Properties

Label 177.10.a.b.1.20
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 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+41.8735 q^{2} -81.0000 q^{3} +1241.39 q^{4} +372.530 q^{5} -3391.75 q^{6} -8199.03 q^{7} +30542.0 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+41.8735 q^{2} -81.0000 q^{3} +1241.39 q^{4} +372.530 q^{5} -3391.75 q^{6} -8199.03 q^{7} +30542.0 q^{8} +6561.00 q^{9} +15599.1 q^{10} -82320.0 q^{11} -100552. q^{12} +203537. q^{13} -343322. q^{14} -30174.9 q^{15} +643310. q^{16} -224449. q^{17} +274732. q^{18} -225175. q^{19} +462454. q^{20} +664121. q^{21} -3.44702e6 q^{22} -1.73087e6 q^{23} -2.47390e6 q^{24} -1.81435e6 q^{25} +8.52279e6 q^{26} -531441. q^{27} -1.01782e7 q^{28} +998535. q^{29} -1.26353e6 q^{30} +3.18733e6 q^{31} +1.13001e7 q^{32} +6.66792e6 q^{33} -9.39847e6 q^{34} -3.05438e6 q^{35} +8.14475e6 q^{36} -1.44250e7 q^{37} -9.42887e6 q^{38} -1.64865e7 q^{39} +1.13778e7 q^{40} +1.46862e7 q^{41} +2.78091e7 q^{42} -4.45514e7 q^{43} -1.02191e8 q^{44} +2.44417e6 q^{45} -7.24776e7 q^{46} -3.24084e7 q^{47} -5.21081e7 q^{48} +2.68705e7 q^{49} -7.59730e7 q^{50} +1.81804e7 q^{51} +2.52668e8 q^{52} -1.75501e7 q^{53} -2.22533e7 q^{54} -3.06666e7 q^{55} -2.50415e8 q^{56} +1.82392e7 q^{57} +4.18121e7 q^{58} -1.21174e7 q^{59} -3.74588e7 q^{60} +4.48800e7 q^{61} +1.33465e8 q^{62} -5.37938e7 q^{63} +1.43800e8 q^{64} +7.58234e7 q^{65} +2.79209e8 q^{66} +1.16824e8 q^{67} -2.78629e8 q^{68} +1.40201e8 q^{69} -1.27898e8 q^{70} +2.10850e8 q^{71} +2.00386e8 q^{72} -2.37679e8 q^{73} -6.04026e8 q^{74} +1.46962e8 q^{75} -2.79530e8 q^{76} +6.74944e8 q^{77} -6.90346e8 q^{78} -2.98225e8 q^{79} +2.39652e8 q^{80} +4.30467e7 q^{81} +6.14961e8 q^{82} +2.78238e8 q^{83} +8.24433e8 q^{84} -8.36140e7 q^{85} -1.86552e9 q^{86} -8.08813e7 q^{87} -2.51422e9 q^{88} +6.35596e8 q^{89} +1.02346e8 q^{90} -1.66880e9 q^{91} -2.14868e9 q^{92} -2.58174e8 q^{93} -1.35705e9 q^{94} -8.38844e7 q^{95} -9.15309e8 q^{96} -1.37463e9 q^{97} +1.12516e9 q^{98} -5.40102e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.8735 1.85056 0.925282 0.379280i \(-0.123828\pi\)
0.925282 + 0.379280i \(0.123828\pi\)
\(3\) −81.0000 −0.577350
\(4\) 1241.39 2.42459
\(5\) 372.530 0.266560 0.133280 0.991078i \(-0.457449\pi\)
0.133280 + 0.991078i \(0.457449\pi\)
\(6\) −3391.75 −1.06842
\(7\) −8199.03 −1.29069 −0.645344 0.763892i \(-0.723286\pi\)
−0.645344 + 0.763892i \(0.723286\pi\)
\(8\) 30542.0 2.63629
\(9\) 6561.00 0.333333
\(10\) 15599.1 0.493287
\(11\) −82320.0 −1.69527 −0.847634 0.530582i \(-0.821974\pi\)
−0.847634 + 0.530582i \(0.821974\pi\)
\(12\) −100552. −1.39984
\(13\) 203537. 1.97650 0.988252 0.152835i \(-0.0488402\pi\)
0.988252 + 0.152835i \(0.0488402\pi\)
\(14\) −343322. −2.38850
\(15\) −30174.9 −0.153899
\(16\) 643310. 2.45403
\(17\) −224449. −0.651775 −0.325888 0.945408i \(-0.605663\pi\)
−0.325888 + 0.945408i \(0.605663\pi\)
\(18\) 274732. 0.616855
\(19\) −225175. −0.396396 −0.198198 0.980162i \(-0.563509\pi\)
−0.198198 + 0.980162i \(0.563509\pi\)
\(20\) 462454. 0.646299
\(21\) 664121. 0.745179
\(22\) −3.44702e6 −3.13720
\(23\) −1.73087e6 −1.28970 −0.644851 0.764308i \(-0.723081\pi\)
−0.644851 + 0.764308i \(0.723081\pi\)
\(24\) −2.47390e6 −1.52206
\(25\) −1.81435e6 −0.928946
\(26\) 8.52279e6 3.65765
\(27\) −531441. −0.192450
\(28\) −1.01782e7 −3.12938
\(29\) 998535. 0.262164 0.131082 0.991372i \(-0.458155\pi\)
0.131082 + 0.991372i \(0.458155\pi\)
\(30\) −1.26353e6 −0.284799
\(31\) 3.18733e6 0.619869 0.309934 0.950758i \(-0.399693\pi\)
0.309934 + 0.950758i \(0.399693\pi\)
\(32\) 1.13001e7 1.90506
\(33\) 6.66792e6 0.978763
\(34\) −9.39847e6 −1.20615
\(35\) −3.05438e6 −0.344046
\(36\) 8.14475e6 0.808196
\(37\) −1.44250e7 −1.26534 −0.632672 0.774420i \(-0.718042\pi\)
−0.632672 + 0.774420i \(0.718042\pi\)
\(38\) −9.42887e6 −0.733556
\(39\) −1.64865e7 −1.14113
\(40\) 1.13778e7 0.702730
\(41\) 1.46862e7 0.811673 0.405836 0.913946i \(-0.366980\pi\)
0.405836 + 0.913946i \(0.366980\pi\)
\(42\) 2.78091e7 1.37900
\(43\) −4.45514e7 −1.98725 −0.993626 0.112724i \(-0.964042\pi\)
−0.993626 + 0.112724i \(0.964042\pi\)
\(44\) −1.02191e8 −4.11032
\(45\) 2.44417e6 0.0888535
\(46\) −7.24776e7 −2.38668
\(47\) −3.24084e7 −0.968763 −0.484381 0.874857i \(-0.660955\pi\)
−0.484381 + 0.874857i \(0.660955\pi\)
\(48\) −5.21081e7 −1.41684
\(49\) 2.68705e7 0.665876
\(50\) −7.59730e7 −1.71907
\(51\) 1.81804e7 0.376303
\(52\) 2.52668e8 4.79220
\(53\) −1.75501e7 −0.305520 −0.152760 0.988263i \(-0.548816\pi\)
−0.152760 + 0.988263i \(0.548816\pi\)
\(54\) −2.22533e7 −0.356141
\(55\) −3.06666e7 −0.451891
\(56\) −2.50415e8 −3.40263
\(57\) 1.82392e7 0.228859
\(58\) 4.18121e7 0.485150
\(59\) −1.21174e7 −0.130189
\(60\) −3.74588e7 −0.373141
\(61\) 4.48800e7 0.415020 0.207510 0.978233i \(-0.433464\pi\)
0.207510 + 0.978233i \(0.433464\pi\)
\(62\) 1.33465e8 1.14711
\(63\) −5.37938e7 −0.430229
\(64\) 1.43800e8 1.07140
\(65\) 7.58234e7 0.526858
\(66\) 2.79209e8 1.81126
\(67\) 1.16824e8 0.708265 0.354132 0.935195i \(-0.384776\pi\)
0.354132 + 0.935195i \(0.384776\pi\)
\(68\) −2.78629e8 −1.58029
\(69\) 1.40201e8 0.744610
\(70\) −1.27898e8 −0.636680
\(71\) 2.10850e8 0.984716 0.492358 0.870393i \(-0.336135\pi\)
0.492358 + 0.870393i \(0.336135\pi\)
\(72\) 2.00386e8 0.878763
\(73\) −2.37679e8 −0.979577 −0.489788 0.871841i \(-0.662926\pi\)
−0.489788 + 0.871841i \(0.662926\pi\)
\(74\) −6.04026e8 −2.34160
