LMFDB - Embedded newform 161.2.o.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(5,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("161.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$161 = 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	161.o (of order $66$ , degree $20$ , 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:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	161.103
Dual form			161.2.o.a.136.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0867328 - 1.82075i) q^{2} +(0.709180 + 1.77144i) q^{3} +(-1.31665 + 0.125725i) q^{4} +(-0.686053 + 2.82795i) q^{5} +(3.16384 - 1.44488i) q^{6} +(1.32416 + 2.29054i) q^{7} +(-0.175716 - 1.22213i) q^{8} +(-0.463879 + 0.442308i) q^{9} +(5.20848 + 1.00385i) q^{10} +(0.771055 + 0.0367299i) q^{11} +(-1.15646 - 2.24321i) q^{12} +(-0.954795 - 0.827335i) q^{13} +(4.05565 - 2.60963i) q^{14} +(-5.49609 + 0.790219i) q^{15} +(-4.80743 + 0.926556i) q^{16} +(2.47986 - 3.48247i) q^{17} +(0.845564 + 0.806243i) q^{18} +(-0.629425 - 0.883904i) q^{19} +(0.547749 - 3.80968i) q^{20} +(-3.11850 + 3.97009i) q^{21} -1.40708i q^{22} +(-3.59065 - 3.17918i) q^{23} +(2.04033 - 1.17798i) q^{24} +(-3.08245 - 1.58911i) q^{25} +(-1.42355 + 1.81020i) q^{26} +(4.09459 + 1.86993i) q^{27} +(-2.03144 - 2.84937i) q^{28} +(-3.69721 - 8.09575i) q^{29} +(1.91548 + 9.93845i) q^{30} +(0.180856 + 0.229977i) q^{31} +(1.52180 + 6.27295i) q^{32} +(0.481751 + 1.39193i) q^{33} +(-6.55578 - 4.21314i) q^{34} +(-7.38599 + 2.17323i) q^{35} +(0.555157 - 0.640686i) q^{36} +(6.61620 + 6.93887i) q^{37} +(-1.55477 + 1.22269i) q^{38} +(0.788457 - 2.27810i) q^{39} +(3.57668 + 0.341531i) q^{40} +(0.283675 + 0.966107i) q^{41} +(7.49900 + 5.33366i) q^{42} +(5.33475 + 0.767022i) q^{43} +(-1.01983 + 0.0485804i) q^{44} +(-0.932578 - 1.61527i) q^{45} +(-5.47706 + 6.81341i) q^{46} +(-5.52188 - 3.18806i) q^{47} +(-5.05067 - 7.85900i) q^{48} +(-3.49318 + 6.06611i) q^{49} +(-2.62602 + 5.75019i) q^{50} +(7.92766 + 1.92323i) q^{51} +(1.36115 + 0.969269i) q^{52} +(-11.3409 - 3.92512i) q^{53} +(3.04954 - 7.61739i) q^{54} +(-0.632855 + 2.15530i) q^{55} +(2.56667 - 2.02079i) q^{56} +(1.11941 - 1.74184i) q^{57} +(-14.4196 + 7.43384i) q^{58} +(-1.25368 + 6.50471i) q^{59} +(7.13708 - 1.73144i) q^{60} +(-3.32793 - 1.33230i) q^{61} +(0.403043 - 0.349239i) q^{62} +(-1.62738 - 0.476847i) q^{63} +(1.89430 - 0.556216i) q^{64} +(2.99470 - 2.13252i) q^{65} +(2.49257 - 0.997873i) q^{66} +(3.15064 - 6.11139i) q^{67} +(-2.82727 + 4.89698i) q^{68} +(3.08533 - 8.61526i) q^{69} +(4.59751 + 13.2595i) q^{70} +(8.76767 - 5.63464i) q^{71} +(0.622069 + 0.489201i) q^{72} +(-0.813474 - 8.51908i) q^{73} +(12.0601 - 12.6483i) q^{74} +(0.629017 - 6.58736i) q^{75} +(0.939862 + 1.08466i) q^{76} +(0.936871 + 1.81477i) q^{77} +(-4.21622 - 1.23799i) q^{78} +(-2.36896 + 0.819906i) q^{79} +(0.677898 - 14.2308i) q^{80} +(-0.500183 + 10.5001i) q^{81} +(1.73443 - 0.600293i) q^{82} +(17.0454 + 5.00499i) q^{83} +(3.60684 - 5.61929i) q^{84} +(8.14693 + 9.40206i) q^{85} +(0.933854 - 9.77976i) q^{86} +(11.7192 - 12.2907i) q^{87} +(-0.0905980 - 0.948785i) q^{88} +(-10.4991 - 8.25662i) q^{89} +(-2.86012 + 1.83809i) q^{90} +(0.630742 - 3.28253i) q^{91} +(5.12734 + 3.73444i) q^{92} +(-0.279132 + 0.483471i) q^{93} +(-5.32571 + 10.3304i) q^{94} +(2.93146 - 1.17358i) q^{95} +(-10.0330 + 7.14444i) q^{96} +(-5.40596 + 1.58733i) q^{97} +(11.3478 + 5.83407i) q^{98} +(-0.373922 + 0.324005i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$280 q - 7 q^{2} - 27 q^{3} + q^{4} - 33 q^{5} - 22 q^{7} - 56 q^{8} - 15 q^{9} - 33 q^{10} - 11 q^{11} - 39 q^{12} - 22 q^{14} - 44 q^{15} + 11 q^{16} - 33 q^{17} - 77 q^{18} - 33 q^{19} + 44 q^{21} + 11 q^{23}+ \cdots - 198 q^{99}+O(q^{100})$ 280 * q - 7 * q^2 - 27 * q^3 + q^4 - 33 * q^5 - 22 * q^7 - 56 * q^8 - 15 * q^9 - 33 * q^10 - 11 * q^11 - 39 * q^12 - 22 * q^14 - 44 * q^15 + 11 * q^16 - 33 * q^17 - 77 * q^18 - 33 * q^19 + 44 * q^21 + 11 * q^23 - 30 * q^24 - 11 * q^25 - 21 * q^26 + 66 * q^28 + 33 * q^30 - 33 * q^31 - 27 * q^32 - 33 * q^33 + 10 * q^35 + 66 * q^36 - 55 * q^37 - 33 * q^38 + 5 * q^39 - 33 * q^40 + 88 * q^42 + 44 * q^43 - 66 * q^44 - 29 * q^46 - 30 * q^47 + 16 * q^49 + 26 * q^50 - 55 * q^51 - 105 * q^52 - 11 * q^53 - 3 * q^54 + 99 * q^56 + 44 * q^57 - 36 * q^58 + 21 * q^59 - 11 * q^60 - 33 * q^61 + 33 * q^63 + 24 * q^64 + 66 * q^65 + 66 * q^66 - 11 * q^67 + 6 * q^70 - 60 * q^71 + 59 * q^72 - 15 * q^73 - 129 * q^75 + 13 * q^77 - 252 * q^78 + 33 * q^79 + 264 * q^80 + 99 * q^81 - 33 * q^82 + 44 * q^84 - 212 * q^85 + 11 * q^86 + 381 * q^87 + 198 * q^88 - 33 * q^89 - 214 * q^92 - 12 * q^93 + 180 * q^94 + 32 * q^95 + 51 * q^96 + 80 * q^98 - 198 * q^99

Character values

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

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (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

)

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

$2$	−0.0867328	−	1.82075i	−0.0613294	−	1.28746i	−0.794436	−	0.607348i	$-0.792233\pi$
$2$	−0.0867328	−	1.82075i	−0.0613294	−	1.28746i	0.733106	−	0.680114i	$-0.238070\pi$
$3$	0.709180	+	1.77144i	0.409445	+	1.02274i	0.979555	+	0.201176i	$0.0644763\pi$
$3$	0.709180	+	1.77144i	0.409445	+	1.02274i	−0.570110	+	0.821568i	$0.693099\pi$
$4$	−1.31665	+	0.125725i	−0.658325	+	0.0628625i
$5$	−0.686053	+	2.82795i	−0.306812	+	1.26470i	0.584532	+	0.811371i	$0.301278\pi$
$5$	−0.686053	+	2.82795i	−0.306812	+	1.26470i	−0.891344	+	0.453327i	$0.850237\pi$
$6$	3.16384	−	1.44488i	1.29163	−	0.589869i
$7$	1.32416	+	2.29054i	0.500487	+	0.865744i
$7$	1.32416	+	2.29054i	0.500487	+	0.865744i
$8$	−0.175716	−	1.22213i	−0.0621250	−	0.432089i
$9$	−0.463879	+	0.442308i	−0.154626	+	0.147436i
$10$	5.20848	+	1.00385i	1.64707	+	0.317446i
$11$	0.771055	+	0.0367299i	0.232482	+	0.0110745i	0.163499	−	0.986543i	$-0.447722\pi$
$11$	0.771055	+	0.0367299i	0.232482	+	0.0110745i	0.0689822	+	0.997618i	$0.478025\pi$
$12$	−1.15646	−	2.24321i	−0.333840	−	0.647560i
$13$	−0.954795	−	0.827335i	−0.264813	−	0.229461i	0.512326	−	0.858791i	$-0.328784\pi$
$13$	−0.954795	−	0.827335i	−0.264813	−	0.229461i	−0.777138	+	0.629330i	$0.783329\pi$
$14$	4.05565	−	2.60963i	1.08392	−	0.697453i
$15$	−5.49609	+	0.790219i	−1.41908	+	0.204034i
$16$	−4.80743	+	0.926556i	−1.20186	+	0.231639i
$17$	2.47986	−	3.48247i	0.601453	−	0.844623i	−0.395827	−	0.918325i	$-0.629542\pi$
$17$	2.47986	−	3.48247i	0.601453	−	0.844623i	0.997280	+	0.0737022i	$0.0234814\pi$
$18$	0.845564	+	0.806243i	0.199301	+	0.190033i
$19$	−0.629425	−	0.883904i	−0.144400	−	0.202782i	0.736041	−	0.676937i	$-0.236693\pi$
$19$	−0.629425	−	0.883904i	−0.144400	−	0.202782i	−0.880441	+	0.474155i	$0.842754\pi$
$20$	0.547749	−	3.80968i	0.122480	−	0.851869i
$21$	−3.11850	+	3.97009i	−0.680513	+	0.866345i
$22$		−	1.40708i		−	0.299991i
$23$	−3.59065	−	3.17918i	−0.748703	−	0.662906i
$23$	−3.59065	−	3.17918i	−0.748703	−	0.662906i
$24$	2.04033	−	1.17798i	0.416480	−	0.240455i
$25$	−3.08245	−	1.58911i	−0.616490	−	0.317823i
$26$	−1.42355	+	1.81020i	−0.279182	+	0.355009i
$27$	4.09459	+	1.86993i	0.788003	+	0.359869i
$28$	−2.03144	−	2.84937i	−0.383906	−	0.538480i
$29$	−3.69721	−	8.09575i	−0.686554	−	1.50334i	−0.855546	−	0.517726i	$-0.826779\pi$
$29$	−3.69721	−	8.09575i	−0.686554	−	1.50334i	0.168992	−	0.985617i	$-0.445949\pi$
$30$	1.91548	+	9.93845i	0.349717	+	1.81450i
$31$	0.180856	+	0.229977i	0.0324826	+	0.0413050i	0.802023	−	0.597293i	$-0.203757\pi$
$31$	0.180856	+	0.229977i	0.0324826	+	0.0413050i	−0.769540	+	0.638598i	$0.779515\pi$
$32$	1.52180	+	6.27295i	0.269019	+	1.10891i
$33$	0.481751	+	1.39193i	0.0838621	+	0.242304i
$34$	−6.55578	−	4.21314i	−1.12431	−	0.722548i
$35$	−7.38599	+	2.17323i	−1.24846	+	0.367343i
$36$	0.555157	−	0.640686i	0.0925262	−	0.106781i
$37$	6.61620	+	6.93887i	1.08770	+	1.14074i	0.989345	+	0.145592i	$0.0465087\pi$
$37$	6.61620	+	6.93887i	1.08770	+	1.14074i	0.0983524	+	0.995152i	$0.468643\pi$
$38$	−1.55477	+	1.22269i	−0.252218	+	0.198346i
$39$	0.788457	−	2.27810i	0.126254	−	0.364787i
$40$	3.57668	+	0.341531i	0.565523	+	0.0540009i
$41$	0.283675	+	0.966107i	0.0443025	+	0.150881i	0.978674	−	0.205420i	$-0.0658561\pi$
$41$	0.283675	+	0.966107i	0.0443025	+	0.150881i	−0.934371	+	0.356301i	$0.884038\pi$
$42$	7.49900	+	5.33366i	1.15712	+	0.823002i
$43$	5.33475	+	0.767022i	0.813543	+	0.116970i	0.536513	−	0.843892i	$-0.319741\pi$
$43$	5.33475	+	0.767022i	0.813543	+	0.116970i	0.277029	+	0.960862i	$0.410650\pi$
$44$	−1.01983	+	0.0485804i	−0.153745	+	0.00732377i
$45$	−0.932578	−	1.61527i	−0.139021	−	0.240791i
$46$	−5.47706	+	6.81341i	−0.807549	+	1.00458i
$47$	−5.52188	−	3.18806i	−0.805448	−	0.465026i	0.0399243	−	0.999203i	$-0.487288\pi$
$47$	−5.52188	−	3.18806i	−0.805448	−	0.465026i	−0.845373	+	0.534177i	$0.820622\pi$
$48$	−5.05067	−	7.85900i	−0.729002	−	1.13435i
$49$	−3.49318	+	6.06611i	−0.499026	+	0.866587i
$50$	−2.62602	+	5.75019i	−0.371376	+	0.813200i
$51$	7.92766	+	1.92323i	1.11010	+	0.269306i
$52$	1.36115	+	0.969269i	0.188757	+	0.134413i
$53$	−11.3409	−	3.92512i	−1.55779	−	0.539157i	−0.593692	−	0.804693i	$-0.702330\pi$
$53$	−11.3409	−	3.92512i	−1.55779	−	0.539157i	−0.964101	+	0.265535i	$0.914451\pi$
