LMFDB - Embedded newform 1260.2.c.e.811.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(811,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1260.811");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.c (of order $2$, degree $1$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$16$
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} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 3x^14 - 4x^13 + 3x^12 + 2x^11 - 7x^10 + 12x^9 - 28x^8 + 24x^7 - 28x^6 + 16x^5 + 48x^4 - 128x^3 + 192x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			811.15
Root			$-1.39396 - 0.238466i$ of defining polynomial
Character	$\chi$	$=$	1260.811
Dual form			1260.2.c.e.811.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39396 - 0.238466i) q^{2} +(1.88627 - 0.664826i) q^{4} -1.00000i q^{5} +(-2.37694 - 1.16196i) q^{7} +(2.47085 - 1.37655i) q^{8} +O(q^{10})$	\(q+(1.39396 - 0.238466i) q^{2} +(1.88627 - 0.664826i) q^{4} -1.00000i q^{5} +(-2.37694 - 1.16196i) q^{7} +(2.47085 - 1.37655i) q^{8} +(-0.238466 - 1.39396i) q^{10} -4.86632i q^{11} +3.63628i q^{13} +(-3.59045 - 1.05292i) q^{14} +(3.11601 - 2.50808i) q^{16} -4.47770i q^{17} +2.70953 q^{19} +(-0.664826 - 1.88627i) q^{20} +(-1.16045 - 6.78348i) q^{22} +1.68651i q^{23} -1.00000 q^{25} +(0.867130 + 5.06885i) q^{26} +(-5.25605 - 0.611525i) q^{28} -8.31929 q^{29} -5.47361 q^{31} +(3.74552 - 4.23924i) q^{32} +(-1.06778 - 6.24175i) q^{34} +(-1.16196 + 2.37694i) q^{35} +7.07032 q^{37} +(3.77698 - 0.646131i) q^{38} +(-1.37655 - 2.47085i) q^{40} -11.5568i q^{41} -7.86152i q^{43} +(-3.23526 - 9.17919i) q^{44} +(0.402175 + 2.35093i) q^{46} +4.75086 q^{47} +(4.29968 + 5.52384i) q^{49} +(-1.39396 + 0.238466i) q^{50} +(2.41750 + 6.85900i) q^{52} +10.1441 q^{53} -4.86632 q^{55} +(-7.47257 + 0.400946i) q^{56} +(-11.5968 + 1.98387i) q^{58} -2.97451 q^{59} -1.18105i q^{61} +(-7.63001 + 1.30527i) q^{62} +(4.21020 - 6.80252i) q^{64} +3.63628 q^{65} +13.1428i q^{67} +(-2.97689 - 8.44614i) q^{68} +(-1.05292 + 3.59045i) q^{70} +14.8383i q^{71} +1.40398i q^{73} +(9.85577 - 1.68603i) q^{74} +(5.11090 - 1.80137i) q^{76} +(-5.65450 + 11.5670i) q^{77} +1.01535i q^{79} +(-2.50808 - 3.11601i) q^{80} +(-2.75589 - 16.1097i) q^{82} +8.22400 q^{83} -4.47770 q^{85} +(-1.87471 - 10.9587i) q^{86} +(-6.69876 - 12.0240i) q^{88} +9.91123i q^{89} +(4.22523 - 8.64322i) q^{91} +(1.12123 + 3.18121i) q^{92} +(6.62252 - 1.13292i) q^{94} -2.70953i q^{95} -13.0383i q^{97} +(7.31084 + 6.67470i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	$ 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	1.39396	−	0.238466i	0.985681	−	0.168621i
$2$	1.39396	−	0.238466i	0.985681	−	0.168621i
$3$		0			0
$3$		0			0
$4$	1.88627	−	0.664826i	0.943134	−	0.332413i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−2.37694	−	1.16196i	−0.898398	−	0.439181i
$7$	−2.37694	−	1.16196i	−0.898398	−	0.439181i
$8$	2.47085	−	1.37655i	0.873577	−	0.486685i
$9$		0			0
$10$	−0.238466	−	1.39396i	−0.0754096	−	0.440810i
$11$		−	4.86632i		−	1.46725i	−0.679554	−	0.733626i	$-0.737826\pi$
$11$		−	4.86632i		−	1.46725i	0.679554	−	0.733626i	$-0.262174\pi$
$12$		0			0
$13$			3.63628i			1.00852i	0.863551	+	0.504262i	$0.168235\pi$
$13$			3.63628i			1.00852i	−0.863551	+	0.504262i	$0.831765\pi$
$14$	−3.59045	−	1.05292i	−0.959589	−	0.281404i
$15$		0			0
$16$	3.11601	−	2.50808i	0.779003	−	0.627020i
$17$		−	4.47770i		−	1.08600i	−0.839732	−	0.543001i	$-0.817288\pi$
$17$		−	4.47770i		−	1.08600i	0.839732	−	0.543001i	$-0.182712\pi$
$18$		0			0
$19$	2.70953			0.621609			0.310804	−	0.950474i	$-0.399402\pi$
$19$	2.70953			0.621609			0.310804	+	0.950474i	$0.399402\pi$
$20$	−0.664826	−	1.88627i	−0.148660	−	0.421782i
$21$		0			0
$22$	−1.16045	−	6.78348i	−0.247410	−	1.44624i
$23$			1.68651i			0.351661i	0.984420	+	0.175831i	$0.0562611\pi$
$23$			1.68651i			0.351661i	−0.984420	+	0.175831i	$0.943739\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	0.867130	+	5.06885i	0.170058	+	0.994082i
$27$		0			0
$28$	−5.25605	−	0.611525i	−0.993300	−	0.115567i
$29$	−8.31929			−1.54485			−0.772427	−	0.635103i	$-0.780957\pi$
$29$	−8.31929			−1.54485			−0.772427	+	0.635103i	$0.780957\pi$
$30$		0			0
$31$	−5.47361			−0.983090			−0.491545	−	0.870852i	$-0.663568\pi$
$31$	−5.47361			−0.983090			−0.491545	+	0.870852i	$0.663568\pi$
$32$	3.74552	−	4.23924i	0.662120	−	0.749398i
$33$		0			0
$34$	−1.06778	−	6.24175i	−0.183123	−	1.07045i
$35$	−1.16196	+	2.37694i	−0.196408	+	0.401776i
$36$		0			0
$37$	7.07032			1.16235			0.581177	−	0.813777i	$-0.302592\pi$
$37$	7.07032			1.16235			0.581177	+	0.813777i	$0.302592\pi$
$38$	3.77698	−	0.646131i	0.612708	−	0.104816i
$39$		0			0
$40$	−1.37655	−	2.47085i	−0.217652	−	0.390676i
$41$		−	11.5568i		−	1.80486i	−0.430835	−	0.902431i	$-0.641781\pi$
$41$		−	11.5568i		−	1.80486i	0.430835	−	0.902431i	$-0.358219\pi$
$42$		0			0
$43$		−	7.86152i		−	1.19887i	−0.800424	−	0.599435i	$-0.795392\pi$
$43$		−	7.86152i		−	1.19887i	0.800424	−	0.599435i	$-0.204608\pi$
$44$	−3.23526	−	9.17919i	−0.487734	−	1.38382i
$45$		0			0
$46$	0.402175	+	2.35093i	0.0592975	+	0.346626i
$47$	4.75086			0.692984			0.346492	−	0.938053i	$-0.387373\pi$
$47$	4.75086			0.692984			0.346492	+	0.938053i	$0.387373\pi$
$48$		0			0
$49$	4.29968	+	5.52384i	0.614240	+	0.789120i
$50$	−1.39396	+	0.238466i	−0.197136	+	0.0337242i
$51$		0			0
$52$	2.41750	+	6.85900i	0.335246	+	0.951173i
$53$	10.1441			1.39340			0.696701	−	0.717362i	$-0.254651\pi$
$53$	10.1441			1.39340			0.696701	+	0.717362i	$0.254651\pi$
$54$		0			0
$55$	−4.86632			−0.656175
$56$	−7.47257	+	0.400946i	−0.998564	+	0.0535786i
$57$		0			0
$58$	−11.5968	+	1.98387i	−1.52273	+	0.260495i
$59$	−2.97451			−0.387248			−0.193624	−	0.981076i	$-0.562024\pi$
$59$	−2.97451			−0.387248			−0.193624	+	0.981076i	$0.562024\pi$
$60$		0			0
$61$		−	1.18105i		−	0.151217i	−0.997138	−	0.0756087i	$-0.975910\pi$
$61$		−	1.18105i		−	0.151217i	0.997138	−	0.0756087i	$-0.0240900\pi$
$62$	−7.63001	+	1.30527i	−0.969013	+	0.165770i
$63$		0			0
$64$	4.21020	−	6.80252i	0.526275	−	0.850315i
$65$	3.63628			0.451025
$66$		0			0
$67$			13.1428i			1.60565i	0.596215	+	0.802825i	$0.296671\pi$
$67$			13.1428i			1.60565i	−0.596215	+	0.802825i	$0.703329\pi$
$68$	−2.97689	−	8.44614i	−0.361001	−	1.02425i
$69$		0			0
$70$	−1.05292	+	3.59045i	−0.125848	+	0.429141i
$71$			14.8383i			1.76098i	0.474060	+	0.880492i	$0.342788\pi$
$71$			14.8383i			1.76098i	−0.474060	+	0.880492i	$0.657212\pi$
$72$		0			0
$73$			1.40398i			0.164323i	0.996619	+	0.0821615i	$0.0261823\pi$
$73$			1.40398i			0.164323i	−0.996619	+	0.0821615i	$0.973818\pi$
$74$	9.85577	−	1.68603i	1.14571	−	0.195997i
$75$		0			0
$76$	5.11090	−	1.80137i	0.586260	−	0.206631i
$77$	−5.65450	+	11.5670i	−0.644390	+	1.31818i
$78$		0			0
