LMFDB - Embedded newform 592.2.be.d.415.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(319,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("592.319");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.be (of order $12$, degree $4$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 14x^{14} + 135x^{12} - 686x^{10} + 2521x^{8} - 4452x^{6} + 5592x^{4} - 2016x^{2} + 576 $ x^16 - 14x^14 + 135x^12 - 686x^10 + 2521x^8 - 4452x^6 + 5592x^4 - 2016*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			415.3
Root			$-1.17183 + 0.676554i$ of defining polynomial
Character	$\chi$	$=$	592.415
Dual form			592.2.be.d.495.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.676554 - 1.17183i) q^{3} +(-1.86603 + 0.500000i) q^{5} +(-1.68397 - 0.972241i) q^{7} +(0.584551 + 1.01247i) q^{9} +O(q^{10})$	\(q+(0.676554 - 1.17183i) q^{3} +(-1.86603 + 0.500000i) q^{5} +(-1.68397 - 0.972241i) q^{7} +(0.584551 + 1.01247i) q^{9} -4.28813 q^{11} +(-5.64462 + 1.51247i) q^{13} +(-0.676554 + 2.52493i) q^{15} +(-0.293946 + 1.09702i) q^{17} +(1.38828 + 5.18115i) q^{19} +(-2.27859 + 1.31555i) q^{21} +(4.50459 - 4.50459i) q^{23} +(-1.09808 + 0.633975i) q^{25} +5.64124 q^{27} +(-2.59702 + 2.59702i) q^{29} +(-7.21081 - 7.21081i) q^{31} +(-2.90115 + 5.02494i) q^{33} +(3.62845 + 0.972241i) q^{35} +(-5.93857 + 1.31660i) q^{37} +(-2.04654 + 7.63777i) q^{39} +(-0.465928 - 0.269004i) q^{41} +(4.65070 - 4.65070i) q^{43} +(-1.59702 - 1.59702i) q^{45} +6.56143i q^{47} +(-1.60949 - 2.78772i) q^{49} +(1.08665 + 1.08665i) q^{51} +(4.84154 + 8.38580i) q^{53} +(8.00177 - 2.14407i) q^{55} +(7.01064 + 1.87850i) q^{57} +(-6.02211 - 1.61362i) q^{59} +(-2.43810 - 9.09913i) q^{61} -2.27330i q^{63} +(9.77677 - 5.64462i) q^{65} +(-3.23666 + 5.60606i) q^{67} +(-2.23100 - 8.32619i) q^{69} +(0.284761 + 0.164407i) q^{71} +3.46410i q^{73} +1.71567i q^{75} +(7.22109 + 4.16910i) q^{77} +(-3.27477 - 12.2216i) q^{79} +(2.06295 - 3.57313i) q^{81} +(-7.09188 + 4.09450i) q^{83} -2.19404i q^{85} +(1.28623 + 4.80028i) q^{87} +(12.7273 + 3.41028i) q^{89} +(10.9759 + 2.94097i) q^{91} +(-13.3283 + 3.57131i) q^{93} +(-5.18115 - 8.97401i) q^{95} +(-8.83638 - 8.83638i) q^{97} +(-2.50663 - 4.34161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{5} - 4 q^{9}+O(q^{10}) $ 16 * q - 16 * q^5 - 4 * q^9	$ 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89} - 60 q^{93} - 4 q^{97}+O(q^{100}) $ 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	0.676554	−	1.17183i	0.390608	−	0.676554i	−0.601922	−	0.798555i	$-0.705598\pi$
$3$	0.676554	−	1.17183i	0.390608	−	0.676554i	0.992530	+	0.122002i	$0.0389313\pi$
$4$		0			0
$5$	−1.86603	+	0.500000i	−0.834512	+	0.223607i	−0.650681	−	0.759351i	$-0.725517\pi$
$5$	−1.86603	+	0.500000i	−0.834512	+	0.223607i	−0.183831	+	0.982958i	$0.558850\pi$
$6$		0			0
$7$	−1.68397	−	0.972241i	−0.636481	−	0.367473i	0.146776	−	0.989170i	$-0.453110\pi$
$7$	−1.68397	−	0.972241i	−0.636481	−	0.367473i	−0.783258	+	0.621697i	$0.786444\pi$
$8$		0			0
$9$	0.584551	+	1.01247i	0.194850	+	0.337490i
$10$		0			0
$11$	−4.28813			−1.29292			−0.646460	−	0.762948i	$-0.723751\pi$
$11$	−4.28813			−1.29292			−0.646460	+	0.762948i	$0.723751\pi$
$12$		0			0
$13$	−5.64462	+	1.51247i	−1.56554	+	0.419484i	−0.934411	−	0.356197i	$-0.884073\pi$
$13$	−5.64462	+	1.51247i	−1.56554	+	0.419484i	−0.631125	+	0.775681i	$0.717406\pi$
$14$		0			0
$15$	−0.676554	+	2.52493i	−0.174685	+	0.651935i
$16$		0			0
$17$	−0.293946	+	1.09702i	−0.0712924	+	0.266067i	−0.992367	−	0.123319i	$-0.960646\pi$
$17$	−0.293946	+	1.09702i	−0.0712924	+	0.266067i	0.921075	+	0.389386i	$0.127313\pi$
$18$		0			0
$19$	1.38828	+	5.18115i	0.318494	+	1.18864i	0.920692	+	0.390290i	$0.127625\pi$
$19$	1.38828	+	5.18115i	0.318494	+	1.18864i	−0.602198	+	0.798347i	$0.705708\pi$
$20$		0			0
$21$	−2.27859	+	1.31555i	−0.497230	+	0.287076i
$22$		0			0
$23$	4.50459	−	4.50459i	0.939272	−	0.939272i	−0.0589865	−	0.998259i	$-0.518787\pi$
$23$	4.50459	−	4.50459i	0.939272	−	0.939272i	0.998259	+	0.0589865i	$0.0187869\pi$
$24$		0			0
$25$	−1.09808	+	0.633975i	−0.219615	+	0.126795i
$26$		0			0
$27$	5.64124			1.08566
$28$		0			0
$29$	−2.59702	+	2.59702i	−0.482255	+	0.482255i	−0.905851	−	0.423596i	$-0.860768\pi$
$29$	−2.59702	+	2.59702i	−0.482255	+	0.482255i	0.423596	+	0.905851i	$0.360768\pi$
$30$		0			0
$31$	−7.21081	−	7.21081i	−1.29510	−	1.29510i	−0.931591	−	0.363508i	$-0.881579\pi$
$31$	−7.21081	−	7.21081i	−1.29510	−	1.29510i	−0.363508	−	0.931591i	$-0.618421\pi$
$32$		0			0
$33$	−2.90115	+	5.02494i	−0.505026	+	0.874730i
$34$		0			0
$35$	3.62845	+	0.972241i	0.613321	+	0.164339i
$36$		0			0
$37$	−5.93857	+	1.31660i	−0.976294	+	0.216448i
$37$	−5.93857	+	1.31660i	−0.976294	+	0.216448i
$38$		0			0
$39$	−2.04654	+	7.63777i	−0.327708	+	1.22302i
$40$		0			0
$41$	−0.465928	−	0.269004i	−0.0727657	−	0.0420113i	0.463176	−	0.886266i	$-0.346710\pi$
$41$	−0.465928	−	0.269004i	−0.0727657	−	0.0420113i	−0.535941	+	0.844255i	$0.680043\pi$
$42$		0			0
$43$	4.65070	−	4.65070i	0.709225	−	0.709225i	−0.257147	−	0.966372i	$-0.582783\pi$
$43$	4.65070	−	4.65070i	0.709225	−	0.709225i	0.966372	+	0.257147i	$0.0827826\pi$
$44$		0			0
$45$	−1.59702	−	1.59702i	−0.238070	−	0.238070i
$46$		0			0
$47$			6.56143i			0.957083i	0.878065	+	0.478541i	$0.158834\pi$
$47$			6.56143i			0.957083i	−0.878065	+	0.478541i	$0.841166\pi$
$48$		0			0
$49$	−1.60949	−	2.78772i	−0.229928	−	0.398246i
$50$		0			0
$51$	1.08665	+	1.08665i	0.152161	+	0.152161i
$52$		0			0
$53$	4.84154	+	8.38580i	0.665037	+	1.15188i	0.979275	+	0.202534i	$0.0649177\pi$
$53$	4.84154	+	8.38580i	0.665037	+	1.15188i	−0.314238	+	0.949344i	$0.601749\pi$
$54$		0			0
$55$	8.00177	−	2.14407i	1.07896	−	0.289106i
$56$		0			0
$57$	7.01064	+	1.87850i	0.928583	+	0.248813i
$58$		0			0
$59$	−6.02211	−	1.61362i	−0.784011	−	0.210075i	−0.155459	−	0.987842i	$-0.549686\pi$
$59$	−6.02211	−	1.61362i	−0.784011	−	0.210075i	−0.628553	+	0.777767i	$0.716352\pi$
$60$		0			0
$61$	−2.43810	−	9.09913i	−0.312167	−	1.16502i	−0.926598	−	0.376053i	$-0.877281\pi$
$61$	−2.43810	−	9.09913i	−0.312167	−	1.16502i	0.614431	−	0.788971i	$-0.289386\pi$
$62$		0			0
$63$		−	2.27330i		−	0.286409i
$64$		0			0
$65$	9.77677	−	5.64462i	1.21266	−	0.700129i
$66$		0			0
$67$	−3.23666	+	5.60606i	−0.395421	+	0.684890i	−0.993155	−	0.116805i	$-0.962735\pi$
$67$	−3.23666	+	5.60606i	−0.395421	+	0.684890i	0.597734	+	0.801695i	$0.296068\pi$
$68$		0			0
$69$	−2.23100	−	8.32619i	−0.268580	−	1.00236i
$70$		0			0
$71$	0.284761	+	0.164407i	0.0337950	+	0.0195115i	0.516802	−	0.856105i	$-0.327122\pi$
$71$	0.284761	+	0.164407i	0.0337950	+	0.0195115i	−0.483007	+	0.875616i	$0.660456\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$		0			0
