LMFDB - Embedded newform 656.2.bs.d.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(33,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("656.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.bs (of order $20$, degree $8$, 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			225.3
Character	$\chi$	$=$	656.225
Dual form			656.2.bs.d.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67347 - 1.67347i) q^{3} +(-1.68856 + 2.32411i) q^{5} +(1.86997 + 0.952797i) q^{7} -2.60102i q^{9} +O(q^{10})$	\(q+(1.67347 - 1.67347i) q^{3} +(-1.68856 + 2.32411i) q^{5} +(1.86997 + 0.952797i) q^{7} -2.60102i q^{9} +(-0.0609104 + 0.384573i) q^{11} +(1.56991 + 3.08112i) q^{13} +(1.06357 + 6.71509i) q^{15} +(5.05100 + 0.800000i) q^{17} +(2.92520 - 5.74102i) q^{19} +(4.72382 - 1.53486i) q^{21} +(-0.410662 + 1.26389i) q^{23} +(-1.00514 - 3.09351i) q^{25} +(0.667682 + 0.667682i) q^{27} +(0.589758 - 0.0934085i) q^{29} +(0.996546 - 0.724033i) q^{31} +(0.541641 + 0.745505i) q^{33} +(-5.37196 + 2.73715i) q^{35} +(-2.07936 - 1.51074i) q^{37} +(7.78337 + 2.52897i) q^{39} +(1.91012 + 6.11158i) q^{41} +(-9.42697 - 3.06301i) q^{43} +(6.04504 + 4.39198i) q^{45} +(1.97205 - 1.00481i) q^{47} +(-1.52553 - 2.09972i) q^{49} +(9.79148 - 7.11393i) q^{51} +(-5.34140 + 0.845995i) q^{53} +(-0.790938 - 0.790938i) q^{55} +(-4.71221 - 14.5027i) q^{57} +(-2.04191 + 6.28435i) q^{59} +(6.08019 - 1.97557i) q^{61} +(2.47824 - 4.86383i) q^{63} +(-9.81174 - 1.55403i) q^{65} +(-0.874252 - 5.51981i) q^{67} +(1.42785 + 2.80231i) q^{69} +(1.09545 - 6.91639i) q^{71} -14.4984i q^{73} +(-6.85898 - 3.49482i) q^{75} +(-0.480321 + 0.661105i) q^{77} +(-4.23136 + 4.23136i) q^{79} +10.0378 q^{81} -15.4232 q^{83} +(-10.3882 + 10.3882i) q^{85} +(0.830627 - 1.14326i) q^{87} +(0.298137 + 0.151908i) q^{89} +7.25741i q^{91} +(0.456043 - 2.87934i) q^{93} +(8.40337 + 16.4925i) q^{95} +(2.25597 + 14.2436i) q^{97} +(1.00028 + 0.158429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	$ 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.67347	−	1.67347i	0.966180	−	0.966180i	−0.0332667	−	0.999447i	$-0.510591\pi$
$3$	1.67347	−	1.67347i	0.966180	−	0.966180i	0.999447	+	0.0332667i	$0.0105911\pi$
$4$		0			0
$5$	−1.68856	+	2.32411i	−0.755148	+	1.03937i	0.242455	+	0.970163i	$0.422047\pi$
$5$	−1.68856	+	2.32411i	−0.755148	+	1.03937i	−0.997602	+	0.0692088i	$0.977953\pi$
$6$		0			0
$7$	1.86997	+	0.952797i	0.706782	+	0.360123i	0.770146	−	0.637867i	$-0.220183\pi$
$7$	1.86997	+	0.952797i	0.706782	+	0.360123i	−0.0633646	+	0.997990i	$0.520183\pi$
$8$		0			0
$9$		−	2.60102i		−	0.867007i
$10$		0			0
$11$	−0.0609104	+	0.384573i	−0.0183652	+	0.115953i	−0.995168	−	0.0981881i	$-0.968695\pi$
$11$	−0.0609104	+	0.384573i	−0.0183652	+	0.115953i	0.976803	+	0.214141i	$0.0686953\pi$
$12$		0			0
$13$	1.56991	+	3.08112i	0.435415	+	0.854549i	0.999583	+	0.0288893i	$0.00919702\pi$
$13$	1.56991	+	3.08112i	0.435415	+	0.854549i	−0.564168	+	0.825660i	$0.690803\pi$
$14$		0			0
$15$	1.06357	+	6.71509i	0.274611	+	1.73383i
$16$		0			0
$17$	5.05100	+	0.800000i	1.22505	+	0.194028i	0.735243	−	0.677804i	$-0.237068\pi$
$17$	5.05100	+	0.800000i	1.22505	+	0.194028i	0.489804	+	0.871832i	$0.337068\pi$
$18$		0			0
$19$	2.92520	−	5.74102i	0.671086	−	1.31708i	−0.264638	−	0.964348i	$-0.585252\pi$
$19$	2.92520	−	5.74102i	0.671086	−	1.31708i	0.935724	−	0.352733i	$-0.114748\pi$
$20$		0			0
$21$	4.72382	−	1.53486i	1.03082	−	0.334934i
$22$		0			0
$23$	−0.410662	+	1.26389i	−0.0856289	+	0.263539i	−0.984698	−	0.174267i	$-0.944244\pi$
$23$	−0.410662	+	1.26389i	−0.0856289	+	0.263539i	0.899069	+	0.437806i	$0.144244\pi$
$24$		0			0
$25$	−1.00514	−	3.09351i	−0.201028	−	0.618701i
$26$		0			0
$27$	0.667682	+	0.667682i	0.128495	+	0.128495i
$28$		0			0
$29$	0.589758	−	0.0934085i	0.109515	−	0.0173455i	−0.101436	−	0.994842i	$-0.532344\pi$
$29$	0.589758	−	0.0934085i	0.109515	−	0.0173455i	0.210952	+	0.977497i	$0.432344\pi$
$30$		0			0
$31$	0.996546	−	0.724033i	0.178985	−	0.130040i	−0.494685	−	0.869072i	$-0.664717\pi$
$31$	0.996546	−	0.724033i	0.178985	−	0.130040i	0.673670	+	0.739032i	$0.264717\pi$
$32$		0			0
$33$	0.541641	+	0.745505i	0.0942876	+	0.129776i
$34$		0			0
$35$	−5.37196	+	2.73715i	−0.908027	+	0.462663i
$36$		0			0
$37$	−2.07936	−	1.51074i	−0.341845	−	0.248365i	0.403595	−	0.914938i	$-0.367761\pi$
$37$	−2.07936	−	1.51074i	−0.341845	−	0.248365i	−0.745440	+	0.666573i	$0.767761\pi$
$38$		0			0
$39$	7.78337	+	2.52897i	1.24634	+	0.404959i
$40$		0			0
$41$	1.91012	+	6.11158i	0.298310	+	0.954469i
$41$	1.91012	+	6.11158i	0.298310	+	0.954469i
$42$		0			0
$43$	−9.42697	−	3.06301i	−1.43760	−	0.467104i	−0.516452	−	0.856316i	$-0.672747\pi$
$43$	−9.42697	−	3.06301i	−1.43760	−	0.467104i	−0.921148	+	0.389212i	$0.872747\pi$
$44$		0			0
$45$	6.04504	+	4.39198i	0.901142	+	0.654718i
$46$		0			0
$47$	1.97205	−	1.00481i	0.287653	−	0.146567i	−0.304210	−	0.952605i	$-0.598393\pi$
$47$	1.97205	−	1.00481i	0.287653	−	0.146567i	0.591863	+	0.806038i	$0.298393\pi$
$48$		0			0
$49$	−1.52553	−	2.09972i	−0.217934	−	0.299960i
$50$		0			0
$51$	9.79148	−	7.11393i	1.37108	−	0.996149i
$52$		0			0
$53$	−5.34140	+	0.845995i	−0.733698	+	0.116206i	−0.512093	−	0.858930i	$-0.671130\pi$
$53$	−5.34140	+	0.845995i	−0.733698	+	0.116206i	−0.221605	+	0.975136i	$0.571130\pi$
$54$		0			0
$55$	−0.790938	−	0.790938i	−0.106650	−	0.106650i
$56$		0			0
$57$	−4.71221	−	14.5027i	−0.624147	−	1.92093i
$58$		0			0
$59$	−2.04191	+	6.28435i	−0.265834	+	0.818153i	0.725666	+	0.688047i	$0.241532\pi$
$59$	−2.04191	+	6.28435i	−0.265834	+	0.818153i	−0.991500	+	0.130106i	$0.958468\pi$
$60$		0			0
$61$	6.08019	−	1.97557i	0.778489	−	0.252946i	0.107294	−	0.994227i	$-0.465781\pi$
$61$	6.08019	−	1.97557i	0.778489	−	0.252946i	0.671195	+	0.741281i	$0.265781\pi$
$62$		0			0
$63$	2.47824	−	4.86383i	0.312229	−	0.612785i
$64$		0			0
$65$	−9.81174	−	1.55403i	−1.21700	−	0.192753i
$66$		0			0
$67$	−0.874252	−	5.51981i	−0.106807	−	0.674352i	−0.981757	−	0.190139i	$-0.939106\pi$
$67$	−0.874252	−	5.51981i	−0.106807	−	0.674352i	0.874950	−	0.484213i	$-0.160894\pi$
$68$		0			0
$69$	1.42785	+	2.80231i	0.171893	+	0.337359i
$70$		0			0
$71$	1.09545	−	6.91639i	0.130006	−	0.820824i	−0.833379	−	0.552702i	$-0.813597\pi$
$71$	1.09545	−	6.91639i	0.130006	−	0.820824i	0.963385	−	0.268123i	$-0.0864032\pi$
$72$		0			0
$73$		−	14.4984i		−	1.69692i	−0.529263	−	0.848458i	$-0.677532\pi$
$73$		−	14.4984i		−	1.69692i	0.529263	−	0.848458i	$-0.322468\pi$
$74$		0			0
$75$	−6.85898	−	3.49482i	−0.792006	−	0.403547i
$76$		0			0
$77$	−0.480321	+	0.661105i	−0.0547376	+	0.0753399i
$78$		0			0
$79$	−4.23136	+	4.23136i	−0.476066	+	0.476066i	−0.903871	−	0.427805i	$-0.859287\pi$
$79$	−4.23136	+	4.23136i	−0.476066	+	0.476066i	0.427805	+	0.903871i	$0.359287\pi$
$80$		0			0
$81$	10.0378			1.11531
$82$		0			0
$83$	−15.4232			−1.69292			−0.846458	−	0.532456i	$-0.821269\pi$
