# Properties

 Label 325.2.n.d.251.2 Level $325$ Weight $2$ Character 325.251 Analytic conductor $2.595$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.n (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.59513806569$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ 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: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 251.2 Root $$1.40994 - 0.109843i$$ of defining polynomial Character $$\chi$$ $$=$$ 325.251 Dual form 325.2.n.d.101.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.05628 - 0.609843i) q^{2} +(1.16612 - 2.01978i) q^{3} +(-0.256182 - 0.443720i) q^{4} +(-2.46350 + 1.42231i) q^{6} +(-3.11786 + 1.80010i) q^{7} +3.06430i q^{8} +(-1.21969 - 2.11256i) q^{9} +O(q^{10})$$ $$q+(-1.05628 - 0.609843i) q^{2} +(1.16612 - 2.01978i) q^{3} +(-0.256182 - 0.443720i) q^{4} +(-2.46350 + 1.42231i) q^{6} +(-3.11786 + 1.80010i) q^{7} +3.06430i q^{8} +(-1.21969 - 2.11256i) q^{9} +(-4.65213 - 2.68591i) q^{11} -1.19496 q^{12} +(-1.81988 - 3.11256i) q^{13} +4.39111 q^{14} +(1.35638 - 2.34932i) q^{16} +(0.565928 + 0.980215i) q^{17} +2.97527i q^{18} +(-1.96410 + 1.13397i) q^{19} +8.39654i q^{21} +(3.27597 + 5.67414i) q^{22} +(1.94644 - 3.37133i) q^{23} +(6.18922 + 3.57335i) q^{24} +(0.0241312 + 4.39758i) q^{26} +1.30752 q^{27} +(1.59748 + 0.922305i) q^{28} +(0.0123639 - 0.0214150i) q^{29} -5.46410i q^{31} +(2.44209 - 1.40994i) q^{32} +(-10.8499 + 6.26420i) q^{33} -1.38051i q^{34} +(-0.624924 + 1.08240i) q^{36} +(-7.53794 - 4.35203i) q^{37} +2.76619 q^{38} +(-8.40891 + 0.0461428i) q^{39} +(3.23205 + 1.86603i) q^{41} +(5.12058 - 8.86910i) q^{42} +(0.565928 + 0.980215i) q^{43} +2.75232i q^{44} +(-4.11196 + 2.37404i) q^{46} -2.58535i q^{47} +(-3.16341 - 5.47918i) q^{48} +(2.98070 - 5.16273i) q^{49} +2.63977 q^{51} +(-0.914884 + 1.60490i) q^{52} +4.43937 q^{53} +(-1.38111 - 0.797382i) q^{54} +(-5.51603 - 9.55405i) q^{56} +5.28942i q^{57} +(-0.0261196 + 0.0150801i) q^{58} +(-0.148458 + 0.0857123i) q^{59} +(-1.68012 - 2.91005i) q^{61} +(-3.33225 + 5.77162i) q^{62} +(7.60563 + 4.39111i) q^{63} -8.86488 q^{64} +15.2807 q^{66} +(-5.54239 - 3.19990i) q^{67} +(0.289961 - 0.502227i) q^{68} +(-4.53957 - 7.86276i) q^{69} +(9.35076 - 5.39866i) q^{71} +(6.47351 - 3.73748i) q^{72} +4.70308i q^{73} +(5.30812 + 9.19393i) q^{74} +(1.00633 + 0.581008i) q^{76} +19.3396 q^{77} +(8.91030 + 5.07938i) q^{78} -11.9826 q^{79} +(5.18379 - 8.97859i) q^{81} +(-2.27597 - 3.94209i) q^{82} -12.1286i q^{83} +(3.72572 - 2.15104i) q^{84} -1.38051i q^{86} +(-0.0288357 - 0.0499450i) q^{87} +(8.23042 - 14.2555i) q^{88} +(13.9898 + 8.07702i) q^{89} +(11.2771 + 6.42856i) q^{91} -1.99457 q^{92} +(-11.0363 - 6.37182i) q^{93} +(-1.57666 + 2.73086i) q^{94} -6.57666i q^{96} +(10.5379 - 6.08408i) q^{97} +(-6.29692 + 3.63553i) q^{98} +13.1039i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9} + O(q^{10})$$ $$8 q - 2 q^{3} + 2 q^{4} - 18 q^{6} + 6 q^{7} - 4 q^{9} - 20 q^{12} + 4 q^{14} - 2 q^{16} + 2 q^{17} + 12 q^{19} + 12 q^{22} + 10 q^{23} - 12 q^{24} + 10 q^{26} + 4 q^{27} + 18 q^{28} - 8 q^{29} - 6 q^{32} - 42 q^{33} + 20 q^{36} - 6 q^{37} + 16 q^{38} + 12 q^{41} - 4 q^{42} + 2 q^{43} - 42 q^{46} - 28 q^{48} + 12 q^{49} - 8 q^{51} + 6 q^{52} + 24 q^{53} + 18 q^{54} + 12 q^{56} - 36 q^{58} - 12 q^{59} - 28 q^{61} - 4 q^{62} + 24 q^{63} - 8 q^{64} + 12 q^{66} - 6 q^{67} + 14 q^{68} - 16 q^{69} + 48 q^{72} + 10 q^{74} + 54 q^{76} + 36 q^{77} + 56 q^{78} - 16 q^{79} + 8 q^{81} - 4 q^{82} - 30 q^{84} - 22 q^{87} + 18 q^{88} + 24 q^{89} + 28 q^{91} - 44 q^{92} + 32 q^{94} + 30 q^{97} - 72 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$301$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.05628 0.609843i −0.746903 0.431224i 0.0776710 0.996979i $$-0.475252\pi$$
−0.824574 + 0.565755i $$0.808585\pi$$
$$3$$ 1.16612 2.01978i 0.673262 1.16612i −0.303712 0.952764i $$-0.598226\pi$$
0.976974 0.213359i $$-0.0684405\pi$$
$$4$$ −0.256182 0.443720i −0.128091 0.221860i
$$5$$ 0 0
$$6$$ −2.46350 + 1.42231i −1.00572 + 0.580654i
$$7$$ −3.11786 + 1.80010i −1.17844 + 0.680373i −0.955653 0.294494i $$-0.904849\pi$$
−0.222787 + 0.974867i $$0.571516\pi$$
$$8$$ 3.06430i 1.08339i
$$9$$ −1.21969 2.11256i −0.406562 0.704187i
$$10$$ 0 0
$$11$$ −4.65213 2.68591i −1.40267 0.809832i −0.408004 0.912980i $$-0.633775\pi$$
−0.994666 + 0.103149i $$0.967108\pi$$
$$12$$ −1.19496 −0.344955
$$13$$ −1.81988 3.11256i −0.504745 0.863269i
$$14$$ 4.39111 1.17357
$$15$$ 0 0
$$16$$ 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 $$0.789505\pi$$
$$18$$ 2.97527i 0.701278i
$$19$$ −1.96410 + 1.13397i −0.450596 + 0.260152i −0.708082 0.706130i $$-0.750439\pi$$
0.257486 + 0.966282i $$0.417106\pi$$
$$20$$ 0 0
$$21$$ 8.39654i 1.83228i
$$22$$ 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 $$0.0336387\pi$$
$$24$$ 6.18922 + 3.57335i 1.26337 + 0.729407i
$$25$$ 0 0
$$26$$ 0.0241312 + 4.39758i 0.00473251 + 0.862436i
$$27$$ 1.30752 0.251632
$$28$$ 1.59748 + 0.922305i 0.301895 + 0.174299i
