LMFDB - Embedded newform 1900.2.s.d.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 17x^{14} + 215x^{12} - 1176x^{10} + 4775x^{8} - 2898x^{6} + 1385x^{4} - 164x^{2} + 16 $ x^16 - 17x^14 + 215x^12 - 1176x^10 + 4775x^8 - 2898x^6 + 1385x^4 - 164*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Root			$-0.614201 - 0.354609i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614201 + 0.354609i) q^{3} +3.11079i q^{7} +(-1.24850 + 2.16247i) q^{9} +O(q^{10})$	\(q+(-0.614201 + 0.354609i) q^{3} +3.11079i q^{7} +(-1.24850 + 2.16247i) q^{9} -3.52922 q^{11} +(0.347770 + 0.200785i) q^{13} +(3.02850 - 1.74850i) q^{17} +(-4.35162 + 0.251824i) q^{19} +(-1.10311 - 1.91065i) q^{21} +(-6.33672 - 3.65851i) q^{23} -3.89858i q^{27} +(-3.96540 + 6.86827i) q^{29} +5.73545 q^{31} +(2.16765 - 1.25150i) q^{33} -10.5292i q^{37} -0.284801 q^{39} +(0.555394 + 0.961971i) q^{41} +(7.45457 - 4.30390i) q^{43} +(-6.51532 - 3.76162i) q^{47} -2.67700 q^{49} +(-1.24007 + 2.14787i) q^{51} +(9.14130 + 5.27773i) q^{53} +(2.58347 - 1.69779i) q^{57} +(-4.25618 - 7.37192i) q^{59} +(4.61079 - 7.98612i) q^{61} +(-6.72700 - 3.88383i) q^{63} +(-7.28540 - 4.20623i) q^{67} +5.18936 q^{69} +(4.31233 + 7.46918i) q^{71} +(-1.50813 + 0.870717i) q^{73} -10.9787i q^{77} +(-4.50544 - 7.80366i) q^{79} +(-2.36304 - 4.09291i) q^{81} -4.07857i q^{83} -5.62466i q^{87} +(-6.61623 + 11.4596i) q^{89} +(-0.624599 + 1.08184i) q^{91} +(-3.52272 + 2.03384i) q^{93} +(-6.67120 + 3.85162i) q^{97} +(4.40625 - 7.63186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−0.614201	+	0.354609i	−0.354609	+	0.204734i	−0.666713	−	0.745314i	$-0.732299\pi$
$3$	−0.614201	+	0.354609i	−0.354609	+	0.204734i	0.312104	+	0.950048i	$0.398966\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.11079i			1.17577i	0.808945	+	0.587884i	$0.200039\pi$
$7$			3.11079i			1.17577i	−0.808945	+	0.587884i	$0.799961\pi$
$8$		0			0
$9$	−1.24850	+	2.16247i	−0.416168	+	0.720825i
$10$		0			0
$11$	−3.52922			−1.06410			−0.532051	−	0.846713i	$-0.678578\pi$
$11$	−3.52922			−1.06410			−0.532051	+	0.846713i	$0.678578\pi$
$12$		0			0
$13$	0.347770	+	0.200785i	0.0964540	+	0.0556877i	0.547451	−	0.836838i	$-0.315598\pi$
$13$	0.347770	+	0.200785i	0.0964540	+	0.0556877i	−0.450997	+	0.892525i	$0.648932\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.02850	−	1.74850i	0.734519	−	0.424075i	−0.0855542	−	0.996334i	$-0.527266\pi$
$17$	3.02850	−	1.74850i	0.734519	−	0.424075i	0.820073	+	0.572259i	$0.193933\pi$
$18$		0			0
$19$	−4.35162	+	0.251824i	−0.998330	+	0.0577725i
$19$	−4.35162	+	0.251824i	−0.998330	+	0.0577725i
$20$		0			0
$21$	−1.10311	−	1.91065i	−0.240719	−	0.416938i
$22$		0			0
$23$	−6.33672	−	3.65851i	−1.32130	−	0.762852i	−0.337362	−	0.941375i	$-0.609535\pi$
$23$	−6.33672	−	3.65851i	−1.32130	−	0.762852i	−0.983936	+	0.178523i	$0.942868\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	3.89858i		−	0.750282i
$28$		0			0
$29$	−3.96540	+	6.86827i	−0.736356	+	1.27541i	0.217770	+	0.976000i	$0.430122\pi$
$29$	−3.96540	+	6.86827i	−0.736356	+	1.27541i	−0.954126	+	0.299406i	$0.903212\pi$
$30$		0			0
$31$	5.73545			1.03012			0.515059	−	0.857155i	$-0.327770\pi$
$31$	5.73545			1.03012			0.515059	+	0.857155i	$0.327770\pi$
$32$		0			0
$33$	2.16765	−	1.25150i	0.377340	−	0.217857i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	10.5292i		−	1.73099i	−0.500914	−	0.865497i	$-0.667003\pi$
$37$		−	10.5292i		−	1.73099i	0.500914	−	0.865497i	$-0.332997\pi$
$38$		0			0
$39$	−0.284801			−0.0456046
$40$		0			0
$41$	0.555394	+	0.961971i	0.0867380	+	0.150235i	0.906130	−	0.422998i	$-0.139022\pi$
$41$	0.555394	+	0.961971i	0.0867380	+	0.150235i	−0.819392	+	0.573233i	$0.805689\pi$
$42$		0			0
$43$	7.45457	−	4.30390i	1.13681	−	0.656338i	0.191172	−	0.981556i	$-0.438771\pi$
$43$	7.45457	−	4.30390i	1.13681	−	0.656338i	0.945639	+	0.325218i	$0.105438\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.51532	−	3.76162i	−0.950357	−	0.548689i	−0.0571653	−	0.998365i	$-0.518206\pi$
$47$	−6.51532	−	3.76162i	−0.950357	−	0.548689i	−0.893192	+	0.449676i	$0.851540\pi$
$48$		0			0
$49$	−2.67700			−0.382429
$50$		0			0
$51$	−1.24007	+	2.14787i	−0.173645	+	0.300762i
$52$		0			0
$53$	9.14130	+	5.27773i	1.25565	+	0.724952i	0.972227	−	0.234042i	$-0.0751953\pi$
$53$	9.14130	+	5.27773i	1.25565	+	0.724952i	0.283427	+	0.958994i	$0.408529\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.58347	−	1.69779i	0.342189	−	0.224878i
$58$		0			0
$59$	−4.25618	−	7.37192i	−0.554107	−	0.959742i	−0.997972	−	0.0636484i	$-0.979726\pi$
$59$	−4.25618	−	7.37192i	−0.554107	−	0.959742i	0.443865	−	0.896094i	$-0.353607\pi$
$60$		0			0
$61$	4.61079	−	7.98612i	0.590351	−	1.02252i	−0.403834	−	0.914832i	$-0.632323\pi$
$61$	4.61079	−	7.98612i	0.590351	−	1.02252i	0.994185	−	0.107686i	$-0.0343440\pi$
$62$		0			0
$63$	−6.72700	−	3.88383i	−0.847522	−	0.489317i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.28540	−	4.20623i	−0.890053	−	0.513873i	−0.0160934	−	0.999870i	$-0.505123\pi$
$67$	−7.28540	−	4.20623i	−0.890053	−	0.513873i	−0.873960	+	0.485998i	$0.838456\pi$
$68$		0			0
$69$	5.18936			0.624726
$70$		0			0
$71$	4.31233	+	7.46918i	0.511780	+	0.886428i	0.999907	+	0.0136558i	$0.00434692\pi$
$71$	4.31233	+	7.46918i	0.511780	+	0.886428i	−0.488127	+	0.872773i	$0.662320\pi$
$72$		0			0
$73$	−1.50813	+	0.870717i	−0.176513	+	0.101910i	−0.585653	−	0.810562i	$-0.699162\pi$
$73$	−1.50813	+	0.870717i	−0.176513	+	0.101910i	0.409140	+	0.912471i	$0.365829\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	10.9787i		−	1.25114i
$78$		0			0
$79$	−4.50544	−	7.80366i	−0.506902	−	0.877980i	−0.999968	−	0.00798806i	$-0.997457\pi$
$79$	−4.50544	−	7.80366i	−0.506902	−	0.877980i	0.493066	−	0.869992i	$-0.335876\pi$
$80$		0			0
$81$	−2.36304	−	4.09291i	−0.262560	−	0.454768i
$82$		0			0
$83$		−	4.07857i		−	0.447682i	−0.974626	−	0.223841i	$-0.928140\pi$
$83$		−	4.07857i		−	0.447682i	0.974626	−	0.223841i	$-0.0718596\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	5.62466i		−	0.603027i