$75$			1.71567i			0.198109i
$76$		0			0
$77$	7.22109	+	4.16910i	0.822920	+	0.475113i
$78$		0			0
$79$	−3.27477	−	12.2216i	−0.368440	−	1.37504i	−0.862697	−	0.505721i	$-0.831226\pi$
$79$	−3.27477	−	12.2216i	−0.368440	−	1.37504i	0.494257	−	0.869316i	$-0.335440\pi$
$80$		0			0
$81$	2.06295	−	3.57313i	0.229217	−	0.397015i
$82$		0			0
$83$	−7.09188	+	4.09450i	−0.778435	+	0.449430i	−0.835875	−	0.548919i	$-0.815039\pi$
$83$	−7.09188	+	4.09450i	−0.778435	+	0.449430i	0.0574405	+	0.998349i	$0.481706\pi$
$84$		0			0
$85$		−	2.19404i		−	0.237977i
$86$		0			0
$87$	1.28623	+	4.80028i	0.137898	+	0.514644i
$88$		0			0
$89$	12.7273	+	3.41028i	1.34910	+	0.361489i	0.859801	−	0.510629i	$-0.170588\pi$
$89$	12.7273	+	3.41028i	1.34910	+	0.361489i	0.489295	+	0.872118i	$0.337254\pi$
$90$		0			0
$91$	10.9759	+	2.94097i	1.15058	+	0.308298i
$92$		0			0
$93$	−13.3283	+	3.57131i	−1.38208	+	0.370327i
$94$		0			0
$95$	−5.18115	−	8.97401i	−0.531574	−	0.920714i
$96$		0			0
$97$	−8.83638	−	8.83638i	−0.897198	−	0.897198i	0.0979894	−	0.995187i	$-0.468759\pi$
$97$	−8.83638	−	8.83638i	−0.897198	−	0.897198i	−0.995187	+	0.0979894i	$0.968759\pi$
$98$		0			0
$99$	−2.50663	−	4.34161i	−0.251926	−	0.436348i
$100$		0			0
$101$			4.58332i			0.456057i	0.973654	+	0.228029i	$0.0732280\pi$
$101$			4.58332i			0.456057i	−0.973654	+	0.228029i	$0.926772\pi$
$102$		0			0
$103$	4.25153	+	4.25153i	0.418916	+	0.418916i	0.884830	−	0.465914i	$-0.154274\pi$
$103$	4.25153	+	4.25153i	0.418916	+	0.418916i	−0.465914	+	0.884830i	$0.654274\pi$
$104$		0			0
$105$	3.59414	−	3.59414i	0.350752	−	0.350752i
$106$		0			0
$107$	−13.4821	−	7.78388i	−1.30336	−	0.752496i	−0.322382	−	0.946610i	$-0.604484\pi$
$107$	−13.4821	−	7.78388i	−1.30336	−	0.752496i	−0.980979	+	0.194113i	$0.937817\pi$
$108$		0			0
$109$	−1.13397	+	4.23205i	−0.108615	+	0.405357i	−0.998730	−	0.0503788i	$-0.983957\pi$
$109$	−1.13397	+	4.23205i	−0.108615	+	0.405357i	0.890115	+	0.455736i	$0.150624\pi$
$110$		0			0
$111$	−2.47493	+	7.84971i	−0.234910	+	0.745062i
$112$		0			0
$113$	7.91468	+	2.12073i	0.744550	+	0.199502i	0.611099	−	0.791554i	$-0.290728\pi$
$113$	7.91468	+	2.12073i	0.744550	+	0.199502i	0.133451	+	0.991055i	$0.457394\pi$
$114$		0			0
$115$	−6.15339	+	10.6580i	−0.573806	+	0.993862i
$116$		0			0
$117$	−4.83090	−	4.83090i	−0.446617	−	0.446617i
$118$		0			0
$119$	1.56157	−	1.56157i	0.143149	−	0.143149i
$120$		0			0
$121$	7.38809			0.671644
$122$		0			0
$123$	−0.630450	+	0.363991i	−0.0568458	+	0.0328199i
$124$		0			0
$125$	8.56218	−	8.56218i	0.765824	−	0.765824i
$126$		0			0
$127$	0.710303	−	0.410094i	0.0630292	−	0.0363899i	−0.468154	−	0.883647i	$-0.655081\pi$
$127$	0.710303	−	0.410094i	0.0630292	−	0.0363899i	0.531183	+	0.847257i	$0.321747\pi$
$128$		0			0
$129$	−2.30336	−	8.59625i	−0.202799	−	0.756858i
$130$		0			0
$131$	5.24350	−	19.5690i	0.458127	−	1.70975i	−0.220603	−	0.975364i	$-0.570802\pi$
$131$	5.24350	−	19.5690i	0.458127	−	1.70975i	0.678729	−	0.734388i	$-0.262531\pi$
$132$		0			0
$133$	2.69949	−	10.0746i	0.234076	−	0.873583i
$134$		0			0
$135$	−10.5267	+	2.82062i	−0.905994	+	0.242760i
$136$		0			0
$137$	12.7554			1.08977			0.544886	−	0.838510i	$-0.316573\pi$
$137$	12.7554			1.08977			0.544886	+	0.838510i	$0.316573\pi$
$138$		0			0
$139$	−6.10134	−	10.5678i	−0.517509	−	0.896351i	−0.999793	−	0.0203365i	$-0.993526\pi$
$139$	−6.10134	−	10.5678i	−0.517509	−	0.896351i	0.482285	−	0.876015i	$-0.339807\pi$
$140$		0			0
$141$	7.68885	+	4.43916i	0.647518	+	0.373845i
$142$		0			0
$143$	24.2049	−	6.48568i	2.02411	−	0.542360i
$144$		0			0
$145$	3.54760	−	6.14462i	0.294612	−	0.510283i
$146$		0			0
$147$	−4.35563			−0.359247
$148$		0			0
$149$	8.82359			0.722857			0.361428	−	0.932400i	$-0.382289\pi$
$149$	8.82359			0.722857			0.361428	+	0.932400i	$0.382289\pi$
$150$		0			0
$151$	−7.88736	+	13.6613i	−0.641864	+	1.11174i	0.343152	+	0.939280i	$0.388505\pi$
$151$	−7.88736	+	13.6613i	−0.641864	+	1.11174i	−0.985016	+	0.172462i	$0.944828\pi$
$152$		0			0
$153$	−1.28253	+	0.343653i	−0.103686	+	0.0277827i
$154$		0			0
$155$	17.0610	+	9.85014i	1.37037	+	0.791183i
$156$		0			0
$157$	−0.401152	−	0.694815i	−0.0320154	−	0.0554523i	0.849574	−	0.527470i	$-0.176859\pi$
$157$	−0.401152	−	0.694815i	−0.0320154	−	0.0554523i	−0.881589	+	0.472018i	$0.843526\pi$
$158$		0			0
$159$	13.1023			1.03908
$160$		0			0
$161$	−11.9652	+	3.20605i	−0.942986	+	0.252672i
$162$		0			0
$163$	0.826136	−	3.08318i	0.0647080	−	0.241493i	−0.925995	−	0.377536i	$-0.876772\pi$
$163$	0.826136	−	3.08318i	0.0647080	−	0.241493i	0.990703	+	0.136042i	$0.0434383\pi$
$164$		0			0
$165$	2.90115	−	10.8272i	0.225854	−	0.842900i
$166$		0			0
$167$	2.64876	+	9.88532i	0.204967	+	0.764949i	0.989459	+	0.144810i	$0.0462571\pi$
$167$	2.64876	+	9.88532i	0.204967	+	0.764949i	−0.784492	+	0.620139i	$0.787076\pi$
$168$		0			0
$169$	18.3158	−	10.5746i	1.40891	−	0.813435i
$170$		0			0
$171$	−4.43424	+	4.43424i	−0.339095	+	0.339095i
$172$		0			0
$173$	−0.406913	+	0.234932i	−0.0309371	+	0.0178615i	−0.515389	−	0.856956i	$-0.672352\pi$
$173$	−0.406913	+	0.234932i	−0.0309371	+	0.0178615i	0.484452	+	0.874818i	$0.339019\pi$
$174$		0			0
$175$	2.46551			0.186375
$176$		0			0
$177$	−5.96516	+	5.96516i	−0.448369	+	0.448369i
$178$		0			0
$179$	5.94041	+	5.94041i	0.444007	+	0.444007i	0.893356	−	0.449349i	$-0.148344\pi$
$179$	5.94041	+	5.94041i	0.444007	+	0.444007i	−0.449349	+	0.893356i	$0.648344\pi$
$180$		0			0
$181$	−10.4623	+	18.1212i	−0.777655	+	1.34694i	0.155635	+	0.987815i	$0.450257\pi$
$181$	−10.4623	+	18.1212i	−0.777655	+	1.34694i	−0.933290	+	0.359123i	$0.883076\pi$
$182$		0			0
$183$	−12.3121	−	3.29902i	−0.910137	−	0.243870i
$184$		0			0
$185$	10.4232	−	5.42609i	0.766330	−	0.398934i
$186$		0			0
$187$	1.26048	−	4.70418i	0.0921754	−	0.344003i
$188$		0			0
$189$	−9.49969	−	5.48465i	−0.691001	−	0.398949i
$190$		0			0
$191$	−9.59106	+	9.59106i	−0.693985	+	0.693985i	−0.963106	−	0.269122i	$-0.913267\pi$
$191$	−9.59106	+	9.59106i	−0.693985	+	0.693985i	0.269122	+	0.963106i	$0.413267\pi$
$192$		0			0
$193$	2.18491	+	2.18491i	0.157274	+	0.157274i	0.781357	−	0.624084i	$-0.214528\pi$
$193$	2.18491	+	2.18491i	0.157274	+	0.157274i	−0.624084	+	0.781357i	$0.714528\pi$
$194$		0			0
$195$		−	15.2755i		−	1.09390i
$196$		0			0
$197$	4.98904	+	8.64128i	0.355455	+	0.615666i	0.987196	−	0.159514i	$-0.0509927\pi$
$197$	4.98904	+	8.64128i	0.355455	+	0.615666i	−0.631741	+	0.775180i	$0.717659\pi$
$198$		0			0
$199$	0.820188	+	0.820188i	0.0581416	+	0.0581416i	0.735580	−	0.677438i	$-0.236910\pi$
$199$	0.820188	+	0.820188i	0.0581416	+	0.0581416i	−0.677438	+	0.735580i	$0.736910\pi$
$200$		0			0
$201$	4.37955	+	7.58560i	0.308910	+	0.535047i
$202$		0			0
$203$	6.89824	−	1.84838i	0.484162	−	0.129731i
