LMFDB - Embedded newform 2070.2.j.h.323.1

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 24 x^{14} - 48 x^{13} + 160 x^{12} - 292 x^{11} + 436 x^{10} - 176 x^{9} - 914 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 24x^14 - 48x^13 + 160x^12 - 292x^11 + 436x^10 - 176x^9 - 914x^8 + 820x^7 + 1624x^6 - 768x^5 - 568x^4 - 636x^3 + 540x^2 + 432*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Root			$-1.03797 - 2.50588i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.h.737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.46791 + 1.68678i) q^{5} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.46791 + 1.68678i) q^{5} +(0.707107 - 0.707107i) q^{8} +(2.23071 - 0.154765i) q^{10} -1.23907i q^{11} +(4.46141 + 4.46141i) q^{13} -1.00000 q^{16} +(-4.78778 - 4.78778i) q^{17} -5.84235i q^{19} +(-1.68678 - 1.46791i) q^{20} +(-0.876155 + 0.876155i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-0.690470 - 4.95210i) q^{25} -6.30939i q^{26} +4.52518 q^{29} -6.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +6.77094i q^{34} +(3.76641 - 3.76641i) q^{37} +(-4.13117 + 4.13117i) q^{38} +(0.154765 + 2.23071i) q^{40} +8.85528i q^{41} +(7.64710 + 7.64710i) q^{43} +1.23907 q^{44} -1.00000 q^{46} +(-1.69675 - 1.69675i) q^{47} +7.00000i q^{49} +(-3.01342 + 3.98990i) q^{50} +(-4.46141 + 4.46141i) q^{52} +(3.04730 - 3.04730i) q^{53} +(2.09004 + 1.81885i) q^{55} +(-3.19979 - 3.19979i) q^{58} -0.693932 q^{59} +14.3656 q^{61} +(4.24264 + 4.24264i) q^{62} -1.00000i q^{64} +(-14.0744 + 0.976472i) q^{65} +(2.96620 - 2.96620i) q^{67} +(4.78778 - 4.78778i) q^{68} -16.2089i q^{71} +(4.66120 + 4.66120i) q^{73} -5.32651 q^{74} +5.84235 q^{76} +8.15188i q^{79} +(1.46791 - 1.68678i) q^{80} +(6.26163 - 6.26163i) q^{82} +(-0.939152 + 0.939152i) q^{83} +(15.1040 - 1.04790i) q^{85} -10.8146i q^{86} +(-0.876155 - 0.876155i) q^{88} -4.52518 q^{89} +(0.707107 + 0.707107i) q^{92} +2.39957i q^{94} +(9.85478 + 8.57606i) q^{95} +(9.57116 - 9.57116i) q^{97} +(4.94975 - 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * 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
$5$	−1.46791	+	1.68678i	−0.656470	+	0.754352i
$5$	−1.46791	+	1.68678i	−0.656470	+	0.754352i
$6$		0			0
$7$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$7$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	2.23071	−	0.154765i	0.705411	−	0.0489410i
$11$		−	1.23907i		−	0.373594i	−0.982399	−	0.186797i	$-0.940189\pi$
$11$		−	1.23907i		−	0.373594i	0.982399	−	0.186797i	$-0.0598106\pi$
$12$		0			0
$13$	4.46141	+	4.46141i	1.23737	+	1.23737i	0.961071	+	0.276302i	$0.0891090\pi$
$13$	4.46141	+	4.46141i	1.23737	+	1.23737i	0.276302	+	0.961071i	$0.410891\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.78778	−	4.78778i	−1.16121	−	1.16121i	−0.984212	−	0.176995i	$-0.943362\pi$
$17$	−4.78778	−	4.78778i	−1.16121	−	1.16121i	−0.176995	−	0.984212i	$-0.556638\pi$
$18$		0			0
$19$		−	5.84235i		−	1.34033i	−0.742213	−	0.670164i	$-0.766224\pi$
$19$		−	5.84235i		−	1.34033i	0.742213	−	0.670164i	$-0.233776\pi$
$20$	−1.68678	−	1.46791i	−0.377176	−	0.328235i
$21$		0			0
$22$	−0.876155	+	0.876155i	−0.186797	+	0.186797i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$23$	0.707107	−	0.707107i	0.147442	−	0.147442i
$24$		0			0
$25$	−0.690470	−	4.95210i	−0.138094	−	0.990419i
$26$		−	6.30939i		−	1.23737i
$27$		0			0
$28$		0			0
$29$	4.52518			0.840305			0.420152	−	0.907454i	$-0.361977\pi$
$29$	4.52518			0.840305			0.420152	+	0.907454i	$0.361977\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			6.77094i			1.16121i
$35$		0			0
$36$		0			0
$37$	3.76641	−	3.76641i	0.619194	−	0.619194i	−0.326131	−	0.945325i	$-0.605745\pi$
$37$	3.76641	−	3.76641i	0.619194	−	0.619194i	0.945325	+	0.326131i	$0.105745\pi$
$38$	−4.13117	+	4.13117i	−0.670164	+	0.670164i
$39$		0			0
$40$	0.154765	+	2.23071i	0.0244705	+	0.352706i
$41$			8.85528i			1.38296i	0.722395	+	0.691481i	$0.243041\pi$
$41$			8.85528i			1.38296i	−0.722395	+	0.691481i	$0.756959\pi$
$42$		0			0
$43$	7.64710	+	7.64710i	1.16617	+	1.16617i	0.983100	+	0.183072i	$0.0586040\pi$
$43$	7.64710	+	7.64710i	1.16617	+	1.16617i	0.183072	+	0.983100i	$0.441396\pi$
$44$	1.23907			0.186797
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−1.69675	−	1.69675i	−0.247497	−	0.247497i	0.572446	−	0.819943i	$-0.305995\pi$
$47$	−1.69675	−	1.69675i	−0.247497	−	0.247497i	−0.819943	+	0.572446i	$0.805995\pi$
$48$		0			0
$49$			7.00000i			1.00000i
$50$	−3.01342	+	3.98990i	−0.426163	+	0.564257i
$51$		0			0
$52$	−4.46141	+	4.46141i	−0.618686	+	0.618686i
$53$	3.04730	−	3.04730i	0.418579	−	0.418579i	−0.466135	−	0.884714i	$-0.654354\pi$
$53$	3.04730	−	3.04730i	0.418579	−	0.418579i	0.884714	+	0.466135i	$0.154354\pi$
$54$		0			0
$55$	2.09004	+	1.81885i	0.281821	+	0.245253i
$56$		0			0
$57$		0			0
$58$	−3.19979	−	3.19979i	−0.420152	−	0.420152i
$59$	−0.693932			−0.0903423			−0.0451711	−	0.998979i	$-0.514383\pi$
$59$	−0.693932			−0.0903423			−0.0451711	+	0.998979i	$0.514383\pi$
$60$		0			0
$61$	14.3656			1.83933			0.919663	−	0.392707i	$-0.128461\pi$
$61$	14.3656			1.83933			0.919663	+	0.392707i	$0.128461\pi$
$62$	4.24264	+	4.24264i	0.538816	+	0.538816i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−14.0744	+	0.976472i	−1.74571	+	0.121116i
$66$		0			0
$67$	2.96620	−	2.96620i	0.362379	−	0.362379i	−0.502309	−	0.864688i	$-0.667516\pi$
$67$	2.96620	−	2.96620i	0.362379	−	0.362379i	0.864688	+	0.502309i	$0.167516\pi$
$68$	4.78778	−	4.78778i	0.580603	−	0.580603i
$69$		0			0
$70$		0			0
$71$		−	16.2089i		−	1.92364i	−0.273682	−	0.961820i	$-0.588242\pi$
$71$		−	16.2089i		−	1.92364i	0.273682	−	0.961820i	$-0.411758\pi$
$72$		0			0
$73$	4.66120	+	4.66120i	0.545552	+	0.545552i	0.925151	−	0.379599i	$-0.123938\pi$
$73$	4.66120	+	4.66120i	0.545552	+	0.545552i	−0.379599	+	0.925151i	$0.623938\pi$
$74$	−5.32651			−0.619194
$75$		0			0
$76$	5.84235			0.670164
$77$		0			0
$78$		0			0
$79$			8.15188i			0.917158i	0.888654	+	0.458579i	$0.151641\pi$
$79$			8.15188i			0.917158i	−0.888654	+	0.458579i	$0.848359\pi$
$80$	1.46791	−	1.68678i	0.164118	−	0.188588i
$81$		0			0
$82$	6.26163	−	6.26163i	0.691481	−	0.691481i
$83$	−0.939152	+	0.939152i	−0.103085	+	0.103085i	−0.756768	−	0.653683i	$-0.773223\pi$
$83$	−0.939152	+	0.939152i	−0.103085	+	0.103085i	0.653683	+	0.756768i	$0.273223\pi$
$84$		0			0
$85$	15.1040	−	1.04790i	1.63826	−	0.113661i
