Properties

Label 1.74.a.a.1.1
Level 1
Weight 74
Character 1.1
Self dual yes
Analytic conductor 33.748
Analytic rank 1
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 74 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.7483973737\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 10073499617947743056 x^{3} + 1429272143092482488433869600 x^{2} + 7661214288514935343595600445215756800 x + 1722510836040319301450745177697157900206688000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.93794e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.59439e11 q^{2} +2.55219e16 q^{3} +1.59761e22 q^{4} +2.70839e25 q^{5} -4.06919e27 q^{6} -5.83802e30 q^{7} -1.04135e33 q^{8} -6.69338e34 q^{9} +O(q^{10})\) \(q-1.59439e11 q^{2} +2.55219e16 q^{3} +1.59761e22 q^{4} +2.70839e25 q^{5} -4.06919e27 q^{6} -5.83802e30 q^{7} -1.04135e33 q^{8} -6.69338e34 q^{9} -4.31824e36 q^{10} +1.33163e38 q^{11} +4.07740e38 q^{12} -6.53481e40 q^{13} +9.30808e41 q^{14} +6.91234e41 q^{15} +1.51423e43 q^{16} +1.34700e45 q^{17} +1.06719e46 q^{18} +4.71630e46 q^{19} +4.32695e47 q^{20} -1.48997e47 q^{21} -2.12314e49 q^{22} -7.28068e48 q^{23} -2.65773e49 q^{24} -3.25252e50 q^{25} +1.04190e52 q^{26} -3.43318e51 q^{27} -9.32686e52 q^{28} -1.30886e53 q^{29} -1.10210e53 q^{30} -6.62177e53 q^{31} +7.42102e54 q^{32} +3.39858e54 q^{33} -2.14764e56 q^{34} -1.58116e56 q^{35} -1.06934e57 q^{36} +1.59006e57 q^{37} -7.51962e57 q^{38} -1.66781e57 q^{39} -2.82039e58 q^{40} -1.09204e59 q^{41} +2.37560e58 q^{42} +6.52415e59 q^{43} +2.12743e60 q^{44} -1.81283e60 q^{45} +1.16082e60 q^{46} +6.06379e60 q^{47} +3.86459e59 q^{48} -1.51393e61 q^{49} +5.18579e61 q^{50} +3.43780e61 q^{51} -1.04401e63 q^{52} -1.02494e63 q^{53} +5.47383e62 q^{54} +3.60659e63 q^{55} +6.07943e63 q^{56} +1.20369e63 q^{57} +2.08683e64 q^{58} -2.47662e64 q^{59} +1.10432e64 q^{60} -8.75008e64 q^{61} +1.05577e65 q^{62} +3.90761e65 q^{63} -1.32621e66 q^{64} -1.76988e66 q^{65} -5.41867e65 q^{66} -2.58164e66 q^{67} +2.15197e67 q^{68} -1.85817e65 q^{69} +2.52099e67 q^{70} -4.91723e67 q^{71} +6.97016e67 q^{72} -1.02422e68 q^{73} -2.53517e68 q^{74} -8.30105e66 q^{75} +7.53479e68 q^{76} -7.77410e68 q^{77} +2.65914e68 q^{78} -2.22461e69 q^{79} +4.10112e68 q^{80} +4.43611e69 q^{81} +1.74113e70 q^{82} -1.44102e70 q^{83} -2.38039e69 q^{84} +3.64820e70 q^{85} -1.04020e71 q^{86} -3.34045e69 q^{87} -1.38670e71 q^{88} +3.70525e70 q^{89} +2.89036e71 q^{90} +3.81503e71 q^{91} -1.16317e71 q^{92} -1.69000e70 q^{93} -9.66804e71 q^{94} +1.27736e72 q^{95} +1.89399e71 q^{96} +3.38939e71 q^{97} +2.41379e72 q^{98} -8.91313e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} + O(q^{10}) \) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} - \)\(10\!\cdots\!00\)\(q^{10} + \)\(50\!\cdots\!60\)\(q^{11} + \)\(13\!\cdots\!92\)\(q^{12} + \)\(47\!\cdots\!86\)\(q^{13} + \)\(26\!\cdots\!20\)\(q^{14} - \)\(50\!\cdots\!00\)\(q^{15} + \)\(57\!\cdots\!80\)\(q^{16} + \)\(66\!\cdots\!02\)\(q^{17} + \)\(69\!\cdots\!16\)\(q^{18} + \)\(31\!\cdots\!00\)\(q^{19} + \)\(68\!\cdots\!00\)\(q^{20} + \)\(87\!\cdots\!60\)\(q^{21} - \)\(94\!\cdots\!16\)\(q^{22} - \)\(41\!\cdots\!24\)\(q^{23} + \)\(16\!\cdots\!00\)\(q^{24} + \)\(32\!\cdots\!75\)\(q^{25} + \)\(44\!\cdots\!60\)\(q^{26} - \)\(12\!\cdots\!80\)\(q^{27} - \)\(37\!\cdots\!16\)\(q^{28} - \)\(21\!\cdots\!50\)\(q^{29} - \)\(80\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!40\)\(q^{31} - \)\(94\!\cdots\!68\)\(q^{32} - \)\(73\!\cdots\!28\)\(q^{33} - \)\(32\!\cdots\!80\)\(q^{34} - \)\(10\!\cdots\!00\)\(q^{35} - \)\(34\!\cdots\!20\)\(q^{36} - \)\(67\!\cdots\!78\)\(q^{37} - \)\(20\!\cdots\!20\)\(q^{38} - \)\(53\!\cdots\!20\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(89\!\cdots\!90\)\(q^{41} + \)\(15\!\cdots\!84\)\(q^{42} + \)\(11\!\cdots\!56\)\(q^{43} + \)\(36\!\cdots\!20\)\(q^{44} + \)\(86\!\cdots\!50\)\(q^{45} + \)\(13\!\cdots\!60\)\(q^{46} + \)\(26\!\cdots\!32\)\(q^{47} - \)\(30\!\cdots\!24\)\(q^{48} - \)\(47\!\cdots\!15\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(66\!\cdots\!40\)\(q^{51} - \)\(18\!\cdots\!28\)\(q^{52} - \)\(22\!\cdots\!54\)\(q^{53} - \)\(98\!\cdots\!00\)\(q^{54} + \)\(52\!\cdots\!00\)\(q^{55} + \)\(17\!\cdots\!00\)\(q^{56} + \)\(39\!\cdots\!40\)\(q^{57} + \)\(63\!\cdots\!20\)\(q^{58} + \)\(49\!\cdots\!00\)\(q^{59} + \)\(91\!\cdots\!00\)\(q^{60} - \)\(20\!\cdots\!90\)\(q^{61} - \)\(45\!\cdots\!96\)\(q^{62} - \)\(14\!\cdots\!44\)\(q^{63} - \)\(26\!\cdots\!40\)\(q^{64} - \)\(22\!\cdots\!00\)\(q^{65} - \)\(79\!\cdots\!80\)\(q^{66} + \)\(17\!\cdots\!52\)\(q^{67} + \)\(25\!\cdots\!04\)\(q^{68} + \)\(43\!\cdots\!80\)\(q^{69} + \)\(60\!\cdots\!00\)\(q^{70} + \)\(29\!\cdots\!60\)\(q^{71} + \)\(59\!\cdots\!60\)\(q^{72} - \)\(23\!\cdots\!74\)\(q^{73} - \)\(38\!\cdots\!80\)\(q^{74} - \)\(78\!\cdots\!00\)\(q^{75} - \)\(40\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!56\)\(q^{77} + \)\(33\!\cdots\!72\)\(q^{78} + \)\(12\!\cdots\!00\)\(q^{79} + \)\(76\!\cdots\!00\)\(q^{80} + \)\(12\!\cdots\!05\)\(q^{81} + \)\(19\!\cdots\!64\)\(q^{82} + \)\(10\!\cdots\!16\)\(q^{83} - \)\(17\!\cdots\!80\)\(q^{84} - \)\(28\!\cdots\!00\)\(q^{85} - \)\(13\!\cdots\!40\)\(q^{86} - \)\(15\!\cdots\!40\)\(q^{87} - \)\(22\!\cdots\!60\)\(q^{88} - \)\(44\!\cdots\!50\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(50\!\cdots\!60\)\(q^{91} + \)\(10\!\cdots\!52\)\(q^{92} + \)\(20\!\cdots\!32\)\(q^{93} + \)\(12\!\cdots\!20\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} - \)\(12\!\cdots\!40\)\(q^{96} - \)\(47\!\cdots\!18\)\(q^{97} - \)\(76\!\cdots\!16\)\(q^{98} - \)\(15\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59439e11 −1.64059 −0.820295 0.571941i \(-0.806191\pi\)
−0.820295 + 0.571941i \(0.806191\pi\)
\(3\) 2.55219e16 0.0981720 0.0490860 0.998795i \(-0.484369\pi\)
0.0490860 + 0.998795i \(0.484369\pi\)
\(4\) 1.59761e22 1.69153
\(5\) 2.70839e25 0.832351 0.416175 0.909284i \(-0.363370\pi\)
0.416175 + 0.909284i \(0.363370\pi\)
\(6\) −4.06919e27 −0.161060