$88$		0			0
$89$	−6.61623	+	11.4596i	−0.701319	+	1.21472i	0.266685	+	0.963784i	$0.414072\pi$
$89$	−6.61623	+	11.4596i	−0.701319	+	1.21472i	−0.968004	+	0.250936i	$0.919262\pi$
$90$		0			0
$91$	−0.624599	+	1.08184i	−0.0654758	+	0.113407i
$92$		0			0
$93$	−3.52272	+	2.03384i	−0.365289	+	0.210900i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.67120	+	3.85162i	−0.677358	+	0.391073i	−0.798859	−	0.601519i	$-0.794563\pi$
$97$	−6.67120	+	3.85162i	−0.677358	+	0.391073i	0.121501	+	0.992591i	$0.461229\pi$
$98$		0			0
$99$	4.40625	−	7.63186i	0.442845	−	0.767030i
$100$		0			0
$101$	−8.68773	+	15.0476i	−0.864462	+	1.49729i	0.00311897	+	0.999995i	$0.499007\pi$
$101$	−8.68773	+	15.0476i	−0.864462	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$102$		0			0
$103$			7.12614i			0.702159i	0.936346	+	0.351080i	$0.114185\pi$
$103$			7.12614i			0.702159i	−0.936346	+	0.351080i	$0.885815\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			0.735452i			0.0710989i	0.999368	+	0.0355494i	$0.0113181\pi$
$107$			0.735452i			0.0710989i	−0.999368	+	0.0355494i	$0.988682\pi$
$108$		0			0
$109$	−8.00468	−	13.8645i	−0.766710	−	1.32798i	−0.939338	−	0.342993i	$-0.888559\pi$
$109$	−8.00468	−	13.8645i	−0.766710	−	1.32798i	0.172628	−	0.984987i	$-0.444774\pi$
$110$		0			0
$111$	3.73376	+	6.46706i	0.354393	+	0.613826i
$112$		0			0
$113$		−	4.34923i		−	0.409141i	−0.978852	−	0.204571i	$-0.934420\pi$
$113$		−	4.34923i		−	0.409141i	0.978852	−	0.204571i	$-0.0655798\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.868384	+	0.501362i	−0.0802822	+	0.0463509i
$118$		0			0
$119$	5.43923	+	9.42102i	0.498613	+	0.863623i
$120$		0			0
$121$	1.45543			0.132312
$122$		0			0
$123$	−0.682247	−	0.393896i	−0.0615162	−	0.0355164i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.02355	+	2.32300i	0.357032	+	0.206133i	0.667778	−	0.744360i	$-0.267245\pi$
$127$	4.02355	+	2.32300i	0.357032	+	0.206133i	−0.310746	+	0.950493i	$0.600579\pi$
$128$		0			0
$129$	−3.05240	+	5.28692i	−0.268749	+	0.465487i
$130$		0			0
$131$	−5.24775	−	9.08936i	−0.458498	−	0.794141i	0.540384	−	0.841418i	$-0.318279\pi$
$131$	−5.24775	−	9.08936i	−0.458498	−	0.794141i	−0.998882	+	0.0472772i	$0.984946\pi$
$132$		0			0
$133$	−0.783372	−	13.5370i	−0.0679270	−	1.17380i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.20568	+	0.696101i	0.103008	+	0.0594719i	0.550619	−	0.834757i	$-0.314392\pi$
$137$	1.20568	+	0.696101i	0.103008	+	0.0594719i	−0.447611	+	0.894228i	$0.647725\pi$
$138$		0			0
$139$	−3.03766	+	5.26138i	−0.257651	+	0.446264i	−0.965612	−	0.259987i	$-0.916282\pi$
$139$	−3.03766	+	5.26138i	−0.257651	+	0.446264i	0.707961	+	0.706251i	$0.249615\pi$
$140$		0			0
$141$	5.33562			0.449340
$142$		0			0
$143$	−1.22736	−	0.708615i	−0.102637	−	0.0592574i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.64422	−	0.949290i	0.135613	−	0.0782961i
$148$		0			0
$149$	−0.0422770	−	0.0732259i	−0.00346347	−	0.00599890i	0.864288	−	0.502996i	$-0.167769\pi$
$149$	−0.0422770	−	0.0732259i	−0.00346347	−	0.00599890i	−0.867752	+	0.496998i	$0.834436\pi$
$150$		0			0
$151$	−15.2216			−1.23871			−0.619357	−	0.785109i	$-0.712607\pi$
$151$	−15.2216			−1.23871			−0.619357	+	0.785109i	$0.712607\pi$
$152$		0			0
$153$			8.73207i			0.705946i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	14.0804	−	8.12935i	1.12374	−	0.648793i	0.181388	−	0.983412i	$-0.441941\pi$
$157$	14.0804	−	8.12935i	1.12374	−	0.648793i	0.942354	+	0.334619i	$0.108608\pi$
$158$		0			0
$159$	−7.48612			−0.593688
$160$		0			0
$161$	11.3808	−	19.7122i	0.896936	−	1.55354i
$162$		0			0
$163$		−	14.9461i		−	1.17067i	−0.810791	−	0.585336i	$-0.800963\pi$
$163$		−	14.9461i		−	1.17067i	0.810791	−	0.585336i	$-0.199037\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.8506	−	6.26461i	−0.839647	−	0.484770i	0.0174974	−	0.999847i	$-0.494430\pi$
$167$	−10.8506	−	6.26461i	−0.839647	−	0.484770i	−0.857144	+	0.515077i	$0.827763\pi$
$168$		0			0
$169$	−6.41937	−	11.1187i	−0.493798	−	0.855283i
$170$		0			0
$171$	4.88845	−	9.72466i	0.373829	−	0.743664i
$172$		0			0
$173$	−15.0557	+	8.69242i	−1.14466	+	0.660872i	−0.947581	−	0.319515i	$-0.896480\pi$
$173$	−15.0557	+	8.69242i	−1.14466	+	0.660872i	−0.197083	+	0.980387i	$0.563147\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.22830	+	3.01856i	0.392983	+	0.226889i
$178$		0			0
$179$	−20.7830			−1.55340			−0.776698	−	0.629873i	$-0.783107\pi$
$179$	−20.7830			−1.55340			−0.776698	+	0.629873i	$0.783107\pi$
$180$		0			0
$181$	−0.814564	+	1.41087i	−0.0605460	+	0.104869i	−0.894710	−	0.446648i	$-0.852618\pi$
$181$	−0.814564	+	1.41087i	−0.0605460	+	0.104869i	0.834164	+	0.551517i	$0.185951\pi$
$182$		0			0
$183$			6.54011i			0.483459i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.6883	+	6.17087i	−0.781603	+	0.451258i
$188$		0			0
$189$	12.1277			0.882157
$190$		0			0
$191$	−13.4016			−0.969704			−0.484852	−	0.874596i	$-0.661126\pi$
$191$	−13.4016			−0.969704			−0.484852	+	0.874596i	$0.661126\pi$
$192$		0			0
$193$	9.26116	−	5.34693i	0.666633	−	0.384881i	−0.128167	−	0.991753i	$-0.540909\pi$
$193$	9.26116	−	5.34693i	0.666633	−	0.384881i	0.794800	+	0.606872i	$0.207576\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.00611i		−	0.499165i	−0.968354	−	0.249582i	$-0.919707\pi$
$197$		−	7.00611i		−	0.499165i	0.968354	−	0.249582i	$-0.0802933\pi$
$198$		0			0
$199$	−10.3909	+	17.9976i	−0.736592	+	1.27581i	0.217430	+	0.976076i	$0.430233\pi$
$199$	−10.3909	+	17.9976i	−0.736592	+	1.27581i	−0.954021	+	0.299738i	$0.903101\pi$
$200$		0			0
$201$	5.96627			0.420828
$202$		0			0
$203$	−21.3657	−	12.3355i	−1.49958	−	0.865783i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	15.8229	−	9.13533i	1.09976	−	0.634949i
$208$		0			0
$209$	15.3578	−	0.888745i	1.06232	−	0.0614758i
$210$		0			0
$211$	5.61623	+	9.72760i	0.386637	+	0.669675i	0.991995	−	0.126278i	$-0.0403032\pi$
$211$	5.61623	+	9.72760i	0.386637	+	0.669675i	−0.605358	+	0.795954i	$0.706970\pi$
$212$		0			0
