LMFDB - Embedded newform 1600.2.s.d.943.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(207,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("1600.207");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.4
Root			$-1.08900 - 0.902261i$ of defining polynomial
Character	$\chi$	$=$	1600.943
Dual form			1600.2.s.d.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.496487 q^{3} +(1.55426 - 1.55426i) q^{7} -2.75350 q^{9} +O(q^{10})$	$q-0.496487 q^{3} +(1.55426 - 1.55426i) q^{7} -2.75350 q^{9} +(4.19607 + 4.19607i) q^{11} -5.09530i q^{13} +(-0.213542 + 0.213542i) q^{17} +(-0.844754 - 0.844754i) q^{19} +(-0.771668 + 0.771668i) q^{21} +(1.70744 + 1.70744i) q^{23} +2.85654 q^{27} +(2.24750 - 2.24750i) q^{29} +0.818209i q^{31} +(-2.08329 - 2.08329i) q^{33} -5.12639i q^{37} +2.52975i q^{39} -3.34727i q^{41} -4.49131i q^{43} +(4.29355 + 4.29355i) q^{47} +2.16858i q^{49} +(0.106021 - 0.106021i) q^{51} +1.00653 q^{53} +(0.419410 + 0.419410i) q^{57} +(7.65005 - 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-4.27964 + 4.27964i) q^{63} -11.0221i q^{67} +(-0.847724 - 0.847724i) q^{69} +10.5331 q^{71} +(-2.70854 + 2.70854i) q^{73} +13.0435 q^{77} +8.32010 q^{79} +6.84226 q^{81} -9.17237 q^{83} +(-1.11585 + 1.11585i) q^{87} -4.25101 q^{89} +(-7.91940 - 7.91940i) q^{91} -0.406230i q^{93} +(7.16000 - 7.16000i) q^{97} +(-11.5539 - 11.5539i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) $ 18 * q + 2 * q^7 + 10 * q^9	$ 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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			0
$2$		0			0
$3$	−0.496487			−0.286647			−0.143324	−	0.989676i	$-0.545779\pi$
$3$	−0.496487			−0.286647			−0.143324	+	0.989676i	$0.545779\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.55426	−	1.55426i	0.587453	−	0.587453i	−0.349488	−	0.936941i	$-0.613644\pi$
$7$	1.55426	−	1.55426i	0.587453	−	0.587453i	0.936941	+	0.349488i	$0.113644\pi$
$8$		0			0
$9$	−2.75350			−0.917833
$10$		0			0
$11$	4.19607	+	4.19607i	1.26516	+	1.26516i	0.948558	+	0.316604i	$0.102543\pi$
$11$	4.19607	+	4.19607i	1.26516	+	1.26516i	0.316604	+	0.948558i	$0.397457\pi$
$12$		0			0
$13$		−	5.09530i		−	1.41318i	−0.707622	−	0.706591i	$-0.750232\pi$
$13$		−	5.09530i		−	1.41318i	0.707622	−	0.706591i	$-0.249768\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	−0.732528	−	0.680737i	$-0.761660\pi$
$17$	−0.213542	+	0.213542i	−0.0517916	+	0.0517916i	0.680737	+	0.732528i	$0.261660\pi$
$18$		0			0
$19$	−0.844754	−	0.844754i	−0.193800	−	0.193800i	0.603536	−	0.797336i	$-0.293758\pi$
$19$	−0.844754	−	0.844754i	−0.193800	−	0.193800i	−0.797336	+	0.603536i	$0.793758\pi$
$20$		0			0
$21$	−0.771668	+	0.771668i	−0.168392	+	0.168392i
$22$		0			0
$23$	1.70744	+	1.70744i	0.356027	+	0.356027i	0.862346	−	0.506319i	$-0.168994\pi$
$23$	1.70744	+	1.70744i	0.356027	+	0.356027i	−0.506319	+	0.862346i	$0.668994\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.85654			0.549741
$28$		0			0
$29$	2.24750	−	2.24750i	0.417350	−	0.417350i	−0.466939	−	0.884289i	$-0.654643\pi$
$29$	2.24750	−	2.24750i	0.417350	−	0.417350i	0.884289	+	0.466939i	$0.154643\pi$
$30$		0			0
$31$			0.818209i			0.146955i	0.997297	+	0.0734773i	$0.0234097\pi$
$31$			0.818209i			0.146955i	−0.997297	+	0.0734773i	$0.976590\pi$
$32$		0			0
$33$	−2.08329	−	2.08329i	−0.362655	−	0.362655i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	5.12639i		−	0.842774i	−0.906881	−	0.421387i	$-0.861543\pi$
$37$		−	5.12639i		−	0.842774i	0.906881	−	0.421387i	$-0.138457\pi$
$38$		0			0
$39$			2.52975i			0.405084i
$40$		0			0
$41$		−	3.34727i		−	0.522756i	−0.965237	−	0.261378i	$-0.915823\pi$
$41$		−	3.34727i		−	0.522756i	0.965237	−	0.261378i	$-0.0841769\pi$
$42$		0			0
$43$		−	4.49131i		−	0.684919i	−0.939533	−	0.342460i	$-0.888740\pi$
$43$		−	4.49131i		−	0.684919i	0.939533	−	0.342460i	$-0.111260\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.29355	+	4.29355i	0.626278	+	0.626278i	0.947130	−	0.320851i	$-0.103969\pi$
$47$	4.29355	+	4.29355i	0.626278	+	0.626278i	−0.320851	+	0.947130i	$0.603969\pi$
$48$		0			0
$49$			2.16858i			0.309797i
$50$		0			0
$51$	0.106021	−	0.106021i	0.0148459	−	0.0148459i
$52$		0			0
$53$	1.00653			0.138258			0.0691291	−	0.997608i	$-0.477978\pi$
$53$	1.00653			0.138258			0.0691291	+	0.997608i	$0.477978\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.419410	+	0.419410i	0.0555521	+	0.0555521i
$58$		0			0
$59$	7.65005	−	7.65005i	0.995952	−	0.995952i	−0.00404030	−	0.999992i	$-0.501286\pi$
$59$	7.65005	−	7.65005i	0.995952	−	0.995952i	0.999992	+	0.00404030i	$0.00128607\pi$
$60$		0			0
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	0.574712	−	0.818355i	$-0.305114\pi$
$61$	−1.90291	−	1.90291i	−0.243643	−	0.243643i	−0.818355	+	0.574712i	$0.805114\pi$
$62$		0			0
$63$	−4.27964	+	4.27964i	−0.539184	+	0.539184i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	11.0221i		−	1.34656i	−0.739387	−	0.673280i	$-0.764885\pi$
$67$		−	11.0221i		−	1.34656i	0.739387	−	0.673280i	$-0.235115\pi$
$68$		0			0
$69$	−0.847724	−	0.847724i	−0.102054	−	0.102054i
$70$		0			0
$71$	10.5331			1.25005			0.625027	−	0.780604i	$-0.285088\pi$
$71$	10.5331			1.25005			0.625027	+	0.780604i	$0.285088\pi$
$72$		0			0
$73$	−2.70854	+	2.70854i	−0.317010	+	0.317010i	−0.847618	−	0.530607i	$-0.821964\pi$
$73$	−2.70854	+	2.70854i	−0.317010	+	0.317010i	0.530607	+	0.847618i	$0.321964\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	13.0435			1.48645
$78$		0			0
$79$	8.32010			0.936085			0.468042	−	0.883706i	$-0.344959\pi$
$79$	8.32010			0.936085			0.468042	+	0.883706i	$0.344959\pi$
$80$		0			0
$81$	6.84226			0.760252
$82$		0			0
$83$	−9.17237			−1.00680			−0.503399	−	0.864054i	$-0.667917\pi$
$83$	−9.17237			−1.00680			−0.503399	+	0.864054i	$0.667917\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.11585	+	1.11585i	−0.119632	+	0.119632i
$88$		0			0
$89$	−4.25101			−0.450606			−0.225303	−	0.974289i	$-0.572337\pi$
