LMFDB - Embedded newform 1890.2.m.d.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(323,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, 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("1890.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.m (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.1
Character	$\chi$	$=$	1890.323
Dual form			1890.2.m.d.1457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.490937 + 2.18151i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.490937 + 2.18151i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.19542 - 1.88970i) q^{10} -3.47893i q^{11} +(0.449625 + 0.449625i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.85435 - 1.85435i) q^{17} -3.23958i q^{19} +(-2.18151 + 0.490937i) q^{20} +(-2.45998 + 2.45998i) q^{22} +(5.77199 - 5.77199i) q^{23} +(-4.51796 + 2.14197i) q^{25} -0.635865i q^{26} +(-0.707107 - 0.707107i) q^{28} -4.75829 q^{29} +2.10225 q^{31} +(0.707107 + 0.707107i) q^{32} +2.62245i q^{34} +(-1.88970 - 1.19542i) q^{35} +(-0.0596053 + 0.0596053i) q^{37} +(-2.29073 + 2.29073i) q^{38} +(1.88970 + 1.19542i) q^{40} -6.47162i q^{41} +(4.16669 + 4.16669i) q^{43} +3.47893 q^{44} -8.16282 q^{46} +(-2.10574 - 2.10574i) q^{47} -1.00000i q^{49} +(4.70928 + 1.68008i) q^{50} +(-0.449625 + 0.449625i) q^{52} +(3.49565 - 3.49565i) q^{53} +(7.58933 - 1.70794i) q^{55} +1.00000i q^{56} +(3.36462 + 3.36462i) q^{58} +8.62525 q^{59} +2.95225 q^{61} +(-1.48651 - 1.48651i) q^{62} -1.00000i q^{64} +(-0.760123 + 1.20160i) q^{65} +(-4.49082 + 4.49082i) q^{67} +(1.85435 - 1.85435i) q^{68} +(0.490937 + 2.18151i) q^{70} -13.6863i q^{71} +(6.20495 + 6.20495i) q^{73} +0.0842946 q^{74} +3.23958 q^{76} +(2.45998 + 2.45998i) q^{77} +10.5800i q^{79} +(-0.490937 - 2.18151i) q^{80} +(-4.57612 + 4.57612i) q^{82} +(10.5057 - 10.5057i) q^{83} +(3.13491 - 4.95565i) q^{85} -5.89260i q^{86} +(-2.45998 - 2.45998i) q^{88} -1.28547 q^{89} -0.635865 q^{91} +(5.77199 + 5.77199i) q^{92} +2.97797i q^{94} +(7.06718 - 1.59043i) q^{95} +(8.72213 - 8.72213i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{5}+O(q^{10}) $ 24 * q + 8 * q^5	$ 24 q + 8 q^{5} + 24 q^{14} - 24 q^{16} + 16 q^{17} + 8 q^{22} - 8 q^{25} - 16 q^{29} - 16 q^{31} - 8 q^{35} - 16 q^{37} + 8 q^{38} + 8 q^{40} - 8 q^{43} + 8 q^{44} + 16 q^{46} + 16 q^{47} + 32 q^{50} - 24 q^{53} + 40 q^{55} + 8 q^{58} + 32 q^{59} + 40 q^{62} - 24 q^{65} - 24 q^{67} - 16 q^{68} + 8 q^{70} - 24 q^{73} - 16 q^{74} - 8 q^{77} - 8 q^{80} - 8 q^{82} + 48 q^{83} - 24 q^{85} + 8 q^{88} + 48 q^{89} + 72 q^{95} + 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^5 + 24 * q^14 - 24 * q^16 + 16 * q^17 + 8 * q^22 - 8 * q^25 - 16 * q^29 - 16 * q^31 - 8 * q^35 - 16 * q^37 + 8 * q^38 + 8 * q^40 - 8 * q^43 + 8 * q^44 + 16 * q^46 + 16 * q^47 + 32 * q^50 - 24 * q^53 + 40 * q^55 + 8 * q^58 + 32 * q^59 + 40 * q^62 - 24 * q^65 - 24 * q^67 - 16 * q^68 + 8 * q^70 - 24 * q^73 - 16 * q^74 - 8 * q^77 - 8 * q^80 - 8 * q^82 + 48 * q^83 - 24 * q^85 + 8 * q^88 + 48 * q^89 + 72 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	0.490937	+	2.18151i	0.219554	+	0.975600i
$5$	0.490937	+	2.18151i	0.219554	+	0.975600i
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	1.19542	−	1.88970i	0.378023	−	0.597577i
$11$		−	3.47893i		−	1.04894i	−0.851429	−	0.524469i	$-0.824264\pi$
$11$		−	3.47893i		−	1.04894i	0.851429	−	0.524469i	$-0.175736\pi$
$12$		0			0
$13$	0.449625	+	0.449625i	0.124703	+	0.124703i	0.766704	−	0.642001i	$-0.221895\pi$
$13$	0.449625	+	0.449625i	0.124703	+	0.124703i	−0.642001	+	0.766704i	$0.721895\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.85435	−	1.85435i	−0.449746	−	0.449746i	0.445524	−	0.895270i	$-0.353017\pi$
$17$	−1.85435	−	1.85435i	−0.449746	−	0.449746i	−0.895270	+	0.445524i	$0.853017\pi$
$18$		0			0
$19$		−	3.23958i		−	0.743212i	−0.928391	−	0.371606i	$-0.878807\pi$
$19$		−	3.23958i		−	0.743212i	0.928391	−	0.371606i	$-0.121193\pi$
$20$	−2.18151	+	0.490937i	−0.487800	+	0.109777i
$21$		0			0
$22$	−2.45998	+	2.45998i	−0.524469	+	0.524469i
$23$	5.77199	−	5.77199i	1.20354	−	1.20354i	0.230461	−	0.973082i	$-0.425977\pi$
$23$	5.77199	−	5.77199i	1.20354	−	1.20354i	0.973082	−	0.230461i	$-0.0740233\pi$
$24$		0			0
$25$	−4.51796	+	2.14197i	−0.903593	+	0.428393i
$26$		−	0.635865i		−	0.124703i
$27$		0			0
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	−4.75829			−0.883592			−0.441796	−	0.897115i	$-0.645659\pi$
$29$	−4.75829			−0.883592			−0.441796	+	0.897115i	$0.645659\pi$
$30$		0			0
$31$	2.10225			0.377575			0.188787	−	0.982018i	$-0.439544\pi$
$31$	2.10225			0.377575			0.188787	+	0.982018i	$0.439544\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$			2.62245i			0.449746i
$35$	−1.88970	−	1.19542i	−0.319418	−	0.202062i
$36$		0			0
$37$	−0.0596053	+	0.0596053i	−0.00979905	+	0.00979905i	−0.711989	−	0.702190i	$-0.752206\pi$
$37$	−0.0596053	+	0.0596053i	−0.00979905	+	0.00979905i	0.702190	+	0.711989i	$0.252206\pi$
$38$	−2.29073	+	2.29073i	−0.371606	+	0.371606i
$39$		0			0
$40$	1.88970	+	1.19542i	0.298788	+	0.189012i
$41$		−	6.47162i		−	1.01070i	−0.862915	−	0.505348i	$-0.831364\pi$
$41$		−	6.47162i		−	1.01070i	0.862915	−	0.505348i	$-0.168636\pi$
$42$		0			0
$43$	4.16669	+	4.16669i	0.635415	+	0.635415i	0.949421	−	0.314006i	$-0.101671\pi$
$43$	4.16669	+	4.16669i	0.635415	+	0.635415i	−0.314006	+	0.949421i	$0.601671\pi$
$44$	3.47893			0.524469
$45$		0			0
$46$	−8.16282			−1.20354
$47$	−2.10574	−	2.10574i	−0.307154	−	0.307154i	0.536651	−	0.843805i	$-0.319689\pi$
$47$	−2.10574	−	2.10574i	−0.307154	−	0.307154i	−0.843805	+	0.536651i	$0.819689\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	4.70928	+	1.68008i	0.665993	+	0.237600i
$51$		0			0
$52$	−0.449625	+	0.449625i	−0.0623517	+	0.0623517i
$53$	3.49565	−	3.49565i	0.480164	−	0.480164i	−0.425020	−	0.905184i	$-0.639733\pi$
$53$	3.49565	−	3.49565i	0.480164	−	0.480164i	0.905184	+	0.425020i	$0.139733\pi$
$54$		0			0
$55$	7.58933	−	1.70794i	1.02334	−	0.230298i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	3.36462	+	3.36462i	0.441796	+	0.441796i
$59$	8.62525			1.12291			0.561456	−	0.827506i	$-0.310241\pi$
$59$	8.62525			1.12291			0.561456	+	0.827506i	$0.310241\pi$
$60$		0			0
$61$	2.95225			0.377997			0.188999	−	0.981977i	$-0.439476\pi$
$61$	2.95225			0.377997			0.188999	+	0.981977i	$0.439476\pi$
$62$	−1.48651	−	1.48651i	−0.188787	−	0.188787i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.760123	+	1.20160i	−0.0942817	+	0.149040i
$66$		0			0
$67$	−4.49082	+	4.49082i	−0.548641	+	0.548641i	−0.926048	−	0.377406i	$-0.876816\pi$
$67$	−4.49082	+	4.49082i	−0.548641	+	0.548641i	0.377406	+	0.926048i	$0.376816\pi$
$68$	1.85435	−	1.85435i	0.224873	−	0.224873i
$69$		0			0
$70$	0.490937	+	2.18151i	0.0586781	+	0.260740i
$71$		−	13.6863i		−	1.62426i	−0.583473	−	0.812132i	$-0.698307\pi$
$71$		−	13.6863i		−	1.62426i	0.583473	−	0.812132i	$-0.301693\pi$
$72$		0			0
$73$	6.20495	+	6.20495i	0.726234	+	0.726234i	0.969867	−	0.243633i	$-0.0783393\pi$
