Properties

Label 177.14.a.c.1.2
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-166.716 q^{2} +729.000 q^{3} +19602.3 q^{4} +43558.7 q^{5} -121536. q^{6} -395203. q^{7} -1.90228e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-166.716 q^{2} +729.000 q^{3} +19602.3 q^{4} +43558.7 q^{5} -121536. q^{6} -395203. q^{7} -1.90228e6 q^{8} +531441. q^{9} -7.26193e6 q^{10} +2.80600e6 q^{11} +1.42901e7 q^{12} +2.66316e7 q^{13} +6.58867e7 q^{14} +3.17543e7 q^{15} +1.56559e8 q^{16} +1.05903e8 q^{17} -8.85998e7 q^{18} +1.56853e8 q^{19} +8.53849e8 q^{20} -2.88103e8 q^{21} -4.67805e8 q^{22} -2.25613e8 q^{23} -1.38676e9 q^{24} +6.76654e8 q^{25} -4.43992e9 q^{26} +3.87420e8 q^{27} -7.74687e9 q^{28} +4.55422e8 q^{29} -5.29395e9 q^{30} +3.56282e9 q^{31} -1.05174e10 q^{32} +2.04557e9 q^{33} -1.76558e10 q^{34} -1.72145e10 q^{35} +1.04175e10 q^{36} +2.68695e10 q^{37} -2.61499e10 q^{38} +1.94144e10 q^{39} -8.28607e10 q^{40} -1.72189e10 q^{41} +4.80314e10 q^{42} +2.91163e10 q^{43} +5.50040e10 q^{44} +2.31489e10 q^{45} +3.76133e10 q^{46} +1.44877e8 q^{47} +1.14131e11 q^{48} +5.92961e10 q^{49} -1.12809e11 q^{50} +7.72036e10 q^{51} +5.22040e11 q^{52} +4.30140e10 q^{53} -6.45893e10 q^{54} +1.22226e11 q^{55} +7.51785e11 q^{56} +1.14346e11 q^{57} -7.59262e10 q^{58} -4.21805e10 q^{59} +6.22456e11 q^{60} -2.11973e11 q^{61} -5.93979e11 q^{62} -2.10027e11 q^{63} +4.70889e11 q^{64} +1.16004e12 q^{65} -3.41030e11 q^{66} -9.17316e11 q^{67} +2.07595e12 q^{68} -1.64472e11 q^{69} +2.86993e12 q^{70} +1.33109e12 q^{71} -1.01095e12 q^{72} -1.30644e12 q^{73} -4.47958e12 q^{74} +4.93281e11 q^{75} +3.07467e12 q^{76} -1.10894e12 q^{77} -3.23670e12 q^{78} +3.47198e12 q^{79} +6.81948e12 q^{80} +2.82430e11 q^{81} +2.87066e12 q^{82} +3.63991e12 q^{83} -5.64747e12 q^{84} +4.61301e12 q^{85} -4.85416e12 q^{86} +3.32003e11 q^{87} -5.33779e12 q^{88} -1.84291e12 q^{89} -3.85929e12 q^{90} -1.05249e13 q^{91} -4.42253e12 q^{92} +2.59729e12 q^{93} -2.41533e10 q^{94} +6.83229e12 q^{95} -7.66717e12 q^{96} -1.21303e13 q^{97} -9.88561e12 q^{98} +1.49122e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −166.716 −1.84197 −0.920985 0.389597i \(-0.872614\pi\)
−0.920985 + 0.389597i \(0.872614\pi\)
\(3\) 729.000 0.577350
\(4\) 19602.3 2.39286
\(5\) 43558.7 1.24672 0.623361 0.781934i \(-0.285767\pi\)
0.623361 + 0.781934i \(0.285767\pi\)
\(6\) −121536. −1.06346
\(7\) −395203. −1.26965 −0.634823 0.772658i \(-0.718927\pi\)
−0.634823 + 0.772658i \(0.718927\pi\)
\(8\) −1.90228e6 −2.56560
\(9\) 531441. 0.333333
\(10\) −7.26193e6 −2.29642
\(11\) 2.80600e6 0.477568 0.238784 0.971073i \(-0.423251\pi\)
0.238784 + 0.971073i \(0.423251\pi\)
\(12\) 1.42901e7 1.38152
\(13\) 2.66316e7 1.53026 0.765131 0.643875i \(-0.222674\pi\)
0.765131 + 0.643875i \(0.222674\pi\)
\(14\) 6.58867e7 2.33865
\(15\) 3.17543e7 0.719795
\(16\) 1.56559e8 2.33290
\(17\) 1.05903e8 1.06412 0.532061 0.846706i \(-0.321418\pi\)
0.532061 + 0.846706i \(0.321418\pi\)
\(18\) −8.85998e7 −0.613990
\(19\) 1.56853e8 0.764880 0.382440 0.923980i \(-0.375084\pi\)
0.382440 + 0.923980i \(0.375084\pi\)
\(20\) 8.53849e8 2.98323
\(21\) −2.88103e8 −0.733030
\(22\) −4.67805e8 −0.879666
\(23\) −2.25613e8 −0.317785 −0.158892 0.987296i \(-0.550792\pi\)
−0.158892 + 0.987296i \(0.550792\pi\)
\(24\) −1.38676e9 −1.48125
\(25\) 6.76654e8 0.554315
\(26\) −4.43992e9 −2.81870
\(27\) 3.87420e8 0.192450
\(28\) −7.74687e9 −3.03808
\(29\) 4.55422e8 0.142176 0.0710881 0.997470i \(-0.477353\pi\)
0.0710881 + 0.997470i \(0.477353\pi\)
\(30\) −5.29395e9 −1.32584
\(31\) 3.56282e9 0.721012 0.360506 0.932757i \(-0.382604\pi\)
0.360506 + 0.932757i \(0.382604\pi\)
\(32\) −1.05174e10 −1.73154
\(33\) 2.04557e9 0.275724
\(34\) −1.76558e10 −1.96008
\(35\) −1.72145e10 −1.58289
\(36\) 1.04175e10 0.797619
\(37\) 2.68695e10 1.72166 0.860831 0.508890i \(-0.169944\pi\)
0.860831 + 0.508890i \(0.169944\pi\)
\(38\) −2.61499e10 −1.40889
\(39\) 1.94144e10 0.883497
\(40\) −8.28607e10 −3.19859
\(41\) −1.72189e10 −0.566121 −0.283061 0.959102i \(-0.591350\pi\)
−0.283061 + 0.959102i \(0.591350\pi\)
\(42\) 4.80314e10 1.35022
\(43\) 2.91163e10 0.702411 0.351206 0.936298i \(-0.385772\pi\)
0.351206 + 0.936298i \(0.385772\pi\)
\(44\) 5.50040e10 1.14275
\(45\) 2.31489e10 0.415574
\(46\) 3.76133e10 0.585350
\(47\) 1.44877e8 0.00196048 0.000980241 1.00000i \(-0.499688\pi\)
0.000980241 1.00000i \(0.499688\pi\)
\(48\) 1.14131e11 1.34690
\(49\) 5.92961e10 0.612000
\(50\) −1.12809e11 −1.02103
\(51\) 7.72036e10 0.614372
\(52\) 5.22040e11 3.66170
\(53\) 4.30140e10 0.266574 0.133287 0.991078i \(-0.457447\pi\)
0.133287 + 0.991078i \(0.457447\pi\)
\(54\) −6.45893e10 −0.354487
\(55\) 1.22226e11 0.595394
\(56\) 7.51785e11 3.25740
\(57\) 1.14346e11 0.441604
\(58\) −7.59262e10 −0.261884
\(59\) −4.21805e10 −0.130189
\(60\) 6.22456e11 1.72237
\(61\) −2.11973e11 −0.526789 −0.263394 0.964688i \(-0.584842\pi\)
−0.263394 + 0.964688i \(0.584842\pi\)
\(62\) −5.93979e11 −1.32808
\(63\) −2.10027e11 −0.423215
\(64\) 4.70889e11 0.856543
\(65\) 1.16004e12 1.90781
\(66\) −3.41030e11 −0.507875
\(67\) −9.17316e11 −1.23889 −0.619445 0.785040i \(-0.712642\pi\)
−0.619445 + 0.785040i \(0.712642\pi\)
\(68\) 2.07595e12 2.54629
\(69\) −1.64472e11 −0.183473
\(70\) 2.86993e12 2.91565
\(71\) 1.33109e12 1.23318 0.616592 0.787283i \(-0.288513\pi\)
0.616592 + 0.787283i \(0.288513\pi\)
\(72\) −1.01095e12 −0.855200
\(73\) −1.30644e12 −1.01039 −0.505196 0.863005i \(-0.668580\pi\)
