LMFDB - Embedded newform 2070.2.j.g.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$-0.0912546 - 1.41127i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.g.737.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.342849 + 2.20963i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.342849 + 2.20963i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.80487 - 1.32001i) q^{10} -1.59083i q^{11} +(-2.64002 - 2.64002i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +1.60975i q^{19} +(-2.20963 - 0.342849i) q^{20} +(-1.12489 + 1.12489i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-4.76491 - 1.51514i) q^{25} +3.73356i q^{26} +(-2.00000 - 2.00000i) q^{28} +6.56198 q^{29} -4.24977 q^{31} +(0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(-3.73356 - 5.10495i) q^{35} +(-0.875115 + 0.875115i) q^{37} +(1.13826 - 1.13826i) q^{38} +(1.32001 + 1.80487i) q^{40} +2.87124i q^{41} +(-2.09461 - 2.09461i) q^{43} +1.59083 q^{44} -1.00000 q^{46} +(-3.51413 - 3.51413i) q^{47} -1.00000i q^{49} +(2.29793 + 4.44066i) q^{50} +(2.64002 - 2.64002i) q^{52} +(3.23818 - 3.23818i) q^{53} +(3.51514 + 0.545414i) q^{55} +2.82843i q^{56} +(-4.64002 - 4.64002i) q^{58} +11.6669 q^{59} -9.85952 q^{61} +(3.00504 + 3.00504i) q^{62} -1.00000i q^{64} +(6.73860 - 4.92834i) q^{65} +(4.79518 - 4.79518i) q^{67} +(1.41421 - 1.41421i) q^{68} +(-0.969724 + 6.24977i) q^{70} -8.32943i q^{71} +(-2.03028 - 2.03028i) q^{73} +1.23760 q^{74} -1.60975 q^{76} +(3.18166 + 3.18166i) q^{77} -7.21949i q^{79} +(0.342849 - 2.20963i) q^{80} +(2.03028 - 2.03028i) q^{82} +(8.60538 - 8.60538i) q^{83} +(3.60975 - 2.64002i) q^{85} +2.96222i q^{86} +(-1.12489 - 1.12489i) q^{88} +16.8575 q^{89} +10.5601 q^{91} +(0.707107 + 0.707107i) q^{92} +4.96972i q^{94} +(-3.55694 - 0.551901i) q^{95} +(1.60975 - 1.60975i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.342849	+	2.20963i	−0.153327	+	0.988176i
$5$	−0.342849	+	2.20963i	−0.153327	+	0.988176i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	1.80487	−	1.32001i	0.570751	−	0.417424i
$11$		−	1.59083i		−	0.479653i	−0.970816	−	0.239826i	$-0.922909\pi$
$11$		−	1.59083i		−	0.479653i	0.970816	−	0.239826i	$-0.0770905\pi$
$12$		0			0
$13$	−2.64002	−	2.64002i	−0.732211	−	0.732211i	0.238847	−	0.971057i	$-0.423231\pi$
$13$	−2.64002	−	2.64002i	−0.732211	−	0.732211i	−0.971057	+	0.238847i	$0.923231\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	0.514496	−	0.857493i	$-0.327979\pi$
$17$	−1.41421	−	1.41421i	−0.342997	−	0.342997i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$			1.60975i			0.369301i	0.982804	+	0.184651i	$0.0591154\pi$
$19$			1.60975i			0.369301i	−0.982804	+	0.184651i	$0.940885\pi$
$20$	−2.20963	−	0.342849i	−0.494088	−	0.0766634i
$21$		0			0
$22$	−1.12489	+	1.12489i	−0.239826	+	0.239826i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	−4.76491	−	1.51514i	−0.952982	−	0.303028i
$26$			3.73356i			0.732211i
$27$		0			0
$28$	−2.00000	−	2.00000i	−0.377964	−	0.377964i
$29$	6.56198			1.21853			0.609265	−	0.792967i	$-0.291465\pi$
$29$	6.56198			1.21853			0.609265	+	0.792967i	$0.291465\pi$
$30$		0			0
$31$	−4.24977			−0.763281			−0.381641	−	0.924311i	$-0.624641\pi$
$31$	−4.24977			−0.763281			−0.381641	+	0.924311i	$0.624641\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			2.00000i			0.342997i
$35$	−3.73356	−	5.10495i	−0.631086	−	0.862895i
$36$		0			0
$37$	−0.875115	+	0.875115i	−0.143868	+	0.143868i	−0.775372	−	0.631504i	$-0.782438\pi$
$37$	−0.875115	+	0.875115i	−0.143868	+	0.143868i	0.631504	+	0.775372i	$0.282438\pi$
$38$	1.13826	−	1.13826i	0.184651	−	0.184651i
$39$		0			0
$40$	1.32001	+	1.80487i	0.208712	+	0.285376i
$41$			2.87124i			0.448413i	0.974542	+	0.224206i	$0.0719790\pi$
$41$			2.87124i			0.448413i	−0.974542	+	0.224206i	$0.928021\pi$
$42$		0			0
$43$	−2.09461	−	2.09461i	−0.319425	−	0.319425i	0.529121	−	0.848546i	$-0.322522\pi$
$43$	−2.09461	−	2.09461i	−0.319425	−	0.319425i	−0.848546	+	0.529121i	$0.822522\pi$
$44$	1.59083			0.239826
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−3.51413	−	3.51413i	−0.512588	−	0.512588i	0.402731	−	0.915319i	$-0.368061\pi$
$47$	−3.51413	−	3.51413i	−0.512588	−	0.512588i	−0.915319	+	0.402731i	$0.868061\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	2.29793	+	4.44066i	0.324977	+	0.628005i
$51$		0			0
$52$	2.64002	−	2.64002i	0.366105	−	0.366105i
$53$	3.23818	−	3.23818i	0.444798	−	0.444798i	−0.448823	−	0.893621i	$-0.648157\pi$
$53$	3.23818	−	3.23818i	0.444798	−	0.444798i	0.893621	+	0.448823i	$0.148157\pi$
$54$		0			0
$55$	3.51514	+	0.545414i	0.473981	+	0.0735436i
$56$			2.82843i			0.377964i
$57$		0			0
$58$	−4.64002	−	4.64002i	−0.609265	−	0.609265i
$59$	11.6669			1.51891			0.759453	−	0.650562i	$-0.225467\pi$
$59$	11.6669			1.51891			0.759453	+	0.650562i	$0.225467\pi$
$60$		0			0
$61$	−9.85952			−1.26238			−0.631191	−	0.775627i	$-0.717434\pi$
$61$	−9.85952			−1.26238			−0.631191	+	0.775627i	$0.717434\pi$
$62$	3.00504	+	3.00504i	0.381641	+	0.381641i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.73860	−	4.92834i	0.835820	−	0.611285i
$66$		0			0
$67$	4.79518	−	4.79518i	0.585825	−	0.585825i	−0.350673	−	0.936498i	$-0.614047\pi$
$67$	4.79518	−	4.79518i	0.585825	−	0.585825i	0.936498	+	0.350673i	$0.114047\pi$
$68$	1.41421	−	1.41421i	0.171499	−	0.171499i
$69$		0			0
$70$	−0.969724	+	6.24977i	−0.115904	+	0.746990i
$71$		−	8.32943i		−	0.988521i	−0.869314	−	0.494261i	$-0.835439\pi$
$71$		−	8.32943i		−	0.988521i	0.869314	−	0.494261i	$-0.164561\pi$
$72$		0			0
$73$	−2.03028	−	2.03028i	−0.237626	−	0.237626i	0.578241	−	0.815866i	$-0.303740\pi$
$73$	−2.03028	−	2.03028i	−0.237626	−	0.237626i	−0.815866	+	0.578241i	$0.803740\pi$
$74$	1.23760			0.143868
$75$		0			0
$76$	−1.60975			−0.184651
$77$	3.18166	+	3.18166i	0.362583	+	0.362583i
$78$		0			0
$79$		−	7.21949i		−	0.812257i	−0.913816	−	0.406128i	$-0.866879\pi$
$79$		−	7.21949i		−	0.812257i	0.913816	−	0.406128i	$-0.133121\pi$
$80$	0.342849	−	2.20963i	0.0383317	−	0.247044i
$81$		0			0
$82$	2.03028	−	2.03028i	0.224206	−	0.224206i
$83$	8.60538	−	8.60538i	0.944563	−	0.944563i	−0.0539792	−	0.998542i	$-0.517190\pi$
$83$	8.60538	−	8.60538i	0.944563	−	0.944563i	0.998542	+	0.0539792i	$0.0171905\pi$
$84$		0			0
$85$	3.60975	−	2.64002i	0.391532	−	0.286351i
$86$			2.96222i			0.319425i
$87$		0			0
$88$	−1.12489	−	1.12489i	−0.119913	−	0.119913i
$89$	16.8575			1.78689			0.893447	−	0.449169i	$-0.148280\pi$
$89$	16.8575			1.78689			0.893447	+	0.449169i	$0.148280\pi$
$90$		0			0
$91$	10.5601			1.10700
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$		0			0
$94$			4.96972i			0.512588i
$95$	−3.55694	−	0.551901i	−0.364935	−	0.0566238i
