Properties

Label 1.94.a.a.1.2
Level 1
Weight 94
Character 1.1
Self dual yes
Analytic conductor 54.773
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 94 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.7725430605\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 160477500301516091326739 x^{5} + 877016488484326647371325741724874 x^{4} + 7260529465737129707868752892581169765229378456 x^{3} - 20781038399188480098606854392326662967337072615105929280 x^{2} - 71309214652872234197294752847774640455181142633761719353245451878000 x - 1353216958878139720025204995487184336935523797943751976847532373756765247900000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.45391e11\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35097e14 q^{2} -1.21702e22 q^{3} +8.34770e27 q^{4} +3.52234e32 q^{5} +1.64416e36 q^{6} -7.46408e38 q^{7} +2.10186e41 q^{8} -8.75419e43 q^{9} +O(q^{10})\) \(q-1.35097e14 q^{2} -1.21702e22 q^{3} +8.34770e27 q^{4} +3.52234e32 q^{5} +1.64416e36 q^{6} -7.46408e38 q^{7} +2.10186e41 q^{8} -8.75419e43 q^{9} -4.75858e46 q^{10} -9.09961e47 q^{11} -1.01593e50 q^{12} -6.25337e51 q^{13} +1.00838e53 q^{14} -4.28675e54 q^{15} -1.11067e56 q^{16} +2.83546e57 q^{17} +1.18267e58 q^{18} -8.20370e57 q^{19} +2.94035e60 q^{20} +9.08391e60 q^{21} +1.22933e62 q^{22} -2.05771e63 q^{23} -2.55800e63 q^{24} +2.30946e64 q^{25} +8.44812e65 q^{26} +3.93336e66 q^{27} -6.23079e66 q^{28} +1.94947e68 q^{29} +5.79127e68 q^{30} +8.59696e68 q^{31} +1.29233e70 q^{32} +1.10744e70 q^{33} -3.83062e71 q^{34} -2.62910e71 q^{35} -7.30774e71 q^{36} +9.63679e71 q^{37} +1.10830e72 q^{38} +7.61046e73 q^{39} +7.40347e73 q^{40} +1.11843e75 q^{41} -1.22721e75 q^{42} -1.49706e76 q^{43} -7.59609e75 q^{44} -3.08352e76 q^{45} +2.77991e77 q^{46} -6.74418e75 q^{47} +1.35171e78 q^{48} -3.37039e78 q^{49} -3.12001e78 q^{50} -3.45080e79 q^{51} -5.22013e79 q^{52} +2.18289e80 q^{53} -5.31386e80 q^{54} -3.20519e80 q^{55} -1.56885e80 q^{56} +9.98404e79 q^{57} -2.63368e82 q^{58} -4.18777e82 q^{59} -3.57845e82 q^{60} +3.83206e82 q^{61} -1.16142e83 q^{62} +6.53420e82 q^{63} -6.45940e83 q^{64} -2.20265e84 q^{65} -1.49612e84 q^{66} +2.76024e84 q^{67} +2.36696e85 q^{68} +2.50427e85 q^{69} +3.55184e85 q^{70} +1.96031e86 q^{71} -1.84001e85 q^{72} -1.54628e86 q^{73} -1.30190e86 q^{74} -2.81065e86 q^{75} -6.84821e85 q^{76} +6.79202e86 q^{77} -1.02815e88 q^{78} +8.28611e87 q^{79} -3.91216e88 q^{80} -2.72400e88 q^{81} -1.51096e89 q^{82} +1.06612e89 q^{83} +7.58298e88 q^{84} +9.98745e89 q^{85} +2.02248e90 q^{86} -2.37254e90 q^{87} -1.91261e89 q^{88} -1.04123e90 q^{89} +4.16575e90 q^{90} +4.66757e90 q^{91} -1.71772e91 q^{92} -1.04627e91 q^{93} +9.11120e89 q^{94} -2.88962e90 q^{95} -1.57278e92 q^{96} -3.92105e92 q^{97} +4.55330e92 q^{98} +7.96597e91 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + O(q^{10}) \) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + \)\(56\!\cdots\!00\)\(q^{10} + \)\(10\!\cdots\!24\)\(q^{11} - \)\(16\!\cdots\!48\)\(q^{12} + \)\(19\!\cdots\!26\)\(q^{13} - \)\(82\!\cdots\!32\)\(q^{14} - \)\(16\!\cdots\!00\)\(q^{15} - \)\(18\!\cdots\!48\)\(q^{16} + \)\(80\!\cdots\!42\)\(q^{17} + \)\(79\!\cdots\!36\)\(q^{18} - \)\(49\!\cdots\!00\)\(q^{19} - \)\(58\!\cdots\!00\)\(q^{20} + \)\(54\!\cdots\!84\)\(q^{21} + \)\(34\!\cdots\!44\)\(q^{22} - \)\(25\!\cdots\!64\)\(q^{23} - \)\(29\!\cdots\!00\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(79\!\cdots\!64\)\(q^{26} - \)\(10\!\cdots\!40\)\(q^{27} + \)\(19\!\cdots\!24\)\(q^{28} + \)\(11\!\cdots\!50\)\(q^{29} - \)\(64\!\cdots\!00\)\(q^{30} - \)\(11\!\cdots\!56\)\(q^{31} - \)\(70\!\cdots\!88\)\(q^{32} + \)\(66\!\cdots\!12\)\(q^{33} + \)\(80\!\cdots\!28\)\(q^{34} - \)\(16\!\cdots\!00\)\(q^{35} + \)\(52\!\cdots\!12\)\(q^{36} + \)\(11\!\cdots\!42\)\(q^{37} - \)\(42\!\cdots\!60\)\(q^{38} - \)\(20\!\cdots\!68\)\(q^{39} + \)\(76\!\cdots\!00\)\(q^{40} - \)\(50\!\cdots\!46\)\(q^{41} - \)\(54\!\cdots\!76\)\(q^{42} - \)\(72\!\cdots\!44\)\(q^{43} + \)\(94\!\cdots\!08\)\(q^{44} + \)\(16\!\cdots\!50\)\(q^{45} - \)\(63\!\cdots\!16\)\(q^{46} - \)\(37\!\cdots\!08\)\(q^{47} - \)\(41\!\cdots\!64\)\(q^{48} + \)\(25\!\cdots\!99\)\(q^{49} - \)\(31\!\cdots\!00\)\(q^{50} - \)\(55\!\cdots\!36\)\(q^{51} - \)\(55\!\cdots\!28\)\(q^{52} - \)\(36\!\cdots\!34\)\(q^{53} - \)\(19\!\cdots\!00\)\(q^{54} - \)\(35\!\cdots\!00\)\(q^{55} - \)\(12\!\cdots\!00\)\(q^{56} - \)\(13\!\cdots\!80\)\(q^{57} - \)\(73\!\cdots\!40\)\(q^{58} - \)\(11\!\cdots\!00\)\(q^{59} - \)\(46\!\cdots\!00\)\(q^{60} - \)\(32\!\cdots\!26\)\(q^{61} - \)\(99\!\cdots\!36\)\(q^{62} - \)\(22\!\cdots\!64\)\(q^{63} - \)\(47\!\cdots\!16\)\(q^{64} + \)\(24\!\cdots\!00\)\(q^{65} + \)\(12\!\cdots\!08\)\(q^{66} + \)\(97\!\cdots\!92\)\(q^{67} + \)\(51\!\cdots\!24\)\(q^{68} + \)\(12\!\cdots\!92\)\(q^{69} + \)\(43\!\cdots\!00\)\(q^{70} + \)\(42\!\cdots\!84\)\(q^{71} + \)\(11\!\cdots\!80\)\(q^{72} + \)\(24\!\cdots\!86\)\(q^{73} + \)\(98\!\cdots\!48\)\(q^{74} + \)\(94\!\cdots\!00\)\(q^{75} - \)\(98\!\cdots\!00\)\(q^{76} - \)\(16\!\cdots\!56\)\(q^{77} - \)\(73\!\cdots\!28\)\(q^{78} - \)\(43\!\cdots\!00\)\(q^{79} - \)\(88\!\cdots\!00\)\(q^{80} - \)\(70\!\cdots\!53\)\(q^{81} - \)\(23\!\cdots\!76\)\(q^{82} - \)\(20\!\cdots\!04\)\(q^{83} + \)\(16\!\cdots\!28\)\(q^{84} + \)\(16\!\cdots\!00\)\(q^{85} + \)\(32\!\cdots\!24\)\(q^{86} + \)\(65\!\cdots\!80\)\(q^{87} + \)\(63\!\cdots\!20\)\(q^{88} + \)\(55\!\cdots\!50\)\(q^{89} + \)\(19\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} - \)\(81\!\cdots\!08\)\(q^{92} - \)\(12\!\cdots\!28\)\(q^{93} - \)\(30\!\cdots\!92\)\(q^{94} - \)\(21\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!16\)\(q^{96} + \)\(43\!\cdots\!42\)\(q^{97} - \)\(69\!\cdots\!56\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35097e14 −1.35754 −0.678768 0.734353i \(-0.737486\pi\)
−0.678768 + 0.734353i \(0.737486\pi\)
\(3\) −1.21702e22 −0.792790 −0.396395 0.918080i \(-0.629739\pi\)
−0.396395 + 0.918080i \(0.629739\pi\)
\(4\) 8.34770e27 0.842903
\(5\) 3.52234e32 1.10848 0.554238 0.832358i \(-0.313010\pi\)
0.554238 + 0.832358i \(0.313010\pi\)
