LMFDB - Embedded newform 1408.2.i.b.351.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1408,2,Mod(351,1408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1408, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1408.351");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1408 = 2^{7} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1408.i (of order $4$, 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:	$11.2429366046$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 176)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			351.13
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} +3.48768i q^{7} +2.63045i q^{9} +O(q^{10})$	\(q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} +3.48768i q^{7} +2.63045i q^{9} +(1.67289 - 2.86382i) q^{11} +(0.438991 - 0.438991i) q^{13} +0.604994i q^{15} -3.89861i q^{17} +(-0.685216 - 0.685216i) q^{19} +(1.49919 + 1.49919i) q^{21} +3.54310 q^{23} +4.00955i q^{25} +(2.42027 + 2.42027i) q^{27} +(-3.67594 + 3.67594i) q^{29} +8.85547i q^{31} +(-0.511925 - 1.95012i) q^{33} +(-2.45436 - 2.45436i) q^{35} +(-4.70899 + 4.70899i) q^{37} -0.377404i q^{39} -6.55941 q^{41} +(-4.01324 + 4.01324i) q^{43} +(-1.85110 - 1.85110i) q^{45} -5.68856i q^{47} -5.16393 q^{49} +(-1.67583 - 1.67583i) q^{51} +(-6.67821 + 6.67821i) q^{53} +(0.838081 + 3.19257i) q^{55} -0.589085 q^{57} +(10.5776 + 10.5776i) q^{59} +(-3.64241 + 3.64241i) q^{61} -9.17418 q^{63} +0.617854i q^{65} +(3.52675 - 3.52675i) q^{67} +(1.52302 - 1.52302i) q^{69} +6.71309 q^{71} +8.28094 q^{73} +(1.72352 + 1.72352i) q^{75} +(9.98808 + 5.83450i) q^{77} +8.89181 q^{79} -5.81063 q^{81} +(1.57109 + 1.57109i) q^{83} +(2.74353 + 2.74353i) q^{85} +3.16023i q^{87} +8.43118i q^{89} +(1.53106 + 1.53106i) q^{91} +(3.80655 + 3.80655i) q^{93} +0.964401 q^{95} -11.5768 q^{97} +(7.53313 + 4.40045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5	$ 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times$.

$n$	$133$	$639$	$1025$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.429854	−	0.429854i	0.248176	−	0.248176i	−0.572046	−	0.820222i	$-0.693850\pi$
$3$	0.429854	−	0.429854i	0.248176	−	0.248176i	0.820222	+	0.572046i	$0.193850\pi$
$4$		0			0
$5$	−0.703721	+	0.703721i	−0.314714	+	0.314714i	−0.846732	−	0.532019i	$-0.821434\pi$
$5$	−0.703721	+	0.703721i	−0.314714	+	0.314714i	0.532019	+	0.846732i	$0.321434\pi$
$6$		0			0
$7$			3.48768i			1.31822i	0.752047	+	0.659110i	$0.229067\pi$
$7$			3.48768i			1.31822i	−0.752047	+	0.659110i	$0.770933\pi$
$8$		0			0
$9$			2.63045i			0.876817i
$10$		0			0
$11$	1.67289	−	2.86382i	0.504395	−	0.863473i
$11$	1.67289	−	2.86382i	0.504395	−	0.863473i
$12$		0			0
$13$	0.438991	−	0.438991i	0.121754	−	0.121754i	−0.643604	−	0.765358i	$-0.722562\pi$
$13$	0.438991	−	0.438991i	0.121754	−	0.121754i	0.765358	+	0.643604i	$0.222562\pi$
$14$		0			0
$15$			0.604994i			0.156209i
$16$		0			0
$17$		−	3.89861i		−	0.945552i	−0.881183	−	0.472776i	$-0.843252\pi$
$17$		−	3.89861i		−	0.945552i	0.881183	−	0.472776i	$-0.156748\pi$
$18$		0			0
$19$	−0.685216	−	0.685216i	−0.157199	−	0.157199i	0.624125	−	0.781324i	$-0.285456\pi$
$19$	−0.685216	−	0.685216i	−0.157199	−	0.157199i	−0.781324	+	0.624125i	$0.785456\pi$
$20$		0			0
$21$	1.49919	+	1.49919i	0.327151	+	0.327151i
$22$		0			0
$23$	3.54310			0.738788			0.369394	−	0.929273i	$-0.379565\pi$
$23$	3.54310			0.738788			0.369394	+	0.929273i	$0.379565\pi$
$24$		0			0
$25$			4.00955i			0.801911i
$26$		0			0
$27$	2.42027	+	2.42027i	0.465781	+	0.465781i
$28$		0			0
$29$	−3.67594	+	3.67594i	−0.682605	+	0.682605i	−0.960586	−	0.277982i	$-0.910335\pi$
$29$	−3.67594	+	3.67594i	−0.682605	+	0.682605i	0.277982	+	0.960586i	$0.410335\pi$
$30$		0			0
$31$			8.85547i			1.59049i	0.606289	+	0.795244i	$0.292657\pi$
$31$			8.85547i			1.59049i	−0.606289	+	0.795244i	$0.707343\pi$
$32$		0			0
$33$	−0.511925	−	1.95012i	−0.0891146	−	0.339472i
$34$		0			0
$35$	−2.45436	−	2.45436i	−0.414862	−	0.414862i
$36$		0			0
$37$	−4.70899	+	4.70899i	−0.774152	+	0.774152i	−0.978830	−	0.204677i	$-0.934386\pi$
$37$	−4.70899	+	4.70899i	−0.774152	+	0.774152i	0.204677	+	0.978830i	$0.434386\pi$
$38$		0			0
$39$		−	0.377404i		−	0.0604330i
$40$		0			0
$41$	−6.55941			−1.02441			−0.512204	−	0.858864i	$-0.671171\pi$
$41$	−6.55941			−1.02441			−0.512204	+	0.858864i	$0.671171\pi$
$42$		0			0
$43$	−4.01324	+	4.01324i	−0.612013	+	0.612013i	−0.943470	−	0.331457i	$-0.892460\pi$
$43$	−4.01324	+	4.01324i	−0.612013	+	0.612013i	0.331457	+	0.943470i	$0.392460\pi$
$44$		0			0
$45$	−1.85110	−	1.85110i	−0.275946	−	0.275946i
$46$		0			0
$47$		−	5.68856i		−	0.829761i	−0.909876	−	0.414881i	$-0.863823\pi$
$47$		−	5.68856i		−	0.829761i	0.909876	−	0.414881i	$-0.136177\pi$
$48$		0			0
$49$	−5.16393			−0.737704
$50$		0			0
$51$	−1.67583	−	1.67583i	−0.234663	−	0.234663i
$52$		0			0
$53$	−6.67821	+	6.67821i	−0.917322	+	0.917322i	−0.996834	−	0.0795118i	$-0.974664\pi$
$53$	−6.67821	+	6.67821i	−0.917322	+	0.917322i	0.0795118	+	0.996834i	$0.474664\pi$
$54$		0			0
$55$	0.838081	+	3.19257i	0.113007	+	0.430487i
$56$		0			0
$57$	−0.589085			−0.0780262
$58$		0			0
$59$	10.5776	+	10.5776i	1.37708	+	1.37708i	0.849510	+	0.527573i	$0.176898\pi$
$59$	10.5776	+	10.5776i	1.37708	+	1.37708i	0.527573	+	0.849510i	$0.323102\pi$
$60$		0			0
$61$	−3.64241	+	3.64241i	−0.466363	+	0.466363i	−0.900734	−	0.434371i	$-0.856971\pi$
$61$	−3.64241	+	3.64241i	−0.466363	+	0.466363i	0.434371	+	0.900734i	$0.356971\pi$
$62$		0			0
$63$	−9.17418			−1.15584
$64$		0			0
$65$			0.617854i			0.0766354i
$66$		0			0
$67$	3.52675	−	3.52675i	0.430862	−	0.430862i	−0.458060	−	0.888921i	$-0.651455\pi$
$67$	3.52675	−	3.52675i	0.430862	−	0.430862i	0.888921	+	0.458060i	$0.151455\pi$
$68$		0			0
$69$	1.52302	−	1.52302i	0.183350	−	0.183350i
$70$		0			0
$71$	6.71309			0.796697			0.398349	−	0.917234i	$-0.369583\pi$
$71$	6.71309			0.796697			0.398349	+	0.917234i	$0.369583\pi$
$72$		0			0
$73$	8.28094			0.969211			0.484605	−	0.874733i	$-0.338963\pi$
$73$	8.28094			0.969211			0.484605	+	0.874733i	$0.338963\pi$
$74$		0			0
$75$	1.72352	+	1.72352i	0.199015	+	0.199015i
$76$		0			0
$77$	9.98808	+	5.83450i	1.13825	+	0.664903i
$78$		0			0
$79$	8.89181			1.00041			0.500203	−	0.865908i	$-0.333259\pi$
$79$	8.89181			1.00041			0.500203	+	0.865908i	$0.333259\pi$
