LMFDB - Embedded newform 380.2.bh.a.117.2

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			117.2
Character	$\chi$	$=$	380.117
Dual form			380.2.bh.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38123 - 1.11039i) q^{3} +(1.56340 - 1.59868i) q^{5} +(0.558906 - 2.08587i) q^{7} +(2.50894 + 2.99004i) q^{9} +O(q^{10})$	\(q+(-2.38123 - 1.11039i) q^{3} +(1.56340 - 1.59868i) q^{5} +(0.558906 - 2.08587i) q^{7} +(2.50894 + 2.99004i) q^{9} +(-0.730936 + 1.26602i) q^{11} +(-0.349226 - 0.748918i) q^{13} +(-5.49797 + 2.07086i) q^{15} +(-0.237149 - 2.71062i) q^{17} +(-4.25189 - 0.959893i) q^{19} +(-3.64700 + 4.34633i) q^{21} +(-5.66631 - 3.96759i) q^{23} +(-0.111572 - 4.99876i) q^{25} +(-0.614204 - 2.29224i) q^{27} +(-1.39280 + 1.16870i) q^{29} +(-1.26371 + 0.729601i) q^{31} +(3.14629 - 2.20306i) q^{33} +(-2.46084 - 4.15455i) q^{35} +(0.309697 - 0.309697i) q^{37} +2.17112i q^{39} +(0.339156 + 0.931825i) q^{41} +(-5.64709 - 8.06488i) q^{43} +(8.70259 + 0.663621i) q^{45} +(10.9192 + 0.955306i) q^{47} +(2.02372 + 1.16839i) q^{49} +(-2.44513 + 6.71794i) q^{51} +(-5.47646 + 7.82119i) q^{53} +(0.881217 + 3.14782i) q^{55} +(9.05889 + 7.00697i) q^{57} +(-4.73412 - 3.97240i) q^{59} +(0.0111039 + 0.0629732i) q^{61} +(7.63907 - 3.56216i) q^{63} +(-1.74326 - 0.612555i) q^{65} +(-0.176397 + 2.01623i) q^{67} +(9.08722 + 15.7395i) q^{69} +(13.0287 + 2.29730i) q^{71} +(6.33800 - 13.5919i) q^{73} +(-5.28487 + 12.0271i) q^{75} +(2.23222 + 2.23222i) q^{77} +(2.02226 - 0.736043i) q^{79} +(0.950647 - 5.39139i) q^{81} +(12.1400 + 3.25291i) q^{83} +(-4.70418 - 3.85865i) q^{85} +(4.61428 - 1.23639i) q^{87} +(11.7510 + 4.27701i) q^{89} +(-1.75733 + 0.309864i) q^{91} +(3.81931 - 0.334147i) q^{93} +(-8.18197 + 5.29673i) q^{95} +(-9.92678 + 0.868480i) q^{97} +(-5.61931 + 0.990836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.38123	−	1.11039i	−1.37480	−	0.641082i	−0.411975	−	0.911195i	$-0.635161\pi$
$3$	−2.38123	−	1.11039i	−1.37480	−	0.641082i	−0.962829	+	0.270113i	$0.912939\pi$
$4$		0			0
$5$	1.56340	−	1.59868i	0.699173	−	0.714953i
$5$	1.56340	−	1.59868i	0.699173	−	0.714953i
$6$		0			0
$7$	0.558906	−	2.08587i	0.211247	−	0.788383i	−0.776208	−	0.630477i	$-0.782859\pi$
$7$	0.558906	−	2.08587i	0.211247	−	0.788383i	0.987454	−	0.157906i	$-0.0504742\pi$
$8$		0			0
$9$	2.50894	+	2.99004i	0.836313	+	0.996679i
$10$		0			0
$11$	−0.730936	+	1.26602i	−0.220385	+	0.381719i	−0.954925	−	0.296847i	$-0.904065\pi$
$11$	−0.730936	+	1.26602i	−0.220385	+	0.381719i	0.734540	+	0.678566i	$0.237398\pi$
$12$		0			0
$13$	−0.349226	−	0.748918i	−0.0968579	−	0.207712i	0.851909	−	0.523691i	$-0.175445\pi$
$13$	−0.349226	−	0.748918i	−0.0968579	−	0.207712i	−0.948766	+	0.315978i	$0.897667\pi$
$14$		0			0
$15$	−5.49797	+	2.07086i	−1.41957	+	0.534693i
$16$		0			0
$17$	−0.237149	−	2.71062i	−0.0575170	−	0.657422i	−0.969159	−	0.246437i	$-0.920740\pi$
$17$	−0.237149	−	2.71062i	−0.0575170	−	0.657422i	0.911642	−	0.410985i	$-0.134815\pi$
$18$		0			0
$19$	−4.25189	−	0.959893i	−0.975451	−	0.220214i
$19$	−4.25189	−	0.959893i	−0.975451	−	0.220214i
$20$		0			0
$21$	−3.64700	+	4.34633i	−0.795841	+	0.948446i
$22$		0			0
$23$	−5.66631	−	3.96759i	−1.18151	−	0.827300i	−0.193407	−	0.981119i	$-0.561954\pi$
$23$	−5.66631	−	3.96759i	−1.18151	−	0.827300i	−0.988099	+	0.153819i	$0.950843\pi$
$24$		0			0
$25$	−0.111572	−	4.99876i	−0.0223144	−	0.999751i
$26$		0			0
$27$	−0.614204	−	2.29224i	−0.118204	−	0.441142i
$28$		0			0
$29$	−1.39280	+	1.16870i	−0.258636	+	0.217022i	−0.762881	−	0.646539i	$-0.776216\pi$
$29$	−1.39280	+	1.16870i	−0.258636	+	0.217022i	0.504244	+	0.863561i	$0.331771\pi$
$30$		0			0
$31$	−1.26371	+	0.729601i	−0.226968	+	0.131040i	−0.609173	−	0.793038i	$-0.708498\pi$
$31$	−1.26371	+	0.729601i	−0.226968	+	0.131040i	0.382204	+	0.924078i	$0.375165\pi$
$32$		0			0
$33$	3.14629	−	2.20306i	0.547700	−	0.383503i
$34$		0			0
$35$	−2.46084	−	4.15455i	−0.415959	−	0.702248i
$36$		0			0
$37$	0.309697	−	0.309697i	0.0509138	−	0.0509138i	−0.681191	−	0.732105i	$-0.738538\pi$
$37$	0.309697	−	0.309697i	0.0509138	−	0.0509138i	0.732105	+	0.681191i	$0.238538\pi$
$38$		0			0
$39$			2.17112i			0.347658i
$40$		0			0
$41$	0.339156	+	0.931825i	0.0529673	+	0.145527i	0.963355	−	0.268230i	$-0.0864387\pi$
$41$	0.339156	+	0.931825i	0.0529673	+	0.145527i	−0.910388	+	0.413757i	$0.864216\pi$
$42$		0			0
$43$	−5.64709	−	8.06488i	−0.861173	−	1.22988i	−0.971749	−	0.236015i	$-0.924159\pi$
$43$	−5.64709	−	8.06488i	−0.861173	−	1.22988i	0.110576	−	0.993868i	$-0.464730\pi$
$44$		0			0
$45$	8.70259	+	0.663621i	1.29731	+	0.0989268i
$46$		0			0
$47$	10.9192	+	0.955306i	1.59273	+	0.139346i	0.848727	−	0.528831i	$-0.177370\pi$
$47$	10.9192	+	0.955306i	1.59273	+	0.139346i	0.744002	+	0.668177i	$0.232925\pi$
$48$		0			0
$49$	2.02372	+	1.16839i	0.289102	+	0.166913i
$50$		0			0
$51$	−2.44513	+	6.71794i	−0.342387	+	0.940699i
$52$		0			0
$53$	−5.47646	+	7.82119i	−0.752249	+	1.07432i	0.242315	+	0.970198i	$0.422093\pi$
$53$	−5.47646	+	7.82119i	−0.752249	+	1.07432i	−0.994564	+	0.104126i	$0.966796\pi$
$54$		0			0
$55$	0.881217	+	3.14782i	0.118823	+	0.424453i
$56$		0			0
$57$	9.05889	+	7.00697i	1.19988	+	0.928096i
$58$		0			0
$59$	−4.73412	−	3.97240i	−0.616330	−	0.517162i	0.280318	−	0.959907i	$-0.409560\pi$
$59$	−4.73412	−	3.97240i	−0.616330	−	0.517162i	−0.896647	+	0.442745i	$0.854005\pi$
$60$		0			0
$61$	0.0111039	+	0.0629732i	0.00142171	+	0.00806290i	0.985510	−	0.169615i	$-0.0542525\pi$
