Properties

Label 1.68.a.a.1.2
Level 1
Weight 68
Character 1.1
Self dual yes
Analytic conductor 28.429
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 68 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.4290351930\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 939384011925257456 x^{3} + 31046449413968483513911200 x^{2} + 156793504704482691874379743265203200 x + 20916736226052669578405116700517591609696000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(6.06038e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.34339e10 q^{2} +7.87958e15 q^{3} +3.28965e19 q^{4} -3.01383e23 q^{5} -1.05854e26 q^{6} -4.20742e26 q^{7} +1.54057e30 q^{8} -3.06216e31 q^{9} +O(q^{10})\) \(q-1.34339e10 q^{2} +7.87958e15 q^{3} +3.28965e19 q^{4} -3.01383e23 q^{5} -1.05854e26 q^{6} -4.20742e26 q^{7} +1.54057e30 q^{8} -3.06216e31 q^{9} +4.04876e33 q^{10} +1.62242e34 q^{11} +2.59210e35 q^{12} -3.08856e37 q^{13} +5.65222e36 q^{14} -2.37477e39 q^{15} -2.55506e40 q^{16} -1.59490e41 q^{17} +4.11369e41 q^{18} +1.03902e43 q^{19} -9.91443e42 q^{20} -3.31527e42 q^{21} -2.17954e44 q^{22} -3.59214e45 q^{23} +1.21390e46 q^{24} +2.30691e46 q^{25} +4.14915e47 q^{26} -9.71798e47 q^{27} -1.38409e46 q^{28} +1.54617e49 q^{29} +3.19025e49 q^{30} +1.52983e50 q^{31} +1.15896e50 q^{32} +1.27840e50 q^{33} +2.14258e51 q^{34} +1.26805e50 q^{35} -1.00734e51 q^{36} +1.16261e52 q^{37} -1.39581e53 q^{38} -2.43366e53 q^{39} -4.64301e53 q^{40} +1.50280e54 q^{41} +4.45371e52 q^{42} +1.43610e54 q^{43} +5.33717e53 q^{44} +9.22884e54 q^{45} +4.82565e55 q^{46} +9.41631e55 q^{47} -2.01328e56 q^{48} -4.18201e56 q^{49} -3.09909e56 q^{50} -1.25671e57 q^{51} -1.01603e57 q^{52} +4.49370e57 q^{53} +1.30551e58 q^{54} -4.88968e57 q^{55} -6.48182e56 q^{56} +8.18704e58 q^{57} -2.07711e59 q^{58} +2.81815e59 q^{59} -7.81216e58 q^{60} -4.42593e59 q^{61} -2.05516e60 q^{62} +1.28838e58 q^{63} +2.21365e60 q^{64} +9.30840e60 q^{65} -1.71739e60 q^{66} +9.71985e60 q^{67} -5.24666e60 q^{68} -2.83045e61 q^{69} -1.70348e60 q^{70} -3.66936e61 q^{71} -4.71748e61 q^{72} -1.52158e61 q^{73} -1.56184e62 q^{74} +1.81775e62 q^{75} +3.41801e62 q^{76} -6.82619e60 q^{77} +3.26936e63 q^{78} -2.59876e63 q^{79} +7.70050e63 q^{80} -4.81844e63 q^{81} -2.01885e64 q^{82} -2.25569e64 q^{83} -1.09061e62 q^{84} +4.80676e64 q^{85} -1.92925e64 q^{86} +1.21832e65 q^{87} +2.49944e64 q^{88} -2.92327e64 q^{89} -1.23980e65 q^{90} +1.29949e64 q^{91} -1.18169e65 q^{92} +1.20544e66 q^{93} -1.26498e66 q^{94} -3.13143e66 q^{95} +9.13215e65 q^{96} -8.79797e65 q^{97} +5.61808e66 q^{98} -4.96810e65 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 5554901256q^{2} + 3443360269119372q^{3} + \)\(35\!\cdots\!40\)\(q^{4} + \)\(33\!\cdots\!50\)\(q^{5} + \)\(14\!\cdots\!60\)\(q^{6} + \)\(33\!\cdots\!56\)\(q^{7} + \)\(32\!\cdots\!80\)\(q^{8} + \)\(27\!\cdots\!85\)\(q^{9} - \)\(52\!\cdots\!00\)\(q^{10} + \)\(20\!\cdots\!60\)\(q^{11} - \)\(20\!\cdots\!24\)\(q^{12} + \)\(17\!\cdots\!02\)\(q^{13} + \)\(29\!\cdots\!80\)\(q^{14} - \)\(93\!\cdots\!00\)\(q^{15} + \)\(18\!\cdots\!80\)\(q^{16} + \)\(75\!\cdots\!06\)\(q^{17} - \)\(10\!\cdots\!68\)\(q^{18} + \)\(39\!\cdots\!00\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(17\!\cdots\!40\)\(q^{21} + \)\(18\!\cdots\!32\)\(q^{22} - \)\(41\!\cdots\!68\)\(q^{23} - \)\(13\!\cdots\!00\)\(q^{24} + \)\(17\!\cdots\!75\)\(q^{25} + \)\(21\!\cdots\!60\)\(q^{26} + \)\(18\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!48\)\(q^{28} + \)\(18\!\cdots\!50\)\(q^{29} + \)\(18\!\cdots\!00\)\(q^{30} + \)\(36\!\cdots\!60\)\(q^{31} + \)\(15\!\cdots\!96\)\(q^{32} + \)\(24\!\cdots\!84\)\(q^{33} + \)\(78\!\cdots\!80\)\(q^{34} + \)\(45\!\cdots\!00\)\(q^{35} - \)\(38\!\cdots\!20\)\(q^{36} - \)\(56\!\cdots\!94\)\(q^{37} - \)\(31\!\cdots\!80\)\(q^{38} - \)\(71\!\cdots\!80\)\(q^{39} - \)\(18\!\cdots\!00\)\(q^{40} + \)\(11\!\cdots\!10\)\(q^{41} + \)\(28\!\cdots\!92\)\(q^{42} + \)\(65\!\cdots\!92\)\(q^{43} + \)\(49\!\cdots\!80\)\(q^{44} + \)\(99\!\cdots\!50\)\(q^{45} + \)\(79\!\cdots\!60\)\(q^{46} - \)\(12\!\cdots\!44\)\(q^{47} - \)\(19\!\cdots\!68\)\(q^{48} - \)\(77\!\cdots\!35\)\(q^{49} - \)\(39\!\cdots\!00\)\(q^{50} - \)\(33\!\cdots\!40\)\(q^{51} + \)\(67\!\cdots\!16\)\(q^{52} + \)\(10\!\cdots\!22\)\(q^{53} + \)\(19\!\cdots\!00\)\(q^{54} + \)\(66\!\cdots\!00\)\(q^{55} + \)\(16\!\cdots\!00\)\(q^{56} - \)\(92\!\cdots\!60\)\(q^{57} - \)\(61\!\cdots\!20\)\(q^{58} - \)\(30\!\cdots\!00\)\(q^{59} - \)\(13\!\cdots\!00\)\(q^{60} - \)\(11\!\cdots\!90\)\(q^{61} - \)\(21\!\cdots\!28\)\(q^{62} - \)\(20\!\cdots\!68\)\(q^{63} + \)\(63\!\cdots\!40\)\(q^{64} + \)\(17\!\cdots\!00\)\(q^{65} + \)\(27\!\cdots\!20\)\(q^{66} - \)\(11\!\cdots\!44\)\(q^{67} + \)\(81\!\cdots\!48\)\(q^{68} + \)\(35\!\cdots\!20\)\(q^{69} - \)\(26\!\cdots\!00\)\(q^{70} - \)\(11\!\cdots\!40\)\(q^{71} - \)\(74\!\cdots\!40\)\(q^{72} - \)\(30\!\cdots\!18\)\(q^{73} + \)\(92\!\cdots\!80\)\(q^{74} + \)\(21\!\cdots\!00\)\(q^{75} + \)\(20\!\cdots\!00\)\(q^{76} + \)\(50\!\cdots\!32\)\(q^{77} + \)\(61\!\cdots\!64\)\(q^{78} + \)\(29\!\cdots\!00\)\(q^{79} - \)\(15\!\cdots\!00\)\(q^{80} - \)\(11\!\cdots\!95\)\(q^{81} - \)\(17\!\cdots\!08\)\(q^{82} - \)\(47\!\cdots\!88\)\(q^{83} - \)\(52\!\cdots\!20\)\(q^{84} - \)\(39\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!60\)\(q^{86} + \)\(35\!\cdots\!60\)\(q^{87} + \)\(43\!\cdots\!60\)\(q^{88} - \)\(11\!\cdots\!50\)\(q^{89} + \)\(47\!\cdots\!00\)\(q^{90} + \)\(23\!\cdots\!60\)\(q^{91} - \)\(98\!\cdots\!44\)\(q^{92} - \)\(18\!\cdots\!36\)\(q^{93} - \)\(49\!\cdots\!20\)\(q^{94} - \)\(20\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!40\)\(q^{96} + \)\(28\!\cdots\!06\)\(q^{97} + \)\(12\!\cdots\!08\)\(q^{98} + \)\(16\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34339e10 −1.10585 −0.552927 0.833229i \(-0.686489\pi\)
−0.552927 + 0.833229i \(0.686489\pi\)
\(3\) 7.87958e15 0.818354 0.409177 0.912455i \(-0.365816\pi\)
0.409177 + 0.912455i \(0.365816\pi\)
\(4\) 3.28965e19 0.222915
