Properties

Label 1.30.a.a.1.2
Level $1$
Weight $30$
Character 1.1
Self dual yes
Analytic conductor $5.328$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.32780423830\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{51349}) \)
Defining polynomial: \(x^{2} - x - 12837\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{6}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-112.802\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} +O(q^{10})\) \(q+26073.9 q^{2} -1.44920e7 q^{3} +1.42978e8 q^{4} -6.21544e9 q^{5} -3.77862e11 q^{6} -3.40335e10 q^{7} -1.02703e13 q^{8} +1.41387e14 q^{9} -1.62061e14 q^{10} -7.97271e14 q^{11} -2.07203e15 q^{12} +1.10490e16 q^{13} -8.87385e14 q^{14} +9.00740e16 q^{15} -3.44548e17 q^{16} -7.47691e17 q^{17} +3.68651e18 q^{18} -2.49040e18 q^{19} -8.88669e17 q^{20} +4.93212e17 q^{21} -2.07880e19 q^{22} -1.63712e18 q^{23} +1.48837e20 q^{24} -1.47633e20 q^{25} +2.88091e20 q^{26} -1.05439e21 q^{27} -4.86602e18 q^{28} +1.87750e21 q^{29} +2.34858e21 q^{30} -4.79819e21 q^{31} -3.46987e21 q^{32} +1.15540e22 q^{33} -1.94952e22 q^{34} +2.11533e20 q^{35} +2.02152e22 q^{36} +7.91036e22 q^{37} -6.49345e22 q^{38} -1.60122e23 q^{39} +6.38347e22 q^{40} -6.06439e21 q^{41} +1.28600e22 q^{42} +6.72526e23 q^{43} -1.13992e23 q^{44} -8.78782e23 q^{45} -4.26862e22 q^{46} -1.90366e24 q^{47} +4.99319e24 q^{48} -3.21875e24 q^{49} -3.84936e24 q^{50} +1.08355e25 q^{51} +1.57976e24 q^{52} -1.65597e24 q^{53} -2.74920e25 q^{54} +4.95539e24 q^{55} +3.49535e23 q^{56} +3.60909e25 q^{57} +4.89537e25 q^{58} -8.93685e25 q^{59} +1.28786e25 q^{60} +4.59924e25 q^{61} -1.25108e26 q^{62} -4.81189e24 q^{63} +9.45048e25 q^{64} -6.86745e25 q^{65} +3.01259e26 q^{66} -1.04774e26 q^{67} -1.06903e26 q^{68} +2.37252e25 q^{69} +5.51549e24 q^{70} +1.75243e26 q^{71} -1.45209e27 q^{72} -4.56674e26 q^{73} +2.06254e27 q^{74} +2.13949e27 q^{75} -3.56072e26 q^{76} +2.71339e25 q^{77} -4.17501e27 q^{78} -3.28137e27 q^{79} +2.14152e27 q^{80} +5.57671e27 q^{81} -1.58122e26 q^{82} -4.40086e27 q^{83} +7.05183e25 q^{84} +4.64723e27 q^{85} +1.75354e28 q^{86} -2.72087e28 q^{87} +8.18824e27 q^{88} -6.06897e26 q^{89} -2.29133e28 q^{90} -3.76036e26 q^{91} -2.34072e26 q^{92} +6.95352e28 q^{93} -4.96357e28 q^{94} +1.54790e28 q^{95} +5.02853e28 q^{96} +1.44471e28 q^{97} -8.39253e28 q^{98} -1.12724e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 8640q^{2} - 4967640q^{3} - 89952256q^{4} - 17477788500q^{5} - 543908756736q^{6} - 3020312682800q^{7} + 3150297169920q^{8} + 163469569523706q^{9} + O(q^{10}) \) \( 2q + 8640q^{2} - 4967640q^{3} - 89952256q^{4} - 17477788500q^{5} - 543908756736q^{6} - 3020312682800q^{7} + 3150297169920q^{8} + 163469569523706q^{9} + 34285866768000q^{10} - 2055380519588616q^{11} - 4290530276229120q^{12} + 17139371179332220q^{13} + 51175123348059648q^{14} - 17192351392506000q^{15} - 453469082063208448q^{16} - 664795927907749980q^{17} + 3301524864881760960q^{18} + 1232169445452155080q^{19} + 1734668101813248000q^{20} - 27949113476248821696q^{21} + 1145797484912974080q^{22} - 18588430504374379920q^{23} + \)\(27\!\cdots\!40\)\(q^{24} - \)\(20\!\cdots\!50\)\(q^{25} + \)\(18\!\cdots\!64\)\(q^{26} - \)\(14\!\cdots\!80\)\(q^{27} + \)\(69\!\cdots\!20\)\(q^{28} + \)\(99\!\cdots\!20\)\(q^{29} + \)\(42\!\cdots\!00\)\(q^{30} - \)\(10\!\cdots\!56\)\(q^{31} - \)\(87\!\cdots\!60\)\(q^{32} - \)\(42\!\cdots\!80\)\(q^{33} - \)\(20\!\cdots\!92\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} + \)\(15\!\cdots\!32\)\(q^{36} + \)\(98\!\cdots\!60\)\(q^{37} - \)\(12\!\cdots\!20\)\(q^{38} - \)\(10\!\cdots\!28\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(10\!\cdots\!76\)\(q^{41} + \)\(50\!\cdots\!20\)\(q^{42} + \)\(51\!\cdots\!00\)\(q^{43} + \)\(17\!\cdots\!48\)\(q^{44} - \)\(11\!\cdots\!00\)\(q^{45} + \)\(25\!\cdots\!64\)\(q^{46} - \)\(45\!\cdots\!20\)\(q^{47} + \)\(39\!\cdots\!80\)\(q^{48} + \)\(24\!\cdots\!14\)\(q^{49} - \)\(28\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!84\)\(q^{51} + \)\(16\!\cdots\!00\)\(q^{52} - \)\(16\!\cdots\!40\)\(q^{53} - \)\(19\!\cdots\!20\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!20\)\(q^{56} + \)\(71\!\cdots\!40\)\(q^{57} + \)\(64\!\cdots\!20\)\(q^{58} - \)\(83\!\cdots\!60\)\(q^{59} + \)\(37\!\cdots\!00\)\(q^{60} - \)\(15\!\cdots\!16\)\(q^{61} - \)\(18\!\cdots\!20\)\(q^{62} - \)\(70\!\cdots\!60\)\(q^{63} + \)\(24\!\cdots\!84\)\(q^{64} - \)\(13\!\cdots\!00\)\(q^{65} + \)\(51\!\cdots\!88\)\(q^{66} + \)\(24\!\cdots\!20\)\(q^{67} - \)\(12\!\cdots\!40\)\(q^{68} - \)\(13\!\cdots\!28\)\(q^{69} - \)\(58\!\cdots\!00\)\(q^{70} - \)\(18\!\cdots\!36\)\(q^{71} - \)\(11\!\cdots\!40\)\(q^{72} + \)\(99\!\cdots\!80\)\(q^{73} + \)\(17\!\cdots\!28\)\(q^{74} + \)\(15\!\cdots\!00\)\(q^{75} - \)\(12\!\cdots\!40\)\(q^{76} + \)\(37\!\cdots\!00\)\(q^{77} - \)\(51\!\cdots\!00\)\(q^{78} - \)\(72\!\cdots\!80\)\(q^{79} + \)\(33\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!58\)\(q^{81} + \)\(15\!\cdots\!80\)\(q^{82} + \)\(22\!\cdots\!40\)\(q^{83} + \)\(66\!\cdots\!88\)\(q^{84} + \)\(37\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!64\)\(q^{86} - \)\(35\!\cdots\!40\)\(q^{87} - \)\(86\!\cdots\!60\)\(q^{88} + \)\(58\!\cdots\!60\)\(q^{89} - \)\(18\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} + \)\(37\!\cdots\!20\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} - \)\(40\!\cdots\!12\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} - \)\(25\!\cdots\!16\)\(q^{96} + \)\(10\!\cdots\!80\)\(q^{97} - \)\(18\!\cdots\!20\)\(q^{98} - \)\(14\!\cdots\!48\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 26073.9 1.12531 0.562654 0.826693i \(-0.309780\pi\)
0.562654 + 0.826693i \(0.309780\pi\)
\(3\) −1.44920e7 −1.74932 −0.874660 0.484736i \(-0.838916\pi\)
−0.874660 + 0.484736i \(0.838916\pi\)
\(4\) 1.42978e8 0.266317
\(5\) −6.21544e9 −0.455415 −0.227707 0.973730i \(-0.573123\pi\)
−0.227707 + 0.973730i \(0.573123\pi\)
\(6\) −3.77862e11 −1.96852
