LMFDB - Embedded newform 483.2.j.a.229.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.18
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.208136 - 0.360502i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.913359 + 1.58198i) q^{4} +(0.648045 - 1.12245i) q^{5} +0.416272i q^{6} +(-0.918903 - 2.48105i) q^{7} +1.59295 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.269763 - 0.467243i) q^{10} +(2.43137 - 1.40375i) q^{11} +(-1.58198 - 0.913359i) q^{12} -3.38323i q^{13} +(-1.08568 - 0.185130i) q^{14} +1.29609i q^{15} +(-1.49517 + 2.58970i) q^{16} +(2.05236 + 3.55480i) q^{17} +(-0.208136 - 0.360502i) q^{18} +(3.04196 - 5.26884i) q^{19} +2.36759 q^{20} +(2.03632 + 1.68920i) q^{21} -1.16868i q^{22} +(-0.594509 + 4.75884i) q^{23} +(-1.37954 + 0.796477i) q^{24} +(1.66008 + 2.87533i) q^{25} +(-1.21966 - 0.704171i) q^{26} +1.00000i q^{27} +(3.08570 - 3.71978i) q^{28} +2.21188 q^{29} +(0.467243 + 0.269763i) q^{30} +(6.23520 - 3.59990i) q^{31} +(2.21535 + 3.83710i) q^{32} +(-1.40375 + 2.43137i) q^{33} +1.70868 q^{34} +(-3.38034 - 0.576414i) q^{35} +1.82672 q^{36} +(-3.56949 - 2.06085i) q^{37} +(-1.26628 - 2.19327i) q^{38} +(1.69161 + 2.92996i) q^{39} +(1.03231 - 1.78801i) q^{40} -0.240997i q^{41} +(1.03279 - 0.382513i) q^{42} -3.36019i q^{43} +(4.44143 + 2.56426i) q^{44} +(-0.648045 - 1.12245i) q^{45} +(1.59183 + 1.20481i) q^{46} +(-3.39835 - 1.96204i) q^{47} -2.99033i q^{48} +(-5.31124 + 4.55969i) q^{49} +1.38208 q^{50} +(-3.55480 - 2.05236i) q^{51} +(5.35221 - 3.09010i) q^{52} +(-6.00452 + 3.46671i) q^{53} +(0.360502 + 0.208136i) q^{54} -3.63878i q^{55} +(-1.46377 - 3.95220i) q^{56} +6.08393i q^{57} +(0.460371 - 0.797386i) q^{58} +(-0.590358 + 0.340843i) q^{59} +(-2.05039 + 1.18380i) q^{60} +(-0.675455 + 1.16992i) q^{61} -2.99707i q^{62} +(-2.60811 - 0.444733i) q^{63} -4.13629 q^{64} +(-3.79749 - 2.19248i) q^{65} +(0.584342 + 1.01211i) q^{66} +(3.27203 - 1.88911i) q^{67} +(-3.74909 + 6.49361i) q^{68} +(-1.86456 - 4.41853i) q^{69} +(-0.911368 + 1.09865i) q^{70} +10.1493 q^{71} +(0.796477 - 1.37954i) q^{72} +(-0.125713 + 0.0725804i) q^{73} +(-1.48588 + 0.857873i) q^{74} +(-2.87533 - 1.66008i) q^{75} +11.1136 q^{76} +(-5.71697 - 4.74244i) q^{77} +1.40834 q^{78} +(-7.09830 - 4.09821i) q^{79} +(1.93787 + 3.35649i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0868798 - 0.0501601i) q^{82} -8.63635 q^{83} +(-0.812401 + 4.76427i) q^{84} +5.32009 q^{85} +(-1.21135 - 0.699375i) q^{86} +(-1.91554 + 1.10594i) q^{87} +(3.87306 - 2.23611i) q^{88} +(1.93681 - 3.35466i) q^{89} -0.539526 q^{90} +(-8.39396 + 3.10885i) q^{91} +(-8.07141 + 3.40602i) q^{92} +(-3.59990 + 6.23520i) q^{93} +(-1.41464 + 0.816740i) q^{94} +(-3.94266 - 6.82889i) q^{95} +(-3.83710 - 2.21535i) q^{96} -8.51417 q^{97} +(0.538318 + 2.86375i) q^{98} -2.80750i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Character values

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

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.208136	−	0.360502i	0.147174	−	0.254913i	−0.783008	−	0.622012i	$-0.786316\pi$
$2$	0.208136	−	0.360502i	0.147174	−	0.254913i	0.930182	+	0.367099i	$0.119649\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.913359	+	1.58198i	0.456679	+	0.790992i
$5$	0.648045	−	1.12245i	0.289815	−	0.501974i	−0.683951	−	0.729528i	$-0.739740\pi$
$5$	0.648045	−	1.12245i	0.289815	−	0.501974i	0.973765	+	0.227555i	$0.0730730\pi$
$6$			0.416272i			0.169942i
$7$	−0.918903	−	2.48105i	−0.347313	−	0.937749i
$7$	−0.918903	−	2.48105i	−0.347313	−	0.937749i
$8$	1.59295			0.563195
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.269763	−	0.467243i	−0.0853065	−	0.147755i
$11$	2.43137	−	1.40375i	0.733086	−	0.423247i	−0.0864644	−	0.996255i	$-0.527557\pi$
$11$	2.43137	−	1.40375i	0.733086	−	0.423247i	0.819550	+	0.573008i	$0.194224\pi$
$12$	−1.58198	−	0.913359i	−0.456679	−	0.263664i
$13$		−	3.38323i		−	0.938338i	−0.883108	−	0.469169i	$-0.844554\pi$
$13$		−	3.38323i		−	0.938338i	0.883108	−	0.469169i	$-0.155446\pi$
$14$	−1.08568	−	0.185130i	−0.290160	−	0.0494780i
$15$			1.29609i			0.334649i
$16$	−1.49517	+	2.58970i	−0.373792	+	0.647426i
$17$	2.05236	+	3.55480i	0.497771	+	0.862165i	0.999997	−	0.00257180i	$-0.000818630\pi$
$17$	2.05236	+	3.55480i	0.497771	+	0.862165i	−0.502226	+	0.864737i	$0.667485\pi$
$18$	−0.208136	−	0.360502i	−0.0490581	−	0.0849711i
$19$	3.04196	−	5.26884i	0.697874	−	1.20875i	−0.271328	−	0.962487i	$-0.587463\pi$
$19$	3.04196	−	5.26884i	0.697874	−	1.20875i	0.969202	−	0.246267i	$-0.0792040\pi$
$20$	2.36759			0.529409
$21$	2.03632	+	1.68920i	0.444361	+	0.368614i
$22$		−	1.16868i		−	0.249164i
$23$	−0.594509	+	4.75884i	−0.123964	+	0.992287i
$23$	−0.594509	+	4.75884i	−0.123964	+	0.992287i
$24$	−1.37954	+	0.796477i	−0.281597	+	0.162580i
$25$	1.66008	+	2.87533i	0.332015	+	0.575067i
$26$	−1.21966	−	0.704171i	−0.239195	−	0.138099i
$27$			1.00000i			0.192450i
$28$	3.08570	−	3.71978i	0.583142	−	0.702972i
$29$	2.21188			0.410735			0.205368	−	0.978685i	$-0.434161\pi$
$29$	2.21188			0.410735			0.205368	+	0.978685i	$0.434161\pi$
$30$	0.467243	+	0.269763i	0.0853065	+	0.0492517i
$31$	6.23520	−	3.59990i	1.11988	−	0.646561i	0.178506	−	0.983939i	$-0.442873\pi$
$31$	6.23520	−	3.59990i	1.11988	−	0.646561i	0.941369	+	0.337378i	$0.109540\pi$
$32$	2.21535	+	3.83710i	0.391622	+	0.678310i
$33$	−1.40375	+	2.43137i	−0.244362	+	0.423247i
$34$	1.70868			0.293036
$35$	−3.38034	−	0.576414i	−0.571382	−	0.0974317i
$36$	1.82672			0.304453
$37$	−3.56949	−	2.06085i	−0.586821	−	0.338801i	0.177018	−	0.984208i	$-0.443355\pi$
$37$	−3.56949	−	2.06085i	−0.586821	−	0.338801i	−0.763840	+	0.645406i	$0.776688\pi$
$38$	−1.26628	−	2.19327i	−0.205418	−	0.355795i
$39$	1.69161	+	2.92996i	0.270875	+	0.469169i
$40$	1.03231	−	1.78801i	0.163222	−	0.282709i
$41$		−	0.240997i		−	0.0376374i	−0.999823	−	0.0188187i	$-0.994009\pi$
$41$		−	0.240997i		−	0.0376374i	0.999823	−	0.0188187i	$-0.00599053\pi$
$42$	1.03279	−	0.382513i	0.159363	−	0.0590231i
$43$		−	3.36019i		−	0.512424i	−0.966621	−	0.256212i	$-0.917526\pi$
$43$		−	3.36019i		−	0.512424i	0.966621	−	0.256212i	$-0.0824744\pi$
$44$	4.44143	+	2.56426i	0.669570	+	0.386577i
$45$	−0.648045	−	1.12245i	−0.0966049	−	0.167325i
$46$	1.59183	+	1.20481i	0.234703	+	0.177639i
$47$	−3.39835	−	1.96204i	−0.495700	−	0.286192i	0.231236	−	0.972898i	$-0.425723\pi$
$47$	−3.39835	−	1.96204i	−0.495700	−	0.286192i	−0.726936	+	0.686705i	$0.759056\pi$
$48$		−	2.99033i		−	0.431617i
$49$	−5.31124	+	4.55969i	−0.758748	+	0.651384i
$50$	1.38208			0.195456
$51$	−3.55480	−	2.05236i	−0.497771	−	0.287388i
$52$	5.35221	−	3.09010i	0.742218	−	0.428520i
$53$	−6.00452	+	3.46671i	−0.824785	+	0.476190i	−0.852064	−	0.523438i	$-0.824649\pi$
$53$	−6.00452	+	3.46671i	−0.824785	+	0.476190i	0.0272789	+	0.999628i	$0.491316\pi$
$54$	0.360502	+	0.208136i	0.0490581	+	0.0283237i