$$29$$ 0.0123639 0.0214150i 0.00229593 0.00397666i −0.864875 0.501987i $$-0.832603\pi$$
0.867171 + 0.498010i $$0.165936\pi$$
$$30$$ 0 0
$$31$$ 5.46410i 0.981382i −0.871334 0.490691i $$-0.836744\pi$$
0.871334 0.490691i $$-0.163256\pi$$
$$32$$ 2.44209 1.40994i 0.431705 0.249245i
$$33$$ −10.8499 + 6.26420i −1.88873 + 1.09046i
$$34$$ 1.38051i 0.236755i
$$35$$ 0 0
$$36$$ −0.624924 + 1.08240i −0.104154 + 0.180400i
$$37$$ −7.53794 4.35203i −1.23923 0.715470i −0.270293 0.962778i $$-0.587121\pi$$
−0.968937 + 0.247309i $$0.920454\pi$$
$$38$$ 2.76619 0.448735
$$39$$ −8.40891 + 0.0461428i −1.34650 + 0.00738877i
$$40$$ 0 0
$$41$$ 3.23205 + 1.86603i 0.504762 + 0.291424i 0.730678 0.682723i $$-0.239204\pi$$
−0.225916 + 0.974147i $$0.572538\pi$$
$$42$$ 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 $$0.805828\pi$$
$$44$$ 2.75232i 0.414929i
$$45$$ 0 0
$$46$$ −4.11196 + 2.37404i −0.606276 + 0.350034i
$$47$$ 2.58535i 0.377113i −0.982062 0.188556i $$-0.939619\pi$$
0.982062 0.188556i $$-0.0603808\pi$$
$$48$$ −3.16341 5.47918i −0.456598 0.790852i
$$49$$ 2.98070 5.16273i 0.425815 0.737533i
$$50$$ 0 0
$$51$$ 2.63977 0.369641
$$52$$ −0.914884 + 1.60490i −0.126872 + 0.222560i
$$53$$ 4.43937 0.609795 0.304897 0.952385i $$-0.401378\pi$$
0.304897 + 0.952385i $$0.401378\pi$$
$$54$$ −1.38111 0.797382i −0.187945 0.108510i
$$55$$ 0 0
$$56$$ −5.51603 9.55405i −0.737111 1.27671i
$$57$$ 5.28942i 0.700600i
$$58$$ −0.0261196 + 0.0150801i −0.00342967 + 0.00198012i
$$59$$ −0.148458 + 0.0857123i −0.0193276 + 0.0111588i −0.509633 0.860392i $$-0.670219\pi$$
0.490305 + 0.871551i $$0.336885\pi$$
$$60$$ 0 0
$$61$$ −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
$$63$$ 7.60563 + 4.39111i 0.958219 + 0.553228i
$$64$$ −8.86488 −1.10811
$$65$$ 0 0
$$66$$ 15.2807 1.88093
$$67$$ −5.54239 3.19990i −0.677111 0.390930i 0.121655 0.992572i $$-0.461180\pi$$
−0.798766 + 0.601642i $$0.794513\pi$$
$$68$$ 0.289961 0.502227i 0.0351629 0.0609040i
$$69$$ −4.53957 7.86276i −0.546500 0.946566i
$$70$$ 0 0
$$71$$ 9.35076 5.39866i 1.10973 0.640703i 0.170971 0.985276i $$-0.445309\pi$$
0.938760 + 0.344573i $$0.111976\pi$$
$$72$$ 6.47351 3.73748i 0.762911 0.440467i
$$73$$ 4.70308i 0.550454i 0.961379 + 0.275227i $$0.0887531\pi$$
−0.961379 + 0.275227i $$0.911247\pi$$
$$74$$ 5.30812 + 9.19393i 0.617056 + 1.06877i
$$75$$ 0 0
$$76$$ 1.00633 + 0.581008i 0.115435 + 0.0666462i
$$77$$ 19.3396 2.20395
$$78$$ 8.91030 + 5.07938i 1.00889 + 0.575126i
$$79$$ −11.9826 −1.34815 −0.674075 0.738663i $$-0.735457\pi$$
−0.674075 + 0.738663i $$0.735457\pi$$
$$80$$ 0 0
$$81$$ 5.18379 8.97859i 0.575976 0.997621i
$$82$$ −2.27597 3.94209i −0.251338 0.435331i
$$83$$ 12.1286i 1.33129i −0.746270 0.665643i $$-0.768157\pi$$
0.746270 0.665643i $$-0.231843\pi$$
$$84$$ 3.72572 2.15104i 0.406509 0.234698i
$$85$$ 0 0
$$86$$ 1.38051i 0.148864i
$$87$$ −0.0288357 0.0499450i −0.00309152 0.00535466i
$$88$$ 8.23042 14.2555i 0.877366 1.51964i
$$89$$ 13.9898 + 8.07702i 1.48292 + 0.856162i 0.999812 0.0194001i $$-0.00617565\pi$$
0.483105 + 0.875562i $$0.339509\pi$$
$$90$$ 0 0
$$91$$ 11.2771 + 6.42856i 1.18216 + 0.673896i
$$92$$ −1.99457 −0.207948
$$93$$ −11.0363 6.37182i −1.14441 0.660727i
$$94$$ −1.57666 + 2.73086i −0.162620 + 0.281666i
$$95$$ 0 0
$$96$$ 6.57666i 0.671228i
$$97$$ 10.5379 6.08408i 1.06997 0.617745i 0.141794 0.989896i $$-0.454713\pi$$
0.928172 + 0.372151i $$0.121380\pi$$
$$98$$ −6.29692 + 3.63553i −0.636085 + 0.367244i
$$99$$ 13.1039i 1.31699i
$$100$$ 0 0
$$101$$ −2.02721 + 3.51122i −0.201714 + 0.349380i −0.949081 0.315032i $$-0.897985\pi$$
0.747366 + 0.664412i $$0.231318\pi$$
$$102$$ −2.78833 1.60984i −0.276086 0.159398i
$$103$$ −17.9035 −1.76408 −0.882041 0.471173i $$-0.843831\pi$$
−0.882041 + 0.471173i $$0.843831\pi$$
$$104$$ 9.53781 5.57666i 0.935259 0.546837i
$$105$$ 0 0
$$106$$ −4.68922 2.70732i −0.455457 0.262958i
$$107$$ −4.56593 + 7.90842i −0.441405 + 0.764536i −0.997794 0.0663862i $$-0.978853\pi$$
0.556389 + 0.830922i $$0.312186\pi$$
$$108$$ −0.334963 0.580172i −0.0322318 0.0558271i
$$109$$ 7.37605i 0.706498i −0.935529 0.353249i $$-0.885077\pi$$
0.935529 0.353249i $$-0.114923\pi$$
$$110$$ 0 0
$$111$$ −17.5803 + 10.1500i −1.66865 + 0.963396i
$$112$$ 9.76645i 0.922843i
$$113$$ 3.53794 + 6.12789i 0.332821 + 0.576463i 0.983064 0.183263i $$-0.0586661\pi$$
−0.650243 + 0.759727i $$0.725333\pi$$
$$114$$ 3.22572 5.58710i 0.302116 0.523280i
$$115$$ 0 0
$$116$$ −0.0126697 −0.00117635
$$117$$ −4.35578 + 7.64096i −0.402692 + 0.706407i
$$118$$ 0.209084 0.0192478
$$119$$ −3.52897 2.03745i −0.323500 0.186773i
$$120$$ 0 0
$$121$$ 8.92820 + 15.4641i 0.811655 + 1.40583i
$$122$$ 4.09843i 0.371055i
$$123$$ 7.53794 4.35203i 0.679673 0.392409i
$$124$$ −2.42453 + 1.39980i −0.217729 + 0.125706i
$$125$$ 0 0
$$126$$ −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 $$-0.00272499\pi$$
$$128$$ 4.47962 + 2.58631i 0.395946 + 0.228600i
$$129$$ 2.63977 0.232418
$$130$$ 0 0
$$131$$ −10.5680 −0.923328 −0.461664 0.887055i $$-0.652747\pi$$
−0.461664 + 0.887055i $$0.652747\pi$$
