Properties

Label 1.94.a.a.1.6
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 1.6
Root \(2.59428e11\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.55678e14 q^{2} +1.43559e22 q^{3} +1.43322e28 q^{4} -3.85879e32 q^{5} +2.23491e36 q^{6} -1.93687e39 q^{7} +6.89447e41 q^{8} -2.95620e43 q^{9} +O(q^{10})\) \(q+1.55678e14 q^{2} +1.43559e22 q^{3} +1.43322e28 q^{4} -3.85879e32 q^{5} +2.23491e36 q^{6} -1.93687e39 q^{7} +6.89447e41 q^{8} -2.95620e43 q^{9} -6.00730e46 q^{10} +4.19320e48 q^{11} +2.05752e50 q^{12} -6.72877e51 q^{13} -3.01529e53 q^{14} -5.53966e54 q^{15} -3.46072e55 q^{16} +7.90484e56 q^{17} -4.60216e57 q^{18} -1.84855e59 q^{19} -5.53049e60 q^{20} -2.78056e61 q^{21} +6.52790e62 q^{22} -3.52814e63 q^{23} +9.89767e63 q^{24} +4.79285e64 q^{25} -1.04752e66 q^{26} -3.80744e66 q^{27} -2.77596e67 q^{28} +6.08060e66 q^{29} -8.62404e68 q^{30} -3.87123e69 q^{31} -1.22155e70 q^{32} +6.01973e70 q^{33} +1.23061e71 q^{34} +7.47399e71 q^{35} -4.23688e71 q^{36} +9.82535e72 q^{37} -2.87779e73 q^{38} -9.65977e73 q^{39} -2.66043e74 q^{40} +1.01031e75 q^{41} -4.32873e75 q^{42} +9.34216e75 q^{43} +6.00977e76 q^{44} +1.14074e76 q^{45} -5.49254e77 q^{46} -5.01133e76 q^{47} -4.96819e77 q^{48} -1.76033e77 q^{49} +7.46143e78 q^{50} +1.13481e79 q^{51} -9.64379e79 q^{52} +1.92932e80 q^{53} -5.92735e80 q^{54} -1.61807e81 q^{55} -1.33537e81 q^{56} -2.65376e81 q^{57} +9.46617e80 q^{58} -2.20461e81 q^{59} -7.93954e82 q^{60} -3.04227e82 q^{61} -6.02666e83 q^{62} +5.72579e82 q^{63} -1.55896e84 q^{64} +2.59649e84 q^{65} +9.37141e84 q^{66} -8.28207e84 q^{67} +1.13294e85 q^{68} -5.06497e85 q^{69} +1.16354e86 q^{70} +1.80973e86 q^{71} -2.03814e85 q^{72} -2.33738e86 q^{73} +1.52959e87 q^{74} +6.88059e86 q^{75} -2.64937e87 q^{76} -8.12170e87 q^{77} -1.50382e88 q^{78} -4.15888e87 q^{79} +1.33542e88 q^{80} -4.76929e88 q^{81} +1.57284e89 q^{82} +5.26808e88 q^{83} -3.98516e89 q^{84} -3.05031e89 q^{85} +1.45437e90 q^{86} +8.72927e88 q^{87} +2.89099e90 q^{88} +3.32123e90 q^{89} +1.77588e90 q^{90} +1.30328e91 q^{91} -5.05660e91 q^{92} -5.55751e91 q^{93} -7.80155e90 q^{94} +7.13316e91 q^{95} -1.75366e92 q^{96} +2.28947e92 q^{97} -2.74045e91 q^{98} -1.23959e92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + O(q^{10}) \) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + \)\(56\!\cdots\!00\)\(q^{10} + \)\(10\!\cdots\!24\)\(q^{11} - \)\(16\!\cdots\!48\)\(q^{12} + \)\(19\!\cdots\!26\)\(q^{13} - \)\(82\!\cdots\!32\)\(q^{14} - \)\(16\!\cdots\!00\)\(q^{15} - \)\(18\!\cdots\!48\)\(q^{16} + \)\(80\!\cdots\!42\)\(q^{17} + \)\(79\!\cdots\!36\)\(q^{18} - \)\(49\!\cdots\!00\)\(q^{19} - \)\(58\!\cdots\!00\)\(q^{20} + \)\(54\!\cdots\!84\)\(q^{21} + \)\(34\!\cdots\!44\)\(q^{22} - \)\(25\!\cdots\!64\)\(q^{23} - \)\(29\!\cdots\!00\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(79\!\cdots\!64\)\(q^{26} - \)\(10\!\cdots\!40\)\(q^{27} + \)\(19\!\cdots\!24\)\(q^{28} + \)\(11\!\cdots\!50\)\(q^{29} - \)\(64\!\cdots\!00\)\(q^{30} - \)\(11\!\cdots\!56\)\(q^{31} - \)\(70\!\cdots\!88\)\(q^{32} + \)\(66\!\cdots\!12\)\(q^{33} + \)\(80\!\cdots\!28\)\(q^{34} - \)\(16\!\cdots\!00\)\(q^{35} + \)\(52\!\cdots\!12\)\(q^{36} + \)\(11\!\cdots\!42\)\(q^{37} - \)\(42\!\cdots\!60\)\(q^{38} - \)\(20\!\cdots\!68\)\(q^{39} + \)\(76\!\cdots\!00\)\(q^{40} - \)\(50\!\cdots\!46\)\(q^{41} - \)\(54\!\cdots\!76\)\(q^{42} - \)\(72\!\cdots\!44\)\(q^{43} + \)\(94\!\cdots\!08\)\(q^{44} + \)\(16\!\cdots\!50\)\(q^{45} - \)\(63\!\cdots\!16\)\(q^{46} - \)\(37\!\cdots\!08\)\(q^{47} - \)\(41\!\cdots\!64\)\(q^{48} + \)\(25\!\cdots\!99\)\(q^{49} - \)\(31\!\cdots\!00\)\(q^{50} - \)\(55\!\cdots\!36\)\(q^{51} - \)\(55\!\cdots\!28\)\(q^{52} - \)\(36\!\cdots\!34\)\(q^{53} - \)\(19\!\cdots\!00\)\(q^{54} - \)\(35\!\cdots\!00\)\(q^{55} - \)\(12\!\cdots\!00\)\(q^{56} - \)\(13\!\cdots\!80\)\(q^{57} - \)\(73\!\cdots\!40\)\(q^{58} - \)\(11\!\cdots\!00\)\(q^{59} - \)\(46\!\cdots\!00\)\(q^{60} - \)\(32\!\cdots\!26\)\(q^{61} - \)\(99\!\cdots\!36\)\(q^{62} - \)\(22\!\cdots\!64\)\(q^{63} - \)\(47\!\cdots\!16\)\(q^{64} + \)\(24\!\cdots\!00\)\(q^{65} + \)\(12\!\cdots\!08\)\(q^{66} + \)\(97\!\cdots\!92\)\(q^{67} + \)\(51\!\cdots\!24\)\(q^{68} + \)\(12\!\cdots\!92\)\(q^{69} + \)\(43\!\cdots\!00\)\(q^{70} + \)\(42\!\cdots\!84\)\(q^{71} + \)\(11\!\cdots\!80\)\(q^{72} + \)\(24\!\cdots\!86\)\(q^{73} + \)\(98\!\cdots\!48\)\(q^{74} + \)\(94\!\cdots\!00\)\(q^{75} - \)\(98\!\cdots\!00\)\(q^{76} - \)\(16\!\cdots\!56\)\(q^{77} - \)\(73\!\cdots\!28\)\(q^{78} - \)\(43\!\cdots\!00\)\(q^{79} - \)\(88\!\cdots\!00\)\(q^{80} - \)\(70\!\cdots\!53\)\(q^{81} - \)\(23\!\cdots\!76\)\(q^{82} - \)\(20\!\cdots\!04\)\(q^{83} + \)\(16\!\cdots\!28\)\(q^{84} + \)\(16\!\cdots\!00\)\(q^{85} + \)\(32\!\cdots\!24\)\(q^{86} + \)\(65\!\cdots\!80\)\(q^{87} + \)\(63\!\cdots\!20\)\(q^{88} + \)\(55\!\cdots\!50\)\(q^{89} + \)\(19\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} - \)\(81\!\cdots\!08\)\(q^{92} - \)\(12\!\cdots\!28\)\(q^{93} - \)\(30\!\cdots\!92\)\(q^{94} - \)\(21\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!16\)\(q^{96} + \)\(43\!\cdots\!42\)\(q^{97} - \)\(69\!\cdots\!56\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55678e14 1.56435 0.782173 0.623061i \(-0.214111\pi\)
0.782173 + 0.623061i \(0.214111\pi\)
\(3\) 1.43559e22 0.935176 0.467588 0.883947i \(-0.345123\pi\)
0.467588 + 0.883947i \(0.345123\pi\)
\(4\) 1.43322e28 1.44718
\(5\) −3.85879e32 −1.21436 −0.607178 0.794566i \(-0.707699\pi\)
−0.607178 + 0.794566i \(0.707699\pi\)
\(6\) 2.23491e36 1.46294
\(7\) −1.93687e39 −0.977333 −0.488666 0.872471i \(-0.662516\pi\)
−0.488666 + 0.872471i \(0.662516\pi\)
\(8\) 6.89447e41 0.699547
\(9\) −2.95620e43 −0.125446
\(10\) −6.00730e46 −1.89967
\(11\) 4.19320e48 1.57683 0.788416 0.615142i \(-0.210901\pi\)
0.788416 + 0.615142i \(0.210901\pi\)
\(12\) 2.05752e50 1.35337
\(13\) −6.72877e51 −1.07046 −0.535229 0.844707i \(-0.679775\pi\)
−0.535229 + 0.844707i \(0.679775\pi\)
\(14\) −3.01529e53 −1.52889
