LMFDB - Embedded newform 380.2.bh.a.33.7

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			33.7
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.377219 + 0.538725i) q^{3} +(2.02714 + 0.943776i) q^{5} +(1.97160 + 0.528288i) q^{7} +(0.878130 - 2.41264i) q^{9} +O(q^{10})$	\(q+(0.377219 + 0.538725i) q^{3} +(2.02714 + 0.943776i) q^{5} +(1.97160 + 0.528288i) q^{7} +(0.878130 - 2.41264i) q^{9} +(-0.906926 + 1.57084i) q^{11} +(-1.44805 - 1.01394i) q^{13} +(0.256239 + 1.44808i) q^{15} +(0.0577770 - 0.123903i) q^{17} +(-2.93922 + 3.21885i) q^{19} +(0.459122 + 1.26143i) q^{21} +(6.07446 + 0.531447i) q^{23} +(3.21857 + 3.82633i) q^{25} +(3.53675 - 0.947670i) q^{27} +(-3.14393 - 1.14430i) q^{29} +(0.680748 - 0.393030i) q^{31} +(-1.18836 + 0.103968i) q^{33} +(3.49811 + 2.93166i) q^{35} +(-4.83846 - 4.83846i) q^{37} -1.16258i q^{39} +(5.31428 + 0.937051i) q^{41} +(0.277984 + 3.17737i) q^{43} +(4.05709 - 4.06200i) q^{45} +(-5.00993 + 2.33617i) q^{47} +(-2.45407 - 1.41686i) q^{49} +(0.0885442 - 0.0156127i) q^{51} +(0.933570 - 10.6708i) q^{53} +(-3.32099 + 2.32838i) q^{55} +(-2.84280 - 0.369220i) q^{57} +(-8.38425 + 3.05162i) q^{59} +(-5.98020 + 5.01798i) q^{61} +(3.00589 - 4.29286i) q^{63} +(-1.97847 - 3.42202i) q^{65} +(-3.83106 - 8.21573i) q^{67} +(2.00510 + 3.47293i) q^{69} +(-1.87804 + 2.23816i) q^{71} +(2.70247 - 1.89229i) q^{73} +(-0.847230 + 3.17729i) q^{75} +(-2.61795 + 2.61795i) q^{77} +(-2.28065 + 12.9342i) q^{79} +(-4.05575 - 3.40318i) q^{81} +(4.13317 - 15.4252i) q^{83} +(0.234059 - 0.196640i) q^{85} +(-0.569489 - 2.12536i) q^{87} +(-1.72877 - 9.80435i) q^{89} +(-2.31932 - 2.76406i) q^{91} +(0.468526 + 0.218477i) q^{93} +(-8.99608 + 3.75108i) q^{95} +(-5.79625 - 2.70284i) q^{97} +(2.99348 + 3.56749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.377219	+	0.538725i	0.217787	+	0.311033i	0.913148	−	0.407628i	$-0.133644\pi$
$3$	0.377219	+	0.538725i	0.217787	+	0.311033i	−0.695360	+	0.718661i	$0.744755\pi$
$4$		0			0
$5$	2.02714	+	0.943776i	0.906563	+	0.422070i
$5$	2.02714	+	0.943776i	0.906563	+	0.422070i
$6$		0			0
$7$	1.97160	+	0.528288i	0.745194	+	0.199674i	0.611385	−	0.791333i	$-0.290613\pi$
$7$	1.97160	+	0.528288i	0.745194	+	0.199674i	0.133809	+	0.991007i	$0.457279\pi$
$8$		0			0
$9$	0.878130	−	2.41264i	0.292710	−	0.804215i
$10$		0			0
$11$	−0.906926	+	1.57084i	−0.273448	+	0.473626i	−0.969742	−	0.244130i	$-0.921498\pi$
$11$	−0.906926	+	1.57084i	−0.273448	+	0.473626i	0.696294	+	0.717757i	$0.254831\pi$
$12$		0			0
$13$	−1.44805	−	1.01394i	−0.401617	−	0.281215i	0.355267	−	0.934765i	$-0.384390\pi$
$13$	−1.44805	−	1.01394i	−0.401617	−	0.281215i	−0.756883	+	0.653550i	$0.773279\pi$
$14$		0			0
$15$	0.256239	+	1.44808i	0.0661607	+	0.373892i
$16$		0			0
$17$	0.0577770	−	0.123903i	0.0140130	−	0.0300509i	−0.899177	−	0.437586i	$-0.855834\pi$
$17$	0.0577770	−	0.123903i	0.0140130	−	0.0300509i	0.913190	+	0.407535i	$0.133611\pi$
$18$		0			0
$19$	−2.93922	+	3.21885i	−0.674304	+	0.738454i
$19$	−2.93922	+	3.21885i	−0.674304	+	0.738454i
$20$		0			0
$21$	0.459122	+	1.26143i	0.100189	+	0.275266i
$22$		0			0
$23$	6.07446	+	0.531447i	1.26661	+	0.110814i	0.700583	−	0.713571i	$-0.252923\pi$
$23$	6.07446	+	0.531447i	1.26661	+	0.110814i	0.566030	+	0.824385i	$0.308479\pi$
$24$		0			0
$25$	3.21857	+	3.82633i	0.643715	+	0.765266i
$26$		0			0
$27$	3.53675	−	0.947670i	0.680649	−	0.182379i
$28$		0			0
$29$	−3.14393	−	1.14430i	−0.583813	−	0.212491i	0.0331929	−	0.999449i	$-0.489432\pi$
$29$	−3.14393	−	1.14430i	−0.583813	−	0.212491i	−0.617006	+	0.786958i	$0.711655\pi$
$30$		0			0
$31$	0.680748	−	0.393030i	0.122266	−	0.0705903i	−0.437620	−	0.899160i	$-0.644178\pi$
$31$	0.680748	−	0.393030i	0.122266	−	0.0705903i	0.559886	+	0.828570i	$0.310845\pi$
$32$		0			0
$33$	−1.18836	+	0.103968i	−0.206867	+	0.0180985i
$34$		0			0
$35$	3.49811	+	2.93166i	0.591289	+	0.495541i
$36$		0			0
$37$	−4.83846	−	4.83846i	−0.795439	−	0.795439i	0.186934	−	0.982372i	$-0.440145\pi$
$37$	−4.83846	−	4.83846i	−0.795439	−	0.795439i	−0.982372	+	0.186934i	$0.940145\pi$
$38$		0			0
$39$		−	1.16258i		−	0.186161i
$40$		0			0
$41$	5.31428	+	0.937051i	0.829951	+	0.146343i	0.572455	−	0.819936i	$-0.305991\pi$
$41$	5.31428	+	0.937051i	0.829951	+	0.146343i	0.257497	+	0.966279i	$0.417102\pi$
$42$		0			0
$43$	0.277984	+	3.17737i	0.0423922	+	0.484545i	0.987482	+	0.157733i	$0.0504186\pi$
$43$	0.277984	+	3.17737i	0.0423922	+	0.484545i	−0.945090	+	0.326811i	$0.894026\pi$
$44$		0			0
$45$	4.05709	−	4.06200i	0.604795	−	0.605527i
$46$		0			0
$47$	−5.00993	+	2.33617i	−0.730773	+	0.340765i	−0.752137	−	0.659007i	$-0.770977\pi$
$47$	−5.00993	+	2.33617i	−0.730773	+	0.340765i	0.0213641	+	0.999772i	$0.493199\pi$
$48$		0			0
$49$	−2.45407	−	1.41686i	−0.350581	−	0.202408i
$50$		0			0
$51$	0.0885442	−	0.0156127i	0.0123987	−	0.00218622i
$52$		0			0
$53$	0.933570	−	10.6708i	0.128236	−	1.46574i	−0.610645	−	0.791905i	$-0.709090\pi$
$53$	0.933570	−	10.6708i	0.128236	−	1.46574i	0.738881	−	0.673836i	$-0.235355\pi$
$54$		0			0
$55$	−3.32099	+	2.32838i	−0.447802	+	0.313958i
$56$		0			0
$57$	−2.84280	−	0.369220i	−0.376538	−	0.0489044i
$58$		0			0
$59$	−8.38425	+	3.05162i	−1.09154	+	0.397287i	−0.824190	−	0.566314i	$-0.808369\pi$
$59$	−8.38425	+	3.05162i	−1.09154	+	0.397287i	−0.267346	+	0.963601i	$0.586147\pi$
$60$		0			0
$61$	−5.98020	+	5.01798i	−0.765686	+	0.642487i	−0.939600	−	0.342274i	$-0.888803\pi$
$61$	−5.98020	+	5.01798i	−0.765686	+	0.642487i	0.173914	+	0.984761i	$0.444359\pi$
$62$		0			0
