# Properties

 Label 700.2.c.e.699.1 Level $700$ Weight $2$ Character 700.699 Analytic conductor $5.590$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$700 = 2^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 700.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.58952814149$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 140) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 699.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 700.699 Dual form 700.2.c.e.699.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(-2.36603 + 0.633975i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$$ $$q+(-0.366025 - 1.36603i) q^{2} -1.73205i q^{3} +(-1.73205 + 1.00000i) q^{4} +(-2.36603 + 0.633975i) q^{6} +(2.00000 + 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} -3.73205i q^{11} +(1.73205 + 3.00000i) q^{12} +6.46410 q^{13} +(1.63397 - 3.36603i) q^{14} +(2.00000 - 3.46410i) q^{16} -0.464102 q^{17} -6.00000 q^{19} +(3.00000 - 3.46410i) q^{21} +(-5.09808 + 1.36603i) q^{22} +5.46410 q^{23} +(3.46410 - 3.46410i) q^{24} +(-2.36603 - 8.83013i) q^{26} -5.19615i q^{27} +(-5.19615 - 1.00000i) q^{28} +5.92820 q^{29} -6.00000 q^{31} +(-5.46410 - 1.46410i) q^{32} -6.46410 q^{33} +(0.169873 + 0.633975i) q^{34} -2.53590i q^{37} +(2.19615 + 8.19615i) q^{38} -11.1962i q^{39} +3.46410i q^{41} +(-5.83013 - 2.83013i) q^{42} -2.00000 q^{43} +(3.73205 + 6.46410i) q^{44} +(-2.00000 - 7.46410i) q^{46} -1.73205i q^{47} +(-6.00000 - 3.46410i) q^{48} +(1.00000 + 6.92820i) q^{49} +0.803848i q^{51} +(-11.1962 + 6.46410i) q^{52} -2.00000i q^{53} +(-7.09808 + 1.90192i) q^{54} +(0.535898 + 7.46410i) q^{56} +10.3923i q^{57} +(-2.16987 - 8.09808i) q^{58} -3.46410 q^{59} +2.53590i q^{61} +(2.19615 + 8.19615i) q^{62} +8.00000i q^{64} +(2.36603 + 8.83013i) q^{66} +3.46410 q^{67} +(0.803848 - 0.464102i) q^{68} -9.46410i q^{69} -0.535898i q^{71} -0.928203 q^{73} +(-3.46410 + 0.928203i) q^{74} +(10.3923 - 6.00000i) q^{76} +(6.46410 - 7.46410i) q^{77} +(-15.2942 + 4.09808i) q^{78} -2.66025i q^{79} -9.00000 q^{81} +(4.73205 - 1.26795i) q^{82} -8.53590i q^{83} +(-1.73205 + 9.00000i) q^{84} +(0.732051 + 2.73205i) q^{86} -10.2679i q^{87} +(7.46410 - 7.46410i) q^{88} -9.46410i q^{89} +(12.9282 + 11.1962i) q^{91} +(-9.46410 + 5.46410i) q^{92} +10.3923i q^{93} +(-2.36603 + 0.633975i) q^{94} +(-2.53590 + 9.46410i) q^{96} -7.39230 q^{97} +(9.09808 - 3.90192i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{13} + 10 q^{14} + 8 q^{16} + 12 q^{17} - 24 q^{19} + 12 q^{21} - 10 q^{22} + 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} - 8 q^{32} - 12 q^{33} + 18 q^{34} - 12 q^{38} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 24 q^{48} + 4 q^{49} - 24 q^{52} - 18 q^{54} + 16 q^{56} - 26 q^{58} - 12 q^{62} + 6 q^{66} + 24 q^{68} + 24 q^{73} + 12 q^{77} - 30 q^{78} - 36 q^{81} + 12 q^{82} - 4 q^{86} + 16 q^{88} + 24 q^{91} - 24 q^{92} - 6 q^{94} - 24 q^{96} + 12 q^{97} + 26 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$351$$ $$477$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.366025 1.36603i −0.258819 0.965926i
$$3$$ 1.73205i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 0 0
$$6$$ −2.36603 + 0.633975i −0.965926 + 0.258819i
$$7$$ 2.00000 + 1.73205i 0.755929 + 0.654654i
$$8$$ 2.00000 + 2.00000i 0.707107 + 0.707107i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.73205i 1.12526i −0.826710 0.562628i $$-0.809790\pi$$
0.826710 0.562628i $$-0.190210\pi$$
$$12$$ 1.73205 + 3.00000i 0.500000 + 0.866025i
$$13$$ 6.46410 1.79282 0.896410 0.443227i $$-0.146166\pi$$
0.896410 + 0.443227i $$0.146166\pi$$
$$14$$ 1.63397 3.36603i 0.436698 0.899608i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ −0.464102 −0.112561 −0.0562806 0.998415i $$-0.517924\pi$$
−0.0562806 + 0.998415i $$0.517924\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ 3.00000 3.46410i 0.654654 0.755929i
$$22$$ −5.09808 + 1.36603i −1.08691 + 0.291238i
$$23$$ 5.46410 1.13934 0.569672 0.821872i $$-0.307070\pi$$
0.569672 + 0.821872i $$0.307070\pi$$
$$24$$ 3.46410 3.46410i 0.707107 0.707107i
$$25$$ 0 0
$$26$$ −2.36603 8.83013i −0.464016 1.73173i
$$27$$ 5.19615i 1.00000i
$$28$$ −5.19615 1.00000i −0.981981 0.188982i
$$29$$ 5.92820 1.10084 0.550420 0.834888i $$-0.314468\pi$$
0.550420 + 0.834888i $$0.314468\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ −5.46410 1.46410i −0.965926 0.258819i
$$33$$ −6.46410 −1.12526
$$34$$ 0.169873 + 0.633975i 0.0291330 + 0.108726i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.53590i 0.416899i −0.978033 0.208450i $$-0.933158\pi$$
0.978033 0.208450i $$-0.0668417\pi$$
$$38$$ 2.19615 + 8.19615i 0.356263 + 1.32959i
$$39$$ 11.1962i 1.79282i
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i 0.962720 + 0.270501i $$0.0871893\pi$$