$96$		0			0
$97$	1.60975	−	1.60975i	0.163445	−	0.163445i	−0.620646	−	0.784091i	$-0.713130\pi$
$97$	1.60975	−	1.60975i	0.163445	−	0.163445i	0.784091	+	0.620646i	$0.213130\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	1.51514	−	4.76491i	0.151514	−	0.476491i
$101$		−	6.91521i		−	0.688089i	−0.938953	−	0.344045i	$-0.888203\pi$
$101$		−	6.91521i		−	0.688089i	0.938953	−	0.344045i	$-0.111797\pi$
$102$		0			0
$103$	4.31032	+	4.31032i	0.424709	+	0.424709i	0.886821	−	0.462113i	$-0.152908\pi$
$103$	4.31032	+	4.31032i	0.424709	+	0.424709i	−0.462113	+	0.886821i	$0.652908\pi$
$104$	−3.73356			−0.366105
$105$		0			0
$106$	−4.57947			−0.444798
$107$	−9.75734	−	9.75734i	−0.943278	−	0.943278i	0.0551976	−	0.998475i	$-0.482421\pi$
$107$	−9.75734	−	9.75734i	−0.943278	−	0.943278i	−0.998475	+	0.0551976i	$0.982421\pi$
$108$		0			0
$109$		−	14.9503i		−	1.43198i	−0.698109	−	0.715992i	$-0.745975\pi$
$109$		−	14.9503i		−	1.43198i	0.698109	−	0.715992i	$-0.254025\pi$
$110$	−2.09991	−	2.87124i	−0.200219	−	0.273762i
$111$		0			0
$112$	2.00000	−	2.00000i	0.188982	−	0.188982i
$113$	−0.0428169	+	0.0428169i	−0.00402787	+	0.00402787i	−0.709118	−	0.705090i	$-0.750907\pi$
$113$	−0.0428169	+	0.0428169i	−0.00402787	+	0.00402787i	0.705090	+	0.709118i	$0.250907\pi$
$114$		0			0
$115$	1.32001	+	1.80487i	0.123092	+	0.168305i
$116$			6.56198i			0.609265i
$117$		0			0
$118$	−8.24977	−	8.24977i	−0.759453	−	0.759453i
$119$	5.65685			0.518563
$120$		0			0
$121$	8.46927			0.769933
$122$	6.97173	+	6.97173i	0.631191	+	0.631191i
$123$		0			0
$124$		−	4.24977i		−	0.381641i
$125$	4.98154	−	10.0092i	0.445562	−	0.895251i
$126$		0			0
$127$	3.64002	−	3.64002i	0.323000	−	0.323000i	−0.526917	−	0.849917i	$-0.676652\pi$
$127$	3.64002	−	3.64002i	0.323000	−	0.323000i	0.849917	+	0.526917i	$0.176652\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−8.24977	−	1.28005i	−0.723553	−	0.112268i
$131$			11.7526i			1.02683i	0.858141	+	0.513413i	$0.171619\pi$
$131$			11.7526i			1.02683i	−0.858141	+	0.513413i	$0.828381\pi$
$132$		0			0
$133$	−3.21949	−	3.21949i	−0.279166	−	0.279166i
$134$	−6.78142			−0.585825
$135$		0			0
$136$	−2.00000			−0.171499
$137$	−9.34759	−	9.34759i	−0.798619	−	0.798619i	0.184259	−	0.982878i	$-0.441012\pi$
$137$	−9.34759	−	9.34759i	−0.798619	−	0.798619i	−0.982878	+	0.184259i	$0.941012\pi$
$138$		0			0
$139$			7.34060i			0.622621i	0.950308	+	0.311311i	$0.100768\pi$
$139$			7.34060i			0.622621i	−0.950308	+	0.311311i	$0.899232\pi$
$140$	5.10495	−	3.73356i	0.431447	−	0.315543i
$141$		0			0
$142$	−5.88979	+	5.88979i	−0.494261	+	0.494261i
$143$	−4.19982	+	4.19982i	−0.351207	+	0.351207i
$144$		0			0
$145$	−2.24977	+	14.4995i	−0.186833	+	1.20412i
$146$			2.87124i			0.237626i
$147$		0			0
$148$	−0.875115	−	0.875115i	−0.0719340	−	0.0719340i
$149$	17.1044			1.40124			0.700622	−	0.713533i	$-0.252906\pi$
$149$	17.1044			1.40124			0.700622	+	0.713533i	$0.252906\pi$
$150$		0			0
$151$	−15.5298			−1.26380			−0.631899	−	0.775050i	$-0.717724\pi$
$151$	−15.5298			−1.26380			−0.631899	+	0.775050i	$0.717724\pi$
$152$	1.13826	+	1.13826i	0.0923253	+	0.0923253i
$153$		0			0
$154$		−	4.49954i		−	0.362583i
$155$	1.45703	−	9.39041i	0.117032	−	0.754256i
$156$		0			0
$157$	−6.65470	+	6.65470i	−0.531103	+	0.531103i	−0.920901	−	0.389797i	$-0.872545\pi$
$157$	−6.65470	+	6.65470i	−0.531103	+	0.531103i	0.389797	+	0.920901i	$0.372545\pi$
$158$	−5.10495	+	5.10495i	−0.406128	+	0.406128i
$159$		0			0
$160$	−1.80487	+	1.32001i	−0.142688	+	0.104356i
$161$			2.82843i			0.222911i
$162$		0			0
$163$	1.21949	+	1.21949i	0.0955182	+	0.0955182i	0.753251	−	0.657733i	$-0.228484\pi$
$163$	1.21949	+	1.21949i	0.0955182	+	0.0955182i	−0.657733	+	0.753251i	$0.728484\pi$
$164$	−2.87124			−0.224206
$165$		0			0
$166$	−12.1698			−0.944563
$167$	−9.01513	−	9.01513i	−0.697611	−	0.697611i	0.266283	−	0.963895i	$-0.414204\pi$
$167$	−9.01513	−	9.01513i	−0.697611	−	0.697611i	−0.963895	+	0.266283i	$0.914204\pi$
$168$		0			0
$169$			0.939448i			0.0722652i
$170$	−4.41926	−	0.685698i	−0.338941	−	0.0525907i
$171$		0			0
$172$	2.09461	−	2.09461i	0.159712	−	0.159712i
$173$	0.396046	−	0.396046i	0.0301108	−	0.0301108i	−0.691891	−	0.722002i	$-0.743222\pi$
$173$	0.396046	−	0.396046i	0.0301108	−	0.0301108i	0.722002	+	0.691891i	$0.243222\pi$
$174$		0			0
$175$	12.5601	−	6.49954i	0.949454	−	0.491319i
$176$			1.59083i			0.119913i
$177$		0			0
$178$	−11.9201	−	11.9201i	−0.893447	−	0.893447i
$179$	−20.4198			−1.52625			−0.763124	−	0.646252i	$-0.776336\pi$
$179$	−20.4198			−1.52625			−0.763124	+	0.646252i	$0.776336\pi$
$180$		0			0
$181$	7.13957			0.530680			0.265340	−	0.964155i	$-0.414516\pi$
$181$	7.13957			0.530680			0.265340	+	0.964155i	$0.414516\pi$
$182$	−7.46711	−	7.46711i	−0.553499	−	0.553499i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−1.63365	−	2.23371i	−0.120108	−	0.164226i
$186$		0			0
$187$	−2.24977	+	2.24977i	−0.164520	+	0.164520i
$188$	3.51413	−	3.51413i	0.256294	−	0.256294i
$189$		0			0
$190$	2.12489	+	2.90539i	0.154155	+	0.210779i
$191$			11.6669i			0.844190i	0.906552	+	0.422095i	$0.138705\pi$
$191$			11.6669i			0.844190i	−0.906552	+	0.422095i	$0.861295\pi$
$192$		0			0
$193$	2.52982	+	2.52982i	0.182100	+	0.182100i	0.792270	−	0.610170i	$-0.208899\pi$
$193$	2.52982	+	2.52982i	0.182100	+	0.182100i	−0.610170	+	0.792270i	$0.708899\pi$
$194$	−2.27653			−0.163445
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.05290	+	6.05290i	0.431251	+	0.431251i	0.889054	−	0.457803i	$-0.151363\pi$
$197$	6.05290	+	6.05290i	0.431251	+	0.431251i	−0.457803	+	0.889054i	$0.651363\pi$
$198$		0			0
$199$		−	12.4995i		−	0.886069i	−0.896505	−	0.443035i	$-0.853902\pi$
$199$		−	12.4995i		−	0.886069i	0.896505	−	0.443035i	$-0.146098\pi$
$200$	−4.44066	+	2.29793i	−0.314002	+	0.162489i
$201$		0			0
$202$	−4.88979	+	4.88979i	−0.344045	+	0.344045i
$203$	−13.1240	+	13.1240i	−0.921122	+	0.921122i
$204$		0			0
$205$	−6.34438	−	0.984404i	−0.443111	−	0.0687537i
$206$		−	6.09572i		−	0.424709i
$207$		0			0
$208$	2.64002	+	2.64002i	0.183053	+	0.183053i
$209$	2.56083			0.177136
$210$		0			0
$211$	6.71995			0.462621			0.231310	−	0.972880i	$-0.425699\pi$
$211$	6.71995			0.462621			0.231310	+	0.972880i	$0.425699\pi$
$212$	3.23818	+	3.23818i	0.222399	+	0.222399i
$213$		0			0
$214$			13.7990i			0.943278i
$215$	5.34644	−	3.91017i	0.364624	−	0.266671i
$216$		0			0
$217$	8.49954	−	8.49954i	0.576986	−	0.576986i
$218$	−10.5715	+	10.5715i	−0.715992	+	0.715992i
$219$		0			0
$220$	−0.545414	+	3.51514i	−0.0367718	+	0.236991i
$221$			7.46711i			0.502292i
$222$		0			0
$223$	−12.6703	−	12.6703i	−0.848466	−	0.848466i	0.141476	−	0.989942i	$-0.454815\pi$
