1.25978
\(207\) −5.44468e9 −0.206113
\(208\) −7.36552e8 −0.0272847
\(209\) −5.70945e9 −0.206984
\(210\) 5.98843e10 2.12484
\(211\) 1.80597e10 0.627250 0.313625 0.949547i \(-0.398457\pi\)
0.313625 + 0.949547i \(0.398457\pi\)
\(212\) −8.06885e9 −0.274347
\(213\) −1.62753e8 −0.00541777
\(214\) −2.69006e10 −0.876800
\(215\) 2.53754e10 0.809915
\(216\) 1.19965e8 0.00374984
\(217\) −9.89898e9 −0.303055
\(218\) 7.98157e10 2.39350
\(219\) 3.49675e10 1.02723
\(220\) 1.62642e10 0.468091
\(221\) −8.52144e8 −0.0240297
\(222\) 7.71385e8 0.0213149
\(223\) −5.79827e10 −1.57010 −0.785048 0.619434i \(-0.787362\pi\)
−0.785048 + 0.619434i \(0.787362\pi\)
\(224\) 1.02572e11 2.72214
\(225\) 1.06002e10 0.275734
\(226\) 5.99456e10 1.52851
\(227\) −1.84397e10 −0.460931 −0.230466 0.973080i \(-0.574025\pi\)
−0.230466 + 0.973080i \(0.574025\pi\)
\(228\) 1.36947e10 0.335619
\(229\) 3.07282e10 0.738376 0.369188 0.929355i \(-0.379636\pi\)
0.369188 + 0.929355i \(0.379636\pi\)
\(230\) −4.99925e10 −1.17796
\(231\) −1.69497e10 −0.391658
\(232\) −2.40879e8 −0.00545887
\(233\) −6.81886e10 −1.51569 −0.757845 0.652435i \(-0.773747\pi\)
−0.757845 + 0.652435i \(0.773747\pi\)
\(234\) −5.79957e8 −0.0126452
\(235\) −4.67464e9 −0.0999868
\(236\) 6.11831e9 0.128389
\(237\) −2.80852e10 −0.578242
\(238\) 1.20310e11 2.43055
\(239\) −7.97104e10 −1.58024 −0.790122 0.612949i \(-0.789983\pi\)
−0.790122 + 0.612949i \(0.789983\pi\)
\(240\) 4.06598e10 0.791069
\(241\) −3.16837e10 −0.605005 −0.302503 0.953149i \(-0.597822\pi\)
−0.302503 + 0.953149i \(0.597822\pi\)
\(242\) 6.59217e10 1.23555
\(243\) 3.48678e9 0.0641500
\(244\) 2.15733e10 0.389640
\(245\) −2.08286e11 −3.69328
\(246\) −2.47288e9 −0.0430522
\(247\) 9.28167e8 0.0158668
\(248\) −1.82081e8 −0.00305655
\(249\) 1.92073e10 0.316642
\(250\) −2.03315e10 −0.329184
\(251\) −1.06582e11 −1.69494 −0.847468 0.530846i \(-0.821874\pi\)
−0.847468 + 0.530846i \(0.821874\pi\)
\(252\) 4.06556e10 0.635064
\(253\) 1.41499e10 0.217125
\(254\) 1.04094e11 1.56918
\(255\) 4.70408e10 0.696697
\(256\) 7.05801e10 1.02708
\(257\) −5.57546e10 −0.797227 −0.398613 0.917119i \(-0.630508\pi\)
−0.398613 + 0.917119i \(0.630508\pi\)
\(258\) 3.46963e10 0.487522
\(259\) −3.66496e9 −0.0506081
\(260\) −2.64402e9 −0.0358826
\(261\) −7.00114e9 −0.0933870
\(262\) −5.66857e10 −0.743221
\(263\) −2.12500e10 −0.273879 −0.136939 0.990579i \(-0.543727\pi\)
−0.136939 + 0.990579i \(0.543727\pi\)
\(264\) −3.11770e8 −0.00395018
\(265\) 3.01888e10 0.376045
\(266\) −1.31043e11 −1.60490
\(267\) 4.27588e10 0.514903
\(268\) −5.30932e10 −0.628684
\(269\) 2.74501e9 0.0319638 0.0159819 0.999872i \(-0.494913\pi\)
0.0159819 + 0.999872i \(0.494913\pi\)
\(270\) 3.20153e10 0.366623
\(271\) 1.67543e11 1.88697 0.943485 0.331414i \(-0.107526\pi\)
0.943485 + 0.331414i \(0.107526\pi\)
\(272\) 8.16869e10 0.904883
\(273\) 2.75545e9 0.0300235
\(274\) 3.00496e10 0.322078
\(275\) −2.75481e10 −0.290466
\(276\) −3.39399e10 −0.352063
\(277\) 1.37791e11 1.40625 0.703123 0.711068i \(-0.251788\pi\)
0.703123 + 0.711068i \(0.251788\pi\)
\(278\) 1.25682e11 1.26204
\(279\) −5.29218e9 −0.0522896
\(280\) −5.23340e9 −0.0508830
\(281\) −1.47914e11 −1.41524 −0.707622 0.706591i \(-0.750232\pi\)
−0.707622 + 0.706591i \(0.750232\pi\)
\(282\) −6.39173e9 −0.0601863
\(283\) 4.45401e10 0.412774 0.206387 0.978470i \(-0.433829\pi\)
0.206387 + 0.978470i \(0.433829\pi\)
\(284\) −1.01454e9 −0.00925412
\(285\) −5.12375e10 −0.460030
\(286\) 1.50722e9 0.0133208
\(287\) 1.17490e10 0.102219
\(288\) 5.48366e10 0.469683
\(289\) −2.40813e10 −0.203067
\(290\) −6.42837e10 −0.533716
\(291\) 7.39886e10 0.604848
\(292\) 2.17973e11 1.75461
\(293\) 1.85472e11 1.47019 0.735097 0.677962i \(-0.237137\pi\)
0.735097 + 0.677962i \(0.237137\pi\)
\(294\) −2.84794e11 −2.22314
\(295\) −2.28911e10 −0.175982
\(296\) −6.74128e7 −0.000510422 0
\(297\) −9.06161e9 −0.0675774
\(298\) −2.78774e11 −2.04776
\(299\) −2.30030e9 −0.0166442
\(300\) 6.60771e10 0.470983
\(301\) −1.64847e11 −1.15753
\(302\) 2.09497e11 1.44926
\(303\) −1.22668e11 −0.836060
\(304\) −8.89745e10 −0.597495
