Properties

Label 177.10.a.b.1.16
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +33357.2 q^{10} +17390.2 q^{11} -7851.63 q^{12} +156345. q^{13} -119224. q^{14} -109494. q^{15} -302378. q^{16} -358347. q^{17} +161903. q^{18} +77701.9 q^{19} +131033. q^{20} +391349. q^{21} +429131. q^{22} +1.04074e6 q^{23} +829636. q^{24} -125828. q^{25} +3.85805e6 q^{26} -531441. q^{27} -468332. q^{28} +4.51161e6 q^{29} -2.70193e6 q^{30} -9.81810e6 q^{31} -2.21753e6 q^{32} -1.40861e6 q^{33} -8.84278e6 q^{34} -6.53106e6 q^{35} +635982. q^{36} +5.36151e6 q^{37} +1.91742e6 q^{38} -1.26639e7 q^{39} -1.38455e7 q^{40} -1.59041e7 q^{41} +9.65715e6 q^{42} -1.04717e7 q^{43} +1.68570e6 q^{44} +8.86900e6 q^{45} +2.56819e7 q^{46} -2.40460e7 q^{47} +2.44926e7 q^{48} -1.70106e7 q^{49} -3.10500e6 q^{50} +2.90261e7 q^{51} +1.51551e7 q^{52} +2.96704e7 q^{53} -1.31141e7 q^{54} +2.35077e7 q^{55} +4.94859e7 q^{56} -6.29385e6 q^{57} +1.11331e8 q^{58} -1.21174e7 q^{59} -1.06136e7 q^{60} -1.50242e8 q^{61} -2.42277e8 q^{62} -3.16992e7 q^{63} +1.00096e8 q^{64} +2.11343e8 q^{65} -3.47596e7 q^{66} -1.05311e8 q^{67} -3.47359e7 q^{68} -8.43000e7 q^{69} -1.61164e8 q^{70} -4.08704e8 q^{71} -6.72005e7 q^{72} +3.83910e8 q^{73} +1.32304e8 q^{74} +1.01921e7 q^{75} +7.53193e6 q^{76} -8.40202e7 q^{77} -3.12502e8 q^{78} +2.66685e8 q^{79} -4.08747e8 q^{80} +4.30467e7 q^{81} -3.92459e8 q^{82} -7.10929e8 q^{83} +3.79349e7 q^{84} -4.84405e8 q^{85} -2.58406e8 q^{86} -3.65441e8 q^{87} -1.78118e8 q^{88} -9.56287e8 q^{89} +2.18857e8 q^{90} -7.55373e8 q^{91} +1.00883e8 q^{92} +7.95266e8 q^{93} -5.93373e8 q^{94} +1.05035e8 q^{95} +1.79620e8 q^{96} +8.46910e8 q^{97} -4.19762e8 q^{98} +1.14097e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.6766 1.09056 0.545281 0.838254i \(-0.316423\pi\)
0.545281 + 0.838254i \(0.316423\pi\)
\(3\) −81.0000 −0.577350
\(4\) 96.9337 0.189324
\(5\) 1351.78 0.967252 0.483626 0.875275i \(-0.339320\pi\)
0.483626 + 0.875275i \(0.339320\pi\)
\(6\) −1998.80 −0.629636
\(7\) −4831.46 −0.760567 −0.380284 0.924870i \(-0.624174\pi\)
−0.380284 + 0.924870i \(0.624174\pi\)
\(8\) −10242.4 −0.884092
\(9\) 6561.00 0.333333
\(10\) 33357.2 1.05485
\(11\) 17390.2 0.358128 0.179064 0.983837i \(-0.442693\pi\)
0.179064 + 0.983837i \(0.442693\pi\)
\(12\) −7851.63 −0.109306
\(13\) 156345. 1.51823 0.759115 0.650956i \(-0.225632\pi\)
0.759115 + 0.650956i \(0.225632\pi\)
\(14\) −119224. −0.829445
\(15\) −109494. −0.558443
\(16\) −302378. −1.15348
\(17\) −358347. −1.04060 −0.520300 0.853984i \(-0.674180\pi\)
−0.520300 + 0.853984i \(0.674180\pi\)
\(18\) 161903. 0.363520
\(19\) 77701.9 0.136786 0.0683928 0.997658i \(-0.478213\pi\)
0.0683928 + 0.997658i \(0.478213\pi\)
\(20\) 131033. 0.183124
\(21\) 391349. 0.439114
\(22\) 429131. 0.390560
\(23\) 1.04074e6 0.775474 0.387737 0.921770i \(-0.373257\pi\)
0.387737 + 0.921770i \(0.373257\pi\)
\(24\) 829636. 0.510431
\(25\) −125828. −0.0644239
\(26\) 3.85805e6 1.65572
\(27\) −531441. −0.192450
\(28\) −468332. −0.143993
\(29\) 4.51161e6 1.18452 0.592258 0.805749i \(-0.298237\pi\)
0.592258 + 0.805749i \(0.298237\pi\)
\(30\) −2.70193e6 −0.609016
\(31\) −9.81810e6 −1.90941 −0.954707 0.297549i \(-0.903831\pi\)
−0.954707 + 0.297549i \(0.903831\pi\)
\(32\) −2.21753e6 −0.373848
\(33\) −1.40861e6 −0.206765
\(34\) −8.84278e6 −1.13484
\(35\) −6.53106e6 −0.735660
\(36\) 635982. 0.0631079
\(37\) 5.36151e6 0.470305 0.235153 0.971958i \(-0.424441\pi\)
0.235153 + 0.971958i \(0.424441\pi\)
\(38\) 1.91742e6 0.149173
\(39\) −1.26639e7 −0.876551
\(40\) −1.38455e7 −0.855140
\(41\) −1.59041e7 −0.878986 −0.439493 0.898246i \(-0.644842\pi\)
−0.439493 + 0.898246i \(0.644842\pi\)
\(42\) 9.65715e6 0.478880
\(43\) −1.04717e7 −0.467099 −0.233550 0.972345i \(-0.575034\pi\)
−0.233550 + 0.972345i \(0.575034\pi\)
\(44\) 1.68570e6 0.0678020
\(45\) 8.86900e6 0.322417
\(46\) 2.56819e7 0.845702
\(47\) −2.40460e7 −0.718790 −0.359395 0.933185i \(-0.617017\pi\)
−0.359395 + 0.933185i \(0.617017\pi\)
\(48\) 2.44926e7 0.665962
\(49\) −1.70106e7 −0.421537
\(50\) −3.10500e6 −0.0702582
\(51\) 2.90261e7 0.600790
\(52\) 1.51551e7 0.287437
\(53\) 2.96704e7 0.516514 0.258257 0.966076i \(-0.416852\pi\)
0.258257 + 0.966076i \(0.416852\pi\)
\(54\) −1.31141e7 −0.209879
\(55\) 2.35077e7 0.346400
\(56\) 4.94859e7 0.672412
\(57\) −6.29385e6 −0.0789732
\(58\) 1.11331e8 1.29179
\(59\) −1.21174e7 −0.130189
\(60\) −1.06136e7 −0.105726
\(61\) −1.50242e8 −1.38934 −0.694668 0.719330i \(-0.744449\pi\)
−0.694668 + 0.719330i \(0.744449\pi\)
\(62\) −2.42277e8 −2.08233
\(63\) −3.16992e7 −0.253522
\(64\) 1.00096e8 0.745776
\(65\) 2.11343e8 1.46851
\(66\) −3.47596e7 −0.225490
\(67\) −1.05311e8 −0.638462 −0.319231 0.947677i \(-0.603425\pi\)
−0.319231 + 0.947677i \(0.603425\pi\)
\(68\) −3.47359e7 −0.197010
\(69\) −8.43000e7 −0.447720
\(70\) −1.61164e8 −0.802282
\(71\) −4.08704e8 −1.90874 −0.954370 0.298626i \(-0.903472\pi\)
−0.954370 + 0.298626i \(0.903472\pi\)
\(72\) −6.72005e7 −0.294697
\(73\) 3.83910e8 1.58225 0.791127 0.611652i \(-0.209495\pi\)
0.791127 + 0.611652i \(0.209495\pi\)
\(74\) 1.32304e8 0.512896
\(75\) 1.01921e7 0.0371951
\(76\) 7.53193e6 0.0258967
\(77\) −8.40202e7 −0.272380
\(78\) −3.12502e8 −0.955932
\(79\) 2.66685e8 0.770329 0.385164 0.922848i \(-0.374145\pi\)
0.385164 + 0.922848i \(0.374145\pi\)
\(80\) −4.08747e8 −1.11571
\(81\) 4.30467e7 0.111111
\(82\) −3.92459e8 −0.958588