$213$	−5.29728	−	3.05838i	−0.362963	−	0.209557i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			17.8418i			1.21118i
$218$		0			0
$219$	0.617528	−	1.06959i	0.0417287	−	0.0722762i
$220$		0			0
$221$	1.40429			0.0944630
$222$		0			0
$223$	9.43976	−	5.45005i	0.632133	−	0.364962i	−0.149445	−	0.988770i	$-0.547749\pi$
$223$	9.43976	−	5.45005i	0.632133	−	0.364962i	0.781578	+	0.623808i	$0.214415\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			3.96627i			0.263250i	0.991300	+	0.131625i	$0.0420195\pi$
$227$			3.96627i			0.263250i	−0.991300	+	0.131625i	$0.957980\pi$
$228$		0			0
$229$	10.9139			0.721213			0.360606	−	0.932718i	$-0.382570\pi$
$229$	10.9139			0.721213			0.360606	+	0.932718i	$0.382570\pi$
$230$		0			0
$231$	3.89314	+	6.74311i	0.256150	+	0.443664i
$232$		0			0
$233$	13.5021	−	7.79547i	0.884555	−	0.510698i	0.0123973	−	0.999923i	$-0.496054\pi$
$233$	13.5021	−	7.79547i	0.884555	−	0.510698i	0.872157	+	0.489225i	$0.162720\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.53450	+	3.19534i	0.359504	+	0.207560i
$238$		0			0
$239$	8.09544			0.523650			0.261825	−	0.965115i	$-0.415676\pi$
$239$	8.09544			0.523650			0.261825	+	0.965115i	$0.415676\pi$
$240$		0			0
$241$	12.6425	−	21.8974i	0.814373	−	1.41054i	−0.0954047	−	0.995439i	$-0.530415\pi$
$241$	12.6425	−	21.8974i	0.814373	−	1.41054i	0.909777	−	0.415096i	$-0.136252\pi$
$242$		0			0
$243$	13.0316	+	7.52378i	0.835976	+	0.482651i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.56392	−	0.786163i	−0.0995101	−	0.0500223i
$248$		0			0
$249$	1.44630	+	2.50506i	0.0916555	+	0.158752i
$250$		0			0
$251$	−3.94461	+	6.83226i	−0.248981	+	0.431248i	−0.963243	−	0.268630i	$-0.913429\pi$
$251$	−3.94461	+	6.83226i	−0.248981	+	0.431248i	0.714262	+	0.699878i	$0.246762\pi$
$252$		0			0
$253$	22.3637	+	12.9117i	1.40599	+	0.811751i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.95540	+	4.59305i	0.496244	+	0.286507i	0.727161	−	0.686467i	$-0.240839\pi$
$257$	7.95540	+	4.59305i	0.496244	+	0.286507i	−0.230917	+	0.972973i	$0.574173\pi$
$258$		0			0
$259$	32.7542			2.03525
$260$		0			0
$261$	−9.90163	−	17.1501i	−0.612896	−	1.06157i
$262$		0			0
$263$	−20.9954	+	12.1217i	−1.29463	+	0.747454i	−0.979471	−	0.201585i	$-0.935391\pi$
$263$	−20.9954	+	12.1217i	−1.29463	+	0.747454i	−0.315158	+	0.949039i	$0.602058\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	9.38470i		−	0.574335i
$268$		0			0
$269$	0.712209	+	1.23358i	0.0434241	+	0.0752128i	0.886921	−	0.461922i	$-0.152840\pi$
$269$	0.712209	+	1.23358i	0.0434241	+	0.0752128i	−0.843496	+	0.537135i	$0.819507\pi$
$270$		0			0
$271$	5.19617	+	9.00002i	0.315645	+	0.546712i	0.979574	−	0.201083i	$-0.0644459\pi$
$271$	5.19617	+	9.00002i	0.315645	+	0.546712i	−0.663930	+	0.747795i	$0.731113\pi$
$272$		0			0
$273$		−	0.885955i		−	0.0536204i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			20.3078i			1.22018i	0.792334	+	0.610088i	$0.208866\pi$
$277$			20.3078i			1.22018i	−0.792334	+	0.610088i	$0.791134\pi$
$278$		0			0
$279$	−7.16074	+	12.4028i	−0.428702	+	0.742534i
$280$		0			0
$281$	−7.79547	+	13.5021i	−0.465038	+	0.805470i	−0.999203	−	0.0399101i	$-0.987293\pi$
$281$	−7.79547	+	13.5021i	−0.465038	+	0.805470i	0.534165	+	0.845380i	$0.320626\pi$
$282$		0			0
$283$	−23.6119	+	13.6323i	−1.40358	+	0.810358i	−0.994758	−	0.102255i	$-0.967394\pi$
$283$	−23.6119	+	13.6323i	−1.40358	+	0.810358i	−0.408824	+	0.912613i	$0.634061\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.99249	+	1.72771i	−0.176641	+	0.101984i
$288$		0			0
$289$	−2.38546	+	4.13174i	−0.140321	+	0.243044i
$290$		0			0
$291$	2.73164	−	4.73134i	0.160131	−	0.277356i
$292$		0			0
$293$			12.6710i			0.740249i	0.928982	+	0.370125i	$0.120685\pi$
$293$			12.6710i			0.740249i	−0.928982	+	0.370125i	$0.879315\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			13.7590i			0.798376i
$298$		0			0
$299$	−1.46915	−	2.54464i	−0.0849630	−	0.147160i
$300$		0			0
$301$	13.3885	+	23.1896i	0.771701	+	1.33663i
$302$		0			0
$303$		−	12.3230i		−	0.707938i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	2.22638	−	1.28540i	0.127066	−	0.0733619i	−0.435119	−	0.900373i	$-0.643294\pi$
$307$	2.22638	−	1.28540i	0.127066	−	0.0733619i	0.562186	+	0.827011i	$0.309961\pi$
$308$		0			0
$309$	−2.52699	−	4.37688i	−0.143756	−	0.248992i
$310$		0			0
$311$	19.7568			1.12030			0.560152	−	0.828390i	$-0.310743\pi$
$311$	19.7568			1.12030			0.560152	+	0.828390i	$0.310743\pi$
$312$		0			0
$313$	19.3777	+	11.1877i	1.09529	+	0.632368i	0.934981	−	0.354698i	$-0.115416\pi$
$313$	19.3777	+	11.1877i	1.09529	+	0.632368i	0.160313	+	0.987066i	$0.448750\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.5236	−	6.65313i	−0.647228	−	0.373677i	0.140166	−	0.990128i	$-0.455236\pi$
$317$	−11.5236	−	6.65313i	−0.647228	−	0.373677i	−0.787393	+	0.616451i	$0.788570\pi$
$318$		0			0
$319$	13.9948	−	24.2397i	0.783557	−	1.35716i
$320$		0			0
$321$	−0.260798	−	0.451716i	−0.0145563	−	0.0252123i
$322$		0			0
$323$	−12.7386	+	8.37148i	−0.708792	+	0.465801i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.83297	+	5.67707i	0.543764	+	0.313943i
$328$		0			0
$329$	11.7016	−	20.2678i	0.645131	−	1.11740i
$330$		0			0
$331$	−19.6173			−1.07826			−0.539132	−	0.842221i	$-0.681248\pi$
$331$	−19.6173			−1.07826			−0.539132	+	0.842221i	$0.681248\pi$
$332$		0			0
$333$	22.7692	+	13.1458i	1.24774	+	0.720385i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−25.2722	+	14.5909i	−1.37667	+	0.794819i	−0.991757	−	0.128136i	$-0.959101\pi$
$337$	−25.2722	+	14.5909i	−1.37667	+	0.794819i	−0.384910	+	0.922954i	$0.625767\pi$
$338$		0			0
$339$	1.54228	+	2.67130i	0.0837650	+	0.145085i
$340$		0			0
$341$	−20.2417			−1.09615
$342$		0			0
$343$			13.4479i			0.726120i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.4605	+	6.03935i	−0.561547	+	0.324209i	−0.753766	−	0.657143i	$-0.771765\pi$
$347$	−10.4605	+	6.03935i	−0.561547	+	0.324209i	0.192219	+	0.981352i	$0.438432\pi$
$348$		0			0
$349$	−20.2894			−1.08607			−0.543033	−	0.839711i	$-0.682724\pi$