−0.962720 + 0.270501i $$0.912811\pi$$
$$42$$ −5.83013 2.83013i −0.899608 0.436698i
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 3.73205 + 6.46410i 0.562628 + 0.974500i
$$45$$ 0 0
$$46$$ −2.00000 7.46410i −0.294884 1.10052i
$$47$$ 1.73205i 0.252646i −0.991989 0.126323i $$-0.959682\pi$$
0.991989 0.126323i $$-0.0403175\pi$$
$$48$$ −6.00000 3.46410i −0.866025 0.500000i
$$49$$ 1.00000 + 6.92820i 0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 0.803848i 0.112561i
$$52$$ −11.1962 + 6.46410i −1.55263 + 0.896410i
$$53$$ 2.00000i 0.274721i −0.990521 0.137361i $$-0.956138\pi$$
0.990521 0.137361i $$-0.0438619\pi$$
$$54$$ −7.09808 + 1.90192i −0.965926 + 0.258819i
$$55$$ 0 0
$$56$$ 0.535898 + 7.46410i 0.0716124 + 0.997433i
$$57$$ 10.3923i 1.37649i
$$58$$ −2.16987 8.09808i −0.284918 1.06333i
$$59$$ −3.46410 −0.450988 −0.225494 0.974245i $$-0.572400\pi$$
−0.225494 + 0.974245i $$0.572400\pi$$
$$60$$ 0 0
$$61$$ 2.53590i 0.324689i 0.986734 + 0.162344i $$0.0519055\pi$$
−0.986734 + 0.162344i $$0.948094\pi$$
$$62$$ 2.19615 + 8.19615i 0.278912 + 1.04091i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 2.36603 + 8.83013i 0.291238 + 1.08691i
$$67$$ 3.46410 0.423207 0.211604 0.977356i $$-0.432131\pi$$
0.211604 + 0.977356i $$0.432131\pi$$
$$68$$ 0.803848 0.464102i 0.0974808 0.0562806i
$$69$$ 9.46410i 1.13934i
$$70$$ 0 0
$$71$$ 0.535898i 0.0635994i −0.999494 0.0317997i $$-0.989876\pi$$
0.999494 0.0317997i $$-0.0101239\pi$$
$$72$$ 0 0
$$73$$ −0.928203 −0.108638 −0.0543190 0.998524i $$-0.517299\pi$$
−0.0543190 + 0.998524i $$0.517299\pi$$
$$74$$ −3.46410 + 0.928203i −0.402694 + 0.107901i
$$75$$ 0 0
$$76$$ 10.3923 6.00000i 1.19208 0.688247i
$$77$$ 6.46410 7.46410i 0.736653 0.850613i
$$78$$ −15.2942 + 4.09808i −1.73173 + 0.464016i
$$79$$ 2.66025i 0.299302i −0.988739 0.149651i $$-0.952185\pi$$
0.988739 0.149651i $$-0.0478150\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 4.73205 1.26795i 0.522568 0.140022i
$$83$$ 8.53590i 0.936937i −0.883480 0.468468i $$-0.844806\pi$$
0.883480 0.468468i $$-0.155194\pi$$
$$84$$ −1.73205 + 9.00000i −0.188982 + 0.981981i
$$85$$ 0 0
$$86$$ 0.732051 + 2.73205i 0.0789391 + 0.294605i
$$87$$ 10.2679i 1.10084i
$$88$$ 7.46410 7.46410i 0.795676 0.795676i
$$89$$ 9.46410i 1.00319i −0.865102 0.501596i $$-0.832746\pi$$
0.865102 0.501596i $$-0.167254\pi$$
$$90$$ 0 0
$$91$$ 12.9282 + 11.1962i 1.35524 + 1.17368i
$$92$$ −9.46410 + 5.46410i −0.986701 + 0.569672i
$$93$$ 10.3923i 1.07763i
$$94$$ −2.36603 + 0.633975i −0.244037 + 0.0653895i
$$95$$ 0 0
$$96$$ −2.53590 + 9.46410i −0.258819 + 0.965926i
$$97$$ −7.39230 −0.750575 −0.375287 0.926908i $$-0.622456\pi$$
−0.375287 + 0.926908i $$0.622456\pi$$
$$98$$ 9.09808 3.90192i 0.919044 0.394154i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.53590i 0.849354i −0.905345 0.424677i $$-0.860388\pi$$
0.905345 0.424677i $$-0.139612\pi$$
$$102$$ 1.09808 0.294229i 0.108726 0.0291330i
$$103$$ 17.1962i 1.69439i 0.531284 + 0.847194i $$0.321710\pi$$
−0.531284 + 0.847194i $$0.678290\pi$$
$$104$$ 12.9282 + 12.9282i 1.26771 + 1.26771i
$$105$$ 0 0
$$106$$ −2.73205 + 0.732051i −0.265360 + 0.0711031i
$$107$$ 18.3923 1.77805 0.889026 0.457857i $$-0.151383\pi$$
0.889026 + 0.457857i $$0.151383\pi$$
$$108$$ 5.19615 + 9.00000i 0.500000 + 0.866025i
$$109$$ −15.9282 −1.52565 −0.762823 0.646608i $$-0.776187\pi$$
−0.762823 + 0.646608i $$0.776187\pi$$
$$110$$ 0 0
$$111$$ −4.39230 −0.416899
$$112$$ 10.0000 3.46410i 0.944911 0.327327i
$$113$$ 1.46410i 0.137731i 0.997626 + 0.0688655i $$0.0219379\pi$$
−0.997626 + 0.0688655i $$0.978062\pi$$
$$114$$ 14.1962 3.80385i 1.32959 0.356263i
$$115$$ 0 0
$$116$$ −10.2679 + 5.92820i −0.953355 + 0.550420i
$$117$$ 0 0
$$118$$ 1.26795 + 4.73205i 0.116724 + 0.435621i
$$119$$ −0.928203 0.803848i −0.0850883 0.0736886i
$$120$$ 0 0
$$121$$ −2.92820 −0.266200
$$122$$ 3.46410 0.928203i 0.313625 0.0840356i
$$123$$ 6.00000 0.541002
$$124$$ 10.3923 6.00000i 0.933257 0.538816i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −8.53590 −0.757438 −0.378719 0.925512i $$-0.623635\pi$$
−0.378719 + 0.925512i $$0.623635\pi$$
$$128$$ 10.9282 2.92820i 0.965926 0.258819i
$$129$$ 3.46410i 0.304997i
$$130$$ 0 0
$$131$$ 9.46410 0.826882 0.413441 0.910531i $$-0.364327\pi$$
0.413441 + 0.910531i $$0.364327\pi$$
$$132$$ 11.1962 6.46410i 0.974500 0.562628i
$$133$$ −12.0000 10.3923i −1.04053 0.901127i
$$134$$ −1.26795 4.73205i −0.109534 0.408787i
$$135$$ 0 0
$$136$$ −0.928203 0.928203i −0.0795928 0.0795928i
$$137$$ 0.392305i 0.0335169i −0.999860 0.0167584i $$-0.994665\pi$$
0.999860 0.0167584i $$-0.00533462\pi$$
$$138$$ −12.9282 + 3.46410i −1.10052 + 0.294884i
$$139$$ 6.92820 0.587643 0.293821 0.955860i $$-0.405073\pi$$
