Properties

Label 29.18.a.b.1.20
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 1.20
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +O(q^{10})\) \(q+652.859 q^{2} +4140.75 q^{3} +295153. q^{4} +358296. q^{5} +2.70332e6 q^{6} +1.05214e7 q^{7} +1.07122e8 q^{8} -1.11994e8 q^{9} +2.33917e8 q^{10} +1.15705e9 q^{11} +1.22215e9 q^{12} -2.51476e9 q^{13} +6.86899e9 q^{14} +1.48361e9 q^{15} +3.12492e10 q^{16} +1.45392e10 q^{17} -7.31166e10 q^{18} +1.40302e11 q^{19} +1.05752e11 q^{20} +4.35664e10 q^{21} +7.55391e11 q^{22} -5.22017e11 q^{23} +4.43565e11 q^{24} -6.34564e11 q^{25} -1.64179e12 q^{26} -9.98477e11 q^{27} +3.10542e12 q^{28} +5.00246e11 q^{29} +9.68589e11 q^{30} +5.44856e12 q^{31} +6.36066e12 q^{32} +4.79105e12 q^{33} +9.49202e12 q^{34} +3.76977e12 q^{35} -3.30555e13 q^{36} +2.38708e13 q^{37} +9.15975e13 q^{38} -1.04130e13 q^{39} +3.83813e13 q^{40} -5.39518e13 q^{41} +2.84428e13 q^{42} +5.68631e13 q^{43} +3.41507e14 q^{44} -4.01271e13 q^{45} -3.40803e14 q^{46} -1.71515e14 q^{47} +1.29395e14 q^{48} -1.21931e14 q^{49} -4.14281e14 q^{50} +6.02029e13 q^{51} -7.42240e14 q^{52} +6.93926e14 q^{53} -6.51865e14 q^{54} +4.14566e14 q^{55} +1.12707e15 q^{56} +5.80955e14 q^{57} +3.26591e14 q^{58} -1.52517e15 q^{59} +4.37893e14 q^{60} -2.52379e14 q^{61} +3.55714e15 q^{62} -1.17834e15 q^{63} +5.67187e13 q^{64} -9.01028e14 q^{65} +3.12788e15 q^{66} -9.07675e14 q^{67} +4.29128e15 q^{68} -2.16154e15 q^{69} +2.46113e15 q^{70} +1.43297e14 q^{71} -1.19971e16 q^{72} +5.43727e15 q^{73} +1.55842e16 q^{74} -2.62757e15 q^{75} +4.14106e16 q^{76} +1.21738e16 q^{77} -6.79822e15 q^{78} -6.13389e15 q^{79} +1.11965e16 q^{80} +1.03285e16 q^{81} -3.52229e16 q^{82} -1.62223e16 q^{83} +1.28588e16 q^{84} +5.20931e15 q^{85} +3.71236e16 q^{86} +2.07139e15 q^{87} +1.23945e17 q^{88} +4.92142e16 q^{89} -2.61973e16 q^{90} -2.64588e16 q^{91} -1.54075e17 q^{92} +2.25611e16 q^{93} -1.11975e17 q^{94} +5.02696e16 q^{95} +2.63379e16 q^{96} -7.93342e16 q^{97} -7.96036e16 q^{98} -1.29583e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 652.859 1.80329 0.901643 0.432481i \(-0.142362\pi\)
0.901643 + 0.432481i \(0.142362\pi\)
\(3\) 4140.75 0.364374 0.182187 0.983264i \(-0.441682\pi\)
0.182187 + 0.983264i \(0.441682\pi\)
\(4\) 295153. 2.25184
\(5\) 358296. 0.410201 0.205100 0.978741i \(-0.434248\pi\)
0.205100 + 0.978741i \(0.434248\pi\)
\(6\) 2.70332e6 0.657071
\(7\) 1.05214e7 0.689827 0.344913 0.938634i \(-0.387908\pi\)
0.344913 + 0.938634i \(0.387908\pi\)
\(8\) 1.07122e8 2.25743
\(9\) −1.11994e8 −0.867231
\(10\) 2.33917e8 0.739709
\(11\) 1.15705e9 1.62747 0.813737 0.581233i \(-0.197430\pi\)
0.813737 + 0.581233i \(0.197430\pi\)
\(12\) 1.22215e9 0.820513
\(13\) −2.51476e9 −0.855024 −0.427512 0.904010i \(-0.640610\pi\)
−0.427512 + 0.904010i \(0.640610\pi\)
\(14\) 6.86899e9 1.24396
\(15\) 1.48361e9 0.149467
\(16\) 3.12492e10 1.81894
\(17\) 1.45392e10 0.505503 0.252751 0.967531i \(-0.418665\pi\)
0.252751 + 0.967531i \(0.418665\pi\)
\(18\) −7.31166e10 −1.56387
\(19\) 1.40302e11 1.89521 0.947607 0.319438i \(-0.103494\pi\)
0.947607 + 0.319438i \(0.103494\pi\)
\(20\) 1.05752e11 0.923706
\(21\) 4.35664e10 0.251355
\(22\) 7.55391e11 2.93480
\(23\) −5.22017e11 −1.38995 −0.694973 0.719036i \(-0.744584\pi\)
−0.694973 + 0.719036i \(0.744584\pi\)
\(24\) 4.43565e11 0.822548
\(25\) −6.34564e11 −0.831735
\(26\) −1.64179e12 −1.54185
\(27\) −9.98477e11 −0.680371
\(28\) 3.10542e12 1.55338
\(29\) 5.00246e11 0.185695
\(30\) 9.68589e11 0.269531
\(31\) 5.44856e12 1.14738 0.573690 0.819073i \(-0.305511\pi\)
0.573690 + 0.819073i \(0.305511\pi\)
\(32\) 6.36066e12 1.02265
\(33\) 4.79105e12 0.593010
\(34\) 9.49202e12 0.911566
\(35\) 3.76977e12 0.282967
\(36\) −3.30555e13 −1.95287
\(37\) 2.38708e13 1.11725 0.558626 0.829419i \(-0.311329\pi\)
0.558626 + 0.829419i \(0.311329\pi\)
\(38\) 9.15975e13 3.41761
\(39\) −1.04130e13 −0.311549
\(40\) 3.83813e13 0.925998
\(41\) −5.39518e13 −1.05522 −0.527610 0.849487i \(-0.676912\pi\)
−0.527610 + 0.849487i \(0.676912\pi\)
\(42\) 2.84428e13 0.453266
\(43\) 5.68631e13 0.741905 0.370953 0.928652i \(-0.379031\pi\)
0.370953 + 0.928652i \(0.379031\pi\)
\(44\) 3.41507e14 3.66481
\(45\) −4.01271e13 −0.355739
\(46\) −3.40803e14 −2.50647
\(47\) −1.71515e14 −1.05068 −0.525339 0.850893i \(-0.676061\pi\)
−0.525339 + 0.850893i \(0.676061\pi\)
\(48\) 1.29395e14 0.662777
\(49\) −1.21931e14 −0.524139
\(50\) −4.14281e14 −1.49986
\(51\) 6.02029e13 0.184192
\(52\) −7.42240e14 −1.92538
\(53\) 6.93926e14 1.53098 0.765488 0.643451i \(-0.222498\pi\)
0.765488 + 0.643451i \(0.222498\pi\)
\(54\) −6.51865e14 −1.22690
\(55\) 4.14566e14 0.667591
\(56\) 1.12707e15 1.55723
\(57\) 5.80955e14 0.690568
\(58\) 3.26591e14 0.334862
\(59\) −1.52517e15 −1.35231 −0.676153 0.736761i \(-0.736354\pi\)
−0.676153 + 0.736761i \(0.736354\pi\)
\(60\) 4.37893e14 0.336575
\(61\) −2.52379e14 −0.168558 −0.0842790 0.996442i \(-0.526859\pi\)
−0.0842790 + 0.996442i \(0.526859\pi\)
\(62\) 3.55714e15 2.06905
\(63\) −1.17834e15 −0.598239
\(64\) 5.67187e13 0.0251882
\(65\) −9.01028e14 −0.350731
\(66\) 3.12788e15 1.06937
\(67\) −9.07675e14 −0.273083 −0.136542 0.990634i \(-0.543599\pi\)
−0.136542 + 0.990634i \(0.543599\pi\)
\(68\) 4.29128e15 1.13831
\(69\) −2.16154e15 −0.506461
\(70\) 2.46113e15 0.510271
\(71\) 1.43297e14 0.0263354 0.0131677 0.999913i \(-0.495808\pi\)
0.0131677 + 0.999913i \(0.495808\pi\)
\(72\) −1.19971e16 −1.95771
\(73\) 5.43727e15 0.789108 0.394554 0.918873i \(-0.370899\pi\)
