Properties

Label 177.12.a.c.1.11
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-11.8207 q^{2} -243.000 q^{3} -1908.27 q^{4} -8832.11 q^{5} +2872.42 q^{6} +19217.9 q^{7} +46765.7 q^{8} +59049.0 q^{9} +104401. q^{10} +413614. q^{11} +463710. q^{12} -2.15678e6 q^{13} -227168. q^{14} +2.14620e6 q^{15} +3.35534e6 q^{16} -6.59896e6 q^{17} -697998. q^{18} +772293. q^{19} +1.68541e7 q^{20} -4.66995e6 q^{21} -4.88919e6 q^{22} +4.19889e7 q^{23} -1.13641e7 q^{24} +2.91781e7 q^{25} +2.54945e7 q^{26} -1.43489e7 q^{27} -3.66730e7 q^{28} -4.25227e7 q^{29} -2.53695e7 q^{30} -6.05374e7 q^{31} -1.35439e8 q^{32} -1.00508e8 q^{33} +7.80040e7 q^{34} -1.69735e8 q^{35} -1.12682e8 q^{36} -5.85646e8 q^{37} -9.12901e6 q^{38} +5.24097e8 q^{39} -4.13040e8 q^{40} -2.62066e8 q^{41} +5.52019e7 q^{42} -1.36297e9 q^{43} -7.89288e8 q^{44} -5.21527e8 q^{45} -4.96337e8 q^{46} -9.55377e8 q^{47} -8.15348e8 q^{48} -1.60800e9 q^{49} -3.44904e8 q^{50} +1.60355e9 q^{51} +4.11572e9 q^{52} -3.76739e9 q^{53} +1.69614e8 q^{54} -3.65309e9 q^{55} +8.98740e8 q^{56} -1.87667e8 q^{57} +5.02646e8 q^{58} -7.14924e8 q^{59} -4.09554e9 q^{60} -1.01945e9 q^{61} +7.15592e8 q^{62} +1.13480e9 q^{63} -5.27076e9 q^{64} +1.90489e10 q^{65} +1.18807e9 q^{66} -1.22341e10 q^{67} +1.25926e10 q^{68} -1.02033e10 q^{69} +2.00638e9 q^{70} -2.13614e10 q^{71} +2.76147e9 q^{72} +7.12398e8 q^{73} +6.92272e9 q^{74} -7.09028e9 q^{75} -1.47374e9 q^{76} +7.94880e9 q^{77} -6.19517e9 q^{78} +4.14934e10 q^{79} -2.96347e10 q^{80} +3.48678e9 q^{81} +3.09779e9 q^{82} -4.23677e9 q^{83} +8.91154e9 q^{84} +5.82828e10 q^{85} +1.61112e10 q^{86} +1.03330e10 q^{87} +1.93430e10 q^{88} +7.44660e9 q^{89} +6.16480e9 q^{90} -4.14487e10 q^{91} -8.01263e10 q^{92} +1.47106e10 q^{93} +1.12932e10 q^{94} -6.82098e9 q^{95} +3.29116e10 q^{96} +1.19796e11 q^{97} +1.90076e10 q^{98} +2.44235e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.8207 −0.261202 −0.130601 0.991435i \(-0.541691\pi\)
−0.130601 + 0.991435i \(0.541691\pi\)
\(3\) −243.000 −0.577350
\(4\) −1908.27 −0.931773
\(5\) −8832.11 −1.26395 −0.631975 0.774989i \(-0.717755\pi\)
−0.631975 + 0.774989i \(0.717755\pi\)
\(6\) 2872.42 0.150805
\(7\) 19217.9 0.432182 0.216091 0.976373i \(-0.430669\pi\)
0.216091 + 0.976373i \(0.430669\pi\)
\(8\) 46765.7 0.504583
\(9\) 59049.0 0.333333
\(10\) 104401. 0.330146
\(11\) 413614. 0.774347 0.387173 0.922007i \(-0.373451\pi\)
0.387173 + 0.922007i \(0.373451\pi\)
\(12\) 463710. 0.537960
\(13\) −2.15678e6 −1.61108 −0.805540 0.592542i \(-0.798124\pi\)
−0.805540 + 0.592542i \(0.798124\pi\)
\(14\) −227168. −0.112887
\(15\) 2.14620e6 0.729741
\(16\) 3.35534e6 0.799975
\(17\) −6.59896e6 −1.12721 −0.563607 0.826043i \(-0.690587\pi\)
−0.563607 + 0.826043i \(0.690587\pi\)
\(18\) −697998. −0.0870674
\(19\) 772293. 0.0715545 0.0357773 0.999360i \(-0.488609\pi\)
0.0357773 + 0.999360i \(0.488609\pi\)
\(20\) 1.68541e7 1.17771
\(21\) −4.66995e6 −0.249521
\(22\) −4.88919e6 −0.202261
\(23\) 4.19889e7 1.36029 0.680145 0.733078i \(-0.261917\pi\)
0.680145 + 0.733078i \(0.261917\pi\)
\(24\) −1.13641e7 −0.291321
\(25\) 2.91781e7 0.597568
\(26\) 2.54945e7 0.420817
\(27\) −1.43489e7 −0.192450
\(28\) −3.66730e7 −0.402696
\(29\) −4.25227e7 −0.384974 −0.192487 0.981299i \(-0.561655\pi\)
−0.192487 + 0.981299i \(0.561655\pi\)
\(30\) −2.53695e7 −0.190610
\(31\) −6.05374e7 −0.379782 −0.189891 0.981805i \(-0.560813\pi\)
−0.189891 + 0.981805i \(0.560813\pi\)
\(32\) −1.35439e8 −0.713538
\(33\) −1.00508e8 −0.447069
\(34\) 7.80040e7 0.294431
\(35\) −1.69735e8 −0.546256
\(36\) −1.12682e8 −0.310591
\(37\) −5.85646e8 −1.38843 −0.694217 0.719765i \(-0.744249\pi\)
−0.694217 + 0.719765i \(0.744249\pi\)
\(38\) −9.12901e6 −0.0186902
\(39\) 5.24097e8 0.930157
\(40\) −4.13040e8 −0.637768
\(41\) −2.62066e8 −0.353264 −0.176632 0.984277i \(-0.556520\pi\)
−0.176632 + 0.984277i \(0.556520\pi\)
\(42\) 5.52019e7 0.0651753
\(43\) −1.36297e9 −1.41387 −0.706935 0.707278i \(-0.749923\pi\)
−0.706935 + 0.707278i \(0.749923\pi\)
\(44\) −7.89288e8 −0.721516
\(45\) −5.21527e8 −0.421316
\(46\) −4.96337e8 −0.355311
\(47\) −9.55377e8 −0.607626 −0.303813 0.952732i \(-0.598260\pi\)
−0.303813 + 0.952732i \(0.598260\pi\)
\(48\) −8.15348e8 −0.461866
\(49\) −1.60800e9 −0.813219
\(50\) −3.44904e8 −0.156086
\(51\) 1.60355e9 0.650797
\(52\) 4.11572e9 1.50116
\(53\) −3.76739e9 −1.23744 −0.618719 0.785613i \(-0.712348\pi\)
−0.618719 + 0.785613i \(0.712348\pi\)
\(54\) 1.69614e8 0.0502684
\(55\) −3.65309e9 −0.978735
\(56\) 8.98740e8 0.218072
\(57\) −1.87667e8 −0.0413120
\(58\) 5.02646e8 0.100556
\(59\) −7.14924e8 −0.130189
\(60\) −4.09554e9 −0.679954
\(61\) −1.01945e9 −0.154545 −0.0772723 0.997010i \(-0.524621\pi\)
−0.0772723 + 0.997010i \(0.524621\pi\)
\(62\) 7.15592e8 0.0991999
\(63\) 1.13480e9 0.144061
\(64\) −5.27076e9 −0.613598
\(65\) 1.90489e10 2.03632
\(66\) 1.18807e9 0.116775
\(67\) −1.22341e10 −1.10703 −0.553514 0.832840i \(-0.686714\pi\)
−0.553514 + 0.832840i \(0.686714\pi\)
\(68\) 1.25926e10 1.05031
\(69\) −1.02033e10 −0.785364
\(70\) 2.00638e9 0.142683
\(71\) −2.13614e10 −1.40510 −0.702551 0.711633i \(-0.747956\pi\)
−0.702551 + 0.711633i \(0.747956\pi\)
\(72\) 2.76147e9 0.168194
\(73\) 7.12398e8 0.0402205 0.0201102 0.999798i \(-0.493598\pi\)
0.0201102 + 0.999798i \(0.493598\pi\)
\(74\) 6.92272e9 0.362662
\(75\) −7.09028e9 −0.345006
\(76\) −1.47374e9 −0.0666726
\(77\) 7.94880e9 0.334659
\(78\) −6.19517e9 −0.242959
\(79\) 4.14934e10 1.51716 0.758578 0.651583i \(-0.225895\pi\)
