# Properties

 Label 370.2.q.a.103.1 Level $370$ Weight $2$ Character 370.103 Analytic conductor $2.954$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.q (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 103.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.103 Dual form 370.2.q.a.97.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +(2.00000 + 1.00000i) q^{10} +2.00000i q^{11} +(-0.500000 - 0.133975i) q^{12} +(2.23205 - 3.86603i) q^{13} +(-2.00000 + 2.00000i) q^{14} +(-0.866025 - 0.767949i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.63397 - 2.09808i) q^{17} +(-2.36603 - 1.36603i) q^{18} +(3.36603 - 0.901924i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(1.26795 - 0.732051i) q^{21} +(1.73205 - 1.00000i) q^{22} +6.00000 q^{23} +(0.133975 + 0.500000i) q^{24} +(1.96410 - 4.59808i) q^{25} -4.46410 q^{26} +(2.09808 + 2.09808i) q^{27} +(2.73205 + 0.732051i) q^{28} +(-1.26795 + 1.26795i) q^{29} +(-0.232051 + 1.13397i) q^{30} +(-1.83013 - 1.83013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 0.267949i) q^{33} +(-3.63397 - 2.09808i) q^{34} +(4.73205 + 4.19615i) q^{35} +2.73205i q^{36} +(-5.50000 + 2.59808i) q^{37} +(-2.46410 - 2.46410i) q^{38} +(2.23205 + 0.598076i) q^{39} +(-1.86603 + 1.23205i) q^{40} +(-0.401924 - 0.232051i) q^{41} +(-1.26795 - 0.732051i) q^{42} -11.0000 q^{43} +(-1.73205 - 1.00000i) q^{44} +(-2.73205 + 5.46410i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(4.19615 - 4.19615i) q^{47} +(0.366025 - 0.366025i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-4.96410 + 0.598076i) q^{50} +(1.53590 + 1.53590i) q^{51} +(2.23205 + 3.86603i) q^{52} +(3.13397 - 11.6962i) q^{53} +(0.767949 - 2.86603i) q^{54} +(-2.46410 - 3.73205i) q^{55} +(-0.732051 - 2.73205i) q^{56} +(0.901924 + 1.56218i) q^{57} +(1.73205 + 0.464102i) q^{58} +(-2.09808 + 7.83013i) q^{59} +(1.09808 - 0.366025i) q^{60} +(-6.46410 + 1.73205i) q^{61} +(-0.669873 + 2.50000i) q^{62} +(-5.46410 - 5.46410i) q^{63} +1.00000 q^{64} +(0.598076 + 9.96410i) q^{65} +(0.732051 + 0.732051i) q^{66} +(13.5622 - 3.63397i) q^{67} +4.19615i q^{68} +(0.803848 + 3.00000i) q^{69} +(1.26795 - 6.19615i) q^{70} +(-5.46410 + 9.46410i) q^{71} +(2.36603 - 1.36603i) q^{72} +(5.00000 + 3.46410i) q^{74} +(2.56218 + 0.366025i) q^{75} +(-0.901924 + 3.36603i) q^{76} +(5.46410 - 1.46410i) q^{77} +(-0.598076 - 2.23205i) q^{78} +(-6.83013 + 1.83013i) q^{79} +(2.00000 + 1.00000i) q^{80} +(3.33013 - 5.76795i) q^{81} +0.464102i q^{82} +(-3.43782 + 12.8301i) q^{83} +1.46410i q^{84} +(-4.19615 + 8.39230i) q^{85} +(5.50000 + 9.52628i) q^{86} +(-0.803848 - 0.464102i) q^{87} +2.00000i q^{88} +(12.5622 + 3.36603i) q^{89} +(6.09808 - 0.366025i) q^{90} +(-12.1962 - 3.26795i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(0.669873 - 1.16025i) q^{93} +(-5.73205 - 1.53590i) q^{94} +(-5.16987 + 5.83013i) q^{95} +(-0.500000 - 0.133975i) q^{96} -5.46410i q^{97} +(0.866025 + 0.500000i) q^{98} +(2.73205 + 4.73205i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9 $$4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9} + 8 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} - 2 q^{16} + 18 q^{17} - 6 q^{18} + 10 q^{19} - 4 q^{20} + 12 q^{21} + 24 q^{23} + 4 q^{24} - 6 q^{25} - 4 q^{26} - 2 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 10 q^{31} - 2 q^{32} - 4 q^{33} - 18 q^{34} + 12 q^{35} - 22 q^{37} + 4 q^{38} + 2 q^{39} - 4 q^{40} - 12 q^{41} - 12 q^{42} - 44 q^{43} - 4 q^{45} - 12 q^{46} - 4 q^{47} - 2 q^{48} - 6 q^{50} + 20 q^{51} + 2 q^{52} + 16 q^{53} + 10 q^{54} + 4 q^{55} + 4 q^{56} + 14 q^{57} + 2 q^{59} - 6 q^{60} - 12 q^{61} - 20 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{66} + 30 q^{67} + 24 q^{69} + 12 q^{70} - 8 q^{71} + 6 q^{72} + 20 q^{74} - 14 q^{75} - 14 q^{76} + 8 q^{77} + 8 q^{78} - 10 q^{79} + 8 q^{80} - 4 q^{81} - 38 q^{83} + 4 q^{85} + 22 q^{86} - 24 q^{87} + 26 q^{89} + 14 q^{90} - 28 q^{91} - 12 q^{92} + 20 q^{93} - 16 q^{94} - 38 q^{95} - 2 q^{96} + 4 q^{99}+O(q^{100})$$ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9 + 8 * q^10 - 2 * q^12 + 2 * q^13 - 8 * q^14 - 2 * q^16 + 18 * q^17 - 6 * q^18 + 10 * q^19 - 4 * q^20 + 12 * q^21 + 24 * q^23 + 4 * q^24 - 6 * q^25 - 4 * q^26 - 2 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 10 * q^31 - 2 * q^32 - 4 * q^33 - 18 * q^34 + 12 * q^35 - 22 * q^37 + 4 * q^38 + 2 * q^39 - 4 * q^40 - 12 * q^41 - 12 * q^42 - 44 * q^43 - 4 * q^45 - 12 * q^46 - 4 * q^47 - 2 * q^48 - 6 * q^50 + 20 * q^51 + 2 * q^52 + 16 * q^53 + 10 * q^54 + 4 * q^55 + 4 * q^56 + 14 * q^57 + 2 * q^59 - 6 * q^60 - 12 * q^61 - 20 * q^62 - 8 * q^63 + 4 * q^64 - 8 * q^65 - 4 * q^66 + 30 * q^67 + 24 * q^69 + 12 * q^70 - 8 * q^71 + 6 * q^72 + 20 * q^74 - 14 * q^75 - 14 * q^76 + 8 * q^77 + 8 * q^78 - 10 * q^79 + 8 * q^80 - 4 * q^81 - 38 * q^83 + 4 * q^85 + 22 * q^86 - 24 * q^87 + 26 * q^89 + 14 * q^90 - 28 * q^91 - 12 * q^92 + 20 * q^93 - 16 * q^94 - 38 * q^95 - 2 * q^96 + 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$3$$ 0.133975 + 0.500000i 0.0773503 + 0.288675i 0.993756 0.111576i $$-0.0355897\pi$$
−0.916406 + 0.400251i $$0.868923\pi$$
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −1.86603 + 1.23205i −0.834512 + 0.550990i
$$6$$ 0.366025 0.366025i 0.149429 0.149429i
$$7$$ −0.732051 2.73205i −0.276689 1.03262i −0.954701 0.297567i $$-0.903825\pi$$
0.678012 0.735051i $$-0.262842\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 2.36603 1.36603i 0.788675 0.455342i
$$10$$ 2.00000 + 1.00000i 0.632456 + 0.316228i
$$11$$ 2.00000i 0.603023i 0.953463 + 0.301511i $$0.0974911\pi$$
−0.953463 + 0.301511i $$0.902509\pi$$
$$12$$ −0.500000 0.133975i −0.144338 0.0386751i
$$13$$ 2.23205 3.86603i 0.619060 1.07224i −0.370598 0.928793i $$-0.620847\pi$$
0.989658 0.143449i $$-0.0458194\pi$$
$$14$$ −2.00000 + 2.00000i −0.534522 + 0.534522i
$$15$$ −0.866025 0.767949i −0.223607 0.198284i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 3.63397 2.09808i 0.881368 0.508858i 0.0102590 0.999947i $$-0.496734\pi$$
0.871109 + 0.491089i $$0.163401\pi$$
$$18$$ −2.36603 1.36603i −0.557678 0.321975i
$$19$$ 3.36603 0.901924i 0.772219 0.206916i 0.148868 0.988857i $$-0.452437\pi$$
