LMFDB - Embedded newform 380.2.bh.a.13.7

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			13.7
Character	$\chi$	$=$	380.13
Dual form			380.2.bh.a.117.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959290 - 0.447324i) q^{3} +(1.57989 + 1.58239i) q^{5} +(0.204631 + 0.763694i) q^{7} +(-1.20823 + 1.43991i) q^{9} +O(q^{10})$	\(q+(0.959290 - 0.447324i) q^{3} +(1.57989 + 1.58239i) q^{5} +(0.204631 + 0.763694i) q^{7} +(-1.20823 + 1.43991i) q^{9} +(2.14248 + 3.71088i) q^{11} +(-1.21768 + 2.61133i) q^{13} +(2.22341 + 0.811249i) q^{15} +(0.544538 - 6.22409i) q^{17} +(0.761826 - 4.29181i) q^{19} +(0.537919 + 0.641067i) q^{21} +(2.67802 - 1.87517i) q^{23} +(-0.00791432 + 4.99999i) q^{25} +(-1.33678 + 4.98893i) q^{27} +(-6.38036 - 5.35376i) q^{29} +(4.23651 + 2.44595i) q^{31} +(3.71522 + 2.60143i) q^{33} +(-0.885167 + 1.53036i) q^{35} +(-1.75916 - 1.75916i) q^{37} +3.04972i q^{39} +(0.896173 - 2.46221i) q^{41} +(5.40483 - 7.71890i) q^{43} +(-4.18735 + 0.363007i) q^{45} +(4.32309 - 0.378221i) q^{47} +(5.52082 - 3.18745i) q^{49} +(-2.26182 - 6.21429i) q^{51} +(-0.286216 - 0.408759i) q^{53} +(-2.48719 + 9.25301i) q^{55} +(-1.18902 - 4.45787i) q^{57} +(-9.10551 + 7.64043i) q^{59} +(-1.00870 + 5.72060i) q^{61} +(-1.34689 - 0.628064i) q^{63} +(-6.05594 + 2.19875i) q^{65} +(-0.376469 - 4.30306i) q^{67} +(1.73019 - 2.99678i) q^{69} +(-15.2125 + 2.68238i) q^{71} +(-5.98076 - 12.8258i) q^{73} +(2.22903 + 4.79998i) q^{75} +(-2.39556 + 2.39556i) q^{77} +(1.72702 + 0.628586i) q^{79} +(-0.0298904 - 0.169517i) q^{81} +(9.12912 - 2.44614i) q^{83} +(10.7092 - 8.97169i) q^{85} +(-8.51548 - 2.28172i) q^{87} +(-12.0968 + 4.40288i) q^{89} +(-2.24343 - 0.395577i) q^{91} +(5.15817 + 0.451282i) q^{93} +(7.99491 - 5.57507i) q^{95} +(-15.3386 - 1.34195i) q^{97} +(-7.93192 - 1.39861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.959290	−	0.447324i	0.553846	−	0.258263i	−0.125484	−	0.992096i	$-0.540048\pi$
$3$	0.959290	−	0.447324i	0.553846	−	0.258263i	0.679330	+	0.733833i	$0.262271\pi$
$4$		0			0
$5$	1.57989	+	1.58239i	0.706547	+	0.707666i
$5$	1.57989	+	1.58239i	0.706547	+	0.707666i
$6$		0			0
$7$	0.204631	+	0.763694i	0.0773433	+	0.288649i	0.993754	−	0.111589i	$-0.0355940\pi$
$7$	0.204631	+	0.763694i	0.0773433	+	0.288649i	−0.916411	+	0.400238i	$0.868927\pi$
$8$		0			0
$9$	−1.20823	+	1.43991i	−0.402742	+	0.479969i
$10$		0			0
$11$	2.14248	+	3.71088i	0.645982	+	1.11887i	0.984074	+	0.177760i	$0.0568851\pi$
$11$	2.14248	+	3.71088i	0.645982	+	1.11887i	−0.338092	+	0.941113i	$0.609782\pi$
$12$		0			0
$13$	−1.21768	+	2.61133i	−0.337724	+	0.724252i	−0.999680	−	0.0252910i	$-0.991949\pi$
$13$	−1.21768	+	2.61133i	−0.337724	+	0.724252i	0.661956	+	0.749543i	$0.269727\pi$
$14$		0			0
$15$	2.22341	+	0.811249i	0.574082	+	0.209463i
$16$		0			0
$17$	0.544538	−	6.22409i	0.132070	−	1.50956i	−0.584125	−	0.811664i	$-0.698562\pi$
$17$	0.544538	−	6.22409i	0.132070	−	1.50956i	0.716195	−	0.697900i	$-0.245882\pi$
$18$		0			0
$19$	0.761826	−	4.29181i	0.174775	−	0.984608i
$19$	0.761826	−	4.29181i	0.174775	−	0.984608i
$20$		0			0
$21$	0.537919	+	0.641067i	0.117384	+	0.139892i
$22$		0			0
$23$	2.67802	−	1.87517i	0.558406	−	0.391000i	−0.260028	−	0.965601i	$-0.583732\pi$
$23$	2.67802	−	1.87517i	0.558406	−	0.391000i	0.818434	+	0.574601i	$0.194843\pi$
$24$		0			0
$25$	−0.00791432	+	4.99999i	−0.00158286	+	0.999999i
$26$		0			0
$27$	−1.33678	+	4.98893i	−0.257264	+	0.960121i
$28$		0			0
$29$	−6.38036	−	5.35376i	−1.18480	−	0.994168i	−0.999935	−	0.0114049i	$-0.996370\pi$
$29$	−6.38036	−	5.35376i	−1.18480	−	0.994168i	−0.184869	−	0.982763i	$-0.559186\pi$
$30$		0			0
$31$	4.23651	+	2.44595i	0.760900	+	0.439306i	0.829619	−	0.558330i	$-0.188558\pi$
$31$	4.23651	+	2.44595i	0.760900	+	0.439306i	−0.0687188	+	0.997636i	$0.521891\pi$
$32$		0			0
$33$	3.71522	+	2.60143i	0.646738	+	0.452851i
$34$		0			0
$35$	−0.885167	+	1.53036i	−0.149621	+	0.258677i
$36$		0			0
$37$	−1.75916	−	1.75916i	−0.289204	−	0.289204i	0.547561	−	0.836766i	$-0.315556\pi$
$37$	−1.75916	−	1.75916i	−0.289204	−	0.289204i	−0.836766	+	0.547561i	$0.815556\pi$
$38$		0			0
$39$			3.04972i			0.488346i
$40$		0			0
$41$	0.896173	−	2.46221i	0.139959	−	0.384533i	−0.849834	−	0.527051i	$-0.823298\pi$
$41$	0.896173	−	2.46221i	0.139959	−	0.384533i	0.989792	+	0.142518i	$0.0455199\pi$
$42$		0			0
$43$	5.40483	−	7.71890i	0.824230	−	1.17712i	−0.157627	−	0.987499i	$-0.550385\pi$
$43$	5.40483	−	7.71890i	0.824230	−	1.17712i	0.981857	−	0.189623i	$-0.0607266\pi$
$44$		0			0
$45$	−4.18735	+	0.363007i	−0.624214	+	0.0541138i
$46$		0			0
$47$	4.32309	−	0.378221i	0.630588	−	0.0551693i	0.232618	−	0.972568i	$-0.425271\pi$
$47$	4.32309	−	0.378221i	0.630588	−	0.0551693i	0.397969	+	0.917399i	$0.369715\pi$
$48$		0			0
$49$	5.52082	−	3.18745i	0.788689	−	0.455350i
$50$		0			0
$51$	−2.26182	−	6.21429i	−0.316718	−	0.870175i
$52$		0			0
$53$	−0.286216	−	0.408759i	−0.0393148	−	0.0561474i	0.799013	−	0.601313i	$-0.205356\pi$
$53$	−0.286216	−	0.408759i	−0.0393148	−	0.0561474i	−0.838328	+	0.545166i	$0.816467\pi$
$54$		0			0
$55$	−2.48719	+	9.25301i	−0.335372	+	1.24768i
$56$		0			0
$57$	−1.18902	−	4.45787i	−0.157489	−	0.590459i
$58$		0			0
$59$	−9.10551	+	7.64043i	−1.18544	+	0.994699i	−0.185509	+	0.982643i	$0.559393\pi$
$59$	−9.10551	+	7.64043i	−1.18544	+	0.994699i	−0.999927	+	0.0120561i	$0.996162\pi$
$60$		0			0
$61$	−1.00870	+	5.72060i	−0.129150	+	0.732448i	0.849606	+	0.527418i	$0.176840\pi$
$61$	−1.00870	+	5.72060i	−0.129150	+	0.732448i	−0.978756	+	0.205029i	$0.934271\pi$