0.758578 + 0.651583i \(0.225895\pi\)
\(80\) −2.96347e10 −1.01113
\(81\) 3.48678e9 0.111111
\(82\) 3.09779e9 0.0922733
\(83\) −4.23677e9 −0.118061 −0.0590304 0.998256i \(-0.518801\pi\)
−0.0590304 + 0.998256i \(0.518801\pi\)
\(84\) 8.91154e9 0.232497
\(85\) 5.82828e10 1.42474
\(86\) 1.61112e10 0.369306
\(87\) 1.03330e10 0.222265
\(88\) 1.93430e10 0.390722
\(89\) 7.44660e9 0.141356 0.0706778 0.997499i \(-0.477484\pi\)
0.0706778 + 0.997499i \(0.477484\pi\)
\(90\) 6.16480e9 0.110049
\(91\) −4.14487e10 −0.696280
\(92\) −8.01263e10 −1.26748
\(93\) 1.47106e10 0.219267
\(94\) 1.12932e10 0.158713
\(95\) −6.82098e9 −0.0904413
\(96\) 3.29116e10 0.411962
\(97\) 1.19796e11 1.41644 0.708218 0.705993i \(-0.249499\pi\)
0.708218 + 0.705993i \(0.249499\pi\)
\(98\) 1.90076e10 0.212414
\(99\) 2.44235e10 0.258116
\(100\) −5.56798e10 −0.556798
\(101\) −7.85276e10 −0.743455 −0.371728 0.928342i \(-0.621234\pi\)
−0.371728 + 0.928342i \(0.621234\pi\)
\(102\) −1.89550e10 −0.169990
\(103\) 6.24296e10 0.530622 0.265311 0.964163i \(-0.414525\pi\)
0.265311 + 0.964163i \(0.414525\pi\)
\(104\) −1.00863e11 −0.812924
\(105\) 4.12455e10 0.315381
\(106\) 4.45330e10 0.323221
\(107\) −2.62553e11 −1.80970 −0.904848 0.425735i \(-0.860016\pi\)
−0.904848 + 0.425735i \(0.860016\pi\)
\(108\) 2.73816e10 0.179320
\(109\) −2.15266e11 −1.34008 −0.670040 0.742325i \(-0.733723\pi\)
−0.670040 + 0.742325i \(0.733723\pi\)
\(110\) 4.31819e10 0.255648
\(111\) 1.42312e11 0.801613
\(112\) 6.44826e10 0.345735
\(113\) 1.01778e11 0.519662 0.259831 0.965654i \(-0.416333\pi\)
0.259831 + 0.965654i \(0.416333\pi\)
\(114\) 2.21835e9 0.0107908
\(115\) −3.70851e11 −1.71934
\(116\) 8.11449e10 0.358709
\(117\) −1.27356e11 −0.537026
\(118\) 8.45087e9 0.0340056
\(119\) −1.26818e11 −0.487162
\(120\) 1.00369e11 0.368215
\(121\) −1.14235e11 −0.400387
\(122\) 1.20506e10 0.0403674
\(123\) 6.36820e10 0.203957
\(124\) 1.15522e11 0.353871
\(125\) 1.73551e11 0.508654
\(126\) −1.34141e10 −0.0376290
\(127\) 6.78964e11 1.82359 0.911793 0.410651i \(-0.134698\pi\)
0.911793 + 0.410651i \(0.134698\pi\)
\(128\) 3.39682e11 0.873811
\(129\) 3.31202e11 0.816298
\(130\) −2.25171e11 −0.531892
\(131\) 3.24480e11 0.734846 0.367423 0.930054i \(-0.380240\pi\)
0.367423 + 0.930054i \(0.380240\pi\)
\(132\) 1.91797e11 0.416567
\(133\) 1.48418e10 0.0309246
\(134\) 1.44615e11 0.289158
\(135\) 1.26731e11 0.243247
\(136\) −3.08605e11 −0.568773
\(137\) 6.17045e11 1.09233 0.546165 0.837678i \(-0.316087\pi\)
0.546165 + 0.837678i \(0.316087\pi\)
\(138\) 1.20610e11 0.205139
\(139\) −7.24498e11 −1.18428 −0.592142 0.805834i \(-0.701717\pi\)
−0.592142 + 0.805834i \(0.701717\pi\)
\(140\) 3.23900e11 0.508987
\(141\) 2.32157e11 0.350813
\(142\) 2.52505e11 0.367016
\(143\) −8.92073e11 −1.24753
\(144\) 1.98129e11 0.266658
\(145\) 3.75565e11 0.486588
\(146\) −8.42102e9 −0.0105057
\(147\) 3.90744e11 0.469512
\(148\) 1.11757e12 1.29371
\(149\) −6.77062e11 −0.755273 −0.377636 0.925954i \(-0.623263\pi\)
−0.377636 + 0.925954i \(0.623263\pi\)
\(150\) 8.38117e10 0.0901162
\(151\) −1.64182e12 −1.70197 −0.850987 0.525187i \(-0.823995\pi\)
−0.850987 + 0.525187i \(0.823995\pi\)
\(152\) 3.61168e10 0.0361052
\(153\) −3.89662e11 −0.375738
\(154\) −9.39600e10 −0.0874136
\(155\) 5.34673e11 0.480025
\(156\) −1.00012e12 −0.866696
\(157\) 7.23872e10 0.0605639 0.0302819 0.999541i \(-0.490359\pi\)
0.0302819 + 0.999541i \(0.490359\pi\)
\(158\) −4.90479e11 −0.396284
\(159\) 9.15475e11 0.714435
\(160\) 1.19621e12 0.901876
\(161\) 8.06939e11 0.587893
\(162\) −4.12161e10 −0.0290225
\(163\) −4.95381e11 −0.337216 −0.168608 0.985683i \(-0.553927\pi\)
−0.168608 + 0.985683i \(0.553927\pi\)
\(164\) 5.00093e11 0.329162
\(165\) 8.87700e11 0.565073
\(166\) 5.00815e10 0.0308377
\(167\) 8.26483e11 0.492372 0.246186 0.969223i \(-0.420823\pi\)
0.246186 + 0.969223i \(0.420823\pi\)
\(168\) −2.18394e11 −0.125904
\(169\) 2.85953e12 1.59558
\(170\) −6.88940e11 −0.372145
\(171\) 4.56031e10 0.0238515
\(172\) 2.60092e12 1.31741
\(173\) 2.96785e11 0.145609 0.0728046 0.997346i \(-0.476805\pi\)
0.0728046 + 0.997346i \(0.476805\pi\)
\(174\) −1.22143e11 −0.0580561
\(175\) 5.60742e11 0.258258
\(176\) 1.38782e12 0.619458
\(177\) 1.73727e11 0.0751646
\(178\) −8.80237e10 −0.0369224
\(179\) −2.19982e12 −0.894737 −0.447369 0.894350i \(-0.647639\pi\)
−0.447369 + 0.894350i \(0.647639\pi\)
\(180\) 9.95216e11 0.392571
\(181\) 2.19331e12 0.839206 0.419603 0.907708i \(-0.362169\pi\)
0.419603 + 0.907708i \(0.362169\pi\)
\(182\) 4.89951e11 0.181870
\(183\) 2.47727e11 0.0892263
\(184\) 1.96364e12 0.686380
\(185\) 5.17249e12 1.75491
\(186\) −1.73889e11 −0.0572731
\(187\) −2.72942e12 −0.872854
\(188\) 1.82312e12 0.566170
\(189\) −2.75756e11 −0.0831735
\(190\) 8.06284e10 0.0236234
\(191\) −1.37402e12 −0.391120 −0.195560 0.980692i \(-0.562652\pi\)
−0.195560 + 0.980692i \(0.562652\pi\)
\(192\) 1.28080e12 0.354261
\(193\) −5.84943e12 −1.57235 −0.786174 0.618006i \(-0.787941\pi\)
−0.786174 + 0.618006i \(0.787941\pi\)
\(194\) −1.41607e12 −0.369976
\(195\) −4.62888e12 −1.17567
\(196\) 3.06850e12 0.757735
\(197\) 3.23289e12 0.776295 0.388148 0.921597i \(-0.373115\pi\)
0.388148 + 0.921597i \(0.373115\pi\)
\(198\) −2.88702e11 −0.0674203
\(199\) −7.57931e12 −1.72162 −0.860811 0.508924i \(-0.830043\pi\)
−0.860811 + 0.508924i \(0.830043\pi\)
\(200\) 1.36454e12 0.301523
\(201\) 2.97287e12 0.639143
\(202\) 9.28248e11 0.194192
\(203\) −8.17197e11 −0.166379
\(204\) −3.06000e12 −0.606396
