Properties

Label 177.10.a.c.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-17.2166 q^{2} -81.0000 q^{3} -215.588 q^{4} +470.596 q^{5} +1394.55 q^{6} -5413.27 q^{7} +12526.6 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-17.2166 q^{2} -81.0000 q^{3} -215.588 q^{4} +470.596 q^{5} +1394.55 q^{6} -5413.27 q^{7} +12526.6 q^{8} +6561.00 q^{9} -8102.07 q^{10} -66383.2 q^{11} +17462.7 q^{12} -154777. q^{13} +93198.2 q^{14} -38118.3 q^{15} -105284. q^{16} +478273. q^{17} -112958. q^{18} +25047.4 q^{19} -101455. q^{20} +438475. q^{21} +1.14289e6 q^{22} +250737. q^{23} -1.01465e6 q^{24} -1.73166e6 q^{25} +2.66474e6 q^{26} -531441. q^{27} +1.16704e6 q^{28} +266117. q^{29} +656268. q^{30} -7.24334e6 q^{31} -4.60098e6 q^{32} +5.37704e6 q^{33} -8.23424e6 q^{34} -2.54747e6 q^{35} -1.41448e6 q^{36} -1.81489e7 q^{37} -431232. q^{38} +1.25370e7 q^{39} +5.89497e6 q^{40} -1.23421e7 q^{41} -7.54906e6 q^{42} -1.58491e7 q^{43} +1.43115e7 q^{44} +3.08758e6 q^{45} -4.31685e6 q^{46} -3.87386e6 q^{47} +8.52803e6 q^{48} -1.10501e7 q^{49} +2.98134e7 q^{50} -3.87401e7 q^{51} +3.33682e7 q^{52} -2.96748e7 q^{53} +9.14961e6 q^{54} -3.12397e7 q^{55} -6.78099e7 q^{56} -2.02884e6 q^{57} -4.58162e6 q^{58} +1.21174e7 q^{59} +8.21786e6 q^{60} -1.03356e8 q^{61} +1.24706e8 q^{62} -3.55165e7 q^{63} +1.33119e8 q^{64} -7.28376e7 q^{65} -9.25744e7 q^{66} -2.36659e8 q^{67} -1.03110e8 q^{68} -2.03097e7 q^{69} +4.38587e7 q^{70} -8.61606e7 q^{71} +8.21871e7 q^{72} -2.99436e8 q^{73} +3.12463e8 q^{74} +1.40265e8 q^{75} -5.39994e6 q^{76} +3.59351e8 q^{77} -2.15844e8 q^{78} +2.81809e7 q^{79} -4.95464e7 q^{80} +4.30467e7 q^{81} +2.12490e8 q^{82} +6.97783e8 q^{83} -9.45302e7 q^{84} +2.25073e8 q^{85} +2.72868e8 q^{86} -2.15554e7 q^{87} -8.31557e8 q^{88} +1.72640e8 q^{89} -5.31577e7 q^{90} +8.37852e8 q^{91} -5.40561e7 q^{92} +5.86711e8 q^{93} +6.66947e7 q^{94} +1.17872e7 q^{95} +3.72680e8 q^{96} -5.76011e8 q^{97} +1.90245e8 q^{98} -4.35540e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17.2166 −0.760874 −0.380437 0.924807i \(-0.624226\pi\)
−0.380437 + 0.924807i \(0.624226\pi\)
\(3\) −81.0000 −0.577350
\(4\) −215.588 −0.421071
\(5\) 470.596 0.336731 0.168366 0.985725i \(-0.446151\pi\)
0.168366 + 0.985725i \(0.446151\pi\)
\(6\) 1394.55 0.439291
\(7\) −5413.27 −0.852156 −0.426078 0.904687i \(-0.640105\pi\)
−0.426078 + 0.904687i \(0.640105\pi\)
\(8\) 12526.6 1.08126
\(9\) 6561.00 0.333333
\(10\) −8102.07 −0.256210
\(11\) −66383.2 −1.36707 −0.683536 0.729917i \(-0.739559\pi\)
−0.683536 + 0.729917i \(0.739559\pi\)
\(12\) 17462.7 0.243106
\(13\) −154777. −1.50301 −0.751506 0.659726i \(-0.770672\pi\)
−0.751506 + 0.659726i \(0.770672\pi\)
\(14\) 93198.2 0.648383
\(15\) −38118.3 −0.194412
\(16\) −105284. −0.401628
\(17\) 478273. 1.38885 0.694426 0.719564i \(-0.255659\pi\)
0.694426 + 0.719564i \(0.255659\pi\)
\(18\) −112958. −0.253625
\(19\) 25047.4 0.0440933 0.0220466 0.999757i \(-0.492982\pi\)
0.0220466 + 0.999757i \(0.492982\pi\)
\(20\) −101455. −0.141788
\(21\) 438475. 0.491992
\(22\) 1.14289e6 1.04017
\(23\) 250737. 0.186829 0.0934144 0.995627i \(-0.470222\pi\)
0.0934144 + 0.995627i \(0.470222\pi\)
\(24\) −1.01465e6 −0.624263
\(25\) −1.73166e6 −0.886612
\(26\) 2.66474e6 1.14360
\(27\) −531441. −0.192450
\(28\) 1.16704e6 0.358818
\(29\) 266117. 0.0698684 0.0349342 0.999390i \(-0.488878\pi\)
0.0349342 + 0.999390i \(0.488878\pi\)
\(30\) 656268. 0.147923
\(31\) −7.24334e6 −1.40868 −0.704338 0.709864i \(-0.748756\pi\)
−0.704338 + 0.709864i \(0.748756\pi\)
\(32\) −4.60098e6 −0.775668
\(33\) 5.37704e6 0.789279
\(34\) −8.23424e6 −1.05674
\(35\) −2.54747e6 −0.286947
\(36\) −1.41448e6 −0.140357
\(37\) −1.81489e7 −1.59200 −0.796000 0.605297i \(-0.793054\pi\)
−0.796000 + 0.605297i \(0.793054\pi\)
\(38\) −431232. −0.0335494
\(39\) 1.25370e7 0.867764
\(40\) 5.89497e6 0.364093
\(41\) −1.23421e7 −0.682124 −0.341062 0.940041i \(-0.610787\pi\)
−0.341062 + 0.940041i \(0.610787\pi\)
\(42\) −7.54906e6 −0.374344
\(43\) −1.58491e7 −0.706965 −0.353482 0.935441i \(-0.615003\pi\)
−0.353482 + 0.935441i \(0.615003\pi\)
\(44\) 1.43115e7 0.575635
\(45\) 3.08758e6 0.112244
\(46\) −4.31685e6 −0.142153
\(47\) −3.87386e6 −0.115799 −0.0578993 0.998322i \(-0.518440\pi\)
−0.0578993 + 0.998322i \(0.518440\pi\)
\(48\) 8.52803e6 0.231880
\(49\) −1.10501e7 −0.273831
\(50\) 2.98134e7 0.674600
\(51\) −3.87401e7 −0.801854
\(52\) 3.33682e7 0.632875
\(53\) −2.96748e7 −0.516591 −0.258295 0.966066i \(-0.583161\pi\)
−0.258295 + 0.966066i \(0.583161\pi\)
\(54\) 9.14961e6 0.146430
\(55\) −3.12397e7 −0.460336
\(56\) −6.78099e7 −0.921398
\(57\) −2.02884e6 −0.0254573
\(58\) −4.58162e6 −0.0531610
\(59\) 1.21174e7 0.130189
\(60\) 8.21786e6 0.0818612
\(61\) −1.03356e8 −0.955763 −0.477882 0.878424i \(-0.658595\pi\)
−0.477882 + 0.878424i \(0.658595\pi\)
\(62\) 1.24706e8 1.07183
\(63\) −3.55165e7 −0.284052
\(64\) 1.33119e8 0.991813
\(65\) −7.28376e7 −0.506111
\(66\) −9.25744e7 −0.600542
\(67\) −2.36659e8 −1.43478 −0.717391 0.696671i \(-0.754664\pi\)
−0.717391 + 0.696671i \(0.754664\pi\)
\(68\) −1.03110e8 −0.584805
\(69\) −2.03097e7 −0.107866
\(70\) 4.38587e7 0.218331
\(71\) −8.61606e7 −0.402389 −0.201195 0.979551i \(-0.564482\pi\)
−0.201195 + 0.979551i \(0.564482\pi\)
\(72\) 8.21871e7 0.360419
\(73\) −2.99436e8 −1.23410 −0.617050 0.786924i \(-0.711672\pi\)
−0.617050 + 0.786924i \(0.711672\pi\)
\(74\) 3.12463e8 1.21131
\(75\) 1.40265e8 0.511886
\(76\) −5.39994e6 −0.0185664
\(77\) 3.59351e8 1.16496