\(15\) −5.53966e54 −1.13564
\(16\) −3.46072e55 −0.352848
\(17\) 7.90484e56 0.480859 0.240430 0.970667i \(-0.422712\pi\)
0.240430 + 0.970667i \(0.422712\pi\)
\(18\) −4.60216e57 −0.196241
\(19\) −1.84855e59 −0.637952 −0.318976 0.947763i \(-0.603339\pi\)
−0.318976 + 0.947763i \(0.603339\pi\)
\(20\) −5.53049e60 −1.75739
\(21\) −2.78056e61 −0.913978
\(22\) 6.52790e62 2.46671
\(23\) −3.52814e63 −1.68733 −0.843667 0.536866i \(-0.819608\pi\)
−0.843667 + 0.536866i \(0.819608\pi\)
\(24\) 9.89767e63 0.654199
\(25\) 4.79285e64 0.474661
\(26\) −1.04752e66 −1.67457
\(27\) −3.80744e66 −1.05249
\(28\) −2.77596e67 −1.41438
\(29\) 6.08060e66 0.0605954 0.0302977 0.999541i \(-0.490354\pi\)
0.0302977 + 0.999541i \(0.490354\pi\)
\(30\) −8.62404e68 −1.77653
\(31\) −3.87123e69 −1.73592 −0.867961 0.496633i \(-0.834570\pi\)
−0.867961 + 0.496633i \(0.834570\pi\)
\(32\) −1.22155e70 −1.25152
\(33\) 6.01973e70 1.47462
\(34\) 1.23061e71 0.752231
\(35\) 7.47399e71 1.18683
\(36\) −4.23688e71 −0.181543
\(37\) 9.82535e72 1.17752 0.588760 0.808308i \(-0.299616\pi\)
0.588760 + 0.808308i \(0.299616\pi\)
\(38\) −2.87779e73 −0.997979
\(39\) −9.65977e73 −1.00107
\(40\) −2.66043e74 −0.849499
\(41\) 1.01031e75 1.02331 0.511654 0.859192i \(-0.329033\pi\)
0.511654 + 0.859192i \(0.329033\pi\)
\(42\) −4.32873e75 −1.42978
\(43\) 9.34216e75 1.03315 0.516576 0.856241i \(-0.327206\pi\)
0.516576 + 0.856241i \(0.327206\pi\)
\(44\) 6.00977e76 2.28196
\(45\) 1.14074e76 0.152336
\(46\) −5.49254e77 −2.63958
\(47\) −5.01133e76 −0.0885937 −0.0442968 0.999018i \(-0.514105\pi\)
−0.0442968 + 0.999018i \(0.514105\pi\)
\(48\) −4.96819e77 −0.329974
\(49\) −1.76033e77 −0.0448204
\(50\) 7.46143e78 0.742535
\(51\) 1.13481e79 0.449688
\(52\) −9.64379e79 −1.54915
\(53\) 1.92932e80 1.27813 0.639066 0.769152i \(-0.279321\pi\)
0.639066 + 0.769152i \(0.279321\pi\)
\(54\) −5.92735e80 −1.64646
\(55\) −1.61807e81 −1.91484
\(56\) −1.33537e81 −0.683690
\(57\) −2.65376e81 −0.596598
\(58\) 9.46617e80 0.0947922
\(59\) −2.20461e81 −0.0997043 −0.0498521 0.998757i \(-0.515875\pi\)
−0.0498521 + 0.998757i \(0.515875\pi\)
\(60\) −7.93954e82 −1.64347
\(61\) −3.04227e82 −0.291985 −0.145992 0.989286i \(-0.546638\pi\)
−0.145992 + 0.989286i \(0.546638\pi\)
\(62\) −6.02666e83 −2.71558
\(63\) 5.72579e82 0.122603
\(64\) −1.55896e84 −1.60497
\(65\) 2.59649e84 1.29992
\(66\) 9.37141e84 2.30681
\(67\) −8.28207e84 −1.01312 −0.506560 0.862205i \(-0.669083\pi\)
−0.506560 + 0.862205i \(0.669083\pi\)
\(68\) 1.13294e85 0.695891
\(69\) −5.06497e85 −1.57795
\(70\) 1.16354e86 1.85661
\(71\) 1.80973e86 1.49314 0.746570 0.665307i \(-0.231699\pi\)
0.746570 + 0.665307i \(0.231699\pi\)
\(72\) −2.03814e85 −0.0877554
\(73\) −2.33738e86 −0.529927 −0.264963 0.964258i \(-0.585360\pi\)
−0.264963 + 0.964258i \(0.585360\pi\)
\(74\) 1.52959e87 1.84205
\(75\) 6.88059e86 0.443892
\(76\) −2.64937e87 −0.923233
\(77\) −8.12170e87 −1.54109
\(78\) −1.50382e88 −1.56601
\(79\) −4.15888e87 −0.239506 −0.119753 0.992804i \(-0.538210\pi\)
−0.119753 + 0.992804i \(0.538210\pi\)
\(80\) 1.33542e88 0.428483
\(81\) −4.76929e88 −0.858817
\(82\) 1.57284e89 1.60081
\(83\) 5.26808e88 0.305155 0.152578 0.988291i \(-0.451243\pi\)
0.152578 + 0.988291i \(0.451243\pi\)
\(84\) −3.98516e89 −1.32269
\(85\) −3.05031e89 −0.583935
\(86\) 1.45437e90 1.61621
\(87\) 8.72927e88 0.0566673
\(88\) 2.89099e90 1.10307
\(89\) 3.32123e90 0.749313 0.374656 0.927164i \(-0.377761\pi\)
0.374656 + 0.927164i \(0.377761\pi\)
\(90\) 1.77588e90 0.238307
\(91\) 1.30328e91 1.04619
\(92\) −5.05660e91 −2.44188
\(93\) −5.55751e91 −1.62339
\(94\) −7.80155e90 −0.138591
\(95\) 7.13316e91 0.774701
\(96\) −1.75366e92 −1.17039
\(97\) 2.28947e92 0.943731 0.471866 0.881670i \(-0.343581\pi\)
0.471866 + 0.881670i \(0.343581\pi\)
\(98\) −2.74045e91 −0.0701147
\(99\) −1.23959e92 −0.197808
\(100\) 6.86921e92 0.686921
\(101\) 7.22314e92 0.454760 0.227380 0.973806i \(-0.426984\pi\)
0.227380 + 0.973806i \(0.426984\pi\)
\(102\) 1.76666e93 0.703468
\(103\) −2.71237e93 −0.686148 −0.343074 0.939308i \(-0.611468\pi\)
−0.343074 + 0.939308i \(0.611468\pi\)
\(104\) −4.63913e93 −0.748835
\(105\) 1.07296e94 1.10990
\(106\) 3.00353e94 1.99944
\(107\) −7.44894e93 −0.320442 −0.160221 0.987081i \(-0.551221\pi\)
−0.160221 + 0.987081i \(0.551221\pi\)
\(108\) −5.45689e94 −1.52314
\(109\) −3.92415e94 −0.713532 −0.356766 0.934194i \(-0.616121\pi\)
−0.356766 + 0.934194i \(0.616121\pi\)
\(110\) −2.51898e95 −2.99547
\(111\) 1.41052e95 1.10119
\(112\) 6.70298e94 0.344849
\(113\) 3.44959e95 1.17387 0.586935 0.809634i \(-0.300335\pi\)
0.586935 + 0.809634i \(0.300335\pi\)
\(114\) −4.13133e95 −0.933286
\(115\) 1.36144e96 2.04903
\(116\) 8.71483e94 0.0876925
\(117\) 1.98916e95 0.134285
\(118\) −3.43210e95 −0.155972
\(119\) −1.53107e96 −0.469960
\(120\) −3.81930e96 −0.794431
\(121\) 1.05113e97 1.48640
\(122\) −4.73615e96 −0.456765
\(123\) 1.45040e97 0.956973
\(124\) −5.54832e97 −2.51219
\(125\) 2.04692e97 0.637949
\(126\) 8.91380e96 0.191793
\(127\) −7.56617e97 −1.12720 −0.563602 0.826046i \(-0.690585\pi\)
−0.563602 + 0.826046i \(0.690585\pi\)
\(128\) −1.21719e98 −1.25920
\(129\) 1.34115e98 0.966178
\(130\) 4.04217e98 2.03352
\(131\) −3.57749e98 −1.26027 −0.630135 0.776486i \(-0.717000\pi\)
−0.630135 + 0.776486i \(0.717000\pi\)
\(132\) 8.62759e98 2.13404
\(133\) 3.58040e98 0.623492
\(134\) −1.28934e99 −1.58487
\(135\) 1.46921e99 1.27810
\(136\) 5.44997e98 0.336384
\(137\) −2.60803e99 −1.14500 −0.572502 0.819904i \(-0.694027\pi\)
−0.572502 + 0.819904i \(0.694027\pi\)
\(138\) −7.88506e99 −2.46847
\(139\) −4.38756e99 −0.981826 −0.490913 0.871208i \(-0.663337\pi\)
−0.490913 + 0.871208i \(0.663337\pi\)
\(140\) 1.07119e100 1.71756
\(141\) −7.19424e98 −0.0828507
\(142\) 2.81735e100 2.33579
\(143\) −2.82151e100 −1.68793
\(144\) 1.02306e99 0.0442633
\(145\) −2.34638e99 −0.0735844
\(146\) −3.63879e100 −0.828990
\(147\) −2.52712e99 −0.0419150
\(148\) 1.40819e101 1.70408
\(149\) 1.00746e101 0.891387 0.445694 0.895186i \(-0.352957\pi\)