$204$		0			0
$205$	1.00394	+	0.269004i	0.0701179	+	0.0187880i
$206$		0			0
$207$	7.19393	+	1.92761i	0.500013	+	0.133978i
$208$		0			0
$209$	−5.95315	−	22.2174i	−0.411788	−	1.53681i
$210$		0			0
$211$			0.457624i			0.0315041i	0.999876	+	0.0157521i	$0.00501424\pi$
$211$			0.457624i			0.0315041i	−0.999876	+	0.0157521i	$0.994986\pi$
$212$		0			0
$213$	0.385313	−	0.222460i	0.0264012	−	0.0152427i
$214$		0			0
$215$	−6.35297	+	11.0037i	−0.433269	+	0.750444i
$216$		0			0
$217$	5.13215	+	19.1534i	0.348393	+	1.30022i
$218$		0			0
$219$	4.05932	+	2.34365i	0.274304	+	0.158369i
$220$		0			0
$221$		−	6.63686i		−	0.446443i
$222$		0			0
$223$			17.9599i			1.20268i	0.798992	+	0.601342i	$0.205367\pi$
$223$			17.9599i			1.20268i	−0.798992	+	0.601342i	$0.794633\pi$
$224$		0			0
$225$	−1.28376	−	0.741180i	−0.0855841	−	0.0494120i
$226$		0			0
$227$	4.62787	+	17.2715i	0.307163	+	1.14635i	0.931068	+	0.364847i	$0.118879\pi$
$227$	4.62787	+	17.2715i	0.307163	+	1.14635i	−0.623905	+	0.781500i	$0.714455\pi$
$228$		0			0
$229$	5.66910	−	9.81917i	0.374625	−	0.648869i	−0.615646	−	0.788023i	$-0.711105\pi$
$229$	5.66910	−	9.81917i	0.374625	−	0.648869i	0.990271	+	0.139154i	$0.0444382\pi$
$230$		0			0
$231$	9.77092	−	5.64124i	0.642879	−	0.371166i
$232$		0			0
$233$			5.84129i			0.382675i	0.981524	+	0.191338i	$0.0612826\pi$
$233$			5.84129i			0.382675i	−0.981524	+	0.191338i	$0.938717\pi$
$234$		0			0
$235$	−3.28072	−	12.2438i	−0.214010	−	0.798697i
$236$		0			0
$237$	−16.5371	−	4.43111i	−1.07420	−	0.287832i
$238$		0			0
$239$	−13.9407	−	3.73541i	−0.901752	−	0.241624i	−0.221983	−	0.975050i	$-0.571253\pi$
$239$	−13.9407	−	3.73541i	−0.901752	−	0.241624i	−0.679768	+	0.733427i	$0.737920\pi$
$240$		0			0
$241$	−17.1358	+	4.59152i	−1.10381	+	0.295766i	−0.764316	−	0.644842i	$-0.776923\pi$
$241$	−17.1358	+	4.59152i	−1.10381	+	0.295766i	−0.339496	+	0.940607i	$0.610257\pi$
$242$		0			0
$243$	5.67047	+	9.82154i	0.363761	+	0.630052i
$244$		0			0
$245$	4.39722	+	4.39722i	0.280928	+	0.280928i
$246$		0			0
$247$	−15.6727	−	27.1459i	−0.997228	−	1.72725i
$248$		0			0
$249$			11.0806i			0.702204i
$250$		0			0
$251$	−12.7763	−	12.7763i	−0.806433	−	0.806433i	0.177659	−	0.984092i	$-0.443147\pi$
$251$	−12.7763	−	12.7763i	−0.806433	−	0.806433i	−0.984092	+	0.177659i	$0.943147\pi$
$252$		0			0
$253$	−19.3163	+	19.3163i	−1.21440	+	1.21440i
$254$		0			0
$255$	−2.57104	−	1.48439i	−0.161004	−	0.0929560i
$256$		0			0
$257$	−4.68569	+	17.4872i	−0.292285	+	1.09082i	0.651065	+	0.759022i	$0.274323\pi$
$257$	−4.68569	+	17.4872i	−0.292285	+	1.09082i	−0.943350	+	0.331800i	$0.892344\pi$
$258$		0			0
$259$	11.2804	+	3.55660i	0.700932	+	0.220996i
$260$		0			0
$261$	−4.14750	−	1.11132i	−0.256724	−	0.0687889i
$262$		0			0
$263$	12.7376	−	22.0622i	0.785437	−	1.36042i	−0.143301	−	0.989679i	$-0.545772\pi$
$263$	12.7376	−	22.0622i	0.785437	−	1.36042i	0.928738	−	0.370737i	$-0.120895\pi$
$264$		0			0
$265$	−13.2273	−	13.2273i	−0.812549	−	0.812549i
$266$		0			0
$267$	12.6070	−	12.6070i	0.771535	−	0.771535i
$268$		0			0
$269$	−29.7585			−1.81441			−0.907203	−	0.420693i	$-0.861787\pi$
$269$	−29.7585			−1.81441			−0.907203	+	0.420693i	$0.861787\pi$
$270$		0			0
$271$	1.51149	−	0.872660i	0.0918166	−	0.0530103i	−0.453389	−	0.891313i	$-0.649785\pi$
$271$	1.51149	−	0.872660i	0.0918166	−	0.0530103i	0.545205	+	0.838303i	$0.316452\pi$
$272$		0			0
$273$	10.8721	−	10.8721i	0.658008	−	0.658008i
$274$		0			0
$275$	4.70870	−	2.71857i	0.283945	−	0.163936i
$276$		0			0
$277$	−0.0892292	−	0.333008i	−0.00536126	−	0.0200085i	0.963193	−	0.268809i	$-0.0866302\pi$
$277$	−0.0892292	−	0.333008i	−0.00536126	−	0.0200085i	−0.968555	+	0.248801i	$0.919964\pi$
$278$		0			0
$279$	3.08565	−	11.5158i	0.184733	−	0.689434i
$280$		0			0
$281$	−2.76661	+	10.3251i	−0.165042	+	0.615946i	0.832993	+	0.553284i	$0.186626\pi$
$281$	−2.76661	+	10.3251i	−0.165042	+	0.615946i	−0.998035	+	0.0626619i	$0.980041\pi$
$282$		0			0
$283$	−17.6914	+	4.74040i	−1.05164	+	0.281787i	−0.742931	−	0.669368i	$-0.766565\pi$
$283$	−17.6914	+	4.74040i	−1.05164	+	0.281787i	−0.308713	+	0.951155i	$0.599898\pi$
$284$		0			0
$285$	−14.0213			−0.830550
$286$		0			0
$287$	0.523073	+	0.905989i	0.0308760	+	0.0534788i
$288$		0			0
$289$	13.6054	+	7.85507i	0.800316	+	0.462063i
$290$		0			0
$291$	−16.3330	+	4.37641i	−0.957456	+	0.256549i
$292$		0			0
$293$	−11.1922	+	19.3855i	−0.653856	+	1.13251i	0.328323	+	0.944566i	$0.393517\pi$
$293$	−11.1922	+	19.3855i	−0.653856	+	1.13251i	−0.982179	+	0.187947i	$0.939817\pi$
$294$		0			0
$295$	12.0442			0.701241
$296$		0			0
$297$	−24.1904			−1.40367
$298$		0			0
$299$	−18.6136	+	32.2398i	−1.07645	+	1.86447i
$300$		0			0
$301$	−12.3532	+	3.31004i	−0.712029	+	0.190788i
$302$		0			0
$303$	5.37085	+	3.10086i	0.308547	+	0.178140i
$304$		0			0
$305$	9.09913	+	15.7602i	0.521015	+	0.902424i
$306$		0			0
$307$	−30.9897			−1.76868			−0.884338	−	0.466846i	$-0.845390\pi$
$307$	−30.9897			−1.76868			−0.884338	+	0.466846i	$0.845390\pi$
$308$		0			0
$309$	7.85844	−	2.10566i	0.447051	−	0.119787i
$310$		0			0
$311$	−5.54023	+	20.6764i	−0.314158	+	1.17245i	0.610613	+	0.791929i	$0.290923\pi$
$311$	−5.54023	+	20.6764i	−0.314158	+	1.17245i	−0.924771	+	0.380524i	$0.875744\pi$
$312$		0			0
$313$	−1.20423	+	4.49424i	−0.0680670	+	0.254029i	−0.991572	−	0.129557i	$-0.958644\pi$
$313$	−1.20423	+	4.49424i	−0.0680670	+	0.254029i	0.923505	+	0.383586i	$0.125311\pi$
$314$		0			0
$315$	1.13665	+	4.24203i	0.0640429	+	0.239011i
$316$		0			0
$317$	27.8142	−	16.0585i	1.56220	−	0.901937i	0.565166	−	0.824977i	$-0.308812\pi$
$317$	27.8142	−	16.0585i	1.56220	−	0.901937i	0.997034	−	0.0769593i	$-0.0245212\pi$
$318$		0			0
$319$	11.1364	−	11.1364i	0.623517	−	0.623517i
$320$		0			0
$321$	−18.2427	+	10.5324i	−1.01821	+	0.587863i
$322$		0			0
$323$	−6.09191			−0.338963
$324$		0			0
$325$	5.23935	−	5.23935i	0.290627	−	0.290627i
$326$		0			0
$327$	4.19203	+	4.19203i	0.231820	+	0.231820i
$328$		0			0
$329$	6.37929	−	11.0493i	0.351702	−	0.609166i
$330$		0			0
$331$	9.17359	+	2.45806i	0.504226	+	0.135107i	0.501961	−	0.864890i	$-0.332612\pi$
$331$	9.17359	+	2.45806i	0.504226	+	0.135107i	0.00226548	+	0.999997i	$0.499279\pi$
$332$		0			0
$333$	−4.80441	−	5.24301i	−0.263280	−	0.287315i
$334$		0			0
$335$	3.23666	−	12.0794i	0.176838	−	0.659968i
$336$		0			0
$337$	−26.3619	−	15.2200i	−1.43602	−	0.829088i	−0.438453	−	0.898754i	$-0.644473\pi$
$337$	−26.3619	−	15.2200i	−1.43602	−	0.829088i	−0.997570	+	0.0696657i	$0.977807\pi$
$338$		0			0
$339$	7.83983	−	7.83983i	0.425801	−	0.425801i
$340$		0			0
$341$	30.9209	+	30.9209i	1.67446	+	1.67446i
$342$		0			0
$343$			19.8706i			1.07291i
$344$		0			0
$345$	8.32619	+	14.4214i	0.448267	+	0.776421i
$346$		0			0
