LMFDB - Embedded newform 2070.2.j.h.737.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 24 x^{14} - 48 x^{13} + 160 x^{12} - 292 x^{11} + 436 x^{10} - 176 x^{9} - 914 x^{8} + \cdots + 81 $ x^16 - 4x^15 + 24x^14 - 48x^13 + 160x^12 - 292x^11 + 436x^10 - 176x^9 - 914x^8 + 820x^7 + 1624x^6 - 768x^5 - 568x^4 - 636x^3 + 540x^2 + 432*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.4
Root			$1.43216 - 3.45754i$ of defining polynomial
Character	$\chi$	$=$	2070.737
Dual form			2070.2.j.h.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.02538 - 0.947538i) q^{5} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.02538 - 0.947538i) q^{5} +(0.707107 + 0.707107i) q^{8} +(-0.762151 + 2.10217i) q^{10} -4.20577i q^{11} +(-1.52430 + 1.52430i) q^{13} -1.00000 q^{16} +(-3.30929 + 3.30929i) q^{17} -7.93299i q^{19} +(-0.947538 - 2.02538i) q^{20} +(2.97393 + 2.97393i) q^{22} +(0.707107 + 0.707107i) q^{23} +(3.20434 - 3.83825i) q^{25} -2.15569i q^{26} +2.98344 q^{29} -6.00000 q^{31} +(0.707107 - 0.707107i) q^{32} -4.68004i q^{34} +(-5.06867 - 5.06867i) q^{37} +(5.60947 + 5.60947i) q^{38} +(2.10217 + 0.762151i) q^{40} -1.93194i q^{41} +(1.70611 - 1.70611i) q^{43} -4.20577 q^{44} -1.00000 q^{46} +(-0.155008 + 0.155008i) q^{47} -7.00000i q^{49} +(0.448241 + 4.97987i) q^{50} +(1.52430 + 1.52430i) q^{52} +(5.80135 + 5.80135i) q^{53} +(-3.98513 - 8.51829i) q^{55} +(-2.10961 + 2.10961i) q^{58} +3.27242 q^{59} -9.20081 q^{61} +(4.24264 - 4.24264i) q^{62} +1.00000i q^{64} +(-1.64296 + 4.53163i) q^{65} +(-6.95906 - 6.95906i) q^{67} +(3.30929 + 3.30929i) q^{68} +7.74381i q^{71} +(-2.41469 + 2.41469i) q^{73} +7.16818 q^{74} -7.93299 q^{76} +1.72865i q^{79} +(-2.02538 + 0.947538i) q^{80} +(1.36609 + 1.36609i) q^{82} +(-7.65955 - 7.65955i) q^{83} +(-3.56690 + 9.83825i) q^{85} +2.41281i q^{86} +(2.97393 - 2.97393i) q^{88} -2.98344 q^{89} +(0.707107 - 0.707107i) q^{92} -0.219215i q^{94} +(-7.51681 - 16.0673i) q^{95} +(8.57043 + 8.57043i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.02538	−	0.947538i	0.905778	−	0.423752i
$5$	2.02538	−	0.947538i	0.905778	−	0.423752i
$6$		0			0
$7$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$7$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.762151	+	2.10217i	−0.241013	+	0.664765i
$11$		−	4.20577i		−	1.26809i	−0.773297	−	0.634044i	$-0.781394\pi$
$11$		−	4.20577i		−	1.26809i	0.773297	−	0.634044i	$-0.218606\pi$
$12$		0			0
$13$	−1.52430	+	1.52430i	−0.422765	+	0.422765i	−0.886155	−	0.463390i	$-0.846633\pi$
$13$	−1.52430	+	1.52430i	−0.422765	+	0.422765i	0.463390	+	0.886155i	$0.346633\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.30929	+	3.30929i	−0.802621	+	0.802621i	−0.983504	−	0.180884i	$-0.942104\pi$
$17$	−3.30929	+	3.30929i	−0.802621	+	0.802621i	0.180884	+	0.983504i	$0.442104\pi$
$18$		0			0
$19$		−	7.93299i		−	1.81995i	−0.414660	−	0.909976i	$-0.636100\pi$
$19$		−	7.93299i		−	1.81995i	0.414660	−	0.909976i	$-0.363900\pi$
$20$	−0.947538	−	2.02538i	−0.211876	−	0.452889i
$21$		0			0
$22$	2.97393	+	2.97393i	0.634044	+	0.634044i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	3.20434	−	3.83825i	0.640869	−	0.767650i
$26$		−	2.15569i		−	0.422765i
$27$		0			0
$28$		0			0
$29$	2.98344			0.554010			0.277005	−	0.960868i	$-0.410658\pi$
$29$	2.98344			0.554010			0.277005	+	0.960868i	$0.410658\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	4.68004i		−	0.802621i
$35$		0			0
$36$		0			0
$37$	−5.06867	−	5.06867i	−0.833284	−	0.833284i	0.154681	−	0.987964i	$-0.450565\pi$
$37$	−5.06867	−	5.06867i	−0.833284	−	0.833284i	−0.987964	+	0.154681i	$0.950565\pi$
$38$	5.60947	+	5.60947i	0.909976	+	0.909976i
$39$		0			0
$40$	2.10217	+	0.762151i	0.332383	+	0.120507i
$41$		−	1.93194i		−	0.301719i	−0.988555	−	0.150860i	$-0.951796\pi$
$41$		−	1.93194i		−	0.301719i	0.988555	−	0.150860i	$-0.0482041\pi$
$42$		0			0
$43$	1.70611	−	1.70611i	0.260180	−	0.260180i	−0.564947	−	0.825127i	$-0.691104\pi$
$43$	1.70611	−	1.70611i	0.260180	−	0.260180i	0.825127	+	0.564947i	$0.191104\pi$
$44$	−4.20577			−0.634044
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−0.155008	+	0.155008i	−0.0226103	+	0.0226103i	−0.718322	−	0.695711i	$-0.755089\pi$
$47$	−0.155008	+	0.155008i	−0.0226103	+	0.0226103i	0.695711	+	0.718322i	$0.255089\pi$
$48$		0			0
$49$		−	7.00000i		−	1.00000i
$50$	0.448241	+	4.97987i	0.0633909	+	0.704260i
$51$		0			0
$52$	1.52430	+	1.52430i	0.211383	+	0.211383i
$53$	5.80135	+	5.80135i	0.796876	+	0.796876i	0.982602	−	0.185725i	$-0.0594635\pi$
$53$	5.80135	+	5.80135i	0.796876	+	0.796876i	−0.185725	+	0.982602i	$0.559463\pi$
$54$		0			0
$55$	−3.98513	−	8.51829i	−0.537355	−	1.14861i
$56$		0			0
$57$		0			0
$58$	−2.10961	+	2.10961i	−0.277005	+	0.277005i
$59$	3.27242			0.426033			0.213016	−	0.977049i	$-0.431671\pi$
$59$	3.27242			0.426033			0.213016	+	0.977049i	$0.431671\pi$
$60$		0			0
$61$	−9.20081			−1.17804			−0.589021	−	0.808118i	$-0.700487\pi$
$61$	−9.20081			−1.17804			−0.589021	+	0.808118i	$0.700487\pi$
$62$	4.24264	−	4.24264i	0.538816	−	0.538816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.64296	+	4.53163i	−0.203784	+	0.562079i
$66$		0			0
$67$	−6.95906	−	6.95906i	−0.850184	−	0.850184i	0.139971	−	0.990156i	$-0.455299\pi$
$67$	−6.95906	−	6.95906i	−0.850184	−	0.850184i	−0.990156	+	0.139971i	$0.955299\pi$
$68$	3.30929	+	3.30929i	0.401310	+	0.401310i
$69$		0			0
$70$		0			0
$71$			7.74381i			0.919021i	0.888172	+	0.459510i	$0.151975\pi$
$71$			7.74381i			0.919021i	−0.888172	+	0.459510i	$0.848025\pi$
$72$		0			0
$73$	−2.41469	+	2.41469i	−0.282619	+	0.282619i	−0.834152	−	0.551534i	$-0.814043\pi$
$73$	−2.41469	+	2.41469i	−0.282619	+	0.282619i	0.551534	+	0.834152i	$0.314043\pi$
$74$	7.16818			0.833284
$75$		0			0
$76$	−7.93299			−0.909976
$77$		0			0
$78$		0			0
$79$			1.72865i			0.194488i	0.995261	+	0.0972439i	$0.0310027\pi$
$79$			1.72865i			0.194488i	−0.995261	+	0.0972439i	$0.968997\pi$
$80$	−2.02538	+	0.947538i	−0.226445	+	0.105938i
$81$		0			0
$82$	1.36609	+	1.36609i	0.150860	+	0.150860i
$83$	−7.65955	−	7.65955i	−0.840745	−	0.840745i	0.148211	−	0.988956i	$-0.452649\pi$
$83$	−7.65955	−	7.65955i	−0.840745	−	0.840745i	−0.988956	+	0.148211i	$0.952649\pi$
$84$		0			0
$85$	−3.56690	+	9.83825i	−0.386884	+	1.06711i
$86$			2.41281i			0.260180i
$87$		0			0
$88$	2.97393	−	2.97393i	0.317022	−	0.317022i
$89$	−2.98344			−0.316244			−0.158122	−	0.987420i	$-0.550544\pi$
$89$	−2.98344			−0.316244			−0.158122	+	0.987420i	$0.550544\pi$
