Properties

Label 177.10.a.c.1.2
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 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-38.2133 q^{2} -81.0000 q^{3} +948.259 q^{4} -2363.53 q^{5} +3095.28 q^{6} +4562.96 q^{7} -16670.9 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-38.2133 q^{2} -81.0000 q^{3} +948.259 q^{4} -2363.53 q^{5} +3095.28 q^{6} +4562.96 q^{7} -16670.9 q^{8} +6561.00 q^{9} +90318.2 q^{10} -48239.1 q^{11} -76809.0 q^{12} +191254. q^{13} -174366. q^{14} +191446. q^{15} +151543. q^{16} +338128. q^{17} -250718. q^{18} +524360. q^{19} -2.24124e6 q^{20} -369600. q^{21} +1.84338e6 q^{22} -1.14530e6 q^{23} +1.35035e6 q^{24} +3.63313e6 q^{25} -7.30844e6 q^{26} -531441. q^{27} +4.32687e6 q^{28} +5.85805e6 q^{29} -7.31577e6 q^{30} +5.88714e6 q^{31} +2.74455e6 q^{32} +3.90737e6 q^{33} -1.29210e7 q^{34} -1.07847e7 q^{35} +6.22153e6 q^{36} -1.22817e7 q^{37} -2.00376e7 q^{38} -1.54915e7 q^{39} +3.94022e7 q^{40} +3.14093e7 q^{41} +1.41236e7 q^{42} +1.58091e7 q^{43} -4.57432e7 q^{44} -1.55071e7 q^{45} +4.37657e7 q^{46} -1.12476e7 q^{47} -1.22750e7 q^{48} -1.95330e7 q^{49} -1.38834e8 q^{50} -2.73883e7 q^{51} +1.81358e8 q^{52} -4.33557e7 q^{53} +2.03081e7 q^{54} +1.14014e8 q^{55} -7.60688e7 q^{56} -4.24732e7 q^{57} -2.23856e8 q^{58} +1.21174e7 q^{59} +1.81540e8 q^{60} -1.55643e8 q^{61} -2.24967e8 q^{62} +2.99376e7 q^{63} -1.82468e8 q^{64} -4.52033e8 q^{65} -1.49314e8 q^{66} -1.33621e8 q^{67} +3.20633e8 q^{68} +9.27693e7 q^{69} +4.12118e8 q^{70} -1.02482e8 q^{71} -1.09378e8 q^{72} -2.90383e8 q^{73} +4.69323e8 q^{74} -2.94283e8 q^{75} +4.97230e8 q^{76} -2.20113e8 q^{77} +5.91983e8 q^{78} +3.11640e8 q^{79} -3.58176e8 q^{80} +4.30467e7 q^{81} -1.20025e9 q^{82} +4.30611e8 q^{83} -3.50477e8 q^{84} -7.99173e8 q^{85} -6.04118e8 q^{86} -4.74502e8 q^{87} +8.04191e8 q^{88} -3.66207e8 q^{89} +5.92578e8 q^{90} +8.72683e8 q^{91} -1.08604e9 q^{92} -4.76858e8 q^{93} +4.29810e8 q^{94} -1.23934e9 q^{95} -2.22308e8 q^{96} -7.50948e8 q^{97} +7.46421e8 q^{98} -3.16497e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −38.2133 −1.68881 −0.844404 0.535708i \(-0.820045\pi\)
−0.844404 + 0.535708i \(0.820045\pi\)
\(3\) −81.0000 −0.577350
\(4\) 948.259 1.85207
\(5\) −2363.53 −1.69120 −0.845601 0.533816i \(-0.820757\pi\)
−0.845601 + 0.533816i \(0.820757\pi\)
\(6\) 3095.28 0.975033
\(7\) 4562.96 0.718299 0.359150 0.933280i \(-0.383067\pi\)
0.359150 + 0.933280i \(0.383067\pi\)
\(8\) −16670.9 −1.43898
\(9\) 6561.00 0.333333
\(10\) 90318.2 2.85611
\(11\) −48239.1 −0.993419 −0.496710 0.867917i \(-0.665459\pi\)
−0.496710 + 0.867917i \(0.665459\pi\)
\(12\) −76809.0 −1.06929
\(13\) 191254. 1.85722 0.928612 0.371051i \(-0.121003\pi\)
0.928612 + 0.371051i \(0.121003\pi\)
\(14\) −174366. −1.21307
\(15\) 191446. 0.976415
\(16\) 151543. 0.578091
\(17\) 338128. 0.981885 0.490942 0.871192i \(-0.336653\pi\)
0.490942 + 0.871192i \(0.336653\pi\)
\(18\) −250718. −0.562936
\(19\) 524360. 0.923079 0.461539 0.887120i \(-0.347297\pi\)
0.461539 + 0.887120i \(0.347297\pi\)
\(20\) −2.24124e6 −3.13222
\(21\) −369600. −0.414710
\(22\) 1.84338e6 1.67769
\(23\) −1.14530e6 −0.853383 −0.426691 0.904397i \(-0.640321\pi\)
−0.426691 + 0.904397i \(0.640321\pi\)
\(24\) 1.35035e6 0.830796
\(25\) 3.63313e6 1.86016
\(26\) −7.30844e6 −3.13649
\(27\) −531441. −0.192450
\(28\) 4.32687e6 1.33034
\(29\) 5.85805e6 1.53802 0.769010 0.639237i \(-0.220750\pi\)
0.769010 + 0.639237i \(0.220750\pi\)
\(30\) −7.31577e6 −1.64898
\(31\) 5.88714e6 1.14492 0.572462 0.819931i \(-0.305988\pi\)
0.572462 + 0.819931i \(0.305988\pi\)
\(32\) 2.74455e6 0.462696
\(33\) 3.90737e6 0.573551
\(34\) −1.29210e7 −1.65821
\(35\) −1.07847e7 −1.21479
\(36\) 6.22153e6 0.617356
\(37\) −1.22817e7 −1.07733 −0.538666 0.842520i \(-0.681071\pi\)
−0.538666 + 0.842520i \(0.681071\pi\)
\(38\) −2.00376e7 −1.55890
\(39\) −1.54915e7 −1.07227
\(40\) 3.94022e7 2.43361
\(41\) 3.14093e7 1.73592 0.867962 0.496630i \(-0.165429\pi\)
0.867962 + 0.496630i \(0.165429\pi\)
\(42\) 1.41236e7 0.700366
\(43\) 1.58091e7 0.705178 0.352589 0.935778i \(-0.385301\pi\)
0.352589 + 0.935778i \(0.385301\pi\)
\(44\) −4.57432e7 −1.83988
\(45\) −1.55071e7 −0.563734
\(46\) 4.37657e7 1.44120
\(47\) −1.12476e7 −0.336218 −0.168109 0.985768i \(-0.553766\pi\)
−0.168109 + 0.985768i \(0.553766\pi\)
\(48\) −1.22750e7 −0.333761
\(49\) −1.95330e7 −0.484046
\(50\) −1.38834e8 −3.14145
\(51\) −2.73883e7 −0.566891
\(52\) 1.81358e8 3.43971
\(53\) −4.33557e7 −0.754753 −0.377377 0.926060i \(-0.623174\pi\)
−0.377377 + 0.926060i \(0.623174\pi\)
\(54\) 2.03081e7 0.325011
\(55\) 1.14014e8 1.68007
\(56\) −7.60688e7 −1.03362
\(57\) −4.24732e7 −0.532940
\(58\) −2.23856e8 −2.59742
\(59\) 1.21174e7 0.130189
\(60\) 1.81540e8 1.80839
\(61\) −1.55643e8 −1.43928 −0.719639 0.694349i \(-0.755692\pi\)
−0.719639 + 0.694349i \(0.755692\pi\)
\(62\) −2.24967e8 −1.93356
\(63\) 2.99376e7 0.239433
\(64\) −1.82468e8 −1.35950
\(65\) −4.52033e8 −3.14094
\(66\) −1.49314e8 −0.968617
\(67\) −1.33621e8 −0.810098 −0.405049 0.914295i \(-0.632745\pi\)
−0.405049 + 0.914295i \(0.632745\pi\)
\(68\) 3.20633e8 1.81852
\(69\) 9.27693e7 0.492701
\(70\) 4.12118e8 2.05154
\(71\) −1.02482e8 −0.478614 −0.239307 0.970944i \(-0.576920\pi\)
−0.239307 + 0.970944i \(0.576920\pi\)
\(72\) −1.09378e8 −0.479660
\(73\) −2.90383e8 −1.19679 −0.598395 0.801202i \(-0.704194\pi\)
−0.598395 + 0.801202i \(0.704194\pi\)
\(74\) 4.69323e8 1.81940
