Properties

Label 177.12.a.c.1.14
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 1.14
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-5.14065 q^{2} -243.000 q^{3} -2021.57 q^{4} +3789.43 q^{5} +1249.18 q^{6} -36302.1 q^{7} +20920.3 q^{8} +59049.0 q^{9} -19480.2 q^{10} -671806. q^{11} +491242. q^{12} +1.37666e6 q^{13} +186616. q^{14} -920832. q^{15} +4.03264e6 q^{16} -4.33060e6 q^{17} -303550. q^{18} +8.25438e6 q^{19} -7.66062e6 q^{20} +8.82141e6 q^{21} +3.45352e6 q^{22} -6.13520e7 q^{23} -5.08362e6 q^{24} -3.44683e7 q^{25} -7.07696e6 q^{26} -1.43489e7 q^{27} +7.33874e7 q^{28} -7.51187e7 q^{29} +4.73368e6 q^{30} +2.73144e8 q^{31} -6.35751e7 q^{32} +1.63249e8 q^{33} +2.22621e7 q^{34} -1.37564e8 q^{35} -1.19372e8 q^{36} -5.71706e8 q^{37} -4.24329e7 q^{38} -3.34530e8 q^{39} +7.92759e7 q^{40} -9.81972e8 q^{41} -4.53478e7 q^{42} +1.36438e9 q^{43} +1.35810e9 q^{44} +2.23762e8 q^{45} +3.15389e8 q^{46} -1.13219e9 q^{47} -9.79931e8 q^{48} -6.59485e8 q^{49} +1.77190e8 q^{50} +1.05234e9 q^{51} -2.78303e9 q^{52} -3.65087e9 q^{53} +7.37628e7 q^{54} -2.54576e9 q^{55} -7.59449e8 q^{56} -2.00581e9 q^{57} +3.86159e8 q^{58} -7.14924e8 q^{59} +1.86153e9 q^{60} +4.73749e9 q^{61} -1.40414e9 q^{62} -2.14360e9 q^{63} -7.93203e9 q^{64} +5.21678e9 q^{65} -8.39206e8 q^{66} -1.18157e10 q^{67} +8.75463e9 q^{68} +1.49085e10 q^{69} +7.07170e8 q^{70} -2.10973e10 q^{71} +1.23532e9 q^{72} -4.85638e9 q^{73} +2.93894e9 q^{74} +8.37580e9 q^{75} -1.66868e10 q^{76} +2.43880e10 q^{77} +1.71970e9 q^{78} -3.22186e10 q^{79} +1.52814e10 q^{80} +3.48678e9 q^{81} +5.04798e9 q^{82} -3.61907e10 q^{83} -1.78331e10 q^{84} -1.64105e10 q^{85} -7.01379e9 q^{86} +1.82538e10 q^{87} -1.40544e10 q^{88} -1.60558e10 q^{89} -1.15028e9 q^{90} -4.99758e10 q^{91} +1.24028e11 q^{92} -6.63739e10 q^{93} +5.82020e9 q^{94} +3.12794e10 q^{95} +1.54487e10 q^{96} +1.28235e11 q^{97} +3.39018e9 q^{98} -3.96695e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.14065 −0.113593 −0.0567967 0.998386i \(-0.518089\pi\)
−0.0567967 + 0.998386i \(0.518089\pi\)
\(3\) −243.000 −0.577350
\(4\) −2021.57 −0.987097
\(5\) 3789.43 0.542299 0.271150 0.962537i \(-0.412596\pi\)
0.271150 + 0.962537i \(0.412596\pi\)
\(6\) 1249.18 0.0655832
\(7\) −36302.1 −0.816380 −0.408190 0.912897i \(-0.633840\pi\)
−0.408190 + 0.912897i \(0.633840\pi\)
\(8\) 20920.3 0.225721
\(9\) 59049.0 0.333333
\(10\) −19480.2 −0.0616017
\(11\) −671806. −1.25772 −0.628860 0.777519i \(-0.716478\pi\)
−0.628860 + 0.777519i \(0.716478\pi\)
\(12\) 491242. 0.569900
\(13\) 1.37666e6 1.02835 0.514174 0.857686i \(-0.328099\pi\)
0.514174 + 0.857686i \(0.328099\pi\)
\(14\) 186616. 0.0927354
\(15\) −920832. −0.313097
\(16\) 4.03264e6 0.961456
\(17\) −4.33060e6 −0.739740 −0.369870 0.929083i \(-0.620598\pi\)
−0.369870 + 0.929083i \(0.620598\pi\)
\(18\) −303550. −0.0378645
\(19\) 8.25438e6 0.764785 0.382393 0.924000i \(-0.375100\pi\)
0.382393 + 0.924000i \(0.375100\pi\)
\(20\) −7.66062e6 −0.535302
\(21\) 8.82141e6 0.471337
\(22\) 3.45352e6 0.142869
\(23\) −6.13520e7 −1.98758 −0.993792 0.111251i \(-0.964514\pi\)
−0.993792 + 0.111251i \(0.964514\pi\)
\(24\) −5.08362e6 −0.130320
\(25\) −3.44683e7 −0.705911
\(26\) −7.07696e6 −0.116814
\(27\) −1.43489e7 −0.192450
\(28\) 7.33874e7 0.805846
\(29\) −7.51187e7 −0.680078 −0.340039 0.940411i \(-0.610440\pi\)
−0.340039 + 0.940411i \(0.610440\pi\)
\(30\) 4.73368e6 0.0355657
\(31\) 2.73144e8 1.71357 0.856785 0.515674i \(-0.172458\pi\)
0.856785 + 0.515674i \(0.172458\pi\)
\(32\) −6.35751e7 −0.334936
\(33\) 1.63249e8 0.726145
\(34\) 2.22621e7 0.0840297
\(35\) −1.37564e8 −0.442722
\(36\) −1.19372e8 −0.329032
\(37\) −5.71706e8 −1.35539 −0.677694 0.735344i \(-0.737021\pi\)
−0.677694 + 0.735344i \(0.737021\pi\)
\(38\) −4.24329e7 −0.0868746
\(39\) −3.34530e8 −0.593717
\(40\) 7.92759e7 0.122408
\(41\) −9.81972e8 −1.32370 −0.661848 0.749638i \(-0.730227\pi\)
−0.661848 + 0.749638i \(0.730227\pi\)
\(42\) −4.53478e7 −0.0535408
\(43\) 1.36438e9 1.41533 0.707666 0.706548i \(-0.249748\pi\)
0.707666 + 0.706548i \(0.249748\pi\)
\(44\) 1.35810e9 1.24149
\(45\) 2.23762e8 0.180766
\(46\) 3.15389e8 0.225777
\(47\) −1.13219e9 −0.720082 −0.360041 0.932937i \(-0.617237\pi\)
−0.360041 + 0.932937i \(0.617237\pi\)
\(48\) −9.79931e8 −0.555097
\(49\) −6.59485e8 −0.333523
\(50\) 1.77190e8 0.0801869
\(51\) 1.05234e9 0.427089
\(52\) −2.78303e9 −1.01508
\(53\) −3.65087e9 −1.19917 −0.599583 0.800312i \(-0.704667\pi\)
−0.599583 + 0.800312i \(0.704667\pi\)
\(54\) 7.37628e7 0.0218611
\(55\) −2.54576e9 −0.682061
\(56\) −7.59449e8 −0.184274
\(57\) −2.00581e9 −0.441549
\(58\) 3.86159e8 0.0772524
\(59\) −7.14924e8 −0.130189
\(60\) 1.86153e9 0.309057
\(61\) 4.73749e9 0.718181 0.359091 0.933303i \(-0.383087\pi\)
0.359091 + 0.933303i \(0.383087\pi\)
\(62\) −1.40414e9 −0.194650
\(63\) −2.14360e9 −0.272127
\(64\) −7.93203e9 −0.923410
\(65\) 5.21678e9 0.557672
\(66\) −8.39206e8 −0.0824853
\(67\) −1.18157e10 −1.06917 −0.534587 0.845113i \(-0.679533\pi\)
−0.534587 + 0.845113i \(0.679533\pi\)
\(68\) 8.75463e9 0.730195
\(69\) 1.49085e10 1.14753
\(70\) 7.07170e8 0.0502904
\(71\) −2.10973e10 −1.38773 −0.693867 0.720103i \(-0.744095\pi\)
−0.693867 + 0.720103i \(0.744095\pi\)
\(72\) 1.23532e9 0.0752404
\(73\) −4.85638e9 −0.274181 −0.137090 0.990559i \(-0.543775\pi\)
−0.137090 + 0.990559i \(0.543775\pi\)
\(74\) 2.93894e9 0.153963
\(75\) 8.37580e9 0.407558
\(76\) −1.66868e10 −0.754917
\(77\) 2.43880e10 1.02678
\(78\) 1.71970e9 0.0674423
