# Properties

 Label 845.2.e.m.191.2 Level $845$ Weight $2$ Character 845.191 Analytic conductor $6.747$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$845 = 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 845.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.74735897080$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.22581504.2 Defining polynomial: $$x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 191.2 Root $$1.40994 + 0.109843i$$ of defining polynomial Character $$\chi$$ $$=$$ 845.191 Dual form 845.2.e.m.146.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$$ $$q+(-0.609843 + 1.05628i) q^{2} +(-1.16612 + 2.01978i) q^{3} +(0.256182 + 0.443720i) q^{4} -1.00000 q^{5} +(-1.42231 - 2.46350i) q^{6} +(-1.80010 - 3.11786i) q^{7} -3.06430 q^{8} +(-1.21969 - 2.11256i) q^{9} +(0.609843 - 1.05628i) q^{10} +(-2.68591 + 4.65213i) q^{11} -1.19496 q^{12} +4.39111 q^{14} +(1.16612 - 2.01978i) q^{15} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +2.97527 q^{18} +(-1.13397 - 1.96410i) q^{19} +(-0.256182 - 0.443720i) q^{20} +8.39654 q^{21} +(-3.27597 - 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} +(3.57335 - 6.18922i) q^{24} +1.00000 q^{25} -1.30752 q^{27} +(0.922305 - 1.59748i) q^{28} +(0.0123639 - 0.0214150i) q^{29} +(1.42231 + 2.46350i) q^{30} +5.46410 q^{31} +(-1.40994 - 2.44209i) q^{32} +(-6.26420 - 10.8499i) q^{33} -1.38051 q^{34} +(1.80010 + 3.11786i) q^{35} +(0.624924 - 1.08240i) q^{36} +(4.35203 - 7.53794i) q^{37} +2.76619 q^{38} +3.06430 q^{40} +(-1.86603 + 3.23205i) q^{41} +(-5.12058 + 8.86910i) q^{42} +(0.565928 + 0.980215i) q^{43} -2.75232 q^{44} +(1.21969 + 2.11256i) q^{45} +(2.37404 + 4.11196i) q^{46} +2.58535 q^{47} +(3.16341 + 5.47918i) q^{48} +(-2.98070 + 5.16273i) q^{49} +(-0.609843 + 1.05628i) q^{50} -2.63977 q^{51} -4.43937 q^{53} +(0.797382 - 1.38111i) q^{54} +(2.68591 - 4.65213i) q^{55} +(5.51603 + 9.55405i) q^{56} +5.28942 q^{57} +(0.0150801 + 0.0261196i) q^{58} +(0.0857123 + 0.148458i) q^{59} +1.19496 q^{60} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} +(-4.39111 + 7.60563i) q^{63} +8.86488 q^{64} +15.2807 q^{66} +(-3.19990 + 5.54239i) q^{67} +(-0.289961 + 0.502227i) q^{68} +(4.53957 + 7.86276i) q^{69} -4.39111 q^{70} +(5.39866 + 9.35076i) q^{71} +(3.73748 + 6.47351i) q^{72} -4.70308 q^{73} +(5.30812 + 9.19393i) q^{74} +(-1.16612 + 2.01978i) q^{75} +(0.581008 - 1.00633i) q^{76} +19.3396 q^{77} -11.9826 q^{79} +(-1.35638 + 2.34932i) q^{80} +(5.18379 - 8.97859i) q^{81} +(-2.27597 - 3.94209i) q^{82} -12.1286 q^{83} +(2.15104 + 3.72572i) q^{84} +(-0.565928 - 0.980215i) q^{85} -1.38051 q^{86} +(0.0288357 + 0.0499450i) q^{87} +(8.23042 - 14.2555i) q^{88} +(8.07702 - 13.9898i) q^{89} -2.97527 q^{90} +1.99457 q^{92} +(-6.37182 + 11.0363i) q^{93} +(-1.57666 + 2.73086i) q^{94} +(1.13397 + 1.96410i) q^{95} +6.57666 q^{96} +(-6.08408 - 10.5379i) q^{97} +(-3.63553 - 6.29692i) q^{98} +13.1039 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + O(q^{10})$$ $$8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$$.

 $$n$$ $$171$$ $$677$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.609843 + 1.05628i −0.431224 + 0.746903i −0.996979 0.0776710i $$-0.975252\pi$$
0.565755 + 0.824574i $$0.308585\pi$$
$$3$$ −1.16612 + 2.01978i −0.673262 + 1.16612i 0.303712 + 0.952764i $$0.401774\pi$$
−0.976974 + 0.213359i $$0.931559\pi$$
$$4$$ 0.256182 + 0.443720i 0.128091 + 0.221860i
$$5$$ −1.00000 −0.447214
$$6$$ −1.42231 2.46350i −0.580654 1.00572i
$$7$$ −1.80010 3.11786i −0.680373 1.17844i −0.974867 0.222787i $$-0.928484\pi$$
0.294494 0.955653i $$-0.404849\pi$$
$$8$$ −3.06430 −1.08339
$$9$$ −1.21969 2.11256i −0.406562 0.704187i
$$10$$ 0.609843 1.05628i 0.192849 0.334025i
$$11$$ −2.68591 + 4.65213i −0.809832 + 1.40267i 0.103149 + 0.994666i $$0.467108\pi$$
−0.912980 + 0.408004i $$0.866225\pi$$
$$12$$ −1.19496 −0.344955
$$13$$ 0 0
$$14$$ 4.39111 1.17357
$$15$$ 1.16612 2.01978i 0.301092 0.521506i
$$16$$ 1.35638 2.34932i 0.339094 0.587329i
$$17$$ 0.565928 + 0.980215i 0.137258 + 0.237737i 0.926458 0.376399i $$-0.122838\pi$$
−0.789200 + 0.614136i $$0.789505\pi$$
$$18$$ 2.97527 0.701278
$$19$$ −1.13397 1.96410i −0.260152 0.450596i 0.706130 0.708082i $$-0.250439\pi$$
−0.966282 + 0.257486i $$0.917106\pi$$
$$20$$ −0.256182 0.443720i −0.0572840 0.0992188i
$$21$$ 8.39654 1.83228
$$22$$ −3.27597 5.67414i −0.698438 1.20973i
$$23$$ 1.94644 3.37133i 0.405860 0.702970i −0.588561 0.808453i $$-0.700305\pi$$
0.994421 + 0.105483i $$0.0336387\pi$$
$$24$$ 3.57335 6.18922i 0.729407 1.26337i
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ −1.30752 −0.251632
$$28$$ 0.922305 1.59748i 0.174299 0.301895i
$$29$$ 0.0123639 0.0214150i 0.00229593 0.00397666i −0.864875 0.501987i $$-0.832603\pi$$
0.867171 + 0.498010i $$0.165936\pi$$
$$30$$ 1.42231 + 2.46350i 0.259676 + 0.449772i
$$31$$ 5.46410 0.981382 0.490691 0.871334i $$-0.336744\pi$$
0.490691 + 0.871334i $$0.336744\pi$$
$$32$$ −1.40994 2.44209i −0.249245 0.431705i
$$33$$ −6.26420 10.8499i −1.09046 1.88873i
$$34$$ −1.38051 −0.236755
$$35$$ 1.80010 + 3.11786i 0.304272 + 0.527015i
$$36$$ 0.624924 1.08240i 0.104154 0.180400i
$$37$$ 4.35203 7.53794i 0.715470 1.23923i −0.247309 0.968937i $$-0.579546\pi$$
0.962778 0.270293i $$-0.0871205\pi$$
$$38$$ 2.76619 0.448735
$$39$$ 0 0
$$40$$ 3.06430 0.484508
$$41$$ −1.86603 + 3.23205i −0.291424 + 0.504762i −0.974147 0.225916i $$-0.927462\pi$$