$349$	−20.2894			−1.08607			−0.543033	+	0.839711i	$0.682724\pi$
$350$		0			0
$351$	0.782776	−	1.35581i	0.0417815	−	0.0723677i
$352$		0			0
$353$		−	6.69387i		−	0.356279i	−0.984005	−	0.178139i	$-0.942992\pi$
$353$		−	6.69387i		−	0.356279i	0.984005	−	0.178139i	$-0.0570078\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.68156	−	3.85760i	−0.353626	−	0.204166i
$358$		0			0
$359$	4.94536	+	8.56562i	0.261006	+	0.452076i	0.966510	−	0.256630i	$-0.0826123\pi$
$359$	4.94536	+	8.56562i	0.261006	+	0.452076i	−0.705503	+	0.708707i	$0.749279\pi$
$360$		0			0
$361$	18.8732	−	2.19169i	0.993325	−	0.115352i
$362$		0			0
$363$	−0.893925	+	0.516108i	−0.0469189	+	0.0270886i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−14.0285	−	8.09936i	−0.732282	−	0.422783i	0.0869742	−	0.996211i	$-0.472280\pi$
$367$	−14.0285	−	8.09936i	−0.732282	−	0.422783i	−0.819257	+	0.573427i	$0.805614\pi$
$368$		0			0
$369$	−2.77365			−0.144390
$370$		0			0
$371$	−16.4179	+	28.4366i	−0.852375	+	1.47636i
$372$		0			0
$373$		−	10.3003i		−	0.533328i	−0.963790	−	0.266664i	$-0.914079\pi$
$373$		−	10.3003i		−	0.533328i	0.963790	−	0.266664i	$-0.0859214\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.75809	+	1.59238i	−0.142049	+	0.0820120i
$378$		0			0
$379$	21.2587			1.09199			0.545993	−	0.837790i	$-0.316153\pi$
$379$	21.2587			1.09199			0.545993	+	0.837790i	$0.316153\pi$
$380$		0			0
$381$	−3.29502			−0.168809
$382$		0			0
$383$	11.7607	−	6.79002i	0.600942	−	0.346954i	−0.168470	−	0.985707i	$-0.553883\pi$
$383$	11.7607	−	6.79002i	0.600942	−	0.346954i	0.769412	+	0.638753i	$0.220549\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			21.4938i			1.09259i
$388$		0			0
$389$	8.98771	−	15.5672i	0.455695	−	0.789287i	−0.543033	−	0.839711i	$-0.682724\pi$
$389$	8.98771	−	15.5672i	0.455695	−	0.789287i	0.998728	+	0.0504248i	$0.0160575\pi$
$390$		0			0
$391$	−25.5877			−1.29402
$392$		0			0
$393$	6.44634	+	3.72180i	0.325175	+	0.187740i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	20.8139	−	12.0169i	1.04462	−	0.603112i	0.123483	−	0.992347i	$-0.460594\pi$
$397$	20.8139	−	12.0169i	1.04462	−	0.603112i	0.921139	+	0.389234i	$0.127260\pi$
$398$		0			0
$399$	5.28148	+	8.03663i	0.264405	+	0.402335i
$400$		0			0
$401$	5.91076	+	10.2377i	0.295169	+	0.511248i	0.975024	−	0.222098i	$-0.0712906\pi$
$401$	5.91076	+	10.2377i	0.295169	+	0.511248i	−0.679855	+	0.733347i	$0.737957\pi$
$402$		0			0
$403$	1.99462	+	1.15159i	0.0993589	+	0.0573649i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			37.1600i			1.84195i
$408$		0			0
$409$	−15.6300	+	27.0719i	−0.772851	+	1.33862i	0.163143	+	0.986602i	$0.447837\pi$
$409$	−15.6300	+	27.0719i	−0.772851	+	1.33862i	−0.935994	+	0.352015i	$0.885496\pi$
$410$		0			0
$411$	−0.987375			−0.0487036
$412$		0			0
$413$	22.9325	−	13.2401i	1.12843	−	0.651501i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	4.30872i		−	0.210999i
$418$		0			0
$419$	22.4217			1.09537			0.547686	−	0.836684i	$-0.315509\pi$
$419$	22.4217			1.09537			0.547686	+	0.836684i	$0.315509\pi$
$420$		0			0
$421$	−13.6431	−	23.6305i	−0.664922	−	1.15168i	−0.979306	−	0.202384i	$-0.935131\pi$
$421$	−13.6431	−	23.6305i	−0.664922	−	1.15168i	0.314384	−	0.949296i	$-0.398202\pi$
$422$		0			0
$423$	16.2688	−	9.39281i	0.791017	−	0.456694i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	24.8431	+	14.3432i	1.20224	+	0.694115i
$428$		0			0
$429$	1.00513			0.0485279
$430$		0			0
$431$	−13.6686	+	23.6748i	−0.658395	+	1.14037i	0.322636	+	0.946523i	$0.395431\pi$
$431$	−13.6686	+	23.6748i	−0.658395	+	1.14037i	−0.981031	+	0.193850i	$0.937902\pi$
$432$		0			0
$433$	−6.36980	−	3.67761i	−0.306113	−	0.176734i	0.339073	−	0.940760i	$-0.389887\pi$
$433$	−6.36980	−	3.67761i	−0.306113	−	0.176734i	−0.645186	+	0.764026i	$0.723220\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	28.4963	+	14.3247i	1.36316	+	0.685243i
$438$		0			0
$439$	2.11862	+	3.66955i	0.101116	+	0.175138i	0.912145	−	0.409868i	$-0.134425\pi$
$439$	2.11862	+	3.66955i	0.101116	+	0.175138i	−0.811029	+	0.585006i	$0.801092\pi$
$440$		0			0
$441$	3.34225	−	5.78895i	0.159155	−	0.275664i
$442$		0			0
$443$	−19.2794	−	11.1310i	−0.915993	−	0.528849i	−0.0336383	−	0.999434i	$-0.510709\pi$
$443$	−19.2794	−	11.1310i	−0.915993	−	0.528849i	−0.882354	+	0.470585i	$0.844043\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.0519332	+	0.0299836i	0.00245635	+	0.00141818i
$448$		0			0
$449$	−4.46328			−0.210635			−0.105318	−	0.994439i	$-0.533586\pi$
$449$	−4.46328			−0.210635			−0.105318	+	0.994439i	$0.533586\pi$
$450$		0			0
$451$	−1.96011	−	3.39501i	−0.0922980	−	0.159865i
$452$		0			0
$453$	9.34911	−	5.39771i	0.439259	−	0.253607i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			10.7463i			0.502692i	0.967897	+	0.251346i	$0.0808733\pi$
$457$			10.7463i			0.502692i	−0.967897	+	0.251346i	$0.919127\pi$
$458$		0			0
$459$	−6.81668	−	11.8068i	−0.318176	−	0.551096i
$460$		0			0
$461$	−11.9163	−	20.6397i	−0.554998	−	0.961285i	−0.997904	−	0.0647167i	$-0.979386\pi$
$461$	−11.9163	−	20.6397i	−0.554998	−	0.961285i	0.442906	−	0.896568i	$-0.353948\pi$
$462$		0			0
$463$			25.3695i			1.17902i	0.807761	+	0.589510i	$0.200679\pi$
$463$			25.3695i			1.17902i	−0.807761	+	0.589510i	$0.799321\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			5.62020i			0.260072i	0.991509	+	0.130036i	$0.0415093\pi$
$467$			5.62020i			0.260072i	−0.991509	+	0.130036i	$0.958491\pi$
$468$		0			0
$469$	13.0847	−	22.6633i	0.604195	−	1.04650i
$470$		0			0
$471$	−5.76548	+	9.98611i	−0.265659	+	0.460136i
$472$		0			0
$473$	−26.3089	+	15.1894i	−1.20968	+	0.698411i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−22.8259	+	13.1785i	−1.04513	+	0.603404i
$478$		0			0
$479$	6.83611	−	11.8405i	0.312350	−	0.541006i	−0.666521	−	0.745487i	$-0.732217\pi$
$479$	6.83611	−	11.8405i	0.312350	−	0.541006i	0.978871	+	0.204480i	$0.0655505\pi$
$480$		0			0
$481$	2.11411	−	3.66175i	0.0963951	−	0.166961i
$482$		0			0
$483$			16.1430i			0.734532i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	7.39233i		−	0.334979i	−0.985874	−	0.167489i	$-0.946434\pi$