$54$	3.04954	−	7.61739i	0.414990	−	1.03659i
$55$	−0.632855	+	2.15530i	−0.0853341	+	0.290621i
$56$	2.56667	−	2.02079i	0.342986	−	0.270039i
$57$	1.11941	−	1.74184i	0.148270	−	0.230712i
$58$	−14.4196	+	7.43384i	−1.89339	+	0.976111i
$59$	−1.25368	+	6.50471i	−0.163215	+	0.846841i	0.804338	+	0.594172i	$0.202520\pi$
$59$	−1.25368	+	6.50471i	−0.163215	+	0.846841i	−0.967553	+	0.252668i	$0.918692\pi$
$60$	7.13708	−	1.73144i	0.921393	−	0.223528i
$61$	−3.32793	−	1.33230i	−0.426098	−	0.170584i	0.148695	−	0.988883i	$-0.452493\pi$
$61$	−3.32793	−	1.33230i	−0.426098	−	0.170584i	−0.574792	+	0.818299i	$0.694917\pi$
$62$	0.403043	−	0.349239i	0.0511865	−	0.0443534i
$63$	−1.62738	−	0.476847i	−0.205030	−	0.0600771i
$64$	1.89430	−	0.556216i	0.236787	−	0.0695270i
$65$	2.99470	−	2.13252i	0.371447	−	0.264506i
$66$	2.49257	−	0.997873i	0.306814	−	0.122830i
$67$	3.15064	−	6.11139i	0.384912	−	0.746625i	−0.614183	−	0.789164i	$-0.710514\pi$
$67$	3.15064	−	6.11139i	0.384912	−	0.746625i	0.999095	+	0.0425385i	$0.0135445\pi$
$68$	−2.82727	+	4.89698i	−0.342857	+	0.593845i
$69$	3.08533	−	8.61526i	0.371430	−	1.03715i
$70$	4.59751	+	13.2595i	0.549508	+	1.58482i
$71$	8.76767	−	5.63464i	1.04053	−	0.668708i	0.0954127	−	0.995438i	$-0.469583\pi$
$71$	8.76767	−	5.63464i	1.04053	−	0.668708i	0.945118	+	0.326729i	$0.105947\pi$
$72$	0.622069	+	0.489201i	0.0733116	+	0.0576529i
$73$	−0.813474	−	8.51908i	−0.0952099	−	0.997083i	−0.909243	−	0.416265i	$-0.863339\pi$
$73$	−0.813474	−	8.51908i	−0.0952099	−	0.997083i	0.814033	−	0.580818i	$-0.197267\pi$
$74$	12.0601	−	12.6483i	1.40196	−	1.47033i
$75$	0.629017	−	6.58736i	0.0726326	−	0.760643i
$76$	0.939862	+	1.08466i	0.107810	+	0.124419i
$77$	0.936871	+	1.81477i	0.106766	+	0.206812i
$78$	−4.21622	−	1.23799i	−0.477393	−	0.140175i
$79$	−2.36896	+	0.819906i	−0.266529	+	0.0922467i	−0.457064	−	0.889434i	$-0.651099\pi$
$79$	−2.36896	+	0.819906i	−0.266529	+	0.0922467i	0.190535	+	0.981680i	$0.438978\pi$
$80$	0.677898	−	14.2308i	0.0757913	−	1.59106i
$81$	−0.500183	+	10.5001i	−0.0555759	+	1.16668i
$82$	1.73443	−	0.600293i	0.191536	−	0.0662912i
$83$	17.0454	+	5.00499i	1.87098	+	0.549369i	0.998113	+	0.0614078i	$0.0195590\pi$
$83$	17.0454	+	5.00499i	1.87098	+	0.549369i	0.872865	+	0.487961i	$0.162259\pi$
$84$	3.60684	−	5.61929i	0.393538	−	0.613115i
$85$	8.14693	+	9.40206i	0.883659	+	1.01980i
$86$	0.933854	−	9.77976i	0.100700	−	1.05458i
$87$	11.7192	−	12.2907i	1.25643	−	1.31771i
$88$	−0.0905980	−	0.948785i	−0.00965778	−	0.101141i
$89$	−10.4991	−	8.25662i	−1.11291	−	0.875200i	−0.119845	−	0.992793i	$-0.538240\pi$
$89$	−10.4991	−	8.25662i	−1.11291	−	0.875200i	−0.993062	+	0.117593i	$0.962482\pi$
$90$	−2.86012	+	1.83809i	−0.301483	+	0.193751i
$91$	0.630742	−	3.28253i	0.0661197	−	0.344102i
$92$	5.12734	+	3.73444i	0.534562	+	0.389342i
$93$	−0.279132	+	0.483471i	−0.0289446	+	0.0501336i
$94$	−5.32571	+	10.3304i	−0.549305	+	1.06550i
$95$	2.93146	−	1.17358i	0.300761	−	0.120407i
$96$	−10.0330	+	7.14444i	−1.02398	+	0.729176i
$97$	−5.40596	+	1.58733i	−0.548892	+	0.161169i	−0.544408	−	0.838821i	$-0.683246\pi$
$97$	−5.40596	+	1.58733i	−0.548892	+	0.161169i	−0.00448422	+	0.999990i	$0.501427\pi$
$98$	11.3478	+	5.83407i	1.14630	+	0.589330i
$99$	−0.373922	+	0.324005i	−0.0375806	+	0.0325637i
$100$	4.25830	+	1.70477i	0.425830	+	0.170477i
$101$	−16.1652	+	3.92163i	−1.60850	+	0.390217i	−0.936592	−	0.350422i	$-0.886038\pi$
$101$	−16.1652	+	3.92163i	−1.60850	+	0.390217i	−0.671904	+	0.740639i	$0.734523\pi$
$102$	2.81413	−	14.6011i	0.278640	−	1.44572i
$103$	−8.24652	+	4.25138i	−0.812554	+	0.418901i	−0.813833	−	0.581098i	$-0.802623\pi$
$103$	−8.24652	+	4.25138i	−0.812554	+	0.418901i	0.00127916	+	0.999999i	$0.499593\pi$
$104$	−0.843340	+	1.31226i	−0.0826963	+	0.128678i
$105$	−9.08775	−	11.5427i	−0.886874	−	1.12645i
$106$	−6.16303	+	20.9893i	−0.598606	+	2.03867i
$107$	3.53298	−	8.82496i	0.341546	−	0.853141i	−0.653790	−	0.756676i	$-0.726822\pi$
$107$	3.53298	−	8.82496i	0.341546	−	0.853141i	0.995336	−	0.0964654i	$-0.0307537\pi$
$108$	−5.62624	−	1.94726i	−0.541385	−	0.187375i
$109$	2.52052	+	1.79485i	0.241422	+	0.171916i	0.694363	−	0.719624i	$-0.255686\pi$
$109$	2.52052	+	1.79485i	0.241422	+	0.171916i	−0.452942	+	0.891540i	$0.649625\pi$
$110$	3.97915	+	0.965332i	0.379397	+	0.0920408i
$111$	−7.59976	+	16.6411i	−0.721337	+	1.57951i
$112$	−8.48814	−	9.78471i	−0.802054	−	0.924569i
$113$	4.53586	+	7.05793i	0.426697	+	0.663954i	0.986329	−	0.164787i	$-0.0526937\pi$
$113$	4.53586	+	7.05793i	0.426697	+	0.663954i	−0.559632	+	0.828741i	$0.689057\pi$
$114$	−3.26854	−	1.88709i	−0.306127	−	0.176742i
$115$	11.4540	−	7.97309i	1.06809	−	0.743495i
$116$	5.88577	+	10.1944i	0.546480	+	0.946531i
$117$	0.808846	−	0.0385301i	0.0747778	−	0.00356211i
$118$	11.9522	+	1.71846i	1.10029	+	0.158197i
$119$	11.2605	+	1.06886i	1.03225	+	0.0979821i
$120$	1.93150	+	6.57810i	0.176321	+	0.600495i
$121$	−10.3570	−	0.988975i	−0.941547	−	0.0899068i
$122$	−2.13714	+	6.17487i	−0.193488	+	0.559046i
$123$	−1.51023	+	1.18766i	−0.136173	+	0.107087i
$124$	−0.267038	−	0.280061i	−0.0239807	−	0.0251502i
$125$	−2.91949	+	3.36927i	−0.261127	+	0.301357i
$126$	−0.727071	+	3.00440i	−0.0647726	+	0.267653i
$127$	10.6761	+	6.86113i	0.947353	+	0.608827i	0.920471	−	0.390812i	$-0.127806\pi$
$127$	10.6761	+	6.86113i	0.947353	+	0.608827i	0.0268827	+	0.999639i	$0.491442\pi$
$128$	3.04536	+	8.79899i	0.269174	+	0.777729i
$129$	2.42456	+	9.99418i	0.213471	+	0.879938i
$130$	−4.14251	−	5.26763i	−0.363322	−	0.462002i
$131$	3.71745	+	19.2879i	0.324795	+	1.68520i	0.666593	+	0.745422i	$0.267752\pi$
$131$	3.71745	+	19.2879i	0.324795	+	1.68520i	−0.341798	+	0.939773i	$0.611036\pi$
$132$	−0.809298	−	1.77212i	−0.0704404	−	0.154243i
$133$	1.19116	−	2.61216i	0.103287	−	0.226503i
$134$	−11.4006	−	5.20646i	−0.984858	−	0.449770i
$135$	−8.09718	+	10.2964i	−0.696895	+	0.886174i
$136$	−4.69179	−	2.41878i	−0.402318	−	0.207409i
$137$	−7.34045	+	4.23801i	−0.627137	+	0.362078i	−0.779643	−	0.626225i	$-0.784599\pi$
$137$	−7.34045	+	4.23801i	−0.627137	+	0.362078i	0.152505	+	0.988303i	$0.451266\pi$
$138$	−15.9538	−	4.87038i	−1.35808	−	0.414595i
$139$			9.59921i			0.814194i	0.913385	+	0.407097i	$0.133459\pi$
$139$			9.59921i			0.814194i	−0.913385	+	0.407097i	$0.866541\pi$
$140$	9.45154	−	3.78999i	0.798801	−	0.320313i
$141$	1.73146	−	12.0426i	0.145816	−	1.01417i
$142$	−11.0197	−	15.4750i	−0.924752	−	1.29863i
$143$	−0.705811	−	0.672990i	−0.0590229	−	0.0562782i
$144$	1.82024	−	2.55617i	0.151687	−	0.213014i
$145$	25.4309	−	4.90140i	2.11192	−	0.407039i
$146$	−15.4405	+	2.22001i	−1.27787	+	0.183730i
$147$	−13.2231	−	1.88602i	−1.09062	−	0.155556i
$148$	−9.58362	−	8.30425i	−0.787769	−	0.682605i
$149$	8.30022	+	16.1002i	0.679981	+	1.31898i	0.935895	+	0.352279i	$0.114593\pi$
$149$	8.30022	+	16.1002i	0.679981	+	1.31898i	−0.255914	+	0.966699i	$0.582377\pi$
$150$	−12.0485	−	0.573939i	−0.983753	−	0.0468619i
$151$	−11.9189	−	2.29717i	−0.969944	−	0.186941i	−0.320414	−	0.947278i	$-0.603822\pi$
$151$	−11.9189	−	2.29717i	−0.969944	−	0.186941i	−0.649530	+	0.760336i	$0.725034\pi$
$152$	−0.969648	+	0.924557i	−0.0786488	+	0.0749915i
$153$	0.389970	+	2.71230i	0.0315272	+	0.219277i
$154$	3.22298	−	1.86320i	0.259715	−	0.150141i
$155$	−0.774439	+	0.353674i	−0.0622044	+	0.0284078i
$156$	−0.751709	+	3.09859i	−0.0601849	+	0.248085i
$157$	15.5506	−	1.48491i	1.24108	−	0.118508i	0.546210	−	0.837648i	$-0.316070\pi$
$157$	15.5506	−	1.48491i	1.24108	−	0.118508i	0.694866	+	0.719140i	$0.255464\pi$
$158$	1.69831	+	4.24217i	0.135110	+	0.337489i
$159$	−1.08959	−	22.8734i	−0.0864104	−	1.81398i
$160$	−18.7836			−1.48498
$161$	2.52745	−	12.4343i	0.199191	−	0.979961i
$162$	19.1615			1.50547
$163$	−0.646012	−	13.5615i	−0.0505996	−	1.06222i	−0.871267	−	0.490810i	$-0.836701\pi$
$163$	−0.646012	−	13.5615i	−0.0505996	−	1.06222i	0.820667	−	0.571406i	$-0.193602\pi$
$164$	−0.494964	−	1.23636i	−0.0386502	−	0.0965435i
$165$	−4.26681	+	0.407431i	−0.332171	+	0.0317185i
$166$	7.63442	−	31.4695i	0.592546	−	2.44251i
$167$	12.1370	−	5.54280i	0.939192	−	0.428914i	0.113818	−	0.993502i	$-0.463692\pi$
$167$	12.1370	−	5.54280i	0.939192	−	0.428914i	0.825373	+	0.564587i	$0.190965\pi$
$168$	5.39995	+	3.11361i	0.416615	+	0.240221i
$169$	−1.62294	−	11.2878i	−0.124842	−	0.868293i
$170$	16.4122	−	15.6490i	1.25876	−	1.20022i
$171$	0.682935	+	0.131625i	0.0522253	+	0.0100656i
$172$	−7.12044	−	0.339188i	−0.542929	−	0.0258629i
$173$	5.24777	+	10.1793i	0.398981	+	0.773915i	0.999673	−	0.0255656i	$-0.00813866\pi$
$173$	5.24777	+	10.1793i	0.398981	+	0.773915i	−0.600692	+	0.799480i	$0.705108\pi$
$174$	−23.3948	−	20.2717i	−1.77355	−	1.53679i
$175$	−0.441734	−	9.16474i	−0.0333920	−	0.692789i
$176$	−3.74082	+	0.537849i	−0.281975	+	0.0405419i
$177$	−12.4118	+	2.39218i	−0.932929	+	0.179807i
$178$	−14.1226	+	19.8324i	−1.05853	+	1.48650i
$179$	5.64624	+	5.38368i	0.422020	+	0.402395i	0.871107	−	0.491093i	$-0.163402\pi$
$179$	5.64624	+	5.38368i	0.422020	+	0.402395i	−0.449088	+	0.893488i	$0.648251\pi$
$180$	1.43096	+	2.00950i	0.106657	+	0.149779i
$181$	−1.43524	+	9.98235i	−0.106681	+	0.741982i	0.864326	+	0.502932i	$0.167745\pi$
