LMFDB - Embedded newform 2070.2.j.e.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.e.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 1.00000i) q^{10} +1.41421i q^{11} +(2.00000 - 2.00000i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +2.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} -2.82843i q^{26} +(2.00000 - 2.00000i) q^{28} +8.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(-2.82843 - 5.65685i) q^{35} +(3.00000 + 3.00000i) q^{37} +(1.41421 + 1.41421i) q^{38} +(1.00000 + 2.00000i) q^{40} +1.41421i q^{41} +(3.00000 - 3.00000i) q^{43} +1.41421 q^{44} +1.00000 q^{46} +(-1.41421 + 1.41421i) q^{47} +1.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(4.24264 + 4.24264i) q^{53} +(1.00000 - 3.00000i) q^{55} -2.82843i q^{56} +11.3137 q^{59} -2.00000 q^{61} +(5.65685 - 5.65685i) q^{62} +1.00000i q^{64} +(-5.65685 + 2.82843i) q^{65} +(1.00000 + 1.00000i) q^{67} +(1.41421 + 1.41421i) q^{68} +(-6.00000 - 2.00000i) q^{70} -9.89949i q^{71} +(5.00000 - 5.00000i) q^{73} +4.24264 q^{74} +2.00000 q^{76} +(-2.82843 + 2.82843i) q^{77} +4.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(1.00000 + 1.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(4.00000 - 2.00000i) q^{85} -4.24264i q^{86} +(1.00000 - 1.00000i) q^{88} +8.00000 q^{91} +(0.707107 - 0.707107i) q^{92} +2.00000i q^{94} +(1.41421 - 4.24264i) q^{95} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{7}+O(q^{10}) $ 4 * q + 8 * q^7	$ 4 q + 8 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{16} + 4 q^{22} + 16 q^{25} + 8 q^{28} + 32 q^{31} + 12 q^{37} + 4 q^{40} + 12 q^{43} + 4 q^{46} - 8 q^{52} + 4 q^{55} - 8 q^{61} + 4 q^{67} - 24 q^{70} + 20 q^{73} + 8 q^{76} + 4 q^{82} + 16 q^{85} + 4 q^{88} + 32 q^{91}+O(q^{100}) $ 4 * q + 8 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^16 + 4 * q^22 + 16 * q^25 + 8 * q^28 + 32 * q^31 + 12 * q^37 + 4 * q^40 + 12 * q^43 + 4 * q^46 - 8 * q^52 + 4 * q^55 - 8 * q^61 + 4 * q^67 - 24 * q^70 + 20 * q^73 + 8 * q^76 + 4 * q^82 + 16 * q^85 + 4 * q^88 + 32 * q^91

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
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	0.975579	−	0.219650i	$-0.0704915\pi$
$7$	2.00000	+	2.00000i	0.755929	+	0.755929i	−0.219650	+	0.975579i	$0.570491\pi$
$8$	−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
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	2.82843			0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$	−1.41421	+	1.41421i	−0.342997	+	0.342997i	0.514496	+	0.857493i	$0.327979\pi$
$18$		0			0
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$	−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
$26$		−	2.82843i		−	0.554700i
$27$		0			0
$28$	2.00000	−	2.00000i	0.377964	−	0.377964i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			2.00000i			0.342997i
$35$	−2.82843	−	5.65685i	−0.478091	−	0.956183i
$36$		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	$0.636609\pi$
$38$	1.41421	+	1.41421i	0.229416	+	0.229416i
$39$		0			0
$40$	1.00000	+	2.00000i	0.158114	+	0.316228i
$41$			1.41421i			0.220863i	0.993884	+	0.110432i	$0.0352233\pi$
$41$			1.41421i			0.220863i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		0			0
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	−0.440337	−	0.897833i	$-0.645141\pi$
$43$	3.00000	−	3.00000i	0.457496	−	0.457496i	0.897833	+	0.440337i	$0.145141\pi$
$44$	1.41421			0.213201
$45$		0			0
$46$	1.00000			0.147442
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	−0.802686	−	0.596402i	$-0.796597\pi$
$47$	−1.41421	+	1.41421i	−0.206284	+	0.206284i	0.596402	+	0.802686i	$0.296597\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$	1.00000	−	3.00000i	0.134840	−	0.404520i
$56$		−	2.82843i		−	0.377964i
$57$		0			0
$58$		0			0
$59$	11.3137			1.47292			0.736460	−	0.676481i	$-0.236496\pi$
$59$	11.3137			1.47292			0.736460	+	0.676481i	$0.236496\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	5.65685	−	5.65685i	0.718421	−	0.718421i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.65685	+	2.82843i	−0.701646	+	0.350823i
$66$		0			0
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	0.765548	−	0.643379i	$-0.222468\pi$
$67$	1.00000	+	1.00000i	0.122169	+	0.122169i	−0.643379	+	0.765548i	$0.722468\pi$
$68$	1.41421	+	1.41421i	0.171499	+	0.171499i
$69$		0			0
$70$	−6.00000	−	2.00000i	−0.717137	−	0.239046i
$71$		−	9.89949i		−	1.17485i	−0.809277	−	0.587427i	$-0.800141\pi$
$71$		−	9.89949i		−	1.17485i	0.809277	−	0.587427i	$-0.199859\pi$
$72$		0			0
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	5.00000	−	5.00000i	0.585206	−	0.585206i	0.936329	+	0.351123i	$0.114200\pi$
$74$	4.24264			0.493197
$75$		0			0
$76$	2.00000			0.229416
$77$	−2.82843	+	2.82843i	−0.322329	+	0.322329i
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	2.12132	+	0.707107i	0.237171	+	0.0790569i
$81$		0			0
$82$	1.00000	+	1.00000i	0.110432	+	0.110432i
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	0.900515	−	0.434825i	$-0.143190\pi$
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	−0.434825	+	0.900515i	$0.643190\pi$
$84$		0			0
$85$	4.00000	−	2.00000i	0.433861	−	0.216930i
$86$		−	4.24264i		−	0.457496i
$87$		0			0
$88$	1.00000	−	1.00000i	0.106600	−	0.106600i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	8.00000			0.838628
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$			2.00000i			0.206284i
$95$	1.41421	−	4.24264i	0.145095	−	0.435286i
$96$		0			0
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$		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
$103$	2.00000	−	2.00000i	0.197066	−	0.197066i	−0.601675	−	0.798741i	$-0.705500\pi$
$103$	2.00000	−	2.00000i	0.197066	−	0.197066i	0.798741	+	0.601675i	$0.205500\pi$
$104$	−2.82843			−0.277350
$105$		0			0
$106$	6.00000			0.582772
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	−0.165848	−	0.986151i	$-0.553036\pi$
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	0.986151	+	0.165848i	$0.0530362\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$	−1.41421	−	2.82843i	−0.134840	−	0.269680i