\(79\) −3.22186e10 −1.17803 −0.589017 0.808121i \(-0.700485\pi\)
−0.589017 + 0.808121i \(0.700485\pi\)
\(80\) 1.52814e10 0.521397
\(81\) 3.48678e9 0.111111
\(82\) 5.04798e9 0.150363
\(83\) −3.61907e10 −1.00848 −0.504240 0.863563i \(-0.668227\pi\)
−0.504240 + 0.863563i \(0.668227\pi\)
\(84\) −1.78331e10 −0.465255
\(85\) −1.64105e10 −0.401161
\(86\) −7.01379e9 −0.160772
\(87\) 1.82538e10 0.392643
\(88\) −1.40544e10 −0.283894
\(89\) −1.60558e10 −0.304779 −0.152390 0.988320i \(-0.548697\pi\)
−0.152390 + 0.988320i \(0.548697\pi\)
\(90\) −1.15028e9 −0.0205339
\(91\) −4.99758e10 −0.839522
\(92\) 1.24028e11 1.96194
\(93\) −6.63739e10 −0.989330
\(94\) 5.82020e9 0.0817966
\(95\) 3.12794e10 0.414743
\(96\) 1.54487e10 0.193376
\(97\) 1.28235e11 1.51622 0.758110 0.652127i \(-0.226123\pi\)
0.758110 + 0.652127i \(0.226123\pi\)
\(98\) 3.39018e9 0.0378861
\(99\) −3.96695e10 −0.419240
\(100\) 6.96803e10 0.696803
\(101\) 1.34185e11 1.27039 0.635196 0.772351i \(-0.280919\pi\)
0.635196 + 0.772351i \(0.280919\pi\)
\(102\) −5.40970e9 −0.0485146
\(103\) 6.70298e10 0.569723 0.284861 0.958569i \(-0.408052\pi\)
0.284861 + 0.958569i \(0.408052\pi\)
\(104\) 2.88002e10 0.232120
\(105\) 3.34281e10 0.255606
\(106\) 1.87679e10 0.136217
\(107\) 2.12026e11 1.46143 0.730716 0.682682i \(-0.239187\pi\)
0.730716 + 0.682682i \(0.239187\pi\)
\(108\) 2.90074e10 0.189967
\(109\) −1.09209e11 −0.679846 −0.339923 0.940453i \(-0.610401\pi\)
−0.339923 + 0.940453i \(0.610401\pi\)
\(110\) 1.30869e10 0.0774776
\(111\) 1.38925e11 0.782534
\(112\) −1.46393e11 −0.784914
\(113\) 3.74403e10 0.191165 0.0955825 0.995422i \(-0.469529\pi\)
0.0955825 + 0.995422i \(0.469529\pi\)
\(114\) 1.03112e10 0.0501571
\(115\) −2.32489e11 −1.07787
\(116\) 1.51858e11 0.671303
\(117\) 8.12907e10 0.342782
\(118\) 3.67518e9 0.0147886
\(119\) 1.57210e11 0.603909
\(120\) −1.92640e10 −0.0706725
\(121\) 1.66011e11 0.581860
\(122\) −2.43538e10 −0.0815807
\(123\) 2.38619e11 0.764236
\(124\) −5.52180e11 −1.69146
\(125\) −3.15646e11 −0.925115
\(126\) 1.10195e10 0.0309118
\(127\) 5.88565e11 1.58079 0.790395 0.612597i \(-0.209875\pi\)
0.790395 + 0.612597i \(0.209875\pi\)
\(128\) 1.70978e11 0.439830
\(129\) −3.31544e11 −0.817142
\(130\) −2.68176e10 −0.0633479
\(131\) −3.19444e11 −0.723440 −0.361720 0.932287i \(-0.617810\pi\)
−0.361720 + 0.932287i \(0.617810\pi\)
\(132\) −3.30020e11 −0.716775
\(133\) −2.99651e11 −0.624356
\(134\) 6.07405e10 0.121451
\(135\) −5.43742e10 −0.104366
\(136\) −9.05974e10 −0.166975
\(137\) −2.28257e11 −0.404074 −0.202037 0.979378i \(-0.564756\pi\)
−0.202037 + 0.979378i \(0.564756\pi\)
\(138\) −7.66396e10 −0.130352
\(139\) 4.86391e11 0.795068 0.397534 0.917587i \(-0.369866\pi\)
0.397534 + 0.917587i \(0.369866\pi\)
\(140\) 2.78096e11 0.437010
\(141\) 2.75123e11 0.415739
\(142\) 1.08454e11 0.157638
\(143\) −9.24852e11 −1.29337
\(144\) 2.38123e11 0.320485
\(145\) −2.84657e11 −0.368806
\(146\) 2.49649e10 0.0311451
\(147\) 1.60255e11 0.192560
\(148\) 1.15575e12 1.33790
\(149\) −3.60386e11 −0.402016 −0.201008 0.979590i \(-0.564422\pi\)
−0.201008 + 0.979590i \(0.564422\pi\)
\(150\) −4.30571e10 −0.0462959
\(151\) −8.20006e11 −0.850049 −0.425024 0.905182i \(-0.639734\pi\)
−0.425024 + 0.905182i \(0.639734\pi\)
\(152\) 1.72684e11 0.172628
\(153\) −2.55718e11 −0.246580
\(154\) −1.25370e11 −0.116635
\(155\) 1.03506e12 0.929268
\(156\) 6.76276e11 0.586056
\(157\) −1.34208e11 −0.112287 −0.0561435 0.998423i \(-0.517880\pi\)
−0.0561435 + 0.998423i \(0.517880\pi\)
\(158\) 1.65625e11 0.133817
\(159\) 8.87162e11 0.692339
\(160\) −2.40914e11 −0.181636
\(161\) 2.22721e12 1.62262
\(162\) −1.79243e10 −0.0126215
\(163\) 1.82174e12 1.24009 0.620046 0.784566i \(-0.287114\pi\)
0.620046 + 0.784566i \(0.287114\pi\)
\(164\) 1.98513e12 1.30662
\(165\) 6.18620e11 0.393788
\(166\) 1.86044e11 0.114557
\(167\) 1.74140e12 1.03743 0.518713 0.854948i \(-0.326411\pi\)
0.518713 + 0.854948i \(0.326411\pi\)
\(168\) 1.84546e11 0.106391
\(169\) 1.03046e11 0.0574982
\(170\) 8.43608e10 0.0455692
\(171\) 4.87413e11 0.254928
\(172\) −2.75819e12 −1.39707
\(173\) 4.58319e11 0.224861 0.112430 0.993660i \(-0.464136\pi\)
0.112430 + 0.993660i \(0.464136\pi\)
\(174\) −9.38366e10 −0.0446017
\(175\) 1.25127e12 0.576292
\(176\) −2.70915e12 −1.20924
\(177\) 1.73727e11 0.0751646
\(178\) 8.25371e10 0.0346210
\(179\) −4.11251e10 −0.0167269 −0.00836345 0.999965i \(-0.502662\pi\)
−0.00836345 + 0.999965i \(0.502662\pi\)
\(180\) −4.52352e11 −0.178434
\(181\) 3.53519e12 1.35264 0.676318 0.736610i \(-0.263575\pi\)
0.676318 + 0.736610i \(0.263575\pi\)
\(182\) 2.56908e11 0.0953642
\(183\) −1.15121e12 −0.414642
\(184\) −1.28350e12 −0.448640
\(185\) −2.16644e12 −0.735026
\(186\) 3.41205e11 0.112381
\(187\) 2.90932e12 0.930386
\(188\) 2.28881e12 0.710790
\(189\) 5.20895e11 0.157112
\(190\) −1.60797e11 −0.0471120
\(191\) 8.11282e11 0.230934 0.115467 0.993311i \(-0.463164\pi\)
0.115467 + 0.993311i \(0.463164\pi\)
\(192\) 1.92748e12 0.533131
\(193\) −1.33845e12 −0.359779 −0.179890 0.983687i \(-0.557574\pi\)
−0.179890 + 0.983687i \(0.557574\pi\)
\(194\) −6.59212e11 −0.172233
\(195\) −1.26768e12 −0.321972
\(196\) 1.33320e12 0.329220
\(197\) 7.58650e12 1.82170 0.910850 0.412737i \(-0.135427\pi\)
0.910850 + 0.412737i \(0.135427\pi\)
\(198\) 2.03927e11 0.0476229
\(199\) 1.86054e12 0.422618 0.211309 0.977419i \(-0.432227\pi\)
0.211309 + 0.977419i \(0.432227\pi\)
\(200\) −7.21087e11 −0.159339
\(201\) 2.87122e12 0.617288
\(202\) −6.89801e11 −0.144308
