LMFDB - Embedded newform 483.2.r.a.412.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(34,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

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

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

chi := DirichletCharacter("483.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.r (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$32$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			412.14
Character	$\chi$	$=$	483.412
Dual form			483.2.r.a.34.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.795109 - 0.510986i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.459738 - 1.00669i) q^{4} +(-1.49456 - 0.438843i) q^{5} +(-0.859737 - 0.392629i) q^{6} +(-2.64381 + 0.101346i) q^{7} +(-0.417877 + 2.90640i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.795109 - 0.510986i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.459738 - 1.00669i) q^{4} +(-1.49456 - 0.438843i) q^{5} +(-0.859737 - 0.392629i) q^{6} +(-2.64381 + 0.101346i) q^{7} +(-0.417877 + 2.90640i) q^{8} +(0.959493 - 0.281733i) q^{9} +(0.964098 + 1.11263i) q^{10} +(-0.572532 - 0.890878i) q^{11} +(-0.598324 - 0.931011i) q^{12} +(-0.623842 + 0.540562i) q^{13} +(2.15390 + 1.27037i) q^{14} +(-1.54180 - 0.221678i) q^{15} +(0.367925 - 0.424608i) q^{16} +(-2.42411 + 5.30805i) q^{17} +(-0.906863 - 0.266279i) q^{18} +(0.166950 + 0.365570i) q^{19} +(0.245330 + 1.70631i) q^{20} +(-2.60248 + 0.476568i) q^{21} +1.00090i q^{22} +(-3.24202 + 3.53402i) q^{23} +2.93629i q^{24} +(-2.16514 - 1.39145i) q^{25} +(0.772242 - 0.111032i) q^{26} +(0.909632 - 0.415415i) q^{27} +(1.31748 + 2.61489i) q^{28} +(-0.929966 + 2.03634i) q^{29} +(1.11263 + 0.964098i) q^{30} +(6.11805 + 0.879642i) q^{31} +(5.12518 - 1.50489i) q^{32} +(-0.693490 - 0.800330i) q^{33} +(4.63977 - 2.98180i) q^{34} +(3.99581 + 1.00875i) q^{35} +(-0.724731 - 0.836384i) q^{36} +(-3.05924 - 10.4188i) q^{37} +(0.0540574 - 0.375978i) q^{38} +(-0.540562 + 0.623842i) q^{39} +(1.90000 - 4.16041i) q^{40} +(-3.48835 + 11.8802i) q^{41} +(2.31277 + 0.950904i) q^{42} +(-11.9776 + 1.72211i) q^{43} +(-0.633619 + 0.985930i) q^{44} -1.55766 q^{45} +(4.38360 - 1.15331i) q^{46} -4.76463i q^{47} +(0.303752 - 0.472647i) q^{48} +(6.97946 - 0.535881i) q^{49} +(1.01051 + 2.21271i) q^{50} +(-1.64402 + 5.59901i) q^{51} +(0.830979 + 0.379495i) q^{52} +(-4.79415 - 4.15415i) q^{53} +(-0.935528 - 0.134509i) q^{54} +(0.464730 + 1.58272i) q^{55} +(0.810235 - 7.72632i) q^{56} +(0.217277 + 0.338090i) q^{57} +(1.77997 - 1.14391i) q^{58} +(-4.32793 + 3.75017i) q^{59} +(0.485665 + 1.65402i) q^{60} +(1.11823 - 7.77749i) q^{61} +(-4.41503 - 3.82565i) q^{62} +(-2.50816 + 0.842088i) q^{63} +(-5.92222 - 1.73892i) q^{64} +(1.16959 - 0.534135i) q^{65} +(0.142443 + 0.990713i) q^{66} +(0.784651 - 1.22094i) q^{67} +6.45799 q^{68} +(-2.70608 + 3.95944i) q^{69} +(-2.66165 - 2.84387i) q^{70} +(8.54463 + 5.49130i) q^{71} +(0.417877 + 2.90640i) q^{72} +(-13.8221 + 6.31233i) q^{73} +(-2.89144 + 9.84734i) q^{74} +(-2.34112 - 1.06915i) q^{75} +(0.291261 - 0.336133i) q^{76} +(1.60395 + 2.29729i) q^{77} +(0.748580 - 0.219803i) q^{78} +(1.45453 - 1.26036i) q^{79} +(-0.736223 + 0.473142i) q^{80} +(0.841254 - 0.540641i) q^{81} +(8.84424 - 7.66358i) q^{82} +(-4.40875 + 1.29453i) q^{83} +(1.67621 + 2.40078i) q^{84} +(5.95238 - 6.86941i) q^{85} +(10.4035 + 4.75110i) q^{86} +(-0.630698 + 2.14796i) q^{87} +(2.82849 - 1.29173i) q^{88} +(-1.25773 - 8.74770i) q^{89} +(1.23851 + 0.795941i) q^{90} +(1.59453 - 1.49237i) q^{91} +(5.04812 + 1.63897i) q^{92} +6.18096 q^{93} +(-2.43466 + 3.78840i) q^{94} +(-0.0890897 - 0.619633i) q^{95} +(4.85885 - 2.21896i) q^{96} +(-4.81079 - 1.41258i) q^{97} +(-5.82326 - 3.14032i) q^{98} +(-0.800330 - 0.693490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	$ 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) $ 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.795109	−	0.510986i	−0.562227	−	0.361321i	0.228449	−	0.973556i	$-0.426635\pi$
$2$	−0.795109	−	0.510986i	−0.562227	−	0.361321i	−0.790676	+	0.612234i	$0.790271\pi$
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i
$3$	0.989821	−	0.142315i	0.571474	−	0.0821655i
$4$	−0.459738	−	1.00669i	−0.229869	−	0.503343i
$5$	−1.49456	−	0.438843i	−0.668388	−	0.196257i	−0.0701032	−	0.997540i	$-0.522333\pi$
$5$	−1.49456	−	0.438843i	−0.668388	−	0.196257i	−0.598285	+	0.801283i	$0.704151\pi$
$6$	−0.859737	−	0.392629i	−0.350986	−	0.160290i
$7$	−2.64381	+	0.101346i	−0.999266	+	0.0383053i
$7$	−2.64381	+	0.101346i	−0.999266	+	0.0383053i
$8$	−0.417877	+	2.90640i	−0.147742	+	1.02757i
$9$	0.959493	−	0.281733i	0.319831	−	0.0939109i
$10$	0.964098	+	1.11263i	0.304874	+	0.351844i
$11$	−0.572532	−	0.890878i	−0.172625	−	0.268610i	0.744151	−	0.668011i	$-0.232854\pi$
$11$	−0.572532	−	0.890878i	−0.172625	−	0.268610i	−0.916776	+	0.399402i	$0.869218\pi$
$12$	−0.598324	−	0.931011i	−0.172721	−	0.268760i
$13$	−0.623842	+	0.540562i	−0.173023	+	0.149925i	−0.737067	−	0.675819i	$-0.763790\pi$
$13$	−0.623842	+	0.540562i	−0.173023	+	0.149925i	0.564045	+	0.825744i	$0.309245\pi$
$14$	2.15390	+	1.27037i	0.575655	+	0.339520i
$15$	−1.54180	−	0.221678i	−0.398092	−	0.0572370i
$16$	0.367925	−	0.424608i	0.0919812	−	0.106152i
$17$	−2.42411	+	5.30805i	−0.587932	+	1.28739i	0.348752	+	0.937215i	$0.386606\pi$
$17$	−2.42411	+	5.30805i	−0.587932	+	1.28739i	−0.936684	+	0.350176i	$0.886122\pi$
$18$	−0.906863	−	0.266279i	−0.213750	−	0.0627626i
$19$	0.166950	+	0.365570i	0.0383011	+	0.0838676i	0.927815	−	0.373040i	$-0.121684\pi$
$19$	0.166950	+	0.365570i	0.0383011	+	0.0838676i	−0.889514	+	0.456907i	$0.848957\pi$
$20$	0.245330	+	1.70631i	0.0548574	+	0.381542i
$21$	−2.60248	+	0.476568i	−0.567907	+	0.103996i
$22$			1.00090i			0.213393i
$23$	−3.24202	+	3.53402i	−0.676008	+	0.736894i
$23$	−3.24202	+	3.53402i	−0.676008	+	0.736894i
$24$			2.93629i			0.599367i
$25$	−2.16514	−	1.39145i	−0.433027	−	0.278290i
$26$	0.772242	−	0.111032i	0.151449	−	0.0217751i
$27$	0.909632	−	0.415415i	0.175059	−	0.0799467i
$28$	1.31748	+	2.61489i	0.248981	+	0.494168i
$29$	−0.929966	+	2.03634i	−0.172690	+	0.378139i	−0.976111	−	0.217273i	$-0.930284\pi$
$29$	−0.929966	+	2.03634i	−0.172690	+	0.378139i	0.803421	+	0.595412i	$0.203011\pi$
$30$	1.11263	+	0.964098i	0.203137	+	0.176019i
$31$	6.11805	+	0.879642i	1.09883	+	0.157988i	0.667795	−	0.744345i	$-0.267238\pi$
$31$	6.11805	+	0.879642i	1.09883	+	0.157988i	0.431038	+	0.902334i	$0.358147\pi$
$32$	5.12518	−	1.50489i	0.906013	−	0.266029i
$33$	−0.693490	−	0.800330i	−0.120721	−	0.139320i
$34$	4.63977	−	2.98180i	0.795713	−	0.511374i
$35$	3.99581	+	1.00875i	0.675416	+	0.170510i
$36$	−0.724731	−	0.836384i	−0.120788	−	0.139397i
$37$	−3.05924	−	10.4188i	−0.502937	−	1.71284i	−0.684097	−	0.729391i	$-0.739804\pi$
$37$	−3.05924	−	10.4188i	−0.502937	−	1.71284i	0.181161	−	0.983454i	$-0.442015\pi$
$38$	0.0540574	−	0.375978i	0.00876928	−	0.0609917i
$39$	−0.540562	+	0.623842i	−0.0865592	+	0.0998946i
$40$	1.90000	−	4.16041i	0.300416	−	0.657819i
$41$	−3.48835	+	11.8802i	−0.544788	+	1.85538i	−0.0274059	+	0.999624i	$0.508725\pi$
$41$	−3.48835	+	11.8802i	−0.544788	+	1.85538i	−0.517382	+	0.855754i	$0.673094\pi$
$42$	2.31277	+	0.950904i	0.356869	+	0.146728i
$43$	−11.9776	+	1.72211i	−1.82656	+	0.262620i	−0.968155	−	0.250350i	$-0.919454\pi$
$43$	−11.9776	+	1.72211i	−1.82656	+	0.262620i	−0.858406	+	0.512970i	$0.828545\pi$
$44$	−0.633619	+	0.985930i	−0.0955216	+	0.148634i
$45$	−1.55766			−0.232202
$46$	4.38360	−	1.15331i	0.646326	−	0.170046i
$47$		−	4.76463i		−	0.694992i	−0.937681	−	0.347496i	$-0.887032\pi$
$47$		−	4.76463i		−	0.694992i	0.937681	−	0.347496i	$-0.112968\pi$
$48$	0.303752	−	0.472647i	0.0438428	−	0.0682208i
$49$	6.97946	−	0.535881i	0.997065	−	0.0765544i
$50$	1.01051	+	2.21271i	0.142908	+	0.312924i
$51$	−1.64402	+	5.59901i	−0.230208	+	0.784018i
$52$	0.830979	+	0.379495i	0.115236	+	0.0526265i
$53$	−4.79415	−	4.15415i	−0.658527	−	0.570617i	0.260179	−	0.965561i	$-0.416219\pi$
$53$	−4.79415	−	4.15415i	−0.658527	−	0.570617i	−0.918705	+	0.394944i	$0.870764\pi$
$54$	−0.935528	−	0.134509i	−0.127309	−	0.0183043i
$55$	0.464730	+	1.58272i	0.0626641	+	0.213414i
$56$	0.810235	−	7.72632i	0.108272	−	1.03247i
$57$	0.217277	+	0.338090i	0.0287791	+	0.0447811i
$58$	1.77997	−	1.14391i	0.233721	−	0.150203i
$59$	−4.32793	+	3.75017i	−0.563448	+	0.488231i	−0.889384	−	0.457161i	$-0.848866\pi$
$59$	−4.32793	+	3.75017i	−0.563448	+	0.488231i	0.325936	+	0.945392i	$0.394321\pi$
$60$	0.485665	+	1.65402i	0.0626991	+	0.213534i
$61$	1.11823	−	7.77749i	0.143175	−	0.995805i	−0.783888	−	0.620902i	$-0.786767\pi$
$61$	1.11823	−	7.77749i	0.143175	−	0.995805i	0.927064	−	0.374904i	$-0.122324\pi$
$62$	−4.41503	−	3.82565i	−0.560709	−	0.485857i
$63$	−2.50816	+	0.842088i	−0.315999	+	0.106093i
$64$	−5.92222	−	1.73892i	−0.740277	−	0.217365i
$65$	1.16959	−	0.534135i	0.145070	−	0.0662513i
$66$	0.142443	+	0.990713i	0.0175335	+	0.121948i
$67$	0.784651	−	1.22094i	0.0958603	−	0.149162i	−0.790011	−	0.613093i	$-0.789925\pi$
$67$	0.784651	−	1.22094i	0.0958603	−	0.149162i	0.885871	+	0.463931i	$0.153562\pi$
$68$	6.45799			0.783146
$69$	−2.70608	+	3.95944i	−0.325774	+	0.476660i
$70$	−2.66165	−	2.84387i	−0.318128	−	0.339907i
$71$	8.54463	+	5.49130i	1.01406	+	0.651697i	0.938441	−	0.345439i	$-0.112270\pi$
$71$	8.54463	+	5.49130i	1.01406	+	0.651697i	0.0756198	+	0.997137i	$0.475906\pi$
$72$	0.417877	+	2.90640i	0.0492473	+	0.342523i