$86$		−	10.8146i		−	1.16617i
$87$		0			0
$88$	−0.876155	−	0.876155i	−0.0933984	−	0.0933984i
$89$	−4.52518			−0.479668			−0.239834	−	0.970814i	$-0.577093\pi$
$89$	−4.52518			−0.479668			−0.239834	+	0.970814i	$0.577093\pi$
$90$		0			0
$91$		0			0
$92$	0.707107	+	0.707107i	0.0737210	+	0.0737210i
$93$		0			0
$94$			2.39957i			0.247497i
$95$	9.85478	+	8.57606i	1.01108	+	0.879885i
$96$		0			0
$97$	9.57116	−	9.57116i	0.971804	−	0.971804i	−0.0278096	−	0.999613i	$-0.508853\pi$
$97$	9.57116	−	9.57116i	0.971804	−	0.971804i	0.999613	+	0.0278096i	$0.00885323\pi$
$98$	4.94975	−	4.94975i	0.500000	−	0.500000i
$99$		0			0
$100$	4.95210	−	0.690470i	0.495210	−	0.0690470i
$101$			9.83175i			0.978295i	0.872201	+	0.489148i	$0.162692\pi$
$101$			9.83175i			0.978295i	−0.872201	+	0.489148i	$0.837308\pi$
$102$		0			0
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	0.346757	−	0.937955i	$-0.387283\pi$
$103$	−6.00000	−	6.00000i	−0.591198	−	0.591198i	−0.937955	+	0.346757i	$0.887283\pi$
$104$	6.30939			0.618686
$105$		0			0
$106$	−4.30953			−0.418579
$107$	7.83508	+	7.83508i	0.757445	+	0.757445i	0.975857	−	0.218411i	$-0.0700875\pi$
$107$	7.83508	+	7.83508i	0.757445	+	0.757445i	−0.218411	+	0.975857i	$0.570087\pi$
$108$		0			0
$109$			10.7091i			1.02575i	0.858465	+	0.512873i	$0.171419\pi$
$109$			10.7091i			1.02575i	−0.858465	+	0.512873i	$0.828581\pi$
$110$	−0.191765	−	2.76400i	−0.0182840	−	0.263537i
$111$		0			0
$112$		0			0
$113$	11.3534	−	11.3534i	1.06803	−	1.06803i	0.0705240	−	0.997510i	$-0.477533\pi$
$113$	11.3534	−	11.3534i	1.06803	−	1.06803i	0.997510	−	0.0705240i	$-0.0224671\pi$
$114$		0			0
$115$	0.154765	+	2.23071i	0.0144319	+	0.208014i
$116$			4.52518i			0.420152i
$117$		0			0
$118$	0.490684	+	0.490684i	0.0451711	+	0.0451711i
$119$		0			0
$120$		0			0
$121$	9.46471			0.860428
$122$	−10.1580	−	10.1580i	−0.919663	−	0.919663i
$123$		0			0
$124$		−	6.00000i		−	0.538816i
$125$	9.36666	+	6.10457i	0.837779	+	0.546009i
$126$		0			0
$127$	9.61329	−	9.61329i	0.853042	−	0.853042i	−0.137465	−	0.990507i	$-0.543895\pi$
$127$	9.61329	−	9.61329i	0.853042	−	0.853042i	0.990507	+	0.137465i	$0.0438954\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	10.6426	+	9.26163i	0.933415	+	0.812298i
$131$			16.1411i			1.41026i	0.709079	+	0.705129i	$0.249111\pi$
$131$			16.1411i			1.41026i	−0.709079	+	0.705129i	$0.750889\pi$
$132$		0			0
$133$		0			0
$134$	−4.19484			−0.362379
$135$		0			0
$136$	−6.77094			−0.580603
$137$	3.65610	+	3.65610i	0.312362	+	0.312362i	0.845824	−	0.533462i	$-0.179109\pi$
$137$	3.65610	+	3.65610i	0.312362	+	0.312362i	−0.533462	+	0.845824i	$0.679109\pi$
$138$		0			0
$139$			2.83855i			0.240762i	0.992728	+	0.120381i	$0.0384117\pi$
$139$			2.83855i			0.240762i	−0.992728	+	0.120381i	$0.961588\pi$
$140$		0			0
$141$		0			0
$142$	−11.4614	+	11.4614i	−0.961820	+	0.961820i
$143$	5.52800	−	5.52800i	0.462275	−	0.462275i
$144$		0			0
$145$	−6.64257	+	7.63300i	−0.551635	+	0.633886i
$146$		−	6.59193i		−	0.545552i
$147$		0			0
$148$	3.76641	+	3.76641i	0.309597	+	0.309597i
$149$	4.76143			0.390072			0.195036	−	0.980796i	$-0.437518\pi$
$149$	4.76143			0.390072			0.195036	+	0.980796i	$0.437518\pi$
$150$		0			0
$151$	−5.90419			−0.480476			−0.240238	−	0.970714i	$-0.577226\pi$
$151$	−5.90419			−0.480476			−0.240238	+	0.970714i	$0.577226\pi$
$152$	−4.13117	−	4.13117i	−0.335082	−	0.335082i
$153$		0			0
$154$		0			0
$155$	8.80747	−	10.1207i	0.707433	−	0.812914i
$156$		0			0
$157$	2.99547	−	2.99547i	0.239064	−	0.239064i	−0.577398	−	0.816463i	$-0.695932\pi$
$157$	2.99547	−	2.99547i	0.239064	−	0.239064i	0.816463	+	0.577398i	$0.195932\pi$
$158$	5.76425	−	5.76425i	0.458579	−	0.458579i
$159$		0			0
$160$	−2.23071	+	0.154765i	−0.176353	+	0.0122352i
$161$		0			0
$162$		0			0
$163$	−11.2851	−	11.2851i	−0.883920	−	0.883920i	0.110011	−	0.993930i	$-0.464911\pi$
$163$	−11.2851	−	11.2851i	−0.883920	−	0.883920i	−0.993930	+	0.110011i	$0.964911\pi$
$164$	−8.85528			−0.691481
$165$		0			0
$166$	1.32816			0.103085
$167$	3.19842	+	3.19842i	0.247501	+	0.247501i	0.819944	−	0.572443i	$-0.194004\pi$
$167$	3.19842	+	3.19842i	0.247501	+	0.247501i	−0.572443	+	0.819944i	$0.694004\pi$
$168$		0			0
$169$			26.8084i			2.06218i
$170$	−11.4211	−	9.93914i	−0.875959	−	0.762298i
$171$		0			0
$172$	−7.64710	+	7.64710i	−0.583086	+	0.583086i
$173$	14.5121	−	14.5121i	1.10334	−	1.10334i	0.109331	−	0.994005i	$-0.465129\pi$
$173$	14.5121	−	14.5121i	1.10334	−	1.10334i	0.994005	−	0.109331i	$-0.0348710\pi$
$174$		0			0
$175$		0			0
$176$			1.23907i			0.0933984i
$177$		0			0
$178$	3.19979	+	3.19979i	0.239834	+	0.239834i
$179$	−8.51852			−0.636704			−0.318352	−	0.947973i	$-0.603129\pi$
$179$	−8.51852			−0.636704			−0.318352	+	0.947973i	$0.603129\pi$
$180$		0			0
$181$	2.36560			0.175834			0.0879169	−	0.996128i	$-0.471979\pi$
$181$	2.36560			0.175834			0.0879169	+	0.996128i	$0.471979\pi$
$182$		0			0
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	0.824357	+	11.8819i	0.0606079	+	0.873573i
$186$		0			0
$187$	−5.93239	+	5.93239i	−0.433820	+	0.433820i
$188$	1.69675	−	1.69675i	0.123748	−	0.123748i
$189$		0			0
$190$	−0.904191	−	13.0326i	−0.0655969	−	0.945482i
$191$			6.39684i			0.462859i	0.972852	+	0.231430i	$0.0743403\pi$
$191$			6.39684i			0.462859i	−0.972852	+	0.231430i	$0.925660\pi$
$192$		0			0
$193$	−8.68470	−	8.68470i	−0.625139	−	0.625139i	0.321702	−	0.946841i	$-0.395745\pi$
$193$	−8.68470	−	8.68470i	−0.625139	−	0.625139i	−0.946841	+	0.321702i	$0.895745\pi$
$194$	−13.5357			−0.971804
$195$		0			0
$196$	−7.00000			−0.500000
$197$	5.50165	+	5.50165i	0.391977	+	0.391977i	0.875391	−	0.483415i	$-0.160604\pi$
$197$	5.50165	+	5.50165i	0.391977	+	0.391977i	−0.483415	+	0.875391i	$0.660604\pi$
$198$		0			0
$199$		−	26.8552i		−	1.90372i	−0.306540	−	0.951858i	$-0.599171\pi$
$199$		−	26.8552i		−	1.90372i	0.306540	−	0.951858i	$-0.400829\pi$
$200$	−3.98990	−	3.01342i	−0.282128	−	0.213081i
$201$		0			0
$202$	6.95210	−	6.95210i	0.489148	−	0.489148i
$203$		0			0
$204$		0			0
$205$	−14.9369	−	12.9988i	−1.04324	−	0.907873i
$206$			8.48528i			0.591198i
$207$		0			0
$208$	−4.46141	−	4.46141i	−0.309343	−	0.309343i
$209$	−7.23908			−0.500738
$210$		0			0
$211$	14.1609			0.974879			0.487440	−	0.873157i	$-0.337931\pi$
$211$	14.1609			0.974879			0.487440	+	0.873157i	$0.337931\pi$
$212$	3.04730	+	3.04730i	0.209289	+	0.209289i
$213$		0			0
$214$		−	11.0805i		−	0.757445i
