LMFDB - Embedded newform 380.2.bh.a.33.2

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			33.2
Character	$\chi$	$=$	380.33
Dual form			380.2.bh.a.357.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +O(q^{10})$	\(q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +(-1.50482 + 2.60643i) q^{11} +(2.49576 + 1.74755i) q^{13} +(-4.78405 + 2.78200i) q^{15} +(1.54457 - 3.31233i) q^{17} +(-2.24349 + 3.73721i) q^{19} +(3.42418 + 9.40786i) q^{21} +(4.38572 + 0.383700i) q^{23} +(-4.92936 - 0.837516i) q^{25} +(0.299637 - 0.0802874i) q^{27} +(-6.16306 - 2.24317i) q^{29} +(0.0797471 - 0.0460420i) q^{31} +(7.42036 - 0.649197i) q^{33} +(-3.06717 + 8.50944i) q^{35} +(-5.63016 - 5.63016i) q^{37} -7.54055i q^{39} +(-0.252048 - 0.0444428i) q^{41} +(-0.986904 - 11.2804i) q^{43} +(6.34288 + 2.93369i) q^{45} +(-12.1390 + 5.66049i) q^{47} +(8.10914 + 4.68182i) q^{49} +(-8.90788 + 1.57070i) q^{51} +(-0.0341343 + 0.390156i) q^{53} +(5.52472 + 3.84283i) q^{55} +(10.7614 - 0.756885i) q^{57} +(6.11253 - 2.22478i) q^{59} +(-5.92709 + 4.97342i) q^{61} +(7.25151 - 10.3562i) q^{63} +(4.36286 - 5.23251i) q^{65} +(-3.18616 - 6.83274i) q^{67} +(-5.44793 - 9.43609i) q^{69} +(10.3566 - 12.3425i) q^{71} +(4.03907 - 2.82818i) q^{73} +(5.29962 + 11.1825i) q^{75} +(8.60875 - 8.60875i) q^{77} +(1.67176 - 9.48103i) q^{79} +(6.59432 + 5.53329i) q^{81} +(-1.31821 + 4.91963i) q^{83} +(-7.09010 - 4.06405i) q^{85} +(4.20119 + 15.6790i) q^{87} +(1.38111 + 7.83264i) q^{89} +(-7.92219 - 9.44130i) q^{91} +(-0.206550 - 0.0963158i) q^{93} +(7.90545 + 5.70121i) q^{95} +(-4.48907 - 2.09329i) q^{97} +(-6.04617 - 7.20554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.41957	−	2.02735i	−0.819588	−	1.17049i	−0.982940	−	0.183925i	$-0.941119\pi$
$3$	−1.41957	−	2.02735i	−0.819588	−	1.17049i	0.163352	−	0.986568i	$-0.447769\pi$
$4$		0			0
$5$	0.187939	−	2.22816i	0.0840490	−	0.996462i
$5$	0.187939	−	2.22816i	0.0840490	−	0.996462i
$6$		0			0
$7$	−3.90736	−	1.04697i	−1.47684	−	0.395719i	−0.571572	−	0.820552i	$-0.693666\pi$
$7$	−3.90736	−	1.04697i	−1.47684	−	0.395719i	−0.905272	+	0.424833i	$0.860333\pi$
$8$		0			0
$9$	−1.06893	+	2.93686i	−0.356310	+	0.978953i
$10$		0			0
$11$	−1.50482	+	2.60643i	−0.453721	+	0.785868i	−0.998614	−	0.0526377i	$-0.983237\pi$
$11$	−1.50482	+	2.60643i	−0.453721	+	0.785868i	0.544892	+	0.838506i	$0.316570\pi$
$12$		0			0
$13$	2.49576	+	1.74755i	0.692199	+	0.484683i	0.865965	−	0.500104i	$-0.166705\pi$
$13$	2.49576	+	1.74755i	0.692199	+	0.484683i	−0.173766	+	0.984787i	$0.555594\pi$
$14$		0			0
$15$	−4.78405	+	2.78200i	−1.23524	+	0.718309i
$16$		0			0
$17$	1.54457	−	3.31233i	0.374612	−	0.803358i	−0.625127	−	0.780523i	$-0.714953\pi$
$17$	1.54457	−	3.31233i	0.374612	−	0.803358i	0.999739	−	0.0228352i	$-0.00726931\pi$
$18$		0			0
$19$	−2.24349	+	3.73721i	−0.514692	+	0.857375i
$19$	−2.24349	+	3.73721i	−0.514692	+	0.857375i
$20$		0			0
$21$	3.42418	+	9.40786i	0.747217	+	2.05296i
$22$		0			0
$23$	4.38572	+	0.383700i	0.914485	+	0.0800071i	0.534675	−	0.845058i	$-0.320434\pi$
$23$	4.38572	+	0.383700i	0.914485	+	0.0800071i	0.379810	+	0.925065i	$0.375989\pi$
$24$		0			0
$25$	−4.92936	−	0.837516i	−0.985872	−	0.167503i
$26$		0			0
$27$	0.299637	−	0.0802874i	0.0576651	−	0.0154513i
$28$		0			0
$29$	−6.16306	−	2.24317i	−1.14445	−	0.416546i	−0.300932	−	0.953645i	$-0.597298\pi$
$29$	−6.16306	−	2.24317i	−1.14445	−	0.416546i	−0.843519	+	0.537099i	$0.819520\pi$
$30$		0			0
$31$	0.0797471	−	0.0460420i	0.0143230	−	0.00826939i	−0.492821	−	0.870130i	$-0.664034\pi$
$31$	0.0797471	−	0.0460420i	0.0143230	−	0.00826939i	0.507144	+	0.861861i	$0.330701\pi$
$32$		0			0
$33$	7.42036	−	0.649197i	1.29172	−	0.113011i
$34$		0			0
$35$	−3.06717	+	8.50944i	−0.518446	+	1.43836i
$36$		0			0
$37$	−5.63016	−	5.63016i	−0.925592	−	0.925592i	0.0718248	−	0.997417i	$-0.477118\pi$
$37$	−5.63016	−	5.63016i	−0.925592	−	0.925592i	−0.997417	+	0.0718248i	$0.977118\pi$
$38$		0			0
$39$		−	7.54055i		−	1.20745i
$40$		0			0
$41$	−0.252048	−	0.0444428i	−0.0393633	−	0.00694081i	0.153932	−	0.988081i	$-0.450806\pi$
$41$	−0.252048	−	0.0444428i	−0.0393633	−	0.00694081i	−0.193295	+	0.981141i	$0.561917\pi$
$42$		0			0
$43$	−0.986904	−	11.2804i	−0.150501	−	1.72024i	−0.577842	−	0.816149i	$-0.696105\pi$
$43$	−0.986904	−	11.2804i	−0.150501	−	1.72024i	0.427340	−	0.904091i	$-0.359451\pi$
$44$		0			0
$45$	6.34288	+	2.93369i	0.945541	+	0.437329i
$46$		0			0
$47$	−12.1390	+	5.66049i	−1.77065	+	0.825667i	−0.794910	+	0.606727i	$0.792482\pi$
$47$	−12.1390	+	5.66049i	−1.77065	+	0.825667i	−0.975738	+	0.218940i	$0.929740\pi$
$48$		0			0
$49$	8.10914	+	4.68182i	1.15845	+	0.668831i
$50$		0			0
$51$	−8.90788	+	1.57070i	−1.24735	+	0.219942i
$52$		0			0
$53$	−0.0341343	+	0.390156i	−0.00468870	+	0.0535921i	−0.998179	−	0.0603282i	$-0.980785\pi$
$53$	−0.0341343	+	0.390156i	−0.00468870	+	0.0535921i	0.993490	+	0.113920i	$0.0363408\pi$
$54$		0			0
$55$	5.52472	+	3.84283i	0.744953	+	0.518167i
$56$		0			0
$57$	10.7614	−	0.756885i	1.42539	−	0.100252i
$58$		0			0
$59$	6.11253	−	2.22478i	0.795784	−	0.289642i	0.0880459	−	0.996116i	$-0.471938\pi$
$59$	6.11253	−	2.22478i	0.795784	−	0.289642i	0.707738	+	0.706475i	$0.249716\pi$
$60$		0			0
$61$	−5.92709	+	4.97342i	−0.758886	+	0.636781i	−0.937837	−	0.347077i	$-0.887174\pi$
$61$	−5.92709	+	4.97342i	−0.758886	+	0.636781i	0.178951	+	0.983858i	$0.442730\pi$
$62$		0			0
$63$	7.25151	−	10.3562i	0.913604	−	1.30476i
$64$		0			0
