Properties

Label 29.18.a.b.1.19
Level $29$
Weight $18$
Character 29.1
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +O(q^{10})\) \(q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +4.73928e8 q^{10} -6.23226e8 q^{11} +4.43138e9 q^{12} +1.86416e9 q^{13} +1.01472e9 q^{14} +1.36447e10 q^{15} +1.23678e10 q^{16} -1.09640e10 q^{17} +1.14939e11 q^{18} -3.02142e10 q^{19} +1.91674e11 q^{20} +2.92144e10 q^{21} -3.84471e11 q^{22} +2.62133e11 q^{23} +1.29760e12 q^{24} -1.72754e11 q^{25} +1.15001e12 q^{26} +1.01550e12 q^{27} +4.10391e11 q^{28} +5.00246e11 q^{29} +8.41747e12 q^{30} -4.65989e12 q^{31} -1.94620e12 q^{32} -1.10692e13 q^{33} -6.76375e12 q^{34} +1.26364e12 q^{35} +4.64857e13 q^{36} +2.56925e13 q^{37} -1.86393e13 q^{38} +3.31094e13 q^{39} +5.61262e13 q^{40} +4.31933e13 q^{41} +1.80225e13 q^{42} -6.43816e13 q^{43} -1.55495e14 q^{44} +1.43134e14 q^{45} +1.61711e14 q^{46} -1.91076e14 q^{47} +2.19665e14 q^{48} -2.29925e14 q^{49} -1.06573e14 q^{50} -1.94733e14 q^{51} +4.65107e14 q^{52} -7.46298e14 q^{53} +6.26465e14 q^{54} -4.78784e14 q^{55} +1.20171e14 q^{56} -5.36637e14 q^{57} +3.08604e14 q^{58} +2.00465e15 q^{59} +3.40434e15 q^{60} +1.38827e15 q^{61} -2.87471e15 q^{62} +3.06463e14 q^{63} -2.82169e15 q^{64} +1.43211e15 q^{65} -6.82862e15 q^{66} -2.66642e15 q^{67} -2.73551e15 q^{68} +4.65576e15 q^{69} +7.79545e14 q^{70} +6.06764e15 q^{71} +1.36119e16 q^{72} +7.52337e15 q^{73} +1.58498e16 q^{74} -3.06829e15 q^{75} -7.53843e15 q^{76} -1.02512e15 q^{77} +2.04254e16 q^{78} +2.43578e16 q^{79} +9.50135e15 q^{80} -6.02451e15 q^{81} +2.66462e16 q^{82} +1.12492e16 q^{83} +7.28899e15 q^{84} -8.42294e15 q^{85} -3.97173e16 q^{86} +8.88491e15 q^{87} -4.55320e16 q^{88} +3.40745e16 q^{89} +8.83002e16 q^{90} +3.06628e15 q^{91} +6.54020e16 q^{92} -8.27646e16 q^{93} -1.17876e17 q^{94} -2.32116e16 q^{95} -3.45666e16 q^{96} -7.90652e16 q^{97} -1.41842e17 q^{98} -1.16117e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 616.905 1.70397 0.851987 0.523562i \(-0.175397\pi\)
0.851987 + 0.523562i \(0.175397\pi\)
\(3\) 17761.1 1.56293 0.781463 0.623951i \(-0.214474\pi\)
0.781463 + 0.623951i \(0.214474\pi\)
\(4\) 249500. 1.90353
\(5\) 768235. 0.879527 0.439764 0.898114i \(-0.355062\pi\)
0.439764 + 0.898114i \(0.355062\pi\)
\(6\) 1.09569e7 2.66319
\(7\) 1.64486e6 0.107844 0.0539219 0.998545i \(-0.482828\pi\)
0.0539219 + 0.998545i \(0.482828\pi\)
\(8\) 7.30585e7 1.53959
\(9\) 1.86316e8 1.44274
\(10\) 4.73928e8 1.49869
\(11\) −6.23226e8 −0.876612 −0.438306 0.898826i \(-0.644421\pi\)
−0.438306 + 0.898826i \(0.644421\pi\)
\(12\) 4.43138e9 2.97508
\(13\) 1.86416e9 0.633817 0.316909 0.948456i \(-0.397355\pi\)
0.316909 + 0.948456i \(0.397355\pi\)
\(14\) 1.01472e9 0.183763
\(15\) 1.36447e10 1.37464
\(16\) 1.23678e10 0.719898
\(17\) −1.09640e10 −0.381200 −0.190600 0.981668i \(-0.561043\pi\)
−0.190600 + 0.981668i \(0.561043\pi\)
\(18\) 1.14939e11 2.45839
\(19\) −3.02142e10 −0.408137 −0.204068 0.978957i \(-0.565416\pi\)
−0.204068 + 0.978957i \(0.565416\pi\)
\(20\) 1.91674e11 1.67421
\(21\) 2.92144e10 0.168552
\(22\) −3.84471e11 −1.49373
\(23\) 2.62133e11 0.697966 0.348983 0.937129i \(-0.386527\pi\)
0.348983 + 0.937129i \(0.386527\pi\)
\(24\) 1.29760e12 2.40627
\(25\) −1.72754e11 −0.226432
\(26\) 1.15001e12 1.08001
\(27\) 1.01550e12 0.691969
\(28\) 4.10391e11 0.205284
\(29\) 5.00246e11 0.185695
\(30\) 8.41747e12 2.34235
\(31\) −4.65989e12 −0.981299 −0.490649 0.871357i \(-0.663240\pi\)
−0.490649 + 0.871357i \(0.663240\pi\)
\(32\) −1.94620e12 −0.312905
\(33\) −1.10692e13 −1.37008
\(34\) −6.76375e12 −0.649556
\(35\) 1.26364e12 0.0948516
\(36\) 4.64857e13 2.74630
\(37\) 2.56925e13 1.20252 0.601258 0.799055i \(-0.294666\pi\)
0.601258 + 0.799055i \(0.294666\pi\)
\(38\) −1.86393e13 −0.695455
\(39\) 3.31094e13 0.990610
\(40\) 5.61262e13 1.35411
\(41\) 4.31933e13 0.844800 0.422400 0.906410i \(-0.361188\pi\)
0.422400 + 0.906410i \(0.361188\pi\)
\(42\) 1.80225e13 0.287208
\(43\) −6.43816e13 −0.840002 −0.420001 0.907524i \(-0.637970\pi\)
−0.420001 + 0.907524i \(0.637970\pi\)
\(44\) −1.55495e14 −1.66866
\(45\) 1.43134e14 1.26893
\(46\) 1.61711e14 1.18932
\(47\) −1.91076e14 −1.17051 −0.585255 0.810849i \(-0.699006\pi\)
−0.585255 + 0.810849i \(0.699006\pi\)
\(48\) 2.19665e14 1.12515
\(49\) −2.29925e14 −0.988370
\(50\) −1.06573e14 −0.385834
\(51\) −1.94733e14 −0.595788
\(52\) 4.65107e14 1.20649
\(53\) −7.46298e14 −1.64652 −0.823260 0.567664i \(-0.807847\pi\)
−0.823260 + 0.567664i \(0.807847\pi\)
\(54\) 6.26465e14 1.17910
\(55\) −4.78784e14 −0.771004
\(56\) 1.20171e14 0.166036
\(57\) −5.36637e14 −0.637888
\(58\) 3.08604e14 0.316420
\(59\) 2.00465e15 1.77744 0.888721 0.458448i \(-0.151594\pi\)
0.888721 + 0.458448i \(0.151594\pi\)
\(60\) 3.40434e15 2.61666
\(61\) 1.38827e15 0.927193 0.463597 0.886046i \(-0.346559\pi\)
0.463597 + 0.886046i \(0.346559\pi\)
\(62\) −2.87471e15 −1.67211
\(63\) 3.06463e14 0.155590
\(64\) −2.82169e15 −1.25308
\(65\) 1.43211e15 0.557460
\(66\) −6.82862e15 −2.33458
\(67\) −2.66642e15 −0.802219 −0.401110 0.916030i \(-0.631375\pi\)
−0.401110 + 0.916030i \(0.631375\pi\)
\(68\) −2.73551e15 −0.725627
\(69\) 4.65576e15 1.09087
\(70\) 7.79545e14 0.161625
\(71\) 6.06764e15 1.11513 0.557563 0.830135i \(-0.311737\pi\)
0.557563 + 0.830135i \(0.311737\pi\)
\(72\) 1.36119e16 2.22123
\(73\) 7.52337e15 1.09186 0.545931 0.837830i \(-0.316176\pi\)
0.545931 + 0.837830i \(0.316176\pi\)
\(74\) 1.58498e16 2.04906
