# Properties

 Label 126.2.f.d.43.1 Level $126$ Weight $2$ Character 126.43 Analytic conductor $1.006$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$126 = 2 \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 126.f (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.00611506547$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-11})$$ Defining polynomial: $$x^{4} - x^{3} - 2 x^{2} - 3 x + 9$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 43.1 Root $$1.68614 - 0.396143i$$ of defining polynomial Character $$\chi$$ $$=$$ 126.43 Dual form 126.2.f.d.85.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} -4.37228 q^{10} +(0.686141 - 1.18843i) q^{11} +(1.18614 + 1.26217i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(5.18614 + 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.37228 q^{17} +(0.186141 - 2.99422i) q^{18} +5.00000 q^{19} +(-2.18614 + 3.78651i) q^{20} +(0.500000 - 1.65831i) q^{21} +(-0.686141 - 1.18843i) q^{22} +(0.813859 + 1.40965i) q^{23} +(1.68614 - 0.396143i) q^{24} +(-7.05842 + 12.2255i) q^{25} -2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +1.00000 q^{28} +(4.37228 - 7.57301i) q^{29} +(7.37228 - 1.73205i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.686141 + 2.27567i) q^{33} +(0.686141 - 1.18843i) q^{34} +4.37228 q^{35} +(-2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(2.18614 + 3.78651i) q^{40} +(-2.31386 - 4.00772i) q^{41} +(-1.18614 - 1.26217i) q^{42} +(4.05842 - 7.02939i) q^{43} -1.37228 q^{44} +(-10.9307 - 7.25061i) q^{45} +1.62772 q^{46} +(0.500000 - 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(7.05842 + 12.2255i) q^{50} +(-2.31386 + 0.543620i) q^{51} +(-1.00000 + 1.73205i) q^{52} -8.74456 q^{53} +(0.872281 + 5.12241i) q^{54} -6.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(-8.43070 + 1.98072i) q^{57} +(-4.37228 - 7.57301i) q^{58} +(5.05842 + 8.76144i) q^{59} +(2.18614 - 7.25061i) q^{60} +(-1.55842 + 2.69927i) q^{61} -2.00000 q^{62} +(-0.186141 + 2.99422i) q^{63} +1.00000 q^{64} +(-4.37228 + 7.57301i) q^{65} +(1.62772 + 1.73205i) q^{66} +(1.05842 + 1.83324i) q^{67} +(-0.686141 - 1.18843i) q^{68} +(-1.93070 - 2.05446i) q^{69} +(2.18614 - 3.78651i) q^{70} -7.11684 q^{71} +(-2.68614 + 1.33591i) q^{72} +12.1168 q^{73} +(1.00000 - 1.73205i) q^{74} +(7.05842 - 23.4101i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(0.686141 + 1.18843i) q^{77} +(3.37228 - 0.792287i) q^{78} +(2.55842 - 4.43132i) q^{79} +4.37228 q^{80} +(5.43070 - 7.17687i) q^{81} -4.62772 q^{82} +(-8.74456 + 15.1460i) q^{83} +(-1.68614 + 0.396143i) q^{84} +(-3.00000 - 5.19615i) q^{85} +(-4.05842 - 7.02939i) q^{86} +(-4.37228 + 14.5012i) q^{87} +(-0.686141 + 1.18843i) q^{88} +14.7446 q^{89} +(-11.7446 + 5.84096i) q^{90} +2.00000 q^{91} +(0.813859 - 1.40965i) q^{92} +(2.37228 + 2.52434i) q^{93} +(-10.9307 - 18.9325i) q^{95} +(-1.18614 - 1.26217i) q^{96} +(4.05842 - 7.02939i) q^{97} -1.00000 q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9} + O(q^{10})$$ $$4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9} - 6 q^{10} - 3 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + 15 q^{15} - 2 q^{16} - 6 q^{17} - 5 q^{18} + 20 q^{19} - 3 q^{20} + 2 q^{21} + 3 q^{22} + 9 q^{23} + q^{24} - 11 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} + 6 q^{29} + 18 q^{30} - 4 q^{31} + 2 q^{32} + 3 q^{33} - 3 q^{34} + 6 q^{35} - 10 q^{36} + 8 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} + q^{42} - q^{43} + 6 q^{44} - 15 q^{45} + 18 q^{46} + 2 q^{48} - 2 q^{49} + 11 q^{50} - 15 q^{51} - 4 q^{52} - 12 q^{53} - 8 q^{54} - 24 q^{55} + 2 q^{56} - 5 q^{57} - 6 q^{58} + 3 q^{59} + 3 q^{60} + 11 q^{61} - 8 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 18 q^{66} - 13 q^{67} + 3 q^{68} + 21 q^{69} + 3 q^{70} + 6 q^{71} - 5 q^{72} + 14 q^{73} + 4 q^{74} + 11 q^{75} - 10 q^{76} - 3 q^{77} + 2 q^{78} - 7 q^{79} + 6 q^{80} - 7 q^{81} - 30 q^{82} - 12 q^{83} - q^{84} - 12 q^{85} + q^{86} - 6 q^{87} + 3 q^{88} + 36 q^{89} - 24 q^{90} + 8 q^{91} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} - 4 q^{98} + 24 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$73$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 0.866025i 0.353553 0.612372i
$$3$$ −1.68614 + 0.396143i −0.973494 + 0.228714i
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −2.18614 3.78651i −0.977672 1.69338i −0.670820 0.741620i $$-0.734058\pi$$
−0.306851 0.951757i $$-0.599275\pi$$
$$6$$ −0.500000 + 1.65831i −0.204124 + 0.677003i
$$7$$ −0.500000 + 0.866025i −0.188982 + 0.327327i
$$8$$ −1.00000 −0.353553
$$9$$ 2.68614 1.33591i 0.895380 0.445302i
$$10$$ −4.37228 −1.38264
$$11$$ 0.686141 1.18843i 0.206879 0.358325i −0.743851 0.668346i $$-0.767003\pi$$
0.950730 + 0.310021i $$0.100336\pi$$
$$12$$ 1.18614 + 1.26217i 0.342409 + 0.364357i
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0.500000 + 0.866025i 0.133631 + 0.231455i
$$15$$ 5.18614 + 5.51856i 1.33906 + 1.42489i
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 1.37228 0.332827 0.166414 0.986056i $$-0.446781\pi$$
0.166414 + 0.986056i $$0.446781\pi$$
$$18$$ 0.186141 2.99422i 0.0438738 0.705744i
$$19$$ 5.00000 1.14708 0.573539 0.819178i $$-0.305570\pi$$
0.573539 + 0.819178i $$0.305570\pi$$
$$20$$ −2.18614 + 3.78651i −0.488836 + 0.846689i
$$21$$ 0.500000 1.65831i 0.109109 0.361873i
$$22$$ −0.686141 1.18843i −0.146286 0.253374i
$$23$$ 0.813859 + 1.40965i 0.169701 + 0.293931i 0.938315 0.345782i $$-0.112386\pi$$
−0.768613 + 0.639713i $$0.779053\pi$$
$$24$$ 1.68614 0.396143i 0.344182 0.0808625i
$$25$$ −7.05842 + 12.2255i −1.41168 + 2.44511i
$$26$$ −2.00000 −0.392232
$$27$$ −4.00000 + 3.31662i −0.769800 + 0.638285i
$$28$$ 1.00000 0.188982
$$29$$ 4.37228 7.57301i 0.811912 1.40627i −0.0996117 0.995026i $$-0.531760\pi$$
0.911524 0.411247i $$-0.134907\pi$$
$$30$$ 7.37228 1.73205i 1.34599 0.316228i
