LMFDB - Embedded newform 630.2.u.d.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(109,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("630.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.2702336256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 $ x^8 + 9x^6 + 56x^4 + 225*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.4
Root			$0.656712 - 2.13746i$ of defining polynomial
Character	$\chi$	$=$	630.109
Dual form			630.2.u.d.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-2.63746 - 0.209313i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-2.63746 - 0.209313i) q^{7} -1.00000i q^{8} +(-0.500000 - 2.17945i) q^{10} +(0.866025 - 1.50000i) q^{11} -2.15068i q^{13} +(-2.38876 + 1.13746i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.13746 - 3.70219i) q^{19} +(-1.52274 - 1.63746i) q^{20} -1.73205i q^{22} +(-3.70219 + 2.13746i) q^{23} +(-4.13746 - 2.80739i) q^{25} +(-1.07534 - 1.86254i) q^{26} +(-1.50000 + 2.17945i) q^{28} +3.88273 q^{29} +(3.63746 - 6.30026i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-2.17945 + 5.50000i) q^{35} +(-4.13746 + 2.38876i) q^{37} +(-3.70219 - 2.13746i) q^{38} +(-2.13746 - 0.656712i) q^{40} +10.8685 q^{41} +2.62685i q^{43} +(-0.866025 - 1.50000i) q^{44} +(-2.13746 + 3.70219i) q^{46} +(-1.49397 + 0.862541i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-4.98684 - 0.362541i) q^{50} +(-1.86254 - 1.07534i) q^{52} +(6.53835 + 3.77492i) q^{53} +(-2.63746 - 2.83616i) q^{55} +(-0.209313 + 2.63746i) q^{56} +(3.36254 - 1.94136i) q^{58} +(-3.67341 + 6.36254i) q^{59} +(-2.27492 - 3.94027i) q^{61} -7.27492i q^{62} -1.00000 q^{64} +(-4.59698 - 1.41238i) q^{65} +(-7.54983 - 4.35890i) q^{67} +(1.73205 - 1.00000i) q^{68} +(0.862541 + 5.85286i) q^{70} +14.8087 q^{71} +(10.5498 + 6.09095i) q^{73} +(-2.38876 + 4.13746i) q^{74} -4.27492 q^{76} +(-2.59808 + 3.77492i) q^{77} +(-1.63746 - 2.83616i) q^{79} +(-2.17945 + 0.500000i) q^{80} +(9.41238 - 5.43424i) q^{82} +0.725083i q^{83} +(3.27492 - 3.04547i) q^{85} +(1.31342 + 2.27492i) q^{86} +(-1.50000 - 0.866025i) q^{88} +(0.418627 + 0.725083i) q^{89} +(-0.450166 + 5.67232i) q^{91} +4.27492i q^{92} +(-0.862541 + 1.49397i) q^{94} +(-9.31697 + 2.13746i) q^{95} -2.20822i q^{97} +(6.53835 - 2.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 6 * q^7	$ 8 q + 4 q^{4} - 6 q^{7} - 4 q^{10} - 4 q^{16} - 2 q^{19} - 18 q^{25} - 12 q^{28} + 14 q^{31} + 16 q^{34} - 18 q^{37} - 2 q^{40} - 2 q^{46} + 10 q^{49} - 30 q^{52} - 6 q^{55} + 42 q^{58} + 12 q^{61} - 8 q^{64} + 22 q^{70} + 24 q^{73} - 4 q^{76} + 2 q^{79} + 30 q^{82} - 4 q^{85} - 12 q^{88} - 64 q^{91} - 22 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 - 6 * q^7 - 4 * q^10 - 4 * q^16 - 2 * q^19 - 18 * q^25 - 12 * q^28 + 14 * q^31 + 16 * q^34 - 18 * q^37 - 2 * q^40 - 2 * q^46 + 10 * q^49 - 30 * q^52 - 6 * q^55 + 42 * q^58 + 12 * q^61 - 8 * q^64 + 22 * q^70 + 24 * q^73 - 4 * q^76 + 2 * q^79 + 30 * q^82 - 4 * q^85 - 12 * q^88 - 64 * q^91 - 22 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.656712	−	2.13746i	0.293691	−	0.955901i
$5$	0.656712	−	2.13746i	0.293691	−	0.955901i
$6$		0			0
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$7$	−2.63746	−	0.209313i	−0.996866	−	0.0791130i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.500000	−	2.17945i	−0.158114	−	0.689202i
$11$	0.866025	−	1.50000i	0.261116	−	0.452267i	−0.705422	−	0.708787i	$-0.749243\pi$
$11$	0.866025	−	1.50000i	0.261116	−	0.452267i	0.966539	+	0.256520i	$0.0825760\pi$
$12$		0			0
$13$		−	2.15068i		−	0.596491i	−0.954489	−	0.298245i	$-0.903599\pi$
$13$		−	2.15068i		−	0.596491i	0.954489	−	0.298245i	$-0.0964014\pi$
$14$	−2.38876	+	1.13746i	−0.638424	+	0.303999i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	−2.13746	−	3.70219i	−0.490367	−	0.849340i	0.509572	−	0.860428i	$-0.329804\pi$
$19$	−2.13746	−	3.70219i	−0.490367	−	0.849340i	−0.999939	+	0.0110882i	$0.996470\pi$
$20$	−1.52274	−	1.63746i	−0.340494	−	0.366147i
$21$		0			0
$22$		−	1.73205i		−	0.369274i
$23$	−3.70219	+	2.13746i	−0.771959	+	0.445691i	−0.833573	−	0.552409i	$-0.813709\pi$
$23$	−3.70219	+	2.13746i	−0.771959	+	0.445691i	0.0616138	+	0.998100i	$0.480375\pi$
$24$		0			0
$25$	−4.13746	−	2.80739i	−0.827492	−	0.561478i
$26$	−1.07534	−	1.86254i	−0.210891	−	0.365274i
$27$		0			0
$28$	−1.50000	+	2.17945i	−0.283473	+	0.411877i
$29$	3.88273			0.721005			0.360502	−	0.932758i	$-0.382605\pi$
$29$	3.88273			0.721005			0.360502	+	0.932758i	$0.382605\pi$
$30$		0			0
$31$	3.63746	−	6.30026i	0.653307	−	1.13156i	−0.329009	−	0.944327i	$-0.606714\pi$
$31$	3.63746	−	6.30026i	0.653307	−	1.13156i	0.982315	−	0.187234i	$-0.0599522\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	2.00000			0.342997
$35$	−2.17945	+	5.50000i	−0.368394	+	0.929670i
$36$		0			0
$37$	−4.13746	+	2.38876i	−0.680194	+	0.392710i	−0.799928	−	0.600096i	$-0.795129\pi$
$37$	−4.13746	+	2.38876i	−0.680194	+	0.392710i	0.119734	+	0.992806i	$0.461796\pi$
$38$	−3.70219	−	2.13746i	−0.600574	−	0.346742i
$39$		0			0
$40$	−2.13746	−	0.656712i	−0.337962	−	0.103835i
$41$	10.8685			1.69737			0.848685	−	0.528898i	$-0.177395\pi$
$41$	10.8685			1.69737			0.848685	+	0.528898i	$0.177395\pi$
$42$		0			0
$43$			2.62685i			0.400591i	0.979736	+	0.200295i	$0.0641902\pi$
$43$			2.62685i			0.400591i	−0.979736	+	0.200295i	$0.935810\pi$
$44$	−0.866025	−	1.50000i	−0.130558	−	0.226134i
$45$		0			0
$46$	−2.13746	+	3.70219i	−0.315151	+	0.545858i
$47$	−1.49397	+	0.862541i	−0.217917	+	0.125815i	−0.604986	−	0.796236i	$-0.706821\pi$
$47$	−1.49397	+	0.862541i	−0.217917	+	0.125815i	0.387068	+	0.922051i	$0.373488\pi$
$48$		0			0
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$	−4.98684	−	0.362541i	−0.705246	−	0.0512711i
$51$		0			0
$52$	−1.86254	−	1.07534i	−0.258288	−	0.149123i
$53$	6.53835	+	3.77492i	0.898111	+	0.518525i	0.876587	−	0.481244i	$-0.159815\pi$
$53$	6.53835	+	3.77492i	0.898111	+	0.518525i	0.0215243	+	0.999768i	$0.493148\pi$
$54$		0			0
$55$	−2.63746	−	2.83616i	−0.355635	−	0.382428i
$56$	−0.209313	+	2.63746i	−0.0279707	+	0.352445i
$57$		0			0
$58$	3.36254	−	1.94136i	0.441523	−	0.254914i
$59$	−3.67341	+	6.36254i	−0.478238	+	0.828332i	−0.999689	−	0.0249490i	$-0.992058\pi$
$59$	−3.67341	+	6.36254i	−0.478238	+	0.828332i	0.521451	+	0.853281i	$0.325391\pi$
$60$		0			0
$61$	−2.27492	−	3.94027i	−0.291273	−	0.504500i	0.682838	−	0.730570i	$-0.260746\pi$
$61$	−2.27492	−	3.94027i	−0.291273	−	0.504500i	−0.974111	+	0.226070i	$0.927412\pi$
$62$		−	7.27492i		−	0.923915i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.59698	−	1.41238i	−0.570186	−	0.175184i
$66$		0			0
$67$	−7.54983	−	4.35890i	−0.922359	−	0.532524i	−0.0379722	−	0.999279i	$-0.512090\pi$
$67$	−7.54983	−	4.35890i	−0.922359	−	0.532524i	−0.884387	+	0.466755i	$0.845423\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$		0			0
$70$	0.862541	+	5.85286i	0.103093	+	0.699551i
$71$	14.8087			1.75748			0.878738	−	0.477305i	$-0.158386\pi$
$71$	14.8087			1.75748			0.878738	+	0.477305i	$0.158386\pi$
$72$		0			0
$73$	10.5498	+	6.09095i	1.23476	+	0.712892i	0.968019	−	0.250875i	$-0.0807184\pi$
$73$	10.5498	+	6.09095i	1.23476	+	0.712892i	0.266745	+	0.963767i	$0.414052\pi$
$74$	−2.38876	+	4.13746i	−0.277688	+	0.480970i
$75$		0			0
$76$	−4.27492			−0.490367
