Properties

Label 8.21.d.b.3.14
Level 8
Weight 21
Character 8.3
Analytic conductor 20.281
Analytic rank 0
Dimension 18
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(20.2811012082\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.14
Root \(7663.46 + 3.49192e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.13

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(607.571 + 824.278i) q^{2}\) \(+24307.8 q^{3}\) \(+(-310291. + 1.00161e6i) q^{4}\) \(-1.39677e7i q^{5}\) \(+(1.47687e7 + 2.00364e7i) q^{6}\) \(+2.84328e8i q^{7}\) \(+(-1.01413e9 + 3.52785e8i) q^{8}\) \(-2.89591e9 q^{9}\) \(+O(q^{10})\) \(q\)\(+(607.571 + 824.278i) q^{2}\) \(+24307.8 q^{3}\) \(+(-310291. + 1.00161e6i) q^{4}\) \(-1.39677e7i q^{5}\) \(+(1.47687e7 + 2.00364e7i) q^{6}\) \(+2.84328e8i q^{7}\) \(+(-1.01413e9 + 3.52785e8i) q^{8}\) \(-2.89591e9 q^{9}\) \(+(1.15133e10 - 8.48636e9i) q^{10}\) \(-4.00855e10 q^{11}\) \(+(-7.54252e9 + 2.43471e10i) q^{12}\) \(+2.05883e11i q^{13}\) \(+(-2.34365e11 + 1.72749e11i) q^{14}\) \(-3.39524e11i q^{15}\) \(+(-9.06950e11 - 6.21585e11i) q^{16}\) \(+2.13586e12 q^{17}\) \(+(-1.75947e12 - 2.38704e12i) q^{18}\) \(-8.51094e12 q^{19}\) \(+(1.39902e13 + 4.33406e12i) q^{20}\) \(+6.91139e12i q^{21}\) \(+(-2.43548e13 - 3.30416e13i) q^{22}\) \(-3.75944e13i q^{23}\) \(+(-2.46514e13 + 8.57545e12i) q^{24}\) \(-9.97290e13 q^{25}\) \(+(-1.69705e14 + 1.25088e14i) q^{26}\) \(-1.55150e14 q^{27}\) \(+(-2.84787e14 - 8.82244e13i) q^{28}\) \(-8.26668e13i q^{29}\) \(+(2.79862e14 - 2.06285e14i) q^{30}\) \(+1.32448e14i q^{31}\) \(+(-3.86781e13 - 1.12524e15i) q^{32}\) \(-9.74392e14 q^{33}\) \(+(1.29769e15 + 1.76055e15i) q^{34}\) \(+3.97140e15 q^{35}\) \(+(8.98577e14 - 2.90059e15i) q^{36}\) \(+5.16964e15i q^{37}\) \(+(-5.17100e15 - 7.01537e15i) q^{38}\) \(+5.00457e15i q^{39}\) \(+(4.92760e15 + 1.41651e16i) q^{40}\) \(+1.72416e16 q^{41}\) \(+(-5.69691e15 + 4.19916e15i) q^{42}\) \(-7.35091e15 q^{43}\) \(+(1.24382e16 - 4.01502e16i) q^{44}\) \(+4.04492e16i q^{45}\) \(+(3.09882e16 - 2.28412e16i) q^{46}\) \(+2.83483e16i q^{47}\) \(+(-2.20460e16 - 1.51094e16i) q^{48}\) \(-1.04993e15 q^{49}\) \(+(-6.05924e16 - 8.22044e16i) q^{50}\) \(+5.19183e16 q^{51}\) \(+(-2.06215e17 - 6.38836e16i) q^{52}\) \(-2.16094e16i q^{53}\) \(+(-9.42644e16 - 1.27886e17i) q^{54}\) \(+5.59902e17i q^{55}\) \(+(-1.00307e17 - 2.88346e17i) q^{56}\) \(-2.06883e17 q^{57}\) \(+(6.81404e16 - 5.02259e16i) q^{58}\) \(-2.04432e17 q^{59}\) \(+(3.40073e17 + 1.05352e17i) q^{60}\) \(+6.34107e17i q^{61}\) \(+(-1.09174e17 + 8.04713e16i) q^{62}\) \(-8.23388e17i q^{63}\) \(+(9.04007e17 - 7.15542e17i) q^{64}\) \(+2.87571e18 q^{65}\) \(+(-5.92012e17 - 8.03169e17i) q^{66}\) \(+5.81095e17 q^{67}\) \(+(-6.62740e17 + 2.13931e18i) q^{68}\) \(-9.13838e17i q^{69}\) \(+(2.41291e18 + 3.27354e18i) q^{70}\) \(+1.90384e18i q^{71}\) \(+(2.93684e18 - 1.02164e18i) q^{72}\) \(-6.95411e18 q^{73}\) \(+(-4.26122e18 + 3.14092e18i) q^{74}\) \(-2.42420e18 q^{75}\) \(+(2.64087e18 - 8.52467e18i) q^{76}\) \(-1.13974e19i q^{77}\) \(+(-4.12515e18 + 3.04063e18i) q^{78}\) \(-3.49017e18i q^{79}\) \(+(-8.68210e18 + 1.26680e19i) q^{80}\) \(+6.32607e18 q^{81}\) \(+(1.04755e19 + 1.42119e19i) q^{82}\) \(-1.42925e19 q^{83}\) \(+(-6.92255e18 - 2.14455e18i) q^{84}\) \(-2.98331e19i q^{85}\) \(+(-4.46620e18 - 6.05919e18i) q^{86}\) \(-2.00945e18i q^{87}\) \(+(4.06520e19 - 1.41416e19i) q^{88}\) \(+2.96835e19 q^{89}\) \(+(-3.33414e19 + 2.45758e19i) q^{90}\) \(-5.85381e19 q^{91}\) \(+(3.76551e19 + 1.16652e19i) q^{92}\) \(+3.21952e18i q^{93}\) \(+(-2.33669e19 + 1.72236e19i) q^{94}\) \(+1.18878e20i q^{95}\) \(+(-9.40182e17 - 2.73520e19i) q^{96}\) \(+6.85825e19 q^{97}\) \(+(-6.37905e17 - 8.65431e17i) q^{98}\) \(+1.16084e20 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 607.571 + 824.278i 0.593331 + 0.804959i
\(3\) 24307.8 0.411655 0.205828 0.978588i \(-0.434011\pi\)
0.205828 + 0.978588i \(0.434011\pi\)
\(4\) −310291. + 1.00161e6i −0.295917 + 0.955214i
\(5\) 1.39677e7i 1.43029i −0.698975 0.715146i \(-0.746360\pi\)
0.698975 0.715146i \(-0.253640\pi\)
\(6\) 1.47687e7 + 2.00364e7i 0.244248 + 0.331366i
\(7\) 2.84328e8i 1.00656i 0.864124 + 0.503279i \(0.167873\pi\)
−0.864124 + 0.503279i \(0.832127\pi\)
\(8\) −1.01413e9 + 3.52785e8i −0.944484 + 0.328557i
\(9\) −2.89591e9 −0.830540
\(10\) 1.15133e10 8.48636e9i 1.15133 0.848636i
\(11\) −4.00855e10 −1.54547 −0.772734 0.634730i \(-0.781111\pi\)
−0.772734 + 0.634730i \(0.781111\pi\)
\(12\) −7.54252e9 + 2.43471e10i −0.121816 + 0.393219i
\(13\) 2.05883e11i 1.49344i 0.665141 + 0.746718i \(0.268371\pi\)
−0.665141 + 0.746718i \(0.731629\pi\)
\(14\) −2.34365e11 + 1.72749e11i −0.810237 + 0.597222i
\(15\) 3.39524e11i 0.588787i
\(16\) −9.06950e11 6.21585e11i −0.824866 0.565328i
\(17\) 2.13586e12 1.05946 0.529730 0.848166i \(-0.322293\pi\)
0.529730 + 0.848166i \(0.322293\pi\)
\(18\) −1.75947e12 2.38704e12i −0.492785 0.668550i
\(19\) −8.51094e12 −1.38817 −0.694083 0.719895i \(-0.744190\pi\)
−0.694083 + 0.719895i \(0.744190\pi\)
\(20\) 1.39902e13 + 4.33406e12i 1.36623 + 0.423248i
\(21\) 6.91139e12i 0.414355i
\(22\) −2.43548e13 3.30416e13i −0.916974 1.24404i
\(23\) 3.75944e13i 0.907496i −0.891130 0.453748i \(-0.850087\pi\)
0.891130 0.453748i \(-0.149913\pi\)
\(24\) −2.46514e13 + 8.57545e12i −0.388802 + 0.135252i
\(25\) −9.97290e13 −1.04573
\(26\) −1.69705e14 + 1.25088e14i −1.20215 + 0.886101i
\(27\) −1.55150e14 −0.753552
\(28\) −2.84787e14 8.82244e13i −0.961478 0.297857i
\(29\) 8.26668e13i 0.196495i −0.995162 0.0982474i \(-0.968676\pi\)
0.995162 0.0982474i \(-0.0313237\pi\)
\(30\) 2.79862e14 2.06285e14i 0.473950 0.349346i
\(31\) 1.32448e14i 0.161595i 0.996731 + 0.0807974i \(0.0257467\pi\)