$62$		0			0
$63$	−1.34689	−	0.628064i	−0.169692	−	0.0791287i
$64$		0			0
$65$	−6.05594	+	2.19875i	−0.751146	+	0.272722i
$66$		0			0
$67$	−0.376469	−	4.30306i	−0.0459930	−	0.525702i	−0.983888	−	0.178784i	$-0.942784\pi$
$67$	−0.376469	−	4.30306i	−0.0459930	−	0.525702i	0.937895	−	0.346918i	$-0.112772\pi$
$68$		0			0
$69$	1.73019	−	2.99678i	0.208290	−	0.360769i
$70$		0			0
$71$	−15.2125	+	2.68238i	−1.80540	+	0.318340i	−0.972114	−	0.234509i	$-0.924652\pi$
$71$	−15.2125	+	2.68238i	−1.80540	+	0.318340i	−0.833282	+	0.552849i	$0.813541\pi$
$72$		0			0
$73$	−5.98076	−	12.8258i	−0.699995	−	1.50114i	−0.857969	−	0.513701i	$-0.828274\pi$
$73$	−5.98076	−	12.8258i	−0.699995	−	1.50114i	0.157974	−	0.987443i	$-0.449504\pi$
$74$		0			0
$75$	2.22903	+	4.79998i	0.257386	+	0.554254i
$76$		0			0
$77$	−2.39556	+	2.39556i	−0.272999	+	0.272999i
$78$		0			0
$79$	1.72702	+	0.628586i	0.194305	+	0.0707214i	0.437340	−	0.899296i	$-0.355921\pi$
$79$	1.72702	+	0.628586i	0.194305	+	0.0707214i	−0.243035	+	0.970018i	$0.578143\pi$
$80$		0			0
$81$	−0.0298904	−	0.169517i	−0.00332115	−	0.0188352i
$82$		0			0
$83$	9.12912	−	2.44614i	1.00205	−	0.268499i	0.279746	−	0.960074i	$-0.409750\pi$
$83$	9.12912	−	2.44614i	1.00205	−	0.268499i	0.722304	+	0.691575i	$0.243083\pi$
$84$		0			0
$85$	10.7092	−	8.97169i	1.16158	−	0.973117i
$86$		0			0
$87$	−8.51548	−	2.28172i	−0.912955	−	0.244626i
$88$		0			0
$89$	−12.0968	+	4.40288i	−1.28226	+	0.466705i	−0.891179	−	0.453652i	$-0.850121\pi$
$89$	−12.0968	+	4.40288i	−1.28226	+	0.466705i	−0.391081	+	0.920356i	$0.627899\pi$
$90$		0			0
$91$	−2.24343	−	0.395577i	−0.235175	−	0.0414677i
$92$		0			0
$93$	5.15817	+	0.451282i	0.534878	+	0.0467957i
$94$		0			0
$95$	7.99491	−	5.57507i	0.820261	−	0.571990i
$96$		0			0
$97$	−15.3386	−	1.34195i	−1.55740	−	0.136254i	−0.724340	−	0.689443i	$-0.757855\pi$
$97$	−15.3386	−	1.34195i	−1.55740	−	0.136254i	−0.833056	+	0.553189i	$0.813411\pi$
$98$		0			0
$99$	−7.93192	−	1.39861i	−0.797188	−	0.140566i
$100$		0			0
$101$	−2.23165	+	0.812253i	−0.222057	+	0.0808222i	−0.450653	−	0.892699i	$-0.648809\pi$
$101$	−2.23165	+	0.812253i	−0.222057	+	0.0808222i	0.228596	+	0.973521i	$0.426587\pi$
$102$		0			0
$103$	12.0305	+	3.22356i	1.18540	+	0.317627i	0.797066	−	0.603892i	$-0.206384\pi$
$103$	12.0305	+	3.22356i	1.18540	+	0.317627i	0.388334	+	0.921519i	$0.373051\pi$
$104$		0			0
$105$	−0.164567	+	1.86401i	−0.0160600	+	0.181909i
$106$		0			0
$107$	−0.562854	+	0.150816i	−0.0544131	+	0.0145799i	−0.285923	−	0.958253i	$-0.592300\pi$
$107$	−0.562854	+	0.150816i	−0.0544131	+	0.0145799i	0.231510	+	0.972833i	$0.425633\pi$
$108$		0			0
$109$	−1.72790	−	9.79939i	−0.165502	−	0.938611i	−0.948545	−	0.316643i	$-0.897444\pi$
$109$	−1.72790	−	9.79939i	−0.165502	−	0.938611i	0.783042	−	0.621968i	$-0.213667\pi$
$110$		0			0
$111$	−2.47446	−	0.900629i	−0.234865	−	0.0854840i
$112$		0			0
$113$	4.74971	−	4.74971i	0.446816	−	0.446816i	−0.447479	−	0.894294i	$-0.647678\pi$
$113$	4.74971	−	4.74971i	0.446816	−	0.446816i	0.894294	+	0.447479i	$0.147678\pi$
$114$		0			0
$115$	7.19822	+	1.27512i	0.671238	+	0.118905i
$116$		0			0
$117$	−2.28883	−	4.90842i	−0.211603	−	0.453783i
$118$		0			0
$119$	4.86473	−	0.857783i	0.445949	−	0.0786329i
$120$		0			0
$121$	−3.68043	+	6.37469i	−0.334585	+	0.579517i
$122$		0			0
$123$	−0.241719	−	2.76286i	−0.0217950	−	0.249118i
$124$		0			0
$125$	−7.92444	+	7.88690i	−0.708784	+	0.705426i
$126$		0			0
$127$	13.0840	+	6.10115i	1.16101	+	0.541389i	0.905053	−	0.425298i	$-0.139831\pi$
$127$	13.0840	+	6.10115i	1.16101	+	0.541389i	0.255960	+	0.966687i	$0.417609\pi$
$128$		0			0
$129$	1.73195	−	9.82238i	0.152490	−	0.864812i
$130$		0			0
$131$	−0.690640	+	0.579516i	−0.0603415	+	0.0506325i	−0.672460	−	0.740134i	$-0.734762\pi$
$131$	−0.690640	+	0.579516i	−0.0603415	+	0.0506325i	0.612118	+	0.790766i	$0.290318\pi$
$132$		0			0
$133$	3.43352	−	0.296436i	0.297724	−	0.0257042i
$134$		0			0
$135$	−10.0064	+	5.76664i	−0.861214	+	0.496314i
$136$		0			0
$137$	−9.71402	−	13.8731i	−0.829925	−	1.18526i	−0.980473	−	0.196653i	$-0.936993\pi$
$137$	−9.71402	−	13.8731i	−0.829925	−	1.18526i	0.150548	−	0.988603i	$-0.451896\pi$
$138$		0			0
$139$	2.65396	+	7.29169i	0.225106	+	0.618473i	0.999906	−	0.0137335i	$-0.00437166\pi$
$139$	2.65396	+	7.29169i	0.225106	+	0.618473i	−0.774800	+	0.632206i	$0.782149\pi$
$140$		0			0
$141$	3.97791	−	2.29665i	0.335000	−	0.193413i
$142$		0			0
$143$	−12.2992	+	1.07604i	−1.02851	+	0.0899829i
$144$		0			0
$145$	−1.60852	−	18.5546i	−0.133580	−	1.54087i
$146$		0			0
$147$	3.87025	−	5.52728i	0.319213	−	0.455883i
$148$		0			0
$149$	−3.32479	+	9.13479i	−0.272378	+	0.748351i	0.725794	+	0.687912i	$0.241472\pi$
$149$	−3.32479	+	9.13479i	−0.272378	+	0.748351i	−0.998172	+	0.0604394i	$0.980750\pi$
$150$		0			0
$151$			2.54056i			0.206748i	0.994643	+	0.103374i	$0.0329638\pi$
$151$			2.54056i			0.206748i	−0.994643	+	0.103374i	$0.967036\pi$
$152$		0			0
$153$	8.30419	+	8.30419i	0.671354	+	0.671354i
$154$		0			0
$155$	2.82276	+	10.5681i	0.226730	+	0.848853i
$156$		0			0
$157$	8.63056	+	6.04318i	0.688794	+	0.482299i	0.864817	−	0.502088i	$-0.167434\pi$
$157$	8.63056	+	6.04318i	0.688794	+	0.482299i	−0.176023	+	0.984386i	$0.556323\pi$
$158$		0			0
$159$	−0.457412	−	0.264087i	−0.0362751	−	0.0209435i
$160$		0			0
$161$	1.98006	+	1.66147i	0.156051	+	0.130942i
$162$		0			0
$163$	0.529807	−	1.97727i	0.0414977	−	0.154871i	−0.942068	−	0.335422i	$-0.891121\pi$
$163$	0.529807	−	1.97727i	0.0414977	−	0.154871i	0.983566	+	0.180550i	$0.0577879\pi$
