Properties

Label 177.10.a.b.1.6
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} -11156.8 q^{10} -48168.1 q^{11} -2732.48 q^{12} +60042.1 q^{13} -36699.1 q^{14} -38684.4 q^{15} -278278. q^{16} +65961.2 q^{17} -153271. q^{18} -314381. q^{19} +16111.0 q^{20} -127248. q^{21} +1.12525e6 q^{22} -1.21197e6 q^{23} -904992. q^{24} -1.72504e6 q^{25} -1.40264e6 q^{26} -531441. q^{27} +52995.3 q^{28} +5.11139e6 q^{29} +903704. q^{30} +2.37877e6 q^{31} +780396. q^{32} +3.90161e6 q^{33} -1.54092e6 q^{34} +750267. q^{35} +221331. q^{36} +1.04291e6 q^{37} +7.34424e6 q^{38} -4.86341e6 q^{39} +5.33593e6 q^{40} -9.06456e6 q^{41} +2.97263e6 q^{42} +3.58131e7 q^{43} -1.62492e6 q^{44} +3.13343e6 q^{45} +2.83128e7 q^{46} +3.00013e7 q^{47} +2.25405e7 q^{48} -3.78857e7 q^{49} +4.02985e7 q^{50} -5.34286e6 q^{51} +2.02548e6 q^{52} -2.45832e7 q^{53} +1.24150e7 q^{54} -2.30043e7 q^{55} +1.75519e7 q^{56} +2.54649e7 q^{57} -1.19407e8 q^{58} -1.21174e7 q^{59} -1.30499e6 q^{60} +6.49807e7 q^{61} -5.55703e7 q^{62} +1.03071e7 q^{63} +1.24248e8 q^{64} +2.86752e7 q^{65} -9.11454e7 q^{66} +2.82563e8 q^{67} +2.22516e6 q^{68} +9.81696e7 q^{69} -1.75269e7 q^{70} -6.33502e7 q^{71} +7.33044e7 q^{72} +3.82696e8 q^{73} -2.43634e7 q^{74} +1.39728e8 q^{75} -1.06054e7 q^{76} -7.56701e7 q^{77} +1.13614e8 q^{78} -5.56447e8 q^{79} -1.32901e8 q^{80} +4.30467e7 q^{81} +2.11757e8 q^{82} +4.81897e7 q^{83} -4.29262e6 q^{84} +3.15021e7 q^{85} -8.36627e8 q^{86} -4.14023e8 q^{87} -5.38169e8 q^{88} +1.06126e9 q^{89} -7.32000e7 q^{90} +9.43237e7 q^{91} -4.08850e7 q^{92} -1.92680e8 q^{93} -7.00858e8 q^{94} -1.50144e8 q^{95} -6.32120e7 q^{96} +1.41946e6 q^{97} +8.85046e8 q^{98} -3.16031e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −23.3610 −1.03242 −0.516209 0.856463i \(-0.672657\pi\)
−0.516209 + 0.856463i \(0.672657\pi\)
\(3\) −81.0000 −0.577350
\(4\) 33.7344 0.0658874
\(5\) 477.585 0.341732 0.170866 0.985294i \(-0.445343\pi\)
0.170866 + 0.985294i \(0.445343\pi\)
\(6\) 1892.24 0.596067
\(7\) 1570.96 0.247300 0.123650 0.992326i \(-0.460540\pi\)
0.123650 + 0.992326i \(0.460540\pi\)
\(8\) 11172.7 0.964395
\(9\) 6561.00 0.333333
\(10\) −11156.8 −0.352810
\(11\) −48168.1 −0.991955 −0.495978 0.868335i \(-0.665190\pi\)
−0.495978 + 0.868335i \(0.665190\pi\)
\(12\) −2732.48 −0.0380401
\(13\) 60042.1 0.583057 0.291528 0.956562i \(-0.405836\pi\)
0.291528 + 0.956562i \(0.405836\pi\)
\(14\) −36699.1 −0.255317
\(15\) −38684.4 −0.197299
\(16\) −278278. −1.06155
\(17\) 65961.2 0.191544 0.0957720 0.995403i \(-0.469468\pi\)
0.0957720 + 0.995403i \(0.469468\pi\)
\(18\) −153271. −0.344139
\(19\) −314381. −0.553433 −0.276716 0.960952i \(-0.589246\pi\)
−0.276716 + 0.960952i \(0.589246\pi\)
\(20\) 16111.0 0.0225158
\(21\) −127248. −0.142779
\(22\) 1.12525e6 1.02411
\(23\) −1.21197e6 −0.903060 −0.451530 0.892256i \(-0.649122\pi\)
−0.451530 + 0.892256i \(0.649122\pi\)
\(24\) −904992. −0.556794
\(25\) −1.72504e6 −0.883219
\(26\) −1.40264e6 −0.601958
\(27\) −531441. −0.192450
\(28\) 52995.3 0.0162939
\(29\) 5.11139e6 1.34199 0.670993 0.741464i \(-0.265868\pi\)
0.670993 + 0.741464i \(0.265868\pi\)
\(30\) 903704. 0.203695
\(31\) 2.37877e6 0.462620 0.231310 0.972880i \(-0.425699\pi\)
0.231310 + 0.972880i \(0.425699\pi\)
\(32\) 780396. 0.131565
\(33\) 3.90161e6 0.572706
\(34\) −1.54092e6 −0.197753
\(35\) 750267. 0.0845102
\(36\) 221331. 0.0219625
\(37\) 1.04291e6 0.0914830 0.0457415 0.998953i \(-0.485435\pi\)
0.0457415 + 0.998953i \(0.485435\pi\)
\(38\) 7.34424e6 0.571374
\(39\) −4.86341e6 −0.336628
\(40\) 5.33593e6 0.329565
\(41\) −9.06456e6 −0.500979 −0.250490 0.968119i \(-0.580592\pi\)
−0.250490 + 0.968119i \(0.580592\pi\)
\(42\) 2.97263e6 0.147407
\(43\) 3.58131e7 1.59747 0.798736 0.601681i \(-0.205502\pi\)
0.798736 + 0.601681i \(0.205502\pi\)
\(44\) −1.62492e6 −0.0653574
\(45\) 3.13343e6 0.113911
\(46\) 2.83128e7 0.932336
\(47\) 3.00013e7 0.896808 0.448404 0.893831i \(-0.351993\pi\)
0.448404 + 0.893831i \(0.351993\pi\)
\(48\) 2.25405e7 0.612884
\(49\) −3.78857e7 −0.938843
\(50\) 4.02985e7 0.911852
\(51\) −5.34286e6 −0.110588
\(52\) 2.02548e6 0.0384161
\(53\) −2.45832e7 −0.427954 −0.213977 0.976839i \(-0.568642\pi\)
−0.213977 + 0.976839i \(0.568642\pi\)
\(54\) 1.24150e7 0.198689
\(55\) −2.30043e7 −0.338983
\(56\) 1.75519e7 0.238495
\(57\) 2.54649e7 0.319525
\(58\) −1.19407e8 −1.38549
\(59\) −1.21174e7 −0.130189
\(60\) −1.30499e6 −0.0129995
\(61\) 6.49807e7 0.600897 0.300448 0.953798i \(-0.402864\pi\)
0.300448 + 0.953798i \(0.402864\pi\)
\(62\) −5.55703e7 −0.477618
\(63\) 1.03071e7 0.0824333
\(64\) 1.24248e8 0.925716
\(65\) 2.86752e7 0.199249
\(66\) −9.11454e7 −0.591272
\(67\) 2.82563e8 1.71309 0.856543 0.516076i \(-0.172608\pi\)
0.856543 + 0.516076i \(0.172608\pi\)
\(68\) 2.22516e6 0.0126203
\(69\) 9.81696e7 0.521382
\(70\) −1.75269e7 −0.0872499
\(71\) −6.33502e7 −0.295860 −0.147930 0.988998i \(-0.547261\pi\)
−0.147930 + 0.988998i \(0.547261\pi\)
\(72\) 7.33044e7 0.321465
\(73\) 3.82696e8 1.57725 0.788626 0.614873i \(-0.210793\pi\)
0.788626 + 0.614873i \(0.210793\pi\)
\(74\) −2.43634e7 −0.0944487
\(75\) 1.39728e8 0.509927
\(76\) −1.06054e7 −0.0364643
\(77\) −7.56701e7 −0.245310
\(78\) 1.13614e8 0.347541
\(79\) −5.56447e8 −1.60732 −0.803660 0.595089i \(-0.797117\pi\)
−0.803660 + 0.595089i \(0.797117\pi\)
\(80\) −1.32901e8 −0.362764
\(81\) 4.30467e7 0.111111
\(82\) 2.11757e8 0.517220
\(83\) 4.81897e7 0.111456 0.0557279 0.998446i \(-0.482252\pi\)
