LMFDB - Embedded newform 1530.2.m.f.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1530.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.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:	$12.2171115093$
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			647.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.f.953.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.585786 - 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.585786 - 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 + 2.12132i) q^{10} -2.82843i q^{11} +(1.41421 - 1.41421i) q^{13} +0.828427 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +0.828427i q^{19} +(-1.00000 - 2.00000i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-3.58579 - 3.58579i) q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000i q^{26} +(-0.585786 + 0.585786i) q^{28} -7.65685 q^{29} +5.07107 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(-1.75736 - 0.585786i) q^{35} +(4.00000 + 4.00000i) q^{37} +(-0.585786 - 0.585786i) q^{38} +(2.12132 + 0.707107i) q^{40} -8.82843i q^{41} +(-4.41421 + 4.41421i) q^{43} -2.82843 q^{44} +5.07107 q^{46} -6.31371i q^{49} +(0.707107 + 4.94975i) q^{50} +(-1.41421 - 1.41421i) q^{52} +(0.242641 + 0.242641i) q^{53} +(-2.82843 - 5.65685i) q^{55} -0.828427i q^{56} +(5.41421 - 5.41421i) q^{58} -10.7279 q^{59} +2.58579 q^{61} +(-3.58579 + 3.58579i) q^{62} +1.00000i q^{64} +(1.41421 - 4.24264i) q^{65} +(0.414214 + 0.414214i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(1.65685 - 0.828427i) q^{70} -5.65685i q^{71} +(0.242641 - 0.242641i) q^{73} -5.65685 q^{74} +0.828427 q^{76} +(-1.65685 + 1.65685i) q^{77} +0.585786i q^{79} +(-2.00000 + 1.00000i) q^{80} +(6.24264 + 6.24264i) q^{82} +(-1.17157 - 1.17157i) q^{83} +(0.707107 - 2.12132i) q^{85} -6.24264i q^{86} +(2.00000 - 2.00000i) q^{88} -2.58579 q^{89} -1.65685 q^{91} +(-3.58579 + 3.58579i) q^{92} +(0.828427 + 1.65685i) q^{95} +(1.41421 + 1.41421i) q^{97} +(4.46447 + 4.46447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 8 * q^5 - 8 * q^7	$ 4 q + 8 q^{5} - 8 q^{7} - 8 q^{14} - 4 q^{16} - 4 q^{20} + 8 q^{22} - 20 q^{23} + 12 q^{25} - 8 q^{28} - 8 q^{29} - 8 q^{31} - 24 q^{35} + 16 q^{37} - 8 q^{38} - 12 q^{43} - 8 q^{46} - 16 q^{53} + 16 q^{58} + 8 q^{59} + 16 q^{61} - 20 q^{62} - 4 q^{67} - 16 q^{70} - 16 q^{73} - 8 q^{76} + 16 q^{77} - 8 q^{80} + 8 q^{82} - 16 q^{83} + 8 q^{88} - 16 q^{89} + 16 q^{91} - 20 q^{92} - 8 q^{95} + 32 q^{98}+O(q^{100}) $ 4 * q + 8 * q^5 - 8 * q^7 - 8 * q^14 - 4 * q^16 - 4 * q^20 + 8 * q^22 - 20 * q^23 + 12 * q^25 - 8 * q^28 - 8 * q^29 - 8 * q^31 - 24 * q^35 + 16 * q^37 - 8 * q^38 - 12 * q^43 - 8 * q^46 - 16 * q^53 + 16 * q^58 + 8 * q^59 + 16 * q^61 - 20 * q^62 - 4 * q^67 - 16 * q^70 - 16 * q^73 - 8 * q^76 + 16 * q^77 - 8 * q^80 + 8 * q^82 - 16 * q^83 + 8 * q^88 - 16 * q^89 + 16 * q^91 - 20 * q^92 - 8 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$		0			0
$7$	−0.585786	−	0.585786i	−0.221406	−	0.221406i	0.587684	−	0.809091i	$-0.300040\pi$
$7$	−0.585786	−	0.585786i	−0.221406	−	0.221406i	−0.809091	+	0.587684i	$0.800040\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.707107	+	2.12132i	−0.223607	+	0.670820i
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	−0.483250	−	0.875482i	$-0.660544\pi$
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	0.875482	+	0.483250i	$0.160544\pi$
$14$	0.828427			0.221406
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$			0.828427i			0.190054i	0.995475	+	0.0950271i	$0.0302938\pi$
$19$			0.828427i			0.190054i	−0.995475	+	0.0950271i	$0.969706\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	−3.58579	−	3.58579i	−0.747688	−	0.747688i	0.226356	−	0.974045i	$-0.427319\pi$
$23$	−3.58579	−	3.58579i	−0.747688	−	0.747688i	−0.974045	+	0.226356i	$0.927319\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$			2.00000i			0.392232i
$27$		0			0
$28$	−0.585786	+	0.585786i	−0.110703	+	0.110703i
$29$	−7.65685			−1.42184			−0.710921	−	0.703272i	$-0.751722\pi$
$29$	−7.65685			−1.42184			−0.710921	+	0.703272i	$0.751722\pi$
$30$		0			0
$31$	5.07107			0.910791			0.455395	−	0.890289i	$-0.349498\pi$
$31$	5.07107			0.910791			0.455395	+	0.890289i	$0.349498\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			1.00000i			0.171499i
$35$	−1.75736	−	0.585786i	−0.297048	−	0.0990160i
$36$		0			0
$37$	4.00000	+	4.00000i	0.657596	+	0.657596i	0.954811	−	0.297215i	$-0.0960577\pi$
$37$	4.00000	+	4.00000i	0.657596	+	0.657596i	−0.297215	+	0.954811i	$0.596058\pi$
$38$	−0.585786	−	0.585786i	−0.0950271	−	0.0950271i
$39$		0			0
$40$	2.12132	+	0.707107i	0.335410	+	0.111803i
$41$		−	8.82843i		−	1.37877i	−0.724396	−	0.689384i	$-0.757881\pi$
$41$		−	8.82843i		−	1.37877i	0.724396	−	0.689384i	$-0.242119\pi$
$42$		0			0
$43$	−4.41421	+	4.41421i	−0.673161	+	0.673161i	−0.958444	−	0.285282i	$-0.907913\pi$
$43$	−4.41421	+	4.41421i	−0.673161	+	0.673161i	0.285282	+	0.958444i	$0.407913\pi$
$44$	−2.82843			−0.426401
$45$		0			0
$46$	5.07107			0.747688
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		0			0
$49$		−	6.31371i		−	0.901958i
$50$	0.707107	+	4.94975i	0.100000	+	0.700000i
$51$		0			0
$52$	−1.41421	−	1.41421i	−0.196116	−	0.196116i
$53$	0.242641	+	0.242641i	0.0333293	+	0.0333293i	0.723575	−	0.690246i	$-0.242498\pi$
$53$	0.242641	+	0.242641i	0.0333293	+	0.0333293i	−0.690246	+	0.723575i	$0.742498\pi$
$54$		0			0
$55$	−2.82843	−	5.65685i	−0.381385	−	0.762770i
$56$		−	0.828427i		−	0.110703i
$57$		0			0
$58$	5.41421	−	5.41421i	0.710921	−	0.710921i
$59$	−10.7279			−1.39666			−0.698328	−	0.715778i	$-0.746072\pi$
$59$	−10.7279			−1.39666			−0.698328	+	0.715778i	$0.746072\pi$
$60$		0			0
$61$	2.58579			0.331076			0.165538	−	0.986203i	$-0.447064\pi$
$61$	2.58579			0.331076			0.165538	+	0.986203i	$0.447064\pi$
$62$	−3.58579	+	3.58579i	−0.455395	+	0.455395i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.41421	−	4.24264i	0.175412	−	0.526235i
$66$		0			0
$67$	0.414214	+	0.414214i	0.0506042	+	0.0506042i	0.731956	−	0.681352i	$-0.238608\pi$
$67$	0.414214	+	0.414214i	0.0506042	+	0.0506042i	−0.681352	+	0.731956i	$0.738608\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	1.65685	−	0.828427i	0.198032	−	0.0990160i
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$		0			0
$73$	0.242641	−	0.242641i	0.0283989	−	0.0283989i	−0.692765	−	0.721164i	$-0.743608\pi$
$73$	0.242641	−	0.242641i	0.0283989	−	0.0283989i	0.721164	+	0.692765i	$0.243608\pi$
$74$	−5.65685			−0.657596
$75$		0			0
$76$	0.828427			0.0950271
$77$	−1.65685	+	1.65685i	−0.188816	+	0.188816i
$78$		0			0
$79$			0.585786i			0.0659061i	0.999457	+	0.0329531i	$0.0104912\pi$
$79$			0.585786i			0.0659061i	−0.999457	+	0.0329531i	$0.989509\pi$
$80$	−2.00000	+	1.00000i	−0.223607	+	0.111803i
