LMFDB - Embedded newform 1408.2.i.b.351.14

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			351.14
Character	$\chi$	$=$	1408.351
Dual form			1408.2.i.b.1055.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} -3.48768i q^{7} +2.63045i q^{9} +O(q^{10})$	\(q+(0.429854 - 0.429854i) q^{3} +(-0.703721 + 0.703721i) q^{5} -3.48768i q^{7} +2.63045i q^{9} +(-2.86382 + 1.67289i) q^{11} +(-0.438991 + 0.438991i) q^{13} +0.604994i q^{15} +3.89861i q^{17} +(0.685216 + 0.685216i) q^{19} +(-1.49919 - 1.49919i) q^{21} +3.54310 q^{23} +4.00955i q^{25} +(2.42027 + 2.42027i) q^{27} +(3.67594 - 3.67594i) q^{29} +8.85547i q^{31} +(-0.511925 + 1.95012i) q^{33} +(2.45436 + 2.45436i) q^{35} +(-4.70899 + 4.70899i) q^{37} +0.377404i q^{39} +6.55941 q^{41} +(4.01324 - 4.01324i) q^{43} +(-1.85110 - 1.85110i) q^{45} -5.68856i q^{47} -5.16393 q^{49} +(1.67583 + 1.67583i) q^{51} +(-6.67821 + 6.67821i) q^{53} +(0.838081 - 3.19257i) q^{55} +0.589085 q^{57} +(10.5776 + 10.5776i) q^{59} +(3.64241 - 3.64241i) q^{61} +9.17418 q^{63} -0.617854i q^{65} +(3.52675 - 3.52675i) q^{67} +(1.52302 - 1.52302i) q^{69} +6.71309 q^{71} -8.28094 q^{73} +(1.72352 + 1.72352i) q^{75} +(5.83450 + 9.98808i) q^{77} -8.89181 q^{79} -5.81063 q^{81} +(-1.57109 - 1.57109i) q^{83} +(-2.74353 - 2.74353i) q^{85} -3.16023i q^{87} +8.43118i q^{89} +(1.53106 + 1.53106i) q^{91} +(3.80655 + 3.80655i) q^{93} -0.964401 q^{95} -11.5768 q^{97} +(-4.40045 - 7.53313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.770933\pi$
$7$		−	3.48768i		−	1.31822i	0.752047	−	0.659110i	$-0.229067\pi$
$8$		0			0
$9$			2.63045i			0.876817i
$10$		0			0
$11$	−2.86382	+	1.67289i	−0.863473	+	0.504395i
$11$	−2.86382	+	1.67289i	−0.863473	+	0.504395i
$12$		0			0
$13$	−0.438991	+	0.438991i	−0.121754	+	0.121754i	−0.765358	−	0.643604i	$-0.777438\pi$
$13$	−0.438991	+	0.438991i	−0.121754	+	0.121754i	0.643604	+	0.765358i	$0.277438\pi$
$14$		0			0
$15$			0.604994i			0.156209i
$16$		0			0
$17$			3.89861i			0.945552i	0.881183	+	0.472776i	$0.156748\pi$
$17$			3.89861i			0.945552i	−0.881183	+	0.472776i	$0.843252\pi$
$18$		0			0
$19$	0.685216	+	0.685216i	0.157199	+	0.157199i	0.781324	−	0.624125i	$-0.214544\pi$
$19$	0.685216	+	0.685216i	0.157199	+	0.157199i	−0.624125	+	0.781324i	$0.714544\pi$
$20$		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	−0.277982	−	0.960586i	$-0.589665\pi$
$29$	3.67594	−	3.67594i	0.682605	−	0.682605i	0.960586	+	0.277982i	$0.0896655\pi$
$30$		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	$-0.328829\pi$
$41$	6.55941			1.02441			0.512204	+	0.858864i	$0.328829\pi$
$42$		0			0
$43$	4.01324	−	4.01324i	0.612013	−	0.612013i	−0.331457	−	0.943470i	$-0.607540\pi$
$43$	4.01324	−	4.01324i	0.612013	−	0.612013i	0.943470	+	0.331457i	$0.107540\pi$
$44$		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	−0.434371	−	0.900734i	$-0.643029\pi$
$61$	3.64241	−	3.64241i	0.466363	−	0.466363i	0.900734	+	0.434371i	$0.143029\pi$
$62$		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	$-0.661037\pi$
$73$	−8.28094			−0.969211			−0.484605	+	0.874733i	$0.661037\pi$
$74$		0			0
$75$	1.72352	+	1.72352i	0.199015	+	0.199015i
