LMFDB - Embedded newform 603.2.u.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (of order $11$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.1
Root			$0.142315 - 0.989821i$ of defining polynomial
Character	$\chi$	$=$	603.64
Dual form			603.2.u.a.424.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.459493 + 0.134919i) q^{2} +(-1.48958 - 0.957293i) q^{4} +(0.345139 + 0.755750i) q^{5} +(1.04408 + 0.306569i) q^{7} +(-1.18251 - 1.36469i) q^{8} +O(q^{10})$	\(q+(0.459493 + 0.134919i) q^{2} +(-1.48958 - 0.957293i) q^{4} +(0.345139 + 0.755750i) q^{5} +(1.04408 + 0.306569i) q^{7} +(-1.18251 - 1.36469i) q^{8} +(0.0566239 + 0.393828i) q^{10} +(-1.19505 - 2.61680i) q^{11} +(2.87491 - 3.31782i) q^{13} +(0.438384 + 0.281733i) q^{14} +(1.11189 + 2.43470i) q^{16} +(2.76321 - 1.77580i) q^{17} +(-3.40746 + 1.00052i) q^{19} +(0.209362 - 1.45615i) q^{20} +(-0.196061 - 1.36364i) q^{22} +(0.912860 - 6.34908i) q^{23} +(2.82227 - 3.25707i) q^{25} +(1.76864 - 1.13663i) q^{26} +(-1.26176 - 1.45615i) q^{28} +1.97270 q^{29} +(-1.76031 - 2.03151i) q^{31} +(0.696384 + 4.84346i) q^{32} +(1.50926 - 0.443160i) q^{34} +(0.128663 + 0.894870i) q^{35} +8.07686 q^{37} -1.70069 q^{38} +(0.623231 - 1.36469i) q^{40} +(2.28074 - 1.46575i) q^{41} +(-6.51473 + 4.18676i) q^{43} +(-0.724922 + 5.04194i) q^{44} +(1.27607 - 2.79420i) q^{46} +(1.56014 - 10.8510i) q^{47} +(-4.89266 - 3.14432i) q^{49} +(1.73625 - 1.11582i) q^{50} +(-7.45852 + 2.19002i) q^{52} +(-6.30856 - 4.05427i) q^{53} +(1.56519 - 1.80632i) q^{55} +(-0.816259 - 1.78736i) q^{56} +(0.906440 + 0.266155i) q^{58} +(6.97706 + 8.05195i) q^{59} +(-3.84302 + 8.41503i) q^{61} +(-0.534760 - 1.17096i) q^{62} +(0.428340 - 2.97917i) q^{64} +(3.49969 + 1.02760i) q^{65} +(7.85223 - 2.31139i) q^{67} -5.81597 q^{68} +(-0.0616156 + 0.428546i) q^{70} +(1.45889 + 0.937571i) q^{71} +(-0.608158 + 1.33168i) q^{73} +(3.71126 + 1.08972i) q^{74} +(6.03346 + 1.77158i) q^{76} +(-0.445499 - 3.09851i) q^{77} +(-10.1410 + 11.7033i) q^{79} +(-1.45626 + 1.68062i) q^{80} +(1.24574 - 0.365783i) q^{82} +(3.35960 + 7.35650i) q^{83} +(2.29575 + 1.47539i) q^{85} +(-3.55835 + 1.04483i) q^{86} +(-2.15795 + 4.72526i) q^{88} +(2.19746 + 15.2836i) q^{89} +(4.01877 - 2.58271i) q^{91} +(-7.43771 + 8.58357i) q^{92} +(2.18089 - 4.77548i) q^{94} +(-1.93219 - 2.22987i) q^{95} +1.03304 q^{97} +(-1.82391 - 2.10491i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	$ 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) $ 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$

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 $

$2$	0.459493	+	0.134919i	0.324911	+	0.0954024i	0.440120	−	0.897939i	$-0.354936\pi$
$2$	0.459493	+	0.134919i	0.324911	+	0.0954024i	−0.115210	+	0.993341i	$0.536754\pi$
$3$		0			0
$3$		0			0
$4$	−1.48958	−	0.957293i	−0.744788	−	0.478646i
$5$	0.345139	+	0.755750i	0.154351	+	0.337981i	0.970972	−	0.239193i	$-0.0768827\pi$
$5$	0.345139	+	0.755750i	0.154351	+	0.337981i	−0.816621	+	0.577174i	$0.804155\pi$
$6$		0			0
$7$	1.04408	+	0.306569i	0.394624	+	0.115872i	0.473023	−	0.881050i	$-0.343163\pi$
$7$	1.04408	+	0.306569i	0.394624	+	0.115872i	−0.0783990	+	0.996922i	$0.524981\pi$
$8$	−1.18251	−	1.36469i	−0.418079	−	0.482489i
$9$		0			0
$10$	0.0566239	+	0.393828i	0.0179060	+	0.124539i
$11$	−1.19505	−	2.61680i	−0.360322	−	0.788995i	−0.999796	−	0.0201827i	$-0.993575\pi$
$11$	−1.19505	−	2.61680i	−0.360322	−	0.788995i	0.639474	−	0.768812i	$-0.279152\pi$
$12$		0			0
$13$	2.87491	−	3.31782i	0.797356	−	0.920198i	−0.200877	−	0.979616i	$-0.564379\pi$
$13$	2.87491	−	3.31782i	0.797356	−	0.920198i	0.998233	+	0.0594185i	$0.0189247\pi$
$14$	0.438384	+	0.281733i	0.117163	+	0.0752962i
$15$		0			0
$16$	1.11189	+	2.43470i	0.277972	+	0.608674i
$17$	2.76321	−	1.77580i	0.670176	−	0.430696i	−0.160813	−	0.986985i	$-0.551412\pi$
$17$	2.76321	−	1.77580i	0.670176	−	0.430696i	0.830989	+	0.556289i	$0.187775\pi$
$18$		0			0
$19$	−3.40746	+	1.00052i	−0.781724	+	0.229535i	−0.648159	−	0.761505i	$-0.724461\pi$
$19$	−3.40746	+	1.00052i	−0.781724	+	0.229535i	−0.133565	+	0.991040i	$0.542643\pi$
$20$	0.209362	−	1.45615i	0.0468148	−	0.325604i
$21$		0			0
$22$	−0.196061	−	1.36364i	−0.0418004	−	0.290728i
$23$	0.912860	−	6.34908i	0.190345	−	1.32388i	−0.640752	−	0.767748i	$-0.721377\pi$
$23$	0.912860	−	6.34908i	0.190345	−	1.32388i	0.831097	−	0.556128i	$-0.187714\pi$
$24$		0			0
$25$	2.82227	−	3.25707i	0.564453	−	0.651414i
$26$	1.76864	−	1.13663i	0.346858	−	0.222912i
$27$		0			0
$28$	−1.26176	−	1.45615i	−0.238450	−	0.275186i
$29$	1.97270			0.366320			0.183160	−	0.983083i	$-0.441367\pi$
$29$	1.97270			0.366320			0.183160	+	0.983083i	$0.441367\pi$
$30$		0			0
$31$	−1.76031	−	2.03151i	−0.316161	−	0.364869i	0.575319	−	0.817929i	$-0.304878\pi$
$31$	−1.76031	−	2.03151i	−0.316161	−	0.364869i	−0.891480	+	0.453060i	$0.850332\pi$
$32$	0.696384	+	4.84346i	0.123104	+	0.856211i
$33$		0			0
$34$	1.50926	−	0.443160i	0.258837	−	0.0760013i
$35$	0.128663	+	0.894870i	0.0217480	+	0.151261i
$36$		0			0
$37$	8.07686			1.32783			0.663914	−	0.747809i	$-0.268894\pi$
$37$	8.07686			1.32783			0.663914	+	0.747809i	$0.268894\pi$
$38$	−1.70069			−0.275889
$39$		0			0
$40$	0.623231	−	1.36469i	0.0985415	−	0.215776i
$41$	2.28074	−	1.46575i	0.356192	−	0.228911i	−0.350290	−	0.936641i	$-0.613917\pi$
$41$	2.28074	−	1.46575i	0.356192	−	0.228911i	0.706483	+	0.707730i	$0.250281\pi$
$42$		0			0
$43$	−6.51473	+	4.18676i	−0.993487	+	0.638476i	−0.933069	−	0.359698i	$-0.882880\pi$
$43$	−6.51473	+	4.18676i	−0.993487	+	0.638476i	−0.0604184	+	0.998173i	$0.519244\pi$
$44$	−0.724922	+	5.04194i	−0.109286	+	0.760101i
$45$		0			0
$46$	1.27607	−	2.79420i	0.188146	−	0.411982i
$47$	1.56014	−	10.8510i	0.227570	−	1.58278i	−0.480727	−	0.876870i	$-0.659627\pi$
$47$	1.56014	−	10.8510i	0.227570	−	1.58278i	0.708297	−	0.705914i	$-0.249464\pi$
$48$		0			0
$49$	−4.89266	−	3.14432i	−0.698951	−	0.449189i
$50$	1.73625	−	1.11582i	0.245543	−	0.157801i
$51$		0			0
$52$	−7.45852	+	2.19002i	−1.03431	+	0.303701i
$53$	−6.30856	−	4.05427i	−0.866548	−	0.556896i	0.0301473	−	0.999545i	$-0.490402\pi$
$53$	−6.30856	−	4.05427i	−0.866548	−	0.556896i	−0.896695	+	0.442649i	$0.854039\pi$
$54$		0			0
$55$	1.56519	−	1.80632i	0.211050	−	0.243564i
$56$	−0.816259	−	1.78736i	−0.109077	−	0.238846i
$57$		0			0
$58$	0.906440	+	0.266155i	0.119021	+	0.0349478i
$59$	6.97706	+	8.05195i	0.908336	+	1.04828i	0.998628	+	0.0523599i	$0.0166743\pi$
$59$	6.97706	+	8.05195i	0.908336	+	1.04828i	−0.0902927	+	0.995915i	$0.528780\pi$
$60$		0			0
$61$	−3.84302	+	8.41503i	−0.492048	+	1.07743i	0.486925	+	0.873444i	$0.338119\pi$
$61$	−3.84302	+	8.41503i	−0.492048	+	1.07743i	−0.978973	+	0.203991i	$0.934609\pi$
$62$	−0.534760	−	1.17096i	−0.0679146	−	0.148712i
$63$		0			0
$64$	0.428340	−	2.97917i	0.0535425	−	0.372396i
$65$	3.49969	+	1.02760i	0.434083	+	0.127458i
$66$		0			0
$67$	7.85223	−	2.31139i	0.959302	−	0.282381i
$67$	7.85223	−	2.31139i	0.959302	−	0.282381i
$68$	−5.81597			−0.705290
$69$		0			0
$70$	−0.0616156	+	0.428546i	−0.00736447	+	0.0512210i
$71$	1.45889	+	0.937571i	0.173138	+	0.111269i	0.624340	−	0.781153i	$-0.285368\pi$
$71$	1.45889	+	0.937571i	0.173138	+	0.111269i	−0.451202	+	0.892422i	$0.649004\pi$
$72$		0			0
$73$	−0.608158	+	1.33168i	−0.0711796	+	0.155862i	−0.941877	−	0.335957i	$-0.890940\pi$
$73$	−0.608158	+	1.33168i	−0.0711796	+	0.155862i	0.870698	+	0.491818i	$0.163668\pi$
$74$	3.71126	+	1.08972i	0.431425	+	0.126678i
$75$		0			0
$76$	6.03346	+	1.77158i	0.692085	+	0.203214i
$77$	−0.445499	−	3.09851i	−0.0507693	−	0.353108i
$78$		0			0
$79$	−10.1410	+	11.7033i	−1.14095	+	1.31672i	−0.199370	+	0.979924i	$0.563890\pi$
$79$	−10.1410	+	11.7033i	−1.14095	+	1.31672i	−0.941577	+	0.336799i	$0.890656\pi$
$80$	−1.45626	+	1.68062i	−0.162815	+	0.187899i
