# Properties

 Label 495.2.n.h.361.3 Level $495$ Weight $2$ Character 495.361 Analytic conductor $3.953$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$495 = 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 495.n (of order $$5$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.95259490005$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$4$$ over $$\Q(\zeta_{5})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1$$ x^16 - 2*x^15 + 5*x^14 - 8*x^13 + 47*x^12 + 32*x^11 + 171*x^10 + 26*x^9 + 360*x^8 - 172*x^7 + 471*x^6 - 430*x^5 + 383*x^4 + 70*x^3 + 17*x^2 + 4*x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 361.3 Root $$0.735494 + 0.534368i$$ of defining polynomial Character $$\chi$$ $$=$$ 495.361 Dual form 495.2.n.h.181.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.0280832 + 0.0864312i) q^{2} +(1.61135 + 1.17072i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.98801 + 1.44438i) q^{7} +(-0.293484 + 0.213228i) q^{8} +O(q^{10})$$ $$q+(-0.0280832 + 0.0864312i) q^{2} +(1.61135 + 1.17072i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.98801 + 1.44438i) q^{7} +(-0.293484 + 0.213228i) q^{8} +0.0908791 q^{10} +(0.242484 + 3.30775i) q^{11} +(0.0999755 - 0.307693i) q^{13} +(-0.180669 + 0.131264i) q^{14} +(1.22078 + 3.75716i) q^{16} +(-1.13260 - 3.48579i) q^{17} +(-0.437853 + 0.318119i) q^{19} +(0.615482 - 1.89426i) q^{20} +(-0.292702 - 0.0719339i) q^{22} +4.62543 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.0237866 + 0.0172820i) q^{26} +(1.51244 + 4.65480i) q^{28} +(1.19403 + 0.867515i) q^{29} +(0.275312 - 0.847323i) q^{31} -1.08455 q^{32} +0.333088 q^{34} +(0.759354 - 2.33705i) q^{35} +(1.84899 + 1.34337i) q^{37} +(-0.0151991 - 0.0467779i) q^{38} +(0.293484 + 0.213228i) q^{40} +(-7.26541 + 5.27863i) q^{41} +6.31964 q^{43} +(-3.48171 + 5.61383i) q^{44} +(-0.129897 + 0.399782i) q^{46} +(-1.18347 + 0.859844i) q^{47} +(-0.297142 - 0.914509i) q^{49} +(-0.0280832 - 0.0864312i) q^{50} +(0.521317 - 0.378759i) q^{52} +(3.19196 - 9.82385i) q^{53} +(3.07092 - 1.25277i) q^{55} -0.891432 q^{56} +(-0.108513 + 0.0788390i) q^{58} +(5.09137 + 3.69910i) q^{59} +(-2.00101 - 6.15847i) q^{61} +(0.0655035 + 0.0475911i) q^{62} +(-2.41109 + 7.42059i) q^{64} -0.323527 q^{65} -7.05634 q^{67} +(2.25585 - 6.94279i) q^{68} +(0.180669 + 0.131264i) q^{70} +(2.87940 + 8.86188i) q^{71} +(-5.01044 - 3.64030i) q^{73} +(-0.168034 + 0.122084i) q^{74} -1.07796 q^{76} +(-4.29557 + 6.92609i) q^{77} +(3.58612 - 11.0369i) q^{79} +(3.19603 - 2.32205i) q^{80} +(-0.252202 - 0.776199i) q^{82} +(-5.36887 - 16.5237i) q^{83} +(-2.96519 + 2.15434i) q^{85} +(-0.177476 + 0.546214i) q^{86} +(-0.776471 - 0.919066i) q^{88} -4.70270 q^{89} +(0.643177 - 0.467296i) q^{91} +(7.45320 + 5.41507i) q^{92} +(-0.0410816 - 0.126436i) q^{94} +(0.437853 + 0.318119i) q^{95} +(3.40155 - 10.4689i) q^{97} +0.0873867 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10})$$ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 $$16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100})$$ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$397$$ $$\chi(n)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.0280832 + 0.0864312i −0.0198578 + 0.0611161i −0.960494 0.278299i $$-0.910229\pi$$
0.940637 + 0.339415i $$0.110229\pi$$
$$3$$ 0 0
$$4$$ 1.61135 + 1.17072i 0.805676 + 0.585358i
$$5$$ −0.309017 0.951057i −0.138197 0.425325i
$$6$$ 0 0
$$7$$ 1.98801 + 1.44438i 0.751399 + 0.545923i 0.896260 0.443529i $$-0.146274\pi$$
−0.144861 + 0.989452i $$0.546274\pi$$
$$8$$ −0.293484 + 0.213228i −0.103762 + 0.0753876i
$$9$$ 0 0
$$10$$ 0.0908791 0.0287385
$$11$$ 0.242484 + 3.30775i 0.0731117 + 0.997324i
$$12$$ 0 0
$$13$$ 0.0999755 0.307693i 0.0277282 0.0853386i −0.936235 0.351375i $$-0.885714\pi$$
0.963963 + 0.266037i $$0.0857142\pi$$
$$14$$ −0.180669 + 0.131264i −0.0482858 + 0.0350817i
$$15$$ 0 0
$$16$$ 1.22078 + 3.75716i 0.305194 + 0.939291i
$$17$$ −1.13260 3.48579i −0.274696 0.845428i −0.989300 0.145898i $$-0.953393\pi$$
0.714604 0.699530i $$-0.246607\pi$$
$$18$$ 0 0
$$19$$ −0.437853 + 0.318119i −0.100450 + 0.0729815i −0.636877 0.770966i $$-0.719774\pi$$
0.536426 + 0.843947i $$0.319774\pi$$
$$20$$ 0.615482 1.89426i 0.137626 0.423569i
$$21$$ 0 0
$$22$$ −0.292702 0.0719339i −0.0624043 0.0153364i
$$23$$ 4.62543 0.964470 0.482235 0.876042i $$-0.339825\pi$$
0.482235 + 0.876042i $$0.339825\pi$$
$$24$$ 0 0
$$25$$ −0.809017 + 0.587785i −0.161803 + 0.117557i
$$26$$ 0.0237866 + 0.0172820i 0.00466494 + 0.00338928i
$$27$$ 0 0
$$28$$ 1.51244 + 4.65480i 0.285824 + 0.879675i
$$29$$ 1.19403 + 0.867515i 0.221726 + 0.161094i 0.693103 0.720838i $$-0.256243\pi$$
−0.471377 + 0.881932i $$0.656243\pi$$
$$30$$ 0 0
$$31$$ 0.275312 0.847323i 0.0494475 0.152184i −0.923284 0.384118i $$-0.874506\pi$$
0.972731 + 0.231935i $$0.0745055\pi$$
$$32$$ −1.08455 −0.191723
$$33$$ 0 0
$$34$$ 0.333088 0.0571241
$$35$$ 0.759354 2.33705i 0.128354 0.395034i
$$36$$ 0 0
$$37$$ 1.84899 + 1.34337i 0.303971 + 0.220848i 0.729305 0.684188i $$-0.239843\pi$$
