Properties

Label 1.54.a.a.1.2
Level $1$
Weight $54$
Character 1.1
Self dual yes
Analytic conductor $17.790$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 54 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.7903107608\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 2315873743412 x^{2} - 421178019174503472 x + 612167648493870378955584\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-708531.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} +O(q^{10})\) \(q-8.51381e7 q^{2} +6.54009e12 q^{3} -1.75871e15 q^{4} +2.26338e17 q^{5} -5.56810e20 q^{6} -3.24923e22 q^{7} +9.16589e23 q^{8} +2.33895e25 q^{9} -1.92700e25 q^{10} +4.70740e27 q^{11} -1.15021e28 q^{12} -5.49891e29 q^{13} +2.76633e30 q^{14} +1.48027e30 q^{15} -6.21955e31 q^{16} -1.83884e32 q^{17} -1.99134e33 q^{18} -8.16294e33 q^{19} -3.98062e32 q^{20} -2.12502e35 q^{21} -4.00779e35 q^{22} +8.36591e35 q^{23} +5.99457e36 q^{24} -1.10510e37 q^{25} +4.68167e37 q^{26} +2.62013e37 q^{27} +5.71444e37 q^{28} -7.80382e38 q^{29} -1.26027e38 q^{30} -3.24461e39 q^{31} -2.96069e39 q^{32} +3.07868e40 q^{33} +1.56555e40 q^{34} -7.35423e39 q^{35} -4.11353e40 q^{36} -2.65824e40 q^{37} +6.94977e41 q^{38} -3.59634e42 q^{39} +2.07459e41 q^{40} +5.60775e41 q^{41} +1.80920e43 q^{42} +2.91200e42 q^{43} -8.27894e42 q^{44} +5.29393e42 q^{45} -7.12258e43 q^{46} -3.43769e43 q^{47} -4.06764e44 q^{48} +4.38874e44 q^{49} +9.40861e44 q^{50} -1.20262e45 q^{51} +9.67099e44 q^{52} +5.37279e45 q^{53} -2.23073e45 q^{54} +1.06546e45 q^{55} -2.97820e46 q^{56} -5.33864e46 q^{57} +6.64402e46 q^{58} +1.17524e47 q^{59} -2.60336e45 q^{60} -6.10529e46 q^{61} +2.76240e47 q^{62} -7.59978e47 q^{63} +8.12275e47 q^{64} -1.24461e47 q^{65} -2.62113e48 q^{66} +5.08562e47 q^{67} +3.23399e47 q^{68} +5.47138e48 q^{69} +6.26125e47 q^{70} -2.80926e48 q^{71} +2.14386e49 q^{72} -1.95202e49 q^{73} +2.26317e48 q^{74} -7.22745e49 q^{75} +1.43562e49 q^{76} -1.52954e50 q^{77} +3.06185e50 q^{78} +1.95888e50 q^{79} -1.40772e49 q^{80} -2.82006e50 q^{81} -4.77433e49 q^{82} -9.78793e49 q^{83} +3.73730e50 q^{84} -4.16200e49 q^{85} -2.47922e50 q^{86} -5.10376e51 q^{87} +4.31475e51 q^{88} +4.98452e50 q^{89} -4.50715e50 q^{90} +1.78672e52 q^{91} -1.47132e51 q^{92} -2.12201e52 q^{93} +2.92678e51 q^{94} -1.84758e51 q^{95} -1.93632e52 q^{96} -1.99451e52 q^{97} -3.73649e52 q^{98} +1.10104e53 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + O(q^{10}) \) \( 4q - 68476320q^{2} - 1048411007280q^{3} + 7829639419798528q^{4} - 4563895793294313000q^{5} + \)\(36\!\cdots\!28\)\(q^{6} - \)\(22\!\cdots\!00\)\(q^{7} + \)\(13\!\cdots\!40\)\(q^{8} + \)\(11\!\cdots\!12\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(24\!\cdots\!28\)\(q^{11} - \)\(36\!\cdots\!40\)\(q^{12} + \)\(38\!\cdots\!40\)\(q^{13} - \)\(23\!\cdots\!24\)\(q^{14} + \)\(10\!\cdots\!00\)\(q^{15} - \)\(15\!\cdots\!36\)\(q^{16} - \)\(86\!\cdots\!60\)\(q^{17} - \)\(67\!\cdots\!80\)\(q^{18} - \)\(25\!\cdots\!60\)\(q^{19} - \)\(13\!\cdots\!00\)\(q^{20} - \)\(45\!\cdots\!32\)\(q^{21} - \)\(93\!\cdots\!40\)\(q^{22} + \)\(69\!\cdots\!60\)\(q^{23} + \)\(80\!\cdots\!20\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} + \)\(88\!\cdots\!88\)\(q^{26} + \)\(85\!\cdots\!40\)\(q^{27} - \)\(56\!\cdots\!60\)\(q^{28} - \)\(14\!\cdots\!40\)\(q^{29} - \)\(57\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!32\)\(q^{31} + \)\(34\!\cdots\!80\)\(q^{32} + \)\(26\!\cdots\!40\)\(q^{33} + \)\(14\!\cdots\!36\)\(q^{34} + \)\(61\!\cdots\!00\)\(q^{35} + \)\(74\!\cdots\!84\)\(q^{36} - \)\(28\!\cdots\!80\)\(q^{37} - \)\(21\!\cdots\!40\)\(q^{38} - \)\(36\!\cdots\!16\)\(q^{39} - \)\(53\!\cdots\!00\)\(q^{40} + \)\(81\!\cdots\!88\)\(q^{41} + \)\(34\!\cdots\!40\)\(q^{42} + \)\(45\!\cdots\!00\)\(q^{43} + \)\(36\!\cdots\!96\)\(q^{44} - \)\(52\!\cdots\!00\)\(q^{45} - \)\(28\!\cdots\!52\)\(q^{46} - \)\(45\!\cdots\!40\)\(q^{47} - \)\(30\!\cdots\!40\)\(q^{48} + \)\(61\!\cdots\!28\)\(q^{49} + \)\(52\!\cdots\!00\)\(q^{50} + \)\(48\!\cdots\!48\)\(q^{51} + \)\(64\!\cdots\!00\)\(q^{52} + \)\(38\!\cdots\!20\)\(q^{53} - \)\(90\!\cdots\!60\)\(q^{54} - \)\(25\!\cdots\!00\)\(q^{55} - \)\(41\!\cdots\!60\)\(q^{56} - \)\(78\!\cdots\!20\)\(q^{57} + \)\(23\!\cdots\!40\)\(q^{58} + \)\(16\!\cdots\!20\)\(q^{59} + \)\(40\!\cdots\!00\)\(q^{60} + \)\(65\!\cdots\!28\)\(q^{61} + \)\(39\!\cdots\!60\)\(q^{62} - \)\(30\!\cdots\!20\)\(q^{63} - \)\(10\!\cdots\!32\)\(q^{64} - \)\(34\!\cdots\!00\)\(q^{65} - \)\(65\!\cdots\!04\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} + \)\(28\!\cdots\!20\)\(q^{68} + \)\(77\!\cdots\!64\)\(q^{69} + \)\(33\!\cdots\!00\)\(q^{70} + \)\(35\!\cdots\!48\)\(q^{71} + \)\(26\!\cdots\!20\)\(q^{72} - \)\(70\!\cdots\!40\)\(q^{73} - \)\(24\!\cdots\!44\)\(q^{74} - \)\(21\!\cdots\!00\)\(q^{75} + \)\(45\!\cdots\!80\)\(q^{76} - \)\(16\!\cdots\!00\)\(q^{77} + \)\(51\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!40\)\(q^{79} + \)\(11\!\cdots\!00\)\(q^{80} - \)\(49\!\cdots\!56\)\(q^{81} + \)\(15\!\cdots\!60\)\(q^{82} - \)\(26\!\cdots\!20\)\(q^{83} - \)\(76\!\cdots\!24\)\(q^{84} - \)\(23\!\cdots\!00\)\(q^{85} - \)\(77\!\cdots\!32\)\(q^{86} - \)\(45\!\cdots\!80\)\(q^{87} + \)\(56\!\cdots\!80\)\(q^{88} - \)\(37\!\cdots\!20\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(12\!\cdots\!28\)\(q^{91} + \)\(89\!\cdots\!40\)\(q^{92} - \)\(99\!\cdots\!60\)\(q^{93} - \)\(37\!\cdots\!84\)\(q^{94} - \)\(17\!\cdots\!00\)\(q^{95} - \)\(11\!\cdots\!92\)\(q^{96} + \)\(10\!\cdots\!60\)\(q^{97} - \)\(88\!\cdots\!40\)\(q^{98} + \)\(20\!\cdots\!84\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.51381e7 −0.897075 −0.448538 0.893764i \(-0.648055\pi\)
−0.448538 + 0.893764i \(0.648055\pi\)
\(3\) 6.54009e12 1.48549 0.742746 0.669573i \(-0.233523\pi\)
0.742746 + 0.669573i \(0.233523\pi\)
\(4\) −1.75871e15 −0.195256
\(5\) 2.26338e17 0.0679285 0.0339643 0.999423i \(-0.489187\pi\)
0.0339643 + 0.999423i \(0.489187\pi\)
\(6\) −5.56810e20 −1.33260