\(78\) −2.15844e8 −0.660259
\(79\) 2.81809e7 0.0814016 0.0407008 0.999171i \(-0.487041\pi\)
0.0407008 + 0.999171i \(0.487041\pi\)
\(80\) −4.95464e7 −0.135241
\(81\) 4.30467e7 0.111111
\(82\) 2.12490e8 0.519010
\(83\) 6.97783e8 1.61387 0.806936 0.590639i \(-0.201124\pi\)
0.806936 + 0.590639i \(0.201124\pi\)
\(84\) −9.45302e7 −0.207164
\(85\) 2.25073e8 0.467670
\(86\) 2.72868e8 0.537911
\(87\) −2.15554e7 −0.0403386
\(88\) −8.31557e8 −1.47815
\(89\) 1.72640e8 0.291666 0.145833 0.989309i \(-0.453414\pi\)
0.145833 + 0.989309i \(0.453414\pi\)
\(90\) −5.31577e7 −0.0854033
\(91\) 8.37852e8 1.28080
\(92\) −5.40561e7 −0.0786682
\(93\) 5.86711e8 0.813300
\(94\) 6.66947e7 0.0881082
\(95\) 1.17872e7 0.0148476
\(96\) 3.72680e8 0.447832
\(97\) −5.76011e8 −0.660630 −0.330315 0.943871i \(-0.607155\pi\)
−0.330315 + 0.943871i \(0.607155\pi\)
\(98\) 1.90245e8 0.208351
\(99\) −4.35540e8 −0.455691
\(100\) 3.73327e8 0.373327
\(101\) −4.89774e8 −0.468327 −0.234164 0.972197i \(-0.575235\pi\)
−0.234164 + 0.972197i \(0.575235\pi\)
\(102\) 6.66973e8 0.610109
\(103\) 5.42890e8 0.475274 0.237637 0.971354i \(-0.423627\pi\)
0.237637 + 0.971354i \(0.423627\pi\)
\(104\) −1.93884e9 −1.62514
\(105\) 2.06345e8 0.165669
\(106\) 5.10900e8 0.393060
\(107\) 8.99458e8 0.663367 0.331684 0.943391i \(-0.392383\pi\)
0.331684 + 0.943391i \(0.392383\pi\)
\(108\) 1.14573e8 0.0810352
\(109\) 8.82309e8 0.598689 0.299345 0.954145i \(-0.403232\pi\)
0.299345 + 0.954145i \(0.403232\pi\)
\(110\) 5.37842e8 0.350257
\(111\) 1.47006e9 0.919141
\(112\) 5.69933e8 0.342249
\(113\) −1.92955e9 −1.11328 −0.556640 0.830754i \(-0.687910\pi\)
−0.556640 + 0.830754i \(0.687910\pi\)
\(114\) 3.49298e7 0.0193698
\(115\) 1.17996e8 0.0629111
\(116\) −5.73717e7 −0.0294196
\(117\) −1.01549e9 −0.501004
\(118\) −2.08620e8 −0.0990573
\(119\) −2.58902e9 −1.18352
\(120\) −4.77493e8 −0.210209
\(121\) 2.04879e9 0.868886
\(122\) 1.77944e9 0.727215
\(123\) 9.99714e8 0.393824
\(124\) 1.56158e9 0.593153
\(125\) −1.73405e9 −0.635281
\(126\) 6.11474e8 0.216128
\(127\) −2.78609e7 −0.00950340 −0.00475170 0.999989i \(-0.501513\pi\)
−0.00475170 + 0.999989i \(0.501513\pi\)
\(128\) 6.38474e7 0.0210232
\(129\) 1.28378e9 0.408166
\(130\) 1.25402e9 0.385087
\(131\) −6.39360e8 −0.189681 −0.0948407 0.995492i \(-0.530234\pi\)
−0.0948407 + 0.995492i \(0.530234\pi\)
\(132\) −1.15923e9 −0.332343
\(133\) −1.35589e8 −0.0375743
\(134\) 4.07446e9 1.09169
\(135\) −2.50094e8 −0.0648039
\(136\) 5.99114e9 1.50170
\(137\) 3.13151e9 0.759472 0.379736 0.925095i \(-0.376015\pi\)
0.379736 + 0.925095i \(0.376015\pi\)
\(138\) 3.49665e8 0.0820721
\(139\) 5.67256e9 1.28888 0.644440 0.764655i \(-0.277090\pi\)
0.644440 + 0.764655i \(0.277090\pi\)
\(140\) 5.49204e8 0.120825
\(141\) 3.13783e8 0.0668564
\(142\) 1.48339e9 0.306167
\(143\) 1.02746e10 2.05473
\(144\) −6.90771e8 −0.133876
\(145\) 1.25233e8 0.0235269
\(146\) 5.15526e9 0.938995
\(147\) 8.95055e8 0.158096
\(148\) 3.91270e9 0.670345
\(149\) 6.34326e9 1.05432 0.527162 0.849765i \(-0.323256\pi\)
0.527162 + 0.849765i \(0.323256\pi\)
\(150\) −2.41488e9 −0.389480
\(151\) −3.66715e9 −0.574028 −0.287014 0.957926i \(-0.592663\pi\)
−0.287014 + 0.957926i \(0.592663\pi\)
\(152\) 3.13759e8 0.0476761
\(153\) 3.13795e9 0.462950
\(154\) −6.18680e9 −0.886386
\(155\) −3.40869e9 −0.474345
\(156\) −2.70283e9 −0.365391
\(157\) −4.89732e9 −0.643295 −0.321647 0.946859i \(-0.604237\pi\)
−0.321647 + 0.946859i \(0.604237\pi\)
\(158\) −4.85180e8 −0.0619364
\(159\) 2.40366e9 0.298254
\(160\) −2.16520e9 −0.261191
\(161\) −1.35731e9 −0.159207
\(162\) −7.41118e8 −0.0845415
\(163\) 1.47341e10 1.63486 0.817430 0.576028i \(-0.195398\pi\)
0.817430 + 0.576028i \(0.195398\pi\)
\(164\) 2.66082e9 0.287223
\(165\) 2.53042e9 0.265775
\(166\) −1.20135e10 −1.22795
\(167\) −5.19742e9 −0.517087 −0.258543 0.966000i \(-0.583243\pi\)
−0.258543 + 0.966000i \(0.583243\pi\)
\(168\) 5.49261e9 0.531969
\(169\) 1.33515e10 1.25904
\(170\) −3.87500e9 −0.355837
\(171\) 1.64336e8 0.0146978
\(172\) 3.41689e9 0.297682
\(173\) −7.79075e9 −0.661259 −0.330630 0.943761i \(-0.607261\pi\)
−0.330630 + 0.943761i \(0.607261\pi\)
\(174\) 3.71112e8 0.0306925
\(175\) 9.37397e9 0.755531
\(176\) 6.98912e9 0.549054
\(177\) −9.81506e8 −0.0751646
\(178\) −2.97227e9 −0.221921
\(179\) 2.93195e9 0.213461 0.106730 0.994288i \(-0.465962\pi\)
0.106730 + 0.994288i \(0.465962\pi\)
\(180\) −6.65647e8 −0.0472626
\(181\) 1.63487e10 1.13222 0.566110 0.824330i \(-0.308448\pi\)
0.566110 + 0.824330i \(0.308448\pi\)
\(182\) −1.44250e10 −0.974527
\(183\) 8.37181e9 0.551810
\(184\) 3.14089e9 0.202010
\(185\) −8.54081e9 −0.536076
\(186\) −1.01012e10 −0.618819
\(187\) −3.17493e10 −1.89866
\(188\) 8.35159e8 0.0487595
\(189\) 2.87684e9 0.163997
\(190\) −2.02936e8 −0.0112971
\(191\) 4.61139e9 0.250716 0.125358 0.992112i \(-0.459992\pi\)
0.125358 + 0.992112i \(0.459992\pi\)
\(192\) −1.07826e10 −0.572623
\(193\) −1.79012e10 −0.928700 −0.464350 0.885652i \(-0.653712\pi\)
−0.464350 + 0.885652i \(0.653712\pi\)
\(194\) 9.91696e9 0.502656
\(195\) 5.89985e9 0.292203
\(196\) 2.38227e9 0.115302
\(197\) −1.06899e10 −0.505678 −0.252839 0.967508i \(-0.581364\pi\)
−0.252839 + 0.967508i \(0.581364\pi\)
\(198\) 7.49853e9 0.346723
\(199\) 3.32999e10 1.50523 0.752617 0.658458i \(-0.228791\pi\)
0.752617 + 0.658458i \(0.228791\pi\)
\(200\) −2.16919e10 −0.958654
\(201\) 1.91694e10 0.828372
\(202\) 8.43225e9 0.356338
\(203\) −1.44056e9 −0.0595388