$215$	−24.1243	+	1.67373i	−1.64526	+	0.114147i
$216$		0			0
$217$		0			0
$218$	7.57248	−	7.57248i	0.512873	−	0.512873i
$219$		0			0
$220$	−1.81885	+	2.09004i	−0.122627	+	0.140911i
$221$		−	42.7205i		−	2.87369i
$222$		0			0
$223$	17.4849	+	17.4849i	1.17088	+	1.17088i	0.982001	+	0.188876i	$0.0604843\pi$
$223$	17.4849	+	17.4849i	1.17088	+	1.17088i	0.188876	+	0.982001i	$0.439516\pi$
$224$		0			0
$225$		0			0
$226$	−16.0561			−1.06803
$227$	17.4106	+	17.4106i	1.15558	+	1.15558i	0.985415	+	0.170170i	$0.0544315\pi$
$227$	17.4106	+	17.4106i	1.15558	+	1.15558i	0.170170	+	0.985415i	$0.445568\pi$
$228$		0			0
$229$			5.93816i			0.392405i	0.980563	+	0.196202i	$0.0628609\pi$
$229$			5.93816i			0.392405i	−0.980563	+	0.196202i	$0.937139\pi$
$230$	1.46791	−	1.68678i	0.0967912	−	0.111223i
$231$		0			0
$232$	3.19979	−	3.19979i	0.210076	−	0.210076i
$233$	0.437741	−	0.437741i	0.0286774	−	0.0286774i	−0.692623	−	0.721300i	$-0.743545\pi$
$233$	0.437741	−	0.437741i	0.0286774	−	0.0286774i	0.721300	+	0.692623i	$0.243545\pi$
$234$		0			0
$235$	5.35274	−	0.371370i	0.349174	−	0.0242255i
$236$		−	0.693932i		−	0.0451711i
$237$		0			0
$238$		0			0
$239$	26.1808			1.69349			0.846747	−	0.531996i	$-0.178558\pi$
$239$	26.1808			1.69349			0.846747	+	0.531996i	$0.178558\pi$
$240$		0			0
$241$	−15.3618			−0.989540			−0.494770	−	0.869024i	$-0.664748\pi$
$241$	−15.3618			−0.989540			−0.494770	+	0.869024i	$0.664748\pi$
$242$	−6.69256	−	6.69256i	−0.430214	−	0.430214i
$243$		0			0
$244$			14.3656i			0.919663i
$245$	−11.8075	−	10.2754i	−0.754352	−	0.656470i
$246$		0			0
$247$	26.0651	−	26.0651i	1.65848	−	1.65848i
$248$	−4.24264	+	4.24264i	−0.269408	+	0.269408i
$249$		0			0
$250$	−2.30665	−	10.9398i	−0.145885	−	0.691894i
$251$		−	21.1174i		−	1.33292i	−0.745543	−	0.666458i	$-0.767810\pi$
$251$		−	21.1174i		−	1.33292i	0.745543	−	0.666458i	$-0.232190\pi$
$252$		0			0
$253$	−0.876155	−	0.876155i	−0.0550834	−	0.0550834i
$254$	−13.5952			−0.853042
$255$		0			0
$256$	1.00000			0.0625000
$257$	10.8346	+	10.8346i	0.675842	+	0.675842i	0.959057	−	0.283215i	$-0.0914009\pi$
$257$	10.8346	+	10.8346i	0.675842	+	0.675842i	−0.283215	+	0.959057i	$0.591401\pi$
$258$		0			0
$259$		0			0
$260$	−0.976472	−	14.0744i	−0.0605582	−	0.872857i
$261$		0			0
$262$	11.4135	−	11.4135i	0.705129	−	0.705129i
$263$	12.6602	−	12.6602i	0.780660	−	0.780660i	−0.199282	−	0.979942i	$-0.563861\pi$
$263$	12.6602	−	12.6602i	0.780660	−	0.780660i	0.979942	+	0.199282i	$0.0638611\pi$
$264$		0			0
$265$	0.666964	+	9.61329i	0.0409713	+	0.590540i
$266$		0			0
$267$		0			0
$268$	2.96620	+	2.96620i	0.181189	+	0.181189i
$269$	−11.6226			−0.708642			−0.354321	−	0.935124i	$-0.615288\pi$
$269$	−11.6226			−0.708642			−0.354321	+	0.935124i	$0.615288\pi$
$270$		0			0
$271$	−28.1121			−1.70769			−0.853846	−	0.520526i	$-0.825736\pi$
$271$	−28.1121			−1.70769			−0.853846	+	0.520526i	$0.825736\pi$
$272$	4.78778	+	4.78778i	0.290302	+	0.290302i
$273$		0			0
$274$		−	5.17051i		−	0.312362i
$275$	−6.13599	+	0.855541i	−0.370014	+	0.0515911i
$276$		0			0
$277$	8.09004	−	8.09004i	0.486083	−	0.486083i	−0.420984	−	0.907068i	$-0.638315\pi$
$277$	8.09004	−	8.09004i	0.486083	−	0.486083i	0.907068	+	0.420984i	$0.138315\pi$
$278$	2.00716	−	2.00716i	0.120381	−	0.120381i
$279$		0			0
$280$		0			0
$281$		−	3.60981i		−	0.215343i	−0.994187	−	0.107672i	$-0.965660\pi$
$281$		−	3.60981i		−	0.215343i	0.994187	−	0.107672i	$-0.0343395\pi$
$282$		0			0
$283$	−21.6413	−	21.6413i	−1.28644	−	1.28644i	−0.936932	−	0.349511i	$-0.886348\pi$
$283$	−21.6413	−	21.6413i	−1.28644	−	1.28644i	−0.349511	−	0.936932i	$-0.613652\pi$
$284$	16.2089			0.961820
$285$		0			0
$286$	−7.81777			−0.462275
$287$		0			0
$288$		0			0
$289$			28.8456i			1.69680i
$290$	10.0943	−	0.700339i	0.592760	−	0.0411253i
$291$		0			0
$292$	−4.66120	+	4.66120i	−0.272776	+	0.272776i
$293$	−6.63566	+	6.63566i	−0.387659	+	0.387659i	−0.873852	−	0.486193i	$-0.838385\pi$
$293$	−6.63566	+	6.63566i	−0.387659	+	0.387659i	0.486193	+	0.873852i	$0.338385\pi$
$294$		0			0
$295$	1.01863	−	1.17051i	0.0593070	−	0.0681499i
$296$		−	5.32651i		−	0.309597i
$297$		0			0
$298$	−3.36684	−	3.36684i	−0.195036	−	0.195036i
$299$	6.30939			0.364881
$300$		0			0
$301$		0			0
$302$	4.17489	+	4.17489i	0.240238	+	0.240238i
$303$		0			0
$304$			5.84235i			0.335082i
$305$	−21.0874	+	24.2316i	−1.20746	+	1.38750i
$306$		0			0
$307$	17.5419	−	17.5419i	1.00117	−	1.00117i	0.00116880	−	0.999999i	$-0.499628\pi$
$307$	17.5419	−	17.5419i	1.00117	−	1.00117i	0.999999	−	0.00116880i	$-0.000372040\pi$
$308$		0			0
$309$		0			0
$310$	−13.3842	+	0.928590i	−0.760173	+	0.0527404i
$311$			25.3053i			1.43493i	0.696594	+	0.717466i	$0.254698\pi$
$311$			25.3053i			1.43493i	−0.696594	+	0.717466i	$0.745302\pi$
$312$		0			0
$313$	10.6086	+	10.6086i	0.599633	+	0.599633i	0.940215	−	0.340582i	$-0.110624\pi$
$313$	10.6086	+	10.6086i	0.599633	+	0.599633i	−0.340582	+	0.940215i	$0.610624\pi$
$314$	−4.23623			−0.239064
$315$		0			0
$316$	−8.15188			−0.458579
$317$	−6.67938	−	6.67938i	−0.375152	−	0.375152i	0.494198	−	0.869349i	$-0.335462\pi$
$317$	−6.67938	−	6.67938i	−0.375152	−	0.375152i	−0.869349	+	0.494198i	$0.835462\pi$
$318$		0			0
$319$		−	5.60702i		−	0.313933i
$320$	1.68678	+	1.46791i	0.0942940	+	0.0820588i
$321$		0			0
$322$		0			0
$323$	−27.9719	+	27.9719i	−1.55640	+	1.55640i
$324$		0			0
$325$	19.0129	−	25.1738i	1.05464	−	1.39639i
$326$			15.9596i			0.883920i
$327$		0			0
$328$	6.26163	+	6.26163i	0.345740	+	0.345740i
$329$		0			0
$330$		0			0
$331$	−35.7498			−1.96499			−0.982494	−	0.186292i	$-0.940353\pi$
$331$	−35.7498			−1.96499			−0.982494	+	0.186292i	$0.940353\pi$
$332$	−0.939152	−	0.939152i	−0.0515427	−	0.0515427i
$333$		0			0
$334$		−	4.52325i		−	0.247501i
$335$	0.649214	+	9.35744i	0.0354703	+	0.511252i
$336$		0			0
$337$	−23.1600	+	23.1600i	−1.26161	+	1.26161i	−0.311295	+	0.950313i	$0.600763\pi$
$337$	−23.1600	+	23.1600i	−1.26161	+	1.26161i	−0.950313	+	0.311295i	$0.899237\pi$
$338$	18.9564	−	18.9564i	1.03109	−	1.03109i
$339$		0			0
$340$	1.04790	+	15.1040i	0.0568306	+	0.819128i
$341$			7.43442i			0.402596i
$342$		0			0
$343$		0			0
$344$	10.8146			0.583086
$345$		0			0
$346$	−20.5233			−1.10334
$347$	6.47812	+	6.47812i	0.347764	+	0.347764i	0.859276	−	0.511512i	$-0.170914\pi$
$347$	6.47812	+	6.47812i	0.347764	+	0.347764i	−0.511512	+	0.859276i	$0.670914\pi$
$348$		0			0
