Properties

Label 29.18.a.b.1.6
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 1.6
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +O(q^{10})\) \(q-332.840 q^{2} -18225.8 q^{3} -20289.6 q^{4} -318485. q^{5} +6.06628e6 q^{6} +9.82044e6 q^{7} +5.03792e7 q^{8} +2.03040e8 q^{9} +1.06005e8 q^{10} +9.36358e6 q^{11} +3.69795e8 q^{12} -3.20633e9 q^{13} -3.26863e9 q^{14} +5.80466e9 q^{15} -1.41088e10 q^{16} +8.46481e9 q^{17} -6.75799e10 q^{18} -7.69200e10 q^{19} +6.46194e9 q^{20} -1.78986e11 q^{21} -3.11657e9 q^{22} +1.60829e11 q^{23} -9.18202e11 q^{24} -6.61507e11 q^{25} +1.06720e12 q^{26} -1.34689e12 q^{27} -1.99253e11 q^{28} +5.00246e11 q^{29} -1.93202e12 q^{30} -4.63610e12 q^{31} -1.90733e12 q^{32} -1.70659e11 q^{33} -2.81742e12 q^{34} -3.12767e12 q^{35} -4.11961e12 q^{36} +4.51018e12 q^{37} +2.56020e13 q^{38} +5.84380e13 q^{39} -1.60450e13 q^{40} -1.95332e13 q^{41} +5.95735e13 q^{42} -2.62720e13 q^{43} -1.89983e11 q^{44} -6.46654e13 q^{45} -5.35304e13 q^{46} -2.05312e14 q^{47} +2.57145e14 q^{48} -1.36189e14 q^{49} +2.20176e14 q^{50} -1.54278e14 q^{51} +6.50552e13 q^{52} -1.23971e14 q^{53} +4.48300e14 q^{54} -2.98216e12 q^{55} +4.94746e14 q^{56} +1.40193e15 q^{57} -1.66502e14 q^{58} +6.96656e13 q^{59} -1.17774e14 q^{60} +2.14181e15 q^{61} +1.54308e15 q^{62} +1.99395e15 q^{63} +2.48410e15 q^{64} +1.02117e15 q^{65} +5.68021e13 q^{66} -1.15108e15 q^{67} -1.71748e14 q^{68} -2.93124e15 q^{69} +1.04101e15 q^{70} -2.06784e14 q^{71} +1.02290e16 q^{72} +2.75508e14 q^{73} -1.50117e15 q^{74} +1.20565e16 q^{75} +1.56068e15 q^{76} +9.19545e13 q^{77} -1.94505e16 q^{78} -1.64938e16 q^{79} +4.49345e15 q^{80} -1.67245e15 q^{81} +6.50144e15 q^{82} +1.11291e16 q^{83} +3.63155e15 q^{84} -2.69592e15 q^{85} +8.74436e15 q^{86} -9.11740e15 q^{87} +4.71729e14 q^{88} -6.18759e16 q^{89} +2.15232e16 q^{90} -3.14876e16 q^{91} -3.26316e15 q^{92} +8.44967e16 q^{93} +6.83361e16 q^{94} +2.44979e16 q^{95} +3.47626e16 q^{96} +1.57070e15 q^{97} +4.53293e16 q^{98} +1.90118e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \) \( 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −332.840 −0.919349 −0.459675 0.888087i \(-0.652034\pi\)
−0.459675 + 0.888087i \(0.652034\pi\)
\(3\) −18225.8 −1.60382 −0.801912 0.597443i \(-0.796183\pi\)
−0.801912 + 0.597443i \(0.796183\pi\)
\(4\) −20289.6 −0.154797
\(5\) −318485. −0.364623 −0.182312 0.983241i \(-0.558358\pi\)
−0.182312 + 0.983241i \(0.558358\pi\)
\(6\) 6.06628e6 1.47447
\(7\) 9.82044e6 0.643869 0.321935 0.946762i \(-0.395667\pi\)
0.321935 + 0.946762i \(0.395667\pi\)
\(8\) 5.03792e7 1.06166
\(9\) 2.03040e8 1.57225
\(10\) 1.06005e8 0.335216
\(11\) 9.36358e6 0.0131706 0.00658528 0.999978i \(-0.497904\pi\)
0.00658528 + 0.999978i \(0.497904\pi\)
\(12\) 3.69795e8 0.248268
\(13\) −3.20633e9 −1.09016 −0.545080 0.838384i \(-0.683501\pi\)
−0.545080 + 0.838384i \(0.683501\pi\)
\(14\) −3.26863e9 −0.591940
\(15\) 5.80466e9 0.584791
\(16\) −1.41088e10 −0.821240
\(17\) 8.46481e9 0.294307 0.147154 0.989114i \(-0.452989\pi\)
0.147154 + 0.989114i \(0.452989\pi\)
\(18\) −6.75799e10 −1.44544
\(19\) −7.69200e10 −1.03904 −0.519522 0.854457i \(-0.673890\pi\)
−0.519522 + 0.854457i \(0.673890\pi\)
\(20\) 6.46194e9 0.0564427
\(21\) −1.78986e11 −1.03265
\(22\) −3.11657e9 −0.0121083
\(23\) 1.60829e11 0.428231 0.214116 0.976808i \(-0.431313\pi\)
0.214116 + 0.976808i \(0.431313\pi\)
\(24\) −9.18202e11 −1.70272
\(25\) −6.61507e11 −0.867050
\(26\) 1.06720e12 1.00224
\(27\) −1.34689e12 −0.917785
\(28\) −1.99253e11 −0.0996692
\(29\) 5.00246e11 0.185695
\(30\) −1.93202e12 −0.537627
\(31\) −4.63610e12 −0.976289 −0.488144 0.872763i \(-0.662326\pi\)
−0.488144 + 0.872763i \(0.662326\pi\)
\(32\) −1.90733e12 −0.306655
\(33\) −1.70659e11 −0.0211232
\(34\) −2.81742e12 −0.270571
\(35\) −3.12767e12 −0.234770
\(36\) −4.11961e12 −0.243380
\(37\) 4.51018e12 0.211096 0.105548 0.994414i \(-0.466340\pi\)
0.105548 + 0.994414i \(0.466340\pi\)
\(38\) 2.56020e13 0.955244
\(39\) 5.84380e13 1.74842
\(40\) −1.60450e13 −0.387107
\(41\) −1.95332e13 −0.382042 −0.191021 0.981586i \(-0.561180\pi\)
−0.191021 + 0.981586i \(0.561180\pi\)
\(42\) 5.95735e13 0.949368
\(43\) −2.62720e13 −0.342776 −0.171388 0.985204i \(-0.554825\pi\)
−0.171388 + 0.985204i \(0.554825\pi\)
\(44\) −1.89983e11 −0.00203877
\(45\) −6.46654e13 −0.573278
\(46\) −5.35304e13 −0.393694
\(47\) −2.05312e14 −1.25772 −0.628859 0.777519i \(-0.716478\pi\)
−0.628859 + 0.777519i \(0.716478\pi\)
\(48\) 2.57145e14 1.31712
\(49\) −1.36189e14 −0.585433
\(50\) 2.20176e14 0.797121
\(51\) −1.54278e14 −0.472017
\(52\) 6.50552e13 0.168754
\(53\) −1.23971e14 −0.273511 −0.136755 0.990605i \(-0.543667\pi\)
−0.136755 + 0.990605i \(0.543667\pi\)
\(54\) 4.48300e14 0.843765
\(55\) −2.98216e12 −0.00480229
\(56\) 4.94746e14 0.683571
\(57\) 1.40193e15 1.66644
\(58\) −1.66502e14 −0.170719
\(59\) 6.96656e13 0.0617698 0.0308849 0.999523i \(-0.490167\pi\)
0.0308849 + 0.999523i \(0.490167\pi\)
\(60\) −1.17774e14 −0.0905241
\(61\) 2.14181e15 1.43047 0.715233 0.698886i \(-0.246320\pi\)
0.715233 + 0.698886i \(0.246320\pi\)
\(62\) 1.54308e15 0.897550
\(63\) 1.99395e15 1.01232
\(64\) 2.48410e15 1.10316
\(65\) 1.02117e15 0.397497
\(66\) 5.68021e13 0.0194196
\(67\) −1.15108e15 −0.346314 −0.173157 0.984894i \(-0.555397\pi\)
−0.173157 + 0.984894i \(0.555397\pi\)
\(68\) −1.71748e14 −0.0455580
\(69\) −2.93124e15 −0.686807
\(70\) 1.04101e15 0.215835
\(71\) −2.06784e14 −0.0380033 −0.0190016 0.999819i \(-0.506049\pi\)
−0.0190016 + 0.999819i \(0.506049\pi\)
