Properties

Label 29.12.a.a.1.6
Level $29$
Weight $12$
Character 29.1
Self dual yes
Analytic conductor $22.282$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.2819522362\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + 1279291654973975 x^{2} - 65244901875230266 x - 758324542468966858\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-18.9987\) of defining polynomial
Character \(\chi\) \(=\) 29.1

$q$-expansion

\(f(q)\) \(=\) \(q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +O(q^{10})\) \(q-21.9987 q^{2} +310.394 q^{3} -1564.06 q^{4} -886.321 q^{5} -6828.28 q^{6} +44263.6 q^{7} +79460.6 q^{8} -80802.4 q^{9} +19497.9 q^{10} -480464. q^{11} -485474. q^{12} +729102. q^{13} -973741. q^{14} -275109. q^{15} +1.45516e6 q^{16} +6.80915e6 q^{17} +1.77755e6 q^{18} -1.56192e7 q^{19} +1.38626e6 q^{20} +1.37392e7 q^{21} +1.05696e7 q^{22} -3.18252e7 q^{23} +2.46641e7 q^{24} -4.80426e7 q^{25} -1.60393e7 q^{26} -8.00660e7 q^{27} -6.92307e7 q^{28} +2.05111e7 q^{29} +6.05205e6 q^{30} -3.08016e8 q^{31} -1.94747e8 q^{32} -1.49133e8 q^{33} -1.49793e8 q^{34} -3.92317e7 q^{35} +1.26379e8 q^{36} +4.28251e8 q^{37} +3.43602e8 q^{38} +2.26309e8 q^{39} -7.04276e7 q^{40} -1.00915e9 q^{41} -3.02244e8 q^{42} +3.53819e8 q^{43} +7.51473e8 q^{44} +7.16169e7 q^{45} +7.00114e8 q^{46} -2.87373e9 q^{47} +4.51672e8 q^{48} -1.80646e7 q^{49} +1.05687e9 q^{50} +2.11352e9 q^{51} -1.14036e9 q^{52} -1.08796e9 q^{53} +1.76135e9 q^{54} +4.25846e8 q^{55} +3.51721e9 q^{56} -4.84810e9 q^{57} -4.51219e8 q^{58} +9.69237e9 q^{59} +4.30286e8 q^{60} +2.73036e9 q^{61} +6.77597e9 q^{62} -3.57660e9 q^{63} +1.30402e9 q^{64} -6.46218e8 q^{65} +3.28074e9 q^{66} +5.53037e9 q^{67} -1.06499e10 q^{68} -9.87837e9 q^{69} +8.63048e8 q^{70} +1.51715e10 q^{71} -6.42060e9 q^{72} +2.05445e10 q^{73} -9.42097e9 q^{74} -1.49121e10 q^{75} +2.44293e10 q^{76} -2.12671e10 q^{77} -4.97851e9 q^{78} -2.27864e10 q^{79} -1.28974e9 q^{80} -1.05381e10 q^{81} +2.21999e10 q^{82} -6.37446e9 q^{83} -2.14888e10 q^{84} -6.03510e9 q^{85} -7.78357e9 q^{86} +6.36654e9 q^{87} -3.81780e10 q^{88} -2.92283e10 q^{89} -1.57548e9 q^{90} +3.22726e10 q^{91} +4.97764e10 q^{92} -9.56066e10 q^{93} +6.32185e10 q^{94} +1.38436e10 q^{95} -6.04483e10 q^{96} -1.24338e11 q^{97} +3.97399e8 q^{98} +3.88226e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} + O(q^{10}) \) \( 11q - 32q^{2} - 982q^{3} + 9146q^{4} - 2740q^{5} - 28202q^{6} - 49432q^{7} - 150054q^{8} + 330749q^{9} - 685834q^{10} - 612246q^{11} + 2578538q^{12} + 1510364q^{13} + 3955400q^{14} - 2462818q^{15} + 3024818q^{16} - 3291098q^{17} - 27885614q^{18} - 44121388q^{19} - 49472662q^{20} - 46916800q^{21} - 43435618q^{22} - 88684076q^{23} - 224700678q^{24} - 44195521q^{25} - 324999762q^{26} - 236304286q^{27} - 391274848q^{28} + 225622639q^{29} - 494910382q^{30} - 292235934q^{31} - 632542514q^{32} - 1079766410q^{33} - 1113307936q^{34} - 1312820120q^{35} - 2236726492q^{36} - 1380429338q^{37} - 1222857284q^{38} - 1186931090q^{39} - 2713154106q^{40} - 1062067494q^{41} + 205598960q^{42} + 74588594q^{43} + 52891466q^{44} + 4527996830q^{45} - 87670324q^{46} - 1821239394q^{47} + 2666035542q^{48} + 4692522003q^{49} + 9494259926q^{50} + 8768158380q^{51} + 3266669866q^{52} + 7818635688q^{53} + 17402728558q^{54} - 191002682q^{55} + 11263587512q^{56} + 15495358340q^{57} - 656356768q^{58} + 1230002712q^{59} + 31834046430q^{60} - 18602654230q^{61} + 22075953162q^{62} - 9964531456q^{63} + 11813658086q^{64} + 32245789334q^{65} + 42677188354q^{66} + 27481284652q^{67} + 29588811820q^{68} - 20565315068q^{69} + 42862666712q^{70} - 20347168516q^{71} + 47061083616q^{72} - 57740010478q^{73} - 2640709564q^{74} - 23544691000q^{75} - 33350650772q^{76} + 871959792q^{77} - 15384525342q^{78} - 120245016462q^{79} - 84319695274q^{80} - 48880047865q^{81} - 111495532412q^{82} - 142463983824q^{83} - 134146226376q^{84} - 181628566552q^{85} + 47870165542q^{86} - 20141948318q^{87} - 180608014462q^{88} - 96700717270q^{89} - 25522461244q^{90} - 355162031176q^{91} - 22429477796q^{92} - 172582115142q^{93} + 172608565078q^{94} - 195922150708q^{95} + 226391047758q^{96} - 303190852014q^{97} - 123776497136q^{98} - 139125462440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −21.9987 −0.486107 −0.243054 0.970013i \(-0.578149\pi\)
−0.243054 + 0.970013i \(0.578149\pi\)
\(3\) 310.394 0.737474 0.368737 0.929534i \(-0.379790\pi\)
0.368737 + 0.929534i \(0.379790\pi\)
\(4\) −1564.06 −0.763700
\(5\) −886.321 −0.126840 −0.0634200 0.997987i \(-0.520201\pi\)
−0.0634200 + 0.997987i \(0.520201\pi\)
\(6\) −6828.28 −0.358492
\(7\) 44263.6 0.995422 0.497711 0.867343i \(-0.334174\pi\)
0.497711 + 0.867343i \(0.334174\pi\)
\(8\) 79460.6 0.857348
\(9\) −80802.4 −0.456132
\(10\) 19497.9 0.0616579
\(11\) −480464. −0.899500 −0.449750 0.893154i \(-0.648487\pi\)
−0.449750 + 0.893154i \(0.648487\pi\)
\(12\) −485474. −0.563209
\(13\) 729102. 0.544627 0.272314 0.962209i \(-0.412211\pi\)
0.272314 + 0.962209i \(0.412211\pi\)
\(14\) −973741. −0.483882
\(15\) −275109. −0.0935412
\(16\) 1.45516e6 0.346936
\(17\) 6.80915e6 1.16312 0.581559 0.813504i \(-0.302443\pi\)
0.581559 + 0.813504i \(0.302443\pi\)
\(18\) 1.77755e6 0.221729
\(19\) −1.56192e7 −1.44715 −0.723574 0.690246i \(-0.757502\pi\)
−0.723574 + 0.690246i \(0.757502\pi\)
\(20\) 1.38626e6 0.0968676
\(21\) 1.37392e7 0.734098
\(22\) 1.05696e7 0.437254
\(23\) −3.18252e7 −1.03102 −0.515511 0.856883i \(-0.672398\pi\)
−0.515511 + 0.856883i \(0.672398\pi\)
\(24\) 2.46641e7 0.632272
\(25\) −4.80426e7 −0.983912
\(26\) −1.60393e7 −0.264748
\(27\) −8.00660e7 −1.07386
\(28\) −6.92307e7 −0.760203
\(29\) 2.05111e7 0.185695
\(30\) 6.05205e6 0.0454711
\(31\) −3.08016e8 −1.93234 −0.966172 0.257898i \(-0.916970\pi\)
−0.966172 + 0.257898i \(0.916970\pi\)
