LMFDB - Embedded newform 728.2.ds.b.461.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(293,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.293"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 6, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.ds (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 8x^{12} + 40x^{10} - 161x^{8} + 360x^{6} + 648x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 8x^12 + 40x^10 - 161x^8 + 360x^6 + 648x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 13 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			461.4
Root			$-0.197958 + 1.72070i$ of defining polynomial
Character	$\chi$	$=$	728.461
Dual form			728.2.ds.b.349.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(1.72070 - 2.98034i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.25964 - 1.25964i) q^{5} +(-4.70104 - 1.25964i) q^{6} +(0.684771 - 2.55560i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.42162 - 7.65848i) q^{9} +(-2.18176 - 1.25964i) q^{10} +6.88280i q^{12} +(0.833829 + 3.50781i) q^{13} -3.74166 q^{14} +(-1.58669 - 5.92162i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-8.84325 + 8.84325i) q^{18} +(2.32794 + 0.623770i) q^{19} +(-0.922121 + 3.44140i) q^{20} +(-6.43827 - 6.43827i) q^{21} +(8.21056 + 4.74037i) q^{23} +(9.40209 - 2.51928i) q^{24} +1.82661i q^{25} +(4.48655 - 2.42298i) q^{26} -20.1090 q^{27} +(1.36954 + 5.11120i) q^{28} +(-7.50832 + 4.33493i) q^{30} +(-5.46410 - 1.46410i) q^{32} +(-2.35657 - 4.08170i) q^{35} +(15.3170 + 8.84325i) q^{36} -3.40834i q^{38} +(11.8892 + 3.55080i) q^{39} +5.03856 q^{40} +(-6.43827 + 11.1514i) q^{42} +(-15.2166 - 4.07727i) q^{45} +(3.47019 - 12.9509i) q^{46} +(-6.88280 - 11.9214i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(2.49520 - 0.668586i) q^{50} +(-4.95204 - 5.24188i) q^{52} +(7.36040 + 27.4694i) q^{54} +(6.48074 - 3.74166i) q^{56} +(5.86474 - 5.86474i) q^{57} +(-3.79545 + 14.1648i) q^{59} +(8.66986 + 8.66986i) q^{60} +(-1.28827 - 2.23135i) q^{61} +(-22.5998 + 6.05560i) q^{63} +8.00000i q^{64} +(5.46890 + 3.36825i) q^{65} +(28.2558 - 16.3135i) q^{69} +(-4.71314 + 4.71314i) q^{70} +(10.5472 + 2.82612i) q^{71} +(6.47371 - 24.1602i) q^{72} +(5.44392 + 3.14305i) q^{75} +(-4.65588 + 1.24754i) q^{76} +(0.498713 - 17.5407i) q^{78} +15.7417 q^{79} +(-1.84424 - 6.88280i) q^{80} +(-21.3367 + 36.9562i) q^{81} +(-11.4889 + 11.4889i) q^{83} +(17.5897 + 4.71314i) q^{84} +22.2786i q^{90} +(9.53554 + 0.271112i) q^{91} -18.9615 q^{92} +(3.71810 - 2.14664i) q^{95} +(-13.7656 + 13.7656i) q^{96} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 q^{57} - 32 q^{60} - 112 q^{63} + 16 q^{65} - 16 q^{71}+ \cdots + 56 q^{98}+O(q^{100}) $ 16 * q + 8 * q^2 + 32 * q^8 - 16 * q^9 - 56 * q^15 + 32 * q^16 - 32 * q^18 - 96 * q^30 - 32 * q^32 + 48 * q^36 + 72 * q^39 - 24 * q^46 + 56 * q^50 + 88 * q^57 - 32 * q^60 - 112 * q^63 + 16 * q^65 - 16 * q^71 + 16 * q^72 + 16 * q^78 + 192 * q^79 - 48 * q^81 - 96 * q^92 + 120 * q^95 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$	1.72070	−	2.98034i	0.993447	−	1.72070i	0.397744	−	0.917496i	$-0.369793\pi$
$3$	1.72070	−	2.98034i	0.993447	−	1.72070i	0.595703	−	0.803205i	$-0.296874\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	1.25964	−	1.25964i	0.563328	−	0.563328i	−0.366923	−	0.930251i	$-0.619589\pi$
$5$	1.25964	−	1.25964i	0.563328	−	0.563328i	0.930251	+	0.366923i	$0.119589\pi$
$6$	−4.70104	−	1.25964i	−1.91919	−	0.514246i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$7$	0.684771	−	2.55560i	0.258819	−	0.965926i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−4.42162	−	7.65848i	−1.47387	−	2.55283i
$10$	−2.18176	−	1.25964i	−0.689934	−	0.398333i
$11$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$11$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$12$			6.88280i			1.98689i
$13$	0.833829	+	3.50781i	0.231263	+	0.972891i
$13$	0.833829	+	3.50781i	0.231263	+	0.972891i
$14$	−3.74166			−1.00000
$15$	−1.58669	−	5.92162i	−0.409683	−	1.52896i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−8.84325	+	8.84325i	−2.08437	+	2.08437i
$19$	2.32794	+	0.623770i	0.534066	+	0.143103i	0.515765	−	0.856730i	$-0.327508\pi$
$19$	2.32794	+	0.623770i	0.534066	+	0.143103i	0.0183009	+	0.999833i	$0.494174\pi$
$20$	−0.922121	+	3.44140i	−0.206193	+	0.769521i
$21$	−6.43827	−	6.43827i	−1.40495	−	1.40495i
$22$		0			0
$23$	8.21056	+	4.74037i	1.71202	+	0.988436i	0.931831	+	0.362892i	$0.118211\pi$
$23$	8.21056	+	4.74037i	1.71202	+	0.988436i	0.780189	+	0.625543i	$0.215123\pi$
$24$	9.40209	−	2.51928i	1.91919	−	0.514246i
$25$			1.82661i			0.365322i
$26$	4.48655	−	2.42298i	0.879886	−	0.475185i
$27$	−20.1090			−3.86997
$28$	1.36954	+	5.11120i	0.258819	+	0.965926i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−7.50832	+	4.33493i	−1.37083	+	0.791446i
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$		0			0
$34$		0			0
$35$	−2.35657	−	4.08170i	−0.398333	−	0.689934i
$36$	15.3170	+	8.84325i	2.55283	+	1.47387i
$37$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$37$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$38$		−	3.40834i		−	0.552906i
$39$	11.8892	+	3.55080i	1.90380	+	0.568582i
$40$	5.03856			0.796667
$41$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$41$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$42$	−6.43827	+	11.1514i	−0.993447	+	1.72070i
$43$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$43$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$44$		0			0
$45$	−15.2166	−	4.07727i	−2.26836	−	0.607804i
$46$	3.47019	−	12.9509i	0.511652	−	1.90951i
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$	−6.88280	−	11.9214i	−0.993447	−	1.72070i
$49$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$50$	2.49520	−	0.668586i	0.352874	−	0.0945523i
$51$		0			0
$52$	−4.95204	−	5.24188i	−0.686725	−	0.726917i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	7.36040	+	27.4694i	1.00162	+	3.73811i
$55$		0			0
$56$	6.48074	−	3.74166i	0.866025	−	0.500000i
$57$	5.86474	−	5.86474i	0.776804	−	0.776804i
$58$		0			0