\(204\) 8.35192e9 0.337637
\(205\) −5.80817e9 −0.229692
\(206\) −9.34672e9 −0.361624
\(207\) 1.64509e9 0.0622763
\(208\) 1.62956e10 0.603651
\(209\) −1.66273e9 −0.0602787
\(210\) −3.55256e9 −0.126053
\(211\) −8.48875e9 −0.294831 −0.147415 0.989075i \(-0.547095\pi\)
−0.147415 + 0.989075i \(0.547095\pi\)
\(212\) 6.39755e9 0.217522
\(213\) 6.97901e9 0.232320
\(214\) −1.54856e10 −0.504739
\(215\) −7.45855e9 −0.238057
\(216\) −6.65715e9 −0.208088
\(217\) 3.92102e10 1.20041
\(218\) −1.51904e10 −0.455527
\(219\) 2.42543e10 0.712508
\(220\) 6.73492e9 0.193834
\(221\) −7.40259e10 −2.08746
\(222\) −2.53095e10 −0.699350
\(223\) 7.04918e10 1.90883 0.954414 0.298485i \(-0.0964814\pi\)
0.954414 + 0.298485i \(0.0964814\pi\)
\(224\) 2.49064e10 0.660989
\(225\) −1.13614e10 −0.295537
\(226\) 3.32204e10 0.847065
\(227\) −5.81539e10 −1.45366 −0.726829 0.686818i \(-0.759007\pi\)
−0.726829 + 0.686818i \(0.759007\pi\)
\(228\) 4.37395e8 0.0107193
\(229\) −6.21009e10 −1.49224 −0.746119 0.665813i \(-0.768085\pi\)
−0.746119 + 0.665813i \(0.768085\pi\)
\(230\) −2.03149e9 −0.0478674
\(231\) −2.91074e10 −0.672589
\(232\) 3.33354e9 0.0755456
\(233\) −3.61242e9 −0.0802966 −0.0401483 0.999194i \(-0.512783\pi\)
−0.0401483 + 0.999194i \(0.512783\pi\)
\(234\) 1.74834e10 0.381201
\(235\) −1.82302e9 −0.0389930
\(236\) −2.61236e9 −0.0548188
\(237\) −2.28265e9 −0.0469973
\(238\) 4.45742e10 0.900507
\(239\) −2.98723e10 −0.592214 −0.296107 0.955155i \(-0.595688\pi\)
−0.296107 + 0.955155i \(0.595688\pi\)
\(240\) 4.01326e9 0.0780812
\(241\) −8.16207e10 −1.55856 −0.779280 0.626675i \(-0.784415\pi\)
−0.779280 + 0.626675i \(0.784415\pi\)
\(242\) −3.52732e10 −0.661112
\(243\) −3.48678e9 −0.0641500
\(244\) 2.22823e10 0.402444
\(245\) −5.20012e9 −0.0922074
\(246\) −1.72117e10 −0.299651
\(247\) −3.87678e9 −0.0662727
\(248\) −9.07345e10 −1.52314
\(249\) −5.65204e10 −0.931769
\(250\) 2.98544e10 0.483369
\(251\) −1.06367e11 −1.69152 −0.845758 0.533567i \(-0.820851\pi\)
−0.845758 + 0.533567i \(0.820851\pi\)
\(252\) 7.65695e9 0.119606
\(253\) −1.66448e10 −0.255408
\(254\) 4.79671e8 0.00723089
\(255\) −1.82309e10 −0.270009
\(256\) −6.92561e10 −1.00781
\(257\) 4.23776e10 0.605951 0.302975 0.952998i \(-0.402020\pi\)
0.302975 + 0.952998i \(0.402020\pi\)
\(258\) −2.21023e10 −0.310563
\(259\) 9.82450e10 1.35663
\(260\) 1.57030e10 0.213109
\(261\) 1.74599e9 0.0232895
\(262\) 1.10076e10 0.144324
\(263\) 6.13808e10 0.791101 0.395550 0.918444i \(-0.370554\pi\)
0.395550 + 0.918444i \(0.370554\pi\)
\(264\) 6.73561e10 0.853413
\(265\) −1.39649e10 −0.173952
\(266\) 2.33438e9 0.0285893
\(267\) −1.39838e10 −0.168394
\(268\) 5.10209e10 0.604145
\(269\) 5.72181e10 0.666266 0.333133 0.942880i \(-0.391894\pi\)
0.333133 + 0.942880i \(0.391894\pi\)
\(270\) 4.30577e9 0.0493076
\(271\) −1.60471e10 −0.180732 −0.0903661 0.995909i \(-0.528804\pi\)
−0.0903661 + 0.995909i \(0.528804\pi\)
\(272\) −5.03547e10 −0.557801
\(273\) −6.78661e10 −0.739470
\(274\) −5.39140e10 −0.577862
\(275\) 1.14953e11 1.21206
\(276\) 4.37854e9 0.0454191
\(277\) −5.03692e10 −0.514051 −0.257026 0.966405i \(-0.582742\pi\)
−0.257026 + 0.966405i \(0.582742\pi\)
\(278\) −9.76623e10 −0.980675
\(279\) −4.75236e10 −0.469559
\(280\) −3.19111e10 −0.310263
\(281\) 6.43753e10 0.615943 0.307972 0.951396i \(-0.400350\pi\)
0.307972 + 0.951396i \(0.400350\pi\)
\(282\) −5.40227e9 −0.0508693
\(283\) −5.77949e10 −0.535612 −0.267806 0.963473i \(-0.586299\pi\)
−0.267806 + 0.963473i \(0.586299\pi\)
\(284\) 1.85752e10 0.169435
\(285\) −9.54766e8 −0.00857225
\(286\) −1.76894e11 −1.56339
\(287\) 6.68114e10 0.581276
\(288\) −3.01870e10 −0.258556
\(289\) 1.10157e11 0.928908
\(290\) −2.15609e9 −0.0179010
\(291\) 4.66569e10 0.381415
\(292\) 6.45548e10 0.519644
\(293\) 5.15641e10 0.408736 0.204368 0.978894i \(-0.434486\pi\)
0.204368 + 0.978894i \(0.434486\pi\)
\(294\) −1.54098e10 −0.120291
\(295\) 5.70238e9 0.0438387
\(296\) −2.27344e11 −1.72136
\(297\) 3.52788e10 0.263093
\(298\) −1.09209e11 −0.802208
\(299\) −3.88085e10 −0.280806
\(300\) −3.02395e10 −0.215540
\(301\) 8.57958e10 0.602444
\(302\) 6.31359e10 0.436763
\(303\) 3.96717e10 0.270389
\(304\) −2.63710e9 −0.0177091
\(305\) −4.86388e10 −0.321835
\(306\) −5.40248e10 −0.352247
\(307\) 1.84862e11 1.18775 0.593874 0.804558i \(-0.297598\pi\)
0.593874 + 0.804558i \(0.297598\pi\)
\(308\) −7.74719e10 −0.490530
\(309\) −4.39741e10 −0.274400
\(310\) 5.86861e10 0.360917
\(311\) 9.51423e10 0.576703 0.288351 0.957525i \(-0.406893\pi\)
0.288351 + 0.957525i \(0.406893\pi\)
\(312\) 1.57046e11 0.938275
\(313\) −1.37755e11 −0.811255 −0.405628 0.914038i \(-0.632947\pi\)
−0.405628 + 0.914038i \(0.632947\pi\)
\(314\) 8.43153e10 0.489466
\(315\) −1.67139e10 −0.0956491
\(316\) −6.07548e9 −0.0342759
\(317\) 5.17222e10 0.287681 0.143840 0.989601i \(-0.454055\pi\)
0.143840 + 0.989601i \(0.454055\pi\)
\(318\) −4.13829e10 −0.226934
\(319\) −1.76657e10 −0.0955152
\(320\) 6.26452e10 0.333974
\(321\) −7.28561e10 −0.382995
\(322\) 2.33683e10 0.121137
\(323\) 1.19795e10 0.0612390
\(324\) −9.28038e9 −0.0467857
\(325\) 2.68022e11 1.33259
\(326\) −2.53672e11 −1.24392
\(327\) −7.14670e10 −0.345653
\(328\) −1.54605e11 −0.737550
\(329\) 2.09703e10 0.0986785
\(330\) −4.35652e10 −0.202221
\(331\) 1.57884e11 0.722959 0.361479 0.932380i \(-0.382272\pi\)
0.361479 + 0.932380i \(0.382272\pi\)
\(332\) −1.50434e11 −0.679555
\(333\) −1.19075e11 −0.530666
\(334\) 8.94819e10 0.393438
\(335\) −1.11371e11 −0.483136