−0.505196 + 0.863005i \(0.668580\pi\)
\(74\) −4.47958e12 −3.17125
\(75\) 4.93281e11 0.320034
\(76\) 3.07467e12 1.83025
\(77\) −1.10894e12 −0.606342
\(78\) −3.23670e12 −1.62738
\(79\) 3.47198e12 1.60694 0.803472 0.595343i \(-0.202984\pi\)
0.803472 + 0.595343i \(0.202984\pi\)
\(80\) 6.81948e12 2.90848
\(81\) 2.82430e11 0.111111
\(82\) 2.87066e12 1.04278
\(83\) 3.63991e12 1.22203 0.611017 0.791618i \(-0.290761\pi\)
0.611017 + 0.791618i \(0.290761\pi\)
\(84\) −5.64747e12 −1.75404
\(85\) 4.61301e12 1.32667
\(86\) −4.85416e12 −1.29382
\(87\) 3.32003e11 0.0820855
\(88\) −5.33779e12 −1.22525
\(89\) −1.84291e12 −0.393070 −0.196535 0.980497i \(-0.562969\pi\)
−0.196535 + 0.980497i \(0.562969\pi\)
\(90\) −3.85929e12 −0.765475
\(91\) −1.05249e13 −1.94289
\(92\) −4.42253e12 −0.760413
\(93\) 2.59729e12 0.416276
\(94\) −2.41533e10 −0.00361115
\(95\) 6.83229e12 0.953592
\(96\) −7.66717e12 −0.999705
\(97\) −1.21303e13 −1.47862 −0.739310 0.673365i \(-0.764848\pi\)
−0.739310 + 0.673365i \(0.764848\pi\)
\(98\) −9.88561e12 −1.12729
\(99\) 1.49122e12 0.159189
\(100\) 1.32640e13 1.32640
\(101\) 9.46306e12 0.887038 0.443519 0.896265i \(-0.353730\pi\)
0.443519 + 0.896265i \(0.353730\pi\)
\(102\) −1.28711e13 −1.13165
\(103\) 3.13670e11 0.0258840 0.0129420 0.999916i \(-0.495880\pi\)
0.0129420 + 0.999916i \(0.495880\pi\)
\(104\) −5.06607e13 −3.92604
\(105\) −1.25494e13 −0.913885
\(106\) −7.17114e12 −0.491021
\(107\) 1.29230e13 0.832470 0.416235 0.909257i \(-0.363349\pi\)
0.416235 + 0.909257i \(0.363349\pi\)
\(108\) 7.59432e12 0.460505
\(109\) 6.73016e12 0.384373 0.192187 0.981358i \(-0.438442\pi\)
0.192187 + 0.981358i \(0.438442\pi\)
\(110\) −2.03770e13 −1.09670
\(111\) 1.95879e13 0.994003
\(112\) −6.18723e13 −2.96196
\(113\) 9.15347e12 0.413596 0.206798 0.978384i \(-0.433696\pi\)
0.206798 + 0.978384i \(0.433696\pi\)
\(114\) −1.90632e13 −0.813421
\(115\) −9.82740e12 −0.396189
\(116\) 8.92731e12 0.340207
\(117\) 1.41531e13 0.510087
\(118\) 7.03218e12 0.239804
\(119\) −4.18533e13 −1.35106
\(120\) −6.04054e13 −1.84671
\(121\) −2.66491e13 −0.771929
\(122\) 3.53393e13 0.970330
\(123\) −1.25526e13 −0.326850
\(124\) 6.98393e13 1.72528
\(125\) −2.36980e13 −0.555645
\(126\) 3.50149e13 0.779550
\(127\) 1.74328e13 0.368674 0.184337 0.982863i \(-0.440986\pi\)
0.184337 + 0.982863i \(0.440986\pi\)
\(128\) 7.65350e12 0.153814
\(129\) 2.12258e13 0.405537
\(130\) −1.93397e14 −3.51413
\(131\) −2.37102e13 −0.409894 −0.204947 0.978773i \(-0.565702\pi\)
−0.204947 + 0.978773i \(0.565702\pi\)
\(132\) 4.00979e13 0.659767
\(133\) −6.19885e13 −0.971126
\(134\) 1.52931e14 2.28200
\(135\) 1.68755e13 0.239932
\(136\) −2.01458e14 −2.73011
\(137\) 9.22184e13 1.19161 0.595805 0.803129i \(-0.296833\pi\)
0.595805 + 0.803129i \(0.296833\pi\)
\(138\) 2.74201e13 0.337952
\(139\) −4.30398e13 −0.506144 −0.253072 0.967447i \(-0.581441\pi\)
−0.253072 + 0.967447i \(0.581441\pi\)
\(140\) −3.37443e14 −3.78764
\(141\) 1.05615e11 0.00113189
\(142\) −2.21914e14 −2.27149
\(143\) 7.47283e13 0.730803
\(144\) 8.32016e13 0.777635
\(145\) 1.98376e13 0.177254
\(146\) 2.17804e14 1.86111
\(147\) 4.32268e13 0.353338
\(148\) 5.26703e14 4.11969
\(149\) −8.82130e13 −0.660423 −0.330211 0.943907i \(-0.607120\pi\)
−0.330211 + 0.943907i \(0.607120\pi\)
\(150\) −8.22379e13 −0.589493
\(151\) −2.27439e13 −0.156140 −0.0780701 0.996948i \(-0.524876\pi\)
−0.0780701 + 0.996948i \(0.524876\pi\)
\(152\) −2.98377e14 −1.96238
\(153\) 5.62814e13 0.354708
\(154\) 1.84878e14 1.11686
\(155\) 1.55192e14 0.898901
\(156\) 3.80567e14 2.11408
\(157\) −3.12906e14 −1.66750 −0.833750 0.552143i \(-0.813810\pi\)
−0.833750 + 0.552143i \(0.813810\pi\)
\(158\) −5.78835e14 −2.95994
\(159\) 3.13572e13 0.153906
\(160\) −4.58123e14 −2.15875
\(161\) 8.91628e13 0.403474
\(162\) −4.70856e13 −0.204663
\(163\) 3.26303e14 1.36270 0.681352 0.731955i \(-0.261392\pi\)
0.681352 + 0.731955i \(0.261392\pi\)
\(164\) −3.37529e14 −1.35465
\(165\) 8.91024e13 0.343751
\(166\) −6.06832e14 −2.25095
\(167\) −4.85092e14 −1.73048 −0.865241 0.501356i \(-0.832835\pi\)
−0.865241 + 0.501356i \(0.832835\pi\)
\(168\) 5.48051e14 1.88066
\(169\) 4.06368e14 1.34170
\(170\) −7.69063e14 −2.44368
\(171\) 8.33579e13 0.254960
\(172\) 5.70746e14 1.68077
\(173\) −3.13899e14 −0.890206 −0.445103 0.895479i \(-0.646833\pi\)
−0.445103 + 0.895479i \(0.646833\pi\)
\(174\) −5.53502e13 −0.151199
\(175\) −2.67416e14 −0.703784
\(176\) 4.39303e14 1.11412
\(177\) −3.07496e13 −0.0751646
\(178\) 3.07243e14 0.724023
\(179\) 5.26309e14 1.19590 0.597952 0.801532i \(-0.295981\pi\)
0.597952 + 0.801532i \(0.295981\pi\)
\(180\) 4.53770e14 0.994409
\(181\) −1.41686e14 −0.299513 −0.149757 0.988723i \(-0.547849\pi\)
−0.149757 + 0.988723i \(0.547849\pi\)
\(182\) 1.75467e15 3.57875
\(183\) −1.54528e14 −0.304142
\(184\) 4.29178e14 0.815309
\(185\) 1.17040e15 2.14643
\(186\) −4.33011e14 −0.766769
\(187\) 2.97165e14 0.508191
\(188\) 2.83992e12 0.00469115
\(189\) −1.53110e14 −0.244343
\(190\) −1.13905e15 −1.75649
\(191\) −1.13302e14 −0.168857 −0.0844285 0.996430i \(-0.526906\pi\)
−0.0844285 + 0.996430i \(0.526906\pi\)
\(192\) 3.43278e14 0.494525
\(193\) −5.04772e14 −0.703028 −0.351514 0.936183i \(-0.614333\pi\)
−0.351514 + 0.936183i \(0.614333\pi\)
\(194\) 2.02232e15 2.72358
\(195\) 8.45667e14 1.10147
\(196\) 1.16234e15 1.46443
\(197\) −1.14653e15 −1.39751 −0.698756 0.715360i \(-0.746263\pi\)
−0.698756 + 0.715360i \(0.746263\pi\)
\(198\) −2.48611e14 −0.293222
