LMFDB - Embedded newform 1080.2.bt.a.233.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(17,1080)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1080.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.bt (of order $12$, degree $4$, not 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.3
Character	$\chi$	$=$	1080.233
Dual form			1080.2.bt.a.737.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06252 - 0.863710i) q^{5} +(2.64986 + 0.710029i) q^{7} +O(q^{10})$	$q+(-2.06252 - 0.863710i) q^{5} +(2.64986 + 0.710029i) q^{7} +(0.765403 - 0.441906i) q^{11} +(1.35352 - 0.362674i) q^{13} +(-3.83033 - 3.83033i) q^{17} -4.46618i q^{19} +(1.01575 + 3.79082i) q^{23} +(3.50801 + 3.56284i) q^{25} +(0.874378 + 1.51447i) q^{29} +(2.74056 - 4.74679i) q^{31} +(-4.85215 - 3.75316i) q^{35} +(4.41426 - 4.41426i) q^{37} +(5.85416 + 3.37990i) q^{41} +(-1.28815 + 4.80743i) q^{43} +(2.90134 - 10.8280i) q^{47} +(0.455456 + 0.262958i) q^{49} +(6.79105 - 6.79105i) q^{53} +(-1.96034 + 0.250355i) q^{55} +(4.02430 - 6.97029i) q^{59} +(-4.25649 - 7.37246i) q^{61} +(-3.10491 - 0.421023i) q^{65} +(-3.87853 - 14.4749i) q^{67} -11.1410i q^{71} +(10.1583 + 10.1583i) q^{73} +(2.34198 - 0.627531i) q^{77} +(-8.28119 + 4.78115i) q^{79} +(-4.49329 - 1.20397i) q^{83} +(4.59186 + 11.2085i) q^{85} +11.3300 q^{89} +3.84415 q^{91} +(-3.85749 + 9.21161i) q^{95} +(11.0528 + 2.96160i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q - 24 q^{23} - 12 q^{41} + 36 q^{47} + 12 q^{61} + 72 q^{65} + 48 q^{77} + 60 q^{83} + 24 q^{85} + 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q - 24 * q^23 - 12 * q^41 + 36 * q^47 + 12 * q^61 + 72 * q^65 + 48 * q^77 + 60 * q^83 + 24 * q^85 + 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.06252	−	0.863710i	−0.922389	−	0.386263i
$5$	−2.06252	−	0.863710i	−0.922389	−	0.386263i
$6$		0			0
$7$	2.64986	+	0.710029i	1.00155	+	0.268366i	0.722096	−	0.691792i	$-0.243179\pi$
$7$	2.64986	+	0.710029i	1.00155	+	0.268366i	0.279458	+	0.960158i	$0.409845\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.765403	−	0.441906i	0.230778	−	0.133240i	−0.380153	−	0.924924i	$-0.624129\pi$
$11$	0.765403	−	0.441906i	0.230778	−	0.133240i	0.610931	+	0.791684i	$0.290795\pi$
$12$		0			0
$13$	1.35352	−	0.362674i	0.375399	−	0.100588i	−0.0661862	−	0.997807i	$-0.521083\pi$
$13$	1.35352	−	0.362674i	0.375399	−	0.100588i	0.441585	+	0.897220i	$0.354416\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.83033	−	3.83033i	−0.928992	−	0.928992i	0.0686484	−	0.997641i	$-0.478131\pi$
$17$	−3.83033	−	3.83033i	−0.928992	−	0.928992i	−0.997641	+	0.0686484i	$0.978131\pi$
$18$		0			0
$19$		−	4.46618i		−	1.02461i	−0.858803	−	0.512306i	$-0.828791\pi$
$19$		−	4.46618i		−	1.02461i	0.858803	−	0.512306i	$-0.171209\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.01575	+	3.79082i	0.211798	+	0.790440i	0.987269	+	0.159058i	$0.0508456\pi$
$23$	1.01575	+	3.79082i	0.211798	+	0.790440i	−0.775471	+	0.631383i	$0.782488\pi$
$24$		0			0
$25$	3.50801	+	3.56284i	0.701602	+	0.712569i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.874378	+	1.51447i	0.162368	+	0.281229i	0.935717	−	0.352750i	$-0.114754\pi$
$29$	0.874378	+	1.51447i	0.162368	+	0.281229i	−0.773350	+	0.633980i	$0.781420\pi$
$30$		0			0
$31$	2.74056	−	4.74679i	0.492219	−	0.852548i	−0.507741	−	0.861510i	$-0.669519\pi$
$31$	2.74056	−	4.74679i	0.492219	−	0.852548i	0.999960	+	0.00896169i	$0.00285263\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.85215	−	3.75316i	−0.820163	−	0.634400i
$36$		0			0
$37$	4.41426	−	4.41426i	0.725699	−	0.725699i	−0.244061	−	0.969760i	$-0.578480\pi$
$37$	4.41426	−	4.41426i	0.725699	−	0.725699i	0.969760	+	0.244061i	$0.0784796\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.85416	+	3.37990i	0.914266	+	0.527852i	0.881801	−	0.471621i	$-0.156331\pi$
$41$	5.85416	+	3.37990i	0.914266	+	0.527852i	0.0324645	+	0.999473i	$0.489664\pi$
$42$		0			0
$43$	−1.28815	+	4.80743i	−0.196441	+	0.733127i	0.795449	+	0.606021i	$0.207235\pi$
$43$	−1.28815	+	4.80743i	−0.196441	+	0.733127i	−0.991889	+	0.127105i	$0.959431\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.90134	−	10.8280i	0.423205	−	1.57942i	−0.344608	−	0.938747i	$-0.611988\pi$
$47$	2.90134	−	10.8280i	0.423205	−	1.57942i	0.767813	−	0.640674i	$-0.221345\pi$
$48$		0			0
$49$	0.455456	+	0.262958i	0.0650651	+	0.0375654i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.79105	−	6.79105i	0.932823	−	0.932823i	−0.0650586	−	0.997881i	$-0.520723\pi$
$53$	6.79105	−	6.79105i	0.932823	−	0.932823i	0.997881	+	0.0650586i	$0.0207234\pi$
$54$		0			0
$55$	−1.96034	+	0.250355i	−0.264332	+	0.0337579i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.02430	−	6.97029i	0.523919	−	0.907455i	−0.475693	−	0.879611i	$-0.657803\pi$
$59$	4.02430	−	6.97029i	0.523919	−	0.907455i	0.999612	−	0.0278435i	$-0.00886401\pi$
$60$		0			0
$61$	−4.25649	−	7.37246i	−0.544988	−	0.943947i	−0.998608	−	0.0527517i	$-0.983201\pi$
$61$	−4.25649	−	7.37246i	−0.544988	−	0.943947i	0.453620	−	0.891195i	$-0.350133\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.10491	−	0.421023i	−0.385117	−	0.0522215i
$66$		0			0
$67$	−3.87853	−	14.4749i	−0.473837	−	1.76839i	−0.625784	−	0.779996i	$-0.715221\pi$
$67$	−3.87853	−	14.4749i	−0.473837	−	1.76839i	0.151947	−	0.988389i	$-0.451446\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.1410i		−	1.32219i	−0.750302	−	0.661095i	$-0.770092\pi$
$71$		−	11.1410i		−	1.32219i	0.750302	−	0.661095i	$-0.229908\pi$
$72$		0			0
$73$	10.1583	+	10.1583i	1.18894	+	1.18894i	0.977361	+	0.211580i	$0.0678609\pi$
$73$	10.1583	+	10.1583i	1.18894	+	1.18894i	0.211580	+	0.977361i	$0.432139\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.34198	−	0.627531i	0.266893	−	0.0715138i
$78$		0			0
$79$	−8.28119	+	4.78115i	−0.931707	+	0.537921i	−0.887351	−	0.461095i	$-0.847457\pi$
$79$	−8.28119	+	4.78115i	−0.931707	+	0.537921i	−0.0443558	+	0.999016i	$0.514124\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.49329	−	1.20397i	−0.493203	−	0.132153i	0.00364075	−	0.999993i	$-0.498841\pi$