\(72\) 1.02290e16 1.66920
\(73\) 2.75508e14 0.0399844 0.0199922 0.999800i \(-0.493636\pi\)
0.0199922 + 0.999800i \(0.493636\pi\)
\(74\) −1.50117e15 −0.194071
\(75\) 1.20565e16 1.39059
\(76\) 1.56068e15 0.160841
\(77\) 9.19545e13 0.00848011
\(78\) −1.94505e16 −1.60741
\(79\) −1.64938e16 −1.22318 −0.611591 0.791174i \(-0.709470\pi\)
−0.611591 + 0.791174i \(0.709470\pi\)
\(80\) 4.49345e15 0.299443
\(81\) −1.67245e15 −0.100284
\(82\) 6.50144e15 0.351230
\(83\) 1.11291e16 0.542371 0.271185 0.962527i \(-0.412584\pi\)
0.271185 + 0.962527i \(0.412584\pi\)
\(84\) 3.63155e15 0.159852
\(85\) −2.69592e15 −0.107311
\(86\) 8.74436e15 0.315131
\(87\) −9.11740e15 −0.297822
\(88\) 4.71729e14 0.0139827
\(89\) −6.18759e16 −1.66612 −0.833061 0.553182i \(-0.813414\pi\)
−0.833061 + 0.553182i \(0.813414\pi\)
\(90\) 2.15232e16 0.527043
\(91\) −3.14876e16 −0.701920
\(92\) −3.26316e15 −0.0662890
\(93\) 8.44967e16 1.56579
\(94\) 6.83361e16 1.15628
\(95\) 2.44979e16 0.378859
\(96\) 3.47626e16 0.491821
\(97\) 1.57070e15 0.0203485 0.0101743 0.999948i \(-0.496761\pi\)
0.0101743 + 0.999948i \(0.496761\pi\)
\(98\) 4.53293e16 0.538217
\(99\) 1.90118e15 0.0207074
\(100\) 1.34217e16 0.134217
\(101\) 1.07285e17 0.985840 0.492920 0.870075i \(-0.335930\pi\)
0.492920 + 0.870075i \(0.335930\pi\)
\(102\) 5.13499e16 0.433948
\(103\) −3.50328e15 −0.0272495 −0.0136248 0.999907i \(-0.504337\pi\)
−0.0136248 + 0.999907i \(0.504337\pi\)
\(104\) −1.61532e17 −1.15738
\(105\) 5.70043e16 0.376529
\(106\) 4.12624e16 0.251452
\(107\) −3.49430e17 −1.96607 −0.983034 0.183422i \(-0.941283\pi\)
−0.983034 + 0.183422i \(0.941283\pi\)
\(108\) 2.73279e16 0.142071
\(109\) −2.87690e17 −1.38293 −0.691464 0.722411i \(-0.743034\pi\)
−0.691464 + 0.722411i \(0.743034\pi\)
\(110\) 9.92583e14 0.00441498
\(111\) −8.22018e16 −0.338560
\(112\) −1.38555e17 −0.528771
\(113\) −1.91324e17 −0.677023 −0.338511 0.940962i \(-0.609923\pi\)
−0.338511 + 0.940962i \(0.609923\pi\)
\(114\) −4.66618e17 −1.53204
\(115\) −5.12217e16 −0.156143
\(116\) −1.01498e16 −0.0287451
\(117\) −6.51015e17 −1.71400
\(118\) −2.31875e16 −0.0567880
\(119\) 8.31281e16 0.189495
\(120\) 2.92434e17 0.620851
\(121\) −5.05359e17 −0.999827
\(122\) −7.12881e17 −1.31510
\(123\) 3.56009e17 0.612728
\(124\) 9.40646e16 0.151127
\(125\) 4.53665e17 0.680770
\(126\) −6.63665e17 −0.930677
\(127\) 1.24826e18 1.63672 0.818359 0.574708i \(-0.194884\pi\)
0.818359 + 0.574708i \(0.194884\pi\)
\(128\) −5.76812e17 −0.707537
\(129\) 4.78828e17 0.549753
\(130\) −3.39886e17 −0.365439
\(131\) 7.84941e17 0.790735 0.395368 0.918523i \(-0.370617\pi\)
0.395368 + 0.918523i \(0.370617\pi\)
\(132\) 3.46260e15 0.00326982
\(133\) −7.55388e17 −0.669008
\(134\) 3.83126e17 0.318384
\(135\) 4.28965e17 0.334646
\(136\) 4.26450e17 0.312455
\(137\) −7.82588e17 −0.538776 −0.269388 0.963032i \(-0.586821\pi\)
−0.269388 + 0.963032i \(0.586821\pi\)
\(138\) 9.75635e17 0.631415
\(139\) 2.40417e18 1.46332 0.731661 0.681669i \(-0.238745\pi\)
0.731661 + 0.681669i \(0.238745\pi\)
\(140\) 6.34591e16 0.0363417
\(141\) 3.74199e18 2.01716
\(142\) 6.88259e16 0.0349383
\(143\) −3.00227e16 −0.0143580
\(144\) −2.86466e18 −1.29119
\(145\) −1.59321e17 −0.0677088
\(146\) −9.17002e16 −0.0367596
\(147\) 2.48216e18 0.938930
\(148\) −9.15098e16 −0.0326771
\(149\) 2.84020e18 0.957779 0.478890 0.877875i \(-0.341039\pi\)
0.478890 + 0.877875i \(0.341039\pi\)
\(150\) −4.01288e18 −1.27844
\(151\) 2.96188e18 0.891791 0.445895 0.895085i \(-0.352885\pi\)
0.445895 + 0.895085i \(0.352885\pi\)
\(152\) −3.87517e18 −1.10311
\(153\) 1.71870e18 0.462724
\(154\) −3.06061e16 −0.00779618
\(155\) 1.47653e18 0.355978
\(156\) −1.18568e18 −0.270651
\(157\) 1.90893e18 0.412707 0.206354 0.978478i \(-0.433840\pi\)
0.206354 + 0.978478i \(0.433840\pi\)
\(158\) 5.48980e18 1.12453
\(159\) 2.25947e18 0.438663
\(160\) 6.07456e17 0.111814
\(161\) 1.57941e18 0.275725
\(162\) 5.56658e17 0.0921957
\(163\) −7.02547e18 −1.10428 −0.552142 0.833750i \(-0.686189\pi\)
−0.552142 + 0.833750i \(0.686189\pi\)
\(164\) 3.96322e17 0.0591391
\(165\) 5.43524e16 0.00770202
\(166\) −3.70421e18 −0.498628
\(167\) 4.80741e18 0.614923 0.307462 0.951560i \(-0.400520\pi\)
0.307462 + 0.951560i \(0.400520\pi\)
\(168\) −9.01715e18 −1.09633
\(169\) 1.63015e18 0.188447
\(170\) 8.97308e17 0.0986566
\(171\) −1.56179e19 −1.63363
\(172\) 5.33048e17 0.0530609
\(173\) 1.45503e19 1.37874 0.689369 0.724411i \(-0.257888\pi\)
0.689369 + 0.724411i \(0.257888\pi\)
\(174\) 3.03464e18 0.273803
\(175\) −6.49629e18 −0.558267
\(176\) −1.32109e17 −0.0108162
\(177\) −1.26971e18 −0.0990679
\(178\) 2.05948e19 1.53175
\(179\) 1.08261e19 0.767751 0.383875 0.923385i \(-0.374589\pi\)
0.383875 + 0.923385i \(0.374589\pi\)
\(180\) 1.31203e18 0.0887420
\(181\) 1.14959e19 0.741777 0.370889 0.928677i \(-0.379053\pi\)
0.370889 + 0.928677i \(0.379053\pi\)
\(182\) 1.04803e19 0.645309
\(183\) −3.90363e19 −2.29422
\(184\) 8.10244e18 0.454637
\(185\) −1.43643e18 −0.0769704
\(186\) −2.81239e19 −1.43951
\(187\) 7.92609e16 0.00387619
\(188\) 4.16571e18 0.194691
\(189\) −1.32271e19 −0.590933
\(190\) −8.15388e18 −0.348304
\(191\) −6.91419e18 −0.282461 −0.141230 0.989977i \(-0.545106\pi\)
−0.141230 + 0.989977i \(0.545106\pi\)
\(192\) −4.52748e19 −1.76928
\(193\) 1.71091e19 0.639721 0.319861 0.947465i \(-0.396364\pi\)
0.319861 + 0.947465i \(0.396364\pi\)
\(194\) −5.22791e17 −0.0187074
\(195\) −1.86117e19 −0.637516
\(196\) 2.76323e18 0.0906234
\(197\) −1.88385e19 −0.591675 −0.295838 0.955238i \(-0.595599\pi\)