\(7\) −3.40335e10 −0.0189664 −0.00948319 0.999955i \(-0.503019\pi\)
−0.00948319 + 0.999955i \(0.503019\pi\)
\(8\) −1.02703e13 −0.825619
\(9\) 1.41387e14 2.06012
\(10\) −1.62061e14 −0.512481
\(11\) −7.97271e14 −0.633012 −0.316506 0.948590i \(-0.602510\pi\)
−0.316506 + 0.948590i \(0.602510\pi\)
\(12\) −2.07203e15 −0.465873
\(13\) 1.10490e16 0.778296 0.389148 0.921175i \(-0.372769\pi\)
0.389148 + 0.921175i \(0.372769\pi\)
\(14\) −8.87385e14 −0.0213430
\(15\) 9.00740e16 0.796666
\(16\) −3.44548e17 −1.19539
\(17\) −7.47691e17 −1.07699 −0.538496 0.842628i \(-0.681007\pi\)
−0.538496 + 0.842628i \(0.681007\pi\)
\(18\) 3.68651e18 2.31827
\(19\) −2.49040e18 −0.715060 −0.357530 0.933902i \(-0.616381\pi\)
−0.357530 + 0.933902i \(0.616381\pi\)
\(20\) −8.88669e17 −0.121284
\(21\) 4.93212e17 0.0331783
\(22\) −2.07880e19 −0.712333
\(23\) −1.63712e18 −0.0294461 −0.0147231 0.999892i \(-0.504687\pi\)
−0.0147231 + 0.999892i \(0.504687\pi\)
\(24\) 1.48837e20 1.44427
\(25\) −1.47633e20 −0.792598
\(26\) 2.88091e20 0.875822
\(27\) −1.05439e21 −1.85449
\(28\) −4.86602e18 −0.00505106
\(29\) 1.87750e21 1.17168 0.585839 0.810427i \(-0.300765\pi\)
0.585839 + 0.810427i \(0.300765\pi\)
\(30\) 2.34858e21 0.896494
\(31\) −4.79819e21 −1.13850 −0.569250 0.822165i \(-0.692766\pi\)
−0.569250 + 0.822165i \(0.692766\pi\)
\(32\) −3.46987e21 −0.519564
\(33\) 1.15540e22 1.10734
\(34\) −1.94952e22 −1.21195
\(35\) 2.11533e20 0.00863757
\(36\) 2.02152e22 0.548645
\(37\) 7.91036e22 1.44302 0.721508 0.692406i \(-0.243449\pi\)
0.721508 + 0.692406i \(0.243449\pi\)
\(38\) −6.49345e22 −0.804662
\(39\) −1.60122e23 −1.36149
\(40\) 6.38347e22 0.375999
\(41\) −6.06439e21 −0.0249702 −0.0124851 0.999922i \(-0.503974\pi\)
−0.0124851 + 0.999922i \(0.503974\pi\)
\(42\) 1.28600e22 0.0373358
\(43\) 6.72526e23 1.38809 0.694044 0.719933i \(-0.255827\pi\)
0.694044 + 0.719933i \(0.255827\pi\)
\(44\) −1.13992e23 −0.168582
\(45\) −8.78782e23 −0.938210
\(46\) −4.26862e22 −0.0331359
\(47\) −1.90366e24 −1.08186 −0.540928 0.841069i \(-0.681927\pi\)
−0.540928 + 0.841069i \(0.681927\pi\)
\(48\) 4.99319e24 2.09112
\(49\) −3.21875e24 −0.999640
\(50\) −3.84936e24 −0.891916
\(51\) 1.08355e25 1.88401
\(52\) 1.57976e24 0.207273
\(53\) −1.65597e24 −0.164836 −0.0824181 0.996598i \(-0.526264\pi\)
−0.0824181 + 0.996598i \(0.526264\pi\)
\(54\) −2.74920e25 −2.08688
\(55\) 4.95539e24 0.288283
\(56\) 3.49535e23 0.0156590
\(57\) 3.60909e25 1.25087
\(58\) 4.89537e25 1.31850
\(59\) −8.93685e25 −1.87858 −0.939292 0.343120i \(-0.888516\pi\)
−0.939292 + 0.343120i \(0.888516\pi\)
\(60\) 1.28786e25 0.212165
\(61\) 4.59924e25 0.596216 0.298108 0.954532i \(-0.403644\pi\)
0.298108 + 0.954532i \(0.403644\pi\)
\(62\) −1.25108e26 −1.28116
\(63\) −4.81189e24 −0.0390731
\(64\) 9.45048e25 0.610723
\(65\) −6.86745e25 −0.354447
\(66\) 3.01259e26 1.24610
\(67\) −1.04774e26 −0.348472 −0.174236 0.984704i \(-0.555746\pi\)
−0.174236 + 0.984704i \(0.555746\pi\)
\(68\) −1.06903e26 −0.286821
\(69\) 2.37252e25 0.0515107
\(70\) 5.51549e24 0.00971992
\(71\) 1.75243e26 0.251417 0.125709 0.992067i \(-0.459880\pi\)
0.125709 + 0.992067i \(0.459880\pi\)
\(72\) −1.45209e27 −1.70088
\(73\) −4.56674e26 −0.437950 −0.218975 0.975730i \(-0.570271\pi\)
−0.218975 + 0.975730i \(0.570271\pi\)
\(74\) 2.06254e27 1.62384
\(75\) 2.13949e27 1.38651
\(76\) −3.56072e26 −0.190432
\(77\) 2.71339e25 0.0120059
\(78\) −4.17501e27 −1.53209
\(79\) −3.28137e27 −1.00107 −0.500533 0.865717i \(-0.666863\pi\)
−0.500533 + 0.865717i \(0.666863\pi\)
\(80\) 2.14152e27 0.544399
\(81\) 5.57671e27 1.18398
\(82\) −1.58122e26 −0.0280991
\(83\) −4.40086e27 −0.656002 −0.328001 0.944677i \(-0.606375\pi\)
−0.328001 + 0.944677i \(0.606375\pi\)
\(84\) 7.05183e25 0.00883593
\(85\) 4.64723e27 0.490478
\(86\) 1.75354e28 1.56202
\(87\) −2.72087e28 −2.04964
\(88\) 8.18824e27 0.522627
\(89\) −6.06897e26 −0.0328821 −0.0164411 0.999865i \(-0.505234\pi\)
−0.0164411 + 0.999865i \(0.505234\pi\)
\(90\) −2.29133e28 −1.05577
\(91\) −3.76036e26 −0.0147615
\(92\) −2.34072e26 −0.00784199
\(93\) 6.95352e28 1.99160
\(94\) −4.96357e28 −1.21742
\(95\) 1.54790e28 0.325649
\(96\) 5.02853e28 0.908884
\(97\) 1.44471e28 0.224694 0.112347 0.993669i \(-0.464163\pi\)
0.112347 + 0.993669i \(0.464163\pi\)
\(98\) −8.39253e28 −1.12490
\(99\) −1.12724e29 −1.30408
\(100\) −2.11082e28 −0.211082
\(101\) −4.90236e28 −0.424371 −0.212185 0.977229i \(-0.568058\pi\)
−0.212185 + 0.977229i \(0.568058\pi\)
\(102\) 2.82524e29 2.12009
\(103\) 1.31966e29 0.859654 0.429827 0.902911i \(-0.358574\pi\)
0.429827 + 0.902911i \(0.358574\pi\)
\(104\) −1.13477e29 −0.642576
\(105\) −3.06553e27 −0.0151099
\(106\) −4.31776e28 −0.185491
\(107\) −2.31447e29 −0.867733 −0.433867 0.900977i \(-0.642851\pi\)
−0.433867 + 0.900977i \(0.642851\pi\)
\(108\) −1.50754e29 −0.493882
\(109\) 6.73768e29 1.93119 0.965597 0.260043i \(-0.0837367\pi\)
0.965597 + 0.260043i \(0.0837367\pi\)
\(110\) 1.29206e29 0.324407
\(111\) −1.14637e30 −2.52430
\(112\) 1.17262e28 0.0226723
\(113\) 5.10156e28 0.0867092 0.0433546 0.999060i \(-0.486195\pi\)
0.0433546 + 0.999060i \(0.486195\pi\)
\(114\) 9.41029e29 1.40761
\(115\) 1.01755e28 0.0134102
\(116\) 2.68440e29 0.312037
\(117\) 1.56219e30 1.60339
\(118\) −2.33019e30 −2.11398
\(119\) 2.54465e28 0.0204267
\(120\) −9.25091e29 −0.657743
\(121\) −9.50668e29 −0.599296
\(122\) 1.19920e30 0.670926
\(123\) 8.78850e28 0.0436808
\(124\) −6.86034e29 −0.303201
\(125\) 2.07532e30 0.816375
\(126\) −1.25465e29 −0.0439692
\(127\) 3.46836e30 1.08385 0.541926 0.840426i \(-0.317695\pi\)
0.541926 + 0.840426i \(0.317695\pi\)
\(128\) 4.32698e30 1.20681
\(129\) −9.74624e30 −2.42821
\(130\) −1.79061e30 −0.398862
\(131\) −1.16207e30 −0.231631 −0.115816 0.993271i \(-0.536948\pi\)
−0.115816 + 0.993271i \(0.536948\pi\)
\(132\) 1.65197e30 0.294903
\(133\) 8.47570e28 0.0135621
\(134\) −2.73186e30 −0.392138
\(135\) 6.55348e30 0.844564
\(136\) 7.67904e30 0.889186
\(137\) −1.12214e31 −1.16842 −0.584210 0.811603i \(-0.698596\pi\)
−0.584210 + 0.811603i \(0.698596\pi\)
