# Properties

 Label 370.2.g.c.43.2 Level $370$ Weight $2$ Character 370.43 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.g (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 43.2 Root $$0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.43 Dual form 370.2.g.c.327.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +(1.41421 - 1.41421i) q^{3} -1.00000 q^{4} +(2.12132 - 0.707107i) q^{5} +(-1.41421 - 1.41421i) q^{6} +(2.70711 - 2.70711i) q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-0.707107 - 2.12132i) q^{10} +3.82843i q^{11} +(-1.41421 + 1.41421i) q^{12} +2.24264i q^{13} +(-2.70711 - 2.70711i) q^{14} +(2.00000 - 4.00000i) q^{15} +1.00000 q^{16} -1.82843 q^{17} -1.00000 q^{18} +(-5.82843 + 5.82843i) q^{19} +(-2.12132 + 0.707107i) q^{20} -7.65685i q^{21} +3.82843 q^{22} -2.58579i q^{23} +(1.41421 + 1.41421i) q^{24} +(4.00000 - 3.00000i) q^{25} +2.24264 q^{26} +(2.82843 + 2.82843i) q^{27} +(-2.70711 + 2.70711i) q^{28} +(-6.70711 - 6.70711i) q^{29} +(-4.00000 - 2.00000i) q^{30} +(-4.12132 + 4.12132i) q^{31} -1.00000i q^{32} +(5.41421 + 5.41421i) q^{33} +1.82843i q^{34} +(3.82843 - 7.65685i) q^{35} +1.00000i q^{36} +(-4.94975 - 3.53553i) q^{37} +(5.82843 + 5.82843i) q^{38} +(3.17157 + 3.17157i) q^{39} +(0.707107 + 2.12132i) q^{40} +7.00000i q^{41} -7.65685 q^{42} -7.00000i q^{43} -3.82843i q^{44} +(-0.707107 - 2.12132i) q^{45} -2.58579 q^{46} +(-8.24264 + 8.24264i) q^{47} +(1.41421 - 1.41421i) q^{48} -7.65685i q^{49} +(-3.00000 - 4.00000i) q^{50} +(-2.58579 + 2.58579i) q^{51} -2.24264i q^{52} +(2.12132 + 2.12132i) q^{53} +(2.82843 - 2.82843i) q^{54} +(2.70711 + 8.12132i) q^{55} +(2.70711 + 2.70711i) q^{56} +16.4853i q^{57} +(-6.70711 + 6.70711i) q^{58} +(-1.17157 + 1.17157i) q^{59} +(-2.00000 + 4.00000i) q^{60} +(9.29289 - 9.29289i) q^{61} +(4.12132 + 4.12132i) q^{62} +(-2.70711 - 2.70711i) q^{63} -1.00000 q^{64} +(1.58579 + 4.75736i) q^{65} +(5.41421 - 5.41421i) q^{66} +(1.24264 + 1.24264i) q^{67} +1.82843 q^{68} +(-3.65685 - 3.65685i) q^{69} +(-7.65685 - 3.82843i) q^{70} -0.343146 q^{71} +1.00000 q^{72} +(6.00000 - 6.00000i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(1.41421 - 9.89949i) q^{75} +(5.82843 - 5.82843i) q^{76} +(10.3640 + 10.3640i) q^{77} +(3.17157 - 3.17157i) q^{78} +(9.65685 - 9.65685i) q^{79} +(2.12132 - 0.707107i) q^{80} +11.0000 q^{81} +7.00000 q^{82} +(-0.828427 - 0.828427i) q^{83} +7.65685i q^{84} +(-3.87868 + 1.29289i) q^{85} -7.00000 q^{86} -18.9706 q^{87} -3.82843 q^{88} +(7.41421 + 7.41421i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(6.07107 + 6.07107i) q^{91} +2.58579i q^{92} +11.6569i q^{93} +(8.24264 + 8.24264i) q^{94} +(-8.24264 + 16.4853i) q^{95} +(-1.41421 - 1.41421i) q^{96} -7.00000 q^{97} -7.65685 q^{98} +3.82843 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{4} + 8q^{7} + O(q^{10})$$ $$4q - 4q^{4} + 8q^{7} - 8q^{14} + 8q^{15} + 4q^{16} + 4q^{17} - 4q^{18} - 12q^{19} + 4q^{22} + 16q^{25} - 8q^{26} - 8q^{28} - 24q^{29} - 16q^{30} - 8q^{31} + 16q^{33} + 4q^{35} + 12q^{38} + 24q^{39} - 8q^{42} - 16q^{46} - 16q^{47} - 12q^{50} - 16q^{51} + 8q^{55} + 8q^{56} - 24q^{58} - 16q^{59} - 8q^{60} + 40q^{61} + 8q^{62} - 8q^{63} - 4q^{64} + 12q^{65} + 16q^{66} - 12q^{67} - 4q^{68} + 8q^{69} - 8q^{70} - 24q^{71} + 4q^{72} + 24q^{73} + 12q^{76} + 16q^{77} + 24q^{78} + 16q^{79} + 44q^{81} + 28q^{82} + 8q^{83} - 24q^{85} - 28q^{86} - 8q^{87} - 4q^{88} + 24q^{89} - 4q^{91} + 16q^{94} - 16q^{95} - 28q^{97} - 8q^{98} + 4q^{99} + O(q^{100})$$

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.41421 1.41421i 0.816497 0.816497i −0.169102 0.985599i $$-0.554087\pi$$
0.985599 + 0.169102i $$0.0540867\pi$$
$$4$$ −1.00000 −0.500000
$$5$$ 2.12132 0.707107i 0.948683 0.316228i
$$6$$ −1.41421 1.41421i −0.577350 0.577350i
$$7$$ 2.70711 2.70711i 1.02319 1.02319i 0.0234655 0.999725i $$-0.492530\pi$$
0.999725 0.0234655i $$-0.00747000\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000i 0.333333i
$$10$$ −0.707107 2.12132i −0.223607 0.670820i
$$11$$ 3.82843i 1.15431i 0.816633 + 0.577157i $$0.195838\pi$$
−0.816633 + 0.577157i $$0.804162\pi$$
$$12$$ −1.41421 + 1.41421i −0.408248 + 0.408248i
$$13$$ 2.24264i 0.621997i 0.950410 + 0.310998i $$0.100663\pi$$
−0.950410 + 0.310998i $$0.899337\pi$$
$$14$$ −2.70711 2.70711i −0.723505 0.723505i
$$15$$ 2.00000 4.00000i 0.516398 1.03280i
$$16$$ 1.00000 0.250000
$$17$$ −1.82843 −0.443459 −0.221729 0.975108i $$-0.571170\pi$$
−0.221729 + 0.975108i $$0.571170\pi$$
$$18$$ −1.00000 −0.235702
$$19$$ −5.82843 + 5.82843i −1.33713 + 1.33713i −0.438308 + 0.898825i $$0.644422\pi$$
−0.898825 + 0.438308i $$0.855578\pi$$
$$20$$ −2.12132 + 0.707107i −0.474342 + 0.158114i
$$21$$ 7.65685i 1.67086i
$$22$$ 3.82843 0.816223
$$23$$ 2.58579i 0.539174i −0.962976 0.269587i $$-0.913113\pi$$
0.962976 0.269587i $$-0.0868871\pi$$
$$24$$ 1.41421 + 1.41421i 0.288675 + 0.288675i
$$25$$ 4.00000 3.00000i 0.800000 0.600000i
$$26$$ 2.24264 0.439818
$$27$$ 2.82843 + 2.82843i 0.544331 + 0.544331i
$$28$$ −2.70711 + 2.70711i −0.511595 + 0.511595i
$$29$$ −6.70711 6.70711i −1.24548 1.24548i −0.957696 0.287783i $$-0.907082\pi$$
−0.287783 0.957696i $$-0.592918\pi$$
$$30$$ −4.00000 2.00000i −0.730297 0.365148i
$$31$$ −4.12132 + 4.12132i −0.740211 + 0.740211i −0.972619 0.232408i $$-0.925340\pi$$
0.232408 + 0.972619i $$0.425340\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 5.41421 + 5.41421i 0.942494 + 0.942494i
$$34$$ 1.82843i 0.313573i
$$35$$ 3.82843 7.65685i 0.647122 1.29424i
$$36$$ 1.00000i 0.166667i