\(203\) 2.72696e12 0.555202
\(204\) −2.12738e12 −0.421578
\(205\) −3.72112e12 −0.717839
\(206\) −3.44577e11 −0.0647168
\(207\) −3.62277e12 −0.662528
\(208\) 5.55159e12 0.988711
\(209\) −5.54534e12 −0.961886
\(210\) −1.71842e11 −0.0290352
\(211\) 7.60940e12 1.25256 0.626278 0.779600i \(-0.284578\pi\)
0.626278 + 0.779600i \(0.284578\pi\)
\(212\) 7.38051e12 1.18369
\(213\) 5.12665e12 0.801209
\(214\) −1.08995e12 −0.166009
\(215\) 5.17022e12 0.767533
\(216\) −3.00183e11 −0.0434401
\(217\) −9.91569e12 −1.39892
\(218\) 5.61403e11 0.0772261
\(219\) 1.18010e12 0.158298
\(220\) 5.14645e12 0.673260
\(221\) −5.96179e12 −0.760710
\(222\) −7.14164e11 −0.0888907
\(223\) 1.12582e13 1.36708 0.683539 0.729914i \(-0.260440\pi\)
0.683539 + 0.729914i \(0.260440\pi\)
\(224\) 2.30791e12 0.273435
\(225\) −2.03532e12 −0.235304
\(226\) −1.92468e11 −0.0217151
\(227\) 6.67768e12 0.735332 0.367666 0.929958i \(-0.380157\pi\)
0.367666 + 0.929958i \(0.380157\pi\)
\(228\) 4.05490e12 0.435851
\(229\) −4.01035e12 −0.420812 −0.210406 0.977614i \(-0.567479\pi\)
−0.210406 + 0.977614i \(0.567479\pi\)
\(230\) 1.19515e12 0.122439
\(231\) −5.92627e12 −0.592810
\(232\) −1.57150e12 −0.153508
\(233\) −1.74443e12 −0.166416 −0.0832080 0.996532i \(-0.526517\pi\)
−0.0832080 + 0.996532i \(0.526517\pi\)
\(234\) −4.17887e11 −0.0389378
\(235\) −4.29036e12 −0.390500
\(236\) 1.44527e12 0.128509
\(237\) 7.82912e12 0.680138
\(238\) −8.08162e11 −0.0686002
\(239\) −9.98034e12 −0.827860 −0.413930 0.910309i \(-0.635844\pi\)
−0.413930 + 0.910309i \(0.635844\pi\)
\(240\) −3.71338e12 −0.301029
\(241\) −5.80164e12 −0.459682 −0.229841 0.973228i \(-0.573821\pi\)
−0.229841 + 0.973228i \(0.573821\pi\)
\(242\) −8.53407e11 −0.0660955
\(243\) −8.47289e11 −0.0641500
\(244\) −9.57718e12 −0.708914
\(245\) −2.49907e12 −0.180870
\(246\) −1.22666e12 −0.0868122
\(247\) 1.13635e13 0.786465
\(248\) 5.71424e12 0.386789
\(249\) 8.79434e12 0.582246
\(250\) 1.62263e12 0.105087
\(251\) −1.51372e13 −0.959048 −0.479524 0.877529i \(-0.659191\pi\)
−0.479524 + 0.877529i \(0.659191\pi\)
\(252\) 4.33345e12 0.268615
\(253\) 4.12166e13 2.49983
\(254\) −3.02561e12 −0.179567
\(255\) 3.98776e12 0.231610
\(256\) 1.53659e13 0.873448
\(257\) −2.53545e13 −1.41066 −0.705332 0.708877i \(-0.749202\pi\)
−0.705332 + 0.708877i \(0.749202\pi\)
\(258\) 1.70435e12 0.0928220
\(259\) 2.07541e13 1.10651
\(260\) −1.05461e13 −0.550476
\(261\) −4.43568e12 −0.226693
\(262\) 1.64215e12 0.0821780
\(263\) −9.49565e12 −0.465338 −0.232669 0.972556i \(-0.574746\pi\)
−0.232669 + 0.972556i \(0.574746\pi\)
\(264\) 3.41521e12 0.163906
\(265\) −1.38347e13 −0.650307
\(266\) 1.54040e12 0.0709227
\(267\) 3.90155e12 0.175965
\(268\) 2.38863e13 1.05538
\(269\) 2.00720e13 0.868868 0.434434 0.900704i \(-0.356948\pi\)
0.434434 + 0.900704i \(0.356948\pi\)
\(270\) 2.79519e11 0.0118552
\(271\) −1.65588e12 −0.0688172 −0.0344086 0.999408i \(-0.510955\pi\)
−0.0344086 + 0.999408i \(0.510955\pi\)
\(272\) −1.74638e13 −0.711228
\(273\) 1.21441e13 0.484698
\(274\) 1.17339e12 0.0459002
\(275\) 2.31560e13 0.887839
\(276\) −3.01387e13 −1.13273
\(277\) −2.74139e13 −1.01002 −0.505012 0.863112i \(-0.668512\pi\)
−0.505012 + 0.863112i \(0.668512\pi\)
\(278\) −2.50037e12 −0.0903146
\(279\) 1.61289e13 0.571190
\(280\) −2.87788e12 −0.0999318
\(281\) 2.30957e13 0.786404 0.393202 0.919452i \(-0.371367\pi\)
0.393202 + 0.919452i \(0.371367\pi\)
\(282\) −1.41431e12 −0.0472253
\(283\) 3.22107e13 1.05481 0.527405 0.849614i \(-0.323165\pi\)
0.527405 + 0.849614i \(0.323165\pi\)
\(284\) 4.26498e13 1.36983
\(285\) −7.60089e12 −0.239452
\(286\) 4.75434e12 0.146919
\(287\) 3.56477e13 1.08064
\(288\) −3.75405e12 −0.111645
\(289\) −1.55178e13 −0.452784
\(290\) 1.46332e12 0.0418939
\(291\) −3.11611e13 −0.875390
\(292\) 9.81752e12 0.270643
\(293\) −6.10603e13 −1.65191 −0.825957 0.563734i \(-0.809364\pi\)
−0.825957 + 0.563734i \(0.809364\pi\)
\(294\) −8.23814e11 −0.0218735
\(295\) −2.70916e12 −0.0706014
\(296\) −1.19603e13 −0.305940
\(297\) 9.63968e12 0.242048
\(298\) 1.85262e12 0.0456664
\(299\) −8.44612e13 −2.04393
\(300\) −1.69323e13 −0.402299
\(301\) −4.95298e13 −1.15545
\(302\) 4.21537e12 0.0965600
\(303\) −3.26071e13 −0.733462
\(304\) 3.32869e13 0.735307
\(305\) 1.79524e13 0.389469
\(306\) 1.31456e12 0.0280099
\(307\) 4.45828e13 0.933052 0.466526 0.884507i \(-0.345505\pi\)
0.466526 + 0.884507i \(0.345505\pi\)
\(308\) −4.93021e13 −1.01353
\(309\) −1.62883e13 −0.328930
\(310\) −5.32088e12 −0.105559
\(311\) 2.92875e13 0.570822 0.285411 0.958405i \(-0.407870\pi\)
0.285411 + 0.958405i \(0.407870\pi\)
\(312\) −6.99845e12 −0.134014
\(313\) −1.04478e14 −1.96576 −0.982881 0.184239i \(-0.941018\pi\)
−0.982881 + 0.184239i \(0.941018\pi\)
\(314\) 6.89916e11 0.0127551
\(315\) −8.12303e12 −0.147574
\(316\) 6.51323e13 1.16283
\(317\) 9.29865e13 1.63153 0.815763 0.578386i \(-0.196317\pi\)
0.815763 + 0.578386i \(0.196317\pi\)
\(318\) −4.56059e12 −0.0786452
\(319\) 5.04651e13 0.855348
\(320\) −3.00579e13 −0.500764
\(321\) −5.15223e13 −0.843758
\(322\) −1.14493e13 −0.184320
\(323\) −3.57464e13 −0.565743
\(324\) −7.04879e12 −0.109677
\(325\) −4.74513e13 −0.725922
\(326\) −9.36491e12 −0.140866
\(327\) 2.65377e13 0.392509
\(328\) −2.05431e13 −0.298786
\(329\) 4.11009e13 0.587860
\(330\) −3.18011e12 −0.0447317
\(331\) 3.70812e13 0.512979 0.256489 0.966547i \(-0.417434\pi\)
0.256489 + 0.966547i \(0.417434\pi\)
\(332\) 7.31622e13 0.995467
\(333\) −3.37587e13 −0.451796