\(205\) 2.31460e12 0.446508
\(206\) −7.37958e11 −0.138600
\(207\) 2.47940e12 0.453430
\(208\) −7.23672e12 −1.28882
\(209\) 3.19431e11 0.0554080
\(210\) −4.87549e11 −0.0823782
\(211\) 2.14129e12 0.352469 0.176235 0.984348i \(-0.443608\pi\)
0.176235 + 0.984348i \(0.443608\pi\)
\(212\) 7.18920e12 1.15301
\(213\) 5.19081e12 0.811236
\(214\) 3.10354e12 0.472696
\(215\) 1.20379e13 1.78706
\(216\) −6.71037e11 −0.0971071
\(217\) −1.16340e12 −0.164135
\(218\) 2.54459e12 0.350032
\(219\) −1.73113e11 −0.0232213
\(220\) 6.97108e12 0.911959
\(221\) 1.42325e13 1.81603
\(222\) −1.68222e12 −0.209383
\(223\) 5.58025e12 0.677606 0.338803 0.940857i \(-0.389978\pi\)
0.338803 + 0.940857i \(0.389978\pi\)
\(224\) −2.60285e12 −0.308379
\(225\) 1.72294e12 0.199189
\(226\) −1.20308e12 −0.135737
\(227\) −4.01000e12 −0.441572 −0.220786 0.975322i \(-0.570862\pi\)
−0.220786 + 0.975322i \(0.570862\pi\)
\(228\) 3.58120e11 0.0384934
\(229\) −2.06203e11 −0.0216372 −0.0108186 0.999941i \(-0.503444\pi\)
−0.0108186 + 0.999941i \(0.503444\pi\)
\(230\) 4.38370e12 0.449095
\(231\) −1.93156e12 −0.193215
\(232\) −1.98860e12 −0.194252
\(233\) −6.77586e12 −0.646408 −0.323204 0.946329i \(-0.604760\pi\)
−0.323204 + 0.946329i \(0.604760\pi\)
\(234\) 1.50543e12 0.140272
\(235\) 8.43800e12 0.768009
\(236\) 1.36427e12 0.121307
\(237\) −1.00829e13 −0.875930
\(238\) 1.49907e12 0.127248
\(239\) −1.19720e12 −0.0993066 −0.0496533 0.998767i \(-0.515812\pi\)
−0.0496533 + 0.998767i \(0.515812\pi\)
\(240\) 7.20124e12 0.583775
\(241\) 2.15690e13 1.70898 0.854490 0.519468i \(-0.173870\pi\)
0.854490 + 0.519468i \(0.173870\pi\)
\(242\) 1.35033e12 0.104582
\(243\) −8.47289e11 −0.0641500
\(244\) 1.94540e12 0.144001
\(245\) 1.42020e13 1.02787
\(246\) −7.52763e11 −0.0532740
\(247\) −1.66566e12 −0.115280
\(248\) −2.83108e12 −0.191632
\(249\) 1.02954e12 0.0681625
\(250\) −2.05149e12 −0.132862
\(251\) −1.46993e13 −0.931306 −0.465653 0.884967i \(-0.654181\pi\)
−0.465653 + 0.884967i \(0.654181\pi\)
\(252\) −2.16550e12 −0.134232
\(253\) 1.73672e13 1.05334
\(254\) −8.02580e12 −0.476324
\(255\) −1.41627e13 −0.822575
\(256\) 6.77926e12 0.385356
\(257\) −1.15394e13 −0.642021 −0.321011 0.947076i \(-0.604023\pi\)
−0.321011 + 0.947076i \(0.604023\pi\)
\(258\) −3.91502e12 −0.213219
\(259\) −1.12549e13 −0.600057
\(260\) −3.63505e13 −1.89739
\(261\) −2.51092e12 −0.128325
\(262\) −3.83557e12 −0.191943
\(263\) 2.68522e13 1.31590 0.657951 0.753060i \(-0.271423\pi\)
0.657951 + 0.753060i \(0.271423\pi\)
\(264\) −4.70034e12 −0.225584
\(265\) 3.32740e13 1.56406
\(266\) −1.75440e11 −0.00807757
\(267\) −1.80952e12 −0.0816117
\(268\) 2.33459e13 1.03150
\(269\) −2.32608e12 −0.100690 −0.0503451 0.998732i \(-0.516032\pi\)
−0.0503451 + 0.998732i \(0.516032\pi\)
\(270\) −1.49805e12 −0.0635367
\(271\) −1.78154e13 −0.740398 −0.370199 0.928952i \(-0.620711\pi\)
−0.370199 + 0.928952i \(0.620711\pi\)
\(272\) −2.21417e13 −0.901743
\(273\) 1.00720e13 0.401997
\(274\) −7.29387e12 −0.285319
\(275\) 1.20685e13 0.462724
\(276\) 1.94707e13 0.731781
\(277\) 1.49786e13 0.551866 0.275933 0.961177i \(-0.411013\pi\)
0.275933 + 0.961177i \(0.411013\pi\)
\(278\) 8.56404e12 0.309337
\(279\) −3.57467e12 −0.126594
\(280\) −7.93777e12 −0.275632
\(281\) −3.35026e13 −1.14076 −0.570380 0.821381i \(-0.693204\pi\)
−0.570380 + 0.821381i \(0.693204\pi\)
\(282\) −2.74424e12 −0.0916331
\(283\) −5.75554e12 −0.188478 −0.0942390 0.995550i \(-0.530042\pi\)
−0.0942390 + 0.995550i \(0.530042\pi\)
\(284\) 4.07633e13 1.30924
\(285\) 1.65750e12 0.0522163
\(286\) 1.05449e13 0.325858
\(287\) −5.03636e12 −0.152674
\(288\) −7.99751e12 −0.237846
\(289\) 9.27436e12 0.270611
\(290\) −4.43943e12 −0.127098
\(291\) −2.91104e13 −0.817780
\(292\) −1.35945e12 −0.0374764
\(293\) −2.09331e13 −0.566319 −0.283159 0.959073i \(-0.591383\pi\)
−0.283159 + 0.959073i \(0.591383\pi\)
\(294\) −4.61885e12 −0.122637
\(295\) 6.31429e12 0.164552
\(296\) −2.73882e13 −0.700581
\(297\) −5.93491e12 −0.149023
\(298\) 8.00331e12 0.197279
\(299\) −9.05607e13 −2.19154
\(300\) 1.35302e13 0.321467
\(301\) −2.61934e13 −0.611050
\(302\) 1.94074e13 0.444559
\(303\) 1.90822e13 0.429234
\(304\) 2.59130e12 0.0572418
\(305\) 9.00394e12 0.195336
\(306\) 4.60606e12 0.0981435
\(307\) 4.90108e13 1.02572 0.512862 0.858471i \(-0.328585\pi\)
0.512862 + 0.858471i \(0.328585\pi\)
\(308\) −1.51685e13 −0.311826
\(309\) −1.51704e13 −0.306355
\(310\) −6.32019e12 −0.125384
\(311\) −3.13688e13 −0.611386 −0.305693 0.952130i \(-0.598888\pi\)
−0.305693 + 0.952130i \(0.598888\pi\)
\(312\) 2.45098e13 0.469342
\(313\) 8.03328e13 1.51147 0.755734 0.654879i \(-0.227280\pi\)
0.755734 + 0.654879i \(0.227280\pi\)
\(314\) −8.55664e11 −0.0158194
\(315\) −1.00227e13 −0.182085
\(316\) −7.91807e13 −1.41364
\(317\) −9.56777e13 −1.67875 −0.839373 0.543556i \(-0.817077\pi\)
−0.839373 + 0.543556i \(0.817077\pi\)
\(318\) −1.08215e13 −0.186612
\(319\) −1.75880e13 −0.298104
\(320\) 4.65520e13 0.775556
\(321\) 6.38003e13 1.04483
\(322\) −9.53855e12 −0.153559
\(323\) −5.09633e12 −0.0806572
\(324\) −6.65373e12 −0.103530
\(325\) −6.29307e13 −0.962729
\(326\) 5.85573e12 0.0880814
\(327\) 5.23098e13 0.773695
\(328\) −1.22557e13 −0.178251
\(329\) −1.83603e13 −0.262605
\(330\) −1.04932e13 −0.147598
\(331\) 4.55274e13 0.629823 0.314911 0.949121i \(-0.398025\pi\)
0.314911 + 0.949121i \(0.398025\pi\)
\(332\) 8.08492e12 0.110006
\(333\) −3.45818e13 −0.462812
\(334\) −9.76958e12 −0.128609
\(335\) 1.08053e14 1.39923
