# Properties

 Label 700.2.c.e.699.4 Level $700$ Weight $2$ Character 700.699 Analytic conductor $5.590$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## 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 699.4 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 700.699 Dual form 700.2.c.e.699.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.36603 + 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(2.00000 - 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$$ $$q+(1.36603 + 0.366025i) q^{2} +1.73205i q^{3} +(1.73205 + 1.00000i) q^{4} +(-0.633975 + 2.36603i) q^{6} +(2.00000 - 1.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} -0.267949i q^{11} +(-1.73205 + 3.00000i) q^{12} -0.464102 q^{13} +(3.36603 - 1.63397i) q^{14} +(2.00000 + 3.46410i) q^{16} +6.46410 q^{17} -6.00000 q^{19} +(3.00000 + 3.46410i) q^{21} +(0.0980762 - 0.366025i) q^{22} -1.46410 q^{23} +(-3.46410 + 3.46410i) q^{24} +(-0.633975 - 0.169873i) q^{26} +5.19615i q^{27} +(5.19615 - 1.00000i) q^{28} -7.92820 q^{29} -6.00000 q^{31} +(1.46410 + 5.46410i) q^{32} +0.464102 q^{33} +(8.83013 + 2.36603i) q^{34} -9.46410i q^{37} +(-8.19615 - 2.19615i) q^{38} -0.803848i q^{39} -3.46410i q^{41} +(2.83013 + 5.83013i) q^{42} -2.00000 q^{43} +(0.267949 - 0.464102i) q^{44} +(-2.00000 - 0.535898i) q^{46} +1.73205i q^{47} +(-6.00000 + 3.46410i) q^{48} +(1.00000 - 6.92820i) q^{49} +11.1962i q^{51} +(-0.803848 - 0.464102i) q^{52} -2.00000i q^{53} +(-1.90192 + 7.09808i) q^{54} +(7.46410 + 0.535898i) q^{56} -10.3923i q^{57} +(-10.8301 - 2.90192i) q^{58} +3.46410 q^{59} +9.46410i q^{61} +(-8.19615 - 2.19615i) q^{62} +8.00000i q^{64} +(0.633975 + 0.169873i) q^{66} -3.46410 q^{67} +(11.1962 + 6.46410i) q^{68} -2.53590i q^{69} -7.46410i q^{71} +12.9282 q^{73} +(3.46410 - 12.9282i) q^{74} +(-10.3923 - 6.00000i) q^{76} +(-0.464102 - 0.535898i) q^{77} +(0.294229 - 1.09808i) q^{78} +14.6603i q^{79} -9.00000 q^{81} +(1.26795 - 4.73205i) q^{82} -15.4641i q^{83} +(1.73205 + 9.00000i) q^{84} +(-2.73205 - 0.732051i) q^{86} -13.7321i q^{87} +(0.535898 - 0.535898i) q^{88} -2.53590i q^{89} +(-0.928203 + 0.803848i) q^{91} +(-2.53590 - 1.46410i) q^{92} -10.3923i q^{93} +(-0.633975 + 2.36603i) q^{94} +(-9.46410 + 2.53590i) q^{96} +13.3923 q^{97} +(3.90192 - 9.09808i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + O(q^{10})$$ $$4 q + 2 q^{2} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{13} + 10 q^{14} + 8 q^{16} + 12 q^{17} - 24 q^{19} + 12 q^{21} - 10 q^{22} + 8 q^{23} - 6 q^{26} - 4 q^{29} - 24 q^{31} - 8 q^{32} - 12 q^{33} + 18 q^{34} - 12 q^{38} - 6 q^{42} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 24 q^{48} + 4 q^{49} - 24 q^{52} - 18 q^{54} + 16 q^{56} - 26 q^{58} - 12 q^{62} + 6 q^{66} + 24 q^{68} + 24 q^{73} + 12 q^{77} - 30 q^{78} - 36 q^{81} + 12 q^{82} - 4 q^{86} + 16 q^{88} + 24 q^{91} - 24 q^{92} - 6 q^{94} - 24 q^{96} + 12 q^{97} + 26 q^{98} + O(q^{100})$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.36603 + 0.366025i 0.965926 + 0.258819i
$$3$$ 1.73205i 1.00000i 0.866025 + 0.500000i $$0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$4$$ 1.73205 + 1.00000i 0.866025 + 0.500000i
$$5$$ 0 0
$$6$$ −0.633975 + 2.36603i −0.258819 + 0.965926i
$$7$$ 2.00000 1.73205i 0.755929 0.654654i
$$8$$ 2.00000 + 2.00000i 0.707107 + 0.707107i
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 0.267949i 0.0807897i −0.999184 0.0403949i $$-0.987138\pi$$
0.999184 0.0403949i $$-0.0128616\pi$$
$$12$$ −1.73205 + 3.00000i −0.500000 + 0.866025i
$$13$$ −0.464102 −0.128719 −0.0643593 0.997927i $$-0.520500\pi$$
−0.0643593 + 0.997927i $$0.520500\pi$$
$$14$$ 3.36603 1.63397i 0.899608 0.436698i
$$15$$ 0 0
$$16$$ 2.00000 + 3.46410i 0.500000 + 0.866025i
$$17$$ 6.46410 1.56777 0.783887 0.620903i $$-0.213234\pi$$
0.783887 + 0.620903i $$0.213234\pi$$
$$18$$ 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
$$22$$ 0.0980762 0.366025i 0.0209099 0.0780369i
$$23$$ −1.46410 −0.305286 −0.152643 0.988281i $$-0.548779\pi$$
−0.152643 + 0.988281i $$0.548779\pi$$
$$24$$ −3.46410 + 3.46410i −0.707107 + 0.707107i
$$25$$ 0 0
$$26$$ −0.633975 0.169873i −0.124333 0.0333148i
$$27$$ 5.19615i 1.00000i
$$28$$ 5.19615 1.00000i 0.981981 0.188982i
$$29$$ −7.92820 −1.47223 −0.736115 0.676856i $$-0.763342\pi$$
−0.736115 + 0.676856i $$0.763342\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ 1.46410 + 5.46410i 0.258819 + 0.965926i
$$33$$ 0.464102 0.0807897
$$34$$ 8.83013 + 2.36603i 1.51435 + 0.405770i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 9.46410i 1.55589i −0.628333 0.777944i $$-0.716263\pi$$
0.628333 0.777944i $$-0.283737\pi$$
$$38$$ −8.19615 2.19615i −1.32959 0.356263i
$$39$$ 0.803848i 0.128719i