$$31$$ −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i $$-0.224149\pi$$
−0.941745 + 0.336327i $$0.890815\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −0.686141 + 2.27567i −0.119442 + 0.396143i
$$34$$ 0.686141 1.18843i 0.117672 0.203814i
$$35$$ 4.37228 0.739050
$$36$$ −2.50000 1.65831i −0.416667 0.276385i
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 2.50000 4.33013i 0.405554 0.702439i
$$39$$ 2.37228 + 2.52434i 0.379869 + 0.404218i
$$40$$ 2.18614 + 3.78651i 0.345659 + 0.598699i
$$41$$ −2.31386 4.00772i −0.361364 0.625901i 0.626821 0.779163i $$-0.284356\pi$$
−0.988186 + 0.153262i $$0.951022\pi$$
$$42$$ −1.18614 1.26217i −0.183025 0.194757i
$$43$$ 4.05842 7.02939i 0.618904 1.07197i −0.370783 0.928720i $$-0.620910\pi$$
0.989686 0.143253i $$-0.0457562\pi$$
$$44$$ −1.37228 −0.206879
$$45$$ −10.9307 7.25061i −1.62945 1.08086i
$$46$$ 1.62772 0.239994
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ 0.500000 1.65831i 0.0721688 0.239357i
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ 7.05842 + 12.2255i 0.998212 + 1.72895i
$$51$$ −2.31386 + 0.543620i −0.324005 + 0.0761221i
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ −8.74456 −1.20116 −0.600579 0.799565i $$-0.705063\pi$$
−0.600579 + 0.799565i $$0.705063\pi$$
$$54$$ 0.872281 + 5.12241i 0.118702 + 0.697072i
$$55$$ −6.00000 −0.809040
$$56$$ 0.500000 0.866025i 0.0668153 0.115728i
$$57$$ −8.43070 + 1.98072i −1.11667 + 0.262352i
$$58$$ −4.37228 7.57301i −0.574109 0.994385i
$$59$$ 5.05842 + 8.76144i 0.658550 + 1.14064i 0.980991 + 0.194053i $$0.0621634\pi$$
−0.322441 + 0.946590i $$0.604503\pi$$
$$60$$ 2.18614 7.25061i 0.282230 0.936050i
$$61$$ −1.55842 + 2.69927i −0.199535 + 0.345606i −0.948378 0.317142i $$-0.897277\pi$$
0.748842 + 0.662748i $$0.230610\pi$$
$$62$$ −2.00000 −0.254000
$$63$$ −0.186141 + 2.99422i −0.0234515 + 0.377236i
$$64$$ 1.00000 0.125000
$$65$$ −4.37228 + 7.57301i −0.542315 + 0.939317i
$$66$$ 1.62772 + 1.73205i 0.200358 + 0.213201i
$$67$$ 1.05842 + 1.83324i 0.129307 + 0.223966i 0.923408 0.383819i $$-0.125391\pi$$
−0.794101 + 0.607785i $$0.792058\pi$$
$$68$$ −0.686141 1.18843i −0.0832068 0.144118i
$$69$$ −1.93070 2.05446i −0.232429 0.247327i
$$70$$ 2.18614 3.78651i 0.261294 0.452574i
$$71$$ −7.11684 −0.844614 −0.422307 0.906453i $$-0.638780\pi$$
−0.422307 + 0.906453i $$0.638780\pi$$
$$72$$ −2.68614 + 1.33591i −0.316565 + 0.157438i
$$73$$ 12.1168 1.41817 0.709085 0.705123i $$-0.249108\pi$$
0.709085 + 0.705123i $$0.249108\pi$$
$$74$$ 1.00000 1.73205i 0.116248 0.201347i
$$75$$ 7.05842 23.4101i 0.815036 2.70317i
$$76$$ −2.50000 4.33013i −0.286770 0.496700i
$$77$$ 0.686141 + 1.18843i 0.0781930 + 0.135434i
$$78$$ 3.37228 0.792287i 0.381836 0.0897088i
$$79$$ 2.55842 4.43132i 0.287845 0.498562i −0.685450 0.728120i $$-0.740395\pi$$
0.973295 + 0.229557i $$0.0737279\pi$$
$$80$$ 4.37228 0.488836
$$81$$ 5.43070 7.17687i 0.603411 0.797430i
$$82$$ −4.62772 −0.511046
$$83$$ −8.74456 + 15.1460i −0.959840 + 1.66249i −0.236960 + 0.971519i $$0.576151\pi$$
−0.722881 + 0.690973i $$0.757182\pi$$
$$84$$ −1.68614 + 0.396143i −0.183973 + 0.0432228i
$$85$$ −3.00000 5.19615i −0.325396 0.563602i
$$86$$ −4.05842 7.02939i −0.437631 0.757999i
$$87$$ −4.37228 + 14.5012i −0.468758 + 1.55469i
$$88$$ −0.686141 + 1.18843i −0.0731428 + 0.126687i
$$89$$ 14.7446 1.56292 0.781460 0.623955i $$-0.214475\pi$$
0.781460 + 0.623955i $$0.214475\pi$$
$$90$$ −11.7446 + 5.84096i −1.23799 + 0.615692i
$$91$$ 2.00000 0.209657
$$92$$ 0.813859 1.40965i 0.0848507 0.146966i
$$93$$ 2.37228 + 2.52434i 0.245994 + 0.261762i
$$94$$ 0 0
$$95$$ −10.9307 18.9325i −1.12147 1.94244i
$$96$$ −1.18614 1.26217i −0.121060 0.128820i
$$97$$ 4.05842 7.02939i 0.412070 0.713727i −0.583046 0.812439i $$-0.698139\pi$$
0.995116 + 0.0987127i $$0.0314725\pi$$
$$98$$ −1.00000 −0.101015
$$99$$ 0.255437 4.10891i 0.0256724 0.412961i
$$100$$ 14.1168 1.41168
$$101$$ −0.813859 + 1.40965i −0.0809820 + 0.140265i −0.903672 0.428225i $$-0.859139\pi$$
0.822690 + 0.568490i $$0.192472\pi$$
$$102$$ −0.686141 + 2.27567i −0.0679380 + 0.225325i
$$103$$ 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i $$-0.00268960\pi$$
−0.507300 + 0.861770i $$0.669356\pi$$
$$104$$ 1.00000 + 1.73205i 0.0980581 + 0.169842i
$$105$$ −7.37228 + 1.73205i −0.719461 + 0.169031i
$$106$$ −4.37228 + 7.57301i −0.424674 + 0.735556i
$$107$$ −7.37228 −0.712705 −0.356353 0.934352i $$-0.615980\pi$$
−0.356353 + 0.934352i $$0.615980\pi$$
$$108$$ 4.87228 + 1.80579i 0.468835 + 0.173762i
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ −3.00000 + 5.19615i −0.286039 + 0.495434i
$$111$$ −3.37228 + 0.792287i −0.320083 + 0.0752006i
$$112$$ −0.500000 0.866025i −0.0472456 0.0818317i
$$113$$ 2.18614 + 3.78651i 0.205655 + 0.356205i 0.950341 0.311210i $$-0.100734\pi$$
−0.744686 + 0.667415i $$0.767401\pi$$
$$114$$ −2.50000 + 8.29156i −0.234146 + 0.776576i
$$115$$ 3.55842 6.16337i 0.331825 0.574737i
$$116$$ −8.74456 −0.811912
$$117$$ −5.00000 3.31662i −0.462250 0.306622i
$$118$$ 10.1168 0.931331
$$119$$ −0.686141 + 1.18843i −0.0628984 + 0.108943i
$$120$$ −5.18614 5.51856i −0.473428 0.503773i
$$121$$ 4.55842 + 7.89542i 0.414402 + 0.717765i
$$122$$ 1.55842 + 2.69927i 0.141093 + 0.244380i
$$123$$ 5.48913 + 5.84096i 0.494938 + 0.526662i
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ 39.8614 3.56531
$$126$$ 2.50000 + 1.65831i 0.222718 + 0.147734i
$$127$$ 3.11684 0.276575 0.138288 0.990392i $$-0.455840\pi$$
0.138288 + 0.990392i $$0.455840\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ −4.05842 + 13.4603i −0.357324 + 1.18511i
$$130$$ 4.37228 + 7.57301i 0.383474 + 0.664197i
$$131$$ 0.813859 + 1.40965i 0.0711072 + 0.123161i 0.899387 0.437154i $$-0.144013\pi$$
−0.828280 + 0.560315i $$0.810680\pi$$
$$132$$ 2.31386 0.543620i 0.201396 0.0473161i
$$133$$ −2.50000 + 4.33013i −0.216777 + 0.375470i