\(336\) −4.61646e10 −0.197598
\(337\) 1.74853e11 0.738480 0.369240 0.929334i \(-0.379618\pi\)
0.369240 + 0.929334i \(0.379618\pi\)
\(338\) −2.29868e11 −0.957974
\(339\) 1.56294e11 0.642752
\(340\) −4.85232e10 −0.196922
\(341\) 4.80837e11 1.92576
\(342\) −2.82931e9 −0.0111831
\(343\) 2.78262e11 1.08550
\(344\) −1.98536e11 −0.764410
\(345\) −9.55768e9 −0.0363217
\(346\) 1.34130e11 0.503135
\(347\) −1.25277e11 −0.463863 −0.231931 0.972732i \(-0.574505\pi\)
−0.231931 + 0.972732i \(0.574505\pi\)
\(348\) 4.64710e9 0.0169854
\(349\) −2.06778e11 −0.746086 −0.373043 0.927814i \(-0.621686\pi\)
−0.373043 + 0.927814i \(0.621686\pi\)
\(350\) −1.61388e11 −0.574864
\(351\) 8.22550e10 0.289255
\(352\) 3.05428e11 1.06039
\(353\) −2.24191e11 −0.768480 −0.384240 0.923233i \(-0.625536\pi\)
−0.384240 + 0.923233i \(0.625536\pi\)
\(354\) 1.68982e10 0.0571908
\(355\) −4.05469e10 −0.135497
\(356\) −3.72192e10 −0.122812
\(357\) 2.09711e11 0.683304
\(358\) −5.04782e10 −0.162417
\(359\) 1.17207e10 0.0372416 0.0186208 0.999827i \(-0.494072\pi\)
0.0186208 + 0.999827i \(0.494072\pi\)
\(360\) 3.86769e10 0.121364
\(361\) −3.22060e11 −0.998056
\(362\) −2.81470e11 −0.861477
\(363\) −1.65952e11 −0.501651
\(364\) −1.80631e11 −0.539308
\(365\) −1.40913e11 −0.415560
\(366\) −1.44134e11 −0.419858
\(367\) 2.53136e11 0.728376 0.364188 0.931325i \(-0.381346\pi\)
0.364188 + 0.931325i \(0.381346\pi\)
\(368\) −2.63987e10 −0.0750356
\(369\) −8.09768e10 −0.227375
\(370\) 1.47044e11 0.407886
\(371\) 1.60638e11 0.440216
\(372\) −1.26488e11 −0.342457
\(373\) −4.56903e11 −1.22218 −0.611089 0.791562i \(-0.709268\pi\)
−0.611089 + 0.791562i \(0.709268\pi\)
\(374\) 5.46615e11 1.44464
\(375\) 1.40458e11 0.366780
\(376\) −4.85263e10 −0.125208
\(377\) −4.11888e10 −0.105013
\(378\) −4.95294e10 −0.124781
\(379\) 5.82504e11 1.45018 0.725090 0.688654i \(-0.241798\pi\)
0.725090 + 0.688654i \(0.241798\pi\)
\(380\) −2.54119e9 −0.00625189
\(381\) 2.25674e9 0.00548679
\(382\) −7.93926e10 −0.190763
\(383\) 6.37704e11 1.51434 0.757172 0.653215i \(-0.226580\pi\)
0.757172 + 0.653215i \(0.226580\pi\)
\(384\) −5.17164e9 −0.0121377
\(385\) 1.69109e11 0.392278
\(386\) 3.08199e11 0.706623
\(387\) −1.03986e11 −0.235655
\(388\) 1.24181e11 0.278172
\(389\) −2.82852e11 −0.626306 −0.313153 0.949703i \(-0.601385\pi\)
−0.313153 + 0.949703i \(0.601385\pi\)
\(390\) −1.01575e11 −0.222330
\(391\) 1.19921e11 0.259477
\(392\) −1.38420e11 −0.296081
\(393\) 5.17882e10 0.109513
\(394\) 1.84043e11 0.384757
\(395\) 1.32618e10 0.0274105
\(396\) 9.38975e10 0.191878
\(397\) −7.08379e8 −0.00143123 −0.000715613 1.00000i \(-0.500228\pi\)
−0.000715613 1.00000i \(0.500228\pi\)
\(398\) −5.73312e11 −1.14529
\(399\) 1.09827e10 0.0216935
\(400\) 1.82317e11 0.356088
\(401\) 8.61044e11 1.66294 0.831468 0.555573i \(-0.187501\pi\)
0.831468 + 0.555573i \(0.187501\pi\)
\(402\) −3.30031e11 −0.630286
\(403\) 1.12111e12 2.11726
\(404\) 1.05590e11 0.197199
\(405\) 2.02576e10 0.0374146
\(406\) 2.48016e10 0.0453015
\(407\) 1.20478e12 2.17638
\(408\) −4.85282e11 −0.867009
\(409\) −2.41126e11 −0.426078 −0.213039 0.977044i \(-0.568336\pi\)
−0.213039 + 0.977044i \(0.568336\pi\)
\(410\) 9.99969e10 0.174767
\(411\) −2.53653e11 −0.438481
\(412\) −1.17041e11 −0.200124
\(413\) −6.55946e10 −0.110941
\(414\) −2.83228e10 −0.0473844
\(415\) 3.28374e11 0.543441
\(416\) 7.12128e11 1.16584
\(417\) −4.59477e11 −0.744135
\(418\) 2.86266e10 0.0458644
\(419\) −1.03648e12 −1.64284 −0.821421 0.570322i \(-0.806818\pi\)
−0.821421 + 0.570322i \(0.806818\pi\)
\(420\) −4.44855e10 −0.0697585
\(421\) 1.50236e11 0.233080 0.116540 0.993186i \(-0.462820\pi\)
0.116540 + 0.993186i \(0.462820\pi\)
\(422\) 1.46147e11 0.224329
\(423\) −2.54164e10 −0.0385996
\(424\) −3.71725e11 −0.558567
\(425\) −8.28208e11 −1.23137
\(426\) −1.20155e11 −0.176766
\(427\) 5.59493e11 0.814459
\(428\) −1.93913e11 −0.279325
\(429\) −8.32245e11 −1.18630
\(430\) 1.28411e11 0.181131
\(431\) −1.15250e12 −1.60877 −0.804384 0.594110i \(-0.797504\pi\)
−0.804384 + 0.594110i \(0.797504\pi\)
\(432\) 5.59524e10 0.0772933
\(433\) −6.40176e11 −0.875193 −0.437596 0.899171i \(-0.644170\pi\)
−0.437596 + 0.899171i \(0.644170\pi\)
\(434\) −6.75067e11 −0.913362
\(435\) −1.01439e10 −0.0135832
\(436\) −1.90216e11 −0.252091
\(437\) 6.28033e9 0.00823789
\(438\) −4.17576e11 −0.542129
\(439\) −6.22464e11 −0.799878 −0.399939 0.916542i \(-0.630969\pi\)
−0.399939 + 0.916542i \(0.630969\pi\)
\(440\) −3.91327e11 −0.497741
\(441\) −7.24995e10 −0.0912770
\(442\) 1.27447e12 1.58829
\(443\) 2.06954e11 0.255304 0.127652 0.991819i \(-0.459256\pi\)
0.127652 + 0.991819i \(0.459256\pi\)
\(444\) −3.16928e11 −0.387024
\(445\) 8.12436e10 0.0982131
\(446\) −1.21363e12 −1.45238
\(447\) −5.13804e11 −0.608715
\(448\) −7.20609e11 −0.845179
\(449\) 1.49258e12 1.73312 0.866562 0.499070i \(-0.166325\pi\)
0.866562 + 0.499070i \(0.166325\pi\)
\(450\) 1.95606e11 0.224867
\(451\) 8.19311e11 0.932512
\(452\) 4.15990e11 0.468770
\(453\) 2.97039e11 0.331415
\(454\) 1.00121e12 1.10605
\(455\) 3.94290e11 0.431285
\(456\) −2.54145e10 −0.0275258
\(457\) 1.39765e11 0.149891 0.0749457 0.997188i \(-0.476122\pi\)
0.0749457 + 0.997188i \(0.476122\pi\)
\(458\) 1.06917e12 1.13540
\(459\) −2.54174e11 −0.267285
\(460\) −2.54386e10 −0.0264900
\(461\) 1.62785e12 1.67865 0.839326 0.543628i \(-0.182950\pi\)
0.839326 + 0.543628i \(0.182950\pi\)
\(462\) 5.01131e11 0.511755
\(463\) −8.20961e9 −0.00830249 −0.00415124 0.999991i \(-0.501321\pi\)