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 2.83013 + 5.83013i 0.436698 + 0.899608i
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0.267949 0.464102i 0.0403949 0.0699660i
$$45$$ 0 0
$$46$$ −2.00000 0.535898i −0.294884 0.0790139i
$$47$$ 1.73205i 0.252646i 0.991989 + 0.126323i $$0.0403175\pi$$
−0.991989 + 0.126323i $$0.959682\pi$$
$$48$$ −6.00000 + 3.46410i −0.866025 + 0.500000i
$$49$$ 1.00000 6.92820i 0.142857 0.989743i
$$50$$ 0 0
$$51$$ 11.1962i 1.56777i
$$52$$ −0.803848 0.464102i −0.111474 0.0643593i
$$53$$ 2.00000i 0.274721i −0.990521 0.137361i $$-0.956138\pi$$
0.990521 0.137361i $$-0.0438619\pi$$
$$54$$ −1.90192 + 7.09808i −0.258819 + 0.965926i
$$55$$ 0 0
$$56$$ 7.46410 + 0.535898i 0.997433 + 0.0716124i
$$57$$ 10.3923i 1.37649i
$$58$$ −10.8301 2.90192i −1.42207 0.381041i
$$59$$ 3.46410 0.450988 0.225494 0.974245i $$-0.427600\pi$$
0.225494 + 0.974245i $$0.427600\pi$$
$$60$$ 0 0
$$61$$ 9.46410i 1.21175i 0.795558 + 0.605877i $$0.207178\pi$$
−0.795558 + 0.605877i $$0.792822\pi$$
$$62$$ −8.19615 2.19615i −1.04091 0.278912i
$$63$$ 0 0
$$64$$ 8.00000i 1.00000i
$$65$$ 0 0
$$66$$ 0.633975 + 0.169873i 0.0780369 + 0.0209099i
$$67$$ −3.46410 −0.423207 −0.211604 0.977356i $$-0.567869\pi$$
−0.211604 + 0.977356i $$0.567869\pi$$
$$68$$ 11.1962 + 6.46410i 1.35773 + 0.783887i
$$69$$ 2.53590i 0.305286i
$$70$$ 0 0
$$71$$ 7.46410i 0.885826i −0.896565 0.442913i $$-0.853945\pi$$
0.896565 0.442913i $$-0.146055\pi$$
$$72$$ 0 0
$$73$$ 12.9282 1.51313 0.756566 0.653917i $$-0.226876\pi$$
0.756566 + 0.653917i $$0.226876\pi$$
$$74$$ 3.46410 12.9282i 0.402694 1.50287i
$$75$$ 0 0
$$76$$ −10.3923 6.00000i −1.19208 0.688247i
$$77$$ −0.464102 0.535898i −0.0528893 0.0610713i
$$78$$ 0.294229 1.09808i 0.0333148 0.124333i
$$79$$ 14.6603i 1.64941i 0.565565 + 0.824704i $$0.308658\pi$$
−0.565565 + 0.824704i $$0.691342\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 1.26795 4.73205i 0.140022 0.522568i
$$83$$ 15.4641i 1.69741i −0.528870 0.848703i $$-0.677384\pi$$
0.528870 0.848703i $$-0.322616\pi$$
$$84$$ 1.73205 + 9.00000i 0.188982 + 0.981981i
$$85$$ 0 0
$$86$$ −2.73205 0.732051i −0.294605 0.0789391i
$$87$$ 13.7321i 1.47223i
$$88$$ 0.535898 0.535898i 0.0571270 0.0571270i
$$89$$ 2.53590i 0.268805i −0.990927 0.134402i $$-0.957089\pi$$
0.990927 0.134402i $$-0.0429115\pi$$
$$90$$ 0 0
$$91$$ −0.928203 + 0.803848i −0.0973021 + 0.0842661i
$$92$$ −2.53590 1.46410i −0.264386 0.152643i
$$93$$ 10.3923i 1.07763i
$$94$$ −0.633975 + 2.36603i −0.0653895 + 0.244037i
$$95$$ 0 0
$$96$$ −9.46410 + 2.53590i −0.965926 + 0.258819i
$$97$$ 13.3923 1.35978 0.679891 0.733313i $$-0.262027\pi$$
0.679891 + 0.733313i $$0.262027\pi$$
$$98$$ 3.90192 9.09808i 0.394154 0.919044i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 15.4641i 1.53874i −0.638806 0.769368i $$-0.720571\pi$$
0.638806 0.769368i $$-0.279429\pi$$
$$102$$ −4.09808 + 15.2942i −0.405770 + 1.51435i
$$103$$ 6.80385i 0.670403i 0.942146 + 0.335202i $$0.108804\pi$$
−0.942146 + 0.335202i $$0.891196\pi$$
$$104$$ −0.928203 0.928203i −0.0910178 0.0910178i
$$105$$ 0 0
$$106$$ 0.732051 2.73205i 0.0711031 0.265360i
$$107$$ −2.39230 −0.231273 −0.115636 0.993292i $$-0.536891\pi$$
−0.115636 + 0.993292i $$0.536891\pi$$
$$108$$ −5.19615 + 9.00000i −0.500000 + 0.866025i
$$109$$ −2.07180 −0.198442 −0.0992211 0.995065i $$-0.531635\pi$$
−0.0992211 + 0.995065i $$0.531635\pi$$
$$110$$ 0 0
$$111$$ 16.3923 1.55589
$$112$$ 10.0000 + 3.46410i 0.944911 + 0.327327i
$$113$$ 5.46410i 0.514019i −0.966409 0.257010i $$-0.917263\pi$$
0.966409 0.257010i $$-0.0827372\pi$$
$$114$$ 3.80385 14.1962i 0.356263 1.32959i
$$115$$ 0 0
$$116$$ −13.7321 7.92820i −1.27499 0.736115i
$$117$$ 0 0
$$118$$ 4.73205 + 1.26795i 0.435621 + 0.116724i
$$119$$ 12.9282 11.1962i 1.18513 1.02635i
$$120$$ 0 0
$$121$$ 10.9282 0.993473
$$122$$ −3.46410 + 12.9282i −0.313625 + 1.17046i
$$123$$ 6.00000 0.541002
$$124$$ −10.3923 6.00000i −0.933257 0.538816i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −15.4641 −1.37222 −0.686109 0.727499i $$-0.740683\pi$$
−0.686109 + 0.727499i $$0.740683\pi$$
$$128$$ −2.92820 + 10.9282i −0.258819 + 0.965926i
$$129$$ 3.46410i 0.304997i
$$130$$ 0 0
$$131$$ 2.53590 0.221562 0.110781 0.993845i $$-0.464665\pi$$
0.110781 + 0.993845i $$0.464665\pi$$
$$132$$ 0.803848 + 0.464102i 0.0699660 + 0.0403949i
$$133$$ −12.0000 + 10.3923i −1.04053 + 0.901127i
$$134$$ −4.73205 1.26795i −0.408787 0.109534i
$$135$$ 0 0
$$136$$ 12.9282 + 12.9282i 1.10858 + 1.10858i
$$137$$ 20.3923i 1.74223i 0.491077 + 0.871116i $$0.336603\pi$$
−0.491077 + 0.871116i $$0.663397\pi$$
$$138$$ 0.928203 3.46410i 0.0790139 0.294884i
$$139$$ −6.92820 −0.587643 −0.293821 0.955860i $$-0.594927\pi$$