\(5\) −3.01383e23 −1.15777 −0.578887 0.815408i \(-0.696513\pi\)
−0.578887 + 0.815408i \(0.696513\pi\)
\(6\) −1.05854e26 −0.904981
\(7\) −4.20742e26 −0.0205699 −0.0102849 0.999947i \(-0.503274\pi\)
−0.0102849 + 0.999947i \(0.503274\pi\)
\(8\) 1.54057e30 0.859343
\(9\) −3.06216e31 −0.330297
\(10\) 4.04876e33 1.28033
\(11\) 1.62242e34 0.210624 0.105312 0.994439i \(-0.466416\pi\)
0.105312 + 0.994439i \(0.466416\pi\)
\(12\) 2.59210e35 0.182423
\(13\) −3.08856e37 −1.48817 −0.744087 0.668082i \(-0.767115\pi\)
−0.744087 + 0.668082i \(0.767115\pi\)
\(14\) 5.65222e36 0.0227473
\(15\) −2.37477e39 −0.947469
\(16\) −2.55506e40 −1.17322
\(17\) −1.59490e41 −0.960936 −0.480468 0.877012i \(-0.659533\pi\)
−0.480468 + 0.877012i \(0.659533\pi\)
\(18\) 4.11369e41 0.365260
\(19\) 1.03902e43 1.50792 0.753959 0.656921i \(-0.228141\pi\)
0.753959 + 0.656921i \(0.228141\pi\)
\(20\) −9.91443e42 −0.258085
\(21\) −3.31527e42 −0.0168334
\(22\) −2.17954e44 −0.232919
\(23\) −3.59214e45 −0.865905 −0.432953 0.901417i \(-0.642528\pi\)
−0.432953 + 0.901417i \(0.642528\pi\)
\(24\) 1.21390e46 0.703247
\(25\) 2.30691e46 0.340440
\(26\) 4.14915e47 1.64571
\(27\) −9.71798e47 −1.08865
\(28\) −1.38409e46 −0.00458534
\(29\) 1.54617e49 1.58097 0.790486 0.612480i \(-0.209828\pi\)
0.790486 + 0.612480i \(0.209828\pi\)
\(30\) 3.19025e49 1.04776
\(31\) 1.52983e50 1.67504 0.837521 0.546405i \(-0.184004\pi\)
0.837521 + 0.546405i \(0.184004\pi\)
\(32\) 1.15896e50 0.438072
\(33\) 1.27840e50 0.172365
\(34\) 2.14258e51 1.06266
\(35\) 1.26805e50 0.0238153
\(36\) −1.00734e51 −0.0736281
\(37\) 1.16261e52 0.339372 0.169686 0.985498i \(-0.445725\pi\)
0.169686 + 0.985498i \(0.445725\pi\)
\(38\) −1.39581e53 −1.66754
\(39\) −2.43366e53 −1.21785
\(40\) −4.64301e53 −0.994925
\(41\) 1.50280e54 1.40813 0.704064 0.710137i \(-0.251367\pi\)
0.704064 + 0.710137i \(0.251367\pi\)
\(42\) 4.45371e52 0.0186153
\(43\) 1.43610e54 0.272893 0.136447 0.990647i \(-0.456432\pi\)
0.136447 + 0.990647i \(0.456432\pi\)
\(44\) 5.33717e53 0.0469512
\(45\) 9.22884e54 0.382409
\(46\) 4.82565e55 0.957565
\(47\) 9.41631e55 0.909081 0.454540 0.890726i \(-0.349804\pi\)
0.454540 + 0.890726i \(0.349804\pi\)
\(48\) −2.01328e56 −0.960112
\(49\) −4.18201e56 −0.999577
\(50\) −3.09909e56 −0.376477
\(51\) −1.25671e57 −0.786386
\(52\) −1.01603e57 −0.331737
\(53\) 4.49370e57 0.775109 0.387554 0.921847i \(-0.373320\pi\)
0.387554 + 0.921847i \(0.373320\pi\)
\(54\) 1.30551e58 1.20389
\(55\) −4.88968e57 −0.243854
\(56\) −6.48182e56 −0.0176766
\(57\) 8.18704e58 1.23401
\(58\) −2.07711e59 −1.74833
\(59\) 2.81815e59 1.33789 0.668947 0.743310i \(-0.266745\pi\)
0.668947 + 0.743310i \(0.266745\pi\)
\(60\) −7.81216e58 −0.211205
\(61\) −4.42593e59 −0.687789 −0.343894 0.939008i \(-0.611746\pi\)
−0.343894 + 0.939008i \(0.611746\pi\)
\(62\) −2.05516e60 −1.85235
\(63\) 1.28838e58 0.00679417
\(64\) 2.21365e60 0.688780
\(65\) 9.30840e60 1.72297
\(66\) −1.71739e60 −0.190610
\(67\) 9.71985e60 0.651859 0.325930 0.945394i \(-0.394323\pi\)
0.325930 + 0.945394i \(0.394323\pi\)
\(68\) −5.24666e60 −0.214207
\(69\) −2.83045e61 −0.708617
\(70\) −1.70348e60 −0.0263362
\(71\) −3.66936e61 −0.352725 −0.176362 0.984325i \(-0.556433\pi\)
−0.176362 + 0.984325i \(0.556433\pi\)
\(72\) −4.71748e61 −0.283838
\(73\) −1.52158e61 −0.0576740 −0.0288370 0.999584i \(-0.509180\pi\)
−0.0288370 + 0.999584i \(0.509180\pi\)
\(74\) −1.56184e62 −0.375296
\(75\) 1.81775e62 0.278600
\(76\) 3.41801e62 0.336138
\(77\) −6.82619e60 −0.00433250
\(78\) 3.26936e63 1.34677
\(79\) −2.59876e63 −0.698649 −0.349325 0.937002i \(-0.613589\pi\)
−0.349325 + 0.937002i \(0.613589\pi\)
\(80\) 7.70050e63 1.35833
\(81\) −4.81844e63 −0.560607
\(82\) −2.01885e64 −1.55719
\(83\) −2.25569e64 −1.15921 −0.579607 0.814896i \(-0.696794\pi\)
−0.579607 + 0.814896i \(0.696794\pi\)
\(84\) −1.09061e62 −0.00375243
\(85\) 4.80676e64 1.11255
\(86\) −1.92925e64 −0.301780
\(87\) 1.21832e65 1.29379
\(88\) 2.49944e64 0.180998
\(89\) −2.92327e64 −0.144978 −0.0724892 0.997369i \(-0.523094\pi\)
−0.0724892 + 0.997369i \(0.523094\pi\)
\(90\) −1.23980e65 −0.422889
\(91\) 1.29949e64 0.0306116
\(92\) −1.18169e65 −0.193023
\(93\) 1.20544e66 1.37078
\(94\) −1.26498e66 −1.00531
\(95\) −3.13143e66 −1.74583
\(96\) 9.13215e65 0.358498
\(97\) −8.79797e65 −0.244078 −0.122039 0.992525i \(-0.538943\pi\)
−0.122039 + 0.992525i \(0.538943\pi\)
\(98\) 5.61808e66 1.10539
\(99\) −4.96810e65 −0.0695683
\(100\) 7.58891e65 0.0758891
\(101\) 1.50109e67 1.07558 0.537789 0.843080i \(-0.319260\pi\)
0.537789 + 0.843080i \(0.319260\pi\)
\(102\) 1.68826e67 0.869629
\(103\) −1.56772e67 −0.582398 −0.291199 0.956662i \(-0.594054\pi\)
−0.291199 + 0.956662i \(0.594054\pi\)
\(104\) −4.75814e67 −1.27885
\(105\) 9.99167e65 0.0194893
\(106\) −6.03681e67 −0.857158
\(107\) −2.27147e67 −0.235478 −0.117739 0.993045i \(-0.537565\pi\)
−0.117739 + 0.993045i \(0.537565\pi\)
\(108\) −3.19687e67 −0.242677
\(109\) 2.18578e68 1.21848 0.609240 0.792986i \(-0.291474\pi\)
0.609240 + 0.792986i \(0.291474\pi\)
\(110\) 6.56877e67 0.269668
\(111\) 9.16088e67 0.277727
\(112\) 1.07502e67 0.0241331
\(113\) 2.20699e68 0.367851 0.183926 0.982940i \(-0.441119\pi\)
0.183926 + 0.982940i \(0.441119\pi\)
\(114\) −1.09984e69 −1.36464
\(115\) 1.08261e69 1.00252
\(116\) 5.08635e68 0.352422
\(117\) 9.45768e68 0.491539
\(118\) −3.78588e69 −1.47952
\(119\) 6.71042e67 0.0197663
\(120\) −3.65850e69 −0.814201
\(121\) −5.67026e69 −0.955638
\(122\) 5.94576e69 0.760594
\(123\) 1.18414e70 1.15235
\(124\) 5.03259e69 0.373392
\(125\) 1.34699e70 0.763621
\(126\) −1.73080e68 −0.00751336
\(127\) 1.39984e70 0.466288 0.233144 0.972442i \(-0.425099\pi\)
0.233144 + 0.972442i \(0.425099\pi\)
\(128\) −4.68413e70 −1.19976
\(129\) 1.13159e70 0.223323
\(130\) −1.25048e71 −1.90535
\(131\) 7.06278e70 0.832506 0.416253 0.909249i \(-0.363343\pi\)
0.416253 + 0.909249i \(0.363343\pi\)
\(132\) 4.20547e69 0.0384227
\(133\) −4.37159e69 −0.0310177
\(134\) −1.30576e71 −0.720862