\(138\) 6.18608e29 0.0579654
\(139\) −2.10245e30 −0.177423 −0.0887117 0.996057i \(-0.528275\pi\)
−0.0887117 + 0.996057i \(0.528275\pi\)
\(140\) 3.02445e28 0.00230033
\(141\) 2.75877e31 1.89251
\(142\) 4.56927e30 0.282922
\(143\) −8.80906e30 −0.492671
\(144\) −4.87146e31 −2.46265
\(145\) −1.16695e31 −0.533600
\(146\) −1.19073e31 −0.492828
\(147\) 4.66460e31 1.74869
\(148\) 1.13100e31 0.384299
\(149\) −4.28030e30 −0.131909 −0.0659543 0.997823i \(-0.521009\pi\)
−0.0659543 + 0.997823i \(0.521009\pi\)
\(150\) 5.57849e31 1.56025
\(151\) −9.32731e30 −0.236914 −0.118457 0.992959i \(-0.537795\pi\)
−0.118457 + 0.992959i \(0.537795\pi\)
\(152\) 2.55773e31 0.590367
\(153\) −1.05714e32 −2.21874
\(154\) 7.07486e29 0.0135104
\(155\) 2.98229e31 0.518489
\(156\) −2.28939e31 −0.362587
\(157\) 2.58823e31 0.373644 0.186822 0.982394i \(-0.440181\pi\)
0.186822 + 0.982394i \(0.440181\pi\)
\(158\) −8.55583e31 −1.12651
\(159\) 2.39983e31 0.288351
\(160\) 2.15668e31 0.236617
\(161\) 5.57170e28 0.000558486 0
\(162\) 1.45407e32 1.33234
\(163\) 1.19680e31 0.100300 0.0501501 0.998742i \(-0.484030\pi\)
0.0501501 + 0.998742i \(0.484030\pi\)
\(164\) −8.67072e29 −0.00664997
\(165\) −7.18134e31 −0.504299
\(166\) −1.14748e32 −0.738204
\(167\) 1.07804e32 0.635692 0.317846 0.948142i \(-0.397041\pi\)
0.317846 + 0.948142i \(0.397041\pi\)
\(168\) −5.06545e30 −0.0273926
\(169\) −7.94575e31 −0.394255
\(170\) 1.21171e32 0.551939
\(171\) −3.52110e32 −1.47311
\(172\) 9.61562e31 0.369671
\(173\) 3.82198e32 1.35089 0.675446 0.737410i \(-0.263951\pi\)
0.675446 + 0.737410i \(0.263951\pi\)
\(174\) −7.09436e32 −2.30648
\(175\) 5.02445e30 0.0150327
\(176\) 2.74698e32 0.756698
\(177\) 1.29513e33 3.28624
\(178\) −1.58242e31 −0.0370025
\(179\) −5.24041e32 −1.12979 −0.564893 0.825164i \(-0.691083\pi\)
−0.564893 + 0.825164i \(0.691083\pi\)
\(180\) −1.25646e32 −0.249861
\(181\) −7.54402e32 −1.38441 −0.692203 0.721703i \(-0.743360\pi\)
−0.692203 + 0.721703i \(0.743360\pi\)
\(182\) −9.80473e30 −0.0166112
\(183\) −6.66521e32 −1.04297
\(184\) 1.68138e31 0.0243113
\(185\) −4.91664e32 −0.657170
\(186\) 1.81306e33 2.24116
\(187\) 5.96112e32 0.681750
\(188\) −2.72180e32 −0.288116
\(189\) 3.58844e31 0.0351730
\(190\) 4.03597e32 0.366455
\(191\) −1.08024e33 −0.908947 −0.454473 0.890760i \(-0.650173\pi\)
−0.454473 + 0.890760i \(0.650173\pi\)
\(192\) −1.36956e33 −1.06835
\(193\) 1.91169e33 1.38305 0.691524 0.722354i \(-0.256940\pi\)
0.691524 + 0.722354i \(0.256940\pi\)
\(194\) 3.76693e32 0.252849
\(195\) 9.95229e32 0.620042
\(196\) −4.60209e32 −0.266221
\(197\) −2.82411e33 −1.51747 −0.758737 0.651397i \(-0.774183\pi\)
−0.758737 + 0.651397i \(0.774183\pi\)
\(198\) −2.93915e33 −1.46749
\(199\) 2.05181e33 0.952288 0.476144 0.879367i \(-0.342034\pi\)
0.476144 + 0.879367i \(0.342034\pi\)
\(200\) 1.51624e33 0.654384
\(201\) 1.51838e33 0.609590
\(202\) −1.27824e33 −0.477547
\(203\) −6.38978e31 −0.0222225
\(204\) 1.54924e33 0.501742
\(205\) 3.76929e31 0.0113718
\(206\) 3.44088e33 0.967375
\(207\) −2.31468e32 −0.0606626
\(208\) −3.80692e33 −0.930369
\(209\) 1.98553e33 0.452641
\(210\) −7.99303e31 −0.0170032
\(211\) −4.24073e33 −0.842063 −0.421032 0.907046i \(-0.638332\pi\)
−0.421032 + 0.907046i \(0.638332\pi\)
\(212\) −2.36767e32 −0.0438986
\(213\) −2.53962e33 −0.439809
\(214\) −6.03472e33 −0.976466
\(215\) −4.18005e33 −0.632155
\(216\) 1.08289e34 1.53111
\(217\) 1.63299e32 0.0215932
\(218\) 1.75678e34 2.17319
\(219\) 6.61810e33 0.766115
\(220\) 7.08510e32 0.0767745
\(221\) −8.26125e33 −0.838219
\(222\) −2.98903e34 −2.84061
\(223\) 1.95826e34 1.74362 0.871808 0.489848i \(-0.162948\pi\)
0.871808 + 0.489848i \(0.162948\pi\)
\(224\) 1.18092e32 0.00985425
\(225\) −2.08734e34 −1.63285
\(226\) 1.33017e33 0.0975745
\(227\) 1.22424e34 0.842345 0.421173 0.906980i \(-0.361619\pi\)
0.421173 + 0.906980i \(0.361619\pi\)
\(228\) 5.16018e33 0.333127
\(229\) 5.07275e33 0.307347 0.153673 0.988122i \(-0.450890\pi\)
0.153673 + 0.988122i \(0.450890\pi\)
\(230\) 2.65314e32 0.0150906
\(231\) −3.93224e32 −0.0210023
\(232\) −1.92825e34 −0.967361
\(233\) −2.33456e34 −1.10038 −0.550192 0.835038i \(-0.685446\pi\)
−0.550192 + 0.835038i \(0.685446\pi\)
\(234\) 4.07323e34 1.80430
\(235\) 1.18321e34 0.492693
\(236\) −1.27777e34 −0.500298
\(237\) 4.75536e34 1.75119
\(238\) 6.63490e32 0.0229863
\(239\) −1.69274e34 −0.551849 −0.275925 0.961179i \(-0.588984\pi\)
−0.275925 + 0.961179i \(0.588984\pi\)
\(240\) −3.10349e34 −0.952328
\(241\) −2.26884e34 −0.655476 −0.327738 0.944769i \(-0.606286\pi\)
−0.327738 + 0.944769i \(0.606286\pi\)
\(242\) −2.47876e34 −0.674392
\(243\) −8.45454e33 −0.216670
\(244\) 6.57588e33 0.158782
\(245\) 2.00059e34 0.455251
\(246\) 2.29151e33 0.0491543
\(247\) −2.75165e34 −0.556528
\(248\) 4.92790e34 0.939967
\(249\) 6.37771e34 1.14756
\(250\) 5.41117e34 0.918673
\(251\) −9.82834e34 −1.57475 −0.787374 0.616475i \(-0.788560\pi\)
−0.787374 + 0.616475i \(0.788560\pi\)
\(252\) −6.87992e32 −0.0104058
\(253\) 1.30523e33 0.0186398
\(254\) 9.04337e34 1.21967
\(255\) −6.73475e34 −0.858004
\(256\) 6.20845e34 0.747315
\(257\) −8.53561e34 −0.970966 −0.485483 0.874246i \(-0.661356\pi\)
−0.485483 + 0.874246i \(0.661356\pi\)
\(258\) −2.54122e35 −2.73248
\(259\) −2.69217e33 −0.0273688
\(260\) −9.81891e33 −0.0943952
\(261\) 2.65454e35 2.41380
\(262\) −3.02996e34 −0.260656
\(263\) 2.07906e35 1.69243 0.846213 0.532845i \(-0.178877\pi\)
0.846213 + 0.532845i \(0.178877\pi\)
\(264\) −1.18664e35 −0.914242
\(265\) 1.02926e34 0.0750688
\(266\) 2.20995e33 0.0152615
\(267\) 8.79513e33 0.0575214
\(268\) −1.49803e34 −0.0928039
\(269\) −2.34883e35 −1.37862 −0.689309 0.724468i \(-0.742086\pi\)
−0.689309 + 0.724468i \(0.742086\pi\)
\(270\) 1.70875e35 0.950394
\(271\) −8.82959e34 −0.465463 −0.232732 0.972541i \(-0.574766\pi\)
−0.232732 + 0.972541i \(0.574766\pi\)
\(272\) 2.57616e35 1.28743
\(273\) 5.44951e33 0.0258225
\(274\) −2.92586e35 −1.31483
\(275\) 1.17703e35 0.501724
\(276\) 3.39217e33 0.0137182