$80$		0			0
$81$	−5.81063			−0.645626
$82$		0			0
$83$	1.57109	+	1.57109i	0.172449	+	0.172449i	0.788055	−	0.615605i	$-0.211088\pi$
$83$	1.57109	+	1.57109i	0.172449	+	0.172449i	−0.615605	+	0.788055i	$0.711088\pi$
$84$		0			0
$85$	2.74353	+	2.74353i	0.297578	+	0.297578i
$86$		0			0
$87$			3.16023i			0.338812i
$88$		0			0
$89$			8.43118i			0.893703i	0.894608	+	0.446851i	$0.147455\pi$
$89$			8.43118i			0.893703i	−0.894608	+	0.446851i	$0.852545\pi$
$90$		0			0
$91$	1.53106	+	1.53106i	0.160499	+	0.160499i
$92$		0			0
$93$	3.80655	+	3.80655i	0.394721	+	0.394721i
$94$		0			0
$95$	0.964401			0.0989455
$96$		0			0
$97$	−11.5768			−1.17545			−0.587724	−	0.809062i	$-0.699976\pi$
$97$	−11.5768			−1.17545			−0.587724	+	0.809062i	$0.699976\pi$
$98$		0			0
$99$	7.53313	+	4.40045i	0.757108	+	0.442262i
$100$		0			0
$101$	−11.8302	−	11.8302i	−1.17715	−	1.17715i	−0.980467	−	0.196683i	$-0.936983\pi$
$101$	−11.8302	−	11.8302i	−1.17715	−	1.17715i	−0.196683	−	0.980467i	$-0.563017\pi$
$102$		0			0
$103$	−3.87104			−0.381425			−0.190713	−	0.981646i	$-0.561080\pi$
$103$	−3.87104			−0.381425			−0.190713	+	0.981646i	$0.561080\pi$
$104$		0			0
$105$	−2.11003			−0.205918
$106$		0			0
$107$	5.15332	−	5.15332i	0.498190	−	0.498190i	−0.412684	−	0.910874i	$-0.635409\pi$
$107$	5.15332	−	5.15332i	0.498190	−	0.498190i	0.910874	+	0.412684i	$0.135409\pi$
$108$		0			0
$109$	11.6593	−	11.6593i	1.11676	−	1.11676i	0.124545	−	0.992214i	$-0.460253\pi$
$109$	11.6593	−	11.6593i	1.11676	−	1.11676i	0.992214	−	0.124545i	$-0.0397472\pi$
$110$		0			0
$111$			4.04835i			0.384252i
$112$		0			0
$113$	13.2747			1.24878			0.624392	−	0.781111i	$-0.285347\pi$
$113$	13.2747			1.24878			0.624392	+	0.781111i	$0.285347\pi$
$114$		0			0
$115$	−2.49336	+	2.49336i	−0.232507	+	0.232507i
$116$		0			0
$117$	1.15474	+	1.15474i	0.106756	+	0.106756i
$118$		0			0
$119$	13.5971			1.24645
$120$		0			0
$121$	−5.40289	−	9.58169i	−0.491171	−	0.871063i
$122$		0			0
$123$	−2.81958	+	2.81958i	−0.254233	+	0.254233i
$124$		0			0
$125$	−6.34021	−	6.34021i	−0.567086	−	0.567086i
$126$		0			0
$127$	3.51958			0.312312			0.156156	−	0.987732i	$-0.450090\pi$
$127$	3.51958			0.312312			0.156156	+	0.987732i	$0.450090\pi$
$128$		0			0
$129$			3.45021i			0.303774i
$130$		0			0
$131$	5.50159	+	5.50159i	0.480676	+	0.480676i	0.905348	−	0.424672i	$-0.139610\pi$
$131$	5.50159	+	5.50159i	0.480676	+	0.480676i	−0.424672	+	0.905348i	$0.639610\pi$
$132$		0			0
$133$	2.38981	−	2.38981i	0.207223	−	0.207223i
$134$		0			0
$135$	−3.40639			−0.293175
$136$		0			0
$137$			0.493241i			0.0421404i	0.999778	+	0.0210702i	$0.00670735\pi$
$137$			0.493241i			0.0421404i	−0.999778	+	0.0210702i	$0.993293\pi$
$138$		0			0
$139$	−10.4765	+	10.4765i	−0.888605	+	0.888605i	−0.994389	−	0.105785i	$-0.966265\pi$
$139$	−10.4765	+	10.4765i	−0.888605	+	0.888605i	0.105785	+	0.994389i	$0.466265\pi$
$140$		0			0
$141$	−2.44525	−	2.44525i	−0.205927	−	0.205927i
$142$		0			0
$143$	−0.522806	−	1.99157i	−0.0437193	−	0.166544i
$144$		0			0
$145$		−	5.17367i		−	0.429650i
$146$		0			0
$147$	−2.21973	+	2.21973i	−0.183080	+	0.183080i
$148$		0			0
$149$	−3.86542	−	3.86542i	−0.316667	−	0.316667i	0.530818	−	0.847486i	$-0.321885\pi$
$149$	−3.86542	−	3.86542i	−0.316667	−	0.316667i	−0.847486	+	0.530818i	$0.821885\pi$
$150$		0			0
$151$		−	17.9891i		−	1.46393i	−0.681341	−	0.731966i	$-0.738603\pi$
$151$		−	17.9891i		−	1.46393i	0.681341	−	0.731966i	$-0.261397\pi$
$152$		0			0
$153$	10.2551			0.829076
$154$		0			0
$155$	−6.23178	−	6.23178i	−0.500548	−	0.500548i
$156$		0			0
$157$	−3.64970	−	3.64970i	−0.291278	−	0.291278i	0.546307	−	0.837585i	$-0.316033\pi$
$157$	−3.64970	−	3.64970i	−0.291278	−	0.291278i	−0.837585	+	0.546307i	$0.816033\pi$
$158$		0			0
$159$			5.74130i			0.455315i
$160$		0			0
$161$			12.3572i			0.973886i
$162$		0			0
$163$	−3.44307	+	3.44307i	−0.269682	+	0.269682i	−0.828972	−	0.559290i	$-0.811074\pi$
$163$	−3.44307	+	3.44307i	−0.269682	+	0.269682i	0.559290	+	0.828972i	$0.311074\pi$
$164$		0			0
$165$	1.73259	+	1.01209i	0.134882	+	0.0787909i
$166$		0			0
$167$		−	10.4302i		−	0.807110i	−0.914955	−	0.403555i	$-0.867774\pi$
$167$		−	10.4302i		−	0.807110i	0.914955	−	0.403555i	$-0.132226\pi$
$168$		0			0
$169$			12.6146i			0.970352i
$170$		0			0
$171$	1.80243	−	1.80243i	0.137835	−	0.137835i
$172$		0			0
$173$	−3.96494	+	3.96494i	−0.301449	+	0.301449i	−0.841581	−	0.540131i	$-0.818375\pi$
$173$	−3.96494	+	3.96494i	−0.301449	+	0.301449i	0.540131	+	0.841581i	$0.318375\pi$
$174$		0			0
$175$	−13.9840			−1.05709
$176$		0			0
$177$	9.09362			0.683518
$178$		0			0
$179$	6.01484	−	6.01484i	0.449570	−	0.449570i	−0.445642	−	0.895211i	$-0.647024\pi$
$179$	6.01484	−	6.01484i	0.449570	−	0.449570i	0.895211	+	0.445642i	$0.147024\pi$
$180$		0			0
$181$	1.56251	−	1.56251i	0.116140	−	0.116140i	−0.646648	−	0.762788i	$-0.723830\pi$
$181$	1.56251	−	1.56251i	0.116140	−	0.116140i	0.762788	+	0.646648i	$0.223830\pi$
$182$		0			0
$183$			3.13141i			0.231480i
$184$		0			0
$185$		−	6.62762i		−	0.487273i
$186$		0			0
$187$	−11.1649	−	6.52194i	−0.816459	−	0.476932i
$188$		0			0
$189$	−8.44113	+	8.44113i	−0.614002	+	0.614002i
$190$		0			0
$191$		−	12.3597i		−	0.894318i	−0.894455	−	0.447159i	$-0.852436\pi$
$191$		−	12.3597i		−	0.894318i	0.894455	−	0.447159i	$-0.147564\pi$
$192$		0			0
$193$			23.5392i			1.69439i	0.531281	+	0.847195i	$0.321711\pi$
$193$			23.5392i			1.69439i	−0.531281	+	0.847195i	$0.678289\pi$
$194$		0			0
$195$	0.265587	+	0.265587i	0.0190191	+	0.0190191i
$196$		0			0
$197$	7.01740	+	7.01740i	0.499969	+	0.499969i	0.911428	−	0.411459i	$-0.134981\pi$
$197$	7.01740	+	7.01740i	0.499969	+	0.499969i	−0.411459	+	0.911428i	$0.634981\pi$
$198$		0			0
$199$	−9.97331			−0.706989			−0.353495	−	0.935437i	$-0.615007\pi$
$199$	−9.97331			−0.706989			−0.353495	+	0.935437i	$0.615007\pi$
$200$		0			0
$201$		−	3.03198i		−	0.213859i
$202$		0			0
$203$	−12.8205	−	12.8205i	−0.899823	−	0.899823i
$204$		0			0
$205$	4.61599	−	4.61599i	0.322395	−	0.322395i
$206$		0			0
$207$			9.31997i			0.647782i
$208$		0			0
$209$	−3.10862	+	0.816042i	−0.215028	+	0.0564468i
$210$		0			0
$211$	−9.92341	−	9.92341i	−0.683156	−	0.683156i	0.277554	−	0.960710i	$-0.410476\pi$
$211$	−9.92341	−	9.92341i	−0.683156	−	0.683156i	−0.960710	+	0.277554i	$0.910476\pi$