0.623352 + 0.781942i $$0.285771\pi$$
$$20$$ −0.133975 2.23205i −0.0299576 0.499102i
$$21$$ 1.26795 0.732051i 0.276689 0.159747i
$$22$$ 1.73205 1.00000i 0.369274 0.213201i
$$23$$ 6.00000 1.25109 0.625543 0.780189i $$-0.284877\pi$$
0.625543 + 0.780189i $$0.284877\pi$$
$$24$$ 0.133975 + 0.500000i 0.0273474 + 0.102062i
$$25$$ 1.96410 4.59808i 0.392820 0.919615i
$$26$$ −4.46410 −0.875482
$$27$$ 2.09808 + 2.09808i 0.403775 + 0.403775i
$$28$$ 2.73205 + 0.732051i 0.516309 + 0.138345i
$$29$$ −1.26795 + 1.26795i −0.235452 + 0.235452i −0.814964 0.579512i $$-0.803243\pi$$
0.579512 + 0.814964i $$0.303243\pi$$
$$30$$ −0.232051 + 1.13397i −0.0423665 + 0.207034i
$$31$$ −1.83013 1.83013i −0.328701 0.328701i 0.523392 0.852092i $$-0.324666\pi$$
−0.852092 + 0.523392i $$0.824666\pi$$
$$32$$ −0.500000 + 0.866025i −0.0883883 + 0.153093i
$$33$$ −1.00000 + 0.267949i −0.174078 + 0.0466440i
$$34$$ −3.63397 2.09808i −0.623222 0.359817i
$$35$$ 4.73205 + 4.19615i 0.799863 + 0.709279i
$$36$$ 2.73205i 0.455342i
$$37$$ −5.50000 + 2.59808i −0.904194 + 0.427121i
$$38$$ −2.46410 2.46410i −0.399730 0.399730i
$$39$$ 2.23205 + 0.598076i 0.357414 + 0.0957688i
$$40$$ −1.86603 + 1.23205i −0.295045 + 0.194804i
$$41$$ −0.401924 0.232051i −0.0627700 0.0362402i 0.468287 0.883577i $$-0.344871\pi$$
−0.531057 + 0.847336i $$0.678205\pi$$
$$42$$ −1.26795 0.732051i −0.195649 0.112958i
$$43$$ −11.0000 −1.67748 −0.838742 0.544529i $$-0.816708\pi$$
−0.838742 + 0.544529i $$0.816708\pi$$
$$44$$ −1.73205 1.00000i −0.261116 0.150756i
$$45$$ −2.73205 + 5.46410i −0.407270 + 0.814540i
$$46$$ −3.00000 5.19615i −0.442326 0.766131i
$$47$$ 4.19615 4.19615i 0.612072 0.612072i −0.331414 0.943486i $$-0.607526\pi$$
0.943486 + 0.331414i $$0.107526\pi$$
$$48$$ 0.366025 0.366025i 0.0528312 0.0528312i
$$49$$ −0.866025 + 0.500000i −0.123718 + 0.0714286i
$$50$$ −4.96410 + 0.598076i −0.702030 + 0.0845807i
$$51$$ 1.53590 + 1.53590i 0.215069 + 0.215069i
$$52$$ 2.23205 + 3.86603i 0.309530 + 0.536121i
$$53$$ 3.13397 11.6962i 0.430485 1.60659i −0.321162 0.947024i $$-0.604073\pi$$
0.751647 0.659566i $$-0.229260\pi$$
$$54$$ 0.767949 2.86603i 0.104505 0.390017i
$$55$$ −2.46410 3.73205i −0.332259 0.503230i
$$56$$ −0.732051 2.73205i −0.0978244 0.365086i
$$57$$ 0.901924 + 1.56218i 0.119463 + 0.206916i
$$58$$ 1.73205 + 0.464102i 0.227429 + 0.0609395i
$$59$$ −2.09808 + 7.83013i −0.273146 + 1.01940i 0.683927 + 0.729550i $$0.260271\pi$$
−0.957073 + 0.289845i $$0.906396\pi$$
$$60$$ 1.09808 0.366025i 0.141761 0.0472537i
$$61$$ −6.46410 + 1.73205i −0.827643 + 0.221766i −0.647685 0.761908i $$-0.724263\pi$$
−0.179958 + 0.983674i $$0.557596\pi$$
$$62$$ −0.669873 + 2.50000i −0.0850740 + 0.317500i
$$63$$ −5.46410 5.46410i −0.688412 0.688412i
$$64$$ 1.00000 0.125000
$$65$$ 0.598076 + 9.96410i 0.0741822 + 1.23589i
$$66$$ 0.732051 + 0.732051i 0.0901092 + 0.0901092i
$$67$$ 13.5622 3.63397i 1.65688 0.443961i 0.695355 0.718666i $$-0.255247\pi$$
0.961528 + 0.274705i $$0.0885803\pi$$
$$68$$ 4.19615i 0.508858i
$$69$$ 0.803848 + 3.00000i 0.0967719 + 0.361158i
$$70$$ 1.26795 6.19615i 0.151549 0.740582i
$$71$$ −5.46410 + 9.46410i −0.648470 + 1.12318i 0.335019 + 0.942211i $$0.391257\pi$$
−0.983488 + 0.180971i $$0.942076\pi$$
$$72$$ 2.36603 1.36603i 0.278839 0.160988i
$$73$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$74$$ 5.00000 + 3.46410i 0.581238 + 0.402694i
$$75$$ 2.56218 + 0.366025i 0.295855 + 0.0422650i
$$76$$ −0.901924 + 3.36603i −0.103458 + 0.386110i
$$77$$ 5.46410 1.46410i 0.622692 0.166850i
$$78$$ −0.598076 2.23205i −0.0677188 0.252730i
$$79$$ −6.83013 + 1.83013i −0.768449 + 0.205905i −0.621686 0.783266i $$-0.713552\pi$$
−0.146763 + 0.989172i $$0.546885\pi$$
$$80$$ 2.00000 + 1.00000i 0.223607 + 0.111803i
$$81$$ 3.33013 5.76795i 0.370014 0.640883i
$$82$$ 0.464102i 0.0512514i
$$83$$ −3.43782 + 12.8301i −0.377350 + 1.40829i 0.472531 + 0.881314i $$0.343341\pi$$
−0.849881 + 0.526975i $$0.823326\pi$$
$$84$$ 1.46410i 0.159747i
$$85$$ −4.19615 + 8.39230i −0.455137 + 0.910273i
$$86$$ 5.50000 + 9.52628i 0.593080 + 1.02725i
$$87$$ −0.803848 0.464102i −0.0861815 0.0497569i
$$88$$ 2.00000i 0.213201i
$$89$$ 12.5622 + 3.36603i 1.33159 + 0.356798i 0.853307 0.521409i $$-0.174593\pi$$
0.478281 + 0.878207i $$0.341260\pi$$
$$90$$ 6.09808 0.366025i 0.642794 0.0385825i
$$91$$ −12.1962 3.26795i −1.27850 0.342574i
$$92$$ −3.00000 + 5.19615i −0.312772 + 0.541736i
$$93$$ 0.669873 1.16025i 0.0694626 0.120313i
$$94$$ −5.73205 1.53590i −0.591216 0.158416i
$$95$$ −5.16987 + 5.83013i −0.530418 + 0.598158i
$$96$$ −0.500000 0.133975i −0.0510310 0.0136737i
$$97$$ 5.46410i 0.554795i −0.960755 0.277398i $$-0.910528\pi$$
0.960755 0.277398i $$-0.0894720\pi$$
$$98$$ 0.866025 + 0.500000i 0.0874818 + 0.0505076i
$$99$$ 2.73205 + 4.73205i 0.274581 + 0.475589i
$$100$$ 3.00000 + 4.00000i 0.300000 + 0.400000i
$$101$$ 10.1962i 1.01456i −0.861783 0.507278i $$-0.830652\pi$$
0.861783 0.507278i $$-0.169348\pi$$
$$102$$ 0.562178 2.09808i 0.0556639 0.207741i
$$103$$ 4.19615i 0.413459i 0.978398 + 0.206730i $$0.0662820\pi$$
−0.978398 + 0.206730i $$0.933718\pi$$
$$104$$ 2.23205 3.86603i 0.218871 0.379095i
$$105$$ −1.46410 + 2.92820i −0.142882 + 0.285763i
$$106$$ −11.6962 + 3.13397i −1.13603 + 0.304399i
$$107$$ 0.428203 + 1.59808i 0.0413960 + 0.154492i 0.983530 0.180744i $$-0.0578506\pi$$
−0.942134 + 0.335236i $$0.891184\pi$$
$$108$$ −2.86603 + 0.767949i −0.275783 + 0.0738959i
$$109$$ −1.00000 + 3.73205i −0.0957826 + 0.357466i −0.997137 0.0756168i $$-0.975907\pi$$
0.901354 + 0.433082i $$0.142574\pi$$
$$110$$ −2.00000 + 4.00000i −0.190693 + 0.381385i
$$111$$ −2.03590 2.40192i −0.193239 0.227981i
$$112$$ −2.00000 + 2.00000i −0.188982 + 0.188982i
$$113$$ 5.19615 3.00000i 0.488813 0.282216i −0.235269 0.971930i $$-0.575597\pi$$
0.724082 + 0.689714i $$0.242264\pi$$
$$114$$ 0.901924 1.56218i 0.0844729 0.146311i
$$115$$ −11.1962 + 7.39230i −1.04405 + 0.689336i
$$116$$ −0.464102 1.73205i −0.0430908 0.160817i
$$117$$ 12.1962i 1.12753i
$$118$$ 7.83013 2.09808i 0.720822 0.193144i
$$119$$ −8.39230 8.39230i −0.769321 0.769321i
$$120$$ −0.866025 0.767949i −0.0790569 0.0701038i
$$121$$ 7.00000 0.636364
$$122$$ 4.73205 + 4.73205i 0.428420 + 0.428420i
