LMFDB - Embedded newform 44.2.g.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [44,2,Mod(7,44)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(44, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("44.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$44 = 2^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	44.g (of order $10$ , degree $4$ , 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:	$0.351341768894$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256$ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.2
Root			$1.06665 - 0.928579i$ of defining polynomial
Character	$\chi$	$=$	44.35
Dual form			44.2.g.a.39.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06665 - 0.928579i) q^{2} +(1.59814 + 2.19965i) q^{3} +(0.275480 + 1.98094i) q^{4} +(-0.720859 - 2.21858i) q^{5} +(0.337896 - 3.83025i) q^{6} +(-1.04462 - 0.758960i) q^{7} +(1.54562 - 2.36877i) q^{8} +(-1.35736 + 4.17752i) q^{9} +(-1.29122 + 3.03582i) q^{10} +(-3.29387 - 0.387833i) q^{11} +(-3.91711 + 3.77177i) q^{12} +(-0.279141 - 0.0906984i) q^{13} +(0.409487 + 1.77956i) q^{14} +(3.72806 - 5.13123i) q^{15} +(-3.84822 + 1.09142i) q^{16} +(2.82281 - 0.917186i) q^{17} +(5.32698 - 3.19553i) q^{18} +(-1.38671 + 1.00751i) q^{19} +(4.19628 - 2.03915i) q^{20} -3.51072i q^{21} +(3.15327 + 3.47230i) q^{22} -0.525735i q^{23} +(7.68057 - 0.385808i) q^{24} +(-0.357358 + 0.259635i) q^{25} +(0.213525 + 0.355948i) q^{26} +(-3.60079 + 1.16997i) q^{27} +(1.21568 - 2.27840i) q^{28} +(-4.84416 + 6.66742i) q^{29} +(-8.74128 + 2.01142i) q^{30} +(4.22806 + 1.37378i) q^{31} +(5.11817 + 2.40922i) q^{32} +(-4.41097 - 7.86517i) q^{33} +(-3.86263 - 1.64289i) q^{34} +(-0.930788 + 2.86467i) q^{35} +(-8.64932 - 1.53802i) q^{36} +(4.22613 + 3.07046i) q^{37} +(2.41469 + 0.213018i) q^{38} +(-0.246601 - 0.758960i) q^{39} +(-6.36947 - 1.72152i) q^{40} +(3.28821 + 4.52583i) q^{41} +(-3.25998 + 3.74471i) q^{42} +3.49429 q^{43} +(-0.139124 - 6.63179i) q^{44} +10.2466 q^{45} +(-0.488187 + 0.560775i) q^{46} +(-4.50223 - 6.19679i) q^{47} +(-8.55073 - 6.72050i) q^{48} +(-1.64791 - 5.07175i) q^{49} +(0.622267 + 0.0548950i) q^{50} +(6.52872 + 4.74340i) q^{51} +(0.102770 - 0.577946i) q^{52} +(0.484791 - 1.49203i) q^{53} +(4.92719 + 2.09567i) q^{54} +(1.51398 + 7.58728i) q^{55} +(-3.41238 + 1.30140i) q^{56} +(-4.43232 - 1.44015i) q^{57} +(11.3582 - 2.61360i) q^{58} +(-8.27247 + 11.3861i) q^{59} +(11.1916 + 5.97149i) q^{60} +(-8.98451 + 2.91924i) q^{61} +(-3.23419 - 5.39143i) q^{62} +(4.58849 - 3.33373i) q^{63} +(-3.22214 - 7.32242i) q^{64} +0.684676i q^{65} +(-2.59848 + 12.4853i) q^{66} -10.4249i q^{67} +(2.59452 + 5.33914i) q^{68} +(1.15643 - 0.840198i) q^{69} +(3.65290 - 2.19129i) q^{70} +(3.41904 - 1.11091i) q^{71} +(7.79762 + 9.67211i) q^{72} +(2.51668 - 3.46391i) q^{73} +(-1.65663 - 7.19940i) q^{74} +(-1.14221 - 0.371128i) q^{75} +(-2.37782 - 2.46944i) q^{76} +(3.14649 + 2.90506i) q^{77} +(-0.441718 + 1.03853i) q^{78} +(3.04387 - 9.36807i) q^{79} +(5.19542 + 7.75081i) q^{80} +(2.33275 + 1.69484i) q^{81} +(0.695229 - 7.88083i) q^{82} +(-1.16185 - 3.57581i) q^{83} +(6.95451 - 0.967134i) q^{84} +(-4.06969 - 5.60145i) q^{85} +(-3.72718 - 3.24473i) q^{86} -22.4076 q^{87} +(-6.00975 + 7.20298i) q^{88} +0.598152 q^{89} +(-10.9295 - 9.51479i) q^{90} +(0.222760 + 0.306602i) q^{91} +(1.04145 - 0.144830i) q^{92} +(3.73519 + 11.4957i) q^{93} +(-0.951912 + 10.7905i) q^{94} +(3.23485 + 2.35026i) q^{95} +(2.88011 + 15.1084i) q^{96} +(-2.57295 + 7.91872i) q^{97} +(-2.95178 + 6.93999i) q^{98} +(6.09114 - 13.2338i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9} - 22 q^{12} - 10 q^{13} + 8 q^{14} + 23 q^{16} - 10 q^{17} + 20 q^{18} + 16 q^{20} + 17 q^{22} + 25 q^{24} + 6 q^{25} - 4 q^{26} + 20 q^{28}+ \cdots - 68 q^{97}+O(q^{100})$ 16 * q - 5 * q^2 - q^4 - 6 * q^5 - 5 * q^6 - 5 * q^8 - 10 * q^9 - 22 * q^12 - 10 * q^13 + 8 * q^14 + 23 * q^16 - 10 * q^17 + 20 * q^18 + 16 * q^20 + 17 * q^22 + 25 * q^24 + 6 * q^25 - 4 * q^26 + 20 * q^28 - 10 * q^29 - 12 * q^33 - 6 * q^34 - 30 * q^36 + 18 * q^37 - 38 * q^38 - 40 * q^40 + 10 * q^41 - 26 * q^42 - 28 * q^44 + 40 * q^45 - 30 * q^46 - 36 * q^48 + 6 * q^49 - 15 * q^50 - 10 * q^52 + 38 * q^53 - 12 * q^56 + 30 * q^58 + 52 * q^60 - 10 * q^61 + 70 * q^62 + 23 * q^64 + 36 * q^66 + 60 * q^68 - 16 * q^69 + 12 * q^70 + 45 * q^72 - 30 * q^73 + 40 * q^74 + 2 * q^77 + 4 * q^78 - 28 * q^80 - 4 * q^81 - 59 * q^82 - 10 * q^84 - 50 * q^85 - 39 * q^86 - 53 * q^88 - 36 * q^89 - 50 * q^90 + 36 * q^92 - 38 * q^93 - 30 * q^94 - 68 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$ .

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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

)

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

$2$	−1.06665	−	0.928579i	−0.754235	−	0.656605i
$2$	−1.06665	−	0.928579i	−0.754235	−	0.656605i
$3$	1.59814	+	2.19965i	0.922686	+	1.26997i	0.962645	+	0.270767i	$0.0872771\pi$
$3$	1.59814	+	2.19965i	0.922686	+	1.26997i	−0.0399594	+	0.999201i	$0.512723\pi$
$4$	0.275480	+	1.98094i	0.137740	+	0.990468i
$5$	−0.720859	−	2.21858i	−0.322378	−	0.992177i	−0.972610	−	0.232442i	$-0.925328\pi$
$5$	−0.720859	−	2.21858i	−0.322378	−	0.992177i	0.650232	−	0.759735i	$-0.274672\pi$
$6$	0.337896	−	3.83025i	0.137945	−	1.56369i
$7$	−1.04462	−	0.758960i	−0.394829	−	0.286860i	0.372602	−	0.927991i	$-0.378466\pi$
$7$	−1.04462	−	0.758960i	−0.394829	−	0.286860i	−0.767431	+	0.641131i	$0.778466\pi$
$8$	1.54562	−	2.36877i	0.546458	−	0.837487i
$9$	−1.35736	+	4.17752i	−0.452453	+	1.39251i
$10$	−1.29122	+	3.03582i	−0.408320	+	0.960010i
$11$	−3.29387	−	0.387833i	−0.993139	−	0.116936i
$11$	−3.29387	−	0.387833i	−0.993139	−	0.116936i
$12$	−3.91711	+	3.77177i	−1.13077	+	1.08882i
$13$	−0.279141	−	0.0906984i	−0.0774198	−	0.0251552i	0.270051	−	0.962846i	$-0.412959\pi$
$13$	−0.279141	−	0.0906984i	−0.0774198	−	0.0251552i	−0.347471	+	0.937691i	$0.612959\pi$
$14$	0.409487	+	1.77956i	0.109440	+	0.475607i
$15$	3.72806	−	5.13123i	0.962580	−	1.32488i
$16$	−3.84822	+	1.09142i	−0.962055	+	0.272854i
$17$	2.82281	−	0.917186i	0.684631	−	0.222450i	0.0540095	−	0.998540i	$-0.482800\pi$
$17$	2.82281	−	0.917186i	0.684631	−	0.222450i	0.630622	+	0.776090i	$0.282800\pi$
$18$	5.32698	−	3.19553i	1.25558	−	0.753194i
$19$	−1.38671	+	1.00751i	−0.318134	+	0.231138i	−0.735379	−	0.677656i	$-0.762996\pi$
$19$	−1.38671	+	1.00751i	−0.318134	+	0.231138i	0.417245	+	0.908794i	$0.362996\pi$
$20$	4.19628	−	2.03915i	0.938316	−	0.455968i
$21$		−	3.51072i		−	0.766102i
$22$	3.15327	+	3.47230i	0.672280	+	0.740297i
$23$		−	0.525735i		−	0.109623i	−0.998497	−	0.0548117i	$-0.982544\pi$
$23$		−	0.525735i		−	0.109623i	0.998497	−	0.0548117i	$-0.0174559\pi$
$24$	7.68057	−	0.385808i	1.56779	−	0.0787527i
$25$	−0.357358	+	0.259635i	−0.0714715	+	0.0519271i
$26$	0.213525	+	0.355948i	0.0418756	+	0.0698071i
$27$	−3.60079	+	1.16997i	−0.692972	+	0.225160i
$28$	1.21568	−	2.27840i	0.229742	−	0.430578i
$29$	−4.84416	+	6.66742i	−0.899538	+	1.23811i	0.0710771	+	0.997471i	$0.477356\pi$
$29$	−4.84416	+	6.66742i	−0.899538	+	1.23811i	−0.970615	+	0.240637i	$0.922644\pi$
$30$	−8.74128	+	2.01142i	−1.59593	+	0.367234i
$31$	4.22806	+	1.37378i	0.759382	+	0.246738i	0.663013	−	0.748608i	$-0.269277\pi$
$31$	4.22806	+	1.37378i	0.759382	+	0.246738i	0.0963686	+	0.995346i	$0.469277\pi$
$32$	5.11817	+	2.40922i	0.904773	+	0.425894i
$33$	−4.41097	−	7.86517i	−0.767851	−	1.36915i
$34$	−3.86263	−	1.64289i	−0.662435	−	0.281753i
$35$	−0.930788	+	2.86467i	−0.157332	+	0.484218i
$36$	−8.64932	−	1.53802i	−1.44155	−	0.256336i
$37$	4.22613	+	3.07046i	0.694771	+	0.504781i	0.878225	−	0.478248i	$-0.158728\pi$
$37$	4.22613	+	3.07046i	0.694771	+	0.504781i	−0.183454	+	0.983028i	$0.558728\pi$
$38$	2.41469	+	0.213018i	0.391714	+	0.0345561i
$39$	−0.246601	−	0.758960i	−0.0394878	−	0.121531i
$40$	−6.36947	−	1.72152i	−1.00710	−	0.272196i
$41$	3.28821	+	4.52583i	0.513531	+	0.706815i	0.984510	−	0.175329i	$-0.0560990\pi$
$41$	3.28821	+	4.52583i	0.513531	+	0.706815i	−0.470978	+	0.882145i	$0.656099\pi$
$42$	−3.25998	+	3.74471i	−0.503026	+	0.577821i
$43$	3.49429			0.532874			0.266437	−	0.963852i	$-0.414154\pi$
$43$	3.49429			0.532874			0.266437	+	0.963852i	$0.414154\pi$
$44$	−0.139124	−	6.63179i	−0.0209737	−	0.999780i
$45$	10.2466			1.52747
$46$	−0.488187	+	0.560775i	−0.0719793	+	0.0826818i
$47$	−4.50223	−	6.19679i	−0.656718	−	0.903895i	0.342649	−	0.939463i	$-0.388676\pi$
$47$	−4.50223	−	6.19679i	−0.656718	−	0.903895i	−0.999367	+	0.0355685i	$0.988676\pi$
$48$	−8.55073	−	6.72050i	−1.23419	−	0.970020i
$49$	−1.64791	−	5.07175i	−0.235416	−	0.724535i
$50$	0.622267	+	0.0548950i	0.0880019	+	0.00776332i
$51$	6.52872	+	4.74340i	0.914204	+	0.664208i
$52$	0.102770	−	0.577946i	0.0142516	−	0.0801467i
$53$	0.484791	−	1.49203i	0.0665912	−	0.204947i	−0.912224	−	0.409691i	$-0.865636\pi$
$53$	0.484791	−	1.49203i	0.0665912	−	0.204947i	0.978815	+	0.204745i	$0.0656364\pi$
$54$	4.92719	+	2.09567i	0.670505	+	0.285185i
$55$	1.51398	+	7.58728i	0.204145	+	1.02307i
$56$	−3.41238	+	1.30140i	−0.455999	+	0.173907i
$57$	−4.43232	−	1.44015i	−0.587075	−	0.190752i