$111$		0			0
$112$	−2.00000	−	2.00000i	−0.188982	−	0.188982i
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	0.877920	−	0.478806i	$-0.158930\pi$
$113$	4.24264	+	4.24264i	0.399114	+	0.399114i	−0.478806	+	0.877920i	$0.658930\pi$
$114$		0			0
$115$	−1.00000	−	2.00000i	−0.0932505	−	0.186501i
$116$		0			0
$117$		0			0
$118$	8.00000	−	8.00000i	0.736460	−	0.736460i
$119$	−5.65685			−0.518563
$120$		0			0
$121$	9.00000			0.818182
$122$	−1.41421	+	1.41421i	−0.128037	+	0.128037i
$123$		0			0
$124$		−	8.00000i		−	0.718421i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$		0			0
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	0.827570	−	0.561363i	$-0.189723\pi$
$127$	3.00000	+	3.00000i	0.266207	+	0.266207i	−0.561363	+	0.827570i	$0.689723\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−2.00000	+	6.00000i	−0.175412	+	0.526235i
$131$		−	19.7990i		−	1.72985i	−0.501905	−	0.864923i	$-0.667367\pi$
$131$		−	19.7990i		−	1.72985i	0.501905	−	0.864923i	$-0.332633\pi$
$132$		0			0
$133$	−4.00000	+	4.00000i	−0.346844	+	0.346844i
$134$	1.41421			0.122169
$135$		0			0
$136$	2.00000			0.171499
$137$	−1.41421	+	1.41421i	−0.120824	+	0.120824i	−0.764934	−	0.644109i	$-0.777228\pi$
$137$	−1.41421	+	1.41421i	−0.120824	+	0.120824i	0.644109	+	0.764934i	$0.277228\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	−5.65685	+	2.82843i	−0.478091	+	0.239046i
$141$		0			0
$142$	−7.00000	−	7.00000i	−0.587427	−	0.587427i
$143$	2.82843	+	2.82843i	0.236525	+	0.236525i
$144$		0			0
$145$		0			0
$146$		−	7.07107i		−	0.585206i
$147$		0			0
$148$	3.00000	−	3.00000i	0.246598	−	0.246598i
$149$	−24.0416			−1.96957			−0.984784	−	0.173785i	$-0.944400\pi$
$149$	−24.0416			−1.96957			−0.984784	+	0.173785i	$0.944400\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$	1.41421	−	1.41421i	0.114708	−	0.114708i
$153$		0			0
$154$			4.00000i			0.322329i
$155$	−16.9706	−	5.65685i	−1.36311	−	0.454369i
$156$		0			0
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	0.249974	−	0.968252i	$-0.419578\pi$
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	−0.968252	+	0.249974i	$0.919578\pi$
$158$	2.82843	+	2.82843i	0.225018	+	0.225018i
$159$		0			0
$160$	2.00000	−	1.00000i	0.158114	−	0.0790569i
$161$			2.82843i			0.222911i
$162$		0			0
$163$	2.00000	−	2.00000i	0.156652	−	0.156652i	−0.624429	−	0.781081i	$-0.714668\pi$
$163$	2.00000	−	2.00000i	0.156652	−	0.156652i	0.781081	+	0.624429i	$0.214668\pi$
$164$	1.41421			0.110432
$165$		0			0
$166$	6.00000			0.465690
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	1.41421	−	4.24264i	0.108465	−	0.325396i
$171$		0			0
$172$	−3.00000	−	3.00000i	−0.228748	−	0.228748i
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	0.527187	−	0.849749i	$-0.323247\pi$
$173$	−4.24264	−	4.24264i	−0.322562	−	0.322562i	−0.849749	+	0.527187i	$0.823247\pi$
$174$		0			0
$175$	2.00000	+	14.0000i	0.151186	+	1.05830i
$176$		−	1.41421i		−	0.106600i
$177$		0			0
$178$		0			0
$179$	−11.3137			−0.845626			−0.422813	−	0.906217i	$-0.638957\pi$
$179$	−11.3137			−0.845626			−0.422813	+	0.906217i	$0.638957\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$	5.65685	−	5.65685i	0.419314	−	0.419314i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	−4.24264	−	8.48528i	−0.311925	−	0.623850i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	1.41421	+	1.41421i	0.103142	+	0.103142i
$189$		0			0
$190$	−2.00000	−	4.00000i	−0.145095	−	0.290191i
$191$			16.9706i			1.22795i	0.789327	+	0.613973i	$0.210430\pi$
$191$			16.9706i			1.22795i	−0.789327	+	0.613973i	$0.789570\pi$
$192$		0			0
$193$	−11.0000	+	11.0000i	−0.791797	+	0.791797i	−0.981786	−	0.189989i	$-0.939155\pi$
$193$	−11.0000	+	11.0000i	−0.791797	+	0.791797i	0.189989	+	0.981786i	$0.439155\pi$
$194$		0			0
$195$		0			0
$196$	1.00000			0.0714286
$197$	12.7279	−	12.7279i	0.906827	−	0.906827i	−0.0891879	−	0.996015i	$-0.528427\pi$
$197$	12.7279	−	12.7279i	0.906827	−	0.906827i	0.996015	+	0.0891879i	$0.0284272\pi$
$198$		0			0
$199$			20.0000i			1.41776i	0.705328	+	0.708881i	$0.250800\pi$
$199$			20.0000i			1.41776i	−0.705328	+	0.708881i	$0.749200\pi$
$200$	−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
$205$	1.00000	−	3.00000i	0.0698430	−	0.209529i
$206$		−	2.82843i		−	0.197066i
$207$		0			0
$208$	−2.00000	+	2.00000i	−0.138675	+	0.138675i
$209$	−2.82843			−0.195646
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$		−	12.0000i		−	0.820303i
$215$	−8.48528	+	4.24264i	−0.578691	+	0.289346i
$216$		0			0
$217$	16.0000	+	16.0000i	1.08615	+	1.08615i
$218$	2.82843	+	2.82843i	0.191565	+	0.191565i
$219$		0			0
$220$	−3.00000	−	1.00000i	−0.202260	−	0.0674200i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	−13.0000	+	13.0000i	−0.870544	+	0.870544i	−0.992532	−	0.121987i	$-0.961073\pi$
$223$	−13.0000	+	13.0000i	−0.870544	+	0.870544i	0.121987	+	0.992532i	$0.461073\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	6.00000			0.399114
$227$	2.82843	−	2.82843i	0.187729	−	0.187729i	−0.606984	−	0.794714i	$-0.707621\pi$
$227$	2.82843	−	2.82843i	0.187729	−	0.187729i	0.794714	+	0.606984i	$0.207621\pi$
$228$		0			0
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$	−2.12132	−	0.707107i	−0.139876	−	0.0466252i
$231$		0			0
$232$		0			0
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	18.3848	+	18.3848i	1.20443	+	1.20443i	0.231621	+	0.972806i	$0.425597\pi$
$234$		0			0
$235$	4.00000	−	2.00000i	0.260931	−	0.130466i
$236$		−	11.3137i		−	0.736460i
$237$		0			0
$238$	−4.00000	+	4.00000i	−0.259281	+	0.259281i
$239$	−9.89949			−0.640345			−0.320173	−	0.947359i	$-0.603741\pi$
$239$	−9.89949			−0.640345			−0.320173	+	0.947359i	$0.603741\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	6.36396	−	6.36396i	0.409091	−	0.409091i
$243$		0			0
$244$			2.00000i			0.128037i
$245$	0.707107	−	2.12132i	0.0451754	−	0.135526i
$246$		0			0
$247$	4.00000	+	4.00000i	0.254514	+	0.254514i
$248$	−5.65685	−	5.65685i	−0.359211	−	0.359211i
$249$		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
$254$	4.24264			0.266207