$61$	0.0111039	+	0.0629732i	0.00142171	+	0.00806290i	−0.984089	+	0.177678i	$0.943141\pi$
$62$		0			0
$63$	7.63907	−	3.56216i	0.962433	−	0.448790i
$64$		0			0
$65$	−1.74326	−	0.612555i	−0.216225	−	0.0759781i
$66$		0			0
$67$	−0.176397	+	2.01623i	−0.0215504	+	0.246322i	0.977777	+	0.209648i	$0.0672318\pi$
$67$	−0.176397	+	2.01623i	−0.0215504	+	0.246322i	−0.999327	+	0.0366737i	$0.988324\pi$
$68$		0			0
$69$	9.08722	+	15.7395i	1.09397	+	1.89482i
$70$		0			0
$71$	13.0287	+	2.29730i	1.54622	+	0.272640i	0.880675	−	0.473720i	$-0.157089\pi$
$71$	13.0287	+	2.29730i	1.54622	+	0.272640i	0.665542	+	0.746360i	$0.268200\pi$
$72$		0			0
$73$	6.33800	−	13.5919i	0.741807	−	1.59081i	−0.0635204	−	0.997981i	$-0.520233\pi$
$73$	6.33800	−	13.5919i	0.741807	−	1.59081i	0.805328	−	0.592830i	$-0.201989\pi$
$74$		0			0
$75$	−5.28487	+	12.0271i	−0.610244	+	1.38877i
$76$		0			0
$77$	2.23222	+	2.23222i	0.254385	+	0.254385i
$78$		0			0
$79$	2.02226	−	0.736043i	0.227522	−	0.0828113i	−0.225743	−	0.974187i	$-0.572481\pi$
$79$	2.02226	−	0.736043i	0.227522	−	0.0828113i	0.453266	+	0.891375i	$0.350259\pi$
$80$		0			0
$81$	0.950647	−	5.39139i	0.105627	−	0.599043i
$82$		0			0
$83$	12.1400	+	3.25291i	1.33254	+	0.357053i	0.853661	−	0.520829i	$-0.174377\pi$
$83$	12.1400	+	3.25291i	1.33254	+	0.357053i	0.478878	+	0.877882i	$0.341044\pi$
$84$		0			0
$85$	−4.70418	−	3.85865i	−0.510240	−	0.418530i
$86$		0			0
$87$	4.61428	−	1.23639i	0.494703	−	0.132555i
$88$		0			0
$89$	11.7510	+	4.27701i	1.24560	+	0.453362i	0.878913	−	0.476982i	$-0.158269\pi$
$89$	11.7510	+	4.27701i	1.24560	+	0.453362i	0.366688	+	0.930344i	$0.380492\pi$
$90$		0			0
$91$	−1.75733	+	0.309864i	−0.184218	+	0.0324826i
$92$		0			0
$93$	3.81931	−	0.334147i	0.396044	−	0.0346494i
$94$		0			0
$95$	−8.18197	+	5.29673i	−0.839452	+	0.543434i
$96$		0			0
$97$	−9.92678	+	0.868480i	−1.00791	+	0.0881808i	−0.579137	−	0.815231i	$-0.696610\pi$
$97$	−9.92678	+	0.868480i	−1.00791	+	0.0881808i	−0.428775	+	0.903411i	$0.641055\pi$
$98$		0			0
$99$	−5.61931	+	0.990836i	−0.564762	+	0.0995828i
$100$		0			0
$101$	−6.98936	−	2.54392i	−0.695468	−	0.253130i	−0.0299932	−	0.999550i	$-0.509549\pi$
$101$	−6.98936	−	2.54392i	−0.695468	−	0.253130i	−0.665475	+	0.746421i	$0.731771\pi$
$102$		0			0
$103$	13.0684	−	3.50166i	1.28767	−	0.345029i	0.450893	−	0.892578i	$-0.351106\pi$
$103$	13.0684	−	3.50166i	1.28767	−	0.345029i	0.836774	+	0.547549i	$0.184439\pi$
$104$		0			0
$105$	1.24668	+	12.6254i	0.121664	+	1.23212i
$106$		0			0
$107$	−2.00090	−	0.536140i	−0.193435	−	0.0518306i	0.160801	−	0.986987i	$-0.448592\pi$
$107$	−2.00090	−	0.536140i	−0.193435	−	0.0518306i	−0.354236	+	0.935156i	$0.615259\pi$
$108$		0			0
$109$	3.56668	−	20.2276i	0.341626	−	1.93746i	−0.00642372	−	0.999979i	$-0.502045\pi$
$109$	3.56668	−	20.2276i	0.341626	−	1.93746i	0.348049	−	0.937476i	$-0.386844\pi$
$110$		0			0
$111$	−1.08134	+	0.393576i	−0.102636	+	0.0373566i
$112$		0			0
$113$	−13.3811	−	13.3811i	−1.25879	−	1.25879i	−0.951670	−	0.307122i	$-0.900634\pi$
$113$	−13.3811	−	13.3811i	−1.25879	−	1.25879i	−0.307122	−	0.951670i	$-0.599366\pi$
$114$		0			0
$115$	−15.2016	+	2.85570i	−1.41756	+	0.266296i
$116$		0			0
$117$	1.36310	−	2.92319i	0.126019	−	0.270249i
$118$		0			0
$119$	−5.78654	−	1.02032i	−0.530451	−	0.0935328i
$120$		0			0
$121$	4.43147	+	7.67552i	0.402861	+	0.697775i
$122$		0			0
$123$	0.227075	−	2.59548i	0.0204747	−	0.234027i
$124$		0			0
$125$	−8.16585	−	7.63668i	−0.730376	−	0.683045i
$126$		0			0
$127$	−11.4484	+	5.33846i	−1.01588	+	0.473712i	−0.857947	−	0.513738i	$-0.828260\pi$
$127$	−11.4484	+	5.33846i	−1.01588	+	0.473712i	−0.157931	+	0.987450i	$0.550483\pi$
$128$		0			0
$129$	4.49189	+	25.4748i	0.395489	+	2.24293i
$130$		0			0
$131$	10.5177	+	8.82537i	0.918933	+	0.771076i	0.973797	−	0.227418i	$-0.0730283\pi$
$131$	10.5177	+	8.82537i	0.918933	+	0.771076i	−0.0548646	+	0.998494i	$0.517473\pi$
$132$		0			0
$133$	−4.37862	+	8.33239i	−0.379674	+	0.722510i
$134$		0			0
$135$	−4.62481	−	2.60177i	−0.398040	−	0.223925i
$136$		0			0
$137$	−3.96702	+	5.66550i	−0.338926	+	0.484036i	−0.952047	−	0.305953i	$-0.901025\pi$
$137$	−3.96702	+	5.66550i	−0.338926	+	0.484036i	0.613121	+	0.789989i	$0.289914\pi$
$138$		0			0
$139$	6.75859	−	18.5691i	0.573256	−	1.57501i	−0.226069	−	0.974111i	$-0.572588\pi$
$139$	6.75859	−	18.5691i	0.573256	−	1.57501i	0.799326	−	0.600898i	$-0.205190\pi$
$140$		0			0
$141$	−24.9404	−	14.3993i	−2.10036	−	1.21264i
$142$		0			0
$143$	1.20341	+	0.105284i	0.100634	+	0.00880432i
$144$		0			0
$145$	−0.309124	+	4.05379i	−0.0256714	+	0.336649i
$146$		0			0
$147$	−3.52157	−	5.02932i	−0.290454	−	0.414811i
$148$		0			0
$149$	4.11924	+	11.3175i	0.337461	+	0.927167i	0.986112	+	0.166081i	$0.0531113\pi$
$149$	4.11924	+	11.3175i	0.337461	+	0.927167i	−0.648651	+	0.761086i	$0.724666\pi$
$150$		0			0
$151$		−	21.7280i		−	1.76820i	−0.467296	−	0.884101i	$-0.654772\pi$
$151$		−	21.7280i		−	1.76820i	0.467296	−	0.884101i	$-0.345228\pi$
$152$		0			0
$153$	7.50986	−	7.50986i	0.607136	−	0.607136i
$154$		0			0
$155$	−0.809275	+	3.16092i	−0.0650026	+	0.253891i
$156$		0			0
$157$	6.53099	−	4.57305i	0.521230	−	0.364969i	−0.283158	−	0.959073i	$-0.591382\pi$
$157$	6.53099	−	4.57305i	0.521230	−	0.364969i	0.804388	+	0.594104i	$0.202493\pi$
$158$		0			0
$159$	21.7253	−	12.5431i	1.72292	−	0.994731i
$160$		0			0
$161$	−11.4428	+	9.60165i	−0.901819	+	0.756716i
$162$		0			0
$163$	1.40873	+	5.25745i	0.110340	+	0.411795i	0.998896	−	0.0469731i	$-0.0149575\pi$
$163$	1.40873	+	5.25745i	0.110340	+	0.411795i	−0.888556	+	0.458768i	$0.848291\pi$