−0.996731 + 0.0807974i \(0.974253\pi\)
\(32\) −3.86781e13 1.12524e15i −0.0343531 0.999410i
\(33\) −9.74392e14 −0.636201
\(34\) 1.29769e15 + 1.76055e15i 0.628610 + 0.852821i
\(35\) 3.97140e15 1.43967
\(36\) 8.98577e14 2.90059e15i 0.245771 0.793343i
\(37\) 5.16964e15i 1.07509i 0.843236 + 0.537543i \(0.180647\pi\)
−0.843236 + 0.537543i \(0.819353\pi\)
\(38\) −5.17100e15 7.01537e15i −0.823642 1.11742i
\(39\) 5.00457e15i 0.614781i
\(40\) 4.92760e15 + 1.41651e16i 0.469932 + 1.35089i
\(41\) 1.72416e16 1.28452 0.642258 0.766489i \(-0.277998\pi\)
0.642258 + 0.766489i \(0.277998\pi\)
\(42\) −5.69691e15 + 4.19916e15i −0.333539 + 0.245850i
\(43\) −7.35091e15 −0.340139 −0.170069 0.985432i \(-0.554399\pi\)
−0.170069 + 0.985432i \(0.554399\pi\)
\(44\) 1.24382e16 4.01502e16i 0.457330 1.47625i
\(45\) 4.04492e16i 1.18791i
\(46\) 3.09882e16 2.28412e16i 0.730497 0.538445i
\(47\) 2.83483e16i 0.538950i 0.963007 + 0.269475i \(0.0868501\pi\)
−0.963007 + 0.269475i \(0.913150\pi\)
\(48\) −2.20460e16 1.51094e16i −0.339561 0.232720i
\(49\) −1.04993e15 −0.0131583
\(50\) −6.05924e16 8.22044e16i −0.620466 0.841773i
\(51\) 5.19183e16 0.436132
\(52\) −2.06215e17 6.38836e16i −1.42655 0.441933i
\(53\) 2.16094e16i 0.123562i −0.998090 0.0617810i \(-0.980322\pi\)
0.998090 0.0617810i \(-0.0196780\pi\)
\(54\) −9.42644e16 1.27886e17i −0.447106 0.606578i
\(55\) 5.59902e17i 2.21047i
\(56\) −1.00307e17 2.88346e17i −0.330711 0.950678i
\(57\) −2.06883e17 −0.571446
\(58\) 6.81404e16 5.02259e16i 0.158170 0.116586i
\(59\) −2.04432e17 −0.399970 −0.199985 0.979799i \(-0.564089\pi\)
−0.199985 + 0.979799i \(0.564089\pi\)
\(60\) 3.40073e17 + 1.05352e17i 0.562418 + 0.174232i
\(61\) 6.34107e17i 0.888923i 0.895798 + 0.444462i \(0.146605\pi\)
−0.895798 + 0.444462i \(0.853395\pi\)
\(62\) −1.09174e17 + 8.04713e16i −0.130077 + 0.0958792i
\(63\) 8.23388e17i 0.835986i
\(64\) 9.04007e17 7.15542e17i 0.784101 0.620633i
\(65\) 2.87571e18 2.13605
\(66\) −5.92012e17 8.03169e17i −0.377477 0.512115i
\(67\) 5.81095e17 0.318786 0.159393 0.987215i \(-0.449046\pi\)
0.159393 + 0.987215i \(0.449046\pi\)
\(68\) −6.62740e17 + 2.13931e18i −0.313512 + 1.01201i
\(69\) 9.13838e17i 0.373576i
\(70\) 2.41291e18 + 3.27354e18i 0.854201 + 1.15888i
\(71\) 1.90384e18i 0.584852i 0.956288 + 0.292426i \(0.0944625\pi\)
−0.956288 + 0.292426i \(0.905537\pi\)
\(72\) 2.93684e18 1.02164e18i 0.784432 0.272880i
\(73\) −6.95411e18 −1.61813 −0.809064 0.587720i \(-0.800025\pi\)
−0.809064 + 0.587720i \(0.800025\pi\)
\(74\) −4.26122e18 + 3.14092e18i −0.865399 + 0.637881i
\(75\) −2.42420e18 −0.430482
\(76\) 2.64087e18 8.52467e18i 0.410782 1.32599i
\(77\) 1.13974e19i 1.55560i
\(78\) −4.12515e18 + 3.04063e18i −0.494873 + 0.364768i
\(79\) 3.49017e18i 0.368617i −0.982868 0.184309i \(-0.940995\pi\)
0.982868 0.184309i \(-0.0590046\pi\)
\(80\) −8.68210e18 + 1.26680e19i −0.808584 + 1.17980i
\(81\) 6.32607e18 0.520336
\(82\) 1.04755e19 + 1.42119e19i 0.762143 + 1.03398i
\(83\) −1.42925e19 −0.921144 −0.460572 0.887622i \(-0.652356\pi\)
−0.460572 + 0.887622i \(0.652356\pi\)
\(84\) −6.92255e18 2.14455e18i −0.395798 0.122615i
\(85\) 2.98331e19i 1.51534i
\(86\) −4.46620e18 6.05919e18i −0.201815 0.273798i
\(87\) 2.00945e18i 0.0808882i
\(88\) 4.06520e19 1.41416e19i 1.45967 0.507774i
\(89\) 2.96835e19 0.951953 0.475976 0.879458i \(-0.342095\pi\)
0.475976 + 0.879458i \(0.342095\pi\)
\(90\) −3.33414e19 + 2.45758e19i −0.956222 + 0.704826i
\(91\) −5.85381e19 −1.50323
\(92\) 3.76551e19 + 1.16652e19i 0.866852 + 0.268543i
\(93\) 3.21952e18i 0.0665214i
\(94\) −2.33669e19 + 1.72236e19i −0.433832 + 0.319776i
\(95\) 1.18878e20i 1.98548i
\(96\) −9.40182e17 2.73520e19i −0.0141416 0.411413i
\(97\) 6.85825e19 0.930028 0.465014 0.885303i \(-0.346049\pi\)
0.465014 + 0.885303i \(0.346049\pi\)
\(98\) −6.37905e17 8.65431e17i −0.00780720 0.0105918i
\(99\) 1.16084e20 1.28357
\(100\) 3.09451e19 9.98900e19i 0.309451 0.998900i
\(101\) 1.09960e20i 0.995451i −0.867335 0.497726i \(-0.834169\pi\)
0.867335 0.497726i \(-0.165831\pi\)
\(102\) 3.15440e19 + 4.27951e19i 0.258771 + 0.351069i
\(103\) 1.81814e20i 1.35287i 0.736502 + 0.676435i \(0.236476\pi\)
−0.736502 + 0.676435i \(0.763524\pi\)
\(104\) −7.26324e19 2.08792e20i −0.490678 1.41053i
\(105\) 9.65362e19 0.592648
\(106\) 1.78122e19 1.31293e19i 0.0994623 0.0733131i
\(107\) −2.14467e20 −1.09024 −0.545121 0.838357i \(-0.683516\pi\)
−0.545121 + 0.838357i \(0.683516\pi\)
\(108\) 4.81416e19 1.55400e20i 0.222989 0.719803i
\(109\) 1.20761e20i 0.510109i 0.966927 + 0.255054i \(0.0820933\pi\)
−0.966927 + 0.255054i \(0.917907\pi\)
\(110\) −4.61514e20 + 3.40180e20i −1.77934 + 1.31154i
\(111\) 1.25663e20i 0.442565i
\(112\) 1.76734e20 2.57871e20i 0.569035 0.830275i
\(113\) −1.03816e20 −0.305830 −0.152915 0.988239i \(-0.548866\pi\)
−0.152915 + 0.988239i \(0.548866\pi\)
\(114\) −1.25696e20 1.70529e20i −0.339057 0.459990i
\(115\) −5.25107e20 −1.29798
\(116\) 8.28002e19 + 2.56508e19i 0.187695 + 0.0581462i
\(117\) 5.96218e20i 1.24036i
\(118\) −1.24207e20 1.68508e20i −0.237315 0.321960i
\(119\) 6.07285e20i 1.06641i
\(120\) 1.19779e20 + 3.44323e20i 0.193450 + 0.556100i
\(121\) 9.34095e20 1.38847
\(122\) −5.22680e20 + 3.85265e20i −0.715547 + 0.527426i
\(123\) 4.19106e20 0.528778
\(124\) −1.32661e20 4.10974e19i −0.154358 0.0478186i
\(125\) 6.09209e19i 0.0654134i
\(126\) 6.78700e20 5.00267e20i 0.672934 0.496016i
\(127\) 1.27937e21i 1.17208i −0.810282 0.586040i \(-0.800686\pi\)
0.810282 0.586040i \(-0.199314\pi\)
\(128\) 1.13905e21 + 3.10410e20i 0.964816 + 0.262928i
\(129\) −1.78685e20 −0.140020
\(130\) 1.74720e21 + 2.37038e21i 1.26738 + 1.71943i