\(199\) −1.38430e15 −1.58010 −0.790049 0.613044i \(-0.789945\pi\)
−0.790049 + 0.613044i \(0.789945\pi\)
\(200\) −1.28718e15 −1.42215
\(201\) −6.68723e14 −0.715273
\(202\) −1.57764e15 −1.63390
\(203\) −1.79984e14 −0.180513
\(204\) 1.51337e15 1.47010
\(205\) −7.50031e14 −0.705796
\(206\) −5.22939e13 −0.0476775
\(207\) −1.19900e14 −0.105928
\(208\) 4.16940e15 3.56995
\(209\) 4.40128e14 0.365282
\(210\) 2.09218e15 1.68335
\(211\) −2.36304e15 −1.84347 −0.921734 0.387823i \(-0.873227\pi\)
−0.921734 + 0.387823i \(0.873227\pi\)
\(212\) 8.43173e14 0.637872
\(213\) 9.70364e14 0.711979
\(214\) −2.15447e15 −1.53339
\(215\) 1.26827e15 0.875711
\(216\) −7.36981e14 −0.493750
\(217\) −1.40803e15 −0.915430
\(218\) −1.12203e15 −0.708004
\(219\) −9.52393e14 −0.583350
\(220\) 2.39590e15 1.42469
\(221\) 2.82038e15 1.62839
\(222\) −3.26561e15 −1.83092
\(223\) −1.11944e15 −0.609563 −0.304782 0.952422i \(-0.598583\pi\)
−0.304782 + 0.952422i \(0.598583\pi\)
\(224\) 4.15649e15 2.19844
\(225\) 3.59602e14 0.184772
\(226\) −1.52603e15 −0.761831
\(227\) 3.69508e15 1.79249 0.896244 0.443562i \(-0.146286\pi\)
0.896244 + 0.443562i \(0.146286\pi\)
\(228\) 2.24143e15 1.05669
\(229\) 1.30647e15 0.598646 0.299323 0.954152i \(-0.403239\pi\)
0.299323 + 0.954152i \(0.403239\pi\)
\(230\) 1.63839e15 0.729769
\(231\) −8.08416e14 −0.350072
\(232\) −8.66339e14 −0.364767
\(233\) 2.77607e15 1.13662 0.568312 0.822813i \(-0.307597\pi\)
0.568312 + 0.822813i \(0.307597\pi\)
\(234\) −2.35956e15 −0.939566
\(235\) 6.31064e12 0.00244418
\(236\) −8.26834e14 −0.311523
\(237\) 2.53107e15 0.927770
\(238\) 6.97762e15 2.48861
\(239\) 2.48628e15 0.862908 0.431454 0.902135i \(-0.358001\pi\)
0.431454 + 0.902135i \(0.358001\pi\)
\(240\) 4.97140e15 1.67921
\(241\) 4.45058e15 1.46321 0.731603 0.681731i \(-0.238772\pi\)
0.731603 + 0.681731i \(0.238772\pi\)
\(242\) 4.44283e15 1.42187
\(243\) 2.05891e14 0.0641500
\(244\) −4.15515e15 −1.26053
\(245\) 2.58286e15 0.762994
\(246\) 2.09271e15 0.602049
\(247\) 4.17724e15 1.17047
\(248\) −6.77746e15 −1.84983
\(249\) 2.65349e15 0.705541
\(250\) 3.95085e15 1.02348
\(251\) 2.69542e15 0.680374 0.340187 0.940358i \(-0.389510\pi\)
0.340187 + 0.940358i \(0.389510\pi\)
\(252\) −4.11700e15 −1.01269
\(253\) −6.33070e14 −0.151764
\(254\) −2.90632e15 −0.679086
\(255\) 3.36288e15 0.765951
\(256\) −5.13349e15 −1.13986
\(257\) 1.37462e15 0.297589 0.148794 0.988868i \(-0.452461\pi\)
0.148794 + 0.988868i \(0.452461\pi\)
\(258\) −3.53868e15 −0.746988
\(259\) −1.06189e16 −2.18590
\(260\) 2.27394e16 4.56511
\(261\) 2.42030e14 0.0473921
\(262\) 3.95287e15 0.755013
\(263\) 1.00126e16 1.86567 0.932835 0.360303i \(-0.117327\pi\)
0.932835 + 0.360303i \(0.117327\pi\)
\(264\) −3.89125e15 −0.707397
\(265\) 1.87363e15 0.332343
\(266\) 1.03345e16 1.78879
\(267\) −1.34348e15 −0.226939
\(268\) −1.79815e16 −2.96449
\(269\) −5.49516e15 −0.884281 −0.442141 0.896946i \(-0.645781\pi\)
−0.442141 + 0.896946i \(0.645781\pi\)
\(270\) −2.81342e15 −0.441947
\(271\) 8.53635e15 1.30910 0.654549 0.756020i \(-0.272859\pi\)
0.654549 + 0.756020i \(0.272859\pi\)
\(272\) 1.65801e16 2.48250
\(273\) −7.67264e15 −1.12173
\(274\) −1.53743e16 −2.19491
\(275\) 1.89869e15 0.264723
\(276\) −3.22402e15 −0.439025
\(277\) −1.03907e16 −1.38205 −0.691027 0.722829i \(-0.742842\pi\)
−0.691027 + 0.722829i \(0.742842\pi\)
\(278\) 7.17544e15 0.932303
\(279\) 1.89343e15 0.240337
\(280\) 3.27467e16 4.06107
\(281\) 3.02542e14 0.0366601 0.0183301 0.999832i \(-0.494165\pi\)
0.0183301 + 0.999832i \(0.494165\pi\)
\(282\) −1.76078e13 −0.00208490
\(283\) 1.43459e16 1.66003 0.830017 0.557739i \(-0.188331\pi\)
0.830017 + 0.557739i \(0.188331\pi\)
\(284\) 2.60924e16 2.95083
\(285\) 4.98074e15 0.550557
\(286\) −1.24584e16 −1.34612
\(287\) 6.80494e15 0.718774
\(288\) −5.58937e15 −0.577180
\(289\) 1.31095e15 0.132358
\(290\) −3.30724e15 −0.326497
\(291\) −8.84302e15 −0.853682
\(292\) −2.56091e16 −2.41772
\(293\) −1.07037e16 −0.988316 −0.494158 0.869372i \(-0.664524\pi\)
−0.494158 + 0.869372i \(0.664524\pi\)
\(294\) −7.20661e15 −0.650839
\(295\) −1.83733e15 −0.162309
\(296\) −5.11132e16 −4.41710
\(297\) 1.08710e15 0.0919079
\(298\) 1.47065e16 1.21648
\(299\) −6.00844e15 −0.486294
\(300\) 9.66943e15 0.765795
\(301\) −1.15068e16 −0.891813
\(302\) 3.79178e15 0.287606
\(303\) 6.89857e15 0.512132
\(304\) 2.45566e16 1.78439
\(305\) −9.23326e15 −0.656759
\(306\) −9.38302e15 −0.653361
\(307\) 5.22880e15 0.356453 0.178227 0.983989i \(-0.442964\pi\)
0.178227 + 0.983989i \(0.442964\pi\)
\(308\) −2.17377e16 −1.45089
\(309\) 2.28665e14 0.0149441
\(310\) −2.58729e16 −1.65575
\(311\) −2.44661e15 −0.153328 −0.0766641 0.997057i \(-0.524427\pi\)
−0.0766641 + 0.997057i \(0.524427\pi\)
\(312\) −3.69317e16 −2.26670
\(313\) −1.71237e15 −0.102934 −0.0514670 0.998675i \(-0.516390\pi\)
−0.0514670 + 0.998675i \(0.516390\pi\)
\(314\) 5.21664e16 3.07148
\(315\) −9.14849e15 −0.527632
\(316\) 6.80587e16 3.84519
\(317\) −2.84323e16 −1.57372 −0.786859 0.617133i \(-0.788294\pi\)
−0.786859 + 0.617133i \(0.788294\pi\)
\(318\) −5.22776e15 −0.283491
\(319\) 1.27791e15 0.0678988
\(320\) 2.05113e16 1.06787
\(321\) 9.42086e15 0.480627
\(322\) −1.48649e16 −0.743187
\(323\) 1.66112e16 0.813926
\(324\) 5.53626e15 0.265873
\(325\) 1.80204e16 0.848247
\(326\) −5.44000e16 −2.51006
\(327\) 4.90629e15 0.221918
\(328\) 3.27551e16 1.45244
\(329\) −5.72557e13 −0.00248912
\(330\) −1.48548e16 −0.633179
\(331\) −3.78376e16 −1.58140 −0.790700 0.612204i \(-0.790283\pi\)
