Properties

Label 3.42.a.b.1.1
Level $3$
Weight $42$
Character 3.1
Self dual yes
Analytic conductor $31.942$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 42 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9415011369\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 196497525461 x^{2} + 10360343667016365 x + 6095744045744274504000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13}\cdot 3^{10}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(330995.\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +O(q^{10})\) \(q-2.00342e6 q^{2} +3.48678e9 q^{3} +1.81468e12 q^{4} -3.43221e14 q^{5} -6.98551e15 q^{6} -2.11939e17 q^{7} +7.69998e17 q^{8} +1.21577e19 q^{9} +6.87617e20 q^{10} -2.68951e21 q^{11} +6.32741e21 q^{12} -4.84491e22 q^{13} +4.24604e23 q^{14} -1.19674e24 q^{15} -5.53316e24 q^{16} -2.66383e25 q^{17} -2.43570e25 q^{18} +4.14274e24 q^{19} -6.22838e26 q^{20} -7.38986e26 q^{21} +5.38824e27 q^{22} -6.80863e27 q^{23} +2.68482e27 q^{24} +7.23261e28 q^{25} +9.70641e28 q^{26} +4.23912e28 q^{27} -3.84602e29 q^{28} -1.53939e30 q^{29} +2.39757e30 q^{30} -6.13330e29 q^{31} +9.39202e30 q^{32} -9.37775e30 q^{33} +5.33678e31 q^{34} +7.27420e31 q^{35} +2.20623e31 q^{36} +1.47726e32 q^{37} -8.29967e30 q^{38} -1.68932e32 q^{39} -2.64280e32 q^{40} +1.43312e33 q^{41} +1.48050e33 q^{42} +1.93562e33 q^{43} -4.88061e33 q^{44} -4.17277e33 q^{45} +1.36406e34 q^{46} -1.54236e34 q^{47} -1.92929e34 q^{48} +3.50578e32 q^{49} -1.44900e35 q^{50} -9.28821e34 q^{51} -8.79197e34 q^{52} +2.77827e35 q^{53} -8.49274e34 q^{54} +9.23098e35 q^{55} -1.63193e35 q^{56} +1.44449e34 q^{57} +3.08404e36 q^{58} -2.82191e36 q^{59} -2.17170e36 q^{60} +3.86057e36 q^{61} +1.22876e36 q^{62} -2.57669e36 q^{63} -6.64865e36 q^{64} +1.66288e37 q^{65} +1.87876e37 q^{66} -4.59962e36 q^{67} -4.83401e37 q^{68} -2.37402e37 q^{69} -1.45733e38 q^{70} +9.12164e37 q^{71} +9.36137e36 q^{72} -6.94314e36 q^{73} -2.95957e38 q^{74} +2.52185e38 q^{75} +7.51776e36 q^{76} +5.70013e38 q^{77} +3.38441e38 q^{78} +5.97141e38 q^{79} +1.89910e39 q^{80} +1.47809e38 q^{81} -2.87114e39 q^{82} -3.36804e39 q^{83} -1.34103e39 q^{84} +9.14284e39 q^{85} -3.87787e39 q^{86} -5.36751e39 q^{87} -2.07092e39 q^{88} -1.32775e40 q^{89} +8.35982e39 q^{90} +1.02683e40 q^{91} -1.23555e40 q^{92} -2.13855e39 q^{93} +3.09000e40 q^{94} -1.42188e39 q^{95} +3.27479e40 q^{96} -9.71560e40 q^{97} -7.02357e38 q^{98} -3.26982e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + O(q^{10}) \) \( 4q - 69822q^{2} + 13947137604q^{3} + 5352947588932q^{4} + 118536963776280q^{5} - 243454260446622q^{6} + 150256264888927136q^{7} + 6279626248119395784q^{8} + 48630661836227715204q^{9} + \)\(72\!\cdots\!40\)\(q^{10} + \)\(72\!\cdots\!56\)\(q^{11} + \)\(18\!\cdots\!32\)\(q^{12} - \)\(88\!\cdots\!08\)\(q^{13} + \)\(49\!\cdots\!68\)\(q^{14} + \)\(41\!\cdots\!80\)\(q^{15} - \)\(59\!\cdots\!00\)\(q^{16} - \)\(38\!\cdots\!88\)\(q^{17} - \)\(84\!\cdots\!22\)\(q^{18} + \)\(26\!\cdots\!48\)\(q^{19} + \)\(78\!\cdots\!60\)\(q^{20} + \)\(52\!\cdots\!36\)\(q^{21} - \)\(63\!\cdots\!76\)\(q^{22} - \)\(15\!\cdots\!32\)\(q^{23} + \)\(21\!\cdots\!84\)\(q^{24} + \)\(11\!\cdots\!00\)\(q^{25} - \)\(62\!\cdots\!52\)\(q^{26} + \)\(16\!\cdots\!04\)\(q^{27} + \)\(68\!\cdots\!12\)\(q^{28} - \)\(10\!\cdots\!64\)\(q^{29} + \)\(25\!\cdots\!40\)\(q^{30} + \)\(92\!\cdots\!04\)\(q^{31} + \)\(19\!\cdots\!56\)\(q^{32} + \)\(25\!\cdots\!56\)\(q^{33} + \)\(92\!\cdots\!04\)\(q^{34} + \)\(20\!\cdots\!40\)\(q^{35} + \)\(65\!\cdots\!32\)\(q^{36} + \)\(20\!\cdots\!56\)\(q^{37} + \)\(11\!\cdots\!28\)\(q^{38} - \)\(30\!\cdots\!08\)\(q^{39} + \)\(25\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!04\)\(q^{41} + \)\(17\!\cdots\!68\)\(q^{42} + \)\(39\!\cdots\!60\)\(q^{43} - \)\(18\!\cdots\!04\)\(q^{44} + \)\(14\!\cdots\!80\)\(q^{45} - \)\(44\!\cdots\!16\)\(q^{46} - \)\(88\!\cdots\!20\)\(q^{47} - \)\(20\!\cdots\!00\)\(q^{48} - \)\(33\!\cdots\!80\)\(q^{49} - \)\(21\!\cdots\!50\)\(q^{50} - \)\(13\!\cdots\!88\)\(q^{51} - \)\(59\!\cdots\!08\)\(q^{52} + \)\(95\!\cdots\!28\)\(q^{53} - \)\(29\!\cdots\!22\)\(q^{54} + \)\(12\!\cdots\!60\)\(q^{55} + \)\(19\!\cdots\!20\)\(q^{56} + \)\(91\!\cdots\!48\)\(q^{57} + \)\(38\!\cdots\!16\)\(q^{58} - \)\(18\!\cdots\!08\)\(q^{59} + \)\(27\!\cdots\!60\)\(q^{60} + \)\(53\!\cdots\!40\)\(q^{61} + \)\(14\!\cdots\!52\)\(q^{62} + \)\(18\!\cdots\!36\)\(q^{63} - \)\(38\!\cdots\!92\)\(q^{64} - \)\(97\!\cdots\!80\)\(q^{65} - \)\(22\!\cdots\!76\)\(q^{66} - \)\(73\!\cdots\!28\)\(q^{67} - \)\(89\!\cdots\!24\)\(q^{68} - \)\(53\!\cdots\!32\)\(q^{69} - \)\(12\!\cdots\!80\)\(q^{70} - \)\(84\!\cdots\!52\)\(q^{71} + \)\(76\!\cdots\!84\)\(q^{72} - \)\(44\!\cdots\!32\)\(q^{73} - \)\(29\!\cdots\!12\)\(q^{74} + \)\(40\!\cdots\!00\)\(q^{75} + \)\(11\!\cdots\!72\)\(q^{76} + \)\(83\!\cdots\!52\)\(q^{77} - \)\(21\!\cdots\!52\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(15\!\cdots\!80\)\(q^{80} + \)\(59\!\cdots\!04\)\(q^{81} + \)\(61\!\cdots\!12\)\(q^{82} + \)\(15\!\cdots\!04\)\(q^{83} + \)\(23\!\cdots\!12\)\(q^{84} - \)\(28\!\cdots\!60\)\(q^{85} - \)\(12\!\cdots\!24\)\(q^{86} - \)\(36\!\cdots\!64\)\(q^{87} - \)\(13\!\cdots\!96\)\(q^{88} - \)\(39\!\cdots\!72\)\(q^{89} + \)\(88\!\cdots\!40\)\(q^{90} - \)\(88\!\cdots\!16\)\(q^{91} - \)\(65\!\cdots\!44\)\(q^{92} + \)\(32\!\cdots\!04\)\(q^{93} + \)\(98\!\cdots\!32\)\(q^{94} + \)\(78\!\cdots\!00\)\(q^{95} + \)\(68\!\cdots\!56\)\(q^{96} + \)\(36\!\cdots\!52\)\(q^{97} - \)\(68\!\cdots\!22\)\(q^{98} + \)\(88\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00342e6 −1.35101 −0.675504 0.737356i \(-0.736074\pi\)
−0.675504 + 0.737356i \(0.736074\pi\)
\(3\) 3.48678e9 0.577350
\(4\) 1.81468e12 0.825222
\(5\) −3.43221e14 −1.60949 −0.804746 0.593619i \(-0.797699\pi\)
−0.804746 + 0.593619i \(0.797699\pi\)
\(6\) −6.98551e15 −0.780005
\(7\) −2.11939e17 −1.00393 −0.501963 0.864889i \(-0.667389\pi\)
−0.501963 + 0.864889i \(0.667389\pi\)
