LMFDB - Embedded newform 810.2.f.c.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(323,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("810.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.f (of order $4$, degree $2$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.7
Root			$0.500000 - 2.00333i$ of defining polynomial
Character	$\chi$	$=$	810.647
Dual form			810.2.f.c.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.930573 - 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.930573 - 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +1.96950i q^{11} +(2.87542 - 2.87542i) q^{13} -2.01658 q^{14} -1.00000 q^{16} +(-2.35877 + 2.35877i) q^{17} -3.70753i q^{19} +(-2.03323 + 0.930573i) q^{20} +(1.39264 + 1.39264i) q^{22} +(-4.43138 - 4.43138i) q^{23} +(-3.26807 + 3.78414i) q^{25} -4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} -7.49726 q^{29} -6.97674 q^{31} +(-0.707107 + 0.707107i) q^{32} +3.33580i q^{34} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-2.62162 - 2.62162i) q^{38} +(-0.779698 + 2.09573i) q^{40} +7.08526i q^{41} +(6.65957 - 6.65957i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(5.48696 - 5.48696i) q^{47} -2.93342i q^{49} +(0.364918 + 4.98667i) q^{50} +(-2.87542 - 2.87542i) q^{52} +(-7.03027 - 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +2.01658i q^{56} +(-5.30136 + 5.30136i) q^{58} +2.69933 q^{59} +8.74707 q^{61} +(-4.93330 + 4.93330i) q^{62} +1.00000i q^{64} +(-8.52220 - 3.17062i) q^{65} +(5.99026 + 5.99026i) q^{67} +(2.35877 + 2.35877i) q^{68} +(1.87657 + 4.10017i) q^{70} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +6.03434 q^{74} -3.70753 q^{76} +(2.80837 - 2.80837i) q^{77} -11.6088i q^{79} +(0.930573 + 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(1.20473 + 1.20473i) q^{83} +(6.99092 + 2.60092i) q^{85} -9.41805i q^{86} +(1.39264 - 1.39264i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(-4.43138 + 4.43138i) q^{92} -7.75974i q^{94} +(-7.53826 + 3.45012i) q^{95} +(7.11484 + 7.11484i) q^{97} +(-2.07424 - 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{7}+O(q^{10}) $ 16 * q - 16 * q^7	$ 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82} + 8 q^{85} - 16 q^{88} + 96 q^{97}+O(q^{100}) $ 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.930573	−	2.03323i	−0.416165	−	0.909289i
$5$	−0.930573	−	2.03323i	−0.416165	−	0.909289i
$6$		0			0
$7$	−1.42594	−	1.42594i	−0.538953	−	0.538953i	0.384269	−	0.923221i	$-0.374454\pi$
$7$	−1.42594	−	1.42594i	−0.538953	−	0.538953i	−0.923221	+	0.384269i	$0.874454\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.09573	−	0.779698i	−0.662727	−	0.246562i
$11$			1.96950i			0.593825i	0.954905	+	0.296913i	$0.0959570\pi$
$11$			1.96950i			0.593825i	−0.954905	+	0.296913i	$0.904043\pi$
$12$		0			0
$13$	2.87542	−	2.87542i	0.797499	−	0.797499i	−0.185201	−	0.982701i	$-0.559294\pi$
$13$	2.87542	−	2.87542i	0.797499	−	0.797499i	0.982701	+	0.185201i	$0.0592937\pi$
$14$	−2.01658			−0.538953
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	−0.932711	−	0.360626i	$-0.882563\pi$
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	0.360626	+	0.932711i	$0.382563\pi$
$18$		0			0
$19$		−	3.70753i		−	0.850565i	−0.905061	−	0.425282i	$-0.860175\pi$
$19$		−	3.70753i		−	0.850565i	0.905061	−	0.425282i	$-0.139825\pi$
$20$	−2.03323	+	0.930573i	−0.454645	+	0.208082i
$21$		0			0
$22$	1.39264	+	1.39264i	0.296913	+	0.296913i
$23$	−4.43138	−	4.43138i	−0.924007	−	0.924007i	0.0733025	−	0.997310i	$-0.476646\pi$
$23$	−4.43138	−	4.43138i	−0.924007	−	0.924007i	−0.997310	+	0.0733025i	$0.976646\pi$
$24$		0			0
$25$	−3.26807	+	3.78414i	−0.653614	+	0.756828i
$26$		−	4.06647i		−	0.797499i
$27$		0			0
$28$	−1.42594	+	1.42594i	−0.269476	+	0.269476i
$29$	−7.49726			−1.39221			−0.696103	−	0.717942i	$-0.745084\pi$
$29$	−7.49726			−1.39221			−0.696103	+	0.717942i	$0.745084\pi$
$30$		0			0
$31$	−6.97674			−1.25306			−0.626530	−	0.779397i	$-0.715525\pi$
$31$	−6.97674			−1.25306			−0.626530	+	0.779397i	$0.715525\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			3.33580i			0.572085i
$35$	−1.57232	+	4.22619i	−0.265771	+	0.714357i
$36$		0			0
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	0.964728	−	0.263250i	$-0.0847944\pi$
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	−0.263250	+	0.964728i	$0.584794\pi$
$38$	−2.62162	−	2.62162i	−0.425282	−	0.425282i
$39$		0			0
$40$	−0.779698	+	2.09573i	−0.123281	+	0.331363i
$41$			7.08526i			1.10653i	0.833005	+	0.553266i	$0.186619\pi$
$41$			7.08526i			1.10653i	−0.833005	+	0.553266i	$0.813381\pi$
$42$		0			0
$43$	6.65957	−	6.65957i	1.01557	−	1.01557i	0.0156976	−	0.999877i	$-0.495003\pi$
$43$	6.65957	−	6.65957i	1.01557	−	1.01557i	0.999877	−	0.0156976i	$-0.00499689\pi$
$44$	1.96950			0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	5.48696	−	5.48696i	0.800356	−	0.800356i	−0.182795	−	0.983151i	$-0.558515\pi$
$47$	5.48696	−	5.48696i	0.800356	−	0.800356i	0.983151	+	0.182795i	$0.0585146\pi$
$48$		0			0
$49$		−	2.93342i		−	0.419060i
$50$	0.364918	+	4.98667i	0.0516072	+	0.705221i
$51$		0			0
$52$	−2.87542	−	2.87542i	−0.398750	−	0.398750i
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	0.0337485	−	0.999430i	$-0.489255\pi$
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	−0.999430	+	0.0337485i	$0.989255\pi$
$54$		0			0
$55$	4.00444	−	1.83276i	0.539959	−	0.247129i
$56$			2.01658i			0.269476i
$57$		0			0
$58$	−5.30136	+	5.30136i	−0.696103	+	0.696103i
$59$	2.69933			0.351423			0.175712	−	0.984442i	$-0.443777\pi$
$59$	2.69933			0.351423			0.175712	+	0.984442i	$0.443777\pi$
$60$		0			0
$61$	8.74707			1.11995			0.559973	−	0.828511i	$-0.310811\pi$
$61$	8.74707			1.11995			0.559973	+	0.828511i	$0.310811\pi$
$62$	−4.93330	+	4.93330i	−0.626530	+	0.626530i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−8.52220	−	3.17062i	−1.05705	−	0.393266i
$66$		0			0
$67$	5.99026	+	5.99026i	0.731827	+	0.731827i	0.970982	−	0.239154i	$-0.0768702\pi$
$67$	5.99026	+	5.99026i	0.731827	+	0.731827i	−0.239154	+	0.970982i	$0.576870\pi$
$68$	2.35877	+	2.35877i	0.286042	+	0.286042i
$69$		0			0
$70$	1.87657	+	4.10017i	0.224293	+	0.490064i
$71$		−	5.68481i		−	0.674663i	−0.941386	−	0.337332i	$-0.890476\pi$
$71$		−	5.68481i		−	0.674663i	0.941386	−	0.337332i	$-0.109524\pi$
$72$		0			0
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	−0.636645	−	0.771157i	$-0.719678\pi$
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	0.771157	+	0.636645i	$0.219678\pi$
$74$	6.03434			0.701478
$75$		0			0
$76$	−3.70753			−0.425282
$77$	2.80837	−	2.80837i	0.320044	−	0.320044i
$78$		0			0
$79$		−	11.6088i		−	1.30609i	−0.757318	−	0.653046i	$-0.773491\pi$
$79$		−	11.6088i		−	1.30609i	0.757318	−	0.653046i	$-0.226509\pi$
$80$	0.930573	+	2.03323i	0.104041	+	0.227322i
$81$		0			0
$82$	5.01003	+	5.01003i	0.553266	+	0.553266i
