# Properties

 Label 1110.2.u.b.191.2 Level $1110$ Weight $2$ Character 1110.191 Analytic conductor $8.863$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1110 = 2 \cdot 3 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1110.u (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 191.2 Root $$0.707107 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1110.191 Dual form 1110.2.u.b.401.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +(-1.41421 - 1.00000i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.292893 - 1.70711i) q^{6} +4.00000 q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +1.00000 q^{10} +4.24264 q^{11} +(1.00000 - 1.41421i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(2.82843 + 2.82843i) q^{14} +(-1.70711 + 0.292893i) q^{15} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +(-1.29289 + 2.70711i) q^{18} +(-2.00000 - 2.00000i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-5.65685 - 4.00000i) q^{21} +(3.00000 + 3.00000i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(1.70711 - 0.292893i) q^{24} -1.00000i q^{25} -1.41421i q^{26} +(1.41421 - 5.00000i) q^{27} +4.00000i q^{28} +(-1.41421 - 1.00000i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-6.00000 - 4.24264i) q^{33} -2.00000 q^{34} +(2.82843 - 2.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(6.00000 - 1.00000i) q^{37} -2.82843i q^{38} +(0.414214 + 2.41421i) q^{39} +1.00000i q^{40} +5.65685 q^{41} +(-1.17157 - 6.82843i) q^{42} +(9.00000 + 9.00000i) q^{43} +4.24264i q^{44} +(2.70711 + 1.29289i) q^{45} -6.00000 q^{46} +1.41421i q^{47} +(1.41421 + 1.00000i) q^{48} +9.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.41421 - 0.585786i) q^{51} +(1.00000 - 1.00000i) q^{52} +2.82843i q^{53} +(4.53553 - 2.53553i) q^{54} +(3.00000 - 3.00000i) q^{55} +(-2.82843 + 2.82843i) q^{56} +(0.828427 + 4.82843i) q^{57} +(-2.82843 + 2.82843i) q^{59} +(-0.292893 - 1.70711i) q^{60} +(4.00000 - 4.00000i) q^{61} +7.07107 q^{62} +(4.00000 + 11.3137i) q^{63} -1.00000i q^{64} -1.41421 q^{65} +(-1.24264 - 7.24264i) q^{66} +2.00000i q^{67} +(-1.41421 - 1.41421i) q^{68} +(10.2426 - 1.75736i) q^{69} +4.00000 q^{70} -2.82843i q^{71} +(-2.70711 - 1.29289i) q^{72} -6.00000i q^{73} +(4.94975 + 3.53553i) q^{74} +(-1.00000 + 1.41421i) q^{75} +(2.00000 - 2.00000i) q^{76} +16.9706 q^{77} +(-1.41421 + 2.00000i) q^{78} +(-3.00000 - 3.00000i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(4.00000 + 4.00000i) q^{82} -2.82843i q^{83} +(4.00000 - 5.65685i) q^{84} +2.00000i q^{85} +12.7279i q^{86} +(-3.00000 + 3.00000i) q^{88} +(-12.7279 - 12.7279i) q^{89} +(1.00000 + 2.82843i) q^{90} +(-4.00000 - 4.00000i) q^{91} +(-4.24264 - 4.24264i) q^{92} +(-12.0711 + 2.07107i) q^{93} +(-1.00000 + 1.00000i) q^{94} -2.82843 q^{95} +(0.292893 + 1.70711i) q^{96} +(-12.0000 - 12.0000i) q^{97} +(6.36396 + 6.36396i) q^{98} +(4.24264 + 12.0000i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{6} + 16q^{7} + 4q^{9} + O(q^{10})$$ $$4q - 4q^{6} + 16q^{7} + 4q^{9} + 4q^{10} + 4q^{12} - 4q^{13} - 4q^{15} - 4q^{16} - 8q^{18} - 8q^{19} + 12q^{22} + 4q^{24} + 20q^{31} - 24q^{33} - 8q^{34} + 24q^{37} - 4q^{39} - 16q^{42} + 36q^{43} + 8q^{45} - 24q^{46} + 36q^{49} + 8q^{51} + 4q^{52} + 4q^{54} + 12q^{55} - 8q^{57} - 4q^{60} + 16q^{61} + 16q^{63} + 12q^{66} + 24q^{69} + 16q^{70} - 8q^{72} - 4q^{75} + 8q^{76} - 12q^{79} - 28q^{81} + 16q^{82} + 16q^{84} - 12q^{88} + 4q^{90} - 16q^{91} - 20q^{93} - 4q^{94} + 4q^{96} - 48q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$667$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.500000 + 0.500000i
$$3$$ −1.41421 1.00000i −0.816497 0.577350i
$$4$$ 1.00000i 0.500000i
$$5$$ 0.707107 0.707107i 0.316228 0.316228i
$$6$$ −0.292893 1.70711i −0.119573 0.696923i
$$7$$ 4.00000 1.51186 0.755929 0.654654i $$-0.227186\pi$$
0.755929 + 0.654654i $$0.227186\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ 1.00000 + 2.82843i 0.333333 + 0.942809i
$$10$$ 1.00000 0.316228
$$11$$ 4.24264 1.27920 0.639602 0.768706i $$-0.279099\pi$$
0.639602 + 0.768706i $$0.279099\pi$$
$$12$$ 1.00000 1.41421i 0.288675 0.408248i
$$13$$ −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i $$-0.312833\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ 2.82843 + 2.82843i 0.755929 + 0.755929i
$$15$$ −1.70711 + 0.292893i −0.440773 + 0.0756247i
$$16$$ −1.00000 −0.250000
$$17$$ −1.41421 + 1.41421i −0.342997 + 0.342997i −0.857493 0.514496i $$-0.827979\pi$$
0.514496 + 0.857493i $$0.327979\pi$$
$$18$$ −1.29289 + 2.70711i −0.304738 + 0.638071i
$$19$$ −2.00000 2.00000i −0.458831 0.458831i 0.439440 0.898272i $$-0.355177\pi$$
−0.898272 + 0.439440i $$0.855177\pi$$
$$20$$ 0.707107 + 0.707107i 0.158114 + 0.158114i
$$21$$ −5.65685 4.00000i −1.23443 0.872872i
$$22$$ 3.00000 + 3.00000i 0.639602 + 0.639602i
$$23$$ −4.24264 + 4.24264i −0.884652 + 0.884652i −0.994003 0.109351i $$-0.965123\pi$$
0.109351 + 0.994003i $$0.465123\pi$$
$$24$$ 1.70711 0.292893i 0.348462 0.0597866i
$$25$$ 1.00000i 0.200000i
$$26$$ 1.41421i 0.277350i
$$27$$ 1.41421 5.00000i 0.272166 0.962250i
$$28$$ 4.00000i 0.755929i
$$29$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$30$$ −1.41421 1.00000i −0.258199 0.182574i
$$31$$ 5.00000 5.00000i 0.898027 0.898027i −0.0972349 0.995261i $$-0.531000\pi$$
0.995261 + 0.0972349i $$0.0309998\pi$$
$$32$$ −0.707107 0.707107i −0.125000 0.125000i
$$33$$ −6.00000 4.24264i −1.04447 0.738549i
$$34$$ −2.00000 −0.342997
