LMFDB - Embedded newform 161.2.g.a.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(45,161)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.2
Character	$\chi$	$=$	161.68
Dual form			161.2.g.a.45.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.23299 + 2.13559i) q^{2} +(0.854402 - 0.493289i) q^{3} +(-2.04051 - 3.53426i) q^{4} +(1.24346 - 2.15373i) q^{5} +2.43287i q^{6} +(2.57635 + 0.602017i) q^{7} +5.13171 q^{8} +(-1.01333 + 1.75514i) q^{9} +(3.06632 + 5.31103i) q^{10} +(3.89415 - 2.24829i) q^{11} +(-3.48683 - 2.01312i) q^{12} +2.10932i q^{13} +(-4.46226 + 4.75976i) q^{14} -2.45353i q^{15} +(-2.24632 + 3.89073i) q^{16} +(-2.00823 - 3.47836i) q^{17} +(-2.49885 - 4.32813i) q^{18} +(-2.91949 + 5.05671i) q^{19} -10.1491 q^{20} +(2.49821 - 0.756521i) q^{21} +11.0884i q^{22} +(0.792981 - 4.72982i) q^{23} +(4.38455 - 2.53142i) q^{24} +(-0.592363 - 1.02600i) q^{25} +(-4.50465 - 2.60076i) q^{26} +4.95920i q^{27} +(-3.12937 - 10.3339i) q^{28} +2.64981 q^{29} +(5.23975 + 3.02517i) q^{30} +(-4.85302 + 2.80189i) q^{31} +(-0.407637 - 0.706048i) q^{32} +(2.21811 - 3.84188i) q^{33} +9.90448 q^{34} +(4.50016 - 4.80017i) q^{35} +8.27083 q^{36} +(-0.674116 - 0.389201i) q^{37} +(-7.19938 - 12.4697i) q^{38} +(1.04051 + 1.80221i) q^{39} +(6.38106 - 11.0523i) q^{40} +1.68118i q^{41} +(-1.46463 + 6.26793i) q^{42} -8.94389i q^{43} +(-15.8921 - 9.17528i) q^{44} +(2.52006 + 4.36488i) q^{45} +(9.12323 + 7.52528i) q^{46} +(-6.98642 - 4.03361i) q^{47} +4.43234i q^{48} +(6.27515 + 3.10201i) q^{49} +2.92150 q^{50} +(-3.43167 - 1.98128i) q^{51} +(7.45489 - 4.30408i) q^{52} +(-5.49706 + 3.17373i) q^{53} +(-10.5908 - 6.11462i) q^{54} -11.1826i q^{55} +(13.2211 + 3.08938i) q^{56} +5.76061i q^{57} +(-3.26717 + 5.65891i) q^{58} +(-10.5475 + 6.08961i) q^{59} +(-8.67142 + 5.00645i) q^{60} +(2.93570 - 5.08478i) q^{61} -13.8188i q^{62} +(-3.66732 + 3.91181i) q^{63} -6.97482 q^{64} +(4.54291 + 2.62285i) q^{65} +(5.46980 + 9.47397i) q^{66} +(-13.6208 + 7.86395i) q^{67} +(-8.19562 + 14.1952i) q^{68} +(-1.65564 - 4.43234i) q^{69} +(4.70259 + 15.5290i) q^{70} +5.33546 q^{71} +(-5.20013 + 9.00688i) q^{72} +(3.15749 - 1.82298i) q^{73} +(1.66235 - 0.959758i) q^{74} +(-1.01223 - 0.584413i) q^{75} +23.8290 q^{76} +(11.3862 - 3.44803i) q^{77} -5.13171 q^{78} +(4.37340 + 2.52498i) q^{79} +(5.58639 + 9.67591i) q^{80} +(-0.593674 - 1.02827i) q^{81} +(-3.59033 - 2.07288i) q^{82} -0.851415 q^{83} +(-7.77135 - 7.28563i) q^{84} -9.98859 q^{85} +(19.1005 + 11.0277i) q^{86} +(2.26400 - 1.30712i) q^{87} +(19.9836 - 11.5376i) q^{88} +(3.97758 - 6.88938i) q^{89} -12.4288 q^{90} +(-1.26985 + 5.43435i) q^{91} +(-18.3345 + 6.84862i) q^{92} +(-2.76429 + 4.78788i) q^{93} +(17.2283 - 9.94677i) q^{94} +(7.26051 + 12.5756i) q^{95} +(-0.696572 - 0.402166i) q^{96} -2.72009 q^{97} +(-14.3618 + 9.57643i) q^{98} +9.11304i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) $ 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.23299	+	2.13559i	−0.871852	+	1.51009i	−0.0117739	+	0.999931i	$0.503748\pi$
$2$	−1.23299	+	2.13559i	−0.871852	+	1.51009i	−0.860078	+	0.510162i	$0.829586\pi$
$3$	0.854402	−	0.493289i	0.493289	−	0.284801i	−0.232649	−	0.972561i	$-0.574739\pi$
$3$	0.854402	−	0.493289i	0.493289	−	0.284801i	0.725938	+	0.687760i	$0.241406\pi$
$4$	−2.04051	−	3.53426i	−1.02025	−	1.76713i
$5$	1.24346	−	2.15373i	0.556090	−	0.963176i	−0.441728	−	0.897149i	$-0.645634\pi$
$5$	1.24346	−	2.15373i	0.556090	−	0.963176i	0.997818	−	0.0660272i	$-0.0210324\pi$
$6$			2.43287i			0.993217i
$7$	2.57635	+	0.602017i	0.973768	+	0.227541i
$7$	2.57635	+	0.602017i	0.973768	+	0.227541i
$8$	5.13171			1.81433
$9$	−1.01333	+	1.75514i	−0.337777	+	0.585047i
$10$	3.06632	+	5.31103i	0.969657	+	1.67950i
$11$	3.89415	−	2.24829i	1.17413	−	0.677884i	0.219480	−	0.975617i	$-0.429564\pi$
$11$	3.89415	−	2.24829i	1.17413	−	0.677884i	0.954649	+	0.297733i	$0.0962305\pi$
$12$	−3.48683	−	2.01312i	−1.00656	−	0.581138i
$13$			2.10932i			0.585021i	0.956262	+	0.292510i	$0.0944906\pi$
$13$			2.10932i			0.585021i	−0.956262	+	0.292510i	$0.905509\pi$
$14$	−4.46226	+	4.75976i	−1.19259	+	1.27210i
$15$		−	2.45353i		−	0.633500i
$16$	−2.24632	+	3.89073i	−0.561579	+	0.972684i
$17$	−2.00823	−	3.47836i	−0.487068	−	0.843626i	0.512822	−	0.858495i	$-0.328600\pi$
$17$	−2.00823	−	3.47836i	−0.487068	−	0.843626i	−0.999889	+	0.0148691i	$0.995267\pi$
$18$	−2.49885	−	4.32813i	−0.588983	−	1.02015i
$19$	−2.91949	+	5.05671i	−0.669777	+	1.16009i	0.308189	+	0.951325i	$0.400277\pi$
$19$	−2.91949	+	5.05671i	−0.669777	+	1.16009i	−0.977966	+	0.208763i	$0.933056\pi$
$20$	−10.1491			−2.26941
$21$	2.49821	−	0.756521i	0.545153	−	0.165086i
$22$			11.0884i			2.36406i
$23$	0.792981	−	4.72982i	0.165348	−	0.986235i
$23$	0.792981	−	4.72982i	0.165348	−	0.986235i
$24$	4.38455	−	2.53142i	0.894992	−	0.516724i
$25$	−0.592363	−	1.02600i	−0.118473	−	0.205201i
$26$	−4.50465	−	2.60076i	−0.883435	−	0.510052i
$27$			4.95920i			0.954398i
$28$	−3.12937	−	10.3339i	−0.591396	−	1.95292i
$29$	2.64981			0.492057			0.246028	−	0.969263i	$-0.420874\pi$
$29$	2.64981			0.492057			0.246028	+	0.969263i	$0.420874\pi$
$30$	5.23975	+	3.02517i	0.956643	+	0.552318i
$31$	−4.85302	+	2.80189i	−0.871628	+	0.503234i	−0.867889	−	0.496759i	$-0.834523\pi$
$31$	−4.85302	+	2.80189i	−0.871628	+	0.503234i	−0.00373884	+	0.999993i	$0.501190\pi$
$32$	−0.407637	−	0.706048i	−0.0720607	−	0.124813i
$33$	2.21811	−	3.84188i	0.386124	−	0.668786i
$34$	9.90448			1.69860
$35$	4.50016	−	4.80017i	0.760665	−	0.811378i
$36$	8.27083			1.37847
$37$	−0.674116	−	0.389201i	−0.110824	−	0.0639842i	0.443563	−	0.896243i	$-0.353714\pi$
$37$	−0.674116	−	0.389201i	−0.110824	−	0.0639842i	−0.554387	+	0.832259i	$0.687047\pi$
$38$	−7.19938	−	12.4697i	−1.16789	−	2.02285i
$39$	1.04051	+	1.80221i	0.166614	+	0.288584i
$40$	6.38106	−	11.0523i	1.00893	−	1.74752i
$41$			1.68118i			0.262557i	0.991346	+	0.131278i	$0.0419082\pi$
$41$			1.68118i			0.262557i	−0.991346	+	0.131278i	$0.958092\pi$
$42$	−1.46463	+	6.26793i	−0.225998	+	0.967163i
$43$		−	8.94389i		−	1.36393i	−0.731384	−	0.681965i	$-0.761125\pi$
$43$		−	8.94389i		−	1.36393i	0.731384	−	0.681965i	$-0.238875\pi$
$44$	−15.8921	−	9.17528i	−2.39582	−	1.38323i
$45$	2.52006	+	4.36488i	0.375669	+	0.650678i
$46$	9.12323	+	7.52528i	1.34515	+	1.10954i
$47$	−6.98642	−	4.03361i	−1.01907	−	0.588363i	−0.105239	−	0.994447i	$-0.533561\pi$
$47$	−6.98642	−	4.03361i	−1.01907	−	0.588363i	−0.913836	+	0.406084i	$0.866894\pi$
$48$			4.43234i			0.639753i
$49$	6.27515	+	3.10201i	0.896450	+	0.443145i
$50$	2.92150			0.413162
$51$	−3.43167	−	1.98128i	−0.480531	−	0.277434i
$52$	7.45489	−	4.30408i	1.03381	−	0.596869i
$53$	−5.49706	+	3.17373i	−0.755079	+	0.435945i	−0.827526	−	0.561427i	$-0.810253\pi$
$53$	−5.49706	+	3.17373i	−0.755079	+	0.435945i	0.0724468	+	0.997372i	$0.476919\pi$
$54$	−10.5908	−	6.11462i	−1.44123	−	0.832094i
$55$		−	11.1826i		−	1.50786i
$56$	13.2211	+	3.08938i	1.76674	+	0.412836i
$57$			5.76061i			0.763012i
$58$	−3.26717	+	5.65891i	−0.429001	+	0.743051i
$59$	−10.5475	+	6.08961i	−1.37317	+	0.792799i	−0.991326	−	0.131428i	$-0.958044\pi$
$59$	−10.5475	+	6.08961i	−1.37317	+	0.792799i	−0.381843	+	0.924227i	$0.624711\pi$
$60$	−8.67142	+	5.00645i	−1.11948	+	0.646330i
$61$	2.93570	−	5.08478i	0.375878	−	0.651039i	−0.614580	−	0.788854i	$-0.710675\pi$
$61$	2.93570	−	5.08478i	0.375878	−	0.651039i	0.990458	+	0.137815i	$0.0440080\pi$
$62$		−	13.8188i		−	1.75498i
$63$	−3.66732	+	3.91181i	−0.462039	+	0.492842i
$64$	−6.97482			−0.871853
$65$	4.54291	+	2.62285i	0.563478	+	0.325324i
$66$	5.46980	+	9.47397i	0.673286	+	1.16617i
$67$	−13.6208	+	7.86395i	−1.66404	+	0.960734i	−0.693284	+	0.720664i	$0.743837\pi$
$67$	−13.6208	+	7.86395i	−1.66404	+	0.960734i	−0.970756	+	0.240070i	$0.922830\pi$
$68$	−8.19562	+	14.1952i	−0.993864	+	1.72142i
$69$	−1.65564	−	4.43234i	−0.199316	−	0.533591i
$70$	4.70259	+	15.5290i	0.562067	+	1.85608i
$71$	5.33546			0.633203			0.316601	−	0.948559i	$-0.397458\pi$
$71$	5.33546			0.633203			0.316601	+	0.948559i	$0.397458\pi$
$72$	−5.20013	+	9.00688i	−0.612841	+	1.06147i
$73$	3.15749	−	1.82298i	0.369556	−	0.213364i	−0.303708	−	0.952765i	$-0.598225\pi$
$73$	3.15749	−	1.82298i	0.369556	−	0.213364i	0.673265	+	0.739402i	$0.264891\pi$
$74$	1.66235	−	0.959758i	0.193244	−	0.111570i
$75$	−1.01223	−	0.584413i	−0.116883	−	0.0674822i
$76$	23.8290			2.73337
$77$	11.3862	−	3.44803i	1.29758	−	0.392939i
$78$	−5.13171			−0.581052
$79$	4.37340	+	2.52498i	0.492046	+	0.284083i	0.725423	−	0.688304i	$-0.241644\pi$
$79$	4.37340	+	2.52498i	0.492046	+	0.284083i	−0.233377	+	0.972386i	$0.574978\pi$