$73$	6.20495	+	6.20495i	0.726234	+	0.726234i	−0.243633	+	0.969867i	$0.578339\pi$
$74$	0.0842946			0.00979905
$75$		0			0
$76$	3.23958			0.371606
$77$	2.45998	+	2.45998i	0.280341	+	0.280341i
$78$		0			0
$79$			10.5800i			1.19034i	0.803599	+	0.595171i	$0.202916\pi$
$79$			10.5800i			1.19034i	−0.803599	+	0.595171i	$0.797084\pi$
$80$	−0.490937	−	2.18151i	−0.0548884	−	0.243900i
$81$		0			0
$82$	−4.57612	+	4.57612i	−0.505348	+	0.505348i
$83$	10.5057	−	10.5057i	1.15315	−	1.15315i	0.167229	−	0.985918i	$-0.446518\pi$
$83$	10.5057	−	10.5057i	1.15315	−	1.15315i	0.985918	−	0.167229i	$-0.0534818\pi$
$84$		0			0
$85$	3.13491	−	4.95565i	0.340029	−	0.537516i
$86$		−	5.89260i		−	0.635415i
$87$		0			0
$88$	−2.45998	−	2.45998i	−0.262235	−	0.262235i
$89$	−1.28547			−0.136260			−0.0681299	−	0.997676i	$-0.521703\pi$
$89$	−1.28547			−0.136260			−0.0681299	+	0.997676i	$0.521703\pi$
$90$		0			0
$91$	−0.635865			−0.0666568
$92$	5.77199	+	5.77199i	0.601771	+	0.601771i
$93$		0			0
$94$			2.97797i			0.307154i
$95$	7.06718	−	1.59043i	0.725078	−	0.163175i
$96$		0			0
$97$	8.72213	−	8.72213i	0.885598	−	0.885598i	−0.108499	−	0.994097i	$-0.534604\pi$
$97$	8.72213	−	8.72213i	0.885598	−	0.885598i	0.994097	+	0.108499i	$0.0346043\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−2.14197	−	4.51796i	−0.214197	−	0.451796i
$101$		−	9.77064i		−	0.972215i	−0.873899	−	0.486108i	$-0.838416\pi$
$101$		−	9.77064i		−	0.972215i	0.873899	−	0.486108i	$-0.161584\pi$
$102$		0			0
$103$	9.11889	+	9.11889i	0.898511	+	0.898511i	0.995305	−	0.0967933i	$-0.0308586\pi$
$103$	9.11889	+	9.11889i	0.898511	+	0.898511i	−0.0967933	+	0.995305i	$0.530859\pi$
$104$	0.635865			0.0623517
$105$		0			0
$106$	−4.94359			−0.480164
$107$	11.2524	+	11.2524i	1.08781	+	1.08781i	0.995754	+	0.0920569i	$0.0293442\pi$
$107$	11.2524	+	11.2524i	1.08781	+	1.08781i	0.0920569	+	0.995754i	$0.470656\pi$
$108$		0			0
$109$		−	13.3922i		−	1.28274i	−0.767232	−	0.641370i	$-0.778366\pi$
$109$		−	13.3922i		−	1.28274i	0.767232	−	0.641370i	$-0.221634\pi$
$110$	−6.57416	−	4.15877i	−0.626821	−	0.396523i
$111$		0			0
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−5.87982	+	5.87982i	−0.553127	+	0.553127i	−0.927342	−	0.374215i	$-0.877912\pi$
$113$	−5.87982	+	5.87982i	−0.553127	+	0.553127i	0.374215	+	0.927342i	$0.377912\pi$
$114$		0			0
$115$	15.4253	+	9.75796i	1.43842	+	0.909934i
$116$		−	4.75829i		−	0.441796i
$117$		0			0
$118$	−6.09898	−	6.09898i	−0.561456	−	0.561456i
$119$	2.62245			0.240399
$120$		0			0
$121$	−1.10299			−0.100271
$122$	−2.08756	−	2.08756i	−0.188999	−	0.188999i
$123$		0			0
$124$			2.10225i			0.188787i
$125$	−6.89075	−	8.80441i	−0.616327	−	0.787490i
$126$		0			0
$127$	5.98264	−	5.98264i	0.530874	−	0.530874i	−0.389959	−	0.920832i	$-0.627511\pi$
$127$	5.98264	−	5.98264i	0.530874	−	0.530874i	0.920832	+	0.389959i	$0.127511\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1.38715	−	0.312170i	0.121661	−	0.0273791i
$131$			19.7896i			1.72903i	0.502610	+	0.864513i	$0.332373\pi$
$131$			19.7896i			1.72903i	−0.502610	+	0.864513i	$0.667627\pi$
$132$		0			0
$133$	2.29073	+	2.29073i	0.198632	+	0.198632i
$134$	6.35098			0.548641
$135$		0			0
$136$	−2.62245			−0.224873
$137$	−5.68489	−	5.68489i	−0.485693	−	0.485693i	0.421251	−	0.906944i	$-0.361591\pi$
$137$	−5.68489	−	5.68489i	−0.485693	−	0.485693i	−0.906944	+	0.421251i	$0.861591\pi$
$138$		0			0
$139$		−	7.27284i		−	0.616875i	−0.951245	−	0.308437i	$-0.900194\pi$
$139$		−	7.27284i		−	0.616875i	0.951245	−	0.308437i	$-0.0998060\pi$
$140$	1.19542	−	1.88970i	0.101031	−	0.159709i
$141$		0			0
$142$	−9.67767	+	9.67767i	−0.812132	+	0.812132i
$143$	1.56421	−	1.56421i	0.130806	−	0.130806i
$144$		0			0
$145$	−2.33602	−	10.3803i	−0.193996	−	0.862033i
$146$		−	8.77512i		−	0.726234i
$147$		0			0
$148$	−0.0596053	−	0.0596053i	−0.00489952	−	0.00489952i
$149$	2.82065			0.231077			0.115538	−	0.993303i	$-0.463141\pi$
$149$	2.82065			0.231077			0.115538	+	0.993303i	$0.463141\pi$
$150$		0			0
$151$	−17.6663			−1.43767			−0.718833	−	0.695183i	$-0.755324\pi$
$151$	−17.6663			−1.43767			−0.718833	+	0.695183i	$0.755324\pi$
$152$	−2.29073	−	2.29073i	−0.185803	−	0.185803i
$153$		0			0
$154$		−	3.47893i		−	0.280341i
$155$	1.03207	+	4.58607i	0.0828979	+	0.368362i
$156$		0			0
$157$	3.31278	−	3.31278i	0.264389	−	0.264389i	−0.562445	−	0.826834i	$-0.690139\pi$
$157$	3.31278	−	3.31278i	0.264389	−	0.264389i	0.826834	+	0.562445i	$0.190139\pi$
$158$	7.48118	−	7.48118i	0.595171	−	0.595171i
$159$		0			0
$160$	−1.19542	+	1.88970i	−0.0945059	+	0.149394i
$161$			8.16282i			0.643320i
$162$		0			0
$163$	−4.34747	−	4.34747i	−0.340520	−	0.340520i	0.516043	−	0.856563i	$-0.327405\pi$
$163$	−4.34747	−	4.34747i	−0.340520	−	0.340520i	−0.856563	+	0.516043i	$0.827405\pi$
$164$	6.47162			0.505348
$165$		0			0
$166$	−14.8573			−1.15315
$167$	−3.40504	−	3.40504i	−0.263490	−	0.263490i	0.562980	−	0.826470i	$-0.309655\pi$
$167$	−3.40504	−	3.40504i	−0.263490	−	0.263490i	−0.826470	+	0.562980i	$0.809655\pi$
$168$		0			0
$169$		−	12.5957i		−	0.968898i
$170$	−5.72089	+	1.28745i	−0.438772	+	0.0987433i
$171$		0			0
$172$	−4.16669	+	4.16669i	−0.317707	+	0.317707i
$173$	14.0825	−	14.0825i	1.07067	−	1.07067i	0.0733668	−	0.997305i	$-0.476626\pi$
$173$	14.0825	−	14.0825i	1.07067	−	1.07067i	0.997305	−	0.0733668i	$-0.0233744\pi$
$174$		0			0
$175$	1.68008	−	4.70928i	0.127002	−	0.355988i
$176$			3.47893i			0.262235i
$177$		0			0
$178$	0.908966	+	0.908966i	0.0681299	+	0.0681299i
$179$	−22.4158			−1.67544			−0.837719	−	0.546102i	$-0.816111\pi$
$179$	−22.4158			−1.67544			−0.837719	+	0.546102i	$0.816111\pi$
$180$		0			0
$181$	−16.4453			−1.22237			−0.611183	−	0.791489i	$-0.709306\pi$
$181$	−16.4453			−1.22237			−0.611183	+	0.791489i	$0.709306\pi$
$182$	0.449625	+	0.449625i	0.0333284	+	0.0333284i
$183$		0			0
$184$		−	8.16282i		−	0.601771i
$185$	−0.159292	−	0.100767i	−0.0117114	−	0.00740854i
$186$		0			0
$187$	−6.45116	+	6.45116i	−0.471756	+	0.471756i
$188$	2.10574	−	2.10574i	0.153577	−	0.153577i
$189$		0			0
$190$	−6.12186	−	3.87265i	−0.444126	−	0.280951i
$191$			6.41085i			0.463873i	0.972731	+	0.231936i	$0.0745061\pi$
$191$			6.41085i			0.463873i	−0.972731	+	0.231936i	$0.925494\pi$
$192$		0			0
$193$	2.14415	+	2.14415i	0.154339	+	0.154339i	0.780053	−	0.625714i	$-0.215192\pi$
$193$	2.14415	+	2.14415i	0.154339	+	0.154339i	−0.625714	+	0.780053i	$0.715192\pi$
$194$	−12.3350			−0.885598
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.91076	+	6.91076i	0.492371	+	0.492371i	0.909053	−	0.416681i	$-0.136807\pi$
$197$	6.91076	+	6.91076i	0.492371	+	0.492371i	−0.416681	+	0.909053i	$0.636807\pi$
$198$		0			0
$199$		−	18.4417i		−	1.30730i	−0.756799	−	0.653648i	$-0.773238\pi$
$199$		−	18.4417i		−	1.30730i	0.756799	−	0.653648i	$-0.226762\pi$
$200$	−1.68008	+	4.70928i	−0.118800	+	0.332996i
$201$		0			0
$202$	−6.90889	+	6.90889i	−0.486108	+	0.486108i
$203$	3.36462	−	3.36462i	0.236150	−	0.236150i
$204$		0			0
