Properties

Label 177.10.a.c.1.5
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
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: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-27.1769 q^{2} -81.0000 q^{3} +226.586 q^{4} -1812.37 q^{5} +2201.33 q^{6} -9882.92 q^{7} +7756.68 q^{8} +6561.00 q^{9} +49254.6 q^{10} +62941.6 q^{11} -18353.4 q^{12} +89682.6 q^{13} +268587. q^{14} +146802. q^{15} -326815. q^{16} -98165.2 q^{17} -178308. q^{18} -608747. q^{19} -410657. q^{20} +800517. q^{21} -1.71056e6 q^{22} -1.34425e6 q^{23} -628291. q^{24} +1.33155e6 q^{25} -2.43730e6 q^{26} -531441. q^{27} -2.23933e6 q^{28} +1.65081e6 q^{29} -3.98962e6 q^{30} -3.82270e6 q^{31} +4.91040e6 q^{32} -5.09827e6 q^{33} +2.66783e6 q^{34} +1.79115e7 q^{35} +1.48663e6 q^{36} -243314. q^{37} +1.65439e7 q^{38} -7.26429e6 q^{39} -1.40580e7 q^{40} -3.05708e7 q^{41} -2.17556e7 q^{42} -9.67346e6 q^{43} +1.42617e7 q^{44} -1.18909e7 q^{45} +3.65327e7 q^{46} -1.94397e7 q^{47} +2.64720e7 q^{48} +5.73185e7 q^{49} -3.61875e7 q^{50} +7.95138e6 q^{51} +2.03208e7 q^{52} -6.14911e7 q^{53} +1.44429e7 q^{54} -1.14073e8 q^{55} -7.66587e7 q^{56} +4.93085e7 q^{57} -4.48639e7 q^{58} +1.21174e7 q^{59} +3.32632e7 q^{60} -1.88500e8 q^{61} +1.03889e8 q^{62} -6.48418e7 q^{63} +3.38795e7 q^{64} -1.62538e8 q^{65} +1.38555e8 q^{66} +7.34365e7 q^{67} -2.22428e7 q^{68} +1.08884e8 q^{69} -4.86779e8 q^{70} -1.30229e8 q^{71} +5.08916e7 q^{72} +3.50993e7 q^{73} +6.61254e6 q^{74} -1.07856e8 q^{75} -1.37934e8 q^{76} -6.22047e8 q^{77} +1.97421e8 q^{78} -1.62826e8 q^{79} +5.92309e8 q^{80} +4.30467e7 q^{81} +8.30822e8 q^{82} +1.68987e8 q^{83} +1.81386e8 q^{84} +1.77911e8 q^{85} +2.62895e8 q^{86} -1.33716e8 q^{87} +4.88218e8 q^{88} -9.09234e8 q^{89} +3.23159e8 q^{90} -8.86326e8 q^{91} -3.04588e8 q^{92} +3.09639e8 q^{93} +5.28311e8 q^{94} +1.10327e9 q^{95} -3.97743e8 q^{96} +2.90211e7 q^{97} -1.55774e9 q^{98} +4.12960e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −27.1769 −1.20106 −0.600531 0.799601i \(-0.705044\pi\)
−0.600531 + 0.799601i \(0.705044\pi\)
\(3\) −81.0000 −0.577350
\(4\) 226.586 0.442550
\(5\) −1812.37 −1.29682 −0.648412 0.761289i \(-0.724567\pi\)
−0.648412 + 0.761289i \(0.724567\pi\)
\(6\) 2201.33 0.693434
\(7\) −9882.92 −1.55577 −0.777883 0.628409i \(-0.783706\pi\)
−0.777883 + 0.628409i \(0.783706\pi\)
\(8\) 7756.68 0.669532
\(9\) 6561.00 0.333333
\(10\) 49254.6 1.55757
\(11\) 62941.6 1.29620 0.648098 0.761557i \(-0.275565\pi\)
0.648098 + 0.761557i \(0.275565\pi\)
\(12\) −18353.4 −0.255507
\(13\) 89682.6 0.870890 0.435445 0.900215i \(-0.356591\pi\)
0.435445 + 0.900215i \(0.356591\pi\)
\(14\) 268587. 1.86857
\(15\) 146802. 0.748722
\(16\) −326815. −1.24670
\(17\) −98165.2 −0.285061 −0.142530 0.989790i \(-0.545524\pi\)
−0.142530 + 0.989790i \(0.545524\pi\)
\(18\) −178308. −0.400354
\(19\) −608747. −1.07163 −0.535816 0.844335i \(-0.679996\pi\)
−0.535816 + 0.844335i \(0.679996\pi\)
\(20\) −410657. −0.573910
\(21\) 800517. 0.898222
\(22\) −1.71056e6 −1.55681
\(23\) −1.34425e6 −1.00163 −0.500813 0.865556i \(-0.666966\pi\)
−0.500813 + 0.865556i \(0.666966\pi\)
\(24\) −628291. −0.386554
\(25\) 1.33155e6 0.681755
\(26\) −2.43730e6 −1.04599
\(27\) −531441. −0.192450
\(28\) −2.23933e6 −0.688505
\(29\) 1.65081e6 0.433417 0.216708 0.976236i \(-0.430468\pi\)
0.216708 + 0.976236i \(0.430468\pi\)
\(30\) −3.98962e6 −0.899262
\(31\) −3.82270e6 −0.743435 −0.371718 0.928346i \(-0.621231\pi\)
−0.371718 + 0.928346i \(0.621231\pi\)
\(32\) 4.91040e6 0.827832
\(33\) −5.09827e6 −0.748360
\(34\) 2.66783e6 0.342376
\(35\) 1.79115e7 2.01756
\(36\) 1.48663e6 0.147517
\(37\) −243314. −0.0213432 −0.0106716 0.999943i \(-0.503397\pi\)
−0.0106716 + 0.999943i \(0.503397\pi\)
\(38\) 1.65439e7 1.28710
\(39\) −7.26429e6 −0.502808
\(40\) −1.40580e7 −0.868265
\(41\) −3.05708e7 −1.68959 −0.844793 0.535094i \(-0.820276\pi\)
−0.844793 + 0.535094i \(0.820276\pi\)
\(42\) −2.17556e7 −1.07882
\(43\) −9.67346e6 −0.431493 −0.215746 0.976449i \(-0.569218\pi\)
−0.215746 + 0.976449i \(0.569218\pi\)
\(44\) 1.42617e7 0.573632
\(45\) −1.18909e7 −0.432275
\(46\) 3.65327e7 1.20301
\(47\) −1.94397e7 −0.581097 −0.290549 0.956860i \(-0.593838\pi\)
−0.290549 + 0.956860i \(0.593838\pi\)
\(48\) 2.64720e7 0.719782
\(49\) 5.73185e7 1.42041
\(50\) −3.61875e7 −0.818830
\(51\) 7.95138e6 0.164580
\(52\) 2.03208e7 0.385413
\(53\) −6.14911e7 −1.07046 −0.535231 0.844706i \(-0.679775\pi\)
−0.535231 + 0.844706i \(0.679775\pi\)
\(54\) 1.44429e7 0.231145
\(55\) −1.14073e8 −1.68094
\(56\) −7.66587e7 −1.04163
\(57\) 4.93085e7 0.618707
\(58\) −4.48639e7 −0.520561
\(59\) 1.21174e7 0.130189
\(60\) 3.32632e7 0.331347
\(61\) −1.88500e8 −1.74312 −0.871558 0.490293i \(-0.836890\pi\)
−0.871558 + 0.490293i \(0.836890\pi\)
\(62\) 1.03889e8 0.892912
\(63\) −6.48418e7 −0.518589
\(64\) 3.38795e7 0.252422
\(65\) −1.62538e8 −1.12939
\(66\) 1.38555e8 0.898827
\(67\) 7.34365e7 0.445221 0.222610 0.974907i \(-0.428542\pi\)
0.222610 + 0.974907i \(0.428542\pi\)
\(68\) −2.22428e7 −0.126154
\(69\) 1.08884e8 0.578289
\(70\) −4.86779e8 −2.42321
\(71\) −1.30229e8 −0.608196 −0.304098 0.952641i \(-0.598355\pi\)
−0.304098 + 0.952641i \(0.598355\pi\)
\(72\) 5.08916e7 0.223177
\(73\) 3.50993e7 0.144659 0.0723295 0.997381i \(-0.476957\pi\)
0.0723295 + 0.997381i \(0.476957\pi\)
\(74\) 6.61254e6 0.0256345
\(75\) −1.07856e8 −0.393611
\(76\) −1.37934e8 −0.474251
\(77\) −6.22047e8 −2.01658