$$134$$ 2.11684 0.182867
$$135$$ 21.3030 + 7.89542i 1.83347 + 0.679529i
$$136$$ −1.37228 −0.117672
$$137$$ −5.31386 + 9.20387i −0.453994 + 0.786340i −0.998630 0.0523324i $$-0.983334\pi$$
0.544636 + 0.838672i $$0.316668\pi$$
$$138$$ −2.74456 + 0.644810i −0.233633 + 0.0548899i
$$139$$ −6.61684 11.4607i −0.561233 0.972085i −0.997389 0.0722136i $$-0.976994\pi$$
0.436156 0.899871i $$-0.356340\pi$$
$$140$$ −2.18614 3.78651i −0.184763 0.320018i
$$141$$ 0 0
$$142$$ −3.55842 + 6.16337i −0.298616 + 0.517218i
$$143$$ −2.74456 −0.229512
$$144$$ −0.186141 + 2.99422i −0.0155117 + 0.249518i
$$145$$ −38.2337 −3.17513
$$146$$ 6.05842 10.4935i 0.501399 0.868448i
$$147$$ 1.18614 + 1.26217i 0.0978312 + 0.104102i
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ −1.62772 2.81929i −0.133348 0.230965i 0.791617 0.611017i $$-0.209239\pi$$
−0.924965 + 0.380052i $$0.875906\pi$$
$$150$$ −16.7446 17.8178i −1.36719 1.45482i
$$151$$ −4.55842 + 7.89542i −0.370959 + 0.642520i −0.989713 0.143065i $$-0.954304\pi$$
0.618754 + 0.785585i $$0.287638\pi$$
$$152$$ −5.00000 −0.405554
$$153$$ 3.68614 1.83324i 0.298007 0.148209i
$$154$$ 1.37228 0.110582
$$155$$ −4.37228 + 7.57301i −0.351190 + 0.608279i
$$156$$ 1.00000 3.31662i 0.0800641 0.265543i
$$157$$ −4.55842 7.89542i −0.363802 0.630123i 0.624781 0.780800i $$-0.285188\pi$$
−0.988583 + 0.150677i $$0.951855\pi$$
$$158$$ −2.55842 4.43132i −0.203537 0.352537i
$$159$$ 14.7446 3.46410i 1.16932 0.274721i
$$160$$ 2.18614 3.78651i 0.172830 0.299350i
$$161$$ −1.62772 −0.128282
$$162$$ −3.50000 8.29156i −0.274986 0.651447i
$$163$$ −18.2337 −1.42817 −0.714086 0.700058i $$-0.753158\pi$$
−0.714086 + 0.700058i $$0.753158\pi$$
$$164$$ −2.31386 + 4.00772i −0.180682 + 0.312951i
$$165$$ 10.1168 2.37686i 0.787595 0.185038i
$$166$$ 8.74456 + 15.1460i 0.678710 + 1.17556i
$$167$$ 2.74456 + 4.75372i 0.212381 + 0.367854i 0.952459 0.304666i $$-0.0985450\pi$$
−0.740078 + 0.672521i $$0.765212\pi$$
$$168$$ −0.500000 + 1.65831i −0.0385758 + 0.127942i
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ −6.00000 −0.460179
$$171$$ 13.4307 6.67954i 1.02707 0.510797i
$$172$$ −8.11684 −0.618904
$$173$$ 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i $$-0.760087\pi$$
0.957241 + 0.289292i $$0.0934200\pi$$
$$174$$ 10.3723 + 11.0371i 0.786321 + 0.836722i
$$175$$ −7.05842 12.2255i −0.533567 0.924164i
$$176$$ 0.686141 + 1.18843i 0.0517198 + 0.0895813i
$$177$$ −12.0000 12.7692i −0.901975 0.959789i
$$178$$ 7.37228 12.7692i 0.552576 0.957089i
$$179$$ 3.25544 0.243323 0.121661 0.992572i $$-0.461178\pi$$
0.121661 + 0.992572i $$0.461178\pi$$
$$180$$ −0.813859 + 13.0916i −0.0606615 + 0.975788i
$$181$$ 0.883156 0.0656445 0.0328222 0.999461i $$-0.489550\pi$$
0.0328222 + 0.999461i $$0.489550\pi$$
$$182$$ 1.00000 1.73205i 0.0741249 0.128388i
$$183$$ 1.55842 5.16870i 0.115202 0.382081i
$$184$$ −0.813859 1.40965i −0.0599985 0.103920i
$$185$$ −4.37228 7.57301i −0.321457 0.556779i
$$186$$ 3.37228 0.792287i 0.247268 0.0580933i
$$187$$ 0.941578 1.63086i 0.0688550 0.119260i
$$188$$ 0 0
$$189$$ −0.872281 5.12241i −0.0634491 0.372601i
$$190$$ −21.8614 −1.58599
$$191$$ 9.55842 16.5557i 0.691623 1.19793i −0.279683 0.960092i $$-0.590229\pi$$
0.971306 0.237834i $$-0.0764374\pi$$
$$192$$ −1.68614 + 0.396143i −0.121687 + 0.0285892i
$$193$$ 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i $$-0.0855996\pi$$
−0.712123 + 0.702055i $$0.752266\pi$$
$$194$$ −4.05842 7.02939i −0.291378 0.504681i
$$195$$ 4.37228 14.5012i 0.313106 1.03845i
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ −6.00000 −0.427482 −0.213741 0.976890i $$-0.568565\pi$$
−0.213741 + 0.976890i $$0.568565\pi$$
$$198$$ −3.43070 2.27567i −0.243809 0.161725i
$$199$$ −10.0000 −0.708881 −0.354441 0.935079i $$-0.615329\pi$$
−0.354441 + 0.935079i $$0.615329\pi$$
$$200$$ 7.05842 12.2255i 0.499106 0.864477i
$$201$$ −2.51087 2.67181i −0.177103 0.188455i
$$202$$ 0.813859 + 1.40965i 0.0572629 + 0.0991823i
$$203$$ 4.37228 + 7.57301i 0.306874 + 0.531521i
$$204$$ 1.62772 + 1.73205i 0.113963 + 0.121268i
$$205$$ −10.1168 + 17.5229i −0.706591 + 1.22385i
$$206$$ 10.0000 0.696733
$$207$$ 4.06930 + 2.69927i 0.282836 + 0.187612i
$$208$$ 2.00000 0.138675
$$209$$ 3.43070 5.94215i 0.237307 0.411027i
$$210$$ −2.18614 + 7.25061i −0.150858 + 0.500340i
$$211$$ 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i $$0.0189888\pi$$
−0.447478 + 0.894295i $$0.647678\pi$$
$$212$$ 4.37228 + 7.57301i 0.300290 + 0.520117i
$$213$$ 12.0000 2.81929i 0.822226 0.193175i
$$214$$ −3.68614 + 6.38458i −0.251979 + 0.436441i
$$215$$ −35.4891 −2.42034
$$216$$ 4.00000 3.31662i 0.272166 0.225668i
$$217$$ 2.00000 0.135769
$$218$$ 7.00000 12.1244i 0.474100 0.821165i
$$219$$ −20.4307 + 4.80001i −1.38058 + 0.324355i
$$220$$ 3.00000 + 5.19615i 0.202260 + 0.350325i
$$221$$ −1.37228 2.37686i −0.0923096 0.159885i
$$222$$ −1.00000 + 3.31662i −0.0671156 + 0.222597i
$$223$$ 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i $$-0.790574\pi$$
0.925188 + 0.379509i $$0.123907\pi$$
$$224$$ −1.00000 −0.0668153
$$225$$ −2.62772 + 42.2689i −0.175181 + 2.81793i
$$226$$ 4.37228 0.290840
$$227$$ 6.12772 10.6135i 0.406711 0.704444i −0.587808 0.809000i $$-0.700009\pi$$
0.994519 + 0.104556i $$0.0333423\pi$$
$$228$$ 5.93070 + 6.31084i 0.392770 + 0.417946i
$$229$$ 1.44158 + 2.49689i 0.0952622 + 0.164999i 0.909718 0.415227i $$-0.136298\pi$$
−0.814456 + 0.580226i $$0.802964\pi$$
$$230$$ −3.55842 6.16337i −0.234635 0.406400i
$$231$$ −1.62772 1.73205i −0.107096 0.113961i
$$232$$ −4.37228 + 7.57301i −0.287054 + 0.497193i
$$233$$ −0.255437 −0.0167343 −0.00836713 0.999965i $$-0.502663\pi$$
−0.00836713 + 0.999965i $$0.502663\pi$$
$$234$$ −5.37228 + 2.67181i −0.351197 + 0.174662i
$$235$$ 0 0
$$236$$ 5.05842 8.76144i 0.329275 0.570321i
$$237$$ −2.55842 + 8.48533i −0.166187 + 0.551181i