−0.295838 + 0.955238i \(0.595599\pi\)
\(198\) −6.32790e17 −0.0190373
\(199\) −2.19879e19 −0.633773 −0.316886 0.948464i \(-0.602637\pi\)
−0.316886 + 0.948464i \(0.602637\pi\)
\(200\) −3.33262e19 −0.920514
\(201\) 2.09794e19 0.555427
\(202\) −3.57087e19 −0.906331
\(203\) 4.91264e18 0.119563
\(204\) 3.13024e18 0.0730670
\(205\) 6.22105e18 0.139302
\(206\) 1.16603e18 0.0250518
\(207\) 3.26548e19 0.673285
\(208\) 4.52375e19 0.895283
\(209\) −7.20246e17 −0.0136848
\(210\) −1.89733e19 −0.346162
\(211\) 8.36965e19 1.46658 0.733291 0.679915i \(-0.237983\pi\)
0.733291 + 0.679915i \(0.237983\pi\)
\(212\) 2.51532e18 0.0423387
\(213\) 3.76881e18 0.0609505
\(214\) 1.16304e20 1.80750
\(215\) 8.36724e18 0.124984
\(216\) −6.78553e19 −0.974377
\(217\) −4.55285e19 −0.628602
\(218\) 9.57547e19 1.27139
\(219\) −5.02137e18 −0.0641279
\(220\) 6.05069e16 0.000743382 0
\(221\) −2.71410e19 −0.320842
\(222\) 2.73600e19 0.311255
\(223\) −1.36177e20 −1.49112 −0.745558 0.666440i \(-0.767817\pi\)
−0.745558 + 0.666440i \(0.767817\pi\)
\(224\) −1.87308e19 −0.197446
\(225\) −1.34313e20 −1.36322
\(226\) 6.36803e19 0.622420
\(227\) −1.32204e20 −1.24459 −0.622294 0.782784i \(-0.713799\pi\)
−0.622294 + 0.782784i \(0.713799\pi\)
\(228\) −2.84446e19 −0.257961
\(229\) 9.74665e19 0.851635 0.425818 0.904809i \(-0.359986\pi\)
0.425818 + 0.904809i \(0.359986\pi\)
\(230\) 1.70486e19 0.143550
\(231\) −1.67595e18 −0.0136006
\(232\) 2.52020e19 0.197146
\(233\) −1.48581e20 −1.12057 −0.560283 0.828301i \(-0.689308\pi\)
−0.560283 + 0.828301i \(0.689308\pi\)
\(234\) 2.16684e20 1.57577
\(235\) 6.53890e19 0.458593
\(236\) −1.41349e18 −0.00956181
\(237\) 3.00613e20 1.96177
\(238\) −2.76684e19 −0.174212
\(239\) 1.89117e19 0.114908 0.0574538 0.998348i \(-0.481702\pi\)
0.0574538 + 0.998348i \(0.481702\pi\)
\(240\) −8.18968e19 −0.480254
\(241\) −4.04261e19 −0.228832 −0.114416 0.993433i \(-0.536500\pi\)
−0.114416 + 0.993433i \(0.536500\pi\)
\(242\) 1.68204e20 0.919190
\(243\) 2.04420e20 1.07862
\(244\) −4.34565e19 −0.221433
\(245\) 4.33743e19 0.213462
\(246\) −1.18494e20 −0.563311
\(247\) 2.46631e20 1.13272
\(248\) −2.33563e20 −1.03649
\(249\) −2.02837e20 −0.869866
\(250\) −1.50998e20 −0.625865
\(251\) 2.84259e20 1.13890 0.569452 0.822025i \(-0.307156\pi\)
0.569452 + 0.822025i \(0.307156\pi\)
\(252\) −4.04564e19 −0.156705
\(253\) 1.50594e18 0.00564004
\(254\) −4.15471e20 −1.50471
\(255\) 4.91353e19 0.172108
\(256\) −1.33611e20 −0.452690
\(257\) 2.56438e20 0.840524 0.420262 0.907403i \(-0.361938\pi\)
0.420262 + 0.907403i \(0.361938\pi\)
\(258\) −1.59373e20 −0.505415
\(259\) 4.42920e19 0.135918
\(260\) −2.07191e19 −0.0615316
\(261\) 1.01570e20 0.291959
\(262\) −2.61260e20 −0.726962
\(263\) 2.38051e20 0.641277 0.320639 0.947202i \(-0.396103\pi\)
0.320639 + 0.947202i \(0.396103\pi\)
\(264\) −8.59766e18 −0.0224257
\(265\) 3.94828e19 0.0997283
\(266\) 2.51423e20 0.615052
\(267\) 1.12774e21 2.67216
\(268\) 2.33550e19 0.0536085
\(269\) 4.64530e20 1.03305 0.516523 0.856273i \(-0.327226\pi\)
0.516523 + 0.856273i \(0.327226\pi\)
\(270\) −1.42777e20 −0.307656
\(271\) 6.34118e20 1.32413 0.662066 0.749446i \(-0.269680\pi\)
0.662066 + 0.749446i \(0.269680\pi\)
\(272\) −1.19428e20 −0.241697
\(273\) 5.73887e20 1.12576
\(274\) 2.60476e20 0.495323
\(275\) −6.19407e18 −0.0114195
\(276\) 5.94737e19 0.106316
\(277\) 4.44454e19 0.0770458 0.0385229 0.999258i \(-0.487735\pi\)
0.0385229 + 0.999258i \(0.487735\pi\)
\(278\) −8.00205e20 −1.34530
\(279\) −9.41315e20 −1.53497
\(280\) −1.57569e20 −0.249246
\(281\) −8.82170e20 −1.35378 −0.676891 0.736083i \(-0.736673\pi\)
−0.676891 + 0.736083i \(0.736673\pi\)
\(282\) −1.24548e21 −1.85447
\(283\) 1.15837e21 1.67364 0.836822 0.547475i \(-0.184411\pi\)
0.836822 + 0.547475i \(0.184411\pi\)
\(284\) 4.19556e18 0.00588280
\(285\) −4.46494e20 −0.607623
\(286\) 9.99276e18 0.0132000
\(287\) −1.91825e20 −0.245985
\(288\) −3.87265e20 −0.482138
\(289\) −7.55587e20 −0.913383
\(290\) 5.30284e19 0.0622481
\(291\) −2.86273e19 −0.0326354
\(292\) −5.58996e18 −0.00618948
\(293\) −1.59557e21 −1.71609 −0.858047 0.513571i \(-0.828322\pi\)
−0.858047 + 0.513571i \(0.828322\pi\)
\(294\) −8.26164e20 −0.863205
\(295\) −2.21875e19 −0.0225227
\(296\) 2.27219e20 0.224112
\(297\) −1.26117e19 −0.0120877
\(298\) −9.45331e20 −0.880533
\(299\) −5.15672e20 −0.466840
\(300\) −2.44622e20 −0.215260
\(301\) −2.58002e20 −0.220703
\(302\) −9.85831e20 −0.819867
\(303\) −1.95535e21 −1.58111
\(304\) 1.08525e21 0.853304
\(305\) −6.82136e20 −0.521582
\(306\) −5.72051e20 −0.425405
\(307\) 1.77466e21 1.28362 0.641812 0.766862i \(-0.278183\pi\)
0.641812 + 0.766862i \(0.278183\pi\)
\(308\) −1.86572e18 −0.00131270
\(309\) 6.38502e19 0.0437034
\(310\) −4.91448e20 −0.327268
\(311\) 1.63898e21 1.06197 0.530984 0.847382i \(-0.321823\pi\)
0.530984 + 0.847382i \(0.321823\pi\)
\(312\) 2.94406e21 1.85623
\(313\) −7.94089e19 −0.0487240 −0.0243620 0.999703i \(-0.507755\pi\)
−0.0243620 + 0.999703i \(0.507755\pi\)
\(314\) −6.35366e20 −0.379422
\(315\) −6.35043e20 −0.369116
\(316\) 3.34653e20 0.189345
\(317\) −2.25505e21 −1.24209 −0.621044 0.783776i \(-0.713291\pi\)
−0.621044 + 0.783776i \(0.713291\pi\)
\(318\) −7.52041e20 −0.403284
\(319\) 4.68410e18 0.00244571
\(320\) −7.91151e20 −0.402239
\(321\) 6.36866e21 3.15323
\(322\) −5.25692e20 −0.253487
\(323\) −6.51113e20 −0.305798
\(324\) 3.39333e19 0.0155236
\(325\) 2.12101e21 0.945222
\(326\) 2.33836e21 1.01522
\(327\) 5.24339e21 2.21797
\(328\) −9.84068e20 −0.405600
\(329\) −2.01626e21 −0.809806
