LMFDB - Embedded newform 380.2.bh.a.33.1

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			33.1
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +O(q^{10})$	\(q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +(1.71018 - 2.96212i) q^{11} +(1.74848 + 1.22430i) q^{13} +(-5.54820 - 2.94613i) q^{15} +(-2.63830 + 5.65786i) q^{17} +(1.56004 - 4.07017i) q^{19} +(-4.88905 - 13.4325i) q^{21} +(-2.25262 - 0.197079i) q^{23} +(2.93449 - 4.04831i) q^{25} +(5.13536 - 1.37602i) q^{27} +(-5.51312 - 2.00661i) q^{29} +(-0.923557 + 0.533216i) q^{31} +(-9.57244 + 0.837480i) q^{33} +(11.1277 - 2.37165i) q^{35} +(-2.20652 - 2.20652i) q^{37} -5.99656i q^{39} +(-2.29610 - 0.404865i) q^{41} +(-0.102775 - 1.17473i) q^{43} +(1.33919 + 10.8575i) q^{45} +(-2.83672 + 1.32278i) q^{47} +(16.3593 + 9.44505i) q^{49} +(17.2716 - 3.04546i) q^{51} +(-1.09089 + 12.4689i) q^{53} +(0.396085 - 7.63791i) q^{55} +(-11.8804 + 2.96849i) q^{57} +(1.32531 - 0.482374i) q^{59} +(-8.84468 + 7.42157i) q^{61} +(-14.2785 + 20.3919i) q^{63} +(4.72681 + 0.661666i) q^{65} +(2.33207 + 5.00114i) q^{67} +(3.17628 + 5.50149i) q^{69} +(-2.27536 + 2.71167i) q^{71} +(-1.61028 + 1.12753i) q^{73} +(-14.0449 - 0.229741i) q^{75} +(12.3062 - 12.3062i) q^{77} +(1.00143 - 5.67937i) q^{79} +(-0.198129 - 0.166250i) q^{81} +(0.0567325 - 0.211729i) q^{83} +(0.494822 + 13.9505i) q^{85} +(4.26593 + 15.9207i) q^{87} +(-2.79291 - 15.8394i) q^{89} +(6.98122 + 8.31989i) q^{91} +(2.71528 + 1.26616i) q^{93} +(-1.02903 - 9.69232i) q^{95} +(12.8386 + 5.98673i) q^{97} +(10.7564 + 12.8189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.61138	−	2.30128i	−0.930328	−	1.32865i	−0.944418	−	0.328746i	$-0.893374\pi$
$3$	−1.61138	−	2.30128i	−0.930328	−	1.32865i	0.0140900	−	0.999901i	$-0.495515\pi$
$4$		0			0
$5$	1.99179	−	1.01625i	0.890757	−	0.454479i
$5$	1.99179	−	1.01625i	0.890757	−	0.454479i
$6$		0			0
$7$	4.91485	+	1.31693i	1.85764	+	0.497753i	0.999868	−	0.0162764i	$-0.00518117\pi$
$7$	4.91485	+	1.31693i	1.85764	+	0.497753i	0.857772	+	0.514030i	$0.171848\pi$
$8$		0			0
$9$	−1.67331	+	4.59739i	−0.557771	+	1.53246i
$10$		0			0
$11$	1.71018	−	2.96212i	0.515640	−	0.893114i	−0.484195	−	0.874960i	$-0.660888\pi$
$11$	1.71018	−	2.96212i	0.515640	−	0.893114i	0.999835	−	0.0181543i	$-0.00577902\pi$
$12$		0			0
$13$	1.74848	+	1.22430i	0.484942	+	0.339560i	0.790344	−	0.612664i	$-0.209902\pi$
$13$	1.74848	+	1.22430i	0.484942	+	0.339560i	−0.305402	+	0.952224i	$0.598791\pi$
$14$		0			0
$15$	−5.54820	−	2.94613i	−1.43254	−	0.760687i
$16$		0			0
$17$	−2.63830	+	5.65786i	−0.639882	+	1.37223i	0.272206	+	0.962239i	$0.412247\pi$
$17$	−2.63830	+	5.65786i	−0.639882	+	1.37223i	−0.912089	+	0.409993i	$0.865531\pi$
$18$		0			0
$19$	1.56004	−	4.07017i	0.357897	−	0.933761i
$19$	1.56004	−	4.07017i	0.357897	−	0.933761i
$20$		0			0
$21$	−4.88905	−	13.4325i	−1.06688	−	2.93122i
$22$		0			0
$23$	−2.25262	−	0.197079i	−0.469704	−	0.0410938i	−0.150153	−	0.988663i	$-0.547977\pi$
$23$	−2.25262	−	0.197079i	−0.469704	−	0.0410938i	−0.319551	+	0.947569i	$0.603532\pi$
$24$		0			0
$25$	2.93449	−	4.04831i	0.586897	−	0.809661i
$26$		0			0
$27$	5.13536	−	1.37602i	0.988301	−	0.264814i
$28$		0			0
$29$	−5.51312	−	2.00661i	−1.02376	−	0.372618i	−0.225059	−	0.974345i	$-0.572257\pi$
$29$	−5.51312	−	2.00661i	−1.02376	−	0.372618i	−0.798702	+	0.601727i	$0.794480\pi$
$30$		0			0
$31$	−0.923557	+	0.533216i	−0.165876	+	0.0957684i	−0.580640	−	0.814161i	$-0.697197\pi$
$31$	−0.923557	+	0.533216i	−0.165876	+	0.0957684i	0.414764	+	0.909929i	$0.363864\pi$
$32$		0			0
$33$	−9.57244	+	0.837480i	−1.66635	+	0.145787i
$34$		0			0
$35$	11.1277	−	2.37165i	1.88092	−	0.400881i
$36$		0			0
$37$	−2.20652	−	2.20652i	−0.362749	−	0.362749i	0.502075	−	0.864824i	$-0.332570\pi$
$37$	−2.20652	−	2.20652i	−0.362749	−	0.362749i	−0.864824	+	0.502075i	$0.832570\pi$
$38$		0			0
$39$		−	5.99656i		−	0.960219i
$40$		0			0
$41$	−2.29610	−	0.404865i	−0.358591	−	0.0632293i	−0.00854966	−	0.999963i	$-0.502721\pi$
$41$	−2.29610	−	0.404865i	−0.358591	−	0.0632293i	−0.350042	+	0.936734i	$0.613833\pi$
$42$		0			0
$43$	−0.102775	−	1.17473i	−0.0156731	−	0.179144i	−0.999996	−	0.00276953i	$-0.999118\pi$
$43$	−0.102775	−	1.17473i	−0.0156731	−	0.179144i	0.984323	−	0.176375i	$-0.0564371\pi$
$44$		0			0
$45$	1.33919	+	10.8575i	0.199634	+	1.61855i
$46$		0			0
$47$	−2.83672	+	1.32278i	−0.413778	+	0.192948i	−0.618349	−	0.785904i	$-0.712198\pi$
$47$	−2.83672	+	1.32278i	−0.413778	+	0.192948i	0.204570	+	0.978852i	$0.434420\pi$
$48$		0			0
$49$	16.3593	+	9.44505i	2.33704	+	1.34929i
$50$		0			0
$51$	17.2716	−	3.04546i	2.41851	−	0.426449i
$52$		0			0
$53$	−1.09089	+	12.4689i	−0.149845	+	1.71274i	0.434030	+	0.900898i	$0.357091\pi$
$53$	−1.09089	+	12.4689i	−0.149845	+	1.71274i	−0.583876	+	0.811843i	$0.698465\pi$
$54$		0			0
$55$	0.396085	−	7.63791i	0.0534081	−	1.02990i
$56$		0			0
$57$	−11.8804	+	2.96849i	−1.57360	+	0.393186i
$58$		0			0
$59$	1.32531	−	0.482374i	0.172541	−	0.0627998i	−0.254305	−	0.967124i	$-0.581847\pi$
$59$	1.32531	−	0.482374i	0.172541	−	0.0627998i	0.426846	+	0.904324i	$0.359625\pi$
$60$		0			0
$61$	−8.84468	+	7.42157i	−1.13244	+	0.950234i	−0.999166	−	0.0408444i	$-0.986995\pi$
$61$	−8.84468	+	7.42157i	−1.13244	+	0.950234i	−0.133279	+	0.991079i	$0.542551\pi$
$62$		0			0
$63$	−14.2785	+	20.3919i	−1.79893	+	2.56913i
$64$		0			0
$65$	4.72681	+	0.661666i	0.586289	+	0.0820696i
$66$		0			0