\(7\) −5.83802e30 −0.832122 −0.416061 0.909337i \(-0.636590\pi\)
−0.416061 + 0.909337i \(0.636590\pi\)
\(8\) −1.04135e33 −1.13452
\(9\) −6.69338e34 −0.990362
\(10\) −4.31824e36 −1.36555
\(11\) 1.33163e38 1.29883 0.649414 0.760435i \(-0.275014\pi\)
0.649414 + 0.760435i \(0.275014\pi\)
\(12\) 4.07740e38 0.166061
\(13\) −6.53481e40 −1.43318 −0.716590 0.697495i \(-0.754298\pi\)
−0.716590 + 0.697495i \(0.754298\pi\)
\(14\) 9.30808e41 1.36517
\(15\) 6.91234e41 0.0817135
\(16\) 1.51423e43 0.169750
\(17\) 1.34700e45 1.65189 0.825945 0.563750i \(-0.190642\pi\)
0.825945 + 0.563750i \(0.190642\pi\)
\(18\) 1.06719e46 1.62478
\(19\) 4.71630e46 0.997918 0.498959 0.866626i \(-0.333716\pi\)
0.498959 + 0.866626i \(0.333716\pi\)
\(20\) 4.32695e47 1.40795
\(21\) −1.48997e47 −0.0816911
\(22\) −2.12314e49 −2.13084
\(23\) −7.28068e48 −0.144247 −0.0721234 0.997396i \(-0.522978\pi\)
−0.0721234 + 0.997396i \(0.522978\pi\)
\(24\) −2.65773e49 −0.111378
\(25\) −3.25252e50 −0.307192
\(26\) 1.04190e52 2.35126
\(27\) −3.43318e51 −0.195398
\(28\) −9.32686e52 −1.40756
\(29\) −1.30886e53 −0.548738 −0.274369 0.961624i \(-0.588469\pi\)
−0.274369 + 0.961624i \(0.588469\pi\)
\(30\) −1.10210e53 −0.134058
\(31\) −6.62177e53 −0.243373 −0.121686 0.992569i \(-0.538830\pi\)
−0.121686 + 0.992569i \(0.538830\pi\)
\(32\) 7.42102e54 0.856030
\(33\) 3.39858e54 0.127508
\(34\) −2.14764e56 −2.71007
\(35\) −1.58116e56 −0.692618
\(36\) −1.06934e57 −1.67523
\(37\) 1.59006e57 0.916326 0.458163 0.888868i \(-0.348508\pi\)
0.458163 + 0.888868i \(0.348508\pi\)
\(38\) −7.51962e57 −1.63717
\(39\) −1.66781e57 −0.140698
\(40\) −2.82039e58 −0.944320
\(41\) −1.09204e59 −1.48466 −0.742328 0.670036i \(-0.766278\pi\)
−0.742328 + 0.670036i \(0.766278\pi\)
\(42\) 2.37560e58 0.134021
\(43\) 6.52415e59 1.55928 0.779642 0.626225i \(-0.215401\pi\)
0.779642 + 0.626225i \(0.215401\pi\)
\(44\) 2.12743e60 2.19701
\(45\) −1.81283e60 −0.824329
\(46\) 1.16082e60 0.236650
\(47\) 6.06379e60 0.563861 0.281931 0.959435i \(-0.409025\pi\)
0.281931 + 0.959435i \(0.409025\pi\)
\(48\) 3.86459e59 0.0166647
\(49\) −1.51393e61 −0.307573
\(50\) 5.18579e61 0.503976
\(51\) 3.43780e61 0.162169
\(52\) −1.04401e63 −2.42427
\(53\) −1.02494e63 −1.18749 −0.593745 0.804654i \(-0.702351\pi\)
−0.593745 + 0.804654i \(0.702351\pi\)
\(54\) 5.47383e62 0.320567
\(55\) 3.60659e63 1.08108
\(56\) 6.07943e63 0.944060
\(57\) 1.20369e63 0.0979676
\(58\) 2.08683e64 0.900254
\(59\) −2.47662e64 −0.572481 −0.286241 0.958158i \(-0.592406\pi\)
−0.286241 + 0.958158i \(0.592406\pi\)
\(60\) 1.10432e64 0.138221
\(61\) −8.75008e64 −0.599064 −0.299532 0.954086i \(-0.596831\pi\)
−0.299532 + 0.954086i \(0.596831\pi\)
\(62\) 1.05577e65 0.399275
\(63\) 3.90761e65 0.824102
\(64\) −1.32621e66 −1.57414
\(65\) −1.76988e66 −1.19291
\(66\) −5.41867e65 −0.209189
\(67\) −2.58164e66 −0.575659 −0.287830 0.957682i \(-0.592934\pi\)
−0.287830 + 0.957682i \(0.592934\pi\)
\(68\) 2.15197e67 2.79423
\(69\) −1.85817e65 −0.0141610
\(70\) 2.52099e67 1.13630
\(71\) −4.91723e67 −1.32066 −0.660330 0.750975i \(-0.729584\pi\)
−0.660330 + 0.750975i \(0.729584\pi\)
\(72\) 6.97016e67 1.12359
\(73\) −1.02422e68 −0.997948 −0.498974 0.866617i \(-0.666290\pi\)
−0.498974 + 0.866617i \(0.666290\pi\)
\(74\) −2.53517e68 −1.50332
\(75\) −8.30105e66 −0.0301576
\(76\) 7.53479e68 1.68801
\(77\) −7.77410e68 −1.08078
\(78\) 2.65914e68 0.230828
\(79\) −2.22461e69 −1.21301 −0.606505 0.795080i \(-0.707429\pi\)
−0.606505 + 0.795080i \(0.707429\pi\)
\(80\) 4.10112e68 0.141292
\(81\) 4.43611e69 0.971180
\(82\) 1.74113e70 2.43571
\(83\) −1.44102e70 −1.29515 −0.647575 0.762001i \(-0.724217\pi\)
−0.647575 + 0.762001i \(0.724217\pi\)
\(84\) −2.38039e69 −0.138183
\(85\) 3.64820e70 1.37495
\(86\) −1.04020e71 −2.55815
\(87\) −3.34045e69 −0.0538707
\(88\) −1.38670e71 −1.47355
\(89\) 3.70525e70 0.260664 0.130332 0.991470i \(-0.458396\pi\)
0.130332 + 0.991470i \(0.458396\pi\)
\(90\) 2.89036e71 1.35239
\(91\) 3.81503e71 1.19258
\(92\) −1.16317e71 −0.243998
\(93\) −1.69000e70 −0.0238924
\(94\) −9.66804e71 −0.925064
\(95\) 1.27736e72 0.830618
\(96\) 1.89399e71 0.0840382
\(97\) 3.38939e71 0.103027 0.0515137 0.998672i \(-0.483595\pi\)
0.0515137 + 0.998672i \(0.483595\pi\)
\(98\) 2.41379e72 0.504601
\(99\) −8.91313e72 −1.28631
\(100\) −5.19625e72 −0.519625
\(101\) −6.71007e71 −0.0466656 −0.0233328 0.999728i \(-0.507428\pi\)
−0.0233328 + 0.999728i \(0.507428\pi\)
\(102\) −5.48119e72 −0.266053
\(103\) −2.69369e73 −0.915775 −0.457888 0.889010i \(-0.651394\pi\)
−0.457888 + 0.889010i \(0.651394\pi\)
\(104\) 6.80503e73 1.62597
\(105\) −4.03544e72 −0.0679956
\(106\) 1.63416e74 1.94818
\(107\) 4.79460e73 0.405737 0.202869 0.979206i \(-0.434974\pi\)
0.202869 + 0.979206i \(0.434974\pi\)
\(108\) −5.48488e73 −0.330522
\(109\) −2.34717e74 −1.01036 −0.505182 0.863013i \(-0.668575\pi\)
−0.505182 + 0.863013i \(0.668575\pi\)
\(110\) −5.75031e74 −1.77361
\(111\) 4.05813e73 0.0899576
\(112\) −8.84007e73 −0.141253
\(113\) 1.03352e75 1.19386 0.596931 0.802293i \(-0.296387\pi\)
0.596931 + 0.802293i \(0.296387\pi\)
\(114\) −1.91915e74 −0.160725
\(115\) −1.97189e74 −0.120064
\(116\) −2.09104e75 −0.928209
\(117\) 4.37400e75 1.41937
\(118\) 3.94870e75 0.939207
\(119\) −7.86380e75 −1.37457
\(120\) −7.19817e74 −0.0927057
\(121\) 7.22094e75 0.686954
\(122\) 1.39510e76 0.982818
\(123\) −2.78708e75 −0.145752
\(124\) −1.05790e76 −0.411673
\(125\) −3.74853e76 −1.08804
\(126\) −6.23026e76 −1.35201
\(127\) −6.92602e76 −1.12628 −0.563142 0.826360i \(-0.690408\pi\)
−0.563142 + 0.826360i \(0.690408\pi\)
\(128\) 1.41361e77 1.72649
\(129\) 1.66509e76 0.153078
\(130\) 2.82188e77 1.95707
\(131\) −1.76015e76 −0.0922887 −0.0461444 0.998935i \(-0.514693\pi\)
−0.0461444 + 0.998935i \(0.514693\pi\)
\(132\) 5.42960e76 0.215685
\(133\) −2.75338e77 −0.830389
\(134\) 4.11614e77 0.944420
\(135\) −9.29841e76 −0.162640
\(136\) −1.40270e78 −1.87411
\(137\) −4.61954e77 −0.472387 −0.236193 0.971706i \(-0.575900\pi\)
−0.236193 + 0.971706i \(0.575900\pi\)
\(138\) 2.96265e76 0.0232324