$89$	−4.25101			−0.450606			−0.225303	+	0.974289i	$0.572337\pi$
$90$		0			0
$91$	−7.91940	−	7.91940i	−0.830178	−	0.830178i
$92$		0			0
$93$		−	0.406230i		−	0.0421241i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.16000	−	7.16000i	0.726987	−	0.726987i	−0.243031	−	0.970019i	$-0.578142\pi$
$97$	7.16000	−	7.16000i	0.726987	−	0.726987i	0.970019	+	0.243031i	$0.0781417\pi$
$98$		0			0
$99$	−11.5539	−	11.5539i	−1.16121	−	1.16121i
$100$		0			0
$101$	8.38846	−	8.38846i	0.834683	−	0.834683i	−0.153470	−	0.988153i	$-0.549045\pi$
$101$	8.38846	−	8.38846i	0.834683	−	0.834683i	0.988153	+	0.153470i	$0.0490448\pi$
$102$		0			0
$103$	−5.16478	−	5.16478i	−0.508901	−	0.508901i	0.405288	−	0.914189i	$-0.367171\pi$
$103$	−5.16478	−	5.16478i	−0.508901	−	0.508901i	−0.914189	+	0.405288i	$0.867171\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.97973			0.868103			0.434052	−	0.900888i	$-0.357084\pi$
$107$	8.97973			0.868103			0.434052	+	0.900888i	$0.357084\pi$
$108$		0			0
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.0458592	−	0.998948i	$-0.485397\pi$
$109$	10.9081	−	10.9081i	1.04481	−	1.04481i	0.998948	−	0.0458592i	$-0.0146025\pi$
$110$		0			0
$111$			2.54519i			0.241579i
$112$		0			0
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	0.879715	−	0.475502i	$-0.157734\pi$
$113$	4.29684	+	4.29684i	0.404212	+	0.404212i	−0.475502	+	0.879715i	$0.657734\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$			14.0299i			1.29707i
$118$		0			0
$119$			0.663798i			0.0608503i
$120$		0			0
$121$			24.2140i			2.20127i
$122$		0			0
$123$			1.66188i			0.149846i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.759686	+	0.759686i	0.0674112	+	0.0674112i	0.740009	−	0.672597i	$-0.234821\pi$
$127$	0.759686	+	0.759686i	0.0674112	+	0.0674112i	−0.672597	+	0.740009i	$0.734821\pi$
$128$		0			0
$129$			2.22988i			0.196330i
$130$		0			0
$131$	−7.59995	+	7.59995i	−0.664010	+	0.664010i	−0.956323	−	0.292312i	$-0.905575\pi$
$131$	−7.59995	+	7.59995i	−0.664010	+	0.664010i	0.292312	+	0.956323i	$0.405575\pi$
$132$		0			0
$133$	−2.62593			−0.227697
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.995339	−	0.0964376i	$-0.969255\pi$
$137$	−12.7789	−	12.7789i	−1.09178	−	1.09178i	−0.0964376	−	0.995339i	$-0.530745\pi$
$138$		0			0
$139$	−7.74227	+	7.74227i	−0.656691	+	0.656691i	−0.954596	−	0.297905i	$-0.903712\pi$
$139$	−7.74227	+	7.74227i	−0.656691	+	0.656691i	0.297905	+	0.954596i	$0.403712\pi$
$140$		0			0
$141$	−2.13169	−	2.13169i	−0.179521	−	0.179521i
$142$		0			0
$143$	21.3802	−	21.3802i	1.78790	−	1.78790i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		−	1.07667i		−	0.0888024i
$148$		0			0
$149$	9.57165	+	9.57165i	0.784140	+	0.784140i	0.980527	−	0.196386i	$-0.0629207\pi$
$149$	9.57165	+	9.57165i	0.784140	+	0.784140i	−0.196386	+	0.980527i	$0.562921\pi$
$150$		0			0
$151$	9.68791			0.788391			0.394195	−	0.919027i	$-0.371023\pi$
$151$	9.68791			0.788391			0.394195	+	0.919027i	$0.371023\pi$
$152$		0			0
$153$	0.587989	−	0.587989i	0.0475361	−	0.0475361i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.97637			0.796201			0.398101	−	0.917342i	$-0.369669\pi$
$157$	9.97637			0.796201			0.398101	+	0.917342i	$0.369669\pi$
$158$		0			0
$159$	−0.499732			−0.0396313
$160$		0			0
$161$	5.30761			0.418298
$162$		0			0
$163$	9.48267			0.742740			0.371370	−	0.928485i	$-0.378888\pi$
$163$	9.48267			0.742740			0.371370	+	0.928485i	$0.378888\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.43528	+	9.43528i	−0.730124	+	0.730124i	−0.970644	−	0.240520i	$-0.922682\pi$
$167$	−9.43528	+	9.43528i	−0.730124	+	0.730124i	0.240520	+	0.970644i	$0.422682\pi$
$168$		0			0
$169$	−12.9621			−0.997082
$170$		0			0
$171$	2.32603	+	2.32603i	0.177876	+	0.177876i
$172$		0			0
$173$		−	8.94716i		−	0.680240i	−0.940382	−	0.340120i	$-0.889532\pi$
$173$		−	8.94716i		−	0.680240i	0.940382	−	0.340120i	$-0.110468\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.79815	+	3.79815i	−0.285487	+	0.285487i
$178$		0			0
$179$	3.02430	+	3.02430i	0.226047	+	0.226047i	0.811039	−	0.584992i	$-0.198902\pi$
$179$	3.02430	+	3.02430i	0.226047	+	0.226047i	−0.584992	+	0.811039i	$0.698902\pi$
$180$		0			0
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	−0.762309	−	0.647213i	$-0.775934\pi$
$181$	−1.54845	+	1.54845i	−0.115095	+	0.115095i	0.647213	+	0.762309i	$0.275934\pi$
$182$		0			0
$183$	0.944773	+	0.944773i	0.0698396	+	0.0698396i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.79208			−0.131050
$188$		0			0
$189$	4.43979	−	4.43979i	0.322947	−	0.322947i
$190$		0			0
$191$		−	20.1005i		−	1.45442i	−0.686415	−	0.727210i	$-0.740817\pi$
$191$		−	20.1005i		−	1.45442i	0.686415	−	0.727210i	$-0.259183\pi$
$192$		0			0
$193$	−3.82483	−	3.82483i	−0.275317	−	0.275317i	0.555919	−	0.831236i	$-0.312366\pi$
$193$	−3.82483	−	3.82483i	−0.275317	−	0.275317i	−0.831236	+	0.555919i	$0.812366\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.11758i		−	0.0796246i	−0.999207	−	0.0398123i	$-0.987324\pi$
$197$		−	1.11758i		−	0.0796246i	0.999207	−	0.0398123i	$-0.0126760\pi$
$198$		0			0
$199$			25.5830i			1.81353i	0.421635	+	0.906766i	$0.361456\pi$
$199$			25.5830i			1.81353i	−0.421635	+	0.906766i	$0.638544\pi$
$200$		0			0
$201$			5.47232i			0.385988i
$202$		0			0
$203$		−	6.98637i		−	0.490347i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−4.70145	−	4.70145i	−0.326773	−	0.326773i
$208$		0			0
$209$		−	7.08929i		−	0.490376i
$210$		0			0
$211$	−0.411613	+	0.411613i	−0.0283366	+	0.0283366i	−0.721133	−	0.692797i	$-0.756378\pi$
$211$	−0.411613	+	0.411613i	−0.0283366	+	0.0283366i	0.692797	+	0.721133i	$0.256378\pi$
$212$		0			0
$213$	−5.22957			−0.358324
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.27171	+	1.27171i	0.0863290	+	0.0863290i
$218$		0			0
$219$	1.34475	−	1.34475i	0.0908701	−	0.0908701i
$220$		0			0
$221$	1.08806	+	1.08806i	0.0731909	+	0.0731909i
$222$		0			0
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.129908	+	0.991526i	$0.541468\pi$