\(131\) −4.67394e20 −0.314029 −0.157015 0.987596i \(-0.550187\pi\)
−0.157015 + 0.987596i \(0.550187\pi\)
\(132\) 3.02345e20 9.75964e20i 0.188263 0.607708i
\(133\) 2.41989e21i 1.39727i
\(134\) 3.53056e20 + 4.78984e20i 0.189145 + 0.256609i
\(135\) 2.16708e21i 1.07780i
\(136\) −2.16605e21 + 7.53501e20i −1.00064 + 0.348093i
\(137\) −1.74801e21 −0.750479 −0.375239 0.926928i \(-0.622440\pi\)
−0.375239 + 0.926928i \(0.622440\pi\)
\(138\) 7.53257e20 5.55222e20i 0.300713 0.221654i
\(139\) 9.57638e20 0.355675 0.177837 0.984060i \(-0.443090\pi\)
0.177837 + 0.984060i \(0.443090\pi\)
\(140\) −1.23229e21 + 3.97781e21i −0.426023 + 1.37519i
\(141\) 6.89086e20i 0.221862i
\(142\) −1.56929e21 + 1.15672e21i −0.470782 + 0.347011i
\(143\) 8.25291e21i 2.30806i
\(144\) 2.62645e21 + 1.80005e21i 0.685084 + 0.469527i
\(145\) −1.15466e21 −0.281045
\(146\) −4.22511e21 5.73212e21i −0.960085 1.30253i
\(147\) −2.55215e19 −0.00541667
\(148\) −5.17798e21 1.60409e21i −1.02694 0.318136i
\(149\) 8.57844e21i 1.59054i 0.606252 + 0.795272i \(0.292672\pi\)
−0.606252 + 0.795272i \(0.707328\pi\)
\(150\) −1.47287e21 1.99821e21i −0.255418 0.346520i
\(151\) 6.24048e18i 0.00101262i −1.00000 0.000506312i \(-0.999839\pi\)
1.00000 0.000506312i \(-0.000161164\pi\)
\(152\) 8.63121e21 3.00253e21i 1.31110 0.456091i
\(153\) −6.18528e21 −0.879923
\(154\) 9.39463e21 6.92473e21i 1.25220 0.922987i
\(155\) 1.84999e21 0.231128
\(156\) −5.01264e21 1.55287e21i −0.587247 0.181924i
\(157\) 8.84474e21i 0.972050i 0.873945 + 0.486025i \(0.161554\pi\)
−0.873945 + 0.486025i \(0.838446\pi\)
\(158\) 2.87687e21 2.12053e21i 0.296722 0.218712i
\(159\) 5.25279e20i 0.0508650i
\(160\) −1.57169e22 + 5.40244e20i −1.42945 + 0.0491349i
\(161\) 1.06891e22 0.913447
\(162\) 3.84354e21 + 5.21444e21i 0.308731 + 0.418849i
\(163\) 1.69388e22 1.27940 0.639701 0.768624i \(-0.279058\pi\)
0.639701 + 0.768624i \(0.279058\pi\)
\(164\) −5.34992e21 + 1.72694e22i −0.380110 + 1.22699i
\(165\) 1.36100e22i 0.909952i
\(166\) −8.68371e21 1.17810e22i −0.546543 0.741483i
\(167\) 1.22986e22i 0.728940i 0.931215 + 0.364470i \(0.118750\pi\)
−0.931215 + 0.364470i \(0.881250\pi\)
\(168\) −2.43824e21 7.00906e21i −0.136139 0.391352i
\(169\) −2.33827e22 −1.23035
\(170\) 2.45908e22 1.81257e22i 1.21978 0.899096i
\(171\) 2.46469e22 1.15293
\(172\) 2.28092e21 7.36277e21i 0.100653 0.324905i
\(173\) 2.44986e21i 0.102019i −0.998698 0.0510093i \(-0.983756\pi\)
0.998698 0.0510093i \(-0.0162438\pi\)
\(174\) 1.65635e21 1.22088e21i 0.0651116 0.0479935i
\(175\) 2.83557e22i 1.05259i
\(176\) 3.63555e22 + 2.49165e22i 1.27480 + 0.873696i
\(177\) −4.96929e21 −0.164650
\(178\) 1.80348e22 + 2.44675e22i 0.564823 + 0.766283i
\(179\) −3.04158e22 −0.900675 −0.450338 0.892858i \(-0.648696\pi\)
−0.450338 + 0.892858i \(0.648696\pi\)
\(180\) −4.05145e22 1.25510e22i −1.13471 0.351524i
\(181\) 2.35703e21i 0.0624566i 0.999512 + 0.0312283i \(0.00994190\pi\)
−0.999512 + 0.0312283i \(0.990058\pi\)
\(182\) −3.55661e22 4.82517e22i −0.891912 1.21004i
\(183\) 1.54138e22i 0.365930i
\(184\) 1.32627e22 + 3.81257e22i 0.298164 + 0.857115i
\(185\) 7.22079e22 1.53769
\(186\) −2.65378e21 + 1.95609e21i −0.0535470 + 0.0394692i
\(187\) −8.56171e22 −1.63736
\(188\) −2.83941e22 8.79623e21i −0.514812 0.159484i
\(189\) 4.41133e22i 0.758493i
\(190\) −9.79886e22 + 7.22269e22i −1.59823 + 1.17805i
\(191\) 1.20961e23i 1.87203i −0.351966 0.936013i \(-0.614487\pi\)
0.351966 0.936013i \(-0.385513\pi\)
\(192\) 2.19745e22 1.73933e22i 0.322779 0.255487i
\(193\) −1.36921e23 −1.90940 −0.954702 0.297564i \(-0.903826\pi\)
−0.954702 + 0.297564i \(0.903826\pi\)
\(194\) 4.16687e22 + 5.65310e22i 0.551814 + 0.748634i
\(195\) 6.99022e22 0.879316
\(196\) 3.25783e20 1.05162e21i 0.00389375 0.0125689i
\(197\) 2.38694e22i 0.271131i −0.990768 0.135566i \(-0.956715\pi\)
0.990768 0.135566i \(-0.0432851\pi\)
\(198\) 7.05293e22 + 9.56855e22i 0.761584 + 1.03322i
\(199\) 1.43271e23i 1.47105i 0.677497 + 0.735526i \(0.263065\pi\)
−0.677497 + 0.735526i \(0.736935\pi\)
\(200\) 1.01138e23 3.51829e22i 0.987680 0.343583i
\(201\) 1.41252e22 0.131230
\(202\) 9.06374e22 6.68083e22i 0.801297 0.590632i
\(203\) 2.35045e22 0.197783
\(204\) −1.61098e22 + 5.20021e22i −0.129059 + 0.416600i
\(205\) 2.40826e23i 1.83723i
\(206\) −1.49866e23 + 1.10465e23i −1.08900 + 0.802700i
\(207\) 1.08870e23i 0.753711i
\(208\) 1.27974e23 1.86725e23i 0.844280 1.23188i
\(209\) 3.41165e23 2.14537
\(210\) 5.86526e22 + 7.95726e22i 0.351637 + 0.477058i
\(211\) −7.39581e22 −0.422826 −0.211413 0.977397i \(-0.567806\pi\)
−0.211413 + 0.977397i \(0.567806\pi\)
\(212\) 2.16443e22 + 6.70522e21i 0.118028 + 0.0365641i
\(213\) 4.62781e22i 0.240758i
\(214\) −1.30304e23 1.76781e23i −0.646875 0.877601i
\(215\) 1.02675e23i 0.486498i
\(216\) 1.57342e23 5.47345e22i 0.711718 0.247585i
\(217\) −3.76585e22 −0.162655
\(218\) −9.95408e22 + 7.33710e22i −0.410616 + 0.302663i
\(219\) −1.69039e23 −0.666111
\(220\) −5.60805e23 1.73733e23i −2.11147 0.654116i
\(221\) 4.39737e23i 1.58223i
\(222\) −1.03581e23 + 7.63491e22i −0.356246 + 0.262587i
\(223\) 3.94167e23i 1.29608i 0.761606 + 0.648040i \(0.224411\pi\)
−0.761606 + 0.648040i \(0.775589\pi\)
\(224\) 3.19935e23 1.09973e22i 1.00596 0.0345784i
\(225\) 2.88806e23 0.868524
\(226\) −6.30755e22 8.55731e22i −0.181458 0.246180i
\(227\) −4.13516e23 −1.13824 −0.569119 0.822255i \(-0.692716\pi\)
−0.569119 + 0.822255i \(0.692716\pi\)
\(228\) 6.41939e22 2.07216e23i 0.169101 0.545853i
\(229\) 5.15394e23i 1.29953i −0.760137 0.649763i \(-0.774868\pi\)
0.760137 0.649763i \(-0.225132\pi\)
\(230\) −3.19040e23 4.32834e23i −0.770134 1.04482i
\(231\) 2.77046e23i 0.640373i
\(232\) 2.91636e22 + 8.38351e22i 0.0645597 + 0.185586i