$164$		0			0
$165$	1.75316	+	9.98890i	0.136483	+	0.777635i
$166$		0			0
$167$	12.0210	−	8.41717i	0.930210	−	0.651340i	−0.00704874	−	0.999975i	$-0.502244\pi$
$167$	12.0210	−	8.41717i	0.930210	−	0.651340i	0.937258	+	0.348635i	$0.113355\pi$
$168$		0			0
$169$	3.01996	+	3.59905i	0.232305	+	0.276850i
$170$		0			0
$171$	5.25935	+	6.28243i	0.402192	+	0.480429i
$172$		0			0
$173$	−2.06684	+	23.6241i	−0.157139	+	1.79611i	0.352596	+	0.935776i	$0.385299\pi$
$173$	−2.06684	+	23.6241i	−0.157139	+	1.79611i	−0.509735	+	0.860332i	$0.670256\pi$
$174$		0			0
$175$	−3.82008	+	1.01711i	−0.288771	+	0.0768863i
$176$		0			0
$177$	−5.31707	+	11.4025i	−0.399655	+	0.857064i
$178$		0			0
$179$	0.252534	+	0.437403i	0.0188753	+	0.0326930i	0.875309	−	0.483564i	$-0.160658\pi$
$179$	0.252534	+	0.437403i	0.0188753	+	0.0326930i	−0.856433	+	0.516257i	$0.827325\pi$
$180$		0			0
$181$	5.94759	−	7.08806i	0.442081	−	0.526851i	−0.498286	−	0.867012i	$-0.666037\pi$
$181$	5.94759	−	7.08806i	0.442081	−	0.526851i	0.940367	+	0.340161i	$0.110482\pi$
$182$		0			0
$183$	1.59133	+	5.93892i	0.117634	+	0.439018i
$184$		0			0
$185$	0.00440270	−	5.56295i	0.000323693	−	0.408996i
$186$		0			0
$187$	24.2635	−	11.3143i	1.77433	−	0.827381i
$188$		0			0
$189$	−4.08357			−0.297036
$190$		0			0
$191$	−10.1212			−0.732344			−0.366172	−	0.930547i	$-0.619332\pi$
$191$	−10.1212			−0.732344			−0.366172	+	0.930547i	$0.619332\pi$
$192$		0			0
$193$	12.6672	−	5.90682i	0.911806	−	0.425182i	0.0906480	−	0.995883i	$-0.471106\pi$
$193$	12.6672	−	5.90682i	0.911806	−	0.425182i	0.821158	+	0.570701i	$0.193328\pi$
$194$		0			0
$195$	−4.82584	+	4.81821i	−0.345586	+	0.345039i
$196$		0			0
$197$	4.65700	+	17.3802i	0.331798	+	1.23829i	0.907299	+	0.420485i	$0.138140\pi$
$197$	4.65700	+	17.3802i	0.331798	+	1.23829i	−0.575502	+	0.817801i	$0.695193\pi$
$198$		0			0
$199$	−0.246173	+	0.293378i	−0.0174508	+	0.0207970i	−0.774699	−	0.632330i	$-0.782099\pi$
$199$	−0.246173	+	0.293378i	−0.0174508	+	0.0207970i	0.757248	+	0.653127i	$0.226543\pi$
$200$		0			0
$201$	−2.28600	−	3.95947i	−0.161242	−	0.279280i
$202$		0			0
$203$	2.78301	−	5.96819i	0.195329	−	0.418885i
$204$		0			0
$205$	5.31203	−	2.47193i	0.371008	−	0.172647i
$206$		0			0
$207$	−0.535582	+	6.12173i	−0.0372255	+	0.425490i
$208$		0			0
$209$	17.5586	−	6.36806i	1.21455	−	0.440488i
$210$		0			0
$211$	6.35759	+	7.57668i	0.437675	+	0.521600i	0.939120	−	0.343589i	$-0.111643\pi$
$211$	6.35759	+	7.57668i	0.437675	+	0.521600i	−0.501446	+	0.865189i	$0.667198\pi$
$212$		0			0
$213$	−13.3933	+	9.37811i	−0.917696	+	0.642578i
$214$		0			0
$215$	20.7533	−	3.64244i	1.41537	−	0.248412i
$216$		0			0
$217$	−1.00104	+	3.73592i	−0.0679547	+	0.253610i
$218$		0			0
$219$	−11.4746	−	9.62830i	−0.775379	−	0.650620i
$220$		0			0
$221$	15.5901	+	9.00093i	1.04870	+	0.605468i
$222$		0			0
$223$	6.43140	+	4.50331i	0.430678	+	0.301564i	0.768742	−	0.639559i	$-0.220883\pi$
$223$	6.43140	+	4.50331i	0.430678	+	0.301564i	−0.338064	+	0.941123i	$0.609772\pi$
$224$		0			0
$225$	−7.18996	−	6.05251i	−0.479331	−	0.403501i
$226$		0			0
$227$	−19.1073	−	19.1073i	−1.26820	−	1.26820i	−0.947018	−	0.321181i	$-0.895920\pi$
$227$	−19.1073	−	19.1073i	−1.26820	−	1.26820i	−0.321181	−	0.947018i	$-0.604080\pi$
$228$		0			0
$229$			14.4257i			0.953279i	0.879099	+	0.476640i	$0.158145\pi$
$229$			14.4257i			0.953279i	−0.879099	+	0.476640i	$0.841855\pi$
$230$		0			0
$231$	−1.22644	+	3.36963i	−0.0806941	+	0.221705i
$232$		0			0
$233$	−4.07581	+	5.82086i	−0.267015	+	0.381337i	−0.930160	−	0.367154i	$-0.880332\pi$
$233$	−4.07581	+	5.82086i	−0.267015	+	0.381337i	0.663145	+	0.748491i	$0.269221\pi$
$234$		0			0
$235$	7.42849	+	6.24327i	0.484581	+	0.407266i
$236$		0			0
$237$	1.93790	−	0.169544i	0.125880	−	0.0110131i
$238$		0			0
$239$	−14.3994	+	8.31351i	−0.931422	+	0.537756i	−0.887261	−	0.461268i	$-0.847395\pi$
$239$	−14.3994	+	8.31351i	−0.931422	+	0.537756i	−0.0441606	+	0.999024i	$0.514061\pi$
$240$		0			0
$241$	0.560232	+	1.53922i	0.0360877	+	0.0991501i	0.956428	−	0.291969i	$-0.0943103\pi$
$241$	0.560232	+	1.53922i	0.0360877	+	0.0991501i	−0.920340	+	0.391119i	$0.872088\pi$
$242$		0			0
$243$	−8.99194	−	12.8418i	−0.576833	−	0.823803i
$244$		0			0
$245$	13.7661	+	3.70029i	0.879482	+	0.236403i
$246$		0			0
$247$	10.2797	+	7.21543i	0.654079	+	0.459107i
$248$		0			0
$249$	7.66325	−	6.43023i	0.485639	−	0.407499i
$250$		0			0
$251$	0.267163	−	1.51516i	0.0168632	−	0.0956358i	−0.975215	−	0.221261i	$-0.928983\pi$
$251$	0.267163	−	1.51516i	0.0168632	−	0.0956358i	0.992078	+	0.125625i	$0.0400938\pi$
$252$		0			0
$253$	12.6961	+	5.92031i	0.798200	+	0.372207i
$254$		0			0
$255$	6.26002	−	13.3970i	0.392017	−	0.838950i
$256$		0			0
$257$	−0.886586	−	10.1337i	−0.0553037	−	0.632124i	−0.972379	−	0.233409i	$-0.925012\pi$
$257$	−0.886586	−	10.1337i	−0.0553037	−	0.632124i	0.917075	−	0.398715i	$-0.130544\pi$
$258$		0			0
$259$	0.983481	−	1.70344i	0.0611105	−	0.105847i
$260$		0			0
$261$	15.4178	−	2.71858i	0.954339	−	0.168276i
$262$		0			0
$263$	−7.47170	−	16.0231i	−0.460725	−	0.988028i	−0.990194	−	0.139699i	$-0.955387\pi$
$263$	−7.47170	−	16.0231i	−0.460725	−	0.988028i	0.529469	−	0.848329i	$-0.322391\pi$
$264$		0			0
$265$	0.194627	−	1.09870i	0.0119558	−	0.0674926i
$266$		0			0
$267$	−9.63484	+	9.63484i	−0.589643	+	0.589643i
$268$		0			0
$269$	23.2323	+	8.45587i	1.41650	+	0.515564i	0.933030	−	0.359798i	$-0.117154\pi$
$269$	23.2323	+	8.45587i	1.41650	+	0.515564i	0.483469	+	0.875362i	$0.339377\pi$
$270$		0			0