\(78\) 1.97421e8 0.603904
\(79\) −1.62826e8 −0.470330 −0.235165 0.971955i \(-0.575563\pi\)
−0.235165 + 0.971955i \(0.575563\pi\)
\(80\) 5.92309e8 1.61675
\(81\) 4.30467e7 0.111111
\(82\) 8.30822e8 2.02930
\(83\) 1.68987e8 0.390843 0.195422 0.980719i \(-0.437392\pi\)
0.195422 + 0.980719i \(0.437392\pi\)
\(84\) 1.81386e8 0.397508
\(85\) 1.77911e8 0.369674
\(86\) 2.62895e8 0.518250
\(87\) −1.33716e8 −0.250233
\(88\) 4.88218e8 0.867845
\(89\) −9.09234e8 −1.53610 −0.768052 0.640387i \(-0.778774\pi\)
−0.768052 + 0.640387i \(0.778774\pi\)
\(90\) 3.23159e8 0.519189
\(91\) −8.86326e8 −1.35490
\(92\) −3.04588e8 −0.443270
\(93\) 3.09639e8 0.429223
\(94\) 5.28311e8 0.697934
\(95\) 1.10327e9 1.38972
\(96\) −3.97743e8 −0.477949
\(97\) 2.90211e7 0.0332844 0.0166422 0.999862i \(-0.494702\pi\)
0.0166422 + 0.999862i \(0.494702\pi\)
\(98\) −1.55774e9 −1.70600
\(99\) 4.12960e8 0.432066
\(100\) 3.01711e8 0.301711
\(101\) −1.28615e9 −1.22983 −0.614915 0.788593i \(-0.710810\pi\)
−0.614915 + 0.788593i \(0.710810\pi\)
\(102\) −2.16094e8 −0.197671
\(103\) 6.45125e8 0.564776 0.282388 0.959300i \(-0.408873\pi\)
0.282388 + 0.959300i \(0.408873\pi\)
\(104\) 6.95640e8 0.583088
\(105\) −1.45083e9 −1.16484
\(106\) 1.67114e9 1.28569
\(107\) −1.70524e9 −1.25765 −0.628824 0.777548i \(-0.716463\pi\)
−0.628824 + 0.777548i \(0.716463\pi\)
\(108\) −1.20417e8 −0.0851689
\(109\) 6.77929e8 0.460008 0.230004 0.973190i \(-0.426126\pi\)
0.230004 + 0.973190i \(0.426126\pi\)
\(110\) 3.10017e9 2.01891
\(111\) 1.97085e7 0.0123225
\(112\) 3.22988e9 1.93957
\(113\) −1.94114e9 −1.11996 −0.559981 0.828506i \(-0.689191\pi\)
−0.559981 + 0.828506i \(0.689191\pi\)
\(114\) −1.34005e9 −0.743106
\(115\) 2.43628e9 1.29893
\(116\) 3.74050e8 0.191809
\(117\) 5.88408e8 0.290297
\(118\) −3.29313e8 −0.156365
\(119\) 9.70159e8 0.443487
\(120\) 1.13870e9 0.501293
\(121\) 1.60370e9 0.680127
\(122\) 5.12284e9 2.09359
\(123\) 2.47624e9 0.975483
\(124\) −8.66171e8 −0.329008
\(125\) 1.12652e9 0.412708
\(126\) 1.76220e9 0.622857
\(127\) 3.92610e9 1.33920 0.669598 0.742724i \(-0.266466\pi\)
0.669598 + 0.742724i \(0.266466\pi\)
\(128\) −3.43487e9 −1.13101
\(129\) 7.83550e8 0.249123
\(130\) 4.41728e9 1.35647
\(131\) 1.25295e9 0.371717 0.185859 0.982576i \(-0.440493\pi\)
0.185859 + 0.982576i \(0.440493\pi\)
\(132\) −1.15520e9 −0.331187
\(133\) 6.01620e9 1.66721
\(134\) −1.99578e9 −0.534738
\(135\) 9.63167e8 0.249574
\(136\) −7.61436e8 −0.190857
\(137\) −5.77814e9 −1.40135 −0.700674 0.713482i \(-0.747117\pi\)
−0.700674 + 0.713482i \(0.747117\pi\)
\(138\) −2.95914e9 −0.694561
\(139\) −5.20118e8 −0.118178 −0.0590888 0.998253i \(-0.518820\pi\)
−0.0590888 + 0.998253i \(0.518820\pi\)
\(140\) 4.05849e9 0.892870
\(141\) 1.57461e9 0.335497
\(142\) 3.53921e9 0.730482
\(143\) 5.64477e9 1.12884
\(144\) −2.14423e9 −0.415567
\(145\) −2.99187e9 −0.562066
\(146\) −9.53892e8 −0.173745
\(147\) −4.64280e9 −0.820072
\(148\) −5.51316e7 −0.00944545
\(149\) −2.06805e9 −0.343734 −0.171867 0.985120i \(-0.554980\pi\)
−0.171867 + 0.985120i \(0.554980\pi\)
\(150\) 2.93119e9 0.472752
\(151\) −4.21433e9 −0.659678 −0.329839 0.944037i \(-0.606994\pi\)
−0.329839 + 0.944037i \(0.606994\pi\)
\(152\) −4.72186e9 −0.717492
\(153\) −6.44062e8 −0.0950202
\(154\) 1.69053e10 2.42204
\(155\) 6.92815e9 0.964105
\(156\) −1.64599e9 −0.222518
\(157\) −1.39983e9 −0.183876 −0.0919381 0.995765i \(-0.529306\pi\)
−0.0919381 + 0.995765i \(0.529306\pi\)
\(158\) 4.42512e9 0.564896
\(159\) 4.98078e9 0.618031
\(160\) −8.89946e9 −1.07355
\(161\) 1.32851e10 1.55829
\(162\) −1.16988e9 −0.133451
\(163\) −1.41964e10 −1.57519 −0.787595 0.616193i \(-0.788674\pi\)
−0.787595 + 0.616193i \(0.788674\pi\)
\(164\) −6.92692e9 −0.747727
\(165\) 9.23995e9 0.970492
\(166\) −4.59256e9 −0.469427
\(167\) 8.20821e9 0.816628 0.408314 0.912841i \(-0.366117\pi\)
0.408314 + 0.912841i \(0.366117\pi\)
\(168\) 6.20935e9 0.601388
\(169\) −2.56153e9 −0.241551
\(170\) −4.83509e9 −0.444001
\(171\) −3.99399e9 −0.357211
\(172\) −2.19187e9 −0.190957
\(173\) 1.55232e10 1.31757 0.658784 0.752332i \(-0.271071\pi\)
0.658784 + 0.752332i \(0.271071\pi\)
\(174\) 3.63398e9 0.300546
\(175\) −1.31596e10 −1.06065
\(176\) −2.05703e10 −1.61597
\(177\) −9.81506e8 −0.0751646
\(178\) 2.47102e10 1.84496
\(179\) −3.36293e9 −0.244838 −0.122419 0.992478i \(-0.539065\pi\)
−0.122419 + 0.992478i \(0.539065\pi\)
\(180\) −2.69432e9 −0.191303
\(181\) 1.83171e10 1.26854 0.634268 0.773113i \(-0.281301\pi\)
0.634268 + 0.773113i \(0.281301\pi\)
\(182\) 2.40876e10 1.62732
\(183\) 1.52685e10 1.00639
\(184\) −1.04269e10 −0.670620
\(185\) 4.40975e8 0.0276784
\(186\) −8.41504e9 −0.515523
\(187\) −6.17868e9 −0.369495
\(188\) −4.40476e9 −0.257165
\(189\) 5.25219e9 0.299407
\(190\) −2.99836e10 −1.66914
\(191\) −1.90964e10 −1.03825 −0.519125 0.854698i \(-0.673742\pi\)
−0.519125 + 0.854698i \(0.673742\pi\)
\(192\) −2.74424e9 −0.145736
\(193\) −3.18478e9 −0.165224 −0.0826118 0.996582i \(-0.526326\pi\)
−0.0826118 + 0.996582i \(0.526326\pi\)
\(194\) −7.88705e8 −0.0399767
\(195\) 1.31656e10 0.652054
\(196\) 1.29876e10 0.628601
\(197\) 2.09373e10 0.990428 0.495214 0.868771i \(-0.335090\pi\)
0.495214 + 0.868771i \(0.335090\pi\)
\(198\) −1.12230e10 −0.518938
\(199\) −2.41219e9 −0.109037 −0.0545183 0.998513i \(-0.517362\pi\)
−0.0545183 + 0.998513i \(0.517362\pi\)
\(200\) 1.03284e10 0.456457
\(201\) −5.94836e9 −0.257048
\(202\) 3.49536e10 1.47710
\(203\) −1.63148e10 −0.674295