\(330\) −1.80906e19 −0.00708085
\(331\) 5.11331e21 1.95058 0.975290 0.220927i \(-0.0709084\pi\)
0.975290 + 0.220927i \(0.0709084\pi\)
\(332\) −2.25805e20 −0.0839575
\(333\) 9.15749e20 0.331895
\(334\) −1.60010e21 −0.565329
\(335\) 3.66602e20 0.126274
\(336\) 2.52527e21 0.848056
\(337\) −1.78584e21 −0.584773 −0.292387 0.956300i \(-0.594449\pi\)
−0.292387 + 0.956300i \(0.594449\pi\)
\(338\) −5.42578e20 −0.173249
\(339\) 3.48704e21 1.08582
\(340\) 5.46991e19 0.0166115
\(341\) −4.34105e19 −0.0128583
\(342\) 5.19825e21 1.50188
\(343\) −3.62197e21 −1.02081
\(344\) −1.32356e21 −0.363913
\(345\) 9.33558e20 0.250426
\(346\) −4.84294e21 −1.26754
\(347\) −4.18884e21 −1.06978 −0.534889 0.844922i \(-0.679647\pi\)
−0.534889 + 0.844922i \(0.679647\pi\)
\(348\) 1.84988e20 0.0461021
\(349\) 2.00753e21 0.488254 0.244127 0.969743i \(-0.421499\pi\)
0.244127 + 0.969743i \(0.421499\pi\)
\(350\) 2.16222e21 0.513242
\(351\) 4.31858e21 1.00053
\(352\) −1.78594e19 −0.00403882
\(353\) −2.68437e21 −0.592595 −0.296298 0.955096i \(-0.595752\pi\)
−0.296298 + 0.955096i \(0.595752\pi\)
\(354\) 4.22611e20 0.0910780
\(355\) 6.58576e19 0.0138569
\(356\) 1.25544e21 0.257911
\(357\) −1.51508e21 −0.303917
\(358\) −3.60335e21 −0.705831
\(359\) −9.74174e21 −1.86352 −0.931759 0.363077i \(-0.881726\pi\)
−0.931759 + 0.363077i \(0.881726\pi\)
\(360\) −3.25779e21 −0.608628
\(361\) 4.36301e20 0.0796113
\(362\) −3.82628e21 −0.681952
\(363\) 9.21059e21 1.60354
\(364\) 6.38871e20 0.108655
\(365\) −8.77454e19 −0.0145792
\(366\) 1.29928e22 2.10919
\(367\) 3.91305e21 0.620660 0.310330 0.950629i \(-0.399560\pi\)
0.310330 + 0.950629i \(0.399560\pi\)
\(368\) −2.26911e21 −0.351681
\(369\) −3.96604e21 −0.600665
\(370\) 4.78100e20 0.0707627
\(371\) −1.21745e21 −0.176105
\(372\) −1.71440e21 −0.242381
\(373\) 2.02358e20 0.0279638 0.0139819 0.999902i \(-0.495549\pi\)
0.0139819 + 0.999902i \(0.495549\pi\)
\(374\) −2.63812e19 −0.00356357
\(375\) −8.26842e21 −1.09183
\(376\) −1.03435e22 −1.33527
\(377\) −1.60396e21 −0.202437
\(378\) 4.40250e21 0.543274
\(379\) 1.06563e21 0.128579 0.0642897 0.997931i \(-0.479522\pi\)
0.0642897 + 0.997931i \(0.479522\pi\)
\(380\) −4.97052e20 −0.0586464
\(381\) −2.27506e22 −2.62501
\(382\) 2.30132e21 0.259680
\(383\) 8.39158e21 0.926092 0.463046 0.886334i \(-0.346756\pi\)
0.463046 + 0.886334i \(0.346756\pi\)
\(384\) 1.05129e22 1.13476
\(385\) −2.92861e19 −0.00309205
\(386\) −5.69460e21 −0.588127
\(387\) −5.33427e21 −0.538930
\(388\) −3.18688e19 −0.00314990
\(389\) 1.40638e22 1.35997 0.679985 0.733226i \(-0.261986\pi\)
0.679985 + 0.733226i \(0.261986\pi\)
\(390\) 6.19470e21 0.586099
\(391\) 1.36139e21 0.126032
\(392\) −6.86111e21 −0.621531
\(393\) −1.43062e22 −1.26820
\(394\) 6.27020e21 0.543956
\(395\) 5.25304e21 0.446001
\(396\) −3.85743e19 −0.00320545
\(397\) −7.22062e21 −0.587293 −0.293647 0.955914i \(-0.594869\pi\)
−0.293647 + 0.955914i \(0.594869\pi\)
\(398\) 7.31846e21 0.582658
\(399\) 1.37676e22 1.07297
\(400\) 9.33307e21 0.712056
\(401\) −5.40980e21 −0.404067 −0.202034 0.979379i \(-0.564755\pi\)
−0.202034 + 0.979379i \(0.564755\pi\)
\(402\) −6.98278e21 −0.510631
\(403\) 1.48649e22 1.06431
\(404\) −2.17677e21 −0.152605
\(405\) 5.32650e20 0.0365658
\(406\) −1.63512e21 −0.109921
\(407\) 4.22315e19 0.00278025
\(408\) −7.77240e21 −0.501122
\(409\) −2.89928e21 −0.183080 −0.0915402 0.995801i \(-0.529179\pi\)
−0.0915402 + 0.995801i \(0.529179\pi\)
\(410\) −2.07061e21 −0.128067
\(411\) 1.42633e22 0.864101
\(412\) 7.10802e19 0.00421816
\(413\) 6.84147e20 0.0397717
\(414\) −1.08688e22 −0.618984
\(415\) −3.54445e21 −0.197761
\(416\) 6.11552e21 0.334303
\(417\) −4.38180e22 −2.34691
\(418\) 2.39727e20 0.0125811
\(419\) −1.52164e21 −0.0782513 −0.0391257 0.999234i \(-0.512457\pi\)
−0.0391257 + 0.999234i \(0.512457\pi\)
\(420\) −1.15659e21 −0.0582857
\(421\) −1.72305e22 −0.850944 −0.425472 0.904971i \(-0.639892\pi\)
−0.425472 + 0.904971i \(0.639892\pi\)
\(422\) −2.78575e22 −1.34830
\(423\) −4.16867e22 −1.97745
\(424\) −6.24554e21 −0.290376
\(425\) −5.59952e21 −0.255179
\(426\) −1.25441e21 −0.0560348
\(427\) 2.10335e22 0.921034
\(428\) 7.08980e21 0.304342
\(429\) 5.47189e20 0.0230277
\(430\) −2.78495e21 −0.114904
\(431\) 1.14752e22 0.464198 0.232099 0.972692i \(-0.425441\pi\)
0.232099 + 0.972692i \(0.425441\pi\)
\(432\) 1.90030e22 0.753722
\(433\) 2.22821e22 0.866579 0.433289 0.901255i \(-0.357353\pi\)
0.433289 + 0.901255i \(0.357353\pi\)
\(434\) 1.51537e22 0.577905
\(435\) 2.90376e21 0.108593
\(436\) 5.83712e21 0.214074
\(437\) −1.23710e22 −0.444951
\(438\) 1.67131e21 0.0589559
\(439\) 8.42409e21 0.291457 0.145729 0.989325i \(-0.453447\pi\)
0.145729 + 0.989325i \(0.453447\pi\)
\(440\) −1.50239e20 −0.00509841
\(441\) −2.76520e22 −0.920445
\(442\) 9.03360e21 0.294966
\(443\) 2.61533e22 0.837712 0.418856 0.908053i \(-0.362431\pi\)
0.418856 + 0.908053i \(0.362431\pi\)
\(444\) 1.66784e21 0.0524082
\(445\) 1.97066e22 0.607507
\(446\) 4.53251e22 1.37086
\(447\) −5.17649e22 −1.53611
\(448\) 2.43950e22 0.710293
\(449\) −2.97454e22 −0.849819 −0.424909 0.905236i \(-0.639694\pi\)
−0.424909 + 0.905236i \(0.639694\pi\)
\(450\) 4.47046e22 1.25327
\(451\) −1.82901e20 −0.00503171
\(452\) 3.88189e21 0.104801
\(453\) −5.39826e22 −1.43027
\(454\) 4.40028e22 1.14421
\(455\) 1.00283e22 0.255936
\(456\) 7.06281e22 1.76920
\(457\) 6.40802e22 1.57557 0.787783 0.615953i \(-0.211229\pi\)
0.787783 + 0.615953i \(0.211229\pi\)
\(458\) −3.24407e22 −0.782950
\(459\) −1.14012e22 −0.270111
\(460\) 1.03927e21 0.0241705