$73$	−13.8221	+	6.31233i	−1.61775	+	0.738802i	−0.998908	−	0.0467134i	$-0.985125\pi$
$73$	−13.8221	+	6.31233i	−1.61775	+	0.738802i	−0.618842	+	0.785515i	$0.712398\pi$
$74$	−2.89144	+	9.84734i	−0.336123	+	1.14473i
$75$	−2.34112	−	1.06915i	−0.270329	−	0.123455i
$76$	0.291261	−	0.336133i	0.0334099	−	0.0385571i
$77$	1.60395	+	2.29729i	0.182787	+	0.261800i
$78$	0.748580	−	0.219803i	0.0847600	−	0.0248878i
$79$	1.45453	−	1.26036i	0.163647	−	0.141801i	−0.569188	−	0.822208i	$-0.692742\pi$
$79$	1.45453	−	1.26036i	0.163647	−	0.141801i	0.732835	+	0.680406i	$0.238197\pi$
$80$	−0.736223	+	0.473142i	−0.0823122	+	0.0528989i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	8.84424	−	7.66358i	0.976683	−	0.846301i
$83$	−4.40875	+	1.29453i	−0.483923	+	0.142093i	−0.514589	−	0.857437i	$-0.672055\pi$
$83$	−4.40875	+	1.29453i	−0.483923	+	0.142093i	0.0306656	+	0.999530i	$0.490237\pi$
$84$	1.67621	+	2.40078i	0.182890	+	0.261946i
$85$	5.95238	−	6.86941i	0.645626	−	0.745092i
$86$	10.4035	+	4.75110i	1.12183	+	0.512324i
$87$	−0.630698	+	2.14796i	−0.0676180	+	0.230286i
$88$	2.82849	−	1.29173i	0.301519	−	0.137699i
$89$	−1.25773	−	8.74770i	−0.133319	−	0.927254i	−0.941186	−	0.337889i	$-0.890287\pi$
$89$	−1.25773	−	8.74770i	−0.133319	−	0.927254i	0.807867	−	0.589365i	$-0.200622\pi$
$90$	1.23851	+	0.795941i	0.130550	+	0.0838996i
$91$	1.59453	−	1.49237i	0.167153	−	0.156443i
$92$	5.04812	+	1.63897i	0.526303	+	0.170875i
$93$	6.18096			0.640936
$94$	−2.43466	+	3.78840i	−0.251116	+	0.390744i
$95$	−0.0890897	−	0.619633i	−0.00914042	−	0.0635730i
$96$	4.85885	−	2.21896i	0.495904	−	0.226472i
$97$	−4.81079	−	1.41258i	−0.488462	−	0.143425i	0.0282218	−	0.999602i	$-0.491016\pi$
$97$	−4.81079	−	1.41258i	−0.488462	−	0.143425i	−0.516684	+	0.856176i	$0.672834\pi$
$98$	−5.82326	−	3.14032i	−0.588238	−	0.317220i
$99$	−0.800330	−	0.693490i	−0.0804362	−	0.0696984i
$100$	−0.405356	+	2.81931i	−0.0405356	+	0.281931i
$101$	−3.57035	−	12.1595i	−0.355263	−	1.20991i	−0.922382	−	0.386278i	$-0.873760\pi$
$101$	−3.57035	−	12.1595i	−0.355263	−	1.20991i	0.567119	−	0.823636i	$-0.308058\pi$
$102$	4.16819	−	3.61175i	0.412712	−	0.357617i
$103$	1.10932	−	0.712920i	0.109305	−	0.0702461i	−0.484846	−	0.874599i	$-0.661124\pi$
$103$	1.10932	−	0.712920i	0.109305	−	0.0702461i	0.594151	+	0.804353i	$0.297488\pi$
$104$	−1.31040	−	2.03902i	−0.128495	−	0.199943i
$105$	4.09870	+	0.429818i	0.399992	+	0.0419459i
$106$	1.68916	+	5.75274i	0.164066	+	0.558756i
$107$	−13.3226	−	1.91551i	−1.28795	−	0.185179i	−0.535897	−	0.844283i	$-0.680026\pi$
$107$	−13.3226	−	1.91551i	−1.28795	−	0.185179i	−0.752051	+	0.659104i	$0.770935\pi$
$108$	−0.836384	−	0.724731i	−0.0804811	−	0.0697373i
$109$	7.36542	+	3.36368i	0.705480	+	0.322182i	0.735649	−	0.677363i	$-0.236877\pi$
$109$	7.36542	+	3.36368i	0.705480	+	0.322182i	−0.0301692	+	0.999545i	$0.509605\pi$
$110$	0.439238	−	1.49591i	0.0418797	−	0.142629i
$111$	−4.51086	−	9.87740i	−0.428152	−	0.937522i
$112$	−0.929691	+	1.15987i	−0.0878475	+	0.109597i
$113$	3.83446	−	5.96654i	0.360716	−	0.561285i	−0.612704	−	0.790313i	$-0.709918\pi$
$113$	3.83446	−	5.96654i	0.360716	−	0.561285i	0.973420	+	0.229027i	$0.0735545\pi$
$114$		−	0.379844i		−	0.0355757i
$115$	6.39628	−	3.85907i	0.596456	−	0.359860i
$116$	2.47749			0.230030
$117$	−0.446278	+	0.694422i	−0.0412584	+	0.0641993i
$118$	5.35746	−	0.770286i	0.493194	−	0.0709106i
$119$	5.87092	−	14.2791i	0.538186	−	1.30897i
$120$	1.28857	−	4.38846i	0.117630	−	0.400610i
$121$	4.10370	−	8.98584i	0.373063	−	0.816894i
$122$	−4.86330	+	5.61255i	−0.440303	+	0.508137i
$123$	−1.76211	+	12.2557i	−0.158884	+	1.10506i
$124$	−1.92717	−	6.56335i	−0.173065	−	0.589406i
$125$	7.72555	+	8.91576i	0.690994	+	0.797450i
$126$	2.42456	+	0.612084i	0.215997	+	0.0545288i
$127$	15.1987	−	9.76761i	1.34867	−	0.866735i	0.351092	−	0.936341i	$-0.385811\pi$
$127$	15.1987	−	9.76761i	1.34867	−	0.866735i	0.997575	+	0.0696058i	$0.0221741\pi$
$128$	−3.17570	−	3.66496i	−0.280695	−	0.323939i
$129$	−11.6106	+	3.40917i	−1.02225	+	0.300161i
$130$	−1.20289	−	0.172949i	−0.105500	−	0.0151687i
$131$	−10.9999	−	9.53145i	−0.961064	−	0.832767i	0.0249060	−	0.999690i	$-0.492071\pi$
$131$	−10.9999	−	9.53145i	−0.961064	−	0.832767i	−0.985970	+	0.166923i	$0.946617\pi$
$132$	−0.486857	+	1.06607i	−0.0423754	+	0.0927893i
$133$	−0.478434	−	0.949579i	−0.0414855	−	0.0823389i
$134$	−1.24777	+	0.569836i	−0.107791	+	0.0492263i
$135$	−1.54180	+	0.221678i	−0.132697	+	0.0190790i
$136$	−14.4143	−	9.26353i	−1.23602	−	0.794341i
$137$		−	13.6523i		−	1.16639i	−0.812331	−	0.583196i	$-0.801802\pi$
$137$		−	13.6523i		−	1.16639i	0.812331	−	0.583196i	$-0.198198\pi$
$138$	4.17484	−	1.76542i	0.355386	−	0.150282i
$139$			9.52668i			0.808043i	0.914750	+	0.404021i	$0.132388\pi$
$139$			9.52668i			0.808043i	−0.914750	+	0.404021i	$0.867612\pi$
$140$	−0.821533	−	4.48628i	−0.0694322	−	0.379160i
$141$	−0.678077	−	4.71613i	−0.0571044	−	0.397170i
$142$	−3.98794	−	8.73237i	−0.334660	−	0.732804i
$143$	0.838744	+	0.246277i	0.0701393	+	0.0205948i
$144$	0.233396	−	0.511065i	0.0194496	−	0.0425887i
$145$	2.28352	−	2.63533i	0.189636	−	0.218852i
$146$	14.2156	+	2.04389i	1.17649	+	0.169153i
$147$	6.83215	−	1.52371i	0.563506	−	0.125673i
$148$	−9.08203	+	7.86962i	−0.746538	+	0.646879i
$149$	9.93721	+	15.4626i	0.814088	+	1.26675i	0.960710	+	0.277554i	$0.0895236\pi$
$149$	9.93721	+	15.4626i	0.814088	+	1.26675i	−0.146622	+	0.989193i	$0.546840\pi$
$150$	1.31512	+	2.04637i	0.107379	+	0.167086i
$151$	−4.25045	−	4.90528i	−0.345897	−	0.399186i	0.555969	−	0.831203i	$-0.312347\pi$
$151$	−4.25045	−	4.90528i	−0.345897	−	0.399186i	−0.901865	+	0.432017i	$0.857802\pi$
$152$	−1.13226	+	0.332461i	−0.0918383	+	0.0269662i
$153$	−0.830461	+	5.77599i	−0.0671388	+	0.466961i
$154$	−0.101438	−	2.64619i	−0.00817408	−	0.213236i
$155$	−8.75777	−	3.99954i	−0.703441	−	0.321251i
$156$	0.876529	+	0.257372i	0.0701785	+	0.0206063i
$157$	4.71456	+	10.3235i	0.376263	+	0.823901i	0.999135	+	0.0415777i	$0.0132384\pi$
$157$	4.71456	+	10.3235i	0.376263	+	0.823901i	−0.622872	+	0.782324i	$0.714034\pi$
$158$	−1.80053	+	0.258878i	−0.143243	+	0.0205952i
$159$	−5.33655	−	3.42959i	−0.423216	−	0.271984i
$160$	−8.32032			−0.657779
$161$	8.21313	−	9.67184i	0.647285	−	0.762248i
$162$	−0.945148			−0.0742579
$163$	9.93087	+	6.38218i	0.777846	+	0.499891i	0.868318	−	0.496008i	$-0.165201\pi$
$163$	9.93087	+	6.38218i	0.777846	+	0.499891i	−0.0904723	+	0.995899i	$0.528838\pi$
$164$	13.5634	−	1.95012i	1.05912	−	0.152279i
$165$	0.685244	+	1.50048i	0.0533462	+	0.116812i
$166$	4.16692	+	1.22352i	0.323416	+	0.0949635i
$167$	−1.56423	−	0.714359i	−0.121044	−	0.0552787i	0.353973	−	0.935256i	$-0.384831\pi$
$167$	−1.56423	−	0.714359i	−0.121044	−	0.0552787i	−0.475016	+	0.879977i	$0.657558\pi$
$168$	−0.297582	−	7.76298i	−0.0229590	−	0.598927i
$169$	−1.75312	+	12.1932i	−0.134856	+	0.937941i
$170$	−8.24296	+	2.42035i	−0.632206	+	0.185632i
$171$	0.263181	+	0.303727i	0.0201259	+	0.0232266i
$172$	7.24016	+	11.2659i	0.552057	+	0.859018i
$173$	0.0274912	+	0.0427771i	0.00209011	+	0.00325228i	0.842297	−	0.539014i	$-0.181203\pi$
$173$	0.0274912	+	0.0427771i	0.00209011	+	0.00325228i	−0.840207	+	0.542266i	$0.817567\pi$
$174$	1.59905	−	1.38559i	0.121224	−	0.105041i
$175$	5.86522	+	3.45929i	0.443369	+	0.261498i
$176$	−0.588923	−	0.0846743i	−0.0443917	−	0.00638257i
$177$	−3.75017	+	4.32793i	−0.281880	+	0.325307i
$178$	−3.46992	+	7.59806i	−0.260081	+	0.569499i
$179$	−12.1769	−	3.57546i	−0.910144	−	0.267242i	−0.207042	−	0.978332i	$-0.566384\pi$
$179$	−12.1769	−	3.57546i	−0.910144	−	0.267242i	−0.703101	+	0.711090i	$0.748202\pi$
$180$	0.716114	+	1.56807i	0.0533760	+	0.116877i
$181$	−1.74477	−	12.1351i	−0.129688	−	0.901997i	−0.945949	−	0.324314i	$-0.894866\pi$
$181$	−1.74477	−	12.1351i	−0.129688	−	0.901997i	0.816262	−	0.577682i	$-0.196043\pi$
$182$	−2.03041	+	0.371810i	−0.150504	+	0.0275604i
$183$		−	7.85747i		−	0.580841i
$184$	−8.91651	−	10.8994i	−0.657334	−	0.803514i
$185$			16.9141i			1.24355i
$186$	−4.91454	−	3.15838i	−0.360351	−	0.231584i
$187$	6.11670	−	0.879449i	0.447298	−	0.0643117i
$188$	−4.79648	+	2.19048i	−0.349819	+	0.159757i
$189$	−2.36279	+	1.19047i	−0.171868	+	0.0865937i
$190$	−0.245787	+	0.538199i	−0.0178313	+	0.0390451i
$191$	6.41247	+	5.55644i	0.463990	+	0.402050i	0.855238	−	0.518236i	$-0.173411\pi$
$191$	6.41247	+	5.55644i	0.463990	+	0.402050i	−0.391248	+	0.920285i	$0.627956\pi$
$192$	−6.10941	−	0.878401i	−0.440909	−	0.0633931i
$193$	−5.66336	+	1.66291i	−0.407657	+	0.119699i	−0.479131	−	0.877744i	$-0.659048\pi$
$193$	−5.66336	+	1.66291i	−0.407657	+	0.119699i	0.0714735	+	0.997442i	$0.477230\pi$
$194$	3.10330	+	3.58140i	0.222804	+	0.257129i
$195$	1.08167	−	0.695148i	0.0774601	−	0.0497806i
$196$	−3.74818	−	6.77975i	−0.267727	−	0.484268i
$197$	−0.684320	−	0.789748i	−0.0487558	−	0.0562672i	0.730848	−	0.682540i	$-0.239125\pi$
$197$	−0.684320	−	0.789748i	−0.0487558	−	0.0562672i	−0.779604	+	0.626273i	$0.784579\pi$
$198$	0.281986	+	0.960357i	0.0200399	+	0.0682496i
$199$	−3.13182	+	21.7823i	−0.222009	+	1.54410i	0.508417	+	0.861111i	$0.330231\pi$
$199$	−3.13182	+	21.7823i	−0.222009	+	1.54410i	−0.730426	+	0.682992i	$0.760678\pi$
$200$	4.94886	−	5.71129i	0.349938	−	0.403850i
$201$	0.602906	−	1.32018i	0.0425257	−	0.0931183i
$202$	−3.37451	+	11.4925i	−0.237430	+	0.808611i
$203$	2.25228	−	5.47795i	0.158079	−	0.384476i
$204$	6.39225	−	0.919067i	0.447547	−	0.0643476i
$205$	10.4271	−	16.2249i	0.728260	−	1.13320i
$206$	−1.24633			−0.0868357