$59$	−3.79545	+	14.1648i	−0.494126	+	1.84410i	0.0407464	+	0.999170i	$0.487026\pi$
$59$	−3.79545	+	14.1648i	−0.494126	+	1.84410i	−0.534872	+	0.844933i	$0.679640\pi$
$60$	8.66986	+	8.66986i	1.11927	+	1.11927i
$61$	−1.28827	−	2.23135i	−0.164946	−	0.285695i	0.771690	−	0.635999i	$-0.219412\pi$
$61$	−1.28827	−	2.23135i	−0.164946	−	0.285695i	−0.936636	+	0.350304i	$0.886078\pi$
$62$		0			0
$63$	−22.5998	+	6.05560i	−2.84731	+	0.762934i
$64$			8.00000i			1.00000i
$65$	5.46890	+	3.36825i	0.678334	+	0.417781i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$		0			0
$69$	28.2558	−	16.3135i	3.40160	−	1.96392i
$70$	−4.71314	+	4.71314i	−0.563328	+	0.563328i
$71$	10.5472	+	2.82612i	1.25173	+	0.335399i	0.823003	−	0.568037i	$-0.192297\pi$
$71$	10.5472	+	2.82612i	1.25173	+	0.335399i	0.428723	+	0.903436i	$0.358964\pi$
$72$	6.47371	−	24.1602i	0.762934	−	2.84731i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	5.44392	+	3.14305i	0.628610	+	0.362928i
$76$	−4.65588	+	1.24754i	−0.534066	+	0.143103i
$77$		0			0
$78$	0.498713	−	17.5407i	0.0564681	−	1.98609i
$79$	15.7417			1.77107			0.885537	−	0.464568i	$-0.153790\pi$
$79$	15.7417			1.77107			0.885537	+	0.464568i	$0.153790\pi$
$80$	−1.84424	−	6.88280i	−0.206193	−	0.769521i
$81$	−21.3367	+	36.9562i	−2.37074	+	4.10624i
$82$		0			0
$83$	−11.4889	+	11.4889i	−1.26107	+	1.26107i	−0.310502	+	0.950573i	$0.600497\pi$
$83$	−11.4889	+	11.4889i	−1.26107	+	1.26107i	−0.950573	+	0.310502i	$0.899503\pi$
$84$	17.5897	+	4.71314i	1.91919	+	0.514246i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$89$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$90$			22.2786i			2.34837i
$91$	9.53554	+	0.271112i	0.999596	+	0.0284203i
$92$	−18.9615			−1.97687
$93$		0			0
$94$		0			0
$95$	3.71810	−	2.14664i	0.381469	−	0.220241i
$96$	−13.7656	+	13.7656i	−1.40495	+	1.40495i
$97$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$97$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$98$	−2.56218	+	9.56218i	−0.258819	+	0.965926i
$99$		0			0
$100$	−1.82661	−	3.16378i	−0.182661	−	0.316378i
$101$	−11.4256	−	6.59655i	−1.13689	−	0.656382i	−0.191229	−	0.981546i	$-0.561247\pi$
$101$	−11.4256	−	6.59655i	−1.13689	−	0.656382i	−0.945658	+	0.325164i	$0.894581\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−5.34796	+	8.68328i	−0.524411	+	0.851465i
$105$	−16.2198			−1.58289
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	34.8298	−	20.1090i	3.35150	−	1.93499i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$		0			0
$111$		0			0
$112$	−7.48331	−	7.48331i	−0.707107	−	0.707107i
$113$	−10.6125	−	18.3814i	−0.998339	−	1.72917i	−0.549068	−	0.835778i	$-0.685017\pi$
$113$	−10.6125	−	18.3814i	−0.998339	−	1.72917i	−0.449271	−	0.893396i	$-0.648316\pi$
$114$	−10.1580	−	5.86474i	−0.951386	−	0.549283i
$115$	16.3135	−	4.37119i	1.52124	−	0.407616i
$116$		0			0
$117$	23.1776	−	21.8961i	2.14277	−	2.02429i
$118$	20.7387			1.90916
$119$		0			0
$120$	8.66986	−	15.0166i	0.791446	−	1.37083i
$121$	9.52628	−	5.50000i	0.866025	−	0.500000i
$122$	−2.57654	+	2.57654i	−0.233269	+	0.233269i
$123$		0			0
$124$		0			0
$125$	8.59908	+	8.59908i	0.769125	+	0.769125i
$126$	16.5442	+	28.6554i	1.47387	+	2.55283i
$127$	−11.2211	−	6.47851i	−0.995713	−	0.574875i	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−11.2211	−	6.47851i	−0.995713	−	0.574875i	−0.906977	+	0.421180i	$0.861616\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$		0			0
$130$	2.59936	−	8.70353i	0.227979	−	0.763350i
$131$	−15.4531			−1.35014			−0.675071	−	0.737752i	$-0.735887\pi$
$131$	−15.4531			−1.35014			−0.675071	+	0.737752i	$0.735887\pi$
$132$		0			0
$133$	3.18821	−	5.52215i	0.276453	−	0.478831i
$134$		0			0
$135$	−25.3301	+	25.3301i	−2.18007	+	2.18007i
$136$		0			0
$137$	2.53589	−	9.46406i	0.216655	−	0.808569i	−0.768922	−	0.639343i	$-0.779207\pi$
$137$	2.53589	−	9.46406i	0.216655	−	0.808569i	0.985577	−	0.169226i	$-0.0541268\pi$
$138$	−32.6270	−	32.6270i	−2.77740	−	2.77740i
$139$	−10.0049	−	17.3290i	−0.848604	−	1.46983i	−0.882454	−	0.470399i	$-0.844110\pi$
$139$	−10.0049	−	17.3290i	−0.848604	−	1.46983i	0.0338497	−	0.999427i	$-0.489223\pi$
$140$	8.16340	+	4.71314i	0.689934	+	0.398333i
$141$		0			0
$142$		−	15.4422i		−	1.29588i
$143$		0			0
$144$	−35.3730			−2.94775
$145$		0			0
$146$		0			0
$147$	−20.8624	+	12.0449i	−1.72070	+	0.993447i
$148$		0			0
$149$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$149$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$150$	2.30087	−	8.58698i	0.187866	−	0.701124i
$151$	−2.72150	−	2.72150i	−0.221473	−	0.221473i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−2.72150	−	2.72150i	−0.221473	−	0.221473i	−0.809118	+	0.587646i	$0.800055\pi$
$152$	3.40834	+	5.90342i	0.276453	+	0.478831i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−24.1436	+	5.73908i	−1.93303	+	0.459494i
$157$	9.78477			0.780909			0.390455	−	0.920622i	$-0.372318\pi$
$157$	9.78477			0.780909			0.390455	+	0.920622i	$0.372318\pi$
$158$	−5.76185	−	21.5035i	−0.458388	−	1.71073i
$159$		0			0
$160$	−8.72705	+	5.03856i	−0.689934	+	0.398333i
$161$	17.7368	−	17.7368i	1.39786	−	1.39786i
$162$	58.2928	+	15.6195i	4.57992	+	1.22719i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$		0			0
$165$		0			0
$166$	19.8994	+	11.4889i	1.54449	+	0.891715i
$167$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$167$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$168$		−	25.7531i		−	1.98689i
$169$	−11.6095	+	5.84983i	−0.893035	+	0.449987i
$170$		0			0
$171$	−5.51615	−	20.5866i	−0.421831	−	1.57429i
$172$		0			0
$173$	−20.0715	+	11.5883i	−1.52601	+	0.881040i	−0.526483	+	0.850186i	$0.676490\pi$
$173$	−20.0715	+	11.5883i	−1.52601	+	0.881040i	−0.999524	+	0.0308546i	$0.990177\pi$
$174$		0			0
$175$	4.66809	+	1.25081i	0.352874	+	0.0945523i
$176$		0			0
$177$	35.6852	+	35.6852i	2.68226	+	2.68226i
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	30.4332	−	8.15455i	2.26836	−	0.607804i
$181$		−	6.59930i		−	0.490522i	−0.969457	−	0.245261i	$-0.921126\pi$
$181$		−	6.59930i		−	0.490522i	0.969457	−	0.245261i	$-0.0788737\pi$