$67$	2.33207	+	5.00114i	0.284907	+	0.610986i	0.995723	−	0.0923928i	$-0.0294516\pi$
$67$	2.33207	+	5.00114i	0.284907	+	0.610986i	−0.710815	+	0.703379i	$0.751674\pi$
$68$		0			0
$69$	3.17628	+	5.50149i	0.382380	+	0.662301i
$70$		0			0
$71$	−2.27536	+	2.71167i	−0.270036	+	0.321816i	−0.883972	−	0.467539i	$-0.845141\pi$
$71$	−2.27536	+	2.71167i	−0.270036	+	0.321816i	0.613937	+	0.789355i	$0.289585\pi$
$72$		0			0
$73$	−1.61028	+	1.12753i	−0.188468	+	0.131967i	−0.664003	−	0.747730i	$-0.731144\pi$
$73$	−1.61028	+	1.12753i	−0.188468	+	0.131967i	0.475534	+	0.879697i	$0.342255\pi$
$74$		0			0
$75$	−14.0449	−	0.229741i	−1.62176	−	0.0265282i
$76$		0			0
$77$	12.3062	−	12.3062i	1.40242	−	1.40242i
$78$		0			0
$79$	1.00143	−	5.67937i	0.112669	−	0.638979i	−0.875209	−	0.483746i	$-0.839276\pi$
$79$	1.00143	−	5.67937i	0.112669	−	0.638979i	0.987878	−	0.155233i	$-0.0496129\pi$
$80$		0			0
$81$	−0.198129	−	0.166250i	−0.0220144	−	0.0184722i
$82$		0			0
$83$	0.0567325	−	0.211729i	0.00622720	−	0.0232402i	−0.962742	−	0.270420i	$-0.912837\pi$
$83$	0.0567325	−	0.211729i	0.00622720	−	0.0232402i	0.968970	+	0.247180i	$0.0795040\pi$
$84$		0			0
$85$	0.494822	+	13.9505i	0.0536710	+	1.51314i
$86$		0			0
$87$	4.26593	+	15.9207i	0.457355	+	1.70687i
$88$		0			0
$89$	−2.79291	−	15.8394i	−0.296048	−	1.67897i	−0.662912	−	0.748697i	$-0.730680\pi$
$89$	−2.79291	−	15.8394i	−0.296048	−	1.67897i	0.366864	−	0.930275i	$-0.380432\pi$
$90$		0			0
$91$	6.98122	+	8.31989i	0.731831	+	0.872162i
$92$		0			0
$93$	2.71528	+	1.26616i	0.281561	+	0.131294i
$94$		0			0
$95$	−1.02903	−	9.69232i	−0.105576	−	0.994411i
$96$		0			0
$97$	12.8386	+	5.98673i	1.30356	+	0.607860i	0.945434	−	0.325813i	$-0.105638\pi$
$97$	12.8386	+	5.98673i	1.30356	+	0.607860i	0.358126	+	0.933673i	$0.383416\pi$
$98$		0			0
$99$	10.7564	+	12.8189i	1.08106	+	1.28835i
$100$		0			0
$101$	−2.10879	−	11.9595i	−0.209832	−	1.19002i	−0.889652	−	0.456639i	$-0.849053\pi$
$101$	−2.10879	−	11.9595i	−0.209832	−	1.19002i	0.679820	−	0.733379i	$-0.262058\pi$
$102$		0			0
$103$	−4.25223	−	15.8695i	−0.418984	−	1.56367i	−0.776719	−	0.629848i	$-0.783117\pi$
$103$	−4.25223	−	15.8695i	−0.418984	−	1.56367i	0.357734	−	0.933823i	$-0.383549\pi$
$104$		0			0
$105$	−23.3887	−	21.7864i	−2.28251	−	2.12613i
$106$		0			0
$107$	1.05878	−	3.95143i	0.102356	−	0.381999i	−0.895676	−	0.444708i	$-0.853307\pi$
$107$	1.05878	−	3.95143i	0.102356	−	0.381999i	0.998032	+	0.0627092i	$0.0199741\pi$
$108$		0			0
$109$	1.02714	+	0.861870i	0.0983818	+	0.0825522i	0.690652	−	0.723187i	$-0.257324\pi$
$109$	1.02714	+	0.861870i	0.0983818	+	0.0825522i	−0.592270	+	0.805740i	$0.701768\pi$
$110$		0			0
$111$	−1.52229	+	8.63335i	−0.144490	+	0.819441i
$112$		0			0
$113$	1.49986	−	1.49986i	0.141095	−	0.141095i	−0.633031	−	0.774126i	$-0.718190\pi$
$113$	1.49986	−	1.49986i	0.141095	−	0.141095i	0.774126	+	0.633031i	$0.218190\pi$
$114$		0			0
$115$	−4.68704	+	1.89668i	−0.437068	+	0.176866i
$116$		0			0
$117$	−8.55435	+	5.98982i	−0.790850	+	0.553759i
$118$		0			0
$119$	−20.4179	+	24.3331i	−1.87170	+	2.23061i
$120$		0			0
$121$	−0.349455	−	0.605274i	−0.0317686	−	0.0550249i
$122$		0			0
$123$	2.76818	+	5.93638i	0.249598	+	0.535265i
$124$		0			0
$125$	1.73082	−	11.0456i	0.154809	−	0.987944i
$126$		0			0
$127$	−8.69236	+	12.4140i	−0.771322	+	1.10156i	0.220681	+	0.975346i	$0.429172\pi$
$127$	−8.69236	+	12.4140i	−0.771322	+	1.10156i	−0.992003	+	0.126216i	$0.959717\pi$
$128$		0			0
$129$	−2.53777	+	2.12945i	−0.223439	+	0.187487i
$130$		0			0
$131$	−0.988864	+	0.359917i	−0.0863974	+	0.0314461i	−0.384857	−	0.922976i	$-0.625749\pi$
$131$	−0.988864	+	0.359917i	−0.0863974	+	0.0314461i	0.298460	+	0.954422i	$0.403527\pi$
$132$		0			0
$133$	13.0275	−	17.9498i	1.12963	−	1.55645i
$134$		0			0
$135$	8.83021	−	7.95954i	0.759984	−	0.685048i
$136$		0			0
$137$	−1.29449	+	14.7961i	−0.110596	+	1.26412i	0.714705	+	0.699426i	$0.246561\pi$
$137$	−1.29449	+	14.7961i	−0.110596	+	1.26412i	−0.825301	+	0.564692i	$0.808995\pi$
$138$		0			0
$139$	−5.53858	+	0.976601i	−0.469776	+	0.0828342i	−0.403525	−	0.914969i	$-0.632215\pi$
$139$	−5.53858	+	0.976601i	−0.469776	+	0.0828342i	−0.0662515	+	0.997803i	$0.521104\pi$
$140$		0			0
$141$	7.61513	+	4.39660i	0.641309	+	0.370260i
$142$		0			0
$143$	6.61676	−	3.08545i	0.553321	−	0.258018i
$144$		0			0
$145$	−13.0202	+	1.60593i	−1.08127	+	0.133365i
$146$		0			0
$147$	−4.62526	−	52.8669i	−0.381485	−	4.36039i
$148$		0			0
$149$	14.2507	+	2.51279i	1.16746	+	0.205856i	0.723588	−	0.690232i	$-0.242492\pi$
$149$	14.2507	+	2.51279i	1.16746	+	0.205856i	0.443877	+	0.896088i	$0.353603\pi$
$150$		0			0
$151$			10.6963i			0.870457i	0.900320	+	0.435228i	$0.143332\pi$
$151$			10.6963i			0.870457i	−0.900320	+	0.435228i	$0.856668\pi$
$152$		0			0
$153$	−21.5967	−	21.5967i	−1.74599	−	1.74599i
$154$		0			0
$155$	−1.29766	+	2.00062i	−0.104230	+	0.160694i
$156$		0			0
$157$	11.8321	−	1.03517i	0.944303	−	0.0826159i	0.395407	−	0.918506i	$-0.370604\pi$
$157$	11.8321	−	1.03517i	0.944303	−	0.0826159i	0.548897	+	0.835890i	$0.315048\pi$
$158$		0			0
$159$	30.4524	−	17.5817i	2.41503	−	1.39432i
$160$		0			0
$161$	−10.8118	−	3.93516i	−0.852086	−	0.310134i
$162$		0			0
$163$	−3.09224	+	0.828563i	−0.242203	+	0.0648981i	−0.377878	−	0.925855i	$-0.623346\pi$
$163$	−3.09224	+	0.828563i	−0.242203	+	0.0648981i	0.135675	+	0.990753i	$0.456680\pi$
$164$		0			0
$165$	−18.2152	+	11.3960i	−1.41805	+	0.887181i
$166$		0			0
$167$	−1.39419	−	0.121976i	−0.107886	−	0.00943880i	0.0330849	−	0.999453i	$-0.489467\pi$
