LMFDB - Embedded newform 810.2.f.c.647.2

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			647.2
Root			$0.500000 + 1.74530i$ of defining polynomial
Character	$\chi$	$=$	810.647
Dual form			810.2.f.c.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.930573 + 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.930573 + 2.03323i) q^{5} +(-1.42594 - 1.42594i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} -1.96950i q^{11} +(2.87542 - 2.87542i) q^{13} +2.01658 q^{14} -1.00000 q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(2.03323 - 0.930573i) q^{20} +(1.39264 + 1.39264i) q^{22} +(4.43138 + 4.43138i) q^{23} +(-3.26807 + 3.78414i) q^{25} +4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} +7.49726 q^{29} -6.97674 q^{31} +(0.707107 - 0.707107i) q^{32} +3.33580i q^{34} +(1.57232 - 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(2.62162 + 2.62162i) q^{38} +(-0.779698 + 2.09573i) q^{40} -7.08526i q^{41} +(6.65957 - 6.65957i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(-5.48696 + 5.48696i) q^{47} -2.93342i q^{49} +(-0.364918 - 4.98667i) q^{50} +(-2.87542 - 2.87542i) q^{52} +(7.03027 + 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} -2.01658i q^{56} +(-5.30136 + 5.30136i) q^{58} -2.69933 q^{59} +8.74707 q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(8.52220 + 3.17062i) q^{65} +(5.99026 + 5.99026i) q^{67} +(-2.35877 - 2.35877i) q^{68} +(1.87657 + 4.10017i) q^{70} +5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} -6.03434 q^{74} -3.70753 q^{76} +(-2.80837 + 2.80837i) q^{77} -11.6088i q^{79} +(-0.930573 - 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(-1.20473 - 1.20473i) q^{83} +(6.99092 + 2.60092i) q^{85} +9.41805i q^{86} +(1.39264 - 1.39264i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(4.43138 - 4.43138i) q^{92} -7.75974i q^{94} +(7.53826 - 3.45012i) q^{95} +(7.11484 + 7.11484i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.904043\pi$
$11$		−	1.96950i		−	0.593825i	0.954905	−	0.296913i	$-0.0959570\pi$
$12$		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	−0.360626	−	0.932711i	$-0.617437\pi$
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	0.932711	+	0.360626i	$0.117437\pi$
$18$		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	0.997310	−	0.0733025i	$-0.0233538\pi$
$23$	4.43138	+	4.43138i	0.924007	+	0.924007i	−0.0733025	+	0.997310i	$0.523354\pi$
$24$		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	$-0.254916\pi$
$29$	7.49726			1.39221			0.696103	+	0.717942i	$0.254916\pi$
$30$		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	$-0.813381\pi$
$41$		−	7.08526i		−	1.10653i	0.833005	−	0.553266i	$-0.186619\pi$
$42$		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	−0.983151	−	0.182795i	$-0.941485\pi$
$47$	−5.48696	+	5.48696i	−0.800356	+	0.800356i	0.182795	+	0.983151i	$0.441485\pi$
$48$		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	0.999430	−	0.0337485i	$-0.0107445\pi$
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	−0.0337485	+	0.999430i	$0.510745\pi$
$54$		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	$-0.556223\pi$
$59$	−2.69933			−0.351423			−0.175712	+	0.984442i	$0.556223\pi$
$60$		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	$0.109524\pi$
$71$			5.68481i			0.674663i	−0.941386	+	0.337332i	$0.890476\pi$
$72$		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	0.637891	−	0.770127i	$-0.279807\pi$
$83$	−1.20473	−	1.20473i	−0.132236	−	0.132236i	−0.770127	+	0.637891i	$0.779807\pi$
$84$		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	$-0.534651\pi$
$89$	−2.04989			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$90$		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	$-0.924500\pi$
$101$		−	4.72288i		−	0.469944i	0.972002	−	0.234972i	$-0.0754999\pi$
$102$		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	−0.918273	−	0.395949i	$-0.870416\pi$
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	0.395949	+	0.918273i	$0.370416\pi$
$108$		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	0.601561	−	0.798827i	$-0.294546\pi$
$113$	−2.09697	−	2.09697i	−0.197266	−	0.197266i	−0.798827	+	0.601561i	$0.794546\pi$
$114$		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	$0.00660403\pi$
$131$			0.474890i			0.0414913i	−0.999785	+	0.0207457i	$0.993396\pi$
$132$		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	−0.939024	−	0.343851i	$-0.888268\pi$