\(233\) −4.42845e23 −0.939058 −0.469529 0.882917i \(-0.655576\pi\)
−0.469529 + 0.882917i \(0.655576\pi\)
\(234\) 4.91450e23 3.62245e23i 0.998436 0.735942i
\(235\) 3.95960e23 0.770855
\(236\) 6.34334e22 2.04762e23i 0.118358 0.382057i
\(237\) 8.48386e22i 0.151743i
\(238\) −5.00572e23 + 3.68969e23i −0.858414 + 0.632732i
\(239\) 8.87412e23i 1.45931i 0.683818 + 0.729653i \(0.260318\pi\)
−0.683818 + 0.729653i \(0.739682\pi\)
\(240\) −2.11043e23 + 3.07932e23i −0.332858 + 0.485671i
\(241\) −5.69966e22 −0.0862340 −0.0431170 0.999070i \(-0.513729\pi\)
−0.0431170 + 0.999070i \(0.513729\pi\)
\(242\) 5.67529e23 + 7.69954e23i 0.823824 + 1.11766i
\(243\) 6.94746e23 0.967751
\(244\) −6.35131e23 1.96758e23i −0.849112 0.263048i
\(245\) 1.46651e22i 0.0188201i
\(246\) 2.54637e23 + 3.45460e23i 0.313740 + 0.425644i
\(247\) 1.75225e24i 2.07314i
\(248\) −4.67256e22 1.34319e23i −0.0530931 0.152624i
\(249\) −3.47420e23 −0.379194
\(250\) −5.02158e22 + 3.70138e22i −0.0526551 + 0.0388118i
\(251\) 5.20650e23 0.524576 0.262288 0.964990i \(-0.415523\pi\)
0.262288 + 0.964990i \(0.415523\pi\)
\(252\) 8.24717e23 + 2.55490e23i 0.798545 + 0.247382i
\(253\) 1.50699e24i 1.40251i
\(254\) 1.05455e24 7.77305e23i 0.943476 0.695431i
\(255\) 7.25178e23i 0.623796i
\(256\) 4.36191e23 + 1.12749e24i 0.360809 + 0.932640i
\(257\) 6.80863e22 0.0541662 0.0270831 0.999633i \(-0.491378\pi\)
0.0270831 + 0.999633i \(0.491378\pi\)
\(258\) −1.08564e23 1.47286e23i −0.0830782 0.112710i
\(259\) −1.46987e24 −1.08214
\(260\) −8.92307e23 + 2.88035e24i −0.632093 + 2.04038i
\(261\) 2.39396e23i 0.163197i
\(262\) −2.83975e23 3.85263e23i −0.186323 0.252781i
\(263\) 1.19590e24i 0.755333i −0.925942 0.377666i \(-0.876727\pi\)
0.925942 0.377666i \(-0.123273\pi\)
\(264\) 9.88162e23 3.43751e23i 0.600881 0.209028i
\(265\) −3.01834e23 −0.176730
\(266\) 1.99466e24 1.47026e24i 1.12474 0.829043i
\(267\) 7.21543e23 0.391877
\(268\) −1.80309e23 + 5.82033e23i −0.0943341 + 0.304509i
\(269\) 2.10757e24i 1.06233i −0.847269 0.531165i \(-0.821755\pi\)
0.847269 0.531165i \(-0.178245\pi\)
\(270\) −1.78628e24 + 1.31666e24i −0.867583 + 0.639491i
\(271\) 1.72548e24i 0.807640i −0.914839 0.403820i \(-0.867682\pi\)
0.914839 0.403820i \(-0.132318\pi\)
\(272\) −1.93712e24 1.32762e24i −0.873913 0.598942i
\(273\) −1.42294e24 −0.618812
\(274\) −1.06204e24 1.44085e24i −0.445282 0.604105i
\(275\) 3.99768e24 1.61615
\(276\) 9.15313e23 + 2.83556e23i 0.356844 + 0.110547i
\(277\) 1.47149e24i 0.553299i 0.960971 + 0.276649i \(0.0892240\pi\)
−0.960971 + 0.276649i \(0.910776\pi\)
\(278\) 5.81833e23 + 7.89360e23i 0.211033 + 0.286304i
\(279\) 3.83557e23i 0.134211i
\(280\) −4.02753e24 + 1.40105e24i −1.35975 + 0.473014i
\(281\) −3.14997e24 −1.02623 −0.513113 0.858321i \(-0.671508\pi\)
−0.513113 + 0.858321i \(0.671508\pi\)
\(282\) −5.67998e23 + 4.18669e23i −0.178589 + 0.131637i
\(283\) −5.42512e24 −1.64644 −0.823218 0.567725i \(-0.807824\pi\)
−0.823218 + 0.567725i \(0.807824\pi\)
\(284\) −1.90691e24 5.90744e23i −0.558659 0.173068i
\(285\) 2.88967e24i 0.817334i
\(286\) 6.80269e24 5.01422e24i 1.85789 1.36944i
\(287\) 4.90227e24i 1.29294i
\(288\) 1.12009e23 + 3.25858e24i 0.0285316 + 0.830050i
\(289\) 4.97684e23 0.122455
\(290\) −7.01540e23 9.51764e23i −0.166753 0.226230i
\(291\) 1.66709e24 0.382851
\(292\) 2.15780e24 6.96533e24i 0.478832 1.54566i
\(293\) 2.74098e24i 0.587800i 0.955836 + 0.293900i \(0.0949532\pi\)
−0.955836 + 0.293900i \(0.905047\pi\)
\(294\) −1.55061e22 2.10368e22i −0.00321388 0.00436019i
\(295\) 2.85544e24i 0.572074i
\(296\) −1.82377e24 5.24270e24i −0.353227 1.01540i
\(297\) 6.21925e24 1.16459
\(298\) −7.07102e24 + 5.21201e24i −1.28032 + 0.943719i
\(299\) 7.74003e24 1.35529
\(300\) 7.52208e23 2.42811e24i 0.127387 0.411203i
\(301\) 2.09007e24i 0.342369i
\(302\) 5.14389e21 3.79153e21i 0.000815121 0.000600821i
\(303\) 2.67288e24i 0.409783i
\(304\) 7.71899e24 + 5.29027e24i 1.14505 + 0.784769i
\(305\) 8.85701e24 1.27142
\(306\) −3.75799e24 5.09839e24i −0.522086 0.708302i
\(307\) −2.09763e24 −0.282062 −0.141031 0.990005i \(-0.545042\pi\)
−0.141031 + 0.990005i \(0.545042\pi\)
\(308\) 1.14158e25 + 3.53652e24i 1.48593 + 0.460329i
\(309\) 4.41952e24i 0.556916i
\(310\) 1.12400e24 + 1.52490e24i 0.137135 + 0.186048i
\(311\) 4.77389e24i 0.563986i 0.959417 + 0.281993i \(0.0909955\pi\)
−0.959417 + 0.281993i \(0.909005\pi\)
\(312\) −1.76554e24 5.07529e24i −0.201990 0.580651i
\(313\) −4.62194e24 −0.512130 −0.256065 0.966660i \(-0.582426\pi\)
−0.256065 + 0.966660i \(0.582426\pi\)
\(314\) −7.29052e24 + 5.37380e24i −0.782460 + 0.576747i
\(315\) −1.15008e25 −1.19570
\(316\) 3.49581e24 + 1.08297e24i 0.352108 + 0.109080i
\(317\) 1.06496e25i 1.03929i −0.854381 0.519647i \(-0.826063\pi\)
0.854381 0.519647i \(-0.173937\pi\)
\(318\) 4.32976e23 3.19144e23i 0.0409442 0.0301798i
\(319\) 3.31374e24i 0.303677i
\(320\) −9.99447e24 1.26269e25i −0.887687 1.12149i
\(321\) −5.21324e24 −0.448805
\(322\) 6.49440e24 + 8.81080e24i 0.541976 + 0.735287i
\(323\) −1.81782e25 −1.47071
\(324\) −1.96293e24 + 6.33628e24i −0.153976 + 0.497032i
\(325\) 2.05325e25i 1.56174i
\(326\) 1.02915e25 + 1.39623e25i 0.759108 + 1.02987i
\(327\) 2.93545e24i 0.209989i
\(328\) −1.74853e25 + 6.08259e24i −1.21320 + 0.422036i
\(329\) −8.06020e24 −0.542484
\(330\) −1.12184e25 + 8.26904e24i −0.732474 + 0.539903i
\(331\) 1.49182e25 0.945011 0.472506 0.881328i \(-0.343350\pi\)
0.472506 + 0.881328i \(0.343350\pi\)
\(332\) 4.43484e24 1.43156e25i 0.272582 0.879889i
\(333\) 1.49708e25i 0.892901i
\(334\) −1.01375e25 + 7.47229e24i −0.586767 + 0.432503i
\(335\) 8.11655e24i 0.455957i
\(336\) 4.29601e24 6.26829e24i 0.234246 0.341787i
\(337\) 3.10066e25 1.64118 0.820588 0.571520i \(-0.193646\pi\)