$205$	14.1179	−	3.17715i	0.986036	−	0.221902i
$206$		−	12.8961i		−	0.898511i
$207$		0			0
$208$	−0.449625	−	0.449625i	−0.0311759	−	0.0311759i
$209$	−11.2703			−0.779583
$210$		0			0
$211$	−10.9041			−0.750669			−0.375334	−	0.926889i	$-0.622472\pi$
$211$	−10.9041			−0.750669			−0.375334	+	0.926889i	$0.622472\pi$
$212$	3.49565	+	3.49565i	0.240082	+	0.240082i
$213$		0			0
$214$		−	15.9133i		−	1.08781i
$215$	−7.04410	+	11.1353i	−0.480404	+	0.759419i
$216$		0			0
$217$	−1.48651	+	1.48651i	−0.100911	+	0.100911i
$218$	−9.46972	+	9.46972i	−0.641370	+	0.641370i
$219$		0			0
$220$	1.70794	+	7.58933i	0.115149	+	0.511672i
$221$		−	1.66752i		−	0.112170i
$222$		0			0
$223$	3.84275	+	3.84275i	0.257330	+	0.257330i	0.823967	−	0.566638i	$-0.191756\pi$
$223$	3.84275	+	3.84275i	0.257330	+	0.257330i	−0.566638	+	0.823967i	$0.691756\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	8.31532			0.553127
$227$	4.28065	+	4.28065i	0.284117	+	0.284117i	0.834748	−	0.550632i	$-0.185613\pi$
$227$	4.28065	+	4.28065i	0.284117	+	0.284117i	−0.550632	+	0.834748i	$0.685613\pi$
$228$		0			0
$229$		−	19.3523i		−	1.27884i	−0.768859	−	0.639418i	$-0.779175\pi$
$229$		−	19.3523i		−	1.27884i	0.768859	−	0.639418i	$-0.220825\pi$
$230$	−4.00743	−	17.8073i	−0.264242	−	1.17418i
$231$		0			0
$232$	−3.36462	+	3.36462i	−0.220898	+	0.220898i
$233$	−2.21851	+	2.21851i	−0.145339	+	0.145339i	−0.776032	−	0.630693i	$-0.782771\pi$
$233$	−2.21851	+	2.21851i	−0.145339	+	0.145339i	0.630693	+	0.776032i	$0.282771\pi$
$234$		0			0
$235$	3.55991	−	5.62748i	0.232223	−	0.367096i
$236$			8.62525i			0.561456i
$237$		0			0
$238$	−1.85435	−	1.85435i	−0.120200	−	0.120200i
$239$	−8.35839			−0.540659			−0.270330	−	0.962768i	$-0.587133\pi$
$239$	−8.35839			−0.540659			−0.270330	+	0.962768i	$0.587133\pi$
$240$		0			0
$241$	22.7172			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$241$	22.7172			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$242$	0.779929	+	0.779929i	0.0501357	+	0.0501357i
$243$		0			0
$244$			2.95225i			0.188999i
$245$	2.18151	−	0.490937i	0.139371	−	0.0313648i
$246$		0			0
$247$	1.45660	−	1.45660i	0.0926811	−	0.0926811i
$248$	1.48651	−	1.48651i	0.0943937	−	0.0943937i
$249$		0			0
$250$	−1.35316	+	11.0982i	−0.0855813	+	0.701909i
$251$		−	8.86426i		−	0.559507i	−0.960072	−	0.279753i	$-0.909747\pi$
$251$		−	8.86426i		−	0.559507i	0.960072	−	0.279753i	$-0.0902527\pi$
$252$		0			0
$253$	−20.0804	−	20.0804i	−1.26244	−	1.26244i
$254$	−8.46074			−0.530874
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.23740	+	5.23740i	0.326700	+	0.326700i	0.851330	−	0.524630i	$-0.175796\pi$
$257$	5.23740	+	5.23740i	0.326700	+	0.326700i	−0.524630	+	0.851330i	$0.675796\pi$
$258$		0			0
$259$		−	0.0842946i		−	0.00523781i
$260$	−1.20160	−	0.760123i	−0.0745199	−	0.0471408i
$261$		0			0
$262$	13.9934	−	13.9934i	0.864513	−	0.864513i
$263$	18.9772	−	18.9772i	1.17018	−	1.17018i	0.188016	−	0.982166i	$-0.439794\pi$
$263$	18.9772	−	18.9772i	1.17018	−	1.17018i	0.982166	−	0.188016i	$-0.0602057\pi$
$264$		0			0
$265$	9.34192	+	5.90964i	0.573870	+	0.363026i
$266$		−	3.23958i		−	0.198632i
$267$		0			0
$268$	−4.49082	−	4.49082i	−0.274321	−	0.274321i
$269$	−13.3283			−0.812639			−0.406320	−	0.913731i	$-0.633188\pi$
$269$	−13.3283			−0.812639			−0.406320	+	0.913731i	$0.633188\pi$
$270$		0			0
$271$	−3.35089			−0.203552			−0.101776	−	0.994807i	$-0.532452\pi$
$271$	−3.35089			−0.203552			−0.101776	+	0.994807i	$0.532452\pi$
$272$	1.85435	+	1.85435i	0.112436	+	0.112436i
$273$		0			0
$274$			8.03965i			0.485693i
$275$	7.45176	+	15.7177i	0.449358	+	0.947813i
$276$		0			0
$277$	−9.13047	+	9.13047i	−0.548597	+	0.548597i	−0.926035	−	0.377438i	$-0.876805\pi$
$277$	−9.13047	+	9.13047i	−0.548597	+	0.548597i	0.377438	+	0.926035i	$0.376805\pi$
$278$	−5.14268	+	5.14268i	−0.308437	+	0.308437i
$279$		0			0
$280$	−2.18151	+	0.490937i	−0.130370	+	0.0293391i
$281$			7.47274i			0.445786i	0.974843	+	0.222893i	$0.0715501\pi$
$281$			7.47274i			0.445786i	−0.974843	+	0.222893i	$0.928450\pi$
$282$		0			0
$283$	19.4066	+	19.4066i	1.15360	+	1.15360i	0.985824	+	0.167780i	$0.0536600\pi$
$283$	19.4066	+	19.4066i	1.15360	+	1.15360i	0.167780	+	0.985824i	$0.446340\pi$
$284$	13.6863			0.812132
$285$		0			0
$286$	−2.21213			−0.130806
$287$	4.57612	+	4.57612i	0.270120	+	0.270120i
$288$		0			0
$289$		−	10.1228i		−	0.595457i
$290$	−5.68813	+	8.99176i	−0.334019	+	0.528014i
$291$		0			0
$292$	−6.20495	+	6.20495i	−0.363117	+	0.363117i
$293$	−15.3607	+	15.3607i	−0.897382	+	0.897382i	−0.995204	−	0.0978223i	$-0.968812\pi$
$293$	−15.3607	+	15.3607i	−0.897382	+	0.897382i	0.0978223	+	0.995204i	$0.468812\pi$
$294$		0			0
$295$	4.23445	+	18.8161i	0.246539	+	1.09551i
$296$			0.0842946i			0.00489952i
$297$		0			0
$298$	−1.99450	−	1.99450i	−0.115538	−	0.115538i
$299$	5.19045			0.300172
$300$		0			0
$301$	−5.89260			−0.339644
$302$	12.4920	+	12.4920i	0.718833	+	0.718833i
$303$		0			0
$304$			3.23958i			0.185803i
$305$	1.44937	+	6.44037i	0.0829907	+	0.368774i
$306$		0			0
$307$	1.05294	−	1.05294i	0.0600942	−	0.0600942i	−0.676421	−	0.736515i	$-0.736470\pi$
$307$	1.05294	−	1.05294i	0.0600942	−	0.0600942i	0.736515	+	0.676421i	$0.236470\pi$
$308$	−2.45998	+	2.45998i	−0.140170	+	0.140170i
$309$		0			0
$310$	2.51306	−	3.97263i	0.142732	−	0.225630i
$311$		−	15.9629i		−	0.905175i	−0.891720	−	0.452587i	$-0.850501\pi$
$311$		−	15.9629i		−	0.905175i	0.891720	−	0.452587i	$-0.149499\pi$
$312$		0			0
$313$	−3.08942	−	3.08942i	−0.174624	−	0.174624i	0.614383	−	0.789008i	$-0.289405\pi$
$313$	−3.08942	−	3.08942i	−0.174624	−	0.174624i	−0.789008	+	0.614383i	$0.789405\pi$
$314$	−4.68498			−0.264389
$315$		0			0
$316$	−10.5800			−0.595171
$317$	5.92004	+	5.92004i	0.332502	+	0.332502i	0.853536	−	0.521034i	$-0.174453\pi$
$317$	5.92004	+	5.92004i	0.332502	+	0.332502i	−0.521034	+	0.853536i	$0.674453\pi$
$318$		0			0
$319$			16.5538i			0.926834i
$320$	2.18151	−	0.490937i	0.121950	−	0.0274442i
$321$		0			0
$322$	5.77199	−	5.77199i	0.321660	−	0.321660i
$323$	−6.00732	+	6.00732i	−0.334256	+	0.334256i
$324$		0			0
$325$	−2.99447	−	1.06831i	−0.166103	−	0.0592590i
$326$			6.14825i			0.340520i
$327$		0			0
$328$	−4.57612	−	4.57612i	−0.252674	−	0.252674i
$329$	2.97797			0.164181
$330$		0			0
$331$	27.6578			1.52021			0.760105	−	0.649800i	$-0.225147\pi$
$331$	27.6578			1.52021			0.760105	+	0.649800i	$0.225147\pi$
$332$	10.5057	+	10.5057i	0.576573	+	0.576573i
$333$		0			0
$334$			4.81546i			0.263490i
$335$	−12.0015	−	7.59206i	−0.655711	−	0.414799i
$336$		0			0
$337$	−18.2760	+	18.2760i	−0.995558	+	0.995558i	−0.999990	−	0.00443230i	$-0.998589\pi$
$337$	−18.2760	+	18.2760i	−0.995558	+	0.995558i	0.00443230	+	0.999990i	$0.498589\pi$
$338$	−8.90649	+	8.90649i	−0.484449	+	0.484449i
$339$		0			0
$340$	4.95565	+	3.13491i	0.268758	+	0.170014i
$341$		−	7.31358i		−	0.396053i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	5.89260			0.317707
$345$		0			0
$346$	−19.9156			−1.07067