$77$	−2.59808	+	3.77492i	−0.296078	+	0.430192i
$78$		0			0
$79$	−1.63746	−	2.83616i	−0.184228	−	0.319093i	0.759088	−	0.650988i	$-0.225645\pi$
$79$	−1.63746	−	2.83616i	−0.184228	−	0.319093i	−0.943316	+	0.331895i	$0.892312\pi$
$80$	−2.17945	+	0.500000i	−0.243670	+	0.0559017i
$81$		0			0
$82$	9.41238	−	5.43424i	1.03942	−	0.600111i
$83$			0.725083i			0.0795882i	0.999208	+	0.0397941i	$0.0126702\pi$
$83$			0.725083i			0.0795882i	−0.999208	+	0.0397941i	$0.987330\pi$
$84$		0			0
$85$	3.27492	−	3.04547i	0.355215	−	0.330328i
$86$	1.31342	+	2.27492i	0.141630	+	0.245311i
$87$		0			0
$88$	−1.50000	−	0.866025i	−0.159901	−	0.0923186i
$89$	0.418627	+	0.725083i	0.0443743	+	0.0768586i	0.887360	−	0.461078i	$-0.152537\pi$
$89$	0.418627	+	0.725083i	0.0443743	+	0.0768586i	−0.842985	+	0.537937i	$0.819204\pi$
$90$		0			0
$91$	−0.450166	+	5.67232i	−0.0471902	+	0.594621i
$92$			4.27492i			0.445691i
$93$		0			0
$94$	−0.862541	+	1.49397i	−0.0889644	+	0.154091i
$95$	−9.31697	+	2.13746i	−0.955901	+	0.219299i
$96$		0			0
$97$		−	2.20822i		−	0.224211i	−0.993696	−	0.112105i	$-0.964241\pi$
$97$		−	2.20822i		−	0.224211i	0.993696	−	0.112105i	$-0.0357594\pi$
$98$	6.53835	−	2.50000i	0.660473	−	0.252538i
$99$		0			0
$100$	−4.50000	+	2.17945i	−0.450000	+	0.217945i
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	−0.282656	−	0.959221i	$-0.591216\pi$
$101$	6.92820	−	12.0000i	0.689382	−	1.19404i	0.972038	−	0.234823i	$-0.0754512\pi$
$102$		0			0
$103$	13.5498	−	7.82300i	1.33510	−	0.770823i	0.349028	−	0.937112i	$-0.386512\pi$
$103$	13.5498	−	7.82300i	1.33510	−	0.770823i	0.986077	+	0.166289i	$0.0531785\pi$
$104$	−2.15068			−0.210891
$105$		0			0
$106$	7.54983			0.733305
$107$	−6.77643	+	3.91238i	−0.655103	+	0.378224i	−0.790408	−	0.612580i	$-0.790132\pi$
$107$	−6.77643	+	3.91238i	−0.655103	+	0.378224i	0.135306	+	0.990804i	$0.456798\pi$
$108$		0			0
$109$	−9.54983	+	16.5408i	−0.914708	+	1.58432i	−0.107380	+	0.994218i	$0.534246\pi$
$109$	−9.54983	+	16.5408i	−0.914708	+	1.58432i	−0.807328	+	0.590103i	$0.799087\pi$
$110$	−3.70219	−	1.13746i	−0.352990	−	0.108452i
$111$		0			0
$112$	1.13746	+	2.38876i	0.107480	+	0.225717i
$113$		−	0.549834i		−	0.0517241i	−0.999666	−	0.0258620i	$-0.991767\pi$
$113$		−	0.549834i		−	0.0517241i	0.999666	−	0.0258620i	$-0.00823306\pi$
$114$		0			0
$115$	2.13746	+	9.31697i	0.199319	+	0.868812i
$116$	1.94136	−	3.36254i	0.180251	−	0.312204i
$117$		0			0
$118$			7.34683i			0.676331i
$119$	−4.35890	−	3.00000i	−0.399580	−	0.275010i
$120$		0			0
$121$	4.00000	+	6.92820i	0.363636	+	0.629837i
$122$	−3.94027	−	2.27492i	−0.356735	−	0.205961i
$123$		0			0
$124$	−3.63746	−	6.30026i	−0.326653	−	0.565780i
$125$	−8.71780	+	7.00000i	−0.779744	+	0.626099i
$126$		0			0
$127$			21.6794i			1.92374i	0.273514	+	0.961868i	$0.411814\pi$
$127$			21.6794i			1.92374i	−0.273514	+	0.961868i	$0.588186\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−4.68729	+	1.07534i	−0.411103	+	0.0943134i
$131$	7.85177	+	13.5997i	0.686013	+	1.18821i	0.973117	+	0.230309i	$0.0739738\pi$
$131$	7.85177	+	13.5997i	0.686013	+	1.18821i	−0.287105	+	0.957899i	$0.592693\pi$
$132$		0			0
$133$	4.86254	+	10.2118i	0.421636	+	0.885472i
$134$	−8.71780			−0.753103
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	16.0646	+	9.27492i	1.37249	+	0.792410i	0.991242	−	0.132061i	$-0.0421596\pi$
$137$	16.0646	+	9.27492i	1.37249	+	0.792410i	0.381252	+	0.924471i	$0.375493\pi$
$138$		0			0
$139$	−2.54983			−0.216274			−0.108137	−	0.994136i	$-0.534489\pi$
$139$	−2.54983			−0.216274			−0.108137	+	0.994136i	$0.534489\pi$
$140$	3.67341	+	4.63746i	0.310460	+	0.391937i
$141$		0			0
$142$	12.8248	−	7.40437i	1.07623	−	0.621361i
$143$	−3.22602	−	1.86254i	−0.269773	−	0.155754i
$144$		0			0
$145$	2.54983	−	8.29917i	0.211752	−	0.689209i
$146$	12.1819			1.00818
$147$		0			0
$148$			4.77753i			0.392710i
$149$	−10.8685	−	18.8248i	−0.890380	−	1.54218i	−0.839420	−	0.543483i	$-0.817105\pi$
$149$	−10.8685	−	18.8248i	−0.890380	−	1.54218i	−0.0509601	−	0.998701i	$-0.516228\pi$
$150$		0			0
$151$	−10.1873	+	17.6449i	−0.829030	+	1.43592i	0.0697697	+	0.997563i	$0.477774\pi$
$151$	−10.1873	+	17.6449i	−0.829030	+	1.43592i	−0.898800	+	0.438359i	$0.855560\pi$
$152$	−3.70219	+	2.13746i	−0.300287	+	0.173371i
$153$		0			0
$154$	−0.362541	+	4.56821i	−0.0292144	+	0.368117i
$155$	−11.0778	−	11.9124i	−0.889789	−	0.956825i
$156$		0			0
$157$	2.58762	+	1.49397i	0.206515	+	0.119231i	0.599691	−	0.800232i	$-0.295290\pi$
$157$	2.58762	+	1.49397i	0.206515	+	0.119231i	−0.393176	+	0.919463i	$0.628624\pi$
$158$	−2.83616	−	1.63746i	−0.225633	−	0.130269i
$159$		0			0
$160$	−1.63746	+	1.52274i	−0.129452	+	0.120383i
$161$	10.2118	−	4.86254i	0.804800	−	0.383222i
$162$		0			0
$163$	3.82475	−	2.20822i	0.299578	−	0.172961i	−0.342675	−	0.939454i	$-0.611333\pi$
$163$	3.82475	−	2.20822i	0.299578	−	0.172961i	0.642253	+	0.766493i	$0.278000\pi$
$164$	5.43424	−	9.41238i	0.424343	−	0.734983i
$165$		0			0
$166$	0.362541	+	0.627940i	0.0281387	+	0.0487376i
$167$		−	20.2749i		−	1.56892i	−0.620179	−	0.784460i	$-0.712940\pi$
$167$		−	20.2749i		−	1.56892i	0.620179	−	0.784460i	$-0.287060\pi$
$168$		0			0
$169$	8.37459			0.644199
$170$	1.31342	−	4.27492i	0.100735	−	0.327871i
$171$		0			0
$172$	2.27492	+	1.31342i	0.173461	+	0.100148i
$173$	17.5586	−	10.1375i	1.33496	−	0.770737i	0.348901	−	0.937160i	$-0.386555\pi$
$173$	17.5586	−	10.1375i	1.33496	−	0.770737i	0.986054	+	0.166423i	$0.0532217\pi$
$174$		0			0
$175$	10.3248	+	8.27040i	0.780478	+	0.625183i
$176$	−1.73205			−0.130558
$177$		0			0
$178$	0.725083	+	0.418627i	0.0543473	+	0.0313774i
$179$	−5.85286	+	10.1375i	−0.437464	+	0.757709i	−0.997493	−	0.0707634i	$-0.977456\pi$
$179$	−5.85286	+	10.1375i	−0.437464	+	0.757709i	0.560029	+	0.828473i	$0.310790\pi$
$180$		0			0
$181$	−20.5498			−1.52746			−0.763729	−	0.645537i	$-0.776633\pi$
$181$	−20.5498			−1.52746			−0.763729	+	0.645537i	$0.776633\pi$
$182$	2.44631	+	5.13746i	0.181332	+	0.380814i
$183$		0			0
$184$	2.13746	+	3.70219i	0.157576	+	0.272929i
$185$	2.38876	+	10.4124i	0.175625	+	0.765533i
$186$		0			0
$187$	3.00000	−	1.73205i	0.219382	−	0.126660i
$188$			1.72508i			0.125815i
$189$		0			0
$190$	−7.00000	+	6.50958i	−0.507833	+	0.472254i
$191$	−0.837253	−	1.45017i	−0.0605815	−	0.104930i	0.834144	−	0.551547i	$-0.185962\pi$
$191$	−0.837253	−	1.45017i	−0.0605815	−	0.104930i	−0.894726	+	0.446616i	$0.852629\pi$
$192$		0			0
$193$	−10.1873	−	5.88164i	−0.733297	−	0.423369i	0.0863299	−	0.996267i	$-0.472486\pi$
$193$	−10.1873	−	5.88164i	−0.733297	−	0.423369i	−0.819627	+	0.572897i	$0.805819\pi$
$194$	−1.10411	−	1.91238i	−0.0792705	−	0.137301i
$195$		0			0
$196$	4.41238	−	5.43424i	0.315170	−	0.388160i
$197$		−	13.3746i		−	0.952900i	−0.879202	−	0.476450i	$-0.841923\pi$
$197$		−	13.3746i		−	0.952900i	0.879202	−	0.476450i	$-0.158077\pi$
$198$		0			0
$199$	2.27492	−	3.94027i	0.161265	−	0.279318i	−0.774058	−	0.633115i	$-0.781776\pi$
$199$	2.27492	−	3.94027i	0.161265	−	0.279318i	0.935322	+	0.353796i	$0.115109\pi$
$200$	−2.80739	+	4.13746i	−0.198512	+	0.292563i
$201$		0			0
$202$		−	13.8564i		−	0.974933i
$203$	−10.2405	−	0.812707i	−0.718745	−	0.0570408i
$204$		0			0
$205$	7.13746	−	23.2309i	0.498502	−	1.62252i
$206$	7.82300	−	13.5498i	0.545054	−	0.944062i
$207$		0			0