0.820588 + 0.571520i \(0.193646\pi\)
\(338\) −1.42067e25 1.92739e25i −0.730004 0.990380i
\(339\) −2.52354e24 −0.125896
\(340\) 2.98812e25 + 9.25695e24i 1.44747 + 0.448414i
\(341\) 5.30923e24i 0.249740i
\(342\) 1.49748e25 + 2.03159e25i 0.684067 + 0.928058i
\(343\) 2.23886e25i 0.993313i
\(344\) 7.45479e24 2.59329e24i 0.321256 0.111755i
\(345\) −1.27642e25 −0.534322
\(346\) 2.01936e24 1.48846e24i 0.0821208 0.0605308i
\(347\) −2.79742e25 −1.10526 −0.552628 0.833428i \(-0.686375\pi\)
−0.552628 + 0.833428i \(0.686375\pi\)
\(348\) 2.01270e24 + 6.23516e23i 0.0772655 + 0.0239362i
\(349\) 2.94131e24i 0.109720i 0.998494 + 0.0548601i \(0.0174713\pi\)
−0.998494 + 0.0548601i \(0.982529\pi\)
\(350\) 2.33730e25 1.72281e25i 0.847293 0.624535i
\(351\) 3.19426e25i 1.12538i
\(352\) 1.55043e24 + 4.51056e25i 0.0530916 + 1.54456i
\(353\) −1.82153e24 −0.0606302 −0.0303151 0.999540i \(-0.509651\pi\)
−0.0303151 + 0.999540i \(0.509651\pi\)
\(354\) −3.01920e24 4.09608e24i −0.0976919 0.132536i
\(355\) 2.65922e25 0.836509
\(356\) −9.21054e24 + 2.97314e25i −0.281699 + 0.909318i
\(357\) 1.47618e25i 0.438992i
\(358\) −1.84797e25 2.50710e25i −0.534398 0.725006i
\(359\) 3.11321e25i 0.875517i 0.899093 + 0.437758i \(0.144227\pi\)
−0.899093 + 0.437758i \(0.855773\pi\)
\(360\) −1.42699e25 4.10209e25i −0.390297 1.12197i
\(361\) 3.48461e25 0.927004
\(362\) −1.94284e24 + 1.43206e24i −0.0502750 + 0.0370574i
\(363\) 2.27058e25 0.571573
\(364\) 1.81639e25 5.86326e25i 0.444831 1.43590i
\(365\) 9.71329e25i 2.31440i
\(366\) −1.27052e25 + 9.36496e24i −0.294559 + 0.217118i
\(367\) 4.62723e25i 1.04390i −0.852975 0.521952i \(-0.825204\pi\)
0.852975 0.521952i \(-0.174796\pi\)
\(368\) −2.33681e25 + 3.40962e25i −0.513033 + 0.748563i
\(369\) −4.99302e25 −1.06684
\(370\) 4.38714e25 + 5.95194e25i 0.912357 + 1.23777i
\(371\) 6.14416e24 0.124372
\(372\) −3.22471e24 9.98989e23i −0.0635421 0.0196848i
\(373\) 7.18562e24i 0.137840i −0.997622 0.0689201i \(-0.978045\pi\)
0.997622 0.0689201i \(-0.0219554\pi\)
\(374\) −5.20185e25 7.05723e25i −0.971497 1.31801i
\(375\) 1.48086e24i 0.0269278i
\(376\) −1.00009e25 2.87489e25i −0.177076 0.509030i
\(377\) 1.70197e25 0.293452
\(378\) 3.63616e25 2.68020e25i 0.610556 0.450037i
\(379\) 5.99644e25 0.980621 0.490311 0.871548i \(-0.336883\pi\)
0.490311 + 0.871548i \(0.336883\pi\)
\(380\) −1.19070e26 3.68869e25i −1.89656 0.587538i
\(381\) 3.10986e25i 0.482493i
\(382\) 9.97055e25 7.34924e25i 1.50690 1.11073i
\(383\) 6.57084e25i 0.967460i 0.875217 + 0.483730i \(0.160718\pi\)
−0.875217 + 0.483730i \(0.839282\pi\)
\(384\) 2.76879e25 + 7.54541e24i 0.397172 + 0.108236i
\(385\) −1.59195e26 −2.22497
\(386\) −8.31893e25 1.12861e26i −1.13291 1.53699i
\(387\) 2.12876e25 0.282499
\(388\) −2.12806e25 + 6.86932e25i −0.275211 + 0.888376i
\(389\) 7.85873e25i 0.990504i 0.868749 + 0.495252i \(0.164924\pi\)
−0.868749 + 0.495252i \(0.835076\pi\)
\(390\) 4.24706e25 + 5.76188e25i 0.521725 + 0.707813i
\(391\) 8.02965e25i 0.961455i
\(392\) 1.06476e24 3.70399e23i 0.0124278 0.00432323i
\(393\) −1.13613e25 −0.129272
\(394\) 1.96750e25 1.45024e25i 0.218249 0.160870i
\(395\) −4.87496e25 −0.527231
\(396\) −3.60199e25 + 1.16271e26i −0.379831 + 1.22609i
\(397\) 7.66767e25i 0.788421i 0.919020 + 0.394211i \(0.128982\pi\)
−0.919020 + 0.394211i \(0.871018\pi\)
\(398\) −1.18095e26 + 8.70473e25i −1.18414 + 0.872820i
\(399\) 5.88224e25i 0.575193i
\(400\) 9.04492e25 + 6.19900e25i 0.862591 + 0.591183i
\(401\) 1.45021e26 1.34892 0.674462 0.738310i \(-0.264376\pi\)
0.674462 + 0.738310i \(0.264376\pi\)
\(402\) 8.58204e24 + 1.16431e25i 0.0778628 + 0.105635i
\(403\) −2.72687e25 −0.241331
\(404\) 1.10137e26 + 3.41196e25i 0.950869 + 0.294571i
\(405\) 8.83606e25i 0.744232i
\(406\) 1.42806e25 + 1.93742e25i 0.117351 + 0.159207i
\(407\) 2.07227e26i 1.66151i
\(408\) −5.26520e25 + 1.83160e25i −0.411920 + 0.143294i
\(409\) 7.43957e25 0.567956 0.283978 0.958831i \(-0.408346\pi\)
0.283978 + 0.958831i \(0.408346\pi\)
\(410\) 1.98507e26 1.46319e26i 1.47890 1.09009i
\(411\) −4.24904e25 −0.308939
\(412\) −1.82108e26 5.64155e25i −1.29228 0.400337i
\(413\) 5.81255e25i 0.402593i
\(414\) −8.97392e25 + 6.61463e25i −0.606706 + 0.447200i
\(415\) 1.99633e26i 1.31750i
\(416\) 2.31667e26 7.96316e24i 1.49255 0.0513041i
\(417\) 2.32781e25 0.146416
\(418\) 2.07282e26 + 2.81215e26i 1.27291 + 1.72693i
\(419\) 1.90766e26 1.14383 0.571914 0.820314i \(-0.306201\pi\)
0.571914 + 0.820314i \(0.306201\pi\)
\(420\) −2.99544e25 + 9.66920e25i −0.175375 + 0.566106i
\(421\) 1.28355e26i 0.733827i −0.930255 0.366913i \(-0.880415\pi\)
0.930255 0.366913i \(-0.119585\pi\)
\(422\) −4.49348e25 6.09620e25i −0.250876 0.340357i
\(423\) 8.20942e25i 0.447619i
\(424\) 7.62349e24 + 2.19148e25i 0.0405971 + 0.116702i
\(425\) −2.13008e26 −1.10791
\(426\) −3.81460e25 + 2.81173e25i −0.193800 + 0.142849i
\(427\) −1.80294e26 −0.894753
\(428\) 6.65474e25 2.14813e26i 0.322621 1.04141i
\(429\) 2.00610e26i 0.950124i
\(430\) −8.46329e25 + 6.23825e25i −0.391611 + 0.288654i
\(431\) 2.45768e26i 1.11110i 0.831484 + 0.555549i \(0.187492\pi\)
−0.831484 + 0.555549i \(0.812508\pi\)
\(432\) 1.40713e26 + 9.64386e25i 0.621579 + 0.426004i
\(433\) −7.14228e25 −0.308289 −0.154145 0.988048i \(-0.549262\pi\)
−0.154145 + 0.988048i \(0.549262\pi\)
\(434\) −2.28802e25 3.10411e25i −0.0965079 0.130930i
\(435\) −2.80674e25 −0.115694
\(436\) −1.20956e26 3.74712e25i −0.487263 0.150950i
\(437\) 3.19963e26i 1.25975i
\(438\) −1.02703e26 1.39335e26i −0.395224 0.536192i
\(439\) 1.50251e26i 0.565162i −0.959243 0.282581i \(-0.908809\pi\)
0.959243 0.282581i \(-0.0911907\pi\)
\(440\) −1.97525e26 5.67814e26i −0.726265 2.08775i