$81$		0			0
$82$	6.24264	+	6.24264i	0.689384	+	0.689384i
$83$	−1.17157	−	1.17157i	−0.128597	−	0.128597i	0.639879	−	0.768476i	$-0.278984\pi$
$83$	−1.17157	−	1.17157i	−0.128597	−	0.128597i	−0.768476	+	0.639879i	$0.778984\pi$
$84$		0			0
$85$	0.707107	−	2.12132i	0.0766965	−	0.230089i
$86$		−	6.24264i		−	0.673161i
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	−2.58579			−0.274093			−0.137046	−	0.990565i	$-0.543761\pi$
$89$	−2.58579			−0.274093			−0.137046	+	0.990565i	$0.543761\pi$
$90$		0			0
$91$	−1.65685			−0.173686
$92$	−3.58579	+	3.58579i	−0.373844	+	0.373844i
$93$		0			0
$94$		0			0
$95$	0.828427	+	1.65685i	0.0849948	+	0.169990i
$96$		0			0
$97$	1.41421	+	1.41421i	0.143592	+	0.143592i	0.775248	−	0.631657i	$-0.217625\pi$
$97$	1.41421	+	1.41421i	0.143592	+	0.143592i	−0.631657	+	0.775248i	$0.717625\pi$
$98$	4.46447	+	4.46447i	0.450979	+	0.450979i
$99$		0			0
$100$	−4.00000	−	3.00000i	−0.400000	−	0.300000i
$101$		−	18.0000i		−	1.79107i	−0.444994	−	0.895533i	$-0.646794\pi$
$101$		−	18.0000i		−	1.79107i	0.444994	−	0.895533i	$-0.353206\pi$
$102$		0			0
$103$	3.17157	−	3.17157i	0.312504	−	0.312504i	−0.533375	−	0.845879i	$-0.679076\pi$
$103$	3.17157	−	3.17157i	0.312504	−	0.312504i	0.845879	+	0.533375i	$0.179076\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−0.343146			−0.0333293
$107$	−6.82843	+	6.82843i	−0.660129	+	0.660129i	−0.955410	−	0.295281i	$-0.904587\pi$
$107$	−6.82843	+	6.82843i	−0.660129	+	0.660129i	0.295281	+	0.955410i	$0.404587\pi$
$108$		0			0
$109$		−	12.2426i		−	1.17263i	−0.810082	−	0.586316i	$-0.800578\pi$
$109$		−	12.2426i		−	1.17263i	0.810082	−	0.586316i	$-0.199422\pi$
$110$	6.00000	+	2.00000i	0.572078	+	0.190693i
$111$		0			0
$112$	0.585786	+	0.585786i	0.0553516	+	0.0553516i
$113$	11.0711	+	11.0711i	1.04148	+	1.04148i	0.999102	+	0.0423768i	$0.0134930\pi$
$113$	11.0711	+	11.0711i	1.04148	+	1.04148i	0.0423768	+	0.999102i	$0.486507\pi$
$114$		0			0
$115$	−10.7574	−	3.58579i	−1.00313	−	0.334376i
$116$			7.65685i			0.710921i
$117$		0			0
$118$	7.58579	−	7.58579i	0.698328	−	0.698328i
$119$	−0.828427			−0.0759418
$120$		0			0
$121$	3.00000			0.272727
$122$	−1.82843	+	1.82843i	−0.165538	+	0.165538i
$123$		0			0
$124$		−	5.07107i		−	0.455395i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	2.00000	+	4.00000i	0.175412	+	0.350823i
$131$		−	5.65685i		−	0.494242i	−0.968985	−	0.247121i	$-0.920516\pi$
$131$		−	5.65685i		−	0.494242i	0.968985	−	0.247121i	$-0.0794845\pi$
$132$		0			0
$133$	0.485281	−	0.485281i	0.0420792	−	0.0420792i
$134$	−0.585786			−0.0506042
$135$		0			0
$136$	1.00000			0.0857493
$137$	13.4142	−	13.4142i	1.14605	−	1.14605i	0.158732	−	0.987322i	$-0.449259\pi$
$137$	13.4142	−	13.4142i	1.14605	−	1.14605i	0.987322	−	0.158732i	$-0.0507405\pi$
$138$		0			0
$139$			3.31371i			0.281065i	0.990076	+	0.140533i	$0.0448815\pi$
$139$			3.31371i			0.281065i	−0.990076	+	0.140533i	$0.955119\pi$
$140$	−0.585786	+	1.75736i	−0.0495080	+	0.148524i
$141$		0			0
$142$	4.00000	+	4.00000i	0.335673	+	0.335673i
$143$	−4.00000	−	4.00000i	−0.334497	−	0.334497i
$144$		0			0
$145$	−15.3137	+	7.65685i	−1.27173	+	0.635867i
$146$			0.343146i			0.0283989i
$147$		0			0
$148$	4.00000	−	4.00000i	0.328798	−	0.328798i
$149$	22.4853			1.84207			0.921033	−	0.389485i	$-0.127347\pi$
$149$	22.4853			1.84207			0.921033	+	0.389485i	$0.127347\pi$
$150$		0			0
$151$	−10.1421			−0.825355			−0.412678	−	0.910877i	$-0.635406\pi$
$151$	−10.1421			−0.825355			−0.412678	+	0.910877i	$0.635406\pi$
$152$	−0.585786	+	0.585786i	−0.0475136	+	0.0475136i
$153$		0			0
$154$		−	2.34315i		−	0.188816i
$155$	10.1421	−	5.07107i	0.814636	−	0.407318i
$156$		0			0
$157$	5.75736	+	5.75736i	0.459487	+	0.459487i	0.898487	−	0.439000i	$-0.144667\pi$
$157$	5.75736	+	5.75736i	0.459487	+	0.459487i	−0.439000	+	0.898487i	$0.644667\pi$
$158$	−0.414214	−	0.414214i	−0.0329531	−	0.0329531i
$159$		0			0
$160$	0.707107	−	2.12132i	0.0559017	−	0.167705i
$161$			4.20101i			0.331086i
$162$		0			0
$163$	15.6569	−	15.6569i	1.22634	−	1.22634i	0.261001	−	0.965339i	$-0.415947\pi$
$163$	15.6569	−	15.6569i	1.22634	−	1.22634i	0.965339	−	0.261001i	$-0.0840526\pi$
$164$	−8.82843			−0.689384
$165$		0			0
$166$	1.65685			0.128597
$167$	6.75736	−	6.75736i	0.522900	−	0.522900i	−0.395546	−	0.918446i	$-0.629445\pi$
$167$	6.75736	−	6.75736i	0.522900	−	0.522900i	0.918446	+	0.395546i	$0.129445\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$	1.00000	+	2.00000i	0.0766965	+	0.153393i
$171$		0			0
$172$	4.41421	+	4.41421i	0.336581	+	0.336581i
$173$	10.6569	+	10.6569i	0.810226	+	0.810226i	0.984667	−	0.174442i	$-0.0558121\pi$
$173$	10.6569	+	10.6569i	0.810226	+	0.810226i	−0.174442	+	0.984667i	$0.555812\pi$
$174$		0			0
$175$	−4.10051	+	0.585786i	−0.309969	+	0.0442813i
$176$			2.82843i			0.213201i
$177$		0			0
$178$	1.82843	−	1.82843i	0.137046	−	0.137046i
$179$	−1.75736			−0.131351			−0.0656756	−	0.997841i	$-0.520920\pi$
$179$	−1.75736			−0.131351			−0.0656756	+	0.997841i	$0.520920\pi$
$180$		0			0
$181$	0.242641			0.0180353			0.00901767	−	0.999959i	$-0.497130\pi$
$181$	0.242641			0.0180353			0.00901767	+	0.999959i	$0.497130\pi$
$182$	1.17157	−	1.17157i	0.0868428	−	0.0868428i
$183$		0			0
$184$		−	5.07107i		−	0.373844i
$185$	12.0000	+	4.00000i	0.882258	+	0.294086i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$		0			0
$190$	−1.75736	−	0.585786i	−0.127492	−	0.0424974i
$191$		−	0.686292i		−	0.0496583i	−0.999692	−	0.0248292i	$-0.992096\pi$
$191$		−	0.686292i		−	0.0496583i	0.999692	−	0.0248292i	$-0.00790418\pi$
$192$		0			0
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	−0.345208	−	0.938526i	$-0.612192\pi$
$193$	8.24264	−	8.24264i	0.593318	−	0.593318i	0.938526	+	0.345208i	$0.112192\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−6.31371			−0.450979
$197$	−7.82843	+	7.82843i	−0.557752	+	0.557752i	−0.928667	−	0.370915i	$-0.879044\pi$
$197$	−7.82843	+	7.82843i	−0.557752	+	0.557752i	0.370915	+	0.928667i	$0.379044\pi$
$198$		0			0
$199$			4.10051i			0.290677i	0.989382	+	0.145339i	$0.0464271\pi$
$199$			4.10051i			0.290677i	−0.989382	+	0.145339i	$0.953573\pi$
$200$	4.94975	−	0.707107i	0.350000	−	0.0500000i
$201$		0			0
$202$	12.7279	+	12.7279i	0.895533	+	0.895533i
$203$	4.48528	+	4.48528i	0.314805	+	0.314805i
$204$		0			0
$205$	−8.82843	−	17.6569i	−0.616604	−	1.23321i
$206$			4.48528i			0.312504i
$207$		0			0
$208$	−1.41421	+	1.41421i	−0.0980581	+	0.0980581i
$209$	2.34315			0.162079
$210$		0			0
$211$	26.1421			1.79970			0.899849	−	0.436201i	$-0.143676\pi$
$211$	26.1421			1.79970			0.899849	+	0.436201i	$0.143676\pi$
$212$	0.242641	−	0.242641i	0.0166646	−	0.0166646i
$213$		0			0
$214$		−	9.65685i		−	0.660129i
$215$	−4.41421	+	13.2426i	−0.301047	+	0.903141i
$216$		0			0