\(7\) −3.24923e22 −1.30822 −0.654112 0.756398i \(-0.726957\pi\)
−0.654112 + 0.756398i \(0.726957\pi\)
\(8\) 9.16589e23 1.07223
\(9\) 2.33895e25 1.20669
\(10\) −1.92700e25 −0.0609370
\(11\) 4.70740e27 1.19090 0.595449 0.803393i \(-0.296974\pi\)
0.595449 + 0.803393i \(0.296974\pi\)
\(12\) −1.15021e28 −0.290051
\(13\) −5.49891e29 −1.66256 −0.831282 0.555852i \(-0.812392\pi\)
−0.831282 + 0.555852i \(0.812392\pi\)
\(14\) 2.76633e30 1.17357
\(15\) 1.48027e30 0.100907
\(16\) −6.21955e31 −0.766619
\(17\) −1.83884e32 −0.454620 −0.227310 0.973823i \(-0.572993\pi\)
−0.227310 + 0.973823i \(0.572993\pi\)
\(18\) −1.99134e33 −1.08249
\(19\) −8.16294e33 −1.05895 −0.529476 0.848325i \(-0.677611\pi\)
−0.529476 + 0.848325i \(0.677611\pi\)
\(20\) −3.98062e32 −0.0132634
\(21\) −2.12502e35 −1.94336
\(22\) −4.00779e35 −1.06833
\(23\) 8.36591e35 0.686635 0.343317 0.939219i \(-0.388449\pi\)
0.343317 + 0.939219i \(0.388449\pi\)
\(24\) 5.99457e36 1.59280
\(25\) −1.10510e37 −0.995386
\(26\) 4.68167e37 1.49144
\(27\) 2.62013e37 0.307032
\(28\) 5.71444e37 0.255438
\(29\) −7.80382e38 −1.37645 −0.688224 0.725498i \(-0.741610\pi\)
−0.688224 + 0.725498i \(0.741610\pi\)
\(30\) −1.26027e38 −0.0905214
\(31\) −3.24461e39 −0.977413 −0.488707 0.872448i \(-0.662531\pi\)
−0.488707 + 0.872448i \(0.662531\pi\)
\(32\) −2.96069e39 −0.384519
\(33\) 3.07868e40 1.76907
\(34\) 1.56555e40 0.407828
\(35\) −7.35423e39 −0.0888657
\(36\) −4.11353e40 −0.235613
\(37\) −2.65824e40 −0.0736628 −0.0368314 0.999321i \(-0.511726\pi\)
−0.0368314 + 0.999321i \(0.511726\pi\)
\(38\) 6.94977e41 0.949960
\(39\) −3.59634e42 −2.46972
\(40\) 2.07459e41 0.0728353
\(41\) 5.60775e41 0.102333 0.0511666 0.998690i \(-0.483706\pi\)
0.0511666 + 0.998690i \(0.483706\pi\)
\(42\) 1.80920e43 1.74334
\(43\) 2.91200e42 0.150410 0.0752050 0.997168i \(-0.476039\pi\)
0.0752050 + 0.997168i \(0.476039\pi\)
\(44\) −8.27894e42 −0.232530
\(45\) 5.29393e42 0.0819684
\(46\) −7.12258e43 −0.615963
\(47\) −3.43769e43 −0.168141 −0.0840705 0.996460i \(-0.526792\pi\)
−0.0840705 + 0.996460i \(0.526792\pi\)
\(48\) −4.06764e44 −1.13881
\(49\) 4.38874e44 0.711448
\(50\) 9.40861e44 0.892936
\(51\) −1.20262e45 −0.675334
\(52\) 9.67099e44 0.324625
\(53\) 5.37279e45 1.08865 0.544327 0.838873i \(-0.316785\pi\)
0.544327 + 0.838873i \(0.316785\pi\)
\(54\) −2.23073e45 −0.275430
\(55\) 1.06546e45 0.0808959
\(56\) −2.97820e46 −1.40272
\(57\) −5.33864e46 −1.57307
\(58\) 6.64402e46 1.23478
\(59\) 1.17524e47 1.38851 0.694256 0.719728i \(-0.255733\pi\)
0.694256 + 0.719728i \(0.255733\pi\)
\(60\) −2.60336e45 −0.0197027
\(61\) −6.10529e46 −0.298171 −0.149086 0.988824i \(-0.547633\pi\)
−0.149086 + 0.988824i \(0.547633\pi\)
\(62\) 2.76240e47 0.876813
\(63\) −7.59978e47 −1.57862
\(64\) 8.12275e47 1.11156
\(65\) −1.24461e47 −0.112935
\(66\) −2.62113e48 −1.58699
\(67\) 5.08562e47 0.206710 0.103355 0.994645i \(-0.467042\pi\)
0.103355 + 0.994645i \(0.467042\pi\)
\(68\) 3.23399e47 0.0887671
\(69\) 5.47138e48 1.01999
\(70\) 6.26125e47 0.0797192
\(71\) −2.80926e48 −0.245610 −0.122805 0.992431i \(-0.539189\pi\)
−0.122805 + 0.992431i \(0.539189\pi\)
\(72\) 2.14386e49 1.29385
\(73\) −1.95202e49 −0.817389 −0.408695 0.912671i \(-0.634016\pi\)
−0.408695 + 0.912671i \(0.634016\pi\)
\(74\) 2.26317e48 0.0660811
\(75\) −7.22745e49 −1.47864
\(76\) 1.43562e49 0.206767
\(77\) −1.52954e50 −1.55796
\(78\) 3.06185e50 2.21553
\(79\) 1.95888e50 1.01132 0.505662 0.862732i \(-0.331248\pi\)
0.505662 + 0.862732i \(0.331248\pi\)
\(80\) −1.40772e49 −0.0520753
\(81\) −2.82006e50 −0.750594
\(82\) −4.77433e49 −0.0918005
\(83\) −9.78793e49 −0.136496 −0.0682482 0.997668i \(-0.521741\pi\)
−0.0682482 + 0.997668i \(0.521741\pi\)
\(84\) 3.73730e50 0.379452
\(85\) −4.16200e49 −0.0308816
\(86\) −2.47922e50 −0.134929
\(87\) −5.10376e51 −2.04470
\(88\) 4.31475e51 1.27692
\(89\) 4.98452e50 0.109342 0.0546712 0.998504i \(-0.482589\pi\)
0.0546712 + 0.998504i \(0.482589\pi\)
\(90\) −4.50715e50 −0.0735318
\(91\) 1.78672e52 2.17500
\(92\) −1.47132e51 −0.134069
\(93\) −2.12201e52 −1.45194
\(94\) 2.92678e51 0.150835
\(95\) −1.84758e51 −0.0719330
\(96\) −1.93632e52 −0.571200
\(97\) −1.99451e52 −0.447079 −0.223540 0.974695i \(-0.571761\pi\)
−0.223540 + 0.974695i \(0.571761\pi\)
\(98\) −3.73649e52 −0.638223
\(99\) 1.10104e53 1.43704
\(100\) 1.94355e52 0.194355
\(101\) 1.70262e52 0.130798 0.0653990 0.997859i \(-0.479168\pi\)
0.0653990 + 0.997859i \(0.479168\pi\)
\(102\) 1.02389e53 0.605825
\(103\) 1.87090e53 0.854799 0.427400 0.904063i \(-0.359430\pi\)
0.427400 + 0.904063i \(0.359430\pi\)
\(104\) −5.04024e53 −1.78266
\(105\) −4.80973e52 −0.132009
\(106\) −4.57429e53 −0.976604
\(107\) 1.10378e54 1.83743 0.918716 0.394918i \(-0.129227\pi\)
0.918716 + 0.394918i \(0.129227\pi\)
\(108\) −4.60804e52 −0.0599497
\(109\) −1.44235e54 −1.46984 −0.734919 0.678155i \(-0.762780\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(110\) −9.07114e52 −0.0725697
\(111\) −1.73851e53 −0.109426
\(112\) 2.02087e54 1.00291
\(113\) 1.79503e53 0.0703869 0.0351935 0.999381i \(-0.488795\pi\)
0.0351935 + 0.999381i \(0.488795\pi\)
\(114\) 4.54521e54 1.41116
\(115\) 1.89352e53 0.0466421
\(116\) 1.37246e54 0.268760
\(117\) −1.28617e55 −2.00619
\(118\) −1.00058e55 −1.24560
\(119\) 5.97481e54 0.594744
\(120\) 1.35680e54 0.108196
\(121\) 6.53486e54 0.418238
\(122\) 5.19793e54 0.267482
\(123\) 3.66752e54 0.152015
\(124\) 5.70633e54 0.190846
\(125\) −5.01411e54 −0.135544
\(126\) 6.47031e55 1.41614
\(127\) −4.95049e55 −0.878719 −0.439359 0.898311i \(-0.644794\pi\)
−0.439359 + 0.898311i \(0.644794\pi\)
\(128\) −4.24880e55 −0.612636
\(129\) 1.90447e55 0.223433
\(130\) 1.05964e55 0.101312
\(131\) −1.71039e56 −1.33477 −0.667386 0.744712i \(-0.732587\pi\)
−0.667386 + 0.744712i \(0.732587\pi\)
\(132\) −5.41450e55 −0.345421
\(133\) 2.65233e56 1.38535
\(134\) −4.32979e55 −0.185434
\(135\) 5.93034e54 0.0208562
\(136\) −1.68546e56 −0.487459
\(137\) 4.96948e56 1.18363 0.591815 0.806074i \(-0.298412\pi\)