\(336\) −1.56693e13 −0.199610
\(337\) −1.39734e13 −0.175121 −0.0875603 0.996159i \(-0.527907\pi\)
−0.0875603 + 0.996159i \(0.527907\pi\)
\(338\) −3.38015e13 −0.416768
\(339\) −2.47320e13 −0.300027
\(340\) −1.11219e14 −1.32754
\(341\) −2.50391e13 −0.294083
\(342\) −5.39059e11 −0.00623006
\(343\) −6.89025e13 −0.783641
\(344\) −6.37403e13 −0.713415
\(345\) 9.01168e13 0.992660
\(346\) −3.50820e12 −0.0380334
\(347\) −5.88577e13 −0.628046 −0.314023 0.949415i \(-0.601677\pi\)
−0.314023 + 0.949415i \(0.601677\pi\)
\(348\) −1.97182e13 −0.207101
\(349\) 4.78263e13 0.494455 0.247227 0.968957i \(-0.420481\pi\)
0.247227 + 0.968957i \(0.420481\pi\)
\(350\) −6.62834e12 −0.0674575
\(351\) 3.09474e13 0.310052
\(352\) −5.60193e13 −0.552526
\(353\) −8.23195e13 −0.799359 −0.399680 0.916655i \(-0.630879\pi\)
−0.399680 + 0.916655i \(0.630879\pi\)
\(354\) −2.05356e12 −0.0196332
\(355\) 1.88666e14 1.77598
\(356\) −1.42101e13 −0.131711
\(357\) 3.08168e13 0.281263
\(358\) 2.60033e13 0.233707
\(359\) −2.06967e14 −1.83182 −0.915909 0.401386i \(-0.868529\pi\)
−0.915909 + 0.401386i \(0.868529\pi\)
\(360\) −2.43896e13 −0.212589
\(361\) −1.15894e14 −0.994880
\(362\) −2.59264e13 −0.219202
\(363\) 2.77591e13 0.231164
\(364\) 7.90955e13 0.648775
\(365\) −6.29198e12 −0.0508366
\(366\) −2.92830e12 −0.0233061
\(367\) 1.12211e14 0.879773 0.439886 0.898053i \(-0.355019\pi\)
0.439886 + 0.898053i \(0.355019\pi\)
\(368\) 1.40887e14 1.08820
\(369\) −1.54747e13 −0.117755
\(370\) −6.11422e13 −0.458386
\(371\) −7.24013e13 −0.534798
\(372\) −2.80718e13 −0.204307
\(373\) 8.02486e13 0.575491 0.287746 0.957707i \(-0.407094\pi\)
0.287746 + 0.957707i \(0.407094\pi\)
\(374\) 3.22636e13 0.227991
\(375\) −4.21730e13 −0.293672
\(376\) −4.46789e13 −0.306598
\(377\) 9.17120e13 0.620224
\(378\) 3.25962e12 0.0217251
\(379\) 2.22349e13 0.146056 0.0730279 0.997330i \(-0.476734\pi\)
0.0730279 + 0.997330i \(0.476734\pi\)
\(380\) 1.30163e13 0.0842708
\(381\) −1.64988e14 −1.05285
\(382\) 1.62418e13 0.102161
\(383\) 2.88958e14 1.79160 0.895800 0.444457i \(-0.146603\pi\)
0.895800 + 0.444457i \(0.146603\pi\)
\(384\) −8.25427e13 −0.504495
\(385\) −7.02047e13 −0.422992
\(386\) 6.91441e13 0.410700
\(387\) −8.04820e13 −0.471290
\(388\) −2.28603e14 −1.31980
\(389\) −2.50047e14 −1.42331 −0.711654 0.702530i \(-0.752054\pi\)
−0.711654 + 0.702530i \(0.752054\pi\)
\(390\) 5.47164e13 0.307088
\(391\) −2.77083e14 −1.53334
\(392\) −7.51992e13 −0.410336
\(393\) −7.88487e13 −0.424263
\(394\) −3.82149e13 −0.202770
\(395\) −3.66474e14 −1.91761
\(396\) −4.66067e13 −0.240505
\(397\) 1.55567e14 0.791715 0.395857 0.918312i \(-0.370447\pi\)
0.395857 + 0.918312i \(0.370447\pi\)
\(398\) 8.95924e13 0.449691
\(399\) −3.60657e12 −0.0178543
\(400\) 9.79024e13 0.478039
\(401\) 5.47621e13 0.263746 0.131873 0.991267i \(-0.457901\pi\)
0.131873 + 0.991267i \(0.457901\pi\)
\(402\) −3.51413e13 −0.166946
\(403\) 1.30566e14 0.611859
\(404\) 1.49852e14 0.692732
\(405\) −3.07957e13 −0.140439
\(406\) 9.65981e12 0.0434586
\(407\) −2.42231e14 −1.07513
\(408\) 7.49910e13 0.328381
\(409\) 2.94979e14 1.27442 0.637212 0.770689i \(-0.280088\pi\)
0.637212 + 0.770689i \(0.280088\pi\)
\(410\) −2.73600e13 −0.116629
\(411\) −1.49942e14 −0.630657
\(412\) −1.19133e14 −0.494420
\(413\) −1.37393e13 −0.0562653
\(414\) −2.93082e13 −0.118437
\(415\) 3.74197e13 0.149223
\(416\) 2.92111e14 1.14957
\(417\) 1.76053e14 0.683746
\(418\) −3.77588e12 −0.0144727
\(419\) 9.05972e13 0.342719 0.171359 0.985209i \(-0.445184\pi\)
0.171359 + 0.985209i \(0.445184\pi\)
\(420\) −7.87077e13 −0.293864
\(421\) −5.24734e13 −0.193369 −0.0966847 0.995315i \(-0.530824\pi\)
−0.0966847 + 0.995315i \(0.530824\pi\)
\(422\) −2.53114e13 −0.0920657
\(423\) −5.64141e13 −0.202542
\(424\) −1.76185e14 −0.624390
\(425\) −1.92545e14 −0.673586
\(426\) −6.13588e13 −0.211897
\(427\) −1.95918e13 −0.0667914
\(428\) 5.01022e14 1.68623
\(429\) 2.16774e14 0.720264
\(430\) −1.42296e14 −0.466784
\(431\) −2.30277e14 −0.745806 −0.372903 0.927870i \(-0.621638\pi\)
−0.372903 + 0.927870i \(0.621638\pi\)
\(432\) −4.81455e13 −0.153955
\(433\) 4.93132e14 1.55697 0.778485 0.627664i \(-0.215989\pi\)
0.778485 + 0.627664i \(0.215989\pi\)
\(434\) 1.37522e13 0.0428724
\(435\) −9.12624e13 −0.280932
\(436\) 4.10787e14 1.24865
\(437\) 3.24277e13 0.0973349
\(438\) 2.04631e12 0.00606545
\(439\) −3.84393e14 −1.12518 −0.562589 0.826737i \(-0.690195\pi\)
−0.562589 + 0.826737i \(0.690195\pi\)
\(440\) −1.70839e14 −0.493853
\(441\) −9.49507e13 −0.271073
\(442\) −1.68237e14 −0.474351
\(443\) 6.90847e14 1.92381 0.961903 0.273390i \(-0.0881448\pi\)
0.961903 + 0.273390i \(0.0881448\pi\)
\(444\) −2.71570e14 −0.746922
\(445\) −6.57692e13 −0.178666
\(446\) −6.59622e13 −0.176992
\(447\) 1.64526e14 0.436057
\(448\) −1.01293e14 −0.265186
\(449\) 1.63534e14 0.422915 0.211457 0.977387i \(-0.432179\pi\)
0.211457 + 0.977387i \(0.432179\pi\)
\(450\) −2.03663e13 −0.0520286
\(451\) −1.08394e14 −0.273549
\(452\) −1.94219e14 −0.484207
\(453\) 3.98963e14 0.982635
\(454\) 4.74008e13 0.115340
\(455\) 3.66080e14 0.880062
\(456\) −8.77639e12 −0.0208454
\(457\) −3.63750e14 −0.853620 −0.426810 0.904341i \(-0.640363\pi\)
−0.426810 + 0.904341i \(0.640363\pi\)
\(458\) 2.43746e12 0.00565167
\(459\) 9.46878e13 0.216932
\(460\) 7.07684e14 1.60203
\(461\) −4.90161e14 −1.09644 −0.548218 0.836335i \(-0.684694\pi\)
−0.548218 + 0.836335i \(0.684694\pi\)
\(462\) 2.28323e13 0.0504683
\(463\) 3.68532e13 0.0804971 0.0402485 0.999190i \(-0.487185\pi\)