$$37$$ −4.94975 3.53553i −0.813733 0.581238i
$$38$$ 5.82843 + 5.82843i 0.945496 + 0.945496i
$$39$$ 3.17157 + 3.17157i 0.507858 + 0.507858i
$$40$$ 0.707107 + 2.12132i 0.111803 + 0.335410i
$$41$$ 7.00000i 1.09322i 0.837389 + 0.546608i $$0.184081\pi$$
−0.837389 + 0.546608i $$0.815919\pi$$
$$42$$ −7.65685 −1.18148
$$43$$ 7.00000i 1.06749i −0.845645 0.533745i $$-0.820784\pi$$
0.845645 0.533745i $$-0.179216\pi$$
$$44$$ 3.82843i 0.577157i
$$45$$ −0.707107 2.12132i −0.105409 0.316228i
$$46$$ −2.58579 −0.381253
$$47$$ −8.24264 + 8.24264i −1.20231 + 1.20231i −0.228851 + 0.973461i $$0.573497\pi$$
−0.973461 + 0.228851i $$0.926503\pi$$
$$48$$ 1.41421 1.41421i 0.204124 0.204124i
$$49$$ 7.65685i 1.09384i
$$50$$ −3.00000 4.00000i −0.424264 0.565685i
$$51$$ −2.58579 + 2.58579i −0.362083 + 0.362083i
$$52$$ 2.24264i 0.310998i
$$53$$ 2.12132 + 2.12132i 0.291386 + 0.291386i 0.837628 0.546242i $$-0.183942\pi$$
−0.546242 + 0.837628i $$0.683942\pi$$
$$54$$ 2.82843 2.82843i 0.384900 0.384900i
$$55$$ 2.70711 + 8.12132i 0.365026 + 1.09508i
$$56$$ 2.70711 + 2.70711i 0.361752 + 0.361752i
$$57$$ 16.4853i 2.18353i
$$58$$ −6.70711 + 6.70711i −0.880686 + 0.880686i
$$59$$ −1.17157 + 1.17157i −0.152526 + 0.152526i −0.779245 0.626719i $$-0.784397\pi$$
0.626719 + 0.779245i $$0.284397\pi$$
$$60$$ −2.00000 + 4.00000i −0.258199 + 0.516398i
$$61$$ 9.29289 9.29289i 1.18983 1.18983i 0.212720 0.977113i $$-0.431768\pi$$
0.977113 0.212720i $$-0.0682322\pi$$
$$62$$ 4.12132 + 4.12132i 0.523408 + 0.523408i
$$63$$ −2.70711 2.70711i −0.341063 0.341063i
$$64$$ −1.00000 −0.125000
$$65$$ 1.58579 + 4.75736i 0.196693 + 0.590078i
$$66$$ 5.41421 5.41421i 0.666444 0.666444i
$$67$$ 1.24264 + 1.24264i 0.151813 + 0.151813i 0.778927 0.627114i $$-0.215764\pi$$
−0.627114 + 0.778927i $$0.715764\pi$$
$$68$$ 1.82843 0.221729
$$69$$ −3.65685 3.65685i −0.440234 0.440234i
$$70$$ −7.65685 3.82843i −0.915169 0.457585i
$$71$$ −0.343146 −0.0407239 −0.0203620 0.999793i $$-0.506482\pi$$
−0.0203620 + 0.999793i $$0.506482\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 6.00000 6.00000i 0.702247 0.702247i −0.262646 0.964892i $$-0.584595\pi$$
0.964892 + 0.262646i $$0.0845950\pi$$
$$74$$ −3.53553 + 4.94975i −0.410997 + 0.575396i
$$75$$ 1.41421 9.89949i 0.163299 1.14310i
$$76$$ 5.82843 5.82843i 0.668566 0.668566i
$$77$$ 10.3640 + 10.3640i 1.18108 + 1.18108i
$$78$$ 3.17157 3.17157i 0.359110 0.359110i
$$79$$ 9.65685 9.65685i 1.08648 1.08648i 0.0905930 0.995888i $$-0.471124\pi$$
0.995888 0.0905930i $$-0.0288762\pi$$
$$80$$ 2.12132 0.707107i 0.237171 0.0790569i
$$81$$ 11.0000 1.22222
$$82$$ 7.00000 0.773021
$$83$$ −0.828427 0.828427i −0.0909317 0.0909317i 0.660178 0.751109i $$-0.270481\pi$$
−0.751109 + 0.660178i $$0.770481\pi$$
$$84$$ 7.65685i 0.835431i
$$85$$ −3.87868 + 1.29289i −0.420702 + 0.140234i
$$86$$ −7.00000 −0.754829
$$87$$ −18.9706 −2.03386
$$88$$ −3.82843 −0.408112
$$89$$ 7.41421 + 7.41421i 0.785905 + 0.785905i 0.980820 0.194915i $$-0.0624431\pi$$
−0.194915 + 0.980820i $$0.562443\pi$$
$$90$$ −2.12132 + 0.707107i −0.223607 + 0.0745356i
$$91$$ 6.07107 + 6.07107i 0.636421 + 0.636421i
$$92$$ 2.58579i 0.269587i
$$93$$ 11.6569i 1.20876i
$$94$$ 8.24264 + 8.24264i 0.850163 + 0.850163i
$$95$$ −8.24264 + 16.4853i −0.845677 + 1.69135i
$$96$$ −1.41421 1.41421i −0.144338 0.144338i
$$97$$ −7.00000 −0.710742 −0.355371 0.934725i $$-0.615646\pi$$
−0.355371 + 0.934725i $$0.615646\pi$$
$$98$$ −7.65685 −0.773459
$$99$$ 3.82843 0.384771
$$100$$ −4.00000 + 3.00000i −0.400000 + 0.300000i
$$101$$ 11.0711i 1.10161i −0.834633 0.550806i $$-0.814320\pi$$
0.834633 0.550806i $$-0.185680\pi$$
$$102$$ 2.58579 + 2.58579i 0.256031 + 0.256031i
$$103$$ 13.5563 1.33575 0.667873 0.744275i $$-0.267205\pi$$
0.667873 + 0.744275i $$0.267205\pi$$
$$104$$ −2.24264 −0.219909
$$105$$ −5.41421 16.2426i −0.528373 1.58512i
$$106$$ 2.12132 2.12132i 0.206041 0.206041i
$$107$$ −9.07107 + 9.07107i −0.876933 + 0.876933i −0.993216 0.116283i $$-0.962902\pi$$
0.116283 + 0.993216i $$0.462902\pi$$
$$108$$ −2.82843 2.82843i −0.272166 0.272166i
$$109$$ −0.949747 + 0.949747i −0.0909693 + 0.0909693i −0.751127 0.660158i $$-0.770489\pi$$
0.660158 + 0.751127i $$0.270489\pi$$
$$110$$ 8.12132 2.70711i 0.774338 0.258113i
$$111$$ −12.0000 + 2.00000i −1.13899 + 0.189832i
$$112$$ 2.70711 2.70711i 0.255798 0.255798i
$$113$$ −3.82843 −0.360148 −0.180074 0.983653i $$-0.557634\pi$$
−0.180074 + 0.983653i $$0.557634\pi$$
$$114$$ 16.4853 1.54399
$$115$$ −1.82843 5.48528i −0.170502 0.511505i
$$116$$ 6.70711 + 6.70711i 0.622739 + 0.622739i
$$117$$ 2.24264 0.207332
$$118$$ 1.17157 + 1.17157i 0.107852 + 0.107852i
$$119$$ −4.94975 + 4.94975i −0.453743 + 0.453743i
$$120$$ 4.00000 + 2.00000i 0.365148 + 0.182574i
$$121$$ −3.65685 −0.332441
$$122$$ −9.29289 9.29289i −0.841339 0.841339i
$$123$$ 9.89949 + 9.89949i 0.892607 + 0.892607i
$$124$$ 4.12132 4.12132i 0.370105 0.370105i
$$125$$ 6.36396 9.19239i 0.569210 0.822192i
$$126$$ −2.70711 + 2.70711i −0.241168 + 0.241168i
$$127$$ 2.58579 2.58579i 0.229451 0.229451i −0.583012 0.812464i $$-0.698126\pi$$
0.812464 + 0.583012i $$0.198126\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −9.89949 9.89949i −0.871602 0.871602i
$$130$$ 4.75736 1.58579i 0.417248 0.139083i
$$131$$ 0.414214 0.414214i 0.0361900 0.0361900i −0.688780 0.724970i $$-0.741853\pi$$
0.724970 + 0.688780i $$0.241853\pi$$
$$132$$ −5.41421 5.41421i −0.471247 0.471247i
$$133$$ 31.5563i 2.73628i
$$134$$ 1.24264 1.24264i 0.107348 0.107348i
$$135$$ 8.00000 + 4.00000i 0.688530 + 0.344265i
$$136$$ 1.82843i 0.156786i