0.445694 + 0.895186i \(0.352957\pi\)
\(150\) 1.07116e101 0.694401
\(151\) −1.51245e101 −0.719869 −0.359934 0.932978i \(-0.617201\pi\)
−0.359934 + 0.932978i \(0.617201\pi\)
\(152\) −1.27448e101 −0.446277
\(153\) −2.33683e100 −0.0603219
\(154\) −1.26437e102 −2.41080
\(155\) 1.49383e102 2.10803
\(156\) −1.38446e102 −1.44872
\(157\) −1.66159e102 −1.29179 −0.645894 0.763427i \(-0.723515\pi\)
−0.645894 + 0.763427i \(0.723515\pi\)
\(158\) −6.47447e101 −0.374671
\(159\) 2.76972e102 1.19528
\(160\) 4.71372e102 1.51979
\(161\) 6.83356e102 1.64909
\(162\) −7.42475e102 −1.34349
\(163\) −2.86054e99 −0.000388798 0 −0.000194399 1.00000i \(-0.500062\pi\)
−0.000194399 1.00000i \(0.500062\pi\)
\(164\) 1.44800e103 1.48091
\(165\) −2.32289e103 −1.79071
\(166\) 8.20125e102 0.477369
\(167\) −3.04310e102 −0.133968 −0.0669839 0.997754i \(-0.521338\pi\)
−0.0669839 + 0.997754i \(0.521338\pi\)
\(168\) −1.91705e103 −0.639370
\(169\) 5.76403e102 0.145880
\(170\) −4.74867e103 −0.913476
\(171\) 5.46468e102 0.0800286
\(172\) 1.33894e104 1.49516
\(173\) −1.26480e104 −1.07864 −0.539321 0.842100i \(-0.681319\pi\)
−0.539321 + 0.842100i \(0.681319\pi\)
\(174\) 1.35896e103 0.0886473
\(175\) −9.28315e103 −0.463902
\(176\) −1.45115e104 −0.556382
\(177\) −3.16493e103 −0.0932410
\(178\) 5.17043e104 1.17219
\(179\) 5.12887e104 0.896099 0.448049 0.894009i \(-0.352119\pi\)
0.448049 + 0.894009i \(0.352119\pi\)
\(180\) 1.63492e104 0.220458
\(181\) 2.14822e104 0.223885 0.111943 0.993715i \(-0.464293\pi\)
0.111943 + 0.993715i \(0.464293\pi\)
\(182\) 2.02892e105 1.63661
\(183\) −4.36746e104 −0.273057
\(184\) −2.43247e105 −1.18037
\(185\) −3.79140e105 −1.42993
\(186\) −8.65184e105 −2.53955
\(187\) 3.31466e105 0.758235
\(188\) −7.18234e104 −0.128211
\(189\) 7.37453e105 1.02863
\(190\) 1.11048e106 1.21190
\(191\) 1.28582e106 1.09933 0.549664 0.835386i \(-0.314756\pi\)
0.549664 + 0.835386i \(0.314756\pi\)
\(192\) −2.23803e106 −1.50093
\(193\) −2.06907e106 −1.08983 −0.544917 0.838490i \(-0.683439\pi\)
−0.544917 + 0.838490i \(0.683439\pi\)
\(194\) 3.56420e106 1.47632
\(195\) 3.72751e106 1.21565
\(196\) −2.52294e105 −0.0648633
\(197\) −2.95791e106 −0.600212 −0.300106 0.953906i \(-0.597022\pi\)
−0.300106 + 0.953906i \(0.597022\pi\)
\(198\) −1.92978e106 −0.309440
\(199\) −2.16795e106 −0.275031 −0.137515 0.990500i \(-0.543912\pi\)
−0.137515 + 0.990500i \(0.543912\pi\)
\(200\) 3.30442e106 0.332048
\(201\) −1.18897e107 −0.947445
\(202\) 1.12449e107 0.711402
\(203\) −1.17774e106 −0.0592218
\(204\) 1.62644e107 0.650780
\(205\) −3.89859e107 −1.24266
\(206\) −4.22257e107 −1.07337
\(207\) 1.04299e107 0.211670
\(208\) 2.32864e107 0.377708
\(209\) −7.75133e107 −1.00594
\(210\) 1.67037e108 1.73626
\(211\) −5.65431e107 −0.471244 −0.235622 0.971845i \(-0.575713\pi\)
−0.235622 + 0.971845i \(0.575713\pi\)
\(212\) 2.76513e108 1.84969
\(213\) 2.59804e108 1.39635
\(214\) −1.15964e108 −0.501282
\(215\) −3.60494e108 −1.25461
\(216\) −2.62503e108 −0.736266
\(217\) 7.49808e108 1.69657
\(218\) −6.10905e108 −1.11621
\(219\) −3.35553e108 −0.495575
\(220\) −2.31905e109 −2.77112
\(221\) −5.31898e108 −0.514740
\(222\) 2.19588e109 1.72264
\(223\) 5.40231e108 0.343877 0.171938 0.985108i \(-0.444997\pi\)
0.171938 + 0.985108i \(0.444997\pi\)
\(224\) 2.36600e109 1.22315
\(225\) −1.41686e108 −0.0595444
\(226\) 5.37026e109 1.83634
\(227\) −3.58190e109 −0.997496 −0.498748 0.866747i \(-0.666207\pi\)
−0.498748 + 0.866747i \(0.666207\pi\)
\(228\) −3.80342e109 −0.863385
\(229\) −1.02602e110 −1.90023 −0.950116 0.311898i \(-0.899035\pi\)
−0.950116 + 0.311898i \(0.899035\pi\)
\(230\) 2.11946e110 3.20539
\(231\) −1.16595e110 −1.44119
\(232\) 4.19225e108 0.0423893
\(233\) 8.36616e109 0.692589 0.346295 0.938126i \(-0.387440\pi\)
0.346295 + 0.938126i \(0.387440\pi\)
\(234\) 3.09669e109 0.210068
\(235\) 1.93377e109 0.107584
\(236\) −3.15969e109 −0.144290
\(237\) −5.97046e109 −0.223980
\(238\) −2.38354e110 −0.735180
\(239\) −6.35040e110 −1.61175 −0.805877 0.592083i \(-0.798306\pi\)
−0.805877 + 0.592083i \(0.798306\pi\)
\(240\) 1.91712e110 0.400707
\(241\) −8.57088e110 −1.47650 −0.738249 0.674528i \(-0.764347\pi\)
−0.738249 + 0.674528i \(0.764347\pi\)
\(242\) 1.63638e111 2.32525
\(243\) 2.12565e110 0.249345
\(244\) −4.36024e110 −0.422555
\(245\) 6.79274e109 0.0544280
\(246\) 2.25796e111 1.49704
\(247\) 1.24384e111 0.682901
\(248\) −2.66901e111 −1.21436
\(249\) 7.56282e110 0.285374
\(250\) 3.18661e111 0.997973
\(251\) 2.56709e111 0.667749 0.333874 0.942618i \(-0.391644\pi\)
0.333874 + 0.942618i \(0.391644\pi\)
\(252\) 8.20631e110 0.177428
\(253\) −1.47942e112 −2.66065
\(254\) −1.17789e112 −1.76334
\(255\) −4.37901e111 −0.546082
\(256\) −3.50986e111 −0.364864
\(257\) 1.84481e112 1.59978 0.799892 0.600143i \(-0.204890\pi\)
0.799892 + 0.600143i \(0.204890\pi\)
\(258\) 2.08789e112 1.51144
\(259\) −1.90305e112 −1.15083
\(260\) 3.72134e112 1.88122
\(261\) −1.79755e110 −0.00760145
\(262\) −5.56938e112 −1.97150
\(263\) 3.59863e112 1.06707 0.533537 0.845777i \(-0.320862\pi\)
0.533537 + 0.845777i \(0.320862\pi\)
\(264\) 4.15029e112 1.03156
\(265\) −7.44483e112 −1.55211
\(266\) 5.57391e112 0.975357
\(267\) 4.76793e112 0.700739
\(268\) −1.18700e113 −1.46617
\(269\) −5.66507e112 −0.588470 −0.294235 0.955733i \(-0.595065\pi\)
−0.294235 + 0.955733i \(0.595065\pi\)
\(270\) 2.28724e113 1.99939
\(271\) −7.88661e112 −0.580521 −0.290261 0.956948i \(-0.593742\pi\)
−0.290261 + 0.956948i \(0.593742\pi\)
\(272\) −2.73564e112 −0.169670
\(273\) 1.87098e113 0.978375
\(274\) −4.06014e113 −1.79118
\(275\) 2.00974e113 0.748461
\(276\) −7.25922e113 −2.28359
\(277\) 3.52207e113 0.936459 0.468230 0.883607i \(-0.344892\pi\)
0.468230 + 0.883607i \(0.344892\pi\)
\(278\) −6.83047e113 −1.53592
\(279\) 1.14441e113 0.217765
\(280\) 5.15293e113 0.830243
\(281\) 1.16368e114 1.58851 0.794254 0.607585i \(-0.207862\pi\)
0.794254 + 0.607585i \(0.207862\pi\)
\(282\) −1.11999e113 −0.129607
\(283\) 8.32067e113 0.816750 0.408375 0.912814i \(-0.366096\pi\)