$167$	−1.39419	−	0.121976i	−0.107886	−	0.00943880i	−0.140971	+	0.990014i	$0.545022\pi$
$168$		0			0
$169$	−2.88798	−	7.93466i	−0.222152	−	0.610359i
$170$		0			0
$171$	16.1017	+	13.9828i	1.23133	+	1.06929i
$172$		0			0
$173$	−8.28676	+	17.7710i	−0.630031	+	1.35111i	0.289155	+	0.957282i	$0.406626\pi$
$173$	−8.28676	+	17.7710i	−0.630031	+	1.35111i	−0.919186	+	0.393823i	$0.871152\pi$
$174$		0			0
$175$	19.7539	−	16.0323i	1.49326	−	1.21193i
$176$		0			0
$177$	−3.24566	−	2.27263i	−0.243959	−	0.170822i
$178$		0			0
$179$	−5.18896	+	8.98755i	−0.387841	+	0.671761i	−0.992159	−	0.124983i	$-0.960112\pi$
$179$	−5.18896	+	8.98755i	−0.387841	+	0.671761i	0.604318	+	0.796743i	$0.293446\pi$
$180$		0			0
$181$	0.294087	−	0.807997i	0.0218593	−	0.0600579i	−0.928283	−	0.371874i	$-0.878715\pi$
$181$	0.294087	−	0.807997i	0.0218593	−	0.0600579i	0.950142	+	0.311816i	$0.100937\pi$
$182$		0			0
$183$	31.3312	+	8.39518i	2.31607	+	0.620589i
$184$		0			0
$185$	−6.63729	−	2.15256i	−0.487983	−	0.158260i
$186$		0			0
$187$	12.2473	+	17.4910i	0.895611	+	1.27907i
$188$		0			0
$189$	27.0517			1.96772
$190$		0			0
$191$	−12.3532			−0.893844			−0.446922	−	0.894573i	$-0.647480\pi$
$191$	−12.3532			−0.893844			−0.446922	+	0.894573i	$0.647480\pi$
$192$		0			0
$193$	14.4146	+	20.5862i	1.03759	+	1.48183i	0.868159	+	0.496287i	$0.165304\pi$
$193$	14.4146	+	20.5862i	1.03759	+	1.48183i	0.169429	+	0.985542i	$0.445808\pi$
$194$		0			0
$195$	−6.09399	−	11.9439i	−0.436399	−	0.855322i
$196$		0			0
$197$	2.73612	+	0.733141i	0.194940	+	0.0522341i	0.354968	−	0.934878i	$-0.384492\pi$
$197$	2.73612	+	0.733141i	0.194940	+	0.0522341i	−0.160028	+	0.987113i	$0.551158\pi$
$198$		0			0
$199$	−3.69566	+	10.1538i	−0.261979	+	0.719781i	0.737055	+	0.675833i	$0.236216\pi$
$199$	−3.69566	+	10.1538i	−0.261979	+	0.719781i	−0.999034	+	0.0439479i	$0.986006\pi$
$200$		0			0
$201$	7.75119	−	13.4255i	0.546727	−	0.946959i
$202$		0			0
$203$	−24.4536	−	17.1226i	−1.71631	−	1.20177i
$204$		0			0
$205$	−4.98481	+	1.52700i	−0.348154	+	0.106650i
$206$		0			0
$207$	4.67539	−	10.0264i	0.324962	−	0.696883i
$208$		0			0
$209$	−9.38841	−	11.5818i	−0.649410	−	0.801127i
$210$		0			0
$211$	3.91671	+	10.7611i	0.269637	+	0.740822i	0.998426	+	0.0560837i	$0.0178614\pi$
$211$	3.91671	+	10.7611i	0.269637	+	0.740822i	−0.728789	+	0.684739i	$0.759916\pi$
$212$		0			0
$213$	9.90678	+	0.866731i	0.678801	+	0.0593874i
$214$		0			0
$215$	−1.39852	−	2.23537i	−0.0953784	−	0.152451i
$216$		0			0
$217$	−5.24136	+	1.40442i	−0.355807	+	0.0953381i
$218$		0			0
$219$	5.18952	+	1.88883i	0.350675	+	0.127635i
$220$		0			0
$221$	−11.5399	+	6.66259i	−0.776261	+	0.448174i
$222$		0			0
$223$	7.31669	−	0.640127i	0.489962	−	0.0428661i	0.160502	−	0.987036i	$-0.448689\pi$
$223$	7.31669	−	0.640127i	0.489962	−	0.0428661i	0.329460	+	0.944170i	$0.393133\pi$
$224$		0			0
$225$	13.7013	+	20.2651i	0.913422	+	1.35100i
$226$		0			0
$227$	−17.3630	−	17.3630i	−1.15243	−	1.15243i	−0.986065	−	0.166361i	$-0.946798\pi$
$227$	−17.3630	−	17.3630i	−1.15243	−	1.15243i	−0.166361	−	0.986065i	$-0.553202\pi$
$228$		0			0
$229$		−	23.0335i		−	1.52210i	−0.648695	−	0.761049i	$-0.724685\pi$
$229$		−	23.0335i		−	1.52210i	0.648695	−	0.761049i	$-0.275315\pi$
$230$		0			0
$231$	−48.1500	−	8.49015i	−3.16804	−	0.558611i
$232$		0			0
$233$	−0.808518	−	9.24140i	−0.0529678	−	0.605424i	−0.975573	−	0.219678i	$-0.929499\pi$
$233$	−0.808518	−	9.24140i	−0.0529678	−	0.605424i	0.922605	−	0.385747i	$-0.126056\pi$
$234$		0			0
$235$	−4.30589	+	5.51752i	−0.280885	+	0.359923i
$236$		0			0
$237$	−14.6835	+	6.84703i	−0.953796	+	0.444763i
$238$		0			0
$239$	1.41871	+	0.819094i	0.0917689	+	0.0529828i	0.545182	−	0.838318i	$-0.316460\pi$
$239$	1.41871	+	0.819094i	0.0917689	+	0.0529828i	−0.453413	+	0.891300i	$0.649794\pi$
$240$		0			0
$241$	19.4770	−	3.43432i	1.25462	−	0.221224i	0.493450	−	0.869774i	$-0.335736\pi$
$241$	19.4770	−	3.43432i	1.25462	−	0.221224i	0.761172	+	0.648550i	$0.224624\pi$
$242$		0			0
$243$	1.32677	−	15.1650i	0.0851122	−	0.972837i
$244$		0			0
$245$	42.1828	+	2.18751i	2.69496	+	0.139755i
$246$		0			0
$247$	7.71081	−	5.20667i	0.490627	−	0.331293i
$248$		0			0
$249$	−0.578665	+	0.210617i	−0.0366714	+	0.0133473i
$250$		0			0
$251$	7.88691	−	6.61790i	0.497817	−	0.417718i	−0.359001	−	0.933337i	$-0.616882\pi$
$251$	7.88691	−	6.61790i	0.497817	−	0.417718i	0.856818	+	0.515619i	$0.172438\pi$
$252$		0			0
$253$	−4.43617	+	6.33550i	−0.278899	+	0.398310i
$254$		0			0
$255$	31.3066	−	23.6182i	1.96050	−	1.47903i
$256$		0			0
$257$	−2.50140	−	5.36428i	−0.156033	−	0.334615i	0.812715	−	0.582662i	$-0.197989\pi$
$257$	−2.50140	−	5.36428i	−0.156033	−	0.334615i	−0.968748	+	0.248047i	$0.920211\pi$
$258$		0			0
$259$	−7.93888	−	13.7505i	−0.493298	−	0.854417i
$260$		0			0
$261$	18.4503	−	21.9883i	1.14205	−	1.36104i
$262$		0			0
$263$	−4.51813	+	3.16363i	−0.278600	+	0.195078i	−0.704522	−	0.709682i	$-0.748839\pi$
$263$	−4.51813	+	3.16363i	−0.278600	+	0.195078i	0.425922	+	0.904760i	$0.359950\pi$
$264$		0			0
$265$	10.4987	+	25.9442i	0.644929	+	1.59374i
$266$		0			0
$267$	−31.9505	+	31.9505i	−1.95534	+	1.95534i
$268$		0			0
$269$	−2.13669	+	12.1178i	−0.130276	+	0.738832i	0.847757	+	0.530384i	$0.177952\pi$
$269$	−2.13669	+	12.1178i	−0.130276	+	0.738832i	−0.978033	+	0.208448i	$0.933159\pi$
$270$		0			0
$271$	−5.15712	−	4.32734i	−0.313273	−	0.262867i	0.472570	−	0.881293i	$-0.343326\pi$