$81$		0			0
$82$	1.24574	−	0.365783i	0.137569	−	0.0403940i
$83$	3.35960	+	7.35650i	0.368764	+	0.807480i	0.999504	+	0.0314863i	$0.0100241\pi$
$83$	3.35960	+	7.35650i	0.368764	+	0.807480i	−0.630740	+	0.775994i	$0.717249\pi$
$84$		0			0
$85$	2.29575	+	1.47539i	0.249010	+	0.160029i
$86$	−3.55835	+	1.04483i	−0.383707	+	0.112666i
$87$		0			0
$88$	−2.15795	+	4.72526i	−0.230039	+	0.503714i
$89$	2.19746	+	15.2836i	0.232930	+	1.62006i	0.685319	+	0.728243i	$0.259663\pi$
$89$	2.19746	+	15.2836i	0.232930	+	1.62006i	−0.452389	+	0.891821i	$0.649428\pi$
$90$		0			0
$91$	4.01877	−	2.58271i	0.421281	−	0.270741i
$92$	−7.43771	+	8.58357i	−0.775435	+	0.894899i
$93$		0			0
$94$	2.18089	−	4.77548i	0.224941	−	0.492553i
$95$	−1.93219	−	2.22987i	−0.198238	−	0.228779i
$96$		0			0
$97$	1.03304			0.104890			0.0524448	−	0.998624i	$-0.483299\pi$
$97$	1.03304			0.104890			0.0524448	+	0.998624i	$0.483299\pi$
$98$	−1.82391	−	2.10491i	−0.184243	−	0.212628i
$99$		0			0
$100$	−7.32195	+	2.14992i	−0.732195	+	0.214992i
$101$	−14.7982	+	4.34515i	−1.47248	+	0.432359i	−0.916904	−	0.399108i	$-0.869320\pi$
$101$	−14.7982	+	4.34515i	−1.47248	+	0.432359i	−0.555575	+	0.831466i	$0.687502\pi$
$102$		0			0
$103$	2.64709	+	3.05490i	0.260825	+	0.301009i	0.871025	−	0.491239i	$-0.163456\pi$
$103$	2.64709	+	3.05490i	0.260825	+	0.301009i	−0.610199	+	0.792248i	$0.708911\pi$
$104$	−7.92738			−0.777344
$105$		0			0
$106$	−2.35174	−	2.71405i	−0.228421	−	0.263612i
$107$	−4.27363	+	9.35794i	−0.413147	+	0.904667i	0.582619	+	0.812745i	$0.302028\pi$
$107$	−4.27363	+	9.35794i	−0.413147	+	0.904667i	−0.995766	+	0.0919211i	$0.970699\pi$
$108$		0			0
$109$	5.18000	−	5.97804i	0.496154	−	0.572592i	−0.451346	−	0.892349i	$-0.649056\pi$
$109$	5.18000	−	5.97804i	0.496154	−	0.572592i	0.947500	+	0.319757i	$0.103601\pi$
$110$	0.962900	−	0.618818i	0.0918089	−	0.0590020i
$111$		0			0
$112$	0.414496	+	2.88288i	0.0391662	+	0.272407i
$113$	5.47815	−	11.9955i	0.515341	−	1.12844i	−0.455832	−	0.890066i	$-0.650658\pi$
$113$	5.47815	−	11.9955i	0.515341	−	1.12844i	0.971173	−	0.238374i	$-0.0766144\pi$
$114$		0			0
$115$	5.11338	−	1.50142i	0.476825	−	0.140009i
$116$	−2.93848	−	1.88845i	−0.272831	−	0.175338i
$117$		0			0
$118$	2.11955	+	4.64116i	0.195120	+	0.427253i
$119$	3.42941	−	1.00697i	0.314373	−	0.0923084i
$120$		0			0
$121$	1.78397	−	2.05881i	0.162179	−	0.187165i
$122$	−2.90119	+	3.34815i	−0.262661	+	0.303127i
$123$		0			0
$124$	0.677370	+	4.71121i	0.0608296	+	0.423079i
$125$	7.42148	+	2.17914i	0.663798	+	0.194909i
$126$		0			0
$127$	−1.08241	−	0.317824i	−0.0960483	−	0.0282023i	0.233355	−	0.972392i	$-0.425029\pi$
$127$	−1.08241	−	0.317824i	−0.0960483	−	0.0282023i	−0.329404	+	0.944189i	$0.606848\pi$
$128$	4.66424	−	10.2133i	0.412264	−	0.902733i
$129$		0			0
$130$	1.46944	+	0.944350i	0.128878	+	0.0828250i
$131$	0.304226	−	2.11594i	0.0265803	−	0.184870i	−0.972206	−	0.234128i	$-0.924777\pi$
$131$	0.304226	−	2.11594i	0.0265803	−	0.184870i	0.998786	+	0.0492579i	$0.0156856\pi$
$132$		0			0
$133$	−3.86438			−0.335084
$134$	3.91989	−	0.00264966i	0.338627	−	0.000228895i
$135$		0			0
$136$	−5.69093	−	1.67101i	−0.487993	−	0.143288i
$137$	−1.51982	+	10.5706i	−0.129847	+	0.903107i	0.815898	+	0.578196i	$0.196243\pi$
$137$	−1.51982	+	10.5706i	−0.129847	+	0.903107i	−0.945745	+	0.324910i	$0.894666\pi$
$138$		0			0
$139$	0.348882	+	0.763945i	0.0295918	+	0.0647970i	0.923851	−	0.382753i	$-0.125024\pi$
$139$	0.348882	+	0.763945i	0.0295918	+	0.0647970i	−0.894259	+	0.447550i	$0.852297\pi$
$140$	0.665000	−	1.45615i	0.0562027	−	0.123067i
$141$		0			0
$142$	0.543853	+	0.627640i	0.0456391	+	0.0526703i
$143$	−12.1177	−	3.55809i	−1.01334	−	0.297542i
$144$		0			0
$145$	0.680855	+	1.49086i	0.0565419	+	0.123810i
$146$	−0.459114	+	0.529846i	−0.0379966	+	0.0438504i
$147$		0			0
$148$	−12.0311	−	7.73192i	−0.988950	−	0.635560i
$149$	11.8242	−	3.47190i	0.968676	−	0.284429i	0.241134	−	0.970492i	$-0.422481\pi$
$149$	11.8242	−	3.47190i	0.968676	−	0.284429i	0.727542	+	0.686063i	$0.240663\pi$
$150$		0			0
$151$	−9.27257	+	5.95912i	−0.754591	+	0.484946i	−0.860513	−	0.509428i	$-0.829857\pi$
$151$	−9.27257	+	5.95912i	−0.754591	+	0.484946i	0.105922	+	0.994374i	$0.466221\pi$
$152$	5.39474	+	3.46699i	0.437571	+	0.281210i
$153$		0			0
$154$	0.213345	−	1.48385i	0.0171919	−	0.119572i
$155$	0.927757	−	2.03151i	0.0745193	−	0.163174i
$156$		0			0
$157$	−1.18301	+	8.22804i	−0.0944148	+	0.656669i	0.886571	+	0.462592i	$0.153080\pi$
$157$	−1.18301	+	8.22804i	−0.0944148	+	0.656669i	−0.980986	+	0.194077i	$0.937829\pi$
$158$	−6.23870	+	4.00937i	−0.496324	+	0.318968i
$159$		0			0
$160$	−3.42009	+	2.19796i	−0.270382	+	0.173764i
$161$	2.89953	−	6.34908i	0.228515	−	0.500378i
$162$		0			0
$163$	6.95133			0.544470			0.272235	−	0.962231i	$-0.412237\pi$
$163$	6.95133			0.544470			0.272235	+	0.962231i	$0.412237\pi$
$164$	−4.80049			−0.374855
$165$		0			0
$166$	0.551179	+	3.83353i	0.0427798	+	0.297540i
$167$	−18.2260	+	5.35164i	−1.41037	+	0.414122i	−0.896232	−	0.443585i	$-0.853706\pi$
$167$	−18.2260	+	5.35164i	−1.41037	+	0.414122i	−0.514138	+	0.857707i	$0.671888\pi$
$168$		0			0
$169$	−0.892745	−	6.20918i	−0.0686727	−	0.477629i
$170$	0.855824	+	0.987674i	0.0656387	+	0.0757511i
$171$		0			0
$172$	13.7122			1.04554
$173$	6.43299	+	7.42406i	0.489091	+	0.564441i	0.945622	−	0.325266i	$-0.105454\pi$
$173$	6.43299	+	7.42406i	0.489091	+	0.564441i	−0.456532	+	0.889707i	$0.650908\pi$
$174$		0			0
$175$	3.94518	−	2.53542i	0.298228	−	0.191659i
$176$	5.04235	−	5.81918i	0.380082	−	0.438637i
$177$		0			0
$178$	−1.05234	+	7.31921i	−0.0788765	+	0.548598i
$179$	−3.09043	−	21.4944i	−0.230990	−	1.60657i	−0.693839	−	0.720130i	$-0.744082\pi$
$179$	−3.09043	−	21.4944i	−0.230990	−	1.60657i	0.462849	−	0.886437i	$-0.346827\pi$
$180$		0			0
$181$	3.66805	−	25.5118i	0.272644	−	1.89628i	−0.147894	−	0.989003i	$-0.547249\pi$
$181$	3.66805	−	25.5118i	0.272644	−	1.89628i	0.420537	−	0.907275i	$-0.361842\pi$
$182$	2.19505	−	0.644526i	0.162708	−	0.0477754i
$183$		0			0
$184$	−9.74397	+	6.26207i	−0.718335	+	0.461646i
$185$	2.78764	+	6.10408i	0.204951	+	0.448781i
$186$		0			0
$187$	−7.94911	−	5.10858i	−0.581296	−	0.373576i
$188$	−12.7116	+	14.6699i	−0.927085	+	1.06991i
$189$		0			0
$190$	−0.586975	−	1.28530i	−0.0425837	−	0.0932452i
$191$	2.29093	+	15.9338i	0.165766	+	1.15293i	0.887517	+	0.460775i	$0.152428\pi$
$191$	2.29093	+	15.9338i	0.165766	+	1.15293i	−0.721751	+	0.692153i	$0.756662\pi$
$192$		0			0
$193$	−16.3152	−	18.8288i	−1.17440	−	1.35533i	−0.921758	−	0.387766i	$-0.873247\pi$
$193$	−16.3152	−	18.8288i	−1.17440	−	1.35533i	−0.252639	−	0.967561i	$-0.581299\pi$
$194$	0.474676	+	0.139377i	0.0340797	+	0.0100067i
$195$		0			0
$196$	4.27796	+	9.36742i	0.305568	+	0.669101i
$197$	10.1617	+	6.53055i	0.723993	+	0.465282i	0.850024	−	0.526744i	$-0.176587\pi$
$197$	10.1617	+	6.53055i	0.723993	+	0.465282i	−0.126031	+	0.992026i	$0.540224\pi$
$198$		0			0
$199$	2.26261	+	0.664361i	0.160392	+	0.0470953i	0.360943	−	0.932588i	$-0.382455\pi$
$199$	2.26261	+	0.664361i	0.160392	+	0.0470953i	−0.200551	+	0.979683i	$0.564273\pi$
$200$	−7.78223			−0.550287
$201$		0			0
$202$	−7.38593			−0.519672
$203$	2.05965	+	0.604767i	0.144559	+	0.0424464i
$204$		0			0
$205$	1.89491	+	1.21779i	0.132346	+	0.0850538i
$206$	0.804153	+	1.76085i	0.0560280	+	0.122684i
$207$		0			0
$208$	11.2745	+	3.31048i	0.781744	+	0.229541i
$209$	6.69025	+	7.72096i	0.462774	+	0.534070i
$210$		0			0
$211$	0.100070	+	0.696002i	0.00688910	+	0.0479147i	0.992976	−	0.118316i	$-0.0377495\pi$
$211$	0.100070	+	0.696002i	0.00688910	+	0.0479147i	−0.986087	+	0.166231i	$0.946840\pi$
$212$	5.51597	+	12.0783i	0.378838	+	0.829540i
$213$		0			0
$214$	−3.22627	+	3.72331i	−0.220543	+	0.254521i
$215$	−5.41264	−	3.47849i	−0.369139	−	0.237231i