$223$	−16.7466	+	16.7466i	−1.12143	+	1.12143i	−0.991526	+	0.129908i	$0.958532\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	13.7807i		−	0.914659i	−0.889297	−	0.457330i	$-0.848806\pi$
$227$		−	13.7807i		−	0.914659i	0.889297	−	0.457330i	$-0.151194\pi$
$228$		0			0
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	0.395694	−	0.918382i	$-0.370504\pi$
$229$	−7.90971	−	7.90971i	−0.522688	−	0.522688i	−0.918382	+	0.395694i	$0.870504\pi$
$230$		0			0
$231$	−6.47594			−0.426086
$232$		0			0
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	−0.649933	−	0.759991i	$-0.725203\pi$
$233$	1.67997	−	1.67997i	0.110058	−	0.110058i	0.759991	+	0.649933i	$0.225203\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.13083			−0.268326
$238$		0			0
$239$	−11.7685			−0.761241			−0.380620	−	0.924731i	$-0.624290\pi$
$239$	−11.7685			−0.761241			−0.380620	+	0.924731i	$0.624290\pi$
$240$		0			0
$241$	−13.2730			−0.854991			−0.427495	−	0.904018i	$-0.640604\pi$
$241$	−13.2730			−0.854991			−0.427495	+	0.904018i	$0.640604\pi$
$242$		0			0
$243$	−11.9667			−0.767665
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.30427	+	4.30427i	−0.273874	+	0.273874i
$248$		0			0
$249$	4.55396			0.288596
$250$		0			0
$251$	−10.3795	−	10.3795i	−0.655149	−	0.655149i	0.299079	−	0.954228i	$-0.403321\pi$
$251$	−10.3795	−	10.3795i	−0.655149	−	0.655149i	−0.954228	+	0.299079i	$0.903321\pi$
$252$		0			0
$253$			14.3291i			0.900863i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.331140	+	0.943582i	$0.607433\pi$
$257$	−20.4353	+	20.4353i	−1.27472	+	1.27472i	−0.943582	+	0.331140i	$0.892567\pi$
$258$		0			0
$259$	−7.96772	−	7.96772i	−0.495090	−	0.495090i
$260$		0			0
$261$	−6.18848	+	6.18848i	−0.383058	+	0.383058i
$262$		0			0
$263$	14.0611	+	14.0611i	0.867047	+	0.867047i	0.992144	−	0.125098i	$-0.0399244\pi$
$263$	14.0611	+	14.0611i	0.867047	+	0.867047i	−0.125098	+	0.992144i	$0.539924\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.11057			0.129165
$268$		0			0
$269$	−6.61443	+	6.61443i	−0.403289	+	0.403289i	−0.879390	−	0.476101i	$-0.842050\pi$
$269$	−6.61443	+	6.61443i	−0.403289	+	0.403289i	0.476101	+	0.879390i	$0.342050\pi$
$270$		0			0
$271$			10.6219i			0.645237i	0.946529	+	0.322619i	$0.104563\pi$
$271$			10.6219i			0.645237i	−0.946529	+	0.322619i	$0.895437\pi$
$272$		0			0
$273$	3.93188	+	3.93188i	0.237968	+	0.237968i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	8.28511i		−	0.497804i	−0.968529	−	0.248902i	$-0.919930\pi$
$277$		−	8.28511i		−	0.497804i	0.968529	−	0.248902i	$-0.0800697\pi$
$278$		0			0
$279$		−	2.25294i		−	0.134880i
$280$		0			0
$281$		−	21.0176i		−	1.25380i	−0.779098	−	0.626902i	$-0.784323\pi$
$281$		−	21.0176i		−	1.25380i	0.779098	−	0.626902i	$-0.215677\pi$
$282$		0			0
$283$			14.4748i			0.860436i	0.902725	+	0.430218i	$0.141563\pi$
$283$			14.4748i			0.860436i	−0.902725	+	0.430218i	$0.858437\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.20251	−	5.20251i	−0.307095	−	0.307095i
$288$		0			0
$289$			16.9088i			0.994635i
$290$		0			0
$291$	−3.55485	+	3.55485i	−0.208389	+	0.208389i
$292$		0			0
$293$	11.9165			0.696171			0.348086	−	0.937463i	$-0.386832\pi$
$293$	11.9165			0.696171			0.348086	+	0.937463i	$0.386832\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.9862	+	11.9862i	0.695512	+	0.695512i
$298$		0			0
$299$	8.69993	−	8.69993i	0.503130	−	0.503130i
$300$		0			0
$301$	−6.98065	−	6.98065i	−0.402358	−	0.402358i
$302$		0			0
$303$	−4.16477	+	4.16477i	−0.239260	+	0.239260i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			25.4511i			1.45257i	0.687392	+	0.726287i	$0.258755\pi$
$307$			25.4511i			1.45257i	−0.687392	+	0.726287i	$0.741245\pi$
$308$		0			0
$309$	2.56425	+	2.56425i	0.145875	+	0.145875i
$310$		0			0
$311$	−21.4775			−1.21788			−0.608939	−	0.793217i	$-0.708404\pi$
$311$	−21.4775			−1.21788			−0.608939	+	0.793217i	$0.708404\pi$
$312$		0			0
$313$	−18.7965	+	18.7965i	−1.06244	+	1.06244i	−0.0645277	+	0.997916i	$0.520554\pi$
$313$	−18.7965	+	18.7965i	−1.06244	+	1.06244i	−0.997916	+	0.0645277i	$0.979446\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.2531			−0.912864			−0.456432	−	0.889758i	$-0.650873\pi$
$317$	−16.2531			−0.912864			−0.456432	+	0.889758i	$0.650873\pi$
$318$		0			0
$319$	18.8613			1.05603
$320$		0			0
$321$	−4.45832			−0.248839
$322$		0			0
$323$	0.360781			0.0200744
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.41574	+	5.41574i	−0.299491	+	0.299491i
$328$		0			0
$329$	13.3465			0.735818
$330$		0			0
$331$	8.71558	+	8.71558i	0.479052	+	0.479052i	0.904828	−	0.425777i	$-0.139999\pi$
$331$	8.71558	+	8.71558i	0.479052	+	0.479052i	−0.425777	+	0.904828i	$0.639999\pi$
$332$		0			0
$333$			14.1155i			0.773526i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0406874	+	0.0406874i	−0.00221638	+	0.00221638i	−0.708214	−	0.705998i	$-0.750499\pi$
$337$	−0.0406874	+	0.0406874i	−0.00221638	+	0.00221638i	0.705998	+	0.708214i	$0.250499\pi$
$338$		0			0
$339$	−2.13333	−	2.13333i	−0.115866	−	0.115866i
$340$		0			0
$341$	−3.43326	+	3.43326i	−0.185921	+	0.185921i
$342$		0			0
$343$	14.2503	+	14.2503i	0.769445	+	0.769445i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−35.7094			−1.91698			−0.958491	−	0.285124i	$-0.907965\pi$
$347$	−35.7094			−1.91698			−0.958491	+	0.285124i	$0.907965\pi$
$348$		0			0
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	−0.714414	−	0.699723i	$-0.753307\pi$
$349$	−0.274452	+	0.274452i	−0.0146911	+	0.0146911i	0.699723	+	0.714414i	$0.253307\pi$
$350$		0			0
$351$		−	14.5549i		−	0.776884i
$352$		0			0
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	0.987715	−	0.156268i	$-0.0499464\pi$
$353$	15.6215	+	15.6215i	0.831446	+	0.831446i	−0.156268	+	0.987715i	$0.549946\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	0.329567i		−	0.0174426i
$358$		0			0
$359$		−	0.768787i		−	0.0405750i	−0.999794	−	0.0202875i	$-0.993542\pi$
$359$		−	0.768787i		−	0.0405750i	0.999794	−	0.0202875i	$-0.00645816\pi$