$83$	1.20473	+	1.20473i	0.132236	+	0.132236i	0.770127	−	0.637891i	$-0.220193\pi$
$83$	1.20473	+	1.20473i	0.132236	+	0.132236i	−0.637891	+	0.770127i	$0.720193\pi$
$84$		0			0
$85$	6.99092	+	2.60092i	0.758272	+	0.282109i
$86$		−	9.41805i		−	1.01557i
$87$		0			0
$88$	1.39264	−	1.39264i	0.148456	−	0.148456i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	−4.43138	+	4.43138i	−0.462004	+	0.462004i
$93$		0			0
$94$		−	7.75974i		−	0.800356i
$95$	−7.53826	+	3.45012i	−0.773409	+	0.353975i
$96$		0			0
$97$	7.11484	+	7.11484i	0.722402	+	0.722402i	0.969094	−	0.246692i	$-0.0793435\pi$
$97$	7.11484	+	7.11484i	0.722402	+	0.722402i	−0.246692	+	0.969094i	$0.579343\pi$
$98$	−2.07424	−	2.07424i	−0.209530	−	0.209530i
$99$		0			0
$100$	3.78414	+	3.26807i	0.378414	+	0.326807i
$101$			4.72288i			0.469944i	0.972002	+	0.234972i	$0.0754999\pi$
$101$			4.72288i			0.469944i	−0.972002	+	0.234972i	$0.924500\pi$
$102$		0			0
$103$	2.83210	−	2.83210i	0.279055	−	0.279055i	−0.553677	−	0.832732i	$-0.686776\pi$
$103$	2.83210	−	2.83210i	0.279055	−	0.279055i	0.832732	+	0.553677i	$0.186776\pi$
$104$	−4.06647			−0.398750
$105$		0			0
$106$	−9.94230			−0.965682
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	−0.395949	−	0.918273i	$-0.629584\pi$
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	0.918273	+	0.395949i	$0.129584\pi$
$108$		0			0
$109$		−	4.35357i		−	0.416996i	−0.978023	−	0.208498i	$-0.933142\pi$
$109$		−	4.35357i		−	0.416996i	0.978023	−	0.208498i	$-0.0668575\pi$
$110$	1.53561	−	4.12753i	0.146415	−	0.393544i
$111$		0			0
$112$	1.42594	+	1.42594i	0.134738	+	0.134738i
$113$	2.09697	+	2.09697i	0.197266	+	0.197266i	0.798827	−	0.601561i	$-0.205454\pi$
$113$	2.09697	+	2.09697i	0.197266	+	0.197266i	−0.601561	+	0.798827i	$0.705454\pi$
$114$		0			0
$115$	−4.88631	+	13.1338i	−0.455651	+	1.22473i
$116$			7.49726i			0.696103i
$117$		0			0
$118$	1.90872	−	1.90872i	0.175712	−	0.175712i
$119$	6.72689			0.616653
$120$		0			0
$121$	7.12109			0.647371
$122$	6.18511	−	6.18511i	0.559973	−	0.559973i
$123$		0			0
$124$			6.97674i			0.626530i
$125$	10.7352	+	3.12333i	0.960187	+	0.279359i
$126$		0			0
$127$	−3.41734	−	3.41734i	−0.303240	−	0.303240i	0.539040	−	0.842280i	$-0.318787\pi$
$127$	−3.41734	−	3.41734i	−0.303240	−	0.303240i	−0.842280	+	0.539040i	$0.818787\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−8.26807	+	3.78414i	−0.725158	+	0.331891i
$131$		−	0.474890i		−	0.0414913i	−0.999785	−	0.0207457i	$-0.993396\pi$
$131$		−	0.474890i		−	0.0414913i	0.999785	−	0.0207457i	$-0.00660403\pi$
$132$		0			0
$133$	−5.28669	+	5.28669i	−0.458414	+	0.458414i
$134$	8.47151			0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	6.96632	−	6.96632i	0.595173	−	0.595173i	−0.343851	−	0.939024i	$-0.611732\pi$
$137$	6.96632	−	6.96632i	0.595173	−	0.595173i	0.939024	+	0.343851i	$0.111732\pi$
$138$		0			0
$139$		−	0.702425i		−	0.0595789i	−0.999556	−	0.0297894i	$-0.990516\pi$
$139$		−	0.702425i		−	0.0595789i	0.999556	−	0.0297894i	$-0.00948368\pi$
$140$	4.22619	+	1.57232i	0.357179	+	0.132885i
$141$		0			0
$142$	−4.01977	−	4.01977i	−0.337332	−	0.337332i
$143$	5.66314	+	5.66314i	0.473575	+	0.473575i
$144$		0			0
$145$	6.97674	+	15.2437i	0.579387	+	1.26592i
$146$		−	1.62532i		−	0.134513i
$147$		0			0
$148$	4.26692	−	4.26692i	0.350739	−	0.350739i
$149$	8.11219			0.664576			0.332288	−	0.943178i	$-0.392179\pi$
$149$	8.11219			0.664576			0.332288	+	0.943178i	$0.392179\pi$
$150$		0			0
$151$	−9.23478			−0.751516			−0.375758	−	0.926718i	$-0.622618\pi$
$151$	−9.23478			−0.751516			−0.375758	+	0.926718i	$0.622618\pi$
$152$	−2.62162	+	2.62162i	−0.212641	+	0.212641i
$153$		0			0
$154$		−	3.97164i		−	0.320044i
$155$	6.49237	+	14.1853i	0.521479	+	1.13939i
$156$		0			0
$157$	−7.67538	−	7.67538i	−0.612562	−	0.612562i	0.331051	−	0.943613i	$-0.392597\pi$
$157$	−7.67538	−	7.67538i	−0.612562	−	0.612562i	−0.943613	+	0.331051i	$0.892597\pi$
$158$	−8.20866	−	8.20866i	−0.653046	−	0.653046i
$159$		0			0
$160$	2.09573	+	0.779698i	0.165682	+	0.0616406i
$161$			12.6377i			0.995993i
$162$		0			0
$163$	9.68197	−	9.68197i	0.758351	−	0.758351i	−0.217671	−	0.976022i	$-0.569846\pi$
$163$	9.68197	−	9.68197i	0.758351	−	0.758351i	0.976022	+	0.217671i	$0.0698461\pi$
$164$	7.08526			0.553266
$165$		0			0
$166$	1.70374			0.132236
$167$	−3.61325	+	3.61325i	−0.279602	+	0.279602i	−0.832950	−	0.553348i	$-0.813350\pi$
$167$	−3.61325	+	3.61325i	−0.279602	+	0.279602i	0.553348	+	0.832950i	$0.313350\pi$
$168$		0			0
$169$		−	3.53614i		−	0.272011i
$170$	6.78245	−	3.10420i	0.520190	−	0.238081i
$171$		0			0
$172$	−6.65957	−	6.65957i	−0.507787	−	0.507787i
$173$	5.24323	+	5.24323i	0.398636	+	0.398636i	0.877752	−	0.479116i	$-0.159043\pi$
$173$	5.24323	+	5.24323i	0.398636	+	0.398636i	−0.479116	+	0.877752i	$0.659043\pi$
$174$		0			0
$175$	10.0560	−	0.735886i	0.760162	−	0.0556277i
$176$		−	1.96950i		−	0.148456i
$177$		0			0
$178$	1.44949	−	1.44949i	0.108644	−	0.108644i
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	−5.79852	+	5.79852i	−0.429815	+	0.429815i
$183$		0			0
$184$			6.26692i			0.462004i
$185$	4.70496	−	12.6463i	0.345916	−	0.929776i
$186$		0			0
$187$	−4.64558	−	4.64558i	−0.339718	−	0.339718i
$188$	−5.48696	−	5.48696i	−0.400178	−	0.400178i
$189$		0			0
$190$	−2.89075	+	7.76996i	−0.209717	+	0.563692i
$191$			1.28350i			0.0928706i	0.998921	+	0.0464353i	$0.0147861\pi$
$191$			1.28350i			0.0928706i	−0.998921	+	0.0464353i	$0.985214\pi$
$192$		0			0
$193$	3.86569	−	3.86569i	0.278258	−	0.278258i	−0.554155	−	0.832413i	$-0.686959\pi$
$193$	3.86569	−	3.86569i	0.278258	−	0.278258i	0.832413	+	0.554155i	$0.186959\pi$
$194$	10.0619			0.722402
$195$		0			0
$196$	−2.93342			−0.209530
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	−0.133353	−	0.991069i	$-0.542574\pi$
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	0.991069	+	0.133353i	$0.0425744\pi$
$198$		0			0
$199$		−	4.43831i		−	0.314623i	−0.987549	−	0.157312i	$-0.949717\pi$
$199$		−	4.43831i		−	0.314623i	0.987549	−	0.157312i	$-0.0502827\pi$
$200$	4.98667	−	0.364918i	0.352611	−	0.0258036i
$201$		0			0
$202$	3.33958	+	3.33958i	0.234972	+	0.234972i
$203$	10.6906	+	10.6906i	0.750333	+	0.750333i
$204$		0			0
$205$	14.4060	−	6.59335i	1.00616	−	0.460499i
$206$		−	4.00520i		−	0.279055i
$207$		0			0
$208$	−2.87542	+	2.87542i	−0.199375	+	0.199375i
$209$	7.30196			0.505087
$210$		0			0
$211$	−24.0849			−1.65808			−0.829038	−	0.559192i	$-0.811111\pi$
$211$	−24.0849			−1.65808			−0.829038	+	0.559192i	$0.811111\pi$
$212$	−7.03027	+	7.03027i	−0.482841	+	0.482841i
$213$		0			0
$214$		−	7.64094i		−	0.522324i
$215$	−19.7377	−	7.34324i	−1.34610	−	0.500805i
$216$		0			0
$217$	9.94838	+	9.94838i	0.675340	+	0.675340i
$218$	−3.07844	−	3.07844i	−0.208498	−	0.208498i
$219$		0			0
$220$	−1.83276	−	4.00444i	−0.123565	−	0.269979i
$221$			13.5649i			0.912474i
$222$		0			0
$223$	11.8645	−	11.8645i	0.794508	−	0.794508i	−0.187715	−	0.982224i	$-0.560108\pi$