$$35$$ 2.82843 2.82843i 0.478091 0.478091i
$$36$$ −2.82843 + 1.00000i −0.471405 + 0.166667i
$$37$$ 6.00000 1.00000i 0.986394 0.164399i
$$38$$ 2.82843i 0.458831i
$$39$$ 0.414214 + 2.41421i 0.0663273 + 0.386584i
$$40$$ 1.00000i 0.158114i
$$41$$ 5.65685 0.883452 0.441726 0.897150i $$-0.354366\pi$$
0.441726 + 0.897150i $$0.354366\pi$$
$$42$$ −1.17157 6.82843i −0.180778 1.05365i
$$43$$ 9.00000 + 9.00000i 1.37249 + 1.37249i 0.856742 + 0.515745i $$0.172485\pi$$
0.515745 + 0.856742i $$0.327515\pi$$
$$44$$ 4.24264i 0.639602i
$$45$$ 2.70711 + 1.29289i 0.403552 + 0.192733i
$$46$$ −6.00000 −0.884652
$$47$$ 1.41421i 0.206284i 0.994667 + 0.103142i $$0.0328896\pi$$
−0.994667 + 0.103142i $$0.967110\pi$$
$$48$$ 1.41421 + 1.00000i 0.204124 + 0.144338i
$$49$$ 9.00000 1.28571
$$50$$ 0.707107 0.707107i 0.100000 0.100000i
$$51$$ 3.41421 0.585786i 0.478086 0.0820265i
$$52$$ 1.00000 1.00000i 0.138675 0.138675i
$$53$$ 2.82843i 0.388514i 0.980951 + 0.194257i $$0.0622296\pi$$
−0.980951 + 0.194257i $$0.937770\pi$$
$$54$$ 4.53553 2.53553i 0.617208 0.345042i
$$55$$ 3.00000 3.00000i 0.404520 0.404520i
$$56$$ −2.82843 + 2.82843i −0.377964 + 0.377964i
$$57$$ 0.828427 + 4.82843i 0.109728 + 0.639541i
$$58$$ 0 0
$$59$$ −2.82843 + 2.82843i −0.368230 + 0.368230i −0.866831 0.498601i $$-0.833847\pi$$
0.498601 + 0.866831i $$0.333847\pi$$
$$60$$ −0.292893 1.70711i −0.0378124 0.220387i
$$61$$ 4.00000 4.00000i 0.512148 0.512148i −0.403036 0.915184i $$-0.632045\pi$$
0.915184 + 0.403036i $$0.132045\pi$$
$$62$$ 7.07107 0.898027
$$63$$ 4.00000 + 11.3137i 0.503953 + 1.42539i
$$64$$ 1.00000i 0.125000i
$$65$$ −1.41421 −0.175412
$$66$$ −1.24264 7.24264i −0.152958 0.891507i
$$67$$ 2.00000i 0.244339i 0.992509 + 0.122169i $$0.0389851\pi$$
−0.992509 + 0.122169i $$0.961015\pi$$
$$68$$ −1.41421 1.41421i −0.171499 0.171499i
$$69$$ 10.2426 1.75736i 1.23307 0.211561i
$$70$$ 4.00000 0.478091
$$71$$ 2.82843i 0.335673i −0.985815 0.167836i $$-0.946322\pi$$
0.985815 0.167836i $$-0.0536780\pi$$
$$72$$ −2.70711 1.29289i −0.319036 0.152369i
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 4.94975 + 3.53553i 0.575396 + 0.410997i
$$75$$ −1.00000 + 1.41421i −0.115470 + 0.163299i
$$76$$ 2.00000 2.00000i 0.229416 0.229416i
$$77$$ 16.9706 1.93398
$$78$$ −1.41421 + 2.00000i −0.160128 + 0.226455i
$$79$$ −3.00000 3.00000i −0.337526 0.337526i 0.517909 0.855436i $$-0.326710\pi$$
−0.855436 + 0.517909i $$0.826710\pi$$
$$80$$ −0.707107 + 0.707107i −0.0790569 + 0.0790569i
$$81$$ −7.00000 + 5.65685i −0.777778 + 0.628539i
$$82$$ 4.00000 + 4.00000i 0.441726 + 0.441726i
$$83$$ 2.82843i 0.310460i −0.987878 0.155230i $$-0.950388\pi$$
0.987878 0.155230i $$-0.0496119\pi$$
$$84$$ 4.00000 5.65685i 0.436436 0.617213i
$$85$$ 2.00000i 0.216930i
$$86$$ 12.7279i 1.37249i
$$87$$ 0 0
$$88$$ −3.00000 + 3.00000i −0.319801 + 0.319801i
$$89$$ −12.7279 12.7279i −1.34916 1.34916i −0.886578 0.462579i $$-0.846924\pi$$
−0.462579 0.886578i $$-0.653076\pi$$
$$90$$ 1.00000 + 2.82843i 0.105409 + 0.298142i
$$91$$ −4.00000 4.00000i −0.419314 0.419314i
$$92$$ −4.24264 4.24264i −0.442326 0.442326i
$$93$$ −12.0711 + 2.07107i −1.25171 + 0.214760i
$$94$$ −1.00000 + 1.00000i −0.103142 + 0.103142i
$$95$$ −2.82843 −0.290191
$$96$$ 0.292893 + 1.70711i 0.0298933 + 0.174231i
$$97$$ −12.0000 12.0000i −1.21842 1.21842i −0.968187 0.250229i $$-0.919494\pi$$
−0.250229 0.968187i $$-0.580506\pi$$
$$98$$ 6.36396 + 6.36396i 0.642857 + 0.642857i
$$99$$ 4.24264 + 12.0000i 0.426401 + 1.20605i
$$100$$ 1.00000 0.100000
$$101$$ 15.5563 1.54791 0.773957 0.633238i $$-0.218274\pi$$
0.773957 + 0.633238i $$0.218274\pi$$
$$102$$ 2.82843 + 2.00000i 0.280056 + 0.198030i
$$103$$ −10.0000 + 10.0000i −0.985329 + 0.985329i −0.999894 0.0145647i $$-0.995364\pi$$
0.0145647 + 0.999894i $$0.495364\pi$$
$$104$$ 1.41421 0.138675
$$105$$ −6.82843 + 1.17157i −0.666386 + 0.114334i
$$106$$ −2.00000 + 2.00000i −0.194257 + 0.194257i
$$107$$ 14.1421i 1.36717i −0.729870 0.683586i $$-0.760419\pi$$
0.729870 0.683586i $$-0.239581\pi$$
$$108$$ 5.00000 + 1.41421i 0.481125 + 0.136083i
$$109$$ 12.0000 + 12.0000i 1.14939 + 1.14939i 0.986672 + 0.162719i $$0.0520264\pi$$
0.162719 + 0.986672i $$0.447974\pi$$
$$110$$ 4.24264 0.404520
$$111$$ −9.48528 4.58579i −0.900303 0.435264i
$$112$$ −4.00000 −0.377964
$$113$$ 4.24264 + 4.24264i 0.399114 + 0.399114i 0.877920 0.478806i $$-0.158930\pi$$
−0.478806 + 0.877920i $$0.658930\pi$$
$$114$$ −2.82843 + 4.00000i −0.264906 + 0.374634i
$$115$$ 6.00000i 0.559503i
$$116$$ 0 0
$$117$$ 1.82843 3.82843i 0.169038 0.353938i
$$118$$ −4.00000 −0.368230
$$119$$ −5.65685 + 5.65685i −0.518563 + 0.518563i
$$120$$ 1.00000 1.41421i 0.0912871 0.129099i
$$121$$ 7.00000 0.636364
$$122$$ 5.65685 0.512148
$$123$$ −8.00000 5.65685i −0.721336 0.510061i
$$124$$ 5.00000 + 5.00000i 0.449013 + 0.449013i
$$125$$ −0.707107 0.707107i −0.0632456 0.0632456i
$$126$$ −5.17157 + 10.8284i −0.460720 + 0.964673i
$$127$$ −12.0000 −1.06483 −0.532414 0.846484i $$-0.678715\pi$$
−0.532414 + 0.846484i $$0.678715\pi$$
$$128$$ 0.707107 0.707107i 0.0625000 0.0625000i
$$129$$ −3.72792 21.7279i −0.328225 1.91304i
$$130$$ −1.00000 1.00000i −0.0877058 0.0877058i
$$131$$ 8.48528 + 8.48528i 0.741362 + 0.741362i 0.972840 0.231478i $$-0.0743560\pi$$
−0.231478 + 0.972840i $$0.574356\pi$$
$$132$$ 4.24264 6.00000i 0.369274 0.522233i
$$133$$ −8.00000 8.00000i −0.693688 0.693688i
$$134$$ −1.41421 + 1.41421i −0.122169 + 0.122169i
$$135$$ −2.53553 4.53553i −0.218224 0.390357i
$$136$$ 2.00000i 0.171499i