$$123$$ 0.0621778 0.232051i 0.00560639 0.0209233i
$$124$$ 2.50000 0.669873i 0.224507 0.0601564i
$$125$$ 2.00000 + 11.0000i 0.178885 + 0.983870i
$$126$$ −2.00000 + 7.46410i −0.178174 + 0.664955i
$$127$$ 0.633975 + 0.169873i 0.0562561 + 0.0150738i 0.286837 0.957979i $$-0.407396\pi$$
−0.230581 + 0.973053i $$0.574063\pi$$
$$128$$ −0.500000 0.866025i −0.0441942 0.0765466i
$$129$$ −1.47372 5.50000i −0.129754 0.484248i
$$130$$ 8.33013 5.50000i 0.730600 0.482382i
$$131$$ −2.73205 + 10.1962i −0.238700 + 0.890842i 0.737745 + 0.675079i $$0.235890\pi$$
−0.976446 + 0.215763i $$0.930776\pi$$
$$132$$ 0.267949 1.00000i 0.0233220 0.0870388i
$$133$$ −4.92820 8.53590i −0.427329 0.740156i
$$134$$ −9.92820 9.92820i −0.857666 0.857666i
$$135$$ −6.50000 1.33013i −0.559431 0.114479i
$$136$$ 3.63397 2.09808i 0.311611 0.179909i
$$137$$ 2.00000 2.00000i 0.170872 0.170872i −0.616491 0.787362i $$-0.711446\pi$$
0.787362 + 0.616491i $$0.211446\pi$$
$$138$$ 2.19615 2.19615i 0.186949 0.186949i
$$139$$ 1.46410 + 2.53590i 0.124183 + 0.215092i 0.921413 0.388584i $$-0.127036\pi$$
−0.797230 + 0.603676i $$0.793702\pi$$
$$140$$ −6.00000 + 2.00000i −0.507093 + 0.169031i
$$141$$ 2.66025 + 1.53590i 0.224034 + 0.129346i
$$142$$ 10.9282 0.917074
$$143$$ 7.73205 + 4.46410i 0.646587 + 0.373307i
$$144$$ −2.36603 1.36603i −0.197169 0.113835i
$$145$$ 0.803848 3.92820i 0.0667559 0.326220i
$$146$$ 0 0
$$147$$ −0.366025 0.366025i −0.0301893 0.0301893i
$$148$$ 0.500000 6.06218i 0.0410997 0.498308i
$$149$$ 19.2679i 1.57849i 0.614077 + 0.789246i $$0.289528\pi$$
−0.614077 + 0.789246i $$0.710472\pi$$
$$150$$ −0.964102 2.40192i −0.0787186 0.196116i
$$151$$ −6.23205 3.59808i −0.507157 0.292807i 0.224507 0.974472i $$-0.427923\pi$$
−0.731664 + 0.681665i $$0.761256\pi$$
$$152$$ 3.36603 0.901924i 0.273021 0.0731557i
$$153$$ 5.73205 9.92820i 0.463409 0.802648i
$$154$$ −4.00000 4.00000i −0.322329 0.322329i
$$155$$ 5.66987 + 1.16025i 0.455415 + 0.0931938i
$$156$$ −1.63397 + 1.63397i −0.130823 + 0.130823i
$$157$$ 17.2583 + 4.62436i 1.37736 + 0.369064i 0.870163 0.492764i $$-0.164013\pi$$
0.507202 + 0.861827i $$0.330680\pi$$
$$158$$ 5.00000 + 5.00000i 0.397779 + 0.397779i
$$159$$ 6.26795 0.497081
$$160$$ −0.133975 2.23205i −0.0105916 0.176459i
$$161$$ −4.39230 16.3923i −0.346162 1.29189i
$$162$$ −6.66025 −0.523279
$$163$$ −9.06218 + 5.23205i −0.709805 + 0.409806i −0.810989 0.585062i $$-0.801070\pi$$
0.101184 + 0.994868i $$0.467737\pi$$
$$164$$ 0.401924 0.232051i 0.0313850 0.0181201i
$$165$$ 1.53590 1.73205i 0.119570 0.134840i
$$166$$ 12.8301 3.43782i 0.995811 0.266827i
$$167$$ −14.9545 8.63397i −1.15721 0.668117i −0.206578 0.978430i $$-0.566233\pi$$
−0.950634 + 0.310313i $$0.899566\pi$$
$$168$$ 1.26795 0.732051i 0.0978244 0.0564789i
$$169$$ −3.46410 6.00000i −0.266469 0.461538i
$$170$$ 9.36603 0.562178i 0.718341 0.0431171i
$$171$$ 6.73205 6.73205i 0.514813 0.514813i
$$172$$ 5.50000 9.52628i 0.419371 0.726372i
$$173$$ −9.29423 2.49038i −0.706627 0.189340i −0.112430 0.993660i $$-0.535863\pi$$
−0.594197 + 0.804319i $$0.702530\pi$$
$$174$$ 0.928203i 0.0703669i
$$175$$ −14.0000 2.00000i −1.05830 0.151186i
$$176$$ 1.73205 1.00000i 0.130558 0.0753778i
$$177$$ −4.19615 −0.315402
$$178$$ −3.36603 12.5622i −0.252294 0.941575i
$$179$$ −10.3923 + 10.3923i −0.776757 + 0.776757i −0.979278 0.202521i $$-0.935087\pi$$
0.202521 + 0.979278i $$0.435087\pi$$
$$180$$ −3.36603 5.09808i −0.250889 0.379988i
$$181$$ 12.0981 20.9545i 0.899243 1.55753i 0.0707790 0.997492i $$-0.477451\pi$$
0.828464 0.560042i $$-0.189215\pi$$
$$182$$ 3.26795 + 12.1962i 0.242237 + 0.904039i
$$183$$ −1.73205 3.00000i −0.128037 0.221766i
$$184$$ 6.00000 0.442326
$$185$$ 7.06218 11.6244i 0.519222 0.854640i
$$186$$ −1.33975 −0.0982349
$$187$$ 4.19615 + 7.26795i 0.306853 + 0.531485i
$$188$$ 1.53590 + 5.73205i 0.112017 + 0.418053i
$$189$$ 4.19615 7.26795i 0.305225 0.528666i
$$190$$ 7.63397 + 1.56218i 0.553827 + 0.113332i
$$191$$ 6.83013 6.83013i 0.494211 0.494211i −0.415419 0.909630i $$-0.636365\pi$$
0.909630 + 0.415419i $$0.136365\pi$$
$$192$$ 0.133975 + 0.500000i 0.00966878 + 0.0360844i
$$193$$ −17.6603 −1.27121 −0.635606 0.772013i $$-0.719250\pi$$
−0.635606 + 0.772013i $$0.719250\pi$$
$$194$$ −4.73205 + 2.73205i −0.339741 + 0.196150i
$$195$$ −4.90192 + 1.63397i −0.351034 + 0.117011i
$$196$$ 1.00000i 0.0714286i
$$197$$ −22.8923 6.13397i −1.63101 0.437028i −0.676800 0.736167i $$-0.736634\pi$$
−0.954209 + 0.299140i $$0.903300\pi$$
$$198$$ 2.73205 4.73205i 0.194158 0.336292i
$$199$$ 7.75833 7.75833i 0.549973 0.549973i −0.376460 0.926433i $$-0.622859\pi$$
0.926433 + 0.376460i $$0.122859\pi$$
$$200$$ 1.96410 4.59808i 0.138883 0.325133i
$$201$$ 3.63397 + 6.29423i 0.256321 + 0.443961i
$$202$$ −8.83013 + 5.09808i −0.621286 + 0.358699i
$$203$$ 4.39230 + 2.53590i 0.308279 + 0.177985i
$$204$$ −2.09808 + 0.562178i −0.146895 + 0.0393603i
$$205$$ 1.03590 0.0621778i 0.0723503 0.00434269i
$$206$$ 3.63397 2.09808i 0.253191 0.146180i
$$207$$ 14.1962 8.19615i 0.986701 0.569672i
$$208$$ −4.46410 −0.309530
$$209$$ 1.80385 + 6.73205i 0.124775 + 0.465666i
$$210$$ 3.26795 0.196152i 0.225510 0.0135358i
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 8.56218 + 8.56218i 0.588053 + 0.588053i
$$213$$ −5.46410 1.46410i −0.374394 0.100319i
$$214$$ 1.16987 1.16987i 0.0799709 0.0799709i
$$215$$ 20.5263 13.5526i 1.39988 0.924277i
$$216$$ 2.09808 + 2.09808i 0.142756 + 0.142756i
$$217$$ −3.66025 + 6.33975i −0.248474 + 0.430370i
$$218$$ 3.73205 1.00000i 0.252766 0.0677285i
$$219$$ 0 0
$$220$$ 4.46410 0.267949i 0.300970 0.0180651i
$$221$$ 18.7321i 1.26005i
$$222$$ −1.06218 + 2.96410i −0.0712887 + 0.198937i
$$223$$ 0.928203 + 0.928203i 0.0621571 + 0.0621571i 0.737502 0.675345i $$-0.236005\pi$$
−0.675345 + 0.737502i $$0.736005\pi$$
$$224$$ 2.73205 + 0.732051i 0.182543 + 0.0489122i
$$225$$ −1.63397 13.5622i −0.108932 0.904145i
$$226$$ −5.19615 3.00000i −0.345643 0.199557i
$$227$$ −12.6962 7.33013i −0.842673 0.486518i 0.0154988 0.999880i $$-0.495066\pi$$
−0.858172 + 0.513362i $$0.828400\pi$$
$$228$$ −1.80385 −0.119463
$$229$$ 0.294229 + 0.169873i 0.0194432 + 0.0112255i 0.509690 0.860358i $$-0.329760\pi$$