\(75\) 1.46962e8 0.536327
\(76\) −2.79530e8 −0.961096
\(77\) 6.74944e8 2.18806
\(78\) −6.90346e8 −2.11174
\(79\) −2.98225e8 −0.861434 −0.430717 0.902487i \(-0.641739\pi\)
−0.430717 + 0.902487i \(0.641739\pi\)
\(80\) 2.39652e8 0.654148
\(81\) 4.30467e7 0.111111
\(82\) 6.14961e8 1.50205
\(83\) 2.78238e8 0.643525 0.321762 0.946820i \(-0.395725\pi\)
0.321762 + 0.946820i \(0.395725\pi\)
\(84\) 8.24433e8 1.80675
\(85\) −8.36140e7 −0.173738
\(86\) −1.86552e9 −3.67754
\(87\) −8.08813e7 −0.151360
\(88\) −2.51422e9 −4.46921
\(89\) 6.35596e8 1.07381 0.536903 0.843644i \(-0.319594\pi\)
0.536903 + 0.843644i \(0.319594\pi\)
\(90\) 1.02346e8 0.164429
\(91\) −1.66880e9 −2.55105
\(92\) −2.14868e9 −3.12700
\(93\) −2.58174e8 −0.357881
\(94\) −1.35705e9 −1.79276
\(95\) −8.38844e7 −0.105664
\(96\) −9.15309e8 −1.09989
\(97\) −1.37463e9 −1.57656 −0.788282 0.615314i \(-0.789029\pi\)
−0.788282 + 0.615314i \(0.789029\pi\)
\(98\) 1.12516e9 1.23225
\(99\) −5.40102e8 −0.565089
\(100\) −2.25231e9 −2.25231
\(101\) −6.16790e8 −0.589781 −0.294891 0.955531i \(-0.595283\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(102\) 7.61276e8 0.696372
\(103\) 1.44347e9 1.26369 0.631846 0.775094i \(-0.282297\pi\)
0.631846 + 0.775094i \(0.282297\pi\)
\(104\) 6.21642e9 5.21063
\(105\) 2.47405e8 0.198635
\(106\) −7.34886e8 −0.565384
\(107\) −6.76419e8 −0.498872 −0.249436 0.968391i \(-0.580245\pi\)
−0.249436 + 0.968391i \(0.580245\pi\)
\(108\) −6.59725e8 −0.466612
\(109\) 1.17743e9 0.798945 0.399472 0.916745i \(-0.369193\pi\)
0.399472 + 0.916745i \(0.369193\pi\)
\(110\) −1.28412e9 −0.836254
\(111\) 1.16843e9 0.730547
\(112\) −5.27452e9 −3.16739
\(113\) −3.37282e9 −1.94599 −0.972995 0.230824i \(-0.925858\pi\)
−0.972995 + 0.230824i \(0.925858\pi\)
\(114\) 7.63738e8 0.423519
\(115\) −6.44801e8 −0.343784
\(116\) 1.23957e9 0.635638
\(117\) 1.33540e9 0.658835
\(118\) −5.07396e8 −0.240923
\(119\) 1.84027e9 0.841239
\(120\) −9.21603e8 −0.405722
\(121\) 4.41863e9 1.87393
\(122\) 1.87928e9 0.768021
\(123\) −1.18958e9 −0.468619
\(124\) 3.95672e9 1.50293
\(125\) −1.40349e9 −0.514181
\(126\) −2.25254e9 −0.796167
\(127\) −3.14508e9 −1.07279 −0.536395 0.843967i \(-0.680214\pi\)
−0.536395 + 0.843967i \(0.680214\pi\)
\(128\) 2.35763e8 0.0776304
\(129\) 3.60866e9 1.14734
\(130\) 3.17499e9 0.974984
\(131\) 2.96230e9 0.878837 0.439419 0.898282i \(-0.355184\pi\)
0.439419 + 0.898282i \(0.355184\pi\)
\(132\) 8.27748e9 2.37310
\(133\) 1.84622e9 0.511624
\(134\) 4.89183e9 1.31069
\(135\) −1.97978e8 −0.0512996
\(136\) −6.85513e9 −1.71827
\(137\) 3.48056e9 0.844125 0.422063 0.906567i \(-0.361306\pi\)
0.422063 + 0.906567i \(0.361306\pi\)
\(138\) 5.87069e9 1.37795
\(139\) −4.66126e9 −1.05910 −0.529550 0.848279i \(-0.677639\pi\)
−0.529550 + 0.848279i \(0.677639\pi\)
\(140\) −3.79167e9 −0.834170
\(141\) 2.62508e9 0.559316
\(142\) 8.82903e9 1.82228
\(143\) −1.67551e10 −3.35070
\(144\) 4.22076e9 0.818011
\(145\) 3.71984e8 0.0698825
\(146\) −9.95246e9 −1.81277
\(147\) −2.17651e9 −0.384444
\(148\) −1.79071e10 −3.06794
\(149\) 3.70108e9 0.615162 0.307581 0.951522i \(-0.400480\pi\)
0.307581 + 0.951522i \(0.400480\pi\)
\(150\) 6.15381e9 0.992507
\(151\) 2.16470e9 0.338845 0.169423 0.985543i \(-0.445810\pi\)
0.169423 + 0.985543i \(0.445810\pi\)
\(152\) −6.87731e9 −1.04501
\(153\) −1.47261e9 −0.217258
\(154\) 2.82623e10 4.04915
\(155\) 1.18738e9 0.165233
\(156\) −2.04661e10 −2.76678
\(157\) −1.50369e9 −0.197520 −0.0987600 0.995111i \(-0.531488\pi\)
−0.0987600 + 0.995111i \(0.531488\pi\)
\(158\) −1.24877e10 −1.59414
\(159\) 1.42156e9 0.176392
\(160\) 4.20963e9 0.507813
\(161\) 1.41915e10 1.66460
\(162\) 1.80252e9 0.205618
\(163\) 3.43583e9 0.381231 0.190615 0.981665i \(-0.438952\pi\)
0.190615 + 0.981665i \(0.438952\pi\)
\(164\) 1.82312e10 1.96797
\(165\) 2.48400e9 0.260900
\(166\) 1.16508e10 1.19088
\(167\) −6.06963e9 −0.603863 −0.301931 0.953330i \(-0.597631\pi\)
−0.301931 + 0.953330i \(0.597631\pi\)
\(168\) 2.02836e10 1.96451
\(169\) 3.08227e10 2.90657
\(170\) −3.50121e9 −0.321512
\(171\) −1.47737e9 −0.132132
\(172\) −5.53056e10 −4.81827
\(173\) 7.07674e9 0.600656 0.300328 0.953836i \(-0.402904\pi\)
0.300328 + 0.953836i \(0.402904\pi\)
\(174\) −3.38678e9 −0.280102
\(175\) 1.48759e10 1.19898
\(176\) −5.29573e10 −4.16024
\(177\) 9.81506e8 0.0751646
\(178\) 2.66146e10 1.98715
\(179\) 2.00822e10 1.46209 0.731044 0.682331i \(-0.239034\pi\)
0.731044 + 0.682331i \(0.239034\pi\)
\(180\) 3.03416e9 0.215433
\(181\) −3.54268e9 −0.245345 −0.122673 0.992447i \(-0.539147\pi\)
−0.122673 + 0.992447i \(0.539147\pi\)
\(182\) −6.98786e10 −4.72088
\(183\) −3.63528e9 −0.239612
\(184\) −5.28643e10 −3.40003
\(185\) −5.37375e9 −0.337291
\(186\) −1.08106e10 −0.662282
\(187\) 1.84767e10 1.10493
\(188\) −4.02314e10 −2.34885
\(189\) 4.35730e9 0.248393
\(190\) −3.51253e9 −0.195537
\(191\) −1.49540e9 −0.0813030 −0.0406515 0.999173i \(-0.512943\pi\)
−0.0406515 + 0.999173i \(0.512943\pi\)
\(192\) −1.16478e10 −0.618571
\(193\) 3.24875e10 1.68542 0.842711 0.538367i \(-0.180959\pi\)
0.842711 + 0.538367i \(0.180959\pi\)
\(194\) −5.75604e10 −2.91753
\(195\) −6.14170e9 −0.304181
\(196\) 3.33567e10 1.61447
\(197\) 2.59561e10 1.22784 0.613920 0.789368i \(-0.289592\pi\)
0.613920 + 0.789368i \(0.289592\pi\)
\(198\) −2.26159e10 −1.04573
\(199\) −1.62559e10 −0.734806 −0.367403 0.930062i \(-0.619753\pi\)
−0.367403 + 0.930062i \(0.619753\pi\)
\(200\) −5.54138e10 −2.44897