$$132$$ 5.55910 + 3.20955i 0.483858 + 0.279355i
$$133$$ 4.08253 7.07115i 0.354000 0.613146i
$$134$$ 3.90288 + 6.75998i 0.337157 + 0.583974i
$$135$$ 0 0
$$136$$ −3.00367 + 1.73417i −0.257563 + 0.148704i
$$137$$ −3.27940 + 1.89336i −0.280178 + 0.161761i −0.633504 0.773739i $$-0.718384\pi$$
0.353326 + 0.935500i $$0.385051\pi$$
$$138$$ 11.0737i 0.942656i
$$139$$ −1.00693 1.74406i −0.0854068 0.147929i 0.820158 0.572138i $$-0.193886\pi$$
−0.905564 + 0.424209i $$0.860552\pi$$
$$140$$ 0 0
$$141$$ −5.22186 3.01484i −0.439760 0.253895i
$$142$$ −13.1694 −1.10515
$$143$$ 0.106280 + 19.3681i 0.00888757 + 1.61964i
$$144$$ −6.61742 −0.551452
$$145$$ 0 0
$$146$$ 2.86814 4.96777i 0.237369 0.411136i
$$147$$ −6.95174 12.0408i −0.573370 0.993105i
$$148$$ 4.45965i 0.366581i
$$149$$ 4.77855 2.75890i 0.391474 0.226018i −0.291324 0.956624i $$-0.594096\pi$$
0.682799 + 0.730607i $$0.260763\pi$$
$$150$$ 0 0
$$151$$ 4.88961i 0.397911i −0.980009 0.198956i $$-0.936245\pi$$
0.980009 0.198956i $$-0.0637549\pi$$
$$152$$ −3.47484 6.01859i −0.281846 0.488172i
$$153$$ 1.38051 2.39111i 0.111608 0.193310i
$$154$$ −20.4280 11.7941i −1.64614 0.950397i
$$155$$ 0 0
$$156$$ 2.17469 + 3.71938i 0.174114 + 0.297789i
$$157$$ −10.0405 −0.801323 −0.400661 0.916226i $$-0.631220\pi$$
−0.400661 + 0.916226i $$0.631220\pi$$
$$158$$ 12.6570 + 7.30752i 1.00694 + 0.581355i
$$159$$ 5.17686 8.96658i 0.410551 0.711096i
$$160$$ 0 0
$$161$$ 14.0151i 1.10454i
$$162$$ −10.9511 + 6.32260i −0.860397 + 0.496750i
$$163$$ −5.87273 + 3.39062i −0.459988 + 0.265574i −0.712039 0.702140i $$-0.752228\pi$$
0.252051 + 0.967714i $$0.418895\pi$$
$$164$$ 1.91217i 0.149315i
$$165$$ 0 0
$$166$$ −7.39654 + 12.8112i −0.574083 + 0.994341i
$$167$$ 9.08444 + 5.24490i 0.702975 + 0.405863i 0.808455 0.588559i $$-0.200304\pi$$
−0.105479 + 0.994421i $$0.533638\pi$$
$$168$$ −25.7295 −1.98507
$$169$$ −6.37605 + 11.3290i −0.490466 + 0.871460i
$$170$$ 0 0
$$171$$ 4.79118 + 2.76619i 0.366391 + 0.211536i
$$172$$ 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 $$0.779123\pi$$
$$174$$ 0.0703412i 0.00533255i
$$175$$ 0 0
$$176$$ −12.6201 + 7.28621i −0.951275 + 0.549219i
$$177$$ 0.399804i 0.0300511i
$$178$$ −9.85143 17.0632i −0.738396 1.27894i
$$179$$ 9.31564 16.1352i 0.696284 1.20600i −0.273462 0.961883i $$-0.588169\pi$$
0.969746 0.244116i $$-0.0784979\pi$$
$$180$$ 0 0
$$181$$ −18.0900 −1.34462 −0.672310 0.740270i $$-0.734698\pi$$
−0.672310 + 0.740270i $$0.734698\pi$$
$$182$$ −7.99131 13.6676i −0.592355 1.01311i
$$183$$ −7.83690 −0.579320
$$184$$ 10.3307 + 5.96446i 0.761593 + 0.439706i
$$185$$ 0 0
$$186$$ 7.77162 + 13.4608i 0.569843 + 0.986997i
$$187$$ 6.08012i 0.444622i
$$188$$ −1.14717 + 0.662321i −0.0836662 + 0.0483047i
$$189$$ −4.07666 + 2.35366i −0.296533 + 0.171204i
$$190$$ 0 0
$$191$$ −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
$$193$$ 18.8511 + 10.8837i 1.35693 + 0.783425i 0.989209 0.146510i $$-0.0468041\pi$$
0.367723 + 0.929935i $$0.380137\pi$$
$$194$$ −14.8413 −1.06555
$$195$$ 0 0
$$196$$ −3.05441 −0.218172
$$197$$ 1.46940 + 0.848360i 0.104691 + 0.0604432i 0.551431 0.834220i $$-0.314082\pi$$
−0.446741 + 0.894664i $$0.647415\pi$$
$$198$$ 7.99131 13.8413i 0.567917 0.983662i
$$199$$ 12.6627 + 21.9325i 0.897637 + 1.55475i 0.830506 + 0.557009i $$0.188051\pi$$
0.0671309 + 0.997744i $$0.478615\pi$$
$$200$$ 0 0
$$201$$ −12.9262 + 7.46296i −0.911746 + 0.526397i
$$202$$ 4.28259 2.47256i 0.301322 0.173968i
$$203$$ 0.0890252i 0.00624834i
$$204$$ −0.676260 1.17132i −0.0473477 0.0820086i
$$205$$ 0 0
$$206$$ 18.9111 + 10.9183i 1.31760 + 0.760715i
$$207$$ −9.49617 −0.660030
$$208$$ −9.78083 + 0.0536711i −0.678179 + 0.00372142i
$$209$$ 12.1830 0.842716
$$210$$ 0 0
$$211$$ 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
$$213$$ 25.1820i 1.72544i
$$214$$ 9.64579 5.56900i 0.659373 0.380689i
$$215$$ 0 0
$$216$$ 4.00663i 0.272616i
$$217$$ 9.83592 + 17.0363i 0.667706 + 1.15650i
$$218$$ −4.49824 + 7.79118i −0.304659 + 0.527685i
$$219$$ 9.49922 + 5.48438i 0.641898 + 0.370600i
$$220$$ 0 0
$$221$$ 2.02106 3.54536i 0.135951 0.238487i
$$222$$ 24.7597 1.66176
$$223$$ 10.6493 + 6.14838i 0.713130 + 0.411726i 0.812219 0.583353i $$-0.198259\pi$$
−0.0990887 + 0.995079i $$0.531593\pi$$
$$224$$ −5.07606 + 8.79200i −0.339159 + 0.587440i
$$225$$ 0 0
$$226$$ 8.63036i 0.574083i
$$227$$ −6.60974 + 3.81613i −0.438704 + 0.253286i −0.703048 0.711143i $$-0.748178\pi$$
0.264344 + 0.964428i $$0.414845\pi$$
$$228$$ 2.34702 1.35505i 0.155435 0.0897406i
$$229$$ 14.4008i 0.951631i −0.879545 0.475815i $$-0.842153\pi$$
0.879545 0.475815i $$-0.157847\pi$$
$$230$$ 0 0
$$231$$ 22.5523 39.0618i 1.48384 2.57008i
$$232$$ 0.0656218 + 0.0378868i 0.00430828 + 0.00248739i
$$233$$ 9.49617 0.622115 0.311057 0.950391i $$-0.399317\pi$$
0.311057 + 0.950391i $$0.399317\pi$$
$$234$$ 9.26071 5.41465i 0.605392 0.353966i
$$235$$ 0 0
$$236$$ 0.0760645 + 0.0439159i 0.00495138 + 0.00285868i
$$237$$ −13.9732 + 24.2023i −0.907657 + 1.57211i
$$238$$ 2.48505 + 4.30423i 0.161082 + 0.279002i