$90$		0			0
$91$		0			0
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$		0			0
$94$		−	0.219215i		−	0.0226103i
$95$	−7.51681	−	16.0673i	−0.771208	−	1.64847i
$96$		0			0
$97$	8.57043	+	8.57043i	0.870196	+	0.870196i	0.992493	−	0.122298i	$-0.0390263\pi$
$97$	8.57043	+	8.57043i	0.870196	+	0.870196i	−0.122298	+	0.992493i	$0.539026\pi$
$98$	4.94975	+	4.94975i	0.500000	+	0.500000i
$99$		0			0
$100$	−3.83825	−	3.20434i	−0.383825	−	0.320434i
$101$			2.59968i			0.258678i	0.991600	+	0.129339i	$0.0412855\pi$
$101$			2.59968i			0.258678i	−0.991600	+	0.129339i	$0.958714\pi$
$102$		0			0
$103$	−6.00000	+	6.00000i	−0.591198	+	0.591198i	−0.937955	−	0.346757i	$-0.887283\pi$
$103$	−6.00000	+	6.00000i	−0.591198	+	0.591198i	0.346757	+	0.937955i	$0.387283\pi$
$104$	−2.15569			−0.211383
$105$		0			0
$106$	−8.20434			−0.796876
$107$	9.11064	−	9.11064i	0.880758	−	0.880758i	−0.112853	−	0.993612i	$-0.535999\pi$
$107$	9.11064	−	9.11064i	0.880758	−	0.880758i	0.993612	+	0.112853i	$0.0359990\pi$
$108$		0			0
$109$		−	12.4236i		−	1.18996i	−0.803740	−	0.594981i	$-0.797160\pi$
$109$		−	12.4236i		−	1.18996i	0.803740	−	0.594981i	$-0.202840\pi$
$110$	8.84126	+	3.20543i	0.842981	+	0.305626i
$111$		0			0
$112$		0			0
$113$	−8.06466	−	8.06466i	−0.758659	−	0.758659i	0.217419	−	0.976078i	$-0.430236\pi$
$113$	−8.06466	−	8.06466i	−0.758659	−	0.758659i	−0.976078	+	0.217419i	$0.930236\pi$
$114$		0			0
$115$	2.10217	+	0.762151i	0.196029	+	0.0710709i
$116$		−	2.98344i		−	0.277005i
$117$		0			0
$118$	−2.31395	+	2.31395i	−0.213016	+	0.213016i
$119$		0			0
$120$		0			0
$121$	−6.68852			−0.608047
$122$	6.50595	−	6.50595i	0.589021	−	0.589021i
$123$		0			0
$124$			6.00000i			0.538816i
$125$	2.85313	−	10.8102i	0.255192	−	0.966890i
$126$		0			0
$127$	−6.25295	−	6.25295i	−0.554859	−	0.554859i	0.372980	−	0.927839i	$-0.378336\pi$
$127$	−6.25295	−	6.25295i	−0.554859	−	0.554859i	−0.927839	+	0.372980i	$0.878336\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−2.04260	−	4.36609i	−0.179148	−	0.382932i
$131$			4.75537i			0.415479i	0.978184	+	0.207739i	$0.0666106\pi$
$131$			4.75537i			0.415479i	−0.978184	+	0.207739i	$0.933389\pi$
$132$		0			0
$133$		0			0
$134$	9.84160			0.850184
$135$		0			0
$136$	−4.68004			−0.401310
$137$	0.635871	−	0.635871i	0.0543261	−	0.0543261i	−0.679422	−	0.733748i	$-0.737769\pi$
$137$	0.635871	−	0.635871i	0.0543261	−	0.0543261i	0.733748	+	0.679422i	$0.237769\pi$
$138$		0			0
$139$		−	20.5982i		−	1.74711i	−0.486723	−	0.873557i	$-0.661808\pi$
$139$		−	20.5982i		−	1.74711i	0.486723	−	0.873557i	$-0.338192\pi$
$140$		0			0
$141$		0			0
$142$	−5.47570	−	5.47570i	−0.459510	−	0.459510i
$143$	6.41086	+	6.41086i	0.536103	+	0.536103i
$144$		0			0
$145$	6.04260	−	2.82692i	0.501810	−	0.234763i
$146$		−	3.41489i		−	0.282619i
$147$		0			0
$148$	−5.06867	+	5.06867i	−0.416642	+	0.416642i
$149$	−4.64977			−0.380924			−0.190462	−	0.981695i	$-0.560999\pi$
$149$	−4.64977			−0.380924			−0.190462	+	0.981695i	$0.560999\pi$
$150$		0			0
$151$	11.6765			0.950220			0.475110	−	0.879926i	$-0.342408\pi$
$151$	11.6765			0.950220			0.475110	+	0.879926i	$0.342408\pi$
$152$	5.60947	−	5.60947i	0.454988	−	0.454988i
$153$		0			0
$154$		0			0
$155$	−12.1523	+	5.68523i	−0.976096	+	0.456648i
$156$		0			0
$157$	−3.74871	−	3.74871i	−0.299179	−	0.299179i	0.541513	−	0.840692i	$-0.317852\pi$
$157$	−3.74871	−	3.74871i	−0.299179	−	0.299179i	−0.840692	+	0.541513i	$0.817852\pi$
$158$	−1.22234	−	1.22234i	−0.0972439	−	0.0972439i
$159$		0			0
$160$	0.762151	−	2.10217i	0.0602533	−	0.166191i
$161$		0			0
$162$		0			0
$163$	14.0852	−	14.0852i	1.10324	−	1.10324i	0.109220	−	0.994018i	$-0.465165\pi$
$163$	14.0852	−	14.0852i	1.10324	−	1.10324i	0.994018	−	0.109220i	$-0.0348352\pi$
$164$	−1.93194			−0.150860
$165$		0			0
$166$	10.8322			0.840745
$167$	−3.72491	+	3.72491i	−0.288242	+	0.288242i	−0.836385	−	0.548143i	$-0.815335\pi$
$167$	−3.72491	+	3.72491i	−0.288242	+	0.288242i	0.548143	+	0.836385i	$0.315335\pi$
$168$		0			0
$169$			8.35301i			0.642539i
$170$	−4.43452	−	9.47887i	−0.340112	−	0.726996i
$171$		0			0
$172$	−1.70611	−	1.70611i	−0.130090	−	0.130090i
$173$	7.58880	+	7.58880i	0.576966	+	0.576966i	0.934066	−	0.357100i	$-0.116235\pi$
$173$	7.58880	+	7.58880i	0.576966	+	0.576966i	−0.357100	+	0.934066i	$0.616235\pi$
$174$		0			0
$175$		0			0
$176$			4.20577i			0.317022i
$177$		0			0
$178$	2.10961	−	2.10961i	0.158122	−	0.158122i
$179$	20.4372			1.52755			0.763774	−	0.645484i	$-0.223344\pi$
$179$	20.4372			1.52755			0.763774	+	0.645484i	$0.223344\pi$
$180$		0			0
$181$	−21.2008			−1.57584			−0.787922	−	0.615775i	$-0.788843\pi$
$181$	−21.2008			−1.57584			−0.787922	+	0.615775i	$0.788843\pi$
$182$		0			0
$183$		0			0
$184$			1.00000i			0.0737210i
$185$	−15.0687	−	5.46323i	−1.10788	−	0.401665i
$186$		0			0
$187$	13.9181	+	13.9181i	1.01779	+	1.01779i
$188$	0.155008	+	0.155008i	0.0113051	+	0.0113051i
$189$		0			0
$190$	16.6765	+	6.04613i	1.20984	+	0.438633i
$191$			7.44982i			0.539050i	0.962993	+	0.269525i	$0.0868667\pi$
$191$			7.44982i			0.539050i	−0.962993	+	0.269525i	$0.913133\pi$
$192$		0			0
$193$	18.8660	−	18.8660i	1.35800	−	1.35800i	0.481626	−	0.876377i	$-0.340046\pi$
$193$	18.8660	−	18.8660i	1.35800	−	1.35800i	0.876377	−	0.481626i	$-0.159954\pi$
$194$	−12.1204			−0.870196
$195$		0			0
$196$	−7.00000			−0.500000
$197$	−1.54819	+	1.54819i	−0.110304	+	0.110304i	−0.760105	−	0.649801i	$-0.774852\pi$
$197$	−1.54819	+	1.54819i	−0.110304	+	0.110304i	0.649801	+	0.760105i	$0.274852\pi$
$198$		0			0
$199$		−	4.96672i		−	0.352081i	−0.984383	−	0.176041i	$-0.943671\pi$
$199$		−	4.96672i		−	0.352081i	0.984383	−	0.176041i	$-0.0563290\pi$
$200$	4.97987	−	0.448241i	0.352130	−	0.0316954i
$201$		0			0
$202$	−1.83825	−	1.83825i	−0.129339	−	0.129339i
$203$		0			0
$204$		0			0
$205$	−1.83059	−	3.91293i	−0.127854	−	0.273291i
$206$		−	8.48528i		−	0.591198i
$207$		0			0
$208$	1.52430	−	1.52430i	0.105691	−	0.105691i
$209$	−33.3643			−2.30786
$210$		0			0
$211$	17.7688			1.22325			0.611626	−	0.791147i	$-0.290516\pi$
$211$	17.7688			1.22325			0.611626	+	0.791147i	$0.290516\pi$
$212$	5.80135	−	5.80135i	0.398438	−	0.398438i
$213$		0			0
$214$			12.8844i			0.880758i
$215$	1.83892	−	5.07213i	0.125413	−	0.345917i
$216$		0			0
$217$		0			0
$218$	8.78478	+	8.78478i	0.594981	+	0.594981i
$219$		0			0
$220$	−8.51829	+	3.98513i	−0.574303	+	0.268677i
$221$		−	10.0887i		−	0.678640i
$222$		0			0