\(139\) 2.47006e78 1.48822 0.744111 0.668056i \(-0.232873\pi\)
0.744111 + 0.668056i \(0.232873\pi\)
\(140\) −2.52608e78 −1.17159
\(141\) 1.54759e77 0.0553554
\(142\) 7.83999e78 2.16666
\(143\) −8.70197e78 −1.86145
\(144\) −1.01353e78 −0.168114
\(145\) −3.54490e78 −0.456743
\(146\) 1.63300e79 1.63722
\(147\) −3.86383e77 −0.0301950
\(148\) 2.54029e79 1.55000
\(149\) −2.10744e79 −1.00567 −0.502835 0.864382i \(-0.667710\pi\)
−0.502835 + 0.864382i \(0.667710\pi\)
\(150\) 1.32351e78 0.0494763
\(151\) −2.80175e79 −0.821808 −0.410904 0.911679i \(-0.634787\pi\)
−0.410904 + 0.911679i \(0.634787\pi\)
\(152\) −4.91132e79 −1.13216
\(153\) −9.01597e79 −1.63597
\(154\) 1.23949e80 1.77312
\(155\) −1.79344e79 −0.202572
\(156\) −2.66450e79 −0.237995
\(157\) 4.31233e79 0.305053 0.152526 0.988299i \(-0.451259\pi\)
0.152526 + 0.988299i \(0.451259\pi\)
\(158\) 3.54689e80 1.99005
\(159\) −2.61585e79 −0.116578
\(160\) 2.00990e80 0.712518
\(161\) 4.25048e79 0.120031
\(162\) −7.07290e80 −1.59331
\(163\) 2.42638e80 0.436628 0.218314 0.975879i \(-0.429944\pi\)
0.218314 + 0.975879i \(0.429944\pi\)
\(164\) −1.74464e81 −2.51135
\(165\) 9.20470e79 0.106132
\(166\) 2.29755e81 2.12481
\(167\) −7.19837e80 −0.534666 −0.267333 0.963604i \(-0.586142\pi\)
−0.267333 + 0.963604i \(0.586142\pi\)
\(168\) 1.55159e80 0.0926802
\(169\) 2.19132e81 1.05400
\(170\) −5.81666e81 −2.25573
\(171\) −3.15680e81 −0.988300
\(172\) 1.04230e82 2.63758
\(173\) −7.61563e80 −0.155963 −0.0779817 0.996955i \(-0.524848\pi\)
−0.0779817 + 0.996955i \(0.524848\pi\)
\(174\) 5.32599e80 0.0883797
\(175\) 1.89883e81 0.255621
\(176\) 2.01639e81 0.220477
\(177\) −6.32082e80 −0.0562016
\(178\) −5.90761e81 −0.427643
\(179\) 2.45288e82 1.44724 0.723621 0.690197i \(-0.242476\pi\)
0.723621 + 0.690197i \(0.242476\pi\)
\(180\) −2.89619e82 −1.39438
\(181\) −1.01305e82 −0.398442 −0.199221 0.979955i \(-0.563841\pi\)
−0.199221 + 0.979955i \(0.563841\pi\)
\(182\) −6.08265e82 −1.95653
\(183\) −2.23319e81 −0.0588113
\(184\) 7.58174e81 0.163651
\(185\) 4.30650e82 0.762705
\(186\) 2.69452e81 0.0391976
\(187\) 1.79371e83 2.14552
\(188\) 9.68755e82 0.953790
\(189\) 2.00430e82 0.162595
\(190\) −2.03661e83 −1.36270
\(191\) −1.22649e83 −0.677559 −0.338780 0.940866i \(-0.610014\pi\)
−0.338780 + 0.940866i \(0.610014\pi\)
\(192\) −3.38475e82 −0.154537
\(193\) −2.37981e82 −0.0898876 −0.0449438 0.998990i \(-0.514311\pi\)
−0.0449438 + 0.998990i \(0.514311\pi\)
\(194\) −5.40401e82 −0.169026
\(195\) −4.51708e82 −0.117110
\(196\) −2.41866e83 −0.520270
\(197\) −1.97247e83 −0.352366 −0.176183 0.984357i \(-0.556375\pi\)
−0.176183 + 0.984357i \(0.556375\pi\)
\(198\) 1.42110e84 2.11031
\(199\) −1.25645e84 −1.55241 −0.776206 0.630480i \(-0.782858\pi\)
−0.776206 + 0.630480i \(0.782858\pi\)
\(200\) 3.38702e83 0.348516
\(201\) −6.58884e82 −0.0565136
\(202\) 1.06985e83 0.0765591
\(203\) 7.64113e83 0.456617
\(204\) 5.49225e83 0.274315
\(205\) −2.95766e84 −1.23576
\(206\) 4.29479e84 1.50241
\(207\) 4.87324e83 0.142857
\(208\) −9.89517e83 −0.243283
\(209\) 6.28038e84 1.29612
\(210\) 6.43406e83 0.111553
\(211\) −1.14628e85 −1.67101 −0.835505 0.549482i \(-0.814825\pi\)
−0.835505 + 0.549482i \(0.814825\pi\)
\(212\) −1.63745e85 −2.00868
\(213\) −1.25497e84 −0.129652
\(214\) −7.64447e84 −0.665648
\(215\) 1.76700e85 1.29787
\(216\) 3.57515e84 0.221683
\(217\) 3.86580e84 0.202516
\(218\) 3.74231e85 1.65759
\(219\) −2.61400e84 −0.0979706
\(220\) 5.76191e85 1.82868
\(221\) −8.80238e85 −2.36746
\(222\) −6.47025e84 −0.147583
\(223\) 6.90864e85 1.33741 0.668705 0.743527i \(-0.266849\pi\)
0.668705 + 0.743527i \(0.266849\pi\)
\(224\) −4.33240e85 −0.712322
\(225\) 2.17704e85 0.304231
\(226\) −1.64783e86 −1.95864
\(227\) −1.09495e86 −1.10777 −0.553885 0.832593i \(-0.686855\pi\)
−0.553885 + 0.832593i \(0.686855\pi\)
\(228\) 1.92302e85 0.165715
\(229\) 2.05799e86 1.51164 0.755819 0.654781i \(-0.227239\pi\)
0.755819 + 0.654781i \(0.227239\pi\)
\(230\) 3.14397e85 0.196976
\(231\) −1.98410e85 −0.106103
\(232\) 1.36298e86 0.622555
\(233\) 3.11195e86 1.21490 0.607451 0.794358i \(-0.292192\pi\)
0.607451 + 0.794358i \(0.292192\pi\)
\(234\) −6.97386e86 −2.32860
\(235\) 1.64231e86 0.469330
\(236\) −3.95667e86 −0.968371
\(237\) −5.67762e85 −0.119084
\(238\) 1.25380e87 2.25511
\(239\) 5.50425e86 0.849522 0.424761 0.905305i \(-0.360358\pi\)
0.424761 + 0.905305i \(0.360358\pi\)
\(240\) 1.04668e85 0.0138709
\(241\) −3.36564e86 −0.383218 −0.191609 0.981471i \(-0.561371\pi\)
−0.191609 + 0.981471i \(0.561371\pi\)
\(242\) −1.15130e87 −1.12701
\(243\) 3.45251e86 0.290740
\(244\) −1.39792e87 −1.01334
\(245\) −4.10031e86 −0.256009
\(246\) 4.44370e86 0.239119
\(247\) −3.08201e87 −1.43020
\(248\) 6.89559e86 0.276112
\(249\) −3.67777e86 −0.127148
\(250\) 5.97662e87 1.78503
\(251\) −2.95049e87 −0.761735 −0.380867 0.924630i \(-0.624375\pi\)
−0.380867 + 0.924630i \(0.624375\pi\)
\(252\) 6.24283e87 1.39400
\(253\) −9.69520e86 −0.187352
\(254\) 1.10428e88 1.84777
\(255\) 9.31091e86 0.134982
\(256\) −1.00127e88 −1.25832
\(257\) −3.50489e87 −0.382046 −0.191023 0.981586i \(-0.561181\pi\)
−0.191023 + 0.981586i \(0.561181\pi\)
\(258\) −2.65480e87 −0.251138
\(259\) −9.28279e87 −0.762495
\(260\) −2.82758e88 −2.01784
\(261\) 8.76068e87 0.543450
\(262\) 2.80637e87 0.151408
\(263\) 3.88636e88 1.82456 0.912279 0.409569i \(-0.134321\pi\)
0.912279 + 0.409569i \(0.134321\pi\)
\(264\) −3.53912e87 −0.144661
\(265\) −2.77594e88 −0.988408
\(266\) 4.38997e88 1.36233
\(267\) 9.45650e86 0.0255899
\(268\) −4.12445e88 −0.973746
\(269\) 9.19679e87 0.189530 0.0947650 0.995500i \(-0.469790\pi\)
0.0947650 + 0.995500i \(0.469790\pi\)
\(270\) 1.48253e88 0.266825
\(271\) −4.14063e87 −0.0651159 −0.0325580 0.999470i \(-0.510365\pi\)
−0.0325580 + 0.999470i \(0.510365\pi\)
\(272\) 2.03966e88 0.280409
\(273\) 9.73670e87 0.117078
\(274\) 7.36535e88 0.774993
\(275\) −4.33116e88 −0.398989
\(276\) −2.96863e87 −0.0239538
\(277\) 1.14938e89 0.812737 0.406369 0.913709i \(-0.366795\pi\)
0.406369 + 0.913709i \(0.366795\pi\)