$63$	3.00589	−	4.29286i	0.378707	−	0.540849i
$64$		0			0
$65$	−1.97847	−	3.42202i	−0.245399	−	0.424449i
$66$		0			0
$67$	−3.83106	−	8.21573i	−0.468038	−	1.00371i	−0.988694	−	0.149944i	$-0.952091\pi$
$67$	−3.83106	−	8.21573i	−0.468038	−	1.00371i	0.520657	−	0.853766i	$-0.325687\pi$
$68$		0			0
$69$	2.00510	+	3.47293i	0.241386	+	0.418092i
$70$		0			0
$71$	−1.87804	+	2.23816i	−0.222883	+	0.265621i	−0.865885	−	0.500243i	$-0.833244\pi$
$71$	−1.87804	+	2.23816i	−0.222883	+	0.265621i	0.643002	+	0.765864i	$0.277688\pi$
$72$		0			0
$73$	2.70247	−	1.89229i	0.316300	−	0.221476i	−0.404635	−	0.914478i	$-0.632601\pi$
$73$	2.70247	−	1.89229i	0.316300	−	0.221476i	0.720935	+	0.693003i	$0.243713\pi$
$74$		0			0
$75$	−0.847230	+	3.17729i	−0.0978297	+	0.366882i
$76$		0			0
$77$	−2.61795	+	2.61795i	−0.298343	+	0.298343i
$78$		0			0
$79$	−2.28065	+	12.9342i	−0.256593	+	1.45521i	0.535357	+	0.844626i	$0.320177\pi$
$79$	−2.28065	+	12.9342i	−0.256593	+	1.45521i	−0.791950	+	0.610586i	$0.790934\pi$
$80$		0			0
$81$	−4.05575	−	3.40318i	−0.450639	−	0.378131i
$82$		0			0
$83$	4.13317	−	15.4252i	0.453674	−	1.69313i	−0.238284	−	0.971196i	$-0.576585\pi$
$83$	4.13317	−	15.4252i	0.453674	−	1.69313i	0.691957	−	0.721938i	$-0.256749\pi$
$84$		0			0
$85$	0.234059	−	0.196640i	0.0253872	−	0.0213286i
$86$		0			0
$87$	−0.569489	−	2.12536i	−0.0610557	−	0.227863i
$88$		0			0
$89$	−1.72877	−	9.80435i	−0.183249	−	1.03926i	−0.928184	−	0.372121i	$-0.878631\pi$
$89$	−1.72877	−	9.80435i	−0.183249	−	1.03926i	0.744935	−	0.667137i	$-0.232481\pi$
$90$		0			0
$91$	−2.31932	−	2.76406i	−0.243131	−	0.289752i
$92$		0			0
$93$	0.468526	+	0.218477i	0.0485839	+	0.0226550i
$94$		0			0
$95$	−8.99608	+	3.75108i	−0.922978	+	0.384853i
$96$		0			0
$97$	−5.79625	−	2.70284i	−0.588520	−	0.274431i	0.105462	−	0.994423i	$-0.466368\pi$
$97$	−5.79625	−	2.70284i	−0.588520	−	0.274431i	−0.693982	+	0.719992i	$0.744145\pi$
$98$		0			0
$99$	2.99348	+	3.56749i	0.300856	+	0.358546i
$100$		0			0
$101$	−0.454754	−	2.57904i	−0.0452497	−	0.256624i	0.953788	−	0.300480i	$-0.0971469\pi$
$101$	−0.454754	−	2.57904i	−0.0452497	−	0.256624i	−0.999038	+	0.0438559i	$0.986036\pi$
$102$		0			0
$103$	−0.187345	−	0.699181i	−0.0184596	−	0.0688923i	0.956082	−	0.293101i	$-0.0946871\pi$
$103$	−0.187345	−	0.699181i	−0.0184596	−	0.0688923i	−0.974541	+	0.224208i	$0.928020\pi$
$104$		0			0
$105$	−0.259802	+	2.99040i	−0.0253541	+	0.291833i
$106$		0			0
$107$	−1.34364	+	5.01454i	−0.129895	+	0.484774i	−0.999967	−	0.00815086i	$-0.997405\pi$
$107$	−1.34364	+	5.01454i	−0.129895	+	0.484774i	0.870072	+	0.492925i	$0.164072\pi$
$108$		0			0
$109$	−10.4748	−	8.78943i	−1.00331	−	0.841875i	−0.0158679	−	0.999874i	$-0.505051\pi$
$109$	−10.4748	−	8.78943i	−1.00331	−	0.841875i	−0.987439	+	0.157999i	$0.949496\pi$
$110$		0			0
$111$	0.781439	−	4.43176i	0.0741709	−	0.420644i
$112$		0			0
$113$	8.31069	−	8.31069i	0.781804	−	0.781804i	−0.198331	−	0.980135i	$-0.563552\pi$
$113$	8.31069	−	8.31069i	0.781804	−	0.781804i	0.980135	+	0.198331i	$0.0635522\pi$
$114$		0			0
$115$	11.8122	+	6.81025i	1.10149	+	0.635059i
$116$		0			0
$117$	−3.71784	+	2.60326i	−0.343714	+	0.240671i
$118$		0			0
$119$	0.179370	−	0.213764i	0.0164428	−	0.0195957i
$120$		0			0
$121$	3.85497	+	6.67701i	0.350452	+	0.607001i
$122$		0			0
$123$	1.49984	+	3.21641i	0.135236	+	0.290014i
$124$		0			0
$125$	2.91329	+	10.7941i	0.260573	+	0.965454i
$126$		0			0
$127$	−0.391459	+	0.559061i	−0.0347363	+	0.0496086i	−0.836145	−	0.548509i	$-0.815196\pi$
$127$	−0.391459	+	0.559061i	−0.0347363	+	0.0496086i	0.801408	+	0.598118i	$0.204084\pi$
$128$		0			0
$129$	−1.60687	+	1.34832i	−0.141477	+	0.118713i
$130$		0			0
$131$	−2.88051	+	1.04842i	−0.251671	+	0.0916007i	−0.464775	−	0.885429i	$-0.653865\pi$
$131$	−2.88051	+	1.04842i	−0.251671	+	0.0916007i	0.213104	+	0.977029i	$0.431643\pi$
$132$		0			0
$133$	−7.49544	+	4.79352i	−0.649937	+	0.415651i
$134$		0			0
$135$	8.06387	+	1.41685i	0.694028	+	0.121943i
$136$		0			0
$137$	0.652163	−	7.45426i	0.0557180	−	0.636860i	−0.916072	−	0.401013i	$-0.868658\pi$
$137$	0.652163	−	7.45426i	0.0557180	−	0.636860i	0.971790	−	0.235847i	$-0.0757863\pi$
$138$		0			0
$139$	−16.6418	+	2.93440i	−1.41154	+	0.248892i	−0.826876	−	0.562384i	$-0.809884\pi$
$139$	−16.6418	+	2.93440i	−1.41154	+	0.248892i	−0.584663	+	0.811276i	$0.698773\pi$
$140$		0			0
$141$	−3.14839	−	1.81772i	−0.265142	−	0.153080i
$142$		0			0
$143$	2.90600	−	1.35509i	0.243012	−	0.113318i
$144$		0			0
$145$	−5.29322	−	5.28682i	−0.439578	−	0.439046i
$146$		0			0
$147$	−0.162425	−	1.85653i	−0.0133966	−	0.153124i
$148$		0			0
$149$	17.2889	+	3.04850i	1.41636	+	0.249743i	0.828849	−	0.559473i	$-0.188996\pi$
$149$	17.2889	+	3.04850i	1.41636	+	0.249743i	0.587512	+	0.809216i	$0.300108\pi$
$150$		0			0
$151$			3.52091i			0.286528i	0.989685	+	0.143264i	$0.0457598\pi$
$151$			3.52091i			0.286528i	−0.989685	+	0.143264i	$0.954240\pi$
$152$		0			0
$153$	−0.248198	−	0.248198i	−0.0200657	−	0.0200657i
$154$		0			0
$155$	1.75090	−	0.154252i	0.140636	−	0.0123898i
$156$		0			0
$157$	−8.11439	+	0.709917i	−0.647599	+	0.0566576i	−0.406223	−	0.913774i	$-0.633154\pi$
$157$	−8.11439	+	0.709917i	−0.647599	+	0.0566576i	−0.241376	+	0.970432i	$0.577599\pi$
$158$		0			0
$159$	6.10076	−	3.52227i	0.483822	−	0.279335i
$160$		0			0
$161$	11.6956	+	4.25686i	0.921746	+	0.335488i
$162$		0			0
$163$	11.2866	−	3.02424i	0.884036	−	0.236877i	0.211889	−	0.977294i	$-0.432039\pi$
$163$	11.2866	−	3.02424i	0.884036	−	0.236877i	0.672148	+	0.740417i	$0.265372\pi$