\(75\) −2.94283e8 −1.07396
\(76\) 4.97230e8 1.70961
\(77\) −2.20113e8 −0.713572
\(78\) 5.91983e8 1.81086
\(79\) 3.11640e8 0.900184 0.450092 0.892982i \(-0.351391\pi\)
0.450092 + 0.892982i \(0.351391\pi\)
\(80\) −3.58176e8 −0.977668
\(81\) 4.30467e7 0.111111
\(82\) −1.20025e9 −2.93164
\(83\) 4.30611e8 0.995940 0.497970 0.867194i \(-0.334079\pi\)
0.497970 + 0.867194i \(0.334079\pi\)
\(84\) −3.50477e8 −0.768072
\(85\) −7.99173e8 −1.66056
\(86\) −6.04118e8 −1.19091
\(87\) −4.74502e8 −0.887976
\(88\) 8.04191e8 1.42951
\(89\) −3.66207e8 −0.618689 −0.309344 0.950950i \(-0.600110\pi\)
−0.309344 + 0.950950i \(0.600110\pi\)
\(90\) 5.92578e8 0.952037
\(91\) 8.72683e8 1.33404
\(92\) −1.08604e9 −1.58052
\(93\) −4.76858e8 −0.661022
\(94\) 4.29810e8 0.567808
\(95\) −1.23934e9 −1.56111
\(96\) −2.22308e8 −0.267138
\(97\) −7.50948e8 −0.861265 −0.430633 0.902527i \(-0.641710\pi\)
−0.430633 + 0.902527i \(0.641710\pi\)
\(98\) 7.46421e8 0.817460
\(99\) −3.16497e8 −0.331140
\(100\) 3.44515e9 3.44515
\(101\) 1.14111e9 1.09114 0.545572 0.838064i \(-0.316312\pi\)
0.545572 + 0.838064i \(0.316312\pi\)
\(102\) 1.04660e9 0.957370
\(103\) −1.57759e8 −0.138111 −0.0690554 0.997613i \(-0.521999\pi\)
−0.0690554 + 0.997613i \(0.521999\pi\)
\(104\) −3.18838e9 −2.67251
\(105\) 8.73559e8 0.701359
\(106\) 1.65677e9 1.27463
\(107\) 2.12531e9 1.56745 0.783727 0.621105i \(-0.213316\pi\)
0.783727 + 0.621105i \(0.213316\pi\)
\(108\) −5.03944e8 −0.356431
\(109\) 2.22170e9 1.50753 0.753765 0.657144i \(-0.228236\pi\)
0.753765 + 0.657144i \(0.228236\pi\)
\(110\) −4.35687e9 −2.83732
\(111\) 9.94815e8 0.621998
\(112\) 6.91485e8 0.415243
\(113\) 1.75118e9 1.01037 0.505183 0.863012i \(-0.331425\pi\)
0.505183 + 0.863012i \(0.331425\pi\)
\(114\) 1.62304e9 0.900032
\(115\) 2.70694e9 1.44324
\(116\) 5.55495e9 2.84852
\(117\) 1.25481e9 0.619075
\(118\) −4.63045e8 −0.219864
\(119\) 1.54286e9 0.705287
\(120\) −3.19158e9 −1.40504
\(121\) −3.09325e7 −0.0131184
\(122\) 5.94763e9 2.43066
\(123\) −2.54415e9 −1.00224
\(124\) 5.58254e9 2.12048
\(125\) −3.97073e9 −1.45471
\(126\) −1.14402e9 −0.404356
\(127\) 2.22763e9 0.759849 0.379924 0.925018i \(-0.375950\pi\)
0.379924 + 0.925018i \(0.375950\pi\)
\(128\) 5.56752e9 1.83323
\(129\) −1.28054e9 −0.407135
\(130\) 1.72737e10 5.30444
\(131\) −4.96514e9 −1.47303 −0.736513 0.676423i \(-0.763529\pi\)
−0.736513 + 0.676423i \(0.763529\pi\)
\(132\) 3.70520e9 1.06226
\(133\) 2.39264e9 0.663047
\(134\) 5.10610e9 1.36810
\(135\) 1.25607e9 0.325472
\(136\) −5.63690e9 −1.41291
\(137\) 5.02264e9 1.21812 0.609060 0.793124i \(-0.291547\pi\)
0.609060 + 0.793124i \(0.291547\pi\)
\(138\) −3.54502e9 −0.832077
\(139\) 5.69724e8 0.129449 0.0647244 0.997903i \(-0.479383\pi\)
0.0647244 + 0.997903i \(0.479383\pi\)
\(140\) −1.02267e10 −2.24987
\(141\) 9.11059e8 0.194116
\(142\) 3.91618e9 0.808287
\(143\) −9.22591e9 −1.84500
\(144\) 9.94274e8 0.192697
\(145\) −1.38456e10 −2.60110
\(146\) 1.10965e10 2.02115
\(147\) 1.58217e9 0.279464
\(148\) −1.16462e10 −1.99529
\(149\) −5.80355e9 −0.964618 −0.482309 0.876001i \(-0.660202\pi\)
−0.482309 + 0.876001i \(0.660202\pi\)
\(150\) 1.12455e10 1.81372
\(151\) −3.42073e9 −0.535455 −0.267727 0.963495i \(-0.586273\pi\)
−0.267727 + 0.963495i \(0.586273\pi\)
\(152\) −8.74158e9 −1.32829
\(153\) 2.21846e9 0.327295
\(154\) 8.41127e9 1.20509
\(155\) −1.39144e10 −1.93630
\(156\) −1.46900e10 −1.98592
\(157\) −1.14979e10 −1.51032 −0.755161 0.655540i \(-0.772441\pi\)
−0.755161 + 0.655540i \(0.772441\pi\)
\(158\) −1.19088e10 −1.52024
\(159\) 3.51181e9 0.435757
\(160\) −6.48681e9 −0.782512
\(161\) −5.22596e9 −0.612984
\(162\) −1.64496e9 −0.187645
\(163\) 1.06364e10 1.18019 0.590093 0.807335i \(-0.299091\pi\)
0.590093 + 0.807335i \(0.299091\pi\)
\(164\) 2.97842e10 3.21505
\(165\) −9.23517e9 −0.969990
\(166\) −1.64551e10 −1.68195
\(167\) 1.29150e10 1.28490 0.642452 0.766326i \(-0.277917\pi\)
0.642452 + 0.766326i \(0.277917\pi\)
\(168\) 6.16157e9 0.596760
\(169\) 2.59734e10 2.44928
\(170\) 3.05391e10 2.80437
\(171\) 3.44033e9 0.307693
\(172\) 1.49911e10 1.30604
\(173\) −2.17455e9 −0.184571 −0.0922853 0.995733i \(-0.529417\pi\)
−0.0922853 + 0.995733i \(0.529417\pi\)
\(174\) 1.81323e10 1.49962
\(175\) 1.65778e10 1.33615
\(176\) −7.31031e9 −0.574287
\(177\) −9.81506e8 −0.0751646
\(178\) 1.39940e10 1.04485
\(179\) −1.76354e10 −1.28395 −0.641975 0.766726i \(-0.721885\pi\)
−0.641975 + 0.766726i \(0.721885\pi\)
\(180\) −1.47047e10 −1.04407
\(181\) −7.91381e9 −0.548065 −0.274033 0.961720i \(-0.588358\pi\)
−0.274033 + 0.961720i \(0.588358\pi\)
\(182\) −3.33481e10 −2.25294
\(183\) 1.26071e10 0.830967
\(184\) 1.90932e10 1.22800
\(185\) 2.90280e10 1.82198
\(186\) 1.82224e10 1.11634
\(187\) −1.63110e10 −0.975423
\(188\) −1.06657e10 −0.622700
\(189\) −2.42494e9 −0.138237
\(190\) 4.73593e10 2.63642
\(191\) 2.90520e9 0.157952 0.0789762 0.996877i \(-0.474835\pi\)
0.0789762 + 0.996877i \(0.474835\pi\)
\(192\) 1.47799e10 0.784905
\(193\) −1.06772e10 −0.553923 −0.276962 0.960881i \(-0.589327\pi\)
−0.276962 + 0.960881i \(0.589327\pi\)
\(194\) 2.86962e10 1.45451
\(195\) 3.66146e10 1.81342
\(196\) −1.85223e10 −0.896486
\(197\) 3.49714e10 1.65430 0.827152 0.561979i \(-0.189960\pi\)
0.827152 + 0.561979i \(0.189960\pi\)
\(198\) 1.20944e10 0.559231
\(199\) 2.26366e10 1.02323 0.511614 0.859216i \(-0.329048\pi\)
0.511614 + 0.859216i \(0.329048\pi\)
\(200\) −6.05676e10 −2.67674