$223$	−12.6703	−	12.6703i	−0.848466	−	0.848466i	−0.989942	+	0.141476i	$0.954815\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	0.0605522			0.00402787
$227$	−14.0428	−	14.0428i	−0.932053	−	0.932053i	0.0657807	−	0.997834i	$-0.479046\pi$
$227$	−14.0428	−	14.0428i	−0.932053	−	0.932053i	−0.997834	+	0.0657807i	$0.979046\pi$
$228$		0			0
$229$		−	9.07901i		−	0.599958i	−0.953946	−	0.299979i	$-0.903020\pi$
$229$		−	9.07901i		−	0.599958i	0.953946	−	0.299979i	$-0.0969797\pi$
$230$	0.342849	−	2.20963i	0.0226068	−	0.145699i
$231$		0			0
$232$	4.64002	−	4.64002i	0.304632	−	0.304632i
$233$	−9.52421	+	9.52421i	−0.623952	+	0.623952i	−0.946540	−	0.322588i	$-0.895447\pi$
$233$	−9.52421	+	9.52421i	−0.623952	+	0.623952i	0.322588	+	0.946540i	$0.395447\pi$
$234$		0			0
$235$	8.96972	−	6.56009i	0.585120	−	0.427933i
$236$			11.6669i			0.759453i
$237$		0			0
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	−27.1102			−1.75362			−0.876808	−	0.480840i	$-0.840332\pi$
$239$	−27.1102			−1.75362			−0.876808	+	0.480840i	$0.840332\pi$
$240$		0			0
$241$	25.8401			1.66451			0.832255	−	0.554393i	$-0.187050\pi$
$241$	25.8401			1.66451			0.832255	+	0.554393i	$0.187050\pi$
$242$	−5.98868	−	5.98868i	−0.384967	−	0.384967i
$243$		0			0
$244$		−	9.85952i		−	0.631191i
$245$	2.20963	+	0.342849i	0.141168	+	0.0219038i
$246$		0			0
$247$	4.24977	−	4.24977i	0.270406	−	0.270406i
$248$	−3.00504	+	3.00504i	−0.190820	+	0.190820i
$249$		0			0
$250$	−10.6001	+	3.55510i	−0.670407	+	0.224844i
$251$		−	9.05794i		−	0.571732i	−0.958270	−	0.285866i	$-0.907719\pi$
$251$		−	9.05794i		−	0.571732i	0.958270	−	0.285866i	$-0.0922813\pi$
$252$		0			0
$253$	−1.12489	−	1.12489i	−0.0707209	−	0.0707209i
$254$	−5.14777			−0.323000
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.353229	+	0.353229i	0.0220338	+	0.0220338i	0.718038	−	0.696004i	$-0.245040\pi$
$257$	0.353229	+	0.353229i	0.0220338	+	0.0220338i	−0.696004	+	0.718038i	$0.745040\pi$
$258$		0			0
$259$		−	3.50046i		−	0.217508i
$260$	4.92834	+	6.73860i	0.305643	+	0.417910i
$261$		0			0
$262$	8.31032	−	8.31032i	0.513413	−	0.513413i
$263$	−3.64792	+	3.64792i	−0.224941	+	0.224941i	−0.810575	−	0.585635i	$-0.800845\pi$
$263$	−3.64792	+	3.64792i	−0.224941	+	0.224941i	0.585635	+	0.810575i	$0.300845\pi$
$264$		0			0
$265$	6.04496	+	8.26537i	0.371339	+	0.507737i
$266$			4.55305i			0.279166i
$267$		0			0
$268$	4.79518	+	4.79518i	0.292913	+	0.292913i
$269$	24.1534			1.47266			0.736329	−	0.676624i	$-0.236558\pi$
$269$	24.1534			1.47266			0.736329	+	0.676624i	$0.236558\pi$
$270$		0			0
$271$	−14.4390			−0.877106			−0.438553	−	0.898705i	$-0.644509\pi$
$271$	−14.4390			−0.877106			−0.438553	+	0.898705i	$0.644509\pi$
$272$	1.41421	+	1.41421i	0.0857493	+	0.0857493i
$273$		0			0
$274$			13.2195i			0.798619i
$275$	−2.41032	+	7.58015i	−0.145348	+	0.457100i
$276$		0			0
$277$	−8.82924	+	8.82924i	−0.530498	+	0.530498i	−0.920720	−	0.390223i	$-0.872398\pi$
$277$	−8.82924	+	8.82924i	−0.530498	+	0.530498i	0.390223	+	0.920720i	$0.372398\pi$
$278$	5.19059	−	5.19059i	0.311311	−	0.311311i
$279$		0			0
$280$	−6.24977	−	0.969724i	−0.373495	−	0.0579521i
$281$			15.7537i			0.939788i	0.882723	+	0.469894i	$0.155708\pi$
$281$			15.7537i			0.939788i	−0.882723	+	0.469894i	$0.844292\pi$
$282$		0			0
$283$	−6.73463	−	6.73463i	−0.400332	−	0.400332i	0.478018	−	0.878350i	$-0.341355\pi$
$283$	−6.73463	−	6.73463i	−0.400332	−	0.400332i	−0.878350	+	0.478018i	$0.841355\pi$
$284$	8.32943			0.494261
$285$		0			0
$286$	5.93945			0.351207
$287$	−5.74249	−	5.74249i	−0.338968	−	0.338968i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$	11.8436	−	8.66190i	0.695477	−	0.508644i
$291$		0			0
$292$	2.03028	−	2.03028i	0.118813	−	0.118813i
$293$	4.36274	−	4.36274i	0.254874	−	0.254874i	−0.568092	−	0.822965i	$-0.692318\pi$
$293$	4.36274	−	4.36274i	0.254874	−	0.254874i	0.822965	+	0.568092i	$0.192318\pi$
$294$		0			0
$295$	−4.00000	+	25.7796i	−0.232889	+	1.50095i
$296$			1.23760i			0.0719340i
$297$		0			0
$298$	−12.0946	−	12.0946i	−0.700622	−	0.700622i
$299$	−3.73356			−0.215917
$300$		0			0
$301$	8.37844			0.482925
$302$	10.9812	+	10.9812i	0.631899	+	0.631899i
$303$		0			0
$304$		−	1.60975i		−	0.0923253i
$305$	3.38033	−	21.7859i	0.193557	−	1.24745i
$306$		0			0
$307$	−13.2800	+	13.2800i	−0.757932	+	0.757932i	−0.975946	−	0.218013i	$-0.930042\pi$
$307$	−13.2800	+	13.2800i	−0.757932	+	0.757932i	0.218013	+	0.975946i	$0.430042\pi$
$308$	−3.18166	+	3.18166i	−0.181292	+	0.181292i
$309$		0			0
$310$	−7.67030	+	5.60975i	−0.435644	+	0.318612i
$311$		−	8.06183i		−	0.457145i	−0.973527	−	0.228572i	$-0.926594\pi$
$311$		−	8.06183i		−	0.457145i	0.973527	−	0.228572i	$-0.0734057\pi$
$312$		0			0
$313$	−4.88979	−	4.88979i	−0.276388	−	0.276388i	0.555278	−	0.831665i	$-0.312612\pi$
$313$	−4.88979	−	4.88979i	−0.276388	−	0.276388i	−0.831665	+	0.555278i	$0.812612\pi$
$314$	9.41117			0.531103
$315$		0			0
$316$	7.21949			0.406128
$317$	−21.4534	−	21.4534i	−1.20494	−	1.20494i	−0.972645	−	0.232298i	$-0.925376\pi$
$317$	−21.4534	−	21.4534i	−1.20494	−	1.20494i	−0.232298	−	0.972645i	$-0.574624\pi$
$318$		0			0
$319$		−	10.4390i		−	0.584471i
$320$	2.20963	+	0.342849i	0.123522	+	0.0191659i
$321$		0			0
$322$	2.00000	−	2.00000i	0.111456	−	0.111456i
$323$	2.27653	−	2.27653i	0.126669	−	0.126669i
$324$		0			0
$325$	8.57947	+	16.5795i	0.475903	+	0.919664i
$326$		−	1.72463i		−	0.0955182i
$327$		0			0
$328$	2.03028	+	2.03028i	0.112103	+	0.112103i
$329$	14.0565			0.774960
$330$		0			0
$331$	4.78051			0.262760			0.131380	−	0.991332i	$-0.458059\pi$
$331$	4.78051			0.262760			0.131380	+	0.991332i	$0.458059\pi$
$332$	8.60538	+	8.60538i	0.472281	+	0.472281i
$333$		0			0
$334$			12.7493i			0.697611i
$335$	8.95155	+	12.2396i	0.489075	+	0.668721i
$336$		0			0
$337$	6.57947	−	6.57947i	0.358407	−	0.358407i	−0.504819	−	0.863225i	$-0.668441\pi$
$337$	6.57947	−	6.57947i	0.358407	−	0.358407i	0.863225	+	0.504819i	$0.168441\pi$
$338$	0.664290	−	0.664290i	0.0361326	−	0.0361326i
$339$		0			0
$340$	2.64002	+	3.60975i	0.143175	+	0.195766i
$341$			6.76066i			0.366110i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−2.96222			−0.159712
$345$		0			0
$346$	−0.560094			−0.0301108
$347$	−9.39041	−	9.39041i	−0.504104	−	0.504104i	0.408607	−	0.912711i	$-0.366015\pi$
$347$	−9.39041	−	9.39041i	−0.504104	−	0.504104i	−0.912711	+	0.408607i	$0.866015\pi$
$348$		0			0
$349$			22.9991i			1.23111i	0.788093	+	0.615556i	$0.211069\pi$
$349$			22.9991i			1.23111i	−0.788093	+	0.615556i	$0.788931\pi$
$350$	−13.4772	−	4.28546i	−0.720387	−	0.229067i
$351$		0			0
$352$	1.12489	−	1.12489i	0.0599566	−	0.0599566i
$353$	−0.728515	+	0.728515i	−0.0387750	+	0.0387750i	−0.726228	−	0.687453i	$-0.758729\pi$