$164$		0			0
$165$	−2.50709	−	0.910789i	−0.195177	−	0.0709048i
$166$		0			0
$167$	11.6099	+	1.01573i	0.898400	+	0.0785998i	0.526992	−	0.849870i	$-0.323320\pi$
$167$	11.6099	+	1.01573i	0.898400	+	0.0785998i	0.371408	+	0.928470i	$0.378875\pi$
$168$		0			0
$169$	−3.37748	−	9.27955i	−0.259806	−	0.713811i
$170$		0			0
$171$	5.18491	+	9.91786i	0.396500	+	0.758438i
$172$		0			0
$173$	−0.461058	+	0.988742i	−0.0350536	+	0.0751727i	−0.923055	−	0.384668i	$-0.874316\pi$
$173$	−0.461058	+	0.988742i	−0.0350536	+	0.0751727i	0.888001	+	0.459841i	$0.152094\pi$
$174$		0			0
$175$	4.32433	+	9.24431i	0.326888	+	0.698805i
$176$		0			0
$177$	−4.80668	−	3.36567i	−0.361292	−	0.252979i
$178$		0			0
$179$	8.87732	−	15.3760i	0.663522	−	1.14925i	−0.316162	−	0.948705i	$-0.602394\pi$
$179$	8.87732	−	15.3760i	0.663522	−	1.14925i	0.979684	−	0.200548i	$-0.0642723\pi$
$180$		0			0
$181$	−7.47461	+	20.5363i	−0.555583	+	1.52645i	0.270394	+	0.962750i	$0.412846\pi$
$181$	−7.47461	+	20.5363i	−0.555583	+	1.52645i	−0.825978	+	0.563703i	$0.809376\pi$
$182$		0			0
$183$	−4.95916	−	1.32880i	−0.366591	−	0.0982279i
$184$		0			0
$185$	−5.24180	−	14.3747i	−0.385385	−	1.05685i
$186$		0			0
$187$	0.142233	+	0.203129i	0.0104011	+	0.0148543i
$188$		0			0
$189$	7.47370			0.543632
$190$		0			0
$191$	4.85947			0.351619			0.175810	−	0.984424i	$-0.443746\pi$
$191$	4.85947			0.351619			0.175810	+	0.984424i	$0.443746\pi$
$192$		0			0
$193$	14.6232	+	20.8842i	1.05260	+	1.50327i	0.851957	+	0.523611i	$0.175415\pi$
$193$	14.6232	+	20.8842i	1.05260	+	1.50327i	0.200647	+	0.979664i	$0.435696\pi$
$194$		0			0
$195$	1.09721	−	2.35670i	0.0785729	−	0.168767i
$196$		0			0
$197$	12.7952	+	3.42845i	0.911617	+	0.244267i	0.683999	−	0.729483i	$-0.260239\pi$
$197$	12.7952	+	3.42845i	0.911617	+	0.244267i	0.227619	+	0.973750i	$0.426906\pi$
$198$		0			0
$199$	−5.22333	+	14.3510i	−0.370272	+	1.01731i	0.604984	+	0.796238i	$0.293180\pi$
$199$	−5.22333	+	14.3510i	−0.370272	+	1.01731i	−0.975256	+	0.221077i	$0.929043\pi$
$200$		0			0
$201$	2.98087	−	5.16301i	0.210254	−	0.364171i
$202$		0			0
$203$	−5.59405	−	3.91700i	−0.392625	−	0.274919i
$204$		0			0
$205$	9.88841	+	6.91502i	0.690637	+	0.482966i
$206$		0			0
$207$	6.61636	−	14.1888i	0.459869	−	0.986192i
$208$		0			0
$209$	−2.39064	−	7.53630i	−0.165364	−	0.521297i
$210$		0			0
$211$	1.62398	+	4.46185i	0.111800	+	0.307167i	0.982957	−	0.183838i	$-0.0588521\pi$
$211$	1.62398	+	4.46185i	0.111800	+	0.307167i	−0.871157	+	0.491004i	$0.836630\pi$
$212$		0			0
$213$	−1.91419	−	0.167470i	−0.131158	−	0.0114748i
$214$		0			0
$215$	−2.43522	+	6.70332i	−0.166080	+	0.457163i
$216$		0			0
$217$	1.54979	−	0.415266i	0.105207	−	0.0281901i
$218$		0			0
$219$	2.03884	+	0.742079i	0.137772	+	0.0501450i
$220$		0			0
$221$	−0.209294	+	0.120836i	−0.0140786	+	0.00812829i
$222$		0			0
$223$	−16.5158	+	1.44494i	−1.10598	+	0.0967605i	−0.625483	−	0.780238i	$-0.715098\pi$
$223$	−16.5158	+	1.44494i	−1.10598	+	0.0967605i	−0.480494	+	0.876998i	$0.659543\pi$
$224$		0			0
$225$	12.0579	−	4.40525i	0.803860	−	0.293684i
$226$		0			0
$227$	16.8095	+	16.8095i	1.11569	+	1.11569i	0.992367	+	0.123318i	$0.0393535\pi$
$227$	16.8095	+	16.8095i	1.11569	+	1.11569i	0.123318	+	0.992367i	$0.460647\pi$
$228$		0			0
$229$			11.3431i			0.749574i	0.927111	+	0.374787i	$0.122284\pi$
$229$			11.3431i			0.749574i	−0.927111	+	0.374787i	$0.877716\pi$
$230$		0			0
$231$	−2.39789	−	0.422813i	−0.157770	−	0.0278191i
$232$		0			0
$233$	1.29005	+	14.7454i	0.0845141	+	0.966001i	0.913529	+	0.406774i	$0.133346\pi$
$233$	1.29005	+	14.7454i	0.0845141	+	0.966001i	−0.829015	+	0.559227i	$0.811098\pi$
$234$		0			0
$235$	−12.3606	+	0.00748234i	−0.806318	+	0.000488094i
$236$		0			0
$237$	−7.82827	+	3.65038i	−0.508501	+	0.237118i
$238$		0			0
$239$	1.87782	+	1.08416i	0.121466	+	0.0701283i	0.559502	−	0.828829i	$-0.310992\pi$
$239$	1.87782	+	1.08416i	0.121466	+	0.0701283i	−0.438036	+	0.898957i	$0.644326\pi$
$240$		0			0
$241$	29.6663	−	5.23098i	1.91098	−	0.336957i	0.913432	−	0.406991i	$-0.133422\pi$
$241$	29.6663	−	5.23098i	1.91098	−	0.336957i	0.997545	+	0.0700339i	$0.0223107\pi$
$242$		0			0
$243$	1.26084	−	14.4114i	0.0808827	−	0.924494i
$244$		0			0
$245$	−3.63754	−	5.18825i	−0.232394	−	0.331465i
$246$		0			0
$247$	7.51984	−	1.68087i	0.478476	−	0.106951i
$248$		0			0
$249$	9.86903	−	3.59203i	0.625425	−	0.227636i
$250$		0			0
$251$	7.77884	−	6.52722i	0.490996	−	0.411995i	−0.363387	−	0.931638i	$-0.618380\pi$
$251$	7.77884	−	6.52722i	0.490996	−	0.411995i	0.854383	+	0.519644i	$0.173935\pi$
$252$		0			0
$253$	−6.34390	+	9.06003i	−0.398838	+	0.569599i
$254$		0			0
$255$	0.194226	+	0.0519168i	0.0121629	+	0.00325115i
$256$		0			0
$257$	−5.89006	−	12.6313i	−0.367412	−	0.787917i	−0.999911	−	0.0133560i	$-0.995749\pi$
$257$	−5.89006	−	12.6313i	−0.367412	−	0.787917i	0.632499	−	0.774561i	$-0.282029\pi$
$258$		0			0
$259$	−6.98340	−	12.0956i	−0.433927	−	0.751584i
$260$		0			0
$261$	−5.52156	+	6.58034i	−0.341776	+	0.407313i
$262$		0			0
$263$	−2.91929	+	2.04411i	−0.180011	+	0.126045i	−0.660109	−	0.751170i	$-0.729490\pi$
$263$	−2.91929	+	2.04411i	−0.180011	+	0.126045i	0.480098	+	0.877215i	$0.340601\pi$
$264$		0			0
$265$	11.9633	−	20.7500i	0.734898	−	1.27466i
$266$		0			0
$267$	4.62972	−	4.62972i	0.283334	−	0.283334i
$268$		0			0
$269$	−5.16456	+	29.2897i	−0.314889	+	1.78582i	0.257952	+	0.966158i	$0.416952\pi$
$269$	−5.16456	+	29.2897i	−0.314889	+	1.78582i	−0.572841	+	0.819667i	$0.694159\pi$
$270$		0			0