$$137$$ 8.41421 8.41421i 0.718875 0.718875i −0.249500 0.968375i $$-0.580266\pi$$
0.968375 + 0.249500i $$0.0802663\pi$$
$$138$$ −3.65685 + 3.65685i −0.311292 + 0.311292i
$$139$$ −6.17157 −0.523466 −0.261733 0.965140i $$-0.584294\pi$$
−0.261733 + 0.965140i $$0.584294\pi$$
$$140$$ −3.82843 + 7.65685i −0.323561 + 0.647122i
$$141$$ 23.3137i 1.96337i
$$142$$ 0.343146i 0.0287962i
$$143$$ −8.58579 −0.717980
$$144$$ 1.00000i 0.0833333i
$$145$$ −18.9706 9.48528i −1.57542 0.787710i
$$146$$ −6.00000 6.00000i −0.496564 0.496564i
$$147$$ −10.8284 10.8284i −0.893114 0.893114i
$$148$$ 4.94975 + 3.53553i 0.406867 + 0.290619i
$$149$$ 8.24264i 0.675263i 0.941278 + 0.337632i $$0.109626\pi$$
−0.941278 + 0.337632i $$0.890374\pi$$
$$150$$ −9.89949 1.41421i −0.808290 0.115470i
$$151$$ 12.0000i 0.976546i −0.872691 0.488273i $$-0.837627\pi$$
0.872691 0.488273i $$-0.162373\pi$$
$$152$$ −5.82843 5.82843i −0.472748 0.472748i
$$153$$ 1.82843i 0.147820i
$$154$$ 10.3640 10.3640i 0.835152 0.835152i
$$155$$ −5.82843 + 11.6569i −0.468151 + 0.936301i
$$156$$ −3.17157 3.17157i −0.253929 0.253929i
$$157$$ 5.87868 5.87868i 0.469170 0.469170i −0.432476 0.901646i $$-0.642360\pi$$
0.901646 + 0.432476i $$0.142360\pi$$
$$158$$ −9.65685 9.65685i −0.768258 0.768258i
$$159$$ 6.00000 0.475831
$$160$$ −0.707107 2.12132i −0.0559017 0.167705i
$$161$$ −7.00000 7.00000i −0.551677 0.551677i
$$162$$ 11.0000i 0.864242i
$$163$$ −14.6569 −1.14801 −0.574007 0.818851i $$-0.694612\pi$$
−0.574007 + 0.818851i $$0.694612\pi$$
$$164$$ 7.00000i 0.546608i
$$165$$ 15.3137 + 7.65685i 1.19217 + 0.596085i
$$166$$ −0.828427 + 0.828427i −0.0642984 + 0.0642984i
$$167$$ −1.17157 −0.0906590 −0.0453295 0.998972i $$-0.514434\pi$$
−0.0453295 + 0.998972i $$0.514434\pi$$
$$168$$ 7.65685 0.590739
$$169$$ 7.97056 0.613120
$$170$$ 1.29289 + 3.87868i 0.0991604 + 0.297481i
$$171$$ 5.82843 + 5.82843i 0.445711 + 0.445711i
$$172$$ 7.00000i 0.533745i
$$173$$ 6.02082 6.02082i 0.457754 0.457754i −0.440164 0.897918i $$-0.645080\pi$$
0.897918 + 0.440164i $$0.145080\pi$$
$$174$$ 18.9706i 1.43815i
$$175$$ 2.70711 18.9497i 0.204638 1.43247i
$$176$$ 3.82843i 0.288579i
$$177$$ 3.31371i 0.249074i
$$178$$ 7.41421 7.41421i 0.555719 0.555719i
$$179$$ −14.4853 14.4853i −1.08268 1.08268i −0.996259 0.0864222i $$-0.972457\pi$$
−0.0864222 0.996259i $$-0.527543\pi$$
$$180$$ 0.707107 + 2.12132i 0.0527046 + 0.158114i
$$181$$ 7.65685 0.569129 0.284565 0.958657i $$-0.408151\pi$$
0.284565 + 0.958657i $$0.408151\pi$$
$$182$$ 6.07107 6.07107i 0.450017 0.450017i
$$183$$ 26.2843i 1.94299i
$$184$$ 2.58579 0.190627
$$185$$ −13.0000 4.00000i −0.955779 0.294086i
$$186$$ 11.6569 0.854722
$$187$$ 7.00000i 0.511891i
$$188$$ 8.24264 8.24264i 0.601156 0.601156i
$$189$$ 15.3137 1.11391
$$190$$ 16.4853 + 8.24264i 1.19597 + 0.597984i
$$191$$ 1.53553 + 1.53553i 0.111107 + 0.111107i 0.760475 0.649367i $$-0.224966\pi$$
−0.649367 + 0.760475i $$0.724966\pi$$
$$192$$ −1.41421 + 1.41421i −0.102062 + 0.102062i
$$193$$ 20.4853i 1.47456i −0.675586 0.737281i $$-0.736109\pi$$
0.675586 0.737281i $$-0.263891\pi$$
$$194$$ 7.00000i 0.502571i
$$195$$ 8.97056 + 4.48528i 0.642395 + 0.321198i
$$196$$ 7.65685i 0.546918i
$$197$$ −2.00000 + 2.00000i −0.142494 + 0.142494i −0.774755 0.632261i $$-0.782127\pi$$
0.632261 + 0.774755i $$0.282127\pi$$
$$198$$ 3.82843i 0.272074i
$$199$$ −3.89949 3.89949i −0.276428 0.276428i 0.555253 0.831681i $$-0.312621\pi$$
−0.831681 + 0.555253i $$0.812621\pi$$
$$200$$ 3.00000 + 4.00000i 0.212132 + 0.282843i
$$201$$ 3.51472 0.247909
$$202$$ −11.0711 −0.778958
$$203$$ −36.3137 −2.54872
$$204$$ 2.58579 2.58579i 0.181041 0.181041i
$$205$$ 4.94975 + 14.8492i 0.345705 + 1.03712i
$$206$$ 13.5563i 0.944516i
$$207$$ −2.58579 −0.179725
$$208$$ 2.24264i 0.155499i
$$209$$ −22.3137 22.3137i −1.54347 1.54347i
$$210$$ −16.2426 + 5.41421i −1.12085 + 0.373616i
$$211$$ −9.00000 −0.619586 −0.309793 0.950804i $$-0.600260\pi$$
−0.309793 + 0.950804i $$0.600260\pi$$
$$212$$ −2.12132 2.12132i −0.145693 0.145693i
$$213$$ −0.485281 + 0.485281i −0.0332509 + 0.0332509i
$$214$$ 9.07107 + 9.07107i 0.620085 + 0.620085i
$$215$$ −4.94975 14.8492i −0.337570 1.01271i
$$216$$ −2.82843 + 2.82843i −0.192450 + 0.192450i
$$217$$ 22.3137i 1.51475i
$$218$$ 0.949747 + 0.949747i 0.0643250 + 0.0643250i
$$219$$ 16.9706i 1.14676i
$$220$$ −2.70711 8.12132i −0.182513 0.547539i
$$221$$ 4.10051i 0.275830i
$$222$$ 2.00000 + 12.0000i 0.134231 + 0.805387i
$$223$$ 13.8787 + 13.8787i 0.929385 + 0.929385i 0.997666 0.0682810i $$-0.0217514\pi$$
−0.0682810 + 0.997666i $$0.521751\pi$$
$$224$$ −2.70711 2.70711i −0.180876 0.180876i
$$225$$ −3.00000 4.00000i −0.200000 0.266667i
$$226$$ 3.82843i 0.254663i
$$227$$ −7.48528 −0.496816 −0.248408 0.968656i $$-0.579907\pi$$
−0.248408 + 0.968656i $$0.579907\pi$$
$$228$$ 16.4853i 1.09176i
$$229$$ 1.41421i 0.0934539i −0.998908 0.0467269i $$-0.985121\pi$$
0.998908 0.0467269i $$-0.0148791\pi$$
$$230$$ −5.48528 + 1.82843i −0.361689 + 0.120563i
$$231$$ 29.3137 1.92870
$$232$$ 6.70711 6.70711i 0.440343 0.440343i
$$233$$ 0.0710678 0.0710678i 0.00465581 0.00465581i −0.704775 0.709431i $$-0.748952\pi$$
0.709431 + 0.704775i $$0.248952\pi$$
$$234$$ 2.24264i 0.146606i
$$235$$ −11.6569 + 23.3137i −0.760409 + 1.52082i
$$236$$ 1.17157 1.17157i 0.0762629 0.0762629i
$$237$$ 27.3137i 1.77422i
$$238$$ 4.94975 + 4.94975i 0.320844 + 0.320844i
$$239$$ 7.05025 7.05025i 0.456043 0.456043i −0.441311 0.897354i $$-0.645487\pi$$
0.897354 + 0.441311i $$0.145487\pi$$
$$240$$ 2.00000 4.00000i 0.129099 0.258199i
$$241$$ 0.757359 + 0.757359i 0.0487858 + 0.0487858i 0.731079 0.682293i $$-0.239017\pi$$