$207$	−2.11505	+	4.30425i	−0.147006	+	0.299166i
$208$			0.463774i			0.0321570i
$209$	0.230094	−	0.358033i	0.0159159	−	0.0247657i
$210$	−3.03928	−	2.43613i	−0.209731	−	0.168109i
$211$	2.24439	+	4.91453i	0.154510	+	0.338330i	0.971019	−	0.239003i	$-0.0768206\pi$
$211$	2.24439	+	4.91453i	0.154510	+	0.338330i	−0.816509	+	0.577333i	$0.804093\pi$
$212$	−1.97787	+	6.73601i	−0.135841	+	0.462631i
$213$	9.23915	+	4.21938i	0.633056	+	0.289107i
$214$	9.61416	+	8.33072i	0.657210	+	0.569476i
$215$	18.6570	+	2.68246i	1.27239	+	0.182943i
$216$	0.827248	+	2.81735i	0.0562871	+	0.191696i
$217$	−16.2641	−	1.70556i	−1.10408	−	0.115781i
$218$	−4.13753	−	6.43812i	−0.280229	−	0.436044i
$219$	−12.7830	+	8.21516i	−0.863798	+	0.555129i
$220$	1.37965	−	1.19547i	0.0930160	−	0.0805988i
$221$	−1.35707	−	4.62176i	−0.0912865	−	0.310893i
$222$	−1.46059	+	10.1586i	−0.0980281	+	0.681800i
$223$	14.9294	+	12.9364i	0.999749	+	0.866287i	0.991025	−	0.133675i	$-0.0426777\pi$
$223$	14.9294	+	12.9364i	0.999749	+	0.866287i	0.00872368	+	0.999962i	$0.497223\pi$
$224$	−13.3975	+	4.49806i	−0.895158	+	0.300539i
$225$	−2.46945	−	0.725095i	−0.164630	−	0.0483397i
$226$	−6.09764	+	2.78470i	−0.405609	+	0.185235i
$227$	0.701231	+	4.87717i	0.0465423	+	0.323709i	0.999770	+	0.0214552i	$0.00682994\pi$
$227$	0.701231	+	4.87717i	0.0465423	+	0.323709i	−0.953227	+	0.302254i	$0.902261\pi$
$228$	0.240460	−	0.374162i	0.0159248	−	0.0247795i
$229$	−20.9952			−1.38740			−0.693702	−	0.720262i	$-0.744022\pi$
$229$	−20.9952			−1.38740			−0.693702	+	0.720262i	$0.744022\pi$
$230$	−7.05767	−	0.200023i	−0.465369	−	0.0131892i
$231$	1.91457	+	2.04564i	0.125969	+	0.134593i
$232$	−5.52981	−	3.55379i	−0.363050	−	0.233318i
$233$	1.19941	+	8.34209i	0.0785760	+	0.546508i	0.990644	+	0.136470i	$0.0435756\pi$
$233$	1.19941	+	8.34209i	0.0785760	+	0.546508i	−0.912068	+	0.410038i	$0.865515\pi$
$234$	0.709679	−	0.324100i	0.0463932	−	0.0211871i
$235$	−2.09092	+	7.12103i	−0.136397	+	0.464525i
$236$	5.76495	+	2.63277i	0.375266	+	0.171378i
$237$	1.26036	−	1.45453i	0.0818690	−	0.0944818i
$238$	−11.9645	+	8.35353i	−0.775541	+	0.541479i
$239$	−1.78705	+	0.524725i	−0.115595	+	0.0339416i	−0.339018	−	0.940780i	$-0.610095\pi$
$239$	−1.78705	+	0.524725i	−0.115595	+	0.0339416i	0.223424	+	0.974721i	$0.428277\pi$
$240$	−0.661394	+	0.573101i	−0.0426928	+	0.0369935i
$241$	7.83054	−	5.03239i	0.504410	−	0.324164i	−0.263568	−	0.964641i	$-0.584899\pi$
$241$	7.83054	−	5.03239i	0.504410	−	0.324164i	0.767978	+	0.640476i	$0.221263\pi$
$242$	−7.85452	+	5.04779i	−0.504908	+	0.324485i
$243$	0.755750	−	0.654861i	0.0484814	−	0.0420093i
$244$	−8.34358	+	2.44990i	−0.534143	+	0.156838i
$245$	−10.6664	−	2.26198i	−0.681451	−	0.144513i
$246$	7.66358	−	8.84424i	0.488612	−	0.563888i
$247$	−0.301764	−	0.137811i	−0.0192008	−	0.00876871i
$248$	−5.11318	+	17.4139i	−0.324688	+	1.10578i
$249$	−4.17965	+	1.90878i	−0.264874	+	0.120964i
$250$	−1.58683	−	11.0366i	−0.100360	−	0.698019i
$251$	3.83302	+	2.46333i	0.241938	+	0.155484i	0.655991	−	0.754769i	$-0.272251\pi$
$251$	3.83302	+	2.46333i	0.241938	+	0.155484i	−0.414053	+	0.910253i	$0.635887\pi$
$252$	2.00082	+	2.13779i	0.126040	+	0.134668i
$253$	5.00454	+	0.864904i	0.314633	+	0.0543760i
$254$	−17.0757			−1.07143
$255$	4.91417	−	7.64660i	0.307737	−	0.478849i
$256$	2.40909	+	16.7556i	0.150568	+	1.04723i
$257$	−3.46291	+	1.58146i	−0.216011	+	0.0986487i	−0.520482	−	0.853873i	$-0.674248\pi$
$257$	−3.46291	+	1.58146i	−0.216011	+	0.0986487i	0.304471	+	0.952522i	$0.401520\pi$
$258$	10.9737	+	3.22217i	0.683193	+	0.200604i
$259$	9.14397	+	27.2353i	0.568178	+	1.69232i
$260$	−1.07541	−	0.931849i	−0.0666942	−	0.0577908i
$261$	−0.318592	+	2.21586i	−0.0197203	+	0.137158i
$262$	3.87567	+	13.1993i	0.239440	+	0.815457i
$263$	−6.17816	+	5.35341i	−0.380962	+	0.330105i	−0.824200	−	0.566299i	$-0.808375\pi$
$263$	−6.17816	+	5.35341i	−0.380962	+	0.330105i	0.443238	+	0.896404i	$0.353829\pi$
$264$	2.61587	−	1.68112i	0.160996	−	0.103466i
$265$	5.34213	+	8.31251i	0.328164	+	0.510634i
$266$	−0.104814	+	0.999492i	−0.00642653	+	0.0612828i
$267$	−2.48986	−	8.47967i	−0.152377	−	0.518947i
$268$	−1.58984	−	0.228584i	−0.0971147	−	0.0139630i
$269$	−11.3787	−	9.85968i	−0.693770	−	0.601155i	0.234919	−	0.972015i	$-0.424518\pi$
$269$	−11.3787	−	9.85968i	−0.693770	−	0.601155i	−0.928689	+	0.370860i	$0.879063\pi$
$270$	1.33918	+	0.611581i	0.0814997	+	0.0372197i
$271$	−7.95208	+	27.0823i	−0.483055	+	1.64513i	0.252447	+	0.967611i	$0.418765\pi$
$271$	−7.95208	+	27.0823i	−0.483055	+	1.64513i	−0.735502	+	0.677523i	$0.763054\pi$
$272$	1.36195	+	2.98226i	0.0825805	+	0.180826i
$273$	1.36592	−	1.70410i	0.0826692	−	0.103137i
$274$	−6.97612	+	10.8551i	−0.421443	+	0.655778i
$275$			2.72552i			0.164355i
$276$	5.22999	+	0.903867i	0.314809	+	0.0544064i
$277$	−15.4698			−0.929493			−0.464746	−	0.885444i	$-0.653855\pi$
$277$	−15.4698			−0.929493			−0.464746	+	0.885444i	$0.653855\pi$
$278$	4.86800	−	7.57475i	0.291963	−	0.454303i
$279$	6.11805	−	0.879642i	0.366278	−	0.0526628i
$280$	−4.60159	+	11.1919i	−0.274997	+	0.668844i
$281$	−4.63731	+	15.7932i	−0.276639	+	0.942145i	0.697574	+	0.716513i	$0.254263\pi$
$281$	−4.63731	+	15.7932i	−0.276639	+	0.942145i	−0.974213	+	0.225632i	$0.927555\pi$
$282$	−1.87073	+	4.09633i	−0.111400	+	0.243933i
$283$	−7.64541	+	8.82328i	−0.454473	+	0.524489i	−0.936028	−	0.351926i	$-0.885527\pi$
$283$	−7.64541	+	8.82328i	−0.454473	+	0.524489i	0.481555	+	0.876416i	$0.340072\pi$
$284$	1.59972	−	11.1263i	0.0949260	−	0.660225i
$285$	−0.176366	−	0.600647i	−0.0104470	−	0.0355793i
$286$	−0.541049	−	0.624404i	−0.0319929	−	0.0369218i
$287$	8.01851	−	31.7626i	0.473318	−	1.87489i
$288$	4.49360	−	2.88786i	0.264788	−	0.170169i
$289$	−11.1665	−	12.8868i	−0.656852	−	0.758047i
$290$	−3.16227	+	0.928525i	−0.185695	+	0.0545249i
$291$	−4.96286	−	0.713551i	−0.290928	−	0.0418291i
$292$	12.7090	+	11.0125i	0.743741	+	0.644455i
$293$	5.61741	−	12.3004i	0.328173	−	0.718598i	−0.671578	−	0.740934i	$-0.734383\pi$
$293$	5.61741	−	12.3004i	0.328173	−	0.718598i	0.999751	+	0.0223360i	$0.00711036\pi$
$294$	−6.21090	−	2.27962i	−0.362227	−	0.132950i
$295$	8.11409	−	3.70558i	0.472421	−	0.215747i
$296$	31.5597	−	4.53759i	1.83437	−	0.263742i
$297$	−0.890878	−	0.572532i	−0.0516940	−	0.0332217i
$298$		−	17.3722i		−	1.00635i
$299$	0.112152	−	3.95718i	0.00648589	−	0.228850i
$300$			2.84830i			0.164447i
$301$	31.4919	−	5.76682i	1.81516	−	0.332394i
$302$	0.873043	+	6.07215i	0.0502380	+	0.349413i
$303$	−5.26448	−	11.5276i	−0.302437	−	0.662244i
$304$	0.216649	+	0.0636140i	0.0124257	+	0.00364851i
$305$	−5.08437	+	11.1332i	−0.291130	+	0.637486i
$306$	3.61175	−	4.16819i	0.206470	−	0.238279i
$307$	16.5839	+	2.38441i	0.946493	+	0.136085i	0.598242	−	0.801316i	$-0.295866\pi$
$307$	16.5839	+	2.38441i	0.946493	+	0.136085i	0.348252	+	0.937401i	$0.386775\pi$
$308$	1.57525	−	2.67083i	0.0897580	−	0.152184i
$309$	0.996574	−	0.863537i	0.0566931	−	0.0491249i
$310$	4.91968	+	7.65517i	0.279419	+	0.434784i
$311$	−5.11122	−	7.95322i	−0.289831	−	0.450985i	0.665554	−	0.746350i	$-0.268195\pi$
$311$	−5.11122	−	7.95322i	−0.289831	−	0.450985i	−0.955385	+	0.295364i	$0.904559\pi$
$312$	−1.58724	−	1.83178i	−0.0898601	−	0.103704i
$313$	−15.5101	+	4.55417i	−0.876682	+	0.257417i	−0.688955	−	0.724804i	$-0.741930\pi$
$313$	−15.5101	+	4.55417i	−0.876682	+	0.257417i	−0.187727	+	0.982221i	$0.560112\pi$
$314$	1.52654	−	10.6174i	0.0861479	−	0.599172i
$315$	4.11815	−	0.157863i	0.232032	−	0.00889457i
$316$	−1.93748	−	0.884819i	−0.108992	−	0.0497750i
$317$	6.01183	+	1.76523i	0.337658	+	0.0991453i	0.446166	−	0.894950i	$-0.352789\pi$
$317$	6.01183	+	1.76523i	0.337658	+	0.0991453i	−0.108508	+	0.994096i	$0.534607\pi$
$318$	2.49067	+	5.45380i	0.139670	+	0.305834i
$319$	2.34657	−	0.337385i	0.131382	−	0.0188899i
$320$	8.08801	+	5.19785i	0.452133	+	0.290568i
$321$	−13.4596			−0.751244
$322$	−11.4725	+	3.49338i	−0.639338	+	0.194679i
$323$	−2.34517			−0.130489
$324$	−0.931011	−	0.598324i	−0.0517228	−	0.0332402i
$325$	2.10287	−	0.302346i	0.116646	−	0.0167712i
$326$	−4.63492	−	10.1491i	−0.256705	−	0.562105i
$327$	7.76916	+	2.28123i	0.429635	+	0.126152i
$328$	−33.0710	−	15.1030i	−1.82604	−	0.833924i
$329$	0.482878	+	12.5968i	0.0266219	+	0.694482i
$330$	0.221878	−	1.54319i	0.0122140	−	0.0849499i
$331$	15.7091	−	4.61261i	0.863450	−	0.253532i	0.180123	−	0.983644i	$-0.442350\pi$
$331$	15.7091	−	4.61261i	0.863450	−	0.253532i	0.683327	+	0.730112i	$0.260532\pi$
$332$	3.33005	+	3.84308i	0.182760	+	0.210917i
$333$	−5.87065	−	9.13490i	−0.321709	−	0.500590i
$334$	0.878705	+	1.36729i	0.0480806	+	0.0748149i
$335$	−1.70851	+	1.48043i	−0.0933459	+	0.0808847i
$336$	−0.755161	+	1.28037i	−0.0411974	+	0.0698501i
$337$	−16.1093	−	2.31616i	−0.877527	−	0.126169i	−0.311195	−	0.950346i	$-0.600729\pi$
$337$	−16.1093	−	2.31616i	−0.877527	−	0.126169i	−0.566332	+	0.824177i	$0.691638\pi$
$338$	7.62449	−	8.79913i	0.414718	−	0.478610i
$339$	2.94631	−	6.45151i	0.160021	−	0.350398i
$340$	−9.65186	−	2.83404i	−0.523446	−	0.153698i
$341$	−2.71913	−	5.95405i	−0.147249	−	0.322430i
$342$	−0.0540574	−	0.375978i	−0.00292309	−	0.0203306i
$343$	−18.3980	+	2.12411i	−0.993401	+	0.114691i
$344$		−	35.5312i		−	1.91572i
$345$	5.78197	−	4.73008i	0.311291	−	0.254659i
$346$		−	0.0480600i		−	0.00258372i
$347$	24.0503	+	15.4562i	1.29109	+	0.829732i	0.992212	−	0.124560i	$-0.0397520\pi$
$347$	24.0503	+	15.4562i	1.29109	+	0.829732i	0.298876	+	0.954292i	$0.403388\pi$
$348$	2.45228	−	0.352584i	0.131456	−	0.0189005i