$164$		0			0
$165$	1.39692	−	8.47419i	0.108750	−	0.659714i
$166$		0			0
$167$	15.2439	+	10.6739i	1.17961	+	0.825973i	0.987841	−	0.155467i	$-0.0496882\pi$
$167$	15.2439	+	10.6739i	1.17961	+	0.825973i	0.191770	+	0.981440i	$0.438577\pi$
$168$		0			0
$169$	7.91732	−	9.43549i	0.609025	−	0.725807i
$170$		0			0
$171$	−7.79763	−	15.1216i	−0.596299	−	1.15638i
$172$		0			0
$173$	1.11462	+	12.7401i	0.0847429	+	0.968616i	0.912917	+	0.408145i	$0.133824\pi$
$173$	1.11462	+	12.7401i	0.0847429	+	0.968616i	−0.828174	+	0.560471i	$0.810620\pi$
$174$		0			0
$175$	−10.4891	−	2.56111i	−0.792901	−	0.193602i
$176$		0			0
$177$	6.86213	+	14.7159i	0.515789	+	1.10611i
$178$		0			0
$179$	−6.86857	+	11.8967i	−0.513381	+	0.889202i	0.486499	+	0.873681i	$0.338274\pi$
$179$	−6.86857	+	11.8967i	−0.513381	+	0.889202i	−0.999880	+	0.0155204i	$0.995060\pi$
$180$		0			0
$181$	−1.26467	−	1.50718i	−0.0940024	−	0.112028i	0.716993	−	0.697081i	$-0.245518\pi$
$181$	−1.26467	−	1.50718i	−0.0940024	−	0.112028i	−0.810995	+	0.585053i	$0.801074\pi$
$182$		0			0
$183$	0.0434837	−	0.162283i	0.00321441	−	0.0119963i
$184$		0			0
$185$	−0.0109274	−	0.979286i	−0.000803401	−	0.0719985i
$186$		0			0
$187$	3.60503	+	1.68106i	0.263626	+	0.122931i
$188$		0			0
$189$	−5.12459			−0.372759
$190$		0			0
$191$	−7.72276			−0.558799			−0.279400	−	0.960175i	$-0.590135\pi$
$191$	−7.72276			−0.558799			−0.279400	+	0.960175i	$0.590135\pi$
$192$		0			0
$193$	−1.56066	−	0.727748i	−0.112339	−	0.0523845i	0.365636	−	0.930758i	$-0.380851\pi$
$193$	−1.56066	−	0.727748i	−0.112339	−	0.0523845i	−0.477975	+	0.878373i	$0.658629\pi$
$194$		0			0
$195$	3.47093	+	3.39433i	0.248559	+	0.243073i
$196$		0			0
$197$	−0.701434	+	2.61779i	−0.0499751	+	0.186510i	−0.986401	−	0.164355i	$-0.947446\pi$
$197$	−0.701434	+	2.61779i	−0.0499751	+	0.186510i	0.936426	+	0.350865i	$0.114112\pi$
$198$		0			0
$199$	10.4768	+	12.4858i	0.742680	+	0.885091i	0.996622	−	0.0821280i	$-0.0261716\pi$
$199$	10.4768	+	12.4858i	0.742680	+	0.885091i	−0.253942	+	0.967219i	$0.581727\pi$
$200$		0			0
$201$	2.65884	−	4.60524i	0.187540	−	0.324828i
$202$		0			0
$203$	1.65930	+	3.55839i	0.116460	+	0.249750i
$204$		0			0
$205$	2.01993	+	0.914609i	0.141078	+	0.0638791i
$206$		0			0
$207$	−2.35317	−	26.8969i	−0.163557	−	1.86946i
$208$		0			0
$209$	4.32310	−	4.68135i	0.299035	−	0.323816i
$210$		0			0
$211$	8.61100	−	10.2622i	0.592806	−	0.706479i	−0.383337	−	0.923609i	$-0.625225\pi$
$211$	8.61100	−	10.2622i	0.592806	−	0.706479i	0.976143	+	0.217130i	$0.0696696\pi$
$212$		0			0
$213$	−28.4733	−	19.9372i	−1.95096	−	1.36608i
$214$		0			0
$215$	−21.7218	−	3.58072i	−1.48142	−	0.244203i
$216$		0			0
$217$	0.815557	+	3.04370i	0.0553636	+	0.206620i
$218$		0			0
$219$	−30.1845	+	25.3278i	−2.03968	+	1.71149i
$220$		0			0
$221$	−1.94721	+	1.12422i	−0.130984	+	0.0756235i
$222$		0			0
$223$	−5.94978	+	4.16608i	−0.398427	+	0.278982i	−0.755570	−	0.655068i	$-0.772640\pi$
$223$	−5.94978	+	4.16608i	−0.398427	+	0.278982i	0.357143	+	0.934050i	$0.383751\pi$
$224$		0			0
$225$	14.6665	−	12.8752i	0.977769	−	0.858345i
$226$		0			0
$227$	11.2519	−	11.2519i	0.746813	−	0.746813i	−0.227067	−	0.973879i	$-0.572913\pi$
$227$	11.2519	−	11.2519i	0.746813	−	0.746813i	0.973879	+	0.227067i	$0.0729135\pi$
$228$		0			0
$229$		−	17.1090i		−	1.13059i	−0.824888	−	0.565296i	$-0.808762\pi$
$229$		−	17.1090i		−	1.13059i	0.824888	−	0.565296i	$-0.191238\pi$
$230$		0			0
$231$	−2.83680	−	7.79405i	−0.186648	−	0.512811i
$232$		0			0
$233$	7.89205	+	11.2710i	0.517025	+	0.738389i	0.989748	−	0.142822i	$-0.0456178\pi$
$233$	7.89205	+	11.2710i	0.517025	+	0.738389i	−0.472723	+	0.881211i	$0.656729\pi$
$234$		0			0
$235$	18.5983	−	15.9628i	1.21322	−	1.04130i
$236$		0			0
$237$	−5.63276	−	0.492803i	−0.365887	−	0.0320110i
$238$		0			0
$239$	−10.0336	−	5.79288i	−0.649017	−	0.374710i	0.139062	−	0.990284i	$-0.455591\pi$
$239$	−10.0336	−	5.79288i	−0.649017	−	0.374710i	−0.788080	+	0.615573i	$0.788924\pi$
$240$		0			0
$241$	−1.49523	+	4.10811i	−0.0963161	+	0.264626i	−0.978489	−	0.206300i	$-0.933858\pi$
$241$	−1.49523	+	4.10811i	−0.0963161	+	0.264626i	0.882173	+	0.470926i	$0.156080\pi$
$242$		0			0
$243$	−12.3337	+	17.6144i	−0.791207	+	1.12996i
$244$		0			0
$245$	5.03177	−	1.40862i	0.321468	−	0.0899932i
$246$		0			0
$247$	0.765992	+	3.51954i	0.0487389	+	0.223943i
$248$		0			0
$249$	−25.2962	−	21.2260i	−1.60308	−	1.34514i
$250$		0			0
$251$	4.34823	+	24.6600i	0.274458	+	1.55653i	0.740679	+	0.671859i	$0.234504\pi$
$251$	4.34823	+	24.6600i	0.274458	+	1.55653i	−0.466221	+	0.884668i	$0.654385\pi$
$252$		0			0
$253$	9.16475	−	4.27359i	0.576183	−	0.268678i
$254$		0			0
$255$	6.91714	+	14.4118i	0.433168	+	0.902502i
$256$		0			0
$257$	1.22664	−	14.0206i	0.0765157	−	0.874579i	−0.856830	−	0.515599i	$-0.827569\pi$
$257$	1.22664	−	14.0206i	0.0765157	−	0.874579i	0.933346	−	0.358979i	$-0.116875\pi$
$258$		0			0
$259$	−0.472894	−	0.819077i	−0.0293842	−	0.0508950i
$260$		0			0
$261$	−6.98890	−	1.23233i	−0.432602	−	0.0762794i
$262$		0			0
$263$	−0.0563004	+	0.120737i	−0.00347163	+	0.00744493i	−0.908036	−	0.418892i	$-0.862419\pi$
$263$	−0.0563004	+	0.120737i	−0.00347163	+	0.00744493i	0.904564	+	0.426337i	$0.140196\pi$
$264$		0			0
$265$	3.94172	+	20.9828i	0.242138	+	1.28896i
$266$		0			0
$267$	−23.2327	−	23.2327i	−1.42182	−	1.42182i
$268$		0			0
$269$	4.35873	−	1.58645i	0.265756	−	0.0967274i	−0.205705	−	0.978614i	$-0.565949\pi$
$269$	4.35873	−	1.58645i	0.265756	−	0.0967274i	0.471462	+	0.881887i	$0.343727\pi$