0.394554 + 0.918873i \(0.370899\pi\)
\(74\) 1.55842e16 2.01473
\(75\) −2.62757e15 −0.303063
\(76\) 4.14106e16 4.26772
\(77\) 1.21738e16 1.12268
\(78\) −6.79822e15 −0.561812
\(79\) −6.13389e15 −0.454889 −0.227445 0.973791i \(-0.573037\pi\)
−0.227445 + 0.973791i \(0.573037\pi\)
\(80\) 1.11965e16 0.746132
\(81\) 1.03285e16 0.619321
\(82\) −3.52229e16 −1.90286
\(83\) −1.62223e16 −0.790584 −0.395292 0.918556i \(-0.629357\pi\)
−0.395292 + 0.918556i \(0.629357\pi\)
\(84\) 1.28588e16 0.566012
\(85\) 5.20931e15 0.207357
\(86\) 3.71236e16 1.33787
\(87\) 2.07139e15 0.0676626
\(88\) 1.23945e17 3.67390
\(89\) 4.92142e16 1.32518 0.662590 0.748982i \(-0.269457\pi\)
0.662590 + 0.748982i \(0.269457\pi\)
\(90\) −2.61973e16 −0.641499
\(91\) −2.64588e16 −0.589819
\(92\) −1.54075e17 −3.12994
\(93\) 2.25611e16 0.418076
\(94\) −1.11975e17 −1.89467
\(95\) 5.02696e16 0.777418
\(96\) 2.63379e16 0.372628
\(97\) −7.93342e16 −1.02778 −0.513891 0.857856i \(-0.671796\pi\)
−0.513891 + 0.857856i \(0.671796\pi\)
\(98\) −7.96036e16 −0.945172
\(99\) −1.29583e17 −1.41140
\(100\) −1.87294e17 −1.87294
\(101\) −6.32559e16 −0.581259 −0.290629 0.956836i \(-0.593865\pi\)
−0.290629 + 0.956836i \(0.593865\pi\)
\(102\) 3.93041e16 0.332151
\(103\) −1.77368e17 −1.37961 −0.689807 0.723993i \(-0.742305\pi\)
−0.689807 + 0.723993i \(0.742305\pi\)
\(104\) −2.69386e17 −1.93015
\(105\) 1.56097e16 0.103106
\(106\) 4.53036e17 2.76079
\(107\) −1.42311e17 −0.800714 −0.400357 0.916359i \(-0.631114\pi\)
−0.400357 + 0.916359i \(0.631114\pi\)
\(108\) −2.94704e17 −1.53209
\(109\) −1.29421e17 −0.622128 −0.311064 0.950389i \(-0.600685\pi\)
−0.311064 + 0.950389i \(0.600685\pi\)
\(110\) 2.70653e17 1.20386
\(111\) 9.88427e16 0.407098
\(112\) 3.28786e17 1.25476
\(113\) 1.59967e17 0.566063 0.283032 0.959111i \(-0.408660\pi\)
0.283032 + 0.959111i \(0.408660\pi\)
\(114\) 3.79282e17 1.24529
\(115\) −1.87036e17 −0.570157
\(116\) 1.47649e17 0.418156
\(117\) 2.81639e17 0.741504
\(118\) −9.95718e17 −2.43859
\(119\) 1.52972e17 0.348709
\(120\) 1.58927e17 0.337410
\(121\) 8.33317e17 1.64867
\(122\) −1.64768e17 −0.303958
\(123\) −2.23401e17 −0.384495
\(124\) 1.60816e18 2.58372
\(125\) −5.00719e17 −0.751379
\(126\) −7.69289e17 −1.07880
\(127\) −6.38435e17 −0.837115 −0.418558 0.908190i \(-0.637464\pi\)
−0.418558 + 0.908190i \(0.637464\pi\)
\(128\) −7.96676e17 −0.977230
\(129\) 2.35456e17 0.270331
\(130\) −5.88244e17 −0.632469
\(131\) −1.43449e18 −1.44508 −0.722538 0.691332i \(-0.757024\pi\)
−0.722538 + 0.691332i \(0.757024\pi\)
\(132\) 1.41409e18 1.33536
\(133\) 1.47617e18 1.30737
\(134\) −5.92584e17 −0.492447
\(135\) −3.57750e17 −0.279089
\(136\) 1.55746e18 1.14113
\(137\) −2.34038e18 −1.61124 −0.805622 0.592431i \(-0.798168\pi\)
−0.805622 + 0.592431i \(0.798168\pi\)
\(138\) −1.41118e18 −0.913293
\(139\) 6.13804e17 0.373597 0.186799 0.982398i \(-0.440189\pi\)
0.186799 + 0.982398i \(0.440189\pi\)
\(140\) 1.11266e18 0.637198
\(141\) −7.10199e17 −0.382840
\(142\) 9.35526e16 0.0474903
\(143\) −2.90970e18 −1.39153
\(144\) −3.49974e18 −1.57745
\(145\) 1.79236e17 0.0761724
\(146\) 3.54977e18 1.42299
\(147\) −5.04884e17 −0.190983
\(148\) 7.04553e18 2.51588
\(149\) −3.00916e18 −1.01476 −0.507379 0.861723i \(-0.669386\pi\)
−0.507379 + 0.861723i \(0.669386\pi\)
\(150\) −1.71543e18 −0.546509
\(151\) 2.14548e17 0.0645983 0.0322991 0.999478i \(-0.489717\pi\)
0.0322991 + 0.999478i \(0.489717\pi\)
\(152\) 1.50294e19 4.27831
\(153\) −1.62830e18 −0.438388
\(154\) 7.94777e18 2.02451
\(155\) 1.95219e18 0.470656
\(156\) −3.07343e18 −0.701558
\(157\) −5.18646e18 −1.12131 −0.560653 0.828051i \(-0.689450\pi\)
−0.560653 + 0.828051i \(0.689450\pi\)
\(158\) −4.00457e18 −0.820295
\(159\) 2.87337e18 0.557848
\(160\) 2.27900e18 0.419492
\(161\) −5.49235e18 −0.958822
\(162\) 6.74308e18 1.11681
\(163\) −2.17414e18 −0.341737 −0.170869 0.985294i \(-0.554657\pi\)
−0.170869 + 0.985294i \(0.554657\pi\)
\(164\) −1.59240e19 −2.37619
\(165\) 1.71661e18 0.243253
\(166\) −1.05909e19 −1.42565
\(167\) 7.99349e18 1.02246 0.511230 0.859444i \(-0.329190\pi\)
0.511230 + 0.859444i \(0.329190\pi\)
\(168\) 4.66692e18 0.567416
\(169\) −2.32639e18 −0.268934
\(170\) 3.40095e18 0.373925
\(171\) −1.57130e19 −1.64359
\(172\) 1.67833e19 1.67065
\(173\) 5.81820e18 0.551311 0.275656 0.961256i \(-0.411105\pi\)
0.275656 + 0.961256i \(0.411105\pi\)
\(174\) 1.35233e18 0.122015
\(175\) −6.67650e18 −0.573753
\(176\) 3.61569e19 2.96029
\(177\) −6.31532e18 −0.492746
\(178\) 3.21299e19 2.38968
\(179\) 2.24434e19 1.59161 0.795806 0.605552i \(-0.207048\pi\)
0.795806 + 0.605552i \(0.207048\pi\)
\(180\) −1.18436e19 −0.801067
\(181\) 1.47666e19 0.952822 0.476411 0.879223i \(-0.341937\pi\)
0.476411 + 0.879223i \(0.341937\pi\)
\(182\) −1.72739e19 −1.06361
\(183\) −1.04504e18 −0.0614182
\(184\) −5.59195e19 −3.13770
\(185\) 8.55279e18 0.458298
\(186\) 1.47292e19 0.753910
\(187\) 1.68225e19 0.822692
\(188\) −5.06231e19 −2.36596
\(189\) −1.05054e19 −0.469338
\(190\) 3.28190e19 1.40191
\(191\) −8.66002e18 −0.353781 −0.176891 0.984230i \(-0.556604\pi\)
−0.176891 + 0.984230i \(0.556604\pi\)
\(192\) 2.34858e17 0.00917793
\(193\) 4.09075e19 1.52956 0.764779 0.644293i \(-0.222848\pi\)
0.764779 + 0.644293i \(0.222848\pi\)
\(194\) −5.17941e19 −1.85338
\(195\) −3.73093e18 −0.127798
\(196\) −3.59882e19 −1.18028
\(197\) −4.27580e19 −1.34293 −0.671466 0.741035i \(-0.734335\pi\)
−0.671466 + 0.741035i \(0.734335\pi\)