$487$		−	7.39233i		−	0.334979i	0.985874	−	0.167489i	$-0.0535660\pi$
$488$		0			0
$489$	5.30004	+	9.17994i	0.239676	+	0.415131i
$490$		0			0
$491$	−0.979053	−	1.69577i	−0.0441840	−	0.0765290i	0.843088	−	0.537776i	$-0.180735\pi$
$491$	−0.979053	−	1.69577i	−0.0441840	−	0.0765290i	−0.887272	+	0.461247i	$0.847402\pi$
$492$		0			0
$493$			27.7341i			1.24908i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.2350	+	13.4148i	−1.04223	+	0.601734i
$498$		0			0
$499$	2.72234	+	4.71522i	0.121868	+	0.211082i	0.920505	−	0.390732i	$-0.127778\pi$
$499$	2.72234	+	4.71522i	0.121868	+	0.211082i	−0.798636	+	0.601814i	$0.794445\pi$
$500$		0			0
$501$	8.88595			0.396995
$502$		0			0
$503$	−14.3696	−	8.29629i	−0.640709	−	0.369913i	0.144179	−	0.989552i	$-0.453946\pi$
$503$	−14.3696	−	8.29629i	−0.640709	−	0.369913i	−0.784887	+	0.619638i	$0.787279\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.88557	+	4.55273i	0.350210	+	0.202194i
$508$		0			0
$509$	6.06552	−	10.5058i	0.268849	−	0.465661i	−0.699716	−	0.714422i	$-0.746690\pi$
$509$	6.06552	−	10.5058i	0.268849	−	0.465661i	0.968565	+	0.248761i	$0.0800232\pi$
$510$		0			0
$511$	−2.70862	−	4.69146i	−0.119822	−	0.207538i
$512$		0			0
$513$	0.981757	+	16.9651i	0.0433456	+	0.749029i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	22.9940	+	13.2756i	1.01128	+	0.583861i
$518$		0			0
$519$	6.16482	−	10.6778i	0.270606	−	0.468703i
$520$		0			0
$521$	14.1249			0.618824			0.309412	−	0.950928i	$-0.399868\pi$
$521$	14.1249			0.618824			0.309412	+	0.950928i	$0.399868\pi$
$522$		0			0
$523$	−22.8353	−	13.1840i	−0.998519	−	0.576495i	−0.0907094	−	0.995877i	$-0.528913\pi$
$523$	−22.8353	−	13.1840i	−0.998519	−	0.576495i	−0.907810	+	0.419382i	$0.862247\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.3698	−	10.0285i	0.756641	−	0.436847i
$528$		0			0
$529$	15.2694	+	26.4473i	0.663885	+	1.14988i
$530$		0			0
$531$	21.2554			0.922407
$532$		0			0
$533$			0.446059i			0.0193210i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	12.7649	−	7.36985i	0.550848	−	0.318032i
$538$		0			0
$539$	9.44775			0.406943
$540$		0			0
$541$	14.6986	−	25.4586i	0.631940	−	1.09455i	−0.355214	−	0.934785i	$-0.615592\pi$
$541$	14.6986	−	25.4586i	0.631940	−	1.09455i	0.987155	−	0.159768i	$-0.0510745\pi$
$542$		0			0
$543$		−	1.15541i		−	0.0495833i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−18.8381	−	10.8762i	−0.805457	−	0.465031i	0.0399185	−	0.999203i	$-0.487290\pi$
$547$	−18.8381	−	10.8762i	−0.805457	−	0.465031i	−0.845376	+	0.534172i	$0.820623\pi$
$548$		0			0
$549$	11.5132	+	19.9414i	0.491371	+	0.851079i
$550$		0			0
$551$	15.5263	−	30.8867i	0.661443	−	1.31582i
$552$		0			0
$553$	24.2755	−	14.0155i	1.03230	−	0.595999i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.9086	+	12.0716i	0.885924	+	0.511489i	0.872607	−	0.488423i	$-0.162428\pi$
$557$	20.9086	+	12.0716i	0.885924	+	0.511489i	0.0133172	+	0.999911i	$0.495761\pi$
$558$		0			0
$559$	3.45663			0.146200
$560$		0			0
$561$	4.37649	−	7.58030i	0.184776	−	0.320041i
$562$		0			0
$563$			15.0693i			0.635097i	0.948242	+	0.317548i	$0.102860\pi$
$563$			15.0693i			0.635097i	−0.948242	+	0.317548i	$0.897140\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	12.7322	−	7.35092i	0.534701	−	0.308710i
$568$		0			0
$569$	−0.302873			−0.0126971			−0.00634855	−	0.999980i	$-0.502021\pi$
$569$	−0.302873			−0.0126971			−0.00634855	+	0.999980i	$0.502021\pi$
$570$		0			0
$571$	30.3107			1.26846			0.634232	−	0.773143i	$-0.281316\pi$
$571$	30.3107			1.26846			0.634232	+	0.773143i	$0.281316\pi$
$572$		0			0
$573$	8.23126	−	4.75232i	0.343866	−	0.198531i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			18.6601i			0.776832i	0.921484	+	0.388416i	$0.126978\pi$
$577$			18.6601i			0.776832i	−0.921484	+	0.388416i	$0.873022\pi$
$578$		0			0
$579$	−3.79214	+	6.56819i	−0.157596	+	0.272964i
$580$		0			0
$581$	12.6876			0.526369
$582$		0			0
$583$	−32.2617	−	18.6263i	−1.33614	−	0.771422i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−23.5535	+	13.5986i	−0.972156	+	0.561275i	−0.899893	−	0.436111i	$-0.856355\pi$
$587$	−23.5535	+	13.5986i	−0.972156	+	0.561275i	−0.0722631	+	0.997386i	$0.523022\pi$
$588$		0			0
$589$	−24.9585	+	1.44433i	−1.02840	+	0.0595124i
$590$		0			0
$591$	2.48443	+	4.30316i	0.102196	+	0.177008i
$592$		0			0
$593$	−25.6321	−	14.7987i	−1.05258	−	0.607709i	−0.129211	−	0.991617i	$-0.541245\pi$
$593$	−25.6321	−	14.7987i	−1.05258	−	0.607709i	−0.923371	+	0.383908i	$0.874578\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	14.7388i		−	0.603221i
$598$		0			0
$599$	7.54404	−	13.0667i	0.308241	−	0.533889i	−0.669737	−	0.742599i	$-0.733593\pi$
$599$	7.54404	−	13.0667i	0.308241	−	0.533889i	0.977978	+	0.208710i	$0.0669264\pi$
$600$		0			0
$601$	−44.9249			−1.83253			−0.916263	−	0.400576i	$-0.868810\pi$
$601$	−44.9249			−1.83253			−0.916263	+	0.400576i	$0.868810\pi$
$602$		0			0
$603$	18.1917	−	10.5030i	0.740824	−	0.427715i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	24.9570i		−	1.01297i	−0.862247	−	0.506487i	$-0.830944\pi$
$607$		−	24.9570i		−	1.01297i	0.862247	−	0.506487i	$-0.169056\pi$
$608$		0			0
$609$	17.4971			0.709020
$610$		0			0
$611$	−1.51055	−	2.61636i	−0.0611105	−	0.105846i
$612$		0			0
$613$	16.7024	−	9.64316i	0.674605	−	0.389484i	−0.123214	−	0.992380i	$-0.539320\pi$
$613$	16.7024	−	9.64316i	0.674605	−	0.389484i	0.797819	+	0.602897i	$0.205987\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.8406	−	9.72294i	−0.677978	−	0.391431i	0.121115	−	0.992639i	$-0.461353\pi$
$617$	−16.8406	−	9.72294i	−0.677978	−	0.391431i	−0.799093	+	0.601208i	$0.794686\pi$
$618$		0			0
$619$	1.70324			0.0684589			0.0342294	−	0.999414i	$-0.489102\pi$
$619$	1.70324			0.0684589			0.0342294	+	0.999414i	$0.489102\pi$
$620$		0			0
$621$	−14.2630	+	24.7042i	−0.572354	+	0.991346i
$622$		0			0
$623$	−35.6485	−	20.5817i	−1.42823	−	0.824588i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−9.11764	+	5.99190i	−0.364124	+	0.239293i
