Properties

Label 177.12.a.c.1.12
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 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-10.6257 q^{2} -243.000 q^{3} -1935.10 q^{4} -9082.46 q^{5} +2582.03 q^{6} +57618.4 q^{7} +42323.0 q^{8} +59049.0 q^{9} +96507.1 q^{10} +814898. q^{11} +470228. q^{12} +2.09899e6 q^{13} -612233. q^{14} +2.20704e6 q^{15} +3.51337e6 q^{16} -428820. q^{17} -627434. q^{18} +2.07408e7 q^{19} +1.75754e7 q^{20} -1.40013e7 q^{21} -8.65883e6 q^{22} -2.39961e7 q^{23} -1.02845e7 q^{24} +3.36629e7 q^{25} -2.23032e7 q^{26} -1.43489e7 q^{27} -1.11497e8 q^{28} +2.13616e8 q^{29} -2.34512e7 q^{30} +1.63056e8 q^{31} -1.24009e8 q^{32} -1.98020e8 q^{33} +4.55649e6 q^{34} -5.23316e8 q^{35} -1.14265e8 q^{36} +2.02526e8 q^{37} -2.20385e8 q^{38} -5.10055e8 q^{39} -3.84397e8 q^{40} -7.88296e8 q^{41} +1.48773e8 q^{42} +5.39420e8 q^{43} -1.57691e9 q^{44} -5.36310e8 q^{45} +2.54974e8 q^{46} +4.74636e8 q^{47} -8.53748e8 q^{48} +1.34255e9 q^{49} -3.57690e8 q^{50} +1.04203e8 q^{51} -4.06175e9 q^{52} +1.49336e9 q^{53} +1.52467e8 q^{54} -7.40128e9 q^{55} +2.43858e9 q^{56} -5.04003e9 q^{57} -2.26980e9 q^{58} -7.14924e8 q^{59} -4.27083e9 q^{60} +2.95600e9 q^{61} -1.73258e9 q^{62} +3.40231e9 q^{63} -5.87769e9 q^{64} -1.90640e10 q^{65} +2.10410e9 q^{66} +1.73111e10 q^{67} +8.29807e8 q^{68} +5.83105e9 q^{69} +5.56058e9 q^{70} +2.37102e10 q^{71} +2.49913e9 q^{72} +1.89758e10 q^{73} -2.15198e9 q^{74} -8.18008e9 q^{75} -4.01355e10 q^{76} +4.69531e10 q^{77} +5.41967e9 q^{78} +2.68055e10 q^{79} -3.19100e10 q^{80} +3.48678e9 q^{81} +8.37617e9 q^{82} +1.55416e10 q^{83} +2.70938e10 q^{84} +3.89474e9 q^{85} -5.73170e9 q^{86} -5.19086e10 q^{87} +3.44889e10 q^{88} -5.66575e10 q^{89} +5.69865e9 q^{90} +1.20940e11 q^{91} +4.64347e10 q^{92} -3.96226e10 q^{93} -5.04332e9 q^{94} -1.88378e11 q^{95} +3.01343e10 q^{96} -7.99557e10 q^{97} -1.42655e10 q^{98} +4.81189e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.6257 −0.234796 −0.117398 0.993085i \(-0.537455\pi\)
−0.117398 + 0.993085i \(0.537455\pi\)
\(3\) −243.000 −0.577350
\(4\) −1935.10 −0.944871
\(5\) −9082.46 −1.29978 −0.649888 0.760030i \(-0.725184\pi\)
−0.649888 + 0.760030i \(0.725184\pi\)
\(6\) 2582.03 0.135560
\(7\) 57618.4 1.29575 0.647876 0.761746i \(-0.275658\pi\)
0.647876 + 0.761746i \(0.275658\pi\)
\(8\) 42323.0 0.456648
\(9\) 59049.0 0.333333
\(10\) 96507.1 0.305182
\(11\) 814898. 1.52561 0.762805 0.646628i \(-0.223821\pi\)
0.762805 + 0.646628i \(0.223821\pi\)
\(12\) 470228. 0.545521
\(13\) 2.09899e6 1.56791 0.783957 0.620815i \(-0.213198\pi\)
0.783957 + 0.620815i \(0.213198\pi\)
\(14\) −612233. −0.304237
\(15\) 2.20704e6 0.750426
\(16\) 3.51337e6 0.837652
\(17\) −428820. −0.0732496 −0.0366248 0.999329i \(-0.511661\pi\)
−0.0366248 + 0.999329i \(0.511661\pi\)
\(18\) −627434. −0.0782653
\(19\) 2.07408e7 1.92168 0.960841 0.277099i \(-0.0893731\pi\)
0.960841 + 0.277099i \(0.0893731\pi\)
\(20\) 1.75754e7 1.22812
\(21\) −1.40013e7 −0.748102
\(22\) −8.65883e6 −0.358207
\(23\) −2.39961e7 −0.777387 −0.388693 0.921367i \(-0.627073\pi\)
−0.388693 + 0.921367i \(0.627073\pi\)
\(24\) −1.02845e7 −0.263646
\(25\) 3.36629e7 0.689416
\(26\) −2.23032e7 −0.368140
\(27\) −1.43489e7 −0.192450
\(28\) −1.11497e8 −1.22432
\(29\) 2.13616e8 1.93394 0.966972 0.254883i \(-0.0820371\pi\)
0.966972 + 0.254883i \(0.0820371\pi\)
\(30\) −2.34512e7 −0.176197
\(31\) 1.63056e8 1.02293 0.511467 0.859303i \(-0.329102\pi\)
0.511467 + 0.859303i \(0.329102\pi\)
\(32\) −1.24009e8 −0.653325
\(33\) −1.98020e8 −0.880812
\(34\) 4.55649e6 0.0171987
\(35\) −5.23316e8 −1.68419
\(36\) −1.14265e8 −0.314957
\(37\) 2.02526e8 0.480145 0.240072 0.970755i \(-0.422829\pi\)
0.240072 + 0.970755i \(0.422829\pi\)
\(38\) −2.20385e8 −0.451203
\(39\) −5.10055e8 −0.905236
\(40\) −3.84397e8 −0.593540
\(41\) −7.88296e8 −1.06262 −0.531310 0.847177i \(-0.678300\pi\)
−0.531310 + 0.847177i \(0.678300\pi\)
\(42\) 1.48773e8 0.175651
\(43\) 5.39420e8 0.559565 0.279783 0.960063i \(-0.409738\pi\)
0.279783 + 0.960063i \(0.409738\pi\)
\(44\) −1.57691e9 −1.44151
\(45\) −5.36310e8 −0.433258
\(46\) 2.54974e8 0.182527
\(47\) 4.74636e8 0.301872 0.150936 0.988544i \(-0.451771\pi\)
0.150936 + 0.988544i \(0.451771\pi\)
\(48\) −8.53748e8 −0.483618
\(49\) 1.34255e9 0.678972
\(50\) −3.57690e8 −0.161872
\(51\) 1.04203e8 0.0422907
\(52\) −4.06175e9 −1.48148
\(53\) 1.49336e9 0.490511 0.245255 0.969459i \(-0.421128\pi\)
0.245255 + 0.969459i \(0.421128\pi\)
\(54\) 1.52467e8 0.0451865
\(55\) −7.40128e9 −1.98295
\(56\) 2.43858e9 0.591702
\(57\) −5.04003e9 −1.10948
\(58\) −2.26980e9 −0.454082
\(59\) −7.14924e8 −0.130189
\(60\) −4.27083e9 −0.709055
\(61\) 2.95600e9 0.448117 0.224058 0.974576i \(-0.428069\pi\)
0.224058 + 0.974576i \(0.428069\pi\)
\(62\) −1.73258e9 −0.240181
\(63\) 3.40231e9 0.431917
\(64\) −5.87769e9 −0.684254
\(65\) −1.90640e10 −2.03794
\(66\) 2.10410e9 0.206811
\(67\) 1.73111e10 1.56644 0.783218 0.621747i \(-0.213577\pi\)
0.783218 + 0.621747i \(0.213577\pi\)
\(68\) 8.29807e8 0.0692114
\(69\) 5.83105e9 0.448825
\(70\) 5.56058e9 0.395440
\(71\) 2.37102e10 1.55961 0.779803 0.626025i \(-0.215319\pi\)
0.779803 + 0.626025i \(0.215319\pi\)
\(72\) 2.49913e9 0.152216
\(73\) 1.89758e10 1.07133 0.535666 0.844430i \(-0.320061\pi\)
0.535666 + 0.844430i \(0.320061\pi\)
\(74\) −2.15198e9 −0.112736
\(75\) −8.18008e9 −0.398035
\(76\) −4.01355e10 −1.81574
\(77\) 4.69531e10 1.97681
\(78\) 5.41967e9 0.212546