$$137$$ 9.89949i 0.845771i 0.906183 + 0.422885i $$0.138983\pi$$
−0.906183 + 0.422885i $$0.861017\pi$$
$$138$$ 8.48528 + 6.00000i 0.722315 + 0.510754i
$$139$$ 16.0000i 1.35710i 0.734553 + 0.678551i $$0.237392\pi$$
−0.734553 + 0.678551i $$0.762608\pi$$
$$140$$ 2.82843 + 2.82843i 0.239046 + 0.239046i
$$141$$ 1.41421 2.00000i 0.119098 0.168430i
$$142$$ 2.00000 2.00000i 0.167836 0.167836i
$$143$$ −4.24264 4.24264i −0.354787 0.354787i
$$144$$ −1.00000 2.82843i −0.0833333 0.235702i
$$145$$ 0 0
$$146$$ 4.24264 4.24264i 0.351123 0.351123i
$$147$$ −12.7279 9.00000i −1.04978 0.742307i
$$148$$ 1.00000 + 6.00000i 0.0821995 + 0.493197i
$$149$$ 9.89949i 0.810998i −0.914095 0.405499i $$-0.867098\pi$$
0.914095 0.405499i $$-0.132902\pi$$
$$150$$ −1.70711 + 0.292893i −0.139385 + 0.0239146i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 2.82843 0.229416
$$153$$ −5.41421 2.58579i −0.437713 0.209048i
$$154$$ 12.0000 + 12.0000i 0.966988 + 0.966988i
$$155$$ 7.07107i 0.567962i
$$156$$ −2.41421 + 0.414214i −0.193292 + 0.0331636i
$$157$$ −18.0000 −1.43656 −0.718278 0.695756i $$-0.755069\pi$$
−0.718278 + 0.695756i $$0.755069\pi$$
$$158$$ 4.24264i 0.337526i
$$159$$ 2.82843 4.00000i 0.224309 0.317221i
$$160$$ −1.00000 −0.0790569
$$161$$ −16.9706 + 16.9706i −1.33747 + 1.33747i
$$162$$ −8.94975 0.949747i −0.703159 0.0746192i
$$163$$ −5.00000 + 5.00000i −0.391630 + 0.391630i −0.875268 0.483638i $$-0.839315\pi$$
0.483638 + 0.875268i $$0.339315\pi$$
$$164$$ 5.65685i 0.441726i
$$165$$ −7.24264 + 1.24264i −0.563839 + 0.0967394i
$$166$$ 2.00000 2.00000i 0.155230 0.155230i
$$167$$ −12.7279 + 12.7279i −0.984916 + 0.984916i −0.999888 0.0149717i $$-0.995234\pi$$
0.0149717 + 0.999888i $$0.495234\pi$$
$$168$$ 6.82843 1.17157i 0.526825 0.0903888i
$$169$$ 11.0000i 0.846154i
$$170$$ −1.41421 + 1.41421i −0.108465 + 0.108465i
$$171$$ 3.65685 7.65685i 0.279647 0.585534i
$$172$$ −9.00000 + 9.00000i −0.686244 + 0.686244i
$$173$$ −2.82843 −0.215041 −0.107521 0.994203i $$-0.534291\pi$$
−0.107521 + 0.994203i $$0.534291\pi$$
$$174$$ 0 0
$$175$$ 4.00000i 0.302372i
$$176$$ −4.24264 −0.319801
$$177$$ 6.82843 1.17157i 0.513256 0.0880608i
$$178$$ 18.0000i 1.34916i
$$179$$ −12.7279 12.7279i −0.951330 0.951330i 0.0475398 0.998869i $$-0.484862\pi$$
−0.998869 + 0.0475398i $$0.984862\pi$$
$$180$$ −1.29289 + 2.70711i −0.0963666 + 0.201776i
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 5.65685i 0.419314i
$$183$$ −9.65685 + 1.65685i −0.713855 + 0.122478i
$$184$$ 6.00000i 0.442326i
$$185$$ 3.53553 4.94975i 0.259938 0.363913i
$$186$$ −10.0000 7.07107i −0.733236 0.518476i
$$187$$ −6.00000 + 6.00000i −0.438763 + 0.438763i
$$188$$ −1.41421 −0.103142
$$189$$ 5.65685 20.0000i 0.411476 1.45479i
$$190$$ −2.00000 2.00000i −0.145095 0.145095i
$$191$$ 2.82843 2.82843i 0.204658 0.204658i −0.597334 0.801992i $$-0.703773\pi$$
0.801992 + 0.597334i $$0.203773\pi$$
$$192$$ −1.00000 + 1.41421i −0.0721688 + 0.102062i
$$193$$ 18.0000 + 18.0000i 1.29567 + 1.29567i 0.931226 + 0.364442i $$0.118740\pi$$
0.364442 + 0.931226i $$0.381260\pi$$
$$194$$ 16.9706i 1.21842i
$$195$$ 2.00000 + 1.41421i 0.143223 + 0.101274i
$$196$$ 9.00000i 0.642857i
$$197$$ 19.7990i 1.41062i −0.708899 0.705310i $$-0.750808\pi$$
0.708899 0.705310i $$-0.249192\pi$$
$$198$$ −5.48528 + 11.4853i −0.389822 + 0.816223i
$$199$$ −3.00000 + 3.00000i −0.212664 + 0.212664i −0.805398 0.592734i $$-0.798049\pi$$
0.592734 + 0.805398i $$0.298049\pi$$
$$200$$ 0.707107 + 0.707107i 0.0500000 + 0.0500000i
$$201$$ 2.00000 2.82843i 0.141069 0.199502i
$$202$$ 11.0000 + 11.0000i 0.773957 + 0.773957i
$$203$$ 0 0
$$204$$ 0.585786 + 3.41421i 0.0410133 + 0.239043i
$$205$$ 4.00000 4.00000i 0.279372 0.279372i
$$206$$ −14.1421 −0.985329
$$207$$ −16.2426 7.75736i −1.12894 0.539174i
$$208$$ 1.00000 + 1.00000i 0.0693375 + 0.0693375i
$$209$$ −8.48528 8.48528i −0.586939 0.586939i
$$210$$ −5.65685 4.00000i −0.390360 0.276026i
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ −2.82843 −0.194257
$$213$$ −2.82843 + 4.00000i −0.193801 + 0.274075i
$$214$$ 10.0000 10.0000i 0.683586 0.683586i
$$215$$ 12.7279 0.868037
$$216$$ 2.53553 + 4.53553i 0.172521 + 0.308604i
$$217$$ 20.0000 20.0000i 1.35769 1.35769i
$$218$$ 16.9706i 1.14939i
$$219$$ −6.00000 + 8.48528i −0.405442 + 0.573382i
$$220$$ 3.00000 + 3.00000i 0.202260 + 0.202260i
$$221$$ 2.82843 0.190261
$$222$$ −3.46447 9.94975i −0.232520 0.667783i
$$223$$ −12.0000 −0.803579 −0.401790 0.915732i $$-0.631612\pi$$
−0.401790 + 0.915732i $$0.631612\pi$$
$$224$$ −2.82843 2.82843i −0.188982 0.188982i
$$225$$ 2.82843 1.00000i 0.188562 0.0666667i
$$226$$ 6.00000i 0.399114i
$$227$$ −19.7990 + 19.7990i −1.31411 + 1.31411i −0.395744 + 0.918361i $$0.629513\pi$$
−0.918361 + 0.395744i $$0.870487\pi$$
$$228$$ −4.82843 + 0.828427i −0.319770 + 0.0548639i
$$229$$ 26.0000 1.71813 0.859064 0.511868i $$-0.171046\pi$$
0.859064 + 0.511868i $$0.171046\pi$$
$$230$$ −4.24264 + 4.24264i −0.279751 + 0.279751i
$$231$$ −24.0000 16.9706i −1.57908 1.11658i
$$232$$ 0 0
$$233$$ −7.07107 −0.463241 −0.231621 0.972806i $$-0.574403\pi$$
−0.231621 + 0.972806i $$0.574403\pi$$
$$234$$ 4.00000 1.41421i 0.261488 0.0924500i
$$235$$ 1.00000 + 1.00000i 0.0652328 + 0.0652328i
$$236$$ −2.82843 2.82843i −0.184115 0.184115i
$$237$$ 1.24264 + 7.24264i 0.0807182 + 0.470460i
$$238$$ −8.00000 −0.518563
$$239$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$240$$ 1.70711 0.292893i 0.110193 0.0189062i