−0.790700 + 0.612204i \(0.790283\pi\)
\(332\) 7.13505e16 2.92415
\(333\) 1.42795e16 0.573888
\(334\) 8.08727e16 3.18750
\(335\) −3.99571e16 −1.54455
\(336\) −4.51049e16 −1.71009
\(337\) −5.01871e16 −1.86637 −0.933185 0.359396i \(-0.882983\pi\)
−0.933185 + 0.359396i \(0.882983\pi\)
\(338\) −6.77480e16 −2.47137
\(339\) 6.67288e15 0.238790
\(340\) 9.04255e16 3.17452
\(341\) 9.99726e15 0.344332
\(342\) −1.38971e16 −0.469629
\(343\) 1.48568e16 0.492622
\(344\) −5.53873e16 −1.80211
\(345\) −7.16417e15 −0.228740
\(346\) 5.23321e16 1.63973
\(347\) −9.80701e15 −0.301575 −0.150787 0.988566i \(-0.548181\pi\)
−0.150787 + 0.988566i \(0.548181\pi\)
\(348\) 6.50801e15 0.196419
\(349\) −1.70944e16 −0.506395 −0.253197 0.967415i \(-0.581482\pi\)
−0.253197 + 0.967415i \(0.581482\pi\)
\(350\) 4.45825e16 1.29635
\(351\) 1.03176e16 0.294499
\(352\) −2.95117e16 −0.826928
\(353\) 6.53098e16 1.79656 0.898282 0.439419i \(-0.144816\pi\)
0.898282 + 0.439419i \(0.144816\pi\)
\(354\) 5.12646e15 0.138451
\(355\) 5.79805e16 1.53744
\(356\) −3.61253e16 −0.940560
\(357\) −3.05110e16 −0.780034
\(358\) −8.77442e16 −2.20282
\(359\) −6.09707e16 −1.50317 −0.751583 0.659638i \(-0.770710\pi\)
−0.751583 + 0.659638i \(0.770710\pi\)
\(360\) −4.40356e16 −1.06620
\(361\) −1.74503e16 −0.414959
\(362\) 2.36213e16 0.551695
\(363\) −1.94272e16 −0.445673
\(364\) −2.06312e17 −4.64906
\(365\) −5.69067e16 −1.25968
\(366\) 2.57624e16 0.560220
\(367\) 2.21422e16 0.473033 0.236516 0.971627i \(-0.423994\pi\)
0.236516 + 0.971627i \(0.423994\pi\)
\(368\) −3.53216e16 −0.741361
\(369\) −9.15081e15 −0.188707
\(370\) −1.95124e17 −3.95367
\(371\) −1.69993e16 −0.338454
\(372\) 5.09129e16 0.996089
\(373\) 5.12228e16 0.984818 0.492409 0.870364i \(-0.336117\pi\)
0.492409 + 0.870364i \(0.336117\pi\)
\(374\) −4.95422e16 −0.936072
\(375\) −1.72759e16 −0.320802
\(376\) −2.75596e14 −0.00502981
\(377\) 1.21286e16 0.217567
\(378\) 2.55258e16 0.450073
\(379\) −2.65278e16 −0.459775 −0.229888 0.973217i \(-0.573836\pi\)
−0.229888 + 0.973217i \(0.573836\pi\)
\(380\) 1.33928e17 2.28181
\(381\) 1.27085e16 0.212854
\(382\) 1.88892e16 0.311030
\(383\) 6.59095e16 1.06698 0.533490 0.845806i \(-0.320880\pi\)
0.533490 + 0.845806i \(0.320880\pi\)
\(384\) 5.57940e15 0.0888045
\(385\) −4.83039e16 −0.755939
\(386\) 8.41536e16 1.29496
\(387\) 1.54736e16 0.234137
\(388\) −2.37782e17 −3.53813
\(389\) 9.18217e15 0.134361 0.0671804 0.997741i \(-0.478600\pi\)
0.0671804 + 0.997741i \(0.478600\pi\)
\(390\) −1.40986e17 −2.02888
\(391\) −2.38932e16 −0.338162
\(392\) −1.12798e17 −1.57015
\(393\) −1.72847e16 −0.236652
\(394\) 1.91145e17 2.57418
\(395\) 1.51235e17 2.00341
\(396\) 2.92314e16 0.380917
\(397\) 7.78847e16 0.998421 0.499210 0.866481i \(-0.333623\pi\)
0.499210 + 0.866481i \(0.333623\pi\)
\(398\) 2.30784e17 2.91049
\(399\) −4.51896e16 −0.560680
\(400\) 1.05936e17 1.29316
\(401\) −1.77085e16 −0.212688 −0.106344 0.994329i \(-0.533914\pi\)
−0.106344 + 0.994329i \(0.533914\pi\)
\(402\) 1.11487e17 1.31751
\(403\) 9.48835e16 1.10334
\(404\) 1.85497e17 2.12256
\(405\) 1.23023e16 0.138525
\(406\) 3.00062e16 0.332500
\(407\) 7.53957e16 0.822211
\(408\) −1.46863e17 −1.57623
\(409\) 5.64265e16 0.596048 0.298024 0.954558i \(-0.403672\pi\)
0.298024 + 0.954558i \(0.403672\pi\)
\(410\) 1.25042e17 1.30006
\(411\) 6.72272e16 0.687976
\(412\) 6.14865e15 0.0619366
\(413\) 1.66699e16 0.165294
\(414\) 1.99893e16 0.195117
\(415\) 1.58550e17 1.52354
\(416\) −2.80095e17 −2.64971
\(417\) −3.13760e16 −0.292223
\(418\) −7.33765e16 −0.672839
\(419\) 9.61919e16 0.868455 0.434228 0.900803i \(-0.357021\pi\)
0.434228 + 0.900803i \(0.357021\pi\)
\(420\) −2.45996e17 −2.18679
\(421\) −5.22604e16 −0.457445 −0.228722 0.973492i \(-0.573455\pi\)
−0.228722 + 0.973492i \(0.573455\pi\)
\(422\) 3.93957e17 3.39561
\(423\) 7.69935e13 0.000653494 0
\(424\) −8.18246e16 −0.683921
\(425\) 7.16600e16 0.589860
\(426\) −1.61775e17 −1.31145
\(427\) 8.37723e16 0.668835
\(428\) 2.53320e17 1.99198
\(429\) 5.44769e16 0.421930
\(430\) −2.11441e17 −1.61303
\(431\) 1.12144e17 0.842702 0.421351 0.906898i \(-0.361556\pi\)
0.421351 + 0.906898i \(0.361556\pi\)
\(432\) 6.06540e16 0.448967
\(433\) 3.70819e16 0.270390 0.135195 0.990819i \(-0.456834\pi\)
0.135195 + 0.990819i \(0.456834\pi\)
\(434\) 2.34742e17 1.68619
\(435\) 1.44616e16 0.102338
\(436\) 1.31926e17 0.919750
\(437\) −3.53880e16 −0.243067
\(438\) 1.58779e17 1.07451
\(439\) −1.76562e17 −1.17728 −0.588638 0.808396i \(-0.700336\pi\)
−0.588638 + 0.808396i \(0.700336\pi\)
\(440\) −2.32507e17 −1.52754
\(441\) 3.15124e16 0.204000
\(442\) −4.70202e17 −2.99944
\(443\) 1.96195e17 1.23329 0.616644 0.787242i \(-0.288492\pi\)
0.616644 + 0.787242i \(0.288492\pi\)
\(444\) 3.83967e17 2.37850
\(445\) −8.02748e16 −0.490049
\(446\) 1.86629e17 1.12280
\(447\) −6.43073e16 −0.381295
\(448\) −1.86097e17 −1.08751
\(449\) −1.36970e17 −0.788905 −0.394452 0.918916i \(-0.629066\pi\)
−0.394452 + 0.918916i \(0.629066\pi\)
\(450\) −5.99514e16 −0.340344
\(451\) −4.83161e16 −0.270361
\(452\) 1.79429e17 0.989675
\(453\) −1.65803e16 −0.0901476
\(454\) −6.16030e17 −3.30171
\(455\) −4.58450e17 −2.42224
\(456\) −2.17517e17 −1.13298
\(457\) 1.20278e17 0.617636 0.308818 0.951121i \(-0.400067\pi\)
0.308818 + 0.951121i \(0.400067\pi\)
\(458\) −2.17810e17 −1.10269
\(459\) 4.10291e16 0.204791
\(460\) −1.92639e17 −0.948024
\(461\) 2.94491e17 1.42895 0.714474 0.699662i \(-0.246666\pi\)
