Properties

Label 12.20.b.a.11.4
Level 12
Weight 20
Character 12.11
Analytic conductor 27.458
Analytic rank 0
Dimension 36
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 20 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(27.4580035868\)
Analytic rank: \(0\)
Dimension: \(36\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) = 12.11
Dual form 12.20.b.a.11.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +O(q^{10})\) \(q+(-706.401 + 159.015i) q^{2} +(-32549.6 + 10138.3i) q^{3} +(473717. - 224656. i) q^{4} -5.54418e6i q^{5} +(2.13809e7 - 1.23376e7i) q^{6} -1.49965e8i q^{7} +(-2.98910e8 + 2.34025e8i) q^{8} +(9.56692e8 - 6.59995e8i) q^{9} +(8.81605e8 + 3.91641e9i) q^{10} -2.49508e6 q^{11} +(-1.31417e10 + 1.21151e10i) q^{12} +4.88082e10 q^{13} +(2.38467e10 + 1.05936e11i) q^{14} +(5.62085e10 + 1.80461e11i) q^{15} +(1.73937e11 - 2.12847e11i) q^{16} -4.51471e11i q^{17} +(-5.70859e11 + 6.18349e11i) q^{18} +6.03024e11i q^{19} +(-1.24553e12 - 2.62637e12i) q^{20} +(1.52039e12 + 4.88132e12i) q^{21} +(1.76253e9 - 3.96754e8i) q^{22} +7.40098e12 q^{23} +(7.35680e12 - 1.06479e13i) q^{24} -1.16644e13 q^{25} +(-3.44782e13 + 7.76122e12i) q^{26} +(-2.44487e13 + 3.11818e13i) q^{27} +(-3.36906e13 - 7.10412e13i) q^{28} -1.10755e14i q^{29} +(-6.84016e13 - 1.18540e14i) q^{30} -2.18703e14i q^{31} +(-8.90238e13 + 1.78014e14i) q^{32} +(8.12138e10 - 2.52958e10i) q^{33} +(7.17904e13 + 3.18919e14i) q^{34} -8.31435e14 q^{35} +(3.04929e14 - 5.27577e14i) q^{36} +4.99785e14 q^{37} +(-9.58896e13 - 4.25977e14i) q^{38} +(-1.58869e15 + 4.94832e14i) q^{39} +(1.29748e15 + 1.65721e15i) q^{40} -1.26797e13i q^{41} +(-1.85021e15 - 3.20640e15i) q^{42} -3.26952e15i q^{43} +(-1.18196e12 + 5.60534e11i) q^{44} +(-3.65913e15 - 5.30407e15i) q^{45} +(-5.22806e15 + 1.17686e15i) q^{46} +1.12738e16 q^{47} +(-3.50369e15 + 8.69150e15i) q^{48} -1.10907e16 q^{49} +(8.23976e15 - 1.85481e15i) q^{50} +(4.57714e15 + 1.46952e16i) q^{51} +(2.31213e16 - 1.09651e16i) q^{52} +3.23098e16i q^{53} +(1.23122e16 - 2.59145e16i) q^{54} +1.38332e13i q^{55} +(3.50957e16 + 4.48262e16i) q^{56} +(-6.11364e15 - 1.96282e16i) q^{57} +(1.76117e16 + 7.82375e16i) q^{58} +6.67474e16 q^{59} +(6.71685e16 + 7.28597e16i) q^{60} -1.62842e17 q^{61} +(3.47770e16 + 1.54492e17i) q^{62} +(-9.89764e16 - 1.43471e17i) q^{63} +(3.45797e16 - 1.39905e17i) q^{64} -2.70602e17i q^{65} +(-5.33471e13 + 3.07832e13i) q^{66} -4.88693e15i q^{67} +(-1.01426e17 - 2.13869e17i) q^{68} +(-2.40899e17 + 7.50333e16i) q^{69} +(5.87327e17 - 1.32210e17i) q^{70} -2.98345e17 q^{71} +(-1.31510e17 + 4.21169e17i) q^{72} -9.07454e17 q^{73} +(-3.53049e17 + 7.94731e16i) q^{74} +(3.79672e17 - 1.18257e17i) q^{75} +(1.35473e17 + 2.85663e17i) q^{76} +3.74176e14i q^{77} +(1.04357e18 - 6.02175e17i) q^{78} -3.92004e17i q^{79} +(-1.18006e18 - 9.64339e17i) q^{80} +(4.79666e17 - 1.26282e18i) q^{81} +(2.01625e15 + 8.95693e15i) q^{82} -8.04463e17 q^{83} +(1.81685e18 + 1.97080e18i) q^{84} -2.50303e18 q^{85} +(5.19901e17 + 2.30959e18i) q^{86} +(1.12287e18 + 3.60503e18i) q^{87} +(7.45805e14 - 5.83911e14i) q^{88} -1.37583e18i q^{89} +(3.42824e18 + 3.16494e18i) q^{90} -7.31955e18i q^{91} +(3.50597e18 - 1.66267e18i) q^{92} +(2.21728e18 + 7.11870e18i) q^{93} +(-7.96384e18 + 1.79270e18i) q^{94} +3.34327e18 q^{95} +(1.09293e18 - 6.69682e18i) q^{96} -1.68560e18 q^{97} +(7.83452e18 - 1.76359e18i) q^{98} +(-2.38702e15 + 1.64674e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} + O(q^{10}) \) \( 36q - 47880q^{4} + 21771144q^{6} - 809473644q^{9} - 4162950000q^{10} - 2268767880q^{12} - 25913431656q^{13} + 791689296672q^{16} + 2852271258192q^{18} - 1650825908424q^{21} + 7247870602416q^{22} + 23719435803936q^{24} - 118879690462380q^{25} - 7629081673968q^{28} + 37456727138640q^{30} + 529254701828640q^{33} - 248241675948480q^{34} - 1177548745309416q^{36} + 1847838600168120q^{37} - 40433256181440q^{40} - 2709671988768336q^{42} - 4365410114088000q^{45} + 17206125364795104q^{46} + 1561106052682272q^{48} - 49399737041580084q^{49} + 16558671470242896q^{52} + 40087412948587896q^{54} + 44803667812766472q^{57} - 34645536255764880q^{58} + 50260381053157440q^{60} + 174742350239997144q^{61} - 139766490424918656q^{64} - 87772097712685968q^{66} - 957190369821780672q^{69} + 244663962371376480q^{70} + 54134736422921280q^{72} - 1445122541399481432q^{73} + 2744130151937256048q^{76} + 1125465917961999024q^{78} + 1033298241353042436q^{81} + 1064985418859680800q^{82} + 1920709484261873424q^{84} - 1802899595088057600q^{85} - 9209792381828477760q^{88} - 5194944179528261040q^{90} + 6719944190337314136q^{93} - 3835186345170303552q^{94} - 11947184361208227456q^{96} + 12765226159947004488q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −706.401 + 159.015i −0.975588 + 0.219610i
\(3\) −32549.6 + 10138.3i −0.954759 + 0.297381i
\(4\) 473717. 224656.i 0.903543 0.428497i
\(5\) 5.54418e6i 1.26947i −0.772730 0.634735i \(-0.781109\pi\)
0.772730 0.634735i \(-0.218891\pi\)
\(6\) 2.13809e7 1.23376e7i 0.866143 0.499795i
\(7\) 1.49965e8i 1.40462i −0.711870 0.702312i \(-0.752151\pi\)
0.711870 0.702312i \(-0.247849\pi\)
\(8\) −2.98910e8 + 2.34025e8i −0.787383 + 0.616464i
\(9\) 9.56692e8 6.59995e8i 0.823129 0.567854i
\(10\) 8.81605e8 + 3.91641e9i 0.278788 + 1.23848i
\(11\) −2.49508e6 −0.000319046 −0.000159523 1.00000i \(-0.500051\pi\)
−0.000159523 1.00000i \(0.500051\pi\)
\(12\) −1.31417e10 + 1.21151e10i −0.735239 + 0.677808i
\(13\) 4.88082e10 1.27653 0.638265 0.769816i \(-0.279652\pi\)
0.638265 + 0.769816i \(0.279652\pi\)
\(14\) 2.38467e10 + 1.05936e11i 0.308469 + 1.37033i
\(15\) 5.62085e10 + 1.80461e11i 0.377516 + 1.21204i
\(16\) 1.73937e11 2.12847e11i 0.632780 0.774332i
\(17\) 4.51471e11i 0.923347i −0.887050 0.461673i \(-0.847249\pi\)
0.887050 0.461673i \(-0.152751\pi\)
\(18\) −5.70859e11 + 6.18349e11i −0.678329 + 0.734759i
\(19\) 6.03024e11i 0.428722i 0.976755 + 0.214361i \(0.0687669\pi\)
−0.976755 + 0.214361i \(0.931233\pi\)
\(20\) −1.24553e12 2.62637e12i −0.543964 1.14702i
\(21\) 1.52039e12 + 4.88132e12i 0.417708 + 1.34108i
\(22\) 1.76253e9 3.96754e8i 0.000311258 7.00657e-5i
\(23\) 7.40098e12 0.856791 0.428395 0.903591i \(-0.359079\pi\)
0.428395 + 0.903591i \(0.359079\pi\)