$55$		−	3.63878i		−	0.490653i
$56$	−1.46377	−	3.95220i	−0.195605	−	0.528135i
$57$			6.08393i			0.805836i
$58$	0.460371	−	0.797386i	0.0604497	−	0.104702i
$59$	−0.590358	+	0.340843i	−0.0768581	+	0.0443740i	−0.537937	−	0.842985i	$-0.680796\pi$
$59$	−0.590358	+	0.340843i	−0.0768581	+	0.0443740i	0.461078	+	0.887359i	$0.347463\pi$
$60$	−2.05039	+	1.18380i	−0.264705	+	0.152827i
$61$	−0.675455	+	1.16992i	−0.0864831	+	0.149793i	−0.906022	−	0.423230i	$-0.860896\pi$
$61$	−0.675455	+	1.16992i	−0.0864831	+	0.149793i	0.819539	+	0.573023i	$0.194230\pi$
$62$		−	2.99707i		−	0.380628i
$63$	−2.60811	−	0.444733i	−0.328590	−	0.0560311i
$64$	−4.13629			−0.517036
$65$	−3.79749	−	2.19248i	−0.471021	−	0.271944i
$66$	0.584342	+	1.01211i	0.0719276	+	0.124582i
$67$	3.27203	−	1.88911i	0.399742	−	0.230791i	−0.286630	−	0.958041i	$-0.592535\pi$
$67$	3.27203	−	1.88911i	0.399742	−	0.230791i	0.686373	+	0.727250i	$0.259202\pi$
$68$	−3.74909	+	6.49361i	−0.454644	+	0.787466i
$69$	−1.86456	−	4.41853i	−0.224467	−	0.531929i
$70$	−0.911368	+	1.09865i	−0.108929	+	0.131313i
$71$	10.1493			1.20450			0.602248	−	0.798309i	$-0.294272\pi$
$71$	10.1493			1.20450			0.602248	+	0.798309i	$0.294272\pi$
$72$	0.796477	−	1.37954i	0.0938658	−	0.162580i
$73$	−0.125713	+	0.0725804i	−0.0147136	+	0.00849490i	−0.507339	−	0.861747i	$-0.669371\pi$
$73$	−0.125713	+	0.0725804i	−0.0147136	+	0.00849490i	0.492625	+	0.870242i	$0.336037\pi$
$74$	−1.48588	+	0.857873i	−0.172730	+	0.0997257i
$75$	−2.87533	−	1.66008i	−0.332015	−	0.191689i
$76$	11.1136			1.27482
$77$	−5.71697	−	4.74244i	−0.651510	−	0.540452i
$78$	1.40834			0.159463
$79$	−7.09830	−	4.09821i	−0.798621	−	0.461084i	0.0443675	−	0.999015i	$-0.485873\pi$
$79$	−7.09830	−	4.09821i	−0.798621	−	0.461084i	−0.842989	+	0.537931i	$0.819206\pi$
$80$	1.93787	+	3.35649i	0.216661	+	0.375267i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.0868798	−	0.0501601i	−0.00959427	−	0.00553926i
$83$	−8.63635			−0.947962			−0.473981	−	0.880535i	$-0.657184\pi$
$83$	−8.63635			−0.947962			−0.473981	+	0.880535i	$0.657184\pi$
$84$	−0.812401	+	4.76427i	−0.0886403	+	0.519825i
$85$	5.32009			0.577045
$86$	−1.21135	−	0.699375i	−0.130624	−	0.0754156i
$87$	−1.91554	+	1.10594i	−0.205368	+	0.118569i
$88$	3.87306	−	2.23611i	0.412870	−	0.238370i
$89$	1.93681	−	3.35466i	0.205302	−	0.355593i	−0.744927	−	0.667146i	$-0.767516\pi$
$89$	1.93681	−	3.35466i	0.205302	−	0.355593i	0.950229	+	0.311553i	$0.100849\pi$
$90$	−0.539526			−0.0568710
$91$	−8.39396	+	3.10885i	−0.879926	+	0.325897i
$92$	−8.07141	+	3.40602i	−0.841503	+	0.355103i
$93$	−3.59990	+	6.23520i	−0.373292	+	0.646561i
$94$	−1.41464	+	0.816740i	−0.145908	+	0.0842403i
$95$	−3.94266	−	6.82889i	−0.404508	−	0.700629i
$96$	−3.83710	−	2.21535i	−0.391622	−	0.226103i
$97$	−8.51417			−0.864483			−0.432241	−	0.901758i	$-0.642277\pi$
$97$	−8.51417			−0.864483			−0.432241	+	0.901758i	$0.642277\pi$
$98$	0.538318	+	2.86375i	0.0543784	+	0.289282i
$99$		−	2.80750i		−	0.282165i
$100$	−3.03249	+	5.25242i	−0.303249	+	0.525242i
$101$	−10.2093	+	5.89435i	−1.01587	+	0.586510i	−0.912904	−	0.408175i	$-0.866165\pi$
$101$	−10.2093	+	5.89435i	−1.01587	+	0.586510i	−0.102962	+	0.994685i	$0.532832\pi$
$102$	−1.47976	+	0.854341i	−0.146518	+	0.0845923i
$103$	−6.53852	+	11.3250i	−0.644259	+	1.11589i	0.340213	+	0.940349i	$0.389501\pi$
$103$	−6.53852	+	11.3250i	−0.644259	+	1.11589i	−0.984472	+	0.175542i	$0.943832\pi$
$104$		−	5.38932i		−	0.528467i
$105$	3.21567	−	1.19098i	0.313817	−	0.116228i
$106$			2.88619i			0.280332i
$107$	−4.36810	−	2.52193i	−0.422280	−	0.243804i	0.273772	−	0.961795i	$-0.411729\pi$
$107$	−4.36810	−	2.52193i	−0.422280	−	0.243804i	−0.696053	+	0.717991i	$0.745062\pi$
$108$	−1.58198	+	0.913359i	−0.152226	+	0.0878880i
$109$	−1.85827	+	1.07287i	−0.177990	+	0.102762i	−0.586348	−	0.810059i	$-0.699435\pi$
$109$	−1.85827	+	1.07287i	−0.177990	+	0.102762i	0.408358	+	0.912822i	$0.366101\pi$
$110$	−1.31179	−	0.757360i	−0.125074	−	0.0722115i
$111$	4.12170			0.391214
$112$	7.79910	+	1.32990i	0.736946	+	0.125664i
$113$			20.6577i			1.94331i	0.236400	+	0.971656i	$0.424033\pi$
$113$			20.6577i			1.94331i	−0.236400	+	0.971656i	$0.575967\pi$
$114$	2.19327	+	1.26628i	0.205418	+	0.118598i
$115$	4.95628	+	3.75125i	0.462175	+	0.349806i
$116$	2.02024	+	3.49915i	0.187574	+	0.324888i
$117$	−2.92996	−	1.69161i	−0.270875	−	0.156390i
$118$			0.283767i			0.0261229i
$119$	6.93371	−	8.35853i	0.635612	−	0.766225i
$120$			2.06461i			0.188473i
$121$	−1.55896	+	2.70020i	−0.141724	+	0.245473i
$122$	0.281173	+	0.487005i	0.0254562	+	0.0440914i
$123$	0.120498	+	0.208709i	0.0108650	+	0.0188187i
$124$	11.3900	+	6.57600i	1.02285	+	0.590542i
$125$	10.7837			0.964520
$126$	−0.703167	+	0.847662i	−0.0626431	+	0.0755157i
$127$	13.6774			1.21367			0.606836	−	0.794827i	$-0.292438\pi$
$127$	13.6774			1.21367			0.606836	+	0.794827i	$0.292438\pi$
$128$	−5.29161	+	9.16534i	−0.467717	+	0.810109i
$129$	1.68009	+	2.91001i	0.147924	+	0.256212i
$130$	−1.58079	+	0.912669i	−0.138644	+	0.0800463i
$131$	3.88592	+	2.24354i	0.339515	+	0.196019i	0.660057	−	0.751215i	$-0.270532\pi$
$131$	3.88592	+	2.24354i	0.339515	+	0.196019i	−0.320543	+	0.947234i	$0.603865\pi$
$132$	−5.12852			−0.446380
$133$	−15.8675	−	2.70572i	−1.37589	−	0.234616i
$134$		−	1.57277i		−	0.135866i
$135$	1.12245	+	0.648045i	0.0966049	+	0.0557748i
$136$	3.26932	+	5.66263i	0.280342	+	0.485567i
$137$	−20.1289	+	11.6214i	−1.71973	+	0.992885i	−0.800327	+	0.599564i	$0.795341\pi$
$137$	−20.1289	+	11.6214i	−1.71973	+	0.992885i	−0.919401	+	0.393322i	$0.871326\pi$
$138$	−1.98097	−	0.247477i	−0.168631	−	0.0210667i
$139$		−	11.1536i		−	0.946034i	−0.881053	−	0.473017i	$-0.843165\pi$
$139$		−	11.1536i		−	0.946034i	0.881053	−	0.473017i	$-0.156835\pi$
$140$	−2.17559	−	5.87412i	−0.183871	−	0.496453i
$141$	3.92407			0.330466
$142$	2.11243	−	3.65883i	0.177271	−	0.307042i
$143$	−4.74921	−	8.22587i	−0.397149	−	0.687882i
$144$	1.49517	+	2.58970i	0.124597	+	0.215809i
$145$	1.43340	−	2.48271i	0.119037	−	0.206178i
$146$			0.0604264i			0.00500092i
$147$	2.31982	−	6.60443i	0.191336	−	0.544724i
$148$		−	7.52918i		−	0.618895i
$149$	10.4621	+	6.04029i	0.857088	+	0.494840i	0.863036	−	0.505142i	$-0.168560\pi$
$149$	10.4621	+	6.04029i	0.857088	+	0.494840i	−0.00594789	+	0.999982i	$0.501893\pi$
$150$	−1.19692	+	0.691042i	−0.0977282	+	0.0564234i
$151$	−5.50309	−	9.53164i	−0.447835	−	0.775674i	0.550409	−	0.834895i	$-0.314472\pi$
$151$	−5.50309	−	9.53164i	−0.447835	−	0.775674i	−0.998245	+	0.0592211i	$0.981138\pi$
$152$	4.84571	−	8.39302i	0.393039	−	0.680764i
$153$	4.10473			0.331847
$154$	−2.89957	+	1.07391i	−0.233654	+	0.0865379i
$155$		−	9.33158i		−	0.749531i
$156$	−3.09010	+	5.35221i	−0.247406	+	0.428520i
$157$	−10.6817	−	18.5013i	−0.852493	−	1.47656i	−0.878951	−	0.476912i	$-0.841756\pi$