0.0402485 + 0.999190i \(0.487185\pi\)
\(464\) −1.42678e14 −0.307970
\(465\) −1.29926e14 −0.277143
\(466\) 8.00951e13 0.168843
\(467\) −1.25519e14 −0.261496 −0.130748 0.991416i \(-0.541738\pi\)
−0.130748 + 0.991416i \(0.541738\pi\)
\(468\) 2.43029e14 0.500387
\(469\) −2.35113e14 −0.478438
\(470\) −9.97427e13 −0.200605
\(471\) −1.75901e13 −0.0349666
\(472\) −3.34340e13 −0.0656911
\(473\) −5.63743e14 −1.09483
\(474\) 1.19186e14 0.228795
\(475\) 2.25340e13 0.0427587
\(476\) 2.42004e14 0.453924
\(477\) −2.22461e14 −0.412479
\(478\) 1.41517e13 0.0259391
\(479\) 1.91334e14 0.346694 0.173347 0.984861i \(-0.444542\pi\)
0.173347 + 0.984861i \(0.444542\pi\)
\(480\) −2.90679e14 −0.520699
\(481\) 1.26311e15 2.23688
\(482\) −2.54960e14 −0.446389
\(483\) −1.96086e14 −0.339420
\(484\) 2.17992e14 0.373070
\(485\) −1.05805e15 −1.79030
\(486\) 1.00155e13 0.0167561
\(487\) 1.83560e14 0.303646 0.151823 0.988408i \(-0.451486\pi\)
0.151823 + 0.988408i \(0.451486\pi\)
\(488\) −4.76755e13 −0.0779806
\(489\) 1.20378e14 0.194692
\(490\) −1.67877e14 −0.268481
\(491\) 1.00643e15 1.59160 0.795799 0.605561i \(-0.207051\pi\)
0.795799 + 0.605561i \(0.207051\pi\)
\(492\) −1.21523e14 −0.190042
\(493\) 2.80605e14 0.433948
\(494\) 1.96892e13 0.0301114
\(495\) −2.15711e14 −0.326245
\(496\) −2.03124e14 −0.303816
\(497\) −4.10521e14 −0.607260
\(498\) −1.21698e13 −0.0178042
\(499\) 2.56147e14 0.370627 0.185313 0.982679i \(-0.440670\pi\)
0.185313 + 0.982679i \(0.440670\pi\)
\(500\) −3.31183e14 −0.473951
\(501\) −2.00835e14 −0.284271
\(502\) 1.73756e14 0.243259
\(503\) 1.31881e15 1.82624 0.913121 0.407689i \(-0.133665\pi\)
0.913121 + 0.407689i \(0.133665\pi\)
\(504\) 5.30697e13 0.0726906
\(505\) 6.93565e14 0.939689
\(506\) −2.05292e14 −0.275134
\(507\) −6.94865e14 −0.921206
\(508\) −1.29565e15 −1.69917
\(509\) 9.41159e14 1.22100 0.610499 0.792017i \(-0.290969\pi\)
0.610499 + 0.792017i \(0.290969\pi\)
\(510\) 1.67413e14 0.214858
\(511\) 1.36908e13 0.0173826
\(512\) −7.75804e14 −0.974467
\(513\) −1.10816e13 −0.0137707
\(514\) 1.36403e14 0.167697
\(515\) −5.51385e14 −0.670680
\(516\) −6.32023e14 −0.760605
\(517\) −3.95157e14 −0.470513
\(518\) 1.33040e14 0.156736
\(519\) −7.21188e13 −0.0840675
\(520\) 8.90836e14 1.02749
\(521\) 1.96814e14 0.224620 0.112310 0.993673i \(-0.464175\pi\)
0.112310 + 0.993673i \(0.464175\pi\)
\(522\) 2.96808e13 0.0335187
\(523\) 1.74097e14 0.194551 0.0972753 0.995258i \(-0.468987\pi\)
0.0972753 + 0.995258i \(0.468987\pi\)
\(524\) −6.19196e14 −0.684710
\(525\) −1.36260e14 −0.149105
\(526\) −3.17411e14 −0.343716
\(527\) 3.99484e14 0.428096
\(528\) −3.37239e14 −0.357644
\(529\) 8.10259e14 0.850389
\(530\) −3.93321e14 −0.408535
\(531\) −4.22156e13 −0.0433963
\(532\) −2.83223e13 −0.0288147
\(533\) 5.65218e14 0.569136
\(534\) 2.13898e13 0.0213171
\(535\) 2.31889e15 2.28736
\(536\) −5.72134e14 −0.558588
\(537\) 5.34556e14 0.516577
\(538\) 2.74958e13 0.0263005
\(539\) −6.65091e14 −0.629713
\(540\) −2.41838e14 −0.226651
\(541\) 1.76596e15 1.63830 0.819152 0.573576i \(-0.194444\pi\)
0.819152 + 0.573576i \(0.194444\pi\)
\(542\) 2.10590e14 0.193394
\(543\) −5.32975e14 −0.484516
\(544\) 8.93753e14 0.804310
\(545\) 1.90126e15 1.69379
\(546\) −1.19058e14 −0.105003
\(547\) −9.13558e14 −0.797638 −0.398819 0.917030i \(-0.630580\pi\)
−0.398819 + 0.917030i \(0.630580\pi\)
\(548\) −1.17749e15 −1.01780
\(549\) −6.01978e13 −0.0515149
\(550\) −1.42657e14 −0.120865
\(551\) −3.28400e13 −0.0275467
\(552\) −4.77165e14 −0.396281
\(553\) 7.97416e14 0.655687
\(554\) −1.77057e14 −0.144149
\(555\) −1.25691e15 −1.01320
\(556\) 1.38254e15 1.10348
\(557\) 2.06801e15 1.63437 0.817183 0.576379i \(-0.195535\pi\)
0.817183 + 0.576379i \(0.195535\pi\)
\(558\) 4.22550e13 0.0330666
\(559\) 2.93962e15 2.27786
\(560\) −5.69518e14 −0.436992
\(561\) 6.63249e14 0.503943
\(562\) 3.96023e14 0.297969
\(563\) −8.03448e14 −0.598634 −0.299317 0.954154i \(-0.596759\pi\)
−0.299317 + 0.954154i \(0.596759\pi\)
\(564\) −4.43018e14 −0.326878
\(565\) −8.98911e14 −0.656826
\(566\) 6.80343e13 0.0492309
\(567\) 6.70087e13 0.0480202
\(568\) −9.98980e14 −0.708991
\(569\) −2.72353e15 −1.91432 −0.957162 0.289553i \(-0.906493\pi\)
−0.957162 + 0.289553i \(0.906493\pi\)
\(570\) −1.95927e13 −0.0136390
\(571\) 1.83330e15 1.26396 0.631981 0.774984i \(-0.282242\pi\)
0.631981 + 0.774984i \(0.282242\pi\)
\(572\) 1.70232e15 1.16242
\(573\) 3.33887e14 0.225813
\(574\) 5.95331e13 0.0398789
\(575\) 1.22516e15 0.812865
\(576\) −3.11233e14 −0.204533
\(577\) 1.93168e15 1.25738 0.628692 0.777655i \(-0.283591\pi\)
0.628692 + 0.777655i \(0.283591\pi\)
\(578\) −1.09629e14 −0.0706842
\(579\) 1.42141e15 0.907795
\(580\) −7.16681e14 −0.453390
\(581\) −8.14219e13 −0.0510238
\(582\) 3.44104e14 0.213606
\(583\) −1.55824e15 −0.958205
\(584\) 3.33158e13 0.0202946
\(585\) 1.12482e15 0.678774
\(586\) 2.47443e14 0.147924
\(587\) −9.17137e14 −0.543156 −0.271578 0.962416i \(-0.587546\pi\)
−0.271578 + 0.962416i \(0.587546\pi\)
\(588\) −7.45645e14 −0.437479
\(589\) −4.67526e13 −0.0271751
\(590\) −7.46391e13 −0.0429814
\(591\) −7.85593e14 −0.448194
\(592\) −1.96504e15 −1.11071
\(593\) 6.89190e14 0.385956 0.192978 0.981203i \(-0.438185\pi\)
0.192978 + 0.981203i \(0.438185\pi\)
\(594\) 7.01545e13 0.0389251
\(595\) 1.12007e15 0.615748
\(596\) 1.29202e15 0.703743
\(597\) 1.84177e15 0.993979
\(598\) 1.07049e15 0.572434
\(599\) −2.08381e15 −1.10410 −0.552052 0.833809i \(-0.686155\pi\)