$347$	−10.6669	−	10.6669i	−0.572627	−	0.572627i	0.360235	−	0.932862i	$-0.382697\pi$
$347$	−10.6669	−	10.6669i	−0.572627	−	0.572627i	−0.932862	+	0.360235i	$0.882697\pi$
$348$		0			0
$349$	−2.97781	−	5.15771i	−0.159398	−	0.276086i	0.775254	−	0.631650i	$-0.217622\pi$
$349$	−2.97781	−	5.15771i	−0.159398	−	0.276086i	−0.934652	+	0.355564i	$0.884289\pi$
$350$		0			0
$351$	−31.8427	+	8.53221i	−1.69964	+	0.455416i
$352$		0			0
$353$	3.10201	+	0.831181i	0.165103	+	0.0442393i	0.340424	−	0.940272i	$-0.389429\pi$
$353$	3.10201	+	0.831181i	0.165103	+	0.0442393i	−0.175320	+	0.984511i	$0.556096\pi$
$354$		0			0
$355$	−0.613576	−	0.164407i	−0.0325652	−	0.00872582i
$356$		0			0
$357$	−0.773400	−	2.88637i	−0.0409327	−	0.152763i
$358$		0			0
$359$			3.07163i			0.162115i	0.996709	+	0.0810573i	$0.0258297\pi$
$359$			3.07163i			0.162115i	−0.996709	+	0.0810573i	$0.974170\pi$
$360$		0			0
$361$	−8.46245	+	4.88580i	−0.445392	+	0.257147i
$362$		0			0
$363$	4.99844	−	8.65755i	0.262350	−	0.454403i
$364$		0			0
$365$	−1.73205	−	6.46410i	−0.0906597	−	0.338347i
$366$		0			0
$367$	9.46476	+	5.46448i	0.494056	+	0.285244i	0.726256	−	0.687425i	$-0.241259\pi$
$367$	9.46476	+	5.46448i	0.494056	+	0.285244i	−0.232199	+	0.972668i	$0.574592\pi$
$368$		0			0
$369$		−	0.628985i		−	0.0327436i
$370$		0			0
$371$		−	18.8286i		−	0.977532i
$372$		0			0
$373$	18.6061	+	10.7422i	0.963387	+	0.556212i	0.897214	−	0.441596i	$-0.145588\pi$
$373$	18.6061	+	10.7422i	0.963387	+	0.556212i	0.0661733	+	0.997808i	$0.478921\pi$
$374$		0			0
$375$	−4.24060	−	15.8261i	−0.218984	−	0.817259i
$376$		0			0
$377$	10.7313	−	18.5871i	0.552689	−	0.957285i
$378$		0			0
$379$	−8.98938	+	5.19002i	−0.461753	+	0.266594i	−0.712781	−	0.701386i	$-0.752565\pi$
$379$	−8.98938	+	5.19002i	−0.461753	+	0.266594i	0.251028	+	0.967980i	$0.419231\pi$
$380$		0			0
$381$		−	1.10980i		−	0.0568569i
$382$		0			0
$383$	−2.37100	−	8.84867i	−0.121152	−	0.452146i	0.878521	−	0.477703i	$-0.158531\pi$
$383$	−2.37100	−	8.84867i	−0.121152	−	0.452146i	−0.999673	+	0.0255573i	$0.991864\pi$
$384$		0			0
$385$	−15.5593	−	4.16910i	−0.792975	−	0.212477i
$386$		0			0
$387$	7.42726	+	1.99013i	0.377549	+	0.101164i
$388$		0			0
$389$	4.53119	−	1.21413i	0.229741	−	0.0615588i	−0.142112	−	0.989851i	$-0.545389\pi$
$389$	4.53119	−	1.21413i	0.229741	−	0.0615588i	0.371853	+	0.928292i	$0.378723\pi$
$390$		0			0
$391$	3.61753	+	6.26574i	0.182946	+	0.316872i
$392$		0			0
$393$	−19.3839	−	19.3839i	−0.977791	−	0.977791i
$394$		0			0
$395$	12.2216	+	21.1684i	0.614935	+	1.06510i
$396$		0			0
$397$			18.1430i			0.910570i	0.890346	+	0.455285i	$0.150463\pi$
$397$			18.1430i			0.910570i	−0.890346	+	0.455285i	$0.849537\pi$
$398$		0			0
$399$	−9.97937	−	9.97937i	−0.499594	−	0.499594i
$400$		0			0
$401$	−25.9906	+	25.9906i	−1.29791	+	1.29791i	−0.368136	+	0.929772i	$0.620004\pi$
$401$	−25.9906	+	25.9906i	−1.29791	+	1.29791i	−0.929772	+	0.368136i	$0.879996\pi$
$402$		0			0
$403$	51.6084	+	29.7961i	2.57080	+	1.48425i
$404$		0			0
$405$	−2.06295	+	7.69903i	−0.102509	+	0.382568i
$406$		0			0
$407$	25.4654	−	5.64576i	1.26227	−	0.279850i
$408$		0			0
$409$	−9.99529	−	2.67823i	−0.494235	−	0.132430i	0.00308795	−	0.999995i	$-0.499017\pi$
$409$	−9.99529	−	2.67823i	−0.494235	−	0.132430i	−0.497323	+	0.867565i	$0.665684\pi$
$410$		0			0
$411$	8.62974	−	14.9472i	0.425674	−	0.737289i
$412$		0			0
$413$	8.57223	+	8.57223i	0.421812	+	0.421812i
$414$		0			0
$415$	11.1864	−	11.1864i	0.549118	−	0.549118i
$416$		0			0
$417$	−16.5115			−0.808573
$418$		0			0
$419$	30.9026	−	17.8416i	1.50969	−	0.871620i	0.509753	−	0.860321i	$-0.329737\pi$
$419$	30.9026	−	17.8416i	1.50969	−	0.871620i	0.999936	−	0.0112988i	$-0.00359661\pi$
$420$		0			0
$421$	20.2026	−	20.2026i	0.984612	−	0.984612i	−0.0152713	−	0.999883i	$-0.504861\pi$
$421$	20.2026	−	20.2026i	0.984612	−	0.984612i	0.999883	+	0.0152713i	$0.00486119\pi$
$422$		0			0
$423$	−6.64326	+	3.83549i	−0.323006	+	0.186488i
$424$		0			0
$425$	−0.372709	−	1.39097i	−0.0180790	−	0.0674719i
$426$		0			0
$427$	−4.74085	+	17.6931i	−0.229426	+	0.856229i
$428$		0			0
$429$	8.77582	−	32.7518i	0.423700	−	1.58127i
$430$		0			0
$431$	−8.12007	+	2.17577i	−0.391130	+	0.104803i	−0.449024	−	0.893520i	$-0.648228\pi$
$431$	−8.12007	+	2.17577i	−0.391130	+	0.104803i	0.0578938	+	0.998323i	$0.481562\pi$
$432$		0			0
$433$	−15.6253			−0.750906			−0.375453	−	0.926842i	$-0.622513\pi$
$433$	−15.6253			−0.750906			−0.375453	+	0.926842i	$0.622513\pi$
$434$		0			0
$435$	−4.80028	−	8.31433i	−0.230156	−	0.398642i
$436$		0			0
$437$	29.5926	+	17.0853i	1.41561	+	0.817300i
$438$		0			0
$439$	−10.9354	+	2.93012i	−0.521916	+	0.139847i	−0.510153	−	0.860084i	$-0.670411\pi$
$439$	−10.9354	+	2.93012i	−0.521916	+	0.139847i	−0.0117636	+	0.999931i	$0.503745\pi$
$440$		0			0
$441$	1.88166	−	3.25913i	0.0896029	−	0.155197i
$442$		0			0
$443$	9.14989			0.434724			0.217362	−	0.976091i	$-0.430255\pi$
$443$	9.14989			0.434724			0.217362	+	0.976091i	$0.430255\pi$
$444$		0			0
$445$	−25.4547			−1.20667
$446$		0			0
$447$	5.96963	−	10.3397i	0.282354	−	0.489051i
$448$		0			0
$449$	−4.72063	+	1.26489i	−0.222780	+	0.0596939i	−0.368483	−	0.929635i	$-0.620123\pi$
$449$	−4.72063	+	1.26489i	−0.222780	+	0.0596939i	0.145702	+	0.989329i	$0.453456\pi$
$450$		0			0
$451$	1.99796	+	1.15352i	0.0940803	+	0.0543173i
$452$		0			0
$453$	10.6724	+	18.4852i	0.501435	+	0.868511i
$454$		0			0
$455$	−21.9517			−1.02911
$456$		0			0
$457$	−5.97611	+	1.60129i	−0.279551	+	0.0749054i	−0.395870	−	0.918306i	$-0.629557\pi$
$457$	−5.97611	+	1.60129i	−0.279551	+	0.0749054i	0.116320	+	0.993212i	$0.462890\pi$
$458$		0			0
$459$	−1.65822	+	6.18856i	−0.0773991	+	0.288857i
$460$		0			0
$461$	7.82195	−	29.1919i	0.364304	−	1.35960i	−0.504057	−	0.863670i	$-0.668160\pi$
$461$	7.82195	−	29.1919i	0.364304	−	1.35960i	0.868361	−	0.495932i	$-0.165174\pi$
$462$		0			0
$463$	−1.23435	−	4.60664i	−0.0573650	−	0.214089i	0.931294	−	0.364269i	$-0.118681\pi$
$463$	−1.23435	−	4.60664i	−0.0573650	−	0.214089i	−0.988659	+	0.150180i	$0.952015\pi$
$464$		0			0
$465$	23.0853	−	13.3283i	1.07055	−	0.618085i
$466$		0			0
$467$	−25.4822	+	25.4822i	−1.17918	+	1.17918i	−0.199223	+	0.979954i	$0.563842\pi$
$467$	−25.4822	+	25.4822i	−1.17918	+	1.17918i	−0.979954	+	0.199223i	$0.936158\pi$
$468$		0			0
$469$	10.9009	−	6.29364i	0.503357	−	0.290613i
$470$		0			0
$471$	−1.08560			−0.0500219
$472$		0			0
$473$	−19.9428	+	19.9428i	−0.916971	+	0.916971i
$474$		0			0
$475$	−4.80916	−	4.80916i	−0.220659	−	0.220659i
$476$		0			0
$477$	−5.66025	+	9.80385i	−0.259165	+	0.448887i
$478$		0			0
$479$	−20.9351	−	5.60954i	−0.956549	−	0.256306i	−0.253410	−	0.967359i	$-0.581552\pi$
$479$	−20.9351	−	5.60954i	−0.956549	−	0.256306i	−0.703139	+	0.711053i	$0.748219\pi$