\(6\) 1.64416e36 1.07624
\(7\) −7.46408e38 −0.376632 −0.188316 0.982108i \(-0.560303\pi\)
−0.188316 + 0.982108i \(0.560303\pi\)
\(8\) 2.10186e41 0.213265
\(9\) −8.75419e43 −0.371483
\(10\) −4.75858e46 −1.50479
\(11\) −9.09961e47 −0.342187 −0.171093 0.985255i \(-0.554730\pi\)
−0.171093 + 0.985255i \(0.554730\pi\)
\(12\) −1.01593e50 −0.668245
\(13\) −6.25337e51 −0.994829 −0.497414 0.867513i \(-0.665717\pi\)
−0.497414 + 0.867513i \(0.665717\pi\)
\(14\) 1.00838e53 0.511291
\(15\) −4.28675e54 −0.878789
\(16\) −1.11067e56 −1.13242
\(17\) 2.83546e57 1.72484 0.862420 0.506194i \(-0.168948\pi\)
0.862420 + 0.506194i \(0.168948\pi\)
\(18\) 1.18267e58 0.504302
\(19\) −8.20370e57 −0.0283118 −0.0141559 0.999900i \(-0.504506\pi\)
−0.0141559 + 0.999900i \(0.504506\pi\)
\(20\) 2.94035e60 0.934337
\(21\) 9.08391e60 0.298590
\(22\) 1.22933e62 0.464531
\(23\) −2.05771e63 −0.984102 −0.492051 0.870566i \(-0.663753\pi\)
−0.492051 + 0.870566i \(0.663753\pi\)
\(24\) −2.55800e63 −0.169075
\(25\) 2.30946e64 0.228717
\(26\) 8.44812e65 1.35052
\(27\) 3.93336e66 1.08730
\(28\) −6.23079e66 −0.317464
\(29\) 1.94947e68 1.94272 0.971360 0.237611i \(-0.0763645\pi\)
0.971360 + 0.237611i \(0.0763645\pi\)
\(30\) 5.79127e68 1.19299
\(31\) 8.59696e68 0.385502 0.192751 0.981248i \(-0.438259\pi\)
0.192751 + 0.981248i \(0.438259\pi\)
\(32\) 1.29233e70 1.32403
\(33\) 1.10744e70 0.271282
\(34\) −3.83062e71 −2.34153
\(35\) −2.62910e71 −0.417487
\(36\) −7.30774e71 −0.313124
\(37\) 9.63679e71 0.115492 0.0577461 0.998331i \(-0.481609\pi\)
0.0577461 + 0.998331i \(0.481609\pi\)
\(38\) 1.10830e72 0.0384343
\(39\) 7.61046e73 0.788691
\(40\) 7.40347e73 0.236399
\(41\) 1.11843e75 1.13281 0.566406 0.824126i \(-0.308333\pi\)
0.566406 + 0.824126i \(0.308333\pi\)
\(42\) −1.22721e75 −0.405347
\(43\) −1.49706e76 −1.65560 −0.827799 0.561025i \(-0.810407\pi\)
−0.827799 + 0.561025i \(0.810407\pi\)
\(44\) −7.59609e75 −0.288430
\(45\) −3.08352e76 −0.411780
\(46\) 2.77991e77 1.33595
\(47\) −6.74418e75 −0.0119228 −0.00596141 0.999982i \(-0.501898\pi\)
−0.00596141 + 0.999982i \(0.501898\pi\)
\(48\) 1.35171e78 0.897770
\(49\) −3.37039e78 −0.858148
\(50\) −3.12001e78 −0.310492
\(51\) −3.45080e79 −1.36744
\(52\) −5.22013e79 −0.838544
\(53\) 2.18289e80 1.44612 0.723060 0.690785i \(-0.242735\pi\)
0.723060 + 0.690785i \(0.242735\pi\)
\(54\) −5.31386e80 −1.47605
\(55\) −3.20519e80 −0.379305
\(56\) −1.56885e80 −0.0803225
\(57\) 9.98404e79 0.0224453
\(58\) −2.63368e82 −2.63731
\(59\) −4.18777e82 −1.89393 −0.946965 0.321337i \(-0.895868\pi\)
−0.946965 + 0.321337i \(0.895868\pi\)
\(60\) −3.57845e82 −0.740733
\(61\) 3.83206e82 0.367786 0.183893 0.982946i \(-0.441130\pi\)
0.183893 + 0.982946i \(0.441130\pi\)
\(62\) −1.16142e83 −0.523332
\(63\) 6.53420e82 0.139913
\(64\) −6.45940e83 −0.665003
\(65\) −2.20265e84 −1.10274
\(66\) −1.49612e84 −0.368275
\(67\) 2.76024e84 0.337651 0.168826 0.985646i \(-0.446003\pi\)
0.168826 + 0.985646i \(0.446003\pi\)
\(68\) 2.36696e85 1.45387
\(69\) 2.50427e85 0.780187
\(70\) 3.55184e85 0.566754
\(71\) 1.96031e86 1.61738 0.808691 0.588234i \(-0.200176\pi\)
0.808691 + 0.588234i \(0.200176\pi\)
\(72\) −1.84001e85 −0.0792244
\(73\) −1.54628e86 −0.350570 −0.175285 0.984518i \(-0.556085\pi\)
−0.175285 + 0.984518i \(0.556085\pi\)
\(74\) −1.30190e86 −0.156785
\(75\) −2.81065e86 −0.181325
\(76\) −6.84821e85 −0.0238641
\(77\) 6.79202e86 0.128878
\(78\) −1.02815e88 −1.07068
\(79\) 8.28611e87 0.477190 0.238595 0.971119i \(-0.423313\pi\)
0.238595 + 0.971119i \(0.423313\pi\)
\(80\) −3.91216e88 −1.25526
\(81\) −2.72400e88 −0.490517
\(82\) −1.51096e89 −1.53783
\(83\) 1.06612e89 0.617552 0.308776 0.951135i \(-0.400081\pi\)
0.308776 + 0.951135i \(0.400081\pi\)
\(84\) 7.58298e88 0.251683
\(85\) 9.98745e89 1.91194
\(86\) 2.02248e90 2.24753
\(87\) −2.37254e90 −1.54017
\(88\) −1.91261e89 −0.0729765
\(89\) −1.04123e90 −0.234916 −0.117458 0.993078i \(-0.537475\pi\)
−0.117458 + 0.993078i \(0.537475\pi\)
\(90\) 4.16575e90 0.559006
\(91\) 4.66757e90 0.374684
\(92\) −1.71772e91 −0.829503
\(93\) −1.04627e91 −0.305622
\(94\) 9.11120e89 0.0161857
\(95\) −2.88962e90 −0.0313829
\(96\) −1.57278e92 −1.04968
\(97\) −3.92105e92 −1.61628 −0.808141 0.588990i \(-0.799526\pi\)
−0.808141 + 0.588990i \(0.799526\pi\)
\(98\) 4.55330e92 1.16497
\(99\) 7.96597e91 0.127117
\(100\) 1.92787e92 0.192787
\(101\) 9.67912e92 0.609385 0.304693 0.952451i \(-0.401446\pi\)
0.304693 + 0.952451i \(0.401446\pi\)
\(102\) 4.66194e93 1.85634
\(103\) 9.38508e92 0.237414 0.118707 0.992929i \(-0.462125\pi\)
0.118707 + 0.992929i \(0.462125\pi\)
\(104\) −1.31437e93 −0.212162
\(105\) 3.19966e93 0.330980
\(106\) −2.94902e94 −1.96316
\(107\) −8.54504e93 −0.367594 −0.183797 0.982964i \(-0.558839\pi\)
−0.183797 + 0.982964i \(0.558839\pi\)
\(108\) 3.28345e94 0.916487
\(109\) −7.14180e94 −1.29860 −0.649300 0.760532i \(-0.724938\pi\)
−0.649300 + 0.760532i \(0.724938\pi\)
\(110\) 4.33012e94 0.514921
\(111\) −1.17281e94 −0.0915611
\(112\) 8.29014e94 0.426505
\(113\) −2.74778e95 −0.935050 −0.467525 0.883980i \(-0.654854\pi\)
−0.467525 + 0.883980i \(0.654854\pi\)
\(114\) −1.34882e94 −0.0304703
\(115\) −7.24796e95 −1.09085
\(116\) 1.62736e96 1.63752
\(117\) 5.47432e95 0.369562
\(118\) 5.65755e96 2.57108
\(119\) −2.11641e96 −0.649630
\(120\) −9.01015e95 −0.187415
\(121\) −6.24360e96 −0.882908
\(122\) −5.17701e96 −0.499283
\(123\) −1.36114e97 −0.898083
\(124\) 7.17649e96 0.324940
\(125\) −2.74319e97 −0.854948
\(126\) −8.82751e96 −0.189936
\(127\) 2.13172e97 0.317582 0.158791 0.987312i \(-0.449240\pi\)
0.158791 + 0.987312i \(0.449240\pi\)
\(128\) −4.07212e97 −0.421267
\(129\) 1.82194e98 1.31254
\(130\) 2.97572e98 1.49701
\(131\) −3.85452e98 −1.35786 −0.678929 0.734204i \(-0.737556\pi\)
−0.678929 + 0.734204i \(0.737556\pi\)
\(132\) 9.24457e97 0.228665
\(133\) 6.12330e96 0.0106631
\(134\) −3.72900e98 −0.458374
\(135\) 1.38546e99 1.20524
\(136\) 5.95974e98 0.367848
\(137\) −1.13582e98 −0.0498660 −0.0249330 0.999689i \(-0.507937\pi\)
−0.0249330 + 0.999689i \(0.507937\pi\)
\(138\) −3.38320e99 −1.05913