\(8\) 7.69998e17 0.236126
\(9\) 1.21577e19 0.333333
\(10\) 6.87617e20 2.17444
\(11\) −2.68951e21 −1.20538 −0.602690 0.797976i \(-0.705904\pi\)
−0.602690 + 0.797976i \(0.705904\pi\)
\(12\) 6.32741e21 0.476442
\(13\) −4.84491e22 −0.707045 −0.353522 0.935426i \(-0.615016\pi\)
−0.353522 + 0.935426i \(0.615016\pi\)
\(14\) 4.24604e23 1.35631
\(15\) −1.19674e24 −0.929241
\(16\) −5.53316e24 −1.14423
\(17\) −2.66383e25 −1.58966 −0.794830 0.606833i \(-0.792440\pi\)
−0.794830 + 0.606833i \(0.792440\pi\)
\(18\) −2.43570e25 −0.450336
\(19\) 4.14274e24 0.0252836 0.0126418 0.999920i \(-0.495976\pi\)
0.0126418 + 0.999920i \(0.495976\pi\)
\(20\) −6.22838e26 −1.32819
\(21\) −7.38986e26 −0.579617
\(22\) 5.38824e27 1.62848
\(23\) −6.80863e27 −0.827254 −0.413627 0.910446i \(-0.635738\pi\)
−0.413627 + 0.910446i \(0.635738\pi\)
\(24\) 2.68482e27 0.136328
\(25\) 7.23261e28 1.59047
\(26\) 9.70641e28 0.955223
\(27\) 4.23912e28 0.192450
\(28\) −3.84602e29 −0.828461
\(29\) −1.53939e30 −1.61506 −0.807530 0.589827i \(-0.799196\pi\)
−0.807530 + 0.589827i \(0.799196\pi\)
\(30\) 2.39757e30 1.25541
\(31\) −6.13330e29 −0.163976 −0.0819878 0.996633i \(-0.526127\pi\)
−0.0819878 + 0.996633i \(0.526127\pi\)
\(32\) 9.39202e30 1.30974
\(33\) −9.37775e30 −0.695926
\(34\) 5.33678e31 2.14764
\(35\) 7.27420e31 1.61581
\(36\) 2.20623e31 0.275074
\(37\) 1.47726e32 1.05032 0.525160 0.851004i \(-0.324006\pi\)
0.525160 + 0.851004i \(0.324006\pi\)
\(38\) −8.29967e30 −0.0341584
\(39\) −1.68932e32 −0.408213
\(40\) −2.64280e32 −0.380044
\(41\) 1.43312e33 1.24226 0.621131 0.783707i \(-0.286674\pi\)
0.621131 + 0.783707i \(0.286674\pi\)
\(42\) 1.48050e33 0.783067
\(43\) 1.93562e33 0.632001 0.316000 0.948759i \(-0.397660\pi\)
0.316000 + 0.948759i \(0.397660\pi\)
\(44\) −4.88061e33 −0.994706
\(45\) −4.17277e33 −0.536498
\(46\) 1.36406e34 1.11763
\(47\) −1.54236e34 −0.813168 −0.406584 0.913614i \(-0.633280\pi\)
−0.406584 + 0.913614i \(0.633280\pi\)
\(48\) −1.92929e34 −0.660622
\(49\) 3.50578e32 0.00786621
\(50\) −1.44900e35 −2.14873
\(51\) −9.28821e34 −0.917790
\(52\) −8.79197e34 −0.583469
\(53\) 2.77827e35 1.24773 0.623863 0.781534i \(-0.285562\pi\)
0.623863 + 0.781534i \(0.285562\pi\)
\(54\) −8.49274e34 −0.260002
\(55\) 9.23098e35 1.94005
\(56\) −1.63193e35 −0.237053
\(57\) 1.44449e34 0.0145975
\(58\) 3.08404e36 2.18196
\(59\) −2.82191e36 −1.40630 −0.703148 0.711044i \(-0.748223\pi\)
−0.703148 + 0.711044i \(0.748223\pi\)
\(60\) −2.17170e36 −0.766830
\(61\) 3.86057e36 0.971382 0.485691 0.874130i \(-0.338568\pi\)
0.485691 + 0.874130i \(0.338568\pi\)
\(62\) 1.22876e36 0.221532
\(63\) −2.57669e36 −0.334642
\(64\) −6.64865e36 −0.625236
\(65\) 1.66288e37 1.13798
\(66\) 1.87876e37 0.940202
\(67\) −4.59962e36 −0.169118 −0.0845588 0.996418i \(-0.526948\pi\)
−0.0845588 + 0.996418i \(0.526948\pi\)
\(68\) −4.83401e37 −1.31182
\(69\) −2.37402e37 −0.477615
\(70\) −1.45733e38 −2.18297
\(71\) 9.12164e37 1.02159 0.510795 0.859703i \(-0.329351\pi\)
0.510795 + 0.859703i \(0.329351\pi\)
\(72\) 9.36137e36 0.0787088
\(73\) −6.94314e36 −0.0439985 −0.0219992 0.999758i \(-0.507003\pi\)
−0.0219992 + 0.999758i \(0.507003\pi\)
\(74\) −2.95957e38 −1.41899
\(75\) 2.52185e38 0.918257
\(76\) 7.51776e36 0.0208646
\(77\) 5.70013e38 1.21011
\(78\) 3.38441e38 0.551498
\(79\) 5.97141e38 0.749414 0.374707 0.927143i \(-0.377743\pi\)
0.374707 + 0.927143i \(0.377743\pi\)
\(80\) 1.89910e39 1.84163
\(81\) 1.47809e38 0.111111
\(82\) −2.87114e39 −1.67830
\(83\) −3.36804e39 −1.53559 −0.767797 0.640694i \(-0.778647\pi\)
−0.767797 + 0.640694i \(0.778647\pi\)
\(84\) −1.34103e39 −0.478312
\(85\) 9.14284e39 2.55854
\(86\) −3.87787e39 −0.853838
\(87\) −5.36751e39 −0.932455
\(88\) −2.07092e39 −0.284622
\(89\) −1.32775e40 −1.44750 −0.723752 0.690060i \(-0.757584\pi\)
−0.723752 + 0.690060i \(0.757584\pi\)
\(90\) 8.35982e39 0.724812
\(91\) 1.02683e40 0.709820
\(92\) −1.23555e40 −0.682668
\(93\) −2.13855e39 −0.0946714
\(94\) 3.09000e40 1.09860
\(95\) −1.42188e39 −0.0406938
\(96\) 3.27479e40 0.756178
\(97\) −9.71560e40 −1.81405 −0.907025 0.421077i \(-0.861652\pi\)
−0.907025 + 0.421077i \(0.861652\pi\)
\(98\) −7.02357e38 −0.0106273
\(99\) −3.26982e40 −0.401793
\(100\) 1.31249e41 1.31249
\(101\) −4.41832e40 −0.360304 −0.180152 0.983639i \(-0.557659\pi\)
−0.180152 + 0.983639i \(0.557659\pi\)
\(102\) 1.86082e41 1.23994
\(103\) 2.87560e41 1.56879 0.784395 0.620262i \(-0.212974\pi\)
0.784395 + 0.620262i \(0.212974\pi\)
\(104\) −3.73057e40 −0.166952
\(105\) 2.53636e41 0.932889
\(106\) −5.56605e41 −1.68569
\(107\) −9.23802e40 −0.230787 −0.115394 0.993320i \(-0.536813\pi\)
−0.115394 + 0.993320i \(0.536813\pi\)
\(108\) 7.69265e40 0.158814
\(109\) −7.45590e41 −1.27426 −0.637128 0.770758i \(-0.719878\pi\)
−0.637128 + 0.770758i \(0.719878\pi\)
\(110\) −1.84936e42 −2.62102
\(111\) 5.15088e41 0.606402
\(112\) 1.17269e42 1.14872
\(113\) −1.06665e42 −0.870791 −0.435396 0.900239i \(-0.643391\pi\)
−0.435396 + 0.900239i \(0.643391\pi\)
\(114\) −2.89392e40 −0.0197213
\(115\) 2.33686e42 1.33146
\(116\) −2.79350e42 −1.33278
\(117\) −5.89028e41 −0.235682
\(118\) 5.65348e42 1.89992
\(119\) 5.64570e42 1.59590
\(120\) −9.21486e41 −0.219418
\(121\) 2.25497e42 0.452939
\(122\) −7.73436e42 −1.31235
\(123\) 4.99698e42 0.717220
\(124\) −1.11300e42 −0.135316
\(125\) −9.21595e42 −0.950353
\(126\) 5.16219e42 0.452104
\(127\) 3.83161e42 0.285368 0.142684 0.989768i \(-0.454427\pi\)
0.142684 + 0.989768i \(0.454427\pi\)
\(128\) −7.33322e42 −0.465040
\(129\) 6.74910e42 0.364886
\(130\) −3.33144e43 −1.53742
\(131\) 2.73831e43 1.07999 0.539996 0.841667i \(-0.318426\pi\)
0.539996 + 0.841667i \(0.318426\pi\)
\(132\) −1.70176e43 −0.574294
\(133\) −8.78010e41 −0.0253829
\(134\) 9.21500e42 0.228479
\(135\) −1.45495e43 −0.309747
\(136\) −2.05114e43 −0.375361
\(137\) −4.47383e42 −0.0704544 −0.0352272 0.999379i \(-0.511215\pi\)
−0.0352272 + 0.999379i \(0.511215\pi\)
\(138\) 4.75617e43 0.645262