\(277\) −7.48695e34 −0.287308 −0.143654 0.989628i \(-0.545885\pi\)
−0.143654 + 0.989628i \(0.545885\pi\)
\(278\) −5.48191e34 −0.199656
\(279\) −6.78402e35 −2.34545
\(280\) −2.17251e33 −0.00713134
\(281\) 3.79424e35 1.18272 0.591361 0.806407i \(-0.298591\pi\)
0.591361 + 0.806407i \(0.298591\pi\)
\(282\) 7.19320e35 2.12966
\(283\) 5.23811e35 1.47323 0.736616 0.676311i \(-0.236422\pi\)
0.736616 + 0.676311i \(0.236422\pi\)
\(284\) 2.50558e34 0.0669566
\(285\) −2.24321e35 −0.569664
\(286\) −2.29686e35 −0.554406
\(287\) 2.06392e32 0.000473593 0
\(288\) −4.90595e35 −1.07037
\(289\) 7.70734e34 0.159914
\(290\) −3.04269e35 −0.600464
\(291\) −2.09367e35 −0.393061
\(292\) −6.52941e34 −0.116633
\(293\) −8.91980e35 −1.51626 −0.758131 0.652102i \(-0.773887\pi\)
−0.758131 + 0.652102i \(0.773887\pi\)
\(294\) 1.21624e36 1.96782
\(295\) 5.55465e35 0.855534
\(296\) −8.12420e35 −1.19138
\(297\) 8.40632e35 1.17392
\(298\) −1.11604e35 −0.148438
\(299\) −1.80886e34 −0.0229178
\(300\) 3.05899e35 0.369250
\(301\) −2.28884e34 −0.0263270
\(302\) −2.43200e35 −0.266601
\(303\) 7.10449e35 0.742360
\(304\) 8.58064e35 0.854777
\(305\) −2.85863e35 −0.271525
\(306\) −2.75637e36 −2.49676
\(307\) 6.34791e35 0.548434 0.274217 0.961668i \(-0.411581\pi\)
0.274217 + 0.961668i \(0.411581\pi\)
\(308\) 3.87954e33 0.00319738
\(309\) −1.91246e36 −1.50381
\(310\) 7.77599e35 0.583460
\(311\) 1.79660e36 1.28655 0.643273 0.765637i \(-0.277576\pi\)
0.643273 + 0.765637i \(0.277576\pi\)
\(312\) 1.64451e36 1.12407
\(313\) −2.68729e36 −1.75357 −0.876783 0.480886i \(-0.840315\pi\)
−0.876783 + 0.480886i \(0.840315\pi\)
\(314\) 6.74853e35 0.420465
\(315\) 2.99080e34 0.0177944
\(316\) −4.69163e35 −0.266601
\(317\) 1.03006e36 0.559119 0.279559 0.960128i \(-0.409812\pi\)
0.279559 + 0.960128i \(0.409812\pi\)
\(318\) 6.25729e35 0.324484
\(319\) −1.49687e36 −0.741687
\(320\) −5.87389e35 −0.278132
\(321\) 3.35412e36 1.51794
\(322\) 1.45276e33 0.000628469 0
\(323\) 1.86205e36 0.770114
\(324\) 7.97344e35 0.315314
\(325\) −1.63120e36 −0.616876
\(326\) 3.12053e35 0.112869
\(327\) −9.76422e36 −3.37828
\(328\) 6.22833e34 0.0206158
\(329\) 6.47880e34 0.0205189
\(330\) −1.87246e36 −0.567492
\(331\) 1.57492e36 0.456827 0.228414 0.973564i \(-0.426646\pi\)
0.228414 + 0.973564i \(0.426646\pi\)
\(332\) −6.29224e35 −0.174704
\(333\) 1.11842e37 2.97279
\(334\) 2.81087e36 0.715348
\(335\) 6.51216e35 0.158699
\(336\) −1.69935e35 −0.0396611
\(337\) −3.02595e36 −0.676438 −0.338219 0.941067i \(-0.609824\pi\)
−0.338219 + 0.941067i \(0.609824\pi\)
\(338\) −2.07177e36 −0.443658
\(339\) −7.39316e35 −0.151682
\(340\) 6.64450e35 0.130622
\(341\) 3.82546e36 0.720684
\(342\) −9.18090e36 −1.65770
\(343\) 2.19130e35 0.0379259
\(344\) −6.90707e36 −1.14603
\(345\) −1.47462e35 −0.0234587
\(346\) 9.96541e36 1.52017
\(347\) 4.44778e36 0.650678 0.325339 0.945597i \(-0.394522\pi\)
0.325339 + 0.945597i \(0.394522\pi\)
\(348\) −3.89023e36 −0.545854
\(349\) −9.68519e35 −0.130359 −0.0651793 0.997874i \(-0.520762\pi\)
−0.0651793 + 0.997874i \(0.520762\pi\)
\(350\) 1.31007e35 0.0169164
\(351\) −1.16499e37 −1.44335
\(352\) 2.76643e36 0.328890
\(353\) −9.40660e36 −1.07325 −0.536623 0.843822i \(-0.680300\pi\)
−0.536623 + 0.843822i \(0.680300\pi\)
\(354\) 3.37690e37 3.69804
\(355\) −1.08921e36 −0.114499
\(356\) −8.67726e34 −0.00875705
\(357\) −3.68770e35 −0.0357328
\(358\) −1.36638e37 −1.27136
\(359\) 2.90920e36 0.259958 0.129979 0.991517i \(-0.458509\pi\)
0.129979 + 0.991517i \(0.458509\pi\)
\(360\) 9.02539e36 0.774604
\(361\) −5.92772e36 −0.488690
\(362\) −1.96702e37 −1.55788
\(363\) 1.37771e37 1.04836
\(364\) −5.37647e34 −0.00393122
\(365\) 2.83843e36 0.199449
\(366\) −1.73788e37 −1.17366
\(367\) 3.00435e36 0.195026 0.0975131 0.995234i \(-0.468911\pi\)
0.0975131 + 0.995234i \(0.468911\pi\)
\(368\) 5.64069e35 0.0351997
\(369\) −8.57426e35 −0.0514416
\(370\) −1.28196e37 −0.739519
\(371\) 5.63584e34 0.00312634
\(372\) 9.94198e36 0.530396
\(373\) 2.82375e37 1.44893 0.724466 0.689310i \(-0.242086\pi\)
0.724466 + 0.689310i \(0.242086\pi\)
\(374\) 1.55430e37 0.767178
\(375\) −3.00755e37 −1.42810
\(376\) 1.95512e37 0.893201
\(377\) 2.07445e37 0.911913
\(378\) 9.35647e35 0.0395805
\(379\) 1.51814e37 0.618079 0.309039 0.951049i \(-0.399993\pi\)
0.309039 + 0.951049i \(0.399993\pi\)
\(380\) 2.21314e36 0.0867256
\(381\) −5.02634e37 −1.89601
\(382\) −2.81662e37 −1.02284
\(383\) −2.59896e37 −0.908692 −0.454346 0.890825i \(-0.650127\pi\)
−0.454346 + 0.890825i \(0.650127\pi\)
\(384\) −6.27065e37 −2.11111
\(385\) −1.68649e35 −0.00546768
\(386\) 4.98453e37 1.55635
\(387\) 9.50865e37 2.85963
\(388\) 2.06561e36 0.0598397
\(389\) −4.80732e37 −1.34163 −0.670816 0.741623i \(-0.734056\pi\)
−0.670816 + 0.741623i \(0.734056\pi\)
\(390\) 2.59495e37 0.697738
\(391\) 1.22406e36 0.0317133
\(392\) 3.30576e37 0.825322
\(393\) 1.68406e37 0.405197
\(394\) −7.36356e37 −1.70762
\(395\) 2.03952e37 0.455900
\(396\) −1.61170e37 −0.347299
\(397\) −4.33277e37 −0.900126 −0.450063 0.892997i \(-0.648599\pi\)
−0.450063 + 0.892997i \(0.648599\pi\)
\(398\) 5.34988e37 1.07162
\(399\) −1.22830e36 −0.0237245
\(400\) 5.08666e37 0.947465
\(401\) −2.87417e37 −0.516320 −0.258160 0.966102i \(-0.583116\pi\)
−0.258160 + 0.966102i \(0.583116\pi\)
\(402\) 3.95901e37 0.685976
\(403\) −5.30153e37 −0.886090
\(404\) −7.00928e36 −0.113017
\(405\) −3.46617e37 −0.539203
\(406\) −1.66606e36 −0.0250072
\(407\) −6.30670e37 −0.913446
\(408\) −1.11284e38 −1.55547
\(409\) 8.54677e37 1.15296 0.576480 0.817112i \(-0.304426\pi\)
0.576480 + 0.817112i \(0.304426\pi\)
\(410\) 9.82800e35 0.0127967
\(411\) 1.62620e38 2.04394
\(412\) 1.88683e37 0.228940
\(413\) 3.04152e36 0.0356299
\(414\) −6.03528e36 −0.0682641
\(415\) 2.73533e37 0.298753
\(416\) −3.83387e37 −0.404375
\(417\) 3.04686e37 0.310370
\(418\) 5.17704e37 0.509361
\(419\) −5.26548e37 −0.500420 −0.250210 0.968192i \(-0.580500\pi\)
−0.250210 + 0.968192i \(0.580500\pi\)
\(420\) −4.38302e35 −0.00402401