$76$		0			0
$77$	5.83450	+	9.98808i	0.664903	+	1.13825i
$78$		0			0
$79$	−8.89181			−1.00041			−0.500203	−	0.865908i	$-0.666741\pi$
$79$	−8.89181			−1.00041			−0.500203	+	0.865908i	$0.666741\pi$
$80$		0			0
$81$	−5.81063			−0.645626
$82$		0			0
$83$	−1.57109	−	1.57109i	−0.172449	−	0.172449i	0.615605	−	0.788055i	$-0.288912\pi$
$83$	−1.57109	−	1.57109i	−0.172449	−	0.172449i	−0.788055	+	0.615605i	$0.788912\pi$
$84$		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
$99$	−4.40045	−	7.53313i	−0.442262	−	0.757108i
$100$		0			0
$101$	11.8302	+	11.8302i	1.17715	+	1.17715i	0.980467	+	0.196683i	$0.0630169\pi$
$101$	11.8302	+	11.8302i	1.17715	+	1.17715i	0.196683	+	0.980467i	$0.436983\pi$
$102$		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	−0.910874	−	0.412684i	$-0.864591\pi$
$107$	−5.15332	+	5.15332i	−0.498190	+	0.498190i	0.412684	+	0.910874i	$0.364591\pi$
$108$		0			0
$109$	−11.6593	+	11.6593i	−1.11676	+	1.11676i	−0.124545	+	0.992214i	$0.539747\pi$
$109$	−11.6593	+	11.6593i	−1.11676	+	1.11676i	−0.992214	+	0.124545i	$0.960253\pi$
$110$		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	$-0.549910\pi$
$127$	−3.51958			−0.312312			−0.156156	+	0.987732i	$0.549910\pi$
$128$		0			0
$129$		−	3.45021i		−	0.303774i
$130$		0			0
$131$	−5.50159	−	5.50159i	−0.480676	−	0.480676i	0.424672	−	0.905348i	$-0.360390\pi$
$131$	−5.50159	−	5.50159i	−0.480676	−	0.480676i	−0.905348	+	0.424672i	$0.860390\pi$
$132$		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	−0.105785	−	0.994389i	$-0.533735\pi$
$139$	10.4765	−	10.4765i	0.888605	−	0.888605i	0.994389	+	0.105785i	$0.0337354\pi$
$140$		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	0.847486	−	0.530818i	$-0.178115\pi$
$149$	3.86542	+	3.86542i	0.316667	+	0.316667i	−0.530818	+	0.847486i	$0.678115\pi$
$150$		0			0
$151$			17.9891i			1.46393i	0.681341	+	0.731966i	$0.261397\pi$
$151$			17.9891i			1.46393i	−0.681341	+	0.731966i	$0.738603\pi$
$152$		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
$165$	−1.01209	−	1.73259i	−0.0787909	−	0.134882i
$166$		0			0
$167$			10.4302i			0.807110i	0.914955	+	0.403555i	$0.132226\pi$
$167$			10.4302i			0.807110i	−0.914955	+	0.403555i	$0.867774\pi$
$168$		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	−0.540131	−	0.841581i	$-0.681625\pi$
$173$	3.96494	−	3.96494i	0.301449	−	0.301449i	0.841581	+	0.540131i	$0.181625\pi$
$174$		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
$187$	−6.52194	−	11.1649i	−0.476932	−	0.816459i
$188$		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	$-0.678289\pi$
$193$		−	23.5392i		−	1.69439i	0.531281	−	0.847195i	$-0.321711\pi$
$194$		0			0
$195$	−0.265587	−	0.265587i	−0.0190191	−	0.0190191i
$196$		0			0
$197$	−7.01740	−	7.01740i	−0.499969	−	0.499969i	0.411459	−	0.911428i	$-0.365019\pi$
$197$	−7.01740	−	7.01740i	−0.499969	−	0.499969i	−0.911428	+	0.411459i	$0.865019\pi$
$198$		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	0.960710	−	0.277554i	$-0.0895238\pi$
$211$	9.92341	+	9.92341i	0.683156	+	0.683156i	−0.277554	+	0.960710i	$0.589524\pi$
$212$		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	0.371803	−	0.928311i	$-0.378740\pi$