$58$	11.3582	−	2.61360i	1.49141	−	0.343183i
$59$	−8.27247	+	11.3861i	−1.07698	+	1.48234i	−0.214185	+	0.976793i	$0.568710\pi$
$59$	−8.27247	+	11.3861i	−1.07698	+	1.48234i	−0.862799	+	0.505548i	$0.831290\pi$
$60$	11.1916	+	5.97149i	1.44484	+	0.770916i
$61$	−8.98451	+	2.91924i	−1.15035	+	0.373771i	−0.821274	−	0.570533i	$-0.806737\pi$
$61$	−8.98451	+	2.91924i	−1.15035	+	0.373771i	−0.329074	+	0.944304i	$0.606737\pi$
$62$	−3.23419	−	5.39143i	−0.410743	−	0.684712i
$63$	4.58849	−	3.33373i	0.578096	−	0.420011i
$64$	−3.22214	−	7.32242i	−0.402767	−	0.915302i
$65$			0.684676i			0.0849236i
$66$	−2.59848	+	12.4853i	−0.319851	+	1.53684i
$67$		−	10.4249i		−	1.27361i	−0.771026	−	0.636803i	$-0.780256\pi$
$67$		−	10.4249i		−	1.27361i	0.771026	−	0.636803i	$-0.219744\pi$
$68$	2.59452	+	5.33914i	0.314631	+	0.647466i
$69$	1.15643	−	0.840198i	0.139218	−	0.101148i
$70$	3.65290	−	2.19129i	0.436605	−	0.261909i
$71$	3.41904	−	1.11091i	0.405765	−	0.131841i	−0.0990215	−	0.995085i	$-0.531571\pi$
$71$	3.41904	−	1.11091i	0.405765	−	0.131841i	0.504786	+	0.863244i	$0.331571\pi$
$72$	7.79762	+	9.67211i	0.918958	+	1.13987i
$73$	2.51668	−	3.46391i	0.294555	−	0.405420i	−0.635932	−	0.771745i	$-0.719384\pi$
$73$	2.51668	−	3.46391i	0.294555	−	0.405420i	0.930487	+	0.366325i	$0.119384\pi$
$74$	−1.65663	−	7.19940i	−0.192579	−	0.836913i
$75$	−1.14221	−	0.371128i	−0.131891	−	0.0428541i
$76$	−2.37782	−	2.46944i	−0.272754	−	0.283265i
$77$	3.14649	+	2.90506i	0.358576	+	0.331062i
$78$	−0.441718	+	1.03853i	−0.0500147	+	0.117591i
$79$	3.04387	−	9.36807i	0.342462	−	1.05399i	−0.620467	−	0.784233i	$-0.713057\pi$
$79$	3.04387	−	9.36807i	0.342462	−	1.05399i	0.962929	−	0.269757i	$-0.0869433\pi$
$80$	5.19542	+	7.75081i	0.580866	+	0.866567i
$81$	2.33275	+	1.69484i	0.259194	+	0.188316i
$82$	0.695229	−	7.88083i	0.0767752	−	0.870292i
$83$	−1.16185	−	3.57581i	−0.127530	−	0.392496i	0.866824	−	0.498615i	$-0.166158\pi$
$83$	−1.16185	−	3.57581i	−0.127530	−	0.392496i	−0.994354	+	0.106118i	$0.966158\pi$
$84$	6.95451	−	0.967134i	0.758800	−	0.105523i
$85$	−4.06969	−	5.60145i	−0.441420	−	0.607563i
$86$	−3.72718	−	3.24473i	−0.401912	−	0.349888i
$87$	−22.4076			−2.40235
$88$	−6.00975	+	7.20298i	−0.640641	+	0.767840i
$89$	0.598152			0.0634039			0.0317020	−	0.999497i	$-0.489907\pi$
$89$	0.598152			0.0634039			0.0317020	+	0.999497i	$0.489907\pi$
$90$	−10.9295	−	9.51479i	−1.15207	−	1.00295i
$91$	0.222760	+	0.306602i	0.0233515	+	0.0321406i
$92$	1.04145	−	0.144830i	0.108579	−	0.0150995i
$93$	3.73519	+	11.4957i	0.387321	+	1.19205i
$94$	−0.951912	+	10.7905i	−0.0981822	+	1.11295i
$95$	3.23485	+	2.35026i	0.331889	+	0.241131i
$96$	2.88011	+	15.1084i	0.293950	+	1.54200i
$97$	−2.57295	+	7.91872i	−0.261243	+	0.804024i	0.731292	+	0.682065i	$0.238918\pi$
$97$	−2.57295	+	7.91872i	−0.261243	+	0.804024i	−0.992535	+	0.121960i	$0.961082\pi$
$98$	−2.95178	+	6.93999i	−0.298175	+	0.701045i
$99$	6.09114	−	13.2338i	0.612182	−	1.33004i
$100$	−0.612766	−	0.636378i	−0.0612766	−	0.0636378i
$101$	−7.30672	−	2.37410i	−0.727046	−	0.236232i	−0.0779707	−	0.996956i	$-0.524844\pi$
$101$	−7.30672	−	2.37410i	−0.727046	−	0.236232i	−0.649075	+	0.760724i	$0.724844\pi$
$102$	−2.55924	−	11.1220i	−0.253402	−	1.10124i
$103$	0.242398	−	0.333632i	0.0238841	−	0.0328737i	−0.796908	−	0.604101i	$-0.793532\pi$
$103$	0.242398	−	0.333632i	0.0238841	−	0.0328737i	0.820792	+	0.571227i	$0.193532\pi$
$104$	−0.646288	+	0.521036i	−0.0633738	+	0.0510917i
$105$	−7.78880	+	2.53073i	−0.760109	+	0.246974i
$106$	−1.90257	+	1.14131i	−0.184794	+	0.110854i
$107$	4.18738	−	3.04231i	0.404809	−	0.294111i	−0.366688	−	0.930344i	$-0.619508\pi$
$107$	4.18738	−	3.04231i	0.404809	−	0.294111i	0.771497	+	0.636233i	$0.219508\pi$
$108$	−3.30958	−	6.81063i	−0.318464	−	0.655353i
$109$		−	12.5948i		−	1.20636i	−0.797604	−	0.603181i	$-0.793899\pi$
$109$		−	12.5948i		−	1.20636i	0.797604	−	0.603181i	$-0.206101\pi$
$110$	5.43050	−	9.49881i	0.517778	−	0.905676i
$111$			14.2030i			1.34809i
$112$	4.84827	+	1.78053i	0.458118	+	0.168244i
$113$	2.15258	−	1.56394i	0.202498	−	0.147123i	−0.481915	−	0.876218i	$-0.660059\pi$
$113$	2.15258	−	1.56394i	0.202498	−	0.147123i	0.684413	+	0.729095i	$0.260059\pi$
$114$	3.39044	+	5.65189i	0.317543	+	0.529348i
$115$	−1.16638	+	0.378981i	−0.108766	+	0.0353402i
$116$	−14.5422	−	7.75924i	−1.35021	−	0.720427i
$117$	0.757788	−	1.04301i	0.0700575	−	0.0964259i
$118$	19.3967	−	4.46330i	1.78561	−	0.410880i
$119$	−3.64487	−	1.18429i	−0.334124	−	0.108564i
$120$	−6.39255	−	16.7618i	−0.583558	−	1.53014i
$121$	10.6992	+	2.55494i	0.972652	+	0.232267i
$122$	12.2941	+	5.22902i	1.11305	+	0.473413i
$123$	−4.70022	+	14.4658i	−0.423805	+	1.30434i
$124$	−1.55662	+	8.75397i	−0.139789	+	0.786130i
$125$	−8.60254	−	6.25011i	−0.769435	−	0.559027i
$126$	−7.98995	−	0.704855i	−0.711801	−	0.0627935i
$127$	6.16979	+	18.9887i	0.547481	+	1.68497i	0.715018	+	0.699107i	$0.246419\pi$
$127$	6.16979	+	18.9887i	0.547481	+	1.68497i	−0.167537	+	0.985866i	$0.553581\pi$
$128$	−3.36256	+	10.8025i	−0.297211	+	0.954812i
$129$	5.58436	+	7.68621i	0.491676	+	0.676733i
$130$	0.635776	−	0.730309i	0.0557613	−	0.0640523i
$131$	20.5136			1.79228			0.896139	−	0.443773i	$-0.146360\pi$
$131$	20.5136			1.79228			0.896139	+	0.443773i	$0.146360\pi$
$132$	14.3653	−	10.9045i	1.25034	−	0.949119i
$133$	2.21324			0.191913
$134$	−9.68037	+	11.1197i	−0.836256	+	0.960598i
$135$	5.19132	+	7.14524i	0.446798	+	0.614965i
$136$	2.19038	−	8.10420i	0.187823	−	0.694929i
$137$	−1.93612	−	5.95875i	−0.165414	−	0.509091i	0.833653	−	0.552289i	$-0.186245\pi$
$137$	−1.93612	−	5.95875i	−0.165414	−	0.509091i	−0.999067	+	0.0431981i	$0.986245\pi$
$138$	−2.01370	−	0.177644i	−0.171417	−	0.0151221i
$139$	−10.9058	−	7.92352i	−0.925017	−	0.672064i	0.0197506	−	0.999805i	$-0.493713\pi$
$139$	−10.9058	−	7.92352i	−0.925017	−	0.672064i	−0.944768	+	0.327741i	$0.893713\pi$
$140$	−5.93115	−	1.05467i	−0.501273	−	0.0891361i
$141$	6.43557	−	19.8067i	0.541973	−	1.66802i
$142$	−4.67848	−	1.98989i	−0.392609	−	0.166988i
$143$	0.884278	+	0.407009i	0.0739471	+	0.0340358i
$144$	0.663995	−	17.5575i	0.0553329	−	1.46312i
$145$	18.2841	+	5.94087i	1.51841	+	0.493363i
$146$	−5.90093	+	1.35784i	−0.488365	+	0.112376i
$147$	8.52247	−	11.7302i	0.702922	−	0.967489i
$148$	−4.91817	+	9.21754i	−0.404271	+	0.757677i
$149$	16.5960	−	5.39238i	1.35960	−	0.441761i	0.463690	−	0.885997i	$-0.346525\pi$
$149$	16.5960	−	5.39238i	1.35960	−	0.441761i	0.895910	+	0.444237i	$0.146525\pi$
$150$	0.873719	+	1.45650i	0.0713389	+	0.118923i
$151$	−7.94818	+	5.77469i	−0.646814	+	0.469938i	−0.862184	−	0.506595i	$-0.830904\pi$
$151$	−7.94818	+	5.77469i	−0.646814	+	0.469938i	0.215370	+	0.976532i	$0.430904\pi$
$152$	0.243223	+	4.84202i	0.0197280	+	0.392740i
$153$			13.0373i			1.05400i
$154$	−0.658628	−	6.02044i	−0.0530737	−	0.485141i
$155$		−	10.3706i		−	0.832985i
$156$	1.43552	−	0.697580i	0.114934	−	0.0558511i
$157$	−12.4622	+	9.05431i	−0.994591	+	0.722613i	−0.960922	−	0.276820i	$-0.910719\pi$
$157$	−12.4622	+	9.05431i	−0.994591	+	0.722613i	−0.0336696	+	0.999433i	$0.510719\pi$
$158$	−11.9457	+	7.16596i	−0.950351	+	0.570093i
$159$	4.05671	−	1.31811i	0.321718	−	0.104533i
$160$	1.65556	−	13.0918i	0.130883	−	1.03499i
$161$	−0.399012	+	0.549193i	−0.0314466	+	0.0432825i
$162$	−0.914430	−	3.97394i	−0.0718444	−	0.312223i
$163$	−10.2403	−	3.32727i	−0.802080	−	0.260612i	−0.120840	−	0.992672i	$-0.538559\pi$
$163$	−10.2403	−	3.32727i	−0.802080	−	0.260612i	−0.681240	+	0.732060i	$0.738559\pi$
$164$	−8.05954	+	7.76050i	−0.629344	+	0.605994i
$165$	−14.2698	+	15.4557i	−1.11090	+	1.20323i
$166$	−2.08114	+	4.89301i	−0.161528	+	0.379771i
$167$	−1.98451	+	6.10771i	−0.153566	+	0.472629i	−0.998013	−	0.0630114i	$-0.979930\pi$
$167$	−1.98451	+	6.10771i	−0.153566	+	0.472629i	0.844446	+	0.535640i	$0.179930\pi$
$168$	−8.31609	−	5.42623i	−0.641600	−	0.418642i
$169$	−10.4475	−	7.59057i	−0.803656	−	0.583890i
$170$	−0.860459	+	9.75382i	−0.0659942	+	0.748084i
$171$	−2.32661	−	7.16056i	−0.177920	−	0.547582i
$172$	0.962608	+	6.92197i	0.0733982	+	0.527795i
$173$	−2.12650	−	2.92688i	−0.161675	−	0.222527i	0.720492	−	0.693463i	$-0.243916\pi$
$173$	−2.12650	−	2.92688i	−0.161675	−	0.222527i	−0.882167	+	0.470937i	$0.843916\pi$
$174$	23.9011	+	20.8072i	1.81193	+	1.57739i
$175$	0.570356			0.0431148
$176$	13.0988	−	2.10252i	0.987362	−	0.158484i
$177$	−38.2659			−2.87624
$178$	−0.638018	−	0.555431i	−0.0478214	−	0.0416313i
$179$	2.94347	+	4.05134i	0.220006	+	0.302812i	0.904726	−	0.425994i	$-0.140076\pi$
$179$	2.94347	+	4.05134i	0.220006	+	0.302812i	−0.684720	+	0.728806i	$0.740076\pi$
$180$	2.82274	+	20.2979i	0.210394	+	1.51291i
$181$	3.02897	+	9.32220i	0.225141	+	0.692914i	0.998277	+	0.0586734i	$0.0186871\pi$
$181$	3.02897	+	9.32220i	0.225141	+	0.692914i	−0.773136	+	0.634240i	$0.781313\pi$
$182$	0.0470983	−	0.533887i	0.00349116	−	0.0395743i
$183$	−20.7798	−	15.0974i	−1.53609	−	1.11603i
$184$	−1.24535	−	0.812585i	−0.0918081	−	0.0599046i
$185$	3.76561	−	11.5894i	0.276853	−	0.852066i
$186$	6.69057	−	15.7303i	0.490576	−	1.15340i
$187$	−9.65368	+	1.92631i	−0.705947	+	0.140866i
$188$	11.0352	−	10.6257i	0.804823	−	0.774961i