0.682723 + 0.730678i $$0.260796\pi$$
$$42$$ −5.12058 + 8.86910i −0.790122 + 1.36853i
$$43$$ 0.565928 + 0.980215i 0.0863031 + 0.149481i 0.905946 0.423394i $$-0.139161\pi$$
−0.819643 + 0.572875i $$0.805828\pi$$
$$44$$ −2.75232 −0.414929
$$45$$ 1.21969 + 2.11256i 0.181820 + 0.314922i
$$46$$ 2.37404 + 4.11196i 0.350034 + 0.606276i
$$47$$ 2.58535 0.377113 0.188556 0.982062i $$-0.439619\pi$$
0.188556 + 0.982062i $$0.439619\pi$$
$$48$$ 3.16341 + 5.47918i 0.456598 + 0.790852i
$$49$$ −2.98070 + 5.16273i −0.425815 + 0.737533i
$$50$$ −0.609843 + 1.05628i −0.0862449 + 0.149381i
$$51$$ −2.63977 −0.369641
$$52$$ 0 0
$$53$$ −4.43937 −0.609795 −0.304897 0.952385i $$-0.598622\pi$$
−0.304897 + 0.952385i $$0.598622\pi$$
$$54$$ 0.797382 1.38111i 0.108510 0.187945i
$$55$$ 2.68591 4.65213i 0.362168 0.627293i
$$56$$ 5.51603 + 9.55405i 0.737111 + 1.27671i
$$57$$ 5.28942 0.700600
$$58$$ 0.0150801 + 0.0261196i 0.00198012 + 0.00342967i
$$59$$ 0.0857123 + 0.148458i 0.0111588 + 0.0193276i 0.871551 0.490305i $$-0.163115\pi$$
−0.860392 + 0.509633i $$0.829781\pi$$
$$60$$ 1.19496 0.154269
$$61$$ −1.68012 2.91005i −0.215117 0.372594i 0.738192 0.674591i $$-0.235680\pi$$
−0.953309 + 0.301997i $$0.902347\pi$$
$$62$$ −3.33225 + 5.77162i −0.423196 + 0.732997i
$$63$$ −4.39111 + 7.60563i −0.553228 + 0.958219i
$$64$$ 8.86488 1.10811
$$65$$ 0 0
$$66$$ 15.2807 1.88093
$$67$$ −3.19990 + 5.54239i −0.390930 + 0.677111i −0.992572 0.121655i $$-0.961180\pi$$
0.601642 + 0.798766i $$0.294513\pi$$
$$68$$ −0.289961 + 0.502227i −0.0351629 + 0.0609040i
$$69$$ 4.53957 + 7.86276i 0.546500 + 0.946566i
$$70$$ −4.39111 −0.524838
$$71$$ 5.39866 + 9.35076i 0.640703 + 1.10973i 0.985276 + 0.170971i $$0.0546905\pi$$
−0.344573 + 0.938760i $$0.611976\pi$$
$$72$$ 3.73748 + 6.47351i 0.440467 + 0.762911i
$$73$$ −4.70308 −0.550454 −0.275227 0.961379i $$-0.588753\pi$$
−0.275227 + 0.961379i $$0.588753\pi$$
$$74$$ 5.30812 + 9.19393i 0.617056 + 1.06877i
$$75$$ −1.16612 + 2.01978i −0.134652 + 0.233225i
$$76$$ 0.581008 1.00633i 0.0666462 0.115435i
$$77$$ 19.3396 2.20395
$$78$$ 0 0
$$79$$ −11.9826 −1.34815 −0.674075 0.738663i $$-0.735457\pi$$
−0.674075 + 0.738663i $$0.735457\pi$$
$$80$$ −1.35638 + 2.34932i −0.151648 + 0.262661i
$$81$$ 5.18379 8.97859i 0.575976 0.997621i
$$82$$ −2.27597 3.94209i −0.251338 0.435331i
$$83$$ −12.1286 −1.33129 −0.665643 0.746270i $$-0.731843\pi$$
−0.665643 + 0.746270i $$0.731843\pi$$
$$84$$ 2.15104 + 3.72572i 0.234698 + 0.406509i
$$85$$ −0.565928 0.980215i −0.0613835 0.106319i
$$86$$ −1.38051 −0.148864
$$87$$ 0.0288357 + 0.0499450i 0.00309152 + 0.00535466i
$$88$$ 8.23042 14.2555i 0.877366 1.51964i
$$89$$ 8.07702 13.9898i 0.856162 1.48292i −0.0194001 0.999812i $$-0.506176\pi$$
0.875562 0.483105i $$-0.160491\pi$$
$$90$$ −2.97527 −0.313621
$$91$$ 0 0
$$92$$ 1.99457 0.207948
$$93$$ −6.37182 + 11.0363i −0.660727 + 1.14441i
$$94$$ −1.57666 + 2.73086i −0.162620 + 0.281666i
$$95$$ 1.13397 + 1.96410i 0.116343 + 0.201513i
$$96$$ 6.57666 0.671228
$$97$$ −6.08408 10.5379i −0.617745 1.06997i −0.989896 0.141794i $$-0.954713\pi$$
0.372151 0.928172i $$-0.378620\pi$$
$$98$$ −3.63553 6.29692i −0.367244 0.636085i
$$99$$ 13.1039 1.31699
$$100$$ 0.256182 + 0.443720i 0.0256182 + 0.0443720i
$$101$$ 2.02721 3.51122i 0.201714 0.349380i −0.747366 0.664412i $$-0.768682\pi$$
0.949081 + 0.315032i $$0.102015\pi$$
$$102$$ 1.60984 2.78833i 0.159398 0.276086i
$$103$$ −17.9035 −1.76408 −0.882041 0.471173i $$-0.843831\pi$$
−0.882041 + 0.471173i $$0.843831\pi$$
$$104$$ 0 0
$$105$$ −8.39654 −0.819419
$$106$$ 2.70732 4.68922i 0.262958 0.455457i
$$107$$ 4.56593 7.90842i 0.441405 0.764536i −0.556389 0.830922i $$-0.687814\pi$$
0.997794 + 0.0663862i $$0.0211469\pi$$
$$108$$ −0.334963 0.580172i −0.0322318 0.0558271i
$$109$$ 7.37605 0.706498 0.353249 0.935529i $$-0.385077\pi$$
0.353249 + 0.935529i $$0.385077\pi$$
$$110$$ 3.27597 + 5.67414i 0.312351 + 0.541008i
$$111$$ 10.1500 + 17.5803i 0.963396 + 1.66865i
$$112$$ −9.76645 −0.922843
$$113$$ −3.53794 6.12789i −0.332821 0.576463i 0.650243 0.759727i $$-0.274667\pi$$
−0.983064 + 0.183263i $$0.941334\pi$$
$$114$$ −3.22572 + 5.58710i −0.302116 + 0.523280i
$$115$$ −1.94644 + 3.37133i −0.181506 + 0.314378i
$$116$$ 0.0126697 0.00117635
$$117$$ 0 0
$$118$$ −0.209084 −0.0192478
$$119$$ 2.03745 3.52897i 0.186773 0.323500i
$$120$$ −3.57335 + 6.18922i −0.326201 + 0.564996i
$$121$$ −8.92820 15.4641i −0.811655 1.40583i
$$122$$ 4.09843 0.371055
$$123$$ −4.35203 7.53794i −0.392409 0.679673i
$$124$$ 1.39980 + 2.42453i 0.125706 + 0.217729i
$$125$$ −1.00000 −0.0894427
$$126$$ −5.35578 9.27648i −0.477131 0.826415i
$$127$$ 5.71806 9.90396i 0.507395 0.878835i −0.492568 0.870274i $$-0.663942\pi$$
0.999963 0.00856072i $$-0.00272499\pi$$
$$128$$ −2.58631 + 4.47962i −0.228600 + 0.395946i
$$129$$ −2.63977 −0.232418
$$130$$ 0 0
$$131$$ −10.5680 −0.923328 −0.461664 0.887055i $$-0.652747\pi$$
−0.461664 + 0.887055i $$0.652747\pi$$
$$132$$ 3.20955 5.55910i 0.279355 0.483858i
$$133$$ −4.08253 + 7.07115i −0.354000 + 0.613146i
$$134$$ −3.90288 6.75998i −0.337157 0.583974i
$$135$$ 1.30752 0.112533
$$136$$ −1.73417 3.00367i −0.148704 0.257563i
$$137$$ −1.89336 3.27940i −0.161761 0.280178i 0.773739 0.633504i $$-0.218384\pi$$
−0.935500 + 0.353326i $$0.885051\pi$$
$$138$$ −11.0737 −0.942656
$$139$$ −1.00693 1.74406i −0.0854068 0.147929i 0.820158 0.572138i $$-0.193886\pi$$
−0.905564 + 0.424209i $$0.860552\pi$$