\(198\) −8.45995e19 −2.54515
\(199\) 1.19856e19 0.345467 0.172734 0.984969i \(-0.444740\pi\)
0.172734 + 0.984969i \(0.444740\pi\)
\(200\) −6.79757e19 −1.87758
\(201\) −3.75845e18 −0.0995045
\(202\) −4.12972e19 −1.04818
\(203\) 5.26329e18 0.128098
\(204\) 1.77691e19 0.414771
\(205\) −1.93307e19 −0.432852
\(206\) −1.15796e20 −2.48784
\(207\) 5.84629e19 1.20540
\(208\) −7.85844e19 −1.55524
\(209\) 1.62336e20 3.08441
\(210\) 1.01909e19 0.185930
\(211\) −5.40899e19 −0.947798 −0.473899 0.880579i \(-0.657154\pi\)
−0.473899 + 0.880579i \(0.657154\pi\)
\(212\) 2.04814e20 3.44751
\(213\) 5.93355e17 0.00959596
\(214\) −9.29093e19 −1.44392
\(215\) 2.03738e19 0.304330
\(216\) −1.06959e20 −1.53589
\(217\) 5.73265e19 0.791494
\(218\) −8.44937e19 −1.12187
\(219\) 2.25144e19 0.287531
\(220\) 1.22360e20 1.50331
\(221\) −3.65625e19 −0.432217
\(222\) 6.45304e19 0.734115
\(223\) −1.98803e19 −0.217686 −0.108843 0.994059i \(-0.534715\pi\)
−0.108843 + 0.994059i \(0.534715\pi\)
\(224\) 6.69231e19 0.705453
\(225\) 7.10676e19 0.721307
\(226\) 1.04436e20 1.02077
\(227\) 1.25506e20 1.18153 0.590764 0.806845i \(-0.298826\pi\)
0.590764 + 0.806845i \(0.298826\pi\)
\(228\) 1.71471e20 1.55505
\(229\) −4.26961e19 −0.373067 −0.186533 0.982449i \(-0.559725\pi\)
−0.186533 + 0.982449i \(0.559725\pi\)
\(230\) −1.22108e20 −1.02816
\(231\) 5.04085e19 0.409074
\(232\) 5.35874e19 0.419194
\(233\) 8.91859e18 0.0672621 0.0336311 0.999434i \(-0.489293\pi\)
0.0336311 + 0.999434i \(0.489293\pi\)
\(234\) 1.83871e20 1.33714
\(235\) −6.14529e19 −0.430989
\(236\) −4.50158e20 −3.04518
\(237\) −2.53989e19 −0.165750
\(238\) 9.98694e19 0.628823
\(239\) 2.26702e20 1.37744 0.688720 0.725027i \(-0.258173\pi\)
0.688720 + 0.725027i \(0.258173\pi\)
\(240\) 4.63617e19 0.271872
\(241\) 1.86486e20 1.05560 0.527802 0.849368i \(-0.323016\pi\)
0.527802 + 0.849368i \(0.323016\pi\)
\(242\) 5.44039e20 2.97303
\(243\) 1.71711e20 0.906036
\(244\) −7.44904e19 −0.379566
\(245\) −4.36872e19 −0.215002
\(246\) −1.45849e20 −0.693355
\(247\) −3.52826e20 −1.62045
\(248\) 5.83660e20 2.59013
\(249\) −6.71723e19 −0.288069
\(250\) −3.26899e20 −1.35495
\(251\) 3.50739e20 1.40526 0.702631 0.711554i \(-0.252009\pi\)
0.702631 + 0.711554i \(0.252009\pi\)
\(252\) −3.47790e20 −1.34714
\(253\) −6.03999e20 −2.26210
\(254\) −4.16808e20 −1.50956
\(255\) 2.15704e19 0.0755558
\(256\) −5.27551e20 −1.78741
\(257\) 6.98794e19 0.229043 0.114522 0.993421i \(-0.463466\pi\)
0.114522 + 0.993421i \(0.463466\pi\)
\(258\) 1.53719e20 0.487485
\(259\) 2.51154e20 0.770711
\(260\) −2.65941e20 −0.789791
\(261\) −5.60248e19 −0.161041
\(262\) −9.36518e20 −2.60588
\(263\) 3.37246e20 0.908496 0.454248 0.890875i \(-0.349908\pi\)
0.454248 + 0.890875i \(0.349908\pi\)
\(264\) 5.13226e20 1.33868
\(265\) 2.48631e20 0.628007
\(266\) 9.63734e20 2.35756
\(267\) 2.03783e20 0.482862
\(268\) −2.67903e20 −0.614939
\(269\) 5.58156e20 1.24126 0.620628 0.784105i \(-0.286878\pi\)
0.620628 + 0.784105i \(0.286878\pi\)
\(270\) −2.33560e20 −0.503277
\(271\) 5.37531e20 1.12244 0.561221 0.827666i \(-0.310332\pi\)
0.561221 + 0.827666i \(0.310332\pi\)
\(272\) 4.54337e20 0.919481
\(273\) −1.09559e20 −0.214915
\(274\) −1.52794e21 −2.90553
\(275\) −7.34222e20 −1.35363
\(276\) −6.37985e20 −1.14047
\(277\) 1.98272e19 0.0343703 0.0171852 0.999852i \(-0.494530\pi\)
0.0171852 + 0.999852i \(0.494530\pi\)
\(278\) 4.00727e20 0.673703
\(279\) −6.10208e20 −0.995044
\(280\) 4.03825e20 0.638778
\(281\) 1.12948e21 1.73330 0.866649 0.498918i \(-0.166269\pi\)
0.866649 + 0.498918i \(0.166269\pi\)
\(282\) −4.63660e20 −0.690370
\(283\) 7.43230e19 0.107384 0.0536919 0.998558i \(-0.482901\pi\)
0.0536919 + 0.998558i \(0.482901\pi\)
\(284\) 4.22945e19 0.0593032
\(285\) 2.08154e20 0.283271
\(286\) −1.89963e21 −2.50933
\(287\) −5.67648e20 −0.727919
\(288\) −7.12359e20 −0.886875
\(289\) −6.15853e20 −0.744467
\(290\) 1.17016e20 0.137361
\(291\) −3.28503e20 −0.374497
\(292\) 1.60483e21 1.77695
\(293\) 5.50391e20 0.591966 0.295983 0.955193i \(-0.404353\pi\)
0.295983 + 0.955193i \(0.404353\pi\)
\(294\) −3.29618e20 −0.344397
\(295\) −5.46460e20 −0.554717
\(296\) 2.55708e21 2.52212
\(297\) −1.15529e21 −1.10729
\(298\) −1.96456e21 −1.82990
\(299\) 1.31275e21 1.18844
\(300\) −7.75535e20 −0.682450
\(301\) 5.98279e20 0.511786
\(302\) 1.40070e20 0.116489
\(303\) −2.61927e20 −0.211796
\(304\) 4.38433e21 3.44729
\(305\) −9.04262e19 −0.0691426
\(306\) −1.06305e21 −0.790538
\(307\) −5.62539e20 −0.406889 −0.203445 0.979086i \(-0.565214\pi\)
−0.203445 + 0.979086i \(0.565214\pi\)
\(308\) 3.59313e21 2.52809
\(309\) −7.34434e20 −0.502696
\(310\) 1.27451e21 0.848727
\(311\) −1.38771e21 −0.899156 −0.449578 0.893241i \(-0.648426\pi\)
−0.449578 + 0.893241i \(0.648426\pi\)
\(312\) −1.11546e21 −0.703299
\(313\) 2.65655e21 1.63001 0.815007 0.579451i \(-0.196733\pi\)
0.815007 + 0.579451i \(0.196733\pi\)
\(314\) −3.38603e21 −2.02204
\(315\) −4.22193e20 −0.245398
\(316\) −1.81044e21 −1.02434
\(317\) −1.53955e21 −0.847988 −0.423994 0.905665i \(-0.639372\pi\)
−0.423994 + 0.905665i \(0.639372\pi\)
\(318\) 1.87591e21 1.00596
\(319\) 5.78810e20 0.302214
\(320\) 2.03221e19 0.0103322
\(321\) −5.89275e20 −0.291760
\(322\) −3.58573e21 −1.72903
\(323\) 2.03987e21 0.958036
\(324\) 3.04850e21 1.39461
\(325\) 1.59578e21 0.711154
\(326\) −1.41941e21 −0.616250
\(327\) −5.35900e20 −0.226688
\(328\) −5.77942e21 −2.38208
\(329\) −1.80457e21 −0.724786
\(330\) 1.12071e21 0.438655