$83$	−15.4232			−1.69292			−0.846458	+	0.532456i	$0.821269\pi$
$84$		0			0
$85$	−10.3882	+	10.3882i	−1.12676	+	1.12676i
$86$		0			0
$87$	0.830627	−	1.14326i	0.0890526	−	0.122570i
$88$		0			0
$89$	0.298137	+	0.151908i	0.0316024	+	0.0161022i	0.469720	−	0.882815i	$-0.344355\pi$
$89$	0.298137	+	0.151908i	0.0316024	+	0.0161022i	−0.438118	+	0.898918i	$0.644355\pi$
$90$		0			0
$91$			7.25741i			0.760783i
$92$		0			0
$93$	0.456043	−	2.87934i	0.0472895	−	0.298574i
$94$		0			0
$95$	8.40337	+	16.4925i	0.862167	+	1.69210i
$96$		0			0
$97$	2.25597	+	14.2436i	0.229059	+	1.44622i	0.787315	+	0.616551i	$0.211470\pi$
$97$	2.25597	+	14.2436i	0.229059	+	1.44622i	−0.558257	+	0.829668i	$0.688530\pi$
$98$		0			0
$99$	1.00028	+	0.158429i	0.100532	+	0.0159227i
$100$		0			0
$101$	−5.20975	+	10.2247i	−0.518389	+	1.01740i	0.472323	+	0.881425i	$0.343415\pi$
$101$	−5.20975	+	10.2247i	−0.518389	+	1.01740i	−0.990713	+	0.135971i	$0.956585\pi$
$102$		0			0
$103$	12.4376	−	4.04121i	1.22551	−	0.398192i	0.376423	−	0.926448i	$-0.377154\pi$
$103$	12.4376	−	4.04121i	1.22551	−	0.398192i	0.849085	+	0.528256i	$0.177154\pi$
$104$		0			0
$105$	−4.40928	+	13.5704i	−0.430302	+	1.32433i
$106$		0			0
$107$	2.13126	+	6.55935i	0.206037	+	0.634116i	0.999669	+	0.0257185i	$0.00818734\pi$
$107$	2.13126	+	6.55935i	0.206037	+	0.634116i	−0.793632	+	0.608397i	$0.791813\pi$
$108$		0			0
$109$	−5.79514	−	5.79514i	−0.555074	−	0.555074i	0.372827	−	0.927901i	$-0.378389\pi$
$109$	−5.79514	−	5.79514i	−0.555074	−	0.555074i	−0.927901	+	0.372827i	$0.878389\pi$
$110$		0			0
$111$	−6.00794	+	0.951565i	−0.570249	+	0.0903185i
$112$		0			0
$113$	−2.92382	+	2.12428i	−0.275049	+	0.199835i	−0.716755	−	0.697325i	$-0.754374\pi$
$113$	−2.92382	+	2.12428i	−0.275049	+	0.199835i	0.441706	+	0.897160i	$0.354374\pi$
$114$		0			0
$115$	−2.24398	−	3.08857i	−0.209252	−	0.288011i
$116$		0			0
$117$	8.01406	−	4.08337i	0.740900	−	0.377507i
$118$		0			0
$119$	8.68297	+	6.30855i	0.795967	+	0.578304i
$120$		0			0
$121$	10.3174	+	3.35234i	0.937949	+	0.304758i
$122$		0			0
$123$	13.4241	+	7.03103i	1.21041	+	0.633967i
$124$		0			0
$125$	−4.77387	−	1.55112i	−0.426988	−	0.138737i
$126$		0			0
$127$	−8.27813	−	6.01442i	−0.734566	−	0.533693i	0.156439	−	0.987688i	$-0.449999\pi$
$127$	−8.27813	−	6.01442i	−0.734566	−	0.533693i	−0.891004	+	0.453995i	$0.849999\pi$
$128$		0			0
$129$	−20.9016	+	10.6499i	−1.84029	+	0.937673i
$130$		0			0
$131$	−6.10182	−	8.39844i	−0.533119	−	0.733775i	0.454483	−	0.890755i	$-0.349824\pi$
$131$	−6.10182	−	8.39844i	−0.533119	−	0.733775i	−0.987602	+	0.156981i	$0.949824\pi$
$132$		0			0
$133$	10.9401	−	7.94842i	0.948623	−	0.689215i
$134$		0			0
$135$	−2.67919	+	0.424341i	−0.230588	+	0.0365215i
$136$		0			0
$137$	2.71426	+	2.71426i	0.231895	+	0.231895i	0.813483	−	0.581588i	$-0.197569\pi$
$137$	2.71426	+	2.71426i	0.231895	+	0.231895i	−0.581588	+	0.813483i	$0.697569\pi$
$138$		0			0
$139$	−2.09647	−	6.45229i	−0.177821	−	0.547276i	0.821930	−	0.569588i	$-0.192897\pi$
$139$	−2.09647	−	6.45229i	−0.177821	−	0.547276i	−0.999751	+	0.0223122i	$0.992897\pi$
$140$		0			0
$141$	1.61865	−	4.98170i	0.136315	−	0.419534i
$142$		0			0
$143$	−1.28054	+	0.416073i	−0.107084	+	0.0347938i
$144$		0			0
$145$	−0.778751	+	1.52839i	−0.0646718	+	0.126926i
$146$		0			0
$147$	−6.06676	−	0.960881i	−0.500378	−	0.0792521i
$148$		0			0
$149$	−1.99565	−	12.6001i	−0.163490	−	1.03224i	−0.923856	−	0.382741i	$-0.874980\pi$
$149$	−1.99565	−	12.6001i	−0.163490	−	1.03224i	0.760365	−	0.649496i	$-0.225020\pi$
$150$		0			0
$151$	−1.21997	−	2.39432i	−0.0992794	−	0.194847i	0.836025	−	0.548692i	$-0.184874\pi$
$151$	−1.21997	−	2.39432i	−0.0992794	−	0.194847i	−0.935304	+	0.353845i	$0.884874\pi$
$152$		0			0
$153$	2.08081	−	13.1377i	0.168224	−	1.06212i
$154$		0			0
$155$			3.53865i			0.284231i
$156$		0			0
$157$	9.25397	+	4.71513i	0.738547	+	0.376308i	0.782438	−	0.622728i	$-0.213976\pi$
$157$	9.25397	+	4.71513i	0.738547	+	0.376308i	−0.0438917	+	0.999036i	$0.513976\pi$
$158$		0			0
$159$	−7.52294	+	10.3544i	−0.596608	+	0.821160i
$160$		0			0
$161$	−1.97215	+	1.97215i	−0.155427	+	0.155427i
$162$		0			0
$163$	−3.48663			−0.273094			−0.136547	−	0.990634i	$-0.543601\pi$
$163$	−3.48663			−0.273094			−0.136547	+	0.990634i	$0.543601\pi$
$164$		0			0
$165$	−2.64723			−0.206086
$166$		0			0
$167$	−13.8248	+	13.8248i	−1.06980	+	1.06980i	−0.0724237	+	0.997374i	$0.523073\pi$
$167$	−13.8248	+	13.8248i	−1.06980	+	1.06980i	−0.997374	+	0.0724237i	$0.976927\pi$
$168$		0			0
$169$	0.612517	−	0.843057i	0.0471167	−	0.0648505i
$170$		0			0
$171$	−14.9325	−	7.60850i	−1.14192	−	0.581836i
$172$		0			0
$173$		−	12.0871i		−	0.918962i	−0.888187	−	0.459481i	$-0.848035\pi$
$173$		−	12.0871i		−	0.918962i	0.888187	−	0.459481i	$-0.151965\pi$
$174$		0			0
$175$	1.06790	−	6.74246i	0.0807257	−	0.509682i
$176$		0			0
$177$	7.09961	+	13.9338i	0.533639	+	1.04733i
$178$		0			0
$179$	−0.311865	−	1.96904i	−0.0233099	−	0.147173i	0.973288	−	0.229586i	$-0.0737372\pi$
$179$	−0.311865	−	1.96904i	−0.0233099	−	0.147173i	−0.996598	+	0.0824133i	$0.973737\pi$
$180$		0			0
$181$	−16.0347	−	2.53965i	−1.19185	−	0.188771i	−0.471174	−	0.882040i	$-0.656170\pi$
$181$	−16.0347	−	2.53965i	−1.19185	−	0.188771i	−0.720678	+	0.693269i	$0.756170\pi$
$182$		0			0
$183$	6.86897	−	13.4811i	0.507769	−	0.996552i
$184$		0			0
$185$	7.02226	−	2.28167i	0.516287	−	0.167752i
$186$		0			0
$187$	−0.615317	+	1.89375i	−0.0449964	+	0.138485i
$188$		0			0
$189$	0.612379	+	1.88471i	0.0445440	+	0.137092i
$190$		0			0
$191$	−3.91166	−	3.91166i	−0.283038	−	0.283038i	0.551282	−	0.834319i	$-0.314139\pi$
$191$	−3.91166	−	3.91166i	−0.283038	−	0.283038i	−0.834319	+	0.551282i	$0.814139\pi$
$192$		0			0
$193$	−8.30947	+	1.31609i	−0.598129	+	0.0947343i	−0.448155	−	0.893956i	$-0.647919\pi$
$193$	−8.30947	+	1.31609i	−0.598129	+	0.0947343i	−0.149974	+	0.988690i	$0.547919\pi$
$194$		0			0
$195$	−19.0203	+	13.8191i	−1.36207	+	0.989603i
$196$		0			0
$197$	−15.4090	−	21.2087i	−1.09785	−	1.51106i	−0.838206	−	0.545354i	$-0.816395\pi$
$197$	−15.4090	−	21.2087i	−1.09785	−	1.51106i	−0.259643	−	0.965705i	$-0.583605\pi$
$198$		0			0
$199$	−10.0682	+	5.13001i	−0.713716	+	0.363657i	−0.772846	−	0.634594i	$-0.781167\pi$
$199$	−10.0682	+	5.13001i	−0.713716	+	0.363657i	0.0591296	+	0.998250i	$0.481167\pi$
$200$		0			0
$201$	−10.7003	−	7.77422i	−0.754740	−	0.548351i
$202$		0			0
$203$	1.19183	+	0.387249i	0.0836500	+	0.0271795i
$204$		0			0
$205$	−17.4293	−	5.88047i	−1.21732	−	0.410710i
$206$		0			0
$207$	3.28740	+	1.06814i	0.228490	+	0.0742409i
$208$		0			0
$209$	2.02967	+	1.47464i	0.140395	+	0.102003i
$210$		0			0
$211$	4.73888	−	2.41458i	0.326238	−	0.166226i	−0.283199	−	0.959061i	$-0.591396\pi$
$211$	4.73888	−	2.41458i	0.326238	−	0.166226i	0.609437	+	0.792835i	$0.291396\pi$
$212$		0			0
$213$	−9.74118	−	13.4076i	−0.667455	−	0.918673i
$214$		0			0
$215$	23.0368	−	16.7372i	1.57110	−	1.14147i
$216$		0			0