$83$	−4.49329	−	1.20397i	−0.493203	−	0.132153i	−0.496844	+	0.867840i	$0.665508\pi$
$84$		0			0
$85$	4.59186	+	11.2085i	0.498057	+	1.21573i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	11.3300			1.20097			0.600486	−	0.799635i	$-0.294974\pi$
$89$	11.3300			1.20097			0.600486	+	0.799635i	$0.294974\pi$
$90$		0			0
$91$	3.84415			0.402976
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.85749	+	9.21161i	−0.395770	+	0.945091i
$96$		0			0
$97$	11.0528	+	2.96160i	1.12225	+	0.300705i	0.771792	−	0.635875i	$-0.219361\pi$
$97$	11.0528	+	2.96160i	1.12225	+	0.300705i	0.350454	+	0.936580i	$0.386027\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.3287	+	6.54062i	−1.12725	+	0.650816i	−0.943241	−	0.332109i	$-0.892240\pi$
$101$	−11.3287	+	6.54062i	−1.12725	+	0.650816i	−0.184005	+	0.982925i	$0.558906\pi$
$102$		0			0
$103$	−5.22569	+	1.40022i	−0.514902	+	0.137968i	−0.506908	−	0.862000i	$-0.669211\pi$
$103$	−5.22569	+	1.40022i	−0.514902	+	0.137968i	−0.00799468	+	0.999968i	$0.502545\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.25184	+	5.25184i	0.507715	+	0.507715i	0.913824	−	0.406110i	$-0.133115\pi$
$107$	5.25184	+	5.25184i	0.507715	+	0.507715i	−0.406110	+	0.913824i	$0.633115\pi$
$108$		0			0
$109$		−	10.2761i		−	0.984270i	−0.870519	−	0.492135i	$-0.836217\pi$
$109$		−	10.2761i		−	0.984270i	0.870519	−	0.492135i	$-0.163783\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.46206	+	16.6526i	0.419755	+	1.56655i	0.775116	+	0.631818i	$0.217691\pi$
$113$	4.46206	+	16.6526i	0.419755	+	1.56655i	−0.355361	+	0.934729i	$0.615642\pi$
$114$		0			0
$115$	1.17916	−	8.69596i	0.109958	−	0.810903i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.43021	−	12.8695i	−0.681127	−	1.17975i
$120$		0			0
$121$	−5.10944	+	8.84981i	−0.464494	+	0.804528i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.15809	−	10.3784i	−0.371911	−	0.928268i
$126$		0			0
$127$	−10.6609	+	10.6609i	−0.946006	+	0.946006i	−0.998615	−	0.0526093i	$-0.983246\pi$
$127$	−10.6609	+	10.6609i	−0.946006	+	0.946006i	0.0526093	+	0.998615i	$0.483246\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.743908	+	0.429496i	0.0649956	+	0.0375252i	0.532146	−	0.846653i	$-0.321386\pi$
$131$	0.743908	+	0.429496i	0.0649956	+	0.0375252i	−0.467150	+	0.884178i	$0.654719\pi$
$132$		0			0
$133$	3.17112	−	11.8348i	0.274971	−	1.02620i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.70813	+	13.8389i	−0.316807	+	1.18234i	0.605488	+	0.795854i	$0.292978\pi$
$137$	−3.70813	+	13.8389i	−0.316807	+	1.18234i	−0.922295	+	0.386486i	$0.873689\pi$
$138$		0			0
$139$	−9.63362	−	5.56197i	−0.817113	−	0.471760i	0.0323071	−	0.999478i	$-0.489715\pi$
$139$	−9.63362	−	5.56197i	−0.817113	−	0.471760i	−0.849420	+	0.527718i	$0.823048\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.875720	−	0.875720i	0.0732314	−	0.0732314i
$144$		0			0
$145$	−0.495365	−	3.87883i	−0.0411379	−	0.322119i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.728908	+	1.26251i	−0.0597144	+	0.103428i	−0.894337	−	0.447394i	$-0.852352\pi$
$149$	−0.728908	+	1.26251i	−0.0597144	+	0.103428i	0.834623	+	0.550822i	$0.185686\pi$
$150$		0			0
$151$	5.74576	+	9.95194i	0.467583	+	0.809878i	0.999314	−	0.0370357i	$-0.0117915\pi$
$151$	5.74576	+	9.95194i	0.467583	+	0.809878i	−0.531731	+	0.846913i	$0.678458\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.75231	+	7.42331i	−0.783325	+	0.596255i
$156$		0			0
$157$	1.12353	+	4.19308i	0.0896675	+	0.334644i	0.996157	−	0.0875844i	$-0.0279147\pi$
$157$	1.12353	+	4.19308i	0.0896675	+	0.334644i	−0.906490	+	0.422228i	$0.861248\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			10.7664i			0.848508i
$162$		0			0
$163$	10.7949	+	10.7949i	0.845523	+	0.845523i	0.989571	−	0.144048i	$-0.0460120\pi$
$163$	10.7949	+	10.7949i	0.845523	+	0.845523i	−0.144048	+	0.989571i	$0.546012\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.3964	−	4.66134i	1.34617	−	0.360705i	0.487451	−	0.873150i	$-0.337927\pi$
$167$	17.3964	−	4.66134i	1.34617	−	0.360705i	0.858720	+	0.512445i	$0.171260\pi$
$168$		0			0
$169$	−9.55785	+	5.51823i	−0.735219	+	0.424479i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.8049	+	3.43108i	0.973542	+	0.260860i	0.710323	−	0.703876i	$-0.248549\pi$
$173$	12.8049	+	3.43108i	0.973542	+	0.260860i	0.263219	+	0.964736i	$0.415216\pi$
$174$		0			0
$175$	6.76603	+	11.9318i	0.511464	+	0.901962i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.78241			−0.282711			−0.141355	−	0.989959i	$-0.545146\pi$
$179$	−3.78241			−0.282711			−0.141355	+	0.989959i	$0.545146\pi$
$180$		0			0
$181$	−23.0071			−1.71010			−0.855052	−	0.518541i	$-0.826475\pi$
$181$	−23.0071			−1.71010			−0.855052	+	0.518541i	$0.826475\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.9171	+	5.29187i	−0.949688	+	0.389066i
$186$		0			0
$187$	−4.62440	−	1.23910i	−0.338169	−	0.0906122i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.51688	+	5.49457i	−0.688617	+	0.397573i	−0.803094	−	0.595853i	$-0.796814\pi$
$191$	−9.51688	+	5.49457i	−0.688617	+	0.397573i	0.114476	+	0.993426i	$0.463481\pi$
$192$		0			0
$193$	10.5657	−	2.83107i	0.760536	−	0.203785i	0.142349	−	0.989816i	$-0.454534\pi$
$193$	10.5657	−	2.83107i	0.760536	−	0.203785i	0.618186	+	0.786031i	$0.287868\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.49711	−	4.49711i	−0.320406	−	0.320406i	0.528517	−	0.848923i	$-0.322748\pi$
$197$	−4.49711	−	4.49711i	−0.320406	−	0.320406i	−0.848923	+	0.528517i	$0.822748\pi$
$198$		0			0
$199$		−	14.3650i		−	1.01831i	−0.860676	−	0.509154i	$-0.829958\pi$
$199$		−	14.3650i		−	1.01831i	0.860676	−	0.509154i	$-0.170042\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.24167	+	4.63396i	0.0871479	+	0.325240i
$204$		0			0
$205$	−9.15509	−	12.0274i	−0.639419	−	0.840031i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.97363	−	3.41843i	−0.136519	−	0.236458i
$210$		0			0
$211$	0.167767	−	0.290581i	0.0115496	−	0.0200044i	−0.860193	−	0.509969i	$-0.829657\pi$