\(79\) 2.68055e10 0.980111 0.490055 0.871691i \(-0.336977\pi\)
0.490055 + 0.871691i \(0.336977\pi\)
\(80\) −3.19100e10 −1.08876
\(81\) 3.48678e9 0.111111
\(82\) 8.37617e9 0.249499
\(83\) 1.55416e10 0.433079 0.216540 0.976274i \(-0.430523\pi\)
0.216540 + 0.976274i \(0.430523\pi\)
\(84\) 2.70938e10 0.706860
\(85\) 3.89474e9 0.0952081
\(86\) −5.73170e9 −0.131384
\(87\) −5.19086e10 −1.11656
\(88\) 3.44889e10 0.696667
\(89\) −5.66575e10 −1.07550 −0.537752 0.843103i \(-0.680726\pi\)
−0.537752 + 0.843103i \(0.680726\pi\)
\(90\) 5.69865e9 0.101727
\(91\) 1.20940e11 2.03163
\(92\) 4.64347e10 0.734530
\(93\) −3.96226e10 −0.590591
\(94\) −5.04332e9 −0.0708782
\(95\) −1.88378e11 −2.49776
\(96\) 3.01343e10 0.377197
\(97\) −7.99557e10 −0.945377 −0.472688 0.881230i \(-0.656716\pi\)
−0.472688 + 0.881230i \(0.656716\pi\)
\(98\) −1.42655e10 −0.159420
\(99\) 4.81189e10 0.508537
\(100\) −6.51409e10 −0.651409
\(101\) −1.15204e10 −0.109069 −0.0545345 0.998512i \(-0.517367\pi\)
−0.0545345 + 0.998512i \(0.517367\pi\)
\(102\) −1.10723e9 −0.00992969
\(103\) 6.79276e9 0.0577353 0.0288677 0.999583i \(-0.490810\pi\)
0.0288677 + 0.999583i \(0.490810\pi\)
\(104\) 8.88356e10 0.715985
\(105\) 1.27166e11 0.972365
\(106\) −1.58680e10 −0.115170
\(107\) −2.79927e9 −0.0192945 −0.00964726 0.999953i \(-0.503071\pi\)
−0.00964726 + 0.999953i \(0.503071\pi\)
\(108\) 2.77665e10 0.181840
\(109\) −1.89624e11 −1.18045 −0.590225 0.807239i \(-0.700961\pi\)
−0.590225 + 0.807239i \(0.700961\pi\)
\(110\) 7.86435e10 0.465589
\(111\) −4.92139e10 −0.277212
\(112\) 2.02434e11 1.08539
\(113\) −3.78979e11 −1.93501 −0.967507 0.252844i \(-0.918634\pi\)
−0.967507 + 0.252844i \(0.918634\pi\)
\(114\) 5.35536e10 0.260502
\(115\) 2.17943e11 1.01043
\(116\) −4.13366e11 −1.82733
\(117\) 1.23943e11 0.522638
\(118\) 7.59654e9 0.0305678
\(119\) −2.47079e10 −0.0949133
\(120\) 9.34084e10 0.342680
\(121\) 3.78748e11 1.32749
\(122\) −3.14095e10 −0.105216
\(123\) 1.91556e11 0.613505
\(124\) −3.15529e11 −0.966541
\(125\) 1.37738e11 0.403689
\(126\) −3.61517e10 −0.101412
\(127\) −5.74444e11 −1.54286 −0.771431 0.636313i \(-0.780459\pi\)
−0.771431 + 0.636313i \(0.780459\pi\)
\(128\) 3.16425e11 0.813985
\(129\) −1.31079e11 −0.323065
\(130\) 2.02567e11 0.478499
\(131\) −3.55520e11 −0.805142 −0.402571 0.915389i \(-0.631883\pi\)
−0.402571 + 0.915389i \(0.631883\pi\)
\(132\) 3.83188e11 0.832253
\(133\) 1.19505e12 2.49002
\(134\) −1.83942e11 −0.367793
\(135\) 1.30323e11 0.250142
\(136\) −1.81489e10 −0.0334493
\(137\) 4.73661e11 0.838502 0.419251 0.907870i \(-0.362293\pi\)
0.419251 + 0.907870i \(0.362293\pi\)
\(138\) −6.19587e10 −0.105382
\(139\) 8.42358e11 1.37694 0.688470 0.725265i \(-0.258283\pi\)
0.688470 + 0.725265i \(0.258283\pi\)
\(140\) 1.01267e12 1.59134
\(141\) −1.15336e11 −0.174286
\(142\) −2.51937e11 −0.366189
\(143\) 1.71046e12 2.39203
\(144\) 2.07461e11 0.279217
\(145\) −1.94015e12 −2.51369
\(146\) −2.01630e11 −0.251544
\(147\) −3.26239e11 −0.392004
\(148\) −3.91908e11 −0.453675
\(149\) 8.19778e11 0.914474 0.457237 0.889345i \(-0.348839\pi\)
0.457237 + 0.889345i \(0.348839\pi\)
\(150\) 8.69188e10 0.0934569
\(151\) −1.77194e12 −1.83686 −0.918431 0.395580i \(-0.870543\pi\)
−0.918431 + 0.395580i \(0.870543\pi\)
\(152\) 8.77815e11 0.877532
\(153\) −2.53214e10 −0.0244165
\(154\) −4.98908e11 −0.464148
\(155\) −1.48095e12 −1.32958
\(156\) 9.87005e11 0.855331
\(157\) 1.14069e12 0.954376 0.477188 0.878801i \(-0.341656\pi\)
0.477188 + 0.878801i \(0.341656\pi\)
\(158\) −2.84826e11 −0.230126
\(159\) −3.62888e11 −0.283196
\(160\) 1.12631e12 0.849176
\(161\) −1.38261e12 −1.00730
\(162\) −3.70494e10 −0.0260884
\(163\) −1.12504e12 −0.765837 −0.382919 0.923782i \(-0.625081\pi\)
−0.382919 + 0.923782i \(0.625081\pi\)
\(164\) 1.52543e12 1.00404
\(165\) 1.79851e12 1.14486
\(166\) −1.65140e11 −0.101685
\(167\) 1.15989e12 0.690995 0.345498 0.938420i \(-0.387710\pi\)
0.345498 + 0.938420i \(0.387710\pi\)
\(168\) −5.92575e11 −0.341619
\(169\) 2.61360e12 1.45835
\(170\) −4.13841e10 −0.0223545
\(171\) 1.22473e12 0.640561
\(172\) −1.04383e12 −0.528717
\(173\) 6.58060e11 0.322859 0.161429 0.986884i \(-0.448390\pi\)
0.161429 + 0.986884i \(0.448390\pi\)
\(174\) 5.51563e11 0.262165
\(175\) 1.93960e12 0.893312
\(176\) 2.86304e12 1.27793
\(177\) 1.73727e11 0.0751646
\(178\) 6.02023e11 0.252524
\(179\) 9.77714e11 0.397667 0.198834 0.980033i \(-0.436285\pi\)
0.198834 + 0.980033i \(0.436285\pi\)
\(180\) 1.03781e12 0.409373
\(181\) −1.86516e12 −0.713646 −0.356823 0.934172i \(-0.616140\pi\)
−0.356823 + 0.934172i \(0.616140\pi\)
\(182\) −1.28507e12 −0.477018
\(183\) −7.18309e11 −0.258720
\(184\) −1.01559e12 −0.354992
\(185\) −1.83944e12 −0.624080
\(186\) 4.21016e11 0.138669
\(187\) −3.49444e11 −0.111750
\(188\) −9.18465e11 −0.285230
\(189\) −8.26760e11 −0.249367
\(190\) 2.00164e12 0.586463
\(191\) −5.90311e12 −1.68034 −0.840171 0.542322i \(-0.817545\pi\)
−0.840171 + 0.542322i \(0.817545\pi\)
\(192\) 1.42828e12 0.395054
\(193\) 2.99243e12 0.804376 0.402188 0.915557i \(-0.368250\pi\)
0.402188 + 0.915557i \(0.368250\pi\)
\(194\) 8.49582e11 0.221971
\(195\) 4.63255e12 1.17660
\(196\) −2.59796e12 −0.641540
\(197\) 3.54798e12 0.851955 0.425977 0.904734i \(-0.359930\pi\)
0.425977 + 0.904734i \(0.359930\pi\)
\(198\) −5.11295e11 −0.119402
\(199\) −7.86492e12 −1.78650 −0.893248 0.449564i \(-0.851579\pi\)
−0.893248 + 0.449564i \(0.851579\pi\)
\(200\) 1.42471e12 0.314820
\(201\) −4.20659e12 −0.904382
\(202\) 1.22412e11 0.0256089