\(32\) −1.94747e8 −1.02600
\(33\) −1.49133e8 −0.663358
\(34\) −1.49793e8 −0.565401
\(35\) −3.92317e7 −0.126259
\(36\) 1.26379e8 0.348348
\(37\) 4.28251e8 1.01529 0.507643 0.861567i \(-0.330517\pi\)
0.507643 + 0.861567i \(0.330517\pi\)
\(38\) 3.43602e8 0.703470
\(39\) 2.26309e8 0.401649
\(40\) −7.04276e7 −0.108746
\(41\) −1.00915e9 −1.36033 −0.680163 0.733061i \(-0.738091\pi\)
−0.680163 + 0.733061i \(0.738091\pi\)
\(42\) −3.02244e8 −0.356850
\(43\) 3.53819e8 0.367033 0.183516 0.983017i \(-0.441252\pi\)
0.183516 + 0.983017i \(0.441252\pi\)
\(44\) 7.51473e8 0.686948
\(45\) 7.16169e7 0.0578557
\(46\) 7.00114e8 0.501188
\(47\) −2.87373e9 −1.82772 −0.913858 0.406035i \(-0.866911\pi\)
−0.913858 + 0.406035i \(0.866911\pi\)
\(48\) 4.51672e8 0.255857
\(49\) −1.80646e7 −0.00913589
\(50\) 1.05687e9 0.478287
\(51\) 2.11352e9 0.857770
\(52\) −1.14036e9 −0.415932
\(53\) −1.08796e9 −0.357353 −0.178676 0.983908i \(-0.557182\pi\)
−0.178676 + 0.983908i \(0.557182\pi\)
\(54\) 1.76135e9 0.522011
\(55\) 4.25846e8 0.114093
\(56\) 3.51721e9 0.853422
\(57\) −4.84810e9 −1.06724
\(58\) −4.51219e8 −0.0902679
\(59\) 9.69237e9 1.76500 0.882499 0.470315i \(-0.155860\pi\)
0.882499 + 0.470315i \(0.155860\pi\)
\(60\) 4.30286e8 0.0714374
\(61\) 2.73036e9 0.413910 0.206955 0.978350i \(-0.433645\pi\)
0.206955 + 0.978350i \(0.433645\pi\)
\(62\) 6.77597e9 0.939327
\(63\) −3.57660e9 −0.454043
\(64\) 1.30402e9 0.151808
\(65\) −6.46218e8 −0.0690805
\(66\) 3.28074e9 0.322463
\(67\) 5.53037e9 0.500429 0.250215 0.968190i \(-0.419499\pi\)
0.250215 + 0.968190i \(0.419499\pi\)
\(68\) −1.06499e10 −0.888273
\(69\) −9.87837e9 −0.760353
\(70\) 8.63048e8 0.0613756
\(71\) 1.51715e10 0.997949 0.498974 0.866617i \(-0.333710\pi\)
0.498974 + 0.866617i \(0.333710\pi\)
\(72\) −6.42060e9 −0.391063
\(73\) 2.05445e10 1.15990 0.579949 0.814653i \(-0.303072\pi\)
0.579949 + 0.814653i \(0.303072\pi\)
\(74\) −9.42097e9 −0.493538
\(75\) −1.49121e10 −0.725610
\(76\) 2.44293e10 1.10519
\(77\) −2.12671e10 −0.895382
\(78\) −4.97851e9 −0.195244
\(79\) −2.27864e10 −0.833158 −0.416579 0.909100i \(-0.636771\pi\)
−0.416579 + 0.909100i \(0.636771\pi\)
\(80\) −1.28974e9 −0.0440054
\(81\) −1.05381e10 −0.335812
\(82\) 2.21999e10 0.661265
\(83\) −6.37446e9 −0.177629 −0.0888144 0.996048i \(-0.528308\pi\)
−0.0888144 + 0.996048i \(0.528308\pi\)
\(84\) −2.14888e10 −0.560630
\(85\) −6.03510e9 −0.147530
\(86\) −7.78357e9 −0.178417
\(87\) 6.36654e9 0.136946
\(88\) −3.81780e10 −0.771184
\(89\) −2.92283e10 −0.554828 −0.277414 0.960751i \(-0.589477\pi\)
−0.277414 + 0.960751i \(0.589477\pi\)
\(90\) −1.57548e9 −0.0281241
\(91\) 3.22726e10 0.542134
\(92\) 4.97764e10 0.787392
\(93\) −9.56066e10 −1.42505
\(94\) 6.32185e10 0.888466
\(95\) 1.38436e10 0.183556
\(96\) −6.04483e10 −0.756646
\(97\) −1.24338e11 −1.47014 −0.735069 0.677992i \(-0.762850\pi\)
−0.735069 + 0.677992i \(0.762850\pi\)
\(98\) 3.97399e8 0.00444103
\(99\) 3.88226e10 0.410291
\(100\) 7.51413e10 0.751413
\(101\) −2.60286e10 −0.246424 −0.123212 0.992380i \(-0.539320\pi\)
−0.123212 + 0.992380i \(0.539320\pi\)
\(102\) −4.64948e10 −0.416968
\(103\) −1.19818e11 −1.01840 −0.509200 0.860648i \(-0.670059\pi\)
−0.509200 + 0.860648i \(0.670059\pi\)
\(104\) 5.79348e10 0.466935
\(105\) −1.21773e10 −0.0931130
\(106\) 2.39338e10 0.173712
\(107\) −1.11393e11 −0.767795 −0.383897 0.923376i \(-0.625418\pi\)
−0.383897 + 0.923376i \(0.625418\pi\)
\(108\) 1.25228e11 0.820106
\(109\) 1.17465e11 0.731247 0.365624 0.930763i \(-0.380856\pi\)
0.365624 + 0.930763i \(0.380856\pi\)
\(110\) −9.36806e9 −0.0554613
\(111\) 1.32927e11 0.748748
\(112\) 6.44104e10 0.345348
\(113\) 3.69905e11 1.88868 0.944340 0.328972i \(-0.106702\pi\)
0.944340 + 0.328972i \(0.106702\pi\)
\(114\) 1.06652e11 0.518791
\(115\) 2.82074e10 0.130775
\(116\) −3.20806e10 −0.141815
\(117\) −5.89131e10 −0.248422
\(118\) −2.13220e11 −0.857978
\(119\) 3.01397e11 1.15779
\(120\) −2.18603e10 −0.0801973
\(121\) −5.44658e10 −0.190899
\(122\) −6.00645e10 −0.201205
\(123\) −3.13233e11 −1.00321
\(124\) 4.81755e11 1.47573
\(125\) 8.58586e10 0.251639
\(126\) 7.86806e10 0.220714
\(127\) −5.07350e11 −1.36266 −0.681329 0.731977i \(-0.738598\pi\)
−0.681329 + 0.731977i \(0.738598\pi\)
\(128\) 3.70155e11 0.952201
\(129\) 1.09823e11 0.270677
\(130\) 1.42160e10 0.0335806
\(131\) 3.44791e11 0.780843 0.390422 0.920636i \(-0.372329\pi\)
0.390422 + 0.920636i \(0.372329\pi\)
\(132\) 2.33253e11 0.506606
\(133\) −6.91360e11 −1.44052
\(134\) −1.21661e11 −0.243262
\(135\) 7.09642e10 0.136208
\(136\) 5.41059e11 0.997197
\(137\) 5.50954e11 0.975332 0.487666 0.873030i \(-0.337848\pi\)
0.487666 + 0.873030i \(0.337848\pi\)
\(138\) 2.17311e11 0.369613
\(139\) −9.76916e11 −1.59689 −0.798447 0.602065i \(-0.794345\pi\)
−0.798447 + 0.602065i \(0.794345\pi\)
\(140\) 6.13606e10 0.0964241
\(141\) −8.91991e11 −1.34789
\(142\) −3.33754e11 −0.485110
\(143\) −3.50307e11 −0.489893
\(144\) −1.17580e11 −0.158249
\(145\) −1.81795e10 −0.0235536
\(146\) −4.51953e11 −0.563835
\(147\) −5.60716e9 −0.00673749
\(148\) −6.69808e11 −0.775374
\(149\) −5.22457e9 −0.00582809 −0.00291404 0.999996i \(-0.500928\pi\)
−0.00291404 + 0.999996i \(0.500928\pi\)
\(150\) 3.28048e11 0.352724
\(151\) 2.71454e11 0.281400 0.140700 0.990052i \(-0.455065\pi\)
0.140700 + 0.990052i \(0.455065\pi\)
\(152\) −1.24111e12 −1.24071
\(153\) −5.50195e11 −0.530535
\(154\) 4.67848e11 0.435252
\(155\) 2.73002e11 0.245099
\(156\) −3.53960e11 −0.306739
\(157\) −8.51389e11 −0.712328 −0.356164 0.934424i \(-0.615915\pi\)
−0.356164 + 0.934424i \(0.615915\pi\)
\(158\) 5.01272e11 0.405004
\(159\) −3.37698e11 −0.263539
\(160\) 1.72608e11 0.130137
\(161\) −1.40870e12 −1.02630
\(162\) 2.31826e11 0.163241
\(163\) 1.66971e12 1.13661 0.568304 0.822819i \(-0.307600\pi\)
0.568304 + 0.822819i \(0.307600\pi\)