$217$	−2.97056	−	2.97056i	−0.201655	−	0.201655i
$218$	8.65685	+	8.65685i	0.586316	+	0.586316i
$219$		0			0
$220$	−5.65685	+	2.82843i	−0.381385	+	0.190693i
$221$		−	2.00000i		−	0.134535i
$222$		0			0
$223$	−16.8284	+	16.8284i	−1.12691	+	1.12691i	−0.136239	+	0.990676i	$0.543501\pi$
$223$	−16.8284	+	16.8284i	−1.12691	+	1.12691i	−0.990676	+	0.136239i	$0.956499\pi$
$224$	−0.828427			−0.0553516
$225$		0			0
$226$	−15.6569			−1.04148
$227$	7.17157	−	7.17157i	0.475994	−	0.475994i	−0.427854	−	0.903848i	$-0.640730\pi$
$227$	7.17157	−	7.17157i	0.475994	−	0.475994i	0.903848	+	0.427854i	$0.140730\pi$
$228$		0			0
$229$			1.31371i			0.0868123i	0.999058	+	0.0434062i	$0.0138209\pi$
$229$			1.31371i			0.0868123i	−0.999058	+	0.0434062i	$0.986179\pi$
$230$	10.1421	−	5.07107i	0.668753	−	0.334376i
$231$		0			0
$232$	−5.41421	−	5.41421i	−0.355461	−	0.355461i
$233$	0.100505	+	0.100505i	0.00658431	+	0.00658431i	0.710391	−	0.703807i	$-0.248518\pi$
$233$	0.100505	+	0.100505i	0.00658431	+	0.00658431i	−0.703807	+	0.710391i	$0.748518\pi$
$234$		0			0
$235$		0			0
$236$			10.7279i			0.698328i
$237$		0			0
$238$	0.585786	−	0.585786i	0.0379709	−	0.0379709i
$239$	−22.1421			−1.43226			−0.716128	−	0.697969i	$-0.754087\pi$
$239$	−22.1421			−1.43226			−0.716128	+	0.697969i	$0.754087\pi$
$240$		0			0
$241$	−18.4853			−1.19074			−0.595371	−	0.803451i	$-0.702995\pi$
$241$	−18.4853			−1.19074			−0.595371	+	0.803451i	$0.702995\pi$
$242$	−2.12132	+	2.12132i	−0.136364	+	0.136364i
$243$		0			0
$244$		−	2.58579i		−	0.165538i
$245$	−6.31371	−	12.6274i	−0.403368	−	0.806736i
$246$		0			0
$247$	1.17157	+	1.17157i	0.0745454	+	0.0745454i
$248$	3.58579	+	3.58579i	0.227698	+	0.227698i
$249$		0			0
$250$	6.36396	+	9.19239i	0.402492	+	0.581378i
$251$			2.92893i			0.184873i	0.995719	+	0.0924363i	$0.0294654\pi$
$251$			2.92893i			0.184873i	−0.995719	+	0.0924363i	$0.970535\pi$
$252$		0			0
$253$	−10.1421	+	10.1421i	−0.637631	+	0.637631i
$254$		0			0
$255$		0			0
$256$	1.00000			0.0625000
$257$	−17.6569	+	17.6569i	−1.10140	+	1.10140i	−0.107163	+	0.994241i	$0.534177\pi$
$257$	−17.6569	+	17.6569i	−1.10140	+	1.10140i	−0.994241	+	0.107163i	$0.965823\pi$
$258$		0			0
$259$		−	4.68629i		−	0.291192i
$260$	−4.24264	−	1.41421i	−0.263117	−	0.0877058i
$261$		0			0
$262$	4.00000	+	4.00000i	0.247121	+	0.247121i
$263$	16.1421	+	16.1421i	0.995367	+	0.995367i	0.999989	−	0.00462259i	$-0.00147142\pi$
$263$	16.1421	+	16.1421i	0.995367	+	0.995367i	−0.00462259	+	0.999989i	$0.501471\pi$
$264$		0			0
$265$	0.727922	+	0.242641i	0.0447159	+	0.0149053i
$266$			0.686292i			0.0420792i
$267$		0			0
$268$	0.414214	−	0.414214i	0.0253021	−	0.0253021i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$		0			0
$271$	−30.1421			−1.83100			−0.915502	−	0.402313i	$-0.868206\pi$
$271$	−30.1421			−1.83100			−0.915502	+	0.402313i	$0.868206\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$		0			0
$274$			18.9706i			1.14605i
$275$	−11.3137	−	8.48528i	−0.682242	−	0.511682i
$276$		0			0
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	0.909956	−	0.414704i	$-0.136115\pi$
$277$	8.24264	+	8.24264i	0.495252	+	0.495252i	−0.414704	+	0.909956i	$0.636115\pi$
$278$	−2.34315	−	2.34315i	−0.140533	−	0.140533i
$279$		0			0
$280$	−0.828427	−	1.65685i	−0.0495080	−	0.0990160i
$281$			0.242641i			0.0144747i	0.999974	+	0.00723736i	$0.00230374\pi$
$281$			0.242641i			0.0144747i	−0.999974	+	0.00723736i	$0.997696\pi$
$282$		0			0
$283$	−13.3137	+	13.3137i	−0.791418	+	0.791418i	−0.981725	−	0.190307i	$-0.939052\pi$
$283$	−13.3137	+	13.3137i	−0.791418	+	0.791418i	0.190307	+	0.981725i	$0.439052\pi$
$284$	−5.65685			−0.335673
$285$		0			0
$286$	5.65685			0.334497
$287$	−5.17157	+	5.17157i	−0.305268	+	0.305268i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	5.41421	−	16.2426i	0.317934	−	0.953801i
$291$		0			0
$292$	−0.242641	−	0.242641i	−0.0141995	−	0.0141995i
$293$	12.2426	+	12.2426i	0.715223	+	0.715223i	0.967623	−	0.252400i	$-0.0812199\pi$
$293$	12.2426	+	12.2426i	0.715223	+	0.715223i	−0.252400	+	0.967623i	$0.581220\pi$
$294$		0			0
$295$	−21.4558	+	10.7279i	−1.24921	+	0.624604i
$296$			5.65685i			0.328798i
$297$		0			0
$298$	−15.8995	+	15.8995i	−0.921033	+	0.921033i
$299$	−10.1421			−0.586535
$300$		0			0
$301$	5.17157			0.298085
$302$	7.17157	−	7.17157i	0.412678	−	0.412678i
$303$		0			0
$304$		−	0.828427i		−	0.0475136i
$305$	5.17157	−	2.58579i	0.296123	−	0.148062i
$306$		0			0
$307$	−2.89949	−	2.89949i	−0.165483	−	0.165483i	0.619508	−	0.784991i	$-0.287332\pi$
$307$	−2.89949	−	2.89949i	−0.165483	−	0.165483i	−0.784991	+	0.619508i	$0.787332\pi$
$308$	1.65685	+	1.65685i	0.0944080	+	0.0944080i
$309$		0			0
$310$	−3.58579	+	10.7574i	−0.203659	+	0.610977i
$311$		−	32.9706i		−	1.86959i	−0.355189	−	0.934795i	$-0.615583\pi$
$311$		−	32.9706i		−	1.86959i	0.355189	−	0.934795i	$-0.384417\pi$
$312$		0			0
$313$	2.58579	−	2.58579i	0.146157	−	0.146157i	−0.630242	−	0.776399i	$-0.717044\pi$
$313$	2.58579	−	2.58579i	0.146157	−	0.146157i	0.776399	+	0.630242i	$0.217044\pi$
$314$	−8.14214			−0.459487
$315$		0			0
$316$	0.585786			0.0329531
$317$	2.17157	−	2.17157i	0.121968	−	0.121968i	−0.643488	−	0.765456i	$-0.722513\pi$
$317$	2.17157	−	2.17157i	0.121968	−	0.121968i	0.765456	+	0.643488i	$0.222513\pi$
$318$		0			0
$319$			21.6569i			1.21255i
$320$	1.00000	+	2.00000i	0.0559017	+	0.111803i
$321$		0			0
$322$	−2.97056	−	2.97056i	−0.165543	−	0.165543i
$323$	0.585786	+	0.585786i	0.0325940	+	0.0325940i
$324$		0			0
$325$	−1.41421	−	9.89949i	−0.0784465	−	0.549125i
$326$			22.1421i			1.22634i
$327$		0			0
$328$	6.24264	−	6.24264i	0.344692	−	0.344692i
$329$		0			0
$330$		0			0
$331$	17.5147			0.962696			0.481348	−	0.876530i	$-0.340147\pi$
$331$	17.5147			0.962696			0.481348	+	0.876530i	$0.340147\pi$
$332$	−1.17157	+	1.17157i	−0.0642984	+	0.0642984i
$333$		0			0
$334$			9.55635i			0.522900i
$335$	1.24264	+	0.414214i	0.0678927	+	0.0226309i
$336$		0			0
$337$	−7.75736	−	7.75736i	−0.422570	−	0.422570i	0.463517	−	0.886088i	$-0.346587\pi$
$337$	−7.75736	−	7.75736i	−0.422570	−	0.422570i	−0.886088	+	0.463517i	$0.846587\pi$
$338$	−6.36396	−	6.36396i	−0.346154	−	0.346154i
$339$		0			0
$340$	−2.12132	−	0.707107i	−0.115045	−	0.0383482i
$341$		−	14.3431i		−	0.776725i
$342$		0			0
$343$	−7.79899	+	7.79899i	−0.421106	+	0.421106i
$344$	−6.24264			−0.336581
$345$		0			0
$346$	−15.0711			−0.810226
$347$	−17.3137	+	17.3137i	−0.929449	+	0.929449i	−0.997670	−	0.0682216i	$-0.978268\pi$
$347$	−17.3137	+	17.3137i	−0.929449	+	0.929449i	0.0682216	+	0.997670i	$0.478268\pi$
$348$		0			0
$349$			16.6274i			0.890045i	0.895519	+	0.445023i	$0.146804\pi$
$349$			16.6274i			0.890045i	−0.895519	+	0.445023i	$0.853196\pi$
$350$	2.48528	−	3.31371i	0.132844	−	0.177125i
$351$		0			0