$217$	2.55337	−	0.404414i	0.173334	−	0.0274534i
$218$		0			0
$219$	−24.2628	−	24.2628i	−1.63953	−	1.63953i
$220$		0			0
$221$	5.46472	+	16.8187i	0.367597	+	1.13135i
$222$		0			0
$223$	−2.16692	+	6.66908i	−0.145107	+	0.446595i	−0.997025	−	0.0770815i	$-0.975440\pi$
$223$	−2.16692	+	6.66908i	−0.145107	+	0.446595i	0.851917	+	0.523676i	$0.175440\pi$
$224$		0			0
$225$	−8.04627	+	2.61439i	−0.536418	+	0.174293i
$226$		0			0
$227$	9.20507	−	18.0660i	0.610962	−	1.19908i	−0.353643	−	0.935380i	$-0.615057\pi$
$227$	9.20507	−	18.0660i	0.610962	−	1.19908i	0.964605	−	0.263699i	$-0.0849427\pi$
$228$		0			0
$229$	0.332243	+	0.0526221i	0.0219552	+	0.00347736i	0.167402	−	0.985889i	$-0.446462\pi$
$229$	0.332243	+	0.0526221i	0.0219552	+	0.00347736i	−0.145447	+	0.989366i	$0.546462\pi$
$230$		0			0
$231$	0.302537	+	1.91014i	0.0199055	+	0.125678i
$232$		0			0
$233$	5.88436	+	11.5487i	0.385497	+	0.756581i	0.999464	−	0.0327513i	$-0.0104269\pi$
$233$	5.88436	+	11.5487i	0.385497	+	0.756581i	−0.613966	+	0.789332i	$0.710427\pi$
$234$		0			0
$235$	−0.994645	+	6.27994i	−0.0648835	+	0.409658i
$236$		0			0
$237$			14.1621i			0.919930i
$238$		0			0
$239$	10.5772	+	5.38936i	0.684183	+	0.348609i	0.761288	−	0.648414i	$-0.224568\pi$
$239$	10.5772	+	5.38936i	0.684183	+	0.348609i	−0.0771047	+	0.997023i	$0.524568\pi$
$240$		0			0
$241$	15.9932	−	22.0128i	1.03021	−	1.41797i	0.125428	−	0.992103i	$-0.459970\pi$
$241$	15.9932	−	22.0128i	1.03021	−	1.41797i	0.904787	−	0.425865i	$-0.140030\pi$
$242$		0			0
$243$	14.7949	−	14.7949i	0.949091	−	0.949091i
$244$		0			0
$245$	7.45593			0.476342
$246$		0			0
$247$	22.2811			1.41771
$248$		0			0
$249$	−25.8103	+	25.8103i	−1.63566	+	1.63566i
$250$		0			0
$251$	0.796453	−	1.09622i	0.0502716	−	0.0691930i	−0.783141	−	0.621844i	$-0.786384\pi$
$251$	0.796453	−	1.09622i	0.0502716	−	0.0691930i	0.833413	+	0.552651i	$0.186384\pi$
$252$		0			0
$253$	−0.461044	−	0.234914i	−0.0289856	−	0.0147689i
$254$		0			0
$255$			34.7687i			2.17730i
$256$		0			0
$257$	−0.826496	+	5.21829i	−0.0515554	+	0.325508i	0.948409	+	0.317050i	$0.102692\pi$
$257$	−0.826496	+	5.21829i	−0.0515554	+	0.325508i	−0.999964	+	0.00845795i	$0.997308\pi$
$258$		0			0
$259$	−2.44891	−	4.80625i	−0.152168	−	0.298646i
$260$		0			0
$261$	−0.242957	−	1.53397i	−0.0150387	−	0.0949505i
$262$		0			0
$263$	2.33090	+	0.369179i	0.143730	+	0.0227645i	0.227885	−	0.973688i	$-0.426819\pi$
$263$	2.33090	+	0.369179i	0.143730	+	0.0227645i	−0.0841550	+	0.996453i	$0.526819\pi$
$264$		0			0
$265$	7.05310	−	13.8425i	0.433269	−	0.850338i
$266$		0			0
$267$	0.753138	−	0.244709i	0.0460913	−	0.0149760i
$268$		0			0
$269$	−5.22162	+	16.0705i	−0.318368	+	0.979835i	0.655978	+	0.754780i	$0.272256\pi$
$269$	−5.22162	+	16.0705i	−0.318368	+	0.979835i	−0.974346	+	0.225055i	$0.927744\pi$
$270$		0			0
$271$	−6.54109	−	20.1314i	−0.397343	−	1.22290i	−0.927122	−	0.374760i	$-0.877725\pi$
$271$	−6.54109	−	20.1314i	−0.397343	−	1.22290i	0.529779	−	0.848136i	$-0.322275\pi$
$272$		0			0
$273$	12.1451	+	12.1451i	0.735053	+	0.735053i
$274$		0			0
$275$	1.25090	−	0.198124i	0.0754323	−	0.0119473i
$276$		0			0
$277$	−9.22338	+	6.70118i	−0.554179	+	0.402635i	−0.829324	−	0.558768i	$-0.811274\pi$
$277$	−9.22338	+	6.70118i	−0.554179	+	0.402635i	0.275145	+	0.961403i	$0.411274\pi$
$278$		0			0
$279$	−1.88322	−	2.59204i	−0.112746	−	0.155181i
$280$		0			0
$281$	24.0979	−	12.2785i	1.43756	−	0.732474i	0.450494	−	0.892779i	$-0.351248\pi$
$281$	24.0979	−	12.2785i	1.43756	−	0.732474i	0.987068	+	0.160305i	$0.0512477\pi$
$282$		0			0
$283$	9.07709	+	6.59489i	0.539577	+	0.392026i	0.823928	−	0.566695i	$-0.191778\pi$
$283$	9.07709	+	6.59489i	0.539577	+	0.392026i	−0.284351	+	0.958720i	$0.591778\pi$
$284$		0			0
$285$	41.6626	+	13.5370i	2.46788	+	0.801863i
$286$		0			0
$287$	−2.25123	+	13.2484i	−0.132886	+	0.782030i
$288$		0			0
$289$	8.70462	+	2.82830i	0.512037	+	0.166371i
$290$		0			0
$291$	27.6116	+	20.0610i	1.61862	+	1.17600i
$292$		0			0
$293$	19.3154	−	9.84170i	1.12842	−	0.574958i	0.212837	−	0.977088i	$-0.431730\pi$
$293$	19.3154	−	9.84170i	1.12842	−	0.574958i	0.915583	+	0.402129i	$0.131730\pi$
$294$		0			0
$295$	−11.1576	−	15.3571i	−0.649621	−	0.894127i
$296$		0			0
$297$	−0.297441	+	0.216104i	−0.0172593	+	0.0125396i
$298$		0			0
$299$	−4.53889	+	0.718890i	−0.262491	+	0.0415745i
$300$		0			0
$301$	−14.7097	−	14.7097i	−0.847854	−	0.847854i
$302$		0			0
$303$	8.39239	+	25.8291i	0.482130	+	1.48385i
$304$		0			0
$305$	−5.67534	+	17.4669i	−0.324969	+	1.00015i
$306$		0			0
$307$	16.4573	−	5.34729i	0.939267	−	0.305186i	0.200920	−	0.979608i	$-0.435607\pi$
$307$	16.4573	−	5.34729i	0.939267	−	0.305186i	0.738347	+	0.674421i	$0.235607\pi$
$308$		0			0
$309$	14.0511	−	27.5767i	0.799337	−	1.56879i
$310$		0			0
$311$	11.9416	+	1.89137i	0.677148	+	0.107250i	0.485530	−	0.874220i	$-0.338627\pi$
$311$	11.9416	+	1.89137i	0.677148	+	0.107250i	0.191618	+	0.981470i	$0.438627\pi$
$312$		0			0
$313$	−3.39130	−	21.4118i	−0.191688	−	1.21027i	−0.876447	−	0.481499i	$-0.840093\pi$
$313$	−3.39130	−	21.4118i	−0.191688	−	1.21027i	0.684759	−	0.728770i	$-0.259907\pi$
$314$		0			0
$315$	7.11938	+	13.9726i	0.401132	+	0.787265i
$316$		0			0
$317$	−3.09471	+	19.5392i	−0.173816	+	1.09743i	0.734334	+	0.678788i	$0.237494\pi$
$317$	−3.09471	+	19.5392i	−0.173816	+	1.09743i	−0.908150	+	0.418644i	$0.862506\pi$
$318$		0			0
$319$			0.232495i			0.0130172i
$320$		0			0
$321$	14.5435	+	7.41028i	0.811739	+	0.413601i
$322$		0			0
$323$	19.3680	−	26.6577i	1.07766	−	1.48328i
$324$		0			0
$325$	7.95349	−	7.95349i	0.441180	−	0.441180i
$326$		0			0
$327$	−19.3960			−1.07260
$328$		0			0
$329$	4.64505			0.256090
$330$		0			0
$331$	−20.3952	+	20.3952i	−1.12102	+	1.12102i	−0.129436	+	0.991588i	$0.541317\pi$
$331$	−20.3952	+	20.3952i	−1.12102	+	1.12102i	−0.991588	+	0.129436i	$0.958683\pi$
$332$		0			0
$333$	−3.92948	+	5.40846i	−0.215334	+	0.296382i
$334$		0			0
$335$	14.3049	+	7.28869i	0.781558	+	0.398224i
$336$		0			0
$337$			23.4367i			1.27668i	0.769754	+	0.638340i	$0.220379\pi$
$337$			23.4367i			1.27668i	−0.769754	+	0.638340i	$0.779621\pi$
$338$		0			0
$339$	−1.33801	+	8.44784i	−0.0726706	+	0.458824i
$340$		0			0
$341$	0.217744	+	0.427346i	0.0117915	+	0.0231421i
$342$		0			0
$343$	−3.15028	−	19.8901i	−0.170099	−	1.07396i
$344$		0			0
$345$	−8.92388	−	1.41340i	−0.480446	−	0.0760951i
$346$		0			0
$347$	−6.09771	+	11.9674i	−0.327342	+	0.642445i	−0.994760	−	0.102238i	$-0.967400\pi$
$347$	−6.09771	+	11.9674i	−0.327342	+	0.642445i	0.667418	+	0.744684i	$0.267400\pi$
$348$		0			0
$349$	−10.5919	+	3.44151i	−0.566970	+	0.184220i	−0.578455	−	0.815714i	$-0.696344\pi$
$349$	−10.5919	+	3.44151i	−0.566970	+	0.184220i	0.0114848	+	0.999934i	$0.496344\pi$
$350$		0			0
$351$	−1.00901	+	3.10541i	−0.0538569	+	0.165755i
$352$		0			0
$353$	−4.34026	−	13.3579i	−0.231009	−	0.710971i	−0.997626	−	0.0688670i	$-0.978062\pi$