$$239$$ 19.9143i 1.28815i 0.764962 + 0.644076i $$0.222758\pi$$
−0.764962 + 0.644076i $$0.777242\pi$$
$$240$$ 0 0
$$241$$ 20.1493 11.6332i 1.29793 0.749360i 0.317883 0.948130i $$-0.397028\pi$$
0.980046 + 0.198770i $$0.0636947\pi$$
$$242$$ 21.7792i 1.40002i
$$243$$ −10.1286 17.5432i −0.649750 1.12540i
$$244$$ −0.860832 + 1.49100i −0.0551091 + 0.0954518i
$$245$$ 0 0
$$246$$ −10.6162 −0.676866
$$247$$ 7.10400 + 4.04968i 0.452017 + 0.257675i
$$248$$ 16.7436 1.06322
$$249$$ −24.4972 14.1434i −1.55244 0.896304i
$$250$$ 0 0
$$251$$ 5.92008 + 10.2539i 0.373672 + 0.647219i 0.990127 0.140171i $$-0.0447652\pi$$
−0.616455 + 0.787390i $$0.711432\pi$$
$$252$$ 4.49969i 0.283454i
$$253$$ −18.1101 + 10.4559i −1.13858 + 0.657357i
$$254$$ −12.0797 + 6.97424i −0.757950 + 0.437603i
$$255$$ 0 0
$$256$$ 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 $$0.111288\pi$$
$$258$$ −2.78833 1.60984i −0.173594 0.100224i
$$259$$ 31.3363 1.94714
$$260$$ 0 0
$$261$$ −0.0603205 −0.00373375
$$262$$ 11.1627 + 6.44481i 0.689636 + 0.398161i
$$263$$ 3.42983 5.94065i 0.211493 0.366316i −0.740689 0.671848i $$-0.765501\pi$$
0.952182 + 0.305532i $$0.0988342\pi$$
$$264$$ −19.1954 33.2474i −1.18139 2.04623i
$$265$$ 0 0
$$266$$ −8.62459 + 4.97941i −0.528807 + 0.305307i
$$267$$ 32.6277 18.8376i 1.99678 1.15284i
$$268$$ 3.27903i 0.200299i
$$269$$ 0.710994 + 1.23148i 0.0433501 + 0.0750845i 0.886886 0.461988i $$-0.152864\pi$$
−0.843536 + 0.537072i $$0.819530\pi$$
$$270$$ 0 0
$$271$$ 8.63381 + 4.98473i 0.524467 + 0.302801i 0.738760 0.673968i $$-0.235412\pi$$
−0.214294 + 0.976769i $$0.568745\pi$$
$$272$$ 3.07045 0.186173
$$273$$ 26.1347 15.2807i 1.58175 0.924831i
$$274$$ 4.61862 0.279021
$$275$$ 0 0
$$276$$ −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 $$0.656856\pi$$
$$278$$ 2.45628i 0.147318i
$$279$$ −11.5432 + 6.66449i −0.691076 + 0.398993i
$$280$$ 0 0
$$281$$ 10.7352i 0.640406i 0.947349 + 0.320203i $$0.103751\pi$$
−0.947349 + 0.320203i $$0.896249\pi$$
$$282$$ 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 $$0.179143\pi$$
$$284$$ −4.79099 2.76608i −0.284293 0.164137i
$$285$$ 0 0
$$286$$ 11.6992 20.5229i 0.691790 1.21355i
$$287$$ −13.4361 −0.793109
$$288$$ −5.95717 3.43937i −0.351030 0.202667i
$$289$$ 7.85945 13.6130i 0.462321 0.800763i
$$290$$ 0 0
$$291$$ 28.3792i 1.66362i
$$292$$ 2.08685 1.20485i 0.122124 0.0705082i
$$293$$ −16.2316 + 9.37133i −0.948261 + 0.547479i −0.892540 0.450968i $$-0.851079\pi$$
−0.0557207 + 0.998446i $$0.517746\pi$$
$$294$$ 16.9579i 0.989004i
$$295$$ 0 0
$$296$$ 13.3359 23.0985i 0.775134 1.34257i
$$297$$ −6.08275 3.51187i −0.352957 0.203780i
$$298$$ −6.72998 −0.389857
$$299$$ −14.0357 + 0.0770194i −0.811708 + 0.00445415i
$$300$$ 0 0
$$301$$ −3.52897 2.03745i −0.203406 0.117437i
$$302$$ −2.98190 + 5.16480i −0.171589 + 0.297201i
$$303$$ 4.72794 + 8.18904i 0.271613 + 0.470448i
$$304$$ 6.15239i 0.352864i
$$305$$ 0 0
$$306$$ −2.91641 + 1.68379i −0.166720 + 0.0962558i
$$307$$ 14.3043i 0.816387i −0.912895 0.408194i $$-0.866159\pi$$
0.912895 0.408194i $$-0.133841\pi$$
$$308$$ −4.95445 8.58137i −0.282306 0.488969i
$$309$$ −20.8777 + 36.1612i −1.18769 + 2.05714i
$$310$$ 0 0
$$311$$ −2.76102 −0.156563 −0.0782815 0.996931i $$-0.524943\pi$$
−0.0782815 + 0.996931i $$0.524943\pi$$
$$312$$ −0.141395 25.7674i −0.00800494 1.45879i
$$313$$ 16.3858 0.926179 0.463090 0.886311i $$-0.346741\pi$$
0.463090 + 0.886311i $$0.346741\pi$$
$$314$$ 10.6056 + 6.12316i 0.598510 + 0.345550i
$$315$$ 0 0
$$316$$ 3.06973 + 5.31693i 0.172686 + 0.299101i
$$317$$ 1.78575i 0.100297i 0.998742 + 0.0501487i $$0.0159695\pi$$
−0.998742 + 0.0501487i $$0.984030\pi$$
$$318$$ −10.9364 + 6.31414i −0.613284 + 0.354080i
$$319$$ −0.115037 + 0.0664168i −0.00644085 + 0.00371863i
$$320$$ 0 0
$$321$$ 10.6489 + 18.4444i 0.594362 + 1.02946i
$$322$$ 8.54702 14.8039i 0.476307 0.824987i
$$323$$ −2.22308 1.28349i −0.123695 0.0714156i
$$324$$ −5.31197 −0.295110
$$325$$ 0 0
$$326$$ 8.27099 0.458088
$$327$$ −14.8980 8.60139i −0.823864 0.475658i
$$328$$ −5.71806 + 9.90396i −0.315727 + 0.546855i
$$329$$ 4.65389 + 8.06077i 0.256577 + 0.444405i
$$330$$ 0 0
$$331$$ −6.25652 + 3.61220i −0.343889 + 0.198545i −0.661991 0.749512i $$-0.730288\pi$$
0.318101 + 0.948057i $$0.396955\pi$$
$$332$$ −5.38170 + 3.10713i −0.295359 + 0.170526i
$$333$$ 21.2325i 1.16353i
$$334$$ −6.39714 11.0802i −0.350036 0.606280i
$$335$$ 0 0
$$336$$ 19.7261 + 11.3889i 1.07615 + 0.621315i
$$337$$ −4.36219 −0.237624 −0.118812 0.992917i $$-0.537909\pi$$
−0.118812 + 0.992917i $$0.537909\pi$$
$$338$$ 13.6438 8.07818i 0.742125 0.439395i
$$339$$ 16.5027 0.896303
$$340$$ 0 0
$$341$$ −14.6761 + 25.4197i −0.794754 + 1.37655i
$$342$$ −3.37388 5.84374i −0.182439 0.315993i
$$343$$ 3.73913i 0.201894i
$$344$$ −3.00367 + 1.73417i −0.161947 + 0.0935002i
$$345$$ 0 0
$$346$$ 5.43792i 0.292344i
$$347$$ −13.3536 23.1291i −0.716858 1.24163i −0.962239 0.272207i $$-0.912246\pi$$
0.245381 0.969427i $$-0.421087\pi$$
$$348$$ −0.0147744 + 0.0255900i −0.000791991 + 0.00137177i