−0.293821 + 0.955860i $$0.594927\pi$$
$$140$$ 0 0
$$141$$ −3.00000 −0.252646
$$142$$ 2.73205 10.1962i 0.229269 0.855642i
$$143$$ 0.124356i 0.0103991i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 17.6603 + 4.73205i 1.46157 + 0.391627i
$$147$$ 12.0000 + 1.73205i 0.989743 + 0.142857i
$$148$$ 9.46410 16.3923i 0.777944 1.34744i
$$149$$ −3.07180 −0.251651 −0.125826 0.992052i $$-0.540158\pi$$
−0.125826 + 0.992052i $$0.540158\pi$$
$$150$$ 0 0
$$151$$ 15.1962i 1.23665i −0.785924 0.618323i $$-0.787812\pi$$
0.785924 0.618323i $$-0.212188\pi$$
$$152$$ −12.0000 12.0000i −0.973329 0.973329i
$$153$$ 0 0
$$154$$ −0.437822 0.901924i −0.0352807 0.0726791i
$$155$$ 0 0
$$156$$ 0.803848 1.39230i 0.0643593 0.111474i
$$157$$ −7.85641 −0.627009 −0.313505 0.949587i $$-0.601503\pi$$
−0.313505 + 0.949587i $$0.601503\pi$$
$$158$$ −5.36603 + 20.0263i −0.426898 + 1.59321i
$$159$$ 3.46410 0.274721
$$160$$ 0 0
$$161$$ −2.92820 + 2.53590i −0.230775 + 0.199857i
$$162$$ −12.2942 3.29423i −0.965926 0.258819i
$$163$$ 20.7846 1.62798 0.813988 0.580881i $$-0.197292\pi$$
0.813988 + 0.580881i $$0.197292\pi$$
$$164$$ 3.46410 6.00000i 0.270501 0.468521i
$$165$$ 0 0
$$166$$ 5.66025 21.1244i 0.439321 1.63957i
$$167$$ 5.19615i 0.402090i −0.979582 0.201045i $$-0.935566\pi$$
0.979582 0.201045i $$-0.0644338\pi$$
$$168$$ −0.928203 + 12.9282i −0.0716124 + 0.997433i
$$169$$ −12.7846 −0.983432
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −3.46410 2.00000i −0.264135 0.152499i
$$173$$ −14.3205 −1.08877 −0.544384 0.838836i $$-0.683237\pi$$
−0.544384 + 0.838836i $$0.683237\pi$$
$$174$$ 5.02628 18.7583i 0.381041 1.42207i
$$175$$ 0 0
$$176$$ 0.928203 0.535898i 0.0699660 0.0403949i
$$177$$ 6.00000i 0.450988i
$$178$$ 0.928203 3.46410i 0.0695718 0.259645i
$$179$$ 6.39230i 0.477783i −0.971046 0.238892i $$-0.923216\pi$$
0.971046 0.238892i $$-0.0767841\pi$$
$$180$$ 0 0
$$181$$ 0.928203i 0.0689928i −0.999405 0.0344964i $$-0.989017\pi$$
0.999405 0.0344964i $$-0.0109827\pi$$
$$182$$ −1.56218 + 0.758330i −0.115796 + 0.0562112i
$$183$$ −16.3923 −1.21175
$$184$$ −2.92820 2.92820i −0.215870 0.215870i
$$185$$ 0 0
$$186$$ 3.80385 14.1962i 0.278912 1.04091i
$$187$$ 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
$$191$$ 7.19615i 0.520695i −0.965515 0.260348i $$-0.916163\pi$$
0.965515 0.260348i $$-0.0838372\pi$$
$$192$$ −13.8564 −1.00000
$$193$$ 9.46410i 0.681241i 0.940201 + 0.340620i $$0.110637\pi$$
−0.940201 + 0.340620i $$0.889363\pi$$
$$194$$ 18.2942 + 4.90192i 1.31345 + 0.351938i
$$195$$ 0 0
$$196$$ 8.66025 11.0000i 0.618590 0.785714i
$$197$$ 13.3205i 0.949047i −0.880243 0.474523i $$-0.842620\pi$$
0.880243 0.474523i $$-0.157380\pi$$
$$198$$ 0 0
$$199$$ −3.46410 −0.245564 −0.122782 0.992434i $$-0.539182\pi$$
−0.122782 + 0.992434i $$0.539182\pi$$
$$200$$ 0 0
$$201$$ 6.00000i 0.423207i
$$202$$ 5.66025 21.1244i 0.398254 1.48630i
$$203$$ −15.8564 + 13.7321i −1.11290 + 0.963801i
$$204$$ −11.1962 + 19.3923i −0.783887 + 1.35773i
$$205$$ 0 0
$$206$$ −2.49038 + 9.29423i −0.173513 + 0.647560i
$$207$$ 0 0
$$208$$ −0.928203 1.60770i −0.0643593 0.111474i
$$209$$ 1.60770i 0.111207i
$$210$$ 0 0
$$211$$ 3.19615i 0.220032i −0.993930 0.110016i $$-0.964910\pi$$
0.993930 0.110016i $$-0.0350902\pi$$
$$212$$ 2.00000 3.46410i 0.137361 0.237915i
$$213$$ 12.9282 0.885826
$$214$$ −3.26795 0.875644i −0.223392 0.0598578i
$$215$$ 0 0
$$216$$ −10.3923 + 10.3923i −0.707107 + 0.707107i
$$217$$ −12.0000 + 10.3923i −0.814613 + 0.705476i
$$218$$ −2.83013 0.758330i −0.191680 0.0513606i
$$219$$ 22.3923i 1.51313i
$$220$$ 0 0
$$221$$ −3.00000 −0.201802
$$222$$ 22.3923 + 6.00000i 1.50287 + 0.402694i
$$223$$ 13.7321i 0.919566i 0.888031 + 0.459783i $$0.152073\pi$$
−0.888031 + 0.459783i $$0.847927\pi$$
$$224$$ 12.3923 + 8.39230i 0.827996 + 0.560734i
$$225$$ 0 0
$$226$$ 2.00000 7.46410i 0.133038 0.496505i
$$227$$ 20.6603i 1.37127i 0.727946 + 0.685635i $$0.240475\pi$$
−0.727946 + 0.685635i $$0.759525\pi$$
$$228$$ 10.3923 18.0000i 0.688247 1.19208i
$$229$$ 8.53590i 0.564068i 0.959404 + 0.282034i $$0.0910091\pi$$
−0.959404 + 0.282034i $$0.908991\pi$$
$$230$$ 0 0
$$231$$ 0.928203 0.803848i 0.0610713 0.0528893i
$$232$$ −15.8564 15.8564i −1.04102 1.04102i
$$233$$ 9.07180i 0.594313i 0.954829 + 0.297157i $$0.0960383\pi$$
−0.954829 + 0.297157i $$0.903962\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 6.00000 + 3.46410i 0.390567 + 0.225494i
$$237$$ −25.3923 −1.64941
$$238$$ 21.7583 10.5622i 1.41038 0.684644i
$$239$$ 23.9808i 1.55119i −0.631233 0.775593i $$-0.717451\pi$$
0.631233 0.775593i $$-0.282549\pi$$
$$240$$ 0 0
$$241$$ 16.3923i 1.05592i 0.849269 + 0.527961i $$0.177043\pi$$
−0.849269 + 0.527961i $$0.822957\pi$$