$270$		0			0
$271$	−1.42075	+	8.05748i	−0.0863045	+	0.489457i	0.910763	+	0.412930i	$0.135494\pi$
$271$	−1.42075	+	8.05748i	−0.0863045	+	0.489457i	−0.997067	+	0.0765276i	$0.975617\pi$
$272$		0			0
$273$	4.52867	+	1.21345i	0.274088	+	0.0734415i
$274$		0			0
$275$	6.41007	+	3.51252i	0.386541	+	0.211813i
$276$		0			0
$277$	−26.5790	+	7.12181i	−1.59697	+	0.427908i	−0.944127	−	0.329581i	$-0.893092\pi$
$277$	−26.5790	+	7.12181i	−1.59697	+	0.427908i	−0.652848	+	0.757489i	$0.726426\pi$
$278$		0			0
$279$	−5.35209	−	1.94800i	−0.320421	−	0.116624i
$280$		0			0
$281$	23.1580	−	4.08337i	1.38149	−	0.243594i	0.566973	−	0.823736i	$-0.308114\pi$
$281$	23.1580	−	4.08337i	1.38149	−	0.243594i	0.814515	+	0.580143i	$0.197003\pi$
$282$		0			0
$283$	−15.7284	+	1.37605i	−0.934955	+	0.0817980i	−0.544441	−	0.838799i	$-0.683258\pi$
$283$	−15.7284	+	1.37605i	−0.934955	+	0.0817980i	−0.390514	+	0.920597i	$0.627703\pi$
$284$		0			0
$285$	25.3646	−	3.52760i	1.50247	−	0.208957i
$286$		0			0
$287$	2.13322	−	0.186632i	0.125920	−	0.0110166i
$288$		0			0
$289$	9.45051	−	1.66638i	0.555912	−	0.0980223i
$290$		0			0
$291$	24.6023	+	8.95450i	1.44221	+	0.524922i
$292$		0			0
$293$	−7.04746	+	1.88836i	−0.411717	+	0.110319i	−0.458732	−	0.888575i	$-0.651696\pi$
$293$	−7.04746	+	1.88836i	−0.411717	+	0.110319i	0.0470143	+	0.998894i	$0.485029\pi$
$294$		0			0
$295$	−13.7519	+	1.35791i	−0.800667	+	0.0790608i
$296$		0			0
$297$	3.35096	+	0.897888i	0.194443	+	0.0521007i
$298$		0			0
$299$	−0.992577	+	5.62918i	−0.0574022	+	0.325544i
$300$		0			0
$301$	−19.9785	+	7.27156i	−1.15154	+	0.419126i
$302$		0			0
$303$	13.8186	+	13.8186i	0.793855	+	0.793855i
$304$		0			0
$305$	0.118034	+	0.0807007i	0.00675861	+	0.00462091i
$306$		0			0
$307$	5.40813	−	11.5978i	0.308658	−	0.661920i	−0.689388	−	0.724392i	$-0.742121\pi$
$307$	5.40813	−	11.5978i	0.308658	−	0.661920i	0.998047	+	0.0624721i	$0.0198984\pi$
$308$		0			0
$309$	−35.0070	−	6.17269i	−1.99148	−	0.351152i
$310$		0			0
$311$	−0.789525	−	1.36750i	−0.0447699	−	0.0775437i	0.842772	−	0.538271i	$-0.180922\pi$
$311$	−0.789525	−	1.36750i	−0.0447699	−	0.0775437i	−0.887542	+	0.460727i	$0.847589\pi$
$312$		0			0
$313$	−0.0435813	+	0.498136i	−0.00246336	+	0.0281563i	−0.997327	−	0.0730689i	$-0.976721\pi$
$313$	−0.0435813	+	0.498136i	−0.00246336	+	0.0281563i	0.994864	+	0.101225i	$0.0322763\pi$
$314$		0			0
$315$	6.24815	−	17.7815i	0.352044	−	1.00188i
$316$		0			0
$317$	−7.77864	+	3.62724i	−0.436892	+	0.203726i	−0.628605	−	0.777725i	$-0.716374\pi$
$317$	−7.77864	+	3.62724i	−0.436892	+	0.203726i	0.191713	+	0.981451i	$0.438596\pi$
$318$		0			0
$319$	−0.461545	−	2.61755i	−0.0258416	−	0.146555i
$320$		0			0
$321$	4.16929	+	3.49845i	0.232707	+	0.195264i
$322$		0			0
$323$	−1.59357	+	11.7529i	−0.0886688	+	0.653949i
$324$		0			0
$325$	−3.70469	+	1.82925i	−0.205499	+	0.101469i
$326$		0			0
$327$	−30.9536	+	44.2063i	−1.71174	+	2.44461i
$328$		0			0
$329$	8.09545	−	22.2421i	0.446317	−	1.22624i
$330$		0			0
$331$	28.8818	+	16.6749i	1.58749	+	0.916535i	0.993720	+	0.111897i	$0.0356927\pi$
$331$	28.8818	+	16.6749i	1.58749	+	0.916535i	0.593766	+	0.804638i	$0.297641\pi$
$332$		0			0
$333$	1.70301	+	0.148994i	0.0933246	+	0.00816484i
$334$		0			0
$335$	2.94753	+	3.43417i	0.161041	+	0.187629i
$336$		0			0
$337$	3.29091	+	4.69991i	0.179267	+	0.256020i	0.898722	−	0.438519i	$-0.144497\pi$
$337$	3.29091	+	4.69991i	0.179267	+	0.256020i	−0.719454	+	0.694540i	$0.755608\pi$
$338$		0			0
$339$	17.0053	+	46.7218i	0.923604	+	2.53758i
$340$		0			0
$341$		−	2.13317i		−	0.115517i
$342$		0			0
$343$	14.2569	−	14.2569i	0.769800	−	0.769800i
$344$		0			0
$345$	39.3695	+	10.0796i	2.11958	+	0.542666i
$346$		0			0
$347$	21.1673	−	14.8215i	1.13632	−	0.795659i	0.154975	−	0.987918i	$-0.450470\pi$
$347$	21.1673	−	14.8215i	1.13632	−	0.795659i	0.981344	+	0.192259i	$0.0615814\pi$
$348$		0			0
$349$	−13.6620	+	7.88776i	−0.731310	+	0.422222i	−0.818901	−	0.573935i	$-0.805416\pi$
$349$	−13.6620	+	7.88776i	−0.731310	+	0.422222i	0.0875913	+	0.996156i	$0.472083\pi$
$350$		0			0
$351$	−1.50220	+	1.26050i	−0.0801817	+	0.0672805i
$352$		0			0
$353$	1.48906	+	5.55725i	0.0792547	+	0.295783i	0.994164	−	0.107876i	$-0.0344050\pi$
$353$	1.48906	+	5.55725i	0.0792547	+	0.295783i	−0.914910	+	0.403659i	$0.867738\pi$
$354$		0			0
$355$	24.0416	−	17.2371i	1.27600	−	0.914850i
$356$		0			0
$357$	12.6461	+	8.85491i	0.669304	+	0.468651i
$358$		0			0
$359$	2.00499	−	2.38946i	0.105820	−	0.126111i	−0.710535	−	0.703662i	$-0.751547\pi$
$359$	2.00499	−	2.38946i	0.105820	−	0.126111i	0.816355	+	0.577551i	$0.195992\pi$
$360$		0			0
$361$	17.1572	+	8.16273i	0.903011	+	0.429617i
$362$		0			0
$363$	−2.02955	−	23.1978i	−0.106524	−	1.21757i
$364$		0			0
$365$	−11.8203	−	31.3820i	−0.618703	−	1.64261i
$366$		0			0
$367$	1.66951	+	3.58028i	0.0871478	+	0.186889i	0.945052	−	0.326921i	$-0.106011\pi$
$367$	1.66951	+	3.58028i	0.0871478	+	0.186889i	−0.857904	+	0.513810i	$0.828233\pi$
$368$		0			0
$369$	−1.93527	+	3.35198i	−0.100746	+	0.174497i
$370$		0			0
$371$	13.2531	+	15.7945i	0.688068	+	0.820008i
$372$		0			0
$373$	−2.74928	+	10.2605i	−0.142352	+	0.531266i	0.857507	+	0.514473i	$0.172012\pi$
$373$	−2.74928	+	10.2605i	−0.142352	+	0.531266i	−0.999859	+	0.0167934i	$0.994654\pi$
$374$		0			0
$375$	10.9651	+	27.2519i	0.566236	+	1.40728i
$376$		0			0
$377$	1.36166	+	0.634953i	0.0701291	+	0.0327017i
$378$		0			0
$379$	−1.77489			−0.0911701			−0.0455850	−	0.998960i	$-0.514515\pi$