$189$	4.64941	+	1.51069i	0.338195	+	0.109886i
$190$	−1.26805	−	5.51072i	−0.0919941	−	0.399790i
$191$	6.87102	−	9.45715i	0.497170	−	0.684295i	−0.484521	−	0.874780i	$-0.661006\pi$
$191$	6.87102	−	9.45715i	0.497170	−	0.684295i	0.981690	+	0.190485i	$0.0610059\pi$
$192$	10.9573	−	18.7898i	0.790777	−	1.35604i
$193$	−1.09807	+	0.356784i	−0.0790406	+	0.0256818i	−0.348270	−	0.937394i	$-0.613231\pi$
$193$	−1.09807	+	0.356784i	−0.0790406	+	0.0256818i	0.269230	+	0.963076i	$0.413231\pi$
$194$	10.0976	−	6.05731i	0.724965	−	0.434890i
$195$	−1.50605	+	1.09421i	−0.107850	+	0.0783578i
$196$	9.59284	−	4.66157i	0.685203	−	0.332969i
$197$			15.6248i			1.11322i	0.830774	+	0.556610i	$0.187898\pi$
$197$			15.6248i			1.11322i	−0.830774	+	0.556610i	$0.812102\pi$
$198$	−18.7857	+	8.45969i	−1.33504	+	0.601204i
$199$			10.9684i			0.777526i	0.921338	+	0.388763i	$0.127098\pi$
$199$			10.9684i			0.777526i	−0.921338	+	0.388763i	$0.872902\pi$
$200$	0.0626788	+	1.24779i	0.00443206	+	0.0882324i
$201$	22.9312	−	16.6605i	1.61744	−	1.17514i
$202$	5.58917	+	9.31720i	0.393253	+	0.655556i
$203$	10.1206	−	3.28839i	0.710328	−	0.230799i
$204$	−7.59783	+	14.2397i	−0.531955	+	0.996979i
$205$	7.67056	−	10.5576i	0.535735	−	0.737376i
$206$	−0.568357	+	0.130782i	−0.0395993	+	0.00911204i
$207$	2.19627	+	0.713611i	0.152651	+	0.0495994i
$208$	1.17319	+	0.0443680i	0.0813458	+	0.00307637i
$209$	4.95840	−	2.78078i	0.342980	−	0.192351i
$210$	10.6579	+	4.53311i	0.735465	+	0.312815i
$211$	5.96517	−	18.3589i	0.410659	−	1.26388i	−0.505417	−	0.862875i	$-0.668661\pi$
$211$	5.96517	−	18.3589i	0.410659	−	1.26388i	0.916076	−	0.401004i	$-0.131339\pi$
$212$	3.08917	+	0.549315i	0.212165	+	0.0377271i
$213$	7.90771	+	5.74529i	0.541827	+	0.393661i
$214$	−7.29149	−	0.643239i	−0.498436	−	0.0439709i
$215$	−2.51889	−	7.75235i	−0.171787	−	0.528706i
$216$	−2.79406	+	10.3378i	−0.190111	+	0.703395i
$217$	−3.37407	−	4.64401i	−0.229047	−	0.315256i
$218$	−11.6953	+	13.4342i	−0.792104	+	0.909881i
$219$	11.6414			0.786652
$220$	−14.6128	+	5.08924i	−0.985198	+	0.343117i
$221$	−0.871148			−0.0585998
$222$	13.1886	−	15.1496i	0.885163	−	1.01678i
$223$	−6.37102	−	8.76895i	−0.426635	−	0.587212i	0.540542	−	0.841317i	$-0.318219\pi$
$223$	−6.37102	−	8.76895i	−0.426635	−	0.587212i	−0.967177	+	0.254105i	$0.918219\pi$
$224$	−3.51804	−	6.40121i	−0.235059	−	0.427699i
$225$	−0.599570	−	1.84529i	−0.0399713	−	0.123019i
$226$	−3.74830	−	0.330666i	−0.249333	−	0.0219956i
$227$	19.4139	+	14.1050i	1.28854	+	0.936181i	0.999775	−	0.0212179i	$-0.00675437\pi$
$227$	19.4139	+	14.1050i	1.28854	+	0.936181i	0.288768	+	0.957399i	$0.406754\pi$
$228$	1.63183	−	9.17688i	0.108070	−	0.607753i
$229$	−7.59603	+	23.3782i	−0.501960	+	1.54487i	0.303862	+	0.952716i	$0.401724\pi$
$229$	−7.59603	+	23.3782i	−0.501960	+	1.54487i	−0.805822	+	0.592158i	$0.798276\pi$
$230$	1.59604	+	0.678840i	0.105240	+	0.0447614i
$231$	−1.36157	+	11.5639i	−0.0895849	+	0.760846i
$232$	8.30636	+	21.7800i	0.545339	+	1.42992i
$233$	−13.6046	−	4.42039i	−0.891264	−	0.289589i	−0.172637	−	0.984985i	$-0.555229\pi$
$233$	−13.6046	−	4.42039i	−0.891264	−	0.289589i	−0.718627	+	0.695396i	$0.755229\pi$
$234$	−1.77681	+	0.408855i	−0.116154	+	0.0267277i
$235$	−10.5026	+	14.4556i	−0.685113	+	0.942977i
$236$	−24.8340	−	13.2506i	−1.61656	−	0.862541i
$237$	25.4710	−	8.27602i	1.65452	−	0.537585i
$238$	2.78809	+	4.64777i	0.180725	+	0.301270i
$239$	−15.9893	+	11.6169i	−1.03426	+	0.751436i	−0.969157	−	0.246442i	$-0.920738\pi$
$239$	−15.9893	+	11.6169i	−1.03426	+	0.751436i	−0.0651055	+	0.997878i	$0.520738\pi$
$240$	−8.74607	+	23.8150i	−0.564556	+	1.53725i
$241$			6.53055i			0.420669i	0.977629	+	0.210335i	$0.0674554\pi$
$241$			6.53055i			0.420669i	−0.977629	+	0.210335i	$0.932545\pi$
$242$	−9.03979	−	12.6603i	−0.581100	−	0.813832i
$243$			19.1981i			1.23156i
$244$	−8.25789	−	16.9936i	−0.528657	−	1.08790i
$245$	−10.0641	+	7.31203i	−0.642975	+	0.467148i
$246$	18.4461	−	11.0654i	1.17608	−	0.705504i
$247$	0.478467	−	0.155464i	0.0304442	−	0.00989191i
$248$	9.78913	−	7.89196i	0.621610	−	0.501140i
$249$	6.00873	−	8.27031i	0.380788	−	0.524109i
$250$	3.37217	+	14.6548i	0.213275	+	0.926852i
$251$	−4.53708	−	1.47419i	−0.286378	−	0.0930498i	0.162306	−	0.986741i	$-0.448107\pi$
$251$	−4.53708	−	1.47419i	−0.286378	−	0.0930498i	−0.448684	+	0.893691i	$0.648107\pi$
$252$	7.86796	+	8.17114i	0.495635	+	0.514733i
$253$	−0.203897	+	1.73170i	−0.0128189	+	0.108871i
$254$	11.0515	−	25.9834i	0.693432	−	1.63034i
$255$	5.81729	−	17.9038i	0.364293	−	1.12118i
$256$	13.6176	−	8.40004i	0.851101	−	0.525002i
$257$	2.45693	+	1.78506i	0.153259	+	0.111349i	0.661772	−	0.749705i	$-0.269805\pi$
$257$	2.45693	+	1.78506i	0.153259	+	0.111349i	−0.508513	+	0.861054i	$0.669805\pi$
$258$	1.18071	−	13.3840i	0.0735076	−	0.833252i
$259$	−2.08434	−	6.41493i	−0.129514	−	0.398604i
$260$	−1.35630	+	0.188615i	−0.0841142	+	0.0116974i
$261$	−21.2780	−	29.2866i	−1.31707	−	1.81280i
$262$	−21.8808	−	19.0485i	−1.35180	−	1.17682i
$263$	14.1671			0.873580			0.436790	−	0.899564i	$-0.356115\pi$
$263$	14.1671			0.873580			0.436790	+	0.899564i	$0.356115\pi$
$264$	−25.4484	−	1.70798i	−1.56624	−	0.105119i
$265$	−3.65966			−0.224811
$266$	−2.36076	−	2.05517i	−0.144747	−	0.126011i
$267$	0.955929	+	1.31572i	0.0585019	+	0.0805210i
$268$	20.6511	−	2.87186i	1.26147	−	0.175427i
$269$	0.309559	+	0.952724i	0.0188741	+	0.0580886i	0.960050	−	0.279829i	$-0.0902776\pi$
$269$	0.309559	+	0.952724i	0.0188741	+	0.0580886i	−0.941176	+	0.337917i	$0.890278\pi$
$270$	1.09761	−	12.4420i	0.0667982	−	0.757197i
$271$	14.3933	+	10.4573i	0.874330	+	0.635238i	0.931745	−	0.363113i	$-0.118286\pi$
$271$	14.3933	+	10.4573i	0.874330	+	0.635238i	−0.0574157	+	0.998350i	$0.518286\pi$
$272$	−9.86176	+	6.61040i	−0.597957	+	0.400814i
$273$	−0.318417	+	0.979986i	−0.0192714	+	0.0593114i
$274$	−3.46802	+	8.15373i	−0.209511	+	0.492585i
$275$	1.27778	−	0.716611i	0.0770533	−	0.0432133i
$276$	1.98295	+	2.05936i	0.119360	+	0.123959i
$277$	18.4378	+	5.99082i	1.10782	+	0.359953i	0.805108	−	0.593128i	$-0.202107\pi$
$277$	18.4378	+	5.99082i	1.10782	+	0.359953i	0.302714	+	0.953081i	$0.402107\pi$
$278$	4.27503	+	18.5785i	0.256399	+	1.11427i
$279$	−11.4780	+	15.7981i	−0.687169	+	0.945806i
$280$	5.34711	+	6.63251i	0.319551	+	0.396368i
$281$	−13.9771	+	4.54142i	−0.833802	+	0.270919i	−0.694646	−	0.719352i	$-0.744439\pi$
$281$	−13.9771	+	4.54142i	−0.833802	+	0.270919i	−0.139156	+	0.990270i	$0.544439\pi$
$282$	−25.2566	+	15.1508i	−1.50401	+	0.902218i
$283$	2.02002	−	1.46763i	0.120078	−	0.0872415i	−0.526126	−	0.850407i	$-0.676356\pi$
$283$	2.02002	−	1.46763i	0.120078	−	0.0872415i	0.646203	+	0.763165i	$0.276356\pi$
$284$	3.14252	+	6.46686i	0.186474	+	0.383738i
$285$			10.8716i			0.643977i
$286$	−0.565275	−	1.25526i	−0.0334254	−	0.0742250i
$287$		−	7.22339i		−	0.426383i
$288$	−17.0117	+	18.1111i	−1.00243	+	1.06720i
$289$	−6.62627	+	4.81427i	−0.389781	+	0.283192i
$290$	−13.9862	−	23.3151i	−0.821296	−	1.36911i
$291$	−21.5303	+	6.99563i	−1.26213	+	0.410091i
$292$	7.55509	+	4.03114i	0.442128	+	0.235905i
$293$	4.41949	−	6.08290i	0.258189	−	0.355367i	−0.660169	−	0.751117i	$-0.729515\pi$
$293$	4.41949	−	6.08290i	0.258189	−	0.355367i	0.918358	+	0.395750i	$0.129515\pi$
$294$	−19.9829	+	4.59819i	−1.16543	+	0.268172i
$295$	31.2242	+	10.1453i	1.81794	+	0.590685i
$296$	13.8052	−	5.26497i	0.802410	−	0.306020i
$297$	12.3143	−	2.45722i	0.714547	−	0.142582i
$298$	−22.7094	−	9.65896i	−1.31552	−	0.559529i
$299$	−0.0476833	+	0.146754i	−0.00275760	+	0.00848702i
$300$	0.420523	−	2.36489i	0.0242789	−	0.136537i
$301$	−3.65020	−	2.65203i	−0.210394	−	0.152860i
$302$	13.8402	+	1.22095i	0.796413	+	0.0702577i
$303$	−6.45497	−	19.8664i	−0.370828	−	1.14129i
$304$	4.23677	−	5.39059i	0.242995	−	0.309171i
$305$	12.9531	+	17.8285i	0.741694	+	1.02085i
$306$	12.1061	−	13.9062i	0.692062	−	0.794964i
$307$	−25.7991			−1.47243			−0.736216	−	0.676747i	$-0.763389\pi$
$307$	−25.7991			−1.47243			−0.736216	+	0.676747i	$0.763389\pi$
$308$	−4.88794	+	7.03329i	−0.278516	+	0.400759i
$309$	1.12126			0.0637861
$310$	−9.62990	+	11.0618i	−0.546942	+	0.628266i
$311$	−1.74241	−	2.39822i	−0.0988030	−	0.135991i	0.756753	−	0.653701i	$-0.226785\pi$
$311$	−1.74241	−	2.39822i	−0.0988030	−	0.135991i	−0.855556	+	0.517710i	$0.826785\pi$
$312$	−2.17895	−	0.588920i	−0.123359	−	0.0333411i
$313$	0.186644	+	0.574432i	0.0105498	+	0.0324688i	0.956193	−	0.292738i	$-0.0945662\pi$
$313$	0.186644	+	0.574432i	0.0105498	+	0.0324688i	−0.945643	+	0.325206i	$0.894566\pi$
$314$	21.7004	+	1.91436i	1.22463	+	0.108034i
$315$	−10.7038	−	7.77677i	−0.603091	−	0.438171i
$316$	19.3961	+	3.44900i	1.09111	+	0.194021i
$317$	7.09054	−	21.8224i	0.398244	−	1.22567i	−0.528162	−	0.849144i	$-0.677119\pi$
$317$	7.09054	−	21.8224i	0.398244	−	1.22567i	0.926406	−	0.376526i	$-0.122881\pi$
$318$	−5.55106	−	2.36102i	−0.311288	−	0.132400i
$319$	18.5419	−	20.0829i	1.03815	−	1.12443i
$320$	−13.9226	+	12.4270i	−0.778299	+	0.694690i
$321$	13.3840	+	4.34874i	0.747024	+	0.242723i
$322$	0.935576	−	0.215282i	0.0521376	−	0.0119972i
$323$	−2.99035	+	4.11587i	−0.166388	+	0.229013i
$324$	−2.71475	+	5.08792i	−0.150819	+	0.282662i