$$241$$ 3.00000 + 3.00000i 0.193247 + 0.193247i 0.797098 0.603851i $$-0.206368\pi$$
−0.603851 + 0.797098i $$0.706368\pi$$
$$242$$ 4.94975 + 4.94975i 0.318182 + 0.318182i
$$243$$ 15.5563 1.00000i 0.997940 0.0641500i
$$244$$ 4.00000 + 4.00000i 0.256074 + 0.256074i
$$245$$ 6.36396 6.36396i 0.406579 0.406579i
$$246$$ −1.65685 9.65685i −0.105637 0.615699i
$$247$$ 4.00000i 0.254514i
$$248$$ 7.07107i 0.449013i
$$249$$ −2.82843 + 4.00000i −0.179244 + 0.253490i
$$250$$ 1.00000i 0.0632456i
$$251$$ −2.82843 2.82843i −0.178529 0.178529i 0.612185 0.790714i $$-0.290291\pi$$
−0.790714 + 0.612185i $$0.790291\pi$$
$$252$$ −11.3137 + 4.00000i −0.712697 + 0.251976i
$$253$$ −18.0000 + 18.0000i −1.13165 + 1.13165i
$$254$$ −8.48528 8.48528i −0.532414 0.532414i
$$255$$ 2.00000 2.82843i 0.125245 0.177123i
$$256$$ 1.00000 0.0625000
$$257$$ 2.82843 2.82843i 0.176432 0.176432i −0.613366 0.789799i $$-0.710185\pi$$
0.789799 + 0.613366i $$0.210185\pi$$
$$258$$ 12.7279 18.0000i 0.792406 1.12063i
$$259$$ 24.0000 4.00000i 1.49129 0.248548i
$$260$$ 1.41421i 0.0877058i
$$261$$ 0 0
$$262$$ 12.0000i 0.741362i
$$263$$ −26.8701 −1.65688 −0.828439 0.560079i $$-0.810771\pi$$
−0.828439 + 0.560079i $$0.810771\pi$$
$$264$$ 7.24264 1.24264i 0.445754 0.0764792i
$$265$$ 2.00000 + 2.00000i 0.122859 + 0.122859i
$$266$$ 11.3137i 0.693688i
$$267$$ 5.27208 + 30.7279i 0.322646 + 1.88052i
$$268$$ −2.00000 −0.122169
$$269$$ 21.2132i 1.29339i −0.762748 0.646696i $$-0.776150\pi$$
0.762748 0.646696i $$-0.223850\pi$$
$$270$$ 1.41421 5.00000i 0.0860663 0.304290i
$$271$$ −8.00000 −0.485965 −0.242983 0.970031i $$-0.578126\pi$$
−0.242983 + 0.970031i $$0.578126\pi$$
$$272$$ 1.41421 1.41421i 0.0857493 0.0857493i
$$273$$ 1.65685 + 9.65685i 0.100277 + 0.584459i
$$274$$ −7.00000 + 7.00000i −0.422885 + 0.422885i
$$275$$ 4.24264i 0.255841i
$$276$$ 1.75736 + 10.2426i 0.105781 + 0.616535i
$$277$$ −15.0000 + 15.0000i −0.901263 + 0.901263i −0.995545 0.0942828i $$-0.969944\pi$$
0.0942828 + 0.995545i $$0.469944\pi$$
$$278$$ −11.3137 + 11.3137i −0.678551 + 0.678551i
$$279$$ 19.1421 + 9.14214i 1.14601 + 0.547325i
$$280$$ 4.00000i 0.239046i
$$281$$ −7.07107 + 7.07107i −0.421825 + 0.421825i −0.885832 0.464007i $$-0.846411\pi$$
0.464007 + 0.885832i $$0.346411\pi$$
$$282$$ 2.41421 0.414214i 0.143764 0.0246661i
$$283$$ −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i $$-0.967149\pi$$
0.103022 + 0.994679i $$0.467149\pi$$
$$284$$ 2.82843 0.167836
$$285$$ 4.00000 + 2.82843i 0.236940 + 0.167542i
$$286$$ 6.00000i 0.354787i
$$287$$ 22.6274 1.33565
$$288$$ 1.29289 2.70711i 0.0761845 0.159518i
$$289$$ 13.0000i 0.764706i
$$290$$ 0 0
$$291$$ 4.97056 + 28.9706i 0.291380 + 1.69828i
$$292$$ 6.00000 0.351123
$$293$$ 28.2843i 1.65238i −0.563388 0.826192i $$-0.690502\pi$$
0.563388 0.826192i $$-0.309498\pi$$
$$294$$ −2.63604 15.3640i −0.153737 0.896044i
$$295$$ 4.00000i 0.232889i
$$296$$ −3.53553 + 4.94975i −0.205499 + 0.287698i
$$297$$ 6.00000 21.2132i 0.348155 1.23091i
$$298$$ 7.00000 7.00000i 0.405499 0.405499i
$$299$$ 8.48528 0.490716
$$300$$ −1.41421 1.00000i −0.0816497 0.0577350i
$$301$$ 36.0000 + 36.0000i 2.07501 + 2.07501i
$$302$$ 0 0
$$303$$ −22.0000 15.5563i −1.26387 0.893689i
$$304$$ 2.00000 + 2.00000i 0.114708 + 0.114708i
$$305$$ 5.65685i 0.323911i
$$306$$ −2.00000 5.65685i −0.114332 0.323381i
$$307$$ 4.00000i 0.228292i −0.993464 0.114146i $$-0.963587\pi$$
0.993464 0.114146i $$-0.0364132\pi$$
$$308$$ 16.9706i 0.966988i
$$309$$ 24.1421 4.14214i 1.37340 0.235638i
$$310$$ 5.00000 5.00000i 0.283981 0.283981i
$$311$$ −8.48528 8.48528i −0.481156 0.481156i 0.424345 0.905501i $$-0.360505\pi$$
−0.905501 + 0.424345i $$0.860505\pi$$
$$312$$ −2.00000 1.41421i −0.113228 0.0800641i
$$313$$ 6.00000 + 6.00000i 0.339140 + 0.339140i 0.856044 0.516904i $$-0.172915\pi$$
−0.516904 + 0.856044i $$0.672915\pi$$
$$314$$ −12.7279 12.7279i −0.718278 0.718278i
$$315$$ 10.8284 + 5.17157i 0.610113 + 0.291385i
$$316$$ 3.00000 3.00000i 0.168763 0.168763i
$$317$$ 8.48528 0.476581 0.238290 0.971194i $$-0.423413\pi$$
0.238290 + 0.971194i $$0.423413\pi$$
$$318$$ 4.82843 0.828427i 0.270765 0.0464559i
$$319$$ 0 0
$$320$$ −0.707107 0.707107i −0.0395285 0.0395285i
$$321$$ −14.1421 + 20.0000i −0.789337 + 1.11629i
$$322$$ −24.0000 −1.33747
$$323$$ 5.65685 0.314756
$$324$$ −5.65685 7.00000i −0.314270 0.388889i
$$325$$ −1.00000 + 1.00000i −0.0554700 + 0.0554700i
$$326$$ −7.07107 −0.391630
$$327$$ −4.97056 28.9706i −0.274873 1.60208i
$$328$$ −4.00000 + 4.00000i −0.220863 + 0.220863i
$$329$$ 5.65685i 0.311872i
$$330$$ −6.00000 4.24264i −0.330289 0.233550i
$$331$$ −4.00000 4.00000i −0.219860 0.219860i 0.588579 0.808439i $$-0.299687\pi$$
−0.808439 + 0.588579i $$0.799687\pi$$
$$332$$ 2.82843 0.155230
$$333$$ 8.82843 + 15.9706i 0.483795 + 0.875181i
$$334$$ −18.0000 −0.984916
$$335$$ 1.41421 + 1.41421i 0.0772667 + 0.0772667i
$$336$$ 5.65685 + 4.00000i 0.308607 + 0.218218i
$$337$$ 2.00000i 0.108947i −0.998515 0.0544735i $$-0.982652\pi$$
0.998515 0.0544735i $$-0.0173480\pi$$
$$338$$ 7.77817 7.77817i 0.423077 0.423077i
$$339$$ −1.75736 10.2426i −0.0954467 0.556304i
$$340$$ −2.00000 −0.108465
$$341$$ 21.2132 21.2132i 1.14876 1.14876i
$$342$$ 8.00000 2.82843i 0.432590 0.152944i
$$343$$ 8.00000 0.431959
$$344$$ −12.7279 −0.686244
$$345$$ 6.00000 8.48528i 0.323029 0.456832i
$$346$$ −2.00000 2.00000i −0.107521 0.107521i
$$347$$ 8.48528 + 8.48528i 0.455514 + 0.455514i 0.897180 0.441666i $$-0.145612\pi$$
−0.441666 + 0.897180i $$0.645612\pi$$
$$348$$ 0 0
