LMFDB - Embedded newform 1148.2.ba.a.113.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.9
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +O(q^{10})$	\(q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +(0.409185 + 0.132952i) q^{11} +(2.74295 - 3.77534i) q^{13} +(0.819748 - 0.266352i) q^{15} +(-4.29238 - 1.39468i) q^{17} +(1.21601 + 1.67369i) q^{19} +(-0.175310 + 0.127370i) q^{21} +(1.13883 + 0.827411i) q^{23} +(-8.75484 + 6.36076i) q^{25} +1.29000i q^{27} +(-0.472988 + 0.153683i) q^{29} +(1.57517 - 4.84788i) q^{31} +(-0.0288101 + 0.0886683i) q^{33} +(2.33799 - 3.21797i) q^{35} +(-3.01426 - 9.27694i) q^{37} +(0.818098 + 0.594383i) q^{39} +(-6.19055 - 1.63618i) q^{41} +(5.23055 + 3.80022i) q^{43} +(-3.62975 - 11.1712i) q^{45} +(2.13941 - 2.94464i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.302220 - 0.930139i) q^{51} +(3.39420 - 1.10284i) q^{53} -1.71135i q^{55} +(-0.362680 + 0.263503i) q^{57} +(-11.4286 - 8.30337i) q^{59} +(5.50434 - 3.99914i) q^{61} +(1.73576 + 2.38906i) q^{63} +(-17.6535 - 5.73596i) q^{65} +(-4.97041 + 1.61498i) q^{67} +(-0.179296 + 0.246780i) q^{69} +(-11.2847 - 3.66663i) q^{71} +3.95893 q^{73} +(-1.37835 - 1.89713i) q^{75} +(0.132952 + 0.409185i) q^{77} +2.17988i q^{79} +8.57959 q^{81} +3.14995 q^{83} +17.9522i q^{85} +(-0.0333024 - 0.102494i) q^{87} +(-6.28917 - 8.65631i) q^{89} +4.66658 q^{91} +(1.05051 + 0.341332i) q^{93} +(4.83683 - 6.65733i) q^{95} +(10.7442 - 3.49101i) q^{97} +(1.20834 + 0.392613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.216695i			0.125109i	0.998042	+	0.0625545i	$0.0199247\pi$
$3$			0.216695i			0.125109i	−0.998042	+	0.0625545i	$0.980075\pi$
$4$		0			0
$5$	−1.22916	−	3.78295i	−0.549696	−	1.69179i	−0.709556	−	0.704649i	$-0.751104\pi$
$5$	−1.22916	−	3.78295i	−0.549696	−	1.69179i	0.159860	−	0.987140i	$-0.448896\pi$
$6$		0			0
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$7$	0.587785	+	0.809017i	0.222162	+	0.305780i
$8$		0			0
$9$	2.95304			0.984348
$10$		0			0
$11$	0.409185	+	0.132952i	0.123374	+	0.0400866i	0.370053	−	0.929011i	$-0.379339\pi$
$11$	0.409185	+	0.132952i	0.123374	+	0.0400866i	−0.246679	+	0.969097i	$0.579339\pi$
$12$		0			0
$13$	2.74295	−	3.77534i	0.760757	−	1.04709i	−0.236394	−	0.971657i	$-0.575966\pi$
$13$	2.74295	−	3.77534i	0.760757	−	1.04709i	0.997151	−	0.0754345i	$-0.0240344\pi$
$14$		0			0
$15$	0.819748	−	0.266352i	0.211658	−	0.0687719i
$16$		0			0
$17$	−4.29238	−	1.39468i	−1.04106	−	0.338260i	−0.261904	−	0.965094i	$-0.584350\pi$
$17$	−4.29238	−	1.39468i	−1.04106	−	0.338260i	−0.779152	+	0.626834i	$0.784350\pi$
$18$		0			0
$19$	1.21601	+	1.67369i	0.278971	+	0.383971i	0.925393	−	0.379010i	$-0.123735\pi$
$19$	1.21601	+	1.67369i	0.278971	+	0.383971i	−0.646422	+	0.762980i	$0.723735\pi$
$20$		0			0
$21$	−0.175310	+	0.127370i	−0.0382558	+	0.0277945i
$22$		0			0
$23$	1.13883	+	0.827411i	0.237463	+	0.172527i	0.700152	−	0.713993i	$-0.253115\pi$
$23$	1.13883	+	0.827411i	0.237463	+	0.172527i	−0.462689	+	0.886521i	$0.653115\pi$
$24$		0			0
$25$	−8.75484	+	6.36076i	−1.75097	+	1.27215i
$26$		0			0
$27$			1.29000i			0.248260i
$28$		0			0
$29$	−0.472988	+	0.153683i	−0.0878318	+	0.0285383i	−0.352603	−	0.935773i	$-0.614703\pi$
$29$	−0.472988	+	0.153683i	−0.0878318	+	0.0285383i	0.264771	+	0.964311i	$0.414703\pi$
$30$		0			0
$31$	1.57517	−	4.84788i	0.282909	−	0.870705i	−0.704108	−	0.710093i	$-0.748653\pi$
$31$	1.57517	−	4.84788i	0.282909	−	0.870705i	0.987018	−	0.160613i	$-0.0513470\pi$
$32$		0			0
$33$	−0.0288101	+	0.0886683i	−0.00501519	+	0.0154352i
$34$		0			0
$35$	2.33799	−	3.21797i	0.395193	−	0.543937i
$36$		0			0
$37$	−3.01426	−	9.27694i	−0.495542	−	1.52512i	−0.816111	−	0.577895i	$-0.803874\pi$
$37$	−3.01426	−	9.27694i	−0.495542	−	1.52512i	0.320570	−	0.947225i	$-0.396126\pi$
$38$		0			0
$39$	0.818098	+	0.594383i	0.131001	+	0.0951775i
$40$		0			0
$41$	−6.19055	−	1.63618i	−0.966801	−	0.255529i
$41$	−6.19055	−	1.63618i	−0.966801	−	0.255529i
$42$		0			0
$43$	5.23055	+	3.80022i	0.797651	+	0.579527i	0.910224	−	0.414116i	$-0.135909\pi$
$43$	5.23055	+	3.80022i	0.797651	+	0.579527i	−0.112573	+	0.993643i	$0.535909\pi$
$44$		0			0
$45$	−3.62975	−	11.1712i	−0.541092	−	1.66531i
$46$		0			0
$47$	2.13941	−	2.94464i	0.312065	−	0.429520i	−0.623959	−	0.781457i	$-0.714477\pi$
$47$	2.13941	−	2.94464i	0.312065	−	0.429520i	0.936024	+	0.351937i	$0.114477\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	0.302220	−	0.930139i	0.0423193	−	0.130245i
$52$		0			0
$53$	3.39420	−	1.10284i	0.466229	−	0.151487i	−0.0664757	−	0.997788i	$-0.521175\pi$
$53$	3.39420	−	1.10284i	0.466229	−	0.151487i	0.532705	+	0.846301i	$0.321175\pi$
$54$		0			0
$55$		−	1.71135i		−	0.230758i
$56$		0			0
$57$	−0.362680	+	0.263503i	−0.0480382	+	0.0349018i
$58$		0			0
$59$	−11.4286	−	8.30337i	−1.48788	−	1.08101i	−0.974910	−	0.222600i	$-0.928546\pi$
$59$	−11.4286	−	8.30337i	−1.48788	−	1.08101i	−0.512969	−	0.858407i	$-0.671454\pi$
$60$		0			0
$61$	5.50434	−	3.99914i	0.704759	−	0.512037i	−0.176720	−	0.984261i	$-0.556549\pi$
$61$	5.50434	−	3.99914i	0.704759	−	0.512037i	0.881479	+	0.472224i	$0.156549\pi$
$62$		0			0
$63$	1.73576	+	2.38906i	0.218685	+	0.300994i
$64$		0			0
$65$	−17.6535	−	5.73596i	−2.18964	−	0.711458i
$66$		0			0
$67$	−4.97041	+	1.61498i	−0.607233	+	0.197302i	−0.596464	−	0.802640i	$-0.703428\pi$
$67$	−4.97041	+	1.61498i	−0.607233	+	0.197302i	−0.0107690	+	0.999942i	$0.503428\pi$
$68$		0			0
$69$	−0.179296	+	0.246780i	−0.0215847	+	0.0297088i
$70$		0			0
$71$	−11.2847	−	3.66663i	−1.33925	−	0.435149i	−0.450189	−	0.892933i	$-0.648643\pi$
$71$	−11.2847	−	3.66663i	−1.33925	−	0.435149i	−0.889064	+	0.457784i	$0.848643\pi$
$72$		0			0
$73$	3.95893			0.463358			0.231679	−	0.972792i	$-0.425578\pi$
$73$	3.95893			0.463358			0.231679	+	0.972792i	$0.425578\pi$
$74$		0			0
$75$	−1.37835	−	1.89713i	−0.159158	−	0.219062i
$76$		0			0
$77$	0.132952	+	0.409185i	0.0151513	+	0.0466309i
$78$		0			0
$79$			2.17988i			0.245256i	0.992453	+	0.122628i	$0.0391322\pi$
$79$			2.17988i			0.245256i	−0.992453	+	0.122628i	$0.960868\pi$
$80$		0			0
$81$	8.57959			0.953288
$82$		0			0
$83$	3.14995			0.345751			0.172876	−	0.984944i	$-0.444694\pi$
$83$	3.14995			0.345751			0.172876	+	0.984944i	$0.444694\pi$
$84$		0			0
$85$			17.9522i			1.94719i
$86$		0			0
$87$	−0.0333024	−	0.102494i	−0.00357039	−	0.0109885i
$88$		0			0
$89$	−6.28917	−	8.65631i	−0.666651	−	0.917567i	0.333027	−	0.942917i	$-0.391930\pi$