$182$	−3.11990	−	13.1250i	−0.231263	−	0.972891i
$183$	−8.86692			−0.655462
$184$	6.94038	+	25.9019i	0.511652	+	1.90951i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−13.7700	+	51.3905i	−1.00162	+	3.73811i
$190$	−4.29329	−	4.29329i	−0.311468	−	0.311468i
$191$	2.38751	+	4.13530i	0.172754	+	0.299219i	0.939382	−	0.342873i	$-0.111400\pi$
$191$	2.38751	+	4.13530i	0.172754	+	0.299219i	−0.766627	+	0.642092i	$0.778067\pi$
$192$	23.8427	+	13.7656i	1.72070	+	0.993447i
$193$	19.8761	−	5.32578i	1.43071	−	0.383358i	0.541440	−	0.840739i	$-0.317879\pi$
$193$	19.8761	−	5.32578i	1.43071	−	0.383358i	0.889271	+	0.457381i	$0.151213\pi$
$194$		0			0
$195$	19.4489	−	10.5034i	1.39276	−	0.752167i
$196$	14.0000			1.00000
$197$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$197$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−3.65322	+	3.65322i	−0.258322	+	0.258322i
$201$		0			0
$202$	−4.82901	+	18.0221i	−0.339768	+	1.26803i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	83.8406i		−	5.82732i
$208$	13.8191	+	4.12715i	0.958180	+	0.286166i
$209$		0			0
$210$	5.93687	+	22.1567i	0.409683	+	1.52896i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	26.5714	−	26.5714i	1.82065	−	1.82065i
$214$		0			0
$215$		0			0
$216$	−40.2179	−	40.2179i	−2.73648	−	2.73648i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$223$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$224$	−7.48331	+	12.9615i	−0.500000	+	0.866025i
$225$	13.9891	−	8.07659i	0.932604	−	0.538439i
$226$	−21.2250	+	21.2250i	−1.41186	+	1.41186i
$227$	−22.8649	−	6.12664i	−1.51760	−	0.406639i	−0.598647	−	0.801013i	$-0.704295\pi$
$227$	−22.8649	−	6.12664i	−1.51760	−	0.406639i	−0.918950	+	0.394374i	$0.870962\pi$
$228$	−4.29329	+	16.0228i	−0.284330	+	1.06113i
$229$	21.2737	+	21.2737i	1.40581	+	1.40581i	0.779893	+	0.625913i	$0.215274\pi$
$229$	21.2737	+	21.2737i	1.40581	+	1.40581i	0.625913	+	0.779893i	$0.284726\pi$
$230$	−11.9423	−	20.6847i	−0.787454	−	1.36391i
$231$		0			0
$232$		0			0
$233$		−	9.77048i		−	0.640085i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$		−	9.77048i		−	0.640085i	0.947403	−	0.320043i	$-0.103697\pi$
$234$	−38.3942	−	23.6467i	−2.50991	−	1.54583i
$235$		0			0
$236$	−7.59090	−	28.3296i	−0.494126	−	1.84410i
$237$	27.0867	−	46.9155i	1.75947	−	3.04749i
$238$		0			0
$239$	−10.6016	+	10.6016i	−0.685759	+	0.685759i	−0.961292	−	0.275533i	$-0.911146\pi$
$239$	−10.6016	+	10.6016i	−0.685759	+	0.685759i	0.275533	+	0.961292i	$0.411146\pi$
$240$	−23.6865	−	6.34678i	−1.52896	−	0.409683i
$241$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$241$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$242$	−11.0000	−	11.0000i	−0.707107	−	0.707107i
$243$	43.2646	+	74.9364i	2.77542	+	4.80717i
$244$	4.46270	+	2.57654i	0.285695	+	0.164946i
$245$	−12.0449	+	3.22742i	−0.769521	+	0.206193i
$246$		0			0
$247$	−0.246961	+	8.68609i	−0.0157138	+	0.552683i
$248$		0			0
$249$	14.4719	+	54.0100i	0.917122	+	3.42274i
$250$	8.59908	−	14.8940i	0.543853	−	0.941982i
$251$	27.0553	−	15.6204i	1.70772	−	0.985950i	0.770338	−	0.637636i	$-0.220087\pi$
$251$	27.0553	−	15.6204i	1.70772	−	0.985950i	0.937378	−	0.348315i	$-0.113246\pi$
$252$	33.0884	−	33.0884i	2.08437	−	2.08437i
$253$		0			0
$254$	−4.74260	+	17.6996i	−0.297577	+	1.11057i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$		0			0
$260$	−12.8407	−	0.365083i	−0.796345	−	0.0226415i
$261$		0			0
$262$	5.65622	+	21.1093i	0.349443	+	1.30414i
$263$	−4.00654	+	6.93954i	−0.247054	+	0.427910i	−0.962707	−	0.270546i	$-0.912796\pi$
$263$	−4.00654	+	6.93954i	−0.247054	+	0.427910i	0.715653	+	0.698456i	$0.246129\pi$
$264$		0			0
$265$		0			0
$266$	−8.71036	−	2.33393i	−0.534066	−	0.143103i
$267$		0			0
$268$		0			0
$269$	−11.8415	−	20.5100i	−0.721987	−	1.25052i	−0.960202	−	0.279306i	$-0.909896\pi$
$269$	−11.8415	−	20.5100i	−0.721987	−	1.25052i	0.238215	−	0.971212i	$-0.423438\pi$
$270$	43.8730	+	25.3301i	2.67002	+	1.54154i
$271$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$271$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$272$		0			0
$273$	17.2158	−	27.9527i	1.04195	−	1.69177i
$274$	−13.8563			−0.837092
$275$		0			0
$276$	−32.6270	+	56.5117i	−1.96392	+	3.40160i
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	−20.0098	+	20.0098i	−1.20011	+	1.20011i
$279$		0			0
$280$	3.45026	−	12.8765i	0.206193	−	0.769521i
$281$	−7.51669	−	7.51669i	−0.448408	−	0.448408i	0.446417	−	0.894825i	$-0.352700\pi$
$281$	−7.51669	−	7.51669i	−0.448408	−	0.448408i	−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	23.6754	+	13.6690i	1.40736	+	0.812539i	0.995133	−	0.0985428i	$-0.0314181\pi$
$283$	23.6754	+	13.6690i	1.40736	+	0.812539i	0.412226	+	0.911082i	$0.364751\pi$
$284$	−21.0945	+	5.65225i	−1.25173	+	0.335399i
$285$		−	14.7749i		−	0.875191i
$286$		0			0
$287$		0			0
$288$	12.9474	+	48.3204i	0.762934	+	2.84731i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.53918	+	24.4045i	−0.382023	+	1.42573i	0.460784	+	0.887512i	$0.347568\pi$
$293$	−6.53918	+	24.4045i	−0.382023	+	1.42573i	−0.842807	+	0.538216i	$0.819098\pi$
$294$	24.0898	+	24.0898i	1.40495	+	1.40495i
$295$	13.0617	+	22.6235i	0.760480	+	1.31719i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.78211	+	32.7537i	−0.565714	+	1.89420i
$300$	−12.5722			−0.725857
$301$		0			0
$302$	−2.72150	+	4.71378i	−0.156605	+	0.271248i
$303$	−39.3200	+	22.7014i	−2.25887	+	1.30416i
$304$	6.81668	−	6.81668i	0.390964	−	0.390964i
$305$	−4.43346	−	1.18794i	−0.253859	−	0.0680214i
$306$		0			0
$307$	21.6818	+	21.6818i	1.23745	+	1.23745i	0.961041	+	0.276405i	$0.0891433\pi$
$307$	21.6818	+	21.6818i	1.23745	+	1.23745i	0.276405	+	0.961041i	$0.410857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	16.6769	+	30.8801i	0.944143	+	1.74824i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−3.58147	−	13.3662i	−0.202114	−	0.754301i
$315$	−20.8398	+	36.0955i	−1.17419	+	2.03375i
$316$	−27.2654	+	15.7417i	−1.53380	+	0.885537i
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$		0			0
$320$	10.0771	+	10.0771i	0.563328	+	0.563328i
$321$		0			0