$223$	11.8645	−	11.8645i	0.794508	−	0.794508i	0.982224	+	0.187715i	$0.0601082\pi$
$224$	2.01658			0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	5.26010	−	5.26010i	0.349125	−	0.349125i	−0.510659	−	0.859784i	$-0.670598\pi$
$227$	5.26010	−	5.26010i	0.349125	−	0.349125i	0.859784	+	0.510659i	$0.170598\pi$
$228$		0			0
$229$			8.93950i			0.590738i	0.955383	+	0.295369i	$0.0954427\pi$
$229$			8.93950i			0.590738i	−0.955383	+	0.295369i	$0.904557\pi$
$230$	5.83183	+	12.7421i	0.384539	+	0.840190i
$231$		0			0
$232$	5.30136	+	5.30136i	0.348051	+	0.348051i
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	0.999911	−	0.0133533i	$-0.00425061\pi$
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	−0.0133533	+	0.999911i	$0.504251\pi$
$234$		0			0
$235$	−16.2623	−	6.05025i	−1.06083	−	0.394675i
$236$		−	2.69933i		−	0.175712i
$237$		0			0
$238$	4.75663	−	4.75663i	0.308327	−	0.308327i
$239$	10.8546			0.702128			0.351064	−	0.936352i	$-0.385820\pi$
$239$	10.8546			0.702128			0.351064	+	0.936352i	$0.385820\pi$
$240$		0			0
$241$	−23.3318			−1.50293			−0.751467	−	0.659771i	$-0.770653\pi$
$241$	−23.3318			−1.50293			−0.751467	+	0.659771i	$0.770653\pi$
$242$	5.03537	−	5.03537i	0.323686	−	0.323686i
$243$		0			0
$244$		−	8.74707i		−	0.559973i
$245$	−5.96432	+	2.72976i	−0.381046	+	0.174398i
$246$		0			0
$247$	−10.6607	−	10.6607i	−0.678325	−	0.678325i
$248$	4.93330	+	4.93330i	0.313265	+	0.313265i
$249$		0			0
$250$	9.79947	−	5.38242i	0.619773	−	0.340414i
$251$			13.3860i			0.844914i	0.906383	+	0.422457i	$0.138832\pi$
$251$			13.3860i			0.844914i	−0.906383	+	0.422457i	$0.861168\pi$
$252$		0			0
$253$	8.72759	−	8.72759i	0.548699	−	0.548699i
$254$	−4.83286			−0.303240
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.34100	−	5.34100i	0.333163	−	0.333163i	−0.520624	−	0.853786i	$-0.674301\pi$
$257$	5.34100	−	5.34100i	0.333163	−	0.333163i	0.853786	+	0.520624i	$0.174301\pi$
$258$		0			0
$259$		−	12.1687i		−	0.756127i
$260$	−3.17062	+	8.52220i	−0.196633	+	0.528524i
$261$		0			0
$262$	−0.335798	−	0.335798i	−0.0207457	−	0.0207457i
$263$	−7.88385	−	7.88385i	−0.486139	−	0.486139i	0.420947	−	0.907085i	$-0.361698\pi$
$263$	−7.88385	−	7.88385i	−0.486139	−	0.486139i	−0.907085	+	0.420947i	$0.861698\pi$
$264$		0			0
$265$	−7.75200	+	20.8364i	−0.476201	+	1.27997i
$266$			7.47651i			0.458414i
$267$		0			0
$268$	5.99026	−	5.99026i	0.365914	−	0.365914i
$269$	−13.4707			−0.821326			−0.410663	−	0.911787i	$-0.634703\pi$
$269$	−13.4707			−0.821326			−0.410663	+	0.911787i	$0.634703\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	2.35877	−	2.35877i	0.143021	−	0.143021i
$273$		0			0
$274$		−	9.85187i		−	0.595173i
$275$	−7.45285	−	6.43645i	−0.449424	−	0.388132i
$276$		0			0
$277$	17.1389	+	17.1389i	1.02977	+	1.02977i	0.999543	+	0.0302313i	$0.00962438\pi$
$277$	17.1389	+	17.1389i	1.02977	+	1.02977i	0.0302313	+	0.999543i	$0.490376\pi$
$278$	−0.496689	−	0.496689i	−0.0297894	−	0.0297894i
$279$		0			0
$280$	4.10017	−	1.87657i	0.245032	−	0.112147i
$281$		−	22.5656i		−	1.34615i	−0.739574	−	0.673076i	$-0.764973\pi$
$281$		−	22.5656i		−	1.34615i	0.739574	−	0.673076i	$-0.235027\pi$
$282$		0			0
$283$	1.50170	−	1.50170i	0.0892668	−	0.0892668i	−0.661063	−	0.750330i	$-0.729895\pi$
$283$	1.50170	−	1.50170i	0.0892668	−	0.0892668i	0.750330	+	0.661063i	$0.229895\pi$
$284$	−5.68481			−0.337332
$285$		0			0
$286$	8.00889			0.473575
$287$	10.1031	−	10.1031i	0.596368	−	0.596368i
$288$		0			0
$289$			5.87245i			0.345438i
$290$	15.7122	+	5.84560i	0.922652	+	0.343265i
$291$		0			0
$292$	−1.14928	−	1.14928i	−0.0672563	−	0.0672563i
$293$	−2.58563	−	2.58563i	−0.151054	−	0.151054i	0.627535	−	0.778589i	$-0.284064\pi$
$293$	−2.58563	−	2.58563i	−0.151054	−	0.151054i	−0.778589	+	0.627535i	$0.784064\pi$
$294$		0			0
$295$	−2.51193	−	5.48837i	−0.146250	−	0.319545i
$296$		−	6.03434i		−	0.350739i
$297$		0			0
$298$	5.73618	−	5.73618i	0.332288	−	0.332288i
$299$	−25.4842			−1.47379
$300$		0			0
$301$	−18.9922			−1.09469
$302$	−6.52997	+	6.52997i	−0.375758	+	0.375758i
$303$		0			0
$304$			3.70753i			0.212641i
$305$	−8.13978	−	17.7848i	−0.466082	−	1.01836i
$306$		0			0
$307$	−10.5436	−	10.5436i	−0.601754	−	0.601754i	0.339024	−	0.940778i	$-0.389903\pi$
$307$	−10.5436	−	10.5436i	−0.601754	−	0.601754i	−0.940778	+	0.339024i	$0.889903\pi$
$308$	−2.80837	−	2.80837i	−0.160022	−	0.160022i
$309$		0			0
$310$	14.6213	+	5.43975i	0.830437	+	0.308957i
$311$		−	10.4897i		−	0.594817i	−0.954750	−	0.297408i	$-0.903878\pi$
$311$		−	10.4897i		−	0.594817i	0.954750	−	0.297408i	$-0.0961223\pi$
$312$		0			0
$313$	−12.4828	+	12.4828i	−0.705569	+	0.705569i	−0.965600	−	0.260032i	$-0.916267\pi$
$313$	−12.4828	+	12.4828i	−0.705569	+	0.705569i	0.260032	+	0.965600i	$0.416267\pi$
$314$	−10.8546			−0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	−16.3959	+	16.3959i	−0.920885	+	0.920885i	−0.997092	−	0.0762073i	$-0.975719\pi$
$317$	−16.3959	+	16.3959i	−0.920885	+	0.920885i	0.0762073	+	0.997092i	$0.475719\pi$
$318$		0			0
$319$		−	14.7658i		−	0.826727i
$320$	2.03323	−	0.930573i	0.113661	−	0.0520206i
$321$		0			0
$322$	8.93623	+	8.93623i	0.497996	+	0.497996i
$323$	8.74518	+	8.74518i	0.486595	+	0.486595i
$324$		0			0
$325$	1.48393	+	20.2781i	0.0823135	+	1.12483i
$326$		−	13.6924i		−	0.758351i
$327$		0			0
$328$	5.01003	−	5.01003i	0.276633	−	0.276633i
$329$	−15.6481			−0.862708
$330$		0			0
$331$	−25.8259			−1.41952			−0.709761	−	0.704443i	$-0.751197\pi$
$331$	−25.8259			−1.41952			−0.709761	+	0.704443i	$0.751197\pi$
$332$	1.20473	−	1.20473i	0.0661180	−	0.0661180i
$333$		0			0
$334$			5.10991i			0.279602i
$335$	6.60522	−	17.7540i	0.360882	−	0.970003i
$336$		0			0
$337$	22.6854	+	22.6854i	1.23575	+	1.23575i	0.961720	+	0.274033i	$0.0883577\pi$
$337$	22.6854	+	22.6854i	1.23575	+	1.23575i	0.274033	+	0.961720i	$0.411642\pi$
$338$	−2.50043	−	2.50043i	−0.136005	−	0.136005i
$339$		0			0
$340$	2.60092	−	6.99092i	0.141054	−	0.379136i
$341$		−	13.7407i		−	0.744099i
$342$		0			0
$343$	−14.1644	+	14.1644i	−0.764806	+	0.764806i
$344$	−9.41805			−0.507787
$345$		0			0
$346$	7.41505			0.398636
$347$	10.4684	−	10.4684i	0.561973	−	0.561973i	−0.367894	−	0.929868i	$-0.619921\pi$
$347$	10.4684	−	10.4684i	0.561973	−	0.561973i	0.929868	+	0.367894i	$0.119921\pi$
$348$		0			0
$349$			15.4430i			0.826646i	0.910584	+	0.413323i	$0.135632\pi$
$349$			15.4430i			0.826646i	−0.910584	+	0.413323i	$0.864368\pi$
$350$	6.59031	−	7.63101i	0.352267	−	0.407895i
$351$		0			0
$352$	−1.39264	−	1.39264i	−0.0742282	−	0.0742282i
$353$	14.7469	+	14.7469i	0.784898	+	0.784898i	0.980653	−	0.195754i	$-0.0627156\pi$
$353$	14.7469	+	14.7469i	0.784898	+	0.784898i	−0.195754	+	0.980653i	$0.562716\pi$
$354$		0			0
$355$	−11.5585	+	5.29013i	−0.613464	+	0.280771i
$356$		−	2.04989i		−	0.108644i
$357$		0			0
$358$	−1.93342	+	1.93342i	−0.102184	+	0.102184i