−0.682293 + 0.731079i $$0.739017\pi$$
$$242$$ 3.65685i 0.235071i
$$243$$ 7.07107 7.07107i 0.453609 0.453609i
$$244$$ −9.29289 + 9.29289i −0.594917 + 0.594917i
$$245$$ −5.41421 16.2426i −0.345901 1.03770i
$$246$$ 9.89949 9.89949i 0.631169 0.631169i
$$247$$ −13.0711 13.0711i −0.831692 0.831692i
$$248$$ −4.12132 4.12132i −0.261704 0.261704i
$$249$$ −2.34315 −0.148491
$$250$$ −9.19239 6.36396i −0.581378 0.402492i
$$251$$ −17.8995 + 17.8995i −1.12981 + 1.12981i −0.139598 + 0.990208i $$0.544581\pi$$
−0.990208 + 0.139598i $$0.955419\pi$$
$$252$$ 2.70711 + 2.70711i 0.170532 + 0.170532i
$$253$$ 9.89949 0.622376
$$254$$ −2.58579 2.58579i −0.162247 0.162247i
$$255$$ −3.65685 + 7.31371i −0.229001 + 0.458002i
$$256$$ 1.00000 0.0625000
$$257$$ 18.8284 1.17449 0.587243 0.809411i $$-0.300213\pi$$
0.587243 + 0.809411i $$0.300213\pi$$
$$258$$ −9.89949 + 9.89949i −0.616316 + 0.616316i
$$259$$ −22.9706 + 3.82843i −1.42732 + 0.237887i
$$260$$ −1.58579 4.75736i −0.0983463 0.295039i
$$261$$ −6.70711 + 6.70711i −0.415159 + 0.415159i
$$262$$ −0.414214 0.414214i −0.0255902 0.0255902i
$$263$$ −14.6066 + 14.6066i −0.900682 + 0.900682i −0.995495 0.0948134i $$-0.969775\pi$$
0.0948134 + 0.995495i $$0.469775\pi$$
$$264$$ −5.41421 + 5.41421i −0.333222 + 0.333222i
$$265$$ 6.00000 + 3.00000i 0.368577 + 0.184289i
$$266$$ 31.5563 1.93484
$$267$$ 20.9706 1.28338
$$268$$ −1.24264 1.24264i −0.0759064 0.0759064i
$$269$$ 17.7990i 1.08522i 0.839984 + 0.542612i $$0.182565\pi$$
−0.839984 + 0.542612i $$0.817435\pi$$
$$270$$ 4.00000 8.00000i 0.243432 0.486864i
$$271$$ −3.07107 −0.186554 −0.0932770 0.995640i $$-0.529734\pi$$
−0.0932770 + 0.995640i $$0.529734\pi$$
$$272$$ −1.82843 −0.110865
$$273$$ 17.1716 1.03927
$$274$$ −8.41421 8.41421i −0.508321 0.508321i
$$275$$ 11.4853 + 15.3137i 0.692589 + 0.923451i
$$276$$ 3.65685 + 3.65685i 0.220117 + 0.220117i
$$277$$ 7.79899i 0.468596i −0.972165 0.234298i $$-0.924721\pi$$
0.972165 0.234298i $$-0.0752791\pi$$
$$278$$ 6.17157i 0.370146i
$$279$$ 4.12132 + 4.12132i 0.246737 + 0.246737i
$$280$$ 7.65685 + 3.82843i 0.457585 + 0.228792i
$$281$$ 4.00000 + 4.00000i 0.238620 + 0.238620i 0.816279 0.577659i $$-0.196033\pi$$
−0.577659 + 0.816279i $$0.696033\pi$$
$$282$$ 23.3137 1.38831
$$283$$ 28.0000 1.66443 0.832214 0.554455i $$-0.187073\pi$$
0.832214 + 0.554455i $$0.187073\pi$$
$$284$$ 0.343146 0.0203620
$$285$$ 11.6569 + 34.9706i 0.690492 + 2.07148i
$$286$$ 8.58579i 0.507688i
$$287$$ 18.9497 + 18.9497i 1.11857 + 1.11857i
$$288$$ −1.00000 −0.0589256
$$289$$ −13.6569 −0.803344
$$290$$ −9.48528 + 18.9706i −0.556995 + 1.11399i
$$291$$ −9.89949 + 9.89949i −0.580319 + 0.580319i
$$292$$ −6.00000 + 6.00000i −0.351123 + 0.351123i
$$293$$ −1.77817 1.77817i −0.103882 0.103882i 0.653255 0.757138i $$-0.273403\pi$$
−0.757138 + 0.653255i $$0.773403\pi$$
$$294$$ −10.8284 + 10.8284i −0.631527 + 0.631527i
$$295$$ −1.65685 + 3.31371i −0.0964658 + 0.192932i
$$296$$ 3.53553 4.94975i 0.205499 0.287698i
$$297$$ −10.8284 + 10.8284i −0.628329 + 0.628329i
$$298$$ 8.24264 0.477483
$$299$$ 5.79899 0.335364
$$300$$ −1.41421 + 9.89949i −0.0816497 + 0.571548i
$$301$$ −18.9497 18.9497i −1.09225 1.09225i
$$302$$ −12.0000 −0.690522
$$303$$ −15.6569 15.6569i −0.899463 0.899463i
$$304$$ −5.82843 + 5.82843i −0.334283 + 0.334283i
$$305$$ 13.1421 26.2843i 0.752516 1.50503i
$$306$$ 1.82843 0.104524
$$307$$ −1.89949 1.89949i −0.108410 0.108410i 0.650821 0.759231i $$-0.274425\pi$$
−0.759231 + 0.650821i $$0.774425\pi$$
$$308$$ −10.3640 10.3640i −0.590541 0.590541i
$$309$$ 19.1716 19.1716i 1.09063 1.09063i
$$310$$ 11.6569 + 5.82843i 0.662065 + 0.331032i
$$311$$ −11.7782 + 11.7782i −0.667879 + 0.667879i −0.957225 0.289346i $$-0.906562\pi$$
0.289346 + 0.957225i $$0.406562\pi$$
$$312$$ −3.17157 + 3.17157i −0.179555 + 0.179555i
$$313$$ 0.686292i 0.0387915i −0.999812 0.0193957i $$-0.993826\pi$$
0.999812 0.0193957i $$-0.00617424\pi$$
$$314$$ −5.87868 5.87868i −0.331753 0.331753i
$$315$$ −7.65685 3.82843i −0.431415 0.215707i
$$316$$ −9.65685 + 9.65685i −0.543240 + 0.543240i
$$317$$ 15.5355 + 15.5355i 0.872563 + 0.872563i 0.992751 0.120189i $$-0.0383499\pi$$
−0.120189 + 0.992751i $$0.538350\pi$$
$$318$$ 6.00000i 0.336463i
$$319$$ 25.6777 25.6777i 1.43767 1.43767i
$$320$$ −2.12132 + 0.707107i −0.118585 + 0.0395285i
$$321$$ 25.6569i 1.43203i
$$322$$ −7.00000 + 7.00000i −0.390095 + 0.390095i
$$323$$ 10.6569 10.6569i 0.592963 0.592963i
$$324$$ −11.0000 −0.611111
$$325$$ 6.72792 + 8.97056i 0.373198 + 0.497597i
$$326$$ 14.6569i 0.811768i
$$327$$ 2.68629i 0.148552i
$$328$$ −7.00000 −0.386510
$$329$$ 44.6274i 2.46039i
$$330$$ 7.65685 15.3137i 0.421496 0.842992i
$$331$$ 2.58579 + 2.58579i 0.142128 + 0.142128i 0.774591 0.632463i $$-0.217956\pi$$
−0.632463 + 0.774591i $$0.717956\pi$$
$$332$$ 0.828427 + 0.828427i 0.0454658 + 0.0454658i
$$333$$ −3.53553 + 4.94975i −0.193746 + 0.271244i
$$334$$ 1.17157i 0.0641056i
$$335$$ 3.51472 + 1.75736i 0.192030 + 0.0960148i
$$336$$ 7.65685i 0.417716i
$$337$$ 5.65685 + 5.65685i 0.308148 + 0.308148i 0.844191 0.536043i $$-0.180081\pi$$
−0.536043 + 0.844191i $$0.680081\pi$$
$$338$$ 7.97056i 0.433541i
$$339$$ −5.41421 + 5.41421i −0.294060 + 0.294060i
$$340$$ 3.87868 1.29289i 0.210351 0.0701170i
$$341$$ −15.7782 15.7782i −0.854436 0.854436i
$$342$$ 5.82843 5.82843i 0.315165 0.315165i
$$343$$ −1.77817 1.77817i −0.0960124 0.0960124i
$$344$$ 7.00000 0.377415
$$345$$ −10.3431 5.17157i −0.556856 0.278428i
$$346$$ −6.02082 6.02082i −0.323681 0.323681i
$$347$$ 17.3137i 0.929449i 0.885455 + 0.464724i $$0.153847\pi$$