0.293821 + 0.955860i $$0.405073\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ −0.732051 + 0.196152i −0.0614323 + 0.0164607i
$$143$$ 24.1244i 2.01738i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0.339746 + 1.26795i 0.0281176 + 0.104936i
$$147$$ 12.0000 1.73205i 0.989743 0.142857i
$$148$$ 2.53590 + 4.39230i 0.208450 + 0.361045i
$$149$$ −16.9282 −1.38681 −0.693406 0.720547i $$-0.743891\pi$$
−0.693406 + 0.720547i $$0.743891\pi$$
$$150$$ 0 0
$$151$$ 4.80385i 0.390932i −0.980711 0.195466i $$-0.937378\pi$$
0.980711 0.195466i $$-0.0626219\pi$$
$$152$$ −12.0000 12.0000i −0.973329 0.973329i
$$153$$ 0 0
$$154$$ −12.5622 6.09808i −1.01229 0.491397i
$$155$$ 0 0
$$156$$ 11.1962 + 19.3923i 0.896410 + 1.55263i
$$157$$ 19.8564 1.58471 0.792357 0.610058i $$-0.208854\pi$$
0.792357 + 0.610058i $$0.208854\pi$$
$$158$$ −3.63397 + 0.973721i −0.289103 + 0.0774650i
$$159$$ −3.46410 −0.274721
$$160$$ 0 0
$$161$$ 10.9282 + 9.46410i 0.861263 + 0.745876i
$$162$$ 3.29423 + 12.2942i 0.258819 + 0.965926i
$$163$$ −20.7846 −1.62798 −0.813988 0.580881i $$-0.802708\pi$$
−0.813988 + 0.580881i $$0.802708\pi$$
$$164$$ −3.46410 6.00000i −0.270501 0.468521i
$$165$$ 0 0
$$166$$ −11.6603 + 3.12436i −0.905011 + 0.242497i
$$167$$ 5.19615i 0.402090i 0.979582 + 0.201045i $$0.0644338\pi$$
−0.979582 + 0.201045i $$0.935566\pi$$
$$168$$ 12.9282 0.928203i 0.997433 0.0716124i
$$169$$ 28.7846 2.21420
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 3.46410 2.00000i 0.264135 0.152499i
$$173$$ 20.3205 1.54494 0.772470 0.635051i $$-0.219021\pi$$
0.772470 + 0.635051i $$0.219021\pi$$
$$174$$ −14.0263 + 3.75833i −1.06333 + 0.284918i
$$175$$ 0 0
$$176$$ −12.9282 7.46410i −0.974500 0.562628i
$$177$$ 6.00000i 0.450988i
$$178$$ −12.9282 + 3.46410i −0.969010 + 0.259645i
$$179$$ 14.3923i 1.07573i 0.843031 + 0.537866i $$0.180769\pi$$
−0.843031 + 0.537866i $$0.819231\pi$$
$$180$$ 0 0
$$181$$ 12.9282i 0.960946i 0.877010 + 0.480473i $$0.159535\pi$$
−0.877010 + 0.480473i $$0.840465\pi$$
$$182$$ 10.5622 21.7583i 0.782921 1.61283i
$$183$$ 4.39230 0.324689
$$184$$ 10.9282 + 10.9282i 0.805638 + 0.805638i
$$185$$ 0 0
$$186$$ 14.1962 3.80385i 1.04091 0.278912i
$$187$$ 1.73205i 0.126660i
$$188$$ 1.73205 + 3.00000i 0.126323 + 0.218797i
$$189$$ 9.00000 10.3923i 0.654654 0.755929i
$$190$$ 0 0
$$191$$ 3.19615i 0.231265i 0.993292 + 0.115633i $$0.0368896\pi$$
−0.993292 + 0.115633i $$0.963110\pi$$
$$192$$ 13.8564 1.00000
$$193$$ 2.53590i 0.182538i 0.995826 + 0.0912690i $$0.0290923\pi$$
−0.995826 + 0.0912690i $$0.970908\pi$$
$$194$$ 2.70577 + 10.0981i 0.194263 + 0.725000i
$$195$$ 0 0
$$196$$ −8.66025 11.0000i −0.618590 0.785714i
$$197$$ 21.3205i 1.51902i 0.650494 + 0.759512i $$0.274562\pi$$
−0.650494 + 0.759512i $$0.725438\pi$$
$$198$$ 0 0
$$199$$ 3.46410 0.245564 0.122782 0.992434i $$-0.460818\pi$$
0.122782 + 0.992434i $$0.460818\pi$$
$$200$$ 0 0
$$201$$ 6.00000i 0.423207i
$$202$$ −11.6603 + 3.12436i −0.820413 + 0.219829i
$$203$$ 11.8564 + 10.2679i 0.832157 + 0.720669i
$$204$$ −0.803848 1.39230i −0.0562806 0.0974808i
$$205$$ 0 0
$$206$$ 23.4904 6.29423i 1.63665 0.438540i
$$207$$ 0 0
$$208$$ 12.9282 22.3923i 0.896410 1.55263i
$$209$$ 22.3923i 1.54891i
$$210$$ 0 0
$$211$$ 7.19615i 0.495404i 0.968836 + 0.247702i $$0.0796753\pi$$
−0.968836 + 0.247702i $$0.920325\pi$$
$$212$$ 2.00000 + 3.46410i 0.137361 + 0.237915i
$$213$$ −0.928203 −0.0635994
$$214$$ −6.73205 25.1244i −0.460194 1.71747i
$$215$$ 0 0
$$216$$ 10.3923 10.3923i 0.707107 0.707107i
$$217$$ −12.0000 10.3923i −0.814613 0.705476i
$$218$$ 5.83013 + 21.7583i 0.394866 + 1.47366i
$$219$$ 1.60770i 0.108638i
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ 1.60770 + 6.00000i 0.107901 + 0.402694i
$$223$$ 10.2679i 0.687593i 0.939044 + 0.343796i $$0.111713\pi$$
−0.939044 + 0.343796i $$0.888287\pi$$
$$224$$ −8.39230 12.3923i −0.560734 0.827996i
$$225$$ 0 0
$$226$$ 2.00000 0.535898i 0.133038 0.0356474i
$$227$$ 3.33975i 0.221667i 0.993839 + 0.110833i $$0.0353520\pi$$
−0.993839 + 0.110833i $$0.964648\pi$$
$$228$$ −10.3923 18.0000i −0.688247 1.19208i
$$229$$ 15.4641i 1.02190i 0.859611 + 0.510948i $$0.170706\pi$$
−0.859611 + 0.510948i $$0.829294\pi$$
$$230$$ 0 0
$$231$$ −12.9282 11.1962i −0.850613 0.736653i
$$232$$ 11.8564 + 11.8564i 0.778411 + 0.778411i
$$233$$ 22.9282i 1.50208i 0.660259 + 0.751038i $$0.270447\pi$$
−0.660259 + 0.751038i $$0.729553\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 6.00000 3.46410i 0.390567 0.225494i
$$237$$ −4.60770 −0.299302
$$238$$ −0.758330 + 1.56218i −0.0491552 + 0.101261i
$$239$$ 27.9808i 1.80993i 0.425491 + 0.904963i $$0.360101\pi$$
−0.425491 + 0.904963i $$0.639899\pi$$
$$240$$ 0 0
$$241$$ 4.39230i 0.282933i −0.989943 0.141467i $$-0.954818\pi$$
0.989943 0.141467i $$-0.0451818\pi$$
$$242$$ 1.07180 + 4.00000i 0.0688977 + 0.257130i
