LMFDB - Embedded newform 2070.2.j.c.737.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.c.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} +1.41421i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.00000 q^{16} +(-4.24264 + 4.24264i) q^{17} +6.00000i q^{19} +(0.707107 - 2.12132i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} +5.65685i q^{26} +5.65685 q^{29} +(-0.707107 + 0.707107i) q^{32} +6.00000i q^{34} +(3.00000 + 3.00000i) q^{37} +(4.24264 + 4.24264i) q^{38} +(-1.00000 - 2.00000i) q^{40} +4.24264i q^{41} +(1.00000 - 1.00000i) q^{43} +1.41421 q^{44} +1.00000 q^{46} +(-7.07107 + 7.07107i) q^{47} -7.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-1.00000 + 3.00000i) q^{55} +(4.00000 - 4.00000i) q^{58} +2.82843 q^{59} +2.00000 q^{61} +1.00000i q^{64} +(-11.3137 + 5.65685i) q^{65} +(-9.00000 - 9.00000i) q^{67} +(4.24264 + 4.24264i) q^{68} -4.24264i q^{71} +(9.00000 - 9.00000i) q^{73} +4.24264 q^{74} +6.00000 q^{76} -4.00000i q^{79} +(-2.12132 - 0.707107i) q^{80} +(3.00000 + 3.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(-12.0000 + 6.00000i) q^{85} -1.41421i q^{86} +(1.00000 - 1.00000i) q^{88} +2.82843 q^{89} +(0.707107 - 0.707107i) q^{92} +10.0000i q^{94} +(-4.24264 + 12.7279i) q^{95} +(8.00000 + 8.00000i) q^{97} +(-4.94975 - 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q+O(q^{10}) $ 4 * q	$ 4 q + 8 q^{10} - 16 q^{13} - 4 q^{16} + 4 q^{22} + 16 q^{25} + 12 q^{37} - 4 q^{40} + 4 q^{43} + 4 q^{46} + 16 q^{52} - 4 q^{55} + 16 q^{58} + 8 q^{61} - 36 q^{67} + 36 q^{73} + 24 q^{76} + 12 q^{82} - 48 q^{85} + 4 q^{88} + 32 q^{97}+O(q^{100}) $ 4 * q + 8 * q^10 - 16 * q^13 - 4 * q^16 + 4 * q^22 + 16 * q^25 + 12 * q^37 - 4 * q^40 + 4 * q^43 + 4 * q^46 + 16 * q^52 - 4 * q^55 + 16 * q^58 + 8 * q^61 - 36 * q^67 + 36 * q^73 + 24 * q^76 + 12 * q^82 - 48 * q^85 + 4 * q^88 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$		0			0
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.0294245	+	0.999567i	$0.509367\pi$
$17$	−4.24264	+	4.24264i	−1.02899	+	1.02899i	−0.999567	+	0.0294245i	$0.990633\pi$
$18$		0			0
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$			5.65685i			1.10940i
$27$		0			0
$28$		0			0
$29$	5.65685			1.05045			0.525226	−	0.850963i	$-0.323981\pi$
$29$	5.65685			1.05045			0.525226	+	0.850963i	$0.323981\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			6.00000i			1.02899i
$35$		0			0
$36$		0			0
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$	4.24264	+	4.24264i	0.688247	+	0.688247i
$39$		0			0
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$			4.24264i			0.662589i	0.943527	+	0.331295i	$0.107485\pi$
$41$			4.24264i			0.662589i	−0.943527	+	0.331295i	$0.892515\pi$
$42$		0			0
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	1.41421			0.213201
$45$		0			0
$46$	1.00000			0.147442
$47$	−7.07107	+	7.07107i	−1.03142	+	1.03142i	−0.0319312	+	0.999490i	$0.510166\pi$
$47$	−7.07107	+	7.07107i	−1.03142	+	1.03142i	−0.999490	+	0.0319312i	$0.989834\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$	−1.00000	+	3.00000i	−0.134840	+	0.404520i
$56$		0			0
$57$		0			0
$58$	4.00000	−	4.00000i	0.525226	−	0.525226i
$59$	2.82843			0.368230			0.184115	−	0.982905i	$-0.441058\pi$
$59$	2.82843			0.368230			0.184115	+	0.982905i	$0.441058\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−11.3137	+	5.65685i	−1.40329	+	0.701646i
$66$		0			0
$67$	−9.00000	−	9.00000i	−1.09952	−	1.09952i	−0.994466	−	0.105059i	$-0.966497\pi$
$67$	−9.00000	−	9.00000i	−1.09952	−	1.09952i	−0.105059	−	0.994466i	$-0.533503\pi$
$68$	4.24264	+	4.24264i	0.514496	+	0.514496i
$69$		0			0
$70$		0			0
$71$		−	4.24264i		−	0.503509i	−0.967791	−	0.251754i	$-0.918992\pi$
$71$		−	4.24264i		−	0.503509i	0.967791	−	0.251754i	$-0.0810075\pi$
$72$		0			0
$73$	9.00000	−	9.00000i	1.05337	−	1.05337i	0.0548772	−	0.998493i	$-0.482523\pi$
$73$	9.00000	−	9.00000i	1.05337	−	1.05337i	0.998493	−	0.0548772i	$-0.0174767\pi$
$74$	4.24264			0.493197
$75$		0			0
$76$	6.00000			0.688247
$77$		0			0
$78$		0			0
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	−2.12132	−	0.707107i	−0.237171	−	0.0790569i
$81$		0			0
$82$	3.00000	+	3.00000i	0.331295	+	0.331295i
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	0.625219	−	0.780449i	$-0.285010\pi$
$83$	−1.41421	−	1.41421i	−0.155230	−	0.155230i	−0.780449	+	0.625219i	$0.785010\pi$
$84$		0			0
$85$	−12.0000	+	6.00000i	−1.30158	+	0.650791i
$86$		−	1.41421i		−	0.152499i
$87$		0			0
$88$	1.00000	−	1.00000i	0.106600	−	0.106600i
$89$	2.82843			0.299813			0.149906	−	0.988700i	$-0.452103\pi$
$89$	2.82843			0.299813			0.149906	+	0.988700i	$0.452103\pi$
$90$		0			0
$91$		0			0
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			10.0000i			1.03142i
$95$	−4.24264	+	12.7279i	−0.435286	+	1.30586i
$96$		0			0
$97$	8.00000	+	8.00000i	0.812277	+	0.812277i	0.984975	−	0.172698i	$-0.0552484\pi$
$97$	8.00000	+	8.00000i	0.812277	+	0.812277i	−0.172698	+	0.984975i	$0.555248\pi$
$98$	−4.94975	−	4.94975i	−0.500000	−	0.500000i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$			5.65685i			0.562878i	0.959579	+	0.281439i	$0.0908117\pi$
$101$			5.65685i			0.562878i	−0.959579	+	0.281439i	$0.909188\pi$
$102$		0			0
$103$	12.0000	−	12.0000i	1.18240	−	1.18240i	0.203273	−	0.979122i	$-0.434842\pi$
$103$	12.0000	−	12.0000i	1.18240	−	1.18240i	0.979122	−	0.203273i	$-0.0651579\pi$
$104$	5.65685			0.554700
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	−0.986151	−	0.165848i	$-0.946964\pi$
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	0.165848	+	0.986151i	$0.446964\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$	1.41421	+	2.82843i	0.134840	+	0.269680i
$111$		0			0
$112$		0			0
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$		0			0
$115$	1.00000	+	2.00000i	0.0932505	+	0.186501i
$116$		−	5.65685i		−	0.525226i
$117$		0			0
$118$	2.00000	−	2.00000i	0.184115	−	0.184115i