0.591815 + 0.806074i \(0.298412\pi\)
\(138\) −4.65823e56 −0.915008
\(139\) 9.49018e56 1.53951 0.769755 0.638340i \(-0.220379\pi\)
0.769755 + 0.638340i \(0.220379\pi\)
\(140\) 1.29339e55 0.0173515
\(141\) −2.24828e56 −0.249772
\(142\) 2.39175e56 0.220331
\(143\) −2.58856e57 −1.97994
\(144\) −1.45472e57 −0.925069
\(145\) −1.76630e56 −0.0935001
\(146\) 1.66191e57 0.733260
\(147\) 2.87027e57 1.05685
\(148\) 4.67507e55 0.0143831
\(149\) 3.22647e57 0.830407 0.415204 0.909728i \(-0.363710\pi\)
0.415204 + 0.909728i \(0.363710\pi\)
\(150\) 6.15331e57 1.32645
\(151\) −7.49843e57 −1.35544 −0.677721 0.735319i \(-0.737032\pi\)
−0.677721 + 0.735319i \(0.737032\pi\)
\(152\) −7.48206e57 −1.13545
\(153\) −4.30096e57 −0.548583
\(154\) 1.30222e58 1.39761
\(155\) −7.34379e56 −0.0663942
\(156\) 6.32491e57 0.482228
\(157\) −2.71453e58 −1.74725 −0.873624 0.486602i \(-0.838236\pi\)
−0.873624 + 0.486602i \(0.838236\pi\)
\(158\) −1.66775e58 −0.907233
\(159\) 3.51385e58 1.61719
\(160\) −6.70116e56 −0.0261198
\(161\) −2.71827e58 −0.898272
\(162\) 2.40094e58 0.673339
\(163\) 5.10046e58 1.21517 0.607586 0.794254i \(-0.292138\pi\)
0.607586 + 0.794254i \(0.292138\pi\)
\(164\) −9.86239e56 −0.0199811
\(165\) 6.96821e57 0.120170
\(166\) 8.33325e57 0.122448
\(167\) −1.89473e58 −0.237444 −0.118722 0.992928i \(-0.537880\pi\)
−0.118722 + 0.992928i \(0.537880\pi\)
\(168\) −1.94777e59 −2.08373
\(169\) 1.92986e59 1.76412
\(170\) 3.54344e57 0.0277031
\(171\) −1.90927e59 −1.27782
\(172\) −5.12135e57 −0.0293684
\(173\) −3.74302e59 −1.84078 −0.920388 0.391006i \(-0.872127\pi\)
−0.920388 + 0.391006i \(0.872127\pi\)
\(174\) 4.34525e59 1.83425
\(175\) 3.59072e59 1.30219
\(176\) −2.92779e59 −0.912965
\(177\) 7.68620e59 2.06262
\(178\) −4.24373e58 −0.0980883
\(179\) −3.52065e59 −0.701483 −0.350741 0.936472i \(-0.614070\pi\)
−0.350741 + 0.936472i \(0.614070\pi\)
\(180\) −9.31048e57 −0.0160048
\(181\) 3.15641e58 0.0468501 0.0234251 0.999726i \(-0.492543\pi\)
0.0234251 + 0.999726i \(0.492543\pi\)
\(182\) −1.52118e60 −1.95114
\(183\) −3.99292e59 −0.442931
\(184\) 7.66810e59 0.736233
\(185\) −6.01660e57 −0.00500380
\(186\) 1.80664e60 1.30250
\(187\) −8.65616e59 −0.541406
\(188\) 6.04590e58 0.0328305
\(189\) −8.51339e59 −0.401666
\(190\) 1.57300e59 0.0645294
\(191\) −2.50150e60 −0.892927 −0.446464 0.894802i \(-0.647317\pi\)
−0.446464 + 0.894802i \(0.647317\pi\)
\(192\) 5.31235e60 1.65122
\(193\) 1.82350e60 0.493899 0.246949 0.969028i \(-0.420572\pi\)
0.246949 + 0.969028i \(0.420572\pi\)
\(194\) 1.69808e60 0.401064
\(195\) −8.13987e59 −0.167765
\(196\) −7.71851e59 −0.138914
\(197\) −4.11846e60 −0.647709 −0.323855 0.946107i \(-0.604979\pi\)
−0.323855 + 0.946107i \(0.604979\pi\)
\(198\) −9.37401e60 −1.28913
\(199\) 2.79044e60 0.335789 0.167895 0.985805i \(-0.446303\pi\)
0.167895 + 0.985805i \(0.446303\pi\)
\(200\) −1.01292e61 −1.06729
\(201\) 3.32604e60 0.307066
\(202\) −1.44958e60 −0.117336
\(203\) 2.53564e61 1.80070
\(204\) 2.11506e60 0.131863
\(205\) 1.26925e59 0.00695133
\(206\) −1.59285e61 −0.766819
\(207\) 1.95675e61 0.828553
\(208\) 3.42008e61 1.27455
\(209\) −3.84262e61 −1.26110
\(210\) 4.09491e60 0.118422
\(211\) −9.61153e60 −0.245080 −0.122540 0.992464i \(-0.539104\pi\)
−0.122540 + 0.992464i \(0.539104\pi\)
\(212\) −9.44918e60 −0.212566
\(213\) −1.83728e61 −0.364852
\(214\) −9.39735e61 −1.64832
\(215\) 6.59095e59 0.0102171
\(216\) 2.40158e61 0.329210
\(217\) 1.05425e62 1.27867
\(218\) 1.22799e62 1.31856
\(219\) −1.27664e62 −1.21423
\(220\) −1.87384e60 −0.0157954
\(221\) 1.01116e62 0.755834
\(222\) 1.48014e61 0.0981629
\(223\) −8.79461e61 −0.517771 −0.258885 0.965908i \(-0.583355\pi\)
−0.258885 + 0.965908i \(0.583355\pi\)
\(224\) 9.61994e61 0.503037
\(225\) −2.58477e62 −1.20112
\(226\) −1.52825e61 −0.0631424
\(227\) 3.14689e62 1.15664 0.578318 0.815811i \(-0.303709\pi\)
0.578318 + 0.815811i \(0.303709\pi\)
\(228\) 9.38911e61 0.307150
\(229\) −4.50545e61 −0.131250 −0.0656248 0.997844i \(-0.520904\pi\)
−0.0656248 + 0.997844i \(0.520904\pi\)
\(230\) −1.61211e61 −0.0418414
\(231\) −1.00033e63 −2.31434
\(232\) −7.15289e62 −1.47588
\(233\) 6.26152e62 1.15278 0.576392 0.817173i \(-0.304460\pi\)
0.576392 + 0.817173i \(0.304460\pi\)
\(234\) 1.09502e63 1.79971
\(235\) −7.78080e60 −0.0114216
\(236\) −2.06691e62 −0.271115
\(237\) 1.28113e63 1.50231
\(238\) −5.08684e62 −0.533530
\(239\) 1.59379e63 1.49585 0.747923 0.663785i \(-0.231051\pi\)
0.747923 + 0.663785i \(0.231051\pi\)
\(240\) −9.20662e61 −0.0773574
\(241\) −1.86546e63 −1.40390 −0.701948 0.712228i \(-0.747686\pi\)
−0.701948 + 0.712228i \(0.747686\pi\)
\(242\) −5.56365e62 −0.375191
\(243\) −2.35221e63 −1.42203
\(244\) 1.07374e62 0.0582197
\(245\) 9.93337e61 0.0483276
\(246\) −3.12245e62 −0.136369
\(247\) 4.48873e63 1.76058
\(248\) −2.97398e63 −1.04802
\(249\) −6.40139e62 −0.202764
\(250\) 4.26892e62 0.121593
\(251\) −1.23471e62 −0.0316382 −0.0158191 0.999875i \(-0.505036\pi\)
−0.0158191 + 0.999875i \(0.505036\pi\)
\(252\) 1.33658e63 0.308234
\(253\) 3.93817e63 0.817712
\(254\) 4.21475e63 0.788277
\(255\) −2.72198e62 −0.0458744
\(256\) −3.69897e63 −0.561982
\(257\) −2.57030e63 −0.352174 −0.176087 0.984375i \(-0.556344\pi\)
−0.176087 + 0.984375i \(0.556344\pi\)
\(258\) −1.62143e63 −0.200436
\(259\) 8.63722e62 0.0963674
\(260\) 2.18891e62 0.0220513
\(261\) −1.82527e64 −1.66094
\(262\) 1.45620e64 1.19739
\(263\) −1.92105e64 −1.42794 −0.713972 0.700174i \(-0.753106\pi\)
−0.713972 + 0.700174i \(0.753106\pi\)
\(264\) 2.82188e64 1.89686
\(265\) 1.21607e63 0.0739506
\(266\) −2.25814e64 −1.24276
\(267\) 3.25992e63 0.162427
\(268\) −8.94411e62 −0.0403613
\(269\) 1.72508e64 0.705301 0.352651 0.935755i \(-0.385280\pi\)
0.352651 + 0.935755i \(0.385280\pi\)
\(270\) −5.04898e62 −0.0187096
\(271\) −1.11722e64 −0.375365 −0.187682 0.982230i \(-0.560098\pi\)
−0.187682 + 0.982230i \(0.560098\pi\)
\(272\) 1.14368e64 0.348520
\(273\) 1.16853e65 3.23095
\(274\) −4.23092e64 −1.06180
