LMFDB - Embedded newform 320.3.r.a.111.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (of order $4$, degree $2$, 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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.6
Character	$\chi$	$=$	320.111
Dual form			320.3.r.a.271.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91324 + 1.91324i) q^{3} +(-1.58114 + 1.58114i) q^{5} -1.82022 q^{7} +1.67900i q^{9} +O(q^{10})$	\(q+(-1.91324 + 1.91324i) q^{3} +(-1.58114 + 1.58114i) q^{5} -1.82022 q^{7} +1.67900i q^{9} +(-8.81874 - 8.81874i) q^{11} +(-6.87697 - 6.87697i) q^{13} -6.05021i q^{15} +18.7800 q^{17} +(3.65220 - 3.65220i) q^{19} +(3.48251 - 3.48251i) q^{21} +3.89907 q^{23} -5.00000i q^{25} +(-20.4315 - 20.4315i) q^{27} +(-28.8574 - 28.8574i) q^{29} -58.4285i q^{31} +33.7448 q^{33} +(2.87801 - 2.87801i) q^{35} +(-18.6187 + 18.6187i) q^{37} +26.3146 q^{39} -39.0372i q^{41} +(21.4550 + 21.4550i) q^{43} +(-2.65474 - 2.65474i) q^{45} -1.17993i q^{47} -45.6868 q^{49} +(-35.9307 + 35.9307i) q^{51} +(36.9128 - 36.9128i) q^{53} +27.8873 q^{55} +13.9751i q^{57} +(64.8124 + 64.8124i) q^{59} +(-81.7334 - 81.7334i) q^{61} -3.05615i q^{63} +21.7469 q^{65} +(-49.8013 + 49.8013i) q^{67} +(-7.45987 + 7.45987i) q^{69} -67.8785 q^{71} +94.5184i q^{73} +(9.56621 + 9.56621i) q^{75} +(16.0520 + 16.0520i) q^{77} -55.2351i q^{79} +63.0699 q^{81} +(-51.2318 + 51.2318i) q^{83} +(-29.6938 + 29.6938i) q^{85} +110.423 q^{87} +114.419i q^{89} +(12.5176 + 12.5176i) q^{91} +(111.788 + 111.788i) q^{93} +11.5493i q^{95} -66.1629 q^{97} +(14.8067 - 14.8067i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.91324	+	1.91324i	−0.637748	+	0.637748i	−0.949999	−	0.312252i	$-0.898917\pi$
$3$	−1.91324	+	1.91324i	−0.637748	+	0.637748i	0.312252	+	0.949999i	$0.398917\pi$
$4$		0			0
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$6$		0			0
$7$	−1.82022			−0.260031			−0.130015	−	0.991512i	$-0.541503\pi$
$7$	−1.82022			−0.260031			−0.130015	+	0.991512i	$0.541503\pi$
$8$		0			0
$9$			1.67900i			0.186556i
$10$		0			0
$11$	−8.81874	−	8.81874i	−0.801704	−	0.801704i	0.181658	−	0.983362i	$-0.441854\pi$
$11$	−8.81874	−	8.81874i	−0.801704	−	0.801704i	−0.983362	+	0.181658i	$0.941854\pi$
$12$		0			0
$13$	−6.87697	−	6.87697i	−0.528998	−	0.528998i	0.391276	−	0.920273i	$-0.372034\pi$
$13$	−6.87697	−	6.87697i	−0.528998	−	0.528998i	−0.920273	+	0.391276i	$0.872034\pi$
$14$		0			0
$15$		−	6.05021i		−	0.403347i
$16$		0			0
$17$	18.7800			1.10471			0.552353	−	0.833610i	$-0.313730\pi$
$17$	18.7800			1.10471			0.552353	+	0.833610i	$0.313730\pi$
$18$		0			0
$19$	3.65220	−	3.65220i	0.192221	−	0.192221i	−0.604434	−	0.796655i	$-0.706601\pi$
$19$	3.65220	−	3.65220i	0.192221	−	0.192221i	0.796655	+	0.604434i	$0.206601\pi$
$20$		0			0
$21$	3.48251	−	3.48251i	0.165834	−	0.165834i
$22$		0			0
$23$	3.89907			0.169525			0.0847624	−	0.996401i	$-0.472987\pi$
$23$	3.89907			0.169525			0.0847624	+	0.996401i	$0.472987\pi$
$24$		0			0
$25$		−	5.00000i		−	0.200000i
$26$		0			0
$27$	−20.4315	−	20.4315i	−0.756723	−	0.756723i
$28$		0			0
$29$	−28.8574	−	28.8574i	−0.995084	−	0.995084i	0.00490387	−	0.999988i	$-0.498439\pi$
$29$	−28.8574	−	28.8574i	−0.995084	−	0.995084i	−0.999988	+	0.00490387i	$0.998439\pi$
$30$		0			0
$31$		−	58.4285i		−	1.88479i	−0.334503	−	0.942395i	$-0.608568\pi$
$31$		−	58.4285i		−	1.88479i	0.334503	−	0.942395i	$-0.391432\pi$
$32$		0			0
$33$	33.7448			1.02257
$34$		0			0
$35$	2.87801	−	2.87801i	0.0822290	−	0.0822290i
$36$		0			0
$37$	−18.6187	+	18.6187i	−0.503208	+	0.503208i	−0.912433	−	0.409226i	$-0.865799\pi$
$37$	−18.6187	+	18.6187i	−0.503208	+	0.503208i	0.409226	+	0.912433i	$0.365799\pi$
$38$		0			0
$39$	26.3146			0.674734
$40$		0			0
$41$		−	39.0372i		−	0.952127i	−0.879411	−	0.476063i	$-0.842063\pi$
$41$		−	39.0372i		−	0.952127i	0.879411	−	0.476063i	$-0.157937\pi$
$42$		0			0
$43$	21.4550	+	21.4550i	0.498955	+	0.498955i	0.911112	−	0.412158i	$-0.135225\pi$
$43$	21.4550	+	21.4550i	0.498955	+	0.498955i	−0.412158	+	0.911112i	$0.635225\pi$
$44$		0			0
$45$	−2.65474	−	2.65474i	−0.0589942	−	0.0589942i
$46$		0			0
$47$		−	1.17993i		−	0.0251049i	−0.999921	−	0.0125525i	$-0.996004\pi$
$47$		−	1.17993i		−	0.0251049i	0.999921	−	0.0125525i	$-0.00399568\pi$
$48$		0			0
$49$	−45.6868			−0.932384
$50$		0			0
$51$	−35.9307	+	35.9307i	−0.704524	+	0.704524i
$52$		0			0
$53$	36.9128	−	36.9128i	0.696469	−	0.696469i	−0.267178	−	0.963647i	$-0.586091\pi$
$53$	36.9128	−	36.9128i	0.696469	−	0.696469i	0.963647	+	0.267178i	$0.0860913\pi$
$54$		0			0
$55$	27.8873			0.507042
$56$		0			0
$57$			13.9751i			0.245177i
$58$		0			0
$59$	64.8124	+	64.8124i	1.09851	+	1.09851i	0.994585	+	0.103930i	$0.0331419\pi$
$59$	64.8124	+	64.8124i	1.09851	+	1.09851i	0.103930	+	0.994585i	$0.466858\pi$
$60$		0			0
$61$	−81.7334	−	81.7334i	−1.33989	−	1.33989i	−0.896158	−	0.443734i	$-0.853653\pi$
$61$	−81.7334	−	81.7334i	−1.33989	−	1.33989i	−0.443734	−	0.896158i	$-0.646347\pi$
$62$		0			0
$63$		−	3.05615i		−	0.0485103i
$64$		0			0
$65$	21.7469			0.334567
$66$		0			0
$67$	−49.8013	+	49.8013i	−0.743304	+	0.743304i	−0.973212	−	0.229909i	$-0.926157\pi$
$67$	−49.8013	+	49.8013i	−0.743304	+	0.743304i	0.229909	+	0.973212i	$0.426157\pi$
$68$		0			0
$69$	−7.45987	+	7.45987i	−0.108114	+	0.108114i
$70$		0			0
$71$	−67.8785			−0.956036			−0.478018	−	0.878350i	$-0.658645\pi$
$71$	−67.8785			−0.956036			−0.478018	+	0.878350i	$0.658645\pi$
$72$		0			0
$73$			94.5184i			1.29477i	0.762162	+	0.647386i	$0.224138\pi$
$73$			94.5184i			1.29477i	−0.762162	+	0.647386i	$0.775862\pi$
$74$		0			0
$75$	9.56621	+	9.56621i	0.127550	+	0.127550i
$76$		0			0
$77$	16.0520	+	16.0520i	0.208468	+	0.208468i
$78$		0			0
$79$		−	55.2351i		−	0.699179i	−0.936903	−	0.349589i	$-0.886321\pi$
$79$		−	55.2351i		−	0.699179i	0.936903	−	0.349589i	$-0.113679\pi$
$80$		0			0
$81$	63.0699			0.778641
$82$		0			0
$83$	−51.2318	+	51.2318i	−0.617251	+	0.617251i	−0.944825	−	0.327574i	$-0.893769\pi$
$83$	−51.2318	+	51.2318i	−0.617251	+	0.617251i	0.327574	+	0.944825i	$0.393769\pi$
$84$		0			0