$211$	0.167767	−	0.290581i	0.0115496	−	0.0200044i	0.871742	+	0.489964i	$0.162990\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.80906	−	8.80286i	0.464374	−	0.600350i
$216$		0			0
$217$	10.6325	−	10.6325i	0.721778	−	0.721778i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.57359	−	3.79527i	−0.442188	−	0.255297i
$222$		0			0
$223$	2.22007	−	8.28540i	0.148667	−	0.554832i	−0.850898	−	0.525331i	$-0.823942\pi$
$223$	2.22007	−	8.28540i	0.148667	−	0.554832i	0.999565	−	0.0295007i	$-0.00939174\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.57688	+	17.0812i	−0.303778	+	1.13372i	0.630214	+	0.776422i	$0.282967\pi$
$227$	−4.57688	+	17.0812i	−0.303778	+	1.13372i	−0.933992	+	0.357294i	$0.883699\pi$
$228$		0			0
$229$	4.82045	+	2.78309i	0.318544	+	0.183912i	0.650743	−	0.759298i	$-0.274457\pi$
$229$	4.82045	+	2.78309i	0.318544	+	0.183912i	−0.332199	+	0.943209i	$0.607791\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.1252	+	12.1252i	−0.794347	+	0.794347i	−0.982198	−	0.187851i	$-0.939848\pi$
$233$	−12.1252	+	12.1252i	−0.794347	+	0.794347i	0.187851	+	0.982198i	$0.439848\pi$
$234$		0			0
$235$	−15.3363	+	19.8270i	−1.00043	+	1.29337i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.849620	−	1.47159i	0.0549574	−	0.0951889i	−0.837238	−	0.546839i	$-0.815831\pi$
$239$	0.849620	−	1.47159i	0.0549574	−	0.0951889i	0.892195	+	0.451650i	$0.149164\pi$
$240$		0			0
$241$	−3.86365	−	6.69204i	−0.248880	−	0.431072i	0.714336	−	0.699803i	$-0.246729\pi$
$241$	−3.86365	−	6.69204i	−0.248880	−	0.431072i	−0.963215	+	0.268731i	$0.913396\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.712270	−	0.935738i	−0.0455052	−	0.0597821i
$246$		0			0
$247$	−1.61977	−	6.04506i	−0.103063	−	0.384638i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	8.29943i		−	0.523855i	−0.965088	−	0.261928i	$-0.915642\pi$
$251$		−	8.29943i		−	0.523855i	0.965088	−	0.261928i	$-0.0843582\pi$
$252$		0			0
$253$	2.45264	+	2.45264i	0.154196	+	0.154196i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.35423	−	1.97056i	0.458744	−	0.122920i	−0.0220439	−	0.999757i	$-0.507017\pi$
$257$	7.35423	−	1.97056i	0.458744	−	0.122920i	0.480788	+	0.876837i	$0.340351\pi$
$258$		0			0
$259$	14.8314	−	8.56293i	0.921580	−	0.532074i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.77517	−	0.743605i	−0.171124	−	0.0458527i	0.172239	−	0.985055i	$-0.444900\pi$
$263$	−2.77517	−	0.743605i	−0.171124	−	0.0458527i	−0.343364	+	0.939202i	$0.611566\pi$
$264$		0			0
$265$	−19.8722	+	8.14121i	−1.22074	+	0.500111i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	23.8609			1.45483			0.727413	−	0.686200i	$-0.240723\pi$
$269$	23.8609			1.45483			0.727413	+	0.686200i	$0.240723\pi$
$270$		0			0
$271$	−20.4742			−1.24372			−0.621859	−	0.783129i	$-0.713622\pi$
$271$	−20.4742			−1.24372			−0.621859	+	0.783129i	$0.713622\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.25948	+	1.17680i	0.256857	+	0.0709638i
$276$		0			0
$277$	−0.0780948	−	0.0209254i	−0.00469226	−	0.00125729i	0.256472	−	0.966552i	$-0.417440\pi$
$277$	−0.0780948	−	0.0209254i	−0.00469226	−	0.00125729i	−0.261164	+	0.965294i	$0.584106\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.1783	+	9.91792i	−1.02477	+	0.591654i	−0.915483	−	0.402356i	$-0.868191\pi$
$281$	−17.1783	+	9.91792i	−1.02477	+	0.591654i	−0.109291	+	0.994010i	$0.534858\pi$
$282$		0			0
$283$	15.1034	−	4.04694i	0.897803	−	0.240565i	0.219730	−	0.975561i	$-0.429482\pi$
$283$	15.1034	−	4.04694i	0.897803	−	0.240565i	0.678072	+	0.734995i	$0.262816\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.1129	+	13.1129i	0.774029	+	0.774029i
$288$		0			0
$289$			12.3429i			0.726054i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.44532	+	20.3222i	0.318119	+	1.18724i	0.921051	+	0.389443i	$0.127332\pi$
$293$	5.44532	+	20.3222i	0.318119	+	1.18724i	−0.602932	+	0.797793i	$0.706001\pi$
$294$		0			0
$295$	−14.3205	+	10.9006i	−0.833773	+	0.634656i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.74966	+	4.76256i	0.159017	+	0.275426i
$300$		0			0
$301$	−6.82683	+	11.8244i	−0.393492	+	0.681548i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.41145	+	18.8823i	0.138079	+	1.08119i
$306$		0			0
$307$	−13.6057	+	13.6057i	−0.776518	+	0.776518i	−0.979237	−	0.202719i	$-0.935022\pi$
$307$	−13.6057	+	13.6057i	−0.776518	+	0.776518i	0.202719	+	0.979237i	$0.435022\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.94616	−	3.43302i	−0.337176	−	0.194669i	0.321847	−	0.946792i	$-0.395696\pi$
$311$	−5.94616	−	3.43302i	−0.337176	−	0.194669i	−0.659022	+	0.752123i	$0.729030\pi$
$312$		0			0
$313$	−2.87818	+	10.7415i	−0.162684	+	0.607146i	0.835640	+	0.549278i	$0.185097\pi$
$313$	−2.87818	+	10.7415i	−0.162684	+	0.607146i	−0.998324	+	0.0578684i	$0.981570\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.55850	−	17.0126i	0.256031	−	0.955520i	−0.711483	−	0.702703i	$-0.751976\pi$
$317$	4.55850	−	17.0126i	0.256031	−	0.955520i	0.967514	−	0.252817i	$-0.0813571\pi$
$318$		0			0
$319$	1.33850	+	0.772785i	0.0749418	+	0.0432676i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−17.1070	+	17.1070i	−0.951857	+	0.951857i
$324$		0			0
$325$	6.04031	+	3.55011i	0.335056	+	0.196925i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	15.3763	−	26.6326i	0.847725	−	1.46830i
$330$		0			0
$331$	11.0665	+	19.1677i	0.608269	+	1.05355i	0.991526	+	0.129910i	$0.0414689\pi$
$331$	11.0665	+	19.1677i	0.608269	+	1.05355i	−0.383257	+	0.923642i	$0.625198\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.50252	+	33.2047i	−0.245999	+	1.81416i
$336$		0			0
$337$	−4.91267	−	18.3343i	−0.267610	−	0.998735i	−0.960633	−	0.277820i	$-0.910388\pi$
$337$	−4.91267	−	18.3343i	−0.267610	−	0.998735i	0.693023	−	0.720916i	$-0.256278\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	4.84427i		−	0.262332i
$342$		0			0
$343$	−12.5587	−	12.5587i	−0.678104	−	0.678104i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.854912	−	0.229073i	0.0458941	−	0.0122973i	−0.235799	−	0.971802i	$-0.575771\pi$
$347$	0.854912	−	0.229073i	0.0458941	−	0.0122973i	0.281693	+	0.959505i	$0.409104\pi$