\(278\) −3.93825e89 −2.44156
\(279\) 4.43220e88 0.241027
\(280\) 1.64655e89 0.785789
\(281\) −4.90170e88 −0.205384 −0.102692 0.994713i \(-0.532746\pi\)
−0.102692 + 0.994713i \(0.532746\pi\)
\(282\) −2.46747e88 −0.0908154
\(283\) −2.46352e89 −0.796805 −0.398402 0.917211i \(-0.630435\pi\)
−0.398402 + 0.917211i \(0.630435\pi\)
\(284\) −7.85581e89 −2.23394
\(285\) 3.26006e88 0.0815434
\(286\) 1.38743e90 3.05388
\(287\) 6.37532e89 1.23542
\(288\) −4.96717e89 −0.847780
\(289\) 1.14948e90 1.72874
\(290\) 5.65195e89 0.749328
\(291\) 8.65037e87 0.0101144
\(292\) −1.63630e90 −1.68806
\(293\) −1.49279e90 −1.35935 −0.679675 0.733514i \(-0.737879\pi\)
−0.679675 + 0.733514i \(0.737879\pi\)
\(294\) 6.16046e88 0.0495376
\(295\) −6.70767e89 −0.476506
\(296\) −1.65581e90 −1.03959
\(297\) −4.57174e89 −0.253788
\(298\) 3.36008e90 1.64989
\(299\) 4.75779e89 0.206731
\(300\) −1.32618e89 −0.0510126
\(301\) −3.80881e90 −1.29751
\(302\) 4.46708e90 1.34825
\(303\) −1.71254e88 −0.00458125
\(304\) 7.14154e89 0.169397
\(305\) −2.36987e90 −0.498631
\(306\) 1.43750e91 2.68396
\(307\) −3.33315e90 −0.552464 −0.276232 0.961091i \(-0.589086\pi\)
−0.276232 + 0.961091i \(0.589086\pi\)
\(308\) −1.24200e91 −1.82818
\(309\) −6.87481e89 −0.0899035
\(310\) 2.85944e90 0.332337
\(311\) −7.99091e90 −0.825738 −0.412869 0.910791i \(-0.635473\pi\)
−0.412869 + 0.910791i \(0.635473\pi\)
\(312\) 1.73677e90 0.159625
\(313\) 2.38998e91 1.95445 0.977227 0.212197i \(-0.0680620\pi\)
0.977227 + 0.212197i \(0.0680620\pi\)
\(314\) −6.87555e90 −0.500466
\(315\) 1.05833e91 0.685942
\(316\) −3.55405e91 −2.05185
\(317\) 3.26000e90 0.167708 0.0838542 0.996478i \(-0.473277\pi\)
0.0838542 + 0.996478i \(0.473277\pi\)
\(318\) 4.17068e90 0.191257
\(319\) −1.74292e91 −0.712717
\(320\) −3.59191e91 −1.31024
\(321\) 1.22367e90 0.0398320
\(322\) −6.77692e90 −0.196921
\(323\) 6.35284e91 1.64845
\(324\) 7.08717e91 1.64278
\(325\) 2.12546e91 0.440261
\(326\) −3.86860e91 −0.716328
\(327\) −5.99043e90 −0.0991894
\(328\) 1.13719e92 1.68437
\(329\) −3.54005e91 −0.469201
\(330\) −1.46759e91 −0.174119
\(331\) −8.71306e90 −0.0925654 −0.0462827 0.998928i \(-0.514738\pi\)
−0.0462827 + 0.998928i \(0.514738\pi\)
\(332\) −2.30219e92 −2.19079
\(333\) −1.06429e92 −0.907495
\(334\) 1.14770e92 0.877168
\(335\) −6.99210e91 −0.479150
\(336\) −2.25616e90 −0.0138671
\(337\) 9.82568e91 0.541840 0.270920 0.962602i \(-0.412672\pi\)
0.270920 + 0.962602i \(0.412672\pi\)
\(338\) −3.49383e92 −1.72919
\(339\) 2.63773e91 0.117204
\(340\) 5.82839e92 2.32578
\(341\) −8.81777e91 −0.316099
\(342\) 5.03317e92 1.62139
\(343\) 3.75741e92 1.08806
\(344\) −6.79393e92 −1.76904
\(345\) −5.03265e90 −0.0117869
\(346\) 1.21423e92 0.255872
\(347\) −5.42783e92 −1.02944 −0.514719 0.857359i \(-0.672104\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(348\) −5.33674e91 −0.0911241
\(349\) −1.13207e92 −0.174079 −0.0870395 0.996205i \(-0.527741\pi\)
−0.0870395 + 0.996205i \(0.527741\pi\)
\(350\) −3.02747e92 −0.419369
\(351\) 2.24352e92 0.280040
\(352\) 9.88207e92 1.11184
\(353\) 2.43382e92 0.246895 0.123447 0.992351i \(-0.460605\pi\)
0.123447 + 0.992351i \(0.460605\pi\)
\(354\) 1.00778e92 0.0922038
\(355\) −1.33178e93 −1.09925
\(356\) 5.91953e92 0.440922
\(357\) −2.00699e92 −0.134945
\(358\) −3.91085e93 −2.37433
\(359\) 1.41112e92 0.0773776 0.0386888 0.999251i \(-0.487682\pi\)
0.0386888 + 0.999251i \(0.487682\pi\)
\(360\) 1.88779e93 0.935219
\(361\) −9.29175e90 −0.00415991
\(362\) 1.61520e93 0.653679
\(363\) 1.84292e92 0.0674396
\(364\) 6.09493e93 2.01729
\(365\) −2.77399e93 −0.830643
\(366\) 3.56057e92 0.0964851
\(367\) −1.09116e93 −0.267656 −0.133828 0.991005i \(-0.542727\pi\)
−0.133828 + 0.991005i \(0.542727\pi\)
\(368\) −1.10246e92 −0.0244860
\(369\) 7.30941e93 1.47035
\(370\) −6.86625e93 −1.25129
\(371\) 5.98363e93 0.988136
\(372\) −2.69996e92 −0.0404148
\(373\) −1.92037e93 −0.260623 −0.130311 0.991473i \(-0.541598\pi\)
−0.130311 + 0.991473i \(0.541598\pi\)
\(374\) −2.85987e94 −3.51992
\(375\) −9.56697e92 −0.106815
\(376\) −6.31453e93 −0.639712
\(377\) 8.55313e93 0.786441
\(378\) −3.19564e93 −0.266751
\(379\) 1.21975e94 0.924567 0.462283 0.886732i \(-0.347030\pi\)
0.462283 + 0.886732i \(0.347030\pi\)
\(380\) 2.04072e94 1.40502
\(381\) −1.76765e93 −0.110570
\(382\) 1.95551e94 1.11160
\(383\) 1.64774e94 0.851400 0.425700 0.904864i \(-0.360028\pi\)
0.425700 + 0.904864i \(0.360028\pi\)
\(384\) 3.60780e93 0.169493
\(385\) −2.10553e94 −0.899591
\(386\) 3.79434e93 0.147469
\(387\) −4.36686e94 −1.54426
\(388\) 5.41491e93 0.174274
\(389\) −1.57842e93 −0.0462447 −0.0231223 0.999733i \(-0.507361\pi\)
−0.0231223 + 0.999733i \(0.507361\pi\)
\(390\) 7.20199e93 0.192130
\(391\) −9.80706e93 −0.238280
\(392\) 1.57653e94 0.348948
\(393\) −4.49225e92 −0.00906016
\(394\) 3.14489e94 0.578087
\(395\) −6.02511e94 −1.00965
\(396\) −1.42397e95 −2.17584
\(397\) 4.97423e94 0.693223 0.346611 0.938009i \(-0.387332\pi\)
0.346611 + 0.938009i \(0.387332\pi\)
\(398\) 2.00327e95 2.54687
\(399\) −7.02716e93 −0.0815210
\(400\) −4.92505e93 −0.0521460
\(401\) −1.84398e95 −1.78233 −0.891163 0.453682i \(-0.850110\pi\)
−0.891163 + 0.453682i \(0.850110\pi\)
\(402\) 1.05052e94 0.0927156
\(403\) 4.32720e94 0.348797
\(404\) −1.07201e94 −0.0789364
\(405\) 1.20147e95 0.808362
\(406\) −1.21830e95 −0.749121
\(407\) 2.11737e95 1.19015
\(408\) −3.57995e94 −0.183985
\(409\) 3.46318e94 0.162770 0.0813850 0.996683i \(-0.474066\pi\)
0.0813850 + 0.996683i \(0.474066\pi\)
\(410\) 4.71567e95 2.02737
\(411\) −1.17899e94 −0.0463751
\(412\) −4.30346e95 −1.54906
\(413\) 1.44586e95 0.476374
\(414\) −7.76984e94 −0.234369
\(415\) −3.90285e95 −1.07802
\(416\) −4.84949e95 −1.22685
\(417\) 6.30408e94 0.146102
\(418\) −1.00134e96 −2.12641
\(419\) 4.03746e95 0.785772 0.392886 0.919587i \(-0.371477\pi\)
0.392886 + 0.919587i \(0.371477\pi\)
\(420\) −6.44704e94 −0.115017
\(421\) 7.10860e94 0.116275 0.0581377 0.998309i \(-0.481484\pi\)
0.0581377 + 0.998309i \(0.481484\pi\)