$347$	−15.9006	−	15.9006i	−0.853588	−	0.853588i	0.136985	−	0.990573i	$-0.456259\pi$
$347$	−15.9006	−	15.9006i	−0.853588	−	0.853588i	−0.990573	+	0.136985i	$0.956259\pi$
$348$		0			0
$349$		−	0.558074i		−	0.0298730i	−0.999888	−	0.0149365i	$-0.995245\pi$
$349$		−	0.558074i		−	0.0298730i	0.999888	−	0.0149365i	$-0.00475462\pi$
$350$	−4.51796	+	2.14197i	−0.241495	+	0.114493i
$351$		0			0
$352$	2.45998	−	2.45998i	0.131117	−	0.131117i
$353$	1.02703	−	1.02703i	0.0546631	−	0.0546631i	−0.679247	−	0.733910i	$-0.737693\pi$
$353$	1.02703	−	1.02703i	0.0546631	−	0.0546631i	0.733910	+	0.679247i	$0.237693\pi$
$354$		0			0
$355$	29.8568	−	6.71910i	1.58463	−	0.356613i
$356$		−	1.28547i		−	0.0681299i
$357$		0			0
$358$	15.8504	+	15.8504i	0.837719	+	0.837719i
$359$	−3.92909			−0.207370			−0.103685	−	0.994610i	$-0.533063\pi$
$359$	−3.92909			−0.207370			−0.103685	+	0.994610i	$0.533063\pi$
$360$		0			0
$361$	8.50509			0.447636
$362$	11.6286	+	11.6286i	0.611183	+	0.611183i
$363$		0			0
$364$		−	0.635865i		−	0.0333284i
$365$	−10.4899	+	16.5824i	−0.549067	+	0.867962i
$366$		0			0
$367$	−6.92801	+	6.92801i	−0.361639	+	0.361639i	−0.864416	−	0.502777i	$-0.832312\pi$
$367$	−6.92801	+	6.92801i	−0.361639	+	0.361639i	0.502777	+	0.864416i	$0.332312\pi$
$368$	−5.77199	+	5.77199i	−0.300886	+	0.300886i
$369$		0			0
$370$	0.0413833	+	0.183889i	0.00215141	+	0.00955995i
$371$			4.94359i			0.256658i
$372$		0			0
$373$	5.90666	+	5.90666i	0.305835	+	0.305835i	0.843292	−	0.537456i	$-0.180615\pi$
$373$	5.90666	+	5.90666i	0.305835	+	0.305835i	−0.537456	+	0.843292i	$0.680615\pi$
$374$	9.12332			0.471756
$375$		0			0
$376$	−2.97797			−0.153577
$377$	−2.13944	−	2.13944i	−0.110187	−	0.110187i
$378$		0			0
$379$		−	25.0764i		−	1.28809i	−0.764989	−	0.644044i	$-0.777255\pi$
$379$		−	25.0764i		−	1.28809i	0.764989	−	0.644044i	$-0.222745\pi$
$380$	1.59043	+	7.06718i	0.0815874	+	0.362539i
$381$		0			0
$382$	4.53315	−	4.53315i	0.231936	−	0.231936i
$383$	−23.5479	+	23.5479i	−1.20324	+	1.20324i	−0.230069	+	0.973174i	$0.573895\pi$
$383$	−23.5479	+	23.5479i	−1.20324	+	1.20324i	−0.973174	+	0.230069i	$0.926105\pi$
$384$		0			0
$385$	−4.15877	+	6.57416i	−0.211951	+	0.335050i
$386$		−	3.03228i		−	0.154339i
$387$		0			0
$388$	8.72213	+	8.72213i	0.442799	+	0.442799i
$389$	−8.13778			−0.412602			−0.206301	−	0.978489i	$-0.566143\pi$
$389$	−8.13778			−0.412602			−0.206301	+	0.978489i	$0.566143\pi$
$390$		0			0
$391$	−21.4066			−1.08258
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	9.77329i		−	0.492371i
$395$	−23.0803	+	5.19410i	−1.16130	+	0.261344i
$396$		0			0
$397$	12.2370	−	12.2370i	0.614156	−	0.614156i	−0.329870	−	0.944026i	$-0.607005\pi$
$397$	12.2370	−	12.2370i	0.614156	−	0.614156i	0.944026	+	0.329870i	$0.107005\pi$
$398$	−13.0402	+	13.0402i	−0.653648	+	0.653648i
$399$		0			0
$400$	4.51796	−	2.14197i	0.225898	−	0.107098i
$401$			35.8850i			1.79201i	0.444044	+	0.896005i	$0.353544\pi$
$401$			35.8850i			1.79201i	−0.444044	+	0.896005i	$0.646456\pi$
$402$		0			0
$403$	0.945222	+	0.945222i	0.0470849	+	0.0470849i
$404$	9.77064			0.486108
$405$		0			0
$406$	−4.75829			−0.236150
$407$	0.207363	+	0.207363i	0.0102786	+	0.0102786i
$408$		0			0
$409$		−	2.15655i		−	0.106635i	−0.998578	−	0.0533174i	$-0.983021\pi$
$409$		−	2.15655i		−	0.106635i	0.998578	−	0.0533174i	$-0.0169795\pi$
$410$	−12.2294	−	7.73627i	−0.603969	−	0.382067i
$411$		0			0
$412$	−9.11889	+	9.11889i	−0.449256	+	0.449256i
$413$	−6.09898	+	6.09898i	−0.300111	+	0.300111i
$414$		0			0
$415$	28.0758	+	17.7606i	1.37819	+	0.871833i
$416$			0.635865i			0.0311759i
$417$		0			0
$418$	7.96931	+	7.96931i	0.389792	+	0.389792i
$419$	−15.0242			−0.733982			−0.366991	−	0.930225i	$-0.619612\pi$
$419$	−15.0242			−0.733982			−0.366991	+	0.930225i	$0.619612\pi$
$420$		0			0
$421$	10.2682			0.500442			0.250221	−	0.968189i	$-0.419497\pi$
$421$	10.2682			0.500442			0.250221	+	0.968189i	$0.419497\pi$
$422$	7.71036	+	7.71036i	0.375334	+	0.375334i
$423$		0			0
$424$		−	4.94359i		−	0.240082i
$425$	12.3498	+	4.40593i	0.599055	+	0.213719i
$426$		0			0
$427$	−2.08756	+	2.08756i	−0.101024	+	0.101024i
$428$	−11.2524	+	11.2524i	−0.543905	+	0.543905i
$429$		0			0
$430$	12.8548	−	2.89289i	0.619911	−	0.139508i
$431$		−	1.57507i		−	0.0758686i	−0.999280	−	0.0379343i	$-0.987922\pi$
$431$		−	1.57507i		−	0.0758686i	0.999280	−	0.0379343i	$-0.0120778\pi$
$432$		0			0
$433$	−15.6100	−	15.6100i	−0.750170	−	0.750170i	0.224340	−	0.974511i	$-0.427977\pi$
$433$	−15.6100	−	15.6100i	−0.750170	−	0.750170i	−0.974511	+	0.224340i	$0.927977\pi$
$434$	2.10225			0.100911
$435$		0			0
$436$	13.3922			0.641370
$437$	−18.6988	−	18.6988i	−0.894487	−	0.894487i
$438$		0			0
$439$		−	3.34939i		−	0.159858i	−0.996801	−	0.0799288i	$-0.974531\pi$
$439$		−	3.34939i		−	0.159858i	0.996801	−	0.0799288i	$-0.0254693\pi$
$440$	4.15877	−	6.57416i	0.198262	−	0.313411i
$441$		0			0
$442$	−1.17912	+	1.17912i	−0.0560849	+	0.0560849i
$443$	−10.8536	+	10.8536i	−0.515668	+	0.515668i	−0.916258	−	0.400590i	$-0.868805\pi$
$443$	−10.8536	+	10.8536i	−0.515668	+	0.515668i	0.400590	+	0.916258i	$0.368805\pi$
$444$		0			0
$445$	−0.631085	−	2.80427i	−0.0299163	−	0.132935i
$446$		−	5.43447i		−	0.257330i
$447$		0			0
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	36.2781			1.71207			0.856035	−	0.516918i	$-0.172921\pi$
$449$	36.2781			1.71207			0.856035	+	0.516918i	$0.172921\pi$
$450$		0			0
$451$	−22.5143			−1.06016
$452$	−5.87982	−	5.87982i	−0.276563	−	0.276563i
$453$		0			0
$454$		−	6.05375i		−	0.284117i
$455$	−0.312170	−	1.38715i	−0.0146347	−	0.0650304i
$456$		0			0
$457$	−24.1076	+	24.1076i	−1.12771	+	1.12771i	−0.137159	+	0.990549i	$0.543797\pi$
$457$	−24.1076	+	24.1076i	−1.12771	+	1.12771i	−0.990549	+	0.137159i	$0.956203\pi$
$458$	−13.6842	+	13.6842i	−0.639418	+	0.639418i
$459$		0			0
$460$	−9.75796	+	15.4253i	−0.454967	+	0.719209i
$461$		−	29.7770i		−	1.38686i	−0.720526	−	0.693428i	$-0.756100\pi$
$461$		−	29.7770i		−	1.38686i	0.720526	−	0.693428i	$-0.243900\pi$
$462$		0			0
$463$	−0.240054	−	0.240054i	−0.0111563	−	0.0111563i	0.701507	−	0.712663i	$-0.252511\pi$
$463$	−0.240054	−	0.240054i	−0.0111563	−	0.0111563i	−0.712663	+	0.701507i	$0.752511\pi$
$464$	4.75829			0.220898
$465$		0			0
$466$	3.13744			0.145339
$467$	20.6969	+	20.6969i	0.957740	+	0.957740i	0.999143	−	0.0414021i	$-0.0131825\pi$
$467$	20.6969	+	20.6969i	0.957740	+	0.957740i	−0.0414021	+	0.999143i	$0.513182\pi$
$468$		0			0
$469$		−	6.35098i		−	0.293261i
$470$	−6.49647	+	1.46199i	−0.299660	+	0.0674368i
$471$		0			0
$472$	6.09898	−	6.09898i	0.280728	−	0.280728i
$473$	14.4957	−	14.4957i	0.666511	−	0.666511i
$474$		0			0
$475$	6.93908	+	14.6363i	0.318387	+	0.671560i
$476$			2.62245i			0.120200i
$477$		0			0
$478$	5.91027	+	5.91027i	0.270330	+	0.270330i
$479$	6.32950			0.289202			0.144601	−	0.989490i	$-0.453810\pi$
$479$	6.32950			0.289202			0.144601	+	0.989490i	$0.453810\pi$
$480$		0			0
$481$	−0.0536000			−0.00244395
$482$	−16.0635	−	16.0635i	−0.731673	−	0.731673i
$483$		0			0