$227$	−8.38464	−	8.38464i	−0.556508	−	0.556508i	−0.928311	+	0.371803i	$0.878740\pi$
$228$		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	$-0.822193\pi$
$233$	−25.8883			−1.69600			−0.848000	+	0.529996i	$0.822193\pi$
$234$		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	$-0.450687\pi$
$239$	4.77090			0.308604			0.154302	+	0.988024i	$0.450687\pi$
$240$		0			0
$241$			17.0966i			1.10129i	0.834740	+	0.550645i	$0.185618\pi$
$241$			17.0966i			1.10129i	−0.834740	+	0.550645i	$0.814382\pi$
$242$		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
$253$	−10.1468	+	5.92722i	−0.637924	+	0.372641i
$254$		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	$-0.720592\pi$
$263$		−	24.9527i		−	1.53865i	0.638856	−	0.769326i	$-0.279408\pi$
$264$		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	$-0.859540\pi$
$271$	−29.7704			−1.80842			−0.904211	+	0.427086i	$0.859540\pi$
$272$		0			0
$273$	1.31626			0.0796640
$274$		0			0
$275$	−6.70754	−	11.4826i	−0.404480	−	0.692428i
$276$		0			0
$277$	−7.99051	−	7.99051i	−0.480103	−	0.480103i	0.425061	−	0.905164i	$-0.360252\pi$
$277$	−7.99051	−	7.99051i	−0.480103	−	0.480103i	−0.905164	+	0.425061i	$0.860252\pi$
$278$		0			0
$279$	−23.2939			−1.39457
$280$		0			0
$281$	10.4093			0.620970			0.310485	−	0.950578i	$-0.399509\pi$
$281$	10.4093			0.620970			0.310485	+	0.950578i	$0.399509\pi$
$282$		0			0
$283$	−13.8378	+	13.8378i	−0.822572	+	0.822572i	−0.986476	−	0.163904i	$-0.947591\pi$
$283$	−13.8378	+	13.8378i	−0.822572	+	0.822572i	0.163904	+	0.986476i	$0.447591\pi$
$284$		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	0.846713	−	0.532050i	$-0.178578\pi$
$293$	5.38617	+	5.38617i	0.314663	+	0.314663i	−0.532050	+	0.846713i	$0.678578\pi$
$294$		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	0.394376	−	0.918949i	$-0.370961\pi$
$307$	−9.19127	−	9.19127i	−0.524573	−	0.524573i	−0.918949	+	0.394376i	$0.870961\pi$
$308$		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	$0.180299\pi$
$337$			19.7020i			1.07324i	−0.843825	+	0.536618i	$0.819701\pi$
$338$		0			0
$339$	5.70620	−	5.70620i	0.309918	−	0.309918i
$340$		0			0
$341$	−14.8142	−	25.3604i	−0.802234	−	1.37334i
$342$		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	−0.720391	−	0.693568i	$-0.756038\pi$
$347$	−0.499662	+	0.499662i	−0.0268233	+	0.0268233i	0.693568	+	0.720391i	$0.256038\pi$
$348$		0			0
$349$	11.4338	−	11.4338i	0.612037	−	0.612037i	−0.331439	−	0.943477i	$-0.607534\pi$
$349$	11.4338	−	11.4338i	0.612037	−	0.612037i	0.943477	+	0.331439i	$0.107534\pi$
$350$		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	$-0.914605\pi$
$359$		−	10.0447i		−	0.530139i	0.964229	−	0.265069i	$-0.0853949\pi$
$360$		0			0
$361$		−	18.0610i		−	0.950577i
$362$		0			0
$363$	−1.79628	−	6.44118i	−0.0942800	−	0.338074i
$364$		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	0.194967	−	0.980810i	$-0.437540\pi$
$373$	−15.1771	−	15.1771i	−0.785842	−	0.785842i	−0.980810	+	0.194967i	$0.937540\pi$
$374$		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	$-0.256009\pi$