$223$	−8.97558	+	8.97558i	−0.601050	+	0.601050i	−0.940591	−	0.339541i	$-0.889728\pi$
$223$	−8.97558	+	8.97558i	−0.601050	+	0.601050i	0.339541	+	0.940591i	$0.389728\pi$
$224$		0			0
$225$		0			0
$226$	11.4052			0.758659
$227$	15.7292	−	15.7292i	1.04398	−	1.04398i	0.0449976	−	0.998987i	$-0.485672\pi$
$227$	15.7292	−	15.7292i	1.04398	−	1.04398i	0.998987	−	0.0449976i	$-0.0143280\pi$
$228$		0			0
$229$		−	9.74352i		−	0.643870i	−0.946762	−	0.321935i	$-0.895667\pi$
$229$		−	9.74352i		−	0.643870i	0.946762	−	0.321935i	$-0.104333\pi$
$230$	−2.02538	+	0.947538i	−0.133550	+	0.0624788i
$231$		0			0
$232$	2.10961	+	2.10961i	0.138503	+	0.138503i
$233$	5.94584	+	5.94584i	0.389525	+	0.389525i	0.874518	−	0.484993i	$-0.161178\pi$
$233$	5.94584	+	5.94584i	0.389525	+	0.389525i	−0.484993	+	0.874518i	$0.661178\pi$
$234$		0			0
$235$	−0.167075	+	0.460827i	−0.0108988	+	0.0300611i
$236$		−	3.27242i		−	0.213016i
$237$		0			0
$238$		0			0
$239$	15.7681			1.01995			0.509977	−	0.860188i	$-0.329654\pi$
$239$	15.7681			1.01995			0.509977	+	0.860188i	$0.329654\pi$
$240$		0			0
$241$	−23.3303			−1.50284			−0.751420	−	0.659825i	$-0.770631\pi$
$241$	−23.3303			−1.50284			−0.751420	+	0.659825i	$0.770631\pi$
$242$	4.72950	−	4.72950i	0.304024	−	0.304024i
$243$		0			0
$244$			9.20081i			0.589021i
$245$	−6.63277	−	14.1777i	−0.423752	−	0.905778i
$246$		0			0
$247$	12.0923	+	12.0923i	0.769412	+	0.769412i
$248$	−4.24264	−	4.24264i	−0.269408	−	0.269408i
$249$		0			0
$250$	5.62647	+	9.66141i	0.355849	+	0.611041i
$251$		−	23.1635i		−	1.46207i	−0.682341	−	0.731034i	$-0.739038\pi$
$251$		−	23.1635i		−	1.46207i	0.682341	−	0.731034i	$-0.260962\pi$
$252$		0			0
$253$	2.97393	−	2.97393i	0.186969	−	0.186969i
$254$	8.84300			0.554859
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.827748	−	0.827748i	0.0516335	−	0.0516335i	−0.680819	−	0.732452i	$-0.738376\pi$
$257$	0.827748	−	0.827748i	0.0516335	−	0.0516335i	0.732452	+	0.680819i	$0.238376\pi$
$258$		0			0
$259$		0			0
$260$	4.53163	+	1.64296i	0.281040	+	0.101892i
$261$		0			0
$262$	−3.36255	−	3.36255i	−0.207739	−	0.207739i
$263$	0.228746	+	0.228746i	0.0141051	+	0.0141051i	0.714124	−	0.700019i	$-0.246825\pi$
$263$	0.228746	+	0.228746i	0.0141051	+	0.0141051i	−0.700019	+	0.714124i	$0.746825\pi$
$264$		0			0
$265$	17.2469	+	6.25295i	1.05947	+	0.384115i
$266$		0			0
$267$		0			0
$268$	−6.95906	+	6.95906i	−0.425092	+	0.425092i
$269$	−18.0136			−1.09831			−0.549153	−	0.835722i	$-0.685050\pi$
$269$	−18.0136			−1.09831			−0.549153	+	0.835722i	$0.685050\pi$
$270$		0			0
$271$	26.8103			1.62861			0.814305	−	0.580437i	$-0.197118\pi$
$271$	26.8103			1.62861			0.814305	+	0.580437i	$0.197118\pi$
$272$	3.30929	−	3.30929i	0.200655	−	0.200655i
$273$		0			0
$274$			0.899257i			0.0543261i
$275$	−16.1428	−	13.4767i	−0.973448	−	0.812678i
$276$		0			0
$277$	2.01487	+	2.01487i	0.121062	+	0.121062i	0.765042	−	0.643980i	$-0.222718\pi$
$277$	2.01487	+	2.01487i	0.121062	+	0.121062i	−0.643980	+	0.765042i	$0.722718\pi$
$278$	14.5651	+	14.5651i	0.873557	+	0.873557i
$279$		0			0
$280$		0			0
$281$		−	5.73813i		−	0.342308i	−0.985244	−	0.171154i	$-0.945250\pi$
$281$		−	5.73813i		−	0.342308i	0.985244	−	0.171154i	$-0.0547495\pi$
$282$		0			0
$283$	7.95552	−	7.95552i	0.472907	−	0.472907i	−0.429947	−	0.902854i	$-0.641468\pi$
$283$	7.95552	−	7.95552i	0.472907	−	0.472907i	0.902854	+	0.429947i	$0.141468\pi$
$284$	7.74381			0.459510
$285$		0			0
$286$	−9.06633			−0.536103
$287$		0			0
$288$		0			0
$289$		−	4.90279i		−	0.288400i
$290$	−2.27383	+	6.27169i	−0.133524	+	0.368287i
$291$		0			0
$292$	2.41469	+	2.41469i	0.141309	+	0.141309i
$293$	6.06196	+	6.06196i	0.354143	+	0.354143i	0.861649	−	0.507505i	$-0.169432\pi$
$293$	6.06196	+	6.06196i	0.354143	+	0.354143i	−0.507505	+	0.861649i	$0.669432\pi$
$294$		0			0
$295$	6.62790	−	3.10074i	0.385891	−	0.180532i
$296$		−	7.16818i		−	0.416642i
$297$		0			0
$298$	3.28788	−	3.28788i	0.190462	−	0.190462i
$299$	−2.15569			−0.124667
$300$		0			0
$301$		0			0
$302$	−8.25654	+	8.25654i	−0.475110	+	0.475110i
$303$		0			0
$304$			7.93299i			0.454988i
$305$	−18.6351	+	8.71811i	−1.06705	+	0.499198i
$306$		0			0
$307$	13.3601	+	13.3601i	0.762500	+	0.762500i	0.976774	−	0.214273i	$-0.0687384\pi$
$307$	13.3601	+	13.3601i	0.762500	+	0.762500i	−0.214273	+	0.976774i	$0.568738\pi$
$308$		0			0
$309$		0			0
$310$	4.57290	−	12.6130i	0.259724	−	0.716372i
$311$		−	3.87643i		−	0.219812i	−0.993942	−	0.109906i	$-0.964945\pi$
$311$		−	3.87643i		−	0.219812i	0.993942	−	0.109906i	$-0.0350550\pi$
$312$		0			0
$313$	−23.4626	+	23.4626i	−1.32619	+	1.32619i	−0.417516	+	0.908670i	$0.637099\pi$
$313$	−23.4626	+	23.4626i	−1.32619	+	1.32619i	−0.908670	+	0.417516i	$0.862901\pi$
$314$	5.30147			0.299179
$315$		0			0
$316$	1.72865			0.0972439
$317$	8.70902	−	8.70902i	0.489148	−	0.489148i	−0.418890	−	0.908037i	$-0.637581\pi$
$317$	8.70902	−	8.70902i	0.489148	−	0.489148i	0.908037	+	0.418890i	$0.137581\pi$
$318$		0			0
$319$		−	12.5476i		−	0.702533i
$320$	0.947538	+	2.02538i	0.0529690	+	0.113222i
$321$		0			0
$322$		0			0
$323$	26.2526	+	26.2526i	1.46073	+	1.46073i
$324$		0			0
$325$	0.966268	+	10.7350i	0.0535989	+	0.595473i
$326$			19.9195i			1.10324i
$327$		0			0
$328$	1.36609	−	1.36609i	0.0754298	−	0.0754298i
$329$		0			0
$330$		0			0
$331$	5.77371			0.317352			0.158676	−	0.987331i	$-0.449277\pi$
$331$	5.77371			0.317352			0.158676	+	0.987331i	$0.449277\pi$
$332$	−7.65955	+	7.65955i	−0.420373	+	0.420373i
$333$		0			0
$334$		−	5.26782i		−	0.288242i
$335$	−20.6887	−	7.50078i	−1.13035	−	0.409811i
$336$		0			0
$337$	22.9720	+	22.9720i	1.25137	+	1.25137i	0.955107	+	0.296260i	$0.0957394\pi$
$337$	22.9720	+	22.9720i	1.25137	+	1.25137i	0.296260	+	0.955107i	$0.404261\pi$
$338$	−5.90647	−	5.90647i	−0.321270	−	0.321270i
$339$		0			0
$340$	9.83825	+	3.56690i	0.533554	+	0.193442i
$341$			25.2346i			1.36653i
$342$		0			0
$343$		0			0
$344$	2.41281			0.130090
$345$		0			0
$346$	−10.7322			−0.576966
$347$	−6.07982	+	6.07982i	−0.326382	+	0.326382i	−0.851209	−	0.524827i	$-0.824130\pi$
$347$	−6.07982	+	6.07982i	−0.326382	+	0.326382i	0.524827	+	0.851209i	$0.324130\pi$
$348$		0			0
$349$		−	16.6208i		−	0.889693i	−0.895607	−	0.444846i	$-0.853258\pi$
$349$		−	16.6208i		−	0.889693i	0.895607	−	0.444846i	$-0.146742\pi$
$350$		0			0
$351$		0			0
$352$	−2.97393	−	2.97393i	−0.158511	−	0.158511i
$353$	17.3283	+	17.3283i	0.922291	+	0.922291i	0.997191	−	0.0748996i	$-0.0238636\pi$