$628$		0			0
$629$	−18.4104	−	31.8877i	−0.734071	−	1.27145i
$630$		0			0
$631$	4.39314	−	7.60914i	0.174888	−	0.302915i	−0.765235	−	0.643752i	$-0.777377\pi$
$631$	4.39314	−	7.60914i	0.174888	−	0.302915i	0.940123	+	0.340837i	$0.110710\pi$
$632$		0			0
$633$	−6.89899	−	3.98313i	−0.274210	−	0.158315i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.930981	−	0.537502i	−0.0368868	−	0.0212966i
$638$		0			0
$639$	−21.5359			−0.851946
$640$		0			0
$641$	17.9033	+	31.0095i	0.707139	+	1.22480i	0.965914	+	0.258863i	$0.0833478\pi$
$641$	17.9033	+	31.0095i	0.707139	+	1.22480i	−0.258775	+	0.965938i	$0.583319\pi$
$642$		0			0
$643$	−2.26480	+	1.30758i	−0.0893150	+	0.0515661i	−0.543992	−	0.839090i	$-0.683088\pi$
$643$	−2.26480	+	1.30758i	−0.0893150	+	0.0515661i	0.454677	+	0.890656i	$0.349755\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			30.8849i			1.21421i	0.794622	+	0.607105i	$0.207669\pi$
$647$			30.8849i			1.21421i	−0.794622	+	0.607105i	$0.792331\pi$
$648$		0			0
$649$	15.0210	+	26.0172i	0.589626	+	1.02126i
$650$		0			0
$651$	−6.32686	−	10.9584i	−0.247969	−	0.429495i
$652$		0			0
$653$			17.2198i			0.673864i	0.941529	+	0.336932i	$0.109389\pi$
$653$			17.2198i			0.673864i	−0.941529	+	0.336932i	$0.890611\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	4.34838i		−	0.169646i
$658$		0			0
$659$	−0.0769444	+	0.133272i	−0.00299733	+	0.00519153i	−0.867520	−	0.497402i	$-0.834287\pi$
$659$	−0.0769444	+	0.133272i	−0.00299733	+	0.00519153i	0.864523	+	0.502594i	$0.167621\pi$
$660$		0			0
$661$	13.8595	−	24.0054i	0.539073	−	0.933701i	−0.459882	−	0.887980i	$-0.652108\pi$
$661$	13.8595	−	24.0054i	0.539073	−	0.933701i	0.998954	−	0.0457209i	$-0.0145585\pi$
$662$		0			0
$663$	−0.862519	+	0.497975i	−0.0334975	+	0.0193398i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	50.2552	−	29.0149i	1.94589	−	1.12346i
$668$		0			0
$669$	−3.86527	+	6.69485i	−0.149440	+	0.258838i
$670$		0			0
$671$	−16.2725	+	28.1848i	−0.628193	+	1.08806i
$672$		0			0
$673$			48.0820i			1.85342i	0.375773	+	0.926712i	$0.377377\pi$
$673$			48.0820i			1.85342i	−0.375773	+	0.926712i	$0.622623\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	42.8392i		−	1.64644i	−0.567720	−	0.823222i	$-0.692174\pi$
$677$		−	42.8392i		−	1.64644i	0.567720	−	0.823222i	$-0.307826\pi$
$678$		0			0
$679$	−11.9816	−	20.7527i	−0.459810	−	0.796415i
$680$		0			0
$681$	−1.40647	−	2.43609i	−0.0538962	−	0.0933510i
$682$		0			0
$683$		−	41.4022i		−	1.58421i	−0.610383	−	0.792106i	$-0.708985\pi$
$683$		−	41.4022i		−	1.58421i	0.610383	−	0.792106i	$-0.291015\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−6.70335	+	3.87018i	−0.255749	+	0.147657i
$688$		0			0
$689$	2.11938	+	3.67087i	0.0807418	+	0.139849i
$690$		0			0
$691$	16.9248			0.643850			0.321925	−	0.946765i	$-0.395670\pi$
$691$	16.9248			0.643850			0.321925	+	0.946765i	$0.395670\pi$
$692$		0			0
$693$	23.7411	+	13.7069i	0.901849	+	0.520683i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.36402	+	1.94222i	0.127421	+	0.0735668i
$698$		0			0
$699$	−5.52869	+	9.57597i	−0.209114	+	0.362196i
$700$		0			0
$701$	18.7780	+	32.5244i	0.709233	+	1.22843i	0.965142	+	0.261727i	$0.0842921\pi$
$701$	18.7780	+	32.5244i	0.709233	+	1.22843i	−0.255908	+	0.966701i	$0.582375\pi$
$702$		0			0
$703$	2.65152	+	45.8192i	0.100004	+	1.72810i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−46.8099	−	27.0257i	−1.76047	−	1.01641i
$708$		0			0
$709$	−15.3872	+	26.6514i	−0.577879	+	1.00092i	0.417843	+	0.908519i	$0.362786\pi$
$709$	−15.3872	+	26.6514i	−0.577879	+	1.00092i	−0.995722	+	0.0923969i	$0.970547\pi$
$710$		0			0
$711$	22.5003			0.843826
$712$		0			0
$713$	−36.3440	−	20.9832i	−1.36109	−	0.785827i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.97223	+	2.87072i	−0.185691	+	0.107209i
$718$		0			0
$719$	−23.1509	−	40.0985i	−0.863383	−	1.49542i	−0.868644	−	0.495437i	$-0.835008\pi$
$719$	−23.1509	−	40.0985i	−0.863383	−	1.49542i	0.00526119	−	0.999986i	$-0.498325\pi$
$720$		0			0
$721$	−22.1679			−0.825576
$722$		0			0
$723$			17.9325i			0.666918i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−5.08278	+	2.93454i	−0.188510	+	0.108836i	−0.591285	−	0.806463i	$-0.701379\pi$
$727$	−5.08278	+	2.93454i	−0.188510	+	0.108836i	0.402775	+	0.915299i	$0.368046\pi$
$728$		0			0
$729$	3.50625			0.129861
$730$		0			0
$731$	15.0508	−	26.0687i	0.556673	−	0.964186i
$732$		0			0
$733$		−	11.3955i		−	0.420901i	−0.977605	−	0.210450i	$-0.932507\pi$
$733$		−	11.3955i		−	0.420901i	0.977605	−	0.210450i	$-0.0674931\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.7118	+	14.8447i	0.947107	+	0.546812i
$738$		0			0
$739$	6.86621	+	11.8926i	0.252578	+	0.437477i	0.964235	−	0.265050i	$-0.0853884\pi$
$739$	6.86621	+	11.8926i	0.252578	+	0.437477i	−0.711657	+	0.702527i	$0.752055\pi$
$740$		0			0
$741$	1.23934	−	0.0717198i	0.0455284	−	0.00263469i
$742$		0			0
$743$	7.51300	−	4.33763i	0.275625	−	0.159132i	−0.355816	−	0.934556i	$-0.615797\pi$
$743$	7.51300	−	4.33763i	0.275625	−	0.159132i	0.631441	+	0.775424i	$0.282464\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.81981	+	5.09212i	0.322700	+	0.186311i
$748$		0			0
$749$	−2.28784			−0.0835957
$750$		0			0
$751$	−3.35314	+	5.80780i	−0.122358	+	0.211930i	−0.920697	−	0.390278i	$-0.872379\pi$
$751$	−3.35314	+	5.80780i	−0.122358	+	0.211930i	0.798339	+	0.602208i	$0.205712\pi$
$752$		0			0
$753$		−	5.59517i		−	0.203899i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	12.4618	−	7.19480i	0.452931	−	0.261500i	−0.256136	−	0.966641i	$-0.582450\pi$
$757$	12.4618	−	7.19480i	0.452931	−	0.261500i	0.709067	+	0.705141i	$0.249116\pi$
$758$		0			0
$759$	−18.3144			−0.664771
$760$		0			0
$761$	−50.9650			−1.84748			−0.923740	−	0.383020i	$-0.874884\pi$
$761$	−50.9650			−1.84748			−0.923740	+	0.383020i	$0.874884\pi$
$762$		0			0
$763$	43.1296	−	24.9009i	1.56140	−	0.901472i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	3.41831i		−	0.123428i
$768$		0			0