$271$	−5.15712	−	4.32734i	−0.313273	−	0.262867i	−0.785843	+	0.618426i	$0.787771\pi$
$272$		0			0
$273$	7.89706	−	29.4722i	0.477952	−	1.78374i
$274$		0			0
$275$	−6.97308	−	15.6157i	−0.420492	−	0.941660i
$276$		0			0
$277$	6.11754	+	22.8310i	0.367567	+	1.37178i	0.863907	+	0.503652i	$0.168011\pi$
$277$	6.11754	+	22.8310i	0.367567	+	1.37178i	−0.496339	+	0.868129i	$0.665323\pi$
$278$		0			0
$279$	−0.906001	−	5.13819i	−0.0542409	−	0.307615i
$280$		0			0
$281$	−0.197508	−	0.235381i	−0.0117824	−	0.0140417i	0.760121	−	0.649781i	$-0.225140\pi$
$281$	−0.197508	−	0.235381i	−0.0117824	−	0.0140417i	−0.771903	+	0.635740i	$0.780695\pi$
$282$		0			0
$283$	−18.6762	−	8.70885i	−1.11018	−	0.517687i	−0.221017	−	0.975270i	$-0.570938\pi$
$283$	−18.6762	−	8.70885i	−1.11018	−	0.517687i	−0.889167	+	0.457583i	$0.848715\pi$
$284$		0			0
$285$	−20.6466	+	17.9861i	−1.22300	+	1.06540i
$286$		0			0
$287$	−10.7518	−	5.01367i	−0.634661	−	0.295947i
$288$		0			0
$289$	−14.1233	−	16.8315i	−0.830784	−	0.990090i
$290$		0			0
$291$	−6.91062	−	39.1921i	−0.405108	−	2.29748i
$292$		0			0
$293$	1.62270	+	6.05601i	0.0947993	+	0.353796i	0.996989	−	0.0775438i	$-0.0247078\pi$
$293$	1.62270	+	6.05601i	0.0947993	+	0.353796i	−0.902190	+	0.431340i	$0.858041\pi$
$294$		0			0
$295$	2.14954	−	2.30763i	0.125151	−	0.134356i
$296$		0			0
$297$	4.70648	−	17.5648i	0.273098	−	1.01921i
$298$		0			0
$299$	−3.69739	−	3.10247i	−0.213825	−	0.179421i
$300$		0			0
$301$	1.04191	−	5.90897i	0.0600547	−	0.340587i
$302$		0			0
$303$	−24.1242	+	24.1242i	−1.38590	+	1.38590i
$304$		0			0
$305$	−10.0746	+	23.7706i	−0.576872	+	1.36110i
$306$		0			0
$307$	−19.6087	+	13.7302i	−1.11913	+	0.783621i	−0.978460	−	0.206436i	$-0.933814\pi$
$307$	−19.6087	+	13.7302i	−1.11913	+	0.783621i	−0.140667	+	0.990057i	$0.544925\pi$
$308$		0			0
$309$	−29.6683	+	35.3574i	−1.68777	+	2.01141i
$310$		0			0
$311$	1.54478	+	2.67563i	0.0875963	+	0.151721i	0.906495	−	0.422217i	$-0.138748\pi$
$311$	1.54478	+	2.67563i	0.0875963	+	0.151721i	−0.818898	+	0.573939i	$0.805415\pi$
$312$		0			0
$313$	1.10064	+	2.36034i	0.0622121	+	0.133414i	0.934956	−	0.354765i	$-0.115439\pi$
$313$	1.10064	+	2.36034i	0.0622121	+	0.133414i	−0.872744	+	0.488179i	$0.837661\pi$
$314$		0			0
$315$	−7.71674	+	55.1269i	−0.434789	+	3.10605i
$316$		0			0
$317$	16.8842	−	24.1131i	0.948310	−	1.35433i	0.0132217	−	0.999913i	$-0.495791\pi$
$317$	16.8842	−	24.1131i	0.948310	−	1.35433i	0.935088	−	0.354415i	$-0.115320\pi$
$318$		0			0
$319$	−15.3723	+	12.8989i	−0.860682	+	0.722198i
$320$		0			0
$321$	−10.7995	+	3.93068i	−0.602767	+	0.219389i
$322$		0			0
$323$	18.9126	+	19.5648i	1.05233	+	1.08861i
$324$		0			0
$325$	10.0872	−	3.48570i	0.559540	−	0.193352i
$326$		0			0
$327$	0.328304	−	3.75253i	0.0181552	−	0.207515i
$328$		0			0
$329$	−15.6841	+	2.76553i	−0.864692	+	0.152468i
$330$		0			0
$331$	12.6138	+	7.28259i	0.693318	+	0.400288i	0.804854	−	0.593473i	$-0.202244\pi$
$331$	12.6138	+	7.28259i	0.693318	+	0.400288i	−0.111536	+	0.993760i	$0.535577\pi$
$332$		0			0
$333$	13.8364	−	6.45202i	0.758231	−	0.353569i
$334$		0			0
$335$	9.72739	+	7.59128i	0.531464	+	0.414756i
$336$		0			0
$337$	−0.211469	−	2.41711i	−0.0115195	−	0.131668i	0.988257	−	0.152799i	$-0.0488288\pi$
$337$	−0.211469	−	2.41711i	−0.0115195	−	0.131668i	−0.999777	+	0.0211311i	$0.993273\pi$
$338$		0			0
$339$	−5.86844	−	1.03476i	−0.318730	−	0.0562007i
$340$		0			0
$341$			3.64759i			0.197528i
$342$		0			0
$343$	42.7796	+	42.7796i	2.30988	+	2.30988i
$344$		0			0
$345$	11.9174	+	7.72994i	0.641610	+	0.416166i
$346$		0			0
$347$	20.0577	−	1.75482i	1.07675	−	0.0942037i	0.465045	−	0.885287i	$-0.346038\pi$
$347$	20.0577	−	1.75482i	1.07675	−	0.0942037i	0.611708	+	0.791083i	$0.290483\pi$
$348$		0			0
$349$	−12.2272	+	7.05939i	−0.654509	+	0.377881i	−0.790181	−	0.612873i	$-0.790014\pi$
$349$	−12.2272	+	7.05939i	−0.654509	+	0.377881i	0.135673	+	0.990754i	$0.456680\pi$
$350$		0			0
$351$	10.6638	+	3.88129i	0.569189	+	0.207168i
$352$		0			0
$353$	−16.1175	+	4.31866i	−0.857846	+	0.229859i	−0.660825	−	0.750540i	$-0.729793\pi$
$353$	−16.1175	+	4.31866i	−0.857846	+	0.229859i	−0.197021	+	0.980399i	$0.563127\pi$
$354$		0			0
$355$	−1.77633	+	7.71341i	−0.0942776	+	0.409385i
$356$		0			0
$357$	88.8982	+	7.77758i	4.70499	+	0.411633i
$358$		0			0
$359$	−7.37703	−	20.2682i	−0.389345	−	1.06972i	−0.967297	−	0.253645i	$-0.918370\pi$
$359$	−7.37703	−	20.2682i	−0.389345	−	1.06972i	0.577953	−	0.816070i	$-0.303852\pi$
$360$		0			0
$361$	−14.1326	−	12.6992i	−0.743820	−	0.668380i
$362$		0			0
$363$	−0.829803	+	1.77952i	−0.0435534	+	0.0934005i
$364$		0			0
$365$	−2.06149	+	3.88224i	−0.107903	+	0.203206i
$366$		0			0
$367$	6.66787	+	4.66890i	0.348060	+	0.243714i	0.734513	−	0.678595i	$-0.237411\pi$
$367$	6.66787	+	4.66890i	0.348060	+	0.243714i	−0.386453	+	0.922309i	$0.626300\pi$
$368$		0			0
$369$	5.70342	−	9.87862i	0.296908	−	0.514260i
$370$		0			0
$371$	−21.7823	+	59.8464i	−1.13088	+	3.10707i
$372$		0			0
$373$	−23.0493	−	6.17604i	−1.19345	−	0.319783i	−0.393200	−	0.919453i	$-0.628632\pi$
$373$	−23.0493	−	6.17604i	−1.19345	−	0.319783i	−0.800248	+	0.599670i	$0.795299\pi$
$374$		0			0
$375$	−28.2079	+	13.8154i	−1.45665	+	0.713426i
$376$		0			0
$377$	−7.18290	−	10.2582i	−0.369938	−	0.528326i
$378$		0			0
$379$	36.8691			1.89384			0.946918	−	0.321474i	$-0.104178\pi$
$379$	36.8691			1.89384			0.946918	+	0.321474i	$0.104178\pi$
$380$		0			0
$381$	42.5747			2.18117
$382$		0			0