0.0557279 + 0.998446i \(0.482252\pi\)
\(84\) −4.29262e6 −0.00940731
\(85\) 3.15021e7 0.0654567
\(86\) −8.36627e8 −1.64926
\(87\) −4.14023e8 −0.774796
\(88\) −5.38169e8 −0.956637
\(89\) 1.06126e9 1.79294 0.896471 0.443103i \(-0.146122\pi\)
0.896471 + 0.443103i \(0.146122\pi\)
\(90\) −7.32000e7 −0.117603
\(91\) 9.43237e7 0.144190
\(92\) −4.08850e7 −0.0595003
\(93\) −1.92680e8 −0.267094
\(94\) −7.00858e8 −0.925880
\(95\) −1.50144e8 −0.189126
\(96\) −6.32120e7 −0.0759590
\(97\) 1.41946e6 0.00162799 0.000813994 1.00000i \(-0.499741\pi\)
0.000813994 1.00000i \(0.499741\pi\)
\(98\) 8.85046e8 0.969278
\(99\) −3.16031e8 −0.330652
\(100\) −5.81930e7 −0.0581930
\(101\) −1.20629e9 −1.15347 −0.576736 0.816931i \(-0.695674\pi\)
−0.576736 + 0.816931i \(0.695674\pi\)
\(102\) 1.24814e8 0.114173
\(103\) −1.98483e9 −1.73762 −0.868811 0.495144i \(-0.835115\pi\)
−0.868811 + 0.495144i \(0.835115\pi\)
\(104\) 6.70835e8 0.562297
\(105\) −6.07716e7 −0.0487920
\(106\) 5.74287e8 0.441827
\(107\) −1.19300e9 −0.879859 −0.439930 0.898032i \(-0.644997\pi\)
−0.439930 + 0.898032i \(0.644997\pi\)
\(108\) −1.79278e7 −0.0126800
\(109\) −1.66774e9 −1.13164 −0.565821 0.824528i \(-0.691441\pi\)
−0.565821 + 0.824528i \(0.691441\pi\)
\(110\) 5.37403e8 0.349972
\(111\) −8.44760e7 −0.0528177
\(112\) −4.37163e8 −0.262520
\(113\) 2.96330e9 1.70971 0.854857 0.518864i \(-0.173645\pi\)
0.854857 + 0.518864i \(0.173645\pi\)
\(114\) −5.94883e8 −0.329883
\(115\) −5.78819e8 −0.308605
\(116\) 1.72429e8 0.0884200
\(117\) 3.93936e8 0.194352
\(118\) 2.83073e8 0.134409
\(119\) 1.03622e8 0.0473688
\(120\) −4.32211e8 −0.190274
\(121\) −3.77854e7 −0.0160247
\(122\) −1.51801e9 −0.620377
\(123\) 7.34230e8 0.289240
\(124\) 8.02463e7 0.0304809
\(125\) −1.75663e9 −0.643556
\(126\) −2.40783e8 −0.0851056
\(127\) −1.29615e9 −0.442120 −0.221060 0.975260i \(-0.570952\pi\)
−0.221060 + 0.975260i \(0.570952\pi\)
\(128\) −3.30210e9 −1.08729
\(129\) −2.90086e9 −0.922301
\(130\) −6.69880e8 −0.205708
\(131\) 1.95690e9 0.580562 0.290281 0.956941i \(-0.406251\pi\)
0.290281 + 0.956941i \(0.406251\pi\)
\(132\) 1.31618e8 0.0377341
\(133\) −4.93880e8 −0.136864
\(134\) −6.60095e9 −1.76862
\(135\) −2.53808e8 −0.0657663
\(136\) 7.36968e8 0.184724
\(137\) 1.14427e9 0.277515 0.138757 0.990326i \(-0.455689\pi\)
0.138757 + 0.990326i \(0.455689\pi\)
\(138\) −2.29334e9 −0.538284
\(139\) −8.49846e9 −1.93096 −0.965481 0.260474i \(-0.916121\pi\)
−0.965481 + 0.260474i \(0.916121\pi\)
\(140\) 2.53098e7 0.00556816
\(141\) −2.43010e9 −0.517772
\(142\) 1.47992e9 0.305451
\(143\) −2.89211e9 −0.578366
\(144\) −1.82578e9 −0.353849
\(145\) 2.44112e9 0.458600
\(146\) −8.94014e9 −1.62838
\(147\) 3.06874e9 0.542041
\(148\) 3.51820e7 0.00602758
\(149\) 2.92284e9 0.485811 0.242905 0.970050i \(-0.421900\pi\)
0.242905 + 0.970050i \(0.421900\pi\)
\(150\) −3.26418e9 −0.526458
\(151\) 1.67412e9 0.262054 0.131027 0.991379i \(-0.458173\pi\)
0.131027 + 0.991379i \(0.458173\pi\)
\(152\) −3.51250e9 −0.533728
\(153\) 4.32772e8 0.0638480
\(154\) 1.76773e9 0.253263
\(155\) 1.13606e9 0.158092
\(156\) −1.64064e8 −0.0221795
\(157\) −7.62113e9 −1.00108 −0.500542 0.865712i \(-0.666866\pi\)
−0.500542 + 0.865712i \(0.666866\pi\)
\(158\) 1.29991e10 1.65943
\(159\) 1.99124e9 0.247079
\(160\) 3.72705e8 0.0449599
\(161\) −1.90396e9 −0.223327
\(162\) −1.00561e9 −0.114713
\(163\) −1.78418e10 −1.97968 −0.989839 0.142193i \(-0.954585\pi\)
−0.989839 + 0.142193i \(0.954585\pi\)
\(164\) −3.05787e8 −0.0330082
\(165\) 1.86335e9 0.195712
\(166\) −1.12576e9 −0.115069
\(167\) 1.14867e10 1.14280 0.571400 0.820672i \(-0.306400\pi\)
0.571400 + 0.820672i \(0.306400\pi\)
\(168\) −1.42171e9 −0.137695
\(169\) −6.99945e9 −0.660045
\(170\) −7.35919e8 −0.0675787
\(171\) −2.06265e9 −0.184478
\(172\) 1.20813e9 0.105253
\(173\) −8.09192e9 −0.686822 −0.343411 0.939185i \(-0.611582\pi\)
−0.343411 + 0.939185i \(0.611582\pi\)
\(174\) 9.67197e9 0.799914
\(175\) −2.70996e9 −0.218420
\(176\) 1.34041e10 1.05301
\(177\) 9.81506e8 0.0751646
\(178\) −2.47920e10 −1.85107
\(179\) −1.44994e10 −1.05563 −0.527814 0.849360i \(-0.676988\pi\)
−0.527814 + 0.849360i \(0.676988\pi\)
\(180\) 1.05704e8 0.00750528
\(181\) 1.31916e10 0.913574 0.456787 0.889576i \(-0.349000\pi\)
0.456787 + 0.889576i \(0.349000\pi\)
\(182\) −2.20349e9 −0.148864
\(183\) −5.26343e9 −0.346928
\(184\) −1.35410e10 −0.870907
\(185\) 4.98079e8 0.0312627
\(186\) 4.50120e9 0.275753
\(187\) −3.17722e9 −0.190003
\(188\) 1.01207e9 0.0590883
\(189\) −8.34872e8 −0.0475929
\(190\) 3.50750e9 0.195257
\(191\) 1.40593e10 0.764387 0.382193 0.924082i \(-0.375169\pi\)
0.382193 + 0.924082i \(0.375169\pi\)
\(192\) −1.00641e10 −0.534463
\(193\) 2.42504e10 1.25809 0.629044 0.777369i \(-0.283446\pi\)
0.629044 + 0.777369i \(0.283446\pi\)
\(194\) −3.31600e7 −0.00168076
\(195\) −2.32269e9 −0.115036
\(196\) −1.27805e9 −0.0618579
\(197\) 2.25575e10 1.06707 0.533536 0.845777i \(-0.320863\pi\)
0.533536 + 0.845777i \(0.320863\pi\)
\(198\) 7.38278e9 0.341371
\(199\) −2.75426e10 −1.24499 −0.622495 0.782624i \(-0.713881\pi\)
−0.622495 + 0.782624i \(0.713881\pi\)
\(200\) −1.92734e10 −0.851772
\(201\) −2.28876e10 −0.989050
\(202\) 2.81802e10 1.19087
\(203\) 8.02979e9 0.331873
\(204\) −1.80238e8 −0.00728636
\(205\) −4.32910e9 −0.171201
\(206\) 4.63675e10 1.79395
\(207\) −7.95174e9 −0.301020
\(208\) −1.67084e10 −0.618941
\(209\) 1.51431e10 0.548981
\(210\) 1.41968e9 0.0503738