−0.885455 + 0.464724i $$0.846153\pi$$
$$348$$ 18.9706 1.01693
$$349$$ 4.14214i 0.221723i −0.993836 0.110862i $$-0.964639\pi$$
0.993836 0.110862i $$-0.0353611\pi$$
$$350$$ −18.9497 2.70711i −1.01291 0.144701i
$$351$$ −6.34315 + 6.34315i −0.338572 + 0.338572i
$$352$$ 3.82843 0.204056
$$353$$ 7.34315 0.390836 0.195418 0.980720i $$-0.437394\pi$$
0.195418 + 0.980720i $$0.437394\pi$$
$$354$$ 3.31371 0.176122
$$355$$ −0.727922 + 0.242641i −0.0386341 + 0.0128780i
$$356$$ −7.41421 7.41421i −0.392953 0.392953i
$$357$$ 14.0000i 0.740959i
$$358$$ −14.4853 + 14.4853i −0.765571 + 0.765571i
$$359$$ 30.5269i 1.61115i 0.592495 + 0.805574i $$0.298143\pi$$
−0.592495 + 0.805574i $$0.701857\pi$$
$$360$$ 2.12132 0.707107i 0.111803 0.0372678i
$$361$$ 48.9411i 2.57585i
$$362$$ 7.65685i 0.402435i
$$363$$ −5.17157 + 5.17157i −0.271437 + 0.271437i
$$364$$ −6.07107 6.07107i −0.318210 0.318210i
$$365$$ 8.48528 16.9706i 0.444140 0.888280i
$$366$$ −26.2843 −1.37390
$$367$$ 13.0919 13.0919i 0.683391 0.683391i −0.277372 0.960763i $$-0.589463\pi$$
0.960763 + 0.277372i $$0.0894634\pi$$
$$368$$ 2.58579i 0.134793i
$$369$$ 7.00000 0.364405
$$370$$ −4.00000 + 13.0000i −0.207950 + 0.675838i
$$371$$ 11.4853 0.596286
$$372$$ 11.6569i 0.604380i
$$373$$ −10.8284 + 10.8284i −0.560675 + 0.560675i −0.929499 0.368824i $$-0.879760\pi$$
0.368824 + 0.929499i $$0.379760\pi$$
$$374$$ −7.00000 −0.361961
$$375$$ −4.00000 22.0000i −0.206559 1.13608i
$$376$$ −8.24264 8.24264i −0.425082 0.425082i
$$377$$ 15.0416 15.0416i 0.774683 0.774683i
$$378$$ 15.3137i 0.787652i
$$379$$ 18.0000i 0.924598i 0.886724 + 0.462299i $$0.152975\pi$$
−0.886724 + 0.462299i $$0.847025\pi$$
$$380$$ 8.24264 16.4853i 0.422839 0.845677i
$$381$$ 7.31371i 0.374693i
$$382$$ 1.53553 1.53553i 0.0785647 0.0785647i
$$383$$ 16.5858i 0.847494i −0.905781 0.423747i $$-0.860715\pi$$
0.905781 0.423747i $$-0.139285\pi$$
$$384$$ 1.41421 + 1.41421i 0.0721688 + 0.0721688i
$$385$$ 29.3137 + 14.6569i 1.49396 + 0.746982i
$$386$$ −20.4853 −1.04267
$$387$$ −7.00000 −0.355830
$$388$$ 7.00000 0.355371
$$389$$ −3.77817 + 3.77817i −0.191561 + 0.191561i −0.796370 0.604809i $$-0.793249\pi$$
0.604809 + 0.796370i $$0.293249\pi$$
$$390$$ 4.48528 8.97056i 0.227121 0.454242i
$$391$$ 4.72792i 0.239101i
$$392$$ 7.65685 0.386730
$$393$$ 1.17157i 0.0590980i
$$394$$ 2.00000 + 2.00000i 0.100759 + 0.100759i
$$395$$ 13.6569 27.3137i 0.687151 1.37430i
$$396$$ −3.82843 −0.192386
$$397$$ 8.48528 + 8.48528i 0.425864 + 0.425864i 0.887217 0.461353i $$-0.152636\pi$$
−0.461353 + 0.887217i $$0.652636\pi$$
$$398$$ −3.89949 + 3.89949i −0.195464 + 0.195464i
$$399$$ 44.6274 + 44.6274i 2.23417 + 2.23417i
$$400$$ 4.00000 3.00000i 0.200000 0.150000i
$$401$$ −7.07107 + 7.07107i −0.353112 + 0.353112i −0.861266 0.508154i $$-0.830328\pi$$
0.508154 + 0.861266i $$0.330328\pi$$
$$402$$ 3.51472i 0.175298i
$$403$$ −9.24264 9.24264i −0.460409 0.460409i
$$404$$ 11.0711i 0.550806i
$$405$$ 23.3345 7.77817i 1.15950 0.386501i
$$406$$ 36.3137i 1.80222i
$$407$$ 13.5355 18.9497i 0.670932 0.939304i
$$408$$ −2.58579 2.58579i −0.128016 0.128016i
$$409$$ −19.7990 19.7990i −0.978997 0.978997i 0.0207869 0.999784i $$-0.493383\pi$$
−0.999784 + 0.0207869i $$0.993383\pi$$
$$410$$ 14.8492 4.94975i 0.733352 0.244451i
$$411$$ 23.7990i 1.17392i
$$412$$ −13.5563 −0.667873
$$413$$ 6.34315i 0.312126i
$$414$$ 2.58579i 0.127084i
$$415$$ −2.34315 1.17157i −0.115021 0.0575103i
$$416$$ 2.24264 0.109955
$$417$$ −8.72792 + 8.72792i −0.427408 + 0.427408i
$$418$$ −22.3137 + 22.3137i −1.09140 + 1.09140i
$$419$$ 26.9706i 1.31760i −0.752319 0.658799i $$-0.771065\pi$$
0.752319 0.658799i $$-0.228935\pi$$
$$420$$ 5.41421 + 16.2426i 0.264187 + 0.792560i
$$421$$ −25.3137 + 25.3137i −1.23371 + 1.23371i −0.271188 + 0.962526i $$0.587417\pi$$
−0.962526 + 0.271188i $$0.912583\pi$$
$$422$$ 9.00000i 0.438113i
$$423$$ 8.24264 + 8.24264i 0.400771 + 0.400771i
$$424$$ −2.12132 + 2.12132i −0.103020 + 0.103020i
$$425$$ −7.31371 + 5.48528i −0.354767 + 0.266075i
$$426$$ 0.485281 + 0.485281i 0.0235120 + 0.0235120i
$$427$$ 50.3137i 2.43485i
$$428$$ 9.07107 9.07107i 0.438467 0.438467i
$$429$$ −12.1421 + 12.1421i −0.586228 + 0.586228i
$$430$$ −14.8492 + 4.94975i −0.716094 + 0.238698i
$$431$$ −20.5061 + 20.5061i −0.987744 + 0.987744i −0.999926 0.0121819i $$-0.996122\pi$$
0.0121819 + 0.999926i $$0.496122\pi$$
$$432$$ 2.82843 + 2.82843i 0.136083 + 0.136083i
$$433$$ 5.14214 + 5.14214i 0.247115 + 0.247115i 0.819786 0.572670i $$-0.194093\pi$$
−0.572670 + 0.819786i $$0.694093\pi$$
$$434$$ 22.3137 1.07109
$$435$$ −40.2426 + 13.4142i −1.92949 + 0.643162i
$$436$$ 0.949747 0.949747i 0.0454847 0.0454847i
$$437$$ 15.0711 + 15.0711i 0.720947 + 0.720947i
$$438$$ −16.9706 −0.810885
$$439$$ 2.22183 + 2.22183i 0.106042 + 0.106042i 0.758137 0.652095i $$-0.226110\pi$$
−0.652095 + 0.758137i $$0.726110\pi$$
$$440$$ −8.12132 + 2.70711i −0.387169 + 0.129056i
$$441$$ −7.65685 −0.364612
$$442$$ −4.10051 −0.195041
$$443$$ −5.34315 + 5.34315i −0.253861 + 0.253861i −0.822551 0.568691i $$-0.807450\pi$$
0.568691 + 0.822551i $$0.307450\pi$$
$$444$$ 12.0000 2.00000i 0.569495 0.0949158i
$$445$$ 20.9706 + 10.4853i 0.994100 + 0.497050i
$$446$$ 13.8787 13.8787i 0.657175 0.657175i
$$447$$ 11.6569 + 11.6569i 0.551350 + 0.551350i
$$448$$ −2.70711 + 2.70711i −0.127899 + 0.127899i
$$449$$ −25.6274 + 25.6274i −1.20943 + 1.20943i −0.238222 + 0.971211i $$0.576565\pi$$
−0.971211 + 0.238222i $$0.923435\pi$$
$$450$$ −4.00000 + 3.00000i −0.188562 + 0.141421i
$$451$$ −26.7990 −1.26192
$$452$$ 3.82843 0.180074