$769$	11.9988	−	20.7825i	0.432687	−	0.749435i	−0.564417	−	0.825490i	$-0.690899\pi$
$769$	11.9988	−	20.7825i	0.432687	−	0.749435i	0.997104	+	0.0760546i	$0.0242323\pi$
$770$		0			0
$771$	−6.51495			−0.234630
$772$		0			0
$773$	−38.0920	−	21.9925i	−1.37008	−	0.791014i	−0.379139	−	0.925340i	$-0.623780\pi$
$773$	−38.0920	−	21.9925i	−1.37008	−	0.791014i	−0.990937	+	0.134326i	$0.957113\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−20.1177	+	11.6149i	−0.721717	+	0.416683i
$778$		0			0
$779$	−2.65911	−	4.04627i	−0.0952725	−	0.144973i
$780$		0			0
$781$	−15.2192	−	26.3604i	−0.544585	−	0.943250i
$782$		0			0
$783$	26.7765	+	15.4594i	0.956914	+	0.552474i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			16.4815i			0.587501i	0.955882	+	0.293751i	$0.0949035\pi$
$787$			16.4815i			0.587501i	−0.955882	+	0.293751i	$0.905096\pi$
$788$		0			0
$789$	8.59691	−	14.8903i	0.306058	−	0.530108i
$790$		0			0
$791$	13.5295			0.481055
$792$		0			0
$793$	3.20699	−	1.85155i	0.113883	−	0.0657506i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	47.9346i		−	1.69793i	−0.528448	−	0.848966i	$-0.677226\pi$
$797$		−	47.9346i		−	1.69793i	0.528448	−	0.848966i	$-0.322774\pi$
$798$		0			0
$799$	−26.3089			−0.930740
$800$		0			0
$801$	−16.5208	−	28.6149i	−0.583733	−	1.01106i
$802$		0			0
$803$	5.32251	−	3.07295i	0.187827	−	0.108442i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.874879	−	0.505111i	−0.0307972	−	0.0177808i
$808$		0			0
$809$	−11.7879			−0.414441			−0.207221	−	0.978294i	$-0.566442\pi$
$809$	−11.7879			−0.414441			−0.207221	+	0.978294i	$0.566442\pi$
$810$		0			0
$811$	−15.9432	+	27.6144i	−0.559840	+	0.969671i	0.437669	+	0.899136i	$0.355804\pi$
$811$	−15.9432	+	27.6144i	−0.559840	+	0.969671i	−0.997509	+	0.0705351i	$0.977529\pi$
$812$		0			0
$813$	−6.38298	−	3.68522i	−0.223861	−	0.129246i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−31.3556	+	20.6062i	−1.09699	+	0.720919i
$818$		0			0
$819$	−1.55963	−	2.70136i	−0.0544979	−	0.0943932i
$820$		0			0
$821$	−16.2579	+	28.1596i	−0.567406	+	0.982776i	0.429415	+	0.903107i	$0.358720\pi$
$821$	−16.2579	+	28.1596i	−0.567406	+	0.982776i	−0.996821	+	0.0796688i	$0.974614\pi$
$822$		0			0
$823$	42.7790	+	24.6985i	1.49118	+	0.860934i	0.999949	−	0.0100940i	$-0.00321308\pi$
$823$	42.7790	+	24.6985i	1.49118	+	0.860934i	0.491233	+	0.871028i	$0.336546\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−20.8101	−	12.0147i	−0.723640	−	0.417794i	0.0924511	−	0.995717i	$-0.470530\pi$
$827$	−20.8101	−	12.0147i	−0.723640	−	0.417794i	−0.816091	+	0.577924i	$0.803863\pi$
$828$		0			0
$829$	−8.42673			−0.292672			−0.146336	−	0.989235i	$-0.546748\pi$
$829$	−8.42673			−0.292672			−0.146336	+	0.989235i	$0.546748\pi$
$830$		0			0
$831$	−7.20132	−	12.4731i	−0.249811	−	0.432686i
$832$		0			0
$833$	−8.10730	+	4.68075i	−0.280901	+	0.162178i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	22.3601i		−	0.772879i
$838$		0			0
$839$	11.0809	+	19.1926i	0.382554	+	0.662603i	0.991427	−	0.130665i	$-0.0417112\pi$
$839$	11.0809	+	19.1926i	0.382554	+	0.662603i	−0.608872	+	0.793268i	$0.708378\pi$
$840$		0			0
$841$	−16.9488	−	29.3561i	−0.584440	−	1.01228i
$842$		0			0
$843$		−	11.0574i		−	0.380836i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			4.52752i			0.155568i
$848$		0			0
$849$	9.66830	−	16.7460i	0.331815	−	0.574721i
$850$		0			0
$851$	−38.5213	+	66.7208i	−1.32049	+	2.28716i
$852$		0			0
$853$	33.6283	−	19.4153i	1.15141	−	0.664767i	0.202180	−	0.979348i	$-0.435198\pi$
$853$	33.6283	−	19.4153i	1.15141	−	0.664767i	0.949230	+	0.314582i	$0.101864\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.0409	+	17.9215i	−1.06034	+	0.612186i	−0.925526	−	0.378685i	$-0.876376\pi$
$857$	−31.0409	+	17.9215i	−1.06034	+	0.612186i	−0.134812	+	0.990871i	$0.543043\pi$
$858$		0			0
$859$	−9.06313	+	15.6978i	−0.309230	+	0.535602i	−0.978194	−	0.207692i	$-0.933405\pi$
$859$	−9.06313	+	15.6978i	−0.309230	+	0.535602i	0.668964	+	0.743295i	$0.266738\pi$
$860$		0			0
$861$	1.22533	−	2.12233i	0.0417590	−	0.0723287i
$862$		0			0
$863$		−	48.5099i		−	1.65130i	−0.564186	−	0.825648i	$-0.690810\pi$
$863$		−	48.5099i		−	1.65130i	0.564186	−	0.825648i	$-0.309190\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	3.38363i		−	0.114914i
$868$		0			0
$869$	15.9007	+	27.5409i	0.539395	+	0.934259i
$870$		0			0
$871$	−1.68909	−	2.92560i	−0.0572328	−	0.0991301i
$872$		0			0
$873$		−	19.2351i		−	0.651008i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.3322	−	13.4708i	0.787872	−	0.454878i	−0.0513410	−	0.998681i	$-0.516350\pi$
$877$	23.3322	−	13.4708i	0.787872	−	0.454878i	0.839213	+	0.543803i	$0.183016\pi$
$878$		0			0
$879$	−4.49326	−	7.78255i	−0.151554	−	0.262499i
$880$		0			0
$881$	27.0603			0.911685			0.455843	−	0.890060i	$-0.349338\pi$
$881$	27.0603			0.911685			0.455843	+	0.890060i	$0.349338\pi$
$882$		0			0
$883$	31.7118	+	18.3088i	1.06719	+	0.616140i	0.927411	−	0.374043i	$-0.122029\pi$
$883$	31.7118	+	18.3088i	1.06719	+	0.616140i	0.139775	+	0.990183i	$0.455362\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−36.7786	−	21.2342i	−1.23491	−	0.712973i	−0.266857	−	0.963736i	$-0.585985\pi$
$887$	−36.7786	−	21.2342i	−1.23491	−	0.712973i	−0.968049	+	0.250763i	$0.919319\pi$
$888$		0			0
$889$	−7.22635	+	12.5164i	−0.242364	+	0.419787i
$890$		0			0
$891$	8.33971	+	14.4448i	0.279391	+	0.483919i
$892$		0			0
$893$	29.2995	+	14.7284i	0.980469	+	0.492868i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.80470	+	1.04195i	0.0602573	+	0.0347896i
$898$		0			0
$899$	−22.7433	+	39.3926i	−0.758533	+	1.31382i
$900$		0			0
$901$	36.9125			1.22973
$902$		0			0
$903$	−16.4465	−	9.49538i	−0.547305	−	0.315986i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	46.4433	−	26.8140i	1.54212	−	0.890345i	0.543418	−	0.839462i	$-0.317130\pi$
$907$	46.4433	−	26.8140i	1.54212	−	0.890345i	0.998705	−	0.0508831i	$-0.0162036\pi$
$908$		0			0
$909$	−21.6934	−	37.5740i	−0.719523	−	1.24625i
$910$		0			0
$911$	−10.1631			−0.336719			−0.168360	−	0.985726i	$-0.553847\pi$
