Properties

Label 177.10.a.c.1.17
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 1.17
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+26.7529 q^{2} -81.0000 q^{3} +203.719 q^{4} -302.298 q^{5} -2166.99 q^{6} -5739.31 q^{7} -8247.43 q^{8} +6561.00 q^{9} -8087.35 q^{10} +8930.69 q^{11} -16501.2 q^{12} -34150.1 q^{13} -153543. q^{14} +24486.1 q^{15} -324947. q^{16} +25141.2 q^{17} +175526. q^{18} +41188.0 q^{19} -61583.7 q^{20} +464884. q^{21} +238922. q^{22} -1.88606e6 q^{23} +668042. q^{24} -1.86174e6 q^{25} -913614. q^{26} -531441. q^{27} -1.16920e6 q^{28} +4.48207e6 q^{29} +655075. q^{30} -2.37511e6 q^{31} -4.47059e6 q^{32} -723386. q^{33} +672599. q^{34} +1.73498e6 q^{35} +1.33660e6 q^{36} +1.10711e7 q^{37} +1.10190e6 q^{38} +2.76616e6 q^{39} +2.49318e6 q^{40} +2.38530e7 q^{41} +1.24370e7 q^{42} +3.14335e7 q^{43} +1.81935e6 q^{44} -1.98338e6 q^{45} -5.04577e7 q^{46} +2.63227e7 q^{47} +2.63207e7 q^{48} -7.41390e6 q^{49} -4.98070e7 q^{50} -2.03643e6 q^{51} -6.95700e6 q^{52} -2.61342e7 q^{53} -1.42176e7 q^{54} -2.69973e6 q^{55} +4.73346e7 q^{56} -3.33623e6 q^{57} +1.19909e8 q^{58} +1.21174e7 q^{59} +4.98828e6 q^{60} -1.33430e7 q^{61} -6.35411e7 q^{62} -3.76556e7 q^{63} +4.67714e7 q^{64} +1.03235e7 q^{65} -1.93527e7 q^{66} +1.72934e8 q^{67} +5.12172e6 q^{68} +1.52771e8 q^{69} +4.64158e7 q^{70} +1.07910e8 q^{71} -5.41114e7 q^{72} -4.60374e8 q^{73} +2.96185e8 q^{74} +1.50801e8 q^{75} +8.39076e6 q^{76} -5.12560e7 q^{77} +7.40027e7 q^{78} +2.14806e8 q^{79} +9.82306e7 q^{80} +4.30467e7 q^{81} +6.38138e8 q^{82} +3.37429e8 q^{83} +9.47056e7 q^{84} -7.60012e6 q^{85} +8.40938e8 q^{86} -3.63048e8 q^{87} -7.36553e7 q^{88} +1.74288e8 q^{89} -5.30611e7 q^{90} +1.95998e8 q^{91} -3.84226e8 q^{92} +1.92384e8 q^{93} +7.04210e8 q^{94} -1.24510e7 q^{95} +3.62118e8 q^{96} +8.52762e8 q^{97} -1.98344e8 q^{98} +5.85943e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26.7529 1.18232 0.591162 0.806553i \(-0.298670\pi\)
0.591162 + 0.806553i \(0.298670\pi\)
\(3\) −81.0000 −0.577350
\(4\) 203.719 0.397888
\(5\) −302.298 −0.216307 −0.108153 0.994134i \(-0.534494\pi\)
−0.108153 + 0.994134i \(0.534494\pi\)
\(6\) −2166.99 −0.682615
\(7\) −5739.31 −0.903480 −0.451740 0.892150i \(-0.649197\pi\)
−0.451740 + 0.892150i \(0.649197\pi\)
\(8\) −8247.43 −0.711891
\(9\) 6561.00 0.333333
\(10\) −8087.35 −0.255744
\(11\) 8930.69 0.183915 0.0919577 0.995763i \(-0.470688\pi\)
0.0919577 + 0.995763i \(0.470688\pi\)
\(12\) −16501.2 −0.229721
\(13\) −34150.1 −0.331624 −0.165812 0.986157i \(-0.553025\pi\)
−0.165812 + 0.986157i \(0.553025\pi\)
\(14\) −153543. −1.06821
\(15\) 24486.1 0.124885
\(16\) −324947. −1.23957
\(17\) 25141.2 0.0730071 0.0365036 0.999334i \(-0.488378\pi\)
0.0365036 + 0.999334i \(0.488378\pi\)
\(18\) 175526. 0.394108
\(19\) 41188.0 0.0725069 0.0362535 0.999343i \(-0.488458\pi\)
0.0362535 + 0.999343i \(0.488458\pi\)
\(20\) −61583.7 −0.0860658
\(21\) 464884. 0.521625
\(22\) 238922. 0.217447
\(23\) −1.88606e6 −1.40534 −0.702670 0.711516i \(-0.748009\pi\)
−0.702670 + 0.711516i \(0.748009\pi\)
\(24\) 668042. 0.411011
\(25\) −1.86174e6 −0.953211
\(26\) −913614. −0.392087
\(27\) −531441. −0.192450
\(28\) −1.16920e6 −0.359484
\(29\) 4.48207e6 1.17676 0.588380 0.808584i \(-0.299766\pi\)
0.588380 + 0.808584i \(0.299766\pi\)
\(30\) 655075. 0.147654
\(31\) −2.37511e6 −0.461909 −0.230954 0.972965i \(-0.574185\pi\)
−0.230954 + 0.972965i \(0.574185\pi\)
\(32\) −4.47059e6 −0.753685
\(33\) −723386. −0.106184
\(34\) 672599. 0.0863180
\(35\) 1.73498e6 0.195429
\(36\) 1.33660e6 0.132629
\(37\) 1.10711e7 0.971147 0.485573 0.874196i \(-0.338611\pi\)
0.485573 + 0.874196i \(0.338611\pi\)
\(38\) 1.10190e6 0.0857266
\(39\) 2.76616e6 0.191463
\(40\) 2.49318e6 0.153987
\(41\) 2.38530e7 1.31831 0.659153 0.752009i \(-0.270915\pi\)
0.659153 + 0.752009i \(0.270915\pi\)
\(42\) 1.24370e7 0.616729
\(43\) 3.14335e7 1.40212 0.701060 0.713103i \(-0.252711\pi\)
0.701060 + 0.713103i \(0.252711\pi\)
\(44\) 1.81935e6 0.0731777
\(45\) −1.98338e6 −0.0721022
\(46\) −5.04577e7 −1.66157
\(47\) 2.63227e7 0.786848 0.393424 0.919357i \(-0.371291\pi\)
0.393424 + 0.919357i \(0.371291\pi\)
\(48\) 2.63207e7 0.715668
\(49\) −7.41390e6 −0.183723
\(50\) −4.98070e7 −1.12700
\(51\) −2.03643e6 −0.0421507
\(52\) −6.95700e6 −0.131949
\(53\) −2.61342e7 −0.454955 −0.227478 0.973783i \(-0.573048\pi\)
−0.227478 + 0.973783i \(0.573048\pi\)
\(54\) −1.42176e7 −0.227538
\(55\) −2.69973e6 −0.0397821
\(56\) 4.73346e7 0.643180
\(57\) −3.33623e6 −0.0418619
\(58\) 1.19909e8 1.39131
\(59\) 1.21174e7 0.130189
\(60\) 4.98828e6 0.0496901
\(61\) −1.33430e7 −0.123387 −0.0616935 0.998095i \(-0.519650\pi\)
−0.0616935 + 0.998095i \(0.519650\pi\)
\(62\) −6.35411e7 −0.546125
\(63\) −3.76556e7 −0.301160
\(64\) 4.67714e7 0.348474
\(65\) 1.03235e7 0.0717326
\(66\) −1.93527e7 −0.125543
\(67\) 1.72934e8 1.04844 0.524222 0.851582i \(-0.324356\pi\)
0.524222 + 0.851582i \(0.324356\pi\)
\(68\) 5.12172e6 0.0290486
\(69\) 1.52771e8 0.811373
\(70\) 4.64158e7 0.231060
\(71\) 1.07910e8 0.503965 0.251982 0.967732i \(-0.418918\pi\)
0.251982 + 0.967732i \(0.418918\pi\)
\(72\) −5.41114e7 −0.237297
\(73\) −4.60374e8 −1.89740 −0.948699 0.316182i \(-0.897599\pi\)
−0.948699 + 0.316182i \(0.897599\pi\)
\(74\) 2.96185e8 1.14821
\(75\) 1.50801e8 0.550337
\(76\) 8.39076e6 0.0288496
\(77\) −5.12560e7 −0.166164
\(78\) 7.40027e7 0.226372
\(79\) 2.14806e8 0.620474 0.310237 0.950659i \(-0.399592\pi\)