$$349$$ −20.4131 11.7855i −1.09269 0.630865i −0.158399 0.987375i $$-0.550633\pi$$
−0.934292 + 0.356510i $$0.883967\pi$$
$$350$$ 0 0
$$351$$ −2.37953 4.06973i −0.127010 0.217226i
$$352$$ −15.1479 −0.807385
$$353$$ −4.96862 2.86863i −0.264453 0.152682i 0.361911 0.932213i $$-0.382124\pi$$
−0.626364 + 0.779531i $$0.715458\pi$$
$$354$$ 0.243818 0.422305i 0.0129588 0.0224453i
$$355$$ 0 0
$$356$$ 8.27675i 0.438667i
$$357$$ −8.23042 + 4.75184i −0.435600 + 0.251494i
$$358$$ −19.6799 + 11.3622i −1.04011 + 0.600509i
$$359$$ 24.7583i 1.30669i −0.757059 0.653347i $$-0.773364\pi$$
0.757059 0.653347i $$-0.226636\pi$$
$$360$$ 0 0
$$361$$ −6.92820 + 12.0000i −0.364642 + 0.631579i
$$362$$ 19.1081 + 11.0321i 1.00430 + 0.579833i
$$363$$ 41.6455 2.18582
$$364$$ −0.0364951 6.65074i −0.00191286 0.348593i
$$365$$ 0 0
$$366$$ 8.27796 + 4.77928i 0.432696 + 0.249817i
$$367$$ 13.0268 22.5630i 0.679992 1.17778i −0.294991 0.955500i $$-0.595317\pi$$
0.974983 0.222280i $$-0.0713500\pi$$
$$368$$ −5.28021 9.14558i −0.275250 0.476747i
$$369$$ 9.10387i 0.473928i
$$370$$ 0 0
$$371$$ −13.8413 + 7.99131i −0.718607 + 0.414888i
$$372$$ 6.52938i 0.338532i
$$373$$ 6.60224 + 11.4354i 0.341851 + 0.592103i 0.984776 0.173826i $$-0.0556129\pi$$
−0.642926 + 0.765929i $$0.722280\pi$$
$$374$$ −3.70792 + 6.42231i −0.191732 + 0.332089i
$$375$$ 0 0
$$376$$ 7.92229 0.408561
$$377$$ −0.0891563 0.000489234i −0.00459178 2.51968e-5i
$$378$$ 5.74146 0.295309
$$379$$ 22.5147 + 12.9989i 1.15650 + 0.667707i 0.950463 0.310837i $$-0.100609\pi$$
0.206039 + 0.978544i $$0.433943\pi$$
$$380$$ 0 0
$$381$$ −13.3359 23.0985i −0.683220 1.18337i
$$382$$ 33.3418i 1.70591i
$$383$$ −8.31401 + 4.80010i −0.424826 + 0.245274i −0.697140 0.716935i $$-0.745544\pi$$
0.272314 + 0.962208i $$0.412211\pi$$
$$384$$ 10.4476 6.03191i 0.533151 0.307815i
$$385$$ 0 0
$$386$$ −13.2747 22.9924i −0.675664 1.17028i
$$387$$ 1.38051 2.39111i 0.0701752 0.121547i
$$388$$ −5.39926 3.11726i −0.274106 0.158255i
$$389$$ −5.63129 −0.285518 −0.142759 0.989758i $$-0.545597\pi$$
−0.142759 + 0.989758i $$0.545597\pi$$
$$390$$ 0 0
$$391$$ 4.40617 0.222829
$$392$$ 15.8201 + 9.13376i 0.799038 + 0.461325i
$$393$$ −12.3236 + 21.3450i −0.621641 + 1.07671i
$$394$$ −1.03473 1.79221i −0.0521291 0.0902903i
$$395$$ 0 0
$$396$$ 5.81445 3.35697i 0.292187 0.168694i
$$397$$ 14.5196 8.38291i 0.728719 0.420726i −0.0892344 0.996011i $$-0.528442\pi$$
0.817953 + 0.575285i $$0.195109\pi$$
$$398$$ 30.8891i 1.54833i
$$399$$ −9.52147 16.4917i −0.476670 0.825616i
$$400$$ 0 0
$$401$$ 12.0187 + 6.93902i 0.600187 + 0.346518i 0.769115 0.639110i $$-0.220697\pi$$
−0.168928 + 0.985628i $$0.554031\pi$$
$$402$$ 18.2050 0.907980
$$403$$ −17.0073 + 9.94402i −0.847196 + 0.495347i
$$404$$ 2.07733 0.103351
$$405$$ 0 0
$$406$$ 0.0542914 0.0940355i 0.00269444 0.00466690i
$$407$$ 23.3783 + 40.4924i 1.15882 + 2.00713i
$$408$$ 8.08903i 0.400466i
$$409$$ −25.4829 + 14.7125i −1.26005 + 0.727489i −0.973083 0.230453i $$-0.925979\pi$$
−0.286964 + 0.957941i $$0.592646\pi$$
$$410$$ 0 0
$$411$$ 8.83157i 0.435629i
$$412$$ 4.58655 + 7.94413i 0.225963 + 0.391379i
$$413$$ 0.308581 0.534478i 0.0151843 0.0262999i
$$414$$ 10.0306 + 5.79118i 0.492978 + 0.284621i
$$415$$ 0 0
$$416$$ −8.83284 5.03522i −0.433066 0.246872i
$$417$$ −4.69683 −0.230005
$$418$$ −12.8687 7.42973i −0.629427 0.363400i
$$419$$ −3.48397 + 6.03440i −0.170203 + 0.294800i −0.938491 0.345305i $$-0.887776\pi$$
0.768288 + 0.640104i $$0.221109\pi$$
$$420$$ 0 0
$$421$$ 7.12125i 0.347069i −0.984828 0.173534i $$-0.944481\pi$$
0.984828 0.173534i $$-0.0555188\pi$$
$$422$$ −0.354389 + 0.204607i −0.0172514 + 0.00996010i
$$423$$ −5.46171 + 3.15332i −0.265558 + 0.153320i
$$424$$ 13.6036i 0.660647i
$$425$$ 0 0
$$426$$ −15.3571 + 26.5993i −0.744054 + 1.28874i
$$427$$ 10.4767 + 6.04875i 0.507005 + 0.292720i
$$428$$ 4.67883 0.226160
$$429$$ 39.2433 + 22.3709i 1.89468 + 1.08008i
$$430$$ 0 0
$$431$$ 26.1664 + 15.1072i 1.26039 + 0.727687i 0.973150 0.230171i $$-0.0739286\pi$$
0.287241 + 0.957858i $$0.407262\pi$$
$$432$$ 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 $$0.842514\pi$$
$$434$$ 23.9935i 1.15172i
$$435$$ 0 0
$$436$$ −3.27290 + 1.88961i −0.156744 + 0.0904960i
$$437$$ 8.82884i 0.422341i
$$438$$ −6.68922 11.5861i −0.319623 0.553604i
$$439$$ −8.27705 + 14.3363i −0.395042 + 0.684233i −0.993107 0.117215i $$-0.962603\pi$$
0.598064 + 0.801448i $$0.295937\pi$$
$$440$$ 0 0
$$441$$ −14.5421 −0.692481
$$442$$ −4.29692 + 2.51236i −0.204383 + 0.119501i
$$443$$ −4.55949 −0.216628 −0.108314 0.994117i $$-0.534545\pi$$
−0.108314 + 0.994117i $$0.534545\pi$$
$$444$$ 9.00753 + 5.20050i 0.427478 + 0.246805i
$$445$$ 0 0
$$446$$ −7.49910 12.9888i −0.355093 0.615038i
$$447$$ 12.8689i 0.608676i
$$448$$ 27.6395 15.9577i 1.30584 0.753929i
$$449$$ 11.9963 6.92608i 0.566142 0.326862i −0.189465 0.981887i $$-0.560675\pi$$
0.755607 + 0.655025i $$0.227342\pi$$
$$450$$ 0 0
$$451$$ −10.0239 17.3620i −0.472009 0.817544i
$$452$$ 1.81271 3.13971i 0.0852628 0.147680i
$$453$$ −9.87596 5.70189i −0.464013 0.267898i
$$454$$ 9.30897 0.436892