\(139\) −1.16575e99 −0.260867 −0.130433 0.991457i \(-0.541637\pi\)
−0.130433 + 0.991457i \(0.541637\pi\)
\(140\) −2.19470e99 −0.351901
\(141\) 8.20779e97 0.00945230
\(142\) −2.64833e100 −2.19565
\(143\) 5.69033e99 0.340417
\(144\) 9.72303e99 0.420674
\(145\) 6.86671e100 2.15346
\(146\) 2.08897e100 0.475911
\(147\) 4.10182e100 0.680332
\(148\) 8.04451e99 0.0973486
\(149\) −8.82955e100 −0.781227 −0.390613 0.920555i \(-0.627737\pi\)
−0.390613 + 0.920555i \(0.627737\pi\)
\(150\) 3.79710e100 0.246155
\(151\) −2.05344e101 −0.977357 −0.488679 0.872464i \(-0.662521\pi\)
−0.488679 + 0.872464i \(0.662521\pi\)
\(152\) −1.72430e99 −0.00603791
\(153\) −2.48222e101 −0.640749
\(154\) −9.17583e100 −0.174957
\(155\) 3.02814e101 0.427319
\(156\) 6.35299e101 0.664790
\(157\) −7.80688e101 −0.606937 −0.303469 0.952841i \(-0.598145\pi\)
−0.303469 + 0.952841i \(0.598145\pi\)
\(158\) −1.11943e102 −0.647802
\(159\) −2.65662e102 −1.14647
\(160\) 4.55202e102 1.46766
\(161\) 1.53589e102 0.370645
\(162\) 3.68005e102 0.665894
\(163\) −3.76190e102 −0.511309 −0.255655 0.966768i \(-0.582291\pi\)
−0.255655 + 0.966768i \(0.582291\pi\)
\(164\) 9.33629e102 0.954850
\(165\) 3.90078e102 0.300710
\(166\) −1.44029e103 −0.838348
\(167\) 2.37736e103 1.04659 0.523297 0.852150i \(-0.324702\pi\)
0.523297 + 0.852150i \(0.324702\pi\)
\(168\) 1.90931e102 0.0636789
\(169\) −4.07583e101 −0.0103154
\(170\) −1.34928e104 −2.59553
\(171\) 7.18167e101 0.0105174
\(172\) −1.24970e104 −1.39551
\(173\) −5.20572e102 −0.0443953 −0.0221976 0.999754i \(-0.507066\pi\)
−0.0221976 + 0.999754i \(0.507066\pi\)
\(174\) 3.20524e104 2.09084
\(175\) −1.72380e103 −0.0861423
\(176\) 1.01067e104 0.387498
\(177\) 5.09658e104 1.50149
\(178\) 1.40668e104 0.318907
\(179\) −7.50757e104 −1.31170 −0.655849 0.754893i \(-0.727689\pi\)
−0.655849 + 0.754893i \(0.727689\pi\)
\(180\) −2.57403e104 −0.347091
\(181\) 8.74638e104 0.911538 0.455769 0.890098i \(-0.349364\pi\)
0.455769 + 0.890098i \(0.349364\pi\)
\(182\) −6.30575e104 −0.508648
\(183\) −4.66369e104 −0.291577
\(184\) −4.32503e104 −0.209875
\(185\) 3.39441e104 0.128020
\(186\) 1.41347e105 0.414893
\(187\) −2.58016e105 −0.590217
\(188\) −5.62985e103 −0.0100498
\(189\) −2.93589e105 −0.409512
\(190\) 3.90379e104 0.0426034
\(191\) −1.94469e106 −1.66264 −0.831320 0.555795i \(-0.812414\pi\)
−0.831320 + 0.555795i \(0.812414\pi\)
\(192\) 7.86121e105 0.527208
\(193\) 3.62395e105 0.190883 0.0954415 0.995435i \(-0.469574\pi\)
0.0954415 + 0.995435i \(0.469574\pi\)
\(194\) 5.29723e106 2.19416
\(195\) 2.68066e106 0.874244
\(196\) −2.81350e106 −0.723336
\(197\) 3.73179e106 0.757247 0.378623 0.925551i \(-0.376398\pi\)
0.378623 + 0.925551i \(0.376398\pi\)
\(198\) −1.07618e106 −0.172565
\(199\) −5.95317e106 −0.755232 −0.377616 0.925962i \(-0.623256\pi\)
−0.377616 + 0.925962i \(0.623256\pi\)
\(200\) 4.85416e105 0.0487774
\(201\) −3.35926e106 −0.267687
\(202\) −1.30762e107 −0.827262
\(203\) −1.45510e107 −0.731691
\(204\) −2.88063e107 −1.15262
\(205\) 3.93948e107 1.25569
\(206\) −1.26790e107 −0.322299
\(207\) 1.80136e107 0.365578
\(208\) 6.94545e107 1.12656
\(209\) 7.46505e105 0.00968792
\(210\) −4.32265e107 −0.449317
\(211\) 1.07157e108 0.893071 0.446535 0.894766i \(-0.352658\pi\)
0.446535 + 0.894766i \(0.352658\pi\)
\(212\) 1.82221e108 1.21894
\(213\) −2.38574e108 −1.28225
\(214\) 1.15441e108 0.499022
\(215\) −5.27314e108 −1.83519
\(216\) 8.26738e107 0.231883
\(217\) −6.41684e107 −0.145192
\(218\) 9.64837e108 1.76290
\(219\) 1.88185e108 0.277928
\(220\) −2.67560e108 −0.319718
\(221\) −1.77312e109 −1.71592
\(222\) 1.58444e108 0.124297
\(223\) −1.79075e109 −1.13988 −0.569939 0.821687i \(-0.693033\pi\)
−0.569939 + 0.821687i \(0.693033\pi\)
\(224\) −9.64603e108 −0.498673
\(225\) −2.02174e108 −0.0849647
\(226\) 3.71217e109 1.26936
\(227\) 5.85209e109 1.62970 0.814851 0.579670i \(-0.196819\pi\)
0.814851 + 0.579670i \(0.196819\pi\)
\(228\) 8.33439e107 0.0189192
\(229\) −2.36374e109 −0.437774 −0.218887 0.975750i \(-0.570243\pi\)
−0.218887 + 0.975750i \(0.570243\pi\)
\(230\) 9.79179e109 1.48087
\(231\) −8.26601e108 −0.102174
\(232\) 4.09752e109 0.414314
\(233\) −1.31479e110 −1.08845 −0.544224 0.838940i \(-0.683176\pi\)
−0.544224 + 0.838940i \(0.683176\pi\)
\(234\) −7.39565e109 −0.501694
\(235\) −2.37553e108 −0.0132162
\(236\) −3.49582e110 −1.59640
\(237\) −1.00843e110 −0.378311
\(238\) 2.85921e110 0.881896
\(239\) −5.33449e110 −1.35391 −0.676957 0.736023i \(-0.736702\pi\)
−0.676957 + 0.736023i \(0.736702\pi\)
\(240\) 4.76117e110 0.995156
\(241\) 2.92728e110 0.504280 0.252140 0.967691i \(-0.418866\pi\)
0.252140 + 0.967691i \(0.418866\pi\)
\(242\) 8.43493e110 1.19858
\(243\) −5.95401e110 −0.698422
\(244\) 3.19889e110 0.310008
\(245\) −1.18717e111 −0.951236
\(246\) 1.83887e111 1.21918
\(247\) 5.13008e109 0.0281654
\(248\) 1.80696e110 0.0822140
\(249\) −1.29748e111 −0.489589
\(250\) 3.70596e111 1.16062
\(251\) −4.28523e111 −1.11467 −0.557334 0.830288i \(-0.688176\pi\)
−0.557334 + 0.830288i \(0.688176\pi\)
\(252\) 5.45455e110 0.117933
\(253\) 1.87244e111 0.336747
\(254\) −2.87989e111 −0.431129
\(255\) −1.21549e112 −1.51577
\(256\) 1.18984e112 1.23689
\(257\) 9.96450e111 0.864102 0.432051 0.901849i \(-0.357790\pi\)
0.432051 + 0.901849i \(0.357790\pi\)
\(258\) −2.46139e112 −1.78182
\(259\) −7.19298e110 −0.0434980
\(260\) −1.83871e112 −0.929505
\(261\) −1.70661e112 −0.721688
\(262\) 5.20734e112 1.84334
\(263\) 3.07644e112 0.912233 0.456116 0.889920i \(-0.349240\pi\)
0.456116 + 0.889920i \(0.349240\pi\)
\(264\) 2.32768e111 0.0578550
\(265\) 7.68889e112 1.60299
\(266\) −8.27241e110 −0.0144756
\(267\) 1.26720e112 0.186239
\(268\) 2.30417e112 0.284607
\(269\) −8.31534e112 −0.863771 −0.431886 0.901928i \(-0.642152\pi\)
−0.431886 + 0.901928i \(0.642152\pi\)
\(270\) −1.87172e113 −1.63616
\(271\) 1.06596e113 0.784638 0.392319 0.919829i \(-0.371673\pi\)
0.392319 + 0.919829i \(0.371673\pi\)
\(272\) −3.14927e113 −1.95324
\(273\) −5.68051e112 −0.297046
\(274\) 1.53447e112 0.0676949
\(275\) −2.10152e112 −0.0782641
\(276\) 2.09049e113 0.657622