$$238$$ 0.686141 + 1.18843i 0.0444759 + 0.0770345i
$$239$$ −4.93070 8.54023i −0.318941 0.552421i 0.661327 0.750098i $$-0.269994\pi$$
−0.980267 + 0.197677i $$0.936660\pi$$
$$240$$ −7.37228 + 1.73205i −0.475879 + 0.111803i
$$241$$ −9.05842 + 15.6896i −0.583504 + 1.01066i 0.411556 + 0.911385i $$0.364986\pi$$
−0.995060 + 0.0992745i $$0.968348\pi$$
$$242$$ 9.11684 0.586053
$$243$$ −6.31386 + 14.2525i −0.405034 + 0.914302i
$$244$$ 3.11684 0.199535
$$245$$ −2.18614 + 3.78651i −0.139667 + 0.241911i
$$246$$ 7.80298 1.83324i 0.497500 0.116883i
$$247$$ −5.00000 8.66025i −0.318142 0.551039i
$$248$$ 1.00000 + 1.73205i 0.0635001 + 0.109985i
$$249$$ 8.74456 29.0024i 0.554164 1.83795i
$$250$$ 19.9307 34.5210i 1.26053 2.18330i
$$251$$ −9.00000 −0.568075 −0.284037 0.958813i $$-0.591674\pi$$
−0.284037 + 0.958813i $$0.591674\pi$$
$$252$$ 2.68614 1.33591i 0.169211 0.0841543i
$$253$$ 2.23369 0.140431
$$254$$ 1.55842 2.69927i 0.0977841 0.169367i
$$255$$ 7.11684 + 7.57301i 0.445674 + 0.474240i
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 3.43070 + 5.94215i 0.214001 + 0.370661i 0.952963 0.303086i $$-0.0980170\pi$$
−0.738962 + 0.673747i $$0.764684\pi$$
$$258$$ 9.62772 + 10.2448i 0.599396 + 0.637815i
$$259$$ −1.00000 + 1.73205i −0.0621370 + 0.107624i
$$260$$ 8.74456 0.542315
$$261$$ 1.62772 26.1831i 0.100753 1.62070i
$$262$$ 1.62772 0.100561
$$263$$ −3.81386 + 6.60580i −0.235173 + 0.407331i −0.959323 0.282311i $$-0.908899\pi$$
0.724150 + 0.689642i $$0.242232\pi$$
$$264$$ 0.686141 2.27567i 0.0422290 0.140058i
$$265$$ 19.1168 + 33.1113i 1.17434 + 2.03401i
$$266$$ 2.50000 + 4.33013i 0.153285 + 0.265497i
$$267$$ −24.8614 + 5.84096i −1.52149 + 0.357461i
$$268$$ 1.05842 1.83324i 0.0646534 0.111983i
$$269$$ −1.62772 −0.0992438 −0.0496219 0.998768i $$-0.515802\pi$$
−0.0496219 + 0.998768i $$0.515802\pi$$
$$270$$ 17.4891 14.5012i 1.06435 0.882516i
$$271$$ 16.2337 0.986126 0.493063 0.869994i $$-0.335877\pi$$
0.493063 + 0.869994i $$0.335877\pi$$
$$272$$ −0.686141 + 1.18843i −0.0416034 + 0.0720592i
$$273$$ −3.37228 + 0.792287i −0.204100 + 0.0479514i
$$274$$ 5.31386 + 9.20387i 0.321022 + 0.556026i
$$275$$ 9.68614 + 16.7769i 0.584096 + 1.01168i
$$276$$ −0.813859 + 2.69927i −0.0489886 + 0.162477i
$$277$$ 6.11684 10.5947i 0.367526 0.636573i −0.621652 0.783293i $$-0.713538\pi$$
0.989178 + 0.146720i $$0.0468717\pi$$
$$278$$ −13.2337 −0.793704
$$279$$ −5.00000 3.31662i −0.299342 0.198561i
$$280$$ −4.37228 −0.261294
$$281$$ −8.18614 + 14.1788i −0.488344 + 0.845837i −0.999910 0.0134071i $$-0.995732\pi$$
0.511566 + 0.859244i $$0.329066\pi$$
$$282$$ 0 0
$$283$$ −13.5584 23.4839i −0.805965 1.39597i −0.915638 0.402004i $$-0.868314\pi$$
0.109673 0.993968i $$-0.465019\pi$$
$$284$$ 3.55842 + 6.16337i 0.211153 + 0.365729i
$$285$$ 25.9307 + 27.5928i 1.53600 + 1.63446i
$$286$$ −1.37228 + 2.37686i −0.0811447 + 0.140547i
$$287$$ 4.62772 0.273166
$$288$$ 2.50000 + 1.65831i 0.147314 + 0.0977170i
$$289$$ −15.1168 −0.889226
$$290$$ −19.1168 + 33.1113i −1.12258 + 1.94437i
$$291$$ −4.05842 + 13.4603i −0.237909 + 0.789055i
$$292$$ −6.05842 10.4935i −0.354542 0.614085i
$$293$$ 5.18614 + 8.98266i 0.302978 + 0.524773i 0.976809 0.214113i $$-0.0686859\pi$$
−0.673831 + 0.738885i $$0.735353\pi$$
$$294$$ 1.68614 0.396143i 0.0983377 0.0231036i
$$295$$ 22.1168 38.3075i 1.28769 2.23035i
$$296$$ −2.00000 −0.116248
$$297$$ 1.19702 + 7.02939i 0.0694579 + 0.407887i
$$298$$ −3.25544 −0.188582
$$299$$ 1.62772 2.81929i 0.0941334 0.163044i
$$300$$ −23.8030 + 5.59230i −1.37427 + 0.322871i
$$301$$ 4.05842 + 7.02939i 0.233924 + 0.405167i
$$302$$ 4.55842 + 7.89542i 0.262308 + 0.454330i
$$303$$ 0.813859 2.69927i 0.0467550 0.155069i
$$304$$ −2.50000 + 4.33013i −0.143385 + 0.248350i
$$305$$ 13.6277 0.780321
$$306$$ 0.255437 4.10891i 0.0146024 0.234891i
$$307$$ −13.0000 −0.741949 −0.370975 0.928643i $$-0.620976\pi$$
−0.370975 + 0.928643i $$0.620976\pi$$
$$308$$ 0.686141 1.18843i 0.0390965 0.0677171i
$$309$$ −11.8614 12.6217i −0.674772 0.718023i
$$310$$ 4.37228 + 7.57301i 0.248329 + 0.430118i
$$311$$ −4.11684 7.13058i −0.233445 0.404338i 0.725375 0.688354i $$-0.241666\pi$$
−0.958820 + 0.284016i $$0.908333\pi$$
$$312$$ −2.37228 2.52434i −0.134304 0.142912i
$$313$$ 10.0584 17.4217i 0.568536 0.984733i −0.428175 0.903696i $$-0.640843\pi$$
0.996711 0.0810370i $$-0.0258232\pi$$
$$314$$ −9.11684 −0.514493
$$315$$ 11.7446 5.84096i 0.661731 0.329101i
$$316$$ −5.11684 −0.287845
$$317$$ 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i $$-0.779442\pi$$
0.937892 + 0.346929i $$0.112775\pi$$
$$318$$ 4.37228 14.5012i 0.245185 0.813188i
$$319$$ −6.00000 10.3923i −0.335936 0.581857i
$$320$$ −2.18614 3.78651i −0.122209 0.211672i
$$321$$ 12.4307 2.92048i 0.693814 0.163005i
$$322$$ −0.813859 + 1.40965i −0.0453546 + 0.0785565i
$$323$$ 6.86141 0.381779
$$324$$ −8.93070 1.11469i −0.496150 0.0619273i
$$325$$ 28.2337 1.56612
$$326$$ −9.11684 + 15.7908i −0.504935 + 0.874574i
$$327$$ −23.6060 + 5.54601i −1.30541 + 0.306695i
$$328$$ 2.31386 + 4.00772i 0.127762 + 0.221289i
$$329$$ 0 0
$$330$$ 3.00000 9.94987i 0.165145 0.547723i
$$331$$ −11.1168 + 19.2549i −0.611037 + 1.05835i 0.380029 + 0.924975i $$0.375914\pi$$
−0.991066 + 0.133373i $$0.957419\pi$$
$$332$$ 17.4891 0.959840
$$333$$ 5.37228 2.67181i 0.294399 0.146415i
$$334$$ 5.48913 0.300352
$$335$$ 4.62772 8.01544i 0.252839 0.437930i
$$336$$ 1.18614 + 1.26217i 0.0647093 + 0.0688570i
$$337$$ 4.05842 + 7.02939i 0.221076 + 0.382915i 0.955135 0.296171i $$-0.0957097\pi$$
−0.734059 + 0.679086i $$0.762376\pi$$
$$338$$ −4.50000 7.79423i −0.244768 0.423950i
$$339$$ −5.18614 5.51856i −0.281672 0.299727i
$$340$$ −3.00000 + 5.19615i −0.162698 + 0.281801i
$$341$$ −2.74456 −0.148626
$$342$$ 0.930703 14.9711i 0.0503267 0.809544i
$$343$$ 1.00000 0.0539949
$$344$$ −4.05842 + 7.02939i −0.218815 + 0.378999i
$$345$$ −3.55842 + 11.8020i −0.191579 + 0.635396i