\(201\) −9.46275e9 −0.408917
\(202\) −2.58271e10 −1.09143
\(203\) −8.18702e9 −0.338371
\(204\) 2.25689e10 0.912379
\(205\) 5.47103e9 0.216360
\(206\) 6.04433e10 2.33854
\(207\) −1.13563e10 −0.429901
\(208\) 1.30937e11 4.85041
\(209\) 1.85364e10 0.671997
\(210\) 1.03597e10 0.367587
\(211\) −5.52198e10 −1.91789 −0.958944 0.283594i \(-0.908473\pi\)
−0.958944 + 0.283594i \(0.908473\pi\)
\(212\) −2.17865e10 −0.740759
\(213\) −1.70789e10 −0.568526
\(214\) −2.83240e10 −0.923194
\(215\) −1.65967e10 −0.529723
\(216\) −1.62313e10 −0.507354
\(217\) −2.61330e10 −0.800057
\(218\) 4.93032e10 1.47850
\(219\) 1.92520e10 0.565559
\(220\) −3.80692e10 −1.09565
\(221\) −4.56837e10 −1.28824
\(222\) 4.89261e10 1.35192
\(223\) −2.88799e10 −0.782030 −0.391015 0.920384i \(-0.627876\pi\)
−0.391015 + 0.920384i \(0.627876\pi\)
\(224\) −9.26500e10 −2.45883
\(225\) −1.19039e10 −0.309649
\(226\) −1.41232e11 −3.60118
\(227\) 4.19030e10 1.04744 0.523720 0.851891i \(-0.324544\pi\)
0.523720 + 0.851891i \(0.324544\pi\)
\(228\) 2.26419e10 0.554889
\(229\) 5.35398e10 1.28652 0.643261 0.765647i \(-0.277581\pi\)
0.643261 + 0.765647i \(0.277581\pi\)
\(230\) −2.70001e10 −0.636194
\(231\) −5.46705e10 −1.26328
\(232\) 3.04973e10 0.691139
\(233\) −1.84191e10 −0.409418 −0.204709 0.978823i \(-0.565625\pi\)
−0.204709 + 0.978823i \(0.565625\pi\)
\(234\) 5.59180e10 1.21922
\(235\) −1.20731e10 −0.258234
\(236\) −1.50424e10 −0.315654
\(237\) 2.41562e10 0.497349
\(238\) 7.70583e10 1.55677
\(239\) 2.04847e9 0.0406107 0.0203053 0.999794i \(-0.493536\pi\)
0.0203053 + 0.999794i \(0.493536\pi\)
\(240\) −1.94118e10 −0.377673
\(241\) 8.48874e10 1.62094 0.810469 0.585781i \(-0.199212\pi\)
0.810469 + 0.585781i \(0.199212\pi\)
\(242\) 1.85024e11 3.46783
\(243\) −3.48678e9 −0.0641500
\(244\) 5.57135e10 1.00625
\(245\) 1.00101e10 0.177496
\(246\) −4.98118e10 −0.867210
\(247\) −4.58314e10 −0.783478
\(248\) 9.73476e10 1.63415
\(249\) −2.25373e10 −0.371539
\(250\) −5.87692e10 −0.951524
\(251\) −1.69028e10 −0.268799 −0.134399 0.990927i \(-0.542910\pi\)
−0.134399 + 0.990927i \(0.542910\pi\)
\(252\) −6.67790e10 −1.04313
\(253\) 1.42485e11 2.18639
\(254\) −1.31695e11 −1.98527
\(255\) 6.77273e9 0.100307
\(256\) −6.37536e10 −0.927736
\(257\) −5.99284e10 −0.856906 −0.428453 0.903564i \(-0.640941\pi\)
−0.428453 + 0.903564i \(0.640941\pi\)
\(258\) 1.51107e11 2.12323
\(259\) 1.18271e11 1.63317
\(260\) 9.41263e10 1.27741
\(261\) 6.55139e9 0.0873879
\(262\) 1.24042e11 1.62634
\(263\) 3.62736e10 0.467509 0.233754 0.972296i \(-0.424899\pi\)
0.233754 + 0.972296i \(0.424899\pi\)
\(264\) 2.03652e11 2.58030
\(265\) −6.53795e9 −0.0814395
\(266\) 7.73076e10 0.946792
\(267\) −5.14833e10 −0.619962
\(268\) 1.45024e11 1.71725
\(269\) 1.15892e11 1.34948 0.674740 0.738055i \(-0.264256\pi\)
0.674740 + 0.738055i \(0.264256\pi\)
\(270\) −8.29001e9 −0.0949332
\(271\) 1.71493e11 1.93146 0.965730 0.259548i \(-0.0835735\pi\)
0.965730 + 0.259548i \(0.0835735\pi\)
\(272\) −1.44390e11 −1.59948
\(273\) 1.35173e11 1.47285
\(274\) 1.45743e11 1.56211
\(275\) 1.49357e11 1.57481
\(276\) 1.74043e11 1.80537
\(277\) 1.50131e11 1.53219 0.766094 0.642729i \(-0.222198\pi\)
0.766094 + 0.642729i \(0.222198\pi\)
\(278\) −1.95183e11 −1.95993
\(279\) 2.09121e10 0.206623
\(280\) −9.32870e10 −0.907006
\(281\) 2.66008e10 0.254517 0.127258 0.991870i \(-0.459382\pi\)
0.127258 + 0.991870i \(0.459382\pi\)
\(282\) 1.09921e11 1.03505
\(283\) −1.02268e11 −0.947765 −0.473883 0.880588i \(-0.657148\pi\)
−0.473883 + 0.880588i \(0.657148\pi\)
\(284\) 2.61747e11 2.38753
\(285\) 6.79464e9 0.0610049
\(286\) −7.01596e11 −6.20069
\(287\) −1.20412e11 −1.04762
\(288\) 7.41401e10 0.635019
\(289\) −6.82104e10 −0.575189
\(290\) 1.55763e10 0.129322
\(291\) 1.11345e11 0.910230
\(292\) −2.95052e11 −2.37507
\(293\) −9.53748e10 −0.756014 −0.378007 0.925803i \(-0.623390\pi\)
−0.378007 + 0.925803i \(0.623390\pi\)
\(294\) −9.11380e10 −0.711437
\(295\) −4.51408e9 −0.0347032
\(296\) −4.40570e11 −3.33581
\(297\) 4.37482e10 0.326254
\(298\) 1.54977e11 1.13840
\(299\) −3.52296e11 −2.54910
\(300\) 1.82437e11 1.30037
\(301\) 3.65278e11 2.56492
\(302\) 9.06435e10 0.627055
\(303\) 4.99600e10 0.340510
\(304\) −1.44857e11 −0.972769
\(305\) 1.67191e10 0.110628
\(306\) −6.16634e10 −0.402051
\(307\) −1.98423e11 −1.27488 −0.637440 0.770500i \(-0.720006\pi\)
−0.637440 + 0.770500i \(0.720006\pi\)
\(308\) 8.37868e11 5.30514
\(309\) −1.16921e11 −0.729593
\(310\) 4.97196e10 0.305773
\(311\) −1.02604e11 −0.621930 −0.310965 0.950421i \(-0.600652\pi\)
−0.310965 + 0.950421i \(0.600652\pi\)
\(312\) −5.03530e11 −3.00836
\(313\) −1.93173e11 −1.13762 −0.568809 0.822470i \(-0.692595\pi\)
−0.568809 + 0.822470i \(0.692595\pi\)
\(314\) −6.29649e10 −0.365523
\(315\) −2.00398e10 −0.114682
\(316\) −3.70213e11 −2.08862
\(317\) 1.17454e11 0.653280 0.326640 0.945149i \(-0.394084\pi\)
0.326640 + 0.945149i \(0.394084\pi\)
\(318\) 5.95257e10 0.326425
\(319\) −8.21994e10 −0.444437
\(320\) 5.35699e10 0.285592
\(321\) 5.47900e10 0.288024
\(322\) 5.94246e11 3.08046
\(323\) 5.05404e10 0.258361
\(324\) 5.34377e10 0.269399
\(325\) −3.69286e11 −1.83606
\(326\) 1.43870e11 0.705492
\(327\) −9.53720e10 −0.461271
\(328\) 4.48545e11 2.13980
\(329\) 2.65718e11 1.25037
\(330\) 1.04014e11 0.482811
\(331\) 7.74826e10 0.354796 0.177398 0.984139i \(-0.443232\pi\)
0.177398 + 0.984139i \(0.443232\pi\)
\(332\) 3.45402e11 1.56028
\(333\) −9.46426e10 −0.421782