\(422\) 1.82761e96 2.74144
\(423\) −4.05873e95 −0.558427
\(424\) 1.06732e96 1.34723
\(425\) −4.38114e95 −0.507447
\(426\) 2.00092e95 0.212705
\(427\) 5.10831e95 0.498494
\(428\) 7.65989e95 0.686318
\(429\) −2.22091e95 −0.182743
\(430\) −2.81728e96 −2.12927
\(431\) 8.97999e95 0.623528 0.311764 0.950160i \(-0.399080\pi\)
0.311764 + 0.950160i \(0.399080\pi\)
\(432\) −5.19861e94 −0.0331689
\(433\) 5.49073e95 0.321975 0.160987 0.986956i \(-0.448532\pi\)
0.160987 + 0.986956i \(0.448532\pi\)
\(434\) −6.16360e95 −0.332245
\(435\) −9.04726e94 −0.0448394
\(436\) −3.74986e96 −1.70906
\(437\) −3.43379e95 −0.143946
\(438\) 4.16774e95 0.160729
\(439\) 2.02667e96 0.719165 0.359583 0.933113i \(-0.382919\pi\)
0.359583 + 0.933113i \(0.382919\pi\)
\(440\) −3.75572e96 −1.22651
\(441\) 1.01333e96 0.304609
\(442\) 1.40344e97 3.88402
\(443\) −6.68470e96 −1.70351 −0.851757 0.523937i \(-0.824463\pi\)
−0.851757 + 0.523937i \(0.824463\pi\)
\(444\) 6.48331e95 0.152166
\(445\) 1.00353e96 0.216964
\(446\) −1.10151e97 −2.19414
\(447\) −5.37858e95 −0.0987287
\(448\) 7.74246e96 1.30988
\(449\) 4.18030e96 0.651953 0.325976 0.945378i \(-0.394307\pi\)
0.325976 + 0.945378i \(0.394307\pi\)
\(450\) −3.47105e96 −0.499118
\(451\) −1.45419e97 −1.92831
\(452\) 1.65115e97 2.01946
\(453\) −7.15059e95 −0.0806785
\(454\) 1.74577e97 1.81740
\(455\) 1.03326e97 0.992645
\(456\) −1.25346e96 −0.111146
\(457\) −1.11555e97 −0.913162 −0.456581 0.889682i \(-0.650926\pi\)
−0.456581 + 0.889682i \(0.650926\pi\)
\(458\) −3.28124e97 −2.47998
\(459\) −4.62449e96 −0.322776
\(460\) −3.15031e96 −0.203092
\(461\) −2.25234e97 −1.34137 −0.670687 0.741740i \(-0.734001\pi\)
−0.670687 + 0.741740i \(0.734001\pi\)
\(462\) 3.16343e96 0.174071
\(463\) 3.51982e97 1.78984 0.894919 0.446228i \(-0.147233\pi\)
0.894919 + 0.446228i \(0.147233\pi\)
\(464\) −1.98190e96 −0.0931486
\(465\) −4.57719e95 −0.0198869
\(466\) −4.96166e97 −1.99315
\(467\) 1.56243e97 0.580410 0.290205 0.956965i \(-0.406277\pi\)
0.290205 + 0.956965i \(0.406277\pi\)
\(468\) 6.98793e97 2.40091
\(469\) 1.50717e97 0.479019
\(470\) −2.61849e97 −0.769978
\(471\) 1.10059e96 0.0299476
\(472\) 2.57903e97 0.649492
\(473\) 8.68777e97 2.02524
\(474\) 9.05235e96 0.195367
\(475\) −1.53399e97 −0.306552
\(476\) −1.25633e98 −2.32514
\(477\) 6.86032e97 1.17604
\(478\) −8.77592e97 −1.39372
\(479\) −9.54291e97 −1.40422 −0.702109 0.712069i \(-0.747758\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(480\) 5.12966e96 0.0699493
\(481\) −1.03907e98 −1.31326
\(482\) 5.36615e97 0.628704
\(483\) 1.08480e96 0.0117837
\(484\) 1.15362e98 1.16200
\(485\) 9.17979e96 0.0857550
\(486\) −5.50464e97 −0.476986
\(487\) 1.64586e98 1.32308 0.661539 0.749911i \(-0.269904\pi\)
0.661539 + 0.749911i \(0.269904\pi\)
\(488\) 9.11191e97 0.679651
\(489\) 6.19260e96 0.0428647
\(490\) 6.53749e97 0.420005
\(491\) −2.78063e98 −1.65832 −0.829159 0.559012i \(-0.811180\pi\)
−0.829159 + 0.559012i \(0.811180\pi\)
\(492\) −4.45267e97 −0.246544
\(493\) −1.76303e98 −0.906456
\(494\) 4.91393e98 2.34636
\(495\) −2.41403e98 −1.07066
\(496\) −1.00268e97 −0.0413127
\(497\) 2.87069e98 1.09895
\(498\) 5.86379e97 0.208597
\(499\) 1.33205e98 0.440404 0.220202 0.975454i \(-0.429328\pi\)
0.220202 + 0.975454i \(0.429328\pi\)
\(500\) −5.98868e98 −1.84046
\(501\) −1.83716e97 −0.0524892
\(502\) 4.70424e98 1.24969
\(503\) 8.13928e96 0.0201073 0.0100537 0.999949i \(-0.496800\pi\)
0.0100537 + 0.999949i \(0.496800\pi\)
\(504\) −4.06919e98 −0.934962
\(505\) −1.81735e97 −0.0388422
\(506\) 1.54579e98 0.307367
\(507\) 5.59268e97 0.103474
\(508\) −1.10651e99 −1.90515
\(509\) −1.29772e98 −0.207961 −0.103981 0.994579i \(-0.533158\pi\)
−0.103981 + 0.994579i \(0.533158\pi\)
\(510\) −1.48452e98 −0.221450
\(511\) 5.97941e98 0.830415
\(512\) 2.61299e98 0.337897
\(513\) −1.61919e98 −0.194991
\(514\) 5.58817e98 0.626781
\(515\) −7.29557e98 −0.762247
\(516\) 2.66016e98 0.258936
\(517\) 8.07474e98 0.732358
\(518\) 1.48004e99 1.25094
\(519\) −1.94365e97 −0.0153112
\(520\) 1.84307e99 1.35338
\(521\) 1.96905e99 1.34797 0.673984 0.738746i \(-0.264582\pi\)
0.673984 + 0.738746i \(0.264582\pi\)
\(522\) −1.39679e99 −0.891578
\(523\) −2.52411e99 −1.50244 −0.751220 0.660052i \(-0.770534\pi\)
−0.751220 + 0.660052i \(0.770534\pi\)
\(524\) −2.81204e98 −0.156109
\(525\) 4.84617e97 0.0250948
\(526\) −6.19637e99 −2.99335
\(527\) −8.91951e98 −0.402025
\(528\) 5.14622e97 0.0216446
\(529\) −2.49460e99 −0.979193
\(530\) 4.42594e99 1.62157
\(531\) 1.65770e99 0.566964
\(532\) −4.39883e99 −1.40463
\(533\) 7.13624e99 2.12778
\(534\) −1.50774e98 −0.0419826
\(535\) 1.29857e99 0.337716
\(536\) 2.68839e99 0.653098
\(537\) 6.26023e98 0.142079
\(538\) −1.46633e99 −0.310941
\(539\) −2.01600e99 −0.399484
\(540\) −1.48552e99 −0.275110
\(541\) 2.76758e99 0.479071 0.239536 0.970888i \(-0.423005\pi\)
0.239536 + 0.970888i \(0.423005\pi\)
\(542\) 6.60178e98 0.106828
\(543\) −2.58551e98 −0.0391158
\(544\) 9.99610e99 1.41407
\(545\) −6.35706e99 −0.840977
\(546\) −1.55241e99 −0.192077
\(547\) −1.06027e100 −1.22710 −0.613549 0.789657i \(-0.710259\pi\)
−0.613549 + 0.789657i \(0.710259\pi\)
\(548\) −7.38021e99 −0.799058
\(549\) 5.85676e99 0.593290
\(550\) 6.90557e99 0.654578
\(551\) −6.17296e99 −0.547596
\(552\) 1.93501e98 0.0160659
\(553\) 1.29873e100 1.00937
\(554\) −1.83255e100 −1.33337
\(555\) 1.09910e99 0.0748763
\(556\) 3.94619e100 2.51738
\(557\) −2.06065e100 −1.23109 −0.615544 0.788102i \(-0.711064\pi\)
−0.615544 + 0.788102i \(0.711064\pi\)
\(558\) −7.06666e99 −0.395427
\(559\) −4.26341e100 −2.23473
\(560\) −2.39424e99 −0.117572
\(561\) 4.57788e99 0.210630
\(562\) 7.81523e99 0.336951
\(563\) 1.21330e100 0.490245 0.245122 0.969492i \(-0.421172\pi\)
0.245122 + 0.969492i \(0.421172\pi\)
\(564\) 2.47245e99 0.0936354
\(565\) 2.79917e100 0.993711
\(566\) 3.92782e100 1.30723
\(567\) −2.58981e100 −0.808140
\(568\) 5.12057e100 1.49832
\(569\) 4.59237e100 1.26020 0.630100 0.776514i \(-0.283014\pi\)
0.630100 + 0.776514i \(0.283014\pi\)
\(570\) −5.19782e99 −0.133779