$353$	−4.34026	−	13.3579i	−0.231009	−	0.710971i	0.766617	−	0.642104i	$-0.221938\pi$
$354$		0			0
$355$	14.2247	+	14.2247i	0.754968	+	0.754968i
$356$		0			0
$357$	25.0879	−	3.97353i	1.32779	−	0.210302i
$358$		0			0
$359$	−23.2237	+	16.8730i	−1.22570	+	0.890521i	−0.996560	−	0.0828726i	$-0.973591\pi$
$359$	−23.2237	+	16.8730i	−1.22570	+	0.890521i	−0.229137	+	0.973394i	$0.573591\pi$
$360$		0			0
$361$	−13.2346	−	18.2159i	−0.696560	−	0.958733i
$362$		0			0
$363$	22.8760	−	11.6559i	1.20068	−	0.611776i
$364$		0			0
$365$	33.6959	+	24.4815i	1.76373	+	1.28142i
$366$		0			0
$367$	21.1292	+	6.86529i	1.10293	+	0.358365i	0.803231	−	0.595667i	$-0.203112\pi$
$367$	21.1292	+	6.86529i	1.10293	+	0.358365i	0.299703	+	0.954032i	$0.403112\pi$
$368$		0			0
$369$	15.8963	−	4.96826i	0.827531	−	0.258637i
$370$		0			0
$371$	−10.7943	−	3.50729i	−0.560413	−	0.182089i
$372$		0			0
$373$	14.0050	+	10.1752i	0.725149	+	0.526852i	0.888025	−	0.459795i	$-0.152077\pi$
$373$	14.0050	+	10.1752i	0.725149	+	0.526852i	−0.162876	+	0.986647i	$0.552077\pi$
$374$		0			0
$375$	−10.5847	+	5.39318i	−0.546592	+	0.278502i
$376$		0			0
$377$	1.21367	+	1.67047i	0.0625072	+	0.0860337i
$378$		0			0
$379$	2.13917	−	1.55420i	0.109882	−	0.0798339i	−0.531487	−	0.847066i	$-0.678367\pi$
$379$	2.13917	−	1.55420i	0.109882	−	0.0798339i	0.641369	+	0.767232i	$0.278367\pi$
$380$		0			0
$381$	−23.9182	+	3.78827i	−1.22537	+	0.194079i
$382$		0			0
$383$	−20.4903	−	20.4903i	−1.04701	−	1.04701i	−0.998839	−	0.0481661i	$-0.984662\pi$
$383$	−20.4903	−	20.4903i	−1.04701	−	1.04701i	−0.0481661	−	0.998839i	$-0.515338\pi$
$384$		0			0
$385$	−0.725426	−	2.23263i	−0.0369711	−	0.113785i
$386$		0			0
$387$	−7.96695	+	24.5197i	−0.404983	+	1.24641i
$388$		0			0
$389$	20.1771	−	6.55595i	1.02302	−	0.332400i	0.250994	−	0.967989i	$-0.419243\pi$
$389$	20.1771	−	6.55595i	1.02302	−	0.332400i	0.772028	+	0.635589i	$0.219243\pi$
$390$		0			0
$391$	−3.08536	+	6.05536i	−0.156033	+	0.306233i
$392$		0			0
$393$	−24.2658	−	3.84332i	−1.22405	−	0.193870i
$394$		0			0
$395$	−2.68922	−	16.9791i	−0.135309	−	0.854309i
$396$		0			0
$397$	2.06513	+	4.05305i	0.103646	+	0.203417i	0.937006	−	0.349315i	$-0.113586\pi$
$397$	2.06513	+	4.05305i	0.103646	+	0.203417i	−0.833359	+	0.552731i	$0.813586\pi$
$398$		0			0
$399$	5.00643	−	31.6093i	0.250635	−	1.58245i
$400$		0			0
$401$		−	7.53484i		−	0.376272i	−0.982143	−	0.188136i	$-0.939755\pi$
$401$		−	7.53484i		−	0.376272i	0.982143	−	0.188136i	$-0.0602446\pi$
$402$		0			0
$403$	3.79532	+	1.93381i	0.189058	+	0.0963301i
$404$		0			0
$405$	−16.9494	+	23.3288i	−0.842221	+	1.15922i
$406$		0			0
$407$	0.707647	−	0.707647i	0.0350767	−	0.0350767i
$408$		0			0
$409$	1.03548			0.0512013			0.0256007	−	0.999672i	$-0.491850\pi$
$409$	1.03548			0.0512013			0.0256007	+	0.999672i	$0.491850\pi$
$410$		0			0
$411$	9.08448			0.448104
$412$		0			0
$413$	−9.80602	+	9.80602i	−0.482523	+	0.482523i
$414$		0			0
$415$	26.0430	−	35.8451i	1.27840	−	1.75957i
$416$		0			0
$417$	−14.3061	−	7.28933i	−0.700573	−	0.356960i
$418$		0			0
$419$		−	5.57406i		−	0.272310i	−0.990688	−	0.136155i	$-0.956525\pi$
$419$		−	5.57406i		−	0.272310i	0.990688	−	0.136155i	$-0.0434746\pi$
$420$		0			0
$421$	4.88611	−	30.8497i	0.238134	−	1.50352i	−0.521546	−	0.853223i	$-0.674644\pi$
$421$	4.88611	−	30.8497i	0.238134	−	1.50352i	0.759680	−	0.650297i	$-0.225356\pi$
$422$		0			0
$423$	−2.61353	−	5.12934i	−0.127074	−	0.249397i
$424$		0			0
$425$	−2.60216	−	16.4294i	−0.126223	−	0.796944i
$426$		0			0
$427$	13.2521	+	2.09893i	0.641314	+	0.101574i
$428$		0			0
$429$	−1.44666	+	2.83924i	−0.0698456	+	0.137080i
$430$		0			0
$431$	−14.2216	+	4.62089i	−0.685031	+	0.222580i	−0.630797	−	0.775948i	$-0.717272\pi$
$431$	−14.2216	+	4.62089i	−0.685031	+	0.222580i	−0.0542346	+	0.998528i	$0.517272\pi$
$432$		0			0
$433$	5.42213	−	16.6876i	0.260571	−	0.801955i	−0.732110	−	0.681187i	$-0.761464\pi$
$433$	5.42213	−	16.6876i	0.260571	−	0.801955i	0.992681	−	0.120769i	$-0.0385359\pi$
$434$		0			0
$435$	1.25449	+	3.86093i	0.0601483	+	0.185117i
$436$		0			0
$437$	6.05474	+	6.05474i	0.289637	+	0.289637i
$438$		0			0
$439$	6.74843	−	1.06885i	0.322085	−	0.0510133i	0.00670154	−	0.999978i	$-0.497867\pi$
$439$	6.74843	−	1.06885i	0.322085	−	0.0510133i	0.315384	+	0.948964i	$0.397867\pi$
$440$		0			0
$441$	−5.46141	+	3.96795i	−0.260067	+	0.188950i
$442$		0			0
$443$	−4.96856	−	6.83863i	−0.236063	−	0.324913i	0.674506	−	0.738269i	$-0.264357\pi$
$443$	−4.96856	−	6.83863i	−0.236063	−	0.324913i	−0.910570	+	0.413356i	$0.864357\pi$
$444$		0			0
$445$	−0.856473	+	0.436395i	−0.0406007	+	0.0206871i
$446$		0			0
$447$	−24.4255	−	17.7462i	−1.15529	−	0.839365i
$448$		0			0
$449$	2.96928	+	0.964777i	0.140129	+	0.0455307i	0.378242	−	0.925707i	$-0.376529\pi$
$449$	2.96928	+	0.964777i	0.140129	+	0.0455307i	−0.238113	+	0.971238i	$0.576529\pi$
$450$		0			0
$451$	−2.46670	+	0.362322i	−0.116152	+	0.0170611i
$452$		0			0
$453$	−6.04840	−	1.96525i	−0.284179	−	0.0923353i
$454$		0			0
$455$	−16.8670	−	12.2546i	−0.790736	−	0.574503i
$456$		0			0
$457$	9.87764	−	5.03291i	0.462057	−	0.235430i	−0.207436	−	0.978249i	$-0.566512\pi$
$457$	9.87764	−	5.03291i	0.462057	−	0.235430i	0.669492	+	0.742819i	$0.266512\pi$
$458$		0			0
$459$	2.83832	+	3.90661i	0.132481	+	0.182345i
$460$		0			0
$461$	−14.4831	+	10.5226i	−0.674543	+	0.490084i	−0.871543	−	0.490319i	$-0.836880\pi$
$461$	−14.4831	+	10.5226i	−0.674543	+	0.490084i	0.197000	+	0.980404i	$0.436880\pi$
$462$		0			0
$463$	16.2174	−	2.56859i	0.753689	−	0.119373i	0.232244	−	0.972658i	$-0.425393\pi$
$463$	16.2174	−	2.56859i	0.753689	−	0.119373i	0.521445	+	0.853285i	$0.325393\pi$
$464$		0			0
$465$	5.92184	+	5.92184i	0.274619	+	0.274619i
$466$		0			0
$467$	3.86982	+	11.9101i	0.179074	+	0.551132i	0.999796	−	0.0201950i	$-0.00642870\pi$
$467$	3.86982	+	11.9101i	0.179074	+	0.551132i	−0.820722	+	0.571327i	$0.806429\pi$
$468$		0			0
$469$	3.62443	−	11.1549i	0.167361	−	0.515084i
$470$		0			0
$471$	23.3769	−	7.59561i	1.07715	−	0.349987i
$472$		0			0
$473$	1.75215	−	3.43879i	0.0805640	−	0.158116i
$474$		0			0
$475$	−20.7001	−	3.27858i	−0.949787	−	0.150432i
$476$		0			0
$477$	2.20045	+	13.8931i	0.100752	+	0.636121i
$478$		0			0
$479$	3.18557	+	6.25203i	0.145552	+	0.285663i	0.952260	−	0.305288i	$-0.0987528\pi$
$479$	3.18557	+	6.25203i	0.145552	+	0.285663i	−0.806708	+	0.590951i	$0.798753\pi$
$480$		0			0
$481$	1.39038	−	8.77850i	0.0633958	−	0.400265i
$482$		0			0
$483$			6.60069i			0.300342i
$484$		0			0
$485$	−36.9130	−	18.8081i	−1.67613	−	0.854032i
$486$		0			0
$487$	−17.4933	+	24.0774i	−0.792695	+	1.09105i	0.201072	+	0.979576i	$0.435557\pi$
$487$	−17.4933	+	24.0774i	−0.792695	+	1.09105i	−0.993767	+	0.111475i	$0.964443\pi$
$488$		0			0
$489$	−5.83479	+	5.83479i	−0.263858	+	0.263858i
$490$		0			0
$491$	31.3635			1.41542			0.707708	−	0.706505i	$-0.249729\pi$
$491$	31.3635			1.41542			0.707708	+	0.706505i	$0.249729\pi$
$492$		0			0
