LMFDB - Embedded newform 380.2.bh.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +O(q^{10})$	\(q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +(2.73107 + 4.73035i) q^{11} +(-0.160884 + 0.345016i) q^{13} +(5.63692 + 3.76578i) q^{15} +(-0.0144528 + 0.165196i) q^{17} +(1.45553 + 4.10870i) q^{19} +(2.78783 + 3.32240i) q^{21} +(0.363161 - 0.254288i) q^{23} +(-2.30799 + 4.43544i) q^{25} +(-2.50399 + 9.34503i) q^{27} +(1.09856 + 0.921802i) q^{29} +(6.67979 + 3.85658i) q^{31} +(-13.5648 - 9.49816i) q^{33} +(-2.21187 + 2.31094i) q^{35} +(6.77341 + 6.77341i) q^{37} -1.15412i q^{39} +(2.40119 - 6.59722i) q^{41} +(6.61211 - 9.44307i) q^{43} +(-13.6830 - 2.10482i) q^{45} +(-3.11441 + 0.272476i) q^{47} +(4.28980 - 2.47672i) q^{49} +(-0.171947 - 0.472419i) q^{51} +(6.56681 + 9.37838i) q^{53} +(5.87375 - 10.7086i) q^{55} +(-9.26357 - 9.42437i) q^{57} +(-8.39207 + 7.04179i) q^{59} +(2.07149 - 11.7480i) q^{61} +(-8.02716 - 3.74313i) q^{63} +(0.846167 - 0.0927428i) q^{65} +(0.773226 + 8.83802i) q^{67} +(-0.672034 + 1.16400i) q^{69} +(-0.325803 + 0.0574478i) q^{71} +(-0.964863 - 2.06915i) q^{73} +(0.658643 - 15.1442i) q^{75} +(5.52535 - 5.52535i) q^{77} +(-2.57267 - 0.936374i) q^{79} +(-1.86796 - 10.5937i) q^{81} +(-11.1195 + 2.97945i) q^{83} +(0.332548 - 0.164029i) q^{85} +(-4.19952 - 1.12526i) q^{87} +(-5.02263 + 1.82809i) q^{89} +(0.536325 + 0.0945686i) q^{91} +(-23.2950 - 2.03804i) q^{93} +(6.16528 - 7.54912i) q^{95} +(0.497197 + 0.0434991i) q^{97} +(33.3033 + 5.87227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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			0
$2$		0			0
$3$	−2.74765	+	1.28125i	−1.58636	+	0.739730i	−0.997643	−	0.0686122i	$-0.978143\pi$
$3$	−2.74765	+	1.28125i	−1.58636	+	0.739730i	−0.588713	+	0.808342i	$0.700365\pi$
$4$		0			0
$5$	−1.16017	−	1.91154i	−0.518846	−	0.854868i
$5$	−1.16017	−	1.91154i	−0.518846	−	0.854868i
$6$		0			0
$7$	−0.370262	−	1.38184i	−0.139946	−	0.522285i	−0.999928	−	0.0119616i	$-0.996192\pi$
$7$	−0.370262	−	1.38184i	−0.139946	−	0.522285i	0.859983	−	0.510323i	$-0.170474\pi$
$8$		0			0
$9$	3.97961	−	4.74272i	1.32654	−	1.58091i
$10$		0			0
$11$	2.73107	+	4.73035i	0.823448	+	1.42625i	0.903100	+	0.429431i	$0.141286\pi$
$11$	2.73107	+	4.73035i	0.823448	+	1.42625i	−0.0796521	+	0.996823i	$0.525381\pi$
$12$		0			0
$13$	−0.160884	+	0.345016i	−0.0446211	+	0.0956903i	−0.927355	−	0.374184i	$-0.877923\pi$
$13$	−0.160884	+	0.345016i	−0.0446211	+	0.0956903i	0.882733	+	0.469874i	$0.155701\pi$
$14$		0			0
$15$	5.63692	+	3.76578i	1.45545	+	0.972320i
$16$		0			0
$17$	−0.0144528	+	0.165196i	−0.00350532	+	0.0400660i	−0.997746	−	0.0671051i	$-0.978624\pi$
$17$	−0.0144528	+	0.165196i	−0.00350532	+	0.0400660i	0.994241	+	0.107171i	$0.0341793\pi$
$18$		0			0
$19$	1.45553	+	4.10870i	0.333922	+	0.942601i
$19$	1.45553	+	4.10870i	0.333922	+	0.942601i
$20$		0			0
$21$	2.78783	+	3.32240i	0.608354	+	0.725008i
$22$		0			0
$23$	0.363161	−	0.254288i	0.0757244	−	0.0530228i	−0.535101	−	0.844788i	$-0.679727\pi$
$23$	0.363161	−	0.254288i	0.0757244	−	0.0530228i	0.610826	+	0.791765i	$0.290838\pi$
$24$		0			0
$25$	−2.30799	+	4.43544i	−0.461599	+	0.887089i
$26$		0			0
$27$	−2.50399	+	9.34503i	−0.481894	+	1.79845i
$28$		0			0
$29$	1.09856	+	0.921802i	0.203998	+	0.171174i	0.739063	−	0.673636i	$-0.235269\pi$
$29$	1.09856	+	0.921802i	0.203998	+	0.171174i	−0.535065	+	0.844811i	$0.679713\pi$
$30$		0			0
$31$	6.67979	+	3.85658i	1.19973	+	0.692662i	0.960494	−	0.278301i	$-0.0897712\pi$
$31$	6.67979	+	3.85658i	1.19973	+	0.692662i	0.239231	+	0.970963i	$0.423105\pi$
$32$		0			0
$33$	−13.5648	−	9.49816i	−2.36132	−	1.65342i
$34$		0			0
$35$	−2.21187	+	2.31094i	−0.373874	+	0.390620i
$36$		0			0
$37$	6.77341	+	6.77341i	1.11354	+	1.11354i	0.992668	+	0.120874i	$0.0385699\pi$
$37$	6.77341	+	6.77341i	1.11354	+	1.11354i	0.120874	+	0.992668i	$0.461430\pi$
$38$		0			0
$39$		−	1.15412i		−	0.184807i
$40$		0			0
$41$	2.40119	−	6.59722i	0.375003	−	1.03031i	−0.598397	−	0.801200i	$-0.704195\pi$
$41$	2.40119	−	6.59722i	0.375003	−	1.03031i	0.973400	−	0.229112i	$-0.0735824\pi$
$42$		0			0
$43$	6.61211	−	9.44307i	1.00834	−	1.44005i	0.113565	−	0.993531i	$-0.463773\pi$
$43$	6.61211	−	9.44307i	1.00834	−	1.44005i	0.894772	−	0.446524i	$-0.147338\pi$
$44$		0			0
$45$	−13.6830	−	2.10482i	−2.03973	−	0.313769i
$46$		0			0
$47$	−3.11441	+	0.272476i	−0.454284	+	0.0397447i	−0.312002	−	0.950081i	$-0.601000\pi$
$47$	−3.11441	+	0.272476i	−0.454284	+	0.0397447i	−0.142282	+	0.989826i	$0.545444\pi$
$48$		0			0
$49$	4.28980	−	2.47672i	0.612829	−	0.353817i
$50$		0			0
$51$	−0.171947	−	0.472419i	−0.0240773	−	0.0661519i
$52$		0			0
$53$	6.56681	+	9.37838i	0.902021	+	1.28822i	0.957106	+	0.289738i	$0.0935681\pi$
$53$	6.56681	+	9.37838i	0.902021	+	1.28822i	−0.0550851	+	0.998482i	$0.517543\pi$
$54$		0			0
$55$	5.87375	−	10.7086i	0.792016	−	1.44394i
$56$		0			0
$57$	−9.26357	−	9.42437i	−1.22699	−	1.24829i
$58$		0			0
$59$	−8.39207	+	7.04179i	−1.09255	+	0.916762i	−0.996902	−	0.0786523i	$-0.974938\pi$
$59$	−8.39207	+	7.04179i	−1.09255	+	0.916762i	−0.0956529	+	0.995415i	$0.530494\pi$
$60$		0			0
$61$	2.07149	−	11.7480i	0.265227	−	1.50418i	−0.503159	−	0.864194i	$-0.667829\pi$
$61$	2.07149	−	11.7480i	0.265227	−	1.50418i	0.768387	−	0.639986i	$-0.221060\pi$
$62$		0			0
$63$	−8.02716	−	3.74313i	−1.01133	−	0.471589i
$64$		0			0
$65$	0.846167	−	0.0927428i	0.104954	−	0.0115033i
$66$		0			0