\(83\) −7.10929e8 −1.64428 −0.822138 0.569288i \(-0.807219\pi\)
−0.822138 + 0.569288i \(0.807219\pi\)
\(84\) 3.79349e7 0.0831346
\(85\) −4.84405e8 −1.00652
\(86\) −2.58406e8 −0.509400
\(87\) −3.65441e8 −0.683880
\(88\) −1.78118e8 −0.316618
\(89\) −9.56287e8 −1.61560 −0.807799 0.589459i \(-0.799341\pi\)
−0.807799 + 0.589459i \(0.799341\pi\)
\(90\) 2.18857e8 0.351616
\(91\) −7.55373e8 −1.15472
\(92\) 1.00883e8 0.146816
\(93\) 7.95266e8 1.10240
\(94\) −5.93373e8 −0.783885
\(95\) 1.05035e8 0.132306
\(96\) 1.79620e8 0.215841
\(97\) 8.46910e8 0.971324 0.485662 0.874147i \(-0.338579\pi\)
0.485662 + 0.874147i \(0.338579\pi\)
\(98\) −4.19762e8 −0.459712
\(99\) 1.14097e8 0.119376
\(100\) −1.21970e7 −0.0121970
\(101\) −1.06321e9 −1.01665 −0.508327 0.861164i \(-0.669736\pi\)
−0.508327 + 0.861164i \(0.669736\pi\)
\(102\) 7.16265e8 0.655199
\(103\) −2.15338e9 −1.88518 −0.942591 0.333948i \(-0.891619\pi\)
−0.942591 + 0.333948i \(0.891619\pi\)
\(104\) −1.60135e9 −1.34226
\(105\) 5.29016e8 0.424734
\(106\) 7.32165e8 0.563290
\(107\) 2.51024e9 1.85135 0.925675 0.378319i \(-0.123498\pi\)
0.925675 + 0.378319i \(0.123498\pi\)
\(108\) −5.15145e7 −0.0364353
\(109\) −8.42739e8 −0.571839 −0.285919 0.958254i \(-0.592299\pi\)
−0.285919 + 0.958254i \(0.592299\pi\)
\(110\) 5.80089e8 0.377770
\(111\) −4.34283e8 −0.271531
\(112\) 1.46093e9 0.877299
\(113\) −9.11969e8 −0.526171 −0.263085 0.964773i \(-0.584740\pi\)
−0.263085 + 0.964773i \(0.584740\pi\)
\(114\) −1.55311e8 −0.0861251
\(115\) 1.40685e9 0.750079
\(116\) 4.37327e8 0.224257
\(117\) 1.02578e9 0.506077
\(118\) −2.99015e8 −0.141979
\(119\) 1.73134e9 0.791446
\(120\) 1.12148e9 0.493715
\(121\) −2.05553e9 −0.871745
\(122\) −3.70746e9 −1.51516
\(123\) 1.28823e9 0.507483
\(124\) −9.51705e8 −0.361497
\(125\) −2.81028e9 −1.02957
\(126\) −7.82229e8 −0.276482
\(127\) −4.28296e9 −1.46092 −0.730461 0.682954i \(-0.760695\pi\)
−0.730461 + 0.682954i \(0.760695\pi\)
\(128\) 3.60541e9 1.18716
\(129\) 8.48208e8 0.269680
\(130\) 5.21522e9 1.60150
\(131\) −3.46692e8 −0.102854 −0.0514272 0.998677i \(-0.516377\pi\)
−0.0514272 + 0.998677i \(0.516377\pi\)
\(132\) −1.36541e8 −0.0391455
\(133\) −3.75414e8 −0.104035
\(134\) −2.59870e9 −0.696282
\(135\) −7.18389e8 −0.186148
\(136\) 3.67034e9 0.919986
\(137\) −6.09826e9 −1.47898 −0.739492 0.673165i \(-0.764934\pi\)
−0.739492 + 0.673165i \(0.764934\pi\)
\(138\) −2.08024e9 −0.488266
\(139\) 1.61338e9 0.366581 0.183291 0.983059i \(-0.441325\pi\)
0.183291 + 0.983059i \(0.441325\pi\)
\(140\) −6.33079e8 −0.139278
\(141\) 1.94773e9 0.414994
\(142\) −1.00854e10 −2.08160
\(143\) 2.71887e9 0.543720
\(144\) −1.98390e9 −0.384493
\(145\) 6.09869e9 1.14572
\(146\) 9.47358e9 1.72554
\(147\) 1.37786e9 0.243375
\(148\) 5.19711e8 0.0890398
\(149\) 8.58258e9 1.42653 0.713263 0.700897i \(-0.247217\pi\)
0.713263 + 0.700897i \(0.247217\pi\)
\(150\) 2.51505e8 0.0405636
\(151\) 2.61006e9 0.408558 0.204279 0.978913i \(-0.434515\pi\)
0.204279 + 0.978913i \(0.434515\pi\)
\(152\) −7.95855e8 −0.120931
\(153\) −2.35111e9 −0.346866
\(154\) −2.07333e9 −0.297047
\(155\) −1.32719e10 −1.84688
\(156\) −1.22756e9 −0.165952
\(157\) −7.15014e9 −0.939218 −0.469609 0.882875i \(-0.655605\pi\)
−0.469609 + 0.882875i \(0.655605\pi\)
\(158\) 6.58086e9 0.840090
\(159\) −2.40330e9 −0.298210
\(160\) −2.99761e9 −0.361606
\(161\) −5.02830e9 −0.589800
\(162\) 1.06225e9 0.121173
\(163\) 1.40975e10 1.56422 0.782112 0.623138i \(-0.214142\pi\)
0.782112 + 0.623138i \(0.214142\pi\)
\(164\) −1.54164e9 −0.166413
\(165\) −1.90412e9 −0.199994
\(166\) −1.75433e10 −1.79318
\(167\) 3.55226e9 0.353412 0.176706 0.984264i \(-0.443456\pi\)
0.176706 + 0.984264i \(0.443456\pi\)
\(168\) −4.00836e9 −0.388217
\(169\) 1.38391e10 1.30502
\(170\) −1.19534e10 −1.09767
\(171\) 5.09802e8 0.0455952
\(172\) −1.01506e9 −0.0884329
\(173\) 1.07116e10 0.909177 0.454589 0.890702i \(-0.349786\pi\)
0.454589 + 0.890702i \(0.349786\pi\)
\(174\) −9.01782e9 −0.745813
\(175\) 6.07933e8 0.0489987
\(176\) −5.25842e9 −0.413093
\(177\) 9.81506e8 0.0751646
\(178\) −2.35979e10 −1.76191
\(179\) −2.47669e10 −1.80315 −0.901576 0.432621i \(-0.857589\pi\)
−0.901576 + 0.432621i \(0.857589\pi\)
\(180\) 8.59705e8 0.0610412
\(181\) −4.03191e9 −0.279227 −0.139613 0.990206i \(-0.544586\pi\)
−0.139613 + 0.990206i \(0.544586\pi\)
\(182\) −1.86400e10 −1.25929
\(183\) 1.21696e10 0.802134
\(184\) −1.06597e10 −0.685591
\(185\) 7.24756e9 0.454903
\(186\) 1.96245e10 1.20223
\(187\) −6.23173e9 −0.372667
\(188\) −2.33087e9 −0.136084
\(189\) 2.56764e9 0.146371
\(190\) 2.59192e9 0.144288
\(191\) −3.18277e10 −1.73043 −0.865216 0.501399i \(-0.832819\pi\)
−0.865216 + 0.501399i \(0.832819\pi\)
\(192\) −8.10780e9 −0.430574
\(193\) 2.72496e10 1.41368 0.706842 0.707371i \(-0.250119\pi\)
0.706842 + 0.707371i \(0.250119\pi\)
\(194\) 2.08988e10 1.05929
\(195\) −1.71188e10 −0.847846
\(196\) −1.64890e9 −0.0798070
\(197\) 3.38740e10 1.60239 0.801196 0.598402i \(-0.204198\pi\)
0.801196 + 0.598402i \(0.204198\pi\)
\(198\) 2.81553e9 0.130187
\(199\) 1.53426e10 0.693520 0.346760 0.937954i \(-0.387282\pi\)
0.346760 + 0.937954i \(0.387282\pi\)
\(200\) 1.28878e9 0.0569566
\(201\) 8.53015e9 0.368616
\(202\) −2.62364e10 −1.10872
\(203\) −2.17977e10 −0.900904
\(204\) 2.81361e9 0.113744
\(205\) −2.14988e10 −0.850201
\(206\) −5.31381e10 −2.05591
\(207\) 6.82830e9 0.258491
\(208\) −4.72752e10 −1.75125
\(209\) 1.35125e9 0.0489867
\(210\) 1.30543e10 0.463198