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	−16.0571	+	16.0571i	−0.843941	+	0.843941i
$363$		0			0
$364$			8.20034i			0.429815i
$365$	−3.40623	−	1.26726i	−0.178290	−	0.0663314i
$366$		0			0
$367$	15.5399	+	15.5399i	0.811177	+	0.811177i	0.984810	−	0.173633i	$-0.0555507\pi$
$367$	15.5399	+	15.5399i	0.811177	+	0.811177i	−0.173633	+	0.984810i	$0.555551\pi$
$368$	4.43138	+	4.43138i	0.231002	+	0.231002i
$369$		0			0
$370$	−5.61539	−	12.2692i	−0.291930	−	0.637846i
$371$			20.0494i			1.04091i
$372$		0			0
$373$	−1.04103	+	1.04103i	−0.0539025	+	0.0539025i	−0.733544	−	0.679642i	$-0.762135\pi$
$373$	−1.04103	+	1.04103i	−0.0539025	+	0.0539025i	0.679642	+	0.733544i	$0.262135\pi$
$374$	−6.56984			−0.339718
$375$		0			0
$376$	−7.75974			−0.400178
$377$	−21.5578	+	21.5578i	−1.11028	+	1.11028i
$378$		0			0
$379$			30.1323i			1.54779i	0.633314	+	0.773895i	$0.281694\pi$
$379$			30.1323i			1.54779i	−0.633314	+	0.773895i	$0.718306\pi$
$380$	3.45012	+	7.53826i	0.176988	+	0.386705i
$381$		0			0
$382$	0.907570	+	0.907570i	0.0464353	+	0.0464353i
$383$	−12.1256	−	12.1256i	−0.619587	−	0.619587i	0.325838	−	0.945425i	$-0.394353\pi$
$383$	−12.1256	−	12.1256i	−0.619587	−	0.619587i	−0.945425	+	0.325838i	$0.894353\pi$
$384$		0			0
$385$	−8.32347	−	3.09668i	−0.424203	−	0.157821i
$386$		−	5.46691i		−	0.278258i
$387$		0			0
$388$	7.11484	−	7.11484i	0.361201	−	0.361201i
$389$	30.2139			1.53191			0.765953	−	0.642897i	$-0.222268\pi$
$389$	30.2139			1.53191			0.765953	+	0.642897i	$0.222268\pi$
$390$		0			0
$391$	20.9052			1.05722
$392$	−2.07424	+	2.07424i	−0.104765	+	0.104765i
$393$		0			0
$394$		−	17.0252i		−	0.857716i
$395$	−23.6034	+	10.8028i	−1.18762	+	0.543549i
$396$		0			0
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	0.650561	−	0.759454i	$-0.274534\pi$
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	−0.759454	+	0.650561i	$0.774534\pi$
$398$	−3.13836	−	3.13836i	−0.157312	−	0.157312i
$399$		0			0
$400$	3.26807	−	3.78414i	0.163403	−	0.189207i
$401$		−	14.2269i		−	0.710458i	−0.934779	−	0.355229i	$-0.884403\pi$
$401$		−	14.2269i		−	0.710458i	0.934779	−	0.355229i	$-0.115597\pi$
$402$		0			0
$403$	−20.0611	+	20.0611i	−0.999314	+	0.999314i
$404$	4.72288			0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	−8.40369	+	8.40369i	−0.416555	+	0.416555i
$408$		0			0
$409$			11.8891i			0.587879i	0.955824	+	0.293939i	$0.0949664\pi$
$409$			11.8891i			0.587879i	−0.955824	+	0.293939i	$0.905034\pi$
$410$	5.52436	−	14.8488i	0.272829	−	0.733328i
$411$		0			0
$412$	−2.83210	−	2.83210i	−0.139528	−	0.139528i
$413$	−3.84907	−	3.84907i	−0.189401	−	0.189401i
$414$		0			0
$415$	1.32840	−	3.57058i	0.0652088	−	0.175273i
$416$			4.06647i			0.199375i
$417$		0			0
$418$	5.16326	−	5.16326i	0.252543	−	0.252543i
$419$	−39.2708			−1.91850			−0.959251	−	0.282555i	$-0.908818\pi$
$419$	−39.2708			−1.91850			−0.959251	+	0.282555i	$0.908818\pi$
$420$		0			0
$421$	24.4985			1.19398			0.596992	−	0.802247i	$-0.296362\pi$
$421$	24.4985			1.19398			0.596992	+	0.802247i	$0.296362\pi$
$422$	−17.0306	+	17.0306i	−0.829038	+	0.829038i
$423$		0			0
$424$			9.94230i			0.482841i
$425$	−1.21729	−	16.6345i	−0.0590474	−	0.806892i
$426$		0			0
$427$	−12.4727	−	12.4727i	−0.603599	−	0.603599i
$428$	−5.40296	−	5.40296i	−0.261162	−	0.261162i
$429$		0			0
$430$	−19.1491	+	8.76418i	−0.923451	+	0.422646i
$431$			6.10703i			0.294165i	0.989124	+	0.147083i	$0.0469883\pi$
$431$			6.10703i			0.294165i	−0.989124	+	0.147083i	$0.953012\pi$
$432$		0			0
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	−0.416190	−	0.909278i	$-0.636635\pi$
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	0.909278	+	0.416190i	$0.136635\pi$
$434$	14.0691			0.675340
$435$		0			0
$436$	−4.35357			−0.208498
$437$	−16.4295	+	16.4295i	−0.785928	+	0.785928i
$438$		0			0
$439$			2.27019i			0.108350i	0.998531	+	0.0541752i	$0.0172529\pi$
$439$			2.27019i			0.108350i	−0.998531	+	0.0541752i	$0.982747\pi$
$440$	−4.12753	−	1.53561i	−0.196772	−	0.0732075i
$441$		0			0
$442$	9.59184	+	9.59184i	0.456237	+	0.456237i
$443$	−19.6716	−	19.6716i	−0.934626	−	0.934626i	0.0633641	−	0.997990i	$-0.479817\pi$
$443$	−19.6716	−	19.6716i	−0.934626	−	0.934626i	−0.997990	+	0.0633641i	$0.979817\pi$
$444$		0			0
$445$	−1.90757	−	4.16790i	−0.0904275	−	0.197577i
$446$		−	16.7790i		−	0.794508i
$447$		0			0
$448$	1.42594	−	1.42594i	0.0673691	−	0.0673691i
$449$	−11.7712			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$449$	−11.7712			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	2.09697	−	2.09697i	0.0986331	−	0.0986331i
$453$		0			0
$454$		−	7.43890i		−	0.349125i
$455$	7.63101	+	16.6732i	0.357747	+	0.781652i
$456$		0			0
$457$	−27.5229	−	27.5229i	−1.28747	−	1.28747i	−0.936320	−	0.351147i	$-0.885792\pi$
$457$	−27.5229	−	27.5229i	−1.28747	−	1.28747i	−0.351147	−	0.936320i	$-0.614208\pi$
$458$	6.32118	+	6.32118i	0.295369	+	0.295369i
$459$		0			0
$460$	13.1338	+	4.88631i	0.612365	+	0.227825i
$461$			3.02763i			0.141011i	0.997511	+	0.0705053i	$0.0224612\pi$
$461$			3.02763i			0.141011i	−0.997511	+	0.0705053i	$0.977539\pi$
$462$		0			0
$463$	4.83410	−	4.83410i	0.224660	−	0.224660i	−0.585798	−	0.810457i	$-0.699219\pi$
$463$	4.83410	−	4.83410i	0.224660	−	0.224660i	0.810457	+	0.585798i	$0.199219\pi$
$464$	7.49726			0.348051
$465$		0			0
$466$	21.2969			0.986558
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	−0.495775	−	0.868451i	$-0.665116\pi$
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	0.868451	+	0.495775i	$0.165116\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$	−15.7773	+	7.22100i	−0.727755	+	0.333080i
$471$		0			0
$472$	−1.90872	−	1.90872i	−0.0878558	−	0.0878558i
$473$	13.1160	+	13.1160i	0.603074	+	0.603074i
$474$		0			0
$475$	14.0298	+	12.1165i	0.643731	+	0.555941i
$476$		−	6.72689i		−	0.308327i
$477$		0			0
$478$	7.67538	−	7.67538i	0.351064	−	0.351064i
$479$	−33.1423			−1.51431			−0.757154	−	0.653236i	$-0.773411\pi$
$479$	−33.1423			−1.51431			−0.757154	+	0.653236i	$0.773411\pi$
$480$		0			0
$481$	24.5384			1.11886
$482$	−16.4981	+	16.4981i	−0.751467	+	0.751467i
$483$		0			0
$484$		−	7.12109i		−	0.323686i
$485$	7.84525	−	21.0870i	0.356234	−	0.957511i
$486$		0			0
$487$	−14.8248	−	14.8248i	−0.671777	−	0.671777i	0.286349	−	0.958126i	$-0.407558\pi$
$487$	−14.8248	−	14.8248i	−0.671777	−	0.671777i	−0.958126	+	0.286349i	$0.907558\pi$
$488$	−6.18511	−	6.18511i	−0.279987	−	0.279987i
$489$		0			0
$490$	−2.28718	+	6.14764i	−0.103324	+	0.277722i
$491$			18.6490i			0.841617i	0.907150	+	0.420808i	$0.138253\pi$
$491$			18.6490i			0.841617i	−0.907150	+	0.420808i	$0.861747\pi$
$492$		0			0
$493$	17.6843	−	17.6843i	0.796459	−	0.796459i
$494$	−15.0765			−0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	−8.10617	+	8.10617i	−0.363612	+	0.363612i
$498$		0			0
$499$		−	22.6540i		−	1.01413i	−0.861908	−	0.507065i	$-0.830730\pi$
$499$		−	22.6540i		−	1.01413i	0.861908	−	0.507065i	$-0.169270\pi$