$$453$$ −16.9706 16.9706i −0.797347 0.797347i
$$454$$ 7.48528i 0.351302i
$$455$$ 17.1716 + 8.58579i 0.805016 + 0.402508i
$$456$$ −16.4853 −0.771994
$$457$$ −3.68629 −0.172437 −0.0862187 0.996276i $$-0.527478\pi$$
−0.0862187 + 0.996276i $$0.527478\pi$$
$$458$$ −1.41421 −0.0660819
$$459$$ −5.17157 5.17157i −0.241388 0.241388i
$$460$$ 1.82843 + 5.48528i 0.0852509 + 0.255753i
$$461$$ 10.4645 + 10.4645i 0.487379 + 0.487379i 0.907478 0.420099i $$-0.138005\pi$$
−0.420099 + 0.907478i $$0.638005\pi$$
$$462$$ 29.3137i 1.36380i
$$463$$ 29.9411i 1.39148i 0.718293 + 0.695741i $$0.244924\pi$$
−0.718293 + 0.695741i $$0.755076\pi$$
$$464$$ −6.70711 6.70711i −0.311370 0.311370i
$$465$$ 8.24264 + 24.7279i 0.382243 + 1.14673i
$$466$$ −0.0710678 0.0710678i −0.00329215 0.00329215i
$$467$$ 2.31371 0.107066 0.0535328 0.998566i $$-0.482952\pi$$
0.0535328 + 0.998566i $$0.482952\pi$$
$$468$$ −2.24264 −0.103666
$$469$$ 6.72792 0.310667
$$470$$ 23.3137 + 11.6569i 1.07538 + 0.537691i
$$471$$ 16.6274i 0.766151i
$$472$$ −1.17157 1.17157i −0.0539260 0.0539260i
$$473$$ 26.7990 1.23222
$$474$$ −27.3137 −1.25456
$$475$$ −5.82843 + 40.7990i −0.267427 + 1.87199i
$$476$$ 4.94975 4.94975i 0.226871 0.226871i
$$477$$ 2.12132 2.12132i 0.0971286 0.0971286i
$$478$$ −7.05025 7.05025i −0.322471 0.322471i
$$479$$ 15.5563 15.5563i 0.710788 0.710788i −0.255912 0.966700i $$-0.582376\pi$$
0.966700 + 0.255912i $$0.0823758\pi$$
$$480$$ −4.00000 2.00000i −0.182574 0.0912871i
$$481$$ 7.92893 11.1005i 0.361528 0.506139i
$$482$$ 0.757359 0.757359i 0.0344968 0.0344968i
$$483$$ −19.7990 −0.900885
$$484$$ 3.65685 0.166221
$$485$$ −14.8492 + 4.94975i −0.674269 + 0.224756i
$$486$$ −7.07107 7.07107i −0.320750 0.320750i
$$487$$ 26.9706 1.22215 0.611076 0.791572i $$-0.290737\pi$$
0.611076 + 0.791572i $$0.290737\pi$$
$$488$$ 9.29289 + 9.29289i 0.420670 + 0.420670i
$$489$$ −20.7279 + 20.7279i −0.937349 + 0.937349i
$$490$$ −16.2426 + 5.41421i −0.733768 + 0.244589i
$$491$$ 17.7990 0.803257 0.401629 0.915803i $$-0.368444\pi$$
0.401629 + 0.915803i $$0.368444\pi$$
$$492$$ −9.89949 9.89949i −0.446304 0.446304i
$$493$$ 12.2635 + 12.2635i 0.552318 + 0.552318i
$$494$$ −13.0711 + 13.0711i −0.588095 + 0.588095i
$$495$$ 8.12132 2.70711i 0.365026 0.121675i
$$496$$ −4.12132 + 4.12132i −0.185053 + 0.185053i
$$497$$ −0.928932 + 0.928932i −0.0416683 + 0.0416683i
$$498$$ 2.34315i 0.104999i
$$499$$ −10.2426 10.2426i −0.458524 0.458524i 0.439647 0.898171i $$-0.355104\pi$$
−0.898171 + 0.439647i $$0.855104\pi$$
$$500$$ −6.36396 + 9.19239i −0.284605 + 0.411096i
$$501$$ −1.65685 + 1.65685i −0.0740228 + 0.0740228i
$$502$$ 17.8995 + 17.8995i 0.798894 + 0.798894i
$$503$$ 32.5858i 1.45293i −0.687204 0.726464i $$-0.741162\pi$$
0.687204 0.726464i $$-0.258838\pi$$
$$504$$ 2.70711 2.70711i 0.120584 0.120584i
$$505$$ −7.82843 23.4853i −0.348360 1.04508i
$$506$$ 9.89949i 0.440086i
$$507$$ 11.2721 11.2721i 0.500611 0.500611i
$$508$$ −2.58579 + 2.58579i −0.114726 + 0.114726i
$$509$$ 1.27208 0.0563839 0.0281919 0.999603i $$-0.491025\pi$$
0.0281919 + 0.999603i $$0.491025\pi$$
$$510$$ 7.31371 + 3.65685i 0.323856 + 0.161928i
$$511$$ 32.4853i 1.43706i
$$512$$ 1.00000i 0.0441942i
$$513$$ −32.9706 −1.45569
$$514$$ 18.8284i 0.830486i
$$515$$ 28.7574 9.58579i 1.26720 0.422400i
$$516$$ 9.89949 + 9.89949i 0.435801 + 0.435801i
$$517$$ −31.5563 31.5563i −1.38785 1.38785i
$$518$$ 3.82843 + 22.9706i 0.168211 + 1.00927i
$$519$$ 17.0294i 0.747509i
$$520$$ −4.75736 + 1.58579i −0.208624 + 0.0695413i
$$521$$ 27.6274i 1.21038i −0.796081 0.605190i $$-0.793097\pi$$
0.796081 0.605190i $$-0.206903\pi$$
$$522$$ 6.70711 + 6.70711i 0.293562 + 0.293562i
$$523$$ 43.6569i 1.90898i 0.298241 + 0.954490i $$0.403600\pi$$
−0.298241 + 0.954490i $$0.596400\pi$$
$$524$$ −0.414214 + 0.414214i −0.0180950 + 0.0180950i
$$525$$ −22.9706 30.6274i −1.00252 1.33669i
$$526$$ 14.6066 + 14.6066i 0.636878 + 0.636878i
$$527$$ 7.53553 7.53553i 0.328253 0.328253i
$$528$$ 5.41421 + 5.41421i 0.235623 + 0.235623i
$$529$$ 16.3137 0.709292
$$530$$ 3.00000 6.00000i 0.130312 0.260623i
$$531$$ 1.17157 + 1.17157i 0.0508419 + 0.0508419i
$$532$$ 31.5563i 1.36814i
$$533$$ −15.6985 −0.679977
$$534$$ 20.9706i 0.907485i
$$535$$ −12.8284 + 25.6569i −0.554621 + 1.10924i
$$536$$ −1.24264 + 1.24264i −0.0536739 + 0.0536739i
$$537$$ −40.9706 −1.76801
$$538$$ 17.7990 0.767369
$$539$$ 29.3137 1.26263
$$540$$ −8.00000 4.00000i −0.344265 0.172133i
$$541$$ −27.7990 27.7990i −1.19517 1.19517i −0.975595 0.219577i $$-0.929532\pi$$
−0.219577 0.975595i $$-0.570468\pi$$
$$542$$ 3.07107i 0.131914i
$$543$$ 10.8284 10.8284i 0.464692 0.464692i
$$544$$ 1.82843i 0.0783932i
$$545$$ −1.34315 + 2.68629i −0.0575340 + 0.115068i
$$546$$ 17.1716i 0.734875i
$$547$$ 27.8284i 1.18986i 0.803778 + 0.594929i $$0.202820\pi$$
−0.803778 + 0.594929i $$0.797180\pi$$
$$548$$ −8.41421 + 8.41421i −0.359437 + 0.359437i
$$549$$ −9.29289 9.29289i −0.396611 0.396611i
$$550$$ 15.3137 11.4853i 0.652979 0.489734i
$$551$$ 78.1838 3.33074
$$552$$ 3.65685 3.65685i 0.155646 0.155646i
$$553$$ 52.2843i 2.22335i
$$554$$ −7.79899 −0.331347
$$555$$ −24.0416 + 12.7279i −1.02051 + 0.540270i
$$556$$ 6.17157 0.261733
$$557$$ 23.2132i 0.983575i −0.870715 0.491787i $$-0.836344\pi$$
0.870715 0.491787i $$-0.163656\pi$$
$$558$$ 4.12132 4.12132i 0.174469 0.174469i
$$559$$ 15.6985 0.663975
$$560$$ 3.82843 7.65685i 0.161781 0.323561i
$$561$$ −9.89949 9.89949i −0.417957 0.417957i
$$562$$ 4.00000 4.00000i 0.168730 0.168730i
$$563$$ 24.1127i 1.01623i −0.861290 0.508115i $$-0.830343\pi$$