\(421\) 9.94249e37 0.881870 0.440935 0.897539i \(-0.354647\pi\)
0.440935 + 0.897539i \(0.354647\pi\)
\(422\) −1.10572e38 −0.947580
\(423\) −2.69152e38 −2.22876
\(424\) 1.70074e37 0.136092
\(425\) 1.10384e38 0.853622
\(426\) −6.62178e37 −0.494921
\(427\) −1.56528e36 −0.0113081
\(428\) −3.30917e37 −0.231092
\(429\) 1.27661e38 0.861839
\(430\) −1.08990e38 −0.711369
\(431\) −1.96737e38 −1.24155 −0.620777 0.783987i \(-0.713183\pi\)
−0.620777 + 0.783987i \(0.713183\pi\)
\(432\) 3.63287e38 2.21685
\(433\) 8.93739e37 0.527396 0.263698 0.964605i \(-0.415058\pi\)
0.263698 + 0.964605i \(0.415058\pi\)
\(434\) 4.25784e36 0.0242990
\(435\) 1.69114e38 0.933437
\(436\) 9.63337e37 0.514309
\(437\) 4.07710e36 0.0210557
\(438\) 1.72560e38 0.862115
\(439\) −3.31662e38 −1.60310 −0.801548 0.597930i \(-0.795990\pi\)
−0.801548 + 0.597930i \(0.795990\pi\)
\(440\) −5.08935e37 −0.238012
\(441\) −4.55089e38 −2.05938
\(442\) −2.15403e38 −0.943254
\(443\) 2.62823e38 1.11380 0.556902 0.830578i \(-0.311990\pi\)
0.556902 + 0.830578i \(0.311990\pi\)
\(444\) −1.63905e38 −0.672262
\(445\) 3.77213e36 0.0149750
\(446\) 5.10596e38 1.96210
\(447\) 6.20299e37 0.230750
\(448\) −3.21632e36 −0.0115832
\(449\) 1.08508e38 0.378348 0.189174 0.981944i \(-0.439419\pi\)
0.189174 + 0.981944i \(0.439419\pi\)
\(450\) −5.44250e38 −1.83746
\(451\) 4.83496e36 0.0158064
\(452\) 7.29408e36 0.0230921
\(453\) 1.35171e38 0.414439
\(454\) 3.19206e38 0.947897
\(455\) 2.33723e36 0.00672258
\(456\) −3.70665e38 −1.03274
\(457\) −3.49142e38 −0.942360 −0.471180 0.882037i \(-0.656172\pi\)
−0.471180 + 0.882037i \(0.656172\pi\)
\(458\) 1.32266e38 0.345860
\(459\) 7.88356e38 1.99728
\(460\) 1.45486e36 0.00357136
\(461\) 5.84500e38 1.39034 0.695171 0.718845i \(-0.255329\pi\)
0.695171 + 0.718845i \(0.255329\pi\)
\(462\) −1.02529e37 −0.0236340
\(463\) 2.77160e38 0.619164 0.309582 0.950873i \(-0.399811\pi\)
0.309582 + 0.950873i \(0.399811\pi\)
\(464\) −6.46889e38 −1.40062
\(465\) −4.32192e38 −0.907004
\(466\) −6.08712e38 −1.23827
\(467\) −9.01377e38 −1.77751 −0.888754 0.458384i \(-0.848429\pi\)
−0.888754 + 0.458384i \(0.848429\pi\)
\(468\) 2.23358e38 0.427008
\(469\) 3.56582e36 0.00660926
\(470\) 3.08508e38 0.554431
\(471\) −3.75086e38 −0.653623
\(472\) 9.17845e38 1.55099
\(473\) −5.36186e38 −0.878676
\(474\) 1.23991e39 1.97062
\(475\) 3.67665e38 0.566755
\(476\) 3.63828e36 0.00543996
\(477\) −2.34133e38 −0.339583
\(478\) −4.41363e38 −0.621000
\(479\) 5.62143e38 0.767330 0.383665 0.923472i \(-0.374662\pi\)
0.383665 + 0.923472i \(0.374662\pi\)
\(480\) −3.12546e38 −0.413919
\(481\) 8.74016e38 1.12309
\(482\) −5.91575e38 −0.737612
\(483\) −8.07450e35 −0.000976972 0
\(484\) −1.35924e38 −0.159602
\(485\) −8.97952e37 −0.102329
\(486\) −2.20443e38 −0.243820
\(487\) −1.05085e39 −1.12816 −0.564081 0.825720i \(-0.690769\pi\)
−0.564081 + 0.825720i \(0.690769\pi\)
\(488\) −4.72358e38 −0.492247
\(489\) −1.73440e38 −0.175457
\(490\) 5.21633e38 0.512297
\(491\) 7.99399e38 0.762223 0.381112 0.924529i \(-0.375541\pi\)
0.381112 + 0.924529i \(0.375541\pi\)
\(492\) 1.25656e37 0.0116329
\(493\) −1.40379e39 −1.26189
\(494\) −7.17462e38 −0.626265
\(495\) 7.00628e38 0.593898
\(496\) 1.65321e39 1.36095
\(497\) −5.96413e36 −0.00476848
\(498\) 1.66292e39 1.29136
\(499\) 1.14067e39 0.860401 0.430201 0.902733i \(-0.358443\pi\)
0.430201 + 0.902733i \(0.358443\pi\)
\(500\) 2.96724e38 0.217414
\(501\) −1.56229e39 −1.11203
\(502\) −2.56263e39 −1.77208
\(503\) 3.45164e38 0.231894 0.115947 0.993255i \(-0.463010\pi\)
0.115947 + 0.993255i \(0.463010\pi\)
\(504\) 4.94197e37 0.0322595
\(505\) 3.04703e38 0.193265
\(506\) 3.40325e37 0.0209755
\(507\) 1.15150e39 0.689679
\(508\) 4.95898e38 0.288648
\(509\) −7.06121e37 −0.0399458 −0.0199729 0.999801i \(-0.506358\pi\)
−0.0199729 + 0.999801i \(0.506358\pi\)
\(510\) −1.75601e39 −0.965518
\(511\) 1.55422e37 0.00830633
\(512\) −7.04246e38 −0.365856
\(513\) 2.62585e39 1.32607
\(514\) −2.22557e39 −1.09264
\(515\) −8.20230e38 −0.391499
\(516\) −1.39349e39 −0.646672
\(517\) 1.51773e39 0.684828
\(518\) −7.01953e37 −0.0307983
\(519\) −5.53881e39 −2.36314
\(520\) 7.05310e38 0.292639
\(521\) 3.46255e39 1.39717 0.698585 0.715528i \(-0.253814\pi\)
0.698585 + 0.715528i \(0.253814\pi\)
\(522\) 6.92142e39 2.71627
\(523\) −1.15392e39 −0.440453 −0.220227 0.975449i \(-0.570680\pi\)
−0.220227 + 0.975449i \(0.570680\pi\)
\(524\) −1.66149e38 −0.0616872
\(525\) −7.28143e37 −0.0262970
\(526\) 5.42093e39 1.90450
\(527\) 3.58756e39 1.22616
\(528\) −3.98092e39 −1.32371
\(529\) −3.08838e39 −0.999133
\(530\) 2.68368e38 0.0844754
\(531\) −1.26355e40 −3.87011
\(532\) 1.21184e37 0.00361181
\(533\) −6.70055e37 −0.0194342
\(534\) 2.29323e38 0.0647292
\(535\) 1.43854e39 0.395178
\(536\) 1.07606e39 0.287705
\(537\) 7.59439e39 1.97636
\(538\) −6.12432e39 −1.55137
\(539\) 2.56621e39 0.632784
\(540\) 9.37001e38 0.224921
\(541\) −2.74672e39 −0.641879 −0.320940 0.947100i \(-0.603999\pi\)
−0.320940 + 0.947100i \(0.603999\pi\)
\(542\) −2.30222e39 −0.523789
\(543\) 1.09328e40 2.42177
\(544\) 2.59439e39 0.559567
\(545\) −4.18776e39 −0.879494
\(546\) 1.42090e38 0.0290583
\(547\) −5.50487e39 −1.09630 −0.548152 0.836379i \(-0.684669\pi\)
−0.548152 + 0.836379i \(0.684669\pi\)
\(548\) −1.60441e39 −0.311170
\(549\) 6.50273e39 1.22828
\(550\) 3.06899e39 0.564593
\(551\) −4.67573e39 −0.837820
\(552\) −2.43666e38 −0.0425282
\(553\) 1.11677e38 0.0189866
\(554\) −1.95214e39 −0.323310
\(555\) 7.12518e39 1.14960
\(556\) −3.00603e38 −0.0472508
\(557\) −4.48537e39 −0.686908 −0.343454 0.939170i \(-0.611597\pi\)
−0.343454 + 0.939170i \(0.611597\pi\)
\(558\) −1.76886e40 −2.63935
\(559\) 7.43075e39 1.08034
\(560\) −7.28833e37 −0.0103253
\(561\) −8.63885e39 −1.19260
\(562\) 9.89305e39 1.33093
\(563\) 6.55822e38 0.0859834 0.0429917 0.999075i \(-0.486311\pi\)
0.0429917 + 0.999075i \(0.486311\pi\)
\(564\) 3.94443e39 0.504008
\(565\) −3.17084e38 −0.0394886
\(566\) 1.36578e40 1.65784
\(567\) −1.89795e38 −0.0224559
\(568\) −1.79981e39 −0.207575