$$140$$ −0.922305 + 1.59748i −0.0779490 + 0.135012i
$$141$$ −3.01484 + 5.22186i −0.253895 + 0.439760i
$$142$$ −13.1694 −1.10515
$$143$$ 0 0
$$144$$ −6.61742 −0.551452
$$145$$ −0.0123639 + 0.0214150i −0.00102677 + 0.00177842i
$$146$$ 2.86814 4.96777i 0.237369 0.411136i
$$147$$ −6.95174 12.0408i −0.573370 0.993105i
$$148$$ 4.45965 0.366581
$$149$$ 2.75890 + 4.77855i 0.226018 + 0.391474i 0.956624 0.291324i $$-0.0940959\pi$$
−0.730607 + 0.682799i $$0.760763\pi$$
$$150$$ −1.42231 2.46350i −0.116131 0.201144i
$$151$$ −4.88961 −0.397911 −0.198956 0.980009i $$-0.563755\pi$$
−0.198956 + 0.980009i $$0.563755\pi$$
$$152$$ 3.47484 + 6.01859i 0.281846 + 0.488172i
$$153$$ 1.38051 2.39111i 0.111608 0.193310i
$$154$$ −11.7941 + 20.4280i −0.950397 + 1.64614i
$$155$$ −5.46410 −0.438887
$$156$$ 0 0
$$157$$ 10.0405 0.801323 0.400661 0.916226i $$-0.368780\pi$$
0.400661 + 0.916226i $$0.368780\pi$$
$$158$$ 7.30752 12.6570i 0.581355 1.00694i
$$159$$ 5.17686 8.96658i 0.410551 0.711096i
$$160$$ 1.40994 + 2.44209i 0.111466 + 0.193064i
$$161$$ −14.0151 −1.10454
$$162$$ 6.32260 + 10.9511i 0.496750 + 0.860397i
$$163$$ −3.39062 5.87273i −0.265574 0.459988i 0.702140 0.712039i $$-0.252228\pi$$
−0.967714 + 0.252051i $$0.918895\pi$$
$$164$$ −1.91217 −0.149315
$$165$$ 6.26420 + 10.8499i 0.487667 + 0.844664i
$$166$$ 7.39654 12.8112i 0.574083 0.994341i
$$167$$ −5.24490 + 9.08444i −0.405863 + 0.702975i −0.994421 0.105479i $$-0.966362\pi$$
0.588559 + 0.808455i $$0.299696\pi$$
$$168$$ −25.7295 −1.98507
$$169$$ 0 0
$$170$$ 1.38051 0.105880
$$171$$ −2.76619 + 4.79118i −0.211536 + 0.366391i
$$172$$ −0.289961 + 0.502227i −0.0221093 + 0.0382944i
$$173$$ 2.22923 + 3.86113i 0.169485 + 0.293557i 0.938239 0.345988i $$-0.112456\pi$$
−0.768754 + 0.639545i $$0.779123\pi$$
$$174$$ −0.0703412 −0.00533255
$$175$$ −1.80010 3.11786i −0.136075 0.235688i
$$176$$ 7.28621 + 12.6201i 0.549219 + 0.951275i
$$177$$ −0.399804 −0.0300511
$$178$$ 9.85143 + 17.0632i 0.738396 + 1.27894i
$$179$$ −9.31564 + 16.1352i −0.696284 + 1.20600i 0.273462 + 0.961883i $$0.411831\pi$$
−0.969746 + 0.244116i $$0.921502\pi$$
$$180$$ −0.624924 + 1.08240i −0.0465791 + 0.0806773i
$$181$$ 18.0900 1.34462 0.672310 0.740270i $$-0.265302\pi$$
0.672310 + 0.740270i $$0.265302\pi$$
$$182$$ 0 0
$$183$$ 7.83690 0.579320
$$184$$ −5.96446 + 10.3307i −0.439706 + 0.761593i
$$185$$ −4.35203 + 7.53794i −0.319968 + 0.554200i
$$186$$ −7.77162 13.4608i −0.569843 0.986997i
$$187$$ −6.08012 −0.444622
$$188$$ 0.662321 + 1.14717i 0.0483047 + 0.0836662i
$$189$$ 2.35366 + 4.07666i 0.171204 + 0.296533i
$$190$$ −2.76619 −0.200680
$$191$$ −13.6682 23.6740i −0.988994 1.71299i −0.622632 0.782515i $$-0.713937\pi$$
−0.366361 0.930473i $$-0.619397\pi$$
$$192$$ −10.3375 + 17.9052i −0.746048 + 1.29219i
$$193$$ −10.8837 + 18.8511i −0.783425 + 1.35693i 0.146510 + 0.989209i $$0.453196\pi$$
−0.929935 + 0.367723i $$0.880137\pi$$
$$194$$ 14.8413 1.06555
$$195$$ 0 0
$$196$$ −3.05441 −0.218172
$$197$$ 0.848360 1.46940i 0.0604432 0.104691i −0.834220 0.551431i $$-0.814082\pi$$
0.894664 + 0.446741i $$0.147415\pi$$
$$198$$ −7.99131 + 13.8413i −0.567917 + 0.983662i
$$199$$ −12.6627 21.9325i −0.897637 1.55475i −0.830506 0.557009i $$-0.811949\pi$$
−0.0671309 0.997744i $$-0.521385\pi$$
$$200$$ −3.06430 −0.216679
$$201$$ −7.46296 12.9262i −0.526397 0.911746i
$$202$$ 2.47256 + 4.28259i 0.173968 + 0.301322i
$$203$$ −0.0890252 −0.00624834
$$204$$ −0.676260 1.17132i −0.0473477 0.0820086i
$$205$$ 1.86603 3.23205i 0.130329 0.225736i
$$206$$ 10.9183 18.9111i 0.760715 1.31760i
$$207$$ −9.49617 −0.660030
$$208$$ 0 0
$$209$$ 12.1830 0.842716
$$210$$ 5.12058 8.86910i 0.353353 0.612026i
$$211$$ 0.167753 0.290558i 0.0115486 0.0200028i −0.860193 0.509968i $$-0.829657\pi$$
0.871742 + 0.489965i $$0.162991\pi$$
$$212$$ −1.13729 1.96984i −0.0781092 0.135289i
$$213$$ −25.1820 −1.72544
$$214$$ 5.56900 + 9.64579i 0.380689 + 0.659373i
$$215$$ −0.565928 0.980215i −0.0385959 0.0668501i
$$216$$ 4.00663 0.272616
$$217$$ −9.83592 17.0363i −0.667706 1.15650i
$$218$$ −4.49824 + 7.79118i −0.304659 + 0.527685i
$$219$$ 5.48438 9.49922i 0.370600 0.641898i
$$220$$ 2.75232 0.185562
$$221$$ 0 0
$$222$$ −24.7597 −1.66176
$$223$$ 6.14838 10.6493i 0.411726 0.713130i −0.583353 0.812219i $$-0.698259\pi$$
0.995079 + 0.0990887i $$0.0315928\pi$$
$$224$$ −5.07606 + 8.79200i −0.339159 + 0.587440i
$$225$$ −1.21969 2.11256i −0.0813125 0.140837i
$$226$$ 8.63036 0.574083
$$227$$ 3.81613 + 6.60974i 0.253286 + 0.438704i 0.964428 0.264344i $$-0.0851554\pi$$
−0.711143 + 0.703048i $$0.751822\pi$$
$$228$$ 1.35505 + 2.34702i 0.0897406 + 0.155435i
$$229$$ −14.4008 −0.951631 −0.475815 0.879545i $$-0.657847\pi$$
−0.475815 + 0.879545i $$0.657847\pi$$
$$230$$ −2.37404 4.11196i −0.156540 0.271135i
$$231$$ −22.5523 + 39.0618i −1.48384 + 2.57008i
$$232$$ −0.0378868 + 0.0656218i −0.00248739 + 0.00430828i
$$233$$ 9.49617 0.622115 0.311057 0.950391i $$-0.399317\pi$$
0.311057 + 0.950391i $$0.399317\pi$$
$$234$$ 0 0
$$235$$ −2.58535 −0.168650
$$236$$ −0.0439159 + 0.0760645i −0.00285868 + 0.00495138i
$$237$$ 13.9732 24.2023i 0.907657 1.57211i
$$238$$ 2.48505 + 4.30423i 0.161082 + 0.279002i
$$239$$ −19.9143 −1.28815 −0.644076 0.764962i $$-0.722758\pi$$
−0.644076 + 0.764962i $$0.722758\pi$$
$$240$$ −3.16341 5.47918i −0.204197 0.353680i
$$241$$ −11.6332 20.1493i −0.749360 1.29793i −0.948130 0.317883i $$-0.897028\pi$$
0.198770 0.980046i $$-0.436305\pi$$
$$242$$ 21.7792 1.40002