$85$	−29.6938	+	29.6938i	−0.349339	+	0.349339i
$86$		0			0
$87$	110.423			1.26923
$88$		0			0
$89$			114.419i			1.28561i	0.766030	+	0.642805i	$0.222229\pi$
$89$			114.419i			1.28561i	−0.766030	+	0.642805i	$0.777771\pi$
$90$		0			0
$91$	12.5176	+	12.5176i	0.137556	+	0.137556i
$92$		0			0
$93$	111.788	+	111.788i	1.20202	+	1.20202i
$94$		0			0
$95$			11.5493i			0.121571i
$96$		0			0
$97$	−66.1629			−0.682091			−0.341046	−	0.940047i	$-0.610781\pi$
$97$	−66.1629			−0.682091			−0.341046	+	0.940047i	$0.610781\pi$
$98$		0			0
$99$	14.8067	−	14.8067i	0.149563	−	0.149563i
$100$		0			0
$101$	−57.8537	+	57.8537i	−0.572809	+	0.572809i	−0.932912	−	0.360103i	$-0.882741\pi$
$101$	−57.8537	+	57.8537i	−0.572809	+	0.572809i	0.360103	+	0.932912i	$0.382741\pi$
$102$		0			0
$103$	−24.5893			−0.238731			−0.119365	−	0.992850i	$-0.538086\pi$
$103$	−24.5893			−0.238731			−0.119365	+	0.992850i	$0.538086\pi$
$104$		0			0
$105$			11.0127i			0.104883i
$106$		0			0
$107$	−89.3039	−	89.3039i	−0.834616	−	0.834616i	0.153529	−	0.988144i	$-0.450936\pi$
$107$	−89.3039	−	89.3039i	−0.834616	−	0.834616i	−0.988144	+	0.153529i	$0.950936\pi$
$108$		0			0
$109$	8.79326	+	8.79326i	0.0806721	+	0.0806721i	0.746291	−	0.665619i	$-0.231833\pi$
$109$	8.79326	+	8.79326i	0.0806721	+	0.0806721i	−0.665619	+	0.746291i	$0.731833\pi$
$110$		0			0
$111$		−	71.2441i		−	0.641839i
$112$		0			0
$113$	182.798			1.61769			0.808843	−	0.588025i	$-0.200094\pi$
$113$	182.798			1.61769			0.808843	+	0.588025i	$0.200094\pi$
$114$		0			0
$115$	−6.16497	+	6.16497i	−0.0536085	+	0.0536085i
$116$		0			0
$117$	11.5465	−	11.5465i	0.0986876	−	0.0986876i
$118$		0			0
$119$	−34.1837			−0.287258
$120$		0			0
$121$			34.5404i			0.285458i
$122$		0			0
$123$	74.6876	+	74.6876i	0.607216	+	0.607216i
$124$		0			0
$125$	7.90569	+	7.90569i	0.0632456	+	0.0632456i
$126$		0			0
$127$			189.543i			1.49247i	0.665685	+	0.746233i	$0.268139\pi$
$127$			189.543i			1.49247i	−0.665685	+	0.746233i	$0.731861\pi$
$128$		0			0
$129$	−82.0974			−0.636414
$130$		0			0
$131$	−8.74616	+	8.74616i	−0.0667646	+	0.0667646i	−0.739701	−	0.672936i	$-0.765033\pi$
$131$	−8.74616	+	8.74616i	−0.0667646	+	0.0667646i	0.672936	+	0.739701i	$0.265033\pi$
$132$		0			0
$133$	−6.64780	+	6.64780i	−0.0499835	+	0.0499835i
$134$		0			0
$135$	64.6102			0.478594
$136$		0			0
$137$		−	206.974i		−	1.51076i	−0.655285	−	0.755381i	$-0.727452\pi$
$137$		−	206.974i		−	1.51076i	0.655285	−	0.755381i	$-0.272548\pi$
$138$		0			0
$139$	−92.4013	−	92.4013i	−0.664757	−	0.664757i	0.291740	−	0.956498i	$-0.405766\pi$
$139$	−92.4013	−	92.4013i	−0.664757	−	0.664757i	−0.956498	+	0.291740i	$0.905766\pi$
$140$		0			0
$141$	2.25750	+	2.25750i	0.0160106	+	0.0160106i
$142$		0			0
$143$			121.292i			0.848199i
$144$		0			0
$145$	91.2552			0.629346
$146$		0			0
$147$	87.4100	−	87.4100i	0.594626	−	0.594626i
$148$		0			0
$149$	110.011	−	110.011i	0.738329	−	0.738329i	−0.233926	−	0.972254i	$-0.575157\pi$
$149$	110.011	−	110.011i	0.738329	−	0.738329i	0.972254	+	0.233926i	$0.0751572\pi$
$150$		0			0
$151$	−153.594			−1.01718			−0.508590	−	0.861009i	$-0.669833\pi$
$151$	−153.594			−1.01718			−0.508590	+	0.861009i	$0.669833\pi$
$152$		0			0
$153$			31.5317i			0.206089i
$154$		0			0
$155$	92.3835	+	92.3835i	0.596023	+	0.596023i
$156$		0			0
$157$	−56.5598	−	56.5598i	−0.360253	−	0.360253i	0.503653	−	0.863906i	$-0.331989\pi$
$157$	−56.5598	−	56.5598i	−0.360253	−	0.360253i	−0.863906	+	0.503653i	$0.831989\pi$
$158$		0			0
$159$			141.246i			0.888342i
$160$		0			0
$161$	−7.09715			−0.0440817
$162$		0			0
$163$	150.640	−	150.640i	0.924170	−	0.924170i	−0.0731507	−	0.997321i	$-0.523305\pi$
$163$	150.640	−	150.640i	0.924170	−	0.924170i	0.997321	+	0.0731507i	$0.0233054\pi$
$164$		0			0
$165$	−53.3552	+	53.3552i	−0.323365	+	0.323365i
$166$		0			0
$167$	−116.060			−0.694969			−0.347485	−	0.937686i	$-0.612964\pi$
$167$	−116.060			−0.694969			−0.347485	+	0.937686i	$0.612964\pi$
$168$		0			0
$169$		−	74.4146i		−	0.440323i
$170$		0			0
$171$	6.13206	+	6.13206i	0.0358600	+	0.0358600i
$172$		0			0
$173$	63.7240	+	63.7240i	0.368347	+	0.368347i	0.866874	−	0.498527i	$-0.166126\pi$
$173$	63.7240	+	63.7240i	0.368347	+	0.368347i	−0.498527	+	0.866874i	$0.666126\pi$
$174$		0			0
$175$			9.10108i			0.0520062i
$176$		0			0
$177$	−248.004			−1.40115
$178$		0			0
$179$	86.6633	−	86.6633i	0.484153	−	0.484153i	−0.422302	−	0.906455i	$-0.638778\pi$
$179$	86.6633	−	86.6633i	0.484153	−	0.484153i	0.906455	+	0.422302i	$0.138778\pi$
$180$		0			0
$181$	−185.317	+	185.317i	−1.02385	+	1.02385i	−0.0241425	+	0.999709i	$0.507686\pi$
$181$	−185.317	+	185.317i	−1.02385	+	1.02385i	−0.999709	+	0.0241425i	$0.992314\pi$
$182$		0			0
$183$	312.752			1.70903
$184$		0			0
$185$		−	58.8775i		−	0.318257i
$186$		0			0
$187$	−165.616	−	165.616i	−0.885647	−	0.885647i
$188$		0			0
$189$	37.1898	+	37.1898i	0.196771	+	0.196771i
$190$		0			0
$191$		−	159.221i		−	0.833617i	−0.908994	−	0.416809i	$-0.863148\pi$
$191$		−	159.221i		−	0.833617i	0.908994	−	0.416809i	$-0.136852\pi$
$192$		0			0
$193$	−295.152			−1.52929			−0.764643	−	0.644454i	$-0.777085\pi$
$193$	−295.152			−1.52929			−0.764643	+	0.644454i	$0.777085\pi$
$194$		0			0
$195$	−41.6071	+	41.6071i	−0.213370	+	0.213370i
$196$		0			0
$197$	116.425	−	116.425i	0.590990	−	0.590990i	−0.346909	−	0.937899i	$-0.612769\pi$
$197$	116.425	−	116.425i	0.590990	−	0.590990i	0.937899	+	0.346909i	$0.112769\pi$
$198$		0			0
$199$	−165.779			−0.833060			−0.416530	−	0.909122i	$-0.636754\pi$
$199$	−165.779			−0.833060			−0.416530	+	0.909122i	$0.636754\pi$
$200$		0			0
$201$		−	190.564i		−	0.948080i
$202$		0			0
$203$	52.5268	+	52.5268i	0.258753	+	0.258753i
$204$		0			0
$205$	61.7232	+	61.7232i	0.301089	+	0.301089i
$206$		0			0
$207$			6.54655i			0.0316259i
$208$		0			0
$209$	−64.4157			−0.308209
$210$		0			0
$211$	−140.271	+	140.271i	−0.664792	+	0.664792i	−0.956506	−	0.291713i	$-0.905775\pi$
$211$	−140.271	+	140.271i	−0.664792	+	0.664792i	0.291713	+	0.956506i	$0.405775\pi$
$212$		0			0
$213$	129.868	−	129.868i	0.609709	−	0.609709i