$325$	0.123302	−	0.0400631i	0.00683954	−	0.00222230i
$326$	7.83315	+	13.0579i	0.433838	+	0.723212i
$327$	27.7041	−	20.1282i	1.53204	−	1.11309i
$328$	15.8029	−	0.793809i	0.872572	−	0.0438308i
$329$			9.89031i			0.545270i
$330$	29.5727	−	3.23522i	1.62793	−	0.178093i
$331$			4.43442i			0.243738i	0.992546	+	0.121869i	$0.0388887\pi$
$331$			4.43442i			0.243738i	−0.992546	+	0.121869i	$0.961111\pi$
$332$	6.76339	−	3.28662i	0.371189	−	0.180377i
$333$	−18.5633	+	13.4870i	−1.01726	+	0.739083i
$334$	7.78827	−	4.67200i	0.426155	−	0.255641i
$335$	−23.1285	+	7.51490i	−1.26364	+	0.410583i
$336$	3.83166	+	13.5100i	0.209034	+	0.737032i
$337$	10.4401	−	14.3696i	0.568711	−	0.782763i	−0.423691	−	0.905807i	$-0.639266\pi$
$337$	10.4401	−	14.3696i	0.568711	−	0.782763i	0.992401	+	0.123044i	$0.0392656\pi$
$338$	4.09539	+	17.7978i	0.222760	+	0.968075i
$339$	6.88025	+	2.23553i	0.373684	+	0.121417i
$340$	9.97500	−	9.60490i	0.540971	−	0.520899i
$341$	−13.3939	−	6.16483i	−0.725320	−	0.333844i
$342$	−4.16748	+	9.79825i	−0.225351	+	0.529829i
$343$	−4.92088	+	15.1449i	−0.265703	+	0.817748i
$344$	5.40083	−	8.27717i	0.291193	−	0.446275i
$345$	−2.69767	−	1.95997i	−0.145238	−	0.105521i
$346$	−0.449609	+	5.09659i	−0.0241711	+	0.273994i
$347$	−1.19913	−	3.69054i	−0.0643726	−	0.198119i	0.913697	−	0.406396i	$-0.133214\pi$
$347$	−1.19913	−	3.69054i	−0.0643726	−	0.198119i	−0.978070	+	0.208277i	$0.933214\pi$
$348$	−6.17285	−	44.3881i	−0.330900	−	2.37945i
$349$	−11.5900	−	15.9522i	−0.620396	−	0.853903i	0.376985	−	0.926219i	$-0.376961\pi$
$349$	−11.5900	−	15.9522i	−0.620396	−	0.853903i	−0.997382	+	0.0723168i	$0.976961\pi$
$350$	−0.608369	−	0.529621i	−0.0325187	−	0.0283094i
$351$	1.11124			0.0593137
$352$	−15.9242	−	9.92065i	−0.848764	−	0.528773i
$353$	−1.59623			−0.0849587			−0.0424794	−	0.999097i	$-0.513526\pi$
$353$	−1.59623			−0.0849587			−0.0424794	+	0.999097i	$0.513526\pi$
$354$	40.8163	+	35.5329i	2.16936	+	1.88855i
$355$	−4.92929	−	6.78458i	−0.261619	−	0.360088i
$356$	0.164779	+	1.18490i	0.00873327	+	0.0627996i
$357$	−3.21998	−	9.91009i	−0.170420	−	0.524497i
$358$	0.622342	−	7.05461i	0.0328918	−	0.372848i
$359$	−12.4772	−	9.06523i	−0.658522	−	0.478445i	0.207641	−	0.978205i	$-0.433421\pi$
$359$	−12.4772	−	9.06523i	−0.658522	−	0.478445i	−0.866164	+	0.499760i	$0.833421\pi$
$360$	15.8373	−	24.2718i	0.834700	−	1.27924i
$361$	−4.96342	+	15.2758i	−0.261233	+	0.803991i
$362$	5.42556	−	12.7562i	0.285161	−	0.670449i
$363$	11.4788	+	27.6176i	0.602480	+	1.44955i
$364$	−0.545994	+	0.525735i	−0.0286178	+	0.0275560i
$365$	−9.49912	−	3.08645i	−0.497207	−	0.161552i
$366$	8.14561	+	35.3993i	0.425778	+	1.85035i
$367$	6.20229	−	8.53673i	0.323757	−	0.445613i	−0.615853	−	0.787861i	$-0.711188\pi$
$367$	6.20229	−	8.53673i	0.323757	−	0.445613i	0.939610	+	0.342248i	$0.111188\pi$
$368$	0.573797	+	2.02315i	0.0299112	+	0.105464i
$369$	−23.3700	+	7.59337i	−1.21659	+	0.395295i
$370$	−14.7782	+	8.86511i	−0.768283	+	0.460875i
$371$	−1.63882	+	1.19067i	−0.0850831	+	0.0618165i
$372$	−21.7434	+	10.5660i	−1.12734	+	0.547823i
$373$		−	37.4953i		−	1.94143i	−0.240225	−	0.970717i	$-0.577221\pi$
$373$		−	37.4953i		−	1.94143i	0.240225	−	0.970717i	$-0.422779\pi$
$374$	12.0858	+	6.90951i	0.624943	+	0.357282i
$375$		−	28.9111i		−	1.49296i
$376$	−21.6375	+	1.08689i	−1.11587	+	0.0560520i
$377$	1.95693	−	1.42179i	0.100787	−	0.0732259i
$378$	−3.55650	−	5.92872i	−0.182927	−	0.304941i
$379$	20.2850	−	6.59100i	1.04197	−	0.338557i	0.262459	−	0.964943i	$-0.415467\pi$
$379$	20.2850	−	6.59100i	1.04197	−	0.338557i	0.779513	+	0.626386i	$0.215467\pi$
$380$	−3.76458	+	7.05549i	−0.193119	+	0.361939i
$381$	−31.9082	+	43.9179i	−1.63471	+	2.24998i
$382$	−16.1107	+	3.70717i	−0.824294	+	0.189675i
$383$	−27.4201	−	8.90933i	−1.40110	−	0.455245i	−0.491554	−	0.870847i	$-0.663571\pi$
$383$	−27.4201	−	8.90933i	−1.40110	−	0.455245i	−0.909547	+	0.415602i	$0.863571\pi$
$384$	−29.1355	+	9.86739i	−1.48681	+	0.503543i
$385$	4.17691	−	9.07487i	0.212875	−	0.462498i
$386$	1.50255	+	0.639079i	0.0764780	+	0.0325283i
$387$	−4.74300	+	14.5975i	−0.241100	+	0.742031i
$388$	−16.3953	−	2.91540i	−0.832345	−	0.148007i
$389$	28.2179	+	20.5015i	1.43070	+	1.03947i	0.989885	+	0.141869i	$0.0453112\pi$
$389$	28.2179	+	20.5015i	1.43070	+	1.03947i	0.440817	+	0.897597i	$0.354689\pi$
$390$	2.62248	+	0.231349i	0.132795	+	0.0117148i
$391$	−0.482197	−	1.48405i	−0.0243858	−	0.0750516i
$392$	−14.5608	−	3.93545i	−0.735433	−	0.198770i
$393$	32.7835	+	45.1226i	1.65371	+	2.27614i
$394$	14.5088	−	16.6662i	0.730945	−	0.839629i
$395$	−22.9780			−1.15615
$396$	27.8933	+	8.42052i	1.40169	+	0.423147i
$397$	16.9102			0.848698			0.424349	−	0.905499i	$-0.360503\pi$
$397$	16.9102			0.848698			0.424349	+	0.905499i	$0.360503\pi$
$398$	10.1850	−	11.6994i	0.510528	−	0.586437i
$399$	3.53707	+	4.86836i	0.177075	+	0.243723i
$400$	1.09182	−	1.38916i	0.0545910	−	0.0694581i
$401$	4.90100	+	15.0837i	0.244744	+	0.753246i	0.995678	+	0.0928687i	$0.0296037\pi$
$401$	4.90100	+	15.0837i	0.244744	+	0.753246i	−0.750934	+	0.660377i	$0.770396\pi$
$402$	−39.9301	−	3.52254i	−1.99153	−	0.175688i
$403$	−1.05562	−	0.766956i	−0.0525844	−	0.0382048i
$404$	2.69008	−	15.1282i	0.133837	−	0.752655i
$405$	2.07855	−	6.39712i	0.103284	−	0.317876i
$406$	−13.8487	−	5.89024i	−0.687298	−	0.292328i
$407$	−12.7295	−	11.7527i	−0.630977	−	0.582561i
$408$	21.3269	−	8.13357i	1.05584	−	0.402672i
$409$	−26.3195	−	8.55173i	−1.30142	−	0.422856i	−0.425343	−	0.905032i	$-0.639846\pi$
$409$	−26.3195	−	8.55173i	−1.30142	−	0.422856i	−0.876074	+	0.482176i	$0.839846\pi$
$410$	−17.9854	+	4.13855i	−0.888235	+	0.204388i
$411$	10.0130	−	13.7817i	0.493904	−	0.679800i
$412$	0.727679	+	0.388265i	0.0358502	+	0.0191285i
$413$	17.2832	−	5.61564i	0.850449	−	0.276328i
$414$	−1.68000	−	2.80058i	−0.0825677	−	0.137641i
$415$	−7.09568	+	5.15531i	−0.348313	+	0.253064i
$416$	−1.21018	−	1.13672i	−0.0593339	−	0.0557324i
$417$		−	36.6518i		−	1.79485i
$418$	−7.87105	−	1.63815i	−0.384985	−	0.0801244i
$419$			22.9710i			1.12221i	0.827746	+	0.561103i	$0.189623\pi$
$419$			22.9710i			1.12221i	−0.827746	+	0.561103i	$0.810377\pi$
$420$	−7.15889	−	14.7320i	−0.349318	−	0.718846i
$421$	24.3592	−	17.6980i	1.18719	−	0.862546i	0.194229	−	0.980956i	$-0.437780\pi$
$421$	24.3592	−	17.6980i	1.18719	−	0.862546i	0.992965	+	0.118410i	$0.0377796\pi$
$422$	−23.4104	+	14.0434i	−1.13960	+	0.683621i
$423$	31.9983	−	10.3969i	1.55581	−	0.505514i
$424$	−2.78498	−	3.45447i	−0.135251	−	0.167764i
$425$	−0.770618	+	1.06066i	−0.0373804	+	0.0514498i
$426$	−3.09979	−	13.4711i	−0.150186	−	0.652679i
$427$	11.6010	+	3.76939i	0.561411	+	0.182413i
$428$	7.18017	+	7.45684i	0.347066	+	0.360440i
$429$	0.517923	+	2.59556i	0.0250055	+	0.125315i
$430$	−4.51190	+	10.6080i	−0.217583	+	0.511565i
$431$	−3.14369	+	9.67528i	−0.151426	+	0.466042i	−0.997781	−	0.0665771i	$-0.978792\pi$
$431$	−3.14369	+	9.67528i	−0.151426	+	0.466042i	0.846355	+	0.532619i	$0.178792\pi$
$432$	12.5797	−	8.43226i	0.605241	−	0.405697i
$433$	−22.2763	−	16.1847i	−1.07053	−	0.777785i	−0.0945224	−	0.995523i	$-0.530132\pi$
$433$	−22.2763	−	16.1847i	−1.07053	−	0.777785i	−0.976007	+	0.217737i	$0.930132\pi$
$434$	−0.713383	+	8.08662i	−0.0342435	+	0.388170i
$435$	16.1527	+	49.7130i	0.774464	+	2.38356i
$436$	24.9495	−	3.46962i	1.19486	−	0.166165i
$437$	0.529682	+	0.729044i	0.0253381	+	0.0348749i
$438$	−12.4173	−	10.8100i	−0.593321	−	0.516520i
$439$	11.5438			0.550957			0.275479	−	0.961307i	$-0.411164\pi$
$439$	11.5438			0.550957			0.275479	+	0.961307i	$0.411164\pi$
$440$	20.3125	+	8.14075i	0.968362	+	0.388095i
$441$	23.4241			1.11543
$442$	0.929210	+	0.808931i	0.0441980	+	0.0384769i
$443$	9.98691	+	13.7458i	0.474492	+	0.653083i	0.977435	−	0.211237i	$-0.0677492\pi$
$443$	9.98691	+	13.7458i	0.474492	+	0.653083i	−0.502942	+	0.864320i	$0.667749\pi$
$444$	−28.1353	+	3.91265i	−1.33524	+	0.185686i
$445$	−0.431183	−	1.32704i	−0.0204400	−	0.0629080i
$446$	−1.34703	+	15.2694i	−0.0637837	+	0.723027i
$447$	38.3841	+	27.8877i	1.81551	+	1.31904i
$448$	−2.19152	+	10.0946i	−0.103539	+	0.476926i
$449$	1.89015	−	5.81730i	0.0892019	−	0.274535i	−0.896497	−	0.443049i	$-0.853897\pi$
$449$	1.89015	−	5.81730i	0.0892019	−	0.274535i	0.985699	+	0.168514i	$0.0538968\pi$
$450$	−1.07396	+	2.52502i	−0.0506271	+	0.119031i
$451$	−9.07566	−	16.1828i	−0.427356	−	0.762017i
$452$	3.69107	+	3.83330i	0.173613	+	0.180303i
$453$	−25.4046	−	8.25445i	−1.19361	−	0.387828i
$454$	−7.61016	−	33.0724i	−0.357163	−	1.55216i
$455$	0.519642	−	0.715226i	0.0243612	−	0.0335303i
$456$	−10.2620	+	8.27323i	−0.480564	+	0.387429i
$457$	−6.20446	+	2.01595i	−0.290232	+	0.0943022i	−0.450515	−	0.892769i	$-0.648760\pi$
$457$	−6.20446	+	2.01595i	−0.290232	+	0.0943022i	0.160282	+	0.987071i	$0.448760\pi$
$458$	29.8108	−	17.8828i	1.39297	−	0.835608i
$459$	−9.09126	+	6.60518i	−0.424344	+	0.308304i
$460$	−1.07205	−	2.20613i	−0.0499848	−	0.102861i
$461$			19.0882i			0.889026i	0.895773	+	0.444513i	$0.146623\pi$
$461$			19.0882i			0.889026i	−0.895773	+	0.444513i	$0.853377\pi$
$462$	12.1903	−	11.0703i	0.567143	−	0.515035i
$463$		−	13.0359i		−	0.605829i	−0.953018	−	0.302915i	$-0.902040\pi$