$67$	0.773226	+	8.83802i	0.0944646	+	1.07974i	0.884458	+	0.466620i	$0.154528\pi$
$67$	0.773226	+	8.83802i	0.0944646	+	1.07974i	−0.789993	+	0.613116i	$0.789916\pi$
$68$		0			0
$69$	−0.672034	+	1.16400i	−0.0809033	+	0.140129i
$70$		0			0
$71$	−0.325803	+	0.0574478i	−0.0386657	+	0.00681780i	−0.192948	−	0.981209i	$-0.561805\pi$
$71$	−0.325803	+	0.0574478i	−0.0386657	+	0.00681780i	0.154282	+	0.988027i	$0.450694\pi$
$72$		0			0
$73$	−0.964863	−	2.06915i	−0.112929	−	0.242176i	0.841718	−	0.539917i	$-0.181545\pi$
$73$	−0.964863	−	2.06915i	−0.112929	−	0.242176i	−0.954647	+	0.297741i	$0.903767\pi$
$74$		0			0
$75$	0.658643	−	15.1442i	0.0760535	−	1.74870i
$76$		0			0
$77$	5.52535	−	5.52535i	0.629672	−	0.629672i
$78$		0			0
$79$	−2.57267	−	0.936374i	−0.289447	−	0.105350i	0.193216	−	0.981156i	$-0.438108\pi$
$79$	−2.57267	−	0.936374i	−0.289447	−	0.105350i	−0.482663	+	0.875806i	$0.660330\pi$
$80$		0			0
$81$	−1.86796	−	10.5937i	−0.207551	−	1.17708i
$82$		0			0
$83$	−11.1195	+	2.97945i	−1.22052	+	0.327037i	−0.810881	−	0.585211i	$-0.801012\pi$
$83$	−11.1195	+	2.97945i	−1.22052	+	0.327037i	−0.409638	+	0.912248i	$0.634345\pi$
$84$		0			0
$85$	0.332548	−	0.164029i	0.0360698	−	0.0177915i
$86$		0			0
$87$	−4.19952	−	1.12526i	−0.450236	−	0.120640i
$88$		0			0
$89$	−5.02263	+	1.82809i	−0.532397	+	0.193777i	−0.594208	−	0.804311i	$-0.702535\pi$
$89$	−5.02263	+	1.82809i	−0.532397	+	0.193777i	0.0618111	+	0.998088i	$0.480312\pi$
$90$		0			0
$91$	0.536325	+	0.0945686i	0.0562222	+	0.00991348i
$92$		0			0
$93$	−23.2950	−	2.03804i	−2.41557	−	0.211335i
$94$		0			0
$95$	6.16528	−	7.54912i	0.632545	−	0.774524i
$96$		0			0
$97$	0.497197	+	0.0434991i	0.0504827	+	0.00441667i	0.112369	−	0.993667i	$-0.464156\pi$
$97$	0.497197	+	0.0434991i	0.0504827	+	0.00441667i	−0.0618864	+	0.998083i	$0.519712\pi$
$98$		0			0
$99$	33.3033	+	5.87227i	3.34711	+	0.590185i
$100$		0			0
$101$	1.05706	−	0.384738i	0.105181	−	0.0382828i	−0.288893	−	0.957361i	$-0.593287\pi$
$101$	1.05706	−	0.384738i	0.105181	−	0.0382828i	0.394075	+	0.919078i	$0.371065\pi$
$102$		0			0
$103$	14.9080	+	3.99460i	1.46893	+	0.393599i	0.902565	−	0.430554i	$-0.141682\pi$
$103$	14.9080	+	3.99460i	1.46893	+	0.393599i	0.566367	+	0.824153i	$0.308348\pi$
$104$		0			0
$105$	3.11655	−	9.18362i	0.304144	−	0.896229i
$106$		0			0
$107$	−7.95396	+	2.13126i	−0.768938	+	0.206036i	−0.621902	−	0.783095i	$-0.713640\pi$
$107$	−7.95396	+	2.13126i	−0.768938	+	0.206036i	−0.147036	+	0.989131i	$0.546973\pi$
$108$		0			0
$109$	1.54408	+	8.75691i	0.147896	+	0.838760i	0.964996	+	0.262264i	$0.0844692\pi$
$109$	1.54408	+	8.75691i	0.147896	+	0.838760i	−0.817100	+	0.576496i	$0.804420\pi$
$110$		0			0
$111$	−27.2894	−	9.93253i	−2.59020	−	0.942754i
$112$		0			0
$113$	−6.62544	+	6.62544i	−0.623269	+	0.623269i	−0.946366	−	0.323097i	$-0.895276\pi$
$113$	−6.62544	+	6.62544i	−0.623269	+	0.623269i	0.323097	+	0.946366i	$0.395276\pi$
$114$		0			0
$115$	−0.907414	−	0.399180i	−0.0846168	−	0.0372237i
$116$		0			0
$117$	0.996061	+	2.13606i	0.0920858	+	0.197479i
$118$		0			0
$119$	0.233625	−	0.0411945i	0.0214164	−	0.00377629i
$120$		0			0
$121$	−9.41746	+	16.3115i	−0.856132	+	1.48286i
$122$		0			0
$123$	1.85505	+	21.2034i	0.167265	+	1.91184i
$124$		0			0
$125$	11.1562	−	0.734059i	0.997842	−	0.0656562i
$126$		0			0
$127$	4.55705	+	2.12499i	0.404373	+	0.188562i	0.614154	−	0.789186i	$-0.289497\pi$
$127$	4.55705	+	2.12499i	0.404373	+	0.188562i	−0.209781	+	0.977748i	$0.567275\pi$
$128$		0			0
$129$	−6.06882	+	34.4180i	−0.534330	+	3.03034i
$130$		0			0
$131$	−8.78769	+	7.37375i	−0.767784	+	0.644247i	−0.940140	−	0.340787i	$-0.889306\pi$
$131$	−8.78769	+	7.37375i	−0.767784	+	0.644247i	0.172356	+	0.985035i	$0.444862\pi$
$132$		0			0
$133$	5.13862	−	3.53260i	0.445575	−	0.306316i
$134$		0			0
$135$	20.7685	−	6.05537i	1.78747	−	0.521163i
$136$		0			0
$137$	0.732633	+	1.04631i	0.0625931	+	0.0893922i	0.849228	−	0.528026i	$-0.177068\pi$
$137$	0.732633	+	1.04631i	0.0625931	+	0.0893922i	−0.786635	+	0.617418i	$0.788179\pi$
$138$		0			0
$139$	−1.80645	−	4.96319i	−0.153222	−	0.420973i	0.839205	−	0.543816i	$-0.183021\pi$
$139$	−1.80645	−	4.96319i	−0.153222	−	0.420973i	−0.992426	+	0.122843i	$0.960799\pi$
$140$		0			0
$141$	8.20821	−	4.73901i	0.691256	−	0.399097i
$142$		0			0
$143$	−2.07143	+	0.181227i	−0.173222	+	0.0151549i
$144$		0			0
$145$	0.487542	−	3.16940i	0.0404882	−	0.263204i
$146$		0			0
$147$	−8.61358	+	12.3015i	−0.710436	+	1.01461i
$148$		0			0
$149$	4.81272	−	13.2229i	0.394274	−	1.08326i	−0.570756	−	0.821119i	$-0.693350\pi$
$149$	4.81272	−	13.2229i	0.394274	−	1.08326i	0.965030	−	0.262139i	$-0.0844278\pi$
$150$		0			0
$151$		−	20.4283i		−	1.66243i	−0.555948	−	0.831217i	$-0.687644\pi$
$151$		−	20.4283i		−	1.66243i	0.555948	−	0.831217i	$-0.312356\pi$
$152$		0			0
$153$	0.725963	+	0.725963i	0.0586906	+	0.0586906i
$154$		0			0
$155$	−0.377702	−	17.2430i	−0.0303378	−	1.38499i
$156$		0			0
$157$	13.4852	+	9.44244i	1.07624	+	0.753589i	0.970572	−	0.240813i	$-0.0774140\pi$
$157$	13.4852	+	9.44244i	1.07624	+	0.753589i	0.105665	+	0.994402i	$0.466303\pi$
$158$		0			0
$159$	−30.0593	−	17.3548i	−2.38386	−	1.37632i
$160$		0			0
$161$	−0.485850	−	0.407676i	−0.0382903	−	0.0321294i
$162$		0			0
$163$	2.35672	−	8.79540i	0.184593	−	0.688909i	−0.810125	−	0.586258i	$-0.800601\pi$
$163$	2.35672	−	8.79540i	0.184593	−	0.688909i	0.994717	−	0.102652i	$-0.0327327\pi$
$164$		0			0
$165$	−2.41864	+	36.9492i	−0.188291	+	2.87649i
$166$		0			0