\(204\) 1.80167e9 0.0728349
\(205\) 5.54056e10 2.19110
\(206\) −1.75325e10 −0.678331
\(207\) −8.81964e9 −0.333875
\(208\) −2.93096e10 −1.08574
\(209\) −3.83156e10 −1.38905
\(210\) 3.94291e10 1.39904
\(211\) −2.71223e10 −0.942011 −0.471005 0.882130i \(-0.656109\pi\)
−0.471005 + 0.882130i \(0.656109\pi\)
\(212\) −1.39330e10 −0.473733
\(213\) 1.05485e10 0.351142
\(214\) 4.63433e10 1.51051
\(215\) 1.75319e10 0.559571
\(216\) −4.12222e9 −0.128851
\(217\) 3.77795e10 1.15661
\(218\) −1.84240e10 −0.552498
\(219\) −2.84304e9 −0.0835190
\(220\) −2.58474e10 −0.743901
\(221\) −8.80371e9 −0.248256
\(222\) −5.35616e8 −0.0148001
\(223\) −2.52230e9 −0.0683006 −0.0341503 0.999417i \(-0.510872\pi\)
−0.0341503 + 0.999417i \(0.510872\pi\)
\(224\) −4.85291e10 −1.28791
\(225\) 8.73632e9 0.227252
\(226\) 5.27541e10 1.34514
\(227\) 5.18221e10 1.29538 0.647692 0.761902i \(-0.275734\pi\)
0.647692 + 0.761902i \(0.275734\pi\)
\(228\) 1.11726e10 0.273809
\(229\) −3.31362e10 −0.796239 −0.398120 0.917334i \(-0.630337\pi\)
−0.398120 + 0.917334i \(0.630337\pi\)
\(230\) −6.62106e10 −1.56010
\(231\) 5.03858e10 1.16427
\(232\) 1.28048e10 0.290186
\(233\) −7.47758e10 −1.66211 −0.831054 0.556192i \(-0.812262\pi\)
−0.831054 + 0.556192i \(0.812262\pi\)
\(234\) −1.59911e10 −0.348664
\(235\) 3.52319e10 0.753582
\(236\) 2.74562e9 0.0576152
\(237\) 1.31889e10 0.271545
\(238\) −2.63659e10 −0.532656
\(239\) −9.52011e10 −1.88735 −0.943673 0.330881i \(-0.892654\pi\)
−0.943673 + 0.330881i \(0.892654\pi\)
\(240\) −4.79770e10 −0.933432
\(241\) −5.45165e10 −1.04100 −0.520501 0.853861i \(-0.674255\pi\)
−0.520501 + 0.853861i \(0.674255\pi\)
\(242\) −4.35837e10 −0.816874
\(243\) −3.48678e9 −0.0641500
\(244\) −4.27113e10 −0.771416
\(245\) −1.03882e11 −1.84202
\(246\) −6.72966e10 −1.17162
\(247\) −5.45940e10 −0.933274
\(248\) −2.96515e10 −0.497753
\(249\) −1.36880e10 −0.225654
\(250\) −3.06153e10 −0.495688
\(251\) 7.23992e10 1.15134 0.575668 0.817684i \(-0.304742\pi\)
0.575668 + 0.817684i \(0.304742\pi\)
\(252\) −1.46922e10 −0.229502
\(253\) −8.46094e10 −1.29830
\(254\) −1.06699e11 −1.60846
\(255\) −1.44108e10 −0.213431
\(256\) 7.60029e10 1.10599
\(257\) −2.94793e10 −0.421520 −0.210760 0.977538i \(-0.567594\pi\)
−0.210760 + 0.977538i \(0.567594\pi\)
\(258\) −2.12945e10 −0.299212
\(259\) 2.40466e9 0.0332051
\(260\) −3.68288e10 −0.499813
\(261\) 1.08310e10 0.144472
\(262\) −3.40513e10 −0.446456
\(263\) −1.25248e11 −1.61425 −0.807125 0.590381i \(-0.798978\pi\)
−0.807125 + 0.590381i \(0.798978\pi\)
\(264\) −3.95457e10 −0.501050
\(265\) 1.11445e11 1.38820
\(266\) −1.63502e11 −2.00242
\(267\) 7.36479e10 0.886870
\(268\) 1.66397e10 0.197033
\(269\) 1.23969e11 1.44354 0.721771 0.692132i \(-0.243329\pi\)
0.721771 + 0.692132i \(0.243329\pi\)
\(270\) −2.61759e10 −0.299754
\(271\) 1.03554e11 1.16628 0.583142 0.812370i \(-0.301823\pi\)
0.583142 + 0.812370i \(0.301823\pi\)
\(272\) 3.20818e10 0.355385
\(273\) 7.17924e10 0.782252
\(274\) 1.57032e11 1.68311
\(275\) 8.38101e10 0.883689
\(276\) 2.46717e10 0.255922
\(277\) 1.34895e11 1.37669 0.688344 0.725384i \(-0.258338\pi\)
0.688344 + 0.725384i \(0.258338\pi\)
\(278\) 1.41352e10 0.141939
\(279\) −2.50808e10 −0.247812
\(280\) 1.38934e11 1.35082
\(281\) −1.34882e11 −1.29055 −0.645274 0.763951i \(-0.723257\pi\)
−0.645274 + 0.763951i \(0.723257\pi\)
\(282\) −4.27932e10 −0.402952
\(283\) 1.81349e11 1.68065 0.840324 0.542085i \(-0.182365\pi\)
0.840324 + 0.542085i \(0.182365\pi\)
\(284\) −2.95080e10 −0.269158
\(285\) −8.93652e10 −0.802355
\(286\) −1.53408e11 −1.35581
\(287\) 3.02129e11 2.62860
\(288\) 3.22172e10 0.275944
\(289\) −1.08951e11 −0.918740
\(290\) 8.13100e10 0.675076
\(291\) −2.35071e9 −0.0192168
\(292\) 7.95301e9 0.0640189
\(293\) −2.12229e11 −1.68229 −0.841145 0.540809i \(-0.818118\pi\)
−0.841145 + 0.540809i \(0.818118\pi\)
\(294\) 1.26177e11 0.984957
\(295\) −2.19611e10 −0.168832
\(296\) −1.88731e9 −0.0142900
\(297\) −3.34498e10 −0.249453
\(298\) 5.62032e10 0.412845
\(299\) −1.20556e11 −0.872305
\(300\) −2.44386e10 −0.174193
\(301\) 9.56020e10 0.671302
\(302\) 1.14532e11 0.792314
\(303\) 1.04178e11 0.710043
\(304\) 1.98948e11 1.33600
\(305\) 3.41631e11 2.26052
\(306\) 1.75036e10 0.114125
\(307\) 2.37092e10 0.152333 0.0761665 0.997095i \(-0.475732\pi\)
0.0761665 + 0.997095i \(0.475732\pi\)
\(308\) −1.40947e11 −0.892438
\(309\) −5.22551e10 −0.326074
\(310\) −1.88286e11 −1.15795
\(311\) −2.29292e11 −1.38985 −0.694924 0.719083i \(-0.744562\pi\)
−0.694924 + 0.719083i \(0.744562\pi\)
\(312\) −5.63468e10 −0.336646
\(313\) −6.41849e9 −0.0377993 −0.0188996 0.999821i \(-0.506016\pi\)
−0.0188996 + 0.999821i \(0.506016\pi\)
\(314\) 3.80430e10 0.220847
\(315\) 1.17517e11 0.672519
\(316\) −3.68942e10 −0.208145
\(317\) 2.31514e11 1.28769 0.643843 0.765158i \(-0.277339\pi\)
0.643843 + 0.765158i \(0.277339\pi\)
\(318\) −1.35362e11 −0.742294
\(319\) 1.03905e11 0.561794
\(320\) −6.14021e10 −0.327347
\(321\) 1.38125e11 0.726103
\(322\) −3.61049e11 −1.87161
\(323\) 5.97578e10 0.305480
\(324\) 9.75378e9 0.0491723
\(325\) 1.19417e11 0.593733
\(326\) 3.85814e11 1.89190
\(327\) −5.49122e10 −0.265585
\(328\) −2.37128e11 −1.13123
\(329\) 1.92121e11 0.904051
\(330\) −2.51113e11 −1.16562
\(331\) 2.77864e11 1.27235 0.636176 0.771544i \(-0.280515\pi\)
0.636176 + 0.771544i \(0.280515\pi\)
\(332\) 3.82901e10 0.172968
\(333\) −1.59639e9 −0.00711441
\(334\) −2.23074e11 −0.980822
\(335\) −1.33094e11 −0.577373