$349$	−13.4413	+	6.13842i	−0.719495	+	0.328582i	−0.741294	−	0.671180i	$-0.765788\pi$
$349$	−13.4413	+	6.13842i	−0.719495	+	0.328582i	0.0217995	+	0.999762i	$0.493060\pi$
$350$	−2.89584	−	5.74756i	−0.154789	−	0.307220i
$351$	−0.342909	+	0.750866i	−0.0183031	+	0.0400782i
$352$	−4.27501	−	3.70431i	−0.227859	−	0.197441i
$353$	−0.367098	−	0.0527808i	−0.0195387	−	0.00280924i	0.132539	−	0.991178i	$-0.457687\pi$
$353$	−0.367098	−	0.0527808i	−0.0195387	−	0.00280924i	−0.152077	+	0.988369i	$0.548596\pi$
$354$	5.19330	−	1.52489i	0.276021	−	0.0810471i
$355$	−10.3607	−	11.9568i	−0.549887	−	0.634603i
$356$	−8.22795	+	5.28778i	−0.436081	+	0.280252i
$357$	3.77903	−	14.9693i	0.200007	−	0.792261i
$358$	7.85495	+	9.06510i	0.415147	+	0.479105i
$359$	−3.14912	−	10.7249i	−0.166204	−	0.566040i	−0.999904	−	0.0138224i	$-0.995600\pi$
$359$	−3.14912	−	10.7249i	−0.166204	−	0.566040i	0.833700	−	0.552217i	$-0.186218\pi$
$360$	0.650910	−	4.52718i	0.0343060	−	0.238603i
$361$	12.3366	−	14.2372i	0.649294	−	0.749325i
$362$	−4.81359	+	10.5403i	−0.252997	+	0.553986i
$363$	2.78311	−	9.47839i	0.146075	−	0.497487i
$364$	−2.23541	−	0.919097i	−0.117167	−	0.0481738i
$365$	23.4281	−	3.36845i	1.22628	−	0.176313i
$366$	−4.01505	+	6.24755i	−0.209870	+	0.326564i
$367$	−22.5722			−1.17826			−0.589129	−	0.808039i	$-0.700529\pi$
$367$	−22.5722			−1.17826			−0.589129	+	0.808039i	$0.700529\pi$
$368$	0.307753	+	2.67684i	0.0160427	+	0.139540i
$369$			12.3818i			0.644569i
$370$	8.64287	−	13.4486i	0.449321	−	0.699158i
$371$	13.0958	+	10.4969i	0.679901	+	0.544973i
$372$	−2.84162	−	6.22228i	−0.147331	−	0.322610i
$373$	4.36112	−	14.8526i	0.225810	−	0.769039i	−0.766169	−	0.642639i	$-0.777840\pi$
$373$	4.36112	−	14.8526i	0.225810	−	0.769039i	0.991979	−	0.126400i	$-0.0403422\pi$
$374$	−5.31283	−	2.42629i	−0.274720	−	0.125460i
$375$	8.91576	+	7.72555i	0.460408	+	0.398946i
$376$	13.8479	+	1.99103i	0.714152	+	0.102680i
$377$	−0.520617	−	1.77306i	−0.0268131	−	0.0913171i
$378$	2.48699	+	0.260803i	0.127917	+	0.0134142i
$379$	17.5830	+	27.3597i	0.903178	+	1.40537i	0.914125	+	0.405432i	$0.132879\pi$
$379$	17.5830	+	27.3597i	0.903178	+	1.40537i	−0.0109469	+	0.999940i	$0.503485\pi$
$380$	−0.582817	+	0.374554i	−0.0298979	+	0.0192142i
$381$	13.6539	−	11.8312i	0.699512	−	0.606130i
$382$	−2.25936	−	7.69466i	−0.115599	−	0.393693i
$383$	−4.03447	+	28.0604i	−0.206152	+	1.43382i	0.579410	+	0.815036i	$0.303283\pi$
$383$	−4.03447	+	28.0604i	−0.206152	+	1.43382i	−0.785562	+	0.618783i	$0.787626\pi$
$384$	−3.66496	−	3.17570i	−0.187027	−	0.162059i
$385$	−1.38906	−	4.13732i	−0.0707930	−	0.210857i
$386$	5.35271	+	1.57170i	0.272446	+	0.0799973i
$387$	−11.0072	+	5.02683i	−0.559528	+	0.255528i
$388$	0.789683	+	5.49237i	0.0400901	+	0.278833i
$389$	18.0526	−	28.0904i	0.915304	−	1.42424i	0.00977633	−	0.999952i	$-0.496888\pi$
$389$	18.0526	−	28.0904i	0.915304	−	1.42424i	0.905527	−	0.424288i	$-0.139476\pi$
$390$	−1.21526			−0.0615370
$391$	−10.8998	−	25.7757i	−0.551224	−	1.30353i
$392$	−1.35907	+	20.5090i	−0.0686435	+	1.03586i
$393$	−12.2444	−	7.86899i	−0.617647	−	0.396938i
$394$	0.140560	+	0.977614i	0.00708129	+	0.0492515i
$395$	−2.72698	+	1.24537i	−0.137209	+	0.0626614i
$396$	−0.330184	+	1.12450i	−0.0165924	+	0.0565084i
$397$	8.58878	+	3.92236i	0.431059	+	0.196858i	0.619115	−	0.785300i	$-0.287491\pi$
$397$	8.58878	+	3.92236i	0.431059	+	0.196858i	−0.188056	+	0.982158i	$0.560219\pi$
$398$	13.6206	−	15.7190i	0.682737	−	0.787920i
$399$	−0.608704	−	0.871825i	−0.0304733	−	0.0436459i
$400$	−1.38743	+	0.407385i	−0.0693714	+	0.0203693i
$401$	−9.16429	+	7.94090i	−0.457643	+	0.396550i	−0.852944	−	0.522002i	$-0.825185\pi$
$401$	−9.16429	+	7.94090i	−0.457643	+	0.396550i	0.395302	+	0.918551i	$0.370640\pi$
$402$	−1.15397	+	0.741611i	−0.0575548	+	0.0369882i
$403$	−4.29219	+	2.75843i	−0.213809	+	0.137407i
$404$	−10.5993	+	9.18439i	−0.527337	+	0.456940i
$405$	−1.49456	+	0.438843i	−0.0742654	+	0.0218063i
$406$	−4.58996	+	3.20468i	−0.227796	+	0.159046i
$407$	−7.53038	+	8.69053i	−0.373267	+	0.430773i
$408$	−15.5860	−	7.11787i	−0.771620	−	0.352387i
$409$	10.3051	−	35.0961i	0.509557	−	1.73539i	−0.154772	−	0.987950i	$-0.549464\pi$
$409$	10.3051	−	35.0961i	0.509557	−	1.73539i	0.664329	−	0.747440i	$-0.268717\pi$
$410$	−16.5814	+	7.57246i	−0.818896	+	0.373977i
$411$	−1.94292	−	13.5133i	−0.0958373	−	0.666563i
$412$	−1.22768	−	0.788985i	−0.0604837	−	0.0388705i
$413$	11.0622	−	10.3534i	0.544333	−	0.509455i
$414$	3.88110	−	2.34159i	0.190746	−	0.115083i
$415$	7.15725			0.351335
$416$	−2.38382	+	3.70929i	−0.116876	+	0.181863i
$417$	1.35579	+	9.42971i	0.0663932	+	0.461775i
$418$	−0.365900	+	0.167101i	−0.0178967	+	0.00817317i
$419$	−12.8407	−	3.77037i	−0.627308	−	0.184194i	−0.0474000	−	0.998876i	$-0.515094\pi$
$419$	−12.8407	−	3.77037i	−0.627308	−	0.184194i	−0.579909	+	0.814682i	$0.696912\pi$
$420$	−1.45164	−	4.32370i	−0.0708326	−	0.210975i
$421$	−12.7382	−	11.0377i	−0.620821	−	0.537945i	0.286662	−	0.958032i	$-0.407454\pi$
$421$	−12.7382	−	11.0377i	−0.620821	−	0.537945i	−0.907484	+	0.420087i	$0.862000\pi$
$422$	0.726719	−	5.05444i	0.0353761	−	0.246046i
$423$	−1.34235	−	4.57163i	−0.0652673	−	0.222280i
$424$	14.0770	−	12.1978i	0.683639	−	0.592377i
$425$	12.6344	−	8.11963i	0.612858	−	0.393860i
$426$	−5.19009	−	8.07594i	−0.251461	−	0.391281i
$427$	−2.16818	+	20.6755i	−0.104925	+	1.00056i
$428$	4.19661	+	14.2923i	0.202851	+	0.690846i
$429$	0.865256	+	0.124405i	0.0417749	+	0.00600633i
$430$	−13.4636	−	11.6663i	−0.649273	−	0.562598i
$431$	14.0725	+	6.42668i	0.677847	+	0.309562i	0.724426	−	0.689352i	$-0.242105\pi$
$431$	14.0725	+	6.42668i	0.677847	+	0.309562i	−0.0465795	+	0.998915i	$0.514832\pi$
$432$	0.158288	−	0.539079i	0.00761562	−	0.0259364i
$433$	2.32761	+	5.09675i	0.111858	+	0.244934i	0.957279	−	0.289166i	$-0.0933779\pi$
$433$	2.32761	+	5.09675i	0.111858	+	0.244934i	−0.845421	+	0.534100i	$0.820651\pi$
$434$	12.0602	+	9.66683i	0.578909	+	0.464023i
$435$	1.88524	−	2.93348i	0.0903901	−	0.140650i
$436$		−	8.96107i		−	0.429157i
$437$	−1.83319	−	0.595181i	−0.0876934	−	0.0284714i
$438$	14.3617			0.686231
$439$	9.11088	−	14.1768i	0.434839	−	0.676622i	−0.552810	−	0.833307i	$-0.686444\pi$
$439$	9.11088	−	14.1768i	0.434839	−	0.676622i	0.987649	+	0.156685i	$0.0500808\pi$
$440$	−4.79423	+	0.689306i	−0.228556	+	0.0328614i
$441$	6.54577	−	2.48051i	0.311703	−	0.118120i
$442$	−1.28263	+	4.36825i	−0.0610087	+	0.207776i
$443$	−7.40727	+	16.2197i	−0.351930	+	0.770619i	0.648030	+	0.761615i	$0.275593\pi$
$443$	−7.40727	+	16.2197i	−0.351930	+	0.770619i	−0.999959	+	0.00900374i	$0.997134\pi$
$444$	−7.86962	+	9.08203i	−0.373476	+	0.431014i
$445$	−1.95911	+	13.6259i	−0.0928708	+	0.645931i
$446$	−5.26020	−	17.9146i	−0.249078	−	0.848281i
$447$	12.0366	+	13.8910i	0.569313	+	0.657022i
$448$	15.8334	+	3.99718i	0.748060	+	0.188849i
$449$	0.197321	−	0.126811i	0.00931216	−	0.00598456i	−0.535976	−	0.844233i	$-0.680056\pi$
$449$	0.197321	−	0.126811i	0.00931216	−	0.00598456i	0.545289	+	0.838248i	$0.316420\pi$
$450$	1.59297	+	1.83838i	0.0750932	+	0.0866622i
$451$	12.5810	−	3.69412i	0.592417	−	0.173949i
$452$	−7.76928	−	1.11705i	−0.365436	−	0.0525418i
$453$	−4.90528	−	4.25045i	−0.230470	−	0.199703i
$454$	1.93461	−	4.23620i	0.0907957	−	0.198815i
$455$	−3.03805	+	1.53068i	−0.142426	+	0.0717596i
$456$	−1.07342	+	0.490214i	−0.0502675	+	0.0229564i
$457$	12.0197	−	1.72818i	0.562260	−	0.0808408i	0.144676	−	0.989479i	$-0.453786\pi$
$457$	12.0197	−	1.72818i	0.562260	−	0.0808408i	0.417584	+	0.908638i	$0.362877\pi$
$458$	16.6935	+	10.7283i	0.780037	+	0.501299i
$459$			5.83538i			0.272372i
$460$	−6.82548	−	4.66488i	−0.318240	−	0.217501i
$461$		−	38.0249i		−	1.77100i	−0.464642	−	0.885499i	$-0.653817\pi$
$461$		−	38.0249i		−	1.77100i	0.464642	−	0.885499i	$-0.346183\pi$
$462$	−0.476997	−	2.60482i	−0.0221919	−	0.121187i
$463$	3.10829	+	21.6186i	0.144455	+	1.00470i	0.925098	+	0.379727i	$0.123982\pi$
$463$	3.10829	+	21.6186i	0.144455	+	1.00470i	−0.780644	+	0.624976i	$0.785109\pi$
$464$	0.522489	+	1.14409i	0.0242559	+	0.0531131i
$465$	−9.23783	−	2.71247i	−0.428394	−	0.125788i
$466$	3.30902	−	7.24575i	0.153288	−	0.335653i
$467$	1.81684	−	2.09675i	0.0840733	−	0.0970258i	−0.712154	−	0.702023i	$-0.752280\pi$
$467$	1.81684	−	2.09675i	0.0840733	−	0.0970258i	0.796228	+	0.604997i	$0.206826\pi$
$468$	0.904235	+	0.130009i	0.0417983	+	0.00600968i
$469$	−1.95073	+	3.30746i	−0.0900763	+	0.152724i
$470$	5.30126	−	4.59357i	0.244529	−	0.211885i
$471$	6.13576	+	9.54742i	0.282721	+	0.439922i
$472$	−9.09095	−	14.1458i	−0.418445	−	0.651113i
$473$	8.39174	+	9.68458i	0.385852	+	0.445297i
$474$	−1.74536	+	0.512485i	−0.0801673	+	0.0235392i
$475$	0.147202	−	1.02381i	0.00675409	−	0.0469757i
$476$	−17.0737	+	0.654494i	−0.782571	+	0.0299987i
$477$	−5.77031	−	2.63521i	−0.264204	−	0.120658i
$478$	1.68903	+	0.495943i	0.0772542	+	0.0226839i
$479$	15.6147	+	34.1915i	0.713456	+	1.56225i	0.822854	+	0.568253i	$0.192380\pi$
$479$	15.6147	+	34.1915i	0.713456	+	1.56225i	−0.109398	+	0.993998i	$0.534892\pi$
$480$	−8.23563	+	1.18410i	−0.375903	+	0.0540467i
$481$	7.54050	+	4.84599i	0.343817	+	0.220958i
$482$	−8.79762			−0.400720
$483$	6.75308	−	10.7422i	0.307276	−	0.488789i
$484$	−10.9325			−0.496933
$485$	6.57013	+	4.22236i	0.298334	+	0.191728i
$486$	−0.935528	+	0.134509i	−0.0424364	+	0.00610143i
$487$	7.65392	+	16.7598i	0.346832	+	0.759457i	0.999997	+	0.00224146i	$0.000713479\pi$
$487$	7.65392	+	16.7598i	0.346832	+	0.759457i	−0.653165	+	0.757216i	$0.726559\pi$