−0.00415124 + 0.999991i \(0.501321\pi\)
\(464\) −2.80179e10 −0.0280611
\(465\) 2.76104e11 0.273863
\(466\) 6.21937e10 0.0610955
\(467\) −2.13574e11 −0.207789 −0.103895 0.994588i \(-0.533130\pi\)
−0.103895 + 0.994588i \(0.533130\pi\)
\(468\) 2.18929e11 0.210958
\(469\) 1.28110e12 1.22266
\(470\) 3.13863e10 0.0296688
\(471\) 3.96683e11 0.371407
\(472\) 1.51789e11 0.140768
\(473\) 1.05212e12 0.966472
\(474\) 3.92996e10 0.0357590
\(475\) −4.33738e10 −0.0390936
\(476\) 5.58164e11 0.498345
\(477\) −1.94697e11 −0.172197
\(478\) 5.14300e11 0.450600
\(479\) −1.26522e11 −0.109814 −0.0549070 0.998491i \(-0.517486\pi\)
−0.0549070 + 0.998491i \(0.517486\pi\)
\(480\) 1.75382e11 0.150799
\(481\) 2.80904e12 2.39279
\(482\) 1.40523e12 1.18587
\(483\) 1.09942e11 0.0919183
\(484\) −4.41695e11 −0.365863
\(485\) −2.71069e11 −0.222455
\(486\) 6.00306e10 0.0488101
\(487\) 2.31543e12 1.86531 0.932654 0.360771i \(-0.117486\pi\)
0.932654 + 0.360771i \(0.117486\pi\)
\(488\) −1.29470e12 −1.03342
\(489\) −1.19347e12 −0.943887
\(490\) 8.95284e10 0.0701582
\(491\) −1.98934e12 −1.54469 −0.772345 0.635203i \(-0.780916\pi\)
−0.772345 + 0.635203i \(0.780916\pi\)
\(492\) −2.15527e11 −0.165828
\(493\) 1.27276e11 0.0970369
\(494\) 6.67450e10 0.0504251
\(495\) −2.04964e11 −0.153445
\(496\) 7.62611e11 0.565764
\(497\) 4.66411e11 0.342898
\(498\) 9.73090e11 0.708959
\(499\) −1.05952e12 −0.764991 −0.382496 0.923957i \(-0.624935\pi\)
−0.382496 + 0.923957i \(0.624935\pi\)
\(500\) 3.73841e11 0.267499
\(501\) 4.20991e11 0.298540
\(502\) 1.83128e12 1.28703
\(503\) −2.42824e11 −0.169136 −0.0845679 0.996418i \(-0.526951\pi\)
−0.0845679 + 0.996418i \(0.526951\pi\)
\(504\) −4.44901e11 −0.307133
\(505\) −2.30486e11 −0.157700
\(506\) 2.86566e11 0.194333
\(507\) −1.08147e12 −0.726910
\(508\) 6.00650e9 0.00400161
\(509\) −1.40296e12 −0.926439 −0.463219 0.886244i \(-0.653306\pi\)
−0.463219 + 0.886244i \(0.653306\pi\)
\(510\) 3.13875e11 0.205443
\(511\) 1.62093e12 1.05165
\(512\) 1.15967e12 0.745792
\(513\) −1.33112e10 −0.00848575
\(514\) −7.29599e11 −0.461052
\(515\) 2.55482e11 0.160040
\(516\) −2.76768e11 −0.171867
\(517\) 2.57159e11 0.158305
\(518\) −1.69145e12 −1.03222
\(519\) 6.31051e11 0.381778
\(520\) −9.12408e11 −0.547235
\(521\) 2.56574e12 1.52561 0.762804 0.646629i \(-0.223822\pi\)
0.762804 + 0.646629i \(0.223822\pi\)
\(522\) −3.00600e10 −0.0177203
\(523\) −1.55421e12 −0.908348 −0.454174 0.890913i \(-0.650066\pi\)
−0.454174 + 0.890913i \(0.650066\pi\)
\(524\) 1.37839e11 0.0798694
\(525\) −7.59292e11 −0.436206
\(526\) −1.05677e12 −0.601928
\(527\) −3.46430e12 −1.95644
\(528\) −5.66118e11 −0.316997
\(529\) −1.73828e12 −0.965095
\(530\) 2.40427e11 0.132356
\(531\) 7.95020e10 0.0433963
\(532\) 2.92314e10 0.0158215
\(533\) 1.91028e12 1.02524
\(534\) 2.40754e11 0.128126
\(535\) 4.23282e11 0.223376
\(536\) −2.96453e12 −1.55137
\(537\) −2.37488e11 −0.123242
\(538\) −9.85101e11 −0.506945
\(539\) 7.33539e11 0.374347
\(540\) 5.39174e10 0.0272871
\(541\) 1.19331e12 0.598917 0.299459 0.954109i \(-0.403194\pi\)
0.299459 + 0.954109i \(0.403194\pi\)
\(542\) 2.76277e11 0.137514
\(543\) −1.32425e12 −0.653688
\(544\) −2.20053e12 −1.07729
\(545\) 4.15211e11 0.201597
\(546\) 1.16842e12 0.562643
\(547\) −2.51030e12 −1.19890 −0.599450 0.800412i \(-0.704614\pi\)
−0.599450 + 0.800412i \(0.704614\pi\)
\(548\) −6.75118e11 −0.319792
\(549\) −6.78117e11 −0.318588
\(550\) −1.97911e12 −0.922227
\(551\) 6.66554e9 0.00308073
\(552\) −2.54412e11 −0.116630
\(553\) −1.52551e11 −0.0693669
\(554\) 8.67188e11 0.391128
\(555\) 6.91805e11 0.309503
\(556\) −1.22294e12 −0.542710
\(557\) −1.61310e11 −0.0710088 −0.0355044 0.999370i \(-0.511304\pi\)
−0.0355044 + 0.999370i \(0.511304\pi\)
\(558\) 8.18195e11 0.357275
\(559\) 2.45309e12 1.06258
\(560\) 2.68208e11 0.115246
\(561\) 2.57169e12 1.09619
\(562\) −1.10832e12 −0.468655
\(563\) −1.63046e12 −0.683948 −0.341974 0.939710i \(-0.611095\pi\)
−0.341974 + 0.939710i \(0.611095\pi\)
\(564\) −6.76479e10 −0.0281513
\(565\) −9.08041e11 −0.374876
\(566\) 9.95032e11 0.407533
\(567\) −2.33024e11 −0.0946840
\(568\) −1.07930e12 −0.435086
\(569\) 1.42003e12 0.567928 0.283964 0.958835i \(-0.408350\pi\)
0.283964 + 0.958835i \(0.408350\pi\)
\(570\) 1.64378e10 0.00652240
\(571\) 5.28540e11 0.208073 0.104036 0.994573i \(-0.466824\pi\)
0.104036 + 0.994573i \(0.466824\pi\)
\(572\) −2.21509e12 −0.865186
\(573\) −3.73523e11 −0.144751
\(574\) −1.15027e12 −0.442277
\(575\) −4.34193e11 −0.165645
\(576\) 8.73393e11 0.330604
\(577\) −1.43606e12 −0.539364 −0.269682 0.962949i \(-0.586919\pi\)
−0.269682 + 0.962949i \(0.586919\pi\)
\(578\) −1.89653e12 −0.706782
\(579\) 1.45000e12 0.536185
\(580\) −2.69989e10 −0.00990649
\(581\) −3.77729e12 −1.37527
\(582\) −8.03274e11 −0.290208
\(583\) 1.96991e12 0.706217
\(584\) −3.75091e12 −1.33438
\(585\) −4.77888e11 −0.168704
\(586\) −8.87759e11 −0.310997
\(587\) 1.31190e12 0.456069 0.228034 0.973653i \(-0.426770\pi\)
0.228034 + 0.973653i \(0.426770\pi\)
\(588\) −1.92964e11 −0.0665698
\(589\) −1.81427e11 −0.0621132
\(590\) −9.81757e10 −0.0333557
\(591\) 8.65879e11 0.291953
\(592\) 1.91080e12 0.639391
\(593\) −5.85336e12 −1.94383 −0.971917 0.235324i \(-0.924385\pi\)
−0.971917 + 0.235324i \(0.924385\pi\)
\(594\) −6.07381e11 −0.200181
\(595\) −1.21838e12 −0.398527
\(596\) −1.36753e12 −0.443946
\(597\) −2.69729e12 −0.869048
\(598\) 6.68150e11 0.213658
\(599\) −5.40235e12 −1.71460 −0.857298 0.514820i \(-0.827859\pi\)
