LMFDB - Embedded newform 2070.2.j.g.323.5

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			323.5
Root			$1.41127 + 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.g.737.5

$q$-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	$0.0770905\pi$
$11$			1.59083i			0.479653i	−0.970816	+	0.239826i	$0.922909\pi$
$12$		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	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$		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	$-0.708535\pi$
$29$	−6.56198			−1.21853			−0.609265	+	0.792967i	$0.708535\pi$
$30$		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	$-0.928021\pi$
$41$		−	2.87124i		−	0.448413i	0.974542	−	0.224206i	$-0.0719790\pi$
$42$		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	0.915319	−	0.402731i	$-0.131939\pi$
$47$	3.51413	+	3.51413i	0.512588	+	0.512588i	−0.402731	+	0.915319i	$0.631939\pi$
$48$		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	−0.893621	−	0.448823i	$-0.851843\pi$
$53$	−3.23818	+	3.23818i	−0.444798	+	0.444798i	0.448823	+	0.893621i	$0.351843\pi$
$54$		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	$-0.774533\pi$
$59$	−11.6669			−1.51891			−0.759453	+	0.650562i	$0.774533\pi$
$60$		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	$0.164561\pi$
$71$			8.32943i			0.988521i	−0.869314	+	0.494261i	$0.835439\pi$
$72$		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	−0.998542	−	0.0539792i	$-0.982810\pi$
$83$	−8.60538	+	8.60538i	−0.944563	+	0.944563i	0.0539792	+	0.998542i	$0.482810\pi$
$84$		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	$-0.851720\pi$
$89$	−16.8575			−1.78689			−0.893447	+	0.449169i	$0.851720\pi$
$90$		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	$0.111797\pi$
$101$			6.91521i			0.688089i	−0.938953	+	0.344045i	$0.888203\pi$
$102$		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	0.998475	−	0.0551976i	$-0.0175789\pi$
$107$	9.75734	+	9.75734i	0.943278	+	0.943278i	−0.0551976	+	0.998475i	$0.517579\pi$
$108$		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	−0.705090	−	0.709118i	$-0.749093\pi$
$113$	0.0428169	−	0.0428169i	0.00402787	−	0.00402787i	0.709118	+	0.705090i	$0.249093\pi$
$114$		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	$-0.828381\pi$
$131$		−	11.7526i		−	1.02683i	0.858141	−	0.513413i	$-0.171619\pi$
$132$		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	0.982878	−	0.184259i	$-0.0589885\pi$
$137$	9.34759	+	9.34759i	0.798619	+	0.798619i	−0.184259	+	0.982878i	$0.558988\pi$
$138$		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	$-0.747094\pi$
$149$	−17.1044			−1.40124			−0.700622	+	0.713533i	$0.747094\pi$
$150$		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	0.963895	−	0.266283i	$-0.0857957\pi$
$167$	9.01513	+	9.01513i	0.697611	+	0.697611i	−0.266283	+	0.963895i	$0.585796\pi$
$168$		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	−0.722002	−	0.691891i	$-0.756778\pi$
$173$	−0.396046	+	0.396046i	−0.0301108	+	0.0301108i	0.691891	+	0.722002i	$0.256778\pi$
$174$		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	$-0.223664\pi$
$179$	20.4198			1.52625			0.763124	+	0.646252i	$0.223664\pi$
$180$		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	$-0.861295\pi$
$191$		−	11.6669i		−	0.844190i	0.906552	−	0.422095i	$-0.138705\pi$
$192$		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	0.457803	−	0.889054i	$-0.348637\pi$
$197$	−6.05290	−	6.05290i	−0.431251	−	0.431251i	−0.889054	+	0.457803i	$0.848637\pi$
$198$		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	0.997834	−	0.0657807i	$-0.0209538\pi$
$227$	14.0428	+	14.0428i	0.932053	+	0.932053i	−0.0657807	+	0.997834i	$0.520954\pi$
$228$		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	−0.322588	−	0.946540i	$-0.604553\pi$
$233$	9.52421	−	9.52421i	0.623952	−	0.623952i	0.946540	+	0.322588i	$0.104553\pi$
$234$		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	$-0.159668\pi$
$239$	27.1102			1.75362			0.876808	+	0.480840i	$0.159668\pi$
$240$		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	$0.0922813\pi$
$251$			9.05794i			0.571732i	−0.958270	+	0.285866i	$0.907719\pi$
$252$		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	0.696004	−	0.718038i	$-0.254960\pi$
$257$	−0.353229	−	0.353229i	−0.0220338	−	0.0220338i	−0.718038	+	0.696004i	$0.754960\pi$
$258$		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	−0.585635	−	0.810575i	$-0.699155\pi$
$263$	3.64792	−	3.64792i	0.224941	−	0.224941i	0.810575	+	0.585635i	$0.199155\pi$
$264$		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	$-0.763442\pi$