\(334\) −2.54157e11 −1.11749
\(335\) 4.35204e10 0.188795
\(336\) 4.27236e11 1.82869
\(337\) 1.28551e11 0.542928 0.271464 0.962449i \(-0.412492\pi\)
0.271464 + 0.962449i \(0.412492\pi\)
\(338\) 1.29065e12 5.37879
\(339\) 2.73199e11 1.12352
\(340\) −1.03797e11 −0.421242
\(341\) −2.62381e11 −1.05084
\(342\) −6.18628e10 −0.244519
\(343\) 1.10549e11 0.431250
\(344\) −1.36069e12 −5.23897
\(345\) 5.22289e10 0.198484
\(346\) 2.96328e11 1.11155
\(347\) −4.97854e11 −1.84340 −0.921699 0.387906i \(-0.873199\pi\)
−0.921699 + 0.387906i \(0.873199\pi\)
\(348\) −1.00405e11 −0.366986
\(349\) −1.95888e11 −0.706796 −0.353398 0.935473i \(-0.614974\pi\)
−0.353398 + 0.935473i \(0.614974\pi\)
\(350\) 6.22905e11 2.21879
\(351\) −1.08168e11 −0.380378
\(352\) −9.30226e11 −3.22958
\(353\) −1.13791e11 −0.390053 −0.195026 0.980798i \(-0.562479\pi\)
−0.195026 + 0.980798i \(0.562479\pi\)
\(354\) 4.10991e10 0.139097
\(355\) 7.85479e10 0.262486
\(356\) 7.89021e11 2.60354
\(357\) −1.49062e11 −0.485689
\(358\) 8.40913e11 2.70569
\(359\) 5.00230e11 1.58944 0.794722 0.606974i \(-0.207617\pi\)
0.794722 + 0.606974i \(0.207617\pi\)
\(360\) 7.46498e10 0.234243
\(361\) −2.71984e11 −0.842870
\(362\) −1.48344e11 −0.454027
\(363\) −3.57909e11 −1.08192
\(364\) −2.07163e12 −6.18524
\(365\) −8.85426e10 −0.261116
\(366\) −1.52222e11 −0.443417
\(367\) 3.83881e11 1.10459 0.552293 0.833650i \(-0.313753\pi\)
0.552293 + 0.833650i \(0.313753\pi\)
\(368\) −1.11349e12 −3.16497
\(369\) 9.63559e10 0.270558
\(370\) −2.25018e11 −0.624178
\(371\) 1.43894e11 0.394331
\(372\) −3.20494e11 −0.867714
\(373\) −1.51726e10 −0.0405855 −0.0202928 0.999794i \(-0.506460\pi\)
−0.0202928 + 0.999794i \(0.506460\pi\)
\(374\) 7.73682e11 2.04475
\(375\) 1.13683e11 0.296862
\(376\) −9.89819e11 −2.55394
\(377\) 2.03239e11 0.518167
\(378\) 1.82455e11 0.459667
\(379\) −5.48714e11 −1.36606 −0.683030 0.730390i \(-0.739338\pi\)
−0.683030 + 0.730390i \(0.739338\pi\)
\(380\) −1.04133e11 −0.256190
\(381\) 2.54751e11 0.619375
\(382\) −6.26175e10 −0.150456
\(383\) 3.09208e11 0.734272 0.367136 0.930167i \(-0.380338\pi\)
0.367136 + 0.930167i \(0.380338\pi\)
\(384\) −1.90968e10 −0.0448199
\(385\) 2.51437e11 0.583251
\(386\) 1.36036e12 3.11898
\(387\) −2.92302e11 −0.662418
\(388\) −1.70645e12 −3.82252
\(389\) 5.12638e10 0.113511 0.0567554 0.998388i \(-0.481924\pi\)
0.0567554 + 0.998388i \(0.481924\pi\)
\(390\) −2.57174e11 −0.562907
\(391\) 3.88493e11 0.840597
\(392\) 8.20679e11 1.75544
\(393\) −2.39946e11 −0.507397
\(394\) 1.08687e12 2.27220
\(395\) −1.11098e11 −0.229624
\(396\) −6.70476e11 −1.37011
\(397\) −6.87252e11 −1.38854 −0.694271 0.719714i \(-0.744273\pi\)
−0.694271 + 0.719714i \(0.744273\pi\)
\(398\) −6.80692e11 −1.35981
\(399\) −1.49544e11 −0.295386
\(400\) −1.16719e12 −2.27966
\(401\) −6.21415e11 −1.20014 −0.600071 0.799947i \(-0.704861\pi\)
−0.600071 + 0.799947i \(0.704861\pi\)
\(402\) −3.96238e11 −0.756727
\(403\) 6.48739e11 1.22517
\(404\) −7.65676e11 −1.42998
\(405\) 1.60362e10 0.0296178
\(406\) −3.42819e11 −0.626178
\(407\) 1.18747e12 2.14510
\(408\) 5.55266e11 0.992043
\(409\) −6.54379e11 −1.15631 −0.578156 0.815927i \(-0.696227\pi\)
−0.578156 + 0.815927i \(0.696227\pi\)
\(410\) 2.29091e11 0.400388
\(411\) −2.81926e11 −0.487356
\(412\) 1.79191e12 3.06393
\(413\) 9.93506e10 0.168033
\(414\) −4.75526e11 −0.795559
\(415\) 1.03652e11 0.171538
\(416\) 2.29999e12 3.76535
\(417\) 3.77562e11 0.611471
\(418\) 7.76184e11 1.24357
\(419\) −6.68755e11 −1.06000 −0.529998 0.847999i \(-0.677807\pi\)
−0.529998 + 0.847999i \(0.677807\pi\)
\(420\) 3.07126e11 0.481608
\(421\) −1.14702e12 −1.77952 −0.889760 0.456430i \(-0.849128\pi\)
−0.889760 + 0.456430i \(0.849128\pi\)
\(422\) −2.31224e12 −3.54918
\(423\) −2.12632e11 −0.322921
\(424\) −5.36017e11 −0.805438
\(425\) 4.07229e11 0.605464
\(426\) −7.15151e11 −1.05209
\(427\) −3.67973e11 −0.535661
\(428\) −8.39699e11 −1.20956
\(429\) 1.35717e12 1.93453
\(430\) −6.94962e11 −0.980286
\(431\) 4.93513e10 0.0688891 0.0344446 0.999407i \(-0.489034\pi\)
0.0344446 + 0.999407i \(0.489034\pi\)
\(432\) −3.41881e11 −0.472279
\(433\) 6.37595e11 0.871665 0.435833 0.900028i \(-0.356454\pi\)
0.435833 + 0.900028i \(0.356454\pi\)
\(434\) −1.09428e12 −1.48056
\(435\) −3.01307e10 −0.0403467
\(436\) 1.46165e12 1.93711
\(437\) 3.89749e11 0.511233
\(438\) 8.06149e11 1.04660
\(439\) 4.13393e11 0.531218 0.265609 0.964081i \(-0.414427\pi\)
0.265609 + 0.964081i \(0.414427\pi\)
\(440\) −9.36621e11 −1.19132
\(441\) 1.76297e11 0.221959
\(442\) −1.91293e12 −2.38396
\(443\) −3.88092e11 −0.478760 −0.239380 0.970926i \(-0.576944\pi\)
−0.239380 + 0.970926i \(0.576944\pi\)
\(444\) 1.45047e12 1.77127
\(445\) 2.36778e11 0.286234
\(446\) −1.20930e12 −1.44720
\(447\) −2.99787e11 −0.355164
\(448\) −1.17902e12 −1.38284
\(449\) −4.96545e11 −0.576567 −0.288284 0.957545i \(-0.593085\pi\)
−0.288284 + 0.957545i \(0.593085\pi\)
\(450\) −4.98459e11 −0.573024
\(451\) −1.20896e12 −1.37600
\(452\) −4.18699e12 −4.71822
\(453\) −1.75341e11 −0.195632
\(454\) 1.75463e12 1.93835
\(455\) −6.21679e11 −0.680009
\(456\) 5.57062e11 0.603339
\(457\) −3.23978e11 −0.347450 −0.173725 0.984794i \(-0.555580\pi\)
−0.173725 + 0.984794i \(0.555580\pi\)
\(458\) 2.24190e12 2.38079
\(459\) 1.19282e11 0.125434
\(460\) −8.00448e11 −0.833534
\(461\) 8.40893e11 0.867134 0.433567 0.901121i \(-0.357255\pi\)
0.433567 + 0.901121i \(0.357255\pi\)
\(462\) −2.28924e12 −2.33778