$208$	−1.86254	+	1.07534i	−0.129144	+	0.0745613i
$209$	−7.40437			−0.512171
$210$		0			0
$211$	18.8248			1.29595			0.647975	−	0.761662i	$-0.275616\pi$
$211$	18.8248			1.29595			0.647975	+	0.761662i	$0.275616\pi$
$212$	6.53835	−	3.77492i	0.449056	−	0.259262i
$213$		0			0
$214$	−3.91238	+	6.77643i	−0.267445	+	0.463227i
$215$	5.61478	+	1.72508i	0.382925	+	0.117650i
$216$		0			0
$217$	−10.9124	+	15.8553i	−0.740780	+	1.07633i
$218$			19.0997i			1.29359i
$219$		0			0
$220$	−3.77492	+	0.866025i	−0.254505	+	0.0583874i
$221$	2.15068	−	3.72508i	0.144670	−	0.250576i
$222$		0			0
$223$		−	18.6915i		−	1.25167i	−0.779954	−	0.625837i	$-0.784758\pi$
$223$		−	18.6915i		−	1.25167i	0.779954	−	0.625837i	$-0.215242\pi$
$224$	2.17945	+	1.50000i	0.145621	+	0.100223i
$225$		0			0
$226$	−0.274917	−	0.476171i	−0.0182872	−	0.0316744i
$227$	8.50848	+	4.91238i	0.564728	+	0.326046i	0.755041	−	0.655678i	$-0.227617\pi$
$227$	8.50848	+	4.91238i	0.564728	+	0.326046i	−0.190313	+	0.981723i	$0.560950\pi$
$228$		0			0
$229$	−2.54983	−	4.41644i	−0.168498	−	0.291847i	0.769394	−	0.638774i	$-0.220558\pi$
$229$	−2.54983	−	4.41644i	−0.168498	−	0.291847i	−0.937892	+	0.346928i	$0.887225\pi$
$230$	6.50958	+	7.00000i	0.429229	+	0.461566i
$231$		0			0
$232$		−	3.88273i		−	0.254914i
$233$	−12.6005	+	7.27492i	−0.825488	+	0.476596i	−0.852305	−	0.523045i	$-0.824796\pi$
$233$	−12.6005	+	7.27492i	−0.825488	+	0.476596i	0.0268173	+	0.999640i	$0.491463\pi$
$234$		0			0
$235$	0.862541	+	3.75973i	0.0562660	+	0.245258i
$236$	3.67341	+	6.36254i	0.239119	+	0.414166i
$237$		0			0
$238$	−5.27492	−	0.418627i	−0.341922	−	0.0271355i
$239$	−14.6937			−0.950454			−0.475227	−	0.879863i	$-0.657634\pi$
$239$	−14.6937			−0.950454			−0.475227	+	0.879863i	$0.657634\pi$
$240$		0			0
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	−0.516695	−	0.856170i	$-0.672838\pi$
$241$	7.50000	−	12.9904i	0.483117	−	0.836784i	0.999812	+	0.0193858i	$0.00617107\pi$
$242$	6.92820	+	4.00000i	0.445362	+	0.257130i
$243$		0			0
$244$	−4.54983			−0.291273
$245$	6.89943	−	14.0498i	0.440788	−	0.897611i
$246$		0			0
$247$	−7.96221	+	4.59698i	−0.506623	+	0.292499i
$248$	−6.30026	−	3.63746i	−0.400067	−	0.230979i
$249$		0			0
$250$	−4.04983	+	10.4211i	−0.256134	+	0.659087i
$251$	0.0575438			0.00363214			0.00181607	−	0.999998i	$-0.499422\pi$
$251$	0.0575438			0.00363214			0.00181607	+	0.999998i	$0.499422\pi$
$252$		0			0
$253$			7.40437i			0.465509i
$254$	10.8397	+	18.7749i	0.680143	+	1.17804i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		0			0
$259$	11.4124	−	5.43424i	0.709131	−	0.337667i
$260$	−3.52165	+	3.27492i	−0.218403	+	0.203102i
$261$		0			0
$262$	13.5997	+	7.85177i	0.840190	+	0.485084i
$263$	−18.2728	−	10.5498i	−1.12675	−	0.650531i	−0.183636	−	0.982994i	$-0.558787\pi$
$263$	−18.2728	−	10.5498i	−1.12675	−	0.650531i	−0.943116	+	0.332464i	$0.892120\pi$
$264$		0			0
$265$	12.3625	−	11.4964i	0.759425	−	0.706219i
$266$	9.31697	+	6.41238i	0.571260	+	0.393168i
$267$		0			0
$268$	−7.54983	+	4.35890i	−0.461180	+	0.266262i
$269$	−2.41753	+	4.18729i	−0.147400	+	0.255304i	−0.930266	−	0.366887i	$-0.880424\pi$
$269$	−2.41753	+	4.18729i	−0.147400	+	0.255304i	0.782866	+	0.622190i	$0.213757\pi$
$270$		0			0
$271$	−7.91238	−	13.7046i	−0.480643	−	0.832497i	0.519111	−	0.854707i	$-0.326263\pi$
$271$	−7.91238	−	13.7046i	−0.480643	−	0.832497i	−0.999753	+	0.0222096i	$0.992930\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	18.5498			1.12064
$275$	−7.79423	+	3.77492i	−0.470010	+	0.227636i
$276$		0			0
$277$	−21.0997	−	12.1819i	−1.26776	−	0.731939i	−0.293193	−	0.956053i	$-0.594718\pi$
$277$	−21.0997	−	12.1819i	−1.26776	−	0.731939i	−0.974563	+	0.224114i	$0.928051\pi$
$278$	−2.20822	+	1.27492i	−0.132440	+	0.0764645i
$279$		0			0
$280$	5.50000	+	2.17945i	0.328688	+	0.130247i
$281$	14.3326			0.855010			0.427505	−	0.904013i	$-0.359393\pi$
$281$	14.3326			0.855010			0.427505	+	0.904013i	$0.359393\pi$
$282$		0			0
$283$	−20.2749	−	11.7057i	−1.20522	−	0.695833i	−0.243508	−	0.969899i	$-0.578298\pi$
$283$	−20.2749	−	11.7057i	−1.20522	−	0.695833i	−0.961711	+	0.274066i	$0.911631\pi$
$284$	7.40437	−	12.8248i	0.439369	−	0.761009i
$285$		0			0
$286$	−3.72508			−0.220269
$287$	−28.6652	−	2.27492i	−1.69205	−	0.134284i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−1.94136	−	8.46221i	−0.114001	−	0.496918i
$291$		0			0
$292$	10.5498	−	6.09095i	0.617382	−	0.356446i
$293$			13.5498i			0.791590i	0.918339	+	0.395795i	$0.129531\pi$
$293$			13.5498i			0.791590i	−0.918339	+	0.395795i	$0.870469\pi$
$294$		0			0
$295$	11.1873	+	12.0301i	0.651349	+	0.700421i
$296$	2.38876	+	4.13746i	0.138844	+	0.240485i
$297$		0			0
$298$	−18.8248	−	10.8685i	−1.09049	−	0.629594i
$299$	4.59698	+	7.96221i	0.265850	+	0.460467i
$300$		0			0
$301$	0.549834	−	6.92820i	0.0316919	−	0.399335i
$302$			20.3746i			1.17243i
$303$		0			0
$304$	−2.13746	+	3.70219i	−0.122592	+	0.212335i
$305$	−9.91613	+	2.27492i	−0.567796	+	0.130261i
$306$		0			0
$307$			15.6460i			0.892964i	0.894793	+	0.446482i	$0.147323\pi$
$307$			15.6460i			0.892964i	−0.894793	+	0.446482i	$0.852677\pi$
$308$	1.97014	+	4.13746i	0.112259	+	0.235754i
$309$		0			0
$310$	−15.5498	−	4.77753i	−0.883171	−	0.271345i
$311$	−14.3326	+	24.8248i	−0.812726	+	1.40768i	0.0982235	+	0.995164i	$0.468684\pi$
$311$	−14.3326	+	24.8248i	−0.812726	+	1.40768i	−0.910949	+	0.412518i	$0.864649\pi$
$312$		0			0
$313$	−5.63746	+	3.25479i	−0.318648	+	0.183972i	−0.650790	−	0.759258i	$-0.725562\pi$
$313$	−5.63746	+	3.25479i	−0.318648	+	0.183972i	0.332142	+	0.943229i	$0.392229\pi$
$314$	2.98793			0.168619
$315$		0			0
$316$	−3.27492			−0.184228
$317$	23.6208	−	13.6375i	1.32667	−	0.765956i	0.341891	−	0.939740i	$-0.388933\pi$
$317$	23.6208	−	13.6375i	1.32667	−	0.765956i	0.984784	+	0.173784i	$0.0555994\pi$
$318$		0			0
$319$	3.36254	−	5.82409i	0.188266	−	0.326087i
$320$	−0.656712	+	2.13746i	−0.0367113	+	0.119488i
$321$		0			0
$322$	6.41238	−	9.31697i	0.357348	−	0.519214i
$323$		−	8.54983i		−	0.475726i
$324$		0			0
$325$	−6.03779	+	8.89834i	−0.334916	+	0.493591i
$326$	2.20822	−	3.82475i	0.122302	−	0.211833i
$327$		0			0
$328$		−	10.8685i		−	0.600111i
$329$	4.12081	−	1.96221i	0.227188	−	0.108180i
$330$		0			0
$331$	4.58762	+	7.94600i	0.252159	+	0.436752i	0.964120	−	0.265467i	$-0.0855262\pi$
$331$	4.58762	+	7.94600i	0.252159	+	0.436752i	−0.711961	+	0.702219i	$0.752193\pi$
$332$	0.627940	+	0.362541i	0.0344627	+	0.0198970i
$333$		0			0
$334$	−10.1375	−	17.5586i	−0.554697	−	0.960763i
$335$	−14.2750	+	13.2749i	−0.779928	+	0.725286i
$336$		0			0
$337$		−	9.02134i		−	0.491424i	−0.969343	−	0.245712i	$-0.920978\pi$
$337$		−	9.02134i		−	0.491424i	0.969343	−	0.245712i	$-0.0790217\pi$
$338$	7.25260	−	4.18729i	0.394490	−	0.227759i
$339$		0			0
$340$	−1.00000	−	4.35890i	−0.0542326	−	0.236394i
$341$	−6.30026	−	10.9124i	−0.341178	−	0.590938i
$342$		0			0
$343$	−18.0000	−	4.35890i	−0.971909	−	0.235358i
$344$	2.62685			0.141630
$345$		0			0
$346$	10.1375	−	17.5586i	0.544993	−	0.943956i
$347$	2.51176	+	1.45017i	0.134838	+	0.0778490i	0.565902	−	0.824473i	$-0.308528\pi$
$347$	2.51176	+	1.45017i	0.134838	+	0.0778490i	−0.431063	+	0.902322i	$0.641861\pi$
$348$		0			0
$349$	1.45017			0.0776256			0.0388128	−	0.999246i	$-0.487642\pi$
$349$	1.45017			0.0776256			0.0388128	+	0.999246i	$0.487642\pi$