$157$	−10.6817	−	18.5013i	−0.852493	−	1.47656i	0.0264581	−	0.999650i	$-0.491577\pi$
$158$	−2.95482	+	1.70597i	−0.235073	+	0.135720i
$159$	3.46671	−	6.00452i	0.274928	−	0.476190i
$160$	5.74259			0.453991
$161$	12.3532	−	2.89790i	0.973570	−	0.228387i
$162$	−0.416272			−0.0327054
$163$	−6.79092	+	11.7622i	−0.531906	+	0.921288i	0.467400	+	0.884046i	$0.345191\pi$
$163$	−6.79092	+	11.7622i	−0.531906	+	0.921288i	−0.999306	+	0.0372422i	$0.988143\pi$
$164$	0.381253	−	0.220117i	0.0297709	−	0.0171882i
$165$	1.81939	+	3.15127i	0.141639	+	0.245326i
$166$	−1.79753	+	3.11342i	−0.139516	+	0.241648i
$167$			0.426445i			0.0329993i	0.999864	+	0.0164996i	$0.00525223\pi$
$167$			0.426445i			0.0329993i	−0.999864	+	0.0164996i	$0.994748\pi$
$168$	3.24376	+	2.69082i	0.250262	+	0.207602i
$169$	1.55379			0.119522
$170$	1.10730	−	1.91790i	0.0849262	−	0.147097i
$171$	−3.04196	−	5.26884i	−0.232625	−	0.402918i
$172$	5.31576	−	3.06906i	0.405323	−	0.234013i
$173$	12.4084	+	7.16401i	0.943396	+	0.544670i	0.891023	−	0.453958i	$-0.149988\pi$
$173$	12.4084	+	7.16401i	0.943396	+	0.544670i	0.0523727	+	0.998628i	$0.483322\pi$
$174$			0.920742i			0.0698013i
$175$	5.60841	−	6.76088i	0.423956	−	0.511075i
$176$			8.39537i			0.632825i
$177$	0.340843	−	0.590358i	0.0256194	−	0.0443740i
$178$	−0.806241	−	1.39645i	−0.0604303	−	0.104668i
$179$	6.49175	+	11.2440i	0.485216	+	0.840419i	0.999856	−	0.0169877i	$-0.00540760\pi$
$179$	6.49175	+	11.2440i	0.485216	+	0.840419i	−0.514640	+	0.857407i	$0.672074\pi$
$180$	1.18380	−	2.05039i	0.0882349	−	0.152827i
$181$	3.77532			0.280617			0.140309	−	0.990108i	$-0.455191\pi$
$181$	3.77532			0.280617			0.140309	+	0.990108i	$0.455191\pi$
$182$	−0.626336	+	3.67310i	−0.0464271	+	0.272268i
$183$		−	1.35091i		−	0.0998621i
$184$	−0.947026	+	7.58062i	−0.0698157	+	0.558850i
$185$	−4.62639	+	2.67105i	−0.340139	+	0.196379i
$186$	1.49854	+	2.59554i	0.109878	+	0.190314i
$187$	9.98011	+	5.76202i	0.729818	+	0.421360i
$188$		−	7.16817i		−	0.522793i
$189$	2.48105	−	0.918903i	0.180470	−	0.0668403i
$190$	−3.28244			−0.238133
$191$	−2.98440	−	1.72305i	−0.215944	−	0.124675i	0.388127	−	0.921606i	$-0.373122\pi$
$191$	−2.98440	−	1.72305i	−0.215944	−	0.124675i	−0.604071	+	0.796931i	$0.706456\pi$
$192$	3.58213	−	2.06815i	0.258518	−	0.149256i
$193$	−4.32367	−	7.48882i	−0.311225	−	0.539057i	0.667403	−	0.744697i	$-0.267406\pi$
$193$	−4.32367	−	7.48882i	−0.311225	−	0.539057i	−0.978628	+	0.205640i	$0.934073\pi$
$194$	−1.77210	+	3.06937i	−0.127230	+	0.220368i
$195$	4.38497			0.314014
$196$	−12.0644	−	4.23766i	−0.861744	−	0.302690i
$197$	13.0386			0.928962			0.464481	−	0.885583i	$-0.346241\pi$
$197$	13.0386			0.928962			0.464481	+	0.885583i	$0.346241\pi$
$198$	−1.01211	−	0.584342i	−0.0719276	−	0.0415274i
$199$	−4.47236	−	7.74636i	−0.317037	−	0.549125i	0.662831	−	0.748769i	$-0.269355\pi$
$199$	−4.47236	−	7.74636i	−0.317037	−	0.549125i	−0.979868	+	0.199644i	$0.936021\pi$
$200$	2.64442	+	4.58028i	0.186989	+	0.323875i
$201$	−1.88911	+	3.27203i	−0.133247	+	0.230791i
$202$			4.90731i			0.345277i
$203$	−2.03250	−	5.48778i	−0.142653	−	0.385167i
$204$		−	7.49818i		−	0.524977i
$205$	−0.270506	−	0.156177i	−0.0188930	−	0.0109079i
$206$	2.72180	+	4.71430i	0.189637	+	0.328461i
$207$	3.82402	+	2.89428i	0.265788	+	0.201166i
$208$	8.76155	+	5.05849i	0.607505	+	0.350743i
$209$		−	17.0807i		−	1.18149i
$210$	0.239945	−	1.40714i	0.0165578	−	0.0971019i
$211$	−3.23308			−0.222574			−0.111287	−	0.993788i	$-0.535497\pi$
$211$	−3.23308			−0.222574			−0.111287	+	0.993788i	$0.535497\pi$
$212$	−10.9686	−	6.33271i	−0.753325	−	0.434932i
$213$	−8.78952	+	5.07463i	−0.602248	+	0.347708i
$214$	−1.81832	+	1.04981i	−0.124298	+	0.0717633i
$215$	−3.77163	−	2.17755i	−0.257223	−	0.148508i
$216$			1.59295i			0.108387i
$217$	−14.6611	−	12.1619i	−0.995259	−	0.825604i
$218$			0.893211i			0.0604959i
$219$	0.0725804	−	0.125713i	0.00490453	−	0.00849490i
$220$	5.75649	−	3.32351i	0.388102	−	0.224071i
$221$	12.0267	−	6.94361i	0.809002	−	0.467077i
$222$	0.857873	−	1.48588i	0.0575767	−	0.0997257i
$223$		−	15.5726i		−	1.04282i	−0.853307	−	0.521408i	$-0.825407\pi$
$223$		−	15.5726i		−	1.04282i	0.853307	−	0.521408i	$-0.174593\pi$
$224$	7.48435	−	9.02232i	0.500069	−	0.602829i
$225$	3.32015			0.221343
$226$	7.44714	+	4.29961i	0.495376	+	0.286006i
$227$	−12.8041	−	22.1773i	−0.849838	−	1.47196i	−0.881353	−	0.472459i	$-0.843366\pi$
$227$	−12.8041	−	22.1773i	−0.849838	−	1.47196i	0.0315149	−	0.999503i	$-0.489967\pi$
$228$	−9.62468	+	5.55681i	−0.637410	+	0.368009i
$229$	−6.95903	+	12.0534i	−0.459865	+	0.796510i	−0.998953	−	0.0457393i	$-0.985436\pi$
$229$	−6.95903	+	12.0534i	−0.459865	+	0.796510i	0.539088	+	0.842249i	$0.318769\pi$
$230$	2.38391	−	1.00598i	0.157190	−	0.0663322i
$231$	7.32227	+	1.24859i	0.481770	+	0.0821511i
$232$	3.52342			0.231324
$233$	−8.37502	+	14.5060i	−0.548666	+	0.950317i	0.449700	+	0.893179i	$0.351531\pi$
$233$	−8.37502	+	14.5060i	−0.548666	+	0.950317i	−0.998366	+	0.0571377i	$0.981803\pi$
$234$	−1.21966	+	0.704171i	−0.0797316	+	0.0460331i
$235$	−4.40456	+	2.54297i	−0.287322	+	0.165885i
$236$	−1.07842	−	0.622625i	−0.0701990	−	0.0405294i
$237$	8.19641			0.532414
$238$	−1.57011	−	4.23933i	−0.101775	−	0.274795i
$239$	−8.26463			−0.534595			−0.267297	−	0.963614i	$-0.586131\pi$
$239$	−8.26463			−0.534595			−0.267297	+	0.963614i	$0.586131\pi$
$240$	−3.35649	−	1.93787i	−0.216661	−	0.125089i
$241$	13.0474	+	22.5988i	0.840459	+	1.45572i	0.889507	+	0.456922i	$0.151048\pi$
$241$	13.0474	+	22.5988i	0.840459	+	1.45572i	−0.0490478	+	0.998796i	$0.515619\pi$
$242$	0.648951	+	1.12402i	0.0417162	+	0.0722545i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−2.46773			−0.157980
$245$	1.67609	+	8.91647i	0.107081	+	0.569652i
$246$	0.100320			0.00639618
$247$	−17.8257	−	10.2917i	−1.13422	−	0.654842i
$248$	9.93240	−	5.73447i	0.630708	−	0.364139i
$249$	7.47930	−	4.31817i	0.473981	−	0.273653i
$250$	2.24447	−	3.88753i	0.141953	−	0.245869i
$251$	13.6112			0.859131			0.429566	−	0.903036i	$-0.358667\pi$
$251$	13.6112			0.859131			0.429566	+	0.903036i	$0.358667\pi$
$252$	−1.67858	−	4.53218i	−0.105740	−	0.285501i
$253$	5.23476	+	12.4050i	0.329107	+	0.779898i
$254$	2.84676	−	4.93073i	0.178621	−	0.309381i
$255$	−4.60734	+	2.66005i	−0.288523	+	0.166579i
$256$	−1.93354	−	3.34899i	−0.120846	−	0.209312i
$257$	4.03487	+	2.32953i	0.251688	+	0.145312i	0.620537	−	0.784177i	$-0.286915\pi$
$257$	4.03487	+	2.32953i	0.251688	+	0.145312i	−0.368849	+	0.929489i	$0.620248\pi$
$258$	1.39875			0.0870824
$259$	−1.83305	+	10.7498i	−0.113900	+	0.667961i
$260$		−	8.01009i		−	0.496765i
$261$	1.10594	−	1.91554i	0.0684559	−	0.118569i
$262$	1.61760	−	0.933922i	0.0999356	−	0.0576979i
$263$	26.5367	−	15.3210i	1.63632	−	0.944731i	0.654237	−	0.756289i	$-0.272990\pi$
$263$	26.5367	−	15.3210i	1.63632	−	0.944731i	0.982084	−	0.188442i	$-0.0603436\pi$