$255$		0			0
$256$	1.00000			0.0625000
$257$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$257$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$258$		0			0
$259$			12.0000i			0.745644i
$260$	2.82843	+	5.65685i	0.175412	+	0.350823i
$261$		0			0
$262$	−14.0000	−	14.0000i	−0.864923	−	0.864923i
$263$	−2.82843	−	2.82843i	−0.174408	−	0.174408i	0.614505	−	0.788913i	$-0.289356\pi$
$263$	−2.82843	−	2.82843i	−0.174408	−	0.174408i	−0.788913	+	0.614505i	$0.789356\pi$
$264$		0			0
$265$	−6.00000	−	12.0000i	−0.368577	−	0.737154i
$266$			5.65685i			0.346844i
$267$		0			0
$268$	1.00000	−	1.00000i	0.0610847	−	0.0610847i
$269$	14.1421			0.862261			0.431131	−	0.902290i	$-0.358115\pi$
$269$	14.1421			0.862261			0.431131	+	0.902290i	$0.358115\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.41421	−	1.41421i	0.0857493	−	0.0857493i
$273$		0			0
$274$			2.00000i			0.120824i
$275$	−4.24264	+	5.65685i	−0.255841	+	0.341121i
$276$		0			0
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.996368	−	0.0851468i	$-0.972864\pi$
$277$	−18.0000	−	18.0000i	−1.08152	−	1.08152i	−0.0851468	−	0.996368i	$-0.527136\pi$
$278$	2.82843	+	2.82843i	0.169638	+	0.169638i
$279$		0			0
$280$	−2.00000	+	6.00000i	−0.119523	+	0.358569i
$281$			22.6274i			1.34984i	0.737892	+	0.674919i	$0.235822\pi$
$281$			22.6274i			1.34984i	−0.737892	+	0.674919i	$0.764178\pi$
$282$		0			0
$283$	3.00000	−	3.00000i	0.178331	−	0.178331i	−0.612297	−	0.790628i	$-0.709754\pi$
$283$	3.00000	−	3.00000i	0.178331	−	0.178331i	0.790628	+	0.612297i	$0.209754\pi$
$284$	−9.89949			−0.587427
$285$		0			0
$286$	4.00000			0.236525
$287$	−2.82843	+	2.82843i	−0.166957	+	0.166957i
$288$		0			0
$289$			13.0000i			0.764706i
$290$		0			0
$291$		0			0
$292$	−5.00000	−	5.00000i	−0.292603	−	0.292603i
$293$	−16.9706	−	16.9706i	−0.991431	−	0.991431i	0.00853273	−	0.999964i	$-0.497284\pi$
$293$	−16.9706	−	16.9706i	−0.991431	−	0.991431i	−0.999964	+	0.00853273i	$0.997284\pi$
$294$		0			0
$295$	−24.0000	−	8.00000i	−1.39733	−	0.465778i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	−17.0000	+	17.0000i	−0.984784	+	0.984784i
$299$	2.82843			0.163572
$300$		0			0
$301$	12.0000			0.691669
$302$	7.07107	−	7.07107i	0.406894	−	0.406894i
$303$		0			0
$304$		−	2.00000i		−	0.114708i
$305$	4.24264	+	1.41421i	0.242933	+	0.0809776i
$306$		0			0
$307$	−4.00000	−	4.00000i	−0.228292	−	0.228292i	0.583687	−	0.811979i	$-0.301610\pi$
$307$	−4.00000	−	4.00000i	−0.228292	−	0.228292i	−0.811979	+	0.583687i	$0.801610\pi$
$308$	2.82843	+	2.82843i	0.161165	+	0.161165i
$309$		0			0
$310$	−16.0000	+	8.00000i	−0.908739	+	0.454369i
$311$			12.7279i			0.721734i	0.932617	+	0.360867i	$0.117519\pi$
$311$			12.7279i			0.721734i	−0.932617	+	0.360867i	$0.882481\pi$
$312$		0			0
$313$	−14.0000	+	14.0000i	−0.791327	+	0.791327i	−0.981710	−	0.190383i	$-0.939027\pi$
$313$	−14.0000	+	14.0000i	−0.791327	+	0.791327i	0.190383	+	0.981710i	$0.439027\pi$
$314$	−12.7279			−0.718278
$315$		0			0
$316$	4.00000			0.225018
$317$	−15.5563	+	15.5563i	−0.873732	+	0.873732i	−0.992877	−	0.119145i	$-0.961985\pi$
$317$	−15.5563	+	15.5563i	−0.873732	+	0.873732i	0.119145	+	0.992877i	$0.461985\pi$
$318$		0			0
$319$		0			0
$320$	0.707107	−	2.12132i	0.0395285	−	0.118585i
$321$		0			0
$322$	2.00000	+	2.00000i	0.111456	+	0.111456i
$323$	−2.82843	−	2.82843i	−0.157378	−	0.157378i
$324$		0			0
$325$	14.0000	−	2.00000i	0.776580	−	0.110940i
$326$		−	2.82843i		−	0.156652i
$327$		0			0
$328$	1.00000	−	1.00000i	0.0552158	−	0.0552158i
$329$	−5.65685			−0.311872
$330$		0			0
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$	4.24264	−	4.24264i	0.232845	−	0.232845i
$333$		0			0
$334$		0			0
$335$	−1.41421	−	2.82843i	−0.0772667	−	0.154533i
$336$		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	$0.993859\pi$
$338$	3.53553	+	3.53553i	0.192308	+	0.192308i
$339$		0			0
$340$	−2.00000	−	4.00000i	−0.108465	−	0.216930i
$341$			11.3137i			0.612672i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−4.24264			−0.228748
$345$		0			0
$346$	−6.00000			−0.322562
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	−0.441666	−	0.897180i	$-0.645612\pi$
$347$	8.48528	−	8.48528i	0.455514	−	0.455514i	0.897180	+	0.441666i	$0.145612\pi$
$348$		0			0
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$	11.3137	+	8.48528i	0.604743	+	0.453557i
$351$		0			0
$352$	−1.00000	−	1.00000i	−0.0533002	−	0.0533002i
$353$	11.3137	+	11.3137i	0.602168	+	0.602168i	0.940887	−	0.338719i	$-0.109994\pi$
$353$	11.3137	+	11.3137i	0.602168	+	0.602168i	−0.338719	+	0.940887i	$0.609994\pi$
$354$		0			0
$355$	−7.00000	+	21.0000i	−0.371521	+	1.11456i
$356$		0			0
$357$		0			0
$358$	−8.00000	+	8.00000i	−0.422813	+	0.422813i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	15.0000			0.789474
$362$	7.07107	−	7.07107i	0.371647	−	0.371647i
$363$		0			0
$364$		−	8.00000i		−	0.419314i
$365$	−14.1421	+	7.07107i	−0.740233	+	0.370117i
$366$		0			0
$367$	−10.0000	−	10.0000i	−0.521996	−	0.521996i	0.396178	−	0.918174i	$-0.370336\pi$
$367$	−10.0000	−	10.0000i	−0.521996	−	0.521996i	−0.918174	+	0.396178i	$0.870336\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	−9.00000	−	3.00000i	−0.467888	−	0.155963i
$371$			16.9706i			0.881068i
$372$		0			0
$373$	9.00000	−	9.00000i	0.466002	−	0.466002i	−0.434614	−	0.900617i	$-0.643115\pi$
$373$	9.00000	−	9.00000i	0.466002	−	0.466002i	0.900617	+	0.434614i	$0.143115\pi$
$374$	−2.82843			−0.146254
$375$		0			0
$376$	2.00000			0.103142
$377$		0			0
$378$		0			0
$379$			36.0000i			1.84920i	0.380945	+	0.924598i	$0.375599\pi$
$379$			36.0000i			1.84920i	−0.380945	+	0.924598i	$0.624401\pi$
$380$	−4.24264	−	1.41421i	−0.217643	−	0.0725476i
$381$		0			0
$382$	12.0000	+	12.0000i	0.613973	+	0.613973i
$383$	−19.7990	−	19.7990i	−1.01168	−	1.01168i	−0.999931	−	0.0117502i	$-0.996260\pi$
$383$	−19.7990	−	19.7990i	−1.01168	−	1.01168i	−0.0117502	−	0.999931i	$-0.503740\pi$
$384$		0			0
$385$	8.00000	−	4.00000i	0.407718	−	0.203859i
$386$			15.5563i			0.791797i
$387$		0			0
$388$		0			0
$389$	32.5269			1.64918			0.824590	−	0.565731i	$-0.191406\pi$