\(24\) 7.35680e12 1.06479e13i 0.568437 0.822727i
\(25\) −1.16644e13 −0.611552
\(26\) −3.44782e13 + 7.76122e12i −1.24537 + 0.280339i
\(27\) −2.44487e13 + 3.11818e13i −0.617021 + 0.786946i
\(28\) −3.36906e13 7.10412e13i −0.601877 1.26914i
\(29\) 1.10755e14i 1.41770i −0.705362 0.708848i \(-0.749215\pi\)
0.705362 0.708848i \(-0.250785\pi\)
\(30\) −6.84016e13 1.18540e14i −0.634475 1.09954i
\(31\) 2.18703e14i 1.48566i −0.669481 0.742829i \(-0.733483\pi\)
0.669481 0.742829i \(-0.266517\pi\)
\(32\) −8.90238e13 + 1.78014e14i −0.447282 + 0.894393i
\(33\) 8.12138e10 2.52958e10i 0.000304612 9.48782e-5i
\(34\) 7.17904e13 + 3.18919e14i 0.202776 + 0.900806i
\(35\) −8.31435e14 −1.78313
\(36\) 3.04929e14 5.27577e14i 0.500409 0.865789i
\(37\) 4.99785e14 0.632218 0.316109 0.948723i \(-0.397623\pi\)
0.316109 + 0.948723i \(0.397623\pi\)
\(38\) −9.58896e13 4.25977e14i −0.0941515 0.418256i
\(39\) −1.58869e15 + 4.94832e14i −1.21878 + 0.379616i
\(40\) 1.29748e15 + 1.65721e15i 0.782582 + 0.999559i
\(41\) 1.26797e13i 0.00604869i −0.999995 0.00302435i \(-0.999037\pi\)
0.999995 0.00302435i \(-0.000962681\pi\)
\(42\) −1.85021e15 3.20640e15i −0.702024 1.21661i
\(43\) 3.26952e15i 0.992050i −0.868308 0.496025i \(-0.834792\pi\)
0.868308 0.496025i \(-0.165208\pi\)
\(44\) −1.18196e12 + 5.60534e11i −0.000288272 + 0.000136710i
\(45\) −3.65913e15 5.30407e15i −0.720873 1.04494i
\(46\) −5.22806e15 + 1.17686e15i −0.835874 + 0.188160i
\(47\) 1.12738e16 1.46940 0.734702 0.678390i \(-0.237322\pi\)
0.734702 + 0.678390i \(0.237322\pi\)
\(48\) −3.50369e15 + 8.69150e15i −0.373881 + 0.927477i
\(49\) −1.10907e16 −0.972967
\(50\) 8.23976e15 1.85481e15i 0.596622 0.134303i
\(51\) 4.57714e15 + 1.46952e16i 0.274586 + 0.881574i
\(52\) 2.31213e16 1.09651e16i 1.15340 0.546990i
\(53\) 3.23098e16i 1.34497i 0.740109 + 0.672487i \(0.234774\pi\)
−0.740109 + 0.672487i \(0.765226\pi\)
\(54\) 1.23122e16 2.59145e16i 0.429137 0.903239i
\(55\) 1.38332e13i 0.000405019i
\(56\) 3.50957e16 + 4.48262e16i 0.865899 + 1.10598i
\(57\) −6.11364e15 1.96282e16i −0.127494 0.409326i
\(58\) 1.76117e16 + 7.82375e16i 0.311340 + 1.38309i
\(59\) 6.67474e16 1.00309 0.501545 0.865132i \(-0.332765\pi\)
0.501545 + 0.865132i \(0.332765\pi\)
\(60\) 6.71685e16 + 7.28597e16i 0.860456 + 0.933363i
\(61\) −1.62842e17 −1.78293 −0.891464 0.453091i \(-0.850321\pi\)
−0.891464 + 0.453091i \(0.850321\pi\)
\(62\) 3.47770e16 + 1.54492e17i 0.326265 + 1.44939i
\(63\) −9.89764e16 1.43471e17i −0.797621 1.15619i
\(64\) 3.45797e16 1.39905e17i 0.239945 0.970786i
\(65\) 2.70602e17i 1.62052i
\(66\) −5.33471e13 + 3.07832e13i −0.000276340 + 0.000159458i
\(67\) 4.88693e15i 0.0219445i −0.999940 0.0109723i \(-0.996507\pi\)
0.999940 0.0109723i \(-0.00349265\pi\)
\(68\) −1.01426e17 2.13869e17i −0.395652 0.834284i
\(69\) −2.40899e17 + 7.50333e16i −0.818028 + 0.254793i
\(70\) 5.87327e17 1.32210e17i 1.73960 0.391592i
\(71\) −2.98345e17 −0.772261 −0.386131 0.922444i \(-0.626189\pi\)
−0.386131 + 0.922444i \(0.626189\pi\)
\(72\) −1.31510e17 + 4.21169e17i −0.298057 + 0.954548i
\(73\) −9.07454e17 −1.80409 −0.902044 0.431645i \(-0.857933\pi\)
−0.902044 + 0.431645i \(0.857933\pi\)
\(74\) −3.53049e17 + 7.94731e16i −0.616784 + 0.138841i
\(75\) 3.79672e17 1.18257e17i 0.583885 0.181864i
\(76\) 1.35473e17 + 2.85663e17i 0.183706 + 0.387369i
\(77\) 3.74176e14i 0.000448140i
\(78\) 1.04357e18 6.02175e17i 1.10566 0.638004i
\(79\) 3.92004e17i 0.367987i −0.982927 0.183994i \(-0.941097\pi\)
0.982927 0.183994i \(-0.0589026\pi\)
\(80\) −1.18006e18 9.64339e17i −0.982990 0.803295i
\(81\) 4.79666e17 1.26282e18i 0.355084 0.934834i
\(82\) 2.01625e15 + 8.95693e15i 0.00132835 + 0.00590103i
\(83\) −8.04463e17 −0.472350 −0.236175 0.971711i \(-0.575894\pi\)
−0.236175 + 0.971711i \(0.575894\pi\)
\(84\) 1.81685e18 + 1.97080e18i 0.952065 + 1.03273i
\(85\) −2.50303e18 −1.17216
\(86\) 5.19901e17 + 2.30959e18i 0.217864 + 0.967832i
\(87\) 1.12287e18 + 3.60503e18i 0.421595 + 1.35356i
\(88\) 7.45805e14 5.83911e14i 0.000251212 0.000196680i
\(89\) 1.37583e18i 0.416255i −0.978102 0.208127i \(-0.933263\pi\)
0.978102 0.208127i \(-0.0667368\pi\)
\(90\) 3.42824e18 + 3.16494e18i 0.932753 + 0.861117i
\(91\) 7.31955e18i 1.79305i
\(92\) 3.50597e18 1.66267e18i 0.774147 0.367132i
\(93\) 2.21728e18 + 7.11870e18i 0.441806 + 1.41845i
\(94\) −7.96384e18 + 1.79270e18i −1.43353 + 0.322696i
\(95\) 3.34327e18 0.544249
\(96\) 1.09293e18 6.69682e18i 0.161071 0.986943i
\(97\) −1.68560e18 −0.225125 −0.112562 0.993645i \(-0.535906\pi\)
−0.112562 + 0.993645i \(0.535906\pi\)
\(98\) 7.83452e18 1.76359e18i 0.949215 0.213673i
\(99\) −2.38702e15 + 1.64674e15i −0.000262616 + 0.000181172i
\(100\) −5.52563e18 + 2.62048e18i −0.552563 + 0.262048i
\(101\) 2.15370e18i 0.195944i 0.995189 + 0.0979722i \(0.0312356\pi\)
−0.995189 + 0.0979722i \(0.968764\pi\)
\(102\) −5.57005e18 9.65287e18i −0.461485 0.799751i
\(103\) 2.29597e19i 1.73385i 0.498438 + 0.866926i \(0.333907\pi\)
−0.498438 + 0.866926i \(0.666093\pi\)
\(104\) −1.45893e19 + 1.14224e19i −1.00512 + 0.786935i
\(105\) 2.70629e19 8.42933e18i 1.70246 0.530267i
\(106\) −5.13773e18 2.28237e19i −0.295370 1.31214i
\(107\) 5.85665e18 0.307967 0.153983 0.988073i \(-0.450790\pi\)
0.153983 + 0.988073i \(0.450790\pi\)
\(108\) −4.57659e18 + 2.02639e19i −0.220301 + 0.975432i
\(109\) 2.20095e19 0.970641 0.485321 0.874336i \(-0.338703\pi\)
0.485321 + 0.874336i \(0.338703\pi\)
\(110\) −2.19967e15 9.77176e15i −8.89462e−5 0.000395132i
\(111\) −1.62678e19 + 5.06697e18i −0.603616 + 0.188009i
\(112\) −3.19196e19 2.60846e19i −1.08764 0.888818i
\(113\) 3.71474e19i 1.16328i 0.813447 + 0.581639i \(0.197588\pi\)
−0.813447 + 0.581639i \(0.802412\pi\)
\(114\) 7.43985e18 + 1.28932e19i 0.214273 + 0.371335i
\(115\) 4.10323e19i 1.08767i
\(116\) −2.48818e19 5.24666e19i −0.607479 1.28095i
\(117\) 4.66944e19 3.22132e19i 1.05075 0.724883i
\(118\) −4.71504e19 + 1.06138e19i −0.978603 + 0.220288i
\(119\) −6.77050e19 −1.29695
\(120\) −5.90337e19 4.07874e19i −1.04443 0.721613i
\(121\) −6.11591e19 −1.00000
\(122\) 1.15032e20 2.58943e19i 1.73940 0.391549i
\(123\) 1.28550e17 + 4.12718e17i 0.00179876 + 0.00577504i
\(124\) −4.91330e19 1.03603e20i −0.636601 1.34236i
\(125\) 4.10772e19i 0.493123i