\(164\) 1.57836e12 1.03888
\(165\) 1.32180e11 0.0841403
\(166\) 1.40230e11 0.0863467
\(167\) 1.10002e12 0.655328 0.327664 0.944794i \(-0.393739\pi\)
0.327664 + 0.944794i \(0.393739\pi\)
\(168\) 1.09172e12 0.629377
\(169\) −1.26057e12 −0.703381
\(170\) 1.32764e11 0.0717154
\(171\) 1.26207e12 0.660090
\(172\) −5.53393e11 −0.280303
\(173\) −1.93882e12 −0.951225 −0.475612 0.879655i \(-0.657774\pi\)
−0.475612 + 0.879655i \(0.657774\pi\)
\(174\) −1.40056e11 −0.0665703
\(175\) −2.12653e12 −0.979407
\(176\) −6.99151e11 −0.312069
\(177\) 3.00846e12 1.30164
\(178\) 6.42984e11 0.269706
\(179\) 9.66841e11 0.393245 0.196623 0.980479i \(-0.437003\pi\)
0.196623 + 0.980479i \(0.437003\pi\)
\(180\) −1.12013e11 −0.0441844
\(181\) 3.06155e12 1.17141 0.585705 0.810524i \(-0.300818\pi\)
0.585705 + 0.810524i \(0.300818\pi\)
\(182\) −7.09956e11 −0.263535
\(183\) 8.47489e11 0.305248
\(184\) −2.52885e12 −0.883945
\(185\) −3.79568e11 −0.128779
\(186\) 2.10322e12 0.692730
\(187\) −3.27155e12 −1.04623
\(188\) 4.49468e12 1.39583
\(189\) −3.54401e12 −1.06894
\(190\) −3.04542e11 −0.0892281
\(191\) 1.59095e12 0.452869 0.226435 0.974026i \(-0.427293\pi\)
0.226435 + 0.974026i \(0.427293\pi\)
\(192\) 4.04760e11 0.111954
\(193\) −2.02014e12 −0.543021 −0.271511 0.962435i \(-0.587523\pi\)
−0.271511 + 0.962435i \(0.587523\pi\)
\(194\) 2.73527e12 0.714645
\(195\) −2.00582e11 −0.0509451
\(196\) 2.82541e10 0.00697708
\(197\) −1.30724e12 −0.313901 −0.156950 0.987607i \(-0.550166\pi\)
−0.156950 + 0.987607i \(0.550166\pi\)
\(198\) −8.54048e11 −0.199445
\(199\) 2.91409e12 0.661928 0.330964 0.943643i \(-0.392626\pi\)
0.330964 + 0.943643i \(0.392626\pi\)
\(200\) −3.81749e12 −0.843554
\(201\) 1.71659e12 0.369054
\(202\) 5.72595e11 0.119789
\(203\) 9.07896e11 0.184845
\(204\) −3.30567e12 −0.655078
\(205\) 8.94428e11 0.172544
\(206\) 2.63585e12 0.495052
\(207\) 2.57155e12 0.470282
\(208\) 1.06096e12 0.188951
\(209\) 7.50445e12 1.30171
\(210\) 2.67885e11 0.0452629
\(211\) 7.99404e12 1.31587 0.657935 0.753075i \(-0.271430\pi\)
0.657935 + 0.753075i \(0.271430\pi\)
\(212\) 1.70164e12 0.272910
\(213\) 4.70915e12 0.735961
\(214\) 2.45049e12 0.373231
\(215\) −3.13597e11 −0.0465544
\(216\) −6.36209e12 −0.920671
\(217\) −1.36339e13 −1.92350
\(218\) −2.58409e12 −0.355465
\(219\) 6.37690e12 0.855395
\(220\) −6.66047e11 −0.0871325
\(221\) 4.96456e12 0.633466
\(222\) −2.92421e12 −0.363972
\(223\) −8.85549e12 −1.07532 −0.537658 0.843163i \(-0.680691\pi\)
−0.537658 + 0.843163i \(0.680691\pi\)
\(224\) −8.62019e12 −1.02130
\(225\) 3.88195e12 0.448793
\(226\) −8.13743e12 −0.918101
\(227\) −9.57786e12 −1.05469 −0.527347 0.849650i \(-0.676813\pi\)
−0.527347 + 0.849650i \(0.676813\pi\)
\(228\) 7.58271e12 0.815047
\(229\) −1.53613e13 −1.61188 −0.805940 0.591998i \(-0.798339\pi\)
−0.805940 + 0.591998i \(0.798339\pi\)
\(230\) −6.20526e11 −0.0635707
\(231\) −6.60117e12 −0.660321
\(232\) 1.62983e12 0.159205
\(233\) 1.29012e13 1.23076 0.615379 0.788231i \(-0.289003\pi\)
0.615379 + 0.788231i \(0.289003\pi\)
\(234\) 1.29601e12 0.120760
\(235\) 2.54705e12 0.231827
\(236\) −1.51594e13 −1.34793
\(237\) −7.07278e12 −0.614432
\(238\) −6.63035e12 −0.562812
\(239\) −6.63263e12 −0.550170 −0.275085 0.961420i \(-0.588706\pi\)
−0.275085 + 0.961420i \(0.588706\pi\)
\(240\) −4.00327e11 −0.0324529
\(241\) 1.46207e13 1.15845 0.579223 0.815169i \(-0.303356\pi\)
0.579223 + 0.815169i \(0.303356\pi\)
\(242\) 1.19818e12 0.0927976
\(243\) 1.09125e13 0.826207
\(244\) −4.27044e12 −0.316103
\(245\) 1.60111e10 0.00115880
\(246\) 6.89073e12 0.487666
\(247\) −1.13880e13 −0.788157
\(248\) −2.44752e13 −1.65669
\(249\) −1.97859e12 −0.130997
\(250\) −1.88878e12 −0.122324
\(251\) 9.17406e12 0.581241 0.290620 0.956838i \(-0.406138\pi\)
0.290620 + 0.956838i \(0.406138\pi\)
\(252\) 5.59400e12 0.346753
\(253\) 1.52909e13 0.927405
\(254\) 1.11610e13 0.662399
\(255\) −1.87326e12 −0.108800
\(256\) −1.08136e13 −0.614680
\(257\) 1.33408e13 0.742249 0.371125 0.928583i \(-0.378972\pi\)
0.371125 + 0.928583i \(0.378972\pi\)
\(258\) −2.41597e12 −0.131578
\(259\) 1.89559e13 1.01064
\(260\) 1.01072e12 0.0527568
\(261\) −1.65735e12 −0.0847015
\(262\) −7.58496e12 −0.379574
\(263\) 1.17880e13 0.577677 0.288838 0.957378i \(-0.406731\pi\)
0.288838 + 0.957378i \(0.406731\pi\)
\(264\) −1.18502e13 −0.568729
\(265\) 9.64286e11 0.0453266
\(266\) 1.52090e13 0.700249
\(267\) −9.07229e12 −0.409171
\(268\) −8.64981e12 −0.382177
\(269\) 4.69213e12 0.203111 0.101555 0.994830i \(-0.467618\pi\)
0.101555 + 0.994830i \(0.467618\pi\)
\(270\) −1.56112e12 −0.0662119
\(271\) 2.00690e13 0.834056 0.417028 0.908894i \(-0.363072\pi\)
0.417028 + 0.908894i \(0.363072\pi\)
\(272\) 9.90838e12 0.403528
\(273\) 1.00172e13 0.399810
\(274\) −1.21203e13 −0.474116
\(275\) 2.30827e13 0.885029
\(276\) 1.54503e13 0.580681
\(277\) −3.83151e13 −1.41166 −0.705832 0.708379i \(-0.749427\pi\)
−0.705832 + 0.708379i \(0.749427\pi\)
\(278\) 2.14909e13 0.776262
\(279\) 2.48885e13 0.881404
\(280\) −3.11738e12 −0.108248
\(281\) 2.14260e13 0.729552 0.364776 0.931095i \(-0.381146\pi\)
0.364776 + 0.931095i \(0.381146\pi\)
\(282\) 1.96227e13 0.655221
\(283\) −1.96008e13 −0.641873 −0.320936 0.947101i \(-0.603998\pi\)
−0.320936 + 0.947101i \(0.603998\pi\)
\(284\) −2.37291e13 −0.762133
\(285\) 4.29698e12 0.135368
\(286\) 7.70631e12 0.238140
\(287\) −4.46684e13 −1.35410
\(288\) 1.57360e13 0.467989
\(289\) 1.20926e13 0.352844
\(290\) 3.99925e11 0.0114496
\(291\) −3.85937e13 −1.08419
\(292\) −3.21328e13 −0.885814
\(293\) 5.83139e13 1.57761 0.788807 0.614642i \(-0.210699\pi\)
0.788807 + 0.614642i \(0.210699\pi\)
\(294\) 1.23350e11 0.00327514
\(295\) −8.59056e12 −0.223872
\(296\) 3.40291e13 0.870453
\(297\) 3.84689e13 0.965937
\(298\) 1.14934e11 0.00283308