$$242$$ 14.9282 + 4.00000i 0.959621 + 0.257130i
$$243$$ 0 0
$$244$$ −9.46410 + 16.3923i −0.605877 + 1.04941i
$$245$$ 0 0
$$246$$ 8.19615 + 2.19615i 0.522568 + 0.140022i
$$247$$ 2.78461 0.177180
$$248$$ −12.0000 12.0000i −0.762001 0.762001i
$$249$$ 26.7846 1.69741
$$250$$ 0 0
$$251$$ −25.8564 −1.63204 −0.816021 0.578022i $$-0.803825\pi$$
−0.816021 + 0.578022i $$0.803825\pi$$
$$252$$ 0 0
$$253$$ 0.392305i 0.0246640i
$$254$$ −21.1244 5.66025i −1.32546 0.355156i
$$255$$ 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 $$0.559920\pi$$
$$258$$ 1.26795 4.73205i 0.0789391 0.294605i
$$259$$ −16.3923 18.9282i −1.01857 1.17614i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 3.46410 + 0.928203i 0.214013 + 0.0573446i
$$263$$ 11.4641 0.706907 0.353453 0.935452i $$-0.385007\pi$$
0.353453 + 0.935452i $$0.385007\pi$$
$$264$$ 0.928203 + 0.928203i 0.0571270 + 0.0571270i
$$265$$ 0 0
$$266$$ −20.1962 + 9.80385i −1.23831 + 0.601112i
$$267$$ 4.39230 0.268805
$$268$$ −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
$$271$$ 9.46410 0.574903 0.287452 0.957795i $$-0.407192\pi$$
0.287452 + 0.957795i $$0.407192\pi$$
$$272$$ 12.9282 + 22.3923i 0.783887 + 1.35773i
$$273$$ −1.39230 1.60770i −0.0842661 0.0973021i
$$274$$ −7.46410 + 27.8564i −0.450923 + 1.68287i
$$275$$ 0 0
$$276$$ 2.53590 4.39230i 0.152643 0.264386i
$$277$$ 16.7846i 1.00849i 0.863561 + 0.504245i $$0.168229\pi$$
−0.863561 + 0.504245i $$0.831771\pi$$
$$278$$ −9.46410 2.53590i −0.567619 0.152093i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −7.92820 −0.472957 −0.236478 0.971637i $$-0.575993\pi$$
−0.236478 + 0.971637i $$0.575993\pi$$
$$282$$ −4.09808 1.09808i −0.244037 0.0653895i
$$283$$ 12.1244i 0.720718i −0.932814 0.360359i $$-0.882654\pi$$
0.932814 0.360359i $$-0.117346\pi$$
$$284$$ 7.46410 12.9282i 0.442913 0.767148i
$$285$$ 0 0
$$286$$ −0.0455173 + 0.169873i −0.00269150 + 0.0100448i
$$287$$ −6.00000 6.92820i −0.354169 0.408959i
$$288$$ 0 0
$$289$$ 24.7846 1.45792
$$290$$ 0 0
$$291$$ 23.1962i 1.35978i
$$292$$ 22.3923 + 12.9282i 1.31041 + 0.756566i
$$293$$ 20.3205 1.18714 0.593568 0.804784i $$-0.297719\pi$$
0.593568 + 0.804784i $$0.297719\pi$$
$$294$$ 15.7583 + 6.75833i 0.919044 + 0.394154i
$$295$$ 0 0
$$296$$ 18.9282 18.9282i 1.10018 1.10018i
$$297$$ 1.39230 0.0807897
$$298$$ −4.19615 1.12436i −0.243077 0.0651322i
$$299$$ 0.679492 0.0392960
$$300$$ 0 0
$$301$$ −4.00000 + 3.46410i −0.230556 + 0.199667i
$$302$$ 5.56218 20.7583i 0.320067 1.19451i
$$303$$ 26.7846 1.53874
$$304$$ −12.0000 20.7846i −0.688247 1.19208i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 1.73205i 0.0988534i 0.998778 + 0.0494267i $$0.0157394\pi$$
−0.998778 + 0.0494267i $$0.984261\pi$$
$$308$$ −0.267949 1.39230i −0.0152678 0.0793339i
$$309$$ −11.7846 −0.670403
$$310$$ 0 0
$$311$$ 7.85641 0.445496 0.222748 0.974876i $$-0.428497\pi$$
0.222748 + 0.974876i $$0.428497\pi$$
$$312$$ 1.60770 1.60770i 0.0910178 0.0910178i
$$313$$ −17.5359 −0.991188 −0.495594 0.868554i $$-0.665050\pi$$
−0.495594 + 0.868554i $$0.665050\pi$$
$$314$$ −10.7321 2.87564i −0.605645 0.162282i
$$315$$ 0 0
$$316$$ −14.6603 + 25.3923i −0.824704 + 1.42843i
$$317$$ 3.07180i 0.172529i −0.996272 0.0862646i $$-0.972507\pi$$
0.996272 0.0862646i $$-0.0274931\pi$$
$$318$$ 4.73205 + 1.26795i 0.265360 + 0.0711031i
$$319$$ 2.12436i 0.118941i
$$320$$ 0 0
$$321$$ 4.14359i 0.231273i
$$322$$ −4.92820 + 2.39230i −0.274638 + 0.133318i
$$323$$ −38.7846 −2.15803
$$324$$ −15.5885 9.00000i −0.866025 0.500000i
$$325$$ 0 0
$$326$$ 28.3923 + 7.60770i 1.57250 + 0.421351i
$$327$$ 3.58846i 0.198442i
$$328$$ 6.92820 6.92820i 0.382546 0.382546i
$$329$$ 3.00000 + 3.46410i 0.165395 + 0.190982i
$$330$$ 0 0
$$331$$ 26.3923i 1.45065i 0.688405 + 0.725326i $$0.258311\pi$$
−0.688405 + 0.725326i $$0.741689\pi$$
$$332$$ 15.4641 26.7846i 0.848703 1.47000i
$$333$$ 0 0
$$334$$ 1.90192 7.09808i 0.104069 0.388389i
$$335$$ 0 0
$$336$$ −6.00000 + 17.3205i −0.327327 + 0.944911i
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −17.4641 4.67949i −0.949922 0.254531i
$$339$$ 9.46410 0.514019
$$340$$ 0 0
$$341$$ 1.60770i 0.0870616i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ −4.00000 4.00000i −0.215666 0.215666i
$$345$$ 0 0
$$346$$ −19.5622 5.24167i −1.05167 0.281794i
$$347$$ 34.2487 1.83857 0.919284 0.393596i $$-0.128769\pi$$
0.919284 + 0.393596i $$0.128769\pi$$
$$348$$ 13.7321 23.7846i 0.736115 1.27499i
$$349$$ 5.32051i 0.284800i 0.989809 + 0.142400i $$0.0454820\pi$$
−0.989809 + 0.142400i $$0.954518\pi$$
$$350$$ 0 0
$$351$$ 2.41154i 0.128719i
$$352$$ 1.46410 0.392305i 0.0780369 0.0209099i
$$353$$ −7.39230 −0.393453 −0.196726 0.980458i $$-0.563031\pi$$
−0.196726 + 0.980458i $$0.563031\pi$$