$264$	−2.23611	+	3.87306i	−0.137623	+	0.238370i
$265$			8.98635i			0.552027i
$266$	−4.27802	+	5.15712i	−0.262302	+	0.316203i
$267$			3.87363i			0.237062i
$268$	5.97708	+	3.45087i	0.365108	+	0.210795i
$269$	−20.8811	+	12.0557i	−1.27315	+	0.735051i	−0.975579	−	0.219650i	$-0.929509\pi$
$269$	−20.8811	+	12.0557i	−1.27315	+	0.735051i	−0.297567	+	0.954701i	$0.596175\pi$
$270$	0.467243	−	0.269763i	0.0284355	−	0.0164172i
$271$	10.6658	+	6.15787i	0.647898	+	0.374064i	0.787651	−	0.616122i	$-0.211297\pi$
$271$	10.6658	+	6.15787i	0.647898	+	0.374064i	−0.139752	+	0.990187i	$0.544631\pi$
$272$	−12.2745			−0.744251
$273$	5.71495	−	6.88933i	0.345885	−	0.416961i
$274$			9.67534i			0.584509i
$275$	8.07251	+	4.66067i	0.486791	+	0.281049i
$276$	5.28703	−	6.98541i	0.318242	−	0.420472i
$277$	−11.5136	−	19.9422i	−0.691788	−	1.19821i	−0.971252	−	0.238055i	$-0.923490\pi$
$277$	−11.5136	−	19.9422i	−0.691788	−	1.19821i	0.279464	−	0.960156i	$-0.409843\pi$
$278$	−4.02089	−	2.32146i	−0.241157	−	0.139232i
$279$		−	7.19979i		−	0.431040i
$280$	−5.38473	−	0.918201i	−0.321799	−	0.0548730i
$281$		−	18.7454i		−	1.11826i	−0.829081	−	0.559128i	$-0.811136\pi$
$281$		−	18.7454i		−	1.11826i	0.829081	−	0.559128i	$-0.188864\pi$
$282$	0.816740	−	1.41464i	0.0486362	−	0.0842403i
$283$	12.5662	+	21.7654i	0.746985	+	1.29382i	0.949261	+	0.314488i	$0.101833\pi$
$283$	12.5662	+	21.7654i	0.746985	+	1.29382i	−0.202276	+	0.979329i	$0.564834\pi$
$284$	9.26992	+	16.0560i	0.550069	+	0.952747i
$285$	6.82889	+	3.94266i	0.404508	+	0.233543i
$286$	−3.95392			−0.233800
$287$	−0.597926	+	0.221453i	−0.0352944	+	0.0130719i
$288$	4.43070			0.261082
$289$	0.0756136	−	0.130967i	0.00444786	−	0.00770392i
$290$	−0.596682	−	1.03348i	−0.0350384	−	0.0606883i
$291$	7.37349	−	4.25708i	0.432241	−	0.249555i
$292$	−0.229642	−	0.132584i	−0.0134388	−	0.00775889i
$293$	8.60003			0.502419			0.251210	−	0.967933i	$-0.419172\pi$
$293$	8.60003			0.502419			0.251210	+	0.967933i	$0.419172\pi$
$294$	−1.89807	−	2.21092i	−0.110698	−	0.128943i
$295$			0.883527i			0.0514409i
$296$	−5.68604	−	3.28284i	−0.330494	−	0.190811i
$297$	1.40375	+	2.43137i	0.0814539	+	0.141082i
$298$	4.35508	−	2.51440i	0.252283	−	0.145656i
$299$	16.1002	+	2.01136i	0.931100	+	0.116320i
$300$		−	6.06498i		−	0.350162i
$301$	−8.33680	+	3.08768i	−0.480525	+	0.177971i
$302$	−4.58157			−0.263639
$303$	5.89435	−	10.2093i	0.338622	−	0.586510i
$304$	9.09649	+	15.7556i	0.521719	+	0.903644i
$305$	0.875450	+	1.51632i	0.0501281	+	0.0868245i
$306$	0.854341	−	1.47976i	0.0488394	−	0.0845923i
$307$			10.3669i			0.591670i	0.955239	+	0.295835i	$0.0955978\pi$
$307$			10.3669i			0.591670i	−0.955239	+	0.295835i	$0.904402\pi$
$308$	2.28082	−	13.3757i	0.129962	−	0.762152i
$309$		−	13.0770i		−	0.743927i
$310$	−3.36405	−	1.94224i	−0.191065	−	0.110312i
$311$	−25.8773	+	14.9403i	−1.46737	+	0.847184i	−0.999333	−	0.0365262i	$-0.988371\pi$
$311$	−25.8773	+	14.9403i	−1.46737	+	0.847184i	−0.468034	+	0.883711i	$0.655037\pi$
$312$	2.69466	+	4.66729i	0.152555	+	0.264233i
$313$	−7.87441	+	13.6389i	−0.445088	+	0.770915i	−0.998058	−	0.0622857i	$-0.980161\pi$
$313$	−7.87441	+	13.6389i	−0.445088	+	0.770915i	0.552970	+	0.833201i	$0.313494\pi$
$314$	−8.89299			−0.501860
$315$	−2.18936	+	2.63925i	−0.123356	+	0.148705i
$316$		−	14.9725i		−	0.842271i
$317$	17.2999	−	29.9643i	0.971659	−	1.68296i	0.281111	−	0.959675i	$-0.409297\pi$
$317$	17.2999	−	29.9643i	0.971659	−	1.68296i	0.690548	−	0.723287i	$-0.257370\pi$
$318$	−1.44310	−	2.49951i	−0.0809248	−	0.140166i
$319$	5.37789	−	3.10493i	0.301104	−	0.173842i
$320$	−2.68050	+	4.64277i	−0.149845	+	0.259539i
$321$	5.04385			0.281520
$322$	1.52645	−	5.05652i	0.0850657	−	0.281789i
$323$	24.9729			1.38953
$324$	0.913359	−	1.58198i	0.0507422	−	0.0878880i
$325$	9.72790	−	5.61641i	0.539607	−	0.311542i
$326$	2.82687	+	4.89628i	0.156566	+	0.271180i
$327$	1.07287	−	1.85827i	0.0593299	−	0.102762i
$328$		−	0.383897i		−	0.0211972i
$329$	−1.74516	+	10.2344i	−0.0962140	+	0.564240i
$330$	1.51472			0.0833826
$331$	−6.61046	+	11.4497i	−0.363344	+	0.629330i	−0.988509	−	0.151163i	$-0.951698\pi$
$331$	−6.61046	+	11.4497i	−0.363344	+	0.629330i	0.625165	+	0.780492i	$0.285032\pi$
$332$	−7.88809	−	13.6626i	−0.432915	−	0.749831i
$333$	−3.56949	+	2.06085i	−0.195607	+	0.112934i
$334$	0.153734	+	0.0887584i	0.00841195	+	0.00485664i
$335$		−	4.89691i		−	0.267547i
$336$	−7.41917	+	2.74783i	−0.404749	+	0.149906i
$337$			19.0448i			1.03744i	0.854946	+	0.518718i	$0.173590\pi$
$337$			19.0448i			1.03744i	−0.854946	+	0.518718i	$0.826410\pi$
$338$	0.323399	−	0.560143i	0.0175906	−	0.0304678i
$339$	−10.3288	−	17.8901i	−0.560986	−	0.971656i
$340$	4.85916	+	8.41630i	0.263525	+	0.456438i
$341$	10.1067	−	17.5054i	0.547310	−	0.947968i
$342$	−2.53257			−0.136946
$343$	16.1933	+	8.98754i	0.874358	+	0.485282i
$344$		−	5.35262i		−	0.288594i
$345$	−6.16789	−	0.770537i	−0.332068	−	0.0414843i
$346$	5.16528	−	2.98218i	0.277687	−	0.160323i
$347$	9.83637	+	17.0371i	0.528044	+	0.914599i	0.999466	+	0.0326908i	$0.0104077\pi$
$347$	9.83637	+	17.0371i	0.528044	+	0.914599i	−0.471422	+	0.881908i	$0.656259\pi$
$348$	−3.49915	−	2.02024i	−0.187574	−	0.108296i
$349$			35.3155i			1.89040i	0.326499	+	0.945198i	$0.394131\pi$
$349$			35.3155i			1.89040i	−0.326499	+	0.945198i	$0.605869\pi$
$350$	−1.27000	−	3.42902i	−0.0678844	−	0.183289i
$351$	3.38323			0.180583
$352$	10.7727	+	6.21960i	0.574185	+	0.331506i
$353$	−12.5436	+	7.24207i	−0.667630	+	0.385456i	−0.795178	−	0.606376i	$-0.792623\pi$
$353$	−12.5436	+	7.24207i	−0.667630	+	0.385456i	0.127548	+	0.991832i	$0.459289\pi$
$354$	−0.141883	−	0.245749i	−0.00754102	−	0.0130614i
$355$	6.57718	−	11.3920i	0.349081	−	0.604625i
$356$	7.07602			0.375028
$357$	−1.82551	+	10.7056i	−0.0966160	+	0.566598i
$358$	5.40466			0.285645
$359$	−14.0688	−	8.12264i	−0.742524	−	0.428696i	0.0804624	−	0.996758i	$-0.474360\pi$
$359$	−14.0688	−	8.12264i	−0.742524	−	0.428696i	−0.822986	+	0.568061i	$0.807694\pi$
$360$	−1.03231	−	1.78801i	−0.0544073	−	0.0942363i
$361$	−9.00709	−	15.6007i	−0.474057	−	0.821092i
$362$	0.785779	−	1.36101i	0.0412996	−	0.0715331i
$363$		−	3.11792i		−	0.163648i
$364$	−12.5849	−	10.4396i	−0.659626	−	0.547184i
$365$			0.188142i			0.00984778i
$366$	−0.487005	−	0.281173i	−0.0254562	−	0.0146971i
$367$	2.94340	+	5.09812i	0.153644	+	0.266120i	0.932565	−	0.361003i	$-0.117566\pi$
$367$	2.94340	+	5.09812i	0.153644	+	0.266120i	−0.778920	+	0.627123i	$0.784232\pi$
$368$	−11.4351	−	8.65486i	−0.596096	−	0.451166i
$369$	−0.208709	−	0.120498i	−0.0108650	−	0.00627290i
$370$			2.22376i			0.115608i
$371$	14.1187	+	11.7120i	0.733005	+	0.608055i
$372$	−13.1520			−0.681899
$373$	23.0048	+	13.2818i	1.19114	+	0.687708i	0.958566	−	0.284870i	$-0.0919505\pi$
$373$	23.0048	+	13.2818i	1.19114	+	0.687708i	0.232578	+	0.972578i	$0.425284\pi$
$374$	4.15444	−	2.39856i	0.214821	−	0.124027i