$216$		0			0
$217$	−1.21510	−	2.66071i	−0.0824866	−	0.180620i
$218$	3.18673	−	2.04798i	0.215832	−	0.138707i
$219$		0			0
$220$	−4.06064	+	1.19231i	−0.273769	+	0.0803857i
$221$	2.05216	−	14.2731i	0.138043	−	0.960113i
$222$		0			0
$223$	−1.08766	−	7.56487i	−0.0728354	−	0.506581i	−0.993283	−	0.115714i	$-0.963084\pi$
$223$	−1.08766	−	7.56487i	−0.0728354	−	0.506581i	0.920447	−	0.390867i	$-0.127825\pi$
$224$	−0.757775	+	5.27044i	−0.0506309	+	0.352146i
$225$		0			0
$226$	4.13559	−	4.77273i	0.275096	−	0.317477i
$227$	−9.19211	+	5.90741i	−0.610102	+	0.392089i	−0.808895	−	0.587953i	$-0.799934\pi$
$227$	−9.19211	+	5.90741i	−0.610102	+	0.392089i	0.198793	+	0.980041i	$0.436298\pi$
$228$		0			0
$229$	17.4133	+	20.0960i	1.15070	+	1.32798i	0.936286	+	0.351238i	$0.114239\pi$
$229$	17.4133	+	20.0960i	1.15070	+	1.32798i	0.214415	+	0.976743i	$0.431215\pi$
$230$	2.55213			0.168283
$231$		0			0
$232$	−2.33273	−	2.69211i	−0.153151	−	0.176746i
$233$	−0.351538	−	2.44500i	−0.0230301	−	0.160178i	0.975061	−	0.221937i	$-0.0712379\pi$
$233$	−0.351538	−	2.44500i	−0.0230301	−	0.160178i	−0.998091	+	0.0617595i	$0.980329\pi$
$234$		0			0
$235$	8.73912	−	2.56604i	0.570077	−	0.167390i
$236$	−2.68478	−	18.6731i	−0.174765	−	1.21551i
$237$		0			0
$238$	1.71165			0.110950
$239$	15.7639			1.01968			0.509839	−	0.860270i	$-0.329705\pi$
$239$	15.7639			1.01968			0.509839	+	0.860270i	$0.329705\pi$
$240$		0			0
$241$	−7.72379	+	16.9127i	−0.497533	+	1.08945i	0.479730	+	0.877416i	$0.340734\pi$
$241$	−7.72379	+	16.9127i	−0.497533	+	1.08945i	−0.977263	+	0.212029i	$0.931993\pi$
$242$	1.09750	−	0.705318i	0.0705497	−	0.0453396i
$243$		0			0
$244$	13.7801	−	8.85594i	0.882182	−	0.566944i
$245$	0.687671	−	4.78286i	0.0439337	−	0.305565i
$246$		0			0
$247$	−6.47658	+	14.1817i	−0.412095	+	0.902362i
$248$	−0.690788	+	4.80454i	−0.0438651	+	0.305088i
$249$		0			0
$250$	3.11611	+	2.00260i	0.197080	+	0.126656i
$251$	11.4684	−	7.37030i	0.723879	−	0.465209i	−0.126105	−	0.992017i	$-0.540248\pi$
$251$	11.4684	−	7.37030i	0.723879	−	0.465209i	0.849984	+	0.526808i	$0.176611\pi$
$252$		0			0
$253$	−17.7052	+	5.19872i	−1.11312	+	0.326841i
$254$	−0.454479	−	0.292076i	−0.0285165	−	0.0183265i
$255$		0			0
$256$	−0.420855	+	0.485693i	−0.0263035	+	0.0303558i
$257$	2.01878	+	4.42052i	0.125928	+	0.275744i	0.962087	−	0.272743i	$-0.0879310\pi$
$257$	2.01878	+	4.42052i	0.125928	+	0.275744i	−0.836159	+	0.548488i	$0.815204\pi$
$258$		0			0
$259$	8.43287	+	2.47611i	0.523993	+	0.153858i
$260$	−4.22933	−	4.88091i	−0.262292	−	0.302701i
$261$		0			0
$262$	0.425270	−	0.931212i	0.0262733	−	0.0575304i
$263$	−5.18826	−	11.3607i	−0.319922	−	0.700530i	0.679530	−	0.733648i	$-0.262184\pi$
$263$	−5.18826	−	11.3607i	−0.319922	−	0.700530i	−0.999451	+	0.0331174i	$0.989456\pi$
$264$		0			0
$265$	0.886678	−	6.16698i	0.0544682	−	0.378835i
$266$	−1.77565	−	0.521379i	−0.108872	−	0.0319678i
$267$		0			0
$268$	−13.9092	−	4.07389i	−0.849638	−	0.248852i
$269$	10.3046			0.628282			0.314141	−	0.949376i	$-0.398284\pi$
$269$	10.3046			0.628282			0.314141	+	0.949376i	$0.398284\pi$
$270$		0			0
$271$	0.613771	−	4.26887i	0.0372839	−	0.259315i	−0.962651	−	0.270746i	$-0.912730\pi$
$271$	0.613771	−	4.26887i	0.0372839	−	0.259315i	0.999935	+	0.0114309i	$0.00363865\pi$
$272$	7.39592	+	4.75307i	0.448444	+	0.288197i
$273$		0			0
$274$	−2.12452	+	4.65206i	−0.128347	+	0.281041i
$275$	−11.8959	−	3.49294i	−0.717348	−	0.210632i
$276$		0			0
$277$	15.7476	+	4.62392i	0.946183	+	0.277824i	0.718197	−	0.695840i	$-0.244968\pi$
$277$	15.7476	+	4.62392i	0.946183	+	0.277824i	0.227986	+	0.973664i	$0.426786\pi$
$278$	0.0572379	+	0.398098i	0.00343290	+	0.0238764i
$279$		0			0
$280$	1.06907	−	1.23378i	0.0638893	−	0.0737322i
$281$	15.7848	−	18.2166i	0.941642	−	1.08671i	−0.0544616	−	0.998516i	$-0.517344\pi$
$281$	15.7848	−	18.2166i	0.941642	−	1.08671i	0.996103	−	0.0881964i	$-0.0281103\pi$
$282$		0			0
$283$	25.1857	−	7.39518i	1.49713	−	0.439598i	0.572323	−	0.820028i	$-0.306042\pi$
$283$	25.1857	−	7.39518i	1.49713	−	0.439598i	0.924810	+	0.380430i	$0.124224\pi$
$284$	−1.27560	−	2.79317i	−0.0756927	−	0.165744i
$285$		0			0
$286$	−5.08796	−	3.26984i	−0.300858	−	0.193349i
$287$	2.83063	−	0.831147i	0.167087	−	0.0490611i
$288$		0			0
$289$	−2.58023	+	5.64991i	−0.151778	+	0.332348i
$290$	0.111702	+	0.776902i	0.00655935	+	0.0456213i
$291$		0			0
$292$	2.18071	−	1.40146i	0.127616	−	0.0820140i
$293$	11.2167	−	12.9447i	0.655284	−	0.756238i	−0.326715	−	0.945123i	$-0.605942\pi$
$293$	11.2167	−	12.9447i	0.655284	−	0.756238i	0.981999	+	0.188885i	$0.0604873\pi$
$294$		0			0
$295$	−3.67720	+	8.05195i	−0.214095	+	0.468803i
$296$	−9.55094	−	11.0224i	−0.555137	−	0.640662i
$297$		0			0
$298$	5.90156			0.341868
$299$	−18.4407	−	21.2817i	−1.06646	−	1.23075i
$300$		0			0
$301$	−8.08542	+	2.37409i	−0.466036	+	0.136840i
$302$	−5.06468	+	1.48712i	−0.291440	+	0.0855744i
$303$		0			0
$304$	−6.22467	−	7.18366i	−0.357010	−	0.412011i
$305$	−7.68603			−0.440101
$306$		0			0
$307$	−5.78540	−	6.67671i	−0.330190	−	0.381060i	0.566243	−	0.824238i	$-0.308396\pi$
$307$	−5.78540	−	6.67671i	−0.330190	−	0.381060i	−0.896433	+	0.443178i	$0.853851\pi$
$308$	−2.30258	+	5.04194i	−0.131202	+	0.287291i
$309$		0			0
$310$	0.700387	−	0.808290i	0.0397793	−	0.0459078i
$311$	−17.9884	+	11.5604i	−1.02003	+	0.655531i	−0.939969	−	0.341259i	$-0.889147\pi$
$311$	−17.9884	+	11.5604i	−1.02003	+	0.655531i	−0.0800571	+	0.996790i	$0.525510\pi$
$312$		0			0
$313$	−0.415962	−	2.89308i	−0.0235115	−	0.163526i	0.974683	−	0.223592i	$-0.0717782\pi$
$313$	−0.415962	−	2.89308i	−0.0235115	−	0.163526i	−0.998194	+	0.0600653i	$0.980869\pi$
$314$	−1.65371	+	3.62112i	−0.0933241	+	0.204351i
$315$		0			0
$316$	26.3092	−	7.72508i	1.48001	−	0.434570i
$317$	6.54402	+	4.20559i	0.367549	+	0.236209i	0.711357	−	0.702830i	$-0.248081\pi$
$317$	6.54402	+	4.20559i	0.367549	+	0.236209i	−0.343808	+	0.939040i	$0.611717\pi$
$318$		0			0
$319$	−2.35748	−	5.16215i	−0.131993	−	0.289025i
$320$	2.39934	−	0.704511i	0.134127	−	0.0393833i
$321$		0			0
$322$	2.18893	−	2.52616i	0.121984	−	0.140777i
$323$	−7.63878	+	8.81562i	−0.425033	+	0.490514i
$324$		0			0
$325$	−2.69262	−	18.7276i	−0.149359	−	1.03882i
$326$	3.19409	+	0.937868i	0.176904	+	0.0519437i
$327$		0			0
$328$	−4.69728	−	1.37925i	−0.259364	−	0.0761561i
$329$	4.95550	−	10.8510i	0.273205	−	0.598236i
$330$		0			0
$331$	−27.7329	−	17.8228i	−1.52434	−	0.979632i	−0.991020	−	0.133717i	$-0.957309\pi$
$331$	−27.7329	−	17.8228i	−1.52434	−	0.979632i	−0.533318	−	0.845915i	$-0.679055\pi$
$332$	2.03794	−	14.1742i	0.111846	−	0.777909i
$333$		0			0
$334$	−9.09676			−0.497752
$335$	4.45694	+	5.13657i	0.243509	+	0.280641i
$336$		0			0
$337$	26.4246	+	7.75896i	1.43944	+	0.422658i	0.906035	−	0.423203i	$-0.139094\pi$
$337$	26.4246	+	7.75896i	1.43944	+	0.422658i	0.533404	+	0.845860i	$0.320912\pi$
$338$	0.427528	−	2.97352i	0.0232545	−	0.161738i
$339$		0			0
$340$	−2.00732	−	4.39542i	−0.108862	−	0.238375i
$341$	−3.21238	+	7.03414i	−0.173960	+	0.380920i
$342$		0			0
$343$	−9.13250	−	10.5395i	−0.493109	−	0.569078i
$344$	13.4173	+	3.93969i	0.723414	+	0.212414i
$345$		0			0
$346$	1.95426	+	4.27924i	0.105062	+	0.230053i
$347$	5.54126	−	6.39495i	0.297470	−	0.343299i	−0.587263	−	0.809396i	$-0.699795\pi$
$347$	5.54126	−	6.39495i	0.297470	−	0.343299i	0.884734	+	0.466097i	$0.154340\pi$
$348$		0			0
$349$	24.1955	+	15.5495i	1.29516	+	0.832347i	0.992676	−	0.120808i	$-0.0385486\pi$
$349$	24.1955	+	15.5495i	1.29516	+	0.832347i	0.302481	+	0.953155i	$0.402185\pi$
$350$	2.15486	−	0.632724i	0.115182	−	0.0338205i
$351$		0			0
$352$	11.8422	−	7.61049i	0.631189	−	0.405640i
$353$	18.6338	+	11.9752i	0.991778	+	0.637377i	0.932616	−	0.360871i	$-0.117521\pi$
$353$	18.6338	+	11.9752i	0.991778	+	0.637377i	0.0591626	+	0.998248i	$0.481157\pi$