$271$	−9.68046	−	8.12287i	−0.588046	−	0.493429i	0.299532	−	0.954086i	$-0.403169\pi$
$271$	−9.68046	−	8.12287i	−0.588046	−	0.493429i	−0.887578	+	0.460657i	$0.847614\pi$
$272$		0			0
$273$	0.614175	−	2.29213i	0.0371715	−	0.138726i
$274$		0			0
$275$	−8.92956	+	1.58567i	−0.538473	+	0.0956196i
$276$		0			0
$277$	3.58839	+	13.3920i	0.215605	+	0.804650i	0.985953	+	0.167025i	$0.0534162\pi$
$277$	3.58839	+	13.3920i	0.215605	+	0.804650i	−0.770347	+	0.637624i	$0.779917\pi$
$278$		0			0
$279$	−0.350456	−	1.98753i	−0.0209812	−	0.118991i
$280$		0			0
$281$	−11.8512	−	14.1237i	−0.706982	−	0.842549i	0.286315	−	0.958136i	$-0.407570\pi$
$281$	−11.8512	−	14.1237i	−0.706982	−	0.842549i	−0.993297	+	0.115587i	$0.963125\pi$
$282$		0			0
$283$	−22.7099	−	10.5898i	−1.34996	−	0.629498i	−0.392954	−	0.919558i	$-0.628547\pi$
$283$	−22.7099	−	10.5898i	−1.34996	−	0.629498i	−0.957008	+	0.290060i	$0.906325\pi$
$284$		0			0
$285$	−5.41429	−	3.43143i	−0.320715	−	0.203260i
$286$		0			0
$287$	9.98259	+	4.65496i	0.589254	+	0.274774i
$288$		0			0
$289$	10.9154	+	13.0084i	0.642081	+	0.765202i
$290$		0			0
$291$	−0.730372	−	4.14214i	−0.0428151	−	0.242817i
$292$		0			0
$293$	0.419255	+	1.56468i	0.0244931	+	0.0914096i	0.977090	−	0.212824i	$-0.0682662\pi$
$293$	0.419255	+	1.56468i	0.0244931	+	0.0914096i	−0.952597	+	0.304234i	$0.901600\pi$
$294$		0			0
$295$	−19.8761	−	1.72681i	−1.15723	−	0.100539i
$296$		0			0
$297$	−1.71893	+	6.41514i	−0.0997426	+	0.372244i
$298$		0			0
$299$	−8.25727	−	6.92867i	−0.477530	−	0.400695i
$300$		0			0
$301$	−1.13049	+	6.41135i	−0.0651606	+	0.369544i
$302$		0			0
$303$	1.21785	−	1.21785i	0.0699636	−	0.0699636i
$304$		0			0
$305$	−16.8585	+	4.52817i	−0.965317	+	0.259282i
$306$		0			0
$307$	−12.5645	+	8.79773i	−0.717092	+	0.502113i	−0.874259	−	0.485459i	$-0.838653\pi$
$307$	−12.5645	+	8.79773i	−0.717092	+	0.502113i	0.157168	+	0.987572i	$0.449764\pi$
$308$		0			0
$309$	0.305996	−	0.364672i	0.0174075	−	0.0207454i
$310$		0			0
$311$	−13.9713	−	24.1991i	−0.792242	−	1.37220i	−0.924576	−	0.380998i	$-0.875581\pi$
$311$	−13.9713	−	24.1991i	−0.792242	−	1.37220i	0.132334	−	0.991205i	$-0.457753\pi$
$312$		0			0
$313$	14.4856	+	31.0645i	0.818776	+	1.75587i	0.634384	+	0.773018i	$0.281254\pi$
$313$	14.4856	+	31.0645i	0.818776	+	1.75587i	0.184392	+	0.982853i	$0.440968\pi$
$314$		0			0
$315$	10.1449	−	5.86532i	0.571598	−	0.330474i
$316$		0			0
$317$	−20.3150	+	29.0129i	−1.14101	+	1.62952i	−0.485810	+	0.874064i	$0.661475\pi$
$317$	−20.3150	+	29.0129i	−1.14101	+	1.62952i	−0.655195	+	0.755460i	$0.727414\pi$
$318$		0			0
$319$	4.64882	−	3.90082i	0.260284	−	0.218404i
$320$		0			0
$321$	−3.20830	+	1.16773i	−0.179070	+	0.0651761i
$322$		0			0
$323$	0.229006	+	0.550154i	0.0127422	+	0.0306114i
$324$		0			0
$325$	−0.781004	−	8.80414i	−0.0433223	−	0.488366i
$326$		0			0
$327$	0.783775	−	8.95859i	0.0433429	−	0.495411i
$328$		0			0
$329$	−11.1117	+	1.95930i	−0.612609	+	0.108020i
$330$		0			0
$331$	−20.5987	−	11.8927i	−1.13221	−	0.653680i	−0.187718	−	0.982223i	$-0.560109\pi$
$331$	−20.5987	−	11.8927i	−1.13221	−	0.653680i	−0.944489	+	0.328543i	$0.893442\pi$
$332$		0			0
$333$	−15.9223	+	7.42469i	−0.872536	+	0.406870i
$334$		0			0
$335$	−0.0122702	−	20.2701i	−0.000670393	−	1.10747i
$336$		0			0
$337$	−1.60012	−	18.2895i	−0.0871643	−	0.996293i	−0.906284	−	0.422670i	$-0.861093\pi$
$337$	−1.60012	−	18.2895i	−0.0871643	−	0.996293i	0.819119	−	0.573623i	$-0.194463\pi$
$338$		0			0
$339$	7.61212	+	1.34222i	0.413434	+	0.0728995i
$340$		0			0
$341$			1.42580i			0.0772111i
$342$		0			0
$343$	−14.1931	−	14.1931i	−0.766355	−	0.766355i
$344$		0			0
$345$	0.786939	+	8.93248i	0.0423674	+	0.480908i
$346$		0			0
$347$	17.9028	−	1.56629i	0.961072	−	0.0840829i	0.404190	−	0.914675i	$-0.367553\pi$
$347$	17.9028	−	1.56629i	0.961072	−	0.0840829i	0.556881	+	0.830592i	$0.311998\pi$
$348$		0			0
$349$	13.2462	−	7.64767i	0.709050	−	0.409370i	−0.101659	−	0.994819i	$-0.532415\pi$
$349$	13.2462	−	7.64767i	0.709050	−	0.409370i	0.810709	+	0.585449i	$0.199082\pi$
$350$		0			0
$351$	−6.08227	−	2.21377i	−0.324648	−	0.118162i
$352$		0			0
$353$	17.4171	−	4.66689i	0.927017	−	0.248393i	0.236435	−	0.971647i	$-0.424021\pi$
$353$	17.4171	−	4.66689i	0.927017	−	0.248393i	0.690582	+	0.723254i	$0.257354\pi$
$354$		0			0
$355$	−5.91938	+	2.76461i	−0.314168	+	0.146730i
$356$		0			0
$357$	0.182822	+	0.0159948i	0.00967595	+	0.000846536i
$358$		0			0
$359$	−4.24571	−	11.6650i	−0.224080	−	0.615655i	0.775803	−	0.630976i	$-0.217345\pi$
$359$	−4.24571	−	11.6650i	−0.224080	−	0.615655i	−0.999883	+	0.0153210i	$0.995123\pi$
$360$		0			0
$361$	−1.72196	−	18.9218i	−0.0906295	−	0.995885i
$362$		0			0
$363$	−2.14290	+	4.59546i	−0.112473	+	0.241199i
$364$		0			0
$365$	7.26417	−	1.28540i	0.380224	−	0.0672811i
$366$		0			0
$367$	0.492964	+	0.345177i	0.0257325	+	0.0180181i	0.586372	−	0.810042i	$-0.300556\pi$
$367$	0.492964	+	0.345177i	0.0257325	+	0.0180181i	−0.560639	+	0.828060i	$0.689445\pi$
$368$		0			0
$369$	6.92740	−	11.9986i	0.360626	−	0.624623i
$370$		0			0
$371$	7.47786	−	20.5452i	0.388231	−	1.06666i
$372$		0			0
$373$	−13.7423	−	3.68224i	−0.711550	−	0.190659i	−0.115152	−	0.993348i	$-0.536735\pi$
$373$	−13.7423	−	3.68224i	−0.711550	−	0.190659i	−0.596398	+	0.802689i	$0.703402\pi$
$374$		0			0
$375$	−4.71610	+	5.64120i	−0.243538	+	0.291310i
$376$		0			0
$377$	3.39232	+	4.84474i	0.174714	+	0.249517i
$378$		0			0
$379$	13.3727			0.686911			0.343455	−	0.939169i	$-0.388403\pi$
$379$	13.3727			0.686911			0.343455	+	0.939169i	$0.388403\pi$