$348$		0			0
$349$	−28.5844	+	16.5032i	−1.53009	+	0.883395i	−0.530728	+	0.847542i	$0.678082\pi$
$349$	−28.5844	+	16.5032i	−1.53009	+	0.883395i	−0.999357	+	0.0358533i	$0.988585\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.2519	−	3.55083i	−0.705326	−	0.188991i	−0.111711	−	0.993741i	$-0.535633\pi$
$353$	−13.2519	−	3.55083i	−0.705326	−	0.188991i	−0.593615	+	0.804749i	$0.702300\pi$
$354$		0			0
$355$	−9.62257	+	22.9785i	−0.510713	+	1.21957i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.11438			−0.217149			−0.108574	−	0.994088i	$-0.534629\pi$
$359$	−4.11438			−0.217149			−0.108574	+	0.994088i	$0.534629\pi$
$360$		0			0
$361$	−0.946788			−0.0498310
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.1779	−	29.7256i	−0.637422	−	1.55591i
$366$		0			0
$367$	8.89755	+	2.38409i	0.464448	+	0.124449i	0.483452	−	0.875371i	$-0.339383\pi$
$367$	8.89755	+	2.38409i	0.464448	+	0.124449i	−0.0190037	+	0.999819i	$0.506049\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	22.8172	−	13.1735i	1.18461	−	0.683935i
$372$		0			0
$373$	6.70036	−	1.79536i	0.346931	−	0.0929600i	−0.0811456	−	0.996702i	$-0.525858\pi$
$373$	6.70036	−	1.79536i	0.346931	−	0.0929600i	0.428077	+	0.903742i	$0.359191\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.73274	+	1.73274i	0.0892409	+	0.0892409i
$378$		0			0
$379$		−	28.1201i		−	1.44443i	−0.691668	−	0.722216i	$-0.743124\pi$
$379$		−	28.1201i		−	1.44443i	0.691668	−	0.722216i	$-0.256876\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.95085	+	18.4768i	0.252977	+	0.944122i	0.969205	+	0.246256i	$0.0792003\pi$
$383$	4.95085	+	18.4768i	0.252977	+	0.944122i	−0.716228	+	0.697866i	$0.754133\pi$
$384$		0			0
$385$	−5.37239	−	0.728491i	−0.273803	−	0.0371274i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.75380	−	3.03767i	−0.0889211	−	0.154016i	0.818134	−	0.575027i	$-0.195009\pi$
$389$	−1.75380	−	3.03767i	−0.0889211	−	0.154016i	−0.907055	+	0.421011i	$0.861675\pi$
$390$		0			0
$391$	10.6295	−	18.4107i	0.537554	−	0.931072i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	21.2097	−	2.70869i	1.06717	−	0.136289i
$396$		0			0
$397$	−6.39991	+	6.39991i	−0.321202	+	0.321202i	−0.849228	−	0.528026i	$-0.822932\pi$
$397$	−6.39991	+	6.39991i	−0.321202	+	0.321202i	0.528026	+	0.849228i	$0.322932\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.59094	−	2.07323i	−0.179323	−	0.103532i	0.407652	−	0.913138i	$-0.366348\pi$
$401$	−3.59094	−	2.07323i	−0.179323	−	0.103532i	−0.586975	+	0.809605i	$0.699681\pi$
$402$		0			0
$403$	1.98786	−	7.41880i	0.0990224	−	0.369557i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.42800	−	5.32937i	0.0707834	−	0.264167i
$408$		0			0
$409$	27.6500	+	15.9637i	1.36720	+	0.789356i	0.990570	−	0.137006i	$-0.0437479\pi$
$409$	27.6500	+	15.9637i	1.36720	+	0.789356i	0.376635	+	0.926362i	$0.377081\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	15.6130	−	15.6130i	0.768263	−	0.768263i
$414$		0			0
$415$	8.22764	+	6.36413i	0.403879	+	0.312403i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.0895	+	22.6717i	−0.639466	+	1.10759i	0.346085	+	0.938203i	$0.387511\pi$
$419$	−13.0895	+	22.6717i	−0.639466	+	1.10759i	−0.985550	+	0.169384i	$0.945822\pi$
$420$		0			0
$421$	−0.259922	−	0.450198i	−0.0126678	−	0.0219413i	0.859622	−	0.510931i	$-0.170699\pi$
$421$	−0.259922	−	0.450198i	−0.0126678	−	0.0219413i	−0.872290	+	0.488989i	$0.837366\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.210029	−	27.0837i	0.0101879	−	1.31375i
$426$		0			0
$427$	−6.04446	−	22.5583i	−0.292512	−	1.09167i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	19.8196i		−	0.954676i	−0.878720	−	0.477338i	$-0.841602\pi$
$431$		−	19.8196i		−	0.954676i	0.878720	−	0.477338i	$-0.158398\pi$
$432$		0			0
$433$	21.6940	+	21.6940i	1.04254	+	1.04254i	0.999054	+	0.0434911i	$0.0138480\pi$
$433$	21.6940	+	21.6940i	1.04254	+	1.04254i	0.0434911	+	0.999054i	$0.486152\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.9305	−	4.53651i	0.809895	−	0.217011i
$438$		0			0
$439$	11.8104	−	6.81876i	0.563682	−	0.325442i	−0.190940	−	0.981602i	$-0.561154\pi$
$439$	11.8104	−	6.81876i	0.563682	−	0.325442i	0.754622	+	0.656160i	$0.227820\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.60316	+	1.76931i	0.313726	+	0.0840626i	0.412246	−	0.911072i	$-0.364744\pi$
$443$	6.60316	+	1.76931i	0.313726	+	0.0840626i	−0.0985205	+	0.995135i	$0.531411\pi$
$444$		0			0
$445$	−23.3683	−	9.78579i	−1.10776	−	0.463891i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.2468			−1.33305			−0.666525	−	0.745482i	$-0.732219\pi$
$449$	−28.2468			−1.33305			−0.666525	+	0.745482i	$0.732219\pi$
$450$		0			0
$451$	5.97439			0.281323
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.92865	−	3.32023i	−0.371701	−	0.155655i
$456$		0			0
$457$	−21.7176	−	5.81920i	−1.01590	−	0.272211i	−0.287810	−	0.957687i	$-0.592927\pi$
$457$	−21.7176	−	5.81920i	−1.01590	−	0.272211i	−0.728095	+	0.685477i	$0.759594\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	23.2134	−	13.4023i	1.08116	−	0.624206i	0.149948	−	0.988694i	$-0.452089\pi$
$461$	23.2134	−	13.4023i	1.08116	−	0.624206i	0.931208	+	0.364488i	$0.118756\pi$
$462$		0			0
$463$	25.7031	−	6.88713i	1.19452	−	0.320072i	0.393852	−	0.919174i	$-0.371142\pi$
$463$	25.7031	−	6.88713i	1.19452	−	0.320072i	0.800673	+	0.599102i	$0.204476\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.918499	−	0.918499i	−0.0425031	−	0.0425031i	0.685536	−	0.728039i	$-0.259568\pi$
$467$	−0.918499	−	0.918499i	−0.0425031	−	0.0425031i	−0.728039	+	0.685536i	$0.759568\pi$
$468$		0			0
$469$		−	41.1103i		−	1.89830i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.13848	+	4.24886i	0.0523473	+	0.195363i
$474$		0			0
$475$	15.9123	−	15.6674i	0.730107	−	0.718870i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.07290	−	1.85832i	−0.0490222	−	0.0849089i	0.840473	−	0.541853i	$-0.182277\pi$
$479$	−1.07290	−	1.85832i	−0.0490222	−	0.0849089i	−0.889495	+	0.456944i	$0.848944\pi$
$480$		0			0
