Properties

Label 177.10.a.c.1.19
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 1.19
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+34.5007 q^{2} -81.0000 q^{3} +678.300 q^{4} -2125.49 q^{5} -2794.56 q^{6} -11083.2 q^{7} +5737.48 q^{8} +6561.00 q^{9} -73331.0 q^{10} -12849.6 q^{11} -54942.3 q^{12} -98344.5 q^{13} -382379. q^{14} +172165. q^{15} -149342. q^{16} -55245.8 q^{17} +226359. q^{18} +134898. q^{19} -1.44172e6 q^{20} +897739. q^{21} -443321. q^{22} +1.76768e6 q^{23} -464736. q^{24} +2.56459e6 q^{25} -3.39296e6 q^{26} -531441. q^{27} -7.51774e6 q^{28} -1.27561e6 q^{29} +5.93981e6 q^{30} +655974. q^{31} -8.09001e6 q^{32} +1.04082e6 q^{33} -1.90602e6 q^{34} +2.35573e7 q^{35} +4.45033e6 q^{36} -1.12387e7 q^{37} +4.65407e6 q^{38} +7.96591e6 q^{39} -1.21950e7 q^{40} +9.02546e6 q^{41} +3.09727e7 q^{42} -3.12935e7 q^{43} -8.71589e6 q^{44} -1.39454e7 q^{45} +6.09862e7 q^{46} +4.08477e7 q^{47} +1.20967e7 q^{48} +8.24838e7 q^{49} +8.84803e7 q^{50} +4.47491e6 q^{51} -6.67071e7 q^{52} +5.63144e7 q^{53} -1.83351e7 q^{54} +2.73117e7 q^{55} -6.35897e7 q^{56} -1.09267e7 q^{57} -4.40095e7 q^{58} +1.21174e7 q^{59} +1.16780e8 q^{60} -5.05723e7 q^{61} +2.26316e7 q^{62} -7.27169e7 q^{63} -2.02648e8 q^{64} +2.09031e8 q^{65} +3.59090e7 q^{66} -2.08793e8 q^{67} -3.74732e7 q^{68} -1.43182e8 q^{69} +8.12743e8 q^{70} -2.83381e8 q^{71} +3.76436e7 q^{72} +3.02362e8 q^{73} -3.87743e8 q^{74} -2.07732e8 q^{75} +9.15013e7 q^{76} +1.42415e8 q^{77} +2.74830e8 q^{78} -6.85379e6 q^{79} +3.17426e8 q^{80} +4.30467e7 q^{81} +3.11385e8 q^{82} -7.30628e7 q^{83} +6.08937e8 q^{84} +1.17425e8 q^{85} -1.07965e9 q^{86} +1.03324e8 q^{87} -7.37244e7 q^{88} -9.42405e8 q^{89} -4.81125e8 q^{90} +1.08997e9 q^{91} +1.19902e9 q^{92} -5.31339e7 q^{93} +1.40928e9 q^{94} -2.86724e8 q^{95} +6.55291e8 q^{96} +5.45381e8 q^{97} +2.84575e9 q^{98} -8.43063e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 34.5007 1.52473 0.762366 0.647147i \(-0.224038\pi\)
0.762366 + 0.647147i \(0.224038\pi\)
\(3\) −81.0000 −0.577350
\(4\) 678.300 1.32481
\(5\) −2125.49 −1.52088 −0.760439 0.649409i \(-0.775016\pi\)
−0.760439 + 0.649409i \(0.775016\pi\)
\(6\) −2794.56 −0.880304
\(7\) −11083.2 −1.74471 −0.872357 0.488870i \(-0.837409\pi\)
−0.872357 + 0.488870i \(0.837409\pi\)
\(8\) 5737.48 0.495241
\(9\) 6561.00 0.333333
\(10\) −73331.0 −2.31893
\(11\) −12849.6 −0.264620 −0.132310 0.991208i \(-0.542239\pi\)
−0.132310 + 0.991208i \(0.542239\pi\)
\(12\) −54942.3 −0.764877
\(13\) −98344.5 −0.955004 −0.477502 0.878631i \(-0.658458\pi\)
−0.477502 + 0.878631i \(0.658458\pi\)
\(14\) −382379. −2.66022
\(15\) 172165. 0.878080
\(16\) −149342. −0.569696
\(17\) −55245.8 −0.160428 −0.0802138 0.996778i \(-0.525560\pi\)
−0.0802138 + 0.996778i \(0.525560\pi\)
\(18\) 226359. 0.508244
\(19\) 134898. 0.237473 0.118736 0.992926i \(-0.462116\pi\)
0.118736 + 0.992926i \(0.462116\pi\)
\(20\) −1.44172e6 −2.01487
\(21\) 897739. 1.00731
\(22\) −443321. −0.403474
\(23\) 1.76768e6 1.31713 0.658564 0.752524i \(-0.271164\pi\)
0.658564 + 0.752524i \(0.271164\pi\)
\(24\) −464736. −0.285927
\(25\) 2.56459e6 1.31307
\(26\) −3.39296e6 −1.45612
\(27\) −531441. −0.192450
\(28\) −7.51774e6 −2.31141
\(29\) −1.27561e6 −0.334909 −0.167455 0.985880i \(-0.553555\pi\)
−0.167455 + 0.985880i \(0.553555\pi\)
\(30\) 5.93981e6 1.33884
\(31\) 655974. 0.127573 0.0637866 0.997964i \(-0.479682\pi\)
0.0637866 + 0.997964i \(0.479682\pi\)
\(32\) −8.09001e6 −1.36387
\(33\) 1.04082e6 0.152778
\(34\) −1.90602e6 −0.244609
\(35\) 2.35573e7 2.65350
\(36\) 4.45033e6 0.441602
\(37\) −1.12387e7 −0.985843 −0.492922 0.870074i \(-0.664071\pi\)
−0.492922 + 0.870074i \(0.664071\pi\)
\(38\) 4.65407e6 0.362082
\(39\) 7.96591e6 0.551372
\(40\) −1.21950e7 −0.753201
\(41\) 9.02546e6 0.498818 0.249409 0.968398i \(-0.419764\pi\)
0.249409 + 0.968398i \(0.419764\pi\)
\(42\) 3.09727e7 1.53588
\(43\) −3.12935e7 −1.39587 −0.697936 0.716160i \(-0.745898\pi\)
−0.697936 + 0.716160i \(0.745898\pi\)
\(44\) −8.71589e6 −0.350570
\(45\) −1.39454e7 −0.506960
\(46\) 6.09862e7 2.00827
\(47\) 4.08477e7 1.22103 0.610517 0.792003i \(-0.290962\pi\)
0.610517 + 0.792003i \(0.290962\pi\)
\(48\) 1.20967e7 0.328914
\(49\) 8.24838e7 2.04403
\(50\) 8.84803e7 2.00208
\(51\) 4.47491e6 0.0926229
\(52\) −6.67071e7 −1.26519
\(53\) 5.63144e7 0.980344 0.490172 0.871626i \(-0.336934\pi\)
0.490172 + 0.871626i \(0.336934\pi\)
\(54\) −1.83351e7 −0.293435
\(55\) 2.73117e7 0.402455
\(56\) −6.35897e7 −0.864053
\(57\) −1.09267e7 −0.137105
\(58\) −4.40095e7 −0.510647
\(59\) 1.21174e7 0.130189
\(60\) 1.16780e8 1.16328
\(61\) −5.05723e7 −0.467658 −0.233829 0.972278i \(-0.575126\pi\)
−0.233829 + 0.972278i \(0.575126\pi\)
\(62\) 2.26316e7 0.194515
\(63\) −7.27169e7 −0.581571
\(64\) −2.02648e8 −1.50985
\(65\) 2.09031e8 1.45244
\(66\) 3.59090e7 0.232946
\(67\) −2.08793e8 −1.26584 −0.632920 0.774217i \(-0.718144\pi\)
−0.632920 + 0.774217i \(0.718144\pi\)
\(68\) −3.74732e7 −0.212535
\(69\) −1.43182e8 −0.760445
\(70\) 8.12743e8 4.04587
\(71\) −2.83381e8 −1.32345 −0.661727 0.749745i \(-0.730176\pi\)
−0.661727 + 0.749745i \(0.730176\pi\)
\(72\) 3.76436e7 0.165080
\(73\) 3.02362e8 1.24616 0.623081 0.782158i \(-0.285881\pi\)
0.623081 + 0.782158i \(0.285881\pi\)
\(74\) −3.87743e8 −1.50315
\(75\) −2.07732e8 −0.758102
\(76\) 9.15013e7 0.314605
\(77\) 1.42415e8 0.461686
\(78\) 2.74830e8 0.840694