\(334\) −8.95192e12 −0.117845
\(335\) −4.47748e13 −0.579813
\(336\) 3.55736e13 0.453170
\(337\) −1.33995e14 −1.67928 −0.839642 0.543140i \(-0.817235\pi\)
−0.839642 + 0.543140i \(0.817235\pi\)
\(338\) −5.29724e11 −0.00653142
\(339\) −9.09800e12 −0.110369
\(340\) 3.31751e13 0.395984
\(341\) −1.83500e14 −2.15519
\(342\) −2.50562e12 −0.0289582
\(343\) 9.57218e13 1.08866
\(344\) 2.85431e13 0.319470
\(345\) 5.64949e13 0.622306
\(346\) −2.35606e12 −0.0255427
\(347\) −3.33468e13 −0.355830 −0.177915 0.984046i \(-0.556935\pi\)
−0.177915 + 0.984046i \(0.556935\pi\)
\(348\) −3.69015e13 −0.387577
\(349\) −1.75315e13 −0.181250 −0.0906250 0.995885i \(-0.528886\pi\)
−0.0906250 + 0.995885i \(0.528886\pi\)
\(350\) −6.43236e12 −0.0654630
\(351\) −1.97536e13 −0.197906
\(352\) 4.27101e13 0.421256
\(353\) −1.18278e14 −1.14853 −0.574265 0.818670i \(-0.694712\pi\)
−0.574265 + 0.818670i \(0.694712\pi\)
\(354\) −8.93068e11 −0.00853821
\(355\) −7.99469e13 −0.752568
\(356\) 3.24579e13 0.300847
\(357\) −3.82020e13 −0.348667
\(358\) 2.11410e11 0.00190007
\(359\) −5.70555e13 −0.504984 −0.252492 0.967599i \(-0.581250\pi\)
−0.252492 + 0.967599i \(0.581250\pi\)
\(360\) 4.68116e12 0.0408028
\(361\) −4.83555e13 −0.415103
\(362\) −1.81732e13 −0.153651
\(363\) −4.03408e13 −0.335937
\(364\) 1.01030e14 0.828690
\(365\) −1.84029e13 −0.148688
\(366\) 5.91797e12 0.0471006
\(367\) −1.20150e14 −0.942019 −0.471010 0.882128i \(-0.656110\pi\)
−0.471010 + 0.882128i \(0.656110\pi\)
\(368\) −2.47410e14 −1.91098
\(369\) −5.79845e13 −0.441232
\(370\) 1.11369e13 0.0834941
\(371\) 1.32534e14 0.978976
\(372\) 1.34180e14 0.976564
\(373\) −1.94635e14 −1.39580 −0.697899 0.716197i \(-0.745881\pi\)
−0.697899 + 0.716197i \(0.745881\pi\)
\(374\) −1.49558e13 −0.105686
\(375\) 7.67020e13 0.534115
\(376\) −2.36857e13 −0.162538
\(377\) −1.03413e14 −0.699357
\(378\) −2.67774e12 −0.0178469
\(379\) −1.10895e14 −0.728444 −0.364222 0.931312i \(-0.618665\pi\)
−0.364222 + 0.931312i \(0.618665\pi\)
\(380\) −6.32336e13 −0.409391
\(381\) −1.43021e14 −0.912670
\(382\) −4.17052e12 −0.0262326
\(383\) 4.20665e12 0.0260821 0.0130411 0.999915i \(-0.495849\pi\)
0.0130411 + 0.999915i \(0.495849\pi\)
\(384\) −4.15476e13 −0.253936
\(385\) 9.24165e13 0.556821
\(386\) 6.88050e12 0.0408686
\(387\) 8.05651e13 0.471777
\(388\) −2.59237e14 −1.49665
\(389\) 3.28723e14 1.87114 0.935572 0.353137i \(-0.114885\pi\)
0.935572 + 0.353137i \(0.114885\pi\)
\(390\) 6.51669e12 0.0365739
\(391\) 2.65691e14 1.47030
\(392\) −1.37966e13 −0.0752833
\(393\) 7.76249e13 0.417678
\(394\) −3.89995e13 −0.206933
\(395\) −1.22090e14 −0.638847
\(396\) 8.01947e13 0.413830
\(397\) 1.75916e14 0.895277 0.447639 0.894215i \(-0.352265\pi\)
0.447639 + 0.894215i \(0.352265\pi\)
\(398\) −9.56441e12 −0.0480066
\(399\) 7.28152e13 0.360472
\(400\) −1.38998e14 −0.678703
\(401\) 2.10376e14 1.01322 0.506608 0.862176i \(-0.330899\pi\)
0.506608 + 0.862176i \(0.330899\pi\)
\(402\) −1.47599e13 −0.0701199
\(403\) 3.76027e14 1.76215
\(404\) −2.71266e14 −1.25400
\(405\) 1.32129e13 0.0602555
\(406\) −1.40184e13 −0.0630673
\(407\) 3.84076e14 1.70470
\(408\) 2.20152e13 0.0964031
\(409\) −2.70328e14 −1.16792 −0.583960 0.811783i \(-0.698497\pi\)
−0.583960 + 0.811783i \(0.698497\pi\)
\(410\) 1.91290e13 0.0815418
\(411\) 5.54664e13 0.233292
\(412\) −1.35506e14 −0.562371
\(413\) 2.59532e13 0.106284
\(414\) 1.86234e13 0.0752589
\(415\) −1.37142e14 −0.546898
\(416\) −8.75216e13 −0.344431
\(417\) −1.18193e14 −0.459033
\(418\) 2.85067e13 0.109264
\(419\) 6.14097e12 0.0232306 0.0116153 0.999933i \(-0.496303\pi\)
0.0116153 + 0.999933i \(0.496303\pi\)
\(420\) −6.75774e13 −0.252308
\(421\) 2.97576e14 1.09660 0.548298 0.836283i \(-0.315276\pi\)
0.548298 + 0.836283i \(0.315276\pi\)
\(422\) −3.91173e13 −0.142282
\(423\) −6.68548e13 −0.240027
\(424\) −7.63772e13 −0.270677
\(425\) 1.49269e14 0.522191
\(426\) −2.63543e13 −0.0910121
\(427\) −1.71981e14 −0.586309
\(428\) −4.28626e14 −1.44257
\(429\) 2.24739e14 0.746729
\(430\) −2.65783e13 −0.0871867
\(431\) 2.17247e14 0.703605 0.351803 0.936074i \(-0.385569\pi\)
0.351803 + 0.936074i \(0.385569\pi\)
\(432\) −5.78640e13 −0.185032
\(433\) 8.84686e13 0.279322 0.139661 0.990199i \(-0.455399\pi\)
0.139661 + 0.990199i \(0.455399\pi\)
\(434\) 5.09731e13 0.158909
\(435\) 6.91717e13 0.212930
\(436\) 2.20773e14 0.671074
\(437\) −5.06423e14 −1.52008
\(438\) −6.06648e12 −0.0179816
\(439\) −8.15963e13 −0.238845 −0.119422 0.992844i \(-0.538104\pi\)
−0.119422 + 0.992844i \(0.538104\pi\)
\(440\) −5.32580e13 −0.153956
\(441\) −3.89419e13 −0.111174
\(442\) 3.06475e13 0.0864117
\(443\) 1.83777e14 0.511765 0.255883 0.966708i \(-0.417634\pi\)
0.255883 + 0.966708i \(0.417634\pi\)
\(444\) −2.80846e14 −0.772436
\(445\) −6.08422e13 −0.165282
\(446\) −5.78747e13 −0.155291
\(447\) 8.75738e13 0.232104
\(448\) 2.87949e14 0.753853
\(449\) 7.52236e14 1.94536 0.972679 0.232156i \(-0.0745779\pi\)
0.972679 + 0.232156i \(0.0745779\pi\)
\(450\) 1.04629e13 0.0267290
\(451\) 6.59695e14 1.66484
\(452\) −7.56884e13 −0.188698
\(453\) 1.99261e14 0.490776
\(454\) −3.43276e13 −0.0835289
\(455\) −1.89380e14 −0.455272
\(456\) −4.19622e13 −0.0996670
\(457\) 5.85789e14 1.37468 0.687341 0.726335i \(-0.258778\pi\)
0.687341 + 0.726335i \(0.258778\pi\)
\(458\) 2.06158e13 0.0478014
\(459\) 6.21394e13 0.142363
\(460\) 4.69994e14 1.06396
\(461\) −5.91350e14 −1.32279 −0.661393 0.750040i \(-0.730034\pi\)
−0.661393 + 0.750040i \(0.730034\pi\)
\(462\) 3.04649e13 0.0673394