$389$	32.5269			1.64918			0.824590	+	0.565731i	$0.191406\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$		0			0
$394$		−	18.0000i		−	0.906827i
$395$	2.82843	−	8.48528i	0.142314	−	0.426941i
$396$		0			0
$397$	−18.0000	−	18.0000i	−0.903394	−	0.903394i	0.0923340	−	0.995728i	$-0.470567\pi$
$397$	−18.0000	−	18.0000i	−0.903394	−	0.903394i	−0.995728	+	0.0923340i	$0.970567\pi$
$398$	14.1421	+	14.1421i	0.708881	+	0.708881i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$			19.7990i			0.988714i	0.869259	+	0.494357i	$0.164597\pi$
$401$			19.7990i			0.988714i	−0.869259	+	0.494357i	$0.835403\pi$
$402$		0			0
$403$	16.0000	−	16.0000i	0.797017	−	0.797017i
$404$	5.65685			0.281439
$405$		0			0
$406$		0			0
$407$	−4.24264	+	4.24264i	−0.210300	+	0.210300i
$408$		0			0
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$	−1.41421	−	2.82843i	−0.0698430	−	0.139686i
$411$		0			0
$412$	−2.00000	−	2.00000i	−0.0985329	−	0.0985329i
$413$	22.6274	+	22.6274i	1.11342	+	1.11342i
$414$		0			0
$415$	−6.00000	−	12.0000i	−0.294528	−	0.589057i
$416$			2.82843i			0.138675i
$417$		0			0
$418$	−2.00000	+	2.00000i	−0.0978232	+	0.0978232i
$419$	−24.0416			−1.17451			−0.587255	−	0.809402i	$-0.699792\pi$
$419$	−24.0416			−1.17451			−0.587255	+	0.809402i	$0.699792\pi$
$420$		0			0
$421$	20.0000			0.974740			0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000			0.974740			0.487370	+	0.873195i	$0.337956\pi$
$422$	−5.65685	+	5.65685i	−0.275371	+	0.275371i
$423$		0			0
$424$		−	6.00000i		−	0.291386i
$425$	−9.89949	+	1.41421i	−0.480196	+	0.0685994i
$426$		0			0
$427$	−4.00000	−	4.00000i	−0.193574	−	0.193574i
$428$	−8.48528	−	8.48528i	−0.410152	−	0.410152i
$429$		0			0
$430$	−3.00000	+	9.00000i	−0.144673	+	0.434019i
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$		0			0
$433$	12.0000	−	12.0000i	0.576683	−	0.576683i	−0.357305	−	0.933988i	$-0.616304\pi$
$433$	12.0000	−	12.0000i	0.576683	−	0.576683i	0.933988	+	0.357305i	$0.116304\pi$
$434$	22.6274			1.08615
$435$		0			0
$436$	4.00000			0.191565
$437$	−1.41421	+	1.41421i	−0.0676510	+	0.0676510i
$438$		0			0
$439$		−	6.00000i		−	0.286364i	−0.989696	−	0.143182i	$-0.954267\pi$
$439$		−	6.00000i		−	0.286364i	0.989696	−	0.143182i	$-0.0457335\pi$
$440$	−2.82843	+	1.41421i	−0.134840	+	0.0674200i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	−5.65685	−	5.65685i	−0.268765	−	0.268765i	0.559837	−	0.828603i	$-0.310864\pi$
$443$	−5.65685	−	5.65685i	−0.268765	−	0.268765i	−0.828603	+	0.559837i	$0.810864\pi$
$444$		0			0
$445$		0			0
$446$			18.3848i			0.870544i
$447$		0			0
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	−4.24264			−0.200223			−0.100111	−	0.994976i	$-0.531920\pi$
$449$	−4.24264			−0.200223			−0.100111	+	0.994976i	$0.531920\pi$
$450$		0			0
$451$	−2.00000			−0.0941763
$452$	4.24264	−	4.24264i	0.199557	−	0.199557i
$453$		0			0
$454$		−	4.00000i		−	0.187729i
$455$	−16.9706	−	5.65685i	−0.795592	−	0.265197i
$456$		0			0
$457$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$457$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$458$	9.89949	+	9.89949i	0.462573	+	0.462573i
$459$		0			0
$460$	−2.00000	+	1.00000i	−0.0932505	+	0.0466252i
$461$		−	5.65685i		−	0.263466i	−0.991285	−	0.131733i	$-0.957946\pi$
$461$		−	5.65685i		−	0.263466i	0.991285	−	0.131733i	$-0.0420541\pi$
$462$		0			0
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	−0.191446	−	0.981503i	$-0.561318\pi$
$463$	17.0000	−	17.0000i	0.790057	−	0.790057i	0.981503	+	0.191446i	$0.0613177\pi$
$464$		0			0
$465$		0			0
$466$	26.0000			1.20443
$467$	15.5563	−	15.5563i	0.719862	−	0.719862i	−0.248715	−	0.968577i	$-0.580008\pi$
$467$	15.5563	−	15.5563i	0.719862	−	0.719862i	0.968577	+	0.248715i	$0.0800082\pi$
$468$		0			0
$469$			4.00000i			0.184703i
$470$	1.41421	−	4.24264i	0.0652328	−	0.195698i
$471$		0			0
$472$	−8.00000	−	8.00000i	−0.368230	−	0.368230i
$473$	4.24264	+	4.24264i	0.195077	+	0.195077i
$474$		0			0
$475$	−6.00000	+	8.00000i	−0.275299	+	0.367065i
$476$			5.65685i			0.259281i
$477$		0			0
$478$	−7.00000	+	7.00000i	−0.320173	+	0.320173i
$479$	11.3137			0.516937			0.258468	−	0.966020i	$-0.416782\pi$
$479$	11.3137			0.516937			0.258468	+	0.966020i	$0.416782\pi$
$480$		0			0
$481$	12.0000			0.547153
$482$	−7.07107	+	7.07107i	−0.322078	+	0.322078i
$483$		0			0
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$		0			0
$487$	−31.0000	−	31.0000i	−1.40474	−	1.40474i	−0.784064	−	0.620680i	$-0.786856\pi$
$487$	−31.0000	−	31.0000i	−1.40474	−	1.40474i	−0.620680	−	0.784064i	$-0.713144\pi$
$488$	1.41421	+	1.41421i	0.0640184	+	0.0640184i
$489$		0			0
$490$	−1.00000	−	2.00000i	−0.0451754	−	0.0903508i
$491$		−	8.48528i		−	0.382935i	−0.981499	−	0.191468i	$-0.938675\pi$
$491$		−	8.48528i		−	0.382935i	0.981499	−	0.191468i	$-0.0613247\pi$
$492$		0			0
$493$		0			0
$494$	5.65685			0.254514
$495$		0			0
$496$	−8.00000			−0.359211
$497$	19.7990	−	19.7990i	0.888106	−	0.888106i
$498$		0			0
$499$			40.0000i			1.79065i	0.445418	+	0.895323i	$0.353055\pi$
$499$			40.0000i			1.79065i	−0.445418	+	0.895323i	$0.646945\pi$
$500$	−9.19239	+	6.36396i	−0.411096	+	0.284605i
$501$		0			0
$502$	1.00000	+	1.00000i	0.0446322	+	0.0446322i
$503$	5.65685	+	5.65685i	0.252227	+	0.252227i	0.821883	−	0.569656i	$-0.192924\pi$
$503$	5.65685	+	5.65685i	0.252227	+	0.252227i	−0.569656	+	0.821883i	$0.692924\pi$
$504$		0			0
$505$	4.00000	−	12.0000i	0.177998	−	0.533993i
$506$			1.41421i			0.0628695i
$507$		0			0
$508$	3.00000	−	3.00000i	0.133103	−	0.133103i
$509$	16.9706			0.752207			0.376103	−	0.926578i	$-0.377264\pi$
$509$	16.9706			0.752207			0.376103	+	0.926578i	$0.377264\pi$
$510$		0			0
$511$	20.0000			0.884748
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		0			0
$515$	−5.65685	+	2.82843i	−0.249271	+	0.124635i
$516$		0			0
$517$	−2.00000	−	2.00000i	−0.0879599	−	0.0879599i
$518$	8.48528	+	8.48528i	0.372822	+	0.372822i
$519$		0			0
$520$	6.00000	+	2.00000i	0.263117	+	0.0877058i
$521$			28.2843i			1.23916i	0.784935	+	0.619578i	$0.212696\pi$