$349$		−	28.3316i		−	1.51656i	−0.651930	−	0.758279i	$-0.726041\pi$
$349$		−	28.3316i		−	1.51656i	0.651930	−	0.758279i	$-0.273959\pi$
$350$		0			0
$351$		0			0
$352$	0.876155	−	0.876155i	0.0466992	−	0.0466992i
$353$	−5.10997	+	5.10997i	−0.271976	+	0.271976i	−0.829895	−	0.557919i	$-0.811600\pi$
$353$	−5.10997	+	5.10997i	−0.271976	+	0.271976i	0.557919	+	0.829895i	$0.311600\pi$
$354$		0			0
$355$	27.3409	+	23.7932i	1.45110	+	1.26281i
$356$		−	4.52518i		−	0.239834i
$357$		0			0
$358$	6.02351	+	6.02351i	0.318352	+	0.318352i
$359$	29.4937			1.55662			0.778310	−	0.627881i	$-0.216077\pi$
$359$	29.4937			1.55662			0.778310	+	0.627881i	$0.216077\pi$
$360$		0			0
$361$	−15.1331			−0.796477
$362$	−1.67273	−	1.67273i	−0.0879169	−	0.0879169i
$363$		0			0
$364$		0			0
$365$	−14.7047	+	1.02020i	−0.769677	+	0.0533997i
$366$		0			0
$367$	−5.07470	+	5.07470i	−0.264897	+	0.264897i	−0.827040	−	0.562143i	$-0.809977\pi$
$367$	−5.07470	+	5.07470i	−0.264897	+	0.264897i	0.562143	+	0.827040i	$0.309977\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	7.81885	−	8.98466i	0.406482	−	0.467090i
$371$		0			0
$372$		0			0
$373$	−5.77547	−	5.77547i	−0.299043	−	0.299043i	0.541596	−	0.840639i	$-0.317820\pi$
$373$	−5.77547	−	5.77547i	−0.299043	−	0.299043i	−0.840639	+	0.541596i	$0.817820\pi$
$374$	8.38967			0.433820
$375$		0			0
$376$	−2.39957			−0.123748
$377$	20.1887	+	20.1887i	1.03977	+	1.03977i
$378$		0			0
$379$			25.3166i			1.30043i	0.759751	+	0.650214i	$0.225321\pi$
$379$			25.3166i			1.30043i	−0.759751	+	0.650214i	$0.774679\pi$
$380$	−8.57606	+	9.85478i	−0.439942	+	0.505539i
$381$		0			0
$382$	4.52325	−	4.52325i	0.231430	−	0.231430i
$383$	−2.35744	+	2.35744i	−0.120460	+	0.120460i	−0.764767	−	0.644307i	$-0.777146\pi$
$383$	−2.35744	+	2.35744i	−0.120460	+	0.120460i	0.644307	+	0.764767i	$0.277146\pi$
$384$		0			0
$385$		0			0
$386$			12.2820i			0.625139i
$387$		0			0
$388$	9.57116	+	9.57116i	0.485902	+	0.485902i
$389$	−0.457683			−0.0232055			−0.0116027	−	0.999933i	$-0.503693\pi$
$389$	−0.457683			−0.0232055			−0.0116027	+	0.999933i	$0.503693\pi$
$390$		0			0
$391$	−6.77094			−0.342421
$392$	4.94975	+	4.94975i	0.250000	+	0.250000i
$393$		0			0
$394$		−	7.78051i		−	0.391977i
$395$	−13.7505	−	11.9662i	−0.691860	−	0.602087i
$396$		0			0
$397$	−4.09910	+	4.09910i	−0.205728	+	0.205728i	−0.802449	−	0.596721i	$-0.796470\pi$
$397$	−4.09910	+	4.09910i	−0.205728	+	0.205728i	0.596721	+	0.802449i	$0.296470\pi$
$398$	−18.9895	+	18.9895i	−0.951858	+	0.951858i
$399$		0			0
$400$	0.690470	+	4.95210i	0.0345235	+	0.247605i
$401$			28.8474i			1.44057i	0.693679	+	0.720284i	$0.255989\pi$
$401$			28.8474i			1.44057i	−0.693679	+	0.720284i	$0.744011\pi$
$402$		0			0
$403$	−26.7685	−	26.7685i	−1.33343	−	1.33343i
$404$	−9.83175			−0.489148
$405$		0			0
$406$		0			0
$407$	−4.66685	−	4.66685i	−0.231327	−	0.231327i
$408$		0			0
$409$		−	21.3694i		−	1.05665i	−0.849042	−	0.528325i	$-0.822820\pi$
$409$		−	21.3694i		−	1.05665i	0.849042	−	0.528325i	$-0.177180\pi$
$410$	1.37049	+	19.7535i	0.0676835	+	0.975557i
$411$		0			0
$412$	6.00000	−	6.00000i	0.295599	−	0.295599i
$413$		0			0
$414$		0			0
$415$	−0.205553	−	2.96274i	−0.0100902	−	0.145435i
$416$			6.30939i			0.309343i
$417$		0			0
$418$	5.11880	+	5.11880i	0.250369	+	0.250369i
$419$	17.3388			0.847056			0.423528	−	0.905883i	$-0.360791\pi$
$419$	17.3388			0.847056			0.423528	+	0.905883i	$0.360791\pi$
$420$		0			0
$421$	−16.8700			−0.822196			−0.411098	−	0.911591i	$-0.634855\pi$
$421$	−16.8700			−0.822196			−0.411098	+	0.911591i	$0.634855\pi$
$422$	−10.0133	−	10.0133i	−0.487440	−	0.487440i
$423$		0			0
$424$		−	4.30953i		−	0.209289i
$425$	−20.4037	+	27.0154i	−0.989726	+	1.31044i
$426$		0			0
$427$		0			0
$428$	−7.83508	+	7.83508i	−0.378723	+	0.378723i
$429$		0			0
$430$	18.2419	+	15.8749i	0.879704	+	0.765557i
$431$		−	5.88446i		−	0.283445i	−0.989906	−	0.141722i	$-0.954736\pi$
$431$		−	5.88446i		−	0.283445i	0.989906	−	0.141722i	$-0.0452640\pi$
$432$		0			0
$433$	3.97073	+	3.97073i	0.190821	+	0.190821i	0.796051	−	0.605230i	$-0.206919\pi$
$433$	3.97073	+	3.97073i	0.190821	+	0.190821i	−0.605230	+	0.796051i	$0.706919\pi$
$434$		0			0
$435$		0			0
$436$	−10.7091			−0.512873
$437$	−4.13117	−	4.13117i	−0.197620	−	0.197620i
$438$		0			0
$439$			7.64744i			0.364992i	0.983207	+	0.182496i	$0.0584177\pi$
$439$			7.64744i			0.364992i	−0.983207	+	0.182496i	$0.941582\pi$
$440$	2.76400	−	0.191765i	0.131769	−	0.00914202i
$441$		0			0
$442$	−30.2080	+	30.2080i	−1.43685	+	1.43685i
$443$	15.0095	−	15.0095i	0.713121	−	0.713121i	−0.254066	−	0.967187i	$-0.581768\pi$
$443$	15.0095	−	15.0095i	0.713121	−	0.713121i	0.967187	+	0.254066i	$0.0817680\pi$
$444$		0			0
$445$	6.64257	−	7.63300i	0.314888	−	0.361839i
$446$		−	24.7274i		−	1.17088i
$447$		0			0
$448$		0			0
$449$	−16.8282			−0.794171			−0.397085	−	0.917782i	$-0.629978\pi$
$449$	−16.8282			−0.794171			−0.397085	+	0.917782i	$0.629978\pi$
$450$		0			0
$451$	10.9723			0.516666
$452$	11.3534	+	11.3534i	0.534017	+	0.534017i
$453$		0			0
$454$		−	24.6224i		−	1.15558i
$455$		0			0
$456$		0			0
$457$	22.2184	−	22.2184i	1.03933	−	1.03933i	0.0401396	−	0.999194i	$-0.487220\pi$
$457$	22.2184	−	22.2184i	1.03933	−	1.03933i	0.999194	−	0.0401396i	$-0.0127803\pi$
$458$	4.19891	−	4.19891i	0.196202	−	0.196202i
$459$		0			0
$460$	−2.23071	+	0.154765i	−0.104007	+	0.00721595i
$461$			7.47279i			0.348043i	0.984742	+	0.174021i	$0.0556762\pi$
$461$			7.47279i			0.348043i	−0.984742	+	0.174021i	$0.944324\pi$
$462$		0			0
$463$	−16.8514	−	16.8514i	−0.783152	−	0.783152i	0.197210	−	0.980361i	$-0.436812\pi$
$463$	−16.8514	−	16.8514i	−0.783152	−	0.783152i	−0.980361	+	0.197210i	$0.936812\pi$
$464$	−4.52518			−0.210076
$465$		0			0
$466$	−0.619060			−0.0286774
$467$	−6.58785	−	6.58785i	−0.304849	−	0.304849i	0.538058	−	0.842908i	$-0.319158\pi$
$467$	−6.58785	−	6.58785i	−0.304849	−	0.304849i	−0.842908	+	0.538058i	$0.819158\pi$
$468$		0			0
$469$		0			0
$470$	−4.04756	−	3.52236i	−0.186700	−	0.162474i
$471$		0			0
$472$	−0.490684	+	0.490684i	−0.0225856	+	0.0225856i
$473$	9.47529	−	9.47529i	0.435674	−	0.435674i
$474$		0			0
$475$	−28.9319	+	4.03397i	−1.32749	+	0.185091i
$476$		0			0
$477$		0			0
$478$	−18.5126	−	18.5126i	−0.846747	−	0.846747i
$479$	−13.7091			−0.626383			−0.313191	−	0.949690i	$-0.601398\pi$
$479$	−13.7091			−0.626383			−0.313191	+	0.949690i	$0.601398\pi$
$480$		0			0
$481$	33.6070			1.53235