$350$	13.0767	+	2.00000i	0.698979	+	0.106904i
$351$		0			0
$352$	−1.50000	+	0.866025i	−0.0799503	+	0.0461593i
$353$	7.88054	+	4.54983i	0.419439	+	0.242163i	0.694837	−	0.719167i	$-0.255476\pi$
$353$	7.88054	+	4.54983i	0.419439	+	0.242163i	−0.275398	+	0.961330i	$0.588810\pi$
$354$		0			0
$355$	9.72508	−	31.6531i	0.516154	−	1.67997i
$356$	0.837253			0.0443743
$357$		0			0
$358$			11.7057i			0.618667i
$359$	6.50958	+	11.2749i	0.343562	+	0.595067i	0.985091	−	0.172031i	$-0.0550330\pi$
$359$	6.50958	+	11.2749i	0.343562	+	0.595067i	−0.641529	+	0.767099i	$0.721700\pi$
$360$		0			0
$361$	0.362541	−	0.627940i	0.0190811	−	0.0330495i
$362$	−17.7967	+	10.2749i	−0.935373	+	0.540038i
$363$		0			0
$364$	4.68729	+	3.22602i	0.245681	+	0.169089i
$365$	19.9474	−	18.5498i	1.04409	−	0.970943i
$366$		0			0
$367$	−12.7749	−	7.37560i	−0.666845	−	0.385003i	0.128035	−	0.991770i	$-0.459133\pi$
$367$	−12.7749	−	7.37560i	−0.666845	−	0.385003i	−0.794880	+	0.606766i	$0.792466\pi$
$368$	3.70219	+	2.13746i	0.192990	+	0.111423i
$369$		0			0
$370$	7.27492	+	7.82300i	0.378205	+	0.406698i
$371$	−16.4545	−	11.3248i	−0.854274	−	0.587952i
$372$		0			0
$373$	1.45017	−	0.837253i	0.0750867	−	0.0433513i	−0.461987	−	0.886887i	$-0.652863\pi$
$373$	1.45017	−	0.837253i	0.0750867	−	0.0433513i	0.537073	+	0.843536i	$0.319530\pi$
$374$	1.73205	−	3.00000i	0.0895622	−	0.155126i
$375$		0			0
$376$	0.862541	+	1.49397i	0.0444822	+	0.0770454i
$377$		−	8.35050i		−	0.430072i
$378$		0			0
$379$	−22.8248			−1.17243			−0.586214	−	0.810156i	$-0.699382\pi$
$379$	−22.8248			−1.17243			−0.586214	+	0.810156i	$0.699382\pi$
$380$	−2.80739	+	9.13746i	−0.144016	+	0.468742i
$381$		0			0
$382$	−1.45017	−	0.837253i	−0.0741969	−	0.0428376i
$383$	25.4391	−	14.6873i	1.29988	−	0.750486i	0.319496	−	0.947588i	$-0.396486\pi$
$383$	25.4391	−	14.6873i	1.29988	−	0.750486i	0.980383	+	0.197102i	$0.0631530\pi$
$384$		0			0
$385$	6.36254	+	8.03231i	0.324265	+	0.409365i
$386$	−11.7633			−0.598735
$387$		0			0
$388$	−1.91238	−	1.10411i	−0.0970862	−	0.0560527i
$389$	2.98793	−	5.17525i	0.151494	−	0.262396i	−0.780283	−	0.625427i	$-0.784925\pi$
$389$	2.98793	−	5.17525i	0.151494	−	0.262396i	0.931777	+	0.363031i	$0.118258\pi$
$390$		0			0
$391$	−8.54983			−0.432384
$392$	1.10411	−	6.91238i	0.0557660	−	0.349128i
$393$		0			0
$394$	−6.68729	−	11.5827i	−0.336901	−	0.583530i
$395$	−7.13752	+	1.63746i	−0.359127	+	0.0823895i
$396$		0			0
$397$	−16.5498	+	9.55505i	−0.830612	+	0.479554i	−0.854062	−	0.520171i	$-0.825868\pi$
$397$	−16.5498	+	9.55505i	−0.830612	+	0.479554i	0.0234499	+	0.999725i	$0.492535\pi$
$398$		−	4.54983i		−	0.228063i
$399$		0			0
$400$	−0.362541	+	4.98684i	−0.0181271	+	0.249342i
$401$	−1.97014	−	3.41238i	−0.0983839	−	0.170406i	0.812632	−	0.582777i	$-0.198034\pi$
$401$	−1.97014	−	3.41238i	−0.0983839	−	0.170406i	−0.911016	+	0.412371i	$0.864701\pi$
$402$		0			0
$403$	−13.5498	−	7.82300i	−0.674965	−	0.389691i
$404$	−6.92820	−	12.0000i	−0.344691	−	0.597022i
$405$		0			0
$406$	−9.27492	+	4.41644i	−0.460306	+	0.219184i
$407$			8.27492i			0.410172i
$408$		0			0
$409$	1.63746	−	2.83616i	0.0809671	−	0.140239i	−0.822698	−	0.568478i	$-0.807532\pi$
$409$	1.63746	−	2.83616i	0.0809671	−	0.140239i	0.903666	+	0.428239i	$0.140866\pi$
$410$	−5.43424	−	23.6873i	−0.268378	−	1.16983i
$411$		0			0
$412$		−	15.6460i		−	0.770823i
$413$	11.0202	−	16.0120i	0.542271	−	0.787901i
$414$		0			0
$415$	1.54983	+	0.476171i	0.0760784	+	0.0233743i
$416$	−1.07534	+	1.86254i	−0.0527228	+	0.0913186i
$417$		0			0
$418$	−6.41238	+	3.70219i	−0.313640	+	0.181080i
$419$	2.15068			0.105067			0.0525337	−	0.998619i	$-0.483270\pi$
$419$	2.15068			0.105067			0.0525337	+	0.998619i	$0.483270\pi$
$420$		0			0
$421$	25.0997			1.22328			0.611642	−	0.791135i	$-0.290510\pi$
$421$	25.0997			1.22328			0.611642	+	0.791135i	$0.290510\pi$
$422$	16.3027	−	9.41238i	0.793604	−	0.458187i
$423$		0			0
$424$	3.77492	−	6.53835i	0.183326	−	0.317530i
$425$	−4.35890	−	9.00000i	−0.211438	−	0.436564i
$426$		0			0
$427$	5.17525	+	10.8685i	0.250448	+	0.525962i
$428$			7.82475i			0.378224i
$429$		0			0
$430$	5.72508	−	1.31342i	0.276088	−	0.0633389i
$431$	1.31342	−	2.27492i	0.0632654	−	0.109579i	−0.832658	−	0.553788i	$-0.813182\pi$
$431$	1.31342	−	2.27492i	0.0632654	−	0.109579i	0.895923	+	0.444209i	$0.146515\pi$
$432$		0			0
$433$			12.1819i			0.585425i	0.956201	+	0.292712i	$0.0945578\pi$
$433$			12.1819i			0.585425i	−0.956201	+	0.292712i	$0.905442\pi$
$434$	−1.52274	+	19.1873i	−0.0730937	+	0.921020i
$435$		0			0
$436$	9.54983	+	16.5408i	0.457354	+	0.792161i
$437$	15.8265	+	9.13746i	0.757086	+	0.437104i
$438$		0			0
$439$	11.9124	+	20.6328i	0.568547	+	0.984752i	0.996710	+	0.0810504i	$0.0258275\pi$
$439$	11.9124	+	20.6328i	0.568547	+	0.984752i	−0.428163	+	0.903701i	$0.640839\pi$
$440$	−2.83616	+	2.63746i	−0.135209	+	0.125736i
$441$		0			0
$442$		−	4.30136i		−	0.204595i
$443$	−0.627940	+	0.362541i	−0.0298343	+	0.0172249i	−0.514843	−	0.857284i	$-0.672150\pi$
$443$	−0.627940	+	0.362541i	−0.0298343	+	0.0172249i	0.485009	+	0.874509i	$0.338816\pi$
$444$		0			0
$445$	1.82475	−	0.418627i	0.0865015	−	0.0198448i
$446$	−9.34574	−	16.1873i	−0.442534	−	0.766491i
$447$		0			0
$448$	2.63746	+	0.209313i	0.124608	+	0.00988913i
$449$	31.7682			1.49923			0.749616	−	0.661873i	$-0.230238\pi$
$449$	31.7682			1.49923			0.749616	+	0.661873i	$0.230238\pi$
$450$		0			0
$451$	9.41238	−	16.3027i	0.443211	−	0.767665i
$452$	−0.476171	−	0.274917i	−0.0223972	−	0.0129310i
$453$		0			0
$454$	9.82475			0.461098
$455$	11.8287	+	4.68729i	0.554539	+	0.219744i
$456$		0			0
$457$	9.46221	−	5.46301i	0.442624	−	0.255549i	−0.262086	−	0.965044i	$-0.584411\pi$
$457$	9.46221	−	5.46301i	0.442624	−	0.255549i	0.704710	+	0.709496i	$0.251077\pi$
$458$	−4.41644	−	2.54983i	−0.206367	−	0.119146i
$459$		0			0
$460$	9.13746	+	2.80739i	0.426036	+	0.130895i
$461$	−34.8712			−1.62411			−0.812057	−	0.583579i	$-0.801652\pi$
$461$	−34.8712			−1.62411			−0.812057	+	0.583579i	$0.801652\pi$
$462$		0			0
$463$		−	24.8400i		−	1.15441i	−0.816599	−	0.577206i	$-0.804143\pi$
$463$		−	24.8400i		−	1.15441i	0.816599	−	0.577206i	$-0.195857\pi$
$464$	−1.94136	−	3.36254i	−0.0901256	−	0.156102i
$465$		0			0
$466$	−7.27492	+	12.6005i	−0.337004	+	0.583708i
$467$	−13.3802	+	7.72508i	−0.619163	+	0.357474i	−0.776543	−	0.630064i	$-0.783029\pi$
$467$	−13.3802	+	7.72508i	−0.619163	+	0.357474i	0.157380	+	0.987538i	$0.449695\pi$
$468$		0			0
$469$	19.0000	+	13.0767i	0.877338	+	0.603826i
$470$	2.62685	+	2.82475i	0.121167	+	0.130296i
$471$		0			0
$472$	6.36254	+	3.67341i	0.292860	+	0.169083i
$473$	3.94027	+	2.27492i	0.181174	+	0.104601i
$474$		0			0
$475$	−1.54983	+	21.3183i	−0.0711113	+	0.978152i
$476$	−4.77753	+	2.27492i	−0.218978	+	0.104271i
$477$		0			0
$478$	−12.7251	+	7.34683i	−0.582032	+	0.336036i
$479$	−7.88054	+	13.6495i	−0.360071	+	0.623662i	−0.987972	−	0.154632i	$-0.950581\pi$
$479$	−7.88054	+	13.6495i	−0.360071	+	0.623662i	0.627901	+	0.778293i	$0.283914\pi$
$480$		0			0
$481$	5.13746	+	8.89834i	0.234248	+	0.405729i
$482$		−	15.0000i		−	0.683231i
$483$		0			0
$484$	8.00000			0.363636
$485$	−4.71998	−	1.45017i	−0.214323	−	0.0658486i
$486$		0			0
$487$	17.6375	+	10.1830i	0.799230	+	0.461435i	0.843202	−	0.537597i	$-0.180668\pi$