$521$			28.2843i			1.23916i	−0.784935	+	0.619578i	$0.787304\pi$
$522$		0			0
$523$	−11.0000	+	11.0000i	−0.480996	+	0.480996i	−0.905450	−	0.424453i	$-0.860466\pi$
$523$	−11.0000	+	11.0000i	−0.480996	+	0.480996i	0.424453	+	0.905450i	$0.360466\pi$
$524$	−19.7990			−0.864923
$525$		0			0
$526$	−4.00000			−0.174408
$527$	−11.3137	+	11.3137i	−0.492833	+	0.492833i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−12.7279	−	4.24264i	−0.552866	−	0.184289i
$531$		0			0
$532$	4.00000	+	4.00000i	0.173422	+	0.173422i
$533$	2.82843	+	2.82843i	0.122513	+	0.122513i
$534$		0			0
$535$	−24.0000	+	12.0000i	−1.03761	+	0.518805i
$536$		−	1.41421i		−	0.0610847i
$537$		0			0
$538$	10.0000	−	10.0000i	0.431131	−	0.431131i
$539$	−1.41421			−0.0609145
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$		0			0
$544$		−	2.00000i		−	0.0857493i
$545$	2.82843	−	8.48528i	0.121157	−	0.363470i
$546$		0			0
$547$	−24.0000	−	24.0000i	−1.02617	−	1.02617i	−0.999648	−	0.0265176i	$-0.991558\pi$
$547$	−24.0000	−	24.0000i	−1.02617	−	1.02617i	−0.0265176	−	0.999648i	$-0.508442\pi$
$548$	1.41421	+	1.41421i	0.0604122	+	0.0604122i
$549$		0			0
$550$	1.00000	+	7.00000i	0.0426401	+	0.298481i
$551$		0			0
$552$		0			0
$553$	−8.00000	+	8.00000i	−0.340195	+	0.340195i
$554$	−25.4558			−1.08152
$555$		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
$559$		−	12.0000i		−	0.507546i
$560$	2.82843	+	5.65685i	0.119523	+	0.239046i
$561$		0			0
$562$	16.0000	+	16.0000i	0.674919	+	0.674919i
$563$	−24.0416	−	24.0416i	−1.01323	−	1.01323i	−0.999911	−	0.0133227i	$-0.995759\pi$
$563$	−24.0416	−	24.0416i	−1.01323	−	1.01323i	−0.0133227	−	0.999911i	$-0.504241\pi$
$564$		0			0
$565$	−6.00000	−	12.0000i	−0.252422	−	0.504844i
$566$		−	4.24264i		−	0.178331i
$567$		0			0
$568$	−7.00000	+	7.00000i	−0.293713	+	0.293713i
$569$	2.82843			0.118574			0.0592869	−	0.998241i	$-0.481117\pi$
$569$	2.82843			0.118574			0.0592869	+	0.998241i	$0.481117\pi$
$570$		0			0
$571$	−44.0000			−1.84134			−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000			−1.84134			−0.920671	+	0.390339i	$0.872358\pi$
$572$	2.82843	−	2.82843i	0.118262	−	0.118262i
$573$		0			0
$574$			4.00000i			0.166957i
$575$	0.707107	+	4.94975i	0.0294884	+	0.206419i
$576$		0			0
$577$	−27.0000	−	27.0000i	−1.12402	−	1.12402i	−0.991130	−	0.132895i	$-0.957573\pi$
$577$	−27.0000	−	27.0000i	−1.12402	−	1.12402i	−0.132895	−	0.991130i	$-0.542427\pi$
$578$	9.19239	+	9.19239i	0.382353	+	0.382353i
$579$		0			0
$580$		0			0
$581$			16.9706i			0.704058i
$582$		0			0
$583$	−6.00000	+	6.00000i	−0.248495	+	0.248495i
$584$	−7.07107			−0.292603
$585$		0			0
$586$	−24.0000			−0.991431
$587$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$587$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$588$		0			0
$589$			16.0000i			0.659269i
$590$	−22.6274	+	11.3137i	−0.931556	+	0.465778i
$591$		0			0
$592$	−3.00000	−	3.00000i	−0.123299	−	0.123299i
$593$	28.2843	+	28.2843i	1.16150	+	1.16150i	0.984148	+	0.177348i	$0.0567517\pi$
$593$	28.2843	+	28.2843i	1.16150	+	1.16150i	0.177348	+	0.984148i	$0.443248\pi$
$594$		0			0
$595$	12.0000	+	4.00000i	0.491952	+	0.163984i
$596$			24.0416i			0.984784i
$597$		0			0
$598$	2.00000	−	2.00000i	0.0817861	−	0.0817861i
$599$	−32.5269			−1.32901			−0.664507	−	0.747282i	$-0.731358\pi$
$599$	−32.5269			−1.32901			−0.664507	+	0.747282i	$0.731358\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$	8.48528	−	8.48528i	0.345834	−	0.345834i
$603$		0			0
$604$		−	10.0000i		−	0.406894i
$605$	−19.0919	−	6.36396i	−0.776195	−	0.258732i
$606$		0			0
$607$	1.00000	+	1.00000i	0.0405887	+	0.0405887i	0.727110	−	0.686521i	$-0.240863\pi$
$607$	1.00000	+	1.00000i	0.0405887	+	0.0405887i	−0.686521	+	0.727110i	$0.740863\pi$
$608$	−1.41421	−	1.41421i	−0.0573539	−	0.0573539i
$609$		0			0
$610$	4.00000	−	2.00000i	0.161955	−	0.0809776i
$611$			5.65685i			0.228852i
$612$		0			0
$613$	21.0000	−	21.0000i	0.848182	−	0.848182i	−0.141724	−	0.989906i	$-0.545265\pi$
$613$	21.0000	−	21.0000i	0.848182	−	0.848182i	0.989906	+	0.141724i	$0.0452646\pi$
$614$	−5.65685			−0.228292
$615$		0			0
$616$	4.00000			0.161165
$617$	−29.6985	+	29.6985i	−1.19562	+	1.19562i	−0.220150	+	0.975466i	$0.570655\pi$
$617$	−29.6985	+	29.6985i	−1.19562	+	1.19562i	−0.975466	+	0.220150i	$0.929345\pi$
$618$		0			0
$619$		−	46.0000i		−	1.84890i	−0.381308	−	0.924448i	$-0.624526\pi$
$619$		−	46.0000i		−	1.84890i	0.381308	−	0.924448i	$-0.375474\pi$
$620$	−5.65685	+	16.9706i	−0.227185	+	0.681554i
$621$		0			0
$622$	9.00000	+	9.00000i	0.360867	+	0.360867i
$623$		0			0
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$			19.7990i			0.791327i
$627$		0			0
$628$	−9.00000	+	9.00000i	−0.359139	+	0.359139i
$629$	−8.48528			−0.338330
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$	2.82843	−	2.82843i	0.112509	−	0.112509i
$633$		0			0
$634$			22.0000i			0.873732i
$635$	−4.24264	−	8.48528i	−0.168364	−	0.336728i
$636$		0			0
$637$	2.00000	+	2.00000i	0.0792429	+	0.0792429i
$638$		0			0
$639$		0			0
$640$	−1.00000	−	2.00000i	−0.0395285	−	0.0790569i
$641$			11.3137i			0.446865i	0.974719	+	0.223432i	$0.0717262\pi$
$641$			11.3137i			0.446865i	−0.974719	+	0.223432i	$0.928274\pi$
$642$		0			0
$643$	9.00000	−	9.00000i	0.354925	−	0.354925i	−0.507013	−	0.861938i	$-0.669250\pi$
$643$	9.00000	−	9.00000i	0.354925	−	0.354925i	0.861938	+	0.507013i	$0.169250\pi$
$644$	2.82843			0.111456
$645$		0			0
$646$	−4.00000			−0.157378
$647$	4.24264	−	4.24264i	0.166795	−	0.166795i	−0.618774	−	0.785569i	$-0.712370\pi$
$647$	4.24264	−	4.24264i	0.166795	−	0.166795i	0.785569	+	0.618774i	$0.212370\pi$
$648$		0			0
$649$			16.0000i			0.628055i
$650$	8.48528	−	11.3137i	0.332820	−	0.443760i
$651$		0			0
$652$	−2.00000	−	2.00000i	−0.0783260	−	0.0783260i
$653$	29.6985	+	29.6985i	1.16219	+	1.16219i	0.983995	+	0.178197i	$0.0570263\pi$
$653$	29.6985	+	29.6985i	1.16219	+	1.16219i	0.178197	+	0.983995i	$0.442974\pi$
$654$		0			0
$655$	−14.0000	+	42.0000i	−0.547025	+	1.64108i
$656$		−	1.41421i		−	0.0552158i
$657$		0			0
$658$	−4.00000	+	4.00000i	−0.155936	+	0.155936i