\(463\) −5.70931e14 −1.24706 −0.623531 0.781799i \(-0.714303\pi\)
−0.623531 + 0.781799i \(0.714303\pi\)
\(464\) −3.02926e14 −0.653865
\(465\) −2.51519e14 −0.536513
\(466\) 8.96750e12 0.0189038
\(467\) 1.31858e14 0.274704 0.137352 0.990522i \(-0.456141\pi\)
0.137352 + 0.990522i \(0.456141\pi\)
\(468\) −1.64335e14 −0.338359
\(469\) 4.28935e14 0.872853
\(470\) 2.20553e13 0.0443582
\(471\) 3.26125e13 0.0648289
\(472\) −1.49564e13 −0.0293864
\(473\) −9.16597e14 −1.78009
\(474\) −4.02468e13 −0.0772592
\(475\) −2.84515e14 −0.539871
\(476\) −3.17812e14 −0.596117
\(477\) −2.15580e14 −0.399722
\(478\) 5.13054e13 0.0940394
\(479\) −2.92049e14 −0.529189 −0.264595 0.964360i \(-0.585238\pi\)
−0.264595 + 0.964360i \(0.585238\pi\)
\(480\) 5.85420e13 0.104867
\(481\) −7.87048e14 −1.39381
\(482\) 2.98242e13 0.0522168
\(483\) −5.41211e14 −0.936823
\(484\) −3.35604e14 −0.574352
\(485\) 4.85938e14 0.822245
\(486\) 4.35562e12 0.00728702
\(487\) −3.11946e14 −0.516025 −0.258012 0.966142i \(-0.583068\pi\)
−0.258012 + 0.966142i \(0.583068\pi\)
\(488\) 9.91095e13 0.162109
\(489\) −4.42682e14 −0.715967
\(490\) 1.28469e13 0.0205456
\(491\) −8.87961e14 −1.40425 −0.702127 0.712052i \(-0.747766\pi\)
−0.702127 + 0.712052i \(0.747766\pi\)
\(492\) −4.82387e14 −0.754375
\(493\) 3.25309e14 0.503081
\(494\) −5.84159e13 −0.0893373
\(495\) −1.50325e14 −0.227354
\(496\) 1.10149e15 1.64752
\(497\) 7.65877e14 1.13292
\(498\) −4.52086e13 −0.0661394
\(499\) 9.86386e14 1.42723 0.713615 0.700538i \(-0.247057\pi\)
0.713615 + 0.700538i \(0.247057\pi\)
\(500\) 6.38102e14 0.913177
\(501\) −4.23160e14 −0.598959
\(502\) 7.78151e13 0.108942
\(503\) 7.18036e13 0.0994311 0.0497156 0.998763i \(-0.484169\pi\)
0.0497156 + 0.998763i \(0.484169\pi\)
\(504\) −4.48447e13 −0.0614248
\(505\) 5.08487e14 0.688933
\(506\) −2.11880e14 −0.283964
\(507\) −2.50402e13 −0.0331966
\(508\) −1.18983e15 −1.56039
\(509\) 8.78462e14 1.13966 0.569830 0.821763i \(-0.307009\pi\)
0.569830 + 0.821763i \(0.307009\pi\)
\(510\) −2.04997e13 −0.0263094
\(511\) 1.76297e14 0.223836
\(512\) −4.29153e14 −0.539048
\(513\) −1.18441e14 −0.147183
\(514\) 1.30339e14 0.160242
\(515\) 2.54005e14 0.308960
\(516\) 6.70240e14 0.806598
\(517\) 7.60613e14 0.905661
\(518\) −1.06690e14 −0.125692
\(519\) −1.11371e14 −0.129824
\(520\) 1.09136e14 0.125878
\(521\) 1.11109e15 1.26806 0.634031 0.773308i \(-0.281399\pi\)
0.634031 + 0.773308i \(0.281399\pi\)
\(522\) 2.28023e13 0.0257508
\(523\) 1.16878e15 1.30609 0.653047 0.757318i \(-0.273491\pi\)
0.653047 + 0.757318i \(0.273491\pi\)
\(524\) 6.45779e14 0.714105
\(525\) −3.04059e14 −0.332722
\(526\) 4.88138e13 0.0528593
\(527\) −1.18288e15 −1.26760
\(528\) 6.58324e14 0.698157
\(529\) 2.81126e15 2.95049
\(530\) 7.11196e13 0.0738706
\(531\) −4.22156e13 −0.0433963
\(532\) 6.05767e14 0.616299
\(533\) −1.35185e15 −1.36122
\(534\) −2.00565e13 −0.0199884
\(535\) 8.03458e14 0.792533
\(536\) −2.47188e14 −0.241335
\(537\) 9.99340e12 0.00965728
\(538\) −1.03183e14 −0.0986978
\(539\) 4.43046e14 0.419479
\(540\) 1.09921e14 0.103019
\(541\) 1.01970e15 0.945991 0.472996 0.881065i \(-0.343173\pi\)
0.472996 + 0.881065i \(0.343173\pi\)
\(542\) 8.51229e12 0.00781719
\(543\) −8.59051e14 −0.780944
\(544\) 2.75319e14 0.247766
\(545\) −4.13838e14 −0.368680
\(546\) −6.24287e13 −0.0550586
\(547\) −6.38269e14 −0.557280 −0.278640 0.960396i \(-0.589884\pi\)
−0.278640 + 0.960396i \(0.589884\pi\)
\(548\) 4.61438e14 0.398860
\(549\) 2.79744e14 0.239394
\(550\) −1.19037e14 −0.100853
\(551\) −6.20058e14 −0.520114
\(552\) 3.11891e14 0.259022
\(553\) 1.16960e15 0.961723
\(554\) 1.40925e14 0.114732
\(555\) 5.26446e14 0.424367
\(556\) −9.83276e14 −0.784809
\(557\) 4.12961e14 0.326366 0.163183 0.986596i \(-0.447824\pi\)
0.163183 + 0.986596i \(0.447824\pi\)
\(558\) −8.29129e13 −0.0648835
\(559\) 1.87829e15 1.45545
\(560\) −5.54747e14 −0.425658
\(561\) −7.06966e14 −0.537159
\(562\) −1.18727e14 −0.0893304
\(563\) 9.63114e14 0.717598 0.358799 0.933415i \(-0.383186\pi\)
0.358799 + 0.933415i \(0.383186\pi\)
\(564\) −5.56180e14 −0.410375
\(565\) 1.41878e14 0.103669
\(566\) −1.65584e14 −0.119820
\(567\) −1.26578e14 −0.0907089
\(568\) −4.41362e14 −0.313241
\(569\) −1.13387e15 −0.796980 −0.398490 0.917173i \(-0.630466\pi\)
−0.398490 + 0.917173i \(0.630466\pi\)
\(570\) 3.90736e13 0.0272001
\(571\) 4.38349e14 0.302219 0.151109 0.988517i \(-0.451715\pi\)
0.151109 + 0.988517i \(0.451715\pi\)
\(572\) 1.86966e15 1.27668
\(573\) −1.97141e14 −0.133330
\(574\) −1.83252e14 −0.122753
\(575\) 2.11470e15 1.40306
\(576\) −4.68378e14 −0.307803
\(577\) −2.55059e14 −0.166025 −0.0830127 0.996548i \(-0.526454\pi\)
−0.0830127 + 0.996548i \(0.526454\pi\)
\(578\) 7.97715e13 0.0514333
\(579\) 3.25243e14 0.207719
\(580\) 5.75455e14 0.364047
\(581\) 1.31380e15 0.823303
\(582\) 1.60188e14 0.0994385
\(583\) 2.45268e15 1.50822
\(584\) −1.01597e14 −0.0618884
\(585\) 3.08046e14 0.185891
\(586\) 3.13890e14 0.187647
\(587\) 9.94768e14 0.589132 0.294566 0.955631i \(-0.404825\pi\)
0.294566 + 0.955631i \(0.404825\pi\)
\(588\) −3.23967e14 −0.190075
\(589\) 2.25463e15 1.31051
\(590\) 1.39268e13 0.00801985
\(591\) −1.84352e15 −1.05176
\(592\) −2.30549e15 −1.30315
\(593\) −7.78691e14 −0.436078 −0.218039 0.975940i \(-0.569966\pi\)
−0.218039 + 0.975940i \(0.569966\pi\)
\(594\) −4.95542e13 −0.0274951
\(595\) 5.95736e14 0.327500
\(596\) 7.28547e14 0.396829
\(597\) −4.52112e14 −0.243999
\(598\) 4.34185e14 0.232177
\(599\) −1.46914e15 −0.778425 −0.389213 0.921148i \(-0.627253\pi\)