−0.425334 + 0.905036i $$0.639843\pi$$
$$38$$ −0.0151991 0.0467779i −0.00246562 0.00758838i
$$39$$ 0 0
$$40$$ 0.293484 + 0.213228i 0.0464038 + 0.0337144i
$$41$$ −7.26541 + 5.27863i −1.13467 + 0.824384i −0.986367 0.164559i $$-0.947380\pi$$
−0.148299 + 0.988943i $$0.547380\pi$$
$$42$$ 0 0
$$43$$ 6.31964 0.963736 0.481868 0.876244i $$-0.339959\pi$$
0.481868 + 0.876244i $$0.339959\pi$$
$$44$$ −3.48171 + 5.61383i −0.524887 + 0.846317i
$$45$$ 0 0
$$46$$ −0.129897 + 0.399782i −0.0191523 + 0.0589446i
$$47$$ −1.18347 + 0.859844i −0.172627 + 0.125421i −0.670744 0.741689i $$-0.734025\pi$$
0.498117 + 0.867110i $$0.334025\pi$$
$$48$$ 0 0
$$49$$ −0.297142 0.914509i −0.0424488 0.130644i
$$50$$ −0.0280832 0.0864312i −0.00397156 0.0122232i
$$51$$ 0 0
$$52$$ 0.521317 0.378759i 0.0722936 0.0525244i
$$53$$ 3.19196 9.82385i 0.438450 1.34941i −0.451060 0.892494i $$-0.648954\pi$$
0.889510 0.456916i $$-0.151046\pi$$
$$54$$ 0 0
$$55$$ 3.07092 1.25277i 0.414083 0.168923i
$$56$$ −0.891432 −0.119123
$$57$$ 0 0
$$58$$ −0.108513 + 0.0788390i −0.0142484 + 0.0103521i
$$59$$ 5.09137 + 3.69910i 0.662840 + 0.481581i 0.867621 0.497227i $$-0.165648\pi$$
−0.204781 + 0.978808i $$0.565648\pi$$
$$60$$ 0 0
$$61$$ −2.00101 6.15847i −0.256203 0.788511i −0.993590 0.113041i $$-0.963941\pi$$
0.737388 0.675470i $$-0.236059\pi$$
$$62$$ 0.0655035 + 0.0475911i 0.00831895 + 0.00604407i
$$63$$ 0 0
$$64$$ −2.41109 + 7.42059i −0.301387 + 0.927573i
$$65$$ −0.323527 −0.0401286
$$66$$ 0 0
$$67$$ −7.05634 −0.862069 −0.431035 0.902335i $$-0.641851\pi$$
−0.431035 + 0.902335i $$0.641851\pi$$
$$68$$ 2.25585 6.94279i 0.273562 0.841936i
$$69$$ 0 0
$$70$$ 0.180669 + 0.131264i 0.0215941 + 0.0156890i
$$71$$ 2.87940 + 8.86188i 0.341722 + 1.05171i 0.963315 + 0.268372i $$0.0864855\pi$$
−0.621594 + 0.783340i $$0.713515\pi$$
$$72$$ 0 0
$$73$$ −5.01044 3.64030i −0.586428 0.426065i 0.254608 0.967044i $$-0.418054\pi$$
−0.841036 + 0.540980i $$0.818054\pi$$
$$74$$ −0.168034 + 0.122084i −0.0195336 + 0.0141920i
$$75$$ 0 0
$$76$$ −1.07796 −0.123651
$$77$$ −4.29557 + 6.92609i −0.489526 + 0.789301i
$$78$$ 0 0
$$79$$ 3.58612 11.0369i 0.403470 1.24175i −0.518697 0.854958i $$-0.673583\pi$$
0.922166 0.386793i $$-0.126417\pi$$
$$80$$ 3.19603 2.32205i 0.357327 0.259614i
$$81$$ 0 0
$$82$$ −0.252202 0.776199i −0.0278511 0.0857168i
$$83$$ −5.36887 16.5237i −0.589311 1.81371i −0.581223 0.813744i $$-0.697426\pi$$
−0.00808702 0.999967i $$-0.502574\pi$$
$$84$$ 0 0
$$85$$ −2.96519 + 2.15434i −0.321620 + 0.233670i
$$86$$ −0.177476 + 0.546214i −0.0191377 + 0.0588997i
$$87$$ 0 0
$$88$$ −0.776471 0.919066i −0.0827721 0.0979727i
$$89$$ −4.70270 −0.498485 −0.249242 0.968441i $$-0.580182\pi$$
−0.249242 + 0.968441i $$0.580182\pi$$
$$90$$ 0 0
$$91$$ 0.643177 0.467296i 0.0674233 0.0489859i
$$92$$ 7.45320 + 5.41507i 0.777050 + 0.564560i
$$93$$ 0 0
$$94$$ −0.0410816 0.126436i −0.00423724 0.0130409i
$$95$$ 0.437853 + 0.318119i 0.0449228 + 0.0326383i
$$96$$ 0 0
$$97$$ 3.40155 10.4689i 0.345375 1.06296i −0.616007 0.787741i $$-0.711251\pi$$
0.961383 0.275216i $$-0.0887492\pi$$
$$98$$ 0.0873867 0.00882739
$$99$$ 0 0
$$100$$ −1.99174 −0.199174
$$101$$ −2.07395 + 6.38296i −0.206366 + 0.635129i 0.793289 + 0.608846i $$0.208367\pi$$
−0.999655 + 0.0262830i $$0.991633\pi$$
$$102$$ 0 0
$$103$$ −12.6233 9.17139i −1.24381 0.903684i −0.245968 0.969278i $$-0.579106\pi$$
−0.997846 + 0.0655935i $$0.979106\pi$$
$$104$$ 0.0362677 + 0.111620i 0.00355634 + 0.0109453i
$$105$$ 0 0
$$106$$ 0.759446 + 0.551770i 0.0737640 + 0.0535926i
$$107$$ −7.26833 + 5.28075i −0.702656 + 0.510509i −0.880796 0.473496i $$-0.842992\pi$$
0.178140 + 0.984005i $$0.442992\pi$$
$$108$$ 0 0
$$109$$ −10.7685 −1.03144 −0.515719 0.856758i $$-0.672475\pi$$
−0.515719 + 0.856758i $$0.672475\pi$$
$$110$$ 0.0220367 + 0.300605i 0.00210112 + 0.0286616i
$$111$$ 0 0
$$112$$ −2.99984 + 9.23256i −0.283458 + 0.872394i
$$113$$ 16.0953 11.6939i 1.51412 1.10007i 0.549812 0.835288i $$-0.314699\pi$$
0.964308 0.264784i $$-0.0853007\pi$$
$$114$$ 0 0
$$115$$ −1.42934 4.39905i −0.133286 0.410213i
$$116$$ 0.908393 + 2.79575i 0.0843422 + 0.259578i
$$117$$ 0 0
$$118$$ −0.462699 + 0.336170i −0.0425949 + 0.0309470i
$$119$$ 2.78316 8.56570i 0.255132 0.785216i
$$120$$ 0 0
$$121$$ −10.8824 + 1.60415i −0.989309 + 0.145832i
$$122$$ 0.588478 0.0532783
$$123$$ 0 0
$$124$$ 1.43560 1.04302i 0.128921 0.0936663i
$$125$$ 0.809017 + 0.587785i 0.0723607 + 0.0525731i
$$126$$ 0 0
$$127$$ −3.74224 11.5174i −0.332070 1.02201i −0.968147 0.250381i $$-0.919444\pi$$
0.636078 0.771625i $$-0.280556\pi$$
$$128$$ −2.32850 1.69175i −0.205812 0.149531i
$$129$$ 0 0
$$130$$ 0.00908568 0.0279628i 0.000796867 0.00245250i
$$131$$ −18.7043 −1.63420 −0.817099 0.576497i $$-0.804419\pi$$
−0.817099 + 0.576497i $$0.804419\pi$$
$$132$$ 0 0
$$133$$ −1.32994 −0.115321
$$134$$ 0.198165 0.609888i 0.0171188 0.0526863i
$$135$$ 0 0
$$136$$ 1.07567 + 0.781519i 0.0922378 + 0.0670147i
$$137$$ 4.87796 + 15.0128i 0.416752 + 1.28263i 0.910674 + 0.413125i $$0.135563\pi$$