$463$		−	13.0359i		−	0.605829i	0.953018	−	0.302915i	$-0.0979597\pi$
$464$	11.3645	−	30.9447i	0.527582	−	1.43657i
$465$	22.8116	−	16.5736i	1.05786	−	0.768583i
$466$	10.4066	+	17.3479i	0.482077	+	0.803627i
$467$	−14.4349	+	4.69019i	−0.667969	+	0.217036i	−0.623320	−	0.781967i	$-0.714217\pi$
$467$	−14.4349	+	4.69019i	−0.667969	+	0.217036i	−0.0446484	+	0.999003i	$0.514217\pi$
$468$	2.27488	+	1.21380i	0.105157	+	0.0561080i
$469$	−7.91210	+	10.8901i	−0.365347	+	0.502857i
$470$	24.6257	−	5.66653i	1.13590	−	0.261377i
$471$	−39.8326	−	12.9424i	−1.83539	−	0.596355i
$472$	14.1849	+	37.1941i	0.652914	+	1.71200i
$473$	−11.5097	−	1.35520i	−0.529219	−	0.0623122i
$474$	−34.8535	−	14.8242i	−1.60088	−	0.680899i
$475$	0.233968	−	0.720080i	0.0107352	−	0.0330395i
$476$	1.34191	−	7.54650i	0.0615065	−	0.345893i
$477$	5.57496	+	4.05045i	0.255260	+	0.185457i
$478$	27.8422	+	2.45618i	1.27347	+	0.112343i
$479$	8.09752	+	24.9216i	0.369985	+	1.13870i	0.946800	+	0.321822i	$0.104295\pi$
$479$	8.09752	+	24.9216i	0.369985	+	1.13870i	−0.576815	+	0.816875i	$0.695705\pi$
$480$	31.4431	−	17.2808i	1.43517	−	0.788757i
$481$	−0.901199	−	1.24039i	−0.0410911	−	0.0565571i
$482$	6.06413	−	6.96580i	0.276214	−	0.317283i
$483$	−1.84571			−0.0839827
$484$	−2.11377	+	21.8982i	−0.0960804	+	0.995374i
$485$	19.4230			0.881954
$486$	17.8270	−	20.4776i	0.808647	−	0.928884i
$487$	16.0181	+	22.0471i	0.725851	+	0.999048i	0.999309	+	0.0371640i	$0.0118324\pi$
$487$	16.0181	+	22.0471i	0.725851	+	0.999048i	−0.273458	+	0.961884i	$0.588168\pi$
$488$	−6.97159	+	25.7943i	−0.315589	+	1.16765i
$489$	−9.04656	−	27.8424i	−0.409099	−	1.25908i
$490$	17.5247	+	1.54599i	0.791686	+	0.0698407i
$491$	−17.3230	−	12.5859i	−0.781778	−	0.567995i	0.123734	−	0.992315i	$-0.460513\pi$
$491$	−17.3230	−	12.5859i	−0.781778	−	0.567995i	−0.905512	+	0.424320i	$0.860513\pi$
$492$	−29.9506	−	5.32580i	−1.35028	−	0.240106i
$493$	−7.55888	+	23.2638i	−0.340435	+	1.04775i
$494$	−0.654717	−	0.278470i	−0.0294571	−	0.0125290i
$495$	−33.7510	−	3.97397i	−1.51699	−	0.178617i
$496$	−17.7699	−	0.672029i	−0.797891	−	0.0301750i
$497$	−4.41473	−	1.43443i	−0.198028	−	0.0643431i
$498$	−14.0888	+	3.24193i	−0.631336	+	0.145274i
$499$	18.1317	−	24.9561i	0.811685	−	1.11719i	−0.179376	−	0.983781i	$-0.557408\pi$
$499$	18.1317	−	24.9561i	0.811685	−	1.11719i	0.991061	−	0.133408i	$-0.0425920\pi$
$500$	10.0112	−	18.7629i	0.447717	−	0.839101i
$501$	−16.6063	+	5.39573i	−0.741917	+	0.241063i
$502$	3.47057	+	5.78548i	0.154899	+	0.258219i
$503$	25.6773	−	18.6557i	1.14489	−	0.831815i	0.157101	−	0.987583i	$-0.449785\pi$
$503$	25.6773	−	18.6557i	1.14489	−	0.831815i	0.987794	+	0.155768i	$0.0497852\pi$
$504$	−0.804800	−	16.0218i	−0.0358486	−	0.713666i
$505$			17.9219i			0.797515i
$506$	1.82551	−	1.65779i	0.0811539	−	0.0736976i
$507$		−	35.1117i		−	1.55936i
$508$	−35.9157	+	17.4530i	−1.59350	+	0.774351i
$509$	−5.41179	+	3.93190i	−0.239873	+	0.174278i	−0.701227	−	0.712938i	$-0.747364\pi$
$509$	−5.41179	+	3.93190i	−0.239873	+	0.174278i	0.461354	+	0.887216i	$0.347364\pi$
$510$	−22.8301	+	13.6952i	−1.01093	+	0.606436i
$511$	−5.25794	+	1.70841i	−0.232598	+	0.0755756i
$512$	−22.3253	−	3.68515i	−0.986649	−	0.162862i
$513$	3.81451	−	5.25022i	0.168415	−	0.231803i
$514$	−0.963107	−	4.18549i	−0.0424808	−	0.184614i
$515$	−0.914922	−	0.297276i	−0.0403163	−	0.0130995i
$516$	−13.6875	+	13.1797i	−0.602560	+	0.580202i
$517$	12.4265	+	22.1575i	0.546515	+	0.974488i
$518$	−3.73351	+	8.77795i	−0.164041	+	0.385681i
$519$	3.03967	−	9.35513i	0.133426	−	0.410645i
$520$	1.62184	+	1.05825i	0.0711224	+	0.0464072i
$521$	−10.0067	−	7.27028i	−0.438401	−	0.318517i	0.346598	−	0.938014i	$-0.387337\pi$
$521$	−10.0067	−	7.27028i	−0.438401	−	0.318517i	−0.784999	+	0.619497i	$0.787337\pi$
$522$	−4.49883	+	50.9969i	−0.196908	+	2.23207i
$523$	1.92840	+	5.93501i	0.0843231	+	0.259520i	0.984324	−	0.176367i	$-0.0564347\pi$
$523$	1.92840	+	5.93501i	0.0843231	+	0.259520i	−0.900001	+	0.435887i	$0.856435\pi$
$524$	5.65108	+	40.6361i	0.246869	+	1.77519i
$525$	0.911507	+	1.25458i	0.0397814	+	0.0547545i
$526$	−15.1113	−	13.1553i	−0.658884	−	0.573597i
$527$	13.1950			0.574784
$528$	25.5586	+	25.4527i	1.11229	+	1.10769i
$529$	22.7236			0.987983
$530$	3.90357	+	3.39828i	0.169560	+	0.147612i
$531$	−36.3368	−	50.0134i	−1.57688	−	2.17039i
$532$	0.609705	+	4.38430i	0.0264341	+	0.190083i
$533$	−0.507388	−	1.56158i	−0.0219774	−	0.0676395i
$534$	0.202113	−	2.29107i	0.00874629	−	0.0991443i
$535$	−9.76811	−	7.09695i	−0.422312	−	0.306828i
$536$	−24.6942	−	16.1129i	−1.06663	−	0.695972i
$537$	−4.20746	+	12.9492i	−0.181565	+	0.558800i
$538$	0.554489	−	1.30367i	0.0239057	−	0.0562053i
$539$	3.46101	+	17.3448i	0.149076	+	0.747093i
$540$	−12.7242	+	12.2521i	−0.547561	+	0.527245i
$541$	24.6331	+	8.00377i	1.05906	+	0.344109i	0.786217	−	0.617950i	$-0.212037\pi$
$541$	24.6331	+	8.00377i	1.05906	+	0.344109i	0.272841	+	0.962059i	$0.412037\pi$
$542$	−5.64212	−	24.5196i	−0.242350	−	1.05321i
$543$	−15.6649	+	21.5608i	−0.672244	+	0.925264i
$544$	16.6573	+	2.10645i	0.714176	+	0.0903133i
$545$	−27.9425	+	9.07907i	−1.19693	+	0.388905i
$546$	1.24963	−	0.749625i	0.0534794	−	0.0320810i
$547$	−13.5035	+	9.81087i	−0.577368	+	0.419482i	−0.837774	−	0.546017i	$-0.816143\pi$
$547$	−13.5035	+	9.81087i	−0.577368	+	0.419482i	0.260406	+	0.965499i	$0.416143\pi$
$548$	11.2705	−	5.47684i	0.481454	−	0.233959i
$549$		−	41.4954i		−	1.77098i
$550$	−2.02838	−	0.422153i	−0.0864903	−	0.0180006i
$551$		−	14.1263i		−	0.601801i
$552$	−0.202833	−	4.03795i	−0.00863314	−	0.171866i
$553$	−10.2897	+	7.47589i	−0.437562	+	0.317907i
$554$	−14.1038	−	23.5111i	−0.599211	−	0.998891i
$555$	31.5105	−	10.2384i	1.33755	−	0.434595i
$556$	12.6917	−	23.7865i	0.538246	−	1.00877i
$557$	−10.9144	+	15.0224i	−0.462460	+	0.636522i	−0.975017	−	0.222132i	$-0.928698\pi$
$557$	−10.9144	+	15.0224i	−0.462460	+	0.636522i	0.512557	+	0.858653i	$0.328698\pi$
$558$	26.9127	−	6.19279i	1.13931	−	0.262162i
$559$	−0.975400	−	0.316927i	−0.0412550	−	0.0134046i
$560$	0.455325	−	12.0398i	0.0192410	−	0.508773i
$561$	−19.6651	−	18.1562i	−0.830262	−	0.766555i
$562$	19.1257	+	8.13471i	0.806769	+	0.343142i
$563$	7.00832	−	21.5694i	0.295366	−	0.909042i	−0.687733	−	0.725964i	$-0.741394\pi$
$563$	7.00832	−	21.5694i	0.295366	−	0.909042i	0.983098	−	0.183078i	$-0.0586061\pi$
$564$	41.0086	+	7.29212i	1.72677	+	0.307054i
$565$	−5.02144	−	3.64829i	−0.211253	−	0.153485i
$566$	−3.51746	−	0.310302i	−0.147850	−	0.0130430i
$567$	−1.15052	−	3.54093i	−0.0483172	−	0.148705i
$568$	2.65302	−	9.81595i	0.111318	−	0.411868i
$569$	0.0874036	+	0.120301i	0.00366415	+	0.00504327i	0.810845	−	0.585261i	$-0.199008\pi$
$569$	0.0874036	+	0.120301i	0.00366415	+	0.00504327i	−0.807181	+	0.590304i	$0.799008\pi$
$570$	10.0951	−	11.5962i	0.422838	−	0.485710i
$571$	−22.0331			−0.922057			−0.461028	−	0.887385i	$-0.652519\pi$
$571$	−22.0331			−0.922057			−0.461028	+	0.887385i	$0.652519\pi$
$572$	−0.562657	+	1.86382i	−0.0235259	+	0.0779303i
$573$	31.7832			1.32776
$574$	−6.70749	+	7.70482i	−0.279965	+	0.321593i
$575$	0.136500	+	0.187876i	0.00569242	+	0.00783495i
$576$	34.9631	−	3.52140i	1.45680	−	0.146725i
$577$	1.21706	+	3.74573i	0.0506669	+	0.155937i	0.973189	−	0.230008i	$-0.0738754\pi$
$577$	1.21706	+	3.74573i	0.0506669	+	0.155937i	−0.922522	+	0.385945i	$0.873875\pi$
$578$	11.5383	+	1.01789i	0.479932	+	0.0423385i
$579$	−2.53966	−	1.84517i	−0.105545	−	0.0766827i
$580$	−6.73158	+	37.8563i	−0.279514	+	1.57190i
$581$	−1.50021	+	4.61716i	−0.0622391	+	0.191552i
$582$	29.4613	+	12.5307i	1.22121	+	0.519416i
$583$	−2.17550	+	4.72655i	−0.0901000	+	0.195754i
$584$	−4.31539	−	11.3153i	−0.178572	−	0.468231i
$585$	−2.86025	−	0.929350i	−0.118257	−	0.0384239i
$586$	−10.3625	+	2.38448i	−0.428071	+	0.0985019i
$587$	11.1451	−	15.3399i	0.460006	−	0.633144i	−0.514504	−	0.857488i	$-0.672024\pi$
$587$	11.1451	−	15.3399i	0.460006	−	0.633144i	0.974510	+	0.224344i	$0.0720240\pi$
$588$	25.5845	+	13.6510i	1.05509	+	0.562960i
$589$	−7.24720	+	2.35476i	−0.298616	+	0.0970261i
$590$	−23.8845	−	39.8156i	−0.983308	−	1.63918i
$591$	−34.3690	+	24.9706i	−1.41375	+	1.02715i
$592$	−19.6142	−	7.20334i	−0.806140	−	0.296056i
$593$		−	31.9983i		−	1.31401i	−0.753885	−	0.657007i	$-0.771822\pi$
$593$		−	31.9983i		−	1.31401i	0.753885	−	0.657007i	$-0.228178\pi$
$594$	−15.4167	−	8.81380i	−0.632557	−	0.361635i
$595$			8.94012i			0.366509i
$596$	15.2538	+	31.3902i	0.624822	+	1.28579i
$597$	−24.1265	+	17.5290i	−0.987433	+	0.717412i
$598$	0.187134	−	0.112258i	0.00765249	−	0.00459055i
$599$	−8.23336	+	2.67518i	−0.336406	+	0.109305i	−0.472349	−	0.881412i	$-0.656594\pi$
$599$	−8.23336	+	2.67518i	−0.336406	+	0.109305i	0.135943	+	0.990717i	$0.456594\pi$
$600$	−2.64454	+	2.13202i	−0.107963	+	0.0870393i
$601$	−12.9491	+	17.8228i	−0.528203	+	0.727009i	−0.986855	−	0.161607i	$-0.948332\pi$
$601$	−12.9491	+	17.8228i	−0.528203	+	0.727009i	0.458652	+	0.888616i	$0.348332\pi$
$602$	1.43087	+	6.21829i	0.0583178	+	0.253439i
$603$	43.5503	+	14.1503i	1.77350	+	0.576246i
$604$	−13.6289	−	14.1540i	−0.554551	−	0.575919i
$605$	−2.04426	−	25.5787i	−0.0831110	−	1.03992i