\(336\) −2.61621e11 −1.11981
\(337\) −4.22215e11 −1.78320 −0.891599 0.452826i \(-0.850416\pi\)
−0.891599 + 0.452826i \(0.850416\pi\)
\(338\) 6.96145e10 0.290118
\(339\) 1.57232e11 0.646610
\(340\) 4.03122e10 0.163599
\(341\) −2.40607e11 −0.963638
\(342\) 1.08544e11 0.429032
\(343\) −1.67663e11 −0.654054
\(344\) −7.50339e10 −0.288898
\(345\) −1.97339e11 −0.749939
\(346\) −4.21873e11 −1.58248
\(347\) −3.69232e11 −1.36715 −0.683575 0.729880i \(-0.739576\pi\)
−0.683575 + 0.729880i \(0.739576\pi\)
\(348\) −3.02980e10 −0.110741
\(349\) 1.31293e11 0.473725 0.236863 0.971543i \(-0.423881\pi\)
0.236863 + 0.971543i \(0.423881\pi\)
\(350\) 3.57638e11 1.27391
\(351\) −4.76610e10 −0.167603
\(352\) 3.09069e11 1.07303
\(353\) −2.30328e11 −0.789516 −0.394758 0.918785i \(-0.629172\pi\)
−0.394758 + 0.918785i \(0.629172\pi\)
\(354\) 2.66743e10 0.0902774
\(355\) 2.36022e11 0.788724
\(356\) −2.06020e11 −0.679803
\(357\) −7.85828e10 −0.256048
\(358\) 9.13942e10 0.294066
\(359\) −3.73488e11 −1.18673 −0.593364 0.804934i \(-0.702201\pi\)
−0.593364 + 0.804934i \(0.702201\pi\)
\(360\) −9.22343e10 −0.289422
\(361\) 4.78856e10 0.148396
\(362\) −4.97802e11 −1.52359
\(363\) −1.29900e11 −0.392671
\(364\) −2.00829e11 −0.599612
\(365\) −6.36129e10 −0.187598
\(366\) −4.14950e11 −1.20873
\(367\) 3.81640e11 1.09814 0.549069 0.835777i \(-0.314983\pi\)
0.549069 + 0.835777i \(0.314983\pi\)
\(368\) 4.39321e11 1.24873
\(369\) −2.00575e11 −0.563195
\(370\) −1.19844e10 −0.0332435
\(371\) 6.07712e11 1.66539
\(372\) 7.01598e10 0.189953
\(373\) 4.77457e11 1.27716 0.638579 0.769556i \(-0.279523\pi\)
0.638579 + 0.769556i \(0.279523\pi\)
\(374\) 1.67917e11 0.443786
\(375\) −9.12479e10 −0.238277
\(376\) −1.50787e11 −0.389063
\(377\) 1.48049e11 0.377458
\(378\) −1.42738e11 −0.359607
\(379\) −3.30291e11 −0.822281 −0.411141 0.911572i \(-0.634869\pi\)
−0.411141 + 0.911572i \(0.634869\pi\)
\(380\) 2.49986e11 0.615021
\(381\) −3.18014e11 −0.773185
\(382\) 5.18982e11 1.24700
\(383\) 7.45540e11 1.77042 0.885210 0.465191i \(-0.154015\pi\)
0.885210 + 0.465191i \(0.154015\pi\)
\(384\) 2.78224e11 0.652987
\(385\) 1.12738e12 2.61515
\(386\) 8.65527e10 0.198444
\(387\) −6.34675e10 −0.143831
\(388\) 6.57577e9 0.0147300
\(389\) −3.66578e11 −0.811695 −0.405847 0.913941i \(-0.633024\pi\)
−0.405847 + 0.913941i \(0.633024\pi\)
\(390\) −3.57800e11 −0.783158
\(391\) 1.31959e11 0.285524
\(392\) 4.44602e11 0.951007
\(393\) −1.01489e11 −0.214611
\(394\) −5.69012e11 −1.18957
\(395\) 2.95102e11 0.609936
\(396\) 9.35709e10 0.191211
\(397\) 6.83450e11 1.38086 0.690430 0.723399i \(-0.257421\pi\)
0.690430 + 0.723399i \(0.257421\pi\)
\(398\) 6.55558e10 0.130960
\(399\) −4.87312e11 −0.962564
\(400\) −4.35171e11 −0.849944
\(401\) −5.64066e11 −1.08938 −0.544691 0.838637i \(-0.683353\pi\)
−0.544691 + 0.838637i \(0.683353\pi\)
\(402\) 1.61658e11 0.308731
\(403\) −3.42830e11 −0.647450
\(404\) −2.91423e11 −0.544262
\(405\) −7.80165e10 −0.144092
\(406\) 4.43387e11 0.809870
\(407\) −1.53146e10 −0.0276650
\(408\) 6.16763e10 0.110191
\(409\) 2.61742e11 0.462507 0.231253 0.972894i \(-0.425717\pi\)
0.231253 + 0.972894i \(0.425717\pi\)
\(410\) −1.50576e12 −2.63164
\(411\) 4.68030e11 0.809068
\(412\) 1.46176e11 0.249942
\(413\) −1.19755e11 −0.202543
\(414\) 2.39691e11 0.401005
\(415\) −3.06267e11 −0.506855
\(416\) 4.40378e11 0.720950
\(417\) 4.21296e10 0.0682299
\(418\) 1.04130e12 1.66833
\(419\) 2.60416e11 0.412767 0.206384 0.978471i \(-0.433831\pi\)
0.206384 + 0.978471i \(0.433831\pi\)
\(420\) −3.28738e11 −0.515499
\(421\) 4.17072e11 0.647056 0.323528 0.946219i \(-0.395131\pi\)
0.323528 + 0.946219i \(0.395131\pi\)
\(422\) 7.37102e11 1.13141
\(423\) −1.27544e11 −0.193699
\(424\) −4.76967e11 −0.716708
\(425\) −1.30712e11 −0.194342
\(426\) −2.86676e11 −0.421744
\(427\) 1.86293e12 2.71188
\(428\) −3.86384e11 −0.556573
\(429\) −4.57226e11 −0.651739
\(430\) −4.76462e11 −0.672079
\(431\) 6.74040e11 0.940888 0.470444 0.882430i \(-0.344094\pi\)
0.470444 + 0.882430i \(0.344094\pi\)
\(432\) 1.73683e11 0.239927
\(433\) −4.17035e11 −0.570135 −0.285067 0.958508i \(-0.592016\pi\)
−0.285067 + 0.958508i \(0.592016\pi\)
\(434\) −1.02673e12 −1.38916
\(435\) 2.42342e11 0.324509
\(436\) 1.53609e11 0.203577
\(437\) 8.18310e11 1.07337
\(438\) 7.72652e10 0.100311
\(439\) −1.26557e12 −1.62628 −0.813142 0.582065i \(-0.802245\pi\)
−0.813142 + 0.582065i \(0.802245\pi\)
\(440\) −8.84831e11 −1.12544
\(441\) 3.76067e11 0.473469
\(442\) 2.39258e11 0.298171
\(443\) −1.04011e12 −1.28310 −0.641552 0.767079i \(-0.721709\pi\)
−0.641552 + 0.767079i \(0.721709\pi\)
\(444\) 4.46566e9 0.00545333
\(445\) 1.64787e12 1.99206
\(446\) 6.85483e10 0.0820333
\(447\) 1.67512e11 0.198455
\(448\) −3.34828e11 −0.392709
\(449\) 1.09333e12 1.26953 0.634766 0.772704i \(-0.281096\pi\)
0.634766 + 0.772704i \(0.281096\pi\)
\(450\) −2.37426e11 −0.272943
\(451\) −1.92418e12 −2.19004
\(452\) −4.39834e11 −0.495639
\(453\) 3.41360e11 0.380865
\(454\) −1.40837e12 −1.55584
\(455\) 1.60635e12 1.75707
\(456\) 3.82471e11 0.414244
\(457\) 6.82471e10 0.0731917 0.0365958 0.999330i \(-0.488349\pi\)
0.0365958 + 0.999330i \(0.488349\pi\)
\(458\) 9.00541e11 0.956333
\(459\) 5.21690e10 0.0548599
\(460\) 5.52026e11 0.574843
\(461\) 3.89708e11 0.401869 0.200935 0.979605i \(-0.435602\pi\)
0.200935 + 0.979605i \(0.435602\pi\)
\(462\) −1.36933e12 −1.39836
\(463\) 1.41589e12 1.43191 0.715953 0.698149i \(-0.245993\pi\)