$65$	4.36286	−	5.23251i	0.541147	−	0.649013i
$66$		0			0
$67$	−3.18616	−	6.83274i	−0.389251	−	0.834752i	−0.999107	−	0.0422399i	$-0.986551\pi$
$67$	−3.18616	−	6.83274i	−0.389251	−	0.834752i	0.609856	−	0.792512i	$-0.291227\pi$
$68$		0			0
$69$	−5.44793	−	9.43609i	−0.655853	−	1.13597i
$70$		0			0
$71$	10.3566	−	12.3425i	1.22910	−	1.46479i	0.390002	−	0.920814i	$-0.372474\pi$
$71$	10.3566	−	12.3425i	1.22910	−	1.46479i	0.839102	−	0.543975i	$-0.183081\pi$
$72$		0			0
$73$	4.03907	−	2.82818i	0.472737	−	0.331014i	−0.312810	−	0.949816i	$-0.601270\pi$
$73$	4.03907	−	2.82818i	0.472737	−	0.331014i	0.785547	+	0.618802i	$0.212382\pi$
$74$		0			0
$75$	5.29962	+	11.1825i	0.611947	+	1.29124i
$76$		0			0
$77$	8.60875	−	8.60875i	0.981059	−	0.981059i
$78$		0			0
$79$	1.67176	−	9.48103i	0.188088	−	1.06670i	−0.733836	−	0.679327i	$-0.762272\pi$
$79$	1.67176	−	9.48103i	0.188088	−	1.06670i	0.921923	−	0.387372i	$-0.126617\pi$
$80$		0			0
$81$	6.59432	+	5.53329i	0.732702	+	0.614810i
$82$		0			0
$83$	−1.31821	+	4.91963i	−0.144692	+	0.539999i	0.855077	+	0.518502i	$0.173510\pi$
$83$	−1.31821	+	4.91963i	−0.144692	+	0.539999i	−0.999769	+	0.0214974i	$0.993157\pi$
$84$		0			0
$85$	−7.09010	−	4.06405i	−0.769030	−	0.440808i
$86$		0			0
$87$	4.20119	+	15.6790i	0.450414	+	1.68097i
$88$		0			0
$89$	1.38111	+	7.83264i	0.146397	+	0.830258i	0.966235	+	0.257663i	$0.0829523\pi$
$89$	1.38111	+	7.83264i	0.146397	+	0.830258i	−0.819838	+	0.572596i	$0.805937\pi$
$90$		0			0
$91$	−7.92219	−	9.44130i	−0.830472	−	0.989718i
$92$		0			0
$93$	−0.206550	−	0.0963158i	−0.0214182	−	0.00998748i
$94$		0			0
$95$	7.90545	+	5.70121i	0.811082	+	0.584932i
$96$		0			0
$97$	−4.48907	−	2.09329i	−0.455796	−	0.212541i	0.181141	−	0.983457i	$-0.442021\pi$
$97$	−4.48907	−	2.09329i	−0.455796	−	0.212541i	−0.636937	+	0.770916i	$0.719799\pi$
$98$		0			0
$99$	−6.04617	−	7.20554i	−0.607663	−	0.724184i
$100$		0			0
$101$	−1.30683	−	7.41143i	−0.130035	−	0.737465i	−0.978189	−	0.207716i	$-0.933397\pi$
$101$	−1.30683	−	7.41143i	−0.130035	−	0.737465i	0.848154	−	0.529749i	$-0.177714\pi$
$102$		0			0
$103$	−0.958897	−	3.57865i	−0.0944830	−	0.352615i	0.902458	−	0.430779i	$-0.141761\pi$
$103$	−0.958897	−	3.57865i	−0.0944830	−	0.352615i	−0.996941	+	0.0781635i	$0.975094\pi$
$104$		0			0
$105$	21.6057	−	5.86150i	2.10850	−	0.572024i
$106$		0			0
$107$	−0.0632167	+	0.235928i	−0.00611139	+	0.0228080i	−0.968914	−	0.247397i	$-0.920425\pi$
$107$	−0.0632167	+	0.235928i	−0.00611139	+	0.0228080i	0.962803	+	0.270205i	$0.0870915\pi$
$108$		0			0
$109$	−1.41305	−	1.18569i	−0.135346	−	0.113569i	0.572602	−	0.819834i	$-0.305934\pi$
$109$	−1.41305	−	1.18569i	−0.135346	−	0.113569i	−0.707947	+	0.706265i	$0.750379\pi$
$110$		0			0
$111$	−3.42193	+	19.4067i	−0.324795	+	1.84200i
$112$		0			0
$113$	−6.93584	+	6.93584i	−0.652469	+	0.652469i	−0.953587	−	0.301118i	$-0.902640\pi$
$113$	−6.93584	+	6.93584i	−0.652469	+	0.652469i	0.301118	+	0.953587i	$0.402640\pi$
$114$		0			0
$115$	1.67919	−	9.69995i	0.156586	−	0.904525i
$116$		0			0
$117$	−7.80009	+	5.46168i	−0.721119	+	0.504933i
$118$		0			0
$119$	−9.50310	+	11.3254i	−0.871148	+	1.03819i
$120$		0			0
$121$	0.971015	+	1.68185i	0.0882741	+	0.152895i
$122$		0			0
$123$	0.267698	+	0.574080i	0.0241375	+	0.0517631i
$124$		0			0
$125$	−2.79254	+	10.8260i	−0.249772	+	0.968305i
$126$		0			0
$127$	10.8104	−	15.4389i	0.959269	−	1.36998i	0.0304135	−	0.999537i	$-0.490318\pi$
$127$	10.8104	−	15.4389i	0.959269	−	1.36998i	0.928856	−	0.370441i	$-0.120794\pi$
$128$		0			0
$129$	−21.4683	+	18.0141i	−1.89018	+	1.58605i
$130$		0			0
$131$	0.819676	−	0.298338i	0.0716154	−	0.0260659i	−0.305964	−	0.952043i	$-0.598979\pi$
$131$	0.819676	−	0.298338i	0.0716154	−	0.0260659i	0.377579	+	0.925977i	$0.376757\pi$
$132$		0			0
$133$	12.6789	−	12.2538i	1.09940	−	1.06254i
$134$		0			0
$135$	−0.122579	−	0.682726i	−0.0105499	−	0.0587597i
$136$		0			0
$137$	−1.38293	+	15.8070i	−0.118152	+	1.35048i	0.673355	+	0.739319i	$0.264853\pi$
$137$	−1.38293	+	15.8070i	−0.118152	+	1.35048i	−0.791507	+	0.611161i	$0.790703\pi$
$138$		0			0
$139$	−3.31904	+	0.585237i	−0.281518	+	0.0496391i	−0.312624	−	0.949877i	$-0.601208\pi$
$139$	−3.31904	+	0.585237i	−0.281518	+	0.0496391i	0.0311065	+	0.999516i	$0.490097\pi$
$140$		0			0
$141$	28.7079	+	16.5745i	2.41764	+	1.39583i
$142$		0			0
$143$	−8.31054	+	3.87527i	−0.694962	+	0.324066i
$144$		0			0
$145$	−6.15642	+	13.3107i	−0.511262	+	1.10539i
$146$		0			0
$147$	−2.01979	−	23.0863i	−0.166589	−	1.90412i
$148$		0			0
$149$	−2.79030	−	0.492005i	−0.228590	−	0.0403066i	0.0581797	−	0.998306i	$-0.481470\pi$
$149$	−2.79030	−	0.492005i	−0.228590	−	0.0403066i	−0.286770	+	0.958000i	$0.592581\pi$
$150$		0			0
$151$		−	16.7953i		−	1.36678i	−0.730054	−	0.683390i	$-0.760505\pi$
$151$		−	16.7953i		−	1.36678i	0.730054	−	0.683390i	$-0.239495\pi$
$152$		0			0
$153$	8.07681	+	8.07681i	0.652972	+	0.652972i
$154$		0			0
$155$	−0.0876011	−	0.186342i	−0.00703629	−	0.0149674i
$156$		0			0
$157$	−10.6982	+	0.935974i	−0.853812	+	0.0746989i	−0.505653	−	0.862737i	$-0.668749\pi$
$157$	−10.6982	+	0.935974i	−0.853812	+	0.0746989i	−0.348159	+	0.937436i	$0.613193\pi$
$158$		0			0
$159$	0.839441	−	0.484651i	0.0665720	−	0.0384354i
$160$		0			0
$161$	−16.7349	−	6.09099i	−1.31889	−	0.480037i
$162$		0			0
$163$	−18.9792	+	5.08547i	−1.48657	+	0.398325i	−0.908577	−	0.417718i	$-0.862830\pi$
$163$	−18.9792	+	5.08547i	−1.48657	+	0.398325i	−0.577992	+	0.816043i	$0.696163\pi$
$164$		0			0
