# Properties

 Label 1110.2.l.a.697.4 Level $1110$ Weight $2$ Character 1110.697 Analytic conductor $8.863$ Analytic rank $0$ Dimension $36$ CM no Inner twists $2$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$8.86339462436$$ Analytic rank: $$0$$ Dimension: $$36$$ Relative dimension: $$18$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 697.4 Character $$\chi$$ $$=$$ 1110.697 Dual form 1110.2.l.a.43.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(1.11117 - 1.94044i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.636201 + 0.636201i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-1.94044 - 1.11117i) q^{10} +2.26858i q^{11} +(0.707107 + 0.707107i) q^{12} -1.29147i q^{13} +(0.636201 - 0.636201i) q^{14} +(-2.15781 + 0.586380i) q^{15} +1.00000 q^{16} -5.74699 q^{17} +1.00000 q^{18} +(-4.10165 - 4.10165i) q^{19} +(-1.11117 + 1.94044i) q^{20} -0.899724i q^{21} +2.26858 q^{22} -8.53431i q^{23} +(0.707107 - 0.707107i) q^{24} +(-2.53060 - 4.31232i) q^{25} -1.29147 q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.636201 - 0.636201i) q^{28} +(-1.70155 + 1.70155i) q^{29} +(0.586380 + 2.15781i) q^{30} +(-5.81155 - 5.81155i) q^{31} -1.00000i q^{32} +(1.60413 - 1.60413i) q^{33} +5.74699i q^{34} +(1.94144 - 0.527580i) q^{35} -1.00000i q^{36} +(5.19618 + 3.16223i) q^{37} +(-4.10165 + 4.10165i) q^{38} +(-0.913209 + 0.913209i) q^{39} +(1.94044 + 1.11117i) q^{40} +9.02011i q^{41} -0.899724 q^{42} -0.853087i q^{43} -2.26858i q^{44} +(1.94044 + 1.11117i) q^{45} -8.53431 q^{46} +(-0.326713 - 0.326713i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.19050i q^{49} +(-4.31232 + 2.53060i) q^{50} +(4.06374 + 4.06374i) q^{51} +1.29147i q^{52} +(-6.79864 + 6.79864i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(4.40204 + 2.52078i) q^{55} +(-0.636201 + 0.636201i) q^{56} +5.80061i q^{57} +(1.70155 + 1.70155i) q^{58} +(3.51171 + 3.51171i) q^{59} +(2.15781 - 0.586380i) q^{60} +(-2.06460 - 2.06460i) q^{61} +(-5.81155 + 5.81155i) q^{62} +(-0.636201 + 0.636201i) q^{63} -1.00000 q^{64} +(-2.50602 - 1.43505i) q^{65} +(-1.60413 - 1.60413i) q^{66} +(3.98347 - 3.98347i) q^{67} +5.74699 q^{68} +(-6.03467 + 6.03467i) q^{69} +(-0.527580 - 1.94144i) q^{70} -15.2892 q^{71} -1.00000 q^{72} +(-11.8322 - 11.8322i) q^{73} +(3.16223 - 5.19618i) q^{74} +(-1.25987 + 4.83867i) q^{75} +(4.10165 + 4.10165i) q^{76} +(-1.44327 + 1.44327i) q^{77} +(0.913209 + 0.913209i) q^{78} +(9.04382 + 9.04382i) q^{79} +(1.11117 - 1.94044i) q^{80} -1.00000 q^{81} +9.02011 q^{82} +(9.12362 - 9.12362i) q^{83} +0.899724i q^{84} +(-6.38589 + 11.1517i) q^{85} -0.853087 q^{86} +2.40635 q^{87} -2.26858 q^{88} +(-6.32382 + 6.32382i) q^{89} +(1.11117 - 1.94044i) q^{90} +(0.821636 - 0.821636i) q^{91} +8.53431i q^{92} +8.21877i q^{93} +(-0.326713 + 0.326713i) q^{94} +(-12.5166 + 3.40136i) q^{95} +(-0.707107 + 0.707107i) q^{96} +9.28197 q^{97} -6.19050 q^{98} -2.26858 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$36q - 36q^{4} + 4q^{7} + O(q^{10})$$ $$36q - 36q^{4} + 4q^{7} - 4q^{10} + 4q^{14} + 36q^{16} - 32q^{17} + 36q^{18} + 4q^{19} + 8q^{22} - 4q^{25} + 8q^{26} - 4q^{28} + 36q^{29} - 4q^{31} + 4q^{33} - 12q^{35} - 4q^{37} + 4q^{38} + 4q^{39} + 4q^{40} - 16q^{42} + 4q^{45} + 16q^{47} - 16q^{50} - 8q^{53} + 16q^{55} - 4q^{56} - 36q^{58} - 4q^{59} - 4q^{61} - 4q^{62} - 4q^{63} - 36q^{64} + 52q^{65} - 4q^{66} + 16q^{67} + 32q^{68} - 8q^{69} - 28q^{70} - 8q^{71} - 36q^{72} - 4q^{73} + 28q^{74} + 16q^{75} - 4q^{76} + 8q^{77} - 4q^{78} - 12q^{79} - 36q^{81} - 8q^{82} + 8q^{83} + 8q^{85} + 32q^{86} - 8q^{87} - 8q^{88} - 24q^{89} + 56q^{91} + 16q^{94} - 20q^{95} + 40q^{97} - 12q^{98} - 8q^{99} + O(q^{100})$$

## Character values

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

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

## 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
$$3$$ −0.707107 0.707107i −0.408248 0.408248i
$$4$$ −1.00000 −0.500000
$$5$$ 1.11117 1.94044i 0.496931 0.867790i
$$6$$ −0.707107 + 0.707107i −0.288675 + 0.288675i
$$7$$ 0.636201 + 0.636201i 0.240461 + 0.240461i 0.817041 0.576580i $$-0.195613\pi$$
−0.576580 + 0.817041i $$0.695613\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000i 0.333333i
$$10$$ −1.94044 1.11117i −0.613620 0.351383i
$$11$$ 2.26858i 0.684003i 0.939699 + 0.342002i $$0.111105\pi$$
−0.939699 + 0.342002i $$0.888895\pi$$
$$12$$ 0.707107 + 0.707107i 0.204124 + 0.204124i
$$13$$ 1.29147i 0.358190i −0.983832 0.179095i $$-0.942683\pi$$
0.983832 0.179095i $$-0.0573169\pi$$
$$14$$ 0.636201 0.636201i 0.170032 0.170032i
$$15$$ −2.15781 + 0.586380i −0.557145 + 0.151403i
$$16$$ 1.00000 0.250000
$$17$$ −5.74699 −1.39385 −0.696925 0.717144i $$-0.745449\pi$$
−0.696925 + 0.717144i $$0.745449\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −4.10165 4.10165i −0.940982 0.940982i 0.0573705 0.998353i $$-0.481728\pi$$
−0.998353 + 0.0573705i $$0.981728\pi$$
$$20$$ −1.11117 + 1.94044i −0.248465 + 0.433895i
$$21$$ 0.899724i 0.196336i
$$22$$ 2.26858 0.483663
$$23$$ 8.53431i 1.77953i −0.456423 0.889763i $$-0.650869\pi$$
0.456423 0.889763i $$-0.349131\pi$$
$$24$$ 0.707107 0.707107i 0.144338 0.144338i
$$25$$ −2.53060 4.31232i −0.506119 0.862464i
$$26$$ −1.29147 −0.253278
$$27$$ 0.707107 0.707107i 0.136083 0.136083i
$$28$$ −0.636201 0.636201i −0.120231 0.120231i
$$29$$ −1.70155 + 1.70155i −0.315969 + 0.315969i −0.847217 0.531247i $$-0.821723\pi$$
0.531247 + 0.847217i $$0.321723\pi$$
$$30$$ 0.586380 + 2.15781i 0.107058 + 0.393961i
$$31$$ −5.81155 5.81155i −1.04379 1.04379i −0.998996 0.0447888i $$-0.985739\pi$$