$212$		0			0
$213$	2.88565	−	2.88565i	0.197721	−	0.197721i
$214$		0			0
$215$		−	5.64840i		−	0.385218i
$216$		0			0
$217$	−30.8851			−2.09661
$218$		0			0
$219$	3.55959	−	3.55959i	0.240535	−	0.240535i
$220$		0			0
$221$	−1.71146	−	1.71146i	−0.115125	−	0.115125i
$222$		0			0
$223$		−	5.60151i		−	0.375105i	−0.982255	−	0.187552i	$-0.939945\pi$
$223$		−	5.60151i		−	0.375105i	0.982255	−	0.187552i	$-0.0600555\pi$
$224$		0			0
$225$	−10.5469			−0.703129
$226$		0			0
$227$	8.38464	+	8.38464i	0.556508	+	0.556508i	0.928311	−	0.371803i	$-0.121260\pi$
$227$	8.38464	+	8.38464i	0.556508	+	0.556508i	−0.371803	+	0.928311i	$0.621260\pi$
$228$		0			0
$229$	10.5599	−	10.5599i	0.697820	−	0.697820i	−0.266120	−	0.963940i	$-0.585742\pi$
$229$	10.5599	−	10.5599i	0.697820	−	0.697820i	0.963940	+	0.266120i	$0.0857417\pi$
$230$		0			0
$231$	6.80140	−	1.78543i	0.447499	−	0.117473i
$232$		0			0
$233$	25.8883			1.69600			0.848000	−	0.529996i	$-0.177807\pi$
$233$	25.8883			1.69600			0.848000	+	0.529996i	$0.177807\pi$
$234$		0			0
$235$	4.00316	+	4.00316i	0.261137	+	0.261137i
$236$		0			0
$237$	3.82218	−	3.82218i	0.248277	−	0.248277i
$238$		0			0
$239$	−4.77090			−0.308604			−0.154302	−	0.988024i	$-0.549313\pi$
$239$	−4.77090			−0.308604			−0.154302	+	0.988024i	$0.549313\pi$
$240$		0			0
$241$		−	17.0966i		−	1.10129i	−0.834740	−	0.550645i	$-0.814382\pi$
$241$		−	17.0966i		−	1.10129i	0.834740	−	0.550645i	$-0.185618\pi$
$242$		0			0
$243$	−9.75853	+	9.75853i	−0.626010	+	0.626010i
$244$		0			0
$245$	3.63396	−	3.63396i	0.232165	−	0.232165i
$246$		0			0
$247$	−0.601607			−0.0382793
$248$		0			0
$249$	1.35068			0.0855956
$250$		0			0
$251$	−10.5342	−	10.5342i	−0.664912	−	0.664912i	0.291622	−	0.956534i	$-0.405805\pi$
$251$	−10.5342	−	10.5342i	−0.664912	−	0.664912i	−0.956534	+	0.291622i	$0.905805\pi$
$252$		0			0
$253$	5.92722	−	10.1468i	0.372641	−	0.637924i
$254$		0			0
$255$	2.35864			0.147704
$256$		0			0
$257$	28.3584			1.76895			0.884476	−	0.466586i	$-0.154516\pi$
$257$	28.3584			1.76895			0.884476	+	0.466586i	$0.154516\pi$
$258$		0			0
$259$	−16.4234	−	16.4234i	−1.02050	−	1.02050i
$260$		0			0
$261$	−9.66938	−	9.66938i	−0.598519	−	0.598519i
$262$		0			0
$263$			24.9527i			1.53865i	0.638856	+	0.769326i	$0.279408\pi$
$263$			24.9527i			1.53865i	−0.638856	+	0.769326i	$0.720592\pi$
$264$		0			0
$265$		−	9.39919i		−	0.577388i
$266$		0			0
$267$	3.62417	+	3.62417i	0.221796	+	0.221796i
$268$		0			0
$269$	15.1807	+	15.1807i	0.925586	+	0.925586i	0.997417	−	0.0718312i	$-0.0228843\pi$
$269$	15.1807	+	15.1807i	0.925586	+	0.925586i	−0.0718312	+	0.997417i	$0.522884\pi$
$270$		0			0
$271$	29.7704			1.80842			0.904211	−	0.427086i	$-0.140460\pi$
$271$	29.7704			1.80842			0.904211	+	0.427086i	$0.140460\pi$
$272$		0			0
$273$	1.31626			0.0796640
$274$		0			0
$275$	11.4826	+	6.70754i	0.692428	+	0.404480i
$276$		0			0
$277$	7.99051	+	7.99051i	0.480103	+	0.480103i	0.905164	−	0.425061i	$-0.139748\pi$
$277$	7.99051	+	7.99051i	0.480103	+	0.480103i	−0.425061	+	0.905164i	$0.639748\pi$
$278$		0			0
$279$	−23.2939			−1.39457
$280$		0			0
$281$	−10.4093			−0.620970			−0.310485	−	0.950578i	$-0.600491\pi$
$281$	−10.4093			−0.620970			−0.310485	+	0.950578i	$0.600491\pi$
$282$		0			0
$283$	13.8378	−	13.8378i	0.822572	−	0.822572i	−0.163904	−	0.986476i	$-0.552409\pi$
$283$	13.8378	−	13.8378i	0.822572	−	0.822572i	0.986476	+	0.163904i	$0.0524088\pi$
$284$		0			0
$285$	0.414551	−	0.414551i	0.0245559	−	0.0245559i
$286$		0			0
$287$		−	22.8771i		−	1.35039i
$288$		0			0
$289$	1.80084			0.105932
$290$		0			0
$291$	−4.97634	+	4.97634i	−0.291718	+	0.291718i
$292$		0			0
$293$	−5.38617	−	5.38617i	−0.314663	−	0.314663i	0.532050	−	0.846713i	$-0.321422\pi$
$293$	−5.38617	−	5.38617i	−0.314663	−	0.314663i	−0.846713	+	0.532050i	$0.821422\pi$
$294$		0			0
$295$	−14.8873			−0.866773
$296$		0			0
$297$	10.9801	−	2.88237i	0.637127	−	0.167252i
$298$		0			0
$299$	1.55539	−	1.55539i	0.0899506	−	0.0899506i
$300$		0			0
$301$	−13.9969	−	13.9969i	−0.806768	−	0.806768i
$302$		0			0
$303$	−10.1705			−0.584281
$304$		0			0
$305$		−	5.12649i		−	0.293542i
$306$		0			0
$307$	9.19127	+	9.19127i	0.524573	+	0.524573i	0.918949	−	0.394376i	$-0.129039\pi$
$307$	9.19127	+	9.19127i	0.524573	+	0.524573i	−0.394376	+	0.918949i	$0.629039\pi$
$308$		0			0
$309$	−1.66398	+	1.66398i	−0.0946606	+	0.0946606i
$310$		0			0
$311$	−25.2975			−1.43449			−0.717244	−	0.696822i	$-0.754597\pi$
$311$	−25.2975			−1.43449			−0.717244	+	0.696822i	$0.754597\pi$
$312$		0			0
$313$		−	29.0431i		−	1.64161i	−0.571207	−	0.820806i	$-0.693525\pi$
$313$		−	29.0431i		−	1.64161i	0.571207	−	0.820806i	$-0.306475\pi$
$314$		0			0
$315$	6.45606	−	6.45606i	0.363758	−	0.363758i
$316$		0			0
$317$	14.1057	+	14.1057i	0.792253	+	0.792253i	0.981860	−	0.189607i	$-0.0607215\pi$
$317$	14.1057	+	14.1057i	0.792253	+	0.792253i	−0.189607	+	0.981860i	$0.560721\pi$
$318$		0			0
$319$	4.37778	+	16.6766i	0.245108	+	0.933713i
$320$		0			0
$321$		−	4.43035i		−	0.247278i
$322$		0			0
$323$	−2.67139	+	2.67139i	−0.148640	+	0.148640i
$324$		0			0
$325$	1.76016	+	1.76016i	0.0976360	+	0.0976360i
$326$		0			0
$327$		−	10.0236i		−	0.554306i
$328$		0			0
$329$	19.8399			1.09381
$330$		0			0
$331$	15.4577	+	15.4577i	0.849633	+	0.849633i	0.990087	−	0.140454i	$-0.0448563\pi$
$331$	15.4577	+	15.4577i	0.849633	+	0.849633i	−0.140454	+	0.990087i	$0.544856\pi$
$332$		0			0
$333$	−12.3868	−	12.3868i	−0.678790	−	0.678790i
$334$		0			0
$335$			4.96370i			0.271196i
$336$		0			0
$337$		−	19.7020i		−	1.07324i	−0.843825	−	0.536618i	$-0.819701\pi$
$337$		−	19.7020i		−	1.07324i	0.843825	−	0.536618i	$-0.180299\pi$
$338$		0			0
$339$	5.70620	−	5.70620i	0.309918	−	0.309918i
$340$		0			0
$341$	25.3604	+	14.8142i	1.37334	+	0.802234i
$342$		0			0
$343$			6.40364i			0.345764i
$344$		0			0
$345$			2.14356i			0.115405i
$346$		0			0
$347$	0.499662	−	0.499662i	0.0268233	−	0.0268233i	−0.693568	−	0.720391i	$-0.743962\pi$
$347$	0.499662	−	0.499662i	0.0268233	−	0.0268233i	0.720391	+	0.693568i	$0.243962\pi$
$348$		0			0
$349$	−11.4338	+	11.4338i	−0.612037	+	0.612037i	−0.943477	−	0.331439i	$-0.892466\pi$
$349$	−11.4338	+	11.4338i	−0.612037	+	0.612037i	0.331439	+	0.943477i	$0.392466\pi$
$350$		0			0