$484$		−	1.10299i		−	0.0501357i
$485$	23.3094	+	14.7454i	1.05843	+	0.669554i
$486$		0			0
$487$	−13.7901	+	13.7901i	−0.624888	+	0.624888i	−0.946777	−	0.321889i	$-0.895682\pi$
$487$	−13.7901	+	13.7901i	−0.624888	+	0.624888i	0.321889	+	0.946777i	$0.395682\pi$
$488$	2.08756	−	2.08756i	0.0944993	−	0.0944993i
$489$		0			0
$490$	−1.88970	−	1.19542i	−0.0853681	−	0.0540034i
$491$			31.6281i			1.42736i	0.700474	+	0.713678i	$0.252972\pi$
$491$			31.6281i			1.42736i	−0.700474	+	0.713678i	$0.747028\pi$
$492$		0			0
$493$	8.82353	+	8.82353i	0.397392	+	0.397392i
$494$	−2.05994			−0.0926811
$495$		0			0
$496$	−2.10225			−0.0943937
$497$	9.67767	+	9.67767i	0.434103	+	0.434103i
$498$		0			0
$499$			35.9926i			1.61125i	0.592425	+	0.805625i	$0.298171\pi$
$499$			35.9926i			1.61125i	−0.592425	+	0.805625i	$0.701829\pi$
$500$	8.80441	−	6.89075i	0.393745	−	0.308164i
$501$		0			0
$502$	−6.26798	+	6.26798i	−0.279753	+	0.279753i
$503$	31.2985	−	31.2985i	1.39553	−	1.39553i	0.583209	−	0.812322i	$-0.301797\pi$
$503$	31.2985	−	31.2985i	1.39553	−	1.39553i	0.812322	−	0.583209i	$-0.198203\pi$
$504$		0			0
$505$	21.3147	−	4.79677i	0.948494	−	0.213453i
$506$			28.3979i			1.26244i
$507$		0			0
$508$	5.98264	+	5.98264i	0.265437	+	0.265437i
$509$	−8.99647			−0.398761			−0.199381	−	0.979922i	$-0.563893\pi$
$509$	−8.99647			−0.398761			−0.199381	+	0.979922i	$0.563893\pi$
$510$		0			0
$511$	−8.77512			−0.388188
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	7.40680i		−	0.326700i
$515$	−15.4161	+	24.3697i	−0.679317	+	1.07386i
$516$		0			0
$517$	−7.32574	+	7.32574i	−0.322186	+	0.322186i
$518$	−0.0596053	+	0.0596053i	−0.00261890	+	0.00261890i
$519$		0			0
$520$	0.312170	+	1.38715i	0.0136895	+	0.0608304i
$521$			35.1835i			1.54142i	0.637188	+	0.770708i	$0.280097\pi$
$521$			35.1835i			1.54142i	−0.637188	+	0.770708i	$0.719903\pi$
$522$		0			0
$523$	22.2368	+	22.2368i	0.972349	+	0.972349i	0.999628	−	0.0272784i	$-0.00868407\pi$
$523$	22.2368	+	22.2368i	0.972349	+	0.972349i	−0.0272784	+	0.999628i	$0.508684\pi$
$524$	−19.7896			−0.864513
$525$		0			0
$526$	−26.8378			−1.17018
$527$	−3.89830	−	3.89830i	−0.169813	−	0.169813i
$528$		0			0
$529$		−	43.6316i		−	1.89703i
$530$	−2.42699	−	10.7845i	−0.105422	−	0.468448i
$531$		0			0
$532$	−2.29073	+	2.29073i	−0.0993158	+	0.0993158i
$533$	2.90980	−	2.90980i	0.126037	−	0.126037i
$534$		0			0
$535$	−19.0230	+	30.0714i	−0.822436	+	1.30010i
$536$			6.35098i			0.274321i
$537$		0			0
$538$	9.42451	+	9.42451i	0.406320	+	0.406320i
$539$	−3.47893			−0.149848
$540$		0			0
$541$	−44.5317			−1.91457			−0.957284	−	0.289150i	$-0.906627\pi$
$541$	−44.5317			−1.91457			−0.957284	+	0.289150i	$0.906627\pi$
$542$	2.36943	+	2.36943i	0.101776	+	0.101776i
$543$		0			0
$544$		−	2.62245i		−	0.112436i
$545$	29.2152	−	6.57472i	1.25144	−	0.281630i
$546$		0			0
$547$	2.64303	−	2.64303i	0.113008	−	0.113008i	−0.648342	−	0.761349i	$-0.724537\pi$
$547$	2.64303	−	2.64303i	0.113008	−	0.113008i	0.761349	+	0.648342i	$0.224537\pi$
$548$	5.68489	−	5.68489i	0.242847	−	0.242847i
$549$		0			0
$550$	5.84490	−	16.3833i	0.249227	−	0.698585i
$551$			15.4149i			0.656696i
$552$		0			0
$553$	−7.48118	−	7.48118i	−0.318132	−	0.318132i
$554$	12.9124			0.548597
$555$		0			0
$556$	7.27284			0.308437
$557$	2.10355	+	2.10355i	0.0891301	+	0.0891301i	0.750266	−	0.661136i	$-0.229925\pi$
$557$	2.10355	+	2.10355i	0.0891301	+	0.0891301i	−0.661136	+	0.750266i	$0.729925\pi$
$558$		0			0
$559$			3.74690i			0.158477i
$560$	1.88970	+	1.19542i	0.0798546	+	0.0505155i
$561$		0			0
$562$	5.28402	−	5.28402i	0.222893	−	0.222893i
$563$	1.53777	−	1.53777i	0.0648094	−	0.0648094i	−0.673959	−	0.738769i	$-0.735408\pi$
$563$	1.53777	−	1.53777i	0.0648094	−	0.0648094i	0.738769	+	0.673959i	$0.235408\pi$
$564$		0			0
$565$	−15.7135	−	9.94026i	−0.661072	−	0.418190i
$566$		−	27.4451i		−	1.15360i
$567$		0			0
$568$	−9.67767	−	9.67767i	−0.406066	−	0.406066i
$569$	−35.2437			−1.47749			−0.738747	−	0.673983i	$-0.764582\pi$
$569$	−35.2437			−1.47749			−0.738747	+	0.673983i	$0.764582\pi$
$570$		0			0
$571$	39.9934			1.67367			0.836836	−	0.547453i	$-0.184403\pi$
$571$	39.9934			1.67367			0.836836	+	0.547453i	$0.184403\pi$
$572$	1.56421	+	1.56421i	0.0654031	+	0.0654031i
$573$		0			0
$574$		−	6.47162i		−	0.270120i
$575$	−13.7142	+	38.4410i	−0.571923	+	1.60310i
$576$		0			0
$577$	−22.7084	+	22.7084i	−0.945365	+	0.945365i	−0.998583	−	0.0532178i	$-0.983052\pi$
$577$	−22.7084	+	22.7084i	−0.945365	+	0.945365i	0.0532178	+	0.998583i	$0.483052\pi$
$578$	−7.15788	+	7.15788i	−0.297729	+	0.297729i
$579$		0			0
$580$	10.3803	−	2.33602i	0.431017	−	0.0969979i
$581$			14.8573i			0.616383i
$582$		0			0
$583$	−12.1611	−	12.1611i	−0.503662	−	0.503662i
$584$	8.77512			0.363117
$585$		0			0
$586$	21.7233			0.897382
$587$	−17.0928	−	17.0928i	−0.705496	−	0.705496i	0.260089	−	0.965585i	$-0.416248\pi$
$587$	−17.0928	−	17.0928i	−0.705496	−	0.705496i	−0.965585	+	0.260089i	$0.916248\pi$
$588$		0			0
$589$		−	6.81041i		−	0.280618i
$590$	10.3108	−	16.2992i	0.424487	−	0.671027i
$591$		0			0
$592$	0.0596053	−	0.0596053i	0.00244976	−	0.00244976i
$593$	12.6865	−	12.6865i	0.520972	−	0.520972i	−0.396893	−	0.917865i	$-0.629912\pi$
$593$	12.6865	−	12.6865i	0.520972	−	0.520972i	0.917865	+	0.396893i	$0.129912\pi$
$594$		0			0
$595$	1.28745	+	5.72089i	0.0527805	+	0.234534i
$596$			2.82065i			0.115538i
$597$		0			0
$598$	−3.67021	−	3.67021i	−0.150086	−	0.150086i
$599$	−10.7209			−0.438043			−0.219022	−	0.975720i	$-0.570287\pi$
$599$	−10.7209			−0.438043			−0.219022	+	0.975720i	$0.570287\pi$
$600$		0			0
$601$	19.2399			0.784810			0.392405	−	0.919792i	$-0.371643\pi$
$601$	19.2399			0.784810			0.392405	+	0.919792i	$0.371643\pi$
$602$	4.16669	+	4.16669i	0.169822	+	0.169822i
$603$		0			0
$604$		−	17.6663i		−	0.718833i
$605$	−0.541496	−	2.40617i	−0.0220150	−	0.0978249i
$606$		0			0
$607$	21.8902	−	21.8902i	0.888498	−	0.888498i	−0.105881	−	0.994379i	$-0.533766\pi$
$607$	21.8902	−	21.8902i	0.888498	−	0.888498i	0.994379	+	0.105881i	$0.0337663\pi$
$608$	2.29073	−	2.29073i	0.0929015	−	0.0929015i
$609$		0			0
$610$	3.52917	−	5.57889i	0.142892	−	0.225883i
$611$		−	1.89359i		−	0.0766063i
$612$		0			0
$613$	28.3665	+	28.3665i	1.14571	+	1.14571i	0.987387	+	0.158327i	$0.0506099\pi$
$613$	28.3665	+	28.3665i	1.14571	+	1.14571i	0.158327	+	0.987387i	$0.449390\pi$
$614$	−1.48908			−0.0600942
$615$		0			0
$616$	3.47893			0.140170
$617$	−30.5360	−	30.5360i	−1.22933	−	1.22933i	−0.964217	−	0.265116i	$-0.914590\pi$
$617$	−30.5360	−	30.5360i	−1.22933	−	1.22933i	−0.265116	−	0.964217i	$-0.585410\pi$
$618$		0			0
$619$			14.5652i			0.585423i	0.956201	+	0.292712i	$0.0945576\pi$
$619$			14.5652i			0.585423i	−0.956201	+	0.292712i	$0.905442\pi$
$620$	−4.58607	+	1.03207i	−0.184181	+	0.0414489i
$621$		0			0
$622$	−11.2875	+	11.2875i	−0.452587	+	0.452587i
$623$	0.908966	−	0.908966i	0.0364169	−	0.0364169i
$624$		0			0
$625$	15.8240	−	19.3546i	0.632959	−	0.774185i
$626$			4.36910i			0.174624i