\(277\) 5.26210e113 1.39910 0.699551 0.714582i \(-0.253383\pi\)
0.699551 + 0.714582i \(0.253383\pi\)
\(278\) 1.57490e113 0.354136
\(279\) −7.52594e112 −0.143207
\(280\) −5.52601e112 −0.0890355
\(281\) −9.84704e113 −1.34419 −0.672097 0.740463i \(-0.734606\pi\)
−0.672097 + 0.740463i \(0.734606\pi\)
\(282\) −1.10885e112 −0.0128318
\(283\) 8.24676e113 0.809494 0.404747 0.914429i \(-0.367360\pi\)
0.404747 + 0.914429i \(0.367360\pi\)
\(284\) 1.63641e114 1.36330
\(285\) 3.51672e112 0.0248801
\(286\) −7.68747e113 −0.462128
\(287\) −8.34802e113 −0.426653
\(288\) −1.13133e114 −0.491856
\(289\) 5.33743e114 1.97507
\(290\) −9.27672e114 −2.92340
\(291\) 4.77199e114 1.28137
\(292\) −1.29079e114 −0.295496
\(293\) 5.87130e114 1.14654 0.573271 0.819366i \(-0.305674\pi\)
0.573271 + 0.819366i \(0.305674\pi\)
\(294\) −5.54144e114 −0.923575
\(295\) −1.47507e115 −2.09937
\(296\) 2.02552e113 0.0246304
\(297\) −3.57921e114 −0.372059
\(298\) 1.19285e115 1.06054
\(299\) 1.28676e115 0.979014
\(300\) −2.34625e114 −0.152839
\(301\) 1.11741e115 0.623551
\(302\) 2.77413e115 1.32680
\(303\) −1.17797e115 −0.483115
\(304\) 9.11162e113 0.0320608
\(305\) 1.34978e115 0.407682
\(306\) 3.35340e115 0.869840
\(307\) −8.62573e115 −1.92248 −0.961239 0.275716i \(-0.911085\pi\)
−0.961239 + 0.275716i \(0.911085\pi\)
\(308\) 5.66978e114 0.108632
\(309\) −1.14218e115 −0.188220
\(310\) −4.09093e115 −0.580101
\(311\) −1.13306e116 −1.38323 −0.691615 0.722266i \(-0.743100\pi\)
−0.691615 + 0.722266i \(0.743100\pi\)
\(312\) 1.59961e115 0.168200
\(313\) −8.92421e115 −0.808646 −0.404323 0.914616i \(-0.632493\pi\)
−0.404323 + 0.914616i \(0.632493\pi\)
\(314\) 1.05469e116 0.823939
\(315\) 2.30157e115 0.155090
\(316\) 6.91700e115 0.402225
\(317\) 2.05159e116 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(318\) 3.58901e116 1.55637
\(319\) −1.77395e116 −0.664773
\(320\) −2.27522e116 −0.737140
\(321\) 1.03995e116 0.291425
\(322\) −2.07495e116 −0.503163
\(323\) −2.32613e115 −0.0488333
\(324\) −2.27392e116 −0.413458
\(325\) −1.44419e116 −0.227535
\(326\) 5.08222e116 0.694121
\(327\) 8.69170e116 1.02952
\(328\) 2.35078e116 0.241589
\(329\) 5.03391e114 0.00449052
\(330\) −5.26983e116 −0.408224
\(331\) −2.73551e117 −1.84093 −0.920463 0.390830i \(-0.872188\pi\)
−0.920463 + 0.390830i \(0.872188\pi\)
\(332\) 8.89963e116 0.520536
\(333\) −8.43623e115 −0.0429034
\(334\) −3.21174e117 −1.42079
\(335\) 9.72250e116 0.374278
\(336\) −1.00892e117 −0.338129
\(337\) 1.32552e117 0.386897 0.193449 0.981110i \(-0.438033\pi\)
0.193449 + 0.981110i \(0.438033\pi\)
\(338\) 5.50633e115 0.0140035
\(339\) 3.34410e117 0.741298
\(340\) 8.33723e117 1.61158
\(341\) −7.82290e116 −0.131914
\(342\) −9.70223e115 −0.0142777
\(343\) 5.44721e117 0.699838
\(344\) −3.14660e117 −0.353081
\(345\) 8.82089e117 0.864818
\(346\) 7.03278e116 0.0602682
\(347\) −2.48219e118 −1.86001 −0.930003 0.367551i \(-0.880196\pi\)
−0.930003 + 0.367551i \(0.880196\pi\)
\(348\) −1.98053e118 −1.29821
\(349\) 2.09671e118 1.20270 0.601349 0.798986i \(-0.294630\pi\)
0.601349 + 0.798986i \(0.294630\pi\)
\(350\) 2.32880e117 0.116941
\(351\) −2.45968e118 −1.08168
\(352\) −1.17597e118 −0.453066
\(353\) 9.35602e117 0.315913 0.157956 0.987446i \(-0.449509\pi\)
0.157956 + 0.987446i \(0.449509\pi\)
\(354\) −6.88534e118 −2.03833
\(355\) 6.90489e118 1.79283
\(356\) −8.69192e117 −0.198012
\(357\) 2.57571e118 0.515020
\(358\) 1.01425e119 1.78068
\(359\) 5.71223e118 0.880873 0.440437 0.897784i \(-0.354824\pi\)
0.440437 + 0.897784i \(0.354824\pi\)
\(360\) −6.48114e117 −0.0878183
\(361\) −8.38951e118 −0.999198
\(362\) −1.18161e119 −1.23745
\(363\) 7.59857e118 0.699961
\(364\) 3.89635e118 0.315823
\(365\) −5.44651e118 −0.388598
\(366\) 6.30051e118 0.395827
\(367\) −1.03136e119 −0.570740 −0.285370 0.958417i \(-0.592117\pi\)
−0.285370 + 0.958417i \(0.592117\pi\)
\(368\) 2.28544e119 1.11441
\(369\) −9.79091e118 −0.420821
\(370\) −4.58574e118 −0.173792
\(371\) −1.62933e119 −0.544655
\(372\) −8.73391e118 −0.257610
\(373\) −3.06101e119 −0.796900 −0.398450 0.917190i \(-0.630452\pi\)
−0.398450 + 0.917190i \(0.630452\pi\)
\(374\) 3.48572e119 0.801241
\(375\) 3.33850e119 0.677794
\(376\) −1.41753e117 −0.00254272
\(377\) −1.21908e120 −1.93267
\(378\) 3.96631e119 0.555927
\(379\) −6.87675e119 −0.852432 −0.426216 0.904621i \(-0.640154\pi\)
−0.426216 + 0.904621i \(0.640154\pi\)
\(380\) −2.41217e118 −0.0264527
\(381\) −2.59433e119 −0.251776
\(382\) 2.62722e120 2.25709
\(383\) 2.22549e120 1.69310 0.846549 0.532311i \(-0.178676\pi\)
0.846549 + 0.532311i \(0.178676\pi\)
\(384\) 4.95584e119 0.333976
\(385\) 2.39238e119 0.142859
\(386\) −4.89585e119 −0.259130
\(387\) 1.31055e120 0.615027
\(388\) −3.27318e120 −1.36237
\(389\) −3.21512e118 −0.0118724 −0.00593622 0.999982i \(-0.501890\pi\)
−0.00593622 + 0.999982i \(0.501890\pi\)
\(390\) −3.62150e120 −1.18682
\(391\) −5.83456e120 −1.69742
\(392\) −7.08409e119 −0.183013
\(393\) 4.69101e120 1.07650
\(394\) −5.04154e120 −1.02799
\(395\) 2.91865e120 0.528953
\(396\) 6.64976e119 0.107147
\(397\) 3.63725e119 0.0521212 0.0260606 0.999660i \(-0.491704\pi\)
0.0260606 + 0.999660i \(0.491704\pi\)
\(398\) 8.04256e120 1.02525
\(399\) −7.45217e118 −0.00845363
\(400\) −2.56505e120 −0.259004
\(401\) 6.87560e120 0.618155 0.309078 0.951037i \(-0.399980\pi\)
0.309078 + 0.951037i \(0.399980\pi\)
\(402\) 4.53826e120 0.363394
\(403\) −5.37600e120 −0.383508
\(404\) 8.07984e120 0.513653
\(405\) −9.59486e120 −0.543726
\(406\) 1.96580e121 0.993296
\(407\) −8.76911e119 −0.0395199
\(408\) −7.25311e120 −0.291626
\(409\) 6.34026e120 0.227496 0.113748 0.993510i \(-0.463714\pi\)
0.113748 + 0.993510i \(0.463714\pi\)
\(410\) −5.32212e121 −1.70465
\(411\) 1.38232e120 0.0395333
\(412\) 7.83439e120 0.200117
\(413\) 3.12578e121 0.713315
\(414\) −2.43359e121 −0.496285
\(415\) 3.75522e121 0.684541
\(416\) −8.08140e121 −1.31719
\(417\) 1.41874e121 0.206813
\(418\) −1.00851e120 −0.0131517
\(419\) −1.47579e121 −0.172215 −0.0861077 0.996286i \(-0.527443\pi\)
−0.0861077 + 0.996286i \(0.527443\pi\)
\(420\) 2.67098e121 0.278984