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 2.82843 2.82843i 0.151186 0.151186i
$$351$$ −6.41421 + 3.58579i −0.342365 + 0.191395i
$$352$$ −3.00000 3.00000i −0.159901 0.159901i
$$353$$ −24.0416 24.0416i −1.27961 1.27961i −0.940887 0.338719i $$-0.890006\pi$$
−0.338719 0.940887i $$-0.609994\pi$$
$$354$$ 5.65685 + 4.00000i 0.300658 + 0.212598i
$$355$$ −2.00000 2.00000i −0.106149 0.106149i
$$356$$ 12.7279 12.7279i 0.674579 0.674579i
$$357$$ 13.6569 2.34315i 0.722797 0.124012i
$$358$$ 18.0000i 0.951330i
$$359$$ 11.3137i 0.597115i 0.954392 + 0.298557i $$0.0965054\pi$$
−0.954392 + 0.298557i $$0.903495\pi$$
$$360$$ −2.82843 + 1.00000i −0.149071 + 0.0527046i
$$361$$ 11.0000i 0.578947i
$$362$$ 4.24264 + 4.24264i 0.222988 + 0.222988i
$$363$$ −9.89949 7.00000i −0.519589 0.367405i
$$364$$ 4.00000 4.00000i 0.209657 0.209657i
$$365$$ −4.24264 4.24264i −0.222070 0.222070i
$$366$$ −8.00000 5.65685i −0.418167 0.295689i
$$367$$ 8.00000 0.417597 0.208798 0.977959i $$-0.433045\pi$$
0.208798 + 0.977959i $$0.433045\pi$$
$$368$$ 4.24264 4.24264i 0.221163 0.221163i
$$369$$ 5.65685 + 16.0000i 0.294484 + 0.832927i
$$370$$ 6.00000 1.00000i 0.311925 0.0519875i
$$371$$ 11.3137i 0.587378i
$$372$$ −2.07107 12.0711i −0.107380 0.625856i
$$373$$ 34.0000i 1.76045i −0.474554 0.880227i $$-0.657390\pi$$
0.474554 0.880227i $$-0.342610\pi$$
$$374$$ −8.48528 −0.438763
$$375$$ 0.292893 + 1.70711i 0.0151249 + 0.0881546i
$$376$$ −1.00000 1.00000i −0.0515711 0.0515711i
$$377$$ 0 0
$$378$$ 18.1421 10.1421i 0.933131 0.521655i
$$379$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$380$$ 2.82843i 0.145095i
$$381$$ 16.9706 + 12.0000i 0.869428 + 0.614779i
$$382$$ 4.00000 0.204658
$$383$$ 11.3137 11.3137i 0.578103 0.578103i −0.356277 0.934380i $$-0.615954\pi$$
0.934380 + 0.356277i $$0.115954\pi$$
$$384$$ −1.70711 + 0.292893i −0.0871154 + 0.0149466i
$$385$$ 12.0000 12.0000i 0.611577 0.611577i
$$386$$ 25.4558i 1.29567i
$$387$$ −16.4558 + 34.4558i −0.836498 + 1.75149i
$$388$$ 12.0000 12.0000i 0.609208 0.609208i
$$389$$ −8.48528 + 8.48528i −0.430221 + 0.430221i −0.888703 0.458483i $$-0.848393\pi$$
0.458483 + 0.888703i $$0.348393\pi$$
$$390$$ 0.414214 + 2.41421i 0.0209745 + 0.122248i
$$391$$ 12.0000i 0.606866i
$$392$$ −6.36396 + 6.36396i −0.321429 + 0.321429i
$$393$$ −3.51472 20.4853i −0.177294 1.03335i
$$394$$ 14.0000 14.0000i 0.705310 0.705310i
$$395$$ −4.24264 −0.213470
$$396$$ −12.0000 + 4.24264i −0.603023 + 0.213201i
$$397$$ 18.0000i 0.903394i 0.892171 + 0.451697i $$0.149181\pi$$
−0.892171 + 0.451697i $$0.850819\pi$$
$$398$$ −4.24264 −0.212664
$$399$$ 3.31371 + 19.3137i 0.165893 + 0.966895i
$$400$$ 1.00000i 0.0500000i
$$401$$ −15.5563 15.5563i −0.776847 0.776847i 0.202446 0.979293i $$-0.435111\pi$$
−0.979293 + 0.202446i $$0.935111\pi$$
$$402$$ 3.41421 0.585786i 0.170285 0.0292164i
$$403$$ −10.0000 −0.498135
$$404$$ 15.5563i 0.773957i
$$405$$ −0.949747 + 8.94975i −0.0471933 + 0.444717i
$$406$$ 0 0
$$407$$ 25.4558 4.24264i 1.26180 0.210300i
$$408$$ −2.00000 + 2.82843i −0.0990148 + 0.140028i
$$409$$ 9.00000 9.00000i 0.445021 0.445021i −0.448674 0.893695i $$-0.648104\pi$$
0.893695 + 0.448674i $$0.148104\pi$$
$$410$$ 5.65685 0.279372
$$411$$ 9.89949 14.0000i 0.488306 0.690569i
$$412$$ −10.0000 10.0000i −0.492665 0.492665i
$$413$$ −11.3137 + 11.3137i −0.556711 + 0.556711i
$$414$$ −6.00000 16.9706i −0.294884 0.834058i
$$415$$ −2.00000 2.00000i −0.0981761 0.0981761i
$$416$$ 1.41421i 0.0693375i
$$417$$ 16.0000 22.6274i 0.783523 1.10807i
$$418$$ 12.0000i 0.586939i
$$419$$ 12.7279i 0.621800i 0.950443 + 0.310900i $$0.100630\pi$$
−0.950443 + 0.310900i $$0.899370\pi$$
$$420$$ −1.17157 6.82843i −0.0571669 0.333193i
$$421$$ −14.0000 + 14.0000i −0.682318 + 0.682318i −0.960522 0.278204i $$-0.910261\pi$$
0.278204 + 0.960522i $$0.410261\pi$$
$$422$$ −11.3137 11.3137i −0.550743 0.550743i
$$423$$ −4.00000 + 1.41421i −0.194487 + 0.0687614i
$$424$$ −2.00000 2.00000i −0.0971286 0.0971286i
$$425$$ 1.41421 + 1.41421i 0.0685994 + 0.0685994i
$$426$$ −4.82843 + 0.828427i −0.233938 + 0.0401374i
$$427$$ 16.0000 16.0000i 0.774294 0.774294i
$$428$$ 14.1421 0.683586
$$429$$ 1.75736 + 10.2426i 0.0848461 + 0.494519i
$$430$$ 9.00000 + 9.00000i 0.434019 + 0.434019i
$$431$$ 8.48528 + 8.48528i 0.408722 + 0.408722i 0.881293 0.472571i $$-0.156674\pi$$
−0.472571 + 0.881293i $$0.656674\pi$$
$$432$$ −1.41421 + 5.00000i −0.0680414 + 0.240563i
$$433$$ −6.00000 −0.288342 −0.144171 0.989553i $$-0.546051\pi$$
−0.144171 + 0.989553i $$0.546051\pi$$
$$434$$ 28.2843 1.35769
$$435$$ 0 0
$$436$$ −12.0000 + 12.0000i −0.574696 + 0.574696i
$$437$$ 16.9706 0.811812
$$438$$ −10.2426 + 1.75736i −0.489412 + 0.0839699i
$$439$$ 5.00000 5.00000i 0.238637 0.238637i −0.577649 0.816286i $$-0.696030\pi$$
0.816286 + 0.577649i $$0.196030\pi$$
$$440$$ 4.24264i 0.202260i
$$441$$ 9.00000 + 25.4558i 0.428571 + 1.21218i
$$442$$ 2.00000 + 2.00000i 0.0951303 + 0.0951303i
$$443$$ 2.82843 0.134383 0.0671913 0.997740i $$-0.478596\pi$$
0.0671913 + 0.997740i $$0.478596\pi$$
$$444$$ 4.58579 9.48528i 0.217632 0.450152i
$$445$$ −18.0000 −0.853282
$$446$$ −8.48528 8.48528i −0.401790 0.401790i
$$447$$ −9.89949 + 14.0000i −0.468230 + 0.662177i
$$448$$ 4.00000i 0.188982i
$$449$$ −12.7279 + 12.7279i −0.600668 + 0.600668i −0.940490 0.339822i $$-0.889633\pi$$
0.339822 + 0.940490i $$0.389633\pi$$
$$450$$ 2.70711 + 1.29289i 0.127614 + 0.0609476i
$$451$$ 24.0000 1.13012
$$452$$ −4.24264 + 4.24264i −0.199557 + 0.199557i
$$453$$ 0 0