0.861290 0.508115i $$-0.169657\pi$$
$$564$$ 23.3137i 0.981684i
$$565$$ −8.12132 + 2.70711i −0.341667 + 0.113889i
$$566$$ 28.0000i 1.17693i
$$567$$ 29.7782 29.7782i 1.25057 1.25057i
$$568$$ 0.343146i 0.0143981i
$$569$$ −1.68629 1.68629i −0.0706930 0.0706930i 0.670876 0.741569i $$-0.265918\pi$$
−0.741569 + 0.670876i $$0.765918\pi$$
$$570$$ 34.9706 11.6569i 1.46476 0.488252i
$$571$$ 46.7990 1.95848 0.979238 0.202712i $$-0.0649755\pi$$
0.979238 + 0.202712i $$0.0649755\pi$$
$$572$$ 8.58579 0.358990
$$573$$ 4.34315 0.181438
$$574$$ 18.9497 18.9497i 0.790947 0.790947i
$$575$$ −7.75736 10.3431i −0.323504 0.431339i
$$576$$ 1.00000i 0.0416667i
$$577$$ 21.6569 0.901587 0.450793 0.892628i $$-0.351141\pi$$
0.450793 + 0.892628i $$0.351141\pi$$
$$578$$ 13.6569i 0.568050i
$$579$$ −28.9706 28.9706i −1.20398 1.20398i
$$580$$ 18.9706 + 9.48528i 0.787710 + 0.393855i
$$581$$ −4.48528 −0.186081
$$582$$ 9.89949 + 9.89949i 0.410347 + 0.410347i
$$583$$ −8.12132 + 8.12132i −0.336351 + 0.336351i
$$584$$ 6.00000 + 6.00000i 0.248282 + 0.248282i
$$585$$ 4.75736 1.58579i 0.196693 0.0655642i
$$586$$ −1.77817 + 1.77817i −0.0734557 + 0.0734557i
$$587$$ 4.45584i 0.183912i 0.995763 + 0.0919562i $$0.0293120\pi$$
−0.995763 + 0.0919562i $$0.970688\pi$$
$$588$$ 10.8284 + 10.8284i 0.446557 + 0.446557i
$$589$$ 48.0416i 1.97952i
$$590$$ 3.31371 + 1.65685i 0.136423 + 0.0682116i
$$591$$ 5.65685i 0.232692i
$$592$$ −4.94975 3.53553i −0.203433 0.145310i
$$593$$ −26.1421 26.1421i −1.07353 1.07353i −0.997073 0.0764559i $$-0.975640\pi$$
−0.0764559 0.997073i $$-0.524360\pi$$
$$594$$ 10.8284 + 10.8284i 0.444296 + 0.444296i
$$595$$ −7.00000 + 14.0000i −0.286972 + 0.573944i
$$596$$ 8.24264i 0.337632i
$$597$$ −11.0294 −0.451405
$$598$$ 5.79899i 0.237138i
$$599$$ 33.7574i 1.37929i 0.724148 + 0.689644i $$0.242233\pi$$
−0.724148 + 0.689644i $$0.757767\pi$$
$$600$$ 9.89949 + 1.41421i 0.404145 + 0.0577350i
$$601$$ −16.5147 −0.673649 −0.336825 0.941567i $$-0.609353\pi$$
−0.336825 + 0.941567i $$0.609353\pi$$
$$602$$ −18.9497 + 18.9497i −0.772334 + 0.772334i
$$603$$ 1.24264 1.24264i 0.0506042 0.0506042i
$$604$$ 12.0000i 0.488273i
$$605$$ −7.75736 + 2.58579i −0.315382 + 0.105127i
$$606$$ −15.6569 + 15.6569i −0.636016 + 0.636016i
$$607$$ 34.1838i 1.38748i 0.720227 + 0.693738i $$0.244037\pi$$
−0.720227 + 0.693738i $$0.755963\pi$$
$$608$$ 5.82843 + 5.82843i 0.236374 + 0.236374i
$$609$$ −51.3553 + 51.3553i −2.08102 + 2.08102i
$$610$$ −26.2843 13.1421i −1.06422 0.532110i
$$611$$ −18.4853 18.4853i −0.747834 0.747834i
$$612$$ 1.82843i 0.0739098i
$$613$$ −12.1213 + 12.1213i −0.489576 + 0.489576i −0.908172 0.418597i $$-0.862522\pi$$
0.418597 + 0.908172i $$0.362522\pi$$
$$614$$ −1.89949 + 1.89949i −0.0766574 + 0.0766574i
$$615$$ 28.0000 + 14.0000i 1.12907 + 0.564534i
$$616$$ −10.3640 + 10.3640i −0.417576 + 0.417576i
$$617$$ −27.7279 27.7279i −1.11628 1.11628i −0.992282 0.124002i $$-0.960427\pi$$
−0.124002 0.992282i $$-0.539573\pi$$
$$618$$ −19.1716 19.1716i −0.771194 0.771194i
$$619$$ 46.5980 1.87293 0.936465 0.350760i $$-0.114077\pi$$
0.936465 + 0.350760i $$0.114077\pi$$
$$620$$ 5.82843 11.6569i 0.234075 0.468151i
$$621$$ 7.31371 7.31371i 0.293489 0.293489i
$$622$$ 11.7782 + 11.7782i 0.472262 + 0.472262i
$$623$$ 40.1421 1.60826
$$624$$ 3.17157 + 3.17157i 0.126965 + 0.126965i
$$625$$ 7.00000 24.0000i 0.280000 0.960000i
$$626$$ −0.686292 −0.0274297
$$627$$ −63.1127 −2.52048
$$628$$ −5.87868 + 5.87868i −0.234585 + 0.234585i
$$629$$ 9.05025 + 6.46447i 0.360857 + 0.257755i
$$630$$ −3.82843 + 7.65685i −0.152528 + 0.305056i
$$631$$ −18.8492 + 18.8492i −0.750376 + 0.750376i −0.974549 0.224173i $$-0.928032\pi$$
0.224173 + 0.974549i $$0.428032\pi$$
$$632$$ 9.65685 + 9.65685i 0.384129 + 0.384129i
$$633$$ −12.7279 + 12.7279i −0.505889 + 0.505889i
$$634$$ 15.5355 15.5355i 0.616995 0.616995i
$$635$$ 3.65685 7.31371i 0.145118 0.290236i
$$636$$ −6.00000 −0.237915
$$637$$ 17.1716 0.680362
$$638$$ −25.6777 25.6777i −1.01659 1.01659i
$$639$$ 0.343146i 0.0135746i
$$640$$ 0.707107 + 2.12132i 0.0279508 + 0.0838525i
$$641$$ 25.2843 0.998669 0.499334 0.866409i $$-0.333578\pi$$
0.499334 + 0.866409i $$0.333578\pi$$
$$642$$ 25.6569 1.01260
$$643$$ −24.5147 −0.966766 −0.483383 0.875409i $$-0.660592\pi$$
−0.483383 + 0.875409i $$0.660592\pi$$
$$644$$ 7.00000 + 7.00000i 0.275839 + 0.275839i
$$645$$ −28.0000 14.0000i −1.10250 0.551249i
$$646$$ −10.6569 10.6569i −0.419288 0.419288i
$$647$$ 27.3137i 1.07381i −0.843642 0.536906i $$-0.819593\pi$$
0.843642 0.536906i $$-0.180407\pi$$
$$648$$ 11.0000i 0.432121i
$$649$$ −4.48528 4.48528i −0.176063 0.176063i
$$650$$ 8.97056 6.72792i 0.351854 0.263891i
$$651$$ 31.5563 + 31.5563i 1.23679 + 1.23679i
$$652$$ 14.6569 0.574007
$$653$$ −19.6569 −0.769232 −0.384616 0.923077i $$-0.625666\pi$$
−0.384616 + 0.923077i $$0.625666\pi$$
$$654$$ 2.68629 0.105042
$$655$$ 0.585786 1.17157i 0.0228886 0.0457771i
$$656$$ 7.00000i 0.273304i
$$657$$ −6.00000 6.00000i −0.234082 0.234082i
$$658$$ 44.6274 1.73976
$$659$$ −20.1421 −0.784626 −0.392313 0.919832i $$-0.628325\pi$$
−0.392313 + 0.919832i $$0.628325\pi$$
$$660$$ −15.3137 7.65685i −0.596085 0.298043i
$$661$$ −20.2635 + 20.2635i −0.788157 + 0.788157i −0.981192 0.193035i $$-0.938167\pi$$
0.193035 + 0.981192i $$0.438167\pi$$
$$662$$ 2.58579 2.58579i 0.100499 0.100499i
$$663$$ −5.79899 5.79899i −0.225214 0.225214i
$$664$$ 0.828427 0.828427i 0.0321492 0.0321492i
$$665$$ 22.3137 + 66.9411i 0.865289 + 2.59587i
$$666$$ 4.94975 + 3.53553i 0.191799 + 0.136999i
$$667$$ −17.3431 + 17.3431i −0.671529 + 0.671529i
$$668$$ 1.17157 0.0453295