\(201\) 1.08233e10 0.467710
\(202\) −4.36057e10 −1.84273
\(203\) 2.67300e10 1.10476
\(204\) −2.59712e10 −1.04992
\(205\) −7.42367e10 −2.93580
\(206\) 6.02851e9 0.233243
\(207\) −7.51431e9 −0.284461
\(208\) 2.89832e10 1.07365
\(209\) −2.52947e10 −0.917004
\(210\) −3.33816e10 −1.18446
\(211\) −1.62398e10 −0.564040 −0.282020 0.959409i \(-0.591004\pi\)
−0.282020 + 0.959409i \(0.591004\pi\)
\(212\) −4.11125e10 −1.39786
\(213\) 8.30105e9 0.276328
\(214\) −8.12151e10 −2.64713
\(215\) −3.73652e10 −1.19260
\(216\) 8.85962e9 0.276932
\(217\) 2.68628e10 0.822399
\(218\) −8.48985e10 −2.54593
\(219\) 2.35210e10 0.690967
\(220\) 1.08115e11 3.11161
\(221\) 6.46681e10 1.82358
\(222\) −3.80152e10 −1.05043
\(223\) 2.14459e10 0.580727 0.290364 0.956916i \(-0.406224\pi\)
0.290364 + 0.956916i \(0.406224\pi\)
\(224\) 1.25233e10 0.332354
\(225\) 2.38369e10 0.620054
\(226\) −6.69186e10 −1.70631
\(227\) −4.33184e10 −1.08282 −0.541410 0.840759i \(-0.682109\pi\)
−0.541410 + 0.840759i \(0.682109\pi\)
\(228\) −4.02756e10 −0.987041
\(229\) 4.22128e10 1.01434 0.507171 0.861845i \(-0.330691\pi\)
0.507171 + 0.861845i \(0.330691\pi\)
\(230\) −1.03441e11 −2.43736
\(231\) 1.78292e10 0.411981
\(232\) −9.76591e10 −2.21318
\(233\) 2.55810e10 0.568612 0.284306 0.958734i \(-0.408237\pi\)
0.284306 + 0.958734i \(0.408237\pi\)
\(234\) −4.79507e10 −1.04550
\(235\) 2.65841e10 0.568613
\(236\) 1.14904e10 0.241119
\(237\) −2.52428e10 −0.519721
\(238\) −5.89580e10 −1.19109
\(239\) 1.71958e10 0.340905 0.170452 0.985366i \(-0.445477\pi\)
0.170452 + 0.985366i \(0.445477\pi\)
\(240\) 2.90123e10 0.564457
\(241\) −7.20557e9 −0.137592 −0.0687958 0.997631i \(-0.521916\pi\)
−0.0687958 + 0.997631i \(0.521916\pi\)
\(242\) 1.18203e9 0.0221544
\(243\) −3.48678e9 −0.0641500
\(244\) −1.47590e11 −2.66564
\(245\) 4.61667e10 0.818619
\(246\) 9.72206e10 1.69258
\(247\) 1.00286e11 1.71436
\(248\) −9.81441e10 −1.64752
\(249\) −3.48795e10 −0.575006
\(250\) 1.51735e11 2.45672
\(251\) −2.96084e10 −0.470851 −0.235425 0.971892i \(-0.575648\pi\)
−0.235425 + 0.971892i \(0.575648\pi\)
\(252\) 2.83886e10 0.443447
\(253\) 5.52483e10 0.847767
\(254\) −8.51254e10 −1.28324
\(255\) 6.47330e10 0.958727
\(256\) −1.19330e11 −1.73648
\(257\) −1.32586e11 −1.89582 −0.947912 0.318531i \(-0.896810\pi\)
−0.947912 + 0.318531i \(0.896810\pi\)
\(258\) 4.89336e10 0.687572
\(259\) −5.60407e10 −0.773847
\(260\) −4.28644e11 −5.81724
\(261\) 3.84347e10 0.512673
\(262\) 1.89734e11 2.48766
\(263\) 7.10092e10 0.915195 0.457598 0.889159i \(-0.348710\pi\)
0.457598 + 0.889159i \(0.348710\pi\)
\(264\) −6.51395e10 −0.825328
\(265\) 1.02472e11 1.27644
\(266\) −9.14306e10 −1.11976
\(267\) 2.96628e10 0.357200
\(268\) −1.26707e11 −1.50036
\(269\) −4.49779e10 −0.523738 −0.261869 0.965103i \(-0.584339\pi\)
−0.261869 + 0.965103i \(0.584339\pi\)
\(270\) −4.79988e10 −0.549659
\(271\) 1.26724e11 1.42724 0.713620 0.700533i \(-0.247054\pi\)
0.713620 + 0.700533i \(0.247054\pi\)
\(272\) 5.12409e10 0.567619
\(273\) −7.06873e10 −0.770210
\(274\) −1.91932e11 −2.05717
\(275\) −1.75259e11 −1.84792
\(276\) 8.79693e10 0.912516
\(277\) −9.23479e10 −0.942471 −0.471236 0.882007i \(-0.656192\pi\)
−0.471236 + 0.882007i \(0.656192\pi\)
\(278\) −2.17710e10 −0.218614
\(279\) 3.86255e10 0.381641
\(280\) 1.79791e11 1.74806
\(281\) −1.00241e11 −0.959102 −0.479551 0.877514i \(-0.659200\pi\)
−0.479551 + 0.877514i \(0.659200\pi\)
\(282\) −3.48146e10 −0.327824
\(283\) 1.86843e11 1.73156 0.865781 0.500424i \(-0.166822\pi\)
0.865781 + 0.500424i \(0.166822\pi\)
\(284\) −9.71796e10 −0.886426
\(285\) 1.00386e11 0.901308
\(286\) 3.52553e11 3.11585
\(287\) 1.43319e11 1.24691
\(288\) 1.80070e10 0.154232
\(289\) −4.25760e9 −0.0359025
\(290\) 5.29088e11 4.39276
\(291\) 6.08268e10 0.497252
\(292\) −2.75358e11 −2.21654
\(293\) 6.44015e9 0.0510495 0.0255248 0.999674i \(-0.491874\pi\)
0.0255248 + 0.999674i \(0.491874\pi\)
\(294\) −6.04601e10 −0.471961
\(295\) −2.86397e10 −0.220176
\(296\) 2.04747e11 1.55026
\(297\) 2.56363e10 0.191184
\(298\) 2.21773e11 1.62905
\(299\) −2.19043e11 −1.58492
\(300\) −2.79057e11 −1.98906
\(301\) 7.21363e10 0.506529
\(302\) 1.30718e11 0.904280
\(303\) −9.24301e10 −0.629973
\(304\) 7.94632e10 0.533624
\(305\) 3.67865e11 2.43411
\(306\) −8.47746e10 −0.552738
\(307\) −2.39452e11 −1.53849 −0.769246 0.638953i \(-0.779368\pi\)
−0.769246 + 0.638953i \(0.779368\pi\)
\(308\) −2.08725e11 −1.32159
\(309\) 1.27785e10 0.0797383
\(310\) 5.31716e11 3.27003
\(311\) −1.13245e11 −0.686430 −0.343215 0.939257i \(-0.611516\pi\)
−0.343215 + 0.939257i \(0.611516\pi\)
\(312\) 2.58258e11 1.54297
\(313\) 2.21292e11 1.30322 0.651608 0.758556i \(-0.274095\pi\)
0.651608 + 0.758556i \(0.274095\pi\)
\(314\) 4.39373e11 2.55064
\(315\) −7.07582e10 −0.404930
\(316\) 2.95516e11 1.66720
\(317\) −1.70170e11 −0.946493 −0.473246 0.880930i \(-0.656918\pi\)
−0.473246 + 0.880930i \(0.656918\pi\)
\(318\) −1.34198e11 −0.735910
\(319\) −2.82587e11 −1.52790
\(320\) 4.31269e11 2.29918
\(321\) −1.72150e11 −0.904970
\(322\) 1.99701e11 1.03521
\(323\) 1.77301e11 0.906357
\(324\) 4.08195e10 0.205785
\(325\) 6.94849e11 3.45474
\(326\) −4.06453e11 −1.99311
\(327\) −1.79958e11 −0.870373
\(328\) −5.23622e11 −2.49796
\(329\) −5.13226e10 −0.241505
\(330\) 3.52907e11 1.63813
\(331\) −1.49429e11 −0.684241 −0.342121 0.939656i \(-0.611145\pi\)
−0.342121 + 0.939656i \(0.611145\pi\)
\(332\) 4.08331e11 1.84455