$354$		0			0
$355$	−0.205049	+	1.42615i	−0.0108829	+	0.0756920i
$356$	11.3576	−	24.8698i	0.601954	−	1.31810i
$357$		0			0
$358$	1.47998	−	10.2935i	0.0782194	−	0.544028i
$359$	−7.06702	+	4.54170i	−0.372983	+	0.239702i	−0.713681	−	0.700471i	$-0.752973\pi$
$359$	−7.06702	+	4.54170i	−0.372983	+	0.239702i	0.340697	+	0.940173i	$0.389337\pi$
$360$		0			0
$361$	−5.37410	+	3.45372i	−0.282847	+	0.181775i
$362$	5.12748	−	11.2276i	0.269494	−	0.590110i
$363$		0			0
$364$	−8.45867			−0.443355
$365$	−1.21632			−0.0636649
$366$		0			0
$367$	0.527829	+	3.67113i	0.0275524	+	0.191631i	0.998949	−	0.0458308i	$-0.0145935\pi$
$367$	0.527829	+	3.67113i	0.0275524	+	0.191631i	−0.971397	+	0.237462i	$0.923684\pi$
$368$	16.4731	−	4.83694i	0.858719	−	0.252143i
$369$		0			0
$370$	0.457343	+	3.18089i	0.0237761	+	0.165367i
$371$	−5.34372	−	6.16698i	−0.277432	−	0.320174i
$372$		0			0
$373$	11.2150			0.580689			0.290345	−	0.956922i	$-0.406230\pi$
$373$	11.2150			0.580689			0.290345	+	0.956922i	$0.406230\pi$
$374$	−2.96331	−	3.41984i	−0.153229	−	0.176836i
$375$		0			0
$376$	−16.6531	+	10.7023i	−0.858819	+	0.551929i
$377$	5.67132	−	6.54505i	0.292088	−	0.337087i
$378$		0			0
$379$	−0.847495	+	5.89446i	−0.0435329	+	0.302778i	0.956409	+	0.292029i	$0.0943305\pi$
$379$	−0.847495	+	5.89446i	−0.0435329	+	0.302778i	−0.999942	+	0.0107485i	$0.996579\pi$
$380$	0.743510	+	5.17123i	0.0381413	+	0.265278i
$381$		0			0
$382$	−1.09711	+	7.63055i	−0.0561329	+	0.390413i
$383$	−13.6416	+	4.00554i	−0.697054	+	0.204674i	−0.611016	−	0.791618i	$-0.709239\pi$
$383$	−13.6416	+	4.00554i	−0.697054	+	0.204674i	−0.0860383	+	0.996292i	$0.527421\pi$
$384$		0			0
$385$	2.18794	−	1.40610i	0.111508	−	0.0716616i
$386$	−4.95637	−	10.8529i	−0.252273	−	0.552400i
$387$		0			0
$388$	−1.53880	−	0.988924i	−0.0781205	−	0.0502050i
$389$	−9.26185	+	10.6887i	−0.469594	+	0.541941i	−0.940299	−	0.340350i	$-0.889454\pi$
$389$	−9.26185	+	10.6887i	−0.469594	+	0.541941i	0.470704	+	0.882291i	$0.344000\pi$
$390$		0			0
$391$	−8.75231	−	19.1649i	−0.442623	−	0.969210i
$392$	1.49459	+	10.3951i	0.0754884	+	0.525033i
$393$		0			0
$394$	3.78815	+	4.37175i	0.190844	+	0.220246i
$395$	−12.3448	−	3.62476i	−0.621134	−	0.182381i
$396$		0			0
$397$	−0.131292	−	0.287489i	−0.00658935	−	0.0144287i	0.906309	−	0.422616i	$-0.138888\pi$
$397$	−0.131292	−	0.287489i	−0.00658935	−	0.0144287i	−0.912898	+	0.408188i	$0.866161\pi$
$398$	0.950017	+	0.610539i	0.0476200	+	0.0306035i
$399$		0			0
$400$	11.0680	+	3.24987i	0.553401	+	0.162493i
$401$	−30.4915			−1.52267			−0.761336	−	0.648358i	$-0.775456\pi$
$401$	−30.4915			−1.52267			−0.761336	+	0.648358i	$0.775456\pi$
$402$		0			0
$403$	−11.8009			−0.587845
$404$	26.2027	+	7.69380i	1.30363	+	0.382781i
$405$		0			0
$406$	0.864799	+	0.555773i	0.0429193	+	0.0275825i
$407$	−9.65227	−	21.1355i	−0.478445	−	1.04765i
$408$		0			0
$409$	10.2810	+	3.01878i	0.508363	+	0.149269i	0.525849	−	0.850578i	$-0.323748\pi$
$409$	10.2810	+	3.01878i	0.508363	+	0.149269i	−0.0174854	+	0.999847i	$0.505566\pi$
$410$	0.706395	+	0.815224i	0.0348864	+	0.0402610i
$411$		0			0
$412$	−1.01860	−	7.08455i	−0.0501831	−	0.349031i
$413$	4.81611	+	10.5458i	0.236985	+	0.518926i
$414$		0			0
$415$	−4.40014	+	5.07803i	−0.215994	+	0.249271i
$416$	18.0718	+	11.6140i	0.886041	+	0.569424i
$417$		0			0
$418$	2.03242	+	4.45037i	0.0994087	+	0.217675i
$419$	3.70553	−	2.38140i	0.181027	−	0.116339i	−0.446989	−	0.894540i	$-0.647504\pi$
$419$	3.70553	−	2.38140i	0.181027	−	0.116339i	0.628016	+	0.778201i	$0.283867\pi$
$420$		0			0
$421$	2.55888	−	0.751355i	0.124712	−	0.0366188i	−0.218781	−	0.975774i	$-0.570208\pi$
$421$	2.55888	−	0.751355i	0.124712	−	0.0366188i	0.343493	+	0.939155i	$0.388390\pi$
$422$	−0.0479227	+	0.333309i	−0.00233284	+	0.0162252i
$423$		0			0
$424$	1.92712	+	13.4034i	0.0935892	+	0.650927i
$425$	2.01459	−	14.0118i	0.0977218	−	0.679670i
$426$		0			0
$427$	−6.59220	+	7.60780i	−0.319019	+	0.368167i
$428$	15.3242	−	9.84826i	0.740723	−	0.476034i
$429$		0			0
$430$	−2.01775	−	2.32861i	−0.0973047	−	0.112296i
$431$	10.2150			0.492037			0.246019	−	0.969265i	$-0.420878\pi$
$431$	10.2150			0.492037			0.246019	+	0.969265i	$0.420878\pi$
$432$		0			0
$433$	0.136279	+	0.157275i	0.00654917	+	0.00755815i	0.759015	−	0.651073i	$-0.225681\pi$
$433$	0.136279	+	0.157275i	0.00654917	+	0.00755815i	−0.752466	+	0.658632i	$0.771136\pi$
$434$	−0.199351	−	1.38652i	−0.00956915	−	0.0665549i
$435$		0			0
$436$	−13.4387	+	3.94597i	−0.643599	+	0.188978i
$437$	3.24185	+	22.5476i	0.155079	+	1.07860i
$438$		0			0
$439$	−4.44240			−0.212024			−0.106012	−	0.994365i	$-0.533808\pi$
$439$	−4.44240			−0.212024			−0.106012	+	0.994365i	$0.533808\pi$
$440$	−4.31591			−0.205753
$441$		0			0
$442$	2.86867	−	6.28151i	0.136449	−	0.298781i
$443$	−23.5711	+	15.1482i	−1.11990	+	0.719713i	−0.963427	−	0.267970i	$-0.913647\pi$
$443$	−23.5711	+	15.1482i	−1.11990	+	0.719713i	−0.156468	+	0.987683i	$0.550011\pi$
$444$		0			0
$445$	−10.7922	+	6.93571i	−0.511598	+	0.328784i
$446$	0.520873	−	3.62275i	0.0246641	−	0.171542i
$447$		0			0
$448$	1.36054	−	2.97917i	0.0642795	−	0.140752i
$449$	0.0420093	−	0.292181i	0.00198254	−	0.0137889i	−0.988806	−	0.149206i	$-0.952328\pi$
$449$	0.0420093	−	0.292181i	0.00198254	−	0.0137889i	0.990789	+	0.135417i	$0.0432374\pi$
$450$		0			0
$451$	−6.56117	−	4.21661i	−0.308954	−	0.198552i
$452$	−19.6433	+	12.6240i	−0.923943	+	0.593782i
$453$		0			0
$454$	−5.02073	+	1.47422i	−0.235635	+	0.0691886i
$455$	3.33891	+	2.14579i	0.156531	+	0.100596i
$456$		0			0
$457$	−11.6201	+	13.4103i	−0.543565	+	0.627308i	−0.959372	−	0.282145i	$-0.908954\pi$
$457$	−11.6201	+	13.4103i	−0.543565	+	0.627308i	0.415806	+	0.909453i	$0.363499\pi$
$458$	5.28994	+	11.5834i	0.247183	+	0.541255i
$459$		0			0
$460$	−9.05408	−	2.65852i	−0.422148	−	0.123954i
$461$	−14.7043	−	16.9697i	−0.684849	−	0.790357i	0.301774	−	0.953380i	$-0.402421\pi$
$461$	−14.7043	−	16.9697i	−0.684849	−	0.790357i	−0.986622	+	0.163022i	$0.947876\pi$
$462$		0			0
$463$	8.22023	−	17.9998i	0.382027	−	0.836522i	−0.616754	−	0.787156i	$-0.711553\pi$
$463$	8.22023	−	17.9998i	0.382027	−	0.836522i	0.998781	−	0.0493657i	$-0.0157200\pi$
$464$	2.19342	+	4.80292i	0.101827	+	0.222970i
$465$		0			0
$466$	0.168349	−	1.17089i	0.00779861	−	0.0542405i
$467$	21.2742	+	6.24668i	0.984455	+	0.289062i	0.734062	−	0.679082i	$-0.237622\pi$
$467$	21.2742	+	6.24668i	0.984455	+	0.289062i	0.250393	+	0.968144i	$0.419440\pi$
$468$		0			0
$469$	8.90694	−	0.00602065i	0.411284	−	0.000278008i
$470$	4.36177			0.201194
$471$		0			0
$472$	2.73797	−	19.0430i	0.126025	−	0.876524i
$473$	18.7414	+	12.0444i	0.861730	+	0.553800i
$474$		0			0
$475$	−6.35799	+	13.9221i	−0.291725	+	0.638788i
$476$	−6.07233	−	1.78300i	−0.278325	−	0.0817235i
$477$		0			0
$478$	7.24338	+	2.12685i	0.331304	+	0.0972798i
$479$	−0.555874	−	3.86619i	−0.0253985	−	0.176651i	0.973174	−	0.230072i	$-0.0738963\pi$
$479$	−0.555874	−	3.86619i	−0.0253985	−	0.176651i	−0.998572	+	0.0534218i	$0.982987\pi$
$480$		0			0
$481$	23.2202	−	26.7976i	1.05875	−	1.22186i
$482$	−5.83088	+	6.72920i	−0.265589	+	0.306506i
$483$		0			0
$484$	−4.62825	+	1.35898i	−0.210375	+	0.0617717i
$485$	0.356544	+	0.780721i	0.0161898	+	0.0354507i
$486$		0			0
$487$	22.5654	+	14.5019i	1.02253	+	0.657143i	0.940608	−	0.339495i	$-0.110256\pi$
$487$	22.5654	+	14.5019i	1.02253	+	0.657143i	0.0819269	+	0.996638i	$0.473893\pi$
$488$	16.0283	−	4.70633i	0.725566	−	0.213045i
$489$		0			0
$490$	0.961279	−	2.10491i	0.0434262	−	0.0950901i
$491$	5.24247	+	36.4622i	0.236589	+	1.64551i	0.668582	+	0.743638i	$0.266901\pi$
$491$	5.24247	+	36.4622i	0.236589	+	1.64551i	−0.431993	+	0.901877i	$0.642190\pi$
$492$		0			0
$493$	5.45097	−	3.50312i	0.245499	−	0.157773i
$494$	−4.88933	+	5.64259i	−0.219981	+	0.253872i
$495$		0			0