$482$	10.8624	+	10.8624i	0.494770	+	0.494770i
$483$		0			0
$484$			9.46471i			0.430214i
$485$	2.09485	+	30.1941i	0.0951220	+	1.37104i
$486$		0			0
$487$	17.7091	−	17.7091i	0.802476	−	0.802476i	−0.181006	−	0.983482i	$-0.557935\pi$
$487$	17.7091	−	17.7091i	0.802476	−	0.802476i	0.983482	+	0.181006i	$0.0579353\pi$
$488$	10.1580	−	10.1580i	0.459832	−	0.459832i
$489$		0			0
$490$	1.08335	+	15.6149i	0.0489410	+	0.705411i
$491$		−	14.4858i		−	0.653734i	−0.945070	−	0.326867i	$-0.894007\pi$
$491$		−	14.4858i		−	0.653734i	0.945070	−	0.326867i	$-0.105993\pi$
$492$		0			0
$493$	−21.6656	−	21.6656i	−0.975768	−	0.975768i
$494$	−36.8617			−1.65848
$495$		0			0
$496$	6.00000			0.269408
$497$		0			0
$498$		0			0
$499$			0.495380i			0.0221763i	0.999939	+	0.0110881i	$0.00352954\pi$
$499$			0.495380i			0.0221763i	−0.999939	+	0.0110881i	$0.996470\pi$
$500$	−6.10457	+	9.36666i	−0.273005	+	0.418890i
$501$		0			0
$502$	−14.9322	+	14.9322i	−0.666458	+	0.666458i
$503$	6.82177	−	6.82177i	0.304168	−	0.304168i	−0.538474	−	0.842642i	$-0.680999\pi$
$503$	6.82177	−	6.82177i	0.304168	−	0.304168i	0.842642	+	0.538474i	$0.180999\pi$
$504$		0			0
$505$	−16.5840	−	14.4321i	−0.737979	−	0.642222i
$506$			1.23907i			0.0550834i
$507$		0			0
$508$	9.61329	+	9.61329i	0.426521	+	0.426521i
$509$	2.70773			0.120018			0.0600090	−	0.998198i	$-0.480887\pi$
$509$	2.70773			0.120018			0.0600090	+	0.998198i	$0.480887\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	15.3224i		−	0.675842i
$515$	18.9282	−	1.31322i	0.834075	−	0.0578676i
$516$		0			0
$517$	−2.10240	+	2.10240i	−0.0924633	+	0.0924633i
$518$		0			0
$519$		0			0
$520$	−9.26163	+	10.6426i	−0.406149	+	0.466707i
$521$		−	19.5029i		−	0.854438i	−0.904148	−	0.427219i	$-0.859493\pi$
$521$		−	19.5029i		−	0.854438i	0.904148	−	0.427219i	$-0.140507\pi$
$522$		0			0
$523$	19.4555	+	19.4555i	0.850729	+	0.850729i	0.990223	−	0.139494i	$-0.0445477\pi$
$523$	19.4555	+	19.4555i	0.850729	+	0.850729i	−0.139494	+	0.990223i	$0.544548\pi$
$524$	−16.1411			−0.705129
$525$		0			0
$526$	−17.9042			−0.780660
$527$	28.7267	+	28.7267i	1.25135	+	1.25135i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	6.32601	−	7.26924i	0.274784	−	0.315756i
$531$		0			0
$532$		0			0
$533$	−39.5070	+	39.5070i	−1.71124	+	1.71124i
$534$		0			0
$535$	−24.7173	+	1.71487i	−1.06862	+	0.0741402i
$536$		−	4.19484i		−	0.181189i
$537$		0			0
$538$	8.21842	+	8.21842i	0.354321	+	0.354321i
$539$	8.67349			0.373594
$540$		0			0
$541$	17.2754			0.742727			0.371363	−	0.928488i	$-0.378890\pi$
$541$	17.2754			0.742727			0.371363	+	0.928488i	$0.378890\pi$
$542$	19.8783	+	19.8783i	0.853846	+	0.853846i
$543$		0			0
$544$		−	6.77094i		−	0.290302i
$545$	−18.0639	−	15.7200i	−0.773774	−	0.673372i
$546$		0			0
$547$	−12.0561	+	12.0561i	−0.515480	+	0.515480i	−0.916201	−	0.400720i	$-0.868760\pi$
$547$	−12.0561	+	12.0561i	−0.515480	+	0.515480i	0.400720	+	0.916201i	$0.368760\pi$
$548$	−3.65610	+	3.65610i	−0.156181	+	0.156181i
$549$		0			0
$550$	4.94376	+	3.73384i	0.210803	+	0.159212i
$551$		−	26.4377i		−	1.12628i
$552$		0			0
$553$		0			0
$554$	−11.4410			−0.486083
$555$		0			0
$556$	−2.83855			−0.120381
$557$	−7.86143	−	7.86143i	−0.333099	−	0.333099i	0.520663	−	0.853762i	$-0.325685\pi$
$557$	−7.86143	−	7.86143i	−0.333099	−	0.333099i	−0.853762	+	0.520663i	$0.825685\pi$
$558$		0			0
$559$			68.2337i			2.88598i
$560$		0			0
$561$		0			0
$562$	−2.55252	+	2.55252i	−0.107672	+	0.107672i
$563$	−18.8517	+	18.8517i	−0.794504	+	0.794504i	−0.982223	−	0.187719i	$-0.939891\pi$
$563$	−18.8517	+	18.8517i	−0.794504	+	0.794504i	0.187719	+	0.982223i	$0.439891\pi$
$564$		0			0
$565$	2.48492	+	35.8164i	0.104541	+	1.50681i
$566$			30.6055i			1.28644i
$567$		0			0
$568$	−11.4614	−	11.4614i	−0.480910	−	0.480910i
$569$	−7.64770			−0.320608			−0.160304	−	0.987068i	$-0.551247\pi$
$569$	−7.64770			−0.320608			−0.160304	+	0.987068i	$0.551247\pi$
$570$		0			0
$571$	−12.5854			−0.526684			−0.263342	−	0.964703i	$-0.584825\pi$
$571$	−12.5854			−0.526684			−0.263342	+	0.964703i	$0.584825\pi$
$572$	5.52800	+	5.52800i	0.231137	+	0.231137i
$573$		0			0
$574$		0			0
$575$	−3.98990	−	3.01342i	−0.166390	−	0.125668i
$576$		0			0
$577$	−13.2803	+	13.2803i	−0.552864	+	0.552864i	−0.927266	−	0.374402i	$-0.877848\pi$
$577$	−13.2803	+	13.2803i	−0.552864	+	0.552864i	0.374402	+	0.927266i	$0.377848\pi$
$578$	20.3970	−	20.3970i	0.848401	−	0.848401i
$579$		0			0
$580$	−7.63300	−	6.64257i	−0.316943	−	0.275818i
$581$		0			0
$582$		0			0
$583$	−3.77582	−	3.77582i	−0.156378	−	0.156378i
$584$	6.59193			0.272776
$585$		0			0
$586$	9.38423			0.387659
$587$	−22.8883	−	22.8883i	−0.944700	−	0.944700i	0.0538492	−	0.998549i	$-0.482851\pi$
$587$	−22.8883	−	22.8883i	−0.944700	−	0.944700i	−0.998549	+	0.0538492i	$0.982851\pi$
$588$		0			0
$589$			35.0541i			1.44438i
$590$	−1.54796	+	0.107396i	−0.0637285	+	0.00442144i
$591$		0			0
$592$	−3.76641	+	3.76641i	−0.154799	+	0.154799i
$593$	15.2785	−	15.2785i	0.627411	−	0.627411i	−0.320005	−	0.947416i	$-0.603684\pi$
$593$	15.2785	−	15.2785i	0.627411	−	0.627411i	0.947416	+	0.320005i	$0.103684\pi$
$594$		0			0
$595$		0			0
$596$			4.76143i			0.195036i
$597$		0			0
$598$	−4.46141	−	4.46141i	−0.182441	−	0.182441i
$599$	−21.3467			−0.872203			−0.436102	−	0.899897i	$-0.643641\pi$
$599$	−21.3467			−0.872203			−0.436102	+	0.899897i	$0.643641\pi$
$600$		0			0
$601$	−29.2736			−1.19409			−0.597047	−	0.802206i	$-0.703660\pi$
$601$	−29.2736			−1.19409			−0.597047	+	0.802206i	$0.703660\pi$
$602$		0			0
$603$		0			0
$604$		−	5.90419i		−	0.240238i
$605$	−13.8934	+	15.9649i	−0.564845	+	0.649065i
$606$		0			0
$607$	−0.162523	+	0.162523i	−0.00659660	+	0.00659660i	−0.710397	−	0.703801i	$-0.751485\pi$
$607$	−0.162523	+	0.162523i	−0.00659660	+	0.00659660i	0.703801	+	0.710397i	$0.251485\pi$
$608$	4.13117	−	4.13117i	0.167541	−	0.167541i
$609$		0			0
$610$	32.0454	−	2.22329i	1.29748	−	0.0900185i
$611$		−	15.1398i		−	0.612492i
$612$		0			0
$613$	23.3116	+	23.3116i	0.941546	+	0.941546i	0.998383	−	0.0568373i	$-0.0181016\pi$
$613$	23.3116	+	23.3116i	0.941546	+	0.941546i	−0.0568373	+	0.998383i	$0.518102\pi$
$614$	−24.8080			−1.00117
$615$		0			0
$616$		0			0
$617$	28.2825	+	28.2825i	1.13861	+	1.13861i	0.988699	+	0.149912i	$0.0478991\pi$
$617$	28.2825	+	28.2825i	1.13861	+	1.13861i	0.149912	+	0.988699i	$0.452101\pi$
$618$		0			0
$619$		−	17.2414i		−	0.692991i	−0.938052	−	0.346495i	$-0.887372\pi$