\(275\) −5.20214e64 −1.18540
\(276\) −9.62256e63 −0.199159
\(277\) −1.05957e64 −0.199258 −0.0996291 0.995025i \(-0.531766\pi\)
−0.0996291 + 0.995025i \(0.531766\pi\)
\(278\) −8.07976e64 −1.38106
\(279\) −7.58899e64 −1.17943
\(280\) −6.74080e63 −0.0952848
\(281\) 5.57080e64 0.716473 0.358237 0.933631i \(-0.383378\pi\)
0.358237 + 0.933631i \(0.383378\pi\)
\(282\) 1.91414e64 0.224064
\(283\) 1.04527e65 1.11401 0.557003 0.830511i \(-0.311951\pi\)
0.557003 + 0.830511i \(0.311951\pi\)
\(284\) 4.94067e63 0.0479568
\(285\) −1.20834e64 −0.106856
\(286\) 2.20385e65 1.77616
\(287\) −1.82208e64 −0.133875
\(288\) −6.92490e64 −0.463994
\(289\) −1.29790e65 −0.793321
\(290\) 1.50379e64 0.0838766
\(291\) −1.30442e65 −0.664132
\(292\) 3.43304e64 0.159600
\(293\) 2.53583e65 1.07678 0.538392 0.842694i \(-0.319032\pi\)
0.538392 + 0.842694i \(0.319032\pi\)
\(294\) −2.44369e65 −0.948075
\(295\) 2.66002e64 0.0943196
\(296\) −2.43651e64 −0.0789838
\(297\) 1.23340e65 0.365643
\(298\) −2.74695e65 −0.744938
\(299\) −4.60034e65 −1.14157
\(300\) 1.27110e65 0.288713
\(301\) −9.46174e64 −0.196770
\(302\) 6.38402e65 1.21593
\(303\) 1.11353e65 0.194300
\(304\) 5.07699e65 0.811813
\(305\) −1.38186e64 −0.0202543
\(306\) 3.66176e65 0.492121
\(307\) −1.14760e66 −1.41457 −0.707284 0.706930i \(-0.750080\pi\)
−0.707284 + 0.706930i \(0.750080\pi\)
\(308\) 2.69001e65 0.304201
\(309\) 1.22358e66 1.26980
\(310\) 6.25236e64 0.0595606
\(311\) 3.98992e65 0.348991 0.174496 0.984658i \(-0.444171\pi\)
0.174496 + 0.984658i \(0.444171\pi\)
\(312\) −3.29636e66 −2.64812
\(313\) −1.04506e66 −0.771291 −0.385645 0.922647i \(-0.626021\pi\)
−0.385645 + 0.922647i \(0.626021\pi\)
\(314\) 2.31110e66 1.56741
\(315\) −1.72012e65 −0.107233
\(316\) −3.44510e65 −0.197467
\(317\) 1.24693e66 0.657312 0.328656 0.944450i \(-0.393404\pi\)
0.328656 + 0.944450i \(0.393404\pi\)
\(318\) −2.99163e66 −1.45074
\(319\) −3.67357e66 −1.63921
\(320\) 1.83849e65 0.0755067
\(321\) 7.21880e66 2.72949
\(322\) 2.31429e66 0.805817
\(323\) 1.50104e66 0.481420
\(324\) 4.95966e65 0.146558
\(325\) 6.07685e66 1.65489
\(326\) −4.34243e66 −1.09010
\(327\) −9.43312e66 −2.18343
\(328\) 5.14000e65 0.109725
\(329\) 1.11698e66 0.219966
\(330\) −5.93260e65 −0.107802
\(331\) −7.02324e66 −1.17787 −0.588933 0.808182i \(-0.700452\pi\)
−0.588933 + 0.808182i \(0.700452\pi\)
\(332\) 1.72141e65 0.0266517
\(333\) −6.21749e65 −0.0888879
\(334\) 1.61314e66 0.213005
\(335\) 1.15107e65 0.0140415
\(336\) 1.32167e67 1.48981
\(337\) 7.44919e66 0.776098 0.388049 0.921639i \(-0.373149\pi\)
0.388049 + 0.921639i \(0.373149\pi\)
\(338\) −1.64304e67 −1.58254
\(339\) 1.17396e66 0.104559
\(340\) 7.31974e64 0.00602982
\(341\) −1.52737e67 −1.16400
\(342\) 1.62552e67 1.14630
\(343\) 5.78362e66 0.377490
\(344\) 2.66910e66 0.161275
\(345\) 1.23838e66 0.0692864
\(346\) 3.18674e67 1.65131
\(347\) −1.68736e67 −0.809985 −0.404993 0.914320i \(-0.632726\pi\)
−0.404993 + 0.914320i \(0.632726\pi\)
\(348\) 8.97603e66 0.399240
\(349\) −1.94835e67 −0.803143 −0.401571 0.915828i \(-0.631536\pi\)
−0.401571 + 0.915828i \(0.631536\pi\)
\(350\) −3.05707e67 −1.16816
\(351\) −1.44079e67 −0.510459
\(352\) −1.39371e67 −0.457923
\(353\) 4.86893e67 1.48390 0.741948 0.670457i \(-0.233902\pi\)
0.741948 + 0.670457i \(0.233902\pi\)
\(354\) −6.54388e67 −1.85033
\(355\) −6.35842e65 −0.0166839
\(356\) −8.76632e65 −0.0213497
\(357\) 3.90758e67 0.883487
\(358\) 2.99741e67 0.629283
\(359\) 3.23986e67 0.631719 0.315860 0.948806i \(-0.397707\pi\)
0.315860 + 0.948806i \(0.397707\pi\)
\(360\) 4.85236e66 0.0878894
\(361\) 7.21254e66 0.121380
\(362\) −2.68730e66 −0.0420281
\(363\) 4.27385e67 0.621290
\(364\) −3.14232e67 −0.424682
\(365\) −4.41816e66 −0.0555240
\(366\) 3.39949e67 0.397343
\(367\) −4.09627e67 −0.445388 −0.222694 0.974888i \(-0.571485\pi\)
−0.222694 + 0.974888i \(0.571485\pi\)
\(368\) −5.20323e67 −0.526387
\(369\) 1.31162e67 0.123484
\(370\) 5.12242e65 0.00448879
\(371\) −1.74574e68 −1.42420
\(372\) 3.73199e67 0.283500
\(373\) −1.54943e68 −1.09619 −0.548097 0.836415i \(-0.684648\pi\)
−0.548097 + 0.836415i \(0.684648\pi\)
\(374\) 7.36969e67 0.485682
\(375\) −3.27927e67 −0.201349
\(376\) −3.15095e67 −0.180287
\(377\) 4.29125e68 2.28843
\(378\) 7.24814e67 0.360324
\(379\) 1.05294e68 0.488049 0.244025 0.969769i \(-0.421532\pi\)
0.244025 + 0.969769i \(0.421532\pi\)
\(380\) 3.24936e66 0.0140453
\(381\) −3.23767e68 −1.30533
\(382\) 2.12973e68 0.801023
\(383\) 8.24887e67 0.289486 0.144743 0.989469i \(-0.453764\pi\)
0.144743 + 0.989469i \(0.453764\pi\)
\(384\) −2.77875e68 −0.910065
\(385\) −3.46193e67 −0.105830
\(386\) −1.55250e68 −0.443064
\(387\) 6.81102e67 0.181498
\(388\) 3.50775e67 0.0872948
\(389\) 1.89075e68 0.439510 0.219755 0.975555i \(-0.429474\pi\)
0.219755 + 0.975555i \(0.429474\pi\)
\(390\) 6.93013e67 0.150498
\(391\) −1.53836e68 −0.312158
\(392\) 4.02267e68 0.762840
\(393\) −1.11861e69 −1.98279
\(394\) 3.50638e68 0.581044
\(395\) 4.43369e67 0.0686977
\(396\) −1.93640e68 −0.280591
\(397\) −1.41885e69 −1.92304 −0.961518 0.274743i \(-0.911407\pi\)
−0.961518 + 0.274743i \(0.911407\pi\)
\(398\) −2.37573e68 −0.301228
\(399\) 1.73464e69 2.05792
\(400\) 6.87323e68 0.763082
\(401\) 1.07913e69 1.12137 0.560686 0.828028i \(-0.310537\pi\)
0.560686 + 0.828028i \(0.310537\pi\)
\(402\) −2.83172e68 −0.275461
\(403\) 1.78419e69 1.62501
\(404\) −2.99441e67 −0.0255391
\(405\) −6.38286e67 −0.0509867
\(406\) −2.15879e69 −1.61537
\(407\) −1.25134e68 −0.0877249
\(408\) −1.10231e69 −0.724116
\(409\) −1.89009e69 −1.16363 −0.581814 0.813322i \(-0.697657\pi\)
−0.581814 + 0.813322i \(0.697657\pi\)
\(410\) −1.08061e67 −0.00623587
\(411\) 3.25008e69 1.75827
\(412\) −3.29037e68 −0.166905
\(413\) −3.81863e69 −1.81648
\(414\) −1.66594e69 −0.743274
\(415\) −2.21538e67 −0.00927200
\(416\) 1.62806e69 0.639288
\(417\) 6.20666e69 2.28693
\(418\) 3.27153e69 1.13131
\(419\) −5.52165e69 −1.79225 −0.896123 0.443807i \(-0.853628\pi\)