\(75\) −3.06829e15 −0.353896
\(76\) −7.53843e15 −0.776901
\(77\) −1.02512e15 −0.0945372
\(78\) 2.04254e16 1.68797
\(79\) 2.43578e16 1.80637 0.903186 0.429250i \(-0.141222\pi\)
0.903186 + 0.429250i \(0.141222\pi\)
\(80\) 9.50135e15 0.633170
\(81\) −6.02451e15 −0.361243
\(82\) 2.66462e16 1.43952
\(83\) 1.12492e16 0.548223 0.274111 0.961698i \(-0.411616\pi\)
0.274111 + 0.961698i \(0.411616\pi\)
\(84\) 7.28899e15 0.320844
\(85\) −8.42294e15 −0.335276
\(86\) −3.97173e16 −1.43134
\(87\) 8.88491e15 0.290228
\(88\) −4.55320e16 −1.34963
\(89\) 3.40745e16 0.917518 0.458759 0.888561i \(-0.348294\pi\)
0.458759 + 0.888561i \(0.348294\pi\)
\(90\) 8.83002e16 2.16222
\(91\) 3.06628e15 0.0683533
\(92\) 6.54020e16 1.32860
\(93\) −8.27646e16 −1.53370
\(94\) −1.17876e17 −1.99452
\(95\) −2.32116e16 −0.358967
\(96\) −3.45666e16 −0.489048
\(97\) −7.90652e16 −1.02430 −0.512148 0.858897i \(-0.671150\pi\)
−0.512148 + 0.858897i \(0.671150\pi\)
\(98\) −1.41842e17 −1.68416
\(99\) −1.16117e17 −1.26472
\(100\) −4.31020e16 −0.431020
\(101\) −6.86893e16 −0.631186 −0.315593 0.948895i \(-0.602203\pi\)
−0.315593 + 0.948895i \(0.602203\pi\)
\(102\) −1.20131e17 −1.01521
\(103\) 1.98925e16 0.154730 0.0773648 0.997003i \(-0.475349\pi\)
0.0773648 + 0.997003i \(0.475349\pi\)
\(104\) 1.36193e17 0.975821
\(105\) 2.24436e16 0.148246
\(106\) −4.60395e17 −2.80563
\(107\) 2.76501e16 0.155573 0.0777865 0.996970i \(-0.475215\pi\)
0.0777865 + 0.996970i \(0.475215\pi\)
\(108\) 2.53366e17 1.31718
\(109\) −4.89888e16 −0.235490 −0.117745 0.993044i \(-0.537566\pi\)
−0.117745 + 0.993044i \(0.537566\pi\)
\(110\) −2.95364e17 −1.31377
\(111\) 4.56326e17 1.87944
\(112\) 2.03432e16 0.0776365
\(113\) −3.83273e17 −1.35626 −0.678128 0.734944i \(-0.737208\pi\)
−0.678128 + 0.734944i \(0.737208\pi\)
\(114\) −3.31054e17 −1.08694
\(115\) 2.01380e17 0.613880
\(116\) 1.24811e17 0.353477
\(117\) 3.47322e17 0.914433
\(118\) 1.23668e18 3.02872
\(119\) −1.80342e16 −0.0411101
\(120\) 9.96861e17 2.11638
\(121\) −1.17037e17 −0.231551
\(122\) 8.56430e17 1.57991
\(123\) 7.67160e17 1.32036
\(124\) −1.16264e18 −1.86793
\(125\) −7.18833e17 −1.07868
\(126\) 1.89058e17 0.265122
\(127\) 5.70520e17 0.748065 0.374032 0.927416i \(-0.377975\pi\)
0.374032 + 0.927416i \(0.377975\pi\)
\(128\) −1.48562e18 −1.82231
\(129\) −1.14349e18 −1.31286
\(130\) 8.83477e17 0.949897
\(131\) −1.50293e18 −1.51403 −0.757014 0.653399i \(-0.773343\pi\)
−0.757014 + 0.653399i \(0.773343\pi\)
\(132\) −2.76175e18 −2.60799
\(133\) −4.96981e16 −0.0440150
\(134\) −1.64493e18 −1.36696
\(135\) 7.80141e17 0.608606
\(136\) −8.01014e17 −0.586894
\(137\) −7.83173e17 −0.539179 −0.269589 0.962975i \(-0.586888\pi\)
−0.269589 + 0.962975i \(0.586888\pi\)
\(138\) 2.87216e18 1.85882
\(139\) −1.16884e18 −0.711425 −0.355713 0.934595i \(-0.615762\pi\)
−0.355713 + 0.934595i \(0.615762\pi\)
\(140\) 3.15277e17 0.180553
\(141\) −3.39372e18 −1.82942
\(142\) 3.74316e18 1.90015
\(143\) −1.16179e18 −0.555612
\(144\) 2.30431e18 1.03863
\(145\) 3.84307e17 0.163324
\(146\) 4.64120e18 1.86051
\(147\) −4.08371e18 −1.54475
\(148\) 6.41025e18 2.28903
\(149\) 4.95807e18 1.67197 0.835987 0.548749i \(-0.184896\pi\)
0.835987 + 0.548749i \(0.184896\pi\)
\(150\) −1.89284e18 −0.603030
\(151\) 4.70660e18 1.41711 0.708555 0.705656i \(-0.249348\pi\)
0.708555 + 0.705656i \(0.249348\pi\)
\(152\) −2.20741e18 −0.628364
\(153\) −2.04277e18 −0.549973
\(154\) −6.32400e17 −0.161089
\(155\) −3.57989e18 −0.863079
\(156\) 8.26079e18 1.88566
\(157\) −1.05313e18 −0.227686 −0.113843 0.993499i \(-0.536316\pi\)
−0.113843 + 0.993499i \(0.536316\pi\)
\(158\) 1.50264e19 3.07801
\(159\) −1.32550e19 −2.57339
\(160\) −1.49514e18 −0.275209
\(161\) 4.31171e17 0.0752713
\(162\) −3.71655e18 −0.615548
\(163\) 2.80001e18 0.440113 0.220057 0.975487i \(-0.429376\pi\)
0.220057 + 0.975487i \(0.429376\pi\)
\(164\) 1.07767e19 1.60810
\(165\) −8.50372e18 −1.20502
\(166\) 6.93967e18 0.934158
\(167\) −5.93390e18 −0.759015 −0.379508 0.925189i \(-0.623907\pi\)
−0.379508 + 0.925189i \(0.623907\pi\)
\(168\) 2.13436e18 0.259501
\(169\) −5.17533e18 −0.598275
\(170\) −5.19615e18 −0.571302
\(171\) −5.62938e18 −0.588835
\(172\) −1.60632e19 −1.59897
\(173\) −1.40993e19 −1.33599 −0.667997 0.744164i \(-0.732848\pi\)
−0.667997 + 0.744164i \(0.732848\pi\)
\(174\) 5.48115e18 0.494542
\(175\) −2.84155e17 −0.0244193
\(176\) −7.70790e18 −0.631071
\(177\) 3.56047e19 2.77801
\(178\) 2.10207e19 1.56343
\(179\) 3.92554e18 0.278387 0.139193 0.990265i \(-0.455549\pi\)
0.139193 + 0.990265i \(0.455549\pi\)
\(180\) 3.57119e19 2.41544
\(181\) 1.71539e18 0.110687 0.0553433 0.998467i \(-0.482375\pi\)
0.0553433 + 0.998467i \(0.482375\pi\)
\(182\) 1.89160e18 0.116472
\(183\) 2.46572e19 1.44913
\(184\) 1.91510e19 1.07458
\(185\) 1.97379e19 1.05765
\(186\) −5.10579e19 −2.61338
\(187\) 6.83305e18 0.334165
\(188\) −4.76735e19 −2.22810
\(189\) 1.67035e18 0.0746246
\(190\) −1.43194e19 −0.611671
\(191\) −2.17453e18 −0.0888345 −0.0444172 0.999013i \(-0.514143\pi\)
−0.0444172 + 0.999013i \(0.514143\pi\)
\(192\) −5.01162e19 −1.95847
\(193\) −3.43554e19 −1.28457 −0.642286 0.766465i \(-0.722014\pi\)
−0.642286 + 0.766465i \(0.722014\pi\)
\(194\) −4.87757e19 −1.74537
\(195\) 2.54358e19 0.871269
\(196\) −5.73662e19 −1.88139
\(197\) 5.01100e19 1.57384 0.786922 0.617053i \(-0.211674\pi\)
0.786922 + 0.617053i \(0.211674\pi\)
\(198\) −7.16329e19 −2.15506
\(199\) 4.41185e19 1.27166 0.635828 0.771831i \(-0.280659\pi\)