\(79\) −6.85379e6 −0.0197974 −0.00989872 0.999951i \(-0.503151\pi\)
−0.00989872 + 0.999951i \(0.503151\pi\)
\(80\) 3.17426e8 0.866439
\(81\) 4.30467e7 0.111111
\(82\) 3.11385e8 0.760563
\(83\) −7.30628e7 −0.168984 −0.0844919 0.996424i \(-0.526927\pi\)
−0.0844919 + 0.996424i \(0.526927\pi\)
\(84\) 6.08937e8 1.33449
\(85\) 1.17425e8 0.243991
\(86\) −1.07965e9 −2.12833
\(87\) 1.03324e8 0.193360
\(88\) −7.37244e7 −0.131051
\(89\) −9.42405e8 −1.59215 −0.796073 0.605201i \(-0.793093\pi\)
−0.796073 + 0.605201i \(0.793093\pi\)
\(90\) −4.81125e8 −0.772977
\(91\) 1.08997e9 1.66621
\(92\) 1.19902e9 1.74494
\(93\) −5.31339e7 −0.0736544
\(94\) 1.40928e9 1.86175
\(95\) −2.86724e8 −0.361167
\(96\) 6.55291e8 0.787433
\(97\) 5.45381e8 0.625499 0.312750 0.949836i \(-0.398750\pi\)
0.312750 + 0.949836i \(0.398750\pi\)
\(98\) 2.84575e9 3.11659
\(99\) −8.43063e7 −0.0882067
\(100\) 1.73956e9 1.73956
\(101\) −2.91991e8 −0.279205 −0.139603 0.990208i \(-0.544583\pi\)
−0.139603 + 0.990208i \(0.544583\pi\)
\(102\) 1.54388e8 0.141225
\(103\) 8.14008e8 0.712625 0.356313 0.934367i \(-0.384034\pi\)
0.356313 + 0.934367i \(0.384034\pi\)
\(104\) −5.64250e8 −0.472957
\(105\) −1.90814e9 −1.53200
\(106\) 1.94289e9 1.49476
\(107\) −3.35348e8 −0.247325 −0.123663 0.992324i \(-0.539464\pi\)
−0.123663 + 0.992324i \(0.539464\pi\)
\(108\) −3.60477e8 −0.254959
\(109\) 1.00621e9 0.682761 0.341381 0.939925i \(-0.389105\pi\)
0.341381 + 0.939925i \(0.389105\pi\)
\(110\) 9.42275e8 0.613636
\(111\) 9.10334e8 0.569177
\(112\) 1.65519e9 0.993957
\(113\) −3.73099e8 −0.215264 −0.107632 0.994191i \(-0.534327\pi\)
−0.107632 + 0.994191i \(0.534327\pi\)
\(114\) −3.76980e8 −0.209048
\(115\) −3.75719e9 −2.00319
\(116\) −8.65247e8 −0.443690
\(117\) −6.45238e8 −0.318335
\(118\) 4.18058e8 0.198503
\(119\) 6.12300e8 0.279900
\(120\) 9.87793e8 0.434861
\(121\) −2.19284e9 −0.929976
\(122\) −1.74478e9 −0.713053
\(123\) −7.31062e8 −0.287993
\(124\) 4.44947e8 0.169010
\(125\) −1.29967e9 −0.476144
\(126\) −2.50879e9 −0.886740
\(127\) −2.03108e9 −0.692803 −0.346401 0.938086i \(-0.612596\pi\)
−0.346401 + 0.938086i \(0.612596\pi\)
\(128\) −2.84942e9 −0.938234
\(129\) 2.53477e9 0.805907
\(130\) 7.21171e9 2.21459
\(131\) 3.15608e9 0.936326 0.468163 0.883642i \(-0.344916\pi\)
0.468163 + 0.883642i \(0.344916\pi\)
\(132\) 7.05987e8 0.202402
\(133\) −1.49510e9 −0.414322
\(134\) −7.20350e9 −1.93007
\(135\) 1.12957e9 0.292693
\(136\) −3.16972e8 −0.0794503
\(137\) 5.88365e9 1.42693 0.713467 0.700688i \(-0.247124\pi\)
0.713467 + 0.700688i \(0.247124\pi\)
\(138\) −4.93988e9 −1.15947
\(139\) −6.07512e9 −1.38035 −0.690174 0.723643i \(-0.742466\pi\)
−0.690174 + 0.723643i \(0.742466\pi\)
\(140\) 1.59789e10 3.51537
\(141\) −3.30867e9 −0.704964
\(142\) −9.77686e9 −2.01791
\(143\) 1.26369e9 0.252713
\(144\) −9.79836e8 −0.189899
\(145\) 2.71130e9 0.509357
\(146\) 1.04317e10 1.90006
\(147\) −6.68119e9 −1.18012
\(148\) −7.62320e9 −1.30605
\(149\) −1.45458e9 −0.241768 −0.120884 0.992667i \(-0.538573\pi\)
−0.120884 + 0.992667i \(0.538573\pi\)
\(150\) −7.16691e9 −1.15590
\(151\) 4.99891e9 0.782491 0.391245 0.920286i \(-0.372044\pi\)
0.391245 + 0.920286i \(0.372044\pi\)
\(152\) 7.73974e8 0.117606
\(153\) −3.62468e8 −0.0534759
\(154\) 4.91341e9 0.703947
\(155\) −1.39427e9 −0.194023
\(156\) 5.40328e9 0.730460
\(157\) −9.43502e8 −0.123935 −0.0619675 0.998078i \(-0.519738\pi\)
−0.0619675 + 0.998078i \(0.519738\pi\)
\(158\) −2.36461e8 −0.0301858
\(159\) −4.56147e9 −0.566002
\(160\) 1.71953e10 2.07429
\(161\) −1.95915e10 −2.29801
\(162\) 1.48514e9 0.169415
\(163\) −5.47947e9 −0.607987 −0.303994 0.952674i \(-0.598320\pi\)
−0.303994 + 0.952674i \(0.598320\pi\)
\(164\) 6.12197e9 0.660837
\(165\) −2.21225e9 −0.232357
\(166\) −2.52072e9 −0.257655
\(167\) 1.84188e10 1.83247 0.916236 0.400639i \(-0.131212\pi\)
0.916236 + 0.400639i \(0.131212\pi\)
\(168\) 5.15076e9 0.498861
\(169\) −9.32855e8 −0.0879678
\(170\) 4.05123e9 0.372021
\(171\) 8.85065e8 0.0791576
\(172\) −2.12264e10 −1.84926
\(173\) −4.05329e9 −0.344033 −0.172017 0.985094i \(-0.555028\pi\)
−0.172017 + 0.985094i \(0.555028\pi\)
\(174\) 3.56477e9 0.294822
\(175\) −2.84239e10 −2.29093
\(176\) 1.91899e9 0.150753
\(177\) −9.81506e8 −0.0751646
\(178\) −3.25137e10 −2.42759
\(179\) −1.52337e10 −1.10909 −0.554545 0.832154i \(-0.687108\pi\)
−0.554545 + 0.832154i \(0.687108\pi\)
\(180\) −9.45914e9 −0.671623
\(181\) 2.36616e10 1.63866 0.819332 0.573320i \(-0.194345\pi\)
0.819332 + 0.573320i \(0.194345\pi\)
\(182\) 3.76048e10 2.54052
\(183\) 4.09636e9 0.270003
\(184\) 1.01420e10 0.652296
\(185\) 2.38877e10 1.49935
\(186\) −1.83316e9 −0.112303
\(187\) 7.09887e8 0.0424524
\(188\) 2.77070e10 1.61763
\(189\) 5.89007e9 0.335770
\(190\) −9.89220e9 −0.550683
\(191\) 1.67134e10 0.908686 0.454343 0.890827i \(-0.349874\pi\)
0.454343 + 0.890827i \(0.349874\pi\)
\(192\) 1.64145e10 0.871710
\(193\) 2.66584e10 1.38301 0.691507 0.722370i \(-0.256947\pi\)
0.691507 + 0.722370i \(0.256947\pi\)
\(194\) 1.88160e10 0.953718
\(195\) −1.69315e10 −0.838569
\(196\) 5.59488e10 2.70794
\(197\) 1.97136e9 0.0932539 0.0466269 0.998912i \(-0.485153\pi\)
0.0466269 + 0.998912i \(0.485153\pi\)
\(198\) −2.90863e9 −0.134491
\(199\) 4.05270e10 1.83191 0.915957 0.401276i \(-0.131433\pi\)
0.915957 + 0.401276i \(0.131433\pi\)
\(200\) 1.47143e10 0.650287
\(201\) 1.69122e10 0.730833
\(202\) −1.00739e10 −0.425713
\(203\) 1.41379e10 0.584321
\(204\) 3.03533e9 0.122707