$353$	−0.728515	+	0.728515i	−0.0387750	+	0.0387750i	0.687453	+	0.726228i	$0.258729\pi$
$354$		0			0
$355$	18.4049	+	2.85574i	0.976832	+	0.151567i
$356$			16.8575i			0.893447i
$357$		0			0
$358$	14.4390	+	14.4390i	0.763124	+	0.763124i
$359$	−11.6669			−0.615757			−0.307879	−	0.951426i	$-0.599619\pi$
$359$	−11.6669			−0.615757			−0.307879	+	0.951426i	$0.599619\pi$
$360$		0			0
$361$	16.4087			0.863616
$362$	−5.04843	−	5.04843i	−0.265340	−	0.265340i
$363$		0			0
$364$			10.5601i			0.553499i
$365$	5.18223	−	3.79008i	0.271250	−	0.198382i
$366$		0			0
$367$	20.4390	−	20.4390i	1.06691	−	1.06691i	0.0693115	−	0.997595i	$-0.477920\pi$
$367$	20.4390	−	20.4390i	1.06691	−	1.06691i	0.997595	−	0.0693115i	$-0.0220802\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	−0.424310	+	2.73463i	−0.0220588	+	0.142167i
$371$			12.9527i			0.672471i
$372$		0			0
$373$	−1.34530	−	1.34530i	−0.0696568	−	0.0696568i	0.671420	−	0.741077i	$-0.265685\pi$
$373$	−1.34530	−	1.34530i	−0.0696568	−	0.0696568i	−0.741077	+	0.671420i	$0.765685\pi$
$374$	3.18166			0.164520
$375$		0			0
$376$	−4.96972			−0.256294
$377$	−17.3238	−	17.3238i	−0.892221	−	0.892221i
$378$		0			0
$379$			8.35906i			0.429376i	0.976683	+	0.214688i	$0.0688735\pi$
$379$			8.35906i			0.429376i	−0.976683	+	0.214688i	$0.931127\pi$
$380$	0.551901	−	3.55694i	0.0283119	−	0.182467i
$381$		0			0
$382$	8.24977	−	8.24977i	0.422095	−	0.422095i
$383$	−11.1150	+	11.1150i	−0.567952	+	0.567952i	−0.931554	−	0.363602i	$-0.881547\pi$
$383$	−11.1150	+	11.1150i	−0.567952	+	0.567952i	0.363602	+	0.931554i	$0.381547\pi$
$384$		0			0
$385$	−8.12110	+	5.93945i	−0.413890	+	0.302702i
$386$		−	3.57770i		−	0.182100i
$387$		0			0
$388$	1.60975	+	1.60975i	0.0817225	+	0.0817225i
$389$	−15.1811			−0.769710			−0.384855	−	0.922977i	$-0.625749\pi$
$389$	−15.1811			−0.769710			−0.384855	+	0.922977i	$0.625749\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	8.56009i		−	0.431251i
$395$	15.9524	+	2.47520i	0.802652	+	0.124541i
$396$		0			0
$397$	−22.4802	+	22.4802i	−1.12825	+	1.12825i	−0.137785	+	0.990462i	$0.543998\pi$
$397$	−22.4802	+	22.4802i	−1.12825	+	1.12825i	−0.990462	+	0.137785i	$0.956002\pi$
$398$	−8.83851	+	8.83851i	−0.443035	+	0.443035i
$399$		0			0
$400$	4.76491	+	1.51514i	0.238245	+	0.0757569i
$401$		−	21.8494i		−	1.09111i	−0.838075	−	0.545555i	$-0.816319\pi$
$401$		−	21.8494i		−	1.09111i	0.838075	−	0.545555i	$-0.183681\pi$
$402$		0			0
$403$	11.2195	+	11.2195i	0.558883	+	0.558883i
$404$	6.91521			0.344045
$405$		0			0
$406$	18.5601			0.921122
$407$	1.39216	+	1.39216i	0.0690067	+	0.0690067i
$408$		0			0
$409$			15.1202i			0.747645i	0.927500	+	0.373823i	$0.121953\pi$
$409$			15.1202i			0.747645i	−0.927500	+	0.373823i	$0.878047\pi$
$410$	3.79008	+	5.18223i	0.187178	+	0.255932i
$411$		0			0
$412$	−4.31032	+	4.31032i	−0.212354	+	0.212354i
$413$	−23.3339	+	23.3339i	−1.14818	+	1.14818i
$414$		0			0
$415$	16.0643	+	21.9650i	0.788567	+	1.07822i
$416$		−	3.73356i		−	0.183053i
$417$		0			0
$418$	−1.81078	−	1.81078i	−0.0885682	−	0.0885682i
$419$	24.4584			1.19487			0.597436	−	0.801916i	$-0.296186\pi$
$419$	24.4584			1.19487			0.597436	+	0.801916i	$0.296186\pi$
$420$		0			0
$421$	−23.4499			−1.14288			−0.571439	−	0.820645i	$-0.693615\pi$
$421$	−23.4499			−1.14288			−0.571439	+	0.820645i	$0.693615\pi$
$422$	−4.75172	−	4.75172i	−0.231310	−	0.231310i
$423$		0			0
$424$		−	4.57947i		−	0.222399i
$425$	4.59587	+	8.88133i	0.222932	+	0.430808i
$426$		0			0
$427$	19.7190	−	19.7190i	0.954271	−	0.954271i
$428$	9.75734	−	9.75734i	0.471639	−	0.471639i
$429$		0			0
$430$	−6.54541	−	1.01560i	−0.315648	−	0.0489764i
$431$		−	7.82034i		−	0.376693i	−0.982103	−	0.188346i	$-0.939687\pi$
$431$		−	7.82034i		−	0.376693i	0.982103	−	0.188346i	$-0.0603127\pi$
$432$		0			0
$433$	26.8898	+	26.8898i	1.29224	+	1.29224i	0.933398	+	0.358843i	$0.116829\pi$
$433$	26.8898	+	26.8898i	1.29224	+	1.29224i	0.358843	+	0.933398i	$0.383171\pi$
$434$	−12.0202			−0.576986
$435$		0			0
$436$	14.9503			0.715992
$437$	1.13826	+	1.13826i	0.0544505	+	0.0544505i
$438$		0			0
$439$			21.2195i			1.01275i	0.862313	+	0.506376i	$0.169015\pi$
$439$			21.2195i			1.01275i	−0.862313	+	0.506376i	$0.830985\pi$
$440$	2.87124	−	2.09991i	0.136881	−	0.100109i
$441$		0			0
$442$	5.28005	−	5.28005i	0.251146	−	0.251146i
$443$	20.3924	−	20.3924i	0.968873	−	0.968873i	−0.0306573	−	0.999530i	$-0.509760\pi$
$443$	20.3924	−	20.3924i	0.968873	−	0.968873i	0.999530	+	0.0306573i	$0.00976004\pi$
$444$		0			0
$445$	−5.77959	+	37.2489i	−0.273979	+	1.76577i
$446$			17.9185i			0.848466i
$447$		0			0
$448$	2.00000	+	2.00000i	0.0944911	+	0.0944911i
$449$	−4.86347			−0.229521			−0.114761	−	0.993393i	$-0.536610\pi$
$449$	−4.86347			−0.229521			−0.114761	+	0.993393i	$0.536610\pi$
$450$		0			0
$451$	4.56766			0.215083
$452$	−0.0428169	−	0.0428169i	−0.00201394	−	0.00201394i
$453$		0			0
$454$			19.8595i			0.932053i
$455$	−3.62052	+	23.3339i	−0.169733	+	1.09391i
$456$		0			0
$457$	20.9503	−	20.9503i	0.980016	−	0.980016i	−0.0197883	−	0.999804i	$-0.506299\pi$
$457$	20.9503	−	20.9503i	0.980016	−	0.980016i	0.999804	+	0.0197883i	$0.00629923\pi$
$458$	−6.41983	+	6.41983i	−0.299979	+	0.299979i
$459$		0			0
$460$	−1.80487	+	1.32001i	−0.0841527	+	0.0615459i
$461$			2.00893i			0.0935652i	0.998905	+	0.0467826i	$0.0148968\pi$
$461$			2.00893i			0.0935652i	−0.998905	+	0.0467826i	$0.985103\pi$
$462$		0			0
$463$	−3.39025	−	3.39025i	−0.157558	−	0.157558i	0.623925	−	0.781484i	$-0.285537\pi$
$463$	−3.39025	−	3.39025i	−0.157558	−	0.157558i	−0.781484	+	0.623925i	$0.785537\pi$
$464$	−6.56198			−0.304632
$465$		0			0
$466$	13.4693			0.623952
$467$	5.22505	+	5.22505i	0.241786	+	0.241786i	0.817589	−	0.575802i	$-0.195310\pi$
$467$	5.22505	+	5.22505i	0.241786	+	0.241786i	−0.575802	+	0.817589i	$0.695310\pi$
$468$		0			0
$469$			19.1807i			0.885684i
$470$	−10.9812	−	1.70387i	−0.506527	−	0.0785935i
$471$		0			0
$472$	8.24977	−	8.24977i	0.379726	−	0.379726i
$473$	−3.33216	+	3.33216i	−0.153213	+	0.153213i
$474$		0			0
$475$	2.43899	−	7.67030i	0.111909	−	0.351937i
$476$			5.65685i			0.259281i
$477$		0			0
$478$	19.1698	+	19.1698i	0.876808	+	0.876808i
$479$	−19.4873			−0.890397			−0.445198	−	0.895432i	$-0.646867\pi$
$479$	−19.4873			−0.890397			−0.445198	+	0.895432i	$0.646867\pi$
$480$		0			0
$481$	4.62065			0.210683
$482$	−18.2717	−	18.2717i	−0.832255	−	0.832255i
$483$		0			0
$484$			8.46927i			0.384967i
$485$	3.00504	+	4.10884i	0.136452	+	0.186573i
$486$		0			0
$487$	−22.0790	+	22.0790i	−1.00050	+	1.00050i	−0.000495701		1.00000i	$0.500158\pi$
$487$	−22.0790	+	22.0790i	−1.00050	+	1.00050i	−1.00000		0.000495701i	$0.999842\pi$