$269$	−24.1534			−1.47266			−0.736329	+	0.676624i	$0.763442\pi$
$270$		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	$-0.844292\pi$
$281$		−	15.7537i		−	0.939788i	0.882723	−	0.469894i	$-0.155708\pi$
$282$		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	−0.822965	−	0.568092i	$-0.807682\pi$
$293$	−4.36274	+	4.36274i	−0.254874	+	0.254874i	0.568092	+	0.822965i	$0.307682\pi$
$294$		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	$0.0734057\pi$
$311$			8.06183i			0.457145i	−0.973527	+	0.228572i	$0.926594\pi$
$312$		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	$0.0746245\pi$
$317$	21.4534	+	21.4534i	1.20494	+	1.20494i	0.232298	+	0.972645i	$0.425376\pi$
$318$		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	0.912711	−	0.408607i	$-0.133985\pi$
$347$	9.39041	+	9.39041i	0.504104	+	0.504104i	−0.408607	+	0.912711i	$0.633985\pi$
$348$		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	−0.687453	−	0.726228i	$-0.741271\pi$
$353$	0.728515	−	0.728515i	0.0387750	−	0.0387750i	0.726228	+	0.687453i	$0.241271\pi$
$354$		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	$-0.400381\pi$
$359$	11.6669			0.615757			0.307879	+	0.951426i	$0.400381\pi$
$360$		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	−0.363602	−	0.931554i	$-0.618453\pi$
$383$	11.1150	−	11.1150i	0.567952	−	0.567952i	0.931554	+	0.363602i	$0.118453\pi$
$384$		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	$-0.374251\pi$
$389$	15.1811			0.769710			0.384855	+	0.922977i	$0.374251\pi$
$390$		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	$0.183681\pi$
$401$			21.8494i			1.09111i	−0.838075	+	0.545555i	$0.816319\pi$
$402$		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	$-0.703814\pi$
$419$	−24.4584			−1.19487			−0.597436	+	0.801916i	$0.703814\pi$
$420$		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	$0.0603127\pi$
$431$			7.82034i			0.376693i	−0.982103	+	0.188346i	$0.939687\pi$
$432$		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	−0.999530	−	0.0306573i	$-0.990240\pi$
$443$	−20.3924	+	20.3924i	−0.968873	+	0.968873i	0.0306573	+	0.999530i	$0.490240\pi$
$444$		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	$-0.463390\pi$
$449$	4.86347			0.229521			0.114761	+	0.993393i	$0.463390\pi$
$450$		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	$-0.985103\pi$
$461$		−	2.00893i		−	0.0935652i	0.998905	−	0.0467826i	$-0.0148968\pi$
$462$		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	0.575802	−	0.817589i	$-0.304690\pi$
$467$	−5.22505	−	5.22505i	−0.241786	−	0.241786i	−0.817589	+	0.575802i	$0.804690\pi$
$468$		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	$-0.353133\pi$
$479$	19.4873			0.890397			0.445198	+	0.895432i	$0.353133\pi$
$480$		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	$-0.913208\pi$
$491$		−	11.9345i		−	0.538598i	0.963057	−	0.269299i	$-0.0867920\pi$
$492$		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	−0.787106	−	0.616817i	$-0.788422\pi$
$503$	−3.81919	+	3.81919i	−0.170289	+	0.170289i	0.616817	+	0.787106i	$0.288422\pi$
$504$		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	$-0.561029\pi$
$509$	−8.59832			−0.381114			−0.190557	+	0.981676i	$0.561029\pi$
$510$		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	$-0.955971\pi$
$521$		−	6.29439i		−	0.275762i	0.990449	−	0.137881i	$-0.0440292\pi$
$522$		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	$0.0216823\pi$
$557$	25.1525	+	25.1525i	1.06575	+	1.06575i	0.0680643	+	0.997681i	$0.478318\pi$
$558$		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	−0.627490	−	0.778624i	$-0.715918\pi$
$563$	3.58606	−	3.58606i	0.151134	−	0.151134i	0.778624	+	0.627490i	$0.215918\pi$
$564$		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	$-0.646150\pi$
$569$	−21.1430			−0.886360			−0.443180	+	0.896433i	$0.646150\pi$
$570$		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	0.814145	−	0.580662i	$-0.197206\pi$
$587$	5.65685	+	5.65685i	0.233483	+	0.233483i	−0.580662	+	0.814145i	$0.697206\pi$
$588$		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	−0.572853	−	0.819658i	$-0.694164\pi$
$593$	6.01008	−	6.01008i	0.246805	−	0.246805i	0.819658	+	0.572853i	$0.194164\pi$
$594$		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	$-0.849771\pi$
$599$	−43.5978			−1.78136			−0.890680	+	0.454631i	$0.849771\pi$
$600$		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	0.561546	−	0.827445i	$-0.310207\pi$
$617$	−6.60480	−	6.60480i	−0.265899	−	0.265899i	−0.827445	+	0.561546i	$0.810207\pi$
$618$		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	$0.210048\pi$
$641$			31.0412i			1.22605i	−0.790062	+	0.613026i	$0.789952\pi$