$79$			1.01535i			0.114236i	0.998367	+	0.0571181i	$0.0181911\pi$
$79$			1.01535i			0.114236i	−0.998367	+	0.0571181i	$0.981809\pi$
$80$	−2.50808	−	3.11601i	−0.280412	−	0.348381i
$81$		0			0
$82$	−2.75589	−	16.1097i	−0.304338	−	1.77902i
$83$	8.22400			0.902701			0.451351	−	0.892347i	$-0.350942\pi$
$83$	8.22400			0.902701			0.451351	+	0.892347i	$0.350942\pi$
$84$		0			0
$85$	−4.47770			−0.485675
$86$	−1.87471	−	10.9587i	−0.202155	−	1.18170i
$87$		0			0
$88$	−6.69876	−	12.0240i	−0.714090	−	1.28176i
$89$			9.91123i			1.05059i	0.850921	+	0.525294i	$0.176045\pi$
$89$			9.91123i			1.05059i	−0.850921	+	0.525294i	$0.823955\pi$
$90$		0			0
$91$	4.22523	−	8.64322i	0.442925	−	0.906056i
$92$	1.12123	+	3.18121i	0.116897	+	0.331664i
$93$		0			0
$94$	6.62252	−	1.13292i	0.683061	−	0.116852i
$95$		−	2.70953i		−	0.277992i
$96$		0			0
$97$		−	13.0383i		−	1.32384i	−0.749575	−	0.661920i	$-0.769742\pi$
$97$		−	13.0383i		−	1.32384i	0.749575	−	0.661920i	$-0.230258\pi$
$98$	7.31084	+	6.67470i	0.738506	+	0.674246i
$99$		0			0
$100$	−1.88627	+	0.664826i	−0.188627	+	0.0664826i
$101$			10.5101i			1.04579i	0.852396	+	0.522897i	$0.175149\pi$
$101$			10.5101i			1.04579i	−0.852396	+	0.522897i	$0.824851\pi$
$102$		0			0
$103$	17.7530			1.74926			0.874630	−	0.484791i	$-0.161104\pi$
$103$	17.7530			1.74926			0.874630	+	0.484791i	$0.161104\pi$
$104$	5.00554	+	8.98471i	0.490834	+	0.881023i
$105$		0			0
$106$	14.1405	−	2.41903i	1.37345	−	0.234957i
$107$			3.33046i			0.321968i	0.986957	+	0.160984i	$0.0514667\pi$
$107$			3.33046i			0.321968i	−0.986957	+	0.160984i	$0.948533\pi$
$108$		0			0
$109$	−0.497397			−0.0476420			−0.0238210	−	0.999716i	$-0.507583\pi$
$109$	−0.497397			−0.0476420			−0.0238210	+	0.999716i	$0.507583\pi$
$110$	−6.78348	+	1.16045i	−0.646779	+	0.110645i
$111$		0			0
$112$	−10.3209	+	2.34086i	−0.975231	+	0.221190i
$113$	5.49626			0.517045			0.258522	−	0.966005i	$-0.416764\pi$
$113$	5.49626			0.517045			0.258522	+	0.966005i	$0.416764\pi$
$114$		0			0
$115$	1.68651			0.157268
$116$	−15.6924	+	5.53088i	−1.45700	+	0.513530i
$117$		0			0
$118$	−4.14635	+	0.709319i	−0.381703	+	0.0652981i
$119$	−5.20293	+	10.6432i	−0.476952	+	0.975663i
$120$		0			0
$121$	−12.6811			−1.15283
$122$	−0.281640	−	1.64634i	−0.0254984	−	0.149052i
$123$		0			0
$124$	−10.3247	+	3.63900i	−0.927185	+	0.326792i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	2.36124i		−	0.209527i	−0.994497	−	0.104763i	$-0.966592\pi$
$127$		−	2.36124i		−	0.209527i	0.994497	−	0.104763i	$-0.0334085\pi$
$128$	4.24669	−	10.4864i	0.375358	−	0.926880i
$129$		0			0
$130$	5.06885	−	0.867130i	0.444567	−	0.0760524i
$131$	−1.93713			−0.169248			−0.0846239	−	0.996413i	$-0.526969\pi$
$131$	−1.93713			−0.169248			−0.0846239	+	0.996413i	$0.526969\pi$
$132$		0			0
$133$	−6.44039	−	3.14838i	−0.558452	−	0.272999i
$134$	3.13411	+	18.3206i	0.270746	+	1.58266i
$135$		0			0
$136$	−6.16380	−	11.0637i	−0.528541	−	0.948707i
$137$	−15.2841			−1.30581			−0.652903	−	0.757442i	$-0.726449\pi$
$137$	−15.2841			−1.30581			−0.652903	+	0.757442i	$0.726449\pi$
$138$		0			0
$139$	1.84036			0.156097			0.0780487	−	0.996950i	$-0.475131\pi$
$139$	1.84036			0.156097			0.0780487	+	0.996950i	$0.475131\pi$
$140$	−0.611525	+	5.25605i	−0.0516833	+	0.444217i
$141$		0			0
$142$	3.53844	+	20.6841i	0.296939	+	1.73577i
$143$	17.6953			1.47976
$144$		0			0
$145$			8.31929i			0.690880i
$146$	0.334801	+	1.95709i	0.0277083	+	0.161970i
$147$		0			0
$148$	13.3365	−	4.70053i	1.09626	−	0.386382i
$149$	2.97073			0.243371			0.121686	−	0.992569i	$-0.461170\pi$
$149$	2.97073			0.243371			0.121686	+	0.992569i	$0.461170\pi$
$150$		0			0
$151$			15.8192i			1.28735i	0.765300	+	0.643674i	$0.222591\pi$
$151$			15.8192i			1.28735i	−0.765300	+	0.643674i	$0.777409\pi$
$152$	6.69484	−	3.72981i	0.543023	−	0.302528i
$153$		0			0
$154$	−5.12383	+	17.4723i	−0.412890	+	1.40796i
$155$			5.47361i			0.439651i
$156$		0			0
$157$		−	8.59663i		−	0.686086i	−0.939320	−	0.343043i	$-0.888542\pi$
$157$		−	8.59663i		−	0.686086i	0.939320	−	0.343043i	$-0.111458\pi$
$158$	0.242127	+	1.41537i	0.0192626	+	0.112600i
$159$		0			0
$160$	−4.23924	−	3.74552i	−0.335141	−	0.296109i
$161$	1.95966	−	4.00873i	0.154443	−	0.315932i
$162$		0			0
$163$			1.35767i			0.106341i	0.998585	+	0.0531703i	$0.0169326\pi$
$163$			1.35767i			0.106341i	−0.998585	+	0.0531703i	$0.983067\pi$
$164$	−7.68323	−	21.7991i	−0.599959	−	1.70223i
$165$		0			0
$166$	11.4640	−	1.96115i	0.889776	−	0.152214i
$167$	2.53862			0.196444			0.0982220	−	0.995165i	$-0.468684\pi$
$167$	2.53862			0.196444			0.0982220	+	0.995165i	$0.468684\pi$
$168$		0			0
$169$	−0.222556			−0.0171197
$170$	−6.24175	+	1.06778i	−0.478721	+	0.0818950i
$171$		0			0
$172$	−5.22654	−	14.8289i	−0.398520	−	1.13069i
$173$			6.99917i			0.532137i	0.963954	+	0.266069i	$0.0857248\pi$
$173$			6.99917i			0.532137i	−0.963954	+	0.266069i	$0.914275\pi$
$174$		0			0
$175$	2.37694	+	1.16196i	0.179680	+	0.0878363i
$176$	−12.2051	−	15.1635i	−0.919996	−	1.14299i
$177$		0			0
$178$	2.36349	+	13.8159i	0.177151	+	1.03554i
$179$			8.98718i			0.671734i	0.941909	+	0.335867i	$0.109029\pi$
$179$			8.98718i			0.671734i	−0.941909	+	0.335867i	$0.890971\pi$
$180$		0			0
$181$		−	7.23017i		−	0.537414i	−0.963222	−	0.268707i	$-0.913404\pi$
$181$		−	7.23017i		−	0.537414i	0.963222	−	0.268707i	$-0.0865963\pi$
$182$	3.82870	−	13.0559i	0.283802	−	0.967769i
$183$		0			0
$184$	2.32157	+	4.16711i	0.171148	+	0.307203i
$185$		−	7.07032i		−	0.519820i
$186$		0			0
$187$	−21.7899			−1.59344
$188$	8.96139	−	3.15849i	0.653576	−	0.230357i
$189$		0			0
$190$	−0.646131	−	3.77698i	−0.0468753	−	0.274011i
$191$			5.61914i			0.406587i	0.979118	+	0.203293i	$0.0651645\pi$
$191$			5.61914i			0.406587i	−0.979118	+	0.203293i	$0.934835\pi$
$192$		0			0
$193$	5.51737			0.397149			0.198575	−	0.980086i	$-0.436369\pi$
$193$	5.51737			0.397149			0.198575	+	0.980086i	$0.436369\pi$
$194$	−3.10920	−	18.1749i	−0.223227	−	1.30488i
$195$		0			0
$196$	11.7827	+	7.56090i	0.841624	+	0.540064i
$197$	−6.86110			−0.488833			−0.244416	−	0.969670i	$-0.578596\pi$
$197$	−6.86110			−0.488833			−0.244416	+	0.969670i	$0.578596\pi$
$198$		0			0
$199$	1.33434			0.0945888			0.0472944	−	0.998881i	$-0.484940\pi$
$199$	1.33434			0.0945888			0.0472944	+	0.998881i	$0.484940\pi$
$200$	−2.47085	+	1.37655i	−0.174715	+	0.0973371i
$201$		0			0
$202$	2.50630	+	14.6507i	0.176343	+	1.03082i
$203$	19.7745	+	9.66672i	1.38789	+	0.678471i
$204$		0			0
$205$	−11.5568			−0.807158
$206$	24.7471	−	4.23350i	1.72421	−	0.294962i
$207$		0			0
$208$	9.12009	+	11.3307i	0.632364	+	0.785643i
$209$		−	13.1854i		−	0.912057i
$210$		0			0
$211$			22.2190i			1.52962i	0.644256	+	0.764810i	$0.277167\pi$
$211$			22.2190i			1.52962i	−0.644256	+	0.764810i	$0.722833\pi$
$212$	19.1345	−	6.74407i	1.31416	−	0.463185i