$488$	22.1372	+	6.50007i	1.00210	+	0.294244i
$489$	10.7381	+	4.90391i	0.485592	+	0.221763i
$490$	7.32511	+	7.24890i	0.330915	+	0.327472i
$491$	−2.53481	+	17.6300i	−0.114394	+	0.795631i	0.849163	+	0.528130i	$0.177107\pi$
$491$	−2.53481	+	17.6300i	−0.114394	+	0.795631i	−0.963558	+	0.267500i	$0.913802\pi$
$492$	13.1478	−	3.86054i	0.592748	−	0.174046i
$493$	−8.55466	−	9.87261i	−0.385283	−	0.444640i
$494$	0.169516	+	0.263772i	0.00762688	+	0.0118677i
$495$	0.891810	+	1.38768i	0.0400839	+	0.0623717i
$496$	2.62448	−	2.27413i	0.117843	−	0.102111i
$497$	−23.1469	−	13.6520i	−1.03828	−	0.612375i
$498$	4.29864	+	0.618051i	0.192627	+	0.0276955i
$499$	26.8542	−	30.9914i	1.20216	−	1.38737i	0.301145	−	0.953578i	$-0.402631\pi$
$499$	26.8542	−	30.9914i	1.20216	−	1.38737i	0.901015	−	0.433788i	$-0.142823\pi$
$500$	5.42363	−	11.8761i	0.242552	−	0.531115i
$501$	−1.64997	−	0.484475i	−0.0737152	−	0.0216447i
$502$	−1.78894	−	3.91724i	−0.0798444	−	0.174835i
$503$	−2.28783	−	15.9122i	−0.102009	−	0.709491i	−0.975073	−	0.221885i	$-0.928779\pi$
$503$	−2.28783	−	15.9122i	−0.102009	−	0.709491i	0.873063	−	0.487607i	$-0.162130\pi$
$504$	−1.39934	−	7.64162i	−0.0623316	−	0.340385i
$505$			19.7399i			0.878415i
$506$	−3.53720	−	3.24494i	−0.157248	−	0.144255i
$507$			12.3186i			0.547089i
$508$	−16.8203	−	10.8098i	−0.746281	−	0.479606i
$509$	−23.1757	+	3.33217i	−1.02725	+	0.147696i	−0.635278	−	0.772283i	$-0.719115\pi$
$509$	−23.1757	+	3.33217i	−1.02725	+	0.147696i	−0.391967	+	0.919979i	$0.628205\pi$
$510$	−7.81461	+	3.56881i	−0.346037	+	0.158030i
$511$	35.9032	−	18.0894i	1.58826	−	0.800228i
$512$	2.61733	−	5.73115i	0.115671	−	0.253283i
$513$	0.303727	+	0.263181i	0.0134099	+	0.0116197i
$514$	3.56150	+	0.512066i	0.157091	+	0.0225863i
$515$	−1.97081	+	0.578683i	−0.0868445	+	0.0254998i
$516$	8.76978	+	10.1209i	0.386068	+	0.445546i
$517$	−4.24470	+	2.72790i	−0.186682	+	0.119973i
$518$	6.64642	−	26.3275i	0.292027	−	1.15676i
$519$	0.0332991	+	0.0384293i	0.00146167	+	0.00168686i
$520$	1.06366	+	3.62250i	0.0466447	+	0.158857i
$521$	0.844130	−	5.87105i	0.0369820	−	0.257216i	−0.962940	−	0.269716i	$-0.913070\pi$
$521$	0.844130	−	5.87105i	0.0369820	−	0.257216i	0.999922	+	0.0125007i	$0.00397920\pi$
$522$	1.38559	−	1.59905i	0.0606455	−	0.0699886i
$523$	−17.4852	+	38.2872i	−0.764573	+	1.67418i	−0.0263233	+	0.999653i	$0.508380\pi$
$523$	−17.4852	+	38.2872i	−0.764573	+	1.67418i	−0.738250	+	0.674528i	$0.764347\pi$
$524$	−4.53811	+	15.4554i	−0.198248	+	0.675171i
$525$	6.29783	+	2.58938i	0.274860	+	0.113010i
$526$	7.64783	−	1.09959i	0.333461	−	0.0479445i
$527$	−19.5000	+	30.3426i	−0.849432	+	1.32174i
$528$	−0.594979			−0.0258931
$529$	−1.97859	−	22.9147i	−0.0860258	−	0.996293i
$530$		−	9.33911i		−	0.405665i
$531$	−3.09607	+	4.81758i	−0.134358	+	0.209065i
$532$	−0.735973	+	0.918190i	−0.0319085	+	0.0398086i
$533$	−4.24582	−	9.29704i	−0.183907	−	0.402700i
$534$	−2.35328	+	8.01454i	−0.101836	+	0.346823i
$535$	19.0709	+	8.70939i	0.824507	+	0.376540i
$536$	3.22065	+	2.79071i	0.139111	+	0.120540i
$537$	−12.5618	−	1.80611i	−0.542081	−	0.0779395i
$538$	4.00914	+	13.6539i	0.172846	+	0.588660i
$539$	−4.47337	−	5.91103i	−0.192682	−	0.254606i
$540$	0.931985	+	1.45020i	0.0401062	+	0.0624065i
$541$	10.3918	−	6.67843i	0.446780	−	0.287128i	−0.297841	−	0.954615i	$-0.596267\pi$
$541$	10.3918	−	6.67843i	0.446780	−	0.287128i	0.744621	+	0.667487i	$0.232630\pi$
$542$	20.1615	−	17.4700i	0.866009	−	0.750401i
$543$	−3.45402	−	11.7633i	−0.148226	−	0.504812i
$544$	−4.43596	+	30.8527i	−0.190190	+	1.32280i
$545$	−9.53196	−	8.25949i	−0.408304	−	0.353798i
$546$	−1.95683	+	0.656983i	−0.0837445	+	0.0281163i
$547$	−29.7768	−	8.74325i	−1.27316	−	0.373834i	−0.425785	−	0.904824i	$-0.640002\pi$
$547$	−29.7768	−	8.74325i	−1.27316	−	0.373834i	−0.847378	+	0.530990i	$0.821820\pi$
$548$	−13.7435	+	6.27647i	−0.587095	+	0.268117i
$549$	−1.11823	−	7.77749i	−0.0477251	−	0.331935i
$550$	1.39270	−	2.16709i	0.0593850	−	0.0924049i
$551$	−0.899684			−0.0383278
$552$	−10.3769	−	9.51951i	−0.441670	−	0.405177i
$553$	−3.71777	+	3.47955i	−0.158095	+	0.147966i
$554$	12.3002	+	7.90487i	0.522586	+	0.335846i
$555$	2.40713	+	16.7419i	0.102177	+	0.710656i
$556$	9.59037	−	4.37977i	0.406722	−	0.185744i
$557$	1.32302	−	4.50578i	0.0560580	−	0.190916i	−0.926704	−	0.375793i	$-0.877370\pi$
$557$	1.32302	−	4.50578i	0.0560580	−	0.190916i	0.982762	+	0.184877i	$0.0591886\pi$
$558$	−5.31400	−	2.42682i	−0.224960	−	0.102736i
$559$	6.54120	−	7.54894i	0.276663	−	0.319286i
$560$	1.89848	−	1.32551i	0.0802255	−	0.0560130i
$561$	5.92928	−	1.74099i	0.250335	−	0.0735049i
$562$	11.7573	−	10.1877i	0.495951	−	0.429744i
$563$	16.8589	−	10.8345i	0.710517	−	0.456621i	−0.134810	−	0.990872i	$-0.543042\pi$
$563$	16.8589	−	10.8345i	0.710517	−	0.456621i	0.845326	+	0.534250i	$0.179406\pi$
$564$	−4.43592	+	2.85079i	−0.186786	+	0.120040i
$565$	−8.34922	+	7.23464i	−0.351254	+	0.304364i
$566$	10.5875	−	3.10877i	0.445026	−	0.130671i
$567$	−2.16932	+	1.51461i	−0.0911030	+	0.0636076i
$568$	−19.5305	+	22.5394i	−0.819482	+	0.945733i
$569$	−32.2668	−	14.7357i	−1.35269	−	0.617755i	−0.398562	−	0.917141i	$-0.630491\pi$
$569$	−32.2668	−	14.7357i	−1.35269	−	0.617755i	−0.954132	+	0.299387i	$0.903218\pi$
$570$	−0.166692	+	0.567700i	−0.00698196	+	0.0237784i
$571$	7.45264	−	3.40351i	0.311883	−	0.142432i	−0.253323	−	0.967382i	$-0.581524\pi$
$571$	7.45264	−	3.40351i	0.311883	−	0.142432i	0.565207	+	0.824949i	$0.308796\pi$
$572$	−0.137678	−	0.957574i	−0.00575662	−	0.0400382i
$573$	7.13797	+	4.58729i	0.298193	+	0.191637i
$574$	−22.6058	+	21.1574i	−0.943548	+	0.883092i
$575$	11.9368	−	3.14053i	0.497800	−	0.130969i
$576$	−6.17224			−0.257176
$577$	12.1400	−	18.8901i	0.505393	−	0.786407i	−0.491009	−	0.871154i	$-0.663372\pi$
$577$	12.1400	−	18.8901i	0.505393	−	0.786407i	0.996402	+	0.0847473i	$0.0270083\pi$
$578$	2.29360	+	15.9523i	0.0954011	+	0.663529i
$579$	−5.36905	+	2.45196i	−0.223130	+	0.101900i
$580$	−3.70277	−	1.08723i	−0.153749	−	0.0451448i
$581$	11.5247	−	3.86929i	0.478125	−	0.160525i
$582$	3.58140	+	3.10330i	0.148454	+	0.128636i
$583$	−0.956037	+	6.64938i	−0.0395950	+	0.275389i
$584$	−12.5702	−	42.8102i	−0.520159	−	1.77150i
$585$	0.971732	−	0.842011i	0.0401762	−	0.0348129i
$586$	−10.7518	+	6.90976i	−0.444153	+	0.285440i
$587$	−4.18832	−	6.51716i	−0.172871	−	0.268992i	0.743997	−	0.668183i	$-0.232928\pi$
$587$	−4.18832	−	6.51716i	−0.172871	−	0.268992i	−0.916868	+	0.399191i	$0.869291\pi$
$588$	−4.67489	−	6.17732i	−0.192789	−	0.254748i
$589$	0.699839	+	2.38343i	0.0288364	+	0.0982077i
$590$	−8.34509	−	1.19984i	−0.343562	−	0.0493967i
$591$	−0.789748	−	0.684320i	−0.0324859	−	0.0281492i
$592$	−5.54949	−	2.53437i	−0.228083	−	0.104162i
$593$	−10.0833	+	34.3406i	−0.414072	+	1.41020i	0.443702	+	0.896174i	$0.353665\pi$
$593$	−10.0833	+	34.3406i	−0.414072	+	1.41020i	−0.857774	+	0.514026i	$0.828153\pi$
$594$	0.415789	+	0.910452i	0.0170600	+	0.0373563i
$595$	−15.0408	+	18.7647i	−0.616611	+	0.769276i
$596$	10.9975	−	17.1124i	0.450474	−	0.700951i
$597$			22.0063i			0.900656i
$598$	−2.11124	+	3.08908i	−0.0863349	+	0.126322i
$599$	−13.8023			−0.563948			−0.281974	−	0.959422i	$-0.590989\pi$
$599$	−13.8023			−0.563948			−0.281974	+	0.959422i	$0.590989\pi$
$600$	4.08569	−	6.35746i	0.166798	−	0.259542i
$601$	20.2026	−	2.90469i	0.824079	−	0.118485i	0.282642	−	0.959226i	$-0.408789\pi$
$601$	20.2026	−	2.90469i	0.824079	−	0.118485i	0.541438	+	0.840741i	$0.317880\pi$
$602$	−27.9862	−	11.5066i	−1.14063	−	0.468976i
$603$	0.408888	−	1.39255i	0.0166512	−	0.0567088i
$604$	−2.98398	+	6.53400i	−0.121416	+	0.265865i
$605$	−10.0766	+	11.6290i	−0.409672	+	0.472787i
$606$	−1.70460	+	11.8558i	−0.0692448	+	0.481608i
$607$	−2.30162	−	7.83861i	−0.0934200	−	0.318159i	0.899504	−	0.436913i	$-0.143928\pi$
$607$	−2.30162	−	7.83861i	−0.0934200	−	0.318159i	−0.992924	+	0.118754i	$0.962110\pi$
$608$	1.40580	+	1.62237i	0.0570125	+	0.0657960i
$609$	1.44976	−	5.74272i	0.0587472	−	0.232707i
$610$	9.73154	−	6.25408i	0.394019	−	0.253220i
$611$	2.57558	+	2.97237i	0.104197	+	0.120249i
$612$	6.19639	−	1.81943i	0.250474	−	0.0735459i
$613$	8.07931	+	1.16163i	0.326320	+	0.0469178i	0.303528	−	0.952822i	$-0.401835\pi$
$613$	8.07931	+	1.16163i	0.326320	+	0.0469178i	0.0227921	+	0.999740i	$0.492744\pi$
$614$	−11.9676	−	10.3700i	−0.482974	−	0.418499i
$615$	8.01193	−	17.5437i	0.323072	−	0.707429i
$616$	−7.34709	+	3.70175i	−0.296023	+	0.149148i
$617$	6.69526	−	3.05762i	0.269541	−	0.123095i	−0.276060	−	0.961140i	$-0.589029\pi$
$617$	6.69526	−	3.05762i	0.269541	−	0.123095i	0.545601	+	0.838045i	$0.316302\pi$
$618$	−1.23364	+	0.177371i	−0.0496243	+	0.00713490i
$619$	9.08408	+	5.83799i	0.365120	+	0.234648i	0.710317	−	0.703882i	$-0.248552\pi$
$619$	9.08408	+	5.83799i	0.365120	+	0.234648i	−0.345197	+	0.938530i	$0.612188\pi$
$620$			10.6551i			0.427917i
$621$	−1.48096	+	4.56144i	−0.0594289	+	0.183044i
$622$			8.93544i			0.358278i
$623$	4.21175	+	22.9998i	0.168740	+	0.921467i
$624$	0.0660020	+	0.459054i	0.00264219	+	0.0183769i
$625$	−2.28792	−	5.00985i	−0.0915168	−	0.200394i
$626$	14.6593	+	4.30437i	0.585905	+	0.172037i
$627$	0.176799	−	0.387135i	0.00706065	−	0.0154607i
$628$	8.22501	−	9.49216i	0.328213	−	0.378778i
$629$	62.7196	+	9.01771i	2.50079	+	0.359560i
$630$	−3.35505	−	1.97880i	−0.133668	−	0.0788372i
$631$	−5.78062	+	5.00893i	−0.230123	+	0.199403i	−0.762288	−	0.647238i	$-0.775924\pi$
$631$	−5.78062	+	5.00893i	−0.230123	+	0.199403i	0.532165	+	0.846641i	$0.321379\pi$
$632$	3.05529	+	4.75412i	0.121533	+	0.189109i