\(463\) 1.82302e11 0.184364 0.0921822 0.995742i \(-0.470616\pi\)
0.0921822 + 0.995742i \(0.470616\pi\)
\(464\) 6.42368e11 0.643358
\(465\) −9.61774e10 −0.0953970
\(466\) −7.71272e11 −0.757654
\(467\) −5.22333e11 −0.508184 −0.254092 0.967180i \(-0.581777\pi\)
−0.254092 + 0.967180i \(0.581777\pi\)
\(468\) 1.65776e12 1.59740
\(469\) −9.57844e11 −0.914149
\(470\) −5.05543e11 −0.477878
\(471\) 1.21799e11 0.114038
\(472\) −3.70089e11 −0.343216
\(473\) 3.66747e12 3.36892
\(474\) 1.01150e12 0.920376
\(475\) 4.08546e11 0.368230
\(476\) 2.28448e12 2.03966
\(477\) −1.15147e11 −0.101840
\(478\) 8.57768e10 0.0751526
\(479\) 6.54874e11 0.568392 0.284196 0.958766i \(-0.408273\pi\)
0.284196 + 0.958766i \(0.408273\pi\)
\(480\) −3.40980e11 −0.293186
\(481\) −2.93602e12 −2.50096
\(482\) 3.55453e12 2.99965
\(483\) −1.14951e12 −0.961060
\(484\) 5.48524e12 4.54351
\(485\) −5.12089e11 −0.420250
\(486\) −1.46004e11 −0.118714
\(487\) 2.24496e12 1.80854 0.904272 0.426958i \(-0.140415\pi\)
0.904272 + 0.426958i \(0.140415\pi\)
\(488\) 1.37073e12 1.09411
\(489\) −2.78302e11 −0.220104
\(490\) 4.19156e11 0.328468
\(491\) 4.10093e11 0.318431 0.159216 0.987244i \(-0.449104\pi\)
0.159216 + 0.987244i \(0.449104\pi\)
\(492\) −1.47673e12 −1.13621
\(493\) −2.24120e11 −0.170872
\(494\) −1.91912e12 −1.44988
\(495\) −2.01204e11 −0.150630
\(496\) 2.05044e12 1.52118
\(497\) −1.72877e12 −1.27096
\(498\) −9.43715e11 −0.687557
\(499\) 1.22585e11 0.0885087 0.0442544 0.999020i \(-0.485909\pi\)
0.0442544 + 0.999020i \(0.485909\pi\)
\(500\) −1.74228e12 −1.24668
\(501\) 4.91640e11 0.348640
\(502\) −7.07779e11 −0.497429
\(503\) −2.57979e12 −1.79692 −0.898459 0.439057i \(-0.855313\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(504\) −1.64297e12 −1.13421
\(505\) −2.29772e11 −0.157212
\(506\) 5.96636e12 4.04606
\(507\) −2.49664e12 −1.67811
\(508\) −3.90426e12 −2.60107
\(509\) −6.19813e11 −0.409290 −0.204645 0.978836i \(-0.565604\pi\)
−0.204645 + 0.978836i \(0.565604\pi\)
\(510\) 2.83598e11 0.185625
\(511\) 1.94874e12 1.26433
\(512\) −2.79029e12 −1.79447
\(513\) 1.19667e11 0.0762864
\(514\) −2.50941e12 −1.58576
\(515\) 5.37737e11 0.336850
\(516\) 4.47975e12 2.78183
\(517\) 2.66786e12 1.64231
\(518\) 4.95243e12 3.02228
\(519\) −5.73216e11 −0.346789
\(520\) 2.31580e12 1.38895
\(521\) −2.20520e12 −1.31123 −0.655613 0.755097i \(-0.727590\pi\)
−0.655613 + 0.755097i \(0.727590\pi\)
\(522\) 2.74329e11 0.161717
\(523\) −1.83492e12 −1.07241 −0.536205 0.844088i \(-0.680142\pi\)
−0.536205 + 0.844088i \(0.680142\pi\)
\(524\) 3.67737e12 2.13082
\(525\) −1.20495e12 −0.692231
\(526\) 1.51890e12 0.865154
\(527\) −7.15394e11 −0.404015
\(528\) 4.28954e12 2.40192
\(529\) 1.19476e12 0.663333
\(530\) −2.73767e11 −0.150709
\(531\) −7.95020e10 −0.0433963
\(532\) 2.29187e12 1.24048
\(533\) 2.98917e12 1.60427
\(534\) −2.15578e12 −1.14728
\(535\) −2.51986e11 −0.132980
\(536\) 3.56804e12 1.86719
\(537\) −1.62666e12 −0.844136
\(538\) 4.85278e12 2.49730
\(539\) −2.21198e12 −1.12884
\(540\) −2.45767e11 −0.124380
\(541\) −3.44981e12 −1.73144 −0.865720 0.500529i \(-0.833139\pi\)
−0.865720 + 0.500529i \(0.833139\pi\)
\(542\) 7.18103e12 3.57429
\(543\) 2.86957e11 0.141650
\(544\) −2.53630e12 −1.24167
\(545\) 4.38628e11 0.212967
\(546\) 5.66017e12 2.72560
\(547\) −3.36291e12 −1.60610 −0.803050 0.595911i \(-0.796791\pi\)
−0.803050 + 0.595911i \(0.796791\pi\)
\(548\) 4.32073e12 2.04665
\(549\) 2.94458e11 0.138340
\(550\) 6.25410e12 2.91429
\(551\) −2.24845e11 −0.103921
\(552\) 4.28201e12 1.96301
\(553\) 2.44515e12 1.11184
\(554\) 6.28651e12 2.83541
\(555\) 4.35274e11 0.194735
\(556\) −5.78643e12 −2.56788
\(557\) −2.87465e12 −1.26543 −0.632713 0.774387i \(-0.718059\pi\)
−0.632713 + 0.774387i \(0.718059\pi\)
\(558\) 8.75662e11 0.382369
\(559\) −9.06784e12 −3.92781
\(560\) −1.96491e12 −0.844301
\(561\) −1.49661e12 −0.637934
\(562\) 1.11387e12 0.470999
\(563\) −1.48864e10 −0.00624458 −0.00312229 0.999995i \(-0.500994\pi\)
−0.00312229 + 0.999995i \(0.500994\pi\)
\(564\) 3.25875e12 1.35611
\(565\) −1.25648e12 −0.518724
\(566\) −4.28232e12 −1.75390
\(567\) −3.52941e11 −0.143410
\(568\) 6.43979e12 2.59600
\(569\) −3.07730e11 −0.123074 −0.0615368 0.998105i \(-0.519600\pi\)
−0.0615368 + 0.998105i \(0.519600\pi\)
\(570\) 2.84515e11 0.112893
\(571\) −3.34526e12 −1.31694 −0.658472 0.752605i \(-0.728797\pi\)
−0.658472 + 0.752605i \(0.728797\pi\)
\(572\) −2.07996e13 −8.12407
\(573\) 1.21127e11 0.0469403
\(574\) −5.04208e12 −1.93868
\(575\) 3.14040e12 1.19806
\(576\) 9.43474e11 0.357132
\(577\) −2.83923e12 −1.06637 −0.533187 0.845998i \(-0.679006\pi\)
−0.533187 + 0.845998i \(0.679006\pi\)
\(578\) −2.85621e12 −1.06442
\(579\) −2.63149e12 −0.973078
\(580\) 4.61776e11 0.169436
\(581\) −2.28128e12 −0.830590
\(582\) 4.66239e12 1.68444
\(583\) 1.44473e12 0.517938
\(584\) −7.25921e12 −2.58245
\(585\) 4.97478e11 0.175619
\(586\) −3.99368e12 −1.39905
\(587\) 3.42668e12 1.19125 0.595625 0.803263i \(-0.296905\pi\)
0.595625 + 0.803263i \(0.296905\pi\)
\(588\) −2.70189e12 −0.932117
\(589\) −7.17708e11 −0.245714
\(590\) −1.89020e11 −0.0642205
\(591\) −2.10245e12 −0.708894
\(592\) −9.27977e12 −3.10520
\(593\) −7.77079e11 −0.258059 −0.129029 0.991641i \(-0.541186\pi\)
−0.129029 + 0.991641i \(0.541186\pi\)
\(594\) 1.83189e12 0.603755
\(595\) 6.85554e11 0.224241
\(596\) 4.59447e12 1.49151
\(597\) 1.31673e12 0.424240
\(598\) −1.47519e13 −4.71728
\(599\) 2.82723e11 0.0897305 0.0448653 0.998993i \(-0.485714\pi\)