$488$	−6.97173	+	6.97173i	−0.315595	+	0.315595i
$489$		0			0
$490$	−1.32001	−	1.80487i	−0.0596321	−	0.0815359i
$491$			11.9345i			0.538598i	0.963057	+	0.269299i	$0.0867920\pi$
$491$			11.9345i			0.538598i	−0.963057	+	0.269299i	$0.913208\pi$
$492$		0			0
$493$	−9.28005	−	9.28005i	−0.417952	−	0.417952i
$494$	−6.01008			−0.270406
$495$		0			0
$496$	4.24977			0.190820
$497$	16.6589	+	16.6589i	0.747252	+	0.747252i
$498$		0			0
$499$			15.5005i			0.693896i	0.937884	+	0.346948i	$0.112782\pi$
$499$			15.5005i			0.693896i	−0.937884	+	0.346948i	$0.887218\pi$
$500$	10.0092	+	4.98154i	0.447626	+	0.222781i
$501$		0			0
$502$	−6.40493	+	6.40493i	−0.285866	+	0.285866i
$503$	3.81919	−	3.81919i	0.170289	−	0.170289i	−0.616817	−	0.787106i	$-0.711578\pi$
$503$	3.81919	−	3.81919i	0.170289	−	0.170289i	0.787106	+	0.616817i	$0.211578\pi$
$504$		0			0
$505$	15.2800	+	2.37088i	0.679953	+	0.105503i
$506$			1.59083i			0.0707209i
$507$		0			0
$508$	3.64002	+	3.64002i	0.161500	+	0.161500i
$509$	8.59832			0.381114			0.190557	−	0.981676i	$-0.438971\pi$
$509$	8.59832			0.381114			0.190557	+	0.981676i	$0.438971\pi$
$510$		0			0
$511$	8.12110			0.359257
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	0.499542i		−	0.0220338i
$515$	−11.0020	+	8.04642i	−0.484806	+	0.354568i
$516$		0			0
$517$	−5.59037	+	5.59037i	−0.245864	+	0.245864i
$518$	−2.47520	+	2.47520i	−0.108754	+	0.108754i
$519$		0			0
$520$	1.28005	−	8.24977i	0.0561338	−	0.361776i
$521$			6.29439i			0.275762i	0.990449	+	0.137881i	$0.0440292\pi$
$521$			6.29439i			0.275762i	−0.990449	+	0.137881i	$0.955971\pi$
$522$		0			0
$523$	−11.6850	−	11.6850i	−0.510948	−	0.510948i	0.403869	−	0.914817i	$-0.367665\pi$
$523$	−11.6850	−	11.6850i	−0.510948	−	0.510948i	−0.914817	+	0.403869i	$0.867665\pi$
$524$	−11.7526			−0.513413
$525$		0			0
$526$	5.15894			0.224941
$527$	6.01008	+	6.01008i	0.261803	+	0.261803i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	1.57007	−	10.1189i	0.0681994	−	0.439538i
$531$		0			0
$532$	3.21949	−	3.21949i	0.139583	−	0.139583i
$533$	7.58015	−	7.58015i	0.328333	−	0.328333i
$534$		0			0
$535$	24.9054	−	18.2148i	1.07675	−	0.787494i
$536$		−	6.78142i		−	0.292913i
$537$		0			0
$538$	−17.0790	−	17.0790i	−0.736329	−	0.736329i
$539$	−1.59083			−0.0685218
$540$		0			0
$541$	−27.1202			−1.16599			−0.582994	−	0.812476i	$-0.698119\pi$
$541$	−27.1202			−1.16599			−0.582994	+	0.812476i	$0.698119\pi$
$542$	10.2099	+	10.2099i	0.438553	+	0.438553i
$543$		0			0
$544$		−	2.00000i		−	0.0857493i
$545$	33.0347	+	5.12571i	1.41505	+	0.219561i
$546$		0			0
$547$	−2.18922	+	2.18922i	−0.0936042	+	0.0936042i	−0.752358	−	0.658754i	$-0.771084\pi$
$547$	−2.18922	+	2.18922i	−0.0936042	+	0.0936042i	0.658754	+	0.752358i	$0.271084\pi$
$548$	9.34759	−	9.34759i	0.399309	−	0.399309i
$549$		0			0
$550$	7.06433	−	3.65562i	0.301224	−	0.155876i
$551$			10.5631i			0.450005i
$552$		0			0
$553$	14.4390	+	14.4390i	0.614008	+	0.614008i
$554$	12.4864			0.530498
$555$		0			0
$556$	−7.34060			−0.311311
$557$	−25.1525	−	25.1525i	−1.06575	−	1.06575i	−0.997681	−	0.0680643i	$-0.978318\pi$
$557$	−25.1525	−	25.1525i	−1.06575	−	1.06575i	−0.0680643	−	0.997681i	$-0.521682\pi$
$558$		0			0
$559$			11.0596i			0.467773i
$560$	3.73356	+	5.10495i	0.157772	+	0.215724i
$561$		0			0
$562$	11.1396	−	11.1396i	0.469894	−	0.469894i
$563$	−3.58606	+	3.58606i	−0.151134	+	0.151134i	−0.778624	−	0.627490i	$-0.784082\pi$
$563$	−3.58606	+	3.58606i	−0.151134	+	0.151134i	0.627490	+	0.778624i	$0.284082\pi$
$564$		0			0
$565$	−0.0799296	−	0.109289i	−0.00336266	−	0.00459782i
$566$			9.52421i			0.400332i
$567$		0			0
$568$	−5.88979	−	5.88979i	−0.247130	−	0.247130i
$569$	21.1430			0.886360			0.443180	−	0.896433i	$-0.353850\pi$
$569$	21.1430			0.886360			0.443180	+	0.896433i	$0.353850\pi$
$570$		0			0
$571$	−20.1405			−0.842853			−0.421426	−	0.906863i	$-0.638470\pi$
$571$	−20.1405			−0.842853			−0.421426	+	0.906863i	$0.638470\pi$
$572$	−4.19982	−	4.19982i	−0.175603	−	0.175603i
$573$		0			0
$574$			8.12110i			0.338968i
$575$	−4.44066	+	2.29793i	−0.185188	+	0.0958305i
$576$		0			0
$577$	−5.62065	+	5.62065i	−0.233991	+	0.233991i	−0.814356	−	0.580366i	$-0.802910\pi$
$577$	−5.62065	+	5.62065i	−0.233991	+	0.233991i	0.580366	+	0.814356i	$0.302910\pi$
$578$	−9.19239	+	9.19239i	−0.382353	+	0.382353i
$579$		0			0
$580$	−14.4995	−	2.24977i	−0.602061	−	0.0934166i
$581$			34.4215i			1.42804i
$582$		0			0
$583$	−5.15138	−	5.15138i	−0.213348	−	0.213348i
$584$	−2.87124			−0.118813
$585$		0			0
$586$	−6.16984			−0.254874
$587$	−5.65685	−	5.65685i	−0.233483	−	0.233483i	0.580662	−	0.814145i	$-0.302794\pi$
$587$	−5.65685	−	5.65685i	−0.233483	−	0.233483i	−0.814145	+	0.580662i	$0.802794\pi$
$588$		0			0
$589$		−	6.84106i		−	0.281881i
$590$	21.0573	−	15.4005i	0.866917	−	0.634028i
$591$		0			0
$592$	0.875115	−	0.875115i	0.0359670	−	0.0359670i
$593$	−6.01008	+	6.01008i	−0.246805	+	0.246805i	−0.819658	−	0.572853i	$-0.805836\pi$
$593$	−6.01008	+	6.01008i	−0.246805	+	0.246805i	0.572853	+	0.819658i	$0.305836\pi$
$594$		0			0
$595$	−1.93945	+	12.4995i	−0.0795096	+	0.512431i
$596$			17.1044i			0.700622i
$597$		0			0
$598$	2.64002	+	2.64002i	0.107959	+	0.107959i
$599$	43.5978			1.78136			0.890680	−	0.454631i	$-0.150229\pi$
$599$	43.5978			1.78136			0.890680	+	0.454631i	$0.150229\pi$
$600$		0			0
$601$	−21.4693			−0.875750			−0.437875	−	0.899036i	$-0.644269\pi$
$601$	−21.4693			−0.875750			−0.437875	+	0.899036i	$0.644269\pi$
$602$	−5.92445	−	5.92445i	−0.241463	−	0.241463i
$603$		0			0
$604$		−	15.5298i		−	0.631899i
$605$	−2.90368	+	18.7139i	−0.118051	+	0.760829i
$606$		0			0
$607$	18.8595	−	18.8595i	0.765484	−	0.765484i	−0.211824	−	0.977308i	$-0.567940\pi$
$607$	18.8595	−	18.8595i	0.765484	−	0.765484i	0.977308	+	0.211824i	$0.0679403\pi$
$608$	−1.13826	+	1.13826i	−0.0461627	+	0.0461627i
$609$		0			0
$610$	−17.7952	+	13.0147i	−0.720506	+	0.526949i
$611$			18.5547i			0.750645i
$612$		0			0
$613$	30.9239	+	30.9239i	1.24900	+	1.24900i	0.956161	+	0.292842i	$0.0946009\pi$
$613$	30.9239	+	30.9239i	1.24900	+	1.24900i	0.292842	+	0.956161i	$0.405399\pi$
$614$	18.7808			0.757932
$615$		0			0
$616$	4.49954			0.181292
$617$	6.60480	+	6.60480i	0.265899	+	0.265899i	0.827445	−	0.561546i	$-0.189793\pi$
$617$	6.60480	+	6.60480i	0.265899	+	0.265899i	−0.561546	+	0.827445i	$0.689793\pi$
$618$		0			0
$619$		−	39.7290i		−	1.59684i	−0.602098	−	0.798422i	$-0.705668\pi$
$619$		−	39.7290i		−	1.59684i	0.602098	−	0.798422i	$-0.294332\pi$
$620$	9.39041	+	1.45703i	0.377128	+	0.0585158i
$621$		0			0
$622$	−5.70058	+	5.70058i	−0.228572	+	0.228572i
$623$	−33.7151	+	33.7151i	−1.35076	+	1.35076i
$624$		0			0
$625$	20.4087	+	14.4390i	0.816349	+	0.577560i