\(441\) 3.04050e24 0.0109285
\(442\) −3.62466e26 + 2.67172e26i −1.27363 + 0.938788i
\(443\) 1.83787e26 0.631361 0.315680 0.948866i \(-0.397767\pi\)
0.315680 + 0.948866i \(0.397767\pi\)
\(444\) −1.25866e26 3.89921e25i −0.422744 0.130962i
\(445\) 4.14610e26i 1.36157i
\(446\) −3.24903e26 + 2.39485e26i −1.04329 + 0.769004i
\(447\) 2.08523e26i 0.654756i
\(448\) 2.03448e26 + 2.57034e26i 0.624703 + 0.789243i
\(449\) 2.83524e26 0.851386 0.425693 0.904868i \(-0.360030\pi\)
0.425693 + 0.904868i \(0.360030\pi\)
\(450\) 1.75470e26 + 2.38057e26i 0.515322 + 0.699126i
\(451\) −6.91138e26 −1.98518
\(452\) 3.22132e25 1.03983e26i 0.0905001 0.292133i
\(453\) 1.51693e23i 0.000416852i
\(454\) −2.51240e26 3.40852e26i −0.675352 0.916235i
\(455\) 8.17643e26i 2.15006i
\(456\) 2.09806e26 7.29851e25i 0.539722 0.187752i
\(457\) 6.33685e26 1.59482 0.797409 0.603439i \(-0.206203\pi\)
0.797409 + 0.603439i \(0.206203\pi\)
\(458\) 4.24828e26 3.13139e26i 1.04606 0.771049i
\(459\) −3.31379e26 −0.798358
\(460\) 1.62936e26 5.25954e26i 0.384095 1.23985i
\(461\) 3.19396e26i 0.736750i 0.929677 + 0.368375i \(0.120086\pi\)
−0.929677 + 0.368375i \(0.879914\pi\)
\(462\) 2.28363e26 1.68325e26i 0.515473 0.379953i
\(463\) 6.34081e26i 1.40067i −0.713816 0.700333i \(-0.753035\pi\)
0.713816 0.700333i \(-0.246965\pi\)
\(464\) −5.13844e25 + 7.49747e25i −0.111084 + 0.162082i
\(465\) 4.49692e25 0.0951450
\(466\) −2.69059e26 3.65027e26i −0.557172 0.755903i
\(467\) 4.04419e26 0.819716 0.409858 0.912149i \(-0.365578\pi\)
0.409858 + 0.912149i \(0.365578\pi\)
\(468\) 5.97181e26 + 1.85001e26i 1.18481 + 0.367043i
\(469\) 1.65221e26i 0.320876i
\(470\) 2.40574e26 + 3.26381e26i 0.457372 + 0.620507i
\(471\) 2.14997e26i 0.400150i
\(472\) 2.07321e26 7.21204e25i 0.377766 0.131413i
\(473\) 2.94665e26 0.525674
\(474\) 6.99305e25 5.15454e25i 0.122147 0.0900340i
\(475\) 8.48787e26 1.45165
\(476\) −6.08265e26 1.88435e26i −1.01865 0.315568i
\(477\) 6.25791e25i 0.102623i
\(478\) −7.31474e26 + 5.39166e26i −1.17468 + 0.865851i
\(479\) 1.19581e27i 1.88064i 0.340293 + 0.940319i \(0.389474\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(480\) −3.82045e26 + 1.31322e25i −0.588440 + 0.0202267i
\(481\) −1.06434e27 −1.60557
\(482\) −3.46295e25 4.69810e25i −0.0511653 0.0694148i
\(483\) 2.59829e26 0.376025
\(484\) −2.89842e26 + 9.35603e26i −0.410873 + 1.32629i
\(485\) 9.57940e26i 1.33021i
\(486\) 4.22108e26 + 5.72664e26i 0.574197 + 0.779000i
\(487\) 8.77926e25i 0.116995i −0.998288 0.0584976i \(-0.981369\pi\)
0.998288 0.0584976i \(-0.0186310\pi\)
\(488\) −2.23704e26 6.43069e26i −0.292062 0.839574i
\(489\) 4.11746e26 0.526673
\(490\) −1.20881e25 + 8.91006e24i −0.0151494 + 0.0111666i
\(491\) −6.94416e26 −0.852717 −0.426359 0.904554i \(-0.640204\pi\)
−0.426359 + 0.904554i \(0.640204\pi\)
\(492\) −1.30045e26 + 4.19783e26i −0.156474 + 0.505096i
\(493\) 1.76565e26i 0.208178i
\(494\) 1.44434e27 1.06462e27i 1.66879 1.23006i
\(495\) 1.62143e27i 1.83588i
\(496\) 8.23274e25 1.20123e26i 0.0913541 0.133294i
\(497\) −5.41313e26 −0.588687
\(498\) −2.11082e26 2.86371e26i −0.224987 0.305235i
\(499\) −6.25596e26 −0.653565 −0.326782 0.945100i \(-0.605964\pi\)
−0.326782 + 0.945100i \(0.605964\pi\)
\(500\) −6.10193e25 1.89032e25i −0.0624837 0.0193569i
\(501\) 2.98953e26i 0.300072i
\(502\) 3.16331e26 + 4.29160e26i 0.311247 + 0.422262i
\(503\) 1.46764e27i 1.41560i −0.706415 0.707798i \(-0.749689\pi\)
0.706415 0.707798i \(-0.250311\pi\)
\(504\) 2.90479e26 + 8.35024e26i 0.274669 + 0.789576i
\(505\) −1.53588e27 −1.42379
\(506\) −1.24218e27 + 9.15602e26i −1.12896 + 0.832150i
\(507\) −5.68384e26 −0.506480
\(508\) 1.28143e27 + 3.96976e26i 1.11959 + 0.346838i
\(509\) 2.17480e27i 1.86313i 0.363579 + 0.931563i \(0.381555\pi\)
−0.363579 + 0.931563i \(0.618445\pi\)
\(510\) 5.97748e26 4.40597e26i 0.502130 0.370118i
\(511\) 1.97725e27i 1.62874i
\(512\) −6.64350e26 + 1.04457e27i −0.536657 + 0.843800i
\(513\) 1.32047e27 1.04605
\(514\) 4.13673e25 + 5.61220e25i 0.0321385 + 0.0436016i
\(515\) 2.53953e27 1.93500
\(516\) 5.54443e25 1.78973e26i 0.0414343 0.133749i
\(517\) 1.13635e27i 0.832930i
\(518\) −8.93051e26 1.21158e27i −0.642064 0.871074i
\(519\) 5.95507e25i 0.0419965i
\(520\) −2.91635e27 + 1.01451e27i −2.01746 + 0.701813i
\(521\) −1.42093e27 −0.964266 −0.482133 0.876098i \(-0.660138\pi\)
−0.482133 + 0.876098i \(0.660138\pi\)
\(522\) −1.97329e26 + 1.45450e26i −0.131367 + 0.0968297i
\(523\) −5.60940e26 −0.366353 −0.183176 0.983080i \(-0.558638\pi\)
−0.183176 + 0.983080i \(0.558638\pi\)
\(524\) 1.45028e26 4.68149e26i 0.0929267 0.299965i
\(525\) 6.89266e26i 0.433305i
\(526\) 9.85756e26 7.26596e26i 0.608012 0.448162i
\(527\) 2.82890e26i 0.171203i
\(528\) 8.83724e26 + 6.05667e26i 0.524780 + 0.359662i
\(529\) 3.02818e26 0.176452
\(530\) −1.83386e26 2.48795e26i −0.104859 0.142260i
\(531\) 5.92016e26 0.332191
\(532\) 2.42380e27 + 7.50872e26i 1.33469 + 0.413476i
\(533\) 3.54975e27i 1.91834i
\(534\) 4.38388e26 + 5.94751e26i 0.232512 + 0.315444i
\(535\) 2.99561e27i 1.55937i
\(536\) −5.89307e26 + 2.05002e26i −0.301088 + 0.104739i
\(537\) −7.39341e26 −0.370768
\(538\) 1.73722e27 1.28050e27i 0.855131 0.630313i
\(539\) 4.20868e25 0.0203357
\(540\) −2.17058e27 6.72427e26i −1.02953 0.318939i
\(541\) 9.48899e25i 0.0441822i −0.999756 0.0220911i \(-0.992968\pi\)
0.999756 0.0220911i \(-0.00703239\pi\)
\(542\) 1.42228e27 1.04835e27i 0.650117 0.479198i
\(543\) 5.72942e25i 0.0257106i
\(544\) −8.26112e25 2.40335e27i −0.0363957 1.05883i
\(545\) 1.68676e27 0.729604
\(546\) −8.64534e26 1.17289e27i −0.367160 0.498118i
\(547\) 2.21993e27 0.925692 0.462846 0.886439i \(-0.346828\pi\)
0.462846 + 0.886439i \(0.346828\pi\)