\(211\) −3.44676e10 −1.19713 −0.598563 0.801076i \(-0.704261\pi\)
−0.598563 + 0.801076i \(0.704261\pi\)
\(212\) −8.29298e8 −0.0281968
\(213\) 5.13137e9 0.170815
\(214\) 2.78696e10 0.908383
\(215\) 1.71038e10 0.545907
\(216\) −5.93765e9 −0.185598
\(217\) 3.73695e9 0.114406
\(218\) 3.89600e10 1.16833
\(219\) −3.09984e10 −0.910627
\(220\) −7.76037e8 −0.0223347
\(221\) 3.96045e9 0.111681
\(222\) 1.97344e9 0.0545300
\(223\) 1.69066e10 0.457808 0.228904 0.973449i \(-0.426486\pi\)
0.228904 + 0.973449i \(0.426486\pi\)
\(224\) 1.22597e9 0.0325360
\(225\) −1.13180e10 −0.294406
\(226\) −6.92256e10 −1.76514
\(227\) 1.99018e10 0.497482 0.248741 0.968570i \(-0.419983\pi\)
0.248741 + 0.968570i \(0.419983\pi\)
\(228\) 8.59041e8 0.0210527
\(229\) 1.05069e10 0.252473 0.126236 0.992000i \(-0.459710\pi\)
0.126236 + 0.992000i \(0.459710\pi\)
\(230\) 1.35218e10 0.318609
\(231\) 6.12928e9 0.141630
\(232\) 5.71083e10 1.29420
\(233\) 3.44694e10 0.766183 0.383092 0.923710i \(-0.374859\pi\)
0.383092 + 0.923710i \(0.374859\pi\)
\(234\) −9.20272e9 −0.200653
\(235\) 1.43282e10 0.306468
\(236\) −4.08771e8 −0.00857781
\(237\) 4.50722e10 0.927986
\(238\) −2.42072e9 −0.0489044
\(239\) 2.73381e10 0.541974 0.270987 0.962583i \(-0.412650\pi\)
0.270987 + 0.962583i \(0.412650\pi\)
\(240\) 1.07650e10 0.209442
\(241\) −5.47074e9 −0.104465 −0.0522323 0.998635i \(-0.516634\pi\)
−0.0522323 + 0.998635i \(0.516634\pi\)
\(242\) 8.82703e8 0.0165442
\(243\) −3.48678e9 −0.0641500
\(244\) 2.19208e9 0.0395915
\(245\) −1.80936e10 −0.320833
\(246\) −1.71523e10 −0.298617
\(247\) −1.88761e10 −0.322683
\(248\) 2.65774e10 0.446149
\(249\) −3.90336e9 −0.0643490
\(250\) 4.10367e10 0.664419
\(251\) −4.37703e10 −0.696062 −0.348031 0.937483i \(-0.613150\pi\)
−0.348031 + 0.937483i \(0.613150\pi\)
\(252\) 3.47702e8 0.00543132
\(253\) 5.83783e10 0.895795
\(254\) 3.02794e10 0.456453
\(255\) −2.55167e9 −0.0377914
\(256\) 1.35256e10 0.196823
\(257\) 6.50898e10 0.930709 0.465355 0.885124i \(-0.345927\pi\)
0.465355 + 0.885124i \(0.345927\pi\)
\(258\) 6.77668e10 0.952201
\(259\) 1.63837e9 0.0226237
\(260\) 9.67339e8 0.0131280
\(261\) 3.35358e10 0.447329
\(262\) −4.57152e10 −0.599383
\(263\) 1.08038e11 1.39243 0.696215 0.717833i \(-0.254866\pi\)
0.696215 + 0.717833i \(0.254866\pi\)
\(264\) 4.35917e10 0.552314
\(265\) −1.17406e10 −0.146245
\(266\) 1.15375e10 0.141301
\(267\) −8.59619e10 −1.03516
\(268\) 9.53209e9 0.112871
\(269\) −1.42805e11 −1.66287 −0.831437 0.555619i \(-0.812481\pi\)
−0.831437 + 0.555619i \(0.812481\pi\)
\(270\) 5.92920e9 0.0678984
\(271\) −8.54937e10 −0.962880 −0.481440 0.876479i \(-0.659886\pi\)
−0.481440 + 0.876479i \(0.659886\pi\)
\(272\) −1.83556e10 −0.203333
\(273\) −7.64022e9 −0.0832480
\(274\) −2.67313e10 −0.286511
\(275\) 8.30917e10 0.876114
\(276\) 3.31169e9 0.0343525
\(277\) −9.85414e10 −1.00568 −0.502840 0.864380i \(-0.667711\pi\)
−0.502840 + 0.864380i \(0.667711\pi\)
\(278\) 1.98532e11 1.99356
\(279\) 1.56071e10 0.154207
\(280\) 8.38254e9 0.0815012
\(281\) −9.83292e10 −0.940815 −0.470407 0.882449i \(-0.655893\pi\)
−0.470407 + 0.882449i \(0.655893\pi\)
\(282\) 5.67695e10 0.534557
\(283\) 1.36212e11 1.26234 0.631168 0.775646i \(-0.282576\pi\)
0.631168 + 0.775646i \(0.282576\pi\)
\(284\) −2.13708e9 −0.0194934
\(285\) 1.21616e10 0.109192
\(286\) 6.75625e10 0.597116
\(287\) −1.42401e10 −0.123892
\(288\) 5.12018e9 0.0438550
\(289\) −1.14237e11 −0.963311
\(290\) −5.70270e10 −0.473467
\(291\) −1.14976e8 −0.000939919 0
\(292\) 1.29100e10 0.103921
\(293\) 2.49642e10 0.197885 0.0989425 0.995093i \(-0.468454\pi\)
0.0989425 + 0.995093i \(0.468454\pi\)
\(294\) −7.16887e10 −0.559613
\(295\) −5.78707e9 −0.0444897
\(296\) 1.16522e10 0.0882257
\(297\) 2.55985e10 0.190902
\(298\) −6.82804e10 −0.501560
\(299\) −7.27692e10 −0.526535
\(300\) 4.71364e9 0.0335978
\(301\) 5.62609e10 0.395055
\(302\) −3.91091e10 −0.270549
\(303\) 9.77098e10 0.665957
\(304\) 8.74853e10 0.587495
\(305\) 3.10338e10 0.205346
\(306\) −1.01100e10 −0.0659178
\(307\) −8.15988e10 −0.524277 −0.262139 0.965030i \(-0.584428\pi\)
−0.262139 + 0.965030i \(0.584428\pi\)
\(308\) −2.55268e9 −0.0161629
\(309\) 1.60771e11 1.00322
\(310\) −2.65395e10 −0.163217
\(311\) −8.66559e10 −0.525263 −0.262631 0.964896i \(-0.584590\pi\)
−0.262631 + 0.964896i \(0.584590\pi\)
\(312\) −5.43376e10 −0.324642
\(313\) −2.95540e11 −1.74047 −0.870236 0.492636i \(-0.836034\pi\)
−0.870236 + 0.492636i \(0.836034\pi\)
\(314\) 1.78037e11 1.03354
\(315\) 4.92250e9 0.0281701
\(316\) −1.87714e10 −0.105902
\(317\) −3.28835e11 −1.82899 −0.914495 0.404597i \(-0.867412\pi\)
−0.914495 + 0.404597i \(0.867412\pi\)
\(318\) −4.65172e10 −0.255089
\(319\) −2.46206e11 −1.33119
\(320\) 5.93387e10 0.316347
\(321\) 9.66329e10 0.507987
\(322\) 4.44782e10 0.230567
\(323\) −2.07369e10 −0.106007
\(324\) 1.45215e9 0.00732082
\(325\) −1.03575e11 −0.514967
\(326\) 4.16802e11 2.04386
\(327\) 1.35087e11 0.653354
\(328\) −1.01276e11 −0.483142
\(329\) 4.71308e10 0.221780
\(330\) −4.35297e10 −0.202056
\(331\) 1.82900e10 0.0837504 0.0418752 0.999123i \(-0.486667\pi\)
0.0418752 + 0.999123i \(0.486667\pi\)
\(332\) 1.62565e9 0.00734353
\(333\) 6.84255e9 0.0304943
\(334\) −2.68340e11 −1.17985
\(335\) 1.34948e11 0.585416
\(336\) 3.54102e10 0.151566
\(337\) 3.39078e11 1.43207 0.716037 0.698062i \(-0.245954\pi\)
0.716037 + 0.698062i \(0.245954\pi\)
\(338\) 1.63514e11 0.681443
\(339\) −2.40028e11 −0.987104
\(340\) 1.06270e9 0.00431277
\(341\) −1.14581e11 −0.458899