\(139\) −9.98093e43 −1.16780 −0.583899 0.811826i \(-0.698474\pi\)
−0.583899 + 0.811826i \(0.698474\pi\)
\(140\) 1.32004e44 1.33340
\(141\) −5.37788e43 −0.469482
\(142\) −1.82745e44 −1.38018
\(143\) 1.30305e44 0.852257
\(144\) −6.72703e43 −0.381410
\(145\) 5.28350e44 2.59943
\(146\) 1.39101e43 0.0594423
\(147\) 1.22239e42 0.00454156
\(148\) 2.68076e44 0.866746
\(149\) 2.04820e44 0.576837 0.288419 0.957504i \(-0.406870\pi\)
0.288419 + 0.957504i \(0.406870\pi\)
\(150\) −5.05234e44 −1.24057
\(151\) 3.17569e43 0.0680472 0.0340236 0.999421i \(-0.489168\pi\)
0.0340236 + 0.999421i \(0.489168\pi\)
\(152\) 3.18990e42 0.00597013
\(153\) −3.23860e44 −0.529886
\(154\) −1.14198e45 −1.63487
\(155\) 2.10508e44 0.263918
\(156\) −3.06557e44 −0.336866
\(157\) 1.69451e44 0.163343 0.0816715 0.996659i \(-0.473974\pi\)
0.0816715 + 0.996659i \(0.473974\pi\)
\(158\) −1.19633e45 −1.01246
\(159\) 9.68723e44 0.720375
\(160\) −3.22354e45 −2.10801
\(161\) 1.44301e45 0.830501
\(162\) −2.96124e44 −0.150112
\(163\) 4.18577e44 0.187038 0.0935189 0.995618i \(-0.470188\pi\)
0.0935189 + 0.995618i \(0.470188\pi\)
\(164\) 2.60065e45 1.02514
\(165\) 3.21864e45 1.12009
\(166\) 6.74761e45 2.07460
\(167\) 4.36373e45 1.18623 0.593117 0.805117i \(-0.297897\pi\)
0.593117 + 0.805117i \(0.297897\pi\)
\(168\) −5.69018e44 −0.136863
\(169\) −2.34814e45 −0.500088
\(170\) −1.83170e46 −3.45661
\(171\) 5.03661e43 0.00842787
\(172\) 3.51254e45 0.521541
\(173\) −4.54949e44 −0.0599815 −0.0299907 0.999550i \(-0.509548\pi\)
−0.0299907 + 0.999550i \(0.509548\pi\)
\(174\) 1.07534e46 1.25975
\(175\) −1.53287e46 −1.59671
\(176\) 1.48815e46 1.37923
\(177\) −9.83939e45 −0.811925
\(178\) 2.66004e46 1.95559
\(179\) −1.96397e46 −1.28720 −0.643601 0.765361i \(-0.722560\pi\)
−0.643601 + 0.765361i \(0.722560\pi\)
\(180\) −7.57225e45 −0.442730
\(181\) 2.64903e45 0.138254 0.0691268 0.997608i \(-0.477979\pi\)
0.0691268 + 0.997608i \(0.477979\pi\)
\(182\) −2.05717e46 −0.958973
\(183\) 1.34610e46 0.560828
\(184\) −5.24262e45 −0.195336
\(185\) −5.07027e46 −1.69048
\(186\) 4.28442e45 0.127902
\(187\) 7.16441e46 1.91614
\(188\) −2.79890e46 −0.671044
\(189\) −8.98435e45 −0.193206
\(190\) 2.84862e45 0.0549777
\(191\) 2.19040e46 0.379612 0.189806 0.981822i \(-0.439214\pi\)
0.189806 + 0.981822i \(0.439214\pi\)
\(192\) −2.31824e46 −0.360980
\(193\) −1.09612e47 −1.53438 −0.767189 0.641421i \(-0.778345\pi\)
−0.767189 + 0.641421i \(0.778345\pi\)
\(194\) 1.94645e47 2.45080
\(195\) 5.79809e46 0.657015
\(196\) 6.36189e44 0.00649137
\(197\) 6.57368e46 0.604297 0.302149 0.953261i \(-0.402296\pi\)
0.302149 + 0.953261i \(0.402296\pi\)
\(198\) 6.55084e46 0.542826
\(199\) −1.41080e47 −1.05433 −0.527166 0.849762i \(-0.676745\pi\)
−0.527166 + 0.849762i \(0.676745\pi\)
\(200\) 5.56909e46 0.375551
\(201\) −1.60379e46 −0.0976401
\(202\) 8.85177e46 0.486774
\(203\) 3.26256e47 1.62140
\(204\) −1.68551e47 −0.757381
\(205\) −4.91877e47 −1.99941
\(206\) −5.76104e47 −2.11945
\(207\) −8.27770e46 −0.275751
\(208\) 2.68077e47 0.809022
\(209\) −1.11420e46 −0.0304764
\(210\) −5.08140e47 −1.26034
\(211\) −9.71826e46 −0.218675 −0.109337 0.994005i \(-0.534873\pi\)
−0.109337 + 0.994005i \(0.534873\pi\)
\(212\) 5.04168e47 1.02965
\(213\) 3.18052e47 0.589815
\(214\) 1.85077e47 0.311795
\(215\) −6.64347e47 −1.01720
\(216\) 3.26411e46 0.0454426
\(217\) 1.29989e47 0.164619
\(218\) 1.49373e48 1.72153
\(219\) −2.42092e46 −0.0254025
\(220\) 1.67513e48 1.60097
\(221\) 1.29060e48 1.12396
\(222\) −1.03194e48 −0.819254
\(223\) −1.08268e48 −0.783883 −0.391942 0.919990i \(-0.628197\pi\)
−0.391942 + 0.919990i \(0.628197\pi\)
\(224\) −1.99054e48 −1.31488
\(225\) 8.79316e47 0.530156
\(226\) 2.13695e48 1.17645
\(227\) −7.22684e47 −0.363428 −0.181714 0.983351i \(-0.558165\pi\)
−0.181714 + 0.983351i \(0.558165\pi\)
\(228\) 2.62128e46 0.0120462
\(229\) −3.57660e48 −1.50260 −0.751299 0.659962i \(-0.770572\pi\)
−0.751299 + 0.659962i \(0.770572\pi\)
\(230\) −4.68173e48 −1.79881
\(231\) 1.98751e48 0.698658
\(232\) −1.18532e48 −0.381358
\(233\) 5.07597e48 1.49528 0.747640 0.664104i \(-0.231187\pi\)
0.747640 + 0.664104i \(0.231187\pi\)
\(234\) 1.18007e48 0.318408
\(235\) 5.29371e48 1.30879
\(236\) −5.12087e48 −1.16051
\(237\) 2.08210e48 0.432674
\(238\) −1.13107e49 −2.15607
\(239\) −1.80945e48 −0.316512 −0.158256 0.987398i \(-0.550587\pi\)
−0.158256 + 0.987398i \(0.550587\pi\)
\(240\) 6.62175e48 1.06327
\(241\) 2.18958e48 0.322858 0.161429 0.986884i \(-0.448390\pi\)
0.161429 + 0.986884i \(0.448390\pi\)
\(242\) −4.51765e48 −0.611924
\(243\) 5.15378e47 0.0641500
\(244\) 7.00571e48 0.801606
\(245\) −1.20326e47 −0.0126606
\(246\) −1.00111e49 −0.968970
\(247\) −2.00712e47 −0.0178767
\(248\) −4.72262e47 −0.0387190
\(249\) −1.17436e49 −0.886575
\(250\) 1.84635e49 1.28393
\(251\) 1.23621e49 0.792100 0.396050 0.918229i \(-0.370381\pi\)
0.396050 + 0.918229i \(0.370381\pi\)
\(252\) −4.67587e48 −0.276154
\(253\) 1.83119e49 0.997155
\(254\) −7.67635e48 −0.385535
\(255\) 3.18791e49 1.47718
\(256\) 2.93121e49 1.25351
\(257\) −7.95215e48 −0.313946 −0.156973 0.987603i \(-0.550174\pi\)
−0.156973 + 0.987603i \(0.550174\pi\)
\(258\) −1.35213e49 −0.492963
\(259\) −3.13089e49 −1.05444
\(260\) 3.01759e49 0.939089
\(261\) −1.87153e49 −0.538353
\(262\) −5.48599e49 −1.45908
\(263\) −1.51702e49 −0.373162 −0.186581 0.982440i \(-0.559741\pi\)
−0.186581 + 0.982440i \(0.559741\pi\)
\(264\) −7.22085e48 −0.164327
\(265\) −9.53562e49 −2.00821
\(266\) 1.75903e48 0.0342925
\(267\) −4.62956e49 −0.835717
\(268\) −8.34686e48 −0.139560
\(269\) 7.09419e49 1.09896 0.549479 0.835508i \(-0.314826\pi\)
0.549479 + 0.835508i \(0.314826\pi\)
\(270\) 2.91489e49 0.418471
\(271\) 1.55633e49 0.207125 0.103563 0.994623i \(-0.466976\pi\)
0.103563 + 0.994623i \(0.466976\pi\)
\(272\) 1.47394e50 1.81894
\(273\) 3.58032e49 0.409815
\(274\) 8.96298e48 0.0951844
\(275\) −1.94522e50 −1.91712
\(276\) −4.30809e49 −0.394139