\(421\) 2.72550e121 0.254876 0.127438 0.991847i \(-0.459325\pi\)
0.127438 + 0.991847i \(0.459325\pi\)
\(422\) −1.44766e122 −1.21238
\(423\) 5.90399e119 0.00442913
\(424\) 4.58814e121 0.308407
\(425\) 6.54837e121 0.394501
\(426\) 3.22306e122 1.74069
\(427\) −2.86028e121 −0.138520
\(428\) −7.13315e121 −0.309846
\(429\) −6.92523e121 −0.269880
\(430\) 7.12386e122 2.49133
\(431\) 7.42351e121 0.233032 0.116516 0.993189i \(-0.462827\pi\)
0.116516 + 0.993189i \(0.462827\pi\)
\(432\) −4.36868e122 −1.23128
\(433\) −3.19233e122 −0.808016 −0.404008 0.914755i \(-0.632383\pi\)
−0.404008 + 0.914755i \(0.632383\pi\)
\(434\) 8.66896e121 0.197104
\(435\) −8.35690e122 −1.70724
\(436\) −5.96177e122 −1.09459
\(437\) 1.68809e121 0.0278617
\(438\) −2.54232e122 −0.377297
\(439\) −9.54354e121 −0.127382 −0.0636912 0.997970i \(-0.520287\pi\)
−0.0636912 + 0.997970i \(0.520287\pi\)
\(440\) −6.73687e121 −0.0808926
\(441\) 2.95050e122 0.318788
\(442\) 2.39543e123 2.32942
\(443\) −9.34021e122 −0.817680 −0.408840 0.912606i \(-0.634067\pi\)
−0.408840 + 0.912606i \(0.634067\pi\)
\(444\) −9.79031e121 −0.0771771
\(445\) −3.66758e122 −0.260399
\(446\) 2.41925e123 1.54742
\(447\) 1.07457e123 0.619349
\(448\) 4.82135e122 0.250461
\(449\) −9.82334e122 −0.460049 −0.230025 0.973185i \(-0.573881\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(450\) 2.73131e122 0.115343
\(451\) −1.01772e123 −0.387633
\(452\) −2.29377e123 −0.788156
\(453\) 2.49907e123 0.774840
\(454\) −7.90600e123 −2.21238
\(455\) 1.64408e123 0.415328
\(456\) 2.09851e121 0.00478680
\(457\) 3.72271e122 0.0766930 0.0383465 0.999265i \(-0.487791\pi\)
0.0383465 + 0.999265i \(0.487791\pi\)
\(458\) 3.19334e123 0.594293
\(459\) 1.11529e124 1.87542
\(460\) −6.05038e123 −0.919483
\(461\) −3.32371e123 −0.456594 −0.228297 0.973591i \(-0.573316\pi\)
−0.228297 + 0.973591i \(0.573316\pi\)
\(462\) 1.11671e123 0.138704
\(463\) −9.17903e123 −1.03105 −0.515526 0.856874i \(-0.672404\pi\)
−0.515526 + 0.856874i \(0.672404\pi\)
\(464\) −2.16523e124 −2.19997
\(465\) −3.68530e123 −0.338774
\(466\) 1.77625e124 1.47761
\(467\) 1.99340e124 1.50093 0.750464 0.660911i \(-0.229830\pi\)
0.750464 + 0.660911i \(0.229830\pi\)
\(468\) 4.56980e123 0.311505
\(469\) −2.06026e123 −0.127170
\(470\) 3.20927e122 0.0179414
\(471\) 9.50111e123 0.481174
\(472\) −8.80211e123 −0.403909
\(473\) 1.36226e124 0.566524
\(474\) 1.36237e124 0.513571
\(475\) −1.89461e122 −0.00647540
\(476\) −1.76672e124 −0.547575
\(477\) −1.91095e124 −0.537209
\(478\) 7.20675e124 1.83799
\(479\) −1.27783e124 −0.295714 −0.147857 0.989009i \(-0.547238\pi\)
−0.147857 + 0.989009i \(0.547238\pi\)
\(480\) −5.53988e124 −1.16354
\(481\) −6.02625e123 −0.114895
\(482\) −3.95467e124 −0.684578
\(483\) −1.86921e124 −0.293843
\(484\) −5.21198e124 −0.744206
\(485\) −1.38113e125 −1.79161
\(486\) 8.04369e124 0.948132
\(487\) 3.04606e124 0.326319 0.163160 0.986600i \(-0.447831\pi\)
0.163160 + 0.986600i \(0.447831\pi\)
\(488\) 8.05447e123 0.0784360
\(489\) 4.57830e124 0.405361
\(490\) 1.60383e125 1.29134
\(491\) −5.25589e124 −0.384908 −0.192454 0.981306i \(-0.561645\pi\)
−0.192454 + 0.981306i \(0.561645\pi\)
\(492\) −1.13624e125 −0.756996
\(493\) 5.52765e125 3.35088
\(494\) −6.93059e123 −0.0382355
\(495\) 2.80589e124 0.140906
\(496\) −9.54841e124 −0.436549
\(497\) −1.46319e125 −0.609158
\(498\) 1.75286e125 0.664635
\(499\) −4.67925e125 −1.61622 −0.808110 0.589031i \(-0.799509\pi\)
−0.808110 + 0.589031i \(0.799509\pi\)
\(500\) −2.28993e125 −0.720638
\(501\) −2.89329e125 −0.829730
\(502\) 5.78922e125 1.51320
\(503\) −4.59038e125 −1.09380 −0.546899 0.837199i \(-0.684192\pi\)
−0.546899 + 0.837199i \(0.684192\pi\)
\(504\) 1.37340e124 0.0298384
\(505\) 3.40931e125 0.675489
\(506\) −2.52961e125 −0.457146
\(507\) 4.96035e123 0.00817791
\(508\) 1.77949e125 0.267691
\(509\) −7.31205e125 −1.00384 −0.501918 0.864915i \(-0.667372\pi\)
−0.501918 + 0.864915i \(0.667372\pi\)
\(510\) 1.64209e126 2.05771
\(511\) 1.15415e125 0.132036
\(512\) −1.20416e126 −1.25785
\(513\) −3.22681e124 −0.0307834
\(514\) −1.34617e126 −1.17305
\(515\) 3.30574e125 0.263168
\(516\) 1.52090e126 1.10635
\(517\) 6.13695e123 0.00407983
\(518\) 9.71750e124 0.0590501
\(519\) 6.33545e124 0.0351962
\(520\) −4.62967e125 −0.235177
\(521\) 2.01287e126 0.935106 0.467553 0.883965i \(-0.345136\pi\)
0.467553 + 0.883965i \(0.345136\pi\)
\(522\) 2.30557e126 0.979717
\(523\) 2.88184e126 1.12032 0.560159 0.828385i \(-0.310740\pi\)
0.560159 + 0.828385i \(0.310740\pi\)
\(524\) −3.21764e126 −1.14454
\(525\) 2.09789e125 0.0682928
\(526\) −4.15618e126 −1.23839
\(527\) 2.43763e126 0.664929
\(528\) −1.23000e126 −0.307205
\(529\) −1.37907e125 −0.0315425
\(530\) −1.03875e127 −2.17611
\(531\) 3.66605e126 0.703563
\(532\) 5.11155e124 0.00898798
\(533\) −6.99393e126 −1.12695
\(534\) −1.71195e126 −0.252827
\(535\) −3.00985e126 −0.407469
\(536\) 5.80164e125 0.0720092
\(537\) 9.13684e126 1.03990
\(538\) 1.12338e127 1.17260
\(539\) 3.06692e126 0.293647
\(540\) 1.15654e127 1.01590
\(541\) 1.14287e127 0.921133 0.460567 0.887625i \(-0.347646\pi\)
0.460567 + 0.887625i \(0.347646\pi\)
\(542\) −1.44008e127 −1.06517
\(543\) −1.06445e127 −0.722659
\(544\) 3.66434e127 2.28374
\(545\) −2.51559e127 −1.43947
\(546\) 7.67420e126 0.403251
\(547\) −1.73528e127 −0.837450 −0.418725 0.908113i \(-0.637523\pi\)
−0.418725 + 0.908113i \(0.637523\pi\)
\(548\) −9.48152e125 −0.0420322
\(549\) −3.35466e126 −0.136626
\(550\) 2.83909e126 0.106246
\(551\) −1.59929e126 −0.0550019
\(552\) 5.26363e126 0.166387
\(553\) −6.18482e126 −0.179725
\(554\) −7.10894e127 −1.89933
\(555\) −4.13105e126 −0.101493
\(556\) −9.73137e126 −0.219885
\(557\) −3.51533e127 −0.730634 −0.365317 0.930883i \(-0.619039\pi\)
−0.365317 + 0.930883i \(0.619039\pi\)
\(558\) 1.01673e127 0.194409
\(559\) 9.36165e127 1.64704
\(560\) 2.92007e127 0.472770
\(561\) 3.14010e127 0.467919
\(562\) 1.33031e128 1.82479
\(563\) −7.77831e127 −0.982302 −0.491151 0.871074i \(-0.663424\pi\)
−0.491151 + 0.871074i \(0.663424\pi\)
\(564\) 6.85162e125 0.00796737
\(565\) −9.67862e127 −1.03648
\(566\) −1.11411e128 −1.09892