$$354$$ −2.19615 + 8.19615i −0.116724 + 0.435621i
$$355$$ 0 0
$$356$$ 2.53590 4.39230i 0.134402 0.232792i
$$357$$ 19.3923 + 22.3923i 1.02635 + 1.18513i
$$358$$ 2.33975 8.73205i 0.123659 0.461503i
$$359$$ 25.3205i 1.33637i 0.743997 + 0.668183i $$0.232928\pi$$
−0.743997 + 0.668183i $$0.767072\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0.339746 1.26795i 0.0178567 0.0666419i
$$363$$ 18.9282i 0.993473i
$$364$$ −2.41154 + 0.464102i −0.126399 + 0.0243255i
$$365$$ 0 0
$$366$$ −22.3923 6.00000i −1.17046 0.313625i
$$367$$ 11.8756i 0.619904i 0.950752 + 0.309952i $$0.100313\pi$$
−0.950752 + 0.309952i $$0.899687\pi$$
$$368$$ −2.92820 5.07180i −0.152643 0.264386i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3.46410 4.00000i −0.179847 0.207670i
$$372$$ 10.3923 18.0000i 0.538816 0.933257i
$$373$$ 3.60770i 0.186799i 0.995629 + 0.0933997i $$0.0297734\pi$$
−0.995629 + 0.0933997i $$0.970227\pi$$
$$374$$ 0.633975 2.36603i 0.0327820 0.122344i
$$375$$ 0 0
$$376$$ −3.46410 + 3.46410i −0.178647 + 0.178647i
$$377$$ 3.67949 0.189503
$$378$$ 8.49038 + 17.4904i 0.436698 + 0.899608i
$$379$$ 5.60770i 0.288048i 0.989574 + 0.144024i $$0.0460042\pi$$
−0.989574 + 0.144024i $$0.953996\pi$$
$$380$$ 0 0
$$381$$ 26.7846i 1.37222i
$$382$$ 2.63397 9.83013i 0.134766 0.502953i
$$383$$ 27.4641i 1.40335i −0.712497 0.701675i $$-0.752436\pi$$
0.712497 0.701675i $$-0.247564\pi$$
$$384$$ −18.9282 5.07180i −0.965926 0.258819i
$$385$$ 0 0
$$386$$ −3.46410 + 12.9282i −0.176318 + 0.658028i
$$387$$ 0 0
$$388$$ 23.1962 + 13.3923i 1.17761 + 0.679891i
$$389$$ 20.8564 1.05746 0.528731 0.848790i $$-0.322668\pi$$
0.528731 + 0.848790i $$0.322668\pi$$
$$390$$ 0 0
$$391$$ −9.46410 −0.478620
$$392$$ 15.8564 11.8564i 0.800869 0.598839i
$$393$$ 4.39230i 0.221562i
$$394$$ 4.87564 18.1962i 0.245631 0.916709i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −12.4641 −0.625555 −0.312778 0.949826i $$-0.601259\pi$$
−0.312778 + 0.949826i $$0.601259\pi$$
$$398$$ −4.73205 1.26795i −0.237196 0.0635566i
$$399$$ −18.0000 20.7846i −0.901127 1.04053i
$$400$$ 0 0
$$401$$ −10.0718 −0.502962 −0.251481 0.967862i $$-0.580918\pi$$
−0.251481 + 0.967862i $$0.580918\pi$$
$$402$$ 2.19615 8.19615i 0.109534 0.408787i
$$403$$ 2.78461 0.138711
$$404$$ 15.4641 26.7846i 0.769368 1.33258i
$$405$$ 0 0
$$406$$ −26.6865 + 12.9545i −1.32443 + 0.642920i
$$407$$ −2.53590 −0.125700
$$408$$ −22.3923 + 22.3923i −1.10858 + 1.10858i
$$409$$ 4.14359i 0.204888i −0.994739 0.102444i $$-0.967334\pi$$
0.994739 0.102444i $$-0.0326662\pi$$
$$410$$ 0 0
$$411$$ −35.3205 −1.74223
$$412$$ −6.80385 + 11.7846i −0.335202 + 0.580586i
$$413$$ 6.92820 6.00000i 0.340915 0.295241i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.679492 2.53590i −0.0333148 0.124333i
$$417$$ 12.0000i 0.587643i
$$418$$ −0.588457 + 2.19615i −0.0287824 + 0.107417i
$$419$$ 24.2487 1.18463 0.592314 0.805708i $$-0.298215\pi$$
0.592314 + 0.805708i $$0.298215\pi$$
$$420$$ 0 0
$$421$$ 19.0000 0.926003 0.463002 0.886357i $$-0.346772\pi$$
0.463002 + 0.886357i $$0.346772\pi$$
$$422$$ 1.16987 4.36603i 0.0569485 0.212535i
$$423$$ 0 0
$$424$$ 4.00000 4.00000i 0.194257 0.194257i
$$425$$ 0 0
$$426$$ 17.6603 + 4.73205i 0.855642 + 0.229269i
$$427$$ 16.3923 + 18.9282i 0.793279 + 0.916000i
$$428$$ −4.14359 2.39230i −0.200288 0.115636i
$$429$$ −0.215390 −0.0103991
$$430$$ 0 0
$$431$$ 13.5885i 0.654533i 0.944932 + 0.327266i $$0.106127\pi$$
−0.944932 + 0.327266i $$0.893873\pi$$
$$432$$ −18.0000 + 10.3923i −0.866025 + 0.500000i
$$433$$ −31.8564 −1.53092 −0.765461 0.643483i $$-0.777489\pi$$
−0.765461 + 0.643483i $$0.777489\pi$$
$$434$$ −20.1962 + 9.80385i −0.969446 + 0.470600i
$$435$$ 0 0
$$436$$ −3.58846 2.07180i −0.171856 0.0992211i
$$437$$ 8.78461 0.420225
$$438$$ −8.19615 + 30.5885i −0.391627 + 1.46157i
$$439$$ 39.7128 1.89539 0.947695 0.319179i $$-0.103407\pi$$
0.947695 + 0.319179i $$0.103407\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −4.09808 1.09808i −0.194926 0.0522302i
$$443$$ 26.0000 1.23530 0.617649 0.786454i $$-0.288085\pi$$
0.617649 + 0.786454i $$0.288085\pi$$
$$444$$ 28.3923 + 16.3923i 1.34744 + 0.777944i
$$445$$ 0 0
$$446$$ −5.02628 + 18.7583i −0.238001 + 0.888233i
$$447$$ 5.32051i 0.251651i
$$448$$ 13.8564 + 16.0000i 0.654654 + 0.755929i
$$449$$ −11.9282 −0.562927 −0.281463 0.959572i $$-0.590820\pi$$
−0.281463 + 0.959572i $$0.590820\pi$$
$$450$$ 0 0
$$451$$ −0.928203 −0.0437074
$$452$$ 5.46410 9.46410i 0.257010 0.445154i
$$453$$ 26.3205 1.23665
$$454$$ −7.56218 + 28.2224i −0.354911 + 1.32454i
$$455$$ 0 0
$$456$$ 20.7846 20.7846i 0.973329 0.973329i
$$457$$ 20.5359i 0.960629i 0.877096 + 0.480314i $$0.159477\pi$$
−0.877096 + 0.480314i $$0.840523\pi$$
$$458$$ −3.12436 + 11.6603i −0.145992 + 0.544848i