$500$	3.12333	−	10.7352i	0.139679	−	0.480093i
$501$		0			0
$502$	9.46530	+	9.46530i	0.422457	+	0.422457i
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	0.458507	−	0.888691i	$-0.348384\pi$
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	−0.888691	+	0.458507i	$0.848384\pi$
$504$		0			0
$505$	9.60272	−	4.39499i	0.427315	−	0.195574i
$506$		−	12.3427i		−	0.548699i
$507$		0			0
$508$	−3.41734	+	3.41734i	−0.151620	+	0.151620i
$509$	−27.1764			−1.20457			−0.602286	−	0.798280i	$-0.705744\pi$
$509$	−27.1764			−1.20457			−0.602286	+	0.798280i	$0.705744\pi$
$510$		0			0
$511$	−3.27759			−0.144992
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	7.55332i		−	0.333163i
$515$	−8.39380	−	3.12284i	−0.369875	−	0.137609i
$516$		0			0
$517$	10.8065	+	10.8065i	0.475271	+	0.475271i
$518$	−8.60458	−	8.60458i	−0.378063	−	0.378063i
$519$		0			0
$520$	3.78414	+	8.26807i	0.165946	+	0.362579i
$521$			18.3542i			0.804114i	0.915615	+	0.402057i	$0.131705\pi$
$521$			18.3542i			0.804114i	−0.915615	+	0.402057i	$0.868295\pi$
$522$		0			0
$523$	−25.8576	+	25.8576i	−1.13067	+	1.13067i	−0.140607	+	0.990066i	$0.544905\pi$
$523$	−25.8576	+	25.8576i	−1.13067	+	1.13067i	−0.990066	+	0.140607i	$0.955095\pi$
$524$	−0.474890			−0.0207457
$525$		0			0
$526$	−11.1494			−0.486139
$527$	16.4565	−	16.4565i	0.716856	−	0.716856i
$528$		0			0
$529$			16.2743i			0.707579i
$530$	9.25204	+	20.2150i	0.401883	+	0.878084i
$531$		0			0
$532$	5.28669	+	5.28669i	0.229207	+	0.229207i
$533$	20.3731	+	20.3731i	0.882458	+	0.882458i
$534$		0			0
$535$	−16.0133	−	5.95763i	−0.692317	−	0.257571i
$536$		−	8.47151i		−	0.365914i
$537$		0			0
$538$	−9.52525	+	9.52525i	−0.410663	+	0.410663i
$539$	5.77735			0.248848
$540$		0			0
$541$	−4.54804			−0.195536			−0.0977678	−	0.995209i	$-0.531170\pi$
$541$	−4.54804			−0.195536			−0.0977678	+	0.995209i	$0.531170\pi$
$542$	14.4534	−	14.4534i	0.620827	−	0.620827i
$543$		0			0
$544$		−	3.33580i		−	0.143021i
$545$	−8.85182	+	4.05131i	−0.379170	+	0.173539i
$546$		0			0
$547$	−15.8255	−	15.8255i	−0.676648	−	0.676648i	0.282592	−	0.959240i	$-0.408806\pi$
$547$	−15.8255	−	15.8255i	−0.676648	−	0.676648i	−0.959240	+	0.282592i	$0.908806\pi$
$548$	−6.96632	−	6.96632i	−0.297587	−	0.297587i
$549$		0			0
$550$	−9.82122	+	0.718705i	−0.418778	+	0.0306457i
$551$			27.7963i			1.18416i
$552$		0			0
$553$	−16.5534	+	16.5534i	−0.703922	+	0.703922i
$554$	24.2380			1.02977
$555$		0			0
$556$	−0.702425			−0.0297894
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	−0.120914	−	0.992663i	$-0.538583\pi$
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	0.992663	+	0.120914i	$0.0385825\pi$
$558$		0			0
$559$		−	38.2982i		−	1.61984i
$560$	1.57232	−	4.22619i	0.0664427	−	0.178589i
$561$		0			0
$562$	−15.9563	−	15.9563i	−0.673076	−	0.673076i
$563$	25.0749	+	25.0749i	1.05678	+	1.05678i	0.998288	+	0.0584931i	$0.0186296\pi$
$563$	25.0749	+	25.0749i	1.05678	+	1.05678i	0.0584931	+	0.998288i	$0.481370\pi$
$564$		0			0
$565$	2.31224	−	6.21501i	0.0972768	−	0.261467i
$566$		−	2.12372i		−	0.0892668i
$567$		0			0
$568$	−4.01977	+	4.01977i	−0.168666	+	0.168666i
$569$	−24.1185			−1.01110			−0.505549	−	0.862798i	$-0.668710\pi$
$569$	−24.1185			−1.01110			−0.505549	+	0.862798i	$0.668710\pi$
$570$		0			0
$571$	−4.49452			−0.188090			−0.0940448	−	0.995568i	$-0.529980\pi$
$571$	−4.49452			−0.188090			−0.0940448	+	0.995568i	$0.529980\pi$
$572$	5.66314	−	5.66314i	0.236788	−	0.236788i
$573$		0			0
$574$		−	14.2880i		−	0.596368i
$575$	31.2510	−	2.28691i	1.30326	−	0.0953709i
$576$		0			0
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	0.710979	−	0.703214i	$-0.248252\pi$
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	−0.703214	+	0.710979i	$0.748252\pi$
$578$	4.15245	+	4.15245i	0.172719	+	0.172719i
$579$		0			0
$580$	15.2437	−	6.97674i	0.632959	−	0.289693i
$581$		−	3.43572i		−	0.142538i
$582$		0			0
$583$	13.8461	−	13.8461i	0.573446	−	0.573446i
$584$	−1.62532			−0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	31.9628	−	31.9628i	1.31925	−	1.31925i	0.404874	−	0.914372i	$-0.367315\pi$
$587$	31.9628	−	31.9628i	1.31925	−	1.31925i	0.914372	−	0.404874i	$-0.132685\pi$
$588$		0			0
$589$			25.8664i			1.06581i
$590$	−5.65706	−	2.10466i	−0.232898	−	0.0866477i
$591$		0			0
$592$	−4.26692	−	4.26692i	−0.175369	−	0.175369i
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	0.629242	−	0.777209i	$-0.283365\pi$
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	−0.777209	+	0.629242i	$0.783365\pi$
$594$		0			0
$595$	−6.25986	−	13.6773i	−0.256629	−	0.560716i
$596$		−	8.11219i		−	0.332288i
$597$		0			0
$598$	−18.0201	+	18.0201i	−0.736895	+	0.736895i
$599$	46.9162			1.91695			0.958473	−	0.285184i	$-0.0920548\pi$
$599$	46.9162			1.91695			0.958473	+	0.285184i	$0.0920548\pi$
$600$		0			0
$601$	41.1377			1.67804			0.839020	−	0.544100i	$-0.183129\pi$
$601$	41.1377			1.67804			0.839020	+	0.544100i	$0.183129\pi$
$602$	−13.4295	+	13.4295i	−0.547347	+	0.547347i
$603$		0			0
$604$			9.23478i			0.375758i
$605$	−6.62669	−	14.4788i	−0.269413	−	0.588648i
$606$		0			0
$607$	11.6949	+	11.6949i	0.474680	+	0.474680i	0.903425	−	0.428746i	$-0.141044\pi$
$607$	11.6949	+	11.6949i	0.474680	+	0.474680i	−0.428746	+	0.903425i	$0.641044\pi$
$608$	2.62162	+	2.62162i	0.106321	+	0.106321i
$609$		0			0
$610$	−18.3315	−	6.82007i	−0.742219	−	0.276137i
$611$		−	31.5547i		−	1.27657i
$612$		0			0
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	−0.990658	−	0.136368i	$-0.956457\pi$
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	0.136368	+	0.990658i	$0.456457\pi$
$614$	−14.9109			−0.601754
$615$		0			0
$616$	−3.97164			−0.160022
$617$	7.44284	−	7.44284i	0.299637	−	0.299637i	−0.541234	−	0.840872i	$-0.682043\pi$
$617$	7.44284	−	7.44284i	0.299637	−	0.299637i	0.840872	+	0.541234i	$0.182043\pi$
$618$		0			0
$619$		−	3.19902i		−	0.128580i	−0.997931	−	0.0642898i	$-0.979522\pi$
$619$		−	3.19902i		−	0.128580i	0.997931	−	0.0642898i	$-0.0204782\pi$
$620$	14.1853	−	6.49237i	0.569697	−	0.260740i
$621$		0			0
$622$	−7.41734	−	7.41734i	−0.297408	−	0.297408i
$623$	−2.92301	−	2.92301i	−0.117108	−	0.117108i
$624$		0			0
$625$	−3.63945	−	24.7337i	−0.145578	−	0.989347i
$626$			17.6533i			0.705569i
$627$		0			0
$628$	−7.67538	+	7.67538i	−0.306281	+	0.306281i
$629$	−20.1293			−0.802609
$630$		0			0
$631$	21.2335			0.845291			0.422645	−	0.906295i	$-0.361102\pi$
$631$	21.2335			0.845291			0.422645	+	0.906295i	$0.361102\pi$
$632$	−8.20866	+	8.20866i	−0.326523	+	0.326523i
$633$		0			0
$634$			23.1873i			0.920885i
$635$	−3.76817	+	10.1283i	−0.149535	+	0.401931i
$636$		0			0
$637$	−8.43482	−	8.43482i	−0.334200	−	0.334200i
$638$	−10.4410	−	10.4410i	−0.413363	−	0.413363i
$639$		0			0
$640$	0.779698	−	2.09573i	0.0308203	−	0.0828409i
$641$		−	49.2576i		−	1.94556i	−0.231738	−	0.972778i	$-0.574441\pi$