\(205\) −1.91836e10 −0.758642
\(206\) 2.80839e10 1.08656
\(207\) 1.15977e10 0.439043
\(208\) 1.46870e10 0.544062
\(209\) −1.73338e9 −0.0628401
\(210\) −6.58322e10 −2.33588
\(211\) −1.95680e10 −0.679634 −0.339817 0.940492i \(-0.610365\pi\)
−0.339817 + 0.940492i \(0.610365\pi\)
\(212\) 3.81981e10 1.29876
\(213\) 2.29539e10 0.764096
\(214\) −1.15697e10 −0.377104
\(215\) 6.65140e10 2.12295
\(216\) −3.04913e9 −0.0953091
\(217\) −7.27030e9 −0.222579
\(218\) 3.47149e10 1.04103
\(219\) −2.44913e10 −0.719472
\(220\) 1.85256e10 0.533174
\(221\) 5.43312e9 0.153209
\(222\) 3.14072e10 0.867842
\(223\) −4.91878e10 −1.33194 −0.665971 0.745977i \(-0.731983\pi\)
−0.665971 + 0.745977i \(0.731983\pi\)
\(224\) 8.96633e10 2.37957
\(225\) 1.68263e10 0.437691
\(226\) −1.28722e10 −0.328219
\(227\) −4.48168e10 −1.12027 −0.560137 0.828400i \(-0.689252\pi\)
−0.560137 + 0.828400i \(0.689252\pi\)
\(228\) −7.41160e9 −0.181637
\(229\) −4.38357e10 −1.05334 −0.526670 0.850070i \(-0.676560\pi\)
−0.526670 + 0.850070i \(0.676560\pi\)
\(230\) −1.29626e11 −3.05433
\(231\) −1.15356e10 −0.266555
\(232\) −7.31880e9 −0.165861
\(233\) −9.01688e9 −0.200426 −0.100213 0.994966i \(-0.531952\pi\)
−0.100213 + 0.994966i \(0.531952\pi\)
\(234\) −2.22612e10 −0.485375
\(235\) −8.68215e10 −1.85704
\(236\) 8.21921e9 0.172475
\(237\) 5.55157e8 0.0114301
\(238\) 2.11248e10 0.426773
\(239\) −4.04272e10 −0.801463 −0.400731 0.916196i \(-0.631244\pi\)
−0.400731 + 0.916196i \(0.631244\pi\)
\(240\) −2.57115e10 −0.500239
\(241\) −3.52928e9 −0.0673921 −0.0336960 0.999432i \(-0.510728\pi\)
−0.0336960 + 0.999432i \(0.510728\pi\)
\(242\) −7.56544e10 −1.41796
\(243\) −3.48678e9 −0.0641500
\(244\) −3.43032e10 −0.619556
\(245\) −1.75319e11 −3.10871
\(246\) −2.52222e10 −0.439111
\(247\) −1.32665e10 −0.226787
\(248\) 3.76364e9 0.0631794
\(249\) 5.91809e9 0.0975629
\(250\) −4.48396e10 −0.725992
\(251\) 1.08446e11 1.72458 0.862290 0.506414i \(-0.169029\pi\)
0.862290 + 0.506414i \(0.169029\pi\)
\(252\) −4.93239e10 −0.770469
\(253\) −2.27140e10 −0.348539
\(254\) −7.00736e10 −1.05634
\(255\) −9.51139e9 −0.140868
\(256\) 5.44879e9 0.0792904
\(257\) −1.07464e11 −1.53661 −0.768307 0.640082i \(-0.778900\pi\)
−0.768307 + 0.640082i \(0.778900\pi\)
\(258\) 8.74514e10 1.22879
\(259\) 1.24561e11 1.72001
\(260\) 1.41785e11 1.92421
\(261\) −8.36928e9 −0.111636
\(262\) 1.08887e11 1.42765
\(263\) 2.40331e9 0.0309748 0.0154874 0.999880i \(-0.495070\pi\)
0.0154874 + 0.999880i \(0.495070\pi\)
\(264\) 5.97168e9 0.0756621
\(265\) −1.19696e11 −1.49098
\(266\) −5.15821e10 −0.631730
\(267\) 7.63348e10 0.919225
\(268\) −1.41624e11 −1.67699
\(269\) −1.62916e11 −1.89705 −0.948526 0.316699i \(-0.897426\pi\)
−0.948526 + 0.316699i \(0.897426\pi\)
\(270\) 3.89711e10 0.446279
\(271\) 5.27406e10 0.593996 0.296998 0.954878i \(-0.404015\pi\)
0.296998 + 0.954878i \(0.404015\pi\)
\(272\) 8.25054e9 0.0913950
\(273\) −8.82878e10 −0.961986
\(274\) 2.02990e11 2.17569
\(275\) −3.29540e10 −0.347465
\(276\) −9.71204e10 −1.00744
\(277\) −1.30739e11 −1.33427 −0.667137 0.744935i \(-0.732480\pi\)
−0.667137 + 0.744935i \(0.732480\pi\)
\(278\) −2.09596e11 −2.10466
\(279\) 4.30385e9 0.0425244
\(280\) 1.35159e11 1.31412
\(281\) −3.34613e10 −0.320158 −0.160079 0.987104i \(-0.551175\pi\)
−0.160079 + 0.987104i \(0.551175\pi\)
\(282\) −1.14151e11 −1.07488
\(283\) 1.28327e11 1.18926 0.594631 0.803998i \(-0.297298\pi\)
0.594631 + 0.803998i \(0.297298\pi\)
\(284\) −1.92218e11 −1.75332
\(285\) 2.32247e10 0.208520
\(286\) 4.35982e10 0.385320
\(287\) −1.00031e11 −0.870294
\(288\) −5.30786e10 −0.454625
\(289\) −1.15536e11 −0.974263
\(290\) 9.35419e10 0.776632
\(291\) −4.41758e10 −0.361132
\(292\) 2.05092e11 1.65092
\(293\) 1.99282e11 1.57966 0.789832 0.613324i \(-0.210168\pi\)
0.789832 + 0.613324i \(0.210168\pi\)
\(294\) −2.30506e11 −1.79936
\(295\) −2.57554e10 −0.198002
\(296\) −6.44818e10 −0.488230
\(297\) 6.82881e9 0.0509262
\(298\) −5.01840e10 −0.368631
\(299\) −1.73842e11 −1.25786
\(300\) −1.40905e11 −1.00434
\(301\) 3.46832e11 2.43540
\(302\) 1.72466e11 1.19309
\(303\) 2.36513e10 0.161199
\(304\) −2.01460e10 −0.135287
\(305\) 1.07491e11 0.711251
\(306\) −1.25054e10 −0.0815363
\(307\) 1.03383e11 0.664244 0.332122 0.943236i \(-0.392235\pi\)
0.332122 + 0.943236i \(0.392235\pi\)
\(308\) 9.66000e10 0.611644
\(309\) −6.59347e10 −0.411434
\(310\) −4.81033e10 −0.295833
\(311\) 2.01487e11 1.22131 0.610654 0.791898i \(-0.290907\pi\)
0.610654 + 0.791898i \(0.290907\pi\)
\(312\) 4.57042e10 0.273062
\(313\) −1.69614e11 −0.998879 −0.499439 0.866349i \(-0.666461\pi\)
−0.499439 + 0.866349i \(0.666461\pi\)
\(314\) −3.25515e10 −0.188968
\(315\) 1.54559e11 0.884499
\(316\) −4.64893e9 −0.0262277
\(317\) 1.25759e11 0.699474 0.349737 0.936848i \(-0.386271\pi\)
0.349737 + 0.936848i \(0.386271\pi\)
\(318\) −1.57374e11 −0.863001
\(319\) 1.63911e10 0.0886237
\(320\) 4.30727e11 2.29629
\(321\) 2.71632e10 0.142793
\(322\) −6.75923e11 −3.50385
\(323\) −7.45254e9 −0.0380972
\(324\) 2.91986e10 0.147201
\(325\) −2.52214e11 −1.25399
\(326\) −1.89046e11 −0.927017
\(327\) −8.15029e10 −0.394192
\(328\) 5.17834e10 0.247035
\(329\) −4.52724e11 −2.13035
\(330\) −7.63243e10 −0.354283
\(331\) −4.16265e11 −1.90609 −0.953046 0.302827i \(-0.902070\pi\)
−0.953046 + 0.302827i \(0.902070\pi\)
\(332\) −4.95585e10 −0.223871
\(333\) −7.37370e10 −0.328614
\(334\) 6.35462e11 2.79403
\(335\) 4.43787e11 1.92519