$481$	4.37384	−	7.57572i	0.199430	−	0.345423i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.2388	−	15.6548i	−0.918996	−	0.710849i
$486$		0			0
$487$	17.2421	−	17.2421i	0.781316	−	0.781316i	−0.198737	−	0.980053i	$-0.563684\pi$
$487$	17.2421	−	17.2421i	0.781316	−	0.781316i	0.980053	+	0.198737i	$0.0636839\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.57448	−	4.95048i	−0.386961	−	0.223412i	0.293882	−	0.955842i	$-0.405053\pi$
$491$	−8.57448	−	4.95048i	−0.386961	−	0.223412i	−0.680843	+	0.732430i	$0.738386\pi$
$492$		0			0
$493$	2.45175	−	9.15007i	0.110421	−	0.412098i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.91041	−	29.5221i	0.354830	−	1.32425i
$498$		0			0
$499$	7.91417	+	4.56925i	0.354287	+	0.204548i	0.666572	−	0.745441i	$-0.267761\pi$
$499$	7.91417	+	4.56925i	0.354287	+	0.204548i	−0.312285	+	0.949989i	$0.601094\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.7908	+	10.7908i	−0.481138	+	0.481138i	−0.905495	−	0.424357i	$-0.860500\pi$
$503$	−10.7908	+	10.7908i	−0.481138	+	0.481138i	0.424357	+	0.905495i	$0.360500\pi$
$504$		0			0
$505$	29.0149	−	3.70549i	1.29115	−	0.164892i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.74497	+	9.95058i	−0.254641	+	0.441052i	−0.964798	−	0.262992i	$-0.915291\pi$
$509$	−5.74497	+	9.95058i	−0.254641	+	0.441052i	0.710157	+	0.704044i	$0.248624\pi$
$510$		0			0
$511$	19.7054	+	34.1308i	0.871718	+	1.50986i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.9875	+	1.62549i	0.528232	+	0.0716277i
$516$		0			0
$517$	−2.56424	−	9.56988i	−0.112775	−	0.420883i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	9.40066i		−	0.411850i	−0.978568	−	0.205925i	$-0.933980\pi$
$521$		−	9.40066i		−	0.411850i	0.978568	−	0.205925i	$-0.0660203\pi$
$522$		0			0
$523$	1.46556	+	1.46556i	0.0640843	+	0.0640843i	0.738423	−	0.674338i	$-0.235571\pi$
$523$	1.46556	+	1.46556i	0.0640843	+	0.0640843i	−0.674338	+	0.738423i	$0.735571\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−28.6790	+	7.68452i	−1.24928	+	0.334743i
$528$		0			0
$529$	6.58002	−	3.79898i	0.286088	−	0.165173i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.14951	+	2.45160i	0.396309	+	0.106191i
$534$		0			0
$535$	−6.29598	−	15.3681i	−0.272199	−	0.664422i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.464810			0.0200208
$540$		0			0
$541$	−7.78309			−0.334621			−0.167311	−	0.985904i	$-0.553508\pi$
$541$	−7.78309			−0.334621			−0.167311	+	0.985904i	$0.553508\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.87555	+	21.1947i	−0.380187	+	0.907880i
$546$		0			0
$547$	34.6694	+	9.28964i	1.48236	+	0.397196i	0.907148	−	0.420811i	$-0.138254\pi$
$547$	34.6694	+	9.28964i	1.48236	+	0.397196i	0.575208	+	0.818007i	$0.304921\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.76388	−	3.90513i	0.288151	−	0.166364i
$552$		0			0
$553$	−25.3388	+	6.78950i	−1.07751	+	0.288719i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.17130	−	6.17130i	−0.261486	−	0.261486i	0.564171	−	0.825658i	$-0.309196\pi$
$557$	−6.17130	−	6.17130i	−0.261486	−	0.261486i	−0.825658	+	0.564171i	$0.809196\pi$
$558$		0			0
$559$			6.97413i			0.294974i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.65058	−	36.0164i	−0.406723	−	1.51791i	−0.800855	−	0.598858i	$-0.795621\pi$
$563$	−9.65058	−	36.0164i	−0.406723	−	1.51791i	0.394132	−	0.919054i	$-0.371045\pi$
$564$		0			0
$565$	5.17993	−	38.2004i	0.217921	−	1.60710i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.78087	+	15.2089i	0.368113	+	0.637591i	0.989271	−	0.146095i	$-0.0466706\pi$
$569$	8.78087	+	15.2089i	0.368113	+	0.637591i	−0.621157	+	0.783686i	$0.713337\pi$
$570$		0			0
$571$	−3.87707	+	6.71529i	−0.162250	+	0.281026i	−0.935675	−	0.352862i	$-0.885209\pi$
$571$	−3.87707	+	6.71529i	−0.162250	+	0.281026i	0.773425	+	0.633888i	$0.218542\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.94284	+	16.9172i	−0.414645	+	0.705495i
$576$		0			0
$577$	21.1946	−	21.1946i	0.882344	−	0.882344i	−0.111428	−	0.993772i	$-0.535542\pi$
$577$	21.1946	−	21.1946i	0.882344	−	0.882344i	0.993772	+	0.111428i	$0.0355425\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11.0518	−	6.38073i	−0.458504	−	0.264717i
$582$		0			0
$583$	2.19689	−	8.19890i	0.0909858	−	0.339564i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.98989	−	7.42638i	0.0821317	−	0.306520i	−0.912624	−	0.408800i	$-0.865947\pi$
$587$	1.98989	−	7.42638i	0.0821317	−	0.306520i	0.994756	+	0.102281i	$0.0326139\pi$
$588$		0			0
$589$	−21.2000	−	12.2398i	−0.873532	−	0.504334i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.97136	+	2.97136i	−0.122019	+	0.122019i	−0.765479	−	0.643460i	$-0.777498\pi$
$593$	−2.97136	+	2.97136i	−0.122019	+	0.122019i	0.643460	+	0.765479i	$0.277498\pi$
$594$		0			0
$595$	4.20948	+	32.9612i	0.172572	+	1.35128i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.40103	−	9.35485i	0.220680	−	0.382229i	−0.734335	−	0.678788i	$-0.762506\pi$
$599$	5.40103	−	9.35485i	0.220680	−	0.382229i	0.955015	+	0.296559i	$0.0958390\pi$
$600$		0			0
$601$	13.2730	+	22.9895i	0.541418	+	0.937763i	0.998823	+	0.0485045i	$0.0154455\pi$
$601$	13.2730	+	22.9895i	0.541418	+	0.937763i	−0.457405	+	0.889258i	$0.651221\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	18.1820	−	13.8399i	0.739204	−	0.562671i
$606$		0			0
$607$	8.19313	+	30.5772i	0.332549	+	1.24109i	0.906502	+	0.422201i	$0.138742\pi$
$607$	8.19313	+	30.5772i	0.332549	+	1.24109i	−0.573953	+	0.818888i	$0.694591\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	15.7081i		−	0.635482i
$612$		0			0
$613$	15.6780	+	15.6780i	0.633228	+	0.633228i	0.948876	−	0.315648i	$-0.102222\pi$
$613$	15.6780	+	15.6780i	0.633228	+	0.633228i	−0.315648	+	0.948876i	$0.602222\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.01563	−	1.61188i	0.242180	−	0.0648920i	−0.135687	−	0.990752i	$-0.543324\pi$
$617$	6.01563	−	1.61188i	0.242180	−	0.0648920i	0.377867	+	0.925860i	$0.376658\pi$
$618$		0			0
$619$	−12.1759	+	7.02976i	−0.489391	+	0.282550i	−0.724322	−	0.689462i	$-0.757847\pi$