$181$	−1.43524	+	9.98235i	−0.106681	+	0.741982i	−0.971007	+	0.239050i	$0.923164\pi$
$182$	−6.03135	−	0.863718i	−0.447074	−	0.0640230i
$183$		−	6.84008i		−	0.505633i
$184$	−3.25445	+	4.94689i	−0.239921	+	0.364689i
$185$	−24.1619	+	13.9499i	−1.77641	+	1.02561i
$186$	0.904487	+	0.466296i	0.0663202	+	0.0341904i
$187$	2.04001	−	2.59409i	0.149181	−	0.189699i
$188$	7.67120	+	3.50332i	0.559480	+	0.255506i
$189$	1.13873	+	11.8549i	0.0828307	+	0.862319i
$190$	−2.39104	−	5.23565i	−0.173464	−	0.379834i
$191$	0.525788	+	2.72805i	0.0380447	+	0.197395i	0.995978	−	0.0895955i	$-0.0285574\pi$
$191$	0.525788	+	2.72805i	0.0380447	+	0.197395i	−0.957934	+	0.286990i	$0.907345\pi$
$192$	2.32870	+	2.96119i	0.168060	+	0.213705i
$193$	−1.19792	−	4.93789i	−0.0862281	−	0.355437i	0.912309	−	0.409502i	$-0.134297\pi$
$193$	−1.19792	−	4.93789i	−0.0862281	−	0.355437i	−0.998537	+	0.0540647i	$0.982782\pi$
$194$	3.35900	+	9.70521i	0.241162	+	0.696793i
$195$	5.90142	+	3.79261i	0.422609	+	0.271594i
$196$	3.83664	−	8.42613i	0.274046	−	0.601866i
$197$	4.08767	−	4.71743i	0.291235	−	0.336103i	−0.591211	−	0.806517i	$-0.701350\pi$
$197$	4.08767	−	4.71743i	0.291235	−	0.336103i	0.882446	+	0.470414i	$0.155895\pi$
$198$	0.622363	+	0.652715i	0.0442294	+	0.0463864i
$199$	0.862612	−	0.678365i	0.0611489	−	0.0480880i	−0.587117	−	0.809502i	$-0.699737\pi$
$199$	0.862612	−	0.678365i	0.0611489	−	0.0480880i	0.648266	+	0.761414i	$0.275495\pi$
$200$	−1.40047	+	4.04640i	−0.0990283	+	0.286123i
$201$	13.0604	+	1.24711i	0.921207	+	0.0879646i
$202$	8.54235	+	29.0926i	0.601037	+	2.04695i
$203$	13.6480	−	19.1887i	0.957900	−	1.34678i
$204$	−10.6798	−	1.53552i	−0.747733	−	0.107508i
$205$	−2.92672	+	0.139417i	−0.204411	+	0.00973729i
$206$	8.45593	+	14.6461i	0.589152	+	1.02044i
$207$	3.07181	−	0.113416i	0.213505	−	0.00788298i
$208$	5.35668	+	3.09268i	0.371419	+	0.214439i
$209$	−0.452856	−	0.704657i	−0.0313247	−	0.0487422i
$210$	−20.2280	+	17.5476i	−1.39587	+	1.21090i
$211$	−3.53239	+	7.73486i	−0.243180	+	0.532490i	−0.991385	−	0.130978i	$-0.958188\pi$
$211$	−3.53239	+	7.73486i	−0.243180	+	0.532490i	0.748206	+	0.663467i	$0.230916\pi$
$212$	15.4255	+	3.74218i	1.05943	+	0.257014i
$213$	16.1993	+	11.5355i	1.10996	+	0.790397i
$214$	−16.3744	−	5.66725i	−1.11933	−	0.387405i
$215$	−5.82902	+	14.5602i	−0.397536	+	0.992997i
$216$	1.56582	−	5.33270i	0.106541	−	0.362844i
$217$	−0.287289	+	0.718784i	−0.0195025	+	0.0487943i
$218$	3.04936	−	4.74490i	0.206529	−	0.321365i
$219$	14.5142	−	7.48258i	0.980778	−	0.505626i
$220$	0.562273	−	2.91735i	0.0379084	−	0.196688i
$221$	−5.24892	+	1.27337i	−0.353081	+	0.0856564i
$222$	30.9585	+	12.3939i	2.07780	+	0.831824i
$223$	7.08652	−	6.14051i	0.474549	−	0.411199i	−0.384474	−	0.923136i	$-0.625617\pi$
$223$	7.08652	−	6.14051i	0.474549	−	0.411199i	0.859023	+	0.511937i	$0.171072\pi$
$224$	−12.3534	+	11.7922i	−0.825394	+	0.787898i
$225$	2.13276	−	0.626235i	0.142184	−	0.0417490i
$226$	12.4573	−	8.87080i	0.828647	−	0.590077i
$227$	10.4097	−	4.16742i	0.690917	−	0.276602i	0.000486348	−	1.00000i	$-0.499845\pi$
$227$	10.4097	−	4.16742i	0.690917	−	0.276602i	0.690431	+	0.723398i	$0.257421\pi$
$228$	−1.25488	+	2.43413i	−0.0831066	+	0.161204i
$229$	−13.1638	+	22.8004i	−0.869890	+	1.50669i	−0.00778163	+	0.999970i	$0.502477\pi$
$229$	−13.1638	+	22.8004i	−0.869890	+	1.50669i	−0.862108	+	0.506724i	$0.830856\pi$
$230$	−15.5104	−	20.1632i	−1.02273	−	1.32952i
$231$	−2.55036	+	2.94661i	−0.167801	+	0.193873i
$232$	−9.24442	+	5.94103i	−0.606926	+	0.390048i
$233$	−9.49925	−	7.47029i	−0.622316	−	0.489395i	0.256507	−	0.966542i	$-0.417428\pi$
$233$	−9.49925	−	7.47029i	−0.622316	−	0.489395i	−0.878823	+	0.477147i	$0.841671\pi$
$234$	−0.140307	−	1.46936i	−0.00917216	−	0.0960552i
$235$	12.8040	−	13.4284i	0.835238	−	0.875973i
$236$	0.832854	−	8.72205i	0.0542142	−	0.567757i
$237$	−3.13244	−	3.61503i	−0.203474	−	0.234821i
$238$	0.969466	−	20.5952i	0.0628412	−	1.33499i
$239$	−21.1205	−	6.20154i	−1.36617	−	0.401144i	−0.485237	−	0.874383i	$-0.661267\pi$
$239$	−21.1205	−	6.20154i	−1.36617	−	0.401144i	−0.880934	+	0.473239i	$0.843085\pi$
$240$	25.6899	−	8.89135i	1.65827	−	0.573934i
$241$	0.867091	−	18.2025i	0.0558542	−	1.17252i	−0.780796	−	0.624787i	$-0.785186\pi$
$241$	0.867091	−	18.2025i	0.0558542	−	1.17252i	0.836650	−	0.547738i	$-0.184511\pi$
$242$	−0.902379	+	18.9433i	−0.0580071	+	1.21772i
$243$	−6.19374	+	2.14367i	−0.397329	+	0.137517i
$244$	4.54922	+	1.33577i	0.291234	+	0.0855141i
$245$	−14.7581	−	14.0402i	−0.942863	−	0.896996i
$246$	2.29341	+	2.64673i	0.146222	+	0.168750i
$247$	−0.130312	+	1.36469i	−0.00829158	+	0.0868333i
$248$	0.249283	−	0.261440i	0.0158295	−	0.0166015i
$249$	3.22221	+	33.7445i	0.204199	+	2.13847i
$250$	6.38780	+	5.02342i	0.404000	+	0.317709i
$251$	3.93107	−	2.52634i	0.248127	−	0.159461i	−0.410666	−	0.911786i	$-0.634704\pi$
$251$	3.93107	−	2.52634i	0.248127	−	0.159461i	0.658793	+	0.752324i	$0.271067\pi$
$252$	2.20264	+	0.423240i	0.138753	+	0.0266616i
$253$	−2.65182	−	2.58321i	−0.166718	−	0.162405i
$254$	11.5664	−	20.0336i	0.725741	−	1.25702i
$255$	−10.8776	+	21.0996i	−0.681182	+	1.32131i
$256$	19.4223	−	7.77552i	1.21389	−	0.485970i
$257$	−2.97334	+	2.11731i	−0.185472	+	0.132074i	−0.669022	−	0.743243i	$-0.733287\pi$
$257$	−2.97334	+	2.11731i	−0.185472	+	0.132074i	0.483550	+	0.875317i	$0.339347\pi$
$258$	17.9866	−	5.28134i	1.11980	−	0.328802i
$259$	−7.13286	+	24.3429i	−0.443214	+	1.51259i
$260$	−3.67486	+	3.18429i	−0.227905	+	0.197481i
$261$	5.29587	+	2.12015i	0.327806	+	0.131234i
$262$	34.7960	−	8.44142i	2.14971	−	0.521513i
$263$	−2.01688	+	10.4646i	−0.124366	+	0.645272i	0.865227	+	0.501380i	$0.167174\pi$
$263$	−2.01688	+	10.4646i	−0.124366	+	0.645272i	−0.989593	+	0.143892i	$0.954038\pi$
$264$	1.61647	−	0.833348i	0.0994868	−	0.0512890i
$265$	18.8805	−	29.3787i	1.15982	−	1.80472i
$266$	−4.85939	−	1.94224i	−0.297949	−	0.119086i
$267$	7.18036	−	24.4541i	0.439431	−	1.49656i
$268$	−3.37994	+	8.44268i	−0.206463	+	0.515719i
$269$	−18.9285	−	6.55123i	−1.15409	−	0.399436i	−0.318037	−	0.948078i	$-0.603024\pi$
$269$	−18.9285	−	6.55123i	−1.15409	−	0.399436i	−0.836057	+	0.548643i	$0.815145\pi$
$270$	19.4494	+	13.8499i	1.18365	+	0.842877i
$271$	−12.0485	−	2.92294i	−0.731896	−	0.177556i	−0.147543	−	0.989056i	$-0.547136\pi$
$271$	−12.0485	−	2.92294i	−0.731896	−	0.177556i	−0.584353	+	0.811500i	$0.698652\pi$
$272$	−8.69502	+	19.0394i	−0.527213	+	1.15444i
$273$	6.26212	−	1.21058i	0.379001	−	0.0732674i
$274$	8.35300	+	12.9975i	0.504623	+	0.785209i
$275$	−2.31837	−	1.33851i	−0.139803	−	0.0807153i
$276$	−2.97915	+	11.7312i	−0.179324	+	0.706134i
$277$	−2.78792	−	4.82881i	−0.167510	−	0.290135i	0.770034	−	0.638003i	$-0.220239\pi$
$277$	−2.78792	−	4.82881i	−0.167510	−	0.290135i	−0.937544	+	0.347868i	$0.886906\pi$
$278$	17.4777	−	0.832567i	1.04824	−	0.0499340i
$279$	−0.185616	−	0.0266875i	−0.0111125	−	0.00159774i
$280$	3.95381	+	8.64478i	0.236286	+	0.516625i
$281$	−1.49088	−	5.07748i	−0.0889386	−	0.302897i	0.902996	−	0.429649i	$-0.141363\pi$
$281$	−1.49088	−	5.07748i	−0.0889386	−	0.302897i	−0.991934	+	0.126752i	$0.959545\pi$
$282$	−22.0767	−	2.10807i	−1.31465	−	0.125534i
$283$	0.649487	−	1.87657i	0.0386080	−	0.111551i	−0.924049	−	0.382273i	$-0.875141\pi$
$283$	0.649487	−	1.87657i	0.0386080	−	0.111551i	0.962657	+	0.270723i	$0.0872626\pi$
$284$	−10.8355	+	8.52116i	−0.642971	+	0.505638i
$285$	4.15786	+	4.36063i	0.246290	+	0.258302i
$286$	−1.16413	+	1.34347i	−0.0688363	+	0.0794413i
$287$	−1.83728	+	1.92905i	−0.108451	+	0.113868i
$288$	−3.48051	−	2.23679i	−0.205091	−	0.131804i
$289$	−0.417755	−	1.20702i	−0.0245738	−	0.0710014i
$290$	−11.1299	−	45.8780i	−0.653570	−	2.69405i
$291$	−6.64567	−	8.45065i	−0.389576	−	0.495386i
$292$	2.14212	+	11.1144i	0.125358	+	0.650420i
$293$	0.423524	+	0.927387i	0.0247425	+	0.0541785i	0.921600	−	0.388141i	$-0.126883\pi$
$293$	0.423524	+	0.927387i	0.0247425	+	0.0541785i	−0.896857	+	0.442320i	$0.854156\pi$
$294$	−2.28709	+	24.2394i	−0.133386	+	1.41367i
$295$	−17.5349	−	8.00792i	−1.02092	−	0.466239i
$296$	7.31765	−	9.30515i	0.425330	−	0.540851i
$297$	3.08847	+	1.59222i	0.179211	+	0.0923897i
$298$	28.5944	−	16.5090i	1.65643	−	0.956341i
$299$	0.798088	+	6.00614i	0.0461546	+	0.347344i
$300$			8.75234i			0.505316i
$301$	5.30719	+	13.2352i	0.305901	+	0.762862i
$302$	−3.14881	+	21.9005i	−0.181194	+	1.26023i
$303$	−18.4110	−	25.8546i	−1.05768	−	1.48531i
$304$	3.84490	+	3.66611i	0.220520	+	0.210266i
$305$	6.05082	−	8.49718i	0.346469	−	0.486547i
$306$	4.90459	−	0.945283i	0.280377	−	0.0540382i
$307$	8.34158	−	1.19934i	0.476079	−	0.0684499i	0.0999015	−	0.994997i	$-0.468147\pi$
$307$	8.34158	−	1.19934i	0.476079	−	0.0684499i	0.376178	+	0.926547i	$0.377238\pi$
$308$	−1.46169	−	2.27163i	−0.0832877	−	0.129438i
$309$	−13.3793	−	11.5933i	−0.761125	−	0.659518i
$310$	0.711121	+	1.37938i	0.0403889	+	0.0783436i
$311$	−8.92175	−	0.424995i	−0.505906	−	0.0240993i	−0.206922	−	0.978357i	$-0.566345\pi$
$311$	−8.92175	−	0.424995i	−0.505906	−	0.0240993i	−0.298984	+	0.954258i	$0.596648\pi$
$312$	−2.92268	−	0.563300i	−0.165464	−	0.0318906i
$313$	−4.42742	+	4.22154i	−0.250253	+	0.238615i	−0.804814	−	0.593528i	$-0.797735\pi$