\(305\) −8.07146e10 −0.534076
\(306\) 6.43198e10 0.419371
\(307\) 1.62747e11 1.04566 0.522830 0.852437i \(-0.324876\pi\)
0.522830 + 0.852437i \(0.324876\pi\)
\(308\) −1.05657e11 −0.668993
\(309\) −8.27061e10 −0.516089
\(310\) −4.85922e10 −0.298840
\(311\) −1.22720e10 −0.0743862 −0.0371931 0.999308i \(-0.511842\pi\)
−0.0371931 + 0.999308i \(0.511842\pi\)
\(312\) 5.06835e7 0.000302811 0
\(313\) −1.67219e11 −0.984776 −0.492388 0.870376i \(-0.663876\pi\)
−0.492388 + 0.870376i \(0.663876\pi\)
\(314\) −3.30651e11 −1.91949
\(315\) −1.52109e11 −0.870477
\(316\) −1.75072e11 −0.987698
\(317\) −2.57818e11 −1.43399 −0.716996 0.697078i \(-0.754483\pi\)
−0.716996 + 0.697078i \(0.754483\pi\)
\(318\) 4.12778e10 0.226357
\(319\) 1.81949e10 0.0983764
\(320\) 2.46494e11 1.31411
\(321\) 6.83288e10 0.359196
\(322\) 3.24767e11 1.68353
\(323\) −1.02938e11 −0.526216
\(324\) 2.17352e10 0.109575
\(325\) 4.47841e9 0.0222663
\(326\) −2.01277e11 −0.986996
\(327\) −2.02736e11 −0.980539
\(328\) 2.16110e8 0.00103096
\(329\) 3.03680e10 0.142901
\(330\) −8.32027e10 −0.386211
\(331\) 2.79741e11 1.28095 0.640473 0.767981i \(-0.278738\pi\)
0.640473 + 0.767981i \(0.278738\pi\)
\(332\) 1.19730e11 0.540858
\(333\) −1.95935e9 −0.00873200
\(334\) −2.39229e10 −0.105185
\(335\) 1.98643e11 0.861731
\(336\) −2.64139e11 −1.13059
\(337\) 1.93079e11 0.815454 0.407727 0.913104i \(-0.366321\pi\)
0.407727 + 0.913104i \(0.366321\pi\)
\(338\) 3.37924e11 1.40830
\(339\) −1.52264e11 −0.626181
\(340\) 2.93233e11 1.19003
\(341\) 1.37535e10 0.0550833
\(342\) −7.00580e10 −0.276911
\(343\) 8.57862e11 3.34652
\(344\) −3.03217e9 −0.0116746
\(345\) 1.26983e11 0.482570
\(346\) 4.04961e11 1.51904
\(347\) 4.07789e11 1.50992 0.754959 0.655773i \(-0.227657\pi\)
0.754959 + 0.655773i \(0.227657\pi\)
\(348\) −4.36423e10 −0.159515
\(349\) −1.82090e11 −0.657009 −0.328505 0.944502i \(-0.606545\pi\)
−0.328505 + 0.944502i \(0.606545\pi\)
\(350\) −6.32284e11 −2.25219
\(351\) 1.47312e9 0.00518030
\(352\) −1.42512e11 −0.494776
\(353\) −5.32848e10 −0.182649 −0.0913245 0.995821i \(-0.529110\pi\)
−0.0913245 + 0.995821i \(0.529110\pi\)
\(354\) −3.12995e10 −0.105931
\(355\) 3.79579e9 0.0126845
\(356\) 2.66541e11 0.879507
\(357\) −3.05592e11 −0.995716
\(358\) 5.71824e11 1.83988
\(359\) 5.41580e11 1.72083 0.860414 0.509595i \(-0.170205\pi\)
0.860414 + 0.509595i \(0.170205\pi\)
\(360\) −2.79787e9 −0.00877944
\(361\) −2.10566e11 −0.652539
\(362\) 5.47525e11 1.67577
\(363\) −1.67444e11 −0.506162
\(364\) 1.71764e10 0.0512833
\(365\) −8.15526e11 −2.40503
\(366\) −1.10363e11 −0.321483
\(367\) −1.14857e11 −0.330492 −0.165246 0.986252i \(-0.552842\pi\)
−0.165246 + 0.986252i \(0.552842\pi\)
\(368\) 2.20508e11 0.626771
\(369\) 6.28123e9 0.0176370
\(370\) −1.79906e10 −0.0499042
\(371\) −1.96116e11 −0.537442
\(372\) −3.29893e10 −0.0893161
\(373\) −1.42587e11 −0.381409 −0.190705 0.981647i \(-0.561077\pi\)
−0.190705 + 0.981647i \(0.561077\pi\)
\(374\) −1.67157e11 −0.441777
\(375\) 5.16428e10 0.134856
\(376\) 5.58585e8 0.00144127
\(377\) −2.95788e9 −0.00754128
\(378\) −2.07982e11 −0.523976
\(379\) −7.82015e11 −1.94688 −0.973438 0.228949i \(-0.926471\pi\)
−0.973438 + 0.228949i \(0.926471\pi\)
\(380\) −3.19394e11 −0.785778
\(381\) −2.64403e11 −0.642842
\(382\) 8.42432e11 2.02418
\(383\) 3.21255e11 0.762878 0.381439 0.924394i \(-0.375429\pi\)
0.381439 + 0.924394i \(0.375429\pi\)
\(384\) −9.58546e9 −0.0224969
\(385\) 3.95307e11 0.916984
\(386\) 7.16021e11 1.64166
\(387\) −8.81300e10 −0.199721
\(388\) 4.61215e11 1.03314
\(389\) 1.78363e11 0.394939 0.197470 0.980309i \(-0.436728\pi\)
0.197470 + 0.980309i \(0.436728\pi\)
\(390\) 1.35260e10 0.0296059
\(391\) 2.55114e11 0.551999
\(392\) 2.48886e10 0.0532370
\(393\) 1.43984e11 0.304473
\(394\) −8.05055e11 −1.68303
\(395\) 6.55014e11 1.35383
\(396\) −5.64864e10 −0.115429
\(397\) 6.49654e11 1.31258 0.656289 0.754510i \(-0.272125\pi\)
0.656289 + 0.754510i \(0.272125\pi\)
\(398\) −5.07833e11 −1.01449
\(399\) 3.32855e11 0.657472
\(400\) −4.29302e11 −0.838481
\(401\) −1.09019e11 −0.210550 −0.105275 0.994443i \(-0.533572\pi\)