−0.0447888 0.998996i $$-0.514261\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 1.60413 1.60413i 0.279243 0.279243i
$$34$$ 5.74699i 0.985601i
$$35$$ 1.94144 0.527580i 0.328163 0.0891773i
$$36$$ 1.00000i 0.166667i
$$37$$ 5.19618 + 3.16223i 0.854247 + 0.519868i
$$38$$ −4.10165 + 4.10165i −0.665375 + 0.665375i
$$39$$ −0.913209 + 0.913209i −0.146230 + 0.146230i
$$40$$ 1.94044 + 1.11117i 0.306810 + 0.175692i
$$41$$ 9.02011i 1.40870i 0.709851 + 0.704352i $$0.248762\pi$$
−0.709851 + 0.704352i $$0.751238\pi$$
$$42$$ −0.899724 −0.138830
$$43$$ 0.853087i 0.130094i −0.997882 0.0650472i $$-0.979280\pi$$
0.997882 0.0650472i $$-0.0207198\pi$$
$$44$$ 2.26858i 0.342002i
$$45$$ 1.94044 + 1.11117i 0.289263 + 0.165644i
$$46$$ −8.53431 −1.25832
$$47$$ −0.326713 0.326713i −0.0476560 0.0476560i 0.682877 0.730533i $$-0.260728\pi$$
−0.730533 + 0.682877i $$0.760728\pi$$
$$48$$ −0.707107 0.707107i −0.102062 0.102062i
$$49$$ 6.19050i 0.884357i
$$50$$ −4.31232 + 2.53060i −0.609854 + 0.357880i
$$51$$ 4.06374 + 4.06374i 0.569037 + 0.569037i
$$52$$ 1.29147i 0.179095i
$$53$$ −6.79864 + 6.79864i −0.933866 + 0.933866i −0.997945 0.0640792i $$-0.979589\pi$$
0.0640792 + 0.997945i $$0.479589\pi$$
$$54$$ −0.707107 0.707107i −0.0962250 0.0962250i
$$55$$ 4.40204 + 2.52078i 0.593571 + 0.339902i
$$56$$ −0.636201 + 0.636201i −0.0850159 + 0.0850159i
$$57$$ 5.80061i 0.768309i
$$58$$ 1.70155 + 1.70155i 0.223424 + 0.223424i
$$59$$ 3.51171 + 3.51171i 0.457186 + 0.457186i 0.897731 0.440545i $$-0.145215\pi$$
−0.440545 + 0.897731i $$0.645215\pi$$
$$60$$ 2.15781 0.586380i 0.278573 0.0757013i
$$61$$ −2.06460 2.06460i −0.264345 0.264345i 0.562472 0.826817i $$-0.309851\pi$$
−0.826817 + 0.562472i $$0.809851\pi$$
$$62$$ −5.81155 + 5.81155i −0.738068 + 0.738068i
$$63$$ −0.636201 + 0.636201i −0.0801538 + 0.0801538i
$$64$$ −1.00000 −0.125000
$$65$$ −2.50602 1.43505i −0.310834 0.177996i
$$66$$ −1.60413 1.60413i −0.197455 0.197455i
$$67$$ 3.98347 3.98347i 0.486659 0.486659i −0.420591 0.907250i $$-0.638177\pi$$
0.907250 + 0.420591i $$0.138177\pi$$
$$68$$ 5.74699 0.696925
$$69$$ −6.03467 + 6.03467i −0.726489 + 0.726489i
$$70$$ −0.527580 1.94144i −0.0630579 0.232046i
$$71$$ −15.2892 −1.81450 −0.907248 0.420596i $$-0.861821\pi$$
−0.907248 + 0.420596i $$0.861821\pi$$
$$72$$ −1.00000 −0.117851
$$73$$ −11.8322 11.8322i −1.38486 1.38486i −0.835751 0.549108i $$-0.814968\pi$$
−0.549108 0.835751i $$-0.685032\pi$$
$$74$$ 3.16223 5.19618i 0.367602 0.604044i
$$75$$ −1.25987 + 4.83867i −0.145477 + 0.558722i
$$76$$ 4.10165 + 4.10165i 0.470491 + 0.470491i
$$77$$ −1.44327 + 1.44327i −0.164476 + 0.164476i
$$78$$ 0.913209 + 0.913209i 0.103401 + 0.103401i
$$79$$ 9.04382 + 9.04382i 1.01751 + 1.01751i 0.999844 + 0.0176652i $$0.00562329\pi$$
0.0176652 + 0.999844i $$0.494377\pi$$
$$80$$ 1.11117 1.94044i 0.124233 0.216948i
$$81$$ −1.00000 −0.111111
$$82$$ 9.02011 0.996104
$$83$$ 9.12362 9.12362i 1.00145 1.00145i 0.00144791 0.999999i $$-0.499539\pi$$
0.999999 0.00144791i $$-0.000460883\pi$$
$$84$$ 0.899724i 0.0981680i
$$85$$ −6.38589 + 11.1517i −0.692647 + 1.20957i
$$86$$ −0.853087 −0.0919907
$$87$$ 2.40635 0.257988
$$88$$ −2.26858 −0.241832
$$89$$ −6.32382 + 6.32382i −0.670323 + 0.670323i −0.957791 0.287467i $$-0.907187\pi$$
0.287467 + 0.957791i $$0.407187\pi$$
$$90$$ 1.11117 1.94044i 0.117128 0.204540i
$$91$$ 0.821636 0.821636i 0.0861308 0.0861308i
$$92$$ 8.53431i 0.889763i
$$93$$ 8.21877i 0.852247i
$$94$$ −0.326713 + 0.326713i −0.0336979 + 0.0336979i
$$95$$ −12.5166 + 3.40136i −1.28418 + 0.348972i
$$96$$ −0.707107 + 0.707107i −0.0721688 + 0.0721688i
$$97$$ 9.28197 0.942441 0.471220 0.882015i $$-0.343814\pi$$
0.471220 + 0.882015i $$0.343814\pi$$
$$98$$ −6.19050 −0.625335
$$99$$ −2.26858 −0.228001
$$100$$ 2.53060 + 4.31232i 0.253060 + 0.431232i
$$101$$ 1.47408i 0.146677i 0.997307 + 0.0733383i $$0.0233653\pi$$
−0.997307 + 0.0733383i $$0.976635\pi$$
$$102$$ 4.06374 4.06374i 0.402370 0.402370i
$$103$$ 1.02968 0.101458 0.0507289 0.998712i $$-0.483846\pi$$
0.0507289 + 0.998712i $$0.483846\pi$$
$$104$$ 1.29147 0.126639
$$105$$ −1.74586 0.999748i −0.170378 0.0975654i
$$106$$ 6.79864 + 6.79864i 0.660343 + 0.660343i
$$107$$ −13.8598 13.8598i −1.33988 1.33988i −0.896171 0.443708i $$-0.853663\pi$$
−0.443708 0.896171i $$-0.646337\pi$$
$$108$$ −0.707107 + 0.707107i −0.0680414 + 0.0680414i
$$109$$ 5.32683 + 5.32683i 0.510218 + 0.510218i 0.914593 0.404375i $$-0.132511\pi$$
−0.404375 + 0.914593i $$0.632511\pi$$
$$110$$ 2.52078 4.40204i 0.240347 0.419718i
$$111$$ −1.43822 5.91029i −0.136510 0.560980i
$$112$$ 0.636201 + 0.636201i 0.0601153 + 0.0601153i
$$113$$ 17.2755 1.62515 0.812573 0.582859i $$-0.198066\pi$$
0.812573 + 0.582859i $$0.198066\pi$$
$$114$$ 5.80061 0.543276
$$115$$ −16.5603 9.48308i −1.54426 0.884302i
$$116$$ 1.70155 1.70155i 0.157985 0.157985i
$$117$$ 1.29147 0.119397
$$118$$ 3.51171 3.51171i 0.323279 0.323279i
$$119$$ −3.65624 3.65624i −0.335167 0.335167i
$$120$$ −0.586380 2.15781i −0.0535289 0.196981i
$$121$$ 5.85354 0.532140
$$122$$ −2.06460 + 2.06460i −0.186920 + 0.186920i
$$123$$ 6.37818 6.37818i 0.575101 0.575101i
$$124$$ 5.81155 + 5.81155i 0.521893 + 0.521893i
$$125$$ −11.1797 + 0.118740i −0.999944 + 0.0106204i
$$126$$ 0.636201 + 0.636201i 0.0566773 + 0.0566773i
$$127$$ 0.916380 + 0.916380i 0.0813156 + 0.0813156i 0.746595 0.665279i $$-0.231687\pi$$
−0.665279 + 0.746595i $$0.731687\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −0.603223 + 0.603223i −0.0531109 + 0.0531109i
$$130$$ −1.43505 + 2.50602i −0.125862 + 0.219793i
$$131$$ −6.28943 6.28943i −0.549510 0.549510i 0.376789 0.926299i $$-0.377028\pi$$
−0.926299 + 0.376789i $$0.877028\pi$$