\(336\) −1.34071e11 −0.573861
\(337\) 3.94584e11 1.66650 0.833248 0.552899i \(-0.186479\pi\)
0.833248 + 0.552899i \(0.186479\pi\)
\(338\) −3.21842e10 −0.134127
\(339\) 3.02210e10 0.124282
\(340\) 7.96491e10 0.323240
\(341\) −8.42901e9 −0.0337584
\(342\) 3.05354e10 0.120694
\(343\) −4.66937e11 −1.82152
\(344\) −1.79546e11 −0.691293
\(345\) 3.04332e11 1.15654
\(346\) −1.39842e11 −0.524558
\(347\) −2.58895e11 −0.958609 −0.479305 0.877649i \(-0.659111\pi\)
−0.479305 + 0.877649i \(0.659111\pi\)
\(348\) 7.00850e10 0.256164
\(349\) 3.25345e11 1.17390 0.586949 0.809624i \(-0.300329\pi\)
0.586949 + 0.809624i \(0.300329\pi\)
\(350\) −9.80646e11 −3.49306
\(351\) 5.22643e10 0.183791
\(352\) 1.03953e11 0.360908
\(353\) 5.23092e11 1.79305 0.896524 0.442996i \(-0.146084\pi\)
0.896524 + 0.442996i \(0.146084\pi\)
\(354\) −3.38627e10 −0.114606
\(355\) 6.02325e11 2.01281
\(356\) −6.39234e11 −2.10928
\(357\) −4.95963e10 −0.161600
\(358\) −5.25574e11 −1.69106
\(359\) 1.44888e11 0.460369 0.230184 0.973147i \(-0.426067\pi\)
0.230184 + 0.973147i \(0.426067\pi\)
\(360\) −8.00112e10 −0.251067
\(361\) −3.04490e11 −0.943607
\(362\) 8.16341e11 2.49852
\(363\) 1.77620e11 0.536922
\(364\) 7.39329e11 2.20740
\(365\) −6.42668e11 −1.89526
\(366\) 1.41327e11 0.411681
\(367\) 5.33904e11 1.53626 0.768131 0.640292i \(-0.221187\pi\)
0.768131 + 0.640292i \(0.221187\pi\)
\(368\) −2.63990e11 −0.750363
\(369\) 5.92161e10 0.166273
\(370\) 8.24145e11 2.28610
\(371\) −6.24144e11 −1.71042
\(372\) −3.60407e10 −0.0975777
\(373\) 4.21409e11 1.12724 0.563618 0.826036i \(-0.309409\pi\)
0.563618 + 0.826036i \(0.309409\pi\)
\(374\) 2.44916e10 0.0647284
\(375\) 1.05273e11 0.274902
\(376\) 2.34363e11 0.604705
\(377\) 1.25449e11 0.319840
\(378\) 2.03212e11 0.511959
\(379\) −2.78603e11 −0.693600 −0.346800 0.937939i \(-0.612732\pi\)
−0.346800 + 0.937939i \(0.612732\pi\)
\(380\) −1.94485e11 −0.478476
\(381\) 1.64517e11 0.399990
\(382\) 5.76624e11 1.38550
\(383\) −7.13578e11 −1.69452 −0.847260 0.531178i \(-0.821749\pi\)
−0.847260 + 0.531178i \(0.821749\pi\)
\(384\) 2.30803e11 0.541690
\(385\) −3.02702e11 −0.702169
\(386\) 9.19735e11 2.10872
\(387\) −2.05316e11 −0.465291
\(388\) 3.69932e11 0.828665
\(389\) −4.13305e10 −0.0915160 −0.0457580 0.998953i \(-0.514570\pi\)
−0.0457580 + 0.998953i \(0.514570\pi\)
\(390\) −5.84148e11 −1.27859
\(391\) −9.76569e10 −0.211304
\(392\) 4.73249e11 1.01228
\(393\) −2.55642e11 −0.540588
\(394\) 6.80132e10 0.142187
\(395\) 1.45677e10 0.0301095
\(396\) −5.71850e10 −0.116857
\(397\) −8.80592e10 −0.177917 −0.0889585 0.996035i \(-0.528354\pi\)
−0.0889585 + 0.996035i \(0.528354\pi\)
\(398\) 1.39821e12 2.79318
\(399\) 1.21103e11 0.239209
\(400\) −3.83003e11 −0.748052
\(401\) 3.55570e11 0.686714 0.343357 0.939205i \(-0.388436\pi\)
0.343357 + 0.939205i \(0.388436\pi\)
\(402\) 5.83484e11 1.11432
\(403\) −6.45115e10 −0.121833
\(404\) −1.98058e11 −0.369893
\(405\) −9.14955e10 −0.168987
\(406\) 4.87766e11 0.890932
\(407\) 1.44413e11 0.260874
\(408\) 2.56747e10 0.0458706
\(409\) −6.47031e11 −1.14333 −0.571663 0.820488i \(-0.693702\pi\)
−0.571663 + 0.820488i \(0.693702\pi\)
\(410\) −6.61847e11 −1.15672
\(411\) −4.76575e11 −0.823841
\(412\) 5.52142e11 0.944090
\(413\) −1.34299e11 −0.227142
\(414\) 4.00131e11 0.669422
\(415\) 1.55295e11 0.257004
\(416\) 7.95609e11 1.30251
\(417\) 4.92085e11 0.796944
\(418\) −5.98030e10 −0.0958142
\(419\) 6.62242e11 1.04967 0.524836 0.851203i \(-0.324127\pi\)
0.524836 + 0.851203i \(0.324127\pi\)
\(420\) −1.29429e12 −2.02960
\(421\) −7.29715e11 −1.13210 −0.566049 0.824372i \(-0.691529\pi\)
−0.566049 + 0.824372i \(0.691529\pi\)
\(422\) −6.75110e11 −1.03626
\(423\) 2.68002e11 0.407011
\(424\) 3.23103e11 0.485506
\(425\) −1.41683e11 −0.210653
\(426\) 7.91926e11 1.16504
\(427\) 5.60503e11 0.815929
\(428\) −2.27466e11 −0.327658
\(429\) −1.02359e11 −0.145904
\(430\) 2.29478e12 3.23693
\(431\) 1.04484e10 0.0145849 0.00729243 0.999973i \(-0.497679\pi\)
0.00729243 + 0.999973i \(0.497679\pi\)
\(432\) 7.93667e10 0.109638
\(433\) 9.48860e11 1.29720 0.648599 0.761130i \(-0.275355\pi\)
0.648599 + 0.761130i \(0.275355\pi\)
\(434\) −2.50830e11 −0.339372
\(435\) −2.19615e11 −0.294077
\(436\) 6.82512e11 0.904526
\(437\) 2.38456e11 0.312782
\(438\) −8.44968e11 −1.09700
\(439\) 1.41652e12 1.82025 0.910125 0.414335i \(-0.135986\pi\)
0.910125 + 0.414335i \(0.135986\pi\)
\(440\) 1.56701e11 0.199312
\(441\) 5.41176e11 0.681342
\(442\) 1.87447e11 0.233602
\(443\) 4.09272e11 0.504889 0.252444 0.967611i \(-0.418766\pi\)
0.252444 + 0.967611i \(0.418766\pi\)
\(444\) 6.17480e11 0.754048
\(445\) 2.00308e12 2.42146
\(446\) −1.69702e12 −2.03085
\(447\) 1.17821e11 0.139585
\(448\) 2.24599e12 2.63425
\(449\) −3.44730e11 −0.400287 −0.200143 0.979767i \(-0.564141\pi\)
−0.200143 + 0.979767i \(0.564141\pi\)
\(450\) 5.80520e11 0.667361
\(451\) −1.15974e11 −0.131997
\(452\) −2.53073e11 −0.285182
\(453\) −4.04912e11 −0.451771
\(454\) −1.54621e12 −1.70812
\(455\) −2.31673e12 −2.53410
\(456\) −6.26919e10 −0.0679000
\(457\) 9.96315e11 1.06850 0.534249 0.845327i \(-0.320594\pi\)
0.534249 + 0.845327i \(0.320594\pi\)
\(458\) −1.51236e12 −1.60606
\(459\) 2.93599e10 0.0308743
\(460\) −2.54850e12 −2.65384
\(461\) −5.63457e11 −0.581041 −0.290520 0.956869i \(-0.593828\pi\)
−0.290520 + 0.956869i \(0.593828\pi\)
\(462\) −3.97987e11 −0.406424
\(463\) −1.07447e12 −1.08663 −0.543315 0.839529i \(-0.682831\pi\)