$322$	−30.7211	−	17.7368i	−1.71202	−	0.988436i
$323$		0			0
$324$		−	85.3466i		−	4.74148i
$325$	−6.40740	+	1.52308i	−0.355419	+	0.0844854i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$331$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$332$	8.41049	−	31.3884i	0.461585	−	1.72266i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−35.1794	+	9.42629i	−1.91919	+	0.514246i
$337$		−	0.708287i		−	0.0385828i	−0.999814	−	0.0192914i	$-0.993859\pi$
$337$		−	0.708287i		−	0.0385828i	0.999814	−	0.0192914i	$-0.00614103\pi$
$338$	12.2404	+	13.7176i	0.665788	+	0.746141i
$339$	−73.0437			−3.96719
$340$		0			0
$341$		0			0
$342$	−26.1027	+	15.0704i	−1.41147	+	0.814914i
$343$	−13.0958	+	13.0958i	−0.707107	+	0.707107i
$344$		0			0
$345$	15.0430	−	56.1414i	0.809890	−	3.02255i
$346$	23.1766	+	23.1766i	1.24598	+	1.24598i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	−36.0562	+	9.66123i	−1.93004	+	0.517154i	−0.953826	+	0.300360i	$0.902893\pi$
$349$	−36.0562	+	9.66123i	−1.93004	+	0.517154i	−0.976218	+	0.216793i	$0.930440\pi$
$350$		−	6.83455i		−	0.365322i
$351$	−16.7674	−	70.5385i	−0.894980	−	3.76506i
$352$		0			0
$353$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$353$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$354$	35.6852	−	61.8085i	1.89665	−	3.28509i
$355$	16.8456	−	9.72583i	0.894073	−	0.516193i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.4579	+	24.4579i	1.29084	+	1.29084i	0.934268	+	0.356572i	$0.116054\pi$
$359$	24.4579	+	24.4579i	1.29084	+	1.29084i	0.356572	+	0.934268i	$0.383946\pi$
$360$	−22.2786	−	38.5877i	−1.17419	−	2.03375i
$361$	−11.4243	−	6.59580i	−0.601277	−	0.347147i
$362$	−9.01482	+	2.41551i	−0.473808	+	0.126957i
$363$		−	37.8554i		−	1.98689i
$364$	−16.7871	+	9.06596i	−0.879886	+	0.475185i
$365$		0			0
$366$	3.24552	+	12.1124i	0.169646	+	0.633127i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	32.8422	−	18.9615i	1.71202	−	0.988436i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	40.4246	−	10.8317i	2.08752	−	0.559349i
$376$		0			0
$377$		0			0
$378$	75.2409			3.86997
$379$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$379$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$380$	−4.29329	+	7.43619i	−0.220241	+	0.381469i
$381$	−38.6164	+	22.2952i	−1.97838	+	1.14222i
$382$	4.77503	−	4.77503i	0.244312	−	0.244312i
$383$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$383$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$384$	10.0771	−	37.6083i	0.514246	−	1.91919i
$385$		0			0
$386$	−14.5503	−	25.2019i	−0.740591	−	1.28274i
$387$		0			0
$388$		0			0
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−21.4668	−	22.7232i	−1.08701	−	1.15063i
$391$		0			0
$392$	−5.12436	−	19.1244i	−0.258819	−	0.965926i
$393$	−26.5902	+	46.0555i	−1.34130	+	2.32319i
$394$		0			0
$395$	19.8288	−	19.8288i	0.997697	−	0.997697i
$396$		0			0
$397$	−2.01458	+	7.51852i	−0.101109	+	0.377344i	−0.997875	−	0.0651619i	$-0.979244\pi$
$397$	−2.01458	+	7.51852i	−0.101109	+	0.377344i	0.896766	+	0.442505i	$0.145910\pi$
$398$		0			0
$399$	−10.9719	−	19.0039i	−0.549283	−	0.951386i
$400$	6.32757	+	3.65322i	0.316378	+	0.182661i
$401$	−15.3336	+	4.10862i	−0.765723	+	0.205175i	−0.620481	−	0.784221i	$-0.713063\pi$
$401$	−15.3336	+	4.10862i	−0.765723	+	0.205175i	−0.145242	+	0.989396i	$0.546396\pi$
$402$		0			0
$403$		0			0
$404$	26.3862			1.31276
$405$	19.6750	+	73.4280i	0.977658	+	3.64867i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$409$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$410$		0			0
$411$	−23.8426	−	23.8426i	−1.17607	−	1.17607i
$412$		0			0
$413$	33.6006	+	19.3993i	1.65338	+	0.954578i
$414$	−114.528	+	30.6878i	−5.62876	+	1.50822i
$415$			28.9439i			1.42080i
$416$	0.579662	−	20.3878i	0.0284203	−	0.999596i
$417$	−68.8617			−3.37217
$418$		0			0
$419$	−1.48404	+	2.57043i	−0.0725002	+	0.125574i	−0.899996	−	0.435897i	$-0.856431\pi$
$419$	−1.48404	+	2.57043i	−0.0725002	+	0.125574i	0.827496	+	0.561471i	$0.189764\pi$
$420$	28.0936	−	16.2198i	1.37083	−	0.791446i
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−46.0231	−	26.5714i	−2.22983	−	1.28739i
$427$	−6.58461	+	1.76434i	−0.318652	+	0.0853825i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.00644	+	26.1484i	0.337488	+	1.25952i	0.901146	+	0.433515i	$0.142727\pi$
$431$	7.00644	+	26.1484i	0.337488	+	1.25952i	−0.563658	+	0.826008i	$0.690607\pi$
$432$	−40.2179	+	69.6595i	−1.93499	+	3.35150i
$433$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$433$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.1568	+	16.1568i	0.772885	+	0.772885i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$			61.9027i			2.94775i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	20.4448	+	5.47817i	0.965926	+	0.258819i
$449$	−9.50515	+	35.4737i	−0.448576	+	1.67411i	0.257743	+	0.966213i	$0.417021\pi$
$449$	−9.50515	+	35.4737i	−0.448576	+	1.67411i	−0.706319	+	0.707894i	$0.749646\pi$
$450$	−16.1532	−	16.1532i	−0.761468	−	0.761468i
$451$		0			0
$452$	36.7627	+	21.2250i	1.72917	+	0.998339i
$453$	−12.7939	+	3.42811i	−0.601110	+	0.161067i
$454$			33.4766i			1.57113i
$455$	12.3529	−	11.6698i	0.579111	−	0.547091i
$456$	23.4590			1.09857
$457$	−8.82485	−	32.9348i	−0.412809	−	1.54062i	−0.789184	−	0.614157i	$-0.789496\pi$
$457$	−8.82485	−	32.9348i	−0.412809	−	1.54062i	0.376375	−	0.926467i	$-0.377170\pi$
$458$	21.2737	−	36.8471i	0.994055	−	1.72175i
$459$		0			0
$460$	−23.8847	+	23.8847i	−1.11363	+	1.11363i
$461$	11.2857	+	3.02398i	0.525625	+	0.140841i	0.511867	−	0.859064i	$-0.328954\pi$
$461$	11.2857	+	3.02398i	0.525625	+	0.140841i	0.0137580	+	0.999905i	$0.495621\pi$
$462$		0			0
$463$	4.20185	+	4.20185i	0.195277	+	0.195277i	0.797972	−	0.602695i	$-0.205906\pi$
$463$	4.20185	+	4.20185i	0.195277	+	0.195277i	−0.602695	+	0.797972i	$0.705906\pi$
$464$		0			0
$465$		0			0
$466$	−13.3467	+	3.57624i	−0.618275	+	0.165666i
$467$			16.1251i			0.746180i	0.927795	+	0.373090i	$0.121702\pi$
$467$			16.1251i			0.746180i	−0.927795	+	0.373090i	$0.878298\pi$
$468$	−18.2487	+	61.1027i	−0.843547	+	2.82447i