$351$	2.12495			0.113422
$352$		0			0
$353$	−10.2490			−0.545500			−0.272750	−	0.962085i	$-0.587933\pi$
$353$	−10.2490			−0.545500			−0.272750	+	0.962085i	$0.587933\pi$
$354$		0			0
$355$	−4.72414	+	4.72414i	−0.250732	+	0.250732i
$356$		0			0
$357$	5.84477	−	5.84477i	0.309338	−	0.309338i
$358$		0			0
$359$			10.0447i			0.530139i	0.964229	+	0.265069i	$0.0853949\pi$
$359$			10.0447i			0.530139i	−0.964229	+	0.265069i	$0.914605\pi$
$360$		0			0
$361$		−	18.0610i		−	0.950577i
$362$		0			0
$363$	−6.44118	−	1.79628i	−0.338074	−	0.0942800i
$364$		0			0
$365$	−5.82747	+	5.82747i	−0.305024	+	0.305024i
$366$		0			0
$367$		−	12.7079i		−	0.663347i	−0.943394	−	0.331673i	$-0.892387\pi$
$367$		−	12.7079i		−	0.663347i	0.943394	−	0.331673i	$-0.107613\pi$
$368$		0			0
$369$		−	17.2542i		−	0.898218i
$370$		0			0
$371$	−23.2915	−	23.2915i	−1.20923	−	1.20923i
$372$		0			0
$373$	15.1771	+	15.1771i	0.785842	+	0.785842i	0.980810	−	0.194967i	$-0.0624601\pi$
$373$	15.1771	+	15.1771i	0.785842	+	0.785842i	−0.194967	+	0.980810i	$0.562460\pi$
$374$		0			0
$375$	−5.45073			−0.281474
$376$		0			0
$377$			3.22741i			0.166220i
$378$		0			0
$379$	−21.9541	−	21.9541i	−1.12771	−	1.12771i	−0.990549	−	0.137159i	$-0.956203\pi$
$379$	−21.9541	−	21.9541i	−1.12771	−	1.12771i	−0.137159	−	0.990549i	$-0.543797\pi$
$380$		0			0
$381$	1.51290	−	1.51290i	0.0775084	−	0.0775084i
$382$		0			0
$383$		−	34.0345i		−	1.73908i	−0.493859	−	0.869542i	$-0.664414\pi$
$383$		−	34.0345i		−	1.73908i	0.493859	−	0.869542i	$-0.335586\pi$
$384$		0			0
$385$	−11.1347	+	2.92296i	−0.567476	+	0.148968i
$386$		0			0
$387$	−10.5566	−	10.5566i	−0.536623	−	0.536623i
$388$		0			0
$389$	13.7263	−	13.7263i	0.695950	−	0.695950i	−0.267584	−	0.963535i	$-0.586225\pi$
$389$	13.7263	−	13.7263i	0.695950	−	0.695950i	0.963535	+	0.267584i	$0.0862253\pi$
$390$		0			0
$391$		−	13.8132i		−	0.698563i
$392$		0			0
$393$	4.72976			0.238585
$394$		0			0
$395$	−6.25735	+	6.25735i	−0.314842	+	0.314842i
$396$		0			0
$397$	3.40236	+	3.40236i	0.170760	+	0.170760i	0.787313	−	0.616553i	$-0.211472\pi$
$397$	3.40236	+	3.40236i	0.170760	+	0.170760i	−0.616553	+	0.787313i	$0.711472\pi$
$398$		0			0
$399$		−	2.05454i		−	0.102856i
$400$		0			0
$401$	6.02575			0.300912			0.150456	−	0.988617i	$-0.451926\pi$
$401$	6.02575			0.300912			0.150456	+	0.988617i	$0.451926\pi$
$402$		0			0
$403$	3.88747	+	3.88747i	0.193649	+	0.193649i
$404$		0			0
$405$	4.08906	−	4.08906i	0.203187	−	0.203187i
$406$		0			0
$407$	5.60806	+	21.3633i	0.277981	+	1.05894i
$408$		0			0
$409$	−28.0557			−1.38726			−0.693632	−	0.720329i	$-0.743991\pi$
$409$	−28.0557			−1.38726			−0.693632	+	0.720329i	$0.743991\pi$
$410$		0			0
$411$	0.212021	+	0.212021i	0.0104582	+	0.0104582i
$412$		0			0
$413$	−36.8912	+	36.8912i	−1.81530	+	1.81530i
$414$		0			0
$415$	−2.21121			−0.108544
$416$		0			0
$417$			9.00672i			0.441061i
$418$		0			0
$419$	8.42547	−	8.42547i	0.411611	−	0.411611i	−0.470688	−	0.882300i	$-0.655994\pi$
$419$	8.42547	−	8.42547i	0.411611	−	0.411611i	0.882300	+	0.470688i	$0.155994\pi$
$420$		0			0
$421$	−13.1424	+	13.1424i	−0.640523	+	0.640523i	−0.950684	−	0.310161i	$-0.899617\pi$
$421$	−13.1424	+	13.1424i	−0.640523	+	0.640523i	0.310161	+	0.950684i	$0.399617\pi$
$422$		0			0
$423$	14.9635			0.727549
$424$		0			0
$425$	15.6317			0.758248
$426$		0			0
$427$	−12.7036	−	12.7036i	−0.614769	−	0.614769i
$428$		0			0
$429$	−1.08082	−	0.631355i	−0.0521822	−	0.0304821i
$430$		0			0
$431$	−14.1018			−0.679261			−0.339630	−	0.940559i	$-0.610302\pi$
$431$	−14.1018			−0.679261			−0.339630	+	0.940559i	$0.610302\pi$
$432$		0			0
$433$	26.1852			1.25838			0.629190	−	0.777252i	$-0.283387\pi$
$433$	26.1852			1.25838			0.629190	+	0.777252i	$0.283387\pi$
$434$		0			0
$435$	−2.22392	−	2.22392i	−0.106629	−	0.106629i
$436$		0			0
$437$	−2.42779	−	2.42779i	−0.116137	−	0.116137i
$438$		0			0
$439$			1.85297i			0.0884376i	0.999022	+	0.0442188i	$0.0140799\pi$
$439$			1.85297i			0.0884376i	−0.999022	+	0.0442188i	$0.985920\pi$
$440$		0			0
$441$		−	13.5835i		−	0.646831i
$442$		0			0
$443$	12.2887	+	12.2887i	0.583852	+	0.583852i	0.935960	−	0.352107i	$-0.114535\pi$
$443$	12.2887	+	12.2887i	0.583852	+	0.583852i	−0.352107	+	0.935960i	$0.614535\pi$
$444$		0			0
$445$	−5.93320	−	5.93320i	−0.281260	−	0.281260i
$446$		0			0
$447$	−3.32313			−0.157179
$448$		0			0
$449$	21.8043			1.02901			0.514504	−	0.857488i	$-0.327976\pi$
$449$	21.8043			1.02901			0.514504	+	0.857488i	$0.327976\pi$
$450$		0			0
$451$	−10.9732	+	18.7849i	−0.516706	+	0.884548i
$452$		0			0
$453$	−7.73268	−	7.73268i	−0.363313	−	0.363313i
$454$		0			0
$455$	−2.15488			−0.101022
$456$		0			0
$457$	−19.4072			−0.907830			−0.453915	−	0.891045i	$-0.649973\pi$
$457$	−19.4072			−0.907830			−0.453915	+	0.891045i	$0.649973\pi$
$458$		0			0
$459$	9.43569	−	9.43569i	0.440420	−	0.440420i
$460$		0			0
$461$	28.9596	−	28.9596i	1.34878	−	1.34878i	0.461794	−	0.886987i	$-0.347206\pi$
$461$	28.9596	−	28.9596i	1.34878	−	1.34878i	0.886987	−	0.461794i	$-0.152794\pi$
$462$		0			0
$463$			10.7228i			0.498332i	0.968461	+	0.249166i	$0.0801565\pi$
$463$			10.7228i			0.498332i	−0.968461	+	0.249166i	$0.919844\pi$
$464$		0			0
$465$	−5.35751			−0.248448
$466$		0			0
$467$	23.9075	−	23.9075i	1.10631	−	1.10631i	0.112674	−	0.993632i	$-0.464059\pi$
$467$	23.9075	−	23.9075i	1.10631	−	1.10631i	0.993632	−	0.112674i	$-0.0359415\pi$
$468$		0			0
$469$	12.3002	+	12.3002i	0.567970	+	0.567970i
$470$		0			0
$471$	−3.13767			−0.144576
$472$		0			0
$473$	4.77947	+	18.2069i	0.219760	+	0.837153i
$474$		0			0
$475$	2.74741	−	2.74741i	0.126060	−	0.126060i
$476$		0			0
$477$	−17.5667	−	17.5667i	−0.804324	−	0.804324i
$478$		0			0
$479$	−0.223784			−0.0102250			−0.00511248	−	0.999987i	$-0.501627\pi$
$479$	−0.223784			−0.0102250			−0.00511248	+	0.999987i	$0.501627\pi$
$480$		0			0
$481$			4.13440i			0.188513i
$482$		0			0
$483$	5.31180	+	5.31180i	0.241695	+	0.241695i
$484$		0			0
$485$	8.14685	−	8.14685i	0.369929	−	0.369929i
$486$		0			0
$487$	16.6290			0.753532			0.376766	−	0.926308i	$-0.377036\pi$
$487$	16.6290			0.753532			0.376766	+	0.926308i	$0.377036\pi$
$488$		0			0
$489$			2.96004i			0.133857i
$490$		0			0
$491$	7.49218	−	7.49218i	0.338118	−	0.338118i	−0.517541	−	0.855658i	$-0.673152\pi$