$633$	2.92096	+	4.54510i	0.116098	+	0.180651i
$634$	−3.87805	−	4.47551i	−0.154017	−	0.177745i
$635$	−27.0018	+	7.92846i	−1.07154	+	0.314631i
$636$	−0.999106	+	6.94893i	−0.0396171	+	0.275543i
$637$	−4.06440	+	4.10713i	−0.161037	+	0.162731i
$638$	−2.03818	−	0.930803i	−0.0806921	−	0.0368509i
$639$	9.74559	+	2.86156i	0.385530	+	0.113202i
$640$	3.13794	+	6.87114i	0.124038	+	0.271606i
$641$	−7.65897	+	1.10119i	−0.302511	+	0.0434946i	−0.291899	−	0.956449i	$-0.594287\pi$
$641$	−7.65897	+	1.10119i	−0.302511	+	0.0434946i	−0.0106122	+	0.999944i	$0.503378\pi$
$642$	10.7019	+	6.87768i	0.422370	+	0.271441i
$643$	20.4973			0.808336			0.404168	−	0.914685i	$-0.367561\pi$
$643$	20.4973			0.808336			0.404168	+	0.914685i	$0.367561\pi$
$644$	−13.5124	−	3.82152i	−0.532462	−	0.150589i
$645$	18.8488			0.742171
$646$	1.86467	+	1.19835i	0.0733644	+	0.0471484i
$647$	10.9825	−	1.57904i	0.431765	−	0.0620784i	0.0769937	−	0.997032i	$-0.475468\pi$
$647$	10.9825	−	1.57904i	0.431765	−	0.0620784i	0.354771	+	0.934953i	$0.384559\pi$
$648$	1.21978	+	2.67094i	0.0479174	+	0.104924i
$649$	5.81882	+	1.70856i	0.228409	+	0.0670669i
$650$	−1.82650	−	0.834136i	−0.0716413	−	0.0327175i
$651$	−16.3413	+	0.626418i	−0.640465	+	0.0245512i
$652$	1.85925	−	12.9314i	0.0728140	−	0.506432i
$653$	−3.94998	+	1.15982i	−0.154575	+	0.0453873i	−0.358104	−	0.933682i	$-0.616577\pi$
$653$	−3.94998	+	1.15982i	−0.154575	+	0.0453873i	0.203530	+	0.979069i	$0.434759\pi$
$654$	−5.01165	−	5.78376i	−0.195971	−	0.226163i
$655$	12.2572	+	19.0726i	0.478928	+	0.745227i
$656$	3.76099	+	5.85221i	0.146842	+	0.228490i
$657$	−11.4838	+	9.95076i	−0.448025	+	0.388216i
$658$	6.05283	−	10.2626i	0.235964	−	0.400076i
$659$	−43.3481	−	6.23251i	−1.68860	−	0.242784i	−0.770021	−	0.638019i	$-0.779754\pi$
$659$	−43.3481	−	6.23251i	−1.68860	−	0.242784i	−0.918580	+	0.395235i	$0.870663\pi$
$660$	1.19547	−	1.37965i	0.0465338	−	0.0537028i
$661$	5.83023	−	12.7664i	0.226770	−	0.496556i	−0.761709	−	0.647920i	$-0.775639\pi$
$661$	5.83023	−	12.7664i	0.226770	−	0.496556i	0.988478	+	0.151364i	$0.0483665\pi$
$662$	−14.8474	−	4.35960i	−0.577062	−	0.169441i
$663$	−2.00100	−	4.38159i	−0.0777126	−	0.170167i
$664$	−1.92009	−	13.3546i	−0.0745141	−	0.518257i
$665$	0.298334	+	1.62916i	0.0115689	+	0.0631762i
$666$			10.2631i			0.397686i
$667$	−4.18150	−	9.88838i	−0.161908	−	0.382879i
$668$			1.90310i			0.0736332i
$669$	16.6185	+	10.6801i	0.642509	+	0.412916i
$670$	2.11493	−	0.304081i	0.0817070	−	0.0117477i
$671$	−7.56902	+	3.45665i	−0.292199	+	0.133443i
$672$	−12.6210	+	6.35894i	−0.486865	+	0.245301i
$673$	14.1249	−	30.9292i	0.544475	−	1.19223i	−0.414839	−	0.909895i	$-0.636162\pi$
$673$	14.1249	−	30.9292i	0.544475	−	1.19223i	0.959314	−	0.282340i	$-0.0911106\pi$
$674$	11.6251	+	10.0732i	0.447782	+	0.388005i
$675$	−2.54750	−	0.366276i	−0.0980535	−	0.0140980i
$676$	13.0807	−	3.84084i	0.503104	−	0.147725i
$677$	−21.4608	−	24.7670i	−0.824804	−	0.951875i	0.174659	−	0.984629i	$-0.444118\pi$
$677$	−21.4608	−	24.7670i	−0.824804	−	0.951875i	−0.999463	+	0.0327540i	$0.989572\pi$
$678$	−5.63927	+	3.62414i	−0.216575	+	0.139184i
$679$	12.8620	+	3.24703i	0.493597	+	0.124609i
$680$	17.4779	+	20.1706i	0.670246	+	0.773506i
$681$	1.38819	+	4.72773i	0.0531954	+	0.181167i
$682$	−0.880435	+	6.12356i	−0.0337136	+	0.234483i
$683$	14.5853	−	16.8324i	0.558092	−	0.644072i	−0.404658	−	0.914468i	$-0.632609\pi$
$683$	14.5853	−	16.8324i	0.558092	−	0.644072i	0.962749	+	0.270396i	$0.0871547\pi$
$684$	0.184763	−	0.404575i	0.00706460	−	0.0154693i
$685$	−5.99121	+	20.4042i	−0.228912	+	0.779603i
$686$	15.7138	+	7.71224i	0.599958	+	0.294455i
$687$	−20.7815	+	2.98793i	−0.792865	+	0.113997i
$688$	−3.67562	+	5.71938i	−0.140132	+	0.218049i
$689$	5.23636			0.199490
$690$	−7.01430	+	0.806424i	−0.267030	+	0.0307000i
$691$		−	5.63236i		−	0.214265i	−0.994245	−	0.107132i	$-0.965833\pi$
$691$		−	5.63236i		−	0.214265i	0.994245	−	0.107132i	$-0.0341669\pi$
$692$	0.0304243	−	0.0473412i	0.00115656	−	0.00179964i
$693$	2.18620	+	1.75234i	0.0830470	+	0.0665661i
$694$	−11.2247	−	24.5787i	−0.426085	−	0.932996i
$695$	4.18072	−	14.2382i	0.158584	−	0.540086i
$696$	−5.97928	−	2.73065i	−0.226644	−	0.103505i
$697$	−54.6047	−	47.3152i	−2.06830	−	1.79219i
$698$	13.8239	+	1.98758i	0.523243	+	0.0752310i
$699$	2.37441	+	8.08648i	0.0898083	+	0.305859i
$700$	0.785956	−	7.49480i	0.0297064	−	0.283277i
$701$	−5.36738	−	8.35180i	−0.202723	−	0.315443i	0.724975	−	0.688776i	$-0.241851\pi$
$701$	−5.36738	−	8.35180i	−0.202723	−	0.315443i	−0.927698	+	0.373332i	$0.878215\pi$
$702$	0.656332	−	0.421799i	0.0247716	−	0.0159198i
$703$	3.29807	−	2.85780i	0.124389	−	0.107784i
$704$	1.84150	+	6.27156i	0.0694040	+	0.236368i
$705$	−1.05621	+	7.34612i	−0.0397793	+	0.276671i
$706$	0.264913	+	0.229548i	0.00997013	+	0.00863917i
$707$	10.6716	+	31.7855i	0.401348	+	1.19542i
$708$	6.08095	+	1.78553i	0.228536	+	0.0671043i
$709$	−23.8029	+	10.8704i	−0.893938	+	0.408248i	−0.808774	−	0.588119i	$-0.799869\pi$
$709$	−23.8029	+	10.8704i	−0.893938	+	0.408248i	−0.0851639	+	0.996367i	$0.527141\pi$
$710$	2.12808	+	14.8011i	0.0798655	+	0.555477i
$711$	1.04053	−	1.61909i	0.0390228	−	0.0607207i
$712$	25.9499			0.972513
$713$	−22.9435	+	18.7695i	−0.859241	+	0.702922i
$714$	−10.6539	+	9.97122i	−0.398710	+	0.373164i
$715$	−1.14548	−	0.736154i	−0.0428384	−	0.0275306i
$716$	1.99882	+	13.9021i	0.0746993	+	0.519545i
$717$	−1.69418	+	0.773707i	−0.0632704	+	0.0288946i
$718$	−2.97639	+	10.1366i	−0.111078	+	0.378296i
$719$	−13.1777	−	6.01803i	−0.491443	−	0.224435i	0.154249	−	0.988032i	$-0.450704\pi$
$719$	−13.1777	−	6.01803i	−0.491443	−	0.224435i	−0.645693	+	0.763597i	$0.723431\pi$
$720$	−0.573101	+	0.661394i	−0.0213582	+	0.0246487i
$721$	−2.86059	+	1.99725i	−0.106534	+	0.0743815i
$722$	−17.0839	+	5.01629i	−0.635798	+	0.186687i
$723$	7.03466	−	6.09557i	0.261622	−	0.226697i
$724$	−11.4141	+	7.33540i	−0.424202	+	0.272618i
$725$	4.84696	−	3.11495i	0.180012	−	0.115686i
$726$	−7.05620	+	6.11423i	−0.261880	+	0.226920i
$727$	−14.2623	+	4.18779i	−0.528960	+	0.155317i	−0.535298	−	0.844663i	$-0.679801\pi$
$727$	−14.2623	+	4.18779i	−0.528960	+	0.155317i	0.00633825	+	0.999980i	$0.497982\pi$
$728$	3.67110	+	5.25798i	0.136060	+	0.194874i
$729$	0.654861	−	0.755750i	0.0242541	−	0.0279907i
$730$	−20.3491	−	9.29312i	−0.753154	−	0.343954i
$731$	19.8938	−	67.7521i	0.735799	−	2.50590i
$732$	−7.90999	+	3.61237i	−0.292362	+	0.133517i
$733$	−0.472756	−	3.28809i	−0.0174617	−	0.121448i	0.979226	−	0.202771i	$-0.0649947\pi$
$733$	−0.472756	−	3.28809i	−0.0174617	−	0.121448i	−0.996688	+	0.0813225i	$0.974086\pi$
$734$	17.9473	+	11.5341i	0.662449	+	0.425730i
$735$	−10.8797	−	0.720968i	−0.401305	−	0.0265933i
$736$	−11.2976	+	22.9914i	−0.416437	+	0.847474i
$737$	−1.53695			−0.0566141
$738$	6.32691	−	9.84486i	0.232897	−	0.362394i
$739$	−1.08578	−	7.55180i	−0.0399412	−	0.277797i	0.960057	−	0.279805i	$-0.0902699\pi$
$739$	−1.08578	−	7.55180i	−0.0399412	−	0.277797i	−0.999998	+	0.00200802i	$0.999361\pi$
$740$	17.0272	−	7.77605i	0.625932	−	0.285853i
$741$	−0.318305	−	0.0934628i	−0.0116932	−	0.00343344i
$742$	−5.04883	−	15.0380i	−0.185348	−	0.552061i
$743$	−12.0410	−	10.4336i	−0.441742	−	0.382771i	0.405399	−	0.914140i	$-0.367133\pi$
$743$	−12.0410	−	10.4336i	−0.441742	−	0.382771i	−0.847141	+	0.531368i	$0.821678\pi$
$744$	−2.58288	+	17.9643i	−0.0946931	+	0.658605i
$745$	−8.06613	−	27.4707i	−0.295520	−	1.00645i
$746$	−11.0570	+	9.58097i	−0.404827	+	0.350784i
$747$	−3.86546	+	2.48418i	−0.141430	+	0.0908913i
$748$	−3.69741	−	5.75328i	−0.135191	−	0.210361i
$749$	35.4167	+	3.71403i	1.29410	+	0.135708i
$750$	−3.14136	−	10.6985i	−0.114706	−	0.390653i
$751$	5.83277	+	0.838625i	0.212841	+	0.0306019i	0.247910	−	0.968783i	$-0.420256\pi$
$751$	5.83277	+	0.838625i	0.212841	+	0.0306019i	−0.0350695	+	0.999385i	$0.511165\pi$
$752$	−2.02310	−	1.75303i	−0.0737749	−	0.0639263i
$753$	4.14457	+	1.89276i	0.151037	+	0.0689761i
$754$	−0.492060	+	1.67580i	−0.0179198	+	0.0610291i
$755$	4.19991	+	9.19652i	0.152850	+	0.334696i
$756$	2.28469	+	1.83129i	0.0830933	+	0.0666032i
$757$	−4.03001	+	6.27082i	−0.146473	+	0.227917i	−0.906736	−	0.421699i	$-0.861434\pi$
$757$	−4.03001	+	6.27082i	−0.146473	+	0.227917i	0.760263	+	0.649616i	$0.225070\pi$
$758$		−	30.7386i		−	1.11648i
$759$	5.07669	+	0.143880i	0.184272	+	0.00522251i
$760$	1.83813			0.0666760
$761$	−20.8232	+	32.4015i	−0.754840	+	1.17455i	0.224920	+	0.974377i	$0.427788\pi$
$761$	−20.8232	+	32.4015i	−0.754840	+	1.17455i	−0.979760	+	0.200177i	$0.935848\pi$
$762$	−16.9019	+	2.43013i	−0.612292	+	0.0880343i
$763$	−19.8137	−	8.14646i	−0.717303	−	0.294922i
$764$	2.64553	−	9.00984i	0.0957119	−	0.325965i
$765$	3.77593	−	8.26813i	0.136519	−	0.298935i
$766$	17.5463	−	20.2495i	0.633974	−	0.731645i
$767$	0.672742	−	4.67903i	0.0242913	−	0.168950i
$768$	4.76914	+	16.2422i	0.172092	+	0.586090i
$769$	29.0494	+	33.5248i	1.04755	+	1.20893i	0.977400	+	0.211397i	$0.0678013\pi$
$769$	29.0494	+	33.5248i	1.04755	+	1.20893i	0.0701469	+	0.997537i	$0.477653\pi$
$770$	−1.00966	+	3.99941i	−0.0363855	+	0.144129i
$771$	−3.20260	+	2.05819i	−0.115339	+	0.0741238i
$772$	4.27769	+	4.93671i	0.153957	+	0.177676i
$773$	−17.2700	+	5.07092i	−0.621157	+	0.182388i	−0.577144	−	0.816643i	$-0.695833\pi$
$773$	−17.2700	+	5.07092i	−0.621157	+	0.182388i	−0.0440136	+	0.999031i	$0.514014\pi$
$774$	11.3206	+	1.62765i	0.406910	+	0.0585048i
$775$	−12.0224	−	10.4175i	−0.431858	−	0.374207i
$776$	6.11583	−	13.3918i	0.219546	−	0.480738i