$380$		0			0
$381$	−0.448846			−0.0229951
$382$		0			0
$383$	10.8886	+	15.5505i	0.556381	+	0.794594i	0.994546	−	0.104300i	$-0.0332604\pi$
$383$	10.8886	+	15.5505i	0.556381	+	0.794594i	−0.438165	+	0.898895i	$0.644371\pi$
$384$		0			0
$385$	−7.77770	+	2.83618i	−0.396388	+	0.144545i
$386$		0			0
$387$	7.90997	+	2.11947i	0.402086	+	0.107739i
$388$		0			0
$389$	−3.99288	+	10.9703i	−0.202447	+	0.556218i	−0.998819	−	0.0485888i	$-0.984528\pi$
$389$	−3.99288	+	10.9703i	−0.202447	+	0.556218i	0.796372	+	0.604807i	$0.206750\pi$
$390$		0			0
$391$	0.416812	−	0.721940i	0.0210791	−	0.0365100i
$392$		0			0
$393$	−1.65139	−	1.15632i	−0.0833016	−	0.0583284i
$394$		0			0
$395$	−16.8302	+	24.0670i	−0.846818	+	1.21094i
$396$		0			0
$397$	0.567803	−	1.21766i	0.0284972	−	0.0611125i	−0.891544	−	0.452934i	$-0.850377\pi$
$397$	0.567803	−	1.21766i	0.0284972	−	0.0611125i	0.920041	+	0.391822i	$0.128155\pi$
$398$		0			0
$399$	−5.40981	−	2.22977i	−0.270829	−	0.111628i
$400$		0			0
$401$	−2.58253	−	7.09543i	−0.128965	−	0.354329i	0.858358	−	0.513051i	$-0.171485\pi$
$401$	−2.58253	−	7.09543i	−0.128965	−	0.354329i	−0.987323	+	0.158722i	$0.949263\pi$
$402$		0			0
$403$	−1.38426	−	0.121107i	−0.0689551	−	0.00603279i
$404$		0			0
$405$	−5.00973	−	10.7264i	−0.248935	−	0.533001i
$406$		0			0
$407$	11.9886	−	3.21233i	0.594252	−	0.159229i
$408$		0			0
$409$	13.4389	+	4.89136i	0.664510	+	0.241862i	0.652183	−	0.758062i	$-0.273854\pi$
$409$	13.4389	+	4.89136i	0.664510	+	0.241862i	0.0123279	+	0.999924i	$0.496076\pi$
$410$		0			0
$411$	4.26180	−	2.46055i	0.210219	−	0.121370i
$412$		0			0
$413$	−18.1425	+	1.58726i	−0.892734	+	0.0781041i
$414$		0			0
$415$	22.9364	−	27.3682i	1.12590	−	1.34345i
$416$		0			0
$417$	−7.85844	−	7.85844i	−0.384829	−	0.384829i
$418$		0			0
$419$			4.23569i			0.206927i	0.994633	+	0.103463i	$0.0329925\pi$
$419$			4.23569i			0.206927i	−0.994633	+	0.103463i	$0.967008\pi$
$420$		0			0
$421$	12.3792	+	2.18279i	0.603326	+	0.106383i	0.466964	−	0.884276i	$-0.345348\pi$
$421$	12.3792	+	2.18279i	0.603326	+	0.106383i	0.136362	+	0.990659i	$0.456459\pi$
$422$		0			0
$423$	1.23697	+	14.1386i	0.0601435	+	0.687444i
$424$		0			0
$425$	0.660054	−	0.177718i	0.0320173	−	0.00862057i
$426$		0			0
$427$	−14.4415	+	6.73418i	−0.698873	+	0.325890i
$428$		0			0
$429$	1.82622	+	1.05437i	0.0881708	+	0.0509054i
$430$		0			0
$431$	−20.4402	+	3.60415i	−0.984568	+	0.173606i	−0.642680	−	0.766135i	$-0.722177\pi$
$431$	−20.4402	+	3.60415i	−0.984568	+	0.173606i	−0.341888	+	0.939741i	$0.611066\pi$
$432$		0			0
$433$	−1.28181	+	14.6512i	−0.0616001	+	0.704092i	0.901116	+	0.433578i	$0.142749\pi$
$433$	−1.28181	+	14.6512i	−0.0616001	+	0.704092i	−0.962716	+	0.270514i	$0.912806\pi$
$434$		0			0
$435$	0.851434	−	4.84587i	0.0408231	−	0.232342i
$436$		0			0
$437$	−19.5648	+	17.9907i	−0.935913	+	0.860613i
$438$		0			0
$439$	14.5168	−	5.28369i	0.692850	−	0.252177i	0.0284951	−	0.999594i	$-0.490929\pi$
$439$	14.5168	−	5.28369i	0.692850	−	0.252177i	0.664355	+	0.747417i	$0.268706\pi$
$440$		0			0
$441$	−5.57336	+	4.67661i	−0.265398	+	0.222696i
$442$		0			0
$443$	−12.6779	+	18.1059i	−0.602344	+	0.860236i	−0.998315	−	0.0580266i	$-0.981519\pi$
$443$	−12.6779	+	18.1059i	−0.602344	+	0.860236i	0.395971	+	0.918263i	$0.370408\pi$
$444$		0			0
$445$	5.74865	−	21.5063i	0.272512	−	1.01950i
$446$		0			0
$447$	4.87939	+	10.4639i	0.230787	+	0.494925i
$448$		0			0
$449$	−8.29048	−	14.3595i	−0.391252	−	0.677668i	0.601363	−	0.798976i	$-0.294625\pi$
$449$	−8.29048	−	14.3595i	−0.391252	−	0.677668i	−0.992615	+	0.121308i	$0.961291\pi$
$450$		0			0
$451$	−6.29162	+	7.49806i	−0.296261	+	0.353070i
$452$		0			0
$453$	−1.89680	+	1.32816i	−0.0891196	+	0.0624022i
$454$		0			0
$455$	−2.09293	−	7.79205i	−0.0981180	−	0.365297i
$456$		0			0
$457$	7.39801	−	7.39801i	0.346064	−	0.346064i	−0.512577	−	0.858641i	$-0.671309\pi$
$457$	7.39801	−	7.39801i	0.346064	−	0.346064i	0.858641	+	0.512577i	$0.171309\pi$
$458$		0			0
$459$	0.0869236	−	0.492968i	0.00405725	−	0.0230098i
$460$		0			0
$461$	2.82051	+	2.36669i	0.131364	+	0.110228i	0.706103	−	0.708110i	$-0.250452\pi$
$461$	2.82051	+	2.36669i	0.131364	+	0.110228i	−0.574738	+	0.818337i	$0.694896\pi$
$462$		0			0
$463$	4.14385	−	15.4650i	0.192581	−	0.718722i	−0.800299	−	0.599601i	$-0.795326\pi$
$463$	4.14385	−	15.4650i	0.192581	−	0.718722i	0.992880	−	0.119120i	$-0.0380075\pi$
$464$		0			0
$465$	0.743573	+	0.885067i	0.0344824	+	0.0410440i
$466$		0			0
$467$	7.66461	+	28.6047i	0.354676	+	1.32367i	0.880892	+	0.473318i	$0.156944\pi$
$467$	7.66461	+	28.6047i	0.354676	+	1.32367i	−0.526216	+	0.850351i	$0.676390\pi$
$468$		0			0
$469$	−3.21303	−	18.2220i	−0.148364	−	0.841414i
$470$		0			0
$471$	−3.44335	−	4.10363i	−0.158661	−	0.189085i
$472$		0			0
$473$	−5.24326	−	2.44497i	−0.241085	−	0.112420i
$474$		0			0
$475$	−21.7765	−	0.886328i	−0.999173	−	0.0406675i
$476$		0			0
$477$	−24.9249	−	11.6227i	−1.14123	−	0.532166i
$478$		0			0
$479$	22.5979	+	26.9311i	1.03252	+	1.23051i	0.972642	+	0.232308i	$0.0746276\pi$
$479$	22.5979	+	26.9311i	1.03252	+	1.23051i	0.0598807	+	0.998206i	$0.480928\pi$
$480$		0			0
$481$	2.10045	+	11.9122i	0.0957721	+	0.543151i
$482$		0			0
$483$	2.11854	+	7.90650i	0.0963969	+	0.359758i
$484$		0			0
$485$	−9.19892	−	10.9494i	−0.417702	−	0.497186i
$486$		0			0
$487$	2.69013	−	10.0397i	0.121901	−	0.454943i	−0.877809	−	0.479011i	$-0.840995\pi$
$487$	2.69013	−	10.0397i	0.121901	−	0.454943i	0.999710	+	0.0240686i	$0.00766201\pi$
$488$		0			0