0.310237 + 0.950659i \(0.399592\pi\)
\(80\) 9.82306e7 0.268128
\(81\) 4.30467e7 0.111111
\(82\) 6.38138e8 1.55866
\(83\) 3.37429e8 0.780425 0.390212 0.920725i \(-0.372402\pi\)
0.390212 + 0.920725i \(0.372402\pi\)
\(84\) 9.47056e7 0.207548
\(85\) −7.60012e6 −0.0157919
\(86\) 8.40938e8 1.65776
\(87\) −3.63048e8 −0.679403
\(88\) −7.36553e7 −0.130928
\(89\) 1.74288e8 0.294450 0.147225 0.989103i \(-0.452966\pi\)
0.147225 + 0.989103i \(0.452966\pi\)
\(90\) −5.30611e7 −0.0852481
\(91\) 1.95998e8 0.299616
\(92\) −3.84226e8 −0.559167
\(93\) 1.92384e8 0.266683
\(94\) 7.04210e8 0.930308
\(95\) −1.24510e7 −0.0156837
\(96\) 3.62118e8 0.435140
\(97\) 8.52762e8 0.978037 0.489018 0.872274i \(-0.337355\pi\)
0.489018 + 0.872274i \(0.337355\pi\)
\(98\) −1.98344e8 −0.217220
\(99\) 5.85943e7 0.0613051
\(100\) −3.79271e8 −0.379271
\(101\) 6.13488e7 0.0586624 0.0293312 0.999570i \(-0.490662\pi\)
0.0293312 + 0.999570i \(0.490662\pi\)
\(102\) −5.44806e7 −0.0498357
\(103\) 1.83989e9 1.61073 0.805366 0.592777i \(-0.201969\pi\)
0.805366 + 0.592777i \(0.201969\pi\)
\(104\) 2.81650e8 0.236081
\(105\) −1.40533e8 −0.112831
\(106\) −6.99167e8 −0.537904
\(107\) 2.11452e8 0.155950 0.0779748 0.996955i \(-0.475155\pi\)
0.0779748 + 0.996955i \(0.475155\pi\)
\(108\) −1.08264e8 −0.0765735
\(109\) 1.71147e8 0.116132 0.0580658 0.998313i \(-0.481507\pi\)
0.0580658 + 0.998313i \(0.481507\pi\)
\(110\) −7.22256e7 −0.0470353
\(111\) −8.96763e8 −0.560692
\(112\) 1.86497e9 1.11993
\(113\) 3.33129e8 0.192202 0.0961012 0.995372i \(-0.469363\pi\)
0.0961012 + 0.995372i \(0.469363\pi\)
\(114\) −8.92538e7 −0.0494943
\(115\) 5.70153e8 0.303984
\(116\) 9.13082e8 0.468219
\(117\) −2.24059e8 −0.110541
\(118\) 3.24175e8 0.153925
\(119\) −1.44293e8 −0.0659605
\(120\) −2.01947e8 −0.0889043
\(121\) −2.27819e9 −0.966175
\(122\) −3.56965e8 −0.145883
\(123\) −1.93209e9 −0.761124
\(124\) −4.83854e8 −0.183788
\(125\) 1.15323e9 0.422493
\(126\) −1.00740e9 −0.356069
\(127\) −5.28337e8 −0.180216 −0.0901082 0.995932i \(-0.528721\pi\)
−0.0901082 + 0.995932i \(0.528721\pi\)
\(128\) 3.54021e9 1.16569
\(129\) −2.54612e9 −0.809514
\(130\) 2.76183e8 0.0848111
\(131\) 1.10426e8 0.0327605 0.0163803 0.999866i \(-0.494786\pi\)
0.0163803 + 0.999866i \(0.494786\pi\)
\(132\) −1.47367e8 −0.0422492
\(133\) −2.36391e8 −0.0655086
\(134\) 4.62650e9 1.23960
\(135\) 1.60653e8 0.0416282
\(136\) −2.07350e8 −0.0519731
\(137\) −8.18316e8 −0.198462 −0.0992312 0.995064i \(-0.531638\pi\)
−0.0992312 + 0.995064i \(0.531638\pi\)
\(138\) 4.08708e9 0.959305
\(139\) −7.12323e8 −0.161849 −0.0809245 0.996720i \(-0.525787\pi\)
−0.0809245 + 0.996720i \(0.525787\pi\)
\(140\) 3.53448e8 0.0777587
\(141\) −2.13214e9 −0.454287
\(142\) 2.88691e9 0.595849
\(143\) −3.04984e8 −0.0609909
\(144\) −2.13197e9 −0.413191
\(145\) −1.35492e9 −0.254541
\(146\) −1.23164e10 −2.24334
\(147\) 6.00526e8 0.106073
\(148\) 2.25540e9 0.386407
\(149\) 2.50956e9 0.417119 0.208559 0.978010i \(-0.433123\pi\)
0.208559 + 0.978010i \(0.433123\pi\)
\(150\) 4.03437e9 0.650676
\(151\) −1.14855e10 −1.79785 −0.898925 0.438103i \(-0.855651\pi\)
−0.898925 + 0.438103i \(0.855651\pi\)
\(152\) −3.39695e8 −0.0516170
\(153\) 1.64951e8 0.0243357
\(154\) −1.37125e9 −0.196459
\(155\) 7.17990e8 0.0999139
\(156\) 5.63517e8 0.0761810
\(157\) 6.11357e9 0.803057 0.401529 0.915846i \(-0.368479\pi\)
0.401529 + 0.915846i \(0.368479\pi\)
\(158\) 5.74668e9 0.733601
\(159\) 2.11687e9 0.262668
\(160\) 1.35145e9 0.163027
\(161\) 1.08247e10 1.26970
\(162\) 1.15163e9 0.131369
\(163\) −3.77542e9 −0.418910 −0.209455 0.977818i \(-0.567169\pi\)
−0.209455 + 0.977818i \(0.567169\pi\)
\(164\) 4.85930e9 0.524538
\(165\) 2.18678e8 0.0229682
\(166\) 9.02721e9 0.922714
\(167\) −1.45074e10 −1.44333 −0.721664 0.692244i \(-0.756622\pi\)
−0.721664 + 0.692244i \(0.756622\pi\)
\(168\) −3.83410e9 −0.371340
\(169\) −9.43827e9 −0.890025
\(170\) −2.03325e8 −0.0186712
\(171\) 2.70234e8 0.0241690
\(172\) 6.40359e9 0.557886
\(173\) 8.68202e9 0.736908 0.368454 0.929646i \(-0.379887\pi\)
0.368454 + 0.929646i \(0.379887\pi\)
\(174\) −9.71259e9 −0.803274
\(175\) 1.06851e10 0.861208
\(176\) −2.90200e9 −0.227977
\(177\) −9.81506e8 −0.0751646
\(178\) 4.66271e9 0.348135
\(179\) 1.56613e10 1.14022 0.570112 0.821567i \(-0.306900\pi\)
0.570112 + 0.821567i \(0.306900\pi\)
\(180\) −4.04050e8 −0.0286886
\(181\) −1.27073e10 −0.880037 −0.440019 0.897989i \(-0.645028\pi\)
−0.440019 + 0.897989i \(0.645028\pi\)
\(182\) 5.24352e9 0.354243
\(183\) 1.08078e9 0.0712376
\(184\) 1.55552e10 1.00045
\(185\) −3.34678e9 −0.210065
\(186\) 5.14683e9 0.315305
\(187\) 2.24528e8 0.0134271
\(188\) 5.36243e9 0.313077
\(189\) 3.05011e9 0.173875
\(190\) −3.33102e8 −0.0185432
\(191\) 3.61646e10 1.96623 0.983114 0.182994i \(-0.0585789\pi\)
0.983114 + 0.182994i \(0.0585789\pi\)
\(192\) −3.78849e9 −0.201192
\(193\) −4.94541e9 −0.256563 −0.128281 0.991738i \(-0.540946\pi\)
−0.128281 + 0.991738i \(0.540946\pi\)
\(194\) 2.28139e10 1.15636
\(195\) −8.36203e8 −0.0414148
\(196\) −1.51035e9 −0.0731013
\(197\) 3.44918e10 1.63161 0.815807 0.578324i \(-0.196293\pi\)
0.815807 + 0.578324i \(0.196293\pi\)
\(198\) 1.56757e9 0.0724825
\(199\) −1.72131e10 −0.778075 −0.389037 0.921222i \(-0.627192\pi\)
−0.389037 + 0.921222i \(0.627192\pi\)
\(200\) 1.53546e10 0.678583
\(201\) −1.40077e10 −0.605319
\(202\) 1.64126e9 0.0693579
\(203\) −2.57240e10 −1.06318
\(204\) −4.14859e8 −0.0167712
\(205\) −7.21071e9 −0.285158
\(206\) 4.92223e10 1.90441