$480$		0			0
$481$	31.5296	−	16.4136i	1.43763	−	0.748397i
$482$		0			0
$483$	−4.33813	+	16.1901i	−0.197392	+	0.736677i
$484$		0			0
$485$	20.9071	+	12.0707i	0.949342	+	0.548103i
$486$		0			0
$487$	−6.77789	+	6.77789i	−0.307135	+	0.307135i	−0.843797	−	0.536662i	$-0.819685\pi$
$487$	−6.77789	+	6.77789i	−0.307135	+	0.307135i	0.536662	+	0.843797i	$0.319685\pi$
$488$		0			0
$489$	−3.05402	−	3.05402i	−0.138108	−	0.138108i
$490$		0			0
$491$			34.5955i			1.56127i	0.624985	+	0.780637i	$0.285105\pi$
$491$			34.5955i			1.56127i	−0.624985	+	0.780637i	$0.714895\pi$
$492$		0			0
$493$	−2.08560	−	3.61237i	−0.0939309	−	0.162693i
$494$		0			0
$495$	6.84824	+	6.84824i	0.307806	+	0.307806i
$496$		0			0
$497$	−0.319687	−	0.553714i	−0.0143399	−	0.0248375i
$498$		0			0
$499$	29.0611	−	7.78690i	1.30095	−	0.348590i	0.459143	−	0.888362i	$-0.348156\pi$
$499$	29.0611	−	7.78690i	1.30095	−	0.348590i	0.841811	+	0.539773i	$0.181490\pi$
$500$		0			0
$501$	13.3759	+	3.58406i	0.597591	+	0.160124i
$502$		0			0
$503$	−11.1811	−	2.99595i	−0.498538	−	0.133583i	0.000783156	−	1.00000i	$-0.499751\pi$
$503$	−11.1811	−	2.99595i	−0.498538	−	0.133583i	−0.499322	+	0.866417i	$0.666417\pi$
$504$		0			0
$505$	−2.29166	−	8.55259i	−0.101977	−	0.380585i
$506$		0			0
$507$		−	28.6173i		−	1.27094i
$508$		0			0
$509$	26.0353	−	15.0315i	1.15399	−	0.666258i	0.204136	−	0.978943i	$-0.434561\pi$
$509$	26.0353	−	15.0315i	1.15399	−	0.666258i	0.949857	+	0.312684i	$0.101228\pi$
$510$		0			0
$511$	3.36794	−	5.83345i	0.148989	−	0.258057i
$512$		0			0
$513$	7.83164	+	29.2281i	0.345775	+	1.29045i
$514$		0			0
$515$	−10.0592	−	5.80770i	−0.443263	−	0.255918i
$516$		0			0
$517$		−	28.1363i		−	1.23743i
$518$		0			0
$519$			0.635775i			0.0279074i
$520$		0			0
$521$	−16.6433	−	9.60900i	−0.729155	−	0.420978i	0.0889577	−	0.996035i	$-0.471646\pi$
$521$	−16.6433	−	9.60900i	−0.729155	−	0.420978i	−0.818113	+	0.575057i	$0.804980\pi$
$522$		0			0
$523$	−5.73442	−	21.4011i	−0.250749	−	0.935806i	−0.970406	−	0.241477i	$-0.922368\pi$
$523$	−5.73442	−	21.4011i	−0.250749	−	0.935806i	0.719658	−	0.694329i	$-0.244299\pi$
$524$		0			0
$525$	1.66805	−	2.88914i	0.0727995	−	0.126092i
$526$		0			0
$527$	10.0300	−	5.79082i	0.436914	−	0.252252i
$528$		0			0
$529$		−	17.5827i		−	0.764465i
$530$		0			0
$531$	−1.88648	−	7.04045i	−0.0818664	−	0.305530i
$532$		0			0
$533$	3.03685	+	0.813721i	0.131540	+	0.0352461i
$534$		0			0
$535$	29.0498	+	7.78388i	1.25593	+	0.336526i
$536$		0			0
$537$	10.9801	−	2.94211i	0.473827	−	0.126962i
$538$		0			0
$539$	6.90172	+	11.9541i	0.297278	+	0.514901i
$540$		0			0
$541$	3.71048	+	3.71048i	0.159526	+	0.159526i	0.782357	−	0.622831i	$-0.214017\pi$
$541$	3.71048	+	3.71048i	0.159526	+	0.159526i	−0.622831	+	0.782357i	$0.714017\pi$
$542$		0			0
$543$	14.1566	+	24.5199i	0.607517	+	1.05225i
$544$		0			0
$545$		−	8.46410i		−	0.362562i
$546$		0			0
$547$	−11.7821	−	11.7821i	−0.503767	−	0.503767i	0.408840	−	0.912606i	$-0.365934\pi$
$547$	−11.7821	−	11.7821i	−0.503767	−	0.503767i	−0.912606	+	0.408840i	$0.865934\pi$
$548$		0			0
$549$	7.78741	−	7.78741i	0.332359	−	0.332359i
$550$		0			0
$551$	−17.0610	−	9.85014i	−0.726821	−	0.419630i
$552$		0			0
$553$	−6.36773	+	23.7647i	−0.270783	+	1.01058i
$554$		0			0
$555$	0.693428	−	15.8852i	0.0294344	−	0.674290i
$556$		0			0
$557$	−10.0771	−	2.70014i	−0.426979	−	0.114409i	0.0389287	−	0.999242i	$-0.487605\pi$
$557$	−10.0771	−	2.70014i	−0.426979	−	0.114409i	−0.465908	+	0.884833i	$0.654272\pi$
$558$		0			0
$559$	−19.2174	+	33.2855i	−0.812808	+	1.40783i
$560$		0			0
$561$	−4.65969	−	4.65969i	−0.196732	−	0.196732i
$562$		0			0
$563$	−15.6048	+	15.6048i	−0.657665	+	0.657665i	−0.954827	−	0.297162i	$-0.903960\pi$
$563$	−15.6048	+	15.6048i	−0.657665	+	0.657665i	0.297162	+	0.954827i	$0.403960\pi$
$564$		0			0
$565$	−15.8294			−0.665946
$566$		0			0
$567$	−6.94790	+	4.01137i	−0.291784	+	0.168462i
$568$		0			0
$569$	29.1058	−	29.1058i	1.22018	−	1.22018i	0.252611	−	0.967568i	$-0.418711\pi$
$569$	29.1058	−	29.1058i	1.22018	−	1.22018i	0.967568	−	0.252611i	$-0.0812894\pi$
$570$		0			0
$571$	6.58575	−	3.80229i	0.275605	−	0.159121i	−0.355827	−	0.934552i	$-0.615801\pi$
$571$	6.58575	−	3.80229i	0.275605	−	0.159121i	0.631432	+	0.775431i	$0.282467\pi$
$572$		0			0
$573$	4.75018	+	17.7279i	0.198442	+	0.740594i
$574$		0			0
$575$	−2.09059	+	7.80218i	−0.0871836	+	0.325373i
$576$		0			0
$577$	6.60198	−	24.6389i	0.274844	−	1.02573i	−0.681102	−	0.732189i	$-0.738499\pi$
$577$	6.60198	−	24.6389i	0.274844	−	1.02573i	0.955946	−	0.293543i	$-0.0948345\pi$
$578$		0			0
$579$	4.03855	−	1.08213i	0.167836	−	0.0449716i
$580$		0			0
$581$	15.9234			0.660612
$582$		0			0
$583$	−20.7612	−	35.9594i	−0.859840	−	1.48929i
$584$		0			0
$585$	11.4300	+	6.59913i	0.472574	+	0.272840i
$586$		0			0
$587$	24.3063	−	6.51286i	1.00323	−	0.268814i	0.280431	−	0.959874i	$-0.409523\pi$
$587$	24.3063	−	6.51286i	1.00323	−	0.268814i	0.722798	+	0.691060i	$0.242856\pi$
$588$		0			0
$589$	27.3496	−	47.3709i	1.12692	−	1.95188i
$590$		0			0
$591$	13.5014			0.555374
$592$		0			0
$593$	−7.31269			−0.300296			−0.150148	−	0.988664i	$-0.547975\pi$
$593$	−7.31269			−0.300296			−0.150148	+	0.988664i	$0.547975\pi$
$594$		0			0
$595$	−2.13314	+	3.69471i	−0.0874502	+	0.151468i
$596$		0			0
$597$	1.51602	−	0.406216i	0.0620465	−	0.0166253i
$598$		0			0
$599$	11.3365	+	6.54510i	0.463195	+	0.267426i	0.713387	−	0.700771i	$-0.247160\pi$
$599$	11.3365	+	6.54510i	0.463195	+	0.267426i	−0.250192	+	0.968196i	$0.580494\pi$
$600$		0			0
$601$	22.9334	+	39.7218i	0.935473	+	1.62029i	0.773789	+	0.633444i	$0.218359\pi$
$601$	22.9334	+	39.7218i	0.935473	+	1.62029i	0.161684	+	0.986843i	$0.448307\pi$
$602$		0			0
$603$	−7.56797			−0.308192
$604$		0			0
$605$	−13.7864	+	3.69404i	−0.560495	+	0.150184i
$606$		0			0
$607$	−0.989116	+	3.69143i	−0.0401470	+	0.149831i	−0.983090	−	0.183124i	$-0.941379\pi$
$607$	−0.989116	+	3.69143i	−0.0401470	+	0.149831i	0.942943	+	0.332955i	$0.108046\pi$
$608$		0			0
$609$	2.50105	−	9.33406i	0.101348	−	0.378235i
$610$		0			0
$611$	−9.92397	−	37.0368i	−0.401481	−	1.49835i
$612$		0			0
$613$	16.4410	−	9.49221i	0.664045	−	0.383387i	−0.129771	−	0.991544i	$-0.541424\pi$
$613$	16.4410	−	9.49221i	0.664045	−	0.383387i	0.793817	+	0.608157i	$0.208091\pi$
$614$		0			0
$615$	0.994441	−	0.994441i	0.0400997	−	0.0400997i
$616$		0			0
$617$	24.3464	−	14.0564i	0.980148	−	0.565889i	0.0778335	−	0.996966i	$-0.475200\pi$
$617$	24.3464	−	14.0564i	0.980148	−	0.565889i	0.902315	+	0.431077i	$0.141866\pi$
$618$		0			0
$619$	−36.6887			−1.47464			−0.737321	−	0.675543i	$-0.763909\pi$
$619$	−36.6887			−1.47464			−0.737321	+	0.675543i	$0.763909\pi$
$620$		0			0
$621$	25.4115	−	25.4115i	1.01973	−	1.01973i