\(135\) 2.92883e71 1.26041
\(136\) −2.45705e71 −0.825774
\(137\) 6.38583e71 1.67911 0.839553 0.543277i \(-0.182817\pi\)
0.839553 + 0.543277i \(0.182817\pi\)
\(138\) 3.80241e71 0.783627
\(139\) −1.22134e72 −1.97625 −0.988126 0.153649i \(-0.950898\pi\)
−0.988126 + 0.153649i \(0.950898\pi\)
\(140\) 4.17142e69 0.00530878
\(141\) 7.41966e71 0.743950
\(142\) 4.92939e71 0.390062
\(143\) −5.01093e71 −0.313445
\(144\) 7.82400e71 0.387512
\(145\) −4.65989e72 −1.83041
\(146\) 2.04409e71 0.0637791
\(147\) −3.29525e72 −0.818008
\(148\) 3.82457e71 0.0756512
\(149\) 1.00850e73 1.59197 0.795987 0.605314i \(-0.206952\pi\)
0.795987 + 0.605314i \(0.206952\pi\)
\(150\) −2.44195e72 −0.308091
\(151\) 5.44915e72 0.550302 0.275151 0.961401i \(-0.411272\pi\)
0.275151 + 0.961401i \(0.411272\pi\)
\(152\) 1.60068e73 1.29582
\(153\) 4.88385e72 0.317394
\(154\) 9.17025e70 0.00479112
\(155\) −4.61064e73 −1.93932
\(156\) −8.00587e72 −0.271478
\(157\) −4.30932e73 −1.17970 −0.589848 0.807514i \(-0.700813\pi\)
−0.589848 + 0.807514i \(0.700813\pi\)
\(158\) 3.49116e73 0.772605
\(159\) 3.54085e73 0.634313
\(160\) −3.49292e73 −0.507188
\(161\) 1.51136e72 0.0178116
\(162\) 6.47306e73 0.619950
\(163\) −3.31839e73 −0.258608 −0.129304 0.991605i \(-0.541274\pi\)
−0.129304 + 0.991605i \(0.541274\pi\)
\(164\) 4.94368e73 0.313893
\(165\) −3.85287e73 −0.199559
\(166\) 3.03028e74 1.28192
\(167\) −2.50202e74 −0.865544 −0.432772 0.901503i \(-0.642464\pi\)
−0.432772 + 0.901503i \(0.642464\pi\)
\(168\) −5.10741e72 −0.0144657
\(169\) 5.23192e74 1.21466
\(170\) −6.45736e74 −1.23032
\(171\) −3.18165e74 −0.498061
\(172\) 4.72427e73 0.0608320
\(173\) 3.99627e74 0.423751 0.211876 0.977297i \(-0.432043\pi\)
0.211876 + 0.977297i \(0.432043\pi\)
\(174\) −1.63668e75 −1.43075
\(175\) −9.70614e72 −0.00700280
\(176\) −4.14536e74 −0.247109
\(177\) 2.22058e75 1.09487
\(178\) 3.92710e74 0.160325
\(179\) 9.62216e74 0.325609 0.162804 0.986658i \(-0.447946\pi\)
0.162804 + 0.986658i \(0.447946\pi\)
\(180\) 3.03596e74 0.0852447
\(181\) 7.00912e75 1.63468 0.817338 0.576159i \(-0.195449\pi\)
0.817338 + 0.576159i \(0.195449\pi\)
\(182\) −1.74572e74 −0.0338520
\(183\) −3.48745e75 −0.562855
\(184\) −5.53393e75 −0.744110
\(185\) −3.50391e75 −0.392916
\(186\) −1.61938e76 −1.51588
\(187\) −2.58759e75 −0.202396
\(188\) 3.09763e75 0.202648
\(189\) 4.08876e74 0.0223935
\(190\) 4.20674e76 1.93063
\(191\) −1.34239e75 −0.0516725 −0.0258362 0.999666i \(-0.508225\pi\)
−0.0258362 + 0.999666i \(0.508225\pi\)
\(192\) 1.74427e76 0.563665
\(193\) −7.13753e76 −1.93811 −0.969054 0.246849i \(-0.920605\pi\)
−0.969054 + 0.246849i \(0.920605\pi\)
\(194\) 1.18191e76 0.269915
\(195\) 7.33463e76 1.41000
\(196\) −1.37573e76 −0.222821
\(197\) 2.98948e75 0.0408297 0.0204149 0.999792i \(-0.493501\pi\)
0.0204149 + 0.999792i \(0.493501\pi\)
\(198\) 6.67411e75 0.0769325
\(199\) −6.66765e76 −0.649224 −0.324612 0.945847i \(-0.605234\pi\)
−0.324612 + 0.945847i \(0.605234\pi\)
\(200\) 3.55395e76 0.292555
\(201\) 7.65884e76 0.533452
\(202\) −2.01656e77 −1.18943
\(203\) −6.50539e75 −0.0325204
\(204\) −4.13415e76 −0.175297
\(205\) −4.52919e77 −1.63029
\(206\) 2.10606e77 0.644048
\(207\) 1.09997e77 0.286006
\(208\) 7.89145e77 1.74596
\(209\) 1.68572e77 0.317603
\(210\) −1.34227e76 −0.0215524
\(211\) 5.45267e76 0.0746701 0.0373351 0.999303i \(-0.488113\pi\)
0.0373351 + 0.999303i \(0.488113\pi\)
\(212\) 1.47827e77 0.172783
\(213\) −2.89130e77 −0.288654
\(214\) 3.05147e77 0.260404
\(215\) −4.32817e77 −0.315948
\(216\) −1.49712e78 −0.935527
\(217\) −6.43663e76 −0.0344554
\(218\) −2.93636e78 −1.34746
\(219\) −1.19895e77 −0.0471978
\(220\) −1.60853e77 −0.0543588
\(221\) 4.92595e78 1.43004
\(222\) −1.23067e78 −0.307125
\(223\) 6.27402e78 1.34689 0.673446 0.739236i \(-0.264813\pi\)
0.673446 + 0.739236i \(0.264813\pi\)
\(224\) −4.87625e76 −0.00901109
\(225\) −7.06414e77 −0.112446
\(226\) −2.96485e78 −0.406790
\(227\) 3.35983e78 0.397604 0.198802 0.980040i \(-0.436295\pi\)
0.198802 + 0.980040i \(0.436295\pi\)
\(228\) 2.69325e78 0.275080
\(229\) −5.16052e78 −0.455203 −0.227601 0.973754i \(-0.573088\pi\)
−0.227601 + 0.973754i \(0.573088\pi\)
\(230\) −1.45437e79 −1.10864
\(231\) −5.37875e76 −0.00354552
\(232\) 2.38198e79 1.35860
\(233\) 2.55175e78 0.126013 0.0630065 0.998013i \(-0.479931\pi\)
0.0630065 + 0.998013i \(0.479931\pi\)
\(234\) −1.27054e79 −0.543571
\(235\) −2.83791e79 −1.05251
\(236\) 9.27071e78 0.298237
\(237\) −2.04772e79 −0.571742
\(238\) −9.01473e77 −0.0218587
\(239\) −4.05778e79 −0.854985 −0.427492 0.904019i \(-0.640603\pi\)
−0.427492 + 0.904019i \(0.640603\pi\)
\(240\) 6.06768e79 1.11159
\(241\) 4.01993e79 0.640689 0.320345 0.947301i \(-0.396201\pi\)
0.320345 + 0.947301i \(0.396201\pi\)
\(242\) 7.61739e79 1.05680
\(243\) 5.21275e79 0.629879
\(244\) −1.45597e79 −0.153318
\(245\) 1.26039e80 1.15728
\(246\) −1.59077e80 −1.27433
\(247\) −3.20908e80 −2.24405
\(248\) 2.35680e80 1.43944
\(249\) −1.77739e80 −0.948647
\(250\) −1.80953e80 −0.844455
\(251\) 1.29030e80 0.526771 0.263385 0.964691i \(-0.415161\pi\)
0.263385 + 0.964691i \(0.415161\pi\)
\(252\) 4.23832e77 0.00151452
\(253\) −5.82794e79 −0.182380
\(254\) −1.88054e80 −0.515647
\(255\) 3.78753e80 0.910457
\(256\) 3.02586e80 0.637984
\(257\) 5.23305e80 0.968268 0.484134 0.874994i \(-0.339135\pi\)
0.484134 + 0.874994i \(0.339135\pi\)
\(258\) −1.52017e80 −0.246963
\(259\) −4.89159e78 −0.00698084
\(260\) 3.06213e80 0.384076
\(261\) −4.73462e80 −0.522190
\(262\) −9.48809e80 −0.920631
\(263\) 9.85079e80 0.841305 0.420652 0.907222i \(-0.361801\pi\)
0.420652 + 0.907222i \(0.361801\pi\)
\(264\) 1.96946e80 0.148120
\(265\) −1.35433e81 −0.897400
\(266\) 5.87277e79 0.0343011
\(267\) −2.30341e80 −0.118644
\(268\) 3.19749e80 0.145309
\(269\) −1.08276e81 −0.434343 −0.217171 0.976134i \(-0.569683\pi\)
−0.217171 + 0.976134i \(0.569683\pi\)
\(270\) −3.93457e81 −1.39384
\(271\) 4.87334e81 1.52530 0.762650 0.646811i \(-0.223898\pi\)
0.762650 + 0.646811i \(0.223898\pi\)