$89$	−6.28917	−	8.65631i	−0.666651	−	0.917567i	−0.999679	+	0.0253506i	$0.991930\pi$
$90$		0			0
$91$	4.66658			0.489191
$92$		0			0
$93$	1.05051	+	0.341332i	0.108933	+	0.0353945i
$94$		0			0
$95$	4.83683	−	6.65733i	0.496248	−	0.683027i
$96$		0			0
$97$	10.7442	−	3.49101i	1.09091	−	0.354458i	0.292312	−	0.956323i	$-0.405576\pi$
$97$	10.7442	−	3.49101i	1.09091	−	0.354458i	0.798598	+	0.601865i	$0.205576\pi$
$98$		0			0
$99$	1.20834	+	0.392613i	0.121443	+	0.0394591i
$100$		0			0
$101$	1.43053	+	1.96895i	0.142343	+	0.195918i	0.874236	−	0.485502i	$-0.161363\pi$
$101$	1.43053	+	1.96895i	0.142343	+	0.195918i	−0.731893	+	0.681419i	$0.761363\pi$
$102$		0			0
$103$	−1.89414	+	1.37618i	−0.186636	+	0.135599i	−0.677180	−	0.735818i	$-0.736798\pi$
$103$	−1.89414	+	1.37618i	−0.186636	+	0.135599i	0.490544	+	0.871416i	$0.336798\pi$
$104$		0			0
$105$	0.697319	+	0.506632i	0.0680514	+	0.0494422i
$106$		0			0
$107$	14.4690	−	10.5123i	1.39877	−	1.01626i	0.403928	−	0.914791i	$-0.367645\pi$
$107$	14.4690	−	10.5123i	1.39877	−	1.01626i	0.994838	−	0.101473i	$-0.0323554\pi$
$108$		0			0
$109$			12.3115i			1.17923i	0.807685	+	0.589614i	$0.200720\pi$
$109$			12.3115i			1.17923i	−0.807685	+	0.589614i	$0.799280\pi$
$110$		0			0
$111$	2.01027	−	0.653176i	0.190806	−	0.0619967i
$112$		0			0
$113$	−3.14514	+	9.67974i	−0.295870	+	0.910594i	0.687058	+	0.726602i	$0.258902\pi$
$113$	−3.14514	+	9.67974i	−0.295870	+	0.910594i	−0.982928	+	0.183991i	$0.941098\pi$
$114$		0			0
$115$	1.73025	−	5.32518i	0.161347	−	0.496575i
$116$		0			0
$117$	8.10004	−	11.1488i	0.748849	−	1.03070i
$118$		0			0
$119$	−1.39468	−	4.29238i	−0.127850	−	0.393482i
$120$		0			0
$121$	−8.74943	−	6.35683i	−0.795403	−	0.577894i
$122$		0			0
$123$	0.354553	−	1.34146i	0.0319689	−	0.120956i
$124$		0			0
$125$	18.7337	+	13.6108i	1.67559	+	1.21739i
$126$		0			0
$127$	5.14230	+	15.8264i	0.456305	+	1.40436i	0.869596	+	0.493764i	$0.164379\pi$
$127$	5.14230	+	15.8264i	0.456305	+	1.40436i	−0.413291	+	0.910599i	$0.635621\pi$
$128$		0			0
$129$	−0.823488	+	1.13343i	−0.0725041	+	0.0997933i
$130$		0			0
$131$	−5.66436	+	17.4331i	−0.494897	+	1.52314i	0.322220	+	0.946665i	$0.395571\pi$
$131$	−5.66436	+	17.4331i	−0.494897	+	1.52314i	−0.817117	+	0.576472i	$0.804429\pi$
$132$		0			0
$133$	−0.639293	+	1.96754i	−0.0554337	+	0.170607i
$134$		0			0
$135$	4.87999	−	1.58561i	0.420003	−	0.136467i
$136$		0			0
$137$			4.55542i			0.389196i	0.980883	+	0.194598i	$0.0623403\pi$
$137$			4.55542i			0.389196i	−0.980883	+	0.194598i	$0.937660\pi$
$138$		0			0
$139$	7.78156	−	5.65363i	0.660023	−	0.479535i	−0.206648	−	0.978415i	$-0.566255\pi$
$139$	7.78156	−	5.65363i	0.660023	−	0.479535i	0.866671	+	0.498880i	$0.166255\pi$
$140$		0			0
$141$	0.638090	+	0.463599i	0.0537368	+	0.0390421i
$142$		0			0
$143$	1.62431	−	1.18013i	0.135832	−	0.0986876i
$144$		0			0
$145$	1.16275	+	1.60039i	0.0965614	+	0.132905i
$146$		0			0
$147$	−0.206089	−	0.0669625i	−0.0169980	−	0.00552297i
$148$		0			0
$149$	−3.19195	+	1.03713i	−0.261495	+	0.0849649i	−0.436830	−	0.899544i	$-0.643899\pi$
$149$	−3.19195	+	1.03713i	−0.261495	+	0.0849649i	0.175335	+	0.984509i	$0.443899\pi$
$150$		0			0
$151$	7.21015	−	9.92393i	0.586754	−	0.807598i	−0.407661	−	0.913133i	$-0.633656\pi$
$151$	7.21015	−	9.92393i	0.586754	−	0.807598i	0.994416	+	0.105535i	$0.0336556\pi$
$152$		0			0
$153$	−12.6756	−	4.11855i	−1.02476	−	0.332965i
$154$		0			0
$155$	−20.2755			−1.62856
$156$		0			0
$157$	−1.49501	−	2.05771i	−0.119315	−	0.164223i	0.745182	−	0.666861i	$-0.232363\pi$
$157$	−1.49501	−	2.05771i	−0.119315	−	0.164223i	−0.864497	+	0.502638i	$0.832363\pi$
$158$		0			0
$159$	0.238981	+	0.735507i	0.0189524	+	0.0583295i
$160$		0			0
$161$			1.40768i			0.110940i
$162$		0			0
$163$	21.5148			1.68517			0.842585	−	0.538563i	$-0.181033\pi$
$163$	21.5148			1.68517			0.842585	+	0.538563i	$0.181033\pi$
$164$		0			0
$165$	0.370840			0.0288699
$166$		0			0
$167$			10.5967i			0.820000i	0.912085	+	0.410000i	$0.134471\pi$
$167$			10.5967i			0.820000i	−0.912085	+	0.410000i	$0.865529\pi$
$168$		0			0
$169$	−2.71224	−	8.34740i	−0.208633	−	0.642108i
$170$		0			0
$171$	3.59092	+	4.94248i	0.274605	+	0.377961i
$172$		0			0
$173$	3.44807			0.262152			0.131076	−	0.991372i	$-0.458157\pi$
$173$	3.44807			0.262152			0.131076	+	0.991372i	$0.458157\pi$
$174$		0			0
$175$	−10.2919	−	3.34405i	−0.777997	−	0.252786i
$176$		0			0
$177$	1.79930	−	2.47652i	0.135244	−	0.186147i
$178$		0			0
$179$	14.8273	−	4.81770i	1.10825	−	0.360092i	0.302977	−	0.952998i	$-0.402020\pi$
$179$	14.8273	−	4.81770i	1.10825	−	0.360092i	0.805271	+	0.592906i	$0.202020\pi$
$180$		0			0
$181$	5.09614	+	1.65584i	0.378793	+	0.123077i	0.492224	−	0.870469i	$-0.336184\pi$
$181$	5.09614	+	1.65584i	0.378793	+	0.123077i	−0.113431	+	0.993546i	$0.536184\pi$
$182$		0			0
$183$	0.866594	+	1.19276i	0.0640605	+	0.0881717i
$184$		0			0
$185$	−31.3893	+	22.8056i	−2.30778	+	1.67670i
$186$		0			0
$187$	−1.57095	−	1.14136i	−0.114879	−	0.0834647i
$188$		0			0
$189$	−1.04363	+	0.758240i	−0.0759128	+	0.0551539i
$190$		0			0
$191$		−	18.6695i		−	1.35088i	−0.737416	−	0.675439i	$-0.763954\pi$
$191$		−	18.6695i		−	1.35088i	0.737416	−	0.675439i	$-0.236046\pi$
$192$		0			0
$193$	−22.1479	+	7.19628i	−1.59424	+	0.517999i	−0.965674	−	0.259758i	$-0.916357\pi$
$193$	−22.1479	+	7.19628i	−1.59424	+	0.517999i	−0.628565	+	0.777757i	$0.716357\pi$
$194$		0			0
$195$	1.24295	−	3.82542i	0.0890098	−	0.273944i
$196$		0			0
$197$	0.451696	−	1.39018i	0.0321820	−	0.0990460i	−0.933675	−	0.358121i	$-0.883418\pi$
$197$	0.451696	−	1.39018i	0.0321820	−	0.0990460i	0.965857	+	0.259075i	$0.0834176\pi$
$198$		0			0
$199$	−16.1204	+	22.1879i	−1.14275	+	1.57286i	−0.381532	+	0.924356i	$0.624603\pi$
$199$	−16.1204	+	22.1879i	−1.14275	+	1.57286i	−0.761215	+	0.648500i	$0.775397\pi$
$200$		0			0
$201$	−0.349959	−	1.07706i	−0.0246842	−	0.0759703i
$202$		0			0
$203$	−0.402348	−	0.292323i	−0.0282393	−	0.0205170i
$204$		0			0
$205$	1.41955	+	25.4297i	0.0991459	+	1.77609i
$206$		0			0
$207$	3.36303	+	2.44338i	0.233746	+	0.169827i
$208$		0			0
$209$	0.275051	+	0.846519i	0.0190257	+	0.0585549i
$210$		0			0
$211$	−1.60589	+	2.21031i	−0.110554	+	0.152164i	−0.860708	−	0.509098i	$-0.829979\pi$
$211$	−1.60589	+	2.21031i	−0.110554	+	0.152164i	0.750155	+	0.661262i	$0.229979\pi$
$212$		0			0
$213$	0.794542	−	2.44535i	0.0544411	−	0.167553i
$214$		0			0
$215$	7.94688	−	24.4580i	0.541973	−	1.66802i
$216$		0			0
$217$	4.84788	−	1.57517i	0.329096	−	0.106930i