\(333\) −8.05800e10 −0.359110
\(334\) −4.93525e11 −2.16995
\(335\) 3.15816e11 1.37004
\(336\) −5.60103e10 −0.239740
\(337\) 1.22653e11 0.518018 0.259009 0.965875i \(-0.416604\pi\)
0.259009 + 0.965875i \(0.416604\pi\)
\(338\) −9.92532e11 −4.13637
\(339\) −1.41846e11 −0.583335
\(340\) −7.57823e11 −3.07548
\(341\) −2.83991e11 −1.13739
\(342\) −1.31466e11 −0.519634
\(343\) −2.73260e11 −1.06599
\(344\) −2.63552e11 −1.01474
\(345\) −2.19263e11 −0.833256
\(346\) 8.30969e10 0.311704
\(347\) −2.80556e11 −1.03881 −0.519405 0.854528i \(-0.673846\pi\)
−0.519405 + 0.854528i \(0.673846\pi\)
\(348\) −4.49951e11 −1.64459
\(349\) 5.05946e11 1.82553 0.912767 0.408481i \(-0.133941\pi\)
0.912767 + 0.408481i \(0.133941\pi\)
\(350\) −6.33494e11 −2.25650
\(351\) −1.01640e11 −0.357423
\(352\) −1.32395e11 −0.459651
\(353\) 1.15837e11 0.397066 0.198533 0.980094i \(-0.436382\pi\)
0.198533 + 0.980094i \(0.436382\pi\)
\(354\) 3.75066e10 0.126939
\(355\) 2.42219e11 0.809432
\(356\) −3.47260e11 −1.14585
\(357\) −1.24972e11 −0.407198
\(358\) 6.73909e11 2.16834
\(359\) 1.75745e11 0.558416 0.279208 0.960231i \(-0.409928\pi\)
0.279208 + 0.960231i \(0.409928\pi\)
\(360\) 2.58518e11 0.811202
\(361\) −4.77339e10 −0.147926
\(362\) 3.02413e11 0.925576
\(363\) 2.50553e9 0.00757391
\(364\) 8.27529e11 2.47074
\(365\) 6.86327e11 2.02401
\(366\) −4.81758e11 −1.40334
\(367\) −8.79397e10 −0.253039 −0.126520 0.991964i \(-0.540381\pi\)
−0.126520 + 0.991964i \(0.540381\pi\)
\(368\) −1.73562e11 −0.493333
\(369\) 2.06076e11 0.578641
\(370\) −1.10926e12 −3.07698
\(371\) −1.97830e11 −0.542139
\(372\) −4.52186e11 −1.22426
\(373\) 5.88829e11 1.57507 0.787534 0.616271i \(-0.211357\pi\)
0.787534 + 0.616271i \(0.211357\pi\)
\(374\) 6.23297e11 1.64730
\(375\) 3.21629e11 0.839874
\(376\) 1.87509e11 0.483812
\(377\) 1.12037e12 2.85645
\(378\) 9.26652e10 0.233455
\(379\) 4.34936e11 1.08280 0.541401 0.840764i \(-0.317894\pi\)
0.541401 + 0.840764i \(0.317894\pi\)
\(380\) −1.17521e12 −2.89129
\(381\) −1.80438e11 −0.438699
\(382\) −1.11018e11 −0.266751
\(383\) −4.12270e11 −0.979009 −0.489505 0.872001i \(-0.662822\pi\)
−0.489505 + 0.872001i \(0.662822\pi\)
\(384\) −4.50969e11 −1.05842
\(385\) 5.20243e11 1.20679
\(386\) 4.08012e11 0.935469
\(387\) 1.03723e11 0.235059
\(388\) −7.12093e11 −1.59512
\(389\) −2.59030e11 −0.573557 −0.286778 0.957997i \(-0.592584\pi\)
−0.286778 + 0.957997i \(0.592584\pi\)
\(390\) −1.39917e12 −3.06252
\(391\) −3.87257e11 −0.837923
\(392\) 3.25633e11 0.696533
\(393\) 4.02176e11 0.850452
\(394\) −1.33637e12 −2.79380
\(395\) −7.36569e11 −1.52239
\(396\) −3.00121e11 −0.613294
\(397\) −4.46780e11 −0.902685 −0.451343 0.892351i \(-0.649055\pi\)
−0.451343 + 0.892351i \(0.649055\pi\)
\(398\) −8.65019e11 −1.72803
\(399\) −1.93804e11 −0.382810
\(400\) 5.50575e11 1.07534
\(401\) 5.73928e11 1.10843 0.554214 0.832374i \(-0.313019\pi\)
0.554214 + 0.832374i \(0.313019\pi\)
\(402\) −4.13594e11 −0.789872
\(403\) 1.12594e12 2.12638
\(404\) 1.08207e12 2.02088
\(405\) −1.01742e11 −0.187911
\(406\) −1.02144e12 −1.86572
\(407\) 5.92457e11 1.07024
\(408\) 4.56589e11 0.815746
\(409\) −5.94170e11 −1.04992 −0.524960 0.851127i \(-0.675920\pi\)
−0.524960 + 0.851127i \(0.675920\pi\)
\(410\) 2.83683e12 4.95800
\(411\) −4.06834e11 −0.703282
\(412\) −1.49597e11 −0.255791
\(413\) 5.52910e10 0.0935146
\(414\) 2.87147e11 0.480400
\(415\) −1.01776e12 −1.68434
\(416\) 5.24905e11 0.859331
\(417\) −4.61476e10 −0.0747372
\(418\) 9.66595e11 1.54864
\(419\) 9.41632e8 0.00149251 0.000746257 1.00000i \(-0.499762\pi\)
0.000746257 1.00000i \(0.499762\pi\)
\(420\) 8.28360e11 1.29896
\(421\) −4.18727e11 −0.649623 −0.324812 0.945779i \(-0.605301\pi\)
−0.324812 + 0.945779i \(0.605301\pi\)
\(422\) 6.20577e11 0.952555
\(423\) −7.37958e10 −0.112073
\(424\) 7.22780e11 1.08608
\(425\) 1.22846e12 1.82646
\(426\) −3.17211e11 −0.466664
\(427\) −7.10191e11 −1.03383
\(428\) 2.01534e12 2.90303
\(429\) 7.47299e11 1.06521
\(430\) 1.42785e12 2.01407
\(431\) −4.92356e11 −0.687276 −0.343638 0.939102i \(-0.611659\pi\)
−0.343638 + 0.939102i \(0.611659\pi\)
\(432\) −8.05362e10 −0.111254
\(433\) 1.05027e11 0.143584 0.0717922 0.997420i \(-0.477128\pi\)
0.0717922 + 0.997420i \(0.477128\pi\)
\(434\) −1.02652e12 −1.38887
\(435\) 1.12150e12 1.50175
\(436\) 2.10675e12 2.79205
\(437\) −6.00550e11 −0.787739
\(438\) −8.98816e11 −1.16691
\(439\) 1.80110e11 0.231445 0.115722 0.993282i \(-0.463082\pi\)
0.115722 + 0.993282i \(0.463082\pi\)
\(440\) −1.90073e12 −2.41759
\(441\) −1.28156e11 −0.161349
\(442\) −2.47118e12 −3.07968
\(443\) −2.72830e9 −0.00336570 −0.00168285 0.999999i \(-0.500536\pi\)
−0.00168285 + 0.999999i \(0.500536\pi\)
\(444\) 9.43342e11 1.15198
\(445\) 8.65541e11 1.04633
\(446\) −8.19519e11 −0.980737
\(447\) 4.70087e11 0.556922
\(448\) −8.32596e11 −0.976525
\(449\) 9.66096e11 1.12179 0.560895 0.827887i \(-0.310457\pi\)
0.560895 + 0.827887i \(0.310457\pi\)
\(450\) −9.10889e11 −1.04715
\(451\) −1.51516e12 −1.72450
\(452\) 1.66058e12 1.87127
\(453\) 2.77079e11 0.309145
\(454\) 1.65534e12 1.82867
\(455\) −2.06261e12 −2.25614
\(456\) 7.08068e11 0.766890
\(457\) 1.34660e12 1.44416 0.722078 0.691811i \(-0.243187\pi\)
0.722078 + 0.691811i \(0.243187\pi\)
\(458\) −1.61309e12 −1.71303
\(459\) −1.79695e11 −0.188964
\(460\) 2.56689e12 2.67298
\(461\) −1.67447e12 −1.72672 −0.863361 0.504588i \(-0.831645\pi\)
−0.863361 + 0.504588i \(0.831645\pi\)
\(462\) −6.81313e11 −0.695757