\(299\) −2.32038e13 −0.561523
\(300\) 2.33234e13 0.554148
\(301\) 1.56613e13 0.365352
\(302\) −5.97165e12 −0.136790
\(303\) −8.07912e12 −0.181731
\(304\) −2.27283e13 −0.502069
\(305\) −2.41998e12 −0.0525004
\(306\) 1.21036e13 0.257897
\(307\) −8.69471e13 −1.81968 −0.909838 0.414964i \(-0.863794\pi\)
−0.909838 + 0.414964i \(0.863794\pi\)
\(308\) 3.32629e13 0.683803
\(309\) −3.71909e13 −0.751044
\(310\) −6.00568e12 −0.119144
\(311\) 2.77778e13 0.541398 0.270699 0.962664i \(-0.412745\pi\)
0.270699 + 0.962664i \(0.412745\pi\)
\(312\) 1.79826e13 0.344353
\(313\) −1.13541e13 −0.213629 −0.106814 0.994279i \(-0.534065\pi\)
−0.106814 + 0.994279i \(0.534065\pi\)
\(314\) 1.87295e13 0.346268
\(315\) 3.17002e12 0.0575908
\(316\) 3.56393e13 0.636282
\(317\) −3.72872e13 −0.654236 −0.327118 0.944984i \(-0.606077\pi\)
−0.327118 + 0.944984i \(0.606077\pi\)
\(318\) 7.42892e12 0.128108
\(319\) −9.85487e12 −0.167033
\(320\) −1.15578e12 −0.0192553
\(321\) −3.45756e13 −0.566229
\(322\) 3.09895e13 0.498893
\(323\) −1.06353e14 −1.68321
\(324\) 1.64823e13 0.256460
\(325\) −3.50279e13 −0.535865
\(326\) −3.67316e13 −0.552513
\(327\) 3.64606e13 0.539276
\(328\) −8.01874e13 −1.16627
\(329\) −1.27202e14 −1.81935
\(330\) −2.90779e12 −0.0409013
\(331\) −1.28189e14 −1.77336 −0.886678 0.462388i \(-0.846993\pi\)
−0.886678 + 0.462388i \(0.846993\pi\)
\(332\) 9.97001e12 0.135655
\(333\) −3.46037e13 −0.463104
\(334\) −2.41989e13 −0.318560
\(335\) −4.90168e12 −0.0634744
\(336\) 1.99926e13 0.254685
\(337\) 6.54934e13 0.820792 0.410396 0.911907i \(-0.365390\pi\)
0.410396 + 0.911907i \(0.365390\pi\)
\(338\) 2.77309e13 0.341919
\(339\) 1.14816e14 1.39285
\(340\) 9.43923e12 0.112669
\(341\) 1.47991e14 1.73814
\(342\) −2.77638e13 −0.320875
\(343\) −8.83231e13 −1.00452
\(344\) 2.81147e13 0.314675
\(345\) 8.75541e12 0.0964431
\(346\) 4.26515e13 0.462398
\(347\) 8.39610e13 0.895912 0.447956 0.894056i \(-0.352152\pi\)
0.447956 + 0.894056i \(0.352152\pi\)
\(348\) −9.95764e12 −0.104585
\(349\) −1.07463e13 −0.111102 −0.0555509 0.998456i \(-0.517691\pi\)
−0.0555509 + 0.998456i \(0.517691\pi\)
\(350\) 4.67810e13 0.476097
\(351\) −5.83763e13 −0.584853
\(352\) 9.35689e13 0.922884
\(353\) −1.25603e13 −0.121966 −0.0609832 0.998139i \(-0.519424\pi\)
−0.0609832 + 0.998139i \(0.519424\pi\)
\(354\) −6.61822e13 −0.632737
\(355\) −1.34468e13 −0.126580
\(356\) 4.57147e13 0.423722
\(357\) 9.35520e13 0.853843
\(358\) −2.12693e13 −0.191159
\(359\) −1.38150e14 −1.22273 −0.611365 0.791349i \(-0.709379\pi\)
−0.611365 + 0.791349i \(0.709379\pi\)
\(360\) 5.69072e12 0.0496025
\(361\) 1.27468e14 1.09424
\(362\) −6.73502e13 −0.569432
\(363\) −1.69059e13 −0.140783
\(364\) −5.04762e13 −0.414027
\(365\) −1.82090e13 −0.147121
\(366\) −1.86437e13 −0.148383
\(367\) 2.02429e14 1.58712 0.793559 0.608494i \(-0.208226\pi\)
0.793559 + 0.608494i \(0.208226\pi\)
\(368\) −4.63107e13 −0.357699
\(369\) 8.15414e13 0.620488
\(370\) 8.35000e12 0.0626004
\(371\) −4.81572e13 −0.355717
\(372\) 1.49534e14 1.08831
\(373\) 2.52372e13 0.180985 0.0904927 0.995897i \(-0.471156\pi\)
0.0904927 + 0.995897i \(0.471156\pi\)
\(374\) 7.19700e13 0.508578
\(375\) 2.66500e13 0.185578
\(376\) −2.28349e14 −1.56699
\(377\) 1.49547e13 0.101135
\(378\) 7.79636e13 0.519621
\(379\) −5.31941e13 −0.349420 −0.174710 0.984620i \(-0.555899\pi\)
−0.174710 + 0.984620i \(0.555899\pi\)
\(380\) −2.16522e13 −0.140182
\(381\) −1.57479e14 −1.00493
\(382\) −3.49988e13 −0.220143
\(383\) 3.19109e14 1.97854 0.989272 0.146084i \(-0.0466669\pi\)
0.989272 + 0.146084i \(0.0466669\pi\)
\(384\) 1.14894e14 0.702224
\(385\) 1.88494e13 0.113570
\(386\) 4.44405e13 0.263967
\(387\) −2.85894e13 −0.167415
\(388\) 1.94471e14 1.12274
\(389\) −7.65689e13 −0.435842 −0.217921 0.975966i \(-0.569928\pi\)
−0.217921 + 0.975966i \(0.569928\pi\)
\(390\) 4.41256e12 0.0247648
\(391\) −2.16703e14 −1.19920
\(392\) −1.43543e12 −0.00783264
\(393\) 1.07021e14 0.575852
\(394\) 2.87577e13 0.152589
\(395\) 2.01961e13 0.105678
\(396\) −6.07208e13 −0.313339
\(397\) −3.97244e13 −0.202166 −0.101083 0.994878i \(-0.532231\pi\)
−0.101083 + 0.994878i \(0.532231\pi\)
\(398\) −6.41062e13 −0.321768
\(399\) −2.14594e14 −1.06235
\(400\) −6.99095e13 −0.341355
\(401\) 3.19615e14 1.53934 0.769668 0.638444i \(-0.220422\pi\)
0.769668 + 0.638444i \(0.220422\pi\)
\(402\) −3.77629e13 −0.179400
\(403\) −2.24575e14 −1.05241
\(404\) 4.07102e13 0.188194
\(405\) 9.34018e12 0.0425944
\(406\) −1.99726e13 −0.0898546
\(407\) −2.05759e14 −0.913250
\(408\) 1.67942e14 0.735407
\(409\) −1.92549e14 −0.831885 −0.415942 0.909391i \(-0.636548\pi\)
−0.415942 + 0.909391i \(0.636548\pi\)
\(410\) −1.96763e13 −0.0838748
\(411\) 1.71013e14 0.719282
\(412\) 1.87403e14 0.777752
\(413\) 4.29019e14 1.75692
\(414\) −5.65709e13 −0.228608
\(415\) 5.64982e12 0.0225304
\(416\) −1.41990e14 −0.558786
\(417\) −3.03229e14 −1.17767
\(418\) −1.65088e14 −0.632771
\(419\) −4.17916e13 −0.158093 −0.0790464 0.996871i \(-0.525188\pi\)
−0.0790464 + 0.996871i \(0.525188\pi\)
\(420\) 1.90460e13 0.0711103
\(421\) 2.60522e14 0.960048 0.480024 0.877255i \(-0.340628\pi\)
0.480024 + 0.877255i \(0.340628\pi\)
\(422\) −1.75859e14 −0.639654
\(423\) 2.32205e14 0.833679
\(424\) −8.64503e13 −0.306376
\(425\) −3.27129e14 −1.14441
\(426\) −1.03595e14 −0.357756
\(427\) 1.20856e14 0.412015
\(428\) 1.74224e14 0.586365
\(429\) −1.08733e14 −0.361283
\(430\) 6.89874e12 0.0226305
\(431\) −1.31690e14 −0.426508 −0.213254 0.976997i \(-0.568406\pi\)
−0.213254 + 0.976997i \(0.568406\pi\)
\(432\) −1.16509e14 −0.372561
\(433\) −1.19097e13 −0.0376026 −0.0188013 0.999823i \(-0.505985\pi\)
−0.0188013 + 0.999823i \(0.505985\pi\)
\(434\) 2.99928e14 0.935027
\(435\) −5.64280e12 −0.0173702
\(436\) −1.83723e14 −0.558453
\(437\) 4.97084e14 1.49204
\(438\) −1.40284e14 −0.415814