$271$	−4.51647	−	25.6142i	−0.274356	−	1.55595i	−0.741001	−	0.671504i	$-0.765648\pi$
$271$	−4.51647	−	25.6142i	−0.274356	−	1.55595i	0.466645	−	0.884445i	$-0.345463\pi$
$272$		0			0
$273$	−2.32905	+	0.624067i	−0.140961	+	0.0377703i
$274$		0			0
$275$	−18.5713	+	10.6830i	−1.11989	+	0.644210i
$276$		0			0
$277$	7.12392	+	1.90885i	0.428035	+	0.114692i	0.466404	−	0.884572i	$-0.345549\pi$
$277$	7.12392	+	1.90885i	0.428035	+	0.114692i	−0.0383686	+	0.999264i	$0.512216\pi$
$278$		0			0
$279$	−8.64060	+	3.14492i	−0.517299	+	0.188282i
$280$		0			0
$281$	0.322784	+	0.0569155i	0.0192557	+	0.00339529i	0.183268	−	0.983063i	$-0.441332\pi$
$281$	0.322784	+	0.0569155i	0.0192557	+	0.00339529i	−0.164012	+	0.986458i	$0.552444\pi$
$282$		0			0
$283$	−14.6742	−	1.28383i	−0.872292	−	0.0763157i	−0.357787	−	0.933803i	$-0.616469\pi$
$283$	−14.6742	−	1.28383i	−0.872292	−	0.0763157i	−0.514505	+	0.857487i	$0.672024\pi$
$284$		0			0
$285$	5.17558	−	8.92442i	0.306575	−	0.528637i
$286$		0			0
$287$	2.06376	+	0.180556i	0.121820	+	0.0106579i
$288$		0			0
$289$	−21.7011	−	3.82648i	−1.27653	−	0.225087i
$290$		0			0
$291$	−15.3144	+	5.57399i	−0.897747	+	0.326753i
$292$		0			0
$293$	−22.4984	−	6.02843i	−1.31437	−	0.352185i	−0.467505	−	0.883990i	$-0.654847\pi$
$293$	−22.4984	−	6.02843i	−1.31437	−	0.352185i	−0.846866	+	0.531806i	$0.821514\pi$
$294$		0			0
$295$	−26.4758	−	2.33745i	−1.54148	−	0.136091i
$296$		0			0
$297$	−21.3774	+	5.72805i	−1.24044	+	0.332375i
$298$		0			0
$299$	1.63571	+	9.27655i	0.0945953	+	0.536477i
$300$		0			0
$301$	7.00088	+	2.54811i	0.403524	+	0.146871i
$302$		0			0
$303$	−1.77745	+	1.77745i	−0.102112	+	0.102112i
$304$		0			0
$305$	−10.6458	+	7.44175i	−0.609579	+	0.426113i
$306$		0			0
$307$	5.73116	+	12.2905i	0.327095	+	0.701457i	0.999241	−	0.0389619i	$-0.0124051\pi$
$307$	5.73116	+	12.2905i	0.327095	+	0.701457i	−0.672146	+	0.740419i	$0.734627\pi$
$308$		0			0
$309$	12.9827	−	2.28920i	0.738561	−	0.130228i
$310$		0			0
$311$	7.69889	−	13.3349i	0.436564	−	0.756151i	−0.560858	−	0.827912i	$-0.689529\pi$
$311$	7.69889	−	13.3349i	0.436564	−	0.756151i	0.997422	+	0.0717609i	$0.0228619\pi$
$312$		0			0
$313$	−0.815098	−	9.31661i	−0.0460721	−	0.526606i	−0.983804	−	0.179247i	$-0.942634\pi$
$313$	−0.815098	−	9.31661i	−0.0460721	−	0.526606i	0.937732	−	0.347359i	$-0.112922\pi$
$314$		0			0
$315$	−1.13409	−	3.12357i	−0.0638987	−	0.175993i
$316$		0			0
$317$	−7.07467	−	3.29897i	−0.397353	−	0.185289i	0.213662	−	0.976908i	$-0.431461\pi$
$317$	−7.07467	−	3.29897i	−0.397353	−	0.185289i	−0.611015	+	0.791619i	$0.709239\pi$
$318$		0			0
$319$	6.19738	−	35.1471i	0.346987	−	1.96786i
$320$		0			0
$321$	−0.472476	+	0.396454i	−0.0263710	+	0.0221279i
$322$		0			0
$323$	−26.2978	−	7.07873i	−1.46325	−	0.393871i
$324$		0			0
$325$	−13.0470	−	6.10907i	−0.723716	−	0.338870i
$326$		0			0
$327$	−6.04105	−	8.62752i	−0.334071	−	0.477103i
$328$		0			0
$329$	1.17348	+	3.22412i	0.0646963	+	0.177752i
$330$		0			0
$331$	16.9436	−	9.78241i	0.931306	−	0.537690i	0.0440818	−	0.999028i	$-0.485964\pi$
$331$	16.9436	−	9.78241i	0.931306	−	0.537690i	0.887224	+	0.461338i	$0.152630\pi$
$332$		0			0
$333$	4.65849	−	0.407565i	0.255284	−	0.0223344i
$334$		0			0
$335$	6.21433	−	7.39406i	0.339525	−	0.403981i
$336$		0			0
$337$	−19.3607	+	27.6500i	−1.05465	+	1.50619i	−0.205054	+	0.978751i	$0.565737\pi$
$337$	−19.3607	+	27.6500i	−1.05465	+	1.50619i	−0.849592	+	0.527440i	$0.823152\pi$
$338$		0			0
$339$	2.43169	−	6.68101i	0.132071	−	0.362863i
$340$		0			0
$341$			20.9616i			1.13513i
$342$		0			0
$343$	7.47741	+	7.47741i	0.403742	+	0.403742i
$344$		0			0
$345$	7.47557	−	1.99673i	0.402471	−	0.107501i
$346$		0			0
$347$	5.41721	+	3.79317i	0.290811	+	0.203628i	0.709873	−	0.704329i	$-0.248752\pi$
$347$	5.41721	+	3.79317i	0.290811	+	0.203628i	−0.419062	+	0.907958i	$0.637641\pi$
$348$		0			0
$349$	30.1248	+	17.3926i	1.61255	+	0.931004i	0.988778	+	0.149395i	$0.0477325\pi$
$349$	30.1248	+	17.3926i	1.61255	+	0.931004i	0.623768	+	0.781609i	$0.285601\pi$
$350$		0			0
$351$	−11.4000	−	9.56570i	−0.608485	−	0.510580i
$352$		0			0
$353$	−3.09322	+	11.5440i	−0.164635	+	0.614427i	0.833451	+	0.552593i	$0.186362\pi$
$353$	−3.09322	+	11.5440i	−0.164635	+	0.614427i	−0.998086	+	0.0618342i	$0.980305\pi$
$354$		0			0
$355$	−28.2787	−	19.8343i	−1.50088	−	1.05270i
$356$		0			0
$357$	4.28298	−	2.99897i	0.226679	−	0.158723i
$358$		0			0
$359$	11.0702	+	13.1929i	0.584261	+	0.696295i	0.974492	−	0.224422i	$-0.0720494\pi$
$359$	11.0702	+	13.1929i	0.584261	+	0.696295i	−0.390231	+	0.920717i	$0.627605\pi$
$360$		0			0
$361$	−17.8392	−	6.53922i	−0.938907	−	0.344170i
$362$		0			0
$363$	−0.679045	+	7.76152i	−0.0356406	+	0.407374i
$364$		0			0
$365$	10.8465	−	29.7272i	0.567730	−	1.55599i
$366$		0			0
$367$	0.100871	−	0.216319i	0.00526543	−	0.0112917i	−0.903657	−	0.428256i	$-0.859128\pi$
$367$	0.100871	−	0.216319i	0.00526543	−	0.0112917i	0.908923	+	0.416964i	$0.136906\pi$
$368$		0			0
$369$	2.46258	+	4.26531i	0.128197	+	0.222043i
$370$		0			0
$371$	0.253598	−	0.302226i	0.0131662	−	0.0156908i
$372$		0			0
$373$	−1.72019	−	6.41983i	−0.0890679	−	0.332406i	0.906985	−	0.421162i	$-0.138378\pi$
$373$	−1.72019	−	6.41983i	−0.0890679	−	0.332406i	−0.996053	+	0.0887559i	$0.971711\pi$
$374$		0			0
$375$	−4.07383	+	11.1106i	−0.210372	+	0.573750i
$376$		0			0
$377$	21.7497	−	10.1420i	1.12016	−	0.522341i
$378$		0			0
$379$	20.9801			1.07767			0.538837	−	0.842410i	$-0.318864\pi$
$379$	20.9801			1.07767			0.538837	+	0.842410i	$0.318864\pi$
$380$		0			0