$$454$$ −28.0000 −1.31411
$$455$$ −5.65685 −0.265197
$$456$$ −4.00000 2.82843i −0.187317 0.132453i
$$457$$ −12.0000 12.0000i −0.561336 0.561336i 0.368351 0.929687i $$-0.379923\pi$$
−0.929687 + 0.368351i $$0.879923\pi$$
$$458$$ 18.3848 + 18.3848i 0.859064 + 0.859064i
$$459$$ 5.07107 + 9.07107i 0.236697 + 0.423401i
$$460$$ −6.00000 −0.279751
$$461$$ −24.0416 + 24.0416i −1.11973 + 1.11973i −0.127950 + 0.991781i $$0.540840\pi$$
−0.991781 + 0.127950i $$0.959160\pi$$
$$462$$ −4.97056 28.9706i −0.231252 1.34783i
$$463$$ −22.0000 22.0000i −1.02243 1.02243i −0.999743 0.0226840i $$-0.992779\pi$$
−0.0226840 0.999743i $$-0.507221\pi$$
$$464$$ 0 0
$$465$$ −7.07107 + 10.0000i −0.327913 + 0.463739i
$$466$$ −5.00000 5.00000i −0.231621 0.231621i
$$467$$ 8.48528 8.48528i 0.392652 0.392652i −0.482980 0.875632i $$-0.660445\pi$$
0.875632 + 0.482980i $$0.160445\pi$$
$$468$$ 3.82843 + 1.82843i 0.176969 + 0.0845191i
$$469$$ 8.00000i 0.369406i
$$470$$ 1.41421i 0.0652328i
$$471$$ 25.4558 + 18.0000i 1.17294 + 0.829396i
$$472$$ 4.00000i 0.184115i
$$473$$ 38.1838 + 38.1838i 1.75569 + 1.75569i
$$474$$ −4.24264 + 6.00000i −0.194871 + 0.275589i
$$475$$ −2.00000 + 2.00000i −0.0917663 + 0.0917663i
$$476$$ −5.65685 5.65685i −0.259281 0.259281i
$$477$$ −8.00000 + 2.82843i −0.366295 + 0.129505i
$$478$$ 0 0
$$479$$ 25.4558 25.4558i 1.16311 1.16311i 0.179316 0.983792i $$-0.442612\pi$$
0.983792 0.179316i $$-0.0573883\pi$$
$$480$$ 1.41421 + 1.00000i 0.0645497 + 0.0456435i
$$481$$ −7.00000 5.00000i −0.319173 0.227980i
$$482$$ 4.24264i 0.193247i
$$483$$ 40.9706 7.02944i 1.86423 0.319850i
$$484$$ 7.00000i 0.318182i
$$485$$ −16.9706 −0.770594
$$486$$ 11.7071 + 10.2929i 0.531045 + 0.466895i
$$487$$ 22.0000 + 22.0000i 0.996915 + 0.996915i 0.999995 0.00308010i $$-0.000980427\pi$$
−0.00308010 + 0.999995i $$0.500980\pi$$
$$488$$ 5.65685i 0.256074i
$$489$$ 12.0711 2.07107i 0.545873 0.0936569i
$$490$$ 9.00000 0.406579
$$491$$ 21.2132i 0.957338i 0.877995 + 0.478669i $$0.158881\pi$$
−0.877995 + 0.478669i $$0.841119\pi$$
$$492$$ 5.65685 8.00000i 0.255031 0.360668i
$$493$$ 0 0
$$494$$ −2.82843 + 2.82843i −0.127257 + 0.127257i
$$495$$ 11.4853 + 5.48528i 0.516225 + 0.246545i
$$496$$ −5.00000 + 5.00000i −0.224507 + 0.224507i
$$497$$ 11.3137i 0.507489i
$$498$$ −4.82843 + 0.828427i −0.216367 + 0.0371227i
$$499$$ −12.0000 + 12.0000i −0.537194 + 0.537194i −0.922704 0.385510i $$-0.874026\pi$$
0.385510 + 0.922704i $$0.374026\pi$$
$$500$$ 0.707107 0.707107i 0.0316228 0.0316228i
$$501$$ 30.7279 5.27208i 1.37282 0.235539i
$$502$$ 4.00000i 0.178529i
$$503$$ −21.2132 + 21.2132i −0.945850 + 0.945850i −0.998607 0.0527574i $$-0.983199\pi$$
0.0527574 + 0.998607i $$0.483199\pi$$
$$504$$ −10.8284 5.17157i −0.482336 0.230360i
$$505$$ 11.0000 11.0000i 0.489494 0.489494i
$$506$$ −25.4558 −1.13165
$$507$$ −11.0000 + 15.5563i −0.488527 + 0.690882i
$$508$$ 12.0000i 0.532414i
$$509$$ −24.0416 −1.06563 −0.532813 0.846233i $$-0.678865\pi$$
−0.532813 + 0.846233i $$0.678865\pi$$
$$510$$ 3.41421 0.585786i 0.151184 0.0259391i
$$511$$ 24.0000i 1.06170i
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ −12.8284 + 7.17157i −0.566389 + 0.316633i
$$514$$ 4.00000 0.176432
$$515$$ 14.1421i 0.623177i
$$516$$ 21.7279 3.72792i 0.956518 0.164113i
$$517$$ 6.00000i 0.263880i
$$518$$ 19.7990 + 14.1421i 0.869918 + 0.621370i
$$519$$ 4.00000 + 2.82843i 0.175581 + 0.124154i
$$520$$ 1.00000 1.00000i 0.0438529 0.0438529i
$$521$$ 8.48528 0.371747 0.185873 0.982574i $$-0.440489\pi$$
0.185873 + 0.982574i $$0.440489\pi$$
$$522$$ 0 0
$$523$$ −9.00000 9.00000i −0.393543 0.393543i 0.482405 0.875948i $$-0.339763\pi$$
−0.875948 + 0.482405i $$0.839763\pi$$
$$524$$ −8.48528 + 8.48528i −0.370681 + 0.370681i
$$525$$ −4.00000 + 5.65685i −0.174574 + 0.246885i
$$526$$ −19.0000 19.0000i −0.828439 0.828439i
$$527$$ 14.1421i 0.616041i
$$528$$ 6.00000 + 4.24264i 0.261116 + 0.184637i
$$529$$ 13.0000i 0.565217i
$$530$$ 2.82843i 0.122859i
$$531$$ −10.8284 5.17157i −0.469914 0.224427i
$$532$$ 8.00000 8.00000i 0.346844 0.346844i
$$533$$ −5.65685 5.65685i −0.245026 0.245026i
$$534$$ −18.0000 + 25.4558i −0.778936 + 1.10158i
$$535$$ −10.0000 10.0000i −0.432338 0.432338i
$$536$$ −1.41421 1.41421i −0.0610847 0.0610847i
$$537$$ 5.27208 + 30.7279i 0.227507 + 1.32601i
$$538$$ 15.0000 15.0000i 0.646696 0.646696i
$$539$$ 38.1838 1.64469
$$540$$ 4.53553 2.53553i 0.195178 0.109112i
$$541$$ 2.00000 + 2.00000i 0.0859867 + 0.0859867i 0.748792 0.662805i $$-0.230634\pi$$
−0.662805 + 0.748792i $$0.730634\pi$$
$$542$$ −5.65685 5.65685i −0.242983 0.242983i
$$543$$ −8.48528 6.00000i −0.364138 0.257485i
$$544$$ 2.00000 0.0857493
$$545$$ 16.9706 0.726939
$$546$$ −5.65685 + 8.00000i −0.242091 + 0.342368i
$$547$$ −21.0000 + 21.0000i −0.897895 + 0.897895i −0.995250 0.0973546i $$-0.968962\pi$$
0.0973546 + 0.995250i $$0.468962\pi$$
$$548$$ −9.89949 −0.422885
$$549$$ 15.3137 + 7.31371i 0.653573 + 0.312141i
$$550$$ 3.00000 3.00000i 0.127920 0.127920i
$$551$$ 0 0
$$552$$ −6.00000 + 8.48528i −0.255377 + 0.361158i
$$553$$ −12.0000 12.0000i −0.510292 0.510292i
$$554$$ −21.2132 −0.901263
$$555$$ −9.94975 + 3.46447i −0.422343 + 0.147058i
$$556$$ −16.0000 −0.678551
$$557$$ −24.0416 24.0416i −1.01868 1.01868i −0.999822 0.0188543i $$-0.993998\pi$$
−0.0188543 0.999822i $$-0.506002\pi$$
$$558$$ 7.07107 + 20.0000i 0.299342 + 0.846668i
$$559$$ 18.0000i 0.761319i
$$560$$ −2.82843 + 2.82843i −0.119523 + 0.119523i
$$561$$ 14.4853 2.48528i 0.611569 0.104929i
$$562$$ −10.0000 −0.421825