$$243$$ 10.1286 + 17.5432i 0.649750 + 1.12540i
$$244$$ 0.860832 1.49100i 0.0551091 0.0954518i
$$245$$ 2.98070 5.16273i 0.190430 0.329835i
$$246$$ 10.6162 0.676866
$$247$$ 0 0
$$248$$ −16.7436 −1.06322
$$249$$ 14.1434 24.4972i 0.896304 1.55244i
$$250$$ 0.609843 1.05628i 0.0385699 0.0668050i
$$251$$ −5.92008 10.2539i −0.373672 0.647219i 0.616455 0.787390i $$-0.288568\pi$$
−0.990127 + 0.140171i $$0.955235\pi$$
$$252$$ −4.49969 −0.283454
$$253$$ 10.4559 + 18.1101i 0.657357 + 1.13858i
$$254$$ 6.97424 + 12.0797i 0.437603 + 0.757950i
$$255$$ 2.63977 0.165309
$$256$$ 5.71040 + 9.89070i 0.356900 + 0.618169i
$$257$$ 2.77501 4.80646i 0.173100 0.299819i −0.766402 0.642361i $$-0.777955\pi$$
0.939502 + 0.342543i $$0.111288\pi$$
$$258$$ 1.60984 2.78833i 0.100224 0.173594i
$$259$$ −31.3363 −1.94714
$$260$$ 0 0
$$261$$ −0.0603205 −0.00373375
$$262$$ 6.44481 11.1627i 0.398161 0.689636i
$$263$$ −3.42983 + 5.94065i −0.211493 + 0.366316i −0.952182 0.305532i $$-0.901166\pi$$
0.740689 + 0.671848i $$0.234499\pi$$
$$264$$ 19.1954 + 33.2474i 1.18139 + 2.04623i
$$265$$ 4.43937 0.272709
$$266$$ −4.97941 8.62459i −0.305307 0.528807i
$$267$$ 18.8376 + 32.6277i 1.15284 + 1.99678i
$$268$$ −3.27903 −0.200299
$$269$$ 0.710994 + 1.23148i 0.0433501 + 0.0750845i 0.886886 0.461988i $$-0.152864\pi$$
−0.843536 + 0.537072i $$0.819530\pi$$
$$270$$ −0.797382 + 1.38111i −0.0485271 + 0.0840514i
$$271$$ 4.98473 8.63381i 0.302801 0.524467i −0.673968 0.738760i $$-0.735412\pi$$
0.976769 + 0.214294i $$0.0687449\pi$$
$$272$$ 3.07045 0.186173
$$273$$ 0 0
$$274$$ 4.61862 0.279021
$$275$$ −2.68591 + 4.65213i −0.161966 + 0.280534i
$$276$$ −2.32591 + 4.02860i −0.140003 + 0.242493i
$$277$$ 8.76187 + 15.1760i 0.526449 + 0.911837i 0.999525 + 0.0308154i $$0.00981039\pi$$
−0.473076 + 0.881022i $$0.656856\pi$$
$$278$$ 2.45628 0.147318
$$279$$ −6.66449 11.5432i −0.398993 0.691076i
$$280$$ −5.51603 9.55405i −0.329646 0.570964i
$$281$$ 10.7352 0.640406 0.320203 0.947349i $$-0.396249\pi$$
0.320203 + 0.947349i $$0.396249\pi$$
$$282$$ −3.67716 6.36903i −0.218972 0.379270i
$$283$$ −0.659192 + 1.14175i −0.0391849 + 0.0678702i −0.884953 0.465681i $$-0.845809\pi$$
0.845768 + 0.533551i $$0.179143\pi$$
$$284$$ −2.76608 + 4.79099i −0.164137 + 0.284293i
$$285$$ −5.28942 −0.313318
$$286$$ 0 0
$$287$$ 13.4361 0.793109
$$288$$ −3.43937 + 5.95717i −0.202667 + 0.351030i
$$289$$ 7.85945 13.6130i 0.462321 0.800763i
$$290$$ −0.0150801 0.0261196i −0.000885536 0.00153379i
$$291$$ 28.3792 1.66362
$$292$$ −1.20485 2.08685i −0.0705082 0.122124i
$$293$$ −9.37133 16.2316i −0.547479 0.948261i −0.998446 0.0557207i $$-0.982254\pi$$
0.450968 0.892540i $$-0.351079\pi$$
$$294$$ 16.9579 0.989004
$$295$$ −0.0857123 0.148458i −0.00499036 0.00864356i
$$296$$ −13.3359 + 23.0985i −0.775134 + 1.34257i
$$297$$ 3.51187 6.08275i 0.203780 0.352957i
$$298$$ −6.72998 −0.389857
$$299$$ 0 0
$$300$$ −1.19496 −0.0689910
$$301$$ 2.03745 3.52897i 0.117437 0.203406i
$$302$$ 2.98190 5.16480i 0.171589 0.297201i
$$303$$ 4.72794 + 8.18904i 0.271613 + 0.470448i
$$304$$ −6.15239 −0.352864
$$305$$ 1.68012 + 2.91005i 0.0962032 + 0.166629i
$$306$$ 1.68379 + 2.91641i 0.0962558 + 0.166720i
$$307$$ 14.3043 0.816387 0.408194 0.912895i $$-0.366159\pi$$
0.408194 + 0.912895i $$0.366159\pi$$
$$308$$ 4.95445 + 8.58137i 0.282306 + 0.488969i
$$309$$ 20.8777 36.1612i 1.18769 2.05714i
$$310$$ 3.33225 5.77162i 0.189259 0.327806i
$$311$$ 2.76102 0.156563 0.0782815 0.996931i $$-0.475057\pi$$
0.0782815 + 0.996931i $$0.475057\pi$$
$$312$$ 0 0
$$313$$ −16.3858 −0.926179 −0.463090 0.886311i $$-0.653259\pi$$
−0.463090 + 0.886311i $$0.653259\pi$$
$$314$$ −6.12316 + 10.6056i −0.345550 + 0.598510i
$$315$$ 4.39111 7.60563i 0.247411 0.428529i
$$316$$ −3.06973 5.31693i −0.172686 0.299101i
$$317$$ 1.78575 0.100297 0.0501487 0.998742i $$-0.484030\pi$$
0.0501487 + 0.998742i $$0.484030\pi$$
$$318$$ 6.31414 + 10.9364i 0.354080 + 0.613284i
$$319$$ 0.0664168 + 0.115037i 0.00371863 + 0.00644085i
$$320$$ −8.86488 −0.495562
$$321$$ 10.6489 + 18.4444i 0.594362 + 1.02946i
$$322$$ 8.54702 14.8039i 0.476307 0.824987i
$$323$$ 1.28349 2.22308i 0.0714156 0.123695i
$$324$$ 5.31197 0.295110
$$325$$ 0 0
$$326$$ 8.27099 0.458088
$$327$$ −8.60139 + 14.8980i −0.475658 + 0.823864i
$$328$$ 5.71806 9.90396i 0.315727 0.546855i
$$329$$ −4.65389 8.06077i −0.256577 0.444405i
$$330$$ −15.2807 −0.841176
$$331$$ −3.61220 6.25652i −0.198545 0.343889i 0.749512 0.661991i $$-0.230288\pi$$
−0.948057 + 0.318101i $$0.896955\pi$$
$$332$$ −3.10713 5.38170i −0.170526 0.295359i
$$333$$ −21.2325 −1.16353
$$334$$ −6.39714 11.0802i −0.350036 0.606280i
$$335$$ 3.19990 5.54239i 0.174829 0.302813i
$$336$$ 11.3889 19.7261i 0.621315 1.07615i
$$337$$ −4.36219 −0.237624 −0.118812 0.992917i $$-0.537909\pi$$
−0.118812 + 0.992917i $$0.537909\pi$$
$$338$$ 0 0
$$339$$ 16.5027 0.896303
$$340$$ 0.289961 0.502227i 0.0157253 0.0272371i
$$341$$ −14.6761 + 25.4197i −0.794754 + 1.37655i
$$342$$ −3.37388 5.84374i −0.182439 0.315993i
$$343$$ −3.73913 −0.201894
$$344$$ −1.73417 3.00367i −0.0935002 0.161947i
$$345$$ −4.53957 7.86276i −0.244402 0.423317i
$$346$$ −5.43792 −0.292344
$$347$$ 13.3536 + 23.1291i 0.716858 + 1.24163i 0.962239 + 0.272207i $$0.0877537\pi$$
−0.245381 + 0.969427i $$0.578913\pi$$
$$348$$ −0.0147744 + 0.0255900i −0.000791991 + 0.00137177i
$$349$$ −11.7855 + 20.4131i −0.630865 + 1.09269i 0.356510 + 0.934292i $$0.383967\pi$$
−0.987375 + 0.158399i $$0.949367\pi$$