$627$		0			0
$628$	3.31278	+	3.31278i	0.132194	+	0.132194i
$629$	0.221058			0.00881416
$630$		0			0
$631$	−2.67184			−0.106364			−0.0531821	−	0.998585i	$-0.516936\pi$
$631$	−2.67184			−0.106364			−0.0531821	+	0.998585i	$0.516936\pi$
$632$	7.48118	+	7.48118i	0.297585	+	0.297585i
$633$		0			0
$634$		−	8.37219i		−	0.332502i
$635$	15.9883	+	10.1141i	0.634476	+	0.401366i
$636$		0			0
$637$	0.449625	−	0.449625i	0.0178148	−	0.0178148i
$638$	11.7053	−	11.7053i	0.463417	−	0.463417i
$639$		0			0
$640$	−1.88970	−	1.19542i	−0.0746971	−	0.0472529i
$641$		−	38.4977i		−	1.52057i	−0.649591	−	0.760284i	$-0.725060\pi$
$641$		−	38.4977i		−	1.52057i	0.649591	−	0.760284i	$-0.274940\pi$
$642$		0			0
$643$	−22.8716	−	22.8716i	−0.901969	−	0.901969i	0.0936373	−	0.995606i	$-0.470151\pi$
$643$	−22.8716	−	22.8716i	−0.901969	−	0.901969i	−0.995606	+	0.0936373i	$0.970151\pi$
$644$	−8.16282			−0.321660
$645$		0			0
$646$	8.49564			0.334256
$647$	−20.3226	−	20.3226i	−0.798962	−	0.798962i	0.183970	−	0.982932i	$-0.441105\pi$
$647$	−20.3226	−	20.3226i	−0.798962	−	0.798962i	−0.982932	+	0.183970i	$0.941105\pi$
$648$		0			0
$649$		−	30.0067i		−	1.17787i
$650$	1.36200	+	2.87282i	0.0534221	+	0.112681i
$651$		0			0
$652$	4.34747	−	4.34747i	0.170260	−	0.170260i
$653$	−16.0139	+	16.0139i	−0.626671	+	0.626671i	−0.947229	−	0.320558i	$-0.896130\pi$
$653$	−16.0139	+	16.0139i	−0.626671	+	0.626671i	0.320558	+	0.947229i	$0.396130\pi$
$654$		0			0
$655$	−43.1712	+	9.71545i	−1.68684	+	0.379614i
$656$			6.47162i			0.252674i
$657$		0			0
$658$	−2.10574	−	2.10574i	−0.0820904	−	0.0820904i
$659$	38.3204			1.49275			0.746375	−	0.665526i	$-0.231793\pi$
$659$	38.3204			1.49275			0.746375	+	0.665526i	$0.231793\pi$
$660$		0			0
$661$	−30.3937			−1.18218			−0.591088	−	0.806607i	$-0.701301\pi$
$661$	−30.3937			−1.18218			−0.591088	+	0.806607i	$0.701301\pi$
$662$	−19.5570	−	19.5570i	−0.760105	−	0.760105i
$663$		0			0
$664$		−	14.8573i		−	0.576573i
$665$	−3.87265	+	6.12186i	−0.150175	+	0.237395i
$666$		0			0
$667$	−27.4648	+	27.4648i	−1.06344	+	1.06344i
$668$	3.40504	−	3.40504i	0.131745	−	0.131745i
$669$		0			0
$670$	3.11793	+	13.8547i	0.120456	+	0.535255i
$671$		−	10.2707i		−	0.396496i
$672$		0			0
$673$	−35.3227	−	35.3227i	−1.36159	−	1.36159i	−0.871894	−	0.489695i	$-0.837108\pi$
$673$	−35.3227	−	35.3227i	−1.36159	−	1.36159i	−0.489695	−	0.871894i	$-0.662892\pi$
$674$	25.8462			0.995558
$675$		0			0
$676$	12.5957			0.484449
$677$	−2.02200	−	2.02200i	−0.0777116	−	0.0777116i	0.667183	−	0.744894i	$-0.267500\pi$
$677$	−2.02200	−	2.02200i	−0.0777116	−	0.0777116i	−0.744894	+	0.667183i	$0.767500\pi$
$678$		0			0
$679$			12.3350i			0.473372i
$680$	−1.28745	−	5.72089i	−0.0493716	−	0.219386i
$681$		0			0
$682$	−5.17148	+	5.17148i	−0.198026	+	0.198026i
$683$	−23.1572	+	23.1572i	−0.886086	+	0.886086i	−0.994145	−	0.108058i	$-0.965537\pi$
$683$	−23.1572	+	23.1572i	−0.886086	+	0.886086i	0.108058	+	0.994145i	$0.465537\pi$
$684$		0			0
$685$	9.61072	−	15.1926i	0.367207	−	0.580478i
$686$		−	1.00000i		−	0.0381802i
$687$		0			0
$688$	−4.16669	−	4.16669i	−0.158854	−	0.158854i
$689$	3.14346			0.119756
$690$		0			0
$691$	16.9468			0.644685			0.322342	−	0.946623i	$-0.395530\pi$
$691$	16.9468			0.644685			0.322342	+	0.946623i	$0.395530\pi$
$692$	14.0825	+	14.0825i	0.535336	+	0.535336i
$693$		0			0
$694$			22.4868i			0.853588i
$695$	15.8658	−	3.57050i	0.601823	−	0.135437i
$696$		0			0
$697$	−12.0006	+	12.0006i	−0.454557	+	0.454557i
$698$	−0.394618	+	0.394618i	−0.0149365	+	0.0149365i
$699$		0			0
$700$	4.70928	+	1.68008i	0.177994	+	0.0635012i
$701$			25.2193i			0.952521i	0.879304	+	0.476260i	$0.158008\pi$
$701$			25.2193i			0.952521i	−0.879304	+	0.476260i	$0.841992\pi$
$702$		0			0
$703$	0.193096	+	0.193096i	0.00728276	+	0.00728276i
$704$	−3.47893			−0.131117
$705$		0			0
$706$	−1.45243			−0.0546631
$707$	6.90889	+	6.90889i	0.259836	+	0.259836i
$708$		0			0
$709$		−	17.9840i		−	0.675404i	−0.941253	−	0.337702i	$-0.890350\pi$
$709$		−	17.9840i		−	0.675404i	0.941253	−	0.337702i	$-0.109650\pi$
$710$	−25.8631	−	16.3608i	−0.970623	−	0.614010i
$711$		0			0
$712$	−0.908966	+	0.908966i	−0.0340649	+	0.0340649i
$713$	12.1341	−	12.1341i	0.454427	−	0.454427i
$714$		0			0
$715$	4.18028	+	2.64442i	0.156334	+	0.0988956i
$716$		−	22.4158i		−	0.837719i
$717$		0			0
$718$	2.77829	+	2.77829i	0.103685	+	0.103685i
$719$	−48.5409			−1.81027			−0.905135	−	0.425123i	$-0.860231\pi$
$719$	−48.5409			−1.81027			−0.905135	+	0.425123i	$0.860231\pi$
$720$		0			0
$721$	−12.8961			−0.480274
$722$	−6.01401	−	6.01401i	−0.223818	−	0.223818i
$723$		0			0
$724$		−	16.4453i		−	0.611183i
$725$	21.4978	−	10.1921i	0.798407	−	0.378525i
$726$		0			0
$727$	−29.2735	+	29.2735i	−1.08569	+	1.08569i	−0.0897286	+	0.995966i	$0.528600\pi$
$727$	−29.2735	+	29.2735i	−1.08569	+	1.08569i	−0.995966	+	0.0897286i	$0.971400\pi$
$728$	−0.449625	+	0.449625i	−0.0166642	+	0.0166642i
$729$		0			0
$730$	19.1430	−	4.30803i	0.708514	−	0.159447i
$731$		−	15.4530i		−	0.571550i
$732$		0			0
$733$	16.9533	+	16.9533i	0.626183	+	0.626183i	0.947105	−	0.320923i	$-0.103993\pi$
$733$	16.9533	+	16.9533i	0.626183	+	0.626183i	−0.320923	+	0.947105i	$0.603993\pi$
$734$	9.79769			0.361639
$735$		0			0
$736$	8.16282			0.300886
$737$	15.6233	+	15.6233i	0.575491	+	0.575491i
$738$		0			0
$739$		−	2.73583i		−	0.100639i	−0.998733	−	0.0503196i	$-0.983976\pi$
$739$		−	2.73583i		−	0.100639i	0.998733	−	0.0503196i	$-0.0160240\pi$
$740$	0.100767	−	0.159292i	0.00370427	−	0.00585568i
$741$		0			0
$742$	3.49565	−	3.49565i	0.128329	−	0.128329i
$743$	11.2571	−	11.2571i	0.412981	−	0.412981i	−0.469794	−	0.882776i	$-0.655672\pi$
$743$	11.2571	−	11.2571i	0.412981	−	0.412981i	0.882776	+	0.469794i	$0.155672\pi$
$744$		0			0
$745$	1.38476	+	6.15327i	0.0507337	+	0.225439i
$746$		−	8.35327i		−	0.305835i
$747$		0			0
$748$	−6.45116	−	6.45116i	−0.235878	−	0.235878i
$749$	−15.9133			−0.581459
$750$		0			0
$751$	−5.19836			−0.189691			−0.0948454	−	0.995492i	$-0.530236\pi$
$751$	−5.19836			−0.189691			−0.0948454	+	0.995492i	$0.530236\pi$
$752$	2.10574	+	2.10574i	0.0767885	+	0.0767885i
$753$		0			0
$754$			3.02563i			0.110187i
$755$	−8.67305	−	38.5393i	−0.315645	−	1.40259i
$756$		0			0
$757$	3.87070	−	3.87070i	0.140683	−	0.140683i	−0.633258	−	0.773941i	$-0.718283\pi$
$757$	3.87070	−	3.87070i	0.140683	−	0.140683i	0.773941	+	0.633258i	$0.218283\pi$
$758$	−17.7317	+	17.7317i	−0.644044	+	0.644044i
$759$		0			0
$760$	3.87265	−	6.12186i	0.140476	−	0.222063i
$761$			31.4323i			1.13942i	0.821845	+	0.569710i	$0.192945\pi$
$761$			31.4323i			1.13942i	−0.821845	+	0.569710i	$0.807055\pi$
$762$		0			0
$763$	9.46972	+	9.46972i	0.342827	+	0.342827i
$764$	−6.41085			−0.231936
$765$		0			0
$766$	33.3018			1.20324
$767$	3.87813	+	3.87813i	0.140031	+	0.140031i
$768$		0			0
$769$		−	19.1770i		−	0.691539i	−0.938320	−	0.345769i	$-0.887618\pi$
$769$		−	19.1770i		−	0.691539i	0.938320	−	0.345769i	$-0.112382\pi$
$770$	7.58933	−	1.70794i	0.273500	−	0.0615498i