−0.552052 + 0.833809i \(0.686155\pi\)
\(600\) −3.31582e14 −0.174084
\(601\) 3.29466e15 1.71396 0.856980 0.515350i \(-0.172338\pi\)
0.856980 + 0.515350i \(0.172338\pi\)
\(602\) 3.09623e14 0.159607
\(603\) −7.22409e14 −0.369010
\(604\) 3.13304e15 1.58585
\(605\) 1.00894e15 0.506069
\(606\) −2.25564e14 −0.112117
\(607\) 2.77434e15 1.36654 0.683270 0.730166i \(-0.260557\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(608\) −1.04598e14 −0.0510569
\(609\) 1.98579e14 0.0960590
\(610\) −1.06432e14 −0.0510223
\(611\) 2.06054e15 0.978934
\(612\) 7.43581e14 0.350103
\(613\) 3.15429e15 1.47187 0.735934 0.677053i \(-0.236743\pi\)
0.735934 + 0.677053i \(0.236743\pi\)
\(614\) −5.79340e14 −0.267921
\(615\) −5.62447e14 −0.257791
\(616\) 3.71731e14 0.168863
\(617\) −3.58310e15 −1.61321 −0.806604 0.591092i \(-0.798697\pi\)
−0.806604 + 0.591092i \(0.798697\pi\)
\(618\) 1.79324e14 0.0800206
\(619\) 9.09822e14 0.402400 0.201200 0.979550i \(-0.435516\pi\)
0.201200 + 0.979550i \(0.435516\pi\)
\(620\) −1.02030e15 −0.447275
\(621\) −6.02495e14 −0.261788
\(622\) 3.70800e14 0.159695
\(623\) 1.43108e14 0.0610914
\(624\) 1.75852e15 0.744103
\(625\) −2.95754e15 −1.24048
\(626\) −9.49586e14 −0.394799
\(627\) −7.76217e13 −0.0319898
\(628\) −1.38134e14 −0.0564318
\(629\) 3.86465e15 1.56506
\(630\) 1.18475e14 0.0475611
\(631\) −3.37498e15 −1.34311 −0.671553 0.740957i \(-0.734372\pi\)
−0.671553 + 0.740957i \(0.734372\pi\)
\(632\) 1.94047e15 0.765531
\(633\) −5.20332e14 −0.203498
\(634\) 1.13097e15 0.438492
\(635\) −5.99668e15 −2.30492
\(636\) −1.74698e15 −0.665691
\(637\) 3.46810e15 1.31016
\(638\) 2.07901e14 0.0778653
\(639\) −1.26137e15 −0.468368
\(640\) −3.00011e15 −1.10445
\(641\) −2.46885e14 −0.0901106 −0.0450553 0.998984i \(-0.514346\pi\)
−0.0450553 + 0.998984i \(0.514346\pi\)
\(642\) −7.54161e14 −0.272911
\(643\) 4.89646e14 0.175680 0.0878399 0.996135i \(-0.472004\pi\)
0.0878399 + 0.996135i \(0.472004\pi\)
\(644\) −1.53986e15 −0.547783
\(645\) −2.92521e15 −1.03176
\(646\) 6.02419e13 0.0210678
\(647\) −5.07765e15 −1.76072 −0.880358 0.474310i \(-0.842697\pi\)
−0.880358 + 0.474310i \(0.842697\pi\)
\(648\) 1.63062e14 0.0560648
\(649\) −2.95703e14 −0.100811
\(650\) 7.43882e14 0.251467
\(651\) 2.82707e14 0.0947634
\(652\) 9.45322e14 0.314209
\(653\) 5.94866e13 0.0196064 0.00980318 0.999952i \(-0.496880\pi\)
0.00980318 + 0.999952i \(0.496880\pi\)
\(654\) −6.18336e14 −0.202091
\(655\) −2.86585e15 −0.928807
\(656\) −8.79320e14 −0.282602
\(657\) 4.20664e13 0.0134068
\(658\) 2.17031e14 0.0685930
\(659\) −2.60850e15 −0.817561 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(660\) −1.69397e15 −0.526520
\(661\) −1.10457e15 −0.340474 −0.170237 0.985403i \(-0.554453\pi\)
−0.170237 + 0.985403i \(0.554453\pi\)
\(662\) −5.38163e14 −0.164511
\(663\) −3.45849e15 −1.04849
\(664\) −1.98136e14 −0.0595715
\(665\) −1.31085e14 −0.0390871
\(666\) 4.08779e14 0.120887
\(667\) −1.78548e15 −0.523677
\(668\) −1.57716e15 −0.458779
\(669\) −1.35600e15 −0.391216
\(670\) −1.27725e15 −0.365481
\(671\) −4.21661e14 −0.119671
\(672\) 6.32491e14 0.178042
\(673\) −5.41044e15 −1.51060 −0.755301 0.655378i \(-0.772509\pi\)
−0.755301 + 0.655378i \(0.772509\pi\)
\(674\) 1.65175e14 0.0457419
\(675\) −4.18674e14 −0.115002
\(676\) −5.45676e15 −1.48672
\(677\) 2.10769e15 0.569598 0.284799 0.958587i \(-0.408073\pi\)
0.284799 + 0.958587i \(0.408073\pi\)
\(678\) 2.92348e14 0.0783677
\(679\) 2.30223e15 0.612159
\(680\) 2.72564e15 0.718900
\(681\) 9.74429e14 0.254942
\(682\) 2.95979e14 0.0768151
\(683\) −6.58986e15 −1.69653 −0.848266 0.529570i \(-0.822353\pi\)
−0.848266 + 0.529570i \(0.822353\pi\)
\(684\) −8.70231e13 −0.0222242
\(685\) −5.44981e15 −1.38065
\(686\) 8.14472e14 0.204689
\(687\) 5.01074e13 0.0124922
\(688\) −4.57322e15 −1.13106
\(689\) 8.12542e15 1.99361
\(690\) −1.06524e15 −0.259285
\(691\) 1.29015e15 0.311538 0.155769 0.987794i \(-0.450214\pi\)
0.155769 + 0.987794i \(0.450214\pi\)
\(692\) −5.66347e14 −0.135675
\(693\) 4.69368e14 0.111553
\(694\) 6.95737e14 0.164047
\(695\) 6.39885e15 1.49687
\(696\) 4.83231e14 0.112151
\(697\) 1.72936e15 0.398204
\(698\) −5.65338e14 −0.129153
\(699\) 1.64653e15 0.373204
\(700\) −1.07005e15 −0.240638
\(701\) −1.53913e15 −0.343419 −0.171710 0.985148i \(-0.554929\pi\)
−0.171710 + 0.985148i \(0.554929\pi\)
\(702\) −3.65819e14 −0.0809863
\(703\) −4.52290e14 −0.0993488
\(704\) −2.18006e15 −0.475137
\(705\) −2.05043e15 −0.443410
\(706\) 9.73071e14 0.208794
\(707\) −1.50914e15 −0.321308
\(708\) −3.31518e14 −0.0700364
\(709\) −3.68366e15 −0.772191 −0.386096 0.922459i \(-0.626177\pi\)
−0.386096 + 0.922459i \(0.626177\pi\)
\(710\) −2.23016e15 −0.463889
\(711\) 2.45014e15 0.505718
\(712\) 3.48246e14 0.0713257
\(713\) −2.54190e15 −0.516614
\(714\) −3.64275e14 −0.0734665
\(715\) 7.87889e15 1.57682
\(716\) 4.19786e15 0.833693
\(717\) 2.90919e14 0.0573347
\(718\) 2.44649e15 0.478475
\(719\) −6.47613e15 −1.25692 −0.628459 0.777843i \(-0.716314\pi\)
−0.628459 + 0.777843i \(0.716314\pi\)
\(720\) −1.74990e15 −0.337043
\(721\) 1.19977e15 0.229326
\(722\) 1.36994e15 0.259865
\(723\) −5.24128e15 −0.986680
\(724\) −4.18544e15 −0.781950
\(725\) −1.24073e15 −0.230048
\(726\) −3.28131e14 −0.0603804
\(727\) −3.09368e15 −0.564984 −0.282492 0.959270i \(-0.591161\pi\)
−0.282492 + 0.959270i \(0.591161\pi\)
\(728\) −1.93838e15 −0.351331
\(729\) 2.05891e14 0.0370370
\(730\) 7.43754e13 0.0132786
\(731\) 8.99418e15 1.59373
\(732\) −4.72731e14 −0.0831387