$167$	5.11551	−	3.58192i	0.395850	−	0.277177i	−0.358657	−	0.933469i	$-0.616765\pi$
$167$	5.11551	−	3.58192i	0.395850	−	0.277177i	0.754507	+	0.656293i	$0.227876\pi$
$168$		0			0
$169$	8.26309	+	9.84756i	0.635622	+	0.757505i
$170$		0			0
$171$	25.2789	+	9.44785i	1.93312	+	0.722495i
$172$		0			0
$173$	1.37458	−	15.7116i	0.104508	−	1.19453i	−0.745041	−	0.667019i	$-0.767570\pi$
$173$	1.37458	−	15.7116i	0.104508	−	1.19453i	0.849549	−	0.527510i	$-0.176874\pi$
$174$		0			0
$175$	6.98362	+	1.54699i	0.527912	+	0.116942i
$176$		0			0
$177$	14.0362	−	30.1007i	1.05502	−	2.26251i
$178$		0			0
$179$	−10.6511	−	18.4482i	−0.796099	−	1.37888i	−0.922139	−	0.386858i	$-0.873560\pi$
$179$	−10.6511	−	18.4482i	−0.796099	−	1.37888i	0.126041	−	0.992025i	$-0.459773\pi$
$180$		0			0
$181$	−5.65911	+	6.74426i	−0.420638	+	0.501297i	−0.934197	−	0.356757i	$-0.883882\pi$
$181$	−5.65911	+	6.74426i	−0.420638	+	0.501297i	0.513559	+	0.858054i	$0.328327\pi$
$182$		0			0
$183$	9.36041	+	34.9335i	0.691942	+	2.58236i
$184$		0			0
$185$	5.08933	−	20.8060i	0.374175	−	1.52969i
$186$		0			0
$187$	−0.820907	+	0.382795i	−0.0600307	+	0.0279928i
$188$		0			0
$189$	13.8404			1.00674
$190$		0			0
$191$	11.8629			0.858369			0.429185	−	0.903217i	$-0.358801\pi$
$191$	11.8629			0.858369			0.429185	+	0.903217i	$0.358801\pi$
$192$		0			0
$193$	−2.98330	+	1.39114i	−0.214743	+	0.100136i	−0.527013	−	0.849857i	$-0.676688\pi$
$193$	−2.98330	+	1.39114i	−0.214743	+	0.100136i	0.312271	+	0.949993i	$0.398910\pi$
$194$		0			0
$195$	−2.20614	+	1.33898i	−0.157985	+	0.0958861i
$196$		0			0
$197$	5.05223	+	18.8552i	0.359956	+	1.34338i	0.874131	+	0.485690i	$0.161432\pi$
$197$	5.05223	+	18.8552i	0.359956	+	1.34338i	−0.514175	+	0.857685i	$0.671902\pi$
$198$		0			0
$199$	−7.32786	+	8.73301i	−0.519458	+	0.619066i	−0.960453	−	0.278443i	$-0.910182\pi$
$199$	−7.32786	+	8.73301i	−0.519458	+	0.619066i	0.440994	+	0.897510i	$0.354626\pi$
$200$		0			0
$201$	−13.4483	−	23.2931i	−0.948568	−	1.64297i
$202$		0			0
$203$	0.867024	−	1.85934i	0.0608531	−	0.130500i
$204$		0			0
$205$	−15.3967	+	3.06394i	−1.07535	+	0.213995i
$206$		0			0
$207$	0.239224	−	2.73434i	0.0166272	−	0.190050i
$208$		0			0
$209$	−15.4604	+	18.1063i	−1.06942	+	1.25244i
$210$		0			0
$211$	7.39450	+	8.81242i	0.509058	+	0.606672i	0.957957	−	0.286910i	$-0.0926282\pi$
$211$	7.39450	+	8.81242i	0.509058	+	0.606672i	−0.448899	+	0.893582i	$0.648184\pi$
$212$		0			0
$213$	0.821587	−	0.575281i	0.0562942	−	0.0394176i
$214$		0			0
$215$	−25.7220	−	1.68373i	−1.75423	−	0.114829i
$216$		0			0
$217$	2.85589	−	10.6583i	0.193870	−	0.723534i
$218$		0			0
$219$	5.30221	+	4.44908i	0.358290	+	0.300641i
$220$		0			0
$221$	−0.0546702	−	0.0315639i	−0.00367752	−	0.00212322i
$222$		0			0
$223$	−12.8084	−	8.96853i	−0.857713	−	0.600577i	0.0598325	−	0.998208i	$-0.480943\pi$
$223$	−12.8084	−	8.96853i	−0.857713	−	0.600577i	−0.917545	+	0.397632i	$0.869832\pi$
$224$		0			0
$225$	11.8511	+	28.5975i	0.790076	+	1.90650i
$226$		0			0
$227$	6.34919	+	6.34919i	0.421410	+	0.421410i	0.885689	−	0.464279i	$-0.153686\pi$
$227$	6.34919	+	6.34919i	0.421410	+	0.421410i	−0.464279	+	0.885689i	$0.653686\pi$
$228$		0			0
$229$		−	1.24193i		−	0.0820690i	−0.999158	−	0.0410345i	$-0.986935\pi$
$229$		−	1.24193i		−	0.0820690i	0.999158	−	0.0410345i	$-0.0130654\pi$
$230$		0			0
$231$	−8.10238	+	22.2611i	−0.533097	+	1.46467i
$232$		0			0
$233$	10.3258	−	14.7467i	0.676465	−	0.966091i	−0.323339	−	0.946283i	$-0.604806\pi$
$233$	10.3258	−	14.7467i	0.676465	−	0.966091i	0.999804	−	0.0198083i	$-0.00630560\pi$
$234$		0			0
$235$	4.13411	+	5.63722i	0.269680	+	0.367731i
$236$		0			0
$237$	8.26851	−	0.723401i	0.537098	−	0.0469899i
$238$		0			0
$239$	−11.0995	+	6.40830i	−0.717967	+	0.414518i	−0.814004	−	0.580859i	$-0.802717\pi$
$239$	−11.0995	+	6.40830i	−0.717967	+	0.414518i	0.0960369	+	0.995378i	$0.469383\pi$
$240$		0			0
$241$	−4.12415	−	11.3310i	−0.265660	−	0.729894i	−0.998760	−	0.0497742i	$-0.984150\pi$
$241$	−4.12415	−	11.3310i	−0.265660	−	0.729894i	0.733101	−	0.680120i	$-0.238072\pi$
$242$		0			0
$243$	2.05823	+	2.93945i	0.132035	+	0.188566i
$244$		0			0
$245$	−9.71127	−	5.32672i	−0.620430	−	0.340311i
$246$		0			0
$247$	−1.65174	−	0.158840i	−0.105098	−	0.0101068i
$248$		0			0
$249$	26.7350	−	22.4333i	1.69426	−	1.42165i
$250$		0			0
$251$	−2.27798	+	12.9190i	−0.143785	+	0.815443i	0.824550	+	0.565789i	$0.191428\pi$
$251$	−2.27798	+	12.9190i	−0.143785	+	0.815443i	−0.968335	+	0.249654i	$0.919683\pi$
$252$		0			0
$253$	2.19469	+	1.02340i	0.137979	+	0.0643407i
$254$		0			0
$255$	−0.703562	+	0.876772i	−0.0440587	+	0.0549056i
$256$		0			0
$257$	2.27311	+	25.9817i	0.141792	+	1.62070i	0.650328	+	0.759654i	$0.274632\pi$
$257$	2.27311	+	25.9817i	0.141792	+	1.62070i	−0.508535	+	0.861041i	$0.669813\pi$
$258$		0			0
$259$	6.85181	−	11.8677i	0.425751	−	0.737422i
$260$		0			0
$261$	8.74369	−	1.54175i	0.541221	−	0.0954319i
$262$		0			0
$263$	6.36796	+	13.6561i	0.392665	+	0.842073i	0.998905	+	0.0467907i	$0.0148994\pi$
$263$	6.36796	+	13.6561i	0.392665	+	0.842073i	−0.606240	+	0.795282i	$0.707323\pi$
$264$		0			0
$265$	10.3085	−	23.4333i	0.633248	−	1.43950i
$266$		0			0
$267$	11.4582	−	11.4582i	0.701229	−	0.701229i
$268$		0			0
$269$	−15.9217	−	5.79504i	−0.970765	−	0.353330i	−0.192522	−	0.981293i	$-0.561667\pi$
$269$	−15.9217	−	5.79504i	−0.970765	−	0.353330i	−0.778243	+	0.627963i	$0.783889\pi$
$270$		0			0
$271$	5.49996	+	31.1918i	0.334099	+	1.89477i	0.435956	+	0.899968i	$0.356410\pi$