$381$	15.2805			0.782843
$382$		0			0
$383$	−20.2321	+	9.43439i	−1.03381	+	0.482075i	−0.864048	−	0.503410i	$-0.832079\pi$
$383$	−20.2321	+	9.43439i	−1.03381	+	0.482075i	−0.169765	+	0.985485i	$0.554301\pi$
$384$		0			0
$385$	−7.57542	−	0.00599543i	−0.386079	−	0.000305556i
$386$		0			0
$387$	4.58424	+	17.1086i	0.233030	+	0.869680i
$388$		0			0
$389$	5.52075	−	6.57937i	0.279913	−	0.333587i	−0.607709	−	0.794160i	$-0.707911\pi$
$389$	5.52075	−	6.57937i	0.279913	−	0.333587i	0.887622	+	0.460572i	$0.152356\pi$
$390$		0			0
$391$	−10.2130	−	17.6894i	−0.516491	−	0.894589i
$392$		0			0
$393$	−0.403292	+	0.864863i	−0.0203434	+	0.0436266i
$394$		0			0
$395$	1.73384	+	3.72592i	0.0872388	+	0.187471i
$396$		0			0
$397$	−2.16676	+	24.7662i	−0.108747	+	1.24298i	0.724185	+	0.689606i	$0.242216\pi$
$397$	−2.16676	+	24.7662i	−0.108747	+	1.24298i	−0.832932	+	0.553376i	$0.813339\pi$
$398$		0			0
$399$	3.16114	−	1.82026i	0.158255	−	0.0911272i
$400$		0			0
$401$	−20.7376	−	24.7141i	−1.03558	−	1.23416i	−0.971704	−	0.236204i	$-0.924097\pi$
$401$	−20.7376	−	24.7141i	−1.03558	−	1.23416i	−0.0638807	−	0.997958i	$-0.520348\pi$
$402$		0			0
$403$	−11.5459	+	8.08453i	−0.575142	+	0.402719i
$404$		0			0
$405$	0.221018	−	0.315115i	0.0109825	−	0.0156582i
$406$		0			0
$407$	2.75907	−	10.2970i	0.136762	−	0.510403i
$408$		0			0
$409$	−10.6992	−	8.97770i	−0.529042	−	0.443919i	0.338729	−	0.940884i	$-0.390003\pi$
$409$	−10.6992	−	8.97770i	−0.529042	−	0.443919i	−0.867770	+	0.496965i	$0.834448\pi$
$410$		0			0
$411$	−15.5243	−	8.96297i	−0.765758	−	0.442111i
$412$		0			0
$413$	−7.69822	−	5.39035i	−0.378804	−	0.265242i
$414$		0			0
$415$	18.2937	+	10.5812i	0.898003	+	0.519410i
$416$		0			0
$417$	5.80766	+	5.80766i	0.284402	+	0.284402i
$418$		0			0
$419$		−	14.0602i		−	0.686885i	−0.939174	−	0.343442i	$-0.888407\pi$
$419$		−	14.0602i		−	0.686885i	0.939174	−	0.343442i	$-0.111593\pi$
$420$		0			0
$421$	−0.956778	+	2.62873i	−0.0466305	+	0.128116i	−0.960822	−	0.277166i	$-0.910605\pi$
$421$	−0.956778	+	2.62873i	−0.0466305	+	0.128116i	0.914191	+	0.405283i	$0.132827\pi$
$422$		0			0
$423$	−4.67866	+	6.68182i	−0.227484	+	0.324881i
$424$		0			0
$425$	31.1161	+	2.77194i	1.50935	+	0.134459i
$426$		0			0
$427$	−4.57520	+	0.400278i	−0.221409	+	0.0193708i
$428$		0			0
$429$	−11.3171	+	6.53395i	−0.546397	+	0.315462i
$430$		0			0
$431$	4.10004	+	11.2648i	0.197492	+	0.542605i	0.998422	−	0.0561529i	$-0.0178834\pi$
$431$	4.10004	+	11.2648i	0.197492	+	0.542605i	−0.800930	+	0.598758i	$0.795661\pi$
$432$		0			0
$433$	−12.6971	−	18.1333i	−0.610184	−	0.871433i	0.388566	−	0.921421i	$-0.372970\pi$
$433$	−12.6971	−	18.1333i	−0.610184	−	0.871433i	−0.998750	+	0.0499883i	$0.984082\pi$
$434$		0			0
$435$	−9.84293	−	17.0797i	−0.471933	−	0.818907i
$436$		0			0
$437$	−6.00769	−	12.9221i	−0.287387	−	0.618148i
$438$		0			0
$439$	−22.1872	+	18.6173i	−1.05894	+	0.888554i	−0.994005	−	0.109336i	$-0.965128\pi$
$439$	−22.1872	+	18.6173i	−1.05894	+	0.888554i	−0.0649322	+	0.997890i	$0.520683\pi$
$440$		0			0
$441$	−2.08077	+	11.8006i	−0.0990842	+	0.561935i
$442$		0			0
$443$	−5.11419	−	2.38479i	−0.242983	−	0.113305i	0.297313	−	0.954780i	$-0.403910\pi$
$443$	−5.11419	−	2.38479i	−0.242983	−	0.113305i	−0.540295	+	0.841476i	$0.681687\pi$
$444$		0			0
$445$	−26.0787	−	12.1858i	−1.23625	−	0.577664i
$446$		0			0
$447$	0.896774	+	10.2502i	0.0424159	+	0.484816i
$448$		0			0
$449$	11.1013	−	19.2281i	0.523904	−	0.907429i	−0.475709	−	0.879603i	$-0.657808\pi$
$449$	11.1013	−	19.2281i	0.523904	−	0.907429i	0.999613	−	0.0278258i	$-0.00885837\pi$
$450$		0			0
$451$	11.0570	−	1.94965i	0.520654	−	0.0918054i
$452$		0			0
$453$	1.13645	+	2.43713i	0.0533952	+	0.114506i
$454$		0			0
$455$	−2.91841	−	4.17495i	−0.136817	−	0.195725i
$456$		0			0
$457$	−24.1927	+	24.1927i	−1.13169	+	1.13169i	−0.141791	+	0.989897i	$0.545286\pi$
$457$	−24.1927	+	24.1927i	−1.13169	+	1.13169i	−0.989897	+	0.141791i	$0.954714\pi$
$458$		0			0
$459$	30.3237	+	11.0369i	1.41539	+	0.515159i
$460$		0			0
$461$	−0.595868	−	3.37934i	−0.0277524	−	0.157391i	0.967782	−	0.251789i	$-0.0810188\pi$
$461$	−0.595868	−	3.37934i	−0.0277524	−	0.157391i	−0.995535	+	0.0943971i	$0.969908\pi$
$462$		0			0
$463$	−4.85716	+	1.30147i	−0.225731	+	0.0604845i	−0.369912	−	0.929067i	$-0.620612\pi$
$463$	−4.85716	+	1.30147i	−0.225731	+	0.0604845i	0.144180	+	0.989551i	$0.453945\pi$
$464$		0			0
$465$	7.43523	+	8.87522i	0.344801	+	0.411578i
$466$		0			0
$467$	22.1463	+	5.93409i	1.02481	+	0.274597i	0.731805	−	0.681514i	$-0.238678\pi$
$467$	22.1463	+	5.93409i	1.02481	+	0.274597i	0.293004	+	0.956111i	$0.405345\pi$
$468$		0			0
$469$	3.20918	−	1.16805i	0.148186	−	0.0539353i
$470$		0			0
$471$	10.9825	+	1.93651i	0.506045	+	0.0892295i
$472$		0			0
$473$	40.2237	+	3.51912i	1.84949	+	0.161809i
$474$		0			0
$475$	21.4530	+	3.84309i	0.984331	+	0.176333i
$476$		0			0
$477$	0.934389	+	0.0817484i	0.0427827	+	0.00374300i
$478$		0			0
$479$	−38.4413	−	6.77824i	−1.75643	−	0.309706i	−0.799638	−	0.600482i	$-0.794975\pi$
$479$	−38.4413	−	6.77824i	−1.75643	−	0.309706i	−0.956791	+	0.290777i	$0.906086\pi$
$480$		0			0
$481$	6.73584	−	2.45164i	0.307128	−	0.111785i
$482$		0			0
$483$	2.64267	+	0.708101i	0.120246	+	0.0322197i
$484$		0			0
$485$	−22.1097	−	26.3917i	−1.00395	−	1.19839i
$486$		0			0
$487$	10.8774	−	2.91459i	0.492901	−	0.132073i	−0.00380224	−	0.999993i	$-0.501210\pi$
$487$	10.8774	−	2.91459i	0.492901	−	0.132073i	0.496704	+	0.867920i	$0.334544\pi$
$488$		0			0
$489$	−0.376241	−	2.13377i	−0.0170142	−	0.0964923i