\(342\) 4.81856e10 0.190458
\(343\) −1.22911e11 −0.479475
\(344\) 4.00130e11 1.54059
\(345\) 4.68843e10 0.178173
\(346\) 1.89035e11 0.709087
\(347\) −4.74641e11 −1.75745 −0.878724 0.477330i \(-0.841605\pi\)
−0.878724 + 0.477330i \(0.841605\pi\)
\(348\) −1.39668e10 −0.0510493
\(349\) 2.47333e11 0.892417 0.446209 0.894929i \(-0.352774\pi\)
0.446209 + 0.894929i \(0.352774\pi\)
\(350\) 6.33074e10 0.225501
\(351\) −3.19088e10 −0.112209
\(352\) −3.75901e10 −0.130506
\(353\) −1.91987e11 −0.658090 −0.329045 0.944314i \(-0.606727\pi\)
−0.329045 + 0.944314i \(0.606727\pi\)
\(354\) −2.29289e10 −0.0776013
\(355\) −3.02551e10 −0.101105
\(356\) 3.58009e10 0.118132
\(357\) −8.39341e9 −0.0273484
\(358\) 3.38719e11 1.08985
\(359\) −3.99067e9 −0.0126800 −0.00634002 0.999980i \(-0.502018\pi\)
−0.00634002 + 0.999980i \(0.502018\pi\)
\(360\) 3.50091e10 0.109855
\(361\) −2.23852e11 −0.693712
\(362\) −3.08168e11 −0.943190
\(363\) 3.06062e9 0.00925186
\(364\) 3.18195e9 0.00950029
\(365\) 1.82770e11 0.538997
\(366\) 1.22959e11 0.358175
\(367\) −5.84621e11 −1.68220 −0.841098 0.540882i \(-0.818090\pi\)
−0.841098 + 0.540882i \(0.818090\pi\)
\(368\) 3.37265e11 0.958640
\(369\) −5.94726e10 −0.166993
\(370\) −1.16356e10 −0.0322761
\(371\) −3.86192e10 −0.105833
\(372\) −6.49995e9 −0.0175981
\(373\) −5.84664e11 −1.56393 −0.781964 0.623323i \(-0.785782\pi\)
−0.781964 + 0.623323i \(0.785782\pi\)
\(374\) 7.42230e10 0.196163
\(375\) 1.42287e11 0.371557
\(376\) 3.35196e11 0.864877
\(377\) 3.06899e11 0.782454
\(378\) 1.95034e10 0.0491358
\(379\) 1.81625e11 0.452168 0.226084 0.974108i \(-0.427408\pi\)
0.226084 + 0.974108i \(0.427408\pi\)
\(380\) −5.06500e9 −0.0124610
\(381\) 1.04988e11 0.255258
\(382\) −3.28438e11 −0.789167
\(383\) 6.89118e11 1.63644 0.818218 0.574908i \(-0.194962\pi\)
0.818218 + 0.574908i \(0.194962\pi\)
\(384\) 2.67470e11 0.627748
\(385\) −3.61389e10 −0.0838304
\(386\) −5.66513e11 −1.29887
\(387\) 2.34970e11 0.532491
\(388\) 4.78847e7 0.000107264 0
\(389\) −4.98090e11 −1.10290 −0.551449 0.834209i \(-0.685925\pi\)
−0.551449 + 0.834209i \(0.685925\pi\)
\(390\) 5.42603e10 0.118766
\(391\) −7.99430e10 −0.172976
\(392\) −4.23287e11 −0.905415
\(393\) −1.58509e11 −0.335188
\(394\) −5.26966e11 −1.10166
\(395\) −2.65751e11 −0.549272
\(396\) −1.06611e10 −0.0217858
\(397\) −2.97522e11 −0.601122 −0.300561 0.953763i \(-0.597174\pi\)
−0.300561 + 0.953763i \(0.597174\pi\)
\(398\) 6.43421e11 1.28535
\(399\) 4.00043e10 0.0790184
\(400\) 4.80040e11 0.937578
\(401\) −4.84900e11 −0.936489 −0.468244 0.883599i \(-0.655113\pi\)
−0.468244 + 0.883599i \(0.655113\pi\)
\(402\) 5.34677e11 1.02111
\(403\) 1.42826e11 0.269734
\(404\) −4.06936e10 −0.0759993
\(405\) 2.05585e10 0.0379702
\(406\) −1.87584e11 −0.342632
\(407\) −5.02351e10 −0.0907470
\(408\) −5.96944e10 −0.106650
\(409\) 4.31529e11 0.762527 0.381264 0.924466i \(-0.375489\pi\)
0.381264 + 0.924466i \(0.375489\pi\)
\(410\) 1.01132e11 0.176751
\(411\) −9.26859e10 −0.160223
\(412\) −6.69569e10 −0.114487
\(413\) −1.90359e10 −0.0321957
\(414\) 1.85760e11 0.310779
\(415\) 2.30147e10 0.0380880
\(416\) 4.68566e10 0.0767098
\(417\) 6.88375e11 1.11484
\(418\) −3.53758e11 −0.566778
\(419\) −4.45084e11 −0.705471 −0.352736 0.935723i \(-0.614748\pi\)
−0.352736 + 0.935723i \(0.614748\pi\)
\(420\) −2.05009e9 −0.00321478
\(421\) −2.91834e11 −0.452758 −0.226379 0.974039i \(-0.572689\pi\)
−0.226379 + 0.974039i \(0.572689\pi\)
\(422\) 8.05196e11 1.23593
\(423\) 1.96838e11 0.298936
\(424\) −2.74662e11 −0.412716
\(425\) −1.13786e11 −0.169175
\(426\) −1.19874e11 −0.176352
\(427\) 1.02082e11 0.148602
\(428\) −4.02451e10 −0.0579716
\(429\) 2.34261e11 0.333920
\(430\) −3.99561e11 −0.563605
\(431\) −6.26106e11 −0.873978 −0.436989 0.899467i \(-0.643955\pi\)
−0.436989 + 0.899467i \(0.643955\pi\)
\(432\) 1.47888e11 0.204295
\(433\) −6.10341e11 −0.834405 −0.417203 0.908813i \(-0.636989\pi\)
−0.417203 + 0.908813i \(0.636989\pi\)
\(434\) −8.72987e10 −0.118115
\(435\) −1.97731e11 −0.264773
\(436\) −5.62601e10 −0.0745609
\(437\) 3.81020e11 0.499783
\(438\) 7.24152e11 0.940148
\(439\) 7.33210e11 0.942190 0.471095 0.882083i \(-0.343859\pi\)
0.471095 + 0.882083i \(0.343859\pi\)
\(440\) −2.57022e11 −0.326913
\(441\) −2.48568e11 −0.312948
\(442\) −9.25199e10 −0.115301
\(443\) −8.62779e11 −1.06435 −0.532173 0.846636i \(-0.678624\pi\)
−0.532173 + 0.846636i \(0.678624\pi\)
\(444\) −2.84974e9 −0.00348002
\(445\) 5.06841e11 0.612705
\(446\) −3.94954e11 −0.472650
\(447\) −2.36750e11 −0.280483
\(448\) 1.95188e11 0.228929
\(449\) −3.21480e11 −0.373289 −0.186645 0.982427i \(-0.559761\pi\)
−0.186645 + 0.982427i \(0.559761\pi\)
\(450\) 2.64399e11 0.303951
\(451\) 4.36622e11 0.496949
\(452\) 9.99652e10 0.112649
\(453\) −1.35604e11 −0.151297
\(454\) −4.64926e11 −0.513609
\(455\) 4.50476e10 0.0492742
\(456\) 2.84512e11 0.308148
\(457\) −1.73149e12 −1.85693 −0.928467 0.371415i \(-0.878873\pi\)
−0.928467 + 0.371415i \(0.878873\pi\)
\(458\) −2.45451e11 −0.260658
\(459\) −3.50545e10 −0.0368627
\(460\) −1.95261e10 −0.0203332
\(461\) 7.85929e11 0.810455 0.405228 0.914216i \(-0.367192\pi\)
0.405228 + 0.914216i \(0.367192\pi\)
\(462\) −1.43186e11 −0.146221
\(463\) −7.57858e11 −0.766431 −0.383216 0.923659i \(-0.625183\pi\)
−0.383216 + 0.923659i \(0.625183\pi\)
\(464\) −1.42239e12 −1.42458
\(465\) −9.20212e10 −0.0912745
\(466\) −8.05239e11 −0.791022
\(467\) −2.11064e11 −0.205347 −0.102674 0.994715i \(-0.532740\pi\)