$$350$$ 4.39111 0.234715
$$351$$ 0 0
$$352$$ 15.1479 0.807385
$$353$$ −2.86863 + 4.96862i −0.152682 + 0.264453i −0.932213 0.361911i $$-0.882124\pi$$
0.779531 + 0.626364i $$0.215458\pi$$
$$354$$ 0.243818 0.422305i 0.0129588 0.0224453i
$$355$$ −5.39866 9.35076i −0.286531 0.496287i
$$356$$ 8.27675 0.438667
$$357$$ 4.75184 + 8.23042i 0.251494 + 0.435600i
$$358$$ −11.3622 19.6799i −0.600509 1.04011i
$$359$$ −24.7583 −1.30669 −0.653347 0.757059i $$-0.726636\pi$$
−0.653347 + 0.757059i $$0.726636\pi$$
$$360$$ −3.73748 6.47351i −0.196983 0.341184i
$$361$$ 6.92820 12.0000i 0.364642 0.631579i
$$362$$ −11.0321 + 19.1081i −0.579833 + 1.00430i
$$363$$ 41.6455 2.18582
$$364$$ 0 0
$$365$$ 4.70308 0.246171
$$366$$ −4.77928 + 8.27796i −0.249817 + 0.432696i
$$367$$ −13.0268 + 22.5630i −0.679992 + 1.17778i 0.294991 + 0.955500i $$0.404683\pi$$
−0.974983 + 0.222280i $$0.928650\pi$$
$$368$$ −5.28021 9.14558i −0.275250 0.476747i
$$369$$ 9.10387 0.473928
$$370$$ −5.30812 9.19393i −0.275956 0.477969i
$$371$$ 7.99131 + 13.8413i 0.414888 + 0.718607i
$$372$$ −6.52938 −0.338532
$$373$$ −6.60224 11.4354i −0.341851 0.592103i 0.642926 0.765929i $$-0.277720\pi$$
−0.984776 + 0.173826i $$0.944387\pi$$
$$374$$ 3.70792 6.42231i 0.191732 0.332089i
$$375$$ 1.16612 2.01978i 0.0602183 0.104301i
$$376$$ −7.92229 −0.408561
$$377$$ 0 0
$$378$$ −5.74146 −0.295309
$$379$$ −12.9989 + 22.5147i −0.667707 + 1.15650i 0.310837 + 0.950463i $$0.399391\pi$$
−0.978544 + 0.206039i $$0.933943\pi$$
$$380$$ −0.581008 + 1.00633i −0.0298051 + 0.0516239i
$$381$$ 13.3359 + 23.0985i 0.683220 + 1.18337i
$$382$$ 33.3418 1.70591
$$383$$ 4.80010 + 8.31401i 0.245274 + 0.424826i 0.962208 0.272314i $$-0.0877889\pi$$
−0.716935 + 0.697140i $$0.754456\pi$$
$$384$$ −6.03191 10.4476i −0.307815 0.533151i
$$385$$ −19.3396 −0.985637
$$386$$ −13.2747 22.9924i −0.675664 1.17028i
$$387$$ 1.38051 2.39111i 0.0701752 0.121547i
$$388$$ 3.11726 5.39926i 0.158255 0.274106i
$$389$$ 5.63129 0.285518 0.142759 0.989758i $$-0.454403\pi$$
0.142759 + 0.989758i $$0.454403\pi$$
$$390$$ 0 0
$$391$$ 4.40617 0.222829
$$392$$ 9.13376 15.8201i 0.461325 0.799038i
$$393$$ 12.3236 21.3450i 0.621641 1.07671i
$$394$$ 1.03473 + 1.79221i 0.0521291 + 0.0902903i
$$395$$ 11.9826 0.602911
$$396$$ 3.35697 + 5.81445i 0.168694 + 0.292187i
$$397$$ 8.38291 + 14.5196i 0.420726 + 0.728719i 0.996011 0.0892344i $$-0.0284420\pi$$
−0.575285 + 0.817953i $$0.695109\pi$$
$$398$$ 30.8891 1.54833
$$399$$ −9.52147 16.4917i −0.476670 0.825616i
$$400$$ 1.35638 2.34932i 0.0678189 0.117466i
$$401$$ 6.93902 12.0187i 0.346518 0.600187i −0.639110 0.769115i $$-0.720697\pi$$
0.985628 + 0.168928i $$0.0540307\pi$$
$$402$$ 18.2050 0.907980
$$403$$ 0 0
$$404$$ 2.07733 0.103351
$$405$$ −5.18379 + 8.97859i −0.257585 + 0.446149i
$$406$$ 0.0542914 0.0940355i 0.00269444 0.00466690i
$$407$$ 23.3783 + 40.4924i 1.15882 + 2.00713i
$$408$$ 8.08903 0.400466
$$409$$ −14.7125 25.4829i −0.727489 1.26005i −0.957941 0.286964i $$-0.907354\pi$$
0.230453 0.973083i $$-0.425979\pi$$
$$410$$ 2.27597 + 3.94209i 0.112402 + 0.194686i
$$411$$ 8.83157 0.435629
$$412$$ −4.58655 7.94413i −0.225963 0.391379i
$$413$$ 0.308581 0.534478i 0.0151843 0.0262999i
$$414$$ 5.79118 10.0306i 0.284621 0.492978i
$$415$$ 12.1286 0.595369
$$416$$ 0 0
$$417$$ 4.69683 0.230005
$$418$$ −7.42973 + 12.8687i −0.363400 + 0.629427i
$$419$$ −3.48397 + 6.03440i −0.170203 + 0.294800i −0.938491 0.345305i $$-0.887776\pi$$
0.768288 + 0.640104i $$0.221109\pi$$
$$420$$ −2.15104 3.72572i −0.104960 0.181796i
$$421$$ 7.12125 0.347069 0.173534 0.984828i $$-0.444481\pi$$
0.173534 + 0.984828i $$0.444481\pi$$
$$422$$ 0.204607 + 0.354389i 0.00996010 + 0.0172514i
$$423$$ −3.15332 5.46171i −0.153320 0.265558i
$$424$$ 13.6036 0.660647
$$425$$ 0.565928 + 0.980215i 0.0274515 + 0.0475474i
$$426$$ 15.3571 26.5993i 0.744054 1.28874i
$$427$$ −6.04875 + 10.4767i −0.292720 + 0.507005i
$$428$$ 4.67883 0.226160
$$429$$ 0 0
$$430$$ 1.38051 0.0665740
$$431$$ −15.1072 + 26.1664i −0.727687 + 1.26039i 0.230171 + 0.973150i $$0.426071\pi$$
−0.957858 + 0.287241i $$0.907262\pi$$
$$432$$ −1.77349 + 3.07177i −0.0853270 + 0.147791i
$$433$$ −0.600065 1.03934i −0.0288373 0.0499476i 0.851247 0.524766i $$-0.175847\pi$$
−0.880084 + 0.474818i $$0.842514\pi$$
$$434$$ 23.9935 1.15172
$$435$$ −0.0288357 0.0499450i −0.00138257 0.00239468i
$$436$$ 1.88961 + 3.27290i 0.0904960 + 0.156744i
$$437$$ −8.82884 −0.422341
$$438$$ 6.68922 + 11.5861i 0.319623 + 0.553604i
$$439$$ 8.27705 14.3363i 0.395042 0.684233i −0.598064 0.801448i $$-0.704063\pi$$
0.993107 + 0.117215i $$0.0373966\pi$$
$$440$$ −8.23042 + 14.2555i −0.392370 + 0.679605i
$$441$$ 14.5421 0.692481
$$442$$ 0 0
$$443$$ 4.55949 0.216628 0.108314 0.994117i $$-0.465455\pi$$
0.108314 + 0.994117i $$0.465455\pi$$
$$444$$ −5.20050 + 9.00753i −0.246805 + 0.427478i
$$445$$ −8.07702 + 13.9898i −0.382887 + 0.663180i
$$446$$ 7.49910 + 12.9888i 0.355093 + 0.615038i
$$447$$ −12.8689 −0.608676
$$448$$ −15.9577 27.6395i −0.753929 1.30584i
$$449$$ −6.92608 11.9963i −0.326862 0.566142i 0.655025 0.755607i $$-0.272658\pi$$
−0.981887 + 0.189465i $$0.939325\pi$$
$$450$$ 2.97527 0.140256
$$451$$ −10.0239 17.3620i −0.472009 0.817544i
$$452$$ 1.81271 3.13971i 0.0852628 0.147680i
$$453$$ 5.70189 9.87596i 0.267898 0.464013i
$$454$$ −9.30897 −0.436892
$$455$$ 0 0
$$456$$ −16.2083 −0.759025
$$457$$ −20.0573 + 34.7402i −0.938240 + 1.62508i −0.169489 + 0.985532i $$0.554212\pi$$