$119$		0			0
$120$		0			0
$121$	9.00000			0.818182
$122$	1.41421	−	1.41421i	0.128037	−	0.128037i
$123$		0			0
$124$		0			0
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$		0			0
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	0.982878	−	0.184257i	$-0.0589879\pi$
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	−0.184257	+	0.982878i	$0.558988\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−4.00000	+	12.0000i	−0.350823	+	1.05247i
$131$			11.3137i			0.988483i	0.869325	+	0.494242i	$0.164554\pi$
$131$			11.3137i			0.988483i	−0.869325	+	0.494242i	$0.835446\pi$
$132$		0			0
$133$		0			0
$134$	−12.7279			−1.09952
$135$		0			0
$136$	6.00000			0.514496
$137$	−12.7279	+	12.7279i	−1.08742	+	1.08742i	−0.0916263	+	0.995793i	$0.529207\pi$
$137$	−12.7279	+	12.7279i	−1.08742	+	1.08742i	−0.995793	+	0.0916263i	$0.970793\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	−	3.00000i	−0.251754	−	0.251754i
$143$	−5.65685	−	5.65685i	−0.473050	−	0.473050i
$144$		0			0
$145$	12.0000	+	4.00000i	0.996546	+	0.332182i
$146$		−	12.7279i		−	1.05337i
$147$		0			0
$148$	3.00000	−	3.00000i	0.246598	−	0.246598i
$149$	1.41421			0.115857			0.0579284	−	0.998321i	$-0.481550\pi$
$149$	1.41421			0.115857			0.0579284	+	0.998321i	$0.481550\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	4.24264	−	4.24264i	0.344124	−	0.344124i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	0.816612	−	0.577186i	$-0.195849\pi$
$157$	3.00000	+	3.00000i	0.239426	+	0.239426i	−0.577186	+	0.816612i	$0.695849\pi$
$158$	−2.82843	−	2.82843i	−0.225018	−	0.225018i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$		0			0
$163$	14.0000	−	14.0000i	1.09656	−	1.09656i	0.101755	−	0.994809i	$-0.467554\pi$
$163$	14.0000	−	14.0000i	1.09656	−	1.09656i	0.994809	−	0.101755i	$-0.0324458\pi$
$164$	4.24264			0.331295
$165$		0			0
$166$	−2.00000			−0.155230
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	−0.117582	−	0.993063i	$-0.537514\pi$
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	0.993063	+	0.117582i	$0.0375143\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$	−4.24264	+	12.7279i	−0.325396	+	0.976187i
$171$		0			0
$172$	−1.00000	−	1.00000i	−0.0762493	−	0.0762493i
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	0.758820	−	0.651300i	$-0.225776\pi$
$173$	1.41421	+	1.41421i	0.107521	+	0.107521i	−0.651300	+	0.758820i	$0.725776\pi$
$174$		0			0
$175$		0			0
$176$		−	1.41421i		−	0.106600i
$177$		0			0
$178$	2.00000	−	2.00000i	0.149906	−	0.149906i
$179$	−2.82843			−0.211407			−0.105703	−	0.994398i	$-0.533709\pi$
$179$	−2.82843			−0.211407			−0.105703	+	0.994398i	$0.533709\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	4.24264	+	8.48528i	0.311925	+	0.623850i
$186$		0			0
$187$	−6.00000	−	6.00000i	−0.438763	−	0.438763i
$188$	7.07107	+	7.07107i	0.515711	+	0.515711i
$189$		0			0
$190$	6.00000	+	12.0000i	0.435286	+	0.870572i
$191$		−	22.6274i		−	1.63726i	−0.574320	−	0.818631i	$-0.694733\pi$
$191$		−	22.6274i		−	1.63726i	0.574320	−	0.818631i	$-0.305267\pi$
$192$		0			0
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.0831899	+	0.996534i	$0.526511\pi$
$193$	−15.0000	+	15.0000i	−1.07972	+	1.07972i	−0.996534	+	0.0831899i	$0.973489\pi$
$194$	11.3137			0.812277
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−12.7279	+	12.7279i	−0.906827	+	0.906827i	−0.996015	−	0.0891879i	$-0.971573\pi$
$197$	−12.7279	+	12.7279i	−0.906827	+	0.906827i	0.0891879	+	0.996015i	$0.471573\pi$
$198$		0			0
$199$		−	20.0000i		−	1.41776i	−0.705328	−	0.708881i	$-0.749200\pi$
$199$		−	20.0000i		−	1.41776i	0.705328	−	0.708881i	$-0.250800\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$		0			0
$202$	4.00000	+	4.00000i	0.281439	+	0.281439i
$203$		0			0
$204$		0			0
$205$	−3.00000	+	9.00000i	−0.209529	+	0.628587i
$206$		−	16.9706i		−	1.18240i
$207$		0			0
$208$	4.00000	−	4.00000i	0.277350	−	0.277350i
$209$	−8.48528			−0.586939
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$	−4.24264	+	4.24264i	−0.291386	+	0.291386i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	2.82843	−	1.41421i	0.192897	−	0.0964486i
$216$		0			0
$217$		0			0
$218$	−5.65685	−	5.65685i	−0.383131	−	0.383131i
$219$		0			0
$220$	3.00000	+	1.00000i	0.202260	+	0.0674200i
$221$		−	33.9411i		−	2.28313i
$222$		0			0
$223$	5.00000	−	5.00000i	0.334825	−	0.334825i	−0.519591	−	0.854415i	$-0.673916\pi$
$223$	5.00000	−	5.00000i	0.334825	−	0.334825i	0.854415	+	0.519591i	$0.173916\pi$
$224$		0			0
$225$		0			0
$226$	2.00000			0.133038
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	−0.367024	−	0.930212i	$-0.619623\pi$
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	0.930212	+	0.367024i	$0.119623\pi$
$228$		0			0
$229$			26.0000i			1.71813i	0.511868	+	0.859064i	$0.328954\pi$
$229$			26.0000i			1.71813i	−0.511868	+	0.859064i	$0.671046\pi$
$230$	2.12132	+	0.707107i	0.139876	+	0.0466252i
$231$		0			0
$232$	−4.00000	−	4.00000i	−0.262613	−	0.262613i
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	0.899716	−	0.436475i	$-0.143773\pi$
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	−0.436475	+	0.899716i	$0.643773\pi$
$234$		0			0
$235$	−20.0000	+	10.0000i	−1.30466	+	0.652328i
$236$		−	2.82843i		−	0.184115i
$237$		0			0
$238$		0			0
$239$	7.07107			0.457389			0.228695	−	0.973498i	$-0.426554\pi$
$239$	7.07107			0.457389			0.228695	+	0.973498i	$0.426554\pi$
$240$		0			0
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$		0			0
$244$		−	2.00000i		−	0.128037i
$245$	4.94975	−	14.8492i	0.316228	−	0.948683i
$246$		0			0
$247$	−24.0000	−	24.0000i	−1.52708	−	1.52708i
$248$		0			0
$249$		0			0
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$			1.41421i			0.0892644i	0.999003	+	0.0446322i	$0.0142116\pi$
$251$			1.41421i			0.0892644i	−0.999003	+	0.0446322i	$0.985788\pi$
$252$		0			0
$253$	−1.00000	+	1.00000i	−0.0628695	+	0.0628695i
$254$	12.7279			0.798621