−0.105275 + 0.994443i \(0.533572\pi\)
\(402\) 2.71609e11 0.518712
\(403\) −2.23587e9 −0.00422254
\(404\) −7.64660e11 −1.42808
\(405\) −8.13202e10 −0.150193
\(406\) 4.17608e11 0.762784
\(407\) 5.09205e9 0.00919852
\(408\) −5.62103e9 −0.0100426
\(409\) −4.91552e11 −0.868590 −0.434295 0.900771i \(-0.643002\pi\)
−0.434295 + 0.900771i \(0.643002\pi\)
\(410\) 5.76735e10 0.100797
\(411\) −7.63272e10 −0.131944
\(412\) −5.15556e11 −0.881533
\(413\) 1.48708e11 0.251512
\(414\) 1.73627e11 0.290479
\(415\) −4.47960e11 −0.741349
\(416\) 2.31677e10 0.0379282
\(417\) −3.19239e11 −0.517015
\(418\) 1.82070e11 0.291706
\(419\) 1.82329e11 0.288997 0.144499 0.989505i \(-0.453843\pi\)
0.144499 + 0.989505i \(0.453843\pi\)
\(420\) −9.48185e11 −1.48686
\(421\) −1.14800e12 −1.78104 −0.890519 0.454947i \(-0.849658\pi\)
−0.890519 + 0.454947i \(0.849658\pi\)
\(422\) −5.75911e11 −0.883994
\(423\) 1.62353e10 0.0246563
\(424\) −3.60734e9 −0.00542052
\(425\) −4.96676e11 −0.738453
\(426\) 5.19006e9 0.00763536
\(427\) 5.24348e11 0.763299
\(428\) 4.25934e11 0.613544
\(429\) −3.82840e9 −0.00545707
\(430\) −8.09200e11 −1.14143
\(431\) 9.10456e11 1.27090 0.635450 0.772142i \(-0.280815\pi\)
0.635450 + 0.772142i \(0.280815\pi\)
\(432\) −1.41214e11 −0.195074
\(433\) −1.35384e12 −1.85085 −0.925426 0.378929i \(-0.876292\pi\)
−0.925426 + 0.378929i \(0.876292\pi\)
\(434\) 3.15671e11 0.427101
\(435\) 1.63283e11 0.218646
\(436\) −1.26377e12 −1.67486
\(437\) −2.77873e11 −0.364485
\(438\) −1.11508e12 −1.44769
\(439\) −5.31193e11 −0.682593 −0.341297 0.939956i \(-0.610866\pi\)
−0.341297 + 0.939956i \(0.610866\pi\)
\(440\) 7.27124e9 0.00924850
\(441\) 7.23389e11 0.910748
\(442\) 2.71742e10 0.0338654
\(443\) 2.93695e11 0.362309 0.181155 0.983455i \(-0.442017\pi\)
0.181155 + 0.983455i \(0.442017\pi\)
\(444\) −1.22138e10 −0.0149152
\(445\) −9.97239e11 −1.20553
\(446\) 1.84902e12 2.21276
\(447\) 7.08097e11 0.838898
\(448\) −1.60130e12 −1.87812
\(449\) −2.96345e11 −0.344104 −0.172052 0.985088i \(-0.555040\pi\)
−0.172052 + 0.985088i \(0.555040\pi\)
\(450\) −3.38030e11 −0.388597
\(451\) −1.63239e10 −0.0185793
\(452\) −9.49155e11 −1.06958
\(453\) −5.32133e11 −0.593715
\(454\) 5.88026e11 0.649599
\(455\) −6.42638e10 −0.0702935
\(456\) 6.12250e9 0.00663112
\(457\) −1.56401e12 −1.67733 −0.838664 0.544650i \(-0.816663\pi\)
−0.838664 + 0.544650i \(0.816663\pi\)
\(458\) −9.79898e11 −1.04061
\(459\) −1.63375e11 −0.171802
\(460\) 7.91561e11 0.824279
\(461\) −1.01947e12 −1.05128 −0.525642 0.850706i \(-0.676175\pi\)
−0.525642 + 0.850706i \(0.676175\pi\)
\(462\) 5.40512e11 0.551971
\(463\) −3.45994e11 −0.349908 −0.174954 0.984577i \(-0.555978\pi\)
−0.174954 + 0.984577i \(0.555978\pi\)
\(464\) 2.83544e11 0.283981
\(465\) 1.23426e11 0.122425
\(466\) 2.17448e12 2.13609
\(467\) 5.45802e11 0.531018 0.265509 0.964108i \(-0.414460\pi\)
0.265509 + 0.964108i \(0.414460\pi\)
\(468\) 9.18281e9 0.00884850
\(469\) −1.29045e12 −1.23158
\(470\) 1.49071e11 0.140913
\(471\) 8.39869e11 0.786353
\(472\) 2.73532e9 0.00253670
\(473\) 2.29036e11 0.210392
\(474\) 8.95614e11 0.814927
\(475\) 5.40986e11 0.487601
\(476\) −1.90494e12 −1.70079
\(477\) −1.04847e11 −0.0927311
\(478\) 2.54190e12 2.22706
\(479\) −3.74861e11 −0.325357 −0.162679 0.986679i \(-0.552013\pi\)
−0.162679 + 0.986679i \(0.552013\pi\)
\(480\) −1.27892e12 −1.09966
\(481\) −8.27799e8 −0.000705134 0
\(482\) 1.01037e12 0.852644
\(483\) −8.24923e11 −0.689686
\(484\) −1.04378e12 −0.864578
\(485\) −1.72559e12 −1.41612
\(486\) −1.11191e11 −0.0904077
\(487\) −1.96357e12 −1.58185 −0.790924 0.611914i \(-0.790400\pi\)
−0.790924 + 0.611914i \(0.790400\pi\)
\(488\) 9.64480e9 0.00769847
\(489\) 5.11253e11 0.404339
\(490\) 6.64208e12 5.20501
\(491\) −1.40585e12 −1.09162 −0.545809 0.837910i \(-0.683778\pi\)
−0.545809 + 0.837910i \(0.683778\pi\)
\(492\) 3.91546e10 0.0301259
\(493\) 3.28042e11 0.250103
\(494\) −2.95985e10 −0.0223614
\(495\) 2.11339e11 0.158218
\(496\) 2.14331e11 0.159008
\(497\) −2.46587e10 −0.0181287
\(498\) −6.12505e11 −0.446249
\(499\) −1.21146e12 −0.874696 −0.437348 0.899292i \(-0.644082\pi\)