−0.493922 + 0.869506i $$0.664437\pi$$
$$138$$ 0 0
$$139$$ −11.1932 8.13233i −0.949395 0.689776i 0.00126895 0.999999i $$-0.499596\pi$$
−0.950664 + 0.310224i $$0.899596\pi$$
$$140$$ 3.95961 2.87683i 0.334648 0.243136i
$$141$$ 0 0
$$142$$ −0.846805 −0.0710623
$$143$$ 1.04201 + 0.256083i 0.0871375 + 0.0214147i
$$144$$ 0 0
$$145$$ 0.456080 1.40367i 0.0378754 0.116568i
$$146$$ 0.455344 0.330827i 0.0376846 0.0273794i
$$147$$ 0 0
$$148$$ 1.40667 + 4.32927i 0.115627 + 0.355864i
$$149$$ −2.79288 8.59559i −0.228801 0.704178i −0.997883 0.0650280i $$-0.979286\pi$$
0.769082 0.639150i $$-0.220714\pi$$
$$150$$ 0 0
$$151$$ 7.16102 5.20278i 0.582755 0.423397i −0.256961 0.966422i $$-0.582721\pi$$
0.839716 + 0.543025i $$0.182721\pi$$
$$152$$ 0.0606708 0.186725i 0.00492105 0.0151454i
$$153$$ 0 0
$$154$$ −0.477997 0.565778i −0.0385181 0.0455917i
$$155$$ −0.890928 −0.0715611
$$156$$ 0 0
$$157$$ −9.49715 + 6.90008i −0.757955 + 0.550686i −0.898282 0.439419i $$-0.855184\pi$$
0.140328 + 0.990105i $$0.455184\pi$$
$$158$$ 0.853225 + 0.619904i 0.0678789 + 0.0493169i
$$159$$ 0 0
$$160$$ 0.335145 + 1.03147i 0.0264955 + 0.0815448i
$$161$$ 9.19543 + 6.68087i 0.724701 + 0.526526i
$$162$$ 0 0
$$163$$ 2.35476 7.24722i 0.184439 0.567646i −0.815499 0.578759i $$-0.803537\pi$$
0.999938 + 0.0111126i $$0.00353731\pi$$
$$164$$ −17.8869 −1.39673
$$165$$ 0 0
$$166$$ 1.57894 0.122549
$$167$$ −3.12640 + 9.62208i −0.241928 + 0.744579i 0.754198 + 0.656647i $$0.228026\pi$$
−0.996126 + 0.0879319i $$0.971974\pi$$
$$168$$ 0 0
$$169$$ 10.4325 + 7.57968i 0.802503 + 0.583053i
$$170$$ −0.102930 0.316785i −0.00789435 0.0242963i
$$171$$ 0 0
$$172$$ 10.1832 + 7.39850i 0.776459 + 0.564130i
$$173$$ 7.84357 5.69869i 0.596335 0.433263i −0.248241 0.968698i $$-0.579852\pi$$
0.844576 + 0.535435i $$0.179852\pi$$
$$174$$ 0 0
$$175$$ −2.45732 −0.185756
$$176$$ −12.1317 + 4.94907i −0.914464 + 0.373050i
$$177$$ 0 0
$$178$$ 0.132067 0.406459i 0.00989882 0.0304654i
$$179$$ 14.6904 10.6732i 1.09801 0.797751i 0.117276 0.993099i $$-0.462584\pi$$
0.980734 + 0.195348i $$0.0625837\pi$$
$$180$$ 0 0
$$181$$ −1.36254 4.19346i −0.101277 0.311697i 0.887562 0.460688i $$-0.152397\pi$$
−0.988839 + 0.148991i $$0.952397\pi$$
$$182$$ 0.0223264 + 0.0687137i 0.00165495 + 0.00509340i
$$183$$ 0 0
$$184$$ −1.35749 + 0.986274i −0.100075 + 0.0727091i
$$185$$ 0.706250 2.17361i 0.0519245 0.159807i
$$186$$ 0 0
$$187$$ 11.2555 4.59161i 0.823082 0.335772i
$$188$$ −2.91363 −0.212498
$$189$$ 0 0
$$190$$ −0.0397917 + 0.0289104i −0.00288679 + 0.00209738i
$$191$$ 9.93939 + 7.22139i 0.719189 + 0.522521i 0.886125 0.463446i $$-0.153387\pi$$
−0.166936 + 0.985968i $$0.553387\pi$$
$$192$$ 0 0
$$193$$ 7.19896 + 22.1561i 0.518193 + 1.59483i 0.777397 + 0.629010i $$0.216540\pi$$
−0.259204 + 0.965823i $$0.583460\pi$$
$$194$$ 0.809313 + 0.588000i 0.0581053 + 0.0422160i
$$195$$ 0 0
$$196$$ 0.591830 1.82146i 0.0422736 0.130105i
$$197$$ −19.6929 −1.40306 −0.701532 0.712638i $$-0.747500\pi$$
−0.701532 + 0.712638i $$0.747500\pi$$
$$198$$ 0 0
$$199$$ 22.2083 1.57431 0.787154 0.616757i $$-0.211554\pi$$
0.787154 + 0.616757i $$0.211554\pi$$
$$200$$ 0.112101 0.345011i 0.00792672 0.0243959i
$$201$$ 0 0
$$202$$ −0.493444 0.358508i −0.0347186 0.0252245i
$$203$$ 1.12073 + 3.44927i 0.0786601 + 0.242091i
$$204$$ 0 0
$$205$$ 7.26541 + 5.27863i 0.507438 + 0.368676i
$$206$$ 1.14720 0.833488i 0.0799291 0.0580719i
$$207$$ 0 0
$$208$$ 1.27810 0.0886203
$$209$$ −1.15843 1.37117i −0.0801303 0.0948458i
$$210$$ 0 0
$$211$$ −4.01468 + 12.3559i −0.276382 + 0.850616i 0.712469 + 0.701704i $$0.247577\pi$$
−0.988850 + 0.148912i $$0.952423\pi$$
$$212$$ 16.6443 12.0928i 1.14314 0.830537i
$$213$$ 0 0
$$214$$ −0.252304 0.776510i −0.0172471 0.0530812i
$$215$$ −1.95288 6.01033i −0.133185 0.409901i
$$216$$ 0 0
$$217$$ 1.77118 1.28684i 0.120235 0.0873561i
$$218$$ 0.302415 0.930736i 0.0204821 0.0630374i
$$219$$ 0 0
$$220$$ 6.41497 + 1.57653i 0.432498 + 0.106290i
$$221$$ −1.18578 −0.0797645
$$222$$ 0 0
$$223$$ 18.3008 13.2963i 1.22551 0.890387i 0.228968 0.973434i $$-0.426465\pi$$
0.996546 + 0.0830466i $$0.0264650\pi$$
$$224$$ −2.15610 1.56650i −0.144061 0.104666i
$$225$$ 0 0
$$226$$ 0.558712 + 1.71954i 0.0371650 + 0.114382i
$$227$$ 12.7278 + 9.24727i 0.844772 + 0.613763i 0.923700 0.383118i $$-0.125150\pi$$
−0.0789276 + 0.996880i $$0.525150\pi$$
$$228$$ 0 0
$$229$$ −7.50944 + 23.1117i −0.496238 + 1.52726i 0.318781 + 0.947828i $$0.396727\pi$$
−0.815019 + 0.579434i $$0.803273\pi$$
$$230$$ 0.420355 0.0277174
$$231$$ 0 0
$$232$$ −0.535408 −0.0351513
$$233$$ 1.65556 5.09529i 0.108459 0.333804i −0.882067 0.471123i $$-0.843849\pi$$
0.990527 + 0.137319i $$0.0438487\pi$$
$$234$$ 0 0
$$235$$ 1.18347 + 0.859844i 0.0772013 + 0.0560901i
$$236$$ 3.87340 + 11.9211i 0.252137 + 0.775997i
$$237$$ 0 0
$$238$$ 0.662183 + 0.481104i 0.0429230 + 0.0311854i
$$239$$ 0.745637 0.541737i 0.0482312 0.0350420i −0.563408 0.826179i $$-0.690510\pi$$
0.611640 + 0.791136i $$0.290510\pi$$
$$240$$ 0 0
$$241$$ 11.4029 0.734523 0.367262 0.930118i $$-0.380295\pi$$