\(331\) 3.77688e21 1.44077 0.720385 0.693574i \(-0.243965\pi\)
0.720385 + 0.693574i \(0.243965\pi\)
\(332\) −4.78806e21 −1.78027
\(333\) −2.67339e21 −0.968917
\(334\) 5.21863e21 1.84379
\(335\) −3.25216e20 −0.112019
\(336\) 1.36142e21 0.457201
\(337\) −1.21175e21 −0.396788 −0.198394 0.980122i \(-0.563573\pi\)
−0.198394 + 0.980122i \(0.563573\pi\)
\(338\) −1.51881e21 −0.484965
\(339\) 6.62384e20 0.206259
\(340\) 1.53755e21 0.466936
\(341\) 6.30425e21 1.86733
\(342\) −1.02584e22 −2.96386
\(343\) −3.73048e21 −1.05139
\(344\) 6.09128e21 1.67480
\(345\) −7.74470e20 −0.207751
\(346\) 3.79847e21 0.994172
\(347\) −7.01646e21 −1.79192 −0.895958 0.444138i \(-0.853510\pi\)
−0.895958 + 0.444138i \(0.853510\pi\)
\(348\) 6.11378e20 0.152365
\(349\) −7.19973e20 −0.175106 −0.0875528 0.996160i \(-0.527905\pi\)
−0.0875528 + 0.996160i \(0.527905\pi\)
\(350\) −4.35881e21 −1.03464
\(351\) 2.51093e21 0.581734
\(352\) 7.35960e21 1.66434
\(353\) −3.89749e21 −0.860400 −0.430200 0.902734i \(-0.641557\pi\)
−0.430200 + 0.902734i \(0.641557\pi\)
\(354\) −4.12302e21 −0.888561
\(355\) 5.13426e19 0.0108028
\(356\) 1.45257e22 2.98409
\(357\) 6.33419e20 0.127061
\(358\) 1.46524e22 2.87013
\(359\) 2.13839e21 0.409057 0.204529 0.978861i \(-0.434434\pi\)
0.204529 + 0.978861i \(0.434434\pi\)
\(360\) −4.29849e21 −0.803054
\(361\) 1.42043e22 2.59184
\(362\) 9.64049e21 1.71821
\(363\) 3.45055e21 0.600734
\(364\) −7.80940e21 −1.32818
\(365\) 1.94815e21 0.323693
\(366\) −6.82262e20 −0.110755
\(367\) −2.17384e21 −0.344799 −0.172399 0.985027i \(-0.555152\pi\)
−0.172399 + 0.985027i \(0.555152\pi\)
\(368\) −1.63126e22 −2.52823
\(369\) 6.04229e21 0.915119
\(370\) 5.58377e21 0.826442
\(371\) 7.30107e21 1.05611
\(372\) 6.65898e21 0.941440
\(373\) 3.19905e21 0.442074 0.221037 0.975265i \(-0.429056\pi\)
0.221037 + 0.975265i \(0.429056\pi\)
\(374\) 1.09827e22 1.48355
\(375\) −2.07335e21 −0.273783
\(376\) −1.83730e22 −2.37183
\(377\) −1.25800e21 −0.158774
\(378\) −6.85853e21 −0.846352
\(379\) −1.31984e22 −1.59253 −0.796266 0.604947i \(-0.793194\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(380\) 1.48372e22 1.75062
\(381\) −2.64360e21 −0.305023
\(382\) −5.65377e21 −0.637969
\(383\) 4.70891e20 0.0519673 0.0259837 0.999662i \(-0.491728\pi\)
0.0259837 + 0.999662i \(0.491728\pi\)
\(384\) −3.29883e21 −0.356078
\(385\) 4.36181e21 0.460522
\(386\) 2.67068e22 2.75823
\(387\) −6.36835e21 −0.643404
\(388\) −2.34157e22 −2.31440
\(389\) 7.19164e21 0.695434 0.347717 0.937599i \(-0.386957\pi\)
0.347717 + 0.937599i \(0.386957\pi\)
\(390\) −2.43577e21 −0.230456
\(391\) −7.58968e21 −0.702621
\(392\) −1.30615e22 −1.18320
\(393\) −5.93984e21 −0.526548
\(394\) −2.79149e22 −2.42169
\(395\) −2.19774e21 −0.186596
\(396\) −3.82469e22 −3.17824
\(397\) 9.34349e21 0.759959 0.379979 0.924995i \(-0.375931\pi\)
0.379979 + 0.924995i \(0.375931\pi\)
\(398\) 7.82488e21 0.622977
\(399\) 6.11246e21 0.476372
\(400\) −1.98296e22 −1.51288
\(401\) −1.18885e22 −0.887977 −0.443988 0.896033i \(-0.646437\pi\)
−0.443988 + 0.896033i \(0.646437\pi\)
\(402\) −2.45374e21 −0.179435
\(403\) −1.37018e22 −0.981037
\(404\) −1.86702e22 −1.30890
\(405\) 3.70067e21 0.254046
\(406\) 3.43619e21 0.230997
\(407\) 2.76196e22 1.81830
\(408\) 6.44906e21 0.415800
\(409\) 2.42965e22 1.53425 0.767123 0.641500i \(-0.221688\pi\)
0.767123 + 0.641500i \(0.221688\pi\)
\(410\) −1.26202e22 −0.780556
\(411\) −9.69091e21 −0.587096
\(412\) −5.23506e22 −3.10667
\(413\) −1.60469e22 −0.932857
\(414\) 3.81681e22 2.17369
\(415\) −5.81237e21 −0.324298
\(416\) −1.59956e22 −0.874391
\(417\) 2.54161e21 0.136129
\(418\) 1.05983e23 5.56208
\(419\) 2.77211e21 0.142558 0.0712788 0.997456i \(-0.477292\pi\)
0.0712788 + 0.997456i \(0.477292\pi\)
\(420\) 4.60724e21 0.232179
\(421\) −2.03291e22 −1.00397 −0.501985 0.864877i \(-0.667397\pi\)
−0.501985 + 0.864877i \(0.667397\pi\)
\(422\) −3.53131e22 −1.70915
\(423\) 1.92087e22 0.911180
\(424\) 7.43347e22 3.45606
\(425\) −9.22602e21 −0.420444
\(426\) 3.87378e20 0.0173043
\(427\) −2.65538e21 −0.116276
\(428\) −4.20037e22 −1.80308
\(429\) −1.20483e22 −0.507038
\(430\) 1.33012e22 0.548794
\(431\) −1.04255e22 −0.421737 −0.210868 0.977514i \(-0.567629\pi\)
−0.210868 + 0.977514i \(0.567629\pi\)
\(432\) −3.12016e22 −1.23756
\(433\) 3.20282e21 0.124562 0.0622809 0.998059i \(-0.480163\pi\)
0.0622809 + 0.998059i \(0.480163\pi\)
\(434\) 3.74261e22 1.42729
\(435\) 7.42171e20 0.0277553
\(436\) −3.81990e22 −1.40093
\(437\) −7.32400e22 −2.63425
\(438\) 1.46987e22 0.518500
\(439\) 2.99418e22 1.03593 0.517964 0.855402i \(-0.326690\pi\)
0.517964 + 0.855402i \(0.326690\pi\)
\(440\) 4.44091e22 1.50704
\(441\) 1.36556e22 0.454550
\(442\) −2.38702e22 −0.779410
\(443\) 5.67436e22 1.81754 0.908772 0.417292i \(-0.137021\pi\)
0.908772 + 0.417292i \(0.137021\pi\)
\(444\) 2.91737e22 0.916721
\(445\) 1.76332e22 0.543590
\(446\) −1.29790e22 −0.392551
\(447\) −1.24602e22 −0.369752
\(448\) 5.96761e20 0.0173755
\(449\) −2.47369e22 −0.706725 −0.353363 0.935486i \(-0.614962\pi\)
−0.353363 + 0.935486i \(0.614962\pi\)
\(450\) 4.63971e22 1.30072
\(451\) −6.24249e22 −1.71734
\(452\) 4.72149e22 1.27468
\(453\) 8.88390e20 0.0235380
\(454\) 8.19376e22 2.13063
\(455\) −9.48007e21 −0.241944
\(456\) 6.22330e22 1.55891
\(457\) 5.72597e22 1.40787 0.703933 0.710266i \(-0.251425\pi\)
0.703933 + 0.710266i \(0.251425\pi\)
\(458\) −2.78745e22 −0.672746
\(459\) −1.45170e22 −0.343929
\(460\) −5.52044e22 −1.28390
\(461\) −3.33732e22 −0.761973 −0.380987 0.924581i \(-0.624416\pi\)