−0.857298 + 0.514820i \(0.827859\pi\)
\(600\) 1.75704e12 0.553479
\(601\) −4.40596e12 −1.37754 −0.688772 0.724978i \(-0.741850\pi\)
−0.688772 + 0.724978i \(0.741850\pi\)
\(602\) −1.47711e12 −0.458384
\(603\) −1.55272e12 −0.478261
\(604\) 7.90596e11 0.241707
\(605\) 9.64151e11 0.292581
\(606\) −6.83012e11 −0.205732
\(607\) 3.88829e12 1.16254 0.581272 0.813709i \(-0.302555\pi\)
0.581272 + 0.813709i \(0.302555\pi\)
\(608\) −1.15243e11 −0.0342017
\(609\) 1.16686e11 0.0343747
\(610\) 8.37395e11 0.244876
\(611\) 5.99586e11 0.174047
\(612\) −6.76506e11 −0.194935
\(613\) −2.22713e12 −0.637051 −0.318526 0.947914i \(-0.603188\pi\)
−0.318526 + 0.947914i \(0.603188\pi\)
\(614\) −3.18269e12 −0.903726
\(615\) 4.70461e11 0.132613
\(616\) 4.50144e12 1.25962
\(617\) −6.19968e10 −0.0172221 −0.00861105 0.999963i \(-0.502741\pi\)
−0.00861105 + 0.999963i \(0.502741\pi\)
\(618\) 7.57084e11 0.208783
\(619\) 4.07655e12 1.11605 0.558027 0.829823i \(-0.311558\pi\)
0.558027 + 0.829823i \(0.311558\pi\)
\(620\) 7.34874e11 0.199733
\(621\) −1.33252e11 −0.0359552
\(622\) −1.63803e12 −0.438798
\(623\) −9.34547e11 −0.248545
\(624\) −1.31995e12 −0.348518
\(625\) 2.56612e12 0.672693
\(626\) 2.37167e12 0.617263
\(627\) 1.34681e11 0.0348019
\(628\) 1.05581e12 0.270873
\(629\) −8.68014e12 −2.21105
\(630\) 2.87757e11 0.0727769
\(631\) 1.13483e12 0.284969 0.142485 0.989797i \(-0.454491\pi\)
0.142485 + 0.989797i \(0.454491\pi\)
\(632\) 3.53011e11 0.0880160
\(633\) 6.87589e11 0.170221
\(634\) −8.90481e11 −0.218889
\(635\) −1.31112e10 −0.00320009
\(636\) −5.18201e11 −0.125586
\(637\) 1.71030e12 0.411571
\(638\) 3.04143e11 0.0726750
\(639\) −5.65300e11 −0.134130
\(640\) 3.00463e10 0.00707916
\(641\) 1.03670e12 0.242545 0.121272 0.992619i \(-0.461303\pi\)
0.121272 + 0.992619i \(0.461303\pi\)
\(642\) 1.25433e12 0.291411
\(643\) −3.29334e12 −0.759778 −0.379889 0.925032i \(-0.624038\pi\)
−0.379889 + 0.925032i \(0.624038\pi\)
\(644\) 2.92620e11 0.0670375
\(645\) 6.04142e11 0.137442
\(646\) −2.06247e11 −0.0465951
\(647\) 7.47536e12 1.67711 0.838557 0.544814i \(-0.183400\pi\)
0.838557 + 0.544814i \(0.183400\pi\)
\(648\) 5.39229e11 0.120140
\(649\) −8.04390e11 −0.177978
\(650\) −4.61444e12 −1.01393
\(651\) −3.17603e12 −0.693058
\(652\) −3.17651e12 −0.688392
\(653\) 4.84471e12 1.04270 0.521349 0.853343i \(-0.325429\pi\)
0.521349 + 0.853343i \(0.325429\pi\)
\(654\) 1.23042e12 0.262999
\(655\) −3.00880e11 −0.0638716
\(656\) 1.29943e12 0.273960
\(657\) −1.96460e12 −0.411367
\(658\) −3.61037e11 −0.0750819
\(659\) −5.52324e12 −1.14080 −0.570400 0.821367i \(-0.693212\pi\)
−0.570400 + 0.821367i \(0.693212\pi\)
\(660\) −5.45528e11 −0.111910
\(661\) −5.88116e12 −1.19827 −0.599137 0.800646i \(-0.704490\pi\)
−0.599137 + 0.800646i \(0.704490\pi\)
\(662\) −2.71824e12 −0.550080
\(663\) 5.99609e12 1.20520
\(664\) 8.74085e12 1.74501
\(665\) −6.38075e10 −0.0126524
\(666\) 2.05007e12 0.403770
\(667\) 6.67254e10 0.0130534
\(668\) 1.12050e12 0.217730
\(669\) −5.70984e12 −1.10206
\(670\) 1.91743e12 0.367605
\(671\) 6.86109e12 1.30660
\(672\) −2.01742e12 −0.381622
\(673\) 3.55154e11 0.0667343 0.0333672 0.999443i \(-0.489377\pi\)
0.0333672 + 0.999443i \(0.489377\pi\)
\(674\) −3.01038e12 −0.561890
\(675\) 9.20277e11 0.170629
\(676\) −2.87844e12 −0.530147
\(677\) 6.56111e12 1.20041 0.600203 0.799848i \(-0.295086\pi\)
0.600203 + 0.799848i \(0.295086\pi\)
\(678\) −2.69085e12 −0.489053
\(679\) 3.11811e12 0.562959
\(680\) 2.81941e12 0.505670
\(681\) 4.71046e12 0.839270
\(682\) −8.27837e12 −1.46526
\(683\) 5.91763e12 1.04053 0.520265 0.854005i \(-0.325833\pi\)
0.520265 + 0.854005i \(0.325833\pi\)
\(684\) −3.54290e10 −0.00618880
\(685\) 1.47368e12 0.255738
\(686\) −4.79073e12 −0.825930
\(687\) 5.03017e12 0.861544
\(688\) 1.66867e12 0.283937
\(689\) 4.59299e12 0.776442
\(690\) 1.64551e11 0.0276362
\(691\) −7.81874e12 −1.30462 −0.652312 0.757951i \(-0.726201\pi\)
−0.652312 + 0.757951i \(0.726201\pi\)
\(692\) 1.67960e12 0.278437
\(693\) 2.35770e12 0.388319
\(694\) 2.15685e12 0.352941
\(695\) 2.66949e12 0.434006
\(696\) −2.70016e11 −0.0436163
\(697\) −5.90291e12 −0.947369
\(698\) 3.56001e12 0.567678
\(699\) 2.92606e11 0.0463592
\(700\) −2.02092e12 −0.318133
\(701\) −4.19167e12 −0.655626 −0.327813 0.944743i \(-0.606312\pi\)
−0.327813 + 0.944743i \(0.606312\pi\)
\(702\) −1.41615e12 −0.220086
\(703\) −4.54584e11 −0.0701964
\(704\) −8.83686e12 −1.35588
\(705\) 1.47665e11 0.0225126
\(706\) 3.85981e12 0.584716
\(707\) 2.65128e12 0.399088
\(708\) 2.11601e11 0.0316496
\(709\) 4.05279e12 0.602345 0.301173 0.953570i \(-0.402622\pi\)
0.301173 + 0.953570i \(0.402622\pi\)
\(710\) 6.98079e11 0.103096
\(711\) 1.84895e11 0.0271339
\(712\) 2.16259e12 0.315366
\(713\) −1.81618e12 −0.263181
\(714\) −3.61051e12 −0.519908
\(715\) 4.83520e12 0.691890
\(716\) −6.32094e11 −0.0898821
\(717\) 2.41966e12 0.341915
\(718\) −2.01791e11 −0.0283362
\(719\) 9.83134e12 1.37193 0.685966 0.727633i \(-0.259380\pi\)
0.685966 + 0.727633i \(0.259380\pi\)
\(720\) −3.25074e11 −0.0450802
\(721\) −2.93881e12 −0.405008
\(722\) 5.54479e12 0.759394
\(723\) 6.61128e12 0.899836
\(724\) −3.52460e12 −0.476745
\(725\) −4.60825e11 −0.0619462
\(726\) 2.85713e12 0.381693
\(727\) −1.00675e13 −1.33664 −0.668320 0.743874i \(-0.732986\pi\)
−0.668320 + 0.743874i \(0.732986\pi\)
\(728\) 1.04954e13 1.38487
\(729\) 2.82430e11 0.0370370
\(730\) 2.42605e12 0.316189
\(731\) −7.58022e12 −0.981869
\(732\) −1.80487e12 −0.232351