$$132$$ −1.60413 + 1.60413i −0.139622 + 0.139622i
$$133$$ 5.21895i 0.452540i
$$134$$ −3.98347 3.98347i −0.344120 0.344120i
$$135$$ −0.586380 2.15781i −0.0504675 0.185715i
$$136$$ 5.74699i 0.492800i
$$137$$ 10.4523 + 10.4523i 0.893004 + 0.893004i 0.994805 0.101801i $$-0.0324605\pi$$
−0.101801 + 0.994805i $$0.532461\pi$$
$$138$$ 6.03467 + 6.03467i 0.513705 + 0.513705i
$$139$$ −14.4443 −1.22515 −0.612574 0.790414i $$-0.709866\pi$$
−0.612574 + 0.790414i $$0.709866\pi$$
$$140$$ −1.94144 + 0.527580i −0.164081 + 0.0445887i
$$141$$ 0.462042i 0.0389110i
$$142$$ 15.2892i 1.28304i
$$143$$ 2.92981 0.245003
$$144$$ 1.00000i 0.0833333i
$$145$$ 1.41104 + 5.19246i 0.117180 + 0.431210i
$$146$$ −11.8322 + 11.8322i −0.979243 + 0.979243i
$$147$$ −4.37734 + 4.37734i −0.361037 + 0.361037i
$$148$$ −5.19618 3.16223i −0.427123 0.259934i
$$149$$ 19.0997i 1.56471i −0.622831 0.782356i $$-0.714018\pi$$
0.622831 0.782356i $$-0.285982\pi$$
$$150$$ 4.83867 + 1.25987i 0.395076 + 0.102868i
$$151$$ 3.42513i 0.278733i −0.990241 0.139367i $$-0.955493\pi$$
0.990241 0.139367i $$-0.0445067\pi$$
$$152$$ 4.10165 4.10165i 0.332688 0.332688i
$$153$$ 5.74699i 0.464617i
$$154$$ 1.44327 + 1.44327i 0.116302 + 0.116302i
$$155$$ −17.7346 + 4.81932i −1.42448 + 0.387097i
$$156$$ 0.913209 0.913209i 0.0731152 0.0731152i
$$157$$ 12.1068 + 12.1068i 0.966232 + 0.966232i 0.999448 0.0332164i $$-0.0105751\pi$$
−0.0332164 + 0.999448i $$0.510575\pi$$
$$158$$ 9.04382 9.04382i 0.719488 0.719488i
$$159$$ 9.61473 0.762498
$$160$$ −1.94044 1.11117i −0.153405 0.0878458i
$$161$$ 5.42954 5.42954i 0.427907 0.427907i
$$162$$ 1.00000i 0.0785674i
$$163$$ 24.2268 1.89759 0.948795 0.315894i $$-0.102304\pi$$
0.948795 + 0.315894i $$0.102304\pi$$
$$164$$ 9.02011i 0.704352i
$$165$$ −1.33025 4.89518i −0.103560 0.381089i
$$166$$ −9.12362 9.12362i −0.708130 0.708130i
$$167$$ 9.66372 0.747801 0.373900 0.927469i $$-0.378020\pi$$
0.373900 + 0.927469i $$0.378020\pi$$
$$168$$ 0.899724 0.0694152
$$169$$ 11.3321 0.871700
$$170$$ 11.1517 + 6.38589i 0.855295 + 0.489776i
$$171$$ 4.10165 4.10165i 0.313661 0.313661i
$$172$$ 0.853087i 0.0650472i
$$173$$ −6.77556 6.77556i −0.515136 0.515136i 0.400959 0.916096i $$-0.368677\pi$$
−0.916096 + 0.400959i $$0.868677\pi$$
$$174$$ 2.40635i 0.182425i
$$175$$ 1.13353 4.35347i 0.0856870 0.329091i
$$176$$ 2.26858i 0.171001i
$$177$$ 4.96631i 0.373290i
$$178$$ 6.32382 + 6.32382i 0.473990 + 0.473990i
$$179$$ 7.36463 7.36463i 0.550458 0.550458i −0.376115 0.926573i $$-0.622740\pi$$
0.926573 + 0.376115i $$0.122740\pi$$
$$180$$ −1.94044 1.11117i −0.144632 0.0828218i
$$181$$ −13.9651 −1.03802 −0.519008 0.854769i $$-0.673699\pi$$
−0.519008 + 0.854769i $$0.673699\pi$$
$$182$$ −0.821636 0.821636i −0.0609037 0.0609037i
$$183$$ 2.91979i 0.215837i
$$184$$ 8.53431 0.629158
$$185$$ 11.9100 6.56908i 0.875638 0.482969i
$$186$$ 8.21877 0.602630
$$187$$ 13.0375i 0.953398i
$$188$$ 0.326713 + 0.326713i 0.0238280 + 0.0238280i
$$189$$ 0.899724 0.0654453
$$190$$ 3.40136 + 12.5166i 0.246760 + 0.908051i
$$191$$ −11.6459 + 11.6459i −0.842665 + 0.842665i −0.989205 0.146540i $$-0.953186\pi$$
0.146540 + 0.989205i $$0.453186\pi$$
$$192$$ 0.707107 + 0.707107i 0.0510310 + 0.0510310i
$$193$$ 2.80664i 0.202026i 0.994885 + 0.101013i $$0.0322084\pi$$
−0.994885 + 0.101013i $$0.967792\pi$$
$$194$$ 9.28197i 0.666406i
$$195$$ 0.757293 + 2.78676i 0.0542309 + 0.199564i
$$196$$ 6.19050i 0.442178i
$$197$$ 11.5183 + 11.5183i 0.820643 + 0.820643i 0.986200 0.165557i $$-0.0529422\pi$$
−0.165557 + 0.986200i $$0.552942\pi$$
$$198$$ 2.26858i 0.161221i
$$199$$ 10.3470 10.3470i 0.733481 0.733481i −0.237827 0.971308i $$-0.576435\pi$$
0.971308 + 0.237827i $$0.0764350\pi$$
$$200$$ 4.31232 2.53060i 0.304927 0.178940i
$$201$$ −5.63348 −0.397355
$$202$$ 1.47408 0.103716
$$203$$ −2.16505 −0.151957
$$204$$ −4.06374 4.06374i −0.284518 0.284518i
$$205$$ 17.5030 + 10.0229i 1.22246 + 0.700029i
$$206$$ 1.02968i 0.0717414i
$$207$$ 8.53431 0.593175
$$208$$ 1.29147i 0.0895475i
$$209$$ 9.30492 9.30492i 0.643635 0.643635i
$$210$$ −0.999748 + 1.74586i −0.0689892 + 0.120476i
$$211$$ −3.80993 −0.262286 −0.131143 0.991363i $$-0.541865\pi$$
−0.131143 + 0.991363i $$0.541865\pi$$
$$212$$ 6.79864 6.79864i 0.466933 0.466933i
$$213$$ 10.8111 + 10.8111i 0.740765 + 0.740765i
$$214$$ −13.8598 + 13.8598i −0.947438 + 0.947438i
$$215$$ −1.65536 0.947925i −0.112895 0.0646480i
$$216$$ 0.707107 + 0.707107i 0.0481125 + 0.0481125i
$$217$$ 7.39463i 0.501980i
$$218$$ 5.32683 5.32683i 0.360779 0.360779i
$$219$$ 16.7333i 1.13073i
$$220$$ −4.40204 2.52078i −0.296786 0.169951i
$$221$$ 7.42208i 0.499263i
$$222$$ −5.91029 + 1.43822i −0.396673 + 0.0965269i
$$223$$ 16.8923 16.8923i 1.13119 1.13119i 0.141210 0.989980i $$-0.454901\pi$$
0.989980 0.141210i $$-0.0450992\pi$$
$$224$$ 0.636201 0.636201i 0.0425080 0.0425080i
$$225$$ 4.31232 2.53060i 0.287488 0.168706i
$$226$$ 17.2755i 1.14915i
$$227$$ −25.0030 −1.65950 −0.829752 0.558132i $$-0.811518\pi$$
−0.829752 + 0.558132i $$0.811518\pi$$
$$228$$ 5.80061i 0.384154i
$$229$$ 11.3572i 0.750503i −0.926923 0.375252i $$-0.877556\pi$$
0.926923 0.375252i $$-0.122444\pi$$
$$230$$ −9.48308 + 16.5603i −0.625296 + 1.09195i
$$231$$ 2.04110 0.134294
$$232$$ −1.70155 1.70155i −0.111712 0.111712i
$$233$$ 4.77274 + 4.77274i 0.312673 + 0.312673i 0.845944 0.533271i $$-0.179038\pi$$
−0.533271 + 0.845944i $$0.679038\pi$$
$$234$$ 1.29147i 0.0844262i
$$235$$ −0.997001 + 0.270932i −0.0650371 + 0.0176737i
$$236$$ −3.51171 3.51171i −0.228593 0.228593i
$$237$$ 12.7899i 0.830793i
$$238$$ −3.65624 + 3.65624i −0.236999 + 0.236999i
$$239$$ −2.96858 2.96858i −0.192022 0.192022i 0.604547 0.796569i $$-0.293354\pi$$