\(463\) −1.42881e11 −0.144497 −0.0722485 0.997387i \(-0.523017\pi\)
−0.0722485 + 0.997387i \(0.523017\pi\)
\(464\) 8.87747e11 0.889116
\(465\) 1.12707e12 1.11792
\(466\) −9.77536e11 −0.960276
\(467\) 1.65461e12 1.60979 0.804895 0.593417i \(-0.202221\pi\)
0.804895 + 0.593417i \(0.202221\pi\)
\(468\) 1.18989e12 1.14657
\(469\) −6.09706e11 −0.581893
\(470\) −1.01587e12 −0.960277
\(471\) 9.31328e11 0.871985
\(472\) −2.02008e11 −0.187339
\(473\) −7.62617e11 −0.700537
\(474\) 9.64613e11 0.877709
\(475\) 1.90507e12 1.71707
\(476\) 1.46303e12 1.30624
\(477\) −2.84457e11 −0.251584
\(478\) −6.57110e11 −0.575722
\(479\) 1.39599e11 0.121163 0.0605817 0.998163i \(-0.480704\pi\)
0.0605817 + 0.998163i \(0.480704\pi\)
\(480\) 5.25431e11 0.451784
\(481\) −2.34891e12 −2.00085
\(482\) 2.75349e11 0.232366
\(483\) 4.23303e11 0.353907
\(484\) −2.93320e10 −0.0242962
\(485\) 1.77488e12 1.45657
\(486\) 1.33242e11 0.108337
\(487\) 1.19265e12 0.960799 0.480399 0.877050i \(-0.340492\pi\)
0.480399 + 0.877050i \(0.340492\pi\)
\(488\) 2.59471e12 2.07109
\(489\) −8.61549e11 −0.681381
\(490\) −1.76418e12 −1.38249
\(491\) 3.97761e10 0.0308856 0.0154428 0.999881i \(-0.495084\pi\)
0.0154428 + 0.999881i \(0.495084\pi\)
\(492\) −2.41252e12 −1.85621
\(493\) 1.98077e12 1.51016
\(494\) −3.83226e12 −2.89523
\(495\) 7.48049e11 0.560024
\(496\) 8.92156e11 0.661871
\(497\) −4.67622e11 −0.343788
\(498\) 1.33286e12 0.971075
\(499\) −1.61064e12 −1.16291 −0.581455 0.813578i \(-0.697516\pi\)
−0.581455 + 0.813578i \(0.697516\pi\)
\(500\) −3.76528e12 −2.69421
\(501\) −1.04612e12 −0.741839
\(502\) 1.13144e12 0.795176
\(503\) 1.72425e12 1.20100 0.600502 0.799623i \(-0.294967\pi\)
0.600502 + 0.799623i \(0.294967\pi\)
\(504\) −4.99087e11 −0.344540
\(505\) −2.69705e12 −1.84535
\(506\) −2.11122e12 −1.43171
\(507\) −2.10385e12 −1.41409
\(508\) 2.11238e12 1.40729
\(509\) 1.42974e11 0.0944120 0.0472060 0.998885i \(-0.484968\pi\)
0.0472060 + 0.998885i \(0.484968\pi\)
\(510\) −2.47367e12 −1.61911
\(511\) −1.32500e12 −0.859653
\(512\) 1.70942e12 1.09934
\(513\) −2.78667e11 −0.177647
\(514\) 5.06655e12 3.20168
\(515\) 3.72868e11 0.233573
\(516\) −1.21428e12 −0.754042
\(517\) 5.42577e11 0.334006
\(518\) 2.14150e12 1.30688
\(519\) 1.76139e11 0.106562
\(520\) 7.53581e12 4.51975
\(521\) −6.34830e11 −0.377475 −0.188737 0.982028i \(-0.560439\pi\)
−0.188737 + 0.982028i \(0.560439\pi\)
\(522\) −1.46872e12 −0.865806
\(523\) 2.02092e12 1.18112 0.590558 0.806995i \(-0.298908\pi\)
0.590558 + 0.806995i \(0.298908\pi\)
\(524\) −4.70824e12 −2.72815
\(525\) −1.34280e12 −0.771428
\(526\) −2.71350e12 −1.54559
\(527\) 1.99061e12 1.12418
\(528\) 5.92135e11 0.331565
\(529\) −4.89441e11 −0.271738
\(530\) −3.91581e12 −2.15566
\(531\) 7.95020e10 0.0433963
\(532\) 2.26884e12 1.22801
\(533\) 6.00714e12 3.22400
\(534\) −1.13351e12 −0.603242
\(535\) −5.02322e12 −2.65088
\(536\) 2.22758e12 1.16571
\(537\) 1.42847e12 0.741288
\(538\) 1.71876e12 0.884492
\(539\) 9.42255e11 0.480860
\(540\) 1.19108e12 0.602796
\(541\) −9.27669e11 −0.465592 −0.232796 0.972526i \(-0.574787\pi\)
−0.232796 + 0.972526i \(0.574787\pi\)
\(542\) −4.84255e12 −2.41033
\(543\) 6.41019e11 0.316426
\(544\) 9.28007e11 0.454314
\(545\) −5.25104e12 −2.54954
\(546\) 2.70120e12 1.30074
\(547\) 6.16039e11 0.294215 0.147108 0.989121i \(-0.453004\pi\)
0.147108 + 0.989121i \(0.453004\pi\)
\(548\) 4.76277e12 2.25604
\(549\) −1.02117e12 −0.479759
\(550\) 6.69723e12 3.12078
\(551\) 3.07173e12 1.41971
\(552\) −1.54655e12 −0.708987
\(553\) 1.42200e12 0.646602
\(554\) 3.52892e12 1.59165
\(555\) −2.35127e12 −1.05192
\(556\) 5.40246e11 0.239748
\(557\) −1.69936e12 −0.748060 −0.374030 0.927417i \(-0.622024\pi\)
−0.374030 + 0.927417i \(0.622024\pi\)
\(558\) −1.47601e12 −0.644519
\(559\) 3.02355e12 1.30967
\(560\) −1.63434e12 −0.702259
\(561\) 1.32119e12 0.563161
\(562\) 3.83053e12 1.61974
\(563\) −8.96340e11 −0.375998 −0.187999 0.982169i \(-0.560200\pi\)
−0.187999 + 0.982169i \(0.560200\pi\)
\(564\) 8.63921e11 0.359516
\(565\) −4.13897e12 −1.70873
\(566\) −7.13989e12 −2.92427
\(567\) 1.96421e11 0.0798111
\(568\) 1.70847e12 0.688716
\(569\) 1.66602e12 0.666308 0.333154 0.942872i \(-0.391887\pi\)
0.333154 + 0.942872i \(0.391887\pi\)
\(570\) −3.83610e12 −1.52214
\(571\) −2.70908e12 −1.06650 −0.533249 0.845958i \(-0.679029\pi\)
−0.533249 + 0.845958i \(0.679029\pi\)
\(572\) −8.74856e12 −3.41707
\(573\) −2.35321e11 −0.0911939
\(574\) −5.47671e12 −2.10580
\(575\) −4.16102e12 −1.58743
\(576\) −1.19718e12 −0.453165
\(577\) −2.58898e12 −0.972385 −0.486192 0.873852i \(-0.661615\pi\)
−0.486192 + 0.873852i \(0.661615\pi\)
\(578\) 1.62697e11 0.0606323
\(579\) 8.64853e11 0.319808
\(580\) −1.31293e13 −4.81742
\(581\) 1.96486e12 0.715383
\(582\) −2.32439e12 −0.839762
\(583\) 2.09144e12 0.749786
\(584\) 4.84095e12 1.72216
\(585\) −2.96579e12 −1.04698
\(586\) −2.46100e11 −0.0862128
\(587\) 5.21983e12 1.81462 0.907308 0.420466i \(-0.138133\pi\)
0.907308 + 0.420466i \(0.138133\pi\)
\(588\) 1.50031e12 0.517587
\(589\) 3.08698e12 1.05686
\(590\) 1.09442e12 0.371834
\(591\) −2.83268e12 −0.955112
\(592\) −1.86120e12 −0.622796
\(593\) 1.66156e12 0.551785 0.275892 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(594\) −9.79647e11 −0.322872
\(595\) −3.64660e12 −1.19278
\(596\) −5.50327e12 −1.78654
\(597\) −1.83356e12 −0.590760
\(598\) 8.37035e12 2.67663