$375$	−9.33893	+	5.39183i	−0.482260	+	0.278433i
$376$	−5.41341	−	3.12543i	−0.279175	−	0.161182i
$377$		−	7.48328i		−	0.385408i
$378$	0.185130	−	1.08568i	0.00952205	−	0.0558414i
$379$			35.7093i			1.83426i	0.398585	+	0.917131i	$0.369501\pi$
$379$			35.7093i			1.83426i	−0.398585	+	0.917131i	$0.630499\pi$
$380$	7.20213	−	12.4744i	0.369461	−	0.639926i
$381$	−11.8450	+	6.83870i	−0.606836	+	0.350357i
$382$	−1.24232	+	0.717255i	−0.0635627	+	0.0366980i
$383$	−6.39128	+	11.0700i	−0.326579	+	0.565651i	−0.981831	−	0.189759i	$-0.939229\pi$
$383$	−6.39128	+	11.0700i	−0.326579	+	0.565651i	0.655252	+	0.755411i	$0.272563\pi$
$384$		−	10.5832i		−	0.540073i
$385$	−9.02800	+	3.34368i	−0.460109	+	0.170410i
$386$	−3.59965			−0.183217
$387$	−2.91001	−	1.68009i	−0.147924	−	0.0854039i
$388$	−7.77649	−	13.4693i	−0.394792	−	0.683799i
$389$	9.43612	−	5.44795i	0.478430	−	0.276222i	−0.241332	−	0.970443i	$-0.577584\pi$
$389$	9.43612	−	5.44795i	0.478430	−	0.276222i	0.719762	+	0.694221i	$0.244251\pi$
$390$	0.912669	−	1.58079i	0.0462148	−	0.0800463i
$391$	−18.1369	+	7.65351i	−0.917220	+	0.387055i
$392$	−8.46056	+	7.26338i	−0.427323	+	0.366856i
$393$	−4.48708			−0.226343
$394$	2.71380	−	4.70044i	0.136719	−	0.236805i
$395$	−9.20004	+	5.31165i	−0.462904	+	0.267258i
$396$	4.44143	−	2.56426i	0.223190	−	0.128859i
$397$	−29.6816	−	17.1367i	−1.48968	−	0.860066i	−0.489748	−	0.871864i	$-0.662911\pi$
$397$	−29.6816	−	17.1367i	−1.48968	−	0.860066i	−0.999930	+	0.0117982i	$0.996244\pi$
$398$	−3.72343			−0.186639
$399$	15.0945	−	5.59054i	0.755672	−	0.279877i
$400$	−9.92836			−0.496418
$401$	30.8591	+	17.8165i	1.54103	+	0.889713i	0.998774	+	0.0494981i	$0.0157622\pi$
$401$	30.8591	+	17.8165i	1.54103	+	0.889713i	0.542254	+	0.840215i	$0.317571\pi$
$402$	0.786383	+	1.36206i	0.0392212	+	0.0679331i
$403$	−12.1793	−	21.0951i	−0.606692	−	1.05082i
$404$	−18.6495	−	10.7673i	−0.927850	−	0.535694i
$405$	−1.29609			−0.0644032
$406$	−2.40139	−	0.409484i	−0.119179	−	0.0203224i
$407$	−11.5717			−0.573587
$408$	−5.66263	−	3.26932i	−0.280342	−	0.161856i
$409$	17.3884	−	10.0392i	0.859801	−	0.496406i	−0.00414480	−	0.999991i	$-0.501319\pi$
$409$	17.3884	−	10.0392i	0.859801	−	0.496406i	0.863946	+	0.503585i	$0.167986\pi$
$410$	−0.112604	+	0.0650120i	−0.00556112	+	0.00321071i
$411$	11.6214	−	20.1289i	0.573243	−	0.992885i
$412$	−23.8881			−1.17688
$413$	1.38813	+	1.15151i	0.0683055	+	0.0566619i
$414$	1.83931	−	0.776164i	0.0903971	−	0.0381464i
$415$	−5.59674	+	9.69384i	−0.274733	+	0.475852i
$416$	12.9818	−	7.49503i	0.636484	−	0.367474i
$417$	5.57679	+	9.65928i	0.273097	+	0.473017i
$418$	−6.15761	−	3.55510i	−0.301178	−	0.173885i
$419$	14.4789			0.707343			0.353671	−	0.935370i	$-0.384933\pi$
$419$	14.4789			0.707343			0.353671	+	0.935370i	$0.384933\pi$
$420$	4.82117	+	3.99934i	0.235249	+	0.195148i
$421$			5.46052i			0.266129i	0.991107	+	0.133065i	$0.0424818\pi$
$421$			5.46052i			0.266129i	−0.991107	+	0.133065i	$0.957518\pi$
$422$	−0.672919	+	1.16553i	−0.0327572	+	0.0567371i
$423$	−3.39835	+	1.96204i	−0.165233	+	0.0953974i
$424$	−9.56494	+	5.52232i	−0.464514	+	0.268187i
$425$	−6.81415	+	11.8025i	−0.330535	+	0.572503i
$426$			4.22485i			0.204695i
$427$	3.52331	+	0.600794i	0.170505	+	0.0290745i
$428$		−	9.21369i		−	0.445361i
$429$	8.22587	+	4.74921i	0.397149	+	0.229294i
$430$	−1.57002	+	0.906453i	−0.0757132	+	0.0437131i
$431$	−4.07918	+	2.35512i	−0.196487	+	0.113442i	−0.595016	−	0.803714i	$-0.702854\pi$
$431$	−4.07918	+	2.35512i	−0.196487	+	0.113442i	0.398529	+	0.917156i	$0.369521\pi$
$432$	−2.58970	−	1.49517i	−0.124597	−	0.0719362i
$433$	−11.8433			−0.569151			−0.284576	−	0.958654i	$-0.591853\pi$
$433$	−11.8433			−0.569151			−0.284576	+	0.958654i	$0.591853\pi$
$434$	−7.43589	+	2.75402i	−0.356934	+	0.132197i
$435$			2.86679i			0.137452i
$436$	−3.39453	−	1.95983i	−0.162568	−	0.0938589i
$437$	23.2651	+	17.6086i	1.11292	+	0.842333i
$438$	−0.0302132	−	0.0523308i	−0.00144364	−	0.00250046i
$439$	−24.8602	−	14.3530i	−1.18651	−	0.685032i	−0.228999	−	0.973427i	$-0.573545\pi$
$439$	−24.8602	−	14.3530i	−1.18651	−	0.685032i	−0.957512	+	0.288395i	$0.906879\pi$
$440$		−	5.79641i		−	0.276333i
$441$	1.29319	+	6.87951i	0.0615804	+	0.327596i
$442$		−	5.78085i		−	0.274967i
$443$	19.2032	−	33.2609i	0.912372	−	1.58027i	0.101668	−	0.994818i	$-0.467582\pi$
$443$	19.2032	−	33.2609i	0.912372	−	1.58027i	0.810704	−	0.585456i	$-0.199085\pi$
$444$	3.76459	+	6.52046i	0.178659	+	0.309447i
$445$	−2.51028	−	4.34794i	−0.118999	−	0.206112i
$446$	−5.61394	−	3.24121i	−0.265828	−	0.153476i
$447$	−12.0806			−0.571392
$448$	3.80085	+	10.2624i	0.179573	+	0.484851i
$449$	16.2724			0.767941			0.383970	−	0.923345i	$-0.374556\pi$
$449$	16.2724			0.767941			0.383970	+	0.923345i	$0.374556\pi$
$450$	0.691042	−	1.19692i	0.0325761	−	0.0564234i
$451$	−0.338300	−	0.585952i	−0.0159299	−	0.0275914i
$452$	−32.6801	+	18.8679i	−1.53714	+	0.887471i
$453$	9.53164	+	5.50309i	0.447835	+	0.258558i
$454$	−10.6600			−0.500297
$455$	−1.95014	+	11.4364i	−0.0914239	+	0.536149i
$456$			9.69142i			0.453842i
$457$	−27.2086	−	15.7089i	−1.27277	−	0.734832i	−0.297259	−	0.954797i	$-0.596072\pi$
$457$	−27.2086	−	15.7089i	−1.27277	−	0.734832i	−0.975508	+	0.219965i	$0.929406\pi$
$458$	2.89685	+	5.01748i	0.135361	+	0.234452i
$459$	−3.55480	+	2.05236i	−0.165924	+	0.0957961i
$460$	−1.40755	+	11.2670i	−0.0656276	+	0.525326i
$461$			23.0035i			1.07138i	0.844415	+	0.535689i	$0.179948\pi$
$461$			23.0035i			1.07138i	−0.844415	+	0.535689i	$0.820052\pi$
$462$	1.97415	−	2.37981i	0.0918455	−	0.110719i
$463$	17.2955			0.803790			0.401895	−	0.915686i	$-0.368352\pi$
$463$	17.2955			0.803790			0.401895	+	0.915686i	$0.368352\pi$
$464$	−3.30712	+	5.72811i	−0.153529	+	0.265921i
$465$	4.66579	+	8.08139i	0.216371	+	0.374765i
$466$	3.48628	+	6.03842i	0.161499	+	0.279725i
$467$	−17.5237	+	30.3520i	−0.810902	+	1.40452i	0.101331	+	0.994853i	$0.467690\pi$
$467$	−17.5237	+	30.3520i	−0.810902	+	1.40452i	−0.912233	+	0.409671i	$0.865644\pi$
$468$		−	6.18020i		−	0.285680i
$469$	−7.69366	−	6.38218i	−0.355260	−	0.294702i
$470$			2.11714i			0.0976563i
$471$	18.5013	+	10.6817i	0.852493	+	0.492187i
$472$	−0.940413	+	0.542948i	−0.0432860	+	0.0249912i
$473$	−4.71687	−	8.16985i	−0.216882	−	0.375650i
$474$	1.70597	−	2.95482i	0.0783577	−	0.135720i
$475$	20.1996			0.926819
$476$	19.5560	+	3.33469i	0.896349	+	0.152845i
$477$			6.93343i			0.317460i
$478$	−1.72017	+	2.97942i	−0.0786786	+	0.136275i
$479$	−19.6351	−	34.0089i	−0.897149	−	1.55391i	−0.831122	−	0.556090i	$-0.812301\pi$
$479$	−19.6351	−	34.0089i	−0.897149	−	1.55391i	−0.0660270	−	0.997818i	$-0.521032\pi$
$480$	−4.97323	+	2.87129i	−0.226996	+	0.131056i
$481$	−6.97231	+	12.0764i	−0.317910	+	0.550637i
$482$	10.8626			0.494776
$483$	−9.24926	+	8.68627i	−0.420856	+	0.395239i
$484$	−5.69556			−0.258889