$$243$$ 0 0
$$244$$ −2.53590 4.39230i −0.162344 0.281189i
$$245$$ 0 0
$$246$$ −2.19615 8.19615i −0.140022 0.522568i
$$247$$ −38.7846 −2.46781
$$248$$ −12.0000 12.0000i −0.762001 0.762001i
$$249$$ −14.7846 −0.936937
$$250$$ 0 0
$$251$$ 1.85641 0.117175 0.0585877 0.998282i $$-0.481340\pi$$
0.0585877 + 0.998282i $$0.481340\pi$$
$$252$$ 0 0
$$253$$ 20.3923i 1.28205i
$$254$$ 3.12436 + 11.6603i 0.196040 + 0.731629i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −6.00000 −0.374270 −0.187135 0.982334i $$-0.559920\pi$$
−0.187135 + 0.982334i $$0.559920\pi$$
$$258$$ 4.73205 1.26795i 0.294605 0.0789391i
$$259$$ 4.39230 5.07180i 0.272925 0.315146i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.46410 12.9282i −0.214013 0.798707i
$$263$$ 4.53590 0.279695 0.139848 0.990173i $$-0.455339\pi$$
0.139848 + 0.990173i $$0.455339\pi$$
$$264$$ −12.9282 12.9282i −0.795676 0.795676i
$$265$$ 0 0
$$266$$ −9.80385 + 20.1962i −0.601112 + 1.23831i
$$267$$ −16.3923 −1.00319
$$268$$ −6.00000 + 3.46410i −0.366508 + 0.211604i
$$269$$ 12.0000i 0.731653i 0.930683 + 0.365826i $$0.119214\pi$$
−0.930683 + 0.365826i $$0.880786\pi$$
$$270$$ 0 0
$$271$$ 2.53590 0.154045 0.0770224 0.997029i $$-0.475459\pi$$
0.0770224 + 0.997029i $$0.475459\pi$$
$$272$$ −0.928203 + 1.60770i −0.0562806 + 0.0974808i
$$273$$ 19.3923 22.3923i 1.17368 1.35524i
$$274$$ −0.535898 + 0.143594i −0.0323748 + 0.00867480i
$$275$$ 0 0
$$276$$ 9.46410 + 16.3923i 0.569672 + 0.986701i
$$277$$ 24.7846i 1.48916i −0.667532 0.744581i $$-0.732649\pi$$
0.667532 0.744581i $$-0.267351\pi$$
$$278$$ −2.53590 9.46410i −0.152093 0.567619i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5.92820 0.353647 0.176823 0.984243i $$-0.443418\pi$$
0.176823 + 0.984243i $$0.443418\pi$$
$$282$$ 1.09808 + 4.09808i 0.0653895 + 0.244037i
$$283$$ 12.1244i 0.720718i 0.932814 + 0.360359i $$0.117346\pi$$
−0.932814 + 0.360359i $$0.882654\pi$$
$$284$$ 0.535898 + 0.928203i 0.0317997 + 0.0550787i
$$285$$ 0 0
$$286$$ −32.9545 + 8.83013i −1.94864 + 0.522136i
$$287$$ −6.00000 + 6.92820i −0.354169 + 0.408959i
$$288$$ 0 0
$$289$$ −16.7846 −0.987330
$$290$$ 0 0
$$291$$ 12.8038i 0.750575i
$$292$$ 1.60770 0.928203i 0.0940832 0.0543190i
$$293$$ −14.3205 −0.836613 −0.418307 0.908306i $$-0.637376\pi$$
−0.418307 + 0.908306i $$0.637376\pi$$
$$294$$ −6.75833 15.7583i −0.394154 0.919044i
$$295$$ 0 0
$$296$$ 5.07180 5.07180i 0.294792 0.294792i
$$297$$ −19.3923 −1.12526
$$298$$ 6.19615 + 23.1244i 0.358933 + 1.33956i
$$299$$ 35.3205 2.04264
$$300$$ 0 0
$$301$$ −4.00000 3.46410i −0.230556 0.199667i
$$302$$ −6.56218 + 1.75833i −0.377611 + 0.101181i
$$303$$ −14.7846 −0.849354
$$304$$ −12.0000 + 20.7846i −0.688247 + 1.19208i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.73205i 0.0988534i −0.998778 0.0494267i $$-0.984261\pi$$
0.998778 0.0494267i $$-0.0157394\pi$$
$$308$$ −3.73205 + 19.3923i −0.212653 + 1.10498i
$$309$$ 29.7846 1.69439
$$310$$ 0 0
$$311$$ −19.8564 −1.12595 −0.562977 0.826473i $$-0.690344\pi$$
−0.562977 + 0.826473i $$0.690344\pi$$
$$312$$ 22.3923 22.3923i 1.26771 1.26771i
$$313$$ −24.4641 −1.38279 −0.691396 0.722476i $$-0.743004\pi$$
−0.691396 + 0.722476i $$0.743004\pi$$
$$314$$ −7.26795 27.1244i −0.410154 1.53072i
$$315$$ 0 0
$$316$$ 2.66025 + 4.60770i 0.149651 + 0.259203i
$$317$$ 16.9282i 0.950783i −0.879774 0.475391i $$-0.842306\pi$$
0.879774 0.475391i $$-0.157694\pi$$
$$318$$ 1.26795 + 4.73205i 0.0711031 + 0.265360i
$$319$$ 22.1244i 1.23873i
$$320$$ 0 0
$$321$$ 31.8564i 1.77805i
$$322$$ 8.92820 18.3923i 0.497549 1.02496i
$$323$$ 2.78461 0.154940
$$324$$ 15.5885 9.00000i 0.866025 0.500000i
$$325$$ 0 0
$$326$$ 7.60770 + 28.3923i 0.421351 + 1.57250i
$$327$$ 27.5885i 1.52565i
$$328$$ −6.92820 + 6.92820i −0.382546 + 0.382546i
$$329$$ 3.00000 3.46410i 0.165395 0.190982i
$$330$$ 0 0
$$331$$ 5.60770i 0.308227i 0.988053 + 0.154113i $$0.0492521\pi$$
−0.988053 + 0.154113i $$0.950748\pi$$
$$332$$ 8.53590 + 14.7846i 0.468468 + 0.811411i
$$333$$ 0 0
$$334$$ 7.09808 1.90192i 0.388389 0.104069i
$$335$$ 0 0
$$336$$ −6.00000 17.3205i −0.327327 0.944911i
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −10.5359 39.3205i −0.573077 2.13875i
$$339$$ 2.53590 0.137731
$$340$$ 0 0
$$341$$ 22.3923i 1.21261i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ −4.00000 4.00000i −0.215666 0.215666i
$$345$$ 0 0
$$346$$ −7.43782 27.7583i −0.399860 1.49230i
$$347$$ −14.2487 −0.764911 −0.382455 0.923974i $$-0.624921\pi$$
−0.382455 + 0.923974i $$0.624921\pi$$
$$348$$ 10.2679 + 17.7846i 0.550420 + 0.953355i
$$349$$ 29.3205i 1.56949i −0.619818 0.784745i $$-0.712794\pi$$
0.619818 0.784745i $$-0.287206\pi$$
$$350$$ 0 0
$$351$$ 33.5885i 1.79282i
$$352$$ −5.46410 + 20.3923i −0.291238 + 1.08691i
$$353$$ 13.3923 0.712800 0.356400 0.934333i $$-0.384004\pi$$