\(461\) −5.46473e21 −0.124770 −0.0623851 0.998052i \(-0.519871\pi\)
−0.0623851 + 0.998052i \(0.519871\pi\)
\(462\) 5.57822e20 0.0125037
\(463\) 5.22777e22 1.15048 0.575239 0.817986i \(-0.304909\pi\)
0.575239 + 0.817986i \(0.304909\pi\)
\(464\) −7.05788e21 −0.152501
\(465\) −2.69110e22 −0.570925
\(466\) 4.94536e22 1.03019
\(467\) 9.48870e21 0.194095 0.0970473 0.995280i \(-0.469060\pi\)
0.0970473 + 0.995280i \(0.469060\pi\)
\(468\) 1.32088e22 0.265323
\(469\) −1.13041e22 −0.222981
\(470\) −2.17641e22 −0.421607
\(471\) −3.47917e22 −0.661909
\(472\) 3.50970e21 0.0655787
\(473\) −2.46000e20 −0.00451456
\(474\) −1.00056e23 −1.80355
\(475\) 5.08831e22 0.900902
\(476\) −1.68664e21 −0.0293334
\(477\) −2.51711e22 −0.430027
\(478\) −6.29458e21 −0.105640
\(479\) 2.56708e22 0.423240 0.211620 0.977352i \(-0.432126\pi\)
0.211620 + 0.977352i \(0.432126\pi\)
\(480\) −1.10714e22 −0.179329
\(481\) −1.44611e22 −0.230128
\(482\) 1.34554e22 0.210377
\(483\) −2.87861e22 −0.442214
\(484\) 1.02535e22 0.154771
\(485\) −5.00244e20 −0.00741954
\(486\) −6.80390e22 −0.991630
\(487\) −1.28868e23 −1.84565 −0.922825 0.385219i \(-0.874126\pi\)
−0.922825 + 0.385219i \(0.874126\pi\)
\(488\) 1.07903e23 1.51867
\(489\) 1.28045e23 1.77108
\(490\) −1.44367e22 −0.196246
\(491\) 1.27346e23 1.70134 0.850670 0.525700i \(-0.176196\pi\)
0.850670 + 0.525700i \(0.176196\pi\)
\(492\) −7.22329e21 −0.0948487
\(493\) 4.23449e21 0.0546515
\(494\) −8.20887e22 −1.04137
\(495\) −6.05499e20 −0.00755039
\(496\) 6.54098e22 0.801768
\(497\) −2.03071e21 −0.0244691
\(498\) 6.75122e22 0.799711
\(499\) −6.05712e22 −0.705362 −0.352681 0.935744i \(-0.614730\pi\)
−0.352681 + 0.935744i \(0.614730\pi\)
\(500\) −9.20468e21 −0.105381
\(501\) −8.76189e22 −0.986228
\(502\) −9.46126e22 −1.04705
\(503\) −8.97254e21 −0.0976309 −0.0488155 0.998808i \(-0.515545\pi\)
−0.0488155 + 0.998808i \(0.515545\pi\)
\(504\) 1.00453e23 1.07474
\(505\) −3.41686e22 −0.359460
\(506\) −5.01236e20 −0.00518516
\(507\) −2.97108e22 −0.302236
\(508\) −2.53267e22 −0.253360
\(509\) 1.76507e22 0.173644 0.0868220 0.996224i \(-0.472329\pi\)
0.0868220 + 0.996224i \(0.472329\pi\)
\(510\) −1.63542e22 −0.158228
\(511\) 2.70561e21 0.0257447
\(512\) 1.20075e23 1.12372
\(513\) 1.03603e23 0.953618
\(514\) −8.53526e22 −0.772735
\(515\) 1.11574e21 0.00993581
\(516\) −9.71524e21 −0.0851003
\(517\) −1.92246e21 −0.0165648
\(518\) −1.47421e22 −0.124956
\(519\) −2.65192e23 −2.21125
\(520\) 5.14457e22 0.422008
\(521\) 7.01454e22 0.566081 0.283041 0.959108i \(-0.408657\pi\)
0.283041 + 0.959108i \(0.408657\pi\)
\(522\) −3.38066e22 −0.268412
\(523\) 3.66650e22 0.286410 0.143205 0.989693i \(-0.454259\pi\)
0.143205 + 0.989693i \(0.454259\pi\)
\(524\) −1.59261e22 −0.122404
\(525\) 1.18400e23 0.895361
\(526\) −7.92328e22 −0.589557
\(527\) −3.92437e22 −0.287329
\(528\) 2.40779e21 0.0173473
\(529\) −1.15184e23 −0.816618
\(530\) −1.31415e22 −0.0916851
\(531\) 1.41449e22 0.0971175
\(532\) 1.53265e22 0.103561
\(533\) 6.26300e22 0.416487
\(534\) −3.75357e23 −2.45665
\(535\) 1.11288e23 0.716874
\(536\) −5.79905e22 −0.367668
\(537\) −1.97314e23 −1.23134
\(538\) −1.54614e23 −0.949729
\(539\) −1.27522e21 −0.00771047
\(540\) −8.70354e21 −0.0518023
\(541\) 3.22978e23 1.89233 0.946165 0.323686i \(-0.104922\pi\)
0.946165 + 0.323686i \(0.104922\pi\)
\(542\) −2.11060e23 −1.21734
\(543\) −2.09521e23 −1.18968
\(544\) −1.61452e22 −0.0902509
\(545\) 9.16251e22 0.504248
\(546\) −1.91013e23 −1.03496
\(547\) 1.61822e23 0.863267 0.431633 0.902049i \(-0.357937\pi\)
0.431633 + 0.902049i \(0.357937\pi\)
\(548\) 1.58784e22 0.0834011
\(549\) 4.34874e23 2.24905
\(550\) 2.06163e21 0.0104985
\(551\) −3.84790e22 −0.192946
\(552\) −1.47674e23 −0.729157
\(553\) −1.61977e23 −0.787569
\(554\) −1.47932e22 −0.0708319
\(555\) 2.61801e22 0.123447
\(556\) −4.87797e22 −0.226518
\(557\) −1.97039e23 −0.901121 −0.450561 0.892746i \(-0.648776\pi\)
−0.450561 + 0.892746i \(0.648776\pi\)
\(558\) 3.13307e23 1.41117
\(559\) 8.42367e22 0.373681
\(560\) 4.41276e22 0.192802
\(561\) −1.44459e21 −0.00621672
\(562\) 2.93621e23 1.24460
\(563\) −4.24181e23 −1.77104 −0.885522 0.464597i \(-0.846199\pi\)
−0.885522 + 0.464597i \(0.846199\pi\)
\(564\) −7.59234e22 −0.312251
\(565\) 6.09340e22 0.246858
\(566\) −3.85552e23 −1.53866
\(567\) −1.64242e22 −0.0645696
\(568\) −1.04176e22 −0.0403466
\(569\) 3.39173e23 1.29410 0.647049 0.762449i \(-0.276003\pi\)
0.647049 + 0.762449i \(0.276003\pi\)
\(570\) 1.48611e23 0.558618
\(571\) 6.84513e22 0.253498 0.126749 0.991935i \(-0.459546\pi\)
0.126749 + 0.991935i \(0.459546\pi\)
\(572\) 6.09149e20 0.00222258
\(573\) 1.26017e23 0.453017
\(574\) 6.38470e22 0.226146
\(575\) −1.06390e23 −0.371298
\(576\) 5.04373e23 1.73445
\(577\) −1.80057e23 −0.610121 −0.305061 0.952333i \(-0.598677\pi\)
−0.305061 + 0.952333i \(0.598677\pi\)
\(578\) 2.51490e23 0.839718
\(579\) −3.11828e23 −1.02600
\(580\) 3.23256e21 0.0104812
\(581\) 1.09293e23 0.349216
\(582\) 9.52829e21 0.0300033
\(583\) −1.16081e21 −0.00360229
\(584\) 1.38799e22 0.0424499
\(585\) 2.07339e23 0.624965
\(586\) 5.31069e23 1.57769
\(587\) 8.40746e22 0.246173 0.123087 0.992396i \(-0.460721\pi\)
0.123087 + 0.992396i \(0.460721\pi\)
\(588\) −5.03621e22 −0.145344
\(589\) 3.56609e23 1.01441
\(590\) 7.38488e21 0.0207062
\(591\) 3.43347e23 0.948942
\(592\) −6.36333e22 −0.173360
\(593\) −3.81961e23 −1.02578 −0.512890 0.858455i \(-0.671425\pi\)
−0.512890 + 0.858455i \(0.671425\pi\)
\(594\) 4.19769e21 0.0111128
\(595\) −2.64751e22 −0.0690944
\(596\) −5.76265e22 −0.148262
