LMFDB - Embedded newform 2548.2.y.f.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(753,2548)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2548, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2548.753");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.11348687176217973595570176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16x^{14} + 176x^{12} - 1016x^{10} + 4224x^{8} - 8512x^{6} + 12304x^{4} - 8448x^{2} + 4096 $ x^16 - 16x^14 + 176x^12 - 1016x^10 + 4224x^8 - 8512x^6 + 12304x^4 - 8448*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			961.2
Root			$-2.40000 - 1.38564i$ of defining polynomial
Character	$\chi$	$=$	2548.961
Dual form			2548.2.y.f.753.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38564 - 2.40000i) q^{3} +(2.01603 + 1.16396i) q^{5} +(-2.34001 + 4.05302i) q^{9} +(-0.786990 + 0.454369i) q^{11} +(-1.32791 + 3.35211i) q^{13} -6.45131i q^{15} +(-0.966468 - 1.67397i) q^{17} +(3.62904 + 2.09523i) q^{19} +(0.709587 - 1.22904i) q^{23} +(0.209587 + 0.363016i) q^{25} +4.65582 q^{27} -7.75502 q^{29} +(3.35194 - 1.93524i) q^{31} +(2.18097 + 1.25919i) q^{33} +(-10.3870 - 5.99694i) q^{37} +(9.88509 - 1.45784i) q^{39} -6.19839i q^{41} -6.91667 q^{43} +(-9.43507 + 5.44734i) q^{45} +(-2.74494 - 1.58479i) q^{47} +(-2.67836 + 4.63906i) q^{51} +(-5.38961 - 9.33508i) q^{53} -2.11546 q^{55} -11.6130i q^{57} +(4.30917 - 2.48790i) q^{59} +(0.0241992 - 0.0419143i) q^{61} +(-6.57882 + 5.21233i) q^{65} +(3.26412 - 1.88454i) q^{67} -3.93294 q^{69} -15.3381i q^{71} +(-6.20904 + 3.58479i) q^{73} +(0.580826 - 1.00602i) q^{75} +(8.67300 - 15.0221i) q^{79} +(0.568726 + 0.985063i) q^{81} +12.1173i q^{83} -4.49971i q^{85} +(10.7457 + 18.6121i) q^{87} +(-10.2030 - 5.89071i) q^{89} +(-9.28917 - 5.36311i) q^{93} +(4.87751 + 8.44810i) q^{95} -6.37298i q^{97} -4.25291i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} + 4 q^{13} - 4 q^{17} + 6 q^{23} - 2 q^{25} + 24 q^{27} - 4 q^{29} - 12 q^{43} + 8 q^{51} - 22 q^{53} - 40 q^{55} - 8 q^{61} + 6 q^{65} - 40 q^{69} + 20 q^{75} + 26 q^{79} + 24 q^{81} + 32 q^{87}+ \cdots + 18 q^{95}+O(q^{100}) $ 16 * q - 8 * q^9 + 4 * q^13 - 4 * q^17 + 6 * q^23 - 2 * q^25 + 24 * q^27 - 4 * q^29 - 12 * q^43 + 8 * q^51 - 22 * q^53 - 40 * q^55 - 8 * q^61 + 6 * q^65 - 40 * q^69 + 20 * q^75 + 26 * q^79 + 24 * q^81 + 32 * q^87 + 18 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.38564	−	2.40000i	−0.800001	−	1.38564i	−0.919614	−	0.392822i	$-0.871499\pi$
$3$	−1.38564	−	2.40000i	−0.800001	−	1.38564i	0.119613	−	0.992821i	$-0.461835\pi$
$4$		0			0
$5$	2.01603	+	1.16396i	0.901596	+	0.520537i	0.877718	−	0.479178i	$-0.159065\pi$
$5$	2.01603	+	1.16396i	0.901596	+	0.520537i	0.0238786	+	0.999715i	$0.492398\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.34001	+	4.05302i	−0.780004	+	1.35101i
$10$		0			0
$11$	−0.786990	+	0.454369i	−0.237286	+	0.136997i	−0.613929	−	0.789361i	$-0.710412\pi$
$11$	−0.786990	+	0.454369i	−0.237286	+	0.136997i	0.376643	+	0.926359i	$0.377079\pi$
$12$		0			0
$13$	−1.32791	+	3.35211i	−0.368297	+	0.929708i
$13$	−1.32791	+	3.35211i	−0.368297	+	0.929708i
$14$		0			0
$15$		−	6.45131i		−	1.66572i
$16$		0			0
$17$	−0.966468	−	1.67397i	−0.234403	−	0.405998i	0.724696	−	0.689069i	$-0.241980\pi$