$218$		0			0
$219$			0.857881i			0.0579703i
$220$		0			0
$221$	−17.0392	+	12.3797i	−1.14618	+	0.832748i
$222$		0			0
$223$	−1.96039	−	1.42431i	−0.131277	−	0.0953787i	0.520209	−	0.854039i	$-0.325854\pi$
$223$	−1.96039	−	1.42431i	−0.131277	−	0.0953787i	−0.651486	+	0.758661i	$0.725854\pi$
$224$		0			0
$225$	−25.8534	+	18.7836i	−1.72356	+	1.25224i
$226$		0			0
$227$	6.10875	+	8.40797i	0.405452	+	0.558056i	0.962102	−	0.272691i	$-0.0879135\pi$
$227$	6.10875	+	8.40797i	0.405452	+	0.558056i	−0.556650	+	0.830747i	$0.687914\pi$
$228$		0			0
$229$	22.6120	+	7.34710i	1.49425	+	0.485510i	0.938334	−	0.345731i	$-0.112369\pi$
$229$	22.6120	+	7.34710i	1.49425	+	0.485510i	0.555912	+	0.831241i	$0.312369\pi$
$230$		0			0
$231$	−0.0886683	+	0.0288101i	−0.00583395	+	0.00189556i
$232$		0			0
$233$	−14.7786	+	20.3410i	−0.968179	+	1.33258i	−0.0252174	+	0.999682i	$0.508028\pi$
$233$	−14.7786	+	20.3410i	−0.968179	+	1.33258i	−0.942961	+	0.332902i	$0.891972\pi$
$234$		0			0
$235$	−13.7691	−	4.47386i	−0.898198	−	0.291842i
$236$		0			0
$237$	−0.472370			−0.0306837
$238$		0			0
$239$	−4.74998	−	6.53779i	−0.307251	−	0.422894i	0.627271	−	0.778801i	$-0.284172\pi$
$239$	−4.74998	−	6.53779i	−0.307251	−	0.422894i	−0.934521	+	0.355907i	$0.884172\pi$
$240$		0			0
$241$	2.45473	+	7.55489i	0.158123	+	0.486653i	0.998464	−	0.0554053i	$-0.0176451\pi$
$241$	2.45473	+	7.55489i	0.158123	+	0.486653i	−0.840341	+	0.542059i	$0.817645\pi$
$242$		0			0
$243$			5.72914i			0.367525i
$244$		0			0
$245$	3.97763			0.254122
$246$		0			0
$247$	9.65420			0.614282
$248$		0			0
$249$			0.682578i			0.0432566i
$250$		0			0
$251$	−8.43428	−	25.9580i	−0.532367	−	1.63846i	−0.749271	−	0.662264i	$-0.769596\pi$
$251$	−8.43428	−	25.9580i	−0.532367	−	1.63846i	0.216904	−	0.976193i	$-0.430404\pi$
$252$		0			0
$253$	0.355987	+	0.489974i	0.0223807	+	0.0308044i
$254$		0			0
$255$	−3.89015			−0.243611
$256$		0			0
$257$	−1.97795	−	0.642673i	−0.123381	−	0.0400889i	0.246676	−	0.969098i	$-0.420662\pi$
$257$	−1.97795	−	0.642673i	−0.123381	−	0.0400889i	−0.370057	+	0.929009i	$0.620662\pi$
$258$		0			0
$259$	5.73347	−	7.89144i	0.356260	−	0.490350i
$260$		0			0
$261$	−1.39676	+	0.453833i	−0.0864570	+	0.0280916i
$262$		0			0
$263$	22.2119	+	7.21709i	1.36965	+	0.445025i	0.899252	−	0.437431i	$-0.144112\pi$
$263$	22.2119	+	7.21709i	1.36965	+	0.445025i	0.470394	+	0.882456i	$0.344112\pi$
$264$		0			0
$265$	−8.34401	−	11.4845i	−0.512569	−	0.705490i
$266$		0			0
$267$	1.87578	−	1.36283i	0.114796	−	0.0834041i
$268$		0			0
$269$	24.2208	+	17.5975i	1.47677	+	1.07294i	0.978579	+	0.205870i	$0.0660024\pi$
$269$	24.2208	+	17.5975i	1.47677	+	1.07294i	0.498192	+	0.867067i	$0.333998\pi$
$270$		0			0
$271$	15.9323	−	11.5755i	0.967819	−	0.703162i	0.0128656	−	0.999917i	$-0.495905\pi$
$271$	15.9323	−	11.5755i	0.967819	−	0.703162i	0.954953	+	0.296755i	$0.0959046\pi$
$272$		0			0
$273$			1.01123i			0.0612021i
$274$		0			0
$275$	−4.42802	+	1.43875i	−0.267020	+	0.0867600i
$276$		0			0
$277$	−0.667329	+	2.05383i	−0.0400959	+	0.123402i	−0.969101	−	0.246665i	$-0.920665\pi$
$277$	−0.667329	+	2.05383i	−0.0400959	+	0.123402i	0.929005	+	0.370067i	$0.120665\pi$
$278$		0			0
$279$	4.65155	−	14.3160i	0.278481	−	0.857077i
$280$		0			0
$281$	0.975261	−	1.34233i	0.0581792	−	0.0800768i	−0.778936	−	0.627103i	$-0.784240\pi$
$281$	0.975261	−	1.34233i	0.0581792	−	0.0800768i	0.837115	+	0.547027i	$0.184240\pi$
$282$		0			0
$283$	1.44905	+	4.45972i	0.0861371	+	0.265103i	0.984843	−	0.173450i	$-0.0554914\pi$
$283$	1.44905	+	4.45972i	0.0861371	+	0.265103i	−0.898706	+	0.438552i	$0.855491\pi$
$284$		0			0
$285$	1.44261	+	1.04812i	0.0854529	+	0.0620851i
$286$		0			0
$287$	−2.31502	−	5.96998i	−0.136651	−	0.352397i
$288$		0			0
$289$	2.72614	+	1.98066i	0.160361	+	0.116509i
$290$		0			0
$291$	0.756484	+	2.32822i	0.0443459	+	0.136483i
$292$		0			0
$293$	−7.95949	+	10.9553i	−0.464999	+	0.640016i	−0.975536	−	0.219840i	$-0.929446\pi$
$293$	−7.95949	+	10.9553i	−0.464999	+	0.640016i	0.510537	+	0.859856i	$0.329446\pi$
$294$		0			0
$295$	−17.3637	+	53.4401i	−1.01096	+	3.11140i
$296$		0			0
$297$	−0.171508	+	0.527846i	−0.00995188	+	0.0306287i
$298$		0			0
$299$	6.24752	−	2.02994i	0.361304	−	0.117395i
$300$		0			0
$301$			6.46531i			0.372654i
$302$		0			0
$303$	−0.426662	+	0.309988i	−0.0245111	+	0.0178084i
$304$		0			0
$305$	−21.8943	−	15.9071i	−1.25366	−	0.910839i
$306$		0			0
$307$	−12.2669	+	8.91242i	−0.700109	+	0.508659i	−0.879968	−	0.475034i	$-0.842436\pi$
$307$	−12.2669	+	8.91242i	−0.700109	+	0.508659i	0.179859	+	0.983692i	$0.442436\pi$
$308$		0			0
$309$	−0.298211	−	0.410452i	−0.0169646	−	0.0233498i
$310$		0			0
$311$	20.5959	+	6.69200i	1.16788	+	0.379469i	0.827853	−	0.560945i	$-0.189562\pi$
$311$	20.5959	+	6.69200i	1.16788	+	0.379469i	0.340032	+	0.940414i	$0.389562\pi$
$312$		0			0
$313$	32.4813	−	10.5538i	1.83595	−	0.596537i	0.837183	−	0.546923i	$-0.184201\pi$
$313$	32.4813	−	10.5538i	1.83595	−	0.596537i	0.998768	−	0.0496141i	$-0.0157991\pi$
$314$		0			0
$315$	6.90420	−	9.50282i	0.389008	−	0.535423i
$316$		0			0
$317$	24.2007	+	7.86329i	1.35925	+	0.441646i	0.895792	−	0.444474i	$-0.146609\pi$
$317$	24.2007	+	7.86329i	1.35925	+	0.441646i	0.463455	+	0.886120i	$0.346609\pi$
$318$		0			0
$319$	−0.213972			−0.0119801
$320$		0			0
$321$	2.27797	+	3.13535i	0.127144	+	0.174998i
$322$		0			0
$323$	−2.88531	−	8.88006i	−0.160543	−	0.494100i
$324$		0			0
$325$			50.4997i			2.80122i
$326$		0			0
$327$	−2.66784			−0.147532
$328$		0			0
$329$	3.63978			0.200667
$330$		0			0
$331$			12.8792i			0.707904i	0.935264	+	0.353952i	$0.115162\pi$
$331$			12.8792i			0.707904i	−0.935264	+	0.353952i	$0.884838\pi$
$332$		0			0
$333$	−8.90124	−	27.3952i	−0.487785	−	1.50125i
$334$		0			0
$335$	12.2188	+	16.8178i	0.667586	+	0.918853i
$336$		0			0
$337$	−1.96009			−0.106773			−0.0533864	−	0.998574i	$-0.517002\pi$
$337$	−1.96009			−0.106773			−0.0533864	+	0.998574i	$0.517002\pi$
$338$		0			0
$339$	−2.09755	−	0.681536i	−0.113923	−	0.0370160i
$340$		0			0
$341$	1.28907	−	1.77426i	0.0698072	−	0.0960814i
$342$		0			0
$343$	−0.951057	+	0.309017i	−0.0513522	+	0.0166853i
$344$		0			0
$345$	1.15394	+	0.374938i	0.0621260	+	0.0201860i
$346$		0			0
$347$	10.6877	+	14.7104i	0.573748	+	0.789696i	0.992993	−	0.118177i	$-0.0377051\pi$
$347$	10.6877	+	14.7104i	0.573748	+	0.789696i	−0.419245	+	0.907873i	$0.637705\pi$
$348$		0			0
$349$	17.0025	−	12.3531i	0.910125	−	0.661245i	−0.0309213	−	0.999522i	$-0.509844\pi$