\(203\) 1.23082e13 2.50591
\(204\) −2.01643e11 −0.0399592
\(205\) 7.15967e12 1.38117
\(206\) −7.21776e10 −0.0135560
\(207\) −1.41694e12 −0.259129
\(208\) 7.37453e12 1.31337
\(209\) 1.69017e13 2.93174
\(210\) −1.35122e12 −0.228307
\(211\) −2.88185e12 −0.474371 −0.237186 0.971464i \(-0.576225\pi\)
−0.237186 + 0.971464i \(0.576225\pi\)
\(212\) −2.88980e12 −0.463469
\(213\) −5.76158e12 −0.900438
\(214\) 2.97441e10 0.00453028
\(215\) −4.89926e12 −0.727309
\(216\) −6.07289e11 −0.0878819
\(217\) 9.39503e12 1.32547
\(218\) 2.01488e12 0.277165
\(219\) −4.61111e12 −0.618534
\(220\) 1.43222e13 1.87363
\(221\) −9.00089e11 −0.114849
\(222\) 5.22930e11 0.0650882
\(223\) −6.94038e12 −0.842764 −0.421382 0.906883i \(-0.638455\pi\)
−0.421382 + 0.906883i \(0.638455\pi\)
\(224\) −7.14521e12 −0.846547
\(225\) 1.98776e12 0.229805
\(226\) 4.02690e12 0.454334
\(227\) 1.00179e13 1.10315 0.551576 0.834125i \(-0.314027\pi\)
0.551576 + 0.834125i \(0.314027\pi\)
\(228\) 9.75293e12 1.04832
\(229\) 3.77275e12 0.395879 0.197939 0.980214i \(-0.436575\pi\)
0.197939 + 0.980214i \(0.436575\pi\)
\(230\) −2.31579e12 −0.237245
\(231\) −1.14096e13 −1.14131
\(232\) 9.04085e12 0.883131
\(233\) 1.02994e13 0.982552 0.491276 0.871004i \(-0.336531\pi\)
0.491276 + 0.871004i \(0.336531\pi\)
\(234\) −1.31698e12 −0.122713
\(235\) −4.31086e12 −0.392365
\(236\) 1.38345e12 0.123012
\(237\) −6.51374e12 −0.565867
\(238\) 2.62537e11 0.0222853
\(239\) −2.28705e13 −1.89709 −0.948543 0.316650i \(-0.897442\pi\)
−0.948543 + 0.316650i \(0.897442\pi\)
\(240\) 7.75413e12 0.628595
\(241\) −7.49749e11 −0.0594049 −0.0297024 0.999559i \(-0.509456\pi\)
−0.0297024 + 0.999559i \(0.509456\pi\)
\(242\) −4.02444e12 −0.311689
\(243\) −8.47289e11 −0.0641500
\(244\) −5.72015e12 −0.423412
\(245\) −1.21936e13 −0.882511
\(246\) −2.03541e12 −0.144048
\(247\) 4.35349e13 3.01303
\(248\) 6.90102e12 0.467121
\(249\) −3.77662e12 −0.250038
\(250\) −1.46355e12 −0.0947846
\(251\) −9.91526e12 −0.628201 −0.314101 0.949390i \(-0.601703\pi\)
−0.314101 + 0.949390i \(0.601703\pi\)
\(252\) −6.58379e12 −0.408106
\(253\) −1.95544e13 −1.18599
\(254\) 6.10384e12 0.362258
\(255\) −9.46421e11 −0.0549684
\(256\) 8.67529e12 0.493133
\(257\) 1.74196e13 0.969186 0.484593 0.874740i \(-0.338968\pi\)
0.484593 + 0.874740i \(0.338968\pi\)
\(258\) 1.39280e12 0.0758544
\(259\) 1.16692e13 0.622148
\(260\) 3.68907e13 1.92559
\(261\) 1.26138e13 0.644648
\(262\) 3.77764e12 0.189044
\(263\) −1.75510e13 −0.860093 −0.430047 0.902807i \(-0.641503\pi\)
−0.430047 + 0.902807i \(0.641503\pi\)
\(264\) −8.38081e12 −0.402221
\(265\) −1.35634e13 −0.637554
\(266\) −1.26982e13 −0.584647
\(267\) 1.37678e13 0.620943
\(268\) −3.34986e13 −1.48008
\(269\) 1.86255e13 0.806250 0.403125 0.915145i \(-0.367924\pi\)
0.403125 + 0.915145i \(0.367924\pi\)
\(270\) −1.38477e12 −0.0587323
\(271\) 4.14769e13 1.72375 0.861877 0.507117i \(-0.169289\pi\)
0.861877 + 0.507117i \(0.169289\pi\)
\(272\) −1.50660e12 −0.0613577
\(273\) −2.93885e13 −1.17296
\(274\) −5.03295e12 −0.196877
\(275\) 2.74318e13 1.05178
\(276\) −1.12836e13 −0.424081
\(277\) −1.00078e13 −0.368721 −0.184361 0.982859i \(-0.559021\pi\)
−0.184361 + 0.982859i \(0.559021\pi\)
\(278\) −8.95060e12 −0.323300
\(279\) 9.62830e12 0.340978
\(280\) −2.21483e13 −0.769080
\(281\) 2.85559e12 0.0972325 0.0486163 0.998818i \(-0.484519\pi\)
0.0486163 + 0.998818i \(0.484519\pi\)
\(282\) 1.22553e12 0.0409216
\(283\) 3.51199e13 1.15008 0.575040 0.818125i \(-0.304986\pi\)
0.575040 + 0.818125i \(0.304986\pi\)
\(284\) −4.58815e13 −1.47363
\(285\) 4.57758e13 1.44208
\(286\) −1.81748e13 −0.561638
\(287\) −4.54204e13 −1.37689
\(288\) −7.32263e12 −0.217775
\(289\) −3.40880e13 −0.994634
\(290\) 2.06154e13 0.590205
\(291\) 1.94292e13 0.545813
\(292\) −3.67199e13 −1.01227
\(293\) −8.00808e11 −0.0216649 −0.0108324 0.999941i \(-0.503448\pi\)
−0.0108324 + 0.999941i \(0.503448\pi\)
\(294\) 3.46651e12 0.0920411
\(295\) 6.49327e12 0.169216
\(296\) 8.57153e12 0.219257
\(297\) −1.16929e13 −0.293604
\(298\) −8.71067e12 −0.214715
\(299\) −5.03676e13 −1.21888
\(300\) 1.58292e13 0.376091
\(301\) 3.10805e13 0.725058
\(302\) 1.88281e13 0.431288
\(303\) 2.79946e12 0.0629710
\(304\) 7.28702e13 1.60970
\(305\) −2.68478e13 −0.582451
\(306\) 2.69056e11 0.00573291
\(307\) −3.85316e13 −0.806410 −0.403205 0.915110i \(-0.632104\pi\)
−0.403205 + 0.915110i \(0.632104\pi\)
\(308\) −9.08588e13 −1.86783
\(309\) −1.65064e12 −0.0333335
\(310\) 1.57361e13 0.312181
\(311\) −4.84093e13 −0.943510 −0.471755 0.881730i \(-0.656379\pi\)
−0.471755 + 0.881730i \(0.656379\pi\)
\(312\) −2.15871e13 −0.413374
\(313\) 2.56504e13 0.482615 0.241307 0.970449i \(-0.422424\pi\)
0.241307 + 0.970449i \(0.422424\pi\)
\(314\) −1.21206e13 −0.224084
\(315\) −3.09013e13 −0.561395
\(316\) −5.18712e13 −0.926078
\(317\) −9.07687e13 −1.59261 −0.796307 0.604893i \(-0.793216\pi\)
−0.796307 + 0.604893i \(0.793216\pi\)
\(318\) 3.85592e12 0.0664934
\(319\) 1.74075e14 2.95045
\(320\) 5.33839e13 0.889376
\(321\) 6.80223e11 0.0111397
\(322\) 1.46912e13 0.236510
\(323\) −8.89408e12 −0.140763
\(324\) −6.74726e12 −0.104986
\(325\) 7.06581e13 1.08095
\(326\) 1.19543e13 0.179816
\(327\) 4.60787e13 0.681533
\(328\) −3.33631e13 −0.485244
\(329\) 2.73477e13 0.391151
\(330\) −1.91104e13 −0.268808
\(331\) 6.45071e13 0.892387 0.446194 0.894936i \(-0.352779\pi\)
0.446194 + 0.894936i \(0.352779\pi\)
\(332\) −3.00745e13 −0.409204
\(333\) 1.19590e13 0.160048