$383$	3.36428	+	4.80470i	0.171907	+	0.245508i	0.895856	−	0.444345i	$-0.146564\pi$
$383$	3.36428	+	4.80470i	0.171907	+	0.245508i	−0.723949	+	0.689854i	$0.757675\pi$
$384$		0			0
$385$	12.0053	−	37.0176i	0.611847	−	1.88659i
$386$		0			0
$387$	5.57266	+	1.49319i	0.283274	+	0.0759031i
$388$		0			0
$389$	2.40116	−	6.59712i	0.121743	−	0.334487i	−0.863818	−	0.503803i	$-0.831934\pi$
$389$	2.40116	−	6.59712i	0.121743	−	0.334487i	0.985562	+	0.169316i	$0.0541558\pi$
$390$		0			0
$391$	7.05814	−	12.2251i	0.356945	−	0.618248i
$392$		0			0
$393$	2.42170	+	1.69569i	0.122159	+	0.0855364i
$394$		0			0
$395$	−3.77700	−	12.3298i	−0.190042	−	0.620381i
$396$		0			0
$397$	7.81017	−	16.7490i	0.391981	−	0.840607i	−0.606966	−	0.794728i	$-0.707613\pi$
$397$	7.81017	−	16.7490i	0.391981	−	0.840607i	0.998947	−	0.0458786i	$-0.0146087\pi$
$398$		0			0
$399$	−62.2998	−	1.05600i	−3.11889	−	0.0528660i
$400$		0			0
$401$	12.5239	+	34.4092i	0.625414	+	1.71831i	0.693329	+	0.720621i	$0.256143\pi$
$401$	12.5239	+	34.4092i	0.625414	+	1.71831i	−0.0679151	+	0.997691i	$0.521635\pi$
$402$		0			0
$403$	−2.26764	−	0.198393i	−0.112959	−	0.00988265i
$404$		0			0
$405$	−0.563584	−	0.129788i	−0.0280047	−	0.00644921i
$406$		0			0
$407$	−10.3095	+	2.76243i	−0.511024	+	0.136929i
$408$		0			0
$409$	−30.6038	−	11.1389i	−1.51326	−	0.550783i	−0.553808	−	0.832645i	$-0.686826\pi$
$409$	−30.6038	−	11.1389i	−1.51326	−	0.550783i	−0.959455	+	0.281862i	$0.909048\pi$
$410$		0			0
$411$	36.1360	−	20.8631i	1.78246	−	1.02910i
$412$		0			0
$413$	7.14897	−	0.625454i	0.351778	−	0.0307766i
$414$		0			0
$415$	−0.102169	−	0.479374i	−0.00501528	−	0.0235315i
$416$		0			0
$417$	11.1722	+	11.1722i	0.547104	+	0.547104i
$418$		0			0
$419$		−	6.65117i		−	0.324931i	−0.986714	−	0.162465i	$-0.948055\pi$
$419$		−	6.65117i		−	0.324931i	0.986714	−	0.162465i	$-0.0519446\pi$
$420$		0			0
$421$	−10.5514	−	1.86049i	−0.514243	−	0.0906749i	−0.0894963	−	0.995987i	$-0.528526\pi$
$421$	−10.5514	−	1.86049i	−0.514243	−	0.0906749i	−0.424747	+	0.905312i	$0.639637\pi$
$422$		0			0
$423$	−1.33463	−	15.2549i	−0.0648921	−	0.741721i
$424$		0			0
$425$	15.1627	+	27.2836i	0.735498	+	1.32345i
$426$		0			0
$427$	−53.2440	+	24.8281i	−2.57666	+	1.20151i
$428$		0			0
$429$	−17.7626	−	10.2552i	−0.857585	−	0.495127i
$430$		0			0
$431$	27.1926	−	4.79479i	1.30982	−	0.230957i	0.525225	−	0.850963i	$-0.323981\pi$
$431$	27.1926	−	4.79479i	1.30982	−	0.230957i	0.784597	+	0.620006i	$0.212870\pi$
$432$		0			0
$433$	2.80661	−	32.0797i	0.134877	−	1.54165i	−0.563616	−	0.826037i	$-0.690590\pi$
$433$	2.80661	−	32.0797i	0.134877	−	1.54165i	0.698493	−	0.715616i	$-0.253854\pi$
$434$		0			0
$435$	24.6762	+	27.3754i	1.18313	+	1.31255i
$436$		0			0
$437$	−4.31631	+	8.86110i	−0.206477	+	0.423884i
$438$		0			0
$439$	−16.0863	+	5.85492i	−0.767756	+	0.279440i	−0.696057	−	0.717986i	$-0.745064\pi$
$439$	−16.0863	+	5.85492i	−0.767756	+	0.279440i	−0.0716983	+	0.997426i	$0.522842\pi$
$440$		0			0
$441$	−70.7968	+	59.4055i	−3.37127	+	2.82884i
$442$		0			0
$443$	14.2838	−	20.3994i	0.678643	−	0.969203i	−0.321111	−	0.947042i	$-0.604056\pi$
$443$	14.2838	−	20.3994i	0.678643	−	0.969203i	0.999754	−	0.0221615i	$-0.00705480\pi$
$444$		0			0
$445$	−21.6596	−	28.7105i	−1.02676	−	1.36101i
$446$		0			0
$447$	−17.1806	−	36.8440i	−0.812616	−	1.74266i
$448$		0			0
$449$	12.4835	+	21.6220i	0.589131	+	1.02041i	0.994347	+	0.106184i	$0.0338632\pi$
$449$	12.4835	+	21.6220i	0.589131	+	1.02041i	−0.405215	+	0.914221i	$0.632803\pi$
$450$		0			0
$451$	−5.12602	+	6.10896i	−0.241375	+	0.287659i
$452$		0			0
$453$	24.6153	−	17.2358i	1.15653	−	0.809810i
$454$		0			0
$455$	22.3602	+	9.47687i	1.04826	+	0.444283i
$456$		0			0
$457$	−0.449839	+	0.449839i	−0.0210426	+	0.0210426i	−0.717550	−	0.696507i	$-0.754736\pi$
$457$	−0.449839	+	0.449839i	−0.0210426	+	0.0210426i	0.696507	+	0.717550i	$0.254736\pi$
$458$		0			0
$459$	−5.76334	+	32.6855i	−0.269010	+	1.52563i
$460$		0			0
$461$	12.3104	+	10.3297i	0.573353	+	0.481101i	0.882757	−	0.469830i	$-0.155685\pi$
$461$	12.3104	+	10.3297i	0.573353	+	0.481101i	−0.309403	+	0.950931i	$0.600129\pi$
$462$		0			0
$463$	−5.79341	+	21.6213i	−0.269243	+	1.00483i	0.690359	+	0.723467i	$0.257453\pi$
$463$	−5.79341	+	21.6213i	−0.269243	+	1.00483i	−0.959602	+	0.281361i	$0.909214\pi$
$464$		0			0
$465$	6.69500	−	0.237472i	0.310473	−	0.0110125i
$466$		0			0
$467$	−7.20514	−	26.8899i	−0.333414	−	1.24432i	−0.905578	−	0.424179i	$-0.860563\pi$
$467$	−7.20514	−	26.8899i	−0.333414	−	1.24432i	0.572165	−	0.820139i	$-0.306104\pi$
$468$		0			0
$469$	4.87562	+	27.6510i	0.225135	+	1.27681i
$470$		0			0
$471$	−21.4482	−	25.5609i	−0.988280	−	1.17779i
$472$		0			0
$473$	−3.65546	−	1.70457i	−0.168078	−	0.0783761i
$474$		0			0
$475$	−11.8994	−	18.2594i	−0.545982	−	0.837797i
$476$		0			0
$477$	−55.4992	−	25.8797i	−2.54113	−	1.18495i
$478$		0			0
$479$	13.5112	+	16.1020i	0.617340	+	0.735718i	0.980611	−	0.195966i	$-0.0627843\pi$
$479$	13.5112	+	16.1020i	0.617340	+	0.735718i	−0.363270	+	0.931684i	$0.618340\pi$
$480$		0			0
$481$	−1.15662	−	6.55950i	−0.0527372	−	0.299087i
$482$		0			0
$483$	8.36590	+	31.2220i	0.380661	+	1.42065i
$484$		0			0
$485$	31.6558	−	1.12283i	1.43742	−	0.0509851i
$486$		0			0
$487$	8.79135	−	32.8098i	0.398374	−	1.48675i	−0.417583	−	0.908639i	$-0.637123\pi$
$487$	8.79135	−	32.8098i	0.398374	−	1.48675i	0.815957	−	0.578113i	$-0.196211\pi$
$488$		0			0
$489$	6.88952	+	5.78099i	0.311555	+	0.261426i