0.408375 + 0.912814i \(0.366096\pi\)
\(284\) 2.59374e114 2.16084
\(285\) 1.02403e114 0.724482
\(286\) −4.39247e114 −2.64051
\(287\) −1.95685e114 −1.00011
\(288\) 3.61116e113 0.156999
\(289\) −2.07754e114 −0.768774
\(290\) −3.65280e113 −0.115111
\(291\) 3.28674e114 0.882555
\(292\) −3.34998e114 −0.766900
\(293\) −3.53924e114 −0.691140 −0.345570 0.938393i \(-0.612314\pi\)
−0.345570 + 0.938393i \(0.612314\pi\)
\(294\) −3.93417e113 −0.0655696
\(295\) 8.50714e113 0.121076
\(296\) 6.77407e114 0.823730
\(297\) −1.59654e115 −1.65960
\(298\) 1.56840e115 1.39444
\(299\) 2.37400e115 1.80622
\(300\) 9.86139e114 0.642392
\(301\) −1.80946e115 −1.00973
\(302\) −2.35456e115 −1.12612
\(303\) 1.03695e115 0.425280
\(304\) 6.39730e114 0.225100
\(305\) 1.17395e115 0.354574
\(306\) −3.63793e114 −0.0943644
\(307\) 2.44087e115 0.544013 0.272007 0.962295i \(-0.412313\pi\)
0.272007 + 0.962295i \(0.412313\pi\)
\(308\) −1.16402e116 −2.23024
\(309\) −3.89386e115 −0.641669
\(310\) 2.32556e116 3.29769
\(311\) 5.39685e114 0.0658843 0.0329422 0.999457i \(-0.489512\pi\)
0.0329422 + 0.999457i \(0.489512\pi\)
\(312\) −6.65991e115 −0.700293
\(313\) −3.83093e115 −0.347130 −0.173565 0.984822i \(-0.555529\pi\)
−0.173565 + 0.984822i \(0.555529\pi\)
\(314\) −2.58674e116 −2.02080
\(315\) −2.20946e115 −0.148883
\(316\) −5.96059e115 −0.346609
\(317\) −2.64242e116 −1.32662 −0.663309 0.748346i \(-0.730849\pi\)
−0.663309 + 0.748346i \(0.730849\pi\)
\(318\) 4.31184e116 1.86983
\(319\) 2.54972e115 0.0955488
\(320\) 6.01571e116 1.94900
\(321\) −1.06937e116 −0.299669
\(322\) 1.06384e117 2.57975
\(323\) −1.46125e116 −0.306765
\(324\) −6.83544e116 −1.24286
\(325\) −3.22500e116 −0.508105
\(326\) −4.45324e113 −0.000608216 0
\(327\) −5.63349e116 −0.667278
\(328\) 6.96557e116 0.715852
\(329\) 9.70632e115 0.0865855
\(330\) −3.61623e117 −2.80129
\(331\) −2.97400e116 −0.200143 −0.100071 0.994980i \(-0.531907\pi\)
−0.100071 + 0.994980i \(0.531907\pi\)
\(332\) 7.55031e116 0.441615
\(333\) −2.90457e116 −0.147715
\(334\) −4.73744e116 −0.209572
\(335\) 3.19588e117 1.23029
\(336\) 9.62275e116 0.322495
\(337\) 3.75895e117 1.09717 0.548587 0.836093i \(-0.315166\pi\)
0.548587 + 0.836093i \(0.315166\pi\)
\(338\) 8.97334e116 0.228206
\(339\) 4.95221e117 1.09777
\(340\) −4.37177e117 −0.845059
\(341\) −1.62328e118 −2.73726
\(342\) 8.50731e116 0.125193
\(343\) 7.94805e117 1.02114
\(344\) 6.44093e117 0.722738
\(345\) 1.95447e118 1.91620
\(346\) −1.96901e118 −1.68737
\(347\) 3.02947e117 0.227011 0.113505 0.993537i \(-0.463792\pi\)
0.113505 + 0.993537i \(0.463792\pi\)
\(348\) 1.25110e117 0.0820079
\(349\) −1.20438e118 −0.690844 −0.345422 0.938447i \(-0.612264\pi\)
−0.345422 + 0.938447i \(0.612264\pi\)
\(350\) −1.44518e118 −0.725704
\(351\) 2.56194e118 1.12665
\(352\) −5.12222e118 −1.97344
\(353\) 3.83160e118 1.29377 0.646884 0.762589i \(-0.276072\pi\)
0.646884 + 0.762589i \(0.276072\pi\)
\(354\) −4.92710e117 −0.145861
\(355\) −6.98337e118 −1.81320
\(356\) 4.76004e118 1.08439
\(357\) −2.19799e118 −0.439495
\(358\) 7.98454e118 1.40181
\(359\) −3.83119e118 −0.590802 −0.295401 0.955373i \(-0.595453\pi\)
−0.295401 + 0.955373i \(0.595453\pi\)
\(360\) 7.86478e117 0.106566
\(361\) −4.97911e118 −0.593017
\(362\) 3.34432e118 0.350234
\(363\) 1.50899e119 1.39005
\(364\) 1.86788e119 1.51403
\(365\) 9.01946e118 0.643520
\(366\) −6.79919e118 −0.427156
\(367\) −2.15604e119 −1.19312 −0.596561 0.802568i \(-0.703466\pi\)
−0.596561 + 0.802568i \(0.703466\pi\)
\(368\) 1.22099e119 0.595372
\(369\) −2.98669e118 −0.128370
\(370\) −5.90238e119 −2.23690
\(371\) −3.73684e119 −1.24916
\(372\) −7.96513e119 −2.34934
\(373\) 6.59757e119 1.71760 0.858802 0.512307i \(-0.171209\pi\)
0.858802 + 0.512307i \(0.171209\pi\)
\(374\) 5.16020e119 1.18614
\(375\) 2.93855e119 0.596594
\(376\) −3.45505e118 −0.0619754
\(377\) −4.09149e118 −0.0648648
\(378\) 1.14805e120 1.60914
\(379\) −5.17356e119 −0.641307 −0.320654 0.947197i \(-0.603903\pi\)
−0.320654 + 0.947197i \(0.603903\pi\)
\(380\) 1.02234e120 1.12113
\(381\) −1.08619e120 −1.05413
\(382\) 2.00174e120 1.71973
\(383\) −2.08785e120 −1.58839 −0.794194 0.607664i \(-0.792107\pi\)
−0.794194 + 0.607664i \(0.792107\pi\)
\(384\) −1.74740e120 −1.17758
\(385\) 3.13399e120 1.87143
\(386\) −3.22109e120 −1.70488
\(387\) −2.76173e119 −0.129605
\(388\) 3.28130e120 1.36575
\(389\) −1.96484e120 −0.725556 −0.362778 0.931876i \(-0.618172\pi\)
−0.362778 + 0.931876i \(0.618172\pi\)
\(390\) 5.80291e120 1.90170
\(391\) −2.78894e120 −0.811371
\(392\) −1.21365e119 −0.0313540
\(393\) −5.13583e120 −1.17857
\(394\) −4.60482e120 −0.938940
\(395\) 1.60483e120 0.290846
\(396\) −1.77661e120 −0.286263
\(397\) 4.00181e120 0.573454 0.286727 0.958012i \(-0.407433\pi\)
0.286727 + 0.958012i \(0.407433\pi\)
\(398\) −3.37502e120 −0.430243
\(399\) 5.14001e120 0.583074
\(400\) −1.65867e120 −0.167483
\(401\) −3.73524e120 −0.335819 −0.167909 0.985802i \(-0.553702\pi\)
−0.167909 + 0.985802i \(0.553702\pi\)
\(402\) −1.85097e121 −1.48213
\(403\) 2.60486e121 1.85823
\(404\) 1.03523e121 0.658120
\(405\) 1.84037e121 1.04291
\(406\) −1.83348e120 −0.0926435
\(407\) 4.11997e121 1.85675
\(408\) 7.82394e120 0.314578
\(409\) −1.23899e121 −0.444564 −0.222282 0.974982i \(-0.571351\pi\)
−0.222282 + 0.974982i \(0.571351\pi\)
\(410\) −6.06925e121 −1.94395
\(411\) −3.74408e121 −1.07078
\(412\) −3.88742e121 −0.992980
\(413\) 4.27006e120 0.0974443
\(414\) 1.62371e121 0.331125
\(415\) −2.03284e121 −0.370567
\(416\) 8.21955e121 1.33970
\(417\) −6.29875e121 −0.918180
\(418\) −1.20671e122 −1.57365
\(419\) −9.18993e120 −0.107241 −0.0536204 0.998561i \(-0.517076\pi\)
−0.0536204 + 0.998561i \(0.517076\pi\)
\(420\) 1.53779e122 1.60622
\(421\) 1.03836e122 0.971024 0.485512 0.874230i \(-0.338633\pi\)
0.485512 + 0.874230i \(0.338633\pi\)
\(422\) −8.80253e121 −0.737189
\(423\) 1.48145e120 0.0111137
\(424\) 1.33016e122 0.894113
\(425\) 3.78867e121 0.228245
\(426\) 4.04458e122 2.18437
\(427\) 5.89249e121 0.285366