−0.543315 + 0.839529i \(0.682831\pi\)
\(464\) 1.90503e11 0.190797
\(465\) 1.12936e11 0.112019
\(466\) −3.11089e11 −0.305596
\(467\) −1.72279e11 −0.167612 −0.0838062 0.996482i \(-0.526708\pi\)
−0.0838062 + 0.996482i \(0.526708\pi\)
\(468\) −4.37665e11 −0.421731
\(469\) 2.31409e12 2.20853
\(470\) −2.99541e12 −2.83149
\(471\) 7.64236e10 0.0715539
\(472\) 6.95231e10 0.0644749
\(473\) 4.02109e11 0.369376
\(474\) 1.91533e10 0.0174278
\(475\) 3.45958e11 0.311819
\(476\) 4.15324e11 0.370813
\(477\) 3.69479e11 0.326781
\(478\) −1.39477e12 −1.22202
\(479\) 1.17803e12 1.02246 0.511232 0.859443i \(-0.329189\pi\)
0.511232 + 0.859443i \(0.329189\pi\)
\(480\) −1.39282e12 −1.19759
\(481\) 1.10526e12 0.941484
\(482\) −1.21763e11 −0.102755
\(483\) 1.58692e12 1.32676
\(484\) −1.48740e12 −1.23204
\(485\) −1.15920e12 −0.951309
\(486\) −1.20297e11 −0.0978116
\(487\) 1.41964e12 1.14366 0.571830 0.820372i \(-0.306234\pi\)
0.571830 + 0.820372i \(0.306234\pi\)
\(488\) −2.90158e11 −0.231603
\(489\) 4.43837e11 0.351022
\(490\) −6.04862e12 −4.73995
\(491\) −3.65591e11 −0.283876 −0.141938 0.989876i \(-0.545333\pi\)
−0.141938 + 0.989876i \(0.545333\pi\)
\(492\) −4.95880e11 −0.381534
\(493\) 7.04722e10 0.0537287
\(494\) −4.57703e11 −0.345790
\(495\) 1.79192e11 0.134152
\(496\) −9.79648e10 −0.0726779
\(497\) 3.14077e12 2.30905
\(498\) 2.04178e11 0.148757
\(499\) 2.55102e12 1.84188 0.920941 0.389703i \(-0.127422\pi\)
0.920941 + 0.389703i \(0.127422\pi\)
\(500\) −8.81568e11 −0.630799
\(501\) −1.49192e12 −1.05798
\(502\) 3.74148e12 2.62952
\(503\) −1.67849e12 −1.16913 −0.584566 0.811346i \(-0.698735\pi\)
−0.584566 + 0.811346i \(0.698735\pi\)
\(504\) −4.17212e11 −0.288018
\(505\) 6.20625e11 0.424637
\(506\) −7.83649e11 −0.531428
\(507\) 7.55612e10 0.0507883
\(508\) −1.37768e12 −0.917829
\(509\) −1.57010e12 −1.03681 −0.518403 0.855137i \(-0.673473\pi\)
−0.518403 + 0.855137i \(0.673473\pi\)
\(510\) −3.28150e11 −0.214786
\(511\) −3.35114e12 −2.17419
\(512\) 1.64689e12 1.05913
\(513\) −7.16903e10 −0.0457017
\(514\) −3.70759e12 −2.34292
\(515\) −1.73017e12 −1.08382
\(516\) 1.71934e12 1.06767
\(517\) −5.24877e11 −0.323110
\(518\) 4.29743e12 2.62256
\(519\) 3.28317e11 0.198628
\(520\) 1.19931e12 0.719310
\(521\) 1.78780e12 1.06304 0.531519 0.847046i \(-0.321621\pi\)
0.531519 + 0.847046i \(0.321621\pi\)
\(522\) −2.88746e11 −0.170216
\(523\) −1.34218e11 −0.0784431 −0.0392215 0.999231i \(-0.512488\pi\)
−0.0392215 + 0.999231i \(0.512488\pi\)
\(524\) 2.14077e12 1.24045
\(525\) 2.30234e12 1.32267
\(526\) 8.29160e10 0.0472283
\(527\) −3.62398e10 −0.0204662
\(528\) −1.55438e11 −0.0870373
\(529\) 1.32354e12 0.734828
\(530\) −4.12960e12 −2.27335
\(531\) 7.95020e10 0.0433963
\(532\) −1.01413e12 −0.548896
\(533\) −8.87605e11 −0.476373
\(534\) 2.63361e12 1.40157
\(535\) 7.12779e11 0.376152
\(536\) −1.19794e12 −0.626896
\(537\) 1.23393e12 0.640333
\(538\) −5.62073e12 −2.89249
\(539\) −1.05988e12 −0.540890
\(540\) 7.66190e11 0.387762
\(541\) 1.55224e12 0.779060 0.389530 0.921014i \(-0.372637\pi\)
0.389530 + 0.921014i \(0.372637\pi\)
\(542\) 1.81959e12 0.905684
\(543\) −1.91659e12 −0.946083
\(544\) 4.46939e11 0.218803
\(545\) −2.13869e12 −1.03840
\(546\) −3.04599e12 −1.46677
\(547\) 1.87430e12 0.895153 0.447576 0.894246i \(-0.352287\pi\)
0.447576 + 0.894246i \(0.352287\pi\)
\(548\) 3.99088e12 1.89041
\(549\) −3.31805e11 −0.155886
\(550\) −1.13694e12 −0.529791
\(551\) −1.72077e11 −0.0795319
\(552\) −8.21504e11 −0.376603
\(553\) 7.59619e10 0.0345408
\(554\) −4.51058e12 −2.03441
\(555\) −1.93491e12 −0.865649
\(556\) −4.12076e12 −1.82869
\(557\) 3.54150e12 1.55897 0.779486 0.626419i \(-0.215480\pi\)
0.779486 + 0.626419i \(0.215480\pi\)
\(558\) 1.48486e11 0.0648382
\(559\) 3.07754e12 1.33306
\(560\) −3.51810e12 −1.51169
\(561\) −5.75008e10 −0.0245099
\(562\) −1.15444e12 −0.488156
\(563\) −3.12012e12 −1.30883 −0.654416 0.756135i \(-0.727085\pi\)
−0.654416 + 0.756135i \(0.727085\pi\)
\(564\) −2.24427e12 −0.933940
\(565\) 7.93018e11 0.327390
\(566\) 4.42736e12 1.81331
\(567\) −4.77096e11 −0.193857
\(568\) −1.62590e12 −0.655428
\(569\) 1.25747e12 0.502914 0.251457 0.967868i \(-0.419090\pi\)
0.251457 + 0.967868i \(0.419090\pi\)
\(570\) 8.01268e11 0.317937
\(571\) 3.04709e12 1.19956 0.599782 0.800163i \(-0.295254\pi\)
0.599782 + 0.800163i \(0.295254\pi\)
\(572\) 8.57160e11 0.334796
\(573\) −1.35378e12 −0.524630
\(574\) −3.45114e12 −1.32697
\(575\) 4.53338e12 1.72948
\(576\) −1.32957e12 −0.503282
\(577\) 4.93378e12 1.85305 0.926527 0.376227i \(-0.122779\pi\)
0.926527 + 0.376227i \(0.122779\pi\)
\(578\) −3.98607e12 −1.48549
\(579\) −2.15933e12 −0.798483
\(580\) 1.83908e12 0.674798
\(581\) 8.09770e11 0.294828
\(582\) −1.52410e12 −0.550630
\(583\) −7.23618e11 −0.259419
\(584\) 1.73480e12 0.617150
\(585\) 1.37145e12 0.484148
\(586\) 6.87539e12 2.40856
\(587\) −1.04516e12 −0.363338 −0.181669 0.983360i \(-0.558150\pi\)
−0.181669 + 0.983360i \(0.558150\pi\)
\(588\) −4.53185e12 −1.56343
\(589\) 8.84895e10 0.0302951
\(590\) −8.88579e11 −0.301899
\(591\) −1.59680e11 −0.0538401
\(592\) 1.67841e12 0.561631
\(593\) 2.78359e12 0.924397 0.462198 0.886777i \(-0.347061\pi\)
0.462198 + 0.886777i \(0.347061\pi\)
\(594\) 2.35599e11 0.0776487
\(595\) −1.30144e12 −0.425694
\(596\) −9.86641e11 −0.320296
\(597\) −3.28268e12 −1.05766
\(598\) −5.99766e12 −1.91790
\(599\) −1.00164e12 −0.317901 −0.158950 0.987287i \(-0.550811\pi\)