$213$		0			0
$214$	0.794202	+	4.64254i	0.0542905	+	0.317357i
$215$	−7.86152			−0.536151
$216$		0			0
$217$	13.0104	+	6.36014i	0.883206	+	0.431755i
$218$	−0.693353	+	0.118612i	−0.0469598	+	0.00803344i
$219$		0			0
$220$	−9.17919	+	3.23526i	−0.618861	+	0.218121i
$221$	16.2822			1.09526
$222$		0			0
$223$	28.4530			1.90535			0.952677	−	0.303985i	$-0.0983174\pi$
$223$	28.4530			1.90535			0.952677	+	0.303985i	$0.0983174\pi$
$224$	−13.8287	+	5.72425i	−0.923969	+	0.382467i
$225$		0			0
$226$	7.66158	−	1.31067i	0.509641	−	0.0871846i
$227$	−20.5963			−1.36703			−0.683513	−	0.729938i	$-0.739549\pi$
$227$	−20.5963			−1.36703			−0.683513	+	0.729938i	$0.739549\pi$
$228$		0			0
$229$		−	10.6828i		−	0.705937i	−0.935635	−	0.352968i	$-0.885172\pi$
$229$		−	10.6828i		−	0.705937i	0.935635	−	0.352968i	$-0.114828\pi$
$230$	2.35093	−	0.402175i	0.155016	−	0.0265186i
$231$		0			0
$232$	−20.5557	+	11.4520i	−1.34955	+	0.751858i
$233$	−24.6073			−1.61208			−0.806038	−	0.591864i	$-0.798392\pi$
$233$	−24.6073			−1.61208			−0.806038	+	0.591864i	$0.798392\pi$
$234$		0			0
$235$		−	4.75086i		−	0.309912i
$236$	−5.61072	+	1.97753i	−0.365226	+	0.128726i
$237$		0			0
$238$	−4.71465	+	16.0770i	−0.305605	+	1.04212i
$239$		−	9.20971i		−	0.595726i	−0.954609	−	0.297863i	$-0.903726\pi$
$239$		−	9.20971i		−	0.595726i	0.954609	−	0.297863i	$-0.0962739\pi$
$240$		0			0
$241$			11.5159i			0.741807i	0.928671	+	0.370903i	$0.120952\pi$
$241$			11.5159i			0.741807i	−0.928671	+	0.370903i	$0.879048\pi$
$242$	−17.6770	+	3.02402i	−1.13632	+	0.194391i
$243$		0			0
$244$	−0.785190	−	2.22777i	−0.0502667	−	0.142618i
$245$	5.52384	−	4.29968i	0.352905	−	0.274696i
$246$		0			0
$247$			9.85262i			0.626907i
$248$	−13.5245	+	7.53472i	−0.858805	+	0.478455i
$249$		0			0
$250$	0.238466	+	1.39396i	0.0150819	+	0.0881620i
$251$	−1.35391			−0.0854582			−0.0427291	−	0.999087i	$-0.513605\pi$
$251$	−1.35391			−0.0854582			−0.0427291	+	0.999087i	$0.513605\pi$
$252$		0			0
$253$	8.20710			0.515976
$254$	−0.563077	−	3.29149i	−0.0353306	−	0.206526i
$255$		0			0
$256$	3.41907	−	15.6304i	0.213692	−	0.976901i
$257$			19.0856i			1.19053i	0.803531	+	0.595263i	$0.202952\pi$
$257$			19.0856i			1.19053i	−0.803531	+	0.595263i	$0.797048\pi$
$258$		0			0
$259$	−16.8057	−	8.21546i	−1.04426	−	0.510484i
$260$	6.85900	−	2.41750i	0.425377	−	0.149927i
$261$		0			0
$262$	−2.70029	+	0.461940i	−0.166824	+	0.0285387i
$263$		−	23.1978i		−	1.43044i	−0.698899	−	0.715220i	$-0.746326\pi$
$263$		−	23.1978i		−	1.43044i	0.698899	−	0.715220i	$-0.253674\pi$
$264$		0			0
$265$		−	10.1441i		−	0.623148i
$266$	−9.72844	−	2.85291i	−0.596489	−	0.174923i
$267$		0			0
$268$	8.73768	+	24.7909i	0.533739	+	1.51434i
$269$		−	2.77517i		−	0.169205i	−0.996415	−	0.0846025i	$-0.973038\pi$
$269$		−	2.77517i		−	0.169205i	0.996415	−	0.0846025i	$-0.0269621\pi$
$270$		0			0
$271$	−16.6103			−1.00901			−0.504503	−	0.863410i	$-0.668324\pi$
$271$	−16.6103			−1.00901			−0.504503	+	0.863410i	$0.668324\pi$
$272$	−11.2304	−	13.9526i	−0.680945	−	0.845999i
$273$		0			0
$274$	−21.3054	+	3.64473i	−1.28711	+	0.220186i
$275$			4.86632i			0.293450i
$276$		0			0
$277$	−3.08317			−0.185250			−0.0926250	−	0.995701i	$-0.529526\pi$
$277$	−3.08317			−0.185250			−0.0926250	+	0.995701i	$0.529526\pi$
$278$	2.56540	−	0.438864i	0.153862	−	0.0263213i
$279$		0			0
$280$	0.400946	+	7.47257i	0.0239611	+	0.446571i
$281$	12.9179			0.770617			0.385308	−	0.922788i	$-0.374095\pi$
$281$	12.9179			0.770617			0.385308	+	0.922788i	$0.374095\pi$
$282$		0			0
$283$	17.1674			1.02050			0.510249	−	0.860027i	$-0.329553\pi$
$283$	17.1674			1.02050			0.510249	+	0.860027i	$0.329553\pi$
$284$	9.86490	+	27.9890i	0.585374	+	1.66084i
$285$		0			0
$286$	24.6666	−	4.21974i	1.45857	−	0.249518i
$287$	−13.4285	+	27.4697i	−0.792661	+	1.62148i
$288$		0			0
$289$	−3.04981			−0.179401
$290$	1.98387	+	11.5968i	0.116497	+	0.680987i
$291$		0			0
$292$	0.933400	+	2.64827i	0.0546231	+	0.154979i
$293$			1.99319i			0.116443i	0.998304	+	0.0582217i	$0.0185430\pi$
$293$			1.99319i			0.116443i	−0.998304	+	0.0582217i	$0.981457\pi$
$294$		0			0
$295$			2.97451i			0.173182i
$296$	17.4697	−	9.73268i	1.01541	−	0.565701i
$297$		0			0
$298$	4.14108	−	0.708418i	0.239887	−	0.0410375i
$299$	−6.13262			−0.354659
$300$		0			0
$301$	−9.13480	+	18.6863i	−0.526521	+	1.07706i
$302$	3.77234	+	22.0514i	0.217074	+	1.26891i
$303$		0			0
$304$	8.44293	−	6.79572i	0.484235	−	0.389761i
$305$	−1.18105			−0.0676265
$306$		0			0
$307$	−7.80451			−0.445427			−0.222713	−	0.974884i	$-0.571491\pi$
$307$	−7.80451			−0.445427			−0.222713	+	0.974884i	$0.571491\pi$
$308$	−2.97588	+	25.5776i	−0.169566	+	1.45742i
$309$		0			0
$310$	1.30527	+	7.63001i	0.0741344	+	0.433356i
$311$	34.9575			1.98226			0.991130	−	0.132897i	$-0.0424280\pi$
$311$	34.9575			1.98226			0.991130	+	0.132897i	$0.0424280\pi$
$312$		0			0
$313$			17.5160i			0.990065i	0.868875	+	0.495032i	$0.164844\pi$
$313$			17.5160i			0.990065i	−0.868875	+	0.495032i	$0.835156\pi$
$314$	−2.05001	−	11.9834i	−0.115688	−	0.676262i
$315$		0			0
$316$	0.675033	+	1.91523i	0.0379736	+	0.107740i
$317$	9.86500			0.554074			0.277037	−	0.960859i	$-0.410648\pi$
$317$	9.86500			0.554074			0.277037	+	0.960859i	$0.410648\pi$
$318$		0			0
$319$			40.4844i			2.26669i
$320$	−6.80252	−	4.21020i	−0.380272	−	0.235357i
$321$		0			0
$322$	1.77575	−	6.05533i	0.0989588	−	0.337450i
$323$		−	12.1325i		−	0.675068i
$324$		0			0
$325$		−	3.63628i		−	0.201705i
$326$	0.323757	+	1.89254i	0.0179313	+	0.104818i
$327$		0			0
$328$	−15.9085	−	28.5550i	−0.878400	−	1.57669i
$329$	−11.2925	−	5.52033i	−0.622575	−	0.304345i
$330$		0			0
$331$		−	19.7243i		−	1.08414i	−0.840332	−	0.542072i	$-0.817640\pi$
$331$		−	19.7243i		−	1.08414i	0.840332	−	0.542072i	$-0.182360\pi$
$332$	15.5127	−	5.46753i	0.851368	−	0.300070i
$333$		0			0
$334$	3.53874	−	0.605374i	0.193631	−	0.0331246i
$335$	13.1428			0.718068
$336$		0			0
$337$	−13.8674			−0.755405			−0.377702	−	0.925927i	$-0.623286\pi$
$337$	−13.8674			−0.755405			−0.377702	+	0.925927i	$0.623286\pi$
$338$	−0.310235	+	0.0530720i	−0.0168745	+	0.00288674i
$339$		0			0
$340$	−8.44614	+	2.97689i	−0.458056	+	0.161445i
$341$			26.6364i			1.44244i
$342$		0			0
$343$	−3.80157	−	18.1259i	−0.205265	−	0.978706i
$344$	−10.8218	−	19.4246i	−0.583472	−	1.04731i
$345$		0			0
$346$	1.66907	+	9.75659i	0.0897295	+	0.524517i
$347$		−	11.8032i		−	0.633631i	−0.948487	−	0.316815i	$-0.897386\pi$
$347$		−	11.8032i		−	0.633631i	0.948487	−	0.316815i	$-0.102614\pi$
$348$		0			0
$349$		−	25.5589i		−	1.36814i	−0.729417	−	0.684069i	$-0.760209\pi$
$349$		−	25.5589i		−	1.36814i	0.729417	−	0.684069i	$-0.239791\pi$
$350$	3.59045	+	1.05292i	0.191918	+	0.0562808i
$351$		0			0
$352$	−20.6295	−	18.2269i	−1.09956	−	0.971496i