$777$	12.9269	+	25.6568i	0.463750	+	0.920433i
$778$	−28.7076	+	13.1103i	−1.02922	+	0.470028i
$779$	−4.92544	+	0.708171i	−0.176472	+	0.0253729i
$780$	−1.19708	−	0.769317i	−0.0428624	−	0.0275460i
$781$		−	10.7562i		−	0.384886i
$782$	−4.50449	+	26.0641i	−0.161080	+	0.932050i
$783$			2.23864i			0.0800025i
$784$	2.34038	−	3.16070i	0.0835849	−	0.112882i
$785$	−2.51583	−	17.4980i	−0.0897939	−	0.624530i
$786$	5.71468	+	12.5134i	0.203836	+	0.446339i
$787$	19.3268	+	5.67485i	0.688925	+	0.202287i	0.607414	−	0.794386i	$-0.292207\pi$
$787$	19.3268	+	5.67485i	0.688925	+	0.202287i	0.0815114	+	0.996672i	$0.474025\pi$
$788$	−0.480419	+	1.05197i	−0.0171142	+	0.0374749i
$789$	−5.35341	+	6.17816i	−0.190586	+	0.219948i
$790$	2.80462	+	0.403243i	0.0997838	+	0.0143467i
$791$	−9.53291	+	16.1630i	−0.338951	+	0.574691i
$792$	2.35000	−	2.03629i	0.0835036	−	0.0723562i
$793$	3.50661	+	5.45640i	0.124523	+	0.193762i
$794$	−4.82475	−	7.50745i	−0.171224	−	0.266430i
$795$	6.47075	+	7.46764i	0.229494	+	0.264850i
$796$	23.3677	−	6.86137i	0.828246	−	0.243195i
$797$	−5.74409	+	39.9510i	−0.203466	+	1.41514i	0.590432	+	0.807087i	$0.298957\pi$
$797$	−5.74409	+	39.9510i	−0.203466	+	1.41514i	−0.793898	+	0.608051i	$0.791952\pi$
$798$	0.0384958	+	1.00424i	0.00136274	+	0.0355495i
$799$	25.2909	+	11.5500i	0.894727	+	0.408608i
$800$	−13.1907	−	3.87314i	−0.466361	−	0.136936i
$801$	−3.67129	−	8.03901i	−0.129719	−	0.284045i
$802$	11.3443	−	1.63106i	0.400581	−	0.0575949i
$803$	13.5371	+	8.69976i	0.477714	+	0.307008i
$804$	−1.60618			−0.0566458
$805$	−16.5194	+	10.8509i	−0.582234	+	0.382444i
$806$	4.82228			0.169858
$807$	−12.6660	−	8.13997i	−0.445866	−	0.286540i
$808$	36.8323	−	5.29568i	1.29576	−	0.186302i
$809$	9.77842	+	21.4117i	0.343791	+	0.752797i	0.999998	−	0.00178359i	$-0.000567734\pi$
$809$	9.77842	+	21.4117i	0.343791	+	0.752797i	−0.656208	+	0.754580i	$0.727840\pi$
$810$	1.41258	+	0.414772i	0.0496331	+	0.0145736i
$811$	−14.9403	−	6.82299i	−0.524623	−	0.239587i	0.135456	−	0.990783i	$-0.456750\pi$
$811$	−14.9403	−	6.82299i	−0.524623	−	0.239587i	−0.660079	+	0.751196i	$0.729477\pi$
$812$	−6.55002	+	0.251085i	−0.229861	+	0.00881136i
$813$	−4.01693	+	27.9384i	−0.140880	+	0.979841i
$814$	10.4282	−	3.06200i	0.365509	−	0.107323i
$815$	−12.0415	−	13.8967i	−0.421796	−	0.486779i
$816$	1.77251	+	2.75808i	0.0620502	+	0.0965520i
$817$	−2.62921	−	4.09114i	−0.0919846	−	0.143131i
$818$	−26.1273	+	22.6395i	−0.913520	+	0.791570i
$819$	1.10950	−	1.88115i	0.0387689	−	0.0657326i
$820$	−21.1271	−	3.03762i	−0.737790	−	0.106078i
$821$	−30.7568	+	35.4952i	−1.07342	+	1.23879i	−0.103691	+	0.994610i	$0.533065\pi$
$821$	−30.7568	+	35.4952i	−1.07342	+	1.23879i	−0.969729	+	0.244183i	$0.921480\pi$
$822$	−5.36028	+	11.7374i	−0.186961	+	0.409388i
$823$	−17.2260	−	5.05801i	−0.600460	−	0.176311i	−0.0326449	−	0.999467i	$-0.510393\pi$
$823$	−17.2260	−	5.05801i	−0.600460	−	0.176311i	−0.567815	+	0.823156i	$0.692211\pi$
$824$	1.60847	+	3.52205i	0.0560337	+	0.122697i
$825$	0.387882	+	2.69778i	0.0135043	+	0.0939246i
$826$	−14.0860	+	2.57945i	−0.490116	+	0.0897505i
$827$			19.6790i			0.684306i	0.939644	+	0.342153i	$0.111156\pi$
$827$			19.6790i			0.684306i	−0.939644	+	0.342153i	$0.888844\pi$
$828$	5.30539	+	0.150362i	0.184375	+	0.00522542i
$829$		−	27.0191i		−	0.938411i	−0.883089	−	0.469205i	$-0.844540\pi$
$829$		−	27.0191i		−	0.938411i	0.883089	−	0.469205i	$-0.155460\pi$
$830$	−5.69079	−	3.65725i	−0.197530	−	0.126945i
$831$	−15.3124	+	2.20159i	−0.531181	+	0.0763723i
$832$	4.63452	−	2.11651i	0.160673	−	0.0733769i
$833$	−14.0745	+	38.3463i	−0.487651	+	1.32862i
$834$	3.74045	−	8.19044i	0.129521	−	0.283612i
$835$	2.02434	+	1.75410i	0.0700553	+	0.0607033i
$836$	−0.466210	−	0.0670308i	−0.0161242	−	0.00231831i
$837$	5.93059	−	1.74138i	0.204991	−	0.0601908i
$838$	8.28314	+	9.55926i	0.286136	+	0.330219i
$839$	37.9825	−	24.4099i	1.31130	−	0.842722i	0.316906	−	0.948457i	$-0.397356\pi$
$839$	37.9825	−	24.4099i	1.31130	−	0.842722i	0.994394	+	0.105735i	$0.0337196\pi$
$840$	−2.96198	+	11.7329i	−0.102198	+	0.404822i
$841$	15.7091	+	18.1293i	0.541694	+	0.625148i
$842$	4.48814	+	15.2852i	0.154672	+	0.526763i
$843$	−2.34250	+	16.2924i	−0.0806799	+	0.561141i
$844$	3.91555	−	4.51879i	0.134779	−	0.155543i
$845$	7.97106	−	17.4542i	0.274213	−	0.600442i
$846$	−1.26872	+	4.32087i	−0.0436195	+	0.148554i
$847$	−9.93871	+	24.1727i	−0.341498	+	0.830585i
$848$	−3.52777	+	0.507217i	−0.121144	+	0.0174179i
$849$	−6.31191	+	9.82153i	−0.216624	+	0.337074i
$850$	−14.1947			−0.486875
$851$	46.7385	+	22.9666i	1.60217	+	0.787286i
$852$		−	11.2407i		−	0.385101i
$853$	18.2104	−	28.3359i	0.623512	−	0.970204i	−0.375545	−	0.926804i	$-0.622545\pi$
$853$	18.2104	−	28.3359i	0.623512	−	0.970204i	0.999058	−	0.0434003i	$-0.0138191\pi$
$854$	12.2888	−	15.3314i	0.420515	−	0.524630i
$855$	−0.260052	−	0.569434i	−0.00889358	−	0.0194742i
$856$	11.1345	−	37.9205i	0.380568	−	1.29610i
$857$	−20.3056	−	9.27328i	−0.693627	−	0.316769i	0.0372227	−	0.999307i	$-0.488149\pi$
$857$	−20.3056	−	9.27328i	−0.693627	−	0.316769i	−0.730850	+	0.682538i	$0.760876\pi$
$858$	−0.624404	−	0.541049i	−0.0213168	−	0.0184711i
$859$	−15.4983	−	2.22832i	−0.528796	−	0.0760295i	−0.127255	−	0.991870i	$-0.540617\pi$
$859$	−15.4983	−	2.22832i	−0.528796	−	0.0760295i	−0.401542	+	0.915841i	$0.631526\pi$
$860$	−5.87691	−	20.0149i	−0.200401	−	0.682503i
$861$	3.41661	−	32.5804i	0.116438	−	1.11034i
$862$	−7.90521	−	12.3007i	−0.269252	−	0.418965i
$863$	−9.74666	+	6.26379i	−0.331780	+	0.213222i	−0.695915	−	0.718124i	$-0.745001\pi$
$863$	−9.74666	+	6.26379i	−0.331780	+	0.213222i	0.364135	+	0.931346i	$0.381365\pi$
$864$	4.03688	−	3.49797i	0.137337	−	0.119004i
$865$	−0.0223148	−	0.0759973i	−0.000758727	−	0.00258399i
$866$	0.753664	−	5.24185i	0.0256105	−	0.178125i
$867$	−12.8868	−	11.1665i	−0.437659	−	0.379234i
$868$	5.76025	+	17.1569i	0.195516	+	0.582344i
$869$	−1.95559	−	0.574213i	−0.0663388	−	0.0194788i
$870$	−2.99794	+	1.36911i	−0.101640	+	0.0464172i
$871$	0.170496	+	1.18583i	0.00577704	+	0.0401802i
$872$	−12.8540	+	20.0013i	−0.435292	+	0.677328i
$873$	−5.01389			−0.169694
$874$	1.15346	+	1.40997i	0.0390163	+	0.0476929i
$875$	−21.3285	−	22.7886i	−0.721033	−	0.770396i
$876$	14.1469	+	9.09168i	0.477980	+	0.307179i
$877$	−6.90731	−	48.0414i	−0.233243	−	1.62224i	−0.683921	−	0.729556i	$-0.739727\pi$
$877$	−6.90731	−	48.0414i	−0.233243	−	1.62224i	0.450678	−	0.892687i	$-0.351182\pi$
$878$	−14.4883	+	6.61658i	−0.488956	+	0.223299i
$879$	3.80970	−	12.9747i	0.128498	−	0.437624i
$880$	0.843023	+	0.384996i	0.0284183	+	0.0129782i
$881$	−37.9921	+	43.8452i	−1.27999	+	1.47718i	−0.479871	+	0.877339i	$0.659316\pi$
$881$	−37.9921	+	43.8452i	−1.27999	+	1.47718i	−0.800116	+	0.599845i	$0.795229\pi$
$882$	−6.47211	−	1.37251i	−0.217927	−	0.0462149i
$883$	8.24823	−	2.42190i	0.277575	−	0.0815034i	−0.139982	−	0.990154i	$-0.544705\pi$
$883$	8.24823	−	2.42190i	0.277575	−	0.0815034i	0.417557	+	0.908651i	$0.362886\pi$
$884$	−4.02876	+	3.49094i	−0.135502	+	0.117413i
$885$	7.50414	−	4.82262i	0.252249	−	0.162111i
$886$	14.1776	−	9.11139i	0.476306	−	0.306103i
$887$	0.746289	−	0.646663i	0.0250579	−	0.0217128i	−0.642242	−	0.766502i	$-0.721995\pi$
$887$	0.746289	−	0.646663i	0.0250579	−	0.0217128i	0.667300	+	0.744789i	$0.267450\pi$
$888$	30.5927	−	8.98282i	1.02662	−	0.301444i
$889$	−39.1926	+	27.3640i	−1.31448	+	0.917760i
$890$	8.52036	−	9.83302i	0.285603	−	0.329604i
$891$	−0.963290	−	0.439920i	−0.0322714	−	0.0147379i
$892$	6.15929	−	20.9766i	0.206228	−	0.702349i
$893$	1.74181	−	0.795457i	0.0582874	−	0.0266189i
$894$	−2.47233	−	17.1954i	−0.0826870	−	0.575101i
$895$	16.6301	+	10.6875i	0.555882	+	0.357243i
$896$	8.76738	+	9.36760i	0.292898	+	0.312950i
$897$	−0.452156	−	3.93286i	−0.0150970	−	0.131315i
$898$	−0.221690			−0.00739790
$899$	−7.48082	+	11.6404i	−0.249499	+	0.388229i
$900$	0.405356	+	2.81931i	0.0135119	+	0.0939770i
$901$	33.6720	−	15.3775i	1.12178	−	0.512298i
$902$	−11.8909	−	3.49149i	−0.395924	−	0.116254i
$903$	30.3506	−	10.1899i	1.01001	−	0.339098i
$904$	15.7388	+	13.6378i	0.523466	+	0.453586i
$905$	−2.71775	+	18.9024i	−0.0903411	+	0.628336i
$906$	1.72831	+	5.88610i	0.0574194	+	0.195552i
$907$	4.43380	−	3.84191i	0.147222	−	0.127569i	−0.578136	−	0.815940i	$-0.696220\pi$
$907$	4.43380	−	3.84191i	0.147222	−	0.127569i	0.725358	+	0.688372i	$0.241674\pi$
$908$	4.58739	−	2.94814i	0.152238	−	0.0978374i
$909$	−6.85145	−	10.6611i	−0.227248	−	0.353605i
$910$	3.19774	+	0.335337i	0.106004	+	0.0111163i
$911$	−12.0277	−	40.9626i	−0.398496	−	1.35715i	−0.877600	−	0.479394i	$-0.840857\pi$
$911$	−12.0277	−	40.9626i	−0.398496	−	1.35715i	0.479104	−	0.877758i	$-0.340962\pi$
$912$	0.223497	+	0.0321341i	0.00740074	+	0.00106407i
$913$	3.67742	+	3.18650i	0.121705	+	0.105458i
$914$	−10.4401	−	4.76783i	−0.345327	−	0.157706i
$915$	−3.44819	+	11.7435i	−0.113994	+	0.388227i
$916$	9.65230	+	21.1356i	0.318921	+	0.698340i
$917$	30.0476	+	24.0845i	0.992258	+	0.795342i
$918$	2.98180	−	4.63977i	0.0984140	−	0.153135i
$919$			23.7230i			0.782549i	0.920274	+	0.391275i	$0.127966\pi$
$919$			23.7230i			0.782549i	−0.920274	+	0.391275i	$0.872034\pi$
$920$	8.54315	+	20.2028i	0.281659	+	0.666066i
$921$	16.7544			0.552078
$922$	−19.4302	+	30.2340i	−0.639899	+	0.995703i
$923$	−8.29888	+	1.19320i	−0.273161	+	0.0392746i
$924$	1.17911	−	2.86782i	0.0387900	−	0.0943444i
$925$	−7.87358	+	26.8149i	−0.258882	+	0.881670i
$926$	8.57539	−	18.7775i	0.281805	−	0.617066i