$349$	17.0025	−	12.3531i	0.910125	−	0.661245i	0.941047	+	0.338277i	$0.109844\pi$
$350$		0			0
$351$	4.87018	+	3.53839i	0.259951	+	0.188865i
$352$		0			0
$353$	8.32859	−	6.05107i	0.443286	−	0.322066i	−0.343653	−	0.939097i	$-0.611664\pi$
$353$	8.32859	−	6.05107i	0.443286	−	0.322066i	0.786939	+	0.617030i	$0.211664\pi$
$354$		0			0
$355$			47.1965i			2.50493i
$356$		0			0
$357$	0.930139	−	0.302220i	0.0492282	−	0.0159952i
$358$		0			0
$359$	3.99606	−	12.2986i	0.210904	−	0.649096i	−0.788515	−	0.615015i	$-0.789150\pi$
$359$	3.99606	−	12.2986i	0.210904	−	0.649096i	0.999419	−	0.0340804i	$-0.0108502\pi$
$360$		0			0
$361$	4.54876	−	13.9996i	0.239408	−	0.736823i
$362$		0			0
$363$	1.37749	−	1.89596i	0.0722997	−	0.0995120i
$364$		0			0
$365$	−4.86615	−	14.9765i	−0.254706	−	0.783904i
$366$		0			0
$367$	1.48814	+	1.08120i	0.0776803	+	0.0564381i	0.625948	−	0.779865i	$-0.284712\pi$
$367$	1.48814	+	1.08120i	0.0776803	+	0.0564381i	−0.548267	+	0.836303i	$0.684712\pi$
$368$		0			0
$369$	−18.2810	−	4.83172i	−0.951669	−	0.251529i
$370$		0			0
$371$	2.88728	+	2.09773i	0.149900	+	0.108909i
$372$		0			0
$373$	−0.723809	−	2.22765i	−0.0374774	−	0.115344i	0.930568	−	0.366120i	$-0.119314\pi$
$373$	−0.723809	−	2.22765i	−0.0374774	−	0.115344i	−0.968045	+	0.250777i	$0.919314\pi$
$374$		0			0
$375$	−2.94940	+	4.05950i	−0.152306	+	0.209631i
$376$		0			0
$377$	−0.717175	+	2.20724i	−0.0369364	+	0.113679i
$378$		0			0
$379$	1.88762	−	5.80949i	0.0969605	−	0.298414i	−0.890799	−	0.454397i	$-0.849855\pi$
$379$	1.88762	−	5.80949i	0.0969605	−	0.298414i	0.987760	+	0.155984i	$0.0498547\pi$
$380$		0			0
$381$	−3.42950	+	1.11431i	−0.175698	+	0.0570879i
$382$		0			0
$383$		−	29.0345i		−	1.48360i	−0.670624	−	0.741798i	$-0.733973\pi$
$383$		−	29.0345i		−	1.48360i	0.670624	−	0.741798i	$-0.266027\pi$
$384$		0			0
$385$	1.38451	−	1.00590i	0.0705611	−	0.0512656i
$386$		0			0
$387$	15.4460	+	11.2222i	0.785166	+	0.570457i
$388$		0			0
$389$	2.41673	−	1.75585i	0.122533	−	0.0890253i	−0.524831	−	0.851206i	$-0.675871\pi$
$389$	2.41673	−	1.75585i	0.122533	−	0.0890253i	0.647364	+	0.762181i	$0.275871\pi$
$390$		0			0
$391$	−3.73434	−	5.13988i	−0.188854	−	0.259935i
$392$		0			0
$393$	−3.77767	−	1.22744i	−0.190558	−	0.0619161i
$394$		0			0
$395$	8.24639	−	2.67942i	0.414921	−	0.134816i
$396$		0			0
$397$	−9.04581	+	12.4505i	−0.453996	+	0.624872i	−0.973250	−	0.229748i	$-0.926210\pi$
$397$	−9.04581	+	12.4505i	−0.453996	+	0.624872i	0.519254	+	0.854620i	$0.326210\pi$
$398$		0			0
$399$	−0.426356	−	0.138532i	−0.0213445	−	0.00693526i
$400$		0			0
$401$	24.1478			1.20588			0.602942	−	0.797785i	$-0.293995\pi$
$401$	24.1478			1.20588			0.602942	+	0.797785i	$0.293995\pi$
$402$		0			0
$403$	−13.9818	−	19.2443i	−0.696483	−	0.958627i
$404$		0			0
$405$	−10.5457	−	32.4562i	−0.524018	−	1.61276i
$406$		0			0
$407$		−	4.19673i		−	0.208024i
$408$		0			0
$409$	−15.2044			−0.751810			−0.375905	−	0.926658i	$-0.622668\pi$
$409$	−15.2044			−0.751810			−0.375905	+	0.926658i	$0.622668\pi$
$410$		0			0
$411$	−0.987138			−0.0486919
$412$		0			0
$413$		−	14.1265i		−	0.695122i
$414$		0			0
$415$	−3.87178	−	11.9161i	−0.190058	−	0.584938i
$416$		0			0
$417$	1.22511	+	1.68623i	0.0599941	+	0.0825748i
$418$		0			0
$419$	8.21864			0.401507			0.200754	−	0.979642i	$-0.435661\pi$
$419$	8.21864			0.401507			0.200754	+	0.979642i	$0.435661\pi$
$420$		0			0
$421$	−22.1900	−	7.20998i	−1.08148	−	0.351393i	−0.286529	−	0.958072i	$-0.592501\pi$
$421$	−22.1900	−	7.20998i	−1.08148	−	0.351393i	−0.794947	+	0.606679i	$0.792501\pi$
$422$		0			0
$423$	6.31776	−	8.69565i	0.307180	−	0.422797i
$424$		0			0
$425$	46.4503	−	15.0926i	2.25317	−	0.732100i
$426$		0			0
$427$	6.47074	+	2.10247i	0.313141	+	0.101746i
$428$		0			0
$429$	0.255729	+	0.351980i	0.0123467	+	0.0169938i
$430$		0			0
$431$	−16.9722	+	12.3310i	−0.817521	+	0.593964i	−0.916001	−	0.401175i	$-0.868602\pi$
$431$	−16.9722	+	12.3310i	−0.817521	+	0.593964i	0.0984805	+	0.995139i	$0.468602\pi$
$432$		0			0
$433$	1.17329	+	0.852444i	0.0563846	+	0.0409658i	0.615621	−	0.788043i	$-0.288905\pi$
$433$	1.17329	+	0.852444i	0.0563846	+	0.0409658i	−0.559236	+	0.829009i	$0.688905\pi$
$434$		0			0
$435$	−0.346797	+	0.251963i	−0.0166277	+	0.0120807i
$436$		0			0
$437$			2.91219i			0.139309i
$438$		0			0
$439$	2.70574	−	0.879149i	0.129138	−	0.0419595i	−0.243735	−	0.969842i	$-0.578373\pi$
$439$	2.70574	−	0.879149i	0.129138	−	0.0419595i	0.372873	+	0.927882i	$0.378373\pi$
$440$		0			0
$441$	−0.912541	+	2.80851i	−0.0434543	+	0.133739i
$442$		0			0
$443$	8.70423	−	26.7889i	0.413550	−	1.27278i	−0.499991	−	0.866031i	$-0.666663\pi$
$443$	8.70423	−	26.7889i	0.413550	−	1.27278i	0.913541	−	0.406746i	$-0.133337\pi$
$444$		0			0
$445$	−25.0160	+	34.4316i	−1.18587	+	1.63222i
$446$		0			0
$447$	−0.224741	−	0.691681i	−0.0106299	−	0.0327154i
$448$		0			0
$449$	11.2150	+	8.14820i	0.529270	+	0.384537i	0.820085	−	0.572242i	$-0.193926\pi$
$449$	11.2150	+	8.14820i	0.529270	+	0.384537i	−0.290815	+	0.956779i	$0.593926\pi$
$450$		0			0
$451$	−2.31554	−	1.49255i	−0.109035	−	0.0702813i
$452$		0			0
$453$	2.15047	+	1.56241i	0.101038	+	0.0734082i
$454$		0			0
$455$	−5.73596	−	17.6535i	−0.268906	−	0.827607i
$456$		0			0
$457$	−8.48268	+	11.6754i	−0.396803	+	0.546152i	−0.959938	−	0.280213i	$-0.909595\pi$
$457$	−8.48268	+	11.6754i	−0.396803	+	0.546152i	0.563135	+	0.826365i	$0.309595\pi$
$458$		0			0
$459$	1.79913	−	5.53716i	0.0839762	−	0.258452i
$460$		0			0
$461$	8.32203	−	25.6126i	0.387596	−	1.19290i	−0.546984	−	0.837143i	$-0.684224\pi$
$461$	8.32203	−	25.6126i	0.387596	−	1.19290i	0.934580	−	0.355754i	$-0.115776\pi$
$462$		0			0
$463$	−32.3641	+	10.5157i	−1.50409	+	0.488707i	−0.941207	−	0.337831i	$-0.890307\pi$
$463$	−32.3641	+	10.5157i	−1.50409	+	0.488707i	−0.562880	+	0.826539i	$0.690307\pi$
$464$		0			0
$465$		−	4.39359i		−	0.203748i
$466$		0			0
$467$	−21.5943	+	15.6892i	−0.999267	+	0.726010i	−0.961931	−	0.273293i	$-0.911887\pi$
$467$	−21.5943	+	15.6892i	−0.999267	+	0.726010i	−0.0373362	+	0.999303i	$0.511887\pi$
$468$		0			0
$469$	−4.22809	−	3.07188i	−0.195235	−	0.141846i
$470$		0			0
$471$	0.445895	−	0.323962i	0.0205458	−	0.0149274i
$472$		0			0
$473$	1.63501	+	2.25040i	0.0751780	+	0.103474i
$474$		0			0
$475$	−21.2919	−	6.91815i	−0.976939	−	0.317427i
$476$		0			0
$477$	10.0232	−	3.25674i	0.458932	−	0.149116i
$478$		0			0
$479$	−14.4742	+	19.9220i	−0.661343	+	0.910260i	−0.999525	−	0.0308203i	$-0.990188\pi$