$606$	−11.5623	+	27.1844i	−0.469687	+	1.10429i
$607$	−13.2005	+	40.6268i	−0.535790	+	1.64899i	0.206146	+	0.978521i	$0.433908\pi$
$607$	−13.2005	+	40.6268i	−0.535790	+	1.64899i	−0.741936	+	0.670471i	$0.766092\pi$
$608$	−9.52474	+	1.81569i	−0.386279	+	0.0736360i
$609$	23.4074	+	17.0065i	0.948517	+	0.689138i
$610$	2.73869	−	31.0447i	0.110886	−	1.25696i
$611$	0.694718	+	2.13812i	0.0281053	+	0.0864992i
$612$	−25.8260	+	3.59151i	−1.04396	+	0.145178i
$613$	−5.74748	−	7.91073i	−0.232139	−	0.319511i	0.677018	−	0.735967i	$-0.263272\pi$
$613$	−5.74748	−	7.91073i	−0.232139	−	0.319511i	−0.909156	+	0.416456i	$0.863272\pi$
$614$	27.5186	+	23.9565i	1.11056	+	0.966805i
$615$	35.4817			1.43076
$616$	11.7447	−	2.96321i	0.473207	−	0.119391i
$617$	−22.4213			−0.902649			−0.451324	−	0.892360i	$-0.649048\pi$
$617$	−22.4213			−0.902649			−0.451324	+	0.892360i	$0.649048\pi$
$618$	−1.19599	−	1.04118i	−0.0481097	−	0.0418823i
$619$	11.3322	+	15.5975i	0.455481	+	0.626916i	0.973564	−	0.228414i	$-0.0733540\pi$
$619$	11.3322	+	15.5975i	0.455481	+	0.626916i	−0.518083	+	0.855331i	$0.673354\pi$
$620$	20.5435	−	2.85689i	0.825045	−	0.114735i
$621$	0.615093	+	1.89306i	0.0246828	+	0.0759660i
$622$	−0.368399	+	4.17603i	−0.0147715	+	0.167443i
$623$	−0.624841	−	0.453973i	−0.0250337	−	0.0181881i
$624$	1.77732	+	2.65150i	0.0711497	+	0.106145i
$625$	−8.34762	+	25.6913i	−0.333905	+	1.02765i
$626$	0.334322	−	0.786031i	0.0133622	−	0.0314161i
$627$	14.0409	+	6.46266i	0.560741	+	0.258094i
$628$	−21.3691	−	22.1925i	−0.852720	−	0.885579i
$629$	14.7457	+	4.79118i	0.587951	+	0.191037i
$630$	4.19585	+	18.2344i	0.167167	+	0.726476i
$631$	−22.5021	+	30.9715i	−0.895794	+	1.23296i	0.0759958	+	0.997108i	$0.475786\pi$
$631$	−22.5021	+	30.9715i	−0.895794	+	1.23296i	−0.971790	+	0.235847i	$0.924214\pi$
$632$	−17.4861	−	21.6897i	−0.695561	−	0.862768i
$633$	49.9163	−	16.2188i	1.98400	−	0.644639i
$634$	−27.8270	+	16.6927i	−1.10515	+	0.662954i
$635$	37.6803	−	27.3763i	1.49530	−	1.08640i
$636$	3.72863	+	7.67298i	0.147850	+	0.304253i
$637$			1.56519i			0.0620153i
$638$	−38.4262	+	4.20377i	−1.52131	+	0.166429i
$639$			15.7910i			0.624682i
$640$	26.3900	−	0.326965i	1.04316	−	0.0129244i
$641$	25.5946	−	18.5955i	1.01092	−	0.734480i	0.0465216	−	0.998917i	$-0.485186\pi$
$641$	25.5946	−	18.5955i	1.01092	−	0.734480i	0.964403	+	0.264438i	$0.0851864\pi$
$642$	−10.2379	−	17.0667i	−0.404058	−	0.673569i
$643$	−14.1716	+	4.60464i	−0.558874	+	0.181589i	−0.574814	−	0.818284i	$-0.694926\pi$
$643$	−14.1716	+	4.60464i	−0.558874	+	0.181589i	0.0159405	+	0.999873i	$0.494926\pi$
$644$	−1.19784	−	0.639126i	−0.0472014	−	0.0251851i
$645$	13.0269	−	17.9300i	0.512934	−	0.705993i
$646$	7.01157	−	1.61341i	0.275867	−	0.0634786i
$647$	39.0933	+	12.7022i	1.53692	+	0.499374i	0.950523	−	0.310653i	$-0.100548\pi$
$647$	39.0933	+	12.7022i	1.53692	+	0.499374i	0.586393	+	0.810027i	$0.300548\pi$
$648$	7.62022	−	2.90617i	0.299351	−	0.114165i
$649$	31.6643	−	34.2959i	1.24293	−	1.34623i
$650$	−0.168721	−	0.0717621i	−0.00661780	−	0.00281474i
$651$	4.82296	−	14.8435i	0.189027	−	0.581764i
$652$	3.77011	−	21.2019i	0.147649	−	0.830332i
$653$	−3.70761	−	2.69374i	−0.145090	−	0.105414i	0.512872	−	0.858465i	$-0.328581\pi$
$653$	−3.70761	−	2.69374i	−0.145090	−	0.105414i	−0.657962	+	0.753051i	$0.728581\pi$
$654$	−48.2412	−	4.25573i	−1.88638	−	0.166412i
$655$	−14.7874	−	45.5109i	−0.577791	−	1.77826i
$656$	−17.5933	−	13.8276i	−0.686903	−	0.539876i
$657$	11.0545	+	15.2152i	0.431278	+	0.593603i
$658$	9.18394	−	10.5495i	0.358027	−	0.411262i
$659$	−38.0732			−1.48312			−0.741560	−	0.670886i	$-0.765914\pi$
$659$	−38.0732			−1.48312			−0.741560	+	0.670886i	$0.765914\pi$
$660$	−34.5479	−	24.0098i	−1.34478	−	0.934580i
$661$	−9.34038			−0.363299			−0.181649	−	0.983363i	$-0.558144\pi$
$661$	−9.34038			−0.363299			−0.181649	+	0.983363i	$0.558144\pi$
$662$	4.11771	−	4.72997i	0.160039	−	0.183835i
$663$	−1.39222	−	1.91622i	−0.0540692	−	0.0744198i
$664$	−10.2661	−	2.77467i	−0.398400	−	0.107678i
$665$	−1.59544	−	4.91025i	−0.0618684	−	0.190411i
$666$	32.3242	+	2.85157i	1.25254	+	0.110496i
$667$	3.50530	+	2.54675i	0.135726	+	0.0986104i
$668$	−12.6457	−	2.24864i	−0.489276	−	0.0870027i
$669$	9.10685	−	28.0280i	0.352091	−	1.08363i
$670$	31.6481	+	13.4609i	1.22267	+	0.520039i
$671$	30.7260	−	6.13113i	1.18616	−	0.236689i
$672$	8.45810	−	17.9685i	0.326278	−	0.693148i
$673$	13.4864	+	4.38199i	0.519862	+	0.168913i	0.557183	−	0.830390i	$-0.311882\pi$
$673$	13.4864	+	4.38199i	0.519862	+	0.168913i	−0.0373208	+	0.999303i	$0.511882\pi$
$674$	−24.4793	+	5.63284i	−0.942907	+	0.216969i
$675$	0.983004	−	1.35299i	0.0378358	−	0.0520766i
$676$	12.1584	−	22.7869i	0.467629	−	0.876421i
$677$	−4.48196	+	1.45628i	−0.172256	+	0.0559692i	−0.393875	−	0.919164i	$-0.628866\pi$
$677$	−4.48196	+	1.45628i	−0.172256	+	0.0559692i	0.221619	+	0.975133i	$0.428866\pi$
$678$	−5.26295	−	8.77339i	−0.202122	−	0.336940i
$679$	8.69775	−	6.31929i	0.333789	−	0.242512i
$680$	−19.5587	+	0.982468i	−0.750043	+	0.0376759i
$681$			65.2454i			2.50021i
$682$	8.56204	+	19.0130i	0.327857	+	0.728046i
$683$			18.0462i			0.690519i	0.938507	+	0.345260i	$0.112209\pi$
$683$			18.0462i			0.690519i	−0.938507	+	0.345260i	$0.887791\pi$
$684$	13.5437	−	6.58146i	0.517856	−	0.251648i
$685$	−11.8243	+	8.59084i	−0.451782	+	0.328239i
$686$	19.3121	−	11.5849i	0.737340	−	0.442313i
$687$	−63.5633	+	20.6530i	−2.42509	+	0.787960i
$688$	−13.4468	+	3.81373i	−0.512655	+	0.145397i
$689$	−0.270650	+	0.372518i	−0.0103109	+	0.0141918i
$690$	1.05748	+	4.59560i	0.0402575	+	0.174952i
$691$	1.27888	+	0.415533i	0.0486509	+	0.0158076i	0.333241	−	0.942842i	$-0.391858\pi$
$691$	1.27888	+	0.415533i	0.0486509	+	0.0158076i	−0.284590	+	0.958649i	$0.591858\pi$
$692$	5.21216	−	5.01877i	0.198137	−	0.190785i
$693$	−16.4068	+	9.20132i	−0.623244	+	0.349529i
$694$	−2.14791	+	5.05000i	−0.0815336	+	0.191695i
$695$	−9.71740	+	29.9071i	−0.368602	+	1.13444i
$696$	−34.6336	+	53.0785i	−1.31278	+	2.01193i
$697$	13.4330	+	9.75964i	0.508811	+	0.369673i
$698$	−2.45048	+	27.7776i	−0.0927519	+	1.05140i
$699$	−12.0187	−	36.9896i	−0.454587	−	1.39908i
$700$	0.157122	+	1.12984i	0.00593864	+	0.0427039i
$701$	−9.79382	−	13.4800i	−0.369907	−	0.509134i	0.582968	−	0.812495i	$-0.301891\pi$
$701$	−9.79382	−	13.4800i	−0.369907	−	0.509134i	−0.952876	+	0.303361i	$0.901891\pi$
$702$	−1.18530	−	1.03188i	−0.0447364	−	0.0389457i
$703$	−8.95393			−0.337704
$704$	7.77344	+	25.3688i	0.292972	+	0.956121i
$705$	−48.5817			−1.82969
$706$	1.70262	+	1.48223i	0.0640788	+	0.0557843i
$707$	5.83090	+	8.02554i	0.219293	+	0.301832i
$708$	−10.5415	−	75.8024i	−0.396174	−	2.84883i
$709$	7.43557	+	22.8843i	0.279249	+	0.859440i	0.988064	+	0.154045i	$0.0492301\pi$
$709$	7.43557	+	22.8843i	0.279249	+	0.859440i	−0.708815	+	0.705394i	$0.750770\pi$
$710$	−1.04220	+	11.8140i	−0.0391132	+	0.443372i
$711$	35.0036	+	25.4316i	1.31274	+	0.953761i
$712$	0.924513	−	1.41688i	0.0346476	−	0.0530999i
$713$	0.722245	−	2.22284i	0.0270483	−	0.0832460i
$714$	−5.76771	+	13.5606i	−0.215851	+	0.507493i
$715$	0.265540	−	2.25523i	0.00993063	−	0.0843410i
$716$	−7.21459	+	6.94690i	−0.269622	+	0.259618i
$717$	−51.1063	−	16.6054i	−1.90860	−	0.620141i
$718$	4.89103	+	21.2555i	0.182531	+	0.793249i
$719$	6.65923	−	9.16564i	0.248347	−	0.341821i	−0.666584	−	0.745430i	$-0.732244\pi$
$719$	6.65923	−	9.16564i	0.248347	−	0.341821i	0.914932	+	0.403609i	$0.132244\pi$
$720$	−39.4312	+	11.1833i	−1.46951	+	0.416778i
$721$	−0.506426	+	0.164548i	−0.0188603	+	0.00612808i
$722$	19.4790	−	11.6850i	0.724935	−	0.434871i
$723$	−14.3649	+	10.4367i	−0.534237	+	0.388146i
$724$	−17.6323	+	8.56828i	−0.655298	+	0.318437i
$725$		−	3.64037i		−	0.135200i
$726$	13.4013	−	40.1172i	0.497368	−	1.48889i
$727$		−	0.700673i		−	0.0259865i	−0.999916	−	0.0129933i	$-0.995864\pi$
$727$		−	0.700673i		−	0.0259865i	0.999916	−	0.0129933i	$-0.00413600\pi$
$728$	1.07057	−	0.0537766i	0.0396780	−	0.00199309i
$729$	−35.2308	+	25.5967i	−1.30485	+	0.948026i
$730$	7.26621	+	12.1129i	0.268935	+	0.448317i
$731$	9.86371	−	3.20491i	0.364823	−	0.118538i
$732$	24.1826	−	45.3225i	0.893814	−	1.67517i
$733$	17.6206	−	24.2526i	0.650830	−	0.895790i	−0.348305	−	0.937381i	$-0.613243\pi$
$733$	17.6206	−	24.2526i	0.650830	−	0.895790i	0.999135	+	0.0415908i	$0.0132426\pi$
$734$	−14.5427	+	3.34637i	−0.536781	+	0.123517i
$735$	−32.1678	−	10.4519i	−1.18653	−	0.385526i
$736$	1.26661	−	2.69080i	0.0466879	−	0.0991843i
$737$	−4.04313	+	34.3383i	−0.148930	+	1.26487i
$738$	31.9786	+	13.6014i	1.17715	+	0.500676i
$739$	13.4812	−	41.4910i	0.495915	−	1.52627i	−0.319611	−	0.947549i	$-0.603552\pi$
$739$	13.4812	−	41.4910i	0.495915	−	1.52627i	0.815526	−	0.578721i	$-0.196448\pi$
$740$	23.9951	+	4.26680i	0.882078	+	0.156851i
$741$	1.10662	+	0.804008i	0.0406528	+	0.0295360i
$742$	2.85367	+	0.251745i	0.104762	+	0.00924183i
$743$	−10.5703	−	32.5321i	−0.387788	−	1.19349i	−0.934438	−	0.356127i	$-0.884097\pi$
$743$	−10.5703	−	32.5321i	−0.387788	−	1.19349i	0.546650	−	0.837361i	$-0.315903\pi$
$744$	33.0039	+	8.92019i	1.20998	+	0.327030i
$745$	−23.9268	−	32.9324i	−0.876610	−	1.20655i