$379$	−1.77489			−0.0911701			−0.0455850	+	0.998960i	$0.514515\pi$
$380$		0			0
$381$	33.1890			1.70032
$382$		0			0
$383$	24.3069	+	11.3345i	1.24202	+	0.579165i	0.928824	−	0.370522i	$-0.120821\pi$
$383$	24.3069	+	11.3345i	1.24202	+	0.579165i	0.313200	+	0.949687i	$0.398599\pi$
$384$		0			0
$385$	7.05846	−	0.0787623i	0.359732	−	0.00401410i
$386$		0			0
$387$	9.94608	−	37.1193i	0.505588	−	1.88688i
$388$		0			0
$389$	−11.1104	−	13.2408i	−0.563318	−	0.671336i	0.406928	−	0.913460i	$-0.366600\pi$
$389$	−11.1104	−	13.2408i	−0.563318	−	0.671336i	−0.970245	+	0.242125i	$0.922156\pi$
$390$		0			0
$391$	−9.41088	+	16.3001i	−0.475928	+	0.824332i
$392$		0			0
$393$	−15.2454	−	32.6939i	−0.769030	−	1.64919i
$394$		0			0
$395$	1.98490	−	4.38368i	0.0998712	−	0.220567i
$396$		0			0
$397$	0.398077	+	4.55004i	0.0199789	+	0.228360i	0.999619	+	0.0275986i	$0.00878604\pi$
$397$	0.398077	+	4.55004i	0.0199789	+	0.228360i	−0.979640	+	0.200761i	$0.935658\pi$
$398$		0			0
$399$	19.6787	−	14.9794i	0.985166	−	0.749907i
$400$		0			0
$401$	9.78469	−	11.6609i	0.488624	−	0.582320i	−0.464243	−	0.885708i	$-0.653673\pi$
$401$	9.78469	−	11.6609i	0.488624	−	0.582320i	0.952867	+	0.303388i	$0.0981179\pi$
$402$		0			0
$403$	0.987730	+	0.691616i	0.0492023	+	0.0344519i
$404$		0			0
$405$	−7.13288	−	9.94867i	−0.354436	−	0.494354i
$406$		0			0
$407$	0.165713	+	0.618450i	0.00821409	+	0.0306554i
$408$		0			0
$409$	−19.0672	+	15.9993i	−0.942812	+	0.791113i	−0.978072	−	0.208265i	$-0.933218\pi$
$409$	−19.0672	+	15.9993i	−0.942812	+	0.791113i	0.0352604	+	0.999378i	$0.488774\pi$
$410$		0			0
$411$	15.7373	−	9.08593i	0.776263	−	0.448176i
$412$		0			0
$413$	−10.9318	+	7.65454i	−0.537919	+	0.376655i
$414$		0			0
$415$	24.1800	−	14.3224i	1.18695	−	0.703061i
$416$		0			0
$417$	−36.7126	+	36.7126i	−1.79782	+	1.79782i
$418$		0			0
$419$		−	17.8878i		−	0.873877i	−0.899491	−	0.436939i	$-0.856063\pi$
$419$		−	17.8878i		−	0.873877i	0.899491	−	0.436939i	$-0.143937\pi$
$420$		0			0
$421$	−8.99524	−	24.7142i	−0.438401	−	1.20450i	−0.940532	−	0.339706i	$-0.889673\pi$
$421$	−8.99524	−	24.7142i	−0.438401	−	1.20450i	0.502130	−	0.864792i	$-0.332550\pi$
$422$		0			0
$423$	24.5392	+	35.0456i	1.19314	+	1.70398i
$424$		0			0
$425$	−13.5233	+	1.48788i	−0.655975	+	0.0721726i
$426$		0			0
$427$	0.137560	+	0.0120349i	0.00665698	+	0.000582411i
$428$		0			0
$429$	−2.74868	−	1.58695i	−0.132707	−	0.0766187i
$430$		0			0
$431$	−3.69543	+	10.1531i	−0.178002	+	0.489058i	−0.996320	−	0.0857084i	$-0.972685\pi$
$431$	−3.69543	+	10.1531i	−0.178002	+	0.489058i	0.818318	+	0.574766i	$0.194907\pi$
$432$		0			0
$433$	−16.3089	+	23.2915i	−0.783756	+	1.11932i	0.206278	+	0.978493i	$0.433865\pi$
$433$	−16.3089	+	23.2915i	−0.783756	+	1.11932i	−0.990034	+	0.140826i	$0.955024\pi$
$434$		0			0
$435$	5.23736	−	9.30975i	0.251112	−	0.446368i
$436$		0			0
$437$	20.2841	+	22.3088i	0.970319	+	1.06718i
$438$		0			0
$439$	−18.3174	−	15.3701i	−0.874241	−	0.733575i	0.0907456	−	0.995874i	$-0.471075\pi$
$439$	−18.3174	−	15.3701i	−0.874241	−	0.733575i	−0.964987	+	0.262299i	$0.915519\pi$
$440$		0			0
$441$	1.58384	+	8.98241i	0.0754210	+	0.427734i
$442$		0			0
$443$	−16.4312	+	7.66199i	−0.780670	+	0.364032i	−0.771748	−	0.635928i	$-0.780618\pi$
$443$	−16.4312	+	7.66199i	−0.780670	+	0.364032i	−0.00892130	+	0.999960i	$0.502840\pi$
$444$		0			0
$445$	25.2090	−	12.0994i	1.19502	−	0.573568i
$446$		0			0
$447$	2.75795	−	31.5236i	0.130447	−	1.49101i
$448$		0			0
$449$	−5.71905	−	9.90569i	−0.269899	−	0.467478i	0.698937	−	0.715183i	$-0.253657\pi$
$449$	−5.71905	−	9.90569i	−0.269899	−	0.467478i	−0.968835	+	0.247705i	$0.920324\pi$
$450$		0			0
$451$	−1.42761	−	0.251726i	−0.0672234	−	0.0118533i
$452$		0			0
$453$	−24.1265	+	51.7394i	−1.13356	+	2.43093i
$454$		0			0
$455$	−2.25203	+	3.29385i	−0.105577	+	0.154418i
$456$		0			0
$457$	13.9205	+	13.9205i	0.651173	+	0.651173i	0.953276	−	0.302102i	$-0.0976884\pi$
$457$	13.9205	+	13.9205i	0.651173	+	0.651173i	−0.302102	+	0.953276i	$0.597688\pi$
$458$		0			0
$459$	−6.06774	+	2.20848i	−0.283218	+	0.103083i
$460$		0			0
$461$	−2.37062	+	13.4444i	−0.110411	+	0.626170i	0.878510	+	0.477724i	$0.158538\pi$
$461$	−2.37062	+	13.4444i	−0.110411	+	0.626170i	−0.988921	+	0.148446i	$0.952573\pi$
$462$		0			0
$463$	−35.3266	−	9.46574i	−1.64177	−	0.439910i	−0.684476	−	0.729036i	$-0.739969\pi$
$463$	−35.3266	−	9.46574i	−1.64177	−	0.439910i	−0.957291	+	0.289126i	$0.906635\pi$
$464$		0			0
$465$	5.43691	−	6.62827i	0.252131	−	0.307379i
$466$		0			0
$467$	−4.32009	+	1.15756i	−0.199910	+	0.0535657i	−0.357384	−	0.933957i	$-0.616331\pi$
$467$	−4.32009	+	1.15756i	−0.199910	+	0.0535657i	0.157475	+	0.987523i	$0.449665\pi$
$468$		0			0
$469$	4.10700	+	1.49482i	0.189643	+	0.0690246i
$470$		0			0
$471$	−20.6296	+	3.63756i	−0.950564	+	0.167610i
$472$		0			0
$473$	14.3379	−	1.25441i	0.659259	−	0.0576777i
$474$		0			0
$475$	−4.32388	+	21.3613i	−0.198393	+	0.980123i
$476$		0			0
$477$	−37.1257	+	3.24808i	−1.69987	+	0.148719i
$478$		0			0
$479$	15.7074	−	2.76964i	0.717691	−	0.126548i	0.197136	−	0.980376i	$-0.436836\pi$
$479$	15.7074	−	2.76964i	0.717691	−	0.126548i	0.520555	+	0.853828i	$0.325725\pi$
$480$		0			0
$481$	−0.340091	−	0.123783i	−0.0155068	−	0.00564403i
$482$		0			0
$483$	37.9095	−	10.1578i	1.72494	−	0.462196i
$484$		0			0
$485$	−14.1311	+	17.2275i	−0.641659	+	0.782262i
$486$		0			0
$487$	−37.3087	−	9.99684i	−1.69062	−	0.453000i	−0.720069	−	0.693902i	$-0.755890\pi$
$487$	−37.3087	−	9.99684i	−1.69062	−	0.453000i	−0.970549	+	0.240902i	$0.922557\pi$