0.715953 + 0.698149i \(0.245993\pi\)
\(464\) −5.39509e11 −0.540341
\(465\) −5.61180e11 −0.556626
\(466\) 2.03218e12 1.99629
\(467\) 9.91833e11 0.964967 0.482484 0.875905i \(-0.339735\pi\)
0.482484 + 0.875905i \(0.339735\pi\)
\(468\) 1.33325e11 0.128471
\(469\) −7.25767e11 −0.692659
\(470\) −9.57494e11 −0.905098
\(471\) 1.13386e11 0.106161
\(472\) 9.39905e10 0.0871656
\(473\) −6.08863e11 −0.559300
\(474\) −3.58435e11 −0.326143
\(475\) −8.10579e11 −0.730591
\(476\) 2.19824e11 0.196266
\(477\) −4.03443e11 −0.356820
\(478\) 2.58727e12 2.26682
\(479\) 8.44724e11 0.733171 0.366585 0.930384i \(-0.380527\pi\)
0.366585 + 0.930384i \(0.380527\pi\)
\(480\) 7.20856e11 0.619816
\(481\) −2.18211e10 −0.0185876
\(482\) 1.48159e12 1.25031
\(483\) −1.07610e12 −0.899682
\(484\) 3.63376e11 0.300990
\(485\) −5.25969e10 −0.0431641
\(486\) 9.47601e10 0.0770482
\(487\) −1.17244e12 −0.944521 −0.472260 0.881459i \(-0.656562\pi\)
−0.472260 + 0.881459i \(0.656562\pi\)
\(488\) −1.46213e12 −1.16707
\(489\) 1.14991e12 0.909437
\(490\) 2.82320e12 2.21238
\(491\) −2.02446e9 −0.00157196 −0.000785982 1.00000i \(-0.500250\pi\)
−0.000785982 1.00000i \(0.500250\pi\)
\(492\) 5.61081e11 0.431700
\(493\) −1.62052e11 −0.123550
\(494\) 1.48370e12 1.12092
\(495\) −7.48436e11 −0.560314
\(496\) 1.24932e12 0.926840
\(497\) 1.28704e12 0.946211
\(498\) 3.71997e11 0.271024
\(499\) −2.63096e12 −1.89960 −0.949799 0.312861i \(-0.898713\pi\)
−0.949799 + 0.312861i \(0.898713\pi\)
\(500\) 2.55253e11 0.182644
\(501\) −6.64865e11 −0.471481
\(502\) −1.96759e12 −1.38283
\(503\) 2.12291e11 0.147869 0.0739343 0.997263i \(-0.476444\pi\)
0.0739343 + 0.997263i \(0.476444\pi\)
\(504\) −5.02958e11 −0.347211
\(505\) 2.33098e12 1.59487
\(506\) 2.29943e12 1.55934
\(507\) 2.07484e11 0.139460
\(508\) 8.89598e11 0.592662
\(509\) −1.45955e12 −0.963802 −0.481901 0.876226i \(-0.660054\pi\)
−0.481901 + 0.876226i \(0.660054\pi\)
\(510\) 3.91642e11 0.256344
\(511\) −3.46884e11 −0.225056
\(512\) −3.06873e11 −0.197353
\(513\) 3.23513e11 0.206236
\(514\) 8.01157e11 0.506272
\(515\) −1.16920e12 −0.732416
\(516\) 1.77541e11 0.110249
\(517\) −1.22357e12 −0.753217
\(518\) −6.53512e10 −0.0398813
\(519\) −1.25738e12 −0.760699
\(520\) −1.26075e12 −0.756163
\(521\) 1.80721e12 1.07458 0.537291 0.843397i \(-0.319448\pi\)
0.537291 + 0.843397i \(0.319448\pi\)
\(522\) −2.94352e11 −0.173520
\(523\) 1.21170e12 0.708169 0.354084 0.935213i \(-0.384793\pi\)
0.354084 + 0.935213i \(0.384793\pi\)
\(524\) 2.83901e11 0.164504
\(525\) 1.06593e12 0.612367
\(526\) 3.40386e12 1.93881
\(527\) 3.75256e11 0.211924
\(528\) 1.66619e12 0.932980
\(529\) 5.86089e9 0.00325397
\(530\) −3.02872e12 −1.66732
\(531\) 7.95020e10 0.0433963
\(532\) 1.36319e12 0.737824
\(533\) −2.74167e12 −1.47144
\(534\) −2.00153e12 −1.06519
\(535\) 3.09053e12 1.63095
\(536\) 5.69624e11 0.298089
\(537\) 2.72397e11 0.141357
\(538\) −3.36911e12 −1.73378
\(539\) 3.60772e12 1.84113
\(540\) 2.18240e11 0.110449
\(541\) −8.78587e11 −0.440958 −0.220479 0.975392i \(-0.570762\pi\)
−0.220479 + 0.975392i \(0.570762\pi\)
\(542\) −2.81428e12 −1.40078
\(543\) −1.48368e12 −0.732390
\(544\) −4.82030e11 −0.235982
\(545\) −1.22866e12 −0.596549
\(546\) −1.95110e12 −0.939533
\(547\) −5.44010e11 −0.259815 −0.129908 0.991526i \(-0.541468\pi\)
−0.129908 + 0.991526i \(0.541468\pi\)
\(548\) −1.30925e12 −0.620167
\(549\) −1.23675e12 −0.581038
\(550\) −2.27770e12 −1.06137
\(551\) −1.00493e12 −0.464464
\(552\) 8.44582e11 0.387183
\(553\) 1.60920e12 0.731724
\(554\) −3.66602e12 −1.65349
\(555\) −3.57190e10 −0.0159801
\(556\) −1.17851e11 −0.0522996
\(557\) 2.33872e11 0.102951 0.0514754 0.998674i \(-0.483608\pi\)
0.0514754 + 0.998674i \(0.483608\pi\)
\(558\) 6.81618e11 0.297637
\(559\) −8.67541e11 −0.375783
\(560\) −5.85374e12 −2.51529
\(561\) 5.00473e11 0.213328
\(562\) 3.66567e12 1.55003
\(563\) −2.84490e11 −0.119338 −0.0596691 0.998218i \(-0.519005\pi\)
−0.0596691 + 0.998218i \(0.519005\pi\)
\(564\) 3.56785e11 0.148474
\(565\) 3.51805e12 1.45239
\(566\) −4.92851e12 −2.01856
\(567\) −4.25427e11 −0.172863
\(568\) −1.01014e12 −0.407207
\(569\) 1.45327e12 0.581219 0.290609 0.956842i \(-0.406142\pi\)
0.290609 + 0.956842i \(0.406142\pi\)
\(570\) 2.42867e12 0.963678
\(571\) 9.73987e11 0.383434 0.191717 0.981450i \(-0.438594\pi\)
0.191717 + 0.981450i \(0.438594\pi\)
\(572\) 1.27902e12 0.499571
\(573\) 1.54681e12 0.599434
\(574\) −8.21095e12 −3.15711
\(575\) −1.78994e12 −0.682863
\(576\) 2.22283e11 0.0841406
\(577\) −1.87758e12 −0.705193 −0.352597 0.935775i \(-0.614701\pi\)
−0.352597 + 0.935775i \(0.614701\pi\)
\(578\) 2.96097e12 1.10346
\(579\) 2.57967e11 0.0953919
\(580\) −6.77916e11 −0.248742
\(581\) −1.67009e12 −0.608061
\(582\) 6.38851e10 0.0230805
\(583\) −3.87035e12 −1.38753
\(584\) 2.72254e11 0.0968538
\(585\) −1.06641e12 −0.376464
\(586\) 5.76774e12 2.02054
\(587\) −2.01696e12 −0.701172 −0.350586 0.936530i \(-0.614018\pi\)
−0.350586 + 0.936530i \(0.614018\pi\)
\(588\) −1.05199e12 −0.362923
\(589\) 2.32706e12 0.796689
\(590\) 5.96836e11 0.202778
\(591\) −1.69592e12 −0.571824
\(592\) 7.95187e10 0.0266086
\(593\) −2.70917e12 −0.899683 −0.449841 0.893108i \(-0.648520\pi\)
−0.449841 + 0.893108i \(0.648520\pi\)
\(594\) 9.09062e11 0.299609
\(595\) −1.75828e12 −0.575126
\(596\) −4.68590e11 −0.152119
\(597\) 1.95387e11 0.0629523
\(598\) 3.27634e12 1.04769
\(599\) 1.83662e12 0.582906 0.291453 0.956585i \(-0.405861\pi\)