$17$	−0.966468	−	1.67397i	−0.234403	−	0.405998i	−0.959099	+	0.283071i	$0.908647\pi$
$18$		0			0
$19$	3.62904	+	2.09523i	0.832560	+	0.480679i	0.854728	−	0.519076i	$-0.173724\pi$
$19$	3.62904	+	2.09523i	0.832560	+	0.480679i	−0.0221684	+	0.999754i	$0.507057\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.709587	−	1.22904i	0.147959	−	0.256273i	−0.782514	−	0.622633i	$-0.786063\pi$
$23$	0.709587	−	1.22904i	0.147959	−	0.256273i	0.930473	+	0.366360i	$0.119396\pi$
$24$		0			0
$25$	0.209587	+	0.363016i	0.0419174	+	0.0726031i
$26$		0			0
$27$	4.65582			0.896014
$28$		0			0
$29$	−7.75502			−1.44007			−0.720036	−	0.693937i	$-0.755875\pi$
$29$	−7.75502			−1.44007			−0.720036	+	0.693937i	$0.755875\pi$
$30$		0			0
$31$	3.35194	−	1.93524i	0.602026	−	0.347580i	−0.167812	−	0.985819i	$-0.553670\pi$
$31$	3.35194	−	1.93524i	0.602026	−	0.347580i	0.769838	+	0.638239i	$0.220337\pi$
$32$		0			0
$33$	2.18097	+	1.25919i	0.379659	+	0.219196i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−10.3870	−	5.99694i	−1.70761	−	0.985891i	−0.937501	−	0.347982i	$-0.886867\pi$
$37$	−10.3870	−	5.99694i	−1.70761	−	0.985891i	−0.770112	−	0.637909i	$-0.779800\pi$
$38$		0			0
$39$	9.88509	−	1.45784i	1.58288	−	0.233440i
$40$		0			0
$41$		−	6.19839i		−	0.968027i	−0.875061	−	0.484013i	$-0.839179\pi$
$41$		−	6.19839i		−	0.968027i	0.875061	−	0.484013i	$-0.160821\pi$
$42$		0			0
$43$	−6.91667			−1.05478			−0.527391	−	0.849622i	$-0.676830\pi$
$43$	−6.91667			−1.05478			−0.527391	+	0.849622i	$0.676830\pi$
$44$		0			0
$45$	−9.43507	+	5.44734i	−1.40650	+	0.812042i
$46$		0			0
$47$	−2.74494	−	1.58479i	−0.400391	−	0.231166i	0.286262	−	0.958151i	$-0.407587\pi$
$47$	−2.74494	−	1.58479i	−0.400391	−	0.231166i	−0.686653	+	0.726986i	$0.740921\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.67836	+	4.63906i	−0.375045	+	0.649598i
$52$		0			0
$53$	−5.38961	−	9.33508i	−0.740320	−	1.28227i	−0.952350	−	0.305008i	$-0.901341\pi$
$53$	−5.38961	−	9.33508i	−0.740320	−	1.28227i	0.212030	−	0.977263i	$-0.431993\pi$
$54$		0			0
$55$	−2.11546			−0.285249
$56$		0			0
$57$		−	11.6130i		−	1.53817i
$58$		0			0
$59$	4.30917	−	2.48790i	0.561006	−	0.323897i	−0.192543	−	0.981289i	$-0.561674\pi$
$59$	4.30917	−	2.48790i	0.561006	−	0.323897i	0.753549	+	0.657391i	$0.228340\pi$
$60$		0			0
$61$	0.0241992	−	0.0419143i	0.00309840	−	0.00536658i	−0.864472	−	0.502681i	$-0.832347\pi$
$61$	0.0241992	−	0.0419143i	0.00309840	−	0.00536658i	0.867570	+	0.497314i	$0.165680\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.57882	+	5.21233i	−0.816002	+	0.646510i
$66$		0			0
$67$	3.26412	−	1.88454i	0.398775	−	0.230233i	−0.287180	−	0.957877i	$-0.592718\pi$
$67$	3.26412	−	1.88454i	0.398775	−	0.230233i	0.685955	+	0.727644i	$0.259384\pi$
$68$		0			0
$69$	−3.93294			−0.473470
$70$		0			0
$71$		−	15.3381i		−	1.82029i	−0.414287	−	0.910146i	$-0.635969\pi$
$71$		−	15.3381i		−	1.82029i	0.414287	−	0.910146i	$-0.364031\pi$
$72$		0			0
$73$	−6.20904	+	3.58479i	−0.726714	+	0.419568i	−0.817219	−	0.576328i	$-0.804485\pi$
$73$	−6.20904	+	3.58479i	−0.726714	+	0.419568i	0.0905050	+	0.995896i	$0.471152\pi$
$74$		0			0
$75$	0.580826	−	1.00602i	0.0670680	−	0.116165i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.67300	−	15.0221i	0.975788	−	1.69011i	0.298479	−	0.954416i	$-0.403521\pi$