\(599\) −4.97073e12 −1.57761 −0.788805 0.614644i \(-0.789300\pi\)
−0.788805 + 0.614644i \(0.789300\pi\)
\(600\) 4.90598e12 1.54541
\(601\) 2.21641e12 0.692971 0.346485 0.938055i \(-0.387375\pi\)
0.346485 + 0.938055i \(0.387375\pi\)
\(602\) −2.75657e12 −0.855430
\(603\) −8.76686e11 −0.270033
\(604\) −3.24374e12 −0.991699
\(605\) 7.31097e10 0.0221858
\(606\) 3.53206e12 1.06390
\(607\) 2.09162e12 0.625365 0.312682 0.949858i \(-0.398772\pi\)
0.312682 + 0.949858i \(0.398772\pi\)
\(608\) 1.43913e12 0.427105
\(609\) −2.16513e12 −0.637833
\(610\) −1.40574e13 −4.11074
\(611\) −2.15115e12 −0.624433
\(612\) 2.10367e12 0.606173
\(613\) −2.18419e12 −0.624768 −0.312384 0.949956i \(-0.601127\pi\)
−0.312384 + 0.949956i \(0.601127\pi\)
\(614\) 9.15025e12 2.59822
\(615\) 6.01317e12 1.69498
\(616\) 3.66949e12 1.02682
\(617\) 6.28114e12 1.74484 0.872420 0.488757i \(-0.162550\pi\)
0.872420 + 0.488757i \(0.162550\pi\)
\(618\) −4.88310e11 −0.134663
\(619\) −4.31213e12 −1.18055 −0.590275 0.807202i \(-0.700981\pi\)
−0.590275 + 0.807202i \(0.700981\pi\)
\(620\) −1.31945e13 −3.58616
\(621\) 6.08659e11 0.164234
\(622\) 4.32746e12 1.15925
\(623\) −1.67099e12 −0.444404
\(624\) −2.34764e12 −0.619869
\(625\) 2.28896e12 0.600038
\(626\) −8.45631e12 −2.20088
\(627\) 2.04887e12 0.529432
\(628\) −1.09030e13 −2.79722
\(629\) −4.15277e12 −1.05782
\(630\) 2.70391e12 0.683848
\(631\) 5.98678e11 0.150335 0.0751677 0.997171i \(-0.476051\pi\)
0.0751677 + 0.997171i \(0.476051\pi\)
\(632\) −5.19533e12 −1.29535
\(633\) 1.31542e12 0.325649
\(634\) 6.50278e12 1.59844
\(635\) −5.26507e12 −1.28506
\(636\) 3.33011e12 0.807052
\(637\) −3.73576e12 −0.898982
\(638\) 1.07986e13 2.58033
\(639\) −6.72385e11 −0.159538
\(640\) −1.31590e13 −3.10036
\(641\) 2.99122e12 0.699822 0.349911 0.936783i \(-0.386212\pi\)
0.349911 + 0.936783i \(0.386212\pi\)
\(642\) 6.57843e12 1.52832
\(643\) 4.95935e12 1.14413 0.572065 0.820208i \(-0.306142\pi\)
0.572065 + 0.820208i \(0.306142\pi\)
\(644\) −4.95556e12 −1.13529
\(645\) 3.02658e12 0.688547
\(646\) −6.77525e12 −1.53066
\(647\) 2.32061e12 0.520634 0.260317 0.965523i \(-0.416173\pi\)
0.260317 + 0.965523i \(0.416173\pi\)
\(648\) −7.17629e11 −0.159887
\(649\) −5.84531e11 −0.129332
\(650\) −2.65525e13 −5.83438
\(651\) −2.17589e12 −0.474812
\(652\) 1.00861e13 2.18579
\(653\) −5.19501e12 −1.11809 −0.559045 0.829137i \(-0.688832\pi\)
−0.559045 + 0.829137i \(0.688832\pi\)
\(654\) 6.87678e12 1.46989
\(655\) 1.17352e13 2.49118
\(656\) 4.75986e12 1.00352
\(657\) −1.90520e12 −0.398930
\(658\) 1.96121e12 0.407856
\(659\) −2.11587e12 −0.437023 −0.218512 0.975834i \(-0.570120\pi\)
−0.218512 + 0.975834i \(0.570120\pi\)
\(660\) −8.75734e12 −1.79649
\(661\) 3.71417e12 0.756754 0.378377 0.925652i \(-0.376482\pi\)
0.378377 + 0.925652i \(0.376482\pi\)
\(662\) 5.71018e12 1.15555
\(663\) −5.23812e12 −1.05284
\(664\) −7.17868e12 −1.43314
\(665\) −5.65506e12 −1.12135
\(666\) 3.07923e12 0.606468
\(667\) −6.70922e12 −1.31252
\(668\) 1.22468e13 2.37973
\(669\) −1.73712e12 −0.335283
\(670\) −1.20684e13 −2.31373
\(671\) 7.50807e12 1.42981
\(672\) −1.01438e12 −0.191885
\(673\) 1.74039e12 0.327024 0.163512 0.986541i \(-0.447718\pi\)
0.163512 + 0.986541i \(0.447718\pi\)
\(674\) −4.68700e12 −0.874833
\(675\) −1.93079e12 −0.357988
\(676\) 2.46296e13 4.53624
\(677\) 2.29128e12 0.419208 0.209604 0.977786i \(-0.432783\pi\)
0.209604 + 0.977786i \(0.432783\pi\)
\(678\) 5.42041e12 0.985141
\(679\) −3.42654e12 −0.618646
\(680\) 1.33230e13 2.38952
\(681\) 3.50879e12 0.625166
\(682\) 1.08522e13 1.92083
\(683\) 9.87833e12 1.73696 0.868481 0.495722i \(-0.165097\pi\)
0.868481 + 0.495722i \(0.165097\pi\)
\(684\) 3.26232e12 0.569868
\(685\) −1.18711e13 −2.06008
\(686\) 1.04422e13 1.80025
\(687\) −3.41924e12 −0.585631
\(688\) 2.39576e12 0.407657
\(689\) −8.29194e12 −1.40175
\(690\) 8.37875e12 1.40721
\(691\) 3.06402e12 0.511258 0.255629 0.966775i \(-0.417717\pi\)
0.255629 + 0.966775i \(0.417717\pi\)
\(692\) −2.06204e12 −0.341837
\(693\) −1.44416e12 −0.237857
\(694\) 1.07210e13 1.75435
\(695\) −1.34656e12 −0.218924
\(696\) 7.91039e12 1.27778
\(697\) 1.06203e13 1.70448
\(698\) −1.93339e13 −3.08297
\(699\) −2.07206e12 −0.328288
\(700\) 1.57201e13 2.47465
\(701\) −1.12338e13 −1.75710 −0.878550 0.477650i \(-0.841489\pi\)
−0.878550 + 0.477650i \(0.841489\pi\)
\(702\) 3.88400e12 0.603619
\(703\) −6.44002e12 −0.994462
\(704\) 8.80212e12 1.35055
\(705\) −2.15331e12 −0.328289
\(706\) −4.42654e12 −0.670568
\(707\) 5.20685e12 0.783769
\(708\) −9.30723e11 −0.139210
\(709\) 3.23298e12 0.480502 0.240251 0.970711i \(-0.422770\pi\)
0.240251 + 0.970711i \(0.422770\pi\)
\(710\) −9.25600e12 −1.36698
\(711\) 2.04467e12 0.300061
\(712\) 6.10502e12 0.890281
\(713\) −6.74254e12 −0.977059
\(714\) 4.77559e12 0.687679
\(715\) 2.18057e13 3.12027
\(716\) −1.67230e13 −2.37796
\(717\) −1.39286e12 −0.196821
\(718\) −6.71580e12 −0.943056
\(719\) 7.33792e12 1.02398 0.511992 0.858990i \(-0.328908\pi\)
0.511992 + 0.858990i \(0.328908\pi\)
\(720\) −2.34999e12 −0.325889
\(721\) −7.19850e11 −0.0992049
\(722\) 1.82407e12 0.249818
\(723\) 5.83651e11 0.0794385
\(724\) −7.50435e12 −1.01505
\(725\) 2.12830e13 2.86096
\(726\) −9.57447e10 −0.0127909
\(727\) −1.25826e13 −1.67057 −0.835286 0.549816i \(-0.814698\pi\)
−0.835286 + 0.549816i \(0.814698\pi\)
\(728\) −1.45484e13 −1.91966
\(729\) 2.82430e11 0.0370370
\(730\) −2.62268e13 −3.41816
\(731\) 5.34549e12 0.692404
\(732\) 1.19548e13 1.53901