0.291453 + 0.956585i \(0.405861\pi\)
\(600\) −8.36603e11 −0.263535
\(601\) −3.08070e12 −0.963195 −0.481598 0.876393i \(-0.659943\pi\)
−0.481598 + 0.876393i \(0.659943\pi\)
\(602\) −2.59817e12 −0.806275
\(603\) 4.81817e11 0.148407
\(604\) −9.54906e11 −0.291941
\(605\) −2.90650e12 −0.882005
\(606\) −2.83124e12 −0.852806
\(607\) −8.15369e11 −0.243784 −0.121892 0.992543i \(-0.538896\pi\)
−0.121892 + 0.992543i \(0.538896\pi\)
\(608\) −2.98919e12 −0.887132
\(609\) 1.32150e12 0.389304
\(610\) −9.28447e12 −2.71502
\(611\) −1.74340e12 −0.506072
\(612\) −1.45935e11 −0.0420512
\(613\) 4.96108e12 1.41907 0.709535 0.704670i \(-0.248905\pi\)
0.709535 + 0.704670i \(0.248905\pi\)
\(614\) −6.44343e11 −0.182961
\(615\) −4.48786e12 −1.26503
\(616\) −4.82502e12 −1.35016
\(617\) 1.62700e12 0.451965 0.225982 0.974131i \(-0.427441\pi\)
0.225982 + 0.974131i \(0.427441\pi\)
\(618\) 1.42013e12 0.391635
\(619\) 3.32891e12 0.911368 0.455684 0.890142i \(-0.349395\pi\)
0.455684 + 0.890142i \(0.349395\pi\)
\(620\) 1.56982e12 0.426665
\(621\) 7.14391e11 0.192763
\(622\) 6.23145e12 1.66929
\(623\) 8.98589e12 2.38982
\(624\) 2.37408e12 0.626851
\(625\) −4.64235e12 −1.21697
\(626\) 1.74435e11 0.0453993
\(627\) 3.10356e12 0.801967
\(628\) −3.17180e11 −0.0813744
\(629\) 2.38850e10 0.00608411
\(630\) −3.19376e12 −0.807737
\(631\) −7.18145e12 −1.80335 −0.901675 0.432414i \(-0.857662\pi\)
−0.901675 + 0.432414i \(0.857662\pi\)
\(632\) −1.26299e12 −0.314901
\(633\) 2.19691e12 0.543870
\(634\) −6.29183e12 −1.54659
\(635\) −7.11553e12 −1.73670
\(636\) 1.12857e12 0.273510
\(637\) 5.14047e12 1.23702
\(638\) −2.82381e12 −0.674749
\(639\) −8.54430e11 −0.202732
\(640\) 6.22524e12 1.46672
\(641\) 7.98870e12 1.86903 0.934513 0.355930i \(-0.115836\pi\)
0.934513 + 0.355930i \(0.115836\pi\)
\(642\) −3.75380e12 −0.872095
\(643\) −9.48765e11 −0.218882 −0.109441 0.993993i \(-0.534906\pi\)
−0.109441 + 0.993993i \(0.534906\pi\)
\(644\) 3.01022e12 0.689624
\(645\) −1.42008e12 −0.323068
\(646\) −1.62403e12 −0.366901
\(647\) 6.80837e12 1.52747 0.763737 0.645527i \(-0.223362\pi\)
0.763737 + 0.645527i \(0.223362\pi\)
\(648\) 3.33900e11 0.0743924
\(649\) 7.62687e11 0.168750
\(650\) −3.24539e12 −0.713111
\(651\) −3.06014e12 −0.667770
\(652\) −3.21670e12 −0.697101
\(653\) −8.43389e12 −1.81518 −0.907588 0.419862i \(-0.862078\pi\)
−0.907588 + 0.419862i \(0.862078\pi\)
\(654\) 1.49235e12 0.318985
\(655\) −2.27081e12 −0.482052
\(656\) 9.99101e12 2.10641
\(657\) 2.30287e11 0.0482197
\(658\) −5.22126e12 −1.08582
\(659\) 2.96729e12 0.612880 0.306440 0.951890i \(-0.400862\pi\)
0.306440 + 0.951890i \(0.400862\pi\)
\(660\) 2.09364e12 0.429491
\(661\) −3.53359e12 −0.719962 −0.359981 0.932960i \(-0.617217\pi\)
−0.359981 + 0.932960i \(0.617217\pi\)
\(662\) −7.55150e12 −1.52817
\(663\) 7.13100e11 0.143331
\(664\) 1.31078e12 0.261682
\(665\) −1.09036e13 −2.16208
\(666\) 4.33849e10 0.00854485
\(667\) −2.21910e12 −0.434122
\(668\) 1.85986e12 0.361399
\(669\) 2.04306e11 0.0394334
\(670\) 3.61709e12 0.693461
\(671\) −1.18645e13 −2.25942
\(672\) 3.93086e12 0.743577
\(673\) 6.03044e12 1.13313 0.566567 0.824016i \(-0.308271\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(674\) 1.14745e13 2.14173
\(675\) −7.07642e11 −0.131204
\(676\) −5.80406e11 −0.106899
\(677\) −6.99508e12 −1.27981 −0.639903 0.768456i \(-0.721025\pi\)
−0.639903 + 0.768456i \(0.721025\pi\)
\(678\) −4.27309e12 −0.776619
\(679\) −2.86813e11 −0.0517828
\(680\) 1.38000e12 0.247508
\(681\) −4.19759e12 −0.747890
\(682\) 6.53897e12 1.15739
\(683\) 4.39425e11 0.0772666 0.0386333 0.999253i \(-0.487700\pi\)
0.0386333 + 0.999253i \(0.487700\pi\)
\(684\) −9.04982e11 −0.158084
\(685\) 1.04721e13 1.81730
\(686\) 4.55656e12 0.785559
\(687\) 2.68404e12 0.459709
\(688\) 3.16143e12 0.537942
\(689\) −5.51468e12 −0.932254
\(690\) 5.36306e12 0.900724
\(691\) 7.79892e12 1.30132 0.650659 0.759370i \(-0.274493\pi\)
0.650659 + 0.759370i \(0.274493\pi\)
\(692\) 3.51733e12 0.583091
\(693\) −4.08125e12 −0.672193
\(694\) 1.00346e13 1.64203
\(695\) 9.42645e11 0.153256
\(696\) −1.03719e12 −0.167539
\(697\) 3.00099e12 0.481634
\(698\) −3.56814e12 −0.568973
\(699\) 6.05684e12 0.959618
\(700\) −2.98179e12 −0.469392
\(701\) 4.87558e12 0.762597 0.381299 0.924452i \(-0.375477\pi\)
0.381299 + 0.924452i \(0.375477\pi\)
\(702\) 1.29528e12 0.201301
\(703\) 1.48117e11 0.0228721
\(704\) 2.13243e12 0.327188
\(705\) −2.85378e12 −0.435081
\(706\) 6.25962e12 0.948258
\(707\) 1.27109e13 1.91333
\(708\) −2.22395e11 −0.0332641
\(709\) −7.85521e12 −1.16748 −0.583740 0.811940i \(-0.698411\pi\)
−0.583740 + 0.811940i \(0.698411\pi\)
\(710\) −6.41436e12 −0.947307
\(711\) −1.06830e12 −0.156777
\(712\) −7.05264e12 −1.02847
\(713\) 5.13868e12 0.744644
\(714\) 2.13564e12 0.307529
\(715\) −1.02304e13 −1.46391
\(716\) −7.61992e11 −0.108353
\(717\) 7.71129e12 1.08966
\(718\) 1.01503e13 1.42533
\(719\) 6.29800e12 0.878866 0.439433 0.898275i \(-0.355179\pi\)
0.439433 + 0.898275i \(0.355179\pi\)
\(720\) 3.88614e12 0.538917
\(721\) −6.37572e12 −0.878659
\(722\) −1.30139e12 −0.178233
\(723\) 4.41584e12 0.601023
\(724\) 4.15039e12 0.561391
\(725\) 2.19814e12 0.295484
\(726\) 3.53028e12 0.471623
\(727\) 3.63645e12 0.482806 0.241403 0.970425i \(-0.422392\pi\)
0.241403 + 0.970425i \(0.422392\pi\)
\(728\) −6.87495e12 −0.907148
\(729\) 2.82430e11 0.0370370
\(730\) 1.72880e12 0.225316
\(731\) 9.49596e11 0.123002
\(732\) 3.45962e12 0.445377