$496$	2.98883	−	6.54463i	0.134202	−	0.293862i
$497$	1.23576	+	1.42615i	0.0554316	+	0.0639714i
$498$		0			0
$499$	3.06877			0.137377			0.0686885	−	0.997638i	$-0.478119\pi$
$499$	3.06877			0.137377			0.0686885	+	0.997638i	$0.478119\pi$
$500$	−8.96879	−	10.3505i	−0.401096	−	0.462890i
$501$		0			0
$502$	6.26405	−	1.83929i	0.279578	−	0.0820915i
$503$	3.52345	−	1.03458i	0.157103	−	0.0461295i	−0.202235	−	0.979337i	$-0.564821\pi$
$503$	3.52345	−	1.03458i	0.157103	−	0.0461295i	0.359338	+	0.933207i	$0.383002\pi$
$504$		0			0
$505$	−8.39130	−	9.68407i	−0.373408	−	0.430936i
$506$	−8.83683			−0.392845
$507$		0			0
$508$	1.30808	+	1.50961i	0.0580367	+	0.0669779i
$509$	−6.43959	+	14.1007i	−0.285430	+	0.625004i	−0.996982	−	0.0776289i	$-0.975265\pi$
$509$	−6.43959	+	14.1007i	−0.285430	+	0.625004i	0.711553	+	0.702633i	$0.247992\pi$
$510$		0			0
$511$	−1.04322	+	1.20394i	−0.0461492	+	0.0532590i
$512$	−19.1499	+	12.3069i	−0.846315	+	0.543894i
$513$		0			0
$514$	0.331203	+	2.30357i	0.0146088	+	0.101606i
$515$	−1.39513	+	3.05490i	−0.0614767	+	0.134615i
$516$		0			0
$517$	−30.2594	+	8.88497i	−1.33081	+	0.390760i
$518$	3.54077	+	2.27551i	0.155572	+	0.0999803i
$519$		0			0
$520$	−2.73605	−	5.99112i	−0.119984	−	0.262728i
$521$	−10.6289	+	3.12094i	−0.465662	+	0.136731i	−0.506143	−	0.862449i	$-0.668929\pi$
$521$	−10.6289	+	3.12094i	−0.465662	+	0.136731i	0.0404807	+	0.999180i	$0.487111\pi$
$522$		0			0
$523$	−12.6858	+	14.6402i	−0.554711	+	0.640170i	−0.961974	−	0.273140i	$-0.911938\pi$
$523$	−12.6858	+	14.6402i	−0.554711	+	0.640170i	0.407263	+	0.913311i	$0.366483\pi$
$524$	−2.47874	+	2.86061i	−0.108284	+	0.124967i
$525$		0			0
$526$	−0.851190	−	5.92015i	−0.0371136	−	0.258131i
$527$	−8.47165	−	2.48750i	−0.369031	−	0.108357i
$528$		0			0
$529$	−17.4092	−	5.11181i	−0.756922	−	0.222252i
$530$	1.23947	−	2.71405i	0.0538390	−	0.117891i
$531$		0			0
$532$	5.75629	+	3.69934i	0.249567	+	0.160387i
$533$	1.69385	−	11.7810i	0.0733688	−	0.510291i
$534$		0			0
$535$	−8.54726			−0.369530
$536$	−12.4396	−	7.98259i	−0.537310	−	0.344795i
$537$		0			0
$538$	4.73489	+	1.39029i	0.204135	+	0.0599396i
$539$	−2.38108	+	16.5607i	−0.102560	+	0.713322i
$540$		0			0
$541$	−2.86340	−	6.26997i	−0.123107	−	0.269567i	0.838037	−	0.545613i	$-0.183703\pi$
$541$	−2.86340	−	6.26997i	−0.123107	−	0.269567i	−0.961144	+	0.276046i	$0.910976\pi$
$542$	0.857976	−	1.87871i	0.0368532	−	0.0806973i
$543$		0			0
$544$	10.5253	+	12.1468i	0.451268	+	0.520791i
$545$	6.30572	+	1.85153i	0.270107	+	0.0793107i
$546$		0			0
$547$	4.02139	+	8.80562i	0.171942	+	0.376501i	0.975911	−	0.218171i	$-0.0700091\pi$
$547$	4.02139	+	8.80562i	0.171942	+	0.376501i	−0.803968	+	0.594672i	$0.797282\pi$
$548$	12.3830	−	14.2908i	0.528977	−	0.610472i
$549$		0			0
$550$	−4.99480	−	3.20996i	−0.212979	−	0.136873i
$551$	−6.72188	+	1.97372i	−0.286362	+	0.0840833i
$552$		0			0
$553$	−14.1758	+	9.11024i	−0.602817	+	0.387407i
$554$	6.61207	+	4.24932i	0.280920	+	0.180536i
$555$		0			0
$556$	0.211633	−	1.47194i	0.00897522	−	0.0624240i
$557$	−6.76438	+	14.8119i	−0.286616	+	0.627602i	−0.997099	−	0.0761124i	$-0.975749\pi$
$557$	−6.76438	+	14.8119i	−0.286616	+	0.627602i	0.710483	+	0.703714i	$0.248476\pi$
$558$		0			0
$559$	−4.83832	+	33.6513i	−0.204639	+	1.42330i
$560$	−2.03568	+	1.30825i	−0.0860232	+	0.0552837i
$561$		0			0
$562$	9.71077	−	6.24073i	0.409624	−	0.263249i
$563$	5.49481	−	12.0319i	0.231578	−	0.507086i	−0.757793	−	0.652495i	$-0.773722\pi$
$563$	5.49481	−	12.0319i	0.231578	−	0.507086i	0.989372	+	0.145409i	$0.0464497\pi$
$564$		0			0
$565$	10.9563			0.460935
$566$	12.5704			0.528373
$567$		0			0
$568$	−0.445657	−	3.09961i	−0.0186993	−	0.130057i
$569$	−43.5275	+	12.7808i	−1.82477	+	0.535800i	−0.999578	−	0.0290558i	$-0.990750\pi$
$569$	−43.5275	+	12.7808i	−1.82477	+	0.535800i	−0.825190	+	0.564856i	$0.808932\pi$
$570$		0			0
$571$	3.00470	+	20.8982i	0.125743	+	0.874561i	0.950865	+	0.309606i	$0.100197\pi$
$571$	3.00470	+	20.8982i	0.125743	+	0.874561i	−0.825122	+	0.564955i	$0.808894\pi$
$572$	14.6442	+	16.9003i	0.612304	+	0.706636i
$573$		0			0
$574$	1.41279			0.0589687
$575$	−18.1031	−	20.8921i	−0.754950	−	0.871259i
$576$		0			0
$577$	−20.1398	+	12.9431i	−0.838432	+	0.538827i	−0.887947	−	0.459946i	$-0.847869\pi$
$577$	−20.1398	+	12.9431i	−0.838432	+	0.538827i	0.0495150	+	0.998773i	$0.484232\pi$
$578$	−1.94788	+	2.24797i	−0.0810211	+	0.0935033i
$579$		0			0
$580$	0.413008	−	2.87253i	0.0171492	−	0.119275i
$581$	1.25241	+	8.71070i	0.0519587	+	0.361381i
$582$		0			0
$583$	−3.07014	+	21.3533i	−0.127152	+	0.884364i
$584$	2.53648	−	0.744777i	0.104960	−	0.0308191i
$585$		0			0
$586$	6.90046	−	4.43466i	0.285056	−	0.183194i
$587$	15.8332	+	34.6699i	0.653506	+	1.43098i	0.888452	+	0.458970i	$0.151781\pi$
$587$	15.8332	+	34.6699i	0.653506	+	1.43098i	−0.234946	+	0.972008i	$0.575491\pi$
$588$		0			0
$589$	8.03074	+	5.16104i	0.330901	+	0.212657i
$590$	−2.77601	+	3.20369i	−0.114287	+	0.131894i
$591$		0			0
$592$	8.98057	+	19.6647i	0.369099	+	0.808214i
$593$	−3.00793	−	20.9206i	−0.123521	−	0.859106i	−0.953518	−	0.301338i	$-0.902567\pi$
$593$	−3.00793	−	20.9206i	−0.123521	−	0.859106i	0.829997	−	0.557768i	$-0.188342\pi$
$594$		0			0
$595$	1.94464	+	2.24423i	0.0797224	+	0.0920045i
$596$	−20.9367	−	6.14756i	−0.857599	−	0.251814i
$597$		0			0
$598$	−5.60207	−	12.2668i	−0.229086	−	0.501628i
$599$	−9.77166	−	6.27987i	−0.399259	−	0.256588i	0.325568	−	0.945518i	$-0.394444\pi$
$599$	−9.77166	−	6.27987i	−0.399259	−	0.256588i	−0.724828	+	0.688930i	$0.758081\pi$
$600$		0			0
$601$	46.4950	+	13.6522i	1.89657	+	0.556883i	0.991221	+	0.132216i	$0.0422092\pi$
$601$	46.4950	+	13.6522i	1.89657	+	0.556883i	0.905349	+	0.424667i	$0.139609\pi$
$602$	−4.03550			−0.164475
$603$		0			0
$604$	19.5168			0.794128
$605$	2.17167	+	0.637659i	0.0882908	+	0.0259245i
$606$		0			0
$607$	−18.5371	−	11.9131i	−0.752397	−	0.483536i	0.107372	−	0.994219i	$-0.465756\pi$
$607$	−18.5371	−	11.9131i	−0.752397	−	0.483536i	−0.859769	+	0.510683i	$0.829393\pi$
$608$	−7.21887	−	15.8071i	−0.292764	−	0.641064i
$609$		0			0
$610$	−3.53168	−	1.03699i	−0.142993	−	0.0419867i
$611$	−31.5165	−	36.3720i	−1.27502	−	1.47145i
$612$		0			0
$613$	2.76264	+	19.2146i	0.111582	+	0.776071i	0.966382	+	0.257112i	$0.0827710\pi$
$613$	2.76264	+	19.2146i	0.111582	+	0.776071i	−0.854799	+	0.518959i	$0.826320\pi$
$614$	−1.75753	−	3.84846i	−0.0709283	−	0.155311i
$615$		0			0
$616$	−3.70169	+	4.27198i	−0.149145	+	0.172123i
$617$	−6.46427	−	4.15433i	−0.260242	−	0.167247i	0.404014	−	0.914753i	$-0.367615\pi$
$617$	−6.46427	−	4.15433i	−0.260242	−	0.167247i	−0.664255	+	0.747506i	$0.731251\pi$
$618$		0			0
$619$	−11.6926	−	25.6033i	−0.469966	−	1.02908i	−0.985102	−	0.171974i	$-0.944986\pi$
$619$	−11.6926	−	25.6033i	−0.469966	−	1.02908i	0.515135	−	0.857109i	$-0.327742\pi$
$620$	−3.32671	+	2.13795i	−0.133604	+	0.0858620i
$621$		0			0
$622$	−9.82525	+	2.88495i	−0.393957	+	0.115676i
$623$	−2.39118	+	16.6310i	−0.0958004	+	0.666307i
$624$		0			0
$625$	−2.15213	−	14.9684i	−0.0860851	−	0.598735i
$626$	0.199200	−	1.38547i	0.00796165	−	0.0553745i
$627$		0			0
$628$	9.63883	−	11.1238i	0.384631	−	0.443888i
$629$	22.3180	−	14.3429i	0.889878	−	0.571890i
$630$		0			0
$631$	−4.84651	−	5.59318i	−0.192937	−	0.222661i	0.651036	−	0.759047i	$-0.274335\pi$
$631$	−4.84651	−	5.59318i	−0.192937	−	0.222661i	−0.843973	+	0.536386i	$0.819789\pi$
$632$	27.9631			1.11231
$633$		0			0
$634$	2.43952	+	2.81535i	0.0968856	+	0.111812i
$635$	−0.133387	−	0.927724i	−0.00529328	−	0.0368156i
$636$		0			0
$637$	−24.4982	+	7.19333i	−0.970656	+	0.285010i
$638$	−0.386770	−	2.69004i	−0.0153124	−	0.106500i
$639$		0			0
$640$	9.32848			0.368740
$641$	6.58756			0.260193			0.130097	−	0.991501i	$-0.458471\pi$
$641$	6.58756			0.260193			0.130097	+	0.991501i	$0.458471\pi$
