LMFDB - Embedded newform 738.2.u.f.595.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(289,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,8,0,0,4,0,0,-4,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 246)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			595.1
Character	$\chi$	$=$	738.595
Dual form			738.2.u.f.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.84265 + 2.53619i) q^{5} +(0.0346438 - 0.0679922i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.53619 + 1.84265i) q^{10} +(0.100968 + 0.0159917i) q^{11} +(-0.311532 + 0.158733i) q^{13} +(0.0539589 - 0.0539589i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.17013 + 7.38790i) q^{17} +(-2.53277 - 1.29051i) q^{19} +(-2.98147 + 0.968737i) q^{20} +(0.0910845 + 0.0464099i) q^{22} +(-0.669963 + 2.06193i) q^{23} +(-1.49181 - 4.59132i) q^{25} +(-0.345335 + 0.0546958i) q^{26} +(0.0679922 - 0.0346438i) q^{28} +(0.561209 + 3.54333i) q^{29} +(-3.20265 + 2.32686i) q^{31} +1.00000i q^{32} +(-3.39585 + 6.66472i) q^{34} +(0.108605 + 0.213149i) q^{35} +(1.42799 + 1.03749i) q^{37} +(-2.01002 - 2.01002i) q^{38} -3.13490 q^{40} +(-3.57891 - 5.30956i) q^{41} +(0.478727 + 0.155548i) q^{43} +(0.0722851 + 0.0722851i) q^{44} +(-1.27434 + 1.75398i) q^{46} +(-4.55170 - 8.93321i) q^{47} +(4.11107 + 5.65841i) q^{49} -4.82760i q^{50} +(-0.345335 - 0.0546958i) q^{52} +(1.21132 + 7.64797i) q^{53} +(-0.226606 + 0.226606i) q^{55} +(0.0753700 - 0.0119374i) q^{56} +(-0.561209 + 3.54333i) q^{58} +(2.88903 - 8.89152i) q^{59} +(9.07537 - 2.94877i) q^{61} +(-3.76494 + 1.22330i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(0.171466 - 1.08259i) q^{65} +(11.5761 - 1.83347i) q^{67} +(-5.28915 + 5.28915i) q^{68} +(0.0374227 + 0.236277i) q^{70} +(12.4401 + 1.97032i) q^{71} +5.87673i q^{73} +(1.03749 + 1.42799i) q^{74} +(-1.29051 - 2.53277i) q^{76} +(0.00458522 - 0.00631102i) q^{77} +(8.02245 + 8.02245i) q^{79} +(-2.98147 - 0.968737i) q^{80} +(-1.76301 - 6.15563i) q^{82} -6.44344 q^{83} +(-16.5810 - 16.5810i) q^{85} +(0.407229 + 0.295869i) q^{86} +(0.0464099 + 0.0910845i) q^{88} +(3.11099 - 6.10566i) q^{89} +0.0266808i q^{91} +(-1.75398 + 1.27434i) q^{92} +(-1.56841 - 9.90254i) q^{94} +(7.93998 - 4.04562i) q^{95} +(10.2747 - 1.62735i) q^{97} +(2.16132 + 6.65186i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{11} - 12 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 4 q^{19} - 4 q^{22} - 40 q^{23} + 12 q^{25} - 8 q^{26} - 4 q^{28} - 16 q^{29} - 4 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) $ 32 * q + 8 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^11 - 12 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 4 * q^19 - 4 * q^22 - 40 * q^23 + 12 * q^25 - 8 * q^26 - 4 * q^28 - 16 * q^29 - 4 * q^31 - 16 * q^34 + 8 * q^35 - 44 * q^37 + 16 * q^38 - 16 * q^40 + 28 * q^41 - 40 * q^43 + 16 * q^44 - 20 * q^46 + 48 * q^47 - 40 * q^49 - 8 * q^52 + 8 * q^53 + 72 * q^55 + 4 * q^56 + 16 * q^58 - 32 * q^59 + 100 * q^61 + 8 * q^64 - 56 * q^67 - 4 * q^68 + 48 * q^70 + 80 * q^71 + 4 * q^76 + 48 * q^79 + 12 * q^82 - 72 * q^83 - 52 * q^85 - 4 * q^86 + 4 * q^88 - 44 * q^89 - 20 * q^92 + 28 * q^94 + 40 * q^95 + 92 * q^97 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.84265	+	2.53619i	−0.824057	+	1.13422i	0.164943	+	0.986303i	$0.447256\pi$
$5$	−1.84265	+	2.53619i	−0.824057	+	1.13422i	−0.989000	+	0.147914i	$0.952744\pi$
$6$		0			0
$7$	0.0346438	−	0.0679922i	0.0130941	−	0.0256986i	−0.884367	−	0.466793i	$-0.845409\pi$
$7$	0.0346438	−	0.0679922i	0.0130941	−	0.0256986i	0.897461	+	0.441094i	$0.145409\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$		0			0
$10$	−2.53619	+	1.84265i	−0.802013	+	0.582696i
$11$	0.100968	+	0.0159917i	0.0304430	+	0.00482169i	0.171637	−	0.985160i	$-0.445094\pi$
$11$	0.100968	+	0.0159917i	0.0304430	+	0.00482169i	−0.141194	+	0.989982i	$0.545094\pi$
$12$		0			0
$13$	−0.311532	+	0.158733i	−0.0864033	+	0.0440247i	−0.496658	−	0.867946i	$-0.665440\pi$
$13$	−0.311532	+	0.158733i	−0.0864033	+	0.0440247i	0.410255	+	0.911971i	$0.365440\pi$
$14$	0.0539589	−	0.0539589i	0.0144211	−	0.0144211i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.17013	+	7.38790i	−0.283798	+	1.79183i	0.273872	+	0.961766i	$0.411696\pi$
$17$	−1.17013	+	7.38790i	−0.283798	+	1.79183i	−0.557670	+	0.830063i	$0.688304\pi$
$18$		0			0
$19$	−2.53277	−	1.29051i	−0.581057	−	0.296063i	0.138650	−	0.990341i	$-0.455724\pi$
$19$	−2.53277	−	1.29051i	−0.581057	−	0.296063i	−0.719707	+	0.694278i	$0.755724\pi$
$20$	−2.98147	+	0.968737i	−0.666676	+	0.216616i
$21$		0			0
$22$	0.0910845	+	0.0464099i	0.0194193	+	0.00989462i
$23$	−0.669963	+	2.06193i	−0.139697	+	0.429943i	−0.996291	−	0.0860481i	$-0.972576\pi$
$23$	−0.669963	+	2.06193i	−0.139697	+	0.429943i	0.856594	+	0.515991i	$0.172576\pi$
$24$		0			0
$25$	−1.49181	−	4.59132i	−0.298362	−	0.918264i
$26$	−0.345335	+	0.0546958i	−0.0677259	+	0.0107267i
$27$		0			0
$28$	0.0679922	−	0.0346438i	0.0128493	−	0.00654706i
$29$	0.561209	+	3.54333i	0.104214	+	0.657981i	0.983393	+	0.181489i	$0.0580917\pi$
$29$	0.561209	+	3.54333i	0.104214	+	0.657981i	−0.879179	+	0.476492i	$0.841908\pi$
$30$		0			0
$31$	−3.20265	+	2.32686i	−0.575213	+	0.417917i	−0.836995	−	0.547210i	$-0.815690\pi$
$31$	−3.20265	+	2.32686i	−0.575213	+	0.417917i	0.261782	+	0.965127i	$0.415690\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−3.39585	+	6.66472i	−0.582383	+	1.14299i
$35$	0.108605	+	0.213149i	0.0183576	+	0.0360287i
$36$		0			0
$37$	1.42799	+	1.03749i	0.234759	+	0.170563i	0.698945	−	0.715175i	$-0.253653\pi$
$37$	1.42799	+	1.03749i	0.234759	+	0.170563i	−0.464186	+	0.885738i	$0.653653\pi$
$38$	−2.01002	−	2.01002i	−0.326068	−	0.326068i
$39$		0			0
$40$	−3.13490			−0.495671
$41$	−3.57891	−	5.30956i	−0.558932	−	0.829213i
$41$	−3.57891	−	5.30956i	−0.558932	−	0.829213i
$42$		0			0
$43$	0.478727	+	0.155548i	0.0730051	+	0.0237208i	0.345292	−	0.938495i	$-0.387780\pi$
$43$	0.478727	+	0.155548i	0.0730051	+	0.0237208i	−0.272287	+	0.962216i	$0.587780\pi$
$44$	0.0722851	+	0.0722851i	0.0108974	+	0.0108974i
$45$		0			0
$46$	−1.27434	+	1.75398i	−0.187892	+	0.258611i
$47$	−4.55170	−	8.93321i	−0.663934	−	1.30304i	−0.939760	−	0.341836i	$-0.888951\pi$
$47$	−4.55170	−	8.93321i	−0.663934	−	1.30304i	0.275826	−	0.961208i	$-0.411049\pi$
$48$		0			0
$49$	4.11107	+	5.65841i	0.587296	+	0.808344i
$50$		−	4.82760i		−	0.682726i
$51$		0			0
$52$	−0.345335	−	0.0546958i	−0.0478894	−	0.00758494i
$53$	1.21132	+	7.64797i	0.166388	+	1.05053i	0.919630	+	0.392787i	$0.128489\pi$
$53$	1.21132	+	7.64797i	0.166388	+	1.05053i	−0.753242	+	0.657743i	$0.771511\pi$
$54$		0			0
$55$	−0.226606	+	0.226606i	−0.0305556	+	0.0305556i
$56$	0.0753700	−	0.0119374i	0.0100717	−	0.00159521i
$57$		0			0
$58$	−0.561209	+	3.54333i	−0.0736904	+	0.465263i
$59$	2.88903	−	8.89152i	0.376120	−	1.15758i	−0.566601	−	0.823993i	$-0.691742\pi$
$59$	2.88903	−	8.89152i	0.376120	−	1.15758i	0.942720	−	0.333584i	$-0.108258\pi$
$60$		0			0
$61$	9.07537	−	2.94877i	1.16198	−	0.377551i	0.336338	−	0.941741i	$-0.390812\pi$
$61$	9.07537	−	2.94877i	1.16198	−	0.377551i	0.825645	+	0.564190i	$0.190812\pi$
$62$	−3.76494	+	1.22330i	−0.478148	+	0.155360i
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.171466	−	1.08259i	0.0212677	−	0.134279i
$66$		0			0
$67$	11.5761	−	1.83347i	1.41424	−	0.223994i	0.597904	−	0.801567i	$-0.296000\pi$
$67$	11.5761	−	1.83347i	1.41424	−	0.223994i	0.816339	+	0.577573i	$0.196000\pi$
$68$	−5.28915	+	5.28915i	−0.641404	+	0.641404i
$69$		0			0
$70$	0.0374227	+	0.236277i	0.00447286	+	0.0282405i
$71$	12.4401	+	1.97032i	1.47637	+	0.233834i	0.842118	−	0.539294i	$-0.181309\pi$
$71$	12.4401	+	1.97032i	1.47637	+	0.233834i	0.634250	+	0.773128i	$0.281309\pi$
$72$		0			0
$73$			5.87673i			0.687819i	0.939003	+	0.343910i	$0.111751\pi$