$469$		0			0
$470$		0			0
$471$	16.8367	−	29.1619i	0.775792	−	1.34371i
$472$	−35.9205	+	20.7387i	−1.65338	+	0.954578i
$473$		0			0
$474$	−74.0022	−	19.8288i	−3.39903	−	0.910768i
$475$	−1.13938	+	4.25224i	−0.0522786	+	0.195106i
$476$		0			0
$477$		0			0
$478$	18.3625	+	10.6016i	0.839880	+	0.484905i
$479$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$479$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$480$			34.6794i			1.58289i
$481$		0			0
$482$		0			0
$483$	−22.3420	−	83.3817i	−1.01660	−	3.79400i
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	86.5291	−	86.5291i	3.92504	−	3.92504i
$487$	30.4461	+	8.15800i	1.37964	+	0.369674i	0.870992	−	0.491298i	$-0.163477\pi$
$487$	30.4461	+	8.15800i	1.37964	+	0.369674i	0.508652	+	0.860972i	$0.330144\pi$
$488$	1.88616	−	7.03925i	0.0853825	−	0.318652i
$489$		0			0
$490$	8.81748	+	15.2723i	0.398333	+	0.689934i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$	11.9558	−	2.84198i	0.537918	−	0.127867i
$495$		0			0
$496$		0			0
$497$	14.4449	−	25.0193i	0.647941	−	1.12227i
$498$	68.4819	−	39.5381i	3.06875	−	1.77174i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	−23.4931	−	6.29496i	−1.05064	−	0.281519i
$501$		0			0
$502$	−31.2408	−	31.2408i	−1.39434	−	1.39434i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	−57.3108	−	33.0884i	−2.55283	−	1.47387i
$505$	−22.7014	+	6.08282i	−1.01020	+	0.270682i
$506$		0			0
$507$	−2.54192	+	44.6660i	−0.112891	+	1.98368i
$508$	25.9140			1.14975
$509$	−5.18356	−	19.3453i	−0.229757	−	0.857465i	−0.980443	−	0.196805i	$-0.936943\pi$
$509$	−5.18356	−	19.3453i	−0.229757	−	0.857465i	0.750686	−	0.660660i	$-0.229723\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−46.8125	−	12.5434i	−2.06682	−	0.553803i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$			79.7598i			3.50107i
$520$	4.20130	+	17.6743i	0.184239	+	0.775070i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	20.6031	−	35.6856i	0.900910	−	1.56042i	0.0745957	−	0.997214i	$-0.476233\pi$
$523$	20.6031	−	35.6856i	0.900910	−	1.56042i	0.826315	−	0.563209i	$-0.190433\pi$
$524$	26.7655	−	15.4531i	1.16926	−	0.675071i
$525$	11.7602	−	11.7602i	0.513258	−	0.513258i
$526$	10.9461	+	2.93299i	0.477272	+	0.127885i
$527$		0			0
$528$		0			0
$529$	33.4422	+	57.9236i	1.45401	+	2.51842i
$530$		0			0
$531$	125.263	−	33.5641i	5.43595	−	1.45656i
$532$			12.7528i			0.552906i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−23.6829	+	23.6829i	−1.02104	+	1.02104i
$539$		0			0
$540$	18.5429	−	69.2031i	0.797960	−	2.97803i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$	−19.6682	−	11.3554i	−0.844043	−	0.487308i
$544$		0			0
$545$		0			0
$546$	−44.4855	−	13.2859i	−1.90380	−	0.568582i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$	5.07177	+	18.9281i	0.216655	+	0.808569i
$549$	−11.3925	+	19.7324i	−0.486220	+	0.842158i
$550$		0			0
$551$		0			0
$552$	89.1387	+	23.8847i	3.79400	+	1.01660i
$553$	10.7794	−	40.2294i	0.458388	−	1.71073i
$554$		0			0
$555$		0			0
$556$	34.6580	+	20.0098i	1.46983	+	0.848604i
$557$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$557$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$558$		0			0
$559$		0			0
$560$	−18.8526			−0.796667
$561$		0			0
$562$	−7.51669	+	13.0193i	−0.317072	+	0.549185i
$563$	−40.1801	+	23.1980i	−1.69339	+	0.977679i	−0.741644	+	0.670794i	$0.765954\pi$
$563$	−40.1801	+	23.1980i	−1.69339	+	0.977679i	−0.951746	+	0.306886i	$0.900713\pi$
$564$		0			0
$565$	−36.5218	−	9.78600i	−1.53649	−	0.411700i
$566$	10.0064	−	37.3445i	0.420601	−	1.56970i
$567$	79.8345	+	79.8345i	3.35273	+	3.35273i
$568$	15.4422	+	26.7467i	0.647941	+	1.12227i
$569$	8.30850	+	4.79691i	0.348310	+	0.201097i	0.663941	−	0.747785i	$-0.268883\pi$
$569$	8.30850	+	4.79691i	0.348310	+	0.201097i	−0.315631	+	0.948882i	$0.602216\pi$
$570$	−20.1829	+	5.40800i	−0.845370	+	0.226516i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	16.4328			0.686490
$574$		0			0
$575$	−8.65881	+	14.9975i	−0.361097	+	0.625439i
$576$	61.2678	−	35.3730i	2.55283	−	1.47387i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−23.2224	−	6.22243i	−0.965926	−	0.258819i
$579$	18.3281	−	68.4016i	0.761692	−	2.84267i
$580$		0			0
$581$	21.4938	+	37.2284i	0.891715	+	1.54449i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.61426	−	56.7767i	0.0667415	−	2.34743i
$586$	35.7307			1.47602
$587$	−8.31278	−	31.0237i	−0.343105	−	1.28049i	−0.894810	−	0.446447i	$-0.852689\pi$
$587$	−8.31278	−	31.0237i	−0.343105	−	1.28049i	0.551705	−	0.834039i	$-0.313978\pi$
$588$	24.0898	−	41.7248i	0.993447	−	1.72070i
$589$		0			0
$590$	26.1234	−	26.1234i	1.07548	−	1.07548i
$591$		0			0
$592$		0			0
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	48.3230	+	1.37391i	1.97607	+	0.0561833i
$599$	43.0726			1.75990			0.879949	−	0.475068i	$-0.157577\pi$
$599$	43.0726			1.75990			0.879949	+	0.475068i	$0.157577\pi$
$600$	4.60175	+	17.1740i	0.187866	+	0.701124i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	7.43528	+	1.99228i	0.302537	+	0.0810646i
$605$	5.07167	−	18.9277i	0.206193	−	0.769521i
$606$	45.4028	+	45.4028i	1.84436	+	1.84436i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	−11.8068	−	6.81668i	−0.478831	−	0.276453i
$609$		0			0
$610$			6.49104i			0.262814i
$611$		0			0
$612$		0			0
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$	21.6818	−	37.5540i	0.875007	−	1.51556i
$615$		0			0
$616$		0			0
$617$	−11.1703	−	2.99306i	−0.449698	−	0.120496i	0.0268600	−	0.999639i	$-0.491449\pi$
$617$	−11.1703	−	2.99306i	−0.449698	−	0.120496i	−0.476558	+	0.879143i	$0.658116\pi$
$618$		0			0
$619$	35.0197	+	35.0197i	1.40756	+	1.40756i	0.772288	+	0.635273i	$0.219112\pi$
$619$	35.0197	+	35.0197i	1.40756	+	1.40756i	0.635273	+	0.772288i	$0.280888\pi$
$620$		0			0
$621$	−165.106	−	95.3240i	−6.62547	−	3.82522i
$622$		0			0
$623$		0			0
$624$	36.0788	−	34.0840i	1.44431	−	1.36445i
$625$	12.5304			0.501218
$626$		0			0
$627$		0			0
$628$	−16.9477	+	9.78477i	−0.676287	+	0.390455i
$629$		0			0
$630$	56.9353	+	15.2558i	2.26836	+	0.607804i