\(277\) −3.47369e48 −0.0295091 −0.0147546 0.999891i \(-0.504697\pi\)
−0.0147546 + 0.999891i \(0.504697\pi\)
\(278\) 1.99960e50 1.57770
\(279\) −7.45666e48 −0.0546585
\(280\) 5.60112e49 0.381536
\(281\) 1.20363e50 0.762104 0.381052 0.924554i \(-0.375562\pi\)
0.381052 + 0.924554i \(0.375562\pi\)
\(282\) 1.07742e50 0.634275
\(283\) 6.17804e49 0.338243 0.169121 0.985595i \(-0.445907\pi\)
0.169121 + 0.985595i \(0.445907\pi\)
\(284\) 1.65529e50 0.843039
\(285\) −4.95778e48 −0.0234946
\(286\) −2.61055e50 −1.15141
\(287\) −3.03734e50 −1.24714
\(288\) 1.14185e50 0.436579
\(289\) 4.28795e50 1.52702
\(290\) −1.05851e51 −3.51185
\(291\) −3.38762e50 −1.04734
\(292\) −1.25996e49 −0.0363085
\(293\) −6.08165e49 −0.163394 −0.0816968 0.996657i \(-0.526034\pi\)
−0.0816968 + 0.996657i \(0.526034\pi\)
\(294\) −2.44897e48 −0.00613568
\(295\) 9.68539e50 2.26342
\(296\) 1.13749e50 0.248008
\(297\) −1.14012e50 −0.231975
\(298\) −4.10341e50 −0.779312
\(299\) 3.29872e50 0.584906
\(300\) 4.57637e50 0.757766
\(301\) −4.10234e50 −0.634481
\(302\) −6.36224e49 −0.0919323
\(303\) −1.54057e50 −0.208022
\(304\) −2.29225e49 −0.0289303
\(305\) −1.32503e51 −1.56343
\(306\) 6.48828e50 0.715881
\(307\) −2.16833e50 −0.223763 −0.111882 0.993722i \(-0.535688\pi\)
−0.111882 + 0.993722i \(0.535688\pi\)
\(308\) 1.03439e51 0.998610
\(309\) 1.00266e51 0.905741
\(310\) −4.21736e50 −0.356555
\(311\) 4.74537e50 0.375563 0.187781 0.982211i \(-0.439870\pi\)
0.187781 + 0.982211i \(0.439870\pi\)
\(312\) −1.30077e50 −0.0963898
\(313\) −1.32823e51 −0.921749 −0.460875 0.887465i \(-0.652464\pi\)
−0.460875 + 0.887465i \(0.652464\pi\)
\(314\) −3.39481e50 −0.220678
\(315\) 8.84373e50 0.538604
\(316\) 1.08362e51 0.618433
\(317\) 8.98401e50 0.480569 0.240284 0.970703i \(-0.422759\pi\)
0.240284 + 0.970703i \(0.422759\pi\)
\(318\) −1.94076e51 −0.973232
\(319\) 4.14020e51 1.94676
\(320\) 2.28196e51 1.00631
\(321\) −3.22110e50 −0.133245
\(322\) −2.89097e51 −1.12201
\(323\) −1.10356e50 −0.0401923
\(324\) 2.68226e50 0.0916913
\(325\) −3.50413e51 −1.12453
\(326\) −8.38587e50 −0.252690
\(327\) −2.59971e51 −0.735692
\(328\) 1.10350e51 0.293331
\(329\) 3.26887e51 0.816360
\(330\) −6.44831e51 −1.51325
\(331\) −1.36487e51 −0.301036 −0.150518 0.988607i \(-0.548094\pi\)
−0.150518 + 0.988607i \(0.548094\pi\)
\(332\) −6.11192e51 −1.26721
\(333\) 1.79600e51 0.350106
\(334\) −8.74240e51 −1.60261
\(335\) 1.57869e51 0.272194
\(336\) 4.08893e51 0.663215
\(337\) 4.08797e51 0.623871 0.311936 0.950103i \(-0.399023\pi\)
0.311936 + 0.950103i \(0.399023\pi\)
\(338\) 4.70431e51 0.675622
\(339\) −3.71918e51 −0.502751
\(340\) 1.65913e52 2.11137
\(341\) 1.64956e51 0.197653
\(342\) −1.00905e50 −0.0113861
\(343\) 9.37133e51 0.996028
\(344\) 1.49043e51 0.149232
\(345\) 8.14814e51 0.768718
\(346\) 9.11455e50 0.0810354
\(347\) −9.67986e50 −0.0811176 −0.0405588 0.999177i \(-0.512914\pi\)
−0.0405588 + 0.999177i \(0.512914\pi\)
\(348\) −9.74032e51 −0.769482
\(349\) −1.20461e52 −0.897274 −0.448637 0.893714i \(-0.648090\pi\)
−0.448637 + 0.893714i \(0.648090\pi\)
\(350\) 3.07099e52 2.15717
\(351\) −2.05381e51 −0.136071
\(352\) −2.52600e52 −1.57873
\(353\) −1.65328e52 −0.974912 −0.487456 0.873147i \(-0.662075\pi\)
−0.487456 + 0.873147i \(0.662075\pi\)
\(354\) 1.97125e52 1.09692
\(355\) −3.13074e52 −1.64424
\(356\) −2.40944e52 −1.19451
\(357\) 1.96854e52 0.921393
\(358\) 3.93465e52 1.73902
\(359\) −3.30801e52 −1.38080 −0.690399 0.723429i \(-0.742565\pi\)
−0.690399 + 0.723429i \(0.742565\pi\)
\(360\) −3.21302e51 −0.126681
\(361\) −2.68300e52 −0.999361
\(362\) −5.30714e51 −0.186782
\(363\) 7.86258e51 0.261505
\(364\) 1.86336e52 0.585759
\(365\) 2.38303e51 0.0708152
\(366\) −2.69681e52 −0.757683
\(367\) −5.27201e51 −0.140063 −0.0700313 0.997545i \(-0.522310\pi\)
−0.0700313 + 0.997545i \(0.522310\pi\)
\(368\) 3.76732e52 0.946569
\(369\) 1.74234e52 0.414087
\(370\) 1.01579e53 2.28385
\(371\) −5.88825e52 −1.25262
\(372\) −3.88079e51 −0.0781249
\(373\) 2.13564e52 0.406909 0.203455 0.979084i \(-0.434783\pi\)
0.203455 + 0.979084i \(0.434783\pi\)
\(374\) −1.43534e53 −2.58872
\(375\) −3.21340e52 −0.548687
\(376\) −1.18761e52 −0.192010
\(377\) 7.45818e52 1.14192
\(378\) 1.79995e52 0.261022
\(379\) 1.38114e53 1.89729 0.948643 0.316349i \(-0.102457\pi\)
0.948643 + 0.316349i \(0.102457\pi\)
\(380\) −2.58026e51 −0.0335814
\(381\) 1.33600e52 0.164757
\(382\) −4.38831e52 −0.512859
\(383\) 1.09992e53 1.21839 0.609196 0.793020i \(-0.291492\pi\)
0.609196 + 0.793020i \(0.291492\pi\)
\(384\) −2.55693e52 −0.268491
\(385\) −1.95641e53 −1.94766
\(386\) 2.19599e53 2.07296
\(387\) 2.35327e52 0.210667
\(388\) −1.76307e53 −1.49699
\(389\) −6.95194e51 −0.0559937 −0.0279968 0.999608i \(-0.508913\pi\)
−0.0279968 + 0.999608i \(0.508913\pi\)
\(390\) −1.16160e53 −0.887633
\(391\) 1.81370e53 1.31505
\(392\) 2.69945e50 0.00185742
\(393\) 9.54789e52 0.623534
\(394\) −1.31699e53 −0.816410
\(395\) −2.04952e53 −1.20618
\(396\) −5.93369e52 −0.331569
\(397\) 1.86384e53 0.989015 0.494508 0.869173i \(-0.335348\pi\)
0.494508 + 0.869173i \(0.335348\pi\)
\(398\) 2.82643e53 1.42441
\(399\) −3.06143e51 −0.0146548
\(400\) −4.00192e53 −1.81986
\(401\) −7.71907e52 −0.333507 −0.166754 0.985999i \(-0.553328\pi\)
−0.166754 + 0.985999i \(0.553328\pi\)
\(402\) 3.21307e52 0.131913
\(403\) 2.97153e52 0.115938
\(404\) −8.01785e52 −0.297331
\(405\) −5.07311e52 −0.178833
\(406\) −6.53629e53 −2.19052
\(407\) −3.97311e53 −1.26603
\(408\) −7.15190e52 −0.216714
\(409\) −1.12970e52 −0.0325564 −0.0162782 0.999868i \(-0.505182\pi\)
−0.0162782 + 0.999868i \(0.505182\pi\)
\(410\) 9.85437e53 2.70122
\(411\) −1.55993e52 −0.0406768
\(412\) 5.21829e53 1.29460
\(413\) 5.98073e53 1.41182
\(414\) 1.65837e53 0.372542
\(415\) 1.15598e54 2.47153
\(416\) −4.55035e53 −0.926044
\(417\) −3.48014e53 −0.674228
\(418\) 2.23221e52 0.0411738
\(419\) −2.36312e53 −0.415049 −0.207524 0.978230i \(-0.566541\pi\)
−0.207524 + 0.978230i \(0.566541\pi\)