$360$		0			0
$361$		−	17.5728i		−	0.924883i
$362$		0			0
$363$		−	12.0219i		−	0.630988i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.7849	+	13.7849i	0.719568	+	0.719568i	0.968517	−	0.248949i	$-0.0800852\pi$
$367$	13.7849	+	13.7849i	0.719568	+	0.719568i	−0.248949	+	0.968517i	$0.580085\pi$
$368$		0			0
$369$			9.21671i			0.479803i
$370$		0			0
$371$	1.56441	−	1.56441i	0.0812202	−	0.0812202i
$372$		0			0
$373$	21.4003			1.10806			0.554031	−	0.832496i	$-0.313089\pi$
$373$	21.4003			1.10806			0.554031	+	0.832496i	$0.313089\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−11.4517	−	11.4517i	−0.589791	−	0.589791i
$378$		0			0
$379$	−11.3922	+	11.3922i	−0.585180	+	0.585180i	−0.936322	−	0.351142i	$-0.885793\pi$
$379$	−11.3922	+	11.3922i	−0.585180	+	0.585180i	0.351142	+	0.936322i	$0.385793\pi$
$380$		0			0
$381$	−0.377174	−	0.377174i	−0.0193232	−	0.0193232i
$382$		0			0
$383$	4.42635	−	4.42635i	0.226176	−	0.226176i	−0.584917	−	0.811093i	$-0.698873\pi$
$383$	4.42635	−	4.42635i	0.226176	−	0.226176i	0.811093	+	0.584917i	$0.198873\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			12.3668i			0.628642i
$388$		0			0
$389$	12.3502	+	12.3502i	0.626180	+	0.626180i	0.947105	−	0.320924i	$-0.103994\pi$
$389$	12.3502	+	12.3502i	0.626180	+	0.626180i	−0.320924	+	0.947105i	$0.603994\pi$
$390$		0			0
$391$	−0.729222			−0.0368784
$392$		0			0
$393$	3.77328	−	3.77328i	0.190337	−	0.190337i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.9832			−0.902551			−0.451275	−	0.892385i	$-0.649031\pi$
$397$	−17.9832			−0.902551			−0.451275	+	0.892385i	$0.649031\pi$
$398$		0			0
$399$	1.30374			0.0652686
$400$		0			0
$401$	9.06570			0.452720			0.226360	−	0.974044i	$-0.427317\pi$
$401$	9.06570			0.452720			0.226360	+	0.974044i	$0.427317\pi$
$402$		0			0
$403$	4.16902			0.207674
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.5107	−	21.5107i	1.06625	−	1.06625i
$408$		0			0
$409$	−30.0616			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$409$	−30.0616			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$410$		0			0
$411$	6.34457	+	6.34457i	0.312955	+	0.312955i
$412$		0			0
$413$		−	23.7803i		−	1.17015i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.84394	−	3.84394i	0.188239	−	0.188239i
$418$		0			0
$419$	15.3986	+	15.3986i	0.752271	+	0.752271i	0.974903	−	0.222631i	$-0.0714646\pi$
$419$	15.3986	+	15.3986i	0.752271	+	0.752271i	−0.222631	+	0.974903i	$0.571465\pi$
$420$		0			0
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	−0.794984	−	0.606631i	$-0.792521\pi$
$421$	−3.86468	+	3.86468i	−0.188353	+	0.188353i	0.606631	+	0.794984i	$0.292521\pi$
$422$		0			0
$423$	−11.8223	−	11.8223i	−0.574819	−	0.574819i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.91523			−0.286258
$428$		0			0
$429$	−10.6150	+	10.6150i	−0.512497	+	0.512497i
$430$		0			0
$431$			27.2692i			1.31351i	0.754103	+	0.656756i	$0.228072\pi$
$431$			27.2692i			1.31351i	−0.754103	+	0.656756i	$0.771928\pi$
$432$		0			0
$433$	−19.1435	−	19.1435i	−0.919978	−	0.919978i	0.0770497	−	0.997027i	$-0.475450\pi$
$433$	−19.1435	−	19.1435i	−0.919978	−	0.919978i	−0.997027	+	0.0770497i	$0.975450\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	2.88474i		−	0.137996i
$438$		0			0
$439$		−	30.1995i		−	1.44134i	−0.693276	−	0.720672i	$-0.743833\pi$
$439$		−	30.1995i		−	1.44134i	0.693276	−	0.720672i	$-0.256167\pi$
$440$		0			0
$441$		−	5.97118i		−	0.284342i
$442$		0			0
$443$			27.7051i			1.31631i	0.752884	+	0.658153i	$0.228662\pi$
$443$			27.7051i			1.31631i	−0.752884	+	0.658153i	$0.771338\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.75220	−	4.75220i	−0.224772	−	0.224772i
$448$		0			0
$449$		−	9.78315i		−	0.461695i	−0.972990	−	0.230848i	$-0.925850\pi$
$449$		−	9.78315i		−	0.461695i	0.972990	−	0.230848i	$-0.0741499\pi$
$450$		0			0
$451$	14.0454	−	14.0454i	0.661371	−	0.661371i
$452$		0			0
$453$	−4.80992			−0.225990
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.557108	+	0.557108i	0.0260604	+	0.0260604i	0.720017	−	0.693957i	$-0.244134\pi$
$457$	0.557108	+	0.557108i	0.0260604	+	0.0260604i	−0.693957	+	0.720017i	$0.744134\pi$
$458$		0			0
$459$	−0.609992	+	0.609992i	−0.0284720	+	0.0284720i
$460$		0			0
$461$	−12.5791	−	12.5791i	−0.585865	−	0.585865i	0.350644	−	0.936509i	$-0.385963\pi$
$461$	−12.5791	−	12.5791i	−0.585865	−	0.585865i	−0.936509	+	0.350644i	$0.885963\pi$
$462$		0			0
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	−0.779525	−	0.626371i	$-0.784540\pi$
$463$	−3.29549	+	3.29549i	−0.153154	+	0.153154i	0.626371	+	0.779525i	$0.284540\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	10.1995i		−	0.471979i	−0.971756	−	0.235989i	$-0.924167\pi$
$467$		−	10.1995i		−	0.471979i	0.971756	−	0.235989i	$-0.0758331\pi$
$468$		0			0
$469$	−17.1311	−	17.1311i	−0.791042	−	0.791042i
$470$		0			0
$471$	−4.95314			−0.228229
$472$		0			0
$473$	18.8459	−	18.8459i	0.866534	−	0.866534i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.77149			−0.126898
$478$		0			0
$479$	−5.65795			−0.258518			−0.129259	−	0.991611i	$-0.541260\pi$
$479$	−5.65795			−0.258518			−0.129259	+	0.991611i	$0.541260\pi$
$480$		0			0
$481$	−26.1205			−1.19099
$482$		0			0
$483$	−2.63516			−0.119904
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−19.7470	+	19.7470i	−0.894823	+	0.894823i	−0.994972	−	0.100149i	$-0.968068\pi$
$487$	−19.7470	+	19.7470i	−0.894823	+	0.894823i	0.100149	+	0.994972i	$0.468068\pi$
$488$		0			0
$489$	−4.70802			−0.212904
$490$		0			0
$491$	4.21405	+	4.21405i	0.190177	+	0.190177i	0.795773	−	0.605595i	$-0.207065\pi$
$491$	4.21405	+	4.21405i	0.190177	+	0.190177i	−0.605595	+	0.795773i	$0.707065\pi$
$492$		0			0
$493$			0.959871i			0.0432304i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.3712	−	16.3712i	0.734348	−	0.734348i
$498$		0			0
$499$	16.8862	+	16.8862i	0.755928	+	0.755928i	0.975579	−	0.219650i	$-0.0704917\pi$
$499$	16.8862	+	16.8862i	0.755928	+	0.755928i	−0.219650	+	0.975579i	$0.570492\pi$