\(272\) 4.07506e81 1.12739
\(273\) 1.02394e80 0.0250511
\(274\) −8.57868e81 −1.85685
\(275\) 3.74277e80 0.0717047
\(276\) −9.31119e80 −0.157961
\(277\) 8.18997e81 1.23086 0.615432 0.788190i \(-0.288981\pi\)
0.615432 + 0.788190i \(0.288981\pi\)
\(278\) 1.64074e82 2.18545
\(279\) −4.68458e81 −0.553261
\(280\) 1.95351e80 0.0204655
\(281\) 1.82919e81 0.170058 0.0850289 0.996378i \(-0.472902\pi\)
0.0850289 + 0.996378i \(0.472902\pi\)
\(282\) −9.96751e81 −0.822700
\(283\) −1.71714e82 −1.25881 −0.629403 0.777079i \(-0.716701\pi\)
−0.629403 + 0.777079i \(0.716701\pi\)
\(284\) −1.20709e81 −0.0786276
\(285\) −2.46743e82 −1.42871
\(286\) 6.73165e81 0.346625
\(287\) −6.32292e80 −0.0289650
\(288\) −3.54894e81 −0.144694
\(289\) −2.11015e81 −0.0766012
\(290\) 6.26007e82 2.02417
\(291\) −6.93243e81 −0.199742
\(292\) −5.00547e80 −0.0128564
\(293\) 4.86284e82 1.11385 0.556923 0.830564i \(-0.311982\pi\)
0.556923 + 0.830564i \(0.311982\pi\)
\(294\) 4.42681e82 0.904598
\(295\) −8.49342e82 −1.54898
\(296\) 1.79108e82 0.291637
\(297\) −1.57666e82 −0.229296
\(298\) −1.35481e83 −1.76049
\(299\) 1.10945e83 1.28862
\(300\) 5.97975e81 0.0621042
\(301\) −6.04229e80 −0.00561338
\(302\) −7.32035e82 −0.608555
\(303\) 1.18280e83 0.880203
\(304\) −2.65475e83 −1.76913
\(305\) 1.33390e83 0.796304
\(306\) −6.56092e82 −0.350992
\(307\) 5.34655e81 0.0256412 0.0128206 0.999918i \(-0.495919\pi\)
0.0128206 + 0.999918i \(0.495919\pi\)
\(308\) −2.24557e80 −0.000965780 0
\(309\) −1.23529e83 −0.476608
\(310\) 6.19390e83 2.14461
\(311\) −4.84522e82 −0.150605 −0.0753027 0.997161i \(-0.523992\pi\)
−0.0753027 + 0.997161i \(0.523992\pi\)
\(312\) −3.74922e83 −1.04655
\(313\) −1.01435e82 −0.0254363 −0.0127182 0.999919i \(-0.504048\pi\)
−0.0127182 + 0.999919i \(0.504048\pi\)
\(314\) 5.78911e83 1.30457
\(315\) −3.88296e81 −0.00786611
\(316\) −8.54901e82 −0.155739
\(317\) 3.02253e83 0.495319 0.247660 0.968847i \(-0.420339\pi\)
0.247660 + 0.968847i \(0.420339\pi\)
\(318\) −4.75675e83 −0.701458
\(319\) 2.50853e83 0.332990
\(320\) −6.67157e83 −0.797451
\(321\) −1.78982e83 −0.192704
\(322\) −2.03035e82 −0.0196970
\(323\) −1.65713e84 −1.44901
\(324\) −1.58510e83 −0.124968
\(325\) −7.12503e83 −0.506634
\(326\) 4.45790e83 0.285983
\(327\) 1.72230e84 0.997148
\(328\) 2.31517e84 1.21007
\(329\) −3.96184e82 −0.0186997
\(330\) 5.17591e83 0.220684
\(331\) 2.27713e84 0.877303 0.438652 0.898657i \(-0.355456\pi\)
0.438652 + 0.898657i \(0.355456\pi\)
\(332\) −7.42042e83 −0.258406
\(333\) −3.56010e83 −0.112094
\(334\) 3.36120e84 0.957166
\(335\) −2.92940e84 −0.754705
\(336\) 8.47071e82 0.0197494
\(337\) −7.83609e84 −1.65386 −0.826928 0.562308i \(-0.809914\pi\)
−0.826928 + 0.562308i \(0.809914\pi\)
\(338\) −7.02852e84 −1.34324
\(339\) 1.73901e84 0.301033
\(340\) 1.58125e84 0.248003
\(341\) 2.48202e84 0.352803
\(342\) 4.27420e84 0.550783
\(343\) 3.51984e83 0.0411311
\(344\) 2.21242e84 0.234509
\(345\) 8.53051e84 0.820418
\(346\) −5.36856e84 −0.468607
\(347\) −1.79418e85 −1.42177 −0.710884 0.703309i \(-0.751705\pi\)
−0.710884 + 0.703309i \(0.751705\pi\)
\(348\) 4.00783e84 0.288406
\(349\) −3.77493e83 −0.0246750 −0.0123375 0.999924i \(-0.503927\pi\)
−0.0123375 + 0.999924i \(0.503927\pi\)
\(350\) 1.30392e83 0.00774409
\(351\) 3.00146e85 1.62011
\(352\) 1.88032e84 0.0922684
\(353\) 1.83957e85 0.820848 0.410424 0.911895i \(-0.365381\pi\)
0.410424 + 0.911895i \(0.365381\pi\)
\(354\) −2.98312e85 −1.21077
\(355\) 1.10588e85 0.408375
\(356\) −9.61652e83 −0.0323179
\(357\) 5.28753e83 0.0161759
\(358\) −1.29263e85 −0.360076
\(359\) −5.72913e85 −1.45353 −0.726766 0.686885i \(-0.758978\pi\)
−0.726766 + 0.686885i \(0.758978\pi\)
\(360\) 1.42177e85 0.328621
\(361\) 6.04782e85 1.27382
\(362\) −9.41601e85 −1.80771
\(363\) −4.46793e85 −0.782050
\(364\) 4.27486e83 0.00682378
\(365\) 4.58580e84 0.0667735
\(366\) 4.68501e85 0.622435
\(367\) 9.37834e85 1.13714 0.568568 0.822636i \(-0.307497\pi\)
0.568568 + 0.822636i \(0.307497\pi\)
\(368\) 9.17811e85 1.01590
\(369\) −4.60182e85 −0.465100
\(370\) 4.70713e85 0.434508
\(371\) −1.89069e84 −0.0159439
\(372\) 3.96547e85 0.305567
\(373\) −8.38977e85 −0.590886 −0.295443 0.955360i \(-0.595467\pi\)
−0.295443 + 0.955360i \(0.595467\pi\)
\(374\) 3.47615e85 0.223821
\(375\) 1.06137e86 0.624913
\(376\) 1.45065e86 0.781212
\(377\) −4.77544e86 −2.35276
\(378\) −5.49281e84 −0.0247639
\(379\) −3.46586e86 −1.43020 −0.715102 0.699020i \(-0.753620\pi\)
−0.715102 + 0.699020i \(0.753620\pi\)
\(380\) −1.03013e86 −0.389172
\(381\) 1.10302e86 0.381588
\(382\) 1.80335e85 0.0571423
\(383\) 4.41090e86 1.28047 0.640234 0.768180i \(-0.278837\pi\)
0.640234 + 0.768180i \(0.278837\pi\)
\(384\) −3.69090e86 −0.981830
\(385\) 2.05730e84 0.00501606
\(386\) 9.58850e86 2.14327
\(387\) −4.39758e85 −0.0901357
\(388\) −2.89422e85 −0.0544087
\(389\) 2.14221e86 0.369446 0.184723 0.982791i \(-0.440861\pi\)
0.184723 + 0.982791i \(0.440861\pi\)
\(390\) −9.85329e86 −1.55925
\(391\) 5.72910e86 0.832080
\(392\) −6.44267e86 −0.858980
\(393\) 5.56518e86 0.681285
\(394\) −4.01604e85 −0.0451518
\(395\) 7.83223e86 0.808878
\(396\) −1.63433e85 −0.0155078
\(397\) −1.53266e87 −1.33649 −0.668244 0.743942i \(-0.732954\pi\)
−0.668244 + 0.743942i \(0.732954\pi\)
\(398\) 8.95727e86 0.717948
\(399\) −3.44463e85 −0.0253835
\(400\) −5.89428e86 −0.399412
\(401\) 1.77468e87 1.10607 0.553035 0.833158i \(-0.313470\pi\)
0.553035 + 0.833158i \(0.313470\pi\)
\(402\) −1.02888e87 −0.589920
\(403\) −4.72497e87 −2.49276
\(404\) 4.93807e86 0.239762
\(405\) 1.45220e87 0.649056
\(406\) 8.73929e85 0.0359628
\(407\) 1.88624e86 0.0714798
\(408\) −1.93606e87 −0.675776
\(409\) 6.64558e86 0.213699 0.106849 0.994275i \(-0.465924\pi\)
0.106849 + 0.994275i \(0.465924\pi\)
\(410\) 6.08447e87 1.80287
\(411\) 5.03177e87 1.37410
\(412\) −5.15723e86 −0.129825
\(413\) −1.18571e86 −0.0275203
\(414\) −1.47769e87 −0.316281
\(415\) 6.79827e87 1.34211
\(416\) −3.57953e87 −0.651928
\(417\) −9.62368e87 −1.61727
\(418\) −2.26459e87 −0.351223