\(567\) 2.03322e127 0.184744
\(568\) 4.12031e127 0.344931
\(569\) 2.55784e127 0.197312 0.0986559 0.995122i \(-0.468546\pi\)
0.0986559 + 0.995122i \(0.468546\pi\)
\(570\) −4.75099e126 −0.0337756
\(571\) 3.24099e127 0.212373 0.106186 0.994346i \(-0.466136\pi\)
0.106186 + 0.994346i \(0.466136\pi\)
\(572\) 4.75012e127 0.286939
\(573\) 2.36672e128 1.31812
\(574\) 1.12779e128 0.579197
\(575\) −4.75220e127 −0.225081
\(576\) 5.65469e127 0.247038
\(577\) −9.68555e127 −0.390346 −0.195173 0.980769i \(-0.562527\pi\)
−0.195173 + 0.980769i \(0.562527\pi\)
\(578\) −7.21072e128 −2.68123
\(579\) −4.41041e127 −0.151330
\(580\) 5.73212e128 1.81516
\(581\) −7.95758e127 −0.232590
\(582\) −6.44682e128 −1.73951
\(583\) −1.98635e128 −0.494843
\(584\) −3.25006e127 −0.0747642
\(585\) 1.92824e128 0.409651
\(586\) −7.93196e128 −1.55647
\(587\) 4.65657e128 0.844101 0.422050 0.906572i \(-0.361311\pi\)
0.422050 + 0.906572i \(0.361311\pi\)
\(588\) 3.42408e128 0.573454
\(589\) −7.05269e126 −0.0109142
\(590\) 1.99278e129 2.84998
\(591\) −4.54165e128 −0.600338
\(592\) −1.07033e128 −0.130785
\(593\) 1.44616e129 1.63370 0.816850 0.576850i \(-0.195718\pi\)
0.816850 + 0.576850i \(0.195718\pi\)
\(594\) 4.83541e128 0.505084
\(595\) −7.45471e128 −0.720099
\(596\) −7.37065e128 −0.658498
\(597\) 7.24511e128 0.598741
\(598\) −1.73838e129 −1.32905
\(599\) 4.67972e128 0.331034 0.165517 0.986207i \(-0.447071\pi\)
0.165517 + 0.986207i \(0.447071\pi\)
\(600\) −5.90759e127 −0.0386703
\(601\) −6.57416e128 −0.398270 −0.199135 0.979972i \(-0.563813\pi\)
−0.199135 + 0.979972i \(0.563813\pi\)
\(602\) −1.50959e129 −0.846493
\(603\) −2.41637e128 −0.125432
\(604\) −1.71415e129 −0.823817
\(605\) −2.19921e129 −0.978682
\(606\) 1.59140e129 0.655846
\(607\) 2.37428e129 0.906270 0.453135 0.891442i \(-0.350306\pi\)
0.453135 + 0.891442i \(0.350306\pi\)
\(608\) −1.06019e128 −0.0374857
\(609\) 1.77088e129 0.580078
\(610\) −1.82352e129 −0.553443
\(611\) 4.21739e127 0.0118612
\(612\) −2.07208e129 −0.540089
\(613\) 1.90113e129 0.459304 0.229652 0.973273i \(-0.426241\pi\)
0.229652 + 0.973273i \(0.426241\pi\)
\(614\) 1.16531e130 2.60983
\(615\) −4.79441e129 −0.995502
\(616\) 1.42759e128 0.0274853
\(617\) −7.31692e129 −1.30638 −0.653188 0.757196i \(-0.726569\pi\)
−0.653188 + 0.757196i \(0.726569\pi\)
\(618\) 1.54305e129 0.255515
\(619\) 3.74623e129 0.575412 0.287706 0.957719i \(-0.407107\pi\)
0.287706 + 0.957719i \(0.407107\pi\)
\(620\) 2.52780e129 0.360188
\(621\) −8.09373e129 −1.07001
\(622\) 1.53073e130 1.87778
\(623\) 7.77185e128 0.0884770
\(624\) −8.45273e129 −0.893128
\(625\) −1.19944e130 −1.17641
\(626\) 1.20564e130 1.09777
\(627\) −9.08509e127 −0.00768049
\(628\) −6.51696e129 −0.511589
\(629\) 2.73247e129 0.199205
\(630\) −3.10935e129 −0.210540
\(631\) 7.87187e129 0.495122 0.247561 0.968872i \(-0.420371\pi\)
0.247561 + 0.968872i \(0.420371\pi\)
\(632\) 1.74163e129 0.101768
\(633\) −1.30412e130 −0.708018
\(634\) −2.77164e130 −1.39826
\(635\) 7.50863e129 0.352032
\(636\) −2.21767e130 −0.966363
\(637\) 2.10763e130 0.853711
\(638\) 2.39655e130 0.902453
\(639\) −1.71610e130 −0.600830
\(640\) −1.43434e130 −0.466964
\(641\) 2.38312e130 0.721518 0.360759 0.932659i \(-0.382518\pi\)
0.360759 + 0.932659i \(0.382518\pi\)
\(642\) −1.40494e130 −0.395620
\(643\) −1.44463e130 −0.378397 −0.189198 0.981939i \(-0.560589\pi\)
−0.189198 + 0.981939i \(0.560589\pi\)
\(644\) 1.28212e130 0.312417
\(645\) 6.41750e130 1.45492
\(646\) 3.14253e129 0.0662929
\(647\) 8.21550e130 1.61282 0.806409 0.591359i \(-0.201408\pi\)
0.806409 + 0.591359i \(0.201408\pi\)
\(648\) −5.72547e129 −0.104610
\(649\) 3.81071e130 0.648078
\(650\) 1.95106e130 0.308887
\(651\) 7.80940e129 0.115107
\(652\) −3.14032e130 −0.430984
\(653\) −5.09920e130 −0.651687 −0.325843 0.945424i \(-0.605648\pi\)
−0.325843 + 0.945424i \(0.605648\pi\)
\(654\) −1.17422e131 −1.39761
\(655\) −1.35769e131 −1.50515
\(656\) −1.24220e131 −1.28282
\(657\) 1.35364e130 0.130231
\(658\) −6.80067e128 −0.00609604
\(659\) −6.44359e130 −0.538216 −0.269108 0.963110i \(-0.586729\pi\)
−0.269108 + 0.963110i \(0.586729\pi\)
\(660\) 3.25625e130 0.253469
\(661\) −1.07148e131 −0.777348 −0.388674 0.921375i \(-0.627067\pi\)
−0.388674 + 0.921375i \(0.627067\pi\)
\(662\) 3.69559e131 2.49912
\(663\) 2.15792e131 1.36037
\(664\) 2.24083e130 0.131702
\(665\) 2.15684e129 0.0118198
\(666\) 1.13971e130 0.0582429
\(667\) −4.01145e131 −1.91184
\(668\) 1.98455e131 0.882178
\(669\) 2.17937e131 0.903684
\(670\) −1.31348e131 −0.508096
\(671\) −3.48703e130 −0.125852
\(672\) 1.17394e131 0.395343
\(673\) 2.53785e131 0.797563 0.398782 0.917046i \(-0.369433\pi\)
0.398782 + 0.917046i \(0.369433\pi\)
\(674\) −1.79074e131 −0.525226
\(675\) 9.08393e130 0.248684
\(676\) −3.40238e129 −0.00869484
\(677\) −1.49446e131 −0.356543 −0.178271 0.983981i \(-0.557050\pi\)
−0.178271 + 0.983981i \(0.557050\pi\)
\(678\) −4.51778e131 −1.00634
\(679\) 2.92670e131 0.608743
\(680\) 2.09922e131 0.407750
\(681\) −7.12209e131 −1.29201
\(682\) 1.05685e131 0.179077
\(683\) 4.82762e131 0.764136 0.382068 0.924134i \(-0.375212\pi\)
0.382068 + 0.924134i \(0.375212\pi\)
\(684\) 5.99505e129 0.00886511
\(685\) −4.00076e130 −0.0552753
\(686\) −7.35902e131 −0.950055
\(687\) 2.87671e131 0.347063
\(688\) 1.66274e132 1.87483
\(689\) −1.36504e132 −1.43864
\(690\) −1.19168e132 −1.17402
\(691\) −1.60210e132 −1.47557 −0.737786 0.675035i \(-0.764128\pi\)
−0.737786 + 0.675035i \(0.764128\pi\)
\(692\) −4.34558e130 −0.0374209
\(693\) −5.94587e130 −0.0478762
\(694\) 3.35337e132 2.52503
\(695\) −4.10618e131 −0.289164
\(696\) −4.98676e131 −0.328465
\(697\) 3.17125e132 1.95392
\(698\) −2.83260e132 −1.63271
\(699\) 1.60013e132 0.862911
\(700\) −1.43897e131 −0.0726096
\(701\) −6.59869e131 −0.311580 −0.155790 0.987790i \(-0.549792\pi\)
−0.155790 + 0.987790i \(0.549792\pi\)
\(702\) 3.32295e132 1.46841
\(703\) −7.90574e129 −0.00326979
\(704\) 5.87781e131 0.227555
\(705\) 2.89106e130 0.0104776
\(706\) −1.26397e132 −0.428863
\(707\) −7.22457e131 −0.229514
\(708\) 4.25448e132 1.26561
\(709\) −1.94700e132 −0.542397 −0.271198 0.962524i \(-0.587420\pi\)