\(428\) −1.06760e122 −0.463737
\(429\) −4.05054e122 −1.57851
\(430\) −5.61211e122 −1.96265
\(431\) −1.54782e122 −0.485878 −0.242939 0.970042i \(-0.578111\pi\)
−0.242939 + 0.970042i \(0.578111\pi\)
\(432\) 1.31765e122 0.371369
\(433\) −3.09529e122 −0.783455 −0.391728 0.920081i \(-0.628122\pi\)
−0.391728 + 0.920081i \(0.628122\pi\)
\(434\) 1.16729e123 2.65403
\(435\) −3.36844e121 −0.0688143
\(436\) −5.62417e122 −1.03261
\(437\) 6.52193e122 1.07644
\(438\) −5.22382e122 −0.775251
\(439\) 9.67855e122 1.29184 0.645922 0.763404i \(-0.276473\pi\)
0.645922 + 0.763404i \(0.276473\pi\)
\(440\) −1.11557e123 −1.33952
\(441\) 5.20388e120 0.00562255
\(442\) −8.28049e122 −0.805231
\(443\) −2.07254e123 −1.81439 −0.907194 0.420713i \(-0.861780\pi\)
−0.907194 + 0.420713i \(0.861780\pi\)
\(444\) 2.02159e123 1.59362
\(445\) −1.28159e123 −0.909933
\(446\) 8.41021e122 0.537943
\(447\) 1.44630e123 0.833604
\(448\) 3.01951e123 1.56859
\(449\) −1.09500e123 −0.512813 −0.256407 0.966569i \(-0.582539\pi\)
−0.256407 + 0.966569i \(0.582539\pi\)
\(450\) −2.20575e122 −0.0931481
\(451\) 4.23644e123 1.61359
\(452\) 4.94402e123 1.69880
\(453\) −2.17127e123 −0.673204
\(454\) −5.57624e123 −1.56043
\(455\) −5.02907e123 −1.27045
\(456\) −1.82963e123 −0.417348
\(457\) 7.48537e123 1.54209 0.771046 0.636780i \(-0.219734\pi\)
0.771046 + 0.636780i \(0.219734\pi\)
\(458\) −1.59729e124 −2.97262
\(459\) −3.00972e123 −0.506100
\(460\) 1.95123e124 2.96531
\(461\) −5.06600e123 −0.695941 −0.347970 0.937506i \(-0.613129\pi\)
−0.347970 + 0.937506i \(0.613129\pi\)
\(462\) −1.81512e124 −2.25452
\(463\) −7.01263e123 −0.787707 −0.393854 0.919173i \(-0.628858\pi\)
−0.393854 + 0.919173i \(0.628858\pi\)
\(464\) −2.10432e122 −0.0213809
\(465\) 2.14453e124 1.97138
\(466\) 1.30243e124 1.08345
\(467\) 2.44106e123 0.183799 0.0918994 0.995768i \(-0.470706\pi\)
0.0918994 + 0.995768i \(0.470706\pi\)
\(468\) 2.85090e123 0.194334
\(469\) 1.60413e124 0.990155
\(470\) 3.01046e123 0.168299
\(471\) −2.38537e124 −1.20805
\(472\) −1.51996e123 −0.0697478
\(473\) 3.91735e124 1.62911
\(474\) −9.29471e123 −0.350383
\(475\) −8.85982e123 −0.302811
\(476\) −2.19436e124 −0.680117
\(477\) −5.70345e123 −0.160337
\(478\) −9.88619e124 −2.52134
\(479\) 7.42219e124 1.71763 0.858817 0.512283i \(-0.171200\pi\)
0.858817 + 0.512283i \(0.171200\pi\)
\(480\) 6.76699e124 1.42128
\(481\) −6.61125e124 −1.26048
\(482\) −1.33430e125 −2.30976
\(483\) 9.81022e124 1.54219
\(484\) 1.50650e125 2.15109
\(485\) −8.83457e124 −1.14603
\(486\) 3.30918e124 0.390062
\(487\) −8.80631e124 −0.943403 −0.471701 0.881758i \(-0.656360\pi\)
−0.471701 + 0.881758i \(0.656360\pi\)
\(488\) −2.09748e124 −0.204257
\(489\) −4.10657e121 −0.000363595 0
\(490\) 1.05748e124 0.0851442
\(491\) −1.68113e125 −1.23115 −0.615575 0.788078i \(-0.711076\pi\)
−0.615575 + 0.788078i \(0.711076\pi\)
\(492\) 2.07874e125 1.38491
\(493\) 4.80661e123 0.0291378
\(494\) 1.93639e125 1.06829
\(495\) 4.78333e124 0.240209
\(496\) 1.33972e125 0.612516
\(497\) −3.50522e125 −1.45929
\(498\) 1.17737e125 0.446424
\(499\) −1.86037e125 −0.642574 −0.321287 0.946982i \(-0.604115\pi\)
−0.321287 + 0.946982i \(0.604115\pi\)
\(500\) 2.93369e125 0.923227
\(501\) −4.36866e124 −0.125283
\(502\) 3.99640e125 1.04459
\(503\) 5.49090e125 1.30838 0.654188 0.756332i \(-0.273011\pi\)
0.654188 + 0.756332i \(0.273011\pi\)
\(504\) 3.94763e124 0.0857663
\(505\) −2.78726e125 −0.552240
\(506\) −2.30313e126 −4.16217
\(507\) 8.27481e124 0.136423
\(508\) −1.08440e126 −1.63127
\(509\) 3.04129e125 0.417523 0.208762 0.977967i \(-0.433057\pi\)
0.208762 + 0.977967i \(0.433057\pi\)
\(510\) −6.81717e125 −0.854261
\(511\) 4.52721e125 0.517915
\(512\) 6.59042e125 0.688430
\(513\) 7.03823e125 0.671438
\(514\) 2.87197e126 2.50262
\(515\) 1.04665e126 0.833228
\(516\) 1.92217e126 1.39824
\(517\) −2.10135e125 −0.139697
\(518\) −2.96263e126 −1.80029
\(519\) −1.81574e126 −1.00872
\(520\) 1.79014e126 0.909353
\(521\) 1.60621e125 0.0746188 0.0373094 0.999304i \(-0.488121\pi\)
0.0373094 + 0.999304i \(0.488121\pi\)
\(522\) −2.79839e124 −0.0118913
\(523\) 5.34768e125 0.207891 0.103946 0.994583i \(-0.466853\pi\)
0.103946 + 0.994583i \(0.466853\pi\)
\(524\) −5.12733e126 −1.82384
\(525\) −1.33268e126 −0.433830
\(526\) 5.60228e126 1.66927
\(527\) −3.06014e126 −0.834734
\(528\) −2.08326e126 −0.520315
\(529\) 8.07568e126 1.84710
\(530\) −1.15900e127 −2.42803
\(531\) 6.51728e124 0.0125075
\(532\) 5.13150e126 0.902306
\(533\) −6.79816e126 −1.09541
\(534\) 7.42263e126 1.09620
\(535\) 2.87439e126 0.389130
\(536\) −5.71005e126 −0.708725
\(537\) 7.36298e126 0.838010
\(538\) −8.81928e126 −0.920571
\(539\) −7.38141e125 −0.0706743
\(540\) 2.10570e127 1.84964
\(541\) −6.30702e126 −0.508337 −0.254168 0.967160i \(-0.581802\pi\)
−0.254168 + 0.967160i \(0.581802\pi\)
\(542\) −1.22777e127 −0.908137
\(543\) 3.08398e126 0.209372
\(544\) −9.65619e126 −0.601806
\(545\) 1.51425e127 0.866482
\(546\) 2.91270e127 1.53052
\(547\) 6.02623e126 0.290827 0.145414 0.989371i \(-0.453549\pi\)
0.145414 + 0.989371i \(0.453549\pi\)
\(548\) −3.73788e127 −1.65703
\(549\) 8.99356e125 0.0366284
\(550\) 3.12873e127 1.17085
\(551\) −1.12403e126 −0.0386569
\(552\) −3.49203e127 −1.10385
\(553\) 8.05523e126 0.234077
\(554\) 5.48310e127 1.46495
\(555\) −5.44291e127 −1.33723
\(556\) −6.28833e127 −1.42088
\(557\) −6.30406e127 −1.31025 −0.655124 0.755521i \(-0.727384\pi\)
−0.655124 + 0.755521i \(0.727384\pi\)
\(558\) 1.78160e127 0.340659
\(559\) −6.28612e127 −1.10595
\(560\) −2.58654e127 −0.418770
\(561\) 4.75850e127 0.709083
\(562\) 1.81160e128 2.48498
\(563\) 2.39370e127 0.302294 0.151147 0.988511i \(-0.451703\pi\)
0.151147 + 0.988511i \(0.451703\pi\)
\(564\) −1.03109e127 −0.119900
\(565\) −1.33112e128 −1.42550
\(566\) 1.29535e128 1.27768
\(567\) 9.23752e127 0.839350
\(568\) 1.24771e128 1.04452
\(569\) −1.05530e127 −0.0814058 −0.0407029 0.999171i \(-0.512960\pi\)
−0.0407029 + 0.999171i \(0.512960\pi\)
\(570\) 1.59420e128 1.13334