$631$	12.4011	−	46.2815i	0.493680	−	1.84244i	−0.0436231	−	0.999048i	$-0.513890\pi$
$631$	12.4011	−	46.2815i	0.493680	−	1.84244i	0.537303	−	0.843389i	$-0.319443\pi$
$632$	31.4833	+	31.4833i	1.25234	+	1.25234i
$633$		0			0
$634$		0			0
$635$	−22.2952	+	5.97397i	−0.884757	+	0.237070i
$636$		0			0
$637$	7.22251	−	24.1834i	0.286166	−	0.958180i
$638$		0			0
$639$	−24.9921	−	93.2718i	−0.988673	−	3.68978i
$640$	10.0771	−	17.4541i	0.398333	−	0.689934i
$641$	−43.7806	+	25.2767i	−1.72923	+	0.998371i	−0.836090	+	0.548592i	$0.815164\pi$
$641$	−43.7806	+	25.2767i	−1.72923	+	0.998371i	−0.893140	+	0.449780i	$0.851502\pi$
$642$		0			0
$643$	16.7414	+	4.48583i	0.660215	+	0.176904i	0.573343	−	0.819315i	$-0.305646\pi$
$643$	16.7414	+	4.48583i	0.660215	+	0.176904i	0.0868719	+	0.996219i	$0.472313\pi$
$644$	−12.9843	+	48.4580i	−0.511652	+	1.90951i
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−116.586	+	31.2390i	−4.57992	+	1.22719i
$649$		0			0
$650$	4.42584	+	8.19519i	0.173596	+	0.321442i
$651$		0			0
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−19.4653	+	19.4653i	−0.760574	+	0.760574i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−35.7248	+	9.57242i	−1.38953	+	0.372324i	−0.874575	−	0.484891i	$-0.838859\pi$
$661$	−35.7248	+	9.57242i	−1.38953	+	0.372324i	−0.514958	+	0.857215i	$0.672193\pi$
$662$		0			0
$663$		0			0
$664$	−45.9558			−1.78343
$665$	−2.93992	−	10.9719i	−0.114005	−	0.425473i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	25.7531	+	44.6057i	0.993447	+	1.72070i
$673$	−38.8844	−	22.4499i	−1.49889	−	0.865382i	−0.498886	−	0.866668i	$-0.666257\pi$
$673$	−38.8844	−	22.4499i	−1.49889	−	0.865382i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	−0.967538	+	0.259251i	−0.0372682	+	0.00998598i
$675$		−	36.7313i		−	1.41379i
$676$	14.2583	−	21.7417i	0.548398	−	0.836218i
$677$	38.6505			1.48546			0.742729	−	0.669592i	$-0.233531\pi$
$677$	38.6505			1.48546			0.742729	+	0.669592i	$0.233531\pi$
$678$	26.7358	+	99.7795i	1.02678	+	3.83201i
$679$		0			0
$680$		0			0
$681$	−57.6032	+	57.6032i	−2.20736	+	2.20736i
$682$		0			0
$683$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$683$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$684$	30.1408	+	30.1408i	1.15246	+	1.15246i
$685$	−8.72700	−	15.1156i	−0.333442	−	0.577538i
$686$	22.6826	+	13.0958i	0.866025	+	0.500000i
$687$	100.009	−	26.7972i	3.81557	−	1.02238i
$688$		0			0
$689$		0			0
$690$	−82.1967			−3.12917
$691$	7.28537	+	27.1894i	0.277149	+	1.03433i	0.954388	+	0.298570i	$0.0965096\pi$
$691$	7.28537	+	27.1894i	0.277149	+	1.03433i	−0.677239	+	0.735763i	$0.736824\pi$
$692$	23.1766	−	40.1430i	0.881040	−	1.52601i
$693$		0			0
$694$		0			0
$695$	−34.4309	−	9.22572i	−1.30604	−	0.349952i
$696$		0			0
$697$		0			0
$698$	26.3950	+	45.7174i	0.999064	+	1.73043i
$699$	−29.1194	−	16.8121i	−1.10140	−	0.635891i
$700$	−9.33617	+	2.50162i	−0.352874	+	0.0945523i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−90.2200	+	48.7236i	−3.40513	+	1.83895i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.6820	+	24.6820i	−0.928264	+	0.928264i
$708$	−97.4937	−	26.1234i	−3.66404	−	0.981776i
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$	−19.4517	−	19.4517i	−0.730007	−	0.730007i
$711$	−69.6037	−	120.557i	−2.61034	−	4.52125i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	13.3542	+	49.8385i	0.498721	+	1.86125i
$718$	24.4579	−	42.3624i	0.912761	−	1.58095i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−44.5573	+	44.5573i	−1.66055	+	1.66055i
$721$		0			0
$722$	−4.82846	+	18.0201i	−0.179697	+	0.670637i
$723$		0			0
$724$	6.59930	+	11.4303i	0.245261	+	0.424805i
$725$		0			0
$726$	−51.7115	+	13.8560i	−1.91919	+	0.514246i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	18.5289	+	19.6133i	0.686725	+	0.726917i
$729$	169.762			6.28747
$730$		0			0
$731$		0			0
$732$	15.3580	−	8.86692i	0.567646	−	0.327731i
$733$	27.0383	−	27.0383i	0.998682	−	0.998682i	−0.00131730	−	0.999999i	$-0.500419\pi$
$733$	27.0383	−	27.0383i	0.998682	−	0.998682i	0.999999	+	0.00131730i	$0.000419310\pi$
$734$		0			0
$735$	−11.1069	+	41.4514i	−0.409683	+	1.52896i
$736$	−37.9230	−	37.9230i	−1.39786	−	1.39786i
$737$		0			0
$738$		0			0
$739$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$739$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$740$		0			0
$741$	25.4626	+	15.6822i	0.935391	+	0.576100i
$742$		0			0
$743$	8.51314	+	31.7715i	0.312317	+	1.16558i	0.926462	+	0.376389i	$0.122834\pi$
$743$	8.51314	+	31.7715i	0.312317	+	1.16558i	−0.614145	+	0.789193i	$0.710499\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	138.788	+	37.1880i	5.07797	+	1.36064i
$748$		0			0
$749$		0			0
$750$	−29.5929	−	51.2564i	−1.08058	−	1.87162i
$751$	27.7789	+	16.0381i	1.01367	+	0.585240i	0.912263	−	0.409605i	$-0.134333\pi$
$751$	27.7789	+	16.0381i	1.01367	+	0.585240i	0.101403	+	0.994845i	$0.467667\pi$
$752$		0			0
$753$		−	107.512i		−	3.91796i
$754$		0			0
$755$	−6.85623			−0.249524
$756$	−27.5401	−	102.781i	−1.00162	−	3.73811i
$757$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$757$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$758$		0			0
$759$		0			0
$760$	11.7295	+	3.14290i	0.425473	+	0.114005i
$761$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$761$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$762$	44.5903	+	44.5903i	1.61534	+	1.61534i
$763$		0			0
$764$	−8.27059	−	4.77503i	−0.299219	−	0.172754i
$765$		0			0
$766$		0			0
$767$	−52.8523	−	1.50268i	−1.90838	−	0.0542588i
$768$	−55.0624			−1.98689
$769$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$769$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$770$		0			0
$771$		0			0
$772$	−29.1006	+	29.1006i	−1.04735	+	1.04735i
$773$	−34.3177	−	9.19540i	−1.23432	−	0.330736i	−0.418061	−	0.908419i	$-0.637290\pi$
$773$	−34.3177	−	9.19540i	−1.23432	−	0.330736i	−0.816261	+	0.577683i	$0.803957\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−23.1830	+	37.6414i	−0.830086	+	1.34778i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−24.2487	+	14.0000i	−0.866025	+	0.500000i
$785$	12.3253	−	12.3253i	0.439908	−	0.439908i