$746$	−34.8174	+	39.9944i	−1.27476	+	1.46430i
$747$	16.5151			0.604255
$748$	−6.47531	−	18.5927i	−0.236761	−	0.679815i
$749$	−6.68321			−0.244199
$750$	−26.8463	+	30.8380i	−0.980287	+	1.12605i
$751$	−0.851372	−	1.17181i	−0.0310670	−	0.0427600i	0.793201	−	0.608960i	$-0.208413\pi$
$751$	−0.851372	−	1.17181i	−0.0310670	−	0.0427600i	−0.824268	+	0.566200i	$0.808413\pi$
$752$	24.0889	+	18.9328i	0.878431	+	0.690408i
$753$	−4.00819	−	12.3359i	−0.146067	−	0.449546i
$754$	−3.40760	−	0.300611i	−0.124097	−	0.0109476i
$755$	18.5411	+	13.4709i	0.674780	+	0.490257i
$756$	−1.71175	+	9.62636i	−0.0622558	+	0.350107i
$757$	9.41100	−	28.9641i	0.342049	−	1.05272i	−0.621096	−	0.783734i	$-0.713312\pi$
$757$	9.41100	−	28.9641i	0.342049	−	1.05272i	0.963145	−	0.268983i	$-0.0866875\pi$
$758$	−27.7573	−	11.8060i	−1.00819	−	0.428812i
$759$	−4.13500	+	2.31900i	−0.150091	+	0.0841744i
$760$	10.5671	−	4.03002i	0.383308	−	0.146184i
$761$	22.8716	+	7.43142i	0.829094	+	0.269389i	0.692664	−	0.721261i	$-0.256437\pi$
$761$	22.8716	+	7.43142i	0.829094	+	0.269389i	0.136430	+	0.990650i	$0.456437\pi$
$762$	74.8162	−	17.2157i	2.71030	−	0.623658i
$763$	−9.55895	+	13.1568i	−0.346057	+	0.476307i
$764$	20.6268	+	11.0058i	0.746253	+	0.398176i
$765$	28.9242	−	9.39804i	1.04576	−	0.339787i
$766$	20.9746	+	34.9649i	0.757843	+	1.26333i
$767$	3.34188	−	2.42802i	0.120668	−	0.0876707i
$768$	40.2400	+	16.5295i	1.45203	+	0.596459i
$769$			14.6461i			0.528151i	0.964502	+	0.264076i	$0.0850669\pi$
$769$			14.6461i			0.528151i	−0.964502	+	0.264076i	$0.914933\pi$
$770$	−12.8820	+	5.80111i	−0.464236	+	0.209057i
$771$			8.25715i			0.297374i
$772$	−1.00926	−	2.07691i	−0.0363241	−	0.0747498i
$773$	21.4727	−	15.6009i	0.772320	−	0.561124i	−0.130344	−	0.991469i	$-0.541608\pi$
$773$	21.4727	−	15.6009i	0.772320	−	0.561124i	0.902664	+	0.430345i	$0.141608\pi$
$774$	18.6140	−	11.1661i	0.669067	−	0.401358i
$775$	−1.86761	+	0.606824i	−0.0670866	+	0.0217977i
$776$	14.7808	+	18.3340i	0.530601	+	0.658153i
$777$	10.7795	−	14.8367i	0.386713	−	0.532265i
$778$	−11.0613	−	48.0704i	−0.396567	−	1.72341i
$779$	−9.11960	−	2.96314i	−0.326743	−	0.106165i
$780$	−2.58244	−	2.68195i	−0.0924662	−	0.0960293i
$781$	−11.6927	+	2.33319i	−0.418398	+	0.0834880i
$782$	−0.863723	+	2.03072i	−0.0308867	+	0.0726184i
$783$	9.64214	−	29.6755i	0.344582	−	1.06051i
$784$	11.8769	+	17.7186i	0.424176	+	0.632809i
$785$	29.0712	+	21.1214i	1.03759	+	0.753857i
$786$	6.93145	−	78.5721i	0.247237	−	2.80257i
$787$	−6.33834	−	19.5074i	−0.225937	−	0.695364i	−0.998195	−	0.0600544i	$-0.980873\pi$
$787$	−6.33834	−	19.5074i	−0.225937	−	0.695364i	0.772258	−	0.635309i	$-0.219127\pi$
$788$	−30.9517	+	4.30432i	−1.10261	+	0.153335i
$789$	22.6410	+	31.1626i	0.806040	+	1.10942i
$790$	24.5094	+	21.3369i	0.872006	+	0.759132i
$791$	−3.43560			−0.122156
$792$	−21.9332	−	34.8828i	−0.779362	−	1.23951i
$793$	2.77271			0.0984620
$794$	−18.0372	−	15.7024i	−0.640117	−	0.557259i
$795$	−5.84864	−	8.04996i	−0.207430	−	0.285503i
$796$	−21.7276	+	3.02157i	−0.770115	+	0.107097i
$797$	−10.1514	−	31.2427i	−0.359580	−	1.10667i	−0.953306	−	0.302006i	$-0.902344\pi$
$797$	−10.1514	−	31.2427i	−0.359580	−	1.10667i	0.593726	−	0.804667i	$-0.297656\pi$
$798$	0.747847	−	8.47728i	0.0264735	−	0.300093i
$799$	−18.3925	−	13.3630i	−0.650682	−	0.472748i
$800$	−2.45454	+	0.467906i	−0.0867809	+	0.0165430i
$801$	−0.811905	+	2.49879i	−0.0286873	+	0.0882903i
$802$	8.77880	−	20.6400i	0.309990	−	0.728825i
$803$	−9.63304	+	10.4336i	−0.339942	+	0.368195i
$804$	39.3204	+	40.8356i	1.38672	+	1.44016i
$805$	1.50606	+	0.489348i	0.0530816	+	0.0172473i
$806$	0.413801	+	1.79830i	0.0145755	+	0.0633426i
$807$	−1.60094	+	2.20350i	−0.0563557	+	0.0775670i
$808$	−16.9171	+	13.6385i	−0.595141	+	0.479801i
$809$	17.7783	−	5.77654i	0.625053	−	0.203092i	0.0206708	−	0.999786i	$-0.493420\pi$
$809$	17.7783	−	5.77654i	0.625053	−	0.203092i	0.604383	+	0.796694i	$0.293420\pi$
$810$	−8.15732	+	4.89339i	−0.286619	+	0.171936i
$811$	22.1490	−	16.0922i	0.777758	−	0.565074i	−0.126547	−	0.991961i	$-0.540390\pi$
$811$	22.1490	−	16.0922i	0.777758	−	0.565074i	0.904305	+	0.426886i	$0.140390\pi$
$812$	9.30211	+	19.1424i	0.326440	+	0.671767i
$813$			48.3724i			1.69650i
$814$	2.66455	+	24.3564i	0.0933925	+	0.853691i
$815$			25.1173i			0.879821i
$816$	−30.3010	−	11.1281i	−1.06075	−	0.389560i
$817$	−4.84558	+	3.52052i	−0.169525	+	0.123167i
$818$	20.1327	+	33.5615i	0.703925	+	1.17345i
$819$	−1.58320	+	0.514413i	−0.0553215	+	0.0179750i
$820$	23.0271	+	12.2865i	0.804140	+	0.429062i
$821$	5.06427	−	6.97036i	0.176744	−	0.243267i	−0.711449	−	0.702738i	$-0.751961\pi$
$821$	5.06427	−	6.97036i	0.176744	−	0.243267i	0.888193	+	0.459470i	$0.151961\pi$
$822$	−23.4777	+	5.40237i	−0.818880	+	0.188429i
$823$	3.63990	+	1.18267i	0.126879	+	0.0412254i	0.371768	−	0.928326i	$-0.378752\pi$
$823$	3.63990	+	1.18267i	0.126879	+	0.0412254i	−0.244889	+	0.969551i	$0.578752\pi$
$824$	−0.415643	−	1.08985i	−0.0144796	−	0.0379667i
$825$	3.61837	+	1.66543i	0.125975	+	0.0579830i
$826$	−23.6496	−	10.0589i	−0.822876	−	0.349993i
$827$	8.45284	−	26.0152i	0.293934	−	0.904636i	−0.689643	−	0.724149i	$-0.742233\pi$
$827$	8.45284	−	26.0152i	0.293934	−	0.904636i	0.983577	−	0.180487i	$-0.0577674\pi$
$828$	−0.808590	+	4.54726i	−0.0281004	+	0.158028i
$829$	−14.2443	−	10.3491i	−0.494723	−	0.359438i	0.312274	−	0.949992i	$-0.398909\pi$
$829$	−14.2443	−	10.3491i	−0.494723	−	0.359438i	−0.806998	+	0.590554i	$0.798909\pi$
$830$	12.3557	+	1.08999i	0.428873	+	0.0378342i
$831$	16.2885	+	50.1309i	0.565043	+	1.73902i
$832$	0.235299	+	2.33623i	0.00815753	+	0.0809942i
$833$	−9.30347	−	12.8051i	−0.322346	−	0.443671i
$834$	−34.0341	+	39.0946i	−1.17850	+	1.35374i
$835$	14.9810			0.518438
$836$	6.87449	+	9.05622i	0.237759	+	0.313216i
$837$	−16.8316			−0.581786
$838$	21.3304	−	24.5020i	0.736845	−	0.846406i
$839$	0.148971	+	0.205041i	0.00514306	+	0.00707881i	0.811581	−	0.584240i	$-0.198607\pi$
$839$	0.148971	+	0.205041i	0.00514306	+	0.00707881i	−0.806438	+	0.591319i	$0.798607\pi$
$840$	−6.04377	+	22.3614i	−0.208530	+	0.771542i
$841$	−12.0270	−	37.0154i	−0.414726	−	1.27639i
$842$	−42.4167	−	3.74190i	−1.46177	−	0.128954i
$843$	−32.3268	−	23.4868i	−1.11340	−	0.808929i
$844$	38.0111	+	6.75911i	1.30840	+	0.232658i
$845$	−9.30907	+	28.6504i	−0.320242	+	0.985603i
$846$	−43.7853	−	18.6232i	−1.50537	−	0.640278i
$847$	−9.23746	−	10.7892i	−0.317403	−	0.370721i
$848$	−0.237151	+	6.27079i	−0.00814381	+	0.215340i
$849$	6.45654	+	2.09786i	0.221588	+	0.0719983i
$850$	1.80689	−	0.415777i	0.0619758	−	0.0142610i
$851$	1.61425	−	2.22182i	0.0553358	−	0.0761632i
$852$	−9.20263	+	17.2474i	−0.315277	+	0.590886i
$853$	−35.2985	+	11.4692i	−1.20860	+	0.392697i	−0.842917	−	0.538044i	$-0.819163\pi$
$853$	−35.2985	+	11.4692i	−1.20860	+	0.392697i	−0.365680	+	0.930741i	$0.619163\pi$
$854$	−8.87400	−	14.7930i	−0.303662	−	0.506208i
$855$	−14.2091	+	10.3235i	−0.485941	+	0.353057i
$856$	−0.734447	−	14.6212i	−0.0251029	−	0.499742i
$857$		−	20.9360i		−	0.715161i	−0.933882	−	0.357580i	$-0.883602\pi$
$857$		−	20.9360i		−	0.715161i	0.933882	−	0.357580i	$-0.116398\pi$
$858$	1.85774	−	3.24948i	0.0634222	−	0.110935i
$859$			20.6926i			0.706022i	0.935619	+	0.353011i	$0.114842\pi$
$859$			20.6926i			0.706022i	−0.935619	+	0.353011i	$0.885158\pi$
$860$	14.6630	−	7.12538i	0.500005	−	0.242974i
$861$	15.8889	−	11.5440i	0.541493	−	0.393417i
$862$	12.3375	−	7.40097i	0.420216	−	0.252078i
$863$	35.9307	−	11.6746i	1.22309	−	0.397408i	0.374887	−	0.927071i	$-0.377682\pi$
$863$	35.9307	−	11.6746i	1.22309	−	0.397408i	0.848208	+	0.529663i	$0.177682\pi$
$864$	−21.2482	−	2.68700i	−0.722877	−	0.0914136i
$865$	−4.96060	+	6.82768i	−0.168666	+	0.232148i
$866$	8.73222	+	37.9487i	0.296733	+	1.28955i
$867$	−21.1794	−	6.88161i	−0.719290	−	0.233712i
$868$	8.27000	−	7.96315i	0.280702	−	0.270287i
$869$	−13.6594	+	29.6767i	−0.463362	+	1.00671i
$870$	28.9332	−	68.0254i	0.980926	−	2.30628i
$871$	−0.945523	+	2.91002i	−0.0320378	+	0.0986023i
$872$	−29.8342	−	19.4667i	−1.01031	−	0.659227i
$873$	−29.5882	−	21.4971i	−1.00141	−	0.727566i
$874$	0.111991	−	1.26949i	0.00378816	−	0.0429410i
$875$	4.24279	+	13.0580i	0.143433	+	0.441440i
$876$	3.20697	+	23.0609i	0.108354	+	0.779154i
$877$	6.81007	+	9.37325i	0.229960	+	0.316512i	0.908367	−	0.418173i	$-0.137330\pi$
$877$	6.81007	+	9.37325i	0.229960	+	0.316512i	−0.678408	+	0.734686i	$0.737330\pi$
$878$	−12.3132	−	10.7194i	−0.415551	−	0.361761i
$879$	20.4432			0.689532
$880$	−14.1070	−	27.5451i	−0.475548	−	0.928546i
$881$	−24.6157			−0.829325			−0.414662	−	0.909975i	$-0.636100\pi$
$881$	−24.6157			−0.829325			−0.414662	+	0.909975i	$0.636100\pi$
$882$	−24.9853	−	21.7511i	−0.841299	−	0.732399i
$883$	23.0095	+	31.6699i	0.774333	+	1.06578i	0.995885	+	0.0906289i	$0.0288877\pi$
$883$	23.0095	+	31.6699i	0.774333	+	1.06578i	−0.221552	+	0.975149i	$0.571112\pi$
$884$	−0.239984	−	1.72569i	−0.00807154	−	0.0580412i
$885$	27.5843	+	84.8959i	0.927237	+	2.85374i
$886$	2.11154	−	23.9356i	0.0709387	−	0.804132i
$887$	−38.4919	−	27.9660i	−1.29243	−	0.939006i	−0.292580	−	0.956241i	$-0.594514\pi$
$887$	−38.4919	−	27.9660i	−1.29243	−	0.939006i	−0.999851	+	0.0172350i	$0.994514\pi$