$271$	5.49996	+	31.1918i	0.334099	+	1.89477i	−0.101857	+	0.994799i	$0.532479\pi$
$272$		0			0
$273$	−1.59480	+	0.427325i	−0.0965217	+	0.0258629i
$274$		0			0
$275$	−27.2845	+	1.19589i	−1.64532	+	0.0721148i
$276$		0			0
$277$	6.55193	+	1.75558i	0.393667	+	0.105483i	0.450222	−	0.892917i	$-0.351345\pi$
$277$	6.55193	+	1.75558i	0.393667	+	0.105483i	−0.0565546	+	0.998400i	$0.518012\pi$
$278$		0			0
$279$	44.8736	−	16.3327i	2.68651	−	0.977811i
$280$		0			0
$281$	23.1123	+	4.07533i	1.37877	+	0.243114i	0.813389	−	0.581720i	$-0.197620\pi$
$281$	23.1123	+	4.07533i	1.37877	+	0.243114i	0.565376	+	0.824833i	$0.308731\pi$
$282$		0			0
$283$	−13.9218	−	1.21800i	−0.827564	−	0.0724025i	−0.334500	−	0.942396i	$-0.608568\pi$
$283$	−13.9218	−	1.21800i	−0.827564	−	0.0724025i	−0.493064	+	0.869993i	$0.664123\pi$
$284$		0			0
$285$	−7.26773	+	28.6416i	−0.430503	+	1.69658i
$286$		0			0
$287$	−10.0053	−	0.875354i	−0.590597	−	0.0516705i
$288$		0			0
$289$	16.7147	+	2.94724i	0.983215	+	0.173367i
$290$		0			0
$291$	−1.42186	+	0.517514i	−0.0833507	+	0.0303372i
$292$		0			0
$293$	−0.339935	−	0.0910852i	−0.0198592	−	0.00532126i	0.248876	−	0.968535i	$-0.419939\pi$
$293$	−0.339935	−	0.0910852i	−0.0198592	−	0.00532126i	−0.268735	+	0.963214i	$0.586606\pi$
$294$		0			0
$295$	23.1969	+	7.87211i	1.35058	+	0.458332i
$296$		0			0
$297$	−51.0438	+	13.6771i	−2.96186	+	0.793629i
$298$		0			0
$299$	0.0293069	+	0.166208i	0.00169486	+	0.00961203i
$300$		0			0
$301$	−15.4970	−	5.64044i	−0.893231	−	0.325110i
$302$		0			0
$303$	−2.41148	+	2.41148i	−0.138536	+	0.138536i
$304$		0			0
$305$	−24.8601	+	9.67000i	−1.42349	+	0.553702i
$306$		0			0
$307$	−1.53013	−	3.28138i	−0.0873292	−	0.187278i	0.857793	−	0.513996i	$-0.171835\pi$
$307$	−1.53013	−	3.28138i	−0.0873292	−	0.187278i	−0.945122	+	0.326717i	$0.894057\pi$
$308$		0			0
$309$	−46.0801	+	8.12517i	−2.62141	+	0.462225i
$310$		0			0
$311$	12.3076	−	21.3174i	0.697901	−	1.20880i	−0.271291	−	0.962497i	$-0.587451\pi$
$311$	12.3076	−	21.3174i	0.697901	−	1.20880i	0.969193	−	0.246303i	$-0.0792160\pi$
$312$		0			0
$313$	−1.42067	−	16.2383i	−0.0803008	−	0.917842i	−0.924342	−	0.381564i	$-0.875386\pi$
$313$	−1.42067	−	16.2383i	−0.0803008	−	0.917842i	0.844042	−	0.536278i	$-0.180170\pi$
$314$		0			0
$315$	2.15775	+	19.6869i	0.121576	+	1.10923i
$316$		0			0
$317$	−16.7901	−	7.82936i	−0.943027	−	0.439741i	−0.110593	−	0.993866i	$-0.535275\pi$
$317$	−16.7901	−	7.82936i	−0.943027	−	0.439741i	−0.832433	+	0.554125i	$0.813053\pi$
$318$		0			0
$319$	−1.36020	+	7.71407i	−0.0761565	+	0.431905i
$320$		0			0
$321$	19.1240	−	16.0470i	1.06740	−	0.895654i
$322$		0			0
$323$	−0.699779	+	0.181067i	−0.0389367	+	0.0100748i
$324$		0			0
$325$	−1.15898	−	1.50989i	−0.0642888	−	0.0837534i
$326$		0			0
$327$	−15.4624	−	22.0826i	−0.855072	−	1.22117i
$328$		0			0
$329$	1.52967	+	4.20272i	0.0843332	+	0.231704i
$330$		0			0
$331$	−11.8874	+	6.86318i	−0.653389	+	0.377235i	−0.789754	−	0.613424i	$-0.789792\pi$
$331$	−11.8874	+	6.86318i	−0.653389	+	0.377235i	0.136364	+	0.990659i	$0.456458\pi$
$332$		0			0
$333$	59.0800	−	5.16883i	3.23756	−	0.283250i
$334$		0			0
$335$	15.9972	−	11.7317i	0.874019	−	0.640971i
$336$		0			0
$337$	12.9431	−	18.4847i	0.705056	−	1.00692i	−0.293642	−	0.955915i	$-0.594867\pi$
$337$	12.9431	−	18.4847i	0.705056	−	1.00692i	0.998698	−	0.0510088i	$-0.0162437\pi$
$338$		0			0
$339$	9.71555	−	26.6932i	0.527676	−	1.44978i
$340$		0			0
$341$			42.1303i			2.28148i
$342$		0			0
$343$	−12.0918	−	12.0918i	−0.652895	−	0.652895i
$344$		0			0
$345$	3.00470	−	0.0658171i	0.161768	−	0.00354347i
$346$		0			0
$347$	−29.5562	−	20.6955i	−1.58666	−	1.11099i	−0.936207	−	0.351448i	$-0.885689\pi$
$347$	−29.5562	−	20.6955i	−1.58666	−	1.11099i	−0.650455	−	0.759545i	$-0.725422\pi$
$348$		0			0
$349$	4.78794	+	2.76432i	0.256292	+	0.147970i	0.622642	−	0.782507i	$-0.286059\pi$
$349$	4.78794	+	2.76432i	0.256292	+	0.147970i	−0.366350	+	0.930477i	$0.619393\pi$
$350$		0			0
$351$	−2.82134	−	2.36738i	−0.150592	−	0.126362i
$352$		0			0
$353$	−1.95531	+	7.29731i	−0.104071	+	0.388397i	−0.998238	−	0.0593360i	$-0.981102\pi$
$353$	−1.95531	+	7.29731i	−0.104071	+	0.388397i	0.894168	+	0.447733i	$0.147768\pi$
$354$		0			0
$355$	0.487802	+	0.556137i	0.0258898	+	0.0295167i
$356$		0			0
$357$	−0.589141	+	0.412521i	−0.0311806	+	0.0218329i
$358$		0			0
$359$	−2.56312	−	3.05461i	−0.135276	−	0.161216i	0.694153	−	0.719827i	$-0.255779\pi$
$359$	−2.56312	−	3.05461i	−0.135276	−	0.161216i	−0.829430	+	0.558611i	$0.811335\pi$
$360$		0			0
$361$	−14.7628	+	11.9607i	−0.776992	+	0.629511i
$362$		0			0
$363$	4.97674	−	56.8844i	0.261211	−	2.98566i
$364$		0			0
$365$	−2.83587	+	4.24496i	−0.148436	+	0.222191i
$366$		0			0
$367$	14.6703	−	31.4606i	0.765784	−	1.64223i	−0.000727542	−	1.00000i	$-0.500232\pi$
$367$	14.6703	−	31.4606i	0.765784	−	1.64223i	0.766512	−	0.642230i	$-0.221991\pi$
$368$		0			0
$369$	−21.7329	−	37.6426i	−1.13137	−	1.95959i
$370$		0			0
$371$	10.5279	−	12.5467i	0.546583	−	0.651393i
$372$		0			0
$373$	0.766310	+	2.85991i	0.0396781	+	0.148081i	0.982923	−	0.184017i	$-0.0589103\pi$
$373$	0.766310	+	2.85991i	0.0396781	+	0.148081i	−0.943245	+	0.332098i	$0.892244\pi$
$374$		0			0
$375$	−29.7129	+	16.3108i	−1.53437	+	0.842288i
$376$		0			0
$377$	−0.494777	+	0.230718i	−0.0254823	+	0.0118826i
$378$		0			0
$379$	−31.3437			−1.61002			−0.805010	−	0.593262i	$-0.797840\pi$
$379$	−31.3437			−1.61002			−0.805010	+	0.593262i	$0.797840\pi$