$487$	17.6375	+	10.1830i	0.799230	+	0.461435i	−0.0439721	+	0.999033i	$0.514001\pi$
$488$	−3.94027	+	2.27492i	−0.178368	+	0.102981i
$489$		0			0
$490$	−1.04983	−	15.6172i	−0.0474267	−	0.705514i
$491$	−10.0888			−0.455300			−0.227650	−	0.973743i	$-0.573104\pi$
$491$	−10.0888			−0.455300			−0.227650	+	0.973743i	$0.573104\pi$
$492$		0			0
$493$	6.72508	+	3.88273i	0.302882	+	0.174869i
$494$	−4.59698	+	7.96221i	−0.206828	+	0.358237i
$495$		0			0
$496$	−7.27492			−0.326653
$497$	−39.0575	−	3.09967i	−1.75197	−	0.139039i
$498$		0			0
$499$	−4.72508	−	8.18408i	−0.211524	−	0.366370i	0.740668	−	0.671871i	$-0.234509\pi$
$499$	−4.72508	−	8.18408i	−0.211524	−	0.366370i	−0.952192	+	0.305501i	$0.901176\pi$
$500$	1.70328	+	11.0498i	0.0761729	+	0.494164i
$501$		0			0
$502$	0.0498344	−	0.0287719i	0.00222422	−	0.00128415i
$503$			39.6495i			1.76788i	0.467597	+	0.883942i	$0.345120\pi$
$503$			39.6495i			1.76788i	−0.467597	+	0.883942i	$0.654880\pi$
$504$		0			0
$505$	−21.0997	−	22.6893i	−0.938923	−	1.00966i
$506$	3.70219	+	6.41238i	0.164582	+	0.285065i
$507$		0			0
$508$	18.7749	+	10.8397i	0.833002	+	0.480934i
$509$	−12.8098	−	22.1873i	−0.567786	−	0.983434i	−0.996784	−	0.0801292i	$-0.974467\pi$
$509$	−12.8098	−	22.1873i	−0.567786	−	0.983434i	0.428998	−	0.903305i	$-0.358867\pi$
$510$		0			0
$511$	−26.5498	−	18.2728i	−1.17450	−	0.808343i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	−7.82300	−	34.0997i	−0.344723	−	1.50261i
$516$		0			0
$517$			2.98793i			0.131409i
$518$	7.16629	−	10.4124i	0.314869	−	0.457494i
$519$		0			0
$520$	−1.41238	+	4.59698i	−0.0619368	+	0.201591i
$521$	−8.42217	+	14.5876i	−0.368982	+	0.639095i	−0.989407	−	0.145171i	$-0.953627\pi$
$521$	−8.42217	+	14.5876i	−0.368982	+	0.639095i	0.620425	+	0.784266i	$0.286960\pi$
$522$		0			0
$523$	20.3746	−	11.7633i	0.890918	−	0.514372i	0.0166756	−	0.999861i	$-0.494692\pi$
$523$	20.3746	−	11.7633i	0.890918	−	0.514372i	0.874243	+	0.485489i	$0.161358\pi$
$524$	15.7035			0.686013
$525$		0			0
$526$	−21.0997			−0.919989
$527$	12.6005	−	7.27492i	0.548888	−	0.316900i
$528$		0			0
$529$	−2.36254	+	4.09204i	−0.102719	+	0.177915i
$530$	4.95807	−	16.1375i	0.215365	−	0.700966i
$531$		0			0
$532$	11.2749	+	0.894797i	0.488830	+	0.0387944i
$533$		−	23.3746i		−	1.01247i
$534$		0			0
$535$	3.91238	+	17.0537i	0.169147	+	0.737294i
$536$	−4.35890	+	7.54983i	−0.188276	+	0.326103i
$537$		0			0
$538$			4.83507i			0.208455i
$539$	7.64246	−	9.41238i	0.329184	−	0.405420i
$540$		0			0
$541$	12.5498	+	21.7370i	0.539560	+	0.934545i	0.998928	+	0.0462985i	$0.0147425\pi$
$541$	12.5498	+	21.7370i	0.539560	+	0.934545i	−0.459368	+	0.888246i	$0.651924\pi$
$542$	−13.7046	−	7.91238i	−0.588665	−	0.339866i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	29.0838	+	31.2749i	1.24581	+	1.33967i
$546$		0			0
$547$			12.0668i			0.515940i	0.966153	+	0.257970i	$0.0830535\pi$
$547$			12.0668i			0.515940i	−0.966153	+	0.257970i	$0.916946\pi$
$548$	16.0646	−	9.27492i	0.686247	−	0.396205i
$549$		0			0
$550$	−4.86254	+	7.16629i	−0.207339	+	0.305572i
$551$	−8.29917	−	14.3746i	−0.353557	−	0.612378i
$552$		0			0
$553$	3.72508	+	7.82300i	0.158407	+	0.332668i
$554$	−24.3638			−1.03512
$555$		0			0
$556$	−1.27492	+	2.20822i	−0.0540685	+	0.0936494i
$557$	38.6676	+	22.3248i	1.63840	+	0.945930i	0.981385	+	0.192052i	$0.0615142\pi$
$557$	38.6676	+	22.3248i	1.63840	+	0.945930i	0.657014	+	0.753878i	$0.271819\pi$
$558$		0			0
$559$	5.64950			0.238949
$560$	5.85286	−	0.862541i	0.247329	−	0.0364490i
$561$		0			0
$562$	12.4124	−	7.16629i	0.523584	−	0.302292i
$563$	5.04438	+	2.91238i	0.212595	+	0.122742i	0.602517	−	0.798106i	$-0.294165\pi$
$563$	5.04438	+	2.91238i	0.212595	+	0.122742i	−0.389922	+	0.920848i	$0.627498\pi$
$564$		0			0
$565$	−1.17525	−	0.361083i	−0.0494431	−	0.0151909i
$566$	−23.4115			−0.984057
$567$		0			0
$568$		−	14.8087i		−	0.621361i
$569$	18.0348	+	31.2371i	0.756057	+	1.30953i	0.944847	+	0.327511i	$0.106210\pi$
$569$	18.0348	+	31.2371i	0.756057	+	1.30953i	−0.188791	+	0.982017i	$0.560457\pi$
$570$		0			0
$571$	−5.45017	+	9.43996i	−0.228082	+	0.395050i	−0.957240	−	0.289296i	$-0.906579\pi$
$571$	−5.45017	+	9.43996i	−0.228082	+	0.395050i	0.729157	+	0.684346i	$0.239912\pi$
$572$	−3.22602	+	1.86254i	−0.134887	+	0.0778768i
$573$		0			0
$574$	−25.9622	+	12.3624i	−1.08364	+	0.515998i
$575$	21.3183	+	1.54983i	0.889036	+	0.0646326i
$576$		0			0
$577$	15.3625	+	8.86957i	0.639551	+	0.369245i	0.784442	−	0.620203i	$-0.212950\pi$
$577$	15.3625	+	8.86957i	0.639551	+	0.369245i	−0.144891	+	0.989448i	$0.546283\pi$
$578$	−11.2583	−	6.50000i	−0.468285	−	0.270364i
$579$		0			0
$580$	−5.91238	−	6.35781i	−0.245498	−	0.263994i
$581$	0.151770	−	1.91238i	0.00629646	−	0.0793387i
$582$		0			0
$583$	11.3248	−	6.53835i	0.469023	−	0.270791i
$584$	6.09095	−	10.5498i	0.252045	−	0.436555i
$585$		0			0
$586$	6.77492	+	11.7345i	0.279869	+	0.484748i
$587$		−	43.2749i		−	1.78615i	−0.449911	−	0.893073i	$-0.648544\pi$
$587$		−	43.2749i		−	1.78615i	0.449911	−	0.893073i	$-0.351456\pi$
$588$		0			0
$589$	−31.0997			−1.28144
$590$	15.7035	+	4.82475i	0.646505	+	0.198632i
$591$		0			0
$592$	4.13746	+	2.38876i	0.170049	+	0.0981775i
$593$	−31.3495	+	18.0997i	−1.28737	+	0.743264i	−0.978185	−	0.207737i	$-0.933390\pi$
$593$	−31.3495	+	18.0997i	−1.28737	+	0.743264i	−0.309187	+	0.951001i	$0.600057\pi$
$594$		0			0
$595$	−9.27492	+	7.34683i	−0.380235	+	0.301191i
$596$	−21.7370			−0.890380
$597$		0			0
$598$	7.96221	+	4.59698i	0.325599	+	0.187985i
$599$	20.4811	−	35.4743i	0.836834	−	1.44944i	−0.0556947	−	0.998448i	$-0.517737\pi$
$599$	20.4811	−	35.4743i	0.836834	−	1.44944i	0.892529	−	0.450991i	$-0.148929\pi$
$600$		0			0
$601$	−6.17525			−0.251894			−0.125947	−	0.992037i	$-0.540197\pi$
$601$	−6.17525			−0.251894			−0.125947	+	0.992037i	$0.540197\pi$
$602$	−2.98793	−	6.27492i	−0.121779	−	0.255747i
$603$		0			0
$604$	10.1873	+	17.6449i	0.414515	+	0.717961i
$605$	17.4356	−	4.00000i	0.708858	−	0.162623i
$606$		0			0
$607$	−12.7749	+	7.37560i	−0.518518	+	0.299366i	−0.736328	−	0.676625i	$-0.763442\pi$
$607$	−12.7749	+	7.37560i	−0.518518	+	0.299366i	0.217810	+	0.975991i	$0.430109\pi$
$608$			4.27492i			0.173371i
$609$		0			0
$610$	−7.45017	+	6.92820i	−0.301648	+	0.280515i
$611$	1.85505	+	3.21304i	0.0750472	+	0.129986i
$612$		0			0
$613$	38.0619	+	21.9750i	1.53730	+	0.887563i	0.998995	+	0.0448162i	$0.0142702\pi$
$613$	38.0619	+	21.9750i	1.53730	+	0.887563i	0.538310	+	0.842747i	$0.319063\pi$
$614$	7.82300	+	13.5498i	0.315711	+	0.546827i
$615$		0			0
$616$	3.77492	+	2.59808i	0.152096	+	0.104679i
$617$			15.4502i			0.622000i	0.950410	+	0.311000i	$0.100664\pi$
$617$			15.4502i			0.622000i	−0.950410	+	0.311000i	$0.899336\pi$
$618$		0			0
$619$	−9.68729	+	16.7789i	−0.389365	+	0.674400i	−0.992364	−	0.123342i	$-0.960639\pi$
$619$	−9.68729	+	16.7789i	−0.389365	+	0.674400i	0.602999	+	0.797742i	$0.293972\pi$
$620$	−15.8553	+	3.63746i	−0.636765	+	0.146084i
$621$		0			0
$622$			28.6652i			1.14937i
$623$	−0.952341	−	2.00000i	−0.0381547	−	0.0801283i
$624$		0			0
$625$	9.23713	+	23.2309i	0.369485	+	0.929237i
$626$	−3.25479	+	5.63746i	−0.130088	+	0.225318i
$627$		0			0
$628$	2.58762	−	1.49397i	0.103257	−	0.0596157i
$629$	−9.55505			−0.380985
$630$		0			0
$631$	−6.92442			−0.275657			−0.137828	−	0.990456i	$-0.544012\pi$