\(439\) −5.65097e14 −1.65413 −0.827063 0.562110i \(-0.809990\pi\)
−0.827063 + 0.562110i \(0.809990\pi\)
\(440\) 3.38380e13 0.0978170
\(441\) 1.45967e12 0.00416717
\(442\) −1.09214e14 −0.307933
\(443\) −1.77548e14 −0.494419 −0.247210 0.968962i \(-0.579514\pi\)
−0.247210 + 0.968962i \(0.579514\pi\)
\(444\) −2.07905e14 −0.571818
\(445\) 2.59056e13 0.0703743
\(446\) 1.94809e14 0.522719
\(447\) −1.62168e12 −0.00429806
\(448\) 5.77206e13 0.151113
\(449\) −7.83747e13 −0.202685 −0.101342 0.994852i \(-0.532314\pi\)
−0.101342 + 0.994852i \(0.532314\pi\)
\(450\) −8.53980e13 −0.218162
\(451\) 4.84859e14 1.22361
\(452\) −5.78552e14 −1.44238
\(453\) 8.42579e13 0.207525
\(454\) 2.10701e14 0.512694
\(455\) −2.86039e13 −0.0687643
\(456\) −3.85233e14 −0.914991
\(457\) −4.40497e14 −1.03372 −0.516861 0.856069i \(-0.672900\pi\)
−0.516861 + 0.856069i \(0.672900\pi\)
\(458\) 3.37929e14 0.783547
\(459\) −5.45182e14 −1.24903
\(460\) −4.41179e13 −0.0998727
\(461\) 2.97082e14 0.664541 0.332270 0.943184i \(-0.392185\pi\)
0.332270 + 0.943184i \(0.392185\pi\)
\(462\) 1.45217e14 0.320987
\(463\) 1.07028e14 0.233776 0.116888 0.993145i \(-0.462708\pi\)
0.116888 + 0.993145i \(0.462708\pi\)
\(464\) 2.98469e13 0.0644245
\(465\) 8.47381e13 0.180754
\(466\) −2.83810e14 −0.598281
\(467\) −2.59277e14 −0.540158 −0.270079 0.962838i \(-0.587050\pi\)
−0.270079 + 0.962838i \(0.587050\pi\)
\(468\) 9.21435e13 0.189720
\(469\) 2.44794e14 0.498138
\(470\) −5.60319e13 −0.112693
\(471\) −2.64266e14 −0.525323
\(472\) 7.70162e14 1.51322
\(473\) −1.69997e14 −0.330146
\(474\) 1.55592e14 0.298680
\(475\) 7.50385e14 1.42387
\(476\) −4.71402e14 −0.884206
\(477\) 8.79101e13 0.163000
\(478\) 1.45909e14 0.267442
\(479\) −9.69340e13 −0.175643 −0.0878215 0.996136i \(-0.527991\pi\)
−0.0878215 + 0.996136i \(0.527991\pi\)
\(480\) 5.35766e13 0.0959729
\(481\) 3.12238e14 0.552953
\(482\) −3.21637e14 −0.563129
\(483\) −4.37252e14 −0.756872
\(484\) 8.51876e13 0.145790
\(485\) 1.10203e14 0.186472
\(486\) −2.40060e14 −0.401625
\(487\) 4.95544e14 0.819735 0.409867 0.912145i \(-0.365575\pi\)
0.409867 + 0.912145i \(0.365575\pi\)
\(488\) 2.16956e14 0.354865
\(489\) 5.18270e14 0.838219
\(490\) −3.52223e11 −0.000563300 0
\(491\) −9.75658e14 −1.54294 −0.771471 0.636264i \(-0.780479\pi\)
−0.771471 + 0.636264i \(0.780479\pi\)
\(492\) 4.89915e14 0.766147
\(493\) 1.39664e14 0.215986
\(494\) 2.50521e14 0.383129
\(495\) −3.44093e13 −0.0520412
\(496\) −4.48212e14 −0.670401
\(497\) 6.71545e14 0.993380
\(498\) 4.35265e13 0.0636785
\(499\) 1.26831e15 1.83516 0.917579 0.397554i \(-0.130141\pi\)
0.917579 + 0.397554i \(0.130141\pi\)
\(500\) −1.34288e14 −0.192177
\(501\) 3.41439e14 0.483287
\(502\) −2.01817e14 −0.282545
\(503\) 7.13091e14 0.987463 0.493732 0.869614i \(-0.335632\pi\)
0.493732 + 0.869614i \(0.335632\pi\)
\(504\) −2.84199e14 −0.389273
\(505\) 2.30697e13 0.0312564
\(506\) −3.36380e14 −0.450819
\(507\) −3.91274e14 −0.518725
\(508\) 7.93524e14 1.04066
\(509\) −1.47779e14 −0.191719 −0.0958597 0.995395i \(-0.530560\pi\)
−0.0958597 + 0.995395i \(0.530560\pi\)
\(510\) 4.12093e13 0.0528883
\(511\) 9.09373e14 1.15459
\(512\) −5.20193e14 −0.653400
\(513\) 1.25056e15 1.55403
\(514\) −2.93480e14 −0.360813
\(515\) 1.06198e14 0.129174
\(516\) −1.71770e14 −0.206716
\(517\) 1.38073e15 1.64403
\(518\) −4.17005e14 −0.491279
\(519\) −6.01798e14 −0.701504
\(520\) −5.13489e13 −0.0592260
\(521\) 2.60928e14 0.297792 0.148896 0.988853i \(-0.452428\pi\)
0.148896 + 0.988853i \(0.452428\pi\)
\(522\) 3.64596e13 0.0411740
\(523\) 7.01208e14 0.783587 0.391794 0.920053i \(-0.371855\pi\)
0.391794 + 0.920053i \(0.371855\pi\)
\(524\) −5.39273e14 −0.596330
\(525\) −6.60064e14 −0.722287
\(526\) −2.59322e14 −0.280813
\(527\) −2.09733e15 −2.24755
\(528\) −2.17012e14 −0.230143
\(529\) 6.00349e13 0.0630082
\(530\) −2.12130e13 −0.0220336
\(531\) −7.83166e14 −0.805071
\(532\) 1.08133e15 1.10013
\(533\) −7.35770e14 −0.740871
\(534\) 1.99579e14 0.198901
\(535\) 9.87296e13 0.0973871
\(536\) 4.39446e14 0.429042
\(537\) 3.00102e14 0.290008
\(538\) −1.03221e14 −0.0987336
\(539\) 8.67942e12 0.00821774
\(540\) −1.10992e14 −0.104022
\(541\) −1.43669e15 −1.33284 −0.666419 0.745578i \(-0.732174\pi\)
−0.666419 + 0.745578i \(0.732174\pi\)
\(542\) −4.41493e14 −0.405441
\(543\) 9.50288e14 0.863885
\(544\) −1.32606e15 −1.19335
\(545\) −1.04112e14 −0.0927514
\(546\) −2.20366e14 −0.194351
\(547\) −9.61440e14 −0.839444 −0.419722 0.907653i \(-0.637872\pi\)
−0.419722 + 0.907653i \(0.637872\pi\)
\(548\) −8.61724e14 −0.744861
\(549\) −2.20620e14 −0.188798
\(550\) −5.07790e14 −0.430219
\(551\) −3.20367e14 −0.268729
\(552\) −7.84941e14 −0.651887
\(553\) −1.00861e15 −0.829343
\(554\) 8.42884e14 0.686221
\(555\) −1.17816e14 −0.0949711
\(556\) 1.52795e15 1.21955
\(557\) −2.91552e14 −0.230416 −0.115208 0.993341i \(-0.536753\pi\)
−0.115208 + 0.993341i \(0.536753\pi\)
\(558\) −5.47514e14 −0.428457
\(559\) 2.57970e14 0.199896
\(560\) −5.70883e13 −0.0438039
\(561\) −1.01547e15 −0.771564
\(562\) −4.71344e14 −0.354641
\(563\) −6.42960e14 −0.479057 −0.239529 0.970889i \(-0.576993\pi\)
−0.239529 + 0.970889i \(0.576993\pi\)
\(564\) 1.39512e15 1.02939
\(565\) −3.27854e14 −0.239560
\(566\) 4.31193e14 0.312019
\(567\) −4.66456e14 −0.334275
\(568\) 1.20554e15 0.855589
\(569\) 4.54572e14 0.319511 0.159755 0.987157i \(-0.448929\pi\)
0.159755 + 0.987157i \(0.448929\pi\)
\(570\) −9.45280e13 −0.0658034
\(571\) −1.61565e15 −1.11391 −0.556955 0.830543i \(-0.688030\pi\)
−0.556955 + 0.830543i \(0.688030\pi\)
\(572\) 5.47900e14 0.374131
\(573\) 4.93822e14 0.333979
\(574\) 9.82647e14 0.658237
\(575\) 1.52897e15 1.01444
\(576\) −1.05368e14 −0.0692444
\(577\) −3.96128e14 −0.257851 −0.128926 0.991654i \(-0.541153\pi\)
−0.128926 + 0.991654i \(0.541153\pi\)