0.356400 + 0.934333i $$0.384004\pi$$
$$354$$ 8.19615 2.19615i 0.435621 0.116724i
$$355$$ 0 0
$$356$$ 9.46410 + 16.3923i 0.501596 + 0.868790i
$$357$$ −1.39230 + 1.60770i −0.0736886 + 0.0850883i
$$358$$ 19.6603 5.26795i 1.03908 0.278420i
$$359$$ 9.32051i 0.491918i −0.969280 0.245959i $$-0.920897\pi$$
0.969280 0.245959i $$-0.0791028\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 17.6603 4.73205i 0.928202 0.248711i
$$363$$ 5.07180i 0.266200i
$$364$$ −33.5885 6.46410i −1.76051 0.338811i
$$365$$ 0 0
$$366$$ −1.60770 6.00000i −0.0840356 0.313625i
$$367$$ 36.1244i 1.88568i 0.333251 + 0.942838i $$0.391854\pi$$
−0.333251 + 0.942838i $$0.608146\pi$$
$$368$$ 10.9282 18.9282i 0.569672 0.986701i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 3.46410 4.00000i 0.179847 0.207670i
$$372$$ −10.3923 18.0000i −0.538816 0.933257i
$$373$$ 24.3923i 1.26299i 0.775382 + 0.631493i $$0.217557\pi$$
−0.775382 + 0.631493i $$0.782443\pi$$
$$374$$ 2.36603 0.633975i 0.122344 0.0327820i
$$375$$ 0 0
$$376$$ 3.46410 3.46410i 0.178647 0.178647i
$$377$$ 38.3205 1.97361
$$378$$ −17.4904 8.49038i −0.899608 0.436698i
$$379$$ 26.3923i 1.35568i 0.735209 + 0.677841i $$0.237084\pi$$
−0.735209 + 0.677841i $$0.762916\pi$$
$$380$$ 0 0
$$381$$ 14.7846i 0.757438i
$$382$$ 4.36603 1.16987i 0.223385 0.0598559i
$$383$$ 20.5359i 1.04934i −0.851307 0.524668i $$-0.824190\pi$$
0.851307 0.524668i $$-0.175810\pi$$
$$384$$ −5.07180 18.9282i −0.258819 0.965926i
$$385$$ 0 0
$$386$$ 3.46410 0.928203i 0.176318 0.0472443i
$$387$$ 0 0
$$388$$ 12.8038 7.39230i 0.650017 0.375287i
$$389$$ −6.85641 −0.347634 −0.173817 0.984778i $$-0.555610\pi$$
−0.173817 + 0.984778i $$0.555610\pi$$
$$390$$ 0 0
$$391$$ −2.53590 −0.128246
$$392$$ −11.8564 + 15.8564i −0.598839 + 0.800869i
$$393$$ 16.3923i 0.826882i
$$394$$ 29.1244 7.80385i 1.46726 0.393152i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −5.53590 −0.277839 −0.138919 0.990304i $$-0.544363\pi$$
−0.138919 + 0.990304i $$0.544363\pi$$
$$398$$ −1.26795 4.73205i −0.0635566 0.237196i
$$399$$ −18.0000 + 20.7846i −0.901127 + 1.04053i
$$400$$ 0 0
$$401$$ −23.9282 −1.19492 −0.597459 0.801900i $$-0.703823\pi$$
−0.597459 + 0.801900i $$0.703823\pi$$
$$402$$ −8.19615 + 2.19615i −0.408787 + 0.109534i
$$403$$ −38.7846 −1.93200
$$404$$ 8.53590 + 14.7846i 0.424677 + 0.735562i
$$405$$ 0 0
$$406$$ 9.68653 19.9545i 0.480735 0.990324i
$$407$$ −9.46410 −0.469118
$$408$$ −1.60770 + 1.60770i −0.0795928 + 0.0795928i
$$409$$ 31.8564i 1.57520i −0.616188 0.787599i $$-0.711324\pi$$
0.616188 0.787599i $$-0.288676\pi$$
$$410$$ 0 0
$$411$$ −0.679492 −0.0335169
$$412$$ −17.1962 29.7846i −0.847194 1.46738i
$$413$$ −6.92820 6.00000i −0.340915 0.295241i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −35.3205 9.46410i −1.73173 0.464016i
$$417$$ 12.0000i 0.587643i
$$418$$ 30.5885 8.19615i 1.49613 0.400887i
$$419$$ −24.2487 −1.18463 −0.592314 0.805708i $$-0.701785\pi$$
−0.592314 + 0.805708i $$0.701785\pi$$
$$420$$ 0 0
$$421$$ 19.0000 0.926003 0.463002 0.886357i $$-0.346772\pi$$
0.463002 + 0.886357i $$0.346772\pi$$
$$422$$ 9.83013 2.63397i 0.478523 0.128220i
$$423$$ 0 0
$$424$$ 4.00000 4.00000i 0.194257 0.194257i
$$425$$ 0 0
$$426$$ 0.339746 + 1.26795i 0.0164607 + 0.0614323i
$$427$$ −4.39230 + 5.07180i −0.212559 + 0.245441i
$$428$$ −31.8564 + 18.3923i −1.53984 + 0.889026i
$$429$$ −41.7846 −2.01738
$$430$$ 0 0
$$431$$ 17.5885i 0.847206i −0.905848 0.423603i $$-0.860765\pi$$
0.905848 0.423603i $$-0.139235\pi$$
$$432$$ −18.0000 10.3923i −0.866025 0.500000i
$$433$$ −4.14359 −0.199128 −0.0995642 0.995031i $$-0.531745\pi$$
−0.0995642 + 0.995031i $$0.531745\pi$$
$$434$$ −9.80385 + 20.1962i −0.470600 + 0.969446i
$$435$$ 0 0
$$436$$ 27.5885 15.9282i 1.32125 0.762823i
$$437$$ −32.7846 −1.56830
$$438$$ 2.19615 0.588457i 0.104936 0.0281176i
$$439$$ −15.7128 −0.749932 −0.374966 0.927039i $$-0.622346\pi$$
−0.374966 + 0.927039i $$0.622346\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 1.09808 + 4.09808i 0.0522302 + 0.194926i
$$443$$ 26.0000 1.23530 0.617649 0.786454i $$-0.288085\pi$$
0.617649 + 0.786454i $$0.288085\pi$$
$$444$$ 7.60770 4.39230i 0.361045 0.208450i
$$445$$ 0 0
$$446$$ 14.0263 3.75833i 0.664164 0.177962i
$$447$$ 29.3205i 1.38681i
$$448$$ −13.8564 + 16.0000i −0.654654 + 0.755929i
$$449$$ 1.92820 0.0909975 0.0454988 0.998964i $$-0.485512\pi$$
0.0454988 + 0.998964i $$0.485512\pi$$
$$450$$ 0 0
$$451$$ 12.9282 0.608765
$$452$$ −1.46410 2.53590i −0.0688655 0.119279i
$$453$$ −8.32051 −0.390932
$$454$$ 4.56218 1.22243i 0.214114 0.0573716i
$$455$$ 0 0
$$456$$ −20.7846 + 20.7846i −0.973329 + 0.973329i
$$457$$ 27.4641i 1.28472i 0.766405 + 0.642358i $$0.222044\pi$$
−0.766405 + 0.642358i $$0.777956\pi$$
$$458$$ 21.1244 5.66025i 0.987076 0.264486i