\(211\) 3.28168e10 1.13979 0.569895 0.821717i \(-0.306984\pi\)
0.569895 + 0.821717i \(0.306984\pi\)
\(212\) 2.87606e9 0.0977883
\(213\) 3.31051e10 1.10201
\(214\) 6.19442e10 2.01901
\(215\) −1.41554e10 −0.451803
\(216\) 5.44324e9 0.170144
\(217\) 4.74358e10 1.45224
\(218\) −2.07959e10 −0.623625
\(219\) −3.10967e10 −0.913514
\(220\) 2.27868e9 0.0655816
\(221\) −5.60256e10 −1.57987
\(222\) −1.07166e10 −0.296121
\(223\) 4.00825e10 1.08538 0.542692 0.839932i \(-0.317405\pi\)
0.542692 + 0.839932i \(0.317405\pi\)
\(224\) 1.07139e10 0.284337
\(225\) −8.25557e8 −0.0214746
\(226\) −2.25043e10 −0.573822
\(227\) −4.05197e10 −1.01286 −0.506430 0.862281i \(-0.669035\pi\)
−0.506430 + 0.862281i \(0.669035\pi\)
\(228\) −6.10086e8 −0.0149515
\(229\) −7.76259e9 −0.186529 −0.0932646 0.995641i \(-0.529730\pi\)
−0.0932646 + 0.995641i \(0.529730\pi\)
\(230\) 3.47162e10 0.818007
\(231\) 6.80564e9 0.157259
\(232\) −4.62098e10 −1.04722
\(233\) −1.73507e10 −0.385670 −0.192835 0.981231i \(-0.561768\pi\)
−0.192835 + 0.981231i \(0.561768\pi\)
\(234\) 2.53127e10 0.551908
\(235\) −3.25048e10 −0.695251
\(236\) −1.17458e9 −0.0246478
\(237\) −2.16015e10 −0.444749
\(238\) 4.27236e10 0.863120
\(239\) 3.29921e10 0.654063 0.327032 0.945013i \(-0.393952\pi\)
0.327032 + 0.945013i \(0.393952\pi\)
\(240\) 3.31085e10 0.644153
\(241\) 8.91189e8 0.0170174 0.00850870 0.999964i \(-0.497292\pi\)
0.00850870 + 0.999964i \(0.497292\pi\)
\(242\) −5.07234e10 −0.950691
\(243\) −3.48678e9 −0.0641500
\(244\) −1.45635e10 −0.263034
\(245\) −2.29945e10 −0.407733
\(246\) 3.17892e10 0.553441
\(247\) 1.21483e10 0.207672
\(248\) 1.00561e11 1.68810
\(249\) 5.75853e10 0.949323
\(250\) −6.93480e10 −1.12280
\(251\) −9.43867e10 −1.50099 −0.750497 0.660874i \(-0.770186\pi\)
−0.750497 + 0.660874i \(0.770186\pi\)
\(252\) −3.07272e9 −0.0479978
\(253\) 1.80987e10 0.277719
\(254\) −1.05689e11 −1.59323
\(255\) 3.92368e10 0.581116
\(256\) 3.77199e10 0.548897
\(257\) 1.22809e11 1.75603 0.878014 0.478635i \(-0.158868\pi\)
0.878014 + 0.478635i \(0.158868\pi\)
\(258\) 2.09309e10 0.294102
\(259\) −2.59040e10 −0.357699
\(260\) 2.04862e10 0.278024
\(261\) 2.96007e10 0.394838
\(262\) −8.55517e9 −0.112169
\(263\) 5.70567e10 0.735369 0.367685 0.929951i \(-0.380151\pi\)
0.367685 + 0.929951i \(0.380151\pi\)
\(264\) 1.44275e10 0.182799
\(265\) 4.01077e10 0.499599
\(266\) −9.26393e9 −0.113456
\(267\) 7.74592e10 0.932766
\(268\) −1.02081e10 −0.120876
\(269\) 9.42735e10 1.09775 0.548876 0.835904i \(-0.315056\pi\)
0.548876 + 0.835904i \(0.315056\pi\)
\(270\) −1.77274e10 −0.203005
\(271\) 1.72655e11 1.94454 0.972272 0.233855i \(-0.0751340\pi\)
0.972272 + 0.233855i \(0.0751340\pi\)
\(272\) 1.08356e11 1.20031
\(273\) 6.11852e10 0.666676
\(274\) −1.50484e11 −1.61292
\(275\) −2.18817e9 −0.0230720
\(276\) −8.17151e9 −0.0847640
\(277\) 3.21674e10 0.328289 0.164145 0.986436i \(-0.447514\pi\)
0.164145 + 0.986436i \(0.447514\pi\)
\(278\) 3.98127e10 0.399779
\(279\) −6.44166e10 −0.636471
\(280\) 6.68938e10 0.650391
\(281\) 8.73319e10 0.835593 0.417796 0.908541i \(-0.362803\pi\)
0.417796 + 0.908541i \(0.362803\pi\)
\(282\) 4.80632e10 0.452576
\(283\) −4.86603e10 −0.450958 −0.225479 0.974248i \(-0.572395\pi\)
−0.225479 + 0.974248i \(0.572395\pi\)
\(284\) −3.96172e10 −0.361370
\(285\) −8.50787e9 −0.0763869
\(286\) 6.70923e10 0.592960
\(287\) 7.68401e10 0.668528
\(288\) −1.45492e10 −0.124616
\(289\) 9.82464e9 0.0828469
\(290\) 1.50495e11 1.24948
\(291\) −6.85997e10 −0.560794
\(292\) 3.72138e10 0.299558
\(293\) 8.55239e10 0.677927 0.338964 0.940800i \(-0.389924\pi\)
0.338964 + 0.940800i \(0.389924\pi\)
\(294\) 3.40008e10 0.265415
\(295\) −1.63800e10 −0.125925
\(296\) −5.49149e10 −0.415793
\(297\) −9.24187e9 −0.0689217
\(298\) 2.11789e11 1.55571
\(299\) 1.62714e11 1.17735
\(300\) 9.87953e8 0.00704192
\(301\) 5.05937e10 0.355260
\(302\) 6.44073e10 0.445557
\(303\) 8.61202e10 0.586966
\(304\) −2.34953e10 −0.157779
\(305\) −2.03094e11 −1.34384
\(306\) −5.80175e10 −0.378279
\(307\) −6.14259e10 −0.394665 −0.197333 0.980337i \(-0.563228\pi\)
−0.197333 + 0.980337i \(0.563228\pi\)
\(308\) −8.14439e9 −0.0515680
\(309\) 1.74424e11 1.08841
\(310\) −3.27504e11 −2.01414
\(311\) 4.98435e10 0.302125 0.151062 0.988524i \(-0.451731\pi\)
0.151062 + 0.988524i \(0.451731\pi\)
\(312\) 1.29709e11 0.774952
\(313\) 7.67771e9 0.0452150 0.0226075 0.999744i \(-0.492803\pi\)
0.0226075 + 0.999744i \(0.492803\pi\)
\(314\) −1.76441e11 −1.02427
\(315\) −4.28503e10 −0.245220
\(316\) 2.58507e10 0.145841
\(317\) −8.79590e10 −0.489230 −0.244615 0.969620i \(-0.578662\pi\)
−0.244615 + 0.969620i \(0.578662\pi\)
\(318\) −5.93053e10 −0.325216
\(319\) 7.84579e10 0.424208
\(320\) 1.35308e11 0.721353
\(321\) −2.03330e11 −1.06888
\(322\) −1.24081e11 −0.643213
\(323\) −2.78442e10 −0.142339
\(324\) 4.17268e9 0.0210360
\(325\) −1.96725e10 −0.0978103
\(326\) 3.47879e11 1.70588
\(327\) 6.82618e10 0.330151
\(328\) 1.62896e11 0.777104
\(329\) 1.16177e11 0.546689
\(330\) −4.69872e10 −0.218106
\(331\) −7.39306e10 −0.338531 −0.169265 0.985571i \(-0.554139\pi\)
−0.169265 + 0.985571i \(0.554139\pi\)
\(332\) −6.89130e10 −0.311300
\(333\) 3.51769e10 0.156768
\(334\) 8.76577e10 0.385417
\(335\) −1.42356e11 −0.617554
\(336\) −1.18335e11 −0.506509
\(337\) −1.54529e11 −0.652642 −0.326321 0.945259i \(-0.605809\pi\)
−0.326321 + 0.945259i \(0.605809\pi\)
\(338\) 3.41503e11 1.42321
\(339\) 7.38695e10 0.303785