$771$		0			0
$772$	−2.14415	+	2.14415i	−0.0771695	+	0.0771695i
$773$	7.42074	−	7.42074i	0.266906	−	0.266906i	−0.560947	−	0.827852i	$-0.689563\pi$
$773$	7.42074	−	7.42074i	0.266906	−	0.266906i	0.827852	+	0.560947i	$0.189563\pi$
$774$		0			0
$775$	−9.49787	+	4.50294i	−0.341174	+	0.161750i
$776$		−	12.3350i		−	0.442799i
$777$		0			0
$778$	5.75428	+	5.75428i	0.206301	+	0.206301i
$779$	−20.9654			−0.751162
$780$		0			0
$781$	−47.6137			−1.70375
$782$	15.1367	+	15.1367i	0.541288	+	0.541288i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	8.85323	+	5.60050i	0.315985	+	0.199890i
$786$		0			0
$787$	28.6559	−	28.6559i	1.02147	−	1.02147i	0.0217089	−	0.999764i	$-0.493089\pi$
$787$	28.6559	−	28.6559i	1.02147	−	1.02147i	0.999764	−	0.0217089i	$-0.00691071\pi$
$788$	−6.91076	+	6.91076i	−0.246186	+	0.246186i
$789$		0			0
$790$	19.9931	+	12.6475i	0.711321	+	0.449977i
$791$		−	8.31532i		−	0.295659i
$792$		0			0
$793$	1.32741	+	1.32741i	0.0471376	+	0.0471376i
$794$	−17.3057			−0.614156
$795$		0			0
$796$	18.4417			0.653648
$797$	−37.4755	−	37.4755i	−1.32745	−	1.32745i	−0.907587	−	0.419863i	$-0.862078\pi$
$797$	−37.4755	−	37.4755i	−1.32745	−	1.32745i	−0.419863	−	0.907587i	$-0.637922\pi$
$798$		0			0
$799$			7.80956i			0.276283i
$800$	−4.70928	−	1.68008i	−0.166498	−	0.0593999i
$801$		0			0
$802$	25.3745	−	25.3745i	0.896005	−	0.896005i
$803$	21.5866	−	21.5866i	0.761775	−	0.761775i
$804$		0			0
$805$	−17.8073	+	4.00743i	−0.627624	+	0.141243i
$806$		−	1.33675i		−	0.0470849i
$807$		0			0
$808$	−6.90889	−	6.90889i	−0.243054	−	0.243054i
$809$	2.15880			0.0758994			0.0379497	−	0.999280i	$-0.487917\pi$
$809$	2.15880			0.0758994			0.0379497	+	0.999280i	$0.487917\pi$
$810$		0			0
$811$	−15.5609			−0.546417			−0.273208	−	0.961955i	$-0.588085\pi$
$811$	−15.5609			−0.546417			−0.273208	+	0.961955i	$0.588085\pi$
$812$	3.36462	+	3.36462i	0.118075	+	0.118075i
$813$		0			0
$814$		−	0.293255i		−	0.0102786i
$815$	7.34971	−	11.6184i	0.257449	−	0.406974i
$816$		0			0
$817$	13.4984	−	13.4984i	0.472248	−	0.472248i
$818$	−1.52491	+	1.52491i	−0.0533174	+	0.0533174i
$819$		0			0
$820$	3.17715	+	14.1179i	0.110951	+	0.493018i
$821$		−	7.03139i		−	0.245397i	−0.992444	−	0.122699i	$-0.960845\pi$
$821$		−	7.03139i		−	0.245397i	0.992444	−	0.122699i	$-0.0391549\pi$
$822$		0			0
$823$	36.2056	+	36.2056i	1.26205	+	1.26205i	0.950098	+	0.311951i	$0.100982\pi$
$823$	36.2056	+	36.2056i	1.26205	+	1.26205i	0.311951	+	0.950098i	$0.399018\pi$
$824$	12.8961			0.449256
$825$		0			0
$826$	8.62525			0.300111
$827$	17.4804	+	17.4804i	0.607852	+	0.607852i	0.942384	−	0.334533i	$-0.108578\pi$
$827$	17.4804	+	17.4804i	0.607852	+	0.607852i	−0.334533	+	0.942384i	$0.608578\pi$
$828$		0			0
$829$		−	16.0902i		−	0.558836i	−0.960169	−	0.279418i	$-0.909858\pi$
$829$		−	16.0902i		−	0.558836i	0.960169	−	0.279418i	$-0.0901416\pi$
$830$	−7.29397	−	32.4112i	−0.253177	−	1.12501i
$831$		0			0
$832$	0.449625	−	0.449625i	0.0155879	−	0.0155879i
$833$	−1.85435	+	1.85435i	−0.0642494	+	0.0642494i
$834$		0			0
$835$	5.75647	−	9.09979i	0.199211	−	0.314911i
$836$		−	11.2703i		−	0.389792i
$837$		0			0
$838$	10.6237	+	10.6237i	0.366991	+	0.366991i
$839$	−8.10429			−0.279791			−0.139896	−	0.990166i	$-0.544677\pi$
$839$	−8.10429			−0.279791			−0.139896	+	0.990166i	$0.544677\pi$
$840$		0			0
$841$	−6.35867			−0.219265
$842$	−7.26073	−	7.26073i	−0.250221	−	0.250221i
$843$		0			0
$844$		−	10.9041i		−	0.375334i
$845$	27.4776	−	6.18368i	0.945257	−	0.212725i
$846$		0			0
$847$	0.779929	−	0.779929i	0.0267987	−	0.0267987i
$848$	−3.49565	+	3.49565i	−0.120041	+	0.120041i
$849$		0			0
$850$	−5.61719	−	11.8481i	−0.192668	−	0.406387i
$851$			0.688081i			0.0235871i
$852$		0			0
$853$	26.3338	+	26.3338i	0.901653	+	0.901653i	0.995579	−	0.0939259i	$-0.0299417\pi$
$853$	26.3338	+	26.3338i	0.901653	+	0.901653i	−0.0939259	+	0.995579i	$0.529942\pi$
$854$	2.95225			0.101024
$855$		0			0
$856$	15.9133			0.543905
$857$	−7.24195	−	7.24195i	−0.247380	−	0.247380i	0.572514	−	0.819895i	$-0.305968\pi$
$857$	−7.24195	−	7.24195i	−0.247380	−	0.247380i	−0.819895	+	0.572514i	$0.805968\pi$
$858$		0			0
$859$		−	36.4005i		−	1.24197i	−0.783823	−	0.620984i	$-0.786733\pi$
$859$		−	36.4005i		−	1.24197i	0.783823	−	0.620984i	$-0.213267\pi$
$860$	−11.1353	−	7.04410i	−0.379709	−	0.240202i
$861$		0			0
$862$	−1.11375	+	1.11375i	−0.0379343	+	0.0379343i
$863$	27.3154	−	27.3154i	0.929825	−	0.929825i	−0.0678689	−	0.997694i	$-0.521620\pi$
$863$	27.3154	−	27.3154i	0.929825	−	0.929825i	0.997694	+	0.0678689i	$0.0216200\pi$
$864$		0			0
$865$	37.6347	+	23.8075i	1.27962	+	0.809478i
$866$			22.0759i			0.750170i
$867$		0			0
$868$	−1.48651	−	1.48651i	−0.0504555	−	0.0504555i
$869$	36.8071			1.24859
$870$		0			0
$871$	−4.03837			−0.136835
$872$	−9.46972	−	9.46972i	−0.320685	−	0.320685i
$873$		0			0
$874$			26.4441i			0.894487i
$875$	11.0982	+	1.35316i	0.375186	+	0.0457452i
$876$		0			0
$877$	−0.961051	+	0.961051i	−0.0324524	+	0.0324524i	−0.723147	−	0.690694i	$-0.757305\pi$
$877$	−0.961051	+	0.961051i	−0.0324524	+	0.0324524i	0.690694	+	0.723147i	$0.257305\pi$
$878$	−2.36838	+	2.36838i	−0.0799288	+	0.0799288i
$879$		0			0
$880$	−7.58933	+	1.70794i	−0.255836	+	0.0575745i
$881$		−	2.67945i		−	0.0902728i	−0.998981	−	0.0451364i	$-0.985628\pi$
$881$		−	2.67945i		−	0.0902728i	0.998981	−	0.0451364i	$-0.0143722\pi$
$882$		0			0
$883$	29.0695	+	29.0695i	0.978268	+	0.978268i	0.999769	−	0.0215012i	$-0.00684459\pi$
$883$	29.0695	+	29.0695i	0.978268	+	0.978268i	−0.0215012	+	0.999769i	$0.506845\pi$
$884$	1.66752			0.0560849
$885$		0			0
$886$	15.3492			0.515668
$887$	4.50722	+	4.50722i	0.151338	+	0.151338i	0.778715	−	0.627378i	$-0.215872\pi$
$887$	4.50722	+	4.50722i	0.151338	+	0.151338i	−0.627378	+	0.778715i	$0.715872\pi$
$888$		0			0
$889$			8.46074i			0.283764i
$890$	−1.53667	+	2.42916i	−0.0515094	+	0.0814257i
$891$		0			0
$892$	−3.84275	+	3.84275i	−0.128665	+	0.128665i
$893$	−6.82173	+	6.82173i	−0.228280	+	0.228280i
$894$		0			0
$895$	−11.0048	−	48.9003i	−0.367848	−	1.63456i
$896$		−	1.00000i		−	0.0334077i
$897$		0			0
$898$	−25.6525	−	25.6525i	−0.856035	−	0.856035i
$899$	−10.0031			−0.333622
$900$		0			0
$901$	−12.9643			−0.431903
$902$	15.9200	+	15.9200i	0.530079	+	0.530079i
$903$		0			0
$904$			8.31532i			0.276563i
$905$	−8.07358	−	35.8755i	−0.268375	−	1.19254i
$906$		0			0
$907$	−11.0267	+	11.0267i	−0.366137	+	0.366137i	−0.866066	−	0.499929i	$-0.833359\pi$
$907$	−11.0267	+	11.0267i	−0.366137	+	0.366137i	0.499929	+	0.866066i	$0.333359\pi$
$908$	−4.28065	+	4.28065i	−0.142058	+	0.142058i
$909$		0			0
$910$	−0.760123	+	1.20160i	−0.0251978	+	0.0398326i
$911$		−	3.52452i		−	0.116773i	−0.998294	−	0.0583863i	$-0.981404\pi$
$911$		−	3.52452i		−	0.116773i	0.998294	−	0.0583863i	$-0.0185955\pi$
$912$		0			0
$913$	−36.5485	−	36.5485i	−1.20958	−	1.20958i
$914$	34.0934			1.12771
$915$		0			0
$916$	19.3523			0.639418
$917$	−13.9934	−	13.9934i	−0.462102	−	0.462102i
$918$		0			0