$489$	5.88676	+	4.93958i	0.266209	+	0.223375i
$490$		0			0
$491$	1.01529	−	5.75802i	0.0458196	−	0.259856i	−0.953290	−	0.302058i	$-0.902326\pi$
$491$	1.01529	−	5.75802i	0.0458196	−	0.259856i	0.999109	+	0.0422025i	$0.0134375\pi$
$492$		0			0
$493$	−0.323429	+	0.323429i	−0.0145665	+	0.0145665i
$494$		0			0
$495$	2.70128	+	10.0570i	0.121414	+	0.452027i
$496$		0			0
$497$	−4.88514	+	3.42061i	−0.219128	+	0.153435i
$498$		0			0
$499$	9.13280	−	10.8840i	0.408840	−	0.487237i	−0.521854	−	0.853035i	$-0.674759\pi$
$499$	9.13280	−	10.8840i	0.408840	−	0.487237i	0.930694	+	0.365798i	$0.119204\pi$
$500$		0			0
$501$	3.83227	+	6.63769i	0.171213	+	0.296550i
$502$		0			0
$503$	−0.908594	−	1.94849i	−0.0405122	−	0.0868787i	0.885010	−	0.465572i	$-0.154151\pi$
$503$	−0.908594	−	1.94849i	−0.0405122	−	0.0868787i	−0.925522	+	0.378693i	$0.876374\pi$
$504$		0			0
$505$	1.51219	−	5.65725i	0.0672914	−	0.251744i
$506$		0			0
$507$	3.72507	−	5.31995i	0.165436	−	0.236267i
$508$		0			0
$509$	6.22207	−	5.22094i	0.275788	−	0.231414i	−0.494394	−	0.869238i	$-0.664610\pi$
$509$	6.22207	−	5.22094i	0.275788	−	0.231414i	0.770182	+	0.637824i	$0.220165\pi$
$510$		0			0
$511$	6.32785	−	2.30315i	0.279928	−	0.101885i
$512$		0			0
$513$	−7.34489	+	14.1697i	−0.324285	+	0.625607i
$514$		0			0
$515$	0.280096	−	1.59415i	0.0123425	−	0.0702465i
$516$		0			0
$517$	0.873883	−	9.98853i	0.0384333	−	0.439295i
$518$		0			0
$519$	−0.706580	+	0.124589i	−0.0310154	+	0.00546885i
$520$		0			0
$521$	16.1921	+	9.34849i	0.709387	+	0.409565i	0.810834	−	0.585276i	$-0.199014\pi$
$521$	16.1921	+	9.34849i	0.709387	+	0.409565i	−0.101447	+	0.994841i	$0.532347\pi$
$522$		0			0
$523$	−6.12577	+	2.85649i	−0.267861	+	0.124906i	−0.551909	−	0.833904i	$-0.686100\pi$
$523$	−6.12577	+	2.85649i	−0.267861	+	0.124906i	0.284048	+	0.958810i	$0.408323\pi$
$524$		0			0
$525$	−3.34892	+	5.81675i	−0.146159	+	0.253864i
$526$		0			0
$527$	−0.00936609	−	0.107055i	−0.000407993	−	0.00466338i
$528$		0			0
$529$	13.9661	+	2.46260i	0.607221	+	0.107069i
$530$		0			0
$531$			22.9079i			0.994119i
$532$		0			0
$533$	−6.74523	−	6.74523i	−0.292168	−	0.292168i
$534$		0			0
$535$	−7.45635	+	8.89706i	−0.322366	+	0.384653i
$536$		0			0
$537$	11.6321	−	1.01768i	0.501962	−	0.0439160i
$538$		0			0
$539$	4.45131	−	2.56997i	0.191732	−	0.110696i
$540$		0			0
$541$	30.6180	+	11.1440i	1.31637	+	0.479120i	0.902294	−	0.431122i	$-0.141882\pi$
$541$	30.6180	+	11.1440i	1.31637	+	0.479120i	0.414077	+	0.910242i	$0.364104\pi$
$542$		0			0
$543$	−13.8830	+	3.71993i	−0.595776	+	0.159638i
$544$		0			0
$545$	−12.9387	−	27.7033i	−0.554232	−	1.18668i
$546$		0			0
$547$	37.9950	+	3.32414i	1.62455	+	0.142130i	0.862732	−	0.505661i	$-0.168751\pi$
$547$	37.9950	+	3.32414i	1.62455	+	0.142130i	0.761818	+	0.647791i	$0.224307\pi$
$548$		0			0
$549$	6.85521	+	18.8345i	0.292573	+	0.803838i
$550$		0			0
$551$	12.9240	−	6.75649i	0.550582	−	0.287836i
$552$		0			0
$553$	−11.3295	+	24.2962i	−0.481780	+	1.03318i
$554$		0			0
$555$	5.76667	−	8.24628i	0.244782	−	0.350035i
$556$		0			0
$557$	32.8728	+	23.0178i	1.39287	+	0.975295i	0.998409	+	0.0563797i	$0.0179557\pi$
$557$	32.8728	+	23.0178i	1.39287	+	0.975295i	0.394456	+	0.918915i	$0.370933\pi$
$558$		0			0
$559$	2.81911	−	4.88285i	0.119236	−	0.206522i
$560$		0			0
$561$	−0.0557779	+	0.153249i	−0.00235494	+	0.00647016i
$562$		0			0
$563$	38.6358	+	10.3524i	1.62830	+	0.436303i	0.953426	−	0.301627i	$-0.0975297\pi$
$563$	38.6358	+	10.3524i	1.62830	+	0.436303i	0.674878	+	0.737930i	$0.264196\pi$
$564$		0			0
$565$	24.6903	−	9.00348i	1.03873	−	0.378779i
$566$		0			0
$567$	−6.19845	−	8.85231i	−0.260311	−	0.371762i
$568$		0			0
$569$	−10.0913			−0.423048			−0.211524	−	0.977373i	$-0.567843\pi$
$569$	−10.0913			−0.423048			−0.211524	+	0.977373i	$0.567843\pi$
$570$		0			0
$571$	−3.55333			−0.148702			−0.0743510	−	0.997232i	$-0.523689\pi$
$571$	−3.55333			−0.148702			−0.0743510	+	0.997232i	$0.523689\pi$
$572$		0			0
$573$	1.83309	+	2.61792i	0.0765782	+	0.109365i
$574$		0			0
$575$	17.5176	+	24.9534i	0.730535	+	1.04063i
$576$		0			0
$577$	32.7254	+	8.76874i	1.36238	+	0.365047i	0.864688	−	0.502309i	$-0.167516\pi$
$577$	32.7254	+	8.76874i	1.36238	+	0.365047i	0.497687	+	0.867356i	$0.334183\pi$
$578$		0			0
$579$	−5.73464	+	15.7558i	−0.238324	+	0.654789i
$580$		0			0
$581$	16.2979	−	28.2288i	0.676150	−	1.17113i
$582$		0			0
$583$	15.9154	+	11.1441i	0.659148	+	0.461540i
$584$		0			0
$585$	−9.99347	+	1.76836i	−0.413179	+	0.0731125i
$586$		0			0
$587$	12.3061	−	26.3905i	0.507926	−	1.08925i	−0.470452	−	0.882426i	$-0.655909\pi$
$587$	12.3061	−	26.3905i	0.507926	−	1.08925i	0.978378	−	0.206825i	$-0.0663132\pi$
$588$		0			0
$589$	−0.735765	+	3.34643i	−0.0303167	+	0.137887i
$590$		0			0
$591$	2.97959	+	8.18634i	0.122564	+	0.336741i
$592$		0			0
$593$	0.0877813	+	0.00767986i	0.00360474	+	0.000315374i	0.0889580	−	0.996035i	$-0.471646\pi$
$593$	0.0877813	+	0.00767986i	0.00360474	+	0.000315374i	−0.0853532	+	0.996351i	$0.527202\pi$
$594$		0			0
$595$	0.565352	−	0.264045i	0.0231772	−	0.0108248i
$596$		0			0
$597$	−9.70157	+	2.59953i	−0.397059	+	0.106392i
$598$		0			0
$599$	−44.5968	−	16.2319i	−1.82218	−	0.663218i	−0.994833	−	0.101524i	$-0.967628\pi$
$599$	−44.5968	−	16.2319i	−1.82218	−	0.663218i	−0.827345	−	0.561695i	$-0.810150\pi$
$600$		0			0
$601$	−2.87963	+	1.66255i	−0.117462	+	0.0678169i	−0.557580	−	0.830123i	$-0.688270\pi$
$601$	−2.87963	+	1.66255i	−0.117462	+	0.0678169i	0.440118	+	0.897940i	$0.354937\pi$
$602$		0			0