$491$	7.49218	−	7.49218i	0.338118	−	0.338118i	0.855658	+	0.517541i	$0.173152\pi$
$492$		0			0
$493$	14.3311	+	14.3311i	0.645438	+	0.645438i
$494$		0			0
$495$	−8.39791	+	2.20453i	−0.377458	+	0.0990863i
$496$		0			0
$497$			23.4131i			1.05022i
$498$		0			0
$499$	24.7577	−	24.7577i	1.10830	−	1.10830i	0.114931	−	0.993373i	$-0.463335\pi$
$499$	24.7577	−	24.7577i	1.10830	−	1.10830i	0.993373	−	0.114931i	$-0.0366648\pi$
$500$		0			0
$501$	−4.48344	−	4.48344i	−0.200305	−	0.200305i
$502$		0			0
$503$		−	19.7340i		−	0.879898i	−0.898023	−	0.439949i	$-0.854997\pi$
$503$		−	19.7340i		−	0.879898i	0.898023	−	0.439949i	$-0.145003\pi$
$504$		0			0
$505$	16.6503			0.740930
$506$		0			0
$507$	5.42242	+	5.42242i	0.240818	+	0.240818i
$508$		0			0
$509$	−5.77187	−	5.77187i	−0.255834	−	0.255834i	0.567523	−	0.823357i	$-0.307902\pi$
$509$	−5.77187	−	5.77187i	−0.255834	−	0.255834i	−0.823357	+	0.567523i	$0.807902\pi$
$510$		0			0
$511$			28.8813i			1.27763i
$512$		0			0
$513$		−	3.31681i		−	0.146441i
$514$		0			0
$515$	2.72413	−	2.72413i	0.120040	−	0.120040i
$516$		0			0
$517$	−16.2910	−	9.51632i	−0.716476	−	0.418527i
$518$		0			0
$519$			3.40869i			0.149625i
$520$		0			0
$521$			10.3021i			0.451343i	0.974203	+	0.225671i	$0.0724576\pi$
$521$			10.3021i			0.451343i	−0.974203	+	0.225671i	$0.927542\pi$
$522$		0			0
$523$	9.59389	−	9.59389i	0.419511	−	0.419511i	−0.465524	−	0.885035i	$-0.654134\pi$
$523$	9.59389	−	9.59389i	0.419511	−	0.419511i	0.885035	+	0.465524i	$0.154134\pi$
$524$		0			0
$525$	−6.01109	+	6.01109i	−0.262346	+	0.262346i
$526$		0			0
$527$	34.5240			1.50389
$528$		0			0
$529$	−10.4464			−0.454192
$530$		0			0
$531$	−27.8238	+	27.8238i	−1.20745	+	1.20745i
$532$		0			0
$533$	−2.87952	+	2.87952i	−0.124726	+	0.124726i
$534$		0			0
$535$			7.25300i			0.313574i
$536$		0			0
$537$		−	5.17100i		−	0.223145i
$538$		0			0
$539$	−8.63867	+	14.7885i	−0.372094	+	0.636987i
$540$		0			0
$541$	24.0872	−	24.0872i	1.03559	−	1.03559i	0.0362451	−	0.999343i	$-0.488460\pi$
$541$	24.0872	−	24.0872i	1.03559	−	1.03559i	0.999343	−	0.0362451i	$-0.0115397\pi$
$542$		0			0
$543$		−	1.34330i		−	0.0576465i
$544$		0			0
$545$			16.4098i			0.702919i
$546$		0			0
$547$	−9.72015	−	9.72015i	−0.415604	−	0.415604i	0.468082	−	0.883685i	$-0.344945\pi$
$547$	−9.72015	−	9.72015i	−0.415604	−	0.415604i	−0.883685	+	0.468082i	$0.844945\pi$
$548$		0			0
$549$	−9.58119	−	9.58119i	−0.408915	−	0.408915i
$550$		0			0
$551$	5.03762			0.214610
$552$		0			0
$553$			31.0118i			1.31876i
$554$		0			0
$555$	−2.84891	−	2.84891i	−0.120929	−	0.120929i
$556$		0			0
$557$	12.9184	−	12.9184i	0.547371	−	0.547371i	−0.378308	−	0.925680i	$-0.623494\pi$
$557$	12.9184	−	12.9184i	0.547371	−	0.547371i	0.925680	+	0.378308i	$0.123494\pi$
$558$		0			0
$559$			3.52355i			0.149030i
$560$		0			0
$561$	−7.60276	+	1.99579i	−0.320989	+	0.0842625i
$562$		0			0
$563$	21.8628	+	21.8628i	0.921408	+	0.921408i	0.997129	−	0.0757213i	$-0.0241259\pi$
$563$	21.8628	+	21.8628i	0.921408	+	0.921408i	−0.0757213	+	0.997129i	$0.524126\pi$
$564$		0			0
$565$	−9.34172	+	9.34172i	−0.393009	+	0.393009i
$566$		0			0
$567$		−	20.2656i		−	0.851077i
$568$		0			0
$569$	−40.4249			−1.69470			−0.847350	−	0.531035i	$-0.821803\pi$
$569$	−40.4249			−1.69470			−0.847350	+	0.531035i	$0.821803\pi$
$570$		0			0
$571$	−25.0630	+	25.0630i	−1.04886	+	1.04886i	−0.0501119	+	0.998744i	$0.515958\pi$
$571$	−25.0630	+	25.0630i	−1.04886	+	1.04886i	−0.998744	+	0.0501119i	$0.984042\pi$
$572$		0			0
$573$	−5.31287	−	5.31287i	−0.221948	−	0.221948i
$574$		0			0
$575$			14.2063i			0.592442i
$576$		0			0
$577$	−18.0565			−0.751704			−0.375852	−	0.926680i	$-0.622650\pi$
$577$	−18.0565			−0.751704			−0.375852	+	0.926680i	$0.622650\pi$
$578$		0			0
$579$	10.1184	+	10.1184i	0.420507	+	0.420507i
$580$		0			0
$581$	−5.47945	+	5.47945i	−0.227326	+	0.227326i
$582$		0			0
$583$	7.95326	+	30.2970i	0.329390	+	1.25478i
$584$		0			0
$585$	−1.62524			−0.0671953
$586$		0			0
$587$	−13.6375	−	13.6375i	−0.562879	−	0.562879i	0.367245	−	0.930124i	$-0.380301\pi$
$587$	−13.6375	−	13.6375i	−0.562879	−	0.562879i	−0.930124	+	0.367245i	$0.880301\pi$
$588$		0			0
$589$	6.06790	−	6.06790i	0.250024	−	0.250024i
$590$		0			0
$591$	6.03291			0.248161
$592$		0			0
$593$		−	28.8853i		−	1.18618i	−0.805137	−	0.593090i	$-0.797908\pi$
$593$		−	28.8853i		−	1.18618i	0.805137	−	0.593090i	$-0.202092\pi$
$594$		0			0
$595$	−9.56858	+	9.56858i	−0.392273	+	0.392273i
$596$		0			0
$597$	−4.28706	+	4.28706i	−0.175458	+	0.175458i
$598$		0			0
$599$	29.5162			1.20600			0.602999	−	0.797742i	$-0.293972\pi$
$599$	29.5162			1.20600			0.602999	+	0.797742i	$0.293972\pi$
$600$		0			0
$601$	5.62269			0.229354			0.114677	−	0.993403i	$-0.463417\pi$
$601$	5.62269			0.229354			0.114677	+	0.993403i	$0.463417\pi$
$602$		0			0
$603$	9.27696	+	9.27696i	0.377787	+	0.377787i
$604$		0			0
$605$	10.5450	+	2.94071i	0.428714	+	0.119557i
$606$		0			0
$607$	−5.82970			−0.236620			−0.118310	−	0.992977i	$-0.537748\pi$
$607$	−5.82970			−0.236620			−0.118310	+	0.992977i	$0.537748\pi$
$608$		0			0
$609$	−11.0219			−0.446629
$610$		0			0
$611$	−2.49723	−	2.49723i	−0.101027	−	0.101027i
$612$		0			0
$613$	−28.6414	−	28.6414i	−1.15681	−	1.15681i	−0.985157	−	0.171657i	$-0.945088\pi$
$613$	−28.6414	−	28.6414i	−1.15681	−	1.15681i	−0.171657	−	0.985157i	$-0.554912\pi$
$614$		0			0
$615$		−	3.96840i		−	0.160021i
$616$		0			0
$617$			17.7711i			0.715437i	0.933829	+	0.357719i	$0.116445\pi$
$617$			17.7711i			0.715437i	−0.933829	+	0.357719i	$0.883555\pi$
$618$		0			0
$619$	24.6929	+	24.6929i	0.992491	+	0.992491i	0.999972	−	0.00748108i	$-0.00238132\pi$
$619$	24.6929	+	24.6929i	0.992491	+	0.992491i	−0.00748108	+	0.999972i	$0.502381\pi$
$620$		0			0
$621$	8.57527	+	8.57527i	0.344114	+	0.344114i
$622$		0			0
$623$	−29.4053			−1.17810
$624$		0			0
$625$	−11.1243			−0.444971
$626$		0			0
$627$	−0.985474	+	1.68703i	−0.0393560	+	0.0673735i
$628$		0			0
$629$	18.3585	+	18.3585i	0.732001	+	0.732001i
$630$		0			0
$631$	3.02973			0.120612			0.0603058	−	0.998180i	$-0.480792\pi$
$631$	3.02973			0.120612			0.0603058	+	0.998180i	$0.480792\pi$
$632$		0			0
$633$	−8.53123			−0.339086
$634$		0			0
$635$	−2.47680	+	2.47680i	−0.0982889	+	0.0982889i
$636$		0			0
$637$	−2.26692	+	2.26692i	−0.0898185	+	0.0898185i
$638$		0			0