−0.896123 + 0.443807i \(0.853628\pi\)
\(420\) 8.45891e67 0.0257756
\(421\) −1.18435e69 −0.338847 −0.169424 0.985543i \(-0.554191\pi\)
−0.169424 + 0.985543i \(0.554191\pi\)
\(422\) 8.18307e68 0.219855
\(423\) −8.04059e68 −0.202894
\(424\) 4.92464e69 1.16729
\(425\) 2.03210e69 0.452522
\(426\) 1.56423e69 0.327300
\(427\) 1.98375e69 0.390075
\(428\) −1.94122e69 −0.358769
\(429\) −1.69294e70 −2.94119
\(430\) −5.61141e67 −0.00916554
\(431\) 2.27553e69 0.349490 0.174745 0.984614i \(-0.444090\pi\)
0.174745 + 0.984614i \(0.444090\pi\)
\(432\) −1.62960e69 −0.235376
\(433\) 1.18575e70 1.61088 0.805440 0.592677i \(-0.201929\pi\)
0.805440 + 0.592677i \(0.201929\pi\)
\(434\) −8.97567e69 −1.14707
\(435\) −1.15517e69 −0.138894
\(436\) 2.53668e69 0.286994
\(437\) −6.82905e69 −0.727113
\(438\) 1.08691e70 1.08925
\(439\) −1.92587e69 −0.181684 −0.0908422 0.995865i \(-0.528956\pi\)
−0.0908422 + 0.995865i \(0.528956\pi\)
\(440\) 9.76590e68 0.0867394
\(441\) 1.02650e70 0.858495
\(442\) −8.60885e69 −0.678040
\(443\) −1.15476e69 −0.0856626 −0.0428313 0.999082i \(-0.513638\pi\)
−0.0428313 + 0.999082i \(0.513638\pi\)
\(444\) 3.05754e68 0.0213660
\(445\) 1.12819e68 0.00742746
\(446\) 7.48756e69 0.464479
\(447\) 2.11014e70 1.23356
\(448\) −2.63926e70 −1.45417
\(449\) 1.26244e70 0.655664 0.327832 0.944736i \(-0.393682\pi\)
0.327832 + 0.944736i \(0.393682\pi\)
\(450\) 2.20063e70 1.07749
\(451\) 2.63979e69 0.121868
\(452\) −3.15693e68 −0.0137435
\(453\) −4.90404e70 −2.01350
\(454\) −2.67921e70 −1.03759
\(455\) 4.04403e69 0.147745
\(456\) −4.89333e70 −1.68669
\(457\) 1.89960e70 0.617848 0.308924 0.951087i \(-0.400031\pi\)
0.308924 + 0.951087i \(0.400031\pi\)
\(458\) 3.83586e69 0.117741
\(459\) −4.81800e69 −0.139583
\(460\) −3.33015e68 −0.00910714
\(461\) 4.91287e70 1.26841 0.634206 0.773164i \(-0.281327\pi\)
0.634206 + 0.773164i \(0.281327\pi\)
\(462\) 8.51664e70 2.07614
\(463\) −1.61924e70 −0.372748 −0.186374 0.982479i \(-0.559674\pi\)
−0.186374 + 0.982479i \(0.559674\pi\)
\(464\) 4.85363e70 1.05521
\(465\) −4.80290e69 −0.0986281
\(466\) −5.33094e70 −1.03413
\(467\) 9.60677e68 0.0176068 0.00880339 0.999961i \(-0.497198\pi\)
0.00880339 + 0.999961i \(0.497198\pi\)
\(468\) 2.26200e70 0.391721
\(469\) −1.65243e70 −0.270423
\(470\) 6.62442e68 0.0102460
\(471\) −1.77533e71 −2.59552
\(472\) 1.07722e71 1.48881
\(473\) 1.37079e70 0.179123
\(474\) −1.09073e71 −1.34769
\(475\) 9.02087e70 1.05407
\(476\) −1.05080e70 −0.116127
\(477\) 1.25667e71 1.31366
\(478\) −1.35692e71 −1.34189
\(479\) −7.16104e70 −0.670016 −0.335008 0.942215i \(-0.608739\pi\)
−0.335008 + 0.942215i \(0.608739\pi\)
\(480\) −4.38261e69 −0.0388008
\(481\) 1.46174e70 0.122469
\(482\) 1.58822e71 1.25940
\(483\) −1.77778e71 −1.33438
\(484\) −1.14929e70 −0.0816635
\(485\) −4.51432e69 −0.0303694
\(486\) 2.00263e71 1.27567
\(487\) 8.84962e70 0.533835 0.266918 0.963719i \(-0.413995\pi\)
0.266918 + 0.963719i \(0.413995\pi\)
\(488\) −5.59604e70 −0.319710
\(489\) 3.33574e71 1.80513
\(490\) −8.45708e69 −0.0433535
\(491\) −3.37986e71 −1.64149 −0.820747 0.571292i \(-0.806442\pi\)
−0.820747 + 0.571292i \(0.806442\pi\)
\(492\) −6.45009e69 −0.0296818
\(493\) 1.43500e71 0.625760
\(494\) −3.82162e71 −1.57937
\(495\) 2.49206e70 0.0976160
\(496\) 2.01801e71 0.749304
\(497\) 9.12793e70 0.321313
\(498\) 5.45002e70 0.181895
\(499\) −5.44978e71 −1.72470 −0.862352 0.506310i \(-0.831009\pi\)
−0.862352 + 0.506310i \(0.831009\pi\)
\(500\) 8.81836e69 0.0264657
\(501\) −1.23917e71 −0.352722
\(502\) 1.05121e70 0.0283818
\(503\) 5.30455e71 1.35862 0.679308 0.733853i \(-0.262280\pi\)
0.679308 + 0.733853i \(0.262280\pi\)
\(504\) −6.96587e71 −1.69265
\(505\) 3.85367e69 0.00888492
\(506\) −3.35288e71 −0.733549
\(507\) 1.26214e72 2.62058
\(508\) 8.70647e70 0.171575
\(509\) −5.04965e71 −0.944582 −0.472291 0.881443i \(-0.656573\pi\)
−0.472291 + 0.881443i \(0.656573\pi\)
\(510\) 2.31744e70 0.0411528
\(511\) 6.34256e71 1.06933
\(512\) 6.97622e71 1.11678
\(513\) −2.13880e71 −0.325132
\(514\) 2.18831e71 0.315926
\(515\) 4.23455e70 0.0580652
\(516\) −3.34941e70 −0.0436266
\(517\) −1.61826e71 −0.200239
\(518\) −7.35356e70 −0.0864488
\(519\) −2.44797e72 −2.73446
\(520\) −1.14080e71 −0.121093
\(521\) −1.71481e72 −1.72989 −0.864943 0.501870i \(-0.832646\pi\)
−0.864943 + 0.501870i \(0.832646\pi\)
\(522\) 1.55400e72 1.48999
\(523\) −1.17717e72 −1.07287 −0.536433 0.843943i \(-0.680228\pi\)
−0.536433 + 0.843943i \(0.680228\pi\)
\(524\) 3.00808e71 0.260622
\(525\) 2.34836e72 1.93439
\(526\) 1.63554e72 1.28097
\(527\) 5.96633e71 0.444351
\(528\) −1.91480e72 −1.35620
\(529\) −7.84598e71 −0.528533
\(530\) −1.03534e71 −0.0663392
\(531\) 2.74884e72 1.67550
\(532\) −4.66467e71 −0.270497
\(533\) −3.08365e71 −0.170135
\(534\) −2.77543e71 −0.145709
\(535\) 2.49827e71 0.124814
\(536\) 4.66142e71 0.221641
\(537\) −2.30253e72 −1.04205
\(538\) −1.46870e72 −0.632708
\(539\) 2.06595e72 0.847263
\(540\) −1.04297e70 −0.00407229
\(541\) 3.05901e72 1.13724 0.568621 0.822600i \(-0.307477\pi\)
0.568621 + 0.822600i \(0.307477\pi\)
\(542\) 9.51181e71 0.336730
\(543\) 2.06432e71 0.0695955
\(544\) 5.44424e71 0.174810
\(545\) −3.26459e71 −0.0998439
\(546\) −9.94865e72 −2.89841
\(547\) −3.46128e72 −0.960667 −0.480333 0.877086i \(-0.659484\pi\)
−0.480333 + 0.877086i \(0.659484\pi\)
\(548\) −8.73986e71 −0.231111
\(549\) −1.42800e72 −0.359799
\(550\) 4.42901e72 1.06340
\(551\) 6.37021e72 1.45759
\(552\) 5.01501e72 1.09367
\(553\) −6.36485e72 −1.32304
\(554\) 9.02098e71 0.178750
\(555\) −3.93491e70 −0.00743311
\(556\) −1.66905e72 −0.300598
\(557\) 9.15984e72 1.57299 0.786493 0.617599i \(-0.211894\pi\)
0.786493 + 0.617599i \(0.211894\pi\)
\(558\) 6.46112e72 1.05804
\(559\) −1.60128e72 −0.250066
\(560\) 4.57400e71 0.0681261
\(561\) −5.66120e72 −0.804254
\(562\) −4.74287e72 −0.642730
\(563\) 2.99024e72 0.386575 0.193288 0.981142i \(-0.438085\pi\)
0.193288 + 0.981142i \(0.438085\pi\)
\(564\) 3.95407e71 0.0487695