\(571\) 6.52543e127 0.427593 0.213796 0.976878i \(-0.431417\pi\)
0.213796 + 0.976878i \(0.431417\pi\)
\(572\) −4.04384e128 −2.44274
\(573\) 1.84591e128 1.02806
\(574\) −3.04639e128 −1.56452
\(575\) −1.69098e128 −0.800912
\(576\) 4.60860e127 0.201337
\(577\) 5.32992e127 0.214806 0.107403 0.994216i \(-0.465747\pi\)
0.107403 + 0.994216i \(0.465747\pi\)
\(578\) −3.23427e128 −1.20263
\(579\) −2.97034e128 −1.01919
\(580\) −3.36287e127 −0.106490
\(581\) −1.02036e128 −0.298238
\(582\) 5.11674e128 1.38062
\(583\) 8.09001e128 2.01540
\(584\) −1.61150e128 −0.370709
\(585\) −7.67575e127 −0.163070
\(586\) −5.50983e128 −1.08118
\(587\) 5.47325e128 0.992141 0.496070 0.868282i \(-0.334776\pi\)
0.496070 + 0.868282i \(0.334776\pi\)
\(588\) −3.62191e127 −0.0606586
\(589\) 7.15615e128 1.10744
\(590\) 1.32438e128 0.189406
\(591\) −4.24635e128 −0.561304
\(592\) −3.40028e128 −0.415485
\(593\) −2.94362e128 −0.332536 −0.166268 0.986081i \(-0.553172\pi\)
−0.166268 + 0.986081i \(0.553172\pi\)
\(594\) −2.48546e129 −2.59619
\(595\) 5.90807e128 0.570699
\(596\) 1.44391e129 1.29000
\(597\) −3.11229e128 −0.257202
\(598\) 3.69580e129 2.82556
\(599\) 1.66109e129 1.17502 0.587512 0.809216i \(-0.300108\pi\)
0.587512 + 0.809216i \(0.300108\pi\)
\(600\) 4.74381e128 0.310523
\(601\) −1.29386e129 −0.783834 −0.391917 0.920001i \(-0.628188\pi\)
−0.391917 + 0.920001i \(0.628188\pi\)
\(602\) −2.81693e129 −1.57957
\(603\) 2.44835e128 0.127092
\(604\) −2.16767e129 −1.04178
\(605\) −4.05609e129 −1.80502
\(606\) 1.61430e129 0.665286
\(607\) −3.30501e129 −1.26153 −0.630767 0.775972i \(-0.717260\pi\)
−0.630767 + 0.775972i \(0.717260\pi\)
\(608\) 2.25810e129 0.798412
\(609\) −1.69075e128 −0.0553828
\(610\) 1.82758e129 0.554676
\(611\) 3.37201e128 0.0948358
\(612\) −3.34919e128 −0.0872968
\(613\) 2.95847e129 0.714752 0.357376 0.933961i \(-0.383671\pi\)
0.357376 + 0.933961i \(0.383671\pi\)
\(614\) 3.79990e129 0.851026
\(615\) −5.59679e129 −1.16211
\(616\) −5.59948e129 −1.07806
\(617\) 8.56214e129 1.52870 0.764350 0.644802i \(-0.223060\pi\)
0.764350 + 0.644802i \(0.223060\pi\)
\(618\) −6.06189e129 −1.00379
\(619\) −2.56649e129 −0.394207 −0.197104 0.980383i \(-0.563154\pi\)
−0.197104 + 0.980383i \(0.563154\pi\)
\(620\) 2.14098e130 3.05070
\(621\) 1.34332e130 1.77590
\(622\) 8.40172e128 0.103066
\(623\) −6.43280e129 −0.732328
\(624\) 3.34298e129 0.353224
\(625\) −1.27382e130 −1.24936
\(626\) −5.96392e129 −0.543032
\(627\) −1.11278e130 −0.940735
\(628\) −2.38143e130 −1.86945
\(629\) 7.76678e129 0.566221
\(630\) −3.43965e129 −0.232905
\(631\) 6.30881e129 0.396809 0.198405 0.980120i \(-0.436424\pi\)
0.198405 + 0.980120i \(0.436424\pi\)
\(632\) −2.86733e129 −0.167546
\(633\) −8.11730e129 −0.440696
\(634\) −4.11367e130 −2.07529
\(635\) 2.91963e130 1.36883
\(636\) 3.96961e130 1.72978
\(637\) 1.18448e129 0.0479784
\(638\) 3.96935e129 0.149471
\(639\) −5.34992e129 −0.187309
\(640\) 4.69690e130 1.52912
\(641\) 1.41919e130 0.429676 0.214838 0.976650i \(-0.431078\pi\)
0.214838 + 0.976650i \(0.431078\pi\)
\(642\) −1.66477e130 −0.468787
\(643\) −5.43853e130 −1.42453 −0.712264 0.701911i \(-0.752330\pi\)
−0.712264 + 0.701911i \(0.752330\pi\)
\(644\) 9.79399e130 2.38653
\(645\) −5.17524e130 −1.17328
\(646\) −2.27484e130 −0.479887
\(647\) 1.22570e130 0.240622 0.120311 0.992736i \(-0.461611\pi\)
0.120311 + 0.992736i \(0.461611\pi\)
\(648\) −3.28818e130 −0.600783
\(649\) −9.24438e129 −0.157217
\(650\) −5.02062e130 −0.794852
\(651\) 1.07642e131 1.58659
\(652\) −4.09978e127 −0.000562662 0
\(653\) −1.74371e130 −0.222849 −0.111425 0.993773i \(-0.535541\pi\)
−0.111425 + 0.993773i \(0.535541\pi\)
\(654\) −8.77011e130 −1.04385
\(655\) 1.38048e131 1.53042
\(656\) −3.49641e130 −0.361072
\(657\) 6.90976e129 0.0664773
\(658\) 1.51106e130 0.135450
\(659\) 6.85103e130 0.572248 0.286124 0.958193i \(-0.407633\pi\)
0.286124 + 0.958193i \(0.407633\pi\)
\(660\) −3.32921e131 −2.59148
\(661\) 1.41756e131 1.02843 0.514215 0.857661i \(-0.328083\pi\)
0.514215 + 0.857661i \(0.328083\pi\)
\(662\) −4.62987e130 −0.313092
\(663\) −7.63590e130 −0.481372
\(664\) 3.63206e130 0.213470
\(665\) −1.38160e131 −0.757141
\(666\) −4.52179e130 −0.231078
\(667\) −2.14532e130 −0.102245
\(668\) −4.36143e130 −0.193876
\(669\) 7.75552e130 0.321585
\(670\) 4.97529e131 1.92460
\(671\) −1.27568e131 −0.460411
\(672\) 3.39661e131 1.14386
\(673\) 8.30557e130 0.261017 0.130509 0.991447i \(-0.458339\pi\)
0.130509 + 0.991447i \(0.458339\pi\)
\(674\) 5.85186e131 1.71636
\(675\) −1.82485e131 −0.499576
\(676\) 8.26112e130 0.211114
\(677\) −3.55196e131 −0.847413 −0.423707 0.905799i \(-0.639271\pi\)
−0.423707 + 0.905799i \(0.639271\pi\)
\(678\) 7.70951e131 1.71730
\(679\) −4.43441e131 −0.922340
\(680\) −2.10303e131 −0.408490
\(681\) −5.14215e131 −0.932834
\(682\) −2.52710e132 −4.28202
\(683\) 3.18172e131 0.503615 0.251808 0.967777i \(-0.418975\pi\)
0.251808 + 0.967777i \(0.418975\pi\)
\(684\) 7.83208e130 0.115816
\(685\) 1.00639e132 1.39044
\(686\) 1.23734e132 1.59741
\(687\) −1.47295e132 −1.77705
\(688\) −3.23306e131 −0.364545
\(689\) −1.29819e132 −1.36819
\(690\) 3.04268e132 2.99760
\(691\) 5.99865e131 0.552490 0.276245 0.961087i \(-0.410910\pi\)
0.276245 + 0.961087i \(0.410910\pi\)
\(692\) −1.81273e132 −1.56099
\(693\) 2.40094e131 0.193324
\(694\) 4.71623e131 0.355123
\(695\) 1.69307e132 1.19229
\(696\) 6.01837e130 0.0396414
\(697\) 7.98636e131 0.492067
\(698\) −1.87495e132 −1.08072
\(699\) 1.20104e132 0.647693
\(700\) −1.33048e132 −0.671350
\(701\) 2.25248e132 1.06359 0.531793 0.846874i \(-0.321519\pi\)
0.531793 + 0.846874i \(0.321519\pi\)
\(702\) 3.98838e132 1.76247
\(703\) −1.81626e132 −0.751201
\(704\) −6.53703e132 −2.53077
\(705\) 2.77611e131 0.100610
\(706\) 5.96496e132 2.02390
\(707\) −1.39903e132 −0.444452
\(708\) −4.53604e131 −0.134937
\(709\) −5.69127e132 −1.58547 −0.792737 0.609564i \(-0.791344\pi\)
−0.792737 + 0.609564i \(0.791344\pi\)
\(710\) −1.08716e133 −2.83648
\(711\) 1.22945e131 0.0300451