$479$	−14.4742	+	19.9220i	−0.661343	+	0.910260i	0.338182	+	0.941081i	$0.390188\pi$
$480$		0			0
$481$	−43.2916	−	14.0663i	−1.97393	−	0.641368i
$482$		0			0
$483$	−0.305037			−0.0138796
$484$		0			0
$485$	−26.4126	−	36.3539i	−1.19934	−	1.65074i
$486$		0			0
$487$	10.8022	+	33.2458i	0.489496	+	1.50651i	0.825363	+	0.564603i	$0.190971\pi$
$487$	10.8022	+	33.2458i	0.489496	+	1.50651i	−0.335867	+	0.941909i	$0.609029\pi$
$488$		0			0
$489$			4.66216i			0.210830i
$490$		0			0
$491$	−16.3713			−0.738828			−0.369414	−	0.929265i	$-0.620442\pi$
$491$	−16.3713			−0.738828			−0.369414	+	0.929265i	$0.620442\pi$
$492$		0			0
$493$	2.24459			0.101091
$494$		0			0
$495$		−	5.05368i		−	0.227146i
$496$		0			0
$497$	−3.66663	−	11.2847i	−0.164471	−	0.506190i
$498$		0			0
$499$	22.7804	+	31.3545i	1.01979	+	1.40362i	0.912351	+	0.409408i	$0.134265\pi$
$499$	22.7804	+	31.3545i	1.01979	+	1.40362i	0.107438	+	0.994212i	$0.465735\pi$
$500$		0			0
$501$	−2.29626			−0.102589
$502$		0			0
$503$	38.3663	+	12.4660i	1.71067	+	0.555830i	0.990445	−	0.137910i	$-0.0440386\pi$
$503$	38.3663	+	12.4660i	1.71067	+	0.555830i	0.720225	+	0.693741i	$0.244039\pi$
$504$		0			0
$505$	5.69011	−	7.83177i	0.253207	−	0.348509i
$506$		0			0
$507$	1.80884	−	0.587728i	0.0803335	−	0.0261019i
$508$		0			0
$509$	−38.2295	−	12.4215i	−1.69449	−	0.550574i	−0.706858	−	0.707355i	$-0.749888\pi$
$509$	−38.2295	−	12.4215i	−1.69449	−	0.550574i	−0.987633	+	0.156781i	$0.949888\pi$
$510$		0			0
$511$	2.32700	+	3.20284i	0.102941	+	0.141685i
$512$		0			0
$513$	−2.15905	+	1.56864i	−0.0953245	+	0.0692573i
$514$		0			0
$515$	7.53421	+	5.47392i	0.331997	+	0.241210i
$516$		0			0
$517$	1.26691	−	0.920463i	0.0557186	−	0.0404819i
$518$		0			0
$519$			0.747179i			0.0327975i
$520$		0			0
$521$	12.8706	−	4.18191i	0.563871	−	0.183213i	−0.0131915	−	0.999913i	$-0.504199\pi$
$521$	12.8706	−	4.18191i	0.563871	−	0.183213i	0.577062	+	0.816700i	$0.304199\pi$
$522$		0			0
$523$	−10.5194	+	32.3753i	−0.459980	+	1.41567i	0.405208	+	0.914225i	$0.367199\pi$
$523$	−10.5194	+	32.3753i	−0.459980	+	1.41567i	−0.865188	+	0.501448i	$0.832801\pi$
$524$		0			0
$525$	0.724639	−	2.23021i	0.0316259	−	0.0973344i
$526$		0			0
$527$	−13.5225	+	18.6121i	−0.589049	+	0.810756i
$528$		0			0
$529$	−6.49506	−	19.9897i	−0.282394	−	0.869119i
$530$		0			0
$531$	−33.7492	−	24.5202i	−1.46459	−	1.06409i
$532$		0			0
$533$	−23.1575	+	18.8835i	−1.00306	+	0.817935i
$534$		0			0
$535$	−57.5522	−	41.8141i	−2.48820	−	1.80778i
$536$		0			0
$537$	1.04397	+	3.21301i	0.0450507	+	0.138652i
$538$		0			0
$539$	−0.252890	+	0.348073i	−0.0108927	+	0.0149926i
$540$		0			0
$541$	7.97878	−	24.5562i	0.343035	−	1.05575i	−0.619593	−	0.784923i	$-0.712702\pi$
$541$	7.97878	−	24.5562i	0.343035	−	1.05575i	0.962627	−	0.270829i	$-0.0872978\pi$
$542$		0			0
$543$	−0.358811	+	1.10431i	−0.0153981	+	0.0473904i
$544$		0			0
$545$	46.5739	−	15.1328i	1.99501	−	0.648217i
$546$		0			0
$547$		−	15.1067i		−	0.645916i	−0.946413	−	0.322958i	$-0.895323\pi$
$547$		−	15.1067i		−	0.645916i	0.946413	−	0.322958i	$-0.104677\pi$
$548$		0			0
$549$	16.2546	−	11.8096i	0.693728	−	0.504023i
$550$		0			0
$551$	−0.832375	−	0.604756i	−0.0354604	−	0.0257635i
$552$		0			0
$553$	−1.76356	+	1.28130i	−0.0749942	+	0.0544865i
$554$		0			0
$555$	−4.94187	−	6.80190i	−0.209771	−	0.288725i
$556$		0			0
$557$	2.13139	+	0.692529i	0.0903097	+	0.0293434i	0.353823	−	0.935312i	$-0.384881\pi$
$557$	2.13139	+	0.692529i	0.0903097	+	0.0293434i	−0.263514	+	0.964656i	$0.584881\pi$
$558$		0			0
$559$	28.6942	−	9.32332i	1.21364	−	0.394335i
$560$		0			0
$561$	0.247328	−	0.340418i	0.0104422	−	0.0143724i
$562$		0			0
$563$	10.4568	+	3.39762i	0.440701	+	0.143193i	0.520959	−	0.853582i	$-0.325574\pi$
$563$	10.4568	+	3.39762i	0.440701	+	0.143193i	−0.0802578	+	0.996774i	$0.525574\pi$
$564$		0			0
$565$	40.4839			1.70317
$566$		0			0
$567$	5.04296	+	6.94104i	0.211784	+	0.291496i
$568$		0			0
$569$	2.51711	+	7.74688i	0.105523	+	0.324766i	0.989853	−	0.142096i	$-0.0453843\pi$
$569$	2.51711	+	7.74688i	0.105523	+	0.324766i	−0.884330	+	0.466863i	$0.845384\pi$
$570$		0			0
$571$		−	12.4554i		−	0.521244i	−0.965441	−	0.260622i	$-0.916072\pi$
$571$		−	12.4554i		−	0.521244i	0.965441	−	0.260622i	$-0.0839277\pi$
$572$		0			0
$573$	4.04559			0.169007
$574$		0			0
$575$	−15.2333			−0.635271
$576$		0			0
$577$		−	1.17753i		−	0.0490213i	−0.999700	−	0.0245106i	$-0.992197\pi$
$577$		−	1.17753i		−	0.0490213i	0.999700	−	0.0245106i	$-0.00780276\pi$
$578$		0			0
$579$	−1.55940	−	4.79933i	−0.0648064	−	0.199454i
$580$		0			0
$581$	1.85149	+	2.54836i	0.0768128	+	0.105724i
$582$		0			0
$583$	1.53548			0.0635931
$584$		0			0
$585$	−52.1314	−	16.9385i	−2.15537	−	0.700322i
$586$		0			0
$587$	−1.14260	+	1.57265i	−0.0471601	+	0.0649103i	−0.831946	−	0.554857i	$-0.812773\pi$
$587$	−1.14260	+	1.57265i	−0.0471601	+	0.0649103i	0.784786	+	0.619767i	$0.212773\pi$
$588$		0			0
$589$	10.0293	−	3.25871i	0.413249	−	0.134273i
$590$		0			0
$591$	0.301244	+	0.0978802i	0.0123915	+	0.00402626i
$592$		0			0
$593$	−20.4868	−	28.1977i	−0.841292	−	1.15794i	−0.985715	−	0.168423i	$-0.946133\pi$
$593$	−20.4868	−	28.1977i	−0.841292	−	1.15794i	0.144423	−	0.989516i	$-0.453867\pi$
$594$		0			0
$595$	−14.5236	+	10.5520i	−0.595410	+	0.432591i
$596$		0			0
$597$	−4.80800	−	3.49322i	−0.196778	−	0.142968i
$598$		0			0
$599$	29.2814	−	21.2742i	1.19641	−	0.869239i	0.202479	−	0.979287i	$-0.435100\pi$
$599$	29.2814	−	21.2742i	1.19641	−	0.869239i	0.993926	+	0.110047i	$0.0351002\pi$
$600$		0			0
$601$		−	31.9839i		−	1.30465i	−0.757939	−	0.652325i	$-0.773794\pi$
$601$		−	31.9839i		−	1.30465i	0.757939	−	0.652325i	$-0.226206\pi$
$602$		0			0
$603$	−14.6778	+	4.76912i	−0.597728	+	0.194214i
$604$		0			0
$605$	−13.2932	+	40.9122i	−0.540445	+	1.66332i
$606$		0			0
$607$	4.76037	−	14.6509i	0.193217	−	0.594662i	−0.806775	−	0.590858i	$-0.798789\pi$
$607$	4.76037	−	14.6509i	0.193217	−	0.594662i	0.999993	−	0.00380388i	$-0.00121082\pi$
$608$		0			0
$609$	0.0633450	−	0.0871869i	0.00256687	−	0.00353299i
$610$		0			0
$611$	−5.24875	−	16.1540i	−0.212342	−	0.653521i
$612$		0			0
$613$	−8.03801	−	5.83996i	−0.324652	−	0.235874i	0.413506	−	0.910501i	$-0.364304\pi$
$613$	−8.03801	−	5.83996i	−0.324652	−	0.235874i	−0.738158	+	0.674628i	$0.764304\pi$
$614$		0			0
$615$	−5.51049	+	0.307610i	−0.222204	+	0.0124040i
$616$		0			0
$617$	−8.09555	−	5.88176i	−0.325915	−	0.236791i	0.412781	−	0.910831i	$-0.364558\pi$