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	13.6569	+	13.6569i	0.726881	+	0.726881i	0.969997	−	0.243116i	$-0.0781696\pi$
$353$	13.6569	+	13.6569i	0.726881	+	0.726881i	−0.243116	+	0.969997i	$0.578170\pi$
$354$		0			0
$355$	−5.65685	−	11.3137i	−0.300235	−	0.600469i
$356$			2.58579i			0.137046i
$357$		0			0
$358$	1.24264	−	1.24264i	0.0656756	−	0.0656756i
$359$	−34.1421			−1.80195			−0.900976	−	0.433868i	$-0.857148\pi$
$359$	−34.1421			−1.80195			−0.900976	+	0.433868i	$0.857148\pi$
$360$		0			0
$361$	18.3137			0.963879
$362$	−0.171573	+	0.171573i	−0.00901767	+	0.00901767i
$363$		0			0
$364$			1.65685i			0.0868428i
$365$	0.242641	−	0.727922i	0.0127004	−	0.0381012i
$366$		0			0
$367$	10.7279	+	10.7279i	0.559993	+	0.559993i	0.929305	−	0.369312i	$-0.120407\pi$
$367$	10.7279	+	10.7279i	0.559993	+	0.559993i	−0.369312	+	0.929305i	$0.620407\pi$
$368$	3.58579	+	3.58579i	0.186922	+	0.186922i
$369$		0			0
$370$	−11.3137	+	5.65685i	−0.588172	+	0.294086i
$371$		−	0.284271i		−	0.0147586i
$372$		0			0
$373$	−2.72792	+	2.72792i	−0.141246	+	0.141246i	−0.774194	−	0.632948i	$-0.781845\pi$
$373$	−2.72792	+	2.72792i	−0.141246	+	0.141246i	0.632948	+	0.774194i	$0.281845\pi$
$374$	2.82843			0.146254
$375$		0			0
$376$		0			0
$377$	−10.8284	+	10.8284i	−0.557692	+	0.557692i
$378$		0			0
$379$			5.85786i			0.300898i	0.988618	+	0.150449i	$0.0480720\pi$
$379$			5.85786i			0.300898i	−0.988618	+	0.150449i	$0.951928\pi$
$380$	1.65685	−	0.828427i	0.0849948	−	0.0424974i
$381$		0			0
$382$	0.485281	+	0.485281i	0.0248292	+	0.0248292i
$383$	18.9706	+	18.9706i	0.969350	+	0.969350i	0.999544	−	0.0301936i	$-0.00961238\pi$
$383$	18.9706	+	18.9706i	0.969350	+	0.969350i	−0.0301936	+	0.999544i	$0.509612\pi$
$384$		0			0
$385$	−1.65685	+	4.97056i	−0.0844411	+	0.253323i
$386$			11.6569i			0.593318i
$387$		0			0
$388$	1.41421	−	1.41421i	0.0717958	−	0.0717958i
$389$	12.8284			0.650427			0.325214	−	0.945641i	$-0.394564\pi$
$389$	12.8284			0.650427			0.325214	+	0.945641i	$0.394564\pi$
$390$		0			0
$391$	−5.07107			−0.256455
$392$	4.46447	−	4.46447i	0.225490	−	0.225490i
$393$		0			0
$394$		−	11.0711i		−	0.557752i
$395$	0.585786	+	1.17157i	0.0294741	+	0.0589482i
$396$		0			0
$397$	−15.0711	−	15.0711i	−0.756395	−	0.756395i	0.219269	−	0.975664i	$-0.429633\pi$
$397$	−15.0711	−	15.0711i	−0.756395	−	0.756395i	−0.975664	+	0.219269i	$0.929633\pi$
$398$	−2.89949	−	2.89949i	−0.145339	−	0.145339i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$			29.3137i			1.46386i	0.681382	+	0.731928i	$0.261379\pi$
$401$			29.3137i			1.46386i	−0.681382	+	0.731928i	$0.738621\pi$
$402$		0			0
$403$	7.17157	−	7.17157i	0.357241	−	0.357241i
$404$	−18.0000			−0.895533
$405$		0			0
$406$	−6.34315			−0.314805
$407$	11.3137	−	11.3137i	0.560800	−	0.560800i
$408$		0			0
$409$			6.34315i			0.313648i	0.987627	+	0.156824i	$0.0501256\pi$
$409$			6.34315i			0.313648i	−0.987627	+	0.156824i	$0.949874\pi$
$410$	18.7279	+	6.24264i	0.924906	+	0.308302i
$411$		0			0
$412$	−3.17157	−	3.17157i	−0.156252	−	0.156252i
$413$	6.28427	+	6.28427i	0.309229	+	0.309229i
$414$		0			0
$415$	−3.51472	−	1.17157i	−0.172531	−	0.0575103i
$416$		−	2.00000i		−	0.0980581i
$417$		0			0
$418$	−1.65685	+	1.65685i	−0.0810394	+	0.0810394i
$419$	−6.82843			−0.333590			−0.166795	−	0.985992i	$-0.553342\pi$
$419$	−6.82843			−0.333590			−0.166795	+	0.985992i	$0.553342\pi$
$420$		0			0
$421$	−4.82843			−0.235323			−0.117662	−	0.993054i	$-0.537540\pi$
$421$	−4.82843			−0.235323			−0.117662	+	0.993054i	$0.537540\pi$
$422$	−18.4853	+	18.4853i	−0.899849	+	0.899849i
$423$		0			0
$424$			0.343146i			0.0166646i
$425$	−0.707107	−	4.94975i	−0.0342997	−	0.240098i
$426$		0			0
$427$	−1.51472	−	1.51472i	−0.0733024	−	0.0733024i
$428$	6.82843	+	6.82843i	0.330064	+	0.330064i
$429$		0			0
$430$	−6.24264	−	12.4853i	−0.301047	−	0.602094i
$431$		−	24.9706i		−	1.20279i	−0.798952	−	0.601395i	$-0.794612\pi$
$431$		−	24.9706i		−	1.20279i	0.798952	−	0.601395i	$-0.205388\pi$
$432$		0			0
$433$	11.1421	−	11.1421i	0.535457	−	0.535457i	−0.386734	−	0.922191i	$-0.626397\pi$
$433$	11.1421	−	11.1421i	0.535457	−	0.535457i	0.922191	+	0.386734i	$0.126397\pi$
$434$	4.20101			0.201655
$435$		0			0
$436$	−12.2426			−0.586316
$437$	2.97056	−	2.97056i	0.142101	−	0.142101i
$438$		0			0
$439$			26.7279i			1.27565i	0.770180	+	0.637827i	$0.220167\pi$
$439$			26.7279i			1.27565i	−0.770180	+	0.637827i	$0.779833\pi$
$440$	2.00000	−	6.00000i	0.0953463	−	0.286039i
$441$		0			0
$442$	1.41421	+	1.41421i	0.0672673	+	0.0672673i
$443$	−13.7574	−	13.7574i	−0.653632	−	0.653632i	0.300234	−	0.953866i	$-0.402935\pi$
$443$	−13.7574	−	13.7574i	−0.653632	−	0.653632i	−0.953866	+	0.300234i	$0.902935\pi$
$444$		0			0
$445$	−5.17157	+	2.58579i	−0.245156	+	0.122578i
$446$		−	23.7990i		−	1.12691i
$447$		0			0
$448$	0.585786	−	0.585786i	0.0276758	−	0.0276758i
$449$	−0.343146			−0.0161940			−0.00809702	−	0.999967i	$-0.502577\pi$
$449$	−0.343146			−0.0161940			−0.00809702	+	0.999967i	$0.502577\pi$
$450$		0			0
$451$	−24.9706			−1.17582
$452$	11.0711	−	11.0711i	0.520739	−	0.520739i
$453$		0			0
$454$			10.1421i			0.475994i
$455$	−3.31371	+	1.65685i	−0.155349	+	0.0776745i
$456$		0			0
$457$	−13.4853	−	13.4853i	−0.630815	−	0.630815i	0.317458	−	0.948272i	$-0.397171\pi$
$457$	−13.4853	−	13.4853i	−0.630815	−	0.630815i	−0.948272	+	0.317458i	$0.897171\pi$
$458$	−0.928932	−	0.928932i	−0.0434062	−	0.0434062i
$459$		0			0
$460$	−3.58579	+	10.7574i	−0.167188	+	0.501564i
$461$			22.4853i			1.04724i	0.851951	+	0.523622i	$0.175420\pi$
$461$			22.4853i			1.04724i	−0.851951	+	0.523622i	$0.824580\pi$
$462$		0			0
$463$	10.9706	−	10.9706i	0.509845	−	0.509845i	−0.404634	−	0.914479i	$-0.632601\pi$
$463$	10.9706	−	10.9706i	0.509845	−	0.509845i	0.914479	+	0.404634i	$0.132601\pi$
$464$	7.65685			0.355461
$465$		0			0
$466$	−0.142136			−0.00658431
$467$	−30.1421	+	30.1421i	−1.39481	+	1.39481i	−0.580679	+	0.814132i	$0.697213\pi$
$467$	−30.1421	+	30.1421i	−1.39481	+	1.39481i	−0.814132	+	0.580679i	$0.802787\pi$
$468$		0			0
$469$		−	0.485281i		−	0.0224082i
$470$		0			0
$471$		0			0
$472$	−7.58579	−	7.58579i	−0.349164	−	0.349164i
$473$	12.4853	+	12.4853i	0.574074	+	0.574074i
$474$		0			0
$475$	3.31371	+	2.48528i	0.152043	+	0.114033i
$476$			0.828427i			0.0379709i
$477$		0			0
$478$	15.6569	−	15.6569i	0.716128	−	0.716128i
$479$	8.97056			0.409875			0.204938	−	0.978775i	$-0.434301\pi$
$479$	8.97056			0.409875			0.204938	+	0.978775i	$0.434301\pi$
$480$		0			0
$481$	11.3137			0.515861
$482$	13.0711	−	13.0711i	0.595371	−	0.595371i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	4.24264	+	1.41421i	0.192648	+	0.0642161i
$486$		0			0
$487$	28.2843	+	28.2843i	1.28168	+	1.28168i	0.939710	+	0.341973i	$0.111095\pi$
$487$	28.2843	+	28.2843i	1.28168	+	1.28168i	0.341973	+	0.939710i	$0.388905\pi$