$313$	−4.42742	+	4.22154i	−0.250253	+	0.238615i	0.554561	+	0.832143i	$0.312886\pi$
$314$	−4.05239	−	28.1850i	−0.228689	−	1.59057i
$315$	2.46497	−	4.27500i	0.138885	−	0.240869i
$316$	3.01601	−	1.37737i	0.169664	−	0.0774830i
$317$	−6.97512	+	28.7518i	−0.391762	+	1.61486i	0.344926	+	0.938630i	$0.387904\pi$
$317$	−6.97512	+	28.7518i	−0.391762	+	1.61486i	−0.736687	+	0.676233i	$0.763611\pi$
$318$	−41.5522	+	3.96775i	−2.33013	+	0.222500i
$319$	−2.55339	−	6.37807i	−0.142963	−	0.357103i
$320$	0.273362	+	5.73857i	0.0152814	+	0.320796i
$321$	18.1385			1.01239
$322$	−22.8589	−	3.52338i	−1.27388	−	0.196350i
$323$	−4.63905			−0.258124
$324$	−0.661562	−	13.8879i	−0.0367534	−	0.771549i
$325$	1.62838	+	4.06750i	0.0903263	+	0.225624i
$326$	−24.6360	+	2.35245i	−1.36446	+	0.130290i
$327$	−1.39198	+	5.73783i	−0.0769768	+	0.317303i
$328$	1.13086	−	0.516448i	0.0624415	−	0.0285161i
$329$	−0.00948322	−	16.8696i	−0.000522827	−	0.930052i
$330$	1.11190	+	7.73344i	0.0612082	+	0.425712i
$331$	21.4031	−	20.4078i	1.17642	−	1.12172i	0.186157	−	0.982520i	$-0.440397\pi$
$331$	21.4031	−	20.4078i	1.17642	−	1.12172i	0.990265	−	0.139196i	$-0.0444517\pi$
$332$	−23.0721	−	4.44679i	−1.26625	−	0.244049i
$333$	−6.13823	−	0.292400i	−0.336373	−	0.0160234i
$334$	−11.1447	−	21.6177i	−0.609811	−	1.18287i
$335$	15.1212	+	13.1026i	0.826159	+	0.715871i
$336$	11.3135	−	21.9754i	0.617200	−	1.19886i
$337$	−11.9602	+	1.71962i	−0.651515	+	0.0936738i	−0.460144	−	0.887844i	$-0.652202\pi$
$337$	−11.9602	+	1.71962i	−0.651515	+	0.0936738i	−0.191371	+	0.981518i	$0.561293\pi$
$338$	−20.4115	+	3.93399i	−1.11024	+	0.213981i
$339$	−9.28600	+	13.0404i	−0.504346	+	0.708255i
$340$	−11.9087	−	11.3550i	−0.645842	−	0.615809i
$341$	0.131003	+	0.183967i	0.00709419	+	0.00996239i
$342$	0.180423	−	1.25487i	0.00975614	−	0.0678554i
$343$	−18.5202	+	0.0312334i	−0.999999	+	0.00168644i
$344$		−	6.65455i		−	0.358790i
$345$	22.2468	+	14.6357i	1.19773	+	0.787959i
$346$	18.0787	−	10.4377i	0.971917	−	0.561136i
$347$	−14.0571	−	7.24694i	−0.754625	−	0.389036i	0.0375781	−	0.999294i	$-0.488036\pi$
$347$	−14.0571	−	7.24694i	−0.754625	−	0.389036i	−0.792203	+	0.610257i	$0.791066\pi$
$348$	−13.8848	+	17.6560i	−0.744305	+	0.946461i
$349$	−8.20366	−	3.74649i	−0.439132	−	0.200545i	0.183566	−	0.983007i	$-0.441236\pi$
$349$	−8.20366	−	3.74649i	−0.439132	−	0.200545i	−0.622698	+	0.782463i	$0.713963\pi$
$350$	−16.6484	+	1.59917i	−0.889892	+	0.0854792i
$351$	−2.36243	−	5.17300i	−0.126097	−	0.276114i
$352$	0.942988	+	4.89269i	0.0502614	+	0.260781i
$353$	−2.66815	−	3.39283i	−0.142011	−	0.180582i	0.709845	−	0.704358i	$-0.248765\pi$
$353$	−2.66815	−	3.39283i	−0.142011	−	0.180582i	−0.851856	+	0.523776i	$0.824523\pi$
$354$	5.43207	+	22.3913i	0.288711	+	1.19008i
$355$	9.91939	+	28.6602i	0.526466	+	1.52112i
$356$	14.8618	+	9.55108i	0.787672	+	0.506206i
$357$	6.09228	+	20.7053i	0.322438	+	1.09584i
$358$	9.31260	−	10.7473i	0.492186	−	0.568013i
$359$	−5.16810	−	5.42015i	−0.272762	−	0.286064i	0.573079	−	0.819500i	$-0.305749\pi$
$359$	−5.16810	−	5.42015i	−0.272762	−	0.286064i	−0.845840	+	0.533436i	$0.820901\pi$
$360$	−1.81021	+	1.42356i	−0.0954063	+	0.0750284i
$361$	5.82918	−	16.8423i	0.306799	−	0.886437i
$362$	18.2998	+	1.74742i	0.961816	+	0.0918423i
$363$	−5.59307	−	19.0482i	−0.293560	−	0.999773i
$364$	−0.417771	+	4.40124i	−0.0218972	+	0.230688i
$365$	24.6496	+	3.54408i	1.29022	+	0.185506i
$366$	−12.4541	+	0.593260i	−0.650984	+	0.0310102i
$367$	9.18778	+	15.9137i	0.479598	+	0.830689i	0.999726	−	0.0233998i	$-0.00744908\pi$
$367$	9.18778	+	15.9137i	0.479598	+	0.830689i	−0.520128	+	0.854088i	$0.674116\pi$
$368$	20.2075	+	11.9568i	1.05339	+	0.623289i
$369$	−0.558907	−	0.322685i	−0.0290955	−	0.0167983i
$370$	27.4948	+	42.7827i	1.42938	+	2.22417i
$371$	−6.02654	−	31.1743i	−0.312882	−	1.61849i
$372$	0.306735	−	0.671656i	0.0159035	−	0.0348237i
$373$	11.8126	+	2.86570i	0.611633	+	0.148381i	0.529598	−	0.848249i	$-0.322343\pi$
$373$	11.8126	+	2.86570i	0.611633	+	0.148381i	0.0820351	+	0.996629i	$0.473858\pi$
$374$	−4.90011	−	3.48936i	−0.253379	−	0.180430i
$375$	−8.03891	−	2.78230i	−0.415128	−	0.143677i
$376$	−2.92594	+	7.30866i	−0.150894	+	0.376915i
$377$	−3.16782	+	10.7886i	−0.163151	+	0.555642i
$378$	21.4860	−	3.10156i	1.10512	−	0.159527i
$379$	−20.5129	+	31.9187i	−1.05368	+	1.63955i	−0.337959	+	0.941161i	$0.609737\pi$
$379$	−20.5129	+	31.9187i	−1.05368	+	1.63955i	−0.715717	+	0.698391i	$0.753900\pi$
$380$	−3.71216	+	1.91375i	−0.190430	+	0.0981733i
$381$	−4.58282	+	23.7780i	−0.234785	+	1.21818i
$382$	4.92148	−	1.19394i	0.251805	−	0.0610872i
$383$	14.3071	+	5.72771i	0.731060	+	0.292672i	0.707171	−	0.707042i	$-0.249971\pi$
$383$	14.3071	+	5.72771i	0.731060	+	0.292672i	0.0238890	+	0.999715i	$0.492395\pi$
$384$	−13.4272	+	11.6348i	−0.685205	+	0.593734i
$385$	−5.77482	+	1.40439i	−0.294312	+	0.0715746i
$386$	−8.88674	+	2.60938i	−0.452323	+	0.132814i
$387$	−2.81394	+	2.00380i	−0.143041	+	0.101859i
$388$	6.91819	−	2.76963i	0.351218	−	0.140606i
$389$	4.89432	−	9.49366i	0.248152	−	0.481348i	−0.731555	−	0.681782i	$-0.761205\pi$
$389$	4.89432	−	9.49366i	0.248152	−	0.481348i	0.979707	+	0.200435i	$0.0642354\pi$
$390$	6.39353	−	11.0739i	0.323749	−	0.560750i
$391$	−19.9757	+	4.62042i	−1.01022	+	0.233665i
$392$	8.02740	+	3.20322i	0.405445	+	0.161787i
$393$	−31.5312	+	20.2639i	−1.59054	+	1.02218i
$394$	−8.94377	−	7.03346i	−0.450581	−	0.354341i
$395$	−0.693419	−	7.26181i	−0.0348897	−	0.365381i
$396$	0.451589	−	0.473613i	0.0226932	−	0.0237999i
$397$	3.04396	−	31.8778i	0.152772	−	1.59990i	−0.516104	−	0.856526i	$-0.672618\pi$
$397$	3.04396	−	31.8778i	0.152772	−	1.59990i	0.668876	−	0.743374i	$-0.266776\pi$
$398$	−1.30995	−	1.51176i	−0.0656618	−	0.0757777i
$399$	5.47204	+	0.257583i	0.273945	+	0.0128953i
$400$	16.2911	+	4.78349i	0.814553	+	0.239174i
$401$	23.6792	−	8.19544i	1.18248	−	0.409261i	0.336094	−	0.941828i	$-0.390894\pi$
$401$	23.6792	−	8.19544i	1.18248	−	0.409261i	0.846387	+	0.532568i	$0.178773\pi$
$402$	1.13791	−	23.8878i	0.0567540	−	1.19141i
$403$	0.0175876	−	0.369209i	0.000876100	−	0.0183916i
$404$	20.7909	−	7.19578i	1.03438	−	0.358004i
$405$	−29.3507	−	8.61814i	−1.45845	−	0.428239i
$406$	−36.1215	−	23.1852i	−1.79268	−	1.15066i
$407$	4.84659	+	5.59326i	0.240237	+	0.277248i
$408$	0.957424	−	10.0266i	0.0473995	−	0.496390i
$409$	9.69064	−	10.1633i	0.479171	−	0.502541i	−0.439129	−	0.898424i	$-0.644713\pi$
$409$	9.69064	−	10.1633i	0.479171	−	0.502541i	0.918301	+	0.395883i	$0.129562\pi$
$410$	0.507685	+	5.31672i	0.0250728	+	0.262574i
$411$	−12.7131	−	9.99769i	−0.627091	−	0.493150i
$412$	10.3233	−	6.63437i	0.508592	−	0.326852i
$413$	−16.5594	+	5.74169i	−0.814834	+	0.282530i
$414$	−0.472929	−	5.58314i	−0.0232432	−	0.274396i
$415$	−25.8479	+	44.7699i	−1.26882	+	2.19767i
$416$	3.73682	−	7.24843i	0.183213	−	0.355383i
$417$	−17.0045	+	6.80756i	−0.832712	+	0.333368i
$418$	−1.24372	+	0.885652i	−0.0608326	+	0.0433187i
$419$	−32.6724	+	9.59347i	−1.59615	+	0.468672i	−0.954471	−	0.298302i	$-0.903580\pi$
$419$	−32.6724	+	9.59347i	−1.59615	+	0.468672i	−0.641678	+	0.766974i	$0.721761\pi$
$420$	13.4166	+	14.0551i	0.654663	+	0.685818i
$421$	18.3060	−	15.8623i	0.892181	−	0.773079i	−0.0825208	−	0.996589i	$-0.526297\pi$
$421$	18.3060	−	15.8623i	0.892181	−	0.773079i	0.974702	+	0.223510i	$0.0717516\pi$
$422$	14.3896	+	5.76072i	0.700474	+	0.280428i
$423$	3.97158	−	0.963496i	0.193105	−	0.0468468i
$424$	−2.80424	+	14.5498i	−0.136186	+	0.706600i
$425$	−13.1781	+	6.79377i	−0.639231	+	0.329546i
$426$	19.5982	−	30.4953i	0.949534	−	1.47750i
$427$	−1.35503	−	9.38695i	−0.0655743	−	0.454266i
$428$	−3.54219	+	12.0636i	−0.171218	+	0.583115i
$429$	0.691617	−	1.72758i	0.0333916	−	0.0834082i
$430$	27.0160	+	9.35033i	1.30283	+	0.450913i
$431$	29.4125	+	20.9445i	1.41675	+	1.00886i	0.994757	+	0.102264i	$0.0326086\pi$
$431$	29.4125	+	20.9445i	1.41675	+	1.00886i	0.421993	+	0.906599i	$0.361331\pi$
$432$	−21.4170	−	5.19571i	−1.03043	−	0.249979i
$433$	4.59515	−	10.0620i	0.220829	−	0.483548i	−0.766498	−	0.642246i	$-0.778003\pi$
$433$	4.59515	−	10.0620i	0.220829	−	0.483548i	0.987327	+	0.158699i	$0.0507299\pi$
$434$	1.33364	+	0.460739i	0.0640168	+	0.0221162i
$435$	26.7176	+	41.5734i	1.28101	+	1.99329i
$436$	−3.54430	−	2.04630i	−0.169741	−	0.0980001i
$437$	−0.550047	+	5.17485i	−0.0263123	+	0.247547i
$438$	−14.8827	−	25.7777i	−0.711125	−	1.23170i
$439$	1.22656	−	0.0584284i	0.0585407	−	0.00278864i	−0.0182911	−	0.999833i	$-0.505823\pi$
$439$	1.22656	−	0.0584284i	0.0585407	−	0.00278864i	0.0768318	+	0.997044i	$0.475520\pi$
$440$	2.74527	+	0.394710i	0.130876	+	0.0188171i
$441$	−1.06267	−	4.35900i	−0.0506035	−	0.207571i
$442$	2.77375	+	9.44651i	0.131934	+	0.449325i
$443$	−9.37556	−	0.895257i	−0.445446	−	0.0425350i	−0.130077	−	0.991504i	$-0.541522\pi$
$443$	−9.37556	−	0.895257i	−0.445446	−	0.0425350i	−0.315369	+	0.948969i	$0.602128\pi$
$444$	7.91402	−	22.8661i	0.375583	−	1.08517i
$445$	30.5523	−	24.0266i	1.44832	−	1.13897i
$446$	−11.7949	−	12.3702i	−0.558507	−	0.585745i
$447$	−22.6342	+	26.1213i	−1.07056	+	1.23550i
$448$	3.78239	+	3.60245i	0.178701	+	0.170200i
$449$	8.20124	+	5.27062i	0.387041	+	0.248736i	0.719662	−	0.694325i	$-0.244297\pi$