$603$	−23.1858	+	2.02849i	−0.944198	+	0.0826066i
$604$		0			0
$605$	1.51296	+	17.1734i	0.0615105	+	0.698200i
$606$		0			0
$607$	9.34016	+	9.34016i	0.379106	+	0.379106i	0.870779	−	0.491674i	$-0.163615\pi$
$607$	9.34016	+	9.34016i	0.379106	+	0.379106i	−0.491674	+	0.870779i	$0.663615\pi$
$608$		0			0
$609$		−	4.49122i		−	0.181993i
$610$		0			0
$611$	9.62334	+	1.69685i	0.389319	+	0.0686474i
$612$		0			0
$613$	−2.72812	−	31.1826i	−0.110188	−	1.25945i	−0.827006	−	0.562193i	$-0.809958\pi$
$613$	−2.72812	−	31.1826i	−0.110188	−	1.25945i	0.716818	−	0.697260i	$-0.245598\pi$
$614$		0			0
$615$	0.00480371	+	7.93561i	0.000193704	+	0.319995i
$616$		0			0
$617$	10.6078	−	4.94649i	0.427054	−	0.199138i	−0.197195	−	0.980364i	$-0.563183\pi$
$617$	10.6078	−	4.94649i	0.427054	−	0.199138i	0.624248	+	0.781226i	$0.285405\pi$
$618$		0			0
$619$	27.4876	+	15.8700i	1.10482	+	0.637868i	0.937483	−	0.348032i	$-0.113150\pi$
$619$	27.4876	+	15.8700i	1.10482	+	0.637868i	0.167337	+	0.985900i	$0.446483\pi$
$620$		0			0
$621$	21.9875	−	3.87699i	0.882328	−	0.155578i
$622$		0			0
$623$	1.77108	−	20.2435i	0.0709568	−	0.811040i
$624$		0			0
$625$	−4.28158	+	24.6306i	−0.171263	+	0.985225i
$626$		0			0
$627$	3.15820	−	4.13074i	0.126126	−	0.164966i
$628$		0			0
$629$	−0.879053	+	0.319949i	−0.0350501	+	0.0127572i
$630$		0			0
$631$	−27.5987	+	23.1580i	−1.09869	+	0.921907i	−0.997336	−	0.0729443i	$-0.976760\pi$
$631$	−27.5987	+	23.1580i	−1.09869	+	0.921907i	−0.101349	+	0.994851i	$0.532316\pi$
$632$		0			0
$633$	−1.79111	+	2.55797i	−0.0711904	+	0.101670i
$634$		0			0
$635$	−1.32117	+	0.763844i	−0.0524290	+	0.0303122i
$636$		0			0
$637$	2.11701	+	4.53994i	0.0838790	+	0.179879i
$638$		0			0
$639$	3.75073	+	6.49645i	0.148376	+	0.256995i
$640$		0			0
$641$	−14.2560	+	16.9896i	−0.563077	+	0.671050i	−0.970195	−	0.242326i	$-0.922090\pi$
$641$	−14.2560	+	16.9896i	−0.563077	+	0.671050i	0.407117	+	0.913376i	$0.366534\pi$
$642$		0			0
$643$	4.17663	−	2.92451i	0.164710	−	0.115331i	−0.488315	−	0.872667i	$-0.662388\pi$
$643$	4.17663	−	2.92451i	0.164710	−	0.115331i	0.653025	+	0.757336i	$0.273499\pi$
$644$		0			0
$645$	−4.52985	+	1.21671i	−0.178363	+	0.0479079i
$646$		0			0
$647$	8.23341	−	8.23341i	0.323689	−	0.323689i	−0.526492	−	0.850180i	$-0.676493\pi$
$647$	8.23341	−	8.23341i	0.323689	−	0.323689i	0.850180	+	0.526492i	$0.176493\pi$
$648$		0			0
$649$	2.81028	−	15.9379i	0.110313	−	0.625618i
$650$		0			0
$651$	0.808326	+	0.678266i	0.0316808	+	0.0265833i
$652$		0			0
$653$	6.20696	−	23.1647i	0.242897	−	0.906504i	−0.731532	−	0.681808i	$-0.761194\pi$
$653$	6.20696	−	23.1647i	0.242897	−	0.906504i	0.974429	−	0.224697i	$-0.0721392\pi$
$654$		0			0
$655$	−6.82865	−	0.593265i	−0.266818	−	0.0231808i
$656$		0			0
$657$	−2.19230	−	8.18177i	−0.0855297	−	0.319201i
$658$		0			0
$659$	−4.43073	−	25.1279i	−0.172597	−	0.978844i	−0.940881	−	0.338736i	$-0.890001\pi$
$659$	−4.43073	−	25.1279i	−0.172597	−	0.978844i	0.768285	−	0.640108i	$-0.221111\pi$
$660$		0			0
$661$	−4.69706	−	5.59774i	−0.182695	−	0.217727i	0.666922	−	0.745127i	$-0.267611\pi$
$661$	−4.69706	−	5.59774i	−0.182695	−	0.217727i	−0.849617	+	0.527400i	$0.823167\pi$
$662$		0			0
$663$	−0.144047	−	0.0671701i	−0.00559431	−	0.00260867i
$664$		0			0
$665$	−19.7183	+	2.64310i	−0.764643	+	0.102495i
$666$		0			0
$667$	−18.4896	−	8.62182i	−0.715918	−	0.333838i
$668$		0			0
$669$	−7.00849	−	8.35239i	−0.270964	−	0.322922i
$670$		0			0
$671$	−2.45886	−	13.9449i	−0.0949232	−	0.538336i
$672$		0			0
$673$	−8.99066	−	33.5536i	−0.346565	−	1.29340i	−0.890774	−	0.454447i	$-0.849837\pi$
$673$	−8.99066	−	33.5536i	−0.346565	−	1.29340i	0.544209	−	0.838949i	$-0.316830\pi$
$674$		0			0
$675$	15.0094	+	10.4826i	0.577712	+	0.403477i
$676$		0			0
$677$	−9.74556	+	36.3709i	−0.374552	+	1.39785i	0.479446	+	0.877572i	$0.340838\pi$
$677$	−9.74556	+	36.3709i	−0.374552	+	1.39785i	−0.853998	+	0.520277i	$0.825829\pi$
$678$		0			0
$679$	−10.0000	−	8.39100i	−0.383765	−	0.322017i
$680$		0			0
$681$	−2.71483	+	15.3965i	−0.104032	+	0.589997i
$682$		0			0
$683$	−7.84329	+	7.84329i	−0.300115	+	0.300115i	−0.841059	−	0.540944i	$-0.818067\pi$
$683$	−7.84329	+	7.84329i	−0.300115	+	0.300115i	0.540944	+	0.841059i	$0.318067\pi$
$684$		0			0
$685$	8.35717	−	14.4953i	0.319311	−	0.553837i
$686$		0			0
$687$	−6.11081	+	4.27884i	−0.233142	+	0.163248i
$688$		0			0
$689$	−12.1713	+	14.5052i	−0.463690	+	0.552604i
$690$		0			0
$691$	−14.3362	−	24.8310i	−0.545374	−	0.944616i	−0.998583	−	0.0532115i	$-0.983054\pi$
$691$	−14.3362	−	24.8310i	−0.545374	−	0.944616i	0.453209	−	0.891404i	$-0.350279\pi$
$692$		0			0
$693$	4.01728	+	8.61508i	0.152604	+	0.327260i
$694$		0			0
$695$	−36.5046	−	9.75771i	−1.38470	−	0.370131i
$696$		0			0
$697$	0.423147	−	0.604316i	0.0160278	−	0.0228901i
$698$		0			0
$699$	−7.45706	+	6.25721i	−0.282052	+	0.236670i
$700$		0			0
$701$	−19.5726	+	7.12384i	−0.739246	+	0.269064i	−0.684073	−	0.729413i	$-0.739793\pi$
$701$	−19.5726	+	7.12384i	−0.739246	+	0.269064i	−0.0551727	+	0.998477i	$0.517571\pi$
$702$		0			0
$703$	29.7956	−	1.35296i	1.12376	−	0.0510280i
$704$		0			0
$705$	−4.66669	−	6.65615i	−0.175758	−	0.250685i
$706$		0			0
$707$	0.465883	−	5.32507i	0.0175213	−	0.200270i
$708$		0			0
$709$	9.90503	−	1.74652i	0.371991	−	0.0655921i	0.0154726	−	0.999880i	$-0.495075\pi$
$709$	9.90503	−	1.74652i	0.371991	−	0.0655921i	0.356519	+	0.934288i	$0.383964\pi$
$710$		0			0
$711$	29.2029	+	16.8603i	1.09519	+	0.632311i
$712$		0			0
$713$	4.34405	−	2.02566i	0.162686	−	0.0758617i
$714$		0			0