$353$	17.3283	+	17.3283i	0.922291	+	0.922291i	−0.0748996	+	0.997191i	$0.523864\pi$
$354$		0			0
$355$	7.33755	+	15.6842i	0.389437	+	0.832429i
$356$			2.98344i			0.158122i
$357$		0			0
$358$	−14.4513	+	14.4513i	−0.763774	+	0.763774i
$359$	−15.5093			−0.818549			−0.409274	−	0.912411i	$-0.634218\pi$
$359$	−15.5093			−0.818549			−0.409274	+	0.912411i	$0.634218\pi$
$360$		0			0
$361$	−43.9323			−2.31223
$362$	14.9912	−	14.9912i	0.787922	−	0.787922i
$363$		0			0
$364$		0			0
$365$	−2.60266	+	7.17869i	−0.136230	+	0.375750i
$366$		0			0
$367$	16.7772	+	16.7772i	0.875765	+	0.875765i	0.993093	−	0.117328i	$-0.0374329\pi$
$367$	16.7772	+	16.7772i	0.875765	+	0.875765i	−0.117328	+	0.993093i	$0.537433\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	14.5183	−	6.79212i	0.754770	−	0.353105i
$371$		0			0
$372$		0			0
$373$	−10.4288	+	10.4288i	−0.539980	+	0.539980i	−0.923523	−	0.383543i	$-0.874704\pi$
$373$	−10.4288	+	10.4288i	−0.539980	+	0.539980i	0.383543	+	0.923523i	$0.374704\pi$
$374$	−19.6832			−1.01779
$375$		0			0
$376$	−0.219215			−0.0113051
$377$	−4.54766	+	4.54766i	−0.234216	+	0.234216i
$378$		0			0
$379$			12.4910i			0.641621i	0.947143	+	0.320810i	$0.103955\pi$
$379$			12.4910i			0.641621i	−0.947143	+	0.320810i	$0.896045\pi$
$380$	−16.0673	+	7.51681i	−0.824237	+	0.385604i
$381$		0			0
$382$	−5.26782	−	5.26782i	−0.269525	−	0.269525i
$383$	−25.8051	−	25.8051i	−1.31858	−	1.31858i	−0.914902	−	0.403675i	$-0.867733\pi$
$383$	−25.8051	−	25.8051i	−1.31858	−	1.31858i	−0.403675	−	0.914902i	$-0.632267\pi$
$384$		0			0
$385$		0			0
$386$			26.6805i			1.35800i
$387$		0			0
$388$	8.57043	−	8.57043i	0.435098	−	0.435098i
$389$	−4.36078			−0.221100			−0.110550	−	0.993871i	$-0.535261\pi$
$389$	−4.36078			−0.221100			−0.110550	+	0.993871i	$0.535261\pi$
$390$		0			0
$391$	−4.68004			−0.236680
$392$	4.94975	−	4.94975i	0.250000	−	0.250000i
$393$		0			0
$394$		−	2.18947i		−	0.110304i
$395$	1.63796	+	3.50117i	0.0824146	+	0.176163i
$396$		0			0
$397$	−11.5123	−	11.5123i	−0.577785	−	0.577785i	0.356507	−	0.934293i	$-0.383967\pi$
$397$	−11.5123	−	11.5123i	−0.577785	−	0.577785i	−0.934293	+	0.356507i	$0.883967\pi$
$398$	3.51200	+	3.51200i	0.176041	+	0.176041i
$399$		0			0
$400$	−3.20434	+	3.83825i	−0.160217	+	0.191913i
$401$			14.3609i			0.717148i	0.933501	+	0.358574i	$0.116737\pi$
$401$			14.3609i			0.717148i	−0.933501	+	0.358574i	$0.883263\pi$
$402$		0			0
$403$	9.14581	−	9.14581i	0.455585	−	0.455585i
$404$	2.59968			0.129339
$405$		0			0
$406$		0			0
$407$	−21.3177	+	21.3177i	−1.05668	+	1.05668i
$408$		0			0
$409$		−	33.7320i		−	1.66794i	−0.551811	−	0.833969i	$-0.686063\pi$
$409$		−	33.7320i		−	1.66794i	0.551811	−	0.833969i	$-0.313937\pi$
$410$	4.06128	+	1.47243i	0.200572	+	0.0727183i
$411$		0			0
$412$	6.00000	+	6.00000i	0.295599	+	0.295599i
$413$		0			0
$414$		0			0
$415$	−22.7712	−	8.25580i	−1.11780	−	0.405261i
$416$			2.15569i			0.105691i
$417$		0			0
$418$	23.5922	−	23.5922i	1.15393	−	1.15393i
$419$	−13.5013			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$419$	−13.5013			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$420$		0			0
$421$	−22.1923			−1.08159			−0.540794	−	0.841155i	$-0.681876\pi$
$421$	−22.1923			−1.08159			−0.540794	+	0.841155i	$0.681876\pi$
$422$	−12.5644	+	12.5644i	−0.611626	+	0.611626i
$423$		0			0
$424$			8.20434i			0.398438i
$425$	2.09779	+	23.3060i	0.101758	+	1.13051i
$426$		0			0
$427$		0			0
$428$	−9.11064	−	9.11064i	−0.440379	−	0.440379i
$429$		0			0
$430$	2.28623	+	4.88686i	0.110252	+	0.235665i
$431$			10.9867i			0.529211i	0.964357	+	0.264605i	$0.0852417\pi$
$431$			10.9867i			0.529211i	−0.964357	+	0.264605i	$0.914758\pi$
$432$		0			0
$433$	0.789650	−	0.789650i	0.0379481	−	0.0379481i	−0.687878	−	0.725826i	$-0.741458\pi$
$433$	0.789650	−	0.789650i	0.0379481	−	0.0379481i	0.725826	+	0.687878i	$0.241458\pi$
$434$		0			0
$435$		0			0
$436$	−12.4236			−0.594981
$437$	5.60947	−	5.60947i	0.268337	−	0.268337i
$438$		0			0
$439$			31.1218i			1.48536i	0.669646	+	0.742681i	$0.266446\pi$
$439$			31.1218i			1.48536i	−0.669646	+	0.742681i	$0.733554\pi$
$440$	3.20543	−	8.84126i	0.152813	−	0.421490i
$441$		0			0
$442$	7.13380	+	7.13380i	0.339320	+	0.339320i
$443$	−7.42879	−	7.42879i	−0.352952	−	0.352952i	0.508255	−	0.861207i	$-0.330291\pi$
$443$	−7.42879	−	7.42879i	−0.352952	−	0.352952i	−0.861207	+	0.508255i	$0.830291\pi$
$444$		0			0
$445$	−6.04260	+	2.82692i	−0.286447	+	0.134009i
$446$		−	12.6934i		−	0.601050i
$447$		0			0
$448$		0			0
$449$	−28.8537			−1.36169			−0.680846	−	0.732426i	$-0.738388\pi$
$449$	−28.8537			−1.36169			−0.680846	+	0.732426i	$0.738388\pi$
$450$		0			0
$451$	−8.12532			−0.382606
$452$	−8.06466	+	8.06466i	−0.379330	+	0.379330i
$453$		0			0
$454$			22.2445i			1.04398i
$455$		0			0
$456$		0			0
$457$	26.7375	+	26.7375i	1.25073	+	1.25073i	0.955394	+	0.295334i	$0.0954309\pi$
$457$	26.7375	+	26.7375i	1.25073	+	1.25073i	0.295334	+	0.955394i	$0.404569\pi$
$458$	6.88971	+	6.88971i	0.321935	+	0.321935i
$459$		0			0
$460$	0.762151	−	2.10217i	0.0355355	−	0.0980143i
$461$			36.1150i			1.68204i	0.541002	+	0.841021i	$0.318045\pi$
$461$			36.1150i			1.68204i	−0.541002	+	0.841021i	$0.681955\pi$
$462$		0			0
$463$	−16.5644	+	16.5644i	−0.769814	+	0.769814i	−0.978074	−	0.208259i	$-0.933220\pi$
$463$	−16.5644	+	16.5644i	−0.769814	+	0.769814i	0.208259	+	0.978074i	$0.433220\pi$
$464$	−2.98344			−0.138503
$465$		0			0
$466$	−8.40869			−0.389525
$467$	20.1462	−	20.1462i	0.932255	−	0.932255i	−0.0655918	−	0.997847i	$-0.520894\pi$
$467$	20.1462	−	20.1462i	0.932255	−	0.932255i	0.997847	+	0.0655918i	$0.0208935\pi$
$468$		0			0
$469$		0			0
$470$	−0.207714	−	0.443994i	−0.00958115	−	0.0204799i
$471$		0			0
$472$	2.31395	+	2.31395i	0.106508	+	0.106508i
$473$	−7.17552	−	7.17552i	−0.329931	−	0.329931i
$474$		0			0
$475$	−30.4488	−	25.4200i	−1.39709	−	1.16635i
$476$		0			0
$477$		0			0
$478$	−11.1497	+	11.1497i	−0.509977	+	0.509977i
$479$	6.17808			0.282284			0.141142	−	0.989989i	$-0.454923\pi$
$479$	6.17808			0.282284			0.141142	+	0.989989i	$0.454923\pi$
$480$		0			0
$481$	15.4524			0.704567
$482$	16.4970	−	16.4970i	0.751420	−	0.751420i
$483$		0			0
$484$			6.68852i			0.304024i
$485$	25.4792	+	9.23759i	1.15695	+	0.419457i
$486$		0			0
$487$	19.4236	+	19.4236i	0.880165	+	0.880165i	0.993551	−	0.113386i	$-0.0361695\pi$
$487$	19.4236	+	19.4236i	0.880165	+	0.880165i	−0.113386	+	0.993551i	$0.536170\pi$
$488$	−6.50595	−	6.50595i	−0.294511	−	0.294511i