$449$	8.20124	+	5.27062i	0.387041	+	0.248736i	−0.332621	+	0.943060i	$0.607933\pi$
$450$	−1.32520	−	3.82890i	−0.0624704	−	0.180496i
$451$	0.183244	+	0.755340i	0.00862861	+	0.0355676i
$452$	−6.85950	−	8.72256i	−0.322644	−	0.410275i
$453$	−4.38330	−	22.7427i	−0.205946	−	1.06855i
$454$	−8.49068	−	18.5920i	−0.398488	−	0.872566i
$455$	8.85010	+	4.03569i	0.414899	+	0.189196i
$456$	−2.32546	−	1.06200i	−0.108899	−	0.0497327i
$457$	0.400077	−	0.508739i	0.0187148	−	0.0237978i	−0.776606	−	0.629987i	$-0.783060\pi$
$457$	0.400077	−	0.508739i	0.0187148	−	0.0237978i	0.795320	+	0.606189i	$0.207303\pi$
$458$	42.6555	+	21.9904i	1.99316	+	1.02755i
$459$	16.6660	−	9.62210i	0.777901	−	0.449121i
$460$	−14.0784	+	11.9378i	−0.656411	+	0.556604i
$461$		−	30.0146i		−	1.39792i	−0.715161	−	0.698959i	$-0.753647\pi$
$461$		−	30.0146i		−	1.39792i	0.715161	−	0.698959i	$-0.246353\pi$
$462$	5.58624	+	4.38798i	0.259895	+	0.204148i
$463$	3.87941	−	26.9819i	0.180291	−	1.25395i	−0.675783	−	0.737101i	$-0.736194\pi$
$463$	3.87941	−	26.9819i	0.180291	−	1.25395i	0.856074	−	0.516853i	$-0.172897\pi$
$464$	25.2752	+	35.4941i	1.17337	+	1.64777i
$465$	−1.17573	−	1.12106i	−0.0545232	−	0.0519878i
$466$	−12.7776	+	17.9436i	−0.591911	+	0.831223i
$467$	12.6693	−	2.44181i	0.586265	−	0.112993i	0.112511	−	0.993650i	$-0.464111\pi$
$467$	12.6693	−	2.44181i	0.586265	−	0.112993i	0.473754	+	0.880657i	$0.342899\pi$
$468$	−1.06012	+	0.152423i	−0.0490042	+	0.00704574i
$469$	18.1704	−	0.875800i	0.839030	−	0.0404407i
$470$	−25.5603	−	22.1481i	−1.17901	−	1.02161i
$471$	13.6586	+	26.4940i	0.629356	+	1.22078i
$472$	8.16990	+	0.389180i	0.376050	+	0.0179135i
$473$	4.08522	+	0.787361i	0.187838	+	0.0362029i
$474$	−6.31036	+	6.01692i	−0.289845	+	0.276366i
$475$	0.535548	+	3.72482i	0.0245726	+	0.170907i
$476$	−14.9605	+	0.00841002i	−0.685714	+	0.000385472i
$477$	6.99692	−	3.19539i	0.320367	−	0.146307i
$478$	−9.45958	+	38.9929i	−0.432671	+	1.78350i
$479$	−15.0435	+	1.43648i	−0.687353	+	0.0656343i	−0.432888	−	0.901448i	$-0.642505\pi$
$479$	−15.0435	+	1.43648i	−0.687353	+	0.0656343i	−0.254465	+	0.967082i	$0.581899\pi$
$480$	−13.3210	−	33.2742i	−0.608016	−	1.51875i
$481$	−0.576347	−	12.0990i	−0.0262792	−	0.551668i
$482$	−33.2173			−1.51301
$483$	23.8191	−	4.34092i	1.08381	−	0.197519i
$484$	13.7609			0.625496
$485$	−0.780122	−	16.3768i	−0.0354235	−	0.743631i
$486$	4.44029	+	11.0913i	0.201416	+	0.503112i
$487$	6.86721	−	0.655739i	0.311183	−	0.0297144i	0.0617037	−	0.998095i	$-0.480347\pi$
$487$	6.86721	−	0.655739i	0.311183	−	0.0297144i	0.249479	+	0.968380i	$0.419741\pi$
$488$	−1.04348	+	4.30128i	−0.0472360	+	0.194710i
$489$	23.5652	−	10.7619i	1.06566	−	0.486669i
$490$	−24.2837	+	28.0886i	−1.09702	+	1.26891i
$491$	2.59723	+	18.0641i	0.117211	+	0.815223i	0.960603	+	0.277924i	$0.0896463\pi$
$491$	2.59723	+	18.0641i	0.117211	+	0.815223i	−0.843392	+	0.537299i	$0.819445\pi$
$492$	1.83913	−	1.75360i	0.0829142	−	0.0790585i
$493$	−37.3617	−	7.20089i	−1.68269	−	0.324312i
$494$	2.49606	+	0.118902i	0.112303	+	0.00534966i
$495$	−0.659740	−	1.27972i	−0.0296531	−	0.0575190i
$496$	−1.08254	−	0.938023i	−0.0486073	−	0.0421185i
$497$	24.5162	+	12.6215i	1.09970	+	0.566154i
$498$	61.1606	−	8.79357i	2.74067	−	0.394049i
$499$	4.68633	−	0.903216i	0.209789	−	0.0404335i	−0.0832739	−	0.996527i	$-0.526538\pi$
$499$	4.68633	−	0.903216i	0.209789	−	0.0404335i	0.293063	+	0.956093i	$0.405326\pi$
$500$	3.42034	−	4.80320i	0.152962	−	0.214806i
$501$	18.4261	+	17.5692i	0.823217	+	0.784936i
$502$	−4.94078	−	6.93836i	−0.220518	−	0.309674i
$503$	−4.67140	+	32.4903i	−0.208287	+	1.44867i	0.570456	+	0.821328i	$0.306767\pi$
$503$	−4.67140	+	32.4903i	−0.208287	+	1.44867i	−0.778743	+	0.627343i	$0.784142\pi$
$504$	−0.296814	+	2.07266i	−0.0132212	+	0.0923236i
$505$		−	48.4048i		−	2.15398i
$506$	−4.47337	+	5.05234i	−0.198866	+	0.224604i
$507$	18.8448	−	10.8800i	0.836926	−	0.483199i
$508$	−14.9194	−	7.69146i	−0.661939	−	0.341253i
$509$	22.8632	−	29.0729i	1.01339	−	1.28863i	0.0564364	−	0.998406i	$-0.482026\pi$
$509$	22.8632	−	29.0729i	1.01339	−	1.28863i	0.956957	−	0.290229i	$-0.0937314\pi$
$510$	39.3605	+	17.9753i	1.74291	+	0.795960i
$511$	18.4362	−	13.1440i	0.815568	−	0.581454i
$512$	−8.10585	−	17.7493i	−0.358231	−	0.784418i
$513$	−0.924393	−	4.79621i	−0.0408129	−	0.211758i
$514$	4.11297	+	5.23007i	0.181415	+	0.230688i
$515$	−6.36513	−	26.2374i	−0.280481	−	1.15616i
$516$	−4.44882	−	12.8540i	−0.195848	−	0.565867i
$517$	−4.14057	−	2.66098i	−0.182102	−	0.117030i
$518$	44.9409	+	10.8758i	1.97459	+	0.477855i
$519$	−14.3104	+	16.5151i	−0.628156	+	0.724931i
$520$	−3.13244	−	3.28520i	−0.137366	−	0.144066i
$521$	−29.6026	+	23.2797i	−1.29691	+	1.01990i	−0.299073	+	0.954230i	$0.596677\pi$
$521$	−29.6026	+	23.2797i	−1.29691	+	1.01990i	−0.997841	+	0.0656740i	$0.979080\pi$
$522$	3.40092	−	9.82632i	0.148854	−	0.430086i
$523$	−22.8933	−	2.18605i	−1.00106	−	0.0955892i	−0.418361	−	0.908281i	$-0.637395\pi$
$523$	−22.8933	−	2.18605i	−1.00106	−	0.0955892i	−0.582694	+	0.812691i	$0.698002\pi$
$524$	−7.31955	−	24.9281i	−0.319756	−	1.08899i
$525$	15.9216	−	7.28195i	0.694874	−	0.317810i
$526$	19.2282	+	2.76460i	0.838390	+	0.120542i
$527$	1.24938	−	0.0595154i	0.0544240	−	0.00259253i
$528$	−3.60568	−	6.24523i	−0.156917	−	0.271789i
$529$	2.78557	+	22.8307i	0.121112	+	0.992639i
$530$	−55.1286	−	31.8285i	−2.39463	−	1.38254i
$531$	−2.29553	−	3.57191i	−0.0996174	−	0.155008i
$532$	−1.23993	+	3.58906i	−0.0537577	+	0.155606i
$533$	0.528443	−	1.15713i	0.0228894	−	0.0501208i
$534$	−45.1474	−	10.9526i	−1.95372	−	0.473968i
$535$	22.5327	+	16.0455i	0.974175	+	0.693707i
$536$	−8.02255	−	2.77663i	−0.346521	−	0.119932i
$537$	−5.53269	+	13.8200i	−0.238753	+	0.596377i
$538$	−10.2864	+	35.0323i	−0.443479	+	1.51035i
$539$	−2.91624	+	4.54900i	−0.125611	+	0.195939i
$540$	9.36665	−	14.5748i	0.403076	−	0.627199i
$541$	9.63664	−	4.96803i	0.414311	−	0.213592i	−0.238452	−	0.971154i	$-0.576640\pi$
$541$	9.63664	−	4.96803i	0.414311	−	0.213592i	0.652763	+	0.757562i	$0.273610\pi$
$542$	−4.27693	+	22.1908i	−0.183710	+	0.953177i
$543$	−18.7010	+	4.53682i	−0.802538	+	0.194694i
$544$	25.6192	+	10.2564i	1.09841	+	0.439739i
$545$	−6.80496	+	5.89653i	−0.291493	+	0.252580i
$546$	−2.74729	−	11.2967i	−0.117573	−	0.483456i
$547$	41.7491	−	12.2586i	1.78506	−	0.524142i	0.789129	−	0.614228i	$-0.210533\pi$
$547$	41.7491	−	12.2586i	1.78506	−	0.524142i	0.995934	+	0.0900865i	$0.0287144\pi$
$548$	9.13199	−	6.50286i	0.390099	−	0.277788i
$549$	2.13304	−	0.853942i	0.0910361	−	0.0364453i
$550$	−2.23601	+	4.33726i	−0.0953439	+	0.184941i
$551$	−4.82875	+	8.36365i	−0.205712	+	0.356303i
$552$	−11.0711	−	2.25685i	−0.471218	−	0.0960577i
$553$	−5.01493	−	4.34052i	−0.213256	−	0.184578i
$554$	−8.55024	+	5.49491i	−0.363265	+	0.233456i
$555$	−41.8465	−	32.9084i	−1.77628	−	1.39689i
$556$	−1.20686	−	12.6388i	−0.0511822	−	0.536005i
$557$	−12.4749	+	13.0833i	−0.528577	+	0.554356i	−0.932842	−	0.360286i	$-0.882679\pi$
$557$	−12.4749	+	13.0833i	−0.528577	+	0.554356i	0.404265	+	0.914642i	$0.367527\pi$
$558$	−0.0324922	+	0.340274i	−0.00137550	+	0.0144049i
$559$	−4.45901	−	5.14598i	−0.188596	−	0.217652i
$560$	33.4940	−	17.2912i	1.41538	−	0.730686i
$561$	6.04202	+	1.77410i	0.255094	+	0.0749025i
$562$	−9.11549	+	3.15490i	−0.384514	+	0.133082i
$563$	0.178886	−	3.75527i	0.00753914	−	0.158266i	−0.991958	−	0.126565i	$-0.959605\pi$
$563$	0.178886	−	3.75527i	0.00753914	−	0.158266i	0.999497	−	0.0317006i	$-0.0100923\pi$
$564$	−0.765679	+	16.0736i	−0.0322409	+	0.676820i
$565$	−23.0713	+	7.98506i	−0.970617	+	0.335934i
$566$	−3.47309	−	1.01979i	−0.145985	−	0.0428650i
$567$	−24.7133	+	12.7582i	−1.03786	+	0.535794i
$568$	−8.42689	−	9.72515i	−0.353585	−	0.408058i
$569$	1.36314	−	14.2754i	0.0571458	−	0.598457i	−0.920862	−	0.389889i	$-0.872513\pi$
$569$	1.36314	−	14.2754i	0.0571458	−	0.598457i	0.978008	−	0.208569i	$-0.0668805\pi$
$570$	7.57899	−	7.94861i	0.317449	−	0.332931i
$571$	−2.56364	−	26.8477i	−0.107285	−	1.12354i	−0.875457	−	0.483296i	$-0.839439\pi$
$571$	−2.56364	−	26.8477i	−0.107285	−	1.12354i	0.768172	−	0.640244i	$-0.221167\pi$
$572$	1.01392	+	0.797355i	0.0423941	+	0.0333391i
$573$	−4.45971	+	2.86608i	−0.186307	+	0.119732i
$574$	3.67167	+	3.17791i	0.153252	+	0.132643i
$575$	6.01593	+	15.5056i	0.250881	+	0.646630i
$576$	−0.632706	+	1.09588i	−0.0263627	+	0.0456616i
$577$	6.55671	−	12.7182i	0.272959	−	0.529467i	−0.712016	−	0.702163i	$-0.752218\pi$
$577$	6.55671	−	12.7182i	0.272959	−	0.529467i	0.984975	+	0.172696i	$0.0552479\pi$
$578$	−2.16145	+	0.865314i	−0.0899045	+	0.0359923i
$579$	7.89766	−	5.62390i	0.328215	−	0.233721i
$580$	−32.8673	+	9.65072i	−1.36474	+	0.400724i
$581$	11.1068	+	45.6707i	0.460787	+	1.89474i
$582$	−14.8101	+	12.8330i	−0.613898	+	0.531946i
$583$	−8.60029	−	3.44304i	−0.356187	−	0.142596i
$584$	−10.2685	+	2.49111i	−0.424914	+	0.103083i
$585$	−0.445950	+	2.31381i	−0.0184378	+	0.0956642i
$586$	1.65180	−	0.851564i	0.0682354	−	0.0351778i
$587$	1.23134	−	1.91600i	0.0508229	−	0.0790820i	−0.814912	−	0.579584i	$-0.803215\pi$
$587$	1.23134	−	1.91600i	0.0508229	−	0.0790820i	0.865735	+	0.500502i	$0.166851\pi$
$588$	17.6473	+	0.820759i	0.727762	+	0.0338475i
$589$	0.0894422	−	0.304612i	0.00368540	−	0.0125513i