$$455$$ 0 0
$$456$$ −16.2083 −0.759025
$$457$$ −34.7402 20.0573i −1.62508 0.938240i −0.985532 0.169489i $$-0.945788\pi$$
−0.639548 0.768751i $$-0.720878\pi$$
$$458$$ −8.78222 + 15.2113i −0.410366 + 0.710775i
$$459$$ 0.739961 + 1.28165i 0.0345384 + 0.0598223i
$$460$$ 0 0
$$461$$ 6.52897 3.76950i 0.304084 0.175563i −0.340192 0.940356i $$-0.610492\pi$$
0.644276 + 0.764793i $$0.277159\pi$$
$$462$$ −47.6432 + 27.5068i −2.21656 + 1.27973i
$$463$$ 23.3031i 1.08299i −0.840705 0.541494i $$-0.817859\pi$$
0.840705 0.541494i $$-0.182141\pi$$
$$464$$ −0.0335403 0.0580936i −0.00155707 0.00269693i
$$465$$ 0 0
$$466$$ −10.0306 5.79118i −0.464659 0.268271i
$$467$$ −22.6297 −1.04718 −0.523589 0.851971i $$-0.675407\pi$$
−0.523589 + 0.851971i $$0.675407\pi$$
$$468$$ 4.50632 0.0247279i 0.208305 0.00114305i
$$469$$ 23.0405 1.06391
$$470$$ 0 0
$$471$$ −11.7085 + 20.2797i −0.539500 + 0.934441i
$$472$$ −0.262648 0.454919i −0.0120893 0.0209394i
$$473$$ 6.08012i 0.279564i
$$474$$ 29.5192 17.0429i 1.35586 0.782808i
$$475$$ 0 0
$$476$$ 2.08783i 0.0956956i
$$477$$ −5.41465 9.37844i −0.247920 0.429409i
$$478$$ 12.1446 21.0351i 0.555482 0.962124i
$$479$$ −17.8789 10.3224i −0.816910 0.471643i 0.0324399 0.999474i $$-0.489672\pi$$
−0.849350 + 0.527831i $$0.823006\pi$$
$$480$$ 0 0
$$481$$ 0.172207 + 31.3825i 0.00785198 + 1.43092i
$$482$$ −28.3777 −1.29257
$$483$$ 28.3075 + 16.3433i 1.28804 + 0.743648i
$$484$$ 4.57449 7.92325i 0.207931 0.360148i
$$485$$ 0 0
$$486$$ 24.7074i 1.12075i
$$487$$ 2.62929 1.51802i 0.119145 0.0687882i −0.439243 0.898368i $$-0.644753\pi$$
0.558388 + 0.829580i $$0.311420\pi$$
$$488$$ 8.91725 5.14838i 0.403665 0.233056i
$$489$$ 15.8155i 0.715203i
$$490$$ 0 0
$$491$$ 5.33401 9.23877i 0.240720 0.416940i −0.720199 0.693767i $$-0.755950\pi$$
0.960920 + 0.276827i $$0.0892830\pi$$
$$492$$ −3.86217 2.22982i −0.174120 0.100528i
$$493$$ 0.0279884 0.00126053
$$494$$ −5.03414 8.60992i −0.226497 0.387379i
$$495$$ 0 0
$$496$$ −12.8369 7.41139i −0.576394 0.332781i
$$497$$ −19.4362 + 33.6646i −0.871835 + 1.51006i
$$498$$ 17.2506 + 29.8789i 0.773016 + 1.33890i
$$499$$ 33.9143i 1.51821i −0.650966 0.759107i $$-0.725636\pi$$
0.650966 0.759107i $$-0.274364\pi$$
$$500$$ 0 0
$$501$$ 21.1872 12.2324i 0.946572 0.546504i
$$502$$ 14.4413i 0.644546i
$$503$$ −6.31380 10.9358i −0.281518 0.487604i 0.690241 0.723580i $$-0.257505\pi$$
−0.971759 + 0.235976i $$0.924171\pi$$
$$504$$ −13.4557 + 23.3059i −0.599363 + 1.03813i
$$505$$ 0 0
$$506$$ 25.5058 1.13387
$$507$$ 15.4468 + 26.0893i 0.686019 + 1.15866i
$$508$$ −5.85945 −0.259971
$$509$$ −20.9168 12.0763i −0.927120 0.535273i −0.0412201 0.999150i $$-0.513124\pi$$
−0.885899 + 0.463877i $$0.846458\pi$$
$$510$$ 0 0
$$511$$ −8.46601 14.6636i −0.374514 0.648678i
$$512$$ 24.2750i 1.07281i
$$513$$ −2.56810 + 1.48269i −0.113384 + 0.0654625i
$$514$$ −5.86238 + 3.38465i −0.258578 + 0.149290i
$$515$$ 0 0
$$516$$ −0.676260 1.17132i −0.0297707 0.0515644i
$$517$$ −6.94402 + 12.0274i −0.305398 + 0.528964i
$$518$$ −33.0999 19.1103i −1.45433 0.839656i
$$519$$ 10.3982 0.456431
$$520$$ 0 0
$$521$$ −24.7521 −1.08441 −0.542205 0.840246i $$-0.682410\pi$$
−0.542205 + 0.840246i $$0.682410\pi$$
$$522$$ 0.0637154 + 0.0367861i 0.00278875 + 0.00161008i
$$523$$ 18.5163 32.0712i 0.809662 1.40238i −0.103436 0.994636i $$-0.532984\pi$$
0.913098 0.407739i $$-0.133683\pi$$
$$524$$ 2.70732 + 4.68922i 0.118270 + 0.204850i
$$525$$ 0 0
$$526$$ −7.24573 + 4.18332i −0.315929 + 0.182402i
$$527$$ 5.35600 3.09229i 0.233311 0.134702i
$$528$$ 33.9865i 1.47907i
$$529$$ 3.92277 + 6.79444i 0.170555 + 0.295410i
$$530$$ 0 0
$$531$$ 0.362145 + 0.209084i 0.0157157 + 0.00907348i
$$532$$ −4.18348 −0.181377
$$533$$ −0.0738376 13.4559i −0.00319826 0.582840i
$$534$$ −45.9519 −1.98854
$$535$$ 0 0
$$536$$ 9.80545 16.9835i 0.423531 0.733577i
$$537$$ −21.7264 37.6312i −0.937562 1.62391i
$$538$$ 1.73438i 0.0747744i
$$539$$ −27.7332 + 16.0118i −1.19456 + 0.689677i
$$540$$ 0 0
$$541$$ 8.38144i 0.360346i −0.983635 0.180173i $$-0.942334\pi$$
0.983635 0.180173i $$-0.0576658\pi$$
$$542$$ −6.07981 10.5305i −0.261150 0.452326i
$$543$$ −21.0952 + 36.5379i −0.905281 + 1.56799i
$$544$$ 2.76409 + 1.59585i 0.118509 + 0.0684215i
$$545$$ 0 0
$$546$$ −36.9245 + 0.202618i −1.58022 + 0.00867126i
$$547$$ 22.7842 0.974181 0.487091 0.873351i $$-0.338058\pi$$
0.487091 + 0.873351i $$0.338058\pi$$
$$548$$ 1.68025 + 0.970090i 0.0717765 + 0.0414402i
$$549$$ −4.09843 + 7.09870i −0.174917 + 0.302965i
$$550$$ 0 0
$$551$$ 0.0560816i 0.00238915i
$$552$$ 24.0938 13.9106i 1.02550 0.592074i
$$553$$ 37.3601 21.5699i 1.58871 0.917245i
$$554$$ 21.3735i 0.908071i
$$555$$ 0 0
$$556$$ −0.515915 + 0.893592i −0.0218797 + 0.0378967i
$$557$$ −24.3810 14.0764i −1.03306 0.596435i −0.115197 0.993343i $$-0.536750\pi$$
−0.917858 + 0.396908i $$0.870083\pi$$
$$558$$ 16.2572 0.688222
$$559$$ 2.02106 3.54536i 0.0854816 0.149953i
$$560$$ 0 0
$$561$$ −12.2805 7.09017i −0.518484 0.299347i
$$562$$ 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 $$0.708551\pi$$