\(419\) −7.12912e87 −1.02063 −0.510313 0.859989i \(-0.670470\pi\)
−0.510313 + 0.859989i \(0.670470\pi\)
\(420\) 3.28691e85 0.00434446
\(421\) 1.54353e87 0.188393 0.0941965 0.995554i \(-0.469972\pi\)
0.0941965 + 0.995554i \(0.469972\pi\)
\(422\) −7.32508e86 −0.0825744
\(423\) −2.88343e87 −0.300266
\(424\) 6.92286e87 0.666084
\(425\) −3.67929e87 −0.327141
\(426\) 3.88416e87 0.319209
\(427\) 1.86218e86 0.0141477
\(428\) −7.47232e86 −0.0524915
\(429\) −3.94840e87 −0.256509
\(430\) 5.81444e87 0.349393
\(431\) 2.09290e88 1.16348 0.581742 0.813373i \(-0.302371\pi\)
0.581742 + 0.813373i \(0.302371\pi\)
\(432\) 2.48300e88 1.27723
\(433\) −1.32958e87 −0.0632951 −0.0316476 0.999499i \(-0.510075\pi\)
−0.0316476 + 0.999499i \(0.510075\pi\)
\(434\) 8.64692e86 0.0381027
\(435\) −3.67180e88 −1.49792
\(436\) 7.19044e87 0.271618
\(437\) −3.73230e88 −1.30571
\(438\) 1.61065e87 0.0521939
\(439\) 3.72682e88 1.11886 0.559432 0.828876i \(-0.311019\pi\)
0.559432 + 0.828876i \(0.311019\pi\)
\(440\) −7.53290e87 −0.209555
\(441\) 1.28060e88 0.330157
\(442\) −6.61748e88 −1.58142
\(443\) 3.13151e88 0.693793 0.346896 0.937904i \(-0.387236\pi\)
0.346896 + 0.937904i \(0.387236\pi\)
\(444\) 3.01361e87 0.0619094
\(445\) 8.81023e87 0.167852
\(446\) −8.42847e88 −1.48947
\(447\) 7.94656e88 1.30280
\(448\) −9.31377e86 −0.0141681
\(449\) −5.09792e88 −0.719683 −0.359841 0.933014i \(-0.617169\pi\)
−0.359841 + 0.933014i \(0.617169\pi\)
\(450\) 9.48991e87 0.124349
\(451\) 2.43817e88 0.296585
\(452\) 7.26021e87 0.0819996
\(453\) 4.29371e88 0.450342
\(454\) −4.51357e88 −0.439693
\(455\) −3.91644e87 −0.0354413
\(456\) 1.26127e89 1.06044
\(457\) 4.22735e88 0.330275 0.165137 0.986271i \(-0.447193\pi\)
0.165137 + 0.986271i \(0.447193\pi\)
\(458\) 6.93261e88 0.503388
\(459\) 1.54992e89 1.04613
\(460\) 3.56140e88 0.223477
\(461\) −2.47810e89 −1.44590 −0.722949 0.690901i \(-0.757214\pi\)
−0.722949 + 0.690901i \(0.757214\pi\)
\(462\) 7.22577e86 0.00392083
\(463\) −8.10015e88 −0.408818 −0.204409 0.978886i \(-0.565527\pi\)
−0.204409 + 0.978886i \(0.565527\pi\)
\(464\) −3.95055e89 −1.85483
\(465\) −3.63299e89 −1.58705
\(466\) −3.42801e88 −0.139352
\(467\) 3.15046e89 1.19195 0.595977 0.803002i \(-0.296765\pi\)
0.595977 + 0.803002i \(0.296765\pi\)
\(468\) 3.11124e88 0.109572
\(469\) −4.08955e87 −0.0134087
\(470\) 3.81243e89 1.16392
\(471\) −3.39556e89 −0.965410
\(472\) 4.34155e89 1.14971
\(473\) 2.32996e88 0.0574777
\(474\) 2.75089e89 0.632264
\(475\) 2.39692e89 0.513356
\(476\) 2.20749e87 0.00440622
\(477\) −1.37605e89 −0.256016
\(478\) 5.45119e89 0.945489
\(479\) −2.89428e89 −0.468059 −0.234029 0.972230i \(-0.575191\pi\)
−0.234029 + 0.972230i \(0.575191\pi\)
\(480\) −2.75228e89 −0.415060
\(481\) −3.59079e89 −0.505045
\(482\) −5.40035e89 −0.708510
\(483\) 1.19089e88 0.0145762
\(484\) −1.86532e89 −0.213026
\(485\) 2.65156e89 0.282587
\(486\) −7.00277e89 −0.696554
\(487\) 1.75391e90 1.62850 0.814250 0.580514i \(-0.197148\pi\)
0.814250 + 0.580514i \(0.197148\pi\)
\(488\) −6.81845e89 −0.591047
\(489\) −2.61475e89 −0.211633
\(490\) −1.69319e90 −1.27979
\(491\) 8.85050e89 0.624795 0.312398 0.949951i \(-0.398868\pi\)
0.312398 + 0.949951i \(0.398868\pi\)
\(492\) 3.89541e89 0.256876
\(493\) −2.46599e90 −1.51921
\(494\) 4.31105e90 2.48159
\(495\) 1.49730e89 0.0805444
\(496\) −3.90879e90 −1.96520
\(497\) 1.54386e88 0.00725550
\(498\) 2.38773e90 1.04907
\(499\) 4.21399e90 1.73111 0.865555 0.500813i \(-0.166966\pi\)
0.865555 + 0.500813i \(0.166966\pi\)
\(500\) 4.43111e89 0.170223
\(501\) −1.97149e90 −0.708321
\(502\) −1.73338e90 −0.582532
\(503\) 2.77704e90 0.873081 0.436540 0.899685i \(-0.356204\pi\)
0.436540 + 0.899685i \(0.356204\pi\)
\(504\) 1.98484e88 0.00583852
\(505\) −4.52404e90 −1.24528
\(506\) 7.82921e89 0.201686
\(507\) 4.12253e90 0.994026
\(508\) 4.60498e89 0.103943
\(509\) −2.09998e90 −0.443782 −0.221891 0.975071i \(-0.571223\pi\)
−0.221891 + 0.975071i \(0.571223\pi\)
\(510\) −5.08813e90 −1.00683
\(511\) 6.40195e87 0.00118635
\(512\) 2.84765e90 0.494245
\(513\) −1.00972e91 −1.64160
\(514\) −7.03004e90 −1.07076
\(515\) 4.72483e90 0.674285
\(516\) 3.72253e89 0.0497821
\(517\) 1.52772e90 0.191474
\(518\) 6.57133e88 0.00771980
\(519\) 3.14890e90 0.346778
\(520\) 1.43402e91 1.48062
\(521\) 3.31742e90 0.321171 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(522\) 6.36046e90 0.577466
\(523\) 1.46798e91 1.25001 0.625004 0.780622i \(-0.285097\pi\)
0.625004 + 0.780622i \(0.285097\pi\)
\(524\) 2.32340e90 0.185578
\(525\) −7.64803e88 −0.00573077
\(526\) −1.32335e91 −0.930361
\(527\) −2.43992e91 −1.60961
\(528\) −3.26637e90 −0.202222
\(529\) −4.30593e90 −0.250208
\(530\) 1.81939e91 0.992395
\(531\) −8.62964e90 −0.441902
\(532\) −1.43810e89 −0.00691431
\(533\) −4.64149e91 −2.09554
\(534\) 3.09439e90 0.131203
\(535\) 6.84581e90 0.272630
\(536\) 1.49741e91 0.560171
\(537\) 7.58186e90 0.266463
\(538\) 1.45458e91 0.480320
\(539\) −6.78495e90 −0.210535
\(540\) 9.63482e90 0.280965
\(541\) 5.22060e91 1.43091 0.715454 0.698660i \(-0.246220\pi\)
0.715454 + 0.698660i \(0.246220\pi\)
\(542\) −6.54681e91 −1.68676
\(543\) 5.52290e91 1.33774
\(544\) −1.84843e91 −0.420960
\(545\) −6.58757e91 −1.41072
\(546\) −1.37556e90 −0.0277029
\(547\) 2.90185e91 0.549667 0.274834 0.961492i \(-0.411377\pi\)
0.274834 + 0.961492i \(0.411377\pi\)
\(548\) 2.10071e91 0.374298
\(549\) 1.35529e91 0.227174
\(550\) −5.02800e90 −0.0792950
\(551\) 1.60650e92 2.38398
\(552\) −4.36051e91 −0.608945
\(553\) 1.09341e90 0.0143711
\(554\) −1.10024e92 −1.36116
\(555\) −2.76093e91 −0.321544
\(556\) −4.01779e91 −0.440536
\(557\) −5.90102e91 −0.609226 −0.304613 0.952476i \(-0.598527\pi\)
−0.304613 + 0.952476i \(0.598527\pi\)
\(558\) 6.29323e91 0.611826
\(559\) −4.43549e91 −0.406113
\(560\) −3.23993e90 −0.0279406
\(561\) −2.03891e91 −0.165632
\(562\) −2.45732e91 −0.188059
\(563\) −8.31074e91 −0.599251 −0.299625 0.954057i \(-0.596862\pi\)
−0.299625 + 0.954057i \(0.596862\pi\)
\(564\) 2.44080e91 0.165838