−0.389213 + 0.921148i \(0.627253\pi\)
\(600\) 1.75224e14 0.0919945
\(601\) −2.17016e15 −1.12897 −0.564484 0.825444i \(-0.690925\pi\)
−0.564484 + 0.825444i \(0.690925\pi\)
\(602\) 2.54615e14 0.131251
\(603\) −6.97706e14 −0.356392
\(604\) 1.65770e15 0.839080
\(605\) 6.29089e14 0.315542
\(606\) 1.67622e14 0.0833164
\(607\) 2.68103e15 1.32058 0.660289 0.751012i \(-0.270434\pi\)
0.660289 + 0.751012i \(0.270434\pi\)
\(608\) −5.24773e14 −0.256154
\(609\) −6.62652e14 −0.320546
\(610\) −9.22870e13 −0.0442412
\(611\) −1.55865e15 −0.740494
\(612\) 5.16952e14 0.243398
\(613\) −9.22855e14 −0.430627 −0.215313 0.976545i \(-0.569077\pi\)
−0.215313 + 0.976545i \(0.569077\pi\)
\(614\) −2.29185e14 −0.105989
\(615\) 9.04232e14 0.414445
\(616\) 5.10203e14 0.231765
\(617\) −1.46067e15 −0.657635 −0.328817 0.944394i \(-0.606650\pi\)
−0.328817 + 0.944394i \(0.606650\pi\)
\(618\) 8.37323e13 0.0373642
\(619\) −3.42114e15 −1.51312 −0.756559 0.653925i \(-0.773121\pi\)
−0.756559 + 0.653925i \(0.773121\pi\)
\(620\) −2.09245e15 −0.917277
\(621\) 8.80334e14 0.382511
\(622\) −1.50557e14 −0.0648416
\(623\) 5.82857e14 0.248816
\(624\) −1.34904e15 −0.570832
\(625\) 4.86904e14 0.204222
\(626\) 5.37085e14 0.223298
\(627\) 1.34752e15 0.555345
\(628\) 2.71311e14 0.110838
\(629\) 2.47583e15 1.00264
\(630\) 4.17577e13 0.0167635
\(631\) 1.76224e15 0.701298 0.350649 0.936507i \(-0.385961\pi\)
0.350649 + 0.936507i \(0.385961\pi\)
\(632\) −6.74022e14 −0.265907
\(633\) −1.84908e15 −0.723163
\(634\) −4.78011e14 −0.185331
\(635\) 2.23033e15 0.857262
\(636\) −1.79346e15 −0.683405
\(637\) −9.07890e14 −0.342978
\(638\) −2.59424e14 −0.0971619
\(639\) −1.24578e15 −0.462578
\(640\) 6.47908e14 0.238519
\(641\) −4.50632e15 −1.64476 −0.822381 0.568938i \(-0.807355\pi\)
−0.822381 + 0.568938i \(0.807355\pi\)
\(642\) 2.64858e14 0.0958453
\(643\) 2.77063e15 0.994073 0.497036 0.867730i \(-0.334422\pi\)
0.497036 + 0.867730i \(0.334422\pi\)
\(644\) −4.50246e15 −1.60169
\(645\) −1.25636e15 −0.443135
\(646\) 1.83760e14 0.0642647
\(647\) −1.33400e15 −0.462577 −0.231288 0.972885i \(-0.574294\pi\)
−0.231288 + 0.972885i \(0.574294\pi\)
\(648\) 7.29445e13 0.0250801
\(649\) 4.80290e14 0.163741
\(650\) 2.43931e14 0.0824600
\(651\) 2.40951e15 0.807670
\(652\) −3.68277e15 −1.22409
\(653\) 1.99299e15 0.656876 0.328438 0.944526i \(-0.393478\pi\)
0.328438 + 0.944526i \(0.393478\pi\)
\(654\) −1.36421e14 −0.0445865
\(655\) −1.21051e15 −0.392321
\(656\) −3.95994e15 −1.27268
\(657\) −2.86764e14 −0.0913935
\(658\) −2.11286e14 −0.0667771
\(659\) 5.11300e15 1.60253 0.801265 0.598310i \(-0.204161\pi\)
0.801265 + 0.598310i \(0.204161\pi\)
\(660\) −1.25059e15 −0.388707
\(661\) −3.34905e15 −1.03232 −0.516160 0.856492i \(-0.672639\pi\)
−0.516160 + 0.856492i \(0.672639\pi\)
\(662\) −1.90621e14 −0.0582710
\(663\) 1.44871e15 0.439196
\(664\) −7.57119e14 −0.227635
\(665\) −1.13551e15 −0.338588
\(666\) 1.73542e14 0.0513211
\(667\) 4.60868e15 1.35171
\(668\) −3.52036e15 −1.02404
\(669\) −2.73575e15 −0.789283
\(670\) 2.30172e14 0.0658629
\(671\) −3.18267e15 −0.903271
\(672\) −5.60822e14 −0.157868
\(673\) −2.67235e15 −0.746124 −0.373062 0.927806i \(-0.621692\pi\)
−0.373062 + 0.927806i \(0.621692\pi\)
\(674\) 6.88822e14 0.190756
\(675\) 4.94583e14 0.135853
\(676\) −2.08315e14 −0.0567563
\(677\) −3.40990e15 −0.921520 −0.460760 0.887525i \(-0.652423\pi\)
−0.460760 + 0.887525i \(0.652423\pi\)
\(678\) 4.67697e13 0.0125372
\(679\) −4.65520e15 −1.23781
\(680\) −3.43313e14 −0.0905505
\(681\) −1.62268e15 −0.424544
\(682\) 9.43307e14 0.244816
\(683\) 7.32941e15 1.88693 0.943464 0.331476i \(-0.107547\pi\)
0.943464 + 0.331476i \(0.107547\pi\)
\(684\) −9.85341e14 −0.251639
\(685\) −8.64964e14 −0.219129
\(686\) −4.92072e14 −0.123665
\(687\) 9.74516e14 0.242956
\(688\) 5.50204e15 1.36078
\(689\) −5.02603e15 −1.23316
\(690\) −2.90421e14 −0.0706899
\(691\) 7.68618e15 1.85602 0.928008 0.372561i \(-0.121520\pi\)
0.928008 + 0.372561i \(0.121520\pi\)
\(692\) −9.26525e14 −0.221959
\(693\) 1.44008e15 0.342259
\(694\) 1.71424e14 0.0404199
\(695\) 1.84315e15 0.431165
\(696\) 3.81875e14 0.0886279
\(697\) 4.25253e15 0.979191
\(698\) 9.01231e13 0.0205888
\(699\) 4.23896e14 0.0960804
\(700\) −2.52954e15 −0.568856
\(701\) −3.51387e14 −0.0784038 −0.0392019 0.999231i \(-0.512482\pi\)
−0.0392019 + 0.999231i \(0.512482\pi\)
\(702\) 1.01547e14 0.0224808
\(703\) −4.71908e15 −1.03658
\(704\) 5.32878e15 1.16139
\(705\) 1.04256e15 0.225455
\(706\) 6.08025e14 0.130465
\(707\) −4.87121e15 −1.03712
\(708\) −3.51201e14 −0.0741947
\(709\) −4.65146e15 −0.975067 −0.487534 0.873104i \(-0.662103\pi\)
−0.487534 + 0.873104i \(0.662103\pi\)
\(710\) 4.10979e14 0.0854868
\(711\) −1.90248e15 −0.392678
\(712\) −3.35891e14 −0.0687952
\(713\) −1.67579e16 −3.40587
\(714\) 1.96383e14 0.0396063
\(715\) −3.50466e15 −0.701395
\(716\) 8.31374e13 0.0165111
\(717\) 2.42522e15 0.477965
\(718\) 2.93303e14 0.0573629
\(719\) −2.87911e15 −0.558791 −0.279395 0.960176i \(-0.590134\pi\)
−0.279395 + 0.960176i \(0.590134\pi\)
\(720\) 9.02352e14 0.173799
\(721\) −2.43332e15 −0.465110
\(722\) 2.48579e14 0.0471530
\(723\) 1.40980e15 0.265397
\(724\) −7.14665e15 −1.33518
\(725\) 2.58921e15 0.480075
\(726\) 2.07378e14 0.0381602
\(727\) 9.82747e15 1.79474 0.897372 0.441275i \(-0.145474\pi\)
0.897372 + 0.441275i \(0.145474\pi\)
\(728\) −1.04551e15 −0.189498
\(729\) 2.05891e14 0.0370370
\(730\) 9.46030e13 0.0168900
\(731\) −5.90858e15 −1.04698