\(597\) 4.00748e23 1.01646
\(598\) 1.71636e23 0.429189
\(599\) −3.18627e23 −0.785514 −0.392757 0.919642i \(-0.628479\pi\)
−0.392757 + 0.919642i \(0.628479\pi\)
\(600\) 6.07397e23 1.47634
\(601\) 5.82853e23 1.39677 0.698387 0.715720i \(-0.253901\pi\)
0.698387 + 0.715720i \(0.253901\pi\)
\(602\) 8.58735e22 0.202903
\(603\) −2.33716e23 −0.544492
\(604\) −6.00953e22 −0.138047
\(605\) 1.60950e23 0.364560
\(606\) 6.50820e23 1.45359
\(607\) 6.70463e23 1.47663 0.738313 0.674458i \(-0.235623\pi\)
0.738313 + 0.674458i \(0.235623\pi\)
\(608\) 1.46712e23 0.318628
\(609\) −8.95369e22 −0.191759
\(610\) 2.27042e23 0.479515
\(611\) 6.58300e23 1.37111
\(612\) −3.48717e22 −0.0716285
\(613\) −9.15701e23 −1.85498 −0.927491 0.373845i \(-0.878039\pi\)
−0.927491 + 0.373845i \(0.878039\pi\)
\(614\) −5.90676e23 −1.18010
\(615\) −1.13384e23 −0.223415
\(616\) 4.63259e21 0.00900301
\(617\) −9.04813e23 −1.73434 −0.867171 0.498010i \(-0.834064\pi\)
−0.867171 + 0.498010i \(0.834064\pi\)
\(618\) −2.12519e22 −0.0401787
\(619\) −6.78753e23 −1.26573 −0.632865 0.774262i \(-0.718121\pi\)
−0.632865 + 0.774262i \(0.718121\pi\)
\(620\) −2.99582e22 −0.0551044
\(621\) −2.16620e23 −0.393024
\(622\) −5.45519e23 −0.976319
\(623\) −6.07649e23 −1.07276
\(624\) −8.24491e23 −1.43588
\(625\) 3.60204e23 0.618825
\(626\) 2.64305e22 0.0447943
\(627\) 1.31271e22 0.0219480
\(628\) −3.87313e22 −0.0638860
\(629\) 3.81778e22 0.0621270
\(630\) 2.11368e23 0.339347
\(631\) 9.88826e23 1.56628 0.783141 0.621844i \(-0.213616\pi\)
0.783141 + 0.621844i \(0.213616\pi\)
\(632\) −8.30945e23 −1.29861
\(633\) −1.52544e24 −2.35214
\(634\) 7.50571e23 1.14191
\(635\) −3.97553e23 −0.596785
\(636\) −4.58437e22 −0.0679038
\(637\) 4.36669e23 0.638215
\(638\) −1.55905e21 −0.00224846
\(639\) −4.19855e22 −0.0597506
\(640\) 1.83706e23 0.257985
\(641\) 7.46475e23 1.03448 0.517240 0.855840i \(-0.326959\pi\)
0.517240 + 0.855840i \(0.326959\pi\)
\(642\) −2.11974e24 −2.89892
\(643\) −1.60985e23 −0.217266 −0.108633 0.994082i \(-0.534647\pi\)
−0.108633 + 0.994082i \(0.534647\pi\)
\(644\) −3.20457e22 −0.0426815
\(645\) −1.52500e23 −0.200453
\(646\) 2.16716e23 0.281135
\(647\) 1.47953e23 0.189425 0.0947124 0.995505i \(-0.469807\pi\)
0.0947124 + 0.995505i \(0.469807\pi\)
\(648\) −8.42566e22 −0.106467
\(649\) 6.52320e20 0.000813543 0
\(650\) −7.05957e23 −0.868989
\(651\) 8.29795e23 1.00817
\(652\) 1.42544e23 0.170940
\(653\) −8.40989e23 −0.995470 −0.497735 0.867329i \(-0.665835\pi\)
−0.497735 + 0.867329i \(0.665835\pi\)
\(654\) −1.74521e24 −2.03909
\(655\) −2.49992e23 −0.288320
\(656\) 2.75591e23 0.313749
\(657\) 5.59393e22 0.0628654
\(658\) 6.71091e23 0.744494
\(659\) 1.54714e24 1.69435 0.847175 0.531314i \(-0.178302\pi\)
0.847175 + 0.531314i \(0.178302\pi\)
\(660\) −1.10279e21 −0.00119225
\(661\) −2.20956e23 −0.235827 −0.117914 0.993024i \(-0.537621\pi\)
−0.117914 + 0.993024i \(0.537621\pi\)
\(662\) −1.70191e24 −1.79326
\(663\) 4.94667e23 0.514574
\(664\) 5.60675e23 0.575814
\(665\) 2.40580e23 0.243936
\(666\) −3.04798e23 −0.305127
\(667\) 8.04542e22 0.0795205
\(668\) −9.75404e22 −0.0951885
\(669\) 2.48193e24 2.39149
\(670\) −1.22020e23 −0.116090
\(671\) 2.00550e22 0.0188400
\(672\) 3.41384e23 0.316668
\(673\) 1.15979e24 1.06231 0.531157 0.847273i \(-0.321757\pi\)
0.531157 + 0.847273i \(0.321757\pi\)
\(674\) 5.94398e23 0.537611
\(675\) 8.90978e23 0.795765
\(676\) −3.30750e22 −0.0291711
\(677\) −1.91800e24 −1.67050 −0.835248 0.549873i \(-0.814676\pi\)
−0.835248 + 0.549873i \(0.814676\pi\)
\(678\) −1.16063e24 −0.998252
\(679\) 1.54249e22 0.0131018
\(680\) −1.35818e23 −0.113928
\(681\) 2.40953e24 1.99610
\(682\) 1.44487e22 0.0118212
\(683\) −2.26629e24 −1.83121 −0.915607 0.402075i \(-0.868289\pi\)
−0.915607 + 0.402075i \(0.868289\pi\)
\(684\) 3.16880e23 0.252882
\(685\) 2.49243e23 0.196450
\(686\) 1.20554e24 0.938482
\(687\) −1.77641e24 −1.36587
\(688\) 3.70666e23 0.281502
\(689\) 3.97491e23 0.298170
\(690\) −3.10725e23 −0.230229
\(691\) −6.33975e23 −0.463990 −0.231995 0.972717i \(-0.574525\pi\)
−0.231995 + 0.972717i \(0.574525\pi\)
\(692\) −2.95221e23 −0.213425
\(693\) 1.86705e22 0.0133328
\(694\) 1.39421e24 0.983499
\(695\) −7.65694e23 −0.533561
\(696\) −4.59327e23 −0.316187
\(697\) −1.65345e23 −0.112438
\(698\) −6.68185e23 −0.448876
\(699\) 2.70801e24 1.79719
\(700\) 1.31807e23 0.0864182
\(701\) 1.23966e24 0.802971 0.401485 0.915865i \(-0.368494\pi\)
0.401485 + 0.915865i \(0.368494\pi\)
\(702\) −1.43740e24 −0.919838
\(703\) −3.46923e23 −0.219338
\(704\) 2.32601e22 0.0145293
\(705\) −1.19177e24 −0.735502
\(706\) 8.93467e23 0.544802
\(707\) 1.05358e24 0.634752
\(708\) 2.57620e22 0.0153354
\(709\) 1.92953e24 1.13490 0.567450 0.823408i \(-0.307930\pi\)
0.567450 + 0.823408i \(0.307930\pi\)
\(710\) −2.19201e22 −0.0127393
\(711\) −3.34891e24 −1.92315
\(712\) −3.11726e24 −1.76886
\(713\) −7.45620e23 −0.418077
\(714\) 5.04278e23 0.279406
\(715\) 9.56180e21 0.00523526
\(716\) −2.19657e23 −0.118846
\(717\) −3.44682e23 −0.184292
\(718\) 3.24244e24 1.71322
\(719\) 1.24227e24 0.648664 0.324332 0.945943i \(-0.394861\pi\)
0.324332 + 0.945943i \(0.394861\pi\)
\(720\) 9.12351e23 0.470799
\(721\) −3.44038e22 −0.0175451
\(722\) −1.45218e23 −0.0731905
\(723\) 7.36799e23 0.367006
\(724\) −2.33246e23 −0.114825
\(725\) −3.30916e23 −0.161007
\(726\) −3.06565e24 −1.47422
\(727\) 2.83536e24 1.34761 0.673807 0.738907i \(-0.264658\pi\)
0.673807 + 0.738907i \(0.264658\pi\)
\(728\) −1.58632e24 −0.745202
\(729\) −3.50974e24 −1.62964