−0.490247 + 0.871584i $$0.663093\pi$$
$$230$$ 12.0000 + 6.00000i 0.791257 + 0.395628i
$$231$$ 1.46410 + 2.53590i 0.0963308 + 0.166850i
$$232$$ −1.26795 + 1.26795i −0.0832449 + 0.0832449i
$$233$$ −11.8564 + 11.8564i −0.776739 + 0.776739i −0.979275 0.202536i $$-0.935082\pi$$
0.202536 + 0.979275i $$0.435082\pi$$
$$234$$ −10.5622 + 6.09808i −0.690471 + 0.398644i
$$235$$ −2.66025 + 13.0000i −0.173536 + 0.848026i
$$236$$ −5.73205 5.73205i −0.373125 0.373125i
$$237$$ −1.83013 3.16987i −0.118880 0.205905i
$$238$$ −3.07180 + 11.4641i −0.199115 + 0.743107i
$$239$$ −6.16987 + 23.0263i −0.399096 + 1.48945i 0.415594 + 0.909550i $$0.363574\pi$$
−0.814690 + 0.579896i $$0.803093\pi$$
$$240$$ −0.232051 + 1.13397i −0.0149788 + 0.0731977i
$$241$$ −1.02628 3.83013i −0.0661085 0.246720i 0.924962 0.380060i $$-0.124097\pi$$
−0.991070 + 0.133340i $$0.957430\pi$$
$$242$$ −3.50000 6.06218i −0.224989 0.389692i
$$243$$ 11.9282 + 3.19615i 0.765195 + 0.205033i
$$244$$ 1.73205 6.46410i 0.110883 0.413822i
$$245$$ 1.00000 2.00000i 0.0638877 0.127775i
$$246$$ −0.232051 + 0.0621778i −0.0147950 + 0.00396431i
$$247$$ 4.02628 15.0263i 0.256186 0.956099i
$$248$$ −1.83013 1.83013i −0.116213 0.116213i
$$249$$ −6.87564 −0.435726
$$250$$ 8.52628 7.23205i 0.539249 0.457395i
$$251$$ 2.26795 + 2.26795i 0.143152 + 0.143152i 0.775051 0.631899i $$-0.217724\pi$$
−0.631899 + 0.775051i $$0.717724\pi$$
$$252$$ 7.46410 2.00000i 0.470194 0.125988i
$$253$$ 12.0000i 0.754434i
$$254$$ −0.169873 0.633975i −0.0106588 0.0397791i
$$255$$ −4.75833 0.973721i −0.297978 0.0609767i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −15.2942 + 8.83013i −0.954028 + 0.550808i −0.894330 0.447408i $$-0.852347\pi$$
−0.0596980 + 0.998216i $$0.519014\pi$$
$$258$$ −4.02628 + 4.02628i −0.250665 + 0.250665i
$$259$$ 11.1244 + 13.1244i 0.691234 + 0.815508i
$$260$$ −8.92820 4.46410i −0.553704 0.276852i
$$261$$ −1.26795 + 4.73205i −0.0784841 + 0.292907i
$$262$$ 10.1962 2.73205i 0.629920 0.168787i
$$263$$ 5.09808 + 19.0263i 0.314361 + 1.17321i 0.924583 + 0.380980i $$0.124413\pi$$
−0.610222 + 0.792230i $$0.708920\pi$$
$$264$$ −1.00000 + 0.267949i −0.0615457 + 0.0164911i
$$265$$ 8.56218 + 25.6865i 0.525970 + 1.57791i
$$266$$ −4.92820 + 8.53590i −0.302168 + 0.523370i
$$267$$ 6.73205i 0.411995i
$$268$$ −3.63397 + 13.5622i −0.221980 + 0.828442i
$$269$$ 24.5885i 1.49918i −0.661900 0.749592i $$-0.730250\pi$$
0.661900 0.749592i $$-0.269750\pi$$
$$270$$ 2.09808 + 6.29423i 0.127685 + 0.383055i
$$271$$ 1.76795 + 3.06218i 0.107395 + 0.186014i 0.914714 0.404101i $$-0.132416\pi$$
−0.807319 + 0.590115i $$0.799082\pi$$
$$272$$ −3.63397 2.09808i −0.220342 0.127215i
$$273$$ 6.53590i 0.395571i
$$274$$ −2.73205 0.732051i −0.165049 0.0442248i
$$275$$ 9.19615 + 3.92820i 0.554549 + 0.236880i
$$276$$ −3.00000 0.803848i −0.180579 0.0483859i
$$277$$ −0.330127 + 0.571797i −0.0198354 + 0.0343559i −0.875773 0.482724i $$-0.839648\pi$$
0.855937 + 0.517080i $$0.172981\pi$$
$$278$$ 1.46410 2.53590i 0.0878110 0.152093i
$$279$$ −6.83013 1.83013i −0.408909 0.109567i
$$280$$ 4.73205 + 4.19615i 0.282794 + 0.250768i
$$281$$ 23.6244 + 6.33013i 1.40931 + 0.377624i 0.881679 0.471849i $$-0.156413\pi$$
0.527632 + 0.849473i $$0.323080\pi$$
$$282$$ 3.07180i 0.182923i
$$283$$ −11.2583 6.50000i −0.669238 0.386385i 0.126550 0.991960i $$-0.459610\pi$$
−0.795788 + 0.605575i $$0.792943\pi$$
$$284$$ −5.46410 9.46410i −0.324235 0.561591i
$$285$$ −3.60770 1.80385i −0.213701 0.106851i
$$286$$ 8.92820i 0.527936i
$$287$$ −0.339746 + 1.26795i −0.0200546 + 0.0748447i
$$288$$ 2.73205i 0.160988i
$$289$$ 0.303848 0.526279i 0.0178734 0.0309576i
$$290$$ −3.80385 + 1.26795i −0.223370 + 0.0744565i
$$291$$ 2.73205 0.732051i 0.160156 0.0429136i
$$292$$ 0 0
$$293$$ 18.1603 4.86603i 1.06093 0.284276i 0.314170 0.949367i $$-0.398274\pi$$
0.746763 + 0.665090i $$0.231607\pi$$
$$294$$ −0.133975 + 0.500000i −0.00781356 + 0.0291606i
$$295$$ −5.73205 17.1962i −0.333733 1.00120i
$$296$$ −5.50000 + 2.59808i −0.319681 + 0.151010i
$$297$$ −4.19615 + 4.19615i −0.243485 + 0.243485i
$$298$$ 16.6865 9.63397i 0.966625 0.558081i
$$299$$ 13.3923 23.1962i 0.774497 1.34147i
$$300$$ −1.59808 + 2.03590i −0.0922650 + 0.117543i
$$301$$ 8.05256 + 30.0526i 0.464142 + 1.73220i
$$302$$ 7.19615i 0.414092i
$$303$$ 5.09808 1.36603i 0.292877 0.0784761i
$$304$$ −2.46410 2.46410i −0.141326 0.141326i
$$305$$ 9.92820 11.1962i 0.568487 0.641090i
$$306$$ −11.4641 −0.655359
$$307$$ 24.4186 + 24.4186i 1.39364 + 1.39364i 0.816989 + 0.576653i $$0.195642\pi$$
0.576653 + 0.816989i $$0.304358\pi$$
$$308$$ −1.46410 + 5.46410i −0.0834249 + 0.311346i
$$309$$ −2.09808 + 0.562178i −0.119355 + 0.0319812i
$$310$$ −1.83013 5.49038i −0.103944 0.311833i
$$311$$ −7.25833 + 27.0885i −0.411582 + 1.53605i 0.380002 + 0.924986i $$0.375923\pi$$
−0.791584 + 0.611060i $$0.790743\pi$$
$$312$$ 2.23205 + 0.598076i 0.126365 + 0.0338594i
$$313$$ 5.26795 + 9.12436i 0.297762 + 0.515739i 0.975624 0.219451i $$-0.0704265\pi$$
−0.677862 + 0.735190i $$0.737093\pi$$
$$314$$ −4.62436 17.2583i −0.260967 0.973944i
$$315$$ 16.9282 + 3.46410i 0.953796 + 0.195180i
$$316$$ 1.83013 6.83013i 0.102953 0.384225i
$$317$$ −7.82051 + 29.1865i −0.439243 + 1.63928i 0.291459 + 0.956583i $$0.405859\pi$$
−0.730703 + 0.682696i $$0.760807\pi$$
$$318$$ −3.13397 5.42820i −0.175745 0.304399i
$$319$$ −2.53590 2.53590i −0.141983 0.141983i
$$320$$ −1.86603 + 1.23205i −0.104314 + 0.0688737i
$$321$$ −0.741670 + 0.428203i −0.0413960 + 0.0239000i
$$322$$ −12.0000 + 12.0000i −0.668734 + 0.668734i
$$323$$ 10.3397 10.3397i 0.575319 0.575319i
$$324$$ 3.33013 + 5.76795i 0.185007 + 0.320442i
$$325$$ −13.3923 17.8564i −0.742871 0.990495i
$$326$$ 9.06218 + 5.23205i 0.501908 + 0.289776i
$$327$$ −2.00000 −0.110600
$$328$$ −0.401924 0.232051i −0.0221925 0.0128129i
$$329$$ −14.5359 8.39230i −0.801390 0.462683i
$$330$$ −2.26795 0.464102i −0.124846 0.0255480i
$$331$$ −7.83013 2.09808i −0.430383 0.115321i 0.0371231 0.999311i $$-0.488181\pi$$
−0.467506 + 0.883990i $$0.654847\pi$$
$$332$$ −9.39230 9.39230i −0.515470 0.515470i
$$333$$ −9.46410 + 13.6603i −0.518630 + 0.748577i
$$334$$ 17.2679i 0.944860i
$$335$$ −20.8301 + 23.4904i −1.13807 + 1.28342i