$$346$$ −3.00000 5.19615i −0.161281 0.279347i
$$347$$ 5.05842 + 8.76144i 0.271550 + 0.470339i 0.969259 0.246043i $$-0.0791303\pi$$
−0.697709 + 0.716382i $$0.745797\pi$$
$$348$$ 14.7446 3.46410i 0.790392 0.185695i
$$349$$ 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i $$-0.632927\pi$$
0.994388 0.105797i $$-0.0337393\pi$$
$$350$$ −14.1168 −0.754577
$$351$$ 9.74456 + 3.61158i 0.520126 + 0.192772i
$$352$$ 1.37228 0.0731428
$$353$$ 6.68614 11.5807i 0.355867 0.616380i −0.631399 0.775458i $$-0.717519\pi$$
0.987266 + 0.159078i $$0.0508522\pi$$
$$354$$ −17.0584 + 4.00772i −0.906645 + 0.213008i
$$355$$ 15.5584 + 26.9480i 0.825755 + 1.43025i
$$356$$ −7.37228 12.7692i −0.390730 0.676764i
$$357$$ 0.686141 2.27567i 0.0363144 0.120441i
$$358$$ 1.62772 2.81929i 0.0860276 0.149004i
$$359$$ 21.8614 1.15380 0.576900 0.816814i $$-0.304262\pi$$
0.576900 + 0.816814i $$0.304262\pi$$
$$360$$ 10.9307 + 7.25061i 0.576099 + 0.382141i
$$361$$ 6.00000 0.315789
$$362$$ 0.441578 0.764836i 0.0232088 0.0401989i
$$363$$ −10.8139 11.5070i −0.567580 0.603961i
$$364$$ −1.00000 1.73205i −0.0524142 0.0907841i
$$365$$ −26.4891 45.8805i −1.38650 2.40150i
$$366$$ −3.69702 3.93398i −0.193246 0.205633i
$$367$$ 6.11684 10.5947i 0.319297 0.553038i −0.661045 0.750346i $$-0.729887\pi$$
0.980341 + 0.197308i $$0.0632200\pi$$
$$368$$ −1.62772 −0.0848507
$$369$$ −11.5693 7.67420i −0.602274 0.399503i
$$370$$ −8.74456 −0.454608
$$371$$ 4.37228 7.57301i 0.226998 0.393171i
$$372$$ 1.00000 3.31662i 0.0518476 0.171959i
$$373$$ 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i $$-0.0833099\pi$$
−0.707055 + 0.707159i $$0.749977\pi$$
$$374$$ −0.941578 1.63086i −0.0486878 0.0843298i
$$375$$ −67.2119 + 15.7908i −3.47081 + 0.815435i
$$376$$ 0 0
$$377$$ −17.4891 −0.900736
$$378$$ −4.87228 1.80579i −0.250603 0.0928798i
$$379$$ −8.11684 −0.416934 −0.208467 0.978029i $$-0.566847\pi$$
−0.208467 + 0.978029i $$0.566847\pi$$
$$380$$ −10.9307 + 18.9325i −0.560733 + 0.971218i
$$381$$ −5.25544 + 1.23472i −0.269244 + 0.0632565i
$$382$$ −9.55842 16.5557i −0.489051 0.847062i
$$383$$ 16.3723 + 28.3576i 0.836584 + 1.44901i 0.892734 + 0.450584i $$0.148784\pi$$
−0.0561493 + 0.998422i $$0.517882\pi$$
$$384$$ −0.500000 + 1.65831i −0.0255155 + 0.0846254i
$$385$$ 3.00000 5.19615i 0.152894 0.264820i
$$386$$ 7.00000 0.356291
$$387$$ 1.51087 24.3036i 0.0768021 1.23542i
$$388$$ −8.11684 −0.412070
$$389$$ −5.48913 + 9.50744i −0.278310 + 0.482047i −0.970965 0.239222i $$-0.923107\pi$$
0.692655 + 0.721269i $$0.256441\pi$$
$$390$$ −10.3723 11.0371i −0.525221 0.558886i
$$391$$ 1.11684 + 1.93443i 0.0564812 + 0.0978284i
$$392$$ 0.500000 + 0.866025i 0.0252538 + 0.0437409i
$$393$$ −1.93070 2.05446i −0.0973911 0.103634i
$$394$$ −3.00000 + 5.19615i −0.151138 + 0.261778i
$$395$$ −22.3723 −1.12567
$$396$$ −3.68614 + 1.83324i −0.185236 + 0.0921238i
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ −5.00000 + 8.66025i −0.250627 + 0.434099i
$$399$$ 2.50000 8.29156i 0.125157 0.415097i
$$400$$ −7.05842 12.2255i −0.352921 0.611277i
$$401$$ 5.87228 + 10.1711i 0.293248 + 0.507920i 0.974576 0.224058i $$-0.0719306\pi$$
−0.681328 + 0.731978i $$0.738597\pi$$
$$402$$ −3.56930 + 0.838574i −0.178020 + 0.0418243i
$$403$$ −2.00000 + 3.46410i −0.0996271 + 0.172559i
$$404$$ 1.62772 0.0809820
$$405$$ −39.0475 4.87375i −1.94029 0.242178i
$$406$$ 8.74456 0.433985
$$407$$ 1.37228 2.37686i 0.0680215 0.117817i
$$408$$ 2.31386 0.543620i 0.114553 0.0269132i
$$409$$ 11.1753 + 19.3561i 0.552581 + 0.957099i 0.998087 + 0.0618200i $$0.0196905\pi$$
−0.445506 + 0.895279i $$0.646976\pi$$
$$410$$ 10.1168 + 17.5229i 0.499635 + 0.865394i
$$411$$ 5.31386 17.6241i 0.262113 0.869332i
$$412$$ 5.00000 8.66025i 0.246332 0.426660i
$$413$$ −10.1168 −0.497817
$$414$$ 4.37228 2.17448i 0.214886 0.106870i
$$415$$ 76.4674 3.75364
$$416$$ 1.00000 1.73205i 0.0490290 0.0849208i
$$417$$ 15.6970 + 16.7031i 0.768686 + 0.817957i
$$418$$ −3.43070 5.94215i −0.167801 0.290640i
$$419$$ 6.30298 + 10.9171i 0.307921 + 0.533335i 0.977907 0.209039i $$-0.0670334\pi$$
−0.669986 + 0.742373i $$0.733700\pi$$
$$420$$ 5.18614 + 5.51856i 0.253058 + 0.269278i
$$421$$ −17.1168 + 29.6472i −0.834224 + 1.44492i 0.0604368 + 0.998172i $$0.480751\pi$$
−0.894661 + 0.446746i $$0.852583\pi$$
$$422$$ 16.0000 0.778868
$$423$$ 0 0
$$424$$ 8.74456 0.424674
$$425$$ −9.68614 + 16.7769i −0.469847 + 0.813799i
$$426$$ 3.55842 11.8020i 0.172406 0.571806i
$$427$$ −1.55842 2.69927i −0.0754173 0.130627i
$$428$$ 3.68614 + 6.38458i 0.178176 + 0.308610i
$$429$$ 4.62772 1.08724i 0.223428 0.0524925i
$$430$$ −17.7446 + 30.7345i −0.855719 + 1.48215i
$$431$$ −6.51087 −0.313618 −0.156809 0.987629i $$-0.550121\pi$$
−0.156809 + 0.987629i $$0.550121\pi$$
$$432$$ −0.872281 5.12241i −0.0419677 0.246452i
$$433$$ −20.1168 −0.966754 −0.483377 0.875412i $$-0.660590\pi$$
−0.483377 + 0.875412i $$0.660590\pi$$
$$434$$ 1.00000 1.73205i 0.0480015 0.0831411i
$$435$$ 64.4674 15.1460i 3.09097 0.726196i
$$436$$ −7.00000 12.1244i −0.335239 0.580651i
$$437$$ 4.06930 + 7.04823i 0.194661 + 0.337162i
$$438$$ −6.05842 + 20.0935i −0.289483 + 0.960105i
$$439$$ −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i $$-0.894477\pi$$
0.754642 + 0.656136i $$0.227810\pi$$
$$440$$ 6.00000 0.286039
$$441$$ −2.50000 1.65831i −0.119048 0.0789673i
$$442$$ −2.74456 −0.130546
$$443$$ 20.0584 34.7422i 0.953004 1.65065i 0.214134 0.976804i $$-0.431307\pi$$
0.738870 0.673848i $$-0.235360\pi$$
$$444$$ 2.37228 + 2.52434i 0.112583 + 0.119800i
$$445$$ −32.2337 55.8304i −1.52802 2.64661i
$$446$$ −2.00000 3.46410i −0.0947027 0.164030i
$$447$$ 3.86141 + 4.10891i 0.182638 + 0.194345i
$$448$$ −0.500000 + 0.866025i −0.0236228 + 0.0409159i
$$449$$ 33.0000 1.55737 0.778683 0.627417i $$-0.215888\pi$$
0.778683 + 0.627417i $$0.215888\pi$$
$$450$$ 35.2921 + 23.4101i 1.66369 + 1.10356i
$$451$$ −6.35053 −0.299035