$488$		0			0
$489$	2.48329	−	14.0834i	0.112298	−	0.636874i
$490$		0			0
$491$	−27.1611	+	9.88583i	−1.22576	+	0.446141i	−0.872145	−	0.489248i	$-0.837271\pi$
$491$	−27.1611	+	9.88583i	−1.22576	+	0.446141i	−0.353619	+	0.935390i	$0.615049\pi$
$492$		0			0
$493$	3.49820	+	3.49820i	0.157551	+	0.157551i
$494$		0			0
$495$	−7.20119	+	10.5326i	−0.323669	+	0.473404i
$496$		0			0
$497$	12.0737	−	25.8921i	0.541578	−	1.16142i
$498$		0			0
$499$	16.1470	+	2.84716i	0.722841	+	0.127456i	0.522952	−	0.852362i	$-0.324831\pi$
$499$	16.1470	+	2.84716i	0.722841	+	0.127456i	0.199889	+	0.979819i	$0.435942\pi$
$500$		0			0
$501$	−24.4472	−	42.3437i	−1.09222	−	1.89178i
$502$		0			0
$503$	−1.11982	+	12.7996i	−0.0499305	+	0.570708i	0.929486	+	0.368858i	$0.120251\pi$
$503$	−1.11982	+	12.7996i	−0.0499305	+	0.570708i	−0.979416	+	0.201850i	$0.935305\pi$
$504$		0			0
$505$	−14.9941	+	7.19661i	−0.667228	+	0.320245i
$506$		0			0
$507$	−29.3300	+	13.6768i	−1.30259	+	0.607408i
$508$		0			0
$509$	−5.32090	−	30.1763i	−0.235845	−	1.33754i	−0.840828	−	0.541303i	$-0.817931\pi$
$509$	−5.32090	−	30.1763i	−0.235845	−	1.33754i	0.604983	−	0.796238i	$-0.293180\pi$
$510$		0			0
$511$	−24.8085	−	20.8168i	−1.09746	−	0.920882i
$512$		0			0
$513$	0.411226	+	10.3359i	0.0181561	+	0.456343i
$514$		0			0
$515$	14.8330	−	26.3667i	0.653622	−	1.16186i
$516$		0			0
$517$	−9.19067	+	13.1256i	−0.404205	+	0.577265i
$518$		0			0
$519$	11.4923	−	31.5749i	0.504457	−	1.38598i
$520$		0			0
$521$	−32.1106	−	18.5391i	−1.40679	−	0.812211i	−0.411714	−	0.911313i	$-0.635070\pi$
$521$	−32.1106	−	18.5391i	−1.40679	−	0.812211i	−0.995077	+	0.0991015i	$0.968403\pi$
$522$		0			0
$523$	−5.59078	−	0.489130i	−0.244468	−	0.0213882i	−0.0357367	−	0.999361i	$-0.511378\pi$
$523$	−5.59078	−	0.489130i	−0.244468	−	0.0213882i	−0.208731	+	0.977973i	$0.566933\pi$
$524$		0			0
$525$	22.1331	+	17.7455i	0.965969	+	0.774479i
$526$		0			0
$527$	2.27736	+	3.25240i	0.0992032	+	0.141677i
$528$		0			0
$529$	8.49879	+	23.3502i	0.369513	+	1.01523i
$530$		0			0
$531$		−	24.1217i		−	1.04679i
$532$		0			0
$533$	0.579418	−	0.579418i	0.0250974	−	0.0250974i
$534$		0			0
$535$	−3.98533	+	2.36061i	−0.172301	+	0.102058i
$536$		0			0
$537$	29.5656	−	20.7020i	1.27585	−	0.893359i
$538$		0			0
$539$	−2.95841	+	1.70804i	−0.127428	+	0.0735705i
$540$		0			0
$541$	12.9275	−	10.8475i	0.555796	−	0.466369i	−0.321102	−	0.947045i	$-0.604053\pi$
$541$	12.9275	−	10.8475i	0.555796	−	0.466369i	0.876898	+	0.480676i	$0.159609\pi$
$542$		0			0
$543$	1.33793	+	4.99321i	0.0574160	+	0.214279i
$544$		0			0
$545$	−26.7614	−	37.3258i	−1.14633	−	1.59886i
$546$		0			0
$547$	19.1093	+	13.3805i	0.817056	+	0.572109i	0.905683	−	0.423956i	$-0.139359\pi$
$547$	19.1093	+	13.3805i	0.817056	+	0.572109i	−0.0886268	+	0.996065i	$0.528248\pi$
$548$		0			0
$549$	−0.160433	+	0.191197i	−0.00684713	+	0.00816009i
$550$		0			0
$551$	7.04386	−	3.63224i	0.300079	−	0.154739i
$552$		0			0
$553$	−0.405033	−	4.62955i	−0.0172237	−	0.196868i
$554$		0			0
$555$	−1.06136	+	2.34404i	−0.0450524	+	0.0994989i
$556$		0			0
$557$	−7.28427	−	15.6212i	−0.308645	−	0.661890i	0.689401	−	0.724380i	$-0.257874\pi$
$557$	−7.28427	−	15.6212i	−0.308645	−	0.661890i	−0.998046	+	0.0624895i	$0.980096\pi$
$558$		0			0
$559$	−4.06782	+	7.04567i	−0.172051	+	0.298000i
$560$		0			0
$561$	−6.71780	−	8.00596i	−0.283626	−	0.338012i
$562$		0			0
$563$	5.46271	−	20.3871i	0.230226	−	0.859214i	−0.750017	−	0.661418i	$-0.769955\pi$
$563$	5.46271	−	20.3871i	0.230226	−	0.859214i	0.980243	−	0.197796i	$-0.0633784\pi$
$564$		0			0
$565$	−42.3123	+	0.472144i	−1.78009	+	0.0198633i
$566$		0			0
$567$	−10.7144	−	4.99620i	−0.449962	−	0.209821i
$568$		0			0
$569$	−19.7637			−0.828537			−0.414269	−	0.910155i	$-0.635963\pi$
$569$	−19.7637			−0.828537			−0.414269	+	0.910155i	$0.635963\pi$
$570$		0			0
$571$	11.4004			0.477090			0.238545	−	0.971131i	$-0.423330\pi$
$571$	11.4004			0.477090			0.238545	+	0.971131i	$0.423330\pi$
$572$		0			0
$573$	18.3897	+	8.57524i	0.768239	+	0.358236i
$574$		0			0
$575$	−19.2008	+	28.7671i	−0.800729	+	1.19967i
$576$		0			0
$577$	−9.84673	+	36.7485i	−0.409925	+	1.52986i	0.384864	+	0.922973i	$0.374248\pi$
$577$	−9.84673	+	36.7485i	−0.409925	+	1.52986i	−0.794789	+	0.606886i	$0.792418\pi$
$578$		0			0
$579$	2.90821	+	3.46587i	0.120861	+	0.144037i
$580$		0			0
$581$	13.5702	−	23.5044i	0.562989	−	0.975125i
$582$		0			0
$583$	−5.89883	−	12.6501i	−0.244305	−	0.523913i
$584$		0			0
$585$	−2.54217	−	6.74928i	−0.105106	−	0.279048i
$586$		0			0
$587$	0.00532294	+	0.0608415i	0.000219701	+	0.00251120i	0.996304	−	0.0859001i	$-0.0273766\pi$
$587$	0.00532294	+	0.0608415i	0.000219701	+	0.00251120i	−0.996084	+	0.0884113i	$0.971821\pi$
$588$		0			0
$589$	6.07348	−	1.88916i	0.250253	−	0.0778416i
$590$		0			0
$591$	4.57703	−	5.45469i	0.188274	−	0.224376i
$592$		0			0
$593$	−0.467281	−	0.327194i	−0.0191889	−	0.0134362i	0.563943	−	0.825814i	$-0.309284\pi$
$593$	−0.467281	−	0.327194i	−0.0191889	−	0.0134362i	−0.583132	+	0.812378i	$0.698173\pi$
$594$		0			0
$595$	−10.6778	+	7.65566i	−0.437748	+	0.313852i
$596$		0			0
$597$	−11.0836	−	41.3647i	−0.453623	−	1.69295i
$598$		0			0
$599$	−32.9504	+	27.6487i	−1.34632	+	1.12970i	−0.366364	+	0.930472i	$0.619398\pi$
$599$	−32.9504	+	27.6487i	−1.34632	+	1.12970i	−0.979954	+	0.199224i	$0.936158\pi$
$600$		0			0
$601$	25.2979	−	14.6058i	1.03192	−	0.595782i	0.114389	−	0.993436i	$-0.463509\pi$
$601$	25.2979	−	14.6058i	1.03192	−	0.595782i	0.917535	+	0.397655i	$0.130176\pi$