\(569\) −1.62256e40 −1.82420 −0.912099 0.409970i \(-0.865539\pi\)
−0.912099 + 0.409970i \(0.865539\pi\)
\(570\) −5.84891e39 −0.641047
\(571\) 9.28706e39 0.992327 0.496163 0.868229i \(-0.334742\pi\)
0.496163 + 0.868229i \(0.334742\pi\)
\(572\) −1.25950e39 −0.131206
\(573\) 1.56549e40 1.59004
\(574\) 5.38145e36 0.000532938 0
\(575\) 2.41693e38 0.0233389
\(576\) 1.33617e40 1.25816
\(577\) −2.84801e39 −0.261513 −0.130756 0.991415i \(-0.541741\pi\)
−0.130756 + 0.991415i \(0.541741\pi\)
\(578\) 2.00960e39 0.179952
\(579\) −2.77042e40 −2.41939
\(580\) −1.66847e39 −0.142106
\(581\) 1.49776e38 0.0124420
\(582\) −5.45902e39 −0.442315
\(583\) 1.32026e39 0.104343
\(584\) 4.69019e39 0.361580
\(585\) −9.70968e39 −0.730205
\(586\) −2.32574e40 −1.70626
\(587\) −5.47078e39 −0.391559 −0.195779 0.980648i \(-0.562724\pi\)
−0.195779 + 0.980648i \(0.562724\pi\)
\(588\) 6.66934e39 0.465705
\(589\) 1.19494e40 0.814095
\(590\) 1.44831e40 0.962739
\(591\) 4.09269e40 2.65455
\(592\) −2.72550e40 −1.72497
\(593\) 2.22596e40 1.37475 0.687376 0.726302i \(-0.258762\pi\)
0.687376 + 0.726302i \(0.258762\pi\)
\(594\) 2.19186e40 1.32102
\(595\) −1.58161e38 −0.00930260
\(596\) −6.11986e38 −0.0351294
\(597\) −2.97348e40 −1.66586
\(598\) −4.71641e38 −0.0257896
\(599\) 2.08204e39 0.111122 0.0555611 0.998455i \(-0.482305\pi\)
0.0555611 + 0.998455i \(0.482305\pi\)
\(600\) −2.19733e40 −1.14473
\(601\) −1.47384e40 −0.749498 −0.374749 0.927126i \(-0.622271\pi\)
−0.374749 + 0.927126i \(0.622271\pi\)
\(602\) −5.96790e38 −0.0296260
\(603\) −1.48137e40 −0.717895
\(604\) −1.33360e39 −0.0630941
\(605\) 5.90882e39 0.272928
\(606\) 1.85242e40 0.835383
\(607\) 1.37809e40 0.606796 0.303398 0.952864i \(-0.401879\pi\)
0.303398 + 0.952864i \(0.401879\pi\)
\(608\) 8.64138e39 0.371519
\(609\) 9.26005e38 0.0388743
\(610\) −7.45357e39 −0.305550
\(611\) −2.10335e40 −0.842004
\(612\) −1.51147e40 −0.590886
\(613\) 1.47390e40 0.562717 0.281358 0.959603i \(-0.409215\pi\)
0.281358 + 0.959603i \(0.409215\pi\)
\(614\) 1.65515e40 0.617157
\(615\) −5.46244e38 −0.0198929
\(616\) −2.78674e38 −0.00991234
\(617\) 4.06519e39 0.141236 0.0706181 0.997503i \(-0.477503\pi\)
0.0706181 + 0.997503i \(0.477503\pi\)
\(618\) −4.98652e40 −1.69225
\(619\) 3.64687e40 1.20894 0.604472 0.796627i \(-0.293384\pi\)
0.604472 + 0.796627i \(0.293384\pi\)
\(620\) 4.26400e39 0.138082
\(621\) 1.72616e39 0.0546077
\(622\) 4.68444e40 1.44776
\(623\) 2.06548e37 0.000623655 0
\(624\) 5.51698e40 1.62751
\(625\) 1.45997e40 0.420809
\(626\) −7.00682e40 −1.97330
\(627\) −2.87742e40 −0.791815
\(628\) 3.70059e39 0.0995076
\(629\) −5.91450e40 −1.55412
\(630\) 7.79818e38 0.0200242
\(631\) −6.88296e40 −1.72723 −0.863613 0.504155i \(-0.831804\pi\)
−0.863613 + 0.504155i \(0.831804\pi\)
\(632\) 3.37008e40 0.826500
\(633\) 6.14565e40 1.47304
\(634\) 2.68577e40 0.629181
\(635\) −2.15574e40 −0.493602
\(636\) 3.43122e39 0.0767927
\(637\) −3.55640e40 −0.778016
\(638\) −3.90294e40 −0.834626
\(639\) 2.47771e40 0.517950
\(640\) −2.68941e40 −0.549601
\(641\) 5.79208e40 1.15716 0.578580 0.815626i \(-0.303607\pi\)
0.578580 + 0.815626i \(0.303607\pi\)
\(642\) 8.74550e40 1.70815
\(643\) −6.13559e40 −1.17165 −0.585824 0.810439i \(-0.699229\pi\)
−0.585824 + 0.810439i \(0.699229\pi\)
\(644\) 7.96629e36 0.000148734 0
\(645\) 6.05772e40 1.10584
\(646\) 4.85510e40 0.866615
\(647\) −1.10620e40 −0.193074 −0.0965369 0.995329i \(-0.530777\pi\)
−0.0965369 + 0.995329i \(0.530777\pi\)
\(648\) −5.72747e40 −0.977518
\(649\) 7.12509e40 1.18917
\(650\) −4.25317e40 −0.694175
\(651\) −2.36652e39 −0.0377735
\(652\) 1.71116e39 0.0267116
\(653\) 9.61992e40 1.46869 0.734346 0.678776i \(-0.237489\pi\)
0.734346 + 0.678776i \(0.237489\pi\)
\(654\) −2.54591e41 −3.80160
\(655\) 7.22276e39 0.105488
\(656\) 2.08948e39 0.0298491
\(657\) −6.45677e40 −0.902231
\(658\) 1.68928e39 0.0230901
\(659\) 2.42717e40 0.324535 0.162268 0.986747i \(-0.448119\pi\)
0.162268 + 0.986747i \(0.448119\pi\)
\(660\) −1.02677e40 −0.134303
\(661\) −8.66824e40 −1.10920 −0.554600 0.832117i \(-0.687129\pi\)
−0.554600 + 0.832117i \(0.687129\pi\)
\(662\) 4.10643e40 0.514071
\(663\) 1.19722e41 1.46631
\(664\) 4.51983e40 0.541608
\(665\) −5.26802e38 −0.00617638
\(666\) 2.91616e41 3.34530
\(667\) −3.07370e39 −0.0345014
\(668\) 1.54136e40 0.169295
\(669\) −2.83791e41 −3.05014
\(670\) 1.69797e40 0.178585
\(671\) −3.66684e40 −0.377412
\(672\) −1.71138e39 −0.0172382
\(673\) −8.20694e40 −0.809027 −0.404513 0.914532i \(-0.632559\pi\)
−0.404513 + 0.914532i \(0.632559\pi\)
\(674\) −7.88983e40 −0.761201
\(675\) 1.55662e41 1.46987
\(676\) −1.13606e40 −0.104997
\(677\) 1.82761e41 1.65328 0.826640 0.562730i \(-0.190249\pi\)
0.826640 + 0.562730i \(0.190249\pi\)
\(678\) −1.92769e40 −0.170689
\(679\) −4.91685e38 −0.00426163
\(680\) −4.77286e40 −0.404948
\(681\) −1.77416e41 −1.47353
\(682\) 9.97446e40 0.810991
\(683\) −3.66780e39 −0.0291948 −0.0145974 0.999893i \(-0.504647\pi\)
−0.0145974 + 0.999893i \(0.504647\pi\)
\(684\) −5.03439e40 −0.392314
\(685\) 6.97460e40 0.532115
\(686\) 5.71356e39 0.0426783
\(687\) −7.35141e40 −0.537648
\(688\) −2.31718e41 −1.65931
\(689\) −1.82968e40 −0.128291
\(690\) −3.84492e39 −0.0263983
\(691\) 5.62493e40 0.378169 0.189084 0.981961i \(-0.439448\pi\)
0.189084 + 0.981961i \(0.439448\pi\)
\(692\) 5.46458e40 0.359765
\(693\) 3.83638e39 0.0247337
\(694\) 1.15971e41 0.732213
\(695\) 1.30676e40 0.0808012
\(696\) 2.79442e41 1.69222
\(697\) 4.53429e39 0.0268927
\(698\) −2.52531e40 −0.146693
\(699\) 3.38324e41 1.92493
\(700\) 7.18385e38 0.00400346
\(701\) 4.31831e40 0.235724 0.117862 0.993030i \(-0.462396\pi\)
0.117862 + 0.993030i \(0.462396\pi\)
\(702\) −3.03759e41 −1.62421
\(703\) −1.97000e41 −1.03184
\(704\) −7.53459e40 −0.386595
\(705\) −1.71470e41 −0.861878
\(706\) −2.45267e41 −1.20773
\(707\) 1.66844e39 0.00804878
\(708\) 1.85174e41 0.875181
\(709\) 3.70730e41 1.71667 0.858336 0.513088i \(-0.171499\pi\)
0.858336 + 0.513088i \(0.171499\pi\)
\(710\) −2.84001e40 −0.128847
\(711\) −4.63944e41 −2.06232