$626$			6.91521i			0.276388i
$627$		0			0
$628$	−6.65470	−	6.65470i	−0.265552	−	0.265552i
$629$	2.47520			0.0986926
$630$		0			0
$631$	3.05964			0.121802			0.0609011	−	0.998144i	$-0.480603\pi$
$631$	3.05964			0.121802			0.0609011	+	0.998144i	$0.480603\pi$
$632$	−5.10495	−	5.10495i	−0.203064	−	0.203064i
$633$		0			0
$634$			30.3397i			1.20494i
$635$	6.79512	+	9.29108i	0.269656	+	0.368705i
$636$		0			0
$637$	−2.64002	+	2.64002i	−0.104602	+	0.104602i
$638$	−7.38148	+	7.38148i	−0.292236	+	0.292236i
$639$		0			0
$640$	−1.32001	−	1.80487i	−0.0521780	−	0.0713439i
$641$		−	31.0412i		−	1.22605i	−0.790062	−	0.613026i	$-0.789952\pi$
$641$		−	31.0412i		−	1.22605i	0.790062	−	0.613026i	$-0.210048\pi$
$642$		0			0
$643$	0.916289	+	0.916289i	0.0361349	+	0.0361349i	0.724943	−	0.688808i	$-0.241866\pi$
$643$	0.916289	+	0.916289i	0.0361349	+	0.0361349i	−0.688808	+	0.724943i	$0.741866\pi$
$644$	−2.82843			−0.111456
$645$		0			0
$646$	−3.21949			−0.126669
$647$	−32.1022	−	32.1022i	−1.26207	−	1.26207i	−0.950090	−	0.311977i	$-0.899009\pi$
$647$	−32.1022	−	32.1022i	−1.26207	−	1.26207i	−0.311977	−	0.950090i	$-0.600991\pi$
$648$		0			0
$649$		−	18.5601i		−	0.728547i
$650$	5.65685	−	17.7901i	0.221880	−	0.697784i
$651$		0			0
$652$	−1.21949	+	1.21949i	−0.0477591	+	0.0477591i
$653$	19.1769	−	19.1769i	0.750449	−	0.750449i	−0.224114	−	0.974563i	$-0.571949\pi$
$653$	19.1769	−	19.1769i	0.750449	−	0.750449i	0.974563	+	0.224114i	$0.0719488\pi$
$654$		0			0
$655$	−25.9688	−	4.02936i	−1.01469	−	0.157440i
$656$		−	2.87124i		−	0.112103i
$657$		0			0
$658$	−9.93945	−	9.93945i	−0.387480	−	0.387480i
$659$	5.90369			0.229975			0.114988	−	0.993367i	$-0.463317\pi$
$659$	5.90369			0.229975			0.114988	+	0.993367i	$0.463317\pi$
$660$		0			0
$661$	−38.5483			−1.49935			−0.749677	−	0.661804i	$-0.769791\pi$
$661$	−38.5483			−1.49935			−0.749677	+	0.661804i	$0.769791\pi$
$662$	−3.38033	−	3.38033i	−0.131380	−	0.131380i
$663$		0			0
$664$		−	12.1698i		−	0.472281i
$665$	8.21769	−	6.01008i	0.318668	−	0.233061i
$666$		0			0
$667$	4.64002	−	4.64002i	0.179662	−	0.179662i
$668$	9.01513	−	9.01513i	0.348806	−	0.348806i
$669$		0			0
$670$	2.32500	−	14.9844i	0.0898227	−	0.578898i
$671$			15.6848i			0.605505i
$672$		0			0
$673$	16.0596	+	16.0596i	0.619053	+	0.619053i	0.945289	−	0.326235i	$-0.105780\pi$
$673$	16.0596	+	16.0596i	0.619053	+	0.619053i	−0.326235	+	0.945289i	$0.605780\pi$
$674$	−9.30478			−0.358407
$675$		0			0
$676$	−0.939448			−0.0361326
$677$	21.7722	+	21.7722i	0.836772	+	0.836772i	0.988433	−	0.151660i	$-0.0484620\pi$
$677$	21.7722	+	21.7722i	0.836772	+	0.836772i	−0.151660	+	0.988433i	$0.548462\pi$
$678$		0			0
$679$			6.43899i			0.247106i
$680$	0.685698	−	4.41926i	0.0262953	−	0.169471i
$681$		0			0
$682$	4.78051	−	4.78051i	0.183055	−	0.183055i
$683$	10.2099	−	10.2099i	0.390671	−	0.390671i	−0.484255	−	0.874927i	$-0.660909\pi$
$683$	10.2099	−	10.2099i	0.390671	−	0.390671i	0.874927	+	0.484255i	$0.160909\pi$
$684$		0			0
$685$	23.8595	−	17.4499i	0.911625	−	0.666726i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	2.09461	+	2.09461i	0.0798562	+	0.0798562i
$689$	−17.0977			−0.651371
$690$		0			0
$691$	−29.1202			−1.10778			−0.553892	−	0.832588i	$-0.686858\pi$
$691$	−29.1202			−1.10778			−0.553892	+	0.832588i	$0.686858\pi$
$692$	0.396046	+	0.396046i	0.0150554	+	0.0150554i
$693$		0			0
$694$			13.2800i			0.504104i
$695$	−16.2200	−	2.51672i	−0.615259	−	0.0954646i
$696$		0			0
$697$	4.06055	−	4.06055i	0.153804	−	0.153804i
$698$	16.2628	−	16.2628i	0.615556	−	0.615556i
$699$		0			0
$700$	6.49954	+	12.5601i	0.245660	+	0.474727i
$701$			26.8206i			1.01300i	0.862240	+	0.506500i	$0.169061\pi$
$701$			26.8206i			1.01300i	−0.862240	+	0.506500i	$0.830939\pi$
$702$		0			0
$703$	−1.40871	−	1.40871i	−0.0531306	−	0.0531306i
$704$	−1.59083			−0.0599566
$705$		0			0
$706$	1.03028			0.0387750
$707$	13.8304	+	13.8304i	0.520147	+	0.520147i
$708$		0			0
$709$		−	49.2001i		−	1.84775i	−0.382695	−	0.923875i	$-0.625004\pi$
$709$		−	49.2001i		−	1.84775i	0.382695	−	0.923875i	$-0.374996\pi$
$710$	−10.9949	−	15.0336i	−0.412633	−	0.564200i
$711$		0			0
$712$	11.9201	−	11.9201i	0.446724	−	0.446724i
$713$	−3.00504	+	3.00504i	−0.112540	+	0.112540i
$714$		0			0
$715$	−7.84014	−	10.7200i	−0.293205	−	0.400904i
$716$		−	20.4198i		−	0.763124i
$717$		0			0
$718$	8.24977	+	8.24977i	0.307879	+	0.307879i
$719$	−29.1466			−1.08698			−0.543492	−	0.839414i	$-0.682898\pi$
$719$	−29.1466			−1.08698			−0.543492	+	0.839414i	$0.682898\pi$
$720$		0			0
$721$	−17.2413			−0.642099
$722$	−11.6027	−	11.6027i	−0.431808	−	0.431808i
$723$		0			0
$724$			7.13957i			0.265340i
$725$	−31.2673	−	9.94231i	−1.16124	−	0.369248i
$726$		0			0
$727$	33.4986	−	33.4986i	1.24240	−	1.24240i	0.283391	−	0.959005i	$-0.408541\pi$
$727$	33.4986	−	33.4986i	1.24240	−	1.24240i	0.959005	−	0.283391i	$-0.0914593\pi$
$728$	7.46711	−	7.46711i	0.276750	−	0.276750i
$729$		0			0
$730$	−6.34438	−	0.984404i	−0.234816	−	0.0364344i
$731$			5.92445i			0.219124i
$732$		0			0
$733$	−13.7943	−	13.7943i	−0.509503	−	0.509503i	0.404871	−	0.914374i	$-0.367316\pi$
$733$	−13.7943	−	13.7943i	−0.509503	−	0.509503i	−0.914374	+	0.404871i	$0.867316\pi$
$734$	−28.9051			−1.06691
$735$		0			0
$736$	1.00000			0.0368605
$737$	−7.62832	−	7.62832i	−0.280993	−	0.280993i
$738$		0			0
$739$		−	13.7796i		−	0.506890i	−0.967350	−	0.253445i	$-0.918436\pi$
$739$		−	13.7796i		−	0.506890i	0.967350	−	0.253445i	$-0.0815637\pi$
$740$	2.23371	−	1.63365i	0.0821128	−	0.0600540i
$741$		0			0
$742$	9.15894	−	9.15894i	0.336235	−	0.336235i
$743$	−11.1150	+	11.1150i	−0.407771	+	0.407771i	−0.880961	−	0.473189i	$-0.843103\pi$
$743$	−11.1150	+	11.1150i	−0.407771	+	0.407771i	0.473189	+	0.880961i	$0.343103\pi$
$744$		0			0
$745$	−5.86422	+	37.7943i	−0.214848	+	1.38467i
$746$			1.90254i			0.0696568i
$747$		0			0
$748$	−2.24977	−	2.24977i	−0.0822598	−	0.0822598i
$749$	39.0294			1.42610
$750$		0			0
$751$	−37.2800			−1.36037			−0.680184	−	0.733041i	$-0.738100\pi$
$751$	−37.2800			−1.36037			−0.680184	+	0.733041i	$0.738100\pi$
$752$	3.51413	+	3.51413i	0.128147	+	0.128147i
$753$		0			0
$754$			24.4995i			0.892221i
$755$	5.32439	−	34.3151i	0.193774	−	1.24885i
$756$		0			0
$757$	−5.57569	+	5.57569i	−0.202652	+	0.202652i	−0.801135	−	0.598483i	$-0.795770\pi$
$757$	−5.57569	+	5.57569i	−0.202652	+	0.202652i	0.598483	+	0.801135i	$0.295770\pi$
$758$	5.91075	−	5.91075i	0.214688	−	0.214688i
$759$		0			0
$760$	−2.90539	+	2.12489i	−0.105390	+	0.0770777i
$761$			3.66334i			0.132796i	0.997793	+	0.0663979i	$0.0211507\pi$
$761$			3.66334i			0.132796i	−0.997793	+	0.0663979i	$0.978849\pi$
$762$		0			0
$763$	29.9007	+	29.9007i	1.08248	+	1.08248i