$715$	7.16977	−	0.00434012i	0.268134	−	0.000162311i
$716$		0			0
$717$	0.124286	+	1.42059i	0.00464153	+	0.0530529i
$718$		0			0
$719$	21.2738	+	3.75115i	0.793381	+	0.139894i	0.555628	−	0.831431i	$-0.312478\pi$
$719$	21.2738	+	3.75115i	0.793381	+	0.139894i	0.237753	+	0.971326i	$0.423589\pi$
$720$		0			0
$721$		−	1.47748i		−	0.0550241i
$722$		0			0
$723$	14.0088	+	14.0088i	0.520991	+	0.520991i
$724$		0			0
$725$	−5.74051	−	15.7127i	−0.213197	−	0.583556i
$726$		0			0
$727$	−50.1855	+	4.39066i	−1.86128	+	0.162841i	−0.961733	−	0.273989i	$-0.911657\pi$
$727$	−50.1855	+	4.39066i	−1.86128	+	0.162841i	−0.899544	+	0.436829i	$0.856101\pi$
$728$		0			0
$729$	−5.51587	+	3.18459i	−0.204292	+	0.117948i
$730$		0			0
$731$	0.409747	+	0.149136i	0.0151551	+	0.00551599i
$732$		0			0
$733$	16.3259	−	4.37450i	0.603009	−	0.161576i	0.0556171	−	0.998452i	$-0.482287\pi$
$733$	16.3259	−	4.37450i	0.603009	−	0.161576i	0.547392	+	0.836876i	$0.315621\pi$
$734$		0			0
$735$	1.42289	−	3.91674i	0.0524842	−	0.144471i
$736$		0			0
$737$	16.3801	+	1.43307i	0.603368	+	0.0527879i
$738$		0			0
$739$	13.5232	+	37.1547i	0.497459	+	1.36676i	0.893723	+	0.448620i	$0.148084\pi$
$739$	13.5232	+	37.1547i	0.497459	+	1.36676i	−0.396264	+	0.918137i	$0.629694\pi$
$740$		0			0
$741$	3.74215	+	3.41707i	0.137471	+	0.125529i
$742$		0			0
$743$	−5.93144	+	12.7200i	−0.217603	+	0.466652i	−0.984560	−	0.175047i	$-0.943992\pi$
$743$	−5.93144	+	12.7200i	−0.217603	+	0.466652i	0.766957	+	0.641699i	$0.221770\pi$
$744$		0			0
$745$	32.1698	+	22.4966i	1.17861	+	0.824210i
$746$		0			0
$747$	−33.5860	−	23.5172i	−1.22885	−	0.860449i
$748$		0			0
$749$	−5.29824	+	9.17682i	−0.193594	+	0.335314i
$750$		0			0
$751$	−6.39068	+	17.5582i	−0.233199	+	0.640709i	−0.999999	−	0.00117667i	$-0.999625\pi$
$751$	−6.39068	+	17.5582i	−0.233199	+	0.640709i	0.766800	+	0.641886i	$0.221848\pi$
$752$		0			0
$753$	6.45070	+	1.72846i	0.235077	+	0.0629886i
$754$		0			0
$755$	−3.32295	+	7.13738i	−0.120935	+	0.259756i
$756$		0			0
$757$	−25.4177	−	36.3002i	−0.923822	−	1.31935i	−0.947540	−	0.319636i	$-0.896439\pi$
$757$	−25.4177	−	36.3002i	−0.923822	−	1.31935i	0.0237184	−	0.999719i	$-0.492449\pi$
$758$		0			0
$759$	−7.27390			−0.264026
$760$		0			0
$761$	−28.6386			−1.03815			−0.519073	−	0.854730i	$-0.673723\pi$
$761$	−28.6386			−1.03815			−0.519073	+	0.854730i	$0.673723\pi$
$762$		0			0
$763$	−16.0088	−	22.8629i	−0.579558	−	0.827694i
$764$		0			0
$765$	−0.268889	−	0.737376i	−0.00972168	−	0.0266599i
$766$		0			0
$767$	15.2349	+	4.08219i	0.550102	+	0.147399i
$768$		0			0
$769$	16.7378	−	45.9866i	0.603579	−	1.65832i	−0.140382	−	0.990097i	$-0.544833\pi$
$769$	16.7378	−	45.9866i	0.603579	−	1.65832i	0.743961	−	0.668223i	$-0.232945\pi$
$770$		0			0
$771$	4.58293	−	7.93788i	0.165050	−	0.285876i
$772$		0			0
$773$	25.9019	+	18.1367i	0.931626	+	0.652331i	0.937624	−	0.347651i	$-0.113020\pi$
$773$	25.9019	+	18.1367i	0.931626	+	0.652331i	−0.00599844	+	0.999982i	$0.501909\pi$
$774$		0			0
$775$	3.69490	+	1.33977i	0.132725	+	0.0481259i
$776$		0			0
$777$	3.88193	−	8.32482i	0.139263	−	0.298651i
$778$		0			0
$779$	−18.6361	+	14.3517i	−0.667707	+	0.514202i
$780$		0			0
$781$	−1.81255	−	4.97995i	−0.0648583	−	0.178197i
$782$		0			0
$783$	−12.2037	−	1.06769i	−0.436126	−	0.0381560i
$784$		0			0
$785$	−17.1190	−	6.21907i	−0.611003	−	0.221968i
$786$		0			0
$787$	−42.2003	+	11.3075i	−1.50428	+	0.403070i	−0.914531	−	0.404516i	$-0.867440\pi$
$787$	−42.2003	+	11.3075i	−1.50428	+	0.403070i	−0.589749	+	0.807587i	$0.700773\pi$
$788$		0			0
$789$	−2.20242	−	0.801616i	−0.0784083	−	0.0285383i
$790$		0			0
$791$	20.7758	−	11.9949i	0.738701	−	0.426490i

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)

\(f(q)\)	\(=\)	\(q+(0.377219 + 0.538725i) q^{3} +(2.02714 + 0.943776i) q^{5} +(1.97160 + 0.528288i) q^{7} +(0.878130 - 2.41264i) q^{9} +O(q^{10})\)	\(q+(0.377219 + 0.538725i) q^{3} +(2.02714 + 0.943776i) q^{5} +(1.97160 + 0.528288i) q^{7} +(0.878130 - 2.41264i) q^{9} +(-0.906926 + 1.57084i) q^{11} +(-1.44805 - 1.01394i) q^{13} +(0.256239 + 1.44808i) q^{15} +(0.0577770 - 0.123903i) q^{17} +(-2.93922 + 3.21885i) q^{19} +(0.459122 + 1.26143i) q^{21} +(6.07446 + 0.531447i) q^{23} +(3.21857 + 3.82633i) q^{25} +(3.53675 - 0.947670i) q^{27} +(-3.14393 - 1.14430i) q^{29} +(0.680748 - 0.393030i) q^{31} +(-1.18836 + 0.103968i) q^{33} +(3.49811 + 2.93166i) q^{35} +(-4.83846 - 4.83846i) q^{37} -1.16258i q^{39} +(5.31428 + 0.937051i) q^{41} +(0.277984 + 3.17737i) q^{43} +(4.05709 - 4.06200i) q^{45} +(-5.00993 + 2.33617i) q^{47} +(-2.45407 - 1.41686i) q^{49} +(0.0885442 - 0.0156127i) q^{51} +(0.933570 - 10.6708i) q^{53} +(-3.32099 + 2.32838i) q^{55} +(-2.84280 - 0.369220i) q^{57} +(-8.38425 + 3.05162i) q^{59} +(-5.98020 + 5.01798i) q^{61} +(3.00589 - 4.29286i) q^{63} +(-1.97847 - 3.42202i) q^{65} +(-3.83106 - 8.21573i) q^{67} +(2.00510 + 3.47293i) q^{69} +(-1.87804 + 2.23816i) q^{71} +(2.70247 - 1.89229i) q^{73} +(-0.847230 + 3.17729i) q^{75} +(-2.61795 + 2.61795i) q^{77} +(-2.28065 + 12.9342i) q^{79} +(-4.05575 - 3.40318i) q^{81} +(4.13317 - 15.4252i) q^{83} +(0.234059 - 0.196640i) q^{85} +(-0.569489 - 2.12536i) q^{87} +(-1.72877 - 9.80435i) q^{89} +(-2.31932 - 2.76406i) q^{91} +(0.468526 + 0.218477i) q^{93} +(-8.99608 + 3.75108i) q^{95} +(-5.79625 - 2.70284i) q^{97} +(2.99348 + 3.56749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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

Properties

Related objects

Downloads

Learn more