−0.380987 + 0.924581i \(0.624416\pi\)
\(462\) 3.29097e22 0.737678
\(463\) 1.36245e22 0.299834 0.149917 0.988699i \(-0.452099\pi\)
0.149917 + 0.988699i \(0.452099\pi\)
\(464\) 1.56323e22 0.337770
\(465\) 8.08354e21 0.171495
\(466\) 5.82258e21 0.121293
\(467\) 4.49094e22 0.918637 0.459319 0.888272i \(-0.348094\pi\)
0.459319 + 0.888272i \(0.348094\pi\)
\(468\) 8.31267e22 1.66975
\(469\) −9.55002e21 −0.188380
\(470\) −4.01201e22 −0.777196
\(471\) −2.14758e22 −0.408575
\(472\) −1.63379e23 −3.05273
\(473\) 6.57934e22 1.20743
\(474\) −1.65819e22 −0.298895
\(475\) −8.90306e22 −1.57632
\(476\) 4.51503e22 0.785238
\(477\) −7.77158e22 −1.32771
\(478\) 1.48004e23 2.48392
\(479\) −4.24649e22 −0.700130 −0.350065 0.936725i \(-0.613840\pi\)
−0.350065 + 0.936725i \(0.613840\pi\)
\(480\) 9.43675e21 0.152852
\(481\) −6.00293e22 −0.955278
\(482\) 1.21749e23 1.90355
\(483\) −2.27424e22 −0.349370
\(484\) 2.45956e23 3.71255
\(485\) −2.84251e22 −0.421597
\(486\) 1.12103e23 1.63384
\(487\) −1.28110e23 −1.83480 −0.917399 0.397968i \(-0.869715\pi\)
−0.917399 + 0.397968i \(0.869715\pi\)
\(488\) −2.70353e22 −0.380507
\(489\) −9.00255e21 −0.124520
\(490\) −2.85216e22 −0.387710
\(491\) −8.27365e22 −1.10536 −0.552681 0.833393i \(-0.686395\pi\)
−0.552681 + 0.833393i \(0.686395\pi\)
\(492\) −6.59374e22 −0.865821
\(493\) 7.27316e21 0.0938695
\(494\) −2.30346e23 −2.92214
\(495\) −4.64290e22 −0.578956
\(496\) 1.70263e23 2.08702
\(497\) 1.50768e21 0.0181669
\(498\) −4.38541e22 −0.519470
\(499\) 3.00550e22 0.349995 0.174998 0.984569i \(-0.444008\pi\)
0.174998 + 0.984569i \(0.444008\pi\)
\(500\) −1.47789e23 −1.69199
\(501\) 3.30990e22 0.372559
\(502\) 2.28983e23 2.53409
\(503\) 1.76283e23 1.91815 0.959074 0.283156i \(-0.0913815\pi\)
0.959074 + 0.283156i \(0.0913815\pi\)
\(504\) −1.26226e23 −1.35048
\(505\) −2.26643e22 −0.238433
\(506\) −3.94327e23 −4.07921
\(507\) −9.63299e21 −0.0979927
\(508\) −1.88436e23 −1.88505
\(509\) 1.20073e23 1.18126 0.590628 0.806944i \(-0.298880\pi\)
0.590628 + 0.806944i \(0.298880\pi\)
\(510\) 1.40825e22 0.136249
\(511\) 5.72077e22 0.544348
\(512\) −2.39995e23 −2.24599
\(513\) −1.40088e23 −1.28945
\(514\) 4.56214e22 0.413031
\(515\) −6.35500e22 −0.565919
\(516\) 6.94955e22 0.608743
\(517\) −1.98451e23 −1.70995
\(518\) 1.63968e23 1.38981
\(519\) 2.40917e22 0.200884
\(520\) −9.65199e22 −0.791750
\(521\) −1.57336e23 −1.26972 −0.634860 0.772627i \(-0.718942\pi\)
−0.634860 + 0.772627i \(0.718942\pi\)
\(522\) −3.65763e22 −0.290403
\(523\) 9.85721e22 0.769998 0.384999 0.922917i \(-0.374202\pi\)
0.384999 + 0.922917i \(0.374202\pi\)
\(524\) −4.23393e23 −3.25408
\(525\) −2.76457e22 −0.209061
\(526\) 2.20174e23 1.63828
\(527\) 7.92174e22 0.580003
\(528\) 1.49717e23 1.07865
\(529\) 1.31451e23 0.931949
\(530\) 1.62321e23 1.13248
\(531\) 1.70810e23 1.17276
\(532\) 4.35697e23 2.94399
\(533\) 1.35676e23 0.902238
\(534\) 1.33042e23 0.870738
\(535\) −5.09895e22 −0.328454
\(536\) −9.72320e22 −0.616465
\(537\) 9.29322e22 0.579942
\(538\) 3.64397e23 2.23834
\(539\) −1.41080e23 −0.853022
\(540\) −1.05591e23 −0.628463
\(541\) 1.45163e23 0.850507 0.425254 0.905074i \(-0.360185\pi\)
0.425254 + 0.905074i \(0.360185\pi\)
\(542\) 3.50932e23 2.02409
\(543\) 6.11446e22 0.347184
\(544\) 9.24787e22 0.516953
\(545\) −4.63710e22 −0.255197
\(546\) −7.15267e22 −0.387553
\(547\) 1.29272e23 0.689624 0.344812 0.938672i \(-0.387943\pi\)
0.344812 + 0.938672i \(0.387943\pi\)
\(548\) −6.90770e23 −3.62826
\(549\) 2.82650e22 0.146179
\(550\) −4.79343e23 −2.44098
\(551\) 7.01856e22 0.351933
\(552\) −2.31548e23 −1.14330
\(553\) −6.45371e22 −0.313795
\(554\) 1.29444e22 0.0619795
\(555\) 3.54149e22 0.166992
\(556\) 1.81166e23 0.841282
\(557\) 3.02733e22 0.138449 0.0692247 0.997601i \(-0.477947\pi\)
0.0692247 + 0.997601i \(0.477947\pi\)
\(558\) −3.98380e23 −1.79435
\(559\) −1.42997e23 −0.634347
\(560\) 1.17802e23 0.514702
\(561\) 6.96578e22 0.299768
\(562\) 7.37389e23 3.12563
\(563\) −1.19493e23 −0.498907 −0.249454 0.968387i \(-0.580251\pi\)
−0.249454 + 0.968387i \(0.580251\pi\)
\(564\) −2.09617e23 −0.862095
\(565\) 5.73156e22 0.232199
\(566\) 4.85225e22 0.193644
\(567\) 1.08671e23 0.427225
\(568\) 1.53502e22 0.0594503
\(569\) 7.01391e22 0.267612 0.133806 0.991008i \(-0.457280\pi\)
0.133806 + 0.991008i \(0.457280\pi\)
\(570\) 1.35895e23 0.510819
\(571\) −3.81222e23 −1.41179 −0.705896 0.708315i \(-0.749456\pi\)
−0.705896 + 0.708315i \(0.749456\pi\)
\(572\) −8.58808e23 −3.13350
\(573\) −3.58589e22 −0.128909
\(574\) −3.70594e23 −1.31265
\(575\) 3.31253e23 1.15607
\(576\) −6.35218e21 −0.0218440
\(577\) −3.85101e23 −1.30491 −0.652455 0.757827i \(-0.726261\pi\)
−0.652455 + 0.757827i \(0.726261\pi\)
\(578\) −4.02065e23 −1.34249
\(579\) 1.69388e23 0.557332
\(580\) 5.29021e22 0.171528
\(581\) −1.70681e23 −0.545366
\(582\) −2.14466e23 −0.675326
\(583\) 8.02907e23 2.49162
\(584\) 5.82451e23 1.78135
\(585\) 1.00910e23 0.304165
\(586\) 3.59328e23 1.06748
\(587\) −6.75340e23 −1.97742 −0.988709 0.149846i \(-0.952122\pi\)
−0.988709 + 0.149846i \(0.952122\pi\)
\(588\) −1.49018e23 −0.430063
\(589\) 7.64444e23 2.17453
\(590\) −3.56762e23 −1.00031
\(591\) −1.77050e23 −0.489330
\(592\) 7.45943e23 2.03222
\(593\) −1.56859e23 −0.421255 −0.210627 0.977566i \(-0.567551\pi\)
−0.210627 + 0.977566i \(0.567551\pi\)
\(594\) −7.54240e23 −1.99675
\(595\) 5.48093e22 0.143041
\(596\) −8.88164e23 −2.28507
\(597\) 4.96292e22 0.125880