$137$	−6.96632	+	6.96632i	−0.595173	+	0.595173i	0.343851	+	0.939024i	$0.388268\pi$
$138$		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	$-0.607821\pi$
$149$	−8.11219			−0.664576			−0.332288	+	0.943178i	$0.607821\pi$
$150$		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	−0.553348	−	0.832950i	$-0.686650\pi$
$167$	3.61325	−	3.61325i	0.279602	−	0.279602i	0.832950	+	0.553348i	$0.186650\pi$
$168$		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	0.479116	−	0.877752i	$-0.340957\pi$
$173$	−5.24323	−	5.24323i	−0.398636	−	0.398636i	−0.877752	+	0.479116i	$0.840957\pi$
$174$		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	$-0.467417\pi$
$179$	2.73426			0.204369			0.102184	+	0.994765i	$0.467417\pi$
$180$		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	$-0.985214\pi$
$191$		−	1.28350i		−	0.0928706i	0.998921	−	0.0464353i	$-0.0147861\pi$
$192$		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	−0.991069	−	0.133353i	$-0.957426\pi$
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	0.133353	+	0.991069i	$0.457426\pi$
$198$		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	−0.859784	−	0.510659i	$-0.829402\pi$
$227$	−5.26010	+	5.26010i	−0.349125	+	0.349125i	0.510659	+	0.859784i	$0.329402\pi$
$228$		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	0.0133533	−	0.999911i	$-0.495749\pi$
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	−0.999911	+	0.0133533i	$0.995749\pi$
$234$		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	$-0.614180\pi$
$239$	−10.8546			−0.702128			−0.351064	+	0.936352i	$0.614180\pi$
$240$		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	$-0.861168\pi$
$251$		−	13.3860i		−	0.844914i	0.906383	−	0.422457i	$-0.138832\pi$
$252$		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	−0.853786	−	0.520624i	$-0.825699\pi$
$257$	−5.34100	+	5.34100i	−0.333163	+	0.333163i	0.520624	+	0.853786i	$0.325699\pi$
$258$		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	0.907085	−	0.420947i	$-0.138302\pi$
$263$	7.88385	+	7.88385i	0.486139	+	0.486139i	−0.420947	+	0.907085i	$0.638302\pi$
$264$		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	$-0.365297\pi$
$269$	13.4707			0.821326			0.410663	+	0.911787i	$0.365297\pi$
$270$		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	$0.235027\pi$
$281$			22.5656i			1.34615i	−0.739574	+	0.673076i	$0.764973\pi$
$282$		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	0.778589	−	0.627535i	$-0.215936\pi$
$293$	2.58563	+	2.58563i	0.151054	+	0.151054i	−0.627535	+	0.778589i	$0.715936\pi$
$294$		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	$0.0961223\pi$
$311$			10.4897i			0.594817i	−0.954750	+	0.297408i	$0.903878\pi$
$312$		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	−0.0762073	−	0.997092i	$-0.524281\pi$
$317$	16.3959	−	16.3959i	0.920885	−	0.920885i	0.997092	+	0.0762073i	$0.0242811\pi$
$318$		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	−0.929868	−	0.367894i	$-0.880079\pi$
$347$	−10.4684	+	10.4684i	−0.561973	+	0.561973i	0.367894	+	0.929868i	$0.380079\pi$
$348$		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	0.195754	−	0.980653i	$-0.437284\pi$
$353$	−14.7469	−	14.7469i	−0.784898	−	0.784898i	−0.980653	+	0.195754i	$0.937284\pi$
$354$		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	$-0.528553\pi$
$359$	−3.39466			−0.179163			−0.0895815	+	0.995979i	$0.528553\pi$
$360$		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	0.945425	−	0.325838i	$-0.105647\pi$
$383$	12.1256	+	12.1256i	0.619587	+	0.619587i	−0.325838	+	0.945425i	$0.605647\pi$
$384$		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	$-0.777732\pi$
$389$	−30.2139			−1.53191			−0.765953	+	0.642897i	$0.777732\pi$
$390$		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	$0.115597\pi$
$401$			14.2269i			0.710458i	−0.934779	+	0.355229i	$0.884403\pi$
$402$		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	$-0.0911819\pi$
$419$	39.2708			1.91850			0.959251	+	0.282555i	$0.0911819\pi$
$420$		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	$-0.953012\pi$
$431$		−	6.10703i		−	0.294165i	0.989124	−	0.147083i	$-0.0469883\pi$
$432$		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	0.997990	−	0.0633641i	$-0.0201830\pi$
$443$	19.6716	+	19.6716i	0.934626	+	0.934626i	−0.0633641	+	0.997990i	$0.520183\pi$