$489$		0			0
$490$	14.7152	+	5.33506i	0.664765	+	0.241013i
$491$		−	0.370257i		−	0.0167094i	−0.999965	−	0.00835472i	$-0.997341\pi$
$491$		−	0.370257i		−	0.0167094i	0.999965	−	0.00835472i	$-0.00265942\pi$
$492$		0			0
$493$	−9.87305	+	9.87305i	−0.444660	+	0.444660i
$494$	−17.1010			−0.769412
$495$		0			0
$496$	6.00000			0.269408
$497$		0			0
$498$		0			0
$499$		−	15.8957i		−	0.711590i	−0.934564	−	0.355795i	$-0.884210\pi$
$499$		−	15.8957i		−	0.711590i	0.934564	−	0.355795i	$-0.115790\pi$
$500$	−10.8102	−	2.85313i	−0.483445	−	0.127596i
$501$		0			0
$502$	16.3791	+	16.3791i	0.731034	+	0.731034i
$503$	−20.5922	−	20.5922i	−0.918161	−	0.918161i	0.0787344	−	0.996896i	$-0.474912\pi$
$503$	−20.5922	−	20.5922i	−0.918161	−	0.918161i	−0.996896	+	0.0787344i	$0.974912\pi$
$504$		0			0
$505$	2.46330	+	5.26535i	0.109615	+	0.234305i
$506$			4.20577i			0.186969i
$507$		0			0
$508$	−6.25295	+	6.25295i	−0.277430	+	0.277430i
$509$	37.0450			1.64199			0.820996	−	0.570934i	$-0.193419\pi$
$509$	37.0450			1.64199			0.820996	+	0.570934i	$0.193419\pi$
$510$		0			0
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			1.17061i			0.0516335i
$515$	−6.46706	+	17.8375i	−0.284973	+	0.786015i
$516$		0			0
$517$	0.651930	+	0.651930i	0.0286718	+	0.0286718i
$518$		0			0
$519$		0			0
$520$	−4.36609	+	2.04260i	−0.191466	+	0.0895738i
$521$			32.1874i			1.41015i	0.709131	+	0.705077i	$0.249088\pi$
$521$			32.1874i			1.41015i	−0.709131	+	0.705077i	$0.750912\pi$
$522$		0			0
$523$	−21.6469	+	21.6469i	−0.946553	+	0.946553i	−0.998642	−	0.0520897i	$-0.983412\pi$
$523$	−21.6469	+	21.6469i	−0.946553	+	0.946553i	0.0520897	+	0.998642i	$0.483412\pi$
$524$	4.75537			0.207739
$525$		0			0
$526$	−0.323495			−0.0141051
$527$	19.8557	−	19.8557i	0.864929	−	0.864929i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−16.6169	+	7.77393i	−0.721793	+	0.337678i
$531$		0			0
$532$		0			0
$533$	2.94487	+	2.94487i	0.127556	+	0.127556i
$534$		0			0
$535$	9.81984	−	27.0852i	0.424549	−	1.17099i
$536$		−	9.84160i		−	0.425092i
$537$		0			0
$538$	12.7375	−	12.7375i	0.549153	−	0.549153i
$539$	−29.4404			−1.26809
$540$		0			0
$541$	44.0732			1.89485			0.947427	−	0.319972i	$-0.103674\pi$
$541$	44.0732			1.89485			0.947427	+	0.319972i	$0.103674\pi$
$542$	−18.9577	+	18.9577i	−0.814305	+	0.814305i
$543$		0			0
$544$			4.68004i			0.200655i
$545$	−11.7718	−	25.1625i	−0.504248	−	1.07784i
$546$		0			0
$547$	15.4052	+	15.4052i	0.658677	+	0.658677i	0.955067	−	0.296390i	$-0.0957829\pi$
$547$	15.4052	+	15.4052i	0.658677	+	0.658677i	−0.296390	+	0.955067i	$0.595783\pi$
$548$	−0.635871	−	0.635871i	−0.0271630	−	0.0271630i
$549$		0			0
$550$	20.9442	−	1.88520i	0.893063	−	0.0803852i
$551$		−	23.6676i		−	1.00827i
$552$		0			0
$553$		0			0
$554$	−2.84946			−0.121062
$555$		0			0
$556$	−20.5982			−0.873557
$557$	−17.0697	+	17.0697i	−0.723266	+	0.723266i	−0.969269	−	0.246003i	$-0.920883\pi$
$557$	−17.0697	+	17.0697i	−0.723266	+	0.723266i	0.246003	+	0.969269i	$0.420883\pi$
$558$		0			0
$559$			5.20126i			0.219990i
$560$		0			0
$561$		0			0
$562$	4.05747	+	4.05747i	0.171154	+	0.171154i
$563$	21.3232	+	21.3232i	0.898664	+	0.898664i	0.995318	−	0.0966537i	$-0.0308139\pi$
$563$	21.3232	+	21.3232i	0.898664	+	0.898664i	−0.0966537	+	0.995318i	$0.530814\pi$
$564$		0			0
$565$	−23.9756	−	8.69244i	−1.00866	−	0.365694i
$566$			11.2508i			0.472907i
$567$		0			0
$568$	−5.47570	+	5.47570i	−0.229755	+	0.229755i
$569$	46.7033			1.95790			0.978951	−	0.204095i	$-0.0654251\pi$
$569$	46.7033			1.95790			0.978951	+	0.204095i	$0.0654251\pi$
$570$		0			0
$571$	−21.9106			−0.916930			−0.458465	−	0.888713i	$-0.651601\pi$
$571$	−21.9106			−0.916930			−0.458465	+	0.888713i	$0.651601\pi$
$572$	6.41086	−	6.41086i	0.268052	−	0.268052i
$573$		0			0
$574$		0			0
$575$	4.97987	−	0.448241i	0.207675	−	0.0186930i
$576$		0			0
$577$	−13.9940	−	13.9940i	−0.582578	−	0.582578i	0.353033	−	0.935611i	$-0.385150\pi$
$577$	−13.9940	−	13.9940i	−0.582578	−	0.582578i	−0.935611	+	0.353033i	$0.885150\pi$
$578$	3.46680	+	3.46680i	0.144200	+	0.144200i
$579$		0			0
$580$	−2.82692	−	6.04260i	−0.117381	−	0.250905i
$581$		0			0
$582$		0			0
$583$	24.3991	−	24.3991i	1.01051	−	1.01051i
$584$	−3.41489			−0.141309
$585$		0			0
$586$	−8.57290			−0.354143
$587$	0.965218	−	0.965218i	0.0398388	−	0.0398388i	−0.686907	−	0.726746i	$-0.741032\pi$
$587$	0.965218	−	0.965218i	0.0398388	−	0.0398388i	0.726746	+	0.686907i	$0.241032\pi$
$588$		0			0
$589$			47.5979i			1.96124i
$590$	−2.49408	+	6.87919i	−0.102680	+	0.283212i
$591$		0			0
$592$	5.06867	+	5.06867i	0.208321	+	0.208321i
$593$	2.44118	+	2.44118i	0.100247	+	0.100247i	0.755452	−	0.655204i	$-0.227417\pi$
$593$	2.44118	+	2.44118i	0.100247	+	0.100247i	−0.655204	+	0.755452i	$0.727417\pi$
$594$		0			0
$595$		0			0
$596$			4.64977i			0.190462i
$597$		0			0
$598$	1.52430	−	1.52430i	0.0623333	−	0.0623333i
$599$	−6.08482			−0.248619			−0.124309	−	0.992243i	$-0.539672\pi$
$599$	−6.08482			−0.248619			−0.124309	+	0.992243i	$0.539672\pi$
$600$		0			0
$601$	43.4085			1.77067			0.885334	−	0.464956i	$-0.153930\pi$
$601$	43.4085			1.77067			0.885334	+	0.464956i	$0.153930\pi$
$602$		0			0
$603$		0			0
$604$		−	11.6765i		−	0.475110i
$605$	−13.5468	+	6.33763i	−0.550756	+	0.257661i
$606$		0			0
$607$	12.1462	+	12.1462i	0.492999	+	0.492999i	0.909250	−	0.416251i	$-0.136656\pi$
$607$	12.1462	+	12.1462i	0.492999	+	0.492999i	−0.416251	+	0.909250i	$0.636656\pi$
$608$	−5.60947	−	5.60947i	−0.227494	−	0.227494i
$609$		0			0
$610$	7.01240	−	19.3417i	0.283924	−	0.783122i
$611$		−	0.472559i		−	0.0191177i
$612$		0			0
$613$	0.127201	−	0.127201i	0.00513759	−	0.00513759i	−0.704533	−	0.709671i	$-0.748844\pi$
$613$	0.127201	−	0.127201i	0.00513759	−	0.00513759i	0.709671	+	0.704533i	$0.248844\pi$
$614$	−18.8940			−0.762500
$615$		0			0
$616$		0			0
$617$	4.36578	−	4.36578i	0.175760	−	0.175760i	−0.613745	−	0.789505i	$-0.710338\pi$
$617$	4.36578	−	4.36578i	0.175760	−	0.175760i	0.789505	+	0.613745i	$0.210338\pi$
$618$		0			0
$619$			22.6532i			0.910507i	0.890362	+	0.455254i	$0.150451\pi$
$619$			22.6532i			0.910507i	−0.890362	+	0.455254i	$0.849549\pi$
$620$	5.68523	+	12.1523i	0.228324	+	0.488048i
$621$		0			0
$622$	2.74105	+	2.74105i	0.109906	+	0.109906i
$623$		0			0
$624$		0			0
$625$	−4.46436	−	24.5982i	−0.178575	−	0.983926i
$626$		−	33.1812i		−	1.32619i
$627$		0			0
$628$	−3.74871	+	3.74871i	−0.149590	+	0.149590i
$629$	33.5474			1.33762