$590$	−13.0595	+	32.6211i	−0.537653	+	1.34299i
$591$	11.2556	+	3.89559i	0.462992	+	0.160243i
$592$	−38.2362	−	27.2279i	−1.57150	−	1.11906i
$593$	−23.5573	−	5.71493i	−0.967381	−	0.234684i	−0.279208	−	0.960231i	$-0.590072\pi$
$593$	−23.5573	−	5.71493i	−0.967381	−	0.234684i	−0.688173	+	0.725547i	$0.741587\pi$
$594$	2.63115	−	5.76141i	0.107957	−	0.236394i
$595$	−10.7480	+	31.1108i	−0.440624	+	1.27542i
$596$	−12.9527	−	20.1548i	−0.530563	−	0.825572i
$597$	1.81343	+	1.04699i	0.0742189	+	0.0428503i
$598$	10.8664	−	1.97405i	0.444362	−	0.0807247i
$599$	16.1128	+	27.9083i	0.658353	+	1.14030i	0.981042	+	0.193796i	$0.0620800\pi$
$599$	16.1128	+	27.9083i	0.658353	+	1.14030i	−0.322689	+	0.946505i	$0.604587\pi$
$600$	−8.16115	+	0.388764i	−0.333178	+	0.0158712i
$601$	25.6441	+	3.68707i	1.04605	+	0.150399i	0.643847	−	0.765154i	$-0.277337\pi$
$601$	25.6441	+	3.68707i	1.04605	+	0.150399i	0.402198	+	0.915553i	$0.368246\pi$
$602$	23.6375	−	10.8110i	0.963395	−	0.440622i
$603$	1.24160	+	4.22850i	0.0505618	+	0.172198i
$604$	15.9818	+	1.52608i	0.650290	+	0.0620952i
$605$	9.90223	−	28.6106i	0.402583	−	1.16319i
$606$	−45.4778	+	35.7641i	−1.84741	+	1.45282i
$607$	16.4123	+	17.2127i	0.666156	+	0.698644i	0.966927	−	0.255052i	$-0.0820927\pi$
$607$	16.4123	+	17.2127i	0.666156	+	0.698644i	−0.300772	+	0.953696i	$0.597244\pi$
$608$	4.58683	−	5.29348i	0.186021	−	0.214679i
$609$	43.6706	+	10.5684i	1.76962	+	0.428253i
$610$	−15.9960	−	10.2800i	−0.647660	−	0.416226i
$611$	2.63467	+	7.61238i	0.106587	+	0.307964i
$612$	−0.854459	−	3.52213i	−0.0345394	−	0.142374i
$613$	22.5583	+	28.6852i	0.911120	+	1.15858i	0.986880	+	0.161458i	$0.0516195\pi$
$613$	22.5583	+	28.6852i	0.911120	+	1.15858i	−0.0757594	+	0.997126i	$0.524138\pi$
$614$	−2.90718	−	15.0839i	−0.117324	−	0.608736i
$615$	−2.32254	−	5.08565i	−0.0936537	−	0.205073i
$616$	2.05327	−	1.46386i	0.0827285	−	0.0589808i
$617$	30.8074	+	14.0693i	1.24026	+	0.566408i	0.924046	−	0.382280i	$-0.124861\pi$
$617$	30.8074	+	14.0693i	1.24026	+	0.566408i	0.316213	+	0.948688i	$0.397588\pi$
$618$	−19.9480	+	25.3659i	−0.802425	+	1.02037i
$619$	−2.82646	−	1.45714i	−0.113605	−	0.0585674i	0.400487	−	0.916302i	$-0.368841\pi$
$619$	−2.82646	−	1.45714i	−0.113605	−	0.0585674i	−0.514092	+	0.857735i	$0.671871\pi$
$620$	0.975200	−	0.563032i	0.0391650	−	0.0226119i
$621$	−8.75737	−	19.7317i	−0.351421	−	0.791807i
$622$			16.2811i			0.652813i
$623$	5.00956	−	34.9819i	0.200704	−	1.40152i
$624$	−1.67967	+	11.6823i	−0.0672404	+	0.467668i
$625$	−17.5833	−	24.6923i	−0.703332	−	0.987691i
$626$	8.07035	+	7.69507i	0.322556	+	0.307557i
$627$	0.927105	−	1.30194i	0.0370250	−	0.0519944i
$628$	−20.2881	+	3.91020i	−0.809582	+	0.156034i
$629$	40.5716	−	5.83332i	1.61770	−	0.232590i
$630$	−7.99748	−	4.11730i	−0.318627	−	0.164037i
$631$	10.8739	+	9.42230i	0.432884	+	0.375096i	0.843872	−	0.536545i	$-0.180271\pi$
$631$	10.8739	+	9.42230i	0.432884	+	0.375096i	−0.410988	+	0.911641i	$0.634816\pi$
$632$	1.41830	+	2.75112i	0.0564169	+	0.109434i
$633$	−16.2070	−	0.772033i	−0.644169	−	0.0306856i
$634$	52.9548	+	10.2062i	2.10310	+	0.405340i
$635$	−26.7273	+	25.4845i	−1.06064	+	1.01132i
$636$	4.31037	+	29.9793i	0.170917	+	1.18876i
$637$	8.35398	−	2.90186i	0.330997	−	0.114976i
$638$	−11.3914	+	5.20227i	−0.450989	+	0.205960i
$639$	−1.57489	+	6.49180i	−0.0623018	+	0.256811i
$640$	−26.9724	+	2.57555i	−1.06618	+	0.101808i
$641$	2.92486	+	7.30596i	0.115525	+	0.288568i	0.974850	−	0.222862i	$-0.0715401\pi$
$641$	2.92486	+	7.30596i	0.115525	+	0.288568i	−0.859325	+	0.511430i	$0.829116\pi$
$642$	−1.57320	−	33.0255i	−0.0620892	−	1.30341i
$643$	−33.2719			−1.31212			−0.656058	−	0.754711i	$-0.727777\pi$
$643$	−33.2719			−1.31212			−0.656058	+	0.754711i	$0.727777\pi$
$644$	−1.76447	+	16.6894i	−0.0695298	+	0.657655i
$645$	−29.9264			−1.17835
$646$	0.402358	+	8.44654i	0.0158306	+	0.332325i
$647$	4.94683	+	12.3566i	0.194480	+	0.485787i	0.993270	−	0.115823i	$-0.0369505\pi$
$647$	4.94683	+	12.3566i	0.194480	+	0.485787i	−0.798790	+	0.601610i	$0.794526\pi$
$648$	12.9204	−	1.23375i	0.507563	−	0.0484664i
$649$	−1.20557	+	4.96944i	−0.0473229	+	0.195067i
$650$	7.26465	−	3.31765i	0.284943	−	0.130129i
$651$	−1.47703		0.000830308i	−0.0578892		3.25423e-5i
$652$	2.55559	+	17.7745i	0.100084	+	0.696103i
$653$	−7.05530	+	6.72721i	−0.276095	+	0.263256i	−0.815457	−	0.578818i	$-0.803514\pi$
$653$	−7.05530	+	6.72721i	−0.276095	+	0.263256i	0.539362	+	0.842074i	$0.318666\pi$
$654$	10.5679	+	2.03679i	0.413236	+	0.0796447i
$655$	−57.0957	−	2.71980i	−2.23091	−	0.106271i
$656$	−2.25890	−	4.38165i	−0.0881951	−	0.171075i
$657$	4.14541	+	3.59202i	0.161728	+	0.140138i
$658$	−30.7145	+	1.48042i	−1.19737	+	0.0577126i
$659$	1.49163	−	0.214464i	0.0581056	−	0.00835432i	−0.113201	−	0.993572i	$-0.536110\pi$
$659$	1.49163	−	0.214464i	0.0581056	−	0.00835432i	0.171306	+	0.985218i	$0.445201\pi$
$660$	5.56668	−	1.07289i	0.216683	−	0.0417621i
$661$	2.85527	−	4.00967i	0.111057	−	0.155958i	−0.755306	−	0.655372i	$-0.772512\pi$
$661$	2.85527	−	4.00967i	0.111057	−	0.155958i	0.866363	+	0.499414i	$0.166451\pi$
$662$	−39.0138	−	37.1996i	−1.51632	−	1.44580i
$663$	−5.97814	−	8.39512i	−0.232172	−	0.326040i
$664$	3.12160	−	21.7112i	0.121142	−	0.842559i
$665$	6.56986	+	5.16062i	0.254768	+	0.200120i
$666$			11.2015i			0.434050i
$667$	−12.4625	+	40.8231i	−0.482550	+	1.58068i
$668$	−15.2834	+	8.82385i	−0.591331	+	0.341405i
$669$	15.9032	+	8.19866i	0.614853	+	0.316979i
$670$	22.5450	−	28.6683i	0.870989	−	1.10755i
$671$	−2.51708	−	1.14951i	−0.0971708	−	0.0443764i
$672$	−29.6499	−	13.5205i	−1.14377	−	0.521566i
$673$	12.5580	+	27.4982i	0.484076	+	1.05998i	0.981323	+	0.192369i	$0.0616170\pi$
$673$	12.5580	+	27.4982i	0.484076	+	1.05998i	−0.497247	+	0.867609i	$0.665656\pi$
$674$	4.16834	+	21.6274i	0.160558	+	0.833056i
$675$	−9.64982	−	12.2707i	−0.371422	−	0.472301i
$676$	3.55601	+	14.6581i	0.136769	+	0.563771i
$677$	−16.7020	−	48.2572i	−0.641910	−	1.85468i	−0.502808	−	0.864398i	$-0.667700\pi$
$677$	−16.7020	−	48.2572i	−0.641910	−	1.85468i	−0.139102	−	0.990278i	$-0.544422\pi$
$678$	24.5486	+	15.7764i	0.942783	+	0.605890i
$679$	−10.7942	−	10.2807i	−0.414244	−	0.394537i
$680$	10.0590	−	11.6087i	0.385746	−	0.445174i
$681$	14.7647	+	15.4848i	0.565785	+	0.593378i
$682$	0.323596	−	0.254478i	0.0123911	−	0.00974448i
$683$	9.59314	−	27.7175i	0.367071	−	1.06058i	−0.598652	−	0.801009i	$-0.704297\pi$
$683$	9.59314	−	27.7175i	0.367071	−	1.06058i	0.965723	−	0.259573i	$-0.0835819\pi$
$684$	−0.915735	−	0.0874421i	−0.0350140	−	0.00334343i
$685$	−6.94894	−	23.6659i	−0.265505	−	0.904229i
$686$	1.66318	+	33.7179i	0.0635005	+	1.28736i
$687$	−49.7252	−	7.14940i	−1.89713	−	0.272767i
$688$	−26.3571	+	1.25555i	−1.00486	+	0.0478672i
$689$	7.58085	+	13.1304i	0.288807	+	0.500229i
$690$	24.7183	−	41.7752i	0.941011	−	1.59035i
$691$	40.3880	+	23.3180i	1.53643	+	0.887060i	0.999044	+	0.0437264i	$0.0139230\pi$
$691$	40.3880	+	23.3180i	1.53643	+	0.887060i	0.537390	+	0.843334i	$0.319410\pi$
$692$	−8.18927	−	12.7428i	−0.311309	−	0.484407i
$693$	−1.23728	−	0.427449i	−0.0470004	−	0.0162374i
$694$	−11.9756	+	26.2230i	−0.454589	+	0.995411i
$695$	−27.1461	−	6.58557i	−1.02971	−	0.249805i
$696$	−17.0802	−	12.1627i	−0.647422	−	0.461027i
$697$	4.06791	+	1.40792i	0.154083	+	0.0533287i
$698$	−6.10988	+	15.2617i	−0.231262	+	0.577665i
$699$	6.49654	−	22.1252i	0.245722	−	0.836851i
$700$	1.73385	+	12.0112i	0.0655332	+	0.453982i
$701$	10.6460	−	16.5655i	0.402095	−	0.625672i	−0.579876	−	0.814705i	$-0.696899\pi$
$701$	10.6460	−	16.5655i	0.402095	−	0.625672i	0.981971	+	0.189033i	$0.0605353\pi$
$702$	−9.21382	+	4.75005i	−0.347753	+	0.179279i
$703$	1.96889	−	10.2156i	0.0742583	−	0.385288i
$704$	1.48104	−	0.359295i	0.0558186	−	0.0135415i
$705$	32.8680	+	13.1584i	1.23788	+	0.495573i
$706$	−5.94606	+	5.15229i	−0.223783	+	0.193909i
$707$	−30.3880	−	31.8342i	−1.14286	−	1.19725i
$708$	16.0413	−	4.71014i	0.602868	−	0.177018i
$709$	−0.961501	+	0.684682i	−0.0361099	+	0.0257138i	−0.597969	−	0.801519i	$-0.704026\pi$
$709$	−0.961501	+	0.684682i	−0.0361099	+	0.0257138i	0.561859	+	0.827233i	$0.310086\pi$
$710$	51.3226	−	20.5465i	1.92610	−	0.771095i
$711$	0.736261	−	1.42815i	0.0276120	−	0.0535597i
$712$	−8.24581	+	14.2822i	−0.309025	+	0.535247i
$713$	0.0817485	−	1.40074i	0.00306150	−	0.0524581i
$714$	37.1708	−	12.8883i	1.39108	−	0.482334i
$715$	2.38741	−	1.53429i	0.0892839	−	0.0573793i
$716$	−8.11099	−	6.37855i	−0.303122	−	0.238378i
$717$	−3.99254	−	41.8118i	−0.149104	−	1.56149i
$718$	−9.42047	+	9.87990i	−0.351569	+	0.368715i
$719$	2.54244	−	26.6256i	0.0948170	−	0.992969i	−0.815417	−	0.578874i	$-0.803492\pi$
$719$	2.54244	−	26.6256i	0.0948170	−	0.992969i	0.910234	−	0.414094i	$-0.135902\pi$
$720$	5.97994	+	6.90122i	0.222859	+	0.257193i
$721$	−20.6577	−	13.2595i	−0.769334	−	0.493810i
$722$	−31.1712	−	9.15268i	−1.16007	−	0.340627i
$723$	32.8596	−	11.3728i	1.22206	−	0.422960i
$724$	0.634687	−	13.3237i	0.0235879	−	0.495172i
$725$	−1.46862	+	30.8301i	−0.0545430	+	1.14500i
$726$	−34.1969	+	11.8357i	−1.26917	+	0.439263i
$727$	10.5968	+	3.11149i	0.393013	+	0.115399i	0.472267	−	0.881455i	$-0.343436\pi$
$727$	10.5968	+	3.11149i	0.393013	+	0.115399i	−0.0792544	+	0.996854i	$0.525254\pi$