$165$	−0.0519356	−	16.6557i	−0.00404318	−	1.29665i
$166$		0			0
$167$	19.8346	+	1.73530i	1.53484	+	0.134281i	0.822994	−	0.568050i	$-0.192302\pi$
$167$	19.8346	+	1.73530i	1.53484	+	0.134281i	0.711850	+	0.702332i	$0.247858\pi$
$168$		0			0
$169$	−1.27138	−	3.49308i	−0.0977982	−	0.268698i
$170$		0			0
$171$	−8.57753	−	10.5836i	−0.655940	−	0.809350i
$172$		0			0
$173$	1.92203	−	4.12181i	0.146129	−	0.313376i	−0.819596	−	0.572942i	$-0.805802\pi$
$173$	1.92203	−	4.12181i	0.146129	−	0.313376i	0.965725	+	0.259567i	$0.0835797\pi$
$174$		0			0
$175$	18.3839	+	8.43339i	1.38969	+	0.637504i
$176$		0			0
$177$	−13.1876	−	9.23404i	−0.991239	−	0.694073i
$178$		0			0
$179$	−7.24609	+	12.5506i	−0.541598	+	0.938076i	0.457214	+	0.889357i	$0.348847\pi$
$179$	−7.24609	+	12.5506i	−0.541598	+	0.938076i	−0.998813	+	0.0487192i	$0.984486\pi$
$180$		0			0
$181$	7.37746	−	20.2694i	0.548362	−	1.50661i	−0.287559	−	0.957763i	$-0.592844\pi$
$181$	7.37746	−	20.2694i	0.548362	−	1.50661i	0.835921	−	0.548849i	$-0.184934\pi$
$182$		0			0
$183$	18.4968	+	4.95620i	1.36732	+	0.366373i
$184$		0			0
$185$	−13.6030	+	11.4867i	−1.00011	+	0.844522i
$186$		0			0
$187$	6.30906	+	9.01027i	0.461364	+	0.658896i
$188$		0			0
$189$	−1.25485			−0.0912767
$190$		0			0
$191$	−5.89708			−0.426698			−0.213349	−	0.976976i	$-0.568437\pi$
$191$	−5.89708			−0.426698			−0.213349	+	0.976976i	$0.568437\pi$
$192$		0			0
$193$	0.266322	+	0.380347i	0.0191703	+	0.0273780i	0.828623	−	0.559807i	$-0.189125\pi$
$193$	0.266322	+	0.380347i	0.0191703	+	0.0273780i	−0.809453	+	0.587185i	$0.800236\pi$
$194$		0			0
$195$	−16.8015	−	1.41717i	−1.20318	−	0.101485i
$196$		0			0
$197$	7.73822	+	2.07345i	0.551325	+	0.147727i	0.523718	−	0.851892i	$-0.324545\pi$
$197$	7.73822	+	2.07345i	0.551325	+	0.147727i	0.0276072	+	0.999619i	$0.491211\pi$
$198$		0			0
$199$	4.99686	−	13.7288i	0.354218	−	0.973206i	−0.626781	−	0.779195i	$-0.715628\pi$
$199$	4.99686	−	13.7288i	0.354218	−	0.973206i	0.980999	−	0.194011i	$-0.0621497\pi$
$200$		0			0
$201$	−9.32941	+	16.1590i	−0.658046	+	1.13977i
$202$		0			0
$203$	21.7328	+	15.2174i	1.52534	+	1.06806i
$204$		0			0
$205$	−0.146395	+	0.553250i	−0.0102247	+	0.0386406i
$206$		0			0
$207$	−5.81489	+	12.4701i	−0.404163	+	0.866730i
$208$		0			0
$209$	−6.36473	−	11.4713i	−0.440258	−	0.793489i
$210$		0			0
$211$	−2.44195	−	6.70920i	−0.168111	−	0.461880i	0.826817	−	0.562471i	$-0.190149\pi$
$211$	−2.44195	−	6.70920i	−0.168111	−	0.461880i	−0.994928	+	0.100590i	$0.967927\pi$
$212$		0			0
$213$	−39.7246	−	3.47545i	−2.72188	−	0.238134i
$214$		0			0
$215$	−25.3199	+	0.0789521i	−1.72680	+	0.00538449i
$216$		0			0
$217$	−0.359805	+	0.0964096i	−0.0244252	+	0.00654471i
$218$		0			0
$219$	−11.4675	−	4.17381i	−0.774899	−	0.282040i
$220$		0			0
$221$	9.64332	−	5.56758i	0.648680	−	0.374516i
$222$		0			0
$223$	2.79259	−	0.244320i	0.187006	−	0.0163609i	0.00673183	−	0.999977i	$-0.497857\pi$
$223$	2.79259	−	0.244320i	0.187006	−	0.0163609i	0.180274	+	0.983616i	$0.442302\pi$
$224$		0			0
$225$	7.72880	−	13.5816i	0.515253	−	0.905439i
$226$		0			0
$227$	−0.142147	−	0.142147i	−0.00943464	−	0.00943464i	0.702374	−	0.711808i	$-0.252124\pi$
$227$	−0.142147	−	0.142147i	−0.00943464	−	0.00943464i	−0.711808	+	0.702374i	$0.752124\pi$
$228$		0			0
$229$			12.4654i			0.823738i	0.911243	+	0.411869i	$0.135124\pi$
$229$			12.4654i			0.823738i	−0.911243	+	0.411869i	$0.864876\pi$
$230$		0			0
$231$	−29.6737	−	5.23228i	−1.95239	−	0.344258i
$232$		0			0
$233$	−0.501766	−	5.73521i	−0.0328718	−	0.375726i	−0.994757	−	0.102271i	$-0.967389\pi$
$233$	−0.501766	−	5.73521i	−0.0328718	−	0.375726i	0.961885	−	0.273455i	$-0.0881665\pi$
$234$		0			0
$235$	10.3311	+	28.1113i	0.673924	+	1.83378i
$236$		0			0
$237$	−21.5946	+	10.0697i	−1.40272	+	0.654099i
$238$		0			0
$239$	4.96615	+	2.86721i	0.321233	+	0.185464i	0.651942	−	0.758269i	$-0.273954\pi$
$239$	4.96615	+	2.86721i	0.321233	+	0.185464i	−0.330709	+	0.943733i	$0.607288\pi$
$240$		0			0
$241$	7.31256	−	1.28940i	0.471044	−	0.0830577i	0.0669127	−	0.997759i	$-0.478685\pi$
$241$	7.31256	−	1.28940i	0.471044	−	0.0830577i	0.404131	+	0.914701i	$0.367574\pi$
$242$		0			0
$243$	1.93796	−	22.1510i	0.124320	−	1.42099i
$244$		0			0
$245$	11.9558	−	17.1885i	0.763831	−	1.09814i
$246$		0			0
$247$	−12.1302	+	5.40658i	−0.771824	+	0.344012i
$248$		0			0
$249$	11.8451	−	4.31127i	0.750654	−	0.273216i
$250$		0			0
$251$	−0.758712	+	0.636635i	−0.0478895	+	0.0401840i	−0.666418	−	0.745578i	$-0.732173\pi$
$251$	−0.758712	+	0.636635i	−0.0478895	+	0.0401840i	0.618529	+	0.785762i	$0.287729\pi$
$252$		0			0
$253$	−7.59981	+	10.8537i	−0.477796	+	0.682364i
$254$		0			0
$255$	1.82562	+	20.1433i	0.114325	+	1.26143i
$256$		0			0
$257$	6.37083	+	13.6623i	0.397402	+	0.852230i	0.998588	+	0.0531217i	$0.0169171\pi$
$257$	6.37083	+	13.6623i	0.397402	+	0.852230i	−0.601186	+	0.799109i	$0.705305\pi$
$258$		0			0
$259$	16.1044	+	27.8937i	1.00068	+	1.73323i
$260$		0			0
$261$	13.1757	−	15.7022i	0.815558	−	0.971944i
$262$		0			0
$263$	−9.13287	+	6.39491i	−0.563157	+	0.394327i	−0.820203	−	0.572072i	$-0.806140\pi$
$263$	−9.13287	+	6.39491i	−0.563157	+	0.394327i	0.257046	+	0.966399i	$0.417251\pi$
$264$		0			0
$265$	0.862914	+	0.149382i	0.0530084	+	0.00917647i
$266$		0			0
$267$	13.9190	−	13.9190i	0.851827	−	0.851827i
$268$		0			0
$269$	5.10282	−	28.9395i	0.311124	−	1.76447i	−0.282051	−	0.959399i	$-0.591015\pi$
$269$	5.10282	−	28.9395i	0.311124	−	1.76447i	0.593175	−	0.805074i	$-0.297874\pi$