$493$	3.05359			0.137527
$494$		0			0
$495$	−2.05725	+	2.05725i	−0.0924663	+	0.0924663i
$496$		0			0
$497$	8.63837	−	11.8897i	0.387484	−	0.533326i
$498$		0			0
$499$	−23.9083	−	12.1819i	−1.07028	−	0.545335i	−0.172153	−	0.985070i	$-0.555072\pi$
$499$	−23.9083	−	12.1819i	−1.07028	−	0.545335i	−0.898127	+	0.439735i	$0.855072\pi$
$500$		0			0
$501$			46.2710i			2.06723i
$502$		0			0
$503$	−3.75693	+	23.7203i	−0.167513	+	1.05764i	0.750437	+	0.660942i	$0.229843\pi$
$503$	−3.75693	+	23.7203i	−0.167513	+	1.05764i	−0.917950	+	0.396695i	$0.870157\pi$
$504$		0			0
$505$	−14.9663	−	29.3731i	−0.665992	−	1.30708i
$506$		0			0
$507$	−0.385803	−	2.43586i	−0.0171341	−	0.108180i
$508$		0			0
$509$	−14.6108	−	2.31412i	−0.647612	−	0.102572i	−0.176017	−	0.984387i	$-0.556321\pi$
$509$	−14.6108	−	2.31412i	−0.647612	−	0.102572i	−0.471595	+	0.881815i	$0.656321\pi$
$510$		0			0
$511$	13.8141	−	27.1116i	0.611099	−	1.19935i
$512$		0			0
$513$	5.78628	−	1.88008i	0.255470	−	0.0830074i
$514$		0			0
$515$	−11.6094	+	35.7300i	−0.511571	+	1.57445i
$516$		0			0
$517$	0.266305	+	0.819602i	0.0117121	+	0.0360460i
$518$		0			0
$519$	−20.2274	−	20.2274i	−0.887883	−	0.887883i
$520$		0			0
$521$	−16.0123	+	2.53611i	−0.701513	+	0.111109i	−0.496994	−	0.867754i	$-0.665563\pi$
$521$	−16.0123	+	2.53611i	−0.701513	+	0.111109i	−0.204519	+	0.978863i	$0.565563\pi$
$522$		0			0
$523$	−2.29692	+	1.66881i	−0.100437	+	0.0729721i	−0.636870	−	0.770971i	$-0.719771\pi$
$523$	−2.29692	+	1.66881i	−0.100437	+	0.0729721i	0.536433	+	0.843943i	$0.319771\pi$
$524$		0			0
$525$	−9.49621	−	13.0704i	−0.414449	−	0.570440i
$526$		0			0
$527$	5.61278	−	2.85985i	0.244497	−	0.124577i
$528$		0			0
$529$	17.1786	+	12.4810i	0.746897	+	0.542652i
$530$		0			0
$531$	16.3457	+	5.31105i	0.709344	+	0.230480i
$532$		0			0
$533$	−15.8318	+	15.4799i	−0.685752	+	0.670511i
$534$		0			0
$535$	−18.8434	−	6.12258i	−0.814670	−	0.264702i
$536$		0			0
$537$	−3.81703	−	2.77323i	−0.164717	−	0.119674i
$538$		0			0
$539$	0.900417	−	0.458785i	0.0387837	−	0.0197613i
$540$		0			0
$541$	15.1869	+	20.9030i	0.652938	+	0.898691i	0.999222	−	0.0394382i	$-0.0125568\pi$
$541$	15.1869	+	20.9030i	0.652938	+	0.898691i	−0.346284	+	0.938130i	$0.612557\pi$
$542$		0			0
$543$	−31.0837	+	22.5836i	−1.33393	+	0.969157i
$544$		0			0
$545$	23.2540	−	3.68307i	0.996091	−	0.157765i
$546$		0			0
$547$	31.0360	+	31.0360i	1.32700	+	1.32700i	0.907971	+	0.419032i	$0.137631\pi$
$547$	31.0360	+	31.0360i	1.32700	+	1.32700i	0.419032	+	0.907971i	$0.362369\pi$
$548$		0			0
$549$	−5.13851	−	15.8147i	−0.219306	−	0.674955i
$550$		0			0
$551$	1.18890	−	3.65905i	0.0506488	−	0.155881i
$552$		0			0
$553$	−11.9441	+	3.88089i	−0.507917	+	0.165032i
$554$		0			0
$555$	7.93324	−	15.5699i	0.336747	−	0.660904i
$556$		0			0
$557$	36.1001	+	5.71769i	1.52961	+	0.242266i	0.863792	−	0.503849i	$-0.168083\pi$
$557$	36.1001	+	5.71769i	1.52961	+	0.242266i	0.665817	+	0.746115i	$0.268083\pi$
$558$		0			0
$559$	−5.36199	−	33.8543i	−0.226788	−	1.43188i
$560$		0			0
$561$	2.13942	+	4.19886i	0.0903265	+	0.177276i
$562$		0			0
$563$	−1.70284	+	10.7513i	−0.0717661	+	0.453113i	0.925470	+	0.378820i	$0.123670\pi$
$563$	−1.70284	+	10.7513i	−0.0717661	+	0.453113i	−0.997236	+	0.0742931i	$0.976330\pi$
$564$		0			0
$565$		−	10.3822i		−	0.436784i
$566$		0			0
$567$	18.7703	+	9.56394i	0.788278	+	0.401648i
$568$		0			0
$569$	6.39245	−	8.79845i	0.267985	−	0.368850i	−0.653723	−	0.756734i	$-0.726794\pi$
$569$	6.39245	−	8.79845i	0.267985	−	0.368850i	0.921708	+	0.387884i	$0.126794\pi$
$570$		0			0
$571$	3.44644	−	3.44644i	0.144229	−	0.144229i	−0.631305	−	0.775534i	$-0.717481\pi$
$571$	3.44644	−	3.44644i	0.144229	−	0.144229i	0.775534	+	0.631305i	$0.217481\pi$
$572$		0			0
$573$	−13.0921			−0.546931
$574$		0			0
$575$	4.32262			0.180266
$576$		0			0
$577$	−27.6070	+	27.6070i	−1.14930	+	1.14930i	−0.162605	+	0.986691i	$0.551989\pi$
$577$	−27.6070	+	27.6070i	−1.14930	+	1.14930i	−0.986691	+	0.162605i	$0.948011\pi$
$578$		0			0
$579$	−11.7032	+	16.1081i	−0.486370	+	0.669430i
$580$		0			0
$581$	−28.8409	−	14.6952i	−1.19652	−	0.609658i
$582$		0			0
$583$		−	2.10569i		−	0.0872088i
$584$		0			0
$585$	−4.04205	+	25.5205i	−0.167118	+	1.05514i
$586$		0			0
$587$	2.56196	+	5.02813i	0.105743	+	0.207533i	0.937815	−	0.347135i	$-0.112845\pi$
$587$	2.56196	+	5.02813i	0.105743	+	0.207533i	−0.832072	+	0.554668i	$0.812845\pi$
$588$		0			0
$589$	−1.24160	−	7.83913i	−0.0511591	−	0.323006i
$590$		0			0
$591$	−61.2788	−	9.70561i	−2.52067	−	0.399236i
$592$		0			0
$593$	2.04888	−	4.02116i	0.0841376	−	0.165129i	−0.845104	−	0.534602i	$-0.820462\pi$
$593$	2.04888	−	4.02116i	0.0841376	−	0.165129i	0.929242	+	0.369473i	$0.120462\pi$
$594$		0			0
$595$	−29.3235	+	9.52777i	−1.20214	+	0.390601i
$596$		0			0
$597$	−8.26394	+	25.4338i	−0.338221	+	1.04094i
$598$		0			0
$599$	−9.38078	−	28.8711i	−0.383288	−	1.17964i	−0.937715	−	0.347407i	$-0.887062\pi$
$599$	−9.38078	−	28.8711i	−0.383288	−	1.17964i	0.554426	−	0.832233i	$-0.312938\pi$
$600$		0			0
$601$	10.5900	+	10.5900i	0.431977	+	0.431977i	0.889300	−	0.457324i	$-0.151192\pi$
$601$	10.5900	+	10.5900i	0.431977	+	0.431977i	−0.457324	+	0.889300i	$0.651192\pi$
$602$		0			0
$603$	−14.3571	+	2.27395i	−0.584668	+	0.0926023i
$604$		0			0
$605$	−25.2128	+	18.3182i	−1.02505	+	0.744740i
$606$		0			0
$607$	−11.3274	−	15.5908i	−0.459764	−	0.632811i	0.514696	−	0.857373i	$-0.327905\pi$
$607$	−11.3274	−	15.5908i	−0.459764	−	0.632811i	−0.974460	+	0.224562i	$0.927905\pi$
$608$		0			0
$609$	2.64254	−	1.34644i	0.107081	−	0.0545606i
$610$		0			0
$611$	6.19188	+	4.49867i	0.250497	+	0.181997i
$612$		0			0
$613$	11.6005	+	3.76925i	0.468542	+	0.152238i	0.533766	−	0.845632i	$-0.320776\pi$
$613$	11.6005	+	3.76925i	0.468542	+	0.152238i	−0.0652243	+	0.997871i	$0.520776\pi$
$614$		0			0
$615$	−39.0083	+	19.3267i	−1.57297	+	0.779327i
$616$		0			0
$617$	−20.3958	−	6.62699i	−0.821104	−	0.266793i	−0.131810	−	0.991275i	$-0.542079\pi$
$617$	−20.3958	−	6.62699i	−0.821104	−	0.266793i	−0.689293	+	0.724482i	$0.742079\pi$
$618$		0			0
$619$	36.9222	+	26.8256i	1.48403	+	1.07821i	0.976230	+	0.216735i	$0.0695408\pi$
$619$	36.9222	+	26.8256i	1.48403	+	1.07821i	0.507799	+	0.861476i	$0.330459\pi$
$620$		0			0
$621$	−1.11807	+	0.569683i	−0.0448665	+	0.0228606i
$622$		0			0
$623$	0.412769	+	0.568127i	0.0165372	+	0.0227615i
$624$		0			0
$625$	24.8234	−	18.0353i	0.992937	−	0.721411i
$626$		0			0
$627$	5.86437	−	0.928824i	0.234200	−	0.0370937i
$628$		0			0
$629$	−9.29426	−	9.29426i	−0.370586	−	0.370586i
$630$		0			0
$631$	−8.35237	−	25.7059i	−0.332502	−	1.02334i	−0.967939	−	0.251184i	$-0.919180\pi$
$631$	−8.35237	−	25.7059i	−0.332502	−	1.02334i	0.635437	−	0.772153i	$-0.280820\pi$
$632$		0			0
$633$	3.88965	−	11.9711i	0.154600	−	0.475809i
$634$		0			0
$635$	27.9563	−	9.08354i	1.10941	−	0.360469i
$636$		0			0
$637$	4.07454	−	7.99673i	0.161439	−	0.316842i
$638$		0			0