$622$		0			0
$623$	−18.1169	−	18.1169i	−0.725837	−	0.725837i
$624$		0			0
$625$	−8.52628	+	14.7679i	−0.341051	+	0.590718i
$626$		0			0
$627$	−30.0626	−	8.05524i	−1.20058	−	0.321695i
$628$		0			0
$629$	0.301278	−	6.90175i	0.0120127	−	0.275191i
$630$		0			0
$631$	9.57078	−	35.7186i	0.381007	−	1.42194i	−0.463359	−	0.886170i	$-0.653356\pi$
$631$	9.57078	−	35.7186i	0.381007	−	1.42194i	0.844366	−	0.535766i	$-0.179977\pi$
$632$		0			0
$633$	0.536255	+	0.309607i	0.0213142	+	0.0123058i
$634$		0			0
$635$	−1.12040	+	1.12040i	−0.0444616	+	0.0444616i
$636$		0			0
$637$	13.3013	+	13.3013i	0.527018	+	0.527018i
$638$		0			0
$639$			0.384417i			0.0152073i
$640$		0			0
$641$	−19.3236	−	33.4694i	−0.763236	−	1.32196i	−0.941174	−	0.337922i	$-0.890276\pi$
$641$	−19.3236	−	33.4694i	−0.763236	−	1.32196i	0.177938	−	0.984042i	$-0.443057\pi$
$642$		0			0
$643$	−19.7098	−	19.7098i	−0.777278	−	0.777278i	0.202089	−	0.979367i	$-0.435227\pi$
$643$	−19.7098	−	19.7098i	−0.777278	−	0.777278i	−0.979367	+	0.202089i	$0.935227\pi$
$644$		0			0
$645$	8.59625	+	14.8891i	0.338477	+	0.586259i
$646$		0			0
$647$	29.3286	−	7.85859i	1.15303	−	0.308953i	0.368850	−	0.929489i	$-0.379752\pi$
$647$	29.3286	−	7.85859i	1.15303	−	0.308953i	0.784178	+	0.620536i	$0.213085\pi$
$648$		0			0
$649$	25.8236	+	6.91941i	1.01366	+	0.271611i
$650$		0			0
$651$	25.9167	+	6.94435i	1.01575	+	0.272170i
$652$		0			0
$653$	−7.56035	−	28.2156i	−0.295859	−	1.10416i	−0.940532	−	0.339704i	$-0.889673\pi$
$653$	−7.56035	−	28.2156i	−0.295859	−	1.10416i	0.644673	−	0.764458i	$-0.276994\pi$
$654$		0			0
$655$			39.1380i			1.52925i
$656$		0			0
$657$	−3.50730	+	2.02494i	−0.136833	+	0.0790005i
$658$		0			0
$659$	−0.781534	+	1.35366i	−0.0304442	+	0.0527310i	−0.880846	−	0.473403i	$-0.843026\pi$
$659$	−0.781534	+	1.35366i	−0.0304442	+	0.0527310i	0.850402	+	0.526134i	$0.176359\pi$
$660$		0			0
$661$	−8.00139	−	29.8616i	−0.311218	−	1.16148i	−0.927459	−	0.373924i	$-0.878012\pi$
$661$	−8.00139	−	29.8616i	−0.311218	−	1.16148i	0.616241	−	0.787557i	$-0.288655\pi$
$662$		0			0
$663$	−7.77723	−	4.49019i	−0.302043	−	0.174384i
$664$		0			0
$665$			20.1493i			0.781356i
$666$		0			0
$667$			23.3970i			0.905937i
$668$		0			0
$669$	21.0459	+	12.1508i	0.813681	+	0.469779i
$670$		0			0
$671$	10.4549	+	39.0183i	0.403608	+	1.50628i
$672$		0			0
$673$	−23.1819	+	40.1522i	−0.893595	+	1.54775i	−0.0580607	+	0.998313i	$0.518492\pi$
$673$	−23.1819	+	40.1522i	−0.893595	+	1.54775i	−0.835534	+	0.549439i	$0.814842\pi$
$674$		0			0
$675$	−6.19451	+	3.57640i	−0.238427	+	0.137656i
$676$		0			0
$677$			25.8230i			0.992460i	0.868191	+	0.496230i	$0.165283\pi$
$677$			25.8230i			0.992460i	−0.868191	+	0.496230i	$0.834717\pi$
$678$		0			0
$679$	6.28912	+	23.4713i	0.241354	+	0.900746i
$680$		0			0
$681$	23.3701	+	6.26201i	0.895546	+	0.239961i
$682$		0			0
$683$	30.7385	+	8.23636i	1.17618	+	0.315156i	0.793409	−	0.608689i	$-0.208304\pi$
$683$	30.7385	+	8.23636i	1.17618	+	0.315156i	0.382768	+	0.923845i	$0.374971\pi$
$684$		0			0
$685$	−23.8020	+	6.37772i	−0.909427	+	0.243680i
$686$		0			0
$687$	−7.67090	−	13.2864i	−0.292663	−	0.506907i
$688$		0			0
$689$	−40.0120	−	40.0120i	−1.52433	−	1.52433i
$690$		0			0
$691$	−2.42883	−	4.20685i	−0.0923970	−	0.160036i	0.816122	−	0.577879i	$-0.196120\pi$
$691$	−2.42883	−	4.20685i	−0.0923970	−	0.160036i	−0.908519	+	0.417843i	$0.862786\pi$
$692$		0			0
$693$			9.74820i			0.370304i
$694$		0			0
$695$	16.6692	+	16.6692i	0.632297	+	0.632297i
$696$		0			0
$697$	0.432061	−	0.432061i	0.0163655	−	0.0163655i
$698$		0			0
$699$	6.84497	+	3.95194i	0.258900	+	0.149476i
$700$		0			0
$701$	−11.4856	+	42.8647i	−0.433803	+	1.61898i	0.310111	+	0.950700i	$0.399634\pi$
$701$	−11.4856	+	42.8647i	−0.433803	+	1.61898i	−0.743914	+	0.668275i	$0.767033\pi$
$702$		0			0
$703$	−15.0659	−	28.9408i	−0.568222	−	1.09152i
$704$		0			0
$705$	−16.5672	−	4.43916i	−0.623956	−	0.167188i
$706$		0			0
$707$	4.45609	−	7.71818i	0.167589	−	0.290272i
$708$		0			0
$709$	−4.50977	−	4.50977i	−0.169368	−	0.169368i	0.617334	−	0.786702i	$-0.288213\pi$
$709$	−4.50977	−	4.50977i	−0.169368	−	0.169368i	−0.786702	+	0.617334i	$0.788213\pi$
$710$		0			0
$711$	10.4597	−	10.4597i	0.392271	−	0.392271i
$712$		0			0
$713$	−64.9635			−2.43290
$714$		0			0
$715$	−41.9241	+	24.2049i	−1.56787	+	0.905211i
$716$		0			0
$717$	−13.8089	+	13.8089i	−0.515703	+	0.515703i
$718$		0			0
$719$	−15.4122	+	8.89825i	−0.574779	+	0.331849i	−0.759056	−	0.651025i	$-0.774339\pi$
$719$	−15.4122	+	8.89825i	−0.574779	+	0.331849i	0.184277	+	0.982874i	$0.441006\pi$
$720$		0			0
$721$	−3.02594	−	11.2930i	−0.112692	−	0.420572i
$722$		0			0
$723$	−6.21281	+	23.1865i	−0.231057	+	0.862317i
$724$		0			0
$725$	1.20528	−	4.49817i	0.0447630	−	0.167058i
$726$		0			0
$727$	15.8729	−	4.25312i	0.588692	−	0.157740i	0.0478368	−	0.998855i	$-0.484767\pi$
$727$	15.8729	−	4.25312i	0.588692	−	0.157740i	0.540855	+	0.841116i	$0.318101\pi$
$728$		0			0
$729$	27.7232			1.02679
$730$		0			0
$731$	3.73486	+	6.46897i	0.138139	+	0.239264i
$732$		0			0
$733$	11.7859	+	6.80459i	0.435322	+	0.251333i	0.701611	−	0.712560i	$-0.252464\pi$
$733$	11.7859	+	6.80459i	0.435322	+	0.251333i	−0.266289	+	0.963893i	$0.585798\pi$
$734$		0			0
$735$	8.12772	−	2.17782i	0.299796	−	0.0803300i
$736$		0			0
$737$	13.8792	−	24.0395i	0.511248	−	0.885508i
$738$		0			0
$739$	−4.92106			−0.181024			−0.0905120	−	0.995895i	$-0.528850\pi$
$739$	−4.92106			−0.181024			−0.0905120	+	0.995895i	$0.528850\pi$
$740$		0			0
$741$	−42.4136			−1.55810
$742$		0			0
$743$	24.5645	−	42.5470i	0.901185	−	1.56090i	0.0752264	−	0.997166i	$-0.476032\pi$
$743$	24.5645	−	42.5470i	0.901185	−	1.56090i	0.825958	−	0.563731i	$-0.190635\pi$
$744$		0			0
$745$	−16.4650	+	4.41180i	−0.603233	+	0.161636i
$746$		0			0
$747$	−8.29112	−	4.78688i	−0.303356	−	0.175143i
$748$		0			0
$749$	15.1356	+	26.2157i	0.553044	+	0.957900i
$750$		0			0
$751$	36.7619			1.34146			0.670730	−	0.741702i	$-0.265981\pi$
$751$	36.7619			1.34146			0.670730	+	0.741702i	$0.265981\pi$
$752$		0			0
$753$	−23.6154	+	6.32774i	−0.860594	+	0.230596i
$754$		0			0
$755$	7.88736	−	29.4360i	0.287050	−	1.07129i
$756$		0			0
$757$	−1.31130	+	4.89385i	−0.0476601	+	0.177870i	−0.985653	−	0.168785i	$-0.946016\pi$
$757$	−1.31130	+	4.89385i	−0.0476601	+	0.177870i	0.937993	+	0.346655i	$0.112682\pi$
$758$		0			0
$759$	9.56681	+	35.7038i	0.347253	+	1.29597i
$760$		0			0
$761$	−19.6107	+	11.3223i	−0.710888	+	0.410431i	−0.811390	−	0.584505i	$-0.801289\pi$
$761$	−19.6107	+	11.3223i	−0.710888	+	0.410431i	0.100502	+	0.994937i	$0.467955\pi$
$762$		0			0
$763$	6.02416	−	6.02416i	0.218089	−	0.218089i
$764$		0			0
$765$	2.22141	−	1.28253i	0.0803151	−	0.0463699i
$766$		0			0