$270$		0			0
$271$	22.0185	+	18.4757i	1.33753	+	1.12232i	0.982253	+	0.187559i	$0.0600576\pi$
$271$	22.0185	+	18.4757i	1.33753	+	1.12232i	0.355276	+	0.934761i	$0.384387\pi$
$272$		0			0
$273$	−7.89477	+	29.4637i	−0.477813	+	1.78322i
$274$		0			0
$275$	9.60074	−	11.5877i	0.578946	−	0.698765i
$276$		0			0
$277$	−7.48481	−	27.9337i	−0.449719	−	1.67837i	−0.703167	−	0.711025i	$-0.748231\pi$
$277$	−7.48481	−	27.9337i	−0.449719	−	1.67837i	0.253448	−	0.967349i	$-0.418435\pi$
$278$		0			0
$279$	0.0499748	+	0.283421i	0.00299192	+	0.0169680i
$280$		0			0
$281$	8.34382	+	9.94378i	0.497751	+	0.593196i	0.955171	−	0.296055i	$-0.0956710\pi$
$281$	8.34382	+	9.94378i	0.497751	+	0.593196i	−0.457421	+	0.889251i	$0.651227\pi$
$282$		0			0
$283$	15.9414	+	7.43361i	0.947619	+	0.441882i	0.834075	−	0.551651i	$-0.186002\pi$
$283$	15.9414	+	7.43361i	0.947619	+	0.441882i	0.113544	+	0.993533i	$0.463780\pi$
$284$		0			0
$285$	0.336040	−	24.1204i	0.0199053	−	1.42877i
$286$		0			0
$287$	0.938312	+	0.437542i	0.0553868	+	0.0258273i
$288$		0			0
$289$	2.34154	+	2.79054i	0.137737	+	0.164149i
$290$		0			0
$291$	2.12871	+	12.0725i	0.124787	+	0.707702i
$292$		0			0
$293$	−4.18365	−	15.6136i	−0.244412	−	0.912157i	−0.973678	−	0.227927i	$-0.926805\pi$
$293$	−4.18365	−	15.6136i	−0.244412	−	0.912157i	0.729267	−	0.684230i	$-0.239861\pi$
$294$		0			0
$295$	−3.80837	−	14.0378i	−0.221732	−	0.817313i
$296$		0			0
$297$	−0.241637	+	0.901800i	−0.0140212	+	0.0523277i
$298$		0			0
$299$	10.2752	+	8.62188i	0.594228	+	0.498616i
$300$		0			0
$301$	−7.95406	+	45.1097i	−0.458465	+	2.60008i
$302$		0			0
$303$	−13.1704	+	13.1704i	−0.756622	+	0.756622i
$304$		0			0
$305$	9.96762	+	14.1412i	0.570744	+	0.809722i
$306$		0			0
$307$	−21.1366	+	14.8000i	−1.20633	+	0.844682i	−0.991261	−	0.131917i	$-0.957887\pi$
$307$	−21.1366	+	14.8000i	−1.20633	+	0.844682i	−0.215070	+	0.976599i	$0.568998\pi$
$308$		0			0
$309$	−5.89398	+	7.02417i	−0.335297	+	0.399591i
$310$		0			0
$311$	2.85083	+	4.93778i	0.161656	+	0.279996i	0.935463	−	0.353426i	$-0.114983\pi$
$311$	2.85083	+	4.93778i	0.161656	+	0.279996i	−0.773807	+	0.633421i	$0.781650\pi$
$312$		0			0
$313$	−5.49117	−	11.7759i	−0.310379	−	0.665611i	0.687802	−	0.725899i	$-0.258576\pi$
$313$	−5.49117	−	11.7759i	−0.310379	−	0.665611i	−0.998181	+	0.0602879i	$0.980798\pi$
$314$		0			0
$315$	−21.7124	−	18.1038i	−1.22336	−	1.02004i
$316$		0			0
$317$	−10.2972	+	14.7059i	−0.578349	+	0.825967i	−0.996602	−	0.0823629i	$-0.973753\pi$
$317$	−10.2972	+	14.7059i	−0.578349	+	0.825967i	0.418254	+	0.908330i	$0.362642\pi$
$318$		0			0
$319$	15.1210	−	12.6880i	0.846613	−	0.710392i
$320$		0			0
$321$	0.568050	−	0.206753i	0.0317054	−	0.0115398i
$322$		0			0
$323$	8.91367	+	13.2035i	0.495970	+	0.734665i
$324$		0			0
$325$	−10.8389	−	10.7045i	−0.601233	−	0.593781i
$326$		0			0
$327$	−0.397892	+	4.54793i	−0.0220035	+	0.251501i
$328$		0			0
$329$	53.3577	−	9.40840i	2.94170	−	0.518702i
$330$		0			0
$331$	−10.1591	−	5.86535i	−0.558394	−	0.322389i	0.194107	−	0.980980i	$-0.437819\pi$
$331$	−10.1591	−	5.86535i	−0.558394	−	0.322389i	−0.752501	+	0.658592i	$0.771153\pi$
$332$		0			0
$333$	22.5532	−	10.5167i	1.23591	−	0.576314i
$334$		0			0
$335$	−15.8232	+	5.81512i	−0.864514	+	0.317714i
$336$		0			0
$337$	−2.50771	−	28.6632i	−0.136604	−	1.56139i	−0.687109	−	0.726555i	$-0.741120\pi$
$337$	−2.50771	−	28.6632i	−0.136604	−	1.56139i	0.550505	−	0.834832i	$-0.314435\pi$
$338$		0			0
$339$	23.9073	+	4.21550i	1.29847	+	0.228955i
$340$		0			0
$341$			0.277140i			0.0150080i
$342$		0			0
$343$	−6.76091	−	6.76091i	−0.365055	−	0.365055i
$344$		0			0
$345$	−22.0490	+	10.3654i	−1.18708	+	0.558055i
$346$		0			0
$347$	22.4415	−	1.96338i	1.20472	−	0.105400i	0.532944	−	0.846150i	$-0.321086\pi$
$347$	22.4415	−	1.96338i	1.20472	−	0.105400i	0.671780	+	0.740751i	$0.265530\pi$
$348$		0			0
$349$	25.9401	−	14.9765i	1.38854	−	0.801674i	0.395389	−	0.918514i	$-0.370610\pi$
$349$	25.9401	−	14.9765i	1.38854	−	0.801674i	0.993151	+	0.116840i	$0.0372766\pi$
$350$		0			0
$351$	0.888127	+	0.323252i	0.0474047	+	0.0172539i
$352$		0			0
$353$	27.4121	−	7.34506i	1.45900	−	0.390938i	0.559856	−	0.828590i	$-0.310857\pi$
$353$	27.4121	−	7.34506i	1.45900	−	0.390938i	0.899144	+	0.437652i	$0.144190\pi$
$354$		0			0
$355$	−25.5547	−	25.3958i	−1.35630	−	1.34787i
$356$		0			0
$357$	36.4508	+	3.18903i	1.92918	+	0.168781i
$358$		0			0
$359$	−5.18695	−	14.2510i	−0.273757	−	0.752140i	−0.998037	−	0.0626341i	$-0.980050\pi$
$359$	−5.18695	−	14.2510i	−0.273757	−	0.752140i	0.724280	−	0.689506i	$-0.242172\pi$
$360$		0			0
$361$	−8.93352	−	16.7688i	−0.470185	−	0.882568i
$362$		0			0
$363$	2.03128	−	4.35609i	0.106614	−	0.228635i
$364$		0			0
$365$	−5.54254	−	9.53120i	−0.290110	−	0.498886i
$366$		0			0
$367$	15.5424	+	10.8829i	0.811304	+	0.568081i	0.903960	−	0.427617i	$-0.140647\pi$
$367$	15.5424	+	10.8829i	0.811304	+	0.568081i	−0.0926559	+	0.995698i	$0.529536\pi$
$368$		0			0
$369$	0.399944	−	0.692723i	0.0208202	−	0.0360617i
$370$		0			0
$371$	0.541859	−	1.48874i	0.0281319	−	0.0772918i
$372$		0			0
$373$	−15.2545	−	4.08743i	−0.789848	−	0.211639i	−0.158726	−	0.987323i	$-0.550739\pi$
$373$	−15.2545	−	4.08743i	−0.789848	−	0.211639i	−0.631122	+	0.775683i	$0.717405\pi$
$374$		0			0
$375$	25.9123	−	9.70675i	1.33810	−	0.501255i
$376$		0			0
$377$	−11.4615	−	16.3687i	−0.590295	−	0.843029i
$378$		0			0
$379$	21.5930			1.10916			0.554579	−	0.832131i	$-0.312879\pi$