$353$			3.70650i			0.197277i	0.995123	+	0.0986386i	$0.0314488\pi$
$353$			3.70650i			0.197277i	−0.995123	+	0.0986386i	$0.968551\pi$
$354$		0			0
$355$	14.8383			0.787536
$356$	6.58924	+	18.6952i	0.349229	+	0.990845i
$357$		0			0
$358$	2.14314	+	12.5278i	0.113268	+	0.662115i
$359$			15.8922i			0.838758i	0.907811	+	0.419379i	$0.137752\pi$
$359$			15.8922i			0.838758i	−0.907811	+	0.419379i	$0.862248\pi$
$360$		0			0
$361$	−11.6585			−0.613603
$362$	−1.72415	−	10.0786i	−0.0906193	−	0.529719i
$363$		0			0
$364$	2.22368	−	19.1125i	0.116552	−	1.00177i
$365$	1.40398			0.0734874
$366$		0			0
$367$	28.7376			1.50009			0.750046	−	0.661385i	$-0.230031\pi$
$367$	28.7376			1.50009			0.750046	+	0.661385i	$0.230031\pi$
$368$	4.22990	+	5.25518i	0.220499	+	0.273945i
$369$		0			0
$370$	−1.68603	−	9.85577i	−0.0876526	−	0.512377i
$371$	−24.1119	−	11.7871i	−1.25183	−	0.611956i
$372$		0			0
$373$	9.60992			0.497583			0.248791	−	0.968557i	$-0.419967\pi$
$373$	9.60992			0.497583			0.248791	+	0.968557i	$0.419967\pi$
$374$	−30.3744	+	5.19616i	−1.57062	+	0.268687i
$375$		0			0
$376$	11.7387	−	6.53981i	0.605375	−	0.337265i
$377$		−	30.2513i		−	1.55802i
$378$		0			0
$379$		−	8.12824i		−	0.417520i	−0.977967	−	0.208760i	$-0.933057\pi$
$379$		−	8.12824i		−	0.417520i	0.977967	−	0.208760i	$-0.0669427\pi$
$380$	−1.80137	−	5.11090i	−0.0924081	−	0.262184i
$381$		0			0
$382$	1.33997	+	7.83288i	0.0685591	+	0.400765i
$383$	−6.56611			−0.335513			−0.167756	−	0.985828i	$-0.553652\pi$
$383$	−6.56611			−0.335513			−0.167756	+	0.985828i	$0.553652\pi$
$384$		0			0
$385$	11.5670	+	5.65450i	0.589507	+	0.288180i
$386$	7.69102	−	1.31571i	0.391462	−	0.0669677i
$387$		0			0
$388$	−8.66821	−	24.5937i	−0.440062	−	1.24856i
$389$	16.8701			0.855349			0.427675	−	0.903933i	$-0.359333\pi$
$389$	16.8701			0.855349			0.427675	+	0.903933i	$0.359333\pi$
$390$		0			0
$391$	7.55168			0.381905
$392$	18.2277	+	7.72983i	0.920639	+	0.390415i
$393$		0			0
$394$	−9.56412	+	1.63614i	−0.481833	+	0.0824275i
$395$	1.01535			0.0510880
$396$		0			0
$397$			7.42334i			0.372567i	0.982496	+	0.186283i	$0.0596442\pi$
$397$			7.42334i			0.372567i	−0.982496	+	0.186283i	$0.940356\pi$
$398$	1.86002	−	0.318195i	0.0932344	−	0.0159497i
$399$		0			0
$400$	−3.11601	+	2.50808i	−0.155801	+	0.125404i
$401$	11.4462			0.571596			0.285798	−	0.958290i	$-0.407741\pi$
$401$	11.4462			0.571596			0.285798	+	0.958290i	$0.407741\pi$
$402$		0			0
$403$		−	19.9036i		−	0.991469i
$404$	6.98738	+	19.8248i	0.347635	+	0.986323i
$405$		0			0
$406$	29.8701	+	8.75952i	1.48243	+	0.434728i
$407$		−	34.4065i		−	1.70547i
$408$		0			0
$409$			36.0088i			1.78052i	0.455453	+	0.890260i	$0.349477\pi$
$409$			36.0088i			1.78052i	−0.455453	+	0.890260i	$0.650523\pi$
$410$	−16.1097	+	2.75589i	−0.795601	+	0.136104i
$411$		0			0
$412$	33.4870	−	11.8027i	1.64979	−	0.581477i
$413$	7.07022	+	3.45627i	0.347903	+	0.170072i
$414$		0			0
$415$		−	8.22400i		−	0.403700i
$416$	15.4151	+	13.6198i	0.755786	+	0.667763i
$417$		0			0
$418$	−3.14428	−	18.3800i	−0.153792	−	0.898997i
$419$	−39.5569			−1.93248			−0.966240	−	0.257644i	$-0.917054\pi$
$419$	−39.5569			−1.93248			−0.966240	+	0.257644i	$0.917054\pi$
$420$		0			0
$421$	−16.9601			−0.826584			−0.413292	−	0.910599i	$-0.635621\pi$
$421$	−16.9601			−0.826584			−0.413292	+	0.910599i	$0.635621\pi$
$422$	5.29848	+	30.9725i	0.257926	+	1.50772i
$423$		0			0
$424$	25.0646	−	13.9639i	1.21724	−	0.678148i
$425$			4.47770i			0.217200i
$426$		0			0
$427$	−1.37233	+	2.80727i	−0.0664119	+	0.135854i
$428$	2.21418	+	6.28214i	0.107026	+	0.303659i
$429$		0			0
$430$	−10.9587	+	1.87471i	−0.528474	+	0.0904063i
$431$		−	19.0357i		−	0.916918i	−0.888716	−	0.458459i	$-0.848402\pi$
$431$		−	19.0357i		−	0.916918i	0.888716	−	0.458459i	$-0.151598\pi$
$432$		0			0
$433$		−	28.8960i		−	1.38865i	−0.719660	−	0.694326i	$-0.755702\pi$
$433$		−	28.8960i		−	1.38865i	0.719660	−	0.694326i	$-0.244298\pi$
$434$	19.6528	+	5.76326i	0.943363	+	0.276645i
$435$		0			0
$436$	−0.938224	+	0.330683i	−0.0449328	+	0.0158368i
$437$			4.56964i			0.218596i
$438$		0			0
$439$	−22.6953			−1.08319			−0.541593	−	0.840641i	$-0.682179\pi$
$439$	−22.6953			−1.08319			−0.541593	+	0.840641i	$0.682179\pi$
$440$	−12.0240	+	6.69876i	−0.573220	+	0.319351i
$441$		0			0
$442$	22.6968	−	3.88275i	1.07958	−	0.184684i
$443$		−	28.4930i		−	1.35374i	−0.736102	−	0.676871i	$-0.763336\pi$
$443$		−	28.4930i		−	1.35374i	0.736102	−	0.676871i	$-0.236664\pi$
$444$		0			0
$445$	9.91123			0.469837
$446$	39.6624	−	6.78508i	1.87807	−	0.321283i
$447$		0			0
$448$	−17.9117	+	11.2771i	−0.846247	+	0.532791i
$449$	−17.2001			−0.811722			−0.405861	−	0.913935i	$-0.633028\pi$
$449$	−17.2001			−0.811722			−0.405861	+	0.913935i	$0.633028\pi$
$450$		0			0
$451$	−56.2389			−2.64819
$452$	10.3674	−	3.65406i	0.487642	−	0.171872i
$453$		0			0
$454$	−28.7105	+	4.91153i	−1.34745	+	0.230509i
$455$	−8.64322	−	4.22523i	−0.405201	−	0.198082i
$456$		0			0
$457$	25.6609			1.20037			0.600183	−	0.799862i	$-0.295094\pi$
$457$	25.6609			1.20037			0.600183	+	0.799862i	$0.295094\pi$
$458$	−2.54748	−	14.8914i	−0.119036	−	0.695828i
$459$		0			0
$460$	3.18121	−	1.12123i	0.148325	−	0.0522778i
$461$		−	36.4599i		−	1.69811i	−0.528306	−	0.849054i	$-0.677173\pi$
$461$		−	36.4599i		−	1.69811i	0.528306	−	0.849054i	$-0.322827\pi$
$462$		0			0
$463$			26.2427i			1.21960i	0.792555	+	0.609801i	$0.208751\pi$
$463$			26.2427i			1.21960i	−0.792555	+	0.609801i	$0.791249\pi$
$464$	−25.9230	+	20.8655i	−1.20345	+	0.968655i
$465$		0			0
$466$	−34.3016	+	5.86800i	−1.58899	+	0.271830i
$467$	8.40283			0.388837			0.194418	−	0.980919i	$-0.437718\pi$
$467$	8.40283			0.388837			0.194418	+	0.980919i	$0.437718\pi$
$468$		0			0
$469$	15.2715	−	31.2397i	0.705171	−	1.44251i
$470$	−1.13292	−	6.62252i	−0.0522576	−	0.305474i
$471$		0			0
$472$	−7.34956	+	4.09457i	−0.338291	+	0.188468i
$473$	−38.2567			−1.75904
$474$		0			0
$475$	−2.70953			−0.124322
$476$	−2.73823	+	23.5350i	−0.125506	+	1.07873i
$477$		0			0
$478$	−2.19620	−	12.8380i	−0.100452	−	0.587196i
$479$	−17.6650			−0.807136			−0.403568	−	0.914950i	$-0.632230\pi$
$479$	−17.6650			−0.807136			−0.403568	+	0.914950i	$0.632230\pi$
$480$		0			0
$481$			25.7097i			1.17226i
$482$	2.74616	+	16.0528i	0.125084	+	0.731185i
$483$		0			0
$484$	−23.9200	+	8.43073i	−1.08727	+	0.383215i
$485$	−13.0383			−0.592039
$486$		0			0
$487$		−	1.49550i		−	0.0677675i	−0.999426	−	0.0338837i	$-0.989212\pi$
$487$		−	1.49550i		−	0.0677675i	0.999426	−	0.0338837i	$-0.0107876\pi$
$488$	−1.62577	−	2.91819i	−0.0735953	−	0.132100i
$489$		0			0
$490$	6.67470	−	7.31084i	0.301532	−	0.330270i
$491$			3.45902i			0.156103i	0.996949	+	0.0780517i	$0.0248699\pi$
$491$			3.45902i			0.156103i	−0.996949	+	0.0780517i	$0.975130\pi$
$492$		0			0