\(126\) 9.27310e19 + 8.56092e19i 1.03206 + 0.952796i
\(127\) 7.81349e18i 0.0806695i 0.999186 + 0.0403348i \(0.0128424\pi\)
−0.999186 + 0.0403348i \(0.987158\pi\)
\(128\) −2.18021e18 + 1.04328e20i −0.0208932 + 0.999782i
\(129\) 3.31473e19 + 1.06422e20i 0.295016 + 0.947168i
\(130\) 4.30296e19 + 1.91153e20i 0.355881 + 1.58096i
\(131\) 8.54542e19 0.657138 0.328569 0.944480i \(-0.393434\pi\)
0.328569 + 0.944480i \(0.393434\pi\)
\(132\) 3.27895e16 3.02282e16i 0.000234575 0.000216252i
\(133\) 9.04328e19 0.602193
\(134\) 7.77093e17 + 3.45213e18i 0.00481923 + 0.0214088i
\(135\) 1.72877e20 + 1.35548e20i 0.999004 + 0.783289i
\(136\) 1.05655e20 + 1.34949e20i 0.569210 + 0.727028i
\(137\) 1.34424e20i 0.675512i −0.941234 0.337756i \(-0.890332\pi\)
0.941234 0.337756i \(-0.109668\pi\)
\(138\) 1.58240e20 9.13100e19i 0.742104 0.428220i
\(139\) 3.67041e19i 0.160722i −0.996766 0.0803608i \(-0.974393\pi\)
0.996766 0.0803608i \(-0.0256073\pi\)
\(140\) −3.93865e20 + 1.86787e20i −1.61113 + 0.764065i
\(141\) −3.66958e20 + 1.14297e20i −1.40293 + 0.436973i
\(142\) 2.10751e20 4.74412e19i 0.753409 0.169596i
\(143\) −1.21780e17 −0.000407272
\(144\) 2.59266e19 3.18426e20i 0.0811526 0.996702i
\(145\) −6.14046e20 −1.79972
\(146\) 6.41027e20 1.44298e20i 1.76005 0.396195i
\(147\) 3.60999e20 1.12441e20i 0.928949 0.289342i
\(148\) 2.36757e20 1.12280e20i 0.571236 0.270904i
\(149\) 7.43168e19i 0.168197i 0.996457 + 0.0840983i \(0.0268010\pi\)
−0.996457 + 0.0840983i \(0.973199\pi\)
\(150\) −2.49396e20 + 1.43911e20i −0.529692 + 0.305651i
\(151\) 1.53578e20i 0.306231i −0.988208 0.153115i \(-0.951069\pi\)
0.988208 0.153115i \(-0.0489306\pi\)
\(152\) −1.41123e20 1.80250e20i −0.264291 0.337568i
\(153\) −2.97968e20 4.31918e20i −0.524326 0.760034i
\(154\) −5.94993e16 2.64318e17i −9.84159e−5 0.000437200i
\(155\) −1.21253e21 −1.88600
\(156\) −6.41421e20 + 5.91319e20i −0.938555 + 0.865243i
\(157\) 4.76448e20 0.656098 0.328049 0.944661i \(-0.393609\pi\)
0.328049 + 0.944661i \(0.393609\pi\)
\(158\) 6.23343e19 + 2.76912e20i 0.0808137 + 0.359004i
\(159\) −3.27566e20 1.05167e21i −0.399969 1.28413i
\(160\) 9.86939e20 + 4.93564e20i 1.13540 + 0.567810i
\(161\) 1.10989e21i 1.20347i
\(162\) −1.38029e20 + 9.68333e20i −0.141117 + 0.989993i
\(163\) 5.72589e20i 0.552155i 0.961135 + 0.276077i \(0.0890346\pi\)
−0.961135 + 0.276077i \(0.910965\pi\)
\(164\) −2.84856e18 6.00657e18i −0.00259185 0.00546525i
\(165\) −1.40245e17 4.50264e17i −0.000120445 0.000386696i
\(166\) 5.68273e20 1.27921e20i 0.460819 0.103733i
\(167\) −9.88977e19 −0.0757495 −0.0378747 0.999282i \(-0.512059\pi\)
−0.0378747 + 0.999282i \(0.512059\pi\)
\(168\) −1.59681e21 1.10327e21i −1.15562 0.798440i
\(169\) 9.20324e20 0.629531
\(170\) 1.76815e21 3.98019e20i 1.14355 0.257418i
\(171\) 3.97993e20 + 5.76908e20i 0.243451 + 0.352894i
\(172\) −7.34517e20 1.54883e21i −0.425091 0.896360i
\(173\) 2.94806e21i 1.61473i 0.590055 + 0.807363i \(0.299106\pi\)
−0.590055 + 0.807363i \(0.700894\pi\)
\(174\) −1.36645e21 2.36805e21i −0.708558 1.22793i
\(175\) 1.74926e21i 0.859000i
\(176\) −4.33987e17 + 5.31069e17i −0.000201886 + 0.000247048i
\(177\) −2.17260e21 + 6.76704e20i −0.957709 + 0.298300i
\(178\) 2.18777e20 + 9.71886e20i 0.0914136 + 0.406093i
\(179\) 9.70172e20 0.384366 0.192183 0.981359i \(-0.438443\pi\)
0.192183 + 0.981359i \(0.438443\pi\)
\(180\) −2.92498e21 1.69058e21i −1.09909 0.635254i
\(181\) 3.97411e21 1.41675 0.708375 0.705836i \(-0.249429\pi\)
0.708375 + 0.705836i \(0.249429\pi\)
\(182\) 1.16391e21 + 5.17054e21i 0.393770 + 1.74927i
\(183\) 5.30045e21 1.65094e21i 1.70227 0.530209i
\(184\) −2.21223e21 + 1.73201e21i −0.674623 + 0.528180i
\(185\) 2.77090e21i 0.802581i
\(186\) −2.69826e21 4.67608e21i −0.742526 1.28679i
\(187\) 1.12645e18i 0.000294590i
\(188\) 5.34060e21 2.53273e21i 1.32767 0.629636i
\(189\) 4.67619e21 + 3.66646e21i 1.10536 + 0.866683i
\(190\) −2.36169e21 + 5.31629e20i −0.530963 + 0.119522i
\(191\) −5.34922e21 −1.14412 −0.572062 0.820210i \(-0.693856\pi\)
−0.572062 + 0.820210i \(0.693856\pi\)
\(192\) 2.92842e20 + 4.90443e21i 0.0596036 + 0.998222i
\(193\) 2.15483e21 0.417464 0.208732 0.977973i \(-0.433066\pi\)
0.208732 + 0.977973i \(0.433066\pi\)
\(194\) 1.19071e21 2.68035e20i 0.219629 0.0494396i
\(195\) 2.74344e21 + 8.80797e21i 0.481910 + 1.54720i
\(196\) −5.25387e21 + 2.49160e21i −0.879117 + 0.416914i
\(197\) 2.73703e20i 0.0436365i −0.999762 0.0218182i \(-0.993054\pi\)
0.999762 0.0218182i \(-0.00694551\pi\)
\(198\) 1.42434e18 1.54283e18i 0.000216418 0.000234422i
\(199\) 5.79917e21i 0.839965i −0.907532 0.419983i \(-0.862036\pi\)
0.907532 0.419983i \(-0.137964\pi\)
\(200\) 3.48662e21 2.72977e21i 0.481526 0.376999i
\(201\) 4.95451e19 + 1.59068e20i 0.00652587 + 0.0209517i
\(202\) −3.42470e20 1.52138e21i −0.0430313 0.191161i
\(203\) −1.66094e22 −1.99133
\(204\) 5.46963e21 + 5.93308e21i 0.625852 + 0.678881i
\(205\) −7.02984e19 −0.00767863
\(206\) −3.65092e21 1.62187e22i −0.380771 1.69152i
\(207\) 7.08045e21 4.88461e21i 0.705249 0.486532i
\(208\) 8.48957e21 1.03887e22i 0.807763 0.988458i
\(209\) 1.50459e18i 0.000136782i
\(210\) −1.77769e22 + 1.02579e22i −1.54444 + 0.891198i
\(211\) 6.69519e21i 0.556006i −0.960580 0.278003i \(-0.910328\pi\)
0.960580 0.278003i \(-0.0896725\pi\)
\(212\) 7.25860e21 + 1.53057e22i 0.576318 + 1.21524i
\(213\) 9.71101e21 3.02471e21i 0.737323 0.229656i
\(214\) −4.13715e21 + 9.31293e20i −0.300448 + 0.0676325i
\(215\) −1.81268e22 −1.25938
\(216\) 1.06554e19 1.50422e22i 0.000708367 1.00000i
\(217\) −3.27979e22 −2.08679
\(218\) −1.55475e22 + 3.49983e21i −0.946946 + 0.213162i
\(219\) 2.95373e22 9.20004e21i 1.72247 0.536501i
\(220\) 3.10770e18 + 6.55300e18i 0.000173550 + 0.000365952i
\(221\) 2.20355e22i 1.17868i
\(222\) 1.06859e22 6.16613e21i 0.547591 0.315980i
\(223\) 3.42488e22i 1.68170i 0.541265 + 0.840852i \(0.317945\pi\)
−0.541265 + 0.840852i \(0.682055\pi\)
\(224\) 2.66959e22 + 1.33505e22i 1.25629 + 0.628262i
\(225\) −1.11593e22 + 7.69846e21i −0.503386 + 0.347272i
\(226\) −5.90698e21 2.62410e22i −0.255467 1.13488i
\(227\) 9.15468e21 0.379662 0.189831 0.981817i \(-0.439206\pi\)
0.189831 + 0.981817i \(0.439206\pi\)
\(228\) −7.30572e21 7.92474e21i −0.290591 0.315213i
\(229\) −2.34552e22 −0.894957 −0.447479 0.894295i \(-0.647678\pi\)