0.714474 + 0.699662i \(0.246666\pi\)
\(462\) 1.34776e17 0.644822
\(463\) 3.10512e17 1.46488 0.732439 0.680833i \(-0.238382\pi\)
0.732439 + 0.680833i \(0.238382\pi\)
\(464\) 7.13002e16 0.331683
\(465\) 1.13135e17 0.518981
\(466\) −4.62815e17 −2.09363
\(467\) 3.66019e17 1.63284 0.816421 0.577458i \(-0.195955\pi\)
0.816421 + 0.577458i \(0.195955\pi\)
\(468\) 2.77434e17 1.22057
\(469\) 3.62526e17 1.57295
\(470\) −1.05209e15 −0.00450210
\(471\) −2.28108e17 −0.962731
\(472\) 8.02391e16 0.334013
\(473\) 8.17003e16 0.335449
\(474\) −4.21970e17 −1.70892
\(475\) 1.06135e17 0.423985
\(476\) −8.20420e17 −3.23289
\(477\) 2.28594e16 0.0888579
\(478\) −4.14504e17 −1.58945
\(479\) −1.92869e17 −0.729596 −0.364798 0.931087i \(-0.618862\pi\)
−0.364798 + 0.931087i \(0.618862\pi\)
\(480\) −3.33972e17 −1.24635
\(481\) 7.15578e17 2.63459
\(482\) −7.41983e17 −2.69518
\(483\) 6.49997e16 0.232946
\(484\) −5.22383e17 −1.84712
\(485\) −5.28381e17 −1.84343
\(486\) −3.43254e16 −0.118162
\(487\) 9.24807e16 0.314133 0.157066 0.987588i \(-0.449796\pi\)
0.157066 + 0.987588i \(0.449796\pi\)
\(488\) 4.03231e17 1.35153
\(489\) 2.37875e17 0.786758
\(490\) −4.30604e17 −1.40541
\(491\) 5.83125e16 0.187816 0.0939079 0.995581i \(-0.470064\pi\)
0.0939079 + 0.995581i \(0.470064\pi\)
\(492\) −2.46059e17 −0.782106
\(493\) 4.82307e16 0.151293
\(494\) −6.96413e17 −2.15596
\(495\) 6.49557e16 0.198465
\(496\) 5.57789e17 1.68205
\(497\) −5.26050e17 −1.56571
\(498\) −4.42380e17 −1.29959
\(499\) 4.12178e17 1.19517 0.597587 0.801804i \(-0.296126\pi\)
0.597587 + 0.801804i \(0.296126\pi\)
\(500\) −4.64536e17 −1.32958
\(501\) −3.53632e17 −0.999094
\(502\) −4.49371e17 −1.25323
\(503\) 5.29139e17 1.45673 0.728363 0.685192i \(-0.240282\pi\)
0.728363 + 0.685192i \(0.240282\pi\)
\(504\) 3.99529e17 1.08580
\(505\) 4.12198e17 1.10589
\(506\) 1.05543e17 0.279544
\(507\) 2.96242e17 0.774631
\(508\) 3.41722e17 0.882183
\(509\) −3.99011e17 −1.01700 −0.508498 0.861063i \(-0.669799\pi\)
−0.508498 + 0.861063i \(0.669799\pi\)
\(510\) −5.60647e17 −1.41086
\(511\) 5.16307e17 1.28284
\(512\) 7.93138e17 1.94578
\(513\) 6.07679e16 0.147201
\(514\) −2.29171e17 −0.548150
\(515\) 1.36630e16 0.0322701
\(516\) 4.16074e17 0.970392
\(517\) 4.06524e14 0.000936263 0
\(518\) 1.77034e18 4.02637
\(519\) −2.28833e17 −0.513961
\(520\) −2.20671e18 −4.89468
\(521\) 2.52542e17 0.553208 0.276604 0.960984i \(-0.410791\pi\)
0.276604 + 0.960984i \(0.410791\pi\)
\(522\) −4.03503e16 −0.0872948
\(523\) −4.88553e17 −1.04388 −0.521940 0.852982i \(-0.674791\pi\)
−0.521940 + 0.852982i \(0.674791\pi\)
\(524\) −4.64774e17 −0.980818
\(525\) −1.94946e17 −0.406330
\(526\) −1.66926e18 −3.43651
\(527\) 3.77314e17 0.767245
\(528\) 3.20252e17 0.643237
\(529\) −4.53135e17 −0.899013
\(530\) −3.12365e17 −0.612166
\(531\) −2.24165e16 −0.0433963
\(532\) −1.21512e18 −2.32377
\(533\) −4.58566e17 −0.866314
\(534\) 2.23980e17 0.418015
\(535\) 5.62908e17 1.03786
\(536\) 1.74499e18 3.17850
\(537\) 3.83679e17 0.690455
\(538\) 9.16132e17 1.62882
\(539\) 1.66385e17 0.292271
\(540\) 3.30799e17 0.574122
\(541\) 1.11207e17 0.190700 0.0953499 0.995444i \(-0.469603\pi\)
0.0953499 + 0.995444i \(0.469603\pi\)
\(542\) −1.42315e18 −2.41132
\(543\) −1.03289e17 −0.172924
\(544\) −1.11383e18 −1.84257
\(545\) 2.93157e17 0.479206
\(546\) 1.27915e18 2.06619
\(547\) 7.63636e16 0.121890 0.0609451 0.998141i \(-0.480589\pi\)
0.0609451 + 0.998141i \(0.480589\pi\)
\(548\) 1.80769e18 2.85135
\(549\) −1.12651e17 −0.175596
\(550\) −3.16542e17 −0.487612
\(551\) 7.14341e16 0.108748
\(552\) 3.12871e17 0.470719
\(553\) −1.37213e18 −2.04025
\(554\) 1.73229e18 2.54570
\(555\) 8.53221e17 1.23924
\(556\) −8.43679e17 −1.21113
\(557\) 4.01835e17 0.570150 0.285075 0.958505i \(-0.407981\pi\)
0.285075 + 0.958505i \(0.407981\pi\)
\(558\) −3.15665e17 −0.442694
\(559\) 7.75414e17 1.07487
\(560\) −2.69508e18 −3.69274
\(561\) 2.16633e17 0.293404
\(562\) −5.04386e16 −0.0675269
\(563\) 8.18065e17 1.08264 0.541319 0.840817i \(-0.317925\pi\)
0.541319 + 0.840817i \(0.317925\pi\)
\(564\) 2.07030e15 0.00270844
\(565\) 3.98713e17 0.515639
\(566\) −2.39170e18 −3.05773
\(567\) −1.11617e17 −0.141072
\(568\) −2.53210e18 −3.16386
\(569\) 1.02365e18 1.26451 0.632253 0.774762i \(-0.282130\pi\)
0.632253 + 0.774762i \(0.282130\pi\)
\(570\) −8.30370e17 −1.01411
\(571\) 8.02040e16 0.0968415 0.0484207 0.998827i \(-0.484581\pi\)
0.0484207 + 0.998827i \(0.484581\pi\)
\(572\) 1.46484e18 1.74871
\(573\) −8.25969e16 −0.0974896
\(574\) −1.13449e18 −1.32396
\(575\) −1.52662e17 −0.176153
\(576\) 2.50250e17 0.285514
\(577\) −6.55279e16 −0.0739236 −0.0369618 0.999317i \(-0.511768\pi\)
−0.0369618 + 0.999317i \(0.511768\pi\)
\(578\) −2.18556e17 −0.243799
\(579\) −3.67979e17 −0.405893
\(580\) 3.88862e17 0.424144
\(581\) −1.43850e18 −1.55155
\(582\) 1.47427e18 1.57246
\(583\) 1.20697e17 0.127307
\(584\) 2.48521e18 2.59226
\(585\) 6.16491e17 0.635937
\(586\) 1.78449e18 1.82045
\(587\) −1.41001e18 −1.42257 −0.711284 0.702905i \(-0.751886\pi\)
−0.711284 + 0.702905i \(0.751886\pi\)
\(588\) 8.47344e17 0.845488
\(589\) 5.58837e17 0.551487
\(590\) 3.06312e17 0.298969
\(591\) −8.35821e17 −0.806854
\(592\) 4.20665e18 4.01647
\(593\) 1.76703e18 1.66874 0.834368 0.551208i \(-0.185833\pi\)
0.834368 + 0.551208i \(0.185833\pi\)
\(594\) −1.81237e17 −0.169292
\(595\) −1.82307e18 −1.68439
\(596\) −1.72918e18 −1.58030
\(597\) −1.00915e18 −0.912269
\(598\) 1.00170e18 0.895739