\(578\) −2.66022e14 −0.171520
\(579\) −6.27041e14 −0.400464
\(580\) 2.84337e13 0.0179879
\(581\) −2.82156e14 −0.176816
\(582\) 8.49012e14 0.527033
\(583\) 5.22728e14 0.321439
\(584\) 1.63248e15 0.994436
\(585\) 5.22160e13 0.0315098
\(586\) −1.28283e15 −0.766890
\(587\) −6.16212e14 −0.364939 −0.182470 0.983211i \(-0.558409\pi\)
−0.182470 + 0.983211i \(0.558409\pi\)
\(588\) 8.76992e12 0.00514542
\(589\) 4.81096e15 2.79639
\(590\) 1.88981e14 0.108826
\(591\) −4.05761e14 −0.231494
\(592\) 6.23172e14 0.352240
\(593\) −1.04704e15 −0.586360 −0.293180 0.956057i \(-0.594714\pi\)
−0.293180 + 0.956057i \(0.594714\pi\)
\(594\) −8.46265e14 −0.469549
\(595\) −2.67135e14 −0.146854
\(596\) 8.17152e12 0.00445091
\(597\) 9.04516e14 0.488155
\(598\) 5.10454e14 0.272961
\(599\) −3.29250e15 −1.74453 −0.872265 0.489033i \(-0.837350\pi\)
−0.872265 + 0.489033i \(0.837350\pi\)
\(600\) −1.18493e15 −0.622100
\(601\) −2.47950e14 −0.128990 −0.0644949 0.997918i \(-0.520544\pi\)
−0.0644949 + 0.997918i \(0.520544\pi\)
\(602\) −3.44528e14 −0.177600
\(603\) −4.46867e14 −0.228262
\(604\) −4.24570e14 −0.214905
\(605\) 4.82742e13 0.0242137
\(606\) 1.77730e14 0.0883410
\(607\) −2.44547e15 −1.20455 −0.602274 0.798290i \(-0.705738\pi\)
−0.602274 + 0.798290i \(0.705738\pi\)
\(608\) 3.04179e15 1.48477
\(609\) 2.81806e14 0.136319
\(610\) 5.32364e13 0.0255208
\(611\) −2.09524e15 −0.995424
\(612\) 8.60537e14 0.405169
\(613\) 2.10077e15 0.980270 0.490135 0.871646i \(-0.336947\pi\)
0.490135 + 0.871646i \(0.336947\pi\)
\(614\) 1.91272e15 0.884558
\(615\) 2.77625e14 0.127247
\(616\) −1.68989e15 −0.767653
\(617\) −2.30636e14 −0.103839 −0.0519194 0.998651i \(-0.516534\pi\)
−0.0519194 + 0.998651i \(0.516534\pi\)
\(618\) 8.18152e14 0.365088
\(619\) −1.04593e15 −0.462599 −0.231300 0.972883i \(-0.574298\pi\)
−0.231300 + 0.972883i \(0.574298\pi\)
\(620\) −4.26990e14 −0.187182
\(621\) 2.54812e15 1.10717
\(622\) −6.11077e14 −0.263177
\(623\) −1.29375e15 −0.552287
\(624\) 3.29315e14 0.139347
\(625\) 2.26973e15 0.951994
\(626\) 2.49776e14 0.103846
\(627\) 2.32934e15 0.959978
\(628\) 1.33162e15 0.544004
\(629\) 2.91602e15 1.18090
\(630\) −6.97363e13 −0.0279953
\(631\) 8.37986e14 0.333484 0.166742 0.986001i \(-0.446675\pi\)
0.166742 + 0.986001i \(0.446675\pi\)
\(632\) −1.81062e15 −0.714306
\(633\) 2.48130e15 0.970420
\(634\) 8.20271e14 0.318029
\(635\) 4.49675e14 0.172840
\(636\) 5.28179e14 0.201264
\(637\) −1.31710e13 −0.00497566
\(638\) 2.16795e14 0.0811960
\(639\) −1.22589e15 −0.455196
\(640\) −3.28076e14 −0.120777
\(641\) −4.90090e15 −1.78878 −0.894390 0.447288i \(-0.852390\pi\)
−0.894390 + 0.447288i \(0.852390\pi\)
\(642\) 7.60619e14 0.275248
\(643\) 1.71965e15 0.616991 0.308496 0.951226i \(-0.400174\pi\)
0.308496 + 0.951226i \(0.400174\pi\)
\(644\) 2.20328e15 0.783787
\(645\) −9.73389e13 −0.0343327
\(646\) 2.33964e15 0.818219
\(647\) 8.99014e14 0.311740 0.155870 0.987778i \(-0.450182\pi\)
0.155870 + 0.987778i \(0.450182\pi\)
\(648\) −8.37367e14 −0.287908
\(649\) −4.65684e15 −1.58762
\(650\) 7.70569e14 0.260488
\(651\) −4.23189e15 −1.41853
\(652\) −2.61153e15 −0.868026
\(653\) 1.85055e15 0.609927 0.304964 0.952364i \(-0.401356\pi\)
0.304964 + 0.952364i \(0.401356\pi\)
\(654\) −8.02086e14 −0.262146
\(655\) −3.05596e14 −0.0990421
\(656\) −1.46847e15 −0.471947
\(657\) −1.66004e15 −0.529066
\(658\) 2.79827e15 0.884398
\(659\) −8.51169e14 −0.266776 −0.133388 0.991064i \(-0.542586\pi\)
−0.133388 + 0.991064i \(0.542586\pi\)
\(660\) −2.06737e14 −0.0642579
\(661\) 5.25610e15 1.62015 0.810075 0.586326i \(-0.199426\pi\)
0.810075 + 0.586326i \(0.199426\pi\)
\(662\) 2.81999e15 0.862042
\(663\) 1.54097e15 0.467165
\(664\) −5.06518e14 −0.152290
\(665\) 6.12767e14 0.182716
\(666\) 7.61236e14 0.225119
\(667\) −6.52772e14 −0.191456
\(668\) −1.72049e15 −0.500473
\(669\) −2.74869e15 −0.793017
\(670\) 1.07831e14 0.0308554
\(671\) −1.31184e15 −0.372313
\(672\) −2.67566e15 −0.753181
\(673\) 6.49345e14 0.181298 0.0906490 0.995883i \(-0.471106\pi\)
0.0906490 + 0.995883i \(0.471106\pi\)
\(674\) −1.44077e15 −0.398993
\(675\) 3.84658e15 1.05658
\(676\) 1.97160e15 0.537172
\(677\) 4.60763e15 1.24520 0.622601 0.782540i \(-0.286076\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(678\) −2.52581e15 −0.677076
\(679\) −5.50363e15 −1.46341
\(680\) −4.79552e14 −0.126484
\(681\) −2.97291e15 −0.777809
\(682\) −3.25561e15 −0.844925
\(683\) −1.97762e15 −0.509131 −0.254566 0.967056i \(-0.581932\pi\)
−0.254566 + 0.967056i \(0.581932\pi\)
\(684\) −1.97394e15 −0.504111
\(685\) −4.88323e14 −0.123711
\(686\) 1.94299e15 0.488303
\(687\) −4.76806e15 −1.18872
\(688\) 5.14862e14 0.127337
\(689\) −7.93236e14 −0.194624
\(690\) −1.92608e14 −0.0468817
\(691\) −5.65502e15 −1.36554 −0.682770 0.730633i \(-0.739225\pi\)
−0.682770 + 0.730633i \(0.739225\pi\)
\(692\) 3.03242e15 0.726450
\(693\) 1.71843e15 0.408412
\(694\) −1.84703e15 −0.435510
\(695\) 8.65862e14 0.202550
\(696\) 5.05889e14 0.117410
\(697\) −6.87143e15 −1.58222
\(698\) 2.36406e14 0.0540074
\(699\) 4.00446e15 0.907653
\(700\) 3.32602e15 0.747973
\(701\) 6.37840e15 1.42319 0.711595 0.702590i \(-0.247973\pi\)
0.711595 + 0.702590i \(0.247973\pi\)
\(702\) 1.28420e15 0.284302
\(703\) −6.68892e15 −1.46927
\(704\) −6.26535e14 −0.136551
\(705\) 7.90591e14 0.170967
\(706\) 2.76311e14 0.0592887
\(707\) −1.15212e15 −0.245296
\(708\) −4.70540e15 −0.994062
\(709\) −1.82210e15 −0.381961 −0.190980 0.981594i \(-0.561167\pi\)
−0.190980 + 0.981594i \(0.561167\pi\)
\(710\) 2.95813e14 0.0615314
\(711\) 1.84120e15 0.380030
\(712\) −2.32250e15 −0.475680
\(713\) 9.80269e15 1.99229
\(714\) −2.05802e15 −0.415059
\(715\) 3.10485e14 0.0621380
\(716\) −1.51219e15 −0.300321
\(717\) −2.05873e15 −0.405736
\(718\) 3.03912e15 0.594378
\(719\) 4.72441e15 0.916935 0.458467 0.888711i \(-0.348399\pi\)