\(340\) −4.69551e10 −0.190558
\(341\) −1.70739e11 −0.683814
\(342\) 1.25802e10 0.0497243
\(343\) 2.77153e11 1.08117
\(344\) 1.07256e11 0.412959
\(345\) −1.13955e11 −0.433058
\(346\) 2.64327e11 0.991513
\(347\) −1.37596e11 −0.509476 −0.254738 0.967010i \(-0.581989\pi\)
−0.254738 + 0.967010i \(0.581989\pi\)
\(348\) −3.54235e10 −0.129475
\(349\) −2.44352e11 −0.881660 −0.440830 0.897591i \(-0.645316\pi\)
−0.440830 + 0.897591i \(0.645316\pi\)
\(350\) 1.50017e10 0.0534361
\(351\) −8.30879e10 −0.292184
\(352\) −3.85634e10 −0.133885
\(353\) −2.00711e11 −0.687996 −0.343998 0.938970i \(-0.611781\pi\)
−0.343998 + 0.938970i \(0.611781\pi\)
\(354\) 2.42202e10 0.0819716
\(355\) −5.52477e11 −1.84623
\(356\) −9.26964e10 −0.305871
\(357\) −1.40239e11 −0.456941
\(358\) −6.11161e11 −1.96645
\(359\) −2.19071e11 −0.696082 −0.348041 0.937479i \(-0.613153\pi\)
−0.348041 + 0.937479i \(0.613153\pi\)
\(360\) −9.08400e10 −0.285047
\(361\) −3.16650e11 −0.981290
\(362\) −9.94937e10 −0.304514
\(363\) 1.66498e11 0.503302
\(364\) −7.32211e10 −0.218615
\(365\) 5.18960e11 1.53044
\(366\) 3.00304e11 0.874776
\(367\) −3.57591e11 −1.02894 −0.514470 0.857509i \(-0.672011\pi\)
−0.514470 + 0.857509i \(0.672011\pi\)
\(368\) −3.14697e11 −0.894494
\(369\) −1.04347e11 −0.292995
\(370\) 1.78845e11 0.496100
\(371\) −1.43352e11 −0.392844
\(372\) 7.70881e10 0.208710
\(373\) −5.54118e11 −1.48222 −0.741109 0.671384i \(-0.765700\pi\)
−0.741109 + 0.671384i \(0.765700\pi\)
\(374\) −1.53778e11 −0.406417
\(375\) 2.27632e11 0.594420
\(376\) 2.46289e11 0.635477
\(377\) 7.05366e11 1.79837
\(378\) 6.33605e10 0.159627
\(379\) −1.51950e11 −0.378290 −0.189145 0.981949i \(-0.560572\pi\)
−0.189145 + 0.981949i \(0.560572\pi\)
\(380\) 1.01815e10 0.0250487
\(381\) 3.46920e11 0.843464
\(382\) −7.85398e11 −1.88714
\(383\) −4.27773e11 −1.01582 −0.507912 0.861409i \(-0.669583\pi\)
−0.507912 + 0.861409i \(0.669583\pi\)
\(384\) −2.92038e11 −0.685408
\(385\) −1.13576e11 −0.263460
\(386\) 6.72427e11 1.54171
\(387\) −6.87048e10 −0.155700
\(388\) 8.20940e10 0.183895
\(389\) 4.50463e11 0.997438 0.498719 0.866764i \(-0.333804\pi\)
0.498719 + 0.866764i \(0.333804\pi\)
\(390\) −4.22433e11 −0.924627
\(391\) −3.72946e11 −0.806958
\(392\) 1.74229e11 0.372678
\(393\) 2.80820e10 0.0593830
\(394\) 8.35895e11 1.74751
\(395\) 3.60498e11 0.745102
\(396\) 1.10599e10 0.0226007
\(397\) −7.26579e11 −1.46800 −0.734000 0.679150i \(-0.762349\pi\)
−0.734000 + 0.679150i \(0.762349\pi\)
\(398\) 3.78602e11 0.756326
\(399\) 3.04085e10 0.0600644
\(400\) 3.80476e10 0.0743116
\(401\) 5.60206e11 1.08193 0.540964 0.841046i \(-0.318060\pi\)
0.540964 + 0.841046i \(0.318060\pi\)
\(402\) 2.10495e11 0.401999
\(403\) −1.53501e12 −2.89893
\(404\) −1.03061e11 −0.192477
\(405\) 5.81895e10 0.107472
\(406\) −5.37893e11 −0.982490
\(407\) 9.32379e10 0.168429
\(408\) −2.97297e11 −0.531154
\(409\) 6.91262e11 1.22148 0.610742 0.791829i \(-0.290871\pi\)
0.610742 + 0.791829i \(0.290871\pi\)
\(410\) −5.30516e11 −0.927196
\(411\) 4.93959e11 0.853892
\(412\) −2.08735e11 −0.356910
\(413\) 5.85446e10 0.0990174
\(414\) 1.68499e11 0.281901
\(415\) −9.61017e11 −1.59043
\(416\) −3.46700e11 −0.567588
\(417\) −1.30684e11 −0.211646
\(418\) 3.33443e10 0.0534230
\(419\) −2.75312e11 −0.436377 −0.218188 0.975907i \(-0.570015\pi\)
−0.218188 + 0.975907i \(0.570015\pi\)
\(420\) 5.12794e10 0.0804121
\(421\) 4.44239e11 0.689203 0.344602 0.938749i \(-0.388014\pi\)
0.344602 + 0.938749i \(0.388014\pi\)
\(422\) 8.09806e11 1.24301
\(423\) −1.57766e11 −0.239597
\(424\) −3.03897e11 −0.456646
\(425\) 4.50900e10 0.0670394
\(426\) 8.16920e11 1.20181
\(427\) 7.25889e11 1.05668
\(428\) 2.43327e11 0.350504
\(429\) −2.20228e11 −0.313917
\(430\) −3.49307e11 −0.492718
\(431\) −1.10048e12 −1.53616 −0.768079 0.640355i \(-0.778787\pi\)
−0.768079 + 0.640355i \(0.778787\pi\)
\(432\) 1.60696e11 0.221987
\(433\) −2.93842e11 −0.401715 −0.200857 0.979620i \(-0.564373\pi\)
−0.200857 + 0.979620i \(0.564373\pi\)
\(434\) 1.17055e12 1.58375
\(435\) −4.93994e11 −0.661484
\(436\) −8.16897e10 −0.108263
\(437\) 8.08675e10 0.106074
\(438\) −7.67360e11 −0.996243
\(439\) 9.85425e11 1.26629 0.633145 0.774033i \(-0.281764\pi\)
0.633145 + 0.774033i \(0.281764\pi\)
\(440\) −2.40775e11 −0.306249
\(441\) −1.11606e11 −0.140512
\(442\) −1.38252e12 −1.72294
\(443\) −4.56768e11 −0.563480 −0.281740 0.959491i \(-0.590912\pi\)
−0.281740 + 0.959491i \(0.590912\pi\)
\(444\) −4.20966e10 −0.0514072
\(445\) −1.29269e12 −1.56269
\(446\) 9.89100e11 1.18368
\(447\) −6.95189e11 −0.823605
\(448\) −4.83612e11 −0.567212
\(449\) −1.09455e12 −1.27095 −0.635475 0.772121i \(-0.719196\pi\)
−0.635475 + 0.772121i \(0.719196\pi\)
\(450\) −2.03719e10 −0.0234194
\(451\) −2.76576e11 −0.314789
\(452\) −8.84005e10 −0.0996166
\(453\) −2.11415e11 −0.235881
\(454\) −9.99887e11 −1.10459
\(455\) −1.02110e12 −1.11690
\(456\) 6.44642e10 0.0698196
\(457\) 8.18364e11 0.877654 0.438827 0.898571i \(-0.355394\pi\)
0.438827 + 0.898571i \(0.355394\pi\)
\(458\) −1.91554e11 −0.203421
\(459\) 1.90440e11 0.200263
\(460\) 1.36371e11 0.142008
\(461\) 5.03039e11 0.518738 0.259369 0.965778i \(-0.416485\pi\)
0.259369 + 0.965778i \(0.416485\pi\)
\(462\) 1.67940e11 0.171500
\(463\) 1.69189e12 1.71103 0.855515 0.517779i \(-0.173241\pi\)
0.855515 + 0.517779i \(0.173241\pi\)
\(464\) −1.36421e12 −1.36631
\(465\) 1.07502e12 1.06630
\(466\) −4.28156e11 −0.420597