\(548\) 5.42393e26 1.75083e27i 0.222079 0.716868i
\(549\) 1.83632e27i 0.738286i
\(550\) 2.42888e27 + 3.29520e27i 0.958911 + 1.30093i
\(551\) 7.03572e26i 0.272767i
\(552\) 3.22389e26 + 9.26753e26i 0.122741 + 0.352836i
\(553\) 9.92352e26 0.371035
\(554\) −1.21292e27 + 8.94034e26i −0.445383 + 0.328289i
\(555\) 1.75522e27 0.632997
\(556\) −2.97147e26 + 9.59184e26i −0.105250 + 0.339746i
\(557\) 1.37717e27i 0.479111i 0.970883 + 0.239556i \(0.0770017\pi\)
−0.970883 + 0.239556i \(0.922998\pi\)
\(558\) 3.16157e26 2.33038e26i 0.108034 0.0796315i
\(559\) 1.51342e27i 0.507975i
\(560\) −3.60186e27 2.46856e27i −1.18754 0.813886i
\(561\) −2.08117e27 −0.674029
\(562\) −1.91383e27 2.59645e27i −0.608892 0.826070i
\(563\) −3.26206e27 −1.01955 −0.509774 0.860308i \(-0.670271\pi\)
−0.509774 + 0.860308i \(0.670271\pi\)
\(564\) −6.90198e26 2.13817e26i −0.211925 0.0656526i
\(565\) 1.45007e27i 0.437425i
\(566\) −3.29614e27 4.47181e27i −0.976882 1.32531i
\(567\) 1.79868e27i 0.523748i
\(568\) −6.71645e26 1.93074e27i −0.192157 0.552383i
\(569\) 2.95455e27 0.830556 0.415278 0.909695i \(-0.363684\pi\)
0.415278 + 0.909695i \(0.363684\pi\)
\(570\) −2.38189e27 + 1.75568e27i −0.657920 + 0.484950i
\(571\) −6.52375e27 −1.77066 −0.885332 0.464960i \(-0.846069\pi\)
−0.885332 + 0.464960i \(0.846069\pi\)
\(572\) 8.26623e27 + 2.56081e27i 2.20469 + 0.682993i
\(573\) 2.94030e27i 0.770630i
\(574\) −4.04083e27 + 2.97847e27i −1.04076 + 0.767141i
\(575\) 3.74925e27i 0.948999i
\(576\) −2.61792e27 + 2.07215e27i −0.651227 + 0.515461i
\(577\) 4.43876e27 1.08519 0.542593 0.839996i \(-0.317443\pi\)
0.542593 + 0.839996i \(0.317443\pi\)
\(578\) 3.02378e26 + 4.10230e26i 0.0726561 + 0.0985709i
\(579\) −3.32826e27 −0.786016
\(580\) 3.58282e26 1.15653e27i 0.0831660 0.268458i
\(581\) 4.06375e27i 0.927185i
\(582\) 1.01288e27 + 1.37415e27i 0.227157 + 0.308179i
\(583\) 8.66225e26i 0.190961i
\(584\) 7.05239e27 2.45331e27i 1.52830 0.531647i
\(585\) −8.32780e27 −1.77407
\(586\) −2.25933e27 + 1.66534e27i −0.473154 + 0.348760i
\(587\) 1.40751e27 0.289782 0.144891 0.989448i \(-0.453717\pi\)
0.144891 + 0.989448i \(0.453717\pi\)
\(588\) 7.91909e24 2.55627e25i 0.00160288 0.00517407i
\(589\) 1.12725e27i 0.224320i
\(590\) −2.35367e27 + 1.73488e27i −0.460496 + 0.339429i
\(591\) 5.80214e26i 0.111613i
\(592\) 3.21337e27 4.68861e27i 0.607776 0.886802i
\(593\) 1.04753e27 0.194814 0.0974072 0.995245i \(-0.468945\pi\)
0.0974072 + 0.995245i \(0.468945\pi\)
\(594\) 3.77863e27 + 5.12639e27i 0.690988 + 0.937447i
\(595\) 8.48237e27 1.52527
\(596\) −8.59229e27 2.66182e27i −1.51931 0.470669i
\(597\) 3.48261e27i 0.605566i
\(598\) 4.70262e27 + 6.37994e27i 0.804133 + 1.09095i
\(599\) 9.04310e27i 1.52072i −0.649502 0.760360i \(-0.725022\pi\)
0.649502 0.760360i \(-0.274978\pi\)
\(600\) 2.45846e27 8.55221e26i 0.406584 0.141438i
\(601\) 8.61316e27 1.40093 0.700467 0.713685i \(-0.252975\pi\)
0.700467 + 0.713685i \(0.252975\pi\)
\(602\) 1.72279e27 1.26986e27i 0.275593 0.203138i
\(603\) −1.68280e27 −0.264764
\(604\) 6.25055e24 + 1.93637e24i 0.000967273 + 0.000299653i
\(605\) 1.30472e28i 1.98592i
\(606\) 2.20320e27 1.62397e27i 0.329858 0.243137i
\(607\) 1.08110e28i 1.59213i 0.605214 + 0.796063i \(0.293088\pi\)
−0.605214 + 0.796063i \(0.706912\pi\)
\(608\) 3.29187e26 + 9.57681e27i 0.0476878 + 1.38735i
\(609\) 5.71343e26 0.0814186
\(610\) 5.38126e27 + 7.30064e27i 0.754373 + 1.02344i
\(611\) −5.83642e27 −0.804887
\(612\) 1.91924e27 6.19526e27i 0.260384 0.840515i
\(613\) 8.75826e27i 1.16900i −0.811395 0.584498i \(-0.801291\pi\)
0.811395 0.584498i \(-0.198709\pi\)
\(614\) −1.27446e27 1.72903e27i −0.167356 0.227049i
\(615\) 5.85395e27i 0.756307i
\(616\) 4.02084e27 + 1.15585e28i 0.511104 + 1.46924i
\(617\) 2.57137e27 0.321598 0.160799 0.986987i \(-0.448593\pi\)
0.160799 + 0.986987i \(0.448593\pi\)
\(618\) −3.64291e27 + 2.68517e27i −0.448295 + 0.330436i
\(619\) −2.27538e27 −0.275516 −0.137758 0.990466i \(-0.543990\pi\)
−0.137758 + 0.990466i \(0.543990\pi\)
\(620\) −5.74036e26 + 1.85297e27i −0.0683946 + 0.220776i
\(621\) 5.83275e27i 0.683845i
\(622\) −3.93501e27 + 2.90047e27i −0.453985 + 0.334630i
\(623\) 8.43985e27i 0.958195i
\(624\) 3.11076e27 4.53889e27i 0.347553 0.507112i
\(625\) −8.65997e27 −0.952174
\(626\) −2.80815e27 3.80976e27i −0.303863 0.412244i
\(627\) 8.29298e27 0.883152
\(628\) −8.85901e27 2.74445e27i −0.928515 0.287646i
\(629\) 1.10416e28i 1.13901i
\(630\) −6.98757e27 9.47988e27i −0.709448 0.962492i
\(631\) 2.15086e27i 0.214941i −0.994208 0.107470i \(-0.965725\pi\)
0.994208 0.107470i \(-0.0342751\pi\)
\(632\) 1.23128e27 + 3.53950e27i 0.121112 + 0.348153i
\(633\) −1.79776e27 −0.174059
\(634\) 8.77819e27 6.47036e27i 0.836589 0.616646i
\(635\) −1.78698e28 −1.67642
\(636\) 5.26127e26 + 1.62990e26i 0.0485869 + 0.0150518i
\(637\) 2.16162e26i 0.0196510i
\(638\) −2.73144e27 + 2.01333e27i −0.244447 + 0.180181i
\(639\) 5.51334e27i 0.485743i
\(640\) 4.33572e27 1.59099e28i 0.376063 1.37997i
\(641\) −6.68225e27 −0.570614 −0.285307 0.958436i \(-0.592096\pi\)
−0.285307 + 0.958436i \(0.592096\pi\)
\(642\) −3.16741e27 4.29716e27i −0.266290 0.361269i
\(643\) 9.21310e27 0.762599 0.381299 0.924452i \(-0.375477\pi\)
0.381299 + 0.924452i \(0.375477\pi\)
\(644\) −3.31674e27 + 1.07064e28i −0.270304 + 0.872537i
\(645\) 2.49581e27i 0.200270i
\(646\) −1.10445e28 1.49839e28i −0.872615 1.18386i
\(647\) 1.05751e28i 0.822701i −0.911477 0.411351i \(-0.865057\pi\)
0.911477 0.411351i \(-0.134943\pi\)
\(648\) −6.41547e27 + 2.23174e27i −0.491449 + 0.170960i
\(649\) 8.19474e27 0.618142
\(650\) 1.69245e28 1.24749e28i 1.25713 0.926626i
\(651\) −9.15398e26 −0.0669576
\(652\) −5.25597e27 + 1.69662e28i −0.378597 + 1.22210i