$500$		0			0
$501$	4.68450	−	4.68450i	0.209288	−	0.209288i
$502$		0			0
$503$	−20.3714	−	20.3714i	−0.908317	−	0.908317i	0.0878190	−	0.996136i	$-0.472010\pi$
$503$	−20.3714	−	20.3714i	−0.908317	−	0.908317i	−0.996136	+	0.0878190i	$0.972010\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.43550			0.285811
$508$		0			0
$509$	−20.6309	+	20.6309i	−0.914448	+	0.914448i	−0.996618	−	0.0821701i	$-0.973815\pi$
$509$	−20.6309	+	20.6309i	−0.914448	+	0.914448i	0.0821701	+	0.996618i	$0.473815\pi$
$510$		0			0
$511$			8.41952i			0.372458i
$512$		0			0
$513$	−2.41307	−	2.41307i	−0.106540	−	0.106540i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			36.0320i			1.58469i
$518$		0			0
$519$			4.44215i			0.194989i
$520$		0			0
$521$			19.0433i			0.834300i	0.908838	+	0.417150i	$0.136971\pi$
$521$			19.0433i			0.834300i	−0.908838	+	0.417150i	$0.863029\pi$
$522$		0			0
$523$		−	19.1782i		−	0.838603i	−0.907847	−	0.419301i	$-0.862275\pi$
$523$		−	19.1782i		−	0.838603i	0.907847	−	0.419301i	$-0.137725\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.174722	−	0.174722i	−0.00761101	−	0.00761101i
$528$		0			0
$529$		−	17.1693i		−	0.746490i
$530$		0			0
$531$	−21.0644	+	21.0644i	−0.914118	+	0.914118i
$532$		0			0
$533$	−17.0553			−0.738749
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.50153	−	1.50153i	−0.0647957	−	0.0647957i
$538$		0			0
$539$	−9.09950	+	9.09950i	−0.391943	+	0.391943i
$540$		0			0
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	0.946653	−	0.322255i	$-0.104441\pi$
$541$	14.5231	+	14.5231i	0.624398	+	0.624398i	−0.322255	+	0.946653i	$0.604441\pi$
$542$		0			0
$543$	0.768787	−	0.768787i	0.0329918	−	0.0329918i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			9.97058i			0.426311i	0.977018	+	0.213156i	$0.0683742\pi$
$547$			9.97058i			0.426311i	−0.977018	+	0.213156i	$0.931626\pi$
$548$		0			0
$549$	5.23967	+	5.23967i	0.223624	+	0.223624i
$550$		0			0
$551$	−3.79716			−0.161765
$552$		0			0
$553$	12.9316	−	12.9316i	0.549906	−	0.549906i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.4424			−0.484831			−0.242416	−	0.970173i	$-0.577940\pi$
$557$	−11.4424			−0.484831			−0.242416	+	0.970173i	$0.577940\pi$
$558$		0			0
$559$	−22.8846			−0.967915
$560$		0			0
$561$	0.889743			0.0375650
$562$		0			0
$563$	47.0585			1.98328			0.991640	−	0.129034i	$-0.0411876\pi$
$563$	47.0585			1.98328			0.991640	+	0.129034i	$0.0411876\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	10.6346	−	10.6346i	0.446612	−	0.446612i
$568$		0			0
$569$	41.4684			1.73845			0.869224	−	0.494419i	$-0.164619\pi$
$569$	41.4684			1.73845			0.869224	+	0.494419i	$0.164619\pi$
$570$		0			0
$571$	−16.1745	−	16.1745i	−0.676881	−	0.676881i	0.282412	−	0.959293i	$-0.408865\pi$
$571$	−16.1745	−	16.1745i	−0.676881	−	0.676881i	−0.959293	+	0.282412i	$0.908865\pi$
$572$		0			0
$573$			9.97963i			0.416905i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−20.0316	+	20.0316i	−0.833926	+	0.833926i	−0.988051	−	0.154125i	$-0.950744\pi$
$577$	−20.0316	+	20.0316i	−0.833926	+	0.833926i	0.154125	+	0.988051i	$0.450744\pi$
$578$		0			0
$579$	1.89898	+	1.89898i	0.0789189	+	0.0789189i
$580$		0			0
$581$	−14.2562	+	14.2562i	−0.591447	+	0.591447i
$582$		0			0
$583$	4.22349	+	4.22349i	0.174919	+	0.174919i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	29.1190			1.20187			0.600935	−	0.799298i	$-0.294795\pi$
$587$	29.1190			1.20187			0.600935	+	0.799298i	$0.294795\pi$
$588$		0			0
$589$	0.691185	−	0.691185i	0.0284798	−	0.0284798i
$590$		0			0
$591$			0.554866i			0.0228242i
$592$		0			0
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	0.886832	−	0.462092i	$-0.152901\pi$
$593$	10.3431	+	10.3431i	0.424740	+	0.424740i	−0.462092	+	0.886832i	$0.652901\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	12.7016i		−	0.519843i
$598$		0			0
$599$		−	2.59479i		−	0.106020i	−0.998594	−	0.0530101i	$-0.983118\pi$
$599$		−	2.59479i		−	0.106020i	0.998594	−	0.0530101i	$-0.0168816\pi$
$600$		0			0
$601$		−	14.4092i		−	0.587765i	−0.955842	−	0.293882i	$-0.905053\pi$
$601$		−	14.4092i		−	0.587765i	0.955842	−	0.293882i	$-0.0949474\pi$
$602$		0			0
$603$			30.3493i			1.23592i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.8502	−	11.8502i	−0.480985	−	0.480985i	0.424461	−	0.905446i	$-0.360464\pi$
$607$	−11.8502	−	11.8502i	−0.480985	−	0.480985i	−0.905446	+	0.424461i	$0.860464\pi$
$608$		0			0
$609$			3.46864i			0.140557i
$610$		0			0
$611$	21.8769	−	21.8769i	0.885045	−	0.885045i
$612$		0			0
$613$	−16.8256			−0.679579			−0.339789	−	0.940502i	$-0.610356\pi$
$613$	−16.8256			−0.679579			−0.339789	+	0.940502i	$0.610356\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	0.995881	−	0.0906720i	$-0.0289015\pi$
$617$	22.4849	+	22.4849i	0.905209	+	0.905209i	−0.0906720	+	0.995881i	$0.528902\pi$
$618$		0			0
$619$	14.1269	−	14.1269i	0.567809	−	0.567809i	−0.363705	−	0.931514i	$-0.618488\pi$
$619$	14.1269	−	14.1269i	0.567809	−	0.567809i	0.931514	+	0.363705i	$0.118488\pi$
$620$		0			0
$621$	4.87738	+	4.87738i	0.195723	+	0.195723i
$622$		0			0
$623$	−6.60715	+	6.60715i	−0.264710	+	0.264710i
$624$		0			0
$625$		0			0
$626$		0			0
$627$			3.51974i			0.140565i
$628$		0			0
$629$	1.09470	+	1.09470i	0.0436486	+	0.0436486i
$630$		0			0
$631$	33.9235			1.35047			0.675236	−	0.737601i	$-0.264042\pi$
$631$	33.9235			1.35047			0.675236	+	0.737601i	$0.264042\pi$
$632$		0			0
$633$	0.204361	−	0.204361i	0.00812261	−	0.00812261i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	11.0496			0.437799
$638$		0			0
$639$	−29.0030			−1.14734
$640$		0			0
$641$	18.8495			0.744509			0.372254	−	0.928131i	$-0.378585\pi$
$641$	18.8495			0.744509			0.372254	+	0.928131i	$0.378585\pi$
$642$		0			0
$643$	−16.4916			−0.650364			−0.325182	−	0.945652i	$-0.605426\pi$
$643$	−16.4916			−0.650364			−0.325182	+	0.945652i	$0.605426\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.316870	+	0.316870i	−0.0124574	+	0.0124574i	−0.713308	−	0.700851i	$-0.752804\pi$