$641$		−	49.2576i		−	1.94556i	0.231738	−	0.972778i	$-0.425559\pi$
$642$		0			0
$643$	−14.3595	+	14.3595i	−0.566284	+	0.566284i	−0.931085	−	0.364801i	$-0.881137\pi$
$643$	−14.3595	+	14.3595i	−0.566284	+	0.566284i	0.364801	+	0.931085i	$0.381137\pi$
$644$	12.6377			0.497996
$645$		0			0
$646$	12.3676			0.486595
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.154619	+	0.987974i	$0.549415\pi$
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.987974	+	0.154619i	$0.950585\pi$
$648$		0			0
$649$			5.31632i			0.208684i
$650$	15.3881	+	13.2895i	0.603570	+	0.521257i
$651$		0			0
$652$	−9.68197	−	9.68197i	−0.379175	−	0.379175i
$653$	2.01333	+	2.01333i	0.0787879	+	0.0787879i	0.745403	−	0.666615i	$-0.232257\pi$
$653$	2.01333	+	2.01333i	0.0787879	+	0.0787879i	−0.666615	+	0.745403i	$0.732257\pi$
$654$		0			0
$655$	−0.965562	+	0.441920i	−0.0377276	+	0.0172672i
$656$		−	7.08526i		−	0.276633i
$657$		0			0
$658$	−11.0649	+	11.0649i	−0.431354	+	0.431354i
$659$	37.6971			1.46847			0.734236	−	0.678894i	$-0.237540\pi$
$659$	37.6971			1.46847			0.734236	+	0.678894i	$0.237540\pi$
$660$		0			0
$661$	−7.37815			−0.286977			−0.143488	−	0.989652i	$-0.545832\pi$
$661$	−7.37815			−0.286977			−0.143488	+	0.989652i	$0.545832\pi$
$662$	−18.2617	+	18.2617i	−0.709761	+	0.709761i
$663$		0			0
$664$		−	1.70374i		−	0.0661180i
$665$	15.6687	+	5.82942i	0.607607	+	0.226055i
$666$		0			0
$667$	33.2232	+	33.2232i	1.28641	+	1.28641i
$668$	3.61325	+	3.61325i	0.139801	+	0.139801i
$669$		0			0
$670$	−7.88336	−	17.2246i	−0.304561	−	0.665443i
$671$			17.2273i			0.665053i
$672$		0			0
$673$	5.03954	−	5.03954i	0.194260	−	0.194260i	−0.603274	−	0.797534i	$-0.706137\pi$
$673$	5.03954	−	5.03954i	0.194260	−	0.194260i	0.797534	+	0.603274i	$0.206137\pi$
$674$	32.0820			1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	5.92761	−	5.92761i	0.227817	−	0.227817i	−0.583963	−	0.811780i	$-0.698499\pi$
$677$	5.92761	−	5.92761i	0.227817	−	0.227817i	0.811780	+	0.583963i	$0.198499\pi$
$678$		0			0
$679$		−	20.2906i		−	0.778682i
$680$	−3.10420	−	6.78245i	−0.119041	−	0.260095i
$681$		0			0
$682$	−9.71612	−	9.71612i	−0.372049	−	0.372049i
$683$	−15.8873	−	15.8873i	−0.607911	−	0.607911i	0.334488	−	0.942400i	$-0.391436\pi$
$683$	−15.8873	−	15.8873i	−0.607911	−	0.607911i	−0.942400	+	0.334488i	$0.891436\pi$
$684$		0			0
$685$	−20.6468	−	7.68149i	−0.788875	−	0.293494i
$686$			20.0315i			0.764806i
$687$		0			0
$688$	−6.65957	+	6.65957i	−0.253894	+	0.253894i
$689$	−40.4300			−1.54026
$690$		0			0
$691$	−18.3259			−0.697151			−0.348576	−	0.937281i	$-0.613335\pi$
$691$	−18.3259			−0.697151			−0.348576	+	0.937281i	$0.613335\pi$
$692$	5.24323	−	5.24323i	0.199318	−	0.199318i
$693$		0			0
$694$		−	14.8046i		−	0.561973i
$695$	−1.42819	+	0.653657i	−0.0541744	+	0.0247946i
$696$		0			0
$697$	−16.7125	−	16.7125i	−0.633029	−	0.633029i
$698$	10.9199	+	10.9199i	0.413323	+	0.413323i
$699$		0			0
$700$	−0.735886	−	10.0560i	−0.0278139	−	0.380081i
$701$			21.1738i			0.799724i	0.916575	+	0.399862i	$0.130942\pi$
$701$			21.1738i			0.799724i	−0.916575	+	0.399862i	$0.869058\pi$
$702$		0			0
$703$	15.8197	−	15.8197i	0.596652	−	0.596652i
$704$	−1.96950			−0.0742282
$705$		0			0
$706$	20.8553			0.784898
$707$	6.73453	−	6.73453i	0.253278	−	0.253278i
$708$		0			0
$709$			23.6536i			0.888330i	0.895945	+	0.444165i	$0.146500\pi$
$709$			23.6536i			0.888330i	−0.895945	+	0.444165i	$0.853500\pi$
$710$	−4.43244	+	11.9138i	−0.166346	+	0.447117i
$711$		0			0
$712$	−1.44949	−	1.44949i	−0.0543219	−	0.0543219i
$713$	30.9166	+	30.9166i	1.15784	+	1.15784i
$714$		0			0
$715$	6.24451	−	16.7844i	0.233532	−	0.627702i
$716$			2.73426i			0.102184i
$717$		0			0
$718$	2.40038	−	2.40038i	0.0895815	−	0.0895815i
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	3.71532	−	3.71532i	0.138270	−	0.138270i
$723$		0			0
$724$			22.7081i			0.843941i
$725$	24.5015	−	28.3707i	0.909965	−	1.05366i
$726$		0			0
$727$	−2.17529	−	2.17529i	−0.0806772	−	0.0806772i	0.665617	−	0.746294i	$-0.268169\pi$
$727$	−2.17529	−	2.17529i	−0.0806772	−	0.0806772i	−0.746294	+	0.665617i	$0.768169\pi$
$728$	5.79852	+	5.79852i	0.214907	+	0.214907i
$729$		0			0
$730$	−3.30466	+	1.51248i	−0.122311	+	0.0559794i
$731$			31.4167i			1.16199i
$732$		0			0
$733$	−17.2300	+	17.2300i	−0.636404	+	0.636404i	−0.949666	−	0.313263i	$-0.898578\pi$
$733$	−17.2300	+	17.2300i	−0.636404	+	0.636404i	0.313263	+	0.949666i	$0.398578\pi$
$734$	21.9768			0.811177
$735$		0			0
$736$	6.26692			0.231002
$737$	−11.7978	+	11.7978i	−0.434578	+	0.434578i
$738$		0			0
$739$			5.68805i			0.209238i	0.994512	+	0.104619i	$0.0333624\pi$
$739$			5.68805i			0.209238i	−0.994512	+	0.104619i	$0.966638\pi$
$740$	−12.6463	−	4.70496i	−0.464888	−	0.172958i
$741$		0			0
$742$	14.1771	+	14.1771i	0.520457	+	0.520457i
$743$	−11.0613	−	11.0613i	−0.405799	−	0.405799i	0.474471	−	0.880271i	$-0.342639\pi$
$743$	−11.0613	−	11.0613i	−0.405799	−	0.405799i	−0.880271	+	0.474471i	$0.842639\pi$
$744$		0			0
$745$	−7.54898	−	16.4940i	−0.276573	−	0.604292i
$746$			1.47224i			0.0539025i
$747$		0			0
$748$	−4.64558	+	4.64558i	−0.169859	+	0.169859i
$749$	−15.4086			−0.563016
$750$		0			0
$751$	43.2480			1.57814			0.789070	−	0.614303i	$-0.210563\pi$
$751$	43.2480			1.57814			0.789070	+	0.614303i	$0.210563\pi$
$752$	−5.48696	+	5.48696i	−0.200089	+	0.200089i
$753$		0			0
$754$			30.4873i			1.11028i
$755$	8.59363	+	18.7764i	0.312754	+	0.683345i
$756$		0			0
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	0.986963	−	0.160950i	$-0.0514557\pi$
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	−0.160950	+	0.986963i	$0.551456\pi$
$758$	21.3067	+	21.3067i	0.773895	+	0.773895i
$759$		0			0
$760$	7.76996	+	2.89075i	0.281846	+	0.104859i
$761$		−	28.7225i		−	1.04119i	−0.853804	−	0.520595i	$-0.825710\pi$
$761$		−	28.7225i		−	1.04119i	0.853804	−	0.520595i	$-0.174290\pi$
$762$		0			0
$763$	−6.20791	+	6.20791i	−0.224741	+	0.224741i
$764$	1.28350			0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	7.76173	−	7.76173i	0.280260	−	0.280260i
$768$		0			0
$769$		−	33.8971i		−	1.22236i	−0.791491	−	0.611180i	$-0.790695\pi$
$769$		−	33.8971i		−	1.22236i	0.791491	−	0.611180i	$-0.209305\pi$
$770$	−8.07527	+	3.69590i	−0.291012	+	0.133191i
$771$		0			0
$772$	−3.86569	−	3.86569i	−0.139129	−	0.139129i
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.996232	+	0.0867231i	$0.0276395\pi$
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.0867231	+	0.996232i	$0.472360\pi$
$774$		0			0
$775$	22.8005	−	26.4010i	0.819017	−	0.948351i
$776$		−	10.0619i		−	0.361201i
$777$		0			0
$778$	21.3645	−	21.3645i	0.765953	−	0.765953i
$779$	26.2688			0.941176
$780$		0			0
$781$	11.1962			0.400632
$782$	14.7822	−	14.7822i	0.528610	−	0.528610i
$783$		0			0
$784$			2.93342i			0.104765i
$785$	−8.46333	+	22.7483i	−0.302069	+	0.811923i
$786$		0			0
$787$	7.48244	+	7.48244i	0.266720	+	0.266720i	0.827777	−	0.561057i	$-0.189605\pi$