$630$		0			0
$631$	1.42424			0.0566980			0.0283490	−	0.999598i	$-0.490975\pi$
$631$	1.42424			0.0566980			0.0283490	+	0.999598i	$0.490975\pi$
$632$	−1.22234	+	1.22234i	−0.0486219	+	0.0486219i
$633$		0			0
$634$			12.3164i			0.489148i
$635$	−18.5895	−	6.73970i	−0.737702	−	0.267457i
$636$		0			0
$637$	10.6701	+	10.6701i	0.422765	+	0.422765i
$638$	8.87253	+	8.87253i	0.351267	+	0.351267i
$639$		0			0
$640$	−2.10217	−	0.762151i	−0.0830956	−	0.0301267i
$641$			33.3854i			1.31864i	0.751861	+	0.659321i	$0.229156\pi$
$641$			33.3854i			1.31864i	−0.751861	+	0.659321i	$0.770844\pi$
$642$		0			0
$643$	−20.7576	+	20.7576i	−0.818599	+	0.818599i	−0.985905	−	0.167306i	$-0.946493\pi$
$643$	−20.7576	+	20.7576i	−0.818599	+	0.818599i	0.167306	+	0.985905i	$0.446493\pi$
$644$		0			0
$645$		0			0
$646$	−37.1267			−1.46073
$647$	18.7340	−	18.7340i	0.736510	−	0.736510i	−0.235391	−	0.971901i	$-0.575637\pi$
$647$	18.7340	−	18.7340i	0.736510	−	0.736510i	0.971901	+	0.235391i	$0.0756371\pi$
$648$		0			0
$649$		−	13.7631i		−	0.540247i
$650$	−8.27407	−	6.90756i	−0.324536	−	0.270937i
$651$		0			0
$652$	−14.0852	−	14.0852i	−0.551619	−	0.551619i
$653$	−29.4452	−	29.4452i	−1.15228	−	1.15228i	−0.986094	−	0.166186i	$-0.946855\pi$
$653$	−29.4452	−	29.4452i	−1.15228	−	1.15228i	−0.166186	−	0.986094i	$-0.553145\pi$
$654$		0			0
$655$	4.50589	+	9.63144i	0.176060	+	0.376331i
$656$			1.93194i			0.0754298i
$657$		0			0
$658$		0			0
$659$	2.95506			0.115113			0.0575564	−	0.998342i	$-0.481669\pi$
$659$	2.95506			0.115113			0.0575564	+	0.998342i	$0.481669\pi$
$660$		0			0
$661$	−25.2409			−0.981759			−0.490879	−	0.871228i	$-0.663324\pi$
$661$	−25.2409			−0.981759			−0.490879	+	0.871228i	$0.663324\pi$
$662$	−4.08263	+	4.08263i	−0.158676	+	0.158676i
$663$		0			0
$664$		−	10.8322i		−	0.420373i
$665$		0			0
$666$		0			0
$667$	2.10961	+	2.10961i	0.0816843	+	0.0816843i
$668$	3.72491	+	3.72491i	0.144121	+	0.144121i
$669$		0			0
$670$	19.9330	−	9.32529i	0.770079	−	0.360267i
$671$			38.6965i			1.49386i
$672$		0			0
$673$	−10.0912	+	10.0912i	−0.388987	+	0.388987i	−0.874326	−	0.485339i	$-0.838696\pi$
$673$	−10.0912	+	10.0912i	−0.388987	+	0.388987i	0.485339	+	0.874326i	$0.338696\pi$
$674$	−32.4874			−1.25137
$675$		0			0
$676$	8.35301			0.321270
$677$	14.0160	−	14.0160i	0.538679	−	0.538679i	−0.384462	−	0.923141i	$-0.625613\pi$
$677$	14.0160	−	14.0160i	0.538679	−	0.538679i	0.923141	+	0.384462i	$0.125613\pi$
$678$		0			0
$679$		0			0
$680$	−9.47887	+	4.43452i	−0.363498	+	0.170056i
$681$		0			0
$682$	−17.8436	−	17.8436i	−0.683266	−	0.683266i
$683$	3.80365	+	3.80365i	0.145543	+	0.145543i	0.776124	−	0.630581i	$-0.217183\pi$
$683$	3.80365	+	3.80365i	0.145543	+	0.145543i	−0.630581	+	0.776124i	$0.717183\pi$
$684$		0			0
$685$	0.685369	−	1.89039i	0.0261866	−	0.0722282i
$686$		0			0
$687$		0			0
$688$	−1.70611	+	1.70611i	−0.0650449	+	0.0650449i
$689$	−17.6860			−0.673783
$690$		0			0
$691$	27.2487			1.03659			0.518295	−	0.855202i	$-0.326567\pi$
$691$	27.2487			1.03659			0.518295	+	0.855202i	$0.326567\pi$
$692$	7.58880	−	7.58880i	0.288483	−	0.288483i
$693$		0			0
$694$		−	8.59816i		−	0.326382i
$695$	−19.5175	−	41.7191i	−0.740342	−	1.58250i
$696$		0			0
$697$	6.39336	+	6.39336i	0.242166	+	0.242166i
$698$	11.7527	+	11.7527i	0.444846	+	0.444846i
$699$		0			0
$700$		0			0
$701$			10.8846i			0.411105i	0.978646	+	0.205553i	$0.0658992\pi$
$701$			10.8846i			0.411105i	−0.978646	+	0.205553i	$0.934101\pi$
$702$		0			0
$703$	−40.2097	+	40.2097i	−1.51654	+	1.51654i
$704$	4.20577			0.158511
$705$		0			0
$706$	−24.5059			−0.922291
$707$		0			0
$708$		0			0
$709$		−	39.2740i		−	1.47497i	−0.675366	−	0.737483i	$-0.736014\pi$
$709$		−	39.2740i		−	1.47497i	0.675366	−	0.737483i	$-0.263986\pi$
$710$	−16.2788	−	5.90195i	−0.610933	−	0.221496i
$711$		0			0
$712$	−2.10961	−	2.10961i	−0.0790609	−	0.0790609i
$713$	−4.24264	−	4.24264i	−0.158888	−	0.158888i
$714$		0			0
$715$	19.0590	+	6.90991i	0.712766	+	0.258416i
$716$		−	20.4372i		−	0.763774i
$717$		0			0
$718$	10.9667	−	10.9667i	0.409274	−	0.409274i
$719$	5.49684			0.204998			0.102499	−	0.994733i	$-0.467316\pi$
$719$	5.49684			0.204998			0.102499	+	0.994733i	$0.467316\pi$
$720$		0			0
$721$		0			0
$722$	31.0648	−	31.0648i	1.15611	−	1.15611i
$723$		0			0
$724$			21.2008i			0.787922i
$725$	9.55995	−	11.4512i	0.355048	−	0.425286i
$726$		0			0
$727$	−21.3530	−	21.3530i	−0.791939	−	0.791939i	0.189870	−	0.981809i	$-0.439193\pi$
$727$	−21.3530	−	21.3530i	−0.791939	−	0.791939i	−0.981809	+	0.189870i	$0.939193\pi$
$728$		0			0
$729$		0			0
$730$	−3.23574	−	6.91646i	−0.119760	−	0.255990i
$731$			11.2920i			0.417651i
$732$		0			0
$733$	8.54083	−	8.54083i	0.315463	−	0.315463i	−0.531559	−	0.847021i	$-0.678394\pi$
$733$	8.54083	−	8.54083i	0.315463	−	0.315463i	0.847021	+	0.531559i	$0.178394\pi$
$734$	−23.7266			−0.875765
$735$		0			0
$736$	1.00000			0.0368605
$737$	−29.2682	+	29.2682i	−1.07811	+	1.07811i
$738$		0			0
$739$		−	16.6031i		−	0.610755i	−0.952231	−	0.305377i	$-0.901217\pi$
$739$		−	16.6031i		−	0.610755i	0.952231	−	0.305377i	$-0.0987826\pi$
$740$	−5.46323	+	15.0687i	−0.200832	+	0.553938i
$741$		0			0
$742$		0			0
$743$	−12.5679	−	12.5679i	−0.461072	−	0.461072i	0.437935	−	0.899007i	$-0.355710\pi$
$743$	−12.5679	−	12.5679i	−0.461072	−	0.461072i	−0.899007	+	0.437935i	$0.855710\pi$
$744$		0			0
$745$	−9.41755	+	4.40583i	−0.345032	+	0.161417i
$746$		−	14.7485i		−	0.539980i
$747$		0			0
$748$	13.9181	−	13.9181i	0.508897	−	0.508897i
$749$		0			0
$750$		0			0
$751$	39.1739			1.42948			0.714738	−	0.699392i	$-0.246546\pi$
$751$	39.1739			1.42948			0.714738	+	0.699392i	$0.246546\pi$
$752$	0.155008	−	0.155008i	0.00565257	−	0.00565257i
$753$		0			0
$754$		−	6.43136i		−	0.234216i
$755$	23.6494	−	11.0639i	0.860689	−	0.402658i
$756$		0			0
$757$	23.4103	+	23.4103i	0.850863	+	0.850863i	0.990240	−	0.139376i	$-0.0445097\pi$
$757$	23.4103	+	23.4103i	0.850863	+	0.850863i	−0.139376	+	0.990240i	$0.544510\pi$
$758$	−8.83249	−	8.83249i	−0.320810	−	0.320810i
$759$		0			0
$760$	6.04613	−	16.6765i	0.219316	−	0.604920i
$761$		−	6.00355i		−	0.217628i	−0.994062	−	0.108814i	$-0.965295\pi$
$761$		−	6.00355i		−	0.217628i	0.994062	−	0.108814i	$-0.0347054\pi$
$762$		0			0
$763$		0			0
$764$	7.44982			0.269525
$765$		0			0
$766$	36.4939			1.31858
$767$	−4.98816	+	4.98816i	−0.180112	+	0.180112i
$768$		0			0
$769$		−	13.4524i		−	0.485104i	−0.970138	−	0.242552i	$-0.922015\pi$