$$459$$ 33.5885i 1.56777i
$$460$$ 0 0
$$461$$ 27.7128i 1.29071i 0.763881 + 0.645357i $$0.223291\pi$$
−0.763881 + 0.645357i $$0.776709\pi$$
$$462$$ 1.56218 0.758330i 0.0726791 0.0352807i
$$463$$ 16.3923 0.761815 0.380908 0.924613i $$-0.375612\pi$$
0.380908 + 0.924613i $$0.375612\pi$$
$$464$$ −15.8564 27.4641i −0.736115 1.27499i
$$465$$ 0 0
$$466$$ −3.32051 + 12.3923i −0.153820 + 0.574062i
$$467$$ 22.5167i 1.04195i 0.853573 + 0.520973i $$0.174431\pi$$
−0.853573 + 0.520973i $$0.825569\pi$$
$$468$$ 0 0
$$469$$ −6.92820 + 6.00000i −0.319915 + 0.277054i
$$470$$ 0 0
$$471$$ 13.6077i 0.627009i
$$472$$ 6.92820 + 6.92820i 0.318896 + 0.318896i
$$473$$ 0.535898i 0.0246406i
$$474$$ −34.6865 9.29423i −1.59321 0.426898i
$$475$$ 0 0
$$476$$ 33.5885 6.46410i 1.53952 0.296282i
$$477$$ 0 0
$$478$$ 8.77757 32.7583i 0.401477 1.49833i
$$479$$ −25.1769 −1.15036 −0.575181 0.818026i $$-0.695068\pi$$
−0.575181 + 0.818026i $$0.695068\pi$$
$$480$$ 0 0
$$481$$ 4.39230i 0.200272i
$$482$$ −6.00000 + 22.3923i −0.273293 + 1.01994i
$$483$$ −4.39230 5.07180i −0.199857 0.230775i
$$484$$ 18.9282 + 10.9282i 0.860373 + 0.496737i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −12.7846 −0.579326 −0.289663 0.957129i $$-0.593543\pi$$
−0.289663 + 0.957129i $$0.593543\pi$$
$$488$$ −18.9282 + 18.9282i −0.856840 + 0.856840i
$$489$$ 36.0000i 1.62798i
$$490$$ 0 0
$$491$$ 9.87564i 0.445682i 0.974855 + 0.222841i $$0.0715330\pi$$
−0.974855 + 0.222841i $$0.928467\pi$$
$$492$$ 10.3923 + 6.00000i 0.468521 + 0.270501i
$$493$$ −51.2487 −2.30813
$$494$$ 3.80385 + 1.01924i 0.171143 + 0.0458577i
$$495$$ 0 0
$$496$$ −12.0000 20.7846i −0.538816 0.933257i
$$497$$ −12.9282 14.9282i −0.579909 0.669621i
$$498$$ 36.5885 + 9.80385i 1.63957 + 0.439321i
$$499$$ 25.5885i 1.14550i 0.819731 + 0.572748i $$0.194123\pi$$
−0.819731 + 0.572748i $$0.805877\pi$$
$$500$$ 0 0
$$501$$ 9.00000 0.402090
$$502$$ −35.3205 9.46410i −1.57643 0.422404i
$$503$$ 15.5885i 0.695055i 0.937670 + 0.347527i $$0.112979\pi$$
−0.937670 + 0.347527i $$0.887021\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −0.143594 + 0.535898i −0.00638351 + 0.0238236i
$$507$$ 22.1436i 0.983432i
$$508$$ −26.7846 15.4641i −1.18837 0.686109i
$$509$$ 25.8564i 1.14607i −0.819533 0.573033i $$-0.805767\pi$$
0.819533 0.573033i $$-0.194233\pi$$
$$510$$ 0 0
$$511$$ 25.8564 22.3923i 1.14382 0.990577i
$$512$$ −16.0000 + 16.0000i −0.707107 + 0.707107i
$$513$$ 31.1769i 1.37649i
$$514$$ −8.19615 2.19615i −0.361517 0.0968681i
$$515$$ 0 0
$$516$$ 3.46410 6.00000i 0.152499 0.264135i
$$517$$ 0.464102 0.0204112
$$518$$ −15.4641 31.8564i −0.679454 1.39969i
$$519$$ 24.8038i 1.08877i
$$520$$ 0 0
$$521$$ 13.6077i 0.596164i 0.954540 + 0.298082i $$0.0963469\pi$$
−0.954540 + 0.298082i $$0.903653\pi$$
$$522$$ 0 0
$$523$$ 24.2487i 1.06032i 0.847897 + 0.530161i $$0.177869\pi$$
−0.847897 + 0.530161i $$0.822131\pi$$
$$524$$ 4.39230 + 2.53590i 0.191879 + 0.110781i
$$525$$ 0 0
$$526$$ 15.6603 + 4.19615i 0.682820 + 0.182961i
$$527$$ −38.7846 −1.68948
$$528$$ 0.928203 + 1.60770i 0.0403949 + 0.0699660i
$$529$$ −20.8564 −0.906800
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −31.1769 + 6.00000i −1.35169 + 0.260133i
$$533$$ 1.60770i 0.0696370i
$$534$$ 6.00000 + 1.60770i 0.259645 + 0.0695718i
$$535$$ 0 0
$$536$$ −6.92820 6.92820i −0.299253 0.299253i
$$537$$ 11.0718 0.477783
$$538$$ −4.39230 + 16.3923i −0.189366 + 0.706722i
$$539$$ −1.85641 0.267949i −0.0799611 0.0115414i
$$540$$ 0 0
$$541$$ 7.78461 0.334687 0.167343 0.985899i $$-0.446481\pi$$
0.167343 + 0.985899i $$0.446481\pi$$
$$542$$ 12.9282 + 3.46410i 0.555314 + 0.148796i
$$543$$ 1.60770 0.0689928
$$544$$ 9.46410 + 35.3205i 0.405770 + 1.51435i
$$545$$ 0 0
$$546$$ −1.31347 2.70577i −0.0562112 0.115796i
$$547$$ 21.4641 0.917739 0.458869 0.888504i $$-0.348255\pi$$
0.458869 + 0.888504i $$0.348255\pi$$
$$548$$ −20.3923 + 35.3205i −0.871116 + 1.50882i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 47.5692 2.02652
$$552$$ 5.07180 5.07180i 0.215870 0.215870i
$$553$$ 25.3923 + 29.3205i 1.07979 + 1.24683i
$$554$$ −6.14359 + 22.9282i −0.261016 + 0.974126i
$$555$$ 0 0
$$556$$ −12.0000 6.92820i −0.508913 0.293821i
$$557$$ 21.8564i 0.926086i −0.886336 0.463043i $$-0.846758\pi$$
0.886336 0.463043i $$-0.153242\pi$$
$$558$$ 0 0
$$559$$ 0.928203 0.0392588
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ −10.8301 2.90192i −0.456841 0.122410i
$$563$$ 19.1769i 0.808211i −0.914712 0.404105i $$-0.867583\pi$$
0.914712 0.404105i $$-0.132417\pi$$
$$564$$ −5.19615 3.00000i −0.218797 0.126323i
$$565$$ 0 0
$$566$$ 4.43782 16.5622i 0.186536 0.696160i
$$567$$ −18.0000 + 15.5885i −0.755929 + 0.654654i
$$568$$ 14.9282 14.9282i 0.626373 0.626373i