$$564$$ 3.08939i 0.130087i
$$565$$ 0 0
$$566$$ 1.39258 0.804007i 0.0585346 0.0337950i
$$567$$ 37.3253i 1.56752i
$$568$$ 16.5431 + 28.6535i 0.694133 + 1.20227i
$$569$$ 20.2992 35.1593i 0.850988 1.47395i −0.0293292 0.999570i $$-0.509337\pi$$
0.880317 0.474385i $$-0.157330\pi$$
$$570$$ 0 0
$$571$$ −24.7159 −1.03433 −0.517164 0.855886i $$-0.673012\pi$$
−0.517164 + 0.855886i $$0.673012\pi$$
$$572$$ 8.56677 5.00891i 0.358195 0.209433i
$$573$$ −63.7551 −2.66341
$$574$$ 14.1923 + 8.19393i 0.592375 + 0.342008i
$$575$$ 0 0
$$576$$ 10.8124 + 18.7276i 0.450516 + 0.780317i
$$577$$ 23.0691i 0.960379i 0.877165 + 0.480189i $$0.159432\pi$$
−0.877165 + 0.480189i $$0.840568\pi$$
$$578$$ −16.6036 + 9.58607i −0.690617 + 0.398728i
$$579$$ 43.9654 25.3834i 1.82714 1.05490i
$$580$$ 0 0
$$581$$ 21.8327 + 37.8153i 0.905771 + 1.56884i
$$582$$ −17.3068 + 29.9763i −0.717392 + 1.24256i
$$583$$ −20.6525 11.9237i −0.855341 0.493831i
$$584$$ −14.4116 −0.596358
$$585$$ 0 0
$$586$$ 22.8602 0.944345
$$587$$ 17.6256 + 10.1762i 0.727487 + 0.420015i 0.817502 0.575926i $$-0.195358\pi$$
−0.0900152 + 0.995940i $$0.528692\pi$$
$$588$$ −3.56182 + 6.16925i −0.146887 + 0.254416i
$$589$$ 6.19615 + 10.7321i 0.255308 + 0.442206i
$$590$$ 0 0
$$591$$ 3.42701 1.97859i 0.140968 0.0813881i
$$592$$ −20.4486 + 11.8060i −0.840432 + 0.485223i
$$593$$ 10.3834i 0.426395i −0.977009 0.213198i $$-0.931612\pi$$
0.977009 0.213198i $$-0.0683878\pi$$
$$594$$ 4.28339 + 7.41904i 0.175750 + 0.304407i
$$595$$ 0 0
$$596$$ −2.44836 1.41356i −0.100289 0.0579017i
$$597$$ 59.0652 2.41738
$$598$$ 14.8726 + 8.47825i 0.608187 + 0.346701i
$$599$$ −31.5965 −1.29100 −0.645499 0.763761i $$-0.723351\pi$$
−0.645499 + 0.763761i $$0.723351\pi$$
$$600$$ 0 0
$$601$$ 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
$$603$$ 15.6115i 0.635750i
$$604$$ −2.16962 + 1.25263i −0.0882806 + 0.0509688i
$$605$$ 0 0
$$606$$ 11.5332i 0.468505i
$$607$$ 1.08770 + 1.88395i 0.0441484 + 0.0764673i 0.887255 0.461279i $$-0.152609\pi$$
−0.843107 + 0.537746i $$0.819276\pi$$
$$608$$ −3.19768 + 5.53854i −0.129683 + 0.224617i
$$609$$ 0.179812 + 0.103814i 0.00728634 + 0.00420677i
$$610$$ 0 0
$$611$$ −8.04707 + 4.70504i −0.325550 + 0.190346i
$$612$$ −1.41465 −0.0571837
$$613$$ 12.7843 + 7.38100i 0.516352 + 0.298116i 0.735441 0.677589i $$-0.236975\pi$$
−0.219089 + 0.975705i $$0.570309\pi$$
$$614$$ −8.72336 + 15.1093i −0.352046 + 0.609762i
$$615$$ 0 0
$$616$$ 59.2622i 2.38774i
$$617$$ −17.5779 + 10.1486i −0.707659 + 0.408567i −0.810194 0.586162i $$-0.800638\pi$$
0.102535 + 0.994729i $$0.467305\pi$$
$$618$$ 44.1053 25.4642i 1.77418 1.02432i
$$619$$ 9.94207i 0.399605i 0.979836 + 0.199803i $$0.0640301\pi$$
−0.979836 + 0.199803i $$0.935970\pi$$
$$620$$ 0 0
$$621$$ 2.54500 4.40807i 0.102127 0.176890i
$$622$$ 2.91641 + 1.68379i 0.116937 + 0.0675138i
$$623$$ −58.1577 −2.33004
$$624$$ −11.2973 + 19.8178i −0.452252 + 0.793345i
$$625$$ 0 0
$$626$$ −17.3080 9.99276i −0.691766 0.399391i
$$627$$ 14.2069 24.6070i 0.567368 0.982711i
$$628$$ 2.57221 + 4.45519i 0.102642 + 0.177782i
$$629$$ 9.85174i 0.392815i
$$630$$ 0 0
$$631$$ 0.843006 0.486710i 0.0335596 0.0193756i −0.483126 0.875551i $$-0.660499\pi$$
0.516686 + 0.856175i $$0.327165\pi$$
$$632$$ 36.7183i 1.46058i
$$633$$ −0.391243 0.677652i −0.0155505 0.0269342i
$$634$$ 1.08903 1.88625i 0.0432507 0.0749124i
$$635$$ 0 0
$$636$$ −5.30487 −0.210352
$$637$$ −21.4938 + 0.117945i −0.851617 + 0.00467314i
$$638$$ 0.162015 0.00641425
$$639$$ −22.8100 13.1694i −0.902350 0.520972i
$$640$$ 0 0
$$641$$ −6.31047 10.9301i −0.249249 0.431711i 0.714069 0.700075i $$-0.246850\pi$$
−0.963318 + 0.268364i $$0.913517\pi$$
$$642$$ 25.9766i 1.02521i
$$643$$ 8.62599 4.98022i 0.340176 0.196401i −0.320174 0.947359i $$-0.603741\pi$$
0.660350 + 0.750958i $$0.270408\pi$$
$$644$$ 6.21878 3.59042i 0.245054 0.141482i
$$645$$ 0 0
$$646$$ 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 $$-0.0860354\pi$$
$$648$$ 27.5131 + 15.8847i 1.08081 + 0.624009i
$$649$$ 0.920861 0.0361470
$$650$$ 0 0
$$651$$ 45.8796 1.79816
$$652$$ 3.00898 + 1.73723i 0.117841 + 0.0680353i
$$653$$ 6.87769 11.9125i 0.269145 0.466172i −0.699497 0.714636i $$-0.746592\pi$$
0.968641 + 0.248464i $$0.0799257\pi$$
$$654$$ 10.4910 + 18.1709i 0.410231 + 0.710540i
$$655$$ 0 0
$$656$$ 8.76776 5.06207i 0.342324 0.197641i
$$657$$ 9.93555 5.73629i 0.387623 0.223794i
$$658$$ 11.3526i 0.442570i
$$659$$ 1.29092 + 2.23593i 0.0502869 + 0.0870995i 0.890073 0.455818i $$-0.150653\pi$$
−0.839786 + 0.542917i $$0.817320\pi$$
$$660$$ 0 0
$$661$$ −21.5437 12.4382i −0.837951 0.483791i 0.0186163 0.999827i $$-0.494074\pi$$
−0.856567 + 0.516036i $$0.827407\pi$$
$$662$$ 8.81151 0.342469
$$663$$ −4.80406 8.21643i −0.186574 0.319100i
$$664$$ 37.1656 1.44231
$$665$$ 0 0
$$666$$ 12.9485 22.4274i 0.501743 0.869045i
$$667$$ −0.0481312 0.0833657i −0.00186365 0.00322793i
$$668$$ 5.37460i 0.207949i
$$669$$ 24.8368 14.3395i 0.960246 0.554398i
$$670$$ 0 0
$$671$$ 18.0506i 0.696834i
$$672$$ 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 $$0.852149\pi$$