\(467\) 7.40656e9 0.00720594 0.00360297 0.999994i \(-0.498853\pi\)
0.00360297 + 0.999994i \(0.498853\pi\)
\(468\) 9.94323e10 0.0958123
\(469\) 5.08804e11 0.485593
\(470\) −8.02107e11 −0.758214
\(471\) 5.79162e11 0.542258
\(472\) 1.24111e11 0.115099
\(473\) −1.82105e11 −0.167281
\(474\) −5.33050e11 −0.485026
\(475\) −9.77706e9 −0.00881225
\(476\) 1.67825e11 0.149839
\(477\) 1.94668e11 0.172171
\(478\) 8.14133e11 0.713296
\(479\) 8.74214e11 0.758766 0.379383 0.925240i \(-0.376136\pi\)
0.379383 + 0.925240i \(0.376136\pi\)
\(480\) 2.42806e11 0.208773
\(481\) 8.38244e11 0.714032
\(482\) 2.19915e10 0.0185585
\(483\) 4.07293e11 0.340521
\(484\) −1.99250e11 −0.165042
\(485\) 1.14483e12 0.939515
\(486\) −8.60419e10 −0.0699595
\(487\) −1.11634e12 −0.899325 −0.449663 0.893198i \(-0.648456\pi\)
−0.449663 + 0.893198i \(0.648456\pi\)
\(488\) 1.53884e12 1.22830
\(489\) −1.14190e12 −0.903105
\(490\) −5.67425e11 −0.444658
\(491\) −1.09081e11 −0.0846998 −0.0423499 0.999103i \(-0.513484\pi\)
−0.0423499 + 0.999103i \(0.513484\pi\)
\(492\) 1.24873e11 0.0960784
\(493\) −1.61672e12 −1.23261
\(494\) 2.99778e11 0.226479
\(495\) 1.54234e11 0.115467
\(496\) 2.96878e12 2.20247
\(497\) 1.97464e12 1.45173
\(498\) 1.42101e12 1.03530
\(499\) 3.25184e11 0.234788 0.117394 0.993085i \(-0.462546\pi\)
0.117394 + 0.993085i \(0.462546\pi\)
\(500\) −2.72411e11 −0.194921
\(501\) −2.87733e11 −0.204042
\(502\) −2.32914e12 −1.63693
\(503\) −3.82998e11 −0.266772 −0.133386 0.991064i \(-0.542585\pi\)
−0.133386 + 0.991064i \(0.542585\pi\)
\(504\) 3.24677e11 0.224137
\(505\) −1.43722e12 −0.983361
\(506\) 4.46614e11 0.302869
\(507\) −1.12097e12 −0.753457
\(508\) −4.15163e11 −0.276587
\(509\) 2.38906e12 1.57760 0.788800 0.614650i \(-0.210703\pi\)
0.788800 + 0.614650i \(0.210703\pi\)
\(510\) 9.68229e11 0.633742
\(511\) −1.85485e12 −1.20341
\(512\) −9.15172e11 −0.588556
\(513\) −4.12939e10 −0.0263244
\(514\) 3.03051e12 1.91506
\(515\) −2.91089e12 −1.82345
\(516\) 8.22199e10 0.0510568
\(517\) −4.18165e11 −0.257419
\(518\) −6.39221e11 −0.390092
\(519\) −8.67643e11 −0.524914
\(520\) −2.16466e12 −1.29830
\(521\) 5.93917e11 0.353147 0.176574 0.984287i \(-0.443499\pi\)
0.176574 + 0.984287i \(0.443499\pi\)
\(522\) 7.30444e11 0.430595
\(523\) −2.71554e12 −1.58708 −0.793539 0.608519i \(-0.791764\pi\)
−0.793539 + 0.608519i \(0.791764\pi\)
\(524\) −3.36061e10 −0.0194727
\(525\) −4.92426e10 −0.0282894
\(526\) 1.40796e12 0.801965
\(527\) 3.51829e12 1.98693
\(528\) 4.25932e11 0.238499
\(529\) −7.18011e11 −0.398639
\(530\) 9.89722e11 0.544844
\(531\) −7.95020e10 −0.0433963
\(532\) −3.63902e10 −0.0196962
\(533\) −2.48652e12 −1.33450
\(534\) 1.91143e12 1.01724
\(535\) 3.39328e12 1.79072
\(536\) 1.07863e12 0.564459
\(537\) 2.00612e12 1.04105
\(538\) 2.32635e12 1.19717
\(539\) −2.95817e11 −0.150964
\(540\) −6.96361e10 −0.0352421
\(541\) 1.08823e12 0.546177 0.273089 0.961989i \(-0.411955\pi\)
0.273089 + 0.961989i \(0.411955\pi\)
\(542\) 4.26054e12 2.12064
\(543\) 3.26584e11 0.161212
\(544\) 7.94647e11 0.389026
\(545\) −1.13919e12 −0.553112
\(546\) 1.50984e12 0.727051
\(547\) −1.59236e12 −0.760496 −0.380248 0.924885i \(-0.624161\pi\)
−0.380248 + 0.924885i \(0.624161\pi\)
\(548\) −5.91127e11 −0.280007
\(549\) −9.85738e11 −0.463112
\(550\) −5.39966e10 −0.0251614
\(551\) 3.50561e11 0.162025
\(552\) 8.63436e11 0.395826
\(553\) −1.28848e12 −0.585887
\(554\) 7.93781e11 0.358020
\(555\) −5.87053e11 −0.262639
\(556\) 1.56391e11 0.0694025
\(557\) 2.18678e12 0.962623 0.481312 0.876550i \(-0.340161\pi\)
0.481312 + 0.876550i \(0.340161\pi\)
\(558\) −1.58958e12 −0.694111
\(559\) −1.63719e12 −0.709164
\(560\) 1.97485e12 0.848569
\(561\) 5.04770e11 0.215160
\(562\) 2.15505e12 0.911265
\(563\) −1.61621e12 −0.677971 −0.338985 0.940792i \(-0.610084\pi\)
−0.338985 + 0.940792i \(0.610084\pi\)
\(564\) 1.88800e11 0.0785681
\(565\) −1.23278e12 −0.508940
\(566\) −1.20077e12 −0.491797
\(567\) −2.07979e11 −0.0845075
\(568\) 4.18612e12 1.68750
\(569\) −1.93492e12 −0.773851 −0.386926 0.922111i \(-0.626463\pi\)
−0.386926 + 0.922111i \(0.626463\pi\)
\(570\) −2.09945e11 −0.0833046
\(571\) −6.69506e11 −0.263567 −0.131784 0.991278i \(-0.542070\pi\)
−0.131784 + 0.991278i \(0.542070\pi\)
\(572\) 2.63550e11 0.102939
\(573\) 2.57804e12 0.999066
\(574\) 1.89615e12 0.729070
\(575\) −1.30954e11 −0.0499591
\(576\) 6.56732e11 0.248592
\(577\) −4.52091e12 −1.69799 −0.848995 0.528402i \(-0.822792\pi\)
−0.848995 + 0.528402i \(0.822792\pi\)
\(578\) 2.42438e11 0.0903496
\(579\) −2.20722e12 −0.816191
\(580\) 5.91168e11 0.216913
\(581\) 3.43483e12 1.25058
\(582\) −1.69281e12 −0.611580
\(583\) 5.15975e11 0.184978
\(584\) −3.93216e12 −1.39886
\(585\) 1.38662e12 0.489504
\(586\) 2.11044e12 0.739321
\(587\) −2.49172e12 −0.866219 −0.433109 0.901341i \(-0.642584\pi\)
−0.433109 + 0.901341i \(0.642584\pi\)
\(588\) 1.33561e11 0.0460766
\(589\) −7.62885e11 −0.261180
\(590\) −4.04201e11 −0.137329
\(591\) −2.74380e12 −0.925141
\(592\) −1.62120e12 −0.542488
\(593\) 6.67397e11 0.221635 0.110817 0.993841i \(-0.464653\pi\)
0.110817 + 0.993841i \(0.464653\pi\)
\(594\) −2.28058e11 −0.0751633
\(595\) 2.34038e12 0.765527
\(596\) 8.31941e11 0.270075
\(597\) −1.24275e12 −0.400404
\(598\) 4.01523e12 1.28397
\(599\) −1.52637e12 −0.484440 −0.242220 0.970221i \(-0.577876\pi\)
−0.242220 + 0.970221i \(0.577876\pi\)
\(600\) −1.04391e11 −0.0328839
\(601\) 1.37907e11 0.0431174 0.0215587 0.999768i \(-0.493137\pi\)