$380$		0			0
$381$	−15.2438			−0.780965
$382$		0			0
$383$	8.61928	−	4.01924i	0.440425	−	0.205373i	−0.189741	−	0.981834i	$-0.560765\pi$
$383$	8.61928	−	4.01924i	0.440425	−	0.205373i	0.630166	+	0.776461i	$0.282987\pi$
$384$		0			0
$385$	−16.9723	−	4.15158i	−0.864990	−	0.211584i
$386$		0			0
$387$	−18.4722	−	68.9391i	−0.938994	−	3.50437i
$388$		0			0
$389$	6.11064	−	7.28238i	0.309822	−	0.369231i	−0.588555	−	0.808457i	$-0.700303\pi$
$389$	6.11064	−	7.28238i	0.309822	−	0.369231i	0.898377	+	0.439226i	$0.144747\pi$
$390$		0			0
$391$	0.0367588	+	0.0636681i	0.00185897	+	0.00321983i
$392$		0			0
$393$	14.6979	−	31.5197i	0.741410	−	1.58996i
$394$		0			0
$395$	1.19482	+	6.00412i	0.0601180	+	0.302100i
$396$		0			0
$397$	−0.411018	+	4.69796i	−0.0206284	+	0.235784i	0.978880	+	0.204435i	$0.0655358\pi$
$397$	−0.411018	+	4.69796i	−0.0206284	+	0.235784i	−0.999509	+	0.0313487i	$0.990020\pi$
$398$		0			0
$399$	−9.59298	+	16.2902i	−0.480250	+	0.815531i
$400$		0			0
$401$	3.05550	+	3.64140i	0.152584	+	0.181843i	0.836922	−	0.547323i	$-0.184353\pi$
$401$	3.05550	+	3.64140i	0.152584	+	0.181843i	−0.684338	+	0.729165i	$0.739908\pi$
$402$		0			0
$403$	−2.40525	+	1.68418i	−0.119814	+	0.0838948i
$404$		0			0
$405$	−18.0832	+	15.8613i	−0.898563	+	0.788153i
$406$		0			0
$407$	−13.5419	+	50.5392i	−0.671250	+	2.50514i
$408$		0			0
$409$	−16.9851	−	14.2522i	−0.839858	−	0.704724i	0.117674	−	0.993052i	$-0.462456\pi$
$409$	−16.9851	−	14.2522i	−0.839858	−	0.704724i	−0.957532	+	0.288328i	$0.906901\pi$
$410$		0			0
$411$	−3.35360	−	1.93620i	−0.165421	−	0.0955059i
$412$		0			0
$413$	12.8379	+	8.98916i	0.631710	+	0.442328i
$414$		0			0
$415$	18.5958	+	17.7986i	0.912834	+	0.873701i
$416$		0			0
$417$	11.3226	+	11.3226i	0.554470	+	0.554470i
$418$		0			0
$419$		−	27.3929i		−	1.33823i	−0.743159	−	0.669115i	$-0.766673\pi$
$419$		−	27.3929i		−	1.33823i	0.743159	−	0.669115i	$-0.233327\pi$
$420$		0			0
$421$	−4.48082	+	12.3109i	−0.218382	+	0.599999i	−0.999709	−	0.0241228i	$-0.992321\pi$
$421$	−4.48082	+	12.3109i	−0.218382	+	0.599999i	0.781327	+	0.624121i	$0.214543\pi$
$422$		0			0
$423$	−11.1019	+	15.8551i	−0.539792	+	0.770903i
$424$		0			0
$425$	−0.699362	−	0.445376i	−0.0339240	−	0.0216039i
$426$		0			0
$427$	−17.0008	+	1.48738i	−0.822728	+	0.0719793i
$428$		0			0
$429$	5.45937	−	3.15197i	0.263581	−	0.152179i
$430$		0			0
$431$	−10.1249	−	27.8180i	−0.487701	−	1.33995i	−0.902757	−	0.430151i	$-0.858460\pi$
$431$	−10.1249	−	27.8180i	−0.487701	−	1.33995i	0.415056	−	0.909796i	$-0.363762\pi$
$432$		0			0
$433$	0.999898	+	1.42800i	0.0480520	+	0.0686254i	0.842459	−	0.538760i	$-0.181107\pi$
$433$	0.999898	+	1.42800i	0.0480520	+	0.0686254i	−0.794407	+	0.607386i	$0.792218\pi$
$434$		0			0
$435$	2.72119	+	9.33305i	0.130471	+	0.447486i
$436$		0			0
$437$	1.57339	+	1.12200i	0.0752654	+	0.0536724i
$438$		0			0
$439$	−6.39461	+	5.36572i	−0.305198	+	0.256092i	−0.782504	−	0.622646i	$-0.786058\pi$
$439$	−6.39461	+	5.36572i	−0.305198	+	0.256092i	0.477306	+	0.878737i	$0.341613\pi$
$440$		0			0
$441$	5.32538	−	30.2017i	0.253589	−	1.43818i
$442$		0			0
$443$	−21.4646	−	10.0091i	−1.01981	−	0.475547i	−0.160522	−	0.987032i	$-0.551318\pi$
$443$	−21.4646	−	10.0091i	−1.01981	−	0.475547i	−0.859292	+	0.511485i	$0.829095\pi$
$444$		0			0
$445$	9.32159	+	7.48007i	0.441886	+	0.354589i
$446$		0			0
$447$	3.71810	+	42.4981i	0.175860	+	2.01009i
$448$		0			0
$449$	2.36294	−	4.09274i	0.111514	−	0.193148i	−0.804867	−	0.593455i	$-0.797763\pi$
$449$	2.36294	−	4.09274i	0.111514	−	0.193148i	0.916381	+	0.400307i	$0.131097\pi$
$450$		0			0
$451$	37.7649	−	6.65898i	1.77828	−	0.313559i
$452$		0			0
$453$	26.1738	+	56.1299i	1.22975	+	2.63721i
$454$		0			0
$455$	−0.441459	−	1.13492i	−0.0206959	−	0.0532061i
$456$		0			0
$457$	−13.9975	+	13.9975i	−0.654773	+	0.654773i	−0.954139	−	0.299365i	$-0.903225\pi$
$457$	−13.9975	+	13.9975i	−0.654773	+	0.654773i	0.299365	+	0.954139i	$0.403225\pi$
$458$		0			0
$459$	−1.50757	−	0.548712i	−0.0703676	−	0.0256117i
$460$		0			0
$461$	−0.975172	−	5.53048i	−0.0454183	−	0.257580i	0.953641	−	0.300947i	$-0.0973027\pi$
$461$	−0.975172	−	5.53048i	−0.0454183	−	0.257580i	−0.999059	+	0.0433669i	$0.986192\pi$
$462$		0			0
$463$	12.6185	−	3.38111i	0.586430	−	0.157133i	0.0466088	−	0.998913i	$-0.485159\pi$
$463$	12.6185	−	3.38111i	0.586430	−	0.157133i	0.539821	+	0.841780i	$0.318492\pi$
$464$		0			0
$465$	23.1304	+	46.8938i	1.07265	+	2.17465i
$466$		0			0
$467$	30.4453	+	8.15779i	1.40884	+	0.377498i	0.881511	−	0.472164i	$-0.156527\pi$
$467$	30.4453	+	8.15779i	1.40884	+	0.377498i	0.527329	+	0.849661i	$0.323194\pi$
$468$		0			0
$469$	11.9264	−	4.34085i	0.550710	−	0.200442i
$470$		0			0
$471$	−49.1507	−	8.66660i	−2.26475	−	0.399336i
$472$		0			0
$473$	62.7271	+	5.48791i	2.88420	+	0.252334i
$474$		0			0
$475$	−21.5833	−	3.02691i	−0.990309	−	0.138884i
$476$		0			0
$477$	70.6124	+	6.17778i	3.23312	+	0.282861i
$478$		0			0
$479$	28.5377	+	5.03196i	1.30392	+	0.229916i	0.782107	−	0.623144i	$-0.214145\pi$
$479$	28.5377	+	5.03196i	1.30392	+	0.229916i	0.521813	+	0.853060i	$0.325256\pi$
$480$		0			0
$481$	−3.42667	+	1.24721i	−0.156243	+	0.0568677i
$482$		0			0
$483$	1.85728	+	0.497657i	0.0845092	+	0.0226442i
$484$		0			0
$485$	−0.493685	−	1.00088i	−0.0224171	−	0.0454476i
$486$		0			0
$487$	26.8569	−	7.19630i	1.21700	−	0.326095i	0.407498	−	0.913206i	$-0.366401\pi$
$487$	26.8569	−	7.19630i	1.21700	−	0.326095i	0.809507	+	0.587111i	$0.199735\pi$