\(207\) −1.23745e10 −0.468446
\(208\) 1.10970e10 0.411073
\(209\) 3.67837e8 0.0133351
\(210\) −3.75968e9 −0.133403
\(211\) 2.21547e10 0.769477 0.384738 0.923026i \(-0.374292\pi\)
0.384738 + 0.923026i \(0.374292\pi\)
\(212\) −5.32403e9 −0.181021
\(213\) −8.74073e9 −0.290964
\(214\) 5.65695e9 0.184383
\(215\) −9.50228e9 −0.303288
\(216\) 4.38302e9 0.137004
\(217\) 1.36315e10 0.417325
\(218\) 4.57869e9 0.137305
\(219\) 3.72903e10 1.09546
\(220\) −5.49985e8 −0.0158288
\(221\) −8.58573e8 −0.0242109
\(222\) −2.39910e10 −0.662919
\(223\) −4.46986e9 −0.121038 −0.0605190 0.998167i \(-0.519276\pi\)
−0.0605190 + 0.998167i \(0.519276\pi\)
\(224\) 2.56581e10 0.680939
\(225\) −1.22149e10 −0.317737
\(226\) 8.91216e9 0.227245
\(227\) 1.10694e8 0.00276698 0.00138349 0.999999i \(-0.499560\pi\)
0.00138349 + 0.999999i \(0.499560\pi\)
\(228\) −6.79651e8 −0.0166563
\(229\) −6.91253e10 −1.66103 −0.830515 0.556997i \(-0.811954\pi\)
−0.830515 + 0.556997i \(0.811954\pi\)
\(230\) 1.52533e10 0.359408
\(231\) 4.15174e9 0.0959348
\(232\) −3.69656e10 −0.837725
\(233\) −6.67113e9 −0.148285 −0.0741426 0.997248i \(-0.523622\pi\)
−0.0741426 + 0.997248i \(0.523622\pi\)
\(234\) −5.99422e9 −0.130696
\(235\) −7.95730e9 −0.170200
\(236\) 2.46853e9 0.0518006
\(237\) −1.73993e10 −0.358231
\(238\) −3.86026e9 −0.0779866
\(239\) 1.60016e10 0.317229 0.158615 0.987341i \(-0.449297\pi\)
0.158615 + 0.987341i \(0.449297\pi\)
\(240\) −7.95668e9 −0.154804
\(241\) −3.22187e9 −0.0615220 −0.0307610 0.999527i \(-0.509793\pi\)
−0.0307610 + 0.999527i \(0.509793\pi\)
\(242\) −6.09482e10 −1.14233
\(243\) −3.48678e9 −0.0641500
\(244\) −2.71822e9 −0.0490942
\(245\) 2.24121e9 0.0397406
\(246\) −5.16892e10 −0.899894
\(247\) −1.40657e9 −0.0240451
\(248\) 1.95885e10 0.328829
\(249\) −2.73317e10 −0.450578
\(250\) 3.08521e10 0.499523
\(251\) −5.76479e10 −0.916752 −0.458376 0.888758i \(-0.651569\pi\)
−0.458376 + 0.888758i \(0.651569\pi\)
\(252\) −7.67115e9 −0.119828
\(253\) −1.68439e10 −0.258464
\(254\) −1.41345e10 −0.213074
\(255\) 6.15609e8 0.00911747
\(256\) 7.07641e10 1.02975
\(257\) −1.30863e10 −0.187120 −0.0935598 0.995614i \(-0.529825\pi\)
−0.0935598 + 0.995614i \(0.529825\pi\)
\(258\) −6.81160e10 −0.957107
\(259\) −6.35408e10 −0.877412
\(260\) 2.10309e9 0.0285415
\(261\) 2.94069e10 0.392253
\(262\) 2.95422e9 0.0387335
\(263\) −1.22943e11 −1.58454 −0.792270 0.610170i \(-0.791101\pi\)
−0.792270 + 0.610170i \(0.791101\pi\)
\(264\) 5.96608e9 0.0755912
\(265\) 7.90032e9 0.0984098
\(266\) −6.32414e9 −0.0774523
\(267\) −1.41173e10 −0.170001
\(268\) 3.52300e10 0.417163
\(269\) 2.20233e10 0.256447 0.128224 0.991745i \(-0.459072\pi\)
0.128224 + 0.991745i \(0.459072\pi\)
\(270\) 4.29795e9 0.0492180
\(271\) −1.58720e10 −0.178760 −0.0893798 0.995998i \(-0.528488\pi\)
−0.0893798 + 0.995998i \(0.528488\pi\)
\(272\) −8.16954e9 −0.0904977
\(273\) −1.58758e10 −0.172983
\(274\) −2.18923e10 −0.234647
\(275\) −1.66266e10 −0.175310
\(276\) 3.11223e10 0.322835
\(277\) 1.26897e10 0.129506 0.0647532 0.997901i \(-0.479374\pi\)
0.0647532 + 0.997901i \(0.479374\pi\)
\(278\) −1.90567e10 −0.191358
\(279\) −1.55831e10 −0.153970
\(280\) −1.43091e10 −0.139124
\(281\) −1.28463e11 −1.22913 −0.614567 0.788865i \(-0.710669\pi\)
−0.614567 + 0.788865i \(0.710669\pi\)
\(282\) −5.70410e10 −0.537114
\(283\) 8.79744e10 0.815300 0.407650 0.913138i \(-0.366348\pi\)
0.407650 + 0.913138i \(0.366348\pi\)
\(284\) 2.19833e10 0.200521
\(285\) 1.00853e9 0.00905500
\(286\) −8.15921e9 −0.0721109
\(287\) −1.36900e11 −1.19106
\(288\) −2.93315e10 −0.251228
\(289\) −1.17956e11 −0.994670
\(290\) −3.62481e10 −0.300950
\(291\) −6.90737e10 −0.564670
\(292\) −9.37868e10 −0.754951
\(293\) −9.48080e10 −0.751520 −0.375760 0.926717i \(-0.622618\pi\)
−0.375760 + 0.926717i \(0.622618\pi\)
\(294\) 1.60658e10 0.125412
\(295\) −3.66305e9 −0.0281607
\(296\) −9.13085e10 −0.691351
\(297\) −4.74614e9 −0.0353945
\(298\) 6.71381e10 0.493169
\(299\) 6.44092e10 0.466045
\(300\) 3.07210e10 0.218972
\(301\) −1.80407e11 −1.26679
\(302\) −3.07270e11 −2.12564
\(303\) −4.96925e9 −0.0338688
\(304\) −1.33839e10 −0.0898776
\(305\) 4.03356e9 0.0266894
\(306\) 4.41293e9 0.0287727
\(307\) 2.65087e11 1.70320 0.851601 0.524191i \(-0.175632\pi\)
0.851601 + 0.524191i \(0.175632\pi\)
\(308\) −1.04418e10 −0.0661146
\(309\) −1.49031e11 −0.929957
\(310\) 1.92083e10 0.118130
\(311\) 2.17731e11 1.31977 0.659885 0.751367i \(-0.270605\pi\)
0.659885 + 0.751367i \(0.270605\pi\)
\(312\) −2.28137e10 −0.136301
\(313\) −2.32312e11 −1.36811 −0.684056 0.729430i \(-0.739786\pi\)
−0.684056 + 0.729430i \(0.739786\pi\)
\(314\) 1.63556e11 0.949473
\(315\) 1.13832e10 0.0651429
\(316\) 4.37599e10 0.246879
\(317\) 2.47206e11 1.37497 0.687483 0.726200i \(-0.258715\pi\)
0.687483 + 0.726200i \(0.258715\pi\)
\(318\) 5.66325e10 0.310559
\(319\) 4.00280e10 0.216424
\(320\) −1.41389e10 −0.0753773
\(321\) −1.71276e10 −0.0900375
\(322\) 2.89593e11 1.50119
\(323\) 1.03551e9 0.00529352
\(324\) 8.76942e9 0.0442098
\(325\) 6.35786e10 0.316108
\(326\) −1.01003e11 −0.495287
\(327\) −1.38629e10 −0.0670487
\(328\) −1.96726e11 −0.938490
\(329\) −1.51074e11 −0.710901
\(330\) 5.85027e9 0.0271559
\(331\) 1.18106e11 0.540810 0.270405 0.962747i \(-0.412842\pi\)
0.270405 + 0.962747i \(0.412842\pi\)
\(332\) 6.87405e10 0.310521
\(333\) 7.26378e10 0.323716
\(334\) −3.88115e11 −1.70648
\(335\) −5.22777e10 −0.226785
\(336\) −1.51063e11 −0.646592
\(337\) 2.37871e11 1.00463 0.502315 0.864685i \(-0.332482\pi\)