$642$		0			0
$643$	0.143538	−	0.314305i	0.00566059	−	0.0123950i	−0.906781	−	0.421603i	$-0.861468\pi$
$643$	0.143538	−	0.314305i	0.00566059	−	0.0123950i	0.912441	+	0.409208i	$0.134195\pi$
$644$	−10.3970	+	6.68175i	−0.409699	+	0.263298i
$645$		0			0
$646$	−4.69936	+	3.02010i	−0.184894	+	0.118824i
$647$	−1.12118	+	7.79799i	−0.0440782	+	0.306571i	0.955841	+	0.293883i	$0.0949477\pi$
$647$	−1.12118	+	7.79799i	−0.0440782	+	0.306571i	−0.999920	+	0.0126873i	$0.995961\pi$
$648$		0			0
$649$	12.7324	−	27.8801i	0.499791	−	1.09439i
$650$	1.28947	−	8.96847i	0.0505772	−	0.351772i
$651$		0			0
$652$	−10.3545	−	6.65445i	−0.405515	−	0.260609i
$653$	−26.6118	+	17.1024i	−1.04140	+	0.669267i	−0.945333	−	0.326108i	$-0.894263\pi$
$653$	−26.6118	+	17.1024i	−1.04140	+	0.669267i	−0.0960676	+	0.995375i	$0.530626\pi$
$654$		0			0
$655$	1.70412	−	0.500374i	0.0665854	−	0.0195512i
$656$	6.10458	+	3.92317i	0.238344	+	0.153174i
$657$		0			0
$658$	3.74103	−	4.31738i	0.145840	−	0.168309i
$659$	−1.80243	−	3.94677i	−0.0702127	−	0.153744i	0.871272	−	0.490801i	$-0.163296\pi$
$659$	−1.80243	−	3.94677i	−0.0702127	−	0.153744i	−0.941484	+	0.337057i	$0.890569\pi$
$660$		0			0
$661$	8.20594	+	2.40948i	0.319174	+	0.0937180i	0.437395	−	0.899269i	$-0.355901\pi$
$661$	8.20594	+	2.40948i	0.319174	+	0.0937180i	−0.118221	+	0.992987i	$0.537719\pi$
$662$	−10.3384	−	11.9312i	−0.401814	−	0.463718i
$663$		0			0
$664$	6.06656	−	13.2839i	0.235428	−	0.515515i
$665$	−1.33375	−	2.92050i	−0.0517206	−	0.113252i
$666$		0			0
$667$	1.80080	−	12.5248i	0.0697271	−	0.484963i
$668$	32.2721	+	9.47594i	1.24865	+	0.366635i
$669$		0			0
$670$	1.35491	+	2.96154i	0.0523448	+	0.114414i
$671$	26.6131			1.02739
$672$		0			0
$673$	−5.21849	+	36.2954i	−0.201158	+	1.39909i	0.599697	+	0.800227i	$0.295288\pi$
$673$	−5.21849	+	36.2954i	−0.201158	+	1.39909i	−0.800855	+	0.598858i	$0.795621\pi$
$674$	11.0951	+	7.13038i	0.427367	+	0.274652i
$675$		0			0
$676$	−4.61419	+	10.1037i	−0.177469	+	0.388603i
$677$	27.2962	+	8.01488i	1.04908	+	0.308037i	0.760444	−	0.649403i	$-0.224981\pi$
$677$	27.2962	+	8.01488i	1.04908	+	0.308037i	0.288633	+	0.957440i	$0.406799\pi$
$678$		0			0
$679$	1.07858	+	0.316699i	0.0413920	+	0.0121538i
$680$	−0.701300	−	4.87765i	−0.0268936	−	0.187049i
$681$		0			0
$682$	−2.42511	+	2.79872i	−0.0928622	+	0.107169i
$683$	−23.4493	+	27.0620i	−0.897264	+	1.03550i	0.101907	+	0.994794i	$0.467506\pi$
$683$	−23.4493	+	27.0620i	−0.897264	+	1.03550i	−0.999171	+	0.0407041i	$0.987040\pi$
$684$		0			0
$685$	−8.51327	+	2.49972i	−0.325275	+	0.0955095i
$686$	−2.77434	−	6.07496i	−0.105925	−	0.231943i
$687$		0			0
$688$	−17.4372	−	11.2062i	−0.664785	−	0.427232i
$689$	−31.5879	+	9.27503i	−1.20340	+	0.353351i
$690$		0			0
$691$	9.21471	−	20.1774i	0.350544	−	0.767584i	−0.649430	−	0.760421i	$-0.724993\pi$
$691$	9.21471	−	20.1774i	0.350544	−	0.767584i	0.999974	−	0.00716307i	$-0.00228010\pi$
$692$	−2.47543	−	17.2170i	−0.0941015	−	0.654491i
$693$		0			0
$694$	3.40897	−	2.19081i	0.129403	−	0.0831621i
$695$	−0.456938	+	0.527335i	−0.0173327	+	0.0200030i
$696$		0			0
$697$	3.69929	−	8.10031i	0.140121	−	0.306821i
$698$	9.01975	+	10.4093i	0.341402	+	0.393999i
$699$		0			0
$700$	−8.30379			−0.313854
$701$	8.11956	+	9.37047i	0.306672	+	0.353918i	0.888076	−	0.459697i	$-0.152042\pi$
$701$	8.11956	+	9.37047i	0.306672	+	0.353918i	−0.581404	+	0.813615i	$0.697497\pi$
$702$		0			0
$703$	−27.5215	+	8.08105i	−1.03799	+	0.304783i
$704$	−8.30778	+	2.43938i	−0.313111	+	0.0919378i
$705$		0			0
$706$	6.94642	+	8.01660i	0.261432	+	0.301709i
$707$	−16.7826			−0.631174
$708$		0			0
$709$	−16.3609	−	18.8815i	−0.614445	−	0.709108i	0.360197	−	0.932876i	$-0.382710\pi$
$709$	−16.3609	−	18.8815i	−0.614445	−	0.709108i	−0.974642	+	0.223768i	$0.928164\pi$
$710$	−0.286633	+	0.627640i	−0.0107572	+	0.0235549i
$711$		0			0
$712$	18.2589	−	21.0719i	0.684280	−	0.789701i
$713$	−14.5051	+	9.32187i	−0.543221	+	0.349107i
$714$		0			0
$715$	−1.49328	−	10.3860i	−0.0558456	−	0.388415i
$716$	−15.9730	+	34.9760i	−0.596939	+	1.30711i
$717$		0			0
$718$	−3.86001	+	1.13340i	−0.144054	+	0.0422982i
$719$	37.9952	+	24.4180i	1.41698	+	0.910638i	0.999999	+	0.00172296i	$0.000548435\pi$
$719$	37.9952	+	24.4180i	1.41698	+	0.910638i	0.416982	+	0.908915i	$0.363088\pi$
$720$		0			0
$721$	1.82723	+	4.00107i	0.0680496	+	0.149008i
$722$	−2.93533	+	0.861892i	−0.109242	+	0.0320763i
$723$		0			0
$724$	−29.8861	+	34.4904i	−1.11071	+	1.28183i
$725$	5.56748	−	6.42521i	0.206771	−	0.238626i
$726$		0			0
$727$	5.29490	+	36.8268i	0.196377	+	1.36583i	0.814689	+	0.579898i	$0.196908\pi$
$727$	5.29490	+	36.8268i	0.196377	+	1.36583i	−0.618312	+	0.785933i	$0.712183\pi$
$728$	−8.27680	−	2.43029i	−0.306759	−	0.0900725i
$729$		0			0
$730$	−0.558889	−	0.164105i	−0.0206854	−	0.00607379i
$731$	−10.5667	+	23.1378i	−0.390823	+	0.855782i
$732$		0			0
$733$	18.5007	+	11.8897i	0.683339	+	0.439156i	0.835712	−	0.549167i	$-0.185055\pi$
$733$	18.5007	+	11.8897i	0.683339	+	0.439156i	−0.152373	+	0.988323i	$0.548691\pi$
$734$	−0.252773	+	1.75807i	−0.00933001	+	0.0648916i
$735$		0			0
$736$	31.3872			1.15695
$737$	−15.4323	−	17.7855i	−0.568455	−	0.655137i
$738$		0			0
$739$	−26.2427	−	7.70554i	−0.965352	−	0.283453i	−0.239187	−	0.970973i	$-0.576881\pi$
$739$	−26.2427	−	7.70554i	−0.965352	−	0.283453i	−0.726165	+	0.687521i	$0.758699\pi$
$740$	1.69099	−	11.7611i	0.0621620	−	0.432346i
$741$		0			0
$742$	−1.62336	−	3.55465i	−0.0595953	−	0.130495i
$743$	−14.3874	+	31.5041i	−0.527824	+	1.15577i	0.438568	+	0.898698i	$0.355486\pi$
$743$	−14.3874	+	31.5041i	−0.527824	+	1.15577i	−0.966392	+	0.257075i	$0.917241\pi$
$744$		0			0
$745$	6.70488	+	7.73784i	0.245648	+	0.283493i
$746$	5.15320	+	1.51312i	0.188672	+	0.0553991i
$747$		0			0
$748$	6.95039	+	15.2192i	0.254132	+	0.556471i
$749$	−7.33086	+	8.46026i	−0.267864	+	0.309131i
$750$		0			0
$751$	17.1100	+	10.9959i	0.624353	+	0.401247i	0.814215	−	0.580564i	$-0.197168\pi$
$751$	17.1100	+	10.9959i	0.624353	+	0.401247i	−0.189862	+	0.981811i	$0.560804\pi$
$752$	28.1537	−	8.26666i	1.02666	−	0.301454i
$753$		0			0
$754$	3.48899	−	2.24223i	0.127061	−	0.0816574i
$755$	−7.70393	−	4.95101i	−0.280375	−	0.180186i
$756$		0			0
$757$	0.149712	−	1.04127i	0.00544138	−	0.0378456i	−0.986920	−	0.161212i	$-0.948460\pi$
$757$	0.149712	−	1.04127i	0.00544138	−	0.0378456i	0.992361	+	0.123366i	$0.0393689\pi$
$758$	−1.18469	+	2.59412i	−0.0430300	+	0.0942226i
$759$		0			0
$760$	−0.758238	+	5.27366i	−0.0275042	+	0.191296i
$761$	36.0458	−	23.1653i	1.30666	−	0.839740i	0.312740	−	0.949839i	$-0.398753\pi$
$761$	36.0458	−	23.1653i	1.30666	−	0.839740i	0.993921	+	0.110099i	$0.0351168\pi$
$762$		0			0
$763$	7.24101	−	4.65351i	0.262142	−	0.168468i
$764$	11.8408	−	25.9277i	0.428384	−	0.938030i
$765$		0			0
$766$	−6.80865			−0.246007
$767$	46.7733			1.68889
$768$		0			0
$769$	−2.84713	−	19.8023i	−0.102670	−	0.714087i	−0.974518	−	0.224310i	$-0.927987\pi$
$769$	−2.84713	−	19.8023i	−0.102670	−	0.714087i	0.871848	−	0.489777i	$-0.162922\pi$
$770$	1.19505	−	0.350899i	0.0430667	−	0.0126455i
$771$		0			0
$772$	6.27814	+	43.6654i	0.225955	+	1.57155i
$773$	4.37215	+	5.04573i	0.157255	+	0.181482i	0.828910	−	0.559382i	$-0.188962\pi$
$773$	4.37215	+	5.04573i	0.157255	+	0.181482i	−0.671655	+	0.740864i	$0.734416\pi$
$774$		0			0
$775$	−11.5848			−0.416139
$776$	−1.22158	−	1.40978i	−0.0438522	−	0.0506081i
$777$		0			0
$778$	−5.69787	+	3.66180i	−0.204279	+	0.131282i
$779$	−6.30503	+	7.27639i	−0.225901	+	0.260704i
$780$		0			0
$781$	0.709987	−	4.93807i	0.0254053	−	0.176698i
$782$	−1.43591	−	9.98699i	−0.0513481	−	0.357134i
$783$		0			0
$784$	2.21538	−	15.4083i	0.0791206	−	0.550296i
$785$	−6.62664	+	1.94576i	−0.236515	+	0.0694471i
$786$		0			0
$787$	15.4463	−	9.92675i	0.550602	−	0.353850i	−0.235571	−	0.971857i	$-0.575696\pi$