−0.271198 + 0.962524i \(0.587420\pi\)
\(710\) −9.32831e132 −2.43383
\(711\) −7.25382e131 −0.177268
\(712\) −2.18853e131 −0.0500994
\(713\) −1.76901e132 −0.379373
\(714\) −3.47971e132 −0.699159
\(715\) 2.00433e132 0.377344
\(716\) −6.26710e132 −1.10563
\(717\) 6.49217e132 1.07337
\(718\) −7.71705e132 −1.19582
\(719\) 9.78644e132 1.42145 0.710725 0.703470i \(-0.248367\pi\)
0.710725 + 0.703470i \(0.248367\pi\)
\(720\) 3.42478e132 0.466307
\(721\) −7.00510e131 −0.0894179
\(722\) 1.13340e133 1.35645
\(723\) −3.56255e132 −0.399789
\(724\) 7.30122e132 0.768338
\(725\) 4.50222e132 0.444334
\(726\) −1.02655e133 −0.950222
\(727\) 1.78272e133 1.54787 0.773934 0.633266i \(-0.218286\pi\)
0.773934 + 0.633266i \(0.218286\pi\)
\(728\) 9.81058e131 0.0799071
\(729\) 1.36654e133 1.04422
\(730\) 7.35808e132 0.527535
\(731\) −4.24484e133 −2.85564
\(732\) −3.89311e132 −0.245771
\(733\) −2.90840e133 −1.72314 −0.861568 0.507642i \(-0.830517\pi\)
−0.861568 + 0.507642i \(0.830517\pi\)
\(734\) 1.39334e133 0.774800
\(735\) 1.44480e133 0.754131
\(736\) −2.65924e133 −1.30298
\(737\) −2.51171e132 −0.115540
\(738\) 1.32272e133 0.571279
\(739\) 4.45578e132 0.180700 0.0903498 0.995910i \(-0.471201\pi\)
0.0903498 + 0.995910i \(0.471201\pi\)
\(740\) 2.83355e132 0.107909
\(741\) −6.24339e131 −0.0223292
\(742\) 2.20117e133 0.739389
\(743\) −1.62944e132 −0.0514113 −0.0257056 0.999670i \(-0.508183\pi\)
−0.0257056 + 0.999670i \(0.508183\pi\)
\(744\) −2.19910e132 −0.0651785
\(745\) −3.11007e133 −0.865971
\(746\) 4.13534e133 1.08182
\(747\) −9.33299e132 −0.229410
\(748\) −2.15384e133 −0.497496
\(749\) 6.37809e132 0.138448
\(750\) −4.51022e133 −0.920130
\(751\) −8.09455e133 −1.55216 −0.776078 0.630636i \(-0.782794\pi\)
−0.776078 + 0.630636i \(0.782794\pi\)
\(752\) 7.49058e131 0.0135016
\(753\) 5.21519e133 0.883698
\(754\) 1.64694e134 2.62367
\(755\) −7.23290e133 −1.08338
\(756\) −2.45080e133 −0.345178
\(757\) 1.20299e134 1.59332 0.796659 0.604429i \(-0.206599\pi\)
0.796659 + 0.604429i \(0.206599\pi\)
\(758\) 9.29029e133 1.15721
\(759\) −2.27879e133 −0.266970
\(760\) −6.07358e131 −0.00669288
\(761\) −1.47579e133 −0.152982 −0.0764908 0.997070i \(-0.524372\pi\)
−0.0764908 + 0.997070i \(0.524372\pi\)
\(762\) 3.50487e133 0.341795
\(763\) 5.33070e133 0.489095
\(764\) −1.62337e134 −1.40144
\(765\) −8.74321e133 −0.710255
\(766\) −3.00657e134 −2.29844
\(767\) 2.61877e134 1.88414
\(768\) −1.44806e134 −0.980593
\(769\) 6.28699e133 0.400745 0.200372 0.979720i \(-0.435785\pi\)
0.200372 + 0.979720i \(0.435785\pi\)
\(770\) −3.23204e133 −0.193936
\(771\) −1.21270e134 −0.685052
\(772\) 3.02517e133 0.160896
\(773\) 1.07884e134 0.540268 0.270134 0.962823i \(-0.412932\pi\)
0.270134 + 0.962823i \(0.412932\pi\)
\(774\) −1.77052e134 −0.834921
\(775\) 1.98543e133 0.0881710
\(776\) −8.24151e133 −0.344696
\(777\) 8.75398e132 0.0344848
\(778\) 4.34353e132 0.0161173
\(779\) −9.17523e132 −0.0320719
\(780\) 2.23774e134 0.736903
\(781\) −1.78381e134 −0.553447
\(782\) 7.88232e134 2.30431
\(783\) 7.66798e134 2.11232
\(784\) 3.74340e134 0.971782
\(785\) −2.74985e134 −0.672775
\(786\) −6.33742e134 −1.46138
\(787\) −3.41049e134 −0.741297 −0.370648 0.928773i \(-0.620864\pi\)
−0.370648 + 0.928773i \(0.620864\pi\)
\(788\) 3.11519e134 0.638285
\(789\) −3.74408e134 −0.723209
\(790\) −3.94301e134 −0.718072
\(791\) 2.05097e134 0.352170
\(792\) 1.67434e133 0.0271095
\(793\) −2.39633e134 −0.365884
\(794\) −4.91382e133 −0.0707564
\(795\) −9.35751e134 −1.27083
\(796\) −4.96953e134 −0.636587
\(797\) 8.42317e134 1.01780 0.508901 0.860825i \(-0.330052\pi\)
0.508901 + 0.860825i \(0.330052\pi\)
\(798\) 1.00677e133 0.0114761
\(799\) −1.91229e133 −0.0205650
\(800\) 2.98457e134 0.302829
\(801\) 9.11516e133 0.0872675
\(802\) −9.28874e134 −0.839167
\(803\) 1.40705e134 0.119960
\(804\) −2.80421e134 −0.225634
\(805\) 5.40993e134 0.410850
\(806\) 7.26282e134 0.520626
\(807\) 1.01199e135 0.684790
\(808\) 2.03442e134 0.129961
\(809\) 1.32832e135 0.801118 0.400559 0.916271i \(-0.368816\pi\)
0.400559 + 0.916271i \(0.368816\pi\)
\(810\) 1.29624e135 0.738127
\(811\) −2.63000e135 −1.41412 −0.707061 0.707153i \(-0.749979\pi\)
−0.707061 + 0.707153i \(0.749979\pi\)
\(812\) −1.21468e135 −0.616744
\(813\) −1.29729e135 −0.622054
\(814\) 1.18468e134 0.0536496
\(815\) −1.32507e135 −0.566774
\(816\) 3.83271e135 1.54851
\(817\) 1.22814e134 0.0468729
\(818\) −8.56551e134 −0.308833
\(819\) −4.08608e134 −0.139189
\(820\) 3.28856e135 1.05843
\(821\) 3.67231e135 1.11682 0.558409 0.829566i \(-0.311412\pi\)
0.558409 + 0.829566i \(0.311412\pi\)
\(822\) −1.86747e134 −0.0536679
\(823\) −2.12999e135 −0.578475 −0.289238 0.957257i \(-0.593402\pi\)
−0.289238 + 0.957257i \(0.593402\pi\)
\(824\) 1.97261e134 0.0506322
\(825\) 2.55758e134 0.0620470
\(826\) −4.22284e135 −0.968350
\(827\) −4.76247e135 −1.03235 −0.516174 0.856484i \(-0.672644\pi\)
−0.516174 + 0.856484i \(0.672644\pi\)
\(828\) 1.50372e135 0.308146
\(829\) 1.22443e135 0.237218 0.118609 0.992941i \(-0.462157\pi\)
0.118609 + 0.992941i \(0.462157\pi\)
\(830\) −5.07320e135 −0.929289
\(831\) −6.40406e135 −1.10920
\(832\) 4.03931e135 0.661564
\(833\) −9.55661e135 −1.48017
\(834\) −1.91668e135 −0.280756
\(835\) 8.37386e135 1.16012
\(836\) 6.23160e133 0.00816597
\(837\) 3.38150e135 0.419156
\(838\) 1.99375e135 0.233789
\(839\) −2.34326e135 −0.259949 −0.129975 0.991517i \(-0.541490\pi\)
−0.129975 + 0.991517i \(0.541490\pi\)
\(840\) 6.72525e134 0.0705865
\(841\) 2.79348e136 2.77416
\(842\) −3.68207e135 −0.346003
\(843\) 1.19840e136 1.06566
\(844\) 8.94514e135 0.752772
\(845\) −1.43565e134 −0.0114343
\(846\) −7.97611e133 −0.00601270
\(847\) 4.66027e135 0.332532
\(848\) −2.42448e136 −1.63761
\(849\) −1.00364e136 −0.641760
\(850\) −8.84666e135 −0.535549
\(851\) −1.98297e135 −0.113656
\(852\) −1.99154e136 −1.08081
\(853\) −2.56453e135 −0.131789 −0.0658943 0.997827i \(-0.520990\pi\)
−0.0658943 + 0.997827i \(0.520990\pi\)
\(854\) 3.86416e135 0.188046
\(855\) 2.52963e134 0.0116582
\(856\) −1.79605e135 −0.0783950
\(857\) 1.21930e136 0.504082 0.252041 0.967717i \(-0.418898\pi\)