\(733\) 8.12399e12 1.03945 0.519723 0.854335i \(-0.326035\pi\)
0.519723 + 0.854335i \(0.326035\pi\)
\(734\) −1.03718e13 −1.31893
\(735\) 8.41446e12 1.06349
\(736\) −6.60082e12 −0.829178
\(737\) 4.62221e12 0.577094
\(738\) 5.45102e12 0.676432
\(739\) 1.03954e13 1.28215 0.641076 0.767477i \(-0.278488\pi\)
0.641076 + 0.767477i \(0.278488\pi\)
\(740\) 9.99187e10 0.0122491
\(741\) 4.42212e12 0.538826
\(742\) −1.65157e13 −2.00023
\(743\) −1.15331e13 −1.38835 −0.694173 0.719808i \(-0.744230\pi\)
−0.694173 + 0.719808i \(0.744230\pi\)
\(744\) 2.40177e12 0.287378
\(745\) 3.74806e12 0.445762
\(746\) −1.29758e13 −1.53395
\(747\) 1.10873e12 0.130281
\(748\) −1.40000e12 −0.163520
\(749\) 1.68528e13 1.95661
\(750\) 2.47984e12 0.286186
\(751\) −7.55764e12 −0.866975 −0.433488 0.901159i \(-0.642717\pi\)
−0.433488 + 0.901159i \(0.642717\pi\)
\(752\) 6.35318e12 0.724454
\(753\) −5.86433e12 −0.664724
\(754\) −4.02351e12 −0.453351
\(755\) 7.63791e12 0.855487
\(756\) 1.19007e12 0.132503
\(757\) 1.58446e13 1.75367 0.876836 0.480789i \(-0.159650\pi\)
0.876836 + 0.480789i \(0.159650\pi\)
\(758\) 8.97630e12 0.987611
\(759\) 6.85336e12 0.749576
\(760\) 8.55775e12 0.930461
\(761\) 7.10804e12 0.768279 0.384140 0.923275i \(-0.374498\pi\)
0.384140 + 0.923275i \(0.374498\pi\)
\(762\) 8.64264e12 0.928643
\(763\) −6.69992e12 −0.715664
\(764\) −4.32698e12 −0.459478
\(765\) 1.16728e12 0.123225
\(766\) −2.02615e13 −2.12638
\(767\) 1.08672e12 0.113380
\(768\) −6.15623e12 −0.638542
\(769\) 3.71774e12 0.383363 0.191681 0.981457i \(-0.438606\pi\)
0.191681 + 0.981457i \(0.438606\pi\)
\(770\) −3.06387e13 −3.14096
\(771\) 2.38782e12 0.243365
\(772\) −7.21627e11 −0.0731198
\(773\) 8.84238e12 0.890762 0.445381 0.895341i \(-0.353068\pi\)
0.445381 + 0.895341i \(0.353068\pi\)
\(774\) 1.72485e12 0.172750
\(775\) −5.09013e12 −0.506841
\(776\) 2.25107e11 0.0222850
\(777\) −1.94777e11 −0.0191709
\(778\) 9.96246e12 0.974896
\(779\) 1.86099e13 1.81061
\(780\) 2.98313e12 0.288567
\(781\) −8.19680e12 −0.788342
\(782\) −3.58623e12 −0.342932
\(783\) −8.77308e11 −0.0834111
\(784\) −1.87325e13 −1.77082
\(785\) 2.53700e12 0.238455
\(786\) 2.75816e12 0.257761
\(787\) 6.14962e12 0.571428 0.285714 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(788\) 4.74410e12 0.438314
\(789\) 1.01451e13 0.931988
\(790\) −8.01995e12 −0.732571
\(791\) 1.91841e13 1.74240
\(792\) 3.20320e12 0.289282
\(793\) −1.69051e13 −1.51806
\(794\) −1.85741e13 −1.65850
\(795\) −9.02701e12 −0.801478
\(796\) −5.46567e11 −0.0482542
\(797\) 6.17084e11 0.0541729 0.0270864 0.999633i \(-0.491377\pi\)
0.0270864 + 0.999633i \(0.491377\pi\)
\(798\) 1.32437e13 1.15610
\(799\) 1.90830e12 0.165648
\(800\) 6.53846e12 0.564379
\(801\) −5.96548e12 −0.512035
\(802\) 1.53296e13 1.30842
\(803\) 2.20921e12 0.187507
\(804\) −1.34781e12 −0.113757
\(805\) −2.40776e13 −2.02084
\(806\) 9.31707e12 0.777628
\(807\) −1.00415e13 −0.833429
\(808\) −9.97625e12 −0.823410
\(809\) 1.75260e13 1.43851 0.719257 0.694744i \(-0.244482\pi\)
0.719257 + 0.694744i \(0.244482\pi\)
\(810\) 2.12025e12 0.173063
\(811\) 6.99500e11 0.0567798 0.0283899 0.999597i \(-0.490962\pi\)
0.0283899 + 0.999597i \(0.490962\pi\)
\(812\) −3.69671e12 −0.298410
\(813\) −8.38786e12 −0.673354
\(814\) 4.16204e11 0.0332274
\(815\) 2.57290e13 2.04275
\(816\) −2.59863e12 −0.205182
\(817\) 5.88869e12 0.462402
\(818\) −7.11334e12 −0.555499
\(819\) −5.81519e12 −0.451633
\(820\) 1.25541e13 0.969671
\(821\) 1.82627e13 1.40288 0.701440 0.712728i \(-0.252541\pi\)
0.701440 + 0.712728i \(0.252541\pi\)
\(822\) −1.27196e13 −0.971741
\(823\) −9.62438e12 −0.731263 −0.365631 0.930760i \(-0.619147\pi\)
−0.365631 + 0.930760i \(0.619147\pi\)
\(824\) 5.00403e12 0.378135
\(825\) −6.78862e12 −0.510198
\(826\) 3.25457e12 0.243267
\(827\) 2.25132e13 1.67364 0.836819 0.547479i \(-0.184413\pi\)
0.836819 + 0.547479i \(0.184413\pi\)
\(828\) −1.99840e12 −0.147757
\(829\) 1.77818e11 0.0130761 0.00653806 0.999979i \(-0.497919\pi\)
0.00653806 + 0.999979i \(0.497919\pi\)
\(830\) 8.32340e12 0.608765
\(831\) −1.09265e13 −0.794831
\(832\) 3.03840e12 0.219832
\(833\) −5.62668e12 −0.404902
\(834\) −1.14495e12 −0.0819483
\(835\) −1.48763e13 −1.05902
\(836\) −8.68176e12 −0.614723
\(837\) 2.03154e12 0.143074
\(838\) −7.07732e12 −0.495759
\(839\) 1.57674e13 1.09858 0.549289 0.835633i \(-0.314899\pi\)
0.549289 + 0.835633i \(0.314899\pi\)
\(840\) −1.12536e13 −0.779895
\(841\) −1.17820e13 −0.812150
\(842\) −1.13347e13 −0.777154
\(843\) 1.09254e13 0.745099
\(844\) −6.14553e12 −0.416887
\(845\) 4.64244e12 0.313250
\(846\) 3.46625e12 0.232645
\(847\) −1.58493e13 −1.05812
\(848\) 2.00962e13 1.33454
\(849\) −1.46893e13 −0.970322
\(850\) 3.55235e12 0.233416
\(851\) 3.27076e11 0.0213779
\(852\) 2.39014e12 0.155398
\(853\) 2.28592e13 1.47839 0.739197 0.673489i \(-0.235205\pi\)
0.739197 + 0.673489i \(0.235205\pi\)
\(854\) −5.06286e13 −3.25713
\(855\) 7.23858e12 0.463240
\(856\) −1.32270e13 −0.842035
\(857\) −1.78155e13 −1.12820 −0.564099 0.825707i \(-0.690776\pi\)
−0.564099 + 0.825707i \(0.690776\pi\)
\(858\) 1.24260e13 0.782779
\(859\) 1.32240e13 0.828691 0.414346 0.910120i \(-0.364010\pi\)
0.414346 + 0.910120i \(0.364010\pi\)
\(860\) 3.97247e12 0.247638
\(861\) −2.44725e13 −1.51762
\(862\) −1.83184e13 −1.13007
\(863\) 1.97202e13 1.21022 0.605108 0.796143i \(-0.293130\pi\)
0.605108 + 0.796143i \(0.293130\pi\)
\(864\) −2.60959e12 −0.159316
\(865\) −2.81337e13 −1.70866