$444$		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	$-0.410409\pi$
$449$	11.7712			0.555516			0.277758	+	0.960651i	$0.410409\pi$
$450$		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	$-0.977539\pi$
$461$		−	3.02763i		−	0.141011i	0.997511	−	0.0705053i	$-0.0224612\pi$
$462$		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	−0.868451	−	0.495775i	$-0.834884\pi$
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	0.495775	+	0.868451i	$0.334884\pi$
$468$		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	$-0.226589\pi$
$479$	33.1423			1.51431			0.757154	+	0.653236i	$0.226589\pi$
$480$		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	$-0.861747\pi$
$491$		−	18.6490i		−	0.841617i	0.907150	−	0.420808i	$-0.138253\pi$
$492$		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	0.888691	−	0.458507i	$-0.151616\pi$
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	−0.458507	+	0.888691i	$0.651616\pi$
$504$		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	$-0.294256\pi$
$509$	27.1764			1.20457			0.602286	+	0.798280i	$0.294256\pi$
$510$		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	$-0.868295\pi$
$521$		−	18.3542i		−	0.804114i	0.915615	−	0.402057i	$-0.131705\pi$
$522$		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	−0.992663	−	0.120914i	$-0.961417\pi$
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	0.120914	+	0.992663i	$0.461417\pi$
$558$		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	$-0.981370\pi$
$563$	−25.0749	−	25.0749i	−1.05678	−	1.05678i	−0.0584931	−	0.998288i	$-0.518630\pi$
$564$		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	$-0.331290\pi$
$569$	24.1185			1.01110			0.505549	+	0.862798i	$0.331290\pi$
$570$		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	$0.632685\pi$
$587$	−31.9628	+	31.9628i	−1.31925	+	1.31925i	−0.914372	+	0.404874i	$0.867315\pi$
$588$		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	0.777209	−	0.629242i	$-0.216635\pi$
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	−0.629242	+	0.777209i	$0.716635\pi$
$594$		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	$-0.907945\pi$
$599$	−46.9162			−1.91695			−0.958473	+	0.285184i	$0.907945\pi$
$600$		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	−0.840872	−	0.541234i	$-0.817957\pi$
$617$	−7.44284	+	7.44284i	−0.299637	+	0.299637i	0.541234	+	0.840872i	$0.317957\pi$
$618$		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	$0.425559\pi$
$641$			49.2576i			1.94556i	−0.231738	+	0.972778i	$0.574441\pi$
$642$		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	$-0.450585\pi$
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.987974	−	0.154619i	$-0.0494151\pi$
$648$		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	0.666615	−	0.745403i	$-0.267743\pi$
$653$	−2.01333	−	2.01333i	−0.0787879	−	0.0787879i	−0.745403	+	0.666615i	$0.767743\pi$
$654$		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	$-0.762460\pi$
$659$	−37.6971			−1.46847			−0.734236	+	0.678894i	$0.762460\pi$
$660$		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	−0.811780	−	0.583963i	$-0.801501\pi$
$677$	−5.92761	+	5.92761i	−0.227817	+	0.227817i	0.583963	+	0.811780i	$0.301501\pi$
$678$		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	0.942400	−	0.334488i	$-0.108564\pi$
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	−0.334488	+	0.942400i	$0.608564\pi$
$684$		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	$-0.869058\pi$
$701$		−	21.1738i		−	0.799724i	0.916575	−	0.399862i	$-0.130942\pi$
$702$		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	$-0.630460\pi$
$719$	−21.3695			−0.796947			−0.398473	+	0.917180i	$0.630460\pi$
$720$		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	0.880271	−	0.474471i	$-0.157361\pi$
$743$	11.0613	+	11.0613i	0.405799	+	0.405799i	−0.474471	+	0.880271i	$0.657361\pi$
$744$		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	$0.174290\pi$
$761$			28.7225i			1.04119i	−0.853804	+	0.520595i	$0.825710\pi$
$762$		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	$-0.972360\pi$
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.0867231	−	0.996232i	$-0.527640\pi$
$774$		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	−0.856650	−	0.515898i	$-0.827458\pi$
$797$	−9.61983	+	9.61983i	−0.340752	+	0.340752i	0.515898	+	0.856650i	$0.327458\pi$
$798$		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	$-0.700043\pi$