$$452$$ 2.18614 3.78651i 0.102827 0.178102i
$$453$$ 4.55842 15.1186i 0.214173 0.710333i
$$454$$ −6.12772 10.6135i −0.287588 0.498117i
$$455$$ −4.37228 7.57301i −0.204976 0.355028i
$$456$$ 8.43070 1.98072i 0.394804 0.0927556i
$$457$$ 17.7337 30.7156i 0.829547 1.43682i −0.0688472 0.997627i $$-0.521932\pi$$
0.898394 0.439190i $$-0.144735\pi$$
$$458$$ 2.88316 0.134721
$$459$$ −5.48913 + 4.55134i −0.256210 + 0.212438i
$$460$$ −7.11684 −0.331825
$$461$$ −1.06930 + 1.85208i −0.0498021 + 0.0862598i −0.889852 0.456250i $$-0.849192\pi$$
0.840050 + 0.542509i $$0.182526\pi$$
$$462$$ −2.31386 + 0.543620i −0.107650 + 0.0252915i
$$463$$ 11.5584 + 20.0198i 0.537165 + 0.930398i 0.999055 + 0.0434604i $$0.0138382\pi$$
−0.461890 + 0.886937i $$0.652828\pi$$
$$464$$ 4.37228 + 7.57301i 0.202978 + 0.351568i
$$465$$ 4.37228 14.5012i 0.202760 0.672478i
$$466$$ −0.127719 + 0.221215i −0.00591645 + 0.0102476i
$$467$$ 33.0951 1.53146 0.765729 0.643163i $$-0.222378\pi$$
0.765729 + 0.643163i $$0.222378\pi$$
$$468$$ −0.372281 + 5.98844i −0.0172087 + 0.276816i
$$469$$ −2.11684 −0.0977468
$$470$$ 0 0
$$471$$ 10.8139 + 11.5070i 0.498276 + 0.530214i
$$472$$ −5.05842 8.76144i −0.232833 0.403278i
$$473$$ −5.56930 9.64630i −0.256077 0.443538i
$$474$$ 6.06930 + 6.45832i 0.278772 + 0.296641i
$$475$$ −35.2921 + 61.1277i −1.61931 + 2.80473i
$$476$$ 1.37228 0.0628984
$$477$$ −23.4891 + 11.6819i −1.07549 + 0.534879i
$$478$$ −9.86141 −0.451050
$$479$$ −16.3723 + 28.3576i −0.748069 + 1.29569i 0.200679 + 0.979657i $$0.435685\pi$$
−0.948747 + 0.316036i $$0.897648\pi$$
$$480$$ −2.18614 + 7.25061i −0.0997832 + 0.330943i
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ 9.05842 + 15.6896i 0.412600 + 0.714644i
$$483$$ 2.74456 0.644810i 0.124882 0.0293399i
$$484$$ 4.55842 7.89542i 0.207201 0.358883i
$$485$$ −35.4891 −1.61148
$$486$$ 9.18614 + 12.5942i 0.416692 + 0.571286i
$$487$$ 35.3505 1.60189 0.800943 0.598741i $$-0.204332\pi$$
0.800943 + 0.598741i $$0.204332\pi$$
$$488$$ 1.55842 2.69927i 0.0705464 0.122190i
$$489$$ 30.7446 7.22316i 1.39032 0.326642i
$$490$$ 2.18614 + 3.78651i 0.0987598 + 0.171057i
$$491$$ 12.6861 + 21.9730i 0.572518 + 0.991629i 0.996306 + 0.0858685i $$0.0273665\pi$$
−0.423789 + 0.905761i $$0.639300\pi$$
$$492$$ 2.31386 7.67420i 0.104317 0.345980i
$$493$$ 6.00000 10.3923i 0.270226 0.468046i
$$494$$ −10.0000 −0.449921
$$495$$ −16.1168 + 8.01544i −0.724398 + 0.360267i
$$496$$ 2.00000 0.0898027
$$497$$ 3.55842 6.16337i 0.159617 0.276465i
$$498$$ −20.7446 22.0742i −0.929586 0.989170i
$$499$$ −9.05842 15.6896i −0.405511 0.702365i 0.588870 0.808228i $$-0.299573\pi$$
−0.994381 + 0.105863i $$0.966240\pi$$
$$500$$ −19.9307 34.5210i −0.891328 1.54383i
$$501$$ −6.51087 6.92820i −0.290884 0.309529i
$$502$$ −4.50000 + 7.79423i −0.200845 + 0.347873i
$$503$$ −32.2337 −1.43723 −0.718615 0.695409i $$-0.755223\pi$$
−0.718615 + 0.695409i $$0.755223\pi$$
$$504$$ 0.186141 2.99422i 0.00829136 0.133373i
$$505$$ 7.11684 0.316695
$$506$$ 1.11684 1.93443i 0.0496498 0.0859959i
$$507$$ −4.50000 + 14.9248i −0.199852 + 0.662834i
$$508$$ −1.55842 2.69927i −0.0691438 0.119761i
$$509$$ 14.4891 + 25.0959i 0.642219 + 1.11236i 0.984936 + 0.172918i $$0.0553194\pi$$
−0.342717 + 0.939439i $$0.611347\pi$$
$$510$$ 10.1168 2.37686i 0.447981 0.105249i
$$511$$ −6.05842 + 10.4935i −0.268009 + 0.464205i
$$512$$ −1.00000 −0.0441942
$$513$$ −20.0000 + 16.5831i −0.883022 + 0.732163i
$$514$$ 6.86141 0.302644
$$515$$ 21.8614 37.8651i 0.963329 1.66853i
$$516$$ 13.6861 3.21543i 0.602499 0.141552i
$$517$$ 0 0
$$518$$ 1.00000 + 1.73205i 0.0439375 + 0.0761019i
$$519$$ −3.00000 + 9.94987i −0.131685 + 0.436751i
$$520$$ 4.37228 7.57301i 0.191737 0.332099i
$$521$$ −24.8614 −1.08920 −0.544599 0.838697i $$-0.683318\pi$$
−0.544599 + 0.838697i $$0.683318\pi$$
$$522$$ −21.8614 14.5012i −0.956848 0.634701i
$$523$$ −35.1168 −1.53555 −0.767776 0.640718i $$-0.778637\pi$$
−0.767776 + 0.640718i $$0.778637\pi$$
$$524$$ 0.813859 1.40965i 0.0355536 0.0615807i
$$525$$ 16.7446 + 17.8178i 0.730793 + 0.777634i
$$526$$ 3.81386 + 6.60580i 0.166292 + 0.288026i
$$527$$ −1.37228 2.37686i −0.0597775 0.103538i
$$528$$ −1.62772 1.73205i −0.0708374 0.0753778i
$$529$$ 10.1753 17.6241i 0.442403 0.766264i
$$530$$ 38.2337 1.66077
$$531$$ 25.2921 + 16.7769i 1.09758 + 0.728055i
$$532$$ 5.00000 0.216777
$$533$$ −4.62772 + 8.01544i −0.200449 + 0.347187i
$$534$$ −7.37228 + 24.4511i −0.319030 + 1.05810i
$$535$$ 16.1168 + 27.9152i 0.696792 + 1.20688i
$$536$$ −1.05842 1.83324i −0.0457169 0.0791839i
$$537$$ −5.48913 + 1.28962i −0.236873 + 0.0556512i
$$538$$ −0.813859 + 1.40965i −0.0350880 + 0.0607741i
$$539$$ −1.37228 −0.0591083
$$540$$ −3.81386 22.3966i −0.164122 0.963798i
$$541$$ −6.23369 −0.268007 −0.134004 0.990981i $$-0.542783\pi$$
−0.134004 + 0.990981i $$0.542783\pi$$
$$542$$ 8.11684 14.0588i 0.348648 0.603877i
$$543$$ −1.48913 + 0.349857i −0.0639045 + 0.0150138i
$$544$$ 0.686141 + 1.18843i 0.0294180 + 0.0509535i
$$545$$ −30.6060 53.0111i −1.31102 2.27075i
$$546$$ −1.00000 + 3.31662i −0.0427960 + 0.141938i
$$547$$ −9.05842 + 15.6896i −0.387310 + 0.670841i −0.992087 0.125554i $$-0.959929\pi$$
0.604777 + 0.796395i $$0.293262\pi$$
$$548$$ 10.6277 0.453994
$$549$$ −0.580171 + 9.33252i −0.0247611 + 0.398302i
$$550$$ 19.3723 0.826037
$$551$$ 21.8614 37.8651i 0.931327 1.61311i
$$552$$ 1.93070 + 2.05446i 0.0821762 + 0.0874434i
$$553$$ 2.55842 + 4.43132i 0.108795 + 0.188439i
$$554$$ −6.11684 10.5947i −0.259880 0.450125i
$$555$$ 10.3723 + 11.0371i 0.440279 + 0.468499i
$$556$$ −6.61684 + 11.4607i −0.280617 + 0.486042i
$$557$$ 29.4891 1.24949 0.624747 0.780827i $$-0.285202\pi$$
0.624747 + 0.780827i $$0.285202\pi$$
$$558$$ −5.37228 + 2.67181i −0.227427 + 0.113107i
$$559$$ −16.2337 −0.686612
$$560$$ −2.18614 + 3.78651i −0.0923813 + 0.160009i
$$561$$ −0.941578 + 3.12286i −0.0397535 + 0.131847i