$647$	−0.316870	+	0.316870i	−0.0124574	+	0.0124574i	0.700851	+	0.713308i	$0.252804\pi$
$648$		0			0
$649$	64.2002			2.52008
$650$		0			0
$651$	−0.631386	−	0.631386i	−0.0247460	−	0.0247460i
$652$		0			0
$653$			17.0751i			0.668200i	0.942538	+	0.334100i	$0.108432\pi$
$653$			17.0751i			0.668200i	−0.942538	+	0.334100i	$0.891568\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.45796	−	7.45796i	0.290963	−	0.290963i
$658$		0			0
$659$	7.42245	+	7.42245i	0.289138	+	0.289138i	0.836739	−	0.547601i	$-0.184459\pi$
$659$	7.42245	+	7.42245i	0.289138	+	0.289138i	−0.547601	+	0.836739i	$0.684459\pi$
$660$		0			0
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.273507	−	0.961870i	$-0.411816\pi$
$661$	31.7614	−	31.7614i	1.23538	−	1.23538i	0.961870	−	0.273507i	$-0.0881837\pi$
$662$		0			0
$663$	−0.540209	−	0.540209i	−0.0209800	−	0.0209800i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.67495			0.297175
$668$		0			0
$669$	8.31446	−	8.31446i	0.321456	−	0.321456i
$670$		0			0
$671$		−	15.9695i		−	0.616496i
$672$		0			0
$673$	−4.14672	−	4.14672i	−0.159844	−	0.159844i	0.622653	−	0.782498i	$-0.286055\pi$
$673$	−4.14672	−	4.14672i	−0.159844	−	0.159844i	−0.782498	+	0.622653i	$0.786055\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	25.2618i		−	0.970890i	−0.874267	−	0.485445i	$-0.838658\pi$
$677$		−	25.2618i		−	0.970890i	0.874267	−	0.485445i	$-0.161342\pi$
$678$		0			0
$679$		−	22.2569i		−	0.854143i
$680$		0			0
$681$			6.84196i			0.262184i
$682$		0			0
$683$		−	8.20306i		−	0.313881i	−0.987608	−	0.156941i	$-0.949837\pi$
$683$		−	8.20306i		−	0.313881i	0.987608	−	0.156941i	$-0.0501631\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.92707	+	3.92707i	0.149827	+	0.149827i
$688$		0			0
$689$		−	5.12859i		−	0.195384i
$690$		0			0
$691$	7.89158	−	7.89158i	0.300210	−	0.300210i	−0.540886	−	0.841096i	$-0.681911\pi$
$691$	7.89158	−	7.89158i	0.300210	−	0.300210i	0.841096	+	0.540886i	$0.181911\pi$
$692$		0			0
$693$	−35.9153			−1.36431
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.714783	+	0.714783i	0.0270744	+	0.0270744i
$698$		0			0
$699$	−0.834083	+	0.834083i	−0.0315479	+	0.0315479i
$700$		0			0
$701$	1.50228	+	1.50228i	0.0567405	+	0.0567405i	0.734908	−	0.678167i	$-0.237225\pi$
$701$	1.50228	+	1.50228i	0.0567405	+	0.0567405i	−0.678167	+	0.734908i	$0.737225\pi$
$702$		0			0
$703$	−4.33054	+	4.33054i	−0.163329	+	0.163329i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	26.0756i		−	0.980675i
$708$		0			0
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.880228	−	0.474551i	$-0.842610\pi$
$709$	−36.0738	−	36.0738i	−1.35478	−	1.35478i	−0.474551	−	0.880228i	$-0.657390\pi$
$710$		0			0
$711$	−22.9094			−0.859170
$712$		0			0
$713$	−1.39704	+	1.39704i	−0.0523197	+	0.0523197i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.84291			0.218207
$718$		0			0
$719$	35.0340			1.30655			0.653274	−	0.757121i	$-0.273395\pi$
$719$	35.0340			1.30655			0.653274	+	0.757121i	$0.273395\pi$
$720$		0			0
$721$	−16.0548			−0.597911
$722$		0			0
$723$	6.58989			0.245081
$724$		0			0
$725$		0			0
$726$		0			0
$727$	25.4241	−	25.4241i	0.942928	−	0.942928i	−0.0555295	−	0.998457i	$-0.517685\pi$
$727$	25.4241	−	25.4241i	0.942928	−	0.942928i	0.998457	+	0.0555295i	$0.0176847\pi$
$728$		0			0
$729$	−14.5855			−0.540203
$730$		0			0
$731$	0.959085	+	0.959085i	0.0354731	+	0.0354731i
$732$		0			0
$733$			7.37554i			0.272422i	0.990680	+	0.136211i	$0.0434925\pi$
$733$			7.37554i			0.272422i	−0.990680	+	0.136211i	$0.956508\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	46.2494	−	46.2494i	1.70362	−	1.70362i
$738$		0			0
$739$	−5.55025	−	5.55025i	−0.204169	−	0.204169i	0.597614	−	0.801784i	$-0.296115\pi$
$739$	−5.55025	−	5.55025i	−0.204169	−	0.204169i	−0.801784	+	0.597614i	$0.796115\pi$
$740$		0			0
$741$	2.13702	−	2.13702i	0.0785053	−	0.0785053i
$742$		0			0
$743$	−6.78835	−	6.78835i	−0.249040	−	0.249040i	0.571536	−	0.820577i	$-0.306348\pi$
$743$	−6.78835	−	6.78835i	−0.249040	−	0.249040i	−0.820577	+	0.571536i	$0.806348\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	25.2561			0.924073
$748$		0			0
$749$	13.9568	−	13.9568i	0.509970	−	0.509970i
$750$		0			0
$751$			3.93385i			0.143548i	0.997421	+	0.0717742i	$0.0228661\pi$
$751$			3.93385i			0.143548i	−0.997421	+	0.0717742i	$0.977134\pi$
$752$		0			0
$753$	5.15330	+	5.15330i	0.187797	+	0.187797i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	21.8327i		−	0.793525i	−0.917921	−	0.396762i	$-0.870134\pi$
$757$		−	21.8327i		−	0.793525i	0.917921	−	0.396762i	$-0.129866\pi$
$758$		0			0
$759$		−	7.11421i		−	0.258230i
$760$		0			0
$761$			4.27291i			0.154893i	0.996997	+	0.0774464i	$0.0246767\pi$
$761$			4.27291i			0.154893i	−0.996997	+	0.0774464i	$0.975323\pi$
$762$		0			0
$763$		−	33.9080i		−	1.22755i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−38.9793	−	38.9793i	−1.40746	−	1.40746i
$768$		0			0
$769$		−	26.1800i		−	0.944074i	−0.881579	−	0.472037i	$-0.843519\pi$
$769$		−	26.1800i		−	0.944074i	0.881579	−	0.472037i	$-0.156481\pi$
$770$		0			0
$771$	10.1459	−	10.1459i	0.365395	−	0.365395i
$772$		0			0
$773$	15.0077			0.539791			0.269895	−	0.962890i	$-0.413011\pi$
$773$	15.0077			0.539791			0.269895	+	0.962890i	$0.413011\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.95587	+	3.95587i	0.141916	+	0.141916i
$778$		0			0
$779$	−2.82762	+	2.82762i	−0.101310	+	0.101310i
$780$		0			0
$781$	44.1977	+	44.1977i	1.58152	+	1.58152i
$782$		0			0
$783$	6.42007	−	6.42007i	0.229434	−	0.229434i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			42.9223i			1.53001i	0.644022	+	0.765007i	$0.277264\pi$
$787$			42.9223i			1.53001i	−0.644022	+	0.765007i	$0.722736\pi$
$788$		0			0
$789$	−6.98118	−	6.98118i	−0.248536	−	0.248536i
$790$		0			0
$791$	13.3568			0.474912
$792$		0			0
$793$	−9.69591	+	9.69591i	−0.344312	+	0.344312i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.280831			−0.00994753			−0.00497377	−	0.999988i	$-0.501583\pi$