$787$	15.4463	−	9.92675i	0.550602	−	0.353850i	0.786173	+	0.618007i	$0.212060\pi$
$788$	−8.88503	−	19.4555i	−0.316516	−	0.693073i
$789$		0			0
$790$	−5.18330	−	3.33110i	−0.184413	−	0.118515i
$791$	9.39706	−	10.8448i	0.334121	−	0.385596i
$792$		0			0
$793$	16.8713	+	36.9429i	0.599116	+	1.31188i
$794$	−0.0215399	−	0.149813i	−0.000764421	−	0.00531667i
$795$		0			0
$796$	−2.73434	−	3.15559i	−0.0969160	−	0.111847i
$797$	47.4382	+	13.9291i	1.68035	+	0.493395i	0.976239	−	0.216697i	$-0.0695284\pi$
$797$	47.4382	+	13.9291i	1.68035	+	0.493395i	0.704109	+	0.710092i	$0.251347\pi$
$798$		0			0
$799$	−14.9583	−	32.7541i	−0.529187	−	1.15876i
$800$	17.7409	+	11.4014i	0.627234	+	0.403099i
$801$		0			0
$802$	−14.0106	−	4.11389i	−0.494732	−	0.145266i
$803$	4.21153			0.148622
$804$		0			0
$805$	5.79906			0.204390
$806$	−5.42243	−	1.59217i	−0.190997	−	0.0560818i
$807$		0			0
$808$	23.4288	+	15.0568i	0.824222	+	0.529695i
$809$	−20.9457	−	45.8646i	−0.736410	−	1.61251i	−0.789370	−	0.613917i	$-0.789593\pi$
$809$	−20.9457	−	45.8646i	−0.736410	−	1.61251i	0.0529599	−	0.998597i	$-0.483134\pi$
$810$		0			0
$811$	−35.6538	−	10.4689i	−1.25197	−	0.367613i	−0.412473	−	0.910970i	$-0.635335\pi$
$811$	−35.6538	−	10.4689i	−1.25197	−	0.367613i	−0.839502	+	0.543357i	$0.817153\pi$
$812$	−2.48906	−	2.87253i	−0.0873491	−	0.100806i
$813$		0			0
$814$	−1.58356	−	11.0139i	−0.0555038	−	0.386037i
$815$	2.39918	+	5.25346i	0.0840395	+	0.184021i
$816$		0			0
$817$	18.0097	−	20.7843i	0.630081	−	0.727152i
$818$	4.31676	+	2.77421i	0.150932	+	0.0969981i
$819$		0			0
$820$	−1.65684	−	3.62797i	−0.0578593	−	0.126694i
$821$	29.7766	−	19.1363i	1.03921	−	0.667860i	0.0944193	−	0.995533i	$-0.469901\pi$
$821$	29.7766	−	19.1363i	1.03921	−	0.667860i	0.944791	+	0.327672i	$0.106264\pi$
$822$		0			0
$823$	36.5105	−	10.7205i	1.27268	−	0.373692i	0.425479	−	0.904968i	$-0.360106\pi$
$823$	36.5105	−	10.7205i	1.27268	−	0.373692i	0.847198	+	0.531277i	$0.178288\pi$
$824$	1.03878	−	7.22489i	0.0361877	−	0.251691i
$825$		0			0
$826$	0.790136	+	5.49552i	0.0274923	+	0.191213i
$827$	−7.53408	+	52.4007i	−0.261986	+	1.82215i	0.255902	+	0.966703i	$0.417627\pi$
$827$	−7.53408	+	52.4007i	−0.261986	+	1.82215i	−0.517888	+	0.855448i	$0.673282\pi$
$828$		0			0
$829$	−20.4030	+	23.5463i	−0.708626	+	0.817798i	−0.989891	−	0.141832i	$-0.954701\pi$
$829$	−20.4030	+	23.5463i	−0.708626	+	0.817798i	0.281265	+	0.959630i	$0.409246\pi$
$830$	−2.70696	+	1.73966i	−0.0939599	+	0.0603843i
$831$		0			0
$832$	−8.65291	−	9.98599i	−0.299986	−	0.346202i
$833$	−19.1031			−0.661884
$834$		0			0
$835$	−10.3350	−	11.9272i	−0.357658	−	0.412759i
$836$	−2.57442	−	17.9055i	−0.0890382	−	0.619274i
$837$		0			0
$838$	2.02396	−	0.594289i	0.0699166	−	0.0205294i
$839$	−4.56090	−	31.7217i	−0.157460	−	1.09516i	−0.903293	−	0.429023i	$-0.858858\pi$
$839$	−4.56090	−	31.7217i	−0.157460	−	1.09516i	0.745834	−	0.666132i	$-0.232051\pi$
$840$		0			0
$841$	−25.1085			−0.865809
$842$	1.27716			0.0440138
$843$		0			0
$844$	0.517216	−	1.13254i	0.0178033	−	0.0389838i
$845$	4.38446	−	2.81772i	0.150830	−	0.0969326i
$846$		0			0
$847$	2.49377	−	1.60265i	0.0856871	−	0.0550678i
$848$	2.85649	−	19.8673i	0.0980923	−	0.682247i
$849$		0			0
$850$	2.81614	−	6.16650i	0.0965929	−	0.211509i
$851$	7.37304	−	51.2806i	0.252745	−	1.75788i
$852$		0			0
$853$	−9.90519	−	6.36568i	−0.339147	−	0.217957i	0.359970	−	0.932964i	$-0.382787\pi$
$853$	−9.90519	−	6.36568i	−0.339147	−	0.217957i	−0.699117	+	0.715007i	$0.746423\pi$
$854$	−4.05551	+	2.60632i	−0.138777	+	0.0891863i
$855$		0			0
$856$	17.8243	−	5.23367i	0.609220	−	0.178883i
$857$	−27.6259	−	17.7541i	−0.943684	−	0.606469i	−0.0242467	−	0.999706i	$-0.507719\pi$
$857$	−27.6259	−	17.7541i	−0.943684	−	0.606469i	−0.919437	+	0.393237i	$0.871355\pi$
$858$		0			0
$859$	15.1582	−	17.4935i	0.517191	−	0.596871i	−0.435734	−	0.900075i	$-0.643511\pi$
$859$	15.1582	−	17.4935i	0.517191	−	0.596871i	0.952925	+	0.303205i	$0.0980566\pi$
$860$	4.73260	+	10.3630i	0.161380	+	0.353374i
$861$		0			0
$862$	4.69370	+	1.37820i	0.159868	+	0.0469415i
$863$	−13.9719	−	16.1245i	−0.475610	−	0.548883i	0.466354	−	0.884598i	$-0.345567\pi$
$863$	−13.9719	−	16.1245i	−0.475610	−	0.548883i	−0.941963	+	0.335716i	$0.891022\pi$
$864$		0			0
$865$	−3.39046	+	7.42406i	−0.115279	+	0.252426i
$866$	0.0414000	+	0.0906534i	0.00140683	+	0.00308053i
$867$		0			0
$868$	−0.737084	+	5.12653i	−0.0250183	+	0.174006i
$869$	42.7442	+	12.5508i	1.45000	+	0.425757i
$870$		0			0
$871$	14.9057	−	32.6973i	0.505059	−	1.10791i
$872$	−14.2835			−0.483701
$873$		0			0
$874$	−1.55249	+	10.7978i	−0.0525139	+	0.365242i
$875$	7.08055	+	4.55039i	0.239366	+	0.153831i
$876$		0			0
$877$	−1.36599	+	2.99109i	−0.0461261	+	0.101002i	−0.931292	−	0.364273i	$-0.881317\pi$
$877$	−1.36599	+	2.99109i	−0.0461261	+	0.101002i	0.885166	+	0.465275i	$0.154045\pi$
$878$	−2.04125	−	0.599366i	−0.0688890	−	0.0202276i
$879$		0			0
$880$	6.13816	+	1.80233i	0.206917	+	0.0607564i
$881$	−5.42224	−	37.7125i	−0.182680	−	1.27057i	−0.850393	−	0.526148i	$-0.823636\pi$
$881$	−5.42224	−	37.7125i	−0.182680	−	1.27057i	0.667713	−	0.744419i	$-0.267273\pi$
$882$		0			0
$883$	26.8916	−	31.0346i	0.904976	−	1.04440i	−0.0938322	−	0.995588i	$-0.529912\pi$
$883$	26.8916	−	31.0346i	0.904976	−	1.04440i	0.998808	−	0.0488098i	$-0.0155428\pi$
$884$	−16.7204	+	19.2964i	−0.562367	+	0.649007i
$885$		0			0
$886$	−12.8745	+	3.78030i	−0.432528	+	0.127002i
$887$	−15.8290	−	34.6606i	−0.531485	−	1.16379i	−0.964905	−	0.262598i	$-0.915421\pi$
$887$	−15.8290	−	34.6606i	−0.531485	−	1.16379i	0.433420	−	0.901192i	$-0.357307\pi$
$888$		0			0
$889$	−1.03268	−	0.663666i	−0.0346351	−	0.0222586i
$890$	−5.89469	+	1.73084i	−0.197591	+	0.0580178i
$891$		0			0
$892$	−5.62164	+	12.3097i	−0.188226	+	0.412158i
$893$	5.54055	+	38.5353i	0.185407	+	1.28954i
$894$		0			0
$895$	15.1778	−	9.75415i	0.507337	−	0.326045i
$896$	8.00089	−	9.23352i	0.267291	−	0.308470i
$897$		0			0
$898$	0.0587239	−	0.128587i	0.00195964	−	0.00429102i
$899$	−3.47256	−	4.00754i	−0.115816	−	0.133659i
$900$		0			0
$901$	−24.6314			−0.820592
$902$	−2.44591	−	2.82273i	−0.0814399	−	0.0939867i
$903$		0			0
$904$	−22.8480	+	6.70878i	−0.759914	+	0.223131i
$905$	20.5465	−	6.03301i	0.682990	−	0.200544i
$906$		0			0
$907$	−23.9745	−	27.6680i	−0.796060	−	0.918702i	0.202098	−	0.979365i	$-0.435224\pi$
$907$	−23.9745	−	27.6680i	−0.796060	−	0.918702i	−0.998158	+	0.0606632i	$0.980678\pi$
$908$	19.3475			0.642068
$909$		0			0
$910$	1.24470	+	1.43646i	0.0412614	+	0.0476182i
$911$	17.9986	−	39.4115i	0.596322	−	1.30576i	−0.335224	−	0.942138i	$-0.608812\pi$
$911$	17.9986	−	39.4115i	0.596322	−	1.30576i	0.931546	−	0.363624i	$-0.118461\pi$
$912$		0			0
$913$	15.2356	−	17.5828i	0.504224	−	0.581906i
$914$	−7.14866	+	4.59417i	−0.236457	+	0.151962i
$915$		0			0
$916$	−6.70066	−	46.6041i	−0.221396	−	1.53984i
$917$	0.966315	−	2.11594i	0.0319105	−	0.0698743i
$918$		0			0
$919$	−21.9739	+	6.45211i	−0.724851	+	0.212835i	−0.623286	−	0.781994i	$-0.714203\pi$
$919$	−21.9739	+	6.45211i	−0.724851	+	0.212835i	−0.101564	+	0.994829i	$0.532385\pi$
$920$	−8.09558	−	5.20271i	−0.266903	−	0.171528i
$921$		0			0
$922$	−4.46699	−	9.78135i	−0.147113	−	0.322132i
$923$	7.30486	−	2.14490i	0.240443	−	0.0706003i
$924$		0			0
$925$	22.7951	−	26.3069i	0.749497	−	0.864965i
$926$	6.20566	−	7.16171i	0.203931	−	0.235348i
$927$		0			0
$928$	1.37375	+	9.55467i	0.0450957	+	0.313647i
$929$	−26.3881	−	7.74824i	−0.865765	−	0.254212i	−0.181452	−	0.983400i	$-0.558080\pi$
$929$	−26.3881	−	7.74824i	−0.865765	−	0.254212i	−0.684313	+	0.729188i	$0.739898\pi$
$930$		0			0
$931$	19.8175	+	5.81894i	0.649492	+	0.190708i
$932$	−1.81694	+	3.97855i	−0.0595159	+	0.130322i
$933$		0			0
$934$	8.93257	+	5.74061i	0.292283	+	0.187839i