$888$	33.6437	+	21.9524i	1.12901	+	0.736675i
$889$	7.96657	−	24.5186i	0.267190	−	0.822326i
$890$	−0.772346	+	1.81588i	−0.0258891	+	0.0608684i
$891$	−7.02646	−	6.48731i	−0.235395	−	0.217333i
$892$	15.6157	−	15.0363i	0.522851	−	0.503451i
$893$	12.4866	+	4.05715i	0.417848	+	0.135767i
$894$	−15.0464	−	65.3890i	−0.503228	−	2.18694i
$895$	6.86639	−	9.45077i	0.229518	−	0.315904i
$896$	11.7112	−	8.73242i	0.391245	−	0.291730i
$897$	−0.399012	+	0.129647i	−0.0133226	+	0.00432879i
$898$	−7.41795	+	4.44986i	−0.247540	+	0.148494i
$899$	−29.6410	+	21.5354i	−0.988581	+	0.718246i
$900$	3.49022	−	1.69605i	0.116341	−	0.0565350i
$901$		−	4.65637i		−	0.155126i
$902$	−5.34644	+	25.6888i	−0.178017	+	0.855344i
$903$		−	12.2675i		−	0.408236i
$904$	−0.377553	−	7.51623i	−0.0125572	−	0.249986i
$905$	18.4986	−	13.4400i	0.614913	−	0.446760i
$906$	19.4329	+	32.3948i	0.645614	+	1.07624i
$907$	3.43208	−	1.11515i	0.113960	−	0.0370279i	−0.251482	−	0.967862i	$-0.580918\pi$
$907$	3.43208	−	1.11515i	0.113960	−	0.0370279i	0.365442	+	0.930834i	$0.380918\pi$
$908$	−22.5930	+	42.3433i	−0.749774	+	1.40521i
$909$	19.8357	−	27.3015i	0.657908	−	0.905532i
$910$	−1.21842	+	0.280366i	−0.0403902	+	0.00929405i
$911$	29.8894	+	9.71164i	0.990278	+	0.321761i	0.758974	−	0.651121i	$-0.225701\pi$
$911$	29.8894	+	9.71164i	0.990278	+	0.321761i	0.231304	+	0.972881i	$0.425701\pi$
$912$	18.6283	+	0.704495i	0.616846	+	0.0233282i
$913$	2.44017	+	12.2289i	0.0807579	+	0.404716i
$914$	8.48995	+	3.61102i	0.280823	+	0.119442i
$915$	−18.5154	+	56.9847i	−0.612102	+	1.88386i
$916$	−48.4033	−	8.60703i	−1.59929	−	0.284384i
$917$	−21.4289	−	15.5690i	−0.707643	−	0.514133i
$918$	15.8306	+	1.39654i	0.522488	+	0.0460927i
$919$	8.08812	+	24.8927i	0.266802	+	0.821133i	0.991273	+	0.131827i	$0.0420845\pi$
$919$	8.08812	+	24.8927i	0.266802	+	0.821133i	−0.724470	+	0.689306i	$0.757916\pi$
$920$	−0.905064	+	3.34865i	−0.0298391	+	0.110402i
$921$	−41.2305	−	56.7489i	−1.35859	−	1.86994i
$922$	17.7249	−	20.3604i	0.583739	−	0.670534i
$923$	−1.05515			−0.0347307
$924$	−23.2824	+	0.488426i	−0.765933	+	0.0160680i
$925$	−2.30744			−0.0758681
$926$	−12.1049	+	13.9047i	−0.397790	+	0.456938i
$927$	1.06473	+	1.46548i	0.0349704	+	0.0481326i
$928$	−40.8565	+	22.4543i	−1.34118	+	0.737099i
$929$	8.71671	+	26.8273i	0.285986	+	0.880175i	0.986101	+	0.166145i	$0.0531320\pi$
$929$	8.71671	+	26.8273i	0.285986	+	0.880175i	−0.700115	+	0.714030i	$0.746868\pi$
$930$	−39.7219	−	3.50418i	−1.30253	−	0.114906i
$931$	7.39499	+	5.37278i	0.242361	+	0.176086i
$932$	5.00872	−	28.1675i	0.164066	−	0.922657i
$933$	2.49063	−	7.66538i	0.0815397	−	0.250953i
$934$	19.7522	+	8.40119i	0.646312	+	0.274895i
$935$	11.2326	+	20.0288i	0.367346	+	0.655013i
$936$	−1.29939	−	3.40711i	−0.0424719	−	0.111365i
$937$	20.4298	+	6.63805i	0.667413	+	0.216856i	0.623076	−	0.782161i	$-0.285883\pi$
$937$	20.4298	+	6.63805i	0.667413	+	0.216856i	0.0443365	+	0.999017i	$0.485883\pi$
$938$	18.5517	−	4.26887i	0.605736	−	0.139384i
$939$	−0.965265	+	1.32857i	−0.0315002	+	0.0433563i
$940$	−31.5288	−	16.8227i	−1.02836	−	0.548697i
$941$	27.2146	−	8.84257i	0.887172	−	0.288260i	0.170240	−	0.985403i	$-0.445546\pi$
$941$	27.2146	−	8.84257i	0.887172	−	0.288260i	0.716932	+	0.697143i	$0.245546\pi$
$942$	30.4694	+	50.7928i	0.992746	+	1.65492i
$943$	2.37939	−	1.72873i	0.0774835	−	0.0562951i
$944$	19.4073	−	52.8449i	0.631655	−	1.71995i
$945$		−	11.4041i		−	0.370974i
$946$	11.0184	+	12.1332i	0.358241	+	0.394486i
$947$			0.894236i			0.0290588i	0.999894	+	0.0145294i	$0.00462501\pi$
$947$			0.894236i			0.0290588i	−0.999894	+	0.0145294i	$0.995375\pi$
$948$	23.4110	+	48.1765i	0.760355	+	1.56470i
$949$	−1.01668	+	0.738661i	−0.0330028	+	0.0239779i
$950$	−0.918213	+	0.550814i	−0.0297908	+	0.0178708i
$951$	59.3333	−	19.2786i	1.92402	−	0.625150i
$952$	−8.43888	+	6.80340i	−0.273506	+	0.220499i
$953$	−5.07423	+	6.98407i	−0.164370	+	0.226236i	−0.883255	−	0.468893i	$-0.844653\pi$
$953$	−5.07423	+	6.98407i	−0.164370	+	0.226236i	0.718885	+	0.695129i	$0.244653\pi$
$954$	−2.18537	−	9.49720i	−0.0707538	−	0.307483i
$955$	−25.9344	−	8.42661i	−0.839219	−	0.272679i
$956$	−27.4171	−	28.4736i	−0.886733	−	0.920902i
$957$	73.8078	+	8.69041i	2.38587	+	0.280921i
$958$	14.5045	−	34.1018i	0.468618	−	1.10178i
$959$	−2.49995	+	7.69406i	−0.0807277	+	0.248454i
$960$	−49.5853	−	10.7649i	−1.60036	−	0.347434i
$961$	−9.09031	−	6.60449i	−0.293236	−	0.213048i
$962$	−0.190541	+	2.15990i	−0.00614330	+	0.0696380i
$963$	7.02553	+	21.6224i	0.226395	+	0.696771i
$964$	−12.9366	+	1.79904i	−0.416660	+	0.0579431i
$965$	1.58310	+	2.17895i	0.0509619	+	0.0701430i
$966$	1.96872	+	1.71389i	0.0633427	+	0.0551435i
$967$	23.2776			0.748557			0.374278	−	0.927316i	$-0.377890\pi$
$967$	23.2776			0.748557			0.374278	+	0.927316i	$0.377890\pi$
$968$	22.5889	−	21.3949i	0.726034	−	0.687658i
$969$	−13.8325			−0.444363
$970$	−20.7175	−	18.0358i	−0.665200	−	0.579095i
$971$	−18.9657	−	26.1040i	−0.608638	−	0.837718i	0.387827	−	0.921732i	$-0.373226\pi$
$971$	−18.9657	−	26.1040i	−0.608638	−	0.837718i	−0.996465	+	0.0840143i	$0.973226\pi$
$972$	−38.0302	+	5.28870i	−1.21982	+	0.169635i
$973$	5.37876	+	16.5541i	0.172435	+	0.530701i
$974$	3.38673	−	38.3906i	0.108518	−	1.23011i
$975$	0.285178	+	0.207194i	0.00913300	+	0.00663551i
$976$	31.3883	−	21.0397i	1.00471	−	0.673466i
$977$	2.86676	−	8.82297i	0.0917157	−	0.282272i	−0.894668	−	0.446731i	$-0.852588\pi$
$977$	2.86676	−	8.82297i	0.0917157	−	0.282272i	0.986384	+	0.164459i	$0.0525880\pi$
$978$	−16.2044	+	38.0986i	−0.518160	+	1.21826i
$979$	−1.97023	−	0.231983i	−0.0629689	−	0.00741420i
$980$	−17.2571	−	17.9221i	−0.551259	−	0.572501i
$981$	52.6150	+	17.0956i	1.67987	+	0.545822i
$982$	6.79057	+	29.5106i	0.216696	+	0.941721i
$983$	13.6886	−	18.8408i	0.436599	−	0.600927i	−0.532853	−	0.846208i	$-0.678880\pi$
$983$	13.6886	−	18.8408i	0.436599	−	0.600927i	0.969452	+	0.245281i	$0.0788801\pi$
$984$	27.0014	+	33.4923i	0.860773	+	1.06770i
$985$	34.6648	−	11.2633i	1.10451	−	0.358877i
$986$	29.6650	−	17.7953i	0.944725	−	0.566718i
$987$	−21.7552	+	15.8061i	−0.692476	+	0.503113i
$988$	0.439772	+	0.904987i	0.0139910	+	0.0287915i
$989$		−	1.83707i		−	0.0584155i
$990$	32.3103	+	35.5793i	1.02689	+	1.13078i
$991$		−	42.4003i		−	1.34689i	−0.739237	−	0.673446i	$-0.764814\pi$
$991$		−	42.4003i		−	1.34689i	0.739237	−	0.673446i	$-0.235186\pi$
$992$	18.3302	+	17.2176i	0.581984	+	0.546658i
$993$	−9.75417	+	7.08682i	−0.309539	+	0.224893i
$994$	3.37698	+	5.62946i	0.107111	+	0.178556i
$995$	24.3341	−	7.90664i	0.771444	−	0.250657i
$996$	18.0382	+	9.62461i	0.571564	+	0.304967i
$997$	−2.61173	+	3.59473i	−0.0827142	+	0.113846i	−0.848369	−	0.529405i	$-0.822415\pi$
$997$	−2.61173	+	3.59473i	−0.0827142	+	0.113846i	0.765655	+	0.643252i	$0.222415\pi$
$998$	−42.5138	+	9.78270i	−1.34575	+	0.309666i
$999$	−18.8097	−	6.11165i	−0.595113	−	0.193364i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.2.g.a.35.2	yes	16
3.2	odd	2		396.2.r.a.343.3		16
4.3	odd	2	inner	44.2.g.a.35.1	✓	16
8.3	odd	2		704.2.u.c.255.4		16
8.5	even	2		704.2.u.c.255.1		16
11.2	odd	10		484.2.g.f.239.3		16
11.3	even	5		484.2.g.f.403.2		16
11.4	even	5		484.2.c.d.483.9		16
11.5	even	5		484.2.g.i.215.4		16
11.6	odd	10	inner	44.2.g.a.39.1	yes	16
11.7	odd	10		484.2.c.d.483.8		16
11.8	odd	10		484.2.g.j.403.3		16
11.9	even	5		484.2.g.j.239.2		16
11.10	odd	2		484.2.g.i.475.3		16
12.11	even	2		396.2.r.a.343.4		16
33.17	even	10		396.2.r.a.127.4		16
44.3	odd	10		484.2.g.f.403.3		16
44.7	even	10		484.2.c.d.483.10		16
44.15	odd	10		484.2.c.d.483.7		16
44.19	even	10		484.2.g.j.403.2		16
44.27	odd	10		484.2.g.i.215.3		16
44.31	odd	10		484.2.g.j.239.3		16
44.35	even	10		484.2.g.f.239.2		16
44.39	even	10	inner	44.2.g.a.39.2	yes	16
44.43	even	2		484.2.g.i.475.4		16
88.61	odd	10		704.2.u.c.127.4		16
88.83	even	10		704.2.u.c.127.1		16
132.83	odd	10		396.2.r.a.127.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.1	✓	16	4.3	odd	2	inner
44.2.g.a.35.2	yes	16	1.1	even	1	trivial
44.2.g.a.39.1	yes	16	11.6	odd	10	inner
44.2.g.a.39.2	yes	16	44.39	even	10	inner
396.2.r.a.127.3		16	132.83	odd	10
396.2.r.a.127.4		16	33.17	even	10
396.2.r.a.343.3		16	3.2	odd	2
396.2.r.a.343.4		16	12.11	even	2
484.2.c.d.483.7		16	44.15	odd	10
484.2.c.d.483.8		16	11.7	odd	10
484.2.c.d.483.9		16	11.4	even	5
484.2.c.d.483.10		16	44.7	even	10
484.2.g.f.239.2		16	44.35	even	10
484.2.g.f.239.3		16	11.2	odd	10
484.2.g.f.403.2		16	11.3	even	5
484.2.g.f.403.3		16	44.3	odd	10
484.2.g.i.215.3		16	44.27	odd	10
484.2.g.i.215.4		16	11.5	even	5
484.2.g.i.475.3		16	11.10	odd	2
484.2.g.i.475.4		16	44.43	even	2
484.2.g.j.239.2		16	11.9	even	5
484.2.g.j.239.3		16	44.31	odd	10
484.2.g.j.403.2		16	44.19	even	10
484.2.g.j.403.3		16	11.8	odd	10
704.2.u.c.127.1		16	88.83	even	10
704.2.u.c.127.4		16	88.61	odd	10
704.2.u.c.255.1		16	8.5	even	2
704.2.u.c.255.4		16	8.3	odd	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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	44.2.g.a.35.2

Level	$44$
Weight	$2$
Character	44.35
Analytic conductor	$0.351$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$