$$336$$ −1.26795 0.732051i −0.0691723 0.0399366i
$$337$$ −17.0263 + 4.56218i −0.927481 + 0.248518i −0.690780 0.723065i $$-0.742733\pi$$
−0.236701 + 0.971583i $$0.576066\pi$$
$$338$$ −3.46410 + 6.00000i −0.188422 + 0.326357i
$$339$$ 2.19615 + 2.19615i 0.119279 + 0.119279i
$$340$$ −5.16987 7.83013i −0.280376 0.424648i
$$341$$ 3.66025 3.66025i 0.198214 0.198214i
$$342$$ −9.19615 2.46410i −0.497271 0.133243i
$$343$$ −12.0000 12.0000i −0.647939 0.647939i
$$344$$ −11.0000 −0.593080
$$345$$ −5.19615 4.60770i −0.279751 0.248070i
$$346$$ 2.49038 + 9.29423i 0.133884 + 0.499661i
$$347$$ −7.85641 −0.421754 −0.210877 0.977513i $$-0.567632\pi$$
−0.210877 + 0.977513i $$0.567632\pi$$
$$348$$ 0.803848 0.464102i 0.0430908 0.0248785i
$$349$$ 25.9019 14.9545i 1.38650 0.800495i 0.393579 0.919291i $$-0.371237\pi$$
0.992919 + 0.118796i $$0.0379033\pi$$
$$350$$ 5.26795 + 13.1244i 0.281584 + 0.701526i
$$351$$ 12.7942 3.42820i 0.682905 0.182984i
$$352$$ −1.73205 1.00000i −0.0923186 0.0533002i
$$353$$ −7.60770 + 4.39230i −0.404917 + 0.233779i −0.688603 0.725138i $$-0.741776\pi$$
0.283687 + 0.958917i $$0.408442\pi$$
$$354$$ 2.09808 + 3.63397i 0.111511 + 0.193144i
$$355$$ −1.46410 24.3923i −0.0777064 1.29461i
$$356$$ −9.19615 + 9.19615i −0.487395 + 0.487395i
$$357$$ 3.07180 5.32051i 0.162577 0.281591i
$$358$$ 14.1962 + 3.80385i 0.750290 + 0.201040i
$$359$$ 17.3923i 0.917931i 0.888454 + 0.458965i $$0.151780\pi$$
−0.888454 + 0.458965i $$0.848220\pi$$
$$360$$ −2.73205 + 5.46410i −0.143992 + 0.287983i
$$361$$ −5.93782 + 3.42820i −0.312517 + 0.180432i
$$362$$ −24.1962 −1.27172
$$363$$ 0.937822 + 3.50000i 0.0492229 + 0.183702i
$$364$$ 8.92820 8.92820i 0.467965 0.467965i
$$365$$ 0 0
$$366$$ −1.73205 + 3.00000i −0.0905357 + 0.156813i
$$367$$ −6.78461 25.3205i −0.354154 1.32172i −0.881546 0.472098i $$-0.843497\pi$$
0.527392 0.849622i $$-0.323170\pi$$
$$368$$ −3.00000 5.19615i −0.156386 0.270868i
$$369$$ −1.26795 −0.0660068
$$370$$ −13.5981 0.303848i −0.706930 0.0157963i
$$371$$ −34.2487 −1.77810
$$372$$ 0.669873 + 1.16025i 0.0347313 + 0.0601564i
$$373$$ 6.86603 + 25.6244i 0.355509 + 1.32678i 0.879842 + 0.475266i $$0.157648\pi$$
−0.524333 + 0.851513i $$0.675685\pi$$
$$374$$ 4.19615 7.26795i 0.216978 0.375817i
$$375$$ −5.23205 + 2.47372i −0.270182 + 0.127742i
$$376$$ 4.19615 4.19615i 0.216400 0.216400i
$$377$$ 2.07180 + 7.73205i 0.106703 + 0.398221i
$$378$$ −8.39230 −0.431654
$$379$$ 18.5885 10.7321i 0.954825 0.551268i 0.0602485 0.998183i $$-0.480811\pi$$
0.894576 + 0.446915i $$0.147477\pi$$
$$380$$ −2.46410 7.39230i −0.126406 0.379217i
$$381$$ 0.339746i 0.0174057i
$$382$$ −9.33013 2.50000i −0.477371 0.127911i
$$383$$ 4.26795 7.39230i 0.218082 0.377729i −0.736140 0.676830i $$-0.763353\pi$$
0.954222 + 0.299101i $$0.0966866\pi$$
$$384$$ 0.366025 0.366025i 0.0186787 0.0186787i
$$385$$ −8.39230 + 9.46410i −0.427711 + 0.482335i
$$386$$ 8.83013 + 15.2942i 0.449442 + 0.778456i
$$387$$ −26.0263 + 15.0263i −1.32299 + 0.763829i
$$388$$ 4.73205 + 2.73205i 0.240233 + 0.138699i
$$389$$ −6.09808 + 1.63397i −0.309185 + 0.0828458i −0.410075 0.912052i $$-0.634498\pi$$
0.100890 + 0.994898i $$0.467831\pi$$
$$390$$ 3.86603 + 3.42820i 0.195764 + 0.173594i
$$391$$ 21.8038 12.5885i 1.10267 0.636626i
$$392$$ −0.866025 + 0.500000i −0.0437409 + 0.0252538i
$$393$$ −5.46410 −0.275627
$$394$$ 6.13397 + 22.8923i 0.309025 + 1.15330i
$$395$$ 10.4904 11.8301i 0.527828 0.595238i
$$396$$ −5.46410 −0.274581
$$397$$ 24.7583 + 24.7583i 1.24258 + 1.24258i 0.958925 + 0.283660i $$0.0915487\pi$$
0.283660 + 0.958925i $$0.408451\pi$$
$$398$$ −10.5981 2.83975i −0.531234 0.142344i
$$399$$ 3.60770 3.60770i 0.180611 0.180611i
$$400$$ −4.96410 + 0.598076i −0.248205 + 0.0299038i
$$401$$ 8.12436 + 8.12436i 0.405711 + 0.405711i 0.880240 0.474529i $$-0.157382\pi$$
−0.474529 + 0.880240i $$0.657382\pi$$
$$402$$ 3.63397 6.29423i 0.181246 0.313928i
$$403$$ −11.1603 + 2.99038i −0.555932 + 0.148961i
$$404$$ 8.83013 + 5.09808i 0.439315 + 0.253639i
$$405$$ 0.892305 + 14.8660i 0.0443390 + 0.738699i
$$406$$ 5.07180i 0.251709i
$$407$$ −5.19615 11.0000i −0.257564 0.545250i
$$408$$ 1.53590 + 1.53590i 0.0760383 + 0.0760383i
$$409$$ 27.8923 + 7.47372i 1.37919 + 0.369552i 0.870825 0.491593i $$-0.163585\pi$$
0.508360 + 0.861144i $$0.330252\pi$$
$$410$$ −0.571797 0.866025i −0.0282390 0.0427699i
$$411$$ 1.26795 + 0.732051i 0.0625433 + 0.0361094i
$$412$$ −3.63397 2.09808i −0.179033 0.103365i
$$413$$ 22.9282 1.12822
$$414$$ −14.1962 8.19615i −0.697703 0.402819i
$$415$$ −9.39230 28.1769i −0.461050 1.38315i
$$416$$ 2.23205 + 3.86603i 0.109435 + 0.189547i
$$417$$ −1.07180 + 1.07180i −0.0524861 + 0.0524861i
$$418$$ 4.92820 4.92820i 0.241046 0.241046i
$$419$$ 27.4186 15.8301i 1.33949 0.773352i 0.352754 0.935716i $$-0.385245\pi$$
0.986731 + 0.162364i $$0.0519117\pi$$
$$420$$ −1.80385 2.73205i −0.0880187 0.133310i
$$421$$ 8.66025 + 8.66025i 0.422075 + 0.422075i 0.885918 0.463843i $$-0.153530\pi$$
−0.463843 + 0.885918i $$0.653530\pi$$
$$422$$ −2.00000 3.46410i −0.0973585 0.168630i
$$423$$ 4.19615 15.6603i 0.204024 0.761428i
$$424$$ 3.13397 11.6962i 0.152199 0.568015i
$$425$$ −2.50962 20.8301i −0.121734 1.01041i
$$426$$ 1.46410 + 5.46410i 0.0709360 + 0.264737i
$$427$$ 9.46410 + 16.3923i 0.458000 + 0.793279i
$$428$$ −1.59808 0.428203i −0.0772459 0.0206980i
$$429$$ −1.19615 + 4.46410i −0.0577508 + 0.215529i
$$430$$ −22.0000 11.0000i −1.06093 0.530467i
$$431$$ −24.8923 + 6.66987i −1.19902 + 0.321276i −0.802445 0.596726i $$-0.796468\pi$$
−0.396575 + 0.918002i $$0.629801\pi$$
$$432$$ 0.767949 2.86603i 0.0369480 0.137892i
$$433$$ −7.19615 7.19615i −0.345825 0.345825i 0.512727 0.858552i $$-0.328635\pi$$
−0.858552 + 0.512727i $$0.828635\pi$$
$$434$$ 7.32051 0.351396
$$435$$ 2.07180 0.124356i 0.0993351 0.00596240i
$$436$$ −2.73205 2.73205i −0.130842 0.130842i
$$437$$ 20.1962 5.41154i 0.966113 0.258869i
$$438$$ 0 0
$$439$$ 0.866025 + 3.23205i 0.0413331 + 0.154257i 0.983508 0.180864i $$-0.0578894\pi$$
−0.942175 + 0.335121i $$0.891223\pi$$
$$440$$ −2.46410 3.73205i −0.117471 0.177919i
$$441$$ −1.36603 + 2.36603i −0.0650488 + 0.112668i
$$442$$ −16.2224 + 9.36603i −0.771622 + 0.445496i
$$443$$ 3.75833 3.75833i 0.178564 0.178564i −0.612166 0.790729i $$-0.709701\pi$$