$488$		0			0
$489$	4.79367	+	27.1862i	0.216777	+	1.22940i
$490$		0			0
$491$	19.2426	+	7.00372i	0.868404	+	0.316073i	0.737521	−	0.675324i	$-0.235996\pi$
$491$	19.2426	+	7.00372i	0.868404	+	0.316073i	0.130883	+	0.991398i	$0.458219\pi$
$492$		0			0
$493$	−0.168155	+	0.168155i	−0.00757334	+	0.00757334i
$494$		0			0
$495$	−27.4125	−	70.4735i	−1.23210	−	3.16755i
$496$		0			0
$497$	0.200016	+	0.428935i	0.00897194	+	0.0192404i
$498$		0			0
$499$	−11.8732	+	2.09357i	−0.531519	+	0.0937211i	−0.432965	−	0.901411i	$-0.642533\pi$
$499$	−11.8732	+	2.09357i	−0.531519	+	0.0937211i	−0.0985537	+	0.995132i	$0.531422\pi$
$500$		0			0
$501$	−9.46629	+	16.3961i	−0.422923	+	0.732523i
$502$		0			0
$503$	2.40329	+	27.4697i	0.107157	+	1.22481i	0.839302	+	0.543666i	$0.182964\pi$
$503$	2.40329	+	27.4697i	0.107157	+	1.22481i	−0.732145	+	0.681149i	$0.761480\pi$
$504$		0			0
$505$	−1.96181	−	1.57425i	−0.0872996	−	0.0700532i
$506$		0			0
$507$	−35.3213	−	16.4706i	−1.56867	−	0.731484i
$508$		0			0
$509$	2.22736	−	12.6320i	0.0987260	−	0.559903i	−0.894816	−	0.446436i	$-0.852693\pi$
$509$	2.22736	−	12.6320i	0.0987260	−	0.559903i	0.993542	−	0.113467i	$-0.0361957\pi$
$510$		0			0
$511$	−2.50198	+	2.09941i	−0.110681	+	0.0928725i
$512$		0			0
$513$	−42.0406	+	3.31385i	−1.85614	+	0.146310i
$514$		0			0
$515$	−9.66007	−	33.1318i	−0.425674	−	1.45996i
$516$		0			0
$517$	−9.79458	−	13.9881i	−0.430765	−	0.615196i
$518$		0			0
$519$	16.3536	+	44.9311i	0.717842	+	1.97226i
$520$		0			0
$521$	−14.6741	+	8.47209i	−0.642884	+	0.371169i	−0.785725	−	0.618577i	$-0.787710\pi$
$521$	−14.6741	+	8.47209i	−0.642884	+	0.371169i	0.142841	+	0.989746i	$0.454376\pi$
$522$		0			0
$523$	24.1464	−	2.11254i	1.05585	−	0.0923748i	0.454013	−	0.890995i	$-0.349992\pi$
$523$	24.1464	−	2.11254i	1.05585	−	0.0923748i	0.601836	+	0.798620i	$0.294436\pi$
$524$		0			0
$525$	−21.1706	+	4.69717i	−0.923962	+	0.205001i
$526$		0			0
$527$	−0.733634	+	1.04774i	−0.0319576	+	0.0456402i
$528$		0			0
$529$	−7.79924	+	21.4282i	−0.339097	+	0.931662i
$530$		0			0
$531$			67.8248i			2.94335i
$532$		0			0
$533$	1.88984	+	1.88984i	0.0818579	+	0.0818579i
$534$		0			0
$535$	13.3020	+	12.7317i	0.575094	+	0.550439i
$536$		0			0
$537$	52.9022	+	37.0425i	2.28290	+	1.59850i
$538$		0			0
$539$	23.4315	+	13.5282i	1.00926	+	0.582699i
$540$		0			0
$541$	−27.0758	−	22.7193i	−1.16408	−	0.976779i	−0.164126	−	0.986439i	$-0.552480\pi$
$541$	−27.0758	−	22.7193i	−1.16408	−	0.976779i	−0.999953	+	0.00966081i	$0.996925\pi$
$542$		0			0
$543$	6.90816	−	25.7816i	0.296457	−	1.10639i
$544$		0			0
$545$	14.9478	−	13.1111i	0.640294	−	0.561619i
$546$		0			0
$547$	18.0598	−	12.6456i	0.772183	−	0.540689i	−0.119778	−	0.992801i	$-0.538218\pi$
$547$	18.0598	−	12.6456i	0.772183	−	0.540689i	0.891961	+	0.452112i	$0.149329\pi$
$548$		0			0
$549$	−47.4738	−	56.5771i	−2.02613	−	2.41465i
$550$		0			0
$551$	−2.18841	+	5.85537i	−0.0932296	+	0.249447i
$552$		0			0
$553$	−0.341355	+	3.90170i	−0.0145159	+	0.165917i
$554$		0			0
$555$	12.6740	+	63.6883i	0.537981	+	2.70342i
$556$		0			0
$557$	10.4168	−	22.3390i	0.441376	−	0.946534i	−0.552237	−	0.833687i	$-0.686225\pi$
$557$	10.4168	−	22.3390i	0.441376	−	0.946534i	0.993612	−	0.112846i	$-0.0359968\pi$
$558$		0			0
$559$	2.19423	+	3.80052i	0.0928062	+	0.160745i
$560$		0			0
$561$	1.76511	−	2.10358i	0.0745230	−	0.0888130i
$562$		0			0
$563$	0.147798	+	0.551590i	0.00622894	+	0.0232467i	0.968970	−	0.247177i	$-0.0795029\pi$
$563$	0.147798	+	0.551590i	0.00622894	+	0.0232467i	−0.962741	+	0.270424i	$0.912836\pi$
$564$		0			0
$565$	20.3515	+	4.97815i	0.856193	+	0.209432i
$566$		0			0
$567$	−13.9472	+	6.50368i	−0.585727	+	0.273129i
$568$		0			0
$569$	−34.0442			−1.42721			−0.713603	−	0.700551i	$-0.752938\pi$
$569$	−34.0442			−1.42721			−0.713603	+	0.700551i	$0.752938\pi$
$570$		0			0
$571$	26.6659			1.11593			0.557967	−	0.829863i	$-0.311582\pi$
$571$	26.6659			1.11593			0.557967	+	0.829863i	$0.311582\pi$
$572$		0			0
$573$	−32.5951	+	15.1993i	−1.36168	+	0.634962i
$574$		0			0
$575$	0.289708	+	2.19768i	0.0120817	+	0.0916495i
$576$		0			0
$577$	1.99204	+	7.43441i	0.0829298	+	0.309498i	0.994914	−	0.100727i	$-0.0321168\pi$
$577$	1.99204	+	7.43441i	0.0829298	+	0.309498i	−0.911984	+	0.410225i	$0.865450\pi$
$578$		0			0
$579$	6.41467	−	7.64471i	0.266585	−	0.317703i
$580$		0			0
$581$	8.23422	+	14.2621i	0.341613	+	0.591691i
$582$		0			0
$583$	−26.4286	+	56.6763i	−1.09456	+	2.34729i
$584$		0			0
$585$	2.92756	−	4.38221i	0.121040	−	0.181182i
$586$		0			0
$587$	−0.646976	+	7.39497i	−0.0267036	+	0.305223i	0.971084	+	0.238739i	$0.0767339\pi$
$587$	−0.646976	+	7.39497i	−0.0267036	+	0.305223i	−0.997787	+	0.0664847i	$0.978822\pi$
$588$		0			0
$589$	−6.12286	+	33.0586i	−0.252288	+	1.36216i
$590$		0			0
$591$	−38.0399	−	45.3342i	−1.56475	−	1.86480i
$592$		0			0
$593$	−9.53664	+	6.67763i	−0.391623	+	0.274217i	−0.752760	−	0.658296i	$-0.771278\pi$
$593$	−9.53664	+	6.67763i	−0.391623	+	0.274217i	0.361137	+	0.932513i	$0.382389\pi$
$594$		0			0
$595$	−0.349791	−	0.398792i	−0.0143400	−	0.0163489i
$596$		0			0
$597$	8.94523	−	33.3841i	0.366104	−	1.36632i
$598$		0			0
$599$	−1.68646	−	1.41511i	−0.0689069	−	0.0578197i	0.607684	−	0.794179i	$-0.292099\pi$
$599$	−1.68646	−	1.41511i	−0.0689069	−	0.0578197i	−0.676591	+	0.736359i	$0.736543\pi$
$600$		0			0
$601$	−12.0611	−	6.96346i	−0.491981	−	0.284045i	0.233415	−	0.972377i	$-0.425010\pi$