\(420\) 4.60268e53 0.769840
\(421\) 2.89686e53 0.461471 0.230736 0.973016i \(-0.425887\pi\)
0.230736 + 0.973016i \(0.425887\pi\)
\(422\) 1.94698e53 0.295431
\(423\) −1.87515e53 −0.271056
\(424\) 2.13926e53 0.294621
\(425\) −1.92665e54 −2.52830
\(426\) −6.37193e53 −0.796845
\(427\) −8.18207e53 −0.975195
\(428\) −1.67641e53 −0.190451
\(429\) 4.54344e53 0.492051
\(430\) 1.33097e54 1.37425
\(431\) −1.78890e54 −1.76118 −0.880588 0.473883i \(-0.842852\pi\)
−0.880588 + 0.473883i \(0.842852\pi\)
\(432\) −2.34557e53 −0.220207
\(433\) 3.17218e53 0.284025 0.142012 0.989865i \(-0.454643\pi\)
0.142012 + 0.989865i \(0.454643\pi\)
\(434\) −2.60422e53 −0.222402
\(435\) 1.84224e54 1.50078
\(436\) −1.35301e54 −1.05154
\(437\) −2.82064e52 −0.0209160
\(438\) 4.85014e52 0.0343190
\(439\) −2.40172e54 −1.62181 −0.810904 0.585180i \(-0.801024\pi\)
−0.810904 + 0.585180i \(0.801024\pi\)
\(440\) 7.10783e53 0.458097
\(441\) 4.26222e51 0.00262207
\(442\) −2.58562e54 −1.51848
\(443\) 2.77202e54 1.55425 0.777124 0.629348i \(-0.216678\pi\)
0.777124 + 0.629348i \(0.216678\pi\)
\(444\) 9.34722e53 0.500416
\(445\) 4.55710e54 2.32975
\(446\) 2.16907e54 1.05903
\(447\) 7.14162e53 0.333037
\(448\) 1.40911e54 0.627690
\(449\) −6.15902e53 −0.262097 −0.131048 0.991376i \(-0.541834\pi\)
−0.131048 + 0.991376i \(0.541834\pi\)
\(450\) −1.76164e54 −0.716245
\(451\) −3.85439e54 −1.49740
\(452\) −1.93563e54 −0.718596
\(453\) 1.10729e53 0.0392871
\(454\) 1.44784e54 0.490994
\(455\) −3.52429e54 −1.14245
\(456\) 1.11225e52 0.00344686
\(457\) −1.23275e53 −0.0365253 −0.0182626 0.999833i \(-0.505813\pi\)
−0.0182626 + 0.999833i \(0.505813\pi\)
\(458\) 7.16544e54 2.03002
\(459\) −1.12923e54 −0.305930
\(460\) 4.24067e54 1.09875
\(461\) −7.22256e54 −1.78987 −0.894936 0.446195i \(-0.852779\pi\)
−0.894936 + 0.446195i \(0.852779\pi\)
\(462\) −3.98183e54 −0.943892
\(463\) 4.66005e54 1.05677 0.528385 0.849005i \(-0.322798\pi\)
0.528385 + 0.849005i \(0.322798\pi\)
\(464\) 8.51767e54 1.84800
\(465\) 7.33995e53 0.152373
\(466\) −1.01693e55 −2.02014
\(467\) 9.30547e54 1.76906 0.884529 0.466485i \(-0.154480\pi\)
0.884529 + 0.466485i \(0.154480\pi\)
\(468\) −1.06890e54 −0.194490
\(469\) 9.74841e53 0.169781
\(470\) −1.06055e55 −1.76818
\(471\) 5.90838e53 0.0943061
\(472\) −2.17286e54 −0.332064
\(473\) −5.20589e54 −0.761800
\(474\) −4.17133e54 −0.584546
\(475\) 2.99628e53 0.0402128
\(476\) 1.02452e55 1.31697
\(477\) 3.37773e54 0.415909
\(478\) 3.62510e54 0.427610
\(479\) −1.41559e55 −1.59977 −0.799887 0.600151i \(-0.795107\pi\)
−0.799887 + 0.600151i \(0.795107\pi\)
\(480\) −1.12398e55 −1.21706
\(481\) −7.15718e54 −0.742623
\(482\) −4.38665e54 −0.436183
\(483\) 5.03148e54 0.479490
\(484\) 4.09205e54 0.373775
\(485\) 3.33460e55 2.91970
\(486\) −1.03252e54 −0.0866672
\(487\) −2.04972e55 −1.64949 −0.824746 0.565503i \(-0.808682\pi\)
−0.824746 + 0.565503i \(0.808682\pi\)
\(488\) 2.97263e54 0.229369
\(489\) 1.45949e54 0.107986
\(490\) 2.41064e53 0.0171046
\(491\) −4.95694e54 −0.337321 −0.168660 0.985674i \(-0.553944\pi\)
−0.168660 + 0.985674i \(0.553944\pi\)
\(492\) 9.06792e54 0.591866
\(493\) 4.10067e55 2.56739
\(494\) 4.02112e53 0.0241515
\(495\) 1.12227e55 0.646683
\(496\) 3.39365e54 0.187626
\(497\) −1.93323e55 −1.02560
\(498\) 2.35275e55 1.19777
\(499\) −2.14720e55 −1.04909 −0.524543 0.851384i \(-0.675764\pi\)
−0.524543 + 0.851384i \(0.675764\pi\)
\(500\) −1.67240e55 −0.784252
\(501\) 1.52154e55 0.684872
\(502\) −2.47665e55 −1.07013
\(503\) 2.45440e55 1.01813 0.509063 0.860729i \(-0.329992\pi\)
0.509063 + 0.860729i \(0.329992\pi\)
\(504\) −1.98404e54 −0.0790178
\(505\) 1.51646e55 0.579907
\(506\) −3.66865e55 −1.34716
\(507\) −8.18745e54 −0.288726
\(508\) 6.95316e54 0.235492
\(509\) 1.12858e55 0.367130 0.183565 0.983008i \(-0.441236\pi\)
0.183565 + 0.983008i \(0.441236\pi\)
\(510\) −6.38673e55 −1.99568
\(511\) 1.47152e54 0.0441712
\(512\) −4.25986e55 −1.22846
\(513\) 1.75616e53 0.00486584
\(514\) 1.59315e55 0.424144
\(515\) −9.86966e55 −2.52496
\(516\) 1.22475e55 0.301112
\(517\) 4.14820e55 0.980175
\(518\) 6.27250e55 1.42456
\(519\) −1.58631e54 −0.0346303
\(520\) 1.28041e55 0.268708
\(521\) −3.43253e55 −0.692534 −0.346267 0.938136i \(-0.612551\pi\)
−0.346267 + 0.938136i \(0.612551\pi\)
\(522\) 3.74947e55 0.727319
\(523\) −2.52587e54 −0.0471114 −0.0235557 0.999723i \(-0.507499\pi\)
−0.0235557 + 0.999723i \(0.507499\pi\)
\(524\) 4.96916e55 0.891234
\(525\) −5.34480e55 −0.921861
\(526\) 3.03922e55 0.504144
\(527\) 1.63381e55 0.260665
\(528\) 5.18886e55 0.796300
\(529\) −2.13820e55 −0.315651
\(530\) 1.91039e56 2.71310
\(531\) −3.43078e55 −0.468765
\(532\) −1.59331e54 −0.0209465
\(533\) −6.94333e55 −0.878335
\(534\) 9.27497e55 1.12906
\(535\) 3.17069e55 0.371450
\(536\) −3.54170e54 −0.0399331
\(537\) −6.84792e55 −0.743166
\(538\) −1.42127e56 −1.48470
\(539\) −9.42886e53 −0.00948177
\(540\) −2.64028e55 −0.255610
\(541\) −1.02690e56 −0.957158 −0.478579 0.878045i \(-0.658848\pi\)
−0.478579 + 0.878045i \(0.658848\pi\)
\(542\) −3.11800e55 −0.279827
\(543\) 9.23661e54 0.0798208
\(544\) −2.50188e56 −2.08204
\(545\) 2.55902e56 2.05091
\(546\) −7.17290e55 −0.553663
\(547\) 6.01255e55 0.447011 0.223505 0.974703i \(-0.428250\pi\)
0.223505 + 0.974703i \(0.428250\pi\)
\(548\) −8.11858e54 −0.0581405
\(549\) 4.69356e55 0.323794
\(550\) 3.89710e56 2.59004
\(551\) −6.37728e54 −0.0408346
\(552\) −1.82799e55 −0.112778
\(553\) −1.26558e56 −0.752356
\(554\) 6.95928e54 0.0398671
\(555\) −1.76789e56 −0.976000
\(556\) −1.81122e56 −0.963693
\(557\) 3.06039e56 1.56944 0.784721 0.619849i \(-0.212806\pi\)
0.784721 + 0.619849i \(0.212806\pi\)
\(558\) 1.49388e55 0.0738441
\(559\) −9.37792e55 −0.446853
\(560\) −4.02493e56 −1.84886
\(561\) 2.49808e56 1.10629
\(562\) −2.41139e56 −1.02961
\(563\) −3.42167e56 −1.40869 −0.704346 0.709857i \(-0.748760\pi\)
−0.704346 + 0.709857i \(0.748760\pi\)
\(564\) −9.75915e55 −0.387427
\(565\) 3.66097e56 1.40153