$659$	32.5269			1.26707			0.633534	−	0.773715i	$-0.281604\pi$
$659$	32.5269			1.26707			0.633534	+	0.773715i	$0.281604\pi$
$660$		0			0
$661$	20.0000			0.777910			0.388955	−	0.921257i	$-0.372836\pi$
$661$	20.0000			0.777910			0.388955	+	0.921257i	$0.372836\pi$
$662$	−19.7990	+	19.7990i	−0.769510	+	0.769510i
$663$		0			0
$664$		−	6.00000i		−	0.232845i
$665$	11.3137	−	5.65685i	0.438727	−	0.219363i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	−3.00000	−	1.00000i	−0.115900	−	0.0386334i
$671$		−	2.82843i		−	0.109190i
$672$		0			0
$673$	−29.0000	+	29.0000i	−1.11787	+	1.11787i	−0.125814	+	0.992054i	$0.540154\pi$
$673$	−29.0000	+	29.0000i	−1.11787	+	1.11787i	−0.992054	+	0.125814i	$0.959846\pi$
$674$	−25.4558			−0.980522
$675$		0			0
$676$	5.00000			0.192308
$677$	25.4558	−	25.4558i	0.978348	−	0.978348i	−0.0214229	−	0.999771i	$-0.506820\pi$
$677$	25.4558	−	25.4558i	0.978348	−	0.978348i	0.999771	+	0.0214229i	$0.00681965\pi$
$678$		0			0
$679$		0			0
$680$	−4.24264	−	1.41421i	−0.162698	−	0.0542326i
$681$		0			0
$682$	8.00000	+	8.00000i	0.306336	+	0.306336i
$683$	−5.65685	−	5.65685i	−0.216454	−	0.216454i	0.590549	−	0.807002i	$-0.298911\pi$
$683$	−5.65685	−	5.65685i	−0.216454	−	0.216454i	−0.807002	+	0.590549i	$0.798911\pi$
$684$		0			0
$685$	4.00000	−	2.00000i	0.152832	−	0.0764161i
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	−3.00000	+	3.00000i	−0.114374	+	0.114374i
$689$	16.9706			0.646527
$690$		0			0
$691$	−40.0000			−1.52167			−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000			−1.52167			−0.760836	+	0.648944i	$0.775211\pi$
$692$	−4.24264	+	4.24264i	−0.161281	+	0.161281i
$693$		0			0
$694$		−	12.0000i		−	0.455514i
$695$	2.82843	−	8.48528i	0.107288	−	0.321865i
$696$		0			0
$697$	−2.00000	−	2.00000i	−0.0757554	−	0.0757554i
$698$	−21.2132	−	21.2132i	−0.802932	−	0.802932i
$699$		0			0
$700$	14.0000	−	2.00000i	0.529150	−	0.0755929i
$701$		−	12.7279i		−	0.480727i	−0.970683	−	0.240363i	$-0.922733\pi$
$701$		−	12.7279i		−	0.480727i	0.970683	−	0.240363i	$-0.0772666\pi$
$702$		0			0
$703$	−6.00000	+	6.00000i	−0.226294	+	0.226294i
$704$	−1.41421			−0.0533002
$705$		0			0
$706$	16.0000			0.602168
$707$	−11.3137	+	11.3137i	−0.425496	+	0.425496i
$708$		0			0
$709$		−	10.0000i		−	0.375558i	−0.982211	−	0.187779i	$-0.939871\pi$
$709$		−	10.0000i		−	0.375558i	0.982211	−	0.187779i	$-0.0601289\pi$
$710$	9.89949	+	19.7990i	0.371521	+	0.743043i
$711$		0			0
$712$		0			0
$713$	5.65685	+	5.65685i	0.211851	+	0.211851i
$714$		0			0
$715$	−4.00000	−	8.00000i	−0.149592	−	0.299183i
$716$			11.3137i			0.422813i
$717$		0			0
$718$		0			0
$719$	29.6985			1.10757			0.553783	−	0.832661i	$-0.313184\pi$
$719$	29.6985			1.10757			0.553783	+	0.832661i	$0.313184\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$	10.6066	−	10.6066i	0.394737	−	0.394737i
$723$		0			0
$724$		−	10.0000i		−	0.371647i
$725$		0			0
$726$		0			0
$727$	−12.0000	−	12.0000i	−0.445055	−	0.445055i	0.448651	−	0.893707i	$-0.351904\pi$
$727$	−12.0000	−	12.0000i	−0.445055	−	0.445055i	−0.893707	+	0.448651i	$0.851904\pi$
$728$	−5.65685	−	5.65685i	−0.209657	−	0.209657i
$729$		0			0
$730$	−5.00000	+	15.0000i	−0.185058	+	0.555175i
$731$			8.48528i			0.313839i
$732$		0			0
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	−0.203436	−	0.979088i	$-0.565211\pi$
$733$	21.0000	−	21.0000i	0.775653	−	0.775653i	0.979088	+	0.203436i	$0.0652108\pi$
$734$	−14.1421			−0.521996
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−1.41421	+	1.41421i	−0.0520932	+	0.0520932i
$738$		0			0
$739$			28.0000i			1.03000i	0.857191	+	0.514998i	$0.172207\pi$
$739$			28.0000i			1.03000i	−0.857191	+	0.514998i	$0.827793\pi$
$740$	−8.48528	+	4.24264i	−0.311925	+	0.155963i
$741$		0			0
$742$	12.0000	+	12.0000i	0.440534	+	0.440534i
$743$	2.82843	+	2.82843i	0.103765	+	0.103765i	0.757083	−	0.653318i	$-0.226624\pi$
$743$	2.82843	+	2.82843i	0.103765	+	0.103765i	−0.653318	+	0.757083i	$0.726624\pi$
$744$		0			0
$745$	51.0000	+	17.0000i	1.86850	+	0.622832i
$746$		−	12.7279i		−	0.466002i
$747$		0			0
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	33.9411			1.24018
$750$		0			0
$751$	12.0000			0.437886			0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000			0.437886			0.218943	+	0.975738i	$0.429739\pi$
$752$	1.41421	−	1.41421i	0.0515711	−	0.0515711i
$753$		0			0
$754$		0			0
$755$	−21.2132	−	7.07107i	−0.772028	−	0.257343i
$756$		0			0
$757$	−19.0000	−	19.0000i	−0.690567	−	0.690567i	0.271790	−	0.962357i	$-0.412384\pi$
$757$	−19.0000	−	19.0000i	−0.690567	−	0.690567i	−0.962357	+	0.271790i	$0.912384\pi$
$758$	25.4558	+	25.4558i	0.924598	+	0.924598i
$759$		0			0
$760$	−4.00000	+	2.00000i	−0.145095	+	0.0725476i
$761$		−	49.4975i		−	1.79428i	−0.441744	−	0.897141i	$-0.645640\pi$
$761$		−	49.4975i		−	1.79428i	0.441744	−	0.897141i	$-0.354360\pi$
$762$		0			0
$763$	−8.00000	+	8.00000i	−0.289619	+	0.289619i
$764$	16.9706			0.613973
$765$		0			0
$766$	−28.0000			−1.01168
$767$	22.6274	−	22.6274i	0.817029	−	0.817029i
$768$		0			0
$769$			14.0000i			0.504853i	0.967616	+	0.252426i	$0.0812286\pi$
$769$			14.0000i			0.504853i	−0.967616	+	0.252426i	$0.918771\pi$
$770$	2.82843	−	8.48528i	0.101929	−	0.305788i
$771$		0			0
$772$	11.0000	+	11.0000i	0.395899	+	0.395899i
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	0.955676	−	0.294421i	$-0.0951269\pi$
$773$	18.3848	+	18.3848i	0.661254	+	0.661254i	−0.294421	+	0.955676i	$0.595127\pi$
$774$		0			0
$775$	32.0000	+	24.0000i	1.14947	+	0.862105i
$776$		0			0
$777$		0			0
$778$	23.0000	−	23.0000i	0.824590	−	0.824590i
$779$	−2.82843			−0.101339
$780$		0			0
$781$	14.0000			0.500959
$782$	−1.41421	+	1.41421i	−0.0505722	+	0.0505722i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	12.7279	+	25.4558i	0.454279	+	0.908558i
$786$		0			0
$787$	11.0000	+	11.0000i	0.392108	+	0.392108i	0.875438	−	0.483330i	$-0.160573\pi$
$787$	11.0000	+	11.0000i	0.392108	+	0.392108i	−0.483330	+	0.875438i	$0.660573\pi$
$788$	−12.7279	−	12.7279i	−0.453413	−	0.453413i
$789$		0			0
$790$	−4.00000	−	8.00000i	−0.142314	−	0.284627i