−0.796569 + 0.604547i $$0.793354\pi$$
$$240$$ −2.15781 + 0.586380i −0.139286 + 0.0378507i
$$241$$ −5.75647 + 5.75647i −0.370807 + 0.370807i −0.867771 0.496964i $$-0.834448\pi$$
0.496964 + 0.867771i $$0.334448\pi$$
$$242$$ 5.85354i 0.376279i
$$243$$ 0.707107 + 0.707107i 0.0453609 + 0.0453609i
$$244$$ 2.06460 + 2.06460i 0.132172 + 0.132172i
$$245$$ −12.0123 6.87870i −0.767436 0.439464i
$$246$$ −6.37818 6.37818i −0.406658 0.406658i
$$247$$ −5.29716 + 5.29716i −0.337050 + 0.337050i
$$248$$ 5.81155 5.81155i 0.369034 0.369034i
$$249$$ −12.9027 −0.817678
$$250$$ 0.118740 + 11.1797i 0.00750979 + 0.707067i
$$251$$ −14.7749 14.7749i −0.932584 0.932584i 0.0652824 0.997867i $$-0.479205\pi$$
−0.997867 + 0.0652824i $$0.979205\pi$$
$$252$$ 0.636201 0.636201i 0.0400769 0.0400769i
$$253$$ 19.3608 1.21720
$$254$$ 0.916380 0.916380i 0.0574988 0.0574988i
$$255$$ 12.4009 3.36992i 0.776577 0.211033i
$$256$$ 1.00000 0.0625000
$$257$$ 1.80027 0.112298 0.0561488 0.998422i $$-0.482118\pi$$
0.0561488 + 0.998422i $$0.482118\pi$$
$$258$$ 0.603223 + 0.603223i 0.0375550 + 0.0375550i
$$259$$ 1.29400 + 5.31763i 0.0804053 + 0.330421i
$$260$$ 2.50602 + 1.43505i 0.155417 + 0.0889978i
$$261$$ −1.70155 1.70155i −0.105323 0.105323i
$$262$$ −6.28943 + 6.28943i −0.388563 + 0.388563i
$$263$$ −9.25899 9.25899i −0.570934 0.570934i 0.361456 0.932389i $$-0.382280\pi$$
−0.932389 + 0.361456i $$0.882280\pi$$
$$264$$ 1.60413 + 1.60413i 0.0987274 + 0.0987274i
$$265$$ 5.63789 + 20.7468i 0.346333 + 1.27447i
$$266$$ −5.21895 −0.319994
$$267$$ 8.94323 0.547317
$$268$$ −3.98347 + 3.98347i −0.243329 + 0.243329i
$$269$$ 0.689017i 0.0420101i 0.999779 + 0.0210051i $$0.00668661\pi$$
−0.999779 + 0.0210051i $$0.993313\pi$$
$$270$$ −2.15781 + 0.586380i −0.131320 + 0.0356859i
$$271$$ −14.7629 −0.896783 −0.448392 0.893837i $$-0.648003\pi$$
−0.448392 + 0.893837i $$0.648003\pi$$
$$272$$ −5.74699 −0.348462
$$273$$ −1.16197 −0.0703255
$$274$$ 10.4523 10.4523i 0.631449 0.631449i
$$275$$ 9.78285 5.74087i 0.589928 0.346187i
$$276$$ 6.03467 6.03467i 0.363244 0.363244i
$$277$$ 32.3771i 1.94535i −0.232172 0.972675i $$-0.574583\pi$$
0.232172 0.972675i $$-0.425417\pi$$
$$278$$ 14.4443i 0.866310i
$$279$$ 5.81155 5.81155i 0.347928 0.347928i
$$280$$ 0.527580 + 1.94144i 0.0315289 + 0.116023i
$$281$$ 5.74725 5.74725i 0.342852 0.342852i −0.514586 0.857439i $$-0.672054\pi$$
0.857439 + 0.514586i $$0.172054\pi$$
$$282$$ 0.462042 0.0275142
$$283$$ 6.56809 0.390433 0.195216 0.980760i $$-0.437459\pi$$
0.195216 + 0.980760i $$0.437459\pi$$
$$284$$ 15.2892 0.907248
$$285$$ 11.2557 + 6.44547i 0.666731 + 0.381797i
$$286$$ 2.92981i 0.173243i
$$287$$ −5.73860 + 5.73860i −0.338739 + 0.338739i
$$288$$ 1.00000 0.0589256
$$289$$ 16.0279 0.942818
$$290$$ 5.19246 1.41104i 0.304912 0.0828589i
$$291$$ −6.56334 6.56334i −0.384750 0.384750i
$$292$$ 11.8322 + 11.8322i 0.692430 + 0.692430i
$$293$$ −22.0187 + 22.0187i −1.28634 + 1.28634i −0.349353 + 0.936991i $$0.613599\pi$$
−0.936991 + 0.349353i $$0.886401\pi$$
$$294$$ 4.37734 + 4.37734i 0.255292 + 0.255292i
$$295$$ 10.7164 2.91214i 0.623931 0.169551i
$$296$$ −3.16223 + 5.19618i −0.183801 + 0.302022i
$$297$$ 1.60413 + 1.60413i 0.0930811 + 0.0930811i
$$298$$ −19.0997 −1.10642
$$299$$ −11.0218 −0.637408
$$300$$ 1.25987 4.83867i 0.0727385 0.279361i
$$301$$ 0.542735 0.542735i 0.0312827 0.0312827i
$$302$$ −3.42513 −0.197094
$$303$$ 1.04233 1.04233i 0.0598805 0.0598805i
$$304$$ −4.10165 4.10165i −0.235246 0.235246i
$$305$$ −6.30035 + 1.71210i −0.360757 + 0.0980347i
$$306$$ −5.74699 −0.328534
$$307$$ 5.03677 5.03677i 0.287464 0.287464i −0.548613 0.836077i $$-0.684844\pi$$
0.836077 + 0.548613i $$0.184844\pi$$
$$308$$ 1.44327 1.44327i 0.0822382 0.0822382i
$$309$$ −0.728096 0.728096i −0.0414199 0.0414199i
$$310$$ 4.81932 + 17.7346i 0.273719 + 1.00726i
$$311$$ 3.85553 + 3.85553i 0.218627 + 0.218627i 0.807920 0.589293i $$-0.200594\pi$$
−0.589293 + 0.807920i $$0.700594\pi$$
$$312$$ −0.913209 0.913209i −0.0517003 0.0517003i
$$313$$ 19.5460i 1.10481i −0.833577 0.552404i $$-0.813711\pi$$
0.833577 0.552404i $$-0.186289\pi$$
$$314$$ 12.1068 12.1068i 0.683229 0.683229i
$$315$$ 0.527580 + 1.94144i 0.0297258 + 0.109388i
$$316$$ −9.04382 9.04382i −0.508755 0.508755i
$$317$$ 5.03252 5.03252i 0.282655 0.282655i −0.551512 0.834167i $$-0.685949\pi$$
0.834167 + 0.551512i $$0.185949\pi$$
$$318$$ 9.61473i 0.539168i
$$319$$ −3.86010 3.86010i −0.216124 0.216124i
$$320$$ −1.11117 + 1.94044i −0.0621164 + 0.108474i
$$321$$ 19.6007i 1.09401i
$$322$$ −5.42954 5.42954i −0.302576 0.302576i
$$323$$ 23.5721 + 23.5721i 1.31159 + 1.31159i
$$324$$ 1.00000 0.0555556
$$325$$ −5.56924 + 3.26819i −0.308926 + 0.181287i
$$326$$ 24.2268i 1.34180i
$$327$$ 7.53328i 0.416591i
$$328$$ −9.02011 −0.498052
$$329$$ 0.415710i 0.0229189i
$$330$$ −4.89518 + 1.33025i −0.269471 + 0.0732279i
$$331$$ −3.25748 + 3.25748i −0.179048 + 0.179048i −0.790941 0.611893i $$-0.790408\pi$$
0.611893 + 0.790941i $$0.290408\pi$$
$$332$$ −9.12362 + 9.12362i −0.500723 + 0.500723i
$$333$$ −3.16223 + 5.19618i −0.173289 + 0.284749i
$$334$$ 9.66372i 0.528775i
$$335$$ −3.30336 12.1560i −0.180482 0.664154i
$$336$$ 0.899724i 0.0490840i
$$337$$ 15.5648 15.5648i 0.847866 0.847866i −0.142000 0.989867i $$-0.545353\pi$$
0.989867 + 0.142000i $$0.0453534\pi$$
$$338$$ 11.3321i 0.616385i
$$339$$ −12.2157 12.2157i −0.663463 0.663463i
$$340$$ 6.38589 11.1517i 0.346324 0.604785i
$$341$$ 13.1840 13.1840i 0.713953 0.713953i
$$342$$ −4.10165 4.10165i −0.221792 0.221792i
$$343$$ 8.39181 8.39181i 0.453115 0.453115i
$$344$$ 0.853087 0.0459953
$$345$$ 5.00435 + 18.4154i 0.269425 + 0.991454i