$797$	−0.280831			−0.00994753			−0.00497377	+	0.999988i	$0.501583\pi$
$798$		0			0
$799$	−1.83371			−0.0648719
$800$		0			0
$801$	11.7052			0.413581
$802$		0			0
$803$	−22.7304			−0.802139
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.28398	−	3.28398i	0.115602	−	0.115602i
$808$		0			0
$809$	−16.5787			−0.582876			−0.291438	−	0.956590i	$-0.594134\pi$
$809$	−16.5787			−0.582876			−0.291438	+	0.956590i	$0.594134\pi$
$810$		0			0
$811$	−7.25384	−	7.25384i	−0.254717	−	0.254717i	0.568184	−	0.822901i	$-0.307646\pi$
$811$	−7.25384	−	7.25384i	−0.254717	−	0.254717i	−0.822901	+	0.568184i	$0.807646\pi$
$812$		0			0
$813$		−	5.27366i		−	0.184955i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.79405	+	3.79405i	−0.132737	+	0.132737i
$818$		0			0
$819$	21.8061	+	21.8061i	0.761965	+	0.761965i
$820$		0			0
$821$	−15.3525	+	15.3525i	−0.535806	+	0.535806i	−0.922294	−	0.386489i	$-0.873688\pi$
$821$	−15.3525	+	15.3525i	−0.535806	+	0.535806i	0.386489	+	0.922294i	$0.373688\pi$
$822$		0			0
$823$	−26.7794	−	26.7794i	−0.933472	−	0.933472i	0.0644492	−	0.997921i	$-0.479471\pi$
$823$	−26.7794	−	26.7794i	−0.933472	−	0.933472i	−0.997921	+	0.0644492i	$0.979471\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−39.4186			−1.37072			−0.685359	−	0.728205i	$-0.740355\pi$
$827$	−39.4186			−1.37072			−0.685359	+	0.728205i	$0.740355\pi$
$828$		0			0
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	−0.968461	−	0.249165i	$-0.919844\pi$
$829$	−20.7102	+	20.7102i	−0.719296	+	0.719296i	0.249165	+	0.968461i	$0.419844\pi$
$830$		0			0
$831$			4.11345i			0.142694i
$832$		0			0
$833$	−0.463083	−	0.463083i	−0.0160449	−	0.0160449i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			2.33725i			0.0807870i
$838$		0			0
$839$		−	31.8706i		−	1.10029i	−0.835068	−	0.550147i	$-0.814572\pi$
$839$		−	31.8706i		−	1.10029i	0.835068	−	0.550147i	$-0.185428\pi$
$840$		0			0
$841$			18.8975i			0.651638i
$842$		0			0
$843$			10.4350i			0.359399i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	37.6347	+	37.6347i	1.29314	+	1.29314i
$848$		0			0
$849$		−	7.18654i		−	0.246642i
$850$		0			0
$851$	8.75302	−	8.75302i	0.300050	−	0.300050i
$852$		0			0
$853$	26.5538			0.909185			0.454592	−	0.890700i	$-0.349785\pi$
$853$	26.5538			0.909185			0.454592	+	0.890700i	$0.349785\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	0.966104	−	0.258153i	$-0.0831140\pi$
$857$	20.7249	+	20.7249i	0.707951	+	0.707951i	−0.258153	+	0.966104i	$0.583114\pi$
$858$		0			0
$859$	−35.9248	+	35.9248i	−1.22574	+	1.22574i	−0.260176	+	0.965561i	$0.583781\pi$
$859$	−35.9248	+	35.9248i	−1.22574	+	1.22574i	−0.965561	+	0.260176i	$0.916219\pi$
$860$		0			0
$861$	2.58298	+	2.58298i	0.0880278	+	0.0880278i
$862$		0			0
$863$	9.19232	−	9.19232i	0.312910	−	0.312910i	−0.533126	−	0.846036i	$-0.678983\pi$
$863$	9.19232	−	9.19232i	0.312910	−	0.312910i	0.846036	+	0.533126i	$0.178983\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	8.39500i		−	0.285109i
$868$		0			0
$869$	34.9117	+	34.9117i	1.18430	+	1.18430i
$870$		0			0
$871$	−56.1608			−1.90293
$872$		0			0
$873$	−19.7151	+	19.7151i	−0.667253	+	0.667253i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	17.9106			0.604799			0.302399	−	0.953181i	$-0.402212\pi$
$877$	17.9106			0.604799			0.302399	+	0.953181i	$0.402212\pi$
$878$		0			0
$879$	−5.91641			−0.199556
$880$		0			0
$881$	6.01537			0.202663			0.101332	−	0.994853i	$-0.467690\pi$
$881$	6.01537			0.202663			0.101332	+	0.994853i	$0.467690\pi$
$882$		0			0
$883$	19.8374			0.667580			0.333790	−	0.942647i	$-0.391672\pi$
$883$	19.8374			0.667580			0.333790	+	0.942647i	$0.391672\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.3740	−	14.3740i	0.482632	−	0.482632i	−0.423339	−	0.905971i	$-0.639142\pi$
$887$	14.3740	−	14.3740i	0.482632	−	0.482632i	0.905971	+	0.423339i	$0.139142\pi$
$888$		0			0
$889$	2.36149			0.0792019
$890$		0			0
$891$	28.7106	+	28.7106i	0.961842	+	0.961842i
$892$		0			0
$893$		−	7.25398i		−	0.242745i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.31941	+	4.31941i	−0.144221	+	0.144221i
$898$		0			0
$899$	1.83892	+	1.83892i	0.0613315	+	0.0613315i
$900$		0			0
$901$	−0.214938	+	0.214938i	−0.00716061	+	0.00716061i
$902$		0			0
$903$	3.46580	+	3.46580i	0.115335	+	0.115335i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−39.0417			−1.29636			−0.648180	−	0.761487i	$-0.724469\pi$
$907$	−39.0417			−1.29636			−0.648180	+	0.761487i	$0.724469\pi$
$908$		0			0
$909$	−23.0976	+	23.0976i	−0.766100	+	0.766100i
$910$		0			0
$911$		−	14.0166i		−	0.464392i	−0.972669	−	0.232196i	$-0.925409\pi$
$911$		−	14.0166i		−	0.464392i	0.972669	−	0.232196i	$-0.0745911\pi$
$912$		0			0
$913$	−38.4879	−	38.4879i	−1.27376	−	1.27376i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			23.6245i			0.780150i
$918$		0			0
$919$		−	8.15149i		−	0.268893i	−0.990921	−	0.134446i	$-0.957074\pi$
$919$		−	8.15149i		−	0.268893i	0.990921	−	0.134446i	$-0.0429256\pi$
$920$		0			0
$921$		−	12.6362i		−	0.416376i
$922$		0			0
$923$		−	53.6695i		−	1.76655i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	14.2212	+	14.2212i	0.467086	+	0.467086i
$928$		0			0
$929$			13.4779i			0.442196i	0.975252	+	0.221098i	$0.0709641\pi$
$929$			13.4779i			0.442196i	−0.975252	+	0.221098i	$0.929036\pi$
$930$		0			0
$931$	1.83192	−	1.83192i	0.0600386	−	0.0600386i
$932$		0			0
$933$	10.6633			0.349101
$934$		0			0
$935$		0			0
$936$		0			0
$937$	15.8564	+	15.8564i	0.518005	+	0.518005i	0.916967	−	0.398963i	$-0.130630\pi$
$937$	15.8564	+	15.8564i	0.518005	+	0.518005i	−0.398963	+	0.916967i	$0.630630\pi$
$938$		0			0
$939$	9.33225	−	9.33225i	0.304546	−	0.304546i
$940$		0			0
$941$	15.7073	+	15.7073i	0.512044	+	0.512044i	0.915152	−	0.403108i	$-0.132070\pi$
$941$	15.7073	+	15.7073i	0.512044	+	0.512044i	−0.403108	+	0.915152i	$0.632070\pi$
$942$		0			0
$943$	5.71527	−	5.71527i	0.186115	−	0.186115i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			33.6925i			1.09486i	0.836852	+	0.547430i	$0.184394\pi$