0.635828 + 0.771831i \(0.280659\pi\)
\(200\) −1.26211e19 −0.348613
\(201\) −4.73585e19 −1.25381
\(202\) −4.23747e19 −1.07552
\(203\) 8.22834e17 0.0200261
\(204\) −4.85857e19 −1.13410
\(205\) 3.31826e19 0.743024
\(206\) 1.22718e19 0.263655
\(207\) 4.88394e19 1.00698
\(208\) 2.30554e19 0.456284
\(209\) 1.88303e19 0.357778
\(210\) 1.38455e19 0.252607
\(211\) 3.20402e19 0.561428 0.280714 0.959791i \(-0.409429\pi\)
0.280714 + 0.959791i \(0.409429\pi\)
\(212\) −1.86201e20 −3.13420
\(213\) 1.07768e20 1.74286
\(214\) 1.70575e19 0.265093
\(215\) −4.94602e19 −0.738804
\(216\) 7.41907e19 1.06535
\(217\) −7.66486e18 −0.105827
\(218\) −3.02214e19 −0.401268
\(219\) 1.33623e20 1.70650
\(220\) −1.19456e20 −1.46763
\(221\) −2.04386e19 −0.241611
\(222\) 2.81509e20 3.20253
\(223\) −2.15691e19 −0.236179 −0.118089 0.993003i \(-0.537677\pi\)
−0.118089 + 0.993003i \(0.537677\pi\)
\(224\) −3.20123e18 −0.0337449
\(225\) −3.21867e19 −0.326682
\(226\) −2.36443e20 −2.31103
\(227\) 2.49194e19 0.234595 0.117297 0.993097i \(-0.462577\pi\)
0.117297 + 0.993097i \(0.462577\pi\)
\(228\) −1.33891e20 −1.21424
\(229\) 1.43336e19 0.125243 0.0626215 0.998037i \(-0.480054\pi\)
0.0626215 + 0.998037i \(0.480054\pi\)
\(230\) 1.24232e20 1.04604
\(231\) −1.82072e19 −0.147755
\(232\) 3.65473e19 0.285895
\(233\) −2.07402e20 −1.56418 −0.782090 0.623165i \(-0.785847\pi\)
−0.782090 + 0.623165i \(0.785847\pi\)
\(234\) 2.14264e20 1.55817
\(235\) −1.46792e20 −1.02950
\(236\) 5.00158e20 3.38342
\(237\) 4.32620e20 2.82323
\(238\) −1.11254e19 −0.0700506
\(239\) 2.86450e20 1.74047 0.870237 0.492634i \(-0.163966\pi\)
0.870237 + 0.492634i \(0.163966\pi\)
\(240\) 1.68754e20 0.989598
\(241\) 1.88925e19 0.106941 0.0534706 0.998569i \(-0.482972\pi\)
0.0534706 + 0.998569i \(0.482972\pi\)
\(242\) −7.22005e19 −0.394557
\(243\) −2.38143e20 −1.25656
\(244\) 3.46373e20 1.76494
\(245\) −1.76637e20 −0.869298
\(246\) 4.73265e20 2.24986
\(247\) −5.63240e19 −0.258684
\(248\) −3.40445e20 −1.51080
\(249\) 1.99797e20 0.856832
\(250\) −4.43451e20 −1.83804
\(251\) 1.59121e20 0.637530 0.318765 0.947834i \(-0.396732\pi\)
0.318765 + 0.947834i \(0.396732\pi\)
\(252\) 7.64623e19 0.296171
\(253\) −1.63368e20 −0.611846
\(254\) 3.51957e20 1.27468
\(255\) −1.49600e20 −0.524012
\(256\) −5.46642e20 −1.85209
\(257\) −3.68683e19 −0.120843 −0.0604215 0.998173i \(-0.519244\pi\)
−0.0604215 + 0.998173i \(0.519244\pi\)
\(258\) −7.05423e20 −2.23708
\(259\) 4.22604e19 0.129684
\(260\) 3.57311e20 1.06114
\(261\) 9.32037e19 0.267910
\(262\) −9.27167e20 −2.57987
\(263\) 6.68560e20 1.80101 0.900506 0.434844i \(-0.143197\pi\)
0.900506 + 0.434844i \(0.143197\pi\)
\(264\) −8.08697e20 −2.10937
\(265\) −5.73332e20 −1.44816
\(266\) −3.06590e19 −0.0750005
\(267\) 6.05200e20 1.43401
\(268\) −6.65271e20 −1.52705
\(269\) 8.52453e20 1.89573 0.947864 0.318674i \(-0.103237\pi\)
0.947864 + 0.318674i \(0.103237\pi\)
\(270\) 4.81273e20 1.03705
\(271\) 2.06618e19 0.0431448 0.0215724 0.999767i \(-0.493133\pi\)
0.0215724 + 0.999767i \(0.493133\pi\)
\(272\) −1.35600e20 −0.274425
\(273\) 5.44603e19 0.106831
\(274\) −4.83143e20 −0.918747
\(275\) 1.07665e20 0.198493
\(276\) 1.16161e21 2.07650
\(277\) 4.95320e20 0.858633 0.429316 0.903154i \(-0.358755\pi\)
0.429316 + 0.903154i \(0.358755\pi\)
\(278\) −7.21063e20 −1.21225
\(279\) −8.68210e20 −1.41576
\(280\) 9.23196e19 0.146033
\(281\) 6.31720e20 0.969441 0.484720 0.874669i \(-0.338921\pi\)
0.484720 + 0.874669i \(0.338921\pi\)
\(282\) −2.09360e21 −3.11729
\(283\) −7.12915e20 −1.03004 −0.515019 0.857179i \(-0.672215\pi\)
−0.515019 + 0.857179i \(0.672215\pi\)
\(284\) 1.51387e21 2.12268
\(285\) −4.12263e20 −0.561040
\(286\) −7.16715e20 −0.946749
\(287\) 7.10469e19 0.0911064
\(288\) −3.62608e20 −0.451441
\(289\) −7.07031e20 −0.854686
\(290\) 2.37081e20 0.278300
\(291\) −1.40428e21 −1.60090
\(292\) 1.87708e21 2.07839
\(293\) 3.49413e20 0.375806 0.187903 0.982188i \(-0.439831\pi\)
0.187903 + 0.982188i \(0.439831\pi\)
\(294\) −2.51926e21 −2.63221
\(295\) 1.54004e21 1.56331
\(296\) 1.87705e21 1.85139
\(297\) −6.32884e20 −0.606589
\(298\) 3.05866e21 2.84900
\(299\) 4.88657e20 0.442383
\(300\) −7.65537e20 −0.673652
\(301\) −1.05899e20 −0.0905889
\(302\) 2.90352e21 2.41472
\(303\) −1.21999e21 −0.986497
\(304\) −3.73682e20 −0.293817
\(305\) 1.06652e21 0.815492
\(306\) −1.26019e21 −0.937140
\(307\) −4.85152e20 −0.350915 −0.175457 0.984487i \(-0.556140\pi\)
−0.175457 + 0.984487i \(0.556140\pi\)
\(308\) −2.55766e20 −0.179954
\(309\) 3.53313e20 0.241831
\(310\) −2.20845e21 −1.47066
\(311\) 8.15051e19 0.0528106 0.0264053 0.999651i \(-0.491594\pi\)
0.0264053 + 0.999651i \(0.491594\pi\)
\(312\) 2.41893e21 1.52514
\(313\) −6.96402e20 −0.427300 −0.213650 0.976910i \(-0.568535\pi\)
−0.213650 + 0.976910i \(0.568535\pi\)
\(314\) −6.49684e20 −0.387972
\(315\) 2.35436e20 0.136846
\(316\) 6.07725e21 3.43848
\(317\) −1.74073e20 −0.0958798 −0.0479399 0.998850i \(-0.515266\pi\)
−0.0479399 + 0.998850i \(0.515266\pi\)
\(318\) −8.17710e21 −4.38499
\(319\) −3.11766e20 −0.162783
\(320\) −2.16772e21 −1.10212
\(321\) 4.91095e20 0.243149
\(322\) 2.65991e20 0.128260
\(323\) 3.31269e20 0.155582
\(324\) −1.50311e21 −0.687636
\(325\) −3.22040e20 −0.143516
\(326\) 1.72734e21 0.749942
\(327\) −8.70094e20 −0.368053
\(328\) 3.15564e21 1.30065
\(329\) −3.14294e20 −0.126232
\(330\) −5.24599e21 −2.05333
\(331\) 1.98290e21 0.756422 0.378211 0.925719i \(-0.376539\pi\)