$602$		0			0
$603$	−6.47117	+	4.53116i	−0.263526	+	0.184523i
$604$		0			0
$605$	19.1989	+	4.91539i	0.780545	+	0.199839i
$606$		0			0
$607$	21.0882	−	21.0882i	0.855943	−	0.855943i	−0.134914	−	0.990857i	$-0.543076\pi$
$607$	21.0882	−	21.0882i	0.855943	−	0.855943i	0.990857	+	0.134914i	$0.0430758\pi$
$608$		0			0
$609$		−	10.3158i		−	0.418018i
$610$		0			0
$611$	−3.09782	−	8.51120i	−0.125325	−	0.344326i
$612$		0			0
$613$	12.6475	+	18.0625i	0.510828	+	0.729538i	0.988867	−	0.148801i	$-0.0475412\pi$
$613$	12.6475	+	18.0625i	0.510828	+	0.729538i	−0.478039	+	0.878338i	$0.658652\pi$
$614$		0			0
$615$	−3.79434	−	4.42080i	−0.153003	−	0.178264i
$616$		0			0
$617$	21.2792	+	1.86169i	0.856670	+	0.0749489i	0.507023	−	0.861932i	$-0.330746\pi$
$617$	21.2792	+	1.86169i	0.856670	+	0.0749489i	0.349647	+	0.936881i	$0.386301\pi$
$618$		0			0
$619$	12.8655	+	7.42787i	0.517106	+	0.298551i	0.735750	−	0.677253i	$-0.236830\pi$
$619$	12.8655	+	7.42787i	0.517106	+	0.298551i	−0.218644	+	0.975805i	$0.570163\pi$
$620$		0			0
$621$	−5.61441	+	15.4255i	−0.225298	+	0.619002i
$622$		0			0
$623$	15.4890	−	22.1205i	0.620552	−	0.886240i
$624$		0			0
$625$	−24.9751	+	1.11544i	−0.999004	+	0.0446176i
$626$		0			0
$627$	−15.4924	+	6.34707i	−0.618707	+	0.253478i
$628$		0			0
$629$	−0.912914	−	0.766026i	−0.0364003	−	0.0305435i
$630$		0			0
$631$	−4.05803	−	23.0142i	−0.161548	−	0.916182i	−0.952553	−	0.304373i	$-0.901553\pi$
$631$	−4.05803	−	23.0142i	−0.161548	−	0.916182i	0.791005	−	0.611809i	$-0.209558\pi$
$632$		0			0
$633$	−31.8998	+	14.8751i	−1.26790	+	0.591233i
$634$		0			0
$635$	−9.36385	+	26.6485i	−0.371593	+	1.05751i
$636$		0			0
$637$	0.168296	−	1.92363i	0.00666813	−	0.0762170i
$638$		0			0
$639$	25.8191	+	44.7199i	1.02139	+	1.76909i
$640$		0			0
$641$	−28.6687	−	5.05507i	−1.13235	−	0.199663i	−0.424091	−	0.905620i	$-0.639406\pi$
$641$	−28.6687	−	5.05507i	−1.13235	−	0.199663i	−0.708255	+	0.705957i	$0.750517\pi$
$642$		0			0
$643$	4.16938	−	8.94126i	0.164424	−	0.352609i	−0.806782	−	0.590849i	$-0.798793\pi$
$643$	4.16938	−	8.94126i	0.164424	−	0.352609i	0.971206	+	0.238240i	$0.0765706\pi$
$644$		0			0
$645$	47.7487	+	32.6461i	1.88010	+	1.28544i
$646$		0			0
$647$	−29.2498	−	29.2498i	−1.14993	−	1.14993i	−0.986566	−	0.163361i	$-0.947767\pi$
$647$	−29.2498	−	29.2498i	−1.14993	−	1.14993i	−0.163361	−	0.986566i	$-0.552233\pi$
$648$		0			0
$649$	8.48946	−	3.08991i	0.333241	−	0.121290i
$650$		0			0
$651$	1.43765	−	8.15333i	0.0563460	−	0.319554i
$652$		0			0
$653$	35.5780	+	9.53310i	1.39227	+	0.373059i	0.875564	−	0.483101i	$-0.160490\pi$
$653$	35.5780	+	9.53310i	1.39227	+	0.373059i	0.516710	+	0.856160i	$0.327156\pi$
$654$		0			0
$655$	30.5523	−	3.01684i	1.19378	−	0.117878i
$656$		0			0
$657$	56.5419	−	15.1504i	2.20591	−	0.591072i
$658$		0			0
$659$	8.42325	+	3.06581i	0.328123	+	0.119427i	0.500829	−	0.865546i	$-0.333029\pi$
$659$	8.42325	+	3.06581i	0.328123	+	0.119427i	−0.172705	+	0.984974i	$0.555251\pi$
$660$		0			0
$661$	28.3996	−	5.00761i	1.10462	−	0.194774i	0.408539	−	0.912741i	$-0.366038\pi$
$661$	28.3996	−	5.00761i	1.10462	−	0.194774i	0.696077	+	0.717967i	$0.254927\pi$
$662$		0			0
$663$	5.88509	−	0.514878i	0.228558	−	0.0199962i
$664$		0			0
$665$	6.47533	+	20.0269i	0.251102	+	0.776609i
$666$		0			0
$667$	12.5289	−	1.09614i	0.485123	−	0.0424427i
$668$		0			0
$669$	18.7938	−	3.31385i	0.726609	−	0.128121i
$670$		0			0
$671$	−0.0878415	−	0.0319717i	−0.00339108	−	0.00123425i
$672$		0			0
$673$	−16.2163	+	4.34513i	−0.625091	+	0.167493i	−0.557441	−	0.830217i	$-0.688217\pi$
$673$	−16.2163	+	4.34513i	−0.625091	+	0.167493i	−0.0676498	+	0.997709i	$0.521550\pi$
$674$		0			0
$675$	−11.3898	+	3.32601i	−0.438395	+	0.128018i
$676$		0			0
$677$	−19.9380	−	5.34238i	−0.766280	−	0.205324i	−0.145553	−	0.989351i	$-0.546496\pi$
$677$	−19.9380	−	5.34238i	−0.766280	−	0.205324i	−0.620728	+	0.784026i	$0.713163\pi$
$678$		0			0
$679$	−3.73660	+	21.1913i	−0.143398	+	0.813248i
$680$		0			0
$681$	−39.2872	+	14.2994i	−1.50549	+	0.547953i
$682$		0			0
$683$	18.1397	+	18.1397i	0.694095	+	0.694095i	0.963130	−	0.269036i	$-0.0867049\pi$
$683$	18.1397	+	18.1397i	0.694095	+	0.694095i	−0.269036	+	0.963130i	$0.586705\pi$
$684$		0			0
$685$	2.85529	+	15.1994i	0.109095	+	0.580741i
$686$		0			0
$687$	−18.9976	+	40.7404i	−0.724802	+	1.55434i
$688$		0			0
$689$	7.76995	+	1.37005i	0.296012	+	0.0521948i
$690$		0			0
$691$	2.68880	+	4.65714i	0.102287	+	0.177166i	0.912626	−	0.408795i	$-0.134051\pi$
$691$	2.68880	+	4.65714i	0.102287	+	0.177166i	−0.810340	+	0.585960i	$0.800717\pi$
$692$		0			0
$693$	−1.07392	+	12.2749i	−0.0407947	+	0.466285i
$694$		0			0
$695$	−19.1197	−	39.8357i	−0.725251	−	1.51105i
$696$		0			0
$697$	2.44539	−	1.14031i	0.0926258	−	0.0431921i
$698$		0			0
$699$	−6.27761	−	35.6021i	−0.237441	−	1.34660i
$700$		0			0
$701$	23.7726	+	19.9476i	0.897878	+	0.753409i	0.969774	−	0.244003i	$-0.0784607\pi$
$701$	23.7726	+	19.9476i	0.897878	+	0.753409i	−0.0718966	+	0.997412i	$0.522905\pi$
$702$		0			0
$703$	−1.61407	+	1.01952i	−0.0608759	+	0.0384520i
$704$		0			0
$705$	−62.0117	+	17.3599i	−2.33550	+	0.653810i
$706$		0			0
$707$	−9.21268	+	13.1571i	−0.346478	+	0.494822i
$708$		0			0
$709$	10.9635	−	30.1220i	0.411744	−	1.13126i	−0.544519	−	0.838748i	$-0.683288\pi$
$709$	10.9635	−	30.1220i	0.411744	−	1.13126i	0.956263	−	0.292508i	$-0.0944900\pi$
$710$		0			0
$711$	7.27452	+	4.19995i	0.272816	+	0.157510i
$712$		0			0
$713$	10.0553	+	0.879725i	0.376574	+	0.0329460i