$488$	1.82843	+	1.82843i	0.0827690	+	0.0827690i
$489$		0			0
$490$	13.3934	+	4.46447i	0.605052	+	0.201684i
$491$		−	10.7279i		−	0.484144i	−0.970258	−	0.242072i	$-0.922173\pi$
$491$		−	10.7279i		−	0.484144i	0.970258	−	0.242072i	$-0.0778271\pi$
$492$		0			0
$493$	−5.41421	+	5.41421i	−0.243844	+	0.243844i
$494$	−1.65685			−0.0745454
$495$		0			0
$496$	−5.07107			−0.227698
$497$	−3.31371	+	3.31371i	−0.148640	+	0.148640i
$498$		0			0
$499$		−	8.48528i		−	0.379853i	−0.981798	−	0.189927i	$-0.939175\pi$
$499$		−	8.48528i		−	0.379853i	0.981798	−	0.189927i	$-0.0608250\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$		0			0
$502$	−2.07107	−	2.07107i	−0.0924363	−	0.0924363i
$503$	22.8995	+	22.8995i	1.02104	+	1.02104i	0.999774	+	0.0212641i	$0.00676909\pi$
$503$	22.8995	+	22.8995i	1.02104	+	1.02104i	0.0212641	+	0.999774i	$0.493231\pi$
$504$		0			0
$505$	−18.0000	−	36.0000i	−0.800989	−	1.60198i
$506$		−	14.3431i		−	0.637631i
$507$		0			0
$508$		0			0
$509$	13.5147			0.599029			0.299515	−	0.954092i	$-0.403175\pi$
$509$	13.5147			0.599029			0.299515	+	0.954092i	$0.403175\pi$
$510$		0			0
$511$	−0.284271			−0.0125754
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	24.9706i		−	1.10140i
$515$	3.17157	−	9.51472i	0.139756	−	0.419269i
$516$		0			0
$517$		0			0
$518$	3.31371	+	3.31371i	0.145596	+	0.145596i
$519$		0			0
$520$	4.00000	−	2.00000i	0.175412	−	0.0877058i
$521$			14.0000i			0.613351i	0.951814	+	0.306676i	$0.0992167\pi$
$521$			14.0000i			0.613351i	−0.951814	+	0.306676i	$0.900783\pi$
$522$		0			0
$523$	−7.72792	+	7.72792i	−0.337918	+	0.337918i	−0.855583	−	0.517665i	$-0.826801\pi$
$523$	−7.72792	+	7.72792i	−0.337918	+	0.337918i	0.517665	+	0.855583i	$0.326801\pi$
$524$	−5.65685			−0.247121
$525$		0			0
$526$	−22.8284			−0.995367
$527$	3.58579	−	3.58579i	0.156199	−	0.156199i
$528$		0			0
$529$			2.71573i			0.118075i
$530$	−0.686292	+	0.343146i	−0.0298106	+	0.0149053i
$531$		0			0
$532$	−0.485281	−	0.485281i	−0.0210396	−	0.0210396i
$533$	−12.4853	−	12.4853i	−0.540798	−	0.540798i
$534$		0			0
$535$	−6.82843	+	20.4853i	−0.295219	+	0.885656i
$536$			0.585786i			0.0253021i
$537$		0			0
$538$	−1.41421	+	1.41421i	−0.0609711	+	0.0609711i
$539$	−17.8579			−0.769193
$540$		0			0
$541$	−10.5858			−0.455119			−0.227559	−	0.973764i	$-0.573075\pi$
$541$	−10.5858			−0.455119			−0.227559	+	0.973764i	$0.573075\pi$
$542$	21.3137	−	21.3137i	0.915502	−	0.915502i
$543$		0			0
$544$		−	1.00000i		−	0.0428746i
$545$	−12.2426	−	24.4853i	−0.524417	−	1.04883i
$546$		0			0
$547$	20.8284	+	20.8284i	0.890559	+	0.890559i	0.994576	−	0.104016i	$-0.0331694\pi$
$547$	20.8284	+	20.8284i	0.890559	+	0.890559i	−0.104016	+	0.994576i	$0.533169\pi$
$548$	−13.4142	−	13.4142i	−0.573027	−	0.573027i
$549$		0			0
$550$	14.0000	−	2.00000i	0.596962	−	0.0852803i
$551$		−	6.34315i		−	0.270227i
$552$		0			0
$553$	0.343146	−	0.343146i	0.0145920	−	0.0145920i
$554$	−11.6569			−0.495252
$555$		0			0
$556$	3.31371			0.140533
$557$	−13.8995	+	13.8995i	−0.588941	+	0.588941i	−0.937344	−	0.348404i	$-0.886724\pi$
$557$	−13.8995	+	13.8995i	−0.588941	+	0.588941i	0.348404	+	0.937344i	$0.386724\pi$
$558$		0			0
$559$			12.4853i			0.528071i
$560$	1.75736	+	0.585786i	0.0742620	+	0.0247540i
$561$		0			0
$562$	−0.171573	−	0.171573i	−0.00723736	−	0.00723736i
$563$	7.51472	+	7.51472i	0.316708	+	0.316708i	0.847501	−	0.530794i	$-0.178106\pi$
$563$	7.51472	+	7.51472i	0.316708	+	0.316708i	−0.530794	+	0.847501i	$0.678106\pi$
$564$		0			0
$565$	33.2132	+	11.0711i	1.39729	+	0.465763i
$566$		−	18.8284i		−	0.791418i
$567$		0			0
$568$	4.00000	−	4.00000i	0.167836	−	0.167836i
$569$	14.1005			0.591124			0.295562	−	0.955324i	$-0.404493\pi$
$569$	14.1005			0.591124			0.295562	+	0.955324i	$0.404493\pi$
$570$		0			0
$571$	42.4264			1.77549			0.887745	−	0.460336i	$-0.152271\pi$
$571$	42.4264			1.77549			0.887745	+	0.460336i	$0.152271\pi$
$572$	−4.00000	+	4.00000i	−0.167248	+	0.167248i
$573$		0			0
$574$		−	7.31371i		−	0.305268i
$575$	−25.1005	+	3.58579i	−1.04676	+	0.149538i
$576$		0			0
$577$	−5.82843	−	5.82843i	−0.242641	−	0.242641i	0.575301	−	0.817942i	$-0.304885\pi$
$577$	−5.82843	−	5.82843i	−0.242641	−	0.242641i	−0.817942	+	0.575301i	$0.804885\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$	7.65685	+	15.3137i	0.317934	+	0.635867i
$581$			1.37258i			0.0569443i
$582$		0			0
$583$	0.686292	−	0.686292i	0.0284233	−	0.0284233i
$584$	0.343146			0.0141995
$585$		0			0
$586$	−17.3137			−0.715223
$587$	4.58579	−	4.58579i	0.189276	−	0.189276i	−0.606107	−	0.795383i	$-0.707270\pi$
$587$	4.58579	−	4.58579i	0.189276	−	0.189276i	0.795383	+	0.606107i	$0.207270\pi$
$588$		0			0
$589$			4.20101i			0.173100i
$590$	7.58579	−	22.7574i	0.312302	−	0.936906i
$591$		0			0
$592$	−4.00000	−	4.00000i	−0.164399	−	0.164399i
$593$	3.51472	+	3.51472i	0.144332	+	0.144332i	0.775581	−	0.631248i	$-0.217457\pi$
$593$	3.51472	+	3.51472i	0.144332	+	0.144332i	−0.631248	+	0.775581i	$0.717457\pi$
$594$		0			0
$595$	−1.65685	+	0.828427i	−0.0679244	+	0.0339622i
$596$		−	22.4853i		−	0.921033i
$597$		0			0
$598$	7.17157	−	7.17157i	0.293267	−	0.293267i
$599$	12.4853			0.510135			0.255067	−	0.966923i	$-0.417902\pi$
$599$	12.4853			0.510135			0.255067	+	0.966923i	$0.417902\pi$
$600$		0			0
$601$	3.45584			0.140967			0.0704834	−	0.997513i	$-0.477546\pi$
$601$	3.45584			0.140967			0.0704834	+	0.997513i	$0.477546\pi$
$602$	−3.65685	+	3.65685i	−0.149042	+	0.149042i
$603$		0			0
$604$			10.1421i			0.412678i
$605$	6.00000	−	3.00000i	0.243935	−	0.121967i
$606$		0			0
$607$	−16.9706	−	16.9706i	−0.688814	−	0.688814i	0.273156	−	0.961970i	$-0.411933\pi$
$607$	−16.9706	−	16.9706i	−0.688814	−	0.688814i	−0.961970	+	0.273156i	$0.911933\pi$
$608$	0.585786	+	0.585786i	0.0237568	+	0.0237568i
$609$		0			0
$610$	−1.82843	+	5.48528i	−0.0740309	+	0.222093i
$611$		0			0
$612$		0			0
$613$	8.72792	−	8.72792i	0.352517	−	0.352517i	−0.508528	−	0.861045i	$-0.669810\pi$
$613$	8.72792	−	8.72792i	0.352517	−	0.352517i	0.861045	+	0.508528i	$0.169810\pi$
$614$	4.10051			0.165483
$615$		0			0
$616$	−2.34315			−0.0944080
$617$	23.4142	−	23.4142i	0.942621	−	0.942621i	−0.0558201	−	0.998441i	$-0.517777\pi$
$617$	23.4142	−	23.4142i	0.942621	−	0.942621i	0.998441	+	0.0558201i	$0.0177773\pi$
$618$		0			0
$619$			23.3137i			0.937057i	0.883448	+	0.468529i	$0.155216\pi$
$619$			23.3137i			0.937057i	−0.883448	+	0.468529i	$0.844784\pi$
$620$	−5.07107	−	10.1421i	−0.203659	−	0.407318i
$621$		0			0
$622$	23.3137	+	23.3137i	0.934795	+	0.934795i
$623$	1.51472	+	1.51472i	0.0606859	+	0.0606859i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$			3.65685i			0.146157i
$627$		0			0
$628$	5.75736	−	5.75736i	0.229744	−	0.229744i
$629$	5.65685			0.225554
$630$		0			0
$631$	10.1421			0.403752			0.201876	−	0.979411i	$-0.435296\pi$