0.0215587 + 0.999768i \(0.493137\pi\)
\(602\) 1.24848e12 0.387433
\(603\) −6.90942e11 −0.212821
\(604\) 2.53002e11 0.0773496
\(605\) −2.77861e12 −0.843197
\(606\) 2.12515e12 0.640122
\(607\) 4.01371e12 1.20004 0.600021 0.799984i \(-0.295159\pi\)
0.600021 + 0.799984i \(0.295159\pi\)
\(608\) −1.72307e11 −0.0511371
\(609\) 1.76561e12 0.520137
\(610\) −5.01166e12 −1.46554
\(611\) −3.75946e12 −1.09129
\(612\) −2.27902e11 −0.0656700
\(613\) −4.46430e11 −0.127697 −0.0638486 0.997960i \(-0.520337\pi\)
−0.0638486 + 0.997960i \(0.520337\pi\)
\(614\) −1.51578e12 −0.430407
\(615\) 1.74140e12 0.490864
\(616\) 8.60570e11 0.240809
\(617\) −1.66078e12 −0.461349 −0.230674 0.973031i \(-0.574093\pi\)
−0.230674 + 0.973031i \(0.574093\pi\)
\(618\) 4.30419e12 1.18698
\(619\) −2.53835e12 −0.694933 −0.347467 0.937692i \(-0.612958\pi\)
−0.347467 + 0.937692i \(0.612958\pi\)
\(620\) −1.28649e12 −0.349659
\(621\) −5.53093e11 −0.149240
\(622\) 1.22997e12 0.329486
\(623\) 4.62027e12 1.22877
\(624\) 3.82929e12 1.01108
\(625\) −3.55311e12 −0.931426
\(626\) 1.89460e11 0.0493097
\(627\) −1.09451e11 −0.0282825
\(628\) −6.93090e11 −0.177816
\(629\) −1.92128e12 −0.489399
\(630\) −1.05740e12 −0.267427
\(631\) −3.44715e12 −0.865621 −0.432811 0.901485i \(-0.642478\pi\)
−0.432811 + 0.901485i \(0.642478\pi\)
\(632\) −2.73150e12 −0.681041
\(633\) −2.65816e12 −0.658058
\(634\) −2.17053e12 −0.533536
\(635\) −5.78960e12 −1.41308
\(636\) −2.32961e11 −0.0564581
\(637\) −2.65951e12 −0.639991
\(638\) 1.93607e12 0.462624
\(639\) −2.68151e12 −0.636247
\(640\) 4.87371e12 1.14828
\(641\) 6.73195e12 1.57500 0.787498 0.616317i \(-0.211376\pi\)
0.787498 + 0.616317i \(0.211376\pi\)
\(642\) −5.01748e12 −1.16568
\(643\) 2.98977e12 0.689745 0.344873 0.938649i \(-0.387922\pi\)
0.344873 + 0.938649i \(0.387922\pi\)
\(644\) −4.87412e11 −0.111663
\(645\) 1.14659e12 0.260848
\(646\) −6.87100e11 −0.155229
\(647\) 2.00400e12 0.449601 0.224801 0.974405i \(-0.427827\pi\)
0.224801 + 0.974405i \(0.427827\pi\)
\(648\) −4.40903e11 −0.0982325
\(649\) −2.10724e11 −0.0466243
\(650\) −4.85450e11 −0.106668
\(651\) −3.84230e12 −0.838449
\(652\) 1.36653e12 0.296144
\(653\) −8.37262e11 −0.180199 −0.0900994 0.995933i \(-0.528718\pi\)
−0.0900994 + 0.995933i \(0.528718\pi\)
\(654\) 1.68447e12 0.360050
\(655\) −4.68649e11 −0.0994860
\(656\) 4.80905e12 1.01389
\(657\) 2.51883e12 0.527418
\(658\) 2.86686e12 0.596197
\(659\) 5.14455e12 1.06258 0.531291 0.847189i \(-0.321707\pi\)
0.531291 + 0.847189i \(0.321707\pi\)
\(660\) −1.84573e11 −0.0378636
\(661\) 7.96290e12 1.62243 0.811213 0.584751i \(-0.198808\pi\)
0.811213 + 0.584751i \(0.198808\pi\)
\(662\) −1.82435e12 −0.369188
\(663\) 4.53807e12 0.912138
\(664\) 7.28163e12 1.45369
\(665\) −5.07475e11 −0.100628
\(666\) 8.68045e11 0.170965
\(667\) 4.69542e12 0.918561
\(668\) 3.44334e11 0.0669091
\(669\) −3.24668e12 −0.626646
\(670\) −3.51286e12 −0.673480
\(671\) −2.61274e12 −0.497560
\(672\) −8.67829e11 −0.164162
\(673\) −3.95241e12 −0.742667 −0.371334 0.928499i \(-0.621099\pi\)
−0.371334 + 0.928499i \(0.621099\pi\)
\(674\) −3.81324e12 −0.711746
\(675\) 6.68701e10 0.0123984
\(676\) 1.34148e12 0.247072
\(677\) −8.30975e12 −1.52033 −0.760166 0.649728i \(-0.774883\pi\)
−0.760166 + 0.649728i \(0.774883\pi\)
\(678\) 1.82285e12 0.331296
\(679\) −4.09181e12 −0.738757
\(680\) 4.96147e12 0.889858
\(681\) 3.28209e12 0.584775
\(682\) −4.21325e12 −0.745741
\(683\) −2.21459e12 −0.389403 −0.194701 0.980863i \(-0.562374\pi\)
−0.194701 + 0.980863i \(0.562374\pi\)
\(684\) 4.94170e10 0.00863224
\(685\) −8.24348e12 −1.43055
\(686\) 6.83919e12 1.17909
\(687\) 6.28770e11 0.107693
\(688\) 3.16641e12 0.538790
\(689\) 4.63881e12 0.784188
\(690\) −2.81201e12 −0.472277
\(691\) −3.30602e12 −0.551638 −0.275819 0.961210i \(-0.588949\pi\)
−0.275819 + 0.961210i \(0.588949\pi\)
\(692\) 1.03832e12 0.172129
\(693\) −5.51257e11 −0.0907934
\(694\) −3.39540e12 −0.555615
\(695\) 2.18093e12 0.354576
\(696\) 3.74299e12 0.604613
\(697\) 5.69919e12 0.914672
\(698\) −6.02977e12 −0.961505
\(699\) 1.40541e12 0.222667
\(700\) 5.89292e10 0.00927661
\(701\) −1.50916e12 −0.236050 −0.118025 0.993011i \(-0.537656\pi\)
−0.118025 + 0.993011i \(0.537656\pi\)
\(702\) −2.05033e12 −0.318644
\(703\) 4.16600e11 0.0643309
\(704\) 1.74070e12 0.267083
\(705\) 2.63289e12 0.401404
\(706\) −4.95287e12 −0.750301
\(707\) 5.13687e12 0.773234
\(708\) 9.51410e10 0.0142304
\(709\) 4.19952e12 0.624154 0.312077 0.950057i \(-0.398975\pi\)
0.312077 + 0.950057i \(0.398975\pi\)
\(710\) −1.36332e13 −2.01343
\(711\) 1.74972e12 0.256776
\(712\) 9.79469e12 1.42834
\(713\) −1.02181e13 −1.48070
\(714\) −3.46061e12 −0.498323
\(715\) 3.67530e12 0.525915
\(716\) −2.40074e12 −0.341379
\(717\) −2.67236e12 −0.377624
\(718\) −5.40593e12 −0.759120
\(719\) 2.56575e12 0.358042 0.179021 0.983845i \(-0.442707\pi\)
0.179021 + 0.983845i \(0.442707\pi\)
\(720\) −2.68179e12 −0.371902
\(721\) 1.04040e13 1.43381
\(722\) −7.81384e12 −1.07016
\(723\) −7.21863e10 −0.00982500
\(724\) −3.90828e11 −0.0528642
\(725\) −5.67686e11 −0.0763111
\(726\) 4.10860e12 0.548882
\(727\) −3.93388e12 −0.522296 −0.261148 0.965299i \(-0.584101\pi\)
−0.261148 + 0.965299i \(0.584101\pi\)
\(728\) 7.73685e12 1.02088
\(729\) 2.82430e11 0.0370370
\(730\) 1.28061e13 1.66904
\(731\) 3.75250e12 0.486063
\(732\) 1.17964e12 0.151863
\(733\) 5.34623e12 0.684037 0.342019 0.939693i \(-0.388889\pi\)
0.342019 + 0.939693i \(0.388889\pi\)