$73$			5.87673i			0.687819i	−0.939003	+	0.343910i	$0.888249\pi$
$74$	1.03749	+	1.42799i	0.120606	+	0.166000i
$75$		0			0
$76$	−1.29051	−	2.53277i	−0.148032	−	0.290529i
$77$	0.00458522	−	0.00631102i	0.000522535	−	0.000719208i
$78$		0			0
$79$	8.02245	+	8.02245i	0.902596	+	0.902596i	0.995660	−	0.0930639i	$-0.0296661\pi$
$79$	8.02245	+	8.02245i	0.902596	+	0.902596i	−0.0930639	+	0.995660i	$0.529666\pi$
$80$	−2.98147	−	0.968737i	−0.333338	−	0.108308i
$81$		0			0
$82$	−1.76301	−	6.15563i	−0.194691	−	0.679776i
$83$	−6.44344			−0.707259			−0.353629	−	0.935386i	$-0.615053\pi$
$83$	−6.44344			−0.707259			−0.353629	+	0.935386i	$0.615053\pi$
$84$		0			0
$85$	−16.5810	−	16.5810i	−1.79846	−	1.79846i
$86$	0.407229	+	0.295869i	0.0439127	+	0.0319044i
$87$		0			0
$88$	0.0464099	+	0.0910845i	0.00494731	+	0.00970964i
$89$	3.11099	−	6.10566i	0.329764	−	0.647198i	−0.665284	−	0.746590i	$-0.731690\pi$
$89$	3.11099	−	6.10566i	0.329764	−	0.647198i	0.995048	+	0.0993917i	$0.0316897\pi$
$90$		0			0
$91$			0.0266808i			0.00279691i
$92$	−1.75398	+	1.27434i	−0.182866	+	0.132860i
$93$		0			0
$94$	−1.56841	−	9.90254i	−0.161769	−	1.02137i
$95$	7.93998	−	4.04562i	0.814624	−	0.415072i
$96$		0			0
$97$	10.2747	−	1.62735i	1.04324	−	0.165232i	0.388779	−	0.921331i	$-0.372897\pi$
$97$	10.2747	−	1.62735i	1.04324	−	0.165232i	0.654458	+	0.756099i	$0.272897\pi$
$98$	2.16132	+	6.65186i	0.218326	+	0.671939i
$99$		0			0
$100$	1.49181	−	4.59132i	0.149181	−	0.459132i
$101$	0.666935	+	0.339820i	0.0663625	+	0.0338134i	0.486857	−	0.873482i	$-0.338143\pi$
$101$	0.666935	+	0.339820i	0.0663625	+	0.0338134i	−0.420494	+	0.907295i	$0.638143\pi$
$102$		0			0
$103$	−1.83036	+	0.594721i	−0.180351	+	0.0585996i	−0.397800	−	0.917472i	$-0.630226\pi$
$103$	−1.83036	+	0.594721i	−0.180351	+	0.0585996i	0.217449	+	0.976072i	$0.430226\pi$
$104$	−0.311532	−	0.158733i	−0.0305482	−	0.0155651i
$105$		0			0
$106$	−1.21132	+	7.64797i	−0.117654	+	0.742837i
$107$	2.95677	+	9.10000i	0.285842	+	0.879730i	0.986145	+	0.165885i	$0.0530479\pi$
$107$	2.95677	+	9.10000i	0.285842	+	0.879730i	−0.700304	+	0.713845i	$0.746952\pi$
$108$		0			0
$109$	2.13974	−	2.13974i	0.204950	−	0.204950i	−0.597167	−	0.802117i	$-0.703707\pi$
$109$	2.13974	−	2.13974i	0.204950	−	0.204950i	0.802117	+	0.597167i	$0.203707\pi$
$110$	−0.285541	+	0.145490i	−0.0272252	+	0.0138720i
$111$		0			0
$112$	0.0753700	+	0.0119374i	0.00712179	+	0.00112798i
$113$	16.1454	−	11.7303i	1.51883	−	1.10350i	0.556771	−	0.830666i	$-0.312040\pi$
$113$	16.1454	−	11.7303i	1.51883	−	1.10350i	0.962062	−	0.272831i	$-0.0879600\pi$
$114$		0			0
$115$	−3.99494	−	5.49857i	−0.372530	−	0.512744i
$116$	−1.62869	+	3.19649i	−0.151220	+	0.296787i
$117$		0			0
$118$	5.49526	−	7.56358i	0.505880	−	0.696284i
$119$	0.461782	+	0.335504i	0.0423315	+	0.0307556i
$120$		0			0
$121$	−10.4517	−	3.39596i	−0.950153	−	0.308723i
$122$	9.54241			0.863929
$123$		0			0
$124$	−3.95869			−0.355501
$125$	−0.514007	−	0.167011i	−0.0459742	−	0.0149379i
$126$		0			0
$127$	7.22363	+	5.24828i	0.640994	+	0.465709i	0.860191	−	0.509971i	$-0.170344\pi$
$127$	7.22363	+	5.24828i	0.640994	+	0.465709i	−0.219198	+	0.975680i	$0.570344\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$		0			0
$130$	0.497613	−	0.976621i	0.0436435	−	0.0856553i
$131$	−8.99722	−	12.3836i	−0.786091	−	1.08196i	−0.994584	−	0.103938i	$-0.966856\pi$
$131$	−8.99722	−	12.3836i	−0.786091	−	1.08196i	0.208493	−	0.978024i	$-0.433144\pi$
$132$		0			0
$133$	−0.175489	+	0.127500i	−0.0152169	+	0.0110557i
$134$	11.5761	+	1.83347i	1.00002	+	0.158388i
$135$		0			0
$136$	−6.66472	+	3.39585i	−0.571495	+	0.291191i
$137$	−14.2651	+	14.2651i	−1.21875	+	1.21875i	−0.250681	+	0.968070i	$0.580655\pi$
$137$	−14.2651	+	14.2651i	−1.21875	+	1.21875i	−0.968070	+	0.250681i	$0.919345\pi$
$138$		0			0
$139$	−3.23954	−	9.97029i	−0.274775	−	0.845669i	−0.989279	−	0.146038i	$-0.953348\pi$
$139$	−3.23954	−	9.97029i	−0.274775	−	0.845669i	0.714504	−	0.699631i	$-0.246652\pi$
$140$	−0.0374227	+	0.236277i	−0.00316279	+	0.0199691i
$141$		0			0
$142$	11.2224	+	5.71809i	0.941761	+	0.479851i
$143$	−0.0339931	+	0.0110450i	−0.00284265	+	0.000923632i
$144$		0			0
$145$	−10.0207	−	5.10579i	−0.832172	−	0.424013i
$146$	−1.81601	+	5.58910i	−0.150294	+	0.462558i
$147$		0			0
$148$	0.545442	+	1.67870i	0.0448351	+	0.137988i
$149$	−21.0600	+	3.33557i	−1.72530	+	0.273261i	−0.938833	−	0.344373i	$-0.888092\pi$
$149$	−21.0600	+	3.33557i	−1.72530	+	0.273261i	−0.786466	+	0.617634i	$0.788092\pi$
$150$		0			0
$151$	12.8298	−	6.53713i	1.04408	−	0.531984i	0.154132	−	0.988050i	$-0.450742\pi$
$151$	12.8298	−	6.53713i	1.04408	−	0.531984i	0.889946	+	0.456066i	$0.150742\pi$
$152$	−0.444679	−	2.80760i	−0.0360683	−	0.227726i
$153$		0			0
$154$	0.00631102	−	0.00458522i	0.000508557	−	0.000369488i
$155$		−	12.4101i		−	0.996804i
$156$		0			0
$157$	3.37714	−	6.62800i	0.269525	−	0.528972i	−0.716084	−	0.698014i	$-0.754067\pi$
$157$	3.37714	−	6.62800i	0.269525	−	0.528972i	0.985609	+	0.169042i	$0.0540673\pi$
$158$	5.15073	+	10.1089i	0.409770	+	0.804219i
$159$		0			0
$160$	−2.53619	−	1.84265i	−0.200503	−	0.145674i
$161$	0.116985	+	0.116985i	0.00921974	+	0.00921974i
$162$		0			0
$163$	−11.8702			−0.929748			−0.464874	−	0.885377i	$-0.653900\pi$
$163$	−11.8702			−0.929748			−0.464874	+	0.885377i	$0.653900\pi$
$164$	0.225477	−	6.39915i	0.0176068	−	0.499690i
$165$		0			0
$166$	−6.12807	−	1.99113i	−0.475631	−	0.154542i
$167$	15.0057	+	15.0057i	1.16118	+	1.16118i	0.984218	+	0.176958i	$0.0566256\pi$
$167$	15.0057	+	15.0057i	1.16118	+	1.16118i	0.176958	+	0.984218i	$0.443374\pi$
$168$		0			0
$169$	−7.56935	+	10.4183i	−0.582258	+	0.801409i
$170$	−10.6456	−	20.8932i	−0.816483	−	1.60244i
$171$		0			0
$172$	0.295869	+	0.407229i	0.0225598	+	0.0310509i
$173$		−	15.1065i		−	1.14853i	−0.818671	−	0.574263i	$-0.805289\pi$
$173$		−	15.1065i		−	1.14853i	0.818671	−	0.574263i	$-0.194711\pi$
$174$		0			0
$175$	−0.363856	−	0.0576291i	−0.0275049	−	0.00435635i
$176$	0.0159917	+	0.100968i	0.00120542	+	0.00761074i
$177$		0			0
$178$	4.84548	−	4.84548i	0.363184	−	0.363184i
$179$	17.2465	−	2.73158i	1.28906	−	0.204168i	0.525996	−	0.850487i	$-0.323693\pi$
$179$	17.2465	−	2.73158i	1.28906	−	0.204168i	0.763067	+	0.646319i	$0.223693\pi$
$180$		0			0
$181$	−3.37192	+	21.2895i	−0.250633	+	1.58243i	0.465872	+	0.884852i	$0.345741\pi$
$181$	−3.37192	+	21.2895i	−0.250633	+	1.58243i	−0.716505	+	0.697582i	$0.754259\pi$
$182$	−0.00824484	+	0.0253750i	−0.000611148	+	0.00188092i
$183$		0			0
$184$	−2.06193	+	0.669963i	−0.152008	+	0.0493903i
$185$	−5.26255	+	1.70991i	−0.386911	+	0.125715i
$186$		0			0
$187$	−0.236291	+	0.727229i	−0.0172793	+	0.0531802i
$188$	1.56841	−	9.90254i	0.114388	−	0.722217i
$189$		0			0
$190$	8.80153	−	1.39403i	0.638530	−	0.101133i
$191$	14.6503	−	14.6503i	1.06006	−	1.06006i	0.0619807	−	0.998077i	$-0.480258\pi$
$191$	14.6503	−	14.6503i	1.06006	−	1.06006i	0.998077	−	0.0619807i	$-0.0197417\pi$
$192$		0			0
$193$	−0.919085	−	5.80288i	−0.0661572	−	0.417700i	−0.998433	−	0.0559529i	$-0.982180\pi$
$193$	−0.919085	−	5.80288i	−0.0661572	−	0.417700i	0.932276	−	0.361747i	$-0.117820\pi$
$194$	10.2747	+	1.62735i	0.737680	+	0.116837i
$195$		0			0
$196$			6.99418i			0.499584i
$197$	−4.92559	−	6.77950i	−0.350934	−	0.483019i	0.596661	−	0.802493i	$-0.296494\pi$
$197$	−4.92559	−	6.77950i	−0.350934	−	0.483019i	−0.947595	+	0.319474i	$0.896494\pi$
$198$		0			0
$199$	0.232645	+	0.456592i	0.0164918	+	0.0323670i	0.899105	−	0.437732i	$-0.144218\pi$
$199$	0.232645	+	0.456592i	0.0164918	+	0.0323670i	−0.882614	+	0.470099i	$0.844218\pi$
$200$	2.83759	−	3.90561i	0.200648	−	0.276168i
$201$		0			0
$202$	0.529283	+	0.529283i	0.0372402	+	0.0372402i
$203$	0.260362	+	0.0845966i	0.0182738	+	0.00593752i
$204$		0			0