\(599\) 7.43189e17 0.657393 0.328696 0.944436i \(-0.393391\pi\)
0.328696 + 0.944436i \(0.393391\pi\)
\(600\) −9.38357e17 −0.821079
\(601\) 5.45093e15 0.00471831 0.00235916 0.999997i \(-0.499249\pi\)
0.00235916 + 0.999997i \(0.499249\pi\)
\(602\) 1.91838e18 1.64269
\(603\) −4.87499e17 −0.412963
\(604\) −4.45832e17 −0.373621
\(605\) −1.16080e18 −0.962381
\(606\) −1.15010e18 −0.943332
\(607\) 1.82401e18 1.48013 0.740067 0.672534i \(-0.234794\pi\)
0.740067 + 0.672534i \(0.234794\pi\)
\(608\) −1.64968e18 −1.32442
\(609\) −1.31208e17 −0.104219
\(610\) 1.53933e18 1.20973
\(611\) 3.85830e15 0.00300005
\(612\) 1.10324e18 0.848764
\(613\) 2.14261e18 1.63098 0.815492 0.578769i \(-0.196467\pi\)
0.815492 + 0.578769i \(0.196467\pi\)
\(614\) −8.71726e17 −0.656577
\(615\) −5.46773e17 −0.407491
\(616\) 2.10951e18 1.55563
\(617\) −1.47169e18 −1.07390 −0.536949 0.843615i \(-0.680423\pi\)
−0.536949 + 0.843615i \(0.680423\pi\)
\(618\) −3.81222e16 −0.0275266
\(619\) −2.34920e18 −1.67854 −0.839268 0.543718i \(-0.817016\pi\)
−0.839268 + 0.543718i \(0.817016\pi\)
\(620\) 3.04211e18 2.15094
\(621\) −8.74071e16 −0.0611577
\(622\) 4.07889e17 0.282426
\(623\) 7.28324e17 0.499060
\(624\) 3.03950e18 2.06111
\(625\) −1.85825e18 −1.24705
\(626\) 2.85480e17 0.189602
\(627\) 3.20853e17 0.210896
\(628\) −6.13366e18 −3.99009
\(629\) 2.84557e18 1.83206
\(630\) 1.52520e18 0.971882
\(631\) −3.37780e17 −0.213031 −0.106516 0.994311i \(-0.533969\pi\)
−0.106516 + 0.994311i \(0.533969\pi\)
\(632\) −6.60466e18 −4.12278
\(633\) −1.72266e18 −1.06433
\(634\) 4.74012e18 2.89874
\(635\) 7.59348e17 0.459633
\(636\) 6.14673e17 0.368276
\(637\) 1.57915e18 0.936520
\(638\) −2.13049e17 −0.125068
\(639\) 7.07396e17 0.411061
\(640\) 3.33376e17 0.191763
\(641\) −1.95698e17 −0.111432 −0.0557160 0.998447i \(-0.517744\pi\)
−0.0557160 + 0.998447i \(0.517744\pi\)
\(642\) −1.57061e18 −0.885300
\(643\) 2.67575e18 1.49305 0.746526 0.665357i \(-0.231720\pi\)
0.746526 + 0.665357i \(0.231720\pi\)
\(644\) 1.74779e18 0.965455
\(645\) 9.24567e17 0.505592
\(646\) −2.76936e18 −1.49923
\(647\) −1.32947e18 −0.712526 −0.356263 0.934386i \(-0.615949\pi\)
−0.356263 + 0.934386i \(0.615949\pi\)
\(648\) −5.37259e17 −0.285067
\(649\) −1.18359e17 −0.0621740
\(650\) −3.00429e18 −1.56245
\(651\) −1.02646e18 −0.528523
\(652\) 6.39628e18 3.26076
\(653\) −1.93417e17 −0.0976243 −0.0488122 0.998808i \(-0.515544\pi\)
−0.0488122 + 0.998808i \(0.515544\pi\)
\(654\) −8.17957e17 −0.408766
\(655\) −1.03278e18 −0.511024
\(656\) −2.69576e18 −1.32071
\(657\) −6.94294e17 −0.336797
\(658\) 9.54545e15 0.00458488
\(659\) 2.20254e18 1.04753 0.523766 0.851862i \(-0.324526\pi\)
0.523766 + 0.851862i \(0.324526\pi\)
\(660\) 1.74661e18 0.822546
\(661\) −3.58539e18 −1.67196 −0.835982 0.548756i \(-0.815101\pi\)
−0.835982 + 0.548756i \(0.815101\pi\)
\(662\) 6.30814e18 2.91289
\(663\) 2.05606e18 0.940149
\(664\) −6.92412e18 −3.13525
\(665\) −2.70014e18 −1.21072
\(666\) −2.38063e18 −1.05708
\(667\) −1.02749e17 −0.0451814
\(668\) −9.50891e18 −4.14080
\(669\) −8.16071e17 −0.351931
\(670\) 6.66149e18 2.84502
\(671\) −5.94796e17 −0.251577
\(672\) 3.03008e18 1.26927
\(673\) 2.03328e18 0.843529 0.421765 0.906705i \(-0.361411\pi\)
0.421765 + 0.906705i \(0.361411\pi\)
\(674\) 8.36700e18 3.43780
\(675\) 2.62150e17 0.106678
\(676\) 7.96573e18 3.21049
\(677\) −4.31426e18 −1.72219 −0.861093 0.508447i \(-0.830220\pi\)
−0.861093 + 0.508447i \(0.830220\pi\)
\(678\) −1.11248e18 −0.439843
\(679\) 4.79394e18 1.87732
\(680\) −8.77522e18 −3.40369
\(681\) 2.69371e18 1.03489
\(682\) −1.66670e18 −0.634249
\(683\) −3.28300e18 −1.23748 −0.618738 0.785597i \(-0.712356\pi\)
−0.618738 + 0.785597i \(0.712356\pi\)
\(684\) 1.63400e18 0.610082
\(685\) 4.01691e18 1.48561
\(686\) −2.47687e18 −0.907396
\(687\) 9.52420e17 0.345629
\(688\) 4.55841e18 1.63866
\(689\) 1.14553e18 0.407927
\(690\) 1.19438e18 0.421332
\(691\) 2.85949e18 0.999267 0.499633 0.866237i \(-0.333468\pi\)
0.499633 + 0.866237i \(0.333468\pi\)
\(692\) −6.15314e18 −2.13014
\(693\) −5.89335e17 −0.202114
\(694\) 1.63499e18 0.555492
\(695\) −1.87476e18 −0.631021
\(696\) −6.31561e17 −0.210598
\(697\) −1.82354e18 −0.602423
\(698\) 2.84992e18 0.932764
\(699\) 2.02375e18 0.656230
\(700\) −5.24195e18 −1.68405
\(701\) −3.12642e18 −0.995131 −0.497566 0.867426i \(-0.665773\pi\)
−0.497566 + 0.867426i \(0.665773\pi\)
\(702\) −1.72012e18 −0.542458
\(703\) 4.21455e18 1.31687
\(704\) 1.32131e18 0.409057
\(705\) 4.60046e15 0.00141115
\(706\) −1.08882e19 −3.30922
\(707\) −3.73982e18 −1.12622
\(708\) −6.02762e17 −0.179858
\(709\) −6.61539e18 −1.95594 −0.977969 0.208750i \(-0.933060\pi\)
−0.977969 + 0.208750i \(0.933060\pi\)
\(710\) −9.66628e18 −2.83192
\(711\) 1.84515e18 0.535648
\(712\) 3.50573e18 1.00846
\(713\) −8.03818e17 −0.229127
\(714\) 5.08668e18 1.43680
\(715\) 3.25506e18 0.911109
\(716\) 1.03169e19 2.86162
\(717\) 1.81250e18 0.498200
\(718\) 1.01648e19 2.76879
\(719\) 7.26986e18 1.96240 0.981202 0.192984i \(-0.0618166\pi\)
0.981202 + 0.192984i \(0.0618166\pi\)
\(720\) 3.62415e18 0.969494
\(721\) −1.23963e17 −0.0328635
\(722\) 2.90924e18 0.764342
\(723\) 3.24447e18 0.844783
\(724\) −2.77737e18 −0.716692
\(725\) 3.08163e17 0.0788104
\(726\) 3.23883e18 0.820917
\(727\) 7.25236e18 1.82182 0.910910 0.412604i \(-0.135381\pi\)
0.910910 + 0.412604i \(0.135381\pi\)
\(728\) 2.00212e19 4.98468
\(729\) 1.50095e17 0.0370370
\(730\) 9.48726e18 2.32029
\(731\) 3.08352e18 0.747452