\(733\) −1.82162e12 −0.233072 −0.116536 0.993186i \(-0.537179\pi\)
−0.116536 + 0.993186i \(0.537179\pi\)
\(734\) 3.36047e12 0.427334
\(735\) −3.73951e12 −0.472630
\(736\) −3.14333e12 −0.394857
\(737\) 6.44575e12 0.804767
\(738\) −7.87487e12 −0.977214
\(739\) 7.34365e12 0.905757 0.452879 0.891572i \(-0.350397\pi\)
0.452879 + 0.891572i \(0.350397\pi\)
\(740\) 2.75261e13 3.37444
\(741\) −8.12315e12 −0.989789
\(742\) 7.55976e12 0.915568
\(743\) 1.57099e13 1.89114 0.945571 0.325417i \(-0.105505\pi\)
0.945571 + 0.325417i \(0.105505\pi\)
\(744\) 7.94967e12 0.951198
\(745\) 1.37168e13 1.63136
\(746\) −2.25011e13 −2.65999
\(747\) 2.82524e12 0.331980
\(748\) −1.54670e13 −1.80655
\(749\) 9.69770e12 1.12590
\(750\) −1.22905e13 −1.41839
\(751\) −1.32475e13 −1.51969 −0.759843 0.650107i \(-0.774724\pi\)
−0.759843 + 0.650107i \(0.774724\pi\)
\(752\) −1.70450e12 −0.194365
\(753\) 2.39828e12 0.271846
\(754\) −4.28132e13 −4.82399
\(755\) 8.08498e12 0.905561
\(756\) −2.29948e12 −0.256024
\(757\) −4.15927e12 −0.460347 −0.230173 0.973150i \(-0.573929\pi\)
−0.230173 + 0.973150i \(0.573929\pi\)
\(758\) −1.66204e13 −1.82864
\(759\) −4.47511e12 −0.489458
\(760\) 2.06609e13 2.24641
\(761\) 2.81502e12 0.304264 0.152132 0.988360i \(-0.451386\pi\)
0.152132 + 0.988360i \(0.451386\pi\)
\(762\) 6.89515e12 0.740878
\(763\) 1.01375e13 1.08286
\(764\) 2.75489e12 0.292539
\(765\) −5.24338e12 −0.553521
\(766\) 1.57542e13 1.65336
\(767\) 2.31749e12 0.241790
\(768\) 9.66570e12 1.00255
\(769\) −5.58722e12 −0.576139 −0.288069 0.957610i \(-0.593013\pi\)
−0.288069 + 0.957610i \(0.593013\pi\)
\(770\) −1.98802e13 −2.03804
\(771\) 1.07395e13 1.09455
\(772\) −1.01248e13 −1.02590
\(773\) 7.81592e12 0.787358 0.393679 0.919248i \(-0.371202\pi\)
0.393679 + 0.919248i \(0.371202\pi\)
\(774\) −3.96362e12 −0.396970
\(775\) 2.13887e13 2.12974
\(776\) 1.25190e13 1.23934
\(777\) 4.53930e12 0.446781
\(778\) 9.89839e12 0.968627
\(779\) 1.64698e13 1.60239
\(780\) 3.47202e13 3.35858
\(781\) 4.94365e12 0.475464
\(782\) 1.47984e13 1.41509
\(783\) −3.11321e12 −0.295992
\(784\) −2.96009e12 −0.279823
\(785\) 2.71755e13 2.55426
\(786\) −1.53685e13 −1.43625
\(787\) 8.24352e12 0.765995 0.382998 0.923749i \(-0.374892\pi\)
0.382998 + 0.923749i \(0.374892\pi\)
\(788\) 3.31620e13 3.06388
\(789\) −5.75175e12 −0.528388
\(790\) 2.81468e13 2.57103
\(791\) 7.99059e12 0.725746
\(792\) 5.27630e12 0.476504
\(793\) −2.97672e13 −2.67306
\(794\) 1.70730e13 1.52446
\(795\) −8.30026e12 −0.736953
\(796\) 2.14654e13 1.89509
\(797\) −2.08863e13 −1.83358 −0.916789 0.399373i \(-0.869228\pi\)
−0.916789 + 0.399373i \(0.869228\pi\)
\(798\) 7.40588e12 0.646493
\(799\) −3.80314e12 −0.330128
\(800\) 9.97129e12 0.860689
\(801\) −2.40269e12 −0.206230
\(802\) −2.19317e13 −1.87192
\(803\) 1.40078e13 1.18891
\(804\) 1.02633e13 0.866231
\(805\) 1.23517e13 1.03668
\(806\) −4.30258e13 −3.59105
\(807\) 3.64321e12 0.302380
\(808\) −1.90234e13 −1.57014
\(809\) 1.28294e13 1.05302 0.526511 0.850168i \(-0.323500\pi\)
0.526511 + 0.850168i \(0.323500\pi\)
\(810\) 3.88790e12 0.317346
\(811\) −1.28485e13 −1.04294 −0.521468 0.853271i \(-0.674615\pi\)
−0.521468 + 0.853271i \(0.674615\pi\)
\(812\) 2.53470e13 2.04609
\(813\) −1.02646e13 −0.824018
\(814\) −2.26398e13 −1.80743
\(815\) −2.51394e13 −1.99593
\(816\) −4.15051e12 −0.327715
\(817\) 8.28966e12 0.650935
\(818\) 2.27052e13 1.77311
\(819\) 5.72567e12 0.444681
\(820\) −7.03956e13 −5.43730
\(821\) 1.61653e12 0.124177 0.0620883 0.998071i \(-0.480224\pi\)
0.0620883 + 0.998071i \(0.480224\pi\)
\(822\) 1.55465e13 1.18771
\(823\) 1.26509e13 0.961217 0.480608 0.876935i \(-0.340416\pi\)
0.480608 + 0.876935i \(0.340416\pi\)
\(824\) 2.63000e12 0.198739
\(825\) 1.41960e13 1.06690
\(826\) −2.11286e12 −0.157928
\(827\) 9.59649e12 0.713408 0.356704 0.934218i \(-0.383901\pi\)
0.356704 + 0.934218i \(0.383901\pi\)
\(828\) −7.12552e12 −0.526841
\(829\) 1.50373e13 1.10580 0.552898 0.833249i \(-0.313522\pi\)
0.552898 + 0.833249i \(0.313522\pi\)
\(830\) 3.88920e13 2.84452
\(831\) 7.48018e12 0.544136
\(832\) −3.48977e13 −2.52489
\(833\) −6.60465e12 −0.475277
\(834\) 1.76345e12 0.126217
\(835\) −3.05249e13 −2.17303
\(836\) −2.39859e13 −1.69835
\(837\) −3.12867e12 −0.220341
\(838\) −3.59829e10 −0.00252057
\(839\) −7.36679e12 −0.513274 −0.256637 0.966508i \(-0.582615\pi\)
−0.256637 + 0.966508i \(0.582615\pi\)
\(840\) −1.45630e13 −1.00924
\(841\) 1.98096e13 1.36550
\(842\) 1.60010e13 1.09709
\(843\) 8.11948e12 0.553738
\(844\) −1.53996e13 −1.04464
\(845\) −6.13889e13 −4.14223
\(846\) 2.81998e12 0.189269
\(847\) −1.41144e11 −0.00942293
\(848\) −6.57026e12 −0.436316
\(849\) −1.51343e13 −0.999717
\(850\) −4.69436e13 −3.08454
\(851\) 1.40662e13 0.919376
\(852\) 7.87155e12 0.511778
\(853\) −2.43176e13 −1.57272 −0.786359 0.617770i \(-0.788036\pi\)
−0.786359 + 0.617770i \(0.788036\pi\)
\(854\) 2.71388e13 1.74594
\(855\) −8.13130e12 −0.520370
\(856\) −3.54309e13 −2.25554
\(857\) 6.34489e12 0.401800 0.200900 0.979612i \(-0.435613\pi\)
0.200900 + 0.979612i \(0.435613\pi\)
\(858\) −2.85568e13 −1.79894
\(859\) −1.30312e12 −0.0816612 −0.0408306 0.999166i \(-0.513000\pi\)
−0.0408306 + 0.999166i \(0.513000\pi\)
\(860\) −3.54319e13 −2.20877
\(861\) −1.16089e13 −0.719906
\(862\) 1.88146e13 1.16068
\(863\) −6.05800e12 −0.371776 −0.185888 0.982571i \(-0.559516\pi\)
−0.185888 + 0.982571i \(0.559516\pi\)
\(864\) −1.45857e12 −0.0890459