0.790729 + 0.612166i $$0.209701\pi$$
$$444$$ 3.09808 0.562178i 0.147028 0.0266798i
$$445$$ −27.5885 + 9.19615i −1.30782 + 0.435939i
$$446$$ 0.339746 1.26795i 0.0160874 0.0600391i
$$447$$ −9.63397 + 2.58142i −0.455671 + 0.122097i
$$448$$ −0.732051 2.73205i −0.0345861 0.129077i
$$449$$ −13.4282 + 3.59808i −0.633716 + 0.169804i −0.561355 0.827575i $$-0.689720\pi$$
−0.0723607 + 0.997379i $$0.523053\pi$$
$$450$$ −10.9282 + 8.19615i −0.515160 + 0.386370i
$$451$$ 0.464102 0.803848i 0.0218537 0.0378517i
$$452$$ 6.00000i 0.282216i
$$453$$ 0.964102 3.59808i 0.0452974 0.169052i
$$454$$ 14.6603i 0.688040i
$$455$$ 26.7846 8.92820i 1.25568 0.418561i
$$456$$ 0.901924 + 1.56218i 0.0422365 + 0.0731557i
$$457$$ −12.8038 7.39230i −0.598939 0.345797i 0.169685 0.985498i $$-0.445725\pi$$
−0.768624 + 0.639701i $$0.779058\pi$$
$$458$$ 0.339746i 0.0158753i
$$459$$ 12.0263 + 3.22243i 0.561339 + 0.150410i
$$460$$ −0.803848 13.3923i −0.0374796 0.624419i
$$461$$ −11.4641 3.07180i −0.533936 0.143068i −0.0182310 0.999834i $$-0.505803\pi$$
−0.515705 + 0.856766i $$0.672470\pi$$
$$462$$ 1.46410 2.53590i 0.0681162 0.117981i
$$463$$ −12.8301 + 22.2224i −0.596267 + 1.03276i 0.397100 + 0.917775i $$0.370017\pi$$
−0.993367 + 0.114989i $$0.963317\pi$$
$$464$$ 1.73205 + 0.464102i 0.0804084 + 0.0215454i
$$465$$ 0.179492 + 2.99038i 0.00832374 + 0.138676i
$$466$$ 16.1962 + 4.33975i 0.750272 + 0.201035i
$$467$$ 16.0718i 0.743714i −0.928290 0.371857i $$-0.878721\pi$$
0.928290 0.371857i $$-0.121279\pi$$
$$468$$ 10.5622 + 6.09808i 0.488237 + 0.281884i
$$469$$ −19.8564 34.3923i −0.916884 1.58809i
$$470$$ 12.5885 4.19615i 0.580662 0.193554i
$$471$$ 9.24871i 0.426158i
$$472$$ −2.09808 + 7.83013i −0.0965718 + 0.360411i
$$473$$ 22.0000i 1.01156i
$$474$$ −1.83013 + 3.16987i −0.0840605 + 0.145597i
$$475$$ 2.46410 17.2487i 0.113061 0.791425i
$$476$$ 11.4641 3.07180i 0.525456 0.140796i
$$477$$ −8.56218 31.9545i −0.392035 1.46310i
$$478$$ 23.0263 6.16987i 1.05320 0.282203i
$$479$$ −2.96410 + 11.0622i −0.135433 + 0.505444i 0.864562 + 0.502525i $$0.167596\pi$$
−0.999996 + 0.00291847i $$0.999071\pi$$
$$480$$ 1.09808 0.366025i 0.0501201 0.0167067i
$$481$$ −2.23205 + 27.0622i −0.101773 + 1.23393i
$$482$$ −2.80385 + 2.80385i −0.127712 + 0.127712i
$$483$$ 7.60770 4.39230i 0.346162 0.199857i
$$484$$ −3.50000 + 6.06218i −0.159091 + 0.275554i
$$485$$ 6.73205 + 10.1962i 0.305687 + 0.462983i
$$486$$ −3.19615 11.9282i −0.144980 0.541074i
$$487$$ 34.5359i 1.56497i −0.622669 0.782485i $$-0.713952\pi$$
0.622669 0.782485i $$-0.286048\pi$$
$$488$$ −6.46410 + 1.73205i −0.292616 + 0.0784063i
$$489$$ −3.83013 3.83013i −0.173204 0.173204i
$$490$$ −2.23205 + 0.133975i −0.100834 + 0.00605236i
$$491$$ 2.19615 0.0991110 0.0495555 0.998771i $$-0.484220\pi$$
0.0495555 + 0.998771i $$0.484220\pi$$
$$492$$ 0.169873 + 0.169873i 0.00765847 + 0.00765847i
$$493$$ −1.94744 + 7.26795i −0.0877083 + 0.327332i
$$494$$ −15.0263 + 4.02628i −0.676064 + 0.181151i
$$495$$ −10.9282 5.46410i −0.491186 0.245593i
$$496$$ −0.669873 + 2.50000i −0.0300782 + 0.112253i
$$497$$ 29.8564 + 8.00000i 1.33924 + 0.358849i
$$498$$ 3.43782 + 5.95448i 0.154052 + 0.266827i
$$499$$ 4.80385 + 17.9282i 0.215050 + 0.802577i 0.986149 + 0.165862i $$0.0530405\pi$$
−0.771099 + 0.636715i $$0.780293\pi$$
$$500$$ −10.5263 3.76795i −0.470750 0.168508i
$$501$$ 2.31347 8.63397i 0.103358 0.385738i
$$502$$ 0.830127 3.09808i 0.0370504 0.138274i
$$503$$ 13.5622 + 23.4904i 0.604708 + 1.04738i 0.992098 + 0.125468i $$0.0400434\pi$$
−0.387390 + 0.921916i $$0.626623\pi$$
$$504$$ −5.46410 5.46410i −0.243390 0.243390i
$$505$$ 12.5622 + 19.0263i 0.559010 + 0.846658i
$$506$$ 10.3923 6.00000i 0.461994 0.266733i
$$507$$ 2.53590 2.53590i 0.112623 0.112623i
$$508$$ −0.464102 + 0.464102i −0.0205912 + 0.0205912i
$$509$$ −18.9282 32.7846i −0.838978 1.45315i −0.890750 0.454493i $$-0.849820\pi$$
0.0517723 0.998659i $$-0.483513\pi$$
$$510$$ 1.53590 + 4.60770i 0.0680107 + 0.204032i
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 8.95448 + 5.16987i 0.395350 + 0.228255i
$$514$$ 15.2942 + 8.83013i 0.674600 + 0.389480i
$$515$$ −5.16987 7.83013i −0.227812 0.345037i
$$516$$ 5.50000 + 1.47372i 0.242124 + 0.0648769i
$$517$$ 8.39230 + 8.39230i 0.369093 + 0.369093i
$$518$$ 5.80385 16.1962i 0.255006 0.711618i
$$519$$ 4.98076i 0.218631i
$$520$$ 0.598076 + 9.96410i 0.0262274 + 0.436955i
$$521$$ 14.0885 + 8.13397i 0.617227 + 0.356356i 0.775788 0.630993i $$-0.217352\pi$$
−0.158562 + 0.987349i $$0.550686\pi$$
$$522$$ 4.73205 1.26795i 0.207116 0.0554966i
$$523$$ −4.40192 + 7.62436i −0.192483 + 0.333390i −0.946072 0.323955i $$-0.894987\pi$$
0.753590 + 0.657345i $$0.228321\pi$$
$$524$$ −7.46410 7.46410i −0.326071 0.326071i
$$525$$ −0.875644 7.26795i −0.0382163 0.317199i
$$526$$ 13.9282 13.9282i 0.607299 0.607299i
$$527$$ −10.4904 2.81089i −0.456968 0.122444i
$$528$$ 0.732051 + 0.732051i 0.0318584 + 0.0318584i
$$529$$ 13.0000 0.565217
$$530$$ 17.9641 20.2583i 0.780311 0.879966i
$$531$$ 5.73205 + 21.3923i 0.248750 + 0.928347i
$$532$$ 9.85641 0.427329
$$533$$ −1.79423 + 1.03590i −0.0777167 + 0.0448697i
$$534$$ 5.83013 3.36603i 0.252294 0.145662i
$$535$$ −2.76795 2.45448i −0.119669 0.106117i
$$536$$ 13.5622 3.63397i 0.585797 0.156964i
$$537$$ −6.58846 3.80385i −0.284313 0.164148i
$$538$$ −21.2942 + 12.2942i −0.918059 + 0.530042i
$$539$$ −1.00000 1.73205i −0.0430730 0.0746047i
$$540$$ 4.40192 4.96410i 0.189429 0.213621i
$$541$$ 18.9282 18.9282i 0.813787 0.813787i −0.171412 0.985199i $$-0.554833\pi$$
0.985199 + 0.171412i $$0.0548330\pi$$
$$542$$ 1.76795 3.06218i 0.0759399 0.131532i
$$543$$ 12.0981 + 3.24167i 0.519178 + 0.139113i
$$544$$ 4.19615i 0.179909i
$$545$$ −2.73205 8.19615i −0.117028 0.351085i
$$546$$ −5.66025 + 3.26795i −0.242237 + 0.139855i
$$547$$ −33.9808 −1.45291 −0.726456 0.687213i $$-0.758834\pi$$
−0.726456 + 0.687213i $$0.758834\pi$$
$$548$$ 0.732051 + 2.73205i 0.0312717 + 0.116707i
$$549$$ −12.9282 + 12.9282i −0.551762 + 0.551762i
$$550$$ −1.19615 9.92820i −0.0510041 0.423340i
$$551$$ −3.12436 + 5.41154i −0.133102 + 0.230539i
$$552$$ 0.803848 + 3.00000i 0.0342140 + 0.127688i
$$553$$ 10.0000 + 17.3205i 0.425243 + 0.736543i