$619$		−	17.2414i		−	0.692991i	0.938052	−	0.346495i	$-0.112628\pi$
$620$	10.1207	+	8.80747i	0.406457	+	0.353717i
$621$		0			0
$622$	17.8935	−	17.8935i	0.717466	−	0.717466i
$623$		0			0
$624$		0			0
$625$	−24.0465	+	6.83855i	−0.961860	+	0.273542i
$626$		−	15.0028i		−	0.599633i
$627$		0			0
$628$	2.99547	+	2.99547i	0.119532	+	0.119532i
$629$	−36.0655			−1.43802
$630$		0			0
$631$	14.7337			0.586538			0.293269	−	0.956030i	$-0.405257\pi$
$631$	14.7337			0.586538			0.293269	+	0.956030i	$0.405257\pi$
$632$	5.76425	+	5.76425i	0.229290	+	0.229290i
$633$		0			0
$634$			9.44607i			0.375152i
$635$	2.10407	+	30.3270i	0.0834974	+	1.20349i
$636$		0			0
$637$	−31.2299	+	31.2299i	−1.23737	+	1.23737i
$638$	−3.96476	+	3.96476i	−0.156966	+	0.156966i
$639$		0			0
$640$	−0.154765	−	2.23071i	−0.00611762	−	0.0881764i
$641$		−	15.8517i		−	0.626105i	−0.949736	−	0.313052i	$-0.898648\pi$
$641$		−	15.8517i		−	0.626105i	0.949736	−	0.313052i	$-0.101352\pi$
$642$		0			0
$643$	−19.3748	−	19.3748i	−0.764069	−	0.764069i	0.212986	−	0.977055i	$-0.431681\pi$
$643$	−19.3748	−	19.3748i	−0.764069	−	0.764069i	−0.977055	+	0.212986i	$0.931681\pi$
$644$		0			0
$645$		0			0
$646$	39.5582			1.55640
$647$	−4.71362	−	4.71362i	−0.185312	−	0.185312i	0.608354	−	0.793666i	$-0.291830\pi$
$647$	−4.71362	−	4.71362i	−0.185312	−	0.185312i	−0.793666	+	0.608354i	$0.791830\pi$
$648$		0			0
$649$			0.859831i			0.0337513i
$650$	−31.2447	+	4.35644i	−1.22552	+	0.170874i
$651$		0			0
$652$	11.2851	−	11.2851i	0.441960	−	0.441960i
$653$	−35.2327	+	35.2327i	−1.37876	+	1.37876i	−0.532043	+	0.846717i	$0.678576\pi$
$653$	−35.2327	+	35.2327i	−1.37876	+	1.37876i	−0.846717	+	0.532043i	$0.821424\pi$
$654$		0			0
$655$	−27.2266	−	23.6938i	−1.06383	−	0.925792i
$656$		−	8.85528i		−	0.345740i
$657$		0			0
$658$		0			0
$659$	0.0613400			0.00238947			0.00119473	−	0.999999i	$-0.499620\pi$
$659$	0.0613400			0.00238947			0.00119473	+	0.999999i	$0.499620\pi$
$660$		0			0
$661$	−7.94722			−0.309111			−0.154556	−	0.987984i	$-0.549395\pi$
$661$	−7.94722			−0.309111			−0.154556	+	0.987984i	$0.549395\pi$
$662$	25.2790	+	25.2790i	0.982494	+	0.982494i
$663$		0			0
$664$			1.32816i			0.0515427i
$665$		0			0
$666$		0			0
$667$	3.19979	−	3.19979i	0.123896	−	0.123896i
$668$	−3.19842	+	3.19842i	−0.123751	+	0.123751i
$669$		0			0
$670$	6.15765	−	7.07577i	0.237891	−	0.273361i
$671$		−	17.8000i		−	0.687161i
$672$		0			0
$673$	14.5654	+	14.5654i	0.561454	+	0.561454i	0.929720	−	0.368266i	$-0.120048\pi$
$673$	14.5654	+	14.5654i	0.561454	+	0.561454i	−0.368266	+	0.929720i	$0.620048\pi$
$674$	32.7533			1.26161
$675$		0			0
$676$	−26.8084			−1.03109
$677$	−34.4341	−	34.4341i	−1.32341	−	1.32341i	−0.910996	−	0.412416i	$-0.864685\pi$
$677$	−34.4341	−	34.4341i	−1.32341	−	1.32341i	−0.412416	−	0.910996i	$-0.635315\pi$
$678$		0			0
$679$		0			0
$680$	9.93914	−	11.4211i	0.381149	−	0.437979i
$681$		0			0
$682$	5.25693	−	5.25693i	0.201298	−	0.201298i
$683$	35.5898	−	35.5898i	1.36181	−	1.36181i	0.490194	−	0.871613i	$-0.336926\pi$
$683$	35.5898	−	35.5898i	1.36181	−	1.36181i	0.871613	−	0.490194i	$-0.163074\pi$
$684$		0			0
$685$	−11.5339	+	0.800214i	−0.440687	+	0.0305746i
$686$		0			0
$687$		0			0
$688$	−7.64710	−	7.64710i	−0.291543	−	0.291543i
$689$	27.1905			1.03588
$690$		0			0
$691$	−23.3130			−0.886868			−0.443434	−	0.896307i	$-0.646240\pi$
$691$	−23.3130			−0.886868			−0.443434	+	0.896307i	$0.646240\pi$
$692$	14.5121	+	14.5121i	0.551668	+	0.551668i
$693$		0			0
$694$		−	9.16145i		−	0.347764i
$695$	−4.78801	−	4.16674i	−0.181620	−	0.158053i
$696$		0			0
$697$	42.3971	−	42.3971i	1.60590	−	1.60590i
$698$	−20.0335	+	20.0335i	−0.758279	+	0.758279i
$699$		0			0
$700$		0			0
$701$			9.54280i			0.360427i	0.983628	+	0.180213i	$0.0576788\pi$
$701$			9.54280i			0.360427i	−0.983628	+	0.180213i	$0.942321\pi$
$702$		0			0
$703$	−22.0047	−	22.0047i	−0.829923	−	0.829923i
$704$	−1.23907			−0.0466992
$705$		0			0
$706$	7.22659			0.271976
$707$		0			0
$708$		0			0
$709$		−	11.0902i		−	0.416502i	−0.978075	−	0.208251i	$-0.933223\pi$
$709$		−	11.0902i		−	0.416502i	0.978075	−	0.208251i	$-0.0667771\pi$
$710$	−2.50857	−	36.1572i	−0.0941448	−	1.35696i
$711$		0			0
$712$	−3.19979	+	3.19979i	−0.119917	+	0.119917i
$713$	−4.24264	+	4.24264i	−0.158888	+	0.158888i
$714$		0			0
$715$	1.20992	+	17.4392i	0.0452483	+	0.652187i
$716$		−	8.51852i		−	0.318352i
$717$		0			0
$718$	−20.8552	−	20.8552i	−0.778310	−	0.778310i
$719$	−23.8647			−0.890005			−0.445002	−	0.895529i	$-0.646797\pi$
$719$	−23.8647			−0.890005			−0.445002	+	0.895529i	$0.646797\pi$
$720$		0			0
$721$		0			0
$722$	10.7007	+	10.7007i	0.398239	+	0.398239i
$723$		0			0
$724$			2.36560i			0.0879169i
$725$	−3.12450	−	22.4091i	−0.116041	−	0.832254i
$726$		0			0
$727$	13.8084	−	13.8084i	0.512125	−	0.512125i	−0.403052	−	0.915177i	$-0.632051\pi$
$727$	13.8084	−	13.8084i	0.512125	−	0.512125i	0.915177	+	0.403052i	$0.132051\pi$
$728$		0			0
$729$		0			0
$730$	11.1191	+	9.67637i	0.411538	+	0.358138i
$731$		−	73.2252i		−	2.70833i
$732$		0			0
$733$	−13.9801	−	13.9801i	−0.516368	−	0.516368i	0.400102	−	0.916470i	$-0.368975\pi$
$733$	−13.9801	−	13.9801i	−0.516368	−	0.516368i	−0.916470	+	0.400102i	$0.868975\pi$
$734$	7.17672			0.264897
$735$		0			0
$736$	1.00000			0.0368605
$737$	−3.67533	−	3.67533i	−0.135382	−	0.135382i
$738$		0			0
$739$		−	39.0722i		−	1.43730i	−0.695374	−	0.718648i	$-0.744761\pi$
$739$		−	39.0722i		−	1.43730i	0.695374	−	0.718648i	$-0.255239\pi$
$740$	−11.8819	+	0.824357i	−0.436786	+	0.0303040i
$741$		0			0
$742$		0			0
$743$	16.7937	−	16.7937i	0.616100	−	0.616100i	−0.328429	−	0.944529i	$-0.606519\pi$
$743$	16.7937	−	16.7937i	0.616100	−	0.616100i	0.944529	+	0.328429i	$0.106519\pi$
$744$		0			0
$745$	−6.98936	+	8.03150i	−0.256070	+	0.294251i
$746$			8.16775i			0.299043i
$747$		0			0
$748$	−5.93239	−	5.93239i	−0.216910	−	0.216910i
$749$		0			0
$750$		0			0
$751$	8.10487			0.295751			0.147875	−	0.989006i	$-0.452757\pi$
$751$	8.10487			0.295751			0.147875	+	0.989006i	$0.452757\pi$
$752$	1.69675	+	1.69675i	0.0618742	+	0.0618742i
$753$		0			0
$754$		−	28.5511i		−	1.03977i
$755$	8.66683	−	9.95909i	0.315418	−	0.362448i
$756$		0			0
$757$	−6.98970	+	6.98970i	−0.254045	+	0.254045i	−0.822627	−	0.568582i	$-0.807492\pi$
$757$	−6.98970	+	6.98970i	−0.254045	+	0.254045i	0.568582	+	0.822627i	$0.307492\pi$
$758$	17.9016	−	17.9016i	0.650214	−	0.650214i