$947$			33.6925i			1.09486i	−0.836852	+	0.547430i	$0.815606\pi$
$948$		0			0
$949$	13.8008	+	13.8008i	0.447993	+	0.447993i
$950$		0			0
$951$	8.06945			0.261670
$952$		0			0
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.0916550	−	0.995791i	$-0.470784\pi$
$953$	33.5702	−	33.5702i	1.08745	−	1.08745i	0.995791	−	0.0916550i	$-0.0292157\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−9.36440			−0.302708
$958$		0			0
$959$	−39.7234			−1.28274
$960$		0			0
$961$	30.3305			0.978404
$962$		0			0
$963$	−24.7257			−0.796774
$964$		0			0
$965$		0			0
$966$		0			0
$967$	28.6436	−	28.6436i	0.921115	−	0.921115i	−0.0759933	−	0.997108i	$-0.524213\pi$
$967$	28.6436	−	28.6436i	0.921115	−	0.921115i	0.997108	+	0.0759933i	$0.0242128\pi$
$968$		0			0
$969$	−0.179123			−0.00575427
$970$		0			0
$971$	35.7115	+	35.7115i	1.14604	+	1.14604i	0.987325	+	0.158713i	$0.0507345\pi$
$971$	35.7115	+	35.7115i	1.14604	+	1.14604i	0.158713	+	0.987325i	$0.449266\pi$
$972$		0			0
$973$			24.0669i			0.771551i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	−0.811879	−	0.583826i	$-0.801555\pi$
$977$	−7.12822	+	7.12822i	−0.228052	+	0.228052i	0.583826	+	0.811879i	$0.301555\pi$
$978$		0			0
$979$	−17.8375	−	17.8375i	−0.570090	−	0.570090i
$980$		0			0
$981$	−30.0355	+	30.0355i	−0.958959	+	0.958959i
$982$		0			0
$983$	−23.9941	−	23.9941i	−0.765292	−	0.765292i	0.211982	−	0.977274i	$-0.432008\pi$
$983$	−23.9941	−	23.9941i	−0.765292	−	0.765292i	−0.977274	+	0.211982i	$0.932008\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.62639			−0.210920
$988$		0			0
$989$	7.66866	−	7.66866i	0.243849	−	0.243849i
$990$		0			0
$991$			40.6040i			1.28983i	0.764255	+	0.644914i	$0.223107\pi$
$991$			40.6040i			1.28983i	−0.764255	+	0.644914i	$0.776893\pi$
$992$		0			0
$993$	−4.32718	−	4.32718i	−0.137319	−	0.137319i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	54.9087i		−	1.73898i	−0.493953	−	0.869488i	$-0.664449\pi$
$997$		−	54.9087i		−	1.73898i	0.493953	−	0.869488i	$-0.335551\pi$
$998$		0			0
$999$		−	14.6437i		−	0.463308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.s.d.943.4		18
4.3	odd	2		400.2.s.d.243.1		18
5.2	odd	4		1600.2.j.d.1007.6		18
5.3	odd	4		320.2.j.b.47.4		18
5.4	even	2		320.2.s.b.303.6		18
16.5	even	4		400.2.j.d.43.4		18
16.11	odd	4		1600.2.j.d.143.4		18
20.3	even	4		80.2.j.b.67.6	yes	18
20.7	even	4		400.2.j.d.307.4		18
20.19	odd	2		80.2.s.b.3.9	yes	18
40.3	even	4		640.2.j.d.607.4		18
40.13	odd	4		640.2.j.c.607.6		18
40.19	odd	2		640.2.s.d.223.6		18
40.29	even	2		640.2.s.c.223.4		18
60.23	odd	4		720.2.bd.g.307.4		18
60.59	even	2		720.2.z.g.163.1		18
80.3	even	4		640.2.s.c.287.4		18
80.13	odd	4		640.2.s.d.287.6		18
80.19	odd	4		640.2.j.c.543.4		18
80.27	even	4	inner	1600.2.s.d.207.4		18
80.29	even	4		640.2.j.d.543.6		18
80.37	odd	4		400.2.s.d.107.1		18
80.43	even	4		320.2.s.b.207.6		18
80.53	odd	4		80.2.s.b.27.9	yes	18
80.59	odd	4		320.2.j.b.143.6		18
80.69	even	4		80.2.j.b.43.6	✓	18
240.53	even	4		720.2.z.g.667.1		18
240.149	odd	4		720.2.bd.g.523.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.6	✓	18	80.69	even	4
80.2.j.b.67.6	yes	18	20.3	even	4
80.2.s.b.3.9	yes	18	20.19	odd	2
80.2.s.b.27.9	yes	18	80.53	odd	4
320.2.j.b.47.4		18	5.3	odd	4
320.2.j.b.143.6		18	80.59	odd	4
320.2.s.b.207.6		18	80.43	even	4
320.2.s.b.303.6		18	5.4	even	2
400.2.j.d.43.4		18	16.5	even	4
400.2.j.d.307.4		18	20.7	even	4
400.2.s.d.107.1		18	80.37	odd	4
400.2.s.d.243.1		18	4.3	odd	2
640.2.j.c.543.4		18	80.19	odd	4
640.2.j.c.607.6		18	40.13	odd	4
640.2.j.d.543.6		18	80.29	even	4
640.2.j.d.607.4		18	40.3	even	4
640.2.s.c.223.4		18	40.29	even	2
640.2.s.c.287.4		18	80.3	even	4
640.2.s.d.223.6		18	40.19	odd	2
640.2.s.d.287.6		18	80.13	odd	4
720.2.z.g.163.1		18	60.59	even	2
720.2.z.g.667.1		18	240.53	even	4
720.2.bd.g.307.4		18	60.23	odd	4
720.2.bd.g.523.4		18	240.149	odd	4
1600.2.j.d.143.4		18	16.11	odd	4
1600.2.j.d.1007.6		18	5.2	odd	4
1600.2.s.d.207.4		18	80.27	even	4	inner
1600.2.s.d.943.4		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.496487 q^{3} +(1.55426 - 1.55426i) q^{7} -2.75350 q^{9} +O(q^{10})\)	\(q-0.496487 q^{3} +(1.55426 - 1.55426i) q^{7} -2.75350 q^{9} +(4.19607 + 4.19607i) q^{11} -5.09530i q^{13} +(-0.213542 + 0.213542i) q^{17} +(-0.844754 - 0.844754i) q^{19} +(-0.771668 + 0.771668i) q^{21} +(1.70744 + 1.70744i) q^{23} +2.85654 q^{27} +(2.24750 - 2.24750i) q^{29} +0.818209i q^{31} +(-2.08329 - 2.08329i) q^{33} -5.12639i q^{37} +2.52975i q^{39} -3.34727i q^{41} -4.49131i q^{43} +(4.29355 + 4.29355i) q^{47} +2.16858i q^{49} +(0.106021 - 0.106021i) q^{51} +1.00653 q^{53} +(0.419410 + 0.419410i) q^{57} +(7.65005 - 7.65005i) q^{59} +(-1.90291 - 1.90291i) q^{61} +(-4.27964 + 4.27964i) q^{63} -11.0221i q^{67} +(-0.847724 - 0.847724i) q^{69} +10.5331 q^{71} +(-2.70854 + 2.70854i) q^{73} +13.0435 q^{77} +8.32010 q^{79} +6.84226 q^{81} -9.17237 q^{83} +(-1.11585 + 1.11585i) q^{87} -4.25101 q^{89} +(-7.91940 - 7.91940i) q^{91} -0.406230i q^{93} +(7.16000 - 7.16000i) q^{97} +(-11.5539 - 11.5539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{7} + 10 q^{9}+O(q^{10}) \) 18 * q + 2 * q^7 + 10 * q^9	\( 18 q + 2 q^{7} + 10 q^{9} + 2 q^{11} + 6 q^{17} + 2 q^{19} - 16 q^{21} - 2 q^{23} - 24 q^{27} + 14 q^{29} + 8 q^{33} + 38 q^{47} - 8 q^{51} - 12 q^{53} + 24 q^{57} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 44 q^{77} + 16 q^{79} + 2 q^{81} + 40 q^{83} + 24 q^{87} + 12 q^{89} - 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 2 * q^7 + 10 * q^9 + 2 * q^11 + 6 * q^17 + 2 * q^19 - 16 * q^21 - 2 * q^23 - 24 * q^27 + 14 * q^29 + 8 * q^33 + 38 * q^47 - 8 * q^51 - 12 * q^53 + 24 * q^57 - 10 * q^59 + 14 * q^61 - 6 * q^63 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 44 * q^77 + 16 * q^79 + 2 * q^81 + 40 * q^83 + 24 * q^87 + 12 * q^89 - 18 * q^97 - 22 * q^99

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