\(730\) 2.92052e22 0.0134034
\(731\) −2.22387e23 −0.100882
\(732\) 7.92031e23 0.355139
\(733\) 3.76886e24 1.67042 0.835210 0.549931i \(-0.185346\pi\)
0.835210 + 0.549931i \(0.185346\pi\)
\(734\) −1.30242e24 −0.570603
\(735\) −7.90533e23 −0.342356
\(736\) −3.06754e23 −0.131319
\(737\) −1.07782e22 −0.00456115
\(738\) 1.32006e24 0.552221
\(739\) −1.80876e24 −0.748001 −0.374000 0.927429i \(-0.622014\pi\)
−0.374000 + 0.927429i \(0.622014\pi\)
\(740\) 2.91445e22 0.0119148
\(741\) −4.49505e24 −1.81669
\(742\) 4.05215e23 0.161902
\(743\) 2.01400e24 0.795526 0.397763 0.917488i \(-0.369787\pi\)
0.397763 + 0.917488i \(0.369787\pi\)
\(744\) 4.25687e24 1.66234
\(745\) −9.04561e23 −0.349229
\(746\) −6.73529e22 −0.0257085
\(747\) 2.25966e24 0.852741
\(748\) −1.60817e21 −0.000600024 0
\(749\) −3.43156e24 −1.26589
\(750\) 2.75206e24 1.00378
\(751\) 4.23140e24 1.52596 0.762982 0.646420i \(-0.223734\pi\)
0.762982 + 0.646420i \(0.223734\pi\)
\(752\) 2.89671e24 1.03289
\(753\) −5.18085e24 −1.82660
\(754\) 5.33861e23 0.186111
\(755\) −9.43314e23 −0.325168
\(756\) 2.68372e23 0.0914749
\(757\) 2.90411e24 0.978809 0.489404 0.872057i \(-0.337214\pi\)
0.489404 + 0.872057i \(0.337214\pi\)
\(758\) −3.54683e23 −0.118209
\(759\) −2.74469e22 −0.00904562
\(760\) 1.23418e24 0.402221
\(761\) 2.36377e23 0.0761792 0.0380896 0.999274i \(-0.487873\pi\)
0.0380896 + 0.999274i \(0.487873\pi\)
\(762\) 7.57230e24 2.41330
\(763\) −2.82524e24 −0.890425
\(764\) 1.40286e23 0.0437241
\(765\) −5.47380e23 −0.168720
\(766\) −2.79305e24 −0.851402
\(767\) −2.23371e23 −0.0673390
\(768\) 2.43516e24 0.726035
\(769\) 6.49820e24 1.91610 0.958052 0.286594i \(-0.0925230\pi\)
0.958052 + 0.286594i \(0.0925230\pi\)
\(770\) 9.74760e21 0.00284267
\(771\) −4.67378e24 −1.34805
\(772\) −3.47137e23 −0.0990271
\(773\) 4.42844e24 1.24947 0.624734 0.780837i \(-0.285207\pi\)
0.624734 + 0.780837i \(0.285207\pi\)
\(774\) 1.77546e24 0.495464
\(775\) 3.06681e24 0.846491
\(776\) 7.91305e22 0.0216032
\(777\) −8.07258e23 −0.217989
\(778\) −4.68098e24 −1.25029
\(779\) 1.50250e24 0.396959
\(780\) 3.77623e23 0.0986857
\(781\) −1.93624e21 −0.000500524 0
\(782\) −4.53124e23 −0.115867
\(783\) −6.73778e23 −0.170428
\(784\) 1.92147e24 0.480781
\(785\) −6.07965e23 −0.150483
\(786\) 4.76167e24 1.16592
\(787\) 5.90703e24 1.43082 0.715408 0.698707i \(-0.246241\pi\)
0.715408 + 0.698707i \(0.246241\pi\)
\(788\) 3.82225e23 0.0915897
\(789\) −4.33867e24 −1.02849
\(790\) −1.74842e24 −0.410030
\(791\) −1.87889e24 −0.435914
\(792\) 9.57801e22 0.0219842
\(793\) −6.86736e24 −1.55944
\(794\) 2.40331e24 0.539927
\(795\) −7.19607e23 −0.159947
\(796\) 4.46127e23 0.0981063
\(797\) −3.76240e24 −0.818595 −0.409297 0.912401i \(-0.634226\pi\)
−0.409297 + 0.912401i \(0.634226\pi\)
\(798\) −4.58240e24 −0.986434
\(799\) −1.73793e24 −0.370156
\(800\) 1.26171e24 0.265885
\(801\) −1.25633e25 −2.61956
\(802\) 1.80060e24 0.371479
\(803\) 2.57974e21 0.000526617 0
\(804\) −4.25664e23 −0.0859786
\(805\) −5.03020e23 −0.100536
\(806\) −4.94762e24 −0.978472
\(807\) −8.46644e24 −1.65682
\(808\) 5.40492e24 1.04663
\(809\) −2.21471e24 −0.424379 −0.212190 0.977229i \(-0.568059\pi\)
−0.212190 + 0.977229i \(0.568059\pi\)
\(810\) −1.77287e23 −0.0336167
\(811\) −2.92354e24 −0.548569 −0.274284 0.961649i \(-0.588441\pi\)
−0.274284 + 0.961649i \(0.588441\pi\)
\(812\) −9.96755e22 −0.0185081
\(813\) −1.15573e25 −2.12367
\(814\) −1.40563e22 −0.00255602
\(815\) 2.23751e24 0.402648
\(816\) 2.17668e24 0.387639
\(817\) 2.02084e24 0.356160
\(818\) 9.64996e23 0.168315
\(819\) −6.39325e24 −1.10359
\(820\) −1.26223e23 −0.0215635
\(821\) −6.60841e24 −1.11733 −0.558663 0.829395i \(-0.688686\pi\)
−0.558663 + 0.829395i \(0.688686\pi\)
\(822\) −4.74740e24 −0.794411
\(823\) −9.19312e23 −0.152252 −0.0761262 0.997098i \(-0.524255\pi\)
−0.0761262 + 0.997098i \(0.524255\pi\)
\(824\) −1.76493e23 −0.0289298
\(825\) 1.12892e23 0.0183149
\(826\) −2.27711e23 −0.0365641
\(827\) 7.10161e24 1.12865 0.564326 0.825552i \(-0.309136\pi\)
0.564326 + 0.825552i \(0.309136\pi\)
\(828\) −6.62553e23 −0.104223
\(829\) 5.68184e23 0.0884659 0.0442329 0.999021i \(-0.485916\pi\)
0.0442329 + 0.999021i \(0.485916\pi\)
\(830\) 1.17974e24 0.181811
\(831\) −8.10054e23 −0.123568
\(832\) −7.96486e24 −1.20262
\(833\) −1.15282e24 −0.172297
\(834\) 1.45844e25 2.15763
\(835\) −1.53109e24 −0.224215
\(836\) 1.46135e22 0.00211837
\(837\) 6.24433e24 0.896023
\(838\) 5.06461e23 0.0719403
\(839\) 1.11695e25 1.57057 0.785286 0.619133i \(-0.212516\pi\)
0.785286 + 0.619133i \(0.212516\pi\)
\(840\) 2.87183e24 0.399746
\(841\) 2.50246e23 0.0344828
\(842\) 5.73501e24 0.782315
\(843\) 1.60783e25 2.17123
\(844\) −1.69817e24 −0.227023
\(845\) −5.19178e23 −0.0687122
\(846\) 1.38750e25 1.81796
\(847\) −4.96285e24 −0.643757
\(848\) 1.74908e24 0.224618
\(849\) −2.11123e25 −2.68423
\(850\) 1.86374e24 0.234599
\(851\) 7.25369e23 0.0903978
\(852\) −7.64676e22 −0.00943498
\(853\) −8.02812e24 −0.980725 −0.490362 0.871519i \(-0.663136\pi\)
−0.490362 + 0.871519i \(0.663136\pi\)
\(854\) −7.00080e24 −0.846751
\(855\) 4.97406e24 0.595661
\(856\) −1.76040e25 −2.08730
\(857\) 3.15264e24 0.370115 0.185058 0.982728i \(-0.440753\pi\)
0.185058 + 0.982728i \(0.440753\pi\)
\(858\) −1.82126e23 −0.0211705
\(859\) −2.60602e24 −0.299941 −0.149970 0.988691i \(-0.547918\pi\)
−0.149970 + 0.988691i \(0.547918\pi\)
\(860\) −1.69768e23 −0.0193472
\(861\) 3.49617e24 0.394517
\(862\) −3.81940e24 −0.426760
\(863\) 3.85035e24 0.425999 0.213000 0.977052i \(-0.431677\pi\)