$490$		0			0
$491$	−0.327892	+	1.85957i	−0.0147975	+	0.0839210i	−0.991312	−	0.131530i	$-0.958011\pi$
$491$	−0.327892	+	1.85957i	−0.0147975	+	0.0839210i	0.976515	+	0.215451i	$0.0691222\pi$
$492$		0			0
$493$	25.8984	−	25.8984i	1.16641	−	1.16641i
$494$		0			0
$495$	34.4517	+	14.6016i	1.54849	+	0.656292i
$496$		0			0
$497$	−14.7541	+	10.3310i	−0.661814	+	0.463407i
$498$		0			0
$499$	8.60591	−	10.2561i	0.385254	−	0.459127i	−0.538211	−	0.842810i	$-0.680900\pi$
$499$	8.60591	−	10.2561i	0.385254	−	0.459127i	0.923465	+	0.383682i	$0.125344\pi$
$500$		0			0
$501$	1.96587	+	3.40498i	0.0878285	+	0.152123i
$502$		0			0
$503$	−14.6602	−	31.4389i	−0.653667	−	1.40179i	−0.901410	−	0.432967i	$-0.857467\pi$
$503$	−14.6602	−	31.4389i	−0.653667	−	1.40179i	0.247743	−	0.968826i	$-0.420311\pi$
$504$		0			0
$505$	−16.3541	−	21.6779i	−0.727748	−	0.964653i
$506$		0			0
$507$	−13.6063	+	19.4318i	−0.604276	+	0.862996i
$508$		0			0
$509$	1.65253	−	1.38664i	0.0732471	−	0.0614616i	−0.605429	−	0.795899i	$-0.706998\pi$
$509$	1.65253	−	1.38664i	0.0732471	−	0.0614616i	0.678676	+	0.734438i	$0.262554\pi$
$510$		0			0
$511$	−9.39914	+	3.42101i	−0.415794	+	0.151336i
$512$		0			0
$513$	2.41073	−	23.0484i	0.106436	−	1.01761i
$514$		0			0
$515$	−24.5969	−	27.2875i	−1.08387	−	1.20243i
$516$		0			0
$517$	−0.933060	+	10.6649i	−0.0410359	+	0.469043i
$518$		0			0
$519$	54.2493	−	9.56561i	2.38128	−	0.419884i
$520$		0			0
$521$	1.56446	+	0.903239i	0.0685401	+	0.0395716i	0.533878	−	0.845561i	$-0.320734\pi$
$521$	1.56446	+	0.903239i	0.0685401	+	0.0395716i	−0.465338	+	0.885133i	$0.654067\pi$
$522$		0			0
$523$	4.32062	−	2.01474i	0.188928	−	0.0880984i	−0.325853	−	0.945421i	$-0.605651\pi$
$523$	4.32062	−	2.01474i	0.188928	−	0.0880984i	0.514780	+	0.857322i	$0.327874\pi$
$524$		0			0
$525$	−68.7259	−	19.6253i	−2.99944	−	0.856517i
$526$		0			0
$527$	−0.580237	−	6.63214i	−0.0252755	−	0.288901i
$528$		0			0
$529$	−17.6151	−	3.10602i	−0.765875	−	0.135044i
$530$		0			0
$531$			6.90014i			0.299441i
$532$		0			0
$533$	−3.51902	−	3.51902i	−0.152426	−	0.152426i
$534$		0			0
$535$	−1.90675	−	8.94641i	−0.0824359	−	0.386787i
$536$		0			0
$537$	29.0443	−	2.54104i	1.25335	−	0.109654i
$538$		0			0
$539$	55.9548	−	32.3055i	2.41014	−	1.39150i
$540$		0			0
$541$	−15.3734	−	5.59548i	−0.660956	−	0.240568i	−0.0103070	−	0.999947i	$-0.503281\pi$
$541$	−15.3734	−	5.59548i	−0.660956	−	0.240568i	−0.650649	+	0.759379i	$0.725503\pi$
$542$		0			0
$543$	−2.33331	+	0.625210i	−0.100132	+	0.0268303i
$544$		0			0
$545$	2.92172	+	0.672843i	0.125153	+	0.0288214i
$546$		0			0
$547$	2.89754	+	0.253502i	0.123890	+	0.0108390i	0.148932	−	0.988847i	$-0.452416\pi$
$547$	2.89754	+	0.253502i	0.123890	+	0.0108390i	−0.0250420	+	0.999686i	$0.507972\pi$
$548$		0			0
$549$	−19.3199	−	53.0810i	−0.824554	−	2.26544i
$550$		0			0
$551$	−16.7679	+	19.3089i	−0.714337	+	0.822589i
$552$		0			0
$553$	12.4012	−	26.5945i	0.527353	−	1.13091i
$554$		0			0
$555$	5.74152	+	18.7429i	0.243714	+	0.795591i
$556$		0			0
$557$	−16.9680	−	11.8811i	−0.718959	−	0.503420i	0.155916	−	0.987770i	$-0.450167\pi$
$557$	−16.9680	−	11.8811i	−0.718959	−	0.503420i	−0.874874	+	0.484350i	$0.839056\pi$
$558$		0			0
$559$	1.25852	−	2.17982i	0.0532298	−	0.0921966i
$560$		0			0
$561$	20.5166	−	56.3690i	0.866213	−	2.37990i
$562$		0			0
$563$	−13.2883	−	3.56059i	−0.560035	−	0.150061i	−0.0323123	−	0.999478i	$-0.510287\pi$
$563$	−13.2883	−	3.56059i	−0.560035	−	0.150061i	−0.527722	+	0.849417i	$0.676954\pi$
$564$		0			0
$565$	1.46318	−	4.51164i	0.0615566	−	0.189806i
$566$		0			0
$567$	−0.754836	−	1.07802i	−0.0317001	−	0.0452725i
$568$		0			0
$569$	20.1440			0.844479			0.422239	−	0.906484i	$-0.361244\pi$
$569$	20.1440			0.844479			0.422239	+	0.906484i	$0.361244\pi$
$570$		0			0
$571$	−22.1344			−0.926295			−0.463148	−	0.886281i	$-0.653280\pi$
$571$	−22.1344			−0.926295			−0.463148	+	0.886281i	$0.653280\pi$
$572$		0			0
$573$	19.9056	+	28.4282i	0.831569	+	1.18760i
$574$		0			0
$575$	−7.40812	+	8.54097i	−0.308940	+	0.356183i
$576$		0			0
$577$	8.47640	+	2.27124i	0.352877	+	0.0945531i	0.430903	−	0.902398i	$-0.358195\pi$
$577$	8.47640	+	2.27124i	0.352877	+	0.0945531i	−0.0780261	+	0.996951i	$0.524862\pi$
$578$		0			0
$579$	24.1474	−	66.3443i	1.00353	−	2.75718i
$580$		0			0
$581$	0.557664	−	0.965902i	0.0231358	−	0.0400724i
$582$		0			0
$583$	35.0689	+	24.5555i	1.45241	+	1.01699i
$584$		0			0
$585$	−10.9514	+	20.6238i	−0.452783	+	0.852689i
$586$		0			0
$587$	−1.32881	+	2.84965i	−0.0548460	+	0.117618i	−0.931821	−	0.362919i	$-0.881780\pi$
$587$	−1.32881	+	2.84965i	−0.0548460	+	0.117618i	0.876975	+	0.480536i	$0.159558\pi$
$588$		0			0
$589$	0.729498	+	4.59087i	0.0300584	+	0.189164i
$590$		0			0
$591$	−2.72175	−	7.47795i	−0.111958	−	0.307602i
$592$		0			0
$593$	20.9146	+	1.82979i	0.858861	+	0.0751406i	0.508073	−	0.861314i	$-0.330358\pi$
$593$	20.9146	+	1.82979i	0.858861	+	0.0751406i	0.350788	+	0.936455i	$0.385914\pi$
$594$		0			0
$595$	−15.9398	+	69.2161i	−0.653468	+	2.83758i
$596$		0			0
$597$	29.3218	−	7.85675i	1.20006	−	0.321555i
$598$		0			0
$599$	7.54429	+	2.74590i	0.308252	+	0.112194i	0.491514	−	0.870870i	$-0.336444\pi$
$599$	7.54429	+	2.74590i	0.308252	+	0.112194i	−0.183263	+	0.983064i	$0.558666\pi$
$600$		0			0
$601$	24.2230	−	13.9851i	0.988075	−	0.570466i	0.0833769	−	0.996518i	$-0.473429\pi$
$601$	24.2230	−	13.9851i	0.988075	−	0.570466i	0.904698	+	0.426053i	$0.140096\pi$
$602$		0			0