−0.437348 + 0.899292i \(0.644082\pi\)
\(500\) 3.21921e11 0.230348
\(501\) 6.07651e10 0.0430908
\(502\) 3.39882e12 2.38870
\(503\) −1.83565e12 −1.27860 −0.639298 0.768959i \(-0.720775\pi\)
−0.639298 + 0.768959i \(0.720775\pi\)
\(504\) 1.81759e10 0.0125475
\(505\) 2.86090e12 1.95745
\(506\) −4.51228e11 −0.305998
\(507\) −8.58342e11 −0.576932
\(508\) −1.64818e12 −1.09804
\(509\) −7.98947e11 −0.527579 −0.263790 0.964580i \(-0.584972\pi\)
−0.263790 + 0.964580i \(0.584972\pi\)
\(510\) −1.50009e12 −0.981866
\(511\) 5.29792e12 3.43725
\(512\) −2.19015e12 −1.40851
\(513\) 1.77951e11 0.113441
\(514\) 1.77797e12 1.12354
\(515\) 1.92890e12 1.20831
\(516\) −5.49367e11 −0.341145
\(517\) −4.21930e10 −0.0259736
\(518\) 1.16873e11 0.0713228
\(519\) −1.02862e12 −0.622302
\(520\) −1.18206e9 −0.000708965 0
\(521\) 1.73968e12 1.03443 0.517214 0.855856i \(-0.326969\pi\)
0.517214 + 0.855856i \(0.326969\pi\)
\(522\) 2.23261e11 0.131612
\(523\) 1.07649e12 0.629150 0.314575 0.949233i \(-0.398138\pi\)
0.314575 + 0.949233i \(0.398138\pi\)
\(524\) 8.97540e11 0.520072
\(525\) 1.60603e12 0.922649
\(526\) 6.77647e11 0.385982
\(527\) 2.47968e11 0.140039
\(528\) 3.66992e11 0.205496
\(529\) −1.11249e12 −0.617656
\(530\) −9.62698e11 −0.529967
\(531\) 7.95020e10 0.0433963
\(532\) 2.07489e12 1.12303
\(533\) 2.65373e9 0.00142424
\(534\) −1.36354e12 −0.725661
\(535\) −1.59359e12 −0.840980
\(536\) −2.37364e10 −0.0124215
\(537\) −1.45246e12 −0.753736
\(538\) −8.75362e10 −0.0450472
\(539\) −1.87997e12 −0.959406
\(540\) −5.06917e11 −0.256546
\(541\) 6.48663e11 0.325560 0.162780 0.986662i \(-0.447954\pi\)
0.162780 + 0.986662i \(0.447954\pi\)
\(542\) −5.34282e12 −2.65934
\(543\) −1.39074e12 −0.686509
\(544\) −2.56940e12 −1.25787
\(545\) 4.72828e12 2.29572
\(546\) −8.78693e10 −0.0423126
\(547\) −3.36177e12 −1.60555 −0.802777 0.596279i \(-0.796645\pi\)
−0.802777 + 0.596279i \(0.796645\pi\)
\(548\) −4.75793e11 −0.225375
\(549\) 2.80326e11 0.131701
\(550\) 8.78488e11 0.409359
\(551\) −3.57308e11 −0.165143
\(552\) −1.51735e10 −0.00695603
\(553\) −4.25519e12 −1.93489
\(554\) −4.39404e12 −1.98185
\(555\) 4.56968e10 0.0204441
\(556\) −1.99000e12 −0.883116
\(557\) −1.25211e12 −0.551180 −0.275590 0.961275i \(-0.588873\pi\)
−0.275590 + 0.961275i \(0.588873\pi\)
\(558\) 1.68763e11 0.0736927
\(559\) −3.72337e10 −0.0161281
\(560\) 6.16036e12 2.64704
\(561\) 4.24587e11 0.180981
\(562\) 4.71687e12 1.99453
\(563\) −8.31880e11 −0.348958 −0.174479 0.984661i \(-0.555824\pi\)
−0.174479 + 0.984661i \(0.555824\pi\)
\(564\) 1.01204e11 0.0421156
\(565\) 3.55117e12 1.46607
\(566\) −1.42035e12 −0.581730
\(567\) 5.28283e11 0.214656
\(568\) −4.53569e8 −0.000182842 0
\(569\) 1.53041e12 0.612071 0.306035 0.952020i \(-0.400997\pi\)
0.306035 + 0.952020i \(0.400997\pi\)
\(570\) 1.63392e12 0.648328
\(571\) 1.08360e12 0.426586 0.213293 0.976988i \(-0.431581\pi\)
0.213293 + 0.976988i \(0.431581\pi\)
\(572\) −2.38647e10 −0.00932124
\(573\) −2.13982e12 −0.829241
\(574\) −3.74666e11 −0.144059
\(575\) −1.34074e12 −0.511492
\(576\) −8.56087e11 −0.324053
\(577\) 1.84892e12 0.694429 0.347215 0.937786i \(-0.387128\pi\)
0.347215 + 0.937786i \(0.387128\pi\)
\(578\) 7.67932e11 0.286185
\(579\) −1.81873e12 −0.672533
\(580\) 1.01784e12 0.373469
\(581\) 2.91009e12 1.05953
\(582\) −2.35944e12 −0.852423
\(583\) 2.72482e11 0.0976854
\(584\) 9.74493e10 0.0346674
\(585\) −3.43566e10 −0.0121286
\(586\) −5.91456e12 −2.07197
\(587\) −1.65737e11 −0.0576168 −0.0288084 0.999585i \(-0.509171\pi\)
−0.0288084 + 0.999585i \(0.509171\pi\)
\(588\) 4.50931e12 1.55565
\(589\) −2.70090e11 −0.0924676
\(590\) 7.29979e11 0.248014
\(591\) 2.04488e12 0.689483
\(592\) 7.93531e10 0.0265532
\(593\) −1.00017e12 −0.332146 −0.166073 0.986113i \(-0.553109\pi\)
−0.166073 + 0.986113i \(0.553109\pi\)
\(594\) 2.88967e11 0.0952379
\(595\) 7.12715e12 2.33125
\(596\) 4.41399e12 1.43292
\(597\) 1.28992e12 0.415602
\(598\) 7.33547e10 0.0234570
\(599\) −3.62898e12 −1.15176 −0.575882 0.817533i \(-0.695341\pi\)
−0.575882 + 0.817533i \(0.695341\pi\)
\(600\) 2.95411e10 0.00930563