$80$	5.58639	+	9.67591i	0.624577	+	1.08180i
$81$	−0.593674	−	1.02827i	−0.0659638	−	0.114253i
$82$	−3.59033	−	2.07288i	−0.396485	−	0.228911i
$83$	−0.851415			−0.0934550			−0.0467275	−	0.998908i	$-0.514879\pi$
$83$	−0.851415			−0.0934550			−0.0467275	+	0.998908i	$0.514879\pi$
$84$	−7.77135	−	7.28563i	−0.847924	−	0.794927i
$85$	−9.98859			−1.08341
$86$	19.1005	+	11.0277i	2.05966	+	1.18915i
$87$	2.26400	−	1.30712i	0.242726	−	0.140138i
$88$	19.9836	−	11.5376i	2.13026	−	1.22991i
$89$	3.97758	−	6.88938i	0.421623	−	0.730273i	−0.574475	−	0.818522i	$-0.694794\pi$
$89$	3.97758	−	6.88938i	0.421623	−	0.730273i	0.996098	+	0.0882493i	$0.0281272\pi$
$90$	−12.4288			−1.31011
$91$	−1.26985	+	5.43435i	−0.133116	+	0.569675i
$92$	−18.3345	+	6.84862i	−1.91150	+	0.714018i
$93$	−2.76429	+	4.78788i	−0.286643	+	0.496480i
$94$	17.2283	−	9.94677i	1.77696	−	1.02593i
$95$	7.26051	+	12.5756i	0.744913	+	1.29023i
$96$	−0.696572	−	0.402166i	−0.0710936	−	0.0410459i
$97$	−2.72009			−0.276184			−0.138092	−	0.990419i	$-0.544097\pi$
$97$	−2.72009			−0.276184			−0.138092	+	0.990419i	$0.544097\pi$
$98$	−14.3618	+	9.57643i	−1.45076	+	0.967366i
$99$			9.11304i			0.915895i
$100$	−2.41744	+	4.18713i	−0.241744	+	0.418713i
$101$	−12.3302	+	7.11884i	−1.22690	+	0.708351i	−0.966380	−	0.257118i	$-0.917227\pi$
$101$	−12.3302	+	7.11884i	−1.22690	+	0.708351i	−0.260519	+	0.965469i	$0.583894\pi$
$102$	8.46241	−	4.88577i	0.837903	−	0.483764i
$103$	−4.71247	+	8.16223i	−0.464333	+	0.804249i	−0.999171	−	0.0407059i	$-0.987039\pi$
$103$	−4.71247	+	8.16223i	−0.464333	+	0.804249i	0.534838	+	0.844955i	$0.320373\pi$
$104$			10.8244i			1.06142i
$105$	1.47707	−	6.32116i	0.144147	−	0.616882i
$106$		−	15.6527i		−	1.52032i
$107$	−15.3817	−	8.88064i	−1.48701	−	0.858524i	−0.487117	−	0.873337i	$-0.661952\pi$
$107$	−15.3817	−	8.88064i	−1.48701	−	0.858524i	−0.999890	+	0.0148126i	$0.995285\pi$
$108$	17.5271	−	10.1193i	1.68655	−	0.973727i
$109$	5.63239	−	3.25186i	0.539485	−	0.311472i	−0.205385	−	0.978681i	$-0.565845\pi$
$109$	5.63239	−	3.25186i	0.539485	−	0.311472i	0.744870	+	0.667209i	$0.232511\pi$
$110$	23.8814	+	13.7880i	2.27701	+	1.31463i
$111$	−0.767955			−0.0728910
$112$	−8.12958	+	8.67157i	−0.768174	+	0.819386i
$113$			3.54545i			0.333528i	0.985997	+	0.166764i	$0.0533318\pi$
$113$			3.54545i			0.333528i	−0.985997	+	0.166764i	$0.946668\pi$
$114$	−12.3023	−	7.10275i	−1.15222	−	0.665234i
$115$	−9.20071	−	7.58918i	−0.857970	−	0.707695i
$116$	−5.40694	−	9.36510i	−0.502022	−	0.869528i
$117$	−3.70216	−	2.13744i	−0.342265	−	0.197607i
$118$		−	30.0336i		−	2.76482i
$119$	−3.07987	−	10.1705i	−0.282332	−	0.932324i
$120$		−	12.5908i		−	1.14938i
$121$	4.60959	−	7.98404i	0.419053	−	0.725822i
$122$	7.23935	+	12.5389i	0.655420	+	1.13522i
$123$	0.829310	+	1.43641i	0.0747764	+	0.129516i
$124$	19.8052	+	11.4345i	1.77856	+	1.02685i
$125$	9.48825			0.848655
$126$	−3.83229	−	12.6551i	−0.341408	−	1.12741i
$127$	0.227609			0.0201970			0.0100985	−	0.999949i	$-0.496785\pi$
$127$	0.227609			0.0201970			0.0100985	+	0.999949i	$0.496785\pi$
$128$	9.41513	−	16.3075i	0.832188	−	1.44139i
$129$	−4.41193	−	7.64168i	−0.388449	−	0.672813i
$130$	−11.2027	+	6.46787i	−0.982539	+	0.567269i
$131$	8.89889	+	5.13777i	0.777499	+	0.448889i	0.835543	−	0.549425i	$-0.185153\pi$
$131$	8.89889	+	5.13777i	0.777499	+	0.448889i	−0.0580441	+	0.998314i	$0.518486\pi$
$132$	−18.1043			−1.57578
$133$	−10.5659	+	11.2703i	−0.916175	+	0.977255i
$134$		−	38.7845i		−	3.35047i
$135$	10.6808	+	6.16654i	0.919254	+	0.530731i
$136$	−10.3057	−	17.8499i	−0.883704	−	1.53062i
$137$	9.01269	−	5.20348i	0.770006	−	0.444563i	−0.0628708	−	0.998022i	$-0.520026\pi$
$137$	9.01269	−	5.20348i	0.770006	−	0.444563i	0.832877	+	0.553459i	$0.186692\pi$
$138$	11.5071	+	1.92922i	0.979545	+	0.164226i
$139$		−	6.21923i		−	0.527508i	−0.964590	−	0.263754i	$-0.915039\pi$
$139$		−	6.21923i		−	0.527508i	0.964590	−	0.263754i	$-0.0849607\pi$
$140$	−26.1477	−	6.10994i	−2.20988	−	0.516384i
$141$	−7.95895			−0.670265
$142$	−6.57855	+	11.3944i	−0.552059	+	0.956195i
$143$	4.74236	+	8.21401i	0.396576	+	0.686890i
$144$	−4.55253	−	7.88521i	−0.379377	−	0.657100i
$145$	3.29491	−	5.70696i	0.273628	−	0.473937i
$146$			8.99082i			0.744086i
$147$	6.89169	−	0.445099i	0.568417	−	0.0367111i
$148$			3.17667i			0.261120i
$149$	15.3369	+	8.85477i	1.25645	+	0.725411i	0.972382	−	0.233393i	$-0.0749830\pi$
$149$	15.3369	+	8.85477i	1.25645	+	0.725411i	0.284067	+	0.958805i	$0.408316\pi$
$150$	2.49614	−	1.44114i	0.203809	−	0.117669i
$151$	1.79196	+	3.10377i	0.145828	+	0.252581i	0.929681	−	0.368364i	$-0.120082\pi$
$151$	1.79196	+	3.10377i	0.145828	+	0.252581i	−0.783854	+	0.620946i	$0.786749\pi$
$152$	−14.9820	+	25.9496i	−1.21520	+	2.10479i
$153$	8.14002			0.658081
$154$	−6.67542	+	28.5676i	−0.537920	+	2.30205i
$155$			13.9361i			1.11937i
$156$	4.24632	−	7.35484i	0.339977	−	0.588858i
$157$	4.35719	+	7.54688i	0.347742	+	0.602306i	0.985848	−	0.167642i	$-0.0536153\pi$
$157$	4.35719	+	7.54688i	0.347742	+	0.602306i	−0.638106	+	0.769948i	$0.720282\pi$
$158$	−10.7847	+	6.22653i	−0.857983	+	0.495356i
$159$	−3.13113	+	5.42328i	−0.248315	+	0.430094i
$160$	−2.02751			−0.160289
$161$	4.89043	−	11.7083i	0.385420	−	0.922741i
$162$	2.92797			0.230043
$163$	−3.03003	+	5.24816i	−0.237330	+	0.411068i	−0.959947	−	0.280181i	$-0.909606\pi$
$163$	−3.03003	+	5.24816i	−0.237330	+	0.411068i	0.722617	+	0.691248i	$0.242939\pi$
$164$	5.94174	−	3.43047i	0.463972	−	0.267874i
$165$	−5.51625	−	9.55442i	−0.429439	−	0.743811i
$166$	1.04978	−	1.81828i	0.0814789	−	0.141126i
$167$			4.39200i			0.339863i	0.985456	+	0.169931i	$0.0543546\pi$
$167$			4.39200i			0.339863i	−0.985456	+	0.169931i	$0.945645\pi$
$168$	12.8201	−	3.88225i	0.989091	−	0.299522i
$169$	8.55076			0.657751
$170$	12.3158	−	21.3316i	0.944577	−	1.63606i
$171$	−5.91682	−	10.2482i	−0.452471	−	0.783702i
$172$	−31.6100	+	18.2501i	−2.41024	+	1.39155i
$173$	7.29534	+	4.21197i	0.554655	+	0.320230i	0.750997	−	0.660305i	$-0.229573\pi$
$173$	7.29534	+	4.21197i	0.554655	+	0.320230i	−0.196343	+	0.980535i	$0.562906\pi$
$174$			6.44664i			0.488719i
$175$	−0.908463	−	2.99995i	−0.0686733	−	0.226775i
$176$			20.2015i			1.52274i
$177$	−6.00788	+	10.4059i	−0.451580	+	0.782159i
$178$	9.80861	+	16.9890i	0.735186	+	1.27338i
$179$	−3.81304	−	6.60438i	−0.285000	−	0.493634i	0.687609	−	0.726081i	$-0.258660\pi$
$179$	−3.81304	−	6.60438i	−0.285000	−	0.493634i	−0.972609	+	0.232447i	$0.925327\pi$
$180$	10.2844	−	17.8131i	0.766555	−	1.32771i
$181$	−13.6135			−1.01189			−0.505943	−	0.862567i	$-0.668855\pi$
$181$	−13.6135			−1.01189			−0.505943	+	0.862567i	$0.668855\pi$
$182$	−10.0399	−	9.41235i	−0.744204	−	0.697690i
$183$		−	5.79259i		−	0.428201i
$184$	4.06935	−	24.2721i	0.299997	−	1.78936i
$185$	−1.67647	+	0.967908i	−0.123256	+	0.0711620i
$186$	−6.81665	−	11.8068i	−0.499821	−	0.865715i
$187$	−15.6407	−	9.03016i	−1.14376	−	0.660351i
$188$			32.9224i			2.40112i
$189$	−2.98552	+	12.7766i	−0.217165	+	0.929363i
$190$	−35.8084			−2.59782
$191$	−8.68258	−	5.01289i	−0.628249	−	0.362720i	0.151824	−	0.988407i	$-0.451485\pi$
$191$	−8.68258	−	5.01289i	−0.628249	−	0.362720i	−0.780074	+	0.625687i	$0.784819\pi$
$192$	−5.95931	+	3.44061i	−0.430076	+	0.248304i
$193$	6.77881	+	11.7412i	0.487950	+	0.845154i	0.999904	−	0.0138591i	$-0.00441163\pi$
$193$	6.77881	+	11.7412i	0.487950	+	0.845154i	−0.511954	+	0.859013i	$0.671078\pi$
$194$	3.35383	−	5.80901i	0.240791	−	0.417063i
$195$	5.17529			0.370610
$196$	−1.84116	−	28.5077i	−0.131512	−	2.03626i
$197$	24.0652			1.71458			0.857288	−	0.514837i	$-0.172148\pi$
$197$	24.0652			1.71458			0.857288	+	0.514837i	$0.172148\pi$
$198$	−19.4617	−	11.2362i	−1.38309	−	0.798525i
$199$	12.0641	+	20.8956i	0.855198	+	1.48125i	0.876461	+	0.481473i	$0.159898\pi$
$199$	12.0641	+	20.8956i	0.855198	+	1.48125i	−0.0212629	+	0.999774i	$0.506769\pi$
$200$	−3.03984	−	5.26515i	−0.214949	−	0.372302i
$201$	−7.75840	+	13.4379i	−0.547235	+	0.947840i
$202$		−	35.1097i		−	2.47031i
$203$	6.82682	+	1.59523i	0.479149	+	0.111963i
$204$			16.1712i			1.13221i
$205$	3.62081	+	2.09048i	0.252889	+	0.146005i
$206$	−11.6208	−	20.1278i	−0.809660	−	1.40237i
$207$	7.49795	+	6.18467i	0.521143	+	0.429864i
$208$	−8.20681	−	4.73820i	−0.569040	−	0.328535i
$209$			26.2554i			1.81612i
$210$	11.6782	+	10.9483i	0.805874	+	0.755505i
$211$	22.0361			1.51703			0.758515	−	0.651656i	$-0.225925\pi$
$211$	22.0361			1.51703			0.758515	+	0.651656i	$0.225925\pi$
$212$	22.4336	+	12.9520i	1.54074	+	0.889549i
$213$	4.55863	−	2.63193i	0.312352	−	0.180337i
$214$	37.9309	−	21.8994i	2.59290	−	1.49701i