−0.102674 + 0.994715i \(0.532740\pi\)
\(468\) 1.32892e10 0.0128054
\(469\) 4.43895e11 0.423646
\(470\) −3.34719e11 −0.316403
\(471\) 6.17311e11 0.577976
\(472\) −1.35384e11 −0.125554
\(473\) −1.72505e12 −1.58462
\(474\) −1.05293e12 −0.958070
\(475\) 5.42319e11 0.488803
\(476\) 3.49564e9 0.00312101
\(477\) −1.61290e11 −0.142651
\(478\) −6.38645e11 −0.559543
\(479\) −1.00601e12 −0.873158 −0.436579 0.899666i \(-0.643810\pi\)
−0.436579 + 0.899666i \(0.643810\pi\)
\(480\) −3.01891e10 −0.0259576
\(481\) 6.26187e10 0.0533397
\(482\) 1.27802e11 0.107851
\(483\) 1.54220e11 0.128938
\(484\) −1.27467e9 −0.00105583
\(485\) 6.77914e8 0.000556335 0
\(486\) 8.14546e10 0.0662297
\(487\) −1.83444e12 −1.47783 −0.738914 0.673800i \(-0.764661\pi\)
−0.738914 + 0.673800i \(0.764661\pi\)
\(488\) 7.26012e11 0.579502
\(489\) 1.44519e12 1.14297
\(490\) 4.22685e11 0.331233
\(491\) 1.51402e11 0.117562 0.0587808 0.998271i \(-0.481279\pi\)
0.0587808 + 0.998271i \(0.481279\pi\)
\(492\) 2.47688e10 0.0190573
\(493\) 3.37154e11 0.257049
\(494\) 4.40963e11 0.333144
\(495\) −1.50931e11 −0.112994
\(496\) −6.61959e11 −0.491093
\(497\) −9.95206e10 −0.0731660
\(498\) 9.11863e10 0.0664351
\(499\) −1.06835e12 −0.771366 −0.385683 0.922631i \(-0.626034\pi\)
−0.385683 + 0.922631i \(0.626034\pi\)
\(500\) −5.92590e10 −0.0424023
\(501\) −9.30421e11 −0.659796
\(502\) 1.02252e12 0.718627
\(503\) 5.89639e11 0.410705 0.205353 0.978688i \(-0.434166\pi\)
0.205353 + 0.978688i \(0.434166\pi\)
\(504\) 1.15158e11 0.0794982
\(505\) −5.76108e11 −0.394178
\(506\) −1.36377e12 −0.924836
\(507\) 5.66955e11 0.381077
\(508\) −4.37249e10 −0.0291301
\(509\) 1.50529e12 0.994009 0.497005 0.867748i \(-0.334433\pi\)
0.497005 + 0.867748i \(0.334433\pi\)
\(510\) 5.96094e10 0.0390166
\(511\) 6.01200e11 0.390054
\(512\) 1.37471e12 0.884088
\(513\) 1.67075e11 0.106508
\(514\) −1.52056e12 −0.960881
\(515\) −9.47924e11 −0.593801
\(516\) −9.78586e10 −0.0607680
\(517\) −1.44510e12 −0.889593
\(518\) −3.82740e10 −0.0233571
\(519\) 6.55445e11 0.396537
\(520\) 3.20381e11 0.192155
\(521\) 1.04958e12 0.624088 0.312044 0.950068i \(-0.398986\pi\)
0.312044 + 0.950068i \(0.398986\pi\)
\(522\) −7.83429e11 −0.461830
\(523\) −2.30838e12 −1.34912 −0.674558 0.738222i \(-0.735666\pi\)
−0.674558 + 0.738222i \(0.735666\pi\)
\(524\) 6.60149e10 0.0382518
\(525\) 2.19507e11 0.126105
\(526\) −2.52386e12 −1.43757
\(527\) 1.56907e11 0.0886121
\(528\) −1.08573e12 −0.607954
\(529\) −3.32280e11 −0.184482
\(530\) 2.74271e11 0.150986
\(531\) −7.95020e10 −0.0433963
\(532\) −1.66607e10 −0.00901761
\(533\) −5.44255e11 −0.292099
\(534\) 2.00815e12 1.06871
\(535\) −5.69758e11 −0.300676
\(536\) 3.15701e12 1.65209
\(537\) 1.17445e12 0.609467
\(538\) 3.33607e12 1.71678
\(539\) 1.82488e12 0.931290
\(540\) −8.56206e9 −0.00433317
\(541\) 1.72825e12 0.867399 0.433699 0.901058i \(-0.357208\pi\)
0.433699 + 0.901058i \(0.357208\pi\)
\(542\) 1.99722e12 0.994095
\(543\) −1.06852e12 −0.527452
\(544\) 5.14758e10 0.0252005
\(545\) −7.96487e11 −0.386718
\(546\) 1.78483e11 0.0859468
\(547\) −1.36998e12 −0.654292 −0.327146 0.944974i \(-0.606087\pi\)
−0.327146 + 0.944974i \(0.606087\pi\)
\(548\) 3.86012e10 0.0182847
\(549\) 4.26338e11 0.200299
\(550\) −1.94110e12 −0.904516
\(551\) −1.60692e12 −0.742699
\(552\) 1.09682e12 0.502818
\(553\) −8.74156e11 −0.397490
\(554\) 2.30202e12 1.03828
\(555\) −4.03444e10 −0.0180495
\(556\) −2.86690e11 −0.127226
\(557\) 2.50228e12 1.10151 0.550753 0.834668i \(-0.314341\pi\)
0.550753 + 0.834668i \(0.314341\pi\)
\(558\) −3.64597e11 −0.159206
\(559\) 2.15029e12 0.931417
\(560\) −2.08783e11 −0.0897115
\(561\) 2.57355e11 0.109698
\(562\) 2.29706e12 0.971314
\(563\) −1.45935e12 −0.612167 −0.306084 0.952005i \(-0.599019\pi\)
−0.306084 + 0.952005i \(0.599019\pi\)
\(564\) −8.19780e10 −0.0341147
\(565\) 1.41523e12 0.584264
\(566\) −3.18203e12 −1.30326
\(567\) 6.76247e10 0.0274778
\(568\) −7.07796e11 −0.285325
\(569\) 3.11112e12 1.24426 0.622131 0.782913i \(-0.286267\pi\)
0.622131 + 0.782913i \(0.286267\pi\)
\(570\) −2.84107e11 −0.112732
\(571\) 4.63281e12 1.82382 0.911909 0.410391i \(-0.134608\pi\)
0.911909 + 0.410391i \(0.134608\pi\)
\(572\) −9.75635e10 −0.0381070
\(573\) −1.13880e12 −0.441319
\(574\) 3.32661e11 0.127908
\(575\) 2.09069e12 0.797600
\(576\) 8.15188e11 0.308572
\(577\) 3.67714e12 1.38108 0.690540 0.723294i \(-0.257373\pi\)
0.690540 + 0.723294i \(0.257373\pi\)
\(578\) 2.66869e12 0.994540
\(579\) −1.96428e12 −0.726358
\(580\) 8.23497e10 0.0302159
\(581\) 7.57040e10 0.0275630
\(582\) 2.68596e9 0.000970390 0
\(583\) 1.18412e12 0.424511
\(584\) 4.27576e12 1.52109
\(585\) 1.88138e11 0.0664163
\(586\) −5.83187e11 −0.204300
\(587\) 3.18227e12 1.10628 0.553141 0.833088i \(-0.313429\pi\)
0.553141 + 0.833088i \(0.313429\pi\)
\(588\) 1.03522e11 0.0357137
\(589\) −7.47840e11 −0.256029
\(590\) 1.35191e11 0.0459320
\(591\) −1.82716e12 −0.616075
\(592\) −2.90220e11 −0.0971134
\(593\) −1.13721e12 −0.377654 −0.188827 0.982010i \(-0.560469\pi\)
−0.188827 + 0.982010i \(0.560469\pi\)
\(594\) −5.98005e11 −0.197091
\(595\) 4.94885e10 0.0161874
\(596\) 9.86002e10 0.0320088
\(597\) 2.23095e12 0.718795
\(598\) 1.69996e12 0.543605
\(599\) 8.18505e8 0.000259777 0 0.000129888 1.00000i \(-0.499959\pi\)
0.000129888 1.00000i \(0.499959\pi\)
\(600\) 1.56115e12 0.491771
\(601\) −8.21445e11 −0.256828 −0.128414 0.991721i \(-0.540989\pi\)
−0.128414 + 0.991721i \(0.540989\pi\)
\(602\) −1.31431e12 −0.407862