$631$	−6.92442			−0.275657			−0.137828	+	0.990456i	$0.544012\pi$
$632$	−2.83616	+	1.63746i	−0.112816	+	0.0651346i
$633$		0			0
$634$	13.6375	−	23.6208i	0.541613	−	0.938101i
$635$	46.3388	+	14.2371i	1.83890	+	0.564983i
$636$		0			0
$637$	2.37459	−	14.8663i	0.0940845	−	0.589024i
$638$		−	6.72508i		−	0.266249i
$639$		0			0
$640$	0.500000	+	2.17945i	0.0197642	+	0.0861503i
$641$	−20.1279	+	34.8625i	−0.795004	+	1.37699i	0.127832	+	0.991796i	$0.459198\pi$
$641$	−20.1279	+	34.8625i	−0.795004	+	1.37699i	−0.922837	+	0.385192i	$0.874135\pi$
$642$		0			0
$643$			6.81312i			0.268683i	0.990935	+	0.134342i	$0.0428919\pi$
$643$			6.81312i			0.268683i	−0.990935	+	0.134342i	$0.957108\pi$
$644$	0.894797	−	11.2749i	0.0352600	−	0.444294i
$645$		0			0
$646$	−4.27492	−	7.40437i	−0.168194	−	0.291321i
$647$	34.5756	+	19.9622i	1.35931	+	0.784795i	0.989530	−	0.144326i	$-0.0461013\pi$
$647$	34.5756	+	19.9622i	1.35931	+	0.784795i	0.369775	+	0.929121i	$0.379435\pi$
$648$		0			0
$649$	6.36254	+	11.0202i	0.249752	+	0.432582i
$650$	−0.779710	+	10.7251i	−0.0305827	+	0.420672i
$651$		0			0
$652$		−	4.41644i		−	0.172961i
$653$	−16.9307	+	9.77492i	−0.662548	+	0.382522i	−0.793247	−	0.608900i	$-0.791611\pi$
$653$	−16.9307	+	9.77492i	−0.662548	+	0.382522i	0.130699	+	0.991422i	$0.458278\pi$
$654$		0			0
$655$	34.2251	−	7.85177i	1.33728	−	0.306794i
$656$	−5.43424	−	9.41238i	−0.212171	−	0.367492i
$657$		0			0
$658$	2.58762	−	3.75973i	0.100876	−	0.146570i
$659$	24.2487			0.944596			0.472298	−	0.881439i	$-0.343425\pi$
$659$	24.2487			0.944596			0.472298	+	0.881439i	$0.343425\pi$
$660$		0			0
$661$	−0.549834	+	0.952341i	−0.0213861	+	0.0370418i	−0.876520	−	0.481365i	$-0.840141\pi$
$661$	−0.549834	+	0.952341i	−0.0213861	+	0.0370418i	0.855134	+	0.518407i	$0.173475\pi$
$662$	7.94600	+	4.58762i	0.308830	+	0.178303i
$663$		0			0
$664$	0.725083			0.0281387
$665$	25.0205	−	3.68729i	0.970254	−	0.142987i
$666$		0			0
$667$	−14.3746	+	8.29917i	−0.556586	+	0.321345i
$668$	−17.5586	−	10.1375i	−0.679362	−	0.392230i
$669$		0			0
$670$	−5.72508	+	18.6339i	−0.221179	+	0.719892i
$671$	−7.88054			−0.304225
$672$		0			0
$673$			33.5002i			1.29134i	0.763617	+	0.645669i	$0.223422\pi$
$673$			33.5002i			1.29134i	−0.763617	+	0.645669i	$0.776578\pi$
$674$	−4.51067	−	7.81271i	−0.173744	−	0.300934i
$675$		0			0
$676$	4.18729	−	7.25260i	0.161050	−	0.278946i
$677$	−18.6627	+	10.7749i	−0.717266	+	0.414114i	−0.813746	−	0.581221i	$-0.802575\pi$
$677$	−18.6627	+	10.7749i	−0.717266	+	0.414114i	0.0964796	+	0.995335i	$0.469242\pi$
$678$		0			0
$679$	−0.462210	+	5.82409i	−0.0177380	+	0.223508i
$680$	−3.04547	−	3.27492i	−0.116789	−	0.125587i
$681$		0			0
$682$	−10.9124	−	6.30026i	−0.417856	−	0.241250i
$683$	−12.7523	−	7.36254i	−0.487953	−	0.281720i	0.235772	−	0.971808i	$-0.424238\pi$
$683$	−12.7523	−	7.36254i	−0.487953	−	0.281720i	−0.723725	+	0.690089i	$0.757572\pi$
$684$		0			0
$685$	30.3746	−	28.2465i	1.16055	−	1.07924i
$686$	−17.7679	+	5.22508i	−0.678382	+	0.199495i
$687$		0			0
$688$	2.27492	−	1.31342i	0.0867304	−	0.0500738i
$689$	8.11863	−	14.0619i	0.309295	−	0.535715i
$690$		0			0
$691$	7.09967	+	12.2970i	0.270084	+	0.467799i	0.968883	−	0.247519i	$-0.0796151\pi$
$691$	7.09967	+	12.2970i	0.270084	+	0.467799i	−0.698799	+	0.715318i	$0.746282\pi$
$692$		−	20.2749i		−	0.770737i
$693$		0			0
$694$	2.90033			0.110095
$695$	−1.67451	+	5.45017i	−0.0635177	+	0.206737i
$696$		0			0
$697$	18.8248	+	10.8685i	0.713038	+	0.411673i
$698$	1.25588	−	0.725083i	0.0475358	−	0.0274448i
$699$		0			0
$700$	12.3248	−	4.80630i	0.465832	−	0.181661i
$701$	−21.2032			−0.800835			−0.400418	−	0.916333i	$-0.631135\pi$
$701$	−21.2032			−0.800835			−0.400418	+	0.916333i	$0.631135\pi$
$702$		0			0
$703$	17.6873	+	10.2118i	0.667089	+	0.385144i
$704$	−0.866025	+	1.50000i	−0.0326396	+	0.0565334i
$705$		0			0
$706$	9.09967			0.342471
$707$	−20.7846	+	30.1993i	−0.781686	+	1.13576i
$708$		0			0
$709$	−5.27492	−	9.13642i	−0.198104	−	0.343126i	0.749810	−	0.661653i	$-0.230145\pi$
$709$	−5.27492	−	9.13642i	−0.198104	−	0.343126i	−0.947914	+	0.318528i	$0.896812\pi$
$710$	−7.40437	−	32.2749i	−0.277881	−	1.21126i
$711$		0			0
$712$	0.725083	−	0.418627i	0.0271736	−	0.0156887i
$713$			31.0997i			1.16469i
$714$		0			0
$715$	−6.09967	+	5.67232i	−0.228115	+	0.212133i
$716$	5.85286	+	10.1375i	0.218732	+	0.378855i
$717$		0			0
$718$	11.2749	+	6.50958i	0.420776	+	0.242935i
$719$	18.2153	+	31.5498i	0.679316	+	1.17661i	0.975187	+	0.221382i	$0.0710569\pi$
$719$	18.2153	+	31.5498i	0.679316	+	1.17661i	−0.295871	+	0.955228i	$0.595610\pi$
$720$		0			0
$721$	−37.3746	+	17.7967i	−1.39190	+	0.662783i
$722$		−	0.725083i		−	0.0269848i
$723$		0			0
$724$	−10.2749	+	17.7967i	−0.381864	+	0.661408i
$725$	−16.0646	−	10.9003i	−0.596625	−	0.404828i
$726$		0			0
$727$		−	16.4257i		−	0.609196i	−0.952481	−	0.304598i	$-0.901478\pi$
$727$		−	16.4257i		−	0.609196i	0.952481	−	0.304598i	$-0.0985221\pi$
$728$	5.67232	+	0.450166i	0.210230	+	0.0166842i
$729$		0			0
$730$	8.00000	−	26.0383i	0.296093	−	0.963721i
$731$	−2.62685	+	4.54983i	−0.0971575	+	0.168282i
$732$		0			0
$733$	−20.7870	+	12.0014i	−0.767784	+	0.443280i	−0.832084	−	0.554650i	$-0.812852\pi$
$733$	−20.7870	+	12.0014i	−0.767784	+	0.443280i	0.0642996	+	0.997931i	$0.479519\pi$
$734$	−14.7512			−0.544477
$735$		0			0
$736$	4.27492			0.157576
$737$	−13.0767	+	7.54983i	−0.481686	+	0.278102i
$738$		0			0
$739$	6.96221	−	12.0589i	0.256109	−	0.443594i	−0.709087	−	0.705121i	$-0.750893\pi$
$739$	6.96221	−	12.0589i	0.256109	−	0.443594i	0.965196	+	0.261527i	$0.0842260\pi$
$740$	10.2118	+	3.13746i	0.375392	+	0.115335i
$741$		0			0
$742$	−19.9124	−	1.58028i	−0.731006	−	0.0580140i
$743$			12.8248i			0.470495i	0.971936	+	0.235247i	$0.0755900\pi$
$743$			12.8248i			0.470495i	−0.971936	+	0.235247i	$0.924410\pi$
$744$		0			0
$745$	−47.3746	+	10.8685i	−1.73567	+	0.398190i
$746$	0.837253	−	1.45017i	0.0306540	−	0.0530943i
$747$		0			0
$748$		−	3.46410i		−	0.126660i
$749$	18.6915	−	8.90033i	0.682972	−	0.325211i
$750$		0			0
$751$	6.63746	+	11.4964i	0.242204	+	0.419510i	0.961342	−	0.275358i	$-0.0887962\pi$
$751$	6.63746	+	11.4964i	0.242204	+	0.419510i	−0.719138	+	0.694868i	$0.755463\pi$
$752$	1.49397	+	0.862541i	0.0544793	+	0.0314536i
$753$		0			0
$754$	−4.17525	−	7.23174i	−0.152054	−	0.263365i
$755$	31.0251	+	33.3625i	1.12912	+	1.21419i
$756$		0			0
$757$		−	43.4739i		−	1.58009i	−0.613052	−	0.790043i	$-0.710058\pi$
$757$		−	43.4739i		−	1.58009i	0.613052	−	0.790043i	$-0.289942\pi$
$758$	−19.7668	+	11.4124i	−0.717963	+	0.414516i
$759$		0			0
$760$	2.13746	+	9.31697i	0.0775338	+	0.337962i
$761$	15.7690	+	27.3127i	0.571626	+	0.990085i	0.996399	+	0.0847852i	$0.0270204\pi$
$761$	15.7690	+	27.3127i	0.571626	+	0.990085i	−0.424773	+	0.905300i	$0.639646\pi$
$762$		0			0
$763$	28.6495	−	41.6268i	1.03718	−	1.50699i
$764$	−1.67451			−0.0605815
$765$		0			0
$766$	14.6873	−	25.4391i	0.530673	−	0.919153i
$767$	13.6838	+	7.90033i	0.494092	+	0.285264i
$768$		0			0
$769$	−13.0000			−0.468792			−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000			−0.468792			−0.234396	+	0.972141i	$0.575311\pi$
$770$	9.52628	+	3.77492i	0.343303	+	0.136039i
$771$		0			0
$772$	−10.1873	+	5.88164i	−0.366649	+	0.211685i