0.502315 + 0.864685i \(0.332482\pi\)
\(338\) −2.52501e11 −1.05230
\(339\) −2.69834e10 −0.110968
\(340\) −1.54828e9 −0.00628342
\(341\) −2.12114e10 −0.0849521
\(342\) 7.22956e9 0.0285755
\(343\) 2.74153e11 1.06947
\(344\) −2.59246e11 −0.998156
\(345\) −4.61824e10 −0.175505
\(346\) 2.32269e11 0.871263
\(347\) 2.95829e11 1.09536 0.547682 0.836687i \(-0.315510\pi\)
0.547682 + 0.836687i \(0.315510\pi\)
\(348\) −7.39596e10 −0.270326
\(349\) 2.93184e11 1.05785 0.528926 0.848668i \(-0.322595\pi\)
0.528926 + 0.848668i \(0.322595\pi\)
\(350\) 2.85858e11 1.01823
\(351\) 1.81487e10 0.0638212
\(352\) −3.99254e10 −0.138614
\(353\) −1.49690e10 −0.0513104 −0.0256552 0.999671i \(-0.508167\pi\)
−0.0256552 + 0.999671i \(0.508167\pi\)
\(354\) −2.62582e10 −0.0888688
\(355\) −3.26210e10 −0.109011
\(356\) 3.55057e10 0.117158
\(357\) 1.16877e10 0.0380823
\(358\) 4.18986e11 1.34811
\(359\) −4.00848e11 −1.27366 −0.636832 0.771002i \(-0.719756\pi\)
−0.636832 + 0.771002i \(0.719756\pi\)
\(360\) 1.63577e10 0.0513289
\(361\) −3.20991e11 −0.994743
\(362\) −3.39958e11 −1.04049
\(363\) 1.84533e11 0.557821
\(364\) 3.99284e10 0.119214
\(365\) 1.39170e11 0.410420
\(366\) 2.89141e10 0.0842258
\(367\) −1.86564e11 −0.536823 −0.268412 0.963304i \(-0.586499\pi\)
−0.268412 + 0.963304i \(0.586499\pi\)
\(368\) 6.12870e11 1.74202
\(369\) 1.56500e11 0.439435
\(370\) −8.95362e10 −0.248365
\(371\) 1.49993e11 0.411043
\(372\) 3.91922e10 0.106110
\(373\) 1.70506e11 0.456091 0.228045 0.973651i \(-0.426767\pi\)
0.228045 + 0.973651i \(0.426767\pi\)
\(374\) 6.00678e9 0.0158752
\(375\) −9.34113e10 −0.243926
\(376\) −2.17095e11 −0.560150
\(377\) −1.53063e11 −0.390242
\(378\) 8.15992e10 0.205576
\(379\) 6.72931e11 1.67531 0.837653 0.546202i \(-0.183927\pi\)
0.837653 + 0.546202i \(0.183927\pi\)
\(380\) −2.53651e9 −0.00624036
\(381\) 4.27953e10 0.104048
\(382\) 9.67509e11 2.32472
\(383\) −3.81727e11 −0.906480 −0.453240 0.891389i \(-0.649732\pi\)
−0.453240 + 0.891389i \(0.649732\pi\)
\(384\) −2.86757e11 −0.673014
\(385\) 1.54946e10 0.0359424
\(386\) −1.32304e11 −0.303340
\(387\) 2.06235e11 0.467373
\(388\) 1.73723e11 0.389149
\(389\) −2.35278e11 −0.520964 −0.260482 0.965479i \(-0.583881\pi\)
−0.260482 + 0.965479i \(0.583881\pi\)
\(390\) −2.23709e10 −0.0489657
\(391\) −4.74178e10 −0.102600
\(392\) 6.11456e10 0.130791
\(393\) −8.94452e9 −0.0189143
\(394\) 9.22756e11 1.92910
\(395\) −6.49352e10 −0.134213
\(396\) 1.19367e10 0.0243926
\(397\) 1.06947e11 0.216079 0.108040 0.994147i \(-0.465543\pi\)
0.108040 + 0.994147i \(0.465543\pi\)
\(398\) −4.60502e11 −0.919936
\(399\) 1.91476e10 0.0378214
\(400\) 6.04967e11 1.18158
\(401\) −4.34250e11 −0.838667 −0.419334 0.907832i \(-0.637736\pi\)
−0.419334 + 0.907832i \(0.637736\pi\)
\(402\) −3.74747e11 −0.715683
\(403\) 8.11102e10 0.153180
\(404\) 1.24979e10 0.0233411
\(405\) −1.30129e10 −0.0240341
\(406\) −6.88193e11 −1.25702
\(407\) 9.88730e10 0.178609
\(408\) 1.67953e10 0.0300067
\(409\) 9.37763e11 1.65706 0.828530 0.559945i \(-0.189178\pi\)
0.828530 + 0.559945i \(0.189178\pi\)
\(410\) −1.92908e11 −0.337149
\(411\) 6.62836e10 0.114582
\(412\) 3.74819e11 0.640891
\(413\) −6.95453e10 −0.117623
\(414\) −3.31053e11 −0.553855
\(415\) −1.02004e11 −0.168811
\(416\) 1.52671e11 0.249940
\(417\) 5.76981e10 0.0934436
\(418\) 9.84072e9 0.0157664
\(419\) 4.16830e11 0.660687 0.330344 0.943861i \(-0.392835\pi\)
0.330344 + 0.943861i \(0.392835\pi\)
\(420\) −2.86293e10 −0.0448940
\(421\) 5.26815e11 0.817314 0.408657 0.912688i \(-0.365997\pi\)
0.408657 + 0.912688i \(0.365997\pi\)
\(422\) 5.92704e11 0.909770
\(423\) 1.72703e11 0.262283
\(424\) 2.15540e11 0.323878
\(425\) −4.68063e10 −0.0695912
\(426\) −2.33840e11 −0.344013
\(427\) 7.65797e10 0.111478
\(428\) 4.30766e10 0.0620504
\(429\) 2.47037e10 0.0352131
\(430\) −2.54214e11 −0.358584
\(431\) −8.48282e11 −1.18411 −0.592056 0.805897i \(-0.701684\pi\)
−0.592056 + 0.805897i \(0.701684\pi\)
\(432\) 1.72690e11 0.238556
\(433\) 5.30333e11 0.725025 0.362513 0.931979i \(-0.381919\pi\)
0.362513 + 0.931979i \(0.381919\pi\)
\(434\) 3.64682e11 0.493413
\(435\) 1.09749e11 0.146959
\(436\) 3.48659e10 0.0462074
\(437\) −7.76832e10 −0.101897
\(438\) 9.97625e11 1.29519
\(439\) 8.03608e11 1.03265 0.516326 0.856392i \(-0.327299\pi\)
0.516326 + 0.856392i \(0.327299\pi\)
\(440\) 2.22658e10 0.0283205
\(441\) −4.86426e10 −0.0612411
\(442\) −2.29693e10 −0.0286252
\(443\) 1.27320e12 1.57065 0.785323 0.619086i \(-0.212497\pi\)
0.785323 + 0.619086i \(0.212497\pi\)
\(444\) −1.82687e11 −0.223092
\(445\) −5.26868e10 −0.0636915
\(446\) −1.19582e11 −0.143106
\(447\) −2.03275e11 −0.240824
\(448\) −2.68436e11 −0.314840
\(449\) −7.80521e11 −0.906308 −0.453154 0.891432i \(-0.649701\pi\)
−0.453154 + 0.891432i \(0.649701\pi\)
\(450\) −3.26784e11 −0.375668
\(451\) 2.13024e11 0.242457
\(452\) 6.78645e10 0.0764750
\(453\) 9.30325e11 1.03799
\(454\) 2.96138e9 0.00327147
\(455\) −5.92497e10 −0.0648090
\(456\) 2.75153e10 0.0298011
\(457\) 1.61465e12 1.73164 0.865818 0.500359i \(-0.166799\pi\)
0.865818 + 0.500359i \(0.166799\pi\)
\(458\) −1.84930e12 −1.96387
\(459\) −1.33610e10 −0.0140502
\(460\) 1.16151e11 0.120952
\(461\) 6.00901e11 0.619654 0.309827 0.950793i \(-0.399729\pi\)
0.309827 + 0.950793i \(0.399729\pi\)
\(462\) 1.11071e11 0.113426
\(463\) 1.50181e12 1.51880 0.759400 0.650623i \(-0.225492\pi\)
0.759400 + 0.650623i \(0.225492\pi\)
\(464\) −1.45643e12 −1.45868
\(465\) −5.81572e10 −0.0576853