\(598\) 8.57039e23 2.14309
\(599\) 7.90605e23 1.94909 0.974544 0.224195i \(-0.0719754\pi\)
0.974544 + 0.224195i \(0.0719754\pi\)
\(600\) −2.81470e23 −0.684143
\(601\) 1.62928e23 0.390449 0.195224 0.980759i \(-0.437457\pi\)
0.195224 + 0.980759i \(0.437457\pi\)
\(602\) 3.90592e23 0.922897
\(603\) 1.01655e23 0.236826
\(604\) 6.33246e22 0.145465
\(605\) 2.98574e23 0.676287
\(606\) −1.71001e23 −0.381928
\(607\) −1.01319e23 −0.223144 −0.111572 0.993756i \(-0.535589\pi\)
−0.111572 + 0.993756i \(0.535589\pi\)
\(608\) 8.92414e23 1.93814
\(609\) 2.17940e22 0.0466755
\(610\) −5.90356e22 −0.124684
\(611\) 4.31318e23 0.898354
\(612\) −4.80599e23 −0.987179
\(613\) −7.22991e22 −0.146460 −0.0732300 0.997315i \(-0.523331\pi\)
−0.0732300 + 0.997315i \(0.523331\pi\)
\(614\) −3.67258e23 −0.733737
\(615\) −8.00434e22 −0.157720
\(616\) 1.30408e24 2.53436
\(617\) 6.35382e22 0.121790 0.0608949 0.998144i \(-0.480605\pi\)
0.0608949 + 0.998144i \(0.480605\pi\)
\(618\) −4.79482e23 −0.906505
\(619\) −8.00300e22 −0.149239 −0.0746195 0.997212i \(-0.523774\pi\)
−0.0746195 + 0.997212i \(0.523774\pi\)
\(620\) 5.76196e23 1.05984
\(621\) 5.21222e23 0.945679
\(622\) −9.05979e23 −1.62144
\(623\) 5.17802e23 0.914145
\(624\) −3.25398e23 −0.566690
\(625\) 3.04728e23 0.523519
\(626\) 1.73435e24 2.93938
\(627\) 6.72194e23 1.12388
\(628\) −1.53080e24 −2.52500
\(629\) 3.47061e23 0.564774
\(630\) −2.75633e23 −0.442523
\(631\) −7.48894e23 −1.18624 −0.593118 0.805116i \(-0.702103\pi\)
−0.593118 + 0.805116i \(0.702103\pi\)
\(632\) −6.57074e23 −1.02688
\(633\) −2.23973e23 −0.345353
\(634\) −1.00511e24 −1.52916
\(635\) −2.28749e23 −0.343385
\(636\) 8.48085e23 1.25619
\(637\) 3.06627e23 0.448151
\(638\) 3.77881e23 0.544979
\(639\) −1.60484e22 −0.0228389
\(640\) −2.85445e23 −0.400860
\(641\) −2.64145e23 −0.366057 −0.183029 0.983108i \(-0.558590\pi\)
−0.183029 + 0.983108i \(0.558590\pi\)
\(642\) −3.84714e23 −0.526126
\(643\) 4.21965e23 0.569486 0.284743 0.958604i \(-0.408092\pi\)
0.284743 + 0.958604i \(0.408092\pi\)
\(644\) −1.62108e24 −2.15911
\(645\) 8.43627e22 0.110890
\(646\) 1.33175e24 1.72761
\(647\) −8.02812e23 −1.02784 −0.513922 0.857837i \(-0.671808\pi\)
−0.513922 + 0.857837i \(0.671808\pi\)
\(648\) 1.10641e24 1.39807
\(649\) −1.76469e24 −2.20084
\(650\) 1.04182e24 1.28241
\(651\) 2.37374e23 0.288400
\(652\) −6.41704e23 −0.769538
\(653\) −4.64489e23 −0.549811 −0.274905 0.961471i \(-0.588647\pi\)
−0.274905 + 0.961471i \(0.588647\pi\)
\(654\) −3.49867e23 −0.408782
\(655\) −5.13970e23 −0.592771
\(656\) −1.68595e24 −1.91939
\(657\) −6.08944e23 −0.684339
\(658\) −1.17813e24 −1.30700
\(659\) 9.29904e23 1.01838 0.509192 0.860653i \(-0.329944\pi\)
0.509192 + 0.860653i \(0.329944\pi\)
\(660\) 5.06663e23 0.547767
\(661\) 3.40182e23 0.363078 0.181539 0.983384i \(-0.441892\pi\)
0.181539 + 0.983384i \(0.441892\pi\)
\(662\) 2.46577e24 2.59812
\(663\) −1.51396e23 −0.157489
\(664\) −1.73776e24 −1.78468
\(665\) 5.28907e23 0.536284
\(666\) −1.74535e24 −1.74723
\(667\) −2.61137e23 −0.258106
\(668\) 2.35931e24 2.30242
\(669\) −8.23192e22 −0.0793194
\(670\) −2.12320e23 −0.202002
\(671\) −2.92015e23 −0.274324
\(672\) 2.77111e23 0.257049
\(673\) −2.17086e23 −0.198840 −0.0994202 0.995046i \(-0.531699\pi\)
−0.0994202 + 0.995046i \(0.531699\pi\)
\(674\) −7.91101e23 −0.715522
\(675\) 6.33597e23 0.565889
\(676\) −6.86642e23 −0.605596
\(677\) 1.95265e24 1.70067 0.850337 0.526238i \(-0.176398\pi\)
0.850337 + 0.526238i \(0.176398\pi\)
\(678\) 4.32444e23 0.371944
\(679\) −8.34707e23 −0.708991
\(680\) 5.58032e23 0.468094
\(681\) 5.19687e23 0.430518
\(682\) 4.11579e24 3.36733
\(683\) −2.17020e24 −1.75357 −0.876787 0.480879i \(-0.840318\pi\)
−0.876787 + 0.480879i \(0.840318\pi\)
\(684\) −4.63775e24 −3.70110
\(685\) −8.38547e23 −0.660933
\(686\) −2.43548e24 −1.89596
\(687\) −1.76794e23 −0.135936
\(688\) 1.77693e24 1.34949
\(689\) −1.74506e24 −1.30902
\(690\) −5.05620e23 −0.374634
\(691\) 6.12633e23 0.448370 0.224185 0.974547i \(-0.428028\pi\)
0.224185 + 0.974547i \(0.428028\pi\)
\(692\) 1.71726e24 1.24147
\(693\) −1.36340e24 −0.973619
\(694\) −4.58076e24 −3.23134
\(695\) 2.19923e23 0.153250
\(696\) 2.21892e23 0.152743
\(697\) −7.84413e23 −0.533416
\(698\) −4.70041e23 −0.315766
\(699\) 3.69296e22 0.0245086
\(700\) −1.97059e24 −1.29200
\(701\) −1.08874e24 −0.705212 −0.352606 0.935772i \(-0.614704\pi\)
−0.352606 + 0.935772i \(0.614704\pi\)
\(702\) 1.63928e24 1.04903
\(703\) 3.34912e24 2.11743
\(704\) 6.56264e22 0.0409931
\(705\) −2.54461e23 −0.157041
\(706\) −2.54452e24 −1.55155
\(707\) −6.65541e23 −0.400968
\(708\) −1.86399e24 −1.10958
\(709\) 2.72295e24 1.60157 0.800787 0.598950i \(-0.204415\pi\)
0.800787 + 0.598950i \(0.204415\pi\)
\(710\) 3.35195e22 0.0194806
\(711\) 6.86961e23 0.394494
\(712\) 5.27192e24 2.99150
\(713\) −2.84424e24 −1.59480
\(714\) 4.13534e23 0.229127
\(715\) −1.04253e24 −0.570806
\(716\) 6.62423e24 3.58405
\(717\) 9.38715e23 0.501904
\(718\) 1.39607e24 0.737647
\(719\) −6.34749e23 −0.331441 −0.165721 0.986173i \(-0.552995\pi\)
−0.165721 + 0.986173i \(0.552995\pi\)
\(720\) −1.25394e24 −0.647069
\(721\) −1.86615e24 −0.951695
\(722\) 9.27339e24 4.67383
\(723\) 7.72190e23 0.384635
\(724\) 4.35840e24 2.14560
\(725\) −3.17438e23 −0.154449
\(726\) 2.25273e24 1.08330
\(727\) −3.59324e23 −0.170783 −0.0853913 0.996347i \(-0.527214\pi\)
−0.0853913 + 0.996347i \(0.527214\pi\)
\(728\) −2.83432e24 −1.33147
\(729\) −6.22816e23 −0.289185
\(730\) 1.27187e24 0.583711