\(566\) −1.23772e56 −0.456969
\(567\) −3.13265e55 −0.111547
\(568\) 7.02364e55 0.241224
\(569\) 3.07296e56 1.01802 0.509008 0.860762i \(-0.330012\pi\)
0.509008 + 0.860762i \(0.330012\pi\)
\(570\) 9.93254e54 0.0317414
\(571\) 3.57289e56 1.10149 0.550743 0.834675i \(-0.314344\pi\)
0.550743 + 0.834675i \(0.314344\pi\)
\(572\) 2.36461e56 0.703301
\(573\) 7.63746e55 0.219169
\(574\) 6.08508e56 1.68489
\(575\) −4.92441e56 −1.31572
\(576\) −8.08320e55 −0.208412
\(577\) −7.31817e55 −0.182095 −0.0910476 0.995847i \(-0.529022\pi\)
−0.0910476 + 0.995847i \(0.529022\pi\)
\(578\) −8.59057e56 −2.06301
\(579\) −3.82193e56 −0.885874
\(580\) 9.58787e56 2.14510
\(581\) 7.13819e56 1.54162
\(582\) 6.78684e56 1.41497
\(583\) −7.47220e56 −1.50398
\(584\) −5.34620e54 −0.0103892
\(585\) 2.02167e56 0.379328
\(586\) 1.21841e56 0.220746
\(587\) 7.85589e56 1.37440 0.687202 0.726466i \(-0.258839\pi\)
0.687202 + 0.726466i \(0.258839\pi\)
\(588\) 2.21825e54 0.00374779
\(589\) −2.54087e54 −0.00414590
\(590\) −1.94039e57 −3.05790
\(591\) 2.29210e56 0.348891
\(592\) −8.17391e56 −1.20181
\(593\) 1.07054e57 1.52048 0.760240 0.649642i \(-0.225081\pi\)
0.760240 + 0.649642i \(0.225081\pi\)
\(594\) 2.28414e56 0.313401
\(595\) −1.93773e57 −2.56859
\(596\) 3.71683e56 0.476019
\(597\) −4.91916e56 −0.608719
\(598\) −6.60873e56 −0.790212
\(599\) −1.33866e57 −1.54675 −0.773374 0.633950i \(-0.781432\pi\)
−0.773374 + 0.633950i \(0.781432\pi\)
\(600\) 1.94182e56 0.216825
\(601\) −3.44829e55 −0.0372115 −0.0186058 0.999827i \(-0.505923\pi\)
−0.0186058 + 0.999827i \(0.505923\pi\)
\(602\) 8.21873e56 0.857189
\(603\) −5.59207e55 −0.0563725
\(604\) 5.76286e55 0.0561540
\(605\) −7.73952e56 −0.729003
\(606\) 3.08642e56 0.281039
\(607\) 1.12064e57 0.986505 0.493252 0.869886i \(-0.335808\pi\)
0.493252 + 0.869886i \(0.335808\pi\)
\(608\) 3.89087e55 0.0331149
\(609\) 1.13758e57 0.936115
\(610\) 2.65460e57 2.11221
\(611\) 7.47260e56 0.574946
\(612\) −5.87703e56 −0.437274
\(613\) 7.02680e56 0.505612 0.252806 0.967517i \(-0.418646\pi\)
0.252806 + 0.967517i \(0.418646\pi\)
\(614\) 4.34408e56 0.302306
\(615\) −1.71507e57 −1.15436
\(616\) 4.38909e56 0.285739
\(617\) 1.57026e57 0.988842 0.494421 0.869223i \(-0.335380\pi\)
0.494421 + 0.869223i \(0.335380\pi\)
\(618\) −2.00875e57 −1.22366
\(619\) −1.08061e57 −0.636813 −0.318406 0.947954i \(-0.603148\pi\)
−0.318406 + 0.947954i \(0.603148\pi\)
\(620\) 3.82005e56 0.217791
\(621\) −2.88626e56 −0.159205
\(622\) −9.50699e56 −0.507388
\(623\) 2.81401e57 1.45319
\(624\) 9.34725e56 0.467089
\(625\) −1.25898e56 −0.0608807
\(626\) 2.66100e57 1.24529
\(627\) −3.88496e55 −0.0175955
\(628\) 3.07499e56 0.134794
\(629\) −3.93517e57 −1.66965
\(630\) −1.77177e57 −0.727658
\(631\) −1.40291e57 −0.557736 −0.278868 0.960329i \(-0.589959\pi\)
−0.278868 + 0.960329i \(0.589959\pi\)
\(632\) 4.59797e56 0.176956
\(633\) −3.38855e56 −0.126252
\(634\) −1.79988e57 −0.649252
\(635\) −1.31509e57 −0.459298
\(636\) 1.75793e57 0.594469
\(637\) −1.69852e55 −0.00556176
\(638\) −8.29457e57 −2.63009
\(639\) 1.10898e57 0.340530
\(640\) 2.51692e57 0.748478
\(641\) 5.61783e57 1.61800 0.809001 0.587807i \(-0.200009\pi\)
0.809001 + 0.587807i \(0.200009\pi\)
\(642\) 6.45323e56 0.180015
\(643\) −4.94656e57 −1.33653 −0.668265 0.743923i \(-0.732963\pi\)
−0.668265 + 0.743923i \(0.732963\pi\)
\(644\) 2.61861e57 0.685348
\(645\) −2.31643e57 −0.587281
\(646\) 2.21089e56 0.0543002
\(647\) −2.45422e57 −0.583951 −0.291976 0.956426i \(-0.594313\pi\)
−0.291976 + 0.956426i \(0.594313\pi\)
\(648\) 1.13812e56 0.0262363
\(649\) 7.58956e57 1.69512
\(650\) 7.02026e57 1.51925
\(651\) 4.53242e56 0.0950430
\(652\) 7.59584e56 0.154348
\(653\) −3.19886e57 −0.629906 −0.314953 0.949107i \(-0.601989\pi\)
−0.314953 + 0.949107i \(0.601989\pi\)
\(654\) 5.20832e57 0.993926
\(655\) −9.39846e57 −1.73824
\(656\) −7.92967e57 −1.42143
\(657\) −8.44124e55 −0.0146662
\(658\) −6.54893e57 −1.10291
\(659\) −1.37754e57 −0.224882 −0.112441 0.993658i \(-0.535867\pi\)
−0.112441 + 0.993658i \(0.535867\pi\)
\(660\) 5.84082e57 0.924321
\(661\) 7.48119e57 1.14773 0.573867 0.818949i \(-0.305443\pi\)
0.573867 + 0.818949i \(0.305443\pi\)
\(662\) 2.73441e57 0.406701
\(663\) 4.50005e57 0.648919
\(664\) −2.59338e57 −0.362594
\(665\) 3.01352e56 0.0408536
\(666\) −3.59815e57 −0.472996
\(667\) 1.04811e58 1.33606
\(668\) 7.91878e57 0.978906
\(669\) −3.77508e57 −0.452575
\(670\) −3.16278e57 −0.367736
\(671\) −1.03831e58 −1.17088
\(672\) −6.94057e57 −0.759146
\(673\) 1.60993e58 1.70804 0.854022 0.520237i \(-0.174156\pi\)
0.854022 + 0.520237i \(0.174156\pi\)
\(674\) −8.18994e57 −0.842855
\(675\) 3.06599e57 0.306086
\(676\) −4.26112e57 −0.412683
\(677\) 5.61289e57 0.527374 0.263687 0.964608i \(-0.415061\pi\)
0.263687 + 0.964608i \(0.415061\pi\)
\(678\) 7.45109e57 0.679221
\(679\) 2.05912e58 1.82117
\(680\) 7.03996e57 0.604140
\(681\) −2.51984e57 −0.209825
\(682\) −3.30476e57 −0.267030
\(683\) −2.16339e58 −1.69633 −0.848164 0.529733i \(-0.822292\pi\)
−0.848164 + 0.529733i \(0.822292\pi\)
\(684\) 9.13985e55 0.00695487
\(685\) 1.53551e57 0.113396
\(686\) −1.87747e58 −1.34564
\(687\) −1.24708e58 −0.867525
\(688\) −1.07101e58 −0.723154
\(689\) −1.34605e58 −0.882198
\(690\) −1.63242e58 −1.03854
\(691\) −9.86473e57 −0.609236 −0.304618 0.952475i \(-0.598529\pi\)
−0.304618 + 0.952475i \(0.598529\pi\)
\(692\) −8.25587e56 −0.0494980
\(693\) 6.93003e57 0.403370
\(694\) 1.93929e57 0.109590
\(695\) 3.42567e58 1.87956
\(696\) −4.13297e57 −0.220177
\(697\) −3.81759e58 −1.97477
\(698\) 2.41334e58 1.21222
\(699\) 1.76988e58 0.863300
\(700\) −2.78168e58 −1.31764
\(701\) 2.34581e58 1.07913 0.539564 0.841944i \(-0.318589\pi\)
0.539564 + 0.841944i \(0.318589\pi\)
\(702\) 4.11466e57 0.183833
\(703\) 6.11991e56 0.0265559
\(704\) 1.78816e58 0.753646
\(705\) 1.84580e58 0.755629
\(706\) 3.31222e58 1.31711
\(707\) 9.36416e57 0.361719
\(708\) −1.78554e58 −0.670019