−0.158950 + 0.987287i \(0.550811\pi\)
\(600\) −1.19186e12 −0.375443
\(601\) −5.94601e12 −1.85905 −0.929524 0.368761i \(-0.879782\pi\)
−0.929524 + 0.368761i \(0.879782\pi\)
\(602\) 1.19659e13 3.71332
\(603\) −1.36989e12 −0.421947
\(604\) 3.39076e12 1.03665
\(605\) 4.66086e12 1.41438
\(606\) 8.15987e11 0.245786
\(607\) −1.71818e12 −0.513713 −0.256856 0.966450i \(-0.582687\pi\)
−0.256856 + 0.966450i \(0.582687\pi\)
\(608\) −1.09133e12 −0.323883
\(609\) −1.14517e12 −0.337358
\(610\) 3.70852e12 1.08447
\(611\) −4.01715e12 −1.16609
\(612\) −2.45862e11 −0.0708451
\(613\) 4.34986e12 1.24424 0.622119 0.782923i \(-0.286272\pi\)
0.622119 + 0.782923i \(0.286272\pi\)
\(614\) 3.56680e12 1.01279
\(615\) 1.55387e12 0.438002
\(616\) 8.17102e11 0.228646
\(617\) 4.75580e12 1.32111 0.660557 0.750776i \(-0.270320\pi\)
0.660557 + 0.750776i \(0.270320\pi\)
\(618\) −2.27479e12 −0.627327
\(619\) 2.98381e12 0.816891 0.408445 0.912783i \(-0.366071\pi\)
0.408445 + 0.912783i \(0.366071\pi\)
\(620\) −9.45733e11 −0.257043
\(621\) −9.39417e11 −0.253482
\(622\) 6.95144e12 1.86217
\(623\) 1.04449e13 2.77784
\(624\) −1.18965e12 −0.314114
\(625\) −2.24653e12 −0.588914
\(626\) −5.85181e12 −1.52302
\(627\) 1.40404e11 0.0362807
\(628\) −6.39977e11 −0.164190
\(629\) 6.20890e11 0.158156
\(630\) 5.33241e12 1.34862
\(631\) 3.14683e12 0.790206 0.395103 0.918637i \(-0.370709\pi\)
0.395103 + 0.918637i \(0.370709\pi\)
\(632\) −3.93235e10 −0.00980450
\(633\) 1.58501e12 0.392387
\(634\) 4.33877e12 1.06651
\(635\) 4.31704e12 1.05367
\(636\) −3.09405e12 −0.749842
\(637\) −8.11183e12 −1.95205
\(638\) 5.65505e11 0.135127
\(639\) −1.85927e12 −0.441151
\(640\) 6.05642e12 1.42694
\(641\) −6.90121e12 −1.61460 −0.807299 0.590143i \(-0.799071\pi\)
−0.807299 + 0.590143i \(0.799071\pi\)
\(642\) 9.37149e11 0.217721
\(643\) 2.39255e12 0.551965 0.275983 0.961163i \(-0.410997\pi\)
0.275983 + 0.961163i \(0.410997\pi\)
\(644\) −1.32890e13 −3.04442
\(645\) −5.38764e12 −1.22569
\(646\) −2.57118e11 −0.0580880
\(647\) −5.61890e12 −1.26061 −0.630307 0.776346i \(-0.717071\pi\)
−0.630307 + 0.776346i \(0.717071\pi\)
\(648\) 2.46980e11 0.0550268
\(649\) −1.55703e11 −0.0344506
\(650\) −8.70156e12 −1.91200
\(651\) 5.88894e11 0.128506
\(652\) −3.71673e12 −0.805465
\(653\) 4.52224e12 0.973295 0.486647 0.873599i \(-0.338220\pi\)
0.486647 + 0.873599i \(0.338220\pi\)
\(654\) −2.81191e12 −0.601038
\(655\) −6.70822e12 −1.42404
\(656\) −1.34788e12 −0.284175
\(657\) 1.98380e12 0.415387
\(658\) −1.56193e13 −3.24822
\(659\) 1.98801e12 0.410613 0.205307 0.978698i \(-0.434181\pi\)
0.205307 + 0.978698i \(0.434181\pi\)
\(660\) −1.50057e12 −0.307828
\(661\) 3.75691e12 0.765463 0.382731 0.923860i \(-0.374983\pi\)
0.382731 + 0.923860i \(0.374983\pi\)
\(662\) −1.43614e13 −2.90628
\(663\) −4.40083e11 −0.0884552
\(664\) −4.19197e11 −0.0836877
\(665\) 3.17782e12 0.630133
\(666\) −2.54398e12 −0.501049
\(667\) −2.25487e12 −0.441119
\(668\) 1.24935e13 2.42767
\(669\) 3.98421e12 0.768998
\(670\) 1.53110e13 2.93540
\(671\) 6.49834e11 0.123752
\(672\) −7.26273e12 −1.37385
\(673\) −4.50273e12 −0.846074 −0.423037 0.906112i \(-0.639036\pi\)
−0.423037 + 0.906112i \(0.639036\pi\)
\(674\) 1.36134e13 2.54096
\(675\) −1.36293e12 −0.252701
\(676\) −6.32756e11 −0.116540
\(677\) −4.77303e12 −0.873262 −0.436631 0.899641i \(-0.643829\pi\)
−0.436631 + 0.899641i \(0.643829\pi\)
\(678\) 1.04265e12 0.189497
\(679\) −6.04456e12 −1.09132
\(680\) 6.73721e11 0.120834
\(681\) 3.63016e12 0.646791
\(682\) −2.90807e11 −0.0514725
\(683\) 6.92003e12 1.21679 0.608394 0.793635i \(-0.291814\pi\)
0.608394 + 0.793635i \(0.291814\pi\)
\(684\) 6.00340e11 0.104868
\(685\) −1.25056e13 −2.17019
\(686\) −1.61097e13 −2.77734
\(687\) 3.55069e12 0.608146
\(688\) 4.67344e12 0.795223
\(689\) −5.53822e12 −0.936232
\(690\) 1.04997e13 1.76342
\(691\) −3.26738e12 −0.545190 −0.272595 0.962129i \(-0.587882\pi\)
−0.272595 + 0.962129i \(0.587882\pi\)
\(692\) −2.74935e12 −0.455777
\(693\) 9.34383e11 0.153895
\(694\) −8.93208e12 −1.46162
\(695\) 1.29126e13 2.09934
\(696\) 5.92822e11 0.0957598
\(697\) −4.98619e11 −0.0800242
\(698\) 1.12247e13 1.78988
\(699\) 7.30368e11 0.115716
\(700\) −1.92799e13 −3.03504
\(701\) −8.23416e12 −1.28792 −0.643959 0.765060i \(-0.722709\pi\)
−0.643959 + 0.765060i \(0.722709\pi\)
\(702\) 1.80316e12 0.280231
\(703\) −1.51607e12 −0.234111
\(704\) 2.60395e12 0.399535
\(705\) 7.03254e12 1.07216
\(706\) 1.80470e13 2.73391
\(707\) 3.23620e12 0.487133
\(708\) −6.65756e11 −0.0995785
\(709\) 7.57359e12 1.12563 0.562813 0.826584i \(-0.309719\pi\)
0.562813 + 0.826584i \(0.309719\pi\)
\(710\) 2.07807e13 3.06900
\(711\) −4.49677e10 −0.00659914
\(712\) −5.40703e12 −0.788495
\(713\) 1.15955e12 0.168030
\(714\) −1.71111e12 −0.246397
\(715\) −2.68596e12 −0.384346
\(716\) −1.03330e13 −1.46933
\(717\) 3.27461e12 0.462725
\(718\) 4.99872e12 0.701939
\(719\) 8.97769e12 1.25281 0.626404 0.779499i \(-0.284526\pi\)
0.626404 + 0.779499i \(0.284526\pi\)
\(720\) 2.08263e12 0.288813
\(721\) −9.02182e12 −1.24333
\(722\) −1.05051e13 −1.43875
\(723\) 2.85871e11 0.0389088
\(724\) 1.60496e13 2.17091
\(725\) −3.27142e12 −0.439760
\(726\) 6.12801e12 0.818662
\(727\) −9.56364e11 −0.126975 −0.0634875 0.997983i \(-0.520222\pi\)
−0.0634875 + 0.997983i \(0.520222\pi\)
\(728\) 6.25370e12 0.825174
\(729\) 2.82430e11 0.0370370
\(730\) −2.21725e13 −2.88976
\(731\) 1.72883e12 0.223936
\(732\) 2.77856e12 0.357701