$409$	28.0557			1.38726			0.693632	+	0.720329i	$0.256009\pi$
$410$		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
$429$	−0.631355	−	1.08082i	−0.0304821	−	0.0521822i
$430$		0			0
$431$	14.1018			0.679261			0.339630	−	0.940559i	$-0.389698\pi$
$431$	14.1018			0.679261			0.339630	+	0.940559i	$0.389698\pi$
$432$		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	$-0.985920\pi$
$439$		−	1.85297i		−	0.0884376i	0.999022	−	0.0442188i	$-0.0140799\pi$
$440$		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
$451$	−18.7849	+	10.9732i	−0.884548	+	0.516706i
$452$		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	$-0.350027\pi$
$457$	19.4072			0.907830			0.453915	+	0.891045i	$0.350027\pi$
$458$		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	$0.652794\pi$
$461$	−28.9596	+	28.9596i	−1.34878	+	1.34878i	−0.886987	+	0.461794i	$0.847206\pi$
$462$		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	$-0.498373\pi$
$479$	0.223784			0.0102250			0.00511248	+	0.999987i	$0.498373\pi$
$480$		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	−0.855658	−	0.517541i	$-0.826848\pi$
$491$	−7.49218	+	7.49218i	−0.338118	+	0.338118i	0.517541	+	0.855658i	$0.326848\pi$
$492$		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	$0.145003\pi$
$503$			19.7340i			0.879898i	−0.898023	+	0.439949i	$0.854997\pi$
$504$		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
$517$	9.51632	+	16.2910i	0.418527	+	0.716476i
$518$		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	−0.885035	−	0.465524i	$-0.845866\pi$
$523$	−9.59389	+	9.59389i	−0.419511	+	0.419511i	0.465524	+	0.885035i	$0.345866\pi$
$524$		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
$539$	14.7885	−	8.63867i	0.636987	−	0.372094i
$540$		0			0
$541$	−24.0872	+	24.0872i	−1.03559	+	1.03559i	−0.0362451	+	0.999343i	$0.511540\pi$
$541$	−24.0872	+	24.0872i	−1.03559	+	1.03559i	−0.999343	+	0.0362451i	$0.988460\pi$
$542$		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	0.883685	−	0.468082i	$-0.155055\pi$
$547$	9.72015	+	9.72015i	0.415604	+	0.415604i	−0.468082	+	0.883685i	$0.655055\pi$
$548$		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	−0.925680	−	0.378308i	$-0.876506\pi$
$557$	−12.9184	+	12.9184i	−0.547371	+	0.547371i	0.378308	+	0.925680i	$0.376506\pi$
$558$		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	0.0757213	−	0.997129i	$-0.475874\pi$
$563$	−21.8628	−	21.8628i	−0.921408	−	0.921408i	−0.997129	+	0.0757213i	$0.975874\pi$
$564$		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	$-0.178197\pi$
$569$	40.4249			1.69470			0.847350	+	0.531035i	$0.178197\pi$
$570$		0			0
$571$	25.0630	−	25.0630i	1.04886	−	1.04886i	0.0501119	−	0.998744i	$-0.484042\pi$
$571$	25.0630	−	25.0630i	1.04886	−	1.04886i	0.998744	−	0.0501119i	$-0.0159578\pi$
$572$		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	$0.202092\pi$
$593$			28.8853i			1.18618i	−0.805137	+	0.593090i	$0.797908\pi$
$594$		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	$-0.536583\pi$
$601$	−5.62269			−0.229354			−0.114677	+	0.993403i	$0.536583\pi$
$602$		0			0
$603$	9.27696	+	9.27696i	0.377787	+	0.377787i
$604$		0			0