$$554$$ 0.660254 0.0280515
$$555$$ 6.75833 + 1.97372i 0.286875 + 0.0837798i
$$556$$ −2.92820 −0.124183
$$557$$ 8.30385 + 14.3827i 0.351845 + 0.609414i 0.986573 0.163322i $$-0.0522210\pi$$
−0.634727 + 0.772736i $$0.718888\pi$$
$$558$$ 1.83013 + 6.83013i 0.0774755 + 0.289142i
$$559$$ −24.5526 + 42.5263i −1.03846 + 1.79867i
$$560$$ 1.26795 6.19615i 0.0535806 0.261835i
$$561$$ −3.07180 + 3.07180i −0.129691 + 0.129691i
$$562$$ −6.33013 23.6244i −0.267020 0.996533i
$$563$$ 36.3923 1.53375 0.766876 0.641795i $$-0.221810\pi$$
0.766876 + 0.641795i $$0.221810\pi$$
$$564$$ −2.66025 + 1.53590i −0.112017 + 0.0646730i
$$565$$ −6.00000 + 12.0000i −0.252422 + 0.504844i
$$566$$ 13.0000i 0.546431i
$$567$$ −18.1962 4.87564i −0.764167 0.204758i
$$568$$ −5.46410 + 9.46410i −0.229269 + 0.397105i
$$569$$ 14.6340 14.6340i 0.613488 0.613488i −0.330365 0.943853i $$-0.607172\pi$$
0.943853 + 0.330365i $$0.107172\pi$$
$$570$$ 0.241670 + 4.02628i 0.0101224 + 0.168642i
$$571$$ −1.75833 3.04552i −0.0735838 0.127451i 0.826886 0.562370i $$-0.190110\pi$$
−0.900470 + 0.434919i $$0.856777\pi$$
$$572$$ −7.73205 + 4.46410i −0.323293 + 0.186653i
$$573$$ 4.33013 + 2.50000i 0.180894 + 0.104439i
$$574$$ 1.26795 0.339746i 0.0529232 0.0141807i
$$575$$ 11.7846 27.5885i 0.491452 1.15052i
$$576$$ 2.36603 1.36603i 0.0985844 0.0569177i
$$577$$ −16.3923 + 9.46410i −0.682421 + 0.393996i −0.800766 0.598977i $$-0.795574\pi$$
0.118346 + 0.992972i $$0.462241\pi$$
$$578$$ −0.607695 −0.0252768
$$579$$ −2.36603 8.83013i −0.0983287 0.366968i
$$580$$ 3.00000 + 2.66025i 0.124568 + 0.110461i
$$581$$ 37.5692 1.55863
$$582$$ −2.00000 2.00000i −0.0829027 0.0829027i
$$583$$ 23.3923 + 6.26795i 0.968810 + 0.259592i
$$584$$ 0 0
$$585$$ 15.0263 + 22.7583i 0.621260 + 0.940941i
$$586$$ −13.2942 13.2942i −0.549180 0.549180i
$$587$$ −10.1603 + 17.5981i −0.419359 + 0.726350i −0.995875 0.0907352i $$-0.971078\pi$$
0.576516 + 0.817086i $$0.304412\pi$$
$$588$$ 0.500000 0.133975i 0.0206197 0.00552502i
$$589$$ −7.81089 4.50962i −0.321842 0.185816i
$$590$$ −12.0263 + 13.5622i −0.495114 + 0.558346i
$$591$$ 12.2679i 0.504636i
$$592$$ 5.00000 + 3.46410i 0.205499 + 0.142374i
$$593$$ −1.33975 1.33975i −0.0550168 0.0550168i 0.679063 0.734080i $$-0.262386\pi$$
−0.734080 + 0.679063i $$0.762386\pi$$
$$594$$ 5.73205 + 1.53590i 0.235189 + 0.0630187i
$$595$$ 26.0000 + 5.32051i 1.06590 + 0.218120i
$$596$$ −16.6865 9.63397i −0.683507 0.394623i
$$597$$ 4.91858 + 2.83975i 0.201304 + 0.116223i
$$598$$ −26.7846 −1.09530
$$599$$ −36.6051 21.1340i −1.49564 0.863511i −0.495657 0.868518i $$-0.665073\pi$$
−0.999987 + 0.00500751i $$0.998406\pi$$
$$600$$ 2.56218 + 0.366025i 0.104600 + 0.0149429i
$$601$$ −1.79423 3.10770i −0.0731881 0.126766i 0.827109 0.562042i $$-0.189984\pi$$
−0.900297 + 0.435276i $$0.856651\pi$$
$$602$$ 22.0000 22.0000i 0.896653 0.896653i
$$603$$ 27.1244 27.1244i 1.10459 1.10459i
$$604$$ 6.23205 3.59808i 0.253579 0.146404i
$$605$$ −13.0622 + 8.62436i −0.531053 + 0.350630i
$$606$$ −3.73205 3.73205i −0.151604 0.151604i
$$607$$ 12.0263 + 20.8301i 0.488132 + 0.845469i 0.999907 0.0136506i $$-0.00434526\pi$$
−0.511775 + 0.859119i $$0.671012\pi$$
$$608$$ −0.901924 + 3.36603i −0.0365778 + 0.136510i
$$609$$ −0.679492 + 2.53590i −0.0275344 + 0.102760i
$$610$$ −14.6603 3.00000i −0.593576 0.121466i
$$611$$ −6.85641 25.5885i −0.277381 1.03520i
$$612$$ 5.73205 + 9.92820i 0.231704 + 0.401324i
$$613$$ −42.6147 11.4186i −1.72119 0.461192i −0.743069 0.669215i $$-0.766631\pi$$
−0.978124 + 0.208023i $$0.933297\pi$$
$$614$$ 8.93782 33.3564i 0.360701 1.34616i
$$615$$ 0.169873 + 0.509619i 0.00684994 + 0.0205498i
$$616$$ 5.46410 1.46410i 0.220155 0.0589903i
$$617$$ 8.95448 33.4186i 0.360494 1.34538i −0.512934 0.858428i $$-0.671441\pi$$
0.873428 0.486953i $$-0.161892\pi$$
$$618$$ 1.53590 + 1.53590i 0.0617829 + 0.0617829i
$$619$$ 26.9282 1.08234 0.541168 0.840915i $$-0.317982\pi$$
0.541168 + 0.840915i $$0.317982\pi$$
$$620$$ −3.83975 + 4.33013i −0.154208 + 0.173902i
$$621$$ 12.5885 + 12.5885i 0.505157 + 0.505157i
$$622$$ 27.0885 7.25833i 1.08615 0.291033i
$$623$$ 36.7846i 1.47374i
$$624$$ −0.598076 2.23205i −0.0239422 0.0893535i
$$625$$ −17.2846 18.0622i −0.691384 0.722487i
$$626$$ 5.26795 9.12436i 0.210550 0.364683i
$$627$$ −3.12436 + 1.80385i −0.124775 + 0.0720387i
$$628$$ −12.6340 + 12.6340i −0.504150 + 0.504150i
$$629$$ −14.5359 + 20.9808i −0.579584 + 0.836558i
$$630$$ −5.46410 16.3923i −0.217695 0.653085i
$$631$$ 7.06218 26.3564i 0.281141 1.04923i −0.670473 0.741934i $$-0.733909\pi$$
0.951613 0.307298i $$-0.0994247\pi$$
$$632$$ −6.83013 + 1.83013i −0.271688 + 0.0727985i
$$633$$ 0.535898 + 2.00000i 0.0213000 + 0.0794929i
$$634$$ 29.1865 7.82051i 1.15915 0.310592i
$$635$$ −1.39230 + 0.464102i −0.0552519 + 0.0184173i
$$636$$ −3.13397 + 5.42820i −0.124270 + 0.215242i
$$637$$ 4.46410i 0.176874i
$$638$$ −0.928203 + 3.46410i −0.0367479 + 0.137145i
$$639$$ 29.8564i 1.18110i
$$640$$ 2.00000 + 1.00000i 0.0790569 + 0.0395285i
$$641$$ 3.99038 + 6.91154i 0.157611 + 0.272990i 0.934007 0.357256i $$-0.116288\pi$$
−0.776396 + 0.630245i $$0.782954\pi$$
$$642$$ 0.741670 + 0.428203i 0.0292714 + 0.0168998i
$$643$$ 0.267949i 0.0105669i −0.999986 0.00528344i $$-0.998318\pi$$
0.999986 0.00528344i $$-0.00168178\pi$$
$$644$$ 16.3923 + 4.39230i 0.645947 + 0.173081i
$$645$$ 9.52628 + 8.44744i 0.375097 + 0.332618i
$$646$$ −14.1244 3.78461i −0.555715 0.148903i
$$647$$ 10.2224 17.7058i 0.401885 0.696086i −0.592068 0.805888i $$-0.701688\pi$$
0.993953 + 0.109802i $$0.0350217\pi$$
$$648$$ 3.33013 5.76795i 0.130820 0.226586i
$$649$$ −15.6603 4.19615i −0.614719 0.164713i
$$650$$ −8.76795 + 20.5263i −0.343907 + 0.805107i
$$651$$ −3.66025 0.980762i −0.143457 0.0384391i
$$652$$ 10.4641i 0.409806i
$$653$$ −28.7942 16.6244i −1.12681 0.650561i −0.183676 0.982987i $$-0.558800\pi$$
−0.943129 + 0.332426i $$0.892133\pi$$
$$654$$ 1.00000 + 1.73205i 0.0391031 + 0.0677285i
$$655$$ −7.46410 22.3923i −0.291647 0.874940i
$$656$$ 0.464102i 0.0181201i
$$657$$ 0 0
$$658$$ 16.7846i 0.654332i
$$659$$ 0.392305 0.679492i 0.0152820 0.0264692i −0.858283 0.513176i $$-0.828469\pi$$
0.873565 + 0.486707i $$0.161802\pi$$