$485$	−5.51756	+	9.55670i	−0.250540	+	0.433947i
$486$	0.360502	−	0.208136i	0.0163527	−	0.00944124i
$487$	−12.7333	−	22.0547i	−0.576999	−	0.999392i	−0.995821	−	0.0913237i	$-0.970890\pi$
$487$	−12.7333	−	22.0547i	−0.576999	−	0.999392i	0.418822	−	0.908068i	$-0.362443\pi$
$488$	−1.07597	+	1.86363i	−0.0487068	+	0.0843627i
$489$		−	13.5818i		−	0.614192i
$490$	3.56326	+	1.25160i	0.160972	+	0.0565417i
$491$	−18.1317			−0.818274			−0.409137	−	0.912473i	$-0.634170\pi$
$491$	−18.1317			−0.818274			−0.409137	+	0.912473i	$0.634170\pi$
$492$	−0.220117	+	0.381253i	−0.00992362	+	0.0171882i
$493$	4.53957	+	7.86277i	0.204452	+	0.354121i
$494$	−7.42032	+	4.28412i	−0.333856	+	0.192752i
$495$	−3.15127	−	1.81939i	−0.141639	−	0.0817755i
$496$			21.5298i			0.966716i
$497$	−9.32619	−	25.1809i	−0.418337	−	1.12952i
$498$		−	3.59507i		−	0.161099i
$499$	3.93276	−	6.81173i	0.176054	−	0.304935i	−0.764471	−	0.644658i	$-0.777000\pi$
$499$	3.93276	−	6.81173i	0.176054	−	0.304935i	0.940526	+	0.339723i	$0.110333\pi$
$500$	9.84936	+	17.0596i	0.440477	+	0.762928i
$501$	−0.213222	−	0.369312i	−0.00952607	−	0.0164996i
$502$	2.83298	−	4.90686i	0.126442	−	0.219004i
$503$	−34.6468			−1.54482			−0.772412	−	0.635122i	$-0.780950\pi$
$503$	−34.6468			−1.54482			−0.772412	+	0.635122i	$0.780950\pi$
$504$	−4.15459	−	0.708439i	−0.185060	−	0.0315564i
$505$			15.2792i			0.679917i
$506$	5.56158	+	0.694794i	0.247243	+	0.0308873i
$507$	−1.34562	+	0.776893i	−0.0597610	+	0.0345030i
$508$	12.4924	+	21.6374i	0.554259	+	0.960006i
$509$	−2.04296	−	1.17950i	−0.0905527	−	0.0522806i	0.454040	−	0.890981i	$-0.349982\pi$
$509$	−2.04296	−	1.17950i	−0.0905527	−	0.0522806i	−0.544593	+	0.838701i	$0.683316\pi$
$510$			2.21461i			0.0980644i
$511$	0.295594	+	0.245206i	0.0130763	+	0.0108473i
$512$	−22.7762			−1.00658
$513$	5.26884	+	3.04196i	0.232625	+	0.134306i
$514$	1.67960	−	0.969719i	0.0740841	−	0.0427725i
$515$	8.47451	+	14.6783i	0.373432	+	0.646802i
$516$	−3.06906	+	5.31576i	−0.135108	+	0.234013i
$517$	−11.0168			−0.484520
$518$	3.49381	+	2.89824i	0.153509	+	0.127341i
$519$	−14.3280			−0.628931
$520$	−6.04923	−	3.49253i	−0.265276	−	0.153157i
$521$	15.1524	+	26.2447i	0.663839	+	1.14980i	0.979599	+	0.200963i	$0.0644072\pi$
$521$	15.1524	+	26.2447i	0.663839	+	1.14980i	−0.315760	+	0.948839i	$0.602259\pi$
$522$	−0.460371	−	0.797386i	−0.0201499	−	0.0349006i
$523$	13.2982	−	23.0332i	0.581490	−	1.00717i	−0.413813	−	0.910362i	$-0.635803\pi$
$523$	13.2982	−	23.0332i	0.581490	−	1.00717i	0.995303	−	0.0968083i	$-0.0308634\pi$
$524$			8.19662i			0.358071i
$525$	−1.47658	+	8.65930i	−0.0644432	+	0.377923i
$526$		−	12.7554i		−	0.556160i
$527$	25.5938	+	14.7766i	1.11488	+	0.643678i
$528$	−4.19769	−	7.27061i	−0.182681	−	0.316413i
$529$	−22.2931	−	5.65835i	−0.969266	−	0.246015i
$530$	3.23960	+	1.87038i	0.140719	+	0.0812442i
$531$			0.681687i			0.0295827i
$532$	−10.2123	−	27.5735i	−0.442761	−	1.19546i
$533$	−0.815347			−0.0353166
$534$	1.39645	+	0.806241i	0.0604303	+	0.0348894i
$535$	−5.66145	+	3.26864i	−0.244766	+	0.141316i
$536$	5.21220	−	3.00927i	0.225133	−	0.129980i
$537$	−11.2440	−	6.49175i	−0.485216	−	0.280140i
$538$			10.0369i			0.432723i
$539$	−6.51290	+	18.5419i	−0.280531	+	0.798658i
$540$			2.36759i			0.101885i
$541$	12.6830	−	21.9676i	0.545284	−	0.944460i	−0.453305	−	0.891356i	$-0.649755\pi$
$541$	12.6830	−	21.9676i	0.545284	−	0.944460i	0.998589	−	0.0531042i	$-0.0169115\pi$
$542$	4.43985	−	2.56335i	0.190708	−	0.110105i
$543$	−3.26952	+	1.88766i	−0.140309	+	0.0810072i
$544$	−9.09341	+	15.7502i	−0.389877	+	0.675286i
$545$			2.78107i			0.119128i
$546$	−1.29413	−	3.49417i	−0.0553836	−	0.149537i
$547$	−3.00044			−0.128290			−0.0641448	−	0.997941i	$-0.520432\pi$
$547$	−3.00044			−0.128290			−0.0641448	+	0.997941i	$0.520432\pi$
$548$	−36.7698	−	21.2291i	−1.57073	−	0.906861i
$549$	0.675455	+	1.16992i	0.0288277	+	0.0499310i
$550$	3.36036	−	1.94010i	0.143286	−	0.0827263i
$551$	6.72845	−	11.6540i	0.286642	−	0.496478i
$552$	−2.97016	−	7.03852i	−0.126418	−	0.299579i
$553$	−3.64521	+	21.3771i	−0.155010	+	0.909047i
$554$	−9.58561			−0.407253
$555$	2.67105	−	4.62639i	0.113380	−	0.196379i
$556$	17.6448	−	10.1872i	0.748306	−	0.432034i
$557$	−0.716386	+	0.413606i	−0.0303543	+	0.0175250i	−0.515100	−	0.857130i	$-0.672245\pi$
$557$	−0.716386	+	0.413606i	−0.0303543	+	0.0175250i	0.484746	+	0.874655i	$0.338912\pi$
$558$	−2.59554	−	1.49854i	−0.109878	−	0.0634381i
$559$	−11.3683			−0.480826
$560$	6.54691	−	7.89225i	0.276658	−	0.333508i
$561$	−11.5240			−0.486545
$562$	−6.75775	−	3.90159i	−0.285059	−	0.164579i
$563$	−12.5287	−	21.7004i	−0.528023	−	0.914562i	−0.999466	−	0.0326661i	$-0.989600\pi$
$563$	−12.5287	−	21.7004i	−0.528023	−	0.914562i	0.471443	−	0.881896i	$-0.343733\pi$
$564$	3.58409	+	6.20782i	0.150917	+	0.261396i
$565$	23.1872	+	13.3871i	0.975491	+	0.563200i
$566$	10.4619			0.439748
$567$	−1.68920	+	2.03632i	−0.0709398	+	0.0855174i
$568$	16.1673			0.678366
$569$	−5.70825	−	3.29566i	−0.239302	−	0.138161i	0.375554	−	0.926801i	$-0.377453\pi$
$569$	−5.70825	−	3.29566i	−0.239302	−	0.138161i	−0.614856	+	0.788639i	$0.710786\pi$
$570$	2.84267	−	1.64122i	0.119066	−	0.0687431i
$571$	9.07398	−	5.23887i	0.379734	−	0.219240i	−0.297968	−	0.954576i	$-0.596309\pi$
$571$	9.07398	−	5.23887i	0.379734	−	0.219240i	0.677703	+	0.735336i	$0.262976\pi$
$572$	8.67546	−	15.0263i	0.362739	−	0.628283i
$573$	3.44609			0.143962
$574$	−0.0446157	+	0.261646i	−0.00186222	+	0.0109209i
$575$	−14.6702	+	6.19062i	−0.611789	+	0.258167i
$576$	−2.06815	+	3.58213i	−0.0861727	+	0.149256i
$577$	28.5827	−	16.5022i	1.18991	−	0.686996i	0.231626	−	0.972805i	$-0.425596\pi$
$577$	28.5827	−	16.5022i	1.18991	−	0.686996i	0.958287	+	0.285809i	$0.0922622\pi$
$578$	−0.0314758	−	0.0545177i	−0.00130922	−	0.00226764i
$579$	7.48882	+	4.32367i	0.311225	+	0.179686i
$580$	5.23682			0.217447
$581$	7.93596	+	21.4272i	0.329239	+	0.888951i
$582$		−	3.54421i		−	0.146912i
$583$	−9.73281	+	16.8577i	−0.403092	+	0.698176i
$584$	−0.200255	+	0.115617i	−0.00828662	+	0.00478428i
$585$	−3.79749	+	2.19248i	−0.157007	+	0.0906480i
$586$	1.78998	−	3.10033i	0.0739432	−	0.128073i
$587$		−	12.9758i		−	0.535567i	−0.963479	−	0.267783i	$-0.913709\pi$
$587$		−	12.9758i		−	0.535567i	0.963479	−	0.267783i	$-0.0862911\pi$
$588$	12.5669	−	2.36229i	0.518251	−	0.0974193i
$589$		−	43.8030i		−	1.80487i
$590$	0.318513	+	0.183894i	0.0131130	+	0.00757079i
$591$	−11.2918	+	6.51930i	−0.464481	+	0.268168i
$592$	10.6740	−	6.16262i	0.438698	−	0.253282i
$593$	−31.4273	−	18.1446i	−1.29057	−	0.745109i	−0.311811	−	0.950144i	$-0.600936\pi$
$593$	−31.4273	−	18.1446i	−1.29057	−	0.745109i	−0.978755	+	0.205036i	$0.934269\pi$
$594$	1.16868			0.0479517
$595$	−4.88865	−	13.1994i	−0.200415	−	0.541124i
$596$			22.0678i			0.903933i
$597$	7.74636	+	4.47236i	0.317037	+	0.183042i
$598$	4.07613	−	5.38553i	0.166686	−	0.220231i