$639$			17.6585i			0.698558i
$640$		0			0
$641$	−13.2419			−0.523022			−0.261511	−	0.965201i	$-0.584221\pi$
$641$	−13.2419			−0.523022			−0.261511	+	0.965201i	$0.584221\pi$
$642$		0			0
$643$	−19.4121	+	19.4121i	−0.765539	+	0.765539i	−0.977318	−	0.211779i	$-0.932074\pi$
$643$	−19.4121	+	19.4121i	−0.765539	+	0.765539i	0.211779	+	0.977318i	$0.432074\pi$
$644$		0			0
$645$	−2.42798	−	2.42798i	−0.0956018	−	0.0956018i
$646$		0			0
$647$	8.30862			0.326646			0.163323	−	0.986573i	$-0.447779\pi$
$647$	8.30862			0.326646			0.163323	+	0.986573i	$0.447779\pi$
$648$		0			0
$649$	47.9873	−	12.5971i	1.88367	−	0.494480i
$650$		0			0
$651$	−13.2761	+	13.2761i	−0.520330	+	0.520330i
$652$		0			0
$653$	6.95291	+	6.95291i	0.272088	+	0.272088i	0.829940	−	0.557852i	$-0.188374\pi$
$653$	6.95291	+	6.95291i	0.272088	+	0.272088i	−0.557852	+	0.829940i	$0.688374\pi$
$654$		0			0
$655$	−7.74317			−0.302551
$656$		0			0
$657$			21.7826i			0.849821i
$658$		0			0
$659$	18.0679	+	18.0679i	0.703824	+	0.703824i	0.965229	−	0.261405i	$-0.0841858\pi$
$659$	18.0679	+	18.0679i	0.703824	+	0.703824i	−0.261405	+	0.965229i	$0.584186\pi$
$660$		0			0
$661$	−25.9400	+	25.9400i	−1.00895	+	1.00895i	−0.00898951	+	0.999960i	$0.502861\pi$
$661$	−25.9400	+	25.9400i	−1.00895	+	1.00895i	−0.999960	+	0.00898951i	$0.997139\pi$
$662$		0			0
$663$	−1.47135			−0.0571425
$664$		0			0
$665$			3.36353i			0.130432i
$666$		0			0
$667$	−13.0242	+	13.0242i	−0.504300	+	0.504300i
$668$		0			0
$669$	−2.40783	−	2.40783i	−0.0930921	−	0.0930921i
$670$		0			0
$671$	4.33785	+	16.5246i	0.167461	+	0.637923i
$672$		0			0
$673$			2.19817i			0.0847331i	0.999102	+	0.0423666i	$0.0134897\pi$
$673$			2.19817i			0.0847331i	−0.999102	+	0.0423666i	$0.986510\pi$
$674$		0			0
$675$	−9.70420	+	9.70420i	−0.373515	+	0.373515i
$676$		0			0
$677$	−11.3920	−	11.3920i	−0.437830	−	0.437830i	0.453451	−	0.891281i	$-0.350193\pi$
$677$	−11.3920	−	11.3920i	−0.437830	−	0.437830i	−0.891281	+	0.453451i	$0.850193\pi$
$678$		0			0
$679$		−	40.3763i		−	1.54950i
$680$		0			0
$681$	7.20834			0.276224
$682$		0			0
$683$	4.81965	+	4.81965i	0.184419	+	0.184419i	0.793278	−	0.608859i	$-0.208373\pi$
$683$	4.81965	+	4.81965i	0.184419	+	0.184419i	−0.608859	+	0.793278i	$0.708373\pi$
$684$		0			0
$685$	−0.347104	−	0.347104i	−0.0132622	−	0.0132622i
$686$		0			0
$687$		−	9.07845i		−	0.346365i
$688$		0			0
$689$			5.86335i			0.223376i
$690$		0			0
$691$	−8.72767	+	8.72767i	−0.332016	+	0.332016i	−0.853352	−	0.521336i	$-0.825434\pi$
$691$	−8.72767	+	8.72767i	−0.332016	+	0.332016i	0.521336	+	0.853352i	$0.325434\pi$
$692$		0			0
$693$	−15.3474	+	26.2732i	−0.582999	+	0.998035i
$694$		0			0
$695$		−	14.7451i		−	0.559312i
$696$		0			0
$697$			25.5726i			0.968630i
$698$		0			0
$699$	11.1282	−	11.1282i	0.420907	−	0.420907i
$700$		0			0
$701$	−27.2961	+	27.2961i	−1.03096	+	1.03096i	−0.0314550	+	0.999505i	$0.510014\pi$
$701$	−27.2961	+	27.2961i	−1.03096	+	1.03096i	−0.999505	+	0.0314550i	$0.989986\pi$
$702$		0			0
$703$	6.45334			0.243392
$704$		0			0
$705$	3.44154			0.129616
$706$		0			0
$707$	41.2600	−	41.2600i	1.55174	−	1.55174i
$708$		0			0
$709$	−6.06158	+	6.06158i	−0.227647	+	0.227647i	−0.811709	−	0.584062i	$-0.801463\pi$
$709$	−6.06158	+	6.06158i	−0.227647	+	0.227647i	0.584062	+	0.811709i	$0.301463\pi$
$710$		0			0
$711$			23.3895i			0.877174i
$712$		0			0
$713$			31.3758i			1.17503i
$714$		0			0
$715$	1.76942	+	1.03360i	0.0661726	+	0.0386545i
$716$		0			0
$717$	−2.05079	+	2.05079i	−0.0765881	+	0.0765881i
$718$		0			0
$719$		−	8.66986i		−	0.323331i	−0.986846	−	0.161666i	$-0.948313\pi$
$719$		−	8.66986i		−	0.323331i	0.986846	−	0.161666i	$-0.0516866\pi$
$720$		0			0
$721$		−	13.5010i		−	0.502802i
$722$		0			0
$723$	−7.34904	−	7.34904i	−0.273314	−	0.273314i
$724$		0			0
$725$	−14.7389	−	14.7389i	−0.547388	−	0.547388i
$726$		0			0
$727$	17.9981			0.667512			0.333756	−	0.942659i	$-0.391684\pi$
$727$	17.9981			0.667512			0.333756	+	0.942659i	$0.391684\pi$
$728$		0			0
$729$		−	9.04241i		−	0.334904i
$730$		0			0
$731$	15.6460	+	15.6460i	0.578690	+	0.578690i
$732$		0			0
$733$	−8.31257	+	8.31257i	−0.307032	+	0.307032i	−0.843757	−	0.536725i	$-0.819661\pi$
$733$	−8.31257	+	8.31257i	−0.307032	+	0.307032i	0.536725	+	0.843757i	$0.319661\pi$
$734$		0			0
$735$		−	3.12415i		−	0.115236i
$736$		0			0
$737$	−4.20011	−	15.9998i	−0.154713	−	0.589362i
$738$		0			0
$739$	9.37332	+	9.37332i	0.344803	+	0.344803i	0.858170	−	0.513366i	$-0.171602\pi$
$739$	9.37332	+	9.37332i	0.344803	+	0.344803i	−0.513366	+	0.858170i	$0.671602\pi$
$740$		0			0
$741$	−0.258603	+	0.258603i	−0.00950002	+	0.00950002i
$742$		0			0
$743$		−	49.4798i		−	1.81524i	−0.419795	−	0.907619i	$-0.637898\pi$
$743$		−	49.4798i		−	1.81524i	0.419795	−	0.907619i	$-0.362102\pi$
$744$		0			0
$745$	5.44035			0.199319
$746$		0			0
$747$	−4.13267	+	4.13267i	−0.151206	+	0.151206i
$748$		0			0
$749$	17.9731	+	17.9731i	0.656724	+	0.656724i
$750$		0			0
$751$		−	7.22225i		−	0.263543i	−0.991280	−	0.131772i	$-0.957933\pi$
$751$		−	7.22225i		−	0.263543i	0.991280	−	0.131772i	$-0.0420666\pi$
$752$		0			0
$753$	−9.05631			−0.330030
$754$		0			0
$755$	12.6593	+	12.6593i	0.460719	+	0.460719i
$756$		0			0
$757$	13.9267	−	13.9267i	0.506173	−	0.506173i	−0.407176	−	0.913350i	$-0.633487\pi$
$757$	13.9267	−	13.9267i	0.506173	−	0.506173i	0.913350	+	0.407176i	$0.133487\pi$
$758$		0			0
$759$	−1.81380	−	6.90948i	−0.0658368	−	0.250798i
$760$		0			0
$761$	−32.6575			−1.18384			−0.591918	−	0.805998i	$-0.701629\pi$
$761$	−32.6575			−1.18384			−0.591918	+	0.805998i	$0.701629\pi$
$762$		0			0
$763$	40.6640	+	40.6640i	1.47213	+	1.47213i
$764$		0			0
$765$	−7.21673	+	7.21673i	−0.260922	+	0.260922i
$766$		0			0
$767$	9.28692			0.335331
$768$		0			0
$769$			39.4500i			1.42260i	0.702888	+	0.711301i	$0.251894\pi$
$769$			39.4500i			1.42260i	−0.702888	+	0.711301i	$0.748106\pi$
$770$		0			0
$771$	12.1900	−	12.1900i	0.439012	−	0.439012i
$772$		0			0
$773$	2.13615	−	2.13615i	0.0768318	−	0.0768318i	−0.667647	−	0.744478i	$-0.732698\pi$
$773$	2.13615	−	2.13615i	0.0768318	−	0.0768318i	0.744478	+	0.667647i	$0.232698\pi$
$774$		0			0
$775$	−35.5065			−1.27543
$776$		0			0
$777$	−14.1194			−0.506529
$778$		0			0
$779$	4.49461	+	4.49461i	0.161036	+	0.161036i
$780$		0			0