0.367262 + 0.930118i $$0.380295\pi$$
$$242$$ 0.166964 0.985628i 0.0107328 0.0633586i
$$243$$ 0 0
$$244$$ 3.98549 12.2661i 0.255145 0.785255i
$$245$$ −0.777928 + 0.565198i −0.0497000 + 0.0361091i
$$246$$ 0 0
$$247$$ 0.0541084 + 0.166528i 0.00344283 + 0.0105959i
$$248$$ 0.0998738 + 0.307380i 0.00634199 + 0.0195186i
$$249$$ 0 0
$$250$$ −0.0735227 + 0.0534174i −0.00464999 + 0.00337841i
$$251$$ 0.274926 0.846135i 0.0173532 0.0534076i −0.942005 0.335599i $$-0.891061\pi$$
0.959358 + 0.282191i $$0.0910613\pi$$
$$252$$ 0 0
$$253$$ 1.12159 + 15.2998i 0.0705140 + 0.961888i
$$254$$ 1.10056 0.0690551
$$255$$ 0 0
$$256$$ −12.4130 + 9.01860i −0.775815 + 0.563663i
$$257$$ −12.9545 9.41196i −0.808077 0.587102i 0.105196 0.994452i $$-0.466453\pi$$
−0.913272 + 0.407349i $$0.866453\pi$$
$$258$$ 0 0
$$259$$ 1.73548 + 5.34127i 0.107838 + 0.331890i
$$260$$ −0.521317 0.378759i −0.0323307 0.0234896i
$$261$$ 0 0
$$262$$ 0.525275 1.61663i 0.0324516 0.0998757i
$$263$$ −21.2954 −1.31313 −0.656565 0.754269i $$-0.727991\pi$$
−0.656565 + 0.754269i $$0.727991\pi$$
$$264$$ 0 0
$$265$$ −10.3294 −0.634531
$$266$$ 0.0373490 0.114948i 0.00229001 0.00704794i
$$267$$ 0 0
$$268$$ −11.3703 8.26097i −0.694549 0.504619i
$$269$$ 9.35808 + 28.8012i 0.570572 + 1.75604i 0.650783 + 0.759264i $$0.274441\pi$$
−0.0802108 + 0.996778i $$0.525559\pi$$
$$270$$ 0 0
$$271$$ −4.86915 3.53764i −0.295780 0.214897i 0.429991 0.902833i $$-0.358517\pi$$
−0.725771 + 0.687937i $$0.758517\pi$$
$$272$$ 11.7140 8.51073i 0.710267 0.516039i
$$273$$ 0 0
$$274$$ −1.43456 −0.0866651
$$275$$ −2.14042 2.53350i −0.129072 0.152776i
$$276$$ 0 0
$$277$$ −8.66386 + 26.6646i −0.520561 + 1.60212i 0.252369 + 0.967631i $$0.418790\pi$$
−0.772930 + 0.634491i $$0.781210\pi$$
$$278$$ 1.01723 0.739059i 0.0610093 0.0443258i
$$279$$ 0 0
$$280$$ 0.275468 + 0.847802i 0.0164623 + 0.0506659i
$$281$$ −8.10523 24.9453i −0.483517 1.48811i −0.834117 0.551588i $$-0.814022\pi$$
0.350599 0.936526i $$-0.385978\pi$$
$$282$$ 0 0
$$283$$ −10.0324 + 7.28897i −0.596365 + 0.433284i −0.844587 0.535419i $$-0.820154\pi$$
0.248222 + 0.968703i $$0.420154\pi$$
$$284$$ −5.73502 + 17.6506i −0.340311 + 1.04737i
$$285$$ 0 0
$$286$$ −0.0513966 + 0.0828708i −0.00303915 + 0.00490025i
$$287$$ −22.0681 −1.30264
$$288$$ 0 0
$$289$$ 2.88536 2.09634i 0.169727 0.123314i
$$290$$ 0.108513 + 0.0788390i 0.00637208 + 0.00462959i
$$291$$ 0 0
$$292$$ −3.81183 11.7316i −0.223071 0.686540i
$$293$$ 24.0919 + 17.5038i 1.40746 + 1.02258i 0.993685 + 0.112202i $$0.0357902\pi$$
0.413776 + 0.910379i $$0.364210\pi$$
$$294$$ 0 0
$$295$$ 1.94473 5.98526i 0.113227 0.348475i
$$296$$ −0.829091 −0.0481899
$$297$$ 0 0
$$298$$ 0.821359 0.0475801
$$299$$ 0.462430 1.42321i 0.0267430 0.0823065i
$$300$$ 0 0
$$301$$ 12.5635 + 9.12794i 0.724150 + 0.526126i
$$302$$ 0.248578 + 0.765046i 0.0143041 + 0.0440234i
$$303$$ 0 0
$$304$$ −1.72974 1.25673i −0.0992077 0.0720786i
$$305$$ −5.23871 + 3.80614i −0.299967 + 0.217939i
$$306$$ 0 0
$$307$$ 13.5474 0.773194 0.386597 0.922249i $$-0.373650\pi$$
0.386597 + 0.922249i $$0.373650\pi$$
$$308$$ −15.0302 + 6.13148i −0.856423 + 0.349373i
$$309$$ 0 0
$$310$$ 0.0250201 0.0770039i 0.00142105 0.00437353i
$$311$$ 7.08052 5.14430i 0.401499 0.291706i −0.368652 0.929567i $$-0.620181\pi$$
0.770151 + 0.637861i $$0.220181\pi$$
$$312$$ 0 0
$$313$$ 5.00966 + 15.4181i 0.283162 + 0.871484i 0.986943 + 0.161067i $$0.0514936\pi$$
−0.703781 + 0.710417i $$0.748506\pi$$
$$314$$ −0.329672 1.01463i −0.0186045 0.0572586i
$$315$$ 0 0
$$316$$ 18.6996 13.5861i 1.05193 0.764275i
$$317$$ 1.81782 5.59467i 0.102099 0.314228i −0.886940 0.461885i $$-0.847173\pi$$
0.989039 + 0.147657i $$0.0471732\pi$$
$$318$$ 0 0
$$319$$ −2.57999 + 4.15992i −0.144452 + 0.232911i
$$320$$ 7.80247 0.436171
$$321$$ 0 0
$$322$$ −0.835672 + 0.607152i −0.0465702 + 0.0338352i
$$323$$ 1.60481 + 1.16596i 0.0892939 + 0.0648758i
$$324$$ 0 0
$$325$$ 0.0999755 + 0.307693i 0.00554564 + 0.0170677i
$$326$$ 0.560256 + 0.407050i 0.0310297 + 0.0225444i
$$327$$ 0 0
$$328$$ 1.00673 3.09838i 0.0555871 0.171080i
$$329$$ −3.59470 −0.198182
$$330$$ 0 0
$$331$$ 13.4772 0.740775 0.370387 0.928877i $$-0.379225\pi$$
0.370387 + 0.928877i $$0.379225\pi$$
$$332$$ 10.6934 32.9109i 0.586877 1.80622i
$$333$$ 0 0
$$334$$ −0.743848 0.540437i −0.0407016 0.0295714i
$$335$$ 2.18053 + 6.71098i 0.119135 + 0.366660i
$$336$$ 0 0
$$337$$ 12.2650 + 8.91103i 0.668116 + 0.485415i 0.869394 0.494119i $$-0.164509\pi$$
−0.201278 + 0.979534i $$0.564509\pi$$
$$338$$ −0.948100 + 0.688835i −0.0515698 + 0.0374677i
$$339$$ 0 0
$$340$$ −7.30008 −0.395902
$$341$$ 2.86949 + 0.705200i 0.155392 + 0.0381887i
$$342$$ 0 0
$$343$$ 6.04565 18.6066i 0.326435 1.00466i
$$344$$ −1.85471 + 1.34753i −0.0999993 + 0.0726537i
$$345$$ 0 0
$$346$$ 0.272272 + 0.837966i 0.0146374 + 0.0450493i
$$347$$ −5.36400 16.5087i −0.287955 0.886233i −0.985497 0.169690i $$-0.945723\pi$$
0.697543 0.716543i $$-0.254277\pi$$
$$348$$ 0 0
$$349$$ 3.95801 2.87566i 0.211867 0.153931i −0.476791 0.879017i $$-0.658200\pi$$