\(733\) 8.77585e12 1.12285 0.561424 0.827528i \(-0.310254\pi\)
0.561424 + 0.827528i \(0.310254\pi\)
\(734\) 1.84201e13 2.34239
\(735\) 1.42008e13 1.79482
\(736\) −1.43006e13 −1.79640
\(737\) 2.68290e12 0.334967
\(738\) 2.04300e12 0.253521
\(739\) −9.96504e12 −1.22908 −0.614538 0.788887i \(-0.710658\pi\)
−0.614538 + 0.788887i \(0.710658\pi\)
\(740\) 1.62031e13 1.98634
\(741\) 1.07458e12 0.130936
\(742\) −2.15334e13 −2.60793
\(743\) −3.30829e12 −0.398249 −0.199124 0.979974i \(-0.563810\pi\)
−0.199124 + 0.979974i \(0.563810\pi\)
\(744\) −3.04855e11 −0.0364766
\(745\) 3.09170e12 0.367700
\(746\) 1.45389e13 1.71873
\(747\) −4.79365e11 −0.0563279
\(748\) 4.81516e11 0.0562411
\(749\) 3.71673e12 0.431512
\(750\) 3.63201e12 0.419152
\(751\) 6.43513e12 0.738206 0.369103 0.929389i \(-0.379665\pi\)
0.369103 + 0.929389i \(0.379665\pi\)
\(752\) −6.10030e12 −0.695618
\(753\) −8.78416e12 −0.995687
\(754\) 4.32809e12 0.487670
\(755\) −1.06251e13 −1.19007
\(756\) 3.99524e12 0.444830
\(757\) −7.76173e12 −0.859068 −0.429534 0.903051i \(-0.641322\pi\)
−0.429534 + 0.903051i \(0.641322\pi\)
\(758\) −9.61200e12 −1.05755
\(759\) 1.83983e12 0.201229
\(760\) −1.64508e12 −0.178865
\(761\) −9.64688e12 −1.04269 −0.521346 0.853345i \(-0.674570\pi\)
−0.521346 + 0.853345i \(0.674570\pi\)
\(762\) 5.67596e12 0.609877
\(763\) −1.11520e13 −1.19122
\(764\) 1.13367e13 1.20383
\(765\) 7.70422e11 0.0813303
\(766\) −2.46190e13 −2.58369
\(767\) −1.19168e12 −0.124331
\(768\) −4.41352e11 −0.0457783
\(769\) −3.19835e12 −0.329805 −0.164903 0.986310i \(-0.552731\pi\)
−0.164903 + 0.986310i \(0.552731\pi\)
\(770\) −1.04434e13 −1.07062
\(771\) 8.70460e12 0.887164
\(772\) 1.80824e13 1.83222
\(773\) −4.99654e12 −0.503341 −0.251670 0.967813i \(-0.580980\pi\)
−0.251670 + 0.967813i \(0.580980\pi\)
\(774\) −7.08356e12 −0.709443
\(775\) 1.68231e12 0.167513
\(776\) 3.12911e12 0.309773
\(777\) −1.00894e13 −0.993050
\(778\) −1.42593e12 −0.139537
\(779\) 1.21752e12 0.118456
\(780\) −1.14846e13 −1.11094
\(781\) 3.64134e12 0.350212
\(782\) −3.36923e12 −0.322182
\(783\) 6.77912e11 0.0644533
\(784\) −1.23183e13 −1.16447
\(785\) 2.00541e12 0.188490
\(786\) −8.81985e12 −0.824252
\(787\) −2.48095e12 −0.230532 −0.115266 0.993335i \(-0.536772\pi\)
−0.115266 + 0.993335i \(0.536772\pi\)
\(788\) 1.33717e12 0.123543
\(789\) −1.94668e11 −0.0178833
\(790\) 5.02596e11 0.0459089
\(791\) 4.13513e12 0.375573
\(792\) −4.83706e11 −0.0436835
\(793\) 4.97351e12 0.446615
\(794\) −3.03811e12 −0.271275
\(795\) 9.69537e12 0.860820
\(796\) 2.74895e13 2.42693
\(797\) 4.01929e12 0.352847 0.176424 0.984314i \(-0.443547\pi\)
0.176424 + 0.984314i \(0.443547\pi\)
\(798\) 4.17815e12 0.364729
\(799\) −2.25667e12 −0.195887
\(800\) −2.07476e13 −1.79087
\(801\) −6.18312e12 −0.530715
\(802\) 1.22674e13 1.04705
\(803\) −3.88523e12 −0.329759
\(804\) 1.14716e13 0.968212
\(805\) 4.16417e13 3.49500
\(806\) −2.22569e12 −0.185762
\(807\) 1.31962e13 1.09526
\(808\) −1.67529e12 −0.138274
\(809\) −1.76189e13 −1.44614 −0.723068 0.690776i \(-0.757269\pi\)
−0.723068 + 0.690776i \(0.757269\pi\)
\(810\) −3.15666e12 −0.257659
\(811\) 1.43610e13 1.16571 0.582856 0.812576i \(-0.301935\pi\)
0.582856 + 0.812576i \(0.301935\pi\)
\(812\) 9.58971e12 0.774111
\(813\) −4.27199e12 −0.342944
\(814\) 4.98234e12 0.397762
\(815\) 1.16466e13 0.924675
\(816\) −6.68294e11 −0.0527669
\(817\) −4.22142e12 −0.331482
\(818\) −2.23230e13 −1.74327
\(819\) 7.15131e12 0.555403
\(820\) −1.30122e13 −1.00505
\(821\) −1.27547e13 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(822\) −1.64422e13 −1.25614
\(823\) −1.55652e13 −1.18265 −0.591326 0.806433i \(-0.701395\pi\)
−0.591326 + 0.806433i \(0.701395\pi\)
\(824\) 4.67036e12 0.352921
\(825\) 2.66928e12 0.200609
\(826\) −4.63342e12 −0.346331
\(827\) 2.98542e12 0.221937 0.110969 0.993824i \(-0.464605\pi\)
0.110969 + 0.993824i \(0.464605\pi\)
\(828\) 7.86675e12 0.581646
\(829\) 1.23183e13 0.905848 0.452924 0.891549i \(-0.350381\pi\)
0.452924 + 0.891549i \(0.350381\pi\)
\(830\) 5.35777e12 0.391862
\(831\) 1.05898e13 0.770344
\(832\) 1.99293e13 1.44191
\(833\) −4.55688e12 −0.327918
\(834\) 1.69773e13 1.21513
\(835\) −3.91490e13 −2.78697
\(836\) −1.17576e12 −0.0832508
\(837\) −3.48612e11 −0.0245515
\(838\) 2.28478e13 1.60047
\(839\) −1.86372e13 −1.29853 −0.649264 0.760563i \(-0.724923\pi\)
−0.649264 + 0.760563i \(0.724923\pi\)
\(840\) −1.09479e13 −0.758708
\(841\) −1.28800e13 −0.887836
\(842\) −2.51757e13 −1.72614
\(843\) 2.71037e12 0.184844
\(844\) −1.32730e13 −0.900383
\(845\) 1.98278e12 0.133788
\(846\) 9.24626e12 0.620583
\(847\) 2.43036e13 1.62254
\(848\) −8.41014e12 −0.558498
\(849\) −1.03945e13 −0.686621
\(850\) −4.88817e12 −0.321189
\(851\) −1.98664e13 −1.29848
\(852\) 1.55696e13 1.01228
\(853\) 2.02588e13 1.31022 0.655110 0.755534i \(-0.272622\pi\)
0.655110 + 0.755534i \(0.272622\pi\)
\(854\) 1.93378e13 1.24407
\(855\) −1.88120e12 −0.120389
\(856\) −1.92405e12 −0.122486
\(857\) −1.79742e13 −1.13825 −0.569124 0.822252i \(-0.692718\pi\)
−0.569124 + 0.822252i \(0.692718\pi\)
\(858\) −3.53145e12 −0.222464
\(859\) 8.13333e11 0.0509682 0.0254841 0.999675i \(-0.491887\pi\)
0.0254841 + 0.999675i \(0.491887\pi\)
\(860\) 4.51165e13 2.81250
\(861\) 8.10251e12 0.502465
\(862\) 3.60478e11 0.0222380
\(863\) 2.73063e13 1.67577 0.837885 0.545848i \(-0.183792\pi\)
0.837885 + 0.545848i \(0.183792\pi\)
\(864\) 4.29937e12 0.262478
\(865\) 8.61525e12 0.523233