\(601\) 4.56853e12 1.42837 0.714186 0.699956i \(-0.246797\pi\)
0.714186 + 0.699956i \(0.246797\pi\)
\(602\) 5.25683e12 1.63132
\(603\) −6.89898e11 −0.212499
\(604\) −3.31710e12 −1.01413
\(605\) 3.90520e12 1.18507
\(606\) 3.91177e12 1.17827
\(607\) 3.24449e11 0.0970058 0.0485029 0.998823i \(-0.484555\pi\)
0.0485029 + 0.998823i \(0.484555\pi\)
\(608\) 2.79863e12 0.830575
\(609\) −1.06074e12 −0.312487
\(610\) 2.57393e12 0.752682
\(611\) 6.85918e9 0.00199107
\(612\) −1.01842e12 −0.293456
\(613\) −4.26225e12 −1.21918 −0.609588 0.792718i \(-0.708665\pi\)
−0.609588 + 0.792718i \(0.708665\pi\)
\(614\) −5.18988e12 −1.47367
\(615\) −1.46493e11 −0.0412933
\(616\) −4.72363e10 −0.0132179
\(617\) −4.33447e11 −0.120407 −0.0602037 0.998186i \(-0.519175\pi\)
−0.0602037 + 0.998186i \(0.519175\pi\)
\(618\) 2.63743e12 0.727332
\(619\) 1.15536e12 0.316306 0.158153 0.987415i \(-0.449446\pi\)
0.158153 + 0.987415i \(0.449446\pi\)
\(620\) 7.69390e11 0.209114
\(621\) −4.41019e11 −0.119000
\(622\) 3.91343e11 0.104834
\(623\) 6.47839e12 1.72294
\(624\) −5.96607e10 −0.0157528
\(625\) −4.35996e12 −1.14294
\(626\) 5.33250e12 1.38786
\(627\) −4.62466e11 −0.119502
\(628\) 5.23540e12 1.34317
\(629\) 9.18066e10 0.0233855
\(630\) 4.85063e12 1.22678
\(631\) 2.05136e12 0.515121 0.257560 0.966262i \(-0.417081\pi\)
0.257560 + 0.966262i \(0.417081\pi\)
\(632\) −7.82694e10 −0.0195148
\(633\) 1.46284e12 0.362143
\(634\) 8.22161e12 2.02095
\(635\) 6.16652e12 1.50508
\(636\) −6.53577e11 −0.158394
\(637\) 3.05621e11 0.0735455
\(638\) −5.80220e11 −0.138644
\(639\) −1.31830e10 −0.00312795
\(640\) 2.23556e11 0.0526716
\(641\) 7.24358e12 1.69470 0.847349 0.531036i \(-0.178197\pi\)
0.847349 + 0.531036i \(0.178197\pi\)
\(642\) −2.17895e12 −0.506221
\(643\) −9.75907e11 −0.225143 −0.112572 0.993644i \(-0.535909\pi\)
−0.112572 + 0.993644i \(0.535909\pi\)
\(644\) −5.14224e12 −1.17806
\(645\) 2.05540e12 0.467604
\(646\) 3.28261e12 0.741605
\(647\) −5.08148e12 −1.14004 −0.570021 0.821630i \(-0.693065\pi\)
−0.570021 + 0.821630i \(0.693065\pi\)
\(648\) 9.71717e9 0.00216497
\(649\) −2.06613e11 −0.0457148
\(650\) −1.42813e11 −0.0313803
\(651\) −8.01818e11 −0.174969
\(652\) 3.18695e12 0.690654
\(653\) 2.74396e12 0.590565 0.295283 0.955410i \(-0.404586\pi\)
0.295283 + 0.955410i \(0.404586\pi\)
\(654\) 6.46507e12 1.38189
\(655\) −3.35806e12 −0.712858
\(656\) −2.54387e11 −0.0536326
\(657\) 2.83237e12 0.593069
\(658\) −9.68411e11 −0.201392
\(659\) −2.37620e12 −0.490793 −0.245396 0.969423i \(-0.578918\pi\)
−0.245396 + 0.969423i \(0.578918\pi\)
\(660\) 1.31740e12 0.270252
\(661\) −3.46172e12 −0.705319 −0.352659 0.935752i \(-0.614723\pi\)
−0.352659 + 0.935752i \(0.614723\pi\)
\(662\) −8.92073e12 −1.80526
\(663\) −6.90237e10 −0.0138735
\(664\) 5.35279e10 0.0106862
\(665\) −7.76299e12 −1.53933
\(666\) 6.24822e10 0.0123062
\(667\) 8.85526e11 0.173235
\(668\) 3.78785e11 0.0736036
\(669\) −4.69660e12 −0.906496
\(670\) −6.33457e12 −1.21445
\(671\) −7.28524e11 −0.138737
\(672\) 8.30829e12 1.57163
\(673\) −6.67858e12 −1.25492 −0.627461 0.778648i \(-0.715906\pi\)
−0.627461 + 0.778648i \(0.715906\pi\)
\(674\) −6.15712e12 −1.14923
\(675\) 8.58612e11 0.159195
\(676\) −5.35056e12 −0.985460
\(677\) 4.44582e11 0.0813398 0.0406699 0.999173i \(-0.487051\pi\)
0.0406699 + 0.999173i \(0.487051\pi\)
\(678\) 4.85559e12 0.882487
\(679\) 1.12100e13 2.02391
\(680\) 1.31096e11 0.0235125
\(681\) −1.49361e12 −0.266119
\(682\) −4.38590e11 −0.0776298
\(683\) 9.48001e12 1.66692 0.833462 0.552577i \(-0.186355\pi\)
0.833462 + 0.552577i \(0.186355\pi\)
\(684\) 1.10927e12 0.193770
\(685\) 1.78013e12 0.308919
\(686\) −2.73565e13 −4.71631
\(687\) 2.48899e12 0.426302
\(688\) 3.56924e12 0.607334
\(689\) −4.42966e10 −0.00748830
\(690\) −4.04939e12 −0.680093
\(691\) −5.25166e12 −0.876284 −0.438142 0.898906i \(-0.644363\pi\)
−0.438142 + 0.898906i \(0.644363\pi\)
\(692\) −6.41199e12 −1.06296
\(693\) −1.37292e12 −0.226124
\(694\) −1.30041e13 −2.12795
\(695\) 7.44541e12 1.21048
\(696\) −1.95112e10 −0.00315168
\(697\) −2.94310e11 −0.0472344
\(698\) 5.80670e12 0.925934
\(699\) −5.52328e12 −0.875084