0.688658 + 0.725086i $$0.258200\pi$$
$$350$$ 0.0690094 0.212389i 0.00368871 0.0113527i
$$351$$ 0 0
$$352$$ −0.262986 3.58742i −0.0140172 0.191210i
$$353$$ −9.32665 −0.496408 −0.248204 0.968708i $$-0.579840\pi$$
−0.248204 + 0.968708i $$0.579840\pi$$
$$354$$ 0 0
$$355$$ 7.53836 5.47694i 0.400095 0.290686i
$$356$$ −7.57770 5.50552i −0.401617 0.291792i
$$357$$ 0 0
$$358$$ 0.509943 + 1.56944i 0.0269513 + 0.0829477i
$$359$$ 23.4423 + 17.0318i 1.23724 + 0.898904i 0.997411 0.0719119i $$-0.0229101\pi$$
0.239825 + 0.970816i $$0.422910\pi$$
$$360$$ 0 0
$$361$$ −5.78081 + 17.7915i −0.304253 + 0.936394i
$$362$$ 0.400710 0.0210608
$$363$$ 0 0
$$364$$ 1.58346 0.0829956
$$365$$ −1.91382 + 5.89013i −0.100174 + 0.308303i
$$366$$ 0 0
$$367$$ 11.2839 + 8.19820i 0.589013 + 0.427943i 0.841962 0.539537i $$-0.181401\pi$$
−0.252949 + 0.967480i $$0.581401\pi$$
$$368$$ 5.64662 + 17.3785i 0.294350 + 0.905917i
$$369$$ 0 0
$$370$$ 0.168034 + 0.122084i 0.00873568 + 0.00634684i
$$371$$ 20.5350 14.9196i 1.06612 0.774585i
$$372$$ 0 0
$$373$$ −22.0121 −1.13974 −0.569871 0.821734i $$-0.693007\pi$$
−0.569871 + 0.821734i $$0.693007\pi$$
$$374$$ 0.0807685 + 1.10177i 0.00417644 + 0.0569712i
$$375$$ 0 0
$$376$$ 0.163987 0.504701i 0.00845699 0.0260279i
$$377$$ 0.386302 0.280665i 0.0198956 0.0144550i
$$378$$ 0 0
$$379$$ −0.585450 1.80183i −0.0300726 0.0925538i 0.934894 0.354928i $$-0.115495\pi$$
−0.964966 + 0.262374i $$0.915495\pi$$
$$380$$ 0.333109 + 1.02520i 0.0170881 + 0.0525918i
$$381$$ 0 0
$$382$$ −0.903283 + 0.656273i −0.0462160 + 0.0335779i
$$383$$ −0.296274 + 0.911838i −0.0151389 + 0.0465928i −0.958341 0.285628i $$-0.907798\pi$$
0.943202 + 0.332221i $$0.107798\pi$$
$$384$$ 0 0
$$385$$ 7.91451 + 1.94505i 0.403361 + 0.0991292i
$$386$$ −2.11715 −0.107760
$$387$$ 0 0
$$388$$ 17.7372 12.8868i 0.900471 0.654230i
$$389$$ −5.28186 3.83750i −0.267801 0.194569i 0.445778 0.895143i $$-0.352927\pi$$
−0.713579 + 0.700575i $$0.752927\pi$$
$$390$$ 0 0
$$391$$ −5.23877 16.1233i −0.264936 0.815389i
$$392$$ 0.282206 + 0.205034i 0.0142535 + 0.0103558i
$$393$$ 0 0
$$394$$ 0.553040 1.70208i 0.0278618 0.0857497i
$$395$$ −11.6049 −0.583907
$$396$$ 0 0
$$397$$ −21.3621 −1.07213 −0.536066 0.844176i $$-0.680090\pi$$
−0.536066 + 0.844176i $$0.680090\pi$$
$$398$$ −0.623681 + 1.91949i −0.0312623 + 0.0962155i
$$399$$ 0 0
$$400$$ −3.19603 2.32205i −0.159802 0.116103i
$$401$$ −3.90987 12.0334i −0.195250 0.600917i −0.999974 0.00726766i $$-0.997687\pi$$
0.804724 0.593649i $$-0.202313\pi$$
$$402$$ 0 0
$$403$$ −0.233191 0.169423i −0.0116161 0.00843956i
$$404$$ −10.8145 + 7.85719i −0.538042 + 0.390910i
$$405$$ 0 0
$$406$$ −0.329598 −0.0163577
$$407$$ −3.99517 + 6.44173i −0.198033 + 0.319305i
$$408$$ 0 0
$$409$$ 1.54745 4.76256i 0.0765164 0.235493i −0.905481 0.424386i $$-0.860490\pi$$
0.981998 + 0.188893i $$0.0604899\pi$$
$$410$$ −0.660274 + 0.479717i −0.0326086 + 0.0236915i
$$411$$ 0 0
$$412$$ −9.60355 29.5567i −0.473133 1.45615i
$$413$$ 4.77883 + 14.7077i 0.235151 + 0.723719i
$$414$$ 0 0
$$415$$ −14.0559 + 10.2122i −0.689977 + 0.501297i
$$416$$ −0.108428 + 0.333709i −0.00531614 + 0.0163614i
$$417$$ 0 0
$$418$$ 0.151044 0.0616176i 0.00738781 0.00301382i
$$419$$ 9.31728 0.455179 0.227589 0.973757i $$-0.426916\pi$$
0.227589 + 0.973757i $$0.426916\pi$$
$$420$$ 0 0
$$421$$ −19.1562 + 13.9178i −0.933617 + 0.678313i −0.946876 0.321600i $$-0.895780\pi$$
0.0132587 + 0.999912i $$0.495780\pi$$
$$422$$ −0.955191 0.693987i −0.0464980 0.0337827i
$$423$$ 0 0
$$424$$ 1.15794 + 3.56376i 0.0562343 + 0.173071i
$$425$$ 2.96519 + 2.15434i 0.143833 + 0.104501i
$$426$$ 0 0
$$427$$ 4.91712 15.1333i 0.237956 0.732353i
$$428$$ −17.8941 −0.864944
$$429$$ 0 0
$$430$$ 0.574323 0.0276963
$$431$$ 7.94388 24.4488i 0.382643 1.17765i −0.555532 0.831495i $$-0.687485\pi$$
0.938176 0.346160i $$-0.112515\pi$$
$$432$$ 0 0
$$433$$ −16.0949 11.6937i −0.773474 0.561962i 0.129539 0.991574i $$-0.458650\pi$$
−0.903013 + 0.429613i $$0.858650\pi$$
$$434$$ 0.0614824 + 0.189223i 0.00295125 + 0.00908302i
$$435$$ 0 0
$$436$$ −17.3519 12.6069i −0.831005 0.603761i
$$437$$ −2.02526 + 1.47144i −0.0968814 + 0.0703884i
$$438$$ 0 0
$$439$$ −2.83831 −0.135465 −0.0677327 0.997704i $$-0.521577\pi$$
−0.0677327 + 0.997704i $$0.521577\pi$$
$$440$$ −0.634141 + 1.02247i −0.0302315 + 0.0487446i
$$441$$ 0 0
$$442$$ 0.0333006 0.102489i 0.00158395 0.00487489i
$$443$$ −21.9190 + 15.9251i −1.04141 + 0.756625i −0.970559 0.240862i $$-0.922570\pi$$
−0.0708460 + 0.997487i $$0.522570\pi$$
$$444$$ 0 0
$$445$$ 1.45321 + 4.47253i 0.0688889 + 0.212018i
$$446$$ 0.635271 + 1.95516i 0.0300810 + 0.0925797i
$$447$$ 0 0
$$448$$ −15.5114 + 11.2697i −0.732846 + 0.532443i
$$449$$ 8.08057 24.8694i 0.381346 1.17366i −0.557751 0.830009i $$-0.688335\pi$$
0.939097 0.343653i $$-0.111665\pi$$
$$450$$ 0 0
$$451$$ −19.2221 22.7522i −0.905135 1.07136i
$$452$$ 39.6255 1.86383
$$453$$ 0 0
$$454$$ −1.15669 + 0.840383i −0.0542861 + 0.0394412i
$$455$$ −0.643177 0.467296i −0.0301526 0.0219072i
$$456$$ 0 0