$599$	−15.5154	−	26.8734i	−0.633940	−	1.09802i	−0.986739	−	0.162317i	$-0.948103\pi$
$599$	−15.5154	−	26.8734i	−0.633940	−	1.09802i	0.352799	−	0.935699i	$-0.385230\pi$
$600$	−4.58028	−	2.64442i	−0.186989	−	0.107958i
$601$			20.7835i			0.847776i	0.905715	+	0.423888i	$0.139335\pi$
$601$			20.7835i			0.847776i	−0.905715	+	0.423888i	$0.860665\pi$
$602$	−0.622070	+	3.64809i	−0.0253537	+	0.148685i
$603$		−	3.77822i		−	0.153861i
$604$	10.0526	−	17.4116i	0.409035	−	0.708469i
$605$	2.02055	+	3.49970i	0.0821472	+	0.142283i
$606$	−2.45365	−	4.24985i	−0.0996729	−	0.172638i
$607$	16.9902	+	9.80932i	0.689613	+	0.398148i	0.803467	−	0.595349i	$-0.202986\pi$
$607$	16.9902	+	9.80932i	0.689613	+	0.398148i	−0.113854	+	0.993497i	$0.536320\pi$
$608$	26.9561			1.09321
$609$	4.50409	+	3.73631i	0.182515	+	0.151403i
$610$	0.728850			0.0295103
$611$	−6.63801	+	11.4974i	−0.268545	+	0.465134i
$612$	3.74909	+	6.49361i	0.151548	+	0.262489i
$613$	40.0742	−	23.1368i	1.61858	−	0.934488i	0.631292	−	0.775545i	$-0.282525\pi$
$613$	40.0742	−	23.1368i	1.61858	−	0.934488i	0.987288	−	0.158943i	$-0.0508085\pi$
$614$	3.73728	+	2.15772i	0.150824	+	0.0870786i
$615$	0.312354			0.0125953
$616$	−9.10688	−	7.55450i	−0.366927	−	0.304379i
$617$		−	30.5101i		−	1.22829i	−0.789193	−	0.614146i	$-0.789501\pi$
$617$		−	30.5101i		−	1.22829i	0.789193	−	0.614146i	$-0.210499\pi$
$618$	−4.71430	−	2.72180i	−0.189637	−	0.109487i
$619$	−4.76427	−	8.25196i	−0.191492	−	0.331674i	0.754253	−	0.656584i	$-0.227999\pi$
$619$	−4.76427	−	8.25196i	−0.191492	−	0.331674i	−0.945745	+	0.324910i	$0.894666\pi$
$620$	14.7624	−	8.52308i	0.592873	−	0.342295i
$621$	−4.75884	−	0.594509i	−0.190966	−	0.0238568i
$622$			12.4384i			0.498735i
$623$	−10.1028	−	1.72273i	−0.404761	−	0.0690197i
$624$	−10.1170			−0.405003
$625$	−1.31208	+	2.27258i	−0.0524830	+	0.0909032i
$626$	3.27790	+	5.67748i	0.131011	+	0.226918i
$627$	8.54033	+	14.7923i	0.341068	+	0.590747i
$628$	19.5125	−	33.7966i	0.778632	−	1.34863i
$629$		−	16.9184i		−	0.674582i
$630$	0.495772	+	1.33859i	0.0197520	+	0.0533308i
$631$		−	7.71076i		−	0.306960i	−0.988152	−	0.153480i	$-0.950952\pi$
$631$		−	7.71076i		−	0.306960i	0.988152	−	0.153480i	$-0.0490481\pi$
$632$	−11.3073	−	6.52826i	−0.449779	−	0.259680i
$633$	2.79993	−	1.61654i	0.111287	−	0.0642516i
$634$	−7.20146	−	12.4733i	−0.286006	−	0.495378i
$635$	8.86357	−	15.3522i	0.351740	−	0.609232i
$636$	12.6654			0.502216
$637$	15.4265	+	17.9691i	0.611219	+	0.711962i
$638$		−	2.58499i		−	0.102341i
$639$	5.07463	−	8.78952i	0.200749	−	0.347708i
$640$	6.85841	+	11.8791i	0.271102	+	0.469563i
$641$	3.53672	−	2.04193i	0.139692	−	0.0806512i	−0.428525	−	0.903530i	$-0.640967\pi$
$641$	3.53672	−	2.04193i	0.139692	−	0.0806512i	0.568217	+	0.822879i	$0.307633\pi$
$642$	1.04981	−	1.81832i	0.0414326	−	0.0717633i
$643$	12.6742			0.499820			0.249910	−	0.968269i	$-0.419599\pi$
$643$	12.6742			0.499820			0.249910	+	0.968269i	$0.419599\pi$
$644$	15.8674	+	16.8958i	0.625262	+	0.665787i
$645$	4.35510			0.171482
$646$	5.19775	−	9.00276i	0.204503	−	0.354209i
$647$	26.2316	−	15.1448i	1.03127	−	0.595405i	0.113923	−	0.993490i	$-0.463658\pi$
$647$	26.2316	−	15.1448i	1.03127	−	0.595405i	0.917349	+	0.398084i	$0.130325\pi$
$648$	−0.796477	−	1.37954i	−0.0312886	−	0.0541934i
$649$	−0.956919	+	1.65743i	−0.0375624	+	0.0650599i
$650$		−	4.67590i		−	0.183404i
$651$	18.7778	+	3.20198i	0.735961	+	0.125496i
$652$	−24.8102			−0.971642
$653$	−5.64151	+	9.77138i	−0.220769	+	0.382384i	−0.955042	−	0.296471i	$-0.904190\pi$
$653$	−5.64151	+	9.77138i	−0.220769	+	0.382384i	0.734272	+	0.678855i	$0.237523\pi$
$654$	−0.446606	−	0.773544i	−0.0174637	−	0.0302479i
$655$	5.03650	−	2.90783i	0.196793	−	0.113618i
$656$	0.624111	+	0.360330i	0.0243674	+	0.0140685i
$657$			0.145161i			0.00566327i
$658$	3.32629	+	2.75928i	0.129672	+	0.107568i
$659$		−	26.5417i		−	1.03392i	−0.856010	−	0.516960i	$-0.827064\pi$
$659$		−	26.5417i		−	1.03392i	0.856010	−	0.516960i	$-0.172936\pi$
$660$	−3.32351	+	5.75649i	−0.129367	+	0.224071i
$661$	−20.0973	−	34.8095i	−0.781693	−	1.35393i	−0.930955	−	0.365135i	$-0.881023\pi$
$661$	−20.0973	−	34.8095i	−0.781693	−	1.35393i	0.149261	−	0.988798i	$-0.452310\pi$
$662$	2.75175	+	4.76617i	0.106950	+	0.185242i
$663$	−6.94361	+	12.0267i	−0.269667	+	0.467077i
$664$	−13.7573			−0.533887
$665$	−13.3199	+	16.0570i	−0.516524	+	0.622665i
$666$			1.71575i			0.0664838i
$667$	−1.31498	+	10.5260i	−0.0509163	+	0.407567i
$668$	−0.674628	+	0.389497i	−0.0261022	+	0.0150701i
$669$	7.78629	+	13.4862i	0.301035	+	0.521408i
$670$	−1.76535	−	1.01922i	−0.0682013	−	0.0393760i
$671$			3.79268i			0.146415i
$672$	−1.97048	+	11.5557i	−0.0760129	+	0.445772i
$673$	39.8949			1.53784			0.768918	−	0.639348i	$-0.220795\pi$
$673$	39.8949			1.53784			0.768918	+	0.639348i	$0.220795\pi$
$674$	6.86568	+	3.96390i	0.264456	+	0.152684i
$675$	−2.87533	+	1.66008i	−0.110672	+	0.0638963i
$676$	1.41916	+	2.45806i	0.0545832	+	0.0945409i
$677$	−4.92309	+	8.52703i	−0.189210	+	0.327721i	−0.944987	−	0.327108i	$-0.893926\pi$
$677$	−4.92309	+	8.52703i	−0.189210	+	0.327721i	0.755777	+	0.654829i	$0.227259\pi$
$678$	−8.59921			−0.330251
$679$	7.82369	+	21.1241i	0.300246	+	0.810668i
$680$	8.47467			0.324989
$681$	22.1773	+	12.8041i	0.849838	+	0.490654i
$682$	−4.20714	−	7.28699i	−0.161100	−	0.279033i
$683$	−14.4397	−	25.0103i	−0.552520	−	0.956993i	−0.998092	−	0.0617467i	$-0.980333\pi$
$683$	−14.4397	−	25.0103i	−0.552520	−	0.956993i	0.445572	−	0.895246i	$-0.353000\pi$
$684$	5.55681	−	9.62468i	0.212470	−	0.368009i
$685$			30.1248i			1.15101i
$686$	6.61044	−	3.96710i	0.252388	−	0.151465i
$687$		−	13.9181i		−	0.531007i
$688$	8.70189	+	5.02404i	0.331756	+	0.191540i
$689$	11.7287	+	20.3147i	0.446827	+	0.773927i
$690$	−1.56154	+	2.06316i	−0.0594468	+	0.0785431i
$691$	11.3374	+	6.54566i	0.431296	+	0.249009i	0.699899	−	0.714242i	$-0.253229\pi$
$691$	11.3374	+	6.54566i	0.431296	+	0.249009i	−0.268603	+	0.963251i	$0.586562\pi$
$692$			26.1733i			0.994958i
$693$	−6.96556	+	2.57982i	−0.264600	+	0.0979994i
$694$	8.18920			0.310858
$695$	−12.5193	−	7.22802i	−0.474884	−	0.274175i
$696$	−3.05137	+	1.76171i	−0.115662	+	0.0667774i
$697$	0.856695	−	0.494613i	0.0324496	−	0.0187348i
$698$	12.7313	+	7.35042i	0.481887	+	0.278218i
$699$		−	16.7500i		−	0.633545i
$700$	15.8181	+	2.69730i	0.597868	+	0.101948i
$701$			15.0246i			0.567471i	0.958903	+	0.283735i	$0.0915737\pi$
$701$			15.0246i			0.567471i	−0.958903	+	0.283735i	$0.908426\pi$
$702$	0.704171	−	1.21966i	0.0265772	−	0.0460331i
$703$	−21.7165	+	12.5381i	−0.819055	+	0.472882i
$704$	−10.0569	+	5.80633i	−0.379032	+	0.218834i
$705$	2.54297	−	4.40456i	0.0957740	−	0.165885i
$706$			6.02934i			0.226917i
$707$	24.0056	+	19.9135i	0.902822	+	0.748925i
$708$	1.24525			0.0467993
$709$	0.0358729	+	0.0207113i	0.00134724	+	0.000777827i	0.500673	−	0.865636i	$-0.333086\pi$