$603$	−26.8944	+	2.35296i	−1.09523	+	0.0958199i
$604$		0			0
$605$	−1.31115	−	0.850448i	−0.0533058	−	0.0345756i
$606$		0			0
$607$	−25.5906	−	25.5906i	−1.03869	−	1.03869i	−0.999221	−	0.0394685i	$-0.987434\pi$
$607$	−25.5906	−	25.5906i	−1.03869	−	1.03869i	−0.0394685	−	0.999221i	$-0.512566\pi$
$608$		0			0
$609$			83.8656i			3.39841i
$610$		0			0
$611$	−6.57945	−	1.16013i	−0.266176	−	0.0469340i
$612$		0			0
$613$	0.797871	+	9.11970i	0.0322257	+	0.368341i	0.995135	+	0.0985173i	$0.0314100\pi$
$613$	0.797871	+	9.11970i	0.0322257	+	0.368341i	−0.962910	+	0.269824i	$0.913034\pi$
$614$		0			0
$615$	11.5465	+	9.01089i	0.465598	+	0.363354i
$616$		0			0
$617$	0.712827	−	0.332397i	0.0286973	−	0.0133818i	−0.408217	−	0.912885i	$-0.633849\pi$
$617$	0.712827	−	0.332397i	0.0286973	−	0.0133818i	0.436914	+	0.899503i	$0.356071\pi$
$618$		0			0
$619$	−11.9011	−	6.87112i	−0.478347	−	0.276174i	0.241380	−	0.970431i	$-0.422400\pi$
$619$	−11.9011	−	6.87112i	−0.478347	−	0.276174i	−0.719727	+	0.694257i	$0.755733\pi$
$620$		0			0
$621$	−11.8392	+	2.08757i	−0.475091	+	0.0837714i
$622$		0			0
$623$	7.13263	−	81.5264i	0.285763	−	3.26628i
$624$		0			0
$625$	−7.77758	−	23.7594i	−0.311103	−	0.950376i
$626$		0			0
$627$	−11.5247	+	40.2680i	−0.460251	+	1.60815i
$628$		0			0
$629$	18.3056	−	6.66270i	0.729893	−	0.265659i
$630$		0			0
$631$	6.05675	−	5.08222i	0.241115	−	0.202320i	−0.514220	−	0.857658i	$-0.671918\pi$
$631$	6.05675	−	5.08222i	0.241115	−	0.202320i	0.755335	+	0.655339i	$0.227474\pi$
$632$		0			0
$633$	18.4530	−	26.3536i	0.733440	−	1.04746i
$634$		0			0
$635$	−4.69773	+	33.5597i	−0.186424	+	1.33177i
$636$		0			0
$637$	17.0404	+	36.5432i	0.675164	+	1.44789i
$638$		0			0
$639$	−8.65921	−	14.9982i	−0.342553	−	0.593319i
$640$		0			0
$641$	−6.04488	+	7.20401i	−0.238758	+	0.284541i	−0.872096	−	0.489334i	$-0.837240\pi$
$641$	−6.04488	+	7.20401i	−0.238758	+	0.284541i	0.633338	+	0.773875i	$0.281684\pi$
$642$		0			0
$643$	−19.4660	+	13.6303i	−0.767666	+	0.537525i	−0.890544	−	0.454896i	$-0.849676\pi$
$643$	−19.4660	+	13.6303i	−0.767666	+	0.537525i	0.122879	+	0.992422i	$0.460787\pi$
$644$		0			0
$645$	−2.89068	+	6.82042i	−0.113821	+	0.268554i
$646$		0			0
$647$	24.9929	−	24.9929i	0.982571	−	0.982571i	−0.0172799	−	0.999851i	$-0.505501\pi$
$647$	24.9929	−	24.9929i	0.982571	−	0.982571i	0.999851	+	0.0172799i	$0.00550063\pi$
$648$		0			0
$649$	0.837675	−	4.75069i	0.0328816	−	0.186481i
$650$		0			0
$651$	11.6778	+	9.79881i	0.457688	+	0.384045i
$652$		0			0
$653$	−1.60286	+	5.98196i	−0.0627248	+	0.234092i	−0.990170	−	0.139866i	$-0.955333\pi$
$653$	−1.60286	+	5.98196i	−0.0627248	+	0.234092i	0.927446	+	0.373958i	$0.122000\pi$
$654$		0			0
$655$	−1.60385	+	1.72181i	−0.0626675	+	0.0672767i
$656$		0			0
$657$	−2.48919	−	9.28977i	−0.0971124	−	0.362428i
$658$		0			0
$659$	−4.09855	−	23.2441i	−0.159657	−	0.905460i	−0.954404	−	0.298519i	$-0.903507\pi$
$659$	−4.09855	−	23.2441i	−0.159657	−	0.905460i	0.794747	−	0.606941i	$-0.207604\pi$
$660$		0			0
$661$	12.7152	+	15.1534i	0.494566	+	0.589401i	0.954373	−	0.298618i	$-0.0965258\pi$
$661$	12.7152	+	15.1534i	0.494566	+	0.589401i	−0.459807	+	0.888019i	$0.652081\pi$
$662$		0			0
$663$	33.9277	+	15.8208i	1.31764	+	0.614427i
$664$		0			0
$665$	7.70661	−	48.9915i	0.298849	−	1.89981i
$666$		0			0
$667$	12.0235	+	5.60665i	0.465552	+	0.217090i
$668$		0			0
$669$	−13.2630	−	15.8063i	−0.512779	−	0.611106i
$670$		0			0
$671$	6.85758	+	38.8913i	0.264734	+	1.50138i
$672$		0			0
$673$	−4.86798	−	18.1676i	−0.187647	−	0.700308i	−0.994048	−	0.108940i	$-0.965255\pi$
$673$	−4.86798	−	18.1676i	−0.187647	−	0.700308i	0.806401	−	0.591369i	$-0.201412\pi$
$674$		0			0
$675$	9.49912	−	24.8274i	0.365621	−	0.955608i
$676$		0			0
$677$	−10.0879	+	37.6486i	−0.387710	+	1.44695i	0.446141	+	0.894963i	$0.352798\pi$
$677$	−10.0879	+	37.6486i	−0.387710	+	1.44695i	−0.833850	+	0.551990i	$0.813869\pi$
$678$		0			0
$679$	55.2156	+	46.3314i	2.11898	+	1.77804i
$680$		0			0
$681$	−11.9789	+	67.9357i	−0.459032	+	2.60330i
$682$		0			0
$683$	18.0735	−	18.0735i	0.691562	−	0.691562i	−0.271013	−	0.962576i	$-0.587359\pi$
$683$	18.0735	−	18.0735i	0.691562	−	0.691562i	0.962576	+	0.271013i	$0.0873588\pi$
$684$		0			0
$685$	12.4581	+	30.7864i	0.476001	+	1.17629i
$686$		0			0
$687$	−53.0066	+	37.1156i	−2.02233	+	1.41605i
$688$		0			0
$689$	−17.1731	+	20.4662i	−0.654245	+	0.779699i
$690$		0			0
$691$	0.633938	+	1.09801i	0.0241161	+	0.0417704i	0.877832	−	0.478969i	$-0.158990\pi$
$691$	0.633938	+	1.09801i	0.0241161	+	0.0417704i	−0.853715	+	0.520740i	$0.825656\pi$
$692$		0			0
$693$	35.9843	+	77.1686i	1.36693	+	2.93139i
$694$		0			0
$695$	−10.0392	+	7.57375i	−0.380810	+	0.287289i
$696$		0			0
$697$	8.34849	−	11.9229i	0.316222	−	0.451611i
$698$		0			0
$699$	−19.9643	+	16.7520i	−0.755117	+	0.633619i
$700$		0			0
$701$	−37.4222	+	13.6206i	−1.41342	+	0.514441i	−0.932130	−	0.362123i	$-0.882052\pi$
$701$	−37.4222	+	13.6206i	−1.41342	+	0.514441i	−0.481285	+	0.876564i	$0.659830\pi$
$702$		0			0
$703$	−12.4231	+	5.53866i	−0.468548	+	0.208894i
$704$		0			0
$705$	19.6358	+	1.01827i	0.739527	+	0.0383502i
$706$		0			0
$707$	5.38549	−	61.5565i	0.202542	−	2.31507i
$708$		0			0
$709$	−37.2819	+	6.57380i	−1.40015	+	0.246884i	−0.822205	−	0.569192i	$-0.807256\pi$
$709$	−37.2819	+	6.57380i	−1.40015	+	0.246884i	−0.577945	+	0.816076i	$0.696145\pi$
$710$		0			0
$711$	24.4346	+	14.1073i	0.916368	+	0.529065i
$712$		0			0