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.48528	+	8.48528i	−0.529297	+	0.529297i	−0.920363	−	0.391066i	$-0.872107\pi$
$257$	−8.48528	+	8.48528i	−0.529297	+	0.529297i	0.391066	+	0.920363i	$0.372107\pi$
$258$		0			0
$259$		0			0
$260$	5.65685	+	11.3137i	0.350823	+	0.701646i
$261$		0			0
$262$	8.00000	+	8.00000i	0.494242	+	0.494242i
$263$	−19.7990	−	19.7990i	−1.22086	−	1.22086i	−0.967327	−	0.253531i	$-0.918408\pi$
$263$	−19.7990	−	19.7990i	−1.22086	−	1.22086i	−0.253531	−	0.967327i	$-0.581592\pi$
$264$		0			0
$265$	−6.00000	−	12.0000i	−0.368577	−	0.737154i
$266$		0			0
$267$		0			0
$268$	−9.00000	+	9.00000i	−0.549762	+	0.549762i
$269$	−2.82843			−0.172452			−0.0862261	−	0.996276i	$-0.527481\pi$
$269$	−2.82843			−0.172452			−0.0862261	+	0.996276i	$0.527481\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	4.24264	−	4.24264i	0.257248	−	0.257248i
$273$		0			0
$274$			18.0000i			1.08742i
$275$	−4.24264	+	5.65685i	−0.255841	+	0.341121i
$276$		0			0
$277$	20.0000	+	20.0000i	1.20168	+	1.20168i	0.973654	+	0.228029i	$0.0732282\pi$
$277$	20.0000	+	20.0000i	1.20168	+	1.20168i	0.228029	+	0.973654i	$0.426772\pi$
$278$	2.82843	+	2.82843i	0.169638	+	0.169638i
$279$		0			0
$280$		0			0
$281$			19.7990i			1.18111i	0.806998	+	0.590554i	$0.201091\pi$
$281$			19.7990i			1.18111i	−0.806998	+	0.590554i	$0.798909\pi$
$282$		0			0
$283$	13.0000	−	13.0000i	0.772770	−	0.772770i	−0.205820	−	0.978590i	$-0.565986\pi$
$283$	13.0000	−	13.0000i	0.772770	−	0.772770i	0.978590	+	0.205820i	$0.0659862\pi$
$284$	−4.24264			−0.251754
$285$		0			0
$286$	−8.00000			−0.473050
$287$		0			0
$288$		0			0
$289$		−	19.0000i		−	1.11765i
$290$	11.3137	−	5.65685i	0.664364	−	0.332182i
$291$		0			0
$292$	−9.00000	−	9.00000i	−0.526685	−	0.526685i
$293$	11.3137	+	11.3137i	0.660954	+	0.660954i	0.955605	−	0.294651i	$-0.0952034\pi$
$293$	11.3137	+	11.3137i	0.660954	+	0.660954i	−0.294651	+	0.955605i	$0.595203\pi$
$294$		0			0
$295$	6.00000	+	2.00000i	0.349334	+	0.116445i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	1.00000	−	1.00000i	0.0579284	−	0.0579284i
$299$	−5.65685			−0.327144
$300$		0			0
$301$		0			0
$302$	−1.41421	+	1.41421i	−0.0813788	+	0.0813788i
$303$		0			0
$304$		−	6.00000i		−	0.344124i
$305$	4.24264	+	1.41421i	0.242933	+	0.0809776i
$306$		0			0
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	0.440948	−	0.897532i	$-0.354642\pi$
$307$	−8.00000	−	8.00000i	−0.456584	−	0.456584i	−0.897532	+	0.440948i	$0.854642\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			7.07107i			0.400963i	0.979697	+	0.200482i	$0.0642507\pi$
$311$			7.07107i			0.400963i	−0.979697	+	0.200482i	$0.935749\pi$
$312$		0			0
$313$	−10.0000	+	10.0000i	−0.565233	+	0.565233i	−0.930789	−	0.365556i	$-0.880879\pi$
$313$	−10.0000	+	10.0000i	−0.565233	+	0.565233i	0.365556	+	0.930789i	$0.380879\pi$
$314$	4.24264			0.239426
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−24.0416	+	24.0416i	−1.35031	+	1.35031i	−0.465004	+	0.885309i	$0.653947\pi$
$317$	−24.0416	+	24.0416i	−1.35031	+	1.35031i	−0.885309	+	0.465004i	$0.846053\pi$
$318$		0			0
$319$			8.00000i			0.447914i
$320$	−0.707107	+	2.12132i	−0.0395285	+	0.118585i
$321$		0			0
$322$		0			0
$323$	−25.4558	−	25.4558i	−1.41640	−	1.41640i
$324$		0			0
$325$	−28.0000	+	4.00000i	−1.55316	+	0.221880i
$326$		−	19.7990i		−	1.09656i
$327$		0			0
$328$	3.00000	−	3.00000i	0.165647	−	0.165647i
$329$		0			0
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$	−1.41421	+	1.41421i	−0.0776151	+	0.0776151i
$333$		0			0
$334$		−	16.0000i		−	0.875481i
$335$	−12.7279	−	25.4558i	−0.695401	−	1.39080i
$336$		0			0
$337$	−18.0000	−	18.0000i	−0.980522	−	0.980522i	0.0192914	−	0.999814i	$-0.493859\pi$
$337$	−18.0000	−	18.0000i	−0.980522	−	0.980522i	−0.999814	+	0.0192914i	$0.993859\pi$
$338$	−13.4350	−	13.4350i	−0.730769	−	0.730769i
$339$		0			0
$340$	6.00000	+	12.0000i	0.325396	+	0.650791i
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−1.41421			−0.0762493
$345$		0			0
$346$	2.00000			0.107521
$347$	11.3137	−	11.3137i	0.607352	−	0.607352i	−0.334901	−	0.942253i	$-0.608703\pi$
$347$	11.3137	−	11.3137i	0.607352	−	0.607352i	0.942253	+	0.334901i	$0.108703\pi$
$348$		0			0
$349$			14.0000i			0.749403i	0.927146	+	0.374701i	$0.122255\pi$
$349$			14.0000i			0.749403i	−0.927146	+	0.374701i	$0.877745\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	−	1.00000i	−0.0533002	−	0.0533002i
$353$	8.48528	+	8.48528i	0.451626	+	0.451626i	0.895894	−	0.444268i	$-0.146536\pi$
$353$	8.48528	+	8.48528i	0.451626	+	0.451626i	−0.444268	+	0.895894i	$0.646536\pi$
$354$		0			0
$355$	3.00000	−	9.00000i	0.159223	−	0.477670i
$356$		−	2.82843i		−	0.149906i
$357$		0			0
$358$	−2.00000	+	2.00000i	−0.105703	+	0.105703i
$359$	−28.2843			−1.49279			−0.746393	−	0.665505i	$-0.768216\pi$
$359$	−28.2843			−1.49279			−0.746393	+	0.665505i	$0.768216\pi$
$360$		0			0
$361$	−17.0000			−0.894737
$362$	−7.07107	+	7.07107i	−0.371647	+	0.371647i
$363$		0			0
$364$		0			0
$365$	25.4558	−	12.7279i	1.33242	−	0.666210i
$366$		0			0
$367$	4.00000	+	4.00000i	0.208798	+	0.208798i	0.803757	−	0.594958i	$-0.202831\pi$
$367$	4.00000	+	4.00000i	0.208798	+	0.208798i	−0.594958	+	0.803757i	$0.702831\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	9.00000	+	3.00000i	0.467888	+	0.155963i
$371$		0			0
$372$		0			0
$373$	13.0000	−	13.0000i	0.673114	−	0.673114i	−0.285318	−	0.958433i	$-0.592099\pi$
$373$	13.0000	−	13.0000i	0.673114	−	0.673114i	0.958433	+	0.285318i	$0.0920993\pi$
$374$	−8.48528			−0.438763
$375$		0			0
$376$	10.0000			0.515711
$377$	−22.6274	+	22.6274i	−1.16537	+	1.16537i
$378$		0			0
$379$			36.0000i			1.84920i	0.380945	+	0.924598i	$0.375599\pi$
$379$			36.0000i			1.84920i	−0.380945	+	0.924598i	$0.624401\pi$
$380$	12.7279	+	4.24264i	0.652929	+	0.217643i
$381$		0			0
$382$	−16.0000	−	16.0000i	−0.818631	−	0.818631i
$383$	−5.65685	−	5.65685i	−0.289052	−	0.289052i	0.547653	−	0.836705i	$-0.315521\pi$