$379$	21.5930			1.10916			0.554579	+	0.832131i	$0.312879\pi$
$380$		0			0
$381$	−46.6462			−2.38976
$382$		0			0
$383$	−21.7781	−	31.1023i	−1.11281	−	1.58925i	−0.755348	−	0.655324i	$-0.772532\pi$
$383$	−21.7781	−	31.1023i	−1.11281	−	1.58925i	−0.357459	−	0.933929i	$-0.616357\pi$
$384$		0			0
$385$	−17.5637	−	20.7996i	−0.895130	−	1.06004i
$386$		0			0
$387$	34.1838	+	9.15951i	1.73766	+	0.465604i
$388$		0			0
$389$	0.967198	−	2.65735i	0.0490389	−	0.134733i	−0.912755	−	0.408507i	$-0.866050\pi$
$389$	0.967198	−	2.65735i	0.0490389	−	0.134733i	0.961794	+	0.273774i	$0.0882719\pi$
$390$		0			0
$391$	8.04497	−	13.9343i	0.406851	−	0.704687i
$392$		0			0
$393$	−1.76842	−	1.23826i	−0.0892051	−	0.0624621i
$394$		0			0
$395$	−20.8110	−	5.50680i	−1.04712	−	0.277077i
$396$		0			0
$397$	−6.06428	+	13.0049i	−0.304358	+	0.652697i	−0.997691	−	0.0679201i	$-0.978364\pi$
$397$	−6.06428	+	13.0049i	−0.304358	+	0.652697i	0.693333	+	0.720617i	$0.256141\pi$
$398$		0			0
$399$	−42.8413	−	8.30953i	−2.14475	−	0.415997i
$400$		0			0
$401$	3.61702	+	9.93769i	0.180626	+	0.496264i	0.996653	−	0.0817486i	$-0.0260505\pi$
$401$	3.61702	+	9.93769i	0.180626	+	0.496264i	−0.816027	+	0.578013i	$0.803828\pi$
$402$		0			0
$403$	0.279490	+	0.0244522i	0.0139224	+	0.00121805i
$404$		0			0
$405$	13.5684	−	13.6533i	0.674218	−	0.678435i
$406$		0			0
$407$	23.1470	−	6.20222i	1.14735	−	0.307433i
$408$		0			0
$409$	−3.03263	−	1.10379i	−0.149954	−	0.0545788i	0.265953	−	0.963986i	$-0.414313\pi$
$409$	−3.03263	−	1.10379i	−0.149954	−	0.0545788i	−0.415907	+	0.909407i	$0.636536\pi$
$410$		0			0
$411$	34.0095	−	19.6354i	1.67756	−	0.968542i
$412$		0			0
$413$	−26.2132	+	2.29336i	−1.28987	+	0.112849i
$414$		0			0
$415$	10.7140	+	3.86177i	0.525927	+	0.189567i
$416$		0			0
$417$	5.89809	+	5.89809i	0.288831	+	0.288831i
$418$		0			0
$419$			32.1672i			1.57147i	0.618564	+	0.785735i	$0.287715\pi$
$419$			32.1672i			1.57147i	−0.618564	+	0.785735i	$0.712285\pi$
$420$		0			0
$421$	14.6161	+	2.57721i	0.712346	+	0.125606i	0.518066	−	0.855341i	$-0.326652\pi$
$421$	14.6161	+	2.57721i	0.712346	+	0.125606i	0.194279	+	0.980946i	$0.437763\pi$
$422$		0			0
$423$	−3.64837	−	41.7010i	−0.177390	−	2.02757i
$424$		0			0
$425$	−10.3878	+	15.0341i	−0.503884	+	0.729259i
$426$		0			0
$427$	28.3663	−	13.2274i	1.37274	−	0.640120i
$428$		0			0
$429$	19.6539	+	11.3472i	0.948900	+	0.547848i
$430$		0			0
$431$	39.8648	−	7.02923i	1.92022	−	0.338586i	0.921463	−	0.388466i	$-0.126995\pi$
$431$	39.8648	−	7.02923i	1.92022	−	0.338586i	0.998755	+	0.0498802i	$0.0158840\pi$
$432$		0			0
$433$	−3.28124	+	37.5047i	−0.157686	+	1.80236i	0.345746	+	0.938328i	$0.387626\pi$
$433$	−3.28124	+	37.5047i	−0.157686	+	1.80236i	−0.503433	+	0.864034i	$0.667930\pi$
$434$		0			0
$435$	35.7249	−	6.41419i	1.71288	−	0.307537i
$436$		0			0
$437$	−11.2733	+	15.5295i	−0.539274	+	0.742878i
$438$		0			0
$439$	−25.5394	+	9.29559i	−1.21893	+	0.443654i	−0.869793	−	0.493417i	$-0.835748\pi$
$439$	−25.5394	+	9.29559i	−1.21893	+	0.443654i	−0.349137	+	0.937072i	$0.613525\pi$
$440$		0			0
$441$	−22.4179	+	18.8109i	−1.06752	+	0.895756i
$442$		0			0
$443$	9.52548	−	13.6038i	0.452569	−	0.646336i	−0.526425	−	0.850221i	$-0.676468\pi$
$443$	9.52548	−	13.6038i	0.452569	−	0.646336i	0.978995	+	0.203885i	$0.0653570\pi$
$444$		0			0
$445$	17.7119	−	1.60526i	0.839625	−	0.0760965i
$446$		0			0
$447$	2.96355	+	6.35536i	0.140171	+	0.300598i
$448$		0			0
$449$	−19.9824	−	34.6106i	−0.943030	−	1.63338i	−0.759648	−	0.650334i	$-0.774629\pi$
$449$	−19.9824	−	34.6106i	−0.943030	−	1.63338i	−0.183382	−	0.983042i	$-0.558704\pi$
$450$		0			0
$451$	0.495125	−	0.590067i	0.0233145	−	0.0277852i
$452$		0			0
$453$	−34.0500	+	23.8420i	−1.59981	+	1.12020i
$454$		0			0
$455$	−22.5256	+	15.8775i	−1.05602	+	0.744348i
$456$		0			0
$457$	−24.6377	+	24.6377i	−1.15250	+	1.15250i	−0.166452	+	0.986050i	$0.553231\pi$
$457$	−24.6377	+	24.6377i	−1.15250	+	1.15250i	−0.986050	+	0.166452i	$0.946769\pi$
$458$		0			0
$459$	0.196870	−	1.11650i	0.00918910	−	0.0521140i
$460$		0			0
$461$	1.32304	+	1.11016i	0.0616202	+	0.0517055i	0.673078	−	0.739572i	$-0.264972\pi$
$461$	1.32304	+	1.11016i	0.0616202	+	0.0517055i	−0.611457	+	0.791277i	$0.709416\pi$
$462$		0			0
$463$	−0.0346141	+	0.129182i	−0.00160865	+	0.00600358i	−0.966725	−	0.255816i	$-0.917656\pi$
$463$	−0.0346141	+	0.129182i	−0.00160865	+	0.00600358i	0.965117	+	0.261820i	$0.0843225\pi$
$464$		0			0
$465$	−0.253425	+	0.442124i	−0.0117523	+	0.0205030i
$466$		0			0
$467$	3.21248	+	11.9891i	0.148656	+	0.554791i	0.999565	+	0.0294790i	$0.00938481\pi$
$467$	3.21248	+	11.9891i	0.148656	+	0.554791i	−0.850910	+	0.525312i	$0.823949\pi$
$468$		0			0
$469$	5.29577	+	30.0338i	0.244536	+	1.38683i
$470$		0			0
$471$	17.0844	+	20.3604i	0.787209	+	0.938159i
$472$		0			0
$473$	30.8866	+	14.4027i	1.42017	+	0.662235i
$474$		0			0
$475$	14.1889	−	16.5431i	0.651033	−	0.759050i
$476$		0			0
$477$	−1.10935	−	0.517297i	−0.0507935	−	0.0236854i
$478$		0			0
$479$	−4.28350	−	5.10488i	−0.195718	−	0.233248i	0.659256	−	0.751919i	$-0.270871\pi$
$479$	−4.28350	−	5.10488i	−0.195718	−	0.233248i	−0.854974	+	0.518671i	$0.826427\pi$
$480$		0			0
$481$	−4.21254	−	23.8905i	−0.192075	−	1.08931i
$482$		0			0
$483$	11.4077	+	42.5740i	0.519067	+	1.93719i
$484$		0			0
$485$	−5.50784	+	9.60894i	−0.250098	+	0.436319i
$486$		0			0
$487$	−0.882377	+	3.29308i	−0.0399843	+	0.149224i	−0.983032	−	0.183434i	$-0.941279\pi$