$214$		0			0
$215$	−67.8468			−0.315567
$216$		0			0
$217$			106.352i			0.490103i
$218$		0			0
$219$	−180.837	−	180.837i	−0.825738	−	0.825738i
$220$		0			0
$221$	−129.149	−	129.149i	−0.584387	−	0.584387i
$222$		0			0
$223$			176.789i			0.792775i	0.918083	+	0.396387i	$0.129736\pi$
$223$			176.789i			0.792775i	−0.918083	+	0.396387i	$0.870264\pi$
$224$		0			0
$225$	8.39502			0.0373112
$226$		0			0
$227$	285.515	−	285.515i	1.25778	−	1.25778i	0.305624	−	0.952152i	$-0.401135\pi$
$227$	285.515	−	285.515i	1.25778	−	1.25778i	0.952152	−	0.305624i	$-0.0988651\pi$
$228$		0			0
$229$	93.1148	−	93.1148i	0.406615	−	0.406615i	−0.473941	−	0.880556i	$-0.657169\pi$
$229$	93.1148	−	93.1148i	0.406615	−	0.406615i	0.880556	+	0.473941i	$0.157169\pi$
$230$		0			0
$231$	−61.4228			−0.265900
$232$		0			0
$233$		−	130.556i		−	0.560324i	−0.959953	−	0.280162i	$-0.909612\pi$
$233$		−	130.556i		−	0.560324i	0.959953	−	0.280162i	$-0.0903882\pi$
$234$		0			0
$235$	1.86564	+	1.86564i	0.00793887	+	0.00793887i
$236$		0			0
$237$	105.678	+	105.678i	0.445900	+	0.445900i
$238$		0			0
$239$		−	14.5966i		−	0.0610737i	−0.999534	−	0.0305368i	$-0.990278\pi$
$239$		−	14.5966i		−	0.0610737i	0.999534	−	0.0305368i	$-0.00972169\pi$
$240$		0			0
$241$	7.50558			0.0311435			0.0155717	−	0.999879i	$-0.495043\pi$
$241$	7.50558			0.0311435			0.0155717	+	0.999879i	$0.495043\pi$
$242$		0			0
$243$	63.2157	−	63.2157i	0.260147	−	0.260147i
$244$		0			0
$245$	72.2372	−	72.2372i	0.294846	−	0.294846i
$246$		0			0
$247$	−50.2322			−0.203369
$248$		0			0
$249$		−	196.038i		−	0.787301i
$250$		0			0
$251$	301.462	+	301.462i	1.20104	+	1.20104i	0.973850	+	0.227193i	$0.0729548\pi$
$251$	301.462	+	301.462i	1.20104	+	1.20104i	0.227193	+	0.973850i	$0.427045\pi$
$252$		0			0
$253$	−34.3849	−	34.3849i	−0.135909	−	0.135909i
$254$		0			0
$255$		−	113.623i		−	0.445580i
$256$		0			0
$257$	−186.712			−0.726507			−0.363253	−	0.931690i	$-0.618334\pi$
$257$	−186.712			−0.726507			−0.363253	+	0.931690i	$0.618334\pi$
$258$		0			0
$259$	33.8900	−	33.8900i	0.130850	−	0.130850i
$260$		0			0
$261$	48.4517	−	48.4517i	0.185639	−	0.185639i
$262$		0			0
$263$	−139.854			−0.531765			−0.265882	−	0.964005i	$-0.585663\pi$
$263$	−139.854			−0.531765			−0.265882	+	0.964005i	$0.585663\pi$
$264$		0			0
$265$			116.729i			0.440485i
$266$		0			0
$267$	−218.912	−	218.912i	−0.819894	−	0.819894i
$268$		0			0
$269$	162.722	+	162.722i	0.604914	+	0.604914i	0.941612	−	0.336699i	$-0.109310\pi$
$269$	162.722	+	162.722i	0.604914	+	0.604914i	−0.336699	+	0.941612i	$0.609310\pi$
$270$		0			0
$271$		−	418.661i		−	1.54487i	−0.635091	−	0.772437i	$-0.719038\pi$
$271$		−	418.661i		−	1.54487i	0.635091	−	0.772437i	$-0.280962\pi$
$272$		0			0
$273$	−47.8983			−0.175452
$274$		0			0
$275$	−44.0937	+	44.0937i	−0.160341	+	0.160341i
$276$		0			0
$277$	318.143	−	318.143i	1.14853	−	1.14853i	0.161691	−	0.986841i	$-0.448305\pi$
$277$	318.143	−	318.143i	1.14853	−	1.14853i	0.986841	−	0.161691i	$-0.0516948\pi$
$278$		0			0
$279$	98.1016			0.351619
$280$		0			0
$281$		−	277.764i		−	0.988484i	−0.869324	−	0.494242i	$-0.835446\pi$
$281$		−	277.764i		−	0.988484i	0.869324	−	0.494242i	$-0.164554\pi$
$282$		0			0
$283$	−46.0047	−	46.0047i	−0.162561	−	0.162561i	0.621139	−	0.783700i	$-0.286670\pi$
$283$	−46.0047	−	46.0047i	−0.162561	−	0.162561i	−0.783700	+	0.621139i	$0.786670\pi$
$284$		0			0
$285$	−22.0966	−	22.0966i	−0.0775319	−	0.0775319i
$286$		0			0
$287$			71.0561i			0.247582i
$288$		0			0
$289$	63.6885			0.220375
$290$		0			0
$291$	126.586	−	126.586i	0.435002	−	0.435002i
$292$		0			0
$293$	−246.101	+	246.101i	−0.839936	+	0.839936i	−0.988850	−	0.148914i	$-0.952422\pi$
$293$	−246.101	+	246.101i	−0.839936	+	0.839936i	0.148914	+	0.988850i	$0.452422\pi$
$294$		0			0
$295$	−204.955			−0.694762
$296$		0			0
$297$			360.361i			1.21334i
$298$		0			0
$299$	−26.8138	−	26.8138i	−0.0896782	−	0.0896782i
$300$		0			0
$301$	−39.0528	−	39.0528i	−0.129744	−	0.129744i
$302$		0			0
$303$		−	221.376i		−	0.730615i
$304$		0			0
$305$	258.464			0.847422
$306$		0			0
$307$	−197.066	+	197.066i	−0.641908	+	0.641908i	−0.951024	−	0.309117i	$-0.899967\pi$
$307$	−197.066	+	197.066i	−0.641908	+	0.641908i	0.309117	+	0.951024i	$0.399967\pi$
$308$		0			0
$309$	47.0453	−	47.0453i	0.152250	−	0.152250i
$310$		0			0
$311$	104.537			0.336131			0.168066	−	0.985776i	$-0.446248\pi$
$311$	104.537			0.336131			0.168066	+	0.985776i	$0.446248\pi$
$312$		0			0
$313$			136.649i			0.436577i	0.975884	+	0.218288i	$0.0700473\pi$
$313$			136.649i			0.436577i	−0.975884	+	0.218288i	$0.929953\pi$
$314$		0			0
$315$	4.83219	+	4.83219i	0.0153403	+	0.0153403i
$316$		0			0
$317$	300.353	+	300.353i	0.947486	+	0.947486i	0.998688	−	0.0512023i	$-0.0163053\pi$
$317$	300.353	+	300.353i	0.947486	+	0.947486i	−0.0512023	+	0.998688i	$0.516305\pi$
$318$		0			0
$319$			508.973i			1.59553i
$320$		0			0
$321$	341.720			1.06455
$322$		0			0
$323$	68.5884	−	68.5884i	0.212348	−	0.212348i
$324$		0			0
$325$	−34.3848	+	34.3848i	−0.105800	+	0.105800i
$326$		0			0
$327$	−33.6473			−0.102897
$328$		0			0
$329$			2.14773i			0.00652805i
$330$		0			0
$331$	−120.286	−	120.286i	−0.363401	−	0.363401i	0.501662	−	0.865064i	$-0.332722\pi$
$331$	−120.286	−	120.286i	−0.363401	−	0.363401i	−0.865064	+	0.501662i	$0.832722\pi$
$332$		0			0
$333$	−31.2608	−	31.2608i	−0.0938764	−	0.0938764i
$334$		0			0
$335$		−	157.486i		−	0.470106i
$336$		0			0
$337$	−438.291			−1.30057			−0.650283	−	0.759692i	$-0.725350\pi$
$337$	−438.291			−1.30057			−0.650283	+	0.759692i	$0.725350\pi$
$338$		0			0
$339$	−349.738	+	349.738i	−1.03167	+	1.03167i
$340$		0			0
$341$	−515.266	+	515.266i	−1.51104	+	1.51104i
$342$		0			0
$343$	172.350			0.502479
$344$		0			0
$345$		−	23.5902i		−	0.0683773i
$346$		0			0
$347$	387.729	+	387.729i	1.11737	+	1.11737i	0.992125	+	0.125249i	$0.0399730\pi$
$347$	387.729	+	387.729i	1.11737	+	1.11737i	0.125249	+	0.992125i	$0.460027\pi$
$348$		0			0
$349$	121.722	+	121.722i	0.348773	+	0.348773i	0.859652	−	0.510879i	$-0.170680\pi$