\(733\) 2.14364e15 0.374179 0.187089 0.982343i \(-0.440095\pi\)
0.187089 + 0.982343i \(0.440095\pi\)
\(734\) −1.32640e15 −0.229798
\(735\) −3.45109e15 −0.593439
\(736\) −5.68692e15 −0.970619
\(737\) −5.06018e15 −0.857224
\(738\) 1.82921e14 0.0307578
\(739\) 4.32853e15 0.722430 0.361215 0.932483i \(-0.382362\pi\)
0.361215 + 0.932483i \(0.382362\pi\)
\(740\) −9.87052e15 −1.63518
\(741\) 4.04756e14 0.0665569
\(742\) 8.55831e14 0.139690
\(743\) −2.87609e15 −0.465976 −0.232988 0.972480i \(-0.574850\pi\)
−0.232988 + 0.972480i \(0.574850\pi\)
\(744\) 6.87952e14 0.110639
\(745\) 5.97989e15 0.954626
\(746\) −9.48591e14 −0.150320
\(747\) −2.50177e14 −0.0393536
\(748\) 5.20848e15 0.813303
\(749\) −5.04571e15 −0.782118
\(750\) 4.98512e14 0.0767076
\(751\) −1.56156e15 −0.238528 −0.119264 0.992863i \(-0.538053\pi\)
−0.119264 + 0.992863i \(0.538053\pi\)
\(752\) −3.20561e15 −0.486086
\(753\) 3.57194e15 0.537690
\(754\) −1.08410e15 −0.162004
\(755\) 1.45008e16 2.15121
\(756\) 5.26217e14 0.0774989
\(757\) −1.93821e15 −0.283383 −0.141691 0.989911i \(-0.545254\pi\)
−0.141691 + 0.989911i \(0.545254\pi\)
\(758\) −2.62831e14 −0.0381501
\(759\) −4.22023e15 −0.608144
\(760\) −3.18988e14 −0.0456352
\(761\) 9.78831e15 1.39025 0.695124 0.718890i \(-0.255349\pi\)
0.695124 + 0.718890i \(0.255349\pi\)
\(762\) 1.95027e15 0.275006
\(763\) −4.13697e15 −0.579159
\(764\) 2.62200e15 0.364435
\(765\) 3.44154e15 0.474914
\(766\) −3.41567e15 −0.467970
\(767\) 1.54193e15 0.209745
\(768\) −1.64736e15 −0.222486
\(769\) −5.57344e13 −0.00747357 −0.00373678 0.999993i \(-0.501189\pi\)
−0.00373678 + 0.999993i \(0.501189\pi\)
\(770\) 8.29865e14 0.110486
\(771\) 2.80406e15 0.370671
\(772\) 1.11623e16 1.46507
\(773\) 1.11036e16 1.44703 0.723514 0.690310i \(-0.242526\pi\)
0.723514 + 0.690310i \(0.242526\pi\)
\(774\) 9.51350e14 0.123102
\(775\) −1.76637e15 −0.226945
\(776\) 5.60234e15 0.714710
\(777\) 2.73494e15 0.346443
\(778\) 2.95572e15 0.371771
\(779\) −2.02392e14 −0.0252776
\(780\) 8.83317e15 1.09546
\(781\) −8.83536e15 −1.08804
\(782\) 3.27530e15 0.400511
\(783\) 6.10154e14 0.0740883
\(784\) −5.39538e15 −0.650555
\(785\) −6.39332e14 −0.0765497
\(786\) 9.32043e14 0.110818
\(787\) −1.02810e15 −0.121388 −0.0606939 0.998156i \(-0.519331\pi\)
−0.0606939 + 0.998156i \(0.519331\pi\)
\(788\) −6.16924e15 −0.723331
\(789\) −6.52509e15 −0.759737
\(790\) 4.33197e15 0.500883
\(791\) 1.95595e15 0.224589
\(792\) 1.14218e15 0.130241
\(793\) 2.19874e15 0.248984
\(794\) −1.83890e15 −0.206798
\(795\) −8.08558e15 −0.903009
\(796\) 1.44634e16 1.60416
\(797\) −1.08662e16 −1.19690 −0.598450 0.801160i \(-0.704217\pi\)
−0.598450 + 0.801160i \(0.704217\pi\)
\(798\) 4.26320e13 0.00466359
\(799\) 6.30449e15 0.684925
\(800\) −3.95184e15 −0.426387
\(801\) 4.39714e14 0.0471185
\(802\) −6.47324e14 −0.0688911
\(803\) 2.94658e14 0.0311446
\(804\) −5.67305e15 −0.595537
\(805\) −7.12698e15 −0.743067
\(806\) −1.54337e15 −0.159819
\(807\) 5.65237e14 0.0581335
\(808\) −3.67240e15 −0.375135
\(809\) −1.24954e16 −1.26774 −0.633872 0.773438i \(-0.718536\pi\)
−0.633872 + 0.773438i \(0.718536\pi\)
\(810\) 3.64025e14 0.0366829
\(811\) 1.56653e15 0.156792 0.0783958 0.996922i \(-0.475020\pi\)
0.0783958 + 0.996922i \(0.475020\pi\)
\(812\) 1.55943e15 0.155028
\(813\) 4.32915e15 0.427469
\(814\) 2.86333e15 0.280826
\(815\) 4.37526e15 0.426223
\(816\) 5.38044e15 0.520622
\(817\) −1.05261e15 −0.101169
\(818\) −3.48685e15 −0.332882
\(819\) −2.44751e15 −0.232093
\(820\) −4.41688e15 −0.416044
\(821\) −3.01669e15 −0.282256 −0.141128 0.989991i \(-0.545073\pi\)
−0.141128 + 0.989991i \(0.545073\pi\)
\(822\) 1.77241e15 0.164729
\(823\) 6.25430e15 0.577404 0.288702 0.957419i \(-0.406776\pi\)
0.288702 + 0.957419i \(0.406776\pi\)
\(824\) 2.91956e15 0.267743
\(825\) −2.93264e15 −0.267154
\(826\) 1.62408e14 0.0146966
\(827\) −1.65925e16 −1.49153 −0.745764 0.666210i \(-0.767915\pi\)
−0.745764 + 0.666210i \(0.767915\pi\)
\(828\) −4.73138e15 −0.422494
\(829\) 2.08080e16 1.84578 0.922890 0.385063i \(-0.125820\pi\)
0.922890 + 0.385063i \(0.125820\pi\)
\(830\) −4.42325e14 −0.0389773
\(831\) −3.63981e15 −0.318620
\(832\) 1.13679e16 0.988554
\(833\) 1.06111e16 0.916671
\(834\) −2.08106e15 −0.178596
\(835\) −7.29959e15 −0.622333
\(836\) −6.09561e14 −0.0516277
\(837\) 8.68646e14 0.0730891
\(838\) −1.07092e15 −0.0895188
\(839\) −6.74798e15 −0.560381 −0.280190 0.959944i \(-0.590398\pi\)
−0.280190 + 0.959944i \(0.590398\pi\)
\(840\) 1.92888e15 0.159136
\(841\) −1.03923e16 −0.851795
\(842\) 6.20270e14 0.0505085
\(843\) 8.14114e15 0.658618
\(844\) −4.08615e15 −0.328421
\(845\) −2.52557e16 −2.01673
\(846\) 6.66851e14 0.0529044
\(847\) −2.19536e15 −0.173040
\(848\) −1.26409e16 −0.989919
\(849\) 1.39860e15 0.108818
\(850\) 2.27601e15 0.175942
\(851\) −2.45906e16 −1.88867
\(852\) −9.90548e15 −0.755889
\(853\) −1.85964e16 −1.40996 −0.704982 0.709225i \(-0.749045\pi\)
−0.704982 + 0.709225i \(0.749045\pi\)
\(854\) 2.31588e14 0.0174461
\(855\) −4.02772e14 −0.0301471
\(856\) −1.22785e16 −0.913142
\(857\) 1.07425e16 0.793798 0.396899 0.917862i \(-0.370086\pi\)
0.396899 + 0.917862i \(0.370086\pi\)
\(858\) −2.56241e15 −0.188134
\(859\) 1.75952e16 1.28361 0.641803 0.766869i \(-0.278187\pi\)
0.641803 + 0.766869i \(0.278187\pi\)
\(860\) −2.29716e16 −1.66514
\(861\) 1.22383e15 0.0881466
\(862\) 2.72203e15 0.194806
\(863\) 2.42553e16 1.72484 0.862418 0.506197i \(-0.168949\pi\)
0.862418 + 0.506197i \(0.168949\pi\)
\(864\) 1.94340e15 0.137321