$$674$$ 4.60770 + 2.66025i 0.177482 + 0.102469i
$$675$$ 0 0
$$676$$ 6.66033 0.0730977i 0.256167 0.00281145i
$$677$$ 41.3625 1.58969 0.794845 0.606813i $$-0.207552\pi$$
0.794845 + 0.606813i $$0.207552\pi$$
$$678$$ −17.4315 10.0641i −0.669451 0.386508i
$$679$$ −21.9039 + 37.9386i −0.840594 + 1.45595i
$$680$$ 0 0
$$681$$ 17.8003i 0.682110i
$$682$$ 31.0041 17.9002i 1.18721 0.685435i
$$683$$ −2.27495 + 1.31344i −0.0870484 + 0.0502574i −0.542892 0.839802i $$-0.682671\pi$$
0.455844 + 0.890060i $$0.349338\pi$$
$$684$$ 2.83459i 0.108383i
$$685$$ 0 0
$$686$$ −2.28028 + 3.94957i −0.0870617 + 0.150795i
$$687$$ −29.0865 16.7931i −1.10972 0.640696i
$$688$$ 3.07045 0.117060
$$689$$ −8.07914 13.8178i −0.307791 0.526417i
$$690$$ 0 0
$$691$$ −13.2288 7.63765i −0.503247 0.290550i 0.226806 0.973940i $$-0.427172\pi$$
−0.730053 + 0.683390i $$0.760505\pi$$
$$692$$ 1.14218 1.97831i 0.0434190 0.0752039i
$$693$$ −23.5882 40.8560i −0.896043 1.55199i
$$694$$ 32.5744i 1.23651i
$$695$$ 0 0
$$696$$ 0.153046 0.0883613i 0.00580120 0.00334933i
$$697$$ 4.22414i 0.160001i
$$698$$ 14.3747 + 24.8976i 0.544089 + 0.942390i
$$699$$ 11.0737 19.1802i 0.418846 0.725463i
$$700$$ 0 0
$$701$$ 48.1947 1.82029 0.910144 0.414292i $$-0.135971\pi$$
0.910144 + 0.414292i $$0.135971\pi$$
$$702$$ 0.0315519 + 5.74991i 0.00119085 + 0.217017i
$$703$$ 19.7404 0.744522
$$704$$ 41.2406 + 23.8103i 1.55431 + 0.897383i
$$705$$ 0 0
$$706$$ 3.49884 + 6.06016i 0.131680 + 0.228077i
$$707$$ 14.5967i 0.548964i
$$708$$ 0.177401 0.102423i 0.00666715 0.00384928i
$$709$$ −33.6624 + 19.4350i −1.26422 + 0.729896i −0.973887 0.227031i $$-0.927098\pi$$
−0.290329 + 0.956927i $$0.593765\pi$$
$$710$$ 0 0
$$711$$ 14.6150 + 25.3140i 0.548107 + 0.949349i
$$712$$ −24.7504 + 42.8689i −0.927560 + 1.60658i
$$713$$ −18.4213 10.6355i −0.689882 0.398304i
$$714$$ 11.5915 0.433801
$$715$$ 0 0
$$716$$ −9.54600 −0.356751
$$717$$ 40.2227 + 23.2226i 1.50214 + 0.867263i
$$718$$ −15.0987 + 26.1517i −0.563478 + 0.975973i
$$719$$ 3.30830 + 5.73015i 0.123379 + 0.213698i 0.921098 0.389331i $$-0.127294\pi$$
−0.797719 + 0.603029i $$0.793960\pi$$
$$720$$ 0 0
$$721$$ 55.8205 32.2280i 2.07887 1.20023i
$$722$$ 14.6362 8.45024i 0.544705 0.314485i
$$723$$ 54.2629i 2.01806i
$$724$$ 4.63433 + 8.02690i 0.172234 + 0.298317i
$$725$$ 0 0
$$726$$ −43.9893 25.3973i −1.63260 0.942581i
$$727$$ −18.3735 −0.681435 −0.340717 0.940166i $$-0.610670\pi$$
−0.340717 + 0.940166i $$0.610670\pi$$
$$728$$ −19.6990 + 34.5562i −0.730094 + 1.28074i
$$729$$ −16.1420 −0.597853
$$730$$ 0 0
$$731$$ −0.640548 + 1.10946i −0.0236915 + 0.0410349i
$$732$$ 2.00767 + 3.47739i 0.0742057 + 0.128528i
$$733$$ 0.791131i 0.0292211i 0.999893 + 0.0146105i $$0.00465084\pi$$
−0.999893 + 0.0146105i $$0.995349\pi$$
$$734$$ −27.5198 + 15.8886i −1.01578 + 0.586458i
$$735$$ 0 0
$$736$$ 10.9774i 0.404634i
$$737$$ 17.1893 + 29.7727i 0.633175 + 1.09669i
$$738$$ −5.55193 + 9.61623i −0.204369 + 0.353978i
$$739$$ −27.0073 15.5926i −0.993478 0.573585i −0.0871658 0.996194i $$-0.527781\pi$$
−0.906312 + 0.422609i $$0.861114\pi$$
$$740$$ 0 0
$$741$$ 16.4636 9.62612i 0.604806 0.353624i
$$742$$ 19.4938 0.715639
$$743$$ −4.81773 2.78152i −0.176745 0.102044i 0.409017 0.912527i $$-0.365872\pi$$
−0.585763 + 0.810483i $$0.699205\pi$$
$$744$$ 19.5251 33.8185i 0.715826 1.23985i
$$745$$ 0 0
$$746$$ 16.1053i 0.589658i
$$747$$ −25.6224 + 14.7931i −0.937474 + 0.541251i
$$748$$ −2.69787 + 1.55762i −0.0986439 + 0.0569521i
$$749$$ 32.8765i 1.20128i
$$750$$ 0 0
$$751$$ −17.6048 + 30.4925i −0.642410 + 1.11269i 0.342483 + 0.939524i $$0.388732\pi$$
−0.984893 + 0.173163i $$0.944601\pi$$
$$752$$ −6.07381 3.50672i −0.221489 0.127877i
$$753$$ 27.6142 1.00632
$$754$$ 0.0944723 + 0.0538546i 0.00344048 + 0.00196127i
$$755$$ 0 0
$$756$$ 2.08873 + 1.20593i 0.0759665 + 0.0438593i
$$757$$ 25.0223 43.3399i 0.909451 1.57522i 0.0946237 0.995513i $$-0.469835\pi$$
0.814828 0.579703i $$-0.196831\pi$$
$$758$$ −15.8545 27.4609i −0.575863 0.997424i
$$759$$ 48.7715i 1.77029i
$$760$$ 0 0
$$761$$ 38.8161 22.4105i 1.40708 0.812379i 0.411975 0.911195i $$-0.364839\pi$$
0.995106 + 0.0988165i $$0.0315057\pi$$
$$762$$ 32.5313i 1.17848i
$$763$$ 13.2776 + 22.9975i 0.480682 + 0.832566i
$$764$$ −7.00307 + 12.1297i −0.253362 + 0.438836i
$$765$$ 0 0
$$766$$ 11.7092 0.423072
$$767$$ 0.536961 + 0.306098i 0.0193885 + 0.0110526i
$$768$$ 26.6361 0.961148
$$769$$ −34.0897 19.6817i −1.22930 0.709739i −0.262420 0.964954i $$-0.584521\pi$$
−0.966884 + 0.255215i $$0.917854\pi$$
$$770$$ 0 0
$$771$$ −6.47201 11.2099i −0.233084 0.403713i
$$772$$ 11.1528i 0.401399i
$$773$$ 42.2452 24.3902i 1.51945 0.877256i 0.519715 0.854340i $$-0.326038\pi$$
0.999737 0.0229167i $$-0.00729525\pi$$
$$774$$ −2.91641 + 1.68379i −0.104828 + 0.0605225i
$$775$$ 0 0
$$776$$ 18.6434 + 32.2914i 0.669260 + 1.15919i
$$777$$ 36.5420 63.2926i 1.31094 2.27061i
$$778$$ 5.94822 + 3.43420i 0.213254 + 0.123122i
$$779$$ −8.46410 −0.303258
$$780$$ 0 0
$$781$$ −58.0013 −2.07545
$$782$$ −4.65415 2.68707i −0.166432 0.0960895i