$205$	20.0607	+	0.706848i	1.40110	+	0.0493684i
$206$	−1.92456			−0.134090
$207$		0			0
$208$	−0.247233	−	0.247233i	−0.0171425	−	0.0171425i
$209$	−0.235091	−	0.170804i	−0.0162616	−	0.0118147i
$210$		0			0
$211$	0.714967	+	1.40320i	0.0492204	+	0.0966004i	0.914307	−	0.405023i	$-0.132736\pi$
$211$	0.714967	+	1.40320i	0.0492204	+	0.0966004i	−0.865086	+	0.501623i	$0.832736\pi$
$212$	−3.51539	+	6.89934i	−0.241438	+	0.473848i
$213$		0			0
$214$			9.56830i			0.654076i
$215$	−1.27662	+	0.927521i	−0.0870650	+	0.0632564i
$216$		0			0
$217$	0.0472566	+	0.298367i	0.00320799	+	0.0202545i
$218$	2.69623	−	1.37380i	0.182612	−	0.0930453i
$219$		0			0
$220$	−0.316524	+	0.0501325i	−0.0213401	+	0.00337994i
$221$	−0.808174	−	2.48730i	−0.0543637	−	0.167314i
$222$		0			0
$223$	−3.23494	+	9.95613i	−0.216628	+	0.666712i	0.782406	+	0.622768i	$0.213992\pi$
$223$	−3.23494	+	9.95613i	−0.216628	+	0.666712i	−0.999034	+	0.0439434i	$0.986008\pi$
$224$	0.0679922	+	0.0346438i	0.00454292	+	0.00231473i
$225$		0			0
$226$	18.9801	−	6.16700i	1.26254	−	0.410223i
$227$	1.04445	+	0.532171i	0.0693223	+	0.0353215i	0.488308	−	0.872671i	$-0.337614\pi$
$227$	1.04445	+	0.532171i	0.0693223	+	0.0353215i	−0.418986	+	0.907993i	$0.637614\pi$
$228$		0			0
$229$	−1.29154	+	8.15447i	−0.0853474	+	0.538863i	0.907555	+	0.419933i	$0.137946\pi$
$229$	−1.29154	+	8.15447i	−0.0853474	+	0.538863i	−0.992903	+	0.118930i	$0.962054\pi$
$230$	−2.10027	−	6.46395i	−0.138487	−	0.426221i
$231$		0			0
$232$	−2.53675	+	2.53675i	−0.166546	+	0.166546i
$233$	21.1656	−	10.7844i	1.38660	−	0.706510i	0.408138	−	0.912920i	$-0.366178\pi$
$233$	21.1656	−	10.7844i	1.38660	−	0.706510i	0.978466	+	0.206410i	$0.0661781\pi$
$234$		0			0
$235$	31.0435	+	4.91680i	2.02505	+	0.320737i
$236$	7.56358	−	5.49526i	0.492347	−	0.357711i
$237$		0			0
$238$	0.335504	+	0.461782i	0.0217475	+	0.0299329i
$239$	−9.07637	+	17.8134i	−0.587102	+	1.15225i	0.386134	+	0.922443i	$0.373810\pi$
$239$	−9.07637	+	17.8134i	−0.587102	+	1.15225i	−0.973236	+	0.229810i	$0.926190\pi$
$240$		0			0
$241$	−4.67533	+	6.43504i	−0.301165	+	0.414517i	−0.932600	−	0.360911i	$-0.882466\pi$
$241$	−4.67533	+	6.43504i	−0.301165	+	0.414517i	0.631436	+	0.775428i	$0.282466\pi$
$242$	−8.89073	−	6.45950i	−0.571518	−	0.415232i
$243$		0			0
$244$	9.07537	+	2.94877i	0.580991	+	0.188776i
$245$	−21.9260			−1.40080
$246$		0			0
$247$	0.993884			0.0632394
$248$	−3.76494	−	1.22330i	−0.239074	−	0.0776799i
$249$		0			0
$250$	−0.437240	−	0.317674i	−0.0276535	−	0.0200915i
$251$	−2.14543	+	2.95293i	−0.135418	+	0.186387i	−0.871341	−	0.490679i	$-0.836749\pi$
$251$	−2.14543	+	2.95293i	−0.135418	+	0.186387i	0.735922	+	0.677066i	$0.236749\pi$
$252$		0			0
$253$	−0.100619	+	0.197475i	−0.00632584	+	0.0124152i
$254$	5.24828	+	7.22363i	0.329306	+	0.453251i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.665902	−	0.105469i	−0.0415379	−	0.00657895i	0.135631	−	0.990759i	$-0.456694\pi$
$257$	−0.665902	−	0.105469i	−0.0415379	−	0.00657895i	−0.177169	+	0.984180i	$0.556694\pi$
$258$		0			0
$259$	0.120012	−	0.0611493i	0.00745720	−	0.00379963i
$260$	0.775050	−	0.775050i	0.0480666	−	0.0480666i
$261$		0			0
$262$	−4.73012	−	14.5578i	−0.292228	−	0.899385i
$263$	−2.92611	+	18.4747i	−0.180432	+	1.13920i	0.716682	+	0.697400i	$0.245660\pi$
$263$	−2.92611	+	18.4747i	−0.180432	+	1.13920i	−0.897113	+	0.441800i	$0.854340\pi$
$264$		0			0
$265$	−21.6287	−	11.0204i	−1.32864	−	0.676977i
$266$	−0.206300	+	0.0670310i	−0.0126491	+	0.00410993i
$267$		0			0
$268$	10.4429	+	5.32094i	0.637904	+	0.325028i
$269$	−1.07493	+	3.30831i	−0.0655399	+	0.201711i	−0.978464	−	0.206419i	$-0.933819\pi$
$269$	−1.07493	+	3.30831i	−0.0655399	+	0.201711i	0.912924	+	0.408130i	$0.133819\pi$
$270$		0			0
$271$	3.06228	+	9.42473i	0.186020	+	0.572511i	0.999964	−	0.00843170i	$-0.00268392\pi$
$271$	3.06228	+	9.42473i	0.186020	+	0.572511i	−0.813944	+	0.580943i	$0.802684\pi$
$272$	−7.38790	+	1.17013i	−0.447957	+	0.0709495i
$273$		0			0
$274$	−17.9751	+	9.15877i	−1.08592	+	0.553301i
$275$	−0.0772018	−	0.487433i	−0.00465544	−	0.0293933i
$276$		0			0
$277$	6.93279	−	5.03697i	0.416551	−	0.302642i	−0.359697	−	0.933069i	$-0.617120\pi$
$277$	6.93279	−	5.03697i	0.416551	−	0.302642i	0.776249	+	0.630427i	$0.217120\pi$
$278$		−	10.4834i		−	0.628752i
$279$		0			0
$280$	−0.108605	+	0.213149i	−0.00649038	+	0.0127381i
$281$	0.403383	+	0.791683i	0.0240638	+	0.0472279i	0.902725	−	0.430217i	$-0.141563\pi$
$281$	0.403383	+	0.791683i	0.0240638	+	0.0472279i	−0.878662	+	0.477445i	$0.841563\pi$
$282$		0			0
$283$	−19.4643	−	14.1416i	−1.15703	−	0.840633i	−0.167632	−	0.985850i	$-0.553612\pi$
$283$	−19.4643	−	14.1416i	−1.15703	−	0.840633i	−0.989400	+	0.145217i	$0.953612\pi$
$284$	8.90613	+	8.90613i	0.528481	+	0.528481i
$285$		0			0
$286$	−0.0357425			−0.00211350
$287$	−0.484996	+	0.0593952i	−0.0286284	+	0.00350599i
$288$		0			0
$289$	−37.0439	−	12.0363i	−2.17905	−	0.708018i
$290$	−7.95245	−	7.95245i	−0.466984	−	0.466984i
$291$		0			0
$292$	−3.45426	+	4.75438i	−0.202145	+	0.278229i
$293$	−2.02289	−	3.97014i	−0.118178	−	0.231938i	0.824338	−	0.566098i	$-0.191548\pi$
$293$	−2.02289	−	3.97014i	−0.118178	−	0.231938i	−0.942517	+	0.334160i	$0.891548\pi$
$294$		0			0
$295$	17.2271	+	23.7111i	1.00300	+	1.38051i
$296$			1.76509i			0.102594i
$297$		0			0
$298$	−21.0600	−	3.33557i	−1.21997	−	0.193224i
$299$	−0.118583	−	0.748703i	−0.00685782	−	0.0432986i
$300$		0			0
$301$	0.0271609	−	0.0271609i	0.00156553	−	0.00156553i
$302$	14.2220	−	2.25254i	0.818384	−	0.129619i
$303$		0			0
$304$	0.444679	−	2.80760i	0.0255041	−	0.161027i
$305$	−9.24409	+	28.4504i	−0.529315	+	1.62906i
$306$		0			0
$307$	26.9559	−	8.75849i	1.53845	−	0.499874i	0.587504	−	0.809221i	$-0.300111\pi$
$307$	26.9559	−	8.75849i	1.53845	−	0.499874i	0.950949	+	0.309348i	$0.100111\pi$
$308$	0.00741905	−	0.00241060i	0.000422740	−	0.000137356i
$309$		0			0
$310$	3.83494	−	11.8027i	0.217810	−	0.670349i
$311$	−4.45454	+	28.1249i	−0.252594	+	1.59482i	0.456514	+	0.889716i	$0.349098\pi$
$311$	−4.45454	+	28.1249i	−0.252594	+	1.59482i	−0.709108	+	0.705099i	$0.750902\pi$
$312$		0			0
$313$	−22.7528	+	3.60369i	−1.28606	+	0.203692i	−0.761771	−	0.647846i	$-0.775670\pi$
$313$	−22.7528	+	3.60369i	−1.28606	+	0.203692i	−0.524292	+	0.851538i	$0.675670\pi$
$314$	5.26001	−	5.26001i	0.296840	−	0.296840i
$315$		0			0
$316$	1.77482	+	11.2058i	0.0998415	+	0.630374i
$317$	6.37254	+	1.00931i	0.357917	+	0.0566885i	0.332804	−	0.942996i	$-0.392005\pi$
$317$	6.37254	+	1.00931i	0.357917	+	0.0566885i	0.0251135	+	0.999685i	$0.492005\pi$
$318$		0			0
$319$			0.366738i			0.0205334i
$320$	−1.84265	−	2.53619i	−0.103007	−	0.141777i
$321$		0			0
$322$	0.0751092	+	0.147410i	0.00418567	+	0.00821485i
$323$	12.4978	−	17.2018i	0.695398	−	0.957133i
$324$		0			0
$325$	1.19354	+	1.19354i	0.0662058	+	0.0662058i
$326$	−11.2893	−	3.66810i	−0.625254	−	0.203157i
$327$		0			0
$328$	2.19189	−	6.01628i	0.121027	−	0.332193i
$329$	−0.765077			−0.0421801
$330$		0			0
$331$	−24.2411	−	24.2411i	−1.33241	−	1.33241i	−0.903208	−	0.429204i	$-0.858794\pi$
$331$	−24.2411	−	24.2411i	−1.33241	−	1.33241i	−0.429204	−	0.903208i	$-0.641206\pi$
$332$	−5.21285	−	3.78736i	−0.286092	−	0.207858i
$333$		0			0
$334$	9.63426	+	18.9083i	0.527163	+	1.03462i
$335$	−16.6806	+	32.7376i	−0.911359	+	1.78864i
$336$		0			0
$337$			5.87884i			0.320241i	0.987097	+	0.160120i	$0.0511882\pi$
$337$			5.87884i			0.320241i	−0.987097	+	0.160120i	$0.948812\pi$
$338$	−10.4183	+	7.56935i	−0.566682	+	0.411719i
$339$		0			0
$340$	−3.66824	−	23.1603i	−0.198938	−	1.25605i
$341$	−0.360576	+	0.183722i	−0.0195263	+	0.00994913i
$342$		0			0
$343$	1.05474	−	0.167055i	0.0569506	−	0.00902010i
$344$	0.155548	+	0.478727i	0.00838657	+	0.0258112i
$345$		0			0
$346$	4.66817	−	14.3671i	0.250962	−	0.772383i