−0.768751 + 0.639548i $$0.779122\pi$$
$$458$$ 8.78222 15.2113i 0.410366 0.710775i
$$459$$ −0.739961 1.28165i −0.0345384 0.0598223i
$$460$$ −1.99457 −0.0929972
$$461$$ 3.76950 + 6.52897i 0.175563 + 0.304084i 0.940356 0.340192i $$-0.110492\pi$$
−0.764793 + 0.644276i $$0.777159\pi$$
$$462$$ −27.5068 47.6432i −1.27973 2.21656i
$$463$$ 23.3031 1.08299 0.541494 0.840705i $$-0.317859\pi$$
0.541494 + 0.840705i $$0.317859\pi$$
$$464$$ −0.0335403 0.0580936i −0.00155707 0.00269693i
$$465$$ 6.37182 11.0363i 0.295486 0.511797i
$$466$$ −5.79118 + 10.0306i −0.268271 + 0.464659i
$$467$$ −22.6297 −1.04718 −0.523589 0.851971i $$-0.675407\pi$$
−0.523589 + 0.851971i $$0.675407\pi$$
$$468$$ 0 0
$$469$$ 23.0405 1.06391
$$470$$ 1.57666 2.73086i 0.0727260 0.125965i
$$471$$ −11.7085 + 20.2797i −0.539500 + 0.934441i
$$472$$ −0.262648 0.454919i −0.0120893 0.0209394i
$$473$$ −6.08012 −0.279564
$$474$$ 17.0429 + 29.5192i 0.782808 + 1.35586i
$$475$$ −1.13397 1.96410i −0.0520303 0.0901192i
$$476$$ 2.08783 0.0956956
$$477$$ 5.41465 + 9.37844i 0.247920 + 0.429409i
$$478$$ 12.1446 21.0351i 0.555482 0.962124i
$$479$$ −10.3224 + 17.8789i −0.471643 + 0.816910i −0.999474 0.0324399i $$-0.989672\pi$$
0.527831 + 0.849350i $$0.323006\pi$$
$$480$$ −6.57666 −0.300182
$$481$$ 0 0
$$482$$ 28.3777 1.29257
$$483$$ 16.3433 28.3075i 0.743648 1.28804i
$$484$$ 4.57449 7.92325i 0.207931 0.360148i
$$485$$ 6.08408 + 10.5379i 0.276264 + 0.478503i
$$486$$ −24.7074 −1.12075
$$487$$ −1.51802 2.62929i −0.0687882 0.119145i 0.829580 0.558388i $$-0.188580\pi$$
−0.898368 + 0.439243i $$0.855247\pi$$
$$488$$ 5.14838 + 8.91725i 0.233056 + 0.403665i
$$489$$ 15.8155 0.715203
$$490$$ 3.63553 + 6.29692i 0.164236 + 0.284466i
$$491$$ −5.33401 + 9.23877i −0.240720 + 0.416940i −0.960920 0.276827i $$-0.910717\pi$$
0.720199 + 0.693767i $$0.244050\pi$$
$$492$$ 2.22982 3.86217i 0.100528 0.174120i
$$493$$ 0.0279884 0.00126053
$$494$$ 0 0
$$495$$ −13.1039 −0.588975
$$496$$ 7.41139 12.8369i 0.332781 0.576394i
$$497$$ 19.4362 33.6646i 0.871835 1.51006i
$$498$$ 17.2506 + 29.8789i 0.773016 + 1.33890i
$$499$$ 33.9143 1.51821 0.759107 0.650966i $$-0.225636\pi$$
0.759107 + 0.650966i $$0.225636\pi$$
$$500$$ −0.256182 0.443720i −0.0114568 0.0198438i
$$501$$ −12.2324 21.1872i −0.546504 0.946572i
$$502$$ 14.4413 0.644546
$$503$$ 6.31380 + 10.9358i 0.281518 + 0.487604i 0.971759 0.235976i $$-0.0758286\pi$$
−0.690241 + 0.723580i $$0.742495\pi$$
$$504$$ 13.4557 23.3059i 0.599363 1.03813i
$$505$$ −2.02721 + 3.51122i −0.0902095 + 0.156247i
$$506$$ −25.5058 −1.13387
$$507$$ 0 0
$$508$$ 5.85945 0.259971
$$509$$ 12.0763 20.9168i 0.535273 0.927120i −0.463877 0.885899i $$-0.653542\pi$$
0.999150 0.0412201i $$-0.0131245\pi$$
$$510$$ −1.60984 + 2.78833i −0.0712851 + 0.123469i
$$511$$ 8.46601 + 14.6636i 0.374514 + 0.648678i
$$512$$ −24.2750 −1.07281
$$513$$ 1.48269 + 2.56810i 0.0654625 + 0.113384i
$$514$$ 3.38465 + 5.86238i 0.149290 + 0.258578i
$$515$$ 17.9035 0.788921
$$516$$ −0.676260 1.17132i −0.0297707 0.0515644i
$$517$$ −6.94402 + 12.0274i −0.305398 + 0.528964i
$$518$$ 19.1103 33.0999i 0.839656 1.45433i
$$519$$ −10.3982 −0.456431
$$520$$ 0 0
$$521$$ −24.7521 −1.08441 −0.542205 0.840246i $$-0.682410\pi$$
−0.542205 + 0.840246i $$0.682410\pi$$
$$522$$ 0.0367861 0.0637154i 0.00161008 0.00278875i
$$523$$ −18.5163 + 32.0712i −0.809662 + 1.40238i 0.103436 + 0.994636i $$0.467016\pi$$
−0.913098 + 0.407739i $$0.866317\pi$$
$$524$$ −2.70732 4.68922i −0.118270 0.204850i
$$525$$ 8.39654 0.366455
$$526$$ −4.18332 7.24573i −0.182402 0.315929i
$$527$$ 3.09229 + 5.35600i 0.134702 + 0.233311i
$$528$$ −33.9865 −1.47907
$$529$$ 3.92277 + 6.79444i 0.170555 + 0.295410i
$$530$$ −2.70732 + 4.68922i −0.117599 + 0.203687i
$$531$$ 0.209084 0.362145i 0.00907348 0.0157157i
$$532$$ −4.18348 −0.181377
$$533$$ 0 0
$$534$$ −45.9519 −1.98854
$$535$$ −4.56593 + 7.90842i −0.197402 + 0.341911i
$$536$$ 9.80545 16.9835i 0.423531 0.733577i
$$537$$ −21.7264 37.6312i −0.937562 1.62391i
$$538$$ −1.73438 −0.0747744
$$539$$ −16.0118 27.7332i −0.689677 1.19456i
$$540$$ 0.334963 + 0.580172i 0.0144145 + 0.0249666i
$$541$$ −8.38144 −0.360346 −0.180173 0.983635i $$-0.557666\pi$$
−0.180173 + 0.983635i $$0.557666\pi$$
$$542$$ 6.07981 + 10.5305i 0.261150 + 0.452326i
$$543$$ −21.0952 + 36.5379i −0.905281 + 1.56799i
$$544$$ 1.59585 2.76409i 0.0684215 0.118509i
$$545$$ −7.37605 −0.315955
$$546$$ 0 0
$$547$$ −22.7842 −0.974181 −0.487091 0.873351i $$-0.661942\pi$$
−0.487091 + 0.873351i $$0.661942\pi$$
$$548$$ 0.970090 1.68025i 0.0414402 0.0717765i
$$549$$ −4.09843 + 7.09870i −0.174917 + 0.302965i
$$550$$ −3.27597 5.67414i −0.139688 0.241946i
$$551$$ −0.0560816 −0.00238915
$$552$$ −13.9106 24.0938i −0.592074 1.02550i
$$553$$ 21.5699 + 37.3601i 0.917245 + 1.58871i
$$554$$ −21.3735 −0.908071
$$555$$ −10.1500 17.5803i −0.430844 0.746244i
$$556$$ 0.515915 0.893592i 0.0218797 0.0378967i
$$557$$ 14.0764 24.3810i 0.596435 1.03306i −0.396908 0.917858i $$-0.629917\pi$$
0.993343 0.115197i $$-0.0367499\pi$$
$$558$$ 16.2572 0.688222
$$559$$ 0 0
$$560$$ 9.76645 0.412708
$$561$$ 7.09017 12.2805i 0.299347 0.518484i
$$562$$ −6.54676 + 11.3393i −0.276159 + 0.478321i
$$563$$ 9.06514 + 15.7013i 0.382050 + 0.661731i 0.991355 0.131206i $$-0.0418848\pi$$
−0.609305 + 0.792936i $$0.708551\pi$$
$$564$$ −3.08939 −0.130087
$$565$$ 3.53794 + 6.12789i 0.148842 + 0.257802i
$$566$$ −0.804007 1.39258i −0.0337950 0.0585346i