$773$	−11.1066	−	6.41238i	−0.399475	−	0.230637i	0.286782	−	0.957996i	$-0.407414\pi$
$773$	−11.1066	−	6.41238i	−0.399475	−	0.230637i	−0.686258	+	0.727359i	$0.740748\pi$
$774$		0			0
$775$	−32.7371	+	15.8553i	−1.17595	+	0.569540i
$776$	−2.20822			−0.0792705
$777$		0			0
$778$		−	5.97586i		−	0.214245i
$779$	−23.2309	−	40.2371i	−0.832334	−	1.44164i
$780$		0			0
$781$	12.8248	−	22.2131i	0.458906	−	0.794848i
$782$	−7.40437	+	4.27492i	−0.264780	+	0.152871i
$783$		0			0
$784$	−2.50000	−	6.53835i	−0.0892857	−	0.233512i
$785$	4.89261	−	4.54983i	0.174625	−	0.162391i
$786$		0			0
$787$	0.824752	+	0.476171i	0.0293992	+	0.0169736i	0.514628	−	0.857414i	$-0.327930\pi$
$787$	0.824752	+	0.476171i	0.0293992	+	0.0169736i	−0.485228	+	0.874387i	$0.661264\pi$
$788$	−11.5827	−	6.68729i	−0.412618	−	0.238225i
$789$		0			0
$790$	−5.36254	+	4.98684i	−0.190791	+	0.177424i
$791$	−0.115088	+	1.45017i	−0.00409205	+	0.0515620i
$792$		0			0
$793$	−8.47425	+	4.89261i	−0.300930	+	0.173742i
$794$	−9.55505	+	16.5498i	−0.339096	+	0.587332i
$795$		0			0
$796$	−2.27492	−	3.94027i	−0.0806323	−	0.139659i
$797$		−	43.2749i		−	1.53288i	−0.642318	−	0.766438i	$-0.722027\pi$
$797$		−	43.2749i		−	1.53288i	0.642318	−	0.766438i	$-0.277973\pi$
$798$		0			0
$799$	−3.45017			−0.122058
$800$	2.17945	+	4.50000i	0.0770552	+	0.159099i
$801$		0			0
$802$	−3.41238	−	1.97014i	−0.120495	−	0.0695679i
$803$	18.2728	−	10.5498i	0.644835	−	0.372296i
$804$		0			0
$805$	−3.68729	−	25.0205i	−0.129960	−	0.881857i
$806$	−15.6460			−0.551107
$807$		0			0
$808$	−12.0000	−	6.92820i	−0.422159	−	0.243733i
$809$	−18.4534	+	31.9622i	−0.648787	+	1.12373i	0.334626	+	0.942351i	$0.391390\pi$
$809$	−18.4534	+	31.9622i	−0.648787	+	1.12373i	−0.983413	+	0.181381i	$0.941943\pi$
$810$		0			0
$811$	29.3746			1.03148			0.515741	−	0.856745i	$-0.327517\pi$
$811$	29.3746			1.03148			0.515741	+	0.856745i	$0.327517\pi$
$812$	−5.82409	+	8.46221i	−0.204386	+	0.296965i
$813$		0			0
$814$	4.13746	+	7.16629i	0.145018	+	0.251178i
$815$	−2.20822	−	9.62541i	−0.0773506	−	0.337164i
$816$		0			0
$817$	9.72508	−	5.61478i	0.340238	−	0.196436i
$818$		−	3.27492i		−	0.114505i
$819$		0			0
$820$	−16.5498	−	17.7967i	−0.577945	−	0.621487i
$821$	−22.3649	−	38.7371i	−0.780540	−	1.35194i	−0.931627	−	0.363415i	$-0.881611\pi$
$821$	−22.3649	−	38.7371i	−0.780540	−	1.35194i	0.151087	−	0.988520i	$-0.451723\pi$
$822$		0			0
$823$	−1.35050	−	0.779710i	−0.0470754	−	0.0271790i	0.476278	−	0.879295i	$-0.341986\pi$
$823$	−1.35050	−	0.779710i	−0.0470754	−	0.0271790i	−0.523353	+	0.852116i	$0.675319\pi$
$824$	−7.82300	−	13.5498i	−0.272527	−	0.472031i
$825$		0			0
$826$	1.53779	−	19.3770i	0.0535065	−	0.674211i
$827$			32.7251i			1.13796i	0.822350	+	0.568981i	$0.192662\pi$
$827$			32.7251i			1.13796i	−0.822350	+	0.568981i	$0.807338\pi$
$828$		0			0
$829$	21.5498	−	37.3254i	0.748457	−	1.29637i	−0.200106	−	0.979774i	$-0.564129\pi$
$829$	21.5498	−	37.3254i	0.748457	−	1.29637i	0.948562	−	0.316591i	$-0.102538\pi$
$830$	1.58028	−	0.362541i	0.0548524	−	0.0125840i
$831$		0			0
$832$			2.15068i			0.0745613i
$833$	10.8685	+	8.82475i	0.376570	+	0.305760i
$834$		0			0
$835$	−43.3368	−	13.3148i	−1.49973	−	0.460777i
$836$	−3.70219	+	6.41238i	−0.128043	+	0.221777i
$837$		0			0
$838$	1.86254	−	1.07534i	0.0643404	−	0.0371470i
$839$	20.8997			0.721538			0.360769	−	0.932655i	$-0.382514\pi$
$839$	20.8997			0.721538			0.360769	+	0.932655i	$0.382514\pi$
$840$		0			0
$841$	−13.9244			−0.480152
$842$	21.7370	−	12.5498i	0.749105	−	0.432496i
$843$		0			0
$844$	9.41238	−	16.3027i	0.323987	−	0.561163i
$845$	5.49969	−	17.9003i	0.189195	−	0.615790i
$846$		0			0
$847$	−9.09967	−	19.1101i	−0.312668	−	0.656631i
$848$		−	7.54983i		−	0.259262i
$849$		0			0
$850$	−8.27492	−	5.61478i	−0.283827	−	0.192585i
$851$	10.2118	−	17.6873i	0.350055	−	0.606313i
$852$		0			0
$853$			46.5769i			1.59476i	0.603475	+	0.797382i	$0.293782\pi$
$853$			46.5769i			1.59476i	−0.603475	+	0.797382i	$0.706218\pi$
$854$	9.91613	+	6.82475i	0.339323	+	0.233538i
$855$		0			0
$856$	3.91238	+	6.77643i	0.133722	+	0.231614i
$857$	−25.2011	−	14.5498i	−0.860852	−	0.497013i	0.00344581	−	0.999994i	$-0.498903\pi$
$857$	−25.2011	−	14.5498i	−0.860852	−	0.497013i	−0.864297	+	0.502981i	$0.832236\pi$
$858$		0			0
$859$	27.0997	+	46.9380i	0.924629	+	1.60150i	0.792157	+	0.610317i	$0.208958\pi$
$859$	27.0997	+	46.9380i	0.924629	+	1.60150i	0.132472	+	0.991187i	$0.457709\pi$
$860$	4.30136	−	4.00000i	0.146675	−	0.136399i
$861$		0			0
$862$		−	2.62685i		−	0.0894708i
$863$	18.0348	−	10.4124i	0.613911	−	0.354441i	−0.160584	−	0.987022i	$-0.551338\pi$
$863$	18.0348	−	10.4124i	0.613911	−	0.354441i	0.774494	+	0.632581i	$0.218004\pi$
$864$		0			0
$865$	−10.1375	−	44.1882i	−0.344684	−	1.50244i
$866$	6.09095	+	10.5498i	0.206979	+	0.358498i
$867$		0			0
$868$	8.27492	+	17.3781i	0.280869	+	0.589850i
$869$	−5.67232			−0.192420
$870$		0			0
$871$	−9.37459	+	16.2373i	−0.317646	+	0.550179i
$872$	16.5408	+	9.54983i	0.560142	+	0.323398i
$873$		0			0
$874$	18.2749			0.618158
$875$	24.4580	−	16.6375i	0.826832	−	0.562449i
$876$		0			0
$877$	−24.3127	+	14.0369i	−0.820982	+	0.473994i	−0.850755	−	0.525563i	$-0.823855\pi$
$877$	−24.3127	+	14.0369i	−0.820982	+	0.473994i	0.0297731	+	0.999557i	$0.490522\pi$
$878$	20.6328	+	11.9124i	0.696325	+	0.402023i
$879$		0			0
$880$	−1.13746	+	3.70219i	−0.0383437	+	0.124801i
$881$	−28.1890			−0.949711			−0.474855	−	0.880064i	$-0.657500\pi$
$881$	−28.1890			−0.949711			−0.474855	+	0.880064i	$0.657500\pi$
$882$		0			0
$883$		−	52.0766i		−	1.75252i	−0.481841	−	0.876259i	$-0.660032\pi$
$883$		−	52.0766i		−	1.75252i	0.481841	−	0.876259i	$-0.339968\pi$
$884$	−2.15068	−	3.72508i	−0.0723351	−	0.125288i
$885$		0			0
$886$	−0.362541	+	0.627940i	−0.0121798	+	0.0210961i
$887$	−3.76764	+	2.17525i	−0.126505	+	0.0730377i	−0.561917	−	0.827194i	$-0.689936\pi$
$887$	−3.76764	+	2.17525i	−0.126505	+	0.0730377i	0.435412	+	0.900231i	$0.356603\pi$
$888$		0			0
$889$	4.53779	−	57.1785i	0.152193	−	1.91771i
$890$	1.37097	−	1.27492i	0.0459549	−	0.0427353i
$891$		0			0
$892$	−16.1873	−	9.34574i	−0.541991	−	0.312918i
$893$	6.38658	+	3.68729i	0.213719	+	0.123391i
$894$		0			0
$895$	17.8248	+	19.1676i	0.595816	+	0.640704i
$896$	2.38876	−	1.13746i	0.0798030	−	0.0379998i
$897$		0			0
$898$	27.5120	−	15.8841i	0.918089	−	0.530059i
$899$	14.1233	−	24.4622i	0.471037	−	0.815860i
$900$		0			0
$901$	7.54983	+	13.0767i	0.251521	+	0.435648i
$902$		−	18.8248i		−	0.626796i
$903$		0			0
$904$	−0.549834			−0.0182872
$905$	−13.4953	+	43.9244i	−0.448600	+	1.46010i
$906$		0			0
$907$	0.924421	+	0.533714i	0.0306949	+	0.0177217i	0.515269	−	0.857029i	$-0.327692\pi$
$907$	0.924421	+	0.533714i	0.0306949	+	0.0177217i	−0.484574	+	0.874750i	$0.661025\pi$
$908$	8.50848	−	4.91238i	0.282364	−	0.163023i
$909$		0			0
$910$	12.5876	−	1.85505i	0.417276	−	0.0614943i
$911$	−53.0290			−1.75693			−0.878464	−	0.477809i	$-0.841431\pi$
$911$	−53.0290			−1.75693			−0.878464	+	0.477809i	$0.841431\pi$
$912$		0			0
$913$	1.08762	+	0.627940i	0.0359951	+	0.0207818i
$914$	5.46301	−	9.46221i	0.180700	−	0.312982i
$915$		0			0
$916$	−5.09967			−0.168498
$917$	−17.8621	−	37.5120i	−0.589860	−	1.23876i
$918$		0			0
$919$	2.54983	+	4.41644i	0.0841113	+	0.145685i	0.905012	−	0.425386i	$-0.139862\pi$