\(603\) 1.85390e12 0.571028
\(604\) 5.64754e10 0.0172661
\(605\) −1.80457e10 −0.00547615
\(606\) −2.28260e12 −0.687547
\(607\) −1.81063e12 −0.541353 −0.270676 0.962670i \(-0.587247\pi\)
−0.270676 + 0.962670i \(0.587247\pi\)
\(608\) −2.45342e11 −0.0728123
\(609\) −6.50413e11 −0.191607
\(610\) −7.24979e11 −0.212003
\(611\) 1.80134e12 0.522889
\(612\) 1.45993e10 0.00420678
\(613\) 1.14483e12 0.327468 0.163734 0.986505i \(-0.447646\pi\)
0.163734 + 0.986505i \(0.447646\pi\)
\(614\) 1.90623e12 0.541273
\(615\) 3.50657e11 0.0988427
\(616\) −8.45442e11 −0.236576
\(617\) −1.58187e12 −0.439428 −0.219714 0.975564i \(-0.570512\pi\)
−0.219714 + 0.975564i \(0.570512\pi\)
\(618\) −3.75577e12 −1.03574
\(619\) −1.91787e12 −0.525062 −0.262531 0.964924i \(-0.584557\pi\)
−0.262531 + 0.964924i \(0.584557\pi\)
\(620\) 3.83244e10 0.0104163
\(621\) 6.44091e11 0.173794
\(622\) 2.02437e12 0.542291
\(623\) 1.66719e12 0.443394
\(624\) 1.35338e12 0.357346
\(625\) 2.53027e12 0.663296
\(626\) 6.90410e12 1.79689
\(627\) −1.22659e12 −0.316954
\(628\) −2.57094e11 −0.0659589
\(629\) 6.87918e10 0.0175230
\(630\) −1.14994e11 −0.0290833
\(631\) −3.98851e12 −1.00156 −0.500782 0.865573i \(-0.666954\pi\)
−0.500782 + 0.865573i \(0.666954\pi\)
\(632\) −6.21704e12 −1.55009
\(633\) 2.79187e12 0.691161
\(634\) 7.68190e12 1.88828
\(635\) −6.19024e11 −0.151086
\(636\) 6.71732e10 0.0162794
\(637\) −2.27474e12 −0.547398
\(638\) 5.75160e12 1.37435
\(639\) −4.15641e11 −0.0986198
\(640\) −1.57704e12 −0.371562
\(641\) 4.30645e12 1.00753 0.503765 0.863841i \(-0.331948\pi\)
0.503765 + 0.863841i \(0.331948\pi\)
\(642\) −2.25744e12 −0.524455
\(643\) −2.93311e12 −0.676674 −0.338337 0.941025i \(-0.609864\pi\)
−0.338337 + 0.941025i \(0.609864\pi\)
\(644\) −6.42288e10 −0.0147144
\(645\) −1.38541e12 −0.315180
\(646\) 4.84435e11 0.109443
\(647\) 1.29709e12 0.291006 0.145503 0.989358i \(-0.453520\pi\)
0.145503 + 0.989358i \(0.453520\pi\)
\(648\) 4.80950e11 0.107155
\(649\) 5.83670e11 0.129142
\(650\) 2.41961e12 0.531661
\(651\) −3.02693e11 −0.0660523
\(652\) −6.01882e11 −0.130436
\(653\) 4.63066e12 0.996630 0.498315 0.866996i \(-0.333952\pi\)
0.498315 + 0.866996i \(0.333952\pi\)
\(654\) −3.15576e12 −0.674534
\(655\) 9.34588e11 0.198397
\(656\) 2.52247e12 0.531812
\(657\) 2.51087e12 0.525751
\(658\) −1.10102e12 −0.228970
\(659\) 3.08986e11 0.0638196 0.0319098 0.999491i \(-0.489841\pi\)
0.0319098 + 0.999491i \(0.489841\pi\)
\(660\) 6.28590e10 0.0128949
\(661\) 5.48364e12 1.11728 0.558640 0.829410i \(-0.311323\pi\)
0.558640 + 0.829410i \(0.311323\pi\)
\(662\) −4.27271e11 −0.0864654
\(663\) −3.20796e11 −0.0644790
\(664\) 5.38411e11 0.107487
\(665\) −2.35870e11 −0.0467708
\(666\) −1.59849e11 −0.0314829
\(667\) −6.19485e12 −1.21189
\(668\) 3.87496e11 0.0752962
\(669\) −1.36943e12 −0.264316
\(670\) −3.15251e12 −0.604394
\(671\) −3.12999e12 −0.596063
\(672\) −9.93036e10 −0.0187846
\(673\) −4.26313e12 −0.801053 −0.400526 0.916285i \(-0.631173\pi\)
−0.400526 + 0.916285i \(0.631173\pi\)
\(674\) −7.92120e12 −1.47850
\(675\) 9.16756e11 0.169976
\(676\) −2.36122e11 −0.0434887
\(677\) 3.55841e11 0.0651038 0.0325519 0.999470i \(-0.489637\pi\)
0.0325519 + 0.999470i \(0.489637\pi\)
\(678\) 5.60728e12 1.01910
\(679\) 2.22992e9 0.000402601 0
\(680\) 3.51965e11 0.0631261
\(681\) −1.61205e12 −0.287221
\(682\) 2.67671e12 0.473775
\(683\) −5.38485e12 −0.946849 −0.473424 0.880834i \(-0.656982\pi\)
−0.473424 + 0.880834i \(0.656982\pi\)
\(684\) −6.95823e10 −0.0121548
\(685\) 5.46487e11 0.0948357
\(686\) 2.87131e12 0.495019
\(687\) −8.51058e11 −0.145765
\(688\) −9.96599e12 −1.69579
\(689\) −1.47603e12 −0.249521
\(690\) −1.09526e12 −0.183949
\(691\) 2.56126e12 0.427369 0.213684 0.976903i \(-0.431454\pi\)
0.213684 + 0.976903i \(0.431454\pi\)
\(692\) −2.72976e11 −0.0452529
\(693\) −4.96471e11 −0.0817701
\(694\) 1.10881e13 1.81442
\(695\) −4.05874e12 −0.659871
\(696\) −4.62577e12 −0.747209
\(697\) −5.97910e11 −0.0959595
\(698\) −5.77794e12 −0.921348
\(699\) −2.79203e12 −0.442356
\(700\) −9.14189e10 −0.0143911
\(701\) −6.38644e12 −0.998914 −0.499457 0.866339i \(-0.666467\pi\)
−0.499457 + 0.866339i \(0.666467\pi\)
\(702\) 7.45421e11 0.115847
\(703\) −3.27872e11 −0.0506297
\(704\) −5.98476e12 −0.918269
\(705\) −1.16058e12 −0.176939
\(706\) 4.48500e12 0.679425
\(707\) −1.89504e12 −0.285253
\(708\) 3.31105e10 0.00495240
\(709\) 4.71903e12 0.701367 0.350683 0.936494i \(-0.385949\pi\)
0.350683 + 0.936494i \(0.385949\pi\)
\(710\) 7.06788e11 0.104382
\(711\) −3.65085e12 −0.535773
\(712\) 1.18572e13 1.72910
\(713\) −2.88300e12 −0.417774
\(714\) 1.96078e11 0.0282350
\(715\) −1.38123e12 −0.197646
\(716\) −4.89127e11 −0.0695526
\(717\) −2.21439e12 −0.312909
\(718\) 9.32259e10 0.0130911
\(719\) −8.71884e12 −1.21669 −0.608343 0.793674i \(-0.708166\pi\)
−0.608343 + 0.793674i \(0.708166\pi\)
\(720\) −8.71966e11 −0.120921
\(721\) −3.11808e12 −0.429714
\(722\) 5.22940e12 0.716201
\(723\) 4.43130e11 0.0603127
\(724\) 4.45010e11 0.0601930
\(725\) −8.81734e12 −1.18527
\(726\) −7.14990e10 −0.00955179
\(727\) −1.17664e13 −1.56220 −0.781101 0.624405i \(-0.785342\pi\)
−0.781101 + 0.624405i \(0.785342\pi\)
\(728\) 1.05385e12 0.139056
\(729\) 2.82430e11 0.0370370
\(730\) −4.26968e12 −0.556471
\(731\) 2.36227e12 0.305986
\(732\) −1.77559e11 −0.0228582
\(733\) −1.13764e12 −0.145559 −0.0727794 0.997348i \(-0.523187\pi\)
−0.0727794 + 0.997348i \(0.523187\pi\)
\(734\) 1.36573e13 1.73673