\(866\) 3.27363e13 1.97788
\(867\) 9.35840e12 0.562491
\(868\) −4.93144e12 −0.294873
\(869\) 8.80685e10 0.00523880
\(870\) −7.57689e12 −0.448389
\(871\) 2.05336e13 1.20888
\(872\) 5.77311e12 0.338131
\(873\) 3.57824e12 0.208500
\(874\) 8.22691e12 0.476909
\(875\) 1.44045e13 0.830735
\(876\) −1.66125e13 −0.953160
\(877\) 2.50307e13 1.42881 0.714405 0.699732i \(-0.246697\pi\)
0.714405 + 0.699732i \(0.246697\pi\)
\(878\) 4.88708e13 2.77539
\(879\) −1.61419e13 −0.912019
\(880\) −4.07880e12 −0.229277
\(881\) −3.22785e13 −1.80518 −0.902591 0.430499i \(-0.858338\pi\)
−0.902591 + 0.430499i \(0.858338\pi\)
\(882\) 1.86710e13 1.03886
\(883\) 8.95417e12 0.495681 0.247840 0.968801i \(-0.420279\pi\)
0.247840 + 0.968801i \(0.420279\pi\)
\(884\) 3.68529e12 0.202972
\(885\) 2.08618e12 0.114316
\(886\) 1.41202e13 0.769819
\(887\) −1.32363e13 −0.717978 −0.358989 0.933342i \(-0.616879\pi\)
−0.358989 + 0.933342i \(0.616879\pi\)
\(888\) 5.22302e12 0.281880
\(889\) 2.25108e13 1.20874
\(890\) 6.91076e13 3.69208
\(891\) −5.53133e11 −0.0294022
\(892\) −3.33641e13 −1.76456
\(893\) 5.51027e12 0.289962
\(894\) 4.06491e12 0.212829
\(895\) 3.23791e13 1.68679
\(896\) 3.15807e13 1.63695
\(897\) 1.40812e13 0.726227
\(898\) −1.18934e13 −0.610329
\(899\) −8.36768e11 −0.0427254
\(900\) 1.14133e13 0.579855
\(901\) −3.11114e12 −0.157274
\(902\) −4.00118e12 −0.201260
\(903\) −2.80934e13 −1.40608
\(904\) −2.14065e12 −0.106607
\(905\) −5.02925e13 −2.49221
\(906\) −1.39698e13 −0.688830
\(907\) 3.19713e13 1.56866 0.784328 0.620347i \(-0.213008\pi\)
0.784328 + 0.620347i \(0.213008\pi\)
\(908\) −3.03992e13 −1.48415
\(909\) −1.91575e12 −0.0930684
\(910\) −7.99288e13 −3.86382
\(911\) 8.00387e12 0.385006 0.192503 0.981296i \(-0.438340\pi\)
0.192503 + 0.981296i \(0.438340\pi\)
\(912\) 1.63182e12 0.0781082
\(913\) 9.38829e11 0.0447165
\(914\) 3.43736e13 1.62917
\(915\) −8.70677e12 −0.410641
\(916\) −2.97338e13 −1.39547
\(917\) −3.49795e13 −1.63362
\(918\) 1.01294e12 0.0470750
\(919\) −1.03567e13 −0.478965 −0.239482 0.970901i \(-0.576978\pi\)
−0.239482 + 0.970901i \(0.576978\pi\)
\(920\) −2.15568e13 −0.992063
\(921\) −8.37405e12 −0.383501
\(922\) −1.94397e13 −0.885931
\(923\) 2.78690e13 1.26390
\(924\) −7.82460e12 −0.353133
\(925\) −2.88227e13 −1.29448
\(926\) −3.70701e13 −1.65682
\(927\) 5.34071e12 0.237542
\(928\) 1.03197e13 0.456774
\(929\) −3.17313e13 −1.39771 −0.698856 0.715263i \(-0.746307\pi\)
−0.698856 + 0.715263i \(0.746307\pi\)
\(930\) 3.89636e12 0.170799
\(931\) 1.11269e13 0.485400
\(932\) −6.11616e12 −0.265526
\(933\) −1.63204e13 −0.705122
\(934\) −5.94375e12 −0.255564
\(935\) −1.50886e12 −0.0645649
\(936\) −3.70204e12 −0.157652
\(937\) −1.29178e13 −0.547469 −0.273735 0.961805i \(-0.588259\pi\)
−0.273735 + 0.961805i \(0.588259\pi\)
\(938\) 7.98379e13 3.36741
\(939\) 1.37388e13 0.576703
\(940\) −5.88911e13 −2.46022
\(941\) −3.12085e13 −1.29754 −0.648769 0.760986i \(-0.724716\pi\)
−0.648769 + 0.760986i \(0.724716\pi\)
\(942\) 2.63667e12 0.109101
\(943\) 1.59541e13 0.657008
\(944\) −1.80964e12 −0.0741681
\(945\) −1.25193e13 −0.510666
\(946\) 1.38730e13 0.563199
\(947\) 2.66359e13 1.07620 0.538099 0.842882i \(-0.319143\pi\)
0.538099 + 0.842882i \(0.319143\pi\)
\(948\) 3.76563e11 0.0151426
\(949\) −2.97356e13 −1.19009
\(950\) 1.19358e13 0.475440
\(951\) −1.01865e13 −0.403842
\(952\) 3.51306e12 0.138618
\(953\) −3.20298e13 −1.25787 −0.628936 0.777457i \(-0.716509\pi\)
−0.628936 + 0.777457i \(0.716509\pi\)
\(954\) 1.27473e13 0.498254
\(955\) −3.55242e13 −1.38200
\(956\) −2.74218e13 −1.06178
\(957\) −1.32768e12 −0.0511669
\(958\) 4.06430e13 1.55898
\(959\) −6.52097e13 −2.48959
\(960\) −3.48889e13 −1.32576
\(961\) −2.60093e13 −0.983725
\(962\) 3.81324e13 1.43551
\(963\) −2.20022e12 −0.0824417
\(964\) −2.39391e12 −0.0892814
\(965\) −5.66623e13 −2.10340
\(966\) 5.47497e13 2.02295
\(967\) 3.00424e12 0.110488 0.0552440 0.998473i \(-0.482406\pi\)
0.0552440 + 0.998473i \(0.482406\pi\)
\(968\) −1.25814e13 −0.460562
\(969\) 6.03656e11 0.0219954
\(970\) −3.99933e13 −1.45049
\(971\) −1.27149e13 −0.459016 −0.229508 0.973307i \(-0.573712\pi\)
−0.229508 + 0.973307i \(0.573712\pi\)
\(972\) −2.36509e12 −0.0849863
\(973\) 6.73318e13 2.40831
\(974\) 4.89785e13 1.74377
\(975\) 2.04293e13 0.723991
\(976\) 7.55259e12 0.266423
\(977\) 1.84870e13 0.649143 0.324571 0.945861i \(-0.394780\pi\)
0.324571 + 0.945861i \(0.394780\pi\)
\(978\) 1.53127e13 0.535214
\(979\) 1.21095e13 0.421314
\(980\) −1.18919e14 −4.11844
\(981\) 6.60174e12 0.227587
\(982\) −1.26131e13 −0.432834
\(983\) 3.61480e13 1.23479 0.617395 0.786654i \(-0.288188\pi\)
0.617395 + 0.786654i \(0.288188\pi\)
\(984\) −4.19446e12 −0.142626
\(985\) −4.19010e12 −0.141828
\(986\) 2.43134e12 0.0819218
\(987\) 3.66706e13 1.22996
\(988\) −8.99865e12 −0.300449
\(989\) −5.53168e13 −1.83854
\(990\) 6.18227e12 0.204545
\(991\) 3.82897e10 0.00126110 0.000630552 1.00000i \(-0.499799\pi\)
0.000630552 1.00000i \(0.499799\pi\)
\(992\) −5.30684e12 −0.173994
\(993\) 3.37174e13 1.10048
\(994\) 1.08359e14 3.52068
\(995\) −8.61398e13 −2.78612
\(996\) 4.01424e12 0.129252
\(997\) −7.31678e12 −0.234526 −0.117263 0.993101i \(-0.537412\pi\)
−0.117263 + 0.993101i \(0.537412\pi\)
\(998\) 8.80121e13 2.80837
\(999\) 5.97270e12 0.189726
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.1.19 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.19 22 1.1 even 1 trivial