$709$	0.0358729	+	0.0207113i	0.00134724	+	0.000777827i	−0.499326	+	0.866414i	$0.666419\pi$
$710$	−2.73789	−	4.74217i	−0.102751	−	0.177971i
$711$	−7.09830	+	4.09821i	−0.266207	+	0.153695i
$712$	3.08526	−	5.34382i	0.115625	−	0.200268i
$713$	13.4244	+	31.8125i	0.502749	+	1.19139i
$714$	3.47942	+	2.88631i	0.130214	+	0.108017i
$715$	−12.3108			−0.460398
$716$	−11.8586	+	20.5397i	−0.443176	+	0.767604i
$717$	7.15738	−	4.13232i	0.267297	−	0.154324i
$718$	−5.85645	+	3.38122i	−0.218561	+	0.126186i
$719$	2.48281	+	1.43345i	0.0925932	+	0.0534587i	0.545582	−	0.838058i	$-0.316309\pi$
$719$	2.48281	+	1.43345i	0.0925932	+	0.0534587i	−0.452988	+	0.891516i	$0.649642\pi$
$720$	3.87574			0.144440
$721$	34.1063	+	5.81579i	1.27018	+	0.216591i
$722$	−7.49880			−0.279076
$723$	−22.5988	−	13.0474i	−0.840459	−	0.485239i
$724$	3.44822	+	5.97249i	0.128152	+	0.221966i
$725$	3.67188	+	6.35988i	0.136370	+	0.236200i
$726$	−1.12402	−	0.648951i	−0.0417162	−	0.0240848i
$727$	16.1319			0.598300			0.299150	−	0.954206i	$-0.403297\pi$
$727$	16.1319			0.598300			0.299150	+	0.954206i	$0.403297\pi$
$728$	−13.3712	+	4.95226i	−0.495569	+	0.183543i
$729$	−1.00000			−0.0370370
$730$	0.0678254	+	0.0391590i	0.00251033	+	0.00144934i
$731$	11.9448	−	6.89632i	0.441794	−	0.255070i
$732$	2.13712	−	1.23387i	0.0789901	−	0.0456050i
$733$	9.38450	−	16.2544i	0.346624	−	0.600371i	−0.639023	−	0.769187i	$-0.720661\pi$
$733$	9.38450	−	16.2544i	0.346624	−	0.600371i	0.985647	+	0.168817i	$0.0539946\pi$
$734$	2.45051			0.0904500
$735$	−5.90977	−	6.88384i	−0.217985	−	0.253914i
$736$	−19.5772	+	8.26131i	−0.721625	+	0.304516i
$737$	5.30368	−	9.18625i	0.195364	−	0.338380i
$738$	−0.0868798	+	0.0501601i	−0.00319809	+	0.00184642i
$739$	−21.6696	−	37.5329i	−0.797131	−	1.38067i	−0.921477	−	0.388432i	$-0.873017\pi$
$739$	−21.6696	−	37.5329i	−0.797131	−	1.38067i	0.124347	−	0.992239i	$-0.460316\pi$
$740$	−8.45110	−	4.87925i	−0.310669	−	0.179365i
$741$	20.5833			0.756146
$742$	7.16079	−	2.65213i	0.262881	−	0.0973627i
$743$			39.9810i			1.46676i	0.679819	+	0.733380i	$0.262058\pi$
$743$			39.9810i			1.46676i	−0.679819	+	0.733380i	$0.737942\pi$
$744$	−5.73447	+	9.93240i	−0.210236	+	0.364139i
$745$	13.5598	−	7.82876i	0.496793	−	0.286824i
$746$	9.57626	−	5.52886i	0.350612	−	0.202426i
$747$	−4.31817	+	7.47930i	−0.157994	+	0.273653i
$748$			21.0512i			0.769707i
$749$	−2.24317	+	13.1549i	−0.0819635	+	0.480669i
$750$			4.48894i			0.163913i
$751$	40.0065	+	23.0978i	1.45986	+	0.842850i	0.999004	−	0.0446250i	$-0.0142093\pi$
$751$	40.0065	+	23.0978i	1.45986	+	0.842850i	0.460855	+	0.887475i	$0.347543\pi$
$752$	10.1622	−	5.86714i	0.370577	−	0.213953i
$753$	−11.7876	+	6.80560i	−0.429566	+	0.248010i
$754$	−2.69774	−	1.55754i	−0.0982457	−	0.0567222i
$755$	−14.2650			−0.519157
$756$	3.71978	+	3.08570i	0.135287	+	0.112226i
$757$		−	44.6366i		−	1.62235i	−0.584807	−	0.811173i	$-0.698830\pi$
$757$		−	44.6366i		−	1.62235i	0.584807	−	0.811173i	$-0.301170\pi$
$758$	12.8733	+	7.43238i	0.467578	+	0.269956i
$759$	−10.7360	−	8.12570i	−0.389691	−	0.294944i
$760$	−6.28048	−	10.8781i	−0.227817	−	0.394590i
$761$	−18.8170	−	10.8640i	−0.682115	−	0.393819i	0.118536	−	0.992950i	$-0.462180\pi$
$761$	−18.8170	−	10.8640i	−0.682115	−	0.393819i	−0.800651	+	0.599130i	$0.795513\pi$
$762$			5.69352i			0.206254i
$763$	4.36941	+	3.62459i	0.158183	+	0.131219i
$764$		−	6.29503i		−	0.227746i
$765$	2.66005	−	4.60734i	0.0961742	−	0.166579i
$766$	2.66051	+	4.60814i	0.0961281	+	0.166499i
$767$	1.15315	+	1.99731i	0.0416378	+	0.0721188i
$768$	3.34899	+	1.93354i	0.120846	+	0.0697707i
$769$	1.28406			0.0463045			0.0231522	−	0.999732i	$-0.492630\pi$
$769$	1.28406			0.0463045			0.0231522	+	0.999732i	$0.492630\pi$
$770$	−0.673646	+	3.95055i	−0.0242765	+	0.142368i
$771$	−4.65906			−0.167792
$772$	7.89813	−	13.6800i	0.284260	−	0.492353i
$773$	−26.8737	−	46.5465i	−0.966578	−	1.67416i	−0.705314	−	0.708895i	\(-0.749194\

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.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.208136 - 0.360502i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.913359 + 1.58198i) q^{4} +(0.648045 - 1.12245i) q^{5} +0.416272i q^{6} +(-0.918903 - 2.48105i) q^{7} +1.59295 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.269763 - 0.467243i) q^{10} +(2.43137 - 1.40375i) q^{11} +(-1.58198 - 0.913359i) q^{12} -3.38323i q^{13} +(-1.08568 - 0.185130i) q^{14} +1.29609i q^{15} +(-1.49517 + 2.58970i) q^{16} +(2.05236 + 3.55480i) q^{17} +(-0.208136 - 0.360502i) q^{18} +(3.04196 - 5.26884i) q^{19} +2.36759 q^{20} +(2.03632 + 1.68920i) q^{21} -1.16868i q^{22} +(-0.594509 + 4.75884i) q^{23} +(-1.37954 + 0.796477i) q^{24} +(1.66008 + 2.87533i) q^{25} +(-1.21966 - 0.704171i) q^{26} +1.00000i q^{27} +(3.08570 - 3.71978i) q^{28} +2.21188 q^{29} +(0.467243 + 0.269763i) q^{30} +(6.23520 - 3.59990i) q^{31} +(2.21535 + 3.83710i) q^{32} +(-1.40375 + 2.43137i) q^{33} +1.70868 q^{34} +(-3.38034 - 0.576414i) q^{35} +1.82672 q^{36} +(-3.56949 - 2.06085i) q^{37} +(-1.26628 - 2.19327i) q^{38} +(1.69161 + 2.92996i) q^{39} +(1.03231 - 1.78801i) q^{40} -0.240997i q^{41} +(1.03279 - 0.382513i) q^{42} -3.36019i q^{43} +(4.44143 + 2.56426i) q^{44} +(-0.648045 - 1.12245i) q^{45} +(1.59183 + 1.20481i) q^{46} +(-3.39835 - 1.96204i) q^{47} -2.99033i q^{48} +(-5.31124 + 4.55969i) q^{49} +1.38208 q^{50} +(-3.55480 - 2.05236i) q^{51} +(5.35221 - 3.09010i) q^{52} +(-6.00452 + 3.46671i) q^{53} +(0.360502 + 0.208136i) q^{54} -3.63878i q^{55} +(-1.46377 - 3.95220i) q^{56} +6.08393i q^{57} +(0.460371 - 0.797386i) q^{58} +(-0.590358 + 0.340843i) q^{59} +(-2.05039 + 1.18380i) q^{60} +(-0.675455 + 1.16992i) q^{61} -2.99707i q^{62} +(-2.60811 - 0.444733i) q^{63} -4.13629 q^{64} +(-3.79749 - 2.19248i) q^{65} +(0.584342 + 1.01211i) q^{66} +(3.27203 - 1.88911i) q^{67} +(-3.74909 + 6.49361i) q^{68} +(-1.86456 - 4.41853i) q^{69} +(-0.911368 + 1.09865i) q^{70} +10.1493 q^{71} +(0.796477 - 1.37954i) q^{72} +(-0.125713 + 0.0725804i) q^{73} +(-1.48588 + 0.857873i) q^{74} +(-2.87533 - 1.66008i) q^{75} +11.1136 q^{76} +(-5.71697 - 4.74244i) q^{77} +1.40834 q^{78} +(-7.09830 - 4.09821i) q^{79} +(1.93787 + 3.35649i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.0868798 - 0.0501601i) q^{82} -8.63635 q^{83} +(-0.812401 + 4.76427i) q^{84} +5.32009 q^{85} +(-1.21135 - 0.699375i) q^{86} +(-1.91554 + 1.10594i) q^{87} +(3.87306 - 2.23611i) q^{88} +(1.93681 - 3.35466i) q^{89} -0.539526 q^{90} +(-8.39396 + 3.10885i) q^{91} +(-8.07141 + 3.40602i) q^{92} +(-3.59990 + 6.23520i) q^{93} +(-1.41464 + 0.816740i) q^{94} +(-3.94266 - 6.82889i) q^{95} +(-3.83710 - 2.21535i) q^{96} -8.51417 q^{97} +(0.538318 + 2.86375i) q^{98} -2.80750i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

Modular forms

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