\(735\) 1.46558e12 0.185233
\(736\) −9.45816e11 −0.118811
\(737\) −1.36105e13 −1.69930
\(738\) 1.38934e12 0.172407
\(739\) 9.77524e12 1.20567 0.602834 0.797867i \(-0.294038\pi\)
0.602834 + 0.797867i \(0.294038\pi\)
\(740\) 1.68024e10 0.00205982
\(741\) 1.52896e12 0.186301
\(742\) 9.02181e11 0.109264
\(743\) 6.06927e11 0.0730612 0.0365306 0.999333i \(-0.488369\pi\)
0.0365306 + 0.999333i \(0.488369\pi\)
\(744\) −2.15277e12 −0.257584
\(745\) 1.39590e12 0.166017
\(746\) 1.36583e13 1.61463
\(747\) 3.16172e11 0.0371519
\(748\) −1.07182e11 −0.0125188
\(749\) −1.87415e12 −0.217589
\(750\) −3.32397e12 −0.383603
\(751\) −3.40247e12 −0.390315 −0.195157 0.980772i \(-0.562522\pi\)
−0.195157 + 0.980772i \(0.562522\pi\)
\(752\) −8.34869e12 −0.952003
\(753\) 3.54540e12 0.401872
\(754\) −7.16944e12 −0.807820
\(755\) 7.99535e11 0.0895522
\(756\) −2.81639e10 −0.00313577
\(757\) 6.46608e11 0.0715665 0.0357832 0.999360i \(-0.488607\pi\)
0.0357832 + 0.999360i \(0.488607\pi\)
\(758\) −4.24294e12 −0.466827
\(759\) −4.72864e12 −0.517188
\(760\) −1.67752e12 −0.182392
\(761\) −1.30326e13 −1.40864 −0.704320 0.709882i \(-0.748748\pi\)
−0.704320 + 0.709882i \(0.748748\pi\)
\(762\) −2.45263e12 −0.263533
\(763\) −2.61995e12 −0.279855
\(764\) 4.74281e11 0.0503635
\(765\) 2.06685e11 0.0218189
\(766\) −1.60985e13 −1.68949
\(767\) −7.27552e11 −0.0759075
\(768\) −1.09557e12 −0.113636
\(769\) −3.31464e11 −0.0341797 −0.0170898 0.999854i \(-0.505440\pi\)
−0.0170898 + 0.999854i \(0.505440\pi\)
\(770\) 8.44239e11 0.0865480
\(771\) −5.27228e12 −0.537345
\(772\) 8.18072e11 0.0828922
\(773\) −1.11690e13 −1.12514 −0.562568 0.826751i \(-0.690187\pi\)
−0.562568 + 0.826751i \(0.690187\pi\)
\(774\) −5.48911e12 −0.549753
\(775\) −4.10347e12 −0.408595
\(776\) 1.58593e10 0.00157002
\(777\) −1.32708e11 −0.0130618
\(778\) 1.16359e13 1.13865
\(779\) 2.84973e12 0.277258
\(780\) −7.83545e10 −0.00757946
\(781\) 3.05146e12 0.293479
\(782\) 1.86755e12 0.178583
\(783\) −2.71640e12 −0.258265
\(784\) 1.05428e13 0.996625
\(785\) −3.63973e12 −0.342102
\(786\) 3.70293e12 0.346054
\(787\) −1.36913e13 −1.27221 −0.636105 0.771602i \(-0.719456\pi\)
−0.636105 + 0.771602i \(0.719456\pi\)
\(788\) 7.60964e11 0.0703066
\(789\) −8.75104e12 −0.803920
\(790\) 6.20819e12 0.567079
\(791\) 4.65523e12 0.422812
\(792\) −3.53093e12 −0.318879
\(793\) 3.90157e12 0.350357
\(794\) 6.95041e12 0.620609
\(795\) 9.50985e11 0.0844349
\(796\) −9.29132e11 −0.0820292
\(797\) 1.16938e13 1.02658 0.513290 0.858215i \(-0.328427\pi\)
0.513290 + 0.858215i \(0.328427\pi\)
\(798\) −9.34538e11 −0.0815800
\(799\) 1.97892e12 0.171778
\(800\) −1.34621e12 −0.116201
\(801\) 6.96292e12 0.597647
\(802\) 1.13277e13 0.966848
\(803\) −1.84337e13 −1.56456
\(804\) −7.72099e11 −0.0651660
\(805\) −9.09301e11 −0.0763179
\(806\) −3.33656e12 −0.278478
\(807\) 1.15672e13 0.960061
\(808\) −1.34776e13 −1.11240
\(809\) 2.55564e12 0.209765 0.104882 0.994485i \(-0.466553\pi\)
0.104882 + 0.994485i \(0.466553\pi\)
\(810\) −4.80265e11 −0.0392011
\(811\) 9.70911e12 0.788107 0.394054 0.919087i \(-0.371072\pi\)
0.394054 + 0.919087i \(0.371072\pi\)
\(812\) 2.70880e11 0.0218663
\(813\) 6.92499e12 0.555919
\(814\) 1.17354e12 0.0936889
\(815\) −8.52098e12 −0.676519
\(816\) 1.48680e12 0.117394
\(817\) −1.12589e13 −0.884094
\(818\) −1.00809e13 −0.787247
\(819\) 6.18858e11 0.0480633
\(820\) −1.46039e11 −0.0112800
\(821\) −8.51723e12 −0.654265 −0.327133 0.944978i \(-0.606082\pi\)
−0.327133 + 0.944978i \(0.606082\pi\)
\(822\) 2.16523e12 0.165417
\(823\) 1.00520e13 0.763750 0.381875 0.924214i \(-0.375278\pi\)
0.381875 + 0.924214i \(0.375278\pi\)
\(824\) −2.21760e13 −1.67575
\(825\) −6.73043e12 −0.505825
\(826\) 4.44696e11 0.0332394
\(827\) −8.59417e11 −0.0638895 −0.0319447 0.999490i \(-0.510170\pi\)
−0.0319447 + 0.999490i \(0.510170\pi\)
\(828\) −2.68247e11 −0.0198334
\(829\) 1.45843e13 1.07248 0.536242 0.844064i \(-0.319844\pi\)
0.536242 + 0.844064i \(0.319844\pi\)
\(830\) −5.37644e11 −0.0393227
\(831\) 7.98185e12 0.580630
\(832\) 7.46008e12 0.539745
\(833\) −2.49899e12 −0.179830
\(834\) −1.60811e13 −1.15098
\(835\) 5.48586e12 0.390531
\(836\) 5.10844e11 0.0361709
\(837\) −1.26418e12 −0.0890313
\(838\) 1.03976e13 0.728341
\(839\) 1.28668e13 0.896484 0.448242 0.893912i \(-0.352050\pi\)
0.448242 + 0.893912i \(0.352050\pi\)
\(840\) −6.78985e11 −0.0470548
\(841\) 1.16192e13 0.800927
\(842\) 6.81752e12 0.467436
\(843\) 7.96467e12 0.543180
\(844\) −1.16274e12 −0.0788755
\(845\) −3.34283e12 −0.225558
\(846\) −4.59833e12 −0.308627
\(847\) −5.93593e10 −0.00396291
\(848\) 6.84096e12 0.454293
\(849\) −1.10331e13 −0.728810
\(850\) 2.65814e12 0.174660
\(851\) −1.26398e12 −0.0826147
\(852\) 1.73103e11 0.0112545
\(853\) 9.19067e12 0.594397 0.297198 0.954816i \(-0.403948\pi\)
0.297198 + 0.954816i \(0.403948\pi\)
\(854\) −2.38473e12 −0.153419
\(855\) −9.85092e11 −0.0630419
\(856\) −1.33291e13 −0.848532
\(857\) 6.56735e12 0.415888 0.207944 0.978141i \(-0.433323\pi\)
0.207944 + 0.978141i \(0.433323\pi\)
\(858\) −5.47256e12 −0.344745
\(859\) −1.15305e13 −0.722566 −0.361283 0.932456i \(-0.617661\pi\)
−0.361283 + 0.932456i \(0.617661\pi\)
\(860\) 5.76985e11 0.0359684
\(861\) 1.15345e12 0.0715291
\(862\) 1.46264e13 0.902311
\(863\) −3.57238e12 −0.219235 −0.109617 0.993974i \(-0.534963\pi\)
−0.109617 + 0.993974i \(0.534963\pi\)
\(864\) −4.14734e11 −0.0253197
\(865\) −3.86458e12 −0.234709
\(866\) 1.42582e13 0.861455