\(565\) 4.06282e70 0.00478128
\(566\) −8.89922e72 −0.999347
\(567\) 9.16301e72 0.981944
\(568\) −2.57494e72 −0.263352
\(569\) −1.95493e73 −1.90834 −0.954169 0.299270i \(-0.903257\pi\)
−0.954169 + 0.299270i \(0.903257\pi\)
\(570\) 1.02875e72 0.0958579
\(571\) 6.21208e72 0.552561 0.276280 0.961077i \(-0.410898\pi\)
0.276280 + 0.961077i \(0.410898\pi\)
\(572\) 4.55252e72 0.386595
\(573\) −1.63600e73 −1.32644
\(574\) 1.55129e72 0.120096
\(575\) −9.24517e72 −0.683466
\(576\) 1.89987e73 1.34131
\(577\) 3.44976e72 0.232611 0.116305 0.993213i \(-0.462895\pi\)
0.116305 + 0.993213i \(0.462895\pi\)
\(578\) 1.10501e73 0.711669
\(579\) 1.19259e73 0.733682
\(580\) 3.10640e71 0.0182564
\(581\) 3.18032e72 0.178568
\(582\) 1.11056e73 0.595777
\(583\) 2.52919e73 1.29647
\(584\) −1.78920e73 −0.876433
\(585\) −2.91109e72 −0.136278
\(586\) −2.15896e73 −0.965957
\(587\) −3.91303e73 −1.67341 −0.836707 0.547650i \(-0.815522\pi\)
−0.836707 + 0.547650i \(0.815522\pi\)
\(588\) −5.04797e72 −0.206356
\(589\) 2.64856e73 1.03503
\(590\) −2.26469e72 −0.0846118
\(591\) −2.69351e73 −0.962167
\(592\) 1.65331e72 0.0564713
\(593\) 3.03919e73 0.992679 0.496340 0.868128i \(-0.334677\pi\)
0.496340 + 0.868128i \(0.334677\pi\)
\(594\) −1.05009e73 −0.328010
\(595\) 1.35233e72 0.0404001
\(596\) −5.67442e72 −0.162142
\(597\) 1.82497e73 0.498812
\(598\) 3.91664e73 1.02408
\(599\) −4.69569e73 −1.17460 −0.587298 0.809371i \(-0.699808\pi\)
−0.587298 + 0.809371i \(0.699808\pi\)
\(600\) −6.62460e73 −1.58545
\(601\) 3.32571e73 0.761572 0.380786 0.924663i \(-0.375653\pi\)
0.380786 + 0.924663i \(0.375653\pi\)
\(602\) 8.05554e72 0.176517
\(603\) 1.18950e73 0.249434
\(604\) 1.31875e73 0.264658
\(605\) 1.47909e72 0.0284103
\(606\) −9.48037e72 −0.174301
\(607\) −4.03134e73 −0.709495 −0.354747 0.934962i \(-0.615433\pi\)
−0.354747 + 0.934962i \(0.615433\pi\)
\(608\) 2.41679e73 0.407188
\(609\) 1.65833e74 2.67493
\(610\) 1.17649e72 0.0181697
\(611\) 1.89036e73 0.279545
\(612\) 7.56414e72 0.107114
\(613\) −1.16967e74 −1.58621 −0.793103 0.609087i \(-0.791536\pi\)
−0.793103 + 0.609087i \(0.791536\pi\)
\(614\) 9.77045e73 1.26897
\(615\) 8.30098e71 0.0103262
\(616\) −1.40196e74 −1.67050
\(617\) −8.47254e73 −0.967067 −0.483534 0.875326i \(-0.660647\pi\)
−0.483534 + 0.875326i \(0.660647\pi\)
\(618\) −1.04174e74 −1.13910
\(619\) −4.01420e73 −0.420529 −0.210265 0.977644i \(-0.567433\pi\)
−0.210265 + 0.977644i \(0.567433\pi\)
\(620\) 1.29156e72 0.0129639
\(621\) 2.19198e73 0.210818
\(622\) −3.39694e73 −0.313071
\(623\) −1.61958e73 −0.143044
\(624\) 2.23676e74 1.89334
\(625\) 1.21556e74 0.986178
\(626\) 8.89748e73 0.691906
\(627\) −2.51311e74 −1.87336
\(628\) 4.77407e73 0.341160
\(629\) 4.88808e72 0.0334886
\(630\) 1.46447e73 0.0961961
\(631\) 1.79458e74 1.13028 0.565139 0.824996i \(-0.308823\pi\)
0.565139 + 0.824996i \(0.308823\pi\)
\(632\) 1.79549e74 1.08438
\(633\) −6.28603e73 −0.364064
\(634\) −1.06161e74 −0.589658
\(635\) −1.12048e73 −0.0596900
\(636\) −6.17984e73 −0.315765
\(637\) −2.41333e74 −1.18283
\(638\) 3.12760e74 1.47050
\(639\) −6.57073e73 −0.296374
\(640\) −9.61665e72 −0.0416154
\(641\) 9.16136e73 0.380384 0.190192 0.981747i \(-0.439089\pi\)
0.190192 + 0.981747i \(0.439089\pi\)
\(642\) −6.14595e74 −2.44856
\(643\) 2.41149e74 0.921924 0.460962 0.887420i \(-0.347504\pi\)
0.460962 + 0.887420i \(0.347504\pi\)
\(644\) 4.78065e73 0.175393
\(645\) 4.31054e72 0.0151775
\(646\) −1.27795e74 −0.431870
\(647\) −2.73867e74 −0.888334 −0.444167 0.895944i \(-0.646500\pi\)
−0.444167 + 0.895944i \(0.646500\pi\)
\(648\) −2.58483e74 −0.804813
\(649\) 5.53234e74 1.65358
\(650\) −5.17371e74 −1.48456
\(651\) 6.89488e74 1.89946
\(652\) −8.97021e73 −0.237269
\(653\) 2.24596e74 0.570430 0.285215 0.958464i \(-0.407935\pi\)
0.285215 + 0.958464i \(0.407935\pi\)
\(654\) 8.03117e74 1.95870
\(655\) −3.87127e73 −0.0906690
\(656\) −3.48777e73 −0.0784505
\(657\) −4.56568e74 −0.986333
\(658\) −9.50979e73 −0.197326
\(659\) −7.20835e74 −1.43672 −0.718361 0.695671i \(-0.755107\pi\)
−0.718361 + 0.695671i \(0.755107\pi\)
\(660\) −1.22551e73 −0.0234639
\(661\) 2.05504e73 0.0377992 0.0188996 0.999821i \(-0.493984\pi\)
0.0188996 + 0.999821i \(0.493984\pi\)
\(662\) 5.97945e74 1.05663
\(663\) 6.61310e74 1.12278
\(664\) −8.97150e73 −0.146356
\(665\) 6.00322e73 0.0941045
\(666\) 5.29345e73 0.0797392
\(667\) −6.52861e74 −0.945118
\(668\) 3.33228e73 0.0463624
\(669\) −5.75175e74 −0.769144
\(670\) −9.79996e72 −0.0125963
\(671\) −2.87400e74 −0.355092
\(672\) 6.29153e74 0.747258
\(673\) −8.58844e73 −0.0980652 −0.0490326 0.998797i \(-0.515614\pi\)
−0.0490326 + 0.998797i \(0.515614\pi\)
\(674\) −6.34209e74 −0.696218
\(675\) −2.89551e74 −0.305615
\(676\) −3.39405e74 −0.344454
\(677\) −1.28702e75 −1.25599 −0.627993 0.778219i \(-0.716123\pi\)
−0.627993 + 0.778219i \(0.716123\pi\)
\(678\) −9.99489e73 −0.0937975
\(679\) 6.48060e74 0.584879
\(680\) −3.81484e73 −0.0331123
\(681\) 2.05810e75 1.71817
\(682\) 1.30037e75 1.04420
\(683\) 2.32106e75 1.79283 0.896414 0.443218i \(-0.146163\pi\)
0.896414 + 0.443218i \(0.146163\pi\)
\(684\) 3.35785e74 0.249503
\(685\) 1.12478e74 0.0804022
\(686\) −4.92406e74 −0.338637
\(687\) −2.94661e74 −0.194970
\(688\) −1.81113e74 −0.115307
\(689\) −2.95445e75 −1.80995
\(690\) −1.05433e74 −0.0621551
\(691\) 4.45634e74 0.252819 0.126410 0.991978i \(-0.459655\pi\)
0.126410 + 0.991978i \(0.459655\pi\)
\(692\) 6.58289e74 0.359422
\(693\) −3.57752e75 −1.87997
\(694\) 1.43659e75 0.726618
\(695\) 2.14799e74 0.104577
\(696\) −4.67805e75 −2.19240
\(697\) −1.03118e74 −0.0465226
\(698\) 1.65879e75 0.720480
\(699\) 4.09509e75 1.71245
\(700\) −6.31503e74 −0.254260
\(701\) −1.68252e75 −0.652276 −0.326138 0.945322i \(-0.605747\pi\)
−0.326138 + 0.945322i \(0.605747\pi\)
\(702\) 1.22666e75 0.457920
\(703\) 2.16991e74 0.0780054
\(704\) 3.82370e75 1.32376
\(705\) −5.08871e73 −0.0169667
\(706\) −4.14531e75 −1.33117
\(707\) −5.53220e74 −0.171113
\(708\) −1.35178e75 −0.402739