$619$	−12.1759	+	7.02976i	−0.489391	+	0.282550i	0.234931	+	0.972012i	$0.424514\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	30.0228	+	8.04459i	1.20284	+	0.322300i
$624$		0			0
$625$	−0.387717	+	24.9970i	−0.0155087	+	0.999880i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−33.8162			−1.34834
$630$		0			0
$631$	33.2378			1.32318			0.661589	−	0.749867i	$-0.269882\pi$
$631$	33.2378			1.32318			0.661589	+	0.749867i	$0.269882\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	31.1964	−	12.7805i	1.23799	−	0.507178i
$636$		0			0
$637$	0.711836	+	0.190736i	0.0282040	+	0.00755723i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.3490	+	7.12970i	−0.487756	+	0.281606i	−0.723643	−	0.690174i	$-0.757534\pi$
$641$	−12.3490	+	7.12970i	−0.487756	+	0.281606i	0.235887	+	0.971780i	$0.424200\pi$
$642$		0			0
$643$	−35.0630	+	9.39510i	−1.38275	+	0.370507i	−0.872119	−	0.489293i	$-0.837255\pi$
$643$	−35.0630	+	9.39510i	−1.38275	+	0.370507i	−0.510631	+	0.859800i	$0.670588\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.6172	+	11.6172i	0.456718	+	0.456718i	0.897577	−	0.440858i	$-0.145326\pi$
$647$	11.6172	+	11.6172i	0.456718	+	0.456718i	−0.440858	+	0.897577i	$0.645326\pi$
$648$		0			0
$649$		−	7.11345i		−	0.279227i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.43066	−	31.4636i	−0.329917	−	1.23127i	−0.909276	−	0.416194i	$-0.863364\pi$
$653$	−8.43066	−	31.4636i	−0.329917	−	1.23127i	0.579359	−	0.815073i	$-0.303303\pi$
$654$		0			0
$655$	−1.16337	−	1.52837i	−0.0454566	−	0.0597182i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.2138	−	24.6190i	−0.553691	−	0.959021i	−0.998004	−	0.0631491i	$-0.979886\pi$
$659$	−14.2138	−	24.6190i	−0.553691	−	0.959021i	0.444313	−	0.895871i	$-0.353448\pi$
$660$		0			0
$661$	1.00541	−	1.74143i	0.0391060	−	0.0677336i	−0.845810	−	0.533484i	$-0.820882\pi$
$661$	1.00541	−	1.74143i	0.0391060	−	0.0677336i	0.884916	+	0.465751i	$0.154216\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−16.7623	+	21.6706i	−0.650015	+	0.840349i
$666$		0			0
$667$	−4.85292	+	4.85292i	−0.187906	+	0.187906i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.51587	−	3.76194i	−0.251542	−	0.145228i
$672$		0			0
$673$	−5.36532	+	20.0237i	−0.206818	+	0.771855i	0.782070	+	0.623191i	$0.214164\pi$
$673$	−5.36532	+	20.0237i	−0.206818	+	0.771855i	−0.988888	+	0.148664i	$0.952503\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.55998	+	13.2860i	−0.136821	+	0.510623i	0.863163	+	0.504926i	$0.168480\pi$
$677$	−3.55998	+	13.2860i	−0.136821	+	0.510623i	−0.999984	+	0.00569716i	$0.998187\pi$
$678$		0			0
$679$	27.1857	+	15.6957i	1.04329	+	0.602345i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.6518	+	17.6518i	−0.675426	+	0.675426i	−0.958962	−	0.283536i	$-0.908492\pi$
$683$	−17.6518	+	17.6518i	−0.675426	+	0.675426i	0.283536	+	0.958962i	$0.408492\pi$
$684$		0			0
$685$	19.6009	−	25.3404i	0.748913	−	0.968206i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.72888	−	11.6548i	0.256350	−	0.444011i
$690$		0			0
$691$	−5.36784	−	9.29738i	−0.204202	−	0.353689i	0.745676	−	0.666309i	$-0.232127\pi$
$691$	−5.36784	−	9.29738i	−0.204202	−	0.353689i	−0.949878	+	0.312620i	$0.898793\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.0656	+	19.7923i	0.571472	+	0.750767i
$696$		0			0
$697$	−9.47723	−	35.3695i	−0.358976	−	1.33972i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			38.4271i			1.45137i	0.688026	+	0.725686i	$0.258478\pi$
$701$			38.4271i			1.45137i	−0.688026	+	0.725686i	$0.741522\pi$
$702$		0			0
$703$	−19.7149	−	19.7149i	−0.743561	−	0.743561i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−34.6635	+	9.28805i	−1.30365	+	0.349313i
$708$		0			0
$709$	3.01213	−	1.73906i	0.113123	−	0.0653116i	−0.442371	−	0.896832i	$-0.645863\pi$
$709$	3.01213	−	1.73906i	0.113123	−	0.0653116i	0.555494	+	0.831521i	$0.312529\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	20.7779	+	5.56743i	0.778139	+	0.208502i
$714$		0			0
$715$	−2.56256	+	1.04983i	−0.0958343	+	0.0392612i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	19.6808			0.733970			0.366985	−	0.930227i	$-0.380390\pi$
$719$	19.6808			0.733970			0.366985	+	0.930227i	$0.380390\pi$
$720$		0			0
$721$	−14.8416			−0.552728
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.32848	+	8.42804i	−0.0864776	+	0.313009i
$726$		0			0
$727$	−20.1645	−	5.40306i	−0.747860	−	0.200388i	−0.135291	−	0.990806i	$-0.543197\pi$
$727$	−20.1645	−	5.40306i	−0.747860	−	0.200388i	−0.612569	+	0.790417i	$0.709864\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.3481	−	13.4800i	0.863561	−	0.498577i
$732$		0			0
$733$	11.2977	−	3.02722i	0.417291	−	0.111813i	−0.0440635	−	0.999029i	$-0.514030\pi$
$733$	11.2977	−	3.02722i	0.417291	−	0.111813i	0.461354	+	0.887216i	$0.347364\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.36516	−	9.36516i	−0.344970	−	0.344970i
$738$		0			0
$739$			3.09434i			0.113827i	0.998379	+	0.0569136i	$0.0181259\pi$
$739$			3.09434i			0.113827i	−0.998379	+	0.0569136i	$0.981874\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.79197	−	17.8839i	−0.175800	−	0.656096i	−0.996414	−	0.0846124i	$-0.973035\pi$
$743$	−4.79197	−	17.8839i	−0.175800	−	0.656096i	0.820614	−	0.571483i	$-0.193632\pi$
$744$		0			0
$745$	2.59383	−	1.97438i	0.0950305	−	0.0723358i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.1877	+	17.6456i	0.372251	+	0.644757i
$750$		0			0
$751$	27.1986	−	47.1093i	0.992490	−	1.71904i	0.390310	−	0.920684i	$-0.372368\pi$
$751$	27.1986	−	47.1093i	0.992490	−	1.71904i	0.602181	−	0.798360i	$-0.294299\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.25517	−	25.4888i	−0.118468	−	0.927632i
$756$		0			0
$757$	−23.8602	+	23.8602i	−0.867215	+	0.867215i	−0.992163	−	0.124949i	$-0.960123\pi$
$757$	−23.8602	+	23.8602i	−0.867215	+	0.867215i	0.124949	+	0.992163i	$0.460123\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.20716	−	4.73841i	−0.297509	−	0.171767i	0.343814	−	0.939038i	$-0.388281\pi$
$761$	−8.20716	−	4.73841i	−0.297509	−	0.171767i	−0.641323	+	0.767271i	$0.721614\pi$
$762$		0			0