$215$	−19.2627	−	11.1213i	−1.31371	−	0.758469i
$216$			25.4492i			1.73160i
$217$	−14.1899	+	4.29705i	−0.963270	+	0.291703i
$218$			16.0380i			1.08623i
$219$	1.79851	−	3.11511i	0.121532	−	0.210500i
$220$	−39.5221	+	22.8181i	−2.66458	+	1.53840i
$221$	7.33698	−	4.23601i	0.493539	−	0.284945i
$222$	0.946877	−	1.64004i	0.0635502	−	0.110072i
$223$		−	16.7338i		−	1.12058i	−0.828297	−	0.560290i	$-0.810690\pi$
$223$		−	16.7338i		−	1.12058i	0.828297	−	0.560290i	$-0.189310\pi$
$224$	−0.625162	−	2.06443i	−0.0417704	−	0.137936i
$225$	2.40104			0.160069
$226$	−7.57164	−	4.37149i	−0.503658	−	0.290787i
$227$	−14.6339	−	25.3467i	−0.971289	−	1.68232i	−0.691675	−	0.722208i	$-0.743127\pi$
$227$	−14.6339	−	25.3467i	−0.971289	−	1.68232i	−0.279613	−	0.960113i	$-0.590206\pi$
$228$	20.3595	−	11.7546i	1.34834	−	0.778465i
$229$	2.53147	−	4.38464i	0.167284	−	0.289745i	−0.770180	−	0.637827i	$-0.779834\pi$
$229$	2.53147	−	4.38464i	0.167284	−	0.289745i	0.937464	+	0.348082i	$0.113167\pi$
$230$	27.5517	−	10.2916i	1.81671	−	0.678609i
$231$	8.02751	−	8.56269i	0.528171	−	0.563384i
$232$	13.5980			0.892755
$233$	1.05963	−	1.83533i	0.0694186	−	0.120237i	−0.829227	−	0.558912i	$-0.811219\pi$
$233$	1.05963	−	1.83533i	0.0694186	−	0.120237i	0.898646	+	0.438676i	$0.144552\pi$
$234$	9.12941	−	5.27087i	0.596808	−	0.344567i
$235$	−17.3746	+	10.0312i	−1.13339	+	0.654366i
$236$	43.0445	+	24.8518i	2.80196	+	1.61771i
$237$	4.98219			0.323628
$238$	25.5174	+	5.96267i	1.65405	+	0.386502i
$239$	−11.1996			−0.724444			−0.362222	−	0.932092i	$-0.617982\pi$
$239$	−11.1996			−0.724444			−0.362222	+	0.932092i	$0.617982\pi$
$240$	9.54605	+	5.51141i	0.616195	+	0.355760i
$241$	−3.32975	−	5.76730i	−0.214488	−	0.371504i	0.738626	−	0.674115i	$-0.235475\pi$
$241$	−3.32975	−	5.76730i	−0.214488	−	0.371504i	−0.953114	+	0.302611i	$0.902142\pi$
$242$	11.3671	+	19.6884i	0.730705	+	1.26562i
$243$	−13.8988	−	8.02450i	−0.891611	−	0.514772i
$244$	−23.9612			−1.53396
$245$	14.4838	−	9.65775i	0.925334	−	0.617011i
$246$	−4.09011			−0.260776
$247$	−10.6662	−	6.15814i	−0.678675	−	0.391833i
$248$	−24.9043	+	14.3785i	−1.58142	+	0.913036i
$249$	−0.727451	+	0.419994i	−0.0461003	+	0.0266160i
$250$	−11.6989	+	20.2630i	−0.739901	+	1.28155i
$251$	2.15008			0.135712			0.0678559	−	0.997695i	$-0.478384\pi$
$251$	2.15008			0.135712			0.0678559	+	0.997695i	$0.478384\pi$
$252$	21.3086	+	4.97918i	1.34231	+	0.313659i
$253$	−7.54600	−	20.2015i	−0.474413	−	1.27005i
$254$	−0.280638	+	0.486080i	−0.0176088	+	0.0304994i
$255$	−8.53427	+	4.92726i	−0.534437	+	0.308557i
$256$	16.2426	+	28.1330i	1.01516	+	1.75831i
$257$	−24.6604	−	14.2377i	−1.53827	−	0.888122i	−0.998940	−	0.0460288i	$-0.985343\pi$
$257$	−24.6604	−	14.2377i	−1.53827	−	0.888122i	−0.539332	−	0.842093i	$-0.681323\pi$
$258$	21.7594			1.35468
$259$	−1.50245	−	1.40855i	−0.0933578	−	0.0875228i
$260$		−	21.4077i		−	1.32765i
$261$	−2.68513	+	4.65078i	−0.166205	+	0.287876i
$262$	−21.9444	+	12.6696i	−1.35573	+	0.782731i
$263$	10.8838	−	6.28378i	0.671126	−	0.387475i	−0.125377	−	0.992109i	$-0.540014\pi$
$263$	10.8838	−	6.28378i	0.671126	−	0.387475i	0.796503	+	0.604635i	$0.206681\pi$
$264$	11.3827	−	19.7154i	0.700558	−	1.21340i
$265$			15.7856i			0.969700i
$266$	−11.0411	−	36.4604i	−0.676976	−	2.23553i
$267$		−	7.84840i		−	0.480314i
$268$	55.5865	+	32.0929i	3.39548	+	1.96038i
$269$	13.5285	−	7.81069i	0.824848	−	0.476226i	−0.0272372	−	0.999629i	$-0.508671\pi$
$269$	13.5285	−	7.81069i	0.824848	−	0.476226i	0.852086	+	0.523403i	$0.175338\pi$
$270$	−26.3385	+	15.2065i	−1.60291	+	0.925439i
$271$	13.4285	+	7.75294i	0.815722	+	0.470957i	0.848939	−	0.528491i	$-0.177242\pi$
$271$	13.4285	+	7.75294i	0.815722	+	0.470957i	−0.0332170	+	0.999448i	$0.510575\pi$
$272$	18.0445			1.09411
$273$	1.59575	+	5.26952i	0.0965789	+	0.318926i
$274$			25.6632i			1.55037i
$275$	−4.61350	−	2.66360i	−0.278204	−	0.160621i
$276$	−12.2867	+	14.8957i	−0.739571	+	0.896615i
$277$	−0.909988	−	1.57615i	−0.0546759	−	0.0947014i	0.837392	−	0.546603i	$-0.184079\pi$
$277$	−0.909988	−	1.57615i	−0.0546759	−	0.0947014i	−0.892068	+	0.451901i	$0.850746\pi$
$278$	13.2817	+	7.66822i	0.796586	+	0.459909i
$279$		−	11.3570i		−	0.679924i
$280$	23.0935	−	24.6331i	1.38010	−	1.47211i
$281$			16.5334i			0.986301i	0.869944	+	0.493150i	$0.164155\pi$
$281$			16.5334i			0.986301i	−0.869944	+	0.493150i	$0.835845\pi$
$282$	9.81327	−	16.9971i	0.584372	−	1.01216i
$283$	−14.6412	−	25.3592i	−0.870327	−	1.50745i	−0.861659	−	0.507487i	$-0.830574\pi$
$283$	−14.6412	−	25.3592i	−0.870327	−	1.50745i	−0.00866737	−	0.999962i	$-0.502759\pi$
$284$	−10.8870	−	18.8569i	−0.646027	−	1.11895i
$285$	12.4068	+	7.16307i	0.734915	+	0.424303i
$286$	−23.3890			−1.38302
$287$	−1.01210	+	4.33132i	−0.0597425	+	0.255670i
$288$	1.65229			0.0973619
$289$	0.434012	−	0.751731i	0.0255301	−	0.0442195i
$290$	8.12516	+	14.0732i	0.477126	+	0.826407i
$291$	−2.32405	+	1.34179i	−0.136238	+	0.0786573i
$292$	−12.8858	−	7.43960i	−0.754082	−	0.435370i
$293$	−19.5508			−1.14217			−0.571085	−	0.820891i	$-0.693477\pi$
$293$	−19.5508			−1.14217			−0.571085	+	0.820891i	$0.693477\pi$
$294$	−7.54681	+	15.2667i	−0.440139	+	0.890369i
$295$			30.2886i			1.76347i
$296$	−3.45937	−	1.99727i	−0.201072	−	0.116089i
$297$	11.1497	+	19.3118i	0.646971	+	1.12059i
$298$	−37.8204	+	21.8356i	−2.19088	+	1.26490i
$299$	9.97671	+	1.67265i	0.576968	+	0.0967320i
$300$			4.76999i			0.275395i
$301$	5.38438	−	23.0426i	0.310350	−	1.32815i
$302$	−8.83785			−0.508561
$303$	−7.02329	+	12.1647i	−0.403478	+	0.698844i
$304$	−13.1162	−	22.7179i	−0.752266	−	1.30296i
$305$	−7.30082	−	12.6454i	−0.418044	−	0.724073i
$306$	−10.0365	+	17.3838i	−0.573750	+	0.993764i
$307$		−	0.893505i		−	0.0509950i	−0.999675	−	0.0254975i	$-0.991883\pi$
$307$		−	0.893505i		−	0.0509950i	0.999675	−	0.0254975i	$-0.00811699\pi$
$308$	−35.4198	−	33.2060i	−2.01823	−	1.89209i
$309$			9.29844i			0.528970i
$310$	−29.7619	−	17.1830i	−1.69036	−	0.975930i
$311$	−23.5660	+	13.6058i	−1.33630	+	0.771516i	−0.986257	−	0.165216i	$-0.947168\pi$
$311$	−23.5660	+	13.6058i	−1.33630	+	0.771516i	−0.350047	+	0.936732i	$0.613834\pi$
$312$	5.33958	+	9.24842i	0.302294	+	0.523589i
$313$	8.97878	−	15.5517i	0.507511	−	0.879034i	−0.492452	−	0.870340i	$-0.663899\pi$
$313$	8.97878	−	15.5517i	0.507511	−	0.879034i	0.999962	−	0.00869421i	$-0.00276749\pi$
$314$	−21.4894			−1.21272
$315$	3.86483	+	12.7626i	0.217759	+	0.719090i
$316$		−	20.6090i		−	1.15935i
$317$	5.65331	−	9.79182i	0.317522	−	0.549964i	−0.662449	−	0.749107i	$-0.730483\pi$
$317$	5.65331	−	9.79182i	0.317522	−	0.549964i	0.979970	+	0.199144i	$0.0638161\pi$
$318$	−7.72129	−	13.3737i	−0.432988	−	0.749958i
$319$	10.3187	−	5.95752i	0.577738	−	0.333557i
$320$	−8.67288	+	15.0219i	−0.484829	+	0.839748i
$321$	−17.5229			−0.978033
$322$	18.9743	+	24.8801i	1.05740	+	1.38651i
$323$	23.4521			1.30491
$324$	−2.42279	+	4.19640i	−0.134600	+	0.233133i
$325$	2.16417	−	1.24948i	0.120047	−	0.0693089i
$326$	−7.47196	−	12.9418i	−0.413833	−	0.716781i
$327$	3.20822	−	5.55679i	0.177415	−	0.307291i
$328$			8.62736i			0.476366i
$329$	−15.5712	−	14.5979i	−0.858466	−	0.804810i
$330$	27.2058			1.49763
$331$	17.8442	−	30.9071i	0.980808	−	1.69881i	0.321551	−	0.946892i	$-0.395796\pi$
$331$	17.8442	−	30.9071i	0.980808	−	1.69881i	0.659258	−	0.751917i	$-0.270871\pi$
$332$	1.73732	+	3.00912i	0.0953477	+	0.165147i
$333$	1.36621	−	0.788779i	0.0748676	−	0.0432248i
$334$	−9.37952	−	5.41527i	−0.513225	−	0.296310i
$335$			39.1139i			2.13702i
$336$	−2.66834	+	11.4192i	−0.145570	+	0.622971i
$337$		−	17.0125i		−	0.926730i	−0.886167	−	0.463365i	$-0.846642\pi$
$337$		−	17.0125i		−	0.926730i	0.886167	−	0.463365i	$-0.153358\pi$
$338$	−10.5430	+	18.2610i	−0.573462	+	0.993265i
$339$	1.74893	+	3.02924i	0.0949891	+	0.164526i
$340$	20.3818	+	35.3023i	1.10536	+	1.91453i
$341$	−12.5989	+	21.8219i	−0.682269	+	1.18172i
$342$	29.1814			1.57795
$343$	14.2995	+	11.7696i	0.772101	+	0.635500i
$344$		−	45.8975i		−	2.47463i
$345$	−11.6048	−	1.94561i	−0.624780	−	0.104748i
$346$	−17.9901	+	10.3866i	−0.967154	+	0.558387i
$347$	−0.944481	−	1.63589i	−0.0507024	−	0.0878191i	0.839560	−	0.543266i	$-0.182813\pi$
$347$	−0.944481	−	1.63589i	−0.0507024	−	0.0878191i	−0.890263	+	0.455447i	$0.849479\pi$
$348$	−9.23941	−	5.33437i	−0.495284	−	0.285953i
$349$			29.0312i			1.55401i	0.629497	+	0.777003i	$0.283261\pi$
$349$			29.0312i			1.55401i	−0.629497	+	0.777003i	$0.716739\pi$
$350$	7.52680	+	1.75879i	0.402325	+	0.0940114i
$351$	−10.4605			−0.558343
$352$	−3.17480	−	1.83297i	−0.169217	−	0.0976976i
$353$	15.8172	−	9.13208i	0.841866	−	0.486052i	−0.0160319	−	0.999871i	$-0.505103\pi$