$383$	−5.65685	−	5.65685i	−0.289052	−	0.289052i	−0.836705	+	0.547653i	$0.815521\pi$
$384$		0			0
$385$		0			0
$386$			21.2132i			1.07972i
$387$		0			0
$388$	8.00000	−	8.00000i	0.406138	−	0.406138i
$389$	24.0416			1.21896			0.609480	−	0.792802i	$-0.291378\pi$
$389$	24.0416			1.21896			0.609480	+	0.792802i	$0.291378\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	−4.94975	+	4.94975i	−0.250000	+	0.250000i
$393$		0			0
$394$			18.0000i			0.906827i
$395$	2.82843	−	8.48528i	0.142314	−	0.426941i
$396$		0			0
$397$	−16.0000	−	16.0000i	−0.803017	−	0.803017i	0.180549	−	0.983566i	$-0.442213\pi$
$397$	−16.0000	−	16.0000i	−0.803017	−	0.803017i	−0.983566	+	0.180549i	$0.942213\pi$
$398$	−14.1421	−	14.1421i	−0.708881	−	0.708881i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$		−	22.6274i		−	1.12996i	−0.825105	−	0.564980i	$-0.808884\pi$
$401$		−	22.6274i		−	1.12996i	0.825105	−	0.564980i	$-0.191116\pi$
$402$		0			0
$403$		0			0
$404$	5.65685			0.281439
$405$		0			0
$406$		0			0
$407$	−4.24264	+	4.24264i	−0.210300	+	0.210300i
$408$		0			0
$409$		−	26.0000i		−	1.28562i	−0.766027	−	0.642809i	$-0.777769\pi$
$409$		−	26.0000i		−	1.28562i	0.766027	−	0.642809i	$-0.222231\pi$
$410$	4.24264	+	8.48528i	0.209529	+	0.419058i
$411$		0			0
$412$	−12.0000	−	12.0000i	−0.591198	−	0.591198i
$413$		0			0
$414$		0			0
$415$	−2.00000	−	4.00000i	−0.0981761	−	0.196352i
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$	−6.00000	+	6.00000i	−0.293470	+	0.293470i
$419$	15.5563			0.759977			0.379989	−	0.924991i	$-0.375928\pi$
$419$	15.5563			0.759977			0.379989	+	0.924991i	$0.375928\pi$
$420$		0			0
$421$	−40.0000			−1.94948			−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000			−1.94948			−0.974740	+	0.223341i	$0.928304\pi$
$422$	11.3137	−	11.3137i	0.550743	−	0.550743i
$423$		0			0
$424$			6.00000i			0.291386i
$425$	−29.6985	+	4.24264i	−1.44059	+	0.205798i
$426$		0			0
$427$		0			0
$428$	8.48528	+	8.48528i	0.410152	+	0.410152i
$429$		0			0
$430$	1.00000	−	3.00000i	0.0482243	−	0.144673i
$431$		−	33.9411i		−	1.63489i	−0.576009	−	0.817443i	$-0.695391\pi$
$431$		−	33.9411i		−	1.63489i	0.576009	−	0.817443i	$-0.304609\pi$
$432$		0			0
$433$	4.00000	−	4.00000i	0.192228	−	0.192228i	−0.604430	−	0.796658i	$-0.706599\pi$
$433$	4.00000	−	4.00000i	0.192228	−	0.192228i	0.796658	+	0.604430i	$0.206599\pi$
$434$		0			0
$435$		0			0
$436$	−8.00000			−0.383131
$437$	−4.24264	+	4.24264i	−0.202953	+	0.202953i
$438$		0			0
$439$		−	10.0000i		−	0.477274i	−0.971109	−	0.238637i	$-0.923299\pi$
$439$		−	10.0000i		−	0.477274i	0.971109	−	0.238637i	$-0.0767006\pi$
$440$	2.82843	−	1.41421i	0.134840	−	0.0674200i
$441$		0			0
$442$	−24.0000	−	24.0000i	−1.14156	−	1.14156i
$443$	−2.82843	−	2.82843i	−0.134383	−	0.134383i	0.636716	−	0.771099i	$-0.280292\pi$
$443$	−2.82843	−	2.82843i	−0.134383	−	0.134383i	−0.771099	+	0.636716i	$0.780292\pi$
$444$		0			0
$445$	6.00000	+	2.00000i	0.284427	+	0.0948091i
$446$		−	7.07107i		−	0.334825i
$447$		0			0
$448$		0			0
$449$	26.8701			1.26808			0.634038	−	0.773302i	$-0.281396\pi$
$449$	26.8701			1.26808			0.634038	+	0.773302i	$0.281396\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$		0			0
$454$		−	12.0000i		−	0.563188i
$455$		0			0
$456$		0			0
$457$	−20.0000	−	20.0000i	−0.935561	−	0.935561i	0.0624853	−	0.998046i	$-0.480097\pi$
$457$	−20.0000	−	20.0000i	−0.935561	−	0.935561i	−0.998046	+	0.0624853i	$0.980097\pi$
$458$	18.3848	+	18.3848i	0.859064	+	0.859064i
$459$		0			0
$460$	2.00000	−	1.00000i	0.0932505	−	0.0466252i
$461$		−	11.3137i		−	0.526932i	−0.964669	−	0.263466i	$-0.915134\pi$
$461$		−	11.3137i		−	0.526932i	0.964669	−	0.263466i	$-0.0848657\pi$
$462$		0			0
$463$	−5.00000	+	5.00000i	−0.232370	+	0.232370i	−0.813681	−	0.581311i	$-0.802540\pi$
$463$	−5.00000	+	5.00000i	−0.232370	+	0.232370i	0.581311	+	0.813681i	$0.302540\pi$
$464$	−5.65685			−0.262613
$465$		0			0
$466$	10.0000			0.463241
$467$	−18.3848	+	18.3848i	−0.850746	+	0.850746i	−0.990225	−	0.139479i	$-0.955457\pi$
$467$	−18.3848	+	18.3848i	−0.850746	+	0.850746i	0.139479	+	0.990225i	$0.455457\pi$
$468$		0			0
$469$		0			0
$470$	−7.07107	+	21.2132i	−0.326164	+	0.978492i
$471$		0			0
$472$	−2.00000	−	2.00000i	−0.0920575	−	0.0920575i
$473$	1.41421	+	1.41421i	0.0650256	+	0.0650256i
$474$		0			0
$475$	−18.0000	+	24.0000i	−0.825897	+	1.10120i
$476$		0			0
$477$		0			0
$478$	5.00000	−	5.00000i	0.228695	−	0.228695i
$479$	28.2843			1.29234			0.646171	−	0.763193i	$-0.276369\pi$
$479$	28.2843			1.29234			0.646171	+	0.763193i	$0.276369\pi$
$480$		0			0
$481$	−24.0000			−1.09431
$482$	7.07107	−	7.07107i	0.322078	−	0.322078i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$	11.3137	+	22.6274i	0.513729	+	1.02746i
$486$		0			0
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	0.771804	−	0.635861i	$-0.219355\pi$
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	−0.635861	+	0.771804i	$0.719355\pi$
$488$	−1.41421	−	1.41421i	−0.0640184	−	0.0640184i
$489$		0			0
$490$	−7.00000	−	14.0000i	−0.316228	−	0.632456i
$491$		−	5.65685i		−	0.255290i	−0.991820	−	0.127645i	$-0.959258\pi$
$491$		−	5.65685i		−	0.255290i	0.991820	−	0.127645i	$-0.0407419\pi$
$492$		0			0
$493$	−24.0000	+	24.0000i	−1.08091	+	1.08091i
$494$	−33.9411			−1.52708
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$		0			0
$502$	1.00000	+	1.00000i	0.0446322	+	0.0446322i
$503$	25.4558	+	25.4558i	1.13502	+	1.13502i	0.989330	+	0.145690i	$0.0465401\pi$
$503$	25.4558	+	25.4558i	1.13502	+	1.13502i	0.145690	+	0.989330i	$0.453460\pi$
$504$		0			0
$505$	−4.00000	+	12.0000i	−0.177998	+	0.533993i
$506$			1.41421i			0.0628695i
$507$		0			0
$508$	9.00000	−	9.00000i	0.399310	−	0.399310i
$509$	39.5980			1.75515			0.877575	−	0.479440i	$-0.159160\pi$
$509$	39.5980			1.75515			0.877575	+	0.479440i	$0.159160\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			12.0000i			0.529297i