$911$	−10.1631			−0.336719			−0.168360	+	0.985726i	$0.553847\pi$
$912$		0			0
$913$			14.3942i			0.476379i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.2751	−	16.3246i	0.933725	−	0.539087i
$918$		0			0
$919$	16.6831			0.550325			0.275163	−	0.961398i	$-0.411268\pi$
$919$	16.6831			0.550325			0.275163	+	0.961398i	$0.411268\pi$
$920$		0			0
$921$	−0.911632	+	1.57899i	−0.0300393	+	0.0520296i
$922$		0			0
$923$			3.46341i			0.113999i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.4101	−	8.89702i	−0.506134	−	0.292216i
$928$		0			0
$929$	4.49844	+	7.79152i	0.147589	+	0.255631i	0.930336	−	0.366709i	$-0.119515\pi$
$929$	4.49844	+	7.79152i	0.147589	+	0.255631i	−0.782747	+	0.622340i	$0.786182\pi$
$930$		0			0
$931$	11.6493	−	0.674135i	0.381790	−	0.0220939i
$932$		0			0
$933$	−12.1346	+	7.00594i	−0.397270	+	0.229364i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−34.5001	−	19.9187i	−1.12707	−	0.650714i	−0.183874	−	0.982950i	$-0.558864\pi$
$937$	−34.5001	−	19.9187i	−1.12707	−	0.650714i	−0.943196	+	0.332236i	$0.892197\pi$
$938$		0			0
$939$	−15.8691			−0.517868
$940$		0			0
$941$	−5.92236	+	10.2578i	−0.193063	+	0.334396i	−0.946264	−	0.323395i	$-0.895176\pi$
$941$	−5.92236	+	10.2578i	−0.193063	+	0.334396i	0.753201	+	0.657791i	$0.228509\pi$
$942$		0			0
$943$		−	8.12765i		−	0.264673i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.5944	+	6.69404i	−0.376768	+	0.217527i	−0.676411	−	0.736524i	$-0.736466\pi$
$947$	−11.5944	+	6.69404i	−0.376768	+	0.217527i	0.299643	+	0.954051i	$0.403132\pi$
$948$		0			0
$949$	−0.699307			−0.0227005
$950$		0			0
$951$	9.43704			0.306017
$952$		0			0
$953$	−40.0094	+	23.0994i	−1.29603	+	0.748264i	−0.979716	−	0.200390i	$-0.935779\pi$
$953$	−40.0094	+	23.0994i	−1.29603	+	0.748264i	−0.316315	+	0.948654i	$0.602446\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			19.8507i			0.641682i
$958$		0			0
$959$	−2.16542	+	3.75062i	−0.0699252	+	0.121114i
$960$		0			0
$961$	1.89541			0.0611424
$962$		0			0
$963$	−1.59040	−	0.918216i	−0.0512498	−	0.0295891i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	20.5345	−	11.8556i	0.660346	−	0.381251i	−0.132063	−	0.991241i	$-0.542160\pi$
$967$	20.5345	−	11.8556i	0.660346	−	0.381251i	0.792409	+	0.609991i	$0.208827\pi$
$968$		0			0
$969$	4.85543	−	9.65898i	0.155979	−	0.310291i
$970$		0			0
$971$	17.2724	+	29.9166i	0.554296	+	0.960069i	0.997958	+	0.0638748i	$0.0203458\pi$
$971$	17.2724	+	29.9166i	0.554296	+	0.960069i	−0.443662	+	0.896194i	$0.646321\pi$
$972$		0			0
$973$	−16.3670	−	9.44951i	−0.524703	−	0.302937i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	52.4467i		−	1.67792i	−0.544195	−	0.838959i	$-0.683165\pi$
$977$		−	52.4467i		−	1.67792i	0.544195	−	0.838959i	$-0.316835\pi$
$978$		0			0
$979$	23.3502	−	40.4437i	0.746275	−	1.29259i
$980$		0			0
$981$	39.9755			1.27632
$982$		0			0
$983$	−12.1497	+	7.01464i	−0.387515	+	0.223732i	−0.681083	−	0.732206i	$-0.738491\pi$
$983$	−12.1497	+	7.01464i	−0.387515	+	0.223732i	0.293568	+	0.955938i	$0.405157\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			16.5980i			0.528320i
$988$		0			0
$989$	−62.9834			−2.00276
$990$		0			0
$991$	−4.94168	−	8.55924i	−0.156978	−	0.271893i	0.776800	−	0.629748i	$-0.216842\pi$
$991$	−4.94168	−	8.55924i	−0.156978	−	0.271893i	−0.933777	+	0.357854i	$0.883508\pi$
$992$		0			0
$993$	12.0490	−	6.95647i	0.382362	−	0.220757i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	36.7559	+	21.2210i	1.16407	+	0.672077i	0.952276	−	0.305237i	$-0.0987357\pi$
$997$	36.7559	+	21.2210i	1.16407	+	0.672077i	0.211795	+	0.977314i	$0.432069\pi$
$998$		0			0
$999$	−41.0490			−1.29873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.d.349.3		16
5.2	odd	4		1900.2.i.d.501.3		8
5.3	odd	4		380.2.i.c.121.2	✓	8
5.4	even	2	inner	1900.2.s.d.349.6		16
15.8	even	4		3420.2.t.w.1261.4		8
19.11	even	3	inner	1900.2.s.d.49.6		16
20.3	even	4		1520.2.q.m.881.3		8
95.49	even	6	inner	1900.2.s.d.49.3		16
95.68	odd	12		380.2.i.c.201.2	yes	8
95.83	odd	12		7220.2.a.r.1.3		4
95.87	odd	12		1900.2.i.d.201.3		8
95.88	even	12		7220.2.a.p.1.2		4
285.68	even	12		3420.2.t.w.3241.4		8
380.163	even	12		1520.2.q.m.961.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.2	✓	8	5.3	odd	4
380.2.i.c.201.2	yes	8	95.68	odd	12
1520.2.q.m.881.3		8	20.3	even	4
1520.2.q.m.961.3		8	380.163	even	12
1900.2.i.d.201.3		8	95.87	odd	12
1900.2.i.d.501.3		8	5.2	odd	4
1900.2.s.d.49.3		16	95.49	even	6	inner
1900.2.s.d.49.6		16	19.11	even	3	inner
1900.2.s.d.349.3		16	1.1	even	1	trivial
1900.2.s.d.349.6		16	5.4	even	2	inner
3420.2.t.w.1261.4		8	15.8	even	4
3420.2.t.w.3241.4		8	285.68	even	12
7220.2.a.p.1.2		4	95.88	even	12
7220.2.a.r.1.3		4	95.83	odd	12

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.614201 + 0.354609i) q^{3} +3.11079i q^{7} +(-1.24850 + 2.16247i) q^{9} +O(q^{10})\)	\(q+(-0.614201 + 0.354609i) q^{3} +3.11079i q^{7} +(-1.24850 + 2.16247i) q^{9} -3.52922 q^{11} +(0.347770 + 0.200785i) q^{13} +(3.02850 - 1.74850i) q^{17} +(-4.35162 + 0.251824i) q^{19} +(-1.10311 - 1.91065i) q^{21} +(-6.33672 - 3.65851i) q^{23} -3.89858i q^{27} +(-3.96540 + 6.86827i) q^{29} +5.73545 q^{31} +(2.16765 - 1.25150i) q^{33} -10.5292i q^{37} -0.284801 q^{39} +(0.555394 + 0.961971i) q^{41} +(7.45457 - 4.30390i) q^{43} +(-6.51532 - 3.76162i) q^{47} -2.67700 q^{49} +(-1.24007 + 2.14787i) q^{51} +(9.14130 + 5.27773i) q^{53} +(2.58347 - 1.69779i) q^{57} +(-4.25618 - 7.37192i) q^{59} +(4.61079 - 7.98612i) q^{61} +(-6.72700 - 3.88383i) q^{63} +(-7.28540 - 4.20623i) q^{67} +5.18936 q^{69} +(4.31233 + 7.46918i) q^{71} +(-1.50813 + 0.870717i) q^{73} -10.9787i q^{77} +(-4.50544 - 7.80366i) q^{79} +(-2.36304 - 4.09291i) q^{81} -4.07857i q^{83} -5.62466i q^{87} +(-6.61623 + 11.4596i) q^{89} +(-0.624599 + 1.08184i) q^{91} +(-3.52272 + 2.03384i) q^{93} +(-6.67120 + 3.85162i) q^{97} +(4.40625 - 7.63186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Introduction

L-functions

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