$$569$$ −7.07180 −0.296465 −0.148233 0.988953i $$-0.547358\pi$$
−0.148233 + 0.988953i $$0.547358\pi$$
$$570$$ 0 0
$$571$$ 6.67949i 0.279528i 0.990185 + 0.139764i $$0.0446344\pi$$
−0.990185 + 0.139764i $$0.955366\pi$$
$$572$$ −0.124356 + 0.215390i −0.00519957 + 0.00900592i
$$573$$ 12.4641 0.520695
$$574$$ −5.66025 11.6603i −0.236254 0.486690i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −19.3923 −0.807312 −0.403656 0.914911i $$-0.632261\pi$$
−0.403656 + 0.914911i $$0.632261\pi$$
$$578$$ 33.8564 + 9.07180i 1.40824 + 0.377337i
$$579$$ −16.3923 −0.681241
$$580$$ 0 0
$$581$$ −26.7846 30.9282i −1.11121 1.28312i
$$582$$ −8.49038 + 31.6865i −0.351938 + 1.31345i
$$583$$ −0.535898 −0.0221946
$$584$$ 25.8564 + 25.8564i 1.06995 + 1.06995i
$$585$$ 0 0
$$586$$ 27.7583 + 7.43782i 1.14669 + 0.307254i
$$587$$ 20.5359i 0.847607i −0.905754 0.423804i $$-0.860695\pi$$
0.905754 0.423804i $$-0.139305\pi$$
$$588$$ 19.0526 + 15.0000i 0.785714 + 0.618590i
$$589$$ 36.0000 1.48335
$$590$$ 0 0
$$591$$ 23.0718 0.949047
$$592$$ 32.7846 18.9282i 1.34744 0.777944i
$$593$$ 30.4641 1.25101 0.625505 0.780220i $$-0.284893\pi$$
0.625505 + 0.780220i $$0.284893\pi$$
$$594$$ 1.90192 + 0.509619i 0.0780369 + 0.0209099i
$$595$$ 0 0
$$596$$ −5.32051 3.07180i −0.217937 0.125826i
$$597$$ 6.00000i 0.245564i
$$598$$ 0.928203 + 0.248711i 0.0379571 + 0.0101706i
$$599$$ 10.1244i 0.413670i −0.978376 0.206835i $$-0.933684\pi$$
0.978376 0.206835i $$-0.0663163\pi$$
$$600$$ 0 0
$$601$$ 14.7846i 0.603077i −0.953454 0.301538i $$-0.902500\pi$$
0.953454 0.301538i $$-0.0975001\pi$$
$$602$$ −6.73205 + 3.26795i −0.274378 + 0.133192i
$$603$$ 0 0
$$604$$ 15.1962 26.3205i 0.618323 1.07097i
$$605$$ 0 0
$$606$$ 36.5885 + 9.80385i 1.48630 + 0.398254i
$$607$$ 29.1962i 1.18504i −0.805557 0.592518i $$-0.798134\pi$$
0.805557 0.592518i $$-0.201866\pi$$
$$608$$ −8.78461 32.7846i −0.356263 1.32959i
$$609$$ −23.7846 27.4641i −0.963801 1.11290i
$$610$$ 0 0
$$611$$ 0.803848i 0.0325202i
$$612$$ 0 0
$$613$$ 10.0000i 0.403896i 0.979396 + 0.201948i $$0.0647272\pi$$
−0.979396 + 0.201948i $$0.935273\pi$$
$$614$$ −0.633975 + 2.36603i −0.0255851 + 0.0954850i
$$615$$ 0 0
$$616$$ 0.143594 2.00000i 0.00578555 0.0805823i
$$617$$ 22.9282i 0.923055i −0.887126 0.461527i $$-0.847302\pi$$
0.887126 0.461527i $$-0.152698\pi$$
$$618$$ −16.0981 4.31347i −0.647560 0.173513i
$$619$$ −0.679492 −0.0273111 −0.0136555 0.999907i $$-0.504347\pi$$
−0.0136555 + 0.999907i $$0.504347\pi$$
$$620$$ 0 0
$$621$$ 7.60770i 0.305286i
$$622$$ 10.7321 + 2.87564i 0.430316 + 0.115303i
$$623$$ −4.39230 5.07180i −0.175974 0.203197i
$$624$$ 2.78461 1.60770i 0.111474 0.0643593i
$$625$$ 0 0
$$626$$ −23.9545 6.41858i −0.957414 0.256538i
$$627$$ −2.78461 −0.111207
$$628$$ −13.6077 7.85641i −0.543006 0.313505i
$$629$$ 61.1769i 2.43928i
$$630$$ 0 0
$$631$$ 38.9090i 1.54894i −0.632610 0.774471i $$-0.718016\pi$$
0.632610 0.774471i $$-0.281984\pi$$
$$632$$ −29.3205 + 29.3205i −1.16631 + 1.16631i
$$633$$ 5.53590 0.220032
$$634$$ 1.12436 4.19615i 0.0446539 0.166651i
$$635$$ 0 0
$$636$$ 6.00000 + 3.46410i 0.237915 + 0.137361i
$$637$$ −0.464102 + 3.21539i −0.0183884 + 0.127398i
$$638$$ −0.777568 + 2.90192i −0.0307842 + 0.114888i
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.92820 0.352643 0.176321 0.984333i $$-0.443580\pi$$
0.176321 + 0.984333i $$0.443580\pi$$
$$642$$ 1.51666 5.66025i 0.0598578 0.223392i
$$643$$ 7.05256i 0.278126i −0.990284 0.139063i $$-0.955591\pi$$
0.990284 0.139063i $$-0.0444090\pi$$
$$644$$ −7.60770 + 1.46410i −0.299785 + 0.0576937i
$$645$$ 0 0
$$646$$ −52.9808 14.1962i −2.08450 0.558540i
$$647$$ 10.3923i 0.408564i −0.978912 0.204282i $$-0.934514\pi$$
0.978912 0.204282i $$-0.0654859\pi$$
$$648$$ −18.0000 18.0000i −0.707107 0.707107i
$$649$$ 0.928203i 0.0364352i
$$650$$ 0 0
$$651$$ −18.0000 20.7846i −0.705476 0.814613i
$$652$$ 36.0000 + 20.7846i 1.40987 + 0.813988i
$$653$$ 17.6077i 0.689042i −0.938779 0.344521i $$-0.888041\pi$$
0.938779 0.344521i $$-0.111959\pi$$
$$654$$ 1.31347 4.90192i 0.0513606 0.191680i
$$655$$ 0 0
$$656$$ 12.0000 6.92820i 0.468521 0.270501i
$$657$$ 0 0
$$658$$ 2.83013 + 5.83013i 0.110330 + 0.227282i
$$659$$ 31.1962i 1.21523i −0.794232 0.607615i $$-0.792126\pi$$
0.794232 0.607615i $$-0.207874\pi$$
$$660$$ 0 0
$$661$$ 39.7128i 1.54465i 0.635228 + 0.772325i $$0.280906\pi$$
−0.635228 + 0.772325i $$0.719094\pi$$
$$662$$ −9.66025 + 36.0526i −0.375456 + 1.40122i
$$663$$ 5.19615i 0.201802i
$$664$$ 30.9282 30.9282i 1.20025 1.20025i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 11.6077 0.449452
$$668$$ 5.19615 9.00000i 0.201045 0.348220i
$$669$$ −23.7846 −0.919566
$$670$$ 0 0
$$671$$ 2.53590 0.0978973