\(867\) 9.25320e12 0.556168
\(868\) 1.26064e11 0.00753791
\(869\) 2.68030e13 1.59439
\(870\) 4.61918e12 0.273356
\(871\) 1.69657e13 0.998825
\(872\) −1.86332e13 −1.09135
\(873\) 9.31309e9 0.000542663 0
\(874\) −8.90100e12 −0.515985
\(875\) −2.75960e12 −0.159151
\(876\) −1.04571e12 −0.0599988
\(877\) 3.20992e13 1.83230 0.916149 0.400837i \(-0.131281\pi\)
0.916149 + 0.400837i \(0.131281\pi\)
\(878\) −1.71285e13 −0.972734
\(879\) −2.02210e12 −0.114249
\(880\) 6.40160e12 0.359846
\(881\) −2.72871e13 −1.52604 −0.763020 0.646375i \(-0.776284\pi\)
−0.763020 + 0.646375i \(0.776284\pi\)
\(882\) 5.80679e12 0.323093
\(883\) −5.72818e12 −0.317098 −0.158549 0.987351i \(-0.550682\pi\)
−0.158549 + 0.987351i \(0.550682\pi\)
\(884\) 1.33603e11 0.00735837
\(885\) 4.68753e11 0.0256861
\(886\) 2.01554e13 1.09885
\(887\) 9.01105e12 0.488787 0.244393 0.969676i \(-0.421411\pi\)
0.244393 + 0.969676i \(0.421411\pi\)
\(888\) −9.43828e11 −0.0509371
\(889\) −2.03621e12 −0.109336
\(890\) −1.18403e13 −0.632568
\(891\) −2.07348e12 −0.110217
\(892\) 5.70333e11 0.0301638
\(893\) −9.43183e12 −0.496323
\(894\) 5.53071e12 0.289576
\(895\) −6.92468e12 −0.360742
\(896\) −5.18747e12 −0.268887
\(897\) 5.89431e12 0.303995
\(898\) 7.51009e12 0.385391
\(899\) 1.21588e13 0.620830
\(900\) −3.81805e11 −0.0193977
\(901\) −1.62154e12 −0.0819720
\(902\) −1.01999e13 −0.513059
\(903\) −4.55713e12 −0.228085
\(904\) 3.31082e13 1.64884
\(905\) 6.30011e12 0.312197
\(906\) 3.16784e12 0.156202
\(907\) −1.01989e12 −0.0500402 −0.0250201 0.999687i \(-0.507965\pi\)
−0.0250201 + 0.999687i \(0.507965\pi\)
\(908\) 6.71376e11 0.0327778
\(909\) −7.91450e12 −0.384491
\(910\) −1.05235e12 −0.0508716
\(911\) −1.10786e13 −0.532909 −0.266455 0.963847i \(-0.585852\pi\)
−0.266455 + 0.963847i \(0.585852\pi\)
\(912\) −7.08631e12 −0.339190
\(913\) −2.32120e12 −0.110559
\(914\) 4.04492e13 1.91713
\(915\) −2.51374e12 −0.118556
\(916\) 3.54443e11 0.0166348
\(917\) 3.07422e12 0.143573
\(918\) 8.18907e11 0.0380577
\(919\) −1.02036e13 −0.471881 −0.235941 0.971767i \(-0.575817\pi\)
−0.235941 + 0.971767i \(0.575817\pi\)
\(920\) −6.46699e12 −0.297617
\(921\) 6.60950e12 0.302692
\(922\) −1.83601e13 −0.836729
\(923\) −3.80368e12 −0.172503
\(924\) 2.06767e11 0.00933164
\(925\) −1.79906e12 −0.0807995
\(926\) 1.77043e13 0.791278
\(927\) −1.30225e13 −0.579207
\(928\) 3.98891e12 0.176558
\(929\) −3.80349e13 −1.67537 −0.837686 0.546152i \(-0.816092\pi\)
−0.837686 + 0.546152i \(0.816092\pi\)
\(930\) 2.14970e12 0.0942335
\(931\) 1.19105e13 0.519587
\(932\) 1.16280e12 0.0504818
\(933\) 7.01913e12 0.303260
\(934\) 4.93066e12 0.212004
\(935\) −1.51739e12 −0.0649301
\(936\) 4.40135e12 0.187432
\(937\) 3.02627e13 1.28256 0.641282 0.767305i \(-0.278403\pi\)
0.641282 + 0.767305i \(0.278403\pi\)
\(938\) −1.03698e13 −0.437379
\(939\) 2.39387e13 1.00486
\(940\) 4.83351e11 0.0201924
\(941\) 1.55023e12 0.0644531 0.0322266 0.999481i \(-0.489740\pi\)
0.0322266 + 0.999481i \(0.489740\pi\)
\(942\) −1.44210e13 −0.596713
\(943\) 1.09860e13 0.452414
\(944\) 3.37199e12 0.138202
\(945\) −3.98722e11 −0.0162640
\(946\) 4.02987e13 1.63599
\(947\) −3.90879e13 −1.57931 −0.789654 0.613552i \(-0.789740\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(948\) 1.52048e12 0.0611426
\(949\) 2.29779e13 0.919627
\(950\) −1.26691e13 −0.504649
\(951\) 2.66356e13 1.05597
\(952\) 1.15775e12 0.0456822
\(953\) −2.78189e13 −1.09250 −0.546251 0.837622i \(-0.683945\pi\)
−0.546251 + 0.837622i \(0.683945\pi\)
\(954\) 3.76790e12 0.147276
\(955\) 6.71450e12 0.261215
\(956\) 9.22234e11 0.0357092
\(957\) 1.99427e13 0.768563
\(958\) 2.35014e13 0.901464
\(959\) 1.79760e12 0.0686294
\(960\) −4.80644e12 −0.182643
\(961\) −2.07811e13 −0.785982
\(962\) −1.46283e12 −0.0550689
\(963\) −7.82727e12 −0.293286
\(964\) −1.84552e11 −0.00688291
\(965\) 1.15816e13 0.429929
\(966\) −3.60274e12 −0.133118
\(967\) 3.01952e12 0.111050 0.0555250 0.998457i \(-0.482317\pi\)
0.0555250 + 0.998457i \(0.482317\pi\)
\(968\) −4.22167e11 −0.0154541
\(969\) 1.67969e12 0.0612030
\(970\) −1.58367e10 −0.000574371 0
\(971\) 4.22227e13 1.52426 0.762130 0.647424i \(-0.224154\pi\)
0.762130 + 0.647424i \(0.224154\pi\)
\(972\) −1.17624e11 −0.00422668
\(973\) −1.33507e13 −0.477526
\(974\) 4.28543e13 1.52574
\(975\) 8.38956e12 0.297316
\(976\) −1.80827e13 −0.637880
\(977\) 2.06518e12 0.0725159 0.0362579 0.999342i \(-0.488456\pi\)
0.0362579 + 0.999342i \(0.488456\pi\)
\(978\) −3.37609e13 −1.18002
\(979\) −5.11188e13 −1.77852
\(980\) −6.10377e11 −0.0211388
\(981\) −1.09420e13 −0.377214
\(982\) −3.53690e12 −0.121373
\(983\) −2.25904e13 −0.771674 −0.385837 0.922567i \(-0.626087\pi\)
−0.385837 + 0.922567i \(0.626087\pi\)
\(984\) 8.20336e12 0.278942
\(985\) 1.07731e13 0.364653
\(986\) −7.87623e12 −0.265382
\(987\) −3.81759e12 −0.128045
\(988\) −6.36773e11 −0.0212607
\(989\) −4.34044e13 −1.44261
\(990\) 3.52590e12 0.116657
\(991\) 5.55935e12 0.183102 0.0915509 0.995800i \(-0.470818\pi\)
0.0915509 + 0.995800i \(0.470818\pi\)
\(992\) 1.85638e12 0.0608646
\(993\) −1.48149e12 −0.0483533
\(994\) 2.32490e12 0.0755379
\(995\) −1.31539e13 −0.425453
\(996\) −1.31677e11 −0.00423979
\(997\) 2.57742e13 0.826145 0.413073 0.910698i \(-0.364456\pi\)
0.413073 + 0.910698i \(0.364456\pi\)
\(998\) 2.49576e13 0.796372
\(999\) −5.54247e11 −0.0176059
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.b.1.6 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.6 21 1.1 even 1 trivial