$493$			37.2513i			1.67771i
$494$	2.34952	+	13.7342i	0.105710	+	0.617930i
$495$		0			0
$496$	−17.0558	+	13.7283i	−0.765830	+	0.616417i
$497$	17.2416	−	35.2698i	0.773392	−	1.58207i
$498$		0			0
$499$		−	16.3100i		−	0.730135i	−0.930981	−	0.365067i	$-0.881046\pi$
$499$		−	16.3100i		−	0.730135i	0.930981	−	0.365067i	$-0.118954\pi$
$500$	0.664826	+	1.88627i	0.0297319	+	0.0843565i
$501$		0			0
$502$	−1.88731	+	0.322862i	−0.0842346	+	0.0144101i
$503$	27.5175			1.22694			0.613472	−	0.789716i	$-0.289772\pi$
$503$	27.5175			1.22694			0.613472	+	0.789716i	$0.289772\pi$
$504$		0			0
$505$	10.5101			0.467693
$506$	11.4404	−	1.95711i	0.508587	−	0.0870043i
$507$		0			0
$508$	−1.56982	−	4.45394i	−0.0696494	−	0.197612i
$509$		−	7.28185i		−	0.322762i	−0.986892	−	0.161381i	$-0.948405\pi$
$509$		−	7.28185i		−	0.322762i	0.986892	−	0.161381i	$-0.0515949\pi$
$510$		0			0
$511$	1.63137	−	3.33716i	0.0721675	−	0.147627i
$512$	1.03873	−	22.6036i	0.0459058	−	0.998946i
$513$		0			0
$514$	4.55127	+	26.6046i	0.200748	+	1.17348i
$515$		−	17.7530i		−	0.782293i
$516$		0			0
$517$		−	23.1192i		−	1.01678i
$518$	−25.3857	−	7.44446i	−1.11538	−	0.327091i
$519$		0			0
$520$	8.98471	−	5.00554i	0.394006	−	0.219508i
$521$		−	5.22603i		−	0.228957i	−0.993426	−	0.114478i	$-0.963480\pi$
$521$		−	5.22603i		−	0.228957i	0.993426	−	0.114478i	$-0.0365196\pi$
$522$		0			0
$523$	18.0840			0.790756			0.395378	−	0.918518i	$-0.370614\pi$
$523$	18.0840			0.790756			0.395378	+	0.918518i	$0.370614\pi$
$524$	−3.65394	+	1.28785i	−0.159623	+	0.0562602i
$525$		0			0
$526$	−5.53190	−	32.3369i	−0.241202	−	1.40996i
$527$			24.5092i			1.06764i
$528$		0			0
$529$	20.1557			0.876334
$530$	−2.41903	−	14.1405i	−0.105076	−	0.614225i
$531$		0			0
$532$	−14.2414	−	1.65695i	−0.617444	−	0.0718377i
$533$	42.0236			1.82024
$534$		0			0
$535$	3.33046			0.143988
$536$	18.0918	+	32.4739i	0.781446	+	1.40266i
$537$		0			0
$538$	−0.661784	−	3.86848i	−0.0285315	−	0.166782i
$539$	26.8808	−	20.9236i	1.15784	−	0.901244i
$540$		0			0
$541$	24.4454			1.05099			0.525494	−	0.850797i	$-0.323880\pi$
$541$	24.4454			1.05099			0.525494	+	0.850797i	$0.323880\pi$
$542$	−23.1542	+	3.96101i	−0.994559	+	0.170140i
$543$		0			0
$544$	−18.9820	−	16.7713i	−0.813848	−	0.719063i
$545$			0.497397i			0.0213062i
$546$		0			0
$547$		−	19.9093i		−	0.851258i	−0.904898	−	0.425629i	$-0.860053\pi$
$547$		−	19.9093i		−	0.851258i	0.904898	−	0.425629i	$-0.139947\pi$
$548$	−28.8298	+	10.1612i	−1.23155	+	0.434067i
$549$		0			0
$550$	1.16045	+	6.78348i	0.0494819	+	0.289248i
$551$	−22.5414			−0.960295
$552$		0			0
$553$	1.17980	−	2.41343i	0.0501704	−	0.102630i
$554$	−4.29783	+	0.735233i	−0.182597	+	0.0312370i
$555$		0			0
$556$	3.47142	−	1.22352i	0.147221	−	0.0518888i
$557$	−19.7547			−0.837034			−0.418517	−	0.908209i	$-0.637450\pi$
$557$	−19.7547			−0.837034			−0.418517	+	0.908209i	$0.637450\pi$
$558$		0			0
$559$	28.5867			1.20909
$560$	2.34086	+	10.3209i	0.0989193	+	0.436136i
$561$		0			0
$562$	18.0071	−	3.08048i	0.759582	−	0.129942i
$563$	−8.92016			−0.375940			−0.187970	−	0.982175i	$-0.560191\pi$
$563$	−8.92016			−0.375940			−0.187970	+	0.982175i	$0.560191\pi$
$564$		0			0
$565$		−	5.49626i		−	0.231229i
$566$	23.9308	−	4.09385i	1.00589	−	0.172078i
$567$		0			0
$568$	20.4258	+	36.6633i	0.857046	+	1.53836i
$569$	−8.00467			−0.335573			−0.167787	−	0.985823i	$-0.553662\pi$
$569$	−8.00467			−0.335573			−0.167787	+	0.985823i	$0.553662\pi$
$570$		0			0
$571$		−	32.6423i		−	1.36604i	−0.730401	−	0.683019i	$-0.760667\pi$
$571$		−	32.6423i		−	1.36604i	0.730401	−	0.683019i	$-0.239333\pi$
$572$	33.3781	−	11.7643i	1.39561	−	0.491891i
$573$		0			0
$574$	−12.1683	+	41.4940i	−0.507895	+	1.73193i
$575$		−	1.68651i		−	0.0703323i
$576$		0			0
$577$			34.5773i			1.43947i	0.694247	+	0.719737i	$0.255737\pi$
$577$			34.5773i			1.43947i	−0.694247	+	0.719737i	$0.744263\pi$
$578$	−4.25133	+	0.727277i	−0.176832	+	0.0302507i
$579$		0			0
$580$	5.53088	+	15.6924i	0.229657	+	0.651592i
$581$	−19.5479	−	9.55600i	−0.810986	−	0.396450i
$582$		0			0
$583$		−	49.3646i		−	2.04447i
$584$	1.93265	+	3.46901i	0.0799736	+	0.143549i
$585$		0			0
$586$	0.475309	+	2.77844i	0.0196348	+	0.114776i
$587$	38.2214			1.57757			0.788783	−	0.614672i	$-0.210712\pi$
$587$	38.2214			1.57757			0.788783	+	0.614672i	$0.210712\pi$
$588$		0			0
$589$	−14.8309			−0.611097
$590$	0.709319	+	4.14635i	0.0292022	+	0.170703i
$591$		0			0
$592$	22.0312	−	17.7329i	0.905477	−	0.728819i
$593$			28.7500i			1.18062i	0.807176	+	0.590311i	$0.200995\pi$
$593$			28.7500i			1.18062i	−0.807176	+	0.590311i	$0.799005\pi$
$594$		0			0
$595$	10.6432	+	5.20293i	0.436330	+	0.213299i
$596$	5.60359	−	1.97502i	0.229532	−	0.0808998i
$597$		0			0
$598$	−8.54865	+	1.46242i	−0.349580	+	0.0598029i
$599$			13.1500i			0.537296i	0.963238	+	0.268648i	$0.0865769\pi$
$599$			13.1500i			0.537296i	−0.963238	+	0.268648i	$0.913423\pi$
$600$		0			0
$601$		−	32.8895i		−	1.34159i	−0.741643	−	0.670794i	$-0.765953\pi$
$601$		−	32.8895i		−	1.34159i	0.741643	−	0.670794i	$-0.234047\pi$
$602$	−8.27752	+	28.2264i	−0.337366	+	1.15042i
$603$		0			0
$604$	10.5170	+	29.8392i	0.427931	+	1.21414i
$605$			12.6811i			0.515560i
$606$		0			0
$607$	−26.5553			−1.07785			−0.538923	−	0.842355i	$-0.681169\pi$
$607$	−26.5553			−1.07785			−0.538923	+	0.842355i	$0.681169\pi$
$608$	10.1486	−	11.4863i	0.411579	−	0.465832i
$609$		0			0
$610$	−1.64634	+	0.281640i	−0.0666582	+	0.0114033i
$611$			17.2755i			0.698890i
$612$		0			0
$613$	−37.0669			−1.49712			−0.748558	−	0.663069i	$-0.769254\pi$
$613$	−37.0669			−1.49712			−0.748558	+	0.663069i	$0.769254\pi$
$614$	−10.8792	+	1.86111i	−0.439049	+	0.0751083i
$615$		0			0
$616$	1.95113	+	36.3639i	0.0786134	+	1.46514i
$617$	3.72176			0.149832			0.0749162	−	0.997190i	$-0.476131\pi$
$617$	3.72176			0.149832			0.0749162	+	0.997190i	$0.476131\pi$
$618$		0			0
$619$	−45.7106			−1.83726			−0.918632	−	0.395113i	$-0.870705\pi$
$619$	−45.7106			−1.83726			−0.918632	+	0.395113i	$0.870705\pi$
$620$	3.63900	+	10.3247i	0.146146	+	0.414650i
$621$		0			0
$622$	48.7295	−	8.33619i	1.95388	−	0.334251i
$623$	11.5165	−	23.5584i	0.461399	−	0.943847i
$624$		0			0
$625$	1.00000			0.0400000
$626$	4.17698	+	24.4167i	0.166946	+	0.975888i
$627$		0			0
$628$	−5.71526	−	16.2155i	−0.228064	−	0.647071i
$629$		−	31.6588i		−	1.26232i
$630$		0			0
$631$			11.1088i			0.442235i	0.975247	+	0.221117i	$0.0709704\pi$
$631$			11.1088i			0.442235i	−0.975247	+	0.221117i	$0.929030\pi$
$632$	1.39769	+	2.50879i	0.0555971	+	0.0997941i
$633$		0			0
$634$	13.7515	−	2.35247i	0.546140	−	0.0934285i
$635$	−2.36124			−0.0937031
$636$		0			0
$637$	−20.0862	+	15.6348i	−0.795846	+	0.619475i
$638$	9.65415	+	56.4337i	0.382212	+	2.23423i
$639$		0			0
$640$	−10.4864	−	4.24669i	−0.414513	−	0.167865i