$$457$$ −4.35548 13.4048i −0.203741 0.627050i −0.999763 0.0217820i $$-0.993066\pi$$
0.796022 0.605268i $$-0.206934\pi$$
$$458$$ −1.78668 1.29810i −0.0834861 0.0606562i
$$459$$ 0 0
$$460$$ 2.84687 8.76177i 0.132736 0.408519i
$$461$$ 0.212479 0.00989612 0.00494806 0.999988i $$-0.498425\pi$$
0.00494806 + 0.999988i $$0.498425\pi$$
$$462$$ 0 0
$$463$$ −9.01059 −0.418758 −0.209379 0.977835i $$-0.567144\pi$$
−0.209379 + 0.977835i $$0.567144\pi$$
$$464$$ −1.80175 + 5.54522i −0.0836441 + 0.257430i
$$465$$ 0 0
$$466$$ 0.393899 + 0.286184i 0.0182470 + 0.0132572i
$$467$$ −1.83401 5.64451i −0.0848679 0.261197i 0.899613 0.436688i $$-0.143849\pi$$
−0.984481 + 0.175491i $$0.943849\pi$$
$$468$$ 0 0
$$469$$ −14.0281 10.1920i −0.647758 0.470624i
$$470$$ −0.107553 + 0.0781419i −0.00496105 + 0.00360442i
$$471$$ 0 0
$$472$$ −2.28299 −0.105083
$$473$$ 1.53241 + 20.9038i 0.0704604 + 0.961156i
$$474$$ 0 0
$$475$$ 0.167245 0.514727i 0.00767373 0.0236173i
$$476$$ 14.5127 10.5441i 0.665187 0.483286i
$$477$$ 0 0
$$478$$ 0.0258831 + 0.0796599i 0.00118386 + 0.00364356i
$$479$$ −9.48284 29.1852i −0.433282 1.33351i −0.894837 0.446394i $$-0.852708\pi$$
0.461555 0.887112i $$-0.347292\pi$$
$$480$$ 0 0
$$481$$ 0.598198 0.434616i 0.0272755 0.0198168i
$$482$$ −0.320229 + 0.985563i −0.0145860 + 0.0448912i
$$483$$ 0 0
$$484$$ −19.4134 10.1553i −0.882427 0.461607i
$$485$$ −11.0077 −0.499832
$$486$$ 0 0
$$487$$ −32.3998 + 23.5398i −1.46818 + 1.06669i −0.487038 + 0.873381i $$0.661923\pi$$
−0.981138 + 0.193311i $$0.938077\pi$$
$$488$$ 1.90042 + 1.38074i 0.0860281 + 0.0625031i
$$489$$ 0 0
$$490$$ −0.0270040 0.0831097i −0.00121992 0.00375452i
$$491$$ 15.7927 + 11.4740i 0.712713 + 0.517816i 0.884048 0.467397i $$-0.154808\pi$$
−0.171335 + 0.985213i $$0.554808\pi$$
$$492$$ 0 0
$$493$$ 1.67161 5.14469i 0.0752856 0.231705i
$$494$$ −0.0159128 −0.000715950
$$495$$ 0 0
$$496$$ 3.51962 0.158036
$$497$$ −7.07561 + 21.7765i −0.317384 + 0.976809i
$$498$$ 0 0
$$499$$ −7.50690 5.45408i −0.336055 0.244158i 0.406941 0.913455i $$-0.366596\pi$$
−0.742995 + 0.669296i $$0.766596\pi$$
$$500$$ 0.615482 + 1.89426i 0.0275252 + 0.0847138i
$$501$$ 0 0
$$502$$ 0.0654117 + 0.0475243i 0.00291946 + 0.00212112i
$$503$$ −15.7812 + 11.4657i −0.703651 + 0.511232i −0.881119 0.472894i $$-0.843209\pi$$
0.177468 + 0.984126i $$0.443209\pi$$
$$504$$ 0 0
$$505$$ 6.71144 0.298655
$$506$$ −1.35387 0.332726i −0.0601871 0.0147915i
$$507$$ 0 0
$$508$$ 7.45356 22.9397i 0.330698 1.01779i
$$509$$ 8.55440 6.21513i 0.379167 0.275481i −0.381835 0.924231i $$-0.624708\pi$$
0.761002 + 0.648750i $$0.224708\pi$$
$$510$$ 0 0
$$511$$ −4.70287 14.4739i −0.208043 0.640289i
$$512$$ −2.20971 6.80077i −0.0976561 0.300555i
$$513$$ 0 0
$$514$$ 1.17729 0.855351i 0.0519280 0.0377279i
$$515$$ −4.82169 + 14.8396i −0.212469 + 0.653912i
$$516$$ 0 0
$$517$$ −3.13112 3.70614i −0.137707 0.162996i
$$518$$ −0.510390 −0.0224252
$$519$$ 0 0
$$520$$ 0.0949500 0.0689852i 0.00416383 0.00302520i
$$521$$ −6.77644 4.92337i −0.296881 0.215697i 0.429366 0.903131i $$-0.358737\pi$$
−0.726247 + 0.687434i $$0.758737\pi$$
$$522$$ 0 0
$$523$$ 10.6523 + 32.7846i 0.465795 + 1.43357i 0.857980 + 0.513683i $$0.171719\pi$$
−0.392186 + 0.919886i $$0.628281\pi$$
$$524$$ −30.1391 21.8974i −1.31663 0.956591i
$$525$$ 0 0
$$526$$ 0.598043 1.84059i 0.0260759 0.0802534i
$$527$$ −3.26541 −0.142243
$$528$$ 0 0
$$529$$ −1.60536 −0.0697983
$$530$$ 0.290083 0.892783i 0.0126004 0.0387800i
$$531$$ 0 0
$$532$$ −2.14301 1.55698i −0.0929111 0.0675038i
$$533$$ 0.897834 + 2.76325i 0.0388895 + 0.119690i
$$534$$ 0 0
$$535$$ 7.26833 + 5.28075i 0.314237 + 0.228307i
$$536$$ 2.07092 1.50461i 0.0894502 0.0649894i
$$537$$ 0 0
$$538$$ −2.75213 −0.118653
$$539$$ 2.95291 1.20462i 0.127191 0.0518869i
$$540$$ 0 0
$$541$$ −7.43553 + 22.8842i −0.319678 + 0.983868i 0.654108 + 0.756402i $$0.273044\pi$$
−0.973786 + 0.227467i $$0.926956\pi$$
$$542$$ 0.442504 0.321498i 0.0190072 0.0138095i
$$543$$ 0 0
$$544$$ 1.22836 + 3.78051i 0.0526656 + 0.162088i
$$545$$ 3.32766 + 10.2415i 0.142541 + 0.438697i
$$546$$ 0 0
$$547$$ 17.9233 13.0220i 0.766343 0.556781i −0.134506 0.990913i $$-0.542945\pi$$
0.900849 + 0.434132i $$0.142945\pi$$
$$548$$ −9.71563 + 29.9016i −0.415031 + 1.27733i
$$549$$ 0 0
$$550$$ 0.279083 0.113850i 0.0119001 0.00485459i
$$551$$ −0.798784 −0.0340293
$$552$$ 0 0
$$553$$ 23.0707 16.7619i 0.981068 0.712787i
$$554$$ −2.06135 1.49766i −0.0875782 0.0636293i
$$555$$ 0 0
$$556$$ −8.51553 26.2081i −0.361139 1.11147i
$$557$$ −6.22550 4.52309i −0.263783 0.191649i 0.448030 0.894018i $$-0.352126\pi$$
−0.711813 + 0.702369i $$0.752126\pi$$
$$558$$ 0 0
$$559$$ 0.631809 1.94451i 0.0267227 0.0822439i
$$560$$ 9.70768 0.410224
$$561$$ 0 0
$$562$$ 2.38367 0.100549
$$563$$ −10.0877 + 31.0469i −0.425148 + 1.30847i 0.477705 + 0.878520i $$0.341469\pi$$
−0.902853 + 0.429950i $$0.858531\pi$$
$$564$$ 0 0
$$565$$ −16.0953 11.6939i −0.677135 0.491967i
$$566$$ −0.348252 1.07181i −0.0146381 0.0450515i
$$567$$ 0 0
$$568$$ −2.73466 1.98685i −0.114744 0.0833662i