$347$	11.0081	+	5.60890i	0.590945	+	0.301101i	0.723773	−	0.690038i	$-0.242406\pi$
$347$	11.0081	+	5.60890i	0.590945	+	0.301101i	−0.132829	+	0.991139i	$0.542406\pi$
$348$		0			0
$349$	5.63605	−	1.83127i	0.301691	−	0.0980254i	−0.154260	−	0.988030i	$-0.549299\pi$
$349$	5.63605	−	1.83127i	0.301691	−	0.0980254i	0.455951	+	0.890005i	$0.349299\pi$
$350$	−0.328239	−	0.167246i	−0.0175451	−	0.00893969i
$351$		0			0
$352$	−0.0159917	+	0.100968i	−0.000852363	+	0.00538161i
$353$	0.332345	+	1.02285i	0.0176889	+	0.0544409i	0.959511	−	0.281670i	$-0.0908883\pi$
$353$	0.332345	+	1.02285i	0.0176889	+	0.0544409i	−0.941822	+	0.336111i	$0.890888\pi$
$354$		0			0
$355$	−27.9198	+	27.9198i	−1.48183	+	1.48183i
$356$	6.10566	−	3.11099i	0.323599	−	0.164882i
$357$		0			0
$358$	17.2465	+	2.73158i	0.911506	+	0.144368i
$359$	3.02432	−	2.19730i	0.159618	−	0.115969i	−0.505109	−	0.863055i	$-0.668548\pi$
$359$	3.02432	−	2.19730i	0.159618	−	0.115969i	0.664727	+	0.747086i	$0.268548\pi$
$360$		0			0
$361$	−6.41842	−	8.83420i	−0.337811	−	0.464958i
$362$	−9.78570	+	19.2055i	−0.514325	+	1.00942i
$363$		0			0
$364$	−0.0156826	+	0.0215853i	−0.000821992	+	0.00113138i
$365$	−14.9045	−	10.8287i	−0.780137	−	0.566803i
$366$		0			0
$367$	34.4342	+	11.1884i	1.79745	+	0.584028i	0.999817	−	0.0191125i	$-0.00608407\pi$
$367$	34.4342	+	11.1884i	1.79745	+	0.584028i	0.797635	+	0.603140i	$0.206084\pi$
$368$	−2.16804			−0.113017
$369$		0			0
$370$	−5.53337			−0.287666
$371$	0.561968	+	0.182594i	0.0291759	+	0.00947982i
$372$		0			0
$373$	−21.7974	−	15.8368i	−1.12863	−	0.819997i	−0.143134	−	0.989703i	$-0.545718\pi$
$373$	−21.7974	−	15.8368i	−1.12863	−	0.819997i	−0.985495	+	0.169706i	$0.945718\pi$
$374$	−0.449452	+	0.618618i	−0.0232406	+	0.0319880i
$375$		0			0
$376$	4.55170	−	8.93321i	0.234736	−	0.460695i
$377$	−0.737280	−	1.01478i	−0.0379718	−	0.0522637i
$378$		0			0
$379$	22.2040	−	16.1322i	1.14054	−	0.828653i	0.153348	−	0.988172i	$-0.450994\pi$
$379$	22.2040	−	16.1322i	1.14054	−	0.828653i	0.987195	+	0.159519i	$0.0509944\pi$
$380$	8.80153	+	1.39403i	0.451509	+	0.0715120i
$381$		0			0
$382$	18.4604	−	9.40607i	0.944519	−	0.481256i
$383$	−7.29030	+	7.29030i	−0.372517	+	0.372517i	−0.868393	−	0.495876i	$-0.834847\pi$
$383$	−7.29030	+	7.29030i	−0.372517	+	0.372517i	0.495876	+	0.868393i	$0.334847\pi$
$384$		0			0
$385$	0.00755698	+	0.0232580i	0.000385139	+	0.00118534i
$386$	0.919085	−	5.80288i	0.0467802	−	0.295359i
$387$		0			0
$388$	9.26893	+	4.72276i	0.470559	+	0.239762i
$389$	−5.15936	+	1.67638i	−0.261590	+	0.0849957i	−0.436876	−	0.899522i	$-0.643915\pi$
$389$	−5.15936	+	1.67638i	−0.261590	+	0.0849957i	0.175286	+	0.984518i	$0.443915\pi$
$390$		0			0
$391$	−14.4494	−	7.36234i	−0.730738	−	0.372330i
$392$	−2.16132	+	6.65186i	−0.109163	+	0.335970i
$393$		0			0
$394$	−2.58954	−	7.96978i	−0.130459	−	0.401512i
$395$	−35.1290	+	5.56389i	−1.76753	+	0.279950i
$396$		0			0
$397$	−15.7141	+	8.00674i	−0.788669	+	0.401847i	−0.801443	−	0.598071i	$-0.795934\pi$
$397$	−15.7141	+	8.00674i	−0.788669	+	0.401847i	0.0127737	+	0.999918i	$0.495934\pi$
$398$	0.0801641	+	0.506136i	0.00401826	+	0.0253703i
$399$		0			0
$400$	3.90561	−	2.83759i	0.195280	−	0.141880i
$401$		−	20.7188i		−	1.03465i	−0.855790	−	0.517323i	$-0.826929\pi$
$401$		−	20.7188i		−	1.03465i	0.855790	−	0.517323i	$-0.173071\pi$
$402$		0			0
$403$	0.628377	−	1.23326i	0.0313017	−	0.0614330i
$404$	0.339820	+	0.666935i	0.0169067	+	0.0331813i
$405$		0			0
$406$	0.221477	+	0.160912i	0.0109917	+	0.00798595i
$407$	0.127589	+	0.127589i	0.00632438	+	0.00632438i
$408$		0			0
$409$	−10.5239			−0.520375			−0.260187	−	0.965558i	$-0.583784\pi$
$409$	−10.5239			−0.520375			−0.260187	+	0.965558i	$0.583784\pi$
$410$	18.8604	+	6.87135i	0.931451	+	0.339352i
$411$		0			0
$412$	−1.83036	−	0.594721i	−0.0901754	−	0.0292998i
$413$	−0.504467	−	0.504467i	−0.0248232	−	0.0248232i
$414$		0			0
$415$	11.8730	−	16.3418i	0.582822	−	0.802185i
$416$	−0.158733	−	0.311532i	−0.00778254	−	0.0152741i
$417$		0			0
$418$	−0.170804	−	0.235091i	−0.00835427	−	0.0114987i
$419$		−	12.0058i		−	0.586520i	−0.956033	−	0.293260i	$-0.905260\pi$
$419$		−	12.0058i		−	0.586520i	0.956033	−	0.293260i	$-0.0947402\pi$
$420$		0			0
$421$	8.63360	+	1.36743i	0.420776	+	0.0666444i	0.363232	−	0.931699i	$-0.381673\pi$
$421$	8.63360	+	1.36743i	0.420776	+	0.0666444i	0.0575438	+	0.998343i	$0.481673\pi$
$422$	0.246361	+	1.55546i	0.0119927	+	0.0757187i
$423$		0			0
$424$	−5.47535	+	5.47535i	−0.265906	+	0.265906i
$425$	35.6658	−	5.64891i	1.73005	−	0.274012i
$426$		0			0
$427$	0.113912	−	0.719211i	0.00551258	−	0.0348051i
$428$	−2.95677	+	9.10000i	−0.142921	+	0.439865i
$429$		0			0
$430$	−1.50076	+	0.487627i	−0.0723731	+	0.0235154i
$431$	−14.5130	+	4.71556i	−0.699067	+	0.227140i	−0.636924	−	0.770927i	$-0.719793\pi$
$431$	−14.5130	+	4.71556i	−0.699067	+	0.227140i	−0.0621428	+	0.998067i	$0.519793\pi$
$432$		0			0
$433$	−12.0419	+	37.0613i	−0.578698	+	1.78105i	0.0445275	+	0.999008i	$0.485822\pi$
$433$	−12.0419	+	37.0613i	−0.578698	+	1.78105i	−0.623226	+	0.782042i	$0.714178\pi$
$434$	−0.0472566	+	0.298367i	−0.00226839	+	0.0143221i
$435$		0			0
$436$	2.98879	−	0.473378i	0.143137	−	0.0226707i
$437$	4.35781	−	4.35781i	0.208462	−	0.208462i
$438$		0			0
$439$	2.50768	+	15.8329i	0.119685	+	0.755661i	0.972406	+	0.233294i	$0.0749506\pi$
$439$	2.50768	+	15.8329i	0.119685	+	0.755661i	−0.852721	+	0.522366i	$0.825049\pi$
$440$	−0.316524	−	0.0501325i	−0.0150897	−	0.00238998i
$441$		0			0
$442$		−	2.61531i		−	0.124397i
$443$	−11.0705	−	15.2372i	−0.525974	−	0.723941i	0.460536	−	0.887641i	$-0.347657\pi$
$443$	−11.0705	−	15.2372i	−0.525974	−	0.723941i	−0.986510	+	0.163700i	$0.947657\pi$
$444$		0			0
$445$	9.75264	+	19.1406i	0.462319	+	0.907353i
$446$	−6.15323	+	8.46919i	−0.291364	+	0.401028i
$447$		0			0
$448$	0.0539589	+	0.0539589i	0.00254932	+	0.00254932i
$449$	22.5162	+	7.31595i	1.06260	+	0.345261i	0.787603	−	0.616183i	$-0.211322\pi$
$449$	22.5162	+	7.31595i	1.06260	+	0.345261i	0.275001	+	0.961444i	$0.411322\pi$
$450$		0			0
$451$	−0.276446	−	0.593328i	−0.0130174	−	0.0279387i
$452$	19.9568			0.938691
$453$		0			0
$454$	0.828876	+	0.828876i	0.0389011	+	0.0389011i
$455$	−0.0676676	−	0.0491634i	−0.00317231	−	0.00230482i
$456$		0			0
$457$	1.68928	+	3.31539i	0.0790211	+	0.155088i	0.927136	−	0.374724i	$-0.122263\pi$
$457$	1.68928	+	3.31539i	0.0790211	+	0.155088i	−0.848115	+	0.529812i	$0.822263\pi$
$458$	−3.74820	+	7.35625i	−0.175142	+	0.343735i
$459$		0			0
$460$		−	6.79660i		−	0.316893i
$461$	−28.6714	+	20.8310i	−1.33536	+	0.970195i	−0.335758	+	0.941948i	$0.608992\pi$
$461$	−28.6714	+	20.8310i	−1.33536	+	0.970195i	−0.999601	+	0.0282468i	$0.991008\pi$
$462$		0			0
$463$	3.82726	+	24.1644i	0.177868	+	1.12301i	0.901484	+	0.432812i	$0.142479\pi$
$463$	3.82726	+	24.1644i	0.177868	+	1.12301i	−0.723616	+	0.690203i	$0.757521\pi$
$464$	−3.19649	+	1.62869i	−0.148393	+	0.0756101i
$465$		0			0
$466$	23.4622	−	3.71605i	1.08687	−	0.172143i
$467$	3.94825	+	12.1514i	0.182703	+	0.562302i	0.999901	−	0.0140547i	$-0.00447389\pi$
$467$	3.94825	+	12.1514i	0.182703	+	0.562302i	−0.817198	+	0.576357i	$0.804474\pi$
$468$		0			0
$469$	0.276377	−	0.850602i	0.0127619	−	0.0392771i
$470$	28.0047	+	14.2691i	1.29176	+	0.658186i
$471$		0			0
$472$	8.89152	−	2.88903i	0.409265	−	0.132978i
$473$	0.0458486	+	0.0233610i	0.00210812	+	0.00107414i
$474$		0			0
$475$	−2.14673	+	13.5539i	−0.0984989	+	0.621898i
$476$	0.176385	+	0.542858i	0.00808460	+	0.0248818i
$477$		0			0
$478$	−14.1368	+	14.1368i	−0.646602	+	0.646602i
$479$	11.3045	−	5.75996i	0.516518	−	0.263179i	−0.176243	−	0.984347i	$-0.556394\pi$
$479$	11.3045	−	5.75996i	0.516518	−	0.263179i	0.692761	+	0.721168i	$0.256394\pi$
$480$		0			0
$481$	−0.609547	−	0.0965428i	−0.0277930	−	0.00440197i