$787$	7.48244	+	7.48244i	0.266720	+	0.266720i	−0.561057	+	0.827777i	$0.689605\pi$
$788$	−12.0386	−	12.0386i	−0.428858	−	0.428858i
$789$		0			0
$790$	−9.05136	+	24.3289i	−0.322033	+	0.865582i
$791$		−	5.98028i		−	0.212634i
$792$		0			0
$793$	25.1515	−	25.1515i	0.893157	−	0.893157i
$794$	−3.06840			−0.108893
$795$		0			0
$796$	−4.43831			−0.157312
$797$	9.61983	−	9.61983i	0.340752	−	0.340752i	−0.515898	−	0.856650i	$-0.672542\pi$
$797$	9.61983	−	9.61983i	0.340752	−	0.340752i	0.856650	+	0.515898i	$0.172542\pi$
$798$		0			0
$799$			25.8849i			0.915742i
$800$	−0.364918	−	4.98667i	−0.0129018	−	0.176305i
$801$		0			0
$802$	−10.0599	−	10.0599i	−0.355229	−	0.355229i
$803$	2.26349	+	2.26349i	0.0798770	+	0.0798770i
$804$		0			0
$805$	25.6954	−	11.7603i	0.905645	−	0.414497i
$806$			28.3707i			0.999314i
$807$		0			0
$808$	3.33958	−	3.33958i	0.117486	−	0.117486i
$809$	33.4429			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$809$	33.4429			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	10.6906	−	10.6906i	0.375167	−	0.375167i
$813$		0			0
$814$			11.8846i			0.416555i
$815$	−28.6955	−	10.6759i	−1.00516	−	0.373961i
$816$		0			0
$817$	−24.6905	−	24.6905i	−0.863812	−	0.863812i
$818$	8.40687	+	8.40687i	0.293939	+	0.293939i
$819$		0			0
$820$	−6.59335	−	14.4060i	−0.230250	−	0.503078i
$821$			44.4492i			1.55129i	0.631171	+	0.775643i	$0.282574\pi$
$821$			44.4492i			1.55129i	−0.631171	+	0.775643i	$0.717426\pi$
$822$		0			0
$823$	18.0312	−	18.0312i	0.628530	−	0.628530i	−0.319168	−	0.947698i	$-0.603404\pi$
$823$	18.0312	−	18.0312i	0.628530	−	0.628530i	0.947698	+	0.319168i	$0.103404\pi$
$824$	−4.00520			−0.139528
$825$		0			0
$826$	−5.44341			−0.189401
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	−0.494368	−	0.869253i	$-0.664600\pi$
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	0.869253	+	0.494368i	$0.164600\pi$
$828$		0			0
$829$		−	4.02079i		−	0.139648i	−0.997559	−	0.0698239i	$-0.977756\pi$
$829$		−	4.02079i		−	0.139648i	0.997559	−	0.0698239i	$-0.0222437\pi$
$830$	−1.58545	−	3.46410i	−0.0550319	−	0.120241i
$831$		0			0
$832$	2.87542	+	2.87542i	0.0996874	+	0.0996874i
$833$	6.91924	+	6.91924i	0.239738	+	0.239738i
$834$		0			0
$835$	10.7090	+	3.98419i	0.370599	+	0.137878i
$836$		−	7.30196i		−	0.252543i
$837$		0			0
$838$	−27.7686	+	27.7686i	−0.959251	+	0.959251i
$839$	33.5761			1.15918			0.579588	−	0.814910i	$-0.303214\pi$
$839$	33.5761			1.15918			0.579588	+	0.814910i	$0.303214\pi$
$840$		0			0
$841$	27.2088			0.938236
$842$	17.3231	−	17.3231i	0.596992	−	0.596992i
$843$		0			0
$844$			24.0849i			0.829038i
$845$	−7.18979	+	3.29063i	−0.247336	+	0.113201i
$846$		0			0
$847$	−10.1542	−	10.1542i	−0.348903	−	0.348903i
$848$	7.03027	+	7.03027i	0.241420	+	0.241420i
$849$		0			0
$850$	−12.6231	−	10.9016i	−0.432970	−	0.373922i
$851$		−	37.8167i		−	1.29634i
$852$		0			0
$853$	−16.8177	+	16.8177i	−0.575828	+	0.575828i	−0.933751	−	0.357923i	$-0.883485\pi$
$853$	−16.8177	+	16.8177i	−0.575828	+	0.575828i	0.357923	+	0.933751i	$0.383485\pi$
$854$	−17.6391			−0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	8.38017	−	8.38017i	0.286261	−	0.286261i	−0.549339	−	0.835600i	$-0.685120\pi$
$857$	8.38017	−	8.38017i	0.286261	−	0.286261i	0.835600	+	0.549339i	$0.185120\pi$
$858$		0			0
$859$			40.0301i			1.36581i	0.730508	+	0.682904i	$0.239283\pi$
$859$			40.0301i			1.36581i	−0.730508	+	0.682904i	$0.760717\pi$
$860$	−7.34324	+	19.7377i	−0.250402	+	0.673049i
$861$		0			0
$862$	4.31832	+	4.31832i	0.147083	+	0.147083i
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	0.676041	−	0.736864i	$-0.263694\pi$
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	−0.736864	+	0.676041i	$0.763694\pi$
$864$		0			0
$865$	5.78150	−	15.5399i	0.196577	−	0.528373i
$866$		−	14.5105i		−	0.493088i
$867$		0			0
$868$	9.94838	−	9.94838i	0.337670	−	0.337670i
$869$	22.8635			0.775590
$870$		0			0
$871$	34.4491			1.16726
$872$	−3.07844	+	3.07844i	−0.104249	+	0.104249i
$873$		0			0
$874$			23.2348i			0.785928i
$875$	−10.8541	−	19.7614i	−0.366934	−	0.668057i
$876$		0			0
$877$	−4.87772	−	4.87772i	−0.164709	−	0.164709i	0.619940	−	0.784649i	$-0.287157\pi$
$877$	−4.87772	−	4.87772i	−0.164709	−	0.164709i	−0.784649	+	0.619940i	$0.787157\pi$
$878$	1.60527	+	1.60527i	0.0541752	+	0.0541752i
$879$		0			0
$880$	−4.00444	+	1.83276i	−0.134990	+	0.0617823i
$881$			3.01999i			0.101746i	0.998705	+	0.0508731i	$0.0162004\pi$
$881$			3.01999i			0.101746i	−0.998705	+	0.0508731i	$0.983800\pi$
$882$		0			0
$883$	−8.50404	+	8.50404i	−0.286184	+	0.286184i	−0.835569	−	0.549385i	$-0.814862\pi$
$883$	−8.50404	+	8.50404i	−0.286184	+	0.286184i	0.549385	+	0.835569i	$0.314862\pi$
$884$	13.5649			0.456237
$885$		0			0
$886$	−27.8199			−0.934626
$887$	12.5953	−	12.5953i	0.422909	−	0.422909i	−0.463295	−	0.886204i	$-0.653333\pi$
$887$	12.5953	−	12.5953i	0.422909	−	0.422909i	0.886204	+	0.463295i	$0.153333\pi$
$888$		0			0
$889$			9.74583i			0.326864i
$890$	−4.29601	−	1.59829i	−0.144002	−	0.0535749i
$891$		0			0
$892$	−11.8645	−	11.8645i	−0.397254	−	0.397254i
$893$	−20.3431	−	20.3431i	−0.680754	−	0.680754i
$894$		0			0
$895$	2.54443	+	5.55940i	0.0850510	+	0.185830i
$896$		−	2.01658i		−	0.0673691i
$897$		0			0
$898$	−8.32347	+	8.32347i	−0.277758	+	0.277758i
$899$	52.3064			1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	−9.86724	+	9.86724i	−0.328543	+	0.328543i
$903$		0			0
$904$		−	2.96556i		−	0.0986331i
$905$	21.1316	+	46.1709i	0.702437	+	1.53477i
$906$		0			0
$907$	0.887159	+	0.887159i	0.0294576	+	0.0294576i	0.721682	−	0.692225i	$-0.243369\pi$
$907$	0.887159	+	0.887159i	0.0294576	+	0.0294576i	−0.692225	+	0.721682i	$0.743369\pi$
$908$	−5.26010	−	5.26010i	−0.174562	−	0.174562i
$909$		0			0
$910$	17.1857	+	6.39379i	0.569699	+	0.211952i
$911$			27.0184i			0.895161i	0.894244	+	0.447581i	$0.147714\pi$
$911$			27.0184i			0.895161i	−0.894244	+	0.447581i	$0.852286\pi$
$912$		0			0
$913$	−2.37270	+	2.37270i	−0.0785251	+	0.0785251i
$914$	−38.9233			−1.28747
$915$		0			0
$916$	8.93950			0.295369
$917$	−0.677163	+	0.677163i	−0.0223619	+	0.0223619i
$918$		0			0
$919$			54.3202i			1.79186i	0.444196	+	0.895930i	$0.353489\pi$
$919$			54.3202i			1.79186i	−0.444196	+	0.895930i	$0.646511\pi$
$920$	12.7421	−	5.83183i	0.420095	−	0.192270i
$921$		0			0
$922$	2.14086	+	2.14086i	0.0705053	+	0.0705053i
$923$	−16.3463	−	16.3463i	−0.538043	−	0.538043i
$924$		0			0
$925$	−30.0912	+	2.20204i	−0.989394	+	0.0724027i
$926$		−	6.83645i		−	0.224660i
$927$		0			0
$928$	5.30136	−	5.30136i	0.174026	−	0.174026i
$929$	27.8548			0.913888			0.456944	−	0.889496i	$-0.348944\pi$
$929$	27.8548			0.913888			0.456944	+	0.889496i	$0.348944\pi$
$930$		0			0
$931$	−10.8757			−0.356437
$932$	15.0591	−	15.0591i	0.493279	−	0.493279i
$933$		0			0
$934$		−	11.3895i		−	0.372676i
$935$	−5.12249	+	13.7686i	−0.167523	+	0.450281i
$936$		0			0