$631$	10.1421			0.403752			0.201876	+	0.979411i	$0.435296\pi$
$632$	−0.414214	+	0.414214i	−0.0164765	+	0.0164765i
$633$		0			0
$634$			3.07107i			0.121968i
$635$		0			0
$636$		0			0
$637$	−8.92893	−	8.92893i	−0.353777	−	0.353777i
$638$	−15.3137	−	15.3137i	−0.606276	−	0.606276i
$639$		0			0
$640$	−2.12132	−	0.707107i	−0.0838525	−	0.0279508i
$641$			39.9411i			1.57758i	0.614663	+	0.788790i	$0.289292\pi$
$641$			39.9411i			1.57758i	−0.614663	+	0.788790i	$0.710708\pi$
$642$		0			0
$643$	12.6274	−	12.6274i	0.497977	−	0.497977i	−0.412831	−	0.910808i	$-0.635460\pi$
$643$	12.6274	−	12.6274i	0.497977	−	0.497977i	0.910808	+	0.412831i	$0.135460\pi$
$644$	4.20101			0.165543
$645$		0			0
$646$	−0.828427			−0.0325940
$647$	15.1716	−	15.1716i	0.596456	−	0.596456i	−0.342912	−	0.939368i	$-0.611413\pi$
$647$	15.1716	−	15.1716i	0.596456	−	0.596456i	0.939368	+	0.342912i	$0.111413\pi$
$648$		0			0
$649$			30.3431i			1.19107i
$650$	8.00000	+	6.00000i	0.313786	+	0.235339i
$651$		0			0
$652$	−15.6569	−	15.6569i	−0.613170	−	0.613170i
$653$	2.31371	+	2.31371i	0.0905424	+	0.0905424i	0.750927	−	0.660385i	$-0.229607\pi$
$653$	2.31371	+	2.31371i	0.0905424	+	0.0905424i	−0.660385	+	0.750927i	$0.729607\pi$
$654$		0			0
$655$	−5.65685	−	11.3137i	−0.221032	−	0.442063i
$656$			8.82843i			0.344692i
$657$		0			0
$658$		0			0
$659$	−3.89949			−0.151903			−0.0759514	−	0.997112i	$-0.524199\pi$
$659$	−3.89949			−0.151903			−0.0759514	+	0.997112i	$0.524199\pi$
$660$		0			0
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	−12.3848	+	12.3848i	−0.481348	+	0.481348i
$663$		0			0
$664$		−	1.65685i		−	0.0642984i
$665$	0.485281	−	1.45584i	0.0188184	−	0.0564552i
$666$		0			0
$667$	27.4558	+	27.4558i	1.06309	+	1.06309i
$668$	−6.75736	−	6.75736i	−0.261450	−	0.261450i
$669$		0			0
$670$	−1.17157	+	0.585786i	−0.0452618	+	0.0226309i
$671$		−	7.31371i		−	0.282343i
$672$		0			0
$673$	8.72792	−	8.72792i	0.336437	−	0.336437i	−0.518588	−	0.855024i	$-0.673542\pi$
$673$	8.72792	−	8.72792i	0.336437	−	0.336437i	0.855024	+	0.518588i	$0.173542\pi$
$674$	10.9706			0.422570
$675$		0			0
$676$	9.00000			0.346154
$677$	−17.4853	+	17.4853i	−0.672014	+	0.672014i	−0.958180	−	0.286166i	$-0.907619\pi$
$677$	−17.4853	+	17.4853i	−0.672014	+	0.672014i	0.286166	+	0.958180i	$0.407619\pi$
$678$		0			0
$679$		−	1.65685i		−	0.0635842i
$680$	2.00000	−	1.00000i	0.0766965	−	0.0383482i
$681$		0			0
$682$	10.1421	+	10.1421i	0.388362	+	0.388362i
$683$	14.3431	+	14.3431i	0.548825	+	0.548825i	0.926101	−	0.377276i	$-0.123139\pi$
$683$	14.3431	+	14.3431i	0.548825	+	0.548825i	−0.377276	+	0.926101i	$0.623139\pi$
$684$		0			0
$685$	13.4142	−	40.2426i	0.512531	−	1.53759i
$686$		−	11.0294i		−	0.421106i
$687$		0			0
$688$	4.41421	−	4.41421i	0.168290	−	0.168290i
$689$	0.686292			0.0261456
$690$		0			0
$691$	47.7990			1.81836			0.909180	−	0.416404i	$-0.136710\pi$
$691$	47.7990			1.81836			0.909180	+	0.416404i	$0.136710\pi$
$692$	10.6569	−	10.6569i	0.405113	−	0.405113i
$693$		0			0
$694$		−	24.4853i		−	0.929449i
$695$	3.31371	+	6.62742i	0.125696	+	0.251392i
$696$		0			0
$697$	−6.24264	−	6.24264i	−0.236457	−	0.236457i
$698$	−11.7574	−	11.7574i	−0.445023	−	0.445023i
$699$		0			0
$700$	0.585786	+	4.10051i	0.0221406	+	0.154985i
$701$			17.5147i			0.661522i	0.943715	+	0.330761i	$0.107305\pi$
$701$			17.5147i			0.661522i	−0.943715	+	0.330761i	$0.892695\pi$
$702$		0			0
$703$	−3.31371	+	3.31371i	−0.124979	+	0.124979i
$704$	2.82843			0.106600
$705$		0			0
$706$	−19.3137			−0.726881
$707$	−10.5442	+	10.5442i	−0.396554	+	0.396554i
$708$		0			0
$709$			11.2721i			0.423332i	0.977342	+	0.211666i	$0.0678889\pi$
$709$			11.2721i			0.423332i	−0.977342	+	0.211666i	$0.932111\pi$
$710$	12.0000	+	4.00000i	0.450352	+	0.150117i
$711$		0			0
$712$	−1.82843	−	1.82843i	−0.0685232	−	0.0685232i
$713$	−18.1838	−	18.1838i	−0.680987	−	0.680987i
$714$		0			0
$715$	−12.0000	−	4.00000i	−0.448775	−	0.149592i
$716$			1.75736i			0.0656756i
$717$		0			0
$718$	24.1421	−	24.1421i	0.900976	−	0.900976i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−3.71573			−0.138381
$722$	−12.9497	+	12.9497i	−0.481940	+	0.481940i
$723$		0			0
$724$		−	0.242641i		−	0.00901767i
$725$	−22.9706	+	30.6274i	−0.853105	+	1.13747i
$726$		0			0
$727$	−4.48528	−	4.48528i	−0.166350	−	0.166350i	0.619023	−	0.785373i	$-0.287529\pi$
$727$	−4.48528	−	4.48528i	−0.166350	−	0.166350i	−0.785373	+	0.619023i	$0.787529\pi$
$728$	−1.17157	−	1.17157i	−0.0434214	−	0.0434214i
$729$		0			0
$730$	0.343146	+	0.686292i	0.0127004	+	0.0254008i
$731$			6.24264i			0.230892i
$732$		0			0
$733$	34.5269	−	34.5269i	1.27528	−	1.27528i	0.332002	−	0.943279i	$-0.392276\pi$
$733$	34.5269	−	34.5269i	1.27528	−	1.27528i	0.943279	−	0.332002i	$-0.107724\pi$
$734$	−15.1716			−0.559993
$735$		0			0
$736$	−5.07107			−0.186922
$737$	1.17157	−	1.17157i	0.0431554	−	0.0431554i
$738$		0			0
$739$			40.2843i			1.48188i	0.671571	+	0.740940i	$0.265620\pi$
$739$			40.2843i			1.48188i	−0.671571	+	0.740940i	$0.734380\pi$
$740$	4.00000	−	12.0000i	0.147043	−	0.441129i
$741$		0			0
$742$	0.201010	+	0.201010i	0.00737931	+	0.00737931i
$743$	−26.0711	−	26.0711i	−0.956455	−	0.956455i	0.0426360	−	0.999091i	$-0.486424\pi$
$743$	−26.0711	−	26.0711i	−0.956455	−	0.956455i	−0.999091	+	0.0426360i	$0.986424\pi$
$744$		0			0
$745$	44.9706	−	22.4853i	1.64759	−	0.823797i
$746$		−	3.85786i		−	0.141246i
$747$		0			0
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	8.00000			0.292314
$750$		0			0
$751$	−21.2721			−0.776229			−0.388115	−	0.921611i	$-0.626874\pi$
$751$	−21.2721			−0.776229			−0.388115	+	0.921611i	$0.626874\pi$
$752$		0			0
$753$		0			0
$754$		−	15.3137i		−	0.557692i
$755$	−20.2843	+	10.1421i	−0.738220	+	0.369110i
$756$		0			0
$757$	−15.8995	−	15.8995i	−0.577877	−	0.577877i	0.356441	−	0.934318i	$-0.383990\pi$
$757$	−15.8995	−	15.8995i	−0.577877	−	0.577877i	−0.934318	+	0.356441i	$0.883990\pi$
$758$	−4.14214	−	4.14214i	−0.150449	−	0.150449i
$759$		0			0
$760$	−0.585786	+	1.75736i	−0.0212487	+	0.0637461i
$761$		−	16.9289i		−	0.613673i	−0.951762	−	0.306837i	$-0.900729\pi$
$761$		−	16.9289i		−	0.613673i	0.951762	−	0.306837i	$-0.0992705\pi$
$762$		0			0
$763$	−7.17157	+	7.17157i	−0.259628	+	0.259628i
$764$	−0.686292			−0.0248292
$765$		0			0
$766$	−26.8284			−0.969350
$767$	−15.1716	+	15.1716i	−0.547814	+	0.547814i
$768$		0			0
$769$		−	26.0000i		−	0.937584i	−0.883309	−	0.468792i	$-0.844689\pi$
$769$		−	26.0000i		−	0.937584i	0.883309	−	0.468792i	$-0.155311\pi$
$770$	−2.34315	−	4.68629i	−0.0844411	−	0.168882i
$771$		0			0
$772$	−8.24264	−	8.24264i	−0.296659	−	0.296659i
$773$	37.3553	+	37.3553i	1.34358	+	1.34358i	0.892469	+	0.451110i	$0.148972\pi$
$773$	37.3553	+	37.3553i	1.34358	+	1.34358i	0.451110	+	0.892469i	$0.351028\pi$