$601$	−12.0611	−	6.96346i	−0.491981	−	0.284045i	−0.725396	+	0.688332i	$0.758343\pi$
$602$		0			0
$603$	44.9934	+	31.5047i	1.83227	+	1.28297i
$604$		0			0
$605$	42.1060	−	0.922319i	1.71185	−	0.0374976i
$606$		0			0
$607$	−27.3635	−	27.3635i	−1.11065	−	1.11065i	−0.993062	−	0.117588i	$-0.962484\pi$
$607$	−27.3635	−	27.3635i	−1.11065	−	1.11065i	−0.117588	−	0.993062i	$-0.537516\pi$
$608$		0			0
$609$			6.21968i			0.252034i
$610$		0			0
$611$	0.407050	−	1.11836i	0.0164675	−	0.0452440i
$612$		0			0
$613$	−16.0911	+	22.9805i	−0.649913	+	0.928172i	−0.999963	−	0.00855863i	$-0.997276\pi$
$613$	−16.0911	+	22.9805i	−0.649913	+	0.928172i	0.350050	+	0.936731i	$0.386165\pi$
$614$		0			0
$615$	38.3790	−	28.1456i	1.54759	−	1.13494i
$616$		0			0
$617$	1.72373	−	0.150807i	0.0693949	−	0.00607127i	−0.0524054	−	0.998626i	$-0.516689\pi$
$617$	1.72373	−	0.150807i	0.0693949	−	0.00607127i	0.121800	+	0.992555i	$0.461133\pi$
$618$		0			0
$619$	16.7870	−	9.69196i	0.674725	−	0.389553i	−0.123140	−	0.992389i	$-0.539296\pi$
$619$	16.7870	−	9.69196i	0.674725	−	0.389553i	0.797865	+	0.602837i	$0.205963\pi$
$620$		0			0
$621$	1.46698	+	4.03049i	0.0588678	+	0.161738i
$622$		0			0
$623$	4.38580	+	6.26357i	0.175713	+	0.250945i
$624$		0			0
$625$	−14.3463	−	20.4740i	−0.573853	−	0.818958i
$626$		0			0
$627$	19.2811	−	69.5585i	0.770013	−	2.77790i
$628$		0			0
$629$	−1.21684	+	1.02105i	−0.0485185	+	0.0407118i
$630$		0			0
$631$	−1.43123	+	8.11694i	−0.0569766	+	0.323130i	−0.999953	−	0.00973032i	$-0.996903\pi$
$631$	−1.43123	+	8.11694i	−0.0569766	+	0.323130i	0.942976	+	0.332860i	$0.108014\pi$
$632$		0			0
$633$	−31.6084	−	14.7392i	−1.25632	−	0.585832i
$634$		0			0
$635$	−1.22497	−	11.1764i	−0.0486113	−	0.443520i
$636$		0			0
$637$	0.164349	+	1.87852i	0.00651174	+	0.0744295i
$638$		0			0
$639$	−1.02411	+	1.77381i	−0.0405132	+	0.0701709i
$640$		0			0
$641$	3.01863	−	0.532266i	0.119229	−	0.0210232i	−0.113715	−	0.993513i	$-0.536275\pi$
$641$	3.01863	−	0.532266i	0.119229	−	0.0210232i	0.232944	+	0.972490i	$0.425164\pi$
$642$		0			0
$643$	−11.3967	−	24.4403i	−0.449442	−	0.963832i	−0.992283	−	0.123996i	$-0.960429\pi$
$643$	−11.3967	−	24.4403i	−0.449442	−	0.963832i	0.542840	−	0.839836i	$-0.317349\pi$
$644$		0			0
$645$	72.8324	−	28.3301i	2.86777	−	1.11549i
$646$		0			0
$647$	−9.43474	+	9.43474i	−0.370918	+	0.370918i	−0.867812	−	0.496894i	$-0.834474\pi$
$647$	−9.43474	+	9.43474i	−0.370918	+	0.370918i	0.496894	+	0.867812i	$0.334474\pi$
$648$		0			0
$649$	−56.2294	−	20.4658i	−2.20720	−	0.803354i
$650$		0			0
$651$	5.80899	+	32.9444i	0.227672	+	1.29119i
$652$		0			0
$653$	25.7176	−	6.89102i	1.00641	−	0.269666i	0.282281	−	0.959332i	$-0.408909\pi$
$653$	25.7176	−	6.89102i	1.00641	−	0.269666i	0.724128	+	0.689665i	$0.242242\pi$
$654$		0			0
$655$	24.2905	+	8.24322i	0.949108	+	0.322089i
$656$		0			0
$657$	−13.6532	−	3.65836i	−0.532662	−	0.142726i
$658$		0			0
$659$	8.38583	−	3.05219i	0.326666	−	0.118897i	−0.173481	−	0.984837i	$-0.555502\pi$
$659$	8.38583	−	3.05219i	0.326666	−	0.118897i	0.500147	+	0.865941i	$0.333279\pi$
$660$		0			0
$661$	−15.1515	−	2.67162i	−0.589325	−	0.103914i	−0.128970	−	0.991649i	$-0.541167\pi$
$661$	−15.1515	−	2.67162i	−0.589325	−	0.103914i	−0.460356	+	0.887735i	$0.652278\pi$
$662$		0			0
$663$	0.190656	+	0.0166802i	0.00740446	+	0.000647806i
$664$		0			0
$665$	−12.7144	−	5.72426i	−0.493044	−	0.221977i
$666$		0			0
$667$	0.633358	+	0.0554117i	0.0245237	+	0.00214555i
$668$		0			0
$669$	46.6839	+	8.23163i	1.80490	+	0.318253i
$670$		0			0
$671$	61.2296	−	22.2857i	2.36374	−	0.860332i
$672$		0			0
$673$	1.76147	+	0.471984i	0.0678996	+	0.0181936i	0.292609	−	0.956232i	$-0.405477\pi$
$673$	1.76147	+	0.471984i	0.0678996	+	0.0181936i	−0.224709	+	0.974426i	$0.572143\pi$
$674$		0			0
$675$	−35.6702	−	32.6746i	−1.37295	−	1.25765i
$676$		0			0
$677$	2.89080	−	0.774587i	0.111102	−	0.0297698i	−0.202839	−	0.979212i	$-0.565017\pi$
$677$	2.89080	−	0.774587i	0.111102	−	0.0297698i	0.313942	+	0.949442i	$0.398350\pi$
$678$		0			0
$679$	−0.123984	−	0.703151i	−0.00475809	−	0.0269845i
$680$		0			0
$681$	−25.5802	−	9.31045i	−0.980237	−	0.356777i
$682$		0			0
$683$	16.7520	−	16.7520i	0.640998	−	0.640998i	−0.309803	−	0.950801i	$-0.600263\pi$
$683$	16.7520	−	16.7520i	0.640998	−	0.640998i	0.950801	+	0.309803i	$0.100263\pi$
$684$		0			0
$685$	1.15008	−	2.61436i	0.0439424	−	0.0998896i
$686$		0			0
$687$	1.59122	+	3.41239i	0.0607089	+	0.130191i
$688$		0			0
$689$	−4.29219	+	0.756829i	−0.163519	+	0.0288329i
$690$		0			0
$691$	−4.79488	+	8.30497i	−0.182406	+	0.315936i	−0.942699	−	0.333644i	$-0.891722\pi$
$691$	−4.79488	+	8.30497i	−0.182406	+	0.315936i	0.760294	+	0.649580i	$0.225055\pi$
$692$		0			0
$693$	−4.21643	−	48.1940i	−0.160169	−	1.83074i
$694$		0			0
$695$	−7.39156	+	9.21128i	−0.280378	+	0.349404i
$696$		0			0
$697$	1.05513	+	0.492016i	0.0399660	+	0.0186364i
$698$		0			0
$699$	−9.47736	+	53.7488i	−0.358467	+	2.03297i
$700$		0			0
$701$	−30.5097	+	25.6007i	−1.15234	+	0.966925i	−0.999772	−	0.0213689i	$-0.993198\pi$
$701$	−30.5097	+	25.6007i	−1.15234	+	0.966925i	−0.152564	+	0.988294i	$0.548753\pi$
$702$		0			0
$703$	−17.9710	+	37.6889i	−0.677789	+	1.42146i
$704$		0			0
$705$	−18.5818	−	10.1923i	−0.699830	−	0.383863i
$706$		0			0
$707$	−0.923033	−	1.31823i	−0.0347142	−	0.0495770i
$708$		0			0
$709$	−0.312288	−	0.858004i	−0.0117282	−	0.0322230i	0.933690	−	0.358081i	$-0.116569\pi$
$709$	−0.312288	−	0.858004i	−0.0117282	−	0.0322230i	−0.945419	+	0.325858i	$0.894347\pi$