$$569$$ 13.2440 9.62230i 0.555215 0.403388i −0.274489 0.961590i $$-0.588509\pi$$
0.829705 + 0.558203i $$0.188509\pi$$
$$570$$ 0 0
$$571$$ 14.2204 0.595107 0.297554 0.954705i $$-0.403829\pi$$
0.297554 + 0.954705i $$0.403829\pi$$
$$572$$ 1.37925 + 1.63254i 0.0576693 + 0.0682600i
$$573$$ 0 0
$$574$$ 0.619742 1.90737i 0.0258675 0.0796121i
$$575$$ −3.74205 + 2.71876i −0.156054 + 0.113380i
$$576$$ 0 0
$$577$$ 6.75349 + 20.7851i 0.281151 + 0.865295i 0.987526 + 0.157457i $$0.0503295\pi$$
−0.706374 + 0.707838i $$0.749671\pi$$
$$578$$ 0.100159 + 0.308257i 0.00416605 + 0.0128218i
$$579$$ 0 0
$$580$$ 2.37820 1.72787i 0.0987495 0.0717457i
$$581$$ 13.1930 40.6040i 0.547340 1.68454i
$$582$$ 0 0
$$583$$ 33.2688 + 8.17608i 1.37785 + 0.338619i
$$584$$ 2.24670 0.0929690
$$585$$ 0 0
$$586$$ −2.18945 + 1.59073i −0.0904452 + 0.0657123i
$$587$$ 31.1788 + 22.6527i 1.28689 + 0.934977i 0.999738 0.0229093i $$-0.00729289\pi$$
0.287148 + 0.957886i $$0.407293\pi$$
$$588$$ 0 0
$$589$$ 0.149003 + 0.458585i 0.00613957 + 0.0188957i
$$590$$ 0.462699 + 0.336170i 0.0190490 + 0.0138399i
$$591$$ 0 0
$$592$$ −2.79005 + 8.58689i −0.114670 + 0.352919i
$$593$$ 30.7989 1.26476 0.632379 0.774659i $$-0.282079\pi$$
0.632379 + 0.774659i $$0.282079\pi$$
$$594$$ 0 0
$$595$$ −9.00651 −0.369231
$$596$$ 5.56268 17.1202i 0.227856 0.701270i
$$597$$ 0 0
$$598$$ 0.110023 + 0.0799367i 0.00449919 + 0.00326886i
$$599$$ −11.6618 35.8914i −0.476489 1.46648i −0.843939 0.536439i $$-0.819769\pi$$
0.367451 0.930043i $$-0.380231\pi$$
$$600$$ 0 0
$$601$$ 18.5724 + 13.4937i 0.757585 + 0.550417i 0.898169 0.439651i $$-0.144898\pi$$
−0.140584 + 0.990069i $$0.544898\pi$$
$$602$$ −1.14176 + 0.829539i −0.0465348 + 0.0338095i
$$603$$ 0 0
$$604$$ 17.6299 0.717351
$$605$$ 4.88849 + 9.85407i 0.198745 + 0.400625i
$$606$$ 0 0
$$607$$ 3.47703 10.7012i 0.141128 0.434348i −0.855365 0.518027i $$-0.826667\pi$$
0.996493 + 0.0836784i $$0.0266668\pi$$
$$608$$ 0.474874 0.345016i 0.0192587 0.0139923i
$$609$$ 0 0
$$610$$ −0.181850 0.559676i −0.00736288 0.0226606i
$$611$$ 0.146250 + 0.450110i 0.00591662 + 0.0182095i
$$612$$ 0 0
$$613$$ −36.2214 + 26.3164i −1.46297 + 1.06291i −0.480390 + 0.877055i $$0.659505\pi$$
−0.982578 + 0.185853i $$0.940495\pi$$
$$614$$ −0.380455 + 1.17092i −0.0153539 + 0.0472545i
$$615$$ 0 0
$$616$$ −0.216158 2.94863i −0.00870926 0.118804i
$$617$$ −16.4108 −0.660673 −0.330337 0.943863i $$-0.607162\pi$$
−0.330337 + 0.943863i $$0.607162\pi$$
$$618$$ 0 0
$$619$$ −1.21920 + 0.885800i −0.0490037 + 0.0356033i −0.612017 0.790844i $$-0.709642\pi$$
0.563014 + 0.826448i $$0.309642\pi$$
$$620$$ −1.43560 1.04302i −0.0576550 0.0418888i
$$621$$ 0 0
$$622$$ 0.245784 + 0.756446i 0.00985505 + 0.0303307i
$$623$$ −9.34903 6.79247i −0.374561 0.272134i
$$624$$ 0 0
$$625$$ 0.309017 0.951057i 0.0123607 0.0380423i
$$626$$ −1.47329 −0.0588847
$$627$$ 0 0
$$628$$ −23.3813 −0.933015
$$629$$ 2.58853 7.96667i 0.103211 0.317652i
$$630$$ 0 0
$$631$$ 26.9869 + 19.6071i 1.07433 + 0.780548i 0.976686 0.214674i $$-0.0688688\pi$$
0.0976458 + 0.995221i $$0.468869\pi$$
$$632$$ 1.30092 + 4.00382i 0.0517478 + 0.159263i
$$633$$ 0 0
$$634$$ 0.432504 + 0.314232i 0.0171769 + 0.0124798i
$$635$$ −9.79730 + 7.11816i −0.388794 + 0.282475i
$$636$$ 0 0
$$637$$ −0.311095 −0.0123260
$$638$$ −0.287092 0.339815i −0.0113661 0.0134534i
$$639$$ 0 0
$$640$$ −0.889407 + 2.73731i −0.0351569 + 0.108202i
$$641$$ 6.96411 5.05972i 0.275066 0.199847i −0.441697 0.897164i $$-0.645623\pi$$
0.716762 + 0.697318i $$0.245623\pi$$
$$642$$ 0 0
$$643$$ −3.66045 11.2657i −0.144354 0.444276i 0.852573 0.522608i $$-0.175041\pi$$
−0.996927 + 0.0783317i $$0.975041\pi$$
$$644$$ 6.99568 + 21.5305i 0.275668 + 0.848420i
$$645$$ 0 0
$$646$$ −0.145843 + 0.105961i −0.00573813 + 0.00416900i
$$647$$ 6.86541 21.1295i 0.269907 0.830688i −0.720615 0.693335i $$-0.756141\pi$$
0.990522 0.137353i $$-0.0438595\pi$$
$$648$$ 0 0
$$649$$ −11.0011 + 17.7379i −0.431831 + 0.696275i
$$650$$ −0.0294019 −0.00115324
$$651$$ 0 0
$$652$$ 12.2788 8.92107i 0.480875 0.349376i
$$653$$ 5.54195 + 4.02646i 0.216873 + 0.157568i 0.690918 0.722933i $$-0.257207\pi$$
−0.474045 + 0.880501i $$0.657207\pi$$
$$654$$ 0 0
$$655$$ 5.77993 + 17.7888i 0.225841 + 0.695066i
$$656$$ −28.7021 20.8533i −1.12063 0.814185i
$$657$$ 0 0
$$658$$ 0.100951 0.310694i 0.00393547 0.0121121i
$$659$$ 10.7882 0.420248 0.210124 0.977675i $$-0.432613\pi$$
0.210124 + 0.977675i $$0.432613\pi$$
$$660$$ 0 0
$$661$$ 24.3271 0.946214 0.473107 0.881005i $$-0.343132\pi$$
0.473107 + 0.881005i $$0.343132\pi$$
$$662$$ −0.378483 + 1.16485i −0.0147102 + 0.0452732i
$$663$$ 0 0
$$664$$ 5.09900 + 3.70464i 0.197880 + 0.143768i
$$665$$ 0.410975 + 1.26485i 0.0159369 + 0.0490488i
$$666$$ 0 0
$$667$$ 5.52292 + 4.01263i 0.213848 + 0.155370i
$$668$$ −16.3025 + 11.8444i −0.630761 + 0.458275i
$$669$$ 0 0
$$670$$ −0.641274 −0.0247746
$$671$$ 19.8855 8.11216i 0.767669 0.313167i
$$672$$ 0 0
$$673$$ 10.5821 32.5684i 0.407910 1.25542i −0.510530 0.859860i $$-0.670551\pi$$