\(734\) −8.82413e12 −1.12212
\(735\) 1.86255e12 0.235405
\(736\) −2.30788e12 −0.289910
\(737\) −1.83137e12 −0.228651
\(738\) −2.57492e12 −0.319529
\(739\) 2.20679e12 0.272183 0.136091 0.990696i \(-0.456546\pi\)
0.136091 + 0.990696i \(0.456546\pi\)
\(740\) 7.02533e11 0.0861239
\(741\) −9.84009e11 −0.119899
\(742\) −3.53743e12 −0.428420
\(743\) 1.61454e12 0.194356 0.0971782 0.995267i \(-0.469018\pi\)
0.0971782 + 0.995267i \(0.469018\pi\)
\(744\) −8.14545e12 −0.974623
\(745\) 1.16017e13 1.37981
\(746\) −1.36737e13 −1.61645
\(747\) −4.66441e12 −0.548092
\(748\) −6.04064e11 −0.0705547
\(749\) −1.21281e13 −1.40808
\(750\) 5.61719e12 0.648252
\(751\) −3.76703e12 −0.432135 −0.216067 0.976378i \(-0.569323\pi\)
−0.216067 + 0.976378i \(0.569323\pi\)
\(752\) 7.27098e12 0.829111
\(753\) 7.64532e12 0.866599
\(754\) 1.74060e13 1.96123
\(755\) 3.52821e12 0.395178
\(756\) 2.48891e11 0.0277115
\(757\) −1.18381e13 −1.31024 −0.655122 0.755523i \(-0.727383\pi\)
−0.655122 + 0.755523i \(0.727383\pi\)
\(758\) −3.74962e12 −0.412549
\(759\) −1.46600e12 −0.160341
\(760\) −1.07582e12 −0.116971
\(761\) 5.32000e12 0.575017 0.287509 0.957778i \(-0.407173\pi\)
0.287509 + 0.957778i \(0.407173\pi\)
\(762\) 8.56079e12 0.919849
\(763\) 4.07166e12 0.434922
\(764\) −3.08517e12 −0.327612
\(765\) −3.17818e12 −0.335507
\(766\) −1.05560e13 −1.10782
\(767\) −1.89448e12 −0.197657
\(768\) −3.05532e12 −0.316906
\(769\) −5.58489e12 −0.575898 −0.287949 0.957646i \(-0.592973\pi\)
−0.287949 + 0.957646i \(0.592973\pi\)
\(770\) −2.80268e12 −0.287319
\(771\) −9.94754e12 −1.01384
\(772\) 2.64141e12 0.267644
\(773\) −2.34571e12 −0.236301 −0.118151 0.992996i \(-0.537697\pi\)
−0.118151 + 0.992996i \(0.537697\pi\)
\(774\) −1.69540e12 −0.169800
\(775\) 1.23539e12 0.123012
\(776\) −8.67440e12 −0.858740
\(777\) 2.09822e12 0.206517
\(778\) 1.11159e13 1.08777
\(779\) −1.23578e12 −0.120233
\(780\) −1.65939e12 −0.160517
\(781\) −7.10746e12 −0.683573
\(782\) −9.20304e12 −0.880037
\(783\) −2.39766e12 −0.227960
\(784\) 5.14362e12 0.486235
\(785\) −9.66539e12 −0.908460
\(786\) 6.92968e11 0.0647608
\(787\) 1.63539e13 1.51962 0.759812 0.650143i \(-0.225291\pi\)
0.759812 + 0.650143i \(0.225291\pi\)
\(788\) 3.28353e12 0.303371
\(789\) −4.62159e12 −0.424566
\(790\) 8.89585e12 0.812579
\(791\) 4.40614e12 0.400188
\(792\) −1.16863e12 −0.105539
\(793\) −2.34895e13 −2.10933
\(794\) −1.79295e13 −1.60094
\(795\) −3.24873e12 −0.288444
\(796\) 1.48721e12 0.131300
\(797\) 7.98493e12 0.700985 0.350493 0.936565i \(-0.386014\pi\)
0.350493 + 0.936565i \(0.386014\pi\)
\(798\) 7.50378e11 0.0655039
\(799\) 8.61681e12 0.747973
\(800\) 2.79028e11 0.0240848
\(801\) −6.27420e12 −0.538532
\(802\) 1.38240e13 1.17991
\(803\) 6.67627e12 0.566649
\(804\) 8.26859e11 0.0697877
\(805\) −6.79714e12 −0.570486
\(806\) −3.78787e13 −3.16146
\(807\) −7.63615e12 −0.633788
\(808\) 1.08899e13 0.898817
\(809\) 8.18221e12 0.671587 0.335794 0.941936i \(-0.390996\pi\)
0.335794 + 0.941936i \(0.390996\pi\)
\(810\) 1.43592e12 0.117205
\(811\) −1.08175e13 −0.878077 −0.439038 0.898468i \(-0.644681\pi\)
−0.439038 + 0.898468i \(0.644681\pi\)
\(812\) −2.11293e12 −0.170562
\(813\) −1.39851e13 −1.12268
\(814\) 2.30079e12 0.183682
\(815\) 1.90567e13 1.51300
\(816\) −8.77685e12 −0.693000
\(817\) −8.13671e11 −0.0638924
\(818\) 1.70580e13 1.33210
\(819\) −4.95601e12 −0.384906
\(820\) −2.08396e12 −0.160963
\(821\) 2.25816e13 1.73464 0.867322 0.497747i \(-0.165839\pi\)
0.867322 + 0.497747i \(0.165839\pi\)
\(822\) 1.21892e13 0.931221
\(823\) −1.26241e13 −0.959184 −0.479592 0.877492i \(-0.659215\pi\)
−0.479592 + 0.877492i \(0.659215\pi\)
\(824\) 2.20558e13 1.66668
\(825\) 1.77242e11 0.0133206
\(826\) 1.44468e12 0.107985
\(827\) −1.97443e13 −1.46780 −0.733901 0.679256i \(-0.762303\pi\)
−0.733901 + 0.679256i \(0.762303\pi\)
\(828\) 6.61892e11 0.0489385
\(829\) −6.92065e12 −0.508922 −0.254461 0.967083i \(-0.581898\pi\)
−0.254461 + 0.967083i \(0.581898\pi\)
\(830\) −2.37146e13 −1.73446
\(831\) −2.60556e12 −0.189538
\(832\) 1.56495e13 1.13226
\(833\) 6.09568e12 0.438652
\(834\) −3.22483e12 −0.230813
\(835\) 4.80186e12 0.341838
\(836\) 1.30982e11 0.00927433
\(837\) 5.21774e12 0.367467
\(838\) −6.79376e12 −0.475896
\(839\) −1.15417e13 −0.804155 −0.402077 0.915606i \(-0.631712\pi\)
−0.402077 + 0.915606i \(0.631712\pi\)
\(840\) −5.41840e12 −0.375504
\(841\) 5.84749e12 0.403077
\(842\) 1.09623e13 0.751618
\(843\) −7.07389e12 −0.482430
\(844\) 3.18105e12 0.215789
\(845\) 1.87074e13 1.26229
\(846\) −3.89312e12 −0.261295
\(847\) 9.93121e12 0.663020
\(848\) −8.97168e12 −0.595789
\(849\) 3.94148e12 0.260361
\(850\) 1.11267e12 0.0731106
\(851\) 5.57995e12 0.364710
\(852\) 3.20900e12 0.208637
\(853\) 4.10642e11 0.0265579 0.0132789 0.999912i \(-0.495773\pi\)
0.0132789 + 0.999912i \(0.495773\pi\)
\(854\) 1.79125e13 1.15238
\(855\) 6.89138e11 0.0441020
\(856\) −2.57110e13 −1.63676
\(857\) 8.38710e12 0.531126 0.265563 0.964093i \(-0.414442\pi\)
0.265563 + 0.964093i \(0.414442\pi\)
\(858\) −5.43448e12 −0.342346
\(859\) −2.68616e13 −1.68330 −0.841651 0.540022i \(-0.818416\pi\)
−0.841651 + 0.540022i \(0.818416\pi\)
\(860\) −1.37213e12 −0.0855369
\(861\) −6.22405e12 −0.385975
\(862\) −2.71562e13 −1.67527
\(863\) 1.97692e13 1.21322 0.606610 0.795000i \(-0.292529\pi\)
0.606610 + 0.795000i \(0.292529\pi\)
\(864\) 1.17849e12 0.0719472
\(865\) 1.44797e13 0.879403
\(866\) −7.25101e12 −0.438095