\(334\) −1.23246e13 −0.162243
\(335\) −1.57227e14 −2.03602
\(336\) −4.91916e13 −0.626649
\(337\) −1.01245e14 −1.26884 −0.634422 0.772987i \(-0.718762\pi\)
−0.634422 + 0.772987i \(0.718762\pi\)
\(338\) −2.77713e13 −0.342416
\(339\) 9.20920e13 1.11718
\(340\) −7.53668e12 −0.0899593
\(341\) 1.32874e14 1.56060
\(342\) −1.30135e13 −0.150401
\(343\) −3.65749e13 −0.415973
\(344\) 2.28299e13 0.255524
\(345\) −5.29602e13 −0.583371
\(346\) −6.99232e12 −0.0758059
\(347\) −8.83024e13 −0.942238 −0.471119 0.882070i \(-0.656150\pi\)
−0.471119 + 0.882070i \(0.656150\pi\)
\(348\) 1.00448e14 1.05501
\(349\) −8.87236e13 −0.917275 −0.458637 0.888624i \(-0.651662\pi\)
−0.458637 + 0.888624i \(0.651662\pi\)
\(350\) −2.06095e13 −0.209746
\(351\) −3.01182e13 −0.301745
\(352\) −1.01055e14 −0.996720
\(353\) −9.74142e13 −0.945936 −0.472968 0.881080i \(-0.656817\pi\)
−0.472968 + 0.881080i \(0.656817\pi\)
\(354\) −1.84596e12 −0.0176483
\(355\) −2.15347e14 −2.02714
\(356\) 1.09638e14 1.01621
\(357\) 6.00401e12 0.0547982
\(358\) −1.03888e13 −0.0933707
\(359\) −1.64288e14 −1.45407 −0.727035 0.686600i \(-0.759102\pi\)
−0.727035 + 0.686600i \(0.759102\pi\)
\(360\) −2.26982e13 −0.197847
\(361\) 3.13692e14 2.69286
\(362\) 1.98185e13 0.167561
\(363\) −9.20357e13 −0.766426
\(364\) −2.34031e14 −1.91962
\(365\) −1.72347e14 −1.39249
\(366\) 7.63250e12 0.0607465
\(367\) −9.07931e13 −0.711852 −0.355926 0.934514i \(-0.615834\pi\)
−0.355926 + 0.934514i \(0.615834\pi\)
\(368\) −8.43070e13 −0.651179
\(369\) −4.65481e13 −0.354207
\(370\) 1.95452e13 0.146532
\(371\) 8.60452e13 0.635580
\(372\) 7.66736e13 0.558033
\(373\) 2.01891e14 1.44783 0.723917 0.689887i \(-0.242340\pi\)
0.723917 + 0.689887i \(0.242340\pi\)
\(374\) 3.71308e12 0.0262386
\(375\) −3.34702e13 −0.233070
\(376\) 2.00880e13 0.137849
\(377\) 4.48377e14 3.03226
\(378\) 8.78487e12 0.0585505
\(379\) −1.71894e13 −0.112913 −0.0564566 0.998405i \(-0.517980\pi\)
−0.0564566 + 0.998405i \(0.517980\pi\)
\(380\) 3.64529e14 2.36006
\(381\) 1.39590e14 0.890772
\(382\) 6.27244e13 0.394537
\(383\) −4.50671e13 −0.279426 −0.139713 0.990192i \(-0.544618\pi\)
−0.139713 + 0.990192i \(0.544618\pi\)
\(384\) −7.68914e13 −0.469955
\(385\) −4.26450e14 −2.56941
\(386\) −3.17966e13 −0.188864
\(387\) 3.18522e13 0.186522
\(388\) 1.54722e14 0.893259
\(389\) −2.49811e14 −1.42196 −0.710982 0.703210i \(-0.751749\pi\)
−0.710982 + 0.703210i \(0.751749\pi\)
\(390\) −4.92239e13 −0.276262
\(391\) 1.02900e13 0.0569433
\(392\) 5.68207e13 0.310051
\(393\) 8.63915e13 0.464849
\(394\) −3.76996e13 −0.200036
\(395\) −2.43460e14 −1.27392
\(396\) −9.31147e13 −0.480502
\(397\) −2.26483e14 −1.15262 −0.576311 0.817230i \(-0.695508\pi\)
−0.576311 + 0.817230i \(0.695508\pi\)
\(398\) 8.35699e13 0.419462
\(399\) −2.90398e14 −1.43762
\(400\) 1.18270e14 0.577491
\(401\) 9.58388e13 0.461580 0.230790 0.973004i \(-0.425869\pi\)
0.230790 + 0.973004i \(0.425869\pi\)
\(402\) 4.46978e13 0.212345
\(403\) 3.42253e14 1.60387
\(404\) 2.22931e13 0.103056
\(405\) −3.16686e13 −0.144419
\(406\) −1.30782e14 −0.588378
\(407\) 1.65039e14 0.732514
\(408\) 4.41019e12 0.0193120
\(409\) 3.12553e14 1.35035 0.675174 0.737658i \(-0.264069\pi\)
0.675174 + 0.737658i \(0.264069\pi\)
\(410\) −7.60762e13 −0.324293
\(411\) −1.15100e14 −0.484109
\(412\) −1.31446e13 −0.0545524
\(413\) −4.11928e13 −0.168692
\(414\) 1.50560e13 0.0608425
\(415\) −1.41156e14 −0.562906
\(416\) −2.60294e14 −1.02436
\(417\) −2.04693e14 −0.794977
\(418\) −1.79591e14 −0.688361
\(419\) −1.31239e14 −0.496462 −0.248231 0.968701i \(-0.579849\pi\)
−0.248231 + 0.968701i \(0.579849\pi\)
\(420\) −2.46078e14 −0.918759
\(421\) 2.15819e14 0.795311 0.397656 0.917535i \(-0.369824\pi\)
0.397656 + 0.917535i \(0.369824\pi\)
\(422\) 3.06216e13 0.111380
\(423\) 2.80268e13 0.100624
\(424\) 6.32037e13 0.223991
\(425\) −1.44353e13 −0.0504995
\(426\) 6.12206e13 0.211419
\(427\) 1.70320e14 0.580648
\(428\) 5.41685e12 0.0182308
\(429\) −4.15643e14 −1.38104
\(430\) 5.20579e13 0.170769
\(431\) 1.68529e14 0.545820 0.272910 0.962040i \(-0.412014\pi\)
0.272910 + 0.962040i \(0.412014\pi\)
\(432\) −5.04130e13 −0.161206
\(433\) −2.96714e14 −0.936816 −0.468408 0.883512i \(-0.655172\pi\)
−0.468408 + 0.883512i \(0.655172\pi\)
\(434\) −9.98283e13 −0.311215
\(435\) 4.71457e14 1.45128
\(436\) 3.66941e14 1.11537
\(437\) −4.97699e14 −1.49389
\(438\) 4.89961e13 0.145229
\(439\) 1.22210e14 0.357728 0.178864 0.983874i \(-0.442758\pi\)
0.178864 + 0.983874i \(0.442758\pi\)
\(440\) −3.13244e14 −0.905511
\(441\) 7.92762e13 0.226324
\(442\) 9.56403e12 0.0269661
\(443\) 3.82613e14 1.06546 0.532732 0.846284i \(-0.321165\pi\)
0.532732 + 0.846284i \(0.321165\pi\)
\(444\) 9.52337e13 0.261929
\(445\) 5.14589e14 1.39791
\(446\) 7.37460e13 0.197878
\(447\) −1.99206e14 −0.527972
\(448\) −3.38663e14 −0.886622
\(449\) −6.61570e13 −0.171088 −0.0855442 0.996334i \(-0.527263\pi\)
−0.0855442 + 0.996334i \(0.527263\pi\)
\(450\) −2.11213e13 −0.0539574
\(451\) −6.42382e14 −1.62115
\(452\) 7.33361e14 1.82834
\(453\) 4.30582e14 1.06051
\(454\) −1.06447e14 −0.259016
\(455\) −1.09844e15 −2.64066
\(456\) −2.13309e14 −0.506644
\(457\) 7.89022e14 1.85161 0.925806 0.377999i \(-0.123388\pi\)
0.925806 + 0.377999i \(0.123388\pi\)
\(458\) −4.00879e13 −0.0929508
\(459\) 6.15309e12 0.0140969
\(460\) −4.21741e14 −0.954724
\(461\) 6.71616e14 1.50233 0.751167 0.660113i \(-0.229491\pi\)
0.751167 + 0.660113i \(0.229491\pi\)
\(462\) 1.21235e14 0.267976