−0.447479 + 0.894295i \(0.647678\pi\)
\(230\) 6.52474e21 + 2.89853e22i 0.238863 + 1.06112i
\(231\) −3.79350e18 1.21793e19i −0.000133268 0.000427866i
\(232\) 2.59195e22 + 3.31059e22i 0.873958 + 1.11627i
\(233\) 7.75371e21i 0.250974i −0.992095 0.125487i \(-0.959951\pi\)
0.992095 0.125487i \(-0.0400493\pi\)
\(234\) −2.78626e22 + 3.01805e22i −0.865907 + 0.937942i
\(235\) 6.25041e22i 1.86536i
\(236\) 3.16193e22 1.49952e22i 0.906335 0.429821i
\(237\) 3.97425e21 + 1.27596e22i 0.109432 + 0.351339i
\(238\) 4.78269e22 1.07661e22i 1.26529 0.284824i
\(239\) 5.58610e21 0.142013 0.0710066 0.997476i \(-0.477379\pi\)
0.0710066 + 0.997476i \(0.477379\pi\)
\(240\) 4.81872e22 + 1.94251e22i 1.17740 + 0.474631i
\(241\) −7.82487e21 −0.183787 −0.0918935 0.995769i \(-0.529292\pi\)
−0.0918935 + 0.995769i \(0.529292\pi\)
\(242\) 4.32028e22 9.72518e21i 0.975588 0.219610i
\(243\) −2.81006e21 + 4.59674e22i −0.0610177 + 0.998137i
\(244\) −7.71412e22 + 3.65835e22i −1.61095 + 0.763980i
\(245\) 6.14891e22i 1.23515i
\(246\) −1.56436e20 2.71103e20i −0.00302311 0.00523903i
\(247\) 2.94326e22i 0.547277i
\(248\) 5.11820e22 + 6.53727e22i 0.915855 + 1.16978i
\(249\) 2.61849e22 8.15588e21i 0.450981 0.140468i
\(250\) 6.53186e21 + 2.90169e22i 0.108295 + 0.481085i
\(251\) −5.35960e22 −0.855523 −0.427762 0.903892i \(-0.640698\pi\)
−0.427762 + 0.903892i \(0.640698\pi\)
\(252\) −7.91183e22 4.57288e22i −1.21611 0.702886i
\(253\) −1.84660e19 −0.000273356
\(254\) −1.24246e21 5.51945e21i −0.0177158 0.0787002i
\(255\) 8.14728e22 2.53765e22i 1.11913 0.348578i
\(256\) −1.50495e22 7.40439e22i −0.199179 0.979963i
\(257\) 9.24681e22i 1.17931i −0.807656 0.589654i \(-0.799264\pi\)
0.807656 0.589654i \(-0.200736\pi\)
\(258\) −4.03379e22 6.99054e22i −0.495822 0.859257i
\(259\) 7.49505e22i 0.888028i
\(260\) −6.07923e22 1.28189e23i −0.694387 1.46421i
\(261\) −7.30978e22 1.05958e23i −0.805044 1.16695i
\(262\) −6.03650e22 + 1.35885e22i −0.641095 + 0.144314i
\(263\) −7.84375e22 −0.803423 −0.401712 0.915766i \(-0.631585\pi\)
−0.401712 + 0.915766i \(0.631585\pi\)
\(264\) −1.83558e19 + 2.65673e19i −0.000181358 + 0.000262488i
\(265\) 1.79131e23 1.70740
\(266\) −6.38818e22 + 1.43801e22i −0.587492 + 0.132247i
\(267\) 1.39485e22 + 4.47826e22i 0.123786 + 0.397423i
\(268\) −1.09788e21 2.31502e21i −0.00940316 0.0198278i
\(269\) 1.45532e23i 1.20313i 0.798824 + 0.601565i \(0.205456\pi\)
−0.798824 + 0.601565i \(0.794544\pi\)
\(270\) −1.43675e23 6.82612e22i −1.14663 0.544777i
\(271\) 1.50170e23i 1.15711i 0.815642 + 0.578557i \(0.196384\pi\)
−0.815642 + 0.578557i \(0.803616\pi\)
\(272\) −9.60940e22 7.85276e22i −0.714977 0.584275i
\(273\) 7.42077e22 + 2.38248e23i 0.533217 + 1.71193i
\(274\) 2.13754e22 + 9.49575e22i 0.148349 + 0.659021i
\(275\) 2.91036e19 0.000195113
\(276\) −9.72612e22 + 8.96639e22i −0.629946 + 0.580739i
\(277\) 2.52142e23 1.57793 0.788964 0.614439i \(-0.210618\pi\)
0.788964 + 0.614439i \(0.210618\pi\)
\(278\) 5.83649e21 + 2.59278e22i 0.0352960 + 0.156798i
\(279\) −1.44343e23 2.09232e23i −0.843637 1.22289i
\(280\) 2.48525e23 1.94577e23i 1.40400 1.09923i
\(281\) 1.28348e23i 0.700935i −0.936575 0.350467i \(-0.886023\pi\)
0.936575 0.350467i \(-0.113977\pi\)
\(282\) 2.41045e23 1.39091e23i 1.27272 0.734402i
\(283\) 2.88031e23i 1.47051i 0.677789 + 0.735256i \(0.262938\pi\)
−0.677789 + 0.735256i \(0.737062\pi\)
\(284\) −1.41331e23 + 6.70250e22i −0.697771 + 0.330912i
\(285\) −1.08822e23 + 3.38951e22i −0.519627 + 0.161849i
\(286\) 8.60258e19 1.93648e19i 0.000397330 8.94410e-5i
\(287\) −1.90151e21 −0.00849613
\(288\) 3.23198e22 + 2.29059e23i 0.139714 + 0.990192i
\(289\) 3.52466e22 0.147431
\(290\) 4.33763e23 9.76422e22i 1.75578 0.395236i
\(291\) 5.48657e22 1.70891e22i 0.214940 0.0669478i
\(292\) −4.29876e23 + 2.03865e23i −1.63007 + 0.773047i
\(293\) 3.47250e23i 1.27468i −0.770584 0.637338i \(-0.780036\pi\)
0.770584 0.637338i \(-0.219964\pi\)
\(294\) −2.37131e23 + 1.36833e23i −0.842729 + 0.486284i
\(295\) 3.70059e23i 1.27339i
\(296\) −1.49391e23 + 1.16962e23i −0.497798 + 0.389739i
\(297\) 6.10014e19 7.78010e19i 0.000196858 0.000251072i
\(298\) −1.18174e22 5.24975e22i −0.0369376 0.164091i
\(299\) 3.61229e23 1.09372
\(300\) 1.53290e23 1.41316e23i 0.449637 0.414515i
\(301\) −4.90315e23 −1.39346
\(302\) 2.44212e22 + 1.08488e23i 0.0672513 + 0.298755i
\(303\) −2.18349e22 7.01022e22i −0.0582701 0.187080i
\(304\) 1.28352e23 + 1.04888e23i 0.331973 + 0.271287i
\(305\) 9.02827e23i 2.26337i
\(306\) 2.79166e23 + 2.57726e23i 0.678437 + 0.626333i
\(307\) 1.16531e23i 0.274554i 0.990533 + 0.137277i \(0.0438351\pi\)
−0.990533 + 0.137277i \(0.956165\pi\)
\(308\) 8.40608e19 + 1.77253e20i 0.000192027 + 0.000404914i
\(309\) −2.32772e23 7.47328e23i −0.515614 1.65541i
\(310\) 8.56532e23 1.92810e23i 1.83996 0.414184i
\(311\) 6.98423e23 1.45511 0.727553 0.686051i \(-0.240657\pi\)
0.727553 + 0.686051i \(0.240657\pi\)
\(312\) 3.59073e23 5.19704e23i 0.725627 1.05024i
\(313\) −5.99952e22 −0.117610 −0.0588052 0.998269i \(-0.518729\pi\)
−0.0588052 + 0.998269i \(0.518729\pi\)
\(314\) −3.36564e23 + 7.57622e22i −0.640082 + 0.144086i
\(315\) −7.95427e23 + 5.48743e23i −1.46774 + 1.01256i
\(316\) −8.80660e22 1.85699e23i −0.157682 0.332492i
\(317\) 4.40158e23i 0.764796i 0.923998 + 0.382398i \(0.124902\pi\)
−0.923998 + 0.382398i \(0.875098\pi\)
\(318\) 3.98624e23 + 6.90814e23i 0.672212 + 1.16494i
\(319\) 2.76343e20i 0.000452310i
\(320\) −7.75659e23 1.91716e23i −1.23238 0.304603i
\(321\) −1.90632e23 + 5.93765e22i −0.294034 + 0.0915834i
\(322\) 1.76489e23 + 7.84028e23i 0.264293 + 1.17409i
\(323\) 2.72248e23 0.395859
\(324\) −5.64750e22 7.05980e23i −0.0797405 0.996816i
\(325\) −5.69320e23 −0.780665
\(326\) −9.10500e22 4.04478e23i −0.121259 0.538676i
\(327\) −7.16401e23 + 2.23139e23i −0.926728 + 0.288650i
\(328\) 2.96736e21 + 3.79009e21i 0.00372880 + 0.00476264i
\(329\) 1.69068e24i 2.06396i
\(330\) 1.70667e20 + 2.95766e20i 0.000202427 + 0.000350805i
\(331\) 1.20541e24i 1.38921i −0.719392 0.694604i \(-0.755580\pi\)
0.719392 0.694604i \(-0.244420\pi\)
\(332\) −3.81088e23 + 1.80727e23i −0.426789 + 0.202401i
\(333\) 4.78140e23 3.29855e23i 0.520397 0.359007i
\(334\) 6.98614e22 1.57262e22i 0.0739003 0.0166353i