$791$			16.9706i			0.603404i
$792$		0			0
$793$	−4.00000	+	4.00000i	−0.142044	+	0.142044i
$794$	−25.4558			−0.903394
$795$		0			0
$796$	20.0000			0.708881
$797$	1.41421	−	1.41421i	0.0500940	−	0.0500940i	−0.681616	−	0.731710i	$-0.738723\pi$
$797$	1.41421	−	1.41421i	0.0500940	−	0.0500940i	0.731710	+	0.681616i	$0.238723\pi$
$798$		0			0
$799$		−	4.00000i		−	0.141510i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	14.0000	+	14.0000i	0.494357	+	0.494357i
$803$	7.07107	+	7.07107i	0.249533	+	0.249533i
$804$		0			0
$805$	2.00000	−	6.00000i	0.0704907	−	0.211472i
$806$		−	22.6274i		−	0.797017i
$807$		0			0
$808$	4.00000	−	4.00000i	0.140720	−	0.140720i
$809$	−18.3848			−0.646374			−0.323187	−	0.946335i	$-0.604754\pi$
$809$	−18.3848			−0.646374			−0.323187	+	0.946335i	$0.604754\pi$
$810$		0			0
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		0			0
$813$		0			0
$814$			6.00000i			0.210300i
$815$	−5.65685	+	2.82843i	−0.198151	+	0.0990755i
$816$		0			0
$817$	6.00000	+	6.00000i	0.209913	+	0.209913i
$818$	−7.07107	−	7.07107i	−0.247234	−	0.247234i
$819$		0			0
$820$	−3.00000	−	1.00000i	−0.104765	−	0.0349215i
$821$		−	19.7990i		−	0.690990i	−0.938421	−	0.345495i	$-0.887711\pi$
$821$		−	19.7990i		−	0.690990i	0.938421	−	0.345495i	$-0.112289\pi$
$822$		0			0
$823$	17.0000	−	17.0000i	0.592583	−	0.592583i	−0.345746	−	0.938328i	$-0.612374\pi$
$823$	17.0000	−	17.0000i	0.592583	−	0.592583i	0.938328	+	0.345746i	$0.112374\pi$
$824$	−2.82843			−0.0985329
$825$		0			0
$826$	32.0000			1.11342
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	−0.417093	−	0.908864i	$-0.636951\pi$
$827$	14.1421	−	14.1421i	0.491770	−	0.491770i	0.908864	+	0.417093i	$0.136951\pi$
$828$		0			0
$829$			10.0000i			0.347314i	0.984806	+	0.173657i	$0.0555585\pi$
$829$			10.0000i			0.347314i	−0.984806	+	0.173657i	$0.944442\pi$
$830$	−12.7279	−	4.24264i	−0.441793	−	0.147264i
$831$		0			0
$832$	2.00000	+	2.00000i	0.0693375	+	0.0693375i
$833$	−1.41421	−	1.41421i	−0.0489996	−	0.0489996i
$834$		0			0
$835$		0			0
$836$			2.82843i			0.0978232i
$837$		0			0
$838$	−17.0000	+	17.0000i	−0.587255	+	0.587255i
$839$	14.1421			0.488241			0.244120	−	0.969745i	$-0.421501\pi$
$839$	14.1421			0.488241			0.244120	+	0.969745i	$0.421501\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	14.1421	−	14.1421i	0.487370	−	0.487370i
$843$		0			0
$844$			8.00000i			0.275371i
$845$	3.53553	−	10.6066i	0.121626	−	0.364878i
$846$		0			0
$847$	18.0000	+	18.0000i	0.618487	+	0.618487i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$	−6.00000	+	8.00000i	−0.205798	+	0.274398i
$851$			4.24264i			0.145436i
$852$		0			0
$853$	30.0000	−	30.0000i	1.02718	−	1.02718i	0.0275603	−	0.999620i	$-0.491226\pi$
$853$	30.0000	−	30.0000i	1.02718	−	1.02718i	0.999620	−	0.0275603i	$-0.00877382\pi$
$854$	−5.65685			−0.193574
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−11.3137	+	11.3137i	−0.386469	+	0.386469i	−0.873426	−	0.486957i	$-0.838107\pi$
$857$	−11.3137	+	11.3137i	−0.386469	+	0.386469i	0.486957	+	0.873426i	$0.338107\pi$
$858$		0			0
$859$		−	24.0000i		−	0.818869i	−0.912339	−	0.409435i	$-0.865726\pi$
$859$		−	24.0000i		−	0.818869i	0.912339	−	0.409435i	$-0.134274\pi$
$860$	4.24264	+	8.48528i	0.144673	+	0.289346i
$861$		0			0
$862$	4.00000	+	4.00000i	0.136241	+	0.136241i
$863$	−29.6985	−	29.6985i	−1.01095	−	1.01095i	−0.999939	−	0.0110088i	$-0.996496\pi$
$863$	−29.6985	−	29.6985i	−1.01095	−	1.01095i	−0.0110088	−	0.999939i	$-0.503504\pi$
$864$		0			0
$865$	6.00000	+	12.0000i	0.204006	+	0.408012i
$866$		−	16.9706i		−	0.576683i
$867$		0			0
$868$	16.0000	−	16.0000i	0.543075	−	0.543075i
$869$	−5.65685			−0.191896
$870$		0			0
$871$	4.00000			0.135535
$872$	2.82843	−	2.82843i	0.0957826	−	0.0957826i
$873$		0			0
$874$			2.00000i			0.0676510i
$875$	5.65685	−	31.1127i	0.191237	−	1.05180i
$876$		0			0
$877$	2.00000	+	2.00000i	0.0675352	+	0.0675352i	0.740068	−	0.672532i	$-0.234793\pi$
$877$	2.00000	+	2.00000i	0.0675352	+	0.0675352i	−0.672532	+	0.740068i	$0.734793\pi$
$878$	−4.24264	−	4.24264i	−0.143182	−	0.143182i
$879$		0			0
$880$	−1.00000	+	3.00000i	−0.0337100	+	0.101130i
$881$		−	33.9411i		−	1.14351i	−0.820426	−	0.571753i	$-0.806264\pi$
$881$		−	33.9411i		−	1.14351i	0.820426	−	0.571753i	$-0.193736\pi$
$882$		0			0
$883$	30.0000	−	30.0000i	1.00958	−	1.00958i	0.00962672	−	0.999954i	$-0.496936\pi$
$883$	30.0000	−	30.0000i	1.00958	−	1.00958i	0.999954	−	0.00962672i	$-0.00306433\pi$
$884$	5.65685			0.190261
$885$		0			0
$886$	−8.00000			−0.268765
$887$	15.5563	−	15.5563i	0.522331	−	0.522331i	−0.395944	−	0.918275i	$-0.629582\pi$
$887$	15.5563	−	15.5563i	0.522331	−	0.522331i	0.918275	+	0.395944i	$0.129582\pi$
$888$		0			0
$889$			12.0000i			0.402467i
$890$		0			0
$891$		0			0
$892$	13.0000	+	13.0000i	0.435272	+	0.435272i
$893$	−2.82843	−	2.82843i	−0.0946497	−	0.0946497i
$894$		0			0
$895$	24.0000	+	8.00000i	0.802232	+	0.267411i
$896$			2.82843i			0.0944911i
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$		0			0
$901$	−12.0000			−0.399778
$902$	−1.41421	+	1.41421i	−0.0470882	+	0.0470882i
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$	−21.2132	−	7.07107i	−0.705151	−	0.235050i
$906$		0			0
$907$	−15.0000	−	15.0000i	−0.498067	−	0.498067i	0.412769	−	0.910836i	$-0.364562\pi$
$907$	−15.0000	−	15.0000i	−0.498067	−	0.498067i	−0.910836	+	0.412769i	$0.864562\pi$
$908$	−2.82843	−	2.82843i	−0.0938647	−	0.0938647i
$909$		0			0
$910$	−16.0000	+	8.00000i	−0.530395	+	0.265197i
$911$		−	14.1421i		−	0.468550i	−0.972170	−	0.234275i	$-0.924728\pi$
$911$		−	14.1421i		−	0.468550i	0.972170	−	0.234275i	$-0.0752716\pi$
$912$		0			0
$913$	−6.00000	+	6.00000i	−0.198571	+	0.198571i
$914$		0			0
$915$		0			0
$916$	14.0000			0.462573
$917$	39.5980	−	39.5980i	1.30764	−	1.30764i
$918$		0			0
$919$		−	4.00000i		−	0.131948i	−0.997821	−	0.0659739i	$-0.978985\pi$
$919$		−	4.00000i		−	0.131948i	0.997821	−	0.0659739i	$-0.0210154\pi$
$920$	−0.707107	+	2.12132i	−0.0233126	+	0.0699379i
$921$		0			0
$922$	−4.00000	−	4.00000i	−0.131733	−	0.131733i