$$567$$ −37.3253 −1.56752
$$568$$ −16.5431 28.6535i −0.694133 1.20227i
$$569$$ −20.2992 + 35.1593i −0.850988 + 1.47395i 0.0293292 + 0.999570i $$0.490663\pi$$
−0.880317 + 0.474385i $$0.842670\pi$$
$$570$$ 3.22572 5.58710i 0.135110 0.234018i
$$571$$ 24.7159 1.03433 0.517164 0.855886i $$-0.326988\pi$$
0.517164 + 0.855886i $$0.326988\pi$$
$$572$$ 0 0
$$573$$ 63.7551 2.66341
$$574$$ −8.19393 + 14.1923i −0.342008 + 0.592375i
$$575$$ 1.94644 3.37133i 0.0811720 0.140594i
$$576$$ −10.8124 18.7276i −0.450516 0.780317i
$$577$$ 23.0691 0.960379 0.480189 0.877165i $$-0.340568\pi$$
0.480189 + 0.877165i $$0.340568\pi$$
$$578$$ 9.58607 + 16.6036i 0.398728 + 0.690617i
$$579$$ −25.3834 43.9654i −1.05490 1.82714i
$$580$$ −0.0126697 −0.000526079
$$581$$ 21.8327 + 37.8153i 0.905771 + 1.56884i
$$582$$ −17.3068 + 29.9763i −0.717392 + 1.24256i
$$583$$ 11.9237 20.6525i 0.493831 0.855341i
$$584$$ 14.4116 0.596358
$$585$$ 0 0
$$586$$ 22.8602 0.944345
$$587$$ 10.1762 17.6256i 0.420015 0.727487i −0.575926 0.817502i $$-0.695358\pi$$
0.995940 + 0.0900152i $$0.0286916\pi$$
$$588$$ 3.56182 6.16925i 0.146887 0.254416i
$$589$$ −6.19615 10.7321i −0.255308 0.442206i
$$590$$ 0.209084 0.00860786
$$591$$ 1.97859 + 3.42701i 0.0813881 + 0.140968i
$$592$$ −11.8060 20.4486i −0.485223 0.840432i
$$593$$ 10.3834 0.426395 0.213198 0.977009i $$-0.431612\pi$$
0.213198 + 0.977009i $$0.431612\pi$$
$$594$$ 4.28339 + 7.41904i 0.175750 + 0.304407i
$$595$$ −2.03745 + 3.52897i −0.0835273 + 0.144674i
$$596$$ −1.41356 + 2.44836i −0.0579017 + 0.100289i
$$597$$ 59.0652 2.41738
$$598$$ 0 0
$$599$$ −31.5965 −1.29100 −0.645499 0.763761i $$-0.723351\pi$$
−0.645499 + 0.763761i $$0.723351\pi$$
$$600$$ 3.57335 6.18922i 0.145881 0.252674i
$$601$$ 21.9423 38.0051i 0.895044 1.55026i 0.0612928 0.998120i $$-0.480478\pi$$
0.833751 0.552141i $$-0.186189\pi$$
$$602$$ 2.48505 + 4.30423i 0.101283 + 0.175428i
$$603$$ 15.6115 0.635750
$$604$$ −1.25263 2.16962i −0.0509688 0.0882806i
$$605$$ 8.92820 + 15.4641i 0.362983 + 0.628705i
$$606$$ −11.5332 −0.468505
$$607$$ −1.08770 1.88395i −0.0441484 0.0764673i 0.843107 0.537746i $$-0.180724\pi$$
−0.887255 + 0.461279i $$0.847391\pi$$
$$608$$ −3.19768 + 5.53854i −0.129683 + 0.224617i
$$609$$ 0.103814 0.179812i 0.00420677 0.00728634i
$$610$$ −4.09843 −0.165941
$$611$$ 0 0
$$612$$ 1.41465 0.0571837
$$613$$ 7.38100 12.7843i 0.298116 0.516352i −0.677589 0.735441i $$-0.736975\pi$$
0.975705 + 0.219089i $$0.0703085\pi$$
$$614$$ −8.72336 + 15.1093i −0.352046 + 0.609762i
$$615$$ 4.35203 + 7.53794i 0.175491 + 0.303959i
$$616$$ −59.2622 −2.38774
$$617$$ 10.1486 + 17.5779i 0.408567 + 0.707659i 0.994729 0.102535i $$-0.0326953\pi$$
−0.586162 + 0.810194i $$0.699362\pi$$
$$618$$ 25.4642 + 44.1053i 1.02432 + 1.77418i
$$619$$ 9.94207 0.399605 0.199803 0.979836i $$-0.435970\pi$$
0.199803 + 0.979836i $$0.435970\pi$$
$$620$$ −1.39980 2.42453i −0.0562175 0.0973716i
$$621$$ −2.54500 + 4.40807i −0.102127 + 0.176890i
$$622$$ −1.68379 + 2.91641i −0.0675138 + 0.116937i
$$623$$ −58.1577 −2.33004
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 9.99276 17.3080i 0.399391 0.691766i
$$627$$ −14.2069 + 24.6070i −0.567368 + 0.982711i
$$628$$ 2.57221 + 4.45519i 0.102642 + 0.177782i
$$629$$ 9.85174 0.392815
$$630$$ 5.35578 + 9.27648i 0.213379 + 0.369584i
$$631$$ −0.486710 0.843006i −0.0193756 0.0335596i 0.856175 0.516686i $$-0.172835\pi$$
−0.875551 + 0.483126i $$0.839501\pi$$
$$632$$ 36.7183 1.46058
$$633$$ 0.391243 + 0.677652i 0.0155505 + 0.0269342i
$$634$$ −1.08903 + 1.88625i −0.0432507 + 0.0749124i
$$635$$ −5.71806 + 9.90396i −0.226914 + 0.393027i
$$636$$ 5.30487 0.210352
$$637$$ 0 0
$$638$$ −0.162015 −0.00641425
$$639$$ 13.1694 22.8100i 0.520972 0.902350i
$$640$$ 2.58631 4.47962i 0.102233 0.177072i
$$641$$ 6.31047 + 10.9301i 0.249249 + 0.431711i 0.963318 0.268364i $$-0.0864830\pi$$
−0.714069 + 0.700075i $$0.753150\pi$$
$$642$$ −25.9766 −1.02521
$$643$$ −4.98022 8.62599i −0.196401 0.340176i 0.750958 0.660350i $$-0.229592\pi$$
−0.947359 + 0.320174i $$0.896259\pi$$
$$644$$ −3.59042 6.21878i −0.141482 0.245054i
$$645$$ 2.63977 0.103941
$$646$$ 1.56546 + 2.71146i 0.0615923 + 0.106681i
$$647$$ 18.1381 31.4162i 0.713084 1.23510i −0.250610 0.968088i $$-0.580631\pi$$
0.963694 0.267009i $$-0.0860354\pi$$
$$648$$ −15.8847 + 27.5131i −0.624009 + 1.08081i
$$649$$ −0.920861 −0.0361470
$$650$$ 0 0
$$651$$ 45.8796 1.79816
$$652$$ 1.73723 3.00898i 0.0680353 0.117841i
$$653$$ −6.87769 + 11.9125i −0.269145 + 0.466172i −0.968641 0.248464i $$-0.920074\pi$$
0.699497 + 0.714636i $$0.253408\pi$$
$$654$$ −10.4910 18.1709i −0.410231 0.710540i
$$655$$ 10.5680 0.412925
$$656$$ 5.06207 + 8.76776i 0.197641 + 0.342324i
$$657$$ 5.73629 + 9.93555i 0.223794 + 0.387623i
$$658$$ 11.3526 0.442570
$$659$$ 1.29092 + 2.23593i 0.0502869 + 0.0870995i 0.890073 0.455818i $$-0.150653\pi$$
−0.839786 + 0.542917i $$0.817320\pi$$
$$660$$ −3.20955 + 5.55910i −0.124932 + 0.216388i
$$661$$ −12.4382 + 21.5437i −0.483791 + 0.837951i −0.999827 0.0186163i $$-0.994074\pi$$
0.516036 + 0.856567i $$0.327407\pi$$
$$662$$ 8.81151 0.342469
$$663$$ 0 0
$$664$$ 37.1656 1.44231
$$665$$ 4.08253 7.07115i 0.158314 0.274207i
$$666$$ 12.9485 22.4274i 0.501743 0.869045i
$$667$$ −0.0481312 0.0833657i −0.00186365 0.00322793i
$$668$$ −5.37460 −0.207949
$$669$$ 14.3395 + 24.8368i 0.554398 + 0.960246i
$$670$$ 3.90288 + 6.75998i 0.150781 + 0.261161i
$$671$$ 18.0506 0.696834