$353$	15.8172	−	9.13208i	0.841866	−	0.486052i	0.857898	+	0.513820i	$0.171770\pi$
$354$	−14.8152	−	25.6608i	−0.787422	−	1.36385i
$355$	6.63441	−	11.4911i	0.352118	−	0.609886i
$356$	−32.4651			−1.72065
$357$	−7.64843	−	7.17039i	−0.404798	−	0.379497i
$358$	18.8057			0.993911
$359$	4.45099	+	2.56978i	0.234914	+	0.135628i	0.612837	−	0.790209i	$-0.290028\pi$
$359$	4.45099	+	2.56978i	0.234914	+	0.135628i	−0.377923	+	0.925837i	$0.623362\pi$
$360$	12.9323	+	22.3993i	0.681589	+	1.18055i
$361$	−7.54685	−	13.0715i	−0.397203	−	0.687975i
$362$	16.7853	−	29.0730i	0.882215	−	1.52804i
$363$		−	9.09544i		−	0.477387i
$364$	21.7975	−	6.60085i	1.14250	−	0.345979i
$365$		−	9.06717i		−	0.474597i
$366$	12.3706	+	7.14218i	0.646623	+	0.373328i
$367$	4.82808	+	8.36248i	0.252024	+	0.436518i	0.964083	−	0.265602i	$-0.0855706\pi$
$367$	4.82808	+	8.36248i	0.252024	+	0.436518i	−0.712059	+	0.702119i	$0.752237\pi$
$368$	16.6212	+	13.7099i	0.866439	+	0.714680i
$369$	−2.95072	−	1.70360i	−0.153608	−	0.0886857i
$370$		−	4.77367i		−	0.248171i
$371$	−16.0730	+	4.86731i	−0.834468	+	0.252698i
$372$	22.5622			1.16979
$373$	−5.35579	−	3.09216i	−0.277312	−	0.160106i	0.354894	−	0.934907i	$-0.384517\pi$
$373$	−5.35579	−	3.09216i	−0.277312	−	0.160106i	−0.632206	+	0.774800i	$0.717850\pi$
$374$	38.5695	−	22.2681i	1.99438	−	1.15146i
$375$	8.10678	−	4.68045i	0.418632	−	0.241697i
$376$	−35.8523	−	20.6993i	−1.84894	−	1.06749i
$377$			5.58929i			0.287863i
$378$	−23.6046	−	22.1293i	−1.21409	−	1.13821i
$379$		−	13.0402i		−	0.669830i	−0.942248	−	0.334915i	$-0.891292\pi$
$379$		−	13.0402i		−	0.669830i	0.942248	−	0.334915i	$-0.108708\pi$
$380$	29.6302	−	51.3211i	1.52000	−	2.63272i
$381$	0.194469	−	0.112277i	0.00996297	−	0.00575212i
$382$	21.4110	−	12.3616i	1.09548	−	0.632477i
$383$	12.2159	−	21.1585i	0.624201	−	1.08115i	−0.364494	−	0.931206i	$-0.618758\pi$
$383$	12.2159	−	21.1585i	0.624201	−	1.08115i	0.988695	−	0.149942i	$-0.0479087\pi$
$384$		−	18.5775i		−	0.948031i
$385$	6.73210	−	28.8102i	0.343100	−	1.46831i
$386$	−33.4327			−1.70168
$387$	15.6978	+	9.06313i	0.797964	+	0.460705i
$388$	5.55036	+	9.61351i	0.281777	+	0.488052i
$389$	−13.7847	+	7.95860i	−0.698912	+	0.403517i	−0.806942	−	0.590630i	$-0.798879\pi$
$389$	−13.7847	+	7.95860i	−0.698912	+	0.403517i	0.108030	+	0.994148i	$0.465546\pi$
$390$	−6.38106	+	11.0523i	−0.323117	+	0.559656i
$391$	−18.0445	+	6.74030i	−0.912549	+	0.340872i
$392$	32.2023	+	15.9186i	1.62646	+	0.804013i
$393$	10.1376			0.511376
$394$	−29.6721	+	51.3935i	−1.49486	+	2.58917i
$395$	10.8763	−	6.27941i	0.547244	−	0.315951i
$396$	32.2078	−	18.5952i	1.61850	−	0.934444i
$397$	13.7111	+	7.91614i	0.688143	+	0.397299i	0.802916	−	0.596092i	$-0.203281\pi$
$397$	13.7111	+	7.91614i	0.688143	+	0.397299i	−0.114773	+	0.993392i	$0.536614\pi$
$398$	−59.4992			−2.98243
$399$	−3.46799	+	14.8414i	−0.173617	+	0.742997i
$400$	5.32254			0.266127
$401$	0.612134	+	0.353416i	0.0305685	+	0.0176487i	0.515206	−	0.857066i	$-0.327715\pi$
$401$	0.612134	+	0.353416i	0.0305685	+	0.0176487i	−0.484638	+	0.874715i	$0.661049\pi$
$402$	−19.1320	−	33.1376i	−0.954217	−	1.65275i
$403$	−5.91009	−	10.2366i	−0.294402	−	0.509920i
$404$	50.3196	+	29.0520i	2.50349	+	1.44539i
$405$	−2.95283			−0.146727
$406$	−11.8241	+	12.6124i	−0.586822	+	0.625944i
$407$	−3.50014			−0.173496
$408$	−17.6104	−	10.1674i	−0.871843	−	0.503359i
$409$	19.8589	−	11.4655i	0.981960	−	0.566935i	0.0790984	−	0.996867i	$-0.474796\pi$
$409$	19.8589	−	11.4655i	0.981960	−	0.566935i	0.902861	+	0.429932i	$0.141463\pi$
$410$	−8.92882	+	5.15506i	−0.440963	+	0.254590i
$411$	5.13364	−	8.89173i	0.253224	−	0.438596i
$412$	38.4633			1.89495
$413$	−30.8401	+	9.33917i	−1.51754	+	0.459551i
$414$	−22.4528	+	8.38696i	−1.10349	+	0.412197i
$415$	−1.05870	+	1.83372i	−0.0519694	+	0.0900136i
$416$	1.48928	−	0.859838i	0.0730181	−	0.0421570i
$417$	−3.06788	−	5.31372i	−0.150235	−	0.260214i
$418$	−56.0709	−	32.3725i	−2.74252	−	1.58339i
$419$	−8.27756			−0.404385			−0.202193	−	0.979346i	$-0.564807\pi$
$419$	−8.27756			−0.404385			−0.202193	+	0.979346i	$0.564807\pi$
$420$	−25.3546	+	7.67802i	−1.23718	+	0.374649i
$421$		−	2.27003i		−	0.110635i	−0.998469	−	0.0553173i	$-0.982383\pi$
$421$		−	2.27003i		−	0.110635i	0.998469	−	0.0553173i	$-0.0176170\pi$
$422$	−27.1702	+	47.0602i	−1.32263	+	2.29085i
$423$	14.1591	−	8.17477i	0.688440	−	0.397471i
$424$	−28.2093	+	16.2867i	−1.36997	+	0.790951i
$425$	−2.37920	+	4.12090i	−0.115408	+	0.199893i
$426$			12.9805i			0.628908i
$427$	10.6245	−	11.3328i	0.514156	−	0.548434i
$428$			72.4840i			3.50365i
$429$	8.10377	+	4.67871i	0.391253	+	0.225890i
$430$	47.5013	−	27.4249i	2.29072	−	1.32255i
$431$	−0.522666	+	0.301761i	−0.0251759	+	0.0145353i	−0.512535	−	0.858666i	$-0.671294\pi$
$431$	−0.522666	+	0.301761i	−0.0251759	+	0.0145353i	0.487359	+	0.873202i	$0.337960\pi$
$432$	−19.2949	−	11.1399i	−0.928327	−	0.535970i
$433$	27.0009			1.29758			0.648790	−	0.760968i	$-0.275275\pi$
$433$	27.0009			1.29758			0.648790	+	0.760968i	$0.275275\pi$
$434$	8.31913	−	35.6020i	0.399331	−	1.70895i
$435$		−	6.50139i		−	0.311718i
$436$	−22.9858	−	13.2709i	−1.10082	−	0.635560i
$437$	21.6022	+	17.8185i	1.03337	+	0.852376i
$438$	4.43508	+	7.68178i	0.211916	+	0.367050i
$439$	−6.76947	−	3.90836i	−0.323089	−	0.186536i	0.329679	−	0.944093i	$-0.393059\pi$
$439$	−6.76947	−	3.90836i	−0.323089	−	0.186536i	−0.652769	+	0.757557i	$0.726393\pi$
$440$		−	57.3858i		−	2.73576i
$441$	−11.8033	+	7.87041i	−0.562061	+	0.374781i
$442$			20.8917i			0.993718i
$443$	−3.09922	+	5.36801i	−0.147248	+	0.255042i	−0.930210	−	0.367029i	$-0.880375\pi$
$443$	−3.09922	+	5.36801i	−0.147248	+	0.255042i	0.782961	+	0.622071i	$0.213708\pi$
$444$	1.56702	+	2.71415i	0.0743673	+	0.128808i
$445$	−9.89190	−	17.1333i	−0.468921	−	0.812195i
$446$	35.7366	+	20.6325i	1.69218	+	0.976979i
$447$	17.4719			0.826391
$448$	−17.9696	−	4.19896i	−0.848983	−	0.198382i
$449$	−12.0380			−0.568109			−0.284055	−	0.958808i	$-0.591680\pi$
$449$	−12.0380			−0.568109			−0.284055	+	0.958808i	$0.591680\pi$
$450$	−2.96045	+	5.12764i	−0.139557	+	0.241719i
$451$	3.77978	+	6.54678i	0.177983	+	0.308276i
$452$	12.5306	−	7.23452i	0.589388	−	0.340283i
$453$	3.06211	+	1.76791i	0.143871	+	0.0830637i
$454$	72.1737			3.38728
$455$	10.1251	+	9.49228i	0.474673	+	0.445005i
$456$			29.5618i			1.38436i
$457$	−15.5450	−	8.97490i	−0.727164	−	0.419828i	0.0902199	−	0.995922i	$-0.471243\pi$
$457$	−15.5450	−	8.97490i	−0.727164	−	0.419828i	−0.817384	+	0.576094i	$0.804576\pi$
$458$	6.24253	+	10.8124i	0.291694	+	0.505230i
$459$	17.2499	−	9.95922i	0.805155	−	0.464856i
$460$	−8.04805	+	48.0035i	−0.375242	+	2.23817i
$461$			12.3887i			0.577001i	0.957480	+	0.288501i	$0.0931567\pi$
$461$			12.3887i			0.577001i	−0.957480	+	0.288501i	$0.906843\pi$
$462$	8.38862	+	27.7012i	0.390274	+	1.28877i
$463$	12.7244			0.591354			0.295677	−	0.955288i	$-0.404455\pi$
$463$	12.7244			0.591354			0.295677	+	0.955288i	$0.404455\pi$
$464$	−5.95230	+	10.3097i	−0.276329	+	0.478615i
$465$	6.87453	+	11.9070i	0.318799	+	0.552176i
$466$	2.61301	+	4.52587i	0.121046	+	0.209657i
$467$	−2.05265	+	3.55529i	−0.0949853	+	0.164519i	−0.909602	−	0.415480i	$-0.863614\pi$
$467$	−2.05265	+	3.55529i	−0.0949853	+	0.164519i	0.814617	+	0.579999i	$0.196947\pi$
$468$			17.4458i			0.806435i
$469$	−39.8260	+	12.0603i	−1.83900	+	0.556895i
$470$		−	49.4735i		−	2.28204i
$471$	7.44559	+	4.29871i	0.343075	+	0.198074i
$472$	−54.1268	+	31.2501i	−2.49139	+	1.43840i
$473$	−20.1084	−	34.8288i	−0.924587	−	1.60143i
$474$	−6.14297	+	10.6399i	−0.282156	+	0.488708i
$475$	6.91759			0.317401
$476$	−29.6605	+	31.6380i	−1.35949	+	1.45012i
$477$		−	12.8642i		−	0.589009i
$478$	13.8090	−	23.9178i	0.631608	−	1.09398i
$479$	10.0244	+	17.3627i	0.458025	+	0.793323i	0.998857	−	0.0478079i	$-0.0152235\pi$
$479$	10.0244	+	17.3627i	0.458025	+	0.793323i	−0.540831	+	0.841131i	$0.681890\pi$
$480$	−1.73231	+	1.00015i	−0.0790689	+	0.0456504i
$481$	0.820950	−	1.42193i	0.0374321	−	0.0648343i
$482$	16.4221			0.748008
$483$	−1.59718	−	12.4160i	−0.0726740	−	0.564946i
$484$	−37.6236			−1.71016
$485$	−3.38231	+	5.85834i	−0.153583	+	0.266013i
$486$	34.2742	−	19.7882i	1.55471	−	0.897611i
$487$	13.5230	+	23.4226i	0.612787	+	1.06138i	0.990768	+	0.135565i	$0.0432851\pi$
$487$	13.5230	+	23.4226i	0.612787	+	1.06138i	−0.377981	+	0.925813i	$0.623382\pi$
$488$	15.0652	−	26.0936i	0.681968	−	1.18120i
$489$			5.97872i			0.270367i
$490$	2.76677	+	42.8393i	0.124990	+	1.93528i
$491$	10.5974			0.478256			0.239128	−	0.970988i	$-0.423138\pi$
$491$	10.5974			0.478256			0.239128	+	0.970988i	$0.423138\pi$