\(335\) −2.70940e22 −0.0278579
\(336\) 1.30342e24 + 5.25432e23i 1.30276 + 0.525162i
\(337\) −5.16565e23 −0.501928 −0.250964 0.967996i \(-0.580748\pi\)
−0.250964 + 0.967996i \(0.580748\pi\)
\(338\) −6.50118e23 + 1.46345e23i −0.614163 + 0.138251i
\(339\) −3.76612e23 1.20913e24i −0.345937 1.11065i
\(340\) −1.18573e24 + 5.62322e23i −1.05910 + 0.502268i
\(341\) 5.45682e20i 0.000473994i
\(342\) −3.72879e23 3.44242e23i −0.315007 0.290814i
\(343\) 4.62114e22i 0.0379713i
\(344\) 7.65149e23 + 9.77293e23i 0.611563 + 0.781123i
\(345\) 4.15998e23 + 1.33559e24i 0.323452 + 1.03846i
\(346\) −4.68785e23 2.08252e24i −0.354610 1.57531i
\(347\) 1.44732e23 0.106521 0.0532603 0.998581i \(-0.483039\pi\)
0.0532603 + 0.998581i \(0.483039\pi\)
\(348\) 1.34181e24 + 1.45551e24i 0.960925 + 1.04234i
\(349\) −7.90825e23 −0.551110 −0.275555 0.961285i \(-0.588862\pi\)
−0.275555 + 0.961285i \(0.588862\pi\)
\(350\) −2.78158e23 1.23568e24i −0.188645 0.838030i
\(351\) −1.19330e24 + 1.52193e24i −0.787647 + 1.00456i
\(352\) 2.22121e20 4.44158e20i 0.000142704 0.000285353i
\(353\) 3.64188e23i 0.227754i 0.993495 + 0.113877i \(0.0363270\pi\)
−0.993495 + 0.113877i \(0.963673\pi\)
\(354\) 1.42712e24 8.23499e23i 0.868820 0.501340i
\(355\) 1.65408e24i 0.980362i
\(356\) −3.09088e23 6.51753e23i −0.178364 0.376104i
\(357\) 2.20377e24 6.86413e23i 1.23828 0.385689i
\(358\) −6.85330e23 + 1.54271e23i −0.374983 + 0.0844105i
\(359\) 5.80491e23 0.309313 0.154657 0.987968i \(-0.450573\pi\)
0.154657 + 0.987968i \(0.450573\pi\)
\(360\) 2.33504e24 + 7.29114e23i 1.21177 + 0.378374i
\(361\) 1.61478e24 0.816198
\(362\) −2.80731e24 + 6.31941e23i −1.38216 + 0.311132i
\(363\) 1.99070e24 6.20049e23i 0.954759 0.297381i
\(364\) −1.64438e24 3.46739e24i −0.768315 1.62009i
\(365\) 5.03109e24i 2.29023i
\(366\) −3.48172e24 + 2.00908e24i −1.54427 + 0.891100i
\(367\) 7.29018e23i 0.315073i −0.987513 0.157536i \(-0.949645\pi\)
0.987513 0.157536i \(-0.0503551\pi\)
\(368\) 1.28731e24 1.57527e24i 0.542160 0.663440i
\(369\) −8.36852e21 1.21305e22i −0.00343477 0.00497886i
\(370\) 4.40613e23 + 1.95736e24i 0.176255 + 0.782988i
\(371\) 4.84536e24 1.88918
\(372\) 2.64962e24 + 2.87412e24i 1.00699 + 1.09231i
\(373\) 2.85996e24 1.05956 0.529781 0.848135i \(-0.322274\pi\)
0.529781 + 0.848135i \(0.322274\pi\)
\(374\) −1.79123e20 7.95729e20i −6.46949e−5 0.000287399i
\(375\) 4.16452e23 + 1.33705e24i 0.146645 + 0.470814i
\(376\) −3.36986e24 + 2.63836e24i −1.15698 + 0.905835i
\(377\) 5.40576e24i 1.80973i
\(378\) −3.88629e24 1.84641e24i −1.26871 0.602776i
\(379\) 4.82016e24i 1.53458i 0.641301 + 0.767290i \(0.278395\pi\)
−0.641301 + 0.767290i \(0.721605\pi\)
\(380\) 1.58376e24 7.51087e23i 0.491752 0.233209i
\(381\) −7.92154e22 2.54326e23i −0.0239896 0.0770200i
\(382\) 3.77869e24 8.50603e23i 1.11619 0.251261i
\(383\) −5.48430e24 −1.58028 −0.790138 0.612929i \(-0.789991\pi\)
−0.790138 + 0.612929i \(0.789991\pi\)
\(384\) −9.86740e23 3.41793e24i −0.277368 0.960764i
\(385\) 2.07450e21 0.000568900
\(386\) −1.52217e24 + 3.42649e23i −0.407273 + 0.0916791i
\(387\) −2.15786e24 3.12792e24i −0.563339 0.816585i
\(388\) −7.98498e23 + 3.78681e23i −0.203410 + 0.0964654i
\(389\) 3.68660e24i 0.916442i 0.888838 + 0.458221i \(0.151513\pi\)
−0.888838 + 0.458221i \(0.848487\pi\)
\(390\) −3.33856e24 5.78571e24i −0.809927 1.40360i
\(391\) 3.34133e24i 0.791115i
\(392\) 3.31514e24 2.59551e24i 0.766098 0.599799i
\(393\) −2.78150e24 + 8.66360e23i −0.627408 + 0.195420i
\(394\) 4.35227e22 + 1.93344e23i 0.00958300 + 0.0425712i
\(395\) −2.17334e24 −0.467149
\(396\) −7.60822e20 + 1.31635e21i −0.000159654 + 0.000276227i
\(397\) 4.75450e24 0.974082 0.487041 0.873379i \(-0.338076\pi\)
0.487041 + 0.873379i \(0.338076\pi\)
\(398\) 9.22152e23 + 4.09654e24i 0.184465 + 0.819460i
\(399\) −2.94355e24 + 9.16834e23i −0.574949 + 0.179081i
\(400\) −2.02888e24 + 2.48273e24i −0.386978 + 0.473544i
\(401\) 1.08639e24i 0.202356i −0.994868 0.101178i \(-0.967739\pi\)
0.994868 0.101178i \(-0.0322611\pi\)
\(402\) −6.02928e22 1.04487e23i −0.0109678 0.0190071i
\(403\) 1.06745e25i 1.89649i
\(404\) 4.83842e23 + 1.02025e24i 0.0839616 + 0.177044i
\(405\) −7.00131e24 2.65935e24i −1.18674 0.450768i
\(406\) 1.17329e25 2.64114e24i 1.94271 0.437315i
\(407\) −1.24700e21 −0.000201707
\(408\) −4.80720e24 3.32138e24i −0.759662 0.524864i
\(409\) −7.66016e24 −1.18268 −0.591338 0.806423i \(-0.701400\pi\)
−0.591338 + 0.806423i \(0.701400\pi\)
\(410\) 4.96588e22 1.11785e22i 0.00749117 0.00168630i
\(411\) 1.36283e24 + 4.37546e24i 0.200884 + 0.644951i
\(412\) 5.15803e24 + 1.08764e25i 0.742951 + 1.56661i
\(413\) 1.00098e25i 1.40896i
\(414\) −4.22492e24 + 4.57639e24i −0.581186 + 0.629534i
\(415\) 4.46009e24i 0.599634i
\(416\) −4.34509e24 + 8.68853e24i −0.570969 + 1.14172i
\(417\) 3.72117e23 + 1.19470e24i 0.0477955 + 0.153450i
\(418\) 2.39252e20 + 1.06285e21i 3.00387e−5 + 0.000133443i
\(419\) −3.13837e24 −0.385186 −0.192593 0.981279i \(-0.561690\pi\)
−0.192593 + 0.981279i \(0.561690\pi\)
\(420\) 1.09264e25 1.00730e25i 1.31102 1.20862i
\(421\) 3.70615e24 0.434753 0.217377 0.976088i \(-0.430250\pi\)
0.217377 + 0.976088i \(0.430250\pi\)
\(422\) 1.06463e24 + 4.72949e24i 0.122104 + 0.542432i
\(423\) 1.07856e25 7.44066e24i 1.20951 0.834407i
\(424\) −7.56131e24 9.65775e24i −0.829128 1.05901i
\(425\) 5.26615e24i 0.564674i
\(426\) −6.37889e24 + 3.68085e24i −0.668889 + 0.385973i
\(427\) 2.44207e25i 2.50434i
\(428\) 2.77440e24 1.31573e24i 0.278261 0.131963i
\(429\) 3.96390e21 1.23464e21i 0.000388847 0.000121115i
\(430\) 1.28048e25 2.88242e24i 1.22863 0.276571i
\(431\) −3.09919e24 −0.290880 −0.145440 0.989367i \(-0.546460\pi\)
−0.145440 + 0.989367i \(0.546460\pi\)
\(432\) 2.38440e24 + 1.06275e25i 0.218919 + 0.975743i
\(433\) −1.37245e25 −1.23271 −0.616355 0.787468i \(-0.711391\pi\)
−0.616355 + 0.787468i \(0.711391\pi\)
\(434\) 2.31685e25 5.21535e24i 2.03585 0.458280i
\(435\) 1.99870e25 6.22538e24i 1.71830 0.535202i
\(436\) 1.04263e25 4.94457e24i 0.877016 0.415917i
\(437\) 4.46297e24i 0.367325i
\(438\) −1.94022e25 + 1.11958e25i −1.56260 + 0.901675i
\(439\) 1.81655e25i 1.43164i −0.698283 0.715822i \(-0.746052\pi\)
0.698283 0.715822i \(-0.253948\pi\)
\(440\) −3.23731e21 4.13488e21i −0.000249680 0.000318905i