$639$	−17.9897	−	2.84928i	−0.711660	−	0.112716i
$640$		0			0
$641$	2.19761	+	13.8752i	0.0868005	+	0.548037i	0.992317	+	0.123725i	$0.0394840\pi$
$641$	2.19761	+	13.8752i	0.0868005	+	0.548037i	−0.905516	+	0.424312i	$0.860516\pi$
$642$		0			0
$643$	−9.30874	−	18.2694i	−0.367101	−	0.720476i	0.631386	−	0.775469i	$-0.282486\pi$
$643$	−9.30874	−	18.2694i	−0.367101	−	0.720476i	−0.998487	+	0.0549930i	$0.982486\pi$
$644$		0			0
$645$	10.5422	−	66.5607i	0.415098	−	2.62082i
$646$		0			0
$647$		−	15.8806i		−	0.624333i	−0.950027	−	0.312166i	$-0.898945\pi$
$647$		−	15.8806i		−	0.624333i	0.950027	−	0.312166i	$-0.101055\pi$
$648$		0			0
$649$	−2.29242	−	1.16805i	−0.0899854	−	0.0458498i
$650$		0			0
$651$	3.59621	−	4.94976i	0.140947	−	0.193997i
$652$		0			0
$653$	22.9902	−	22.9902i	0.899676	−	0.899676i	−0.0957311	−	0.995407i	$-0.530519\pi$
$653$	22.9902	−	22.9902i	0.899676	−	0.899676i	0.995407	+	0.0957311i	$0.0305189\pi$
$654$		0			0
$655$	29.8222			1.16525
$656$		0			0
$657$	−37.7108			−1.47124
$658$		0			0
$659$	−1.46743	+	1.46743i	−0.0571629	+	0.0571629i	−0.735110	−	0.677947i	$-0.762870\pi$
$659$	−1.46743	+	1.46743i	−0.0571629	+	0.0571629i	0.677947	+	0.735110i	$0.262870\pi$
$660$		0			0
$661$	−18.2310	+	25.0928i	−0.709103	+	0.975997i	0.290713	+	0.956810i	$0.406108\pi$
$661$	−18.2310	+	25.0928i	−0.709103	+	0.975997i	−0.999816	+	0.0191863i	$0.993892\pi$
$662$		0			0
$663$	37.2906	+	19.0005i	1.44825	+	0.737919i
$664$		0			0
$665$			38.8472i			1.50643i
$666$		0			0
$667$	−0.124133	+	0.783747i	−0.00480646	+	0.0303468i
$668$		0			0
$669$	7.53425	+	14.7868i	0.291291	+	0.571691i
$670$		0			0
$671$	0.389406	+	2.45861i	0.0150329	+	0.0949137i
$672$		0			0
$673$	−1.93008	−	0.305695i	−0.0743992	−	0.0117837i	0.119124	−	0.992879i	$-0.461991\pi$
$673$	−1.93008	−	0.305695i	−0.0743992	−	0.0117837i	−0.193523	+	0.981096i	$0.561991\pi$
$674$		0			0
$675$	1.39436	−	2.73659i	0.0536691	−	0.105332i
$676$		0			0
$677$	17.1066	−	5.55828i	0.657461	−	0.213622i	0.0387601	−	0.999249i	$-0.487659\pi$
$677$	17.1066	−	5.55828i	0.657461	−	0.213622i	0.618701	+	0.785626i	$0.287659\pi$
$678$		0			0
$679$	−9.35267	+	28.7846i	−0.358923	+	1.10465i
$680$		0			0
$681$	−14.8285	−	45.6373i	−0.568228	−	1.74883i
$682$		0			0
$683$	11.2813	+	11.2813i	0.431666	+	0.431666i	0.889195	−	0.457529i	$-0.151265\pi$
$683$	11.2813	+	11.2813i	0.431666	+	0.431666i	−0.457529	+	0.889195i	$0.651265\pi$
$684$		0			0
$685$	−10.8914	+	1.72503i	−0.416140	+	0.0659101i
$686$		0			0
$687$	0.644061	−	0.467937i	0.0245724	−	0.0178529i
$688$		0			0
$689$	−10.9921	−	15.1294i	−0.418767	−	0.576383i
$690$		0			0
$691$	−39.1797	+	19.9630i	−1.49046	+	0.759430i	−0.994078	−	0.108672i	$-0.965340\pi$
$691$	−39.1797	+	19.9630i	−1.49046	+	0.759430i	−0.496387	+	0.868102i	$0.665340\pi$
$692$		0			0
$693$	1.71955	+	1.24932i	0.0653202	+	0.0474579i
$694$		0			0
$695$	18.5358	+	6.02265i	0.703104	+	0.228452i
$696$		0			0
$697$	4.75874	+	32.3977i	0.180250	+	1.22715i
$698$		0			0
$699$	29.1738	+	9.47913i	1.10345	+	0.358534i
$700$		0			0
$701$	−2.76681	−	2.01021i	−0.104501	−	0.0759245i	0.534308	−	0.845290i	$-0.320572\pi$
$701$	−2.76681	−	2.01021i	−0.104501	−	0.0759245i	−0.638809	+	0.769366i	$0.720572\pi$
$702$		0			0
$703$	−14.7558	+	7.51844i	−0.556524	+	0.283563i
$704$		0			0
$705$	8.84479	+	12.1738i	0.333114	+	0.458492i
$706$		0			0
$707$	−19.4841	+	14.1561i	−0.732776	+	0.532393i
$708$		0			0
$709$	−4.54201	+	0.719383i	−0.170579	+	0.0270170i	−0.241139	−	0.970490i	$-0.577521\pi$
$709$	−4.54201	+	0.719383i	−0.170579	+	0.0270170i	0.0705608	+	0.997507i	$0.477521\pi$
$710$		0			0
$711$	11.0059	+	11.0059i	0.412752	+	0.412752i
$712$		0			0
$713$	0.505853	+	1.55686i	0.0189443	+	0.0583047i
$714$		0			0
$715$	1.19527	−	3.67868i	0.0447007	−	0.137575i
$716$		0			0
$717$	26.7196	−	8.68173i	0.997862	−	0.324225i
$718$		0			0
$719$	4.48920	−	8.81056i	0.167419	−	0.328578i	−0.792020	−	0.610496i	$-0.790970\pi$
$719$	4.48920	−	8.81056i	0.167419	−	0.328578i	0.959439	+	0.281917i	$0.0909703\pi$
$720$		0			0
$721$	27.1083	+	4.29353i	1.00957	+	0.159899i
$722$		0			0
$723$	−10.0736	−	63.6020i	−0.374640	−	2.36538i
$724$		0			0
$725$	−0.881750	−	1.73053i	−0.0327474	−	0.0642703i
$726$		0			0
$727$	1.74917	−	11.0438i	0.0648730	−	0.409592i	−0.933787	−	0.357831i	$-0.883517\pi$
$727$	1.74917	−	11.0438i	0.0648730	−	0.409592i	0.998659	−	0.0517612i	$-0.0164835\pi$
$728$		0			0
$729$		−	19.4043i		−	0.718678i
$730$		0			0
$731$	−45.1652	−	23.0128i	−1.67050	−	0.851160i
$732$		0			0
$733$	−17.4839	+	24.0645i	−0.645783	+	0.888844i	−0.998907	−	0.0467321i	$-0.985119\pi$
$733$	−17.4839	+	24.0645i	−0.645783	+	0.888844i	0.353124	+	0.935576i	$0.385119\pi$
$734$		0			0
$735$	12.4773	−	12.4773i	0.460232	−	0.460232i
$736$		0			0
$737$	2.17602			0.0801549
$738$		0			0
$739$	−17.1524			−0.630961			−0.315481	−	0.948932i	$-0.602166\pi$
$739$	−17.1524			−0.630961			−0.315481	+	0.948932i	$0.602166\pi$
$740$		0			0
$741$	37.2868	−	37.2868i	1.36976	−	1.36976i
$742$		0			0
$743$	−28.5351	+	39.2752i	−1.04685	+	1.44087i	−0.155343	+	0.987861i	$0.549648\pi$
$743$	−28.5351	+	39.2752i	−1.04685	+	1.44087i	−0.891508	+	0.453006i	$0.850352\pi$
$744$		0			0
$745$	32.6536	+	16.6379i	1.19634	+	0.609564i
$746$		0			0
$747$			40.1160i			1.46777i
$748$		0			0
$749$	−2.26433	+	14.2964i	−0.0827369	+	0.522380i
$750$		0			0
$751$	5.55343	+	10.8992i	0.202647	+	0.397718i	0.969856	−	0.243680i	$-0.0783547\pi$
$751$	5.55343	+	10.8992i	0.202647	+	0.397718i	−0.767208	+	0.641398i	$0.778355\pi$
$752$		0			0
$753$	−0.501657	−	3.16734i	−0.0182814	−	0.115424i
$754$		0			0
$755$	7.62463	+	1.20762i	0.277489	+	0.0439499i
$756$		0			0
$757$	16.8826	−	33.1340i	0.613609	−	1.20427i	−0.349948	−	0.936769i	$-0.613801\pi$
$757$	16.8826	−	33.1340i	0.613609	−	1.20427i	0.963556	−	0.267505i	$-0.0861993\pi$
$758$		0			0
$759$	−1.16467	+	0.378423i	−0.0422747	+	0.0137359i
$760$		0			0
$761$	−2.87532	+	8.84933i	−0.104230	+	0.320788i	−0.989549	−	0.144197i	$-0.953940\pi$
$761$	−2.87532	+	8.84933i	−0.104230	+	0.320788i	0.885319	+	0.464985i	$0.153940\pi$
$762$		0			0
$763$	−5.31514	−	16.3583i	−0.192421	−	0.592211i
$764$		0			0
$765$	27.0199	+	27.0199i	0.976908	+	0.976908i
$766$		0			0
$767$	−22.5685	+	3.57449i	−0.814900	+	0.129067i
$768$		0			0
$769$	−32.0673	+	23.2983i	−1.15638	+	0.840157i	−0.989316	−	0.145789i	$-0.953428\pi$
$769$	−32.0673	+	23.2983i	−1.15638	+	0.840157i	−0.167062	+	0.985946i	$0.553428\pi$
$770$		0			0
$771$	7.34954	+	10.1158i	0.264687	+	0.364311i
$772$		0			0
$773$	−36.3471	+	18.5198i	−1.30731	+	0.666109i	−0.962172	−	0.272441i	$-0.912169\pi$
$773$	−36.3471	+	18.5198i	−1.30731	+	0.666109i	−0.345141	+	0.938551i	$0.612169\pi$
$774$		0			0
$775$	−3.24147	−	2.35507i	−0.116437	−	0.0845965i
$776$		0			0
$777$	−12.1413	−	3.94495i	−0.435567	−	0.141524i
$778$		0			0
$779$	40.6742	+	6.91155i	1.45730	+	0.247632i
$780$		0			0
$781$	2.59313	+	0.842560i	0.0927896	+	0.0301492i