$492$	3.38442	−	5.86199i	0.152582	−	0.264279i
$493$	−5.32142	−	9.21697i	−0.239665	−	0.415112i
$494$	26.3026	−	15.1858i	1.18341	−	0.683242i
$495$	19.6270	+	11.3317i	0.882168	+	0.509320i
$496$		−	25.1757i		−	1.13042i
$497$	13.7460	+	3.21204i	0.616593	+	0.144080i
$498$		−	2.07139i		−	0.0928210i
$499$	−13.8512	+	23.9911i	−0.620067	+	1.07399i	0.369406	+	0.929268i	$0.379561\pi$
$499$	−13.8512	+	23.9911i	−0.620067	+	1.07399i	−0.989473	+	0.144719i	$0.953772\pi$
$500$	−19.3608	−	33.5339i	−0.865842	−	1.49968i
$501$	2.16653	+	3.75253i	0.0967932	+	0.167651i
$502$	−2.65102	+	4.59169i	−0.118321	+	0.204937i
$503$	14.7700			0.658561			0.329280	−	0.944232i	$-0.393194\pi$
$503$	14.7700			0.658561			0.329280	+	0.944232i	$0.393194\pi$
$504$	−18.8196	+	20.0743i	−0.838293	+	0.894181i
$505$			35.4078i			1.57563i
$506$	52.4462	+	8.79290i	2.33152	+	0.390892i
$507$	7.30579	−	4.21800i	0.324462	−	0.187328i
$508$	−0.464437	−	0.804428i	−0.0206061	−	0.0356907i
$509$	10.9718	+	6.33457i	0.486316	+	0.280775i	0.723045	−	0.690801i	$-0.242742\pi$
$509$	10.9718	+	6.33457i	0.486316	+	0.280775i	−0.236729	+	0.971576i	$0.576075\pi$
$510$		−	24.3010i		−	1.07607i
$511$	9.23227	−	2.79577i	0.408411	−	0.123677i
$512$	−42.4471			−1.87591
$513$	−25.0772	−	14.4783i	−1.10719	−	0.639234i
$514$	60.8118	−	35.1097i	2.68229	−	1.54862i
$515$	11.7195	+	20.2987i	0.516422	+	0.894470i
$516$	−18.0051	+	31.1858i	−0.792631	+	1.37288i
$517$	−36.2749			−1.59537
$518$	4.86059	−	1.47191i	0.213562	−	0.0646720i
$519$	8.31088			0.364807
$520$	23.3129	+	13.4597i	1.02234	+	0.590247i
$521$	−3.89689	−	6.74961i	−0.170726	−	0.295706i	0.767948	−	0.640512i	$-0.221278\pi$
$521$	−3.89689	−	6.74961i	−0.170726	−	0.295706i	−0.938674	+	0.344806i	$0.887945\pi$
$522$	−6.62145	−	11.4687i	−0.289813	−	0.501971i
$523$	−1.88214	+	3.25996i	−0.0823002	+	0.142548i	−0.904238	−	0.427030i	$-0.859560\pi$
$523$	−1.88214	+	3.25996i	−0.0823002	+	0.142548i	0.821937	+	0.569578i	$0.192893\pi$
$524$		−	41.9346i		−	1.83192i
$525$	−2.25604	−	2.11503i	−0.0984616	−	0.0923076i
$526$			30.9912i			1.35128i
$527$	19.4920	+	11.2537i	0.849083	+	0.490218i
$528$	9.96516	+	17.2602i	0.433678	+	0.751152i
$529$	−21.7424	−	7.50131i	−0.945320	−	0.326144i
$530$	−33.7116	−	19.4634i	−1.46434	−	0.845435i
$531$		−	24.6832i		−	1.07116i
$532$	61.3917	+	14.3454i	2.66167	+	0.621954i
$533$	−3.54616			−0.153601
$534$	16.7610	+	9.67696i	0.725319	+	0.418763i
$535$	−38.2530	+	22.0854i	−1.65382	+	0.954834i
$536$	−69.8978	+	40.3555i	−3.01913	+	1.74309i
$537$	−6.51574	−	3.76186i	−0.281175	−	0.162336i
$538$			38.5219i			1.66080i
$539$	31.4106	−	2.02865i	1.35295	−	0.0873800i
$540$		−	50.3315i		−	2.16592i
$541$	6.61885	−	11.4642i	0.284567	−	0.492884i	−0.687937	−	0.725770i	$-0.741484\pi$
$541$	6.61885	−	11.4642i	0.284567	−	0.492884i	0.972504	+	0.232886i	$0.0748170\pi$
$542$	−33.1142	+	19.1185i	−1.42238	+	0.821210i
$543$	−11.6314	+	6.71541i	−0.499152	+	0.288186i
$544$	−1.63726	+	2.83582i	−0.0701969	+	0.121585i
$545$		−	16.1742i		−	0.692826i
$546$	−13.2211	−	3.08938i	−0.565810	−	0.132213i
$547$	−40.0668			−1.71313			−0.856567	−	0.516036i	$-0.827407\pi$
$547$	−40.0668			−1.71313			−0.856567	+	0.516036i	$0.827407\pi$
$548$	−36.7809	−	21.2355i	−1.57120	−	0.907134i
$549$	5.94967	+	10.3051i	0.253926	+	0.439812i
$550$	11.3767	−	6.56837i	0.485106	−	0.280076i
$551$	−7.73608	+	13.3993i	−0.329568	+	0.570829i
$552$	−8.49629	−	22.7455i	−0.361626	−	0.968112i
$553$	9.74732	+	9.13810i	0.414498	+	0.388592i
$554$	4.48801			0.190677
$555$	−0.954918	+	1.65397i	−0.0405340	+	0.0702069i
$556$	−21.9804	+	12.6904i	−0.932175	+	0.538192i
$557$	−9.00856	+	5.20109i	−0.381705	+	0.220377i	−0.678560	−	0.734545i	$-0.737396\pi$
$557$	−9.00856	+	5.20109i	−0.381705	+	0.220377i	0.296855	+	0.954923i	$0.404062\pi$
$558$	24.2539	+	14.0030i	1.02675	+	0.592794i
$559$	18.8655			0.797928
$560$	8.56743	+	28.2916i	0.362040	+	1.19554i
$561$	−17.8179			−0.752274
$562$	−35.3086	−	20.3855i	−1.48941	−	0.859909i
$563$	0.976420	+	1.69121i	0.0411512	+	0.0712760i	0.885867	−	0.463938i	$-0.153564\pi$
$563$	0.976420	+	1.69121i	0.0411512	+	0.0712760i	−0.844716	+	0.535214i	$0.820231\pi$
$564$	16.2403	+	28.1290i	0.683839	+	1.18444i
$565$	7.63594	+	4.40861i	0.321246	+	0.185472i
$566$	72.2093			3.03518
$567$	−0.910474	−	3.00660i	−0.0382363	−	0.126265i
$568$	27.3801			1.14884
$569$	11.3311	+	6.54204i	0.475026	+	0.274256i	0.718341	−	0.695691i	$-0.244902\pi$
$569$	11.3311	+	6.54204i	0.475026	+	0.274256i	−0.243315	+	0.969947i	$0.578235\pi$
$570$	−30.5948	+	17.6639i	−1.28148	+	0.739860i
$571$	−15.3278	+	8.84950i	−0.641448	+	0.370340i	−0.785172	−	0.619278i	$-0.787426\pi$
$571$	−15.3278	+	8.84950i	−0.641448	+	0.370340i	0.143724	+	0.989618i	$0.454092\pi$
$572$	19.3536	−	33.5215i	0.809216	−	1.40160i
$573$	−9.89122			−0.413212
$574$	−8.00203	−	7.50189i	−0.333998	−	0.313123i
$575$	−5.32254	+	1.98817i	−0.221965	+	0.0829124i
$576$	7.06781	−	12.2418i	0.294492	−	0.510075i
$577$	−5.88411	+	3.39719i	−0.244959	+	0.141427i	−0.617454	−	0.786607i	$-0.711836\pi$
$577$	−5.88411	+	3.39719i	−0.244959	+	0.141427i	0.372495	+	0.928034i	$0.378502\pi$
$578$	1.07026	+	1.85375i	0.0445170	+	0.0771057i
$579$	11.5837	+	6.68783i	0.481401	+	0.277937i
$580$	−26.8932			−1.11668
$581$	−2.19354	−	0.512567i	−0.0910035	−	0.0212648i
$582$		−	6.61764i		−	0.274310i
$583$	−14.2709	+	24.7179i	−0.591041	+	1.02371i
$584$	16.2033	−	9.35501i	0.670499	−	0.387113i
$585$	−9.20694	+	5.31563i	−0.380660	+	0.219774i
$586$	24.1058	−	41.7525i	0.995803	−	1.72478i
$587$		−	28.6736i		−	1.18349i	−0.806126	−	0.591744i	$-0.798440\pi$
$587$		−	28.6736i		−	1.18349i	0.806126	−	0.591744i	$-0.201560\pi$
$588$	−15.6356	−	23.4488i	−0.644803	−	0.967012i
$589$		−	32.7204i		−	1.34822i
$590$	−64.6842	−	37.3454i	−2.66301	−	1.53749i
$591$	20.5614	−	11.8711i	0.845782	−	0.488312i
$592$	3.02856	−	1.74854i	0.124473	−	0.0718644i
$593$	−13.4997	−	7.79404i	−0.554365	−	0.320063i	0.196515	−	0.980501i	$-0.437037\pi$
$593$	−13.4997	−	7.79404i	−0.554365	−	0.320063i	−0.750881	+	0.660438i	$0.770371\pi$
$594$	−54.9897			−2.25625
$595$	−25.7341	−	6.01330i	−1.05499	−	0.246521i
$596$		−	72.2729i		−	2.96041i
$597$	20.6151	+	11.9021i	0.843720	+	0.487122i
$598$	−15.8732	+	19.2438i	−0.649105	+	0.786939i
$599$	−0.559872	−	0.969726i	−0.0228757	−	0.0396219i	0.854361	−	0.519680i	$-0.173949\pi$
$599$	−0.559872	−	0.969726i	−0.0228757	−	0.0396219i	−0.877237	+	0.480058i	$0.840616\pi$
$600$	−5.19449	−	2.99904i	−0.212064	−	0.122435i
$601$			3.71483i			0.151531i	0.997126	+	0.0757656i	$0.0241401\pi$
$601$			3.71483i			0.151531i	−0.997126	+	0.0757656i	$0.975860\pi$
$602$	42.5707	+	39.9100i	1.73505	+	1.62661i
$603$		−	31.8751i		−	1.29806i
$604$	7.31302	−	12.6665i	0.297562	−	0.515393i
$605$	−11.4636	−	19.8556i	−0.466063	−	0.807245i
$606$	−17.3192	−	29.9978i	−0.703546	−	1.21858i
$607$	8.88138	+	5.12767i	0.360484	+	0.208126i	0.669293	−	0.742999i	$-0.266597\pi$
$607$	8.88138	+	5.12767i	0.360484	+	0.208126i	−0.308809	+	0.951124i	$0.599930\pi$
$608$	4.76037			0.193059
$609$	6.61976	−	2.00463i	0.268246	−	0.0812318i
$610$	36.0072			1.45789
$611$	8.50819	−	14.7366i	0.344204	−	0.596179i
$612$	−16.6097	−	28.7689i	−0.671409	−	1.16292i
$613$	34.1659	−	19.7257i	1.37995	−	0.796714i	0.387796	−	0.921745i	$-0.373237\pi$
$613$	34.1659	−	19.7257i	1.37995	−	0.796714i	0.992153	+	0.125032i	$0.0399033\pi$
$614$	1.90816	+	1.10168i	0.0770072	+	0.0444601i
$615$	4.12484			0.166330
$616$	58.4307	−	17.6943i	2.35424	−	0.712924i
$617$			32.7292i			1.31763i	0.752305	+	0.658815i	$0.228942\pi$
$617$			32.7292i			1.31763i	−0.752305	+	0.658815i	$0.771058\pi$
$618$	−19.8577	−	11.4648i	−0.798793	−	0.461184i
$619$	13.3844	+	23.1825i	0.537965	+	0.931784i	0.999013	+	0.0444084i	$0.0141403\pi$
$619$	13.3844	+	23.1825i	0.537965	+	0.931784i	−0.461048	+	0.887375i	$0.652526\pi$
$620$	49.2538	−	28.4367i	1.97808	−	1.14205i
$621$	23.4561	+	3.93255i	0.941261	+	0.157808i
$622$		−	67.1032i		−	2.69059i
$623$	14.3952	−	15.3549i	0.576730	−	0.615180i
$624$	−9.34922			−0.374268
$625$	14.7600	−	25.5651i	0.590401	−	1.02260i
$626$	22.1414	+	38.3500i	0.884948	+	1.53278i
$627$	12.9515	+	22.4327i	0.517234	+	0.895875i
$628$	17.7818	−	30.7989i	0.709569	−	1.22901i
$629$			3.12642i			0.124659i
$630$	−32.0210	−	7.48236i	−1.27575	−	0.298104i
$631$			3.62895i			0.144466i	0.997388	+	0.0722331i	$0.0230125\pi$
$631$			3.62895i			0.144466i	−0.997388	+	0.0722331i	$0.976987\pi$
$632$	22.4430	+	12.9575i	0.892736	+	0.515421i
$633$	18.8277	−	10.8702i	0.748334	−	0.432051i
$634$	13.9409	+	24.1463i	0.553664	+	0.958974i