\(709\) 4.03690e75 1.15857 0.579286 0.815124i \(-0.303331\pi\)
0.579286 + 0.815124i \(0.303331\pi\)
\(710\) 5.41344e73 0.0149667
\(711\) 4.58173e75 1.22035
\(712\) 4.56876e74 0.117241
\(713\) −2.71442e75 −0.671126
\(714\) −3.32684e75 −0.792555
\(715\) −5.85888e74 −0.134495
\(716\) 6.19179e74 0.136969
\(717\) 1.04235e76 2.22207
\(718\) −2.75836e75 −0.566700
\(719\) −2.29058e75 −0.453555 −0.226778 0.973947i \(-0.572819\pi\)
−0.226778 + 0.973947i \(0.572819\pi\)
\(720\) −3.29259e74 −0.0628386
\(721\) −6.07898e75 −1.11827
\(722\) −6.14062e74 −0.108887
\(723\) −1.22003e76 −2.08548
\(724\) −5.55120e73 −0.00914776
\(725\) 8.62400e75 1.37010
\(726\) −3.63868e75 −0.557344
\(727\) −1.58967e75 −0.234772 −0.117386 0.993086i \(-0.537451\pi\)
−0.117386 + 0.993086i \(0.537451\pi\)
\(728\) 1.63769e76 2.33211
\(729\) −9.91746e75 −1.36182
\(730\) 3.76154e74 0.0498092
\(731\) −5.35470e74 −0.0683793
\(732\) 7.02237e74 0.0864849
\(733\) 8.19933e74 0.0973919 0.0486959 0.998814i \(-0.484493\pi\)
0.0486959 + 0.998814i \(0.484493\pi\)
\(734\) 3.48749e75 0.399546
\(735\) 6.49651e74 0.0717903
\(736\) −2.47689e75 −0.264024
\(737\) 2.39400e75 0.246170
\(738\) −1.11669e75 −0.110774
\(739\) −5.66664e75 −0.542310 −0.271155 0.962536i \(-0.587406\pi\)
−0.271155 + 0.962536i \(0.587406\pi\)
\(740\) 1.05814e73 0.000977022 0
\(741\) 2.93567e76 2.61532
\(742\) 1.48629e76 1.27762
\(743\) −1.25772e76 −1.04323 −0.521615 0.853181i \(-0.674670\pi\)
−0.521615 + 0.853181i \(0.674670\pi\)
\(744\) −1.94501e76 −1.55682
\(745\) 7.30272e74 0.0564083
\(746\) 1.31915e76 0.983369
\(747\) −2.28935e75 −0.164708
\(748\) 1.52237e75 0.105713
\(749\) −3.58642e76 −2.40377
\(750\) 2.79191e75 0.180625
\(751\) −5.86096e75 −0.366025 −0.183012 0.983111i \(-0.558585\pi\)
−0.183012 + 0.983111i \(0.558585\pi\)
\(752\) 2.13809e75 0.128900
\(753\) −8.07512e74 −0.0469983
\(754\) −3.65349e76 −2.05290
\(755\) −1.69718e75 −0.0920732
\(756\) 1.49726e75 0.0784276
\(757\) 3.11946e76 1.57775 0.788877 0.614551i \(-0.210663\pi\)
0.788877 + 0.614551i \(0.210663\pi\)
\(758\) −8.96451e75 −0.437817
\(759\) 2.57560e76 1.21470
\(760\) −1.69347e75 −0.0771291
\(761\) 7.11505e75 0.312957 0.156478 0.987681i \(-0.449986\pi\)
0.156478 + 0.987681i \(0.449986\pi\)
\(762\) 2.75649e76 1.17098
\(763\) 4.68653e76 1.92288
\(764\) 4.39941e75 0.174349
\(765\) −9.73470e74 −0.0372644
\(766\) −7.02293e75 −0.259691
\(767\) −6.46257e76 −2.30849
\(768\) −2.41916e76 −0.834819
\(769\) 2.10631e76 0.702223 0.351112 0.936334i \(-0.385804\pi\)
0.351112 + 0.936334i \(0.385804\pi\)
\(770\) 2.94742e75 0.0949374
\(771\) −1.68100e76 −0.523151
\(772\) −3.20701e75 −0.0964366
\(773\) 3.92297e75 0.113988 0.0569938 0.998375i \(-0.481848\pi\)
0.0569938 + 0.998375i \(0.481848\pi\)
\(774\) −5.79877e75 −0.162817
\(775\) 3.58562e76 0.972903
\(776\) −1.82814e76 −0.479374
\(777\) 5.64882e75 0.143153
\(778\) −1.60975e76 −0.394274
\(779\) −4.57757e75 −0.108366
\(780\) 1.43157e75 0.0327570
\(781\) −1.32243e76 −0.292497
\(782\) 1.30973e76 0.280029
\(783\) −2.04470e76 −0.422613
\(784\) −2.72960e76 −0.545410
\(785\) −6.14402e75 −0.118688
\(786\) 9.52365e76 1.77871
\(787\) −2.38560e76 −0.430792 −0.215396 0.976527i \(-0.569104\pi\)
−0.215396 + 0.976527i \(0.569104\pi\)
\(788\) 7.24317e75 0.126469
\(789\) −1.25638e77 −2.12120
\(790\) −3.77476e75 −0.0616270
\(791\) −5.83244e75 −0.0920818
\(792\) 1.00920e77 1.54084
\(793\) 3.35725e76 0.495729
\(794\) 1.20798e77 1.72511
\(795\) 7.95318e75 0.109853
\(796\) −4.90758e75 −0.0655648
\(797\) 9.89205e76 1.27832 0.639162 0.769072i \(-0.279281\pi\)
0.639162 + 0.769072i \(0.279281\pi\)
\(798\) −1.47684e77 −1.84611
\(799\) 6.32137e75 0.0764402
\(800\) 3.27186e76 0.382745
\(801\) 1.16586e76 0.131942
\(802\) −9.18754e76 −1.00596
\(803\) −9.18894e76 −0.973427
\(804\) −5.84953e75 −0.0599564
\(805\) −6.15248e75 −0.0610182
\(806\) −1.51902e77 −1.45776
\(807\) 1.12822e77 1.04772
\(808\) 1.56060e76 0.140246
\(809\) 1.59609e77 1.38810 0.694050 0.719927i \(-0.255825\pi\)
0.694050 + 0.719927i \(0.255825\pi\)
\(810\) 5.43424e75 0.0457389
\(811\) −2.38631e77 −1.94390 −0.971952 0.235181i \(-0.924432\pi\)
−0.971952 + 0.235181i \(0.924432\pi\)
\(812\) −4.45944e76 −0.351598
\(813\) −7.30673e76 −0.557601
\(814\) 1.06537e76 0.0786959
\(815\) 1.15443e76 0.0825448
\(816\) 7.47976e76 0.517724
\(817\) −2.37705e76 −0.159277
\(818\) 1.60918e77 1.04386
\(819\) 4.17905e77 2.62455
\(820\) −2.23223e74 −0.00135729
\(821\) −2.72431e77 −1.60385 −0.801924 0.597425i \(-0.796190\pi\)
−0.801924 + 0.597425i \(0.796190\pi\)
\(822\) −2.76706e77 −1.57730
\(823\) 2.80427e77 1.54784 0.773918 0.633286i \(-0.218294\pi\)
0.773918 + 0.633286i \(0.218294\pi\)
\(824\) 1.71485e77 0.916545
\(825\) −3.40225e77 −1.76091
\(826\) 3.25111e77 1.62952
\(827\) 3.27438e77 1.58940 0.794700 0.607002i \(-0.207628\pi\)
0.794700 + 0.607002i \(0.207628\pi\)
\(828\) −3.44135e76 −0.161780
\(829\) −1.12060e77 −0.510216 −0.255108 0.966913i \(-0.582111\pi\)
−0.255108 + 0.966913i \(0.582111\pi\)
\(830\) 1.88613e75 0.00831768
\(831\) −6.92969e76 −0.295996
\(832\) −4.46663e77 −1.84804
\(833\) −8.07019e76 −0.323438
\(834\) −5.28423e77 −2.05155
\(835\) −4.28850e75 −0.0161292
\(836\) 6.75805e76 0.246238
\(837\) −8.50131e76 −0.300097
\(838\) 4.70103e77 1.60778
\(839\) −2.49923e77 −0.828159 −0.414079 0.910241i \(-0.635896\pi\)
−0.414079 + 0.910241i \(0.635896\pi\)
\(840\) −4.40854e76 −0.141545
\(841\) 2.87560e77 0.894611
\(842\) 1.00833e77 0.303972
\(843\) 3.64335e77 1.06432
\(844\) 1.69039e76 0.0478533
\(845\) 4.36799e76 0.119834
\(846\) 6.84560e76 0.182011
\(847\) −2.12332e77 −0.547149
\(848\) −3.34164e77 −0.834583
\(849\) 6.83615e77 1.65485
\(850\) −1.73009e77 −0.405946
\(851\) −2.22386e76 −0.0505794
\(852\) 3.23124e76 0.0712394
\(853\) −7.69577e77 −1.64476 −0.822381 0.568937i \(-0.807355\pi\)
−0.822381 + 0.568937i \(0.807355\pi\)
\(854\) −1.68892e77 −0.349926
\(855\) −4.32141e76 −0.0868007
\(856\) 1.01171e78 1.97016