0.378211 + 0.925719i \(0.376539\pi\)
\(332\) 2.80666e21 1.04356
\(333\) 4.78690e21 1.73492
\(334\) −3.66065e21 −1.29334
\(335\) −2.04844e21 −0.705574
\(336\) 3.61317e20 0.121340
\(337\) 3.36216e21 1.10094 0.550471 0.834854i \(-0.314448\pi\)
0.550471 + 0.834854i \(0.314448\pi\)
\(338\) −3.19269e21 −1.01945
\(339\) −6.80734e21 −2.11973
\(340\) −2.10152e21 −0.638208
\(341\) 2.90416e21 0.860218
\(342\) −3.47279e21 −1.00336
\(343\) −7.60838e20 −0.214433
\(344\) −4.70363e21 −1.29326
\(345\) 3.57672e21 0.959450
\(346\) −8.69791e21 −2.27650
\(347\) −6.87056e21 −1.75465 −0.877327 0.479894i \(-0.840675\pi\)
−0.877327 + 0.479894i \(0.840675\pi\)
\(348\) 2.21678e21 0.552458
\(349\) 5.26478e21 1.28045 0.640227 0.768186i \(-0.278840\pi\)
0.640227 + 0.768186i \(0.278840\pi\)
\(350\) −1.75297e20 −0.0416098
\(351\) 1.89305e21 0.438582
\(352\) 1.21292e21 0.274297
\(353\) 7.61718e21 1.68155 0.840774 0.541387i \(-0.182101\pi\)
0.840774 + 0.541387i \(0.182101\pi\)
\(354\) 2.19647e22 4.73366
\(355\) 4.66137e21 0.980783
\(356\) 8.50157e21 1.74652
\(357\) −3.20307e20 −0.0642521
\(358\) 2.42168e21 0.474364
\(359\) 6.16367e20 0.117906 0.0589531 0.998261i \(-0.481224\pi\)
0.0589531 + 0.998261i \(0.481224\pi\)
\(360\) 1.04572e22 1.95363
\(361\) −4.56749e21 −0.833424
\(362\) 1.05823e21 0.188607
\(363\) −2.07870e21 −0.361897
\(364\) 7.65034e20 0.130113
\(365\) 5.77972e21 0.960323
\(366\) 1.52111e22 2.46929
\(367\) −6.11806e21 −0.970403 −0.485201 0.874402i \(-0.661254\pi\)
−0.485201 + 0.874402i \(0.661254\pi\)
\(368\) 3.24199e21 0.502464
\(369\) 8.04759e21 1.21883
\(370\) 1.21764e22 1.80220
\(371\) −1.22755e21 −0.177567
\(372\) −2.06497e22 −2.91944
\(373\) −2.66728e21 −0.368590 −0.184295 0.982871i \(-0.559000\pi\)
−0.184295 + 0.982871i \(0.559000\pi\)
\(374\) 4.21534e21 0.569409
\(375\) −1.27672e22 −1.68590
\(376\) −1.39598e22 −1.80211
\(377\) 9.32538e20 0.117697
\(378\) 1.03045e21 0.127158
\(379\) 7.99626e21 0.964837 0.482418 0.875941i \(-0.339758\pi\)
0.482418 + 0.875941i \(0.339758\pi\)
\(380\) −5.79129e21 −0.683305
\(381\) 1.01330e22 1.16917
\(382\) −1.34148e21 −0.151372
\(383\) −3.17222e21 −0.350085 −0.175043 0.984561i \(-0.556006\pi\)
−0.175043 + 0.984561i \(0.556006\pi\)
\(384\) −2.63862e22 −2.84814
\(385\) −7.87532e20 −0.0831480
\(386\) −2.11940e22 −2.18888
\(387\) −1.19953e22 −1.21190
\(388\) −1.97267e22 −1.94978
\(389\) 1.28849e22 1.24598 0.622988 0.782231i \(-0.285919\pi\)
0.622988 + 0.782231i \(0.285919\pi\)
\(390\) 1.56915e22 1.48462
\(391\) −2.87402e21 −0.266065
\(392\) −1.67980e22 −1.52169
\(393\) −2.66937e22 −2.36631
\(394\) 3.09131e22 2.68179
\(395\) 1.87125e22 1.58875
\(396\) −2.89711e22 −2.40744
\(397\) −8.69038e21 −0.706837 −0.353419 0.935465i \(-0.614981\pi\)
−0.353419 + 0.935465i \(0.614981\pi\)
\(398\) 2.72169e22 2.16687
\(399\) −8.82691e20 −0.0687922
\(400\) −2.13658e21 −0.163008
\(401\) 4.36758e20 0.0326222 0.0163111 0.999867i \(-0.494808\pi\)
0.0163111 + 0.999867i \(0.494808\pi\)
\(402\) −2.92157e22 −2.13646
\(403\) −8.68677e21 −0.621964
\(404\) −1.71379e22 −1.20148
\(405\) −4.62824e21 −0.317723
\(406\) 5.07611e20 0.0341240
\(407\) −1.60122e22 −1.05414
\(408\) −1.42269e22 −0.917272
\(409\) 2.33651e22 1.47543 0.737715 0.675112i \(-0.235905\pi\)
0.737715 + 0.675112i \(0.235905\pi\)
\(410\) 2.04705e22 1.26610
\(411\) −1.39100e22 −0.842697
\(412\) 4.96318e21 0.294533
\(413\) 3.29736e21 0.191686
\(414\) 3.01293e22 1.71587
\(415\) 8.64202e21 0.482177
\(416\) −3.62803e21 −0.198325
\(417\) −2.07599e22 −1.11191
\(418\) 1.16165e22 0.609644
\(419\) 1.48396e22 0.763139 0.381569 0.924340i \(-0.375384\pi\)
0.381569 + 0.924340i \(0.375384\pi\)
\(420\) 5.59966e21 0.282191
\(421\) 2.90867e22 1.43647 0.718236 0.695800i \(-0.244950\pi\)
0.718236 + 0.695800i \(0.244950\pi\)
\(422\) 1.97657e22 0.956659
\(423\) −3.56005e22 −1.68874
\(424\) −5.45234e22 −2.53497
\(425\) 1.89407e21 0.0863159
\(426\) 6.64825e22 2.96979
\(427\) 2.28351e21 0.0999920
\(428\) 6.89868e21 0.296138
\(429\) −2.06347e22 −0.868381
\(430\) −3.05123e22 −1.25890
\(431\) −2.74838e22 −1.11178 −0.555892 0.831255i \(-0.687623\pi\)
−0.555892 + 0.831255i \(0.687623\pi\)
\(432\) 1.25594e22 0.498147
\(433\) 7.84182e21 0.304979 0.152489 0.988305i \(-0.451271\pi\)
0.152489 + 0.988305i \(0.451271\pi\)
\(434\) −4.72849e21 −0.180326
\(435\) 6.82571e21 0.255264
\(436\) −1.22227e22 −0.448262
\(437\) −7.92013e21 −0.284866
\(438\) 8.24328e22 2.90784
\(439\) −1.59731e22 −0.552637 −0.276319 0.961066i \(-0.589115\pi\)
−0.276319 + 0.961066i \(0.589115\pi\)
\(440\) −3.49793e22 −1.18703
\(441\) −4.28386e22 −1.42596
\(442\) −1.26087e22 −0.411700
\(443\) 2.94720e22 0.944013 0.472007 0.881595i \(-0.343530\pi\)
0.472007 + 0.881595i \(0.343530\pi\)
\(444\) 1.13853e23 3.57758
\(445\) 2.61772e22 0.806982
\(446\) −1.33061e22 −0.402443
\(447\) 8.80607e22 2.61317
\(448\) −4.64128e21 −0.135137
\(449\) 6.31767e22 1.80494 0.902470 0.430752i \(-0.141752\pi\)
0.902470 + 0.430752i \(0.141752\pi\)
\(450\) −1.98561e22 −0.556658
\(451\) −2.69192e22 −0.740562
\(452\) −9.56265e22 −2.58167
\(453\) 8.35943e22 2.21484
\(454\) 1.53729e22 0.399744
\(455\) 2.35562e21 0.0601186
\(456\) −3.92059e22 −0.982087
\(457\) −5.41927e22 −1.33246 −0.666228 0.745748i \(-0.732092\pi\)
−0.666228 + 0.745748i \(0.732092\pi\)
\(458\) 8.84246e21 0.213411
\(459\) −1.11339e22 −0.263779
\(460\) 5.02441e22 1.16854
\(461\) −6.10164e22 −1.39312 −0.696560 0.717499i \(-0.745287\pi\)
−0.696560 + 0.717499i \(0.745287\pi\)