$635$	0.283021	−	0.490207i	0.0112314	−	0.0194533i
$636$	25.5564			1.01338
$637$	−6.54314	+	13.2363i	−0.259249	+	0.524442i
$638$			29.3822i			1.16325i
$639$	−5.40659	+	9.36449i	−0.213881	+	0.370453i
$640$	−23.4146	−	40.5553i	−0.925543	−	1.60309i
$641$	−16.2330	+	9.37215i	−0.641166	+	0.370177i	−0.785064	−	0.619415i	$-0.787370\pi$
$641$	−16.2330	+	9.37215i	−0.641166	+	0.370177i	0.143897	+	0.989593i	$0.454036\pi$
$642$	21.6055	−	37.4218i	0.852700	−	1.47692i
$643$	−21.3880			−0.843460			−0.421730	−	0.906722i	$-0.638577\pi$
$643$	−21.3880			−0.843460			−0.421730	+	0.906722i	$0.638577\pi$
$644$	−51.3590	+	6.60676i	−2.02383	+	0.260343i
$645$	−21.9441			−0.864050
$646$	−28.9160	+	50.0840i	−1.13769	+	1.97053i
$647$	9.62615	−	5.55766i	0.378443	−	0.218494i	−0.298698	−	0.954348i	$-0.596552\pi$
$647$	9.62615	−	5.55766i	0.378443	−	0.218494i	0.677141	+	0.735854i	$0.263219\pi$
$648$	−3.04657	−	5.27681i	−0.119680	−	0.207293i
$649$	−27.3824	+	47.4277i	−1.07485	+	1.86170i
$650$			6.16238i			0.241708i
$651$	−10.0042	+	10.6711i	−0.392094	+	0.418234i
$652$	24.7312			0.968547
$653$	−1.47495	+	2.55469i	−0.0577194	+	0.0999729i	−0.893441	−	0.449180i	$-0.851716\pi$
$653$	−1.47495	+	2.55469i	−0.0577194	+	0.0999729i	0.835722	+	0.549153i	$0.185050\pi$
$654$	7.91137	+	13.7029i	0.309359	+	0.535825i
$655$	22.1307	−	12.7772i	0.864719	−	0.499246i
$656$	−6.54104	−	3.77647i	−0.255385	−	0.147446i
$657$			7.38913i			0.288277i
$658$	50.3743	−	15.2546i	1.96379	−	0.594687i
$659$			13.6891i			0.533252i	0.963800	+	0.266626i	$0.0859089\pi$
$659$			13.6891i			0.533252i	−0.963800	+	0.266626i	$0.914091\pi$
$660$	−22.5119	+	38.9917i	−0.876273	+	1.51775i
$661$	−10.1060	−	17.5041i	−0.393078	−	0.680830i	0.599776	−	0.800168i	$-0.295256\pi$
$661$	−10.1060	−	17.5041i	−0.393078	−	0.680830i	−0.992854	+	0.119337i	$0.961923\pi$
$662$	44.0034	+	76.2161i	1.71024	+	2.96222i
$663$	4.17915	−	7.23851i	0.162305	−	0.281120i
$664$	−4.36922			−0.169559
$665$	11.1349	+	36.7700i	0.431793	+	1.42588i
$666$			3.89021i			0.150743i
$667$	2.10125	−	12.5331i	0.0813605	−	0.485283i
$668$	15.5225	−	8.96190i	0.600582	−	0.346746i
$669$	−8.25461	−	14.2974i	−0.319142	−	0.552770i
$670$	−83.5313	−	48.2268i	−3.22710	−	1.86316i
$671$		−	26.4012i		−	1.01921i
$672$	−1.55250	−	1.45547i	−0.0598891	−	0.0561459i
$673$	35.7251			1.37710			0.688551	−	0.725188i	$-0.258247\pi$
$673$	35.7251			1.37710			0.688551	+	0.725188i	$0.258247\pi$
$674$	36.3318	+	20.9762i	1.39945	+	0.807972i
$675$	5.08815	−	2.93765i	0.195843	−	0.113070i
$676$	−17.4479	−	30.2206i	−0.671072	−	1.16233i
$677$	−16.1105	+	27.9042i	−0.619177	+	1.07245i	0.370460	+	0.928849i	$0.379200\pi$
$677$	−16.1105	+	27.9042i	−0.619177	+	1.07245i	−0.989636	+	0.143597i	$0.954133\pi$
$678$	−8.62564			−0.331266
$679$	−7.00791	−	1.63754i	−0.268939	−	0.0628431i
$680$	−51.2586			−1.96568
$681$	−25.0065	−	14.4375i	−0.958253	−	0.553247i
$682$	−31.0685	−	53.8123i	−1.18968	−	2.06058i
$683$	−2.81568	−	4.87691i	−0.107739	−	0.186610i	0.807115	−	0.590394i	$-0.201028\pi$
$683$	−2.81568	−	4.87691i	−0.107739	−	0.186610i	−0.914854	+	0.403785i	$0.867694\pi$
$684$	−24.1466	+	41.8232i	−0.923269	+	1.59915i
$685$		−	25.8812i		−	0.988869i
$686$	−42.7662	+	16.0262i	−1.63282	+	0.611883i
$687$		−	4.99499i		−	0.190571i
$688$	34.7983	+	20.0908i	1.32667	+	0.765955i
$689$	−6.69442	−	11.5951i	−0.255037	−	0.441737i
$690$	18.4635	−	22.3842i	0.702895	−	0.852150i
$691$	−8.76063	−	5.05795i	−0.333270	−	0.192414i	0.324022	−	0.946050i	$-0.394965\pi$
$691$	−8.76063	−	5.05795i	−0.333270	−	0.192414i	−0.657292	+	0.753636i	$0.728298\pi$
$692$		−	34.3782i		−	1.30686i
$693$	−5.48620	+	23.4784i	−0.208404	+	0.891869i
$694$	4.65812			0.176820
$695$	−13.3945	−	7.73333i	−0.508083	−	0.293342i
$696$	11.6182	−	6.70777i	0.440387	−	0.254257i
$697$	5.84776	−	3.37621i	0.221500	−	0.127883i
$698$	−61.9989	−	35.7951i	−2.34669	−	1.35486i
$699$		−	2.09081i		−	0.0790819i
$700$	−8.74889	+	9.33217i	−0.330677	+	0.352723i
$701$			33.1633i			1.25256i	0.779598	+	0.626280i	$0.215423\pi$
$701$			33.1633i			1.25256i	−0.779598	+	0.626280i	$0.784577\pi$
$702$	12.8977	−	22.3395i	0.486792	−	0.843149i
$703$	3.93615	−	2.27254i	0.148455	−	0.0857104i
$704$	−27.1610	+	15.6814i	−1.02367	+	0.591015i
$705$	−9.89660	+	17.1414i	−0.372728	+	0.645583i
$706$			45.0389i			1.69506i
$707$	−36.0525	+	10.9176i	−1.35589	+	0.410599i
$708$	49.0364			1.84290
$709$	−25.8075	−	14.9000i	−0.969221	−	0.559580i	−0.0702227	−	0.997531i	$-0.522371\pi$
$709$	−25.8075	−	14.9000i	−0.969221	−	0.559580i	−0.898999	+	0.437951i	$0.855704\pi$
$710$	16.3603	+	28.3368i	0.613989	+	1.06346i
$711$	−8.86340	+	5.11729i	−0.332404	+	0.191913i
$712$	20.4118	−	35.3543i	0.764965	−	1.32496i
$713$	9.40408	+	25.1757i	0.352186	+	0.942839i
$714$	24.7434	−	7.49295i	0.926000	−	0.280416i
$715$	23.5877			0.882128
$716$	−15.5611	+	26.9525i	−0.581544	+	1.00726i
$717$	−9.56899	+	5.52466i	−0.357360	+	0.206322i
$718$	−10.9760	+	6.33701i	−0.409621	+	0.236495i
$719$	−40.1866	−	23.2017i	−1.49871	−	0.865279i	−0.498708	−	0.866770i	$-0.666192\pi$
$719$	−40.1866	−	23.2017i	−1.49871	−	0.865279i	−0.999999	+	0.00149132i	$0.999525\pi$
$720$	−22.6435			−0.843872
$721$	−17.0548	+	18.1918i	−0.635153	+	0.677497i
$722$	37.2206			1.38521
$723$	−5.68989	−	3.28506i	−0.211609	−	0.122173i
$724$	27.7785	+	48.1138i	1.03238	+	1.78813i
$725$	−1.56965	−	2.71871i	−0.0582952	−	0.100970i
$726$	19.4242	+	11.2145i	0.720898	+	0.416211i
$727$	−2.32964			−0.0864016			−0.0432008	−	0.999066i	$-0.513756\pi$
$727$	−2.32964			−0.0864016			−0.0432008	+	0.999066i	$0.513756\pi$
$728$	−6.51650	+	27.8875i	−0.241517	+	1.03358i
$729$	−12.2716			−0.454502
$730$	19.3638	+	11.1797i	0.716686	+	0.413779i
$731$	−31.1101	+	17.9614i	−1.15065	+	0.664327i
$732$	−20.4725	+	11.8198i	−0.756687	+	0.436873i
$733$	−16.1650	+	27.9986i	−0.597067	+	1.03415i	0.396184	+	0.918171i	$0.370334\pi$
$733$	−16.1650	+	27.9986i	−0.597067	+	1.03415i	−0.993252	+	0.115980i	$0.962999\pi$
$734$	−23.8118			−0.878909
$735$	7.61089	−	15.3963i	0.280732	−	0.567901i
$736$	−3.66273	+	1.36817i	−0.135010	+	0.0504313i
$737$	−35.3608	+	61.2467i	−1.30253	+	2.25605i
$738$	7.27638	−	4.20102i	0.267847	−	0.154642i
$739$	−10.2719	−	17.7914i	−0.377858	−	0.654469i	0.612893	−	0.790166i	$-0.290006\pi$
$739$	−10.2719	−	17.7914i	−0.377858	−	0.654469i	−0.990750	+	0.135697i	$0.956672\pi$
$740$	6.84168	+	3.95004i	0.251505	+	0.145207i
$741$	−12.1510			−0.446378
$742$	9.42316	−	40.3267i	0.345935	−	1.48044i
$743$			7.41754i			0.272123i	0.990700	+	0.136062i	$0.0434445\pi$
$743$			7.41754i			0.272123i	−0.990700	+	0.136062i	$0.956556\pi$
$744$	−14.1855	+	24.5700i	−0.520067	+	0.900782i
$745$	38.1415	−	22.0210i	1.39740	−	0.806788i
$746$	13.2072	−	7.62519i	0.483550	−	0.279178i
$747$	0.862766	−	1.49435i	0.0315669	−	0.0546756i
$748$			73.7044i			2.69490i
$749$	−34.2824	−	32.1397i	−1.25265	−	1.17436i
$750$			23.0837i			0.842898i
$751$	27.3532	+	15.7924i	0.998132	+	0.576272i	0.907695	−	0.419631i	$-0.137840\pi$
$751$	27.3532	+	15.7924i	0.998132	+	0.576272i	0.0904367	+	0.995902i	$0.471174\pi$
$752$	31.3874	−	18.1215i	1.14458	−	0.660825i
$753$	1.83703	−	1.06061i	0.0669452	−	0.0386508i
$754$	−11.9365	−	6.89151i	−0.434700	−	0.250974i
$755$	8.91290			0.324374
$756$	51.2479	−	15.5192i	1.86387	−	0.564427i
$757$		−	31.9227i		−	1.16025i	−0.814528	−	0.580125i	$-0.803004\pi$
$757$		−	31.9227i		−	1.16025i	0.814528	−	0.580125i	$-0.196996\pi$
$758$	27.8485	+	16.0784i	1.01150	+	0.583993i
$759$	−16.4125	−	13.5378i	−0.595735	−	0.491391i
$760$	37.2589	+	64.5343i	1.35152	+	2.34090i
$761$	−3.76130	−	2.17159i	−0.136347	−	0.0787199i	0.430275	−	0.902698i	$-0.358417\pi$
$761$	−3.76130	−	2.17159i	−0.136347	−	0.0787199i	−0.566622	+	0.823978i	$0.691750\pi$
$762$			0.553743i			0.0200600i
$763$	16.4687	−	4.98714i	0.596206	−	0.180546i
$764$			40.9153i			1.48026i
$765$	10.1217	−	17.5314i	0.365953	−	0.633848i
$766$	30.1239	+	52.1762i	1.08842	+	1.88520i
$767$	−12.8449	−	22.2481i	−0.463804	−	0.803332i
$768$	27.7554	+	16.0246i	1.00154	+	0.578238i
$769$	30.9232			1.11512			0.557559	−	0.830137i	$-0.311738\pi$
$769$	30.9232			1.11512			0.557559	+	0.830137i	$0.311738\pi$
$770$	53.2263	+	49.8996i	1.91814	+	1.79826i
$771$	−28.0932			−1.01175
$772$	27.6644	−	47.9162i	0.995664	−	1.72454i
$773$	4.83709	+	8.37808i	0.173978	+	0.301339i	0.939807	−	0.341705i	$-0.111005\pi$
$773$	4.83709	+	8.37808i	0.173978	+	0.301339i	−0.765829	+	0.643044i	$0.777671\pi$
$774$	−38.7103	+	22.3494i	−1.39141	+	0.803333i
$775$	5.74949	+	3.31947i	0.206528	+	0.119239i
$776$	−13.9587			−0.501089
$777$	−1.97852	−	0.462322i	−0.0709790	−	0.0165857i
$778$		−	39.2514i		−	1.40723i