$482$	−6.43504	+	4.67533i	−0.293108	+	0.212955i
$483$		0			0
$484$	−6.45950	−	8.89073i	−0.293613	−	0.404124i
$485$	−14.8054	+	29.0572i	−0.672277	+	1.31942i
$486$		0			0
$487$	16.8887	−	23.2454i	0.765302	−	1.05335i	−0.231453	−	0.972846i	$-0.574348\pi$
$487$	16.8887	−	23.2454i	0.765302	−	1.05335i	0.996754	−	0.0805016i	$-0.0256522\pi$
$488$	7.71997	+	5.60889i	0.349467	+	0.253902i
$489$		0			0
$490$	−20.8529	−	6.77552i	−0.942038	−	0.306087i
$491$	−38.6471			−1.74412			−0.872061	−	0.489398i	$-0.837217\pi$
$491$	−38.6471			−1.74412			−0.872061	+	0.489398i	$0.837217\pi$
$492$		0			0
$493$	−26.8345			−1.20856
$494$	0.945240	+	0.307127i	0.0425284	+	0.0138183i
$495$		0			0
$496$	−3.20265	−	2.32686i	−0.143803	−	0.104479i
$497$	0.564938	−	0.777571i	0.0253409	−	0.0348788i
$498$		0			0
$499$	9.36080	−	18.3716i	0.419047	−	0.822426i	−0.580917	−	0.813963i	$-0.697306\pi$
$499$	9.36080	−	18.3716i	0.419047	−	0.822426i	0.999964	−	0.00846356i	$-0.00269407\pi$
$500$	−0.317674	−	0.437240i	−0.0142068	−	0.0195540i
$501$		0			0
$502$	−2.95293	+	2.14543i	−0.131796	+	0.0957552i
$503$	24.1383	+	3.82313i	1.07627	+	0.170465i	0.669313	−	0.742981i	$-0.266589\pi$
$503$	24.1383	+	3.82313i	1.07627	+	0.170465i	0.406960	+	0.913446i	$0.366589\pi$
$504$		0			0
$505$	−2.09077	+	1.06530i	−0.0930383	+	0.0474054i
$506$	−0.156717	+	0.156717i	−0.00696693	+	0.00696693i
$507$		0			0
$508$	2.75918	+	8.49189i	0.122419	+	0.376767i
$509$	1.97806	−	12.4890i	0.0876760	−	0.553564i	−0.904276	−	0.426949i	$-0.859588\pi$
$509$	1.97806	−	12.4890i	0.0876760	−	0.553564i	0.991952	−	0.126616i	$-0.0404115\pi$
$510$		0			0
$511$	0.399572	+	0.203592i	0.0176760	+	0.00900639i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$		0			0
$514$	−0.600719	−	0.306082i	−0.0264966	−	0.0135007i
$515$	1.86439	−	5.73800i	0.0821548	−	0.252847i
$516$		0			0
$517$	−0.316718	−	0.974758i	−0.0139292	−	0.0428698i
$518$	0.133035	−	0.0210706i	0.00584521	−	0.000925790i
$519$		0			0
$520$	0.976621	−	0.497613i	0.0428276	−	0.0218218i
$521$	−5.86475	−	37.0286i	−0.256939	−	1.62225i	−0.692033	−	0.721866i	$-0.743285\pi$
$521$	−5.86475	−	37.0286i	−0.256939	−	1.62225i	0.435094	−	0.900385i	$-0.356715\pi$
$522$		0			0
$523$	4.02853	−	2.92690i	0.176155	−	0.127984i	−0.496214	−	0.868200i	$-0.665277\pi$
$523$	4.02853	−	2.92690i	0.176155	−	0.127984i	0.672369	+	0.740216i	$0.265277\pi$
$524$		−	15.3070i		−	0.668689i
$525$		0			0
$526$	−8.49190	+	16.6663i	−0.370264	+	0.726685i
$527$	−13.4431	−	26.3836i	−0.585591	−	1.14929i
$528$		0			0
$529$	14.8047	+	10.7562i	0.643681	+	0.467662i
$530$	−17.1647	−	17.1647i	−0.745585	−	0.745585i
$531$		0			0
$532$	−0.216917			−0.00940453
$533$	1.95775	+	1.08600i	0.0847995	+	0.0470400i
$534$		0			0
$535$	−28.5276	−	9.26917i	−1.23335	−	0.400741i
$536$	8.28756	+	8.28756i	0.357968	+	0.357968i
$537$		0			0
$538$	−2.04465	+	2.81421i	−0.0881510	+	0.121329i
$539$	0.324599	+	0.637061i	0.0139815	+	0.0274402i
$540$		0			0
$541$	15.1504	+	20.8527i	0.651366	+	0.896529i	0.999157	−	0.0410431i	$-0.0130681\pi$
$541$	15.1504	+	20.8527i	0.651366	+	0.896529i	−0.347791	+	0.937572i	$0.613068\pi$
$542$			9.90974i			0.425660i
$543$		0			0
$544$	−7.38790	−	1.17013i	−0.316754	−	0.0501689i
$545$	1.48399	+	9.36956i	0.0635673	+	0.401348i
$546$		0			0
$547$	−11.2671	+	11.2671i	−0.481745	+	0.481745i	−0.905689	−	0.423943i	$-0.860646\pi$
$547$	−11.2671	+	11.2671i	−0.481745	+	0.481745i	0.423943	+	0.905689i	$0.360646\pi$
$548$	−19.9255	+	3.15590i	−0.851177	+	0.134813i
$549$		0			0
$550$	0.0772018	−	0.487433i	0.00329189	−	0.0207842i
$551$	3.15130	−	9.69869i	0.134250	−	0.413178i
$552$		0			0
$553$	0.823392	−	0.267536i	0.0350142	−	0.0113768i
$554$	8.14999	−	2.64809i	0.346260	−	0.112507i
$555$		0			0
$556$	3.23954	−	9.97029i	0.137387	−	0.422835i
$557$	−1.32538	+	8.36812i	−0.0561581	+	0.354569i	0.943568	+	0.331178i	$0.107446\pi$
$557$	−1.32538	+	8.36812i	−0.0561581	+	0.354569i	−0.999726	+	0.0233905i	$0.992554\pi$
$558$		0			0
$559$	−0.173829	+	0.0275318i	−0.00735219	+	0.00116447i
$560$	−0.169156	+	0.169156i	−0.00714814	+	0.00714814i
$561$		0			0
$562$	0.138996	+	0.877588i	0.00586320	+	0.0370188i
$563$	15.5576	+	2.46409i	0.655676	+	0.103849i	0.475403	−	0.879768i	$-0.342302\pi$
$563$	15.5576	+	2.46409i	0.655676	+	0.103849i	0.180272	+	0.983617i	$0.442302\pi$
$564$		0			0
$565$			62.5627i			2.63203i
$566$	−14.1416	−	19.4643i	−0.594417	−	0.818145i
$567$		0			0
$568$	5.71809	+	11.2224i	0.239926	+	0.470880i
$569$	−3.44570	+	4.74260i	−0.144451	+	0.198820i	−0.875112	−	0.483921i	$-0.839212\pi$
$569$	−3.44570	+	4.74260i	−0.144451	+	0.198820i	0.730660	+	0.682741i	$0.239212\pi$
$570$		0			0
$571$	−0.103268	−	0.103268i	−0.00432161	−	0.00432161i	0.704943	−	0.709264i	$-0.250973\pi$
$571$	−0.103268	−	0.103268i	−0.00432161	−	0.00432161i	−0.709264	+	0.704943i	$0.750973\pi$
$572$	−0.0339931	−	0.0110450i	−0.00142132	−	0.000461816i
$573$		0			0
$574$	−0.479612	−	0.0933836i	−0.0200186	−	0.00389776i
$575$	10.4665			0.436481
$576$		0			0
$577$	4.85491	+	4.85491i	0.202112	+	0.202112i	0.800905	−	0.598792i	$-0.204352\pi$
$577$	4.85491	+	4.85491i	0.202112	+	0.202112i	−0.598792	+	0.800905i	$0.704352\pi$
$578$	−31.5114	−	22.8944i	−1.31070	−	0.952282i
$579$		0			0
$580$	−5.10579	−	10.0207i	−0.212006	−	0.416086i
$581$	−0.223225	+	0.438104i	−0.00926093	+	0.0181756i
$582$		0			0
$583$			0.791571i			0.0327835i
$584$	−4.75438	+	3.45426i	−0.196737	+	0.142938i
$585$		0			0
$586$	−0.697040	−	4.40094i	−0.0287945	−	0.181801i
$587$	40.6886	−	20.7319i	1.67940	−	0.855697i	0.687868	−	0.725836i	$-0.258547\pi$
$587$	40.6886	−	20.7319i	1.67940	−	0.855697i	0.991532	−	0.129862i	$-0.0414533\pi$
$588$		0			0
$589$	11.1144	−	1.76035i	0.457961	−	0.0725340i
$590$	9.05682	+	27.8740i	0.372863	+	1.14756i
$591$		0			0
$592$	−0.545442	+	1.67870i	−0.0224175	+	0.0689941i
$593$	1.13116	+	0.576353i	0.0464510	+	0.0236680i	0.477062	−	0.878870i	$-0.341702\pi$
$593$	1.13116	+	0.576353i	0.0464510	+	0.0236680i	−0.430611	+	0.902538i	$0.641702\pi$
$594$		0			0
$595$	−1.70180	+	0.552950i	−0.0697672	+	0.0226687i
$596$	−18.9985	−	9.68020i	−0.778207	−	0.396516i
$597$		0			0
$598$	0.118583	−	0.748703i	0.00484921	−	0.0306167i
$599$	−9.29638	−	28.6113i	−0.379840	−	1.16903i	−0.940155	−	0.340747i	$-0.889320\pi$
$599$	−9.29638	−	28.6113i	−0.379840	−	1.16903i	0.560315	−	0.828280i	$-0.310680\pi$
$600$		0			0
$601$	−18.3006	+	18.3006i	−0.746498	+	0.746498i	−0.973820	−	0.227322i	$-0.927003\pi$
$601$	−18.3006	+	18.3006i	−0.746498	+	0.746498i	0.227322	+	0.973820i	$0.427003\pi$
$602$	0.0342248	−	0.0174384i	0.00139490	−	0.000710736i
$603$		0			0
$604$	14.2220	+	2.25254i	0.578685	+	0.0916546i
$605$	27.8716	−	20.2499i	1.13314	−	0.823274i
$606$		0			0
$607$	−10.0423	−	13.8221i	−0.407606	−	0.561022i	0.555026	−	0.831833i	$-0.312708\pi$
$607$	−10.0423	−	13.8221i	−0.407606	−	0.561022i	−0.962633	+	0.270811i	$0.912708\pi$
$608$	1.29051	−	2.53277i	0.0523371	−	0.102717i
$609$		0			0
$610$	−17.5833	+	24.2013i	−0.711927	+	0.979884i
$611$	2.83600	+	2.06047i	0.114732	+	0.0833578i
$612$		0			0
$613$	11.1033	+	3.60769i	0.448459	+	0.145713i	0.524535	−	0.851389i	$-0.324239\pi$
$613$	11.1033	+	3.60769i	0.448459	+	0.145713i	−0.0760759	+	0.997102i	$0.524239\pi$
$614$	28.3431			1.14383
$615$		0			0
$616$	0.00780085			0.000314305
$617$	37.3173	+	12.1251i	1.50234	+	0.488140i	0.940699	−	0.339242i	$-0.110170\pi$
$617$	37.3173	+	12.1251i	1.50234	+	0.488140i	0.561640	+	0.827381i	$0.310170\pi$
$618$		0			0
$619$	−10.8801	−	7.90485i	−0.437308	−	0.317723i	0.347257	−	0.937770i	$-0.387113\pi$
$619$	−10.8801	−	7.90485i	−0.437308	−	0.317723i	−0.784564	+	0.620048i	$0.787113\pi$
$620$	7.29448	−	10.0400i	0.292953	−	0.403216i
$621$		0			0
$622$	−12.9276	+	25.3718i	−0.518349	+	1.01732i
$623$	−0.307361	−	0.423046i	−0.0123142	−	0.0169490i
$624$		0			0