$$459$$ 2.41154i 0.112561i
$$460$$ 0 0
$$461$$ 27.7128i 1.29071i −0.763881 0.645357i $$-0.776709\pi$$
0.763881 0.645357i $$-0.223291\pi$$
$$462$$ −10.5622 + 21.7583i −0.491397 + 1.01229i
$$463$$ −4.39230 −0.204128 −0.102064 0.994778i $$-0.532545\pi$$
−0.102064 + 0.994778i $$0.532545\pi$$
$$464$$ 11.8564 20.5359i 0.550420 0.953355i
$$465$$ 0 0
$$466$$ 31.3205 8.39230i 1.45089 0.388766i
$$467$$ 22.5167i 1.04195i −0.853573 0.520973i $$-0.825569\pi$$
0.853573 0.520973i $$-0.174431\pi$$
$$468$$ 0 0
$$469$$ 6.92820 + 6.00000i 0.319915 + 0.277054i
$$470$$ 0 0
$$471$$ 34.3923i 1.58471i
$$472$$ −6.92820 6.92820i −0.318896 0.318896i
$$473$$ 7.46410i 0.343200i
$$474$$ 1.68653 + 6.29423i 0.0774650 + 0.289103i
$$475$$ 0 0
$$476$$ 2.41154 + 0.464102i 0.110533 + 0.0212721i
$$477$$ 0 0
$$478$$ 38.2224 10.2417i 1.74825 0.468443i
$$479$$ 37.1769 1.69866 0.849328 0.527865i $$-0.177007\pi$$
0.849328 + 0.527865i $$0.177007\pi$$
$$480$$ 0 0
$$481$$ 16.3923i 0.747425i
$$482$$ −6.00000 + 1.60770i −0.273293 + 0.0732285i
$$483$$ 16.3923 18.9282i 0.745876 0.861263i
$$484$$ 5.07180 2.92820i 0.230536 0.133100i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 28.7846 1.30436 0.652178 0.758066i $$-0.273856\pi$$
0.652178 + 0.758066i $$0.273856\pi$$
$$488$$ −5.07180 + 5.07180i −0.229589 + 0.229589i
$$489$$ 36.0000i 1.62798i
$$490$$ 0 0
$$491$$ 34.1244i 1.54001i 0.638037 + 0.770005i $$0.279746\pi$$
−0.638037 + 0.770005i $$0.720254\pi$$
$$492$$ −10.3923 + 6.00000i −0.468521 + 0.270501i
$$493$$ −2.75129 −0.123912
$$494$$ 14.1962 + 52.9808i 0.638715 + 2.38372i
$$495$$ 0 0
$$496$$ −12.0000 + 20.7846i −0.538816 + 0.933257i
$$497$$ 0.928203 1.07180i 0.0416356 0.0480767i
$$498$$ 5.41154 + 20.1962i 0.242497 + 0.905011i
$$499$$ 5.58846i 0.250174i −0.992146 0.125087i $$-0.960079\pi$$
0.992146 0.125087i $$-0.0399210\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ −0.679492 2.53590i −0.0303272 0.113183i
$$503$$ 15.5885i 0.695055i −0.937670 0.347527i $$-0.887021\pi$$
0.937670 0.347527i $$-0.112979\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −27.8564 + 7.46410i −1.23837 + 0.331820i
$$507$$ 49.8564i 2.21420i
$$508$$ 14.7846 8.53590i 0.655961 0.378719i
$$509$$ 1.85641i 0.0822838i 0.999153 + 0.0411419i $$0.0130996\pi$$
−0.999153 + 0.0411419i $$0.986900\pi$$
$$510$$ 0 0
$$511$$ −1.85641 1.60770i −0.0821226 0.0711202i
$$512$$ −16.0000 + 16.0000i −0.707107 + 0.707107i
$$513$$ 31.1769i 1.37649i
$$514$$ 2.19615 + 8.19615i 0.0968681 + 0.361517i
$$515$$ 0 0
$$516$$ −3.46410 6.00000i −0.152499 0.264135i
$$517$$ −6.46410 −0.284291
$$518$$ −8.53590 4.14359i −0.375046 0.182059i
$$519$$ 35.1962i 1.54494i
$$520$$ 0 0
$$521$$ 34.3923i 1.50675i 0.657589 + 0.753377i $$0.271576\pi$$
−0.657589 + 0.753377i $$0.728424\pi$$
$$522$$ 0 0
$$523$$ 24.2487i 1.06032i −0.847897 0.530161i $$-0.822131\pi$$
0.847897 0.530161i $$-0.177869\pi$$
$$524$$ −16.3923 + 9.46410i −0.716101 + 0.413441i
$$525$$ 0 0
$$526$$ −1.66025 6.19615i −0.0723905 0.270165i
$$527$$ 2.78461 0.121300
$$528$$ −12.9282 + 22.3923i −0.562628 + 0.974500i
$$529$$ 6.85641 0.298105
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 31.1769 + 6.00000i 1.35169 + 0.260133i
$$533$$ 22.3923i 0.969918i
$$534$$ 6.00000 + 22.3923i 0.259645 + 0.969010i
$$535$$ 0 0
$$536$$ 6.92820 + 6.92820i 0.299253 + 0.299253i
$$537$$ 24.9282 1.07573
$$538$$ 16.3923 4.39230i 0.706722 0.189366i
$$539$$ 25.8564 3.73205i 1.11371 0.160751i
$$540$$ 0 0
$$541$$ −33.7846 −1.45251 −0.726257 0.687423i $$-0.758742\pi$$
−0.726257 + 0.687423i $$0.758742\pi$$
$$542$$ −0.928203 3.46410i −0.0398697 0.148796i
$$543$$ 22.3923 0.960946
$$544$$ 2.53590 + 0.679492i 0.108726 + 0.0291330i
$$545$$ 0 0
$$546$$ −37.6865 18.2942i −1.61283 0.782921i
$$547$$ 14.5359 0.621510 0.310755 0.950490i $$-0.399418\pi$$
0.310755 + 0.950490i $$0.399418\pi$$
$$548$$ 0.392305 + 0.679492i 0.0167584 + 0.0290265i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −35.5692 −1.51530
$$552$$ 18.9282 18.9282i 0.805638 0.805638i
$$553$$ 4.60770 5.32051i 0.195939 0.226251i
$$554$$ −33.8564 + 9.07180i −1.43842 + 0.385424i
$$555$$ 0 0
$$556$$ −12.0000 + 6.92820i −0.508913 + 0.293821i
$$557$$ 5.85641i 0.248144i 0.992273 + 0.124072i $$0.0395954\pi$$
−0.992273 + 0.124072i $$0.960405\pi$$
$$558$$ 0 0
$$559$$ −12.9282 −0.546805
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ −2.16987 8.09808i −0.0915306 0.341597i
$$563$$ 43.1769i 1.81969i 0.414948 + 0.909845i $$0.363800\pi$$
−0.414948 + 0.909845i $$0.636200\pi$$
$$564$$ 5.19615 3.00000i 0.218797 0.126323i
$$565$$ 0 0
$$566$$ 16.5622 4.43782i 0.696160 0.186536i
$$567$$ −18.0000 15.5885i −0.755929 0.654654i
$$568$$ 1.07180 1.07180i 0.0449716 0.0449716i
$$569$$ −20.9282 −0.877356 −0.438678 0.898644i $$-0.644553\pi$$