$782$		0			0
$783$	0.456138	+	0.331404i	0.0163010	+	0.0118434i
$784$		0			0
$785$	−26.5843	+	13.5454i	−0.948836	+	0.483456i
$786$		0			0
$787$	2.16421	+	2.97878i	0.0771457	+	0.106182i	0.845846	−	0.533427i	$-0.179096\pi$
$787$	2.16421	+	2.97878i	0.0771457	+	0.106182i	−0.768700	+	0.639609i	$0.779096\pi$
$788$		0			0
$789$	4.51851	−	3.28289i	0.160863	−	0.116874i
$790$		0			0
$791$	−7.49145	+	1.18653i	−0.266365	+	0.0421881i
$792$		0			0
$793$	15.6323	+	15.6323i	0.555121	+	0.555121i
$794$		0			0
$795$	−11.3619	−	34.9682i	−0.402964	−	1.24019i
$796$		0			0
$797$	13.3156	−	40.9813i	0.471664	−	1.45163i	−0.378740	−	0.925503i	$-0.623643\pi$
$797$	13.3156	−	40.9813i	0.471664	−	1.45163i	0.850404	−	0.526130i	$-0.176357\pi$
$798$		0			0
$799$	10.7647	−	3.49765i	0.380827	−	0.123738i
$800$		0			0
$801$	0.395116	−	0.775459i	0.0139607	−	0.0273995i
$802$		0			0
$803$	5.57572	+	0.883107i	0.196763	+	0.0311642i
$804$		0			0
$805$	−1.25339	−	7.91359i	−0.0441762	−	0.278918i
$806$		0			0
$807$	18.1553	+	35.6317i	0.639096	+	1.25430i
$808$		0			0
$809$	−2.96962	+	18.7494i	−0.104406	+	0.659195i	0.878868	+	0.477065i	$0.158299\pi$
$809$	−2.96962	+	18.7494i	−0.104406	+	0.659195i	−0.983274	+	0.182130i	$0.941701\pi$
$810$		0			0
$811$		−	8.79807i		−	0.308942i	−0.987997	−	0.154471i	$-0.950633\pi$
$811$		−	8.79807i		−	0.308942i	0.987997	−	0.154471i	$-0.0493673\pi$
$812$		0			0
$813$	−44.6357	−	22.7430i	−1.56544	−	0.797633i
$814$		0			0
$815$	5.88740	−	8.10330i	0.206226	−	0.283846i
$816$		0			0
$817$	−45.1606	+	45.1606i	−1.57997	+	1.57997i
$818$		0			0
$819$	18.8767			0.659604
$820$		0			0
$821$	−54.2917			−1.89479			−0.947397	−	0.320060i	$-0.896297\pi$
$821$	−54.2917			−1.89479			−0.947397	+	0.320060i	$0.896297\pi$
$822$		0			0
$823$	−2.69668	+	2.69668i	−0.0940004	+	0.0940004i	−0.752543	−	0.658543i	$-0.771173\pi$
$823$	−2.69668	+	2.69668i	−0.0940004	+	0.0940004i	0.658543	+	0.752543i	$0.271173\pi$
$824$		0			0
$825$	1.76180	−	2.42491i	0.0613379	−	0.0844244i
$826$		0			0
$827$	26.9294	+	13.7212i	0.936428	+	0.477134i	0.854469	−	0.519502i	$-0.173882\pi$
$827$	26.9294	+	13.7212i	0.936428	+	0.477134i	0.0819589	+	0.996636i	$0.473882\pi$
$828$		0			0
$829$		−	42.4307i		−	1.47368i	−0.676067	−	0.736840i	$-0.736317\pi$
$829$		−	42.4307i		−	1.47368i	0.676067	−	0.736840i	$-0.263683\pi$
$830$		0			0
$831$	−4.22084	+	26.6493i	−0.146419	+	0.924455i
$832$		0			0
$833$	−6.02570	−	11.8261i	−0.208778	−	0.409750i
$834$		0			0
$835$	−8.78629	−	55.4744i	−0.304062	−	1.91977i
$836$		0			0
$837$	1.14880	+	0.181952i	0.0397083	+	0.00628918i
$838$		0			0
$839$	−4.77141	+	9.36443i	−0.164728	+	0.323296i	−0.958584	−	0.284809i	$-0.908070\pi$
$839$	−4.77141	+	9.36443i	−0.164728	+	0.323296i	0.793857	+	0.608105i	$0.208070\pi$
$840$		0			0
$841$	−27.2415	+	8.85132i	−0.939364	+	0.305218i
$842$		0			0
$843$	19.7795	−	60.8750i	0.681241	−	2.09665i
$844$		0			0
$845$	0.925081	+	2.84711i	0.0318237	+	0.0979434i
$846$		0			0
$847$	16.0992	+	16.0992i	0.553175	+	0.553175i
$848$		0			0
$849$	26.2266	−	4.15389i	0.900096	−	0.142561i
$850$		0			0
$851$	2.76333	−	2.00767i	0.0947256	−	0.0688222i
$852$		0			0
$853$	25.0919	+	34.5360i	0.859131	+	1.18249i	0.981776	+	0.190041i	$0.0608622\pi$
$853$	25.0919	+	34.5360i	0.859131	+	1.18249i	−0.122646	+	0.992451i	$0.539138\pi$
$854$		0			0
$855$	42.8974	−	21.8573i	1.46706	−	0.747505i
$856$		0			0
$857$	−0.509355	−	0.370068i	−0.0173992	−	0.0126413i	0.579052	−	0.815291i	$-0.303423\pi$
$857$	−0.509355	−	0.370068i	−0.0173992	−	0.0126413i	−0.596451	+	0.802650i	$0.703423\pi$
$858$		0			0
$859$	−6.63785	−	2.15677i	−0.226480	−	0.0735880i	0.193578	−	0.981085i	$-0.437991\pi$
$859$	−6.63785	−	2.15677i	−0.226480	−	0.0735880i	−0.420059	+	0.907497i	$0.637991\pi$
$860$		0			0
$861$	18.4035	+	25.9383i	0.627189	+	0.883973i
$862$		0			0
$863$	−33.7819	−	10.9764i	−1.14995	−	0.373641i	−0.328826	−	0.944391i	$-0.606653\pi$
$863$	−33.7819	−	10.9764i	−1.14995	−	0.373641i	−0.821124	+	0.570749i	$0.806653\pi$
$864$		0			0
$865$	28.0916	+	20.4098i	0.955143	+	0.693952i
$866$		0			0
$867$	19.3000	−	9.83386i	0.655464	−	0.333975i
$868$		0			0
$869$	−1.36954	−	1.88500i	−0.0464583	−	0.0639444i
$870$		0			0
$871$	15.6347	−	11.3593i	0.529762	−	0.384895i
$872$		0			0
$873$	37.0479	−	5.86781i	1.25388	−	0.198595i
$874$		0			0
$875$	−7.44908	−	7.44908i	−0.251825	−	0.251825i
$876$		0			0
$877$	5.53033	+	17.0206i	0.186746	+	0.574745i	0.999974	−	0.00720030i	$-0.00229195\pi$
$877$	5.53033	+	17.0206i	0.186746	+	0.574745i	−0.813228	+	0.581945i	$0.802292\pi$
$878$		0			0
$879$	15.8540	−	48.7937i	0.534743	−	1.64577i
$880$		0			0
$881$	20.2237	−	6.57108i	0.681354	−	0.221385i	0.0521659	−	0.998638i	$-0.483388\pi$
$881$	20.2237	−	6.57108i	0.681354	−	0.221385i	0.629188	+	0.777253i	$0.283388\pi$
$882$		0			0
$883$	−18.3180	+	35.9511i	−0.616449	+	1.20985i	0.345961	+	0.938249i	$0.387553\pi$
$883$	−18.3180	+	35.9511i	−0.616449	+	1.20985i	−0.962410	+	0.271601i	$0.912447\pi$
$884$		0			0
$885$	−44.3717	−	7.02778i	−1.49154	−	0.236236i
$886$		0			0
$887$	3.95846	+	24.9927i	0.132912	+	0.839174i	0.960590	+	0.277970i	$0.0896617\pi$
$887$	3.95846	+	24.9927i	0.132912	+	0.839174i	−0.827678	+	0.561204i	$0.810338\pi$
$888$		0			0
$889$	−9.74934	−	19.1341i	−0.326982	−	0.641739i
$890$		0			0
$891$	−0.611404	+	3.86025i	−0.0204828	+	0.129323i
$892$		0			0
$893$		−	14.2609i		−	0.477221i
$894$		0			0
$895$	5.10285	+	2.60003i	0.170569	+	0.0869095i
$896$		0			0
$897$	−6.39267	+	8.79876i	−0.213445	+	0.293782i
$898$		0			0
$899$	0.520090	−	0.520090i	0.0173460	−	0.0173460i
$900$		0			0
$901$	−27.6562			−0.921362
$902$		0			0
$903$	−49.2326			−1.63836
$904$		0			0
$905$	32.9781	−	32.9781i	1.09623	−	1.09623i
$906$		0			0
$907$	−23.2631	+	32.0189i	−0.772438	+	1.06317i	0.223638	+	0.974672i	$0.428207\pi$
$907$	−23.2631	+	32.0189i	−0.772438	+	1.06317i	−0.996076	+	0.0884974i	$0.971793\pi$
$908$		0			0
$909$	26.5947	+	13.5507i	0.882089	+	0.449447i
$910$		0			0
$911$		−	34.8374i		−	1.15422i	−0.816668	−	0.577108i	$-0.804181\pi$
$911$		−	34.8374i		−	1.15422i	0.816668	−	0.577108i	$-0.195819\pi$
$912$		0			0
$913$	0.939433	−	5.93135i	0.0310907	−	0.196299i
$914$		0			0
$915$	19.7328	+	38.7279i	0.652347	+	1.28030i
$916$		0			0
$917$	−3.40821	−	21.5186i	−0.112549	−	0.710607i
$918$		0			0
$919$	23.4135	+	3.70833i	0.772339	+	0.122326i	0.530151	−	0.847903i	$-0.322135\pi$
$919$	23.4135	+	3.70833i	0.772339	+	0.122326i	0.242187	+	0.970229i	$0.422135\pi$
$920$		0			0
$921$	18.5923	−	36.4894i	0.612636	−	1.20237i
$922$		0			0
$923$	23.0300	−	7.48290i	0.758041	−	0.246303i
$924$		0			0
$925$	−2.58345	+	7.95103i	−0.0849432	+	0.261428i
$926$		0			0
$927$	−10.5113	−	32.3503i	−0.345235	−	1.06252i
$928$		0			0
$929$	−13.5134	−	13.5134i	−0.443359	−	0.443359i	0.449780	−	0.893139i	$-0.351502\pi$
$929$	−13.5134	−	13.5134i	−0.443359	−	0.443359i	−0.893139	+	0.449780i	$0.851502\pi$