0.458467 + 0.888711i \(0.348399\pi\)
\(720\) 1.04214e14 0.0200723
\(721\) −5.30358e15 −1.01374
\(722\) −2.80414e15 −0.531918
\(723\) 4.53819e15 0.854324
\(724\) −4.78844e15 −0.894606
\(725\) −9.85408e14 −0.182708
\(726\) 3.71908e14 0.0684359
\(727\) 9.76903e15 1.78407 0.892035 0.451966i \(-0.149277\pi\)
0.892035 + 0.451966i \(0.149277\pi\)
\(728\) 2.56440e15 0.464797
\(729\) 5.25397e15 0.945118
\(730\) 4.00575e14 0.0715169
\(731\) 2.40921e15 0.426902
\(732\) −1.32552e15 −0.233118
\(733\) −2.30118e15 −0.401678 −0.200839 0.979624i \(-0.564367\pi\)
−0.200839 + 0.979624i \(0.564367\pi\)
\(734\) −4.45317e15 −0.771510
\(735\) 4.96975e12 0.000854583 0
\(736\) 6.19786e15 1.05783
\(737\) −2.65714e15 −0.450136
\(738\) −1.79381e15 −0.301624
\(739\) 7.78978e15 1.30011 0.650056 0.759886i \(-0.274745\pi\)
0.650056 + 0.759886i \(0.274745\pi\)
\(740\) 5.93665e14 0.0983484
\(741\) −3.53476e15 −0.581246
\(742\) 1.05940e15 0.172917
\(743\) −7.50411e14 −0.121580 −0.0607898 0.998151i \(-0.519362\pi\)
−0.0607898 + 0.998151i \(0.519362\pi\)
\(744\) −7.59695e15 −1.22177
\(745\) 4.63065e12 0.000739234 0
\(746\) −5.55187e14 −0.0879783
\(747\) 5.15071e14 0.0810222
\(748\) 5.11689e15 0.799002
\(749\) −4.93063e15 −0.764280
\(750\) −5.86266e14 −0.0902106
\(751\) −8.59656e15 −1.31312 −0.656561 0.754273i \(-0.727989\pi\)
−0.656561 + 0.754273i \(0.727989\pi\)
\(752\) −4.18174e15 −0.634101
\(753\) 2.84757e15 0.428650
\(754\) −3.28984e14 −0.0491624
\(755\) −2.40596e14 −0.0356927
\(756\) 5.54303e15 0.816351
\(757\) −5.23719e15 −0.765722 −0.382861 0.923806i \(-0.625061\pi\)
−0.382861 + 0.923806i \(0.625061\pi\)
\(758\) 1.17020e15 0.169856
\(759\) 4.74620e15 0.683938
\(760\) 1.10002e15 0.157372
\(761\) −5.40274e15 −0.767358 −0.383679 0.923466i \(-0.625343\pi\)
−0.383679 + 0.923466i \(0.625343\pi\)
\(762\) 3.46432e15 0.488502
\(763\) 5.19944e15 0.727899
\(764\) −2.48834e15 −0.345856
\(765\) 4.87650e14 0.0672931
\(766\) −7.01999e15 −0.961785
\(767\) 7.06672e15 0.961266
\(768\) −3.35647e15 −0.453311
\(769\) 1.68378e15 0.225783 0.112891 0.993607i \(-0.463989\pi\)
0.112891 + 0.993607i \(0.463989\pi\)
\(770\) −4.14663e14 −0.0552073
\(771\) 4.14091e15 0.547390
\(772\) 3.15962e15 0.414705
\(773\) −6.91163e14 −0.0900727 −0.0450363 0.998985i \(-0.514340\pi\)
−0.0450363 + 0.998985i \(0.514340\pi\)
\(774\) 6.28930e14 0.0813818
\(775\) 1.47979e16 1.90126
\(776\) −9.87995e15 −1.26042
\(777\) 5.88380e15 0.745320
\(778\) 1.68442e15 0.211866
\(779\) 1.57620e16 1.96859
\(780\) 3.13722e14 0.0389068
\(781\) −7.28937e15 −0.897655
\(782\) 4.76718e15 0.582941
\(783\) −1.64225e15 −0.199411
\(784\) −2.62869e13 −0.00316957
\(785\) 7.54604e14 0.0903516
\(786\) −2.35433e15 −0.279926
\(787\) −8.76844e15 −1.03529 −0.517644 0.855596i \(-0.673191\pi\)
−0.517644 + 0.855596i \(0.673191\pi\)
\(788\) 2.04460e15 0.239726
\(789\) 3.65894e15 0.426022
\(790\) −4.44288e14 −0.0513707
\(791\) 1.63733e16 1.88003
\(792\) 3.08487e15 0.351762
\(793\) 1.99071e15 0.225427
\(794\) 8.73885e14 0.0982746
\(795\) 2.99309e14 0.0334272
\(796\) −4.55780e15 −0.505514
\(797\) −9.97692e15 −1.09894 −0.549472 0.835512i \(-0.685171\pi\)
−0.549472 + 0.835512i \(0.685171\pi\)
\(798\) 4.72080e15 0.516416
\(799\) −1.95677e16 −2.12585
\(800\) 9.35614e15 1.00949
\(801\) 2.36171e15 0.253074
\(802\) −7.03113e15 −0.748283
\(803\) −9.87090e15 −1.04333
\(804\) −2.68485e15 −0.281846
\(805\) 1.24856e15 0.130176
\(806\) 4.94037e15 0.511583
\(807\) 1.45641e15 0.149789
\(808\) −2.06825e15 −0.211271
\(809\) 1.81464e16 1.84108 0.920540 0.390648i \(-0.127749\pi\)
0.920540 + 0.390648i \(0.127749\pi\)
\(810\) −2.05472e14 −0.0207055
\(811\) 1.48265e16 1.48397 0.741984 0.670418i \(-0.233885\pi\)
0.741984 + 0.670418i \(0.233885\pi\)
\(812\) −1.42000e15 −0.141166
\(813\) 6.22931e15 0.615095
\(814\) 4.52644e15 0.443938
\(815\) −1.47990e15 −0.144167
\(816\) 3.07551e15 0.297592
\(817\) −5.52636e15 −0.531151
\(818\) 4.23583e15 0.404385
\(819\) −2.60770e15 −0.247284
\(820\) −1.39894e15 −0.131772
\(821\) −1.98325e16 −1.85562 −0.927812 0.373048i \(-0.878313\pi\)
−0.927812 + 0.373048i \(0.878313\pi\)
\(822\) −3.76207e15 −0.349649
\(823\) −4.07918e15 −0.376594 −0.188297 0.982112i \(-0.560297\pi\)
−0.188297 + 0.982112i \(0.560297\pi\)
\(824\) −9.52083e15 −0.873123
\(825\) 7.16475e15 0.652686
\(826\) −9.43786e15 −0.854050
\(827\) −1.50273e16 −1.35083 −0.675417 0.737436i \(-0.736036\pi\)
−0.675417 + 0.737436i \(0.736036\pi\)
\(828\) −4.02205e15 −0.359154
\(829\) 1.78355e15 0.158211 0.0791054 0.996866i \(-0.474794\pi\)
0.0791054 + 0.996866i \(0.474794\pi\)
\(830\) −1.24289e14 −0.0109522
\(831\) −1.18928e16 −1.04107
\(832\) 9.50763e14 0.0826787
\(833\) −1.23005e14 −0.0106261
\(834\) 6.67065e15 0.572473
\(835\) −9.74968e14 −0.0831217
\(836\) −1.17374e16 −0.994116
\(837\) 2.46616e16 2.07507
\(838\) 9.19362e14 0.0768501
\(839\) 2.08273e16 1.72959 0.864794 0.502126i \(-0.167449\pi\)
0.864794 + 0.502126i \(0.167449\pi\)
\(840\) −9.67616e14 −0.0798302
\(841\) 4.20707e14 0.0344828
\(842\) −5.73115e15 −0.466686
\(843\) 6.65050e15 0.538026
\(844\) −1.25031e16 −1.00493
\(845\) 1.11727e15 0.0892168
\(846\) −5.10820e15 −0.405257
\(847\) −2.41085e15 −0.190025
\(848\) −1.58316e15 −0.123979
\(849\) −6.08399e15 −0.473365
\(850\) 7.19642e15 0.556304
\(851\) −1.36292e16 −1.04678
\(852\) −7.36538e15 −0.562053
\(853\) −2.58806e16 −1.96225 −0.981126 0.193370i \(-0.938058\pi\)
−0.981126 + 0.193370i \(0.938058\pi\)
\(854\) −2.65867e15 −0.200284
\(855\) −1.11860e15 −0.0837259
\(856\) −8.85132e15 −0.658267
\(857\) −1.86002e16 −1.37443 −0.687215 0.726454i \(-0.741167\pi\)
−0.687215 + 0.726454i \(0.741167\pi\)
\(858\) 2.39199e15 0.175622
\(859\) −1.99564e16 −1.45586 −0.727931 0.685650i \(-0.759518\pi\)
−0.727931 + 0.685650i \(0.759518\pi\)