\(462\) −1.12321e22 −0.251770
\(463\) 2.32813e22 0.512351 0.256176 0.966630i \(-0.417537\pi\)
0.256176 + 0.966630i \(0.417537\pi\)
\(464\) 6.18692e21 0.133682
\(465\) −6.35827e22 −1.34893
\(466\) −1.27947e23 −2.66533
\(467\) −1.94649e22 −0.398161 −0.199080 0.979983i \(-0.563796\pi\)
−0.199080 + 0.979983i \(0.563796\pi\)
\(468\) 8.66566e22 1.74065
\(469\) −4.38589e21 −0.0865144
\(470\) −9.05565e22 −1.75423
\(471\) −1.87048e22 −0.355857
\(472\) 1.46457e23 2.73654
\(473\) 4.01243e22 0.736356
\(474\) 2.66885e23 4.81071
\(475\) 5.21962e21 0.0924151
\(476\) −4.49953e21 −0.0782543
\(477\) −1.39047e23 −2.37550
\(478\) 1.76713e23 2.96572
\(479\) −3.32545e22 −0.548275 −0.274137 0.961691i \(-0.588392\pi\)
−0.274137 + 0.961691i \(0.588392\pi\)
\(480\) −2.65553e22 −0.430131
\(481\) 4.78948e22 0.762176
\(482\) 1.16549e22 0.182225
\(483\) 7.65806e21 0.117644
\(484\) −2.92006e22 −0.440764
\(485\) −6.07407e22 −0.900896
\(486\) −1.46912e23 −2.14115
\(487\) 3.28210e21 0.0470063 0.0235031 0.999724i \(-0.492518\pi\)
0.0235031 + 0.999724i \(0.492518\pi\)
\(488\) 1.01425e23 1.42750
\(489\) 4.97311e22 0.687864
\(490\) −1.08968e23 −1.48126
\(491\) 2.84768e22 0.380450 0.190225 0.981740i \(-0.439078\pi\)
0.190225 + 0.981740i \(0.439078\pi\)
\(492\) 1.91406e23 2.51335
\(493\) −5.48470e21 −0.0707871
\(494\) −3.47466e22 −0.440791
\(495\) −8.92050e22 −1.11236
\(496\) −5.76323e22 −0.706435
\(497\) 9.98040e21 0.120259
\(498\) 1.23256e23 1.46002
\(499\) −3.85028e22 −0.448371 −0.224186 0.974546i \(-0.571972\pi\)
−0.224186 + 0.974546i \(0.571972\pi\)
\(500\) −1.79348e23 −2.05330
\(501\) −1.05392e23 −1.18628
\(502\) 9.81624e22 1.08633
\(503\) −8.27652e22 −0.900575 −0.450287 0.892884i \(-0.648678\pi\)
−0.450287 + 0.892884i \(0.648678\pi\)
\(504\) 2.23897e22 0.239546
\(505\) −5.27695e22 −0.555145
\(506\) −1.00782e23 −1.04257
\(507\) −9.19194e22 −0.935061
\(508\) 1.42344e23 1.42396
\(509\) −1.71083e22 −0.168309 −0.0841543 0.996453i \(-0.526819\pi\)
−0.0841543 + 0.996453i \(0.526819\pi\)
\(510\) −9.22892e22 −0.892903
\(511\) 1.23749e22 0.117751
\(512\) −1.42503e23 −1.33361
\(513\) −3.06824e22 −0.282418
\(514\) −2.27442e22 −0.205913
\(515\) 1.52821e22 0.136089
\(516\) −2.85299e23 −2.49907
\(517\) 1.19084e23 1.02608
\(518\) 2.60707e22 0.220978
\(519\) −2.50418e23 −2.08806
\(520\) 1.04628e23 0.858261
\(521\) −5.27327e22 −0.425559 −0.212779 0.977100i \(-0.568252\pi\)
−0.212779 + 0.977100i \(0.568252\pi\)
\(522\) 5.74978e22 0.456512
\(523\) −9.98311e22 −0.779833 −0.389916 0.920850i \(-0.627496\pi\)
−0.389916 + 0.920850i \(0.627496\pi\)
\(524\) −3.74981e23 −2.88200
\(525\) −5.04691e21 −0.0381655
\(526\) 4.12438e23 3.06888
\(527\) 5.10910e22 0.374071
\(528\) −1.36901e23 −0.986318
\(529\) −7.23365e22 −0.512843
\(530\) −3.53691e23 −2.46763
\(531\) 3.73497e23 2.56439
\(532\) −1.23997e22 −0.0837839
\(533\) 8.05192e22 0.535449
\(534\) 3.73351e23 2.44352
\(535\) 2.12418e22 0.136831
\(536\) −1.94805e23 −1.23509
\(537\) 6.97217e22 0.435098
\(538\) 5.25883e23 3.23027
\(539\) 1.43295e23 0.866417
\(540\) 1.94645e23 1.15850
\(541\) −1.32366e23 −0.775532 −0.387766 0.921758i \(-0.626753\pi\)
−0.387766 + 0.921758i \(0.626753\pi\)
\(542\) 1.27463e22 0.0735176
\(543\) 3.04672e22 0.172995
\(544\) 2.13382e22 0.119280
\(545\) −3.76349e22 −0.207119
\(546\) 3.35968e22 0.182038
\(547\) 2.22866e23 1.18892 0.594458 0.804126i \(-0.297366\pi\)
0.594458 + 0.804126i \(0.297366\pi\)
\(548\) −1.95401e23 −1.02634
\(549\) 2.58656e23 1.33770
\(550\) 6.64188e22 0.338227
\(551\) −1.51145e22 −0.0757891
\(552\) 3.40143e23 1.67950
\(553\) 4.00651e22 0.194806
\(554\) 3.05565e23 1.46309
\(555\) 3.50565e23 1.65302
\(556\) −2.91625e23 −1.35422
\(557\) −2.46656e23 −1.12803 −0.564017 0.825763i \(-0.690745\pi\)
−0.564017 + 0.825763i \(0.690745\pi\)
\(558\) −5.35603e23 −2.41242
\(559\) −1.20018e23 −0.532408
\(560\) 1.56284e22 0.0682834
\(561\) 1.21362e23 0.522275
\(562\) 3.89711e23 1.65190
\(563\) 1.27538e23 0.532500 0.266250 0.963904i \(-0.414215\pi\)
0.266250 + 0.963904i \(0.414215\pi\)
\(564\) −8.46732e23 −3.48236
\(565\) −2.94444e23 −1.19286
\(566\) −4.39801e23 −1.75516
\(567\) −9.90946e21 −0.0389578
\(568\) 4.43293e23 1.71684
\(569\) −9.14120e22 −0.348778 −0.174389 0.984677i \(-0.555795\pi\)
−0.174389 + 0.984677i \(0.555795\pi\)
\(570\) −2.54327e23 −0.955997
\(571\) 4.57553e23 1.69447 0.847237 0.531215i \(-0.178264\pi\)
0.847237 + 0.531215i \(0.178264\pi\)
\(572\) −2.89866e23 −1.05762
\(573\) −3.86220e22 −0.138842
\(574\) 4.38292e22 0.155243
\(575\) −4.52844e22 −0.158042
\(576\) −5.25724e23 −1.80787
\(577\) −2.90602e23 −0.984702 −0.492351 0.870397i \(-0.663862\pi\)
−0.492351 + 0.870397i \(0.663862\pi\)
\(578\) −4.36171e23 −1.45636
\(579\) −6.10190e23 −2.00769
\(580\) 9.58844e22 0.310892
\(581\) 1.85033e22 0.0591224
\(582\) −8.66309e23 −2.72789
\(583\) 4.65112e23 1.44336
\(584\) 5.49646e23 1.68102
\(585\) 2.66825e23 0.804269
\(586\) 2.15554e23 0.640365
\(587\) 4.87166e23 1.42644 0.713219 0.700941i \(-0.247236\pi\)
0.713219 + 0.700941i \(0.247236\pi\)
\(588\) −1.01888e24 −2.94048
\(589\) 1.40795e23 0.400504
\(590\) 9.50058e23 2.66384
\(591\) 8.90008e23 2.45980
\(592\) 3.17758e23 0.865689
\(593\) −1.95140e23 −0.524061 −0.262031 0.965060i \(-0.584392\pi\)
−0.262031 + 0.965060i \(0.584392\pi\)
\(594\) −3.90429e23 −1.03361
\(595\) −1.38545e22 −0.0361575
\(596\) 1.23704e24 3.18265
\(597\) 7.83592e23 1.98750
\(598\) 3.01455e23 0.753810