$927$	0.863537	−	0.996574i	0.0283623	−	0.0327318i
$928$	−1.70178	+	11.8361i	−0.0558636	+	0.388540i
$929$	3.68296	+	12.5430i	0.120834	+	0.411523i	0.997588	−	0.0694169i	$-0.0221139\pi$
$929$	3.68296	+	12.5430i	0.120834	+	0.411523i	−0.876754	+	0.480939i	$0.840296\pi$
$930$	5.95905	+	6.87711i	0.195405	+	0.225509i
$931$	1.36113	+	2.46202i	0.0446091	+	0.0806894i
$932$	7.84644	−	5.04260i	0.257019	−	0.165176i
$933$	−6.19106	−	7.14486i	−0.202686	−	0.233912i
$934$	−2.51599	+	0.738762i	−0.0823258	+	0.0241730i
$935$	−9.52773	−	1.36988i	−0.311590	−	0.0447999i
$936$	−1.83178	−	1.58724i	−0.0598735	−	0.0518807i
$937$	15.6317	−	34.2285i	0.510664	−	1.11820i	−0.462191	−	0.886781i	$-0.652936\pi$
$937$	15.6317	−	34.2285i	0.510664	−	1.11820i	0.972855	−	0.231417i	$-0.0743362\pi$
$938$	3.24111	−	1.63299i	0.105826	−	0.0533191i
$939$	−14.7041	+	6.71513i	−0.479850	+	0.219140i
$940$	8.12991	−	1.16891i	0.265169	−	0.0381255i
$941$	−50.5075	−	32.4592i	−1.64650	−	1.05814i	−0.934505	−	0.355950i	$-0.884157\pi$
$941$	−50.5075	−	32.4592i	−1.64650	−	1.05814i	−0.711991	−	0.702189i	$-0.752206\pi$
$942$		−	10.7265i		−	0.349489i
$943$	−30.6756	−	50.8438i	−0.998936	−	1.65570i
$944$			3.21745i			0.104719i
$945$	4.05377	−	0.742330i	0.131869	−	0.0241480i
$946$	−1.72367	−	11.9884i	−0.0560412	−	0.389775i
$947$	1.08561	+	2.37716i	0.0352776	+	0.0772472i	0.926450	−	0.376417i	$-0.122844\pi$
$947$	1.08561	+	2.37716i	0.0352776	+	0.0772472i	−0.891173	+	0.453664i	$0.850117\pi$
$948$	−2.04369	−	0.600080i	−0.0663758	−	0.0194897i
$949$	5.21058	−	11.4096i	0.169143	−	0.370370i
$950$	−0.640195	+	0.738825i	−0.0207707	+	0.0239706i
$951$	6.20186	+	0.891692i	0.201109	+	0.0289151i
$952$	39.0476	+	23.0302i	1.26554	+	0.746412i
$953$	19.5072	−	16.9031i	0.631902	−	0.547546i	−0.278936	−	0.960310i	$-0.589982\pi$
$953$	19.5072	−	16.9031i	0.631902	−	0.547546i	0.910838	+	0.412764i	$0.135436\pi$
$954$	3.24147	+	5.04383i	0.104946	+	0.163300i
$955$	−7.14543	−	11.1185i	−0.231221	−	0.359787i
$956$	1.34981	+	1.55776i	0.0436558	+	0.0503815i
$957$	2.27467	−	0.667902i	0.0735295	−	0.0215902i
$958$	5.05595	−	35.1649i	0.163350	−	1.13613i
$959$	1.38361	+	36.0940i	0.0446791	+	1.16554i
$960$	8.74541	+	3.99390i	0.282257	+	0.128902i
$961$	6.91243	+	2.02967i	0.222982	+	0.0654733i
$962$	−3.51929	−	7.70618i	−0.113467	−	0.248457i
$963$	−13.3226	+	1.91551i	−0.429316	+	0.0617263i
$964$	−8.66602	−	5.56932i	−0.279114	−	0.179376i
$965$	9.19399			0.295965
$966$	−10.8586	+	5.09053i	−0.349369	+	0.163785i
$967$	24.2871			0.781021			0.390510	−	0.920599i	$-0.372299\pi$
$967$	24.2871			0.781021			0.390510	+	0.920599i	$0.372299\pi$
$968$	24.4016	+	15.6820i	0.784297	+	0.504037i
$969$	−2.32130	+	0.333753i	−0.0745710	+	0.0107217i
$970$	−3.06640	−	6.71448i	−0.0984562	−	0.215589i
$971$	12.3742	+	3.63339i	0.397107	+	0.116601i	0.474188	−	0.880424i	$-0.342742\pi$
$971$	12.3742	+	3.63339i	0.397107	+	0.116601i	−0.0770810	+	0.997025i	$0.524560\pi$
$972$	−1.00669	−	0.459738i	−0.0322894	−	0.0147461i
$973$	−0.965495	−	25.1867i	−0.0309523	−	0.807449i
$974$	2.47829	−	17.2369i	0.0794095	−	0.552305i
$975$	2.03843	−	0.598538i	0.0652821	−	0.0191686i
$976$	−2.89096	−	3.33634i	−0.0925373	−	0.106794i
$977$	−23.1765	−	36.0633i	−0.741482	−	1.15377i	−0.983042	−	0.183383i	$-0.941295\pi$
$977$	−23.1765	−	36.0633i	−0.741482	−	1.15377i	0.241560	−	0.970386i	$-0.422341\pi$
$978$	−6.03211	−	9.38614i	−0.192886	−	0.300136i
$979$	−7.07304	+	6.12882i	−0.226055	+	0.195878i
$980$	2.62665	+	11.7776i	0.0839051	+	0.376222i
$981$	8.01473	+	1.15234i	0.255891	+	0.0367915i
$982$	11.0241	−	12.7225i	0.351794	−	0.405992i
$983$	1.81962	−	3.98441i	0.0580369	−	0.127083i	−0.878392	−	0.477942i	$-0.841383\pi$
$983$	1.81962	−	3.98441i	0.0580369	−	0.127083i	0.936428	+	0.350859i	$0.114110\pi$
$984$	−34.8837	−	10.2428i	−1.11205	−	0.326528i
$985$	0.676184	+	1.48064i	0.0215450	+	0.0471770i
$986$	1.75713	+	12.2211i	0.0559584	+	0.389200i
$987$	2.27067	+	12.3998i	0.0722762	+	0.394691i
$988$			0.367138i			0.0116802i
$989$	32.7455	−	47.9121i	1.04125	−	1.52352i
$990$		−	1.55906i		−	0.0495502i
$991$	−48.1934	−	30.9720i	−1.53091	−	0.983858i	−0.989729	−	0.142953i	$-0.954340\pi$
$991$	−48.1934	−	30.9720i	−1.53091	−	0.983858i	−0.541183	−	0.840905i	$-0.682024\pi$
$992$	32.6799	−	4.69866i	1.03759	−	0.149183i
$993$	14.8928	−	6.80130i	0.472608	−	0.215833i
$994$	11.4283	+	22.6826i	0.362485	+	0.719447i
$995$	14.2397	−	31.1806i	0.451428	−	0.988490i
$996$	3.84308	+	3.33005i	0.121773	+	0.105517i
$997$	18.4896	+	2.65840i	0.585571	+	0.0841924i	0.428732	−	0.903432i	$-0.358961\pi$
$997$	18.4896	+	2.65840i	0.585571	+	0.0841924i	0.156839	+	0.987624i	$0.449870\pi$
$998$	−37.1882	+	10.9194i	−1.17717	+	0.345649i
$999$	−7.11092	−	8.20644i	−0.224980	−	0.259640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.r.a.412.14	yes	320
7.6	odd	2	inner	483.2.r.a.412.13	yes	320
23.11	odd	22	inner	483.2.r.a.34.13	✓	320
161.34	even	22	inner	483.2.r.a.34.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.r.a.34.13	✓	320	23.11	odd	22	inner
483.2.r.a.34.14	yes	320	161.34	even	22	inner
483.2.r.a.412.13	yes	320	7.6	odd	2	inner
483.2.r.a.412.14	yes	320	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.795109 - 0.510986i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.459738 - 1.00669i) q^{4} +(-1.49456 - 0.438843i) q^{5} +(-0.859737 - 0.392629i) q^{6} +(-2.64381 + 0.101346i) q^{7} +(-0.417877 + 2.90640i) q^{8} +(0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.795109 - 0.510986i) q^{2} +(0.989821 - 0.142315i) q^{3} +(-0.459738 - 1.00669i) q^{4} +(-1.49456 - 0.438843i) q^{5} +(-0.859737 - 0.392629i) q^{6} +(-2.64381 + 0.101346i) q^{7} +(-0.417877 + 2.90640i) q^{8} +(0.959493 - 0.281733i) q^{9} +(0.964098 + 1.11263i) q^{10} +(-0.572532 - 0.890878i) q^{11} +(-0.598324 - 0.931011i) q^{12} +(-0.623842 + 0.540562i) q^{13} +(2.15390 + 1.27037i) q^{14} +(-1.54180 - 0.221678i) q^{15} +(0.367925 - 0.424608i) q^{16} +(-2.42411 + 5.30805i) q^{17} +(-0.906863 - 0.266279i) q^{18} +(0.166950 + 0.365570i) q^{19} +(0.245330 + 1.70631i) q^{20} +(-2.60248 + 0.476568i) q^{21} +1.00090i q^{22} +(-3.24202 + 3.53402i) q^{23} +2.93629i q^{24} +(-2.16514 - 1.39145i) q^{25} +(0.772242 - 0.111032i) q^{26} +(0.909632 - 0.415415i) q^{27} +(1.31748 + 2.61489i) q^{28} +(-0.929966 + 2.03634i) q^{29} +(1.11263 + 0.964098i) q^{30} +(6.11805 + 0.879642i) q^{31} +(5.12518 - 1.50489i) q^{32} +(-0.693490 - 0.800330i) q^{33} +(4.63977 - 2.98180i) q^{34} +(3.99581 + 1.00875i) q^{35} +(-0.724731 - 0.836384i) q^{36} +(-3.05924 - 10.4188i) q^{37} +(0.0540574 - 0.375978i) q^{38} +(-0.540562 + 0.623842i) q^{39} +(1.90000 - 4.16041i) q^{40} +(-3.48835 + 11.8802i) q^{41} +(2.31277 + 0.950904i) q^{42} +(-11.9776 + 1.72211i) q^{43} +(-0.633619 + 0.985930i) q^{44} -1.55766 q^{45} +(4.38360 - 1.15331i) q^{46} -4.76463i q^{47} +(0.303752 - 0.472647i) q^{48} +(6.97946 - 0.535881i) q^{49} +(1.01051 + 2.21271i) q^{50} +(-1.64402 + 5.59901i) q^{51} +(0.830979 + 0.379495i) q^{52} +(-4.79415 - 4.15415i) q^{53} +(-0.935528 - 0.134509i) q^{54} +(0.464730 + 1.58272i) q^{55} +(0.810235 - 7.72632i) q^{56} +(0.217277 + 0.338090i) q^{57} +(1.77997 - 1.14391i) q^{58} +(-4.32793 + 3.75017i) q^{59} +(0.485665 + 1.65402i) q^{60} +(1.11823 - 7.77749i) q^{61} +(-4.41503 - 3.82565i) q^{62} +(-2.50816 + 0.842088i) q^{63} +(-5.92222 - 1.73892i) q^{64} +(1.16959 - 0.534135i) q^{65} +(0.142443 + 0.990713i) q^{66} +(0.784651 - 1.22094i) q^{67} +6.45799 q^{68} +(-2.70608 + 3.95944i) q^{69} +(-2.66165 - 2.84387i) q^{70} +(8.54463 + 5.49130i) q^{71} +(0.417877 + 2.90640i) q^{72} +(-13.8221 + 6.31233i) q^{73} +(-2.89144 + 9.84734i) q^{74} +(-2.34112 - 1.06915i) q^{75} +(0.291261 - 0.336133i) q^{76} +(1.60395 + 2.29729i) q^{77} +(0.748580 - 0.219803i) q^{78} +(1.45453 - 1.26036i) q^{79} +(-0.736223 + 0.473142i) q^{80} +(0.841254 - 0.540641i) q^{81} +(8.84424 - 7.66358i) q^{82} +(-4.40875 + 1.29453i) q^{83} +(1.67621 + 2.40078i) q^{84} +(5.95238 - 6.86941i) q^{85} +(10.4035 + 4.75110i) q^{86} +(-0.630698 + 2.14796i) q^{87} +(2.82849 - 1.29173i) q^{88} +(-1.25773 - 8.74770i) q^{89} +(1.23851 + 0.795941i) q^{90} +(1.59453 - 1.49237i) q^{91} +(5.04812 + 1.63897i) q^{92} +6.18096 q^{93} +(-2.43466 + 3.78840i) q^{94} +(-0.0890897 - 0.619633i) q^{95} +(4.85885 - 2.21896i) q^{96} +(-4.81079 - 1.41258i) q^{97} +(-5.82326 - 3.14032i) q^{98} +(-0.800330 - 0.693490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9	\( 320 q + 4 q^{2} - 36 q^{4} + 12 q^{8} + 32 q^{9} - 4 q^{18} + 52 q^{23} - 68 q^{25} - 88 q^{28} + 24 q^{32} + 28 q^{35} + 14 q^{36} - 44 q^{37} + 110 q^{42} - 44 q^{43} - 154 q^{44} + 40 q^{46} - 16 q^{49} - 166 q^{50} - 44 q^{51} + 110 q^{56} - 44 q^{57} - 62 q^{58} - 84 q^{64} + 72 q^{70} - 40 q^{71} - 12 q^{72} + 22 q^{74} + 72 q^{77} - 8 q^{78} - 88 q^{79} - 32 q^{81} - 304 q^{85} + 330 q^{88} - 412 q^{92} + 24 q^{93} + 148 q^{95} - 60 q^{98} + 44 q^{99}+O(q^{100}) \) 320 * q + 4 * q^2 - 36 * q^4 + 12 * q^8 + 32 * q^9 - 4 * q^18 + 52 * q^23 - 68 * q^25 - 88 * q^28 + 24 * q^32 + 28 * q^35 + 14 * q^36 - 44 * q^37 + 110 * q^42 - 44 * q^43 - 154 * q^44 + 40 * q^46 - 16 * q^49 - 166 * q^50 - 44 * q^51 + 110 * q^56 - 44 * q^57 - 62 * q^58 - 84 * q^64 + 72 * q^70 - 40 * q^71 - 12 * q^72 + 22 * q^74 + 72 * q^77 - 8 * q^78 - 88 * q^79 - 32 * q^81 - 304 * q^85 + 330 * q^88 - 412 * q^92 + 24 * q^93 + 148 * q^95 - 60 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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