$$346$$ −6.77556 + 6.77556i −0.364256 + 0.364256i
$$347$$ 19.7799i 1.06184i −0.847422 0.530920i $$-0.821846\pi$$
0.847422 0.530920i $$-0.178154\pi$$
$$348$$ −2.40635 −0.128994
$$349$$ 5.47518i 0.293080i 0.989205 + 0.146540i $$0.0468137\pi$$
−0.989205 + 0.146540i $$0.953186\pi$$
$$350$$ −4.35347 1.13353i −0.232703 0.0605899i
$$351$$ −0.913209 0.913209i −0.0487435 0.0487435i
$$352$$ 2.26858 0.120916
$$353$$ 28.1816 1.49995 0.749976 0.661465i $$-0.230065\pi$$
0.749976 + 0.661465i $$0.230065\pi$$
$$354$$ −4.96631 −0.263956
$$355$$ −16.9889 + 29.6678i −0.901679 + 1.57460i
$$356$$ 6.32382 6.32382i 0.335162 0.335162i
$$357$$ 5.17071i 0.273663i
$$358$$ −7.36463 7.36463i −0.389233 0.389233i
$$359$$ 2.05043i 0.108218i 0.998535 + 0.0541089i $$0.0172318\pi$$
−0.998535 + 0.0541089i $$0.982768\pi$$
$$360$$ −1.11117 + 1.94044i −0.0585639 + 0.102270i
$$361$$ 14.6470i 0.770896i
$$362$$ 13.9651i 0.733988i
$$363$$ −4.13907 4.13907i −0.217245 0.217245i
$$364$$ −0.821636 + 0.821636i −0.0430654 + 0.0430654i
$$365$$ −36.1074 + 9.81208i −1.88995 + 0.513588i
$$366$$ 2.91979 0.152620
$$367$$ −8.13886 8.13886i −0.424845 0.424845i 0.462023 0.886868i $$-0.347124\pi$$
−0.886868 + 0.462023i $$0.847124\pi$$
$$368$$ 8.53431i 0.444882i
$$369$$ −9.02011 −0.469568
$$370$$ −6.56908 11.9100i −0.341510 0.619169i
$$371$$ −8.65061 −0.449117
$$372$$ 8.21877i 0.426124i
$$373$$ −9.78820 9.78820i −0.506814 0.506814i 0.406733 0.913547i $$-0.366668\pi$$
−0.913547 + 0.406733i $$0.866668\pi$$
$$374$$ −13.0375 −0.674154
$$375$$ 7.98921 + 7.82129i 0.412561 + 0.403889i
$$376$$ 0.326713 0.326713i 0.0168489 0.0168489i
$$377$$ 2.19750 + 2.19750i 0.113177 + 0.113177i
$$378$$ 0.899724i 0.0462768i
$$379$$ 22.6146i 1.16164i −0.814034 0.580818i $$-0.802733\pi$$
0.814034 0.580818i $$-0.197267\pi$$
$$380$$ 12.5166 3.40136i 0.642089 0.174486i
$$381$$ 1.29596i 0.0663939i
$$382$$ 11.6459 + 11.6459i 0.595854 + 0.595854i
$$383$$ 9.52538i 0.486724i 0.969936 + 0.243362i $$0.0782503\pi$$
−0.969936 + 0.243362i $$0.921750\pi$$
$$384$$ 0.707107 0.707107i 0.0360844 0.0360844i
$$385$$ 1.19686 + 4.40431i 0.0609976 + 0.224464i
$$386$$ 2.80664 0.142854
$$387$$ 0.853087 0.0433648
$$388$$ −9.28197 −0.471220
$$389$$ 7.75553 + 7.75553i 0.393221 + 0.393221i 0.875834 0.482613i $$-0.160312\pi$$
−0.482613 + 0.875834i $$0.660312\pi$$
$$390$$ 2.78676 0.757293i 0.141113 0.0383470i
$$391$$ 49.0466i 2.48039i
$$392$$ 6.19050 0.312667
$$393$$ 8.89460i 0.448673i
$$394$$ 11.5183 11.5183i 0.580282 0.580282i
$$395$$ 27.5982 7.49973i 1.38862 0.377353i
$$396$$ 2.26858 0.114001
$$397$$ −18.6690 + 18.6690i −0.936970 + 0.936970i −0.998128 0.0611581i $$-0.980521\pi$$
0.0611581 + 0.998128i $$0.480521\pi$$
$$398$$ −10.3470 10.3470i −0.518649 0.518649i
$$399$$ −3.69035 + 3.69035i −0.184749 + 0.184749i
$$400$$ −2.53060 4.31232i −0.126530 0.215616i
$$401$$ 13.9114 + 13.9114i 0.694702 + 0.694702i 0.963263 0.268561i $$-0.0865481\pi$$
−0.268561 + 0.963263i $$0.586548\pi$$
$$402$$ 5.63348i 0.280973i
$$403$$ −7.50545 + 7.50545i −0.373873 + 0.373873i
$$404$$ 1.47408i 0.0733383i
$$405$$ −1.11117 + 1.94044i −0.0552146 + 0.0964211i
$$406$$ 2.16505i 0.107450i
$$407$$ −7.17378 + 11.7880i −0.355591 + 0.584308i
$$408$$ −4.06374 + 4.06374i −0.201185 + 0.201185i
$$409$$ −7.16339 + 7.16339i −0.354207 + 0.354207i −0.861672 0.507465i $$-0.830582\pi$$
0.507465 + 0.861672i $$0.330582\pi$$
$$410$$ 10.0229 17.5030i 0.494995 0.864409i
$$411$$ 14.7818i 0.729134i
$$412$$ −1.02968 −0.0507289
$$413$$ 4.46831i 0.219871i
$$414$$ 8.53431i 0.419438i
$$415$$ −7.56591 27.8417i −0.371396 1.36670i
$$416$$ −1.29147 −0.0633196
$$417$$ 10.2136 + 10.2136i 0.500164 + 0.500164i
$$418$$ −9.30492 9.30492i −0.455119 0.455119i
$$419$$ 23.8546i 1.16537i 0.812698 + 0.582686i $$0.197998\pi$$
−0.812698 + 0.582686i $$0.802002\pi$$
$$420$$ 1.74586 + 0.999748i 0.0851892 + 0.0487827i
$$421$$ −12.3787 12.3787i −0.603301 0.603301i 0.337886 0.941187i $$-0.390288\pi$$
−0.941187 + 0.337886i $$0.890288\pi$$
$$422$$ 3.80993i 0.185464i
$$423$$ 0.326713 0.326713i 0.0158853 0.0158853i
$$424$$ −6.79864 6.79864i −0.330171 0.330171i
$$425$$ 14.5433 + 24.7828i 0.705454 + 1.20214i
$$426$$ 10.8111 10.8111i 0.523800 0.523800i
$$427$$ 2.62700i 0.127130i
$$428$$ 13.8598 + 13.8598i 0.669940 + 0.669940i
$$429$$ −2.07169 2.07169i −0.100022 0.100022i
$$430$$ −0.947925 + 1.65536i −0.0457130 + 0.0798286i
$$431$$ 5.50143 + 5.50143i 0.264995 + 0.264995i 0.827080 0.562085i $$-0.190001\pi$$
−0.562085 + 0.827080i $$0.690001\pi$$
$$432$$ 0.707107 0.707107i 0.0340207 0.0340207i
$$433$$ 4.53175 4.53175i 0.217782 0.217782i −0.589781 0.807563i $$-0.700786\pi$$
0.807563 + 0.589781i $$0.200786\pi$$
$$434$$ −7.39463 −0.354954
$$435$$ 2.67387 4.66938i 0.128202 0.223879i
$$436$$ −5.32683 5.32683i −0.255109 0.255109i
$$437$$ −35.0047 + 35.0047i −1.67450 + 1.67450i
$$438$$ 16.7333 0.799549
$$439$$ 22.7618 22.7618i 1.08636 1.08636i 0.0904591 0.995900i $$-0.471167\pi$$
0.995900 0.0904591i $$-0.0288334\pi$$
$$440$$ −2.52078 + 4.40204i −0.120174 + 0.209859i
$$441$$ 6.19050 0.294786
$$442$$ 7.42208 0.353032
$$443$$ −18.5368 18.5368i −0.880708 0.880708i 0.112899 0.993606i $$-0.463986\pi$$
−0.993606 + 0.112899i $$0.963986\pi$$
$$444$$ 1.43822 + 5.91029i 0.0682549 + 0.280490i
$$445$$ 5.24413 + 19.2978i 0.248596 + 0.914804i
$$446$$ −16.8923 16.8923i −0.799872 0.799872i
$$447$$ −13.5056 + 13.5056i −0.638791 + 0.638791i
$$448$$ −0.636201 0.636201i −0.0300577 0.0300577i
$$449$$ 9.96142 + 9.96142i 0.470109 + 0.470109i 0.901950 0.431841i $$-0.142136\pi$$
−0.431841 + 0.901950i $$0.642136\pi$$
$$450$$ −2.53060 4.31232i −0.119293 0.203285i