\(441\) −1.06104e25 + 7.31984e24i −0.800878 + 0.552503i
\(442\) 3.50396e24 + 1.55659e25i 0.258850 + 1.14991i
\(443\) 5.94482e24 0.429836 0.214918 0.976632i \(-0.431052\pi\)
0.214918 + 0.976632i \(0.431052\pi\)
\(444\) −6.56801e24 + 6.05497e24i −0.464831 + 0.428522i
\(445\) −7.62783e24 −0.528422
\(446\) −5.44606e24 2.41934e25i −0.369319 1.64065i
\(447\) −7.53445e23 2.41898e24i −0.0500185 0.160587i
\(448\) −2.09809e25 5.18576e24i −1.36359 0.337032i
\(449\) 5.95675e24i 0.379026i −0.981878 0.189513i \(-0.939309\pi\)
0.981878 0.189513i \(-0.0606909\pi\)
\(450\) 6.65874e24 7.21268e24i 0.414833 0.449343i
\(451\) 3.16368e19i 1.92981e-6i
\(452\) 8.34539e24 + 1.75974e25i 0.498462 + 1.05107i
\(453\) 1.55702e24 + 4.99891e24i 0.0910672 + 0.292377i
\(454\) −6.46687e24 + 1.45573e24i −0.370394 + 0.0833776i
\(455\) −4.05809e25 −2.27622
\(456\) 6.42092e24 + 4.43633e24i 0.352721 + 0.243701i
\(457\) 2.63035e25 1.41517 0.707587 0.706626i \(-0.249784\pi\)
0.707587 + 0.706626i \(0.249784\pi\)
\(458\) 1.65688e25 3.72972e24i 0.873109 0.196541i
\(459\) 1.40777e25 + 1.10379e25i 0.726625 + 0.569725i
\(460\) −9.21816e24 1.94377e25i −0.466063 0.982756i
\(461\) 1.31846e25i 0.652991i −0.945199 0.326495i \(-0.894132\pi\)
0.945199 0.326495i \(-0.105868\pi\)
\(462\) 4.61641e21 + 8.00022e21i 0.000223978 + 0.000388153i
\(463\) 1.17965e24i 0.0560706i 0.999607 + 0.0280353i \(0.00892508\pi\)
−0.999607 + 0.0280353i \(0.991075\pi\)
\(464\) −2.35739e25 1.92644e25i −1.09777 0.897089i
\(465\) 3.94674e25 1.22930e25i 1.80067 0.560859i
\(466\) 1.23295e24 + 5.47723e24i 0.0551163 + 0.244847i
\(467\) −1.27273e25 −0.557475 −0.278737 0.960367i \(-0.589916\pi\)
−0.278737 + 0.960367i \(0.589916\pi\)
\(468\) 1.48831e25 2.57501e25i 0.638787 1.10521i
\(469\) −7.32871e23 −0.0308238
\(470\) 9.93905e24 + 4.41529e25i 0.409652 + 1.81983i
\(471\) −1.55082e25 + 4.83037e24i −0.626416 + 0.195111i
\(472\) −1.99515e25 + 1.56206e25i −0.789816 + 0.618369i
\(473\) 8.15770e21i 0.000316510i
\(474\) −4.83637e24 8.38141e24i −0.183918 0.318730i
\(475\) 7.03393e24i 0.262186i
\(476\) −3.20730e25 + 1.52103e25i −1.17185 + 0.555742i
\(477\) 2.13243e25 + 3.09105e25i 0.763749 + 1.10709i
\(478\) −3.94603e24 + 8.88272e23i −0.138546 + 0.0311875i
\(479\) −1.58667e25 −0.546135 −0.273067 0.961995i \(-0.588038\pi\)
−0.273067 + 0.961995i \(0.588038\pi\)
\(480\) −3.71284e25 6.05942e24i −1.25289 0.204474i
\(481\) 2.43936e25 0.807046
\(482\) 5.52749e24 1.24427e24i 0.179300 0.0403614i
\(483\) 1.12524e25 + 3.61265e25i 0.357888 + 1.14902i
\(484\) −2.89721e25 + 1.37398e25i −0.903543 + 0.428497i
\(485\) 9.34527e24i 0.285789i
\(486\) −5.32445e24 3.29182e25i −0.159672 0.987170i
\(487\) 2.17055e25i 0.638329i −0.947699 0.319165i \(-0.896598\pi\)
0.947699 0.319165i \(-0.103402\pi\)
\(488\) 4.86753e25 3.81092e25i 1.40385 1.09911i
\(489\) −5.80508e24 1.86376e25i −0.164200 0.527175i
\(490\) −9.77766e24 4.34359e25i −0.271251 1.20500i
\(491\) 5.61079e25 1.52669 0.763343 0.645994i \(-0.223557\pi\)
0.763343 + 0.645994i \(0.223557\pi\)
\(492\) 1.53616e23 + 1.66632e23i 0.00409985 + 0.00444723i
\(493\) −5.00027e25 −1.30902
\(494\) −4.68020e24 2.07912e25i −0.120187 0.533916i
\(495\) 9.12981e21 + 1.32341e22i 0.000229992 + 0.000333383i
\(496\) −4.65502e25 3.80406e25i −1.15039 0.940095i
\(497\) 4.47414e25i 1.08474i
\(498\) −1.72002e25 + 9.92511e24i −0.409123 + 0.236079i
\(499\) 4.70657e25i 1.09837i −0.835700 0.549186i \(-0.814938\pi\)
0.835700 0.549186i \(-0.185062\pi\)
\(500\) −9.22823e24 1.94589e25i −0.211302 0.445558i
\(501\) 3.21908e24 1.00265e24i 0.0723225 0.0225264i
\(502\) 3.78603e25 8.52254e24i 0.834638 0.187881i
\(503\) −1.83438e25 −0.396821 −0.198410 0.980119i \(-0.563578\pi\)
−0.198410 + 0.980119i \(0.563578\pi\)
\(504\) 6.31608e25 + 1.97219e25i 1.34078 + 0.418658i
\(505\) 1.19405e25 0.248745
\(506\) 1.30444e22 2.93636e21i 0.000266683 6.00316e-5i
\(507\) −2.99562e25 + 9.33051e24i −0.601050 + 0.187210i
\(508\) 1.75535e24 + 3.70138e24i 0.0345667 + 0.0728884i
\(509\) 6.09000e25i 1.17706i −0.808475 0.588530i \(-0.799707\pi\)
0.808475 0.588530i \(-0.200293\pi\)
\(510\) −5.35172e25 + 3.08813e25i −1.01526 + 0.585840i
\(511\) 1.36087e26i 2.53406i
\(512\) 2.24051e25 + 4.99116e25i 0.409526 + 0.912298i
\(513\) −1.88034e25 1.47432e25i −0.337381 0.264530i
\(514\) 1.47038e25 + 6.53196e25i 0.258988 + 1.15052i
\(515\) 1.27292e26 2.20107
\(516\) 3.96107e25 + 4.29669e25i 0.672419 + 0.729394i
\(517\) −2.81291e22 −0.000468808
\(518\) 1.19182e25 + 5.29451e25i 0.195020 + 0.866349i
\(519\) −2.98883e25 9.59583e25i −0.480188 1.54167i
\(520\) 6.33276e25 + 8.08856e25i 0.998990 + 1.27597i
\(521\) 8.86506e25i 1.37317i 0.727051 + 0.686584i \(0.240890\pi\)
−0.727051 + 0.686584i \(0.759110\pi\)
\(522\) 6.84853e25 + 6.32256e25i 1.04166 + 0.961663i
\(523\) 2.41404e25i 0.360561i −0.983615 0.180280i \(-0.942299\pi\)
0.983615 0.180280i \(-0.0577005\pi\)
\(524\) 4.04811e25 1.91978e25i 0.593752 0.281582i
\(525\) −1.77345e25 5.69377e25i −0.255450 0.820138i
\(526\) 5.54084e25 1.24727e25i 0.783810 0.176440i
\(527\) −9.87381e25 −1.37178
\(528\) 8.74197e21 2.16860e22i 0.000119285 0.000295908i
\(529\) −1.98410e25 −0.265910
\(530\) −1.26539e26 + 2.84845e25i −1.66572 + 0.374962i
\(531\) 6.38566e25 4.40529e25i 0.825673 0.569609i
\(532\) 4.28395e25 2.03163e25i 0.544107 0.258038i
\(533\) 6.18873e23i 0.00772134i
\(534\) −1.69744e25 2.94165e25i −0.208042 0.360536i
\(535\) 3.24703e25i 0.390954i
\(536\) 1.14366e24 + 1.46076e24i 0.0135280 + 0.0172787i
\(537\) −3.15787e25 + 9.83589e24i −0.366977 + 0.114303i
\(538\) −2.31417e25 1.02804e26i −0.264219 1.17376i
\(539\) 2.76723e22 0.000310421
\(540\) 1.12347e26 + 2.53734e25i 1.23828 + 0.279665i
\(541\) −6.84884e25 −0.741725 −0.370862 0.928688i \(-0.620938\pi\)
−0.370862 + 0.928688i \(0.620938\pi\)
\(542\) −2.38793e25 1.06080e26i −0.254113 1.12887i
\(543\) −1.29356e26 + 4.02907e25i −1.35265 + 0.421314i
\(544\) 8.03680e25 + 4.01916e25i 0.825835 + 0.412996i
\(545\) 1.22025e26i 1.23220i
\(546\) −9.03054e25 1.56499e26i −0.896156 1.55303i
\(547\) 4.11723e25i 0.401537i 0.979639 + 0.200768i \(0.0643438\pi\)
−0.979639 + 0.200768i \(0.935656\pi\)
\(548\) −3.01993e25 6.36791e25i −0.289455 0.610354i