$786$	72.6456	+	19.4653i	2.59118	+	0.694306i
$787$	12.7259	−	47.4939i	0.453631	−	1.69297i	−0.238451	−	0.971154i	$-0.576640\pi$
$787$	12.7259	−	47.4939i	0.453631	−	1.69297i	0.692082	−	0.721819i	$-0.256694\pi$
$788$		0			0
$789$	13.7881	+	23.8817i	0.490870	+	0.850213i
$790$	−34.3445	−	19.8288i	−1.22192	−	0.705478i
$791$	−54.2425	+	14.5342i	−1.92864	+	0.516778i
$792$		0			0
$793$	6.75296	−	6.37958i	0.239805	−	0.226545i
$794$	11.0079			0.390655
$795$		0			0
$796$		0			0
$797$	−0.592072	+	0.341833i	−0.0209723	+	0.0121083i	−0.510449	−	0.859908i	$-0.670521\pi$
$797$	−0.592072	+	0.341833i	−0.0209723	+	0.0121083i	0.489477	+	0.872016i	$0.337188\pi$
$798$	−21.9438	+	21.9438i	−0.776804	+	0.776804i
$799$		0			0
$800$	2.67434	−	9.98079i	0.0945523	−	0.352874i
$801$		0			0
$802$	11.2250	+	19.4422i	0.396368	+	0.686529i
$803$		0			0
$804$		0			0
$805$		−	44.6841i		−	1.57491i
$806$		0			0
$807$	−81.5025			−2.86902
$808$	−9.65803	−	36.0442i	−0.339768	−	1.26803i
$809$	−5.83746	+	10.1108i	−0.205234	+	0.355476i	−0.950207	−	0.311619i	$-0.899129\pi$
$809$	−5.83746	+	10.1108i	−0.205234	+	0.355476i	0.744973	+	0.667094i	$0.232462\pi$
$810$	93.1030	−	53.7530i	3.27131	−	1.88869i
$811$	−25.4687	+	25.4687i	−0.894326	+	0.894326i	−0.994927	−	0.100600i	$-0.967924\pi$
$811$	−25.4687	+	25.4687i	−0.894326	+	0.894326i	0.100600	+	0.994927i	$0.467924\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−40.0863	−	74.2265i	−1.40073	−	2.59368i
$820$		0			0
$821$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$821$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$822$	−23.8426	+	41.2966i	−0.831607	+	1.44039i
$823$	−33.5437	+	19.3665i	−1.16926	+	0.675072i	−0.953506	−	0.301376i	$-0.902554\pi$
$823$	−33.5437	+	19.3665i	−1.16926	+	0.675072i	−0.215754	+	0.976448i	$0.569221\pi$
$824$		0			0
$825$		0			0
$826$	14.2013	−	52.9999i	0.494126	−	1.84410i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	83.8406	+	145.216i	2.91366	+	5.04661i
$829$	5.36861	+	3.09957i	0.186460	+	0.107653i	0.590324	−	0.807166i	$-0.299000\pi$
$829$	5.36861	+	3.09957i	0.186460	+	0.107653i	−0.403864	+	0.914819i	$0.632333\pi$
$830$	39.5381	−	10.5942i	1.37239	−	0.367730i
$831$		0			0
$832$	−28.0625	+	6.67063i	−0.972891	+	0.231263i
$833$		0			0
$834$	25.2051	+	94.0669i	0.872783	+	3.25727i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	4.05448	+	1.08639i	0.140060	+	0.0375288i
$839$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$839$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$840$	−32.4396	−	32.4396i	−1.11927	−	1.11927i
$841$	−14.5000	−	25.1147i	−0.500000	−	0.866025i
$842$		0			0
$843$	−35.3363	+	9.46832i	−1.21705	+	0.326106i
$844$		0			0
$845$	−7.25506	+	21.9924i	−0.249582	+	0.756562i
$846$		0			0
$847$	−7.53248	−	28.1116i	−0.258819	−	0.965926i
$848$		0			0
$849$	81.4767	−	47.0406i	2.79627	−	1.61443i
$850$		0			0
$851$		0			0
$852$	−19.4517	+	72.5945i	−0.666403	+	2.48705i
$853$	−35.8212	−	35.8212i	−1.22650	−	1.22650i	−0.965280	−	0.261216i	$-0.915877\pi$
$853$	−35.8212	−	35.8212i	−1.22650	−	1.22650i	−0.261216	−	0.965280i	$-0.584123\pi$
$854$	4.82027	+	8.34895i	0.164946	+	0.285695i
$855$	−32.8800	−	18.9833i	−1.12447	−	0.649215i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	0.440260			0.0150215			0.00751074	−	0.999972i	$-0.497609\pi$
$859$	0.440260			0.0150215			0.00751074	+	0.999972i	$0.497609\pi$
$860$		0			0
$861$		0			0
$862$	33.1548	−	19.1419i	1.12926	−	0.651977i
$863$	40.2535	−	40.2535i	1.37025	−	1.37025i	0.510174	−	0.860071i	$-0.329581\pi$
$863$	40.2535	−	40.2535i	1.37025	−	1.37025i	0.860071	−	0.510174i	$-0.170419\pi$
$864$	109.877	+	29.4416i	3.73811	+	1.00162i
$865$	−10.6858	+	39.8799i	−0.363328	+	1.35596i
$866$		0			0
$867$	−29.2519	−	50.6658i	−0.993447	−	1.72070i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	16.1568	−	27.9844i	0.546512	−	0.946587i
$875$	27.8642	−	16.0874i	0.941982	−	0.543853i
$876$		0			0
$877$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$877$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$878$		0			0
$879$	61.4819	+	61.4819i	2.07373	+	2.07373i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	84.5607	−	22.6580i	2.84731	−	0.762934i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	89.9010			3.02199
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	−24.2404	+	24.2404i	−0.812996	+	0.812996i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	29.9333i		−	1.00000i
$897$	80.7853	+	85.5134i	2.69734	+	2.85521i
$898$	51.9371			1.73316
$899$		0			0
$900$	−16.1532	+	27.9781i	−0.538439	+	0.932604i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	15.5378	−	57.9877i	0.516778	−	1.92864i
$905$	−8.31275	−	8.31275i	−0.276325	−	0.276325i
$906$	9.36578	+	16.2220i	0.311157	+	0.538940i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	45.7298	−	12.2533i	1.51760	−	0.406639i
$909$			116.670i			3.86970i
$910$	−20.4628	−	12.6029i	−0.678334	−	0.417781i
$911$	−0.210840			−0.00698543			−0.00349271	−	0.999994i	$-0.501112\pi$
$911$	−0.210840			−0.00698543			−0.00349271	+	0.999994i	$0.501112\pi$
$912$	−8.58657	−	32.0455i	−0.284330	−	1.06113i
$913$		0			0
$914$	−41.7596	+	24.1099i	−1.38129	+	0.797486i
$915$	−11.1691	+	11.1691i	−0.369240	+	0.369240i
$916$	−58.1208	−	15.5734i	−1.92037	−	0.514561i
$917$	−10.5818	+	39.4919i	−0.349443	+	1.30414i
$918$		0			0
$919$	−15.7286	−	27.2428i	−0.518840	−	0.898657i	−0.999760	−	0.0218926i	$-0.993031\pi$
$919$	−15.7286	−	27.2428i	−0.518840	−	0.898657i	0.480921	−	0.876764i	$-0.340303\pi$
$920$	41.3694	+	23.8847i	1.36391	+	0.787454i
$921$	101.927	−	27.3113i	3.35861	−	0.899938i
$922$		−	16.5233i		−	0.544167i
$923$	−1.11891	+	39.3542i	−0.0368294	+	1.29536i
$924$		0			0
$925$		0			0
$926$	4.20185	−	7.27782i	0.138081	−	0.239164i
$927$		0			0
$928$		0			0
$929$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$929$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$930$		0			0
$931$	−11.9292	−	11.9292i	−0.390964	−	0.390964i
$932$	9.77048	+	16.9230i	0.320043	+	0.554330i
$933$		0			0
$934$	22.0273	−	5.90219i	0.720755	−	0.193126i