$714$		0			0
$715$	2.04972	−	1.75926i	0.0766551	−	0.0657927i
$716$		0			0
$717$	17.4599	+	24.9353i	0.652052	+	0.931226i
$718$		0			0
$719$	−4.98770	−	13.7036i	−0.186010	−	0.511058i	0.811278	−	0.584661i	$-0.198772\pi$
$719$	−4.98770	−	13.7036i	−0.186010	−	0.511058i	−0.997288	+	0.0736030i	$0.976550\pi$
$720$		0			0
$721$		−	29.2160i		−	1.08806i
$722$		0			0
$723$	8.12207	−	8.12207i	0.302063	−	0.302063i
$724$		0			0
$725$	5.99743	+	6.83187i	0.222739	+	0.253729i
$726$		0			0
$727$	−16.1621	+	11.3169i	−0.599420	+	0.419719i	−0.833516	−	0.552495i	$-0.813676\pi$
$727$	−16.1621	+	11.3169i	−0.599420	+	0.419719i	0.234096	+	0.972214i	$0.424787\pi$
$728$		0			0
$729$	34.7048	−	20.0368i	1.28536	−	0.742104i
$730$		0			0
$731$	−20.5216	+	17.2197i	−0.759020	+	0.636893i
$732$		0			0
$733$	−0.240409	−	0.897220i	−0.00887972	−	0.0331396i	0.961344	−	0.275351i	$-0.0887940\pi$
$733$	−0.240409	−	0.897220i	−0.00887972	−	0.0331396i	−0.970224	+	0.242211i	$0.922127\pi$
$734$		0			0
$735$	−13.5459	−	2.23296i	−0.499648	−	0.0823640i
$736$		0			0
$737$	−2.42365	−	1.69706i	−0.0892762	−	0.0625119i
$738$		0			0
$739$	−27.7319	+	33.0495i	−1.02013	+	1.21575i	−0.0438973	+	0.999036i	$0.513977\pi$
$739$	−27.7319	+	33.0495i	−1.02013	+	1.21575i	−0.976236	+	0.216711i	$0.930467\pi$
$740$		0			0
$741$	2.08404	−	9.23138i	0.0765593	−	0.339123i
$742$		0			0
$743$	−3.26320	−	37.2986i	−0.119715	−	1.36835i	−0.783948	−	0.620827i	$-0.786797\pi$
$743$	−3.26320	−	37.2986i	−0.119715	−	1.36835i	0.664232	−	0.747526i	$-0.268759\pi$
$744$		0			0
$745$	24.5331	+	11.1084i	0.898824	+	0.406981i
$746$		0			0
$747$	20.7322	+	44.4604i	0.758552	+	1.62672i
$748$		0			0
$749$	−2.23663	+	3.87396i	−0.0817248	+	0.141552i
$750$		0			0
$751$	−8.92461	−	10.6359i	−0.325664	−	0.388111i	0.578226	−	0.815877i	$-0.303745\pi$
$751$	−8.92461	−	10.6359i	−0.325664	−	0.388111i	−0.903890	+	0.427766i	$0.859301\pi$
$752$		0			0
$753$	17.0280	−	63.5494i	0.620536	−	2.31587i
$754$		0			0
$755$	−34.7362	−	33.9696i	−1.26418	−	1.23628i
$756$		0			0
$757$	−2.39265	−	1.11571i	−0.0869625	−	0.0405513i	0.378650	−	0.925540i	$-0.376388\pi$
$757$	−2.39265	−	1.11571i	−0.0869625	−	0.0405513i	−0.465613	+	0.884989i	$0.654166\pi$
$758$		0			0
$759$	−26.5687			−0.964383
$760$		0			0
$761$	26.9984			0.978690			0.489345	−	0.872090i	$-0.337236\pi$
$761$	26.9984			0.978690			0.489345	+	0.872090i	$0.337236\pi$
$762$		0			0
$763$	−40.1987	−	18.7450i	−1.45529	−	0.678613i
$764$		0			0
$765$	−0.264980	−	23.7468i	−0.00958038	−	0.858567i
$766$		0			0
$767$	−1.32172	+	4.93273i	−0.0477246	+	0.178111i
$768$		0			0
$769$	13.2323	+	15.7696i	0.477167	+	0.568666i	0.949906	−	0.312537i	$-0.101179\pi$
$769$	13.2323	+	15.7696i	0.477167	+	0.568666i	−0.472738	+	0.881203i	$0.656734\pi$
$770$		0			0
$771$	−18.4891	+	32.0241i	−0.665870	+	1.15332i
$772$		0			0
$773$	4.57366	+	9.80824i	0.164503	+	0.352778i	0.971229	−	0.238148i	$-0.0765403\pi$
$773$	4.57366	+	9.80824i	0.164503	+	0.352778i	−0.806726	+	0.590926i	$0.798763\pi$
$774$		0			0
$775$	3.78809	+	6.23555i	0.136072	+	0.223988i
$776$		0			0
$777$	0.216579	+	2.47551i	0.00776972	+	0.0888083i
$778$		0			0
$779$	−0.547606	−	4.28757i	−0.0196200	−	0.153618i
$780$		0			0
$781$	−12.4315	+	14.8153i	−0.444836	+	0.530134i
$782$		0			0
$783$	3.53440	+	2.47481i	0.126309	+	0.0884426i
$784$		0			0
$785$	2.89969	−	17.5905i	0.103494	−	0.627831i
$786$		0			0
$787$	−7.11287	−	26.5456i	−0.253546	−	0.946248i	−0.968893	−	0.247479i	$-0.920398\pi$
$787$	−7.11287	−	26.5456i	−0.253546	−	0.946248i	0.715347	−	0.698769i	$-0.246269\pi$
$788$		0			0
$789$	0.268128	−	0.224986i	0.00954562	−	0.00800973i
$790$		0			0
$791$	−35.3901	+	20.4325i	−1.25833	+	0.726495i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.38123 - 1.11039i) q^{3} +(1.56340 - 1.59868i) q^{5} +(0.558906 - 2.08587i) q^{7} +(2.50894 + 2.99004i) q^{9} +O(q^{10})\)	\(q+(-2.38123 - 1.11039i) q^{3} +(1.56340 - 1.59868i) q^{5} +(0.558906 - 2.08587i) q^{7} +(2.50894 + 2.99004i) q^{9} +(-0.730936 + 1.26602i) q^{11} +(-0.349226 - 0.748918i) q^{13} +(-5.49797 + 2.07086i) q^{15} +(-0.237149 - 2.71062i) q^{17} +(-4.25189 - 0.959893i) q^{19} +(-3.64700 + 4.34633i) q^{21} +(-5.66631 - 3.96759i) q^{23} +(-0.111572 - 4.99876i) q^{25} +(-0.614204 - 2.29224i) q^{27} +(-1.39280 + 1.16870i) q^{29} +(-1.26371 + 0.729601i) q^{31} +(3.14629 - 2.20306i) q^{33} +(-2.46084 - 4.15455i) q^{35} +(0.309697 - 0.309697i) q^{37} +2.17112i q^{39} +(0.339156 + 0.931825i) q^{41} +(-5.64709 - 8.06488i) q^{43} +(8.70259 + 0.663621i) q^{45} +(10.9192 + 0.955306i) q^{47} +(2.02372 + 1.16839i) q^{49} +(-2.44513 + 6.71794i) q^{51} +(-5.47646 + 7.82119i) q^{53} +(0.881217 + 3.14782i) q^{55} +(9.05889 + 7.00697i) q^{57} +(-4.73412 - 3.97240i) q^{59} +(0.0111039 + 0.0629732i) q^{61} +(7.63907 - 3.56216i) q^{63} +(-1.74326 - 0.612555i) q^{65} +(-0.176397 + 2.01623i) q^{67} +(9.08722 + 15.7395i) q^{69} +(13.0287 + 2.29730i) q^{71} +(6.33800 - 13.5919i) q^{73} +(-5.28487 + 12.0271i) q^{75} +(2.23222 + 2.23222i) q^{77} +(2.02226 - 0.736043i) q^{79} +(0.950647 - 5.39139i) q^{81} +(12.1400 + 3.25291i) q^{83} +(-4.70418 - 3.85865i) q^{85} +(4.61428 - 1.23639i) q^{87} +(11.7510 + 4.27701i) q^{89} +(-1.75733 + 0.309864i) q^{91} +(3.81931 - 0.334147i) q^{93} +(-8.18197 + 5.29673i) q^{95} +(-9.92678 + 0.868480i) q^{97} +(-5.61931 + 0.990836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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

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