$710$		0			0
$711$	−14.6792	+	8.47502i	−0.550512	+	0.317838i
$712$		0			0
$713$	3.40653	−	0.298032i	0.127575	−	0.0111614i
$714$		0			0
$715$	2.74964	+	3.74938i	0.102831	+	0.140219i
$716$		0			0
$717$	22.2869	−	31.8290i	0.832320	−	1.18868i
$718$		0			0
$719$	0.148862	−	0.408995i	0.00555161	−	0.0152529i	−0.936886	−	0.349635i	$-0.886305\pi$
$719$	0.148862	−	0.408995i	0.00555161	−	0.0152529i	0.942437	+	0.334382i	$0.108528\pi$
$720$		0			0
$721$		−	22.0795i		−	0.822284i
$722$		0			0
$723$	25.8496	+	25.8496i	0.961356	+	0.961356i
$724$		0			0
$725$	−6.62407	+	2.74509i	−0.246012	+	0.101950i
$726$		0			0
$727$	17.2496	+	12.0783i	0.639752	+	0.447959i	0.847913	−	0.530135i	$-0.177859\pi$
$727$	17.2496	+	12.0783i	0.639752	+	0.447959i	−0.208161	+	0.978095i	$0.566748\pi$
$728$		0			0
$729$	18.5265	+	10.6963i	0.686166	+	0.396158i
$730$		0			0
$731$	1.46440	+	1.22877i	0.0541627	+	0.0454479i
$732$		0			0
$733$	3.37563	−	12.5980i	0.124682	−	0.465318i	−0.875147	−	0.483858i	$-0.839235\pi$
$733$	3.37563	−	12.5980i	0.124682	−	0.465318i	0.999828	+	0.0185400i	$0.00590180\pi$
$734$		0			0
$735$	33.5080	+	2.19339i	1.23596	+	0.0809043i
$736$		0			0
$737$	−39.6952	+	27.7949i	−1.46219	+	1.02384i
$738$		0			0
$739$	2.05518	+	2.44926i	0.0756009	+	0.0900976i	0.802519	−	0.596626i	$-0.203493\pi$
$739$	2.05518	+	2.44926i	0.0756009	+	0.0900976i	−0.726918	+	0.686724i	$0.759048\pi$
$740$		0			0
$741$	4.74192	−	1.67986i	0.174199	−	0.0617111i
$742$		0			0
$743$	−1.79419	+	20.5077i	−0.0658225	+	0.752355i	0.889528	+	0.456880i	$0.151033\pi$
$743$	−1.79419	+	20.5077i	−0.0658225	+	0.752355i	−0.955351	+	0.295474i	$0.904522\pi$
$744$		0			0
$745$	−30.8596	+	6.14108i	−1.13061	+	0.224992i
$746$		0			0
$747$	−30.1205	+	64.5935i	−1.10205	+	2.36335i
$748$		0			0
$749$	5.89009	+	10.2019i	0.215219	+	0.372771i
$750$		0			0
$751$	9.43710	−	11.2467i	0.344365	−	0.410398i	−0.565867	−	0.824496i	$-0.691459\pi$
$751$	9.43710	−	11.2467i	0.344365	−	0.410398i	0.910232	+	0.414098i	$0.135903\pi$
$752$		0			0
$753$	−10.2934	−	38.4157i	−0.375114	−	1.39994i
$754$		0			0
$755$	−39.0496	+	23.7004i	−1.42116	+	0.862547i
$756$		0			0
$757$	−27.4326	+	12.7920i	−0.997055	+	0.464935i	−0.851466	−	0.524411i	$-0.824286\pi$
$757$	−27.4326	+	12.7920i	−0.997055	+	0.464935i	−0.145590	+	0.989345i	$0.546508\pi$
$758$		0			0
$759$	−7.34147			−0.266479
$760$		0			0
$761$	45.9564			1.66592			0.832958	−	0.553336i	$-0.186645\pi$
$761$	45.9564			1.66592			0.832958	+	0.553336i	$0.186645\pi$
$762$		0			0
$763$	11.5289	−	5.37602i	0.417374	−	0.194625i
$764$		0			0
$765$	0.545466	−	2.22995i	0.0197214	−	0.0806241i
$766$		0			0
$767$	−1.07938	−	4.02831i	−0.0389743	−	0.145454i
$768$		0			0
$769$	−20.5141	+	24.4477i	−0.739757	+	0.881608i	−0.996389	−	0.0849013i	$-0.972943\pi$
$769$	−20.5141	+	24.4477i	−0.739757	+	0.881608i	0.256633	+	0.966509i	$0.417387\pi$
$770$		0			0
$771$	−39.5348	−	68.4762i	−1.42381	−	2.46611i
$772$		0			0
$773$	1.37825	−	2.95567i	0.0495722	−	0.106308i	−0.879962	−	0.475045i	$-0.842432\pi$
$773$	1.37825	−	2.95567i	0.0495722	−	0.106308i	0.929534	+	0.368737i	$0.120210\pi$
$774$		0			0
$775$	−32.5225	+	20.7269i	−1.16824	+	0.744531i
$776$		0			0
$777$	−3.62090	+	41.3871i	−0.129899	+	1.48475i
$778$		0			0
$779$	30.6010	+	0.263299i	1.09639	+	0.00943366i
$780$		0			0
$781$	−1.16154	−	1.38427i	−0.0415631	−	0.0495330i
$782$		0			0
$783$	−11.3651	+	7.95790i	−0.406154	+	0.284392i
$784$		0			0
$785$	2.40445	−	36.7324i	0.0858185	−	1.31104i
$786$		0			0
$787$	−8.61435	+	32.1492i	−0.307068	+	1.14599i	0.624082	+	0.781359i	$0.285473\pi$
$787$	−8.61435	+	32.1492i	−0.307068	+	1.14599i	−0.931150	+	0.364636i	$0.881194\pi$
$788$		0			0
$789$	−34.9938	−	29.3633i	−1.24581	−	1.04536i
$790$		0			0
$791$	11.6084	+	6.70213i	0.412748	+	0.238300i

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +O(q^{10})\)	\(q+(-2.74765 + 1.28125i) q^{3} +(-1.16017 - 1.91154i) q^{5} +(-0.370262 - 1.38184i) q^{7} +(3.97961 - 4.74272i) q^{9} +(2.73107 + 4.73035i) q^{11} +(-0.160884 + 0.345016i) q^{13} +(5.63692 + 3.76578i) q^{15} +(-0.0144528 + 0.165196i) q^{17} +(1.45553 + 4.10870i) q^{19} +(2.78783 + 3.32240i) q^{21} +(0.363161 - 0.254288i) q^{23} +(-2.30799 + 4.43544i) q^{25} +(-2.50399 + 9.34503i) q^{27} +(1.09856 + 0.921802i) q^{29} +(6.67979 + 3.85658i) q^{31} +(-13.5648 - 9.49816i) q^{33} +(-2.21187 + 2.31094i) q^{35} +(6.77341 + 6.77341i) q^{37} -1.15412i q^{39} +(2.40119 - 6.59722i) q^{41} +(6.61211 - 9.44307i) q^{43} +(-13.6830 - 2.10482i) q^{45} +(-3.11441 + 0.272476i) q^{47} +(4.28980 - 2.47672i) q^{49} +(-0.171947 - 0.472419i) q^{51} +(6.56681 + 9.37838i) q^{53} +(5.87375 - 10.7086i) q^{55} +(-9.26357 - 9.42437i) q^{57} +(-8.39207 + 7.04179i) q^{59} +(2.07149 - 11.7480i) q^{61} +(-8.02716 - 3.74313i) q^{63} +(0.846167 - 0.0927428i) q^{65} +(0.773226 + 8.83802i) q^{67} +(-0.672034 + 1.16400i) q^{69} +(-0.325803 + 0.0574478i) q^{71} +(-0.964863 - 2.06915i) q^{73} +(0.658643 - 15.1442i) q^{75} +(5.52535 - 5.52535i) q^{77} +(-2.57267 - 0.936374i) q^{79} +(-1.86796 - 10.5937i) q^{81} +(-11.1195 + 2.97945i) q^{83} +(0.332548 - 0.164029i) q^{85} +(-4.19952 - 1.12526i) q^{87} +(-5.02263 + 1.82809i) q^{89} +(0.536325 + 0.0945686i) q^{91} +(-23.2950 - 2.03804i) q^{93} +(6.16528 - 7.54912i) q^{95} +(0.497197 + 0.0434991i) q^{97} +(33.3033 + 5.87227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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