\(700\) 1.00113e13 1.57598
\(701\) −9.50022e12 −1.48594 −0.742972 0.669323i \(-0.766584\pi\)
−0.742972 + 0.669323i \(0.766584\pi\)
\(702\) −4.69765e10 −0.00730069
\(703\) −9.99970e10 −0.0154414
\(704\) 2.22484e12 0.341367
\(705\) −3.78646e11 −0.0577274
\(706\) 1.69921e12 0.257410
\(707\) −1.85853e13 −2.79759
\(708\) 4.95583e11 0.0741254
\(709\) 3.80257e12 0.565158 0.282579 0.959244i \(-0.408810\pi\)
0.282579 + 0.959244i \(0.408810\pi\)
\(710\) −1.21045e11 −0.0178765
\(711\) −2.27490e12 −0.333848
\(712\) 1.19163e11 0.0173772
\(713\) 6.69371e11 0.0969983
\(714\) 9.74509e12 1.40328
\(715\) 8.92875e10 0.0127765
\(716\) −9.05403e12 −1.28746
\(717\) −6.45654e12 −0.912354
\(718\) −1.72706e13 −2.42519
\(719\) −4.75843e12 −0.664024 −0.332012 0.943275i \(-0.607727\pi\)
−0.332012 + 0.943275i \(0.607727\pi\)
\(720\) 3.29344e12 0.456724
\(721\) −1.25308e13 −1.72691
\(722\) 6.71479e12 0.919634
\(723\) −2.56638e12 −0.349300
\(724\) −8.66930e12 −1.17263
\(725\) −1.72401e12 −0.231750
\(726\) 5.33966e12 0.713343
\(727\) −8.46722e11 −0.112418 −0.0562090 0.998419i \(-0.517901\pi\)
−0.0562090 + 0.998419i \(0.517901\pi\)
\(728\) 7.67906e9 0.00101325
\(729\) 2.82430e11 0.0370370
\(730\) 2.60065e13 3.38944
\(731\) 4.12938e12 0.534881
\(732\) 1.74744e12 0.224959
\(733\) 1.49200e13 1.90898 0.954490 0.298244i \(-0.0964009\pi\)
0.954490 + 0.298244i \(0.0964009\pi\)
\(734\) 3.66270e12 0.465767
\(735\) −1.68712e13 −2.13232
\(736\) −6.93590e12 −0.871270
\(737\) 1.79294e12 0.223852
\(738\) −2.00303e11 −0.0248562
\(739\) −1.33358e12 −0.164482 −0.0822409 0.996612i \(-0.526208\pi\)
−0.0822409 + 0.996612i \(0.526208\pi\)
\(740\) 2.84856e11 0.0349206
\(741\) 7.51816e10 0.00916072
\(742\) 6.25400e12 0.757426
\(743\) 1.73699e12 0.209097 0.104548 0.994520i \(-0.466660\pi\)
0.104548 + 0.994520i \(0.466660\pi\)
\(744\) −1.47485e10 −0.00176470
\(745\) −1.65145e13 −1.96410
\(746\) 4.54700e12 0.537527
\(747\) 1.55579e12 0.182813
\(748\) 2.64670e12 0.309135
\(749\) 1.03525e13 1.20192
\(750\) −1.64685e12 −0.190054
\(751\) −1.71628e12 −0.196883 −0.0984415 0.995143i \(-0.531386\pi\)
−0.0984415 + 0.995143i \(0.531386\pi\)
\(752\) −6.57523e11 −0.0749775
\(753\) −8.63317e12 −0.978572
\(754\) 9.43245e10 0.0106280
\(755\) 1.24106e13 1.39006
\(756\) 3.29310e12 0.366654
\(757\) −1.73787e12 −0.192348 −0.0961739 0.995365i \(-0.530660\pi\)
−0.0961739 + 0.995365i \(0.530660\pi\)
\(758\) 2.49378e13 2.74377
\(759\) 1.14614e12 0.125357
\(760\) −1.42791e11 −0.0155253
\(761\) 2.45314e12 0.265150 0.132575 0.991173i \(-0.457675\pi\)
0.132575 + 0.991173i \(0.457675\pi\)
\(762\) 8.43161e12 0.905968
\(763\) −3.07164e13 −3.28103
\(764\) −1.33387e13 −1.41643
\(765\) 3.81030e12 0.402238
\(766\) −1.02446e13 −1.07514
\(767\) 3.35885e10 0.00350438
\(768\) 5.71699e12 0.592982
\(769\) 6.92178e12 0.713755 0.356878 0.934151i \(-0.383841\pi\)
0.356878 + 0.934151i \(0.383841\pi\)
\(770\) −1.26060e13 −1.29232
\(771\) −4.51612e12 −0.460279
\(772\) −1.13372e13 −1.14876
\(773\) 7.14953e12 0.720228 0.360114 0.932908i \(-0.382738\pi\)
0.360114 + 0.932908i \(0.382738\pi\)
\(774\) 2.81040e12 0.281471
\(775\) −1.30319e12 −0.129762
\(776\) 2.06196e11 0.0204127
\(777\) −2.96861e11 −0.0292186
\(778\) −5.68784e12 −0.556595
\(779\) 3.20567e11 0.0311889
\(780\) −2.14165e11 −0.0207168
\(781\) 3.42605e10 0.00329507
\(782\) −8.13537e12 −0.777941
\(783\) −5.67092e11 −0.0539170
\(784\) −2.92970e13 −2.76950
\(785\) −1.95878e13 −1.84107
\(786\) −4.59155e12 −0.429099
\(787\) 5.46600e12 0.507906 0.253953 0.967217i \(-0.418269\pi\)
0.253953 + 0.967217i \(0.418269\pi\)
\(788\) 1.27469e13 1.17771
\(789\) −1.72125e12 −0.158124
\(790\) −2.08879e13 −1.90797
\(791\) −2.30696e13 −2.09530
\(792\) −2.52534e10 −0.00228064
\(793\) 1.18434e11 0.0106352
\(794\) −2.07170e13 −1.84984
\(795\) 2.44530e12 0.217110
\(796\) 8.04082e12 0.709891
\(797\) −1.83343e13 −1.60954 −0.804770 0.593587i \(-0.797711\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(798\) −1.06145e13 −0.926587
\(799\) −7.60713e11 −0.0660329
\(800\) 1.35034e13 1.16557
\(801\) 3.46346e12 0.297279