$$562$$ 8.18614 + 14.1788i 0.345312 + 0.598097i
$$563$$ −1.50000 2.59808i −0.0632175 0.109496i 0.832684 0.553748i $$-0.186803\pi$$
−0.895902 + 0.444252i $$0.853470\pi$$
$$564$$ 0 0
$$565$$ 9.55842 16.5557i 0.402126 0.696502i
$$566$$ −27.1168 −1.13981
$$567$$ 3.50000 + 8.29156i 0.146986 + 0.348213i
$$568$$ 7.11684 0.298616
$$569$$ −8.05842 + 13.9576i −0.337827 + 0.585133i −0.984024 0.178038i $$-0.943025\pi$$
0.646197 + 0.763171i $$0.276358\pi$$
$$570$$ 36.8614 8.66025i 1.54395 0.362738i
$$571$$ 11.1753 + 19.3561i 0.467670 + 0.810029i 0.999318 0.0369371i $$-0.0117601\pi$$
−0.531647 + 0.846966i $$0.678427\pi$$
$$572$$ 1.37228 + 2.37686i 0.0573780 + 0.0993815i
$$573$$ −9.55842 + 31.7017i −0.399309 + 1.32436i
$$574$$ 2.31386 4.00772i 0.0965786 0.167279i
$$575$$ −22.9783 −0.958259
$$576$$ 2.68614 1.33591i 0.111923 0.0556628i
$$577$$ 9.88316 0.411441 0.205721 0.978611i $$-0.434046\pi$$
0.205721 + 0.978611i $$0.434046\pi$$
$$578$$ −7.55842 + 13.0916i −0.314389 + 0.544538i
$$579$$ −8.30298 8.83518i −0.345060 0.367178i
$$580$$ 19.1168 + 33.1113i 0.793784 + 1.37487i
$$581$$ −8.74456 15.1460i −0.362786 0.628363i
$$582$$ 9.62772 + 10.2448i 0.399082 + 0.424662i
$$583$$ −6.00000 + 10.3923i −0.248495 + 0.430405i
$$584$$ −12.1168 −0.501399
$$585$$ −1.62772 + 26.1831i −0.0672979 + 1.08254i
$$586$$ 10.3723 0.428475
$$587$$ −7.24456 + 12.5480i −0.299015 + 0.517909i −0.975911 0.218170i $$-0.929991\pi$$
0.676896 + 0.736079i $$0.263325\pi$$
$$588$$ 0.500000 1.65831i 0.0206197 0.0683877i
$$589$$ −5.00000 8.66025i −0.206021 0.356840i
$$590$$ −22.1168 38.3075i −0.910536 1.57709i
$$591$$ 10.1168 2.37686i 0.416151 0.0977710i
$$592$$ −1.00000 + 1.73205i −0.0410997 + 0.0711868i
$$593$$ 14.7446 0.605487 0.302743 0.953072i $$-0.402098\pi$$
0.302743 + 0.953072i $$0.402098\pi$$
$$594$$ 6.68614 + 2.47805i 0.274336 + 0.101676i
$$595$$ 6.00000 0.245976
$$596$$ −1.62772 + 2.81929i −0.0666740 + 0.115483i
$$597$$ 16.8614 3.96143i 0.690091 0.162131i
$$598$$ −1.62772 2.81929i −0.0665624 0.115289i
$$599$$ −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i $$-0.329782\pi$$
−0.999938 + 0.0111569i $$0.996449\pi$$
$$600$$ −7.05842 + 23.4101i −0.288159 + 0.955715i
$$601$$ −12.0584 + 20.8858i −0.491873 + 0.851950i −0.999956 0.00935863i $$-0.997021\pi$$
0.508083 + 0.861308i $$0.330354\pi$$
$$602$$ 8.11684 0.330818
$$603$$ 5.29211 + 3.51039i 0.215511 + 0.142954i
$$604$$ 9.11684 0.370959
$$605$$ 19.9307 34.5210i 0.810298 1.40348i
$$606$$ −1.93070 2.05446i −0.0784295 0.0834566i
$$607$$ −11.1168 19.2549i −0.451219 0.781534i 0.547243 0.836974i $$-0.315677\pi$$
−0.998462 + 0.0554398i $$0.982344\pi$$
$$608$$ 2.50000 + 4.33013i 0.101388 + 0.175610i
$$609$$ −10.3723 11.0371i −0.420306 0.447246i
$$610$$ 6.81386 11.8020i 0.275885 0.477847i
$$611$$ 0 0
$$612$$ −3.43070 2.27567i −0.138678 0.0919886i
$$613$$ −36.2337 −1.46346 −0.731732 0.681592i $$-0.761288\pi$$
−0.731732 + 0.681592i $$0.761288\pi$$
$$614$$ −6.50000 + 11.2583i −0.262319 + 0.454349i
$$615$$ 10.1168 33.5538i 0.407951 1.35302i
$$616$$ −0.686141 1.18843i −0.0276454 0.0478832i
$$617$$ −9.43070 16.3345i −0.379666 0.657600i 0.611348 0.791362i $$-0.290628\pi$$
−0.991014 + 0.133762i $$0.957294\pi$$
$$618$$ −16.8614 + 3.96143i −0.678265 + 0.159352i
$$619$$ −22.7337 + 39.3759i −0.913744 + 1.58265i −0.105014 + 0.994471i $$0.533489\pi$$
−0.808730 + 0.588180i $$0.799844\pi$$
$$620$$ 8.74456 0.351190
$$621$$ −7.93070 2.93932i −0.318248 0.117951i
$$622$$ −8.23369 −0.330141
$$623$$ −7.37228 + 12.7692i −0.295364 + 0.511586i
$$624$$ −3.37228 + 0.792287i −0.134999 + 0.0317169i
$$625$$ −51.8505 89.8078i −2.07402 3.59231i
$$626$$ −10.0584 17.4217i −0.402015 0.696311i
$$627$$ −3.43070 + 11.3784i −0.137009 + 0.454408i
$$628$$ −4.55842 + 7.89542i −0.181901 + 0.315061i
$$629$$ 2.74456 0.109433
$$630$$ 0.813859 13.0916i 0.0324249 0.521581i
$$631$$ −37.3505 −1.48690 −0.743451 0.668791i $$-0.766812\pi$$
−0.743451 + 0.668791i $$0.766812\pi$$
$$632$$ −2.55842 + 4.43132i −0.101769 + 0.176268i
$$633$$ −18.9783 20.1947i −0.754318 0.802667i
$$634$$ −3.00000 5.19615i −0.119145 0.206366i
$$635$$ −6.81386 11.8020i −0.270400 0.468346i
$$636$$ −10.3723 11.0371i −0.411288 0.437650i
$$637$$ −1.00000 + 1.73205i −0.0396214 + 0.0686264i
$$638$$ −12.0000 −0.475085
$$639$$ −19.1168 + 9.50744i −0.756251 + 0.376109i
$$640$$ −4.37228 −0.172830
$$641$$ −17.1060 + 29.6284i −0.675645 + 1.17025i 0.300635 + 0.953739i $$0.402802\pi$$
−0.976280 + 0.216512i $$0.930532\pi$$
$$642$$ 3.68614 12.2255i 0.145480 0.482504i
$$643$$ −13.1753 22.8202i −0.519582 0.899942i −0.999741 0.0227606i $$-0.992754\pi$$
0.480159 0.877181i $$-0.340579\pi$$
$$644$$ 0.813859 + 1.40965i 0.0320706 + 0.0555478i
$$645$$ 59.8397 14.0588i 2.35618 0.553564i
$$646$$ 3.43070 5.94215i 0.134979 0.233791i
$$647$$ 5.48913 0.215800 0.107900 0.994162i $$-0.465587\pi$$
0.107900 + 0.994162i $$0.465587\pi$$
$$648$$ −5.43070 + 7.17687i −0.213338 + 0.281934i
$$649$$ 13.8832 0.544962
$$650$$ 14.1168 24.4511i 0.553708 0.959051i
$$651$$ −3.37228 + 0.792287i −0.132170 + 0.0310522i
$$652$$ 9.11684 + 15.7908i 0.357043 + 0.618417i
$$653$$ 13.3723 + 23.1615i 0.523298 + 0.906378i 0.999632 + 0.0271143i $$0.00863179\pi$$
−0.476335 + 0.879264i $$0.658035\pi$$
$$654$$ −7.00000 + 23.2164i −0.273722 + 0.907832i
$$655$$ 3.55842 6.16337i 0.139039 0.240823i
$$656$$ 4.62772 0.180682
$$657$$ 32.5475 16.1870i 1.26980 0.631514i
$$658$$ 0 0
$$659$$ 10.3723 17.9653i 0.404047 0.699829i −0.590163 0.807284i $$-0.700937\pi$$
0.994210 + 0.107454i $$0.0342700\pi$$
$$660$$ −7.11684 7.57301i −0.277023 0.294779i
$$661$$ −13.5584 23.4839i −0.527361 0.913417i −0.999491 0.0318879i $$-0.989848\pi$$
0.472130 0.881529i $$-0.343485\pi$$
$$662$$ 11.1168 + 19.2549i 0.432068 + 0.748364i
$$663$$ 3.25544 + 3.46410i 0.126431 + 0.134535i
$$664$$ 8.74456 15.1460i 0.339355 0.587780i
$$665$$ 21.8614 0.847749