$779$	−8.50125	−	4.90820i	−0.304589	−	0.175855i
$780$	−10.5602	−	18.2908i	−0.378116	−	0.654916i
$781$	20.7771	−	11.9956i	0.743462	−	0.429238i
$782$	7.85406	−	46.8464i	0.280861	−	1.67522i
$783$			13.1409i			0.469618i
$784$	−26.1651	+	17.4468i	−0.934467	+	0.623102i
$785$	21.6719			0.773503
$786$	−12.4996	+	21.6499i	−0.445844	+	0.772225i
$787$	−10.9244	−	18.9216i	−0.389413	−	0.674484i	0.602957	−	0.797773i	$-0.293989\pi$
$787$	−10.9244	−	18.9216i	−0.389413	−	0.674484i	−0.992371	+	0.123290i	$0.960656\pi$
$788$	−49.1052	−	85.0527i	−1.74930	−	3.02988i
$789$	6.19945	−	10.7378i	0.220706	−	0.382274i
$790$			30.9697i			1.10185i
$791$	−2.13442	+	9.13432i	−0.0758913	+	0.324779i
$792$			46.7655i			1.66174i
$793$	10.7254	+	6.19233i	0.380871	+	0.219896i
$794$	−33.8113	+	19.5210i	−1.19992	+	0.692773i
$795$	7.78685	+	13.4872i	0.276171	+	0.478343i
$796$	49.2335	−	85.2750i	1.74504	−	3.02249i
$797$	−21.0566			−0.745864			−0.372932	−	0.927859i	$-0.621648\pi$
$797$	−21.0566			−0.745864			−0.372932	+	0.927859i	$0.621648\pi$
$798$	−27.4191	−	25.7054i	−0.970626	−	0.909961i
$799$			32.4017i			1.14629i
$800$	−0.482938	+	0.836473i	−0.0170744	+	0.0295738i
$801$	8.06122	+	13.9624i	0.284829	+	0.493339i
$802$	−1.50950	+	0.871512i	−0.0533024	+	0.0307742i
$803$	8.19716	−	14.1979i	0.289271	−	0.501033i
$804$	63.3243			2.23327
$805$	−19.1354	−	25.0914i	−0.674435	−	0.884355i
$806$	29.1482			1.02670
$807$	7.70586	−	13.3469i	0.271259	−	0.469835i
$808$	−63.2750	+	36.5318i	−2.22601	+	1.28519i
$809$	10.7424	+	18.6065i	0.377684	+	0.654168i	0.990725	−	0.135883i	$-0.0433871\pi$
$809$	10.7424	+	18.6065i	0.377684	+	0.654168i	−0.613041	+	0.790051i	$0.710054\pi$
$810$	3.64080	−	6.30604i	0.127925	−	0.221572i
$811$			20.3429i			0.714337i	0.934040	+	0.357169i	$0.116258\pi$
$811$			20.3429i			0.714337i	−0.934040	+	0.357169i	$0.883742\pi$
$812$	−8.29222	−	27.3828i	−0.291000	−	0.960949i
$813$	15.2978			0.536516
$814$	4.31562	−	7.47488i	0.151263	−	0.261994i
$815$	7.53541	+	13.0517i	0.263954	+	0.457181i
$816$	15.4173	−	8.90116i	0.539712	−	0.311603i
$817$	45.2266	+	26.1116i	1.58228	+	0.913530i
$818$			56.5474i			1.97713i
$819$	−8.25127	−	7.73556i	−0.288323	−	0.270302i
$820$		−	17.0625i		−	0.595849i
$821$	14.0687	−	24.3678i	0.491003	−	0.850441i	−0.508944	−	0.860800i	$-0.669964\pi$
$821$	14.0687	−	24.3678i	0.491003	−	0.850441i	0.999946	+	0.0103584i	$0.00329722\pi$
$822$	12.6594	+	21.9267i	0.441548	+	0.764783i
$823$	16.7763	+	29.0574i	0.584786	+	1.01288i	0.994902	+	0.100846i	$0.0321548\pi$
$823$	16.7763	+	29.0574i	0.584786	+	1.01288i	−0.410116	+	0.912033i	$0.634512\pi$
$824$	−24.1830	+	41.8862i	−0.842456	+	1.45918i
$825$	−5.25571			−0.182980
$826$	18.0807	−	77.3770i	0.629109	−	2.69229i
$827$		−	27.0254i		−	0.939764i	−0.882729	−	0.469882i	$-0.844297\pi$
$827$		−	27.0254i		−	0.939764i	0.882729	−	0.469882i	$-0.155703\pi$
$828$	6.55861	−	39.1195i	0.227928	−	1.35950i
$829$	14.0246	−	8.09710i	0.487094	−	0.281224i	−0.236274	−	0.971686i	$-0.575926\pi$
$829$	14.0246	−	8.09710i	0.487094	−	0.281224i	0.723368	+	0.690463i	$0.242593\pi$
$830$	−2.61072	−	4.52189i	−0.0906193	−	0.156957i
$831$	−1.55499	−	0.897775i	−0.0539421	−	0.0311435i
$832$		−	14.7121i		−	0.510052i
$833$	−1.81204	−	28.0568i	−0.0627835	−	0.972110i
$834$	15.1306			0.523930
$835$	9.45917	+	5.46125i	0.327348	+	0.188994i
$836$	92.7934	−	53.5743i	3.20933	−	1.85291i
$837$	−13.8951	−	24.0671i	−0.480286	−	0.831880i
$838$	10.2061	−	17.6775i	0.352564	−	0.610659i
$839$	43.1817			1.49080			0.745399	−	0.666618i	$-0.232259\pi$
$839$	43.1817			1.49080			0.745399	+	0.666618i	$0.232259\pi$
$840$	7.57990	−	32.4384i	0.261531	−	1.11923i
$841$	−21.9785			−0.757880
$842$	4.84787	+	2.79892i	0.167069	+	0.0964571i
$843$	8.15576	+	14.1262i	0.280899	+	0.486532i
$844$	−44.9648	−	77.8814i	−1.54775	−	2.68079i
$845$	10.6325	−	18.4160i	0.365769	−	0.633530i
$846$			40.3175i			1.38614i
$847$	16.6824	−	17.7946i	0.573215	−	0.611430i
$848$		−	28.5168i		−	0.979271i
$849$	−25.0189	−	14.4447i	−0.858646	−	0.495739i
$850$	−5.86705	−	10.1620i	−0.201238	−	0.348555i
$851$	−2.37541	+	2.87982i	−0.0814280	+	0.0987188i
$852$	−18.6038	−	10.7409i	−0.637356	−	0.367978i
$853$			18.9128i			0.647562i	0.946132	+	0.323781i	$0.104954\pi$
$853$			18.9128i			0.647562i	−0.946132	+	0.323781i	$0.895046\pi$
$854$	11.1024	+	36.6628i	0.379918	+	1.25458i
$855$	−29.4292			−1.00646
$856$	−78.9346	−	45.5729i	−2.69793	−	1.55765i
$857$	−0.228365	+	0.131846i	−0.00780079	+	0.00450379i	−0.503895	−	0.863765i	$-0.668100\pi$
$857$	−0.228365	+	0.131846i	−0.00780079	+	0.00450379i	0.496095	+	0.868269i	$0.334767\pi$
$858$	−19.9836	+	11.5376i	−0.682231	+	0.393886i
$859$	35.3191	+	20.3915i	1.20507	+	0.695748i	0.961678	−	0.274180i	$-0.0884063\pi$
$859$	35.3191	+	20.3915i	1.20507	+	0.695748i	0.243393	+	0.969928i	$0.421740\pi$
$860$			90.7726i			3.09532i
$861$	1.27185	+	4.19995i	0.0433446	+	0.143134i
$862$		−	1.48827i		−	0.0506907i
$863$	−6.30497	+	10.9205i	−0.214624	+	0.371739i	−0.953156	−	0.302479i	$-0.902186\pi$
$863$	−6.30497	+	10.9205i	−0.214624	+	0.371739i	0.738532	+	0.674218i	$0.235519\pi$
$864$	3.50143	−	2.02155i	0.119121	−	0.0687746i
$865$	18.1429	−	10.4748i	0.616876	−	0.356154i
$866$	−33.2917	+	57.6629i	−1.13130	+	1.95947i
$867$		−	0.856375i		−	0.0290840i
$868$	44.1414	+	41.3825i	1.49826	+	1.40461i
$869$	22.7075			0.770301
$870$	13.8843	+	8.01611i	0.470722	+	0.271772i
$871$	−16.5876	−	28.7306i	−0.562049	−	0.973498i
$872$	28.9038	−	16.6876i	0.978806	−	0.565114i
$873$	2.75635	−	4.77415i	0.0932885	−	0.161580i
$874$	−64.6883	+	24.1635i	−2.18812	+	0.817343i
$875$	24.4450	+	5.71209i	0.826393	+	0.193104i
$876$	−14.6795			−0.495974
$877$	8.44781	−	14.6320i	0.285262	−	0.494089i	−0.687411	−	0.726269i	$-0.741253\pi$
$877$	8.44781	−	14.6320i	0.285262	−	0.494089i	0.972673	+	0.232180i	$0.0745860\pi$
$878$	16.6933	−	9.63789i	0.563372	−	0.325263i
$879$	−16.7042	+	9.64420i	−0.563420	+	0.325291i
$880$	43.5084	+	25.1196i	1.46667	+	0.846782i
$881$	−12.0628			−0.406406			−0.203203	−	0.979137i	$-0.565135\pi$
$881$	−12.0628			−0.406406			−0.203203	+	0.979137i	$0.565135\pi$
$882$	−2.25473	−	34.9111i	−0.0759206	−	1.17552i
$883$	−49.2906			−1.65876			−0.829381	−	0.558684i	$-0.811307\pi$
$883$	−49.2906			−1.65876			−0.829381	+	0.558684i	$0.811307\pi$
$884$	−29.9423	−	17.2872i	−1.00707	−	0.581431i
$885$	14.9411	+	25.8787i	0.502238	+	0.869902i
$886$	−7.64259	−	13.2374i	−0.256758	−	0.444718i
$887$	−5.19931	−	3.00182i	−0.174576	−	0.100791i	0.410166	−	0.912011i	$-0.365471\pi$
$887$	−5.19931	−	3.00182i	−0.174576	−	0.100791i	−0.584742	+	0.811220i	$0.698804\pi$
$888$	−3.94092			−0.132249
$889$	0.586400	+	0.137024i	0.0196672	+	0.00459565i
$890$	48.7863			1.63532
$891$	−4.62371	−	2.66950i	−0.154900	−	0.0894316i
$892$	−59.1416	+	34.1454i	−1.98021	+	1.14327i
$893$	40.7936	−	23.5522i	1.36511	−	0.788144i
$894$	−21.5425	+	37.3128i	−0.720491	+	1.24793i
$895$	−18.9654			−0.633943
$896$	34.0740	−	36.3457i	1.13833	−	1.21422i
$897$	9.34922	−	3.49229i	0.312161	−	0.116604i
$898$	14.8427	−	25.7083i	0.495307	−	0.857897i
$899$	−12.8596	+	7.42447i	−0.428890	+	0.247620i
$900$	−4.89934	−	8.48590i	−0.163311	−	0.282863i
$901$	22.0787	+	12.7472i	0.735550	+	0.424670i
$902$	−18.6417			−0.620700
$903$	−6.76624	−	22.3437i	−0.225166	−	0.743552i
$904$			18.1942i			0.605132i
$905$	−16.9278	+	29.3198i	−0.562700	+	0.974625i
$906$	−7.55108	+	4.35962i	−0.250868	+	0.144839i
$907$	−16.8846	+	9.74834i	−0.560645	+	0.323688i	−0.753404	−	0.657558i	$-0.771590\pi$
$907$	−16.8846	+	9.74834i	−0.560645	+	0.323688i	0.192760	+	0.981246i	$0.438256\pi$
$908$	−59.7213	+	103.440i	−1.98192	+	3.43279i
$909$		−	28.8550i		−	0.957058i
$910$	−32.7558	+	9.91928i	−1.08584	+	0.328821i
$911$		−	39.2121i		−	1.29916i	−0.760295	−	0.649578i	$-0.774946\pi$
$911$		−	39.2121i		−	1.29916i	0.760295	−	0.649578i	$-0.225054\pi$
$912$	−22.4130	−	12.9402i	−0.742169	−	0.428492i
$913$	−3.31554	+	1.91423i	−0.109728	+	0.0633516i
$914$	38.3335	−	22.1318i	1.26796	−	0.732056i
$915$	−12.4757	−	7.20283i	−0.412433	−	0.238118i
$916$	−20.6619			−0.682689
$917$	19.8336	+	18.5940i	0.654963	+	0.614027i
$918$			49.1183i			1.62114i
$919$	35.0711	+	20.2483i	1.15689	+	0.667929i	0.950556	−	0.310553i	$-0.100514\pi$
$919$	35.0711	+	20.2483i	1.15689	+	0.667929i	0.206331	+	0.978482i	$0.433848\pi$
$920$	−47.2154	−	38.9455i	−1.55665	−	1.28400i
$921$	−0.440756	−	0.763412i	−0.0145234	−	0.0251553i
$922$	−26.4573	−	15.2751i	−0.871325	−	0.503060i
$923$			11.2542i			0.370437i
$924$	−46.6429	−	10.8991i	−1.53444	−	0.358554i
$925$			0.922193i			0.0303215i
$926$	−15.6890	+	27.1742i	−0.515573	+	0.892999i