$774$		0			0
$775$	15.2132	−	20.2843i	0.546474	−	0.728633i
$776$			2.00000i			0.0717958i
$777$		0			0
$778$	−9.07107	+	9.07107i	−0.325214	+	0.325214i
$779$	7.31371			0.262041
$780$		0			0
$781$	−16.0000			−0.572525
$782$	3.58579	−	3.58579i	0.128227	−	0.128227i
$783$		0			0
$784$			6.31371i			0.225490i
$785$	17.2721	+	5.75736i	0.616467	+	0.205489i
$786$		0			0
$787$	−7.51472	−	7.51472i	−0.267871	−	0.267871i	0.560371	−	0.828242i	$-0.310659\pi$
$787$	−7.51472	−	7.51472i	−0.267871	−	0.267871i	−0.828242	+	0.560371i	$0.810659\pi$
$788$	7.82843	+	7.82843i	0.278876	+	0.278876i
$789$		0			0
$790$	−1.24264	−	0.414214i	−0.0442112	−	0.0147371i
$791$		−	12.9706i		−	0.461180i
$792$		0			0
$793$	3.65685	−	3.65685i	0.129859	−	0.129859i
$794$	21.3137			0.756395
$795$		0			0
$796$	4.10051			0.145339
$797$	−9.55635	+	9.55635i	−0.338503	+	0.338503i	−0.855804	−	0.517301i	$-0.826937\pi$
$797$	−9.55635	+	9.55635i	−0.338503	+	0.338503i	0.517301	+	0.855804i	$0.326937\pi$
$798$		0			0
$799$		0			0
$800$	−0.707107	−	4.94975i	−0.0250000	−	0.175000i
$801$		0			0
$802$	−20.7279	−	20.7279i	−0.731928	−	0.731928i
$803$	−0.686292	−	0.686292i	−0.0242187	−	0.0242187i
$804$		0			0
$805$	4.20101	+	8.40202i	0.148066	+	0.296132i
$806$			10.1421i			0.357241i
$807$		0			0
$808$	12.7279	−	12.7279i	0.447767	−	0.447767i
$809$	−40.1421			−1.41132			−0.705661	−	0.708549i	$-0.749350\pi$
$809$	−40.1421			−1.41132			−0.705661	+	0.708549i	$0.749350\pi$
$810$		0			0
$811$	22.1421			0.777516			0.388758	−	0.921340i	$-0.372904\pi$
$811$	22.1421			0.777516			0.388758	+	0.921340i	$0.372904\pi$
$812$	4.48528	−	4.48528i	0.157403	−	0.157403i
$813$		0			0
$814$			16.0000i			0.560800i
$815$	15.6569	−	46.9706i	0.548436	−	1.64531i
$816$		0			0
$817$	−3.65685	−	3.65685i	−0.127937	−	0.127937i
$818$	−4.48528	−	4.48528i	−0.156824	−	0.156824i
$819$		0			0
$820$	−17.6569	+	8.82843i	−0.616604	+	0.308302i
$821$		−	56.9706i		−	1.98829i	−0.108071	−	0.994143i	$-0.534467\pi$
$821$		−	56.9706i		−	1.98829i	0.108071	−	0.994143i	$-0.465533\pi$
$822$		0			0
$823$	9.55635	−	9.55635i	0.333113	−	0.333113i	−0.520654	−	0.853768i	$-0.674312\pi$
$823$	9.55635	−	9.55635i	0.333113	−	0.333113i	0.853768	+	0.520654i	$0.174312\pi$
$824$	4.48528			0.156252
$825$		0			0
$826$	−8.88730			−0.309229
$827$	−24.8284	+	24.8284i	−0.863369	+	0.863369i	−0.991728	−	0.128359i	$-0.959029\pi$
$827$	−24.8284	+	24.8284i	−0.863369	+	0.863369i	0.128359	+	0.991728i	$0.459029\pi$
$828$		0			0
$829$		−	8.82843i		−	0.306624i	−0.988178	−	0.153312i	$-0.951006\pi$
$829$		−	8.82843i		−	0.306624i	0.988178	−	0.153312i	$-0.0489939\pi$
$830$	3.31371	−	1.65685i	0.115021	−	0.0575103i
$831$		0			0
$832$	1.41421	+	1.41421i	0.0490290	+	0.0490290i
$833$	−4.46447	−	4.46447i	−0.154685	−	0.154685i
$834$		0			0
$835$	6.75736	−	20.2721i	0.233848	−	0.701544i
$836$		−	2.34315i		−	0.0810394i
$837$		0			0
$838$	4.82843	−	4.82843i	0.166795	−	0.166795i
$839$	38.4853			1.32866			0.664330	−	0.747440i	$-0.268717\pi$
$839$	38.4853			1.32866			0.664330	+	0.747440i	$0.268717\pi$
$840$		0			0
$841$	29.6274			1.02164
$842$	3.41421	−	3.41421i	0.117662	−	0.117662i
$843$		0			0
$844$		−	26.1421i		−	0.899849i
$845$	9.00000	+	18.0000i	0.309609	+	0.619219i
$846$		0			0
$847$	−1.75736	−	1.75736i	−0.0603836	−	0.0603836i
$848$	−0.242641	−	0.242641i	−0.00833232	−	0.00833232i
$849$		0			0
$850$	4.00000	+	3.00000i	0.137199	+	0.102899i
$851$		−	28.6863i		−	0.983353i
$852$		0			0
$853$	17.1716	−	17.1716i	0.587943	−	0.587943i	−0.349131	−	0.937074i	$-0.613523\pi$
$853$	17.1716	−	17.1716i	0.587943	−	0.587943i	0.937074	+	0.349131i	$0.113523\pi$
$854$	2.14214			0.0733024
$855$		0			0
$856$	−9.65685			−0.330064
$857$	38.8701	−	38.8701i	1.32778	−	1.32778i	0.420469	−	0.907307i	$-0.361866\pi$
$857$	38.8701	−	38.8701i	1.32778	−	1.32778i	0.907307	−	0.420469i	$-0.138134\pi$
$858$		0			0
$859$		−	28.1421i		−	0.960197i	−0.877215	−	0.480099i	$-0.840601\pi$
$859$		−	28.1421i		−	0.960197i	0.877215	−	0.480099i	$-0.159399\pi$
$860$	13.2426	+	4.41421i	0.451570	+	0.150523i
$861$		0			0
$862$	17.6569	+	17.6569i	0.601395	+	0.601395i
$863$	−38.0000	−	38.0000i	−1.29354	−	1.29354i	−0.932585	−	0.360950i	$-0.882453\pi$
$863$	−38.0000	−	38.0000i	−1.29354	−	1.29354i	−0.360950	−	0.932585i	$-0.617547\pi$
$864$		0			0
$865$	31.9706	+	10.6569i	1.08703	+	0.362344i
$866$			15.7574i			0.535457i
$867$		0			0
$868$	−2.97056	+	2.97056i	−0.100827	+	0.100827i
$869$	1.65685			0.0562049
$870$		0			0
$871$	1.17157			0.0396972
$872$	8.65685	−	8.65685i	0.293158	−	0.293158i
$873$		0			0
$874$			4.20101i			0.142101i
$875$	−7.61522	+	5.27208i	−0.257442	+	0.178229i
$876$		0			0
$877$	−2.82843	−	2.82843i	−0.0955092	−	0.0955092i	0.657738	−	0.753247i	$-0.271513\pi$
$877$	−2.82843	−	2.82843i	−0.0955092	−	0.0955092i	−0.753247	+	0.657738i	$0.771513\pi$
$878$	−18.8995	−	18.8995i	−0.637827	−	0.637827i
$879$		0			0
$880$	2.82843	+	5.65685i	0.0953463	+	0.190693i
$881$		−	11.1716i		−	0.376380i	−0.982133	−	0.188190i	$-0.939738\pi$
$881$		−	11.1716i		−	0.376380i	0.982133	−	0.188190i	$-0.0602621\pi$
$882$		0			0
$883$	17.3848	−	17.3848i	0.585044	−	0.585044i	−0.351241	−	0.936285i	$-0.614240\pi$
$883$	17.3848	−	17.3848i	0.585044	−	0.585044i	0.936285	+	0.351241i	$0.114240\pi$
$884$	−2.00000			−0.0672673
$885$		0			0
$886$	19.4558			0.653632
$887$	9.10051	−	9.10051i	0.305565	−	0.305565i	−0.537621	−	0.843186i	$-0.680677\pi$
$887$	9.10051	−	9.10051i	0.305565	−	0.305565i	0.843186	+	0.537621i	$0.180677\pi$
$888$		0			0
$889$		0			0
$890$	1.82843	−	5.48528i	0.0612890	−	0.183867i
$891$		0			0
$892$	16.8284	+	16.8284i	0.563457	+	0.563457i
$893$		0			0
$894$		0			0
$895$	−3.51472	+	1.75736i	−0.117484	+	0.0587420i
$896$			0.828427i			0.0276758i
$897$		0			0
$898$	0.242641	−	0.242641i	0.00809702	−	0.00809702i
$899$	−38.8284			−1.29500
$900$		0			0
$901$	0.343146			0.0114318
$902$	17.6569	−	17.6569i	0.587909	−	0.587909i
$903$		0			0
$904$			15.6569i			0.520739i
$905$	0.485281	−	0.242641i	0.0161313	−	0.00806565i
$906$		0			0
$907$	−6.34315	−	6.34315i	−0.210621	−	0.210621i	0.593910	−	0.804531i	$-0.297583\pi$
$907$	−6.34315	−	6.34315i	−0.210621	−	0.210621i	−0.804531	+	0.593910i	$0.797583\pi$
$908$	−7.17157	−	7.17157i	−0.237997	−	0.237997i
$909$		0			0
$910$	1.17157	−	3.51472i	0.0388373	−	0.116512i
$911$			56.9706i			1.88752i	0.330633	+	0.943759i	$0.392738\pi$
$911$			56.9706i			1.88752i	−0.330633	+	0.943759i	$0.607262\pi$
$912$		0			0
$913$	−3.31371	+	3.31371i	−0.109668	+	0.109668i
$914$	19.0711			0.630815
$915$		0			0
$916$	1.31371			0.0434062
$917$	−3.31371	+	3.31371i	−0.109428	+	0.109428i
$918$		0			0
$919$		−	52.7696i		−	1.74071i	−0.492428	−	0.870353i	$-0.663890\pi$
$919$		−	52.7696i		−	1.74071i	0.492428	−	0.870353i	$-0.336110\pi$
$920$	−5.07107	−	10.1421i	−0.167188	−	0.334376i