$490$		0			0
$491$	1.88535	+	0.686210i	0.0850845	+	0.0309682i	0.384212	−	0.923245i	$-0.374473\pi$
$491$	1.88535	+	0.686210i	0.0850845	+	0.0309682i	−0.299127	+	0.954213i	$0.596695\pi$
$492$		0			0
$493$	−36.7966	+	36.7966i	−1.65724	+	1.65724i
$494$		0			0
$495$	−10.3184	−	14.7610i	−0.463777	−	0.663459i
$496$		0			0
$497$	−5.16147	−	11.0688i	−0.231524	−	0.496504i
$498$		0			0
$499$	−15.7656	+	2.77990i	−0.705765	+	0.124445i	−0.515000	−	0.857190i	$-0.672208\pi$
$499$	−15.7656	+	2.77990i	−0.705765	+	0.124445i	−0.190765	+	0.981636i	$0.561097\pi$
$500$		0			0
$501$	7.76638	−	13.4518i	0.346976	−	0.600981i
$502$		0			0
$503$	−1.62410	−	18.5635i	−0.0724149	−	0.827706i	−0.942369	−	0.334574i	$-0.891408\pi$
$503$	−1.62410	−	18.5635i	−0.0724149	−	0.827706i	0.869954	−	0.493132i	$-0.164148\pi$
$504$		0			0
$505$	−4.81105	−	2.24807i	−0.214089	−	0.100038i
$506$		0			0
$507$	4.50696	+	2.10163i	0.200161	+	0.0933367i
$508$		0			0
$509$	−1.88210	+	10.6739i	−0.0834226	+	0.473113i	0.914263	+	0.405121i	$0.132770\pi$
$509$	−1.88210	+	10.6739i	−0.0834226	+	0.473113i	−0.997686	+	0.0679925i	$0.978341\pi$
$510$		0			0
$511$	8.57112	−	7.19202i	0.379164	−	0.318156i
$512$		0			0
$513$	20.3932	+	9.53791i	0.900380	+	0.421109i
$514$		0			0
$515$	13.9059	+	24.1298i	0.612767	+	1.06329i
$516$		0			0
$517$	10.6657	+	15.2321i	0.469075	+	0.669909i
$518$		0			0
$519$	8.58493	+	23.5869i	0.376837	+	1.03535i
$520$		0			0
$521$	−21.5216	+	12.4255i	−0.942879	+	0.544372i	−0.890862	−	0.454274i	$-0.849899\pi$
$521$	−21.5216	+	12.4255i	−0.942879	+	0.544372i	−0.0520176	+	0.998646i	$0.516565\pi$
$522$		0			0
$523$	0.649209	−	0.0567984i	0.0283879	−	0.00248362i	−0.0729529	−	0.997335i	$-0.523242\pi$
$523$	0.649209	−	0.0567984i	0.0283879	−	0.00248362i	0.101341	+	0.994852i	$0.467687\pi$
$524$		0			0
$525$	−3.20959	+	2.68452i	−0.140078	+	0.117162i
$526$		0			0
$527$	17.5308	−	25.0365i	0.763652	−	1.09061i
$528$		0			0
$529$	−4.21093	+	11.5694i	−0.183084	+	0.503019i
$530$		0			0
$531$		−	22.3424i		−	0.969579i
$532$		0			0
$533$	5.33839	+	5.33839i	0.231231	+	0.231231i
$534$		0			0
$535$	−1.12790	−	0.652381i	−0.0487632	−	0.0282049i
$536$		0			0
$537$	0.437914	+	0.306631i	0.0188974	+	0.0132321i
$538$		0			0
$539$	23.6565	+	13.6581i	1.01896	+	0.588295i
$540$		0			0
$541$	27.6333	+	23.1871i	1.18805	+	0.996892i	0.999891	+	0.0147531i	$0.00469623\pi$
$541$	27.6333	+	23.1871i	1.18805	+	0.996892i	0.188158	+	0.982139i	$0.439748\pi$
$542$		0			0
$543$	2.53480	−	9.46000i	0.108779	−	0.405968i
$544$		0			0
$545$	12.7766	−	18.2161i	0.547288	−	0.780293i
$546$		0			0
$547$	18.0766	−	12.6574i	0.772900	−	0.541190i	−0.119285	−	0.992860i	$-0.538060\pi$
$547$	18.0766	−	12.6574i	0.772900	−	0.541190i	0.892185	+	0.451670i	$0.149171\pi$
$548$		0			0
$549$	−7.01839	−	8.36420i	−0.299538	−	0.356975i
$550$		0			0
$551$	−27.8380	+	23.3047i	−1.18594	+	0.992812i
$552$		0			0
$553$	−0.126644	+	1.44755i	−0.00538545	+	0.0615559i
$554$		0			0
$555$	−2.48422	−	5.33845i	−0.105449	−	0.226605i
$556$		0			0
$557$	−6.59144	+	14.1354i	−0.279288	+	0.598936i	−0.995046	−	0.0994127i	$-0.968304\pi$
$557$	−6.59144	+	14.1354i	−0.279288	+	0.598936i	0.715758	+	0.698348i	$0.246081\pi$
$558$		0			0
$559$	13.5752	+	23.5130i	0.574170	+	0.994492i
$560$		0			0
$561$	18.2146	−	21.7073i	0.769021	−	0.916484i
$562$		0			0
$563$	1.66914	+	6.22932i	0.0703459	+	0.262535i	0.992138	−	0.125151i	$-0.0399414\pi$
$563$	1.66914	+	6.22932i	0.0703459	+	0.262535i	−0.921792	+	0.387685i	$0.873275\pi$
$564$		0			0
$565$	15.0199	+	0.0118872i	0.631892	+	0.000500100i
$566$		0			0
$567$	0.123342	−	0.0575155i	0.00517989	−	0.00241542i
$568$		0			0
$569$	12.7396			0.534072			0.267036	−	0.963687i	$-0.413956\pi$
$569$	12.7396			0.534072			0.267036	+	0.963687i	$0.413956\pi$
$570$		0			0
$571$	23.7038			0.991971			0.495986	−	0.868331i	$-0.334807\pi$
$571$	23.7038			0.991971			0.495986	+	0.868331i	$0.334807\pi$
$572$		0			0
$573$	−9.70916	+	4.52746i	−0.405606	+	0.189137i
$574$		0			0
$575$	9.35465	+	13.4049i	0.390116	+	0.559024i
$576$		0			0
$577$	−8.39386	−	31.3263i	−0.349441	−	1.30413i	−0.887337	−	0.461121i	$-0.847447\pi$
$577$	−8.39386	−	31.3263i	−0.349441	−	1.30413i	0.537896	−	0.843011i	$-0.319219\pi$
$578$		0			0
$579$	9.50926	−	11.3327i	0.395192	−	0.470971i
$580$		0			0
$581$	3.73620	+	6.47129i	0.155004	+	0.268474i
$582$		0			0
$583$	0.903645	−	1.93787i	0.0374252	−	0.0802585i
$584$		0			0
$585$	4.15093	−	11.3766i	0.171620	−	0.470363i
$586$		0			0
$587$	−0.938603	+	10.7283i	−0.0387403	+	0.442804i	0.951910	+	0.306378i	$0.0991171\pi$
$587$	−0.938603	+	10.7283i	−0.0387403	+	0.442804i	−0.990650	+	0.136426i	$0.956438\pi$
$588$		0			0
$589$	13.7250	−	16.3189i	0.565530	−	0.672409i
$590$		0			0
$591$	12.2420	+	14.5894i	0.503568	+	0.600129i
$592$		0			0
$593$	−23.4640	+	16.4297i	−0.963551	+	0.674686i	−0.945661	−	0.325154i	$-0.894584\pi$
$593$	−23.4640	+	16.4297i	−0.963551	+	0.674686i	−0.0178902	+	0.999840i	$0.505695\pi$
$594$		0			0
$595$	9.04307	+	6.34270i	0.370730	+	0.260025i
$596$		0			0
$597$	−0.104916	+	0.391554i	−0.00429395	+	0.0160252i
$598$		0			0
$599$	31.3416	+	26.2988i	1.28058	+	1.07454i	0.993163	+	0.116734i	$0.0372424\pi$
$599$	31.3416	+	26.2988i	1.28058	+	1.07454i	0.287421	+	0.957804i	$0.407202\pi$
$600$		0			0
$601$	21.4695	+	12.3954i	0.875759	+	0.505619i	0.869258	−	0.494359i	$-0.164597\pi$
$601$	21.4695	+	12.3954i	0.875759	+	0.505619i	0.00650093	+	0.999979i	$0.497931\pi$
$602$		0			0
$603$	6.65086	+	4.65698i	0.270844	+	0.189647i