$759$		0			0
$760$	13.0326	−	0.904191i	0.472741	−	0.0327985i
$761$			30.6134i			1.10973i	0.831939	+	0.554867i	$0.187231\pi$
$761$			30.6134i			1.10973i	−0.831939	+	0.554867i	$0.812769\pi$
$762$		0			0
$763$		0			0
$764$	−6.39684			−0.231430
$765$		0			0
$766$	3.33393			0.120460
$767$	−3.09592	−	3.09592i	−0.111787	−	0.111787i
$768$		0			0
$769$			31.6070i			1.13978i	0.821722	+	0.569889i	$0.193014\pi$
$769$			31.6070i			1.13978i	−0.821722	+	0.569889i	$0.806986\pi$
$770$		0			0
$771$		0			0
$772$	8.68470	−	8.68470i	0.312569	−	0.312569i
$773$	−20.6622	+	20.6622i	−0.743169	+	0.743169i	−0.973187	−	0.230017i	$-0.926122\pi$
$773$	−20.6622	+	20.6622i	−0.743169	+	0.743169i	0.230017	+	0.973187i	$0.426122\pi$
$774$		0			0
$775$	4.14282	+	29.7126i	0.148815	+	1.06731i
$776$		−	13.5357i		−	0.485902i
$777$		0			0
$778$	0.323631	+	0.323631i	0.0116027	+	0.0116027i
$779$	51.7356			1.85362
$780$		0			0
$781$	−20.0839			−0.718660
$782$	4.78778	+	4.78778i	0.171211	+	0.171211i
$783$		0			0
$784$		−	7.00000i		−	0.250000i
$785$	0.655620	+	9.44979i	0.0234001	+	0.337277i
$786$		0			0
$787$	7.64380	−	7.64380i	0.272472	−	0.272472i	−0.557623	−	0.830095i	$-0.688286\pi$
$787$	7.64380	−	7.64380i	0.272472	−	0.272472i	0.830095	+	0.557623i	$0.188286\pi$
$788$	−5.50165	+	5.50165i	−0.195988	+	0.195988i
$789$		0			0
$790$	1.26163	+	18.1844i	0.0448866	+	0.646974i
$791$		0			0
$792$		0			0
$793$	64.0909	+	64.0909i	2.27593	+	2.27593i
$794$	5.79701			0.205728
$795$		0			0
$796$	26.8552			0.951858
$797$	−6.53641	−	6.53641i	−0.231532	−	0.231532i	0.581800	−	0.813332i	$-0.302349\pi$
$797$	−6.53641	−	6.53641i	−0.231532	−	0.231532i	−0.813332	+	0.581800i	$0.802349\pi$
$798$		0			0
$799$			16.2474i			0.574790i
$800$	3.01342	−	3.98990i	0.106541	−	0.141064i
$801$		0			0
$802$	20.3982	−	20.3982i	0.720284	−	0.720284i
$803$	5.77555	−	5.77555i	0.203815	−	0.203815i
$804$		0			0
$805$		0			0
$806$			37.8563i			1.33343i
$807$		0			0
$808$	6.95210	+	6.95210i	0.244574	+	0.244574i
$809$	−33.6137			−1.18179			−0.590897	−	0.806747i	$-0.701226\pi$
$809$	−33.6137			−1.18179			−0.590897	+	0.806747i	$0.701226\pi$
$810$		0			0
$811$	40.7291			1.43019			0.715095	−	0.699027i	$-0.246383\pi$
$811$	40.7291			1.43019			0.715095	+	0.699027i	$0.246383\pi$
$812$		0			0
$813$		0			0
$814$			6.59992i			0.231327i
$815$	35.6011	−	2.46998i	1.24705	−	0.0865198i
$816$		0			0
$817$	44.6770	−	44.6770i	1.56305	−	1.56305i
$818$	−15.1105	+	15.1105i	−0.528325	+	0.528325i
$819$		0			0
$820$	12.9988	−	14.9369i	0.453937	−	0.521620i
$821$			16.6582i			0.581374i	0.956818	+	0.290687i	$0.0938839\pi$
$821$			16.6582i			0.581374i	−0.956818	+	0.290687i	$0.906116\pi$
$822$		0			0
$823$	−14.4663	−	14.4663i	−0.504263	−	0.504263i	0.408497	−	0.912760i	$-0.366053\pi$
$823$	−14.4663	−	14.4663i	−0.504263	−	0.504263i	−0.912760	+	0.408497i	$0.866053\pi$
$824$	−8.48528			−0.295599
$825$		0			0
$826$		0			0
$827$	39.5175	+	39.5175i	1.37416	+	1.37416i	0.854178	+	0.519980i	$0.174061\pi$
$827$	39.5175	+	39.5175i	1.37416	+	1.37416i	0.519980	+	0.854178i	$0.325939\pi$
$828$		0			0
$829$			33.3875i			1.15960i	0.814760	+	0.579798i	$0.196869\pi$
$829$			33.3875i			1.15960i	−0.814760	+	0.579798i	$0.803131\pi$
$830$	−1.94962	+	2.24032i	−0.0676724	+	0.0777626i
$831$		0			0
$832$	4.46141	−	4.46141i	0.154672	−	0.154672i
$833$	33.5144	−	33.5144i	1.16121	−	1.16121i
$834$		0			0
$835$	−10.0900	+	0.700041i	−0.349180	+	0.0242259i
$836$		−	7.23908i		−	0.250369i
$837$		0			0
$838$	−12.2604	−	12.2604i	−0.423528	−	0.423528i
$839$	−0.591681			−0.0204271			−0.0102135	−	0.999948i	$-0.503251\pi$
$839$	−0.591681			−0.0204271			−0.0102135	+	0.999948i	$0.503251\pi$
$840$		0			0
$841$	−8.52274			−0.293888
$842$	11.9289	+	11.9289i	0.411098	+	0.411098i
$843$		0			0
$844$			14.1609i			0.487440i
$845$	−45.2199	−	39.3523i	−1.55561	−	1.35376i
$846$		0			0
$847$		0			0
$848$	−3.04730	+	3.04730i	−0.104645	+	0.104645i
$849$		0			0
$850$	33.5303	−	4.67513i	1.15008	−	0.160356i
$851$		−	5.32651i		−	0.182590i
$852$		0			0
$853$	−34.3071	−	34.3071i	−1.17465	−	1.17465i	−0.981088	−	0.193564i	$-0.937995\pi$
$853$	−34.3071	−	34.3071i	−1.17465	−	1.17465i	−0.193564	−	0.981088i	$-0.562005\pi$
$854$		0			0
$855$		0			0
$856$	11.0805			0.378723
$857$	14.2559	+	14.2559i	0.486974	+	0.486974i	0.907350	−	0.420376i	$-0.138102\pi$
$857$	14.2559	+	14.2559i	0.486974	+	0.486974i	−0.420376	+	0.907350i	$0.638102\pi$
$858$		0			0
$859$		−	39.2545i		−	1.33934i	−0.742657	−	0.669672i	$-0.766435\pi$
$859$		−	39.2545i		−	1.33934i	0.742657	−	0.669672i	$-0.233565\pi$
$860$	−1.67373	−	24.1243i	−0.0570736	−	0.822630i
$861$		0			0
$862$	−4.16094	+	4.16094i	−0.141722	+	0.141722i
$863$	−17.6300	+	17.6300i	−0.600132	+	0.600132i	−0.940347	−	0.340216i	$-0.889500\pi$
$863$	−17.6300	+	17.6300i	−0.600132	+	0.600132i	0.340216	+	0.940347i	$0.389500\pi$
$864$		0			0
$865$	3.17628	+	45.7813i	0.107997	+	1.55661i
$866$		−	5.61546i		−	0.190821i
$867$		0			0
$868$		0			0
$869$	10.1008			0.342645
$870$		0			0
$871$	26.4668			0.896795
$872$	7.57248	+	7.57248i	0.256436	+	0.256436i
$873$		0			0
$874$			5.84235i			0.197620i
$875$		0			0
$876$		0			0
$877$	9.45184	−	9.45184i	0.319166	−	0.319166i	−0.529281	−	0.848447i	$-0.677538\pi$
$877$	9.45184	−	9.45184i	0.319166	−	0.319166i	0.848447	+	0.529281i	$0.177538\pi$
$878$	5.40756	−	5.40756i	0.182496	−	0.182496i
$879$		0			0
$880$	−2.09004	−	1.81885i	−0.0704553	−	0.0613133i
$881$			23.9576i			0.807151i	0.914946	+	0.403576i	$0.132233\pi$
$881$			23.9576i			0.807151i	−0.914946	+	0.403576i	$0.867767\pi$
$882$		0			0
$883$	−10.9319	−	10.9319i	−0.367887	−	0.367887i	0.498819	−	0.866706i	$-0.333767\pi$
$883$	−10.9319	−	10.9319i	−0.367887	−	0.367887i	−0.866706	+	0.498819i	$0.833767\pi$
$884$	42.7205			1.43685
$885$		0			0
$886$	−21.2266			−0.713121
$887$	−24.0931	−	24.0931i	−0.808966	−	0.808966i	0.175511	−	0.984477i	$-0.443842\pi$
$887$	−24.0931	−	24.0931i	−0.808966	−	0.808966i	−0.984477	+	0.175511i	$0.943842\pi$
$888$		0			0
$889$		0			0
$890$	−10.0943	+	0.700339i	−0.338363	+	0.0234754i
$891$		0			0
$892$	−17.4849	+	17.4849i	−0.585438	+	0.585438i
$893$	−9.91303	+	9.91303i	−0.331727	+	0.331727i
$894$		0			0
$895$	12.5044	−	14.3689i	0.417977	−	0.480299i
$896$		0			0
$897$		0			0
$898$	11.8993	+	11.8993i	0.397085	+	0.397085i
$899$	−27.1511			−0.905539
$900$		0			0
$901$	−29.1796			−0.972113
$902$	−7.75859	−	7.75859i	−0.258333	−	0.258333i