$349$	121.722	+	121.722i	0.348773	+	0.348773i	−0.510879	+	0.859652i	$0.670680\pi$
$350$		0			0
$351$			281.014i			0.800610i
$352$		0			0
$353$	170.477			0.482938			0.241469	−	0.970409i	$-0.422371\pi$
$353$	170.477			0.482938			0.241469	+	0.970409i	$0.422371\pi$
$354$		0			0
$355$	107.325	−	107.325i	0.302325	−	0.302325i
$356$		0			0
$357$	65.4016	−	65.4016i	0.183198	−	0.183198i
$358$		0			0
$359$	90.9393			0.253313			0.126656	−	0.991947i	$-0.459575\pi$
$359$	90.9393			0.253313			0.126656	+	0.991947i	$0.459575\pi$
$360$		0			0
$361$			334.323i			0.926102i
$362$		0			0
$363$	−66.0841	−	66.0841i	−0.182050	−	0.182050i
$364$		0			0
$365$	−149.447	−	149.447i	−0.409443	−	0.409443i
$366$		0			0
$367$			378.705i			1.03189i	0.856621	+	0.515947i	$0.172560\pi$
$367$			378.705i			1.03189i	−0.856621	+	0.515947i	$0.827440\pi$
$368$		0			0
$369$	65.5436			0.177625
$370$		0			0
$371$	−67.1893	+	67.1893i	−0.181103	+	0.181103i
$372$		0			0
$373$	−122.760	+	122.760i	−0.329115	+	0.329115i	−0.852250	−	0.523135i	$-0.824762\pi$
$373$	−122.760	+	122.760i	−0.329115	+	0.329115i	0.523135	+	0.852250i	$0.324762\pi$
$374$		0			0
$375$	−30.2510			−0.0806694
$376$		0			0
$377$			396.903i			1.05279i
$378$		0			0
$379$	9.20473	+	9.20473i	0.0242869	+	0.0242869i	0.719146	−	0.694859i	$-0.244533\pi$
$379$	9.20473	+	9.20473i	0.0242869	+	0.0242869i	−0.694859	+	0.719146i	$0.744533\pi$
$380$		0			0
$381$	−362.642	−	362.642i	−0.951816	−	0.951816i
$382$		0			0
$383$			201.372i			0.525777i	0.964826	+	0.262888i	$0.0846751\pi$
$383$			201.372i			0.525777i	−0.964826	+	0.262888i	$0.915325\pi$
$384$		0			0
$385$	−50.7609			−0.131847
$386$		0			0
$387$	−36.0231	+	36.0231i	−0.0930829	+	0.0930829i
$388$		0			0
$389$	−342.116	+	342.116i	−0.879474	+	0.879474i	−0.993480	−	0.114006i	$-0.963632\pi$
$389$	−342.116	+	342.116i	−0.879474	+	0.879474i	0.114006	+	0.993480i	$0.463632\pi$
$390$		0			0
$391$	73.2246			0.187275
$392$		0			0
$393$		−	33.4670i		−	0.0851579i
$394$		0			0
$395$	87.3344	+	87.3344i	0.221100	+	0.221100i
$396$		0			0
$397$	−213.381	−	213.381i	−0.537483	−	0.537483i	0.385306	−	0.922789i	$-0.374096\pi$
$397$	−213.381	−	213.381i	−0.537483	−	0.537483i	−0.922789	+	0.385306i	$0.874096\pi$
$398$		0			0
$399$		−	25.4377i		−	0.0637537i
$400$		0			0
$401$	691.238			1.72378			0.861892	−	0.507091i	$-0.169279\pi$
$401$	691.238			1.72378			0.861892	+	0.507091i	$0.169279\pi$
$402$		0			0
$403$	−401.811	+	401.811i	−0.997049	+	0.997049i
$404$		0			0
$405$	−99.7223	+	99.7223i	−0.246228	+	0.246228i
$406$		0			0
$407$	328.387			0.806847
$408$		0			0
$409$			118.715i			0.290258i	0.989413	+	0.145129i	$0.0463597\pi$
$409$			118.715i			0.290258i	−0.989413	+	0.145129i	$0.953640\pi$
$410$		0			0
$411$	395.992	+	395.992i	0.963485	+	0.963485i
$412$		0			0
$413$	−117.973	−	117.973i	−0.285648	−	0.285648i
$414$		0			0
$415$		−	162.009i		−	0.390384i
$416$		0			0
$417$	353.572			0.847895
$418$		0			0
$419$	121.061	−	121.061i	0.288929	−	0.288929i	−0.547728	−	0.836657i	$-0.684507\pi$
$419$	121.061	−	121.061i	0.288929	−	0.288929i	0.836657	+	0.547728i	$0.184507\pi$
$420$		0			0
$421$	92.4441	−	92.4441i	0.219582	−	0.219582i	−0.588740	−	0.808322i	$-0.700376\pi$
$421$	92.4441	−	92.4441i	0.219582	−	0.219582i	0.808322	+	0.588740i	$0.200376\pi$
$422$		0			0
$423$	1.98111			0.00468347
$424$		0			0
$425$		−	93.9000i		−	0.220941i
$426$		0			0
$427$	148.773	+	148.773i	0.348413	+	0.348413i
$428$		0			0
$429$	−232.062	−	232.062i	−0.540937	−	0.540937i
$430$		0			0
$431$		−	690.755i		−	1.60268i	−0.598209	−	0.801340i	$-0.704121\pi$
$431$		−	690.755i		−	1.60268i	0.598209	−	0.801340i	$-0.295879\pi$
$432$		0			0
$433$	−133.522			−0.308365			−0.154183	−	0.988042i	$-0.549274\pi$
$433$	−133.522			−0.308365			−0.154183	+	0.988042i	$0.549274\pi$
$434$		0			0
$435$	−174.593	+	174.593i	−0.401364	+	0.401364i
$436$		0			0
$437$	14.2402	−	14.2402i	0.0325863	−	0.0325863i
$438$		0			0
$439$	739.460			1.68442			0.842209	−	0.539151i	$-0.181255\pi$
$439$	739.460			1.68442			0.842209	+	0.539151i	$0.181255\pi$
$440$		0			0
$441$		−	76.7083i		−	0.173942i
$442$		0			0
$443$	−145.910	−	145.910i	−0.329367	−	0.329367i	0.522978	−	0.852346i	$-0.324821\pi$
$443$	−145.910	−	145.910i	−0.329367	−	0.329367i	−0.852346	+	0.522978i	$0.824821\pi$
$444$		0			0
$445$	−180.913	−	180.913i	−0.406545	−	0.406545i
$446$		0			0
$447$			420.956i			0.941735i
$448$		0			0
$449$	298.459			0.664720			0.332360	−	0.943153i	$-0.392155\pi$
$449$	298.459			0.664720			0.332360	+	0.943153i	$0.392155\pi$
$450$		0			0
$451$	−344.259	+	344.259i	−0.763323	+	0.763323i
$452$		0			0
$453$	293.863	−	293.863i	0.648704	−	0.648704i
$454$		0			0
$455$	−39.5840			−0.0869979
$456$		0			0
$457$		−	135.390i		−	0.296258i	−0.988968	−	0.148129i	$-0.952675\pi$
$457$		−	135.390i		−	0.296258i	0.988968	−	0.148129i	$-0.0473250\pi$
$458$		0			0
$459$	−383.704	−	383.704i	−0.835957	−	0.835957i
$460$		0			0
$461$	327.008	+	327.008i	0.709345	+	0.709345i	0.966397	−	0.257052i	$-0.0827513\pi$
$461$	327.008	+	327.008i	0.709345	+	0.709345i	−0.257052	+	0.966397i	$0.582751\pi$
$462$		0			0
$463$		−	206.161i		−	0.445273i	−0.974902	−	0.222637i	$-0.928534\pi$
$463$		−	206.161i		−	0.445273i	0.974902	−	0.222637i	$-0.0714663\pi$
$464$		0			0
$465$	−353.504			−0.760224
$466$		0			0
$467$	136.609	−	136.609i	0.292525	−	0.292525i	−0.545552	−	0.838077i	$-0.683680\pi$
$467$	136.609	−	136.609i	0.292525	−	0.292525i	0.838077	+	0.545552i	$0.183680\pi$
$468$		0			0
$469$	90.6492	−	90.6492i	0.193282	−	0.193282i
$470$		0			0
$471$	216.425			0.459502
$472$		0			0
$473$		−	378.413i		−	0.800027i
$474$		0			0
$475$	−18.2610	−	18.2610i	−0.0384442	−	0.0384442i
$476$		0			0
$477$	61.9768	+	61.9768i	0.129930	+	0.129930i
$478$		0			0
$479$		−	340.656i		−	0.711182i	−0.934642	−	0.355591i	$-0.884280\pi$
$479$		−	340.656i		−	0.711182i	0.934642	−	0.355591i	$-0.115720\pi$
$480$		0			0
$481$	256.080			0.532391
$482$		0			0
$483$	13.5786	−	13.5786i	0.0281130	−	0.0281130i
$484$		0			0
$485$	104.613	−	104.613i	0.215696	−	0.215696i
$486$		0			0
$487$	−35.9505			−0.0738203			−0.0369102	−	0.999319i	$-0.511752\pi$