\(565\) −6.65149e91 −0.425888
\(566\) 2.30679e92 1.39206
\(567\) 2.02732e90 0.0115316
\(568\) −5.65290e91 −0.303112
\(569\) 7.52878e90 0.0380596 0.0190298 0.999819i \(-0.493942\pi\)
0.0190298 + 0.999819i \(0.493942\pi\)
\(570\) 3.31473e92 1.57994
\(571\) 1.98233e92 0.890979 0.445489 0.895287i \(-0.353030\pi\)
0.445489 + 0.895287i \(0.353030\pi\)
\(572\) −1.64842e91 −0.0698716
\(573\) −1.05774e91 −0.0422864
\(574\) 8.49416e90 0.0320311
\(575\) −8.28673e91 −0.294789
\(576\) −6.77857e91 −0.227502
\(577\) −2.56912e91 −0.0813570 −0.0406785 0.999172i \(-0.512952\pi\)
−0.0406785 + 0.999172i \(0.512952\pi\)
\(578\) 2.83476e91 0.0847098
\(579\) −5.62407e92 −1.58606
\(580\) −1.53294e92 −0.408025
\(581\) 9.49064e90 0.0238449
\(582\) 9.31298e91 0.220886
\(583\) 7.29065e91 0.163256
\(584\) −2.34411e91 −0.0495618
\(585\) −2.85039e92 −0.569091
\(586\) −6.53271e92 −1.23175
\(587\) −3.55629e92 −0.633317 −0.316658 0.948540i \(-0.602561\pi\)
−0.316658 + 0.948540i \(0.602561\pi\)
\(588\) −1.08402e92 −0.182346
\(589\) 1.58952e93 2.52583
\(590\) 1.14100e93 1.71294
\(591\) 2.35558e91 0.0334132
\(592\) −2.97053e92 −0.398160
\(593\) 1.39162e92 0.176274 0.0881368 0.996108i \(-0.471909\pi\)
0.0881368 + 0.996108i \(0.471909\pi\)
\(594\) 2.11807e92 0.253568
\(595\) −2.02241e91 −0.0228850
\(596\) 3.31761e92 0.354875
\(597\) −5.25383e92 −0.531295
\(598\) −1.49043e93 −1.42502
\(599\) 7.02635e91 0.0635230 0.0317615 0.999495i \(-0.489888\pi\)
0.0317615 + 0.999495i \(0.489888\pi\)
\(600\) 2.80037e92 0.239413
\(601\) 1.73639e92 0.140395 0.0701977 0.997533i \(-0.477637\pi\)
0.0701977 + 0.997533i \(0.477637\pi\)
\(602\) 8.11717e90 0.00620758
\(603\) −2.97638e92 −0.215307
\(604\) 1.79258e92 0.122671
\(605\) 1.70892e93 1.10641
\(606\) −1.58896e93 −0.973377
\(607\) 8.53328e91 0.0494646 0.0247323 0.999694i \(-0.492127\pi\)
0.0247323 + 0.999694i \(0.492127\pi\)
\(608\) 1.20419e93 0.660577
\(609\) −5.12597e91 −0.0266132
\(610\) −1.79195e93 −0.880596
\(611\) −2.90828e93 −1.35287
\(612\) 1.60661e92 0.0707520
\(613\) 1.00190e93 0.417732 0.208866 0.977944i \(-0.433023\pi\)
0.208866 + 0.977944i \(0.433023\pi\)
\(614\) −7.18251e91 −0.0283554
\(615\) −3.56881e93 −1.33416
\(616\) −1.05162e91 −0.00372311
\(617\) 5.41310e93 1.81507 0.907534 0.419978i \(-0.137962\pi\)
0.907534 + 0.419978i \(0.137962\pi\)
\(618\) 1.65949e93 0.527059
\(619\) 1.39465e93 0.419595 0.209797 0.977745i \(-0.432720\pi\)
0.209797 + 0.977745i \(0.432720\pi\)
\(620\) −1.51674e93 −0.432303
\(621\) 3.49083e93 0.942671
\(622\) 6.50903e92 0.166548
\(623\) 1.22994e91 0.00298219
\(624\) 6.21813e93 1.42882
\(625\) −5.62281e93 −1.22454
\(626\) 1.36268e92 0.0281289
\(627\) 1.32828e93 0.259912
\(628\) −1.41761e93 −0.262972
\(629\) −1.85425e93 −0.326115
\(630\) 5.21635e91 0.00869877
\(631\) −1.08460e94 −1.71508 −0.857541 0.514416i \(-0.828009\pi\)
−0.857541 + 0.514416i \(0.828009\pi\)
\(632\) −4.00358e93 −0.600380
\(633\) 4.29648e92 0.0611066
\(634\) −4.06044e93 −0.547751
\(635\) −4.21888e93 −0.539856
\(636\) 1.16481e93 0.141398
\(637\) 1.29164e94 1.48755
\(638\) −3.36994e93 −0.368239
\(639\) 1.12362e93 0.116504
\(640\) 1.41172e94 1.38905
\(641\) −1.43305e94 −1.33819 −0.669095 0.743177i \(-0.733318\pi\)
−0.669095 + 0.743177i \(0.733318\pi\)
\(642\) 2.40443e93 0.213103
\(643\) 1.53129e94 1.28822 0.644109 0.764934i \(-0.277228\pi\)
0.644109 + 0.764934i \(0.277228\pi\)
\(644\) 4.97185e91 0.00397047
\(645\) −3.41042e93 −0.258558
\(646\) 2.22618e94 1.60240
\(647\) −1.58467e94 −1.08304 −0.541521 0.840687i \(-0.682151\pi\)
−0.541521 + 0.840687i \(0.682151\pi\)
\(648\) −7.42315e93 −0.481754
\(649\) 4.57221e93 0.281792
\(650\) 9.57172e93 0.560264
\(651\) −5.07180e92 −0.0281967
\(652\) −1.09163e93 −0.0576477
\(653\) 1.67109e94 0.838317 0.419159 0.907913i \(-0.362325\pi\)
0.419159 + 0.907913i \(0.362325\pi\)
\(654\) −2.31373e94 −1.10270
\(655\) −2.12860e94 −0.963854
\(656\) −3.83974e94 −1.65205
\(657\) 4.65934e92 0.0190495
\(658\) 5.32230e92 0.0206791
\(659\) 2.14450e94 0.791888 0.395944 0.918275i \(-0.370417\pi\)
0.395944 + 0.918275i \(0.370417\pi\)
\(660\) −1.26746e93 −0.0444848
\(661\) 4.49680e94 1.50022 0.750109 0.661314i \(-0.230001\pi\)
0.750109 + 0.661314i \(0.230001\pi\)
\(662\) −3.05908e94 −0.970170
\(663\) 3.88144e94 1.17028
\(664\) −3.47505e94 −0.996162
\(665\) 1.31752e93 0.0359115
\(666\) 4.78262e93 0.123959
\(667\) −5.55405e94 −1.36897
\(668\) −8.23076e93 −0.192943
\(669\) 4.94366e94 1.10223
\(670\) 3.93533e94 0.834595
\(671\) −7.18070e93 −0.144865
\(672\) −3.84228e92 −0.00737426
\(673\) −4.87646e94 −0.890431 −0.445216 0.895423i \(-0.646873\pi\)
−0.445216 + 0.895423i \(0.646873\pi\)
\(674\) 1.05269e95 1.82892
\(675\) −2.24185e94 −0.370621
\(676\) 1.72112e94 0.270767
\(677\) −8.08569e93 −0.121059 −0.0605294 0.998166i \(-0.519279\pi\)
−0.0605294 + 0.998166i \(0.519279\pi\)
\(678\) −2.33618e94 −0.332898
\(679\) 3.70168e92 0.00502066
\(680\) 7.40514e94 0.956060
\(681\) 2.64741e94 0.325381
\(682\) −3.33432e94 −0.390149
\(683\) 5.83902e93 0.0650499 0.0325249 0.999471i \(-0.489645\pi\)
0.0325249 + 0.999471i \(0.489645\pi\)
\(684\) −1.04665e94 −0.111025
\(685\) −1.92458e95 −1.94403
\(686\) −4.72853e93 −0.0454850
\(687\) −4.06628e94 −0.372517
\(688\) −3.66932e94 −0.320165
\(689\) −1.38791e95 −1.15350
\(690\) −1.14598e95 −0.907263
\(691\) 9.45504e94 0.713098 0.356549 0.934277i \(-0.383953\pi\)
0.356549 + 0.934277i \(0.383953\pi\)
\(692\) 1.31463e94 0.0944605
\(693\) 2.09029e92 0.00143101
\(694\) 2.41029e95 1.57227
\(695\) 3.68092e95 2.28805
\(696\) 1.87690e95 1.11181
\(697\) −2.39682e95 −1.35312
\(698\) 5.07122e93 0.0272870
\(699\) 2.01067e94 0.103123
\(700\) −3.19298e92 −0.00156103
\(701\) 2.89282e95 1.34824 0.674122 0.738620i \(-0.264522\pi\)
0.674122 + 0.738620i \(0.264522\pi\)
\(702\) −4.03214e95 −1.79160
\(703\) 1.20797e95 0.511746
\(704\) 3.59146e94 0.145073
\(705\) −2.23616e95 −0.861325
\(706\) −2.47126e95 −0.907739
\(707\) −6.31573e93 −0.0221245
\(708\) 7.30493e94 0.244063