\(466\) −1.78472e11 −0.175321
\(467\) −4.12507e11 −0.401333 −0.200667 0.979660i \(-0.564311\pi\)
−0.200667 + 0.979660i \(0.564311\pi\)
\(468\) −4.56449e10 −0.0439831
\(469\) −9.92525e11 −0.947248
\(470\) −2.12881e11 −0.201232
\(471\) −4.95199e11 −0.463645
\(472\) −9.99371e10 −0.0926803
\(473\) 2.80723e11 0.257871
\(474\) −4.65481e11 −0.423545
\(475\) −7.66814e10 −0.0691144
\(476\) −2.93952e10 −0.0262449
\(477\) −1.71467e11 −0.151652
\(478\) 4.28090e11 0.375067
\(479\) −1.35808e11 −0.117873 −0.0589365 0.998262i \(-0.518771\pi\)
−0.0589365 + 0.998262i \(0.518771\pi\)
\(480\) −1.09467e11 −0.0941237
\(481\) −3.78080e11 −0.322056
\(482\) −8.61943e10 −0.0727389
\(483\) −8.76802e11 −0.733060
\(484\) −4.64110e11 −0.384429
\(485\) −2.57788e11 −0.211556
\(486\) −9.32817e10 −0.0758461
\(487\) 4.64384e11 0.374108 0.187054 0.982350i \(-0.440106\pi\)
0.187054 + 0.982350i \(0.440106\pi\)
\(488\) 1.10046e11 0.0878382
\(489\) 3.05809e11 0.241858
\(490\) 5.99588e10 0.0469862
\(491\) −2.27566e12 −1.76702 −0.883510 0.468412i \(-0.844826\pi\)
−0.883510 + 0.468412i \(0.844826\pi\)
\(492\) −3.93604e11 −0.302842
\(493\) 1.12685e11 0.0859119
\(494\) −3.76299e10 −0.0284290
\(495\) −1.77129e10 −0.0132607
\(496\) 7.71784e11 0.572569
\(497\) −6.19330e11 −0.455322
\(498\) −7.31204e11 −0.532729
\(499\) −9.59453e11 −0.692742 −0.346371 0.938098i \(-0.612586\pi\)
−0.346371 + 0.938098i \(0.612586\pi\)
\(500\) 2.34933e11 0.168105
\(501\) 1.17510e12 0.833306
\(502\) −1.54225e12 −1.08390
\(503\) 1.59860e12 1.11348 0.556742 0.830685i \(-0.312051\pi\)
0.556742 + 0.830685i \(0.312051\pi\)
\(504\) 3.10562e11 0.214393
\(505\) −1.85456e10 −0.0126891
\(506\) −4.50622e11 −0.305587
\(507\) 7.64500e11 0.513856
\(508\) −1.07632e11 −0.0717059
\(509\) 1.17983e12 0.779096 0.389548 0.921006i \(-0.372631\pi\)
0.389548 + 0.921006i \(0.372631\pi\)
\(510\) 1.64693e10 0.0107798
\(511\) 2.64223e12 1.71426
\(512\) 8.05557e10 0.0518062
\(513\) −2.18890e10 −0.0139540
\(514\) −3.50098e11 −0.221236
\(515\) −5.56193e11 −0.348412
\(516\) −5.18691e11 −0.322096
\(517\) 2.35080e11 0.144713
\(518\) −1.69990e12 −1.03738
\(519\) −7.03243e11 −0.425454
\(520\) −8.51422e10 −0.0510658
\(521\) −7.90131e11 −0.469818 −0.234909 0.972017i \(-0.575479\pi\)
−0.234909 + 0.972017i \(0.575479\pi\)
\(522\) 7.86720e11 0.463770
\(523\) −1.02714e12 −0.600303 −0.300152 0.953891i \(-0.597037\pi\)
−0.300152 + 0.953891i \(0.597037\pi\)
\(524\) 2.24959e10 0.0130350
\(525\) −8.65494e11 −0.497219
\(526\) −3.28909e12 −1.87344
\(527\) −5.97130e10 −0.0337226
\(528\) 2.35062e11 0.131622
\(529\) 1.75609e12 0.974979
\(530\) 2.11357e11 0.116352
\(531\) 7.95020e10 0.0433963
\(532\) −4.81572e10 −0.0260651
\(533\) −8.14582e11 −0.437182
\(534\) −3.77679e11 −0.200996
\(535\) −6.39214e10 −0.0337329
\(536\) −1.42626e12 −0.746377
\(537\) −1.26857e12 −0.658309
\(538\) 5.89188e11 0.303203
\(539\) −6.62113e10 −0.0337896
\(540\) 3.27281e10 0.0165634
\(541\) 2.60129e12 1.30557 0.652786 0.757542i \(-0.273600\pi\)
0.652786 + 0.757542i \(0.273600\pi\)
\(542\) −4.24622e11 −0.211352
\(543\) 1.02929e12 0.508090
\(544\) −1.12396e11 −0.0550244
\(545\) −5.17374e10 −0.0251201
\(546\) −4.24725e11 −0.204522
\(547\) 1.91631e12 0.915215 0.457608 0.889154i \(-0.348706\pi\)
0.457608 + 0.889154i \(0.348706\pi\)
\(548\) −1.66706e11 −0.0789658
\(549\) −8.75435e10 −0.0411290
\(550\) −4.44811e11 −0.207273
\(551\) 1.84608e11 0.0853232
\(552\) −1.25997e12 −0.577609
\(553\) −1.23284e12 −0.560586
\(554\) 3.39485e11 0.153118
\(555\) 2.71089e11 0.121281
\(556\) −1.45113e11 −0.0643978
\(557\) 3.32274e12 1.46267 0.731337 0.682016i \(-0.238897\pi\)
0.731337 + 0.682016i \(0.238897\pi\)
\(558\) −4.16893e11 −0.182042
\(559\) −1.07346e12 −0.464977
\(560\) −5.63776e11 −0.242248
\(561\) −1.81868e10 −0.00775216
\(562\) −3.43676e12 −1.45323
\(563\) 1.35624e12 0.568918 0.284459 0.958688i \(-0.408186\pi\)
0.284459 + 0.958688i \(0.408186\pi\)
\(564\) −4.34357e11 −0.180755
\(565\) −1.00704e11 −0.0415747
\(566\) 2.35357e12 0.963948
\(567\) −2.47059e11 −0.100387
\(568\) −8.89982e11 −0.358768
\(569\) −1.80406e12 −0.721516 −0.360758 0.932659i \(-0.617482\pi\)
−0.360758 + 0.932659i \(0.617482\pi\)
\(570\) 2.69812e10 0.0107059
\(571\) −3.82279e12 −1.50493 −0.752467 0.658629i \(-0.771136\pi\)
−0.752467 + 0.658629i \(0.771136\pi\)
\(572\) −6.21309e10 −0.0242675
\(573\) −2.92934e12 −1.13520
\(574\) −3.66247e12 −1.40822
\(575\) 3.51136e12 1.33959
\(576\) 3.06867e11 0.116158
\(577\) 3.15806e12 1.18612 0.593060 0.805158i \(-0.297920\pi\)
0.593060 + 0.805158i \(0.297920\pi\)
\(578\) −3.15566e12 −1.17602
\(579\) 4.00578e11 0.148127
\(580\) −2.76022e11 −0.101279
\(581\) −1.93661e12 −0.705098
\(582\) −1.84792e12 −0.667622
\(583\) −2.33397e11 −0.0836733
\(584\) 3.79690e12 1.35074
\(585\) 6.77324e10 0.0239109
\(586\) −2.53639e12 −0.888540
\(587\) 2.31843e12 0.805977 0.402988 0.915205i \(-0.367972\pi\)
0.402988 + 0.915205i \(0.367972\pi\)
\(588\) 1.22338e11 0.0422051
\(589\) −9.78260e10 −0.0334916
\(590\) −9.79973e10 −0.0332951
\(591\) −2.79383e12 −0.942013
\(592\) −3.59753e12 −1.20381
\(593\) 3.39023e12 1.12586 0.562928 0.826506i \(-0.309675\pi\)
0.562928 + 0.826506i \(0.309675\pi\)
\(594\) −1.26973e11 −0.0418478
\(595\) 4.36194e10 0.0142677
\(596\) 5.11244e11 0.165966
\(597\) 1.39426e12 0.449222
\(598\) 1.72313e12 0.551016
\(599\) 1.25426e12 0.398076 0.199038 0.979992i \(-0.436218\pi\)
0.199038 + 0.979992i \(0.436218\pi\)
\(600\) −1.24372e12 −0.391780