$728$	−4.12251	−	0.194057i	−0.152791	−	0.00719223i
$729$	12.4619	+	14.3818i	0.461551	+	0.532659i
$730$	4.31494	−	45.1881i	0.159703	−	1.67249i
$731$	15.9005	−	16.6760i	0.588103	−	0.616785i
$732$	0.859969	+	9.00600i	0.0317854	+	0.332871i
$733$	2.06788	+	1.62620i	0.0763790	+	0.0600651i	0.655619	−	0.755092i	$-0.272408\pi$
$733$	2.06788	+	1.62620i	0.0763790	+	0.0600651i	−0.579240	+	0.815157i	$0.696650\pi$
$734$	28.1779	−	18.1089i	1.04007	−	0.668410i
$735$	14.4053	−	36.1003i	0.531347	−	1.33158i
$736$	14.4786	−	27.3621i	0.533689	−	1.00858i
$737$	2.65379	−	4.59649i	0.0977535	−	0.169314i
$738$	−0.539052	+	1.04562i	−0.0198428	+	0.0384896i
$739$	−15.5235	+	6.21469i	−0.571043	+	0.228611i	−0.639170	−	0.769066i	$-0.720722\pi$
$739$	−15.5235	+	6.21469i	−0.571043	+	0.228611i	0.0681271	+	0.997677i	$0.478298\pi$
$740$	30.0589	−	21.4048i	1.10499	−	0.786857i
$741$	−2.50989	+	0.736971i	−0.0922032	+	0.0270733i
$742$	−56.2379	+	13.6766i	−2.06456	+	0.502085i
$743$	16.8451	−	14.5963i	0.617985	−	0.535487i	−0.288633	−	0.957440i	$-0.593201\pi$
$743$	16.8451	−	14.5963i	0.617985	−	0.535487i	0.906618	+	0.421953i	$0.138655\pi$
$744$	0.639913	+	0.256182i	0.0234603	+	0.00939211i
$745$	−51.2249	+	12.4270i	−1.87673	+	0.455291i
$746$	4.19318	−	21.7563i	0.153523	−	0.796554i
$747$	−10.1208	+	5.21761i	−0.370299	+	0.190902i
$748$	−2.35984	+	3.67199i	−0.0862845	+	0.134261i
$749$	24.8922	−	3.59324i	0.909542	−	0.131294i
$750$	−4.36862	+	14.8781i	−0.159519	+	0.543273i
$751$	11.3011	−	28.2288i	0.412383	−	1.03008i	−0.566206	−	0.824264i	$-0.691589\pi$
$751$	11.3011	−	28.2288i	0.412383	−	1.03008i	0.978590	−	0.205821i	$-0.0659863\pi$
$752$	29.4999	+	10.2100i	1.07575	+	0.372321i
$753$	7.26311	+	5.17204i	0.264682	+	0.188479i
$754$	19.9181	+	4.83207i	0.725374	+	0.175974i
$755$	14.6733	−	32.1300i	0.534015	−	1.16933i
$756$	−2.98977	−	15.4656i	−0.108737	−	0.562480i
$757$	−15.9534	−	24.8240i	−0.579836	−	0.902242i	0.420151	−	0.907454i	$-0.361977\pi$
$757$	−15.9534	−	24.8240i	−0.579836	−	0.902242i	−0.999986	+	0.00521239i	$0.998341\pi$
$758$	59.8949	+	34.5804i	2.17548	+	1.25601i
$759$	2.69540	−	6.52951i	0.0978367	−	0.237006i
$760$	−1.94937	−	3.37641i	−0.0707111	−	0.122475i
$761$	8.36274	−	0.398366i	0.303149	−	0.0144408i	0.104544	−	0.994520i	$-0.466662\pi$
$761$	8.36274	−	0.398366i	0.303149	−	0.0144408i	0.198605	+	0.980080i	$0.436359\pi$
$762$	43.6911	+	6.28183i	1.58276	+	0.227567i
$763$	−0.773611	+	8.15003i	−0.0280066	+	0.295051i
$764$	−1.03526	−	3.52578i	−0.0374545	−	0.127558i
$765$	−7.93780	−	0.757968i	−0.286992	−	0.0274044i
$766$	9.18781	−	26.5464i	0.331969	−	0.959162i
$767$	6.57858	−	5.17345i	0.237539	−	0.186802i
$768$	27.5478	+	28.8913i	0.994045	+	1.04252i
$769$	−8.88620	+	10.2552i	−0.320445	+	0.369813i	−0.893003	−	0.450051i	$-0.851406\pi$
$769$	−8.88620	+	10.2552i	−0.320445	+	0.369813i	0.572558	+	0.819864i	$0.305951\pi$
$770$	3.05791	+	10.3927i	0.110200	+	0.374526i
$771$	−5.85933	−	3.76556i	−0.211019	−	0.135613i
$772$	2.19806	+	6.35087i	0.0791098	+	0.228573i
$773$	9.55124	+	39.3707i	0.343534	+	1.41607i	0.837430	+	0.546545i	$0.184057\pi$
$773$	9.55124	+	39.3707i	0.343534	+	1.41607i	−0.493895	+	0.869521i	$0.664427\pi$
$774$	3.89247	+	4.94968i	0.139912	+	0.177912i
$775$	−0.192020	−	0.996292i	−0.00689755	−	0.0357879i
$776$	2.88984	+	6.32788i	0.103739	+	0.227158i
$777$	−48.1806	+	4.62802i	−1.72847	+	0.166029i
$778$	−17.7100	−	8.08791i	−0.634936	−	0.289965i
$779$	0.675394	−	0.858833i	0.0241985	−	0.0307709i
$780$	−8.24693	−	4.25159i	−0.295287	−	0.152231i
$781$	6.96731	−	4.02258i	0.249310	−	0.143939i
$782$	10.1452	+	35.9700i	0.362790	+	1.28628i
$783$		−	40.0623i		−	1.43171i
$784$	11.1726	−	32.3990i	0.399023	−	1.15711i
$785$	−6.46932	+	44.9951i	−0.230900	+	1.60595i
$786$	39.6301	+	55.6527i	1.41356	+	1.98507i
$787$	34.2849	+	32.6906i	1.22213	+	1.16529i	0.980835	+	0.194842i	$0.0624194\pi$
$787$	34.2849	+	32.6906i	1.22213	+	1.16529i	0.241291	+	0.970453i	$0.422429\pi$
$788$	−4.78894	+	6.72513i	−0.170599	+	0.239573i
$789$	−19.9677	+	3.84846i	−0.710869	+	0.137009i
$790$	−13.1618	+	1.89238i	−0.468275	+	0.0673277i
$791$	−10.1603	+	19.7354i	−0.361258	+	0.701711i
$792$	0.461681	+	0.400049i	0.0164051	+	0.0142151i
$793$	2.07523	+	4.02539i	0.0736936	+	0.142946i
$794$	−58.3054	−	2.77743i	−2.06918	−	0.0985672i
$795$	65.4323	+	12.6110i	2.32065	+	0.447268i
$796$	−1.05047	+	1.00162i	−0.0372330	+	0.0355016i
$797$	1.53037	+	10.6439i	0.0542084	+	0.377028i	0.998808	+	0.0488039i	$0.0155409\pi$
$797$	1.53037	+	10.6439i	0.0542084	+	0.377028i	−0.944600	+	0.328224i	$0.893550\pi$
$798$	−0.00561335	−	9.98554i	−0.000198711	−	0.353484i
$799$	−24.7958	+	11.3238i	−0.877211	+	0.400609i
$800$	5.27756	−	21.7544i	0.186590	−	0.769134i
$801$	8.52230	−	0.813781i	0.301120	−	0.0287535i
$802$	−16.9756	−	42.4030i	−0.599429	−	1.49730i
$803$	−0.314328	−	6.59856i	−0.0110924	−	0.232858i
$804$	−17.3527			−0.611984
$805$	33.4296	+	15.6781i	1.17824	+	0.552580i
$806$	−0.673761			−0.0237322
$807$	−1.81859	−	38.1769i	−0.0640174	−	1.34389i
$808$	7.63323	+	19.0669i	0.268536	+	0.670771i
$809$	−11.1200	+	1.06183i	−0.390958	+	0.0373320i	−0.288684	−	0.957424i	$-0.593218\pi$
$809$	−11.1200	+	1.06183i	−0.390958	+	0.0373320i	−0.102274	+	0.994756i	$0.532612\pi$
$810$	−13.1458	+	54.1876i	−0.461895	+	1.90396i
$811$	−22.9185	+	10.4665i	−0.804777	+	0.367529i	−0.774947	−	0.632026i	$-0.782224\pi$
$811$	−22.9185	+	10.4665i	−0.804777	+	0.367529i	−0.0298296	+	0.999555i	$0.509496\pi$
$812$	−15.5571	+	26.9807i	−0.545948	+	0.946838i
$813$	−3.36674	−	23.4162i	−0.118077	−	0.821241i
$814$	9.76356	−	9.30953i	0.342212	−	0.326299i
$815$	38.7943	+	7.47699i	1.35891	+	0.261908i
$816$	−39.8937	−	1.90037i	−1.39656	−	0.0665262i
$817$	−2.67986	−	5.19820i	−0.0937563	−	0.181862i
$818$	−19.3452	−	16.7627i	−0.676389	−	0.586095i
$819$	1.15930	+	1.80168i	0.0405092	+	0.0629557i
$820$	3.83594	−	0.551524i	0.133957	−	0.0192601i
$821$	24.5783	−	4.73709i	0.857790	−	0.165326i	0.258651	−	0.965971i	$-0.416722\pi$
$821$	24.5783	−	4.73709i	0.857790	−	0.165326i	0.599139	+	0.800645i	$0.295510\pi$
$822$	−17.1006	+	24.0145i	−0.596453	+	0.837601i
$823$	−28.2527	−	26.9389i	−0.984826	−	0.939030i	0.0133192	−	0.999911i	$-0.495760\pi$
$823$	−28.2527	−	26.9389i	−0.984826	−	0.939030i	−0.998145	+	0.0608818i	$0.980609\pi$
$824$	6.64479	+	9.33131i	0.231482	+	0.325071i
$825$	0.726959	−	5.05611i	0.0253095	−	0.176031i
$826$	11.8904	+	29.6525i	0.413720	+	1.03174i
$827$			20.6044i			0.716484i	0.933629	+	0.358242i	$0.116624\pi$
$827$			20.6044i			0.716484i	−0.933629	+	0.358242i	$0.883376\pi$
$828$	−4.03024	+	0.535532i	−0.140060	+	0.0186110i
$829$	23.5198	−	13.5792i	0.816878	−	0.471625i	−0.0324608	−	0.999473i	$-0.510334\pi$
$829$	23.5198	−	13.5792i	0.816878	−	0.471625i	0.849339	+	0.527848i	$0.177001\pi$
$830$	83.7565	+	43.1795i	2.90723	+	1.49878i
$831$	6.57684	−	8.36314i	0.228148	−	0.290114i
$832$	−2.26884	−	1.03615i	−0.0786579	−	0.0359219i
$833$	12.4625	+	27.2080i	0.431798	+	0.942700i
$834$	13.8697	+	30.3704i	0.480268	+	1.05164i
$835$	7.34810	+	38.1256i	0.254291	+	1.31939i
$836$	0.684846	+	0.870852i	0.0236859	+	0.0301191i
$837$	0.310488	+	1.27985i	0.0107320	+	0.0442380i
$838$	20.3010	+	58.6560i	0.701288	+	2.02624i
$839$	−20.8861	−	13.4227i	−0.721067	−	0.463402i	0.127941	−	0.991782i	$-0.459163\pi$
$839$	−20.8861	−	13.4227i	−0.721067	−	0.463402i	−0.849008	+	0.528380i	$0.822800\pi$
$840$	−12.5098	+	13.1347i	−0.431629	+	0.453189i
$841$	−32.8809	+	37.9466i	−1.13382	+	1.30850i
$842$	−30.4689	−	31.9548i	−1.05003	−	1.10124i
$843$	7.93717	−	6.24186i	0.273371	−	0.214981i
$844$	3.67846	−	10.6282i	0.126618	−	0.365838i
$845$	33.0348	+	3.15444i	1.13643	+	0.108516i
$846$	−2.09875	−	7.14768i	−0.0721564	−	0.245742i
$847$	−11.4491	−	25.0328i	−0.393395	−	0.860136i
$848$	58.1574	+	8.36177i	1.99713	+	0.287145i
$849$	3.78484	−	0.180294i	0.129895	−	0.00618768i
$850$	13.5127	+	23.4047i	0.463482	+	0.802774i
$851$	−1.69652	−	45.9492i	−0.0581561	−	1.57512i
$852$	−22.7791	−	13.1515i	−0.780400	−	0.450564i
$853$	−0.175412	−	0.272947i	−0.00600600	−	0.00934552i	0.838238	−	0.545305i	$-0.183586\pi$
$853$	−0.175412	−	0.272947i	−0.00600600	−	0.00934552i	−0.844244	+	0.535960i	$0.819950\pi$
$854$	−16.9737	+	3.28132i	−0.580829	+	0.112284i
$855$	−0.840758	+	1.84100i	−0.0287533	+	0.0629610i
$856$	−11.4061	−	2.76708i	−0.389852	−	0.0945770i
$857$	−3.31767	−	2.36250i	−0.113329	−	0.0807016i	0.521987	−	0.852953i	$-0.325191\pi$
$857$	−3.31767	−	2.36250i	−0.113329	−	0.0807016i	−0.635316	+	0.772252i	$0.719130\pi$
$858$	−3.20546	−	1.10942i	−0.109433	−	0.0378750i
$859$	0.762373	−	1.90432i	0.0260118	−	0.0649744i	−0.914793	−	0.403922i	$-0.867647\pi$
$859$	0.762373	−	1.90432i	0.0260118	−	0.0649744i	0.940805	+	0.338948i	$0.110071\pi$
$860$	5.84421	−	19.9036i	0.199286	−	0.678705i
$861$	−4.72017	−	1.88659i	−0.160863	−	0.0642949i
$862$	35.5837	−	55.3693i	1.21198	−	1.88588i
$863$	−22.2586	+	11.4751i	−0.757692	+	0.390617i	−0.793365	−	0.608746i	$-0.791673\pi$
$863$	−22.2586	+	11.4751i	−0.757692	+	0.390617i	0.0356733	+	0.999364i	$0.488642\pi$
$864$	−5.49886	+	28.5308i	−0.187075	+	0.970638i
$865$	−32.3867	+	7.85692i	−1.10118	+	0.267143i