$625$	20.8988	−	15.1838i	0.835950	−	0.607353i
$626$	−22.7528	−	3.60369i	−0.909384	−	0.144032i
$627$		0			0
$628$	6.62800	−	3.37714i	0.264486	−	0.134762i
$629$	−9.33582	+	9.33582i	−0.372244	+	0.372244i
$630$		0			0
$631$	−6.85341	−	21.0926i	−0.272830	−	0.839684i	−0.989785	−	0.142565i	$-0.954465\pi$
$631$	−6.85341	−	21.0926i	−0.272830	−	0.839684i	0.716956	−	0.697119i	$-0.245535\pi$
$632$	−1.77482	+	11.2058i	−0.0705986	+	0.445742i
$633$		0			0
$634$	5.74875	+	2.92913i	0.228312	+	0.116331i
$635$	−26.6212	+	8.64976i	−1.05643	+	0.343255i
$636$		0			0
$637$	−2.17891	−	1.11021i	−0.0863314	−	0.0439881i
$638$	−0.113328	+	0.348788i	−0.00448671	+	0.0138087i
$639$		0			0
$640$	−0.968737	−	2.98147i	−0.0382927	−	0.117853i
$641$	−24.4147	+	3.86690i	−0.964321	+	0.152733i	−0.618689	−	0.785636i	$-0.712336\pi$
$641$	−24.4147	+	3.86690i	−0.964321	+	0.152733i	−0.345633	+	0.938370i	$0.612336\pi$
$642$		0			0
$643$	−3.14347	+	1.60168i	−0.123966	+	0.0631639i	−0.514874	−	0.857266i	$-0.672161\pi$
$643$	−3.14347	+	1.60168i	−0.123966	+	0.0631639i	0.390908	+	0.920430i	$0.372161\pi$
$644$	0.0258809	+	0.163405i	0.00101985	+	0.00643908i
$645$		0			0
$646$	17.2018	−	12.4978i	0.676795	−	0.491720i
$647$			12.6164i			0.496003i	0.968760	+	0.248002i	$0.0797739\pi$
$647$			12.6164i			0.496003i	−0.968760	+	0.248002i	$0.920226\pi$
$648$		0			0
$649$	0.433890	−	0.851558i	0.0170317	−	0.0334266i
$650$	0.766301	+	1.50395i	0.0300568	+	0.0589898i
$651$		0			0
$652$	−9.60322	−	6.97715i	−0.376091	−	0.273246i
$653$	−18.4555	−	18.4555i	−0.722220	−	0.722220i	0.246837	−	0.969057i	$-0.420609\pi$
$653$	−18.4555	−	18.4555i	−0.722220	−	0.722220i	−0.969057	+	0.246837i	$0.920609\pi$
$654$		0			0
$655$	47.9859			1.87496
$656$	3.94374	−	5.04449i	0.153977	−	0.196954i
$657$		0			0
$658$	−0.727632	−	0.236422i	−0.0283660	−	0.00921668i
$659$	−10.7342	−	10.7342i	−0.418144	−	0.418144i	0.466420	−	0.884563i	$-0.345544\pi$
$659$	−10.7342	−	10.7342i	−0.418144	−	0.418144i	−0.884563	+	0.466420i	$0.845544\pi$
$660$		0			0
$661$	29.8730	−	41.1166i	1.16192	−	1.59925i	0.458048	−	0.888928i	$-0.348549\pi$
$661$	29.8730	−	41.1166i	1.16192	−	1.59925i	0.703876	−	0.710323i	$-0.251451\pi$
$662$	−15.5637	−	30.5456i	−0.604902	−	1.18719i
$663$		0			0
$664$	−3.78736	−	5.21285i	−0.146978	−	0.202298i
$665$		−	0.680012i		−	0.0263697i
$666$		0			0
$667$	−7.68211	−	1.21673i	−0.297452	−	0.0471118i
$668$	3.31974	+	20.9600i	0.128445	+	0.810967i
$669$		0			0
$670$	−25.9807	+	25.9807i	−1.00372	+	1.00372i
$671$	0.963478	−	0.152600i	0.0371946	−	0.00589105i
$672$		0			0
$673$	0.0178699	−	0.112826i	0.000688834	−	0.00434912i	−0.987342	−	0.158609i	$-0.949299\pi$
$673$	0.0178699	−	0.112826i	0.000688834	−	0.00434912i	0.988030	+	0.154260i	$0.0492992\pi$
$674$	−1.81666	+	5.59111i	−0.0699752	+	0.215361i
$675$		0			0
$676$	−12.2475	+	3.97944i	−0.471057	+	0.153056i
$677$	33.3233	−	10.8274i	1.28072	−	0.416131i	0.411885	−	0.911236i	$-0.364871\pi$
$677$	33.3233	−	10.8274i	1.28072	−	0.416131i	0.868833	+	0.495105i	$0.164871\pi$
$678$		0			0
$679$	0.245307	−	0.754976i	0.00941401	−	0.0289733i
$680$	3.66824	−	23.1603i	0.140670	−	0.888158i
$681$		0			0
$682$	−0.399701	+	0.0633065i	−0.0153054	+	0.00242413i
$683$	−8.17370	+	8.17370i	−0.312758	+	0.312758i	−0.845977	−	0.533219i	$-0.820982\pi$
$683$	−8.17370	+	8.17370i	−0.312758	+	0.312758i	0.533219	+	0.845977i	$0.320982\pi$
$684$		0			0
$685$	−9.89342	−	62.4646i	−0.378008	−	2.38665i
$686$	1.05474	+	0.167055i	0.0402702	+	0.00637817i
$687$		0			0
$688$			0.503363i			0.0191905i
$689$	−1.59135	−	2.19031i	−0.0606257	−	0.0834441i
$690$		0			0
$691$	−16.9993	−	33.3630i	−0.646683	−	1.26919i	−0.948788	−	0.315913i	$-0.897689\pi$
$691$	−16.9993	−	33.3630i	−0.646683	−	1.26919i	0.302105	−	0.953275i	$-0.402311\pi$
$692$	8.87938	−	12.2214i	0.337544	−	0.464589i
$693$		0			0
$694$	8.73606	+	8.73606i	0.331616	+	0.331616i
$695$	31.2559	+	10.1557i	1.18560	+	0.385226i
$696$		0			0
$697$	43.4143	−	20.2278i	1.64443	−	0.766182i
$698$	5.92610			0.224306
$699$		0			0
$700$	−0.260492	−	0.260492i	−0.00984568	−	0.00984568i
$701$	42.0177	+	30.5277i	1.58699	+	1.15301i	0.908086	+	0.418784i	$0.137544\pi$
$701$	42.0177	+	30.5277i	1.58699	+	1.15301i	0.678901	+	0.734229i	$0.262456\pi$
$702$		0			0
$703$	−2.27786	−	4.47056i	−0.0859113	−	0.168610i
$704$	−0.0464099	+	0.0910845i	−0.00174914	+	0.00343288i
$705$		0			0
$706$			1.07549i			0.0404766i
$707$	0.0462103	−	0.0335737i	0.00173792	−	0.00126267i
$708$		0			0
$709$	−2.35597	−	14.8750i	−0.0884804	−	0.558643i	−0.991609	−	0.129273i	$-0.958736\pi$
$709$	−2.35597	−	14.8750i	−0.0884804	−	0.558643i	0.903129	−	0.429370i	$-0.141264\pi$
$710$	−35.1810	+	17.9256i	−1.32032	+	0.672737i
$711$		0			0
$712$	6.76817	−	1.07197i	0.253648	−	0.0401739i
$713$	−2.65218	−	8.16256i	−0.0993248	−	0.305690i
$714$		0			0
$715$	0.0346251	−	0.106565i	0.00129490	−	0.00398531i
$716$	15.5583	+	7.92734i	0.581441	+	0.296259i
$717$		0			0
$718$	3.55531	−	1.15519i	0.132683	−	0.0431113i
$719$	13.5445	+	6.90127i	0.505125	+	0.257374i	0.687932	−	0.725775i	$-0.258519\pi$
$719$	13.5445	+	6.90127i	0.505125	+	0.257374i	−0.182808	+	0.983149i	$0.558519\pi$
$720$		0			0
$721$	−0.0229743	+	0.145054i	−0.000855606	+	0.00540208i
$722$	−3.37436	−	10.3852i	−0.125581	−	0.386498i
$723$		0			0
$724$	−15.2416	+	15.2416i	−0.566449	+	0.566449i
$725$	15.4314	−	7.86267i	0.573107	−	0.292012i
$726$		0			0
$727$	25.0156	+	3.96208i	0.927776	+	0.146945i	0.601995	−	0.798500i	$-0.294373\pi$
$727$	25.0156	+	3.96208i	0.927776	+	0.146945i	0.325781	+	0.945445i	$0.394373\pi$
$728$	−0.0215853	+	0.0156826i	−0.000800003	+	0.000581236i
$729$		0			0
$730$	−10.8287	−	14.9045i	−0.400790	−	0.551640i
$731$	−1.70934	+	3.35477i	−0.0632223	+	0.124081i
$732$		0			0
$733$	22.8520	−	31.4530i	0.844057	−	1.16174i	−0.141084	−	0.989998i	$-0.545059\pi$
$733$	22.8520	−	31.4530i	0.844057	−	1.16174i	0.985141	−	0.171747i	$-0.0549411\pi$
$734$	29.2915	+	21.2815i	1.08117	+	0.785516i
$735$		0			0
$736$	−2.06193	−	0.669963i	−0.0760039	−	0.0246952i
$737$	1.19813			0.0441338
$738$		0			0
$739$	−20.0669			−0.738173			−0.369087	−	0.929395i	$-0.620329\pi$
$739$	−20.0669			−0.738173			−0.369087	+	0.929395i	$0.620329\pi$
$740$	−5.26255	−	1.70991i	−0.193455	−	0.0628574i
$741$		0			0
$742$	0.478038	+	0.347315i	0.0175493	+	0.0127503i
$743$	16.7059	−	22.9936i	0.612879	−	0.843555i	−0.383932	−	0.923361i	$-0.625430\pi$
$743$	16.7059	−	22.9936i	0.612879	−	0.843555i	0.996810	+	0.0798065i	$0.0254302\pi$
$744$		0			0
$745$	30.3465	−	59.5583i	1.11181	−	2.18205i
$746$	−15.8368	−	21.7974i	−0.579825	−	0.798061i
$747$		0			0
$748$	−0.618618	+	0.449452i	−0.0226189	+	0.0164336i
$749$	0.721163	+	0.114221i	0.0263507	+	0.00417354i
$750$		0			0
$751$	13.9453	−	7.10551i	0.508873	−	0.259284i	−0.180650	−	0.983547i	$-0.557820\pi$
$751$	13.9453	−	7.10551i	0.508873	−	0.259284i	0.689523	+	0.724264i	$0.257820\pi$
$752$	7.08944	−	7.08944i	0.258525	−	0.258525i
$753$		0			0
$754$	−0.387611	−	1.19294i	−0.0141160	−	0.0434444i
$755$	−7.06149	+	44.5845i	−0.256994	+	1.62260i
$756$		0			0
$757$	7.65445	+	3.90014i	0.278206	+	0.141753i	0.587527	−	0.809205i	$-0.300102\pi$
$757$	7.65445	+	3.90014i	0.278206	+	0.141753i	−0.309321	+	0.950958i	$0.600102\pi$
$758$	26.1024	−	8.48117i	0.948081	−	0.308050i
$759$		0			0
$760$	7.93998	+	4.04562i	0.288013	+	0.146750i
$761$	15.5421	−	47.8336i	0.563400	−	1.73397i	−0.109257	−	0.994014i	$-0.534847\pi$
$761$	15.5421	−	47.8336i	0.563400	−	1.73397i	0.672657	−	0.739954i	$-0.265153\pi$
$762$		0			0
$763$	−0.0713570	−	0.219614i	−0.00258330	−	0.00795057i
$764$	20.4636	−	3.24111i	0.740346	−	0.117259i
$765$		0			0
$766$	−9.18631	+	4.68066i	−0.331915	+	0.169119i
$767$	0.511356	+	3.22857i	0.0184640	+	0.116577i
$768$		0			0
$769$	−29.3994	+	21.3599i	−1.06017	+	0.770258i	−0.974120	−	0.226033i	$-0.927424\pi$