0.0448653 + 0.998993i \(0.485714\pi\)
\(600\) 4.48852e12 1.41391
\(601\) −4.20251e10 −0.0131393 −0.00656967 0.999978i \(-0.502091\pi\)
−0.00656967 + 0.999978i \(0.502091\pi\)
\(602\) 1.52955e13 4.74655
\(603\) 7.66482e11 0.236088
\(604\) 2.68723e12 0.821559
\(605\) 1.64607e12 0.499516
\(606\) 2.09200e12 0.630136
\(607\) 2.73203e12 0.816839 0.408420 0.912794i \(-0.366080\pi\)
0.408420 + 0.912794i \(0.366080\pi\)
\(608\) −2.54451e12 −0.755157
\(609\) 6.63149e11 0.195359
\(610\) 7.00088e11 0.204724
\(611\) −6.59630e12 −1.91476
\(612\) −1.82808e12 −0.526762
\(613\) −2.96329e12 −0.847621 −0.423811 0.905751i \(-0.639308\pi\)
−0.423811 + 0.905751i \(0.639308\pi\)
\(614\) −8.30866e12 −2.35925
\(615\) −4.43153e11 −0.124915
\(616\) 2.06142e13 5.76836
\(617\) 5.24158e12 1.45606 0.728030 0.685546i \(-0.240436\pi\)
0.728030 + 0.685546i \(0.240436\pi\)
\(618\) −4.89590e12 −1.35016
\(619\) −2.75552e12 −0.754388 −0.377194 0.926134i \(-0.623111\pi\)
−0.377194 + 0.926134i \(0.623111\pi\)
\(620\) 1.47399e12 0.400621
\(621\) 9.19856e11 0.248203
\(622\) −4.29637e12 −1.15092
\(623\) −5.21127e12 −1.38595
\(624\) −1.06059e13 −2.80038
\(625\) 3.02080e12 0.791885
\(626\) −8.08881e12 −2.10523
\(627\) −1.50145e12 −0.387978
\(628\) −1.86667e12 −0.478904
\(629\) 3.23769e12 0.824721
\(630\) −8.39136e11 −0.212227
\(631\) −9.51357e11 −0.238897 −0.119449 0.992840i \(-0.538113\pi\)
−0.119449 + 0.992840i \(0.538113\pi\)
\(632\) −9.10839e12 −2.27099
\(633\) 4.47280e12 1.10729
\(634\) 4.91819e12 1.20894
\(635\) −1.17163e12 −0.285963
\(636\) 1.76471e12 0.427677
\(637\) 5.46913e12 1.31611
\(638\) −3.44198e12 −0.822460
\(639\) 1.38339e12 0.328239
\(640\) 8.78289e10 0.0206932
\(641\) −2.51210e12 −0.587727 −0.293863 0.955847i \(-0.594941\pi\)
−0.293863 + 0.955847i \(0.594941\pi\)
\(642\) 2.29425e12 0.533007
\(643\) 2.19703e12 0.506858 0.253429 0.967354i \(-0.418442\pi\)
0.253429 + 0.967354i \(0.418442\pi\)
\(644\) 1.76171e13 4.03598
\(645\) 1.34433e12 0.305836
\(646\) 2.11630e12 0.478114
\(647\) −5.47611e11 −0.122858 −0.0614289 0.998111i \(-0.519566\pi\)
−0.0614289 + 0.998111i \(0.519566\pi\)
\(648\) 1.31473e12 0.292921
\(649\) 9.97501e11 0.220705
\(650\) −1.54633e13 −3.39775
\(651\) 2.11678e12 0.461913
\(652\) 4.26520e12 0.924327
\(653\) 2.94473e12 0.633777 0.316888 0.948463i \(-0.397362\pi\)
0.316888 + 0.948463i \(0.397362\pi\)
\(654\) −3.99356e12 −0.853611
\(655\) 1.10355e12 0.234263
\(656\) 9.44776e12 1.99187
\(657\) −1.55941e12 −0.326526
\(658\) 1.11265e13 2.31389
\(659\) 5.47988e12 1.13184 0.565922 0.824459i \(-0.308520\pi\)
0.565922 + 0.824459i \(0.308520\pi\)
\(660\) 3.08361e12 0.632574
\(661\) −1.52775e12 −0.311277 −0.155639 0.987814i \(-0.549743\pi\)
−0.155639 + 0.987814i \(0.549743\pi\)
\(662\) 3.24447e12 0.656572
\(663\) 3.70038e12 0.743764
\(664\) 8.49796e12 1.69652
\(665\) 6.87771e11 0.136379
\(666\) −3.96302e12 −0.780534
\(667\) −1.72834e12 −0.338113
\(668\) −7.53477e12 −1.46412
\(669\) 2.33927e12 0.451505
\(670\) 1.82235e12 0.349378
\(671\) −3.69452e12 −0.703570
\(672\) 7.50465e12 1.41961
\(673\) −9.55006e12 −1.79448 −0.897239 0.441545i \(-0.854431\pi\)
−0.897239 + 0.441545i \(0.854431\pi\)
\(674\) 5.38289e12 1.00472
\(675\) 9.64218e11 0.178776
\(676\) 3.82629e13 7.04722
\(677\) −5.30001e12 −0.969678 −0.484839 0.874603i \(-0.661122\pi\)
−0.484839 + 0.874603i \(0.661122\pi\)
\(678\) 1.14398e13 2.07914
\(679\) 1.12706e13 2.03485
\(680\) −2.55374e12 −0.458022
\(681\) −3.39415e12 −0.604740
\(682\) −1.09868e13 −1.94465
\(683\) −6.30507e12 −1.10866 −0.554328 0.832298i \(-0.687025\pi\)
−0.554328 + 0.832298i \(0.687025\pi\)
\(684\) −1.83400e12 −0.320365
\(685\) 1.29661e12 0.225010
\(686\) 4.62905e12 0.798056
\(687\) −4.33673e12 −0.742774
\(688\) −2.86604e13 −4.87678
\(689\) −3.57210e12 −0.603861
\(690\) 2.18701e12 0.367307
\(691\) −3.35535e12 −0.559869 −0.279935 0.960019i \(-0.590313\pi\)
−0.279935 + 0.960019i \(0.590313\pi\)
\(692\) 8.78498e12 1.45634
\(693\) 4.42831e12 0.729354
\(694\) −2.08469e13 −3.41133
\(695\) −1.73646e12 −0.282314
\(696\) −2.47028e12 −0.399029
\(697\) −3.29630e12 −0.529028
\(698\) −8.20252e12 −1.30797
\(699\) 1.49195e12 0.236378
\(700\) 1.84667e13 2.90703
\(701\) −2.83738e12 −0.443800 −0.221900 0.975069i \(-0.571226\pi\)
−0.221900 + 0.975069i \(0.571226\pi\)
\(702\) −4.52936e12 −0.703914
\(703\) 3.24816e12 0.501578
\(704\) −1.18376e13 −1.81630
\(705\) 9.77921e11 0.149091
\(706\) −4.76484e12 −0.721818
\(707\) 5.05708e12 0.761224
\(708\) 1.21843e12 0.182243
\(709\) −5.61865e12 −0.835072 −0.417536 0.908660i \(-0.637106\pi\)
−0.417536 + 0.908660i \(0.637106\pi\)
\(710\) 3.28907e12 0.485748
\(711\) −1.95665e12 −0.287145
\(712\) 1.94124e13 2.83086
\(713\) −5.51686e12 −0.799447
\(714\) −6.24173e12 −0.898799
\(715\) −6.24179e12 −0.893165
\(716\) 2.49298e13 3.54496
\(717\) −1.65926e11 −0.0234466
\(718\) 2.09464e13 2.94137
\(719\) 1.31079e13 1.82916 0.914582 0.404400i \(-0.132520\pi\)
0.914582 + 0.404400i \(0.132520\pi\)
\(720\) 1.57236e12 0.218049
\(721\) −1.18351e13 −1.63103
\(722\) −1.13889e13 −1.55979
\(723\) −6.87588e12 −0.935849
\(724\) −4.39784e12 −0.594861
\(725\) −1.81169e12 −0.243536
\(726\) −1.49869e13 −2.00215
\(727\) 5.76955e12 0.766015 0.383007 0.923745i \(-0.374888\pi\)
0.383007 + 0.923745i \(0.374888\pi\)
\(728\) −5.09686e13 −6.72530
\(729\) 2.82430e11 0.0370370
\(730\) −3.70759e12 −0.483213
\(731\) 9.99952e12 1.29524