$487$	−0.882377	+	3.29308i	−0.0399843	+	0.149224i	0.943048	+	0.332658i	$0.107945\pi$
$488$		0			0
$489$	37.2524	+	31.2585i	1.68461	+	1.41356i
$490$		0			0
$491$	2.71026	−	15.3706i	0.122312	−	0.693667i	−0.860556	−	0.509356i	$-0.829884\pi$
$491$	2.71026	−	15.3706i	0.122312	−	0.693667i	0.982868	−	0.184311i	$-0.0590052\pi$
$492$		0			0
$493$	−16.9494	+	16.9494i	−0.763361	+	0.763361i
$494$		0			0
$495$	−17.1914	+	12.1176i	−0.772695	+	0.544645i
$496$		0			0
$497$	−53.3893	+	37.3836i	−2.39484	+	1.67688i
$498$		0			0
$499$	−11.9549	+	14.2473i	−0.535174	+	0.637795i	−0.964098	−	0.265545i	$-0.914448\pi$
$499$	−11.9549	+	14.2473i	−0.535174	+	0.637795i	0.428925	+	0.903340i	$0.358893\pi$
$500$		0			0
$501$	−24.6384	−	42.6750i	−1.10076	−	1.90658i
$502$		0			0
$503$	3.84939	+	8.25504i	0.171636	+	0.368074i	0.973243	−	0.229776i	$-0.0737995\pi$
$503$	3.84939	+	8.25504i	0.171636	+	0.368074i	−0.801608	+	0.597850i	$0.796022\pi$
$504$		0			0
$505$	−16.7594	+	1.51893i	−0.745785	+	0.0675916i
$506$		0			0
$507$	−5.27690	+	7.53620i	−0.234355	+	0.334694i
$508$		0			0
$509$	−17.6627	+	14.8208i	−0.782887	+	0.656920i	−0.943974	−	0.330020i	$-0.892944\pi$
$509$	−17.6627	+	14.8208i	−0.782887	+	0.656920i	0.161087	+	0.986940i	$0.448500\pi$
$510$		0			0
$511$	−18.7431	+	6.82194i	−0.829147	+	0.301785i
$512$		0			0
$513$	−0.372180	+	1.29993i	−0.0164322	+	0.0573933i
$514$		0			0
$515$	−8.15401	+	1.46400i	−0.359309	+	0.0645117i
$516$		0			0
$517$	3.51331	−	40.1574i	0.154515	−	1.76612i
$518$		0			0
$519$	−11.0848	+	1.95455i	−0.486570	+	0.0857954i
$520$		0			0
$521$	−2.69016	−	1.55316i	−0.117858	−	0.0680453i	0.439912	−	0.898041i	$-0.355010\pi$
$521$	−2.69016	−	1.55316i	−0.117858	−	0.0680453i	−0.557770	+	0.829996i	$0.688343\pi$
$522$		0			0
$523$	−21.1624	+	9.86821i	−0.925369	+	0.431507i	−0.826080	−	0.563552i	$-0.809434\pi$
$523$	−21.1624	+	9.86821i	−0.925369	+	0.431507i	−0.0992883	+	0.995059i	$0.531657\pi$
$524$		0			0
$525$	−8.99978	−	49.2425i	−0.392782	−	2.14912i
$526$		0			0
$527$	−0.0293318	−	0.335264i	−0.00127771	−	0.0146043i
$528$		0			0
$529$	−3.56330	−	0.628307i	−0.154926	−	0.0273177i
$530$		0			0
$531$			20.3298i			0.882237i
$532$		0			0
$533$	−0.551385	−	0.551385i	−0.0238831	−	0.0238831i
$534$		0			0
$535$	0.513803	+	0.185197i	0.0222136	+	0.00800675i
$536$		0			0
$537$	35.7308	−	3.12604i	1.54190	−	0.134899i
$538$		0			0
$539$	−24.4057	+	14.0906i	−1.05123	+	0.606926i
$540$		0			0
$541$	3.82579	+	1.39247i	0.164484	+	0.0598671i	0.422950	−	0.906153i	$-0.360995\pi$
$541$	3.82579	+	1.39247i	0.164484	+	0.0598671i	−0.258466	+	0.966020i	$0.583217\pi$
$542$		0			0
$543$	−51.5660	+	13.8171i	−2.21291	+	0.592948i
$544$		0			0
$545$	−2.90748	+	2.92566i	−0.124543	+	0.125322i
$546$		0			0
$547$	35.8262	+	3.13438i	1.53182	+	0.134017i	0.821640	−	0.570007i	$-0.193059\pi$
$547$	35.8262	+	3.13438i	1.53182	+	0.134017i	0.710177	+	0.704023i	$0.248615\pi$
$548$		0			0
$549$	−8.27059	−	22.7232i	−0.352980	−	0.969805i
$550$		0			0
$551$	22.2100	−	18.0001i	0.946176	−	0.766832i
$552$		0			0
$553$	−16.4586	+	35.2955i	−0.699890	+	1.50092i
$554$		0			0
$555$	42.5981	+	11.2719i	1.80819	+	0.478465i
$556$		0			0
$557$	−14.4381	−	10.1097i	−0.611762	−	0.428361i	0.226206	−	0.974079i	$-0.427368\pi$
$557$	−14.4381	−	10.1097i	−0.611762	−	0.428361i	−0.837968	+	0.545719i	$0.816257\pi$
$558$		0			0
$559$	17.2499	−	29.8777i	0.729594	−	1.26369i
$560$		0			0
$561$	9.31087	−	25.5814i	0.393105	−	1.08005i
$562$		0			0
$563$	−7.71367	−	2.06687i	−0.325092	−	0.0871083i	0.0925819	−	0.995705i	$-0.470488\pi$
$563$	−7.71367	−	2.06687i	−0.325092	−	0.0871083i	−0.417674	+	0.908597i	$0.637155\pi$
$564$		0			0
$565$	14.1506	+	16.7576i	0.595321	+	0.704999i
$566$		0			0
$567$	−19.9732	−	28.5247i	−0.838795	−	1.19792i
$568$		0			0
$569$	41.8734			1.75542			0.877712	−	0.479188i	$-0.159069\pi$
$569$	41.8734			1.75542			0.877712	+	0.479188i	$0.159069\pi$
$570$		0			0
$571$	−34.7494			−1.45422			−0.727109	−	0.686522i	$-0.759137\pi$
$571$	−34.7494			−1.45422			−0.727109	+	0.686522i	$0.759137\pi$
$572$		0			0
$573$	8.37131	+	11.9555i	0.349716	+	0.499447i
$574$		0			0
$575$	−21.2974	−	5.56450i	−0.888163	−	0.232056i
$576$		0			0
$577$	−0.637746	−	0.170884i	−0.0265497	−	0.00711398i	0.245520	−	0.969392i	$-0.421041\pi$
$577$	−0.637746	−	0.170884i	−0.0265497	−	0.00711398i	−0.272069	+	0.962278i	$0.587708\pi$
$578$		0			0
$579$	0.393036	−	1.07986i	0.0163340	−	0.0448773i
$580$		0			0
$581$	10.3014	−	17.8426i	0.427376	−	0.740237i
$582$		0			0
$583$	−0.965549	−	0.676085i	−0.0399890	−	0.0280006i
$584$		0			0
$585$	10.7035	+	18.4063i	0.442537	+	0.761006i
$586$		0			0
$587$	3.28102	−	7.03616i	0.135422	−	0.290413i	−0.826889	−	0.562365i	$-0.809891\pi$
$587$	3.28102	−	7.03616i	0.135422	−	0.290413i	0.962311	+	0.271952i	$0.0876692\pi$
$588$		0			0
$589$	−0.00684289	+	0.401326i	−0.000281956	+	0.0165364i
$590$		0			0
$591$	−6.78132	−	18.6315i	−0.278946	−	0.766398i
$592$		0			0
$593$	18.4902	+	1.61768i	0.759301	+	0.0664302i	0.460229	−	0.887800i	$-0.347767\pi$
$593$	18.4902	+	1.61768i	0.759301	+	0.0664302i	0.299072	+	0.954231i	$0.403323\pi$
$594$		0			0
$595$	23.4486	+	23.3029i	0.961301	+	0.955324i
$596$		0			0
$597$	−34.9264	+	9.35851i	−1.42944	+	0.383018i
$598$		0			0
$599$	−1.54272	−	0.561504i	−0.0630338	−	0.0229424i	0.310311	−	0.950635i	$-0.399567\pi$
$599$	−1.54272	−	0.561504i	−0.0630338	−	0.0229424i	−0.373345	+	0.927693i	$0.621789\pi$
$600$		0			0
$601$	−12.9768	+	7.49216i	−0.529335	+	0.305612i	−0.740746	−	0.671786i	$-0.765528\pi$