$605$	2.94071	+	10.5450i	0.119557	+	0.428714i
$606$		0			0
$607$	5.82970			0.236620			0.118310	−	0.992977i	$-0.462252\pi$
$607$	5.82970			0.236620			0.118310	+	0.992977i	$0.462252\pi$
$608$		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	$0.0549121\pi$
$613$	28.6414	+	28.6414i	1.15681	+	1.15681i	0.171657	+	0.985157i	$0.445088\pi$
$614$		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
$627$	−1.68703	+	0.985474i	−0.0673735	+	0.0393560i
$628$		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	0.261405	−	0.965229i	$-0.415814\pi$
$659$	−18.0679	−	18.0679i	−0.703824	−	0.703824i	−0.965229	+	0.261405i	$0.915814\pi$
$660$		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	$-0.986510\pi$
$673$		−	2.19817i		−	0.0847331i	0.999102	−	0.0423666i	$-0.0134897\pi$
$674$		0			0
$675$	−9.70420	+	9.70420i	−0.373515	+	0.373515i
$676$		0			0
$677$	11.3920	+	11.3920i	0.437830	+	0.437830i	0.891281	−	0.453451i	$-0.149807\pi$
$677$	11.3920	+	11.3920i	0.437830	+	0.437830i	−0.453451	+	0.891281i	$0.649807\pi$
$678$		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
$693$	−26.2732	+	15.3474i	−0.998035	+	0.582999i
$694$		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	$-0.489986\pi$
$701$	27.2961	−	27.2961i	1.03096	−	1.03096i	0.999505	−	0.0314550i	$-0.0100141\pi$
$702$		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
$715$	1.03360	+	1.76942i	0.0386545	+	0.0661726i
$716$		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	−0.536725	−	0.843757i	$-0.680339\pi$
$733$	8.31257	−	8.31257i	0.307032	−	0.307032i	0.843757	+	0.536725i	$0.180339\pi$
$734$		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	0.513366	−	0.858170i	$-0.328398\pi$
$739$	−9.37332	−	9.37332i	−0.344803	−	0.344803i	−0.858170	+	0.513366i	$0.828398\pi$
$740$		0			0
$741$	−0.258603	+	0.258603i	−0.00950002	+	0.00950002i
$742$		0			0
$743$			49.4798i			1.81524i	0.419795	+	0.907619i	$0.362102\pi$
$743$			49.4798i			1.81524i	−0.419795	+	0.907619i	$0.637898\pi$
$744$		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	$-0.298371\pi$
$761$	32.6575			1.18384			0.591918	+	0.805998i	$0.298371\pi$
$762$		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	$-0.748106\pi$
$769$		−	39.4500i		−	1.42260i	0.702888	−	0.711301i	$-0.251894\pi$
$770$		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
$781$	−19.2251	+	11.2303i	−0.687927	+	0.401850i
$782$		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	0.994648	−	0.103322i	$-0.0329472\pi$
$787$	25.0048	+	25.0048i	0.891326	+	0.891326i	−0.103322	+	0.994648i	$0.532947\pi$
$788$		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
$803$	23.7151	−	13.8531i	0.836887	−	0.488865i
$804$		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	$-0.236273\pi$
$809$	41.9211			1.47387			0.736933	+	0.675966i	$0.236273\pi$
$810$		0			0
$811$	24.2516	−	24.2516i	0.851587	−	0.851587i	−0.138741	−	0.990329i	$-0.544306\pi$
$811$	24.2516	−	24.2516i	0.851587	−	0.851587i	0.990329	+	0.138741i	$0.0443057\pi$
$812$		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	0.467246	−	0.884128i	$-0.345246\pi$