\(601\) 5.55160e12 1.73573 0.867867 0.496797i \(-0.165491\pi\)
0.867867 + 0.496797i \(0.165491\pi\)
\(602\) −4.82641e12 −1.49775
\(603\) 1.13462e12 0.349481
\(604\) −2.33981e12 −0.715342
\(605\) 6.88692e11 0.208990
\(606\) −1.32942e11 −0.0400438
\(607\) 6.35706e12 1.90067 0.950337 0.311223i \(-0.100739\pi\)
0.950337 + 0.311223i \(0.100739\pi\)
\(608\) −1.84135e11 −0.0546473
\(609\) 2.08365e12 0.613827
\(610\) 1.07910e11 0.0315555
\(611\) −8.98923e11 −0.260938
\(612\) 3.36036e10 0.00968288
\(613\) −1.99633e12 −0.571032 −0.285516 0.958374i \(-0.592165\pi\)
−0.285516 + 0.958374i \(0.592165\pi\)
\(614\) 7.09185e12 2.01373
\(615\) 5.84068e11 0.164636
\(616\) 4.22730e11 0.118291
\(617\) 6.38934e9 0.00177489 0.000887447 1.00000i \(-0.499718\pi\)
0.000887447 1.00000i \(0.499718\pi\)
\(618\) −3.98701e12 −1.09951
\(619\) −2.99662e12 −0.820398 −0.410199 0.911996i \(-0.634541\pi\)
−0.410199 + 0.911996i \(0.634541\pi\)
\(620\) 1.46268e11 0.0397545
\(621\) 1.00233e12 0.270458
\(622\) 5.82493e12 1.56039
\(623\) −1.00029e12 −0.266030
\(624\) −8.98853e11 −0.237333
\(625\) 3.28760e12 0.861823
\(626\) −6.21502e12 −1.61755
\(627\) −2.97948e10 −0.00769905
\(628\) 1.24545e12 0.319527
\(629\) 2.78342e11 0.0709006
\(630\) 3.04534e11 0.0770200
\(631\) 1.38378e12 0.347484 0.173742 0.984791i \(-0.444414\pi\)
0.173742 + 0.984791i \(0.444414\pi\)
\(632\) −1.77159e12 −0.441710
\(633\) −1.79453e12 −0.444258
\(634\) 6.61348e12 1.62565
\(635\) 1.59715e11 0.0389820
\(636\) 4.31246e11 0.104513
\(637\) 2.53185e11 0.0609272
\(638\) 1.07087e12 0.255883
\(639\) 7.07999e11 0.167988
\(640\) −1.07020e12 −0.252147
\(641\) −7.20380e12 −1.68539 −0.842695 0.538391i \(-0.819032\pi\)
−0.842695 + 0.538391i \(0.819032\pi\)
\(642\) −4.58213e11 −0.106453
\(643\) −7.58171e10 −0.0174911 −0.00874556 0.999962i \(-0.502784\pi\)
−0.00874556 + 0.999962i \(0.502784\pi\)
\(644\) 2.20519e12 0.505197
\(645\) 7.69685e11 0.175103
\(646\) 2.77030e10 0.00625865
\(647\) 4.30805e11 0.0966522 0.0483261 0.998832i \(-0.484611\pi\)
0.0483261 + 0.998832i \(0.484611\pi\)
\(648\) −3.55025e11 −0.0790990
\(649\) 1.08216e11 0.0239437
\(650\) 1.70091e12 0.373742
\(651\) −1.10415e12 −0.240943
\(652\) −7.69122e11 −0.166679
\(653\) −4.31846e12 −0.929436 −0.464718 0.885459i \(-0.653844\pi\)
−0.464718 + 0.885459i \(0.653844\pi\)
\(654\) −3.70874e11 −0.0792732
\(655\) −3.33816e10 −0.00708632
\(656\) −7.75096e12 −1.63414
\(657\) −3.02052e12 −0.632466
\(658\) −4.04168e12 −0.840515
\(659\) 5.42048e12 1.11958 0.559788 0.828636i \(-0.310883\pi\)
0.559788 + 0.828636i \(0.310883\pi\)
\(660\) 4.45488e10 0.00913878
\(661\) 4.32120e12 0.880437 0.440219 0.897891i \(-0.354901\pi\)
0.440219 + 0.897891i \(0.354901\pi\)
\(662\) 3.15967e12 0.639413
\(663\) 6.95444e10 0.0139782
\(664\) −2.78292e12 −0.555577
\(665\) 7.14604e10 0.0141699
\(666\) 1.94327e12 0.382736
\(667\) −8.45348e12 −1.65375
\(668\) −2.95542e12 −0.574282
\(669\) 3.62058e11 0.0698813
\(670\) −1.39858e12 −0.268133
\(671\) −1.19162e11 −0.0226928
\(672\) −2.07831e12 −0.393140
\(673\) −7.53010e12 −1.41492 −0.707462 0.706751i \(-0.750160\pi\)
−0.707462 + 0.706751i \(0.750160\pi\)
\(674\) 6.36373e12 1.18780
\(675\) 9.89406e11 0.183446
\(676\) −1.92275e12 −0.354130
\(677\) 4.96788e12 0.908912 0.454456 0.890769i \(-0.349834\pi\)
0.454456 + 0.890769i \(0.349834\pi\)
\(678\) −7.21885e11 −0.131200
\(679\) −4.89427e12 −0.883637
\(680\) 6.26814e10 0.0112421
\(681\) −8.96618e9 −0.00159752
\(682\) −5.67466e11 −0.100441
\(683\) 7.07573e11 0.124417 0.0622083 0.998063i \(-0.480186\pi\)
0.0622083 + 0.998063i \(0.480186\pi\)
\(684\) 5.50518e10 0.00961654
\(685\) 2.47375e11 0.0429287
\(686\) 7.33438e12 1.26446
\(687\) 5.59915e12 0.958996
\(688\) −1.02142e13 −1.73803
\(689\) 8.92486e11 0.150874
\(690\) −1.23551e12 −0.207504
\(691\) 2.18601e12 0.364754 0.182377 0.983229i \(-0.441621\pi\)
0.182377 + 0.983229i \(0.441621\pi\)
\(692\) 1.76869e12 0.293207
\(693\) −3.36291e11 −0.0553880
\(694\) 7.91429e12 1.29507
\(695\) 2.15334e11 0.0350090
\(696\) 2.99421e12 0.483661
\(697\) 5.99693e11 0.0962457
\(698\) 7.84352e12 1.25072
\(699\) 5.40362e11 0.0856125
\(700\) 2.17676e12 0.342664
\(701\) 4.70760e12 0.736324 0.368162 0.929762i \(-0.379987\pi\)
0.368162 + 0.929762i \(0.379987\pi\)
\(702\) 4.85532e11 0.0754572
\(703\) 4.55998e11 0.0704148
\(704\) 4.17701e11 0.0640898
\(705\) 6.44542e11 0.0982652
\(706\) −4.00463e11 −0.0606655
\(707\) −3.52100e11 −0.0530004
\(708\) −1.99951e11 −0.0299071
\(709\) −1.54756e12 −0.230006 −0.115003 0.993365i \(-0.536688\pi\)
−0.115003 + 0.993365i \(0.536688\pi\)
\(710\) −8.72707e11 −0.128886
\(711\) 1.40934e12 0.206825
\(712\) −1.43743e12 −0.209617
\(713\) 4.47961e12 0.649138
\(714\) 3.12681e11 0.0450256
\(715\) 9.21959e10 0.0131927
\(716\) 3.19051e12 0.453681
\(717\) −1.29613e12 −0.183152
\(718\) −1.07239e13 −1.50588
\(719\) 2.98027e12 0.415887 0.207944 0.978141i \(-0.433323\pi\)
0.207944 + 0.978141i \(0.433323\pi\)
\(720\) 6.44491e11 0.0893760
\(721\) −1.05597e13 −1.45527
\(722\) −8.58745e12 −1.17611
\(723\) 2.60971e11 0.0355198
\(724\) −2.58872e12 −0.350156
\(725\) −8.34446e12 −1.12170
\(726\) 4.93681e12 0.659525
\(727\) 1.01794e12 0.135150 0.0675751 0.997714i \(-0.478474\pi\)
0.0675751 + 0.997714i \(0.478474\pi\)
\(728\) −1.61648e12 −0.213294
\(729\) 2.82430e11 0.0370370
\(730\) 3.72321e12 0.485249
\(731\) 7.90275e11 0.102365
\(732\) 2.20176e11 0.0283446
\(733\) −3.38521e12 −0.433130 −0.216565 0.976268i \(-0.569485\pi\)