\(867\) −7.95796e11 −0.0478317
\(868\) 4.59813e12 0.274943
\(869\) 4.63770e12 0.275876
\(870\) −1.21901e13 −0.721389
\(871\) −1.64647e13 −0.969333
\(872\) 8.63168e12 0.505558
\(873\) 5.55657e12 0.323775
\(874\) 1.99553e12 0.115680
\(875\) 1.35778e13 0.783054
\(876\) −3.01431e12 −0.172950
\(877\) 9.19482e12 0.524862 0.262431 0.964951i \(-0.415476\pi\)
0.262431 + 0.964951i \(0.415476\pi\)
\(878\) 2.43169e13 1.38097
\(879\) −6.92743e12 −0.391401
\(880\) −7.10820e12 −0.399565
\(881\) 8.80242e12 0.492278 0.246139 0.969235i \(-0.420838\pi\)
0.246139 + 0.969235i \(0.420838\pi\)
\(882\) −2.75406e12 −0.153237
\(883\) 1.54523e13 0.855400 0.427700 0.903921i \(-0.359324\pi\)
0.427700 + 0.903921i \(0.359324\pi\)
\(884\) −5.43077e12 −0.299107
\(885\) 1.32678e12 0.0727031
\(886\) −1.12715e13 −0.614510
\(887\) 2.05990e13 1.11735 0.558676 0.829386i \(-0.311309\pi\)
0.558676 + 0.829386i \(0.311309\pi\)
\(888\) 4.44810e12 0.240058
\(889\) 2.06930e13 1.11113
\(890\) −3.18990e13 −1.70421
\(891\) 7.48592e11 0.0397920
\(892\) 3.88535e12 0.205489
\(893\) −1.86842e12 −0.0983201
\(894\) −1.71549e13 −0.898192
\(895\) −3.34792e13 −1.74410
\(896\) −1.74194e13 −0.902917
\(897\) −1.31799e13 −0.679743
\(898\) −2.70099e13 −1.38605
\(899\) −4.42955e13 −2.26173
\(900\) −8.00242e10 −0.00406565
\(901\) −1.06323e13 −0.537484
\(902\) −6.82494e12 −0.343297
\(903\) −4.09809e12 −0.205110
\(904\) 9.34076e12 0.465184
\(905\) −5.45023e12 −0.270083
\(906\) −5.21699e12 −0.257243
\(907\) 2.40214e13 1.17860 0.589299 0.807915i \(-0.299404\pi\)
0.589299 + 0.807915i \(0.299404\pi\)
\(908\) −3.92772e12 −0.191758
\(909\) −6.97573e12 −0.338885
\(910\) −2.51971e13 −1.21805
\(911\) 5.73966e12 0.276092 0.138046 0.990426i \(-0.455918\pi\)
0.138046 + 0.990426i \(0.455918\pi\)
\(912\) 1.90312e12 0.0910940
\(913\) −1.23632e13 −0.588861
\(914\) 2.01944e13 0.957136
\(915\) 1.64506e13 0.775865
\(916\) −7.52456e11 −0.0353144
\(917\) 1.67503e12 0.0782276
\(918\) 4.69941e12 0.218400
\(919\) 2.83891e13 1.31290 0.656451 0.754368i \(-0.272057\pi\)
0.656451 + 0.754368i \(0.272057\pi\)
\(920\) −1.44095e13 −0.663139
\(921\) 4.97550e12 0.227860
\(922\) 1.24133e13 0.565715
\(923\) −6.38987e13 −2.89791
\(924\) 6.59695e11 0.0297728
\(925\) −6.74628e11 −0.0302989
\(926\) 4.17500e13 1.86598
\(927\) −1.41283e13 −0.628394
\(928\) −1.00047e13 −0.442829
\(929\) −1.44672e13 −0.637257 −0.318628 0.947880i \(-0.603222\pi\)
−0.318628 + 0.947880i \(0.603222\pi\)
\(930\) 2.65279e13 1.16286
\(931\) −1.32175e12 −0.0576602
\(932\) −1.68187e12 −0.0730164
\(933\) −4.03732e12 −0.174432
\(934\) 1.82769e11 0.00785852
\(935\) −8.42390e12 −0.360463
\(936\) −1.05064e13 −0.447419
\(937\) −1.94080e13 −0.822531 −0.411266 0.911515i \(-0.634913\pi\)
−0.411266 + 0.911515i \(0.634913\pi\)
\(938\) 1.25555e13 0.529569
\(939\) −6.21894e11 −0.0261049
\(940\) −3.15081e12 −0.131627
\(941\) 2.21587e13 0.921279 0.460640 0.887587i \(-0.347620\pi\)
0.460640 + 0.887587i \(0.347620\pi\)
\(942\) 1.42917e13 0.591365
\(943\) −1.65521e13 −0.681631
\(944\) 3.66402e12 0.150170
\(945\) 3.47087e12 0.141578
\(946\) −4.49373e12 −0.182430
\(947\) 2.08532e13 0.842552 0.421276 0.906932i \(-0.361582\pi\)
0.421276 + 0.906932i \(0.361582\pi\)
\(948\) −2.09391e12 −0.0842016
\(949\) 6.00222e13 2.40223
\(950\) −2.41264e11 −0.00961030
\(951\) 7.12468e12 0.282457
\(952\) −1.77331e13 −0.699711
\(953\) −6.20564e12 −0.243707 −0.121854 0.992548i \(-0.538884\pi\)
−0.121854 + 0.992548i \(0.538884\pi\)
\(954\) 4.80373e12 0.187763
\(955\) −4.30239e13 −1.67376
\(956\) 3.19805e12 0.123830
\(957\) −6.35509e12 −0.244916
\(958\) 2.15726e13 0.827481
\(959\) 2.94635e13 1.12487
\(960\) −1.09599e13 −0.416473
\(961\) 6.99555e13 2.64586
\(962\) 2.06850e13 0.778695
\(963\) 1.64697e13 0.617117
\(964\) 8.63862e10 0.00322180
\(965\) 3.68354e13 1.36739
\(966\) 1.00506e13 0.371359
\(967\) −4.63676e13 −1.70528 −0.852639 0.522501i \(-0.824999\pi\)
−0.852639 + 0.522501i \(0.824999\pi\)
\(968\) 2.10536e13 0.770703
\(969\) 2.25538e12 0.0821794
\(970\) 2.82505e13 1.02460
\(971\) 4.99705e13 1.80396 0.901980 0.431778i \(-0.142114\pi\)
0.901980 + 0.431778i \(0.142114\pi\)
\(972\) −3.37987e11 −0.0121451
\(973\) −7.79499e12 −0.278810
\(974\) −2.75475e13 −0.980769
\(975\) 1.59347e12 0.0564708
\(976\) 4.54299e13 1.60257
\(977\) 4.70947e13 1.65366 0.826830 0.562452i \(-0.190142\pi\)
0.826830 + 0.562452i \(0.190142\pi\)
\(978\) −2.81782e13 −0.984891
\(979\) −1.66300e13 −0.578590
\(980\) −2.22894e12 −0.0771934
\(981\) −5.52921e12 −0.190613
\(982\) −2.69175e12 −0.0923703
\(983\) 2.86405e13 0.978340 0.489170 0.872189i \(-0.337300\pi\)
0.489170 + 0.872189i \(0.337300\pi\)
\(984\) −1.31946e13 −0.448661
\(985\) 4.57901e13 1.54992
\(986\) −3.98952e13 −1.34423
\(987\) −9.41037e12 −0.315631
\(988\) 1.17758e12 0.0393172
\(989\) −1.08983e13 −0.362223
\(990\) 3.80596e12 0.125923
\(991\) 5.61009e13 1.84773 0.923866 0.382717i \(-0.125012\pi\)
0.923866 + 0.382717i \(0.125012\pi\)
\(992\) 2.17720e13 0.713831
\(993\) 5.98838e12 0.195451
\(994\) 4.87274e13 1.58320
\(995\) 2.07397e13 0.670808
\(996\) 5.58195e12 0.179729
\(997\) 7.32678e12 0.234847 0.117423 0.993082i \(-0.462537\pi\)
0.117423 + 0.993082i \(0.462537\pi\)
\(998\) 8.02442e12 0.256051
\(999\) −2.84933e12 −0.0905102
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 177.10.a.b.1.16 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.16 21 1.1 even 1 trivial