$$660$$ 0.732051 + 2.19615i 0.0284950 + 0.0854851i
$$661$$ −33.4186 + 8.95448i −1.29983 + 0.348289i −0.841387 0.540433i $$-0.818260\pi$$
−0.458446 + 0.888723i $$0.651594\pi$$
$$662$$ 2.09808 + 7.83013i 0.0815440 + 0.304327i
$$663$$ 9.36603 2.50962i 0.363746 0.0974655i
$$664$$ −3.43782 + 12.8301i −0.133413 + 0.497905i
$$665$$ 19.7128 + 9.85641i 0.764430 + 0.382215i
$$666$$ 16.5622 + 1.36603i 0.641771 + 0.0529324i
$$667$$ −7.60770 + 7.60770i −0.294571 + 0.294571i
$$668$$ 14.9545 8.63397i 0.578606 0.334059i
$$669$$ −0.339746 + 0.588457i −0.0131353 + 0.0227511i
$$670$$ 30.7583 + 6.29423i 1.18830 + 0.243167i
$$671$$ −3.46410 12.9282i −0.133730 0.499088i
$$672$$ 1.46410i 0.0564789i
$$673$$ −16.8301 + 4.50962i −0.648754 + 0.173833i −0.568165 0.822914i $$-0.692347\pi$$
−0.0805884 + 0.996747i $$0.525680\pi$$
$$674$$ 12.4641 + 12.4641i 0.480099 + 0.480099i
$$675$$ 13.7679 5.52628i 0.529929 0.212707i
$$676$$ 6.92820 0.266469
$$677$$ −9.39230 9.39230i −0.360976 0.360976i 0.503196 0.864172i $$-0.332157\pi$$
−0.864172 + 0.503196i $$0.832157\pi$$
$$678$$ 0.803848 3.00000i 0.0308716 0.115214i
$$679$$ −14.9282 + 4.00000i −0.572892 + 0.153506i
$$680$$ −4.19615 + 8.39230i −0.160915 + 0.321830i
$$681$$ 1.96410 7.33013i 0.0752645 0.280891i
$$682$$ −5.00000 1.33975i −0.191460 0.0513015i
$$683$$ 3.69615 + 6.40192i 0.141429 + 0.244963i 0.928035 0.372493i $$-0.121497\pi$$
−0.786606 + 0.617456i $$0.788164\pi$$
$$684$$ 2.46410 + 9.19615i 0.0942173 + 0.351624i
$$685$$ −1.26795 + 6.19615i −0.0484458 + 0.236743i
$$686$$ −4.39230 + 16.3923i −0.167699 + 0.625861i
$$687$$ −0.0455173 + 0.169873i −0.00173659 + 0.00648106i
$$688$$ 5.50000 + 9.52628i 0.209686 + 0.363186i
$$689$$ −38.2224 38.2224i −1.45616 1.45616i
$$690$$ −1.39230 + 6.80385i −0.0530041 + 0.259018i
$$691$$ 2.24167 1.29423i 0.0852771 0.0492348i −0.456755 0.889593i $$-0.650988\pi$$
0.542032 + 0.840358i $$0.317655\pi$$
$$692$$ 6.80385 6.80385i 0.258643 0.258643i
$$693$$ 10.9282 10.9282i 0.415128 0.415128i
$$694$$ 3.92820 + 6.80385i 0.149113 + 0.258271i
$$695$$ −5.85641 2.92820i −0.222146 0.111073i
$$696$$ −0.803848 0.464102i −0.0304698 0.0175917i
$$697$$ −1.94744 −0.0737646
$$698$$ −25.9019 14.9545i −0.980402 0.566036i
$$699$$ −7.51666 4.33975i −0.284306 0.164144i
$$700$$ 8.73205 11.1244i 0.330040 0.420461i
$$701$$ −27.4904 7.36603i −1.03830 0.278211i −0.300890 0.953659i $$-0.597284\pi$$
−0.737408 + 0.675448i $$0.763950\pi$$
$$702$$ −9.36603 9.36603i −0.353498 0.353498i
$$703$$ −16.1699 + 13.7058i −0.609858 + 0.516923i
$$704$$ 2.00000i 0.0753778i
$$705$$ −6.85641 + 0.411543i −0.258227 + 0.0154996i
$$706$$ 7.60770 + 4.39230i 0.286319 + 0.165307i
$$707$$ −27.8564 + 7.46410i −1.04765 + 0.280716i
$$708$$ 2.09808 3.63397i 0.0788505 0.136573i
$$709$$ 33.9282 + 33.9282i 1.27420 + 1.27420i 0.943863 + 0.330338i $$0.107163\pi$$
0.330338 + 0.943863i $$0.392837\pi$$
$$710$$ −20.3923 + 13.4641i −0.765310 + 0.505299i
$$711$$ −13.6603 + 13.6603i −0.512300 + 0.512300i
$$712$$ 12.5622 + 3.36603i 0.470788 + 0.126147i
$$713$$ −10.9808 10.9808i −0.411233 0.411233i
$$714$$ −6.14359 −0.229918
$$715$$ −19.9282 + 1.19615i −0.745273 + 0.0447336i
$$716$$ −3.80385 14.1962i −0.142156 0.530535i
$$717$$ −12.3397 −0.460836
$$718$$ 15.0622 8.69615i 0.562115 0.324538i
$$719$$ 30.5718 17.6506i 1.14014 0.658258i 0.193671 0.981066i $$-0.437960\pi$$
0.946464 + 0.322809i $$0.104627\pi$$
$$720$$ 6.09808 0.366025i 0.227262 0.0136410i
$$721$$ 11.4641 3.07180i 0.426945 0.114400i
$$722$$ 5.93782 + 3.42820i 0.220983 + 0.127585i
$$723$$ 1.77757 1.02628i 0.0661085 0.0381677i
$$724$$ 12.0981 + 20.9545i 0.449621 + 0.778767i
$$725$$ 3.33975 + 8.32051i 0.124035 + 0.309016i
$$726$$ 2.56218 2.56218i 0.0950913 0.0950913i
$$727$$ 14.3205 24.8038i 0.531118 0.919924i −0.468222 0.883611i $$-0.655105\pi$$
0.999340 0.0363130i $$-0.0115613\pi$$
$$728$$ −12.1962 3.26795i −0.452019 0.121118i
$$729$$ 13.5885i 0.503276i
$$730$$ 0 0
$$731$$ −39.9737 + 23.0788i −1.47848 + 0.853602i
$$732$$ 3.46410 0.128037
$$733$$ 4.88269 + 18.2224i 0.180346 + 0.673061i 0.995579 + 0.0939276i $$0.0299422\pi$$
−0.815233 + 0.579133i $$0.803391\pi$$
$$734$$ −18.5359 + 18.5359i −0.684172 + 0.684172i
$$735$$ 1.13397 + 0.232051i 0.0418273 + 0.00855932i
$$736$$ −3.00000 + 5.19615i −0.110581 + 0.191533i
$$737$$ 7.26795 + 27.1244i 0.267718 + 0.999138i
$$738$$ 0.633975 + 1.09808i 0.0233369 + 0.0404207i
$$739$$ −7.80385 −0.287069 −0.143535 0.989645i $$-0.545847\pi$$
−0.143535 + 0.989645i $$0.545847\pi$$
$$740$$ 6.53590 + 11.9282i 0.240264 + 0.438489i
$$741$$ 8.05256 0.295818
$$742$$ 17.1244 + 29.6603i 0.628655 + 1.08886i
$$743$$ −8.97372 33.4904i −0.329214 1.22864i −0.910007 0.414592i $$-0.863924\pi$$
0.580794 0.814051i $$-0.302742\pi$$
$$744$$ 0.669873 1.16025i 0.0245587 0.0425370i
$$745$$ −23.7391 35.9545i −0.869733 1.31727i
$$746$$ 18.7583 18.7583i 0.686791 0.686791i
$$747$$ 9.39230 + 35.0526i 0.343646 + 1.28251i
$$748$$ −8.39230 −0.306853
$$749$$ 4.05256 2.33975i 0.148077 0.0854925i
$$750$$ 4.75833 + 3.29423i 0.173750 + 0.120288i
$$751$$ 32.1769i 1.17415i 0.809532 + 0.587076i $$0.199721\pi$$
−0.809532 + 0.587076i $$0.800279\pi$$
$$752$$ −5.73205 1.53590i −0.209026 0.0560085i
$$753$$ −0.830127 + 1.43782i −0.0302515 + 0.0523972i
$$754$$ 5.66025 5.66025i 0.206134 0.206134i
$$755$$ 16.0622 0.964102i 0.584563 0.0350873i
$$756$$ 4.19615 + 7.26795i 0.152613 + 0.264333i
$$757$$ −14.7224 + 8.50000i −0.535096 + 0.308938i −0.743089 0.669193i $$-0.766640\pi$$
0.207993 + 0.978130i $$0.433307\pi$$
$$758$$ −18.5885 10.7321i −0.675163 0.389806i
$$759$$ −6.00000 + 1.60770i −0.217786 + 0.0583556i
$$760$$ −5.16987 + 5.83013i −0.187531 + 0.211481i
$$761$$ −9.46410 + 5.46410i −0.343073 + 0.198074i −0.661630 0.749830i $$-0.730135\pi$$
0.318557 + 0.947904i $$0.396802\pi$$
$$762$$ 0.294229 0.169873i 0.0106588 0.00615385i
$$763$$ 10.9282 0.395628
$$764$$ 2.50000 + 9.33013i 0.0904468 + 0.337552i
$$765$$ 1.53590 + 25.5885i 0.0555305 + 0.925153i
$$766$$ −8.53590 −0.308415
$$767$$ 25.5885 + 25.5885i 0.923946 + 0.923946i
$$768$$ −0.500000 0.133975i −0.0180422 0.00483439i
$$769$$ −20.0718 + 20.0718i −0.723808 + 0.723808i −0.969379 0.245571i $$-0.921025\pi$$
0.245571 + 0.969379i $$0.421025\pi$$