\(732\) 2.32726e15 0.409292
\(733\) 8.35206e15 1.45788 0.728940 0.684578i \(-0.240013\pi\)
0.728940 + 0.684578i \(0.240013\pi\)
\(734\) 6.17648e14 0.107007
\(735\) 6.07275e14 0.104425
\(736\) 3.90046e15 0.665714
\(737\) 7.93787e15 1.34472
\(738\) 2.98078e14 0.0501210
\(739\) −8.08774e15 −1.34984 −0.674920 0.737890i \(-0.735822\pi\)
−0.674920 + 0.737890i \(0.735822\pi\)
\(740\) 4.37962e15 0.725542
\(741\) −2.76133e15 −0.454066
\(742\) −6.81313e14 −0.111205
\(743\) 7.31920e15 1.18584 0.592919 0.805262i \(-0.297975\pi\)
0.592919 + 0.805262i \(0.297975\pi\)
\(744\) −1.38856e15 −0.223313
\(745\) −1.36566e15 −0.218013
\(746\) 1.00055e15 0.158553
\(747\) −2.13702e15 −0.336160
\(748\) −5.88141e15 −0.918381
\(749\) −7.69699e15 −1.19308
\(750\) −3.94299e14 −0.0606720
\(751\) −8.16956e15 −1.24790 −0.623949 0.781465i \(-0.714473\pi\)
−0.623949 + 0.781465i \(0.714473\pi\)
\(752\) −4.56572e15 −0.692327
\(753\) 3.67834e15 0.553706
\(754\) 5.31611e14 0.0794423
\(755\) −3.10736e15 −0.460981
\(756\) −1.05303e15 −0.155085
\(757\) 6.90771e15 1.00997 0.504983 0.863129i \(-0.331499\pi\)
0.504983 + 0.863129i \(0.331499\pi\)
\(758\) 5.70073e14 0.0827465
\(759\) −1.00156e16 −1.44327
\(760\) 6.54373e14 0.0936162
\(761\) 4.39006e15 0.623527 0.311764 0.950160i \(-0.399080\pi\)
0.311764 + 0.950160i \(0.399080\pi\)
\(762\) 7.35223e14 0.103673
\(763\) 3.96450e15 0.555013
\(764\) −1.64007e15 −0.227954
\(765\) −9.69025e14 −0.133720
\(766\) −2.16249e13 −0.00296276
\(767\) −9.84211e14 −0.133879
\(768\) −3.73390e15 −0.504285
\(769\) −2.32170e14 −0.0311323 −0.0155661 0.999879i \(-0.504955\pi\)
−0.0155661 + 0.999879i \(0.504955\pi\)
\(770\) −4.75081e14 −0.0632512
\(771\) 6.16115e15 0.814447
\(772\) 2.70577e15 0.355137
\(773\) 3.33082e15 0.434075 0.217037 0.976163i \(-0.430361\pi\)
0.217037 + 0.976163i \(0.430361\pi\)
\(774\) −4.14157e14 −0.0535908
\(775\) −9.41481e15 −1.20963
\(776\) 2.68271e15 0.342243
\(777\) −5.04326e15 −0.638845
\(778\) −1.68985e15 −0.212550
\(779\) −8.10557e15 −1.01234
\(780\) 2.56270e15 0.317818
\(781\) 1.41733e16 1.74538
\(782\) −1.36583e15 −0.167016
\(783\) 1.07787e15 0.130881
\(784\) −2.65946e15 −0.320668
\(785\) −5.08571e14 −0.0608932
\(786\) −3.99042e14 −0.0474455
\(787\) 8.86494e15 1.04668 0.523341 0.852123i \(-0.324685\pi\)
0.523341 + 0.852123i \(0.324685\pi\)
\(788\) −1.53367e16 −1.79819
\(789\) 2.30744e15 0.268663
\(790\) 6.27623e14 0.0725688
\(791\) −1.35916e15 −0.156063
\(792\) −8.29896e14 −0.0946313
\(793\) 6.52193e15 0.738540
\(794\) −9.04323e14 −0.101698
\(795\) 3.36184e15 0.375455
\(796\) −3.76123e15 −0.417165
\(797\) 1.00296e16 1.10475 0.552373 0.833597i \(-0.313722\pi\)
0.552373 + 0.833597i \(0.313722\pi\)
\(798\) −3.74318e14 −0.0409472
\(799\) 4.90307e15 0.532673
\(800\) 2.19133e15 0.236435
\(801\) −9.48076e14 −0.101593
\(802\) −1.08147e15 −0.115095
\(803\) 3.26254e15 0.344842
\(804\) −5.80438e15 −0.609323
\(805\) 8.43985e15 0.879948
\(806\) −1.93303e15 −0.200168
\(807\) −4.87751e15 −0.501641
\(808\) 2.80720e15 0.286755
\(809\) −1.25713e16 −1.27544 −0.637722 0.770266i \(-0.720123\pi\)
−0.637722 + 0.770266i \(0.720123\pi\)
\(810\) −6.79231e13 −0.00684463
\(811\) 9.04964e15 0.905768 0.452884 0.891570i \(-0.350395\pi\)
0.452884 + 0.891570i \(0.350395\pi\)
\(812\) −5.51276e15 −0.548038
\(813\) 4.02378e14 0.0397316
\(814\) −1.97440e15 −0.193643
\(815\) 6.90334e15 0.672501
\(816\) 4.24369e15 0.410628
\(817\) 1.12621e16 1.08242
\(818\) 1.38966e15 0.132668
\(819\) −2.95102e15 −0.279841
\(820\) 7.52251e15 0.708577
\(821\) 1.28377e16 1.20115 0.600577 0.799567i \(-0.294938\pi\)
0.600577 + 0.799567i \(0.294938\pi\)
\(822\) −2.85134e14 −0.0265005
\(823\) −1.64147e16 −1.51542 −0.757710 0.652591i \(-0.773682\pi\)
−0.757710 + 0.652591i \(0.773682\pi\)
\(824\) 1.40228e15 0.128598
\(825\) −5.62691e15 −0.512594
\(826\) −1.33417e14 −0.0120731
\(827\) 1.04782e16 0.941900 0.470950 0.882160i \(-0.343911\pi\)
0.470950 + 0.882160i \(0.343911\pi\)
\(828\) 7.32371e15 0.653979
\(829\) 8.00579e15 0.710157 0.355079 0.934836i \(-0.384454\pi\)
0.355079 + 0.934836i \(0.384454\pi\)
\(830\) 7.05000e14 0.0621241
\(831\) 6.66158e15 0.583138
\(832\) −1.09197e16 −0.949586
\(833\) 2.85597e15 0.246721
\(834\) 6.07590e14 0.0521431
\(835\) 6.59891e15 0.562596
\(836\) 1.12103e16 0.949474
\(837\) −3.91931e15 −0.329777
\(838\) −3.15686e13 −0.00263884
\(839\) −8.86181e15 −0.735921 −0.367961 0.929841i \(-0.619944\pi\)
−0.367961 + 0.929841i \(0.619944\pi\)
\(840\) 6.99325e14 0.0576957
\(841\) −6.55770e15 −0.537494
\(842\) −1.52974e15 −0.124566
\(843\) −5.61225e15 −0.454031
\(844\) −1.53830e16 −1.23639
\(845\) 3.90486e14 0.0311813
\(846\) 3.43677e14 0.0272655
\(847\) −6.02656e15 −0.475019
\(848\) −1.47227e16 −1.15295
\(849\) −7.82720e15 −0.608995
\(850\) −7.67338e14 −0.0593175
\(851\) 3.50753e16 2.69395
\(852\) −1.03639e16 −0.790871
\(853\) −1.60165e16 −1.21436 −0.607182 0.794563i \(-0.707700\pi\)
−0.607182 + 0.794563i \(0.707700\pi\)
\(854\) 8.84093e14 0.0666009
\(855\) 1.84702e15 0.138248
\(856\) 4.43564e15 0.329876
\(857\) −1.70481e16 −1.25974 −0.629871 0.776699i \(-0.716892\pi\)
−0.629871 + 0.776699i \(0.716892\pi\)
\(858\) −1.15530e15 −0.0848236
\(859\) −5.84317e15 −0.426272 −0.213136 0.977023i \(-0.568368\pi\)
−0.213136 + 0.977023i \(0.568368\pi\)
\(860\) −1.04520e16 −0.757629
\(861\) −8.66238e15 −0.623907
\(862\) −1.11679e15 −0.0799250
\(863\) −9.32399e15 −0.663044 −0.331522 0.943447i \(-0.607562\pi\)
−0.331522 + 0.943447i \(0.607562\pi\)