$767$	36.4330			1.31552
$768$		0			0
$769$	−4.98020	+	4.98020i	−0.179590	+	0.179590i	−0.791177	−	0.611587i	$-0.790532\pi$
$769$	−4.98020	+	4.98020i	−0.179590	+	0.179590i	0.611587	+	0.791177i	$0.290532\pi$
$770$		0			0
$771$	17.3218	+	17.3218i	0.623831	+	0.623831i
$772$		0			0
$773$	−9.76641	+	16.9159i	−0.351273	+	0.608423i	−0.986473	−	0.163925i	$-0.947584\pi$
$773$	−9.76641	+	16.9159i	−0.351273	+	0.608423i	0.635200	+	0.772348i	$0.280918\pi$
$774$		0			0
$775$	12.4895	+	3.34655i	0.448635	+	0.120212i
$776$		0			0
$777$	11.7995	−	10.8125i	0.423306	−	0.387895i
$778$		0			0
$779$	0.746907	−	2.78749i	0.0267607	−	0.0998723i
$780$		0			0
$781$	−1.22109	−	0.704999i	−0.0436942	−	0.0252269i
$782$		0			0
$783$	−14.6504	+	14.6504i	−0.523563	+	0.523563i
$784$		0			0
$785$	1.09597	+	1.09597i	0.0391168	+	0.0391168i
$786$		0			0
$787$		−	35.8475i		−	1.27783i	−0.769279	−	0.638913i	$-0.779384\pi$
$787$		−	35.8475i		−	1.27783i	0.769279	−	0.638913i	$-0.220616\pi$
$788$		0			0
$789$	−17.2354	−	29.8526i	−0.613596	−	1.06278i
$790$		0			0
$791$	−11.2662	−	11.2662i	−0.400581	−	0.400581i
$792$		0			0
$793$	27.5243	+	47.6736i	0.977418	+	1.69294i
$794$		0			0
$795$	−24.4491	+	6.55113i	−0.867122	+	0.232345i
$796$		0			0
$797$	10.8033	+	2.89474i	0.382674	+	0.102537i	0.445027	−	0.895517i	$-0.353194\pi$
$797$	10.8033	+	2.89474i	0.382674	+	0.102537i	−0.0623536	+	0.998054i	$0.519861\pi$
$798$		0			0
$799$	−7.19803	−	1.92871i	−0.254648	−	0.0682327i
$800$		0			0
$801$	3.98696	+	14.8796i	0.140872	+	0.525743i
$802$		0			0
$803$		−	14.8545i		−	0.524205i
$804$		0			0
$805$	20.7243	−	11.9652i	0.730434	−	0.421716i
$806$		0			0
$807$	−20.1332	+	34.8717i	−0.708722	+	1.22754i
$808$		0			0
$809$	−10.4603	−	39.0383i	−0.367764	−	1.37251i	−0.863635	−	0.504118i	$-0.831818\pi$
$809$	−10.4603	−	39.0383i	−0.367764	−	1.37251i	0.495870	−	0.868397i	$-0.334849\pi$
$810$		0			0
$811$	46.4485	+	26.8170i	1.63103	+	0.941674i	0.983777	+	0.179396i	$0.0574142\pi$
$811$	46.4485	+	26.8170i	1.63103	+	0.941674i	0.647250	+	0.762278i	$0.275919\pi$
$812$		0			0
$813$		−	2.36161i		−	0.0828251i
$814$		0			0
$815$			6.16636i			0.215998i
$816$		0			0
$817$	30.5524	+	17.6395i	1.06889	+	0.617126i
$818$		0			0
$819$	3.43830	+	12.8319i	0.120144	+	0.448383i
$820$		0			0
$821$	6.28436	−	10.8848i	0.219326	−	0.379883i	−0.735276	−	0.677767i	$-0.762948\pi$
$821$	6.28436	−	10.8848i	0.219326	−	0.379883i	0.954602	+	0.297884i	$0.0962810\pi$
$822$		0			0
$823$	−43.0093	+	24.8314i	−1.49921	+	0.865569i	−1.00000		0.000911403i	$-0.999710\pi$
$823$	−43.0093	+	24.8314i	−1.49921	+	0.865569i	−0.499210	+	0.866481i	$0.666377\pi$
$824$		0			0
$825$		−	7.35703i		−	0.256139i
$826$		0			0
$827$	−3.34710	−	12.4915i	−0.116390	−	0.434373i	0.882997	−	0.469378i	$-0.155522\pi$
$827$	−3.34710	−	12.4915i	−0.116390	−	0.434373i	−0.999387	+	0.0350051i	$0.988855\pi$
$828$		0			0
$829$	−7.31064	−	1.95888i	−0.253909	−	0.0680347i	0.129619	−	0.991564i	$-0.458624\pi$
$829$	−7.31064	−	1.95888i	−0.253909	−	0.0680347i	−0.383528	+	0.923529i	$0.625291\pi$
$830$		0			0
$831$	−0.450595	−	0.120737i	−0.0156310	−	0.00418831i
$832$		0			0
$833$	3.53130	−	0.946208i	0.122352	−	0.0327842i
$834$		0			0
$835$	−9.88532	−	17.1219i	−0.342096	−	0.592527i
$836$		0			0
$837$	−40.6779	−	40.6779i	−1.40603	−	1.40603i
$838$		0			0
$839$	−11.6911	−	20.2495i	−0.403621	−	0.699092i	0.590539	−	0.807009i	$-0.298915\pi$
$839$	−11.6911	−	20.2495i	−0.403621	−	0.699092i	−0.994160	+	0.107917i	$0.965582\pi$
$840$		0			0
$841$			15.5110i			0.534861i
$842$		0			0
$843$	10.2275	+	10.2275i	0.352254	+	0.352254i
$844$		0			0
$845$	−28.8905	+	28.8905i	−0.993863	+	0.993863i
$846$		0			0
$847$	−12.4413	−	7.18300i	−0.427489	−	0.246811i
$848$		0			0
$849$	−6.41426	+	23.9384i	−0.220137	+	0.821562i
$850$		0			0
$851$	−20.8201	+	32.6816i	−0.713703	+	1.12031i
$852$		0			0
$853$	−27.7885	−	7.44590i	−0.951459	−	0.254943i	−0.250478	−	0.968122i	$-0.580588\pi$
$853$	−27.7885	−	7.44590i	−0.951459	−	0.254943i	−0.700981	+	0.713180i	$0.747254\pi$
$854$		0			0
$855$	6.05728	−	10.4915i	0.207155	−	0.358802i
$856$		0			0
$857$	33.6235	+	33.6235i	1.14856	+	1.14856i	0.986837	+	0.161718i	$0.0517036\pi$
$857$	33.6235	+	33.6235i	1.14856	+	1.14856i	0.161718	+	0.986837i	$0.448296\pi$
$858$		0			0
$859$	12.8863	−	12.8863i	0.439673	−	0.439673i	−0.452229	−	0.891902i	$-0.649371\pi$
$859$	12.8863	−	12.8863i	0.439673	−	0.439673i	0.891902	+	0.452229i	$0.149371\pi$
$860$		0			0
$861$	1.41555			0.0482417
$862$		0			0
$863$	−10.3158	+	5.95585i	−0.351155	+	0.202740i	−0.665194	−	0.746671i	$-0.731651\pi$
$863$	−10.3158	+	5.95585i	−0.351155	+	0.202740i	0.314039	+	0.949410i	$0.398318\pi$
$864$		0			0
$865$	0.641845	−	0.641845i	0.0218234	−	0.0218234i
$866$		0			0
$867$	18.4095	−	10.6288i	0.625221	−	0.360971i
$868$		0			0
$869$	14.0426	+	52.4078i	0.476364	+	1.77781i
$870$		0			0
$871$	9.79072	−	36.5395i	0.331746	−	1.23809i
$872$		0			0
$873$	3.78127	−	14.1119i	0.127977	−	0.477615i
$874$		0			0
$875$	−22.7430	+	6.09396i	−0.768853	+	0.206013i
$876$		0			0
$877$	−48.2013			−1.62764			−0.813821	−	0.581116i	$-0.802616\pi$
$877$	−48.2013			−1.62764			−0.813821	+	0.581116i	$0.802616\pi$
$878$		0			0
$879$	15.1443	+	26.2306i	0.510804	+	0.884738i
$880$		0			0
$881$	−45.0742	−	26.0236i	−1.51859	−	0.876757i	−0.999761	−	0.0218787i	$-0.993035\pi$
$881$	−45.0742	−	26.0236i	−1.51859	−	0.876757i	−0.518828	−	0.854879i	$-0.673631\pi$
$882$		0			0
$883$	1.29608	−	0.347283i	0.0436165	−	0.0116870i	−0.236945	−	0.971523i	$-0.576146\pi$
$883$	1.29608	−	0.347283i	0.0436165	−	0.0116870i	0.280561	+	0.959836i	$0.409479\pi$
$884$		0			0
$885$	8.14855	−	14.1137i	0.273911	−	0.474427i
$886$		0			0
$887$	4.21493			0.141523			0.0707617	−	0.997493i	$-0.477457\pi$
$887$	4.21493			0.141523			0.0707617	+	0.997493i	$0.477457\pi$
$888$		0			0
$889$	−1.59484			−0.0534893
$890$		0			0
$891$	−8.84620	+	15.3221i	−0.296359	+	0.513309i
$892$		0			0
$893$	−33.9957	+	9.10913i	−1.13762	+	0.304825i
$894$		0			0
$895$	−14.0552	−	8.11474i	−0.469812	−	0.271246i
$896$		0			0
$897$	25.1863	+	43.6239i	0.840944	+	1.45656i
$898$		0			0
$899$	37.4532			1.24914
$900$		0			0
$901$	−10.6226	+	2.84631i	−0.353889	+	0.0948242i
$902$		0			0
$903$	−4.47884	+	16.7153i	−0.149046	+	0.556249i
$904$		0			0
$905$	10.4623	−	39.0457i	0.347778	−	1.29792i
$906$		0			0
$907$	−5.76198	−	21.5040i	−0.191323	−	0.714028i	−0.993188	−	0.116523i	$-0.962825\pi$
$907$	−5.76198	−	21.5040i	−0.191323	−	0.714028i	0.801865	−	0.597506i	$-0.203841\pi$
$908$		0			0
$909$	−4.64048	+	2.67918i	−0.153915	+	0.0888628i
$910$		0			0
$911$	11.9081	−	11.9081i	0.394532	−	0.394532i	−0.481767	−	0.876299i	$-0.660005\pi$
$911$	11.9081	−	11.9081i	0.394532	−	0.394532i	0.876299	+	0.481767i	$0.160005\pi$