$781$	11.2303	−	19.2251i	0.401850	−	0.687927i
$782$		0			0
$783$	−17.7935			−0.635889
$784$		0			0
$785$	5.13674			0.183338
$786$		0			0
$787$	−25.0048	−	25.0048i	−0.891326	−	0.891326i	0.103322	−	0.994648i	$-0.467053\pi$
$787$	−25.0048	−	25.0048i	−0.891326	−	0.891326i	−0.994648	+	0.103322i	$0.967053\pi$
$788$		0			0
$789$	10.7260	+	10.7260i	0.381857	+	0.381857i
$790$		0			0
$791$			46.2981i			1.64617i
$792$		0			0
$793$			3.19797i			0.113563i
$794$		0			0
$795$	−4.04028	−	4.04028i	−0.143294	−	0.143294i
$796$		0			0
$797$	30.8223	+	30.8223i	1.09178	+	1.09178i	0.995338	+	0.0964450i	$0.0307472\pi$
$797$	30.8223	+	30.8223i	1.09178	+	1.09178i	0.0964450	+	0.995338i	$0.469253\pi$
$798$		0			0
$799$	−22.1775			−0.784582
$800$		0			0
$801$	−22.1778			−0.783614
$802$		0			0
$803$	13.8531	−	23.7151i	0.488865	−	0.836887i
$804$		0			0
$805$	−8.69604	−	8.69604i	−0.306495	−	0.306495i
$806$		0			0
$807$	13.0510			0.459417
$808$		0			0
$809$	−41.9211			−1.47387			−0.736933	−	0.675966i	$-0.763727\pi$
$809$	−41.9211			−1.47387			−0.736933	+	0.675966i	$0.763727\pi$
$810$		0			0
$811$	−24.2516	+	24.2516i	−0.851587	+	0.851587i	−0.990329	−	0.138741i	$-0.955694\pi$
$811$	−24.2516	+	24.2516i	−0.851587	+	0.851587i	0.138741	+	0.990329i	$0.455694\pi$
$812$		0			0
$813$	12.7969	−	12.7969i	0.448807	−	0.448807i
$814$		0			0
$815$		−	4.84593i		−	0.169745i
$816$		0			0
$817$	5.49987			0.192416
$818$		0			0
$819$	−4.02738	+	4.02738i	−0.140728	+	0.140728i
$820$		0			0
$821$	11.9450	+	11.9450i	0.416882	+	0.416882i	0.884128	−	0.467246i	$-0.154754\pi$
$821$	11.9450	+	11.9450i	0.416882	+	0.416882i	−0.467246	+	0.884128i	$0.654754\pi$
$822$		0			0
$823$	36.9870			1.28928			0.644642	−	0.764484i	$-0.277006\pi$
$823$	36.9870			1.28928			0.644642	+	0.764484i	$0.277006\pi$
$824$		0			0
$825$	7.81911	−	2.05259i	0.272226	−	0.0714620i
$826$		0			0
$827$	11.9732	−	11.9732i	0.416349	−	0.416349i	−0.467594	−	0.883943i	$-0.654879\pi$
$827$	11.9732	−	11.9732i	0.416349	−	0.416349i	0.883943	+	0.467594i	$0.154879\pi$
$828$		0			0
$829$	25.6621	+	25.6621i	0.891280	+	0.891280i	0.994644	−	0.103364i	$-0.0329605\pi$
$829$	25.6621	+	25.6621i	0.891280	+	0.891280i	−0.103364	+	0.994644i	$0.532961\pi$
$830$		0			0
$831$	6.86950			0.238300
$832$		0			0
$833$			20.1321i			0.697537i
$834$		0			0
$835$	7.33992	+	7.33992i	0.254008	+	0.254008i
$836$		0			0
$837$	−21.4326	+	21.4326i	−0.740820	+	0.740820i
$838$		0			0
$839$	−0.101180			−0.00349312			−0.00174656	−	0.999998i	$-0.500556\pi$
$839$	−0.101180			−0.00349312			−0.00174656	+	0.999998i	$0.500556\pi$
$840$		0			0
$841$			1.97496i			0.0681021i
$842$		0			0
$843$	−4.47450	+	4.47450i	−0.154110	+	0.154110i
$844$		0			0
$845$	−8.87714	−	8.87714i	−0.305383	−	0.305383i
$846$		0			0
$847$	33.4179	−	18.8435i	1.14825	−	0.647472i
$848$		0			0
$849$		−	11.8965i		−	0.408285i
$850$		0			0
$851$	−16.6844	+	16.6844i	−0.571935	+	0.571935i
$852$		0			0
$853$	−31.4844	−	31.4844i	−1.07800	−	1.07800i	−0.996688	−	0.0813161i	$-0.974088\pi$
$853$	−31.4844	−	31.4844i	−1.07800	−	1.07800i	−0.0813161	−	0.996688i	$-0.525912\pi$
$854$		0			0
$855$			2.53681i			0.0867571i
$856$		0			0
$857$	25.1124			0.857824			0.428912	−	0.903346i	$-0.358897\pi$
$857$	25.1124			0.857824			0.428912	+	0.903346i	$0.358897\pi$
$858$		0			0
$859$	−22.4623	−	22.4623i	−0.766404	−	0.766404i	0.211068	−	0.977471i	$-0.432306\pi$
$859$	−22.4623	−	22.4623i	−0.766404	−	0.766404i	−0.977471	+	0.211068i	$0.932306\pi$
$860$		0			0
$861$	−9.83382	−	9.83382i	−0.335136	−	0.335136i
$862$		0			0
$863$		−	5.59943i		−	0.190607i	−0.995448	−	0.0953035i	$-0.969618\pi$
$863$		−	5.59943i		−	0.190607i	0.995448	−	0.0953035i	$-0.0303822\pi$
$864$		0			0
$865$		−	5.58043i		−	0.189740i
$866$		0			0
$867$	0.774096	−	0.774096i	0.0262897	−	0.0262897i
$868$		0			0
$869$	14.8750	−	25.4645i	0.504600	−	0.863824i
$870$		0			0
$871$		−	3.09643i		−	0.104918i
$872$		0			0
$873$		−	30.4523i		−	1.03065i
$874$		0			0
$875$	22.1126	−	22.1126i	0.747544	−	0.747544i
$876$		0			0
$877$	−33.8306	+	33.8306i	−1.14238	+	1.14238i	−0.154363	+	0.988014i	$0.549333\pi$
$877$	−33.8306	+	33.8306i	−1.14238	+	1.14238i	−0.988014	+	0.154363i	$0.950667\pi$
$878$		0			0
$879$	−4.63053			−0.156184
$880$		0			0
$881$	−15.3504			−0.517167			−0.258584	−	0.965989i	$-0.583256\pi$
$881$	−15.3504			−0.517167			−0.258584	+	0.965989i	$0.583256\pi$
$882$		0			0
$883$	−10.6592	+	10.6592i	−0.358712	+	0.358712i	−0.863338	−	0.504626i	$-0.831630\pi$
$883$	−10.6592	+	10.6592i	−0.358712	+	0.358712i	0.504626	+	0.863338i	$0.331630\pi$
$884$		0			0
$885$	−6.39937	+	6.39937i	−0.215112	+	0.215112i
$886$		0			0
$887$			1.62841i			0.0546766i	0.999626	+	0.0273383i	$0.00870314\pi$
$887$			1.62841i			0.0546766i	−0.999626	+	0.0273383i	$0.991297\pi$
$888$		0			0
$889$			12.2752i			0.411696i
$890$		0			0
$891$	−9.72054	+	16.6406i	−0.325650	+	0.557480i
$892$		0			0
$893$	−3.89789	+	3.89789i	−0.130438	+	0.130438i
$894$		0			0
$895$			8.46553i			0.282972i
$896$		0			0
$897$		−	1.33718i		−	0.0446472i
$898$		0			0
$899$	−32.5521	−	32.5521i	−1.08567	−	1.08567i
$900$		0			0
$901$	26.0357	+	26.0357i	0.867376	+	0.867376i
$902$		0			0
$903$	−12.0332			−0.400441
$904$		0			0
$905$			2.19914i			0.0731018i
$906$		0			0
$907$	17.7977	+	17.7977i	0.590964	+	0.590964i	0.937892	−	0.346928i	$-0.112775\pi$
$907$	17.7977	+	17.7977i	0.590964	+	0.590964i	−0.346928	+	0.937892i	$0.612775\pi$
$908$		0			0
$909$	31.1188	−	31.1188i	1.03215	−	1.03215i
$910$		0			0
$911$			39.1539i			1.29723i	0.761117	+	0.648614i	$0.224651\pi$
$911$			39.1539i			1.29723i	−0.761117	+	0.648614i	$0.775349\pi$
$912$		0			0
$913$	7.12756	−	1.87105i	0.235888	−	0.0619227i
$914$		0			0
$915$	−2.20364	−	2.20364i	−0.0728501	−	0.0728501i
$916$		0			0
$917$	−19.1878	+	19.1878i	−0.633637	+	0.633637i
$918$		0			0
$919$			32.7281i			1.07960i	0.841793	+	0.539800i	$0.181500\pi$
$919$			32.7281i			1.07960i	−0.841793	+	0.539800i	$0.818500\pi$
$920$		0			0
$921$	7.90180			0.260373
$922$		0			0
$923$	2.94699	−	2.94699i	0.0970013	−	0.0970013i
$924$		0			0
$925$	−18.8809	−	18.8809i	−0.620801	−	0.620801i
$926$		0			0
$927$		−	10.1826i		−	0.334440i
$928$		0			0
$929$	22.9809			0.753979			0.376989	−	0.926218i	$-0.376959\pi$
$929$	22.9809			0.753979			0.376989	+	0.926218i	$0.376959\pi$