$$563$$ 5.65685 5.65685i 0.238408 0.238408i −0.577783 0.816191i $$-0.696082\pi$$
0.816191 + 0.577783i $$0.196082\pi$$
$$564$$ 2.00000 + 1.41421i 0.0842152 + 0.0595491i
$$565$$ 6.00000 0.252422
$$566$$ −21.2132 −0.891657
$$567$$ −28.0000 + 22.6274i −1.17589 + 0.950262i
$$568$$ 2.00000 + 2.00000i 0.0839181 + 0.0839181i
$$569$$ 18.3848 + 18.3848i 0.770730 + 0.770730i 0.978234 0.207504i $$-0.0665341\pi$$
−0.207504 + 0.978234i $$0.566534\pi$$
$$570$$ 0.828427 + 4.82843i 0.0346990 + 0.202241i
$$571$$ 32.0000 1.33916 0.669579 0.742741i $$-0.266474\pi$$
0.669579 + 0.742741i $$0.266474\pi$$
$$572$$ 4.24264 4.24264i 0.177394 0.177394i
$$573$$ −6.82843 + 1.17157i −0.285262 + 0.0489432i
$$574$$ 16.0000 + 16.0000i 0.667827 + 0.667827i
$$575$$ 4.24264 + 4.24264i 0.176930 + 0.176930i
$$576$$ 2.82843 1.00000i 0.117851 0.0416667i
$$577$$ 20.0000 + 20.0000i 0.832611 + 0.832611i 0.987873 0.155262i $$-0.0496223\pi$$
−0.155262 + 0.987873i $$0.549622\pi$$
$$578$$ −9.19239 + 9.19239i −0.382353 + 0.382353i
$$579$$ −7.45584 43.4558i −0.309854 1.80596i
$$580$$ 0 0
$$581$$ 11.3137i 0.469372i
$$582$$ −16.9706 + 24.0000i −0.703452 + 0.994832i
$$583$$ 12.0000i 0.496989i
$$584$$ 4.24264 + 4.24264i 0.175562 + 0.175562i
$$585$$ −1.41421 4.00000i −0.0584705 0.165380i
$$586$$ 20.0000 20.0000i 0.826192 0.826192i
$$587$$ 16.9706 + 16.9706i 0.700450 + 0.700450i 0.964507 0.264057i $$-0.0850607\pi$$
−0.264057 + 0.964507i $$0.585061\pi$$
$$588$$ 9.00000 12.7279i 0.371154 0.524891i
$$589$$ −20.0000 −0.824086
$$590$$ −2.82843 + 2.82843i −0.116445 + 0.116445i
$$591$$ −19.7990 + 28.0000i −0.814422 + 1.15177i
$$592$$ −6.00000 + 1.00000i −0.246598 + 0.0410997i
$$593$$ 15.5563i 0.638823i −0.947616 0.319411i $$-0.896515\pi$$
0.947616 0.319411i $$-0.103485\pi$$
$$594$$ 19.2426 10.7574i 0.789535 0.441380i
$$595$$ 8.00000i 0.327968i
$$596$$ 9.89949 0.405499
$$597$$ 7.24264 1.24264i 0.296422 0.0508579i
$$598$$ 6.00000 + 6.00000i 0.245358 + 0.245358i
$$599$$ 16.9706i 0.693398i −0.937976 0.346699i $$-0.887302\pi$$
0.937976 0.346699i $$-0.112698\pi$$
$$600$$ −0.292893 1.70711i −0.0119573 0.0696923i
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 50.9117i 2.07501i
$$603$$ −5.65685 + 2.00000i −0.230365 + 0.0814463i
$$604$$ 0 0
$$605$$ 4.94975 4.94975i 0.201236 0.201236i
$$606$$ −4.55635 26.5563i −0.185089 1.07878i
$$607$$ −22.0000 + 22.0000i −0.892952 + 0.892952i −0.994800 0.101848i $$-0.967525\pi$$
0.101848 + 0.994800i $$0.467525\pi$$
$$608$$ 2.82843i 0.114708i
$$609$$ 0 0
$$610$$ 4.00000 4.00000i 0.161955 0.161955i
$$611$$ 1.41421 1.41421i 0.0572130 0.0572130i
$$612$$ 2.58579 5.41421i 0.104524 0.218857i
$$613$$ 16.0000i 0.646234i 0.946359 + 0.323117i $$0.104731\pi$$
−0.946359 + 0.323117i $$0.895269\pi$$
$$614$$ 2.82843 2.82843i 0.114146 0.114146i
$$615$$ −9.65685 + 1.65685i −0.389402 + 0.0668108i
$$616$$ −12.0000 + 12.0000i −0.483494 + 0.483494i
$$617$$ −21.2132 −0.854011 −0.427006 0.904249i $$-0.640432\pi$$
−0.427006 + 0.904249i $$0.640432\pi$$
$$618$$ 20.0000 + 14.1421i 0.804518 + 0.568880i
$$619$$ 16.0000i 0.643094i −0.946894 0.321547i $$-0.895797\pi$$
0.946894 0.321547i $$-0.104203\pi$$
$$620$$ 7.07107 0.283981
$$621$$ 15.2132 + 27.2132i 0.610485 + 1.09203i
$$622$$ 12.0000i 0.481156i
$$623$$ −50.9117 50.9117i −2.03973 2.03973i
$$624$$ −0.414214 2.41421i −0.0165818 0.0966459i
$$625$$ −1.00000 −0.0400000
$$626$$ 8.48528i 0.339140i
$$627$$ 3.51472 + 20.4853i 0.140364 + 0.818103i
$$628$$ 18.0000i 0.718278i
$$629$$ −7.07107 + 9.89949i −0.281942 + 0.394719i
$$630$$ 4.00000 + 11.3137i 0.159364 + 0.450749i
$$631$$ 1.00000 1.00000i 0.0398094 0.0398094i −0.686922 0.726731i $$-0.741039\pi$$
0.726731 + 0.686922i $$0.241039\pi$$
$$632$$ 4.24264 0.168763
$$633$$ 22.6274 + 16.0000i 0.899359 + 0.635943i
$$634$$ 6.00000 + 6.00000i 0.238290 + 0.238290i
$$635$$ −8.48528 + 8.48528i −0.336728 + 0.336728i
$$636$$ 4.00000 + 2.82843i 0.158610 + 0.112154i
$$637$$ −9.00000 9.00000i −0.356593 0.356593i
$$638$$ 0 0
$$639$$ 8.00000 2.82843i 0.316475 0.111891i
$$640$$ 1.00000i 0.0395285i
$$641$$ 22.6274i 0.893729i −0.894602 0.446865i $$-0.852541\pi$$
0.894602 0.446865i $$-0.147459\pi$$
$$642$$ −24.1421 + 4.14214i −0.952814 + 0.163477i
$$643$$ 17.0000 17.0000i 0.670415 0.670415i −0.287397 0.957812i $$-0.592790\pi$$
0.957812 + 0.287397i $$0.0927899\pi$$
$$644$$ −16.9706 16.9706i −0.668734 0.668734i
$$645$$ −18.0000 12.7279i −0.708749 0.501161i
$$646$$ 4.00000 + 4.00000i 0.157378 + 0.157378i
$$647$$ 22.6274 + 22.6274i 0.889576 + 0.889576i 0.994482 0.104907i $$-0.0334543\pi$$
−0.104907 + 0.994482i $$0.533454\pi$$
$$648$$ 0.949747 8.94975i 0.0373096 0.351579i
$$649$$ −12.0000 + 12.0000i −0.471041 + 0.471041i
$$650$$ −1.41421 −0.0554700
$$651$$ −48.2843 + 8.28427i −1.89241 + 0.324686i
$$652$$ −5.00000 5.00000i −0.195815 0.195815i
$$653$$ −4.24264 4.24264i −0.166027 0.166027i 0.619203 0.785231i $$-0.287456\pi$$
−0.785231 + 0.619203i $$0.787456\pi$$
$$654$$ 16.9706 24.0000i 0.663602 0.938474i
$$655$$ 12.0000 0.468879
$$656$$ −5.65685 −0.220863
$$657$$ 16.9706 6.00000i 0.662085 0.234082i
$$658$$ −4.00000 + 4.00000i −0.155936 + 0.155936i
$$659$$ 9.89949 0.385630 0.192815 0.981235i $$-0.438238\pi$$
0.192815 + 0.981235i $$0.438238\pi$$
$$660$$ −1.24264 7.24264i −0.0483697 0.281919i
$$661$$ 10.0000 10.0000i 0.388955 0.388955i −0.485360 0.874315i $$-0.661311\pi$$
0.874315 + 0.485360i $$0.161311\pi$$
$$662$$ 5.65685i 0.219860i
$$663$$ −4.00000 2.82843i −0.155347 0.109847i