0.918441 0.395559i $$-0.129449\pi$$
$$674$$ −1.11463 + 0.809826i −0.0429340 + 0.0311933i
$$675$$ 0 0
$$676$$ 7.93684 + 24.4271i 0.305263 + 0.939503i
$$677$$ 5.47487 + 16.8499i 0.210416 + 0.647595i 0.999447 + 0.0332415i $$0.0105831\pi$$
−0.789031 + 0.614353i $$0.789417\pi$$
$$678$$ 0 0
$$679$$ 21.8834 15.8992i 0.839807 0.610156i
$$680$$ 0.410869 1.26452i 0.0157561 0.0484923i
$$681$$ 0 0
$$682$$ −0.141536 + 0.228209i −0.00541968 + 0.00873858i
$$683$$ −19.2788 −0.737683 −0.368842 0.929492i $$-0.620246\pi$$
−0.368842 + 0.929492i $$0.620246\pi$$
$$684$$ 0 0
$$685$$ 12.7707 9.27843i 0.487942 0.354511i
$$686$$ 1.43841 + 1.04507i 0.0549187 + 0.0399008i
$$687$$ 0 0
$$688$$ 7.71486 + 23.7439i 0.294126 + 0.905228i
$$689$$ −2.70361 1.96429i −0.102999 0.0748334i
$$690$$ 0 0
$$691$$ −8.42752 + 25.9372i −0.320598 + 0.986699i 0.652791 + 0.757538i $$0.273598\pi$$
−0.973389 + 0.229161i $$0.926402\pi$$
$$692$$ 19.3103 0.734067
$$693$$ 0 0
$$694$$ 1.57750 0.0598812
$$695$$ −4.27542 + 13.1584i −0.162176 + 0.499126i
$$696$$ 0 0
$$697$$ 26.6290 + 19.3471i 1.00865 + 0.732824i
$$698$$ 0.137393 + 0.422853i 0.00520041 + 0.0160052i
$$699$$ 0 0
$$700$$ −3.95961 2.87683i −0.149659 0.108734i
$$701$$ −31.7252 + 23.0497i −1.19824 + 0.870574i −0.994111 0.108369i $$-0.965437\pi$$
−0.204132 + 0.978943i $$0.565437\pi$$
$$702$$ 0 0
$$703$$ −1.23693 −0.0466519
$$704$$ −25.1301 6.17592i −0.947126 0.232764i
$$705$$ 0 0
$$706$$ 0.261922 0.806113i 0.00985757 0.0303385i
$$707$$ −13.3425 + 9.69386i −0.501794 + 0.364575i
$$708$$ 0 0
$$709$$ 8.72458 + 26.8515i 0.327658 + 1.00843i 0.970226 + 0.242200i $$0.0778691\pi$$
−0.642568 + 0.766229i $$0.722131\pi$$
$$710$$ 0.261677 + 0.805359i 0.00982057 + 0.0302246i
$$711$$ 0 0
$$712$$ 1.38016 1.00275i 0.0517239 0.0375796i
$$713$$ 1.27344 3.91924i 0.0476906 0.146777i
$$714$$ 0 0
$$715$$ −0.0784503 1.07015i −0.00293387 0.0400212i
$$716$$ 36.1666 1.35161
$$717$$ 0 0
$$718$$ −2.13041 + 1.54784i −0.0795063 + 0.0577647i
$$719$$ 34.1565 + 24.8162i 1.27382 + 0.925486i 0.999348 0.0361078i $$-0.0114960\pi$$
0.274475 + 0.961594i $$0.411496\pi$$
$$720$$ 0 0
$$721$$ −11.8484 36.4657i −0.441259 1.35806i
$$722$$ −1.37540 0.999284i −0.0511869 0.0371895i
$$723$$ 0 0
$$724$$ 2.71382 8.35228i 0.100858 0.310410i
$$725$$ −1.47591 −0.0548137
$$726$$ 0 0
$$727$$ 5.10543 0.189350 0.0946750 0.995508i $$-0.469819\pi$$
0.0946750 + 0.995508i $$0.469819\pi$$
$$728$$ −0.0891214 + 0.274287i −0.00330306 + 0.0101658i
$$729$$ 0 0
$$730$$ −0.455344 0.330827i −0.0168531 0.0122445i
$$731$$ −7.15763 22.0289i −0.264734 0.814769i
$$732$$ 0 0
$$733$$ 15.5996 + 11.3338i 0.576185 + 0.418623i 0.837347 0.546672i $$-0.184106\pi$$
−0.261162 + 0.965295i $$0.584106\pi$$
$$734$$ −1.02547 + 0.745045i −0.0378507 + 0.0275001i
$$735$$ 0 0
$$736$$ −5.01652 −0.184911
$$737$$ −1.71105 23.3406i −0.0630274 0.859762i
$$738$$ 0 0
$$739$$ −11.0939 + 34.1435i −0.408096 + 1.25599i 0.510187 + 0.860064i $$0.329576\pi$$
−0.918282 + 0.395926i $$0.870424\pi$$
$$740$$ 3.68270 2.67564i 0.135379 0.0983584i
$$741$$ 0 0
$$742$$ 0.712826 + 2.19385i 0.0261687 + 0.0805389i
$$743$$ −3.81228 11.7330i −0.139859 0.430442i 0.856455 0.516221i $$-0.172662\pi$$
−0.996314 + 0.0857798i $$0.972662\pi$$
$$744$$ 0 0
$$745$$ −7.31184 + 5.31236i −0.267885 + 0.194630i
$$746$$ 0.618169 1.90253i 0.0226328 0.0696565i
$$747$$ 0 0
$$748$$ 23.5120 + 5.77826i 0.859684 + 0.211274i
$$749$$ −22.0769 −0.806674
$$750$$ 0 0
$$751$$ −5.50024 + 3.99616i −0.200707 + 0.145822i −0.683599 0.729858i $$-0.739586\pi$$
0.482892 + 0.875680i $$0.339586\pi$$
$$752$$ −4.67533 3.39683i −0.170492 0.123870i
$$753$$ 0 0
$$754$$ 0.0134096 + 0.0412705i 0.000488349 + 0.00150298i
$$755$$ −7.16102 5.20278i −0.260616 0.189349i
$$756$$ 0 0
$$757$$ −3.16082 + 9.72801i −0.114882 + 0.353571i −0.991922 0.126846i $$-0.959515\pi$$
0.877040 + 0.480417i $$0.159515\pi$$
$$758$$ 0.172176 0.00625370
$$759$$ 0 0
$$760$$ −0.196335 −0.00712181
$$761$$ −7.57503 + 23.3136i −0.274595 + 0.845116i 0.714732 + 0.699399i $$0.246549\pi$$
−0.989326 + 0.145717i $$0.953451\pi$$
$$762$$ 0 0
$$763$$ −21.4080 15.5538i −0.775022 0.563086i
$$764$$ 7.56166 + 23.2724i 0.273571 + 0.841966i
$$765$$ 0 0
$$766$$ −0.0704909 0.0512147i −0.00254694 0.00185046i
$$767$$ 1.64720 1.19676i 0.0594768 0.0432125i
$$768$$ 0 0
$$769$$ 27.2852 0.983930 0.491965 0.870615i $$-0.336279\pi$$
0.491965 + 0.870615i $$0.336279\pi$$
$$770$$ −0.390378 + 0.629437i −0.0140682 + 0.0226833i
$$771$$ 0 0
$$772$$ −14.3385 + 44.1293i −0.516053 + 1.58825i
$$773$$ −7.01865 + 5.09935i −0.252443 + 0.183411i −0.706809 0.707404i $$-0.749866\pi$$
0.454366 + 0.890815i $$0.349866\pi$$
$$774$$ 0 0
$$775$$ 0.275312 + 0.847323i 0.00988950 + 0.0304367i
$$776$$ 1.23397 + 3.79776i 0.0442968 + 0.136332i
$$777$$ 0 0
$$778$$ 0.480011 0.348748i 0.0172092 0.0125032i
$$779$$ 1.50195 4.62253i 0.0538130 0.165619i
$$780$$ 0 0
$$781$$ −28.6147 + 11.6732i −1.02391 + 0.417700i
$$782$$ 1.54067 0.0550944
$$783$$ 0 0
$$784$$ 3.07321 2.23282i 0.109758 0.0797436i
$$785$$ 9.49715 + 6.90008i 0.338968