\(865\) 5.13961e12 0.312146
\(866\) −4.01345e12 −0.242486
\(867\) 3.44865e11 0.0207283
\(868\) 2.54729e13 1.52314
\(869\) −1.50332e13 −0.894260
\(870\) −4.28562e13 −2.53616
\(871\) −2.55555e13 −1.50453
\(872\) −3.70378e13 −2.16931
\(873\) −4.92697e12 −0.287088
\(874\) 2.29490e13 1.33034
\(875\) −1.81183e13 −1.04491
\(876\) 2.23040e13 1.27972
\(877\) 1.99893e13 1.14103 0.570517 0.821286i \(-0.306743\pi\)
0.570517 + 0.821286i \(0.306743\pi\)
\(878\) −6.88260e12 −0.390865
\(879\) −5.21652e11 −0.0294734
\(880\) 1.72781e13 0.971234
\(881\) 1.68758e13 0.943784 0.471892 0.881656i \(-0.343571\pi\)
0.471892 + 0.881656i \(0.343571\pi\)
\(882\) 4.89727e12 0.272487
\(883\) 2.45383e13 1.35838 0.679190 0.733962i \(-0.262331\pi\)
0.679190 + 0.733962i \(0.262331\pi\)
\(884\) 6.13222e13 3.37740
\(885\) 2.31981e12 0.127118
\(886\) 1.04257e11 0.00568402
\(887\) −1.87374e13 −1.01637 −0.508186 0.861247i \(-0.669684\pi\)
−0.508186 + 0.861247i \(0.669684\pi\)
\(888\) −1.65845e13 −0.895042
\(889\) 1.01646e13 0.545799
\(890\) −3.30752e13 −1.76704
\(891\) −2.07654e12 −0.110380
\(892\) 2.03363e13 1.07555
\(893\) −5.89782e12 −0.310356
\(894\) −1.79636e13 −0.940534
\(895\) 4.16818e13 2.17142
\(896\) 2.54044e13 1.31681
\(897\) 1.77425e13 0.915056
\(898\) −3.69177e13 −1.89449
\(899\) 3.44872e13 1.76092
\(900\) 2.26036e13 1.14838
\(901\) −1.46598e13 −0.741081
\(902\) 5.78992e13 2.91235
\(903\) −5.84304e12 −0.292445
\(904\) −2.91939e13 −1.45390
\(905\) 1.87045e13 0.926888
\(906\) −1.05881e13 −0.522086
\(907\) −2.56704e13 −1.25950 −0.629751 0.776797i \(-0.716843\pi\)
−0.629751 + 0.776797i \(0.716843\pi\)
\(908\) −4.10771e13 −2.00546
\(909\) 7.48684e12 0.363715
\(910\) 7.88191e13 3.81018
\(911\) 2.79680e13 1.34533 0.672665 0.739948i \(-0.265150\pi\)
0.672665 + 0.739948i \(0.265150\pi\)
\(912\) −6.43652e12 −0.308088
\(913\) −2.07723e13 −0.989386
\(914\) −5.14579e13 −2.43890
\(915\) −2.97971e13 −1.40533
\(916\) 4.00287e13 1.87863
\(917\) −2.26557e13 −1.05807
\(918\) 6.86674e12 0.319123
\(919\) 3.04175e13 1.40670 0.703352 0.710841i \(-0.251686\pi\)
0.703352 + 0.710841i \(0.251686\pi\)
\(920\) −4.51273e13 −2.07680
\(921\) 1.93956e13 0.888249
\(922\) 6.39869e13 2.91610
\(923\) −1.96001e13 −0.888894
\(924\) 1.69067e13 0.763018
\(925\) −4.46208e13 −2.00401
\(926\) 5.45995e12 0.244028
\(927\) −1.03506e12 −0.0460369
\(928\) 1.60777e13 0.711636
\(929\) −2.73278e12 −0.120374 −0.0601872 0.998187i \(-0.519170\pi\)
−0.0601872 + 0.998187i \(0.519170\pi\)
\(930\) −4.30690e13 −1.88795
\(931\) −1.02423e13 −0.446812
\(932\) 2.42574e13 1.05311
\(933\) 9.17282e12 0.396310
\(934\) −6.32281e13 −2.71863
\(935\) 3.85514e13 1.64964
\(936\) −2.09189e13 −0.890837
\(937\) 1.01855e12 0.0431671 0.0215835 0.999767i \(-0.493129\pi\)
0.0215835 + 0.999767i \(0.493129\pi\)
\(938\) 2.32989e13 0.982705
\(939\) −1.79247e13 −0.752412
\(940\) 2.52086e13 1.05311
\(941\) 3.23933e13 1.34680 0.673399 0.739279i \(-0.264834\pi\)
0.673399 + 0.739279i \(0.264834\pi\)
\(942\) −3.55892e13 −1.47261
\(943\) −3.59731e13 −1.48141
\(944\) 1.83630e12 0.0752611
\(945\) 5.73142e12 0.233786
\(946\) 2.91421e13 1.18307
\(947\) 3.97181e13 1.60477 0.802387 0.596804i \(-0.203563\pi\)
0.802387 + 0.596804i \(0.203563\pi\)
\(948\) −2.39368e13 −0.962560
\(949\) −5.55367e13 −2.22271
\(950\) −7.27990e13 −2.89981
\(951\) 1.37838e13 0.546458
\(952\) −2.57210e13 −1.01489
\(953\) 8.84197e12 0.347241 0.173621 0.984813i \(-0.444453\pi\)
0.173621 + 0.984813i \(0.444453\pi\)
\(954\) 1.08700e13 0.424878
\(955\) −6.86652e12 −0.267129
\(956\) 1.63061e13 0.631379
\(957\) 2.28896e13 0.882132
\(958\) −5.33453e12 −0.204622
\(959\) 2.29181e13 0.874975
\(960\) −3.49328e13 −1.32743
\(961\) 8.21881e12 0.310852
\(962\) 8.97598e13 3.37904
\(963\) 1.39441e13 0.522485
\(964\) −6.83275e12 −0.254829
\(965\) 2.52358e13 0.936795
\(966\) −1.61758e13 −0.597680
\(967\) −2.35370e12 −0.0865628 −0.0432814 0.999063i \(-0.513781\pi\)
−0.0432814 + 0.999063i \(0.513781\pi\)
\(968\) 5.15673e11 0.0188771
\(969\) −1.43614e13 −0.523285
\(970\) −6.78242e13 −2.45987
\(971\) −1.42028e13 −0.512730 −0.256365 0.966580i \(-0.582525\pi\)
−0.256365 + 0.966580i \(0.582525\pi\)
\(972\) −3.30638e12 −0.118810
\(973\) 2.59963e12 0.0929829
\(974\) −4.55751e13 −1.62260
\(975\) −5.62827e13 −1.99459
\(976\) −2.35866e13 −0.832033
\(977\) 1.07523e13 0.377552 0.188776 0.982020i \(-0.439548\pi\)
0.188776 + 0.982020i \(0.439548\pi\)
\(978\) 3.29227e13 1.15072
\(979\) 1.76655e13 0.614617
\(980\) 4.37780e13 1.51614
\(981\) 1.45766e13 0.502510
\(982\) −1.51998e12 −0.0521597
\(983\) 2.17285e13 0.742232 0.371116 0.928587i \(-0.378975\pi\)
0.371116 + 0.928587i \(0.378975\pi\)
\(984\) 4.24134e13 1.44220
\(985\) −8.26558e13 −2.79776
\(986\) −7.56918e13 −2.55037
\(987\) 4.15713e12 0.139433
\(988\) 9.50970e13 3.17512
\(989\) −1.81061e13 −0.601787
\(990\) −2.85854e13 −0.945772
\(991\) 1.05544e13 0.347618 0.173809 0.984779i \(-0.444392\pi\)
0.173809 + 0.984779i \(0.444392\pi\)
\(992\) 1.61575e13 0.529752
\(993\) 1.21038e13 0.395047
\(994\) 1.78694e13 0.580592
\(995\) −5.35021e13 −1.73048
\(996\) −3.30748e13 −1.06495
\(997\) −1.35344e13 −0.433822 −0.216911 0.976191i \(-0.569598\pi\)
−0.216911 + 0.976191i \(0.569598\pi\)
\(998\) 6.15480e13 1.96393
\(999\) 6.52698e12 0.207333
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.1.2 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.2 22 1.1 even 1 trivial