$912$		0			0
$913$	30.4109	−	17.5578i	1.00645	−	0.581077i
$914$		0			0
$915$	24.6242			0.814051
$916$		0			0
$917$	−27.8557	+	27.8557i	−0.919876	+	0.919876i
$918$		0			0
$919$	−23.7967	−	23.7967i	−0.784980	−	0.784980i	0.195687	−	0.980666i	$-0.437306\pi$
$919$	−23.7967	−	23.7967i	−0.784980	−	0.784980i	−0.980666	+	0.195687i	$0.937306\pi$
$920$		0			0
$921$	−20.9662	+	36.3145i	−0.690860	+	1.19660i
$922$		0			0
$923$	−1.85603	−	0.497322i	−0.0610920	−	0.0163696i
$924$		0			0
$925$	5.68631	−	5.21063i	0.186965	−	0.171324i
$926$		0			0
$927$	−1.81932	+	6.78979i	−0.0597542	+	0.223006i
$928$		0			0
$929$	−22.7113	−	13.1124i	−0.745135	−	0.430204i	0.0787984	−	0.996891i	$-0.474892\pi$
$929$	−22.7113	−	13.1124i	−0.745135	−	0.430204i	−0.823933	+	0.566687i	$0.808225\pi$
$930$		0			0
$931$	12.2092	−	12.2092i	0.400139	−	0.400139i
$932$		0			0
$933$	20.4809	+	20.4809i	0.670514	+	0.670514i
$934$		0			0
$935$			9.40835i			0.307686i
$936$		0			0
$937$	−5.25363	−	9.09955i	−0.171628	−	0.297269i	0.767361	−	0.641215i	$-0.221570\pi$
$937$	−5.25363	−	9.09955i	−0.171628	−	0.297269i	−0.938989	+	0.343946i	$0.888236\pi$
$938$		0			0
$939$	4.45174	+	4.45174i	0.145277	+	0.145277i
$940$		0			0
$941$	22.8561	+	39.5880i	0.745088	+	1.29053i	0.950153	+	0.311783i	$0.100926\pi$
$941$	22.8561	+	39.5880i	0.745088	+	1.29053i	−0.205065	+	0.978748i	$0.565741\pi$
$942$		0			0
$943$	−3.31057	+	0.887064i	−0.107807	+	0.0288868i
$944$		0			0
$945$	20.4690	+	5.48465i	0.665856	+	0.178416i
$946$		0			0
$947$	−35.4230	−	9.49155i	−1.15109	−	0.308434i	−0.367689	−	0.929949i	$-0.619851\pi$
$947$	−35.4230	−	9.49155i	−1.15109	−	0.308434i	−0.783402	+	0.621515i	$0.786518\pi$
$948$		0			0
$949$	−5.23935	−	19.5535i	−0.170077	−	0.634735i
$950$		0			0
$951$		−	43.4578i		−	1.40922i
$952$		0			0
$953$	17.3218	−	10.0007i	0.561108	−	0.323956i	−0.192482	−	0.981300i	$-0.561654\pi$
$953$	17.3218	−	10.0007i	0.561108	−	0.323956i	0.753590	+	0.657345i	$0.228320\pi$
$954$		0			0
$955$	13.1016	−	22.6927i	0.423959	−	0.734318i
$956$		0			0
$957$	−5.51553	−	20.5842i	−0.178292	−	0.665394i
$958$		0			0
$959$	−21.4798	−	12.4014i	−0.693619	−	0.400461i
$960$		0			0
$961$			72.9915i			2.35456i
$962$		0			0
$963$		−	18.2003i		−	0.586496i
$964$		0			0
$965$	−5.16956	−	2.98465i	−0.166414	−	0.0960792i
$966$		0			0
$967$	10.8280	+	40.4105i	0.348203	+	1.29951i	0.888825	+	0.458247i	$0.151522\pi$
$967$	10.8280	+	40.4105i	0.348203	+	1.29951i	−0.540621	+	0.841266i	$0.681811\pi$
$968$		0			0
$969$	−4.12150	+	7.13865i	−0.132402	+	0.229327i
$970$		0			0
$971$	13.1578	−	7.59665i	0.422253	−	0.243788i	−0.273788	−	0.961790i	$-0.588277\pi$
$971$	13.1578	−	7.59665i	0.422253	−	0.243788i	0.696041	+	0.718002i	$0.254943\pi$
$972$		0			0
$973$			23.7279i			0.760681i
$974$		0			0
$975$	−2.59490	−	9.68431i	−0.0831034	−	0.310146i
$976$		0			0
$977$	−49.6586	−	13.3060i	−1.58872	−	0.425696i	−0.647108	−	0.762398i	$-0.724022\pi$
$977$	−49.6586	−	13.3060i	−1.58872	−	0.425696i	−0.941611	+	0.336702i	$0.890688\pi$
$978$		0			0
$979$	−54.5765	−	14.6237i	−1.74427	−	0.467377i
$980$		0			0
$981$	−4.94770	+	1.32573i	−0.157968	+	0.0423273i
$982$		0			0
$983$	10.2429	+	17.7412i	0.326698	+	0.565858i	0.981855	−	0.189636i	$-0.0607307\pi$
$983$	10.2429	+	17.7412i	0.326698	+	0.565858i	−0.655157	+	0.755493i	$0.727397\pi$
$984$		0			0
$985$	−13.6303	−	13.6303i	−0.434298	−	0.434298i
$986$		0			0
$987$	−8.63187	−	14.9508i	−0.274755	−	0.475890i
$988$		0			0
$989$		−	41.8990i		−	1.33231i
$990$		0			0
$991$	15.6163	+	15.6163i	0.496067	+	0.496067i	0.910211	−	0.414144i	$-0.135919\pi$
$991$	15.6163	+	15.6163i	0.496067	+	0.496067i	−0.414144	+	0.910211i	$0.635919\pi$
$992$		0			0
$993$	9.08684	−	9.08684i	0.288362	−	0.288362i
$994$		0			0
$995$	−1.94058	−	1.12040i	−0.0615207	−	0.0355190i
$996$		0			0
$997$	−4.82406	+	18.0036i	−0.152779	+	0.570180i	0.846506	+	0.532379i	$0.178702\pi$
$997$	−4.82406	+	18.0036i	−0.152779	+	0.570180i	−0.999285	+	0.0378011i	$0.987965\pi$
$998$		0			0
$999$	−33.5009	+	7.42726i	−1.05992	+	0.234988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.be.d.415.3	yes	16
4.3	odd	2	inner	592.2.be.d.415.2	✓	16
37.14	odd	12	inner	592.2.be.d.495.2	yes	16
148.51	even	12	inner	592.2.be.d.495.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
592.2.be.d.415.2	✓	16	4.3	odd	2	inner
592.2.be.d.415.3	yes	16	1.1	even	1	trivial
592.2.be.d.495.2	yes	16	37.14	odd	12	inner
592.2.be.d.495.3	yes	16	148.51	even	12	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.676554 - 1.17183i) q^{3} +(-1.86603 + 0.500000i) q^{5} +(-1.68397 - 0.972241i) q^{7} +(0.584551 + 1.01247i) q^{9} +O(q^{10})\)	\(q+(0.676554 - 1.17183i) q^{3} +(-1.86603 + 0.500000i) q^{5} +(-1.68397 - 0.972241i) q^{7} +(0.584551 + 1.01247i) q^{9} -4.28813 q^{11} +(-5.64462 + 1.51247i) q^{13} +(-0.676554 + 2.52493i) q^{15} +(-0.293946 + 1.09702i) q^{17} +(1.38828 + 5.18115i) q^{19} +(-2.27859 + 1.31555i) q^{21} +(4.50459 - 4.50459i) q^{23} +(-1.09808 + 0.633975i) q^{25} +5.64124 q^{27} +(-2.59702 + 2.59702i) q^{29} +(-7.21081 - 7.21081i) q^{31} +(-2.90115 + 5.02494i) q^{33} +(3.62845 + 0.972241i) q^{35} +(-5.93857 + 1.31660i) q^{37} +(-2.04654 + 7.63777i) q^{39} +(-0.465928 - 0.269004i) q^{41} +(4.65070 - 4.65070i) q^{43} +(-1.59702 - 1.59702i) q^{45} +6.56143i q^{47} +(-1.60949 - 2.78772i) q^{49} +(1.08665 + 1.08665i) q^{51} +(4.84154 + 8.38580i) q^{53} +(8.00177 - 2.14407i) q^{55} +(7.01064 + 1.87850i) q^{57} +(-6.02211 - 1.61362i) q^{59} +(-2.43810 - 9.09913i) q^{61} -2.27330i q^{63} +(9.77677 - 5.64462i) q^{65} +(-3.23666 + 5.60606i) q^{67} +(-2.23100 - 8.32619i) q^{69} +(0.284761 + 0.164407i) q^{71} +3.46410i q^{73} +1.71567i q^{75} +(7.22109 + 4.16910i) q^{77} +(-3.27477 - 12.2216i) q^{79} +(2.06295 - 3.57313i) q^{81} +(-7.09188 + 4.09450i) q^{83} -2.19404i q^{85} +(1.28623 + 4.80028i) q^{87} +(12.7273 + 3.41028i) q^{89} +(10.9759 + 2.94097i) q^{91} +(-13.3283 + 3.57131i) q^{93} +(-5.18115 - 8.97401i) q^{95} +(-8.83638 - 8.83638i) q^{97} +(-2.50663 - 4.34161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{5} - 4 q^{9}+O(q^{10}) \) 16 * q - 16 * q^5 - 4 * q^9	\( 16 q - 16 q^{5} - 4 q^{9} - 4 q^{13} + 12 q^{17} + 36 q^{21} + 24 q^{25} - 12 q^{29} + 8 q^{33} + 8 q^{37} - 36 q^{41} + 4 q^{45} + 20 q^{49} + 4 q^{53} + 12 q^{57} - 28 q^{61} - 20 q^{69} + 32 q^{81} + 20 q^{89} - 60 q^{93} - 4 q^{97}+O(q^{100}) \) 16 * q - 16 * q^5 - 4 * q^9 - 4 * q^13 + 12 * q^17 + 36 * q^21 + 24 * q^25 - 12 * q^29 + 8 * q^33 + 8 * q^37 - 36 * q^41 + 4 * q^45 + 20 * q^49 + 4 * q^53 + 12 * q^57 - 28 * q^61 - 20 * q^69 + 32 * q^81 + 20 * q^89 - 60 * q^93 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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