\(571\) 1.78384e100 0.430664 0.215332 0.976541i \(-0.430917\pi\)
0.215332 + 0.976541i \(0.430917\pi\)
\(572\) −1.39023e101 −3.14871
\(573\) −3.13025e99 −0.0665173
\(574\) −1.01648e101 −2.02681
\(575\) 2.36806e99 0.0443114
\(576\) 8.87686e100 1.55897
\(577\) 8.01529e100 1.32130 0.660651 0.750693i \(-0.270280\pi\)
0.660651 + 0.750693i \(0.270280\pi\)
\(578\) −1.83272e101 −2.83616
\(579\) −6.07372e98 −0.00882444
\(580\) −5.66336e100 −0.772596
\(581\) 8.41272e100 1.07772
\(582\) −1.37921e99 −0.0165936
\(583\) −1.36485e101 −1.54234
\(584\) 1.06657e101 1.13219
\(585\) 1.18465e101 1.18141
\(586\) 2.38009e101 2.23013
\(587\) −7.04852e100 −0.620594 −0.310297 0.950640i \(-0.600428\pi\)
−0.310297 + 0.950640i \(0.600428\pi\)
\(588\) −6.17289e99 −0.0510759
\(589\) −3.12302e100 −0.242866
\(590\) 1.06946e101 0.781750
\(591\) −5.03413e99 −0.0345924
\(592\) 2.40771e100 0.155547
\(593\) 9.98127e99 0.0606303 0.0303151 0.999540i \(-0.490349\pi\)
0.0303151 + 0.999540i \(0.490349\pi\)
\(594\) 7.28914e100 0.416362
\(595\) −2.12983e101 −1.14413
\(596\) −3.36686e101 −1.70113
\(597\) −3.20669e100 −0.152403
\(598\) −7.58577e100 −0.339161
\(599\) −1.09544e101 −0.460799 −0.230399 0.973096i \(-0.574003\pi\)
−0.230399 + 0.973096i \(0.574003\pi\)
\(600\) 8.64431e99 0.0342145
\(601\) 1.50406e100 0.0560205 0.0280103 0.999608i \(-0.491083\pi\)
0.0280103 + 0.999608i \(0.491083\pi\)
\(602\) 6.07273e101 2.12869
\(603\) 1.72799e101 0.570111
\(604\) −4.47609e101 −1.39011
\(605\) 1.95571e101 0.571787
\(606\) 2.73046e99 0.00751596
\(607\) −5.22503e101 −1.35426 −0.677129 0.735864i \(-0.736776\pi\)
−0.677129 + 0.735864i \(0.736776\pi\)
\(608\) 3.49997e101 0.854248
\(609\) 1.95016e100 0.0448270
\(610\) 3.77849e101 0.818049
\(611\) −3.96257e101 −0.808114
\(612\) −1.44040e102 −2.76730
\(613\) 7.48452e101 1.35474 0.677371 0.735641i \(-0.263119\pi\)
0.677371 + 0.735641i \(0.263119\pi\)
\(614\) 5.31434e101 0.906367
\(615\) −7.54852e100 −0.121317
\(616\) 8.09557e101 1.22617
\(617\) 6.91230e101 0.986765 0.493383 0.869812i \(-0.335760\pi\)
0.493383 + 0.869812i \(0.335760\pi\)
\(618\) 1.09611e101 0.147495
\(619\) −3.46069e101 −0.438989 −0.219495 0.975614i \(-0.570441\pi\)
−0.219495 + 0.975614i \(0.570441\pi\)
\(620\) −2.86521e101 −0.342657
\(621\) 2.49959e100 0.0281855
\(622\) 1.27406e102 1.35470
\(623\) −2.16313e101 −0.216905
\(624\) −2.52544e100 −0.0238836
\(625\) −6.70876e101 −0.598441
\(626\) −3.81056e102 −3.20646
\(627\) 1.60287e101 0.127243
\(628\) 6.88942e101 0.516007
\(629\) 2.14181e102 1.51367
\(630\) −1.68740e102 −1.12535
\(631\) −2.33316e102 −1.46849 −0.734247 0.678882i \(-0.762465\pi\)
−0.734247 + 0.678882i \(0.762465\pi\)
\(632\) 2.31660e102 1.37619
\(633\) −2.92551e101 −0.164046
\(634\) −5.19772e101 −0.275141
\(635\) −1.87584e102 −0.937464
\(636\) −4.17910e101 −0.197196
\(637\) 9.89323e101 0.440807
\(638\) 2.77889e102 1.16928
\(639\) 3.29129e102 1.30793
\(640\) 3.82861e102 1.43705
\(641\) 4.71888e102 1.67310 0.836548 0.547893i \(-0.184570\pi\)
0.836548 + 0.547893i \(0.184570\pi\)
\(642\) −1.95101e101 −0.0653480
\(643\) −4.02862e102 −1.27484 −0.637420 0.770516i \(-0.719998\pi\)
−0.637420 + 0.770516i \(0.719998\pi\)
\(644\) 6.79059e101 0.203036
\(645\) 4.50971e101 0.127415
\(646\) −1.01289e103 −2.70443
\(647\) 3.84535e102 0.970353 0.485177 0.874416i \(-0.338755\pi\)
0.485177 + 0.874416i \(0.338755\pi\)
\(648\) −4.61955e102 −1.10182
\(649\) −3.29795e102 −0.743555
\(650\) −3.38881e102 −0.722287
\(651\) 9.86627e100 0.0198814
\(652\) 3.87641e102 0.738571
\(653\) 4.39591e101 0.0791986 0.0395993 0.999216i \(-0.487392\pi\)
0.0395993 + 0.999216i \(0.487392\pi\)
\(654\) 9.55109e101 0.162729
\(655\) −4.76719e101 −0.0768166
\(656\) −1.65359e102 −0.252021
\(657\) 6.85549e102 0.988331
\(658\) 5.64422e102 0.769767
\(659\) −2.74596e102 −0.354305 −0.177153 0.984183i \(-0.556689\pi\)
−0.177153 + 0.984183i \(0.556689\pi\)
\(660\) 1.47055e102 0.179525
\(661\) −1.38738e103 −1.60267 −0.801334 0.598217i \(-0.795876\pi\)
−0.801334 + 0.598217i \(0.795876\pi\)
\(662\) 1.38920e102 0.151862
\(663\) −2.24654e102 −0.232418
\(664\) 1.50061e103 1.46938
\(665\) −7.45724e102 −0.691175
\(666\) 1.69689e103 1.48883
\(667\) 9.52937e101 0.0791537
\(668\) −1.15002e103 −0.904406
\(669\) 1.76322e102 0.131296
\(670\) 1.11481e103 0.786089
\(671\) −1.16519e103 −0.778081
\(672\) −1.10571e102 −0.0699300
\(673\) −3.23651e102 −0.193877 −0.0969387 0.995290i \(-0.530905\pi\)
−0.0969387 + 0.995290i \(0.530905\pi\)
\(674\) −1.56660e103 −0.888938
\(675\) 1.11665e102 0.0600246
\(676\) 3.50088e103 1.78288
\(677\) 1.27970e103 0.617479 0.308740 0.951147i \(-0.400093\pi\)
0.308740 + 0.951147i \(0.400093\pi\)
\(678\) −4.20557e102 −0.192283
\(679\) −1.97873e102 −0.0857314
\(680\) −3.79906e103 −1.55991
\(681\) −2.79452e102 −0.108752
\(682\) 1.40590e103 0.518589
\(683\) 5.71497e102 0.199829 0.0999144 0.994996i \(-0.468143\pi\)
0.0999144 + 0.994996i \(0.468143\pi\)
\(684\) −5.04333e103 −1.67174
\(685\) −1.25115e103 −0.393192
\(686\) −5.99077e103 −1.78506
\(687\) 5.25238e102 0.148400
\(688\) 9.87903e102 0.264689
\(689\) 6.69780e103 1.70189
\(690\) 8.02401e101 0.0193375
\(691\) 4.49013e103 1.02639 0.513193 0.858273i \(-0.328463\pi\)
0.513193 + 0.858273i \(0.328463\pi\)
\(692\) −1.21668e103 −0.263817
\(693\) 5.20350e103 1.07037
\(694\) 8.65408e103 1.68889
\(695\) 6.68990e103 1.23872
\(696\) 3.47859e102 0.0611175
\(697\) −1.47097e104 −2.45249
\(698\) 1.80497e103 0.285592
\(699\) 7.94228e102 0.119269
\(700\) 3.03358e103 0.432391
\(701\) −1.08120e104 −1.46284 −0.731422 0.681925i \(-0.761143\pi\)
−0.731422 + 0.681925i \(0.761143\pi\)
\(702\) −3.57705e103 −0.459431
\(703\) 7.49919e103 0.914419
\(704\) −1.76603e104 −2.04454
\(705\) 4.19149e102 0.0460751
\(706\) −3.88046e103 −0.405053
\(707\) 3.91735e102 0.0388315
\(708\) −1.00982e103 −0.0950669
\(709\) −1.89558e104 −1.69494 −0.847470 0.530843i \(-0.821875\pi\)
−0.847470 + 0.530843i \(0.821875\pi\)
\(710\) 2.12338e104 1.80342
\(711\) 1.48901e104 1.20132
\(712\) −3.85846e103 −0.295729