$604$		0			0
$605$	−15.9019	+	4.24742i	−0.646505	+	0.172682i
$606$		0			0
$607$	−29.2432	−	29.2432i	−1.18694	−	1.18694i	−0.977908	−	0.209037i	$-0.932967\pi$
$607$	−29.2432	−	29.2432i	−1.18694	−	1.18694i	−0.209037	−	0.977908i	$-0.567033\pi$
$608$		0			0
$609$		−	6.97013i		−	0.282444i
$610$		0			0
$611$	−4.27649	+	11.7496i	−0.173008	+	0.475336i
$612$		0			0
$613$	−8.11686	+	11.5921i	−0.327837	+	0.468200i	−0.948907	−	0.315555i	$-0.897809\pi$
$613$	−8.11686	+	11.5921i	−0.327837	+	0.468200i	0.621070	+	0.783755i	$0.286698\pi$
$614$		0			0
$615$	3.99003	−	4.74749i	0.160893	−	0.191437i
$616$		0			0
$617$	47.3489	−	4.14249i	1.90619	−	0.166770i	0.927739	−	0.373230i	$-0.121750\pi$
$617$	47.3489	−	4.14249i	1.90619	−	0.166770i	0.978455	+	0.206460i	$0.0661943\pi$
$618$		0			0
$619$	−21.2437	+	12.2651i	−0.853858	+	0.492975i	−0.861951	−	0.506992i	$-0.830757\pi$
$619$	−21.2437	+	12.2651i	−0.853858	+	0.492975i	0.00809267	+	0.999967i	$0.497424\pi$
$620$		0			0
$621$	5.77518	+	15.8672i	0.231750	+	0.636728i
$622$		0			0
$623$	−5.83784	−	8.33730i	−0.233888	−	0.334027i
$624$		0			0
$625$	−24.9999	−	0.0791431i	−0.999995	−	0.00316572i
$626$		0			0
$627$	13.9952	−	13.9632i	0.558914	−	0.557636i
$628$		0			0
$629$	−11.9071	+	9.99125i	−0.474767	+	0.398377i
$630$		0			0
$631$	1.85305	−	10.5092i	0.0737687	−	0.418363i	−0.925451	−	0.378867i	$-0.876314\pi$
$631$	1.85305	−	10.5092i	0.0737687	−	0.418363i	0.999220	−	0.0394957i	$-0.0125752\pi$
$632$		0			0
$633$	9.48800	+	4.42433i	0.377114	+	0.175851i
$634$		0			0
$635$	11.0168	+	30.3430i	0.437187	+	1.20413i
$636$		0			0
$637$	1.60086	+	18.2980i	0.0634286	+	0.724992i
$638$		0			0
$639$	14.5178	−	25.1455i	0.574315	−	0.994742i
$640$		0			0
$641$	8.90367	−	1.56996i	0.351674	−	0.0620096i	0.00497910	−	0.999988i	$-0.498415\pi$
$641$	8.90367	−	1.56996i	0.351674	−	0.0620096i	0.346695	+	0.937978i	$0.387304\pi$
$642$		0			0
$643$	8.15348	+	17.4852i	0.321542	+	0.689549i	0.998938	−	0.0460694i	$-0.0146695\pi$
$643$	8.15348	+	17.4852i	0.321542	+	0.689549i	−0.677396	+	0.735618i	$0.736892\pi$
$644$		0			0
$645$	18.2791	−	12.7776i	0.719739	−	0.503119i
$646$		0			0
$647$	−20.9746	+	20.9746i	−0.824598	+	0.824598i	−0.986764	−	0.162166i	$-0.948152\pi$
$647$	−20.9746	+	20.9746i	−0.824598	+	0.824598i	0.162166	+	0.986764i	$0.448152\pi$
$648$		0			0
$649$	−47.8611	−	17.4200i	−1.87871	−	0.683795i
$650$		0			0
$651$	0.710882	+	4.03161i	0.0278617	+	0.158011i
$652$		0			0
$653$	−1.88464	+	0.504988i	−0.0737517	+	0.0197617i	−0.295506	−	0.955341i	$-0.595488\pi$
$653$	−1.88464	+	0.504988i	−0.0737517	+	0.0197617i	0.221755	+	0.975103i	$0.428822\pi$
$654$		0			0
$655$	−2.00815	−	0.177292i	−0.0784650	−	0.00692738i
$656$		0			0
$657$	25.6940	+	6.88469i	1.00242	+	0.268598i
$658$		0			0
$659$	15.5054	−	5.64352i	0.604006	−	0.219840i	−0.0218722	−	0.999761i	$-0.506963\pi$
$659$	15.5054	−	5.64352i	0.604006	−	0.219840i	0.625879	+	0.779920i	$0.284740\pi$
$660$		0			0
$661$	−43.0557	−	7.59189i	−1.67467	−	0.295290i	−0.745934	−	0.666020i	$-0.767996\pi$
$661$	−43.0557	−	7.59189i	−1.67467	−	0.295290i	−0.928741	+	0.370730i	$0.879108\pi$
$662$		0			0
$663$	18.9817	+	1.66069i	0.737189	+	0.0644957i
$664$		0			0
$665$	5.89365	+	4.96483i	0.228546	+	0.192528i
$666$		0			0
$667$	−27.1260	−	2.37321i	−1.05032	−	0.0918912i
$668$		0			0
$669$	8.18402	+	1.44306i	0.316412	+	0.0557920i
$670$		0			0
$671$	−23.3896	+	8.51311i	−0.902944	+	0.328645i
$672$		0			0
$673$	35.3917	+	9.48319i	1.36425	+	0.365550i	0.865376	−	0.501124i	$-0.167080\pi$
$673$	35.3917	+	9.48319i	1.36425	+	0.365550i	0.498875	+	0.866674i	$0.333747\pi$
$674$		0			0
$675$	−24.9341	−	6.72338i	−0.959712	−	0.258783i
$676$		0			0
$677$	6.19366	−	1.65959i	0.238042	−	0.0637831i	−0.137826	−	0.990456i	$-0.544011\pi$
$677$	6.19366	−	1.65959i	0.238042	−	0.0637831i	0.375868	+	0.926673i	$0.377345\pi$
$678$		0			0
$679$	−2.11391	−	11.9886i	−0.0811244	−	0.460079i
$680$		0			0
$681$	−26.8766	−	9.78230i	−1.02992	−	0.374859i
$682$		0			0
$683$	−24.7978	+	24.7978i	−0.948863	+	0.948863i	−0.998755	−	0.0498918i	$-0.984112\pi$
$683$	−24.7978	+	24.7978i	−0.948863	+	0.948863i	0.0498918	+	0.998755i	$0.484112\pi$
$684$		0			0
$685$	6.60553	−	37.2892i	0.252384	−	1.42475i
$686$		0			0
$687$	6.45298	+	13.8385i	0.246196	+	0.527970i
$688$		0			0
$689$	1.41592	−	0.249666i	0.0539424	−	0.00951150i
$690$		0			0
$691$	−17.9204	+	31.0391i	−0.681726	+	1.18078i	0.292728	+	0.956196i	$0.405437\pi$
$691$	−17.9204	+	31.0391i	−0.681726	+	1.18078i	−0.974454	+	0.224588i	$0.927896\pi$
$692$		0			0
$693$	−0.555007	−	6.34376i	−0.0210830	−	0.240979i
$694$		0			0
$695$	−7.34534	+	15.7196i	−0.278625	+	0.596280i
$696$		0			0
$697$	−14.8370	−	6.91863i	−0.561993	−	0.262062i
$698$		0			0
$699$	−1.30607	+	7.40710i	−0.0494002	+	0.280162i
$700$		0			0
$701$	8.46957	−	7.10681i	0.319891	−	0.268421i	−0.468675	−	0.883371i	$-0.655268\pi$
$701$	8.46957	−	7.10681i	0.319891	−	0.268421i	0.788566	+	0.614950i	$0.210824\pi$
$702$		0			0
$703$	−8.89015	+	6.20980i	−0.335298	+	0.234207i
$704$		0			0
$705$	9.91884	+	2.66616i	0.373565	+	0.100413i
$706$		0			0
$707$	−1.07698	−	1.53808i	−0.0405039	−	0.0578455i
$708$		0			0
$709$	−10.3096	−	28.3255i	−0.387186	−	1.06378i	−0.968262	−	0.249936i	$-0.919590\pi$
$709$	−10.3096	−	28.3255i	−0.387186	−	1.06378i	0.581076	−	0.813849i	$-0.302632\pi$
$710$		0			0
$711$	−2.99174	+	1.72728i	−0.112199	+	0.0647781i
$712$		0			0
$713$	15.9320	−	1.39387i	0.596660	−	0.0522010i
$714$		0			0
$715$	−21.1340	−	17.7621i	−0.790368	−	0.664264i
$716$		0			0