$821$	−11.9450	−	11.9450i	−0.416882	−	0.416882i	−0.884128	+	0.467246i	$0.845246\pi$
$822$		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	−0.883943	−	0.467594i	$-0.845121\pi$
$827$	−11.9732	+	11.9732i	−0.416349	+	0.416349i	0.467594	+	0.883943i	$0.345121\pi$
$828$		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	$0.0259123\pi$
$853$	31.4844	+	31.4844i	1.07800	+	1.07800i	0.0813161	+	0.996688i	$0.474088\pi$
$854$		0			0
$855$		−	2.53681i		−	0.0867571i
$856$		0			0
$857$	−25.1124			−0.857824			−0.428912	−	0.903346i	$-0.641103\pi$
$857$	−25.1124			−0.857824			−0.428912	+	0.903346i	$0.641103\pi$
$858$		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
$869$	25.4645	−	14.8750i	0.863824	−	0.504600i
$870$		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	$-0.450667\pi$
$877$	33.8306	−	33.8306i	1.14238	−	1.14238i	0.988014	−	0.154363i	$-0.0493325\pi$
$878$		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	$-0.991297\pi$
$887$		−	1.62841i		−	0.0546766i	0.999626	−	0.0273383i	$-0.00870314\pi$
$888$		0			0
$889$			12.2752i			0.411696i
$890$		0			0
$891$	16.6406	−	9.72054i	0.557480	−	0.325650i
$892$		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	$-0.818500\pi$
$919$		−	32.7281i		−	1.07960i	0.841793	−	0.539800i	$-0.181500\pi$
$920$		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	$-0.551753\pi$
$937$	−9.90997			−0.323745			−0.161872	+	0.986812i	$0.551753\pi$
$938$		0			0
$939$	−12.4843	−	12.4843i	−0.407409	−	0.407409i
$940$		0			0
$941$	−18.8730	+	18.8730i	−0.615242	+	0.615242i	−0.944307	−	0.329065i	$-0.893267\pi$
$941$	−18.8730	+	18.8730i	−0.615242	+	0.615242i	0.329065	+	0.944307i	$0.393267\pi$
$942$		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	$-0.464813\pi$
$953$	6.81124			0.220638			0.110319	+	0.993896i	$0.464813\pi$
$954$		0			0
$955$	8.69779	+	8.69779i	0.281454	+	0.281454i
$956$		0			0
$957$	5.28671	+	9.05032i	0.170895	+	0.292555i
$958$		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	$-0.724321\pi$
$967$		−	47.3782i		−	1.52358i	0.647824	−	0.761790i	$-0.275679\pi$
$968$		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
$979$	−14.1044	−	24.1453i	−0.450779	−	0.771688i
$980$		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	0.0974530	−	0.995240i	$-0.468930\pi$
$997$	−28.3479	−	28.3479i	−0.897787	−	0.897787i	−0.995240	+	0.0974530i	$0.968930\pi$
$998$		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.351.14		44
4.3	odd	2		1408.2.i.a.351.10		44
8.3	odd	2		704.2.i.a.175.14		44
8.5	even	2		176.2.i.a.131.15	yes	44
11.10	odd	2	inner	1408.2.i.b.351.13		44
16.3	odd	4		176.2.i.a.43.8	✓	44
16.5	even	4		1408.2.i.a.1055.9		44
16.11	odd	4	inner	1408.2.i.b.1055.13		44
16.13	even	4		704.2.i.a.527.14		44
44.43	even	2		1408.2.i.a.351.9		44
88.21	odd	2		176.2.i.a.131.8	yes	44
88.43	even	2		704.2.i.a.175.13		44
176.21	odd	4		1408.2.i.a.1055.10		44
176.43	even	4	inner	1408.2.i.b.1055.14		44
176.109	odd	4		704.2.i.a.527.13		44
176.131	even	4		176.2.i.a.43.15	yes	44

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

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

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