$$666$$ 0.372281 5.98844i 0.0144256 0.232047i
$$667$$ 14.2337 0.551131
$$668$$ 2.74456 4.75372i 0.106190 0.183927i
$$669$$ −2.00000 + 6.63325i −0.0773245 + 0.256456i
$$670$$ −4.62772 8.01544i −0.178784 0.309664i
$$671$$ 2.13859 + 3.70415i 0.0825595 + 0.142997i
$$672$$ 1.68614 0.396143i 0.0650443 0.0152816i
$$673$$ 1.44158 2.49689i 0.0555687 0.0962479i −0.836903 0.547351i $$-0.815636\pi$$
0.892472 + 0.451103i $$0.148969\pi$$
$$674$$ 8.11684 0.312649
$$675$$ −12.3139 72.3123i −0.473961 2.78330i
$$676$$ −9.00000 −0.346154
$$677$$ −17.2337 + 29.8496i −0.662344 + 1.14721i 0.317654 + 0.948207i $$0.397105\pi$$
−0.979998 + 0.199007i $$0.936228\pi$$
$$678$$ −7.37228 + 1.73205i −0.283131 + 0.0665190i
$$679$$ 4.05842 + 7.02939i 0.155748 + 0.269763i
$$680$$ 3.00000 + 5.19615i 0.115045 + 0.199263i
$$681$$ −6.12772 + 20.3233i −0.234815 + 0.778792i
$$682$$ −1.37228 + 2.37686i −0.0525474 + 0.0910147i
$$683$$ 29.8397 1.14178 0.570891 0.821026i $$-0.306598\pi$$
0.570891 + 0.821026i $$0.306598\pi$$
$$684$$ −12.5000 8.29156i −0.477949 0.317036i
$$685$$ 46.4674 1.77543
$$686$$ 0.500000 0.866025i 0.0190901 0.0330650i
$$687$$ −3.41983 3.63903i −0.130475 0.138838i
$$688$$ 4.05842 + 7.02939i 0.154726 + 0.267993i
$$689$$ 8.74456 + 15.1460i 0.333141 + 0.577018i
$$690$$ 8.44158 + 8.98266i 0.321365 + 0.341964i
$$691$$ 11.5584 20.0198i 0.439703 0.761588i −0.557963 0.829866i $$-0.688417\pi$$
0.997666 + 0.0682775i $$0.0217503\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 3.43070 + 2.27567i 0.130322 + 0.0864456i
$$694$$ 10.1168 0.384030
$$695$$ −28.9307 + 50.1094i −1.09740 + 1.90076i
$$696$$ 4.37228 14.5012i 0.165731 0.549667i
$$697$$ −3.17527 5.49972i −0.120272 0.208317i
$$698$$ −11.0000 19.0526i −0.416356 0.721150i
$$699$$ 0.430703 0.101190i 0.0162907 0.00382735i
$$700$$ −7.05842 + 12.2255i −0.266783 + 0.462082i
$$701$$ −38.2337 −1.44407 −0.722033 0.691858i $$-0.756792\pi$$
−0.722033 + 0.691858i $$0.756792\pi$$
$$702$$ 8.00000 6.63325i 0.301941 0.250356i
$$703$$ 10.0000 0.377157
$$704$$ 0.686141 1.18843i 0.0258599 0.0447907i
$$705$$ 0 0
$$706$$ −6.68614 11.5807i −0.251636 0.435847i
$$707$$ −0.813859 1.40965i −0.0306083 0.0530152i
$$708$$ −5.05842 + 16.7769i −0.190107 + 0.630514i
$$709$$ −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i $$0.476184\pi$$
−0.900978 + 0.433865i $$0.857149\pi$$
$$710$$ 31.1168 1.16779
$$711$$ 0.952453 15.3210i 0.0357198 0.574581i
$$712$$ −14.7446 −0.552576
$$713$$ 1.62772 2.81929i 0.0609585 0.105583i
$$714$$ −1.62772 1.73205i −0.0609158 0.0648204i
$$715$$ 6.00000 + 10.3923i 0.224387 + 0.388650i
$$716$$ −1.62772 2.81929i −0.0608307 0.105362i
$$717$$ 11.6970 + 12.4468i 0.436833 + 0.464833i
$$718$$ 10.9307 18.9325i 0.407930 0.706556i
$$719$$ 2.74456 0.102355 0.0511775 0.998690i $$-0.483703\pi$$
0.0511775 + 0.998690i $$0.483703\pi$$
$$720$$ 11.7446 5.84096i 0.437694 0.217680i
$$721$$ −10.0000 −0.372419
$$722$$ 3.00000 5.19615i 0.111648 0.193381i
$$723$$ 9.05842 30.0434i 0.336886 1.11733i
$$724$$ −0.441578 0.764836i −0.0164111 0.0284249i
$$725$$ 61.7228 + 106.907i 2.29233 + 3.97043i
$$726$$ −15.3723 + 3.61158i −0.570519 + 0.134038i
$$727$$ 18.1168 31.3793i 0.671917 1.16379i −0.305443 0.952210i $$-0.598805\pi$$
0.977360 0.211583i $$-0.0678620\pi$$
$$728$$ −2.00000 −0.0741249
$$729$$ 5.00000 26.5330i 0.185185 0.982704i
$$730$$ −52.9783 −1.96081
$$731$$ 5.56930 9.64630i 0.205988 0.356781i
$$732$$ −5.25544 + 1.23472i −0.194247 + 0.0456365i
$$733$$ 20.5584 + 35.6082i 0.759343 + 1.31522i 0.943186 + 0.332265i $$0.107813\pi$$
−0.183844 + 0.982956i $$0.558854\pi$$
$$734$$ −6.11684 10.5947i −0.225777 0.391057i
$$735$$ 2.18614 7.25061i 0.0806370 0.267443i
$$736$$ −0.813859 + 1.40965i −0.0299993 + 0.0519602i
$$737$$ 2.90491 0.107004
$$738$$ −12.4307 + 6.18220i −0.457581 + 0.227570i
$$739$$ −8.11684 −0.298583 −0.149291 0.988793i $$-0.547699\pi$$
−0.149291 + 0.988793i $$0.547699\pi$$
$$740$$ −4.37228 + 7.57301i −0.160728 + 0.278390i
$$741$$ 11.8614 + 12.6217i 0.435740 + 0.463669i
$$742$$ −4.37228 7.57301i −0.160511 0.278014i
$$743$$ 6.86141 + 11.8843i 0.251721 + 0.435993i 0.964000 0.265904i $$-0.0856703\pi$$
−0.712279 + 0.701896i $$0.752337\pi$$
$$744$$ −2.37228 2.52434i −0.0869721 0.0925467i
$$745$$ −7.11684 + 12.3267i −0.260741 + 0.451617i
$$746$$ 10.0000 0.366126
$$747$$ −3.25544 + 52.3663i −0.119110 + 1.91598i
$$748$$ −1.88316 −0.0688550
$$749$$ 3.68614 6.38458i 0.134689 0.233288i
$$750$$ −19.9307 + 66.1027i −0.727766 + 2.41373i
$$751$$ 8.55842 + 14.8236i 0.312301 + 0.540922i 0.978860 0.204531i $$-0.0655668\pi$$
−0.666559 + 0.745452i $$0.732234\pi$$
$$752$$ 0 0
$$753$$ 15.1753 3.56529i 0.553017 0.129926i
$$754$$ −8.74456 + 15.1460i −0.318458 + 0.551586i
$$755$$ 39.8614 1.45071
$$756$$ −4.00000 + 3.31662i −0.145479 + 0.120624i
$$757$$ 46.2337 1.68039 0.840196 0.542283i $$-0.182440\pi$$
0.840196 + 0.542283i $$0.182440\pi$$
$$758$$ −4.05842 + 7.02939i −0.147409 + 0.255319i
$$759$$ −3.76631 + 0.884861i −0.136708 + 0.0321184i
$$760$$ 10.9307 + 18.9325i 0.396498 + 0.686755i
$$761$$ −17.7446 30.7345i −0.643240 1.11412i −0.984705 0.174230i $$-0.944256\pi$$
0.341465 0.939894i $$-0.389077\pi$$
$$762$$ −1.55842 + 5.16870i −0.0564557 + 0.187242i
$$763$$ −7.00000 + 12.1244i −0.253417 + 0.438931i
$$764$$ −19.1168 −0.691623
$$765$$ −15.0000 9.94987i −0.542326 0.359738i
$$766$$ 32.7446 1.18311
$$767$$ 10.1168 17.5229i 0.365298 0.632715i
$$768$$ 1.18614 + 1.26217i 0.0428012 + 0.0455446i
$$769$$ 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i $$-0.108958\pi$$
−0.761680 + 0.647954i $$0.775625\pi$$
$$770$$ −3.00000 5.19615i −0.108112 0.187256i
$$771$$ −8.13859 8.66025i −0.293104 0.311891i
$$772$$ 3.50000 6.06218i 0.125968 0.218183i
$$773$$ −39.8614 −1.43372 −0.716858 0.697220i $$-0.754420\pi$$
−0.716858 + 0.697220i $$0.754420\pi$$
$$774$$ −20.2921 13.4603i −0.729385 0.483819i