$919$	2.54983	+	4.41644i	0.0841113	+	0.145685i	−0.820901	+	0.571071i	$0.806528\pi$
$920$	9.31697	−	2.13746i	0.307171	−	0.0704699i
$921$		0			0
$922$	−30.1993	+	17.4356i	−0.994562	+	0.574211i
$923$		−	31.8488i		−	1.04832i
$924$		0			0
$925$	23.8248	+	1.73205i	0.783353	+	0.0569495i
$926$	−12.4200	−	21.5120i	−0.408146	−	0.706930i
$927$		0			0
$928$	−3.36254	−	1.94136i	−0.110381	−	0.0637284i
$929$	12.8386	+	22.2371i	0.421221	+	0.729576i	0.996059	−	0.0886907i	$-0.0282683\pi$
$929$	12.8386	+	22.2371i	0.421221	+	0.729576i	−0.574838	+	0.818267i	$0.694935\pi$
$930$		0			0
$931$	−10.6873	−	27.9509i	−0.350262	−	0.916054i
$932$			14.5498i			0.476596i
$933$		0			0
$934$	−7.72508	+	13.3802i	−0.252772	+	0.437815i
$935$	−1.73205	−	7.54983i	−0.0566441	−	0.246906i
$936$		0			0
$937$		−	9.02134i		−	0.294714i	−0.989083	−	0.147357i	$-0.952923\pi$
$937$		−	9.02134i		−	0.294714i	0.989083	−	0.147357i	$-0.0470767\pi$
$938$	22.9928	+	1.82475i	0.750743	+	0.0595803i
$939$		0			0
$940$	3.68729	+	1.13288i	0.120266	+	0.0369506i
$941$	−0.266857	+	0.462210i	−0.00869930	+	0.0150676i	−0.870342	−	0.492447i	$-0.836102\pi$
$941$	−0.266857	+	0.462210i	−0.00869930	+	0.0150676i	0.861643	+	0.507515i	$0.169436\pi$
$942$		0			0
$943$	−40.2371	+	23.2309i	−1.31030	+	0.756503i
$944$	7.34683			0.239119
$945$		0			0
$946$	4.54983			0.147928
$947$	31.1769	−	18.0000i	1.01311	−	0.584921i	0.101012	−	0.994885i	$-0.467792\pi$
$947$	31.1769	−	18.0000i	1.01311	−	0.584921i	0.912102	+	0.409964i	$0.134459\pi$
$948$		0			0
$949$	13.0997	−	22.6893i	0.425233	−	0.736526i
$950$	9.31697	+	19.2371i	0.302282	+	0.624135i
$951$		0			0
$952$	−3.00000	+	4.35890i	−0.0972306	+	0.141273i
$953$		−	45.0997i		−	1.46092i	−0.682955	−	0.730461i	$-0.739305\pi$
$953$		−	45.0997i		−	1.46092i	0.682955	−	0.730461i	$-0.260695\pi$
$954$		0			0
$955$	−3.64950	+	0.837253i	−0.118095	+	0.0270929i
$956$	−7.34683	+	12.7251i	−0.237613	+	0.411559i
$957$		0			0
$958$			15.7611i			0.509218i
$959$	−40.4284	−	27.8248i	−1.30550	−	0.898508i
$960$		0			0
$961$	−10.9622	−	18.9871i	−0.353620	−	0.612487i
$962$	8.89834	+	5.13746i	0.286894	+	0.165638i
$963$		0			0
$964$	−7.50000	−	12.9904i	−0.241559	−	0.418392i
$965$	−19.2619	+	17.9124i	−0.620062	+	0.576620i
$966$		0			0
$967$			6.50958i			0.209334i	0.994507	+	0.104667i	$0.0333777\pi$
$967$			6.50958i			0.209334i	−0.994507	+	0.104667i	$0.966622\pi$
$968$	6.92820	−	4.00000i	0.222681	−	0.128565i
$969$		0			0
$970$	−4.81271	+	1.10411i	−0.154527	+	0.0354509i
$971$	−4.33013	−	7.50000i	−0.138960	−	0.240686i	0.788143	−	0.615492i	$-0.211043\pi$
$971$	−4.33013	−	7.50000i	−0.138960	−	0.240686i	−0.927103	+	0.374806i	$0.877709\pi$
$972$		0			0
$973$	6.72508	+	0.533714i	0.215596	+	0.0171101i
$974$	20.3660			0.652568
$975$		0			0
$976$	−2.27492	+	3.94027i	−0.0728183	+	0.126125i
$977$	32.6054	+	18.8248i	1.04314	+	0.602257i	0.920721	−	0.390221i	$-0.127602\pi$
$977$	32.6054	+	18.8248i	1.04314	+	0.602257i	0.122419	+	0.992479i	$0.460935\pi$
$978$		0			0
$979$	1.45017			0.0463475
$980$	−8.71780	−	13.0000i	−0.278480	−	0.415270i
$981$		0			0
$982$	−8.73713	+	5.04438i	−0.278813	+	0.160973i
$983$	30.1591	+	17.4124i	0.961927	+	0.555369i	0.896765	−	0.442506i	$-0.145911\pi$
$983$	30.1591	+	17.4124i	0.961927	+	0.555369i	0.0651611	+	0.997875i	$0.479244\pi$
$984$		0			0
$985$	−28.5876	−	8.78325i	−0.910877	−	0.279858i
$986$	7.76546			0.247303
$987$		0			0
$988$			9.19397i			0.292499i
$989$	−5.61478	−	9.72508i	−0.178540	−	0.309240i
$990$		0			0
$991$	21.7371	−	37.6498i	0.690503	−	1.19599i	−0.281171	−	0.959658i	$-0.590723\pi$
$991$	21.7371	−	37.6498i	0.690503	−	1.19599i	0.971673	−	0.236328i	$-0.0759439\pi$
$992$	−6.30026	+	3.63746i	−0.200034	+	0.115489i
$993$		0			0
$994$	−35.3746	+	16.8443i	−1.12201	+	0.534270i
$995$	−6.92820	−	7.45017i	−0.219639	−	0.236186i
$996$		0			0
$997$	−48.9244	−	28.2465i	−1.54945	−	0.894576i	−0.998183	−	0.0602486i	$-0.980811\pi$
$997$	−48.9244	−	28.2465i	−1.54945	−	0.894576i	−0.551269	−	0.834328i	$-0.685856\pi$
$998$	−8.18408	−	4.72508i	−0.259063	−	0.149570i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.u.d.109.4	yes	8
3.2	odd	2	inner	630.2.u.d.109.1	✓	8
5.4	even	2		630.2.u.e.109.1	yes	8
7.2	even	3		630.2.u.e.289.1	yes	8
15.14	odd	2		630.2.u.e.109.4	yes	8
21.2	odd	6		630.2.u.e.289.4	yes	8
35.9	even	6	inner	630.2.u.d.289.4	yes	8
105.44	odd	6	inner	630.2.u.d.289.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.u.d.109.1	✓	8	3.2	odd	2	inner
630.2.u.d.109.4	yes	8	1.1	even	1	trivial
630.2.u.d.289.1	yes	8	105.44	odd	6	inner
630.2.u.d.289.4	yes	8	35.9	even	6	inner
630.2.u.e.109.1	yes	8	5.4	even	2
630.2.u.e.109.4	yes	8	15.14	odd	2
630.2.u.e.289.1	yes	8	7.2	even	3
630.2.u.e.289.4	yes	8	21.2	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-2.63746 - 0.209313i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-2.63746 - 0.209313i) q^{7} -1.00000i q^{8} +(-0.500000 - 2.17945i) q^{10} +(0.866025 - 1.50000i) q^{11} -2.15068i q^{13} +(-2.38876 + 1.13746i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.13746 - 3.70219i) q^{19} +(-1.52274 - 1.63746i) q^{20} -1.73205i q^{22} +(-3.70219 + 2.13746i) q^{23} +(-4.13746 - 2.80739i) q^{25} +(-1.07534 - 1.86254i) q^{26} +(-1.50000 + 2.17945i) q^{28} +3.88273 q^{29} +(3.63746 - 6.30026i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.00000 q^{34} +(-2.17945 + 5.50000i) q^{35} +(-4.13746 + 2.38876i) q^{37} +(-3.70219 - 2.13746i) q^{38} +(-2.13746 - 0.656712i) q^{40} +10.8685 q^{41} +2.62685i q^{43} +(-0.866025 - 1.50000i) q^{44} +(-2.13746 + 3.70219i) q^{46} +(-1.49397 + 0.862541i) q^{47} +(6.91238 + 1.10411i) q^{49} +(-4.98684 - 0.362541i) q^{50} +(-1.86254 - 1.07534i) q^{52} +(6.53835 + 3.77492i) q^{53} +(-2.63746 - 2.83616i) q^{55} +(-0.209313 + 2.63746i) q^{56} +(3.36254 - 1.94136i) q^{58} +(-3.67341 + 6.36254i) q^{59} +(-2.27492 - 3.94027i) q^{61} -7.27492i q^{62} -1.00000 q^{64} +(-4.59698 - 1.41238i) q^{65} +(-7.54983 - 4.35890i) q^{67} +(1.73205 - 1.00000i) q^{68} +(0.862541 + 5.85286i) q^{70} +14.8087 q^{71} +(10.5498 + 6.09095i) q^{73} +(-2.38876 + 4.13746i) q^{74} -4.27492 q^{76} +(-2.59808 + 3.77492i) q^{77} +(-1.63746 - 2.83616i) q^{79} +(-2.17945 + 0.500000i) q^{80} +(9.41238 - 5.43424i) q^{82} +0.725083i q^{83} +(3.27492 - 3.04547i) q^{85} +(1.31342 + 2.27492i) q^{86} +(-1.50000 - 0.866025i) q^{88} +(0.418627 + 0.725083i) q^{89} +(-0.450166 + 5.67232i) q^{91} +4.27492i q^{92} +(-0.862541 + 1.49397i) q^{94} +(-9.31697 + 2.13746i) q^{95} -2.20822i q^{97} +(6.53835 - 2.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 6 * q^7	\( 8 q + 4 q^{4} - 6 q^{7} - 4 q^{10} - 4 q^{16} - 2 q^{19} - 18 q^{25} - 12 q^{28} + 14 q^{31} + 16 q^{34} - 18 q^{37} - 2 q^{40} - 2 q^{46} + 10 q^{49} - 30 q^{52} - 6 q^{55} + 42 q^{58} + 12 q^{61} - 8 q^{64} + 22 q^{70} + 24 q^{73} - 4 q^{76} + 2 q^{79} + 30 q^{82} - 4 q^{85} - 12 q^{88} - 64 q^{91} - 22 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 - 6 * q^7 - 4 * q^10 - 4 * q^16 - 2 * q^19 - 18 * q^25 - 12 * q^28 + 14 * q^31 + 16 * q^34 - 18 * q^37 - 2 * q^40 - 2 * q^46 + 10 * q^49 - 30 * q^52 - 6 * q^55 + 42 * q^58 + 12 * q^61 - 8 * q^64 + 22 * q^70 + 24 * q^73 - 4 * q^76 + 2 * q^79 + 30 * q^82 - 4 * q^85 - 12 * q^88 - 64 * q^91 - 22 * q^94

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