$769$		−	13.4524i		−	0.485104i	0.970138	−	0.242552i	$-0.0779845\pi$
$770$		0			0
$771$		0			0
$772$	−18.8660	−	18.8660i	−0.679001	−	0.679001i
$773$	18.5032	+	18.5032i	0.665515	+	0.665515i	0.956675	−	0.291159i	$-0.0940410\pi$
$773$	18.5032	+	18.5032i	0.665515	+	0.665515i	−0.291159	+	0.956675i	$0.594041\pi$
$774$		0			0
$775$	−19.2261	+	23.0295i	−0.690621	+	0.827245i
$776$			12.1204i			0.435098i
$777$		0			0
$778$	3.08354	−	3.08354i	0.110550	−	0.110550i
$779$	−15.3261			−0.549114
$780$		0			0
$781$	32.5687			1.16540
$782$	3.30929	−	3.30929i	0.118340	−	0.118340i
$783$		0			0
$784$			7.00000i			0.250000i
$785$	−11.1446	−	4.04052i	−0.397768	−	0.144212i
$786$		0			0
$787$	11.8703	+	11.8703i	0.423132	+	0.423132i	0.886280	−	0.463149i	$-0.153280\pi$
$787$	11.8703	+	11.8703i	0.423132	+	0.423132i	−0.463149	+	0.886280i	$0.653280\pi$
$788$	1.54819	+	1.54819i	0.0551520	+	0.0551520i
$789$		0			0
$790$	−3.63391	−	1.31749i	−0.129289	−	0.0468741i
$791$		0			0
$792$		0			0
$793$	14.0248	−	14.0248i	0.498035	−	0.498035i
$794$	16.2808			0.577785
$795$		0			0
$796$	−4.96672			−0.176041
$797$	−34.2798	+	34.2798i	−1.21425	+	1.21425i	−0.244640	+	0.969614i	$0.578670\pi$
$797$	−34.2798	+	34.2798i	−1.21425	+	1.21425i	−0.969614	+	0.244640i	$0.921330\pi$
$798$		0			0
$799$		−	1.02593i		−	0.0362950i
$800$	−0.448241	−	4.97987i	−0.0158477	−	0.176065i
$801$		0			0
$802$	−10.1547	−	10.1547i	−0.358574	−	0.358574i
$803$	10.1557	+	10.1557i	0.358385	+	0.358385i
$804$		0			0
$805$		0			0
$806$			12.9341i			0.455585i
$807$		0			0
$808$	−1.83825	+	1.83825i	−0.0646695	+	0.0646695i
$809$	17.1768			0.603903			0.301951	−	0.953323i	$-0.402362\pi$
$809$	17.1768			0.603903			0.301951	+	0.953323i	$0.402362\pi$
$810$		0			0
$811$	−17.3055			−0.607680			−0.303840	−	0.952723i	$-0.598269\pi$
$811$	−17.3055			−0.607680			−0.303840	+	0.952723i	$0.598269\pi$
$812$		0			0
$813$		0			0
$814$		−	30.1477i		−	1.05668i
$815$	15.1816	−	41.8741i	0.531790	−	1.46679i
$816$		0			0
$817$	−13.5346	−	13.5346i	−0.473515	−	0.473515i
$818$	23.8521	+	23.8521i	0.833969	+	0.833969i
$819$		0			0
$820$	−3.91293	+	1.83059i	−0.136645	+	0.0639270i
$821$			37.5663i			1.31107i	0.755164	+	0.655536i	$0.227557\pi$
$821$			37.5663i			1.31107i	−0.755164	+	0.655536i	$0.772443\pi$
$822$		0			0
$823$	17.6035	−	17.6035i	0.613619	−	0.613619i	−0.330268	−	0.943887i	$-0.607139\pi$
$823$	17.6035	−	17.6035i	0.613619	−	0.613619i	0.943887	+	0.330268i	$0.107139\pi$
$824$	−8.48528			−0.295599
$825$		0			0
$826$		0			0
$827$	23.3306	−	23.3306i	0.811283	−	0.811283i	−0.173543	−	0.984826i	$-0.555522\pi$
$827$	23.3306	−	23.3306i	0.811283	−	0.811283i	0.984826	+	0.173543i	$0.0555217\pi$
$828$		0			0
$829$		−	5.26288i		−	0.182787i	−0.995815	−	0.0913937i	$-0.970868\pi$
$829$		−	5.26288i		−	0.182787i	0.995815	−	0.0913937i	$-0.0291322\pi$
$830$	21.9394	−	10.2640i	0.761529	−	0.356267i
$831$		0			0
$832$	−1.52430	−	1.52430i	−0.0528456	−	0.0528456i
$833$	23.1650	+	23.1650i	0.802621	+	0.802621i
$834$		0			0
$835$	−4.01487	+	11.0739i	−0.138940	+	0.383227i
$836$			33.3643i			1.15393i
$837$		0			0
$838$	9.54683	−	9.54683i	0.329790	−	0.329790i
$839$	57.1933			1.97453			0.987265	−	0.159083i	$-0.0508537\pi$
$839$	57.1933			1.97453			0.987265	+	0.159083i	$0.0508537\pi$
$840$		0			0
$841$	−20.0991			−0.693073
$842$	15.6923	−	15.6923i	0.540794	−	0.540794i
$843$		0			0
$844$		−	17.7688i		−	0.611626i
$845$	7.91479	+	16.9180i	0.272277	+	0.581998i
$846$		0			0
$847$		0			0
$848$	−5.80135	−	5.80135i	−0.199219	−	0.199219i
$849$		0			0
$850$	−17.9632	−	14.9965i	−0.616132	−	0.514374i
$851$		−	7.16818i		−	0.245722i
$852$		0			0
$853$	−4.37849	+	4.37849i	−0.149917	+	0.149917i	−0.778081	−	0.628164i	$-0.783807\pi$
$853$	−4.37849	+	4.37849i	−0.149917	+	0.149917i	0.628164	+	0.778081i	$0.283807\pi$
$854$		0			0
$855$		0			0
$856$	12.8844			0.440379
$857$	16.8071	−	16.8071i	0.574118	−	0.574118i	−0.359158	−	0.933277i	$-0.616936\pi$
$857$	16.8071	−	16.8071i	0.574118	−	0.574118i	0.933277	+	0.359158i	$0.116936\pi$
$858$		0			0
$859$		−	17.6694i		−	0.602873i	−0.953486	−	0.301437i	$-0.902534\pi$
$859$		−	17.6694i		−	0.602873i	0.953486	−	0.301437i	$-0.0974662\pi$
$860$	−5.07213	−	1.83892i	−0.172958	−	0.0627067i
$861$		0			0
$862$	−7.76877	−	7.76877i	−0.264605	−	0.264605i
$863$	27.7235	+	27.7235i	0.943719	+	0.943719i	0.998499	−	0.0547790i	$-0.0174454\pi$
$863$	27.7235	+	27.7235i	0.943719	+	0.943719i	−0.0547790	+	0.998499i	$0.517445\pi$
$864$		0			0
$865$	22.5609	+	8.17954i	0.767093	+	0.278113i
$866$			1.11673i			0.0379481i
$867$		0			0
$868$		0			0
$869$	7.27029			0.246628
$870$		0			0
$871$	21.2154			0.718857
$872$	8.78478	−	8.78478i	0.297490	−	0.297490i
$873$		0			0
$874$			7.93299i			0.268337i
$875$		0			0
$876$		0			0
$877$	11.3452	+	11.3452i	0.383101	+	0.383101i	0.872218	−	0.489117i	$-0.162681\pi$
$877$	11.3452	+	11.3452i	0.383101	+	0.383101i	−0.489117	+	0.872218i	$0.662681\pi$
$878$	−22.0064	−	22.0064i	−0.742681	−	0.742681i
$879$		0			0
$880$	3.98513	+	8.51829i	0.134339	+	0.287152i
$881$			55.3828i			1.86589i	0.360016	+	0.932946i	$0.382771\pi$
$881$			55.3828i			1.86589i	−0.360016	+	0.932946i	$0.617229\pi$
$882$		0			0
$883$	−12.4488	+	12.4488i	−0.418936	+	0.418936i	−0.884837	−	0.465901i	$-0.845730\pi$
$883$	−12.4488	+	12.4488i	−0.418936	+	0.418936i	0.465901	+	0.884837i	$0.345730\pi$
$884$	−10.0887			−0.339320
$885$		0			0
$886$	10.5059			0.352952
$887$	30.3844	−	30.3844i	1.02021	−	1.02021i	0.0204167	−	0.999792i	$-0.493501\pi$
$887$	30.3844	−	30.3844i	1.02021	−	1.02021i	0.999792	−	0.0204167i	$-0.00649930\pi$
$888$		0			0
$889$		0			0
$890$	2.27383	−	6.27169i	0.0762189	−	0.210228i
$891$		0			0
$892$	8.97558	+	8.97558i	0.300525	+	0.300525i
$893$	1.22968	+	1.22968i	0.0411496	+	0.0411496i
$894$		0			0
$895$	41.3931	−	19.3650i	1.38362	−	0.647301i
$896$		0			0
$897$		0			0
$898$	20.4027	−	20.4027i	0.680846	−	0.680846i
$899$	−17.9006			−0.597019
$900$		0			0
$901$	−38.3967			−1.27918
$902$	5.74547	−	5.74547i	0.191303	−	0.191303i
$903$		0			0
$904$		−	11.4052i		−	0.379330i
$905$	−42.9397	+	20.0886i	−1.42736	+	0.667767i
$906$		0			0
$907$	−25.2085	−	25.2085i	−0.837033	−	0.837033i	0.151434	−	0.988467i	$-0.451611\pi$
$907$	−25.2085	−	25.2085i	−0.837033	−	0.837033i	−0.988467	+	0.151434i	$0.951611\pi$
$908$	−15.7292	−	15.7292i	−0.521992	−	0.521992i
$909$		0			0
$910$		0			0
$911$		−	38.8305i		−	1.28651i	−0.765652	−	0.643255i	$-0.777583\pi$
$911$		−	38.8305i		−	1.28651i	0.765652	−	0.643255i	$-0.222417\pi$