$641$	9.74294			0.384823			0.192412	−	0.981314i	$-0.438369\pi$
$641$	9.74294			0.384823			0.192412	+	0.981314i	$0.438369\pi$
$642$		0			0
$643$	9.82459			0.387444			0.193722	−	0.981056i	$-0.437944\pi$
$643$	9.82459			0.387444			0.193722	+	0.981056i	$0.437944\pi$
$644$	1.03134	−	8.86437i	0.0406406	−	0.349305i
$645$		0			0
$646$	−2.89318	−	16.9122i	−0.113831	−	0.665402i
$647$	−43.7691			−1.72074			−0.860370	−	0.509671i	$-0.829767\pi$
$647$	−43.7691			−1.72074			−0.860370	+	0.509671i	$0.829767\pi$
$648$		0			0
$649$			14.4749i			0.568190i
$650$	−0.867130	−	5.06885i	−0.0340117	−	0.198816i
$651$		0			0
$652$	0.902612	+	2.56092i	0.0353490	+	0.100293i
$653$	−6.78003			−0.265323			−0.132661	−	0.991161i	$-0.542352\pi$
$653$	−6.78003			−0.265323			−0.132661	+	0.991161i	$0.542352\pi$
$654$		0			0
$655$			1.93713i			0.0756899i
$656$	−28.9853	−	36.0110i	−1.13168	−	1.40599i
$657$		0			0
$658$	−17.0577	−	5.00225i	−0.664980	−	0.195008i
$659$		−	16.7430i		−	0.652214i	−0.945333	−	0.326107i	$-0.894263\pi$
$659$		−	16.7430i		−	0.652214i	0.945333	−	0.326107i	$-0.105737\pi$
$660$		0			0
$661$		−	33.0783i		−	1.28660i	−0.765616	−	0.643298i	$-0.777566\pi$
$661$		−	33.0783i		−	1.28660i	0.765616	−	0.643298i	$-0.222434\pi$
$662$	−4.70357	−	27.4949i	−0.182810	−	1.06862i
$663$		0			0
$664$	20.3203	−	11.3208i	0.788579	−	0.439332i
$665$	−3.14838	+	6.44039i	−0.122089	+	0.249747i
$666$		0			0
$667$		−	14.0306i		−	0.543265i
$668$	4.78851	−	1.68774i	0.185273	−	0.0653006i
$669$		0			0
$670$	18.3206	−	3.13411i	0.707786	−	0.121081i
$671$	−5.74735			−0.221874
$672$		0			0
$673$	51.0877			1.96929			0.984643	−	0.174578i	$-0.0558560\pi$
$673$	51.0877			1.96929			0.984643	+	0.174578i	$0.0558560\pi$
$674$	−19.3306	+	3.30690i	−0.744588	+	0.127377i
$675$		0			0
$676$	−0.419800	+	0.147961i	−0.0161461	+	0.00569080i
$677$			46.6750i			1.79387i	0.442165	+	0.896934i	$0.354211\pi$
$677$			46.6750i			1.79387i	−0.442165	+	0.896934i	$0.645789\pi$
$678$		0			0
$679$	−15.1501	+	30.9913i	−0.581406	+	1.18934i
$680$	−11.0637	+	6.16380i	−0.424275	+	0.236371i
$681$		0			0
$682$	6.35187	+	37.1301i	0.243226	+	1.42179i
$683$			9.64514i			0.369061i	0.982827	+	0.184530i	$0.0590764\pi$
$683$			9.64514i			0.369061i	−0.982827	+	0.184530i	$0.940924\pi$
$684$		0			0
$685$			15.2841i			0.583974i
$686$	−9.62166	−	24.3603i	−0.367357	−	0.930080i
$687$		0			0
$688$	−19.7173	−	24.4966i	−0.751715	−	0.933923i
$689$			36.8869i			1.40528i
$690$		0			0
$691$	7.87711			0.299659			0.149830	−	0.988712i	$-0.452127\pi$
$691$	7.87711			0.299659			0.149830	+	0.988712i	$0.452127\pi$
$692$	4.65323	+	13.2023i	0.176889	+	0.501877i
$693$		0			0
$694$	−2.81467	−	16.4533i	−0.106843	−	0.624558i
$695$		−	1.84036i		−	0.0698089i
$696$		0			0
$697$	−51.7477			−1.96008
$698$	−6.09494	−	35.6282i	−0.230697	−	1.34855i
$699$		0			0
$700$	5.25605	+	0.611525i	0.198660	+	0.0231135i
$701$	−41.7864			−1.57825			−0.789125	−	0.614233i	$-0.789465\pi$
$701$	−41.7864			−1.57825			−0.789125	+	0.614233i	$0.789465\pi$
$702$		0			0
$703$	19.1572			0.722529
$704$	−33.1033	−	20.4882i	−1.24763	−	0.772177i
$705$		0			0
$706$	0.883875	+	5.16673i	0.0332651	+	0.194452i
$707$	12.2124	−	24.9818i	0.459293	−	0.939539i
$708$		0			0
$709$	−29.4303			−1.10528			−0.552639	−	0.833421i	$-0.686379\pi$
$709$	−29.4303			−1.10528			−0.552639	+	0.833421i	$0.686379\pi$
$710$	20.6841	−	3.53844i	0.776260	−	0.132795i
$711$		0			0
$712$	13.6433	+	24.4892i	0.511306	+	0.917770i
$713$		−	9.23129i		−	0.345715i
$714$		0			0
$715$		−	17.6953i		−	0.661768i
$716$	5.97491	+	16.9522i	0.223293	+	0.633535i
$717$		0			0
$718$	3.78975	+	22.1531i	0.141432	+	0.826748i
$719$	−27.0792			−1.00988			−0.504942	−	0.863153i	$-0.668486\pi$
$719$	−27.0792			−1.00988			−0.504942	+	0.863153i	$0.668486\pi$
$720$		0			0
$721$	−42.1979	−	20.6284i	−1.57153	−	0.768242i
$722$	−16.2515	+	2.78015i	−0.604816	+	0.103466i
$723$		0			0
$724$	−4.80680	−	13.6380i	−0.178643	−	0.506853i
$725$	8.31929			0.308971
$726$		0			0
$727$	−40.2389			−1.49238			−0.746189	−	0.665734i	$-0.768118\pi$
$727$	−40.2389			−1.49238			−0.746189	+	0.665734i	$0.768118\pi$
$728$	−1.45795	−	27.1724i	−0.0540353	−	1.00707i
$729$		0			0
$730$	1.95709	−	0.334801i	0.0724352	−	0.0123915i
$731$	−35.2015			−1.30198
$732$		0			0
$733$			12.5147i			0.462242i	0.972925	+	0.231121i	$0.0742394\pi$
$733$			12.5147i			0.462242i	−0.972925	+	0.231121i	$0.925761\pi$
$734$	40.0592	−	6.85296i	1.47861	−	0.252947i
$735$		0			0
$736$	7.14951	+	6.31684i	0.263534	+	0.232842i
$737$	63.9572			2.35589
$738$		0			0
$739$		−	25.5637i		−	0.940377i	−0.882566	−	0.470188i	$-0.844186\pi$
$739$		−	25.5637i		−	0.940377i	0.882566	−	0.470188i	$-0.155814\pi$
$740$	−4.70053	−	13.3365i	−0.172795	−	0.490260i
$741$		0			0
$742$	−36.4220	−	10.6809i	−1.33709	−	0.392108i
$743$			18.2745i			0.670425i	0.942143	+	0.335212i	$0.108808\pi$
$743$			18.2745i			0.670425i	−0.942143	+	0.335212i	$0.891192\pi$
$744$		0			0
$745$		−	2.97073i		−	0.108839i
$746$	13.3959	−	2.29164i	0.490458	−	0.0839029i
$747$		0			0
$748$	−41.1017	+	14.4865i	−1.50283	+	0.529680i
$749$	3.86988	−	7.91630i	0.141402	−	0.289255i
$750$		0			0
$751$			45.5201i			1.66105i	0.556979	+	0.830527i	$0.311960\pi$
$751$			45.5201i			1.66105i	−0.556979	+	0.830527i	$0.688040\pi$
$752$	14.8037	−	11.9155i	0.539836	−	0.434515i
$753$		0			0
$754$	−7.21391	−	42.1692i	−0.262715	−	1.53571i
$755$	15.8192			0.575719
$756$		0			0
$757$	−0.384669			−0.0139810			−0.00699051	−	0.999976i	$-0.502225\pi$
$757$	−0.384669			−0.0139810			−0.00699051	+	0.999976i	$0.502225\pi$
$758$	−1.93831	−	11.3305i	−0.0704026	−	0.411541i
$759$		0			0
$760$	−3.72981	−	6.69484i	−0.135295	−	0.242847i
$761$		−	21.5937i		−	0.782771i	−0.920227	−	0.391386i	$-0.871996\pi$
$761$		−	21.5937i		−	0.782771i	0.920227	−	0.391386i	$-0.128004\pi$
$762$		0			0
$763$	1.18228	+	0.577958i	0.0428015	+	0.0209235i
$764$	3.73575	+	10.5992i	0.135155	+	0.383466i
$765$		0			0
$766$	−9.15292	+	1.56580i	−0.330709	+	0.0565745i
$767$		−	10.8161i		−	0.390548i
$768$		0			0
$769$		−	6.41120i		−	0.231194i	−0.993296	−	0.115597i	$-0.963122\pi$
$769$		−	6.41120i		−	0.231194i	0.993296	−	0.115597i	$-0.0368781\pi$
$770$	17.4723	+	5.12383i	0.629659	+	0.184650i
$771$		0			0
$772$	10.4072	−	3.66809i	0.374565	−	0.132018i
$773$			20.1678i			0.725385i	0.931909	+	0.362693i	$0.118143\pi$
$773$			20.1678i			0.725385i	−0.931909	+	0.362693i	$0.881857\pi$
$774$		0			0
$775$	5.47361			0.196618
$776$	−17.9479	−	32.2157i	−0.644293	−	1.15648i
$777$		0			0
$778$	23.5163	−	4.02295i	0.843101	−	0.144230i
$779$		−	31.3134i		−	1.12192i
$780$		0			0
$781$	72.2081			2.58381
$782$	10.5268	−	1.80082i	0.376436	−	0.0643972i
$783$		0			0
$784$	27.2521	+	6.42841i	0.973288	+	0.229586i
$785$	−8.59663			−0.306827
$786$		0			0