$487$	−35.9505			−0.0738203			−0.0369102	+	0.999319i	$0.511752\pi$
$488$		0			0
$489$			576.421i			1.17877i
$490$		0			0
$491$	318.629	+	318.629i	0.648938	+	0.648938i	0.952736	−	0.303798i	$-0.0982549\pi$
$491$	318.629	+	318.629i	0.648938	+	0.648938i	−0.303798	+	0.952736i	$0.598255\pi$
$492$		0			0
$493$	−541.943	−	541.943i	−1.09928	−	1.09928i
$494$		0			0
$495$			46.8229i			0.0945917i
$496$		0			0
$497$	123.554			0.248599
$498$		0			0
$499$	17.0700	−	17.0700i	0.0342084	−	0.0342084i	−0.689796	−	0.724004i	$-0.742300\pi$
$499$	17.0700	−	17.0700i	0.0342084	−	0.0342084i	0.724004	+	0.689796i	$0.242300\pi$
$500$		0			0
$501$	222.051	−	222.051i	0.443215	−	0.443215i
$502$		0			0
$503$	−724.584			−1.44052			−0.720262	−	0.693702i	$-0.755979\pi$
$503$	−724.584			−1.44052			−0.720262	+	0.693702i	$0.755979\pi$
$504$		0			0
$505$		−	182.949i		−	0.362276i
$506$		0			0
$507$	142.373	+	142.373i	0.280815	+	0.280815i
$508$		0			0
$509$	67.1923	+	67.1923i	0.132008	+	0.132008i	0.770024	−	0.638015i	$-0.220244\pi$
$509$	67.1923	+	67.1923i	0.132008	+	0.132008i	−0.638015	+	0.770024i	$0.720244\pi$
$510$		0			0
$511$		−	172.044i		−	0.336681i
$512$		0			0
$513$	−149.240			−0.290917
$514$		0			0
$515$	38.8791	−	38.8791i	0.0754933	−	0.0754933i
$516$		0			0
$517$	−10.4055	+	10.4055i	−0.0201267	+	0.0201267i
$518$		0			0
$519$	−243.839			−0.469824
$520$		0			0
$521$			87.2042i			0.167378i	0.996492	+	0.0836892i	$0.0266703\pi$
$521$			87.2042i			0.167378i	−0.996492	+	0.0836892i	$0.973330\pi$
$522$		0			0
$523$	−701.848	−	701.848i	−1.34197	−	1.34197i	−0.894101	−	0.447865i	$-0.852184\pi$
$523$	−701.848	−	701.848i	−1.34197	−	1.34197i	−0.447865	−	0.894101i	$-0.647816\pi$
$524$		0			0
$525$	−17.4126	−	17.4126i	−0.0331668	−	0.0331668i
$526$		0			0
$527$		−	1097.29i		−	2.08214i
$528$		0			0
$529$	−513.797			−0.971261
$530$		0			0
$531$	−108.820	+	108.820i	−0.204934	+	0.204934i
$532$		0			0
$533$	−268.458	+	268.458i	−0.503673	+	0.503673i
$534$		0			0
$535$	282.404			0.527857
$536$		0			0
$537$			331.616i			0.617534i
$538$		0			0
$539$	402.900	+	402.900i	0.747496	+	0.747496i
$540$		0			0
$541$	558.381	+	558.381i	1.03213	+	1.03213i	0.999466	+	0.0326608i	$0.0103981\pi$
$541$	558.381	+	558.381i	1.03213	+	1.03213i	0.0326608	+	0.999466i	$0.489602\pi$
$542$		0			0
$543$		−	709.113i		−	1.30592i
$544$		0			0
$545$	−27.8067			−0.0510215
$546$		0			0
$547$	−2.58611	+	2.58611i	−0.00472780	+	0.00472780i	−0.709467	−	0.704739i	$-0.751064\pi$
$547$	−2.58611	+	2.58611i	−0.00472780	+	0.00472780i	0.704739	+	0.709467i	$0.251064\pi$
$548$		0			0
$549$	137.231	−	137.231i	0.249965	−	0.249965i
$550$		0			0
$551$	−210.786			−0.382553
$552$		0			0
$553$			100.540i			0.181808i
$554$		0			0
$555$	112.647	+	112.647i	0.202967	+	0.202967i
$556$		0			0
$557$	−282.242	−	282.242i	−0.506718	−	0.506718i	0.406799	−	0.913518i	$-0.366645\pi$
$557$	−282.242	−	282.242i	−0.506718	−	0.506718i	−0.913518	+	0.406799i	$0.866645\pi$
$558$		0			0
$559$		−	295.091i		−	0.527892i
$560$		0			0
$561$	633.727			1.12964
$562$		0			0
$563$	−217.133	+	217.133i	−0.385671	+	0.385671i	−0.873140	−	0.487469i	$-0.837920\pi$
$563$	−217.133	+	217.133i	−0.385671	+	0.385671i	0.487469	+	0.873140i	$0.337920\pi$
$564$		0			0
$565$	−289.030	+	289.030i	−0.511557	+	0.511557i
$566$		0			0
$567$	−114.801			−0.202471
$568$		0			0
$569$		−	155.864i		−	0.273927i	−0.990576	−	0.136963i	$-0.956266\pi$
$569$		−	155.864i		−	0.273927i	0.990576	−	0.136963i	$-0.0437343\pi$
$570$		0			0
$571$	−9.44846	−	9.44846i	−0.0165472	−	0.0165472i	0.698785	−	0.715332i	$-0.253725\pi$
$571$	−9.44846	−	9.44846i	−0.0165472	−	0.0165472i	−0.715332	+	0.698785i	$0.753725\pi$
$572$		0			0
$573$	304.628	+	304.628i	0.531638	+	0.531638i
$574$		0			0
$575$		−	19.4954i		−	0.0339050i
$576$		0			0
$577$	79.6924			0.138115			0.0690575	−	0.997613i	$-0.478001\pi$
$577$	79.6924			0.138115			0.0690575	+	0.997613i	$0.478001\pi$
$578$		0			0
$579$	564.698	−	564.698i	0.975299	−	0.975299i
$580$		0			0
$581$	93.2530	−	93.2530i	0.160504	−	0.160504i
$582$		0			0
$583$	−651.050			−1.11672
$584$		0			0
$585$			36.5131i			0.0624155i
$586$		0			0
$587$	−676.274	−	676.274i	−1.15208	−	1.15208i	−0.986134	−	0.165951i	$-0.946931\pi$
$587$	−676.274	−	676.274i	−1.15208	−	1.15208i	−0.165951	−	0.986134i	$-0.553069\pi$
$588$		0			0
$589$	−213.393	−	213.393i	−0.362297	−	0.362297i
$590$		0			0
$591$			445.498i			0.753804i
$592$		0			0
$593$	−339.411			−0.572363			−0.286182	−	0.958175i	$-0.592386\pi$
$593$	−339.411			−0.572363			−0.286182	+	0.958175i	$0.592386\pi$
$594$		0			0
$595$	54.0491	−	54.0491i	0.0908388	−	0.0908388i
$596$		0			0
$597$	317.175	−	317.175i	0.531282	−	0.531282i
$598$		0			0
$599$	−296.342			−0.494728			−0.247364	−	0.968923i	$-0.579564\pi$
$599$	−296.342			−0.494728			−0.247364	+	0.968923i	$0.579564\pi$
$600$		0			0
$601$			180.395i			0.300158i	0.988674	+	0.150079i	$0.0479528\pi$
$601$			180.395i			0.300158i	−0.988674	+	0.150079i	$0.952047\pi$
$602$		0			0
$603$	−83.6166	−	83.6166i	−0.138668	−	0.138668i
$604$		0			0
$605$	−54.6131	−	54.6131i	−0.0902697	−	0.0902697i
$606$		0			0
$607$			722.761i			1.19071i	0.803463	+	0.595355i	$0.202989\pi$
$607$			722.761i			1.19071i	−0.803463	+	0.595355i	$0.797011\pi$
$608$		0			0
$609$	−200.993			−0.330038
$610$		0			0
$611$	−8.11435	+	8.11435i	−0.0132804	+	0.0132804i
$612$		0			0
$613$	518.676	−	518.676i	0.846127	−	0.846127i	−0.143520	−	0.989647i	$-0.545842\pi$
$613$	518.676	−	518.676i	0.846127	−	0.846127i	0.989647	+	0.143520i	$0.0458422\pi$
$614$		0			0
$615$	−236.183			−0.384037
$616$		0			0
$617$		−	777.489i		−	1.26011i	−0.776550	−	0.630056i	$-0.783032\pi$
$617$		−	777.489i		−	1.26011i	0.776550	−	0.630056i	$-0.216968\pi$
$618$		0			0
$619$	396.075	+	396.075i	0.639863	+	0.639863i	0.950522	−	0.310658i	$-0.100550\pi$
$619$	396.075	+	396.075i	0.639863	+	0.639863i	−0.310658	+	0.950522i	$0.600550\pi$
$620$		0			0
$621$	−79.6640	−	79.6640i	−0.128283	−	0.128283i
$622$		0			0
$623$		−	208.268i		−	0.334298i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	123.243	−	123.243i	0.196560	−	0.196560i