$764$	−11.6669			−0.422095
$765$		0			0
$766$	15.7190			0.567952
$767$	−30.8010	−	30.8010i	−1.11216	−	1.11216i
$768$		0			0
$769$		−	31.6197i		−	1.14024i	−0.821563	−	0.570118i	$-0.806897\pi$
$769$		−	31.6197i		−	1.14024i	0.821563	−	0.570118i	$-0.193103\pi$
$770$	9.94231	+	1.54266i	0.358296	+	0.0555938i
$771$		0			0
$772$	−2.52982	+	2.52982i	−0.0910501	+	0.0910501i
$773$	−31.2107	+	31.2107i	−1.12257	+	1.12257i	−0.131219	+	0.991353i	$0.541889\pi$
$773$	−31.2107	+	31.2107i	−1.12257	+	1.12257i	−0.991353	+	0.131219i	$0.958111\pi$
$774$		0			0
$775$	20.2498	+	6.43899i	0.727393	+	0.231295i
$776$		−	2.27653i		−	0.0817225i
$777$		0			0
$778$	10.7346	+	10.7346i	0.384855	+	0.384855i
$779$	−4.62198			−0.165600
$780$		0			0
$781$	−13.2507			−0.474147
$782$	1.41421	+	1.41421i	0.0505722	+	0.0505722i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−12.4229	−	16.9860i	−0.443391	−	0.606255i
$786$		0			0
$787$	−4.17454	+	4.17454i	−0.148806	+	0.148806i	−0.777585	−	0.628778i	$-0.783555\pi$
$787$	−4.17454	+	4.17454i	−0.148806	+	0.148806i	0.628778	+	0.777585i	$0.283555\pi$
$788$	−6.05290	+	6.05290i	−0.215626	+	0.215626i
$789$		0			0
$790$	−9.52982	−	13.0303i	−0.339056	−	0.463596i
$791$		−	0.171267i		−	0.00608957i
$792$		0			0
$793$	26.0294	+	26.0294i	0.924330	+	0.924330i
$794$	31.7918			1.12825
$795$		0			0
$796$	12.4995			0.443035
$797$	27.0383	+	27.0383i	0.957746	+	0.957746i	0.999143	−	0.0413965i	$-0.0131807\pi$
$797$	27.0383	+	27.0383i	0.957746	+	0.957746i	−0.0413965	+	0.999143i	$0.513181\pi$
$798$		0			0
$799$			9.93945i			0.351632i
$800$	−2.29793	−	4.44066i	−0.0812443	−	0.157001i
$801$		0			0
$802$	−15.4499	+	15.4499i	−0.545555	+	0.545555i
$803$	−3.22982	+	3.22982i	−0.113978	+	0.113978i
$804$		0			0
$805$	−6.24977	−	0.969724i	−0.220275	−	0.0341783i
$806$		−	15.8668i		−	0.558883i
$807$		0			0
$808$	−4.88979	−	4.88979i	−0.172022	−	0.172022i
$809$	−2.16479			−0.0761098			−0.0380549	−	0.999276i	$-0.512116\pi$
$809$	−2.16479			−0.0761098			−0.0380549	+	0.999276i	$0.512116\pi$
$810$		0			0
$811$	−36.8780			−1.29496			−0.647480	−	0.762082i	$-0.724177\pi$
$811$	−36.8780			−1.29496			−0.647480	+	0.762082i	$0.724177\pi$
$812$	−13.1240	−	13.1240i	−0.460561	−	0.460561i
$813$		0			0
$814$		−	1.96881i		−	0.0690067i
$815$	−3.11273	+	2.27653i	−0.109034	+	0.0797432i
$816$		0			0
$817$	3.37179	−	3.37179i	0.117964	−	0.117964i
$818$	10.6916	−	10.6916i	0.373823	−	0.373823i
$819$		0			0
$820$	0.984404	−	6.34438i	0.0343769	−	0.221555i
$821$			12.8838i			0.449647i	0.974400	+	0.224823i	$0.0721805\pi$
$821$			12.8838i			0.449647i	−0.974400	+	0.224823i	$0.927819\pi$
$822$		0			0
$823$	−28.4499	−	28.4499i	−0.991701	−	0.991701i	0.00826508	−	0.999966i	$-0.497369\pi$
$823$	−28.4499	−	28.4499i	−0.991701	−	0.991701i	−0.999966	+	0.00826508i	$0.997369\pi$
$824$	6.09572			0.212354
$825$		0			0
$826$	32.9991			1.14818
$827$	−7.91968	−	7.91968i	−0.275394	−	0.275394i	0.555873	−	0.831267i	$-0.312384\pi$
$827$	−7.91968	−	7.91968i	−0.275394	−	0.275394i	−0.831267	+	0.555873i	$0.812384\pi$
$828$		0			0
$829$			54.4372i			1.89068i	0.326085	+	0.945340i	$0.394270\pi$
$829$			54.4372i			1.89068i	−0.326085	+	0.945340i	$0.605730\pi$
$830$	4.17242	−	26.8908i	0.144827	−	0.933394i
$831$		0			0
$832$	−2.64002	+	2.64002i	−0.0915263	+	0.0915263i
$833$	−1.41421	+	1.41421i	−0.0489996	+	0.0489996i
$834$		0			0
$835$	23.0109	−	16.8292i	0.796325	−	0.582400i
$836$			2.56083i			0.0885682i
$837$		0			0
$838$	−17.2947	−	17.2947i	−0.597436	−	0.597436i
$839$	57.6698			1.99098			0.995490	−	0.0948618i	$-0.0302409\pi$
$839$	57.6698			1.99098			0.995490	+	0.0948618i	$0.0302409\pi$
$840$		0			0
$841$	14.0596			0.484815
$842$	16.5816	+	16.5816i	0.571439	+	0.571439i
$843$		0			0
$844$			6.71995i			0.231310i
$845$	−2.07583	−	0.322089i	−0.0714107	−	0.0110802i
$846$		0			0
$847$	−16.9385	+	16.9385i	−0.582015	+	0.582015i
$848$	−3.23818	+	3.23818i	−0.111199	+	0.111199i
$849$		0			0
$850$	3.03028	−	9.52982i	0.103938	−	0.326870i
$851$			1.23760i			0.0424243i
$852$		0			0
$853$	0.860435	+	0.860435i	0.0294607	+	0.0294607i	0.721684	−	0.692223i	$-0.243369\pi$
$853$	0.860435	+	0.860435i	0.0294607	+	0.0294607i	−0.692223	+	0.721684i	$0.743369\pi$
$854$	−27.8869			−0.954271
$855$		0			0
$856$	−13.7990			−0.471639
$857$	−4.57511	−	4.57511i	−0.156283	−	0.156283i	0.624634	−	0.780917i	$-0.285248\pi$
$857$	−4.57511	−	4.57511i	−0.156283	−	0.156283i	−0.780917	+	0.624634i	$0.785248\pi$
$858$		0			0
$859$			13.1589i			0.448977i	0.974477	+	0.224489i	$0.0720712\pi$
$859$			13.1589i			0.448977i	−0.974477	+	0.224489i	$0.927929\pi$
$860$	3.91017	+	5.34644i	0.133336	+	0.182312i
$861$		0			0
$862$	−5.52982	+	5.52982i	−0.188346	+	0.188346i
$863$	−6.08030	+	6.08030i	−0.206976	+	0.206976i	−0.802981	−	0.596005i	$-0.796754\pi$
$863$	−6.08030	+	6.08030i	−0.206976	+	0.206976i	0.596005	+	0.802981i	$0.296754\pi$
$864$		0			0
$865$	0.739330	+	1.01090i	0.0251380	+	0.0343716i
$866$		−	38.0279i		−	1.29224i
$867$		0			0
$868$	8.49954	+	8.49954i	0.288493	+	0.288493i
$869$	−11.4850			−0.389601
$870$		0			0
$871$	−25.3188			−0.857895
$872$	−10.5715	−	10.5715i	−0.357996	−	0.357996i
$873$		0			0
$874$		−	1.60975i		−	0.0544505i
$875$	10.0553	+	29.9815i	0.339933	+	1.01356i
$876$		0			0
$877$	−8.04874	+	8.04874i	−0.271787	+	0.271787i	−0.829819	−	0.558033i	$-0.811556\pi$
$877$	−8.04874	+	8.04874i	−0.271787	+	0.271787i	0.558033	+	0.829819i	$0.311556\pi$
$878$	15.0044	−	15.0044i	0.506376	−	0.506376i
$879$		0			0
$880$	−3.51514	−	0.545414i	−0.118495	−	0.0183859i
$881$			1.92330i			0.0647975i	0.999475	+	0.0323988i	$0.0103147\pi$
$881$			1.92330i			0.0647975i	−0.999475	+	0.0323988i	$0.989685\pi$
$882$		0			0
$883$	3.03028	+	3.03028i	0.101977	+	0.101977i	0.756254	−	0.654278i	$-0.227027\pi$
$883$	3.03028	+	3.03028i	0.101977	+	0.101977i	−0.654278	+	0.756254i	$0.727027\pi$
$884$	−7.46711			−0.251146
$885$		0			0
$886$	−28.8392			−0.968873
$887$	19.1133	+	19.1133i	0.641762	+	0.641762i	0.950988	−	0.309227i	$-0.100070\pi$
$887$	19.1133	+	19.1133i	0.641762	+	0.641762i	−0.309227	+	0.950988i	$0.600070\pi$
$888$		0			0
$889$			14.5601i			0.488330i
$890$	30.4257	−	22.2521i	1.01987	−	0.745893i
$891$		0			0
$892$	12.6703	−	12.6703i	0.424233	−	0.424233i
$893$	5.65685	−	5.65685i	0.189299	−	0.189299i
$894$		0			0
$895$	7.00092	−	45.1202i	0.234015	−	1.50820i
$896$		−	2.82843i		−	0.0944911i
$897$		0			0
$898$	3.43899	+	3.43899i	0.114761	+	0.114761i
$899$	−27.8869			−0.930081
$900$		0			0
$901$	−9.15894			−0.305129
$902$	−3.22982	−	3.22982i	−0.107541	−	0.107541i
$903$		0			0
$904$			0.0605522i			0.00201394i
$905$	−2.44779	+	15.7758i	−0.0813674	+	0.524405i
$906$		0			0