0.252041 + 0.967717i \(0.418898\pi\)
\(858\) 9.35578e135 0.366371
\(859\) −8.42911e135 −0.312679 −0.156340 0.987703i \(-0.549969\pi\)
−0.156340 + 0.987703i \(0.549969\pi\)
\(860\) −4.40186e136 −1.54689
\(861\) 1.01597e136 0.338247
\(862\) −1.00289e136 −0.316350
\(863\) 2.64685e135 0.0791093 0.0395547 0.999217i \(-0.487406\pi\)
0.0395547 + 0.999217i \(0.487406\pi\)
\(864\) 5.08319e136 1.43962
\(865\) −1.83363e135 −0.0492111
\(866\) 4.31274e136 1.09691
\(867\) −6.49575e136 −1.56582
\(868\) −5.35659e135 −0.122383
\(869\) −7.54004e135 −0.163288
\(870\) 1.12899e137 2.31764
\(871\) −1.72608e136 −0.335905
\(872\) −1.50111e136 −0.276946
\(873\) 3.43256e136 0.600421
\(874\) −2.28055e135 −0.0378232
\(875\) 2.04753e136 0.322001
\(876\) 1.57091e136 0.234266
\(877\) −1.12326e137 −1.58854 −0.794271 0.607564i \(-0.792147\pi\)
−0.794271 + 0.607564i \(0.792147\pi\)
\(878\) 1.28930e136 0.172926
\(879\) −7.14548e136 −0.908968
\(880\) 3.55992e136 0.429532
\(881\) 9.16639e136 1.04910 0.524552 0.851378i \(-0.324233\pi\)
0.524552 + 0.851378i \(0.324233\pi\)
\(882\) −3.98604e136 −0.432766
\(883\) −3.80306e136 −0.391706 −0.195853 0.980633i \(-0.562748\pi\)
−0.195853 + 0.980633i \(0.562748\pi\)
\(884\) −1.48015e137 −1.44635
\(885\) 1.79519e137 1.66436
\(886\) 1.26184e137 1.11003
\(887\) −1.22464e137 −1.02226 −0.511130 0.859503i \(-0.670773\pi\)
−0.511130 + 0.859503i \(0.670773\pi\)
\(888\) −2.46509e135 −0.0195268
\(889\) −1.59113e136 −0.119612
\(890\) 4.95479e136 0.353501
\(891\) 2.47874e136 0.167848
\(892\) −1.49486e137 −0.960806
\(893\) 5.53273e133 0.000337556 0
\(894\) −1.45172e137 −0.840789
\(895\) −2.64442e137 −1.45398
\(896\) 3.03946e136 0.158663
\(897\) −1.56601e137 −0.776153
\(898\) 1.32710e137 0.624533
\(899\) 1.67595e137 0.748922
\(900\) −1.68769e136 −0.0716170
\(901\) 6.18950e137 2.49433
\(902\) 1.37492e137 0.526226
\(903\) −1.35991e137 −0.494345
\(904\) −5.77546e136 −0.199413
\(905\) 3.08077e137 1.01042
\(906\) −3.37617e137 −1.05187
\(907\) 2.22783e137 0.659391 0.329696 0.944087i \(-0.393054\pi\)
0.329696 + 0.944087i \(0.393054\pi\)
\(908\) 4.88515e137 1.37368
\(909\) −8.47328e136 −0.226376
\(910\) −2.22110e137 −0.563823
\(911\) 2.69130e136 0.0649169 0.0324585 0.999473i \(-0.489666\pi\)
0.0324585 + 0.999473i \(0.489666\pi\)
\(912\) −1.10890e136 −0.0254175
\(913\) −9.70125e136 −0.211318
\(914\) −5.02927e136 −0.104113
\(915\) −1.64271e137 −0.323206
\(916\) −1.97318e137 −0.369001
\(917\) 2.87704e137 0.511413
\(918\) −1.50672e138 −2.54594
\(919\) −1.16650e138 −1.87376 −0.936882 0.349647i \(-0.886302\pi\)
−0.936882 + 0.349647i \(0.886302\pi\)
\(920\) −1.52342e137 −0.232641
\(921\) 1.04977e138 1.52412
\(922\) 4.49024e137 0.619843
\(923\) −1.22586e138 −1.60902
\(924\) −6.90022e136 −0.0861224
\(925\) 2.22558e136 0.0264151
\(926\) 1.24006e138 1.39969
\(927\) −8.21588e136 −0.0881955
\(928\) 2.51936e138 2.57222
\(929\) 7.30201e137 0.709107 0.354554 0.935036i \(-0.384633\pi\)
0.354554 + 0.935036i \(0.384633\pi\)
\(930\) 4.97873e137 0.459898
\(931\) 2.76497e136 0.0242957
\(932\) −1.09755e138 −0.917456
\(933\) 1.37895e138 1.09661
\(934\) −2.69303e138 −2.03756
\(935\) −9.08820e137 −0.654241
\(936\) 1.15063e137 0.0788147
\(937\) 6.92090e137 0.451098 0.225549 0.974232i \(-0.427582\pi\)
0.225549 + 0.974232i \(0.427582\pi\)
\(938\) 2.78336e137 0.172638
\(939\) 1.08609e138 0.641087
\(940\) −1.98302e136 −0.0111399
\(941\) −2.77400e137 −0.148317 −0.0741583 0.997246i \(-0.523627\pi\)
−0.0741583 + 0.997246i \(0.523627\pi\)
\(942\) −1.28357e138 −0.653211
\(943\) −2.30140e138 −1.11480
\(944\) 4.65124e138 2.14472
\(945\) −1.03412e138 −0.453934
\(946\) −1.84038e138 −0.769076
\(947\) 5.69228e137 0.226471 0.113235 0.993568i \(-0.463879\pi\)
0.113235 + 0.993568i \(0.463879\pi\)
\(948\) −8.41811e137 −0.318880
\(949\) 9.66944e137 0.348757
\(950\) 2.55956e136 0.00879059
\(951\) −2.49683e138 −0.816572
\(952\) −4.44840e137 −0.138543
\(953\) 3.31221e138 0.982423 0.491212 0.871040i \(-0.336554\pi\)
0.491212 + 0.871040i \(0.336554\pi\)
\(954\) 2.58163e138 0.729281
\(955\) −6.84985e138 −1.84299
\(956\) −4.45308e138 −1.14122
\(957\) 2.15892e138 0.527026
\(958\) 1.72631e138 0.401443
\(959\) 8.47788e136 0.0187811
\(960\) 2.76898e138 0.584397
\(961\) −4.23414e138 −0.851388
\(962\) 8.14128e137 0.155974
\(963\) 7.48049e137 0.136555
\(964\) 2.44361e138 0.425059
\(965\) 1.27648e138 0.211589
\(966\) 2.52525e138 0.398903
\(967\) 4.39653e138 0.661879 0.330940 0.943652i \(-0.392634\pi\)
0.330940 + 0.943652i \(0.392634\pi\)
\(968\) −1.31232e138 −0.188293
\(969\) 2.83094e137 0.0387146
\(970\) 1.86586e139 2.43217
\(971\) −1.08160e139 −1.34392 −0.671961 0.740586i \(-0.734548\pi\)
−0.671961 + 0.740586i \(0.734548\pi\)
\(972\) −4.97023e138 −0.588702
\(973\) 8.70128e137 0.0982508
\(974\) −4.11515e138 −0.442990
\(975\) 1.75760e138 0.180387
\(976\) −4.25617e138 −0.416488
\(977\) 1.37620e139 1.28406 0.642031 0.766679i \(-0.278092\pi\)
0.642031 + 0.766679i \(0.278092\pi\)
\(978\) −6.18515e138 −0.550292
\(979\) 9.47483e137 0.0803852
\(980\) −9.91011e138 −0.801800
\(981\) 6.25207e138 0.482408
\(982\) 7.10056e138 0.522527
\(983\) −2.47747e139 −1.73888 −0.869442 0.494036i \(-0.835521\pi\)
−0.869442 + 0.494036i \(0.835521\pi\)
\(984\) −2.86094e138 −0.191530
\(985\) 1.31446e139 0.839389
\(986\) −7.46770e139 −4.54894
\(987\) −6.12636e136 −0.00356004
\(988\) 4.28244e137 0.0237407
\(989\) 3.08051e139 1.62928
\(990\) −3.79067e138 −0.191284
\(991\) 1.75193e139 0.843512 0.421756 0.906709i \(-0.361414\pi\)
0.421756 + 0.906709i \(0.361414\pi\)
\(992\) 1.11101e139 0.510417
\(993\) 3.32916e139 1.45947
\(994\) 1.97673e139 0.826954
\(995\) −2.09691e139 −0.837156
\(996\) −1.08310e139 −0.412676
\(997\) 2.54861e139 0.926786 0.463393 0.886153i \(-0.346632\pi\)
0.463393 + 0.886153i \(0.346632\pi\)
\(998\) 6.32153e139 2.19408
\(999\) 3.79050e138 0.125574
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 1.94.a.a.1.2 7
3.2 odd 2 9.94.a.b.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.94.a.a.1.2 7 1.1 even 1 trivial
9.94.a.b.1.6 7 3.2 odd 2