\(731\) 8.26741e23 0.375035
\(732\) −3.08446e23 −0.138304
\(733\) 1.35860e24 0.602154 0.301077 0.953600i \(-0.402654\pi\)
0.301077 + 0.953600i \(0.402654\pi\)
\(734\) −1.41921e24 −0.621770
\(735\) −1.80898e23 −0.0783413
\(736\) −3.32037e24 −1.42143
\(737\) −1.05023e24 −0.444436
\(738\) 3.94477e24 1.65022
\(739\) 2.92762e23 0.121070 0.0605352 0.998166i \(-0.480719\pi\)
0.0605352 + 0.998166i \(0.480719\pi\)
\(740\) 2.52438e24 1.03201
\(741\) −1.46096e24 −0.590452
\(742\) 4.76657e24 1.90446
\(743\) 1.26938e24 0.501401 0.250701 0.968065i \(-0.419339\pi\)
0.250701 + 0.968065i \(0.419339\pi\)
\(744\) 2.41679e24 0.943776
\(745\) −1.07817e24 −0.416255
\(746\) 2.08853e24 0.797187
\(747\) 1.81680e24 0.685619
\(748\) 4.96522e24 1.85257
\(749\) −1.49732e24 −0.552354
\(750\) −1.35361e24 −0.493710
\(751\) −1.79039e24 −0.645666 −0.322833 0.946456i \(-0.604635\pi\)
−0.322833 + 0.946456i \(0.604635\pi\)
\(752\) −5.35970e24 −1.91112
\(753\) 1.45232e24 0.512042
\(754\) −8.21297e23 −0.286315
\(755\) 7.68717e22 0.0264982
\(756\) −3.10069e24 −1.05688
\(757\) −5.88170e24 −1.98239 −0.991193 0.132425i \(-0.957724\pi\)
−0.991193 + 0.132425i \(0.957724\pi\)
\(758\) −8.61670e24 −2.87179
\(759\) −2.50101e24 −0.824252
\(760\) 5.38498e24 1.75496
\(761\) 6.02417e24 1.94145 0.970727 0.240184i \(-0.0772077\pi\)
0.970727 + 0.240184i \(0.0772077\pi\)
\(762\) −1.72590e24 −0.550045
\(763\) −1.36169e24 −0.429161
\(764\) −2.55603e24 −0.796659
\(765\) −5.83414e23 −0.179827
\(766\) 3.07425e23 0.0937120
\(767\) 3.83543e24 1.15625
\(768\) −2.18446e24 −0.651288
\(769\) 1.47101e24 0.433752 0.216876 0.976199i \(-0.430413\pi\)
0.216876 + 0.976199i \(0.430413\pi\)
\(770\) 2.84765e24 0.830453
\(771\) 2.89353e23 0.0834575
\(772\) 1.20740e25 3.44432
\(773\) 4.34175e24 1.22501 0.612504 0.790468i \(-0.290162\pi\)
0.612504 + 0.790468i \(0.290162\pi\)
\(774\) −4.15763e24 −1.16024
\(775\) −3.45746e24 −0.954316
\(776\) −8.49843e24 −2.32014
\(777\) 1.03996e24 0.280827
\(778\) 4.69513e24 1.25407
\(779\) −7.56954e24 −1.99987
\(780\) −1.10120e24 −0.287780
\(781\) 1.65801e23 0.0428602
\(782\) −4.95499e24 −1.26703
\(783\) −4.99484e23 −0.126342
\(784\) −3.81024e24 −0.953380
\(785\) −1.85829e24 −0.459960
\(786\) −3.87788e24 −0.949517
\(787\) 3.14826e24 0.762580 0.381290 0.924456i \(-0.375480\pi\)
0.381290 + 0.924456i \(0.375480\pi\)
\(788\) −1.26202e25 −3.02407
\(789\) 1.39645e24 0.331033
\(790\) −1.43482e24 −0.336486
\(791\) 1.68308e24 0.390486
\(792\) −1.38812e25 −3.18612
\(793\) 6.34673e23 0.144121
\(794\) 6.09999e24 1.37042
\(795\) 1.02952e24 0.228830
\(796\) 3.53758e24 0.777938
\(797\) −7.09934e23 −0.154462 −0.0772311 0.997013i \(-0.524608\pi\)
−0.0772311 + 0.997013i \(0.524608\pi\)
\(798\) 3.99058e24 0.859035
\(799\) −2.49368e24 −0.531120
\(800\) −4.03625e24 −0.850575
\(801\) −5.51171e24 −1.14924
\(802\) −7.76155e24 −1.60128
\(803\) 6.29119e24 1.28425
\(804\) −1.10932e24 −0.224068
\(805\) −1.96788e24 −0.393309
\(806\) −8.94536e24 −1.76909
\(807\) 2.31118e24 0.452282
\(808\) −6.77610e24 −1.31215
\(809\) −2.23126e24 −0.427551 −0.213776 0.976883i \(-0.568576\pi\)
−0.213776 + 0.976883i \(0.568576\pi\)
\(810\) 2.41602e24 0.458118
\(811\) 8.44506e24 1.58462 0.792311 0.610118i \(-0.208878\pi\)
0.792311 + 0.610118i \(0.208878\pi\)
\(812\) 1.55348e24 0.288455
\(813\) 2.22578e24 0.408989
\(814\) 1.80317e25 3.27892
\(815\) −7.78984e23 −0.140181
\(816\) 1.88130e24 0.335035
\(817\) 7.97801e24 1.40607
\(818\) 1.58622e25 2.76668
\(819\) 2.96324e24 0.511509
\(820\) −5.70551e24 −0.974713
\(821\) −1.52167e24 −0.257278 −0.128639 0.991691i \(-0.541061\pi\)
−0.128639 + 0.991691i \(0.541061\pi\)
\(822\) −6.32680e24 −1.05870
\(823\) 4.82422e24 0.798967 0.399483 0.916740i \(-0.369190\pi\)
0.399483 + 0.916740i \(0.369190\pi\)
\(824\) −1.90000e25 −3.11438
\(825\) −3.04023e24 −0.493227
\(826\) −1.04764e25 −1.68221
\(827\) −1.39875e24 −0.222302 −0.111151 0.993804i \(-0.535454\pi\)
−0.111151 + 0.993804i \(0.535454\pi\)
\(828\) 1.72555e25 2.71438
\(829\) 2.95029e24 0.459358 0.229679 0.973266i \(-0.426232\pi\)
0.229679 + 0.973266i \(0.426232\pi\)
\(830\) −3.79466e24 −0.584802
\(831\) 8.20995e22 0.0125237
\(832\) −1.42634e23 −0.0215365
\(833\) −1.77277e24 −0.264953
\(834\) 1.65931e24 0.245480
\(835\) 2.86403e24 0.419414
\(836\) 4.79141e25 6.94561
\(837\) −5.44026e24 −0.780644
\(838\) 1.80979e24 0.257072
\(839\) −1.00139e25 −1.40807 −0.704036 0.710164i \(-0.748621\pi\)
−0.704036 + 0.710164i \(0.748621\pi\)
\(840\) 1.67214e24 0.232754
\(841\) 2.50246e23 0.0344828
\(842\) −1.32720e25 −1.81044
\(843\) 4.67687e24 0.631570
\(844\) −1.59648e25 −2.13429
\(845\) −8.33535e23 −0.110317
\(846\) 1.25406e25 1.64312
\(847\) 8.76766e24 1.13730
\(848\) 2.16847e25 2.78476
\(849\) 3.07753e23 0.0391279
\(850\) −6.02329e24 −0.758181
\(851\) −1.24609e25 −1.55292
\(852\) 1.75131e23 0.0216086
\(853\) −1.10311e25 −1.34757 −0.673784 0.738929i \(-0.735332\pi\)
−0.673784 + 0.738929i \(0.735332\pi\)
\(854\) −1.73359e24 −0.209679
\(855\) −5.62991e24 −0.674201
\(856\) −1.52447e25 −1.80755
\(857\) 1.11014e25 1.30328 0.651642 0.758527i \(-0.274080\pi\)
0.651642 + 0.758527i \(0.274080\pi\)
\(858\) −7.86587e24 −0.914334
\(859\) −9.60992e24 −1.10606 −0.553029 0.833162i \(-0.686528\pi\)
−0.553029 + 0.833162i \(0.686528\pi\)
\(860\) 6.01339e24 0.685303
\(861\) −2.35049e24 −0.265235
\(862\) −6.80641e24 −0.760512
\(863\) −7.22439e24 −0.799299 −0.399649 0.916668i \(-0.630868\pi\)
−0.399649 + 0.916668i \(0.630868\pi\)