$921$		0			0
$922$	−15.8995	−	15.8995i	−0.523622	−	0.523622i
$923$	−8.00000	−	8.00000i	−0.263323	−	0.263323i
$924$		0			0
$925$	28.0000	−	4.00000i	0.920634	−	0.131519i
$926$			15.5147i			0.509845i
$927$		0			0
$928$	−5.41421	+	5.41421i	−0.177730	+	0.177730i
$929$	46.0833			1.51194			0.755971	−	0.654605i	$-0.227165\pi$
$929$	46.0833			1.51194			0.755971	+	0.654605i	$0.227165\pi$
$930$		0			0
$931$	5.23045			0.171421
$932$	0.100505	−	0.100505i	0.00329215	−	0.00329215i
$933$		0			0
$934$		−	42.6274i		−	1.39481i
$935$	−6.00000	−	2.00000i	−0.196221	−	0.0654070i
$936$		0			0
$937$	22.1716	+	22.1716i	0.724314	+	0.724314i	0.969481	−	0.245167i	$-0.0788428\pi$
$937$	22.1716	+	22.1716i	0.724314	+	0.724314i	−0.245167	+	0.969481i	$0.578843\pi$
$938$	0.343146	+	0.343146i	0.0112041	+	0.0112041i
$939$		0			0
$940$		0			0
$941$		−	45.6569i		−	1.48837i	−0.667973	−	0.744185i	$-0.732838\pi$
$941$		−	45.6569i		−	1.48837i	0.667973	−	0.744185i	$-0.267162\pi$
$942$		0			0
$943$	−31.6569	+	31.6569i	−1.03089	+	1.03089i
$944$	10.7279			0.349164
$945$		0			0
$946$	−17.6569			−0.574074
$947$	−31.7990	+	31.7990i	−1.03333	+	1.03333i	−0.0339032	+	0.999425i	$0.510794\pi$
$947$	−31.7990	+	31.7990i	−1.03333	+	1.03333i	−0.999425	+	0.0339032i	$0.989206\pi$
$948$		0			0
$949$		−	0.686292i		−	0.0222780i
$950$	−4.10051	+	0.585786i	−0.133038	+	0.0190054i
$951$		0			0
$952$	−0.585786	−	0.585786i	−0.0189854	−	0.0189854i
$953$	5.65685	+	5.65685i	0.183243	+	0.183243i	0.792768	−	0.609524i	$-0.208639\pi$
$953$	5.65685	+	5.65685i	0.183243	+	0.183243i	−0.609524	+	0.792768i	$0.708639\pi$
$954$		0			0
$955$	−0.686292	−	1.37258i	−0.0222079	−	0.0444157i
$956$			22.1421i			0.716128i
$957$		0			0
$958$	−6.34315	+	6.34315i	−0.204938	+	0.204938i
$959$	−15.7157			−0.507487
$960$		0			0
$961$	−5.28427			−0.170460
$962$	−8.00000	+	8.00000i	−0.257930	+	0.257930i
$963$		0			0
$964$			18.4853i			0.595371i
$965$	8.24264	−	24.7279i	0.265340	−	0.796020i
$966$		0			0
$967$	−18.6274	−	18.6274i	−0.599017	−	0.599017i	0.341034	−	0.940051i	$-0.389223\pi$
$967$	−18.6274	−	18.6274i	−0.599017	−	0.599017i	−0.940051	+	0.341034i	$0.889223\pi$
$968$	2.12132	+	2.12132i	0.0681818	+	0.0681818i
$969$		0			0
$970$	−4.00000	+	2.00000i	−0.128432	+	0.0642161i
$971$			31.4142i			1.00813i	0.863666	+	0.504065i	$0.168163\pi$
$971$			31.4142i			1.00813i	−0.863666	+	0.504065i	$0.831837\pi$
$972$		0			0
$973$	1.94113	−	1.94113i	0.0622296	−	0.0622296i
$974$	−40.0000			−1.28168
$975$		0			0
$976$	−2.58579			−0.0827690
$977$	−13.2132	+	13.2132i	−0.422728	+	0.422728i	−0.886142	−	0.463414i	$-0.846624\pi$
$977$	−13.2132	+	13.2132i	−0.422728	+	0.422728i	0.463414	+	0.886142i	$0.346624\pi$
$978$		0			0
$979$			7.31371i			0.233747i
$980$	−12.6274	+	6.31371i	−0.403368	+	0.201684i
$981$		0			0
$982$	7.58579	+	7.58579i	0.242072	+	0.242072i
$983$	−27.7279	−	27.7279i	−0.884383	−	0.884383i	0.109593	−	0.993977i	$-0.465045\pi$
$983$	−27.7279	−	27.7279i	−0.884383	−	0.884383i	−0.993977	+	0.109593i	$0.965045\pi$
$984$		0			0
$985$	−7.82843	+	23.4853i	−0.249434	+	0.748303i
$986$		−	7.65685i		−	0.243844i
$987$		0			0
$988$	1.17157	−	1.17157i	0.0372727	−	0.0372727i
$989$	31.6569			1.00663
$990$		0			0
$991$	53.0711			1.68586			0.842929	−	0.538025i	$-0.180829\pi$
$991$	53.0711			1.68586			0.842929	+	0.538025i	$0.180829\pi$
$992$	3.58579	−	3.58579i	0.113849	−	0.113849i
$993$		0			0
$994$		−	4.68629i		−	0.148640i
$995$	4.10051	+	8.20101i	0.129995	+	0.259989i
$996$		0			0
$997$	−3.27208	−	3.27208i	−0.103628	−	0.103628i	0.653392	−	0.757020i	$-0.273345\pi$
$997$	−3.27208	−	3.27208i	−0.103628	−	0.103628i	−0.757020	+	0.653392i	$0.773345\pi$
$998$	6.00000	+	6.00000i	0.189927	+	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.f.647.1	yes	4
3.2	odd	2		1530.2.m.a.647.2	✓	4
5.3	odd	4		1530.2.m.a.953.2	yes	4
15.8	even	4	inner	1530.2.m.f.953.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.a.647.2	✓	4	3.2	odd	2
1530.2.m.a.953.2	yes	4	5.3	odd	4
1530.2.m.f.647.1	yes	4	1.1	even	1	trivial
1530.2.m.f.953.1	yes	4	15.8	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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.585786 - 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.585786 - 0.585786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 + 2.12132i) q^{10} -2.82843i q^{11} +(1.41421 - 1.41421i) q^{13} +0.828427 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +0.828427i q^{19} +(-1.00000 - 2.00000i) q^{20} +(2.00000 + 2.00000i) q^{22} +(-3.58579 - 3.58579i) q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000i q^{26} +(-0.585786 + 0.585786i) q^{28} -7.65685 q^{29} +5.07107 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(-1.75736 - 0.585786i) q^{35} +(4.00000 + 4.00000i) q^{37} +(-0.585786 - 0.585786i) q^{38} +(2.12132 + 0.707107i) q^{40} -8.82843i q^{41} +(-4.41421 + 4.41421i) q^{43} -2.82843 q^{44} +5.07107 q^{46} -6.31371i q^{49} +(0.707107 + 4.94975i) q^{50} +(-1.41421 - 1.41421i) q^{52} +(0.242641 + 0.242641i) q^{53} +(-2.82843 - 5.65685i) q^{55} -0.828427i q^{56} +(5.41421 - 5.41421i) q^{58} -10.7279 q^{59} +2.58579 q^{61} +(-3.58579 + 3.58579i) q^{62} +1.00000i q^{64} +(1.41421 - 4.24264i) q^{65} +(0.414214 + 0.414214i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(1.65685 - 0.828427i) q^{70} -5.65685i q^{71} +(0.242641 - 0.242641i) q^{73} -5.65685 q^{74} +0.828427 q^{76} +(-1.65685 + 1.65685i) q^{77} +0.585786i q^{79} +(-2.00000 + 1.00000i) q^{80} +(6.24264 + 6.24264i) q^{82} +(-1.17157 - 1.17157i) q^{83} +(0.707107 - 2.12132i) q^{85} -6.24264i q^{86} +(2.00000 - 2.00000i) q^{88} -2.58579 q^{89} -1.65685 q^{91} +(-3.58579 + 3.58579i) q^{92} +(0.828427 + 1.65685i) q^{95} +(1.41421 + 1.41421i) q^{97} +(4.46447 + 4.46447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 8 * q^5 - 8 * q^7	\( 4 q + 8 q^{5} - 8 q^{7} - 8 q^{14} - 4 q^{16} - 4 q^{20} + 8 q^{22} - 20 q^{23} + 12 q^{25} - 8 q^{28} - 8 q^{29} - 8 q^{31} - 24 q^{35} + 16 q^{37} - 8 q^{38} - 12 q^{43} - 8 q^{46} - 16 q^{53} + 16 q^{58} + 8 q^{59} + 16 q^{61} - 20 q^{62} - 4 q^{67} - 16 q^{70} - 16 q^{73} - 8 q^{76} + 16 q^{77} - 8 q^{80} + 8 q^{82} - 16 q^{83} + 8 q^{88} - 16 q^{89} + 16 q^{91} - 20 q^{92} - 8 q^{95} + 32 q^{98}+O(q^{100}) \) 4 * q + 8 * q^5 - 8 * q^7 - 8 * q^14 - 4 * q^16 - 4 * q^20 + 8 * q^22 - 20 * q^23 + 12 * q^25 - 8 * q^28 - 8 * q^29 - 8 * q^31 - 24 * q^35 + 16 * q^37 - 8 * q^38 - 12 * q^43 - 8 * q^46 - 16 * q^53 + 16 * q^58 + 8 * q^59 + 16 * q^61 - 20 * q^62 - 4 * q^67 - 16 * q^70 - 16 * q^73 - 8 * q^76 + 16 * q^77 - 8 * q^80 + 8 * q^82 - 16 * q^83 + 8 * q^88 - 16 * q^89 + 16 * q^91 - 20 * q^92 - 8 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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