\(732\) −4.51280e12 −0.580960
\(733\) 9.88540e11 0.126481 0.0632406 0.997998i \(-0.479856\pi\)
0.0632406 + 0.997998i \(0.479856\pi\)
\(734\) 1.60744e13 2.04411
\(735\) −8.10814e11 −0.102477
\(736\) −1.95591e13 −2.45696
\(737\) −9.61695e12 −1.20070
\(738\) 4.03476e12 0.500684
\(739\) 1.28610e13 1.58627 0.793133 0.609048i \(-0.208448\pi\)
0.793133 + 0.609048i \(0.208448\pi\)
\(740\) −6.67091e12 −0.817791
\(741\) 3.71234e12 0.452341
\(742\) 6.02535e12 0.729734
\(743\) 5.72762e12 0.689485 0.344742 0.938697i \(-0.387966\pi\)
0.344742 + 0.938697i \(0.387966\pi\)
\(744\) −7.88516e12 −0.943479
\(745\) 1.37876e12 0.163978
\(746\) −6.35331e11 −0.0751061
\(747\) 1.82552e12 0.214508
\(748\) 2.29367e13 2.67901
\(749\) 5.54598e12 0.643888
\(750\) 4.76031e12 0.549363
\(751\) 4.82243e12 0.553205 0.276602 0.960984i \(-0.410792\pi\)
0.276602 + 0.960984i \(0.410792\pi\)
\(752\) −2.08487e13 −2.37738
\(753\) 1.36913e12 0.155191
\(754\) 8.51030e12 0.958902
\(755\) 8.06415e11 0.0903227
\(756\) 5.40910e12 0.602250
\(757\) 1.28784e13 1.42538 0.712691 0.701478i \(-0.247476\pi\)
0.712691 + 0.701478i \(0.247476\pi\)
\(758\) −2.29766e13 −2.52798
\(759\) −1.15413e13 −1.26231
\(760\) −2.56200e12 −0.278559
\(761\) 9.13156e12 0.986993 0.493497 0.869748i \(-0.335719\pi\)
0.493497 + 0.869748i \(0.335719\pi\)
\(762\) 1.06673e13 1.14619
\(763\) −9.65380e12 −1.03119
\(764\) −1.85637e12 −0.197126
\(765\) −5.48591e11 −0.0579125
\(766\) 1.29476e13 1.35882
\(767\) −2.46633e12 −0.257319
\(768\) 5.16404e12 0.535629
\(769\) −4.64263e12 −0.478735 −0.239368 0.970929i \(-0.576940\pi\)
−0.239368 + 0.970929i \(0.576940\pi\)
\(770\) 1.05285e13 1.07934
\(771\) 4.85420e12 0.494735
\(772\) 4.03296e13 4.08645
\(773\) 2.94706e12 0.296880 0.148440 0.988921i \(-0.452575\pi\)
0.148440 + 0.988921i \(0.452575\pi\)
\(774\) −1.22397e13 −1.22585
\(775\) −5.78293e12 −0.575824
\(776\) −4.19839e13 −4.15628
\(777\) −9.57997e12 −0.942909
\(778\) 2.14659e12 0.210059
\(779\) −3.30696e12 −0.321744
\(780\) −7.62423e12 −0.737514
\(781\) −1.73572e13 −1.66936
\(782\) 1.62675e13 1.55558
\(783\) −5.30663e11 −0.0504534
\(784\) 1.72861e13 1.63408
\(785\) −5.60171e11 −0.0526510
\(786\) −1.00474e13 −0.938971
\(787\) −9.75736e12 −0.906664 −0.453332 0.891342i \(-0.649765\pi\)
−0.453332 + 0.891342i \(0.649765\pi\)
\(788\) 3.22216e13 2.97700
\(789\) −2.93816e12 −0.269916
\(790\) −4.65204e12 −0.424934
\(791\) 2.76539e13 2.51167
\(792\) −1.64958e13 −1.48974
\(793\) 9.13473e12 0.820288
\(794\) −2.87776e13 −2.56958
\(795\) 5.29574e11 0.0470191
\(796\) −2.01799e13 −1.78160
\(797\) 6.01105e12 0.527701 0.263851 0.964564i \(-0.415007\pi\)
0.263851 + 0.964564i \(0.415007\pi\)
\(798\) −6.26191e12 −0.546631
\(799\) 7.27405e12 0.631416
\(800\) −2.05023e13 −1.76969
\(801\) 4.17014e12 0.357936
\(802\) −2.60208e13 −2.22094
\(803\) 1.95658e13 1.66064
\(804\) −1.17469e13 −0.991454
\(805\) 5.28674e12 0.443718
\(806\) 2.71650e13 2.26726
\(807\) −9.38722e12 −0.779123
\(808\) −1.88380e13 −1.55483
\(809\) −1.23728e13 −1.01555 −0.507773 0.861491i \(-0.669531\pi\)
−0.507773 + 0.861491i \(0.669531\pi\)
\(810\) 6.71491e11 0.0548097
\(811\) −8.95950e12 −0.727260 −0.363630 0.931543i \(-0.618463\pi\)
−0.363630 + 0.931543i \(0.618463\pi\)
\(812\) −1.01633e13 −0.820411
\(813\) −1.38910e13 −1.11513
\(814\) 4.97234e13 3.96964
\(815\) 1.27995e12 0.101621
\(816\) 1.16956e13 0.923459
\(817\) 1.00319e13 0.787739
\(818\) −2.74011e13 −2.13983
\(819\) −1.09490e13 −0.850350
\(820\) 6.79167e12 0.524583
\(821\) 1.10018e13 0.845119 0.422560 0.906335i \(-0.361132\pi\)
0.422560 + 0.906335i \(0.361132\pi\)
\(822\) −1.18052e13 −0.901883
\(823\) 2.28493e12 0.173610 0.0868049 0.996225i \(-0.472334\pi\)
0.0868049 + 0.996225i \(0.472334\pi\)
\(824\) 4.40866e13 3.33146
\(825\) −1.20979e13 −0.909218
\(826\) 4.16016e12 0.310956
\(827\) 1.56218e13 1.16133 0.580667 0.814141i \(-0.302792\pi\)
0.580667 + 0.814141i \(0.302792\pi\)
\(828\) −1.40975e13 −1.04233
\(829\) 1.00909e12 0.0742049 0.0371024 0.999311i \(-0.488187\pi\)
0.0371024 + 0.999311i \(0.488187\pi\)
\(830\) 4.34027e12 0.317443
\(831\) −1.21606e13 −0.884609
\(832\) 2.92687e13 2.11762
\(833\) −6.03106e12 −0.434001
\(834\) 1.58098e13 1.13157
\(835\) −2.26112e12 −0.160966
\(836\) 2.30109e13 1.62932
\(837\) −1.69388e12 −0.119294
\(838\) −2.80031e13 −1.96159
\(839\) −3.59545e11 −0.0250509 −0.0125255 0.999922i \(-0.503987\pi\)
−0.0125255 + 0.999922i \(0.503987\pi\)
\(840\) 7.55625e12 0.523660
\(841\) −1.35101e13 −0.931270
\(842\) −4.80298e13 −3.29311
\(843\) −2.15466e12 −0.146945
\(844\) −6.85492e13 −4.65009
\(845\) 1.14824e13 0.774776
\(846\) −8.90363e12 −0.597586
\(847\) −3.62285e13 −2.41866
\(848\) −1.12902e13 −0.749756
\(849\) 8.28371e12 0.547193
\(850\) 1.70521e13 1.12045
\(851\) 2.49679e13 1.63192
\(852\) −2.12015e13 −1.37844
\(853\) 2.42316e13 1.56715 0.783575 0.621297i \(-0.213394\pi\)
0.783575 + 0.621297i \(0.213394\pi\)
\(854\) −1.54083e13 −0.991275
\(855\) −5.50366e11 −0.0352212
\(856\) −2.06592e13 −1.31517
\(857\) 2.80505e13 1.77634 0.888172 0.459511i \(-0.151975\pi\)
0.888172 + 0.459511i \(0.151975\pi\)
\(858\) 5.68293e13 3.57997
\(859\) −1.00252e13 −0.628236 −0.314118 0.949384i \(-0.601709\pi\)
−0.314118 + 0.949384i \(0.601709\pi\)
\(860\) −2.06030e13 −1.28436
\(861\) 9.75339e12 0.604841
\(862\) 2.06651e12 0.127484
\(863\) −3.02313e13 −1.85527 −0.927637 0.373483i \(-0.878163\pi\)
−0.927637 + 0.373483i \(0.878163\pi\)