$$672$$ −14.5359 + 21.4641i −0.560734 + 0.827996i
$$673$$ 13.1769i 0.507933i 0.967213 + 0.253966i $$0.0817353\pi$$
−0.967213 + 0.253966i $$0.918265\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −22.1436 12.7846i −0.851677 0.491716i
$$677$$ 25.3923 0.975906 0.487953 0.872870i $$-0.337744\pi$$
0.487953 + 0.872870i $$0.337744\pi$$
$$678$$ 12.9282 + 3.46410i 0.496505 + 0.133038i
$$679$$ 26.7846 23.1962i 1.02790 0.890187i
$$680$$ 0 0
$$681$$ −35.7846 −1.37127
$$682$$ −0.588457 + 2.19615i −0.0225332 + 0.0840950i
$$683$$ −7.32051 −0.280111 −0.140056 0.990144i $$-0.544728\pi$$
−0.140056 + 0.990144i $$0.544728\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −7.95448 24.9545i −0.303704 0.952767i
$$687$$ −14.7846 −0.564068
$$688$$ −4.00000 6.92820i −0.152499 0.264135i
$$689$$ 0.928203i 0.0353617i
$$690$$ 0 0
$$691$$ −22.6410 −0.861305 −0.430652 0.902518i $$-0.641717\pi$$
−0.430652 + 0.902518i $$0.641717\pi$$
$$692$$ −24.8038 14.3205i −0.942901 0.544384i
$$693$$ 0 0
$$694$$ 46.7846 + 12.5359i 1.77592 + 0.475856i
$$695$$ 0 0
$$696$$ 27.4641 27.4641i 1.04102 1.04102i
$$697$$ 22.3923i 0.848169i
$$698$$ −1.94744 + 7.26795i −0.0737117 + 0.275096i
$$699$$ −15.7128 −0.594313
$$700$$ 0 0
$$701$$ −37.7846 −1.42711 −0.713553 0.700602i $$-0.752915\pi$$
−0.713553 + 0.700602i $$0.752915\pi$$
$$702$$ 0.882686 3.29423i 0.0333148 0.124333i
$$703$$ 56.7846i 2.14167i
$$704$$ 2.14359 0.0807897
$$705$$ 0 0
$$706$$ −10.0981 2.70577i −0.380046 0.101833i
$$707$$ −26.7846 30.9282i −1.00734 1.16317i
$$708$$ −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
$$712$$ 5.07180 5.07180i 0.190074 0.190074i
$$713$$ 8.78461 0.328986
$$714$$ 18.2942 + 37.6865i 0.684644 + 1.41038i
$$715$$ 0 0
$$716$$ 6.39230 11.0718i 0.238892 0.413772i
$$717$$ 41.5359 1.55119
$$718$$ −9.26795 + 34.5885i −0.345877 + 1.29083i
$$719$$ −38.5359 −1.43715 −0.718573 0.695451i $$-0.755205\pi$$
−0.718573 + 0.695451i $$0.755205\pi$$
$$720$$ 0 0
$$721$$ 11.7846 + 13.6077i 0.438882 + 0.506777i
$$722$$ 23.2224 + 6.22243i 0.864249 + 0.231575i
$$723$$ −28.3923 −1.05592
$$724$$ 0.928203 1.60770i 0.0344964 0.0597495i
$$725$$ 0 0
$$726$$ −6.92820 + 25.8564i −0.257130 + 0.959621i
$$727$$ 13.6077i 0.504681i −0.967638 0.252341i $$-0.918800\pi$$
0.967638 0.252341i $$-0.0812004\pi$$
$$728$$ −3.46410 0.248711i −0.128388 0.00921785i
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ −12.9282 −0.478167
$$732$$ −28.3923 16.3923i −1.04941 0.605877i
$$733$$ 11.5359 0.426088 0.213044 0.977043i $$-0.431662\pi$$
0.213044 + 0.977043i $$0.431662\pi$$
$$734$$ −4.34679 + 16.2224i −0.160443 + 0.598781i
$$735$$ 0 0
$$736$$ −2.14359 8.00000i −0.0790139 0.294884i
$$737$$ 0.928203i 0.0341908i
$$738$$ 0 0
$$739$$ 4.26795i 0.156999i −0.996914 0.0784995i $$-0.974987\pi$$
0.996914 0.0784995i $$-0.0250129\pi$$
$$740$$ 0 0
$$741$$ 4.82309i 0.177180i
$$742$$ −3.26795 6.73205i −0.119970 0.247141i
$$743$$ −30.3923 −1.11499 −0.557493 0.830182i $$-0.688237\pi$$
−0.557493 + 0.830182i $$0.688237\pi$$
$$744$$ 20.7846 20.7846i 0.762001 0.762001i
$$745$$ 0 0
$$746$$ −1.32051 + 4.92820i −0.0483472 + 0.180434i
$$747$$ 0 0
$$748$$ 1.73205 3.00000i 0.0633300 0.109691i
$$749$$ −4.78461 + 4.14359i −0.174826 + 0.151404i
$$750$$ 0 0
$$751$$ 25.5885i 0.933736i 0.884327 + 0.466868i $$0.154618\pi$$
−0.884327 + 0.466868i $$0.845382\pi$$
$$752$$ −6.00000 + 3.46410i −0.218797 + 0.126323i
$$753$$ 44.7846i 1.63204i
$$754$$ 5.02628 + 1.34679i 0.183046 + 0.0490471i
$$755$$ 0 0
$$756$$ 5.19615 + 27.0000i 0.188982 + 0.981981i
$$757$$ 37.8564i 1.37591i 0.725751 + 0.687957i $$0.241492\pi$$
−0.725751 + 0.687957i $$0.758508\pi$$
$$758$$ −2.05256 + 7.66025i −0.0745523 + 0.278233i
$$759$$ −0.679492 −0.0246640
$$760$$ 0 0
$$761$$ 42.2487i 1.53151i −0.643130 0.765757i $$-0.722364\pi$$
0.643130 0.765757i $$-0.277636\pi$$
$$762$$ 9.80385 36.5885i 0.355156 1.32546i
$$763$$ −4.14359 + 3.58846i −0.150008 + 0.129911i
$$764$$ 7.19615 12.4641i 0.260348 0.450935i
$$765$$ 0 0
$$766$$ 10.0526 37.5167i 0.363214 1.35553i
$$767$$ −1.60770 −0.0580505
$$768$$ −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
$$772$$ −9.46410 + 16.3923i −0.340620 + 0.589972i
$$773$$ −5.53590 −0.199112 −0.0995562 0.995032i $$-0.531742\pi$$
−0.0995562 + 0.995032i $$0.531742\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 26.7846 + 26.7846i 0.961511 + 0.961511i
$$777$$ 32.7846 28.3923i 1.17614 1.01857i
$$778$$ 28.4904 + 7.63397i 1.02143 + 0.273691i
$$779$$ 20.7846i 0.744686i
$$780$$ 0 0
$$781$$ −2.00000 −0.0715656
$$782$$ −12.9282 3.46410i −0.462312 0.123876i
$$783$$ 41.1962i 1.47223i
$$784$$ 26.0000 10.3923i 0.928571 0.371154i
$$785$$ 0 0
$$786$$ −1.60770 + 6.00000i −0.0573446 + 0.214013i
$$787$$ 32.6603i 1.16421i