$935$	1.11726	−	7.77070i	0.0365383	−	0.254129i
$936$		0			0
$937$	4.58217			0.149693			0.0748464	−	0.997195i	$-0.476153\pi$
$937$	4.58217			0.149693			0.0748464	+	0.997195i	$0.476153\pi$
$938$	4.09349	+	1.19895i	0.133657	+	0.0391472i
$939$		0			0
$940$	−15.4740	−	4.54359i	−0.504708	−	0.148196i
$941$	1.99987	−	13.9094i	0.0651940	−	0.453434i	−0.930910	−	0.365249i	$-0.880984\pi$
$941$	1.99987	−	13.9094i	0.0651940	−	0.453434i	0.996104	−	0.0881858i	$-0.0281069\pi$
$942$		0			0
$943$	−7.22414	−	15.8187i	−0.235250	−	0.515126i
$944$	−11.8464	+	25.9399i	−0.385566	+	0.844272i
$945$		0			0
$946$	6.98652	+	8.06287i	0.227151	+	0.262146i
$947$	−9.40132	−	2.76048i	−0.305502	−	0.0897034i	0.125389	−	0.992108i	$-0.459982\pi$
$947$	−9.40132	−	2.76048i	−0.305502	−	0.0897034i	−0.430890	+	0.902404i	$0.641800\pi$
$948$		0			0
$949$	2.66988	+	5.84622i	0.0866680	+	0.189776i
$950$	−4.79981	+	5.53927i	−0.155726	+	0.179718i
$951$		0			0
$952$	−5.42949	−	3.48932i	−0.175971	−	0.113090i
$953$	27.5145	−	8.07897i	0.891281	−	0.261704i	0.196139	−	0.980576i	$-0.437160\pi$
$953$	27.5145	−	8.07897i	0.891281	−	0.261704i	0.695142	+	0.718873i	$0.255342\pi$
$954$		0			0
$955$	−11.2513	+	7.23074i	−0.364082	+	0.233981i
$956$	−23.4815	−	15.0906i	−0.759445	−	0.488066i
$957$		0			0
$958$	0.266203	−	1.85148i	0.00860064	−	0.0598187i
$959$	−4.82743	+	10.5706i	−0.155886	+	0.341342i
$960$		0			0
$961$	3.38344	−	23.5323i	0.109143	−	0.759107i
$962$	14.2850	−	9.18044i	0.460568	−	0.295989i
$963$		0			0
$964$	27.6956	−	17.7989i	0.892016	−	0.573264i
$965$	8.59882	−	18.8288i	0.276806	−	0.606120i
$966$		0			0
$967$	3.62365			0.116529			0.0582644	−	0.998301i	$-0.481443\pi$
$967$	3.62365			0.116529			0.0582644	+	0.998301i	$0.481443\pi$
$968$	−4.91919			−0.158109
$969$		0			0
$970$	0.0584948	+	0.406841i	0.00187816	+	0.0130629i
$971$	−13.4807	+	3.95828i	−0.432615	+	0.127027i	−0.490787	−	0.871279i	$-0.663291\pi$
$971$	−13.4807	+	3.95828i	−0.432615	+	0.127027i	0.0581725	+	0.998307i	$0.481473\pi$
$972$		0			0
$973$	0.130058	+	0.904575i	0.00416948	+	0.0289993i
$974$	8.41205	+	9.70802i	0.269539	+	0.311065i
$975$		0			0
$976$	−24.7611			−0.792582
$977$	8.59122	+	9.91480i	0.274858	+	0.317203i	0.876349	−	0.481677i	$-0.159972\pi$
$977$	8.59122	+	9.91480i	0.274858	+	0.317203i	−0.601491	+	0.798879i	$0.705427\pi$
$978$		0			0
$979$	37.3682	−	24.0151i	1.19429	−	0.767525i
$980$	−5.60293	+	6.46613i	−0.178979	+	0.206553i
$981$		0			0
$982$	−2.51057	+	17.4614i	−0.0801156	+	0.557216i
$983$	−3.83285	−	26.6581i	−0.122249	−	0.850260i	−0.954999	−	0.296611i	$-0.904144\pi$
$983$	−3.83285	−	26.6581i	−0.122249	−	0.850260i	0.832750	−	0.553650i	$-0.186765\pi$
$984$		0			0
$985$	−1.42825	+	9.93367i	−0.0455077	+	0.316513i
$986$	2.97732	−	0.874220i	0.0948172	−	0.0278408i
$987$		0			0
$988$	23.2234	−	14.9248i	0.738836	−	0.474821i
$989$	20.6351	+	45.1845i	0.656157	+	1.43678i
$990$		0			0
$991$	27.4529	+	17.6429i	0.872069	+	0.560445i	0.898385	−	0.439209i	$-0.144741\pi$
$991$	27.4529	+	17.6429i	0.872069	+	0.560445i	−0.0263159	+	0.999654i	$0.508378\pi$
$992$	8.61366	−	9.94069i	0.273484	−	0.315617i
$993$		0			0
$994$	0.375410	+	0.822033i	0.0119073	+	0.0260733i
$995$	0.278824	+	1.93926i	0.00883931	+	0.0614787i
$996$		0			0
$997$	25.8805	+	29.8677i	0.819645	+	0.945921i	0.999285	−	0.0378119i	$-0.0120388\pi$
$997$	25.8805	+	29.8677i	0.819645	+	0.945921i	−0.179640	+	0.983732i	$0.557493\pi$
$998$	1.41008	+	0.414036i	0.0446352	+	0.0131061i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.a.64.1		10
3.2	odd	2		67.2.e.b.64.1	yes	10
67.22	even	11	inner	603.2.u.a.424.1		10
201.89	odd	22		67.2.e.b.22.1	✓	10
201.92	odd	22		4489.2.a.i.1.3		5
201.176	even	22		4489.2.a.h.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.b.22.1	✓	10	201.89	odd	22
67.2.e.b.64.1	yes	10	3.2	odd	2
603.2.u.a.64.1		10	1.1	even	1	trivial
603.2.u.a.424.1		10	67.22	even	11	inner
4489.2.a.h.1.3		5	201.176	even	22
4489.2.a.i.1.3		5	201.92	odd	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.459493 + 0.134919i) q^{2} +(-1.48958 - 0.957293i) q^{4} +(0.345139 + 0.755750i) q^{5} +(1.04408 + 0.306569i) q^{7} +(-1.18251 - 1.36469i) q^{8} +O(q^{10})\)	\(q+(0.459493 + 0.134919i) q^{2} +(-1.48958 - 0.957293i) q^{4} +(0.345139 + 0.755750i) q^{5} +(1.04408 + 0.306569i) q^{7} +(-1.18251 - 1.36469i) q^{8} +(0.0566239 + 0.393828i) q^{10} +(-1.19505 - 2.61680i) q^{11} +(2.87491 - 3.31782i) q^{13} +(0.438384 + 0.281733i) q^{14} +(1.11189 + 2.43470i) q^{16} +(2.76321 - 1.77580i) q^{17} +(-3.40746 + 1.00052i) q^{19} +(0.209362 - 1.45615i) q^{20} +(-0.196061 - 1.36364i) q^{22} +(0.912860 - 6.34908i) q^{23} +(2.82227 - 3.25707i) q^{25} +(1.76864 - 1.13663i) q^{26} +(-1.26176 - 1.45615i) q^{28} +1.97270 q^{29} +(-1.76031 - 2.03151i) q^{31} +(0.696384 + 4.84346i) q^{32} +(1.50926 - 0.443160i) q^{34} +(0.128663 + 0.894870i) q^{35} +8.07686 q^{37} -1.70069 q^{38} +(0.623231 - 1.36469i) q^{40} +(2.28074 - 1.46575i) q^{41} +(-6.51473 + 4.18676i) q^{43} +(-0.724922 + 5.04194i) q^{44} +(1.27607 - 2.79420i) q^{46} +(1.56014 - 10.8510i) q^{47} +(-4.89266 - 3.14432i) q^{49} +(1.73625 - 1.11582i) q^{50} +(-7.45852 + 2.19002i) q^{52} +(-6.30856 - 4.05427i) q^{53} +(1.56519 - 1.80632i) q^{55} +(-0.816259 - 1.78736i) q^{56} +(0.906440 + 0.266155i) q^{58} +(6.97706 + 8.05195i) q^{59} +(-3.84302 + 8.41503i) q^{61} +(-0.534760 - 1.17096i) q^{62} +(0.428340 - 2.97917i) q^{64} +(3.49969 + 1.02760i) q^{65} +(7.85223 - 2.31139i) q^{67} -5.81597 q^{68} +(-0.0616156 + 0.428546i) q^{70} +(1.45889 + 0.937571i) q^{71} +(-0.608158 + 1.33168i) q^{73} +(3.71126 + 1.08972i) q^{74} +(6.03346 + 1.77158i) q^{76} +(-0.445499 - 3.09851i) q^{77} +(-10.1410 + 11.7033i) q^{79} +(-1.45626 + 1.68062i) q^{80} +(1.24574 - 0.365783i) q^{82} +(3.35960 + 7.35650i) q^{83} +(2.29575 + 1.47539i) q^{85} +(-3.55835 + 1.04483i) q^{86} +(-2.15795 + 4.72526i) q^{88} +(2.19746 + 15.2836i) q^{89} +(4.01877 - 2.58271i) q^{91} +(-7.43771 + 8.58357i) q^{92} +(2.18089 - 4.77548i) q^{94} +(-1.93219 - 2.22987i) q^{95} +1.03304 q^{97} +(-1.82391 - 2.10491i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8}+O(q^{10}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8	\( 10 q - 4 q^{2} - 14 q^{4} + 9 q^{5} + 7 q^{7} + 7 q^{8} - 8 q^{10} + 12 q^{11} + 15 q^{13} - 5 q^{14} + 12 q^{16} - q^{17} - 13 q^{19} - 6 q^{20} - 7 q^{22} + 7 q^{23} + 12 q^{25} - 28 q^{26} + 10 q^{28} + 24 q^{29} - q^{31} + q^{32} - 15 q^{34} + 3 q^{35} + 2 q^{37} + 36 q^{38} + 25 q^{40} + 7 q^{41} - 2 q^{43} - 41 q^{44} + 6 q^{46} - 33 q^{47} + 2 q^{49} + 4 q^{50} - 21 q^{52} - 21 q^{53} + 13 q^{55} + 17 q^{56} - 3 q^{58} + 38 q^{59} - 50 q^{61} - 4 q^{62} - 31 q^{64} + 8 q^{65} + 32 q^{67} + 30 q^{68} - 10 q^{70} + 16 q^{71} + 3 q^{73} + 8 q^{74} + 5 q^{76} - 7 q^{77} - 19 q^{79} - 9 q^{80} - 16 q^{82} - 5 q^{83} - 13 q^{85} - 19 q^{86} + 48 q^{88} - 7 q^{89} - 6 q^{91} - 45 q^{92} + 22 q^{94} - 15 q^{95} + 54 q^{97} - 47 q^{98}+O(q^{100}) \) 10 * q - 4 * q^2 - 14 * q^4 + 9 * q^5 + 7 * q^7 + 7 * q^8 - 8 * q^10 + 12 * q^11 + 15 * q^13 - 5 * q^14 + 12 * q^16 - q^17 - 13 * q^19 - 6 * q^20 - 7 * q^22 + 7 * q^23 + 12 * q^25 - 28 * q^26 + 10 * q^28 + 24 * q^29 - q^31 + q^32 - 15 * q^34 + 3 * q^35 + 2 * q^37 + 36 * q^38 + 25 * q^40 + 7 * q^41 - 2 * q^43 - 41 * q^44 + 6 * q^46 - 33 * q^47 + 2 * q^49 + 4 * q^50 - 21 * q^52 - 21 * q^53 + 13 * q^55 + 17 * q^56 - 3 * q^58 + 38 * q^59 - 50 * q^61 - 4 * q^62 - 31 * q^64 + 8 * q^65 + 32 * q^67 + 30 * q^68 - 10 * q^70 + 16 * q^71 + 3 * q^73 + 8 * q^74 + 5 * q^76 - 7 * q^77 - 19 * q^79 - 9 * q^80 - 16 * q^82 - 5 * q^83 - 13 * q^85 - 19 * q^86 + 48 * q^88 - 7 * q^89 - 6 * q^91 - 45 * q^92 + 22 * q^94 - 15 * q^95 + 54 * q^97 - 47 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more