$713$	2.18551	−	1.01912i	0.0818480	−	0.0381663i
$714$		0			0
$715$	10.0436	−	12.8698i	0.375611	−	0.481304i
$716$		0			0
$717$	−0.401112	−	4.58473i	−0.0149798	−	0.171220i
$718$		0			0
$719$	15.7089	+	2.76990i	0.585842	+	0.103300i	0.458710	−	0.888586i	$-0.348312\pi$
$719$	15.7089	+	2.76990i	0.585842	+	0.103300i	0.127132	+	0.991886i	$0.459423\pi$
$720$		0			0
$721$		−	83.5963i		−	3.11329i
$722$		0			0
$723$	−39.2881	−	39.2881i	−1.46114	−	1.46114i
$724$		0			0
$725$	−24.3016	+	16.4304i	−0.902537	+	0.610211i
$726$		0			0
$727$	10.6694	−	0.933450i	0.395705	−	0.0346197i	0.112433	−	0.993659i	$-0.464136\pi$
$727$	10.6694	−	0.933450i	0.395705	−	0.0346197i	0.283272	+	0.959040i	$0.408580\pi$
$728$		0			0
$729$	−37.7089	+	21.7712i	−1.39663	+	0.806342i
$730$		0			0
$731$	6.91760	+	2.51780i	0.255857	+	0.0931243i
$732$		0			0
$733$	−4.08675	+	1.09504i	−0.150948	+	0.0404463i	−0.333502	−	0.942750i	$-0.608230\pi$
$733$	−4.08675	+	1.09504i	−0.150948	+	0.0404463i	0.182554	+	0.983196i	$0.441564\pi$
$734$		0			0
$735$	−62.9384	−	100.600i	−2.32152	−	3.71067i
$736$		0			0
$737$	18.8023	+	1.64498i	0.692590	+	0.0605938i
$738$		0			0
$739$	−10.5906	−	29.0974i	−0.389581	−	1.07037i	−0.967190	−	0.254052i	$-0.918236\pi$
$739$	−10.5906	−	29.0974i	−0.389581	−	1.07037i	0.577609	−	0.816313i	$-0.303986\pi$
$740$		0			0
$741$	−24.4070	−	9.35486i	−0.896615	−	0.343659i
$742$		0			0
$743$	−11.6395	+	24.9609i	−0.427011	+	0.915728i	0.568642	+	0.822585i	$0.307469\pi$
$743$	−11.6395	+	24.9609i	−0.427011	+	0.915728i	−0.995653	+	0.0931428i	$0.970309\pi$
$744$		0			0
$745$	30.9381	−	9.47729i	1.13349	−	0.347221i
$746$		0			0
$747$	0.878467	+	0.615109i	0.0321414	+	0.0225057i
$748$		0			0
$749$	10.4075	−	18.0263i	0.380282	−	0.658668i
$750$		0			0
$751$	0.801864	−	2.20310i	0.0292604	−	0.0803924i	−0.924202	−	0.381903i	$-0.875269\pi$
$751$	0.801864	−	2.20310i	0.0292604	−	0.0803924i	0.953463	+	0.301511i	$0.0974910\pi$
$752$		0			0
$753$	−27.9385	−	7.48609i	−1.01813	−	0.272808i
$754$		0			0
$755$	10.8701	+	21.3049i	0.395604	+	0.775366i
$756$		0			0
$757$	−19.3741	−	27.6691i	−0.704163	−	1.00565i	−0.998748	−	0.0500237i	$-0.984070\pi$
$757$	−19.3741	−	27.6691i	−0.704163	−	1.00565i	0.294585	−	0.955625i	$-0.404819\pi$
$758$		0			0
$759$	21.7281			0.788681
$760$		0			0
$761$	−40.7538			−1.47733			−0.738663	−	0.674075i	$-0.764542\pi$
$761$	−40.7538			−1.47733			−0.738663	+	0.674075i	$0.764542\pi$
$762$		0			0
$763$	3.91320	+	5.58863i	0.141667	+	0.202322i
$764$		0			0
$765$	−64.9636	−	21.0686i	−2.34877	−	0.761736i
$766$		0			0
$767$	2.90786	+	0.779158i	0.104997	+	0.0281338i
$768$		0			0
$769$	3.46321	−	9.51510i	0.124887	−	0.343123i	−0.861455	−	0.507833i	$-0.830447\pi$
$769$	3.46321	−	9.51510i	0.124887	−	0.343123i	0.986342	+	0.164710i	$0.0526688\pi$
$770$		0			0
$771$	−8.31403	+	14.4003i	−0.299422	+	0.518615i
$772$		0			0
$773$	4.12919	+	2.89129i	0.148517	+	0.103992i	0.645473	−	0.763783i	$-0.276660\pi$
$773$	4.12919	+	2.89129i	0.148517	+	0.103992i	−0.496956	+	0.867775i	$0.665549\pi$
$774$		0			0
$775$	−0.551544	+	5.30356i	−0.0198121	+	0.190509i
$776$		0			0
$777$	−18.8514	+	40.4269i	−0.676289	+	1.45031i
$778$		0			0
$779$	−5.22988	+	8.71393i	−0.187380	+	0.312209i
$780$		0			0
$781$	4.14102	+	11.3774i	0.148177	+	0.407114i
$782$		0			0
$783$	−31.0730	−	2.71853i	−1.11046	−	0.0971525i
$784$		0			0
$785$	22.5151	−	14.0862i	0.803598	−	0.502757i
$786$		0			0
$787$	43.7226	−	11.7154i	1.55854	−	0.417611i	0.626342	−	0.779549i	$-0.284551\pi$
$787$	43.7226	−	11.7154i	1.55854	−	0.417611i	0.932202	+	0.361938i	$0.117885\pi$
$788$		0			0
$789$	14.5608	+	5.29970i	0.518379	+	0.188674i
$790$		0			0
$791$	9.34680	−	5.39638i	0.332334	−	0.191873i

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)

\(f(q)\)	\(=\)	\(q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +O(q^{10})\)	\(q+(-1.61138 - 2.30128i) q^{3} +(1.99179 - 1.01625i) q^{5} +(4.91485 + 1.31693i) q^{7} +(-1.67331 + 4.59739i) q^{9} +(1.71018 - 2.96212i) q^{11} +(1.74848 + 1.22430i) q^{13} +(-5.54820 - 2.94613i) q^{15} +(-2.63830 + 5.65786i) q^{17} +(1.56004 - 4.07017i) q^{19} +(-4.88905 - 13.4325i) q^{21} +(-2.25262 - 0.197079i) q^{23} +(2.93449 - 4.04831i) q^{25} +(5.13536 - 1.37602i) q^{27} +(-5.51312 - 2.00661i) q^{29} +(-0.923557 + 0.533216i) q^{31} +(-9.57244 + 0.837480i) q^{33} +(11.1277 - 2.37165i) q^{35} +(-2.20652 - 2.20652i) q^{37} -5.99656i q^{39} +(-2.29610 - 0.404865i) q^{41} +(-0.102775 - 1.17473i) q^{43} +(1.33919 + 10.8575i) q^{45} +(-2.83672 + 1.32278i) q^{47} +(16.3593 + 9.44505i) q^{49} +(17.2716 - 3.04546i) q^{51} +(-1.09089 + 12.4689i) q^{53} +(0.396085 - 7.63791i) q^{55} +(-11.8804 + 2.96849i) q^{57} +(1.32531 - 0.482374i) q^{59} +(-8.84468 + 7.42157i) q^{61} +(-14.2785 + 20.3919i) q^{63} +(4.72681 + 0.661666i) q^{65} +(2.33207 + 5.00114i) q^{67} +(3.17628 + 5.50149i) q^{69} +(-2.27536 + 2.71167i) q^{71} +(-1.61028 + 1.12753i) q^{73} +(-14.0449 - 0.229741i) q^{75} +(12.3062 - 12.3062i) q^{77} +(1.00143 - 5.67937i) q^{79} +(-0.198129 - 0.166250i) q^{81} +(0.0567325 - 0.211729i) q^{83} +(0.494822 + 13.9505i) q^{85} +(4.26593 + 15.9207i) q^{87} +(-2.79291 - 15.8394i) q^{89} +(6.98122 + 8.31989i) q^{91} +(2.71528 + 1.26616i) q^{93} +(-1.02903 - 9.69232i) q^{95} +(12.8386 + 5.98673i) q^{97} +(10.7564 + 12.8189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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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