\(709\) 2.11154e58 0.769754 0.384877 0.922968i \(-0.374244\pi\)
0.384877 + 0.922968i \(0.374244\pi\)
\(710\) 6.27220e58 2.22138
\(711\) 7.25985e57 0.249805
\(712\) −1.02236e58 −0.341794
\(713\) 4.17593e57 0.135649
\(714\) −3.94381e58 −1.24481
\(715\) −4.47233e58 −1.37170
\(716\) −3.56397e58 −1.06223
\(717\) −6.30917e57 −0.182738
\(718\) 6.62734e58 1.86547
\(719\) −3.21690e58 −0.880024 −0.440012 0.897992i \(-0.645026\pi\)
−0.440012 + 0.897992i \(0.645026\pi\)
\(720\) 2.30886e58 0.613877
\(721\) −6.09451e58 −1.57495
\(722\) 5.37518e58 1.35014
\(723\) 7.63459e57 0.186402
\(724\) 4.80715e57 0.114090
\(725\) −1.11338e59 −2.56870
\(726\) −1.57521e58 −0.353295
\(727\) 1.46981e58 0.320484 0.160242 0.987078i \(-0.448773\pi\)
0.160242 + 0.987078i \(0.448773\pi\)
\(728\) 7.90654e57 0.167607
\(729\) 1.79701e57 0.0370370
\(730\) −4.77423e57 −0.0956719
\(731\) −5.15618e58 −1.00467
\(732\) 2.44274e58 0.462807
\(733\) 4.14987e58 0.764545 0.382273 0.924050i \(-0.375141\pi\)
0.382273 + 0.924050i \(0.375141\pi\)
\(734\) 1.05621e58 0.189226
\(735\) −4.19551e56 −0.00730961
\(736\) −6.39467e58 −1.08349
\(737\) 1.23708e58 0.203851
\(738\) −3.49064e58 −0.559435
\(739\) 4.59350e57 0.0716033 0.0358016 0.999359i \(-0.488602\pi\)
0.0358016 + 0.999359i \(0.488602\pi\)
\(740\) −9.20092e58 −1.39502
\(741\) −6.99840e56 −0.0103211
\(742\) 1.17966e59 1.69230
\(743\) 8.66038e58 1.20855 0.604277 0.796774i \(-0.293462\pi\)
0.604277 + 0.796774i \(0.293462\pi\)
\(744\) −1.64668e57 −0.0223544
\(745\) −7.02985e58 −0.928416
\(746\) −4.27860e58 −0.549738
\(747\) −4.09475e58 −0.511864
\(748\) 1.30011e59 1.58124
\(749\) 1.95790e58 0.231693
\(750\) 6.43781e58 0.741280
\(751\) 1.41094e59 1.58085 0.790426 0.612557i \(-0.209859\pi\)
0.790426 + 0.612557i \(0.209859\pi\)
\(752\) 8.53413e58 0.930451
\(753\) 4.31039e58 0.457319
\(754\) −1.49419e59 −1.54274
\(755\) −1.08996e58 −0.109521
\(756\) −1.63037e58 −0.159437
\(757\) 3.70705e58 0.352828 0.176414 0.984316i \(-0.443550\pi\)
0.176414 + 0.984316i \(0.443550\pi\)
\(758\) −2.76700e59 −2.56325
\(759\) 6.38496e58 0.575707
\(760\) −1.09484e57 −0.00960888
\(761\) −1.86135e59 −1.59017 −0.795084 0.606500i \(-0.792573\pi\)
−0.795084 + 0.606500i \(0.792573\pi\)
\(762\) −2.67658e58 −0.222588
\(763\) 1.58020e59 1.27926
\(764\) 3.97489e58 0.313264
\(765\) 1.11156e59 0.852848
\(766\) −2.20361e59 −1.64606
\(767\) 1.36719e59 0.994314
\(768\) 1.02205e59 0.723713
\(769\) −6.59899e58 −0.454975 −0.227487 0.973781i \(-0.573051\pi\)
−0.227487 + 0.973781i \(0.573051\pi\)
\(770\) 3.91951e59 2.63131
\(771\) −2.77274e58 −0.181257
\(772\) −1.98911e59 −1.26620
\(773\) 1.95752e59 1.21347 0.606733 0.794906i \(-0.292480\pi\)
0.606733 + 0.794906i \(0.292480\pi\)
\(774\) −4.71459e58 −0.284613
\(775\) −4.43597e58 −0.260798
\(776\) −7.48099e58 −0.428345
\(777\) −1.09167e59 −0.608782
\(778\) 1.39277e58 0.0756479
\(779\) 5.93704e57 0.0314089
\(780\) 1.05217e59 0.542183
\(781\) −2.45328e59 −1.23140
\(782\) −3.63362e59 −1.77664
\(783\) −6.52563e58 −0.310818
\(784\) −1.93981e57 −0.00900076
\(785\) −5.81591e58 −0.262899
\(786\) −1.91285e59 −0.842399
\(787\) 2.07905e59 0.892038 0.446019 0.895024i \(-0.352841\pi\)
0.446019 + 0.895024i \(0.352841\pi\)
\(788\) 1.19291e59 0.498679
\(789\) −5.28950e58 −0.215445
\(790\) 4.10605e59 1.62955
\(791\) 2.26065e59 0.874209
\(792\) −2.51775e58 −0.0948740
\(793\) −1.87041e59 −0.686811
\(794\) −3.73406e59 −1.33617
\(795\) −3.32486e59 −1.15944
\(796\) −2.56015e59 −0.870058
\(797\) 1.24780e58 0.0413283 0.0206642 0.999786i \(-0.493422\pi\)
0.0206642 + 0.999786i \(0.493422\pi\)
\(798\) 6.13334e57 0.0197988
\(799\) 4.10859e59 1.29266
\(800\) 6.79288e59 2.08310
\(801\) −1.61423e59 −0.482501
\(802\) 1.54646e59 0.450571
\(803\) 1.86737e58 0.0530348
\(804\) −2.91037e58 −0.0805748
\(805\) −4.95273e59 −1.33669
\(806\) −5.95323e58 −0.156633
\(807\) 2.47359e59 0.634483
\(808\) −3.40210e58 −0.0850774
\(809\) −1.93365e58 −0.0471448 −0.0235724 0.999722i \(-0.507504\pi\)
−0.0235724 + 0.999722i \(0.507504\pi\)
\(810\) 1.01636e59 0.241604
\(811\) 6.76399e59 1.56775 0.783873 0.620921i \(-0.213241\pi\)
0.783873 + 0.620921i \(0.213241\pi\)
\(812\) 5.92051e59 1.33801
\(813\) 5.42660e58 0.119584
\(814\) 7.95982e59 1.71042
\(815\) −1.43665e59 −0.301036
\(816\) 5.13931e59 1.05016
\(817\) 8.01879e57 0.0159793
\(818\) 2.26327e58 0.0439839
\(819\) 1.24838e59 0.236607
\(820\) −8.92600e59 −1.64996
\(821\) −6.71492e59 −1.21061 −0.605307 0.795992i \(-0.706950\pi\)
−0.605307 + 0.795992i \(0.706950\pi\)
\(822\) 3.12520e58 0.0549547
\(823\) −8.16687e59 −1.40074 −0.700372 0.713778i \(-0.746983\pi\)
−0.700372 + 0.713778i \(0.746983\pi\)
\(824\) 2.21420e59 0.370433
\(825\) −6.78256e59 −1.10685
\(826\) −1.19819e60 −1.90737
\(827\) 6.61685e59 1.02752 0.513758 0.857935i \(-0.328253\pi\)
0.513758 + 0.857935i \(0.328253\pi\)
\(828\) −1.50214e59 −0.227556
\(829\) 8.11669e59 1.19953 0.599765 0.800176i \(-0.295261\pi\)
0.599765 + 0.800176i \(0.295261\pi\)
\(830\) −2.31592e60 −3.33905
\(831\) −1.21120e58 −0.0170371
\(832\) 3.22121e59 0.442070
\(833\) −9.33882e57 −0.0125046
\(834\) 6.97219e59 0.910888
\(835\) −1.49772e60 −1.90923
\(836\) −2.02191e58 −0.0251498
\(837\) −2.59998e58 −0.0315571
\(838\) 4.73434e59 0.560734
\(839\) 8.50436e59 0.982927 0.491463 0.870898i \(-0.336462\pi\)
0.491463 + 0.870898i \(0.336462\pi\)
\(840\) 1.95299e59 0.220280
\(841\) 1.46122e60 1.60842
\(842\) −5.80364e59 −0.623451
\(843\) 4.19681e59 0.440001
\(844\) −1.76356e59 −0.180455
\(845\) 8.05931e59 0.804888
\(846\) 3.75672e59 0.366199
\(847\) −4.77916e59 −0.454717
\(848\) −1.53726e60 −1.42769
\(849\) 2.15415e59 0.195285
\(850\) 3.85989e60 3.41575
\(851\) −1.00581e60 −0.868880
\(852\) 5.77163e59 0.486729
\(853\) −2.06137e60 −1.69708 −0.848538 0.529135i \(-0.822516\pi\)
−0.848538 + 0.529135i \(0.822516\pi\)
\(854\) 1.63921e60 1.31750
\(855\) −1.72867e58 −0.0135646
\(856\) −7.11325e58 −0.0544949
\(857\) 1.32928e60 0.994285 0.497142 0.867669i \(-0.334383\pi\)