\(866\) 1.13337e13 0.684767
\(867\) 8.82507e12 0.530435
\(868\) 8.56030e12 0.511859
\(869\) −1.02486e13 −0.609641
\(870\) −6.58611e12 −0.389755
\(871\) 6.58598e12 0.387738
\(872\) 5.25848e12 0.307990
\(873\) 1.90407e11 0.0110948
\(874\) −2.22392e13 −1.28919
\(875\) −1.11333e13 −0.642077
\(876\) −6.44193e11 −0.0369614
\(877\) −3.08255e12 −0.175959 −0.0879797 0.996122i \(-0.528041\pi\)
−0.0879797 + 0.996122i \(0.528041\pi\)
\(878\) 3.43944e13 1.95327
\(879\) 1.71906e13 0.971271
\(880\) 3.72809e13 2.09563
\(881\) 2.76835e12 0.154821 0.0774103 0.996999i \(-0.475335\pi\)
0.0774103 + 0.996999i \(0.475335\pi\)
\(882\) −1.02203e13 −0.568665
\(883\) 2.65376e13 1.46906 0.734529 0.678577i \(-0.237403\pi\)
0.734529 + 0.678577i \(0.237403\pi\)
\(884\) −1.99479e12 −0.109866
\(885\) 1.77885e12 0.0974753
\(886\) 2.82670e13 1.54109
\(887\) 1.05383e13 0.571630 0.285815 0.958285i \(-0.407736\pi\)
0.285815 + 0.958285i \(0.407736\pi\)
\(888\) 1.52872e11 0.00825031
\(889\) −3.88013e13 −2.08347
\(890\) −4.47840e13 −2.39259
\(891\) 2.70943e12 0.144022
\(892\) −5.71517e11 −0.0302265
\(893\) 1.18339e13 0.622723
\(894\) −4.55246e12 −0.238356
\(895\) 6.09487e12 0.317512
\(896\) 3.39465e13 1.75958
\(897\) 9.76504e12 0.503626
\(898\) −2.97134e13 −1.52479
\(899\) −6.31056e12 −0.322217
\(900\) 1.97953e12 0.100570
\(901\) 6.03629e12 0.305146
\(902\) 5.22933e13 2.63037
\(903\) −7.74376e12 −0.387576
\(904\) −1.50568e13 −0.749850
\(905\) −3.31973e13 −1.64507
\(906\) −9.27713e12 −0.457443
\(907\) 2.64723e13 1.29885 0.649425 0.760426i \(-0.275010\pi\)
0.649425 + 0.760426i \(0.275010\pi\)
\(908\) 1.17421e13 0.573273
\(909\) −8.43843e12 −0.409943
\(910\) −4.36556e13 −2.11035
\(911\) 1.81593e13 0.873507 0.436754 0.899581i \(-0.356128\pi\)
0.436754 + 0.899581i \(0.356128\pi\)
\(912\) −1.61148e13 −0.771342
\(913\) 1.06363e13 0.506610
\(914\) −1.85475e12 −0.0879077
\(915\) −2.76721e13 −1.30511
\(916\) −7.50820e12 −0.352376
\(917\) −1.23828e13 −0.578305
\(918\) −1.41779e12 −0.0658902
\(919\) −5.97931e12 −0.276523 −0.138261 0.990396i \(-0.544151\pi\)
−0.138261 + 0.990396i \(0.544151\pi\)
\(920\) 1.88974e13 0.869677
\(921\) −1.92044e12 −0.0879495
\(922\) −1.05911e13 −0.482670
\(923\) −1.16792e13 −0.529672
\(924\) 1.14167e13 0.515249
\(925\) −3.23986e11 −0.0145509
\(926\) −3.84795e13 −1.71981
\(927\) 4.23266e12 0.188259
\(928\) 8.10614e12 0.358796
\(929\) −2.22992e13 −0.982244 −0.491122 0.871091i \(-0.663413\pi\)
−0.491122 + 0.871091i \(0.663413\pi\)
\(930\) 1.52512e13 0.668543
\(931\) −3.48925e13 −1.52215
\(932\) −1.69431e13 −0.735566
\(933\) 1.85727e13 0.802429
\(934\) −2.69550e13 −1.15899
\(935\) 1.11980e13 0.479170
\(936\) 4.56409e12 0.194363
\(937\) −6.70117e12 −0.284003 −0.142001 0.989866i \(-0.545354\pi\)
−0.142001 + 0.989866i \(0.545354\pi\)
\(938\) 1.97241e13 0.831927
\(939\) 5.19898e11 0.0218234
\(940\) 7.98304e12 0.333498
\(941\) −3.16102e13 −1.31424 −0.657120 0.753786i \(-0.728225\pi\)
−0.657120 + 0.753786i \(0.728225\pi\)
\(942\) −3.08148e12 −0.127506
\(943\) 4.10949e13 1.69233
\(944\) −3.96013e12 −0.162306
\(945\) −9.51890e12 −0.388279
\(946\) 1.65470e13 0.671754
\(947\) −3.93533e13 −1.59003 −0.795016 0.606588i \(-0.792538\pi\)
−0.795016 + 0.606588i \(0.792538\pi\)
\(948\) 2.98843e12 0.120173
\(949\) 3.14780e12 0.125982
\(950\) 2.20291e13 0.877485
\(951\) −1.87526e13 −0.743446
\(952\) 7.52521e12 0.296929
\(953\) −2.79941e13 −1.09938 −0.549690 0.835369i \(-0.685254\pi\)
−0.549690 + 0.835369i \(0.685254\pi\)
\(954\) 1.09644e13 0.428564
\(955\) 3.46098e13 1.34643
\(956\) −2.15712e13 −0.835245
\(957\) −8.41628e12 −0.324352
\(958\) −2.29570e13 −0.880584
\(959\) 5.71049e13 2.18017
\(960\) 4.97357e12 0.188994
\(961\) −1.18266e13 −0.447304
\(962\) 5.93030e11 0.0223249
\(963\) −1.11881e13 −0.419216
\(964\) −1.23527e13 −0.460696
\(965\) 5.77200e12 0.214266
\(966\) 2.92450e13 1.08057
\(967\) 2.14122e13 0.787485 0.393743 0.919221i \(-0.371180\pi\)
0.393743 + 0.919221i \(0.371180\pi\)
\(968\) 1.24394e13 0.455366
\(969\) −4.84038e12 −0.176369
\(970\) 1.42942e12 0.0518427
\(971\) −1.75075e12 −0.0632030 −0.0316015 0.999501i \(-0.510061\pi\)
−0.0316015 + 0.999501i \(0.510061\pi\)
\(972\) −7.90056e11 −0.0283896
\(973\) 5.14028e12 0.183857
\(974\) 3.18634e13 1.13443
\(975\) −9.67279e12 −0.342792
\(976\) 6.16044e13 2.17314
\(977\) −5.13484e13 −1.80303 −0.901513 0.432753i \(-0.857542\pi\)
−0.901513 + 0.432753i \(0.857542\pi\)
\(978\) −3.12509e13 −1.09229
\(979\) −5.72287e13 −1.99109
\(980\) −2.35382e13 −0.815186
\(981\) 4.44789e12 0.153336
\(982\) 5.50186e10 0.00188803
\(983\) 4.30211e12 0.146957 0.0734785 0.997297i \(-0.476590\pi\)
0.0734785 + 0.997297i \(0.476590\pi\)
\(984\) 1.92074e13 0.653116
\(985\) −3.79461e13 −1.28441
\(986\) 4.40408e12 0.148391
\(987\) −1.55618e13 −0.521954
\(988\) −1.23702e13 −0.413021
\(989\) 1.30036e13 0.432194
\(990\) 2.03402e13 0.672971
\(991\) −3.17764e13 −1.04658 −0.523291 0.852154i \(-0.675296\pi\)
−0.523291 + 0.852154i \(0.675296\pi\)
\(992\) −1.87710e13 −0.615439
\(993\) −2.25070e13 −0.734592
\(994\) −3.49778e13 −1.13646
\(995\) 4.37177e12 0.141401
\(996\) −3.10150e12 −0.0998630
\(997\) −4.17148e13 −1.33709 −0.668546 0.743670i \(-0.733083\pi\)
−0.668546 + 0.743670i \(0.733083\pi\)
\(998\) 7.15014e13 2.28153
\(999\) 1.29307e11 0.00410751
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.c.1.5 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.5 22 1.1 even 1 trivial