\(802\) 3.47654e12 0.296731
\(803\) −7.36088e12 −0.624755
\(804\) −4.30055e12 −0.362971
\(805\) 1.92392e13 1.61475
\(806\) 7.13001e10 0.00595090
\(807\) 2.22346e11 0.0184543
\(808\) −3.41857e11 −0.0282158
\(809\) 1.45650e13 1.19548 0.597741 0.801689i \(-0.296065\pi\)
0.597741 + 0.801689i \(0.296065\pi\)
\(810\) 2.59324e12 0.211670
\(811\) −7.14300e12 −0.579811 −0.289906 0.957055i \(-0.593624\pi\)
−0.289906 + 0.957055i \(0.593624\pi\)
\(812\) −6.61224e12 −0.533761
\(813\) 1.35710e13 1.08944
\(814\) −1.62381e11 −0.0129636
\(815\) −1.19237e13 −0.946673
\(816\) 6.61664e12 0.522434
\(817\) −4.49778e12 −0.353182
\(818\) 1.56752e13 1.22412
\(819\) 2.23192e11 0.0173341
\(820\) −9.13180e11 −0.0705333
\(821\) 1.86782e13 1.43480 0.717399 0.696663i \(-0.245333\pi\)
0.717399 + 0.696663i \(0.245333\pi\)
\(822\) 2.43401e12 0.185952
\(823\) −1.64592e13 −1.25057 −0.625286 0.780395i \(-0.715018\pi\)
−0.625286 + 0.780395i \(0.715018\pi\)
\(824\) −2.30490e11 −0.0174172
\(825\) −2.23140e12 −0.167701
\(826\) −4.74218e12 −0.354460
\(827\) 1.92951e13 1.43440 0.717202 0.696865i \(-0.245422\pi\)
0.717202 + 0.696865i \(0.245422\pi\)
\(828\) −2.74914e12 −0.203264
\(829\) −2.67671e12 −0.196836 −0.0984182 0.995145i \(-0.531378\pi\)
−0.0984182 + 0.995145i \(0.531378\pi\)
\(830\) 1.42851e13 1.04480
\(831\) 1.11611e13 0.811896
\(832\) −3.61684e11 −0.0261683
\(833\) −3.38948e13 −2.43910
\(834\) 1.01803e13 0.728638
\(835\) −1.41719e12 −0.100888
\(836\) −2.88282e12 −0.204122
\(837\) −4.28666e11 −0.0301894
\(838\) −5.81434e12 −0.407288
\(839\) 2.29406e13 1.59836 0.799182 0.601089i \(-0.205266\pi\)
0.799182 + 0.601089i \(0.205266\pi\)
\(840\) −4.23906e11 −0.0293773
\(841\) −1.33685e13 −0.921510
\(842\) 3.66088e13 2.51005
\(843\) −1.19811e13 −0.817092
\(844\) 9.11875e12 0.618578
\(845\) 2.00186e13 1.35076
\(846\) −5.17730e11 −0.0347486
\(847\) −2.53694e13 −1.69370
\(848\) 4.24629e12 0.281986
\(849\) 3.60775e12 0.238315
\(850\) 1.58386e13 1.04071
\(851\) 2.47825e11 0.0161980
\(852\) −8.21774e10 −0.00534287
\(853\) 2.67496e12 0.173000 0.0865001 0.996252i \(-0.472432\pi\)
0.0865001 + 0.996252i \(0.472432\pi\)
\(854\) −1.67211e13 −1.07573
\(855\) −4.15023e12 −0.265598
\(856\) 1.90423e11 0.0121223
\(857\) 9.53553e12 0.603853 0.301926 0.953331i \(-0.402370\pi\)
0.301926 + 0.953331i \(0.402370\pi\)
\(858\) 1.22085e11 0.00769074
\(859\) 2.42971e13 1.52260 0.761298 0.648402i \(-0.224562\pi\)
0.761298 + 0.648402i \(0.224562\pi\)
\(860\) 1.28126e13 0.798717
\(861\) 9.51668e11 0.0590162
\(862\) −2.90337e13 −1.79110
\(863\) 5.09925e12 0.312938 0.156469 0.987683i \(-0.449989\pi\)
0.156469 + 0.987683i \(0.449989\pi\)
\(864\) 4.44177e12 0.271171
\(865\) 2.39899e13 1.45699
\(866\) 4.31729e13 2.60844
\(867\) −1.95058e12 −0.117241
\(868\) −4.99821e12 −0.298865
\(869\) 5.91211e12 0.351685
\(870\) −5.20698e12 −0.308141
\(871\) −2.91472e11 −0.0171599
\(872\) −5.64995e11 −0.0330918
\(873\) 5.99307e12 0.349209
\(874\) 8.86116e12 0.513676
\(875\) 7.82440e12 0.451248
\(876\) 1.76558e13 1.01302
\(877\) −1.18486e13 −0.676348 −0.338174 0.941084i \(-0.609809\pi\)
−0.338174 + 0.941084i \(0.609809\pi\)
\(878\) 1.69393e13 0.961990
\(879\) 1.50233e13 0.848817
\(880\) −8.55914e12 −0.481125
\(881\) −2.69059e13 −1.50472 −0.752360 0.658752i \(-0.771085\pi\)
−0.752360 + 0.658752i \(0.771085\pi\)
\(882\) −2.30683e13 −1.28353
\(883\) −2.48397e12 −0.137507 −0.0687534 0.997634i \(-0.521902\pi\)
−0.0687534 + 0.997634i \(0.521902\pi\)
\(884\) −4.30266e11 −0.0236975
\(885\) −1.85418e12 −0.101603
\(886\) −9.36569e12 −0.510608
\(887\) −1.74257e13 −0.945223 −0.472611 0.881271i \(-0.656689\pi\)
−0.472611 + 0.881271i \(0.656689\pi\)
\(888\) −5.46043e9 −0.000294692 0
\(889\) −4.00597e13 −2.15105
\(890\) 3.18011e13 1.69898
\(891\) −7.33990e11 −0.0390158
\(892\) −2.92767e13 −1.54839
\(893\) 8.28579e11 0.0436016
\(894\) −2.25807e13 −1.18227
\(895\) 3.38748e13 1.76471
\(896\) −1.45229e12 −0.0752780
\(897\) −1.86324e11 −0.00960956
\(898\) 9.45022e12 0.484951
\(899\) 8.60723e11 0.0439486
\(900\) 5.35224e12 0.271922
\(901\) 4.91269e12 0.248346