$927$	−9.55058	−	16.5421i	−0.313682	−	0.543314i
$928$	−1.08016	−	1.87089i	−0.0354580	−	0.0614150i
$929$	19.1452	+	11.0535i	0.628134	+	0.362653i	0.780029	−	0.625743i	$-0.215204\pi$
$929$	19.1452	+	11.0535i	0.628134	+	0.362653i	−0.151895	+	0.988397i	$0.548538\pi$
$930$	−33.9048			−1.11178
$931$	−34.0062	+	22.6753i	−1.11451	+	0.743153i
$932$	−8.64872			−0.283298
$933$	−13.4232	+	23.2497i	−0.439457	+	0.761161i
$934$	−5.06178	−	8.76725i	−0.165626	−	0.286873i
$935$	−38.8970	+	22.4572i	−1.27207	+	0.734429i
$936$	−18.9984	−	10.9687i	−0.620983	−	0.358524i
$937$	18.7417			0.612266			0.306133	−	0.951989i	$-0.400965\pi$
$937$	18.7417			0.612266			0.306133	+	0.951989i	$0.400965\pi$
$938$	23.3489	−	99.9225i	0.762370	−	3.26258i
$939$		−	17.7165i		−	0.578157i
$940$	70.9060	+	40.9376i	2.31270	+	1.33524i
$941$	−11.2642	−	19.5102i	−0.367203	−	0.636014i	0.621924	−	0.783078i	$-0.286351\pi$
$941$	−11.2642	−	19.5102i	−0.367203	−	0.636014i	−0.989127	+	0.147063i	$0.953018\pi$
$942$	−18.3606	+	10.6005i	−0.598221	+	0.345383i
$943$	7.95169	+	1.33315i	0.258943	+	0.0434132i
$944$		−	54.7167i		−	1.78088i
$945$	23.8050	+	22.3172i	0.774377	+	0.725978i
$946$	99.1736			3.22441
$947$	10.6083	−	18.3742i	0.344724	−	0.597080i	−0.640579	−	0.767892i	$-0.721306\pi$
$947$	10.6083	−	18.3742i	0.344724	−	0.597080i	0.985304	+	0.170812i	$0.0546390\pi$
$948$	−10.1662	−	17.6084i	−0.330182	−	0.571893i
$949$	3.84525	+	6.66017i	0.124822	+	0.216198i
$950$	−8.52929	+	14.7732i	−0.276727	+	0.479305i
$951$		−	11.1549i		−	0.361722i
$952$	−15.8050	−	52.1919i	−0.512244	−	1.69155i
$953$			37.6405i			1.21930i	0.792673	+	0.609648i	$0.208689\pi$
$953$			37.6405i			1.21930i	−0.792673	+	0.609648i	$0.791311\pi$
$954$	27.4726	+	15.8613i	0.889459	+	0.513529i
$955$	−21.5928	+	12.4666i	−0.698727	+	0.403410i
$956$	22.8529	+	39.5824i	0.739116	+	1.28019i
$957$	5.87756	−	10.1802i	0.189995	−	0.329080i
$958$	−49.4396			−1.59732
$959$	26.3524	−	7.98018i	0.850964	−	0.257694i
$960$			17.1130i			0.552319i
$961$	0.201184	−	0.348460i	0.00648979	−	0.0112407i
$962$	2.02444	+	3.50643i	0.0652705	+	0.113052i
$963$	31.1736	−	17.9981i	1.00455	−	0.579980i
$964$	−13.5887	+	23.5364i	−0.437664	+	0.758056i
$965$	33.7166			1.08538
$966$	28.4848	+	11.8978i	0.916482	+	0.382805i
$967$	−22.5027			−0.723636			−0.361818	−	0.932249i	$-0.617844\pi$
$967$	−22.5027			−0.723636			−0.361818	+	0.932249i	$0.617844\pi$
$968$	23.6551	−	40.9718i	0.760303	−	1.31688i
$969$	20.0375	−	11.5686i	0.643697	−	0.371638i
$970$	−8.34069	−	14.4465i	−0.267803	−	0.463849i
$971$	23.5861	−	40.8523i	0.756913	−	1.31101i	−0.187505	−	0.982264i	$-0.560040\pi$
$971$	23.5861	−	40.8523i	0.756913	−	1.31101i	0.944418	−	0.328748i	$-0.106627\pi$
$972$			65.4962i			2.10079i
$973$	3.74408	−	16.0229i	0.120030	−	0.513671i
$974$	−66.6948			−2.13704
$975$	1.23271	−	2.13512i	0.0394784	−	0.0683787i
$976$	13.1890	+	22.8440i	0.422170	+	0.731220i
$977$	−2.11262	+	1.21972i	−0.0675885	+	0.0390223i	−0.533413	−	0.845855i	$-0.679091\pi$
$977$	−2.11262	+	1.21972i	−0.0675885	+	0.0390223i	0.465825	+	0.884877i	$0.345758\pi$
$978$	−12.7681	−	7.37167i	−0.408279	−	0.235720i
$979$		−	35.7710i		−	1.14325i
$980$	−63.6872	−	31.4827i	−2.03441	−	1.00568i
$981$			13.1808i			0.420832i
$982$	−13.0665	+	22.6318i	−0.416968	+	0.722210i
$983$	12.4449	+	21.5553i	0.396932	+	0.687506i	0.993346	−	0.115171i	$-0.0367416\pi$
$983$	12.4449	+	21.5553i	0.396932	+	0.687506i	−0.596414	+	0.802677i	$0.703408\pi$
$984$	4.25578	+	7.37123i	0.135669	+	0.234986i
$985$	29.9240	−	51.8299i	0.953459	−	1.65144i
$986$	26.2449			0.835809
$987$	−20.5050	−	4.79142i	−0.652683	−	0.152513i
$988$			50.2629i			1.59908i
$989$	−42.3030	−	7.09234i	−1.34516	−	0.225523i
$990$	−48.3996	+	27.9435i	−1.53824	+	0.888104i
$991$	12.1383	+	21.0241i	0.385585	+	0.667853i	0.991850	−	0.127410i	$-0.0406663\pi$
$991$	12.1383	+	21.0241i	0.385585	+	0.667853i	−0.606265	+	0.795263i	$0.707333\pi$
$992$	3.95654	+	2.28431i	0.125620	+	0.0725269i
$993$		−	35.2095i		−	1.11734i
$994$	−23.8082	+	25.3955i	−0.755152	+	0.805496i
$995$	60.0045			1.90227
$996$	2.96874	+	1.71400i	0.0940680	+	0.0543102i
$997$	2.87855	−	1.66193i	0.0911647	−	0.0526340i	−0.453725	−	0.891142i	$-0.649905\pi$
$997$	2.87855	−	1.66193i	0.0911647	−	0.0526340i	0.544889	+	0.838508i	$0.316572\pi$
$998$	−34.1568	−	59.1612i	−1.08121	−	1.87272i
$999$	1.93012	−	3.34307i	0.0610664	−	0.105770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.g.a.68.2	yes	28
7.2	even	3		1127.2.c.c.1126.27		28
7.3	odd	6	inner	161.2.g.a.45.1	✓	28
7.5	odd	6		1127.2.c.c.1126.28		28
23.22	odd	2	inner	161.2.g.a.68.1	yes	28
161.45	even	6	inner	161.2.g.a.45.2	yes	28
161.68	even	6		1127.2.c.c.1126.26		28
161.114	odd	6		1127.2.c.c.1126.25		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.g.a.45.1	✓	28	7.3	odd	6	inner
161.2.g.a.45.2	yes	28	161.45	even	6	inner
161.2.g.a.68.1	yes	28	23.22	odd	2	inner
161.2.g.a.68.2	yes	28	1.1	even	1	trivial
1127.2.c.c.1126.25		28	161.114	odd	6
1127.2.c.c.1126.26		28	161.68	even	6
1127.2.c.c.1126.27		28	7.2	even	3
1127.2.c.c.1126.28		28	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23299 + 2.13559i) q^{2} +(0.854402 - 0.493289i) q^{3} +(-2.04051 - 3.53426i) q^{4} +(1.24346 - 2.15373i) q^{5} +2.43287i q^{6} +(2.57635 + 0.602017i) q^{7} +5.13171 q^{8} +(-1.01333 + 1.75514i) q^{9} +(3.06632 + 5.31103i) q^{10} +(3.89415 - 2.24829i) q^{11} +(-3.48683 - 2.01312i) q^{12} +2.10932i q^{13} +(-4.46226 + 4.75976i) q^{14} -2.45353i q^{15} +(-2.24632 + 3.89073i) q^{16} +(-2.00823 - 3.47836i) q^{17} +(-2.49885 - 4.32813i) q^{18} +(-2.91949 + 5.05671i) q^{19} -10.1491 q^{20} +(2.49821 - 0.756521i) q^{21} +11.0884i q^{22} +(0.792981 - 4.72982i) q^{23} +(4.38455 - 2.53142i) q^{24} +(-0.592363 - 1.02600i) q^{25} +(-4.50465 - 2.60076i) q^{26} +4.95920i q^{27} +(-3.12937 - 10.3339i) q^{28} +2.64981 q^{29} +(5.23975 + 3.02517i) q^{30} +(-4.85302 + 2.80189i) q^{31} +(-0.407637 - 0.706048i) q^{32} +(2.21811 - 3.84188i) q^{33} +9.90448 q^{34} +(4.50016 - 4.80017i) q^{35} +8.27083 q^{36} +(-0.674116 - 0.389201i) q^{37} +(-7.19938 - 12.4697i) q^{38} +(1.04051 + 1.80221i) q^{39} +(6.38106 - 11.0523i) q^{40} +1.68118i q^{41} +(-1.46463 + 6.26793i) q^{42} -8.94389i q^{43} +(-15.8921 - 9.17528i) q^{44} +(2.52006 + 4.36488i) q^{45} +(9.12323 + 7.52528i) q^{46} +(-6.98642 - 4.03361i) q^{47} +4.43234i q^{48} +(6.27515 + 3.10201i) q^{49} +2.92150 q^{50} +(-3.43167 - 1.98128i) q^{51} +(7.45489 - 4.30408i) q^{52} +(-5.49706 + 3.17373i) q^{53} +(-10.5908 - 6.11462i) q^{54} -11.1826i q^{55} +(13.2211 + 3.08938i) q^{56} +5.76061i q^{57} +(-3.26717 + 5.65891i) q^{58} +(-10.5475 + 6.08961i) q^{59} +(-8.67142 + 5.00645i) q^{60} +(2.93570 - 5.08478i) q^{61} -13.8188i q^{62} +(-3.66732 + 3.91181i) q^{63} -6.97482 q^{64} +(4.54291 + 2.62285i) q^{65} +(5.46980 + 9.47397i) q^{66} +(-13.6208 + 7.86395i) q^{67} +(-8.19562 + 14.1952i) q^{68} +(-1.65564 - 4.43234i) q^{69} +(4.70259 + 15.5290i) q^{70} +5.33546 q^{71} +(-5.20013 + 9.00688i) q^{72} +(3.15749 - 1.82298i) q^{73} +(1.66235 - 0.959758i) q^{74} +(-1.01223 - 0.584413i) q^{75} +23.8290 q^{76} +(11.3862 - 3.44803i) q^{77} -5.13171 q^{78} +(4.37340 + 2.52498i) q^{79} +(5.58639 + 9.67591i) q^{80} +(-0.593674 - 1.02827i) q^{81} +(-3.59033 - 2.07288i) q^{82} -0.851415 q^{83} +(-7.77135 - 7.28563i) q^{84} -9.98859 q^{85} +(19.1005 + 11.0277i) q^{86} +(2.26400 - 1.30712i) q^{87} +(19.9836 - 11.5376i) q^{88} +(3.97758 - 6.88938i) q^{89} -12.4288 q^{90} +(-1.26985 + 5.43435i) q^{91} +(-18.3345 + 6.84862i) q^{92} +(-2.76429 + 4.78788i) q^{93} +(17.2283 - 9.94677i) q^{94} +(7.26051 + 12.5756i) q^{95} +(-0.696572 - 0.402166i) q^{96} -2.72009 q^{97} +(-14.3618 + 9.57643i) q^{98} +9.11304i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 6 q^{3} - 12 q^{4} + 12 q^{8} + 4 q^{9} + 6 q^{12} + 22 q^{18} - 36 q^{24} - 22 q^{25} - 12 q^{26} - 44 q^{29} - 6 q^{32} - 10 q^{35} - 16 q^{39} + 18 q^{46} - 36 q^{47} + 28 q^{49} + 84 q^{50}+ \cdots - 146 q^{98}+O(q^{100}) \) 28 * q - 4 * q^2 - 6 * q^3 - 12 * q^4 + 12 * q^8 + 4 * q^9 + 6 * q^12 + 22 * q^18 - 36 * q^24 - 22 * q^25 - 12 * q^26 - 44 * q^29 - 6 * q^32 - 10 * q^35 - 16 * q^39 + 18 * q^46 - 36 * q^47 + 28 * q^49 + 84 * q^50 + 72 * q^52 - 30 * q^54 + 14 * q^58 - 54 * q^59 - 68 * q^64 + 38 * q^70 + 16 * q^71 - 4 * q^72 - 18 * q^73 + 96 * q^75 + 20 * q^77 - 12 * q^78 + 22 * q^81 - 52 * q^85 - 18 * q^87 - 28 * q^92 - 10 * q^93 + 84 * q^94 + 56 * q^95 - 84 * q^96 - 146 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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