\(709\) 1.32934e95 0.423632 0.211816 0.977310i \(-0.432062\pi\)
0.211816 + 0.977310i \(0.432062\pi\)
\(710\) −1.48564e95 −0.451604
\(711\) 7.95784e94 0.230762
\(712\) −4.50350e94 −0.124586
\(713\) −5.49535e95 −1.45043
\(714\) −7.10323e93 −0.0178882
\(715\) 1.51021e95 0.362898
\(716\) 3.16535e94 0.0725831
\(717\) −3.19736e95 −0.699680
\(718\) 7.69647e95 1.60740
\(719\) 4.51429e95 0.899853 0.449927 0.893065i \(-0.351450\pi\)
0.449927 + 0.893065i \(0.351450\pi\)
\(720\) −2.35802e95 −0.448651
\(721\) 6.59604e93 0.0119799
\(722\) −8.12460e95 −1.40866
\(723\) 3.16754e95 0.524311
\(724\) 2.30575e95 0.364394
\(725\) 3.56687e95 0.538226
\(726\) 6.00219e95 0.864834
\(727\) −8.14098e95 −1.12014 −0.560072 0.828444i \(-0.689227\pi\)
−0.560072 + 0.828444i \(0.689227\pi\)
\(728\) 2.00195e94 0.0263059
\(729\) 8.57458e95 1.07607
\(730\) −6.16053e94 −0.0738418
\(731\) −2.29044e95 −0.262233
\(732\) −1.14725e95 −0.125469
\(733\) 4.16267e95 0.434899 0.217450 0.976072i \(-0.430226\pi\)
0.217450 + 0.976072i \(0.430226\pi\)
\(734\) −1.25988e96 −1.25751
\(735\) 9.93132e95 0.947068
\(736\) −4.16316e95 −0.379329
\(737\) 1.57696e95 0.137297
\(738\) 6.18205e95 0.514333
\(739\) −7.08509e95 −0.563322 −0.281661 0.959514i \(-0.590885\pi\)
−0.281661 + 0.959514i \(0.590885\pi\)
\(740\) −1.15266e95 −0.0875869
\(741\) −2.52862e96 −1.83642
\(742\) 2.53994e94 0.0176316
\(743\) 2.43728e95 0.161726 0.0808631 0.996725i \(-0.474232\pi\)
0.0808631 + 0.996725i \(0.474232\pi\)
\(744\) 1.85706e96 1.17797
\(745\) −3.03945e96 −1.84315
\(746\) 1.12708e96 0.653435
\(747\) 6.90729e95 0.382885
\(748\) −8.51226e94 −0.0451171
\(749\) 9.55701e93 0.00484375
\(750\) −1.42584e96 −0.691063
\(751\) 2.39345e96 1.10940 0.554698 0.832052i \(-0.312834\pi\)
0.554698 + 0.832052i \(0.312834\pi\)
\(752\) −2.40592e96 −1.06656
\(753\) 1.01670e96 0.431085
\(754\) 6.41529e96 2.60181
\(755\) −1.64228e96 −0.637126
\(756\) 1.34506e94 0.00499184
\(757\) 3.70408e96 1.31513 0.657565 0.753398i \(-0.271586\pi\)
0.657565 + 0.753398i \(0.271586\pi\)
\(758\) 4.65602e96 1.58160
\(759\) −4.59217e95 −0.149251
\(760\) −4.82418e96 −1.50027
\(761\) −3.66225e96 −1.08984 −0.544919 0.838489i \(-0.683440\pi\)
−0.544919 + 0.838489i \(0.683440\pi\)
\(762\) −1.48178e96 −0.421981
\(763\) −9.19650e94 −0.0250640
\(764\) −4.41597e94 −0.0115186
\(765\) −1.47191e96 −0.367471
\(766\) −5.92558e96 −1.41601
\(767\) −8.70403e96 −1.99102
\(768\) 2.38425e96 0.522096
\(769\) 5.83109e96 1.22241 0.611206 0.791472i \(-0.290685\pi\)
0.611206 + 0.791472i \(0.290685\pi\)
\(770\) −2.76376e94 −0.00554703
\(771\) 4.12343e96 0.792386
\(772\) −2.34799e96 −0.432033
\(773\) 2.14263e96 0.377515 0.188757 0.982024i \(-0.439554\pi\)
0.188757 + 0.982024i \(0.439554\pi\)
\(774\) 5.90768e95 0.0996770
\(775\) 3.52917e96 0.570251
\(776\) −1.35539e96 −0.209747
\(777\) −3.85437e94 −0.00571280
\(778\) −2.87783e96 −0.408553
\(779\) 1.56144e97 2.12334
\(780\) 2.41283e96 0.314310
\(781\) −5.95323e95 −0.0742921
\(782\) −7.69643e96 −0.920159
\(783\) −1.50256e97 −1.72113
\(784\) 1.06853e97 1.17273
\(785\) 1.29876e97 1.36582
\(786\) −7.47622e96 −0.753402
\(787\) −9.20529e96 −0.888964 −0.444482 0.895788i \(-0.646612\pi\)
−0.444482 + 0.895788i \(0.646612\pi\)
\(788\) 9.83432e94 0.00910156
\(789\) 7.76201e96 0.688485
\(790\) −1.05218e97 −0.894501
\(791\) −9.28573e94 −0.00756666
\(792\) −7.65371e95 −0.0597831
\(793\) 1.36698e97 1.02355
\(794\) 2.05897e97 1.47796
\(795\) −1.06715e97 −0.734391
\(796\) −2.19342e96 −0.144722
\(797\) −2.70098e97 −1.70871 −0.854355 0.519690i \(-0.826047\pi\)
−0.854355 + 0.519690i \(0.826047\pi\)
\(798\) 4.62749e95 0.0280704
\(799\) −1.50181e97 −0.873569
\(800\) 2.67363e96 0.149137
\(801\) 8.95153e95 0.0478859
\(802\) −2.38409e97 −1.22315
\(803\) −2.46864e95 −0.0121475
\(804\) 2.51949e96 0.118914
\(805\) −4.55499e95 −0.0206218
\(806\) 6.34749e97 2.75663
\(807\) −8.53173e96 −0.355446
\(808\) 2.31254e97 0.924290
\(809\) 6.43872e96 0.246902 0.123451 0.992351i \(-0.460604\pi\)
0.123451 + 0.992351i \(0.460604\pi\)
\(810\) −1.95087e97 −0.717762
\(811\) −3.69417e97 −1.30412 −0.652061 0.758166i \(-0.726095\pi\)
−0.652061 + 0.758166i \(0.726095\pi\)
\(812\) −2.14004e95 −0.00724929
\(813\) 3.83999e97 1.24824
\(814\) −2.53396e96 −0.0790463
\(815\) 1.00011e97 0.299410
\(816\) 3.21098e97 0.922607
\(817\) 1.49214e97 0.411501
\(818\) −8.92763e96 −0.236320
\(819\) −3.97925e95 −0.0101109
\(820\) −1.48994e97 −0.363417
\(821\) 9.41677e96 0.220499 0.110249 0.993904i \(-0.464835\pi\)
0.110249 + 0.993904i \(0.464835\pi\)
\(822\) −6.75964e97 −1.51956
\(823\) −1.85526e97 −0.400415 −0.200208 0.979754i \(-0.564162\pi\)
−0.200208 + 0.979754i \(0.564162\pi\)
\(824\) −2.41517e97 −0.500480
\(825\) 2.94914e96 0.0586798
\(826\) 1.59288e96 0.0304335
\(827\) −8.33671e97 −1.52954 −0.764769 0.644304i \(-0.777147\pi\)
−0.764769 + 0.644304i \(0.777147\pi\)
\(828\) 3.61852e96 0.0637550
\(829\) 5.04318e97 0.853351 0.426675 0.904405i \(-0.359685\pi\)
0.426675 + 0.904405i \(0.359685\pi\)
\(830\) −9.13274e97 −1.48418
\(831\) 6.45336e97 1.00728
\(832\) −6.83700e97 −1.02502
\(833\) 6.66989e97 0.960530
\(834\) 1.29284e98 1.78847
\(835\) 7.54066e97 1.00210
\(836\) 5.54542e96 0.0707986
\(837\) −1.48668e98 −1.82354
\(838\) 9.57721e97 1.12866
\(839\) 1.80988e97 0.204939 0.102469 0.994736i \(-0.467326\pi\)
0.102469 + 0.994736i \(0.467326\pi\)
\(840\) 1.53929e96 0.0167480
\(841\) 1.43418e98 1.49947
\(842\) −2.07357e97 −0.208335
\(843\) 1.44132e97 0.139167
\(844\) 1.79374e96 0.0166451
\(845\) −1.57681e98 −1.40631
\(846\) 3.87358e97 0.332051
\(847\) 2.38572e96 0.0196574
\(848\) −1.14817e98 −0.909376
\(849\) −1.35303e98 −1.03015
\(850\) 4.94273e97 0.361770
\(851\) −4.17625e97 −0.293864
\(852\) −9.51136e96 −0.0643452
\(853\) −6.65760e95 −0.00433037 −0.00216519 0.999998i \(-0.500689\pi\)
−0.00216519 + 0.999998i \(0.500689\pi\)
\(854\) −2.50163e96 −0.0156453
\(855\) 9.58895e97 0.576642
\(856\) −3.49935e97 −0.202356
\(857\) 1.10050e97 0.0611976 0.0305988 0.999532i \(-0.490259\pi\)