$866$	−18.7189	−	7.49390i	−0.636092	−	0.254653i
$867$	1.84191	−	1.59603i	0.0625546	−	0.0542039i
$868$	0.287890	−	0.982508i	0.00977164	−	0.0333485i
$869$	−1.85672	+	0.545181i	−0.0629848	+	0.0184940i
$870$	73.3773	−	52.2517i	2.48772	−	1.77150i
$871$	−8.06438	+	3.22849i	−0.273251	+	0.109393i
$872$	1.75065	−	3.39579i	0.0592845	−	0.114996i
$873$	1.80562	−	3.12743i	0.0611110	−	0.105847i
$874$	9.46980	+	0.552666i	0.320321	+	0.0186942i
$875$	−11.5833	−	2.22575i	−0.391588	−	0.0752442i
$876$	−18.1694	+	11.6767i	−0.613886	+	0.394521i
$877$	27.1616	+	21.3601i	0.917183	+	0.721280i	0.960646	−	0.277775i	$-0.0895968\pi$
$877$	27.1616	+	21.3601i	0.917183	+	0.721280i	−0.0434637	+	0.999055i	$0.513839\pi$
$878$	−0.212767	−	2.22819i	−0.00718053	−	0.0751979i
$879$	−1.34246	+	1.40793i	−0.0452801	+	0.0474884i
$880$	1.04539	−	10.9478i	0.0352402	−	0.369052i
$881$	16.5681	+	19.1206i	0.558192	+	0.644188i	0.962772	−	0.270314i	$-0.0871276\pi$
$881$	16.5681	+	19.1206i	0.558192	+	0.644188i	−0.404580	+	0.914503i	$0.632582\pi$
$882$	−7.84447	+	2.31293i	−0.264137	+	0.0778803i
$883$	−8.28841	−	2.43370i	−0.278927	−	0.0819004i	0.139277	−	0.990253i	$-0.455522\pi$
$883$	−8.28841	−	2.43370i	−0.278927	−	0.0819004i	−0.418204	+	0.908353i	$0.637340\pi$
$884$	6.75090	−	2.33651i	0.227057	−	0.0785853i
$885$	1.75020	−	36.7411i	0.0588322	−	1.23504i
$886$	−0.816867	+	17.1482i	−0.0274432	+	0.576104i
$887$	27.2908	−	9.44544i	0.916336	−	0.317147i	0.172112	−	0.985077i	$-0.444941\pi$
$887$	27.2908	−	9.44544i	0.916336	−	0.317147i	0.744224	+	0.667930i	$0.232820\pi$
$888$	21.6731	+	6.36379i	0.727301	+	0.213555i
$889$	−1.57878	+	33.5394i	−0.0529507	+	1.12488i
$890$	−46.3962	−	53.5440i	−1.55520	−	1.79480i
$891$	−0.771337	+	8.07780i	−0.0258408	+	0.270617i
$892$	−8.55846	+	8.97586i	−0.286558	+	0.300534i
$893$	0.657672	+	6.88745i	0.0220082	+	0.230480i
$894$	49.5234	+	38.9456i	1.65631	+	1.30254i
$895$	−19.0984	+	12.2738i	−0.638389	+	0.410268i
$896$	−16.1219	+	18.6268i	−0.538596	+	0.622279i
$897$	−10.0736	+	5.67320i	−0.336346	+	0.189423i
$898$	8.88514	−	15.3895i	0.296501	−	0.513555i
$899$	1.19317	−	2.31443i	0.0397946	−	0.0771907i
$900$	−2.72937	+	1.09267i	−0.0909790	+	0.0364225i
$901$	−41.7929	+	29.7606i	−1.39232	+	0.991469i
$902$	1.35939	−	0.399153i	0.0452627	−	0.0132903i
$903$	−19.6816	+	18.7875i	−0.654962	+	0.625209i
$904$	7.82870	−	6.78361i	0.260379	−	0.225619i
$905$	−27.2449	−	10.9072i	−0.905652	−	0.362568i
$906$	−41.0286	+	9.95342i	−1.36308	+	0.330680i
$907$	−2.99140	+	15.5209i	−0.0993278	+	0.515362i	0.897851	+	0.440299i	$0.145128\pi$
$907$	−2.99140	+	15.5209i	−0.0993278	+	0.515362i	−0.997179	+	0.0750623i	$0.976084\pi$
$908$	−13.1820	+	6.79580i	−0.437461	+	0.225527i
$909$	5.76412	−	8.96915i	0.191184	−	0.297488i
$910$	6.58038	−	16.4638i	0.218137	−	0.545770i
$911$	10.1736	−	34.6482i	0.337067	−	1.14795i	−0.600350	−	0.799737i	$-0.704972\pi$
$911$	10.1736	−	34.6482i	0.337067	−	1.14795i	0.937417	−	0.348208i	$-0.113210\pi$
$912$	−3.76758	+	9.41096i	−0.124757	+	0.311628i
$913$	12.9591	+	4.48520i	0.428884	+	0.148438i
$914$	−0.960985	−	0.684314i	−0.0317865	−	0.0226351i
$915$	19.3434	+	4.69266i	0.639473	+	0.155135i
$916$	14.4656	−	31.6752i	0.477956	−	1.04658i
$917$	−39.2574	+	34.0554i	−1.29639	+	1.12461i
$918$	−18.9649	−	29.5099i	−0.625935	−	0.973973i
$919$	2.32987	+	1.34515i	0.0768554	+	0.0443725i	0.537935	−	0.842986i	$-0.319204\pi$
$919$	2.32987	+	1.34515i	0.0768554	+	0.0443725i	−0.461080	+	0.887359i	$0.652538\pi$
$920$	−11.7568	−	12.5972i	−0.387611	−	0.415319i
$921$	8.04024	+	13.9261i	0.264935	+	0.458881i
$922$	−54.6489	+	2.60325i	−1.79977	+	0.0857335i
$923$	−13.0331	−	1.87387i	−0.428988	−	0.0616792i
$924$	2.98747	−	4.20030i	0.0982804	−	0.138180i
$925$	−9.36746	−	31.9026i	−0.308000	−	1.04895i
$926$	−49.4636	−	4.72320i	−1.62547	−	0.155214i
$927$	1.94497	−	5.61963i	0.0638812	−	0.184573i
$928$	45.1579	−	35.5125i	1.48238	−	1.16576i
$929$	4.16678	+	4.36999i	0.136707	+	0.143375i	0.788529	−	0.614998i	$-0.210843\pi$
$929$	4.16678	+	4.36999i	0.136707	+	0.143375i	−0.651821	+	0.758373i	$0.725995\pi$
$930$	−1.93919	+	2.23794i	−0.0635884	+	0.0733850i
$931$	7.56056	−	0.730524i	0.247787	−	0.0239420i
$932$	13.4464	+	8.64147i	0.440451	+	0.283061i
$933$	−5.57426	−	16.1058i	−0.182493	−	0.527280i
$934$	−5.54475	−	22.8558i	−0.181430	−	0.747864i
$935$	5.93640	+	7.54874i	0.194141	+	0.246870i
$936$	−0.189216	−	0.981746i	−0.00618472	−	0.0320894i
$937$	0.235501	+	0.515674i	0.00769347	+	0.0168463i	0.913440	−	0.406974i	$-0.133416\pi$
$937$	0.235501	+	0.515674i	0.00769347	+	0.0168463i	−0.905746	+	0.423820i	$0.860689\pi$
$938$	−3.17058	−	33.0077i	−0.103523	−	1.07774i
$939$	−10.6181	−	4.84910i	−0.346507	−	0.158245i
$940$	−15.1701	+	19.2903i	−0.494793	+	0.629180i
$941$	−0.624036	−	0.321713i	−0.0203430	−	0.0104875i	0.448025	−	0.894021i	$-0.352128\pi$
$941$	−0.624036	−	0.321713i	−0.0203430	−	0.0104875i	−0.468368	+	0.883533i	$0.655158\pi$
$942$	47.0543	−	27.1668i	1.53311	−	0.885142i
$943$	2.05286	−	4.37081i	0.0668502	−	0.142333i
$944$		−	32.4325i		−	1.05559i
$945$	−34.3064	−	4.91283i	−1.11599	−	0.159814i
$946$	1.07926	−	7.50643i	0.0350898	−	0.244055i
$947$	11.2644	+	15.8187i	0.366045	+	0.514039i	0.955988	−	0.293406i	$-0.0947889\pi$
$947$	11.2644	+	15.8187i	0.366045	+	0.514039i	−0.589942	+	0.807445i	$0.700850\pi$
$948$	4.57883	+	4.36590i	0.148713	+	0.141798i
$949$	−6.27143	+	8.80699i	−0.203579	+	0.285887i
$950$	6.73551	−	1.29816i	0.218529	−	0.0421179i
$951$	−55.8789	+	8.03417i	−1.81200	+	0.260526i
$952$	−0.672362	−	13.9496i	−0.0217914	−	0.452110i
$953$	17.2409	+	14.9394i	0.558489	+	0.483933i	0.887763	−	0.460301i	$-0.152259\pi$
$953$	17.2409	+	14.9394i	0.558489	+	0.483933i	−0.329274	+	0.944234i	$0.606804\pi$
$954$	−6.42485	−	12.4625i	−0.208012	−	0.403487i
$955$	−8.07550	−	0.384683i	−0.261317	−	0.0124481i
$956$	28.5880	+	5.50989i	0.924602	+	0.178202i
$957$	9.48758	−	9.04639i	0.306690	−	0.292428i
$958$	3.92022	+	27.2657i	0.126657	+	0.880916i
$959$	−19.4273	−	11.2018i	−0.627341	−	0.361725i
$960$	−9.97170	+	4.55392i	−0.321835	+	0.146977i
$961$	7.28835	−	30.0430i	0.235108	−	0.969128i
$962$	−21.9793	+	2.09876i	−0.708640	+	0.0676669i
$963$	2.26447	+	5.65638i	0.0729716	+	0.182274i
$964$	1.14685	+	24.0753i	0.0369375	+	0.775414i
$965$	14.7859			0.475976
$966$	−9.96961	−	42.9920i	−0.320767	−	1.38325i
$967$	−27.3119			−0.878292			−0.439146	−	0.898416i	$-0.644719\pi$
$967$	−27.3119			−0.878292			−0.439146	+	0.898416i	$0.644719\pi$
$968$	0.611236	+	12.8314i	0.0196459	+	0.412417i
$969$	−3.28992	−	8.21783i	−0.105688	−	0.263995i
$970$	−29.7503	+	2.84081i	−0.955224	+	0.0912128i
$971$	3.60943	−	14.8783i	0.115832	−	0.477466i	−0.884116	−	0.467267i	$-0.845239\pi$
$971$	3.60943	−	14.8783i	0.115832	−	0.477466i	0.999948	−	0.0101985i	$-0.00324634\pi$
$972$	7.88548	−	3.60118i	0.252927	−	0.115508i
$973$	−21.9874	+	12.7109i	−0.704884	+	0.407493i
$974$	−1.78955	−	12.4466i	−0.0573408	−	0.398814i
$975$	−6.05053	+	5.76917i	−0.193772	+	0.184761i
$976$	17.2332	+	3.32143i	0.551622	+	0.106316i
$977$	29.6862	+	1.41413i	0.949745	+	0.0452419i	0.516733	−	0.856146i	$-0.327148\pi$
$977$	29.6862	+	1.41413i	0.949745	+	0.0452419i	0.433011	+	0.901388i	$0.357451\pi$
$978$	−21.6385	−	41.9729i	−0.691924	−	1.34215i
$979$	−7.79215	−	6.75193i	−0.249038	−	0.215793i
$980$	21.1965	+	16.6306i	0.677098	+	0.531245i
$981$	−1.96309	+	0.282250i	−0.0626767	+	0.00901155i
$982$	32.6649	−	6.29565i	1.04238	−	0.200902i
$983$	−15.6733	+	22.0101i	−0.499902	+	0.702014i	−0.985021	−	0.172434i	$-0.944837\pi$
$983$	−15.6733	+	22.0101i	−0.499902	+	0.702014i	0.485119	+	0.874448i	$0.338776\pi$
$984$	1.71685	+	1.63701i	0.0547310	+	0.0521859i
$985$	10.5363	+	14.7961i	0.335714	+	0.471444i
$986$	−9.87050	+	68.6508i	−0.314341	+	2.18629i
$987$	29.8769	−	11.9804i	0.950991	−	0.381340i
$988$		−	1.81321i		−	0.0576858i
$989$	−16.7167	−	19.7143i	−0.531562	−	0.626878i
$990$	−2.27282	+	1.31221i	−0.0722349	+	0.0417049i
$991$	25.1753	+	12.9788i	0.799720	+	0.412284i	0.809099	−	0.587672i	$-0.199955\pi$
$991$	25.1753	+	12.9788i	0.799720	+	0.412284i	−0.00937952	+	0.999956i	$0.502986\pi$
$992$	−1.16741	+	1.48448i	−0.0370652	+	0.0471322i
$993$	51.3300	+	23.4416i	1.62891	+	0.743897i
$994$	20.8543	−	45.7325i	0.661457	−	1.45055i
$995$	1.32659	+	2.90482i	0.0420556	+	0.0920889i
$996$	−8.48504	−	44.0246i	−0.268859	−	1.39497i
$997$	−27.4365	−	34.8883i	−0.868922	−	1.10492i	−0.993626	−	0.112730i	$-0.964041\pi$
$997$	−27.4365	−	34.8883i	−0.868922	−	1.10492i	0.124704	−	0.992194i	$-0.460202\pi$
$998$	−2.05099	−	8.45428i	−0.0649228	−	0.267616i
$999$	14.1154	+	40.7837i	0.446591	+	1.29034i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.o.a.103.3	yes	280
7.3	odd	6	inner	161.2.o.a.80.12	✓	280
23.21	odd	22	inner	161.2.o.a.159.12	yes	280
161.136	even	66	inner	161.2.o.a.136.3	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.o.a.80.12	✓	280	7.3	odd	6	inner
161.2.o.a.103.3	yes	280	1.1	even	1	trivial
161.2.o.a.136.3	yes	280	161.136	even	66	inner
161.2.o.a.159.12	yes	280	23.21	odd	22	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	161.2.o.a.103.3

Level	$161$
Weight	$2$
Character	161.103
Analytic conductor	$1.286$
Analytic rank	$0$
Dimension	$280$
Inner twists	$4$