\(549\) −1.55790e26 + 1.07475e26i −1.46758 + 1.01244i
\(550\) −2.05588e22 + 4.62790e21i −0.000190350 + 4.28488e-5i
\(551\) 6.67880e25 0.607797
\(552\) 5.44475e25 7.88046e25i 0.487031 0.704905i
\(553\) −5.87870e25 −0.516884
\(554\) −1.78113e26 + 4.00942e25i −1.53941 + 0.346529i
\(555\) 2.80922e25 + 9.01916e25i 0.238672 + 0.766272i
\(556\) −8.24580e24 1.73874e25i −0.0688688 0.145219i
\(557\) 1.60444e26i 1.31734i −0.752431 0.658671i \(-0.771119\pi\)
0.752431 0.658671i \(-0.228881\pi\)
\(558\) 1.35235e26 + 1.24849e26i 1.09160 + 1.00776i
\(559\) 1.59579e26i 1.26638i
\(560\) −1.44618e26 + 1.76968e26i −1.12833 + 1.38073i
\(561\) −1.14203e22 3.66657e22i −8.76055e−5 0.000281263i
\(562\) 2.04091e25 + 9.06648e25i 0.153932 + 0.683823i
\(563\) 1.71090e26 1.26881 0.634403 0.773002i \(-0.281246\pi\)
0.634403 + 0.773002i \(0.281246\pi\)
\(564\) −1.48157e26 + 1.36584e26i −1.08036 + 0.995974i
\(565\) 2.05952e26 1.47675
\(566\) −4.58012e25 2.03466e26i −0.322939 1.43461i
\(567\) −1.89380e26 7.19333e25i −1.31309 0.498759i
\(568\) 8.91784e25 6.98202e25i 0.608066 0.476071i
\(569\) 1.43332e26i 0.961115i 0.876963 + 0.480558i \(0.159566\pi\)
−0.876963 + 0.480558i \(0.840434\pi\)
\(570\) 7.14823e25 4.12478e25i 0.471398 0.272013i
\(571\) 8.93301e25i 0.579368i 0.957122 + 0.289684i \(0.0935502\pi\)
−0.957122 + 0.289684i \(0.906450\pi\)
\(572\) −5.76894e22 + 2.73587e22i −0.000367988 + 0.000174515i
\(573\) 1.74115e26 5.42319e25i 1.09236 0.340241i
\(574\) 1.34323e24 3.02368e23i 0.00828872 0.00186583i
\(575\) −8.63282e25 −0.523972
\(576\) −5.92545e25 1.56668e26i −0.353759 0.935337i
\(577\) 1.67041e26 0.980961 0.490481 0.871452i \(-0.336821\pi\)
0.490481 + 0.871452i \(0.336821\pi\)
\(578\) −2.48982e25 + 5.60472e24i −0.143831 + 0.0323772i
\(579\) −7.01389e25 + 2.18463e25i −0.398577 + 0.124146i
\(580\) −2.90884e26 + 1.37949e26i −1.62612 + 0.771175i
\(581\) 1.20642e26i 0.663474i
\(582\) −3.60397e25 + 2.07962e25i −0.194990 + 0.112516i
\(583\) 8.06155e22i 0.000429109i
\(584\) 2.71248e26 2.12367e26i 1.42051 1.11215i
\(585\) −1.78596e26 2.58882e26i −0.920217 1.33389i
\(586\) 5.52178e25 + 2.45298e26i 0.279931 + 1.24356i
\(587\) 1.96328e26 0.979311 0.489656 0.871916i \(-0.337122\pi\)
0.489656 + 0.871916i \(0.337122\pi\)
\(588\) 1.45751e26 1.34366e26i 0.715363 0.659485i
\(589\) 1.31883e26 0.636934
\(590\) 5.88448e25 + 2.61410e26i 0.279649 + 1.24231i
\(591\) 2.77488e24 + 8.90891e24i 0.0129766 + 0.0416623i
\(592\) 8.69312e25 1.06378e26i 0.400055 0.489546i
\(593\) 3.26171e26i 1.47715i 0.674170 + 0.738577i \(0.264502\pi\)
−0.674170 + 0.738577i \(0.735498\pi\)
\(594\) −3.07200e22 + 6.46588e22i −0.000136915 + 0.000288175i
\(595\) 3.75369e26i 1.64644i
\(596\) 1.66957e25 + 3.52051e25i 0.0720718 + 0.151973i
\(597\) 5.87936e25 + 1.88761e26i 0.249790 + 0.801964i
\(598\) −2.55172e26 + 5.74406e25i −1.06702 + 0.240192i
\(599\) −1.67035e26 −0.687468 −0.343734 0.939067i \(-0.611692\pi\)
−0.343734 + 0.939067i \(0.611692\pi\)
\(600\) −8.58129e25 + 1.24201e26i −0.347629 + 0.503140i
\(601\) −1.82808e26 −0.728932 −0.364466 0.931217i \(-0.618749\pi\)
−0.364466 + 0.931217i \(0.618749\pi\)
\(602\) 3.46359e26 7.79672e25i 1.35944 0.306017i
\(603\) −3.22535e24 4.67529e24i −0.0124613 0.0180632i
\(604\) −3.45023e25 7.27526e25i −0.131219 0.276693i
\(605\) 3.39077e26i 1.26947i
\(606\) 2.65714e25 + 4.60482e25i 0.0979321 + 0.169716i
\(607\) 5.20544e26i 1.88871i −0.328933 0.944353i \(-0.606689\pi\)
0.328933 0.944353i \(-0.393311\pi\)
\(608\) −1.07347e26 5.36835e25i −0.383446 0.191759i
\(609\) 5.40631e26 1.68391e26i 1.90124 0.592183i
\(610\) −1.43563e26 6.37758e26i −0.497059 2.20812i
\(611\) 5.50255e26 1.87574
\(612\) −2.38186e26 1.37667e26i −0.799424 0.462051i
\(613\) 2.77002e26 0.915396 0.457698 0.889108i \(-0.348674\pi\)
0.457698 + 0.889108i \(0.348674\pi\)
\(614\) −1.85302e25 8.23179e25i −0.0602948 0.267852i
\(615\) 2.28818e24 7.12705e23i 0.00733124 0.00228348i
\(616\) −8.75665e22 1.11845e23i −0.000276262 0.000352858i
\(617\) 6.18374e26i 1.92106i −0.278169 0.960532i \(-0.589727\pi\)
0.278169 0.960532i \(-0.410273\pi\)
\(618\) 2.83266e26 + 4.90899e26i 0.866571 + 1.50176i
\(619\) 2.78796e26i 0.839897i 0.907548 + 0.419948i \(0.137952\pi\)
−0.907548 + 0.419948i \(0.862048\pi\)
\(620\) −5.74396e26 + 2.72402e26i −1.70408 + 0.808145i
\(621\) −1.80944e26 + 2.30776e26i −0.528658 + 0.674248i
\(622\) −4.93367e26 + 1.11059e26i −1.41958 + 0.319556i
\(623\) −2.06327e26 −0.584681
\(624\) −1.71009e26 + 4.24217e26i −0.477271 + 1.18395i
\(625\) −4.50220e26 −1.23756
\(626\) 4.23807e25 9.54011e24i 0.114739 0.0258284i
\(627\) 1.52540e22 + 4.89739e22i 4.06764e−5 + 0.000130594i
\(628\) 2.25702e26 1.07037e26i 0.592813 0.281136i
\(629\) 2.25638e26i 0.583756i
\(630\) 4.74632e26 5.14117e26i 1.20955 1.31017i
\(631\) 2.48783e26i 0.624514i 0.949998 + 0.312257i \(0.101085\pi\)
−0.949998 + 0.312257i \(0.898915\pi\)
\(632\) 9.17387e25 + 1.17174e26i 0.226851 + 0.289747i
\(633\) 6.78777e25 + 2.17926e26i 0.165345 + 0.530852i
\(634\) −6.99915e25 3.10928e26i −0.167957 0.746125i
\(635\) 4.33194e25 0.102407
\(636\) −3.91438e26 4.24605e26i −0.911634 0.988877i
\(637\) −5.41320e26 −1.24202
\(638\) −4.39425e22 1.95209e23i −9.93318e−5 0.000441268i
\(639\) −2.85424e26 + 1.96906e26i −0.635671 + 0.438532i
\(640\) 5.78412e26 + 1.20875e25i 1.26919 + 0.0265232i
\(641\) 3.31518e26i 0.716730i −0.933581 0.358365i \(-0.883334\pi\)
0.933581 0.358365i \(-0.116666\pi\)
\(642\) 1.25221e26 7.22568e25i 0.266743 0.153920i
\(643\) 3.39062e26i 0.711665i −0.934550 0.355832i \(-0.884197\pi\)
0.934550 0.355832i \(-0.115803\pi\)
\(644\) −2.49344e26 5.25774e26i −0.515683 1.08739i
\(645\) 5.90020e26 1.83775e26i 1.20240 0.374514i
\(646\) −1.92316e26 + 4.32914e25i −0.386195 + 0.0869345i
\(647\) −9.61083e26 −1.90182 −0.950912 0.309463i \(-0.899851\pi\)
−0.950912 + 0.309463i \(0.899851\pi\)
\(648\) 1.52155e26 + 4.89725e26i 0.296704 + 0.954969i
\(649\) −1.66540e23 −0.000320032
\(650\) 4.02168e26 9.05301e25i 0.761607 0.171442i
\(651\) 1.06756e27 3.32515e26i 1.99238 0.620572i
\(652\) 1.28636e26 + 2.71245e26i 0.236597 + 0.498896i
\(653\) 4.95688e26i 0.898531i 0.893398 + 0.449265i \(0.148314\pi\)
−0.893398 + 0.449265i \(0.851686\pi\)
\(654\) 4.70584e26 2.71544e26i 0.840714 0.485122i