0.0305988 + 0.999532i \(0.490259\pi\)
\(858\) 5.30426e97 0.283662
\(859\) 1.29581e98 0.666457 0.333228 0.942846i \(-0.391862\pi\)
0.333228 + 0.942846i \(0.391862\pi\)
\(860\) −1.42382e97 −0.0704297
\(861\) −4.98219e96 −0.0237036
\(862\) −2.81159e98 −1.28665
\(863\) 1.83648e98 0.808398 0.404199 0.914671i \(-0.367550\pi\)
0.404199 + 0.914671i \(0.367550\pi\)
\(864\) −1.12628e98 −0.476909
\(865\) −1.20441e98 −0.490608
\(866\) 1.78615e97 0.0699952
\(867\) −1.66271e97 −0.0626869
\(868\) −2.11742e96 −0.00768063
\(869\) −4.21627e97 −0.147152
\(870\) 4.93267e98 1.65648
\(871\) −3.00204e98 −0.970081
\(872\) 3.36734e98 1.04709
\(873\) 2.69408e97 0.0806183
\(874\) 5.01394e98 1.44393
\(875\) −5.66734e96 −0.0157076
\(876\) −3.94410e96 −0.0105211
\(877\) −8.00025e96 −0.0205408 −0.0102704 0.999947i \(-0.503269\pi\)
−0.0102704 + 0.999947i \(0.503269\pi\)
\(878\) −5.00658e98 −1.23730
\(879\) 3.83172e98 0.911520
\(880\) 1.24934e98 0.286096
\(881\) −2.46360e98 −0.543096 −0.271548 0.962425i \(-0.587536\pi\)
−0.271548 + 0.962425i \(0.587536\pi\)
\(882\) −1.72035e98 −0.365106
\(883\) −8.44617e98 −1.72574 −0.862872 0.505423i \(-0.831336\pi\)
−0.862872 + 0.505423i \(0.831336\pi\)
\(884\) 1.62046e98 0.318778
\(885\) −6.69246e98 −1.26761
\(886\) −4.20685e98 −0.767234
\(887\) 4.82704e98 0.847695 0.423848 0.905734i \(-0.360679\pi\)
0.423848 + 0.905734i \(0.360679\pi\)
\(888\) 1.41130e98 0.238662
\(889\) −5.88972e96 −0.00959148
\(890\) −1.18356e98 −0.185620
\(891\) −7.81752e97 −0.118077
\(892\) 2.06393e98 0.300243
\(893\) 9.78372e98 1.37082
\(894\) −1.06753e99 −1.44071
\(895\) −2.89996e98 −0.376981
\(896\) 1.97081e97 0.0246790
\(897\) 8.74203e98 1.05455
\(898\) 6.84851e98 0.795864
\(899\) 2.36537e99 2.64819
\(900\) −2.32385e97 −0.0250659
\(901\) −7.16701e98 −0.744830
\(902\) −3.27542e98 −0.327980
\(903\) −4.76108e96 −0.00459373
\(904\) 3.40002e98 0.316110
\(905\) −2.11243e99 −1.89258
\(906\) −5.76813e98 −0.498013
\(907\) 1.79940e99 1.49722 0.748608 0.663012i \(-0.230722\pi\)
0.748608 + 0.663012i \(0.230722\pi\)
\(908\) 1.10526e98 0.0886320
\(909\) −4.59659e98 −0.355260
\(910\) 5.26131e97 0.0391929
\(911\) 1.49982e98 0.107690 0.0538449 0.998549i \(-0.482852\pi\)
0.0538449 + 0.998549i \(0.482852\pi\)
\(912\) −2.09183e99 −1.44777
\(913\) −3.65967e98 −0.244158
\(914\) −5.67899e98 −0.365236
\(915\) 1.05106e99 0.651658
\(916\) −1.69763e98 −0.101472
\(917\) −2.97161e97 −0.0171245
\(918\) −2.08215e99 −1.15686
\(919\) −2.19761e99 −1.17728 −0.588641 0.808394i \(-0.700337\pi\)
−0.588641 + 0.808394i \(0.700337\pi\)
\(920\) 1.66783e99 0.861511
\(921\) 4.21286e97 0.0209836
\(922\) 3.32906e99 1.59895
\(923\) 1.13330e99 0.524916
\(924\) −1.76942e96 −0.000790350 0
\(925\) 2.68204e98 0.115536
\(926\) 1.08817e99 0.452093
\(927\) 4.80060e98 0.192364
\(928\) 1.79196e99 0.692580
\(929\) −4.06848e99 −1.51672 −0.758361 0.651835i \(-0.774000\pi\)
−0.758361 + 0.651835i \(0.774000\pi\)
\(930\) 4.88054e99 1.75505
\(931\) −4.34519e99 −1.50728
\(932\) 8.39436e97 0.0280902
\(933\) −3.81783e98 −0.123248
\(934\) −4.23231e99 −1.31813
\(935\) 7.79856e98 0.234329
\(936\) 1.45702e99 0.422401
\(937\) 4.26633e99 1.19338 0.596689 0.802473i \(-0.296483\pi\)
0.596689 + 0.802473i \(0.296483\pi\)
\(938\) 5.49388e97 0.0148280
\(939\) −7.99269e97 −0.0208159
\(940\) −9.33573e98 −0.234620
\(941\) 5.86101e99 1.42141 0.710706 0.703489i \(-0.248376\pi\)
0.710706 + 0.703489i \(0.248376\pi\)
\(942\) 4.56158e99 1.06760
\(943\) −5.39826e99 −1.21931
\(944\) −7.20053e99 −1.56965
\(945\) −1.23228e98 −0.0259266
\(946\) −3.13005e98 −0.0635620
\(947\) −4.54626e99 −0.891107 −0.445553 0.895255i \(-0.646993\pi\)
−0.445553 + 0.895255i \(0.646993\pi\)
\(948\) −6.73626e98 −0.127450
\(949\) 4.69951e98 0.0858290
\(950\) −3.22001e99 −0.567697
\(951\) 2.38163e99 0.405347
\(952\) 1.03379e98 0.0169861
\(953\) −5.35590e99 −0.849611 −0.424806 0.905285i \(-0.639658\pi\)
−0.424806 + 0.905285i \(0.639658\pi\)
\(954\) 1.84857e99 0.283117
\(955\) 4.04572e98 0.0598250
\(956\) −1.33486e99 −0.190589
\(957\) 1.97662e99 0.272504
\(958\) 3.88815e99 0.517605
\(959\) −2.68679e98 −0.0345390
\(960\) −5.25692e99 −0.652597
\(961\) 1.50624e100 1.80577
\(962\) 4.82384e99 0.558507
\(963\) 6.95560e98 0.0777775
\(964\) 1.32241e99 0.142819
\(965\) 2.15113e100 2.24389
\(966\) −1.59983e98 −0.0161191
\(967\) 6.14687e99 0.598228 0.299114 0.954217i \(-0.403309\pi\)
0.299114 + 0.954217i \(0.403309\pi\)
\(968\) −8.73543e99 −0.821221
\(969\) −1.30575e100 −1.18581
\(970\) −3.56208e99 −0.312501
\(971\) −1.66038e100 −1.40723 −0.703613 0.710583i \(-0.748431\pi\)
−0.703613 + 0.710583i \(0.748431\pi\)
\(972\) 1.71481e99 0.140409
\(973\) 5.13871e98 0.0406512
\(974\) −2.35619e100 −1.80089
\(975\) −5.61423e99 −0.414606
\(976\) 1.13085e100 0.806930
\(977\) −1.88759e99 −0.130149 −0.0650743 0.997880i \(-0.520728\pi\)
−0.0650743 + 0.997880i \(0.520728\pi\)
\(978\) 3.51264e99 0.234035
\(979\) −4.74276e98 −0.0305359
\(980\) 4.14622e99 0.257976
\(981\) −6.69322e99 −0.402460
\(982\) −1.18897e100 −0.690933
\(983\) −9.21278e97 −0.00517426 −0.00258713 0.999997i \(-0.500824\pi\)
−0.00258713 + 0.999997i \(0.500824\pi\)
\(984\) 1.82426e100 0.990262
\(985\) −9.00977e98 −0.0472716
\(986\) 3.31279e100 1.68003
\(987\) −3.12176e98 −0.0153030
\(988\) −1.05567e100 −0.500232
\(989\) −5.15868e99 −0.236299
\(990\) −2.01146e99 −0.0890704
\(991\) −1.75044e100 −0.749340 −0.374670 0.927158i \(-0.622244\pi\)
−0.374670 + 0.927158i \(0.622244\pi\)
\(992\) 1.77302e100 0.733789
\(993\) 1.79428e100 0.717945
\(994\) −2.07400e98 −0.00802353
\(995\) 2.00952e100 0.751655
\(996\) −5.84698e99 −0.211468
\(997\) 3.70311e100 1.29503 0.647513 0.762054i \(-0.275809\pi\)
0.647513 + 0.762054i \(0.275809\pi\)
\(998\) −5.66104e100 −1.91436
\(999\) −1.12982e100 −0.369459
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 1.68.a.a.1.2 5
3.2 odd 2 9.68.a.a.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.68.a.a.1.2 5 1.1 even 1 trivial
9.68.a.a.1.4 5 3.2 odd 2