$617$	−8.09555	−	5.88176i	−0.325915	−	0.236791i	−0.738695	+	0.674040i	$0.764558\pi$
$618$		0			0
$619$	−0.285586	−	0.878943i	−0.0114787	−	0.0353277i	0.945153	−	0.326628i	$-0.105912\pi$
$619$	−0.285586	−	0.878943i	−0.0114787	−	0.0353277i	−0.956632	+	0.291300i	$0.905912\pi$
$620$		0			0
$621$	−1.06736	+	1.46909i	−0.0428316	+	0.0589526i
$622$		0			0
$623$	3.30641	−	10.1761i	0.132469	−	0.407697i
$624$		0			0
$625$	11.7422	−	36.1388i	0.469688	−	1.44555i
$626$		0			0
$627$	−0.183437	+	0.0596021i	−0.00732575	+	0.00238028i
$628$		0			0
$629$			44.0241i			1.75536i
$630$		0			0
$631$	1.13038	−	0.821273i	0.0449999	−	0.0326944i	−0.565058	−	0.825051i	$-0.691146\pi$
$631$	1.13038	−	0.821273i	0.0449999	−	0.0326944i	0.610058	+	0.792357i	$0.291146\pi$
$632$		0			0
$633$	−0.478964	−	0.347988i	−0.0190371	−	0.0138313i
$634$		0			0
$635$	53.5497	−	38.9062i	2.12506	−	1.54394i
$636$		0			0
$637$	2.74295	+	3.77534i	0.108680	+	0.149585i
$638$		0			0
$639$	−33.3243	−	10.8277i	−1.31829	−	0.428338i
$640$		0			0
$641$	−12.0262	+	3.90755i	−0.475007	+	0.154339i	−0.536730	−	0.843754i	$-0.680340\pi$
$641$	−12.0262	+	3.90755i	−0.475007	+	0.154339i	0.0617229	+	0.998093i	$0.480340\pi$
$642$		0			0
$643$	−7.73287	+	10.6434i	−0.304955	+	0.419734i	−0.933799	−	0.357797i	$-0.883528\pi$
$643$	−7.73287	+	10.6434i	−0.304955	+	0.419734i	0.628845	+	0.777531i	$0.283528\pi$
$644$		0			0
$645$	5.29993	+	1.72205i	0.208684	+	0.0678057i
$646$		0			0
$647$	22.0631			0.867389			0.433695	−	0.901060i	$-0.357210\pi$
$647$	22.0631			0.867389			0.433695	+	0.901060i	$0.357210\pi$
$648$		0			0
$649$	−3.57246	−	4.91707i	−0.140231	−	0.193012i
$650$		0			0
$651$	0.341332	+	1.05051i	0.0133779	+	0.0411728i
$652$		0			0
$653$			24.5879i			0.962198i	0.876666	+	0.481099i	$0.159762\pi$
$653$			24.5879i			0.962198i	−0.876666	+	0.481099i	$0.840238\pi$
$654$		0			0
$655$	72.9110			2.84887
$656$		0			0
$657$	11.6909			0.456105
$658$		0			0
$659$			19.0955i			0.743856i	0.928262	+	0.371928i	$0.121303\pi$
$659$			19.0955i			0.743856i	−0.928262	+	0.371928i	$0.878697\pi$
$660$		0			0
$661$	−0.958737	−	2.95069i	−0.0372906	−	0.114769i	0.930678	−	0.365838i	$-0.119218\pi$
$661$	−0.958737	−	2.95069i	−0.0372906	−	0.114769i	−0.967969	+	0.251070i	$0.919218\pi$
$662$		0			0
$663$	−2.68262	−	3.69231i	−0.104184	−	0.143397i
$664$		0			0
$665$	8.22891			0.319103
$666$		0			0
$667$	−0.665815	−	0.216336i	−0.0257804	−	0.00837657i
$668$		0			0
$669$	0.308640	−	0.424807i	0.0119327	−	0.0164240i
$670$		0			0
$671$	2.78399	−	0.904572i	0.107475	−	0.0349206i
$672$		0			0
$673$	29.7834	+	9.67721i	1.14806	+	0.373029i	0.820414	−	0.571770i	$-0.193743\pi$
$673$	29.7834	+	9.67721i	1.14806	+	0.373029i	0.327651	+	0.944799i	$0.393743\pi$
$674$		0			0
$675$	−8.20535	−	11.2937i	−0.315824	−	0.434695i
$676$		0			0
$677$	23.4802	−	17.0594i	0.902419	−	0.655646i	−0.0366672	−	0.999328i	$-0.511674\pi$
$677$	23.4802	−	17.0594i	0.902419	−	0.655646i	0.939086	+	0.343682i	$0.111674\pi$
$678$		0			0
$679$	9.13957	+	6.64029i	0.350745	+	0.254831i
$680$		0			0
$681$	−1.82197	+	1.32374i	−0.0698179	+	0.0507257i
$682$		0			0
$683$			12.1143i			0.463542i	0.972770	+	0.231771i	$0.0744520\pi$
$683$			12.1143i			0.463542i	−0.972770	+	0.231771i	$0.925548\pi$
$684$		0			0
$685$	17.2330	−	5.59933i	0.658438	−	0.213939i
$686$		0			0
$687$	−1.59208	+	4.89992i	−0.0607417	+	0.186944i
$688$		0			0
$689$	5.14651	−	15.8393i	0.196066	−	0.603430i
$690$		0			0
$691$	9.19916	−	12.6616i	0.349952	−	0.481668i	−0.597363	−	0.801971i	$-0.703785\pi$
$691$	9.19916	−	12.6616i	0.349952	−	0.481668i	0.947315	+	0.320303i	$0.103785\pi$
$692$		0			0
$693$	0.392613	+	1.20834i	0.0149141	+	0.0459010i
$694$		0			0
$695$	−30.9522	−	22.4881i	−1.17408	−	0.853022i
$696$		0			0
$697$	24.2903	+	15.6570i	0.920060	+	0.593050i
$698$		0			0
$699$	−4.40780	−	3.20245i	−0.166718	−	0.121128i
$700$		0			0
$701$	3.19278	+	9.82636i	0.120590	+	0.371136i	0.993072	−	0.117509i	$-0.0374910\pi$
$701$	3.19278	+	9.82636i	0.120590	+	0.371136i	−0.872482	+	0.488646i	$0.837491\pi$
$702$		0			0
$703$	11.8614	−	16.3258i	0.447360	−	0.615738i
$704$		0			0
$705$	0.969463	−	2.98370i	0.0365121	−	0.112373i
$706$		0			0
$707$	−0.752072	+	2.31464i	−0.0282846	+	0.0870510i
$708$		0			0
$709$	0.0188840	−	0.00613579i	0.000709204	−	0.000230434i	−0.308662	−	0.951172i	$-0.599881\pi$
$709$	0.0188840	−	0.00613579i	0.000709204	−	0.000230434i	0.309372	+	0.950941i	$0.399881\pi$
$710$		0			0
$711$			6.43728i			0.241417i
$712$		0			0
$713$	5.80505	−	4.21762i	0.217401	−	0.157951i
$714$		0			0
$715$	−6.46092	−	4.69413i	−0.241625	−	0.175551i
$716$		0			0
$717$	1.41671	−	1.02930i	0.0529079	−	0.0384398i
$718$		0			0
$719$	5.82008	+	8.01065i	0.217052	+	0.298747i	0.903634	−	0.428306i	$-0.140889\pi$
$719$	5.82008	+	8.01065i	0.217052	+	0.298747i	−0.686581	+	0.727053i	$0.740889\pi$
$720$		0			0
$721$	−2.22670	−	0.723499i	−0.0829266	−	0.0269445i
$722$		0			0
$723$	−1.63711	+	0.531928i	−0.0608847	+	0.0197826i
$724$		0			0
$725$	3.16339	−	4.35404i	0.117486	−	0.161705i
$726$		0			0
$727$	14.8932	+	4.83909i	0.552358	+	0.179472i	0.571880	−	0.820338i	$-0.306214\pi$
$727$	14.8932	+	4.83909i	0.552358	+	0.179472i	−0.0195219	+	0.999809i	$0.506214\pi$
$728$		0			0
$729$	24.4973			0.907308
$730$		0			0
$731$	−17.1514	−	23.6069i	−0.634369	−	0.873134i
$732$		0			0
$733$	−12.7297	−	39.1781i	−0.470183	−	1.44707i	−0.852345	−	0.522979i	$-0.824820\pi$
$733$	−12.7297	−	39.1781i	−0.470183	−	1.44707i	0.382162	−	0.924095i	$-0.375180\pi$
$734$		0			0
$735$			0.861934i			0.0317929i
$736$		0			0
$737$	−2.24853			−0.0828257
$738$		0			0
$739$	28.3486			1.04282			0.521410	−	0.853306i	$-0.325406\pi$
$739$	28.3486			1.04282			0.521410	+	0.853306i	$0.325406\pi$
$740$		0			0
$741$			2.09202i			0.0768522i
$742$		0			0
$743$	−1.60008	−	4.92454i	−0.0587013	−	0.180664i	0.917406	−	0.397952i	$-0.130279\pi$
$743$	−1.60008	−	4.92454i	−0.0587013	−	0.180664i	−0.976108	+	0.217288i	$0.930279\pi$
$744$		0			0
$745$	7.84682	+	10.8002i	0.287485	+	0.395690i
$746$		0			0
$747$	9.30193			0.340340
$748$		0			0
$749$	17.0093	+	5.52665i	0.621505	+	0.201939i
$750$		0			0
$751$	−4.88786	+	6.72756i	−0.178360	+	0.245492i	−0.888831	−	0.458235i	$-0.848482\pi$
$751$	−4.88786	+	6.72756i	−0.178360	+	0.245492i	0.710471	+	0.703727i	$0.248482\pi$
$752$		0			0
$753$	5.62498	−	1.82767i	0.204986	−	0.0666039i
$754$		0			0
$755$	−46.4042	−	15.0776i	−1.68882	−	0.548731i
$756$		0			0
$757$	8.49926	+	11.6982i	0.308911	+	0.425179i	0.935041	−	0.354539i	$-0.115362\pi$