\(713\) 4.82110e102 0.0351057
\(714\) 3.19993e103 0.221389
\(715\) −2.35683e104 −1.54938
\(716\) 3.91875e104 2.44806
\(717\) 1.40479e103 0.0833993
\(718\) −2.24987e103 −0.126945
\(719\) 2.05381e103 0.110143 0.0550713 0.998482i \(-0.482461\pi\)
0.0550713 + 0.998482i \(0.482461\pi\)
\(720\) −2.74503e103 −0.139930
\(721\) 1.57258e104 0.762037
\(722\) 1.48147e102 0.00682471
\(723\) −8.58977e102 −0.0376213
\(724\) −1.61846e104 −0.673977
\(725\) 4.25708e103 0.168568
\(726\) −2.93834e103 −0.110641
\(727\) −2.37156e104 −0.849235 −0.424617 0.905373i \(-0.639591\pi\)
−0.424617 + 0.905373i \(0.639591\pi\)
\(728\) −3.97279e104 −1.35301
\(729\) −2.91004e104 −0.942637
\(730\) 4.42282e104 1.36274
\(731\) 8.78802e104 2.57577
\(732\) −3.56776e103 −0.0994812
\(733\) −3.38968e104 −0.899215 −0.449607 0.893226i \(-0.648436\pi\)
−0.449607 + 0.893226i \(0.648436\pi\)
\(734\) 1.73974e104 0.439114
\(735\) −1.04648e103 −0.0251329
\(736\) −5.40301e103 −0.123480
\(737\) −3.43780e104 −0.747682
\(738\) −1.16541e105 −2.41224
\(739\) 7.30628e104 1.43938 0.719689 0.694297i \(-0.244285\pi\)
0.719689 + 0.694297i \(0.244285\pi\)
\(740\) 6.88010e104 1.29014
\(741\) −7.86588e103 −0.140405
\(742\) −9.54024e104 −1.62113
\(743\) −5.81323e104 −0.940429 −0.470214 0.882552i \(-0.655823\pi\)
−0.470214 + 0.882552i \(0.655823\pi\)
\(744\) 1.75989e103 0.0271064
\(745\) −5.70777e104 −0.837071
\(746\) 3.06182e104 0.427575
\(747\) 9.64531e104 1.28267
\(748\) 2.86564e105 3.62922
\(749\) −2.79910e104 −0.337623
\(750\) 1.52535e104 0.175240
\(751\) 2.16876e104 0.237331 0.118665 0.992934i \(-0.462138\pi\)
0.118665 + 0.992934i \(0.462138\pi\)
\(752\) 9.18194e103 0.0957157
\(753\) −7.53023e103 −0.0747810
\(754\) −1.36370e105 −1.29023
\(755\) −7.58823e104 −0.684032
\(756\) 3.20208e104 0.275034
\(757\) 1.98343e105 1.62337 0.811686 0.584095i \(-0.198550\pi\)
0.811686 + 0.584095i \(0.198550\pi\)
\(758\) −1.94475e105 −1.51683
\(759\) −2.47440e103 −0.0183927
\(760\) −1.33018e105 −0.942354
\(761\) −4.55380e104 −0.307492 −0.153746 0.988110i \(-0.549134\pi\)
−0.153746 + 0.988110i \(0.549134\pi\)
\(762\) 2.81833e104 0.181399
\(763\) 1.37028e105 0.840746
\(764\) −1.95945e105 −1.14611
\(765\) −2.44188e105 −1.36170
\(766\) −2.62714e105 −1.39680
\(767\) 1.61843e105 0.820469
\(768\) −2.55543e104 −0.123532
\(769\) 5.60355e104 0.258316 0.129158 0.991624i \(-0.458773\pi\)
0.129158 + 0.991624i \(0.458773\pi\)
\(770\) 3.35704e105 1.47586
\(771\) −8.94516e103 −0.0375062
\(772\) −3.80200e104 −0.152048
\(773\) 3.54192e105 1.35110 0.675549 0.737315i \(-0.263907\pi\)
0.675549 + 0.737315i \(0.263907\pi\)
\(774\) 6.96249e105 2.53349
\(775\) 2.15374e104 0.0747622
\(776\) −3.52954e104 −0.116887
\(777\) −2.36915e104 −0.0748557
\(778\) 2.51661e104 0.0758685
\(779\) −5.15036e105 −1.48157
\(780\) −7.21652e104 −0.198096
\(781\) −6.54795e105 −1.71531
\(782\) 1.56363e105 0.390919
\(783\) 4.49355e104 0.107222
\(784\) −2.29243e104 −0.0522106
\(785\) 1.16795e105 0.253911
\(786\) 7.16240e103 0.0148640
\(787\) −3.56055e105 −0.705407 −0.352704 0.935735i \(-0.614738\pi\)
−0.352704 + 0.935735i \(0.614738\pi\)
\(788\) −3.15124e105 −0.596038
\(789\) 9.91873e104 0.179120
\(790\) 9.60638e105 1.65642
\(791\) −6.03368e105 −0.993438
\(792\) 9.28170e105 1.45935
\(793\) 5.71801e105 0.858566
\(794\) −7.93087e105 −1.13729
\(795\) −7.08474e104 −0.0970339
\(796\) −2.00731e106 −2.62596
\(797\) 5.25518e104 0.0656688 0.0328344 0.999461i \(-0.489547\pi\)
0.0328344 + 0.999461i \(0.489547\pi\)
\(798\) 1.12040e105 0.133742
\(799\) 8.16791e105 0.931437
\(800\) −2.41370e105 −0.262966
\(801\) −2.48006e105 −0.258152
\(802\) 2.94003e106 2.92407
\(803\) −1.36388e106 −1.29616
\(804\) −1.05264e105 −0.0955946
\(805\) 1.15120e105 0.0999078
\(806\) −6.89925e105 −0.572233
\(807\) 2.34720e104 0.0186065
\(808\) 6.98754e104 0.0529431
\(809\) 1.82851e106 1.32427 0.662136 0.749384i \(-0.269650\pi\)
0.662136 + 0.749384i \(0.269650\pi\)
\(810\) −1.91562e106 −1.32619
\(811\) 2.89168e106 1.91376 0.956882 0.290477i \(-0.0938139\pi\)
0.956882 + 0.290477i \(0.0938139\pi\)
\(812\) 1.22075e106 0.772383
\(813\) −1.05677e104 −0.00639256
\(814\) −3.37592e106 −1.95255
\(815\) 6.57160e105 0.363428
\(816\) 5.20560e104 0.0275283
\(817\) 3.07698e106 1.55604
\(818\) −5.52166e105 −0.267039
\(819\) −2.55355e106 −1.18109
\(820\) −4.72518e106 −2.09032
\(821\) −8.16158e105 −0.345342 −0.172671 0.984980i \(-0.555240\pi\)
−0.172671 + 0.984980i \(0.555240\pi\)
\(822\) 1.87978e105 0.0760825
\(823\) −2.88771e106 −1.11805 −0.559024 0.829152i \(-0.688824\pi\)
−0.559024 + 0.829152i \(0.688824\pi\)
\(824\) 2.80508e106 1.03897
\(825\) −1.10540e105 −0.0391696
\(826\) −2.30526e106 −0.781535
\(827\) −3.86945e106 −1.25516 −0.627579 0.778553i \(-0.715954\pi\)
−0.627579 + 0.778553i \(0.715954\pi\)
\(828\) 7.78552e105 0.241646
\(829\) 4.59567e106 1.36492 0.682461 0.730922i \(-0.260910\pi\)
0.682461 + 0.730922i \(0.260910\pi\)
\(830\) 6.22267e106 1.76859
\(831\) 2.93343e105 0.0797880
\(832\) 8.66656e106 2.25603
\(833\) −2.03926e106 −0.508077
\(834\) −1.00512e106 −0.239693
\(835\) −1.94960e106 −0.445030
\(836\) 1.00336e107 2.19244
\(837\) 2.27337e105 0.0475545
\(838\) −6.43729e106 −1.28913
\(839\) −2.07164e106 −0.397193 −0.198597 0.980081i \(-0.563638\pi\)
−0.198597 + 0.980081i \(0.563638\pi\)
\(840\) 4.20231e105 0.0771425
\(841\) −3.97613e106 −0.698886
\(842\) −1.13339e106 −0.190760
\(843\) −1.25101e105 −0.0201629
\(844\) −1.83130e107 −2.82657
\(845\) 5.93497e106 0.877301
\(846\) 6.47119e106 0.916149
\(847\) −4.21560e106 −0.571629
\(848\) −1.55199e106 −0.201577
\(849\) −6.28739e105 −0.0782239
\(850\) 6.98525e106 0.832513
\(851\) −1.15767e106 −0.132177
\(852\) −2.00495e106 −0.219310
\(853\) 1.22138e107 1.28000 0.640002 0.768373i \(-0.278934\pi\)
0.640002 + 0.768373i \(0.278934\pi\)
\(854\) −8.14465e106 −0.817824
\(855\) −8.54985e106 −0.822613
\(856\) −4.99286e106 −0.460317
\(857\) 6.15560e106 0.543839 0.271920 0.962320i \(-0.412341\pi\)
0.271920 + 0.962320i \(0.412341\pi\)
\(858\) 3.54100e106 0.299805