\(902\) 5.20557e11 0.0261842
\(903\) −1.33526e13 −0.668298
\(904\) −4.24339e11 −0.0211327
\(905\) 3.24354e13 1.60731
\(906\) 1.69693e13 0.836733
\(907\) −1.84102e13 −0.903286 −0.451643 0.892199i \(-0.649162\pi\)
−0.451643 + 0.892199i \(0.649162\pi\)
\(908\) −9.31057e12 −0.454559
\(909\) −9.93607e12 −0.482700
\(910\) 2.04932e12 0.0990659
\(911\) 2.95844e13 1.42308 0.711542 0.702644i \(-0.247997\pi\)
0.711542 + 0.702644i \(0.247997\pi\)
\(912\) −7.20693e12 −0.344964
\(913\) −4.04325e12 −0.192581
\(914\) 4.98752e13 2.36389
\(915\) −6.53789e12 −0.308349
\(916\) 1.55153e13 0.728168
\(917\) 2.18151e13 1.01881
\(918\) 5.20991e12 0.242124
\(919\) 2.24233e13 1.03700 0.518501 0.855077i \(-0.326490\pi\)
0.518501 + 0.855077i \(0.326490\pi\)
\(920\) 3.53884e11 0.0162860
\(921\) 1.31825e13 0.603712
\(922\) 3.25101e13 1.48159
\(923\) −5.56963e9 −0.000252591 0
\(924\) −8.55825e12 −0.386244
\(925\) −4.82486e11 −0.0216694
\(926\) 1.10335e13 0.493131
\(927\) −6.69919e12 −0.297964
\(928\) −8.91866e12 −0.394760
\(929\) 2.64278e13 1.16410 0.582050 0.813153i \(-0.302251\pi\)
0.582050 + 0.813153i \(0.302251\pi\)
\(930\) −3.93597e12 −0.172535
\(931\) 3.69187e13 1.61054
\(932\) −3.44299e13 −1.49473
\(933\) −9.94029e11 −0.0429469
\(934\) −1.74052e13 −0.748372
\(935\) −9.90238e12 −0.423728
\(936\) 4.10536e9 0.000174828 0
\(937\) 4.85245e12 0.205652 0.102826 0.994699i \(-0.467212\pi\)
0.102826 + 0.994699i \(0.467212\pi\)
\(938\) 4.11514e13 1.73569
\(939\) −1.35448e13 −0.568560
\(940\) −2.36033e12 −0.0986045
\(941\) 2.17271e13 0.903336 0.451668 0.892186i \(-0.350829\pi\)
0.451668 + 0.892186i \(0.350829\pi\)
\(942\) −2.67827e13 −1.10822
\(943\) −7.94469e11 −0.0327171
\(944\) −3.21980e12 −0.131964
\(945\) −1.23208e13 −0.502570
\(946\) −7.30378e12 −0.296509
\(947\) 2.12970e13 0.860486 0.430243 0.902713i \(-0.358428\pi\)
0.430243 + 0.902713i \(0.358428\pi\)
\(948\) −1.41808e13 −0.570248
\(949\) 1.19663e12 0.0478920
\(950\) −1.72516e13 −0.687185
\(951\) −2.08833e13 −0.827915
\(952\) −8.51642e11 −0.0336040
\(953\) −8.67033e11 −0.0340500 −0.0170250 0.999855i \(-0.505419\pi\)
−0.0170250 + 0.999855i \(0.505419\pi\)
\(954\) 3.34350e12 0.130687
\(955\) 4.99057e13 1.94149
\(956\) −4.02475e13 −1.55840
\(957\) 1.47378e12 0.0567977
\(958\) 1.19540e13 0.458532
\(959\) −1.15643e13 −0.441506
\(960\) 1.99660e13 0.758701
\(961\) −2.57890e13 −0.975392
\(962\) 2.63978e10 0.000993758 0
\(963\) 5.53464e12 0.207382
\(964\) −1.59978e13 −0.596641
\(965\) 4.24171e13 1.57459
\(966\) 2.63061e13 0.971986
\(967\) −4.69969e12 −0.172842 −0.0864212 0.996259i \(-0.527543\pi\)
−0.0864212 + 0.996259i \(0.527543\pi\)
\(968\) −4.66642e11 −0.0170823
\(969\) −8.33797e12 −0.303811
\(970\) 5.50277e13 1.99576
\(971\) 4.65362e13 1.67998 0.839990 0.542602i \(-0.182561\pi\)
0.839990 + 0.542602i \(0.182561\pi\)
\(972\) 1.76055e12 0.0632631
\(973\) −4.83678e13 −1.73001
\(974\) 6.26165e13 2.22933
\(975\) 3.62751e11 0.0128555
\(976\) −1.13531e13 −0.400489
\(977\) −6.68165e12 −0.234616 −0.117308 0.993096i \(-0.537427\pi\)
−0.117308 + 0.993096i \(0.537427\pi\)
\(978\) −1.63035e13 −0.569842
\(979\) −9.00100e12 −0.313162
\(980\) −1.05168e14 −3.64222
\(981\) −1.64216e13 −0.566115
\(982\) 4.48313e13 1.53844
\(983\) −4.01992e13 −1.37318 −0.686589 0.727046i \(-0.740893\pi\)
−0.686589 + 0.727046i \(0.740893\pi\)
\(984\) 1.75049e10 0.000595225 0
\(985\) −4.76914e13 −1.61427
\(986\) −1.04610e13 −0.352474
\(987\) 2.45981e12 0.0825038
\(988\) 4.68651e11 0.0156475
\(989\) 1.11470e13 0.370487
\(990\) −6.73942e12 −0.222979
\(991\) 1.10880e13 0.365191 0.182596 0.983188i \(-0.441550\pi\)
0.182596 + 0.983188i \(0.441550\pi\)
\(992\) −6.74163e12 −0.221036
\(993\) 2.26591e13 0.739555
\(994\) 7.86346e11 0.0255491
\(995\) −3.00840e13 −0.973042
\(996\) 9.69816e12 0.312264
\(997\) −4.99784e13 −1.60197 −0.800985 0.598685i \(-0.795690\pi\)
−0.800985 + 0.598685i \(0.795690\pi\)
\(998\) 3.86325e13 1.23272
\(999\) −1.58708e11 −0.00504142
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 177.10.a.a.1.4 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.4 21 1.1 even 1 trivial