$515$	33.9411	−	16.9706i	1.49562	−	0.747812i
$516$		0			0
$517$	−10.0000	−	10.0000i	−0.439799	−	0.439799i
$518$		0			0
$519$		0			0
$520$	12.0000	+	4.00000i	0.526235	+	0.175412i
$521$		−	14.1421i		−	0.619578i	−0.950805	−	0.309789i	$-0.899742\pi$
$521$		−	14.1421i		−	0.619578i	0.950805	−	0.309789i	$-0.100258\pi$
$522$		0			0
$523$	−13.0000	+	13.0000i	−0.568450	+	0.568450i	−0.931694	−	0.363244i	$-0.881669\pi$
$523$	−13.0000	+	13.0000i	−0.568450	+	0.568450i	0.363244	+	0.931694i	$0.381669\pi$
$524$	11.3137			0.494242
$525$		0			0
$526$	−28.0000			−1.22086
$527$		0			0
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−12.7279	−	4.24264i	−0.552866	−	0.184289i
$531$		0			0
$532$		0			0
$533$	−16.9706	−	16.9706i	−0.735077	−	0.735077i
$534$		0			0
$535$	−24.0000	+	12.0000i	−1.03761	+	0.518805i
$536$			12.7279i			0.549762i
$537$		0			0
$538$	−2.00000	+	2.00000i	−0.0862261	+	0.0862261i
$539$	9.89949			0.426401
$540$		0			0
$541$	−14.0000			−0.601907			−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000			−0.601907			−0.300954	+	0.953639i	$0.597305\pi$
$542$		0			0
$543$		0			0
$544$		−	6.00000i		−	0.257248i
$545$	5.65685	−	16.9706i	0.242313	−	0.726939i
$546$		0			0
$547$	8.00000	+	8.00000i	0.342055	+	0.342055i	0.857140	−	0.515084i	$-0.172239\pi$
$547$	8.00000	+	8.00000i	0.342055	+	0.342055i	−0.515084	+	0.857140i	$0.672239\pi$
$548$	12.7279	+	12.7279i	0.543710	+	0.543710i
$549$		0			0
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$			33.9411i			1.44594i
$552$		0			0
$553$		0			0
$554$	28.2843			1.20168
$555$		0			0
$556$	4.00000			0.169638
$557$	5.65685	−	5.65685i	0.239689	−	0.239689i	−0.577033	−	0.816721i	$-0.695789\pi$
$557$	5.65685	−	5.65685i	0.239689	−	0.239689i	0.816721	+	0.577033i	$0.195789\pi$
$558$		0			0
$559$			8.00000i			0.338364i
$560$		0			0
$561$		0			0
$562$	14.0000	+	14.0000i	0.590554	+	0.590554i
$563$	−29.6985	−	29.6985i	−1.25164	−	1.25164i	−0.954984	−	0.296658i	$-0.904128\pi$
$563$	−29.6985	−	29.6985i	−1.25164	−	1.25164i	−0.296658	−	0.954984i	$-0.595872\pi$
$564$		0			0
$565$	2.00000	+	4.00000i	0.0841406	+	0.168281i
$566$		−	18.3848i		−	0.772770i
$567$		0			0
$568$	−3.00000	+	3.00000i	−0.125877	+	0.125877i
$569$	33.9411			1.42289			0.711443	−	0.702744i	$-0.248042\pi$
$569$	33.9411			1.42289			0.711443	+	0.702744i	$0.248042\pi$
$570$		0			0
$571$	36.0000			1.50655			0.753277	−	0.657704i	$-0.228472\pi$
$571$	36.0000			1.50655			0.753277	+	0.657704i	$0.228472\pi$
$572$	−5.65685	+	5.65685i	−0.236525	+	0.236525i
$573$		0			0
$574$		0			0
$575$	0.707107	+	4.94975i	0.0294884	+	0.206419i
$576$		0			0
$577$	−3.00000	−	3.00000i	−0.124892	−	0.124892i	0.641898	−	0.766790i	$-0.278147\pi$
$577$	−3.00000	−	3.00000i	−0.124892	−	0.124892i	−0.766790	+	0.641898i	$0.778147\pi$
$578$	−13.4350	−	13.4350i	−0.558824	−	0.558824i
$579$		0			0
$580$	4.00000	−	12.0000i	0.166091	−	0.498273i
$581$		0			0
$582$		0			0
$583$	6.00000	−	6.00000i	0.248495	−	0.248495i
$584$	−12.7279			−0.526685
$585$		0			0
$586$	16.0000			0.660954
$587$	−28.2843	+	28.2843i	−1.16742	+	1.16742i	−0.184604	+	0.982813i	$0.559100\pi$
$587$	−28.2843	+	28.2843i	−1.16742	+	1.16742i	−0.982813	+	0.184604i	$0.940900\pi$
$588$		0			0
$589$		0			0
$590$	5.65685	−	2.82843i	0.232889	−	0.116445i
$591$		0			0
$592$	−3.00000	−	3.00000i	−0.123299	−	0.123299i
$593$	−8.48528	−	8.48528i	−0.348449	−	0.348449i	0.511083	−	0.859532i	$-0.329245\pi$
$593$	−8.48528	−	8.48528i	−0.348449	−	0.348449i	−0.859532	+	0.511083i	$0.829245\pi$
$594$		0			0
$595$		0			0
$596$		−	1.41421i		−	0.0579284i
$597$		0			0
$598$	−4.00000	+	4.00000i	−0.163572	+	0.163572i
$599$	24.0416			0.982314			0.491157	−	0.871071i	$-0.336574\pi$
$599$	24.0416			0.982314			0.491157	+	0.871071i	$0.336574\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		0			0
$604$			2.00000i			0.0813788i
$605$	19.0919	+	6.36396i	0.776195	+	0.258732i
$606$		0			0
$607$	27.0000	+	27.0000i	1.09590	+	1.09590i	0.994885	+	0.101011i	$0.0322077\pi$
$607$	27.0000	+	27.0000i	1.09590	+	1.09590i	0.101011	+	0.994885i	$0.467792\pi$
$608$	−4.24264	−	4.24264i	−0.172062	−	0.172062i
$609$		0			0
$610$	4.00000	−	2.00000i	0.161955	−	0.0809776i
$611$		−	56.5685i		−	2.28852i
$612$		0			0
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	−0.274861	−	0.961484i	$-0.588632\pi$
$613$	17.0000	−	17.0000i	0.686624	−	0.686624i	0.961484	+	0.274861i	$0.0886317\pi$
$614$	−11.3137			−0.456584
$615$		0			0
$616$		0			0
$617$	9.89949	−	9.89949i	0.398539	−	0.398539i	−0.479179	−	0.877717i	$-0.659065\pi$
$617$	9.89949	−	9.89949i	0.398539	−	0.398539i	0.877717	+	0.479179i	$0.159065\pi$
$618$		0			0
$619$		−	10.0000i		−	0.401934i	−0.979598	−	0.200967i	$-0.935592\pi$
$619$		−	10.0000i		−	0.401934i	0.979598	−	0.200967i	$-0.0644084\pi$
$620$		0			0
$621$		0			0
$622$	5.00000	+	5.00000i	0.200482	+	0.200482i
$623$		0			0
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			14.1421i			0.565233i
$627$		0			0
$628$	3.00000	−	3.00000i	0.119713	−	0.119713i
$629$	−25.4558			−1.01499
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$	−2.82843	+	2.82843i	−0.112509	+	0.112509i
$633$		0			0
$634$			34.0000i			1.35031i
$635$	12.7279	+	25.4558i	0.505092	+	1.01018i
$636$		0			0
$637$	28.0000	+	28.0000i	1.10940	+	1.10940i
$638$	5.65685	+	5.65685i	0.223957	+	0.223957i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$			8.48528i			0.335148i	0.985859	+	0.167574i	$0.0535934\pi$
$641$			8.48528i			0.335148i	−0.985859	+	0.167574i	$0.946407\pi$
$642$		0			0
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	−0.861938	−	0.507013i	$-0.830750\pi$
$643$	−9.00000	+	9.00000i	−0.354925	+	0.354925i	0.507013	+	0.861938i	$0.330750\pi$
$644$		0			0
$645$		0			0
$646$	−36.0000			−1.41640
$647$	−1.41421	+	1.41421i	−0.0555985	+	0.0555985i	−0.734359	−	0.678761i	$-0.762517\pi$
$647$	−1.41421	+	1.41421i	−0.0555985	+	0.0555985i	0.678761	+	0.734359i	$0.262517\pi$
$648$		0			0