\(859\) −8.34532e105 −0.0677162 −0.0338581 0.999427i \(-0.510779\pi\)
−0.0338581 + 0.999427i \(0.510779\pi\)
\(860\) 2.82297e107 2.19539
\(861\) 1.62710e106 0.121283
\(862\) −1.43176e107 −1.02295
\(863\) 3.81216e106 0.261082 0.130541 0.991443i \(-0.458329\pi\)
0.130541 + 0.991443i \(0.458329\pi\)
\(864\) −2.54777e106 −0.167266
\(865\) −2.06261e106 −0.129816
\(866\) −8.75436e106 −0.528228
\(867\) 2.93370e106 0.169714
\(868\) 6.17603e106 0.342562
\(869\) −2.96236e107 −1.57549
\(870\) 1.44249e106 0.0735630
\(871\) 1.68705e107 0.825023
\(872\) 2.44423e107 1.14628
\(873\) −2.26865e106 −0.102034
\(874\) 5.47480e106 0.236157
\(875\) 2.18840e107 0.905384
\(876\) −4.17615e106 −0.165720
\(877\) 8.06360e105 0.0306933 0.0153467 0.999882i \(-0.495115\pi\)
0.0153467 + 0.999882i \(0.495115\pi\)
\(878\) −3.23131e107 −1.17985
\(879\) −3.80989e106 −0.133450
\(880\) 5.46118e106 0.183514
\(881\) 1.01969e107 0.328735 0.164367 0.986399i \(-0.447442\pi\)
0.164367 + 0.986399i \(0.447442\pi\)
\(882\) −1.61564e107 −0.499738
\(883\) −2.99686e107 −0.889408 −0.444704 0.895678i \(-0.646691\pi\)
−0.444704 + 0.895678i \(0.646691\pi\)
\(884\) −1.40627e108 −4.00463
\(885\) −1.71193e106 −0.0467795
\(886\) 1.06580e108 2.79477
\(887\) −4.43897e107 −1.11704 −0.558522 0.829490i \(-0.688631\pi\)
−0.558522 + 0.829490i \(0.688631\pi\)
\(888\) −4.22594e106 −0.102059
\(889\) 4.04343e107 0.937206
\(890\) −1.60001e107 −0.355949
\(891\) 5.90728e107 1.26140
\(892\) 1.10373e108 2.26227
\(893\) 2.85986e107 0.562687
\(894\) 8.57556e106 0.161973
\(895\) 6.64337e107 1.20461
\(896\) −8.25267e107 −1.43665
\(897\) 1.21428e106 0.0202952
\(898\) −6.66503e107 −1.06959
\(899\) 8.66695e106 0.133548
\(900\) 3.47805e107 0.514617
\(901\) −1.38059e108 −1.96160
\(902\) 2.31855e108 3.16357
\(903\) −9.72082e106 −0.127380
\(904\) −1.07625e108 −1.35446
\(905\) −2.74375e107 −0.331643
\(906\) 1.14008e107 0.132360
\(907\) −5.06142e106 −0.0564426 −0.0282213 0.999602i \(-0.508984\pi\)
−0.0282213 + 0.999602i \(0.508984\pi\)
\(908\) −1.74930e108 −1.87383
\(909\) 4.49131e106 0.0462159
\(910\) −1.64742e108 −1.62852
\(911\) 6.00813e107 0.570583 0.285291 0.958441i \(-0.407910\pi\)
0.285291 + 0.958441i \(0.407910\pi\)
\(912\) 1.82266e106 0.0166300
\(913\) −1.91891e108 −1.68218
\(914\) 1.77862e108 1.49812
\(915\) −6.04835e106 −0.0489516
\(916\) 3.28786e108 2.55698
\(917\) 1.02758e107 0.0767955
\(918\) 7.37325e107 0.529543
\(919\) −2.62509e108 −1.81187 −0.905937 0.423413i \(-0.860832\pi\)
−0.905937 + 0.423413i \(0.860832\pi\)
\(920\) 2.05343e107 0.136215
\(921\) −8.50684e106 −0.0542365
\(922\) 3.59111e108 2.20064
\(923\) 3.21332e108 1.89274
\(924\) −3.16981e107 −0.179476
\(925\) −5.17170e107 −0.281488
\(926\) −5.61196e108 −2.93639
\(927\) 1.80299e108 0.906949
\(928\) −9.71305e107 −0.469737
\(929\) −3.15796e108 −1.46836 −0.734181 0.678954i \(-0.762434\pi\)
−0.734181 + 0.678954i \(0.762434\pi\)
\(930\) 7.29783e106 0.0326262
\(931\) −7.14013e107 −0.306932
\(932\) 4.97167e108 2.05505
\(933\) −2.03943e107 −0.0810643
\(934\) −2.49113e108 −0.952214
\(935\) 4.85806e108 1.78583
\(936\) −4.55487e108 −1.61030
\(937\) 4.12136e108 1.40135 0.700673 0.713482i \(-0.252883\pi\)
0.700673 + 0.713482i \(0.252883\pi\)
\(938\) −2.40301e108 −0.785873
\(939\) 6.09968e107 0.191873
\(940\) 2.62377e108 0.793888
\(941\) −3.47164e108 −1.01045 −0.505224 0.862989i \(-0.668590\pi\)
−0.505224 + 0.862989i \(0.668590\pi\)
\(942\) −1.75477e107 −0.0491318
\(943\) 7.95076e107 0.214157
\(944\) −3.75016e107 −0.0971790
\(945\) 5.42843e107 0.135336
\(946\) −1.38517e109 −3.32259
\(947\) 6.22124e107 0.143583 0.0717914 0.997420i \(-0.477128\pi\)
0.0717914 + 0.997420i \(0.477128\pi\)
\(948\) −9.07062e107 −0.201434
\(949\) 6.69307e108 1.43024
\(950\) 2.44577e108 0.502926
\(951\) 8.32015e106 0.0164643
\(952\) 8.18898e108 1.55948
\(953\) −1.83299e108 −0.335946 −0.167973 0.985792i \(-0.553722\pi\)
−0.167973 + 0.985792i \(0.553722\pi\)
\(954\) −1.09380e109 −1.92941
\(955\) −3.32182e108 −0.563967
\(956\) 8.79363e108 1.43699
\(957\) −4.44826e107 −0.0699688
\(958\) 1.52151e109 2.30375
\(959\) 2.69689e108 0.393083
\(960\) −9.16724e107 −0.128629
\(961\) −6.96445e108 −0.940770
\(962\) 1.65669e109 2.15452
\(963\) −3.20921e108 −0.401827
\(964\) −5.37698e108 −0.648226
\(965\) −6.44545e107 −0.0748181
\(966\) −1.72960e107 −0.0193322
\(967\) −7.58384e108 −0.816250 −0.408125 0.912926i \(-0.633817\pi\)
−0.408125 + 0.912926i \(0.633817\pi\)
\(968\) −7.51953e108 −0.779364
\(969\) 1.62137e108 0.161832
\(970\) −1.46362e108 −0.140689
\(971\) −1.18116e108 −0.109347 −0.0546737 0.998504i \(-0.517412\pi\)
−0.0546737 + 0.998504i \(0.517412\pi\)
\(972\) 5.51575e108 0.491797
\(973\) −1.44203e109 −1.23838
\(974\) −2.62414e109 −2.17063
\(975\) 5.42458e107 0.0432213
\(976\) −1.32496e108 −0.101691
\(977\) −2.49823e108 −0.184706 −0.0923528 0.995726i \(-0.529439\pi\)
−0.0923528 + 0.995726i \(0.529439\pi\)
\(978\) −9.87342e107 −0.0703233
\(979\) 4.93403e108 0.338558
\(980\) −6.55069e108 −0.433047
\(981\) 1.57105e109 1.00063
\(982\) 4.43340e109 2.72062
\(983\) 1.72004e109 1.01703 0.508517 0.861052i \(-0.330194\pi\)
0.508517 + 0.861052i \(0.330194\pi\)
\(984\) 2.90233e108 0.165358
\(985\) −5.34223e108 −0.293292
\(986\) 2.81096e109 1.48712
\(987\) −9.03489e107 −0.0460624
\(988\) −4.92384e109 −2.41922
\(989\) −4.75003e108 −0.224922
\(990\) 3.84890e109 1.75652
\(991\) −1.06575e108 −0.0468777 −0.0234389 0.999725i \(-0.507462\pi\)
−0.0234389 + 0.999725i \(0.507462\pi\)
\(992\) −4.91403e108 −0.208335
\(993\) −2.22374e107 −0.00908733
\(994\) −4.57700e109 −1.80293
\(995\) −3.40295e109 −1.29215
\(996\) −5.87563e108 −0.215074
\(997\) 3.85126e109 1.35903 0.679517 0.733660i \(-0.262190\pi\)
0.679517 + 0.733660i \(0.262190\pi\)
\(998\) −2.12381e109 −0.722522
\(999\) −5.45896e108 −0.179048
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 1.74.a.a.1.1 5
3.2 odd 2 9.74.a.a.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.74.a.a.1.1 5 1.1 even 1 trivial
9.74.a.a.1.5 5 3.2 odd 2