−0.438678 + 0.898644i $$0.644553\pi$$
$$570$$ 0 0
$$571$$ 41.3205i 1.72921i 0.502453 + 0.864605i $$0.332431\pi$$
−0.502453 + 0.864605i $$0.667569\pi$$
$$572$$ 24.1244 + 41.7846i 1.00869 + 1.74710i
$$573$$ 5.53590 0.231265
$$574$$ 11.6603 + 5.66025i 0.486690 + 0.236254i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 1.39230 0.0579624 0.0289812 0.999580i $$-0.490774\pi$$
0.0289812 + 0.999580i $$0.490774\pi$$
$$578$$ 6.14359 + 22.9282i 0.255540 + 0.953688i
$$579$$ 4.39230 0.182538
$$580$$ 0 0
$$581$$ 14.7846 17.0718i 0.613369 0.708257i
$$582$$ 17.4904 4.68653i 0.725000 0.194263i
$$583$$ −7.46410 −0.309132
$$584$$ −1.85641 1.85641i −0.0768186 0.0768186i
$$585$$ 0 0
$$586$$ 5.24167 + 19.5622i 0.216531 + 0.808106i
$$587$$ 27.4641i 1.13356i −0.823868 0.566782i $$-0.808188\pi$$
0.823868 0.566782i $$-0.191812\pi$$
$$588$$ −19.0526 + 15.0000i −0.785714 + 0.618590i
$$589$$ 36.0000 1.48335
$$590$$ 0 0
$$591$$ 36.9282 1.51902
$$592$$ −8.78461 5.07180i −0.361045 0.208450i
$$593$$ 23.5359 0.966504 0.483252 0.875481i $$-0.339456\pi$$
0.483252 + 0.875481i $$0.339456\pi$$
$$594$$ 7.09808 + 26.4904i 0.291238 + 1.08691i
$$595$$ 0 0
$$596$$ 29.3205 16.9282i 1.20101 0.693406i
$$597$$ 6.00000i 0.245564i
$$598$$ −12.9282 48.2487i −0.528674 1.97304i
$$599$$ 14.1244i 0.577106i 0.957464 + 0.288553i $$0.0931741\pi$$
−0.957464 + 0.288553i $$0.906826\pi$$
$$600$$ 0 0
$$601$$ 26.7846i 1.09257i 0.837600 + 0.546284i $$0.183958\pi$$
−0.837600 + 0.546284i $$0.816042\pi$$
$$602$$ −3.26795 + 6.73205i −0.133192 + 0.274378i
$$603$$ 0 0
$$604$$ 4.80385 + 8.32051i 0.195466 + 0.338557i
$$605$$ 0 0
$$606$$ 5.41154 + 20.1962i 0.219829 + 0.820413i
$$607$$ 18.8038i 0.763225i −0.924322 0.381612i $$-0.875369\pi$$
0.924322 0.381612i $$-0.124631\pi$$
$$608$$ 32.7846 + 8.78461i 1.32959 + 0.356263i
$$609$$ 17.7846 20.5359i 0.720669 0.832157i
$$610$$ 0 0
$$611$$ 11.1962i 0.452948i
$$612$$ 0 0
$$613$$ 10.0000i 0.403896i 0.979396 + 0.201948i $$0.0647272\pi$$
−0.979396 + 0.201948i $$0.935273\pi$$
$$614$$ −2.36603 + 0.633975i −0.0954850 + 0.0255851i
$$615$$ 0 0
$$616$$ 27.8564 2.00000i 1.12237 0.0805823i
$$617$$ 9.07180i 0.365217i −0.983186 0.182608i $$-0.941546\pi$$
0.983186 0.182608i $$-0.0584540\pi$$
$$618$$ −10.9019 40.6865i −0.438540 1.63665i
$$619$$ −35.3205 −1.41965 −0.709826 0.704378i $$-0.751226\pi$$
−0.709826 + 0.704378i $$0.751226\pi$$
$$620$$ 0 0
$$621$$ 28.3923i 1.13934i
$$622$$ 7.26795 + 27.1244i 0.291418 + 1.08759i
$$623$$ 16.3923 18.9282i 0.656744 0.758342i
$$624$$ −38.7846 22.3923i −1.55263 0.896410i
$$625$$ 0 0
$$626$$ 8.95448 + 33.4186i 0.357893 + 1.33568i
$$627$$ 38.7846 1.54891
$$628$$ −34.3923 + 19.8564i −1.37240 + 0.792357i
$$629$$ 1.17691i 0.0469267i
$$630$$ 0 0
$$631$$ 26.9090i 1.07123i 0.844463 + 0.535614i $$0.179920\pi$$
−0.844463 + 0.535614i $$0.820080\pi$$
$$632$$ 5.32051 5.32051i 0.211638 0.211638i
$$633$$ 12.4641 0.495404
$$634$$ −23.1244 + 6.19615i −0.918385 + 0.246081i
$$635$$ 0 0
$$636$$ 6.00000 3.46410i 0.237915 0.137361i
$$637$$ 6.46410 + 44.7846i 0.256117 + 1.77443i
$$638$$ −30.2224 + 8.09808i −1.19652 + 0.320606i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −4.92820 −0.194652 −0.0973262 0.995253i $$-0.531029\pi$$
−0.0973262 + 0.995253i $$0.531029\pi$$
$$642$$ −43.5167 + 11.6603i −1.71747 + 0.460194i
$$643$$ 31.0526i 1.22459i 0.790628 + 0.612297i $$0.209754\pi$$
−0.790628 + 0.612297i $$0.790246\pi$$
$$644$$ −28.3923 5.46410i −1.11881 0.215316i
$$645$$ 0 0
$$646$$ −1.01924 3.80385i −0.0401014 0.149660i
$$647$$ 10.3923i 0.408564i 0.978912 + 0.204282i $$0.0654859\pi$$
−0.978912 + 0.204282i $$0.934514\pi$$
$$648$$ −18.0000 18.0000i −0.707107 0.707107i
$$649$$ 12.9282i 0.507476i
$$650$$ 0 0
$$651$$ −18.0000 + 20.7846i −0.705476 + 0.814613i
$$652$$ 36.0000 20.7846i 1.40987 0.813988i
$$653$$ 38.3923i 1.50241i −0.660071 0.751203i $$-0.729474\pi$$
0.660071 0.751203i $$-0.270526\pi$$
$$654$$ 37.6865 10.0981i 1.47366 0.394866i
$$655$$ 0 0
$$656$$ 12.0000 + 6.92820i 0.468521 + 0.270501i
$$657$$ 0 0
$$658$$ −5.83013 2.83013i −0.227282 0.110330i
$$659$$ 20.8038i 0.810403i −0.914227 0.405201i $$-0.867201\pi$$
0.914227 0.405201i $$-0.132799\pi$$
$$660$$ 0 0
$$661$$ 15.7128i 0.611158i −0.952167 0.305579i $$-0.901150\pi$$
0.952167 0.305579i $$-0.0988499\pi$$
$$662$$ 7.66025 2.05256i 0.297724 0.0797750i
$$663$$ 5.19615i 0.201802i
$$664$$ 17.0718 17.0718i 0.662514 0.662514i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 32.3923 1.25424
$$668$$ −5.19615 9.00000i −0.201045 0.348220i
$$669$$ 17.7846 0.687593
$$670$$ 0 0
$$671$$ 9.46410 0.365358
$$672$$ −21.4641 + 14.5359i −0.827996 + 0.560734i
$$673$$ 49.1769i 1.89563i −0.318820 0.947815i $$-0.603286\pi$$
0.318820 0.947815i $$-0.396714\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −49.8564 + 28.7846i −1.91755 + 1.10710i