$649$			4.00000i			0.157014i
$650$	−16.9706	+	22.6274i	−0.665640	+	0.887520i
$651$		0			0
$652$	−14.0000	−	14.0000i	−0.548282	−	0.548282i
$653$	21.2132	+	21.2132i	0.830137	+	0.830137i	0.987535	−	0.157398i	$-0.0503107\pi$
$653$	21.2132	+	21.2132i	0.830137	+	0.830137i	−0.157398	+	0.987535i	$0.550311\pi$
$654$		0			0
$655$	−8.00000	+	24.0000i	−0.312586	+	0.937758i
$656$		−	4.24264i		−	0.165647i
$657$		0			0
$658$		0			0
$659$	−18.3848			−0.716169			−0.358085	−	0.933689i	$-0.616570\pi$
$659$	−18.3848			−0.716169			−0.358085	+	0.933689i	$0.616570\pi$
$660$		0			0
$661$	24.0000			0.933492			0.466746	−	0.884391i	$-0.345426\pi$
$661$	24.0000			0.933492			0.466746	+	0.884391i	$0.345426\pi$
$662$	5.65685	−	5.65685i	0.219860	−	0.219860i
$663$		0			0
$664$			2.00000i			0.0776151i
$665$		0			0
$666$		0			0
$667$	4.00000	+	4.00000i	0.154881	+	0.154881i
$668$	−11.3137	−	11.3137i	−0.437741	−	0.437741i
$669$		0			0
$670$	−27.0000	−	9.00000i	−1.04310	−	0.347700i
$671$			2.82843i			0.109190i
$672$		0			0
$673$	15.0000	−	15.0000i	0.578208	−	0.578208i	−0.356202	−	0.934409i	$-0.615928\pi$
$673$	15.0000	−	15.0000i	0.578208	−	0.578208i	0.934409	+	0.356202i	$0.115928\pi$
$674$	−25.4558			−0.980522
$675$		0			0
$676$	−19.0000			−0.730769
$677$	−2.82843	+	2.82843i	−0.108705	+	0.108705i	−0.759367	−	0.650662i	$-0.774491\pi$
$677$	−2.82843	+	2.82843i	−0.108705	+	0.108705i	0.650662	+	0.759367i	$0.274491\pi$
$678$		0			0
$679$		0			0
$680$	12.7279	+	4.24264i	0.488094	+	0.162698i
$681$		0			0
$682$		0			0
$683$	−33.9411	−	33.9411i	−1.29872	−	1.29872i	−0.929237	−	0.369484i	$-0.879534\pi$
$683$	−33.9411	−	33.9411i	−1.29872	−	1.29872i	−0.369484	−	0.929237i	$-0.620466\pi$
$684$		0			0
$685$	−36.0000	+	18.0000i	−1.37549	+	0.687745i
$686$		0			0
$687$		0			0
$688$	−1.00000	+	1.00000i	−0.0381246	+	0.0381246i
$689$	33.9411			1.29305
$690$		0			0
$691$	44.0000			1.67384			0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000			1.67384			0.836919	+	0.547326i	$0.184354\pi$
$692$	1.41421	−	1.41421i	0.0537603	−	0.0537603i
$693$		0			0
$694$		−	16.0000i		−	0.607352i
$695$	−2.82843	+	8.48528i	−0.107288	+	0.321865i
$696$		0			0
$697$	−18.0000	−	18.0000i	−0.681799	−	0.681799i
$698$	9.89949	+	9.89949i	0.374701	+	0.374701i
$699$		0			0
$700$		0			0
$701$			7.07107i			0.267071i	0.991044	+	0.133535i	$0.0426329\pi$
$701$			7.07107i			0.267071i	−0.991044	+	0.133535i	$0.957367\pi$
$702$		0			0
$703$	−18.0000	+	18.0000i	−0.678883	+	0.678883i
$704$	−1.41421			−0.0533002
$705$		0			0
$706$	12.0000			0.451626
$707$		0			0
$708$		0			0
$709$		−	6.00000i		−	0.225335i	−0.993633	−	0.112667i	$-0.964061\pi$
$709$		−	6.00000i		−	0.225335i	0.993633	−	0.112667i	$-0.0359394\pi$
$710$	−4.24264	−	8.48528i	−0.159223	−	0.318447i
$711$		0			0
$712$	−2.00000	−	2.00000i	−0.0749532	−	0.0749532i
$713$		0			0
$714$		0			0
$715$	−8.00000	−	16.0000i	−0.299183	−	0.598366i
$716$			2.82843i			0.105703i
$717$		0			0
$718$	−20.0000	+	20.0000i	−0.746393	+	0.746393i
$719$	−26.8701			−1.00208			−0.501042	−	0.865423i	$-0.667050\pi$
$719$	−26.8701			−1.00208			−0.501042	+	0.865423i	$0.667050\pi$
$720$		0			0
$721$		0			0
$722$	−12.0208	+	12.0208i	−0.447368	+	0.447368i
$723$		0			0
$724$			10.0000i			0.371647i
$725$	22.6274	+	16.9706i	0.840361	+	0.630271i
$726$		0			0
$727$	−18.0000	−	18.0000i	−0.667583	−	0.667583i	0.289573	−	0.957156i	$-0.406487\pi$
$727$	−18.0000	−	18.0000i	−0.667583	−	0.667583i	−0.957156	+	0.289573i	$0.906487\pi$
$728$		0			0
$729$		0			0
$730$	9.00000	−	27.0000i	0.333105	−	0.999315i
$731$			8.48528i			0.313839i
$732$		0			0
$733$	−35.0000	+	35.0000i	−1.29275	+	1.29275i	−0.359678	+	0.933076i	$0.617113\pi$
$733$	−35.0000	+	35.0000i	−1.29275	+	1.29275i	−0.933076	+	0.359678i	$0.882887\pi$
$734$	5.65685			0.208798
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	12.7279	−	12.7279i	0.468839	−	0.468839i
$738$		0			0
$739$			16.0000i			0.588570i	0.955718	+	0.294285i	$0.0950814\pi$
$739$			16.0000i			0.588570i	−0.955718	+	0.294285i	$0.904919\pi$
$740$	8.48528	−	4.24264i	0.311925	−	0.155963i
$741$		0			0
$742$		0			0
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.999263	+	0.0383863i	$0.0122217\pi$
$743$	28.2843	+	28.2843i	1.03765	+	1.03765i	0.0383863	+	0.999263i	$0.487778\pi$
$744$		0			0
$745$	3.00000	+	1.00000i	0.109911	+	0.0366372i
$746$		−	18.3848i		−	0.673114i
$747$		0			0
$748$	−6.00000	+	6.00000i	−0.219382	+	0.219382i
$749$		0			0
$750$		0			0
$751$	48.0000			1.75154			0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000			1.75154			0.875772	+	0.482724i	$0.160353\pi$
$752$	7.07107	−	7.07107i	0.257855	−	0.257855i
$753$		0			0
$754$			32.0000i			1.16537i
$755$	−4.24264	−	1.41421i	−0.154406	−	0.0514685i
$756$		0			0
$757$	−15.0000	−	15.0000i	−0.545184	−	0.545184i	0.379860	−	0.925044i	$-0.375972\pi$
$757$	−15.0000	−	15.0000i	−0.545184	−	0.545184i	−0.925044	+	0.379860i	$0.875972\pi$
$758$	25.4558	+	25.4558i	0.924598	+	0.924598i
$759$		0			0
$760$	12.0000	−	6.00000i	0.435286	−	0.217643i
$761$		−	1.41421i		−	0.0512652i	−0.999671	−	0.0256326i	$-0.991840\pi$
$761$		−	1.41421i		−	0.0512652i	0.999671	−	0.0256326i	$-0.00816000\pi$
$762$		0			0
$763$		0			0
$764$	−22.6274			−0.818631
$765$		0			0
$766$	−8.00000			−0.289052
$767$	−11.3137	+	11.3137i	−0.408514	+	0.408514i
$768$		0			0
$769$			26.0000i			0.937584i	0.883309	+	0.468792i	$0.155311\pi$
$769$			26.0000i			0.937584i	−0.883309	+	0.468792i	$0.844689\pi$
$770$		0			0
$771$		0			0
$772$	15.0000	+	15.0000i	0.539862	+	0.539862i
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	0.779277	−	0.626680i	$-0.215587\pi$
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	−0.626680	+	0.779277i	$0.715587\pi$
$774$		0			0
$775$		0			0
$776$		−	11.3137i		−	0.406138i
$777$		0			0
$778$	17.0000	−	17.0000i	0.609480	−	0.609480i
$779$	−25.4558			−0.912050
$780$		0			0
$781$	6.00000			0.214697
$782$	−4.24264	+	4.24264i	−0.151717	+	0.151717i