\(653\) 2.34679e28i 1.66472i 0.554232 + 0.832362i \(0.313012\pi\)
−0.554232 + 0.832362i \(0.686988\pi\)
\(654\) −2.41962e27 + 1.78349e27i −0.169032 + 0.124593i
\(655\) 6.52842e27i 0.449154i
\(656\) −1.56373e28 1.07171e28i −1.05955 0.726172i
\(657\) 2.01385e28 1.34392
\(658\) −4.89714e27 6.64385e27i −0.321873 0.436677i
\(659\) 2.82917e28 1.83149 0.915745 0.401760i \(-0.131601\pi\)
0.915745 + 0.401760i \(0.131601\pi\)
\(660\) −1.36320e28 4.22307e27i −0.869199 0.269270i
\(661\) 7.66843e27i 0.481606i 0.970574 + 0.240803i \(0.0774107\pi\)
−0.970574 + 0.240803i \(0.922589\pi\)
\(662\) 9.06387e27 + 1.22968e28i 0.560704 + 0.760695i
\(663\) 1.06891e28i 0.651335i
\(664\) 1.44945e28 5.04219e27i 0.870006 0.302648i
\(665\) −3.38003e28 −1.99850
\(666\) 1.23401e28 9.09584e27i 0.718749 0.529786i
\(667\) −3.10781e27 −0.178318
\(668\) −1.23185e28 3.81616e27i −0.696294 0.215706i
\(669\) 9.58136e27i 0.533539i
\(670\) 6.69029e27 4.93138e27i 0.367026 0.270533i
\(671\) 2.54185e28i 1.37380i
\(672\) 7.77694e27 2.67320e26i 0.414110 0.0142344i
\(673\) −1.51939e28 −0.797108 −0.398554 0.917145i \(-0.630488\pi\)
−0.398554 + 0.917145i \(0.630488\pi\)
\(674\) 1.88387e28 + 2.55581e28i 0.973761 + 1.32108i
\(675\) 1.54729e28 0.788015
\(676\) 7.25546e27 2.34205e28i 0.364081 1.17525i
\(677\) 2.48298e28i 1.22769i −0.789428 0.613843i \(-0.789623\pi\)
0.789428 0.613843i \(-0.210377\pi\)
\(678\) −1.53323e27 2.08010e27i −0.0746982 0.101341i
\(679\) 1.94999e28i 0.936127i
\(680\) 1.05247e28 + 3.02547e28i 0.497874 + 1.43121i
\(681\) −1.00517e28 −0.468562
\(682\) 4.37628e27 3.22573e27i 0.201030 0.148178i
\(683\) 9.69721e27 0.438975 0.219488 0.975615i \(-0.429561\pi\)
0.219488 + 0.975615i \(0.429561\pi\)
\(684\) −7.64773e27 + 2.46867e28i −0.341171 + 1.10129i
\(685\) 2.44157e28i 1.07340i
\(686\) −1.84544e28 + 1.36027e28i −0.799576 + 0.589363i
\(687\) 1.25281e28i 0.534957i
\(688\) 6.66691e27 + 4.56921e27i 0.280569 + 0.192290i
\(689\) 4.44901e27 0.184532
\(690\) −7.75516e27 1.05213e28i −0.317030 0.430107i
\(691\) −9.52315e27 −0.383707 −0.191854 0.981424i \(-0.561450\pi\)
−0.191854 + 0.981424i \(0.561450\pi\)
\(692\) 2.45381e27 + 7.60169e26i 0.0974496 + 0.0301890i
\(693\) 3.30059e28i 1.29199i
\(694\) −1.69963e28 2.30585e28i −0.655782 0.889685i
\(695\) 1.33760e28i 0.508719i
\(696\) 7.08905e26 + 2.03785e27i 0.0265764 + 0.0763976i
\(697\) 3.68257e28 1.36089
\(698\) −2.42445e27 + 1.78705e27i −0.0883202 + 0.0651003i
\(699\) −1.07646e28 −0.386568
\(700\) 2.84015e28 + 8.79853e27i 1.00545 + 0.311480i
\(701\) 5.09671e28i 1.77873i −0.457199 0.889365i \(-0.651147\pi\)
0.457199 0.889365i \(-0.348853\pi\)
\(702\) 2.63296e28 1.94074e28i 0.905885 0.667723i
\(703\) 4.39985e28i 1.49240i
\(704\) −3.62375e28 + 2.86828e28i −1.21180 + 0.959170i
\(705\) 9.62494e27 0.317327
\(706\) −1.10671e27 1.50144e27i −0.0359737 0.0488048i
\(707\) 3.12646e28 1.00198
\(708\) 1.54193e27 4.97731e27i 0.0487227 0.157276i
\(709\) 5.45169e28i 1.69851i −0.527981 0.849256i \(-0.677051\pi\)
0.527981 0.849256i \(-0.322949\pi\)
\(710\) 1.61566e28 + 2.19194e28i 0.496327 + 0.673355i
\(711\) 1.01072e28i 0.306151i
\(712\) −3.01030e28 + 1.04719e28i −0.899104 + 0.312771i
\(713\) 4.97929e27 0.146647
\(714\) −1.21678e28 + 8.96883e27i −0.353371 + 0.260468i
\(715\) −1.15274e29 −3.30119
\(716\) 9.43775e27 3.04648e28i 0.266525 0.860337i
\(717\) 2.15711e28i 0.600731i
\(718\) −2.56615e28 + 1.89150e28i −0.704755 + 0.519471i
\(719\) 9.63091e27i 0.260843i 0.991459 + 0.130421i \(0.0416330\pi\)
−0.991459 + 0.130421i \(0.958367\pi\)
\(720\) 2.51426e28 3.66854e28i 0.671561 0.979870i
\(721\) −5.16949e28 −1.36174
\(722\) 2.11714e28 + 2.87228e28i 0.550020 + 0.746200i
\(723\) −1.38547e27 −0.0354987
\(724\) −2.36083e27 7.31365e26i −0.0596594 0.0184820i
\(725\) 8.24428e27i 0.205481i
\(726\) 1.37954e28 + 1.87159e28i 0.339132 + 0.460092i
\(727\) 5.73358e28i 1.39021i 0.718906 + 0.695107i \(0.244643\pi\)
−0.718906 + 0.695107i \(0.755357\pi\)
\(728\) 5.93654e28 2.06514e28i 1.41978 0.493896i
\(729\) −5.16986e27 −0.121956
\(730\) −8.00644e28 + 5.90151e28i −1.86299 + 1.37320i
\(731\) −1.57005e28 −0.360363
\(732\) −1.54387e28 4.78276e27i −0.349542 0.108285i
\(733\) 4.62077e28i 1.03199i −0.856593 0.515993i \(-0.827423\pi\)
0.856593 0.515993i \(-0.172577\pi\)
\(734\) 3.81413e28 2.81137e28i 0.840300 0.619381i
\(735\) 3.56476e26i 0.00774741i
\(736\) −4.23025e28 + 1.45408e27i −0.906960 + 0.0311753i
\(737\) −2.32935e28 −0.492673
\(738\) −3.03361e28 4.11564e28i −0.632990 0.858763i
\(739\) 6.84208e28 1.40846 0.704229 0.709973i \(-0.251293\pi\)
0.704229 + 0.709973i \(0.251293\pi\)
\(740\) −2.24055e28 + 7.23245e28i −0.455027 + 1.46882i
\(741\) 4.25935e28i 0.853418i
\(742\) 3.73301e27 + 5.06449e27i 0.0737939 + 0.100115i
\(743\) 8.05426e27i 0.157086i −0.996911 0.0785430i \(-0.974973\pi\)
0.996911 0.0785430i \(-0.0250268\pi\)
\(744\) −1.13580e27 3.26502e27i −0.0218561 0.0628284i
\(745\) 1.19821e29 2.27494
\(746\) 5.92295e27 4.36577e27i 0.110956 0.0817849i
\(747\) 4.13899e28 0.765047
\(748\) 2.65663e28 8.57553e28i 0.484523 1.56403i
\(749\) 6.09790e28i 1.09739i
\(750\) −1.22064e27 + 8.99725e26i −0.0216757 + 0.0159771i
\(751\) 1.10694e29i 1.93965i 0.243792 + 0.969827i \(0.421608\pi\)
−0.243792 + 0.969827i \(0.578392\pi\)
\(752\) 1.76209e28 2.57105e28i 0.304683 0.444562i
\(753\) 1.26559e28 0.215945
\(754\) 1.03407e28 + 1.40289e28i 0.174114 + 0.236217i
\(755\) −8.71651e25 −0.00144835
\(756\) 4.41845e28 + 1.36880e28i 0.724523 + 0.224451i
\(757\) 1.05202e29i 1.70242i 0.524827 + 0.851209i \(0.324130\pi\)
−0.524827 + 0.851209i \(0.675870\pi\)
\(758\) 3.64326e28 + 4.94273e28i 0.581833 + 0.789360i
\(759\) 3.66316e28i 0.577349i
\(760\)