$935$		0			0
$936$	90.1474	+	2.56305i	2.94656	+	0.0837759i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.5088	+	24.5088i	−0.798964	+	0.798964i	−0.982932	−	0.183968i	$-0.941106\pi$
$941$	−24.5088	+	24.5088i	−0.798964	+	0.798964i	0.183968	+	0.982932i	$0.441106\pi$
$942$	−45.9986	−	12.3253i	−1.49872	−	0.401580i
$943$		0			0
$944$	41.4775	+	41.4775i	1.34998	+	1.34998i
$945$	47.3882	+	82.0788i	1.54154	+	2.67002i
$946$		0			0
$947$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$947$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$948$			108.347i			3.51894i
$949$		0			0
$950$	6.22571			0.201989
$951$		0			0
$952$		0			0
$953$	−0.932742	+	0.538519i	−0.0302145	+	0.0174443i	−0.515031	−	0.857171i	$-0.672220\pi$
$953$	−0.932742	+	0.538519i	−0.0302145	+	0.0174443i	0.484817	+	0.874616i	$0.338886\pi$
$954$		0			0
$955$	8.21640	+	2.20158i	0.265876	+	0.0712413i
$956$	7.76090	−	28.9641i	0.251005	−	0.936765i
$957$		0			0
$958$		0			0
$959$	−22.4498	−	12.9614i	−0.724943	−	0.418546i
$960$	47.3730	−	12.6936i	1.52896	−	0.409683i
$961$		−	31.0000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	18.3281	−	31.7453i	0.590004	−	1.02192i
$966$	−105.724	+	61.0396i	−3.40160	+	1.96392i
$967$	17.7750	−	17.7750i	0.571606	−	0.571606i	−0.360971	−	0.932577i	$-0.617555\pi$
$967$	17.7750	−	17.7750i	0.571606	−	0.571606i	0.932577	+	0.360971i	$0.117555\pi$
$968$	30.0526	+	8.05256i	0.965926	+	0.258819i
$969$		0			0
$970$		0			0
$971$	−30.9031	−	53.5257i	−0.991728	−	1.71772i	−0.607027	−	0.794681i	$-0.707638\pi$
$971$	−30.9031	−	53.5257i	−0.991728	−	1.71772i	−0.384701	−	0.923041i	$-0.625695\pi$
$972$	−149.873	−	86.5291i	−4.80717	−	2.77542i
$973$	−51.1370	+	13.7021i	−1.63938	+	0.439270i
$974$		−	44.5762i		−	1.42831i
$975$	−6.48592	+	21.7170i	−0.207716	+	0.695501i
$976$	−10.3062			−0.329893
$977$	0.489704	+	1.82760i	0.0156670	+	0.0584701i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	0.489704	+	1.82760i	0.0156670	+	0.0584701i	−0.957650	+	0.287936i	$0.907031\pi$
$978$		0			0
$979$		0			0
$980$	17.6350	−	17.6350i	0.563328	−	0.563328i
$981$		0			0
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−8.25834	−	15.2917i	−0.262733	−	0.486494i
$989$		0			0
$990$		0			0
$991$	−29.3819	+	50.8909i	−0.933345	+	1.61660i	−0.155787	+	0.987791i	$0.549791\pi$
$991$	−29.3819	+	50.8909i	−0.933345	+	1.61660i	−0.777558	+	0.628811i	$0.783542\pi$
$992$		0			0
$993$		0			0
$994$	−39.4641	−	10.5744i	−1.25173	−	0.335399i
$995$		0			0
$996$	−79.0761	−	79.0761i	−2.50562	−	2.50562i
$997$	−17.5488	−	30.3955i	−0.555777	−	0.962635i	−0.997843	−	0.0656519i	$-0.979087\pi$
$997$	−17.5488	−	30.3955i	−0.555777	−	0.962635i	0.442065	−	0.896983i	$-0.354246\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.ds.b.461.4	yes	16
7.6	odd	2	inner	728.2.ds.b.461.1	yes	16
8.5	even	2	inner	728.2.ds.b.461.1	yes	16
13.11	odd	12	inner	728.2.ds.b.349.4	yes	16
56.13	odd	2	CM	728.2.ds.b.461.4	yes	16
91.76	even	12	inner	728.2.ds.b.349.1	✓	16
104.37	odd	12	inner	728.2.ds.b.349.1	✓	16
728.349	even	12	inner	728.2.ds.b.349.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.ds.b.349.1	✓	16	91.76	even	12	inner
728.2.ds.b.349.1	✓	16	104.37	odd	12	inner
728.2.ds.b.349.4	yes	16	13.11	odd	12	inner
728.2.ds.b.349.4	yes	16	728.349	even	12	inner
728.2.ds.b.461.1	yes	16	7.6	odd	2	inner
728.2.ds.b.461.1	yes	16	8.5	even	2	inner
728.2.ds.b.461.4	yes	16	1.1	even	1	trivial
728.2.ds.b.461.4	yes	16	56.13	odd	2	CM

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.ds (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 1.36603i) q^{2} +(1.72070 - 2.98034i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.25964 - 1.25964i) q^{5} +(-4.70104 - 1.25964i) q^{6} +(0.684771 - 2.55560i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-4.42162 - 7.65848i) q^{9} +(-2.18176 - 1.25964i) q^{10} +6.88280i q^{12} +(0.833829 + 3.50781i) q^{13} -3.74166 q^{14} +(-1.58669 - 5.92162i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-8.84325 + 8.84325i) q^{18} +(2.32794 + 0.623770i) q^{19} +(-0.922121 + 3.44140i) q^{20} +(-6.43827 - 6.43827i) q^{21} +(8.21056 + 4.74037i) q^{23} +(9.40209 - 2.51928i) q^{24} +1.82661i q^{25} +(4.48655 - 2.42298i) q^{26} -20.1090 q^{27} +(1.36954 + 5.11120i) q^{28} +(-7.50832 + 4.33493i) q^{30} +(-5.46410 - 1.46410i) q^{32} +(-2.35657 - 4.08170i) q^{35} +(15.3170 + 8.84325i) q^{36} -3.40834i q^{38} +(11.8892 + 3.55080i) q^{39} +5.03856 q^{40} +(-6.43827 + 11.1514i) q^{42} +(-15.2166 - 4.07727i) q^{45} +(3.47019 - 12.9509i) q^{46} +(-6.88280 - 11.9214i) q^{48} +(-6.06218 - 3.50000i) q^{49} +(2.49520 - 0.668586i) q^{50} +(-4.95204 - 5.24188i) q^{52} +(7.36040 + 27.4694i) q^{54} +(6.48074 - 3.74166i) q^{56} +(5.86474 - 5.86474i) q^{57} +(-3.79545 + 14.1648i) q^{59} +(8.66986 + 8.66986i) q^{60} +(-1.28827 - 2.23135i) q^{61} +(-22.5998 + 6.05560i) q^{63} +8.00000i q^{64} +(5.46890 + 3.36825i) q^{65} +(28.2558 - 16.3135i) q^{69} +(-4.71314 + 4.71314i) q^{70} +(10.5472 + 2.82612i) q^{71} +(6.47371 - 24.1602i) q^{72} +(5.44392 + 3.14305i) q^{75} +(-4.65588 + 1.24754i) q^{76} +(0.498713 - 17.5407i) q^{78} +15.7417 q^{79} +(-1.84424 - 6.88280i) q^{80} +(-21.3367 + 36.9562i) q^{81} +(-11.4889 + 11.4889i) q^{83} +(17.5897 + 4.71314i) q^{84} +22.2786i q^{90} +(9.53554 + 0.271112i) q^{91} -18.9615 q^{92} +(3.71810 - 2.14664i) q^{95} +(-13.7656 + 13.7656i) q^{96} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} + 32 q^{8} - 16 q^{9} - 56 q^{15} + 32 q^{16} - 32 q^{18} - 96 q^{30} - 32 q^{32} + 48 q^{36} + 72 q^{39} - 24 q^{46} + 56 q^{50} + 88 q^{57} - 32 q^{60} - 112 q^{63} + 16 q^{65} - 16 q^{71}+ \cdots + 56 q^{98}+O(q^{100}) \) 16 * q + 8 * q^2 + 32 * q^8 - 16 * q^9 - 56 * q^15 + 32 * q^16 - 32 * q^18 - 96 * q^30 - 32 * q^32 + 48 * q^36 + 72 * q^39 - 24 * q^46 + 56 * q^50 + 88 * q^57 - 32 * q^60 - 112 * q^63 + 16 * q^65 - 16 * q^71 + 16 * q^72 + 16 * q^78 + 192 * q^79 - 48 * q^81 - 96 * q^92 + 120 * q^95 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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