\(463\) −3.32485e14 −0.726234 −0.363117 0.931744i \(-0.618287\pi\)
−0.363117 + 0.931744i \(0.618287\pi\)
\(464\) 7.50509e14 1.61997
\(465\) 3.59871e14 0.767636
\(466\) −1.09438e14 −0.230699
\(467\) −7.51124e14 −1.56484 −0.782418 0.622754i \(-0.786014\pi\)
−0.782418 + 0.622754i \(0.786014\pi\)
\(468\) −2.39842e14 −0.493825
\(469\) 9.97436e14 2.02971
\(470\) 4.58057e13 0.0921258
\(471\) −2.77188e14 −0.551010
\(472\) −3.02577e13 −0.0594505
\(473\) 4.39573e14 0.853679
\(474\) 6.92128e13 0.132863
\(475\) 6.98197e14 1.32484
\(476\) 4.78121e13 0.0896808
\(477\) 8.81817e13 0.163504
\(478\) 2.43014e14 0.445428
\(479\) −3.43615e14 −0.622625 −0.311312 0.950308i \(-0.600769\pi\)
−0.311312 + 0.950308i \(0.600769\pi\)
\(480\) −2.73693e14 −0.490272
\(481\) 4.25101e14 0.752826
\(482\) 7.96657e12 0.0139480
\(483\) 3.35975e14 0.581565
\(484\) −7.32913e14 −1.25430
\(485\) 7.26194e14 1.22878
\(486\) 9.00300e12 0.0150622
\(487\) −4.61203e14 −0.762926 −0.381463 0.924384i \(-0.624580\pi\)
−0.381463 + 0.924384i \(0.624580\pi\)
\(488\) 1.25107e14 0.204631
\(489\) 2.73385e14 0.442156
\(490\) 1.29565e14 0.207210
\(491\) −1.06056e15 −1.67721 −0.838604 0.544742i \(-0.816628\pi\)
−0.838604 + 0.544742i \(0.816628\pi\)
\(492\) −3.70679e14 −0.579683
\(493\) −9.16025e13 −0.141661
\(494\) −4.62586e14 −0.707448
\(495\) −4.37038e14 −0.660984
\(496\) 5.72876e14 0.856863
\(497\) 1.36614e15 2.02086
\(498\) 4.01290e13 0.0587080
\(499\) −9.38857e13 −0.135846 −0.0679229 0.997691i \(-0.521637\pi\)
−0.0679229 + 0.997691i \(0.521637\pi\)
\(500\) −2.66535e14 −0.381434
\(501\) −2.81853e14 −0.398946
\(502\) 1.05356e14 0.147499
\(503\) −1.60080e14 −0.221673 −0.110836 0.993839i \(-0.535353\pi\)
−0.110836 + 0.993839i \(0.535353\pi\)
\(504\) 1.43996e14 0.197234
\(505\) 1.04634e14 0.141765
\(506\) 2.07778e14 0.278466
\(507\) −6.35106e14 −0.841981
\(508\) 1.11160e15 1.45781
\(509\) −6.92627e14 −0.898569 −0.449284 0.893389i \(-0.648321\pi\)
−0.449284 + 0.893389i \(0.648321\pi\)
\(510\) 1.00563e13 0.0129064
\(511\) 1.09335e15 1.38818
\(512\) −7.40220e14 −0.929771
\(513\) −2.97608e14 −0.369828
\(514\) −1.85095e14 −0.227561
\(515\) −6.16950e13 −0.0750430
\(516\) 2.53651e14 0.305255
\(517\) 3.86780e14 0.460539
\(518\) −1.23993e14 −0.146078
\(519\) −1.59909e14 −0.186402
\(520\) −8.06846e14 −0.930619
\(521\) −3.38413e14 −0.386224 −0.193112 0.981177i \(-0.561858\pi\)
−0.193112 + 0.981177i \(0.561858\pi\)
\(522\) −1.34030e14 −0.151361
\(523\) 4.64109e14 0.518634 0.259317 0.965792i \(-0.416503\pi\)
0.259317 + 0.965792i \(0.416503\pi\)
\(524\) 6.87966e14 0.760755
\(525\) −4.71323e14 −0.515754
\(526\) 1.86491e14 0.201946
\(527\) −6.99216e13 −0.0749296
\(528\) −6.95718e14 −0.737813
\(529\) −3.76998e14 −0.395670
\(530\) 1.44120e14 0.149695
\(531\) −4.22156e13 −0.0433963
\(532\) −2.31254e15 −2.35275
\(533\) −1.65463e15 −1.66610
\(534\) −1.46292e14 −0.145795
\(535\) 2.54242e13 0.0250785
\(536\) 7.32657e14 0.715310
\(537\) −2.37584e14 −0.229593
\(538\) −1.97908e14 −0.189304
\(539\) 1.09404e15 1.03585
\(540\) −2.52188e14 −0.236352
\(541\) 1.77314e15 1.64497 0.822485 0.568787i \(-0.192587\pi\)
0.822485 + 0.568787i \(0.192587\pi\)
\(542\) −4.40720e14 −0.404731
\(543\) 4.53233e14 0.412024
\(544\) 5.31776e13 0.0478558
\(545\) 1.72225e15 1.53432
\(546\) 3.12272e14 0.275406
\(547\) 3.74364e14 0.326861 0.163431 0.986555i \(-0.447744\pi\)
0.163431 + 0.986555i \(0.447744\pi\)
\(548\) −9.16578e14 −0.792276
\(549\) 1.74549e14 0.149372
\(550\) −2.91481e14 −0.246954
\(551\) 4.43057e15 3.71643
\(552\) 2.46787e14 0.204955
\(553\) 1.54449e15 1.26998
\(554\) 1.06339e14 0.0865742
\(555\) 4.46983e14 0.360313
\(556\) −1.63004e15 −1.30103
\(557\) −1.23516e15 −0.976153 −0.488077 0.872801i \(-0.662301\pi\)
−0.488077 + 0.872801i \(0.662301\pi\)
\(558\) −1.02307e14 −0.0800603
\(559\) 1.13224e15 0.877350
\(560\) −1.83860e15 −1.41076
\(561\) 8.49150e13 0.0645191
\(562\) −3.03425e13 −0.0228298
\(563\) 1.76993e15 1.31874 0.659370 0.751818i \(-0.270823\pi\)
0.659370 + 0.751818i \(0.270823\pi\)
\(564\) 2.23187e14 0.164677
\(565\) 3.44206e15 2.51508
\(566\) −3.73172e14 −0.270034
\(567\) 2.00903e14 0.143972
\(568\) 1.00349e15 0.712190
\(569\) 7.58600e13 0.0533206 0.0266603 0.999645i \(-0.491513\pi\)
0.0266603 + 0.999645i \(0.491513\pi\)
\(570\) −4.86398e14 −0.338595
\(571\) 9.69490e14 0.668413 0.334206 0.942500i \(-0.391532\pi\)
0.334206 + 0.942500i \(0.391532\pi\)
\(572\) −3.30991e15 −2.26016
\(573\) 1.43446e15 0.970146
\(574\) 4.82621e14 0.323289
\(575\) −8.07778e14 −0.535943
\(576\) −3.47072e14 −0.228085
\(577\) 9.50265e14 0.618554 0.309277 0.950972i \(-0.399913\pi\)
0.309277 + 0.950972i \(0.399913\pi\)
\(578\) 3.62207e14 0.233536
\(579\) −7.27161e14 −0.464407
\(580\) 3.75438e15 2.37511
\(581\) 8.95484e14 0.561163
\(582\) −2.06448e14 −0.128155
\(583\) 1.21694e15 0.748328
\(584\) 8.03112e14 0.489221
\(585\) −1.12571e15 −0.679312
\(586\) 8.50911e12 0.00508683
\(587\) 9.57183e14 0.566872 0.283436 0.958991i \(-0.408526\pi\)
0.283436 + 0.958991i \(0.408526\pi\)
\(588\) 6.31304e14 0.370394
\(589\) 3.38192e15 1.96576
\(590\) −6.89952e13 −0.0397313
\(591\) −8.62159e14 −0.491876
\(592\) 7.11550e14 0.402194
\(593\) −1.68405e15 −0.943091 −0.471546 0.881842i \(-0.656304\pi\)
−0.471546 + 0.881842i \(0.656304\pi\)
\(594\) 1.24245e14 0.0689370
\(595\) 2.24408e14 0.123366
\(596\) −1.58635e15 −0.864060
\(597\) 1.91117e15 1.03143
\(598\) 5.35188e14 0.286187
\(599\) 1.09435e15 0.579840 0.289920 0.957051i \(-0.406371\pi\)