\(864\) −6.00534e12 −0.366628
\(865\) 2.63629e12 0.160111
\(866\) 2.66983e13 1.61307
\(867\) 5.52504e12 0.332085
\(868\) −3.24412e13 −1.93981
\(869\) 2.45499e13 1.46036
\(870\) −1.26168e12 −0.0746641
\(871\) 2.37780e13 1.39989
\(872\) 3.59612e13 2.10625
\(873\) −9.01892e12 −0.525522
\(874\) 1.63202e13 0.946069
\(875\) 1.15073e13 0.663647
\(876\) 2.38992e13 1.37125
\(877\) −2.53640e13 −1.44784 −0.723919 0.689885i \(-0.757661\pi\)
−0.723919 + 0.689885i \(0.757661\pi\)
\(878\) 1.73102e13 0.983052
\(879\) 7.72536e12 0.436485
\(880\) −1.97282e13 −1.10896
\(881\) 1.71470e13 0.958954 0.479477 0.877555i \(-0.340826\pi\)
0.479477 + 0.877555i \(0.340826\pi\)
\(882\) 7.38218e12 0.410749
\(883\) −1.20719e13 −0.668270 −0.334135 0.942525i \(-0.608444\pi\)
−0.334135 + 0.942525i \(0.608444\pi\)
\(884\) −5.67112e13 −3.12344
\(885\) 3.65640e11 0.0200359
\(886\) −1.62508e13 −0.885976
\(887\) −2.99407e13 −1.62408 −0.812038 0.583605i \(-0.801642\pi\)
−0.812038 + 0.583605i \(0.801642\pi\)
\(888\) 3.56861e13 1.92593
\(889\) 2.57866e13 1.38464
\(890\) 9.91473e12 0.529695
\(891\) −3.54361e12 −0.188363
\(892\) −3.58511e13 −1.89610
\(893\) 7.29757e12 0.384014
\(894\) −1.25531e13 −0.657254
\(895\) 7.48123e12 0.389735
\(896\) −1.93303e12 −0.100197
\(897\) 2.85360e13 1.47172
\(898\) −2.07921e13 −1.06697
\(899\) 3.18266e12 0.162507
\(900\) −1.47774e13 −0.750770
\(901\) 3.93912e12 0.199130
\(902\) −5.06236e13 −2.54638
\(903\) −2.95875e13 −1.48086
\(904\) −1.03013e14 −5.13019
\(905\) −1.31975e12 −0.0653994
\(906\) −7.34212e12 −0.362030
\(907\) 8.68316e12 0.426035 0.213017 0.977048i \(-0.431671\pi\)
0.213017 + 0.977048i \(0.431671\pi\)
\(908\) 5.20179e13 2.53961
\(909\) −4.04676e12 −0.196594
\(910\) −2.60318e13 −1.25840
\(911\) 1.40229e13 0.674534 0.337267 0.941409i \(-0.390498\pi\)
0.337267 + 0.941409i \(0.390498\pi\)
\(912\) 1.17335e13 0.561628
\(913\) −2.29046e13 −1.09095
\(914\) −1.35661e13 −0.642978
\(915\) −1.35425e12 −0.0638710
\(916\) 6.64637e13 3.11929
\(917\) −2.42880e13 −1.13430
\(918\) 4.99473e12 0.232124
\(919\) −1.36769e13 −0.632511 −0.316255 0.948674i \(-0.602426\pi\)
−0.316255 + 0.948674i \(0.602426\pi\)
\(920\) −1.96935e13 −0.906313
\(921\) 1.60723e13 0.736052
\(922\) 3.52111e13 1.60469
\(923\) 4.29157e13 1.94630
\(924\) −6.78673e13 −3.06293
\(925\) 2.61720e13 1.17544
\(926\) 7.63362e12 0.341178
\(927\) 9.47063e12 0.421231
\(928\) 1.12836e13 0.499437
\(929\) 1.30401e13 0.574392 0.287196 0.957872i \(-0.407277\pi\)
0.287196 + 0.957872i \(0.407277\pi\)
\(930\) −4.02728e12 −0.176538
\(931\) −6.05057e12 −0.263950
\(932\) −2.28653e13 −0.992669
\(933\) 8.31090e12 0.359071
\(934\) −2.18719e13 −0.940428
\(935\) 6.88310e12 0.294532
\(936\) 4.07859e13 1.73688
\(937\) −1.92359e13 −0.815240 −0.407620 0.913152i \(-0.633641\pi\)
−0.407620 + 0.913152i \(0.633641\pi\)
\(938\) −4.01083e13 −1.69169
\(939\) 1.56470e13 0.656804
\(940\) −1.49874e13 −0.626110
\(941\) 1.87901e13 0.781223 0.390611 0.920556i \(-0.372264\pi\)
0.390611 + 0.920556i \(0.372264\pi\)
\(942\) 5.10016e12 0.211035
\(943\) −2.54199e13 −1.04682
\(944\) −7.79522e12 −0.319488
\(945\) 1.62322e12 0.0662118
\(946\) 1.53570e14 6.23441
\(947\) −2.91972e13 −1.17968 −0.589842 0.807519i \(-0.700810\pi\)
−0.589842 + 0.807519i \(0.700810\pi\)
\(948\) 2.99872e13 1.20587
\(949\) −4.83765e13 −1.93614
\(950\) 1.71072e13 0.681434
\(951\) −9.51374e12 −0.377171
\(952\) 5.62055e13 2.21775
\(953\) −4.06016e13 −1.59450 −0.797252 0.603647i \(-0.793714\pi\)
−0.797252 + 0.603647i \(0.793714\pi\)
\(954\) −4.82159e12 −0.188461
\(955\) −5.57080e11 −0.0216722
\(956\) 2.54295e12 0.0984640
\(957\) 6.65815e12 0.256596
\(958\) 2.74219e13 1.05185
\(959\) −2.85372e13 −1.08950
\(960\) −4.33916e12 −0.164887
\(961\) −1.62805e13 −0.615763
\(962\) −1.22941e14 −4.62818
\(963\) −4.43799e12 −0.166291
\(964\) 1.05378e14 3.93010
\(965\) 1.21026e13 0.449267
\(966\) −4.81339e13 −1.77850
\(967\) 2.59922e13 0.955925 0.477962 0.878380i \(-0.341376\pi\)
0.477962 + 0.878380i \(0.341376\pi\)
\(968\) 1.34954e14 4.94023
\(969\) −4.09377e12 −0.149165
\(970\) −2.14429e13 −0.777699
\(971\) −2.78301e13 −1.00468 −0.502340 0.864670i \(-0.667527\pi\)
−0.502340 + 0.864670i \(0.667527\pi\)
\(972\) −4.32845e12 −0.155537
\(973\) 3.82178e13 1.36697
\(974\) 9.40044e13 3.34682
\(975\) 2.99122e13 1.06005
\(976\) 2.88718e13 1.01847
\(977\) 4.04890e13 1.42171 0.710856 0.703338i \(-0.248308\pi\)
0.710856 + 0.703338i \(0.248308\pi\)
\(978\) −1.16535e13 −0.407316
\(979\) −5.23223e13 −1.82039
\(980\) 1.24264e13 0.430355
\(981\) 7.72513e12 0.266315
\(982\) 1.71720e13 0.589277
\(983\) 4.11780e13 1.40661 0.703306 0.710888i \(-0.251707\pi\)
0.703306 + 0.710888i \(0.251707\pi\)
\(984\) −3.63322e13 −1.23542
\(985\) 9.66942e12 0.327294
\(986\) −9.38470e12 −0.316209
\(987\) −2.15231e13 −0.721902
\(988\) −5.68946e13 −1.89961
\(989\) 7.71127e13 2.56297
\(990\) −8.42510e12 −0.278751
\(991\) 4.17856e13 1.37624 0.688122 0.725595i \(-0.258435\pi\)
0.688122 + 0.725595i \(0.258435\pi\)
\(992\) 3.60172e13 1.18089
\(993\) −6.27609e12 −0.204841
\(994\) −7.23895e13 −2.35200
\(995\) −6.05581e12 −0.195870
\(996\) −2.79775e13 −0.900829
\(997\) 4.78707e13 1.53441 0.767206 0.641401i \(-0.221646\pi\)
0.767206 + 0.641401i \(0.221646\pi\)
\(998\) 5.13307e12 0.163791
\(999\) 7.66605e12 0.243516
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.1.20 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.20 21 1.1 even 1 trivial