\(599\) −6.05879e23 −1.49368 −0.746841 0.665003i \(-0.768430\pi\)
−0.746841 + 0.665003i \(0.768430\pi\)
\(600\) −2.24165e23 −0.544856
\(601\) −3.30763e23 −0.792655 −0.396327 0.918109i \(-0.629715\pi\)
−0.396327 + 0.918109i \(0.629715\pi\)
\(602\) −6.53294e22 −0.154361
\(603\) −4.96796e23 −1.15739
\(604\) 1.17429e24 2.69751
\(605\) −8.99117e22 −0.203655
\(606\) −7.52621e23 −1.68097
\(607\) −3.52469e23 −0.776277 −0.388138 0.921601i \(-0.626882\pi\)
−0.388138 + 0.921601i \(0.626882\pi\)
\(608\) 5.88029e22 0.127708
\(609\) 1.46144e22 0.0312993
\(610\) 6.57940e23 1.38958
\(611\) −3.56196e23 −0.741890
\(612\) −5.09669e23 −1.04689
\(613\) −5.57210e22 −0.112877 −0.0564385 0.998406i \(-0.517974\pi\)
−0.0564385 + 0.998406i \(0.517974\pi\)
\(614\) −2.99293e23 −0.597950
\(615\) 5.89359e23 1.16129
\(616\) −7.48936e22 −0.145549
\(617\) 8.07897e23 1.54858 0.774288 0.632834i \(-0.218108\pi\)
0.774288 + 0.632834i \(0.218108\pi\)
\(618\) 2.17960e23 0.412074
\(619\) 8.02898e23 1.49723 0.748617 0.663002i \(-0.230718\pi\)
0.748617 + 0.663002i \(0.230718\pi\)
\(620\) −8.93181e23 −1.64290
\(621\) 2.66195e23 0.482971
\(622\) 5.02809e22 0.0899880
\(623\) 5.60477e22 0.0989486
\(624\) 4.09489e23 0.713138
\(625\) −4.20432e23 −0.722297
\(626\) −4.29614e23 −0.728109
\(627\) 3.34446e23 0.559180
\(628\) −2.62757e23 −0.433408
\(629\) −2.81692e23 −0.458400
\(630\) 1.45241e23 0.233182
\(631\) 8.50827e23 1.34770 0.673848 0.738870i \(-0.264640\pi\)
0.673848 + 0.738870i \(0.264640\pi\)
\(632\) 1.77954e24 2.78108
\(633\) 5.69068e23 0.877471
\(634\) −1.07386e23 −0.163377
\(635\) 4.38294e23 0.657943
\(636\) −3.30713e24 −4.89853
\(637\) −4.28616e23 −0.626446
\(638\) −1.92330e23 −0.277378
\(639\) 1.13050e24 1.60884
\(640\) −1.14131e24 −1.60277
\(641\) 5.24512e23 0.726879 0.363439 0.931618i \(-0.381602\pi\)
0.363439 + 0.931618i \(0.381602\pi\)
\(642\) 3.02959e23 0.414320
\(643\) −4.45693e23 −0.601510 −0.300755 0.953701i \(-0.597239\pi\)
−0.300755 + 0.953701i \(0.597239\pi\)
\(644\) 1.07577e23 0.143281
\(645\) −8.78467e23 −1.15470
\(646\) 2.04361e23 0.265108
\(647\) 1.34835e24 1.72630 0.863151 0.504946i \(-0.168488\pi\)
0.863151 + 0.504946i \(0.168488\pi\)
\(648\) −4.40142e23 −0.556167
\(649\) −1.24935e24 −1.55813
\(650\) −1.98668e23 −0.244548
\(651\) −1.36136e23 −0.165400
\(652\) 6.98600e23 0.837769
\(653\) 5.92522e23 0.701363 0.350681 0.936495i \(-0.385950\pi\)
0.350681 + 0.936495i \(0.385950\pi\)
\(654\) −5.36765e23 −0.627153
\(655\) −1.15461e24 −1.33163
\(656\) 5.34204e23 0.608170
\(657\) 1.40172e24 1.57527
\(658\) −1.93889e23 −0.215097
\(659\) −5.92079e23 −0.648416 −0.324208 0.945986i \(-0.605098\pi\)
−0.324208 + 0.945986i \(0.605098\pi\)
\(660\) −2.12167e24 −2.29380
\(661\) 1.59306e23 0.170028 0.0850138 0.996380i \(-0.472907\pi\)
0.0850138 + 0.996380i \(0.472907\pi\)
\(662\) 1.22326e24 1.28892
\(663\) −3.63012e23 −0.377621
\(664\) 8.21848e23 0.844040
\(665\) −3.81798e22 −0.0387124
\(666\) 2.95306e24 2.95626
\(667\) 1.31131e23 0.129609
\(668\) −1.48051e24 −1.44481
\(669\) −3.83091e23 −0.369130
\(670\) −1.26369e24 −1.20228
\(671\) −8.65205e23 −0.812789
\(672\) −5.68572e22 −0.0527408
\(673\) −1.08833e24 −0.996853 −0.498427 0.866932i \(-0.666089\pi\)
−0.498427 + 0.866932i \(0.666089\pi\)
\(674\) 2.07413e24 1.87598
\(675\) −1.75431e23 −0.156684
\(676\) −1.29124e24 −1.13884
\(677\) −1.36486e24 −1.18873 −0.594365 0.804196i \(-0.702596\pi\)
−0.594365 + 0.804196i \(0.702596\pi\)
\(678\) −4.19948e24 −3.61196
\(679\) −1.30051e23 −0.110464
\(680\) −6.15367e23 −0.516189
\(681\) 4.42596e23 0.366654
\(682\) 1.79159e24 1.46579
\(683\) 1.66169e24 1.34269 0.671344 0.741146i \(-0.265717\pi\)
0.671344 + 0.741146i \(0.265717\pi\)
\(684\) −1.40453e24 −1.12087
\(685\) −6.01661e23 −0.474222
\(686\) −4.69365e23 −0.365389
\(687\) 2.54580e23 0.195746
\(688\) −7.96256e23 −0.604715
\(689\) −1.39122e24 −1.04359
\(690\) 2.20649e24 1.63488
\(691\) −1.86577e24 −1.36551 −0.682756 0.730646i \(-0.739219\pi\)
−0.682756 + 0.730646i \(0.739219\pi\)
\(692\) −3.51776e24 −2.54311
\(693\) −1.90995e23 −0.136393
\(694\) −4.23848e24 −2.98989
\(695\) −8.97945e23 −0.625718
\(696\) 6.49119e23 0.446833
\(697\) −4.73572e23 −0.322038
\(698\) 3.24787e24 2.18186
\(699\) −3.68368e24 −2.44470
\(700\) −7.08966e22 −0.0464828
\(701\) −1.63544e24 −1.05933 −0.529666 0.848206i \(-0.677683\pi\)
−0.529666 + 0.848206i \(0.677683\pi\)
\(702\) 1.16783e24 0.747333
\(703\) −7.76277e23 −0.490791
\(704\) 1.75855e24 1.09847
\(705\) −2.60718e24 −1.60903
\(706\) 4.69907e24 2.86531
\(707\) −1.12984e23 −0.0680695
\(708\) 8.88335e24 5.28803
\(709\) 5.44397e23 0.320201 0.160101 0.987101i \(-0.448818\pi\)
0.160101 + 0.987101i \(0.448818\pi\)
\(710\) 2.87562e24 1.67123
\(711\) 4.53823e24 2.60612
\(712\) 2.48943e24 1.41260
\(713\) −1.22151e24 −0.684913
\(714\) −1.97599e23 −0.109484
\(715\) −8.92529e23 −0.488676
\(716\) 9.79420e23 0.529917
\(717\) 5.08767e24 2.72023
\(718\) 3.80240e23 0.200909
\(719\) −1.75855e24 −0.918247 −0.459123 0.888372i \(-0.651836\pi\)
−0.459123 + 0.888372i \(0.651836\pi\)
\(720\) 1.77025e24 0.913499
\(721\) 3.27204e22 0.0166866
\(722\) −2.81771e24 −1.42013
\(723\) 3.35551e23 0.167141
\(724\) 4.27989e23 0.210695
\(725\) −8.64194e22 −0.0420473
\(726\) −1.28236e24 −0.616663
\(727\) 2.90848e24 1.38237 0.691185 0.722678i \(-0.257089\pi\)
0.691185 + 0.722678i \(0.257089\pi\)
\(728\) 2.24018e23 0.105236
\(729\) −3.45167e24 −1.60268
\(730\) 3.56554e24 1.63637
\(731\) 7.05881e23 0.320209