$787$	22.3873			0.798019			0.399010	−	0.916947i	$-0.369354\pi$
$787$	22.3873			0.798019			0.399010	+	0.916947i	$0.369354\pi$
$788$	−12.9419	+	4.56144i	−0.461035	+	0.162494i
$789$		0			0
$790$	1.41537	−	0.242127i	0.0503564	−	0.00861450i
$791$	−13.0643	−	6.38646i	−0.464512	−	0.227076i
$792$		0			0
$793$	4.29462			0.152506
$794$	1.77021	+	10.3479i	0.0628226	+	0.367232i
$795$		0			0
$796$	2.51692	−	0.887104i	0.0892099	−	0.0314426i
$797$		−	2.24576i		−	0.0795490i	−0.999209	−	0.0397745i	$-0.987336\pi$
$797$		−	2.24576i		−	0.0795490i	0.999209	−	0.0397745i	$-0.0126640\pi$
$798$		0			0
$799$		−	21.2729i		−	0.752582i
$800$	−3.74552	+	4.23924i	−0.132424	+	0.149880i
$801$		0			0
$802$	15.9556	−	2.72953i	0.563411	−	0.0963830i
$803$	6.83220			0.241103
$804$		0			0
$805$	−4.00873	−	1.95966i	−0.141289	−	0.0690690i
$806$	−4.74634	−	27.7449i	−0.167183	−	0.977272i
$807$		0			0
$808$	14.4677	+	25.9689i	0.508972	+	0.913581i
$809$	47.6518			1.67535			0.837674	−	0.546170i	$-0.183915\pi$
$809$	47.6518			1.67535			0.837674	+	0.546170i	$0.183915\pi$
$810$		0			0
$811$	−40.5019			−1.42222			−0.711108	−	0.703083i	$-0.751806\pi$
$811$	−40.5019			−1.42222			−0.711108	+	0.703083i	$0.751806\pi$
$812$	43.7266	+	5.08746i	1.53450	+	0.178535i
$813$		0			0
$814$	−8.20478	−	47.9614i	−0.287577	−	1.68105i
$815$	1.35767			0.0475570
$816$		0			0
$817$		−	21.3010i		−	0.745228i
$818$	8.58687	+	50.1949i	0.300233	+	1.75502i
$819$		0			0
$820$	−21.7991	+	7.68323i	−0.761258	+	0.268310i
$821$	−11.8126			−0.412263			−0.206132	−	0.978524i	$-0.566087\pi$
$821$	−11.8126			−0.412263			−0.206132	+	0.978524i	$0.566087\pi$
$822$		0			0
$823$			14.2178i			0.495602i	0.968811	+	0.247801i	$0.0797079\pi$
$823$			14.2178i			0.495602i	−0.968811	+	0.247801i	$0.920292\pi$
$824$	43.8651	−	24.4380i	1.52811	−	0.851339i
$825$		0			0
$826$	10.6798	+	3.13191i	0.371599	+	0.108973i
$827$		−	11.5710i		−	0.402363i	−0.979554	−	0.201182i	$-0.935522\pi$
$827$		−	11.5710i		−	0.402363i	0.979554	−	0.201182i	$-0.0644781\pi$
$828$		0			0
$829$		−	22.7146i		−	0.788910i	−0.918915	−	0.394455i	$-0.870933\pi$
$829$		−	22.7146i		−	0.788910i	0.918915	−	0.394455i	$-0.129067\pi$
$830$	−1.96115	−	11.4640i	−0.0680724	−	0.397920i
$831$		0			0
$832$	24.7359	+	15.3095i	0.857562	+	0.530760i
$833$	24.7341	−	19.2527i	0.856986	−	0.667066i
$834$		0			0
$835$		−	2.53862i		−	0.0878524i
$836$	−8.76603	−	24.8713i	−0.303180	−	0.860191i
$837$		0			0
$838$	−55.1408	+	9.43298i	−1.90481	+	0.325857i
$839$	−41.1901			−1.42204			−0.711020	−	0.703172i	$-0.751766\pi$
$839$	−41.1901			−1.42204			−0.711020	+	0.703172i	$0.751766\pi$
$840$		0			0
$841$	40.2107			1.38657
$842$	−23.6417	+	4.04440i	−0.814748	+	0.139379i
$843$		0			0
$844$	14.7718	+	41.9110i	0.508466	+	1.44264i
$845$			0.222556i			0.00765615i
$846$		0			0
$847$	30.1422	+	14.7350i	1.03570	+	0.506301i
$848$	31.6092	−	25.4423i	1.08546	−	0.873691i
$849$		0			0
$850$	1.06778	+	6.24175i	0.0366246	+	0.214090i
$851$			11.9242i			0.408755i
$852$		0			0
$853$		−	13.0933i		−	0.448305i	−0.974554	−	0.224152i	$-0.928039\pi$
$853$		−	13.0933i		−	0.448305i	0.974554	−	0.224152i	$-0.0719613\pi$
$854$	−1.24354	+	4.24049i	−0.0425532	+	0.145107i
$855$		0			0
$856$	4.58456	+	8.22907i	0.156697	+	0.281264i
$857$			2.06062i			0.0703895i	0.999380	+	0.0351948i	$0.0112052\pi$
$857$			2.06062i			0.0703895i	−0.999380	+	0.0351948i	$0.988795\pi$
$858$		0			0
$859$	11.2503			0.383856			0.191928	−	0.981409i	$-0.438526\pi$
$859$	11.2503			0.383856			0.191928	+	0.981409i	$0.438526\pi$
$860$	−14.8289	+	5.22654i	−0.505662	+	0.178224i
$861$		0			0
$862$	−4.53937	−	26.5351i	−0.154612	−	0.903789i
$863$			7.30131i			0.248540i	0.992248	+	0.124270i	$0.0396588\pi$
$863$			7.30131i			0.248540i	−0.992248	+	0.124270i	$0.960341\pi$
$864$		0			0
$865$	6.99917			0.237979
$866$	−6.89072	−	40.2800i	−0.234156	−	1.36877i
$867$		0			0
$868$	28.7696	+	3.34725i	0.976503	+	0.113613i
$869$	4.94104			0.167613
$870$		0			0
$871$	−47.7910			−1.61934
$872$	−1.22899	+	0.684694i	−0.0416190	+	0.0231867i
$873$		0			0
$874$	1.08971	+	6.36992i	0.0368598	+	0.215466i
$875$	1.16196	−	2.37694i	0.0392816	−	0.0803552i
$876$		0			0
$877$	16.5634			0.559307			0.279654	−	0.960101i	$-0.409780\pi$
$877$	16.5634			0.559307			0.279654	+	0.960101i	$0.409780\pi$
$878$	−31.6364	+	5.41206i	−1.06768	+	0.182648i
$879$		0			0
$880$	−15.1635	+	12.2051i	−0.511162	+	0.411435i
$881$			47.9064i			1.61401i	0.590546	+	0.807004i	$0.298912\pi$
$881$			47.9064i			1.61401i	−0.590546	+	0.807004i	$0.701088\pi$
$882$		0			0
$883$		−	27.5910i		−	0.928511i	−0.885701	−	0.464255i	$-0.846322\pi$
$883$		−	27.5910i		−	0.928511i	0.885701	−	0.464255i	$-0.153678\pi$
$884$	30.7126	−	10.8248i	1.03298	−	0.364078i
$885$		0			0
$886$	−6.79461	−	39.7181i	−0.228269	−	1.33436i
$887$	37.5247			1.25996			0.629978	−	0.776613i	$-0.283064\pi$
$887$	37.5247			1.25996			0.629978	+	0.776613i	$0.283064\pi$
$888$		0			0
$889$	−2.74368	+	5.61253i	−0.0920201	+	0.188238i
$890$	13.8159	−	2.36349i	0.463110	−	0.0792244i
$891$		0			0
$892$	53.6700	−	18.9163i	1.79700	−	0.633364i
$893$	12.8726			0.430765
$894$		0			0
$895$	8.98718			0.300408
$896$	−22.2790	+	19.9911i	−0.744289	+	0.667857i
$897$		0			0
$898$	−23.9763	+	4.10164i	−0.800099	+	0.136873i
$899$	45.5366			1.51873
$900$		0			0
$901$		−	45.4223i		−	1.51324i
$902$	−78.3950	+	13.4111i	−2.61027	+	0.446540i
$903$		0			0
$904$	13.5804	−	7.56590i	0.451678	−	0.251638i
$905$	−7.23017			−0.240339
$906$		0			0
$907$		−	53.8990i		−	1.78969i	−0.446381	−	0.894843i	$-0.647288\pi$
$907$		−	53.8990i		−	1.78969i	0.446381	−	0.894843i	$-0.352712\pi$
$908$	−38.8502	+	13.6930i	−1.28929	+	0.454417i
$909$		0			0
$910$	−13.0559	−	3.82870i	−0.432799	−	0.126920i
$911$		−	10.7104i		−	0.354851i	−0.984134	−	0.177425i	$-0.943223\pi$
$911$		−	10.7104i		−	0.354851i	0.984134	−	0.177425i	$-0.0567768\pi$
$912$		0			0
$913$		−	40.0207i		−	1.32449i
$914$	35.7704	−	6.11926i	1.18318	−	0.202407i
$915$		0			0
$916$	−7.10218	−	20.1505i	−0.234663	−	0.665793i
$917$	4.60444	+	2.25088i	0.152052	+	0.0743304i
$918$		0			0
$919$		−	19.2285i		−	0.634289i	−0.948377	−	0.317145i	$-0.897276\pi$
$919$		−	19.2285i		−	0.634289i	0.948377	−	0.317145i	$-0.102724\pi$
$920$	4.16711	−	2.32157i	0.137385	−	0.0765399i
$921$		0			0
$922$	−8.69446	−	50.8238i	−0.286337	−	1.67379i
$923$	−53.9563			−1.77599
$924$		0			0
$925$	−7.07032			−0.232471
$926$	6.25799	+	36.5814i	0.205650	+	1.20214i
$927$		0			0
$928$	−31.1600	+	35.2674i	−1.02288	+	1.15771i
$929$			29.2671i			0.960221i	0.877208	+	0.480110i	$0.159403\pi$
$929$			29.2671i			0.960221i	−0.877208	+	0.480110i	$0.840597\pi$
$930$		0			0
$931$	11.6501	+	14.9670i	0.381817	+	0.490524i
$932$	−46.4159	+	16.3596i	−1.52040	+	0.535875i
$933$		0			0
$934$	11.7132	−	2.00379i	0.383269	−	0.0655661i