$$669$$ 39.2548 1.51768
$$670$$ 1.75736 3.51472i 0.0678927 0.135785i
$$671$$ 35.5772 + 35.5772i 1.37344 + 1.37344i
$$672$$ −7.65685 −0.295370
$$673$$ −10.5147 10.5147i −0.405313 0.405313i 0.474788 0.880100i $$-0.342525\pi$$
−0.880100 + 0.474788i $$0.842525\pi$$
$$674$$ 5.65685 5.65685i 0.217894 0.217894i
$$675$$ 19.7990 + 2.82843i 0.762063 + 0.108866i
$$676$$ −7.97056 −0.306560
$$677$$ −13.5147 13.5147i −0.519413 0.519413i 0.397981 0.917394i $$-0.369711\pi$$
−0.917394 + 0.397981i $$0.869711\pi$$
$$678$$ 5.41421 + 5.41421i 0.207932 + 0.207932i
$$679$$ −18.9497 + 18.9497i −0.727225 + 0.727225i
$$680$$ −1.29289 3.87868i −0.0495802 0.148741i
$$681$$ −10.5858 + 10.5858i −0.405648 + 0.405648i
$$682$$ −15.7782 + 15.7782i −0.604178 + 0.604178i
$$683$$ 12.3137i 0.471171i 0.971854 + 0.235585i $$0.0757008\pi$$
−0.971854 + 0.235585i $$0.924299\pi$$
$$684$$ −5.82843 5.82843i −0.222855 0.222855i
$$685$$ 11.8995 23.7990i 0.454656 0.909313i
$$686$$ −1.77817 + 1.77817i −0.0678910 + 0.0678910i
$$687$$ −2.00000 2.00000i −0.0763048 0.0763048i
$$688$$ 7.00000i 0.266872i
$$689$$ −4.75736 + 4.75736i −0.181241 + 0.181241i
$$690$$ −5.17157 + 10.3431i −0.196878 + 0.393757i
$$691$$ 9.97056i 0.379298i 0.981852 + 0.189649i $$0.0607350\pi$$
−0.981852 + 0.189649i $$0.939265\pi$$
$$692$$ −6.02082 + 6.02082i −0.228877 + 0.228877i
$$693$$ 10.3640 10.3640i 0.393694 0.393694i
$$694$$ 17.3137 0.657219
$$695$$ −13.0919 + 4.36396i −0.496603 + 0.165534i
$$696$$ 18.9706i 0.719077i
$$697$$ 12.7990i 0.484796i
$$698$$ −4.14214 −0.156782
$$699$$ 0.201010i 0.00760290i
$$700$$ −2.70711 + 18.9497i −0.102319 + 0.716233i
$$701$$ 4.34315 + 4.34315i 0.164038 + 0.164038i 0.784353 0.620315i $$-0.212995\pi$$
−0.620315 + 0.784353i $$0.712995\pi$$
$$702$$ 6.34315 + 6.34315i 0.239407 + 0.239407i
$$703$$ 49.4558 8.24264i 1.86526 0.310877i
$$704$$ 3.82843i 0.144289i
$$705$$ 16.4853 + 49.4558i 0.620872 + 1.86261i
$$706$$ 7.34315i 0.276363i
$$707$$ −29.9706 29.9706i −1.12716 1.12716i
$$708$$ 3.31371i 0.124537i
$$709$$ 10.7071 10.7071i 0.402114 0.402114i −0.476864 0.878977i $$-0.658226\pi$$
0.878977 + 0.476864i $$0.158226\pi$$
$$710$$ 0.242641 + 0.727922i 0.00910614 + 0.0273184i
$$711$$ −9.65685 9.65685i −0.362160 0.362160i
$$712$$ −7.41421 + 7.41421i −0.277859 + 0.277859i
$$713$$ 10.6569 + 10.6569i 0.399102 + 0.399102i
$$714$$ 14.0000 0.523937
$$715$$ −18.2132 + 6.07107i −0.681135 + 0.227045i
$$716$$ 14.4853 + 14.4853i 0.541340 + 0.541340i
$$717$$ 19.9411i 0.744715i
$$718$$ 30.5269 1.13925
$$719$$ 24.1421i 0.900350i 0.892940 + 0.450175i $$0.148638\pi$$
−0.892940 + 0.450175i $$0.851362\pi$$
$$720$$ −0.707107 2.12132i −0.0263523 0.0790569i
$$721$$ 36.6985 36.6985i 1.36672 1.36672i
$$722$$ −48.9411 −1.82140
$$723$$ 2.14214 0.0796669
$$724$$ −7.65685 −0.284565
$$725$$ −46.9497 6.70711i −1.74367 0.249096i
$$726$$ 5.17157 + 5.17157i 0.191935 + 0.191935i
$$727$$ 13.8579i 0.513960i 0.966417 + 0.256980i $$0.0827274\pi$$
−0.966417 + 0.256980i $$0.917273\pi$$
$$728$$ −6.07107 + 6.07107i −0.225009 + 0.225009i
$$729$$ 13.0000i 0.481481i
$$730$$ −16.9706 8.48528i −0.628109 0.314054i
$$731$$ 12.7990i 0.473388i
$$732$$ 26.2843i 0.971495i
$$733$$ −22.7487 + 22.7487i −0.840244 + 0.840244i −0.988890 0.148647i $$-0.952508\pi$$
0.148647 + 0.988890i $$0.452508\pi$$
$$734$$ −13.0919 13.0919i −0.483230 0.483230i
$$735$$ −30.6274 15.3137i −1.12971 0.564855i
$$736$$ −2.58579 −0.0953134
$$737$$ −4.75736 + 4.75736i −0.175240 + 0.175240i
$$738$$ 7.00000i 0.257674i
$$739$$ −10.7990 −0.397247 −0.198624 0.980076i $$-0.563647\pi$$
−0.198624 + 0.980076i $$0.563647\pi$$
$$740$$ 13.0000 + 4.00000i 0.477890 + 0.147043i
$$741$$ −36.9706 −1.35815
$$742$$ 11.4853i 0.421638i
$$743$$ 5.05025 5.05025i 0.185276 0.185276i −0.608374 0.793650i $$-0.708178\pi$$
0.793650 + 0.608374i $$0.208178\pi$$
$$744$$ −11.6569 −0.427361
$$745$$ 5.82843 + 17.4853i 0.213537 + 0.640611i
$$746$$ 10.8284 + 10.8284i 0.396457 + 0.396457i
$$747$$ −0.828427 + 0.828427i −0.0303106 + 0.0303106i
$$748$$ 7.00000i 0.255945i
$$749$$ 49.1127i 1.79454i
$$750$$ −22.0000 + 4.00000i −0.803326 + 0.146059i
$$751$$ 16.0416i 0.585367i −0.956209 0.292684i $$-0.905452\pi$$
0.956209 0.292684i $$-0.0945483\pi$$
$$752$$ −8.24264 + 8.24264i −0.300578 + 0.300578i
$$753$$ 50.6274i 1.84497i
$$754$$ −15.0416 15.0416i −0.547784 0.547784i
$$755$$ −8.48528 25.4558i −0.308811 0.926433i
$$756$$ −15.3137 −0.556954
$$757$$ 27.6569 1.00521 0.502603 0.864517i $$-0.332376\pi$$
0.502603 + 0.864517i $$0.332376\pi$$
$$758$$ 18.0000 0.653789
$$759$$ 14.0000 14.0000i 0.508168 0.508168i
$$760$$ −16.4853 8.24264i −0.597984 0.298992i
$$761$$ 11.6863i 0.423628i −0.977310 0.211814i $$-0.932063\pi$$
0.977310 0.211814i $$-0.0679371\pi$$
$$762$$ −7.31371 −0.264948
$$763$$ 5.14214i 0.186158i
$$764$$ −1.53553 1.53553i −0.0555537 0.0555537i
$$765$$ 1.29289 + 3.87868i 0.0467447 + 0.140234i
$$766$$ −16.5858 −0.599269
$$767$$ −2.62742 2.62742i −0.0948705 0.0948705i
$$768$$ 1.41421 1.41421i 0.0510310 0.0510310i
$$769$$ −19.1716 19.1716i −0.691345 0.691345i 0.271183 0.962528i $$-0.412585\pi$$
−0.962528 + 0.271183i $$0.912585\pi$$
$$770$$ 14.6569 29.3137i 0.528196 1.05639i
$$771$$ 26.6274 26.6274i 0.958963 0.958963i
$$772$$ 20.4853i 0.737281i
$$773$$ 10.1213 + 10.1213i 0.364039 + 0.364039i 0.865297 0.501259i $$-0.167130\pi$$
−0.501259 + 0.865297i $$0.667130\pi$$
$$774$$ 7.00000i 0.251610i
$$775$$ −4.12132 + 28.8492i −0.148042 + 1.03630i
$$776$$ 7.00000i 0.251285i
$$777$$ −27.0711 + 37.8995i −0.971169 + 1.35964i
$$778$$ 3.77817 + 3.77817i 0.135454