$930$		0			0
$931$	−16.5170	+	2.61604i	−0.541324	+	0.0857372i
$932$		0			0
$933$	23.1491	−	16.8188i	0.757869	−	0.550624i
$934$		0			0
$935$	−3.36228	−	4.62778i	−0.109958	−	0.151344i
$936$		0			0
$937$	−25.3987	+	12.9413i	−0.829739	+	0.422773i	−0.816644	−	0.577141i	$-0.804168\pi$
$937$	−25.3987	+	12.9413i	−0.829739	+	0.422773i	−0.0130943	+	0.999914i	$0.504168\pi$
$938$		0			0
$939$	−41.5074	−	30.1569i	−1.35454	−	0.984132i
$940$		0			0
$941$	6.31488	+	2.05183i	0.205859	+	0.0668877i	0.410131	−	0.912026i	$-0.365483\pi$
$941$	6.31488	+	2.05183i	0.205859	+	0.0668877i	−0.204272	+	0.978914i	$0.565483\pi$
$942$		0			0
$943$	−8.50877	−	0.0956191i	−0.277084	−	0.00311379i
$944$		0			0
$945$	−5.41430	−	1.75921i	−0.176127	−	0.0572272i
$946$		0			0
$947$	24.7639	+	17.9920i	0.804719	+	0.584663i	0.912295	−	0.409534i	$-0.134309\pi$
$947$	24.7639	+	17.9920i	0.804719	+	0.584663i	−0.107575	+	0.994197i	$0.534309\pi$
$948$		0			0
$949$	44.6715	−	22.7613i	1.45010	−	0.738862i
$950$		0			0
$951$	27.5194	+	37.8772i	0.892379	+	1.22825i
$952$		0			0
$953$	−20.8531	+	15.1507i	−0.675499	+	0.490778i	−0.871861	−	0.489753i	$-0.837087\pi$
$953$	−20.8531	+	15.1507i	−0.675499	+	0.490778i	0.196363	+	0.980531i	$0.437087\pi$
$954$		0			0
$955$	15.6962	−	2.48603i	0.507917	−	0.0804461i
$956$		0			0
$957$	0.389074	+	0.389074i	0.0125770	+	0.0125770i
$958$		0			0
$959$	2.48944	+	7.66172i	0.0803883	+	0.247410i
$960$		0			0
$961$	−9.11065	+	28.0397i	−0.293892	+	0.904506i
$962$		0			0
$963$	17.0610	−	5.54345i	0.549783	−	0.178635i
$964$		0			0
$965$	10.9723	−	21.5344i	0.353211	−	0.693217i
$966$		0			0
$967$	−23.6731	−	3.74945i	−0.761274	−	0.120574i	−0.236286	−	0.971684i	$-0.575930\pi$
$967$	−23.6731	−	3.74945i	−0.761274	−	0.120574i	−0.524988	+	0.851109i	$0.675930\pi$
$968$		0			0
$969$	−12.1992	−	77.0228i	−0.391895	−	2.47433i
$970$		0			0
$971$	−5.16430	−	10.1355i	−0.165730	−	0.325264i	0.793173	−	0.608996i	$-0.208427\pi$
$971$	−5.16430	−	10.1355i	−0.165730	−	0.325264i	−0.958904	+	0.283732i	$0.908427\pi$
$972$		0			0
$973$	2.22737	−	14.0631i	0.0714063	−	0.450842i
$974$		0			0
$975$		−	26.6199i		−	0.852519i
$976$		0			0
$977$	31.3256	+	15.9612i	1.00219	+	0.510644i	0.876488	−	0.481424i	$-0.159880\pi$
$977$	31.3256	+	15.9612i	1.00219	+	0.510644i	0.125707	+	0.992067i	$0.459880\pi$
$978$		0			0
$979$	−0.0765795	+	0.105403i	−0.00244749	+	0.00336868i
$980$		0			0
$981$	−15.0733	+	15.0733i	−0.481253	+	0.481253i
$982$		0			0
$983$	−58.6885			−1.87187			−0.935937	−	0.352169i	$-0.885444\pi$
$983$	−58.6885			−1.87187			−0.935937	+	0.352169i	$0.885444\pi$
$984$		0			0
$985$	75.3104			2.39959
$986$		0			0
$987$	7.77337	−	7.77337i	0.247429	−	0.247429i
$988$		0			0
$989$	7.74260	−	10.6568i	0.246200	−	0.338866i
$990$		0			0
$991$	47.5172	+	24.2112i	1.50943	+	0.769095i	0.996027	−	0.0890509i	$-0.0283834\pi$
$991$	47.5172	+	24.2112i	1.50943	+	0.769095i	0.513406	+	0.858146i	$0.328383\pi$
$992$		0			0
$993$			68.2617i			2.16622i
$994$		0			0
$995$	5.07811	−	32.0619i	0.160987	−	1.01643i
$996$		0			0
$997$	20.4658	+	40.1663i	0.648157	+	1.27208i	0.948054	+	0.318108i	$0.103048\pi$
$997$	20.4658	+	40.1663i	0.648157	+	1.27208i	−0.299897	+	0.953971i	$0.596952\pi$
$998$		0			0
$999$	−0.379655	−	2.39705i	−0.0120118	−	0.0758393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.bs.d.225.3		24
4.3	odd	2		41.2.g.a.20.1	✓	24
12.11	even	2		369.2.u.a.307.3		24
41.39	even	20	inner	656.2.bs.d.449.3		24
164.11	even	40		1681.2.a.m.1.1		24
164.39	odd	20		41.2.g.a.39.1	yes	24
164.71	even	40		1681.2.a.m.1.2		24
492.203	even	20		369.2.u.a.244.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.1	✓	24	4.3	odd	2
41.2.g.a.39.1	yes	24	164.39	odd	20
369.2.u.a.244.3		24	492.203	even	20
369.2.u.a.307.3		24	12.11	even	2
656.2.bs.d.225.3		24	1.1	even	1	trivial
656.2.bs.d.449.3		24	41.39	even	20	inner
1681.2.a.m.1.1		24	164.11	even	40
1681.2.a.m.1.2		24	164.71	even	40

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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.bs (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.67347 - 1.67347i) q^{3} +(-1.68856 + 2.32411i) q^{5} +(1.86997 + 0.952797i) q^{7} -2.60102i q^{9} +O(q^{10})\)	\(q+(1.67347 - 1.67347i) q^{3} +(-1.68856 + 2.32411i) q^{5} +(1.86997 + 0.952797i) q^{7} -2.60102i q^{9} +(-0.0609104 + 0.384573i) q^{11} +(1.56991 + 3.08112i) q^{13} +(1.06357 + 6.71509i) q^{15} +(5.05100 + 0.800000i) q^{17} +(2.92520 - 5.74102i) q^{19} +(4.72382 - 1.53486i) q^{21} +(-0.410662 + 1.26389i) q^{23} +(-1.00514 - 3.09351i) q^{25} +(0.667682 + 0.667682i) q^{27} +(0.589758 - 0.0934085i) q^{29} +(0.996546 - 0.724033i) q^{31} +(0.541641 + 0.745505i) q^{33} +(-5.37196 + 2.73715i) q^{35} +(-2.07936 - 1.51074i) q^{37} +(7.78337 + 2.52897i) q^{39} +(1.91012 + 6.11158i) q^{41} +(-9.42697 - 3.06301i) q^{43} +(6.04504 + 4.39198i) q^{45} +(1.97205 - 1.00481i) q^{47} +(-1.52553 - 2.09972i) q^{49} +(9.79148 - 7.11393i) q^{51} +(-5.34140 + 0.845995i) q^{53} +(-0.790938 - 0.790938i) q^{55} +(-4.71221 - 14.5027i) q^{57} +(-2.04191 + 6.28435i) q^{59} +(6.08019 - 1.97557i) q^{61} +(2.47824 - 4.86383i) q^{63} +(-9.81174 - 1.55403i) q^{65} +(-0.874252 - 5.51981i) q^{67} +(1.42785 + 2.80231i) q^{69} +(1.09545 - 6.91639i) q^{71} -14.4984i q^{73} +(-6.85898 - 3.49482i) q^{75} +(-0.480321 + 0.661105i) q^{77} +(-4.23136 + 4.23136i) q^{79} +10.0378 q^{81} -15.4232 q^{83} +(-10.3882 + 10.3882i) q^{85} +(0.830627 - 1.14326i) q^{87} +(0.298137 + 0.151908i) q^{89} +7.25741i q^{91} +(0.456043 - 2.87934i) q^{93} +(8.40337 + 16.4925i) q^{95} +(2.25597 + 14.2436i) q^{97} +(1.00028 + 0.158429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7}+O(q^{10}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7	\( 24 q + 6 q^{3} - 10 q^{5} + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{17} - 16 q^{19} - 10 q^{21} - 12 q^{23} - 8 q^{25} + 6 q^{27} + 40 q^{29} + 12 q^{31} + 10 q^{33} + 36 q^{35} + 50 q^{39} - 4 q^{41} + 16 q^{45} + 12 q^{47} - 30 q^{49} + 24 q^{51} - 26 q^{53} - 20 q^{55} + 10 q^{57} - 6 q^{59} + 30 q^{61} - 92 q^{63} + 68 q^{65} + 22 q^{67} - 38 q^{69} - 4 q^{71} - 4 q^{75} - 20 q^{77} + 2 q^{79} + 28 q^{81} - 80 q^{83} - 56 q^{85} + 10 q^{87} - 72 q^{89} - 6 q^{93} + 40 q^{95} - 22 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 10 * q^5 + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^17 - 16 * q^19 - 10 * q^21 - 12 * q^23 - 8 * q^25 + 6 * q^27 + 40 * q^29 + 12 * q^31 + 10 * q^33 + 36 * q^35 + 50 * q^39 - 4 * q^41 + 16 * q^45 + 12 * q^47 - 30 * q^49 + 24 * q^51 - 26 * q^53 - 20 * q^55 + 10 * q^57 - 6 * q^59 + 30 * q^61 - 92 * q^63 + 68 * q^65 + 22 * q^67 - 38 * q^69 - 4 * q^71 - 4 * q^75 - 20 * q^77 + 2 * q^79 + 28 * q^81 - 80 * q^83 - 56 * q^85 + 10 * q^87 - 72 * q^89 - 6 * q^93 + 40 * q^95 - 22 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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