$642$		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	$0.100991\pi$
$647$	32.1022	+	32.1022i	1.26207	+	1.26207i	0.311977	+	0.950090i	$0.399009\pi$
$648$		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	−0.974563	−	0.224114i	$-0.928051\pi$
$653$	−19.1769	+	19.1769i	−0.750449	+	0.750449i	0.224114	+	0.974563i	$0.428051\pi$
$654$		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	$-0.536683\pi$
$659$	−5.90369			−0.229975			−0.114988	+	0.993367i	$0.536683\pi$
$660$		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	0.151660	−	0.988433i	$-0.451538\pi$
$677$	−21.7722	−	21.7722i	−0.836772	−	0.836772i	−0.988433	+	0.151660i	$0.951538\pi$
$678$		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	−0.874927	−	0.484255i	$-0.839091\pi$
$683$	−10.2099	+	10.2099i	−0.390671	+	0.390671i	0.484255	+	0.874927i	$0.339091\pi$
$684$		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	$-0.830939\pi$
$701$		−	26.8206i		−	1.01300i	0.862240	−	0.506500i	$-0.169061\pi$
$702$		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	$-0.317102\pi$
$719$	29.1466			1.08698			0.543492	+	0.839414i	$0.317102\pi$
$720$		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	−0.473189	−	0.880961i	$-0.656897\pi$
$743$	11.1150	−	11.1150i	0.407771	−	0.407771i	0.880961	+	0.473189i	$0.156897\pi$
$744$		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	$-0.978849\pi$
$761$		−	3.66334i		−	0.132796i	0.997793	−	0.0663979i	$-0.0211507\pi$
$762$		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	$-0.458111\pi$
$773$	31.2107	−	31.2107i	1.12257	−	1.12257i	0.991353	−	0.131219i	$-0.0418890\pi$
$774$		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	0.0413965	−	0.999143i	$-0.486819\pi$
$797$	−27.0383	−	27.0383i	−0.957746	−	0.957746i	−0.999143	+	0.0413965i	$0.986819\pi$
$798$		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	$-0.487884\pi$
$809$	2.16479			0.0761098			0.0380549	+	0.999276i	$0.487884\pi$
$810$		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	$-0.927819\pi$
$821$		−	12.8838i		−	0.449647i	0.974400	−	0.224823i	$-0.0721805\pi$
$822$		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	0.831267	−	0.555873i	$-0.187616\pi$
$827$	7.91968	+	7.91968i	0.275394	+	0.275394i	−0.555873	+	0.831267i	$0.687616\pi$
$828$		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	$-0.969759\pi$
$839$	−57.6698			−1.99098			−0.995490	+	0.0948618i	$0.969759\pi$
$840$		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	0.780917	−	0.624634i	$-0.214752\pi$
$857$	4.57511	+	4.57511i	0.156283	+	0.156283i	−0.624634	+	0.780917i	$0.714752\pi$
$858$		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	−0.596005	−	0.802981i	$-0.703246\pi$
$863$	6.08030	−	6.08030i	0.206976	−	0.206976i	0.802981	+	0.596005i	$0.203246\pi$
$864$		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	$-0.989685\pi$
$881$		−	1.92330i		−	0.0647975i	0.999475	−	0.0323988i	$-0.0103147\pi$
$882$		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	0.309227	−	0.950988i	$-0.399930\pi$
$887$	−19.1133	−	19.1133i	−0.641762	−	0.641762i	−0.950988	+	0.309227i	$0.899930\pi$
$888$		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	$0.141622\pi$
$911$			25.9803i			0.860767i	−0.902646	+	0.430384i	$0.858378\pi$
$912$		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	$-0.493509\pi$
$929$	1.24295			0.0407797			0.0203899	+	0.999792i	$0.493509\pi$
$930$		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	$-0.818450\pi$
$941$		−	33.1257i		−	1.07987i	0.841708	−	0.539933i	$-0.181550\pi$
$942$		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	$0.0388894\pi$
$947$	34.2944	+	34.2944i	1.11442	+	1.11442i	0.121871	+	0.992546i	$0.461111\pi$
$948$		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	−0.946065	−	0.323977i	$-0.894980\pi$
$953$	−19.2043	+	19.2043i	−0.622087	+	0.622087i	0.323977	+	0.946065i	$0.394980\pi$
$954$		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	$0.153574\pi$
$971$			28.9152i			0.927932i	−0.885853	+	0.463966i	$0.846426\pi$
$972$		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	$-0.917479\pi$
$977$	−38.2253	−	38.2253i	−1.22294	−	1.22294i	−0.256352	−	0.966584i	$-0.582521\pi$
$978$		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	−0.769667	−	0.638445i	$-0.779578\pi$
$983$	−4.11419	+	4.11419i	−0.131222	+	0.131222i	0.638445	+	0.769667i	$0.279578\pi$
$984$		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.323.5	yes	12
3.2	odd	2	inner	2070.2.j.g.323.2	✓	12
5.2	odd	4	inner	2070.2.j.g.737.2	yes	12
15.2	even	4	inner	2070.2.j.g.737.5	yes	12

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