−0.216565 + 0.976268i \(0.569485\pi\)
\(734\) −4.99114e12 −0.634699
\(735\) −1.81538e11 −0.0229442
\(736\) 8.43181e12 1.05918
\(737\) 1.54442e12 0.192825
\(738\) 4.18682e12 0.519554
\(739\) −4.84788e12 −0.597932 −0.298966 0.954264i \(-0.596642\pi\)
−0.298966 + 0.954264i \(0.596642\pi\)
\(740\) −6.81802e11 −0.0835825
\(741\) 1.13932e11 0.0138824
\(742\) 4.01274e12 0.485986
\(743\) 6.68869e12 0.805177 0.402589 0.915381i \(-0.368111\pi\)
0.402589 + 0.915381i \(0.368111\pi\)
\(744\) −1.58667e12 −0.189849
\(745\) −7.58635e11 −0.0902256
\(746\) 4.56155e12 0.539247
\(747\) 2.21387e12 0.260142
\(748\) 4.57405e10 0.00534249
\(749\) −1.21359e12 −0.140897
\(750\) −2.49902e12 −0.288400
\(751\) −5.48484e12 −0.629193 −0.314597 0.949225i \(-0.601869\pi\)
−0.314597 + 0.949225i \(0.601869\pi\)
\(752\) −8.55348e12 −0.975355
\(753\) 4.66948e12 0.529287
\(754\) −4.09489e12 −0.461393
\(755\) 3.47204e12 0.388887
\(756\) 6.21363e11 0.0691827
\(757\) 1.19762e12 0.132553 0.0662763 0.997801i \(-0.478888\pi\)
0.0662763 + 0.997801i \(0.478888\pi\)
\(758\) 1.80029e13 1.98075
\(759\) 1.36435e12 0.149224
\(760\) 1.02689e11 0.0111651
\(761\) 4.53518e12 0.490189 0.245094 0.969499i \(-0.421181\pi\)
0.245094 + 0.969499i \(0.421181\pi\)
\(762\) 1.14490e12 0.123018
\(763\) −9.82268e11 −0.104923
\(764\) 7.36741e12 0.782338
\(765\) −4.98644e10 −0.00526398
\(766\) −1.02123e13 −1.07175
\(767\) −4.13809e11 −0.0431738
\(768\) −5.73189e12 −0.594528
\(769\) 3.02965e12 0.312409 0.156205 0.987725i \(-0.450074\pi\)
0.156205 + 0.987725i \(0.450074\pi\)
\(770\) 4.14525e11 0.0424955
\(771\) 1.05999e12 0.108034
\(772\) −1.00747e12 −0.102083
\(773\) 6.30421e11 0.0635072 0.0317536 0.999496i \(-0.489891\pi\)
0.0317536 + 0.999496i \(0.489891\pi\)
\(774\) 5.51740e12 0.552586
\(775\) 4.42184e12 0.440296
\(776\) −7.03309e12 −0.696256
\(777\) 5.14680e12 0.506574
\(778\) −6.29436e12 −0.615947
\(779\) 9.82458e11 0.0955863
\(780\) −1.70350e11 −0.0164785
\(781\) 9.63713e11 0.0926868
\(782\) −1.26857e12 −0.121306
\(783\) −2.38196e12 −0.226468
\(784\) 2.40912e12 0.227739
\(785\) −1.84812e12 −0.173707
\(786\) −2.39292e11 −0.0223628
\(787\) 7.21786e12 0.670691 0.335345 0.942095i \(-0.391147\pi\)
0.335345 + 0.942095i \(0.391147\pi\)
\(788\) 7.02662e12 0.649200
\(789\) 9.95839e12 0.914835
\(790\) −1.73721e12 −0.158683
\(791\) −1.91193e12 −0.173651
\(792\) −4.83252e11 −0.0436426
\(793\) 4.55665e11 0.0409182
\(794\) 2.86115e12 0.255475
\(795\) −6.39926e11 −0.0568169
\(796\) −3.50664e12 −0.309586
\(797\) −1.09692e13 −0.962968 −0.481484 0.876455i \(-0.659902\pi\)
−0.481484 + 0.876455i \(0.659902\pi\)
\(798\) 5.12255e11 0.0447171
\(799\) 6.61784e11 0.0574455
\(800\) 8.32308e12 0.718421
\(801\) 1.14350e12 0.0981501
\(802\) −1.16174e13 −0.991576
\(803\) −4.11146e12 −0.348961
\(804\) −2.85363e12 −0.240849
\(805\) −3.27229e12 −0.274644
\(806\) 2.16993e12 0.181108
\(807\) −1.78389e12 −0.148060
\(808\) −5.05970e11 −0.0417613
\(809\) −9.11493e12 −0.748144 −0.374072 0.927400i \(-0.622039\pi\)
−0.374072 + 0.927400i \(0.622039\pi\)
\(810\) −3.48134e11 −0.0284160
\(811\) −1.70270e11 −0.0138211 −0.00691056 0.999976i \(-0.502200\pi\)
−0.00691056 + 0.999976i \(0.502200\pi\)
\(812\) −5.24046e12 −0.423026
\(813\) 1.28563e12 0.103207
\(814\) 2.64514e12 0.211173
\(815\) 1.14130e12 0.0906130
\(816\) 6.61733e11 0.0522489
\(817\) 1.29468e12 0.101663
\(818\) 2.50879e13 1.95918
\(819\) 1.28594e12 0.0998721
\(820\) −1.46896e12 −0.113461
\(821\) −9.42511e11 −0.0724006 −0.0362003 0.999345i \(-0.511525\pi\)
−0.0362003 + 0.999345i \(0.511525\pi\)
\(822\) 1.77328e12 0.135473
\(823\) 2.08266e13 1.58241 0.791203 0.611553i \(-0.209455\pi\)
0.791203 + 0.611553i \(0.209455\pi\)
\(824\) −1.51743e13 −1.14667
\(825\) 1.34676e12 0.101215
\(826\) −1.86054e12 −0.139069
\(827\) −1.79987e13 −1.33803 −0.669014 0.743250i \(-0.733283\pi\)
−0.669014 + 0.743250i \(0.733283\pi\)
\(828\) −2.52091e12 −0.186389
\(829\) −1.31848e13 −0.969571 −0.484786 0.874633i \(-0.661102\pi\)
−0.484786 + 0.874633i \(0.661102\pi\)
\(830\) −2.72891e12 −0.199589
\(831\) −1.02786e12 −0.0747705
\(832\) −1.59725e12 −0.115563
\(833\) −1.86394e11 −0.0134131
\(834\) 1.54359e12 0.110481
\(835\) 4.38555e12 0.312201
\(836\) 7.49353e10 0.00530589
\(837\) 1.26223e12 0.0888943
\(838\) 1.11514e13 0.781146
\(839\) 6.35148e12 0.442533 0.221267 0.975213i \(-0.428981\pi\)
0.221267 + 0.975213i \(0.428981\pi\)
\(840\) 1.15904e12 0.0803233
\(841\) 5.58184e12 0.384765
\(842\) 1.40938e13 0.966329
\(843\) 1.04055e13 0.709641
\(844\) 4.51333e12 0.306165
\(845\) 2.85317e12 0.192518
\(846\) 4.62032e12 0.310103
\(847\) 1.30752e13 0.872920
\(848\) 8.49224e12 0.563950
\(849\) −7.12592e12 −0.470713
\(850\) −1.25221e12 −0.0822793
\(851\) −2.08809e13 −1.36479
\(852\) −1.78065e12 −0.115771
\(853\) 9.92635e12 0.641976 0.320988 0.947083i \(-0.395985\pi\)
0.320988 + 0.947083i \(0.395985\pi\)
\(854\) 2.04873e12 0.131803
\(855\) −8.16912e10 −0.00522791
\(856\) −1.74393e12 −0.111019
\(857\) −3.48897e12 −0.220945 −0.110472 0.993879i \(-0.535236\pi\)
−0.110472 + 0.993879i \(0.535236\pi\)
\(858\) 6.60896e11 0.0416332
\(859\) 3.68799e12 0.231111 0.115555 0.993301i \(-0.463135\pi\)
0.115555 + 0.993301i \(0.463135\pi\)
\(860\) −1.93579e12 −0.120674
\(861\) 1.10889e13 0.687661
\(862\) −2.26940e13 −1.40000
\(863\) 1.46271e12 0.0897655 0.0448827 0.998992i \(-0.485709\pi\)
0.0448827 + 0.998992i \(0.485709\pi\)
\(864\) 2.37585e12 0.145047
\(865\) −2.62455e12 −0.159398
\(866\) 1.41880e13 0.857214