$$677$$ 4.60770 0.177088 0.0885441 0.996072i $$-0.471779\pi$$
0.0885441 + 0.996072i $$0.471779\pi$$
$$678$$ −0.928203 3.46410i −0.0356474 0.133038i
$$679$$ −14.7846 12.8038i −0.567381 0.491367i
$$680$$ 0 0
$$681$$ 5.78461 0.221667
$$682$$ 30.5885 8.19615i 1.17129 0.313847i
$$683$$ 27.3205 1.04539 0.522695 0.852520i $$-0.324927\pi$$
0.522695 + 0.852520i $$0.324927\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 24.9545 + 7.95448i 0.952767 + 0.303704i
$$687$$ 26.7846 1.02190
$$688$$ −4.00000 + 6.92820i −0.152499 + 0.264135i
$$689$$ 12.9282i 0.492525i
$$690$$ 0 0
$$691$$ 46.6410 1.77431 0.887154 0.461474i $$-0.152679\pi$$
0.887154 + 0.461474i $$0.152679\pi$$
$$692$$ −35.1962 + 20.3205i −1.33796 + 0.772470i
$$693$$ 0 0
$$694$$ 5.21539 + 19.4641i 0.197974 + 0.738847i
$$695$$ 0 0
$$696$$ 20.5359 20.5359i 0.778411 0.778411i
$$697$$ 1.60770i 0.0608958i
$$698$$ −40.0526 + 10.7321i −1.51601 + 0.406214i
$$699$$ 39.7128 1.50208
$$700$$ 0 0
$$701$$ 3.78461 0.142943 0.0714714 0.997443i $$-0.477231\pi$$
0.0714714 + 0.997443i $$0.477231\pi$$
$$702$$ −45.8827 + 12.2942i −1.73173 + 0.464016i
$$703$$ 15.2154i 0.573859i
$$704$$ 29.8564 1.12526
$$705$$ 0 0
$$706$$ −4.90192 18.2942i −0.184486 0.688512i
$$707$$ 14.7846 17.0718i 0.556032 0.642051i
$$708$$ −6.00000 10.3923i −0.225494 0.390567i
$$709$$ −21.0000 −0.788672 −0.394336 0.918966i $$-0.629025\pi$$
−0.394336 + 0.918966i $$0.629025\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 18.9282 18.9282i 0.709364 0.709364i
$$713$$ −32.7846 −1.22779
$$714$$ 2.70577 + 1.31347i 0.101261 + 0.0491552i
$$715$$ 0 0
$$716$$ −14.3923 24.9282i −0.537866 0.931611i
$$717$$ 48.4641 1.80993
$$718$$ −12.7321 + 3.41154i −0.475156 + 0.127318i
$$719$$ −45.4641 −1.69552 −0.847762 0.530376i $$-0.822051\pi$$
−0.847762 + 0.530376i $$0.822051\pi$$
$$720$$ 0 0
$$721$$ −29.7846 + 34.3923i −1.10924 + 1.28084i
$$722$$ −6.22243 23.2224i −0.231575 0.864249i
$$723$$ −7.60770 −0.282933
$$724$$ −12.9282 22.3923i −0.480473 0.832203i
$$725$$ 0 0
$$726$$ 6.92820 1.85641i 0.257130 0.0688977i
$$727$$ 34.3923i 1.27554i −0.770227 0.637770i $$-0.779857\pi$$
0.770227 0.637770i $$-0.220143\pi$$
$$728$$ 3.46410 + 48.2487i 0.128388 + 1.78822i
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0.928203 0.0343308
$$732$$ −7.60770 + 4.39230i −0.281189 + 0.162344i
$$733$$ 18.4641 0.681987 0.340994 0.940066i $$-0.389237\pi$$
0.340994 + 0.940066i $$0.389237\pi$$
$$734$$ 49.3468 13.2224i 1.82142 0.488049i
$$735$$ 0 0
$$736$$ −29.8564 8.00000i −1.10052 0.294884i
$$737$$ 12.9282i 0.476216i
$$738$$ 0 0
$$739$$ 7.73205i 0.284428i −0.989836 0.142214i $$-0.954578\pi$$
0.989836 0.142214i $$-0.0454221\pi$$
$$740$$ 0 0
$$741$$ 67.1769i 2.46781i
$$742$$ −6.73205 3.26795i −0.247141 0.119970i
$$743$$ −9.60770 −0.352472 −0.176236 0.984348i $$-0.556392\pi$$
−0.176236 + 0.984348i $$0.556392\pi$$
$$744$$ −20.7846 + 20.7846i −0.762001 + 0.762001i
$$745$$ 0 0
$$746$$ 33.3205 8.92820i 1.21995 0.326885i
$$747$$ 0 0
$$748$$ −1.73205 3.00000i −0.0633300 0.109691i
$$749$$ 36.7846 + 31.8564i 1.34408 + 1.16401i
$$750$$ 0 0
$$751$$ 5.58846i 0.203926i −0.994788 0.101963i $$-0.967488\pi$$
0.994788 0.101963i $$-0.0325123\pi$$
$$752$$ −6.00000 3.46410i −0.218797 0.126323i
$$753$$ 3.21539i 0.117175i
$$754$$ −14.0263 52.3468i −0.510807 1.90636i
$$755$$ 0 0
$$756$$ −5.19615 + 27.0000i −0.188982 + 0.981981i
$$757$$ 10.1436i 0.368675i 0.982863 + 0.184338i $$0.0590140\pi$$
−0.982863 + 0.184338i $$0.940986\pi$$
$$758$$ 36.0526 9.66025i 1.30949 0.350876i
$$759$$ −35.3205 −1.28205
$$760$$ 0 0
$$761$$ 6.24871i 0.226516i 0.993566 + 0.113258i $$0.0361286\pi$$
−0.993566 + 0.113258i $$0.963871\pi$$
$$762$$ 20.1962 5.41154i 0.731629 0.196040i
$$763$$ −31.8564 27.5885i −1.15328 0.998769i
$$764$$ −3.19615 5.53590i −0.115633 0.200282i
$$765$$ 0 0
$$766$$ −28.0526 + 7.51666i −1.01358 + 0.271588i
$$767$$ −22.3923 −0.808539
$$768$$ −24.0000 + 13.8564i −0.866025 + 0.500000i
$$769$$ 18.0000i 0.649097i −0.945869 0.324548i $$-0.894788\pi$$
0.945869 0.324548i $$-0.105212\pi$$
$$770$$ 0 0
$$771$$ 10.3923i 0.374270i
$$772$$ −2.53590 4.39230i −0.0912690 0.158083i
$$773$$ −12.4641 −0.448303 −0.224151 0.974554i $$-0.571961\pi$$
−0.224151 + 0.974554i $$0.571961\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −14.7846 14.7846i −0.530737 0.530737i
$$777$$ −8.78461 7.60770i −0.315146 0.272925i
$$778$$ 2.50962 + 9.36603i 0.0899742 + 0.335788i
$$779$$ 20.7846i 0.744686i
$$780$$ 0 0
$$781$$ −2.00000 −0.0715656
$$782$$ 0.928203 + 3.46410i 0.0331925 + 0.123876i
$$783$$ 30.8038i 1.10084i
$$784$$ 26.0000 + 10.3923i 0.928571 + 0.371154i
$$785$$ 0 0
$$786$$ −22.3923 + 6.00000i −0.798707 + 0.214013i
$$787$$ 15.3397i 0.546803i 0.961900 + 0.273401i $$0.0881487\pi$$