$930$		0			0
$931$	3.53840	+	3.53840i	0.115966	+	0.115966i
$932$		0			0
$933$	−10.8742	+	10.8742i	−0.356006	+	0.356006i
$934$		0			0
$935$	12.4466	−	3.26735i	0.407048	−	0.106854i
$936$		0			0
$937$	9.90997			0.323745			0.161872	−	0.986812i	$-0.448247\pi$
$937$	9.90997			0.323745			0.161872	+	0.986812i	$0.448247\pi$
$938$		0			0
$939$	−12.4843	−	12.4843i	−0.407409	−	0.407409i
$940$		0			0
$941$	18.8730	−	18.8730i	0.615242	−	0.615242i	−0.329065	−	0.944307i	$-0.606733\pi$
$941$	18.8730	−	18.8730i	0.615242	−	0.615242i	0.944307	+	0.329065i	$0.106733\pi$
$942$		0			0
$943$	−23.2407			−0.756820
$944$		0			0
$945$		−	11.8804i		−	0.386470i
$946$		0			0
$947$	−1.99242	+	1.99242i	−0.0647451	+	0.0647451i	−0.738738	−	0.673993i	$-0.764578\pi$
$947$	−1.99242	+	1.99242i	−0.0647451	+	0.0647451i	0.673993	+	0.738738i	$0.264578\pi$
$948$		0			0
$949$	3.63526	−	3.63526i	0.118005	−	0.118005i
$950$		0			0
$951$	12.1267			0.393236
$952$		0			0
$953$	−6.81124			−0.220638			−0.110319	−	0.993896i	$-0.535187\pi$
$953$	−6.81124			−0.220638			−0.110319	+	0.993896i	$0.535187\pi$
$954$		0			0
$955$	8.69779	+	8.69779i	0.281454	+	0.281454i
$956$		0			0
$957$	9.05032	+	5.28671i	0.292555	+	0.170895i
$958$		0			0
$959$	−1.72027			−0.0555503
$960$		0			0
$961$	−47.4193			−1.52965
$962$		0			0
$963$	13.5556	+	13.5556i	0.436822	+	0.436822i
$964$		0			0
$965$	−16.5651	−	16.5651i	−0.533248	−	0.533248i
$966$		0			0
$967$			47.3782i			1.52358i	0.647824	+	0.761790i	$0.275679\pi$
$967$			47.3782i			1.52358i	−0.647824	+	0.761790i	$0.724321\pi$
$968$		0			0
$969$			2.29661i			0.0737778i
$970$		0			0
$971$	−16.6558	−	16.6558i	−0.534509	−	0.534509i	0.387402	−	0.921911i	$-0.373372\pi$
$971$	−16.6558	−	16.6558i	−0.534509	−	0.534509i	−0.921911	+	0.387402i	$0.873372\pi$
$972$		0			0
$973$	−36.5387	−	36.5387i	−1.17138	−	1.17138i
$974$		0			0
$975$	1.51322			0.0484619
$976$		0			0
$977$	13.1118			0.419482			0.209741	−	0.977757i	$-0.432738\pi$
$977$	13.1118			0.419482			0.209741	+	0.977757i	$0.432738\pi$
$978$		0			0
$979$	24.1453	+	14.1044i	0.771688	+	0.450779i
$980$		0			0
$981$	30.6692	+	30.6692i	0.979194	+	0.979194i
$982$		0			0
$983$	−3.44728			−0.109951			−0.0549756	−	0.998488i	$-0.517508\pi$
$983$	−3.44728			−0.109951			−0.0549756	+	0.998488i	$0.517508\pi$
$984$		0			0
$985$	−9.87658			−0.314694
$986$		0			0
$987$	8.52824	−	8.52824i	0.271457	−	0.271457i
$988$		0			0
$989$	−14.2193	+	14.2193i	−0.452148	+	0.452148i
$990$		0			0
$991$			26.6017i			0.845030i	0.906356	+	0.422515i	$0.138853\pi$
$991$			26.6017i			0.845030i	−0.906356	+	0.422515i	$0.861147\pi$
$992$		0			0
$993$	13.2891			0.421717
$994$		0			0
$995$	7.01843	−	7.01843i	0.222499	−	0.222499i
$996$		0			0
$997$	28.3479	+	28.3479i	0.897787	+	0.897787i	0.995240	−	0.0974530i	$-0.0310696\pi$
$997$	28.3479	+	28.3479i	0.897787	+	0.897787i	−0.0974530	+	0.995240i	$0.531070\pi$
$998$		0			0
$999$	−22.7940			−0.721171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1408.2.i.b.351.13		44
4.3	odd	2		1408.2.i.a.351.9		44
8.3	odd	2		704.2.i.a.175.13		44
8.5	even	2		176.2.i.a.131.8	yes	44
11.10	odd	2	inner	1408.2.i.b.351.14		44
16.3	odd	4		176.2.i.a.43.15	yes	44
16.5	even	4		1408.2.i.a.1055.10		44
16.11	odd	4	inner	1408.2.i.b.1055.14		44
16.13	even	4		704.2.i.a.527.13		44
44.43	even	2		1408.2.i.a.351.10		44
88.21	odd	2		176.2.i.a.131.15	yes	44
88.43	even	2		704.2.i.a.175.14		44
176.21	odd	4		1408.2.i.a.1055.9		44
176.43	even	4	inner	1408.2.i.b.1055.13		44
176.109	odd	4		704.2.i.a.527.14		44
176.131	even	4		176.2.i.a.43.8	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
176.2.i.a.43.8	✓	44	176.131	even	4
176.2.i.a.43.15	yes	44	16.3	odd	4
176.2.i.a.131.8	yes	44	8.5	even	2
176.2.i.a.131.15	yes	44	88.21	odd	2
704.2.i.a.175.13		44	8.3	odd	2
704.2.i.a.175.14		44	88.43	even	2
704.2.i.a.527.13		44	16.13	even	4
704.2.i.a.527.14		44	176.109	odd	4
1408.2.i.a.351.9		44	4.3	odd	2
1408.2.i.a.351.10		44	44.43	even	2
1408.2.i.a.1055.9		44	176.21	odd	4
1408.2.i.a.1055.10		44	16.5	even	4
1408.2.i.b.351.13		44	1.1	even	1	trivial
1408.2.i.b.351.14		44	11.10	odd	2	inner
1408.2.i.b.1055.13		44	176.43	even	4	inner
1408.2.i.b.1055.14		44	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1408.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} +3.48768i q^{7} +2.63045i q^{9} +O(q^{10})\)	\(q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} +3.48768i q^{7} +2.63045i q^{9} +(1.67289 - 2.86382i) q^{11} +(0.438991 - 0.438991i) q^{13} +0.604994i q^{15} -3.89861i q^{17} +(-0.685216 - 0.685216i) q^{19} +(1.49919 + 1.49919i) q^{21} +3.54310 q^{23} +4.00955i q^{25} +(2.42027 + 2.42027i) q^{27} +(-3.67594 + 3.67594i) q^{29} +8.85547i q^{31} +(-0.511925 - 1.95012i) q^{33} +(-2.45436 - 2.45436i) q^{35} +(-4.70899 + 4.70899i) q^{37} -0.377404i q^{39} -6.55941 q^{41} +(-4.01324 + 4.01324i) q^{43} +(-1.85110 - 1.85110i) q^{45} -5.68856i q^{47} -5.16393 q^{49} +(-1.67583 - 1.67583i) q^{51} +(-6.67821 + 6.67821i) q^{53} +(0.838081 + 3.19257i) q^{55} -0.589085 q^{57} +(10.5776 + 10.5776i) q^{59} +(-3.64241 + 3.64241i) q^{61} -9.17418 q^{63} +0.617854i q^{65} +(3.52675 - 3.52675i) q^{67} +(1.52302 - 1.52302i) q^{69} +6.71309 q^{71} +8.28094 q^{73} +(1.72352 + 1.72352i) q^{75} +(9.98808 + 5.83450i) q^{77} +8.89181 q^{79} -5.81063 q^{81} +(1.57109 + 1.57109i) q^{83} +(2.74353 + 2.74353i) q^{85} +3.16023i q^{87} +8.43118i q^{89} +(1.53106 + 1.53106i) q^{91} +(3.80655 + 3.80655i) q^{93} +0.964401 q^{95} -11.5768 q^{97} +(7.53313 + 4.40045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5	\( 44 q + 4 q^{3} + 4 q^{5} + 6 q^{11} - 24 q^{23} - 8 q^{27} - 4 q^{33} + 20 q^{37} - 28 q^{45} - 28 q^{49} - 12 q^{53} - 36 q^{55} + 20 q^{59} - 36 q^{67} + 16 q^{69} - 40 q^{71} - 60 q^{75} - 4 q^{77} - 20 q^{81} - 56 q^{91} - 8 q^{93} - 8 q^{97} + 42 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 + 6 * q^11 - 24 * q^23 - 8 * q^27 - 4 * q^33 + 20 * q^37 - 28 * q^45 - 28 * q^49 - 12 * q^53 - 36 * q^55 + 20 * q^59 - 36 * q^67 + 16 * q^69 - 40 * q^71 - 60 * q^75 - 4 * q^77 - 20 * q^81 - 56 * q^91 - 8 * q^93 - 8 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

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Database

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