$$672$$ −11.8386 20.5051i −0.456685 0.791002i
$$673$$ −21.6611 + 37.5181i −0.834974 + 1.44622i 0.0590774 + 0.998253i $$0.481184\pi$$
−0.894052 + 0.447964i $$0.852149\pi$$
$$674$$ 2.66025 4.60770i 0.102469 0.177482i
$$675$$ −1.30752 −0.0503264
$$676$$ 0 0
$$677$$ −41.3625 −1.58969 −0.794845 0.606813i $$-0.792448\pi$$
−0.794845 + 0.606813i $$0.792448\pi$$
$$678$$ −10.0641 + 17.4315i −0.386508 + 0.669451i
$$679$$ −21.9039 + 37.9386i −0.840594 + 1.45595i
$$680$$ 1.73417 + 3.00367i 0.0665024 + 0.115186i
$$681$$ −17.8003 −0.682110
$$682$$ −17.9002 31.0041i −0.685435 1.18721i
$$683$$ −1.31344 2.27495i −0.0502574 0.0870484i 0.839802 0.542892i $$-0.182671\pi$$
−0.890060 + 0.455844i $$0.849338\pi$$
$$684$$ −2.83459 −0.108383
$$685$$ 1.89336 + 3.27940i 0.0723416 + 0.125299i
$$686$$ 2.28028 3.94957i 0.0870617 0.150795i
$$687$$ 16.7931 29.0865i 0.640696 1.10972i
$$688$$ 3.07045 0.117060
$$689$$ 0 0
$$690$$ 11.0737 0.421569
$$691$$ 7.63765 13.2288i 0.290550 0.503247i −0.683390 0.730053i $$-0.739495\pi$$
0.973940 + 0.226806i $$0.0728285\pi$$
$$692$$ −1.14218 + 1.97831i −0.0434190 + 0.0752039i
$$693$$ −23.5882 40.8560i −0.896043 1.55199i
$$694$$ −32.5744 −1.23651
$$695$$ 1.00693 + 1.74406i 0.0381951 + 0.0661558i
$$696$$ −0.0883613 0.153046i −0.00334933 0.00580120i
$$697$$ −4.22414 −0.160001
$$698$$ −14.3747 24.8976i −0.544089 0.942390i
$$699$$ −11.0737 + 19.1802i −0.418846 + 0.725463i
$$700$$ 0.922305 1.59748i 0.0348599 0.0603790i
$$701$$ −48.1947 −1.82029 −0.910144 0.414292i $$-0.864029\pi$$
−0.910144 + 0.414292i $$0.864029\pi$$
$$702$$ 0 0
$$703$$ −19.7404 −0.744522
$$704$$ −23.8103 + 41.2406i −0.897383 + 1.55431i
$$705$$ 3.01484 5.22186i 0.113546 0.196667i
$$706$$ −3.49884 6.06016i −0.131680 0.228077i
$$707$$ −14.5967 −0.548964
$$708$$ −0.102423 0.177401i −0.00384928 0.00666715i
$$709$$ 19.4350 + 33.6624i 0.729896 + 1.26422i 0.956927 + 0.290329i $$0.0937647\pi$$
−0.227031 + 0.973887i $$0.572902\pi$$
$$710$$ 13.1694 0.494237
$$711$$ 14.6150 + 25.3140i 0.548107 + 0.949349i
$$712$$ −24.7504 + 42.8689i −0.927560 + 1.60658i
$$713$$ 10.6355 18.4213i 0.398304 0.689882i
$$714$$ −11.5915 −0.433801
$$715$$ 0 0
$$716$$ −9.54600 −0.356751
$$717$$ 23.2226 40.2227i 0.867263 1.50214i
$$718$$ 15.0987 26.1517i 0.563478 0.975973i
$$719$$ −3.30830 5.73015i −0.123379 0.213698i 0.797719 0.603029i $$-0.206040\pi$$
−0.921098 + 0.389331i $$0.872706\pi$$
$$720$$ 6.61742 0.246617
$$721$$ 32.2280 + 55.8205i 1.20023 + 2.07887i
$$722$$ 8.45024 + 14.6362i 0.314485 + 0.544705i
$$723$$ 54.2629 2.01806
$$724$$ 4.63433 + 8.02690i 0.172234 + 0.298317i
$$725$$ 0.0123639 0.0214150i 0.000459185 0.000795332i
$$726$$ −25.3973 + 43.9893i −0.942581 + 1.63260i
$$727$$ −18.3735 −0.681435 −0.340717 0.940166i $$-0.610670\pi$$
−0.340717 + 0.940166i $$0.610670\pi$$
$$728$$ 0 0
$$729$$ −16.1420 −0.597853
$$730$$ −2.86814 + 4.96777i −0.106155 + 0.183866i
$$731$$ −0.640548 + 1.10946i −0.0236915 + 0.0410349i
$$732$$ 2.00767 + 3.47739i 0.0742057 + 0.128528i
$$733$$ 0.791131 0.0292211 0.0146105 0.999893i $$-0.495349\pi$$
0.0146105 + 0.999893i $$0.495349\pi$$
$$734$$ −15.8886 27.5198i −0.586458 1.01578i
$$735$$ 6.95174 + 12.0408i 0.256419 + 0.444130i
$$736$$ −10.9774 −0.404634
$$737$$ −17.1893 29.7727i −0.633175 1.09669i
$$738$$ −5.55193 + 9.61623i −0.204369 + 0.353978i
$$739$$ −15.5926 + 27.0073i −0.573585 + 0.993478i 0.422609 + 0.906312i $$0.361114\pi$$
−0.996194 + 0.0871658i $$0.972219\pi$$
$$740$$ −4.45965 −0.163940
$$741$$ 0 0
$$742$$ −19.4938 −0.715639
$$743$$ −2.78152 + 4.81773i −0.102044 + 0.176745i −0.912527 0.409017i $$-0.865872\pi$$
0.810483 + 0.585763i $$0.199205\pi$$
$$744$$ 19.5251 33.8185i 0.715826 1.23985i
$$745$$ −2.75890 4.77855i −0.101078 0.175073i
$$746$$ 16.1053 0.589658
$$747$$ 14.7931 + 25.6224i 0.541251 + 0.937474i
$$748$$ −1.55762 2.69787i −0.0569521 0.0986439i
$$749$$ −32.8765 −1.20128
$$750$$ 1.42231 + 2.46350i 0.0519352 + 0.0899545i
$$751$$ 17.6048 30.4925i 0.642410 1.11269i −0.342483 0.939524i $$-0.611268\pi$$
0.984893 0.173163i $$-0.0553987\pi$$
$$752$$ 3.50672 6.07381i 0.127877 0.221489i
$$753$$ 27.6142 1.00632
$$754$$ 0 0
$$755$$ 4.88961 0.177951
$$756$$ −1.20593 + 2.08873i −0.0438593 + 0.0759665i
$$757$$ −25.0223 + 43.3399i −0.909451 + 1.57522i −0.0946237 + 0.995513i $$0.530165\pi$$
−0.814828 + 0.579703i $$0.803169\pi$$
$$758$$ −15.8545 27.4609i −0.575863 0.997424i
$$759$$ −48.7715 −1.77029
$$760$$ −3.47484 6.01859i −0.126046 0.218317i
$$761$$ −22.4105 38.8161i −0.812379 1.40708i −0.911195 0.411975i $$-0.864839\pi$$
0.0988165 0.995106i $$-0.468494\pi$$
$$762$$ −32.5313 −1.17848
$$763$$ −13.2776 22.9975i −0.480682 0.832566i
$$764$$ 7.00307 12.1297i 0.253362 0.438836i
$$765$$ −1.38051 + 2.39111i −0.0499124 + 0.0864508i
$$766$$ −11.7092 −0.423072
$$767$$ 0 0
$$768$$ −26.6361 −0.961148
$$769$$ 19.6817 34.0897i 0.709739 1.22930i −0.255215 0.966884i $$-0.582146\pi$$
0.964954 0.262420i $$-0.0845205\pi$$
$$770$$ 11.7941 20.4280i 0.425031 0.736175i
$$771$$ 6.47201 + 11.2099i 0.233084 + 0.403713i
$$772$$ −11.1528 −0.401399
$$773$$ −24.3902 42.2452i −0.877256 1.51945i −0.854340 0.519715i $$-0.826038\pi$$
−0.0229167 0.999737i $$-0.507295\pi$$
$$774$$ 1.68379 + 2.91641i 0.0605225 + 0.104828i
$$775$$ 5.46410 0.196276
$$776$$ 18.6434 + 32.2914i 0.669260 + 1.15919i
$$777$$ 36.5420 63.2926i 1.31094 2.27061i
$$778$$ −3.43420 + 5.94822i −0.123122 + 0.213254i
$$779$$ 8.46410 0.303258
$$780$$ 0 0