$$451$$ −20.4629 −0.963558
$$452$$ −17.2755 −0.812573
$$453$$ −2.42193 + 2.42193i −0.113792 + 0.113792i
$$454$$ 25.0030i 1.17345i
$$455$$ −0.681355 2.50731i −0.0319424 0.117545i
$$456$$ −5.80061 −0.271638
$$457$$ −6.81678 −0.318876 −0.159438 0.987208i $$-0.550968\pi$$
−0.159438 + 0.987208i $$0.550968\pi$$
$$458$$ −11.3572 −0.530686
$$459$$ −4.06374 + 4.06374i −0.189679 + 0.189679i
$$460$$ 16.5603 + 9.48308i 0.772128 + 0.442151i
$$461$$ 24.7125 24.7125i 1.15097 1.15097i 0.164617 0.986358i $$-0.447361\pi$$
0.986358 0.164617i $$-0.0526389\pi$$
$$462$$ 2.04110i 0.0949605i
$$463$$ 32.0736i 1.49059i 0.666737 + 0.745293i $$0.267690\pi$$
−0.666737 + 0.745293i $$0.732310\pi$$
$$464$$ −1.70155 + 1.70155i −0.0789924 + 0.0789924i
$$465$$ 15.9480 + 9.13247i 0.739572 + 0.423508i
$$466$$ 4.77274 4.77274i 0.221093 0.221093i
$$467$$ 13.7531 0.636416 0.318208 0.948021i $$-0.396919\pi$$
0.318208 + 0.948021i $$0.396919\pi$$
$$468$$ −1.29147 −0.0596983
$$469$$ 5.06858 0.234045
$$470$$ 0.270932 + 0.997001i 0.0124972 + 0.0459882i
$$471$$ 17.1217i 0.788925i
$$472$$ −3.51171 + 3.51171i −0.161640 + 0.161640i
$$473$$ 1.93530 0.0889851
$$474$$ −12.7899 −0.587459
$$475$$ −7.30799 + 28.0672i −0.335314 + 1.28781i
$$476$$ 3.65624 + 3.65624i 0.167584 + 0.167584i
$$477$$ −6.79864 6.79864i −0.311289 0.311289i
$$478$$ −2.96858 + 2.96858i −0.135780 + 0.135780i
$$479$$ 15.9554 + 15.9554i 0.729021 + 0.729021i 0.970425 0.241404i $$-0.0776079\pi$$
−0.241404 + 0.970425i $$0.577608\pi$$
$$480$$ 0.586380 + 2.15781i 0.0267645 + 0.0984903i
$$481$$ 4.08393 6.71072i 0.186211 0.305983i
$$482$$ 5.75647 + 5.75647i 0.262200 + 0.262200i
$$483$$ −7.67852 −0.349385
$$484$$ −5.85354 −0.266070
$$485$$ 10.3139 18.0111i 0.468328 0.817841i
$$486$$ 0.707107 0.707107i 0.0320750 0.0320750i
$$487$$ 22.5078 1.01992 0.509962 0.860197i $$-0.329659\pi$$
0.509962 + 0.860197i $$0.329659\pi$$
$$488$$ 2.06460 2.06460i 0.0934600 0.0934600i
$$489$$ −17.1309 17.1309i −0.774688 0.774688i
$$490$$ −6.87870 + 12.0123i −0.310748 + 0.542659i
$$491$$ 31.0223 1.40002 0.700008 0.714135i $$-0.253180\pi$$
0.700008 + 0.714135i $$0.253180\pi$$
$$492$$ −6.37818 + 6.37818i −0.287550 + 0.287550i
$$493$$ 9.77878 9.77878i 0.440414 0.440414i
$$494$$ 5.29716 + 5.29716i 0.238331 + 0.238331i
$$495$$ −2.52078 + 4.40204i −0.113301 + 0.197857i
$$496$$ −5.81155 5.81155i −0.260946 0.260946i
$$497$$ −9.72702 9.72702i −0.436316 0.436316i
$$498$$ 12.9027i 0.578186i
$$499$$ 5.68409 5.68409i 0.254455 0.254455i −0.568339 0.822794i $$-0.692414\pi$$
0.822794 + 0.568339i $$0.192414\pi$$
$$500$$ 11.1797 0.118740i 0.499972 0.00531022i
$$501$$ −6.83328 6.83328i −0.305288 0.305288i
$$502$$ −14.7749 + 14.7749i −0.659437 + 0.659437i
$$503$$ 3.69027i 0.164541i −0.996610 0.0822705i $$-0.973783\pi$$
0.996610 0.0822705i $$-0.0262171\pi$$
$$504$$ −0.636201 0.636201i −0.0283386 0.0283386i
$$505$$ 2.86036 + 1.63796i 0.127285 + 0.0728882i
$$506$$ 19.3608i 0.860692i
$$507$$ −8.01300 8.01300i −0.355870 0.355870i
$$508$$ −0.916380 0.916380i −0.0406578 0.0406578i
$$509$$ 5.91876 0.262345 0.131172 0.991360i $$-0.458126\pi$$
0.131172 + 0.991360i $$0.458126\pi$$
$$510$$ −3.36992 12.4009i −0.149223 0.549123i
$$511$$ 15.0554i 0.666010i
$$512$$ 1.00000i 0.0441942i
$$513$$ −5.80061 −0.256103
$$514$$ 1.80027i 0.0794064i
$$515$$ 1.14415 1.99804i 0.0504175 0.0880440i
$$516$$ 0.603223 0.603223i 0.0265554 0.0265554i
$$517$$ 0.741175 0.741175i 0.0325969 0.0325969i
$$518$$ 5.31763 1.29400i 0.233643 0.0568551i
$$519$$ 9.58209i 0.420607i
$$520$$ 1.43505 2.50602i 0.0629310 0.109896i
$$521$$ 21.8007i 0.955107i 0.878603 + 0.477554i $$0.158476\pi$$
−0.878603 + 0.477554i $$0.841524\pi$$
$$522$$ −1.70155 + 1.70155i −0.0744747 + 0.0744747i
$$523$$ 17.1466i 0.749767i 0.927072 + 0.374883i $$0.122317\pi$$
−0.927072 + 0.374883i $$0.877683\pi$$
$$524$$ 6.28943 + 6.28943i 0.274755 + 0.274755i
$$525$$ −3.87990 + 2.27684i −0.169333 + 0.0993694i
$$526$$ −9.25899 + 9.25899i −0.403711 + 0.403711i
$$527$$ 33.3989 + 33.3989i 1.45488 + 1.45488i
$$528$$ 1.60413 1.60413i 0.0698108 0.0698108i
$$529$$ −49.8344 −2.16671
$$530$$ 20.7468 5.63789i 0.901184 0.244894i
$$531$$ −3.51171 + 3.51171i −0.152395 + 0.152395i
$$532$$ 5.21895i 0.226270i
$$533$$ 11.6492 0.504583
$$534$$ 8.94323i 0.387011i
$$535$$ −42.2948 + 11.4935i −1.82856 + 0.496907i
$$536$$ 3.98347 + 3.98347i 0.172060 + 0.172060i
$$537$$ −10.4152 −0.449447
$$538$$ 0.689017 0.0297056
$$539$$ 14.0436 0.604903
$$540$$ 0.586380 + 2.15781i 0.0252338 + 0.0928575i
$$541$$ −11.6362 + 11.6362i −0.500279 + 0.500279i −0.911525 0.411245i $$-0.865094\pi$$
0.411245 + 0.911525i $$0.365094\pi$$
$$542$$ 14.7629i 0.634122i
$$543$$ 9.87480 + 9.87480i 0.423768 + 0.423768i
$$544$$ 5.74699i 0.246400i
$$545$$ 16.2554 4.41736i 0.696305 0.189219i
$$546$$ 1.16197i 0.0497277i
$$547$$ 37.0105i 1.58245i 0.611523 + 0.791226i $$0.290557\pi$$
−0.611523 + 0.791226i $$0.709443\pi$$
$$548$$ −10.4523 10.4523i −0.446502 0.446502i
$$549$$ 2.06460 2.06460i 0.0881150 0.0881150i
$$550$$ −5.74087 9.78285i −0.244791 0.417142i
$$551$$ 13.9583 0.594643
$$552$$ −6.03467 6.03467i −0.256853 0.256853i
$$553$$ 11.5074i 0.489343i
$$554$$ −32.3771 −1.37557
$$555$$ −13.0667 3.77657i −0.554649 0.160307i
$$556$$ 14.4443 0.612574
$$557$$ 5.02764i 0.213028i −0.994311 0.106514i $$-0.966031\pi$$
0.994311 0.106514i $$-0.0339689\pi$$
$$558$$ −5.81155 5.81155i −0.246023 0.246023i
$$559$$ −1.10174 −0.0465985
$$560$$ 1.94144 0.527580i 0.0820407 0.0222943i
$$561$$ −9.21892 + 9.21892i −0.389223 + 0.389223i
$$562$$ −5.74725 5.74725i −0.242433 0.242433i
$$563$$ 14.7235i 0.620522i 0.950651 + 0.310261i $$0.100416\pi$$