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	0.375481	−	0.926830i	$-0.377477\pi$
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	−0.926830	+	0.375481i	$0.877477\pi$
$938$	−12.0798	−	12.0798i	−0.394420	−	0.394420i
$939$		0			0
$940$	−6.05025	+	16.2623i	−0.197337	+	0.530417i
$941$			32.9135i			1.07295i	0.843917	+	0.536474i	$0.180244\pi$
$941$			32.9135i			1.07295i	−0.843917	+	0.536474i	$0.819756\pi$
$942$		0			0
$943$	31.3975	−	31.3975i	1.02244	−	1.02244i
$944$	−2.69933			−0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	8.42386	−	8.42386i	0.273739	−	0.273739i	−0.556865	−	0.830603i	$-0.687996\pi$
$947$	8.42386	−	8.42386i	0.273739	−	0.273739i	0.830603	+	0.556865i	$0.187996\pi$
$948$		0			0
$949$		−	6.60931i		−	0.214547i
$950$	18.4882	−	1.35294i	0.599836	−	0.0438953i
$951$		0			0
$952$	−4.75663	−	4.75663i	−0.154163	−	0.154163i
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	0.454391	−	0.890802i	$-0.349857\pi$
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	−0.890802	+	0.454391i	$0.849857\pi$
$954$		0			0
$955$	2.60965	−	1.19439i	0.0844463	−	0.0386495i
$956$		−	10.8546i		−	0.351064i
$957$		0			0
$958$	−23.4351	+	23.4351i	−0.757154	+	0.757154i
$959$	−19.8671			−0.641541
$960$		0			0
$961$	17.6749			0.570159
$962$	17.3513	−	17.3513i	0.559428	−	0.559428i
$963$		0			0
$964$			23.3318i			0.751467i
$965$	−11.4571	−	4.26254i	−0.368819	−	0.137216i
$966$		0			0
$967$	−6.55790	−	6.55790i	−0.210888	−	0.210888i	0.593757	−	0.804645i	$-0.297644\pi$
$967$	−6.55790	−	6.55790i	−0.210888	−	0.210888i	−0.804645	+	0.593757i	$0.797644\pi$
$968$	−5.03537	−	5.03537i	−0.161843	−	0.161843i
$969$		0			0
$970$	−9.36333	−	20.4582i	−0.300638	−	0.656873i
$971$			24.7290i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$971$			24.7290i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$972$		0			0
$973$	−1.00161	+	1.00161i	−0.0321102	+	0.0321102i
$974$	−20.9655			−0.671777
$975$		0			0
$976$	−8.74707			−0.279987
$977$	−17.3635	+	17.3635i	−0.555507	+	0.555507i	−0.928025	−	0.372518i	$-0.878495\pi$
$977$	−17.3635	+	17.3635i	−0.555507	+	0.555507i	0.372518	+	0.928025i	$0.378495\pi$
$978$		0			0
$979$			4.03725i			0.129031i
$980$	2.72976	+	5.96432i	0.0871989	+	0.190523i
$981$		0			0
$982$	13.1868	+	13.1868i	0.420808	+	0.420808i
$983$	−29.3519	−	29.3519i	−0.936180	−	0.936180i	0.0619019	−	0.998082i	$-0.480283\pi$
$983$	−29.3519	−	29.3519i	−0.936180	−	0.936180i	−0.998082	+	0.0619019i	$0.980283\pi$
$984$		0			0
$985$	−35.6801	−	13.2745i	−1.13686	−	0.422960i
$986$		−	25.0093i		−	0.796459i
$987$		0			0
$988$	−10.6607	+	10.6607i	−0.339162	+	0.339162i
$989$	−59.0222			−1.87680
$990$		0			0
$991$	36.6089			1.16292			0.581460	−	0.813575i	$-0.302481\pi$
$991$	36.6089			1.16292			0.581460	+	0.813575i	$0.302481\pi$
$992$	4.93330	−	4.93330i	0.156632	−	0.156632i
$993$		0			0
$994$			11.4639i			0.363612i
$995$	−9.02412	+	4.13017i	−0.286084	+	0.130935i
$996$		0			0
$997$	8.45888	+	8.45888i	0.267895	+	0.267895i	0.828252	−	0.560356i	$-0.189336\pi$
$997$	8.45888	+	8.45888i	0.267895	+	0.267895i	−0.560356	+	0.828252i	$0.689336\pi$
$998$	−16.0188	−	16.0188i	−0.507065	−	0.507065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.f.c.647.7		16
3.2	odd	2	inner	810.2.f.c.647.2		16
5.3	odd	4	inner	810.2.f.c.323.2		16
9.2	odd	6		90.2.l.b.77.4	yes	16
9.4	even	3		90.2.l.b.47.4	yes	16
9.5	odd	6		270.2.m.b.197.2		16
9.7	even	3		270.2.m.b.17.2		16
15.8	even	4	inner	810.2.f.c.323.7		16
36.11	even	6		720.2.cu.b.257.2		16
36.31	odd	6		720.2.cu.b.497.1		16
45.2	even	12		450.2.p.h.293.1		16
45.4	even	6		450.2.p.h.407.1		16
45.7	odd	12		1350.2.q.h.1043.3		16
45.13	odd	12		90.2.l.b.83.4	yes	16
45.14	odd	6		1350.2.q.h.1007.3		16
45.22	odd	12		450.2.p.h.443.1		16
45.23	even	12		270.2.m.b.143.2		16
45.29	odd	6		450.2.p.h.257.1		16
45.32	even	12		1350.2.q.h.143.4		16
45.34	even	6		1350.2.q.h.557.4		16
45.38	even	12		90.2.l.b.23.4	✓	16
45.43	odd	12		270.2.m.b.233.2		16
180.83	odd	12		720.2.cu.b.113.1		16
180.103	even	12		720.2.cu.b.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	45.38	even	12
90.2.l.b.47.4	yes	16	9.4	even	3
90.2.l.b.77.4	yes	16	9.2	odd	6
90.2.l.b.83.4	yes	16	45.13	odd	12
270.2.m.b.17.2		16	9.7	even	3
270.2.m.b.143.2		16	45.23	even	12
270.2.m.b.197.2		16	9.5	odd	6
270.2.m.b.233.2		16	45.43	odd	12
450.2.p.h.257.1		16	45.29	odd	6
450.2.p.h.293.1		16	45.2	even	12
450.2.p.h.407.1		16	45.4	even	6
450.2.p.h.443.1		16	45.22	odd	12
720.2.cu.b.113.1		16	180.83	odd	12
720.2.cu.b.257.2		16	36.11	even	6
720.2.cu.b.353.2		16	180.103	even	12
720.2.cu.b.497.1		16	36.31	odd	6
810.2.f.c.323.2		16	5.3	odd	4	inner
810.2.f.c.323.7		16	15.8	even	4	inner
810.2.f.c.647.2		16	3.2	odd	2	inner
810.2.f.c.647.7		16	1.1	even	1	trivial
1350.2.q.h.143.4		16	45.32	even	12
1350.2.q.h.557.4		16	45.34	even	6
1350.2.q.h.1007.3		16	45.14	odd	6
1350.2.q.h.1043.3		16	45.7	odd	12

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.930573 - 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.930573 - 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +1.96950i q^{11} +(2.87542 - 2.87542i) q^{13} -2.01658 q^{14} -1.00000 q^{16} +(-2.35877 + 2.35877i) q^{17} -3.70753i q^{19} +(-2.03323 + 0.930573i) q^{20} +(1.39264 + 1.39264i) q^{22} +(-4.43138 - 4.43138i) q^{23} +(-3.26807 + 3.78414i) q^{25} -4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} -7.49726 q^{29} -6.97674 q^{31} +(-0.707107 + 0.707107i) q^{32} +3.33580i q^{34} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-2.62162 - 2.62162i) q^{38} +(-0.779698 + 2.09573i) q^{40} +7.08526i q^{41} +(6.65957 - 6.65957i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(5.48696 - 5.48696i) q^{47} -2.93342i q^{49} +(0.364918 + 4.98667i) q^{50} +(-2.87542 - 2.87542i) q^{52} +(-7.03027 - 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +2.01658i q^{56} +(-5.30136 + 5.30136i) q^{58} +2.69933 q^{59} +8.74707 q^{61} +(-4.93330 + 4.93330i) q^{62} +1.00000i q^{64} +(-8.52220 - 3.17062i) q^{65} +(5.99026 + 5.99026i) q^{67} +(2.35877 + 2.35877i) q^{68} +(1.87657 + 4.10017i) q^{70} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +6.03434 q^{74} -3.70753 q^{76} +(2.80837 - 2.80837i) q^{77} -11.6088i q^{79} +(0.930573 + 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(1.20473 + 1.20473i) q^{83} +(6.99092 + 2.60092i) q^{85} -9.41805i q^{86} +(1.39264 - 1.39264i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(-4.43138 + 4.43138i) q^{92} -7.75974i q^{94} +(-7.53826 + 3.45012i) q^{95} +(7.11484 + 7.11484i) q^{97} +(-2.07424 - 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{7}+O(q^{10}) \) 16 * q - 16 * q^7	\( 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82} + 8 q^{85} - 16 q^{88} + 96 q^{97}+O(q^{100}) \) 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Introduction

L-functions

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