\(865\) −2.62124e15 −0.184043
\(866\) −5.82915e15 −0.406684
\(867\) −2.25367e15 −0.156237
\(868\) 2.22009e15 0.152937
\(869\) 1.71622e16 1.17480
\(870\) 1.07878e15 0.0733799
\(871\) 2.63861e16 1.78351
\(872\) −1.00671e16 −0.676182
\(873\) 7.07382e15 0.472146
\(874\) −3.83317e14 −0.0254241
\(875\) 3.33529e15 0.219831
\(876\) 3.30346e14 0.0216370
\(877\) 2.26640e16 1.47516 0.737579 0.675261i \(-0.235969\pi\)
0.737579 + 0.675261i \(0.235969\pi\)
\(878\) 4.54378e15 0.293899
\(879\) 5.08673e15 0.326964
\(880\) −1.22573e16 −0.782964
\(881\) 1.05560e16 0.670090 0.335045 0.942202i \(-0.391248\pi\)
0.335045 + 0.942202i \(0.391248\pi\)
\(882\) 1.12238e15 0.0708048
\(883\) 2.13315e16 1.33733 0.668663 0.743566i \(-0.266867\pi\)
0.668663 + 0.743566i \(0.266867\pi\)
\(884\) −2.71595e16 −1.69213
\(885\) −1.53437e15 −0.0950042
\(886\) −8.16627e15 −0.502502
\(887\) −1.91504e16 −1.17111 −0.585555 0.810633i \(-0.699123\pi\)
−0.585555 + 0.810633i \(0.699123\pi\)
\(888\) 6.65532e15 0.404481
\(889\) 1.30483e16 0.788121
\(890\) 7.77435e14 0.0466680
\(891\) 1.44218e15 0.0860385
\(892\) −1.06486e16 −0.631375
\(893\) −7.37831e14 −0.0434784
\(894\) −1.94481e15 −0.113899
\(895\) 1.94291e16 1.13090
\(896\) 6.52798e15 0.377646
\(897\) 2.20063e16 1.26528
\(898\) −1.93308e15 −0.110466
\(899\) 2.57421e15 0.146206
\(900\) −3.28783e15 −0.185599
\(901\) 2.48608e16 1.39486
\(902\) 1.28129e15 0.0714515
\(903\) 6.36500e15 0.352790
\(904\) 4.75970e15 0.262213
\(905\) −1.93716e16 −1.06071
\(906\) −4.71600e15 −0.256666
\(907\) −2.80117e16 −1.51530 −0.757651 0.652660i \(-0.773653\pi\)
−0.757651 + 0.652660i \(0.773653\pi\)
\(908\) 7.65217e15 0.411445
\(909\) −4.63698e15 −0.247818
\(910\) −4.32731e15 −0.229874
\(911\) 3.77581e16 1.99370 0.996848 0.0793409i \(-0.0252816\pi\)
0.996848 + 0.0793409i \(0.0252816\pi\)
\(912\) −6.29687e14 −0.0330486
\(913\) −1.75239e15 −0.0914200
\(914\) 4.29977e15 0.222967
\(915\) −2.18796e15 −0.112778
\(916\) 3.93492e14 0.0201609
\(917\) 6.23583e15 0.317587
\(918\) −1.11927e15 −0.0566632
\(919\) 3.75954e16 1.89190 0.945952 0.324306i \(-0.105131\pi\)
0.945952 + 0.324306i \(0.105131\pi\)
\(920\) −1.73431e16 −0.867549
\(921\) −1.19096e16 −0.592203
\(922\) 5.79402e15 0.286391
\(923\) 4.60717e16 2.26373
\(924\) 3.68594e15 0.180033
\(925\) −1.70880e16 −0.829683
\(926\) −4.35629e14 −0.0210260
\(927\) 3.68640e15 0.176874
\(928\) 5.75921e15 0.274694
\(929\) 4.12183e15 0.195436 0.0977178 0.995214i \(-0.468846\pi\)
0.0977178 + 0.995214i \(0.468846\pi\)
\(930\) 1.53581e15 0.0723903
\(931\) −1.24185e15 −0.0581895
\(932\) 1.29302e16 0.602306
\(933\) 7.62262e15 0.352984
\(934\) 1.48371e15 0.0683033
\(935\) 2.41066e16 1.10324
\(936\) −5.95588e15 −0.270975
\(937\) −4.76398e15 −0.215478 −0.107739 0.994179i \(-0.534361\pi\)
−0.107739 + 0.994179i \(0.534361\pi\)
\(938\) 2.77919e15 0.124969
\(939\) −1.95209e16 −0.872646
\(940\) −1.61020e16 −0.715610
\(941\) 2.23412e16 0.987106 0.493553 0.869716i \(-0.335698\pi\)
0.493553 + 0.869716i \(0.335698\pi\)
\(942\) 2.07926e14 0.00913334
\(943\) −1.10039e16 −0.480541
\(944\) −2.39881e15 −0.104148
\(945\) 2.43551e15 0.105127
\(946\) 6.66381e15 0.285971
\(947\) 1.86498e16 0.795701 0.397850 0.917450i \(-0.369756\pi\)
0.397850 + 0.917450i \(0.369756\pi\)
\(948\) 1.92409e16 0.816168
\(949\) −1.53648e15 −0.0647984
\(950\) −2.66367e14 −0.0111686
\(951\) 2.32497e16 0.969224
\(952\) −5.93075e15 −0.245814
\(953\) 2.56240e15 0.105593 0.0527966 0.998605i \(-0.483186\pi\)
0.0527966 + 0.998605i \(0.483186\pi\)
\(954\) 2.62963e15 0.107740
\(955\) 1.21355e16 0.494355
\(956\) 2.28458e15 0.0925312
\(957\) 4.27388e15 0.172110
\(958\) −2.26169e15 −0.0905572
\(959\) 1.18583e16 0.472085
\(960\) −1.13121e16 −0.447768
\(961\) −2.17437e16 −0.855766
\(962\) −1.49308e16 −0.584277
\(963\) −1.55035e16 −0.603232
\(964\) −4.11596e16 −1.59238
\(965\) 5.16628e16 1.98737
\(966\) 2.31787e15 0.0886573
\(967\) −7.38874e15 −0.281012 −0.140506 0.990080i \(-0.544873\pi\)
−0.140506 + 0.990080i \(0.544873\pi\)
\(968\) −5.34229e15 −0.202029
\(969\) 1.23841e15 0.0465675
\(970\) 1.25068e16 0.467631
\(971\) 3.36438e16 1.25083 0.625417 0.780291i \(-0.284929\pi\)
0.625417 + 0.780291i \(0.284929\pi\)
\(972\) 1.61686e15 0.0597733
\(973\) −1.39233e16 −0.511826
\(974\) −2.16980e15 −0.0793130
\(975\) 1.52922e16 0.555832
\(976\) −3.42062e15 −0.123632
\(977\) 5.16295e16 1.85557 0.927786 0.373112i \(-0.121709\pi\)
0.927786 + 0.373112i \(0.121709\pi\)
\(978\) −1.42294e15 −0.0508538
\(979\) 3.08002e15 0.109458
\(980\) −2.71013e16 −0.957739
\(981\) −1.27113e16 −0.446693
\(982\) −1.18966e16 −0.415729
\(983\) 6.14908e15 0.213681 0.106841 0.994276i \(-0.465927\pi\)
0.106841 + 0.994276i \(0.465927\pi\)
\(984\) 2.97814e15 0.102913
\(985\) −2.85533e16 −0.981198
\(986\) −3.31694e15 −0.113348
\(987\) 4.46156e15 0.151615
\(988\) 3.17854e15 0.107415
\(989\) −5.72296e16 −1.92327
\(990\) 2.54985e15 0.0852159
\(991\) 3.09087e16 1.02725 0.513624 0.858015i \(-0.328303\pi\)
0.513624 + 0.858015i \(0.328303\pi\)
\(992\) 8.19910e15 0.270989
\(993\) −1.10631e16 −0.363628
\(994\) 4.85262e15 0.158618
\(995\) 6.69413e16 2.17604
\(996\) −1.96464e15 −0.0635120
\(997\) −2.95763e16 −0.950869 −0.475435 0.879751i \(-0.657709\pi\)
−0.475435 + 0.879751i \(0.657709\pi\)
\(998\) −3.02783e15 −0.0968084
\(999\) 8.40338e15 0.267204
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.c.1.11 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.11 27 1.1 even 1 trivial