\(864\) −6.35098e24 −0.695783
\(865\) 2.08464e24 0.226148
\(866\) 2.09099e24 0.224621
\(867\) −2.55009e24 −0.271265
\(868\) 1.69201e25 1.78232
\(869\) −7.09721e24 −0.740320
\(870\) 4.84533e23 0.0500507
\(871\) 2.28259e24 0.233493
\(872\) −1.38638e25 −1.40441
\(873\) 8.88499e24 0.891324
\(874\) −4.78154e25 −4.75030
\(875\) −5.26827e24 −0.518322
\(876\) 6.64518e24 0.647474
\(877\) 2.91120e24 0.280915 0.140457 0.990087i \(-0.455143\pi\)
0.140457 + 0.990087i \(0.455143\pi\)
\(878\) 1.95478e25 1.86808
\(879\) 2.27903e24 0.215697
\(880\) 1.29549e25 1.21431
\(881\) 7.96627e24 0.739537 0.369769 0.929124i \(-0.379437\pi\)
0.369769 + 0.929124i \(0.379437\pi\)
\(882\) 8.91515e24 0.819683
\(883\) 1.59441e25 1.45190 0.725948 0.687750i \(-0.241401\pi\)
0.725948 + 0.687750i \(0.241401\pi\)
\(884\) −1.07915e25 −0.973283
\(885\) −2.26275e24 −0.202125
\(886\) 3.70456e25 3.27755
\(887\) 6.50168e24 0.569738 0.284869 0.958566i \(-0.408050\pi\)
0.284869 + 0.958566i \(0.408050\pi\)
\(888\) 1.05882e25 0.918995
\(889\) −6.71723e24 −0.577465
\(890\) 1.15120e25 0.980248
\(891\) 1.19506e25 1.00793
\(892\) −5.86773e24 −0.490195
\(893\) −2.40639e25 −1.99126
\(894\) −8.13475e24 −0.666769
\(895\) 8.04135e24 0.652880
\(896\) −8.38214e24 −0.674120
\(897\) 5.43575e24 0.433036
\(898\) −1.61497e25 −1.27443
\(899\) 2.72562e24 0.213063
\(900\) 2.09758e25 1.62427
\(901\) 1.00891e25 0.773912
\(902\) −4.07547e25 −3.09686
\(903\) 2.47732e24 0.186482
\(904\) 1.71360e25 1.27785
\(905\) 5.29080e24 0.390848
\(906\) 5.79993e23 0.0424457
\(907\) −2.19181e25 −1.58906 −0.794531 0.607224i \(-0.792283\pi\)
−0.794531 + 0.607224i \(0.792283\pi\)
\(908\) 3.70434e25 2.66061
\(909\) 7.08431e24 0.504086
\(910\) −6.18915e24 −0.436294
\(911\) −2.64085e25 −1.84433 −0.922164 0.386799i \(-0.873581\pi\)
−0.922164 + 0.386799i \(0.873581\pi\)
\(912\) 1.81544e25 1.25610
\(913\) −1.87700e25 −1.28665
\(914\) 3.73825e25 2.53879
\(915\) −3.74432e23 −0.0251938
\(916\) −1.26019e25 −0.840086
\(917\) −1.50928e25 −0.996852
\(918\) −9.47756e24 −0.620203
\(919\) 1.23626e25 0.801544 0.400772 0.916178i \(-0.368742\pi\)
0.400772 + 0.916178i \(0.368742\pi\)
\(920\) −2.00357e25 −1.28709
\(921\) −2.32933e24 −0.148260
\(922\) −2.17880e25 −1.37406
\(923\) −3.60357e23 −0.0225174
\(924\) 1.48782e25 0.921170
\(925\) −1.51475e25 −0.929259
\(926\) 8.89485e24 0.540686
\(927\) 1.98642e25 1.19644
\(928\) 3.18190e24 0.189902
\(929\) −1.04780e24 −0.0619645 −0.0309823 0.999520i \(-0.509864\pi\)
−0.0309823 + 0.999520i \(0.509864\pi\)
\(930\) 5.27741e24 0.309255
\(931\) −1.71071e25 −0.993355
\(932\) 2.63235e24 0.151464
\(933\) −5.74615e24 −0.327630
\(934\) 2.93195e25 1.65657
\(935\) 6.02744e24 0.337469
\(936\) 3.01697e25 1.67389
\(937\) −7.67856e24 −0.422176 −0.211088 0.977467i \(-0.567701\pi\)
−0.211088 + 0.977467i \(0.567701\pi\)
\(938\) −6.23482e24 −0.339703
\(939\) 1.10001e25 0.593935
\(940\) −1.81380e25 −0.970518
\(941\) −5.84057e24 −0.309701 −0.154851 0.987938i \(-0.549490\pi\)
−0.154851 + 0.987938i \(0.549490\pi\)
\(942\) −1.40207e25 −0.736778
\(943\) 2.81637e25 1.46670
\(944\) −4.76603e25 −2.45977
\(945\) −3.76403e24 −0.192523
\(946\) 4.29538e25 2.17735
\(947\) −7.29245e24 −0.366352 −0.183176 0.983080i \(-0.558638\pi\)
−0.183176 + 0.983080i \(0.558638\pi\)
\(948\) −7.49656e24 −0.373243
\(949\) −1.36734e25 −0.674706
\(950\) −5.81244e25 −2.84255
\(951\) −6.37488e24 −0.308985
\(952\) 1.63867e25 0.787185
\(953\) 1.09843e25 0.522979 0.261490 0.965206i \(-0.415786\pi\)
0.261490 + 0.965206i \(0.415786\pi\)
\(954\) −5.07375e25 −2.39424
\(955\) −3.10285e24 −0.145121
\(956\) 6.69118e25 3.10178
\(957\) 2.39670e24 0.110119
\(958\) −2.77236e25 −1.26253
\(959\) −2.46240e25 −1.11148
\(960\) 8.41485e22 0.00376479
\(961\) 7.13667e24 0.316481
\(962\) −3.91907e25 −1.72264
\(963\) 1.59381e25 0.694405
\(964\) 5.50419e25 2.37705
\(965\) 1.46570e25 0.627426
\(966\) −1.48476e25 −0.630014
\(967\) 2.88717e25 1.21436 0.607179 0.794565i \(-0.292301\pi\)
0.607179 + 0.794565i \(0.292301\pi\)
\(968\) 8.92665e25 3.72176
\(969\) 8.44660e24 0.349084
\(970\) −1.85576e25 −0.760259
\(971\) 3.53970e25 1.43748 0.718742 0.695277i \(-0.244718\pi\)
0.718742 + 0.695277i \(0.244718\pi\)
\(972\) 5.06811e25 2.04025
\(973\) 6.45807e24 0.257718
\(974\) −8.36381e25 −3.30867
\(975\) 6.60770e24 0.259126
\(976\) −7.88665e24 −0.306598
\(977\) −2.78359e25 −1.07276 −0.536378 0.843978i \(-0.680208\pi\)
−0.536378 + 0.843978i \(0.680208\pi\)
\(978\) −5.87740e24 −0.224546
\(979\) 5.69432e25 2.15670
\(980\) −1.28944e25 −0.484150
\(981\) 1.44944e25 0.539529
\(982\) −5.40153e25 −1.99328
\(983\) 4.25993e25 1.55847 0.779234 0.626733i \(-0.215609\pi\)
0.779234 + 0.626733i \(0.215609\pi\)
\(984\) −2.39311e25 −0.867969
\(985\) −1.53200e25 −0.550872
\(986\) 4.74835e24 0.169273
\(987\) −7.47228e24 −0.264093
\(988\) −1.04138e26 −3.64900
\(989\) −2.96835e25 −1.03121
\(990\) −3.03116e25 −1.04402
\(991\) 8.47047e23 0.0289256 0.0144628 0.999895i \(-0.495396\pi\)
0.0144628 + 0.999895i \(0.495396\pi\)
\(992\) 3.46564e25 1.17337
\(993\) 1.56391e25 0.524980
\(994\) 9.84304e23 0.0327601
\(995\) 4.29437e24 0.141711
\(996\) −1.98261e25 −0.648684
\(997\) −3.78529e25 −1.22798 −0.613988 0.789315i \(-0.710436\pi\)
−0.613988 + 0.789315i \(0.710436\pi\)
\(998\) 1.96217e25 0.631141
\(999\) −2.38344e25 −0.760147
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.1.20 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.20 21 1.1 even 1 trivial