\(732\) 6.15195e24 2.75847
\(733\) 2.06719e24 0.916213 0.458106 0.888897i \(-0.348528\pi\)
0.458106 + 0.888897i \(0.348528\pi\)
\(734\) −3.77426e24 −1.65354
\(735\) −3.13725e24 −1.35865
\(736\) −5.10163e23 −0.218397
\(737\) 1.66178e24 0.703235
\(738\) 4.96460e24 2.07685
\(739\) −8.82599e23 −0.364994 −0.182497 0.983206i \(-0.558418\pi\)
−0.182497 + 0.983206i \(0.558418\pi\)
\(740\) 4.92459e24 2.01326
\(741\) −1.00038e24 −0.404304
\(742\) −7.57284e23 −0.302570
\(743\) −4.67097e24 −1.84502 −0.922512 0.385967i \(-0.873868\pi\)
−0.922512 + 0.385967i \(0.873868\pi\)
\(744\) −6.04666e24 −2.36127
\(745\) 3.80897e24 1.47055
\(746\) −1.64546e24 −0.628068
\(747\) 2.09590e24 0.790942
\(748\) 1.70484e24 0.636093
\(749\) 4.54805e22 0.0167776
\(750\) −7.87617e24 −2.87273
\(751\) 4.67198e24 1.68485 0.842426 0.538813i \(-0.181127\pi\)
0.842426 + 0.538813i \(0.181127\pi\)
\(752\) −2.36319e24 −0.842648
\(753\) 2.82616e24 0.996412
\(754\) 5.75287e23 0.200553
\(755\) 3.61578e24 1.24639
\(756\) 4.16751e23 0.142050
\(757\) −4.38253e24 −1.47710 −0.738550 0.674198i \(-0.764489\pi\)
−0.738550 + 0.674198i \(0.764489\pi\)
\(758\) 4.93293e24 1.64406
\(759\) −2.90159e24 −0.956270
\(760\) −1.69581e24 −0.552664
\(761\) −2.60349e24 −0.839046 −0.419523 0.907745i \(-0.637803\pi\)
−0.419523 + 0.907745i \(0.637803\pi\)
\(762\) 6.25113e24 1.99224
\(763\) −8.05796e22 −0.0253961
\(764\) −5.42544e23 −0.169099
\(765\) −1.56932e24 −0.483716
\(766\) −1.95696e24 −0.596537
\(767\) 3.73698e24 1.12657
\(768\) −9.70895e24 −2.89469
\(769\) 4.34175e24 1.28024 0.640119 0.768275i \(-0.278885\pi\)
0.640119 + 0.768275i \(0.278885\pi\)
\(770\) −4.85832e23 −0.141682
\(771\) −6.54821e23 −0.188869
\(772\) −8.57167e24 −2.44522
\(773\) −4.32285e24 −1.21968 −0.609838 0.792526i \(-0.708765\pi\)
−0.609838 + 0.792526i \(0.708765\pi\)
\(774\) −7.39996e24 −2.06505
\(775\) 8.05013e23 0.222197
\(776\) −5.77639e24 −1.57700
\(777\) 7.50591e23 0.202686
\(778\) 7.94876e24 2.12311
\(779\) −1.30505e24 −0.344794
\(780\) 6.34623e24 1.65849
\(781\) −3.78151e24 −0.977533
\(782\) −1.77300e24 −0.453368
\(783\) 5.07999e23 0.128495
\(784\) −2.84365e24 −0.711525
\(785\) −8.09055e23 −0.200256
\(786\) −1.64675e25 −4.03214
\(787\) −2.56312e24 −0.620847 −0.310423 0.950598i \(-0.600471\pi\)
−0.310423 + 0.950598i \(0.600471\pi\)
\(788\) 1.25024e25 2.99586
\(789\) 1.18743e25 2.81485
\(790\) 1.15438e25 2.70720
\(791\) −6.30430e23 −0.146264
\(792\) −8.48331e24 −1.94716
\(793\) 2.58795e24 0.587671
\(794\) −5.36114e24 −1.20443
\(795\) −1.01830e25 −2.26337
\(796\) 1.10075e25 2.42063
\(797\) −2.79968e24 −0.609133 −0.304567 0.952491i \(-0.598512\pi\)
−0.304567 + 0.952491i \(0.598512\pi\)
\(798\) −5.44537e23 −0.117220
\(799\) 2.09496e24 0.446199
\(800\) 3.36214e23 0.0708517
\(801\) 6.34861e24 1.32374
\(802\) 2.69438e23 0.0555874
\(803\) −4.68876e24 −0.957140
\(804\) −1.18159e25 −2.38666
\(805\) 3.31241e23 0.0662032
\(806\) −5.35891e24 −1.05981
\(807\) 1.51405e25 2.96289
\(808\) −5.01834e24 −0.971769
\(809\) −4.86003e24 −0.931272 −0.465636 0.884976i \(-0.654174\pi\)
−0.465636 + 0.884976i \(0.654174\pi\)
\(810\) −2.85518e24 −0.541391
\(811\) −1.04176e25 −1.95476 −0.977378 0.211502i \(-0.932165\pi\)
−0.977378 + 0.211502i \(0.932165\pi\)
\(812\) 2.05297e23 0.0381203
\(813\) 3.66975e23 0.0674321
\(814\) −9.87800e24 −1.79623
\(815\) 2.15106e24 0.387091
\(816\) −2.40840e24 −0.428907
\(817\) 1.94524e24 0.342835
\(818\) 1.44140e25 2.51410
\(819\) 5.71295e23 0.0986160
\(820\) 8.27905e24 1.41437
\(821\) −7.25397e24 −1.22647 −0.613237 0.789899i \(-0.710133\pi\)
−0.613237 + 0.789899i \(0.710133\pi\)
\(822\) −8.58114e24 −1.43593
\(823\) 8.00151e24 1.32518 0.662588 0.748984i \(-0.269458\pi\)
0.662588 + 0.748984i \(0.269458\pi\)
\(824\) 1.45332e24 0.238221
\(825\) 1.91224e24 0.310230
\(826\) 2.03416e24 0.326628
\(827\) −3.05939e24 −0.486226 −0.243113 0.969998i \(-0.578169\pi\)
−0.243113 + 0.969998i \(0.578169\pi\)
\(828\) 1.21854e25 1.91682
\(829\) 8.57946e24 1.33582 0.667908 0.744244i \(-0.267190\pi\)
0.667908 + 0.744244i \(0.267190\pi\)
\(830\) 5.33130e24 0.821617
\(831\) 8.79741e24 1.34198
\(832\) −5.26007e24 −0.794224
\(833\) 2.52090e24 0.376767
\(834\) −1.28069e25 −1.89466
\(835\) −4.55863e24 −0.667575
\(836\) 4.69814e24 0.681041
\(837\) −4.73210e24 −0.679028
\(838\) 9.15463e24 1.30037
\(839\) 1.95760e24 0.275262 0.137631 0.990484i \(-0.456051\pi\)
0.137631 + 0.990484i \(0.456051\pi\)
\(840\) 1.63969e24 0.228239
\(841\) 2.50246e23 0.0344828
\(842\) 1.79437e25 2.44771
\(843\) 1.12200e25 1.51516
\(844\) 7.99401e24 1.06870
\(845\) −3.97587e24 −0.526200
\(846\) −2.19621e25 −2.87757
\(847\) −1.92509e23 −0.0249713
\(848\) −9.23002e24 −1.18533
\(849\) −1.26621e25 −1.60987
\(850\) 1.16846e24 0.147080
\(851\) 6.73483e24 0.839316
\(852\) 2.68880e25 3.31759
\(853\) −9.66703e24 −1.18094 −0.590468 0.807061i \(-0.701057\pi\)
−0.590468 + 0.807061i \(0.701057\pi\)
\(854\) 1.40871e24 0.170384
\(855\) −4.32469e24 −0.517896
\(856\) 2.02007e24 0.239519
\(857\) 1.08428e25 1.27293 0.636465 0.771305i \(-0.280396\pi\)
0.636465 + 0.771305i \(0.280396\pi\)
\(858\) −1.27296e25 −1.47970
\(859\) 1.74432e24 0.200764 0.100382 0.994949i \(-0.467994\pi\)
0.100382 + 0.994949i \(0.467994\pi\)
\(860\) −1.23403e25 −1.40634
\(861\) 1.26187e24 0.142393
\(862\) −1.69549e25 −1.89445
\(863\) −7.07810e24 −0.783114 −0.391557 0.920154i \(-0.628063\pi\)
−0.391557 + 0.920154i \(0.628063\pi\)
\(864\) −1.97636e24 −0.216521