\(864\) 9.12233e14 0.0644585
\(865\) 1.73677e15 0.121942
\(866\) −4.54786e14 −0.0317292
\(867\) 3.77082e15 0.261415
\(868\) 2.00453e16 1.38087
\(869\) 2.16446e16 1.48164
\(870\) −3.55587e14 −0.0241875
\(871\) −1.62663e16 −1.09948
\(872\) −2.28467e15 −0.153456
\(873\) 7.57215e15 0.505406
\(874\) 2.60334e15 0.172671
\(875\) 1.14586e16 0.755245
\(876\) −2.38566e15 −0.156256
\(877\) −1.09528e16 −0.712899 −0.356450 0.934315i \(-0.616013\pi\)
−0.356450 + 0.934315i \(0.616013\pi\)
\(878\) 4.19458e14 0.0271312
\(879\) 1.48377e16 0.953733
\(880\) −1.02661e16 −0.655771
\(881\) 2.13492e16 1.35523 0.677616 0.735416i \(-0.263013\pi\)
0.677616 + 0.735416i \(0.263013\pi\)
\(882\) 2.00187e14 0.0126287
\(883\) 2.06137e15 0.129233 0.0646163 0.997910i \(-0.479418\pi\)
0.0646163 + 0.997910i \(0.479418\pi\)
\(884\) 1.20522e16 0.750894
\(885\) 6.58325e14 0.0407617
\(886\) −9.44734e14 −0.0581332
\(887\) 1.88858e16 1.15493 0.577465 0.816415i \(-0.304042\pi\)
0.577465 + 0.816415i \(0.304042\pi\)
\(888\) 2.90634e15 0.176634
\(889\) −2.13662e16 −1.29053
\(890\) 3.12769e14 0.0187749
\(891\) −2.34244e15 −0.139747
\(892\) −2.27593e16 −1.34944
\(893\) −9.34554e15 −0.550708
\(894\) −4.50186e14 −0.0263655
\(895\) −1.55841e14 −0.00907098
\(896\) −6.20684e15 −0.359068
\(897\) 2.05241e16 1.18006
\(898\) −3.86699e15 −0.220980
\(899\) −2.05182e16 −1.16536
\(900\) 4.11455e15 0.232268
\(901\) 1.58105e16 0.887072
\(902\) −3.39126e15 −0.189115
\(903\) 1.20357e16 0.667098
\(904\) 7.83262e14 0.0431500
\(905\) 1.33964e16 0.733533
\(906\) −1.02433e15 −0.0557489
\(907\) 1.85358e16 1.00270 0.501351 0.865244i \(-0.332836\pi\)
0.501351 + 0.865244i \(0.332836\pi\)
\(908\) −1.34994e16 −0.725843
\(909\) 7.92352e15 0.423464
\(910\) 9.73537e14 0.0517160
\(911\) −3.24212e16 −1.71190 −0.855948 0.517062i \(-0.827026\pi\)
−0.855948 + 0.517062i \(0.827026\pi\)
\(912\) −8.08872e15 −0.424530
\(913\) 2.43131e16 1.26839
\(914\) −3.01134e15 −0.156155
\(915\) −4.36243e15 −0.224860
\(916\) 8.10723e15 0.415382
\(917\) 1.15965e16 0.590602
\(918\) −3.19437e14 −0.0161715
\(919\) 3.51960e15 0.177116 0.0885580 0.996071i \(-0.471774\pi\)
0.0885580 + 0.996071i \(0.471774\pi\)
\(920\) −4.86374e15 −0.243297
\(921\) −1.08336e16 −0.538698
\(922\) 3.03992e15 0.150260
\(923\) −2.90440e16 −1.42707
\(924\) 1.19804e16 0.585161
\(925\) 1.97058e16 0.956784
\(926\) 2.93496e15 0.141658
\(927\) 3.95805e15 0.189908
\(928\) 4.77568e15 0.227783
\(929\) 1.92092e16 0.910799 0.455400 0.890287i \(-0.349496\pi\)
0.455400 + 0.890287i \(0.349496\pi\)
\(930\) 1.29297e15 0.0609444
\(931\) −5.44364e15 −0.255074
\(932\) 3.52649e15 0.164269
\(933\) −7.11687e15 −0.329564
\(934\) −6.77838e14 −0.0312046
\(935\) 1.10247e16 0.504548
\(936\) 1.70062e15 0.0773733
\(937\) −3.60925e16 −1.63248 −0.816242 0.577710i \(-0.803946\pi\)
−0.816242 + 0.577710i \(0.803946\pi\)
\(938\) −2.20501e15 −0.0991504
\(939\) 2.53882e16 1.13493
\(940\) 8.67328e15 0.385461
\(941\) −4.08149e16 −1.80333 −0.901666 0.432433i \(-0.857655\pi\)
−0.901666 + 0.432433i \(0.857655\pi\)
\(942\) −1.67649e14 −0.00736414
\(943\) 6.02460e16 2.63096
\(944\) −2.88303e15 −0.125171
\(945\) 1.97390e15 0.0852020
\(946\) 4.71191e15 0.202207
\(947\) 1.40417e16 0.599095 0.299548 0.954081i \(-0.403164\pi\)
0.299548 + 0.954081i \(0.403164\pi\)
\(948\) −1.58271e16 −0.671362
\(949\) −6.68560e15 −0.281953
\(950\) 1.46259e15 0.0613258
\(951\) −2.25957e16 −0.941962
\(952\) 3.28887e15 0.136315
\(953\) 3.95272e16 1.62886 0.814432 0.580259i \(-0.197049\pi\)
0.814432 + 0.580259i \(0.197049\pi\)
\(954\) 1.10822e15 0.0454058
\(955\) 3.07430e15 0.125235
\(956\) 2.01760e16 0.817177
\(957\) −1.22630e16 −0.493835
\(958\) 1.50132e15 0.0601124
\(959\) 8.28621e15 0.329878
\(960\) 7.30406e15 0.289116
\(961\) 4.91990e16 1.93632
\(962\) 4.04594e15 0.158328
\(963\) 1.25199e16 0.487144
\(964\) 1.17284e16 0.453750
\(965\) −5.07196e15 −0.195108
\(966\) 2.78218e15 0.106417
\(967\) 2.10761e16 0.801577 0.400788 0.916171i \(-0.368736\pi\)
0.400788 + 0.916171i \(0.368736\pi\)
\(968\) 3.47300e15 0.131338
\(969\) 8.68638e15 0.326632
\(970\) −2.49804e15 −0.0934016
\(971\) 1.84689e16 0.686648 0.343324 0.939217i \(-0.388447\pi\)
0.343324 + 0.939217i \(0.388447\pi\)
\(972\) 1.71286e15 0.0633223
\(973\) −1.76570e16 −0.649078
\(974\) 1.60361e15 0.0586171
\(975\) 1.15307e16 0.419111
\(976\) 1.91046e16 0.690500
\(977\) 5.17619e16 1.86033 0.930166 0.367140i \(-0.119663\pi\)
0.930166 + 0.367140i \(0.119663\pi\)
\(978\) 2.27567e15 0.0813292
\(979\) 1.07863e16 0.383327
\(980\) 5.05206e15 0.178536
\(981\) −6.44865e15 −0.226615
\(982\) 4.56470e15 0.159514
\(983\) 2.53882e16 0.882242 0.441121 0.897448i \(-0.354581\pi\)
0.441121 + 0.897448i \(0.354581\pi\)
\(984\) 4.99198e15 0.172504
\(985\) 2.87485e16 0.987907
\(986\) −1.67230e15 −0.0571467
\(987\) −9.98752e15 −0.339401
\(988\) −2.29722e16 −0.776317
\(989\) −8.37073e16 −2.81309
\(990\) 7.72767e14 0.0258259
\(991\) −1.27518e16 −0.423806 −0.211903 0.977291i \(-0.567966\pi\)
−0.211903 + 0.977291i \(0.567966\pi\)
\(992\) −1.73651e16 −0.573937
\(993\) −9.01072e15 −0.296168
\(994\) −3.93711e15 −0.128692
\(995\) 7.05040e15 0.229185
\(996\) −1.77784e16 −0.574733
\(997\) −2.78396e15 −0.0895033 −0.0447516 0.998998i \(-0.514250\pi\)
−0.0447516 + 0.998998i \(0.514250\pi\)
\(998\) −5.07067e15 −0.162124
\(999\) 8.20336e15 0.260845
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.1.14 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.14 27 1.1 even 1 trivial