\(857\) −4.56317e77 −0.861539 −0.430769 0.902462i \(-0.641758\pi\)
−0.430769 + 0.902462i \(0.641758\pi\)
\(858\) 1.44134e78 2.63847
\(859\) −5.50005e77 −0.976219 −0.488110 0.872782i \(-0.662313\pi\)
−0.488110 + 0.872782i \(0.662313\pi\)
\(860\) −1.15916e75 −0.00199495
\(861\) −1.19166e77 −0.198870
\(862\) −1.93734e77 −0.313519
\(863\) 2.27402e77 0.356868 0.178434 0.983952i \(-0.442897\pi\)
0.178434 + 0.983952i \(0.442897\pi\)
\(864\) −7.75738e76 −0.118060
\(865\) −8.47188e76 −0.125041
\(866\) −1.00952e78 −1.44508
\(867\) −8.48839e77 −1.17847
\(868\) −1.85412e77 −0.249669
\(869\) 9.22123e77 1.20438
\(870\) 9.83494e76 0.124598
\(871\) −2.79654e77 −0.343668
\(872\) −1.32204e78 −1.57601
\(873\) −4.66505e77 −0.539484
\(874\) 5.81412e77 0.652276
\(875\) 1.62920e77 0.177321
\(876\) 2.24524e77 0.237085
\(877\) 1.67020e78 1.71111 0.855556 0.517711i \(-0.173216\pi\)
0.855556 + 0.517711i \(0.173216\pi\)
\(878\) 1.63965e77 0.162985
\(879\) 1.65846e78 1.59955
\(880\) −6.62670e76 −0.0620164
\(881\) 1.51231e78 1.37334 0.686672 0.726967i \(-0.259071\pi\)
0.686672 + 0.726967i \(0.259071\pi\)
\(882\) −8.73946e77 −0.770135
\(883\) −7.53014e77 −0.643938 −0.321969 0.946750i \(-0.604345\pi\)
−0.321969 + 0.946750i \(0.604345\pi\)
\(884\) −1.77834e77 −0.147581
\(885\) 1.73968e77 0.140111
\(886\) 9.83137e76 0.0768458
\(887\) −2.01497e78 −1.52859 −0.764296 0.644865i \(-0.776914\pi\)
−0.764296 + 0.644865i \(0.776914\pi\)
\(888\) −1.59350e77 −0.117330
\(889\) 1.60853e78 1.14956
\(890\) −9.60516e75 −0.00666299
\(891\) −1.32751e78 −0.893881
\(892\) 1.54671e77 0.101098
\(893\) 2.80617e77 0.178053
\(894\) −1.79653e78 −1.10660
\(895\) −7.96855e76 −0.0476507
\(896\) 1.38053e78 0.801464
\(897\) −3.00867e78 −1.69580
\(898\) −1.07481e78 −0.588180
\(899\) 2.53204e78 1.34536
\(900\) 4.54586e77 0.234525
\(901\) −9.87972e77 −0.494923
\(902\) −2.24746e77 −0.109325
\(903\) −6.18806e77 −0.292300
\(904\) 1.64530e77 0.0754713
\(905\) 7.14414e75 0.00318246
\(906\) 4.17520e78 1.80626
\(907\) 8.47265e77 0.355980 0.177990 0.984032i \(-0.443040\pi\)
0.177990 + 0.984032i \(0.443040\pi\)
\(908\) −5.53447e77 −0.225840
\(909\) 3.98234e77 0.157832
\(910\) −3.44301e77 −0.132538
\(911\) −5.35967e77 −0.200402 −0.100201 0.994967i \(-0.531949\pi\)
−0.100201 + 0.994967i \(0.531949\pi\)
\(912\) 3.32039e78 1.20594
\(913\) −4.60756e77 −0.162553
\(914\) −1.61728e78 −0.554256
\(915\) −9.03748e76 −0.0300877
\(916\) 7.92378e76 0.0256273
\(917\) 5.55746e78 1.74618
\(918\) 4.10196e77 0.125216
\(919\) −5.43292e78 −1.61129 −0.805643 0.592402i \(-0.798180\pi\)
−0.805643 + 0.592402i \(0.798180\pi\)
\(920\) 1.73558e77 0.0500112
\(921\) −7.50541e78 −2.10133
\(922\) −4.18272e78 −1.13786
\(923\) 1.54479e78 0.408342
\(924\) 1.75929e78 0.451888
\(925\) 2.93762e77 0.0733229
\(926\) 1.37859e78 0.334383
\(927\) 4.37594e78 1.03147
\(928\) 2.31047e78 0.529271
\(929\) −1.48878e78 −0.331446 −0.165723 0.986172i \(-0.552996\pi\)
−0.165723 + 0.986172i \(0.552996\pi\)
\(930\) 4.08910e77 0.0884768
\(931\) −3.58250e78 −0.753390
\(932\) −1.10122e78 −0.225088
\(933\) 2.60945e78 0.518423
\(934\) −8.17902e76 −0.0157946
\(935\) −1.95922e77 −0.0367769
\(936\) −1.17889e79 −2.15111
\(937\) 5.58551e78 0.990749 0.495374 0.868680i \(-0.335031\pi\)
0.495374 + 0.868680i \(0.335031\pi\)
\(938\) 1.40685e78 0.242590
\(939\) −6.83481e78 −1.14575
\(940\) 1.36842e76 0.00223013
\(941\) 9.38809e78 1.48748 0.743742 0.668467i \(-0.233049\pi\)
0.743742 + 0.668467i \(0.233049\pi\)
\(942\) 1.51148e79 2.32838
\(943\) 4.69139e77 0.0702655
\(944\) −7.30950e78 −1.06446
\(945\) −1.92690e77 −0.0272846
\(946\) −1.16707e78 −0.160687
\(947\) 7.56797e78 1.01322 0.506611 0.862174i \(-0.330898\pi\)
0.506611 + 0.862174i \(0.330898\pi\)
\(948\) −2.25313e78 −0.293335
\(949\) 1.07340e79 1.35896
\(950\) −7.68020e78 −0.945577
\(951\) 8.15503e78 0.976431
\(952\) 5.47645e78 0.637705
\(953\) −1.45966e79 −1.65306 −0.826530 0.562892i \(-0.809689\pi\)
−0.826530 + 0.562892i \(0.809689\pi\)
\(954\) −1.06990e79 −1.17845
\(955\) −5.66184e77 −0.0606552
\(956\) −2.80301e78 −0.292073
\(957\) −2.40254e79 −2.43503
\(958\) 6.09677e78 0.601055
\(959\) −1.61470e79 −1.54845
\(960\) 1.20239e78 0.112165
\(961\) −4.92178e77 −0.0446634
\(962\) −1.24450e78 −0.109864
\(963\) 2.58168e79 2.21721
\(964\) 3.28080e78 0.274119
\(965\) 4.12728e77 0.0335498
\(966\) 1.51356e79 1.19704
\(967\) 1.29544e78 0.0996821 0.0498411 0.998757i \(-0.484129\pi\)
0.0498411 + 0.998757i \(0.484129\pi\)
\(968\) 5.98978e78 0.448450
\(969\) 9.81691e78 0.715146
\(970\) 3.84341e77 0.0272436
\(971\) −1.09632e79 −0.756185 −0.378092 0.925768i \(-0.623420\pi\)
−0.378092 + 0.925768i \(0.623420\pi\)
\(972\) 4.13685e78 0.277660
\(973\) −3.08357e79 −2.01402
\(974\) −7.53440e78 −0.478891
\(975\) 3.97431e79 2.45833
\(976\) 3.79722e78 0.228584
\(977\) 2.12309e79 1.24384 0.621918 0.783083i \(-0.286354\pi\)
0.621918 + 0.783083i \(0.286354\pi\)
\(978\) −2.83999e79 −1.61933
\(979\) 2.34641e78 0.130216
\(980\) −1.74699e77 −0.00943625
\(981\) −3.37359e79 −1.77363
\(982\) 2.87755e79 1.47254
\(983\) −1.67774e79 −0.835710 −0.417855 0.908514i \(-0.637218\pi\)
−0.417855 + 0.908514i \(0.637218\pi\)
\(984\) 3.36160e78 0.162996
\(985\) −9.32164e77 −0.0439979
\(986\) −1.22173e79 −0.561354
\(987\) 7.30517e78 0.326758
\(988\) −7.89437e78 −0.343763
\(989\) 2.43615e78 0.103277
\(990\) −2.12169e78 −0.0875689
\(991\) 1.19328e79 0.479502 0.239751 0.970834i \(-0.422934\pi\)
0.239751 + 0.970834i \(0.422934\pi\)
\(992\) 9.60629e78 0.375834
\(993\) −4.59326e79 −1.74971
\(994\) −7.77134e78 −0.288242
\(995\) 6.31583e77 0.0228097
\(996\) 1.12582e78 0.0395909
\(997\) −2.54279e79 −0.870739 −0.435370 0.900252i \(-0.643382\pi\)
−0.435370 + 0.900252i \(0.643382\pi\)
\(998\) 4.63984e79 1.54719
\(999\) −6.96493e77 −0.0226168
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 1.54.a.a.1.2 4
3.2 odd 2 9.54.a.b.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.54.a.a.1.2 4 1.1 even 1 trivial
9.54.a.b.1.3 4 3.2 odd 2