$757$	8.49926	+	11.6982i	0.308911	+	0.425179i	−0.626130	+	0.779718i	$0.715362\pi$
$758$		0			0
$759$	−0.106175	+	0.0771407i	−0.00385391	+	0.00280003i
$760$		0			0
$761$	−23.5850	−	17.1355i	−0.854954	−	0.621161i	0.0715532	−	0.997437i	$-0.477204\pi$
$761$	−23.5850	−	17.1355i	−0.854954	−	0.621161i	−0.926508	+	0.376276i	$0.877204\pi$
$762$		0			0
$763$	−9.96022	+	7.23652i	−0.360584	+	0.261980i
$764$		0			0
$765$			53.0136i			1.91671i
$766$		0			0
$767$	−62.6962	+	20.3712i	−2.26383	+	0.735562i
$768$		0			0
$769$	−15.3565	+	47.2623i	−0.553768	+	1.70432i	0.145407	+	0.989372i	$0.453551\pi$
$769$	−15.3565	+	47.2623i	−0.553768	+	1.70432i	−0.699175	+	0.714951i	$0.746449\pi$
$770$		0			0
$771$	0.139264	−	0.428611i	0.00501548	−	0.0154361i
$772$		0			0
$773$	4.28435	−	5.89690i	0.154097	−	0.212097i	−0.724988	−	0.688762i	$-0.758155\pi$
$773$	4.28435	−	5.89690i	0.154097	−	0.212097i	0.879085	+	0.476665i	$0.158155\pi$
$774$		0			0
$775$	17.0458	+	52.4617i	0.612305	+	1.88448i
$776$		0			0
$777$	1.71004	+	1.24241i	0.0613472	+	0.0445714i
$778$		0			0
$779$	−4.78929	−	12.3507i	−0.171594	−	0.442509i
$780$		0			0
$781$	−4.13006	−	3.00066i	−0.147785	−	0.107372i
$782$		0			0
$783$	−0.198251	−	0.610153i	−0.00708490	−	0.0218051i
$784$		0			0
$785$	−5.94661	+	8.18481i	−0.212244	+	0.292128i
$786$		0			0
$787$	−10.9182	+	33.6028i	−0.389192	+	1.19781i	0.544201	+	0.838955i	$0.316833\pi$
$787$	−10.9182	+	33.6028i	−0.389192	+	1.19781i	−0.933393	+	0.358856i	$0.883167\pi$
$788$		0			0
$789$	−1.56391	+	4.81322i	−0.0556766	+	0.171355i
$790$		0			0
$791$	−9.67974	+	3.14514i	−0.344172	+	0.111828i
$792$		0			0
$793$		−	31.7502i		−	1.12748i
$794$		0			0
$795$	2.48865	−	1.80811i	0.0882631	−	0.0641269i
$796$		0			0
$797$	1.00198	+	0.727979i	0.0354918	+	0.0257863i	0.605390	−	0.795929i	$-0.293017\pi$
$797$	1.00198	+	0.727979i	0.0354918	+	0.0257863i	−0.569898	+	0.821716i	$0.693017\pi$
$798$		0			0
$799$	−13.2900	+	9.65574i	−0.470166	+	0.341596i
$800$		0			0
$801$	−18.5722	−	25.5624i	−0.656217	−	0.903205i
$802$		0			0
$803$	1.61993	+	0.526349i	0.0571662	+	0.0185744i
$804$		0			0
$805$	5.32518	−	1.73025i	0.187688	−	0.0609835i
$806$		0			0
$807$	−3.81329	+	5.24854i	−0.134234	+	0.184757i
$808$		0			0
$809$	26.4385	+	8.59038i	0.929527	+	0.302022i	0.734369	−	0.678750i	$-0.237478\pi$
$809$	26.4385	+	8.59038i	0.929527	+	0.302022i	0.195158	+	0.980772i	$0.437478\pi$
$810$		0			0
$811$	−23.8892			−0.838864			−0.419432	−	0.907787i	$-0.637771\pi$
$811$	−23.8892			−0.838864			−0.419432	+	0.907787i	$0.637771\pi$
$812$		0			0
$813$	2.50836	+	3.45245i	0.0879719	+	0.121083i
$814$		0			0
$815$	−26.4451	−	81.3896i	−0.926331	−	2.85095i
$816$		0			0
$817$			13.3754i			0.467946i
$818$		0			0
$819$	13.7806			0.481534
$820$		0			0
$821$	17.6236			0.615069			0.307534	−	0.951537i	$-0.400496\pi$
$821$	17.6236			0.615069			0.307534	+	0.951537i	$0.400496\pi$
$822$		0			0
$823$			37.8824i			1.32050i	0.751047	+	0.660249i	$0.229549\pi$
$823$			37.8824i			1.32050i	−0.751047	+	0.660249i	$0.770451\pi$
$824$		0			0
$825$	−0.311770	−	0.959531i	−0.0108545	−	0.0334066i
$826$		0			0
$827$	−13.7865	−	18.9755i	−0.479403	−	0.659842i	0.498987	−	0.866610i	$-0.333706\pi$
$827$	−13.7865	−	18.9755i	−0.479403	−	0.659842i	−0.978390	+	0.206768i	$0.933706\pi$
$828$		0			0
$829$	−23.5381			−0.817511			−0.408756	−	0.912644i	$-0.634037\pi$
$829$	−23.5381			−0.817511			−0.408756	+	0.912644i	$0.634037\pi$
$830$		0			0
$831$	−0.445054	−	0.144607i	−0.0154388	−	0.00501636i
$832$		0			0
$833$	2.65284	−	3.65132i	0.0919154	−	0.126511i
$834$		0			0
$835$	40.0870	−	13.0250i	1.38727	−	0.450750i
$836$		0			0
$837$	6.25375	+	2.03197i	0.216161	+	0.0702350i
$838$		0			0
$839$	20.1290	+	27.7052i	0.694931	+	0.956491i	0.999991	+	0.00415772i	$0.00132345\pi$
$839$	20.1290	+	27.7052i	0.694931	+	0.956491i	−0.305060	+	0.952333i	$0.598677\pi$
$840$		0			0
$841$	−23.2614	+	16.9004i	−0.802117	+	0.582772i
$842$		0			0
$843$	0.290877	+	0.211334i	0.0100183	+	0.00727874i
$844$		0			0
$845$	−28.2441	+	20.5205i	−0.971626	+	0.705928i
$846$		0			0
$847$		−	10.8149i		−	0.371604i
$848$		0			0
$849$	−0.966400	+	0.314002i	−0.0331668	+	0.0107765i
$850$		0			0
$851$	4.24310	−	13.0589i	0.145452	−	0.447654i
$852$		0			0
$853$	−7.56599	+	23.2857i	−0.259055	+	0.797288i	0.733949	+	0.679204i	$0.237675\pi$
$853$	−7.56599	+	23.2857i	−0.259055	+	0.797288i	−0.993004	+	0.118084i	$0.962325\pi$
$854$		0			0
$855$	14.2834	−	19.6594i	0.488481	−	0.672336i
$856$		0			0
$857$	−0.832797	−	2.56308i	−0.0284478	−	0.0875533i	0.935825	−	0.352466i	$-0.114657\pi$
$857$	−0.832797	−	2.56308i	−0.0284478	−	0.0875533i	−0.964272	+	0.264913i	$0.914657\pi$
$858$		0			0
$859$	−37.7618	−	27.4356i	−1.28842	−	0.936090i	−0.288645	−	0.957436i	$-0.593205\pi$
$859$	−37.7618	−	27.4356i	−1.28842	−	0.936090i	−0.999772	+	0.0213466i	$0.993205\pi$
$860$		0			0
$861$	1.29367	−	0.501653i	0.0440880	−	0.0170963i
$862$		0			0
$863$	−19.1614	−	13.9216i	−0.652263	−	0.473897i	0.211778	−	0.977318i	$-0.432075\pi$
$863$	−19.1614	−	13.9216i	−0.652263	−	0.473897i	−0.864041	+	0.503421i	$0.832075\pi$
$864$		0			0
$865$	−4.23821	−	13.0439i	−0.144104	−	0.443505i
$866$		0			0
$867$	−0.429199	+	0.590741i	−0.0145763	+	0.0200626i
$868$		0			0
$869$	−0.289820	+	0.891974i	−0.00983147	+	0.0302581i
$870$		0			0
$871$	−7.53646	+	23.1948i	−0.255363	+	0.785927i
$872$		0			0
$873$	31.7281	−	10.3091i	1.07383	−	0.348910i
$874$		0			0
$875$			23.1561i			0.782819i
$876$		0			0
$877$	30.8743	−	22.4315i	1.04255	−	0.757459i	0.0717701	−	0.997421i	$-0.477135\pi$
$877$	30.8743	−	22.4315i	1.04255	−	0.757459i	0.970782	+	0.239963i	$0.0771352\pi$
$878$		0			0
$879$	−2.37396	−	1.72478i	−0.0800717	−	0.0581755i
$880$		0			0
$881$	−10.7143	+	7.78438i	−0.360973	+	0.262262i	−0.753458	−	0.657496i	$-0.771616\pi$
$881$	−10.7143	+	7.78438i	−0.360973	+	0.262262i	0.392485	+	0.919759i	$0.371616\pi$
$882$		0			0
$883$	7.93990	+	10.9283i	0.267199	+	0.367768i	0.921442	−	0.388517i	$-0.127013\pi$
$883$	7.93990	+	10.9283i	0.267199	+	0.367768i	−0.654243	+	0.756285i	$0.727013\pi$
$884$		0			0
$885$	−11.5802	−	3.76264i	−0.389264	−	0.126480i
$886$		0			0
$887$	3.93389	−	1.27820i	0.132087	−	0.0429177i	−0.242228	−	0.970219i	$-0.577878\pi$
$887$	3.93389	−	1.27820i	0.132087	−	0.0429177i	0.374315	+	0.927302i	$0.377878\pi$
$888$		0			0
$889$	−9.78123	+	13.4627i	−0.328052	+	0.451525i
$890$		0			0
$891$	3.51064	+	1.14068i	0.117611	+	0.0382141i
$892$		0			0