$763$	7.29631	−	27.2302i	0.264144	−	0.985800i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.91902	−	10.8939i	0.105400	−	0.393357i
$768$		0			0
$769$	13.0491	+	7.53390i	0.470562	+	0.271679i	0.716475	−	0.697613i	$-0.245754\pi$
$769$	13.0491	+	7.53390i	0.470562	+	0.271679i	−0.245913	+	0.969292i	$0.579088\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	29.1782	−	29.1782i	1.04947	−	1.04947i	0.0507568	−	0.998711i	$-0.483837\pi$
$773$	29.1782	−	29.1782i	1.04947	−	1.04947i	0.998711	−	0.0507568i	$-0.0161633\pi$
$774$		0			0
$775$	26.5260	−	6.88760i	0.952841	−	0.247410i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15.0952	−	26.1457i	0.540843	−	0.936768i
$780$		0			0
$781$	−4.92326	−	8.52734i	−0.176168	−	0.305132i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.30429	−	9.61872i	0.0465521	−	0.343307i
$786$		0			0
$787$	7.77504	+	29.0169i	0.277150	+	1.03434i	0.954387	+	0.298574i	$0.0965108\pi$
$787$	7.77504	+	29.0169i	0.277150	+	1.03434i	−0.677236	+	0.735766i	$0.736823\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			47.2954i			1.68163i
$792$		0			0
$793$	−8.43505	−	8.43505i	−0.299537	−	0.299537i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.09921	−	1.90223i	0.251467	−	0.0673804i	−0.130883	−	0.991398i	$-0.541781\pi$
$797$	7.09921	−	1.90223i	0.251467	−	0.0673804i	0.382350	+	0.924017i	$0.375115\pi$
$798$		0			0
$799$	−52.5878	+	30.3616i	−1.86042	+	1.07412i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.2642	+	3.28619i	0.432795	+	0.115967i
$804$		0			0
$805$	9.29901	−	22.2059i	0.327747	−	0.782654i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.95255			0.349913			0.174957	−	0.984576i	$-0.444021\pi$
$809$	9.95255			0.349913			0.174957	+	0.984576i	$0.444021\pi$
$810$		0			0
$811$	−17.0435			−0.598480			−0.299240	−	0.954178i	$-0.596733\pi$
$811$	−17.0435			−0.598480			−0.299240	+	0.954178i	$0.596733\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.9411	−	31.5884i	−0.453307	−	1.10649i
$816$		0			0
$817$	21.4709	+	5.75310i	0.751171	+	0.201276i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.0949	−	11.6018i	0.701317	−	0.404905i	−0.106521	−	0.994310i	$-0.533971\pi$
$821$	20.0949	−	11.6018i	0.701317	−	0.404905i	0.807838	+	0.589405i	$0.200638\pi$
$822$		0			0
$823$	−36.7186	+	9.83871i	−1.27993	+	0.342956i	−0.833827	−	0.552026i	$-0.813855\pi$
$823$	−36.7186	+	9.83871i	−1.27993	+	0.342956i	−0.446102	+	0.894982i	$0.647188\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.71693	+	5.71693i	0.198797	+	0.198797i	0.799484	−	0.600687i	$-0.205106\pi$
$827$	5.71693	+	5.71693i	0.198797	+	0.198797i	−0.600687	+	0.799484i	$0.705106\pi$
$828$		0			0
$829$			44.6644i			1.55126i	0.631189	+	0.775629i	$0.282567\pi$
$829$			44.6644i			1.55126i	−0.631189	+	0.775629i	$0.717433\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.737333	−	2.75176i	−0.0255471	−	0.0953430i
$834$		0			0
$835$	−39.9065	−	5.41128i	−1.38102	−	0.187265i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.5225	−	18.2255i	−0.363277	−	0.629215i	0.625221	−	0.780448i	$-0.285009\pi$
$839$	−10.5225	−	18.2255i	−0.363277	−	0.629215i	−0.988498	+	0.151233i	$0.951676\pi$
$840$		0			0
$841$	12.9709	−	22.4663i	0.447273	−	0.774700i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.4794	−	3.12627i	0.842118	−	0.107547i
$846$		0			0
$847$	−19.8229	+	19.8229i	−0.681124	+	0.681124i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	21.2174	+	12.2499i	0.727323	+	0.419920i
$852$		0			0
$853$	1.07750	−	4.02129i	0.0368929	−	0.137686i	−0.945023	−	0.327004i	$-0.893961\pi$
$853$	1.07750	−	4.02129i	0.0368929	−	0.137686i	0.981916	+	0.189318i	$0.0606276\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.32222	+	8.66663i	−0.0793254	+	0.296047i	−0.994179	−	0.107739i	$-0.965639\pi$
$857$	−2.32222	+	8.66663i	−0.0793254	+	0.296047i	0.914854	+	0.403785i	$0.132306\pi$
$858$		0			0
$859$	−29.3253	−	16.9310i	−1.00057	−	0.577677i	−0.0921499	−	0.995745i	$-0.529374\pi$
$859$	−29.3253	−	16.9310i	−1.00057	−	0.577677i	−0.908416	+	0.418068i	$0.862707\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−23.6082	+	23.6082i	−0.803631	+	0.803631i	−0.983661	−	0.180030i	$-0.942380\pi$
$863$	−23.6082	+	23.6082i	−0.803631	+	0.803631i	0.180030	+	0.983661i	$0.442380\pi$
$864$		0			0
$865$	−23.4471	−	18.1364i	−0.797224	−	0.616657i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.22563	+	7.31901i	−0.143345	+	0.248280i
$870$		0			0
$871$	−10.4993	−	18.1853i	−0.355756	−	0.616187i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.64945	−	30.4536i	−0.123374	−	1.02952i
$876$		0			0
$877$	10.4930	+	39.1603i	0.354322	+	1.32235i	0.881335	+	0.472491i	$0.156645\pi$
$877$	10.4930	+	39.1603i	0.354322	+	1.32235i	−0.527013	+	0.849857i	$0.676688\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			55.0463i			1.85456i	0.374373	+	0.927278i	$0.377858\pi$
$881$			55.0463i			1.85456i	−0.374373	+	0.927278i	$0.622142\pi$
$882$		0			0
$883$	24.7855	+	24.7855i	0.834098	+	0.834098i	0.988075	−	0.153976i	$-0.0492080\pi$
$883$	24.7855	+	24.7855i	0.834098	+	0.834098i	−0.153976	+	0.988075i	$0.549208\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.54754	+	1.21851i	−0.152692	+	0.0409136i	−0.334355	−	0.942447i	$-0.608518\pi$
$887$	−4.54754	+	1.21851i	−0.152692	+	0.0409136i	0.181664	+	0.983361i	$0.441852\pi$
$888$		0			0
$889$	−35.8196	+	20.6805i	−1.20135	+	0.693601i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−48.3597	−	12.9579i	−1.61829	−	0.433621i
$894$		0			0
$895$	7.80132	+	3.26691i	0.260769	+	0.109201i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.58513			0.319682
$900$		0			0
$901$	−52.0240			−1.73317
$902$		0			0
$903$		0			0
$904$		0			0
$905$	47.4527	+	19.8715i	1.57738	+	0.660550i
$906$		0			0
$907$	37.0766	+	9.93464i	1.23111	+	0.329874i	0.815011	−	0.579446i	$-0.196731\pi$
$907$	37.0766	+	9.93464i	1.23111	+	0.329874i	0.416097	+	0.909320i	$0.363398\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−19.6058	+	11.3194i	−0.649570	+	0.375029i	−0.788291	−	0.615302i	$-0.789034\pi$