0.289920 + 0.957051i \(0.406371\pi\)
\(600\) −3.46206e14 −0.181762
\(601\) −3.67077e15 −1.90962 −0.954812 0.297211i \(-0.903944\pi\)
−0.954812 + 0.297211i \(0.903944\pi\)
\(602\) −3.30251e14 −0.170241
\(603\) 1.02220e15 0.522145
\(604\) 3.42888e15 1.73560
\(605\) −3.43996e15 −1.72544
\(606\) −2.97461e13 −0.0147853
\(607\) 8.87977e14 0.437385 0.218693 0.975794i \(-0.429821\pi\)
0.218693 + 0.975794i \(0.429821\pi\)
\(608\) −2.57206e15 −1.25548
\(609\) −2.99089e15 −1.44679
\(610\) 2.85275e14 0.136757
\(611\) 9.96256e14 0.473309
\(612\) 4.89993e13 0.0230705
\(613\) 1.31161e15 0.612031 0.306015 0.952027i \(-0.401004\pi\)
0.306015 + 0.952027i \(0.401004\pi\)
\(614\) 4.09423e14 0.189342
\(615\) −1.73980e15 −0.797418
\(616\) 1.98720e15 0.902707
\(617\) 2.24011e14 0.100856 0.0504280 0.998728i \(-0.483941\pi\)
0.0504280 + 0.998728i \(0.483941\pi\)
\(618\) 1.75391e13 0.00782658
\(619\) 1.97391e15 0.873031 0.436515 0.899697i \(-0.356212\pi\)
0.436515 + 0.899697i \(0.356212\pi\)
\(620\) 2.86578e15 1.25629
\(621\) 3.44318e14 0.149608
\(622\) 5.14380e14 0.221532
\(623\) −3.26451e15 −1.39359
\(624\) −1.79201e15 −0.758272
\(625\) −2.89469e15 −1.21412
\(626\) −2.72552e14 −0.113316
\(627\) −4.10711e15 −1.69264
\(628\) −2.20734e15 −0.901762
\(629\) −8.68473e13 −0.0351704
\(630\) 3.28347e14 0.131813
\(631\) 3.02278e15 1.20294 0.601471 0.798895i \(-0.294582\pi\)
0.601471 + 0.798895i \(0.294582\pi\)
\(632\) 1.13449e15 0.447566
\(633\) 7.00290e14 0.273878
\(634\) 9.64477e14 0.373939
\(635\) 5.21736e15 2.00538
\(636\) 7.02222e14 0.267584
\(637\) 2.81800e15 1.06457
\(638\) −1.84966e15 −0.692753
\(639\) 1.40006e15 0.519868
\(640\) −2.87392e15 −1.05800
\(641\) −3.09596e15 −1.13000 −0.564998 0.825092i \(-0.691123\pi\)
−0.564998 + 0.825092i \(0.691123\pi\)
\(642\) −7.22781e12 −0.00261556
\(643\) −3.64598e15 −1.30814 −0.654069 0.756435i \(-0.726939\pi\)
−0.654069 + 0.756435i \(0.726939\pi\)
\(644\) 2.67549e15 0.951769
\(645\) 1.19052e15 0.419912
\(646\) 9.45054e13 0.0330505
\(647\) −4.64520e15 −1.61076 −0.805380 0.592759i \(-0.798039\pi\)
−0.805380 + 0.592759i \(0.798039\pi\)
\(648\) 1.47571e14 0.0507387
\(649\) −5.82591e14 −0.198618
\(650\) −7.50789e14 −0.253802
\(651\) −2.28299e15 −0.765260
\(652\) 2.17706e15 0.723617
\(653\) 3.83555e15 1.26417 0.632085 0.774899i \(-0.282199\pi\)
0.632085 + 0.774899i \(0.282199\pi\)
\(654\) −4.89616e14 −0.160021
\(655\) 3.22900e15 1.04650
\(656\) −2.76957e15 −0.890106
\(657\) 1.12050e15 0.357111
\(658\) −2.90588e14 −0.0918406
\(659\) −1.15381e15 −0.361631 −0.180816 0.983517i \(-0.557874\pi\)
−0.180816 + 0.983517i \(0.557874\pi\)
\(660\) −3.48029e15 −1.08174
\(661\) −2.01622e15 −0.621485 −0.310742 0.950494i \(-0.600578\pi\)
−0.310742 + 0.950494i \(0.600578\pi\)
\(662\) −6.85430e14 −0.209529
\(663\) 2.18722e14 0.0663082
\(664\) 6.57769e14 0.197765
\(665\) −1.08540e16 −3.23647
\(666\) −1.27072e14 −0.0375787
\(667\) −5.12594e15 −1.50342
\(668\) −2.24449e15 −0.652901
\(669\) 1.68651e15 0.486570
\(670\) 1.67064e15 0.478048
\(671\) 2.40884e15 0.683651
\(672\) 1.73629e15 0.488754
\(673\) −2.29558e15 −0.640928 −0.320464 0.947261i \(-0.603839\pi\)
−0.320464 + 0.947261i \(0.603839\pi\)
\(674\) 1.07579e15 0.297920
\(675\) −4.83026e14 −0.132678
\(676\) −5.05757e15 −1.37796
\(677\) 1.43072e15 0.386649 0.193325 0.981135i \(-0.438073\pi\)
0.193325 + 0.981135i \(0.438073\pi\)
\(678\) −9.78538e14 −0.262310
\(679\) −4.60692e15 −1.22497
\(680\) 1.64837e14 0.0434766
\(681\) −2.43435e15 −0.636905
\(682\) −1.41188e15 −0.366423
\(683\) 3.67944e15 0.947256 0.473628 0.880725i \(-0.342944\pi\)
0.473628 + 0.880725i \(0.342944\pi\)
\(684\) −2.36996e15 −0.605247
\(685\) −4.30200e15 −1.08986
\(686\) 3.88632e14 0.0976688
\(687\) −9.16777e14 −0.228561
\(688\) 1.89518e15 0.468721
\(689\) 3.13456e15 0.769079
\(690\) 5.62737e14 0.136973
\(691\) −6.73841e15 −1.62715 −0.813576 0.581459i \(-0.802482\pi\)
−0.813576 + 0.581459i \(0.802482\pi\)
\(692\) −1.27341e15 −0.305060
\(693\) 2.77253e15 0.658937
\(694\) 9.38271e14 0.221234
\(695\) −7.65068e15 −1.78971
\(696\) −2.19693e15 −0.509876
\(697\) 3.38037e14 0.0778366
\(698\) 9.42747e14 0.215372
\(699\) −2.50276e15 −0.567277
\(700\) −3.75331e15 −0.844064
\(701\) 3.41642e14 0.0762294 0.0381147 0.999273i \(-0.487865\pi\)
0.0381147 + 0.999273i \(0.487865\pi\)
\(702\) 3.20026e14 0.0708486
\(703\) 4.20057e15 0.922686
\(704\) −4.78972e15 −1.04390
\(705\) 1.04754e15 0.226532
\(706\) 1.03509e15 0.222102
\(707\) −6.63788e14 −0.141326
\(708\) −3.36178e14 −0.0710208
\(709\) −2.14634e15 −0.449929 −0.224965 0.974367i \(-0.572227\pi\)
−0.224965 + 0.974367i \(0.572227\pi\)
\(710\) 2.28820e15 0.475964
\(711\) 1.58284e15 0.326704
\(712\) −2.39791e15 −0.491127
\(713\) −3.91271e15 −0.795216
\(714\) −6.37966e13 −0.0128664
\(715\) −1.55352e16 −3.10910
\(716\) −1.89197e15 −0.375744
\(717\) 5.55753e15 1.09528
\(718\) 1.74566e15 0.341410
\(719\) −3.75354e15 −0.728505 −0.364252 0.931300i \(-0.618675\pi\)
−0.364252 + 0.931300i \(0.618675\pi\)
\(720\) −1.88425e15 −0.362920
\(721\) 3.91388e14 0.0748106
\(722\) −3.33319e15 −0.632274
\(723\) 1.82189e14 0.0342974
\(724\) 3.60925e15 0.674303
\(725\) 7.19092e15 1.33329
\(726\) 9.77940e14 0.179954
\(727\) −4.00725e15 −0.731825 −0.365912 0.930649i \(-0.619243\pi\)
−0.365912 + 0.930649i \(0.619243\pi\)
\(728\) 5.11856e15 0.927738
\(729\) 2.05891e14 0.0370370
\(730\) 1.83130e15 0.326951
\(731\) −2.31314e14 −0.0409880
\(732\) 1.39000e15 0.244457