$893$	7.52995			0.251980
$894$		0			0
$895$	−36.4503	−	50.1695i	−1.21840	−	1.67698i
$896$		0			0
$897$	0.439879	+	1.35381i	0.0146871	+	0.0452023i
$898$		0			0
$899$			2.53507i			0.0845493i
$900$		0			0
$901$	−16.1073			−0.536613
$902$		0			0
$903$	−1.40100			−0.0466224
$904$		0			0
$905$		−	21.3137i		−	0.708493i
$906$		0			0
$907$	14.6171	+	44.9867i	0.485352	+	1.49376i	0.831471	+	0.555568i	$0.187499\pi$
$907$	14.6171	+	44.9867i	0.485352	+	1.49376i	−0.346119	+	0.938191i	$0.612501\pi$
$908$		0			0
$909$	4.22441	+	5.81440i	0.140115	+	0.192851i
$910$		0			0
$911$	−48.5390			−1.60817			−0.804084	−	0.594516i	$-0.797344\pi$
$911$	−48.5390			−1.60817			−0.804084	+	0.594516i	$0.797344\pi$
$912$		0			0
$913$	1.28891	+	0.418792i	0.0426567	+	0.0138600i
$914$		0			0
$915$	3.44699	−	4.74438i	0.113954	−	0.156844i
$916$		0			0
$917$	−17.4331	+	5.66436i	−0.575692	+	0.187054i
$918$		0			0
$919$	21.8807	+	7.10947i	0.721778	+	0.234520i	0.646794	−	0.762665i	$-0.276109\pi$
$919$	21.8807	+	7.10947i	0.721778	+	0.234520i	0.0749840	+	0.997185i	$0.476109\pi$
$920$		0			0
$921$	−1.93128	−	2.65818i	−0.0636378	−	0.0875899i
$922$		0			0
$923$	−44.7963	+	32.5464i	−1.47449	+	1.07128i
$924$		0			0
$925$	85.3978	+	62.0451i	2.80786	+	2.04003i
$926$		0			0
$927$	−5.59349	+	4.06391i	−0.183714	+	0.133476i
$928$		0			0
$929$		−	5.15414i		−	0.169102i	−0.996419	−	0.0845510i	$-0.973054\pi$
$929$		−	5.15414i		−	0.169102i	0.996419	−	0.0845510i	$-0.0269456\pi$
$930$		0			0
$931$	−1.96754	+	0.639293i	−0.0644835	+	0.0209520i
$932$		0			0
$933$	−1.45012	+	4.46302i	−0.0474749	+	0.146113i
$934$		0			0
$935$	−2.38678	+	7.34575i	−0.0780561	+	0.240232i
$936$		0			0
$937$	32.1541	−	44.2564i	1.05043	−	1.44579i	0.161993	−	0.986792i	$-0.448208\pi$
$937$	32.1541	−	44.2564i	1.05043	−	1.44579i	0.888436	−	0.459000i	$-0.151792\pi$
$938$		0			0
$939$	2.28696	+	7.03854i	0.0746321	+	0.229694i
$940$		0			0
$941$	−37.8805	−	27.5218i	−1.23487	−	0.897186i	−0.237625	−	0.971357i	$-0.576369\pi$
$941$	−37.8805	−	27.5218i	−1.23487	−	0.897186i	−0.997246	+	0.0741712i	$0.976369\pi$
$942$		0			0
$943$	−5.69621	−	6.98547i	−0.185494	−	0.227478i
$944$		0			0
$945$	4.15117	+	3.01600i	0.135038	+	0.0981106i
$946$		0			0
$947$	−16.6849	−	51.3508i	−0.542186	−	1.66868i	−0.727589	−	0.686014i	$-0.759359\pi$
$947$	−16.6849	−	51.3508i	−0.542186	−	1.66868i	0.185403	−	0.982663i	$-0.440641\pi$
$948$		0			0
$949$	10.8591	−	14.9463i	0.352503	−	0.485178i
$950$		0			0
$951$	−1.70394	+	5.24418i	−0.0552539	+	0.170054i
$952$		0			0
$953$	10.9565	−	33.7207i	0.354916	−	1.09232i	−0.601142	−	0.799143i	$-0.705287\pi$
$953$	10.9565	−	33.7207i	0.354916	−	1.09232i	0.956058	−	0.293178i	$-0.0947128\pi$
$954$		0			0
$955$	−70.6259	+	22.9477i	−2.28540	+	0.742571i
$956$		0			0
$957$		−	0.0463667i		−	0.00149882i
$958$		0			0
$959$	−3.68542	+	2.67761i	−0.119008	+	0.0864646i
$960$		0			0
$961$	4.05873	+	2.94884i	0.130927	+	0.0951239i
$962$		0			0
$963$	42.7274	−	31.0433i	1.37687	−	1.00036i
$964$		0			0
$965$	54.4464	+	74.9390i	1.75269	+	2.41237i
$966$		0			0
$967$	3.12641	+	1.01583i	0.100539	+	0.0326670i	0.358854	−	0.933394i	$-0.383167\pi$
$967$	3.12641	+	1.01583i	0.100539	+	0.0326670i	−0.258316	+	0.966061i	$0.583167\pi$
$968$		0			0
$969$	1.92427	−	0.625232i	0.0618163	−	0.0200853i
$970$		0			0
$971$	−9.08068	+	12.4985i	−0.291413	+	0.401095i	−0.929472	−	0.368892i	$-0.879737\pi$
$971$	−9.08068	+	12.4985i	−0.291413	+	0.401095i	0.638060	+	0.769987i	$0.279737\pi$
$972$		0			0
$973$	9.14777	+	2.97229i	0.293264	+	0.0952873i
$974$		0			0
$975$	−10.9430			−0.350458
$976$		0			0
$977$	−5.39696	−	7.42827i	−0.172664	−	0.237651i	0.713911	−	0.700236i	$-0.246922\pi$
$977$	−5.39696	−	7.42827i	−0.172664	−	0.237651i	−0.886575	+	0.462585i	$0.846922\pi$
$978$		0			0
$979$	−1.42256	−	4.37819i	−0.0454652	−	0.139927i
$980$		0			0
$981$			36.3564i			1.16077i
$982$		0			0
$983$	−10.2030			−0.325425			−0.162713	−	0.986674i	$-0.552024\pi$
$983$	−10.2030			−0.325425			−0.162713	+	0.986674i	$0.552024\pi$
$984$		0			0
$985$	−5.81418			−0.185255
$986$		0			0
$987$			0.788722i			0.0251053i
$988$		0			0
$989$	2.81238	+	8.65563i	0.0894286	+	0.275233i
$990$		0			0
$991$	−19.5621	−	26.9250i	−0.621411	−	0.855299i	0.376043	−	0.926602i	$-0.377284\pi$
$991$	−19.5621	−	26.9250i	−0.621411	−	0.855299i	−0.997455	+	0.0713026i	$0.977284\pi$
$992$		0			0
$993$	−2.79085			−0.0885651
$994$		0			0
$995$	103.750	+	33.7105i	3.28910	+	1.06869i
$996$		0			0
$997$	8.93403	−	12.2966i	0.282944	−	0.389438i	−0.643763	−	0.765225i	$-0.722628\pi$
$997$	8.93403	−	12.2966i	0.282944	−	0.389438i	0.926706	+	0.375787i	$0.122628\pi$
$998$		0			0
$999$	11.9672	−	3.88838i	0.378626	−	0.123023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.9	✓	80
41.4	even	10	inner	1148.2.ba.a.701.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.9	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.12	yes	80	41.4	even	10	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +O(q^{10})\)	\(q+0.216695i q^{3} +(-1.22916 - 3.78295i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.95304 q^{9} +(0.409185 + 0.132952i) q^{11} +(2.74295 - 3.77534i) q^{13} +(0.819748 - 0.266352i) q^{15} +(-4.29238 - 1.39468i) q^{17} +(1.21601 + 1.67369i) q^{19} +(-0.175310 + 0.127370i) q^{21} +(1.13883 + 0.827411i) q^{23} +(-8.75484 + 6.36076i) q^{25} +1.29000i q^{27} +(-0.472988 + 0.153683i) q^{29} +(1.57517 - 4.84788i) q^{31} +(-0.0288101 + 0.0886683i) q^{33} +(2.33799 - 3.21797i) q^{35} +(-3.01426 - 9.27694i) q^{37} +(0.818098 + 0.594383i) q^{39} +(-6.19055 - 1.63618i) q^{41} +(5.23055 + 3.80022i) q^{43} +(-3.62975 - 11.1712i) q^{45} +(2.13941 - 2.94464i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.302220 - 0.930139i) q^{51} +(3.39420 - 1.10284i) q^{53} -1.71135i q^{55} +(-0.362680 + 0.263503i) q^{57} +(-11.4286 - 8.30337i) q^{59} +(5.50434 - 3.99914i) q^{61} +(1.73576 + 2.38906i) q^{63} +(-17.6535 - 5.73596i) q^{65} +(-4.97041 + 1.61498i) q^{67} +(-0.179296 + 0.246780i) q^{69} +(-11.2847 - 3.66663i) q^{71} +3.95893 q^{73} +(-1.37835 - 1.89713i) q^{75} +(0.132952 + 0.409185i) q^{77} +2.17988i q^{79} +8.57959 q^{81} +3.14995 q^{83} +17.9522i q^{85} +(-0.0333024 - 0.102494i) q^{87} +(-6.28917 - 8.65631i) q^{89} +4.66658 q^{91} +(1.05051 + 0.341332i) q^{93} +(4.83683 - 6.65733i) q^{95} +(10.7442 - 3.49101i) q^{97} +(1.20834 + 0.392613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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