$923$	−19.7990	−	19.7990i	−0.651692	−	0.651692i
$924$		0			0
$925$	3.00000	+	21.0000i	0.0986394	+	0.690476i
$926$		−	24.0416i		−	0.790057i
$927$		0			0
$928$		0			0
$929$	18.3848			0.603185			0.301592	−	0.953437i	$-0.402482\pi$
$929$	18.3848			0.603185			0.301592	+	0.953437i	$0.402482\pi$
$930$		0			0
$931$	−2.00000			−0.0655474
$932$	18.3848	−	18.3848i	0.602213	−	0.602213i
$933$		0			0
$934$		−	22.0000i		−	0.719862i
$935$	2.82843	+	5.65685i	0.0924995	+	0.184999i
$936$		0			0
$937$	−12.0000	−	12.0000i	−0.392023	−	0.392023i	0.483385	−	0.875408i	$-0.339407\pi$
$937$	−12.0000	−	12.0000i	−0.392023	−	0.392023i	−0.875408	+	0.483385i	$0.839407\pi$
$938$	2.82843	+	2.82843i	0.0923514	+	0.0923514i
$939$		0			0
$940$	−2.00000	−	4.00000i	−0.0652328	−	0.130466i
$941$			18.3848i			0.599327i	0.954045	+	0.299663i	$0.0968743\pi$
$941$			18.3848i			0.599327i	−0.954045	+	0.299663i	$0.903126\pi$
$942$		0			0
$943$	−1.00000	+	1.00000i	−0.0325645	+	0.0325645i
$944$	−11.3137			−0.368230
$945$		0			0
$946$	6.00000			0.195077
$947$	5.65685	−	5.65685i	0.183823	−	0.183823i	−0.609196	−	0.793019i	$-0.708508\pi$
$947$	5.65685	−	5.65685i	0.183823	−	0.183823i	0.793019	+	0.609196i	$0.208508\pi$
$948$		0			0
$949$		−	20.0000i		−	0.649227i
$950$	1.41421	+	9.89949i	0.0458831	+	0.321182i
$951$		0			0
$952$	4.00000	+	4.00000i	0.129641	+	0.129641i
$953$	18.3848	+	18.3848i	0.595541	+	0.595541i	0.939123	−	0.343582i	$-0.111640\pi$
$953$	18.3848	+	18.3848i	0.595541	+	0.595541i	−0.343582	+	0.939123i	$0.611640\pi$
$954$		0			0
$955$	12.0000	−	36.0000i	0.388311	−	1.16493i
$956$			9.89949i			0.320173i
$957$		0			0
$958$	8.00000	−	8.00000i	0.258468	−	0.258468i
$959$	−5.65685			−0.182669
$960$		0			0
$961$	33.0000			1.06452
$962$	8.48528	−	8.48528i	0.273576	−	0.273576i
$963$		0			0
$964$			10.0000i			0.322078i
$965$	31.1127	−	15.5563i	1.00155	−	0.500777i
$966$		0			0
$967$	−1.00000	−	1.00000i	−0.0321578	−	0.0321578i	0.690845	−	0.723003i	$-0.257239\pi$
$967$	−1.00000	−	1.00000i	−0.0321578	−	0.0321578i	−0.723003	+	0.690845i	$0.757239\pi$
$968$	−6.36396	−	6.36396i	−0.204545	−	0.204545i
$969$		0			0
$970$		0			0
$971$			18.3848i			0.589996i	0.955498	+	0.294998i	$0.0953189\pi$
$971$			18.3848i			0.589996i	−0.955498	+	0.294998i	$0.904681\pi$
$972$		0			0
$973$	−8.00000	+	8.00000i	−0.256468	+	0.256468i
$974$	−43.8406			−1.40474
$975$		0			0
$976$	2.00000			0.0640184
$977$	1.41421	−	1.41421i	0.0452447	−	0.0452447i	−0.684122	−	0.729367i	$-0.739815\pi$
$977$	1.41421	−	1.41421i	0.0452447	−	0.0452447i	0.729367	+	0.684122i	$0.239815\pi$
$978$		0			0
$979$		0			0
$980$	−2.12132	−	0.707107i	−0.0677631	−	0.0225877i
$981$		0			0
$982$	−6.00000	−	6.00000i	−0.191468	−	0.191468i
$983$	−28.2843	−	28.2843i	−0.902128	−	0.902128i	0.0934919	−	0.995620i	$-0.470197\pi$
$983$	−28.2843	−	28.2843i	−0.902128	−	0.902128i	−0.995620	+	0.0934919i	$0.970197\pi$
$984$		0			0
$985$	−36.0000	+	18.0000i	−1.14706	+	0.573528i
$986$		0			0
$987$		0			0
$988$	4.00000	−	4.00000i	0.127257	−	0.127257i
$989$	4.24264			0.134908
$990$		0			0
$991$	−30.0000			−0.952981			−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000			−0.952981			−0.476491	+	0.879180i	$0.658091\pi$
$992$	−5.65685	+	5.65685i	−0.179605	+	0.179605i
$993$		0			0
$994$		−	28.0000i		−	0.888106i
$995$	14.1421	−	42.4264i	0.448336	−	1.34501i
$996$		0			0
$997$	−2.00000	−	2.00000i	−0.0633406	−	0.0633406i	0.674727	−	0.738068i	$-0.264261\pi$
$997$	−2.00000	−	2.00000i	−0.0633406	−	0.0633406i	−0.738068	+	0.674727i	$0.764261\pi$
$998$	28.2843	+	28.2843i	0.895323	+	0.895323i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.e.323.1	✓	4	5.3	odd	4	inner
2070.2.j.e.323.2	yes	4	15.8	even	4	inner
2070.2.j.e.737.1	yes	4	3.2	odd	2	inner
2070.2.j.e.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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-2.12132 - 0.707107i) q^{5} +(2.00000 + 2.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.00000 + 1.00000i) q^{10} +1.41421i q^{11} +(2.00000 - 2.00000i) q^{13} +2.82843 q^{14} -1.00000 q^{16} +(-1.41421 + 1.41421i) q^{17} +2.00000i q^{19} +(-0.707107 + 2.12132i) q^{20} +(1.00000 + 1.00000i) q^{22} +(0.707107 + 0.707107i) q^{23} +(4.00000 + 3.00000i) q^{25} -2.82843i q^{26} +(2.00000 - 2.00000i) q^{28} +8.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +2.00000i q^{34} +(-2.82843 - 5.65685i) q^{35} +(3.00000 + 3.00000i) q^{37} +(1.41421 + 1.41421i) q^{38} +(1.00000 + 2.00000i) q^{40} +1.41421i q^{41} +(3.00000 - 3.00000i) q^{43} +1.41421 q^{44} +1.00000 q^{46} +(-1.41421 + 1.41421i) q^{47} +1.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-2.00000 - 2.00000i) q^{52} +(4.24264 + 4.24264i) q^{53} +(1.00000 - 3.00000i) q^{55} -2.82843i q^{56} +11.3137 q^{59} -2.00000 q^{61} +(5.65685 - 5.65685i) q^{62} +1.00000i q^{64} +(-5.65685 + 2.82843i) q^{65} +(1.00000 + 1.00000i) q^{67} +(1.41421 + 1.41421i) q^{68} +(-6.00000 - 2.00000i) q^{70} -9.89949i q^{71} +(5.00000 - 5.00000i) q^{73} +4.24264 q^{74} +2.00000 q^{76} +(-2.82843 + 2.82843i) q^{77} +4.00000i q^{79} +(2.12132 + 0.707107i) q^{80} +(1.00000 + 1.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(4.00000 - 2.00000i) q^{85} -4.24264i q^{86} +(1.00000 - 1.00000i) q^{88} +8.00000 q^{91} +(0.707107 - 0.707107i) q^{92} +2.00000i q^{94} +(1.41421 - 4.24264i) q^{95} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{7}+O(q^{10}) \) 4 * q + 8 * q^7	\( 4 q + 8 q^{7} - 8 q^{10} + 8 q^{13} - 4 q^{16} + 4 q^{22} + 16 q^{25} + 8 q^{28} + 32 q^{31} + 12 q^{37} + 4 q^{40} + 12 q^{43} + 4 q^{46} - 8 q^{52} + 4 q^{55} - 8 q^{61} + 4 q^{67} - 24 q^{70} + 20 q^{73} + 8 q^{76} + 4 q^{82} + 16 q^{85} + 4 q^{88} + 32 q^{91}+O(q^{100}) \) 4 * q + 8 * q^7 - 8 * q^10 + 8 * q^13 - 4 * q^16 + 4 * q^22 + 16 * q^25 + 8 * q^28 + 32 * q^31 + 12 * q^37 + 4 * q^40 + 12 * q^43 + 4 * q^46 - 8 * q^52 + 4 * q^55 - 8 * q^61 + 4 * q^67 - 24 * q^70 + 20 * q^73 + 8 * q^76 + 4 * q^82 + 16 * q^85 + 4 * q^88 + 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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