\(655\) 4.73774e26i 0.834216i
\(656\) −2.69883e24 2.20547e24i −0.00468369 0.00382749i
\(657\) −8.68154e26 + 5.98915e26i −1.48500 + 1.02446i
\(658\) 2.68843e26 + 1.19430e27i 0.453266 + 2.01357i
\(659\) −1.20198e27 −1.99750 −0.998749 0.0500136i \(-0.984074\pi\)
−0.998749 + 0.0500136i \(0.984074\pi\)
\(660\) −1.67591e23 1.81791e23i −0.000274525 0.000297786i
\(661\) −2.59952e26 −0.419739 −0.209870 0.977729i \(-0.567304\pi\)
−0.209870 + 0.977729i \(0.567304\pi\)
\(662\) 1.91677e26 + 8.51500e26i 0.305084 + 1.35529i
\(663\) 2.23402e26 + 7.17247e26i 0.350517 + 1.12536i
\(664\) 2.40462e26 1.88265e26i 0.371921 0.291187i
\(665\) 5.01376e26i 0.764465i
\(666\) −2.85307e26 + 3.09041e26i −0.428852 + 0.464528i
\(667\) 8.19696e26i 1.21467i
\(668\) −4.68495e25 + 2.22180e25i −0.0684429 + 0.0324584i
\(669\) −3.47225e26 1.11479e27i −0.500106 1.60562i
\(670\) 1.91392e25 4.30834e24i 0.0271778 0.00611786i
\(671\) 4.06304e23 0.000568837
\(672\) −1.00429e27 1.63902e26i −1.38628 0.226244i
\(673\) 1.96867e26 0.267935 0.133968 0.990986i \(-0.457228\pi\)
0.133968 + 0.990986i \(0.457228\pi\)
\(674\) 3.64902e26 8.21414e25i 0.489675 0.110228i
\(675\) 2.85180e26 3.63718e26i 0.377340 0.481259i
\(676\) 4.35973e26 2.06756e26i 0.568808 0.269752i
\(677\) 6.59183e26i 0.848035i −0.905654 0.424018i \(-0.860619\pi\)
0.905654 0.424018i \(-0.139381\pi\)
\(678\) 4.58309e26 + 7.94247e26i 0.581401 + 1.00757i
\(679\) 2.52782e26i 0.316216i
\(680\) 7.48183e26 5.85773e26i 0.922940 0.722594i
\(681\) −2.97981e26 + 9.28128e25i −0.362486 + 0.112904i
\(682\) −8.67713e22 3.85470e23i −0.000104094 0.000462423i
\(683\) 1.37366e27 1.62511 0.812554 0.582886i \(-0.198077\pi\)
0.812554 + 0.582886i \(0.198077\pi\)
\(684\) 3.18142e26 + 1.83880e26i 0.371183 + 0.214536i
\(685\) −7.45273e26 −0.857541
\(686\) 7.34829e24 + 3.26438e25i 0.00833887 + 0.0370443i
\(687\) 7.63458e26 2.37796e26i 0.854468 0.266143i
\(688\) −6.95906e26 5.68691e26i −0.768175 0.627749i
\(689\) 1.57699e27i 1.71690i
\(690\) −5.06239e26 8.77310e26i −0.543612 0.942077i
\(691\) 1.46759e27i 1.55440i 0.629253 + 0.777201i \(0.283361\pi\)
−0.629253 + 0.777201i \(0.716639\pi\)
\(692\) 6.62300e26 + 1.39655e27i 0.691906 + 1.45897i
\(693\) 2.46954e23 + 3.57971e23i 0.000254478 + 0.000368877i
\(694\) −1.02239e26 + 2.30144e25i −0.103920 + 0.0233930i
\(695\) −2.03494e26 −0.204031
\(696\) −1.17931e27 8.14803e26i −1.16638 0.805870i
\(697\) −5.72450e24 −0.00558504
\(698\) 5.58639e26 1.25753e26i 0.537657 0.121029i
\(699\) 7.86094e25 + 2.52380e26i 0.0746348 + 0.239619i
\(700\) 3.92982e26 + 8.28654e26i 0.368079 + 0.776143i
\(701\) 2.82602e25i 0.0261128i −0.999915 0.0130564i \(-0.995844\pi\)
0.999915 0.0130564i \(-0.00415610\pi\)
\(702\) 6.00939e26 1.26484e27i 0.547807 1.15301i
\(703\) 3.01382e26i 0.271046i
\(704\) −8.62791e22 + 3.49074e23i −7.65536e−5 + 0.000309726i
\(705\) 6.33684e26 + 2.03448e27i 0.554723 + 1.78097i
\(706\) −5.79111e25 2.57263e26i −0.0500170 0.222194i
\(707\) 3.22981e26 0.275228
\(708\) −8.77171e26 + 8.08654e26i −0.737511 + 0.679903i
\(709\) 1.61811e27 1.34236 0.671181 0.741293i \(-0.265787\pi\)
0.671181 + 0.741293i \(0.265787\pi\)
\(710\) −2.63022e26 1.16844e27i −0.215297 0.956429i
\(711\) −2.58720e26 3.75027e26i −0.208963 0.302901i
\(712\) 3.21978e26 + 4.11249e26i 0.256606 + 0.327752i
\(713\) 1.61862e27i 1.27290i
\(714\) −1.44760e27 + 8.35315e26i −1.12335 + 0.648212i
\(715\) 6.75172e23i 0.000517020i
\(716\) 4.59587e26 2.17955e26i 0.347291 0.164700i
\(717\) −1.81825e26 + 5.66336e25i −0.135588 + 0.0422320i
\(718\) −4.10060e26 + 9.23065e25i −0.301762 + 0.0679282i
\(719\) −1.73484e27 −1.25990 −0.629948 0.776638i \(-0.716924\pi\)
−0.629948 + 0.776638i \(0.716924\pi\)
\(720\) −1.76541e27 1.43742e26i −1.26528 0.103021i
\(721\) 3.44316e27 2.43541
\(722\) −1.14068e27 + 2.56774e26i −0.796272 + 0.179245i
\(723\) 2.54696e26 7.93308e25i 0.175472 0.0546547i
\(724\) 1.88260e27 8.92807e26i 1.28009 0.607073i
\(725\) 1.29189e27i 0.866994i
\(726\) −1.30764e27 + 7.54554e26i −0.866143 + 0.499795i
\(727\) 4.19437e26i 0.274214i 0.990556 + 0.137107i \(0.0437804\pi\)
−0.990556 + 0.137107i \(0.956220\pi\)
\(728\) 1.71296e27 + 2.18789e27i 1.10535 + 1.41181i
\(729\) −3.74564e26 1.52471e27i −0.238569 0.971125i
\(730\) −8.00016e26 3.55397e27i −0.502958 2.23432i
\(731\) −1.47609e27 −0.916006
\(732\) 2.14002e27 1.97286e27i 1.31088 1.20848i
\(733\) −9.43357e26 −0.570411 −0.285206 0.958466i \(-0.592062\pi\)
−0.285206 + 0.958466i \(0.592062\pi\)
\(734\) 1.15924e26 + 5.14979e26i 0.0691931 + 0.307381i
\(735\) −6.23394e26 2.00145e27i −0.367310 1.17927i
\(736\) −6.58863e26 + 1.31747e27i −0.383227 + 0.766308i
\(737\) 1.21933e22i 7.00131e-6i
\(738\) 7.84046e24 + 7.23831e24i 0.00444433 + 0.00410300i
\(739\) 8.35344e26i 0.467459i 0.972302 + 0.233729i \(0.0750929\pi\)
−0.972302 + 0.233729i \(0.924907\pi\)
\(740\) −6.22499e26 1.31262e27i −0.343904 0.725167i
\(741\) −2.98396e26 9.58018e26i −0.162750 0.522517i
\(742\) −3.42277e27 + 7.70482e26i −1.84306 + 0.414883i
\(743\) 2.64337e26 0.140528 0.0702642 0.997528i \(-0.477616\pi\)
0.0702642 + 0.997528i \(0.477616\pi\)
\(744\) −2.32872e27 1.60896e27i −1.22229 0.844503i
\(745\) 4.12026e26 0.213520
\(746\) −2.02028e27 + 4.54775e26i −1.03370 + 0.232690i
\(747\) −7.69623e26 + 5.30941e26i −0.388805 + 0.268226i
\(748\) 2.53065e23 + 5.33621e23i 0.000126231 + 0.000266175i
\(749\) 8.78296e26i 0.432577i
\(750\) −5.06792e26 8.78268e26i −0.246461 0.427115i
\(751\) 7.40863e26i 0.355761i −0.984052 0.177881i \(-0.943076\pi\)
0.984052 0.177881i \(-0.0569241\pi\)
\(752\) 1.96094e27 2.39959e27i 0.929810 1.13781i
\(753\) 1.74453e27 5.43372e26i 0.816819 0.254416i
\(754\) 8.59595e26 + 3.81864e27i 0.397435 + 1.76555i
\(755\) −8.51466e26 −0.388751
\(756\) 3.03888e27 + 6.86330e26i 1.37011 + 0.309440i
\(757\) 4.40332e26 0.196051 0.0980256 0.995184i \(-0.468747\pi\)
0.0980256 + 0.995184i \(0.468747\pi\)
\(758\) −7.66476e26 3.40497e27i −0.337009 1.49712i
\(759\) 6.01062e23 1.87214e23i 0.000260989 8.12908e-5i
\(760\) −9.99339e26 + 7.82410e26i −0.428533 + 0.335510i
\(761\) 9.18035e26i 0.388781i 0.980924 + 0.194391i \(0.0622729\pi\)
−0.980924 + 0.194391i \(0.937727\pi\)
\(762\) 9.63993e25 + 1.67060e26i 0.0403183 + 0.0698714i
\(763\)