$919$			34.7655i			1.14681i	0.819273	+	0.573403i	$0.194377\pi$
$919$			34.7655i			1.14681i	−0.819273	+	0.573403i	$0.805623\pi$
$920$	17.8073	−	4.00743i	0.587088	−	0.132121i
$921$		0			0
$922$	−21.0556	+	21.0556i	−0.693428	+	0.693428i
$923$	6.15370	−	6.15370i	0.202551	−	0.202551i
$924$		0			0
$925$	0.141622	−	0.396967i	0.00465650	−	0.0130522i
$926$			0.339488i			0.0111563i
$927$		0			0
$928$	−3.36462	−	3.36462i	−0.110449	−	0.110449i
$929$	15.0329			0.493214			0.246607	−	0.969116i	$-0.420684\pi$
$929$	15.0329			0.493214			0.246607	+	0.969116i	$0.420684\pi$
$930$		0			0
$931$	−3.23958			−0.106173
$932$	−2.21851	−	2.21851i	−0.0726696	−	0.0726696i
$933$		0			0
$934$		−	29.2699i		−	0.957740i
$935$	−17.2404	−	10.9062i	−0.563821	−	0.356669i
$936$		0			0
$937$	15.7017	−	15.7017i	0.512954	−	0.512954i	−0.402477	−	0.915430i	$-0.631851\pi$
$937$	15.7017	−	15.7017i	0.512954	−	0.512954i	0.915430	+	0.402477i	$0.131851\pi$
$938$	−4.49082	+	4.49082i	−0.146631	+	0.146631i
$939$		0			0
$940$	5.62748	+	3.55991i	0.183548	+	0.116111i
$941$			35.2490i			1.14908i	0.818475	+	0.574542i	$0.194820\pi$
$941$			35.2490i			1.14908i	−0.818475	+	0.574542i	$0.805180\pi$
$942$		0			0
$943$	−37.3541	−	37.3541i	−1.21642	−	1.21642i
$944$	−8.62525			−0.280728
$945$		0			0
$946$	−20.5000			−0.666511
$947$	24.6886	+	24.6886i	0.802270	+	0.802270i	0.983450	−	0.181180i	$-0.0579916\pi$
$947$	24.6886	+	24.6886i	0.802270	+	0.802270i	−0.181180	+	0.983450i	$0.557992\pi$
$948$		0			0
$949$			5.57979i			0.181128i
$950$	5.44277	−	15.2561i	0.176587	−	0.494974i
$951$		0			0
$952$	1.85435	−	1.85435i	0.0600998	−	0.0600998i
$953$	−5.94083	+	5.94083i	−0.192442	+	0.192442i	−0.796751	−	0.604308i	$-0.793450\pi$
$953$	−5.94083	+	5.94083i	−0.192442	+	0.192442i	0.604308	+	0.796751i	$0.293450\pi$
$954$		0			0
$955$	−13.9853	+	3.14732i	−0.452554	+	0.101845i
$956$		−	8.35839i		−	0.270330i
$957$		0			0
$958$	−4.47563	−	4.47563i	−0.144601	−	0.144601i
$959$	8.03965			0.259614
$960$		0			0
$961$	−26.5806			−0.857437
$962$	0.0379009	+	0.0379009i	0.00122197	+	0.00122197i
$963$		0			0
$964$			22.7172i			0.731673i
$965$	−3.62484	+	5.73012i	−0.116688	+	0.184459i
$966$		0			0
$967$	−28.1776	+	28.1776i	−0.906130	+	0.906130i	−0.995957	−	0.0898277i	$-0.971368\pi$
$967$	−28.1776	+	28.1776i	−0.906130	+	0.906130i	0.0898277	+	0.995957i	$0.471368\pi$
$968$	−0.779929	+	0.779929i	−0.0250679	+	0.0250679i
$969$		0			0
$970$	−6.05568	−	26.9088i	−0.194436	−	0.863990i
$971$		−	40.8730i		−	1.31168i	−0.754901	−	0.655839i	$-0.772315\pi$
$971$		−	40.8730i		−	1.31168i	0.754901	−	0.655839i	$-0.227685\pi$
$972$		0			0
$973$	5.14268	+	5.14268i	0.164867	+	0.164867i
$974$	19.5021			0.624888
$975$		0			0
$976$	−2.95225			−0.0944993
$977$	−29.2723	−	29.2723i	−0.936503	−	0.936503i	0.0615982	−	0.998101i	$-0.480380\pi$
$977$	−29.2723	−	29.2723i	−0.936503	−	0.936503i	−0.998101	+	0.0615982i	$0.980380\pi$
$978$		0			0
$979$			4.47207i			0.142928i
$980$	0.490937	+	2.18151i	0.0156824	+	0.0696857i
$981$		0			0
$982$	22.3644	−	22.3644i	0.713678	−	0.713678i
$983$	37.0259	−	37.0259i	1.18094	−	1.18094i	0.201442	−	0.979500i	$-0.435437\pi$
$983$	37.0259	−	37.0259i	1.18094	−	1.18094i	0.979500	−	0.201442i	$-0.0645628\pi$
$984$		0			0
$985$	−11.6831	+	18.4686i	−0.372256	+	0.588459i
$986$		−	12.4784i		−	0.397392i
$987$		0			0
$988$	1.45660	+	1.45660i	0.0463405	+	0.0463405i
$989$	48.1002			1.52950
$990$		0			0
$991$	−6.60953			−0.209959			−0.104979	−	0.994474i	$-0.533478\pi$
$991$	−6.60953			−0.209959			−0.104979	+	0.994474i	$0.533478\pi$
$992$	1.48651	+	1.48651i	0.0471968	+	0.0471968i
$993$		0			0
$994$		−	13.6863i		−	0.434103i
$995$	40.2307	−	9.05369i	1.27540	−	0.287021i
$996$		0			0
$997$	26.8107	−	26.8107i	0.849105	−	0.849105i	−0.140917	−	0.990021i	$-0.545005\pi$
$997$	26.8107	−	26.8107i	0.849105	−	0.849105i	0.990021	+	0.140917i	$0.0450050\pi$
$998$	25.4506	−	25.4506i	0.805625	−	0.805625i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.m.d.323.1	yes	24
3.2	odd	2		1890.2.m.a.323.12	✓	24
5.2	odd	4		1890.2.m.a.1457.12	yes	24
15.2	even	4	inner	1890.2.m.d.1457.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.m.a.323.12	✓	24	3.2	odd	2
1890.2.m.a.1457.12	yes	24	5.2	odd	4
1890.2.m.d.323.1	yes	24	1.1	even	1	trivial
1890.2.m.d.1457.1	yes	24	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.490937 + 2.18151i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(0.490937 + 2.18151i) q^{5} +(-0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.19542 - 1.88970i) q^{10} -3.47893i q^{11} +(0.449625 + 0.449625i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-1.85435 - 1.85435i) q^{17} -3.23958i q^{19} +(-2.18151 + 0.490937i) q^{20} +(-2.45998 + 2.45998i) q^{22} +(5.77199 - 5.77199i) q^{23} +(-4.51796 + 2.14197i) q^{25} -0.635865i q^{26} +(-0.707107 - 0.707107i) q^{28} -4.75829 q^{29} +2.10225 q^{31} +(0.707107 + 0.707107i) q^{32} +2.62245i q^{34} +(-1.88970 - 1.19542i) q^{35} +(-0.0596053 + 0.0596053i) q^{37} +(-2.29073 + 2.29073i) q^{38} +(1.88970 + 1.19542i) q^{40} -6.47162i q^{41} +(4.16669 + 4.16669i) q^{43} +3.47893 q^{44} -8.16282 q^{46} +(-2.10574 - 2.10574i) q^{47} -1.00000i q^{49} +(4.70928 + 1.68008i) q^{50} +(-0.449625 + 0.449625i) q^{52} +(3.49565 - 3.49565i) q^{53} +(7.58933 - 1.70794i) q^{55} +1.00000i q^{56} +(3.36462 + 3.36462i) q^{58} +8.62525 q^{59} +2.95225 q^{61} +(-1.48651 - 1.48651i) q^{62} -1.00000i q^{64} +(-0.760123 + 1.20160i) q^{65} +(-4.49082 + 4.49082i) q^{67} +(1.85435 - 1.85435i) q^{68} +(0.490937 + 2.18151i) q^{70} -13.6863i q^{71} +(6.20495 + 6.20495i) q^{73} +0.0842946 q^{74} +3.23958 q^{76} +(2.45998 + 2.45998i) q^{77} +10.5800i q^{79} +(-0.490937 - 2.18151i) q^{80} +(-4.57612 + 4.57612i) q^{82} +(10.5057 - 10.5057i) q^{83} +(3.13491 - 4.95565i) q^{85} -5.89260i q^{86} +(-2.45998 - 2.45998i) q^{88} -1.28547 q^{89} -0.635865 q^{91} +(5.77199 + 5.77199i) q^{92} +2.97797i q^{94} +(7.06718 - 1.59043i) q^{95} +(8.72213 - 8.72213i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{5}+O(q^{10}) \) 24 * q + 8 * q^5	\( 24 q + 8 q^{5} + 24 q^{14} - 24 q^{16} + 16 q^{17} + 8 q^{22} - 8 q^{25} - 16 q^{29} - 16 q^{31} - 8 q^{35} - 16 q^{37} + 8 q^{38} + 8 q^{40} - 8 q^{43} + 8 q^{44} + 16 q^{46} + 16 q^{47} + 32 q^{50} - 24 q^{53} + 40 q^{55} + 8 q^{58} + 32 q^{59} + 40 q^{62} - 24 q^{65} - 24 q^{67} - 16 q^{68} + 8 q^{70} - 24 q^{73} - 16 q^{74} - 8 q^{77} - 8 q^{80} - 8 q^{82} + 48 q^{83} - 24 q^{85} + 8 q^{88} + 48 q^{89} + 72 q^{95} + 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^5 + 24 * q^14 - 24 * q^16 + 16 * q^17 + 8 * q^22 - 8 * q^25 - 16 * q^29 - 16 * q^31 - 8 * q^35 - 16 * q^37 + 8 * q^38 + 8 * q^40 - 8 * q^43 + 8 * q^44 + 16 * q^46 + 16 * q^47 + 32 * q^50 - 24 * q^53 + 40 * q^55 + 8 * q^58 + 32 * q^59 + 40 * q^62 - 24 * q^65 - 24 * q^67 - 16 * q^68 + 8 * q^70 - 24 * q^73 - 16 * q^74 - 8 * q^77 - 8 * q^80 - 8 * q^82 + 48 * q^83 - 24 * q^85 + 8 * q^88 + 48 * q^89 + 72 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more