$783$		0			0
$784$			7.00000i			0.250000i
$785$	4.24264	+	8.48528i	0.151426	+	0.302853i
$786$		0			0
$787$	−19.0000	−	19.0000i	−0.677277	−	0.677277i	0.282106	−	0.959383i	$-0.408967\pi$
$787$	−19.0000	−	19.0000i	−0.677277	−	0.677277i	−0.959383	+	0.282106i	$0.908967\pi$
$788$	12.7279	+	12.7279i	0.453413	+	0.453413i
$789$		0			0
$790$	−4.00000	−	8.00000i	−0.142314	−	0.284627i
$791$		0			0
$792$		0			0
$793$	−8.00000	+	8.00000i	−0.284088	+	0.284088i
$794$	−22.6274			−0.803017
$795$		0			0
$796$	−20.0000			−0.708881
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	−0.731710	−	0.681616i	$-0.761277\pi$
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	0.681616	+	0.731710i	$0.261277\pi$
$798$		0			0
$799$		−	60.0000i		−	2.12265i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	−16.0000	−	16.0000i	−0.564980	−	0.564980i
$803$	12.7279	+	12.7279i	0.449159	+	0.449159i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	4.00000	−	4.00000i	0.140720	−	0.140720i
$809$	−4.24264			−0.149163			−0.0745817	−	0.997215i	$-0.523762\pi$
$809$	−4.24264			−0.149163			−0.0745817	+	0.997215i	$0.523762\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$			6.00000i			0.210300i
$815$	39.5980	−	19.7990i	1.38706	−	0.693528i
$816$		0			0
$817$	6.00000	+	6.00000i	0.209913	+	0.209913i
$818$	−18.3848	−	18.3848i	−0.642809	−	0.642809i
$819$		0			0
$820$	9.00000	+	3.00000i	0.314294	+	0.104765i
$821$		−	48.0833i		−	1.67812i	−0.544041	−	0.839059i	$-0.683106\pi$
$821$		−	48.0833i		−	1.67812i	0.544041	−	0.839059i	$-0.316894\pi$
$822$		0			0
$823$	39.0000	−	39.0000i	1.35945	−	1.35945i	0.484866	−	0.874588i	$-0.338868\pi$
$823$	39.0000	−	39.0000i	1.35945	−	1.35945i	0.874588	−	0.484866i	$-0.161132\pi$
$824$	−16.9706			−0.591198
$825$		0			0
$826$		0			0
$827$	2.82843	−	2.82843i	0.0983540	−	0.0983540i	−0.656218	−	0.754572i	$-0.727845\pi$
$827$	2.82843	−	2.82843i	0.0983540	−	0.0983540i	0.754572	+	0.656218i	$0.227845\pi$
$828$		0			0
$829$		−	46.0000i		−	1.59765i	−0.601566	−	0.798823i	$-0.705456\pi$
$829$		−	46.0000i		−	1.59765i	0.601566	−	0.798823i	$-0.294544\pi$
$830$	−4.24264	−	1.41421i	−0.147264	−	0.0490881i
$831$		0			0
$832$	−4.00000	−	4.00000i	−0.138675	−	0.138675i
$833$	29.6985	+	29.6985i	1.02899	+	1.02899i
$834$		0			0
$835$	32.0000	−	16.0000i	1.10741	−	0.553703i
$836$			8.48528i			0.293470i
$837$		0			0
$838$	11.0000	−	11.0000i	0.379989	−	0.379989i
$839$	−36.7696			−1.26943			−0.634713	−	0.772748i	$-0.718882\pi$
$839$	−36.7696			−1.26943			−0.634713	+	0.772748i	$0.718882\pi$
$840$		0			0
$841$	3.00000			0.103448
$842$	−28.2843	+	28.2843i	−0.974740	+	0.974740i
$843$		0			0
$844$		−	16.0000i		−	0.550743i
$845$	13.4350	−	40.3051i	0.462179	−	1.38654i
$846$		0			0
$847$		0			0
$848$	4.24264	+	4.24264i	0.145693	+	0.145693i
$849$		0			0
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$			4.24264i			0.145436i
$852$		0			0
$853$	20.0000	−	20.0000i	0.684787	−	0.684787i	−0.276288	−	0.961075i	$-0.589104\pi$
$853$	20.0000	−	20.0000i	0.684787	−	0.684787i	0.961075	+	0.276288i	$0.0891043\pi$
$854$		0			0
$855$		0			0
$856$	12.0000			0.410152
$857$	19.7990	−	19.7990i	0.676321	−	0.676321i	−0.282845	−	0.959166i	$-0.591278\pi$
$857$	19.7990	−	19.7990i	0.676321	−	0.676321i	0.959166	+	0.282845i	$0.0912782\pi$
$858$		0			0
$859$		−	40.0000i		−	1.36478i	−0.730987	−	0.682391i	$-0.760940\pi$
$859$		−	40.0000i		−	1.36478i	0.730987	−	0.682391i	$-0.239060\pi$
$860$	−1.41421	−	2.82843i	−0.0482243	−	0.0964486i
$861$		0			0
$862$	−24.0000	−	24.0000i	−0.817443	−	0.817443i
$863$	−35.3553	−	35.3553i	−1.20351	−	1.20351i	−0.973092	−	0.230418i	$-0.925991\pi$
$863$	−35.3553	−	35.3553i	−1.20351	−	1.20351i	−0.230418	−	0.973092i	$-0.574009\pi$
$864$		0			0
$865$	2.00000	+	4.00000i	0.0680020	+	0.136004i
$866$		−	5.65685i		−	0.192228i
$867$		0			0
$868$		0			0
$869$	5.65685			0.191896
$870$		0			0
$871$	72.0000			2.43963
$872$	−5.65685	+	5.65685i	−0.191565	+	0.191565i
$873$		0			0
$874$			6.00000i			0.202953i
$875$		0			0
$876$		0			0
$877$	32.0000	+	32.0000i	1.08056	+	1.08056i	0.996457	+	0.0841064i	$0.0268036\pi$
$877$	32.0000	+	32.0000i	1.08056	+	1.08056i	0.0841064	+	0.996457i	$0.473196\pi$
$878$	−7.07107	−	7.07107i	−0.238637	−	0.238637i
$879$		0			0
$880$	1.00000	−	3.00000i	0.0337100	−	0.101130i
$881$			36.7696i			1.23880i	0.785076	+	0.619399i	$0.212624\pi$
$881$			36.7696i			1.23880i	−0.785076	+	0.619399i	$0.787376\pi$
$882$		0			0
$883$	−30.0000	+	30.0000i	−1.00958	+	1.00958i	−0.00962672	+	0.999954i	$0.503064\pi$
$883$	−30.0000	+	30.0000i	−1.00958	+	1.00958i	−0.999954	+	0.00962672i	$0.996936\pi$
$884$	−33.9411			−1.14156
$885$		0			0
$886$	−4.00000			−0.134383
$887$	−24.0416	+	24.0416i	−0.807239	+	0.807239i	−0.984215	−	0.176976i	$-0.943368\pi$
$887$	−24.0416	+	24.0416i	−0.807239	+	0.807239i	0.176976	+	0.984215i	$0.443368\pi$
$888$		0			0
$889$		0			0
$890$	5.65685	−	2.82843i	0.189618	−	0.0948091i
$891$		0			0
$892$	−5.00000	−	5.00000i	−0.167412	−	0.167412i
$893$	−42.4264	−	42.4264i	−1.41975	−	1.41975i
$894$		0			0
$895$	−6.00000	−	2.00000i	−0.200558	−	0.0668526i
$896$		0			0
$897$		0			0
$898$	19.0000	−	19.0000i	0.634038	−	0.634038i
$899$		0			0
$900$		0			0
$901$	36.0000			1.19933
$902$	−4.24264	+	4.24264i	−0.141264	+	0.141264i
$903$		0			0
$904$		−	2.00000i		−	0.0665190i
$905$	−21.2132	−	7.07107i	−0.705151	−	0.235050i
$906$		0			0
$907$	3.00000	+	3.00000i	0.0996134	+	0.0996134i	0.755157	−	0.655544i	$-0.227561\pi$
$907$	3.00000	+	3.00000i	0.0996134	+	0.0996134i	−0.655544	+	0.755157i	$0.727561\pi$
$908$	−8.48528	−	8.48528i	−0.281594	−	0.281594i
$909$		0			0
$910$		0			0
$911$			2.82843i			0.0937100i	0.998902	+	0.0468550i	$0.0149199\pi$
$911$			2.82843i			0.0937100i	−0.998902	+	0.0468550i	$0.985080\pi$
$912$		0			0
$913$	2.00000	−	2.00000i	0.0661903	−	0.0661903i
$914$	−28.2843			−0.935561
$915$		0			0
$916$	26.0000			0.859064
$917$		0			0