\(712\) 2.28981e132 0.524179
\(713\) 1.36582e133 2.92908
\(714\) −3.42179e132 −0.687523
\(715\) 1.08876e133 2.04975
\(716\) 7.35080e132 1.29682
\(717\) −9.11660e132 −1.50727
\(718\) −5.96433e132 −0.924220
\(719\) −1.04361e133 −1.51581 −0.757903 0.652368i \(-0.773776\pi\)
−0.757903 + 0.652368i \(0.773776\pi\)
\(720\) −3.94777e131 −0.0537515
\(721\) 5.25352e132 0.670595
\(722\) −7.75139e132 −0.927684
\(723\) −1.23043e133 −1.38079
\(724\) 3.07887e132 0.324003
\(725\) 2.91434e131 0.0287623
\(726\) 2.34918e133 2.17452
\(727\) 1.08894e132 0.0945482 0.0472741 0.998882i \(-0.484947\pi\)
0.0472741 + 0.998882i \(0.484947\pi\)
\(728\) 8.98541e132 0.731861
\(729\) 1.42907e133 1.09200
\(730\) 1.40413e133 1.00669
\(731\) 7.38483e132 0.496801
\(732\) −6.25953e132 −0.395163
\(733\) −1.69144e133 −1.00212 −0.501062 0.865411i \(-0.667057\pi\)
−0.501062 + 0.865411i \(0.667057\pi\)
\(734\) −3.35648e133 −1.86646
\(735\) 9.75162e131 0.0508997
\(736\) 4.30981e133 2.11174
\(737\) −3.47284e133 −1.59752
\(738\) −4.64962e132 −0.200815
\(739\) 3.59192e133 1.45667 0.728334 0.685223i \(-0.240295\pi\)
0.728334 + 0.685223i \(0.240295\pi\)
\(740\) −5.43391e133 −2.06937
\(741\) 1.78566e133 0.638632
\(742\) −5.81745e133 −1.95412
\(743\) −2.53993e133 −0.801386 −0.400693 0.916212i \(-0.631231\pi\)
−0.400693 + 0.916212i \(0.631231\pi\)
\(744\) −3.83161e133 −1.13564
\(745\) −3.88758e133 −1.08246
\(746\) 1.02710e134 2.68693
\(747\) −1.55735e132 −0.0382805
\(748\) 4.75063e133 1.09730
\(749\) 1.44277e133 0.313178
\(750\) 4.57468e133 0.933280
\(751\) 1.35458e133 0.259746 0.129873 0.991531i \(-0.458543\pi\)
0.129873 + 0.991531i \(0.458543\pi\)
\(752\) 1.73428e132 0.0312601
\(753\) 3.68530e133 0.624462
\(754\) −6.36956e132 −0.101471
\(755\) 5.83624e133 0.874177
\(756\) 1.05693e134 1.48862
\(757\) −5.95259e133 −0.788402 −0.394201 0.919024i \(-0.628979\pi\)
−0.394201 + 0.919024i \(0.628979\pi\)
\(758\) −8.05410e133 −1.00323
\(759\) −2.12384e134 −2.48817
\(760\) 4.91794e133 0.541940
\(761\) 7.75508e133 0.803896 0.401948 0.915663i \(-0.368333\pi\)
0.401948 + 0.915663i \(0.368333\pi\)
\(762\) −1.69097e134 −1.64903
\(763\) 7.60058e133 0.697358
\(764\) 1.84286e134 1.59093
\(765\) 9.01733e132 0.0732523
\(766\) −3.25033e134 −2.48479
\(767\) 1.48343e133 0.106729
\(768\) −5.03873e133 −0.341212
\(769\) −2.41544e134 −1.53965 −0.769825 0.638255i \(-0.779656\pi\)
−0.769825 + 0.638255i \(0.779656\pi\)
\(770\) 4.87895e134 2.92757
\(771\) 2.64840e134 1.49608
\(772\) −2.96543e134 −1.57719
\(773\) 1.24924e134 0.625605 0.312802 0.949818i \(-0.398732\pi\)
0.312802 + 0.949818i \(0.398732\pi\)
\(774\) −4.29941e133 −0.202747
\(775\) −1.85542e134 −0.823975
\(776\) 1.57847e134 0.660184
\(777\) −2.73200e134 −1.07623
\(778\) −3.05883e134 −1.13502
\(779\) −1.86761e134 −0.652822
\(780\) 5.34233e134 1.75927
\(781\) 7.58856e134 2.35443
\(782\) −4.34177e134 −1.26927
\(783\) −2.31515e133 −0.0637760
\(784\) 6.09200e132 0.0158148
\(785\) 6.41174e134 1.56869
\(786\) −7.99536e134 −1.84370
\(787\) 6.36591e134 1.38368 0.691840 0.722051i \(-0.256800\pi\)
0.691840 + 0.722051i \(0.256800\pi\)
\(788\) −4.23933e134 −0.868616
\(789\) 5.16617e134 0.997902
\(790\) 2.49836e134 0.454984
\(791\) −6.68142e134 −1.14726
\(792\) −8.54635e133 −0.138376
\(793\) 2.04707e134 0.312557
\(794\) 6.22995e134 0.897081
\(795\) −1.06878e135 −1.45149
\(796\) −3.10715e134 −0.398019
\(797\) −6.97769e133 −0.0843141 −0.0421570 0.999111i \(-0.513423\pi\)
−0.0421570 + 0.999111i \(0.513423\pi\)
\(798\) 8.00187e134 0.912131
\(799\) −3.96138e133 −0.0426011
\(800\) −5.85473e134 −0.594049
\(801\) −9.81821e133 −0.0939984
\(802\) −5.81495e134 −0.525337
\(803\) −9.80109e134 −0.835606
\(804\) −1.70405e135 −1.37113
\(805\) −2.63693e135 −2.00258
\(806\) 4.05520e135 2.90692
\(807\) −8.13274e134 −0.550323
\(808\) 4.97997e134 0.318126
\(809\) 1.46485e134 0.0883461 0.0441731 0.999024i \(-0.485935\pi\)
0.0441731 + 0.999024i \(0.485935\pi\)
\(810\) 2.86506e135 1.63147
\(811\) 3.37629e135 1.81539 0.907696 0.419629i \(-0.137840\pi\)
0.907696 + 0.419629i \(0.137840\pi\)
\(812\) −1.68795e134 −0.0857047
\(813\) −1.13220e135 −0.542890
\(814\) 6.41389e135 2.90460
\(815\) 1.10382e132 0.000472140 0
\(816\) −3.92727e134 −0.158671
\(817\) −1.72694e135 −0.659101
\(818\) −1.92884e135 −0.695453
\(819\) −3.85275e134 −0.131241
\(820\) −5.58753e135 −1.79836
\(821\) 1.07325e135 0.326394 0.163197 0.986593i \(-0.447819\pi\)
0.163197 + 0.986593i \(0.447819\pi\)
\(822\) −5.82871e135 −1.67507
\(823\) −2.55029e135 −0.692623 −0.346311 0.938120i \(-0.612566\pi\)
−0.346311 + 0.938120i \(0.612566\pi\)
\(824\) −1.87004e135 −0.479993
\(825\) 2.88517e135 0.699943
\(826\) 6.64755e134 0.152437
\(827\) 1.56864e135 0.340030 0.170015 0.985441i \(-0.445618\pi\)
0.170015 + 0.985441i \(0.445618\pi\)
\(828\) 1.49483e135 0.306324
\(829\) −6.83946e134 −0.132506 −0.0662531 0.997803i \(-0.521104\pi\)
−0.0662531 + 0.997803i \(0.521104\pi\)
\(830\) −3.16469e135 −0.579696
\(831\) 5.05626e135 0.875754
\(832\) 1.04899e136 1.71805
\(833\) −1.39151e134 −0.0215523
\(834\) −9.80579e135 −1.43635
\(835\) 1.17427e135 0.162685
\(836\) −1.11094e136 −1.45578
\(837\) 1.47395e136 1.82704
\(838\) −1.43067e135 −0.167762
\(839\) −7.63481e135 −0.846968 −0.423484 0.905904i \(-0.639193\pi\)
−0.423484 + 0.905904i \(0.639193\pi\)
\(840\) 7.39751e135 0.776423
\(841\) −1.00327e136 −0.996328
\(842\) 1.61650e136 1.51902
\(843\) 1.67057e136 1.48554
\(844\) −8.10387e135 −0.681975
\(845\) −2.22422e135 −0.177150
\(846\) 2.30630e134 0.0173857
\(847\) −2.03590e136 −1.45271
\(848\) −6.67682e135 −0.450986
\(849\) 1.19451e136 0.763804
\(850\) 5.89814e135 0.357055
\(851\) −3.46652e136 −1.98687
\(852\) 3.72355e136 2.02077
\(853\) 2.56337e136 1.31729 0.658644 0.752455i \(-0.271130\pi\)
0.658644 + 0.752455i \(0.271130\pi\)
\(854\) 9.17333e135 0.446412
\(855\) −2.10870e135 −0.0971833
\(856\) −5.13565e135 −0.224164
\(857\) 3.67285e136 1.51843 0.759215 0.650840i \(-0.225583\pi\)
0.759215 + 0.650840i \(0.225583\pi\)