$907$	−0.504239	+	0.504239i	−0.0167430	+	0.0167430i	−0.715429	−	0.698686i	$-0.753769\pi$
$907$	−0.504239	+	0.504239i	−0.0167430	+	0.0167430i	0.698686	+	0.715429i	$0.253769\pi$
$908$	14.0428	−	14.0428i	0.466027	−	0.466027i
$909$		0			0
$910$	19.0596	−	13.9394i	0.631821	−	0.462088i
$911$		−	25.9803i		−	0.860767i	−0.902646	−	0.430384i	$-0.858378\pi$
$911$		−	25.9803i		−	0.860767i	0.902646	−	0.430384i	$-0.141622\pi$
$912$		0			0
$913$	−13.6897	−	13.6897i	−0.453062	−	0.453062i
$914$	−29.6283			−0.980016
$915$		0			0
$916$	9.07901			0.299979
$917$	−23.5051	−	23.5051i	−0.776208	−	0.776208i
$918$		0			0
$919$		−	21.4986i		−	0.709174i	−0.935023	−	0.354587i	$-0.884621\pi$
$919$		−	21.4986i		−	0.709174i	0.935023	−	0.354587i	$-0.115379\pi$
$920$	2.20963	+	0.342849i	0.0728493	+	0.0113034i
$921$		0			0
$922$	1.42053	−	1.42053i	0.0467826	−	0.0467826i
$923$	−21.9899	+	21.9899i	−0.723806	+	0.723806i
$924$		0			0
$925$	5.49576	−	2.84392i	0.180699	−	0.0935076i
$926$			4.79454i			0.157558i
$927$		0			0
$928$	4.64002	+	4.64002i	0.152316	+	0.152316i
$929$	−1.24295			−0.0407797			−0.0203899	−	0.999792i	$-0.506491\pi$
$929$	−1.24295			−0.0407797			−0.0203899	+	0.999792i	$0.506491\pi$
$930$		0			0
$931$	1.60975			0.0527573
$932$	−9.52421	−	9.52421i	−0.311976	−	0.311976i
$933$		0			0
$934$		−	7.38934i		−	0.241786i
$935$	−4.19982	−	5.74249i	−0.137349	−	0.187799i
$936$		0			0
$937$	−34.2380	+	34.2380i	−1.11851	+	1.11851i	−0.126544	+	0.991961i	$0.540389\pi$
$937$	−34.2380	+	34.2380i	−1.11851	+	1.11851i	−0.991961	+	0.126544i	$0.959611\pi$
$938$	13.5628	−	13.5628i	0.442842	−	0.442842i
$939$		0			0
$940$	6.56009	+	8.96972i	0.213967	+	0.292560i
$941$			33.1257i			1.07987i	0.841708	+	0.539933i	$0.181550\pi$
$941$			33.1257i			1.07987i	−0.841708	+	0.539933i	$0.818450\pi$
$942$		0			0
$943$	2.03028	+	2.03028i	0.0661149	+	0.0661149i
$944$	−11.6669			−0.379726
$945$		0			0
$946$	4.71239			0.153213
$947$	−34.2944	−	34.2944i	−1.11442	−	1.11442i	−0.992546	−	0.121871i	$-0.961111\pi$
$947$	−34.2944	−	34.2944i	−1.11442	−	1.11442i	−0.121871	−	0.992546i	$-0.538889\pi$
$948$		0			0
$949$			10.7200i			0.347984i
$950$	−7.14835	+	3.69909i	−0.231923	+	0.120014i
$951$		0			0
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$	19.2043	−	19.2043i	0.622087	−	0.622087i	−0.323977	−	0.946065i	$-0.605020\pi$
$953$	19.2043	−	19.2043i	0.622087	−	0.622087i	0.946065	+	0.323977i	$0.105020\pi$
$954$		0			0
$955$	−25.7796	−	4.00000i	−0.834208	−	0.129437i
$956$		−	27.1102i		−	0.876808i
$957$		0			0
$958$	13.7796	+	13.7796i	0.445198	+	0.445198i
$959$	37.3904			1.20740
$960$		0			0
$961$	−12.9394			−0.417402
$962$	−3.26729	−	3.26729i	−0.105342	−	0.105342i
$963$		0			0
$964$			25.8401i			0.832255i
$965$	−6.45730	+	4.72261i	−0.207868	+	0.152026i
$966$		0			0
$967$	32.6997	−	32.6997i	1.05155	−	1.05155i	0.0529531	−	0.998597i	$-0.483137\pi$
$967$	32.6997	−	32.6997i	1.05155	−	1.05155i	0.998597	−	0.0529531i	$-0.0168634\pi$
$968$	5.98868	−	5.98868i	0.192483	−	0.192483i
$969$		0			0
$970$	0.780505	−	5.03028i	0.0250605	−	0.161512i
$971$		−	28.9152i		−	0.927932i	−0.885853	−	0.463966i	$-0.846426\pi$
$971$		−	28.9152i		−	0.927932i	0.885853	−	0.463966i	$-0.153574\pi$
$972$		0			0
$973$	−14.6812	−	14.6812i	−0.470658	−	0.470658i
$974$	31.2244			1.00050
$975$		0			0
$976$	9.85952			0.315595
$977$	38.2253	+	38.2253i	1.22294	+	1.22294i	0.966584	+	0.256352i	$0.0825205\pi$
$977$	38.2253	+	38.2253i	1.22294	+	1.22294i	0.256352	+	0.966584i	$0.417479\pi$
$978$		0			0
$979$		−	26.8174i		−	0.857089i
$980$	−0.342849	+	2.20963i	−0.0109519	+	0.0705840i
$981$		0			0
$982$	8.43899	−	8.43899i	0.269299	−	0.269299i
$983$	4.11419	−	4.11419i	0.131222	−	0.131222i	−0.638445	−	0.769667i	$-0.720422\pi$
$983$	4.11419	−	4.11419i	0.131222	−	0.131222i	0.769667	+	0.638445i	$0.220422\pi$
$984$		0			0
$985$	−15.4499	+	11.2994i	−0.492274	+	0.360030i
$986$			13.1240i			0.417952i
$987$		0			0
$988$	4.24977	+	4.24977i	0.135203	+	0.135203i
$989$	−2.96222			−0.0941933
$990$		0			0
$991$	−24.8486			−0.789342			−0.394671	−	0.918822i	$-0.629141\pi$
$991$	−24.8486			−0.789342			−0.394671	+	0.918822i	$0.629141\pi$
$992$	−3.00504	−	3.00504i	−0.0954102	−	0.0954102i
$993$		0			0
$994$		−	23.5592i		−	0.747252i
$995$	27.6193	+	4.28546i	0.875592	+	0.135858i
$996$		0			0
$997$	−0.329700	+	0.329700i	−0.0104417	+	0.0104417i	−0.712308	−	0.701867i	$-0.752350\pi$
$997$	−0.329700	+	0.329700i	−0.0104417	+	0.0104417i	0.701867	+	0.712308i	$0.252350\pi$
$998$	10.9605	−	10.9605i	0.346948	−	0.346948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.g.323.2	✓	12
3.2	odd	2	inner	2070.2.j.g.323.5	yes	12
5.2	odd	4	inner	2070.2.j.g.737.5	yes	12
15.2	even	4	inner	2070.2.j.g.737.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.g.323.2	✓	12	1.1	even	1	trivial
2070.2.j.g.323.5	yes	12	3.2	odd	2	inner
2070.2.j.g.737.2	yes	12	15.2	even	4	inner
2070.2.j.g.737.5	yes	12	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.342849 + 2.20963i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-0.342849 + 2.20963i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.80487 - 1.32001i) q^{10} -1.59083i q^{11} +(-2.64002 - 2.64002i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 - 1.41421i) q^{17} +1.60975i q^{19} +(-2.20963 - 0.342849i) q^{20} +(-1.12489 + 1.12489i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-4.76491 - 1.51514i) q^{25} +3.73356i q^{26} +(-2.00000 - 2.00000i) q^{28} +6.56198 q^{29} -4.24977 q^{31} +(0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(-3.73356 - 5.10495i) q^{35} +(-0.875115 + 0.875115i) q^{37} +(1.13826 - 1.13826i) q^{38} +(1.32001 + 1.80487i) q^{40} +2.87124i q^{41} +(-2.09461 - 2.09461i) q^{43} +1.59083 q^{44} -1.00000 q^{46} +(-3.51413 - 3.51413i) q^{47} -1.00000i q^{49} +(2.29793 + 4.44066i) q^{50} +(2.64002 - 2.64002i) q^{52} +(3.23818 - 3.23818i) q^{53} +(3.51514 + 0.545414i) q^{55} +2.82843i q^{56} +(-4.64002 - 4.64002i) q^{58} +11.6669 q^{59} -9.85952 q^{61} +(3.00504 + 3.00504i) q^{62} -1.00000i q^{64} +(6.73860 - 4.92834i) q^{65} +(4.79518 - 4.79518i) q^{67} +(1.41421 - 1.41421i) q^{68} +(-0.969724 + 6.24977i) q^{70} -8.32943i q^{71} +(-2.03028 - 2.03028i) q^{73} +1.23760 q^{74} -1.60975 q^{76} +(3.18166 + 3.18166i) q^{77} -7.21949i q^{79} +(0.342849 - 2.20963i) q^{80} +(2.03028 - 2.03028i) q^{82} +(8.60538 - 8.60538i) q^{83} +(3.60975 - 2.64002i) q^{85} +2.96222i q^{86} +(-1.12489 - 1.12489i) q^{88} +16.8575 q^{89} +10.5601 q^{91} +(0.707107 + 0.707107i) q^{92} +4.96972i q^{94} +(-3.55694 - 0.551901i) q^{95} +(1.60975 - 1.60975i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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