$912$		0			0
$913$	−32.2143	+	32.2143i	−1.06614	+	1.06614i
$914$	−37.8125			−1.25073
$915$		0			0
$916$	−9.74352			−0.321935
$917$		0			0
$918$		0			0
$919$			36.8624i			1.21598i	0.793945	+	0.607990i	$0.208024\pi$
$919$			36.8624i			1.21598i	−0.793945	+	0.607990i	$0.791976\pi$
$920$	0.947538	+	2.02538i	0.0312394	+	0.0667749i
$921$		0			0
$922$	−25.5372	−	25.5372i	−0.841021	−	0.841021i
$923$	−11.8039	−	11.8039i	−0.388530	−	0.388530i
$924$		0			0
$925$	−35.6966	+	3.21307i	−1.17370	+	0.105645i
$926$		−	23.4256i		−	0.769814i
$927$		0			0
$928$	2.10961	−	2.10961i	0.0692513	−	0.0692513i
$929$	37.6070			1.23385			0.616923	−	0.787024i	$-0.288379\pi$
$929$	37.6070			1.23385			0.616923	+	0.787024i	$0.288379\pi$
$930$		0			0
$931$	−55.5309			−1.81995
$932$	5.94584	−	5.94584i	0.194762	−	0.194762i
$933$		0			0
$934$			28.4910i			0.932255i
$935$	41.3774	+	15.0016i	1.35319	+	0.490603i
$936$		0			0
$937$	−28.6676	−	28.6676i	−0.936531	−	0.936531i	0.0615717	−	0.998103i	$-0.480389\pi$
$937$	−28.6676	−	28.6676i	−0.936531	−	0.936531i	−0.998103	+	0.0615717i	$0.980389\pi$
$938$		0			0
$939$		0			0
$940$	0.460827	+	0.167075i	0.0150305	+	0.00544938i
$941$		−	40.4582i		−	1.31890i	−0.751748	−	0.659450i	$-0.770789\pi$
$941$		−	40.4582i		−	1.31890i	0.751748	−	0.659450i	$-0.229211\pi$
$942$		0			0
$943$	1.36609	−	1.36609i	0.0444860	−	0.0444860i
$944$	−3.27242			−0.106508
$945$		0			0
$946$	10.1477			0.329931
$947$	−26.0203	+	26.0203i	−0.845547	+	0.845547i	−0.989574	−	0.144027i	$-0.953995\pi$
$947$	−26.0203	+	26.0203i	−0.845547	+	0.845547i	0.144027	+	0.989574i	$0.453995\pi$
$948$		0			0
$949$		−	7.36144i		−	0.238963i
$950$	39.5052	−	3.55589i	1.28172	−	0.115368i
$951$		0			0
$952$		0			0
$953$	6.94443	+	6.94443i	0.224952	+	0.224952i	0.810580	−	0.585628i	$-0.199152\pi$
$953$	6.94443	+	6.94443i	0.224952	+	0.224952i	−0.585628	+	0.810580i	$0.699152\pi$
$954$		0			0
$955$	7.05899	+	15.0887i	0.228423	+	0.488260i
$956$		−	15.7681i		−	0.509977i
$957$		0			0
$958$	−4.36856	+	4.36856i	−0.141142	+	0.141142i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−10.9265	+	10.9265i	−0.352283	+	0.352283i
$963$		0			0
$964$			23.3303i			0.751420i
$965$	20.3346	−	56.0870i	0.654593	−	1.80551i
$966$		0			0
$967$	−30.6818	−	30.6818i	−0.986661	−	0.986661i	0.0132510	−	0.999912i	$-0.495782\pi$
$967$	−30.6818	−	30.6818i	−0.986661	−	0.986661i	−0.999912	+	0.0132510i	$0.995782\pi$
$968$	−4.72950	−	4.72950i	−0.152012	−	0.152012i
$969$		0			0
$970$	−24.5485	+	11.4846i	−0.788204	+	0.368747i
$971$		−	54.5231i		−	1.74973i	−0.484366	−	0.874865i	$-0.660950\pi$
$971$		−	54.5231i		−	1.74973i	0.484366	−	0.874865i	$-0.339050\pi$
$972$		0			0
$973$		0			0
$974$	−27.4691			−0.880165
$975$		0			0
$976$	9.20081			0.294511
$977$	−20.9216	+	20.9216i	−0.669340	+	0.669340i	−0.957563	−	0.288223i	$-0.906935\pi$
$977$	−20.9216	+	20.9216i	−0.669340	+	0.669340i	0.288223	+	0.957563i	$0.406935\pi$
$978$		0			0
$979$			12.5476i			0.401025i
$980$	−14.1777	+	6.63277i	−0.452889	+	0.211876i
$981$		0			0
$982$	0.261811	+	0.261811i	0.00835472	+	0.00835472i
$983$	20.2009	+	20.2009i	0.644309	+	0.644309i	0.951612	−	0.307303i	$-0.0994264\pi$
$983$	20.2009	+	20.2009i	0.644309	+	0.644309i	−0.307303	+	0.951612i	$0.599426\pi$
$984$		0			0
$985$	−1.66871	+	4.60265i	−0.0531695	+	0.146653i
$986$		−	13.9626i		−	0.444660i
$987$		0			0
$988$	12.0923	−	12.0923i	0.384706	−	0.384706i
$989$	2.41281			0.0767228
$990$		0			0
$991$	33.6836			1.06999			0.534997	−	0.844854i	$-0.320313\pi$
$991$	33.6836			1.06999			0.534997	+	0.844854i	$0.320313\pi$
$992$	−4.24264	+	4.24264i	−0.134704	+	0.134704i
$993$		0			0
$994$		0			0
$995$	−4.70616	−	10.0595i	−0.149195	−	0.318908i
$996$		0			0
$997$	25.1487	+	25.1487i	0.796466	+	0.796466i	0.982536	−	0.186070i	$-0.0595752\pi$
$997$	25.1487	+	25.1487i	0.796466	+	0.796466i	−0.186070	+	0.982536i	$0.559575\pi$
$998$	11.2400	+	11.2400i	0.355795	+	0.355795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.h.737.4	yes	16
3.2	odd	2	inner	2070.2.j.h.737.5	yes	16
5.3	odd	4	inner	2070.2.j.h.323.5	yes	16
15.8	even	4	inner	2070.2.j.h.323.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.h.323.4	✓	16	15.8	even	4	inner
2070.2.j.h.323.5	yes	16	5.3	odd	4	inner
2070.2.j.h.737.4	yes	16	1.1	even	1	trivial
2070.2.j.h.737.5	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.02538 - 0.947538i) q^{5} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.02538 - 0.947538i) q^{5} +(0.707107 + 0.707107i) q^{8} +(-0.762151 + 2.10217i) q^{10} -4.20577i q^{11} +(-1.52430 + 1.52430i) q^{13} -1.00000 q^{16} +(-3.30929 + 3.30929i) q^{17} -7.93299i q^{19} +(-0.947538 - 2.02538i) q^{20} +(2.97393 + 2.97393i) q^{22} +(0.707107 + 0.707107i) q^{23} +(3.20434 - 3.83825i) q^{25} -2.15569i q^{26} +2.98344 q^{29} -6.00000 q^{31} +(0.707107 - 0.707107i) q^{32} -4.68004i q^{34} +(-5.06867 - 5.06867i) q^{37} +(5.60947 + 5.60947i) q^{38} +(2.10217 + 0.762151i) q^{40} -1.93194i q^{41} +(1.70611 - 1.70611i) q^{43} -4.20577 q^{44} -1.00000 q^{46} +(-0.155008 + 0.155008i) q^{47} -7.00000i q^{49} +(0.448241 + 4.97987i) q^{50} +(1.52430 + 1.52430i) q^{52} +(5.80135 + 5.80135i) q^{53} +(-3.98513 - 8.51829i) q^{55} +(-2.10961 + 2.10961i) q^{58} +3.27242 q^{59} -9.20081 q^{61} +(4.24264 - 4.24264i) q^{62} +1.00000i q^{64} +(-1.64296 + 4.53163i) q^{65} +(-6.95906 - 6.95906i) q^{67} +(3.30929 + 3.30929i) q^{68} +7.74381i q^{71} +(-2.41469 + 2.41469i) q^{73} +7.16818 q^{74} -7.93299 q^{76} +1.72865i q^{79} +(-2.02538 + 0.947538i) q^{80} +(1.36609 + 1.36609i) q^{82} +(-7.65955 - 7.65955i) q^{83} +(-3.56690 + 9.83825i) q^{85} +2.41281i q^{86} +(2.97393 - 2.97393i) q^{88} -2.98344 q^{89} +(0.707107 - 0.707107i) q^{92} -0.219215i q^{94} +(-7.51681 - 16.0673i) q^{95} +(8.57043 + 8.57043i) q^{97} +(4.94975 + 4.94975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{13} - 16 q^{16} + 8 q^{22} - 16 q^{25} - 96 q^{31} + 24 q^{37} + 8 q^{43} - 16 q^{46} + 16 q^{52} - 32 q^{58} + 16 q^{61} - 8 q^{67} - 32 q^{73} + 16 q^{76} + 32 q^{82} + 96 q^{85} + 8 q^{88} + 80 q^{97}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^13 - 16 * q^16 + 8 * q^22 - 16 * q^25 - 96 * q^31 + 24 * q^37 + 8 * q^43 - 16 * q^46 + 16 * q^52 - 32 * q^58 + 16 * q^61 - 8 * q^67 - 32 * q^73 + 16 * q^76 + 32 * q^82 + 96 * q^85 + 8 * q^88 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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