$628$		0			0
$629$	−349.659	+	349.659i	−0.555897	+	0.555897i
$630$		0			0
$631$	380.654			0.603255			0.301627	−	0.953426i	$-0.402470\pi$
$631$	380.654			0.603255			0.301627	+	0.953426i	$0.402470\pi$
$632$		0			0
$633$		−	536.746i		−	0.847940i
$634$		0			0
$635$	−299.694	−	299.694i	−0.471959	−	0.471959i
$636$		0			0
$637$	314.187	+	314.187i	0.493229	+	0.493229i
$638$		0			0
$639$		−	113.968i		−	0.178354i
$640$		0			0
$641$	−1226.62			−1.91360			−0.956800	−	0.290747i	$-0.906096\pi$
$641$	−1226.62			−1.91360			−0.956800	+	0.290747i	$0.906096\pi$
$642$		0			0
$643$	116.534	−	116.534i	0.181235	−	0.181235i	−0.610659	−	0.791894i	$-0.709095\pi$
$643$	116.534	−	116.534i	0.181235	−	0.181235i	0.791894	+	0.610659i	$0.209095\pi$
$644$		0			0
$645$	129.807	−	129.807i	0.201252	−	0.201252i
$646$		0			0
$647$	458.116			0.708062			0.354031	−	0.935234i	$-0.384811\pi$
$647$	458.116			0.708062			0.354031	+	0.935234i	$0.384811\pi$
$648$		0			0
$649$		−	1143.13i		−	1.76137i
$650$		0			0
$651$	−203.478	−	203.478i	−0.312562	−	0.312562i
$652$		0			0
$653$	−61.4219	−	61.4219i	−0.0940611	−	0.0940611i	0.658510	−	0.752572i	$-0.271187\pi$
$653$	−61.4219	−	61.4219i	−0.0940611	−	0.0940611i	−0.752572	+	0.658510i	$0.771187\pi$
$654$		0			0
$655$		−	27.6578i		−	0.0422256i
$656$		0			0
$657$	−158.697			−0.241547
$658$		0			0
$659$	−187.983	+	187.983i	−0.285255	+	0.285255i	−0.835200	−	0.549946i	$-0.814648\pi$
$659$	−187.983	+	187.983i	−0.285255	+	0.285255i	0.549946	+	0.835200i	$0.314648\pi$
$660$		0			0
$661$	−43.9961	+	43.9961i	−0.0665600	+	0.0665600i	−0.739603	−	0.673043i	$-0.764987\pi$
$661$	−43.9961	+	43.9961i	−0.0665600	+	0.0665600i	0.673043	+	0.739603i	$0.264987\pi$
$662$		0			0
$663$	494.189			0.745383
$664$		0			0
$665$		−	21.0222i		−	0.0316123i
$666$		0			0
$667$	−112.517	−	112.517i	−0.168691	−	0.168691i
$668$		0			0
$669$	−338.240	−	338.240i	−0.505590	−	0.505590i
$670$		0			0
$671$			1441.57i			2.14839i
$672$		0			0
$673$	898.652			1.33529			0.667647	−	0.744478i	$-0.267302\pi$
$673$	898.652			1.33529			0.667647	+	0.744478i	$0.267302\pi$
$674$		0			0
$675$	−102.158	+	102.158i	−0.151345	+	0.151345i
$676$		0			0
$677$	−363.498	+	363.498i	−0.536925	+	0.536925i	−0.922624	−	0.385700i	$-0.873960\pi$
$677$	−363.498	+	363.498i	−0.536925	+	0.536925i	0.385700	+	0.922624i	$0.373960\pi$
$678$		0			0
$679$	120.431			0.177365
$680$		0			0
$681$			1092.52i			1.60429i
$682$		0			0
$683$	301.288	+	301.288i	0.441125	+	0.441125i	0.892390	−	0.451265i	$-0.149027\pi$
$683$	301.288	+	301.288i	0.441125	+	0.441125i	−0.451265	+	0.892390i	$0.649027\pi$
$684$		0			0
$685$	327.255	+	327.255i	0.477745	+	0.477745i
$686$		0			0
$687$			356.303i			0.518635i
$688$		0			0
$689$	−507.697			−0.736860
$690$		0			0
$691$	701.699	−	701.699i	1.01548	−	1.01548i	0.0156052	−	0.999878i	$-0.495032\pi$
$691$	701.699	−	701.699i	1.01548	−	1.01548i	0.999878	−	0.0156052i	$-0.00496750\pi$
$692$		0			0
$693$	−26.9514	+	26.9514i	−0.0388909	+	0.0388909i
$694$		0			0
$695$	292.198			0.420429
$696$		0			0
$697$		−	733.118i		−	1.05182i
$698$		0			0
$699$	249.784	+	249.784i	0.357345	+	0.357345i
$700$		0			0
$701$	18.0611	+	18.0611i	0.0257648	+	0.0257648i	0.719872	−	0.694107i	$-0.244201\pi$
$701$	18.0611	+	18.0611i	0.0257648	+	0.0257648i	−0.694107	+	0.719872i	$0.744201\pi$
$702$		0			0
$703$			135.998i			0.193454i
$704$		0			0
$705$	−7.13883			−0.0101260
$706$		0			0
$707$	105.306	−	105.306i	0.148948	−	0.148948i
$708$		0			0
$709$	500.672	−	500.672i	0.706167	−	0.706167i	−0.259560	−	0.965727i	$-0.583578\pi$
$709$	500.672	−	500.672i	0.706167	−	0.706167i	0.965727	+	0.259560i	$0.0835775\pi$
$710$		0			0
$711$	92.7400			0.130436
$712$		0			0
$713$		−	227.817i		−	0.319519i
$714$		0			0
$715$	−191.780	−	191.780i	−0.268224	−	0.268224i
$716$		0			0
$717$	27.9269	+	27.9269i	0.0389496	+	0.0389496i
$718$		0			0
$719$			780.627i			1.08571i	0.839826	+	0.542856i	$0.182657\pi$
$719$			780.627i			1.08571i	−0.839826	+	0.542856i	$0.817343\pi$
$720$		0			0
$721$	44.7578			0.0620774
$722$		0			0
$723$	−14.3600	+	14.3600i	−0.0198617	+	0.0198617i
$724$		0			0
$725$	−144.287	+	144.287i	−0.199017	+	0.199017i
$726$		0			0
$727$	412.254			0.567062			0.283531	−	0.958963i	$-0.408494\pi$
$727$	412.254			0.567062			0.283531	+	0.958963i	$0.408494\pi$
$728$		0			0
$729$			809.523i			1.11046i
$730$		0			0
$731$	402.926	+	402.926i	0.551198	+	0.551198i
$732$		0			0
$733$	−424.853	−	424.853i	−0.579608	−	0.579608i	0.355187	−	0.934795i	$-0.384417\pi$
$733$	−424.853	−	424.853i	−0.579608	−	0.579608i	−0.934795	+	0.355187i	$0.884417\pi$
$734$		0			0
$735$			276.415i			0.376074i
$736$		0			0
$737$	878.370			1.19182
$738$		0			0
$739$	381.830	−	381.830i	0.516685	−	0.516685i	−0.399882	−	0.916567i	$-0.630949\pi$
$739$	381.830	−	381.830i	0.516685	−	0.516685i	0.916567	+	0.399882i	$0.130949\pi$
$740$		0			0
$741$	96.1064	−	96.1064i	0.129698	−	0.129698i
$742$		0			0
$743$	−1361.50			−1.83243			−0.916216	−	0.400685i	$-0.868772\pi$
$743$	−1361.50			−1.83243			−0.916216	+	0.400685i	$0.868772\pi$
$744$		0			0
$745$			347.885i			0.466960i
$746$		0			0
$747$	−86.0184	−	86.0184i	−0.115152	−	0.115152i
$748$		0			0
$749$	162.552	+	162.552i	0.217026	+	0.217026i
$750$		0			0
$751$			60.0278i			0.0799305i	0.999201	+	0.0399653i	$0.0127247\pi$
$751$			60.0278i			0.0799305i	−0.999201	+	0.0399653i	$0.987275\pi$
$752$		0			0
$753$	−1153.54			−1.53192
$754$		0			0
$755$	242.854	−	242.854i	0.321660	−	0.321660i
$756$		0			0
$757$	−417.259	+	417.259i	−0.551201	+	0.551201i	−0.926787	−	0.375586i	$-0.877441\pi$
$757$	−417.259	+	417.259i	−0.551201	+	0.551201i	0.375586	+	0.926787i	$0.377441\pi$
$758$		0			0
$759$	131.573			0.173351
$760$		0			0
$761$		−	1265.10i		−	1.66242i	−0.555961	−	0.831209i	$-0.687650\pi$
$761$		−	1265.10i		−	1.66242i	0.555961	−	0.831209i	$-0.312350\pi$
$762$		0			0
$763$	−16.0056	−	16.0056i	−0.0209772	−	0.0209772i
$764$		0			0
$765$	−49.8560	−	49.8560i	−0.0651712	−	0.0651712i
$766$		0			0
$767$		−	891.425i		−	1.16222i