\(865\) −1.08316e25 −1.17504
\(866\) 4.83766e24 0.519676
\(867\) −1.25576e25 −1.33581
\(868\) −1.91238e24 −0.201445
\(869\) −1.51804e25 −1.58349
\(870\) 4.21081e24 0.434963
\(871\) −4.97063e24 −0.508460
\(872\) −3.57905e24 −0.362558
\(873\) −1.47311e25 −1.47779
\(874\) −4.88597e24 −0.485404
\(875\) −1.18238e24 −0.116329
\(876\) 3.33389e25 3.24838
\(877\) −9.33647e24 −0.900920 −0.450460 0.892797i \(-0.648740\pi\)
−0.450460 + 0.892797i \(0.648740\pi\)
\(878\) −9.85387e24 −0.941680
\(879\) 6.20595e24 0.587358
\(880\) −5.92148e24 −0.555045
\(881\) 1.23542e25 1.14688 0.573442 0.819246i \(-0.305608\pi\)
0.573442 + 0.819246i \(0.305608\pi\)
\(882\) −2.64273e25 −2.42980
\(883\) −4.93699e24 −0.449568 −0.224784 0.974409i \(-0.572168\pi\)
−0.224784 + 0.974409i \(0.572168\pi\)
\(884\) −5.09943e24 −0.459915
\(885\) 2.73528e25 2.44334
\(886\) 1.81814e25 1.60857
\(887\) −1.33070e25 −1.16608 −0.583042 0.812442i \(-0.698138\pi\)
−0.583042 + 0.812442i \(0.698138\pi\)
\(888\) 3.33385e25 2.89358
\(889\) 9.38424e23 0.0806741
\(890\) 1.61489e25 1.37508
\(891\) 3.75463e24 0.316670
\(892\) −5.38149e24 −0.449574
\(893\) 5.77322e24 0.477728
\(894\) 5.43251e25 4.45278
\(895\) 3.01574e24 0.244849
\(896\) −2.44363e24 −0.196525
\(897\) 8.67906e24 0.691412
\(898\) 3.89740e25 3.07557
\(899\) −2.33109e24 −0.182223
\(900\) −8.03057e24 −0.621849
\(901\) 8.18241e24 0.627654
\(902\) −1.66066e25 −1.26190
\(903\) −1.88087e24 −0.141584
\(904\) −2.80014e25 −2.08808
\(905\) 1.31782e24 0.0973518
\(906\) 5.15697e25 3.77403
\(907\) −1.02480e25 −0.742977 −0.371488 0.928438i \(-0.621152\pi\)
−0.371488 + 0.928438i \(0.621152\pi\)
\(908\) 6.21739e24 0.446558
\(909\) −1.27979e25 −0.910636
\(910\) 1.45319e24 0.102441
\(911\) −3.99109e24 −0.278731 −0.139365 0.990241i \(-0.544506\pi\)
−0.139365 + 0.990241i \(0.544506\pi\)
\(912\) −6.63699e24 −0.459214
\(913\) −7.01078e24 −0.480579
\(914\) −3.34317e25 −2.27047
\(915\) 1.89425e25 1.27455
\(916\) 3.57622e24 0.238404
\(917\) −2.47211e24 −0.163279
\(918\) −6.86857e24 −0.449473
\(919\) 8.49585e24 0.550839 0.275420 0.961324i \(-0.411183\pi\)
0.275420 + 0.961324i \(0.411183\pi\)
\(920\) 1.47125e25 0.945126
\(921\) −8.61682e24 −0.548454
\(922\) −3.76413e25 −2.37384
\(923\) 1.13110e25 0.706786
\(924\) −4.54269e24 −0.281256
\(925\) −4.43847e24 −0.272288
\(926\) 1.43623e25 0.873034
\(927\) 3.70629e24 0.223235
\(928\) −9.73580e23 −0.0581051
\(929\) −2.88104e25 −1.70379 −0.851895 0.523712i \(-0.824547\pi\)
−0.851895 + 0.523712i \(0.824547\pi\)
\(930\) −3.92245e25 −2.29854
\(931\) 6.94700e24 0.403390
\(932\) −5.17466e25 −2.97747
\(933\) 1.44762e24 0.0825392
\(934\) −1.20080e25 −0.678456
\(935\) 5.24939e24 0.293907
\(936\) 2.53748e25 1.40786
\(937\) 1.04086e25 0.572277 0.286139 0.958188i \(-0.407628\pi\)
0.286139 + 0.958188i \(0.407628\pi\)
\(938\) −2.70567e24 −0.147418
\(939\) −1.23688e25 −0.667839
\(940\) −3.66244e25 −1.95968
\(941\) 2.04560e25 1.08470 0.542349 0.840153i \(-0.317535\pi\)
0.542349 + 0.840153i \(0.317535\pi\)
\(942\) −1.15391e25 −0.606371
\(943\) 1.13224e25 0.589642
\(944\) 2.47930e25 1.27958
\(945\) 1.28322e24 0.0656343
\(946\) 2.47529e25 1.25473
\(947\) −3.70342e25 −1.86049 −0.930247 0.366934i \(-0.880408\pi\)
−0.930247 + 0.366934i \(0.880408\pi\)
\(948\) 1.07938e26 5.37410
\(949\) 1.40247e25 0.692042
\(950\) 3.22001e24 0.157473
\(951\) −3.09172e24 −0.149853
\(952\) −1.31755e24 −0.0632928
\(953\) −1.70689e25 −0.812674 −0.406337 0.913723i \(-0.633194\pi\)
−0.406337 + 0.913723i \(0.633194\pi\)
\(954\) −8.57787e25 −4.04779
\(955\) −1.67055e24 −0.0781323
\(956\) 7.14693e25 3.31304
\(957\) −5.53731e24 −0.254418
\(958\) −2.05148e25 −0.934246
\(959\) −1.28821e24 −0.0581471
\(960\) −3.85010e25 −1.72253
\(961\) −8.35555e23 −0.0370532
\(962\) 2.95465e25 1.29873
\(963\) 5.15164e24 0.224451
\(964\) 4.71367e24 0.203566
\(965\) −2.63931e25 −1.12982
\(966\) 4.72429e24 0.200462
\(967\) 3.65492e25 1.53728 0.768641 0.639681i \(-0.220933\pi\)
0.768641 + 0.639681i \(0.220933\pi\)
\(968\) −8.55052e24 −0.356494
\(969\) 5.88369e24 0.243163
\(970\) −3.74712e25 −1.53510
\(971\) 3.73289e25 1.51594 0.757969 0.652290i \(-0.226192\pi\)
0.757969 + 0.652290i \(0.226192\pi\)
\(972\) −5.94166e25 −2.39191
\(973\) −1.92258e24 −0.0767228
\(974\) 2.02474e24 0.0800975
\(975\) −5.71978e24 −0.224306
\(976\) 1.71698e25 0.667484
\(977\) 4.72931e25 1.82261 0.911305 0.411731i \(-0.135076\pi\)
0.911305 + 0.411731i \(0.135076\pi\)
\(978\) 3.06794e25 1.17210
\(979\) −2.12361e25 −0.804307
\(980\) −4.40707e25 −1.65474
\(981\) −9.12738e24 −0.339750
\(982\) 1.75675e25 0.648278
\(983\) −2.27666e25 −0.832900 −0.416450 0.909159i \(-0.636726\pi\)
−0.416450 + 0.909159i \(0.636726\pi\)
\(984\) 5.60476e25 2.03282
\(985\) 3.84963e25 1.38424
\(986\) −3.38354e24 −0.120620
\(987\) −5.58219e24 −0.197292
\(988\) −1.40528e25 −0.492413
\(989\) −1.68765e25 −0.586293
\(990\) −5.50310e25 −1.89543
\(991\) 6.54550e24 0.223520 0.111760 0.993735i \(-0.464351\pi\)
0.111760 + 0.993735i \(0.464351\pi\)
\(992\) 9.06908e24 0.307054
\(993\) 3.52185e25 1.18223
\(994\) 6.15696e24 0.204919
\(995\) 3.38934e25 1.11846
\(996\) 4.98494e25 1.63101
\(997\) 3.73337e25 1.21113 0.605567 0.795795i \(-0.292947\pi\)
0.605567 + 0.795795i \(0.292947\pi\)
\(998\) −2.37526e25 −0.764014
\(999\) 2.60906e25 0.832104
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 29.18.a.b.1.19 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.19 21 1.1 even 1 trivial