\(867\) 9.55442e12 0.574273
\(868\) 2.77699e12 0.166049
\(869\) 1.91836e12 0.114115
\(870\) 2.93609e12 0.173753
\(871\) −5.90572e12 −0.347689
\(872\) −1.41152e12 −0.0826731
\(873\) 5.59497e12 0.326012
\(874\) −2.07825e12 −0.120475
\(875\) −6.61872e12 −0.381714
\(876\) 7.59673e12 0.435871
\(877\) −4.67161e12 −0.266667 −0.133333 0.991071i \(-0.542568\pi\)
−0.133333 + 0.991071i \(0.542568\pi\)
\(878\) 2.14989e13 1.22093
\(879\) 7.67945e12 0.433891
\(880\) 8.77268e11 0.0493129
\(881\) −1.19601e13 −0.668874 −0.334437 0.942418i \(-0.608546\pi\)
−0.334437 + 0.942418i \(0.608546\pi\)
\(882\) −1.30133e12 −0.0724068
\(883\) 3.43104e13 1.89934 0.949670 0.313252i \(-0.101418\pi\)
0.949670 + 0.313252i \(0.101418\pi\)
\(884\) −1.74907e11 −0.00963324
\(885\) 2.96707e11 0.0162586
\(886\) 3.40617e13 1.85701
\(887\) −7.13921e12 −0.387252 −0.193626 0.981075i \(-0.562025\pi\)
−0.193626 + 0.981075i \(0.562025\pi\)
\(888\) 7.39599e12 0.399152
\(889\) 3.03229e12 0.162822
\(890\) −1.40953e12 −0.0753040
\(891\) 3.84437e11 0.0204350
\(892\) −9.10593e11 −0.0481595
\(893\) 1.08418e12 0.0570519
\(894\) −5.43819e12 −0.284731
\(895\) −4.73439e12 −0.246638
\(896\) −2.03184e13 −1.05318
\(897\) −5.21715e12 −0.269071
\(898\) −2.08812e13 −1.07155
\(899\) −1.06454e13 −0.543556
\(900\) −2.48840e12 −0.126424
\(901\) −6.57045e11 −0.0332150
\(902\) 5.69901e12 0.286662
\(903\) 1.46129e13 0.731380
\(904\) −2.74745e12 −0.136827
\(905\) 3.84140e12 0.190358
\(906\) 2.48889e13 1.22724
\(907\) 1.56876e13 0.769706 0.384853 0.922978i \(-0.374252\pi\)
0.384853 + 0.922978i \(0.374252\pi\)
\(908\) 2.25503e10 0.00110095
\(909\) 4.02510e11 0.0195541
\(910\) −1.58510e12 −0.0766251
\(911\) 5.16410e12 0.248406 0.124203 0.992257i \(-0.460363\pi\)
0.124203 + 0.992257i \(0.460363\pi\)
\(912\) 1.08410e12 0.0518909
\(913\) 3.01347e12 0.143532
\(914\) 4.31967e13 2.04735
\(915\) −3.26719e11 −0.0154092
\(916\) −1.40821e13 −0.660903
\(917\) −6.33770e11 −0.0295985
\(918\) −3.57447e11 −0.0166119
\(919\) 1.96145e13 0.907106 0.453553 0.891229i \(-0.350156\pi\)
0.453553 + 0.891229i \(0.350156\pi\)
\(920\) −4.70230e12 −0.216404
\(921\) −2.14721e13 −0.983344
\(922\) 1.60759e13 0.732631
\(923\) −3.68514e12 −0.167127
\(924\) 8.45786e11 0.0381713
\(925\) −2.06116e13 −0.925708
\(926\) 4.01778e13 1.79571
\(927\) 1.20715e13 0.536911
\(928\) −2.00375e13 −0.886906
\(929\) −2.42990e13 −1.07033 −0.535164 0.844748i \(-0.679750\pi\)
−0.535164 + 0.844748i \(0.679750\pi\)
\(930\) −1.55587e12 −0.0682027
\(931\) −3.05364e11 −0.0133212
\(932\) −1.35903e12 −0.0590009
\(933\) −1.76362e13 −0.761969
\(934\) −1.10358e13 −0.474506
\(935\) −6.78743e10 −0.00290438
\(936\) 1.84791e12 0.0786935
\(937\) −2.65518e12 −0.112529 −0.0562647 0.998416i \(-0.517919\pi\)
−0.0562647 + 0.998416i \(0.517919\pi\)
\(938\) −2.65529e13 −1.11995
\(939\) 1.88173e13 0.789880
\(940\) −1.62105e12 −0.0677207
\(941\) −3.36624e13 −1.39956 −0.699781 0.714358i \(-0.746719\pi\)
−0.699781 + 0.714358i \(0.746719\pi\)
\(942\) −1.32480e13 −0.548179
\(943\) −4.49883e13 −1.85267
\(944\) −3.93750e12 −0.161379
\(945\) −9.22040e11 −0.0376103
\(946\) 7.51016e12 0.304887
\(947\) −2.44759e13 −0.988927 −0.494463 0.869198i \(-0.664635\pi\)
−0.494463 + 0.869198i \(0.664635\pi\)
\(948\) −3.54455e12 −0.142536
\(949\) 1.57218e13 0.629223
\(950\) −2.05145e12 −0.0817156
\(951\) −2.00237e13 −0.793837
\(952\) 1.19005e12 0.0469567
\(953\) −4.04016e13 −1.58665 −0.793324 0.608800i \(-0.791651\pi\)
−0.793324 + 0.608800i \(0.791651\pi\)
\(954\) −4.58724e12 −0.179301
\(955\) −1.09325e13 −0.425308
\(956\) 3.25982e12 0.126222
\(957\) −3.24227e12 −0.124953
\(958\) −3.63325e12 −0.139364
\(959\) 4.69657e12 0.179307
\(960\) 1.14525e12 0.0435191
\(961\) −2.07985e13 −0.786641
\(962\) −1.01148e13 −0.380774
\(963\) 1.38733e12 0.0519832
\(964\) −6.56354e11 −0.0244789
\(965\) 1.49498e12 0.0554963
\(966\) −2.34570e13 −0.866713
\(967\) −7.98913e12 −0.293819 −0.146910 0.989150i \(-0.546933\pi\)
−0.146910 + 0.989150i \(0.546933\pi\)
\(968\) 1.87892e13 0.687812
\(969\) −8.38766e10 −0.00305622
\(970\) −6.89658e12 −0.250127
\(971\) 1.75900e13 0.635009 0.317505 0.948257i \(-0.397155\pi\)
0.317505 + 0.948257i \(0.397155\pi\)
\(972\) −7.10323e11 −0.0255245
\(973\) 4.08824e12 0.146227
\(974\) 1.24236e13 0.442317
\(975\) −5.14987e12 −0.182505
\(976\) 4.33577e12 0.152947
\(977\) −3.46357e13 −1.21618 −0.608091 0.793867i \(-0.708065\pi\)
−0.608091 + 0.793867i \(0.708065\pi\)
\(978\) 8.18127e12 0.285954
\(979\) 1.55651e12 0.0541539
\(980\) 4.56575e11 0.0158123
\(981\) 1.12290e12 0.0387106
\(982\) −6.08807e13 −2.08919
\(983\) 3.17285e13 1.08382 0.541912 0.840435i \(-0.317700\pi\)
0.541912 + 0.840435i \(0.317700\pi\)
\(984\) 1.59348e13 0.541837
\(985\) −1.04268e13 −0.352929
\(986\) 3.01464e12 0.101576
\(987\) 1.22370e13 0.410439
\(988\) −2.86545e11 −0.00956724
\(989\) −5.92856e13 −1.97045
\(990\) −4.73872e11 −0.0156784
\(991\) −4.34623e13 −1.43147 −0.715733 0.698374i \(-0.753907\pi\)
−0.715733 + 0.698374i \(0.753907\pi\)
\(992\) 1.06181e13 0.348133
\(993\) −9.56656e12 −0.312237
\(994\) −1.65689e13 −0.538338
\(995\) 5.20349e12 0.168303
\(996\) −5.56798e12 −0.179280
\(997\) −1.79904e13 −0.576650 −0.288325 0.957533i \(-0.593098\pi\)
−0.288325 + 0.957533i \(0.593098\pi\)
\(998\) −2.56682e13 −0.819045
\(999\) −5.88366e12 −0.186897
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.1.17 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.17 22 1.1 even 1 trivial