$768$		0			0
$769$	85.3884			0.111038			0.0555191	−	0.998458i	$-0.482319\pi$
$769$	85.3884			0.111038			0.0555191	+	0.998458i	$0.482319\pi$
$770$		0			0
$771$	357.226	−	357.226i	0.463328	−	0.463328i
$772$		0			0
$773$	−338.244	+	338.244i	−0.437573	+	0.437573i	−0.891195	−	0.453621i	$-0.850132\pi$
$773$	−338.244	+	338.244i	−0.437573	+	0.437573i	0.453621	+	0.891195i	$0.350132\pi$
$774$		0			0
$775$	−292.142			−0.376958
$776$		0			0
$777$			129.680i			0.166898i
$778$		0			0
$779$	−142.572	−	142.572i	−0.183019	−	0.183019i
$780$		0			0
$781$	598.603	+	598.603i	0.766457	+	0.766457i
$782$		0			0
$783$			1179.20i			1.50601i
$784$		0			0
$785$	178.858			0.227844
$786$		0			0
$787$	−678.971	+	678.971i	−0.862733	+	0.862733i	−0.991655	−	0.128922i	$-0.958848\pi$
$787$	−678.971	+	678.971i	−0.862733	+	0.862733i	0.128922	+	0.991655i	$0.458848\pi$
$788$		0			0
$789$	267.575	−	267.575i	0.339132	−	0.339132i
$790$		0			0
$791$	−332.733			−0.420648
$792$		0			0
$793$			1124.16i			1.41760i
$794$		0			0
$795$	−223.330	−	223.330i	−0.280919	−	0.280919i
$796$		0			0
$797$	792.145	+	792.145i	0.993909	+	0.993909i	0.999982	−	0.00607264i	$-0.00193299\pi$
$797$	792.145	+	792.145i	0.993909	+	0.993909i	−0.00607264	+	0.999982i	$0.501933\pi$
$798$		0			0
$799$		−	22.1591i		−	0.0277336i
$800$		0			0
$801$	−192.110			−0.239838
$802$		0			0
$803$	833.533	−	833.533i	1.03802	−	1.03802i
$804$		0			0
$805$	11.2216	−	11.2216i	0.0139399	−	0.0139399i
$806$		0			0
$807$	−622.653			−0.771565
$808$		0			0
$809$			572.198i			0.707291i	0.935380	+	0.353646i	$0.115058\pi$
$809$			572.198i			0.707291i	−0.935380	+	0.353646i	$0.884942\pi$
$810$		0			0
$811$	−805.791	−	805.791i	−0.993577	−	0.993577i	0.00640283	−	0.999980i	$-0.497962\pi$
$811$	−805.791	−	805.791i	−0.993577	−	0.993577i	−0.999980	+	0.00640283i	$0.997962\pi$
$812$		0			0
$813$	801.000	+	801.000i	0.985240	+	0.985240i
$814$		0			0
$815$			476.365i			0.584497i
$816$		0			0
$817$	156.716			0.191819
$818$		0			0
$819$	−21.0170	+	21.0170i	−0.0256618	+	0.0256618i
$820$		0			0
$821$	340.854	−	340.854i	0.415169	−	0.415169i	−0.468365	−	0.883535i	$-0.655157\pi$
$821$	340.854	−	340.854i	0.415169	−	0.415169i	0.883535	+	0.468365i	$0.155157\pi$
$822$		0			0
$823$	1483.68			1.80277			0.901384	−	0.433021i	$-0.142552\pi$
$823$	1483.68			1.80277			0.901384	+	0.433021i	$0.142552\pi$
$824$		0			0
$825$		−	168.724i		−	0.204514i
$826$		0			0
$827$	428.054	+	428.054i	0.517598	+	0.517598i	0.916844	−	0.399246i	$-0.130728\pi$
$827$	428.054	+	428.054i	0.517598	+	0.517598i	−0.399246	+	0.916844i	$0.630728\pi$
$828$		0			0
$829$	701.861	+	701.861i	0.846636	+	0.846636i	0.989712	−	0.143076i	$-0.0456993\pi$
$829$	701.861	+	701.861i	0.846636	+	0.846636i	−0.143076	+	0.989712i	$0.545699\pi$
$830$		0			0
$831$			1217.37i			1.46495i
$832$		0			0
$833$	−857.999			−1.03001
$834$		0			0
$835$	183.507	−	183.507i	0.219769	−	0.219769i
$836$		0			0
$837$	−1193.78	+	1193.78i	−1.42626	+	1.42626i
$838$		0			0
$839$	−853.285			−1.01703			−0.508513	−	0.861054i	$-0.669805\pi$
$839$	−853.285			−1.01703			−0.508513	+	0.861054i	$0.669805\pi$
$840$		0			0
$841$			824.504i			0.980385i
$842$		0			0
$843$	531.430	+	531.430i	0.630403	+	0.630403i
$844$		0			0
$845$	117.660	+	117.660i	0.139242	+	0.139242i
$846$		0			0
$847$		−	62.8710i		−	0.0742278i
$848$		0			0
$849$	176.036			0.207346
$850$		0			0
$851$	−72.5956	+	72.5956i	−0.0853062	+	0.0853062i
$852$		0			0
$853$	267.904	−	267.904i	0.314072	−	0.314072i	−0.532413	−	0.846485i	$-0.678715\pi$
$853$	267.904	−	267.904i	0.314072	−	0.314072i	0.846485	+	0.532413i	$0.178715\pi$
$854$		0			0
$855$	−19.3913			−0.0226799
$856$		0			0
$857$		−	315.894i		−	0.368605i	−0.982870	−	0.184302i	$-0.940997\pi$
$857$		−	315.894i		−	0.368605i	0.982870	−	0.184302i	$-0.0590026\pi$
$858$		0			0
$859$	434.360	+	434.360i	0.505658	+	0.505658i	0.913191	−	0.407533i	$-0.133611\pi$
$859$	434.360	+	434.360i	0.505658	+	0.505658i	−0.407533	+	0.913191i	$0.633611\pi$
$860$		0			0
$861$	−135.948	−	135.948i	−0.157895	−	0.157895i
$862$		0			0
$863$			274.320i			0.317867i	0.987289	+	0.158934i	$0.0508056\pi$
$863$			274.320i			0.317867i	−0.987289	+	0.158934i	$0.949194\pi$
$864$		0			0
$865$	−201.513			−0.232963
$866$		0			0
$867$	−121.852	+	121.852i	−0.140544	+	0.140544i
$868$		0			0
$869$	−487.104	+	487.104i	−0.560534	+	0.560534i
$870$		0			0
$871$	684.965			0.786412
$872$		0			0
$873$		−	111.088i		−	0.127248i
$874$		0			0
$875$	−14.3901	−	14.3901i	−0.0164458	−	0.0164458i
$876$		0			0
$877$	114.400	+	114.400i	0.130445	+	0.130445i	0.769315	−	0.638870i	$-0.220598\pi$
$877$	114.400	+	114.400i	0.130445	+	0.130445i	−0.638870	+	0.769315i	$0.720598\pi$
$878$		0			0
$879$		−	941.703i		−	1.07133i
$880$		0			0
$881$	−723.294			−0.820992			−0.410496	−	0.911862i	$-0.634645\pi$
$881$	−723.294			−0.820992			−0.410496	+	0.911862i	$0.634645\pi$
$882$		0			0
$883$	−252.380	+	252.380i	−0.285821	+	0.285821i	−0.835425	−	0.549604i	$-0.814779\pi$
$883$	−252.380	+	252.380i	−0.285821	+	0.285821i	0.549604	+	0.835425i	$0.314779\pi$
$884$		0			0
$885$	392.128	−	392.128i	0.443083	−	0.443083i
$886$		0			0
$887$	−729.292			−0.822201			−0.411100	−	0.911590i	$-0.634855\pi$
$887$	−729.292			−0.822201			−0.411100	+	0.911590i	$0.634855\pi$
$888$		0			0
$889$		−	345.009i		−	0.388087i
$890$		0			0
$891$	−556.197	−	556.197i	−0.624239	−	0.624239i
$892$		0			0
$893$	−4.30935	−	4.30935i	−0.00482570	−	0.00482570i
$894$		0			0
$895$			274.053i			0.306205i
$896$		0			0
$897$	102.603			0.114384
$898$		0			0
$899$	−1686.10	+	1686.10i	−1.87552	+	1.87552i
$900$		0			0
$901$	693.223	−	693.223i	0.769393	−	0.769393i
$902$		0			0
$903$	149.435			0.165487
$904$		0			0
$905$		−	586.024i		−	0.647540i
$906$		0			0
$907$	580.040	+	580.040i	0.639515	+	0.639515i	0.950436	−	0.310921i	$-0.100637\pi$
$907$	580.040	+	580.040i	0.639515	+	0.639515i	−0.310921	+	0.950436i	$0.600637\pi$
$908$		0			0
$909$	−97.1366	−	97.1366i	−0.106861	−	0.106861i
$910$		0			0
$911$		−	772.169i		−	0.847606i	−0.905754	−	0.423803i	$-0.860695\pi$