0.213000 + 0.977052i \(0.431677\pi\)
\(864\) 2.56896e24 0.281444
\(865\) −4.63407e24 −0.502720
\(866\) −7.41636e24 −0.796688
\(867\) 1.37712e25 1.46490
\(868\) 9.23756e23 0.0973059
\(869\) −1.54441e23 −0.0161100
\(870\) −9.66487e23 −0.0998349
\(871\) 3.69075e24 0.377538
\(872\) −1.44936e25 −1.46820
\(873\) 3.18915e23 0.0319929
\(874\) 4.11756e24 0.409065
\(875\) 4.45519e24 0.438327
\(876\) 1.01882e23 0.00992683
\(877\) −1.23091e25 −1.18776 −0.593879 0.804554i \(-0.702404\pi\)
−0.593879 + 0.804554i \(0.702404\pi\)
\(878\) −2.80387e24 −0.267951
\(879\) 2.90806e25 2.75231
\(880\) 4.20747e22 0.00394383
\(881\) 6.75609e24 0.627191 0.313596 0.949557i \(-0.398466\pi\)
0.313596 + 0.949557i \(0.398466\pi\)
\(882\) 9.20368e24 0.846210
\(883\) −7.82807e24 −0.712834 −0.356417 0.934327i \(-0.616002\pi\)
−0.356417 + 0.934327i \(0.616002\pi\)
\(884\) 5.50679e23 0.0496655
\(885\) 4.04385e23 0.0361225
\(886\) −8.70486e24 −0.770150
\(887\) 1.67016e25 1.46355 0.731776 0.681545i \(-0.238692\pi\)
0.731776 + 0.681545i \(0.238692\pi\)
\(888\) −4.14126e24 −0.359437
\(889\) 1.22585e25 1.05383
\(890\) −6.55913e24 −0.558511
\(891\) −1.56601e22 −0.00132079
\(892\) 2.76297e24 0.230821
\(893\) 1.57926e25 1.30682
\(894\) 1.72294e25 1.41222
\(895\) −3.44795e24 −0.279940
\(896\) −5.66454e24 −0.455561
\(897\) 9.39854e24 0.748729
\(898\) 9.90046e24 0.781280
\(899\) −2.31919e24 −0.181292
\(900\) 2.72515e24 0.211023
\(901\) −1.04939e24 −0.0804962
\(902\) 6.08767e22 0.00462590
\(903\) 4.70231e24 0.353969
\(904\) −9.63876e24 −0.718769
\(905\) −3.66126e24 −0.270469
\(906\) 1.79676e25 1.31492
\(907\) −1.60753e25 −1.16546 −0.582729 0.812667i \(-0.698015\pi\)
−0.582729 + 0.812667i \(0.698015\pi\)
\(908\) 2.68237e24 0.192659
\(909\) 2.17831e25 1.54999
\(910\) −3.33783e24 −0.235295
\(911\) 5.48262e24 0.382897 0.191449 0.981503i \(-0.438681\pi\)
0.191449 + 0.981503i \(0.438681\pi\)
\(912\) −1.97796e25 −1.36855
\(913\) 1.04208e23 0.00714332
\(914\) −2.13285e25 −1.44849
\(915\) 1.24325e25 0.836525
\(916\) −1.97756e24 −0.131831
\(917\) 7.70847e24 0.509130
\(918\) 3.79477e24 0.248326
\(919\) 3.41215e24 0.221231 0.110616 0.993863i \(-0.464718\pi\)
0.110616 + 0.993863i \(0.464718\pi\)
\(920\) −2.58051e24 −0.165771
\(921\) −3.23446e25 −2.05871
\(922\) 1.81888e24 0.114707
\(923\) 6.63018e23 0.0414296
\(924\) 3.40043e22 0.00210534
\(925\) −2.98352e24 −0.183031
\(926\) −1.74001e25 −1.05769
\(927\) −7.11308e23 −0.0428430
\(928\) −9.54134e23 −0.0569445
\(929\) 1.88183e25 1.11287 0.556437 0.830890i \(-0.312168\pi\)
0.556437 + 0.830890i \(0.312168\pi\)
\(930\) 8.95704e24 0.524879
\(931\) 1.04757e25 0.608290
\(932\) 3.01465e24 0.173461
\(933\) −2.98718e25 −1.70321
\(934\) −3.15822e24 −0.178441
\(935\) −2.52434e22 −0.00141335
\(936\) −3.27976e25 −1.81969
\(937\) 4.65832e24 0.256120 0.128060 0.991766i \(-0.459125\pi\)
0.128060 + 0.991766i \(0.459125\pi\)
\(938\) 3.76246e24 0.204997
\(939\) 1.44729e24 0.0781446
\(940\) −1.32672e24 −0.0709890
\(941\) 6.56604e24 0.348170 0.174085 0.984731i \(-0.444303\pi\)
0.174085 + 0.984731i \(0.444303\pi\)
\(942\) 1.15801e25 0.608525
\(943\) −3.14151e24 −0.163602
\(944\) −9.82899e23 −0.0507279
\(945\) 4.21263e24 0.215468
\(946\) 8.18785e22 0.00415045
\(947\) 2.19819e25 1.10431 0.552153 0.833742i \(-0.313806\pi\)
0.552153 + 0.833742i \(0.313806\pi\)
\(948\) −6.09933e24 −0.303676
\(949\) −8.83371e23 −0.0435894
\(950\) −1.69359e25 −0.828244
\(951\) 4.11001e25 1.99209
\(952\) 4.18793e24 0.201180
\(953\) 3.19472e25 1.52105 0.760525 0.649308i \(-0.224942\pi\)
0.760525 + 0.649308i \(0.224942\pi\)
\(954\) 8.37793e24 0.395344
\(955\) 2.20207e24 0.102992
\(956\) −3.83711e23 −0.0177874
\(957\) −8.53715e22 −0.00392249
\(958\) −8.54426e24 −0.389106
\(959\) −7.68536e24 −0.346901
\(960\) 1.44194e25 0.645120
\(961\) −1.05671e24 −0.0468607
\(962\) 4.81325e24 0.211568
\(963\) −7.09485e25 −3.09115
\(964\) 8.20230e23 0.0354226
\(965\) −5.44901e24 −0.233257
\(966\) 9.58116e24 0.406549
\(967\) −1.36577e25 −0.574449 −0.287224 0.957863i \(-0.592733\pi\)
−0.287224 + 0.957863i \(0.592733\pi\)
\(968\) −2.54596e25 −1.06148
\(969\) 1.18671e25 0.490446
\(970\) 1.66501e23 0.00682115
\(971\) −1.64712e25 −0.668903 −0.334451 0.942413i \(-0.608551\pi\)
−0.334451 + 0.942413i \(0.608551\pi\)
\(972\) −4.14759e24 −0.166968
\(973\) 2.36100e25 0.942188
\(974\) 4.28925e25 1.69680
\(975\) −3.86571e25 −1.51597
\(976\) −3.02184e25 −1.17476
\(977\) −9.34255e24 −0.360049 −0.180024 0.983662i \(-0.557618\pi\)
−0.180024 + 0.983662i \(0.557618\pi\)
\(978\) −4.26185e25 −1.62824
\(979\) −5.79380e23 −0.0219437
\(980\) −8.80048e23 −0.0330434
\(981\) −5.84127e25 −2.17431
\(982\) −4.23857e25 −1.56413
\(983\) 1.14875e25 0.420262 0.210131 0.977673i \(-0.432611\pi\)
0.210131 + 0.977673i \(0.432611\pi\)
\(984\) 1.79355e25 0.650510
\(985\) 5.99978e24 0.215738
\(986\) −1.40941e24 −0.0502438
\(987\) 3.67480e25 1.29879
\(988\) −5.00405e24 −0.175343
\(989\) −4.22530e24 −0.146788
\(990\) 2.01534e23 0.00694145
\(991\) −5.37183e25 −1.83441 −0.917204 0.398418i \(-0.869559\pi\)
−0.917204 + 0.398418i \(0.869559\pi\)
\(992\) 8.84256e24 0.299384
\(993\) −9.31942e25 −3.12839
\(994\) 6.75901e23 0.0224957
\(995\) 7.00284e24 0.231088
\(996\) 4.11548e24 0.134653
\(997\) 3.11554e25 1.01071 0.505353 0.862913i \(-0.331362\pi\)
0.505353 + 0.862913i \(0.331362\pi\)
\(998\) 2.01605e25 0.648473
\(999\) −6.07473e24 −0.193741
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.1.6 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.18.a.b.1.6 21 1.1 even 1 trivial