\(712\) 6.23303e39 0.0271481
\(713\) 7.85524e39 0.0335244
\(714\) −9.61528e39 −0.0402104
\(715\) 5.47522e40 0.224369
\(716\) −7.49262e40 −0.300881
\(717\) 2.45311e41 0.965361
\(718\) 7.58541e40 0.292533
\(719\) −3.14942e40 −0.119031 −0.0595157 0.998227i \(-0.518956\pi\)
−0.0595157 + 0.998227i \(0.518956\pi\)
\(720\) 3.02783e41 1.12153
\(721\) −4.49128e39 −0.0163045
\(722\) −1.54559e41 −0.549926
\(723\) 3.28800e41 1.14664
\(724\) −1.07863e41 −0.368690
\(725\) −2.77180e41 −0.928670
\(726\) 3.59222e41 1.17973
\(727\) 2.91745e41 0.939192 0.469596 0.882881i \(-0.344400\pi\)
0.469596 + 0.882881i \(0.344400\pi\)
\(728\) 3.86202e39 0.0121873
\(729\) −2.60209e41 −0.804957
\(730\) 7.40089e40 0.224441
\(731\) −5.02842e41 −1.49496
\(732\) −9.52976e40 −0.277761
\(733\) −3.81345e41 −1.08971 −0.544854 0.838531i \(-0.683415\pi\)
−0.544854 + 0.838531i \(0.683415\pi\)
\(734\) 7.83352e40 0.219464
\(735\) −2.89926e41 −0.796379
\(736\) 5.68062e39 0.0152991
\(737\) 8.35331e40 0.220587
\(738\) −2.23564e40 −0.0578876
\(739\) 5.69450e41 1.44581 0.722905 0.690947i \(-0.242806\pi\)
0.722905 + 0.690947i \(0.242806\pi\)
\(740\) −7.02969e40 −0.175015
\(741\) 3.98768e41 0.973546
\(742\) 1.46948e39 0.00351810
\(743\) 2.24951e41 0.528140 0.264070 0.964503i \(-0.414935\pi\)
0.264070 + 0.964503i \(0.414935\pi\)
\(744\) −7.14150e41 −1.64430
\(745\) 2.66039e40 0.0600731
\(746\) 7.36262e41 1.63049
\(747\) −6.22224e41 −1.35144
\(748\) 8.52307e40 0.181561
\(749\) 7.87693e39 0.0164578
\(750\) −7.84185e41 −1.60705
\(751\) −6.45261e41 −1.29705 −0.648524 0.761194i \(-0.724614\pi\)
−0.648524 + 0.761194i \(0.724614\pi\)
\(752\) 6.55901e41 1.29324
\(753\) 1.42432e42 2.75474
\(754\) 5.40890e41 1.02618
\(755\) 5.79734e40 0.107894
\(756\) 5.13067e39 0.00936716
\(757\) −8.68640e41 −1.55579 −0.777893 0.628397i \(-0.783711\pi\)
−0.777893 + 0.628397i \(0.783711\pi\)
\(758\) 3.95839e41 0.695528
\(759\) −1.89154e40 −0.0326069
\(760\) −1.58974e41 −0.268862
\(761\) 4.39407e41 0.729104 0.364552 0.931183i \(-0.381222\pi\)
0.364552 + 0.931183i \(0.381222\pi\)
\(762\) −1.31056e42 −2.13359
\(763\) −2.29306e40 −0.0366278
\(764\) −1.54451e41 −0.242068
\(765\) 6.57058e41 1.01045
\(766\) −6.77649e41 −1.02256
\(767\) −9.87434e41 −1.46209
\(768\) −8.99727e41 −1.30729
\(769\) −3.86450e41 −0.551012 −0.275506 0.961299i \(-0.588845\pi\)
−0.275506 + 0.961299i \(0.588845\pi\)
\(770\) −4.39734e39 −0.00615282
\(771\) 1.23698e42 1.69853
\(772\) 2.73329e41 0.368328
\(773\) 3.89700e41 0.515380 0.257690 0.966228i \(-0.417039\pi\)
0.257690 + 0.966228i \(0.417039\pi\)
\(774\) 2.47928e42 3.21796
\(775\) 7.08370e41 0.902372
\(776\) −1.48377e41 −0.185511
\(777\) 3.90148e40 0.0478768
\(778\) −1.25346e42 −1.50975
\(779\) 1.51028e40 0.0178552
\(780\) 1.42295e41 0.165127
\(781\) −1.39716e41 −0.159150
\(782\) 3.19161e40 0.0356872
\(783\) −1.97961e42 −2.17287
\(784\) 1.10901e42 1.19496
\(785\) −1.60870e41 −0.170163
\(786\) 4.39101e41 0.455972
\(787\) 8.84928e41 0.902140 0.451070 0.892488i \(-0.351042\pi\)
0.451070 + 0.892488i \(0.351042\pi\)
\(788\) −4.03784e41 −0.404128
\(789\) −3.01297e42 −2.96059
\(790\) 5.31782e41 0.513028
\(791\) −1.73624e39 −0.00164456
\(792\) 1.15771e42 1.07668
\(793\) 5.08171e41 0.464032
\(794\) −1.12972e42 −1.01292
\(795\) −1.49160e41 −0.131319
\(796\) 2.93363e41 0.253610
\(797\) −6.26660e41 −0.531969 −0.265985 0.963977i \(-0.585697\pi\)
−0.265985 + 0.963977i \(0.585697\pi\)
\(798\) −3.20265e40 −0.0266973
\(799\) 1.42335e42 1.16515
\(800\) 5.12267e41 0.411805
\(801\) −8.58073e40 −0.0677412
\(802\) −7.49409e41 −0.581019
\(803\) 3.64093e41 0.277228
\(804\) 2.17094e41 0.162344
\(805\) −3.46306e38 −0.000254343 0
\(806\) −1.38231e42 −0.997123
\(807\) 3.40392e42 2.41164
\(808\) 5.03489e41 0.350369
\(809\) −8.71861e41 −0.595928 −0.297964 0.954577i \(-0.596308\pi\)
−0.297964 + 0.954577i \(0.596308\pi\)
\(810\) −9.03766e41 −0.606769
\(811\) 9.09697e41 0.599922 0.299961 0.953952i \(-0.403026\pi\)
0.299961 + 0.953952i \(0.403026\pi\)
\(812\) −9.13595e39 −0.00591822
\(813\) 1.27958e42 0.814245
\(814\) −1.64440e42 −1.02791
\(815\) −7.43865e40 −0.0456782
\(816\) −3.73336e42 −2.25213
\(817\) −1.67486e42 −0.992565
\(818\) 2.22848e42 1.29743
\(819\) −5.31666e40 −0.0304104
\(820\) 5.38924e39 0.00302849
\(821\) 1.52548e42 0.842231 0.421115 0.907007i \(-0.361639\pi\)
0.421115 + 0.907007i \(0.361639\pi\)
\(822\) 4.24015e42 2.30006
\(823\) −1.67746e42 −0.894037 −0.447019 0.894525i \(-0.647514\pi\)
−0.447019 + 0.894525i \(0.647514\pi\)
\(824\) −1.35534e42 −0.709747
\(825\) −1.70575e42 −0.877676
\(826\) 7.93043e40 0.0400946
\(827\) −3.12102e42 −1.55048 −0.775242 0.631665i \(-0.782372\pi\)
−0.775242 + 0.631665i \(0.782372\pi\)
\(828\) −3.30948e40 −0.0161555
\(829\) −1.01143e42 −0.485174 −0.242587 0.970130i \(-0.577996\pi\)
−0.242587 + 0.970130i \(0.577996\pi\)
\(830\) 7.13207e41 0.336189
\(831\) 1.08501e42 0.502595
\(832\) 1.04418e42 0.475323
\(833\) 2.40663e42 1.07661
\(834\) 7.94436e41 0.349262
\(835\) −6.70050e41 −0.289503
\(836\) 2.83886e41 0.120546
\(837\) 5.05915e42 2.11134
\(838\) −1.37292e42 −0.563126
\(839\) 1.10356e42 0.444887 0.222443 0.974946i \(-0.428597\pi\)
0.222443 + 0.974946i \(0.428597\pi\)
\(840\) 3.14840e40 0.0124750
\(841\) 9.57314e41 0.372832
\(842\) 2.59240e42 0.992375
\(843\) −5.49860e42 −2.06896
\(844\) −6.06329e41 −0.224255
\(845\) 4.93863e41 0.179550
\(846\) −7.01785e42 −2.50804
\(847\) 3.23545e40 0.0113665
\(848\) 5.70562e41 0.197044
\(849\) −7.59106e42 −2.57716
\(850\) 2.87814e42 0.960587
\(851\) −1.29502e41 −0.0424912
\(852\) −3.63109e41 −0.117129
\(853\) 1.80886e42 0.573646 0.286823 0.957984i \(-0.407401\pi\)
0.286823 + 0.957984i \(0.407401\pi\)
\(854\) −4.08130e40 −0.0127250
\(855\) 2.18852e42 0.670876
\(856\) 2.37704e42 0.716417
\(857\) 3.58273e42 1.06168 0.530838 0.847473i \(-0.321877\pi\)
0.530838 + 0.847473i \(0.321877\pi\)
\(858\) 3.32861e42 0.969834
\(859\) 3.55534e42 1.01855 0.509273 0.860605i \(-0.329914\pi\)
0.509273 + 0.860605i \(0.329914\pi\)