$769$	−29.3994	+	21.3599i	−1.06017	+	0.770258i	−0.0860497	+	0.996291i	$0.527424\pi$
$770$			0.0244549i			0.000881293i
$771$		0			0
$772$	2.66729	−	5.23485i	0.0959979	−	0.188406i
$773$	8.83075	+	17.3313i	0.317620	+	0.623365i	0.993524	−	0.113625i	$-0.0362464\pi$
$773$	8.83075	+	17.3313i	0.317620	+	0.623365i	−0.675904	+	0.736990i	$0.736246\pi$
$774$		0			0
$775$	15.4611	+	11.2332i	0.555380	+	0.403507i
$776$	7.35586	+	7.35586i	0.264060	+	0.264060i
$777$		0			0
$778$	−5.42487			−0.194491
$779$	2.21252	+	18.0665i	0.0792719	+	0.647300i
$780$		0			0
$781$	1.22454	+	0.397878i	0.0438176	+	0.0142372i
$782$	−11.4671	−	11.4671i	−0.410063	−	0.410063i
$783$		0			0
$784$	−4.11107	+	5.65841i	−0.146824	+	0.202086i
$785$	10.5870	+	20.7781i	0.377866	+	0.741603i
$786$		0			0
$787$	−5.54324	−	7.62961i	−0.197595	−	0.271966i	0.698709	−	0.715406i	$-0.253758\pi$
$787$	−5.54324	−	7.62961i	−0.197595	−	0.271966i	−0.896304	+	0.443439i	$0.853758\pi$
$788$		−	8.37992i		−	0.298522i
$789$		0			0
$790$	−35.1290	−	5.56389i	−1.24983	−	0.197954i
$791$	−0.238233	−	1.50415i	−0.00847060	−	0.0534813i
$792$		0			0
$793$	−2.35920	+	2.35920i	−0.0837776	+	0.0837776i
$794$	−17.4192	+	2.75894i	−0.618186	+	0.0979110i
$795$		0			0
$796$	−0.0801641	+	0.506136i	−0.00284134	+	0.0179395i
$797$	9.68767	−	29.8156i	0.343155	−	1.05612i	−0.619409	−	0.785068i	$-0.712628\pi$
$797$	9.68767	−	29.8156i	0.343155	−	1.05612i	0.962564	−	0.271054i	$-0.0873721\pi$
$798$		0			0
$799$	71.3238	−	23.1745i	2.52325	−	0.819855i
$800$	4.59132	−	1.49181i	0.162328	−	0.0527435i
$801$		0			0
$802$	6.40245	−	19.7047i	0.226078	−	0.695798i
$803$	−0.0939792	+	0.593362i	−0.00331646	+	0.0209393i
$804$		0			0
$805$	−0.512260	+	0.0811340i	−0.0180548	+	0.00285960i
$806$	0.978720	−	0.978720i	0.0344739	−	0.0344739i
$807$		0			0
$808$	0.117094	+	0.739303i	0.00411936	+	0.0260086i
$809$	29.3235	+	4.64439i	1.03096	+	0.163288i	0.648919	−	0.760858i	$-0.275221\pi$
$809$	29.3235	+	4.64439i	1.03096	+	0.163288i	0.382041	+	0.924146i	$0.375221\pi$
$810$		0			0
$811$		−	1.62308i		−	0.0569940i	−0.999594	−	0.0284970i	$-0.990928\pi$
$811$		−	1.62308i		−	0.0569940i	0.999594	−	0.0284970i	$-0.00907211\pi$
$812$	0.160912	+	0.221477i	0.00564692	+	0.00777231i
$813$		0			0
$814$	0.0819175	+	0.160772i	0.00287121	+	0.00563506i
$815$	21.8727	−	30.1051i	0.766166	−	1.05454i
$816$		0			0
$817$	−1.01177	−	1.01177i	−0.0353973	−	0.0353973i
$818$	−10.0088	−	3.25207i	−0.349951	−	0.113706i
$819$		0			0
$820$	15.8140	+	12.3632i	0.552248	+	0.431743i
$821$	−31.6850			−1.10581			−0.552907	−	0.833243i	$-0.686482\pi$
$821$	−31.6850			−1.10581			−0.552907	+	0.833243i	$0.686482\pi$
$822$		0			0
$823$	−19.5106	−	19.5106i	−0.680097	−	0.680097i	0.279925	−	0.960022i	$-0.409690\pi$
$823$	−19.5106	−	19.5106i	−0.680097	−	0.680097i	−0.960022	+	0.279925i	$0.909690\pi$
$824$	−1.55700	−	1.13123i	−0.0542406	−	0.0394081i
$825$		0			0
$826$	−0.323888	−	0.635666i	−0.0112695	−	0.0221176i
$827$	7.48768	−	14.6954i	0.260372	−	0.511009i	−0.723400	−	0.690429i	$-0.757422\pi$
$827$	7.48768	−	14.6954i	0.260372	−	0.511009i	0.983773	+	0.179419i	$0.0574219\pi$
$828$		0			0
$829$		−	5.35467i		−	0.185975i	−0.995667	−	0.0929877i	$-0.970358\pi$
$829$		−	5.35467i		−	0.185975i	0.995667	−	0.0929877i	$-0.0296417\pi$
$830$	16.3418	−	11.8730i	0.567231	−	0.412117i
$831$		0			0
$832$	−0.0546958	−	0.345335i	−0.00189623	−	0.0119724i
$833$	−46.6142	+	23.7511i	−1.61509	+	0.822928i
$834$		0			0
$835$	−65.7075	+	10.4070i	−2.27390	+	0.360151i
$836$	−0.0897967	−	0.276366i	−0.00310569	−	0.00955832i
$837$		0			0
$838$	3.70999	−	11.4182i	0.128159	−	0.394434i
$839$	−35.7376	−	18.2092i	−1.23380	−	0.628652i	−0.289323	−	0.957232i	$-0.593430\pi$
$839$	−35.7376	−	18.2092i	−1.23380	−	0.628652i	−0.944476	+	0.328580i	$0.893430\pi$
$840$		0			0
$841$	15.3404	−	4.98439i	0.528978	−	0.171875i
$842$	7.78849	+	3.96843i	0.268409	+	0.136761i
$843$		0			0
$844$	−0.246361	+	1.55546i	−0.00848009	+	0.0535412i
$845$	−12.4752	−	38.3946i	−0.429159	−	1.32081i
$846$		0			0
$847$	−0.592984	+	0.592984i	−0.0203752	+	0.0203752i
$848$	−6.89934	+	3.51539i	−0.236924	+	0.120719i
$849$		0			0
$850$	35.6658	+	5.64891i	1.22333	+	0.193756i
$851$	−3.09594	+	2.24933i	−0.106127	+	0.0771061i
$852$		0			0
$853$	−22.2833	−	30.6703i	−0.762964	−	1.05013i	−0.996962	−	0.0778928i	$-0.975181\pi$
$853$	−22.2833	−	30.6703i	−0.762964	−	1.05013i	0.233998	−	0.972237i	$-0.424819\pi$
$854$	0.330585	−	0.648810i	0.0113124	−	0.0222018i
$855$		0			0
$856$	−5.62411	+	7.74092i	−0.192228	+	0.264579i
$857$	38.3161	+	27.8383i	1.30885	+	0.950937i	1.00000		0.000173000i	$-5.50676e-5\pi$
$857$	38.3161	+	27.8383i	1.30885	+	0.950937i	0.308852	+	0.951110i	$0.400055\pi$
$858$		0			0
$859$	29.5117	+	9.58895i	1.00693	+	0.327171i	0.765631	−	0.643281i	$-0.222427\pi$
$859$	29.5117	+	9.58895i	1.00693	+	0.327171i	0.241297	+	0.970451i	$0.422427\pi$
$860$	−1.57799			−0.0538091
$861$		0			0
$862$	−15.2599			−0.519753
$863$	−41.0186	−	13.3278i	−1.39629	−	0.453682i	−0.488301	−	0.872676i	$-0.662383\pi$
$863$	−41.0186	−	13.3278i	−1.39629	−	0.453682i	−0.907989	+	0.418993i	$0.862383\pi$
$864$		0			0
$865$	38.3129	+	27.8360i	1.30268	+	0.946452i
$866$	−22.9051	+	31.5262i	−0.778347	+	1.07130i
$867$		0			0
$868$	−0.137144	+	0.269160i	−0.00465497	+	0.00913590i
$869$	0.681717	+	0.938303i	0.0231257	+	0.0318298i
$870$		0			0
$871$	−3.31528	+	2.40869i	−0.112334	+	0.0816155i
$872$	2.98879	+	0.473378i	0.101213	+	0.0160306i
$873$		0			0
$874$	5.49116	−	2.79788i	0.185741	−	0.0946398i
$875$	−0.0291626	+	0.0291626i	−0.000985875	+	0.000985875i
$876$		0			0
$877$	9.93757	+	30.5847i	0.335568	+	1.03277i	0.966442	+	0.256886i	$0.0826965\pi$
$877$	9.93757	+	30.5847i	0.335568	+	1.03277i	−0.630874	+	0.775885i	$0.717303\pi$
$878$	−2.50768	+	15.8329i	−0.0846300	+	0.534333i
$879$		0			0
$880$	−0.285541	−	0.145490i	−0.00962558	−	0.00490448i
$881$	−44.0316	+	14.3067i	−1.48346	+	0.482006i	−0.935145	−	0.354265i	$-0.884731\pi$
$881$	−44.0316	+	14.3067i	−1.48346	+	0.482006i	−0.548317	+	0.836271i	$0.684731\pi$
$882$		0			0
$883$	−45.0914	−	22.9752i	−1.51745	−	0.773178i	−0.520698	−	0.853741i	$-0.674328\pi$
$883$	−45.0914	−	22.9752i	−1.51745	−	0.773178i	−0.996750	+	0.0805632i	$0.974328\pi$
$884$	0.808174	−	2.48730i	0.0271818	−	0.0836571i
$885$		0			0
$886$	−5.82009	−	17.9124i	−0.195530	−	0.601779i
$887$	12.6960	−	2.01085i	0.426289	−	0.0675176i	0.0603962	−	0.998174i	$-0.480764\pi$
$887$	12.6960	−	2.01085i	0.426289	−	0.0675176i	0.365893	+	0.930657i	$0.380764\pi$
$888$		0			0
$889$	0.607096	−	0.309331i	0.0203613	−	0.0103746i
$890$	3.36053	+	21.2175i	0.112645	+	0.711214i
$891$		0			0
$892$	−8.46919	+	6.15323i	−0.283569	+	0.206025i
$893$			28.4998i			0.953709i
$894$		0			0
$895$	−24.8514	+	48.7737i	−0.830692	+	1.63032i
$896$	0.0346438	+	0.0679922i	0.00115737	+	0.00227146i
$897$		0			0
$898$	19.1534	+	13.9158i	0.639158	+	0.464375i
$899$	−10.0422	−	10.0422i	−0.334926	−	0.334926i
$900$		0			0
$901$	−57.9199			−1.92959
$902$	−0.0795677	−	0.649715i	−0.00264931	−	0.0216331i
$903$		0			0
$904$	18.9801	+	6.16700i	0.631268	+	0.205111i
$905$	−47.7808	−	47.7808i	−1.58829	−	1.58829i
$906$		0			0
$907$	−19.2845	+	26.5428i	−0.640331	+	0.881339i	−0.998633	−	0.0522661i	$-0.983356\pi$
$907$	−19.2845	+	26.5428i	−0.640331	+	0.881339i	0.358303	+	0.933605i	$0.383356\pi$
$908$	0.532171	+	1.04445i	0.0176607	+	0.0346611i
$909$		0			0
$910$	−0.0491634	−	0.0676676i	−0.00162975	−	0.00224316i
$911$		−	45.2623i		−	1.49961i	−0.661661	−	0.749803i	$-0.730148\pi$
$911$		−	45.2623i		−	1.49961i	0.661661	−	0.749803i	$-0.269852\pi$
$912$		0			0
$913$	−0.650580	−	0.103042i	−0.0215311	−	0.00341019i
$914$	0.582085	+	3.67514i	0.0192537	+	0.121563i
$915$		0			0
$916$	−5.83796	+	5.83796i	−0.192891	+	0.192891i