$717$	−10.0944	+	14.4163i	−0.376982	+	0.538386i
$718$		0			0
$719$	−9.23700	+	25.3784i	−0.344482	+	0.946456i	0.639595	+	0.768712i	$0.279102\pi$
$719$	−9.23700	+	25.3784i	−0.344482	+	0.946456i	−0.984077	+	0.177744i	$0.943120\pi$
$720$		0			0
$721$			9.84726i			0.366731i
$722$		0			0
$723$	1.22596	+	1.22596i	0.0455938	+	0.0455938i
$724$		0			0
$725$	26.8193	−	31.8594i	0.996042	−	1.18323i
$726$		0			0
$727$	14.1072	+	9.87797i	0.523207	+	0.366354i	0.805144	−	0.593079i	$-0.202088\pi$
$727$	14.1072	+	9.87797i	0.523207	+	0.366354i	−0.281937	+	0.959433i	$0.590977\pi$
$728$		0			0
$729$	−13.9231	−	8.03852i	−0.515671	−	0.297723i
$730$		0			0
$731$	−45.1000	−	37.8434i	−1.66809	−	1.39969i
$732$		0			0
$733$	4.40731	−	16.4483i	0.162788	−	0.607532i	−0.835524	−	0.549453i	$-0.814836\pi$
$733$	4.40731	−	16.4483i	0.162788	−	0.607532i	0.998312	−	0.0580783i	$-0.0184973\pi$
$734$		0			0
$735$	14.8609	−	2.60825i	0.548151	−	0.0962066i
$736$		0			0
$737$	15.1616	−	10.6162i	0.558483	−	0.391054i
$738$		0			0
$739$	−3.11289	−	3.70980i	−0.114510	−	0.136467i	0.705745	−	0.708466i	$-0.250613\pi$
$739$	−3.11289	−	3.70980i	−0.114510	−	0.136467i	−0.820254	+	0.571999i	$0.806168\pi$
$740$		0			0
$741$	13.0888	+	2.32335i	0.480829	+	0.0853505i
$742$		0			0
$743$	2.09705	−	23.9694i	0.0769335	−	0.879353i	−0.855451	−	0.517884i	$-0.826720\pi$
$743$	2.09705	−	23.9694i	0.0769335	−	0.879353i	0.932384	−	0.361469i	$-0.117725\pi$
$744$		0			0
$745$	−19.7076	+	9.17082i	−0.722030	+	0.335993i
$746$		0			0
$747$	−7.50781	+	16.1006i	−0.274697	+	0.589089i
$748$		0			0
$749$	−0.230355	−	0.398986i	−0.00841698	−	0.0145786i
$750$		0			0
$751$	17.3348	−	20.6588i	0.632556	−	0.753851i	−0.350619	−	0.936518i	$-0.614029\pi$
$751$	17.3348	−	20.6588i	0.632556	−	0.753851i	0.983175	+	0.182667i	$0.0584731\pi$
$752$		0			0
$753$	−0.421479	−	1.57298i	−0.0153596	−	0.0573226i
$754$		0			0
$755$	−4.02015	+	4.01379i	−0.146308	+	0.146077i
$756$		0			0
$757$	−18.5906	+	8.66892i	−0.675685	+	0.315077i	−0.730000	−	0.683447i	$-0.760480\pi$
$757$	−18.5906	+	8.66892i	−0.675685	+	0.315077i	0.0543153	+	0.998524i	$0.482702\pi$
$758$		0			0
$759$	14.8276			0.538207
$760$		0			0
$761$	22.9024			0.830210			0.415105	−	0.909774i	$-0.363745\pi$
$761$	22.9024			0.830210			0.415105	+	0.909774i	$0.363745\pi$
$762$		0			0
$763$	7.13015	−	3.32484i	0.258129	−	0.120367i
$764$		0			0
$765$	−0.0207831	+	26.2601i	−0.000751415	+	0.949437i
$766$		0			0
$767$	−8.86404	−	33.0811i	−0.320062	−	1.19449i
$768$		0			0
$769$	−23.5626	+	28.0808i	−0.849688	+	1.01262i	0.150025	+	0.988682i	$0.452064\pi$
$769$	−23.5626	+	28.0808i	−0.849688	+	1.01262i	−0.999713	+	0.0239367i	$0.992380\pi$
$770$		0			0
$771$	−5.38355	−	9.32458i	−0.193884	−	0.335817i
$772$		0			0
$773$	−0.550137	+	1.17977i	−0.0197870	+	0.0424334i	−0.915953	−	0.401286i	$-0.868563\pi$
$773$	−0.550137	+	1.17977i	−0.0197870	+	0.0424334i	0.896166	+	0.443719i	$0.146341\pi$
$774$		0			0
$775$	−12.2633	+	21.1632i	−0.440510	+	0.760204i
$776$		0			0
$777$	0.181454	−	2.07403i	0.00650962	−	0.0744053i
$778$		0			0
$779$	−9.88462	−	5.72198i	−0.354153	−	0.205011i
$780$		0			0
$781$	−42.5465	−	50.7050i	−1.52243	−	1.81437i
$782$		0			0
$783$	35.2387	−	24.6744i	1.25933	−	0.881791i
$784$		0			0
$785$	4.07264	+	23.2045i	0.145359	+	0.828202i
$786$		0			0
$787$	5.44028	−	20.3034i	0.193925	−	0.723738i	−0.798617	−	0.601839i	$-0.794435\pi$
$787$	5.44028	−	20.3034i	0.193925	−	0.723738i	0.992542	−	0.121899i	$-0.0388984\pi$
$788$		0			0
$789$	−14.3351	−	12.0285i	−0.510341	−	0.428227i
$790$		0			0
$791$	4.59927	+	2.65539i	0.163531	+	0.0944147i

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)

\(f(q)\)	\(=\)	\(q+(0.959290 - 0.447324i) q^{3} +(1.57989 + 1.58239i) q^{5} +(0.204631 + 0.763694i) q^{7} +(-1.20823 + 1.43991i) q^{9} +O(q^{10})\)	\(q+(0.959290 - 0.447324i) q^{3} +(1.57989 + 1.58239i) q^{5} +(0.204631 + 0.763694i) q^{7} +(-1.20823 + 1.43991i) q^{9} +(2.14248 + 3.71088i) q^{11} +(-1.21768 + 2.61133i) q^{13} +(2.22341 + 0.811249i) q^{15} +(0.544538 - 6.22409i) q^{17} +(0.761826 - 4.29181i) q^{19} +(0.537919 + 0.641067i) q^{21} +(2.67802 - 1.87517i) q^{23} +(-0.00791432 + 4.99999i) q^{25} +(-1.33678 + 4.98893i) q^{27} +(-6.38036 - 5.35376i) q^{29} +(4.23651 + 2.44595i) q^{31} +(3.71522 + 2.60143i) q^{33} +(-0.885167 + 1.53036i) q^{35} +(-1.75916 - 1.75916i) q^{37} +3.04972i q^{39} +(0.896173 - 2.46221i) q^{41} +(5.40483 - 7.71890i) q^{43} +(-4.18735 + 0.363007i) q^{45} +(4.32309 - 0.378221i) q^{47} +(5.52082 - 3.18745i) q^{49} +(-2.26182 - 6.21429i) q^{51} +(-0.286216 - 0.408759i) q^{53} +(-2.48719 + 9.25301i) q^{55} +(-1.18902 - 4.45787i) q^{57} +(-9.10551 + 7.64043i) q^{59} +(-1.00870 + 5.72060i) q^{61} +(-1.34689 - 0.628064i) q^{63} +(-6.05594 + 2.19875i) q^{65} +(-0.376469 - 4.30306i) q^{67} +(1.73019 - 2.99678i) q^{69} +(-15.2125 + 2.68238i) q^{71} +(-5.98076 - 12.8258i) q^{73} +(2.22903 + 4.79998i) q^{75} +(-2.39556 + 2.39556i) q^{77} +(1.72702 + 0.628586i) q^{79} +(-0.0298904 - 0.169517i) q^{81} +(9.12912 - 2.44614i) q^{83} +(10.7092 - 8.97169i) q^{85} +(-8.51548 - 2.28172i) q^{87} +(-12.0968 + 4.40288i) q^{89} +(-2.24343 - 0.395577i) q^{91} +(5.15817 + 0.451282i) q^{93} +(7.99491 - 5.57507i) q^{95} +(-15.3386 - 1.34195i) q^{97} +(-7.93192 - 1.39861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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

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Groups

Database

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