$601$	−12.9768	+	7.49216i	−0.529335	+	0.305612i	0.211411	+	0.977397i	$0.432194\pi$
$602$		0			0
$603$	23.4726	−	2.05358i	0.955876	−	0.0836284i
$604$		0			0
$605$	3.92991	−	1.84749i	0.159774	−	0.0751110i
$606$		0			0
$607$	−12.1188	−	12.1188i	−0.491888	−	0.491888i	0.417013	−	0.908901i	$-0.363077\pi$
$607$	−12.1188	−	12.1188i	−0.491888	−	0.491888i	−0.908901	+	0.417013i	$0.863077\pi$
$608$		0			0
$609$		−	65.6622i		−	2.66077i
$610$		0			0
$611$	−40.1879	−	7.08621i	−1.62583	−	0.286677i
$612$		0			0
$613$	0.449626	+	5.13925i	0.0181602	+	0.207572i	0.999854	+	0.0171046i	$0.00544484\pi$
$613$	0.449626	+	5.13925i	0.0181602	+	0.207572i	−0.981693	+	0.190468i	$0.939000\pi$
$614$		0			0
$615$	1.32945	−	0.488580i	0.0536086	−	0.0197015i
$616$		0			0
$617$	−7.00750	+	3.26765i	−0.282111	+	0.131551i	−0.558524	−	0.829488i	$-0.688632\pi$
$617$	−7.00750	+	3.26765i	−0.282111	+	0.131551i	0.276413	+	0.961039i	$0.410854\pi$
$618$		0			0
$619$	−33.9868	−	19.6223i	−1.36605	−	0.788687i	−0.375626	−	0.926771i	$-0.622572\pi$
$619$	−33.9868	−	19.6223i	−1.36605	−	0.788687i	−0.990421	+	0.138084i	$0.955906\pi$
$620$		0			0
$621$	1.34493	−	0.237147i	0.0539701	−	0.00951638i
$622$		0			0
$623$	2.80409	−	32.0509i	0.112344	−	1.28409i
$624$		0			0
$625$	23.5971	+	8.25683i	0.943885	+	0.330273i
$626$		0			0
$627$	−14.2213	+	29.1879i	−0.567944	+	1.16565i
$628$		0			0
$629$	−27.3451	+	9.95280i	−1.09032	+	0.396844i
$630$		0			0
$631$	−5.25882	+	4.41268i	−0.209350	+	0.175666i	−0.741434	−	0.671026i	$-0.765854\pi$
$631$	−5.25882	+	4.41268i	−0.209350	+	0.175666i	0.532083	+	0.846692i	$0.321409\pi$
$632$		0			0
$633$	−10.1354	+	14.4749i	−0.402846	+	0.575324i
$634$		0			0
$635$	−32.3685	−	26.9889i	−1.28451	−	1.07102i
$636$		0			0
$637$	12.0568	+	25.8558i	0.477706	+	1.02444i
$638$		0			0
$639$	25.1778	+	43.6092i	0.996017	+	1.72515i
$640$		0			0
$641$	26.5316	−	31.6191i	1.04793	−	1.24888i	0.0802335	−	0.996776i	$-0.474433\pi$
$641$	26.5316	−	31.6191i	1.04793	−	1.24888i	0.967700	−	0.252103i	$-0.0811221\pi$
$642$		0			0
$643$	−18.3224	+	12.8295i	−0.722564	+	0.505945i	−0.876059	−	0.482205i	$-0.839836\pi$
$643$	−18.3224	+	12.8295i	−0.722564	+	0.505945i	0.153494	+	0.988150i	$0.450947\pi$
$644$		0			0
$645$	36.1034	+	51.2203i	1.42157	+	2.01680i
$646$		0			0
$647$	−23.4978	+	23.4978i	−0.923793	+	0.923793i	−0.997295	−	0.0735025i	$-0.976582\pi$
$647$	−23.4978	+	23.4978i	−0.923793	+	0.923793i	0.0735025	+	0.997295i	$0.476582\pi$
$648$		0			0
$649$	−3.39955	+	19.2798i	−0.133444	+	0.756798i
$650$		0			0
$651$	0.706225	+	0.592593i	0.0276791	+	0.0232256i
$652$		0			0
$653$	5.51282	−	20.5741i	0.215733	−	0.805128i	−0.770174	−	0.637834i	$-0.779831\pi$
$653$	5.51282	−	20.5741i	0.215733	−	0.805128i	0.985907	−	0.167294i	$-0.0535028\pi$
$654$		0			0
$655$	−0.510693	−	1.88243i	−0.0199544	−	0.0735528i
$656$		0			0
$657$	3.98850	+	14.8853i	0.155606	+	0.580731i
$658$		0			0
$659$	−1.14501	−	6.49368i	−0.0446033	−	0.252958i	0.954350	−	0.298689i	$-0.0965493\pi$
$659$	−1.14501	−	6.49368i	−0.0446033	−	0.252958i	−0.998954	+	0.0457312i	$0.985438\pi$
$660$		0			0
$661$	5.48023	+	6.53109i	0.213156	+	0.254030i	0.862019	−	0.506875i	$-0.169200\pi$
$661$	5.48023	+	6.53109i	0.213156	+	0.254030i	−0.648863	+	0.760905i	$0.724755\pi$
$662$		0			0
$663$	−24.9768	−	11.6469i	−0.970019	−	0.452327i
$664$		0			0
$665$	−24.9204	−	30.5535i	−0.966373	−	1.18481i
$666$		0			0
$667$	−26.1687	−	12.2027i	−1.01326	−	0.472490i
$668$		0			0
$669$	−4.45960	−	5.31474i	−0.172418	−	0.205480i
$670$		0			0
$671$	−4.04365	−	22.9327i	−0.156103	−	0.885305i
$672$		0			0
$673$	0.688405	+	2.56916i	0.0265361	+	0.0990339i	0.977924	−	0.208962i	$-0.0670084\pi$
$673$	0.688405	+	2.56916i	0.0265361	+	0.0990339i	−0.951388	+	0.307996i	$0.900342\pi$
$674$		0			0
$675$	−1.54426	+	0.144815i	−0.0594385	+	0.00557392i
$676$		0			0
$677$	10.9891	−	41.0118i	0.422345	−	1.57621i	−0.347310	−	0.937751i	$-0.612905\pi$
$677$	10.9891	−	41.0118i	0.422345	−	1.57621i	0.769654	−	0.638461i	$-0.220429\pi$
$678$		0			0
$679$	15.3488	+	12.8792i	0.589033	+	0.494257i
$680$		0			0
$681$	−0.0863950	+	0.489970i	−0.00331066	+	0.0187757i
$682$		0			0
$683$	0.655986	−	0.655986i	0.0251006	−	0.0251006i	−0.694445	−	0.719546i	$-0.744350\pi$
$683$	0.655986	−	0.655986i	0.0251006	−	0.0251006i	0.719546	+	0.694445i	$0.244350\pi$
$684$		0			0
$685$	34.9605	+	6.05213i	1.33577	+	0.231240i
$686$		0			0
$687$	25.2718	−	17.6955i	0.964179	−	0.675126i
$688$		0			0
$689$	−0.767008	+	0.914085i	−0.0292207	+	0.0348239i
$690$		0			0
$691$	11.1063	+	19.2366i	0.422503	+	0.731796i	0.996184	−	0.0872827i	$-0.0278183\pi$
$691$	11.1063	+	19.2366i	0.422503	+	0.731796i	−0.573681	+	0.819079i	$0.694485\pi$
$692$		0			0
$693$	16.0805	+	34.4848i	0.610849	+	1.30997i
$694$		0			0
$695$	0.680220	+	7.50533i	0.0258022	+	0.284694i
$696$		0			0
$697$	−0.536514	+	0.766221i	−0.0203219	+	0.0290227i
$698$		0			0
$699$	−10.9150	+	9.15878i	−0.412844	+	0.346417i
$700$		0			0
$701$	−17.6498	+	6.42402i	−0.666625	+	0.242632i	−0.653094	−	0.757277i	$-0.726529\pi$
$701$	−17.6498	+	6.42402i	−0.666625	+	0.242632i	−0.0135312	+	0.999908i	$0.504307\pi$
$702$		0			0
$703$	33.6723	−	8.40991i	1.26997	−	0.317186i
$704$		0			0
$705$	42.3259	−	60.8507i	1.59409	−	2.29177i
$706$		0			0
$707$	−2.65330	+	30.3274i	−0.0997876	+	1.14058i
$708$		0			0
$709$	−29.9735	+	5.28513i	−1.12568	+	0.198487i	−0.705332	−	0.708877i	$-0.749202\pi$
$709$	−29.9735	+	5.28513i	−1.12568	+	0.198487i	−0.420345	+	0.907364i	$0.638091\pi$