$918$		0			0
$919$			48.0000i			1.58337i	0.610927	+	0.791687i	$0.290797\pi$
$919$			48.0000i			1.58337i	−0.610927	+	0.791687i	$0.709203\pi$
$920$	0.707107	−	2.12132i	0.0233126	−	0.0699379i
$921$		0			0
$922$	−8.00000	−	8.00000i	−0.263466	−	0.263466i
$923$	16.9706	+	16.9706i	0.558593	+	0.558593i
$924$		0			0
$925$	3.00000	+	21.0000i	0.0986394	+	0.690476i
$926$			7.07107i			0.232370i
$927$		0			0
$928$	−4.00000	+	4.00000i	−0.131306	+	0.131306i
$929$	4.24264			0.139197			0.0695983	−	0.997575i	$-0.477828\pi$
$929$	4.24264			0.139197			0.0695983	+	0.997575i	$0.477828\pi$
$930$		0			0
$931$	42.0000			1.37649
$932$	7.07107	−	7.07107i	0.231621	−	0.231621i
$933$		0			0
$934$			26.0000i			0.850746i
$935$	−8.48528	−	16.9706i	−0.277498	−	0.554997i
$936$		0			0
$937$	4.00000	+	4.00000i	0.130674	+	0.130674i	0.769419	−	0.638745i	$-0.220546\pi$
$937$	4.00000	+	4.00000i	0.130674	+	0.130674i	−0.638745	+	0.769419i	$0.720546\pi$
$938$		0			0
$939$		0			0
$940$	10.0000	+	20.0000i	0.326164	+	0.652328i
$941$			49.4975i			1.61357i	0.590844	+	0.806786i	$0.298795\pi$
$941$			49.4975i			1.61357i	−0.590844	+	0.806786i	$0.701205\pi$
$942$		0			0
$943$	−3.00000	+	3.00000i	−0.0976934	+	0.0976934i
$944$	−2.82843			−0.0920575
$945$		0			0
$946$	2.00000			0.0650256
$947$	33.9411	−	33.9411i	1.10294	−	1.10294i	0.108884	−	0.994054i	$-0.465272\pi$
$947$	33.9411	−	33.9411i	1.10294	−	1.10294i	0.994054	−	0.108884i	$-0.0347277\pi$
$948$		0			0
$949$			72.0000i			2.33722i
$950$	4.24264	+	29.6985i	0.137649	+	0.963546i
$951$		0			0
$952$		0			0
$953$	−18.3848	−	18.3848i	−0.595541	−	0.595541i	0.343582	−	0.939123i	$-0.388360\pi$
$953$	−18.3848	−	18.3848i	−0.595541	−	0.595541i	−0.939123	+	0.343582i	$0.888360\pi$
$954$		0			0
$955$	16.0000	−	48.0000i	0.517748	−	1.55324i
$956$		−	7.07107i		−	0.228695i
$957$		0			0
$958$	20.0000	−	20.0000i	0.646171	−	0.646171i
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	−16.9706	+	16.9706i	−0.547153	+	0.547153i
$963$		0			0
$964$		−	10.0000i		−	0.322078i
$965$	−42.4264	+	21.2132i	−1.36575	+	0.682877i
$966$		0			0
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.998000	+	0.0632081i	$0.0201332\pi$
$967$	33.0000	+	33.0000i	1.06121	+	1.06121i	0.0632081	+	0.998000i	$0.479867\pi$
$968$	−6.36396	−	6.36396i	−0.204545	−	0.204545i
$969$		0			0
$970$	24.0000	+	8.00000i	0.770594	+	0.256865i
$971$			7.07107i			0.226921i	0.993542	+	0.113461i	$0.0361936\pi$
$971$			7.07107i			0.226921i	−0.993542	+	0.113461i	$0.963806\pi$
$972$		0			0
$973$		0			0
$974$	4.24264			0.135943
$975$		0			0
$976$	−2.00000			−0.0640184
$977$	−1.41421	+	1.41421i	−0.0452447	+	0.0452447i	−0.729367	−	0.684122i	$-0.760185\pi$
$977$	−1.41421	+	1.41421i	−0.0452447	+	0.0452447i	0.684122	+	0.729367i	$0.260185\pi$
$978$		0			0
$979$			4.00000i			0.127841i
$980$	−14.8492	−	4.94975i	−0.474342	−	0.158114i
$981$		0			0
$982$	−4.00000	−	4.00000i	−0.127645	−	0.127645i
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	0.750773	−	0.660560i	$-0.229681\pi$
$983$	2.82843	+	2.82843i	0.0902128	+	0.0902128i	−0.660560	+	0.750773i	$0.729681\pi$
$984$		0			0
$985$	−36.0000	+	18.0000i	−1.14706	+	0.573528i
$986$			33.9411i			1.08091i
$987$		0			0
$988$	−24.0000	+	24.0000i	−0.763542	+	0.763542i
$989$	1.41421			0.0449694
$990$		0			0
$991$	38.0000			1.20711			0.603555	−	0.797321i	$-0.293750\pi$
$991$	38.0000			1.20711			0.603555	+	0.797321i	$0.293750\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.1421	−	42.4264i	0.448336	−	1.34501i
$996$		0			0
$997$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$997$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$998$	−25.4558	−	25.4558i	−0.805791	−	0.805791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.c.737.2	yes	4
3.2	odd	2	inner	2070.2.j.c.737.1	yes	4
5.3	odd	4	inner	2070.2.j.c.323.1	✓	4
15.8	even	4	inner	2070.2.j.c.323.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.c.323.1	✓	4	5.3	odd	4	inner
2070.2.j.c.323.2	yes	4	15.8	even	4	inner
2070.2.j.c.737.1	yes	4	3.2	odd	2	inner
2070.2.j.c.737.2	yes	4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} +1.41421i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.00000 q^{16} +(-4.24264 + 4.24264i) q^{17} +6.00000i q^{19} +(0.707107 - 2.12132i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} +5.65685i q^{26} +5.65685 q^{29} +(-0.707107 + 0.707107i) q^{32} +6.00000i q^{34} +(3.00000 + 3.00000i) q^{37} +(4.24264 + 4.24264i) q^{38} +(-1.00000 - 2.00000i) q^{40} +4.24264i q^{41} +(1.00000 - 1.00000i) q^{43} +1.41421 q^{44} +1.00000 q^{46} +(-7.07107 + 7.07107i) q^{47} -7.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-1.00000 + 3.00000i) q^{55} +(4.00000 - 4.00000i) q^{58} +2.82843 q^{59} +2.00000 q^{61} +1.00000i q^{64} +(-11.3137 + 5.65685i) q^{65} +(-9.00000 - 9.00000i) q^{67} +(4.24264 + 4.24264i) q^{68} -4.24264i q^{71} +(9.00000 - 9.00000i) q^{73} +4.24264 q^{74} +6.00000 q^{76} -4.00000i q^{79} +(-2.12132 - 0.707107i) q^{80} +(3.00000 + 3.00000i) q^{82} +(-1.41421 - 1.41421i) q^{83} +(-12.0000 + 6.00000i) q^{85} -1.41421i q^{86} +(1.00000 - 1.00000i) q^{88} +2.82843 q^{89} +(0.707107 - 0.707107i) q^{92} +10.0000i q^{94} +(-4.24264 + 12.7279i) q^{95} +(8.00000 + 8.00000i) q^{97} +(-4.94975 - 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q+O(q^{10}) \) 4 * q	\( 4 q + 8 q^{10} - 16 q^{13} - 4 q^{16} + 4 q^{22} + 16 q^{25} + 12 q^{37} - 4 q^{40} + 4 q^{43} + 4 q^{46} + 16 q^{52} - 4 q^{55} + 16 q^{58} + 8 q^{61} - 36 q^{67} + 36 q^{73} + 24 q^{76} + 12 q^{82} - 48 q^{85} + 4 q^{88} + 32 q^{97}+O(q^{100}) \) 4 * q + 8 * q^10 - 16 * q^13 - 4 * q^16 + 4 * q^22 + 16 * q^25 + 12 * q^37 - 4 * q^40 + 4 * q^43 + 4 * q^46 + 16 * q^52 - 4 * q^55 + 16 * q^58 + 8 * q^61 - 36 * q^67 + 36 * q^73 + 24 * q^76 + 12 * q^82 - 48 * q^85 + 4 * q^88 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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