\(858\) −6.30580e136 −2.46934
\(859\) −3.23071e136 −1.19844 −0.599220 0.800584i \(-0.704523\pi\)
−0.599220 + 0.800584i \(0.704523\pi\)
\(860\) −5.16667e136 −1.81565
\(861\) −2.80924e136 −0.935281
\(862\) −2.40962e136 −0.760081
\(863\) 2.97873e136 0.890284 0.445142 0.895460i \(-0.353153\pi\)
0.445142 + 0.895460i \(0.353153\pi\)
\(864\) 4.65099e136 1.31722
\(865\) 4.88059e136 1.30986
\(866\) −4.81869e136 −1.22560
\(867\) −2.98250e136 −0.718939
\(868\) 1.07464e137 2.45525
\(869\) −1.74390e136 −0.377661
\(870\) −5.24393e135 −0.107649
\(871\) 5.57281e136 1.08450
\(872\) −2.70549e136 −0.499149
\(873\) −6.76812e135 −0.118387
\(874\) 1.01532e137 1.68392
\(875\) −3.96463e136 −0.623488
\(876\) −4.80920e136 −0.717187
\(877\) 2.20703e136 0.312124 0.156062 0.987747i \(-0.450120\pi\)
0.156062 + 0.987747i \(0.450120\pi\)
\(878\) 1.50674e137 2.02089
\(879\) −5.08092e136 −0.646338
\(880\) 5.59968e136 0.675645
\(881\) −1.02270e137 −1.17049 −0.585243 0.810858i \(-0.699001\pi\)
−0.585243 + 0.810858i \(0.699001\pi\)
\(882\) 8.10131e134 0.00879561
\(883\) −7.00629e136 −0.721632 −0.360816 0.932637i \(-0.617502\pi\)
−0.360816 + 0.932637i \(0.617502\pi\)
\(884\) −7.62326e136 −0.744922
\(885\) 1.22128e136 0.113228
\(886\) −3.22650e137 −2.83833
\(887\) 6.73980e136 0.562599 0.281299 0.959620i \(-0.409235\pi\)
0.281299 + 0.959620i \(0.409235\pi\)
\(888\) 9.72481e136 0.770332
\(889\) 1.46547e137 1.10165
\(890\) −1.99516e137 −1.42345
\(891\) −1.99986e137 −1.35421
\(892\) 7.74269e136 0.497652
\(893\) 9.26369e135 0.0565185
\(894\) 2.25158e137 1.30405
\(895\) −1.97912e137 −1.08818
\(896\) 2.35755e137 1.23066
\(897\) 3.40810e137 1.68913
\(898\) −1.70468e137 −0.802218
\(899\) −2.35394e136 −0.105189
\(900\) −2.03068e136 −0.0861715
\(901\) 1.52509e137 0.614602
\(902\) 6.59522e137 2.52421
\(903\) −2.59765e137 −0.944278
\(904\) 2.37831e137 0.821177
\(905\) −8.28955e136 −0.271877
\(906\) −3.38019e137 −1.05312
\(907\) −3.04304e137 −0.900677 −0.450338 0.892858i \(-0.648697\pi\)
−0.450338 + 0.892858i \(0.648697\pi\)
\(908\) −5.13365e137 −1.44356
\(909\) −2.13530e136 −0.0570478
\(910\) −7.82917e137 −1.98743
\(911\) 6.22207e137 1.50083 0.750413 0.660969i \(-0.229855\pi\)
0.750413 + 0.660969i \(0.229855\pi\)
\(912\) 9.18393e136 0.210508
\(913\) 2.20901e137 0.481179
\(914\) 1.16531e138 2.41237
\(915\) 1.68531e137 0.331589
\(916\) −1.47051e138 −2.74998
\(917\) 6.92915e137 1.23170
\(918\) −4.68548e137 −0.791716
\(919\) 5.38667e137 0.865265 0.432632 0.901570i \(-0.357585\pi\)
0.432632 + 0.901570i \(0.357585\pi\)
\(920\) 9.38638e137 1.43339
\(921\) 3.50409e137 0.508748
\(922\) −7.88666e137 −1.08869
\(923\) −1.21772e138 −1.59834
\(924\) −1.67106e138 −2.08566
\(925\) 4.70915e137 0.558923
\(926\) −1.09171e138 −1.23225
\(927\) 8.01830e136 0.0860746
\(928\) −7.42778e136 −0.0758365
\(929\) −9.52004e137 −0.924503 −0.462251 0.886749i \(-0.652958\pi\)
−0.462251 + 0.886749i \(0.652958\pi\)
\(930\) 3.33856e138 3.08392
\(931\) 3.25405e136 0.0285933
\(932\) 1.19905e138 1.00230
\(933\) 7.74768e136 0.0616134
\(934\) 3.80019e137 0.287525
\(935\) −1.27906e138 −0.920767
\(936\) 1.37142e137 0.0939385
\(937\) 1.63655e138 1.06669 0.533344 0.845898i \(-0.320935\pi\)
0.533344 + 0.845898i \(0.320935\pi\)
\(938\) 2.49729e138 1.54895
\(939\) −5.49966e137 −0.324628
\(940\) 2.77151e137 0.155694
\(941\) 3.22780e138 1.72579 0.862896 0.505381i \(-0.168648\pi\)
0.862896 + 0.505381i \(0.168648\pi\)
\(942\) −3.71351e138 −1.88981
\(943\) −3.56452e138 −1.72666
\(944\) 7.62954e136 0.0351804
\(945\) −2.84568e138 −1.24913
\(946\) 6.09847e138 2.54849
\(947\) −3.71804e138 −1.47924 −0.739622 0.673022i \(-0.764996\pi\)
−0.739622 + 0.673022i \(0.764996\pi\)
\(948\) −8.55698e137 −0.324140
\(949\) 1.57277e138 0.567264
\(950\) −1.37928e138 −0.473702
\(951\) −3.79344e138 −1.24062
\(952\) −1.05559e138 −0.328759
\(953\) 1.89947e138 0.563394 0.281697 0.959503i \(-0.409103\pi\)
0.281697 + 0.959503i \(0.409103\pi\)
\(954\) −8.87902e137 −0.250822
\(955\) −4.96169e138 −1.33498
\(956\) −9.10151e138 −2.33250
\(957\) 3.66036e137 0.0893549
\(958\) 1.15547e139 2.68697
\(959\) 5.05143e138 1.11905
\(960\) 8.63611e138 1.82266
\(961\) 1.00132e139 2.01342
\(962\) −1.02923e139 −1.97184
\(963\) 2.20206e137 0.0401982
\(964\) −1.22840e139 −2.13676
\(965\) 7.98410e138 1.32345
\(966\) 1.52724e139 2.41252
\(967\) −4.15481e138 −0.625489 −0.312745 0.949837i \(-0.601248\pi\)
−0.312745 + 0.949837i \(0.601248\pi\)
\(968\) 7.24698e138 1.03981
\(969\) −2.09776e138 −0.286880
\(970\) −1.37535e139 −1.79278
\(971\) −9.01984e138 −1.12074 −0.560369 0.828243i \(-0.689341\pi\)
−0.560369 + 0.828243i \(0.689341\pi\)
\(972\) 3.04653e138 0.360847
\(973\) 8.49815e138 0.959571
\(974\) −1.37095e139 −1.47581
\(975\) −4.62979e138 −0.475167
\(976\) 1.05284e138 0.103026
\(977\) 8.65113e138 0.807189 0.403595 0.914938i \(-0.367761\pi\)
0.403595 + 0.914938i \(0.367761\pi\)
\(978\) −6.39304e135 −0.000568788 0
\(979\) 1.39266e139 1.18154
\(980\) 9.73548e137 0.0787671
\(981\) 1.16006e138 0.0895098
\(982\) −2.61715e139 −1.92595
\(983\) −2.72893e139 −1.91538 −0.957689 0.287805i \(-0.907074\pi\)
−0.957689 + 0.287805i \(0.907074\pi\)
\(984\) 9.99974e138 0.669447
\(985\) 1.14139e139 0.728872
\(986\) 7.48285e137 0.0455817
\(987\) 1.39343e138 0.0809727
\(988\) 1.78270e139 0.988281
\(989\) −3.29604e139 −1.74327
\(990\) 7.44661e138 0.375770
\(991\) 2.57952e139 1.24198 0.620989 0.783819i \(-0.286731\pi\)
0.620989 + 0.783819i \(0.286731\pi\)
\(992\) 4.72892e139 2.17255
\(993\) −4.26946e138 −0.187168
\(994\) −5.45686e139 −2.28284
\(995\) 8.36566e138 0.333985
\(996\) 1.08392e139 0.412988
\(997\) −1.61311e139 −0.586595 −0.293298 0.956021i \(-0.594753\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(998\) −2.89619e139 −1.00521
\(999\) −3.74094e139 −1.23933
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.1.6 7
3.2 odd 2 9.94.a.b.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.94.a.a.1.6 7 1.1 even 1 trivial
9.94.a.b.1.2 7 3.2 odd 2