−0.950651 + 0.310261i $$0.899584\pi$$
$$564$$ 0.462042i 0.0194555i
$$565$$ 19.1961 33.5221i 0.807586 1.41029i
$$566$$ 6.56809i 0.276078i
$$567$$ −0.636201 0.636201i −0.0267179 0.0267179i
$$568$$ 15.2892i 0.641521i
$$569$$ −15.1302 + 15.1302i −0.634291 + 0.634291i −0.949141 0.314850i $$-0.898046\pi$$
0.314850 + 0.949141i $$0.398046\pi$$
$$570$$ 6.44547 11.2557i 0.269971 0.471450i
$$571$$ −0.732604 −0.0306585 −0.0153293 0.999882i $$-0.504880\pi$$
−0.0153293 + 0.999882i $$0.504880\pi$$
$$572$$ −2.92981 −0.122502
$$573$$ 16.4697 0.688033
$$574$$ 5.73860 + 5.73860i 0.239525 + 0.239525i
$$575$$ −36.8026 + 21.5969i −1.53478 + 0.900653i
$$576$$ 1.00000i 0.0416667i
$$577$$ 13.0938 0.545102 0.272551 0.962141i $$-0.412133\pi$$
0.272551 + 0.962141i $$0.412133\pi$$
$$578$$ 16.0279i 0.666673i
$$579$$ 1.98459 1.98459i 0.0824768 0.0824768i
$$580$$ −1.41104 5.19246i −0.0585901 0.215605i
$$581$$ 11.6089 0.481619
$$582$$ −6.56334 + 6.56334i −0.272059 + 0.272059i
$$583$$ −15.4233 15.4233i −0.638767 0.638767i
$$584$$ 11.8322 11.8322i 0.489622 0.489622i
$$585$$ 1.43505 2.50602i 0.0593319 0.103611i
$$586$$ 22.0187 + 22.0187i 0.909583 + 0.909583i
$$587$$ 25.6946i 1.06053i −0.847832 0.530265i $$-0.822092\pi$$
0.847832 0.530265i $$-0.177908\pi$$
$$588$$ 4.37734 4.37734i 0.180519 0.180519i
$$589$$ 47.6739i 1.96437i
$$590$$ −2.91214 10.7164i −0.119891 0.441186i
$$591$$ 16.2893i 0.670052i
$$592$$ 5.19618 + 3.16223i 0.213562 + 0.129967i
$$593$$ −32.7884 + 32.7884i −1.34646 + 1.34646i −0.456986 + 0.889474i $$0.651071\pi$$
−0.889474 + 0.456986i $$0.848929\pi$$
$$594$$ 1.60413 1.60413i 0.0658182 0.0658182i
$$595$$ −11.1574 + 3.03200i −0.457410 + 0.124300i
$$596$$ 19.0997i 0.782356i
$$597$$ −14.6329 −0.598885
$$598$$ 11.0218i 0.450716i
$$599$$ 32.7946i 1.33995i −0.742383 0.669975i $$-0.766305\pi$$
0.742383 0.669975i $$-0.233695\pi$$
$$600$$ −4.83867 1.25987i −0.197538 0.0514339i
$$601$$ 27.3053 1.11381 0.556904 0.830577i $$-0.311989\pi$$
0.556904 + 0.830577i $$0.311989\pi$$
$$602$$ −0.542735 0.542735i −0.0221202 0.0221202i
$$603$$ 3.98347 + 3.98347i 0.162220 + 0.162220i
$$604$$ 3.42513i 0.139367i
$$605$$ 6.50428 11.3584i 0.264437 0.461785i
$$606$$ −1.04233 1.04233i −0.0423419 0.0423419i
$$607$$ 26.7432i 1.08547i −0.839903 0.542737i $$-0.817388\pi$$
0.839903 0.542737i $$-0.182612\pi$$
$$608$$ −4.10165 + 4.10165i −0.166344 + 0.166344i
$$609$$ 1.53092 + 1.53092i 0.0620362 + 0.0620362i
$$610$$ 1.71210 + 6.30035i 0.0693210 + 0.255094i
$$611$$ −0.421941 + 0.421941i −0.0170699 + 0.0170699i
$$612$$ 5.74699i 0.232308i
$$613$$ −23.6704 23.6704i −0.956040 0.956040i 0.0430339 0.999074i $$-0.486298\pi$$
−0.999074 + 0.0430339i $$0.986298\pi$$
$$614$$ −5.03677 5.03677i −0.203268 0.203268i
$$615$$ −5.28921 19.4637i −0.213281 0.784852i
$$616$$ −1.44327 1.44327i −0.0581512 0.0581512i
$$617$$ 3.77510 3.77510i 0.151980 0.151980i −0.627022 0.779002i $$-0.715726\pi$$
0.779002 + 0.627022i $$0.215726\pi$$
$$618$$ −0.728096 + 0.728096i −0.0292883 + 0.0292883i
$$619$$ 9.65130 0.387918 0.193959 0.981010i $$-0.437867\pi$$
0.193959 + 0.981010i $$0.437867\pi$$
$$620$$ 17.7346 4.81932i 0.712238 0.193549i
$$621$$ −6.03467 6.03467i −0.242163 0.242163i
$$622$$ 3.85553 3.85553i 0.154593 0.154593i
$$623$$ −8.04644 −0.322374
$$624$$ −0.913209 + 0.913209i −0.0365576 + 0.0365576i
$$625$$ −12.1922 + 21.8255i −0.487687 + 0.873019i
$$626$$ −19.5460 −0.781217
$$627$$ −13.1592 −0.525526
$$628$$ −12.1068 12.1068i −0.483116 0.483116i
$$629$$ −29.8624 18.1733i −1.19069 0.724618i
$$630$$ 1.94144 0.527580i 0.0773487 0.0210193i
$$631$$ 9.32454 + 9.32454i 0.371204 + 0.371204i 0.867916 0.496712i $$-0.165459\pi$$
−0.496712 + 0.867916i $$0.665459\pi$$
$$632$$ −9.04382 + 9.04382i −0.359744 + 0.359744i
$$633$$ 2.69402 + 2.69402i 0.107078 + 0.107078i
$$634$$ −5.03252 5.03252i −0.199867 0.199867i
$$635$$ 2.79643 0.759923i 0.110973 0.0301566i
$$636$$ −9.61473 −0.381249
$$637$$ −7.99485 −0.316768
$$638$$ −3.86010 + 3.86010i −0.152823 + 0.152823i
$$639$$ 15.2892i 0.604832i
$$640$$ 1.94044 + 1.11117i 0.0767025 + 0.0439229i
$$641$$ −7.81012 −0.308481 −0.154241 0.988033i $$-0.549293\pi$$
−0.154241 + 0.988033i $$0.549293\pi$$
$$642$$ 19.6007 0.773580
$$643$$ −39.3070 −1.55012 −0.775058 0.631890i $$-0.782279\pi$$
−0.775058 + 0.631890i $$0.782279\pi$$
$$644$$ −5.42954 + 5.42954i −0.213954 + 0.213954i
$$645$$ 0.500233 + 1.84080i 0.0196966 + 0.0724815i
$$646$$ 23.5721 23.5721i 0.927433 0.927433i
$$647$$ 31.8619i 1.25262i −0.779573 0.626311i $$-0.784564\pi$$
0.779573 0.626311i $$-0.215436\pi$$
$$648$$ 1.00000i 0.0392837i
$$649$$ −7.96660 + 7.96660i −0.312716 + 0.312716i
$$650$$ 3.26819 + 5.56924i 0.128189 + 0.218443i
$$651$$ −5.22879 + 5.22879i −0.204933 + 0.204933i
$$652$$ −24.2268 −0.948795
$$653$$ 40.2027 1.57325 0.786626 0.617430i $$-0.211826\pi$$
0.786626 + 0.617430i $$0.211826\pi$$
$$654$$ −7.53328 −0.294575
$$655$$ −19.1929 + 5.21562i −0.749929 + 0.203791i
$$656$$ 9.02011i 0.352176i
$$657$$ 11.8322 11.8322i 0.461620 0.461620i
$$658$$ −0.415710 −0.0162061
$$659$$ −22.6033 −0.880499 −0.440250 0.897875i $$-0.645110\pi$$
−0.440250 + 0.897875i $$0.645110\pi$$
$$660$$ 1.33025 + 4.89518i 0.0517799 + 0.190545i
$$661$$ 20.1421 + 20.1421i 0.783436 + 0.783436i 0.980409 0.196973i $$-0.0631111\pi$$
−0.196973 + 0.980409i $$0.563111\pi$$
$$662$$ 3.25748 + 3.25748i 0.126606 + 0.126606i
$$663$$ 5.24820 5.24820i 0.203823 0.203823i
$$664$$ 9.12362 + 9.12362i 0.354065 + 0.354065i
$$665$$ −10.1270 5.79914i −0.392710 0.224881i
$$666$$ 5.19618 + 3.16223i 0.201348 + 0.122534i
$$667$$ 14.5215 + 14.5215i 0.562276 + 0.562276i
$$668$$ −9.66372 −0.373900