$$664$$ 2.00000 + 2.00000i 0.0776151 + 0.0776151i
$$665$$ −11.3137 −0.438727
$$666$$ −5.05025 + 17.5355i −0.195693 + 0.679488i
$$667$$ 0 0
$$668$$ −12.7279 12.7279i −0.492458 0.492458i
$$669$$ 16.9706 + 12.0000i 0.656120 + 0.463947i
$$670$$ 2.00000i 0.0772667i
$$671$$ 16.9706 16.9706i 0.655141 0.655141i
$$672$$ 1.17157 + 6.82843i 0.0451944 + 0.263412i
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ 1.41421 1.41421i 0.0544735 0.0544735i
$$675$$ −5.00000 1.41421i −0.192450 0.0544331i
$$676$$ 11.0000 0.423077
$$677$$ 28.2843 1.08705 0.543526 0.839392i $$-0.317089\pi$$
0.543526 + 0.839392i $$0.317089\pi$$
$$678$$ 6.00000 8.48528i 0.230429 0.325875i
$$679$$ −48.0000 48.0000i −1.84207 1.84207i
$$680$$ −1.41421 1.41421i −0.0542326 0.0542326i
$$681$$ 47.7990 8.20101i 1.83166 0.314263i
$$682$$ 30.0000 1.14876
$$683$$ 22.6274 22.6274i 0.865814 0.865814i −0.126192 0.992006i $$-0.540275\pi$$
0.992006 + 0.126192i $$0.0402755\pi$$
$$684$$ 7.65685 + 3.65685i 0.292767 + 0.139823i
$$685$$ 7.00000 + 7.00000i 0.267456 + 0.267456i
$$686$$ 5.65685 + 5.65685i 0.215980 + 0.215980i
$$687$$ −36.7696 26.0000i −1.40285 0.991962i
$$688$$ −9.00000 9.00000i −0.343122 0.343122i
$$689$$ 2.82843 2.82843i 0.107754 0.107754i
$$690$$ 10.2426 1.75736i 0.389931 0.0669015i
$$691$$ 28.0000i 1.06517i −0.846376 0.532585i $$-0.821221\pi$$
0.846376 0.532585i $$-0.178779\pi$$
$$692$$ 2.82843i 0.107521i
$$693$$ 16.9706 + 48.0000i 0.644658 + 1.82337i
$$694$$ 12.0000i 0.455514i
$$695$$ 11.3137 + 11.3137i 0.429153 + 0.429153i
$$696$$ 0 0
$$697$$ −8.00000 + 8.00000i −0.303022 + 0.303022i
$$698$$ −9.89949 9.89949i −0.374701 0.374701i
$$699$$ 10.0000 + 7.07107i 0.378235 + 0.267452i
$$700$$ 4.00000 0.151186
$$701$$ −35.3553 + 35.3553i −1.33535 + 1.33535i −0.434850 + 0.900503i $$0.643198\pi$$
−0.900503 + 0.434850i $$0.856802\pi$$
$$702$$ −7.07107 2.00000i −0.266880 0.0754851i
$$703$$ −14.0000 10.0000i −0.528020 0.377157i
$$704$$ 4.24264i 0.159901i
$$705$$ −0.414214 2.41421i −0.0156002 0.0909245i
$$706$$ 34.0000i 1.27961i
$$707$$ 62.2254 2.34023
$$708$$ 1.17157 + 6.82843i 0.0440304 + 0.256628i
$$709$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$710$$ 2.82843i 0.106149i
$$711$$ 5.48528 11.4853i 0.205714 0.430732i
$$712$$ 18.0000 0.674579
$$713$$ 42.4264i 1.58888i
$$714$$ 11.3137 + 8.00000i 0.423405 + 0.299392i
$$715$$ −6.00000 −0.224387
$$716$$ 12.7279 12.7279i 0.475665 0.475665i
$$717$$ 0 0
$$718$$ −8.00000 + 8.00000i −0.298557 + 0.298557i
$$719$$ 19.7990i 0.738378i 0.929354 + 0.369189i $$0.120364\pi$$
−0.929354 + 0.369189i $$0.879636\pi$$
$$720$$ −2.70711 1.29289i −0.100888 0.0481833i
$$721$$ −40.0000 + 40.0000i −1.48968 + 1.48968i
$$722$$ 7.77817 7.77817i 0.289474 0.289474i
$$723$$ −1.24264 7.24264i −0.0462143 0.269357i
$$724$$ 6.00000i 0.222988i
$$725$$ 0 0
$$726$$ −2.05025 11.9497i −0.0760920 0.443497i
$$727$$ 8.00000 8.00000i 0.296704 0.296704i −0.543018 0.839721i $$-0.682718\pi$$
0.839721 + 0.543018i $$0.182718\pi$$
$$728$$ 5.65685 0.209657
$$729$$ −23.0000 14.1421i −0.851852 0.523783i
$$730$$ 6.00000i 0.222070i
$$731$$ −25.4558 −0.941518
$$732$$ −1.65685 9.65685i −0.0612391 0.356928i
$$733$$ 24.0000i 0.886460i 0.896408 + 0.443230i $$0.146168\pi$$
−0.896408 + 0.443230i $$0.853832\pi$$
$$734$$ 5.65685 + 5.65685i 0.208798 + 0.208798i
$$735$$ −15.3640 + 2.63604i −0.566708 + 0.0972318i
$$736$$ 6.00000 0.221163
$$737$$ 8.48528i 0.312559i
$$738$$ −7.31371 + 15.3137i −0.269221 + 0.563705i
$$739$$ 40.0000i 1.47142i 0.677295 + 0.735712i $$0.263152\pi$$
−0.677295 + 0.735712i $$0.736848\pi$$
$$740$$ 4.94975 + 3.53553i 0.181956 + 0.129969i
$$741$$ 4.00000 5.65685i 0.146944 0.207810i
$$742$$ −8.00000 + 8.00000i −0.293689 + 0.293689i
$$743$$ 49.4975 1.81589 0.907943 0.419093i $$-0.137652\pi$$
0.907943 + 0.419093i $$0.137652\pi$$
$$744$$ 7.07107 10.0000i 0.259238 0.366618i
$$745$$ −7.00000 7.00000i −0.256460 0.256460i
$$746$$ 24.0416 24.0416i 0.880227 0.880227i
$$747$$ 8.00000 2.82843i 0.292705 0.103487i
$$748$$ −6.00000 6.00000i −0.219382 0.219382i
$$749$$ 56.5685i 2.06697i
$$750$$ −1.00000 + 1.41421i −0.0365148 + 0.0516398i
$$751$$ 2.00000i 0.0729810i −0.999334 0.0364905i $$-0.988382\pi$$
0.999334 0.0364905i $$-0.0116179\pi$$
$$752$$ 1.41421i 0.0515711i
$$753$$ 1.17157 + 6.82843i 0.0426945 + 0.248842i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 20.0000 + 5.65685i 0.727393 + 0.205738i
$$757$$ −5.00000 5.00000i −0.181728 0.181728i 0.610380 0.792108i $$-0.291017\pi$$
−0.792108 + 0.610380i $$0.791017\pi$$
$$758$$ 0 0
$$759$$ 43.4558 7.45584i 1.57735 0.270630i
$$760$$ 2.00000 2.00000i 0.0725476 0.0725476i
$$761$$ 22.6274 0.820243 0.410122 0.912031i $$-0.365486\pi$$
0.410122 + 0.912031i $$0.365486\pi$$
$$762$$ 3.51472 + 20.4853i 0.127325 + 0.742103i
$$763$$ 48.0000 + 48.0000i 1.73772 + 1.73772i
$$764$$ 2.82843 + 2.82843i 0.102329 + 0.102329i
$$765$$ −5.65685 + 2.00000i −0.204524 + 0.0723102i
$$766$$ 16.0000 0.578103
$$767$$ 5.65685 0.204257
$$768$$ −1.41421 1.00000i −0.0510310 0.0360844i
$$769$$ 19.0000 19.0000i 0.685158 0.685158i −0.276000 0.961158i $$-0.589009\pi$$
0.961158 + 0.276000i $$0.0890090\pi$$
$$770$$ 16.9706 0.611577
$$771$$ −6.82843 + 1.17157i −0.245920 + 0.0421932i
$$772$$ −18.0000 + 18.0000i −0.647834 + 0.647834i
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ −36.0000 + 12.7279i −1.29399 + 0.457496i
$$775$$ −5.00000 5.00000i −0.179605 0.179605i
$$776$$ 16.9706 0.609208
$$777$$ −37.9411 18.3431i −1.36113 0.658057i