\(733\) 5.72837e15 0.999906 0.499953 0.866053i \(-0.333351\pi\)
0.499953 + 0.866053i \(0.333351\pi\)
\(734\) 9.64736e14 0.167140
\(735\) 2.96305e15 0.509518
\(736\) 2.97574e15 0.507886
\(737\) 1.41068e16 2.38977
\(738\) 4.94604e14 0.0831664
\(739\) 3.82007e15 0.637568 0.318784 0.947827i \(-0.396726\pi\)
0.318784 + 0.947827i \(0.396726\pi\)
\(740\) 3.55949e15 0.589675
\(741\) −1.05790e16 −1.73958
\(742\) −9.14287e14 −0.149232
\(743\) 1.15911e16 1.87796 0.938981 0.343969i \(-0.111771\pi\)
0.938981 + 0.343969i \(0.111771\pi\)
\(744\) −1.67695e15 −0.269692
\(745\) −7.44559e15 −1.18861
\(746\) −2.14523e15 −0.339946
\(747\) 9.17718e14 0.144360
\(748\) 6.76208e14 0.105590
\(749\) −1.61289e14 −0.0250009
\(750\) 3.55643e14 0.0547239
\(751\) 7.92089e15 1.20991 0.604956 0.796259i \(-0.293190\pi\)
0.604956 + 0.796259i \(0.293190\pi\)
\(752\) 1.66757e15 0.252863
\(753\) 2.40941e15 0.362692
\(754\) −4.76430e15 −0.711962
\(755\) 1.60936e16 2.38751
\(756\) 1.59986e15 0.235620
\(757\) 1.94070e15 0.283747 0.141874 0.989885i \(-0.454687\pi\)
0.141874 + 0.989885i \(0.454687\pi\)
\(758\) 1.82648e14 0.0265116
\(759\) 4.75171e15 0.684732
\(760\) −7.97272e15 −1.14060
\(761\) −3.75428e15 −0.533225 −0.266613 0.963804i \(-0.585904\pi\)
−0.266613 + 0.963804i \(0.585904\pi\)
\(762\) −1.48323e15 −0.209150
\(763\) −1.09258e16 −1.52957
\(764\) 1.14231e16 1.58771
\(765\) 2.29980e14 0.0317360
\(766\) 4.78868e14 0.0656081
\(767\) −1.50062e15 −0.204125
\(768\) −2.10810e15 −0.284710
\(769\) 8.90458e15 1.19404 0.597020 0.802227i \(-0.296351\pi\)
0.597020 + 0.802227i \(0.296351\pi\)
\(770\) 4.53131e15 0.603288
\(771\) −4.23297e15 −0.559560
\(772\) −5.79064e15 −0.760032
\(773\) −4.45228e14 −0.0580223 −0.0290112 0.999579i \(-0.509236\pi\)
−0.0290112 + 0.999579i \(0.509236\pi\)
\(774\) −3.38451e14 −0.0437946
\(775\) 5.48894e15 0.705228
\(776\) −3.38396e15 −0.431704
\(777\) −2.83563e15 −0.359198
\(778\) 2.65440e15 0.333871
\(779\) −1.63499e16 −2.04202
\(780\) −8.96443e15 −1.11174
\(781\) 1.93214e16 2.37935
\(782\) −1.09338e14 −0.0133701
\(783\) −3.06515e15 −0.372188
\(784\) 4.71686e15 0.568742
\(785\) −1.03603e16 −1.24048
\(786\) −9.17966e14 −0.109145
\(787\) 1.81740e15 0.214580 0.107290 0.994228i \(-0.465783\pi\)
0.107290 + 0.994228i \(0.465783\pi\)
\(788\) −6.86568e15 −0.804987
\(789\) 4.26489e15 0.496575
\(790\) 2.58692e15 0.299112
\(791\) −2.18362e16 −2.50730
\(792\) 2.03654e15 0.232222
\(793\) 6.20463e15 0.702608
\(794\) 2.40652e15 0.270631
\(795\) 3.29591e15 0.368092
\(796\) 1.52194e16 1.68801
\(797\) −5.13538e15 −0.565655 −0.282828 0.959171i \(-0.591272\pi\)
−0.282828 + 0.959171i \(0.591272\pi\)
\(798\) 3.08567e15 0.337546
\(799\) −2.03533e14 −0.0221120
\(800\) −4.17451e15 −0.450413
\(801\) −3.34557e15 −0.358501
\(802\) −1.01835e15 −0.108377
\(803\) 1.54633e16 1.63443
\(804\) 8.14016e15 0.854524
\(805\) 1.25575e16 1.30926
\(806\) −3.63667e15 −0.376583
\(807\) −4.52599e15 −0.465489
\(808\) −4.87579e14 −0.0498061
\(809\) −9.92930e14 −0.100740 −0.0503700 0.998731i \(-0.516040\pi\)
−0.0503700 + 0.998731i \(0.516040\pi\)
\(810\) 3.36499e14 0.0339091
\(811\) 8.87864e15 0.888652 0.444326 0.895865i \(-0.353443\pi\)
0.444326 + 0.895865i \(0.353443\pi\)
\(812\) −2.38175e16 −2.36776
\(813\) −1.00789e16 −0.995210
\(814\) −1.75364e15 −0.171991
\(815\) 1.02181e16 0.995417
\(816\) 3.66104e14 0.0354249
\(817\) 1.11880e16 1.07531
\(818\) −3.32108e15 −0.317056
\(819\) 7.14141e15 0.677209
\(820\) −1.38546e16 −1.30503
\(821\) −1.02137e16 −0.955643 −0.477821 0.878457i \(-0.658573\pi\)
−0.477821 + 0.878457i \(0.658573\pi\)
\(822\) 1.22301e15 0.113667
\(823\) −1.93889e16 −1.79000 −0.895001 0.446063i \(-0.852826\pi\)
−0.895001 + 0.446063i \(0.852826\pi\)
\(824\) 2.87490e14 0.0263647
\(825\) −6.66594e15 −0.607246
\(826\) 4.37700e14 0.0396083
\(827\) −1.63787e16 −1.47231 −0.736153 0.676815i \(-0.763360\pi\)
−0.736153 + 0.676815i \(0.763360\pi\)
\(828\) 2.74192e15 0.244843
\(829\) −1.53869e16 −1.36490 −0.682450 0.730932i \(-0.739086\pi\)
−0.682450 + 0.730932i \(0.739086\pi\)
\(830\) 1.49988e15 0.132168
\(831\) 2.43188e15 0.212881
\(832\) −1.23372e16 −1.07285
\(833\) −5.75711e14 −0.0497344
\(834\) 2.17500e15 0.186657
\(835\) −1.05346e16 −0.898139
\(836\) −3.27064e16 −2.77012
\(837\) −2.33968e15 −0.196864
\(838\) 1.39450e15 0.116567
\(839\) −3.30349e15 −0.274336 −0.137168 0.990548i \(-0.543800\pi\)
−0.137168 + 0.990548i \(0.543800\pi\)
\(840\) 5.38204e15 0.444029
\(841\) 3.34311e16 2.74014
\(842\) −2.29321e15 −0.186736
\(843\) −6.93909e14 −0.0561372
\(844\) 5.57666e15 0.448219
\(845\) −2.37380e16 −1.89553
\(846\) −2.97803e14 −0.0236261
\(847\) 2.18228e16 1.72009
\(848\) 5.24673e15 0.410877
\(849\) −8.53414e15 −0.663999
\(850\) 1.53385e14 0.0118571
\(851\) −4.85984e15 −0.373258
\(852\) 1.11492e16 0.850798
\(853\) 8.53780e15 0.647330 0.323665 0.946172i \(-0.395085\pi\)
0.323665 + 0.946172i \(0.395085\pi\)
\(854\) −1.80976e15 −0.136334
\(855\) −1.11235e16 −0.832585
\(856\) −1.18473e14 −0.00881080
\(857\) 3.51817e15 0.259969 0.129985 0.991516i \(-0.458507\pi\)
0.129985 + 0.991516i \(0.458507\pi\)
\(858\) 4.41648e15 0.324262
\(859\) 2.39282e16 1.74561 0.872806 0.488067i \(-0.162298\pi\)
0.872806 + 0.488067i \(0.162298\pi\)
\(860\) 9.48054e15 0.687213
\(861\) 1.10371e16 0.794949
\(862\) −1.79073e15 −0.128156
\(863\) 4.05306e15 0.288220 0.144110 0.989562i \(-0.453968\pi\)
0.144110 + 0.989562i \(0.453968\pi\)
\(864\) 1.77940e15 0.125732