\(733\) −4.66502e12 −0.596878 −0.298439 0.954429i \(-0.596466\pi\)
−0.298439 + 0.954429i \(0.596466\pi\)
\(734\) −4.35814e12 −0.554202
\(735\) 4.21210e11 0.0532360
\(736\) −1.15364e12 −0.144917
\(737\) 1.57102e13 1.96145
\(738\) 1.39415e12 0.173003
\(739\) −1.77689e12 −0.219159 −0.109580 0.993978i \(-0.534950\pi\)
−0.109580 + 0.993978i \(0.534950\pi\)
\(740\) 1.84130e12 0.225726
\(741\) 3.14019e11 0.0382626
\(742\) −2.76564e12 −0.334949
\(743\) 8.10862e12 0.976106 0.488053 0.872814i \(-0.337707\pi\)
0.488053 + 0.872814i \(0.337707\pi\)
\(744\) 7.34949e12 0.879385
\(745\) 2.98511e12 0.355024
\(746\) 7.86633e12 0.929923
\(747\) 4.57815e12 0.537957
\(748\) 6.84479e12 0.799471
\(749\) −4.86901e12 −0.565292
\(750\) −2.41821e12 −0.279073
\(751\) 1.19190e13 1.36729 0.683646 0.729814i \(-0.260393\pi\)
0.683646 + 0.729814i \(0.260393\pi\)
\(752\) 4.07857e11 0.0465080
\(753\) 8.61575e12 0.976597
\(754\) 7.09132e11 0.0799017
\(755\) −1.72575e12 −0.193293
\(756\) −6.20213e11 −0.0690546
\(757\) −4.03996e12 −0.447143 −0.223571 0.974688i \(-0.571772\pi\)
−0.223571 + 0.974688i \(0.571772\pi\)
\(758\) −1.00287e13 −1.10340
\(759\) 1.34823e12 0.147460
\(760\) 1.47654e11 0.0160540
\(761\) 9.85667e12 1.06537 0.532684 0.846315i \(-0.321184\pi\)
0.532684 + 0.846315i \(0.321184\pi\)
\(762\) −3.88533e10 −0.00417475
\(763\) −4.77618e12 −0.510176
\(764\) −9.94163e11 −0.105569
\(765\) 1.47671e12 0.155890
\(766\) −1.09791e13 −1.15223
\(767\) −1.87549e12 −0.195675
\(768\) 5.60974e12 0.581859
\(769\) 1.69468e13 1.74751 0.873756 0.486365i \(-0.161677\pi\)
0.873756 + 0.486365i \(0.161677\pi\)
\(770\) −2.91148e12 −0.298474
\(771\) −3.43259e12 −0.349846
\(772\) 3.85930e12 0.391049
\(773\) −3.18191e12 −0.320538 −0.160269 0.987073i \(-0.551236\pi\)
−0.160269 + 0.987073i \(0.551236\pi\)
\(774\) 1.79029e12 0.179304
\(775\) 1.25430e13 1.24895
\(776\) −7.21546e12 −0.714310
\(777\) −7.95785e12 −0.783251
\(778\) 4.86976e12 0.476540
\(779\) −3.09139e11 −0.0300771
\(780\) −1.27194e12 −0.123038
\(781\) 5.71962e12 0.550095
\(782\) −2.06463e12 −0.197430
\(783\) −1.41425e11 −0.0134462
\(784\) 1.16340e12 0.109978
\(785\) −2.30466e12 −0.216617
\(786\) −8.91617e11 −0.0833253
\(787\) −4.03160e12 −0.374621 −0.187310 0.982301i \(-0.559977\pi\)
−0.187310 + 0.982301i \(0.559977\pi\)
\(788\) 2.30461e12 0.212926
\(789\) −4.97185e12 −0.456742
\(790\) −2.28324e11 −0.0208559
\(791\) 1.04452e13 0.948687
\(792\) −5.45584e12 −0.492718
\(793\) 1.59971e13 1.43652
\(794\) 1.21959e10 0.00108898
\(795\) 1.13115e12 0.100431
\(796\) −7.17908e12 −0.633811
\(797\) 2.07530e13 1.82187 0.910937 0.412545i \(-0.135360\pi\)
0.910937 + 0.412545i \(0.135360\pi\)
\(798\) −1.89085e11 −0.0165060
\(799\) −1.85276e12 −0.160827
\(800\) 7.96736e12 0.687716
\(801\) 1.13269e12 0.0972220
\(802\) −1.48242e13 −1.26528
\(803\) 1.98775e13 1.68710
\(804\) −4.13269e12 −0.348804
\(805\) −6.38745e11 −0.0536100
\(806\) −1.93016e13 −1.61097
\(807\) −4.63466e12 −0.384669
\(808\) −6.13521e12 −0.506382
\(809\) −2.12249e13 −1.74211 −0.871056 0.491183i \(-0.836565\pi\)
−0.871056 + 0.491183i \(0.836565\pi\)
\(810\) −3.48767e11 −0.0284678
\(811\) −9.19128e12 −0.746075 −0.373037 0.927816i \(-0.621684\pi\)
−0.373037 + 0.927816i \(0.621684\pi\)
\(812\) 3.10569e11 0.0250701
\(813\) 1.29982e12 0.104346
\(814\) −2.07423e13 −1.65595
\(815\) 6.93383e12 0.550508
\(816\) 4.07873e12 0.322047
\(817\) −3.96981e11 −0.0311724
\(818\) 4.15137e12 0.324191
\(819\) 5.49715e12 0.426933
\(820\) 1.25217e12 0.0967168
\(821\) −1.86206e12 −0.143037 −0.0715185 0.997439i \(-0.522785\pi\)
−0.0715185 + 0.997439i \(0.522785\pi\)
\(822\) 4.36704e12 0.333629
\(823\) −3.74901e12 −0.284850 −0.142425 0.989806i \(-0.545490\pi\)
−0.142425 + 0.989806i \(0.545490\pi\)
\(824\) 6.80057e12 0.513893
\(825\) −9.31123e12 −0.699785
\(826\) 1.12932e12 0.0844122
\(827\) −1.23458e13 −0.917790 −0.458895 0.888491i \(-0.651755\pi\)
−0.458895 + 0.888491i \(0.651755\pi\)
\(828\) −3.54662e11 −0.0262227
\(829\) −2.42543e13 −1.78358 −0.891790 0.452449i \(-0.850550\pi\)
−0.891790 + 0.452449i \(0.850550\pi\)
\(830\) −5.65349e12 −0.413490
\(831\) 4.07991e12 0.296788
\(832\) −2.06038e13 −1.49071
\(833\) −5.28495e12 −0.380310
\(834\) 7.91064e12 0.566193
\(835\) −2.44588e12 −0.174119
\(836\) 3.58465e11 0.0253816
\(837\) 3.84941e12 0.271100
\(838\) 1.78446e13 1.25000
\(839\) 9.09790e12 0.633888 0.316944 0.948444i \(-0.397343\pi\)
0.316944 + 0.948444i \(0.397343\pi\)
\(840\) 2.58480e12 0.179131
\(841\) −1.44363e13 −0.995118
\(842\) −2.58656e12 −0.177345
\(843\) −5.21440e12 −0.355615
\(844\) 1.83008e12 0.124145
\(845\) 6.28318e12 0.423960
\(846\) 4.37584e11 0.0293694
\(847\) −1.10906e13 −0.740426
\(848\) 3.12429e12 0.207477
\(849\) 4.68139e12 0.309236
\(850\) 1.42589e13 0.936919
\(851\) −4.55061e12 −0.297431
\(852\) −1.50459e12 −0.0978231
\(853\) 2.03602e13 1.31678 0.658388 0.752679i \(-0.271239\pi\)
0.658388 + 0.752679i \(0.271239\pi\)
\(854\) −9.63257e12 −0.619700
\(855\) 7.73360e10 0.00494919
\(856\) 1.12672e13 0.717269
\(857\) 3.07800e13 1.94920 0.974598 0.223961i \(-0.0718990\pi\)
0.974598 + 0.223961i \(0.0718990\pi\)
\(858\) 1.43284e13 0.902622
\(859\) −1.16944e13 −0.732837 −0.366419 0.930450i \(-0.619416\pi\)
−0.366419 + 0.930450i \(0.619416\pi\)
\(860\) 1.60798e12 0.100239
\(861\) −5.41172e12 −0.335600
\(862\) 1.98421e13 1.22407
\(863\) 5.54534e12 0.340314 0.170157 0.985417i \(-0.445573\pi\)
0.170157 + 0.985417i \(0.445573\pi\)
\(864\) 2.44515e12 0.149277
\(865\) −3.66630e12 −0.222667