\(732\) −3.02911e18 −0.727767
\(733\) 3.90928e18 0.930938 0.465469 0.885064i \(-0.345886\pi\)
0.465469 + 0.885064i \(0.345886\pi\)
\(734\) −3.69146e18 −0.871313
\(735\) 1.88290e18 0.440515
\(736\) 2.37286e18 0.550257
\(737\) −2.57399e18 −0.591654
\(738\) 1.52559e18 0.347593
\(739\) −1.18734e17 −0.0268156 −0.0134078 0.999910i \(-0.504268\pi\)
−0.0134078 + 0.999910i \(0.504268\pi\)
\(740\) 2.29425e19 5.13611
\(741\) 3.04521e18 0.675769
\(742\) 2.83405e18 0.623422
\(743\) 5.62331e18 1.22621 0.613105 0.790002i \(-0.289920\pi\)
0.613105 + 0.790002i \(0.289920\pi\)
\(744\) −4.94077e18 −1.06800
\(745\) −3.84244e18 −0.823363
\(746\) −8.53967e18 −1.81401
\(747\) 1.93440e18 0.407344
\(748\) 5.82510e18 1.21603
\(749\) −5.10720e18 −1.05694
\(750\) 2.88017e18 0.590907
\(751\) −7.12638e17 −0.144947 −0.0724736 0.997370i \(-0.523089\pi\)
−0.0724736 + 0.997370i \(0.523089\pi\)
\(752\) 2.26817e16 0.00457362
\(753\) 1.96496e18 0.392814
\(754\) −2.02204e18 −0.400752
\(755\) −9.90694e17 −0.194663
\(756\) −3.00130e18 −0.584679
\(757\) −6.26409e18 −1.20986 −0.604929 0.796279i \(-0.706799\pi\)
−0.604929 + 0.796279i \(0.706799\pi\)
\(758\) 4.42261e18 0.846893
\(759\) −4.61508e17 −0.0876208
\(760\) −1.29969e19 −2.44654
\(761\) 1.33282e18 0.248755 0.124377 0.992235i \(-0.460307\pi\)
0.124377 + 0.992235i \(0.460307\pi\)
\(762\) −2.11871e18 −0.392070
\(763\) −2.65978e18 −0.488018
\(764\) −2.22097e18 −0.404051
\(765\) 2.45154e18 0.442222
\(766\) −1.09882e19 −1.96535
\(767\) −1.12334e18 −0.199223
\(768\) −3.74231e18 −0.658100
\(769\) −1.52159e17 −0.0265324 −0.0132662 0.999912i \(-0.504223\pi\)
−0.0132662 + 0.999912i \(0.504223\pi\)
\(770\) 8.05303e18 1.39242
\(771\) 1.00210e18 0.171813
\(772\) −9.89468e18 −1.68224
\(773\) −9.30354e18 −1.56849 −0.784244 0.620452i \(-0.786949\pi\)
−0.784244 + 0.620452i \(0.786949\pi\)
\(774\) −2.57970e18 −0.431274
\(775\) 2.41079e18 0.399668
\(776\) 2.30753e19 3.79355
\(777\) −7.74117e18 −1.26203
\(778\) −1.53082e18 −0.247489
\(779\) −2.70082e18 −0.433015
\(780\) 1.65770e19 2.63567
\(781\) 3.73504e18 0.588929
\(782\) 3.98338e18 0.622885
\(783\) 1.76440e17 0.0273618
\(784\) 9.28331e18 1.42774
\(785\) −1.36298e19 −2.07891
\(786\) 2.88164e18 0.435907
\(787\) −7.83821e18 −1.17593 −0.587965 0.808887i \(-0.700071\pi\)
−0.587965 + 0.808887i \(0.700071\pi\)
\(788\) −2.24746e19 −3.34404
\(789\) 7.29919e18 1.07715
\(790\) −2.52133e19 −3.69023
\(791\) −3.61748e18 −0.525120
\(792\) −2.83672e18 −0.408416
\(793\) −5.64518e18 −0.806125
\(794\) −1.29846e19 −1.83906
\(795\) 1.36588e18 0.191878
\(796\) −2.71353e19 −3.78094
\(797\) 4.87347e18 0.673533 0.336767 0.941588i \(-0.390667\pi\)
0.336767 + 0.941588i \(0.390667\pi\)
\(798\) 7.53384e18 1.03276
\(799\) 1.53430e16 0.00208619
\(800\) −7.11663e18 −0.959819
\(801\) −9.79400e17 −0.131023
\(802\) 2.95229e18 0.391765
\(803\) −3.66586e18 −0.482531
\(804\) −1.31085e19 −1.71155
\(805\) 3.88381e18 0.503020
\(806\) −1.58186e19 −2.03231
\(807\) −4.00597e18 −0.510540
\(808\) −1.80014e19 −2.27579
\(809\) −1.56659e18 −0.196467 −0.0982333 0.995163i \(-0.531319\pi\)
−0.0982333 + 0.995163i \(0.531319\pi\)
\(810\) −2.05098e18 −0.255158
\(811\) 1.55373e19 1.91752 0.958762 0.284211i \(-0.0917316\pi\)
0.958762 + 0.284211i \(0.0917316\pi\)
\(812\) −3.52809e18 −0.431943
\(813\) 6.22300e18 0.755808
\(814\) −1.25697e19 −1.51449
\(815\) 1.42133e19 1.69891
\(816\) 1.20869e19 1.43327
\(817\) 4.56697e18 0.537260
\(818\) −9.40720e18 −1.09790
\(819\) −5.59335e18 −0.647630
\(820\) −1.47023e19 −1.68887
\(821\) 6.52725e18 0.743874 0.371937 0.928258i \(-0.378694\pi\)
0.371937 + 0.928258i \(0.378694\pi\)
\(822\) −1.12079e19 −1.26723
\(823\) −1.64640e18 −0.184687 −0.0923435 0.995727i \(-0.529436\pi\)
−0.0923435 + 0.995727i \(0.529436\pi\)
\(824\) −5.96687e17 −0.0664079
\(825\) 1.38415e18 0.152838
\(826\) −2.77913e18 −0.304466
\(827\) −7.15086e18 −0.777271 −0.388635 0.921392i \(-0.627053\pi\)
−0.388635 + 0.921392i \(0.627053\pi\)
\(828\) −2.35031e18 −0.253471
\(829\) −8.31028e18 −0.889224 −0.444612 0.895723i \(-0.646659\pi\)
−0.444612 + 0.895723i \(0.646659\pi\)
\(830\) −2.64328e19 −2.80631
\(831\) −7.57480e18 −0.797930
\(832\) 1.25405e19 1.31073
\(833\) 6.27966e18 0.651243
\(834\) 5.23089e18 0.538265
\(835\) −2.11300e19 −2.15743
\(836\) 8.62751e18 0.874067
\(837\) 1.38031e18 0.138759
\(838\) −1.60367e19 −1.59967
\(839\) 1.80617e18 0.178775 0.0893874 0.995997i \(-0.471509\pi\)
0.0893874 + 0.995997i \(0.471509\pi\)
\(840\) 2.38724e19 2.34466
\(841\) −1.00532e19 −0.979786
\(842\) 8.71265e18 0.842600
\(843\) 2.20553e17 0.0211657
\(844\) −4.63210e19 −4.41115
\(845\) 1.77008e19 1.67273
\(846\) −1.28361e16 −0.00120372
\(847\) 1.05318e19 0.980076
\(848\) 6.73421e18 0.621890
\(849\) 1.04582e19 0.958421
\(850\) −1.19469e19 −1.08650
\(851\) −6.06210e18 −0.547118
\(852\) 1.90213e19 1.70366
\(853\) −6.78932e18 −0.603472 −0.301736 0.953391i \(-0.597566\pi\)
−0.301736 + 0.953391i \(0.597566\pi\)
\(854\) −1.39662e19 −1.23197
\(855\) 3.63096e18 0.317864
\(856\) −2.45831e19 −2.13578
\(857\) 1.28230e19 1.10564 0.552820 0.833301i \(-0.313552\pi\)
0.552820 + 0.833301i \(0.313552\pi\)
\(858\) −9.08218e18 −0.777182
\(859\) −4.19378e18 −0.356164 −0.178082 0.984016i \(-0.556989\pi\)
−0.178082 + 0.984016i \(0.556989\pi\)
\(860\) 2.48609e19 2.09545
\(861\) 4.96080e18 0.414984
\(862\) −1.86962e19 −1.55223
\(863\) 1.77382e18 0.146163 0.0730817 0.997326i \(-0.476717\pi\)
0.0730817 + 0.997326i \(0.476717\pi\)