\(860\) 4.90484e14 0.0355536
\(861\) −1.38648e16 −0.998612
\(862\) 2.89701e15 0.207329
\(863\) 5.86095e14 0.0416782 0.0208391 0.999783i \(-0.493366\pi\)
0.0208391 + 0.999783i \(0.493366\pi\)
\(864\) 1.55926e16 1.10178
\(865\) 1.71841e15 0.120653
\(866\) 2.61998e14 0.0182789
\(867\) 3.75349e15 0.260213
\(868\) 2.13242e16 1.46897
\(869\) 1.09481e16 0.749425
\(870\) 1.24134e14 0.00844377
\(871\) 4.03220e15 0.272547
\(872\) 9.33387e15 0.626933
\(873\) 1.00468e16 0.670577
\(874\) −1.09352e16 −0.725294
\(875\) 3.80040e15 0.250487
\(876\) −9.97383e15 −0.653265
\(877\) −2.50479e16 −1.63032 −0.815162 0.579232i \(-0.803352\pi\)
−0.815162 + 0.579232i \(0.803352\pi\)
\(878\) 1.24314e16 0.804083
\(879\) 1.81003e16 1.16345
\(880\) 6.19672e14 0.0395829
\(881\) −2.71552e16 −1.72379 −0.861896 0.507085i \(-0.830723\pi\)
−0.861896 + 0.507085i \(0.830723\pi\)
\(882\) −3.21108e13 −0.00202569
\(883\) −6.82561e14 −0.0427915 −0.0213958 0.999771i \(-0.506811\pi\)
−0.0213958 + 0.999771i \(0.506811\pi\)
\(884\) −7.76486e15 −0.483778
\(885\) −2.66646e15 −0.165100
\(886\) 3.90583e15 0.240341
\(887\) 1.46682e16 0.897008 0.448504 0.893781i \(-0.351957\pi\)
0.448504 + 0.893781i \(0.351957\pi\)
\(888\) 1.05624e16 0.641937
\(889\) −2.24571e16 −1.35642
\(890\) −5.69891e14 −0.0342095
\(891\) 5.06320e15 0.302063
\(892\) 1.38505e16 0.821218
\(893\) 4.48854e16 2.64498
\(894\) 3.56748e13 0.00208932
\(895\) −8.56932e14 −0.0498792
\(896\) 1.63844e16 0.947841
\(897\) −7.20233e15 −0.414109
\(898\) 1.72414e15 0.0985266
\(899\) −6.31777e15 −0.358827
\(900\) −6.07159e15 −0.342743
\(901\) −7.40811e15 −0.415644
\(902\) −1.06663e16 −0.594808
\(903\) 4.86118e15 0.269438
\(904\) 2.93928e16 1.61925
\(905\) −2.71352e15 −0.148582
\(906\) −1.85356e15 −0.100879
\(907\) 1.65196e16 0.893634 0.446817 0.894625i \(-0.352558\pi\)
0.446817 + 0.894625i \(0.352558\pi\)
\(908\) 1.49803e16 0.805469
\(909\) 2.10317e15 0.112402
\(910\) 6.29249e14 0.0334268
\(911\) −2.65587e16 −1.40235 −0.701173 0.712991i \(-0.747340\pi\)
−0.701173 + 0.712991i \(0.747340\pi\)
\(912\) −7.05475e15 −0.370263
\(913\) 3.06270e15 0.159777
\(914\) 9.69037e15 0.502500
\(915\) −7.51148e14 −0.0387177
\(916\) 2.40259e16 1.23099
\(917\) 1.52617e16 0.777268
\(918\) 1.19933e16 0.607161
\(919\) 1.23677e16 0.622378 0.311189 0.950348i \(-0.399273\pi\)
0.311189 + 0.950348i \(0.399273\pi\)
\(920\) 2.24137e15 0.112120
\(921\) −2.69879e16 −1.34196
\(922\) −6.53543e15 −0.323038
\(923\) 1.10616e16 0.543510
\(924\) 1.03246e16 0.504287
\(925\) −2.05743e16 −0.998952
\(926\) −2.35447e15 −0.113640
\(927\) 9.68160e15 0.464525
\(928\) −3.99448e15 −0.190523
\(929\) −2.12065e16 −1.00550 −0.502751 0.864432i \(-0.667679\pi\)
−0.502751 + 0.864432i \(0.667679\pi\)
\(930\) −1.86413e15 −0.0878658
\(931\) 2.82155e14 0.0132210
\(932\) −2.01782e16 −0.939929
\(933\) 8.62208e15 0.399267
\(934\) 5.70376e15 0.262575
\(935\) 2.89965e15 0.132703
\(936\) −4.68127e15 −0.212984
\(937\) 4.75067e15 0.214876 0.107438 0.994212i \(-0.465735\pi\)
0.107438 + 0.994212i \(0.465735\pi\)
\(938\) −5.38515e15 −0.242149
\(939\) −3.52425e15 −0.157546
\(940\) −3.98373e15 −0.177046
\(941\) 1.38698e16 0.612813 0.306406 0.951901i \(-0.400873\pi\)
0.306406 + 0.951901i \(0.400873\pi\)
\(942\) 5.81352e15 0.255364
\(943\) 3.21163e16 1.40253
\(944\) 1.41039e16 0.612342
\(945\) 3.14113e15 0.135585
\(946\) 3.73972e15 0.160486
\(947\) −5.40709e15 −0.230695 −0.115348 0.993325i \(-0.536798\pi\)
−0.115348 + 0.993325i \(0.536798\pi\)
\(948\) 1.10622e16 0.469242
\(949\) 1.49790e16 0.631713
\(950\) −1.65075e16 −0.692152
\(951\) −1.15737e16 −0.482482
\(952\) 2.39492e16 0.992631
\(953\) −2.32910e16 −0.959793 −0.479896 0.877325i \(-0.659326\pi\)
−0.479896 + 0.877325i \(0.659326\pi\)
\(954\) −1.93391e15 −0.0792355
\(955\) −1.41009e15 −0.0574419
\(956\) 1.03738e16 0.420165
\(957\) −3.05890e15 −0.123183
\(958\) 2.13242e15 0.0853814
\(959\) 2.43872e16 0.970867
\(960\) −3.58748e14 −0.0142003
\(961\) 6.94656e16 2.73396
\(962\) −6.86884e15 −0.268795
\(963\) 9.00078e15 0.350216
\(964\) −2.28677e16 −0.884704
\(965\) 1.79050e15 0.0688768
\(966\) 9.61897e15 0.367921
\(967\) −4.20715e16 −1.60008 −0.800042 0.599944i \(-0.795189\pi\)
−0.800042 + 0.599944i \(0.795189\pi\)
\(968\) −4.32789e15 −0.163667
\(969\) −3.30115e16 −1.24132
\(970\) −2.42433e15 −0.0906456
\(971\) −4.86896e16 −1.81022 −0.905108 0.425181i \(-0.860210\pi\)
−0.905108 + 0.425181i \(0.860210\pi\)
\(972\) −1.70677e16 −0.630974
\(973\) −4.32418e16 −1.58958
\(974\) −1.09013e16 −0.398479
\(975\) −1.08725e16 −0.395187
\(976\) 3.97311e15 0.143601
\(977\) −3.15141e15 −0.113262 −0.0566311 0.998395i \(-0.518036\pi\)
−0.0566311 + 0.998395i \(0.518036\pi\)
\(978\) −1.14013e16 −0.407464
\(979\) 1.40431e16 0.499068
\(980\) −2.50422e13 −0.000884972 0
\(981\) −9.49148e15 −0.333545
\(982\) 2.14632e16 0.750036
\(983\) 1.18477e16 0.411709 0.205855 0.978583i \(-0.434003\pi\)
0.205855 + 0.978583i \(0.434003\pi\)
\(984\) −2.48897e16 −0.860096
\(985\) 1.15864e15 0.0398151
\(986\) −3.07242e15 −0.104992
\(987\) −3.94827e16 −1.34172
\(988\) 1.78114e16 0.601915
\(989\) −1.12604e16 −0.378419
\(990\) 7.56961e14 0.0252976
\(991\) 3.30955e16 1.09993 0.549963 0.835189i \(-0.314642\pi\)
0.549963 + 0.835189i \(0.314642\pi\)
\(992\) 5.99852e16 1.98258
\(993\) −3.97891e16 −1.30780
\(994\) −1.47731e16 −0.482889
\(995\) −2.58282e15 −0.0839589
\(996\) 3.09463e15 0.100042
\(997\) 1.17372e15 0.0377346 0.0188673 0.999822i \(-0.493994\pi\)
0.0188673 + 0.999822i \(0.493994\pi\)
\(998\) −2.79013e16 −0.892084
\(999\) −3.42883e16 −1.09028
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 29.12.a.a.1.6 11
3.2 odd 2 261.12.a.a.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.12.a.a.1.6 11 1.1 even 1 trivial
261.12.a.a.1.6 11 3.2 odd 2