$710$		0			0
$711$	26.0574	+	15.0443i	0.977231	+	0.564204i
$712$		0			0
$713$	0.367414	−	0.171328i	0.0137598	−	0.00641629i
$714$		0			0
$715$	7.07283	+	19.2455i	0.264509	+	0.719741i
$716$		0			0
$717$	−1.23694	−	14.1383i	−0.0461945	−	0.528006i
$718$		0			0
$719$	−28.1643	−	4.96612i	−1.05035	−	0.185205i	−0.378279	−	0.925692i	$-0.623484\pi$
$719$	−28.1643	−	4.96612i	−1.05035	−	0.185205i	−0.672071	+	0.740487i	$0.734595\pi$
$720$		0			0
$721$			14.9870i			0.558146i
$722$		0			0
$723$	−12.9948	−	12.9948i	−0.483280	−	0.483280i
$724$		0			0
$725$	28.5012	+	16.2191i	1.05851	+	0.602360i
$726$		0			0
$727$	34.1776	−	2.99015i	1.26758	−	0.110899i	0.566546	−	0.824030i	$-0.308279\pi$
$727$	34.1776	−	2.99015i	1.26758	−	0.110899i	0.701030	+	0.713132i	$0.252724\pi$
$728$		0			0
$729$	−25.2940	+	14.6035i	−0.936815	+	0.540870i
$730$		0			0
$731$	−38.8886	−	14.1543i	−1.43835	−	0.523516i
$732$		0			0
$733$	42.3237	−	11.3406i	1.56326	−	0.418874i	0.629566	−	0.776947i	$-0.283233\pi$
$733$	42.3237	−	11.3406i	1.56326	−	0.418874i	0.933694	+	0.358073i	$0.116566\pi$
$734$		0			0
$735$	−51.8194	+	0.161582i	−1.91139	+	0.00596006i
$736$		0			0
$737$	22.6037	+	1.97756i	0.832617	+	0.0728445i
$738$		0			0
$739$	−11.7587	−	32.3067i	−0.432550	−	1.18842i	−0.944242	−	0.329252i	$-0.893203\pi$
$739$	−11.7587	−	32.3067i	−0.432550	−	1.18842i	0.511692	−	0.859169i	$-0.329019\pi$
$740$		0			0
$741$	28.1807	+	16.9171i	1.03524	+	0.621467i
$742$		0			0
$743$	4.85465	−	10.4108i	0.178100	−	0.381936i	−0.796910	−	0.604098i	$-0.793534\pi$
$743$	4.85465	−	10.4108i	0.178100	−	0.381936i	0.975010	+	0.222162i	$0.0713113\pi$
$744$		0			0
$745$	−1.62067	+	6.12475i	−0.0593768	+	0.224394i
$746$		0			0
$747$	−13.0392	−	9.13013i	−0.477078	−	0.334054i
$748$		0			0
$749$	0.494021	−	0.855669i	0.0180511	−	0.0312655i
$750$		0			0
$751$	−15.9735	+	43.8868i	−0.582880	+	1.60145i	0.200354	+	0.979724i	$0.435791\pi$
$751$	−15.9735	+	43.8868i	−0.582880	+	1.60145i	−0.783234	+	0.621727i	$0.786431\pi$
$752$		0			0
$753$	2.36773	+	0.634431i	0.0862848	+	0.0231199i
$754$		0			0
$755$	−37.4225	−	3.15649i	−1.36194	−	0.114877i
$756$		0			0
$757$	−3.37238	−	4.81626i	−0.122571	−	0.175050i	0.753177	−	0.657818i	$-0.228520\pi$
$757$	−3.37238	−	4.81626i	−0.122571	−	0.175050i	−0.875748	+	0.482768i	$0.839631\pi$
$758$		0			0
$759$	32.7927			1.19030
$760$		0			0
$761$	25.4796			0.923636			0.461818	−	0.886975i	$-0.347197\pi$
$761$	25.4796			0.923636			0.461818	+	0.886975i	$0.347197\pi$
$762$		0			0
$763$	4.27992	+	6.11236i	0.154944	+	0.221282i
$764$		0			0
$765$	19.5144	−	16.4784i	0.705543	−	0.595780i
$766$		0			0
$767$	19.1433	+	5.12944i	0.691226	+	0.185213i
$768$		0			0
$769$	9.48778	−	26.0675i	0.342138	−	0.940017i	−0.642635	−	0.766172i	$-0.722159\pi$
$769$	9.48778	−	26.0675i	0.342138	−	0.940017i	0.984773	−	0.173844i	$-0.0556189\pi$
$770$		0			0
$771$	18.6545	−	32.3105i	0.671824	−	1.16363i
$772$		0			0
$773$	−3.27286	−	2.29168i	−0.117716	−	0.0824260i	0.513236	−	0.858248i	$-0.328447\pi$
$773$	−3.27286	−	2.29168i	−0.117716	−	0.0824260i	−0.630952	+	0.775822i	$0.717336\pi$
$774$		0			0
$775$	−0.431663	+	0.160168i	−0.0155058	+	0.00575340i
$776$		0			0
$777$	33.6891	−	72.2464i	1.20859	−	2.59183i
$778$		0			0
$779$	0.731559	−	0.842250i	0.0262108	−	0.0301767i
$780$		0			0
$781$	16.5851	+	45.5671i	0.593461	+	1.63052i
$782$		0			0
$783$	−2.02678	−	0.177320i	−0.0724311	−	0.00633690i
$784$		0			0
$785$	0.0748778	+	24.0132i	0.00267250	+	0.857070i
$786$		0			0
$787$	10.5341	−	2.82261i	0.375502	−	0.100615i	−0.0661320	−	0.997811i	$-0.521066\pi$
$787$	10.5341	−	2.82261i	0.375502	−	0.100615i	0.441633	+	0.897196i	$0.354399\pi$
$788$		0			0
$789$	25.9295	+	9.43756i	0.923114	+	0.335986i
$790$		0			0
$791$	34.3625	−	19.8392i	1.22179	−	0.705400i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +O(q^{10})\)	\(q+(-1.41957 - 2.02735i) q^{3} +(0.187939 - 2.22816i) q^{5} +(-3.90736 - 1.04697i) q^{7} +(-1.06893 + 2.93686i) q^{9} +(-1.50482 + 2.60643i) q^{11} +(2.49576 + 1.74755i) q^{13} +(-4.78405 + 2.78200i) q^{15} +(1.54457 - 3.31233i) q^{17} +(-2.24349 + 3.73721i) q^{19} +(3.42418 + 9.40786i) q^{21} +(4.38572 + 0.383700i) q^{23} +(-4.92936 - 0.837516i) q^{25} +(0.299637 - 0.0802874i) q^{27} +(-6.16306 - 2.24317i) q^{29} +(0.0797471 - 0.0460420i) q^{31} +(7.42036 - 0.649197i) q^{33} +(-3.06717 + 8.50944i) q^{35} +(-5.63016 - 5.63016i) q^{37} -7.54055i q^{39} +(-0.252048 - 0.0444428i) q^{41} +(-0.986904 - 11.2804i) q^{43} +(6.34288 + 2.93369i) q^{45} +(-12.1390 + 5.66049i) q^{47} +(8.10914 + 4.68182i) q^{49} +(-8.90788 + 1.57070i) q^{51} +(-0.0341343 + 0.390156i) q^{53} +(5.52472 + 3.84283i) q^{55} +(10.7614 - 0.756885i) q^{57} +(6.11253 - 2.22478i) q^{59} +(-5.92709 + 4.97342i) q^{61} +(7.25151 - 10.3562i) q^{63} +(4.36286 - 5.23251i) q^{65} +(-3.18616 - 6.83274i) q^{67} +(-5.44793 - 9.43609i) q^{69} +(10.3566 - 12.3425i) q^{71} +(4.03907 - 2.82818i) q^{73} +(5.29962 + 11.1825i) q^{75} +(8.60875 - 8.60875i) q^{77} +(1.67176 - 9.48103i) q^{79} +(6.59432 + 5.53329i) q^{81} +(-1.31821 + 4.91963i) q^{83} +(-7.09010 - 4.06405i) q^{85} +(4.20119 + 15.6790i) q^{87} +(1.38111 + 7.83264i) q^{89} +(-7.92219 - 9.44130i) q^{91} +(-0.206550 - 0.0963158i) q^{93} +(7.90545 + 5.70121i) q^{95} +(-4.48907 - 2.09329i) q^{97} +(-6.04617 - 7.20554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 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