\(866\) 1.10217e13 0.665911
\(867\) −8.92274e12 −0.536305
\(868\) −8.45327e12 −0.505459
\(869\) −1.87074e12 −0.111282
\(870\) 1.74644e11 0.0103351
\(871\) 3.66294e13 2.15649
\(872\) 1.10523e13 0.647336
\(873\) −3.77921e12 −0.220210
\(874\) −1.08126e11 −0.00626799
\(875\) 9.38688e12 0.541358
\(876\) −5.22894e12 −0.300017
\(877\) −6.71347e12 −0.383221 −0.191610 0.981471i \(-0.561371\pi\)
−0.191610 + 0.981471i \(0.561371\pi\)
\(878\) 1.07167e13 0.608606
\(879\) −4.17669e12 −0.235984
\(880\) 3.28905e12 0.184884
\(881\) −2.96798e13 −1.65985 −0.829926 0.557873i \(-0.811617\pi\)
−0.829926 + 0.557873i \(0.811617\pi\)
\(882\) 1.24819e12 0.0694502
\(883\) −2.19380e13 −1.21444 −0.607218 0.794535i \(-0.707714\pi\)
−0.607218 + 0.794535i \(0.707714\pi\)
\(884\) 1.59591e13 0.878969
\(885\) −4.61893e11 −0.0253103
\(886\) −3.56305e12 −0.194254
\(887\) 1.77950e13 0.965253 0.482627 0.875826i \(-0.339683\pi\)
0.482627 + 0.875826i \(0.339683\pi\)
\(888\) 1.84149e13 0.993827
\(889\) 1.50819e11 0.00809837
\(890\) −1.39874e12 −0.0747278
\(891\) −2.85758e12 −0.151897
\(892\) −1.51972e13 −0.803753
\(893\) −9.70303e10 −0.00510594
\(894\) 8.84597e12 0.463155
\(895\) 1.37976e12 0.0718789
\(896\) −3.45623e11 −0.0179150
\(897\) 3.14349e12 0.162123
\(898\) −2.56972e13 −1.31869
\(899\) −1.92757e12 −0.0984220
\(900\) 2.44940e12 0.124442
\(901\) −1.41927e13 −0.717468
\(902\) −1.41058e13 −0.709524
\(903\) −6.94946e12 −0.347821
\(904\) −2.41708e13 −1.20374
\(905\) 7.69366e12 0.381254
\(906\) −5.11401e12 −0.252165
\(907\) −3.94863e13 −1.93737 −0.968687 0.248285i \(-0.920133\pi\)
−0.968687 + 0.248285i \(0.920133\pi\)
\(908\) 1.25373e13 0.612093
\(909\) −3.21341e12 −0.156109
\(910\) −6.78834e12 −0.328154
\(911\) −5.40411e12 −0.259951 −0.129975 0.991517i \(-0.541490\pi\)
−0.129975 + 0.991517i \(0.541490\pi\)
\(912\) 2.13605e11 0.0102243
\(913\) −4.63211e13 −2.20628
\(914\) −2.40629e12 −0.114048
\(915\) 3.93974e12 0.185812
\(916\) 1.33882e13 0.628338
\(917\) 3.46103e12 0.161638
\(918\) 4.37601e12 0.203370
\(919\) 2.00688e13 0.928113 0.464056 0.885806i \(-0.346393\pi\)
0.464056 + 0.885806i \(0.346393\pi\)
\(920\) 1.47809e12 0.0680230
\(921\) −1.49738e13 −0.685747
\(922\) −2.80261e13 −1.27724
\(923\) 1.33357e13 0.604796
\(924\) 6.27522e12 0.283208
\(925\) 3.14278e13 1.41149
\(926\) 1.41342e11 0.00631714
\(927\) 3.56190e12 0.158425
\(928\) −1.22440e12 −0.0541947
\(929\) −5.57427e12 −0.245537 −0.122769 0.992435i \(-0.539177\pi\)
−0.122769 + 0.992435i \(0.539177\pi\)
\(930\) −4.75357e12 −0.208376
\(931\) −2.76776e11 −0.0120741
\(932\) 7.78797e11 0.0338106
\(933\) −7.70653e12 −0.332960
\(934\) 3.67703e12 0.158101
\(935\) −1.49411e13 −0.639338
\(936\) −1.27207e13 −0.541713
\(937\) −3.14621e13 −1.33340 −0.666698 0.745328i \(-0.732293\pi\)
−0.666698 + 0.745328i \(0.732293\pi\)
\(938\) −2.20562e13 −0.930288
\(939\) 1.11581e13 0.468378
\(940\) 3.93023e11 0.0164188
\(941\) 3.85392e13 1.60232 0.801160 0.598450i \(-0.204217\pi\)
0.801160 + 0.598450i \(0.204217\pi\)
\(942\) −6.82954e12 −0.282593
\(943\) −3.09464e12 −0.127440
\(944\) −1.27577e12 −0.0522875
\(945\) 1.35383e12 0.0552230
\(946\) −1.81139e13 −0.735363
\(947\) −1.27822e13 −0.516453 −0.258227 0.966084i \(-0.583138\pi\)
−0.258227 + 0.966084i \(0.583138\pi\)
\(948\) 4.92114e11 0.0197892
\(949\) 4.63459e13 1.85487
\(950\) 7.46749e11 0.0297453
\(951\) −4.18950e12 −0.166092
\(952\) −3.24317e13 −1.27968
\(953\) −1.44419e13 −0.567162 −0.283581 0.958948i \(-0.591522\pi\)
−0.283581 + 0.958948i \(0.591522\pi\)
\(954\) 3.35201e12 0.131020
\(955\) 2.17010e12 0.0844239
\(956\) 6.44013e12 0.249364
\(957\) 1.43092e12 0.0551457
\(958\) 2.17829e12 0.0835546
\(959\) −1.69517e13 −0.647188
\(960\) −5.07426e12 −0.192820
\(961\) 2.60264e13 0.984371
\(962\) −4.83622e13 −1.82061
\(963\) 5.90134e12 0.221122
\(964\) 1.75965e13 0.656265
\(965\) −8.42426e12 −0.312722
\(966\) −1.89283e12 −0.0699382
\(967\) −1.85584e13 −0.682531 −0.341266 0.939967i \(-0.610856\pi\)
−0.341266 + 0.939967i \(0.610856\pi\)
\(968\) 2.56643e13 0.939488
\(969\) −9.70341e11 −0.0353563
\(970\) 4.66688e12 0.169260
\(971\) 4.55906e13 1.64584 0.822922 0.568154i \(-0.192342\pi\)
0.822922 + 0.568154i \(0.192342\pi\)
\(972\) 7.51710e11 0.0270117
\(973\) −3.07071e13 −1.09833
\(974\) −3.98638e13 −1.41926
\(975\) −2.17098e13 −0.769370
\(976\) 1.08817e13 0.383861
\(977\) 3.06072e13 1.07473 0.537363 0.843351i \(-0.319420\pi\)
0.537363 + 0.843351i \(0.319420\pi\)
\(978\) 2.05474e13 0.718179
\(979\) −1.14604e13 −0.398729
\(980\) 1.12109e12 0.0388259
\(981\) 5.78883e12 0.199563
\(982\) 3.42496e13 1.17531
\(983\) −1.41046e13 −0.481804 −0.240902 0.970549i \(-0.577443\pi\)
−0.240902 + 0.970549i \(0.577443\pi\)
\(984\) 1.25230e13 0.425825
\(985\) −5.03061e12 −0.170278
\(986\) −2.19127e12 −0.0738328
\(987\) −1.69859e12 −0.0569720
\(988\) 8.35788e11 0.0279055
\(989\) −3.97397e12 −0.132081
\(990\) 3.52878e12 0.116752
\(991\) −5.67071e13 −1.86770 −0.933848 0.357670i \(-0.883571\pi\)
−0.933848 + 0.357670i \(0.883571\pi\)
\(992\) 3.33265e13 1.09267
\(993\) −1.27886e13 −0.417400
\(994\) −8.03002e12 −0.260902
\(995\) 1.56708e13 0.506859
\(996\) 1.21851e13 0.392341
\(997\) 1.81463e13 0.581646 0.290823 0.956777i \(-0.406071\pi\)
0.290823 + 0.956777i \(0.406071\pi\)
\(998\) 1.82413e13 0.582062
\(999\) 9.64508e12 0.306380
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.1.7 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.7 22 1.1 even 1 trivial