$911$	−19.6058	+	11.3194i	−0.649570	+	0.375029i	0.138721	+	0.990331i	$0.455701\pi$
$912$		0			0
$913$	−3.97122	+	1.06409i	−0.131428	+	0.0352161i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.66630	+	1.66630i	0.0550261	+	0.0550261i
$918$		0			0
$919$		−	34.4135i		−	1.13520i	−0.823306	−	0.567598i	$-0.807873\pi$
$919$		−	34.4135i		−	1.13520i	0.823306	−	0.567598i	$-0.192127\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.04055	−	15.0795i	−0.132996	−	0.496348i
$924$		0			0
$925$	31.2126	+	0.242048i	1.02626	+	0.00795848i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	29.2552	+	50.6715i	0.959832	+	1.66248i	0.722901	+	0.690951i	$0.242808\pi$
$929$	29.2552	+	50.6715i	0.959832	+	1.66248i	0.236931	+	0.971527i	$0.423859\pi$
$930$		0			0
$931$	1.17442	−	2.03415i	0.0384899	−	0.0666665i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.46770	+	6.54982i	0.276923	+	0.214202i
$936$		0			0
$937$	−33.6817	+	33.6817i	−1.10033	+	1.10033i	−0.105963	+	0.994370i	$0.533793\pi$
$937$	−33.6817	+	33.6817i	−1.10033	+	1.10033i	−0.994370	+	0.105963i	$0.966207\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.64011	−	2.67897i	−0.151263	−	0.0873320i	0.422458	−	0.906383i	$-0.361167\pi$
$941$	−4.64011	−	2.67897i	−0.151263	−	0.0873320i	−0.573721	+	0.819051i	$0.694501\pi$
$942$		0			0
$943$	−6.86624	+	25.6252i	−0.223596	+	0.834470i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.28954	+	30.9370i	−0.269374	+	1.00532i	0.690145	+	0.723671i	$0.257547\pi$
$947$	−8.28954	+	30.9370i	−0.269374	+	1.00532i	−0.959519	+	0.281646i	$0.909120\pi$
$948$		0			0
$949$	17.4336	+	10.0653i	0.565920	+	0.326734i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	31.7285	−	31.7285i	1.02779	−	1.02779i	0.0281830	−	0.999603i	$-0.491028\pi$
$953$	31.7285	−	31.7285i	1.02779	−	1.02779i	0.999603	−	0.0281830i	$-0.00897210\pi$
$954$		0			0
$955$	24.3745	−	3.11287i	0.788741	−	0.100730i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.6521	+	34.0384i	−0.634599	+	1.09916i
$960$		0			0
$961$	0.478676	+	0.829091i	0.0154412	+	0.0267449i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−24.2372	−	3.28655i	−0.780224	−	0.105798i
$966$		0			0
$967$	−6.48992	−	24.2207i	−0.208702	−	0.778886i	−0.988289	−	0.152592i	$-0.951238\pi$
$967$	−6.48992	−	24.2207i	−0.208702	−	0.778886i	0.779587	−	0.626293i	$-0.215429\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			19.3757i			0.621794i	0.950444	+	0.310897i	$0.100629\pi$
$971$			19.3757i			0.621794i	−0.950444	+	0.310897i	$0.899371\pi$
$972$		0			0
$973$	−21.5786	−	21.5786i	−0.691778	−	0.691778i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−47.6816	+	12.7763i	−1.52547	+	0.408749i	−0.921538	−	0.388287i	$-0.873067\pi$
$977$	−47.6816	+	12.7763i	−1.52547	+	0.408749i	−0.603932	+	0.797036i	$0.706400\pi$
$978$		0			0
$979$	8.67198	−	5.00677i	0.277158	−	0.160017i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.0191	−	2.95256i	−0.351454	−	0.0941719i	0.0787728	−	0.996893i	$-0.474900\pi$
$983$	−11.0191	−	2.95256i	−0.351454	−	0.0941719i	−0.430227	+	0.902721i	$0.641567\pi$
$984$		0			0
$985$	5.39120	+	13.1596i	0.171778	+	0.419300i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.5325			−0.621099
$990$		0			0
$991$	−25.4006			−0.806876			−0.403438	−	0.915007i	$-0.632185\pi$
$991$	−25.4006			−0.806876			−0.403438	+	0.915007i	$0.632185\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.4072	+	29.6282i	−0.393334	+	0.939276i
$996$		0			0
$997$	24.6160	+	6.59585i	0.779598	+	0.208893i	0.626607	−	0.779335i	$-0.284443\pi$
$997$	24.6160	+	6.59585i	0.779598	+	0.208893i	0.152990	+	0.988228i	$0.451110\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.bt.a.233.3		72
3.2	odd	2		360.2.bs.a.113.7	✓	72
5.2	odd	4	inner	1080.2.bt.a.17.4		72
9.2	odd	6	inner	1080.2.bt.a.953.4		72
9.7	even	3		360.2.bs.a.353.4	yes	72
12.11	even	2		720.2.cu.e.113.12		72
15.2	even	4		360.2.bs.a.257.4	yes	72
36.7	odd	6		720.2.cu.e.353.15		72
45.2	even	12	inner	1080.2.bt.a.737.3		72
45.7	odd	12		360.2.bs.a.137.7	yes	72
60.47	odd	4		720.2.cu.e.257.15		72
180.7	even	12		720.2.cu.e.497.12		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.7	✓	72	3.2	odd	2
360.2.bs.a.137.7	yes	72	45.7	odd	12
360.2.bs.a.257.4	yes	72	15.2	even	4
360.2.bs.a.353.4	yes	72	9.7	even	3
720.2.cu.e.113.12		72	12.11	even	2
720.2.cu.e.257.15		72	60.47	odd	4
720.2.cu.e.353.15		72	36.7	odd	6
720.2.cu.e.497.12		72	180.7	even	12
1080.2.bt.a.17.4		72	5.2	odd	4	inner
1080.2.bt.a.233.3		72	1.1	even	1	trivial
1080.2.bt.a.737.3		72	45.2	even	12	inner
1080.2.bt.a.953.4		72	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.bt (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.06252 - 0.863710i) q^{5} +(2.64986 + 0.710029i) q^{7} +O(q^{10})\)	\(q+(-2.06252 - 0.863710i) q^{5} +(2.64986 + 0.710029i) q^{7} +(0.765403 - 0.441906i) q^{11} +(1.35352 - 0.362674i) q^{13} +(-3.83033 - 3.83033i) q^{17} -4.46618i q^{19} +(1.01575 + 3.79082i) q^{23} +(3.50801 + 3.56284i) q^{25} +(0.874378 + 1.51447i) q^{29} +(2.74056 - 4.74679i) q^{31} +(-4.85215 - 3.75316i) q^{35} +(4.41426 - 4.41426i) q^{37} +(5.85416 + 3.37990i) q^{41} +(-1.28815 + 4.80743i) q^{43} +(2.90134 - 10.8280i) q^{47} +(0.455456 + 0.262958i) q^{49} +(6.79105 - 6.79105i) q^{53} +(-1.96034 + 0.250355i) q^{55} +(4.02430 - 6.97029i) q^{59} +(-4.25649 - 7.37246i) q^{61} +(-3.10491 - 0.421023i) q^{65} +(-3.87853 - 14.4749i) q^{67} -11.1410i q^{71} +(10.1583 + 10.1583i) q^{73} +(2.34198 - 0.627531i) q^{77} +(-8.28119 + 4.78115i) q^{79} +(-4.49329 - 1.20397i) q^{83} +(4.59186 + 11.2085i) q^{85} +11.3300 q^{89} +3.84415 q^{91} +(-3.85749 + 9.21161i) q^{95} +(11.0528 + 2.96160i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q - 24 q^{23} - 12 q^{41} + 36 q^{47} + 12 q^{61} + 72 q^{65} + 48 q^{77} + 60 q^{83} + 24 q^{85} + 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q - 24 * q^23 - 12 * q^41 + 36 * q^47 + 12 * q^61 + 72 * q^65 + 48 * q^77 + 60 * q^83 + 24 * q^85 + 60 * q^95 + 24 * q^97

Introduction

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