\(864\) −4.07465e18 −0.333235
\(865\) −1.36730e19 −1.10984
\(866\) −6.18215e18 −0.498051
\(867\) 9.55681e17 0.0764168
\(868\) −2.76007e19 −2.19049
\(869\) 9.74236e18 0.767425
\(870\) −2.41098e18 −0.188503
\(871\) −2.44296e19 −1.89583
\(872\) −1.28026e19 −0.986148
\(873\) −6.44656e18 −0.492873
\(874\) 5.89975e18 0.447723
\(875\) 9.36553e18 0.705472
\(876\) −1.86691e19 −1.39587
\(877\) 1.29299e19 0.959616 0.479808 0.877373i \(-0.340706\pi\)
0.479808 + 0.877373i \(0.340706\pi\)
\(878\) 2.94358e19 2.16851
\(879\) −7.80303e18 −0.570605
\(880\) 1.91354e19 1.38900
\(881\) −2.59331e19 −1.86858 −0.934289 0.356516i \(-0.883964\pi\)
−0.934289 + 0.356516i \(0.883964\pi\)
\(882\) −5.25362e18 −0.375762
\(883\) 1.38109e19 0.980566 0.490283 0.871563i \(-0.336893\pi\)
0.490283 + 0.871563i \(0.336893\pi\)
\(884\) 5.52858e19 3.89649
\(885\) −1.33941e18 −0.0937093
\(886\) −3.27089e19 −2.27168
\(887\) 5.85589e18 0.403729 0.201864 0.979413i \(-0.435300\pi\)
0.201864 + 0.979413i \(0.435300\pi\)
\(888\) −3.72615e19 −2.55021
\(889\) −6.88947e18 −0.468085
\(890\) 1.33831e19 0.902656
\(891\) 7.92497e17 0.0530631
\(892\) −2.19435e19 −1.45860
\(893\) 2.27243e16 0.00149953
\(894\) 1.07211e19 0.702335
\(895\) 2.29253e19 1.49096
\(896\) −3.02468e18 −0.195289
\(897\) −4.38015e18 −0.280762
\(898\) 2.28351e19 1.45314
\(899\) 1.62258e18 0.102511
\(900\) 7.04901e18 0.442132
\(901\) 4.55533e18 0.283667
\(902\) 8.05508e18 0.497998
\(903\) −8.38849e18 −0.514889
\(904\) −1.74124e19 −1.06112
\(905\) −6.17165e18 −0.373410
\(906\) 2.76421e18 0.166049
\(907\) −2.59316e18 −0.154661 −0.0773307 0.997005i \(-0.524640\pi\)
−0.0773307 + 0.997005i \(0.524640\pi\)
\(908\) 7.24320e19 4.28916
\(909\) 5.02906e18 0.295679
\(910\) 7.64310e19 4.46170
\(911\) −1.64343e19 −0.952537 −0.476269 0.879300i \(-0.658011\pi\)
−0.476269 + 0.879300i \(0.658011\pi\)
\(912\) 1.79018e19 1.03022
\(913\) 1.02136e19 0.583604
\(914\) −2.00524e19 −1.13767
\(915\) −6.73105e18 −0.379180
\(916\) 2.56099e19 1.43247
\(917\) 9.37033e18 0.520420
\(918\) −6.84022e18 −0.377218
\(919\) −8.26113e18 −0.452365 −0.226182 0.974085i \(-0.572625\pi\)
−0.226182 + 0.974085i \(0.572625\pi\)
\(920\) 1.86944e19 1.01646
\(921\) 3.81180e18 0.205798
\(922\) −4.90964e19 −2.63208
\(923\) 3.54491e19 1.88709
\(924\) −1.58468e19 −0.837671
\(925\) 1.81814e19 0.954344
\(926\) −5.17673e19 −2.69826
\(927\) 1.66697e17 0.00862799
\(928\) −4.78984e18 −0.246184
\(929\) 6.48641e17 0.0331057 0.0165528 0.999863i \(-0.494731\pi\)
0.0165528 + 0.999863i \(0.494731\pi\)
\(930\) −1.88614e19 −0.955947
\(931\) 9.30074e18 0.468107
\(932\) 5.44172e19 2.71978
\(933\) −1.78358e18 −0.0885240
\(934\) −6.10213e19 −3.00765
\(935\) 1.29441e19 0.633573
\(936\) −2.69232e19 −1.30868
\(937\) 3.08366e19 1.48854 0.744268 0.667881i \(-0.232799\pi\)
0.744268 + 0.667881i \(0.232799\pi\)
\(938\) −6.04389e19 −2.89733
\(939\) −1.24832e18 −0.0594290
\(940\) 1.23703e17 0.00584856
\(941\) 1.48854e19 0.698919 0.349460 0.936951i \(-0.386365\pi\)
0.349460 + 0.936951i \(0.386365\pi\)
\(942\) 3.80293e19 1.77332
\(943\) 3.88480e18 0.179905
\(944\) −6.60372e18 −0.303718
\(945\) −6.66925e18 −0.304628
\(946\) −1.36208e19 −0.617887
\(947\) 1.95065e19 0.878829 0.439415 0.898284i \(-0.355186\pi\)
0.439415 + 0.898284i \(0.355186\pi\)
\(948\) 4.96148e19 2.22002
\(949\) −3.47925e19 −1.54616
\(950\) −1.76944e19 −0.780967
\(951\) −2.07271e19 −0.908586
\(952\) 7.96166e19 3.46628
\(953\) 3.67148e19 1.58759 0.793794 0.608187i \(-0.208103\pi\)
0.793794 + 0.608187i \(0.208103\pi\)
\(954\) −3.81104e18 −0.163674
\(955\) −4.93527e18 −0.210518
\(956\) 4.87368e19 2.06481
\(957\) 9.31599e17 0.0392014
\(958\) 3.21545e19 1.34389
\(959\) −3.64449e19 −1.51292
\(960\) 1.49527e19 0.616535
\(961\) −1.17239e19 −0.480142
\(962\) −1.19298e20 −4.85285
\(963\) 6.86781e18 0.277490
\(964\) 8.72415e19 3.50124
\(965\) −2.19872e19 −0.876480
\(966\) −1.08365e19 −0.429079
\(967\) 2.37395e19 0.933683 0.466841 0.884341i \(-0.345392\pi\)
0.466841 + 0.884341i \(0.345392\pi\)
\(968\) 5.06939e19 1.98046
\(969\) 1.21096e19 0.469921
\(970\) 8.80897e19 3.39554
\(971\) −4.75630e19 −1.82114 −0.910572 0.413350i \(-0.864359\pi\)
−0.910572 + 0.413350i \(0.864359\pi\)
\(972\) 4.03593e18 0.153502
\(973\) 1.70095e19 0.642624
\(974\) −1.54180e19 −0.578623
\(975\) 1.31369e19 0.489736
\(976\) −3.31862e19 −1.22895
\(977\) 1.03472e19 0.380635 0.190317 0.981723i \(-0.439048\pi\)
0.190317 + 0.981723i \(0.439048\pi\)
\(978\) −3.96576e19 −1.44919
\(979\) −5.17121e18 −0.187718
\(980\) 5.06299e19 1.82573
\(981\) 3.57668e18 0.128124
\(982\) −9.72164e18 −0.345951
\(983\) 4.52073e19 1.59813 0.799063 0.601247i \(-0.205329\pi\)
0.799063 + 0.601247i \(0.205329\pi\)
\(984\) 2.38784e19 0.838567
\(985\) −4.99414e19 −1.74231
\(986\) −8.04084e18 −0.278677
\(987\) −4.17394e16 −0.00143709
\(988\) 8.18833e19 2.80076
\(989\) −6.56902e18 −0.223216
\(990\) −1.08292e19 −0.365566
\(991\) 3.34899e19 1.12314 0.561571 0.827428i \(-0.310197\pi\)
0.561571 + 0.827428i \(0.310197\pi\)
\(992\) −3.74715e19 −1.24846
\(993\) −2.75836e19 −0.913021
\(994\) 8.77010e19 2.88399
\(995\) −6.02981e19 −1.96994
\(996\) 5.20145e19 1.68826
\(997\) 3.31750e17 0.0106977 0.00534887 0.999986i \(-0.498297\pi\)
0.00534887 + 0.999986i \(0.498297\pi\)
\(998\) −6.87167e19 −2.20148
\(999\) 1.04098e19 0.331334
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 177.14.a.c.1.2 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.2 31 1.1 even 1 trivial