$935$			21.7899i			0.712607i
$936$		0			0
$937$			23.8800i			0.780127i	0.920788	+	0.390063i	$0.127547\pi$
$937$			23.8800i			0.780127i	−0.920788	+	0.390063i	$0.872453\pi$
$938$	13.8383	−	47.1887i	0.451836	−	1.54076i
$939$		0			0
$940$	−3.15849	−	8.96139i	−0.103019	−	0.292288i
$941$			56.0030i			1.82565i	0.408355	+	0.912823i	$0.366103\pi$
$941$			56.0030i			1.82565i	−0.408355	+	0.912823i	$0.633897\pi$
$942$		0			0
$943$	19.4906			0.634700
$944$	−9.26860	+	7.46030i	−0.301667	+	0.242812i
$945$		0			0
$946$	−53.3284	+	9.12292i	−1.73386	+	0.296612i
$947$		−	6.51797i		−	0.211806i	−0.994376	−	0.105903i	$-0.966227\pi$
$947$		−	6.51797i		−	0.211806i	0.994376	−	0.105903i	$-0.0337733\pi$
$948$		0			0
$949$	−5.10525			−0.165724
$950$	−3.77698	+	0.646131i	−0.122542	+	0.0209633i
$951$		0			0
$952$	1.79532	+	33.4599i	0.0581865	+	1.08444i
$953$	36.4257			1.17994			0.589972	−	0.807424i	$-0.299139\pi$
$953$	36.4257			1.17994			0.589972	+	0.807424i	$0.299139\pi$
$954$		0			0
$955$	5.61914			0.181831
$956$	−6.12285	−	17.3720i	−0.198027	−	0.561850i
$957$		0			0
$958$	−24.6244	+	4.21251i	−0.795579	+	0.136100i
$959$	36.3293	+	17.7595i	1.17313	+	0.573485i
$960$		0			0
$961$	−1.03957			−0.0335345
$962$	6.13089	+	35.8384i	0.197668	+	1.15548i
$963$		0			0
$964$	7.65609	+	21.7221i	0.246586	+	0.699623i
$965$		−	5.51737i		−	0.177611i
$966$		0			0
$967$			33.7820i			1.08636i	0.839618	+	0.543178i	$0.182779\pi$
$967$			33.7820i			1.08636i	−0.839618	+	0.543178i	$0.817221\pi$
$968$	−31.3331	+	17.4562i	−1.00708	+	0.561065i
$969$		0			0
$970$	−18.1749	+	3.10920i	−0.583562	+	0.0998302i
$971$	−29.8443			−0.957749			−0.478875	−	0.877883i	$-0.658955\pi$
$971$	−29.8443			−0.957749			−0.478875	+	0.877883i	$0.658955\pi$
$972$		0			0
$973$	−4.37443	−	2.13844i	−0.140238	−	0.0685551i
$974$	−0.356626	−	2.08467i	−0.0114270	−	0.0667971i
$975$		0			0
$976$	−2.96216	−	3.68015i	−0.0948164	−	0.117799i
$977$	14.9298			0.477646			0.238823	−	0.971063i	$-0.423238\pi$
$977$	14.9298			0.477646			0.238823	+	0.971063i	$0.423238\pi$
$978$		0			0
$979$	48.2313			1.54148
$980$	7.56090	−	11.7827i	0.241524	−	0.376386i
$981$		0			0
$982$	0.824859	+	4.82174i	0.0263223	+	0.153868i
$983$	4.50914			0.143819			0.0719096	−	0.997411i	$-0.477091\pi$
$983$	4.50914			0.143819			0.0719096	+	0.997411i	$0.477091\pi$
$984$		0			0
$985$			6.86110i			0.218613i
$986$	8.88318	+	51.9270i	0.282898	+	1.65369i
$987$		0			0
$988$	6.55028	+	18.5847i	0.208392	+	0.591257i
$989$	13.2585			0.421596
$990$		0			0
$991$			44.9341i			1.42738i	0.700463	+	0.713689i	$0.252977\pi$
$991$			44.9341i			1.42738i	−0.700463	+	0.713689i	$0.747023\pi$
$992$	−20.5015	+	23.2039i	−0.650923	+	0.736726i
$993$		0			0
$994$	15.6235	−	53.2763i	0.495548	−	1.68982i
$995$		−	1.33434i		−	0.0423014i
$996$		0			0
$997$			24.1118i			0.763628i	0.924239	+	0.381814i	$0.124700\pi$
$997$			24.1118i			0.763628i	−0.924239	+	0.381814i	$0.875300\pi$
$998$	−3.88938	−	22.7355i	−0.123116	−	0.719680i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.c.e.811.15		16
3.2	odd	2		420.2.c.b.391.2	yes	16
4.3	odd	2		1260.2.c.d.811.16		16
7.6	odd	2		1260.2.c.d.811.15		16
12.11	even	2		420.2.c.a.391.1	✓	16
21.20	even	2		420.2.c.a.391.2	yes	16
28.27	even	2	inner	1260.2.c.e.811.16		16
84.83	odd	2		420.2.c.b.391.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.c.a.391.1	✓	16	12.11	even	2
420.2.c.a.391.2	yes	16	21.20	even	2
420.2.c.b.391.1	yes	16	84.83	odd	2
420.2.c.b.391.2	yes	16	3.2	odd	2
1260.2.c.d.811.15		16	7.6	odd	2
1260.2.c.d.811.16		16	4.3	odd	2
1260.2.c.e.811.15		16	1.1	even	1	trivial
1260.2.c.e.811.16		16	28.27	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39396 - 0.238466i) q^{2} +(1.88627 - 0.664826i) q^{4} -1.00000i q^{5} +(-2.37694 - 1.16196i) q^{7} +(2.47085 - 1.37655i) q^{8} +O(q^{10})\)	\(q+(1.39396 - 0.238466i) q^{2} +(1.88627 - 0.664826i) q^{4} -1.00000i q^{5} +(-2.37694 - 1.16196i) q^{7} +(2.47085 - 1.37655i) q^{8} +(-0.238466 - 1.39396i) q^{10} -4.86632i q^{11} +3.63628i q^{13} +(-3.59045 - 1.05292i) q^{14} +(3.11601 - 2.50808i) q^{16} -4.47770i q^{17} +2.70953 q^{19} +(-0.664826 - 1.88627i) q^{20} +(-1.16045 - 6.78348i) q^{22} +1.68651i q^{23} -1.00000 q^{25} +(0.867130 + 5.06885i) q^{26} +(-5.25605 - 0.611525i) q^{28} -8.31929 q^{29} -5.47361 q^{31} +(3.74552 - 4.23924i) q^{32} +(-1.06778 - 6.24175i) q^{34} +(-1.16196 + 2.37694i) q^{35} +7.07032 q^{37} +(3.77698 - 0.646131i) q^{38} +(-1.37655 - 2.47085i) q^{40} -11.5568i q^{41} -7.86152i q^{43} +(-3.23526 - 9.17919i) q^{44} +(0.402175 + 2.35093i) q^{46} +4.75086 q^{47} +(4.29968 + 5.52384i) q^{49} +(-1.39396 + 0.238466i) q^{50} +(2.41750 + 6.85900i) q^{52} +10.1441 q^{53} -4.86632 q^{55} +(-7.47257 + 0.400946i) q^{56} +(-11.5968 + 1.98387i) q^{58} -2.97451 q^{59} -1.18105i q^{61} +(-7.63001 + 1.30527i) q^{62} +(4.21020 - 6.80252i) q^{64} +3.63628 q^{65} +13.1428i q^{67} +(-2.97689 - 8.44614i) q^{68} +(-1.05292 + 3.59045i) q^{70} +14.8383i q^{71} +1.40398i q^{73} +(9.85577 - 1.68603i) q^{74} +(5.11090 - 1.80137i) q^{76} +(-5.65450 + 11.5670i) q^{77} +1.01535i q^{79} +(-2.50808 - 3.11601i) q^{80} +(-2.75589 - 16.1097i) q^{82} +8.22400 q^{83} -4.47770 q^{85} +(-1.87471 - 10.9587i) q^{86} +(-6.69876 - 12.0240i) q^{88} +9.91123i q^{89} +(4.22523 - 8.64322i) q^{91} +(1.12123 + 3.18121i) q^{92} +(6.62252 - 1.13292i) q^{94} -2.70953i q^{95} -13.0383i q^{97} +(7.31084 + 6.67470i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8	\( 16 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 2 q^{8} - 10 q^{14} + 6 q^{16} + 24 q^{19} - 12 q^{22} - 16 q^{25} - 12 q^{26} - 22 q^{28} - 16 q^{29} - 8 q^{31} + 18 q^{32} - 24 q^{34} + 24 q^{37} + 28 q^{38} - 12 q^{40} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 16 q^{49} + 2 q^{50} + 20 q^{52} + 32 q^{53} + 2 q^{56} - 32 q^{58} + 8 q^{59} + 16 q^{62} - 2 q^{64} + 8 q^{65} + 4 q^{68} - 20 q^{70} + 4 q^{74} - 16 q^{76} + 8 q^{77} - 16 q^{80} + 4 q^{82} + 8 q^{83} - 64 q^{86} - 52 q^{88} - 16 q^{91} - 64 q^{92} - 16 q^{94} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 2 * q^8 - 10 * q^14 + 6 * q^16 + 24 * q^19 - 12 * q^22 - 16 * q^25 - 12 * q^26 - 22 * q^28 - 16 * q^29 - 8 * q^31 + 18 * q^32 - 24 * q^34 + 24 * q^37 + 28 * q^38 - 12 * q^40 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 16 * q^49 + 2 * q^50 + 20 * q^52 + 32 * q^53 + 2 * q^56 - 32 * q^58 + 8 * q^59 + 16 * q^62 - 2 * q^64 + 8 * q^65 + 4 * q^68 - 20 * q^70 + 4 * q^74 - 16 * q^76 + 8 * q^77 - 16 * q^80 + 4 * q^82 + 8 * q^83 - 64 * q^86 - 52 * q^88 - 16 * q^91 - 64 * q^92 - 16 * q^94 - 2 * q^98

Introduction

L-functions

Modular forms

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Database

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