0.497142 + 0.867669i \(0.334383\pi\)
\(858\) −9.10243e59 −0.664765
\(859\) −1.38551e60 −0.987987 −0.493994 0.869466i \(-0.664463\pi\)
−0.493994 + 0.869466i \(0.664463\pi\)
\(860\) −1.20558e60 −0.839416
\(861\) −1.05905e60 −0.720035
\(862\) 3.58393e60 2.37936
\(863\) −7.45819e59 −0.483517 −0.241759 0.970336i \(-0.577724\pi\)
−0.241759 + 0.970336i \(0.577724\pi\)
\(864\) 3.98139e59 0.252059
\(865\) 1.56148e59 0.0965398
\(866\) −6.35522e59 −0.383719
\(867\) 1.49511e60 0.881623
\(868\) 2.35888e59 0.135847
\(869\) −1.60602e60 −0.903328
\(870\) −3.69079e60 −2.02757
\(871\) 2.22848e59 0.119574
\(872\) −5.74102e59 −0.300885
\(873\) −1.18119e60 −0.604683
\(874\) 5.65093e58 0.0282576
\(875\) 1.95322e60 0.954084
\(876\) −4.39321e58 −0.0209627
\(877\) 2.15621e60 1.00508 0.502538 0.864555i \(-0.332400\pi\)
0.502538 + 0.864555i \(0.332400\pi\)
\(878\) 4.81166e60 2.19107
\(879\) −2.12054e59 −0.0943353
\(880\) −5.10765e60 −2.21986
\(881\) 2.09977e60 0.891589 0.445795 0.895135i \(-0.352921\pi\)
0.445795 + 0.895135i \(0.352921\pi\)
\(882\) −8.53902e57 −0.00354244
\(883\) −2.55719e60 −1.03650 −0.518249 0.855230i \(-0.673416\pi\)
−0.518249 + 0.855230i \(0.673416\pi\)
\(884\) 2.34203e60 0.927517
\(885\) 3.37709e60 1.30679
\(886\) −5.55353e60 −2.09980
\(887\) 1.55710e60 0.575285 0.287642 0.957738i \(-0.407129\pi\)
0.287642 + 0.957738i \(0.407129\pi\)
\(888\) 3.96617e59 0.143188
\(889\) −8.12069e59 −0.286488
\(890\) −9.12981e60 −3.14751
\(891\) −3.97534e59 −0.133931
\(892\) −1.96473e60 −0.646878
\(893\) −6.38961e58 −0.0205598
\(894\) −1.43077e60 −0.449936
\(895\) 6.74075e60 2.07174
\(896\) 1.55420e60 0.466865
\(897\) 1.15019e60 0.337695
\(898\) 1.23391e60 0.354095
\(899\) 9.44151e59 0.264830
\(900\) 1.59568e60 0.437496
\(901\) −7.40085e60 −1.98346
\(902\) 7.72198e60 2.02299
\(903\) −1.43040e60 −0.366318
\(904\) −8.21318e59 −0.205617
\(905\) −9.09204e59 −0.222518
\(906\) −2.21838e59 −0.0530771
\(907\) −1.66650e60 −0.389814 −0.194907 0.980822i \(-0.562440\pi\)
−0.194907 + 0.980822i \(0.562440\pi\)
\(908\) −1.31144e60 −0.299909
\(909\) −5.37165e59 −0.120101
\(910\) 7.06064e60 1.54346
\(911\) 3.26737e60 0.698348 0.349174 0.937058i \(-0.386462\pi\)
0.349174 + 0.937058i \(0.386462\pi\)
\(912\) −7.99257e58 −0.0167029
\(913\) 9.05839e60 1.85097
\(914\) 2.46972e59 0.0493459
\(915\) −4.62010e60 −0.902648
\(916\) −6.49039e60 −1.23998
\(917\) −5.80355e60 −1.08423
\(918\) 2.26232e60 0.413314
\(919\) 3.23443e60 0.577869 0.288934 0.957349i \(-0.406699\pi\)
0.288934 + 0.957349i \(0.406699\pi\)
\(920\) 1.79938e60 0.314393
\(921\) −7.56050e59 −0.129190
\(922\) 1.44698e61 2.41813
\(923\) −4.41935e60 −0.722310
\(924\) 3.60671e60 0.576548
\(925\) 1.06844e61 1.67050
\(926\) −9.33606e60 −1.42770
\(927\) 3.49605e60 0.522930
\(928\) −1.44579e61 −2.11530
\(929\) 3.84037e60 0.549606 0.274803 0.961501i \(-0.411387\pi\)
0.274803 + 0.961501i \(0.411387\pi\)
\(930\) −1.47050e60 −0.205857
\(931\) 1.45236e57 0.000198886 0
\(932\) 9.21127e60 1.23394
\(933\) 1.65461e60 0.216831
\(934\) −1.86428e61 −2.39001
\(935\) −2.45898e61 −3.08402
\(936\) −4.53550e59 −0.0556507
\(937\) 2.56852e60 0.308334 0.154167 0.988045i \(-0.450731\pi\)
0.154167 + 0.988045i \(0.450731\pi\)
\(938\) −1.95302e60 −0.229376
\(939\) −4.63124e60 −0.532172
\(940\) 9.60641e60 1.08004
\(941\) −1.47165e61 −1.61889 −0.809444 0.587197i \(-0.800231\pi\)
−0.809444 + 0.587197i \(0.800231\pi\)
\(942\) −1.18370e60 −0.127408
\(943\) −9.75757e60 −1.02767
\(944\) 1.56141e61 1.60913
\(945\) 3.08362e60 0.310963
\(946\) 1.04296e61 1.02920
\(947\) −1.41745e61 −1.36878 −0.684388 0.729118i \(-0.739930\pi\)
−0.684388 + 0.729118i \(0.739930\pi\)
\(948\) 3.77836e60 0.357052
\(949\) 3.36389e59 0.0311089
\(950\) −6.00283e59 −0.0543278
\(951\) 3.13253e60 0.277456
\(952\) 4.34718e60 0.376834
\(953\) 1.56903e61 1.33115 0.665573 0.746332i \(-0.268187\pi\)
0.665573 + 0.746332i \(0.268187\pi\)
\(954\) −6.76702e60 −0.561896
\(955\) −7.51793e60 −0.610983
\(956\) −3.28358e60 −0.261193
\(957\) 1.44360e61 1.12396
\(958\) 2.83602e61 2.16131
\(959\) 9.48180e59 0.0707309
\(960\) 7.95669e60 0.580995
\(961\) −1.36142e61 −0.973112
\(962\) 1.43389e61 1.00329
\(963\) −1.12313e60 −0.0769290
\(964\) 3.97339e60 0.266429
\(965\) 3.76211e61 2.46957
\(966\) −1.00802e61 −0.647795
\(967\) −8.55928e60 −0.538511 −0.269256 0.963069i \(-0.586778\pi\)
−0.269256 + 0.963069i \(0.586778\pi\)
\(968\) 1.73632e60 0.106951
\(969\) −3.84787e59 −0.0232051
\(970\) −6.68062e61 −3.94454
\(971\) −1.94026e61 −1.12167 −0.560835 0.827928i \(-0.689520\pi\)
−0.560835 + 0.827928i \(0.689520\pi\)
\(972\) 9.35247e59 0.0529380
\(973\) 2.11535e61 1.17238
\(974\) 4.10645e61 2.22848
\(975\) −1.22182e61 −0.649249
\(976\) −2.13612e61 −1.11149
\(977\) 6.21621e60 0.316729 0.158364 0.987381i \(-0.449378\pi\)
0.158364 + 0.987381i \(0.449378\pi\)
\(978\) −2.92397e60 −0.145890
\(979\) 3.57099e61 1.74479
\(980\) −2.18353e59 −0.0104478
\(981\) −9.06463e60 −0.424752
\(982\) 9.93085e60 0.455723
\(983\) −6.48229e60 −0.291327 −0.145664 0.989334i \(-0.546532\pi\)
−0.145664 + 0.989334i \(0.546532\pi\)
\(984\) 3.84766e60 0.169355
\(985\) −2.25623e61 −0.972612
\(986\) −8.21537e61 −3.46857
\(987\) 1.13978e61 0.471325
\(988\) −3.64229e59 −0.0147522
\(989\) −1.31789e61 −0.522825
\(990\) −2.24839e61 −0.873674
\(991\) −2.42504e60 −0.0923016 −0.0461508 0.998934i \(-0.514695\pi\)
−0.0461508 + 0.998934i \(0.514695\pi\)
\(992\) −5.76040e60 −0.214765
\(993\) −4.75901e60 −0.173803
\(994\) 3.87308e61 1.38559
\(995\) 4.84217e61 1.69694
\(996\) −2.13110e61 −0.731621
\(997\) 2.46785e61 0.829979 0.414990 0.909826i \(-0.363785\pi\)
0.414990 + 0.909826i \(0.363785\pi\)
\(998\) 4.30175e61 1.41732
\(999\) 6.26227e60 0.202134
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 3.42.a.b.1.1 4
3.2 odd 2 9.42.a.c.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.42.a.b.1.1 4 1.1 even 1 trivial
9.42.a.c.1.4 4 3.2 odd 2