\(860\) −5.97653e41 −0.168353
\(861\) −2.99103e39 −0.000828467 0
\(862\) −5.12970e42 −1.39713
\(863\) −5.78959e42 −1.55057 −0.775285 0.631612i \(-0.782394\pi\)
−0.775285 + 0.631612i \(0.782394\pi\)
\(864\) 3.65859e42 0.963528
\(865\) −2.37553e42 −0.615216
\(866\) 2.33033e42 0.593482
\(867\) −1.11695e42 −0.279740
\(868\) 2.33481e40 0.00575063
\(869\) 2.61614e42 0.633687
\(870\) 4.40946e42 1.05040
\(871\) −1.15765e42 −0.271215
\(872\) −6.91982e42 −1.59443
\(873\) 2.04263e42 0.462897
\(874\) 1.06306e41 0.0236942
\(875\) −7.06303e40 −0.0154837
\(876\) 9.46241e41 0.204029
\(877\) −1.74620e42 −0.370340 −0.185170 0.982707i \(-0.559284\pi\)
−0.185170 + 0.982707i \(0.559284\pi\)
\(878\) −8.64771e42 −1.80398
\(879\) 1.29265e43 2.65243
\(880\) −1.70737e42 −0.344611
\(881\) 6.11305e42 1.21369 0.606844 0.794821i \(-0.292435\pi\)
0.606844 + 0.794821i \(0.292435\pi\)
\(882\) −1.18659e43 −2.31744
\(883\) −5.67511e42 −1.09029 −0.545147 0.838340i \(-0.683526\pi\)
−0.545147 + 0.838340i \(0.683526\pi\)
\(884\) −1.18117e42 −0.223232
\(885\) −8.04978e42 −1.49660
\(886\) 6.85281e42 1.25337
\(887\) 1.28948e42 0.232019 0.116009 0.993248i \(-0.462990\pi\)
0.116009 + 0.993248i \(0.462990\pi\)
\(888\) 1.17736e43 2.08411
\(889\) −1.18040e41 −0.0205568
\(890\) 9.83542e40 0.0168515
\(891\) −4.44615e42 −0.749475
\(892\) 2.79988e42 0.464354
\(893\) 4.74087e42 0.773592
\(894\) 1.61736e42 0.259665
\(895\) 3.25715e42 0.514521
\(896\) −1.47262e41 −0.0228889
\(897\) 2.62140e41 0.0400906
\(898\) 2.82924e42 0.425758
\(899\) −9.00859e42 −1.33396
\(900\) −2.98442e42 −0.434854
\(901\) 1.23815e42 0.177527
\(902\) 1.26066e41 0.0177871
\(903\) 3.31698e41 0.0460543
\(904\) −5.23947e41 −0.0715888
\(905\) 4.68894e42 0.630478
\(906\) 3.52444e42 0.466371
\(907\) −6.85671e42 −0.892915 −0.446457 0.894805i \(-0.647315\pi\)
−0.446457 + 0.894805i \(0.647315\pi\)
\(908\) 1.75038e42 0.224331
\(909\) −6.93130e42 −0.874255
\(910\) 6.09407e40 0.00756497
\(911\) −6.18262e42 −0.755363 −0.377682 0.925936i \(-0.623279\pi\)
−0.377682 + 0.925936i \(0.623279\pi\)
\(912\) −1.24350e43 −1.49528
\(913\) 3.50868e42 0.415257
\(914\) −9.10348e42 −1.06044
\(915\) 4.14272e42 0.474985
\(916\) 7.25289e41 0.0818516
\(917\) 3.95491e40 0.00439321
\(918\) 2.05555e43 2.24755
\(919\) 7.15141e42 0.769691 0.384846 0.922981i \(-0.374255\pi\)
0.384846 + 0.922981i \(0.374255\pi\)
\(920\) −1.04505e41 −0.0110717
\(921\) −9.19938e42 −0.959387
\(922\) 1.52402e43 1.56456
\(923\) 1.93626e42 0.195677
\(924\) −5.62222e40 −0.00559325
\(925\) −1.16783e43 −1.14373
\(926\) 7.22663e42 0.696749
\(927\) 1.86583e43 1.77099
\(928\) −6.51468e42 −0.608762
\(929\) 1.19347e43 1.09795 0.548975 0.835839i \(-0.315018\pi\)
0.548975 + 0.835839i \(0.315018\pi\)
\(930\) −1.12689e43 −1.02066
\(931\) 8.01598e42 0.714803
\(932\) −3.33790e42 −0.293051
\(933\) −2.60363e43 −2.25058
\(934\) −2.35024e43 −2.00024
\(935\) −3.70510e42 −0.310479
\(936\) −1.60442e43 −1.32379
\(937\) −4.02931e42 −0.327345 −0.163673 0.986515i \(-0.552334\pi\)
−0.163673 + 0.986515i \(0.552334\pi\)
\(938\) 9.29747e40 0.00743744
\(939\) 3.89442e43 3.06755
\(940\) 1.69172e42 0.131212
\(941\) 9.40592e42 0.718376 0.359188 0.933265i \(-0.383054\pi\)
0.359188 + 0.933265i \(0.383054\pi\)
\(942\) −9.77996e42 −0.735527
\(943\) 9.92816e39 0.000735274 0
\(944\) 3.07918e43 2.24564
\(945\) −2.23038e41 −0.0160183
\(946\) −1.39805e43 −0.988781
\(947\) −1.85611e43 −1.29279 −0.646397 0.763001i \(-0.723725\pi\)
−0.646397 + 0.763001i \(0.723725\pi\)
\(948\) 6.79910e42 0.466370
\(949\) −5.04579e42 −0.340855
\(950\) 9.58647e42 0.637773
\(951\) −1.49276e43 −0.978078
\(952\) −2.61344e41 −0.0168646
\(953\) −3.20332e42 −0.203588 −0.101794 0.994805i \(-0.532458\pi\)
−0.101794 + 0.994805i \(0.532458\pi\)
\(954\) −6.10475e42 −0.382135
\(955\) 6.71420e42 0.413948
\(956\) −2.42024e42 −0.146967
\(957\) 2.16927e43 1.29745
\(958\) 1.46573e43 0.863482
\(959\) 3.81903e41 0.0221607
\(960\) 8.51243e42 0.486542
\(961\) 5.26074e42 0.296181
\(962\) 2.27890e43 1.26383
\(963\) −3.27235e43 −1.78764
\(964\) −3.24393e42 −0.174564
\(965\) −1.18820e43 −0.629860
\(966\) −2.10534e40 −0.00109939
\(967\) 5.23025e42 0.269053 0.134527 0.990910i \(-0.457049\pi\)
0.134527 + 0.990910i \(0.457049\pi\)
\(968\) 9.76368e42 0.494790
\(969\) −2.69848e43 −1.34718
\(970\) −2.34131e42 −0.115151
\(971\) −2.58906e43 −1.25448 −0.627239 0.778827i \(-0.715815\pi\)
−0.627239 + 0.778827i \(0.715815\pi\)
\(972\) −1.20881e42 −0.0577028
\(973\) 7.15536e40 0.00336508
\(974\) −2.73998e43 −1.26953
\(975\) 2.36393e43 1.07911
\(976\) −1.58466e43 −0.712712
\(977\) 6.80879e42 0.301716 0.150858 0.988555i \(-0.451796\pi\)
0.150858 + 0.988555i \(0.451796\pi\)
\(978\) −4.52226e42 −0.197443
\(979\) 4.83861e41 0.0208148
\(980\) 2.86040e42 0.121241
\(981\) 9.52620e43 3.97850
\(982\) 2.08435e43 0.857735
\(983\) −4.18545e43 −1.69713 −0.848566 0.529089i \(-0.822534\pi\)
−0.848566 + 0.529089i \(0.822534\pi\)
\(984\) −9.02608e41 −0.0360637
\(985\) 1.75531e43 0.691080
\(986\) −3.66023e43 −1.42001
\(987\) −9.38906e41 −0.0358941
\(988\) −3.93424e42 −0.148213
\(989\) −1.10101e42 −0.0408738
\(990\) 1.82681e43 0.668318
\(991\) 2.63339e43 0.949397 0.474699 0.880148i \(-0.342557\pi\)
0.474699 + 0.880148i \(0.342557\pi\)
\(992\) 1.66491e43 0.591523
\(993\) −2.28237e43 −0.799138
\(994\) −1.55508e41 −0.00536600
\(995\) −1.27529e43 −0.433686
\(996\) 9.11870e42 0.305614
\(997\) −1.61216e43 −0.532511 −0.266255 0.963903i \(-0.585786\pi\)
−0.266255 + 0.963903i \(0.585786\pi\)
\(998\) 2.97416e43 0.968216
\(999\) −8.34058e43 −2.67606
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 1.30.a.a.1.2 2
3.2 odd 2 9.30.a.a.1.1 2
4.3 odd 2 16.30.a.c.1.2 2
5.2 odd 4 25.30.b.a.24.4 4
5.3 odd 4 25.30.b.a.24.1 4
5.4 even 2 25.30.a.a.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.30.a.a.1.2 2 1.1 even 1 trivial
9.30.a.a.1.1 2 3.2 odd 2
16.30.a.c.1.2 2 4.3 odd 2
25.30.a.a.1.1 2 5.4 even 2
25.30.b.a.24.1 4 5.3 odd 4
25.30.b.a.24.4 4 5.2 odd 4