$903$		0			0
$904$		−	16.0561i		−	0.534017i
$905$	−3.47250	+	3.99026i	−0.115430	+	0.132641i
$906$		0			0
$907$	20.2546	−	20.2546i	0.672544	−	0.672544i	−0.285758	−	0.958302i	$-0.592245\pi$
$907$	20.2546	−	20.2546i	0.672544	−	0.672544i	0.958302	+	0.285758i	$0.0922454\pi$
$908$	−17.4106	+	17.4106i	−0.577792	+	0.577792i
$909$		0			0
$910$		0			0
$911$			10.8841i			0.360607i	0.983611	+	0.180304i	$0.0577080\pi$
$911$			10.8841i			0.360607i	−0.983611	+	0.180304i	$0.942292\pi$
$912$		0			0
$913$	1.16368	+	1.16368i	0.0385120	+	0.0385120i
$914$	−31.4216			−1.03933
$915$		0			0
$916$	−5.93816			−0.196202
$917$		0			0
$918$		0			0
$919$			10.3598i			0.341739i	0.985294	+	0.170870i	$0.0546577\pi$
$919$			10.3598i			0.341739i	−0.985294	+	0.170870i	$0.945342\pi$
$920$	1.68678	+	1.46791i	0.0556116	+	0.0483956i
$921$		0			0
$922$	5.28406	−	5.28406i	0.174021	−	0.174021i
$923$	72.3145	−	72.3145i	2.38026	−	2.38026i
$924$		0			0
$925$	−21.2522	−	16.0510i	−0.698769	−	0.527755i
$926$			23.8315i			0.783152i
$927$		0			0
$928$	3.19979	+	3.19979i	0.105038	+	0.105038i
$929$	11.4817			0.376703			0.188352	−	0.982102i	$-0.439686\pi$
$929$	11.4817			0.376703			0.188352	+	0.982102i	$0.439686\pi$
$930$		0			0
$931$	40.8965			1.34033
$932$	0.437741	+	0.437741i	0.0143387	+	0.0143387i
$933$		0			0
$934$			9.31663i			0.304849i
$935$	−1.29843	−	18.7149i	−0.0424631	−	0.612042i
$936$		0			0
$937$	−5.72551	+	5.72551i	−0.187044	+	0.187044i	−0.794417	−	0.607373i	$-0.792223\pi$
$937$	−5.72551	+	5.72551i	−0.187044	+	0.187044i	0.607373	+	0.794417i	$0.292223\pi$
$938$		0			0
$939$		0			0
$940$	0.371370	+	5.35274i	0.0121127	+	0.174587i
$941$		−	42.4347i		−	1.38333i	−0.722218	−	0.691666i	$-0.756877\pi$
$941$		−	42.4347i		−	1.38333i	0.722218	−	0.691666i	$-0.243123\pi$
$942$		0			0
$943$	6.26163	+	6.26163i	0.203907	+	0.203907i
$944$	0.693932			0.0225856
$945$		0			0
$946$	−13.4001			−0.435674
$947$	13.8251	+	13.8251i	0.449255	+	0.449255i	0.895107	−	0.445852i	$-0.147099\pi$
$947$	13.8251	+	13.8251i	0.449255	+	0.449255i	−0.445852	+	0.895107i	$0.647099\pi$
$948$		0			0
$949$			41.5910i			1.35010i
$950$	23.3104	+	17.6055i	0.756289	+	0.571197i
$951$		0			0
$952$		0			0
$953$	9.83815	−	9.83815i	0.318689	−	0.318689i	−0.529574	−	0.848263i	$-0.677648\pi$
$953$	9.83815	−	9.83815i	0.318689	−	0.318689i	0.848263	+	0.529574i	$0.177648\pi$
$954$		0			0
$955$	−10.7901	−	9.39000i	−0.349159	−	0.303853i
$956$			26.1808i			0.846747i
$957$		0			0
$958$	9.69376	+	9.69376i	0.313191	+	0.313191i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−23.7637	−	23.7637i	−0.766174	−	0.766174i
$963$		0			0
$964$		−	15.3618i		−	0.494770i
$965$	27.3976	−	1.90083i	0.881959	−	0.0611898i
$966$		0			0
$967$	1.20902	−	1.20902i	0.0388796	−	0.0388796i	−0.687400	−	0.726279i	$-0.741248\pi$
$967$	1.20902	−	1.20902i	0.0388796	−	0.0388796i	0.726279	+	0.687400i	$0.241248\pi$
$968$	6.69256	−	6.69256i	0.215107	−	0.215107i
$969$		0			0
$970$	19.8692	−	22.8317i	0.637960	−	0.733082i
$971$		−	12.4490i		−	0.399508i	−0.979846	−	0.199754i	$-0.935986\pi$
$971$		−	12.4490i		−	0.399508i	0.979846	−	0.199754i	$-0.0640143\pi$
$972$		0			0
$973$		0			0
$974$	−25.0445			−0.802476
$975$		0			0
$976$	−14.3656			−0.459832
$977$	33.3661	+	33.3661i	1.06748	+	1.06748i	0.997552	+	0.0699252i	$0.0222761\pi$
$977$	33.3661	+	33.3661i	1.06748	+	1.06748i	0.0699252	+	0.997552i	$0.477724\pi$
$978$		0			0
$979$			5.60702i			0.179201i
$980$	10.2754	−	11.8075i	0.328235	−	0.377176i
$981$		0			0
$982$	−10.2430	+	10.2430i	−0.326867	+	0.326867i
$983$	−0.948609	+	0.948609i	−0.0302559	+	0.0302559i	−0.722073	−	0.691817i	$-0.756810\pi$
$983$	−0.948609	+	0.948609i	−0.0302559	+	0.0302559i	0.691817	+	0.722073i	$0.256810\pi$
$984$		0			0
$985$	−17.3560	+	1.20415i	−0.553009	+	0.0383674i
$986$			30.6397i			0.975768i
$987$		0			0
$988$	26.0651	+	26.0651i	0.829242	+	0.829242i
$989$	10.8146			0.343885
$990$		0			0
$991$	55.4461			1.76130			0.880651	−	0.473765i	$-0.157105\pi$
$991$	55.4461			1.76130			0.880651	+	0.473765i	$0.157105\pi$
$992$	−4.24264	−	4.24264i	−0.134704	−	0.134704i
$993$		0			0
$994$		0			0
$995$	45.2989	+	39.4211i	1.43607	+	1.24973i
$996$		0			0
$997$	−6.11791	+	6.11791i	−0.193756	+	0.193756i	−0.797317	−	0.603561i	$-0.793748\pi$
$997$	−6.11791	+	6.11791i	−0.193756	+	0.193756i	0.603561	+	0.797317i	$0.293748\pi$
$998$	0.350287	−	0.350287i	0.0110881	−	0.0110881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.h.323.1	✓	16
3.2	odd	2	inner	2070.2.j.h.323.8	yes	16
5.2	odd	4	inner	2070.2.j.h.737.8	yes	16
15.2	even	4	inner	2070.2.j.h.737.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.h.323.1	✓	16	1.1	even	1	trivial
2070.2.j.h.323.8	yes	16	3.2	odd	2	inner
2070.2.j.h.737.1	yes	16	15.2	even	4	inner
2070.2.j.h.737.8	yes	16	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.46791 + 1.68678i) q^{5} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.46791 + 1.68678i) q^{5} +(0.707107 - 0.707107i) q^{8} +(2.23071 - 0.154765i) q^{10} -1.23907i q^{11} +(4.46141 + 4.46141i) q^{13} -1.00000 q^{16} +(-4.78778 - 4.78778i) q^{17} -5.84235i q^{19} +(-1.68678 - 1.46791i) q^{20} +(-0.876155 + 0.876155i) q^{22} +(0.707107 - 0.707107i) q^{23} +(-0.690470 - 4.95210i) q^{25} -6.30939i q^{26} +4.52518 q^{29} -6.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +6.77094i q^{34} +(3.76641 - 3.76641i) q^{37} +(-4.13117 + 4.13117i) q^{38} +(0.154765 + 2.23071i) q^{40} +8.85528i q^{41} +(7.64710 + 7.64710i) q^{43} +1.23907 q^{44} -1.00000 q^{46} +(-1.69675 - 1.69675i) q^{47} +7.00000i q^{49} +(-3.01342 + 3.98990i) q^{50} +(-4.46141 + 4.46141i) q^{52} +(3.04730 - 3.04730i) q^{53} +(2.09004 + 1.81885i) q^{55} +(-3.19979 - 3.19979i) q^{58} -0.693932 q^{59} +14.3656 q^{61} +(4.24264 + 4.24264i) q^{62} -1.00000i q^{64} +(-14.0744 + 0.976472i) q^{65} +(2.96620 - 2.96620i) q^{67} +(4.78778 - 4.78778i) q^{68} -16.2089i q^{71} +(4.66120 + 4.66120i) q^{73} -5.32651 q^{74} +5.84235 q^{76} +8.15188i q^{79} +(1.46791 - 1.68678i) q^{80} +(6.26163 - 6.26163i) q^{82} +(-0.939152 + 0.939152i) q^{83} +(15.1040 - 1.04790i) q^{85} -10.8146i q^{86} +(-0.876155 - 0.876155i) q^{88} -4.52518 q^{89} +(0.707107 + 0.707107i) q^{92} +2.39957i q^{94} +(9.85478 + 8.57606i) q^{95} +(9.57116 - 9.57116i) q^{97} +(4.94975 - 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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