$917$	−1.15369	+	0.182726i	−0.0380981	+	0.00603415i
$918$		0			0
$919$	6.87308	−	43.3949i	0.226722	−	1.43147i	−0.567267	−	0.823534i	$-0.691999\pi$
$919$	6.87308	−	43.3949i	0.226722	−	1.43147i	0.793989	−	0.607933i	$-0.208001\pi$
$920$	2.10027	−	6.46395i	0.0692437	−	0.213110i
$921$		0			0
$922$	−33.7052	+	10.9515i	−1.11002	+	0.360668i
$923$	−4.18824	+	1.36084i	−0.137858	+	0.0447926i
$924$		0			0
$925$	2.63318	−	8.10408i	0.0865783	−	0.266461i
$926$	−3.82726	+	24.1644i	−0.125772	+	0.794091i
$927$		0			0
$928$	−3.54333	+	0.561209i	−0.116316	+	0.0184226i
$929$	−6.34123	+	6.34123i	−0.208049	+	0.208049i	−0.803438	−	0.595389i	$-0.796998\pi$
$929$	−6.34123	+	6.34123i	−0.208049	+	0.208049i	0.595389	+	0.803438i	$0.296998\pi$
$930$		0			0
$931$	−3.11017	−	19.6368i	−0.101932	−	0.643571i
$932$	23.4622	+	3.71605i	0.768531	+	0.121723i
$933$		0			0
$934$			12.7768i			0.418069i
$935$	−1.40899	−	1.93930i	−0.0460788	−	0.0634220i
$936$		0			0
$937$	11.6366	+	22.8381i	0.380151	+	0.746089i	0.999230	−	0.0392404i	$-0.0124938\pi$
$937$	11.6366	+	22.8381i	0.380151	+	0.746089i	−0.619079	+	0.785329i	$0.712494\pi$
$938$	0.525701	−	0.723565i	0.0171647	−	0.0236252i
$939$		0			0
$940$	22.2247	+	22.2247i	0.724889	+	0.724889i
$941$	−11.2410	−	3.65241i	−0.366445	−	0.119065i	0.120006	−	0.992773i	$-0.461709\pi$
$941$	−11.2410	−	3.65241i	−0.366445	−	0.119065i	−0.486451	+	0.873708i	$0.661709\pi$
$942$		0			0
$943$	13.3457	−	3.82227i	0.434595	−	0.124470i
$944$	9.34910			0.304287
$945$		0			0
$946$	0.0363856	+	0.0363856i	0.00118300	+	0.00118300i
$947$	−3.49686	−	2.54062i	−0.113633	−	0.0825590i	0.529518	−	0.848299i	$-0.322373\pi$
$947$	−3.49686	−	2.54062i	−0.113633	−	0.0825590i	−0.643150	+	0.765740i	$0.722373\pi$
$948$		0			0
$949$	−0.932833	−	1.83079i	−0.0302810	−	0.0594299i
$950$	−6.23007	+	12.2272i	−0.202130	+	0.396703i
$951$		0			0
$952$			0.570794i			0.0184995i
$953$	3.23986	−	2.35389i	0.104949	−	0.0762501i	−0.534073	−	0.845438i	$-0.679339\pi$
$953$	3.23986	−	2.35389i	0.104949	−	0.0762501i	0.639022	+	0.769188i	$0.279339\pi$
$954$		0			0
$955$	10.1606	+	64.1512i	0.328788	+	2.07588i
$956$	−17.8134	+	9.07637i	−0.576126	+	0.293551i
$957$		0			0
$958$	12.5312	−	1.98475i	0.404864	−	0.0641242i
$959$	0.475720	+	1.46411i	0.0153618	+	0.0472787i
$960$		0			0
$961$	−4.73684	+	14.5785i	−0.152801	+	0.470274i
$962$	−0.549881	−	0.280178i	−0.0177289	−	0.00903331i
$963$		0			0
$964$	−7.56484	+	2.45797i	−0.243647	+	0.0791658i
$965$	16.4107	+	8.36169i	0.528280	+	0.269172i
$966$		0			0
$967$	−8.58410	+	54.1979i	−0.276046	+	1.74289i	0.326859	+	0.945073i	$0.394010\pi$
$967$	−8.58410	+	54.1979i	−0.276046	+	1.74289i	−0.602905	+	0.797813i	$0.705990\pi$
$968$	−3.39596	−	10.4517i	−0.109150	−	0.335930i
$969$		0			0
$970$	−23.0599	+	23.0599i	−0.740409	+	0.740409i
$971$	−0.962775	+	0.490558i	−0.0308969	+	0.0157428i	−0.469371	−	0.883001i	$-0.655519\pi$
$971$	−0.962775	+	0.490558i	−0.0308969	+	0.0157428i	0.438474	+	0.898744i	$0.355519\pi$
$972$		0			0
$973$	−0.790133	−	0.125145i	−0.0253305	−	0.00401196i
$974$	23.2454	−	16.8887i	0.744829	−	0.541150i
$975$		0			0
$976$	5.60889	+	7.71997i	0.179536	+	0.247110i
$977$	4.50300	−	8.83764i	0.144064	−	0.282741i	−0.807688	−	0.589610i	$-0.799281\pi$
$977$	4.50300	−	8.83764i	0.144064	−	0.282741i	0.951752	+	0.306869i	$0.0992814\pi$
$978$		0			0
$979$	0.411750	−	0.566725i	0.0131596	−	0.0181126i
$980$	−17.7385	−	12.8878i	−0.566637	−	0.411686i
$981$		0			0
$982$	−36.7556	−	11.9426i	−1.17292	−	0.381104i
$983$	38.2748			1.22078			0.610389	−	0.792102i	$-0.291013\pi$
$983$	38.2748			1.22078			0.610389	+	0.792102i	$0.291013\pi$
$984$		0			0
$985$	26.2702			0.837039
$986$	−25.5211	−	8.29232i	−0.812758	−	0.264081i
$987$		0			0
$988$	0.804069	+	0.584191i	0.0255809	+	0.0185856i
$989$	−0.641458	+	0.882891i	−0.0203972	+	0.0280743i
$990$		0			0
$991$	−8.39811	+	16.4822i	−0.266775	+	0.523575i	−0.985068	−	0.172166i	$-0.944924\pi$
$991$	−8.39811	+	16.4822i	−0.266775	+	0.523575i	0.718293	+	0.695740i	$0.244924\pi$
$992$	−2.32686	−	3.20265i	−0.0738780	−	0.101684i
$993$		0			0
$994$	0.777571	−	0.564938i	0.0246630	−	0.0179188i
$995$	−1.58669	−	0.251306i	−0.0503014	−	0.00796695i
$996$		0			0
$997$	−7.91767	+	4.03425i	−0.250755	+	0.127766i	−0.574851	−	0.818258i	$-0.694940\pi$
$997$	−7.91767	+	4.03425i	−0.250755	+	0.127766i	0.324096	+	0.946024i	$0.394940\pi$
$998$	14.5798	−	14.5798i	0.461515	−	0.461515i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.f.595.1		32
3.2	odd	2		246.2.n.b.103.2	yes	32
41.2	even	20	inner	738.2.u.f.289.1		32
123.2	odd	20		246.2.n.b.43.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
246.2.n.b.43.2	✓	32	123.2	odd	20
246.2.n.b.103.2	yes	32	3.2	odd	2
738.2.u.f.289.1		32	41.2	even	20	inner
738.2.u.f.595.1		32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.809017 + 0.587785i) q^{4} +(-1.84265 + 2.53619i) q^{5} +(0.0346438 - 0.0679922i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.53619 + 1.84265i) q^{10} +(0.100968 + 0.0159917i) q^{11} +(-0.311532 + 0.158733i) q^{13} +(0.0539589 - 0.0539589i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.17013 + 7.38790i) q^{17} +(-2.53277 - 1.29051i) q^{19} +(-2.98147 + 0.968737i) q^{20} +(0.0910845 + 0.0464099i) q^{22} +(-0.669963 + 2.06193i) q^{23} +(-1.49181 - 4.59132i) q^{25} +(-0.345335 + 0.0546958i) q^{26} +(0.0679922 - 0.0346438i) q^{28} +(0.561209 + 3.54333i) q^{29} +(-3.20265 + 2.32686i) q^{31} +1.00000i q^{32} +(-3.39585 + 6.66472i) q^{34} +(0.108605 + 0.213149i) q^{35} +(1.42799 + 1.03749i) q^{37} +(-2.01002 - 2.01002i) q^{38} -3.13490 q^{40} +(-3.57891 - 5.30956i) q^{41} +(0.478727 + 0.155548i) q^{43} +(0.0722851 + 0.0722851i) q^{44} +(-1.27434 + 1.75398i) q^{46} +(-4.55170 - 8.93321i) q^{47} +(4.11107 + 5.65841i) q^{49} -4.82760i q^{50} +(-0.345335 - 0.0546958i) q^{52} +(1.21132 + 7.64797i) q^{53} +(-0.226606 + 0.226606i) q^{55} +(0.0753700 - 0.0119374i) q^{56} +(-0.561209 + 3.54333i) q^{58} +(2.88903 - 8.89152i) q^{59} +(9.07537 - 2.94877i) q^{61} +(-3.76494 + 1.22330i) q^{62} +(-0.309017 + 0.951057i) q^{64} +(0.171466 - 1.08259i) q^{65} +(11.5761 - 1.83347i) q^{67} +(-5.28915 + 5.28915i) q^{68} +(0.0374227 + 0.236277i) q^{70} +(12.4401 + 1.97032i) q^{71} +5.87673i q^{73} +(1.03749 + 1.42799i) q^{74} +(-1.29051 - 2.53277i) q^{76} +(0.00458522 - 0.00631102i) q^{77} +(8.02245 + 8.02245i) q^{79} +(-2.98147 - 0.968737i) q^{80} +(-1.76301 - 6.15563i) q^{82} -6.44344 q^{83} +(-16.5810 - 16.5810i) q^{85} +(0.407229 + 0.295869i) q^{86} +(0.0464099 + 0.0910845i) q^{88} +(3.11099 - 6.10566i) q^{89} +0.0266808i q^{91} +(-1.75398 + 1.27434i) q^{92} +(-1.56841 - 9.90254i) q^{94} +(7.93998 - 4.04562i) q^{95} +(10.2747 - 1.62735i) q^{97} +(2.16132 + 6.65186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{11} - 12 q^{13} - 4 q^{14} - 8 q^{16} + 4 q^{17} - 4 q^{19} - 4 q^{22} - 40 q^{23} + 12 q^{25} - 8 q^{26} - 4 q^{28} - 16 q^{29} - 4 q^{31} - 16 q^{34} + 8 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) \) 32 * q + 8 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^11 - 12 * q^13 - 4 * q^14 - 8 * q^16 + 4 * q^17 - 4 * q^19 - 4 * q^22 - 40 * q^23 + 12 * q^25 - 8 * q^26 - 4 * q^28 - 16 * q^29 - 4 * q^31 - 16 * q^34 + 8 * q^35 - 44 * q^37 + 16 * q^38 - 16 * q^40 + 28 * q^41 - 40 * q^43 + 16 * q^44 - 20 * q^46 + 48 * q^47 - 40 * q^49 - 8 * q^52 + 8 * q^53 + 72 * q^55 + 4 * q^56 + 16 * q^58 - 32 * q^59 + 100 * q^61 + 8 * q^64 - 56 * q^67 - 4 * q^68 + 48 * q^70 + 80 * q^71 + 4 * q^76 + 48 * q^79 + 12 * q^82 - 72 * q^83 - 52 * q^85 - 4 * q^86 + 4 * q^88 - 44 * q^89 - 20 * q^92 + 28 * q^94 + 40 * q^95 + 92 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

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Database

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