$$669$$ −23.8893 −0.923612
$$670$$ −12.1560 + 3.30336i −0.469628 + 0.127620i
$$671$$ 4.68371 4.68371i 0.180813 0.180813i
$$672$$ −0.899724 −0.0347076
$$673$$ 23.9631 23.9631i 0.923709 0.923709i −0.0735806 0.997289i $$-0.523443\pi$$
0.997289 + 0.0735806i $$0.0234426\pi$$
$$674$$ −15.5648 15.5648i −0.599532 0.599532i
$$675$$ −4.83867 1.25987i −0.186241 0.0484923i
$$676$$ −11.3321 −0.435850
$$677$$ −18.3439 + 18.3439i −0.705012 + 0.705012i −0.965482 0.260470i $$-0.916122\pi$$
0.260470 + 0.965482i $$0.416122\pi$$
$$678$$ −12.2157 + 12.2157i −0.469139 + 0.469139i
$$679$$ 5.90520 + 5.90520i 0.226621 + 0.226621i
$$680$$ −11.1517 6.38589i −0.427647 0.244888i
$$681$$ 17.6798 + 17.6798i 0.677490 + 0.677490i
$$682$$ −13.1840 13.1840i −0.504841 0.504841i
$$683$$ 2.79715i 0.107030i −0.998567 0.0535149i $$-0.982958\pi$$
0.998567 0.0535149i $$-0.0170425\pi$$
$$684$$ −4.10165 + 4.10165i −0.156830 + 0.156830i
$$685$$ 31.8965 8.66777i 1.21870 0.331179i
$$686$$ −8.39181 8.39181i −0.320401 0.320401i
$$687$$ −8.03073 + 8.03073i −0.306392 + 0.306392i
$$688$$ 0.853087i 0.0325236i
$$689$$ 8.78026 + 8.78026i 0.334501 + 0.334501i
$$690$$ 18.4154 5.00435i 0.701064 0.190512i
$$691$$ 7.07761i 0.269245i 0.990897 + 0.134623i $$0.0429822\pi$$
−0.990897 + 0.134623i $$0.957018\pi$$
$$692$$ 6.77556 + 6.77556i 0.257568 + 0.257568i
$$693$$ −1.44327 1.44327i −0.0548255 0.0548255i
$$694$$ −19.7799 −0.750835
$$695$$ −16.0501 + 28.0282i −0.608813 + 1.06317i
$$696$$ 2.40635i 0.0912125i
$$697$$ 51.8385i 1.96352i
$$698$$ 5.47518 0.207239
$$699$$ 6.74968i 0.255296i
$$700$$ −1.13353 + 4.35347i −0.0428435 + 0.164546i
$$701$$ −25.0871 + 25.0871i −0.947527 + 0.947527i −0.998690 0.0511635i $$-0.983707\pi$$
0.0511635 + 0.998690i $$0.483707\pi$$
$$702$$ −0.913209 + 0.913209i −0.0344668 + 0.0344668i
$$703$$ −8.34254 34.2833i −0.314645 1.29302i
$$704$$ 2.26858i 0.0855004i
$$705$$ 0.896564 + 0.513408i 0.0337665 + 0.0193361i
$$706$$ 28.1816i 1.06063i
$$707$$ −0.937812 + 0.937812i −0.0352701 + 0.0352701i
$$708$$ 4.96631i 0.186645i
$$709$$ −6.08101 6.08101i −0.228377 0.228377i 0.583637 0.812014i $$-0.301629\pi$$
−0.812014 + 0.583637i $$0.801629\pi$$
$$710$$ 29.6678 + 16.9889i 1.11341 + 0.637584i
$$711$$ −9.04382 + 9.04382i −0.339170 + 0.339170i
$$712$$ −6.32382 6.32382i −0.236995 0.236995i
$$713$$ −49.5976 + 49.5976i −1.85744 + 1.85744i
$$714$$ 5.17071 0.193509
$$715$$ 3.25552 5.68511i 0.121750 0.212611i
$$716$$ −7.36463 + 7.36463i −0.275229 + 0.275229i
$$717$$ 4.19821i 0.156785i
$$718$$ 2.05043 0.0765215
$$719$$ 37.1763i 1.38644i 0.720724 + 0.693222i $$0.243809\pi$$
−0.720724 + 0.693222i $$0.756191\pi$$
$$720$$ 1.94044 + 1.11117i 0.0723158 + 0.0414109i
$$721$$ 0.655086 + 0.655086i 0.0243967 + 0.0243967i
$$722$$ 14.6470 0.545106
$$723$$ 8.14088 0.302762
$$724$$ 13.9651 0.519008
$$725$$ 11.6435 + 3.03168i 0.432430 + 0.112594i
$$726$$ −4.13907 + 4.13907i −0.153615 + 0.153615i
$$727$$ 10.8041i 0.400701i −0.979724 0.200350i $$-0.935792\pi$$
0.979724 0.200350i $$-0.0642081\pi$$
$$728$$ 0.821636 + 0.821636i 0.0304519 + 0.0304519i
$$729$$ 1.00000i 0.0370370i
$$730$$ 9.81208 + 36.1074i 0.363161 + 1.33639i
$$731$$ 4.90268i 0.181332i
$$732$$ 2.91979i 0.107918i
$$733$$ −2.31409 2.31409i −0.0854728 0.0854728i 0.663078 0.748551i $$-0.269250\pi$$
−0.748551 + 0.663078i $$0.769250\pi$$
$$734$$ −8.13886 + 8.13886i −0.300411 + 0.300411i
$$735$$ 3.62998 + 13.3579i 0.133894 + 0.492715i
$$736$$ −8.53431 −0.314579
$$737$$ 9.03684 + 9.03684i 0.332876 + 0.332876i
$$738$$ 9.02011i 0.332035i
$$739$$ −3.59606 −0.132283 −0.0661416 0.997810i $$-0.521069\pi$$
−0.0661416 + 0.997810i $$0.521069\pi$$
$$740$$ −11.9100 + 6.56908i −0.437819 + 0.241484i
$$741$$ 7.49132 0.275201
$$742$$ 8.65061i 0.317574i
$$743$$ 7.78930 + 7.78930i 0.285762 + 0.285762i 0.835402 0.549640i $$-0.185235\pi$$
−0.549640 + 0.835402i $$0.685235\pi$$
$$744$$ −8.21877 −0.301315
$$745$$ −37.0619 21.2231i −1.35784 0.777554i
$$746$$ −9.78820 + 9.78820i −0.358371 + 0.358371i
$$747$$ 9.12362 + 9.12362i 0.333816 + 0.333816i
$$748$$ 13.0375i 0.476699i
$$749$$ 17.6353i 0.644379i
$$750$$ 7.82129 7.98921i 0.285593 0.291725i
$$751$$ 31.8319i 1.16156i 0.814059 + 0.580782i $$0.197253\pi$$
−0.814059 + 0.580782i $$0.802747\pi$$
$$752$$ −0.326713 0.326713i −0.0119140 0.0119140i
$$753$$ 20.8949i 0.761452i
$$754$$ 2.19750 2.19750i 0.0800283 0.0800283i
$$755$$ −6.64625 3.80591i −0.241882 0.138511i
$$756$$ −0.899724 −0.0327227
$$757$$ 2.85691 0.103836 0.0519182 0.998651i $$-0.483467\pi$$
0.0519182 + 0.998651i $$0.483467\pi$$
$$758$$ −22.6146 −0.821400
$$759$$ −13.6901 13.6901i −0.496921 0.496921i
$$760$$ −3.40136 12.5166i −0.123380 0.454026i
$$761$$ 3.11943i 0.113079i −0.998400 0.0565396i $$-0.981993\pi$$
0.998400 0.0565396i $$-0.0180067\pi$$
$$762$$ −1.29596 −0.0469476
$$763$$ 6.77787i 0.245376i
$$764$$ 11.6459 11.6459i 0.421332 0.421332i
$$765$$ −11.1517 6.38589i −0.403190 0.230882i
$$766$$ 9.52538 0.344166
$$767$$ 4.53527 4.53527i 0.163759 0.163759i
$$768$$ −0.707107 0.707107i −0.0255155 0.0255155i
$$769$$ 22.4056 22.4056i 0.807966 0.807966i −0.176360 0.984326i $$-0.556432\pi$$
0.984326 + 0.176360i $$0.0564322\pi$$
$$770$$ 4.40431 1.19686i 0.158720 0.0431318i
$$771$$ −1.27298 1.27298i −0.0458453 0.0458453i
$$772$$ 2.80664i 0.101013i
$$773$$ −1.90608 + 1.90608i −0.0685571 + 0.0685571i −0.740554 0.671997i $$-0.765437\pi$$
0.671997 + 0.740554i $$0.265437\pi$$
$$774$$ 0.853087i 0.0306636i
$$775$$ −10.3546 + 39.7679i −0.371947 + 1.42851i
$$776$$ 9.28197i 0.333203i
$$777$$ 2.84514 4.67513i 0.102069 0.167719i
$$778$$ 7.75553 7.75553i 0.278049 0.278049i
$$779$$ 36.9973 36.9973i 1.32557 1.32557i