\(865\) −5.97681e15 −0.419644
\(866\) 3.15278e15 0.219961
\(867\) 8.28339e15 0.574252
\(868\) −1.81803e16 −1.25240
\(869\) 2.18438e16 1.49527
\(870\) −5.00954e15 −0.340755
\(871\) 3.63358e16 2.45604
\(872\) −8.02546e15 −0.539050
\(873\) −4.72130e15 −0.315126
\(874\) 5.28838e15 0.350760
\(875\) 7.93621e15 0.523081
\(876\) 8.92295e15 0.584434
\(877\) −1.35224e16 −0.880147 −0.440074 0.897962i \(-0.645048\pi\)
−0.440074 + 0.897962i \(0.645048\pi\)
\(878\) −1.29857e15 −0.0839932
\(879\) 1.94596e14 0.0125082
\(880\) −2.60034e16 −1.66102
\(881\) −5.26571e15 −0.334264 −0.167132 0.985935i \(-0.553451\pi\)
−0.167132 + 0.985935i \(0.553451\pi\)
\(882\) −8.42361e14 −0.0531399
\(883\) 9.43476e15 0.591490 0.295745 0.955267i \(-0.404432\pi\)
0.295745 + 0.955267i \(0.404432\pi\)
\(884\) 1.74176e15 0.108518
\(885\) −1.57786e15 −0.0976971
\(886\) −4.06551e15 −0.250167
\(887\) 1.48332e16 0.907097 0.453549 0.891232i \(-0.350158\pi\)
0.453549 + 0.891232i \(0.350158\pi\)
\(888\) −2.08288e15 −0.126588
\(889\) −3.30985e16 −1.99917
\(890\) −5.46785e15 −0.328225
\(891\) 2.84138e15 0.169512
\(892\) 1.34303e16 0.796304
\(893\) 9.84435e15 0.580101
\(894\) 2.11669e15 0.123966
\(895\) −8.88004e15 −0.516878
\(896\) 1.82319e16 1.05472
\(897\) 1.22393e16 0.703718
\(898\) 7.02961e14 0.0401709
\(899\) 3.48313e16 1.97830
\(900\) −3.84651e15 −0.217136
\(901\) −6.40384e14 −0.0359297
\(902\) 6.82573e15 0.380639
\(903\) −7.55257e15 −0.418612
\(904\) −1.60395e16 −0.883620
\(905\) 1.69402e16 0.927580
\(906\) −4.57522e15 −0.249004
\(907\) −4.11603e15 −0.222658 −0.111329 0.993784i \(-0.535511\pi\)
−0.111329 + 0.993784i \(0.535511\pi\)
\(908\) −1.93856e16 −1.04234
\(909\) −6.80270e14 −0.0363563
\(910\) 1.16716e16 0.620016
\(911\) 2.40095e15 0.126775 0.0633873 0.997989i \(-0.479810\pi\)
0.0633873 + 0.997989i \(0.479810\pi\)
\(912\) −1.77075e16 −0.929361
\(913\) 1.26649e16 0.660710
\(914\) −8.38387e15 −0.434751
\(915\) 6.52401e15 0.336278
\(916\) −7.30062e15 −0.374055
\(917\) −2.04845e16 −1.04326
\(918\) −6.53806e13 −0.00330990
\(919\) −2.76545e16 −1.39165 −0.695826 0.718210i \(-0.744962\pi\)
−0.695826 + 0.718210i \(0.744962\pi\)
\(920\) 9.22402e15 0.461410
\(921\) 9.36318e15 0.465581
\(922\) −7.13637e15 −0.352742
\(923\) 4.97676e16 2.44533
\(924\) 2.20787e16 1.07839
\(925\) 6.81763e15 0.331020
\(926\) 3.53287e15 0.170517
\(927\) 4.01106e14 0.0192451
\(928\) −2.64903e16 −1.26349
\(929\) 1.34456e16 0.637519 0.318759 0.947836i \(-0.396734\pi\)
0.318759 + 0.947836i \(0.396734\pi\)
\(930\) −3.82386e15 −0.180238
\(931\) 2.78456e16 1.30477
\(932\) −1.99304e16 −0.928384
\(933\) 1.17635e16 0.544736
\(934\) 7.98119e15 0.367417
\(935\) 3.17381e15 0.145250
\(936\) 5.24565e15 0.238662
\(937\) 4.76557e15 0.215550 0.107775 0.994175i \(-0.465627\pi\)
0.107775 + 0.994175i \(0.465627\pi\)
\(938\) −1.05984e16 −0.476568
\(939\) −6.23305e15 −0.278638
\(940\) 8.34192e15 0.370734
\(941\) 2.65555e16 1.17331 0.586653 0.809839i \(-0.300445\pi\)
0.586653 + 0.809839i \(0.300445\pi\)
\(942\) 2.94530e15 0.129375
\(943\) 1.89160e16 0.826068
\(944\) −2.51179e15 −0.109053
\(945\) 7.50902e15 0.324122
\(946\) −4.67075e15 −0.200440
\(947\) −5.12655e15 −0.218726 −0.109363 0.994002i \(-0.534881\pi\)
−0.109363 + 0.994002i \(0.534881\pi\)
\(948\) 1.26047e16 0.534671
\(949\) 3.98300e16 1.67976
\(950\) −7.41880e15 −0.311067
\(951\) 2.20568e16 0.919496
\(952\) −1.04571e15 −0.0433420
\(953\) −1.77624e16 −0.731966 −0.365983 0.930622i \(-0.619267\pi\)
−0.365983 + 0.930622i \(0.619267\pi\)
\(954\) −9.36988e14 −0.0383900
\(955\) 5.36148e16 2.18407
\(956\) 4.42566e16 1.79250
\(957\) −4.23002e16 −1.70344
\(958\) 3.65113e15 0.146190
\(959\) 2.72915e16 1.08649
\(960\) −1.29723e16 −0.513481
\(961\) 1.17882e15 0.0463947
\(962\) −4.51698e15 −0.176761
\(963\) −1.65294e14 −0.00643151
\(964\) 1.45084e15 0.0561299
\(965\) −2.71786e16 −1.04551
\(966\) −3.56996e15 −0.136549
\(967\) −2.69583e16 −1.02529 −0.512646 0.858600i \(-0.671335\pi\)
−0.512646 + 0.858600i \(0.671335\pi\)
\(968\) 1.60297e16 0.606195
\(969\) 2.16126e15 0.0812693
\(970\) −7.71629e15 −0.288512
\(971\) −9.08427e15 −0.337741 −0.168871 0.985638i \(-0.554012\pi\)
−0.168871 + 0.985638i \(0.554012\pi\)
\(972\) 1.63958e15 0.0606135
\(973\) 4.85353e16 1.78417
\(974\) 4.90058e15 0.179132
\(975\) −1.71699e16 −0.624084
\(976\) 1.03855e16 0.375366
\(977\) −2.83300e16 −1.01819 −0.509093 0.860712i \(-0.670019\pi\)
−0.509093 + 0.860712i \(0.670019\pi\)
\(978\) −2.90489e15 −0.103817
\(979\) −4.61701e16 −1.64080
\(980\) 2.35959e16 0.833859
\(981\) −1.11971e16 −0.393483
\(982\) 1.12691e16 0.393802
\(983\) −1.34904e16 −0.468791 −0.234395 0.972141i \(-0.575311\pi\)
−0.234395 + 0.972141i \(0.575311\pi\)
\(984\) 8.10723e15 0.280156
\(985\) −3.22244e16 −1.10735
\(986\) 9.73337e14 0.0332614
\(987\) −6.64550e15 −0.225831
\(988\) −8.42441e16 −2.84693
\(989\) −1.29440e16 −0.434999
\(990\) 4.64382e15 0.155196
\(991\) 1.42310e15 0.0472967 0.0236483 0.999720i \(-0.492472\pi\)
0.0236483 + 0.999720i \(0.492472\pi\)
\(992\) −2.02205e16 −0.668309
\(993\) −1.56752e16 −0.515220
\(994\) −1.45162e16 −0.474490
\(995\) 7.14328e16 2.32204
\(996\) 7.30812e15 0.236254
\(997\) 2.29775e16 0.738720 0.369360 0.929286i \(-0.379577\pi\)
0.369360 + 0.929286i \(0.379577\pi\)
\(998\) 9.97597e14 0.0318961
\(999\) −2.90603e15 −0.0924039
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.1.12 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.12 27 1.1 even 1 trivial