$911$		−	772.169i		−	0.847606i	0.905754	−	0.423803i	$-0.139305\pi$
$912$		0			0
$913$	903.600			0.989705
$914$		0			0
$915$	−494.504	+	494.504i	−0.540442	+	0.540442i
$916$		0			0
$917$	15.9199	−	15.9199i	0.0173608	−	0.0173608i
$918$		0			0
$919$	−1756.53			−1.91135			−0.955675	−	0.294422i	$-0.904873\pi$
$919$	−1756.53			−1.91135			−0.955675	+	0.294422i	$0.904873\pi$
$920$		0			0
$921$		−	754.069i		−	0.818750i
$922$		0			0
$923$	466.798	+	466.798i	0.505741	+	0.505741i
$924$		0			0
$925$	93.0934	+	93.0934i	0.100642	+	0.100642i
$926$		0			0
$927$		−	41.2855i		−	0.0445366i
$928$		0			0
$929$	947.261			1.01966			0.509828	−	0.860276i	$-0.329709\pi$
$929$	947.261			1.01966			0.509828	+	0.860276i	$0.329709\pi$
$930$		0			0
$931$	−166.858	+	166.858i	−0.179224	+	0.179224i
$932$		0			0
$933$	−200.004	+	200.004i	−0.214367	+	0.214367i
$934$		0			0
$935$	523.724			0.560132
$936$		0			0
$937$			598.355i			0.638586i	0.947656	+	0.319293i	$0.103445\pi$
$937$			598.355i			0.638586i	−0.947656	+	0.319293i	$0.896555\pi$
$938$		0			0
$939$	−261.442	−	261.442i	−0.278426	−	0.278426i
$940$		0			0
$941$	109.630	+	109.630i	0.116503	+	0.116503i	0.762955	−	0.646452i	$-0.223748\pi$
$941$	109.630	+	109.630i	0.116503	+	0.116503i	−0.646452	+	0.762955i	$0.723748\pi$
$942$		0			0
$943$		−	152.209i		−	0.161409i
$944$		0			0
$945$	−117.604			−0.124449
$946$		0			0
$947$	430.282	−	430.282i	0.454364	−	0.454364i	−0.442436	−	0.896800i	$-0.645886\pi$
$947$	430.282	−	430.282i	0.454364	−	0.454364i	0.896800	+	0.442436i	$0.145886\pi$
$948$		0			0
$949$	650.000	−	650.000i	0.684931	−	0.684931i
$950$		0			0
$951$	−1149.30			−1.20851
$952$		0			0
$953$			1062.59i			1.11500i	0.830178	+	0.557499i	$0.188239\pi$
$953$			1062.59i			1.11500i	−0.830178	+	0.557499i	$0.811761\pi$
$954$		0			0
$955$	251.750	+	251.750i	0.263613	+	0.263613i
$956$		0			0
$957$	−973.788	−	973.788i	−1.01754	−	1.01754i
$958$		0			0
$959$			376.738i			0.392845i
$960$		0			0
$961$	−2452.89			−2.55243
$962$		0			0
$963$	149.942	−	149.942i	0.155702	−	0.155702i
$964$		0			0
$965$	466.677	−	466.677i	0.483603	−	0.483603i
$966$		0			0
$967$	945.989			0.978272			0.489136	−	0.872208i	$-0.337312\pi$
$967$	945.989			0.978272			0.489136	+	0.872208i	$0.337312\pi$
$968$		0			0
$969$			262.453i			0.270849i
$970$		0			0
$971$	−908.018	−	908.018i	−0.935137	−	0.935137i	0.0628841	−	0.998021i	$-0.479970\pi$
$971$	−908.018	−	908.018i	−0.935137	−	0.935137i	−0.998021	+	0.0628841i	$0.979970\pi$
$972$		0			0
$973$	168.190	+	168.190i	0.172857	+	0.172857i
$974$		0			0
$975$		−	131.573i		−	0.134947i
$976$		0			0
$977$	503.352			0.515202			0.257601	−	0.966251i	$-0.417068\pi$
$977$	503.352			0.515202			0.257601	+	0.966251i	$0.417068\pi$
$978$		0			0
$979$	1009.03	−	1009.03i	1.03068	−	1.03068i
$980$		0			0
$981$	−14.7639	+	14.7639i	−0.0150499	+	0.0150499i
$982$		0			0
$983$	760.561			0.773714			0.386857	−	0.922140i	$-0.373561\pi$
$983$	760.561			0.773714			0.386857	+	0.922140i	$0.373561\pi$
$984$		0			0
$985$			368.168i			0.373775i
$986$		0			0
$987$	−4.10913	−	4.10913i	−0.00416325	−	0.00416325i
$988$		0			0
$989$	83.6548	+	83.6548i	0.0845852	+	0.0845852i
$990$		0			0
$991$		−	1187.36i		−	1.19814i	−0.800696	−	0.599070i	$-0.795537\pi$
$991$		−	1187.36i		−	1.19814i	0.800696	−	0.599070i	$-0.204463\pi$
$992$		0			0
$993$	460.272			0.463517
$994$		0			0
$995$	262.119	−	262.119i	0.263437	−	0.263437i
$996$		0			0
$997$	−89.9080	+	89.9080i	−0.0901786	+	0.0901786i	−0.750757	−	0.660578i	$-0.770311\pi$
$997$	−89.9080	+	89.9080i	−0.0901786	+	0.0901786i	0.660578	+	0.750757i	$0.270311\pi$
$998$		0			0
$999$	760.816			0.761578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.111.6		32
4.3	odd	2		80.3.r.a.51.12	yes	32
8.3	odd	2		640.3.r.a.351.6		32
8.5	even	2		640.3.r.b.351.11		32
16.3	odd	4		640.3.r.b.31.11		32
16.5	even	4		80.3.r.a.11.12	✓	32
16.11	odd	4	inner	320.3.r.a.271.6		32
16.13	even	4		640.3.r.a.31.6		32
20.3	even	4		400.3.k.h.99.4		32
20.7	even	4		400.3.k.g.99.13		32
20.19	odd	2		400.3.r.f.51.5		32
80.37	odd	4		400.3.k.h.299.4		32
80.53	odd	4		400.3.k.g.299.13		32
80.69	even	4		400.3.r.f.251.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.12	✓	32	16.5	even	4
80.3.r.a.51.12	yes	32	4.3	odd	2
320.3.r.a.111.6		32	1.1	even	1	trivial
320.3.r.a.271.6		32	16.11	odd	4	inner
400.3.k.g.99.13		32	20.7	even	4
400.3.k.g.299.13		32	80.53	odd	4
400.3.k.h.99.4		32	20.3	even	4
400.3.k.h.299.4		32	80.37	odd	4
400.3.r.f.51.5		32	20.19	odd	2
400.3.r.f.251.5		32	80.69	even	4
640.3.r.a.31.6		32	16.13	even	4
640.3.r.a.351.6		32	8.3	odd	2
640.3.r.b.31.11		32	16.3	odd	4
640.3.r.b.351.11		32	8.5	even	2

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91324 + 1.91324i) q^{3} +(-1.58114 + 1.58114i) q^{5} -1.82022 q^{7} +1.67900i q^{9} +O(q^{10})\)	\(q+(-1.91324 + 1.91324i) q^{3} +(-1.58114 + 1.58114i) q^{5} -1.82022 q^{7} +1.67900i q^{9} +(-8.81874 - 8.81874i) q^{11} +(-6.87697 - 6.87697i) q^{13} -6.05021i q^{15} +18.7800 q^{17} +(3.65220 - 3.65220i) q^{19} +(3.48251 - 3.48251i) q^{21} +3.89907 q^{23} -5.00000i q^{25} +(-20.4315 - 20.4315i) q^{27} +(-28.8574 - 28.8574i) q^{29} -58.4285i q^{31} +33.7448 q^{33} +(2.87801 - 2.87801i) q^{35} +(-18.6187 + 18.6187i) q^{37} +26.3146 q^{39} -39.0372i q^{41} +(21.4550 + 21.4550i) q^{43} +(-2.65474 - 2.65474i) q^{45} -1.17993i q^{47} -45.6868 q^{49} +(-35.9307 + 35.9307i) q^{51} +(36.9128 - 36.9128i) q^{53} +27.8873 q^{55} +13.9751i q^{57} +(64.8124 + 64.8124i) q^{59} +(-81.7334 - 81.7334i) q^{61} -3.05615i q^{63} +21.7469 q^{65} +(-49.8013 + 49.8013i) q^{67} +(-7.45987 + 7.45987i) q^{69} -67.8785 q^{71} +94.5184i q^{73} +(9.56621 + 9.56621i) q^{75} +(16.0520 + 16.0520i) q^{77} -55.2351i q^{79} +63.0699 q^{81} +(-51.2318 + 51.2318i) q^{83} +(-29.6938 + 29.6938i) q^{85} +110.423 q^{87} +114.419i q^{89} +(12.5176 + 12.5176i) q^{91} +(111.788 + 111.788i) q^{93} +11.5493i q^{95} -66.1629 q^{97} +(14.8067 - 14.8067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Introduction

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