$809$	−33.4429			−1.17579			−0.587895	+	0.808937i	$0.700043\pi$
$810$		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	$-0.717426\pi$
$821$		−	44.4492i		−	1.55129i	0.631171	−	0.775643i	$-0.282574\pi$
$822$		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	−0.869253	−	0.494368i	$-0.835400\pi$
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	0.494368	+	0.869253i	$0.335400\pi$
$828$		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	$-0.696786\pi$
$839$	−33.5761			−1.15918			−0.579588	+	0.814910i	$0.696786\pi$
$840$		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	−0.835600	−	0.549339i	$-0.814880\pi$
$857$	−8.38017	+	8.38017i	−0.286261	+	0.286261i	0.549339	+	0.835600i	$0.314880\pi$
$858$		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	0.736864	−	0.676041i	$-0.236306\pi$
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	−0.676041	+	0.736864i	$0.736306\pi$
$864$		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	$-0.983800\pi$
$881$		−	3.01999i		−	0.101746i	0.998705	−	0.0508731i	$-0.0162004\pi$
$882$		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	−0.886204	−	0.463295i	$-0.846667\pi$
$887$	−12.5953	+	12.5953i	−0.422909	+	0.422909i	0.463295	+	0.886204i	$0.346667\pi$
$888$		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	$-0.852286\pi$
$911$		−	27.0184i		−	0.895161i	0.894244	−	0.447581i	$-0.147714\pi$
$912$		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	$-0.651056\pi$
$929$	−27.8548			−0.913888			−0.456944	+	0.889496i	$0.651056\pi$
$930$		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	$-0.819756\pi$
$941$		−	32.9135i		−	1.07295i	0.843917	−	0.536474i	$-0.180244\pi$
$942$		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	−0.830603	−	0.556865i	$-0.812004\pi$
$947$	−8.42386	+	8.42386i	−0.273739	+	0.273739i	0.556865	+	0.830603i	$0.312004\pi$
$948$		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	0.890802	−	0.454391i	$-0.150143\pi$
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	−0.454391	+	0.890802i	$0.650143\pi$
$954$		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	$-0.870122\pi$
$971$		−	24.7290i		−	0.793590i	0.917907	−	0.396795i	$-0.129878\pi$
$972$		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	−0.372518	−	0.928025i	$-0.621505\pi$
$977$	17.3635	−	17.3635i	0.555507	−	0.555507i	0.928025	+	0.372518i	$0.121505\pi$
$978$		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	0.998082	−	0.0619019i	$-0.0197166\pi$
$983$	29.3519	+	29.3519i	0.936180	+	0.936180i	−0.0619019	+	0.998082i	$0.519717\pi$
$984$		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.647.2		16
3.2	odd	2	inner	810.2.f.c.647.7		16
5.3	odd	4	inner	810.2.f.c.323.7		16
9.2	odd	6		270.2.m.b.17.2		16
9.4	even	3		270.2.m.b.197.2		16
9.5	odd	6		90.2.l.b.47.4	yes	16
9.7	even	3		90.2.l.b.77.4	yes	16
15.8	even	4	inner	810.2.f.c.323.2		16
36.7	odd	6		720.2.cu.b.257.2		16
36.23	even	6		720.2.cu.b.497.1		16
45.2	even	12		1350.2.q.h.1043.3		16
45.4	even	6		1350.2.q.h.1007.3		16
45.7	odd	12		450.2.p.h.293.1		16
45.13	odd	12		270.2.m.b.143.2		16
45.14	odd	6		450.2.p.h.407.1		16
45.22	odd	12		1350.2.q.h.143.4		16
45.23	even	12		90.2.l.b.83.4	yes	16
45.29	odd	6		1350.2.q.h.557.4		16
45.32	even	12		450.2.p.h.443.1		16
45.34	even	6		450.2.p.h.257.1		16
45.38	even	12		270.2.m.b.233.2		16
45.43	odd	12		90.2.l.b.23.4	✓	16
180.23	odd	12		720.2.cu.b.353.2		16
180.43	even	12		720.2.cu.b.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	45.43	odd	12
90.2.l.b.47.4	yes	16	9.5	odd	6
90.2.l.b.77.4	yes	16	9.7	even	3
90.2.l.b.83.4	yes	16	45.23	even	12
270.2.m.b.17.2		16	9.2	odd	6
270.2.m.b.143.2		16	45.13	odd	12
270.2.m.b.197.2		16	9.4	even	3
270.2.m.b.233.2		16	45.38	even	12
450.2.p.h.257.1		16	45.34	even	6
450.2.p.h.293.1		16	45.7	odd	12
450.2.p.h.407.1		16	45.14	odd	6
450.2.p.h.443.1		16	45.32	even	12
720.2.cu.b.113.1		16	180.43	even	12
720.2.cu.b.257.2		16	36.7	odd	6
720.2.cu.b.353.2		16	180.23	odd	12
720.2.cu.b.497.1		16	36.23	even	6
810.2.f.c.323.2		16	15.8	even	4	inner
810.2.f.c.323.7		16	5.3	odd	4	inner
810.2.f.c.647.2		16	1.1	even	1	trivial
810.2.f.c.647.7		16	3.2	odd	2	inner
1350.2.q.h.143.4		16	45.22	odd	12
1350.2.q.h.557.4		16	45.29	odd	6
1350.2.q.h.1007.3		16	45.4	even	6
1350.2.q.h.1043.3		16	45.2	even	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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