$79$	8.67300	−	15.0221i	0.975788	−	1.69011i	0.677309	−	0.735699i	$-0.263146\pi$
$80$		0			0
$81$	0.568726	+	0.985063i	0.0631918	+	0.109451i
$82$		0			0
$83$			12.1173i			1.33004i	0.746824	+	0.665022i	$0.231578\pi$
$83$			12.1173i			1.33004i	−0.746824	+	0.665022i	$0.768422\pi$
$84$		0			0
$85$		−	4.49971i		−	0.488062i
$86$		0			0
$87$	10.7457	+	18.6121i	1.15206	+	1.99542i
$88$		0			0
$89$	−10.2030	−	5.89071i	−1.08152	−	0.624414i	−0.150212	−	0.988654i	$-0.547996\pi$
$89$	−10.2030	−	5.89071i	−1.08152	−	0.624414i	−0.931305	+	0.364239i	$0.881329\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.28917	−	5.36311i	−0.963242	−	0.556128i
$94$		0			0
$95$	4.87751	+	8.44810i	0.500422	+	0.866756i
$96$		0			0
$97$		−	6.37298i		−	0.647079i	−0.946215	−	0.323539i	$-0.895127\pi$
$97$		−	6.37298i		−	0.647079i	0.946215	−	0.323539i	$-0.104873\pi$
$98$		0			0
$99$		−	4.25291i		−	0.427434i
$100$		0			0
$101$	−3.80482	−	6.59014i	−0.378593	−	0.655743i	0.612264	−	0.790653i	$-0.290259\pi$
$101$	−3.80482	−	6.59014i	−0.378593	−	0.655743i	−0.990858	+	0.134910i	$0.956925\pi$
$102$		0			0
$103$	1.86255	−	3.22603i	0.183522	−	0.317870i	−0.759555	−	0.650443i	$-0.774583\pi$
$103$	1.86255	−	3.22603i	0.183522	−	0.317870i	0.943078	+	0.332573i	$0.107917\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.47384	−	7.74893i	0.432503	−	0.749117i	−0.564585	−	0.825375i	$-0.690964\pi$
$107$	4.47384	−	7.74893i	0.432503	−	0.749117i	0.997088	+	0.0762578i	$0.0242972\pi$
$108$		0			0
$109$	0.232774	−	0.134392i	0.0222957	−	0.0128724i	−0.488811	−	0.872390i	$-0.662569\pi$
$109$	0.232774	−	0.134392i	0.0222957	−	0.0128724i	0.511106	+	0.859517i	$0.329236\pi$
$110$		0			0
$111$			33.2385i			3.15486i
$112$		0			0
$113$	12.1718			1.14503			0.572513	−	0.819896i	$-0.305969\pi$
$113$	12.1718			1.14503			0.572513	+	0.819896i	$0.305969\pi$
$114$		0			0
$115$	2.86110	−	1.65186i	0.266799	−	0.154036i
$116$		0			0
$117$	−10.4788	−	13.2260i	−0.968769	−	1.22275i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.08710	+	8.81111i	−0.462463	+	0.801010i
$122$		0			0
$123$	−14.8762	+	8.58876i	−1.34134	+	0.774422i
$124$		0			0
$125$		−	10.6638i		−	0.953796i
$126$		0			0
$127$	−11.1742			−0.991550			−0.495775	−	0.868451i	$-0.665116\pi$
$127$	−11.1742			−0.991550			−0.495775	+	0.868451i	$0.665116\pi$
$128$		0			0
$129$	9.58404	+	16.6000i	0.843827	+	1.46155i
$130$		0			0
$131$	−0.771285	+	1.33591i	−0.0673875	+	0.116719i	−0.897751	−	0.440504i	$-0.854800\pi$
$131$	−0.771285	+	1.33591i	−0.0673875	+	0.116719i	0.830363	+	0.557223i	$0.188133\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	9.38629	+	5.41917i	0.807843	+	0.466408i
$136$		0			0
$137$	−13.2131	+	7.62856i	−1.12887	+	0.651752i	−0.943650	−	0.330945i	$-0.892632\pi$
$137$	−13.2131	+	7.62856i	−1.12887	+	0.651752i	−0.185218	+	0.982697i	$0.559299\pi$
$138$		0			0
$139$	9.49138			0.805048			0.402524	−	0.915409i	$-0.368133\pi$
$139$	9.49138			0.805048			0.402524	+	0.915409i	$0.368133\pi$
$140$		0			0
$141$			8.78383i			0.739732i
$142$		0			0
$143$	−0.478042	−	3.24144i	−0.0399758	−	0.271063i
$144$		0			0
$145$	−15.6344	−	9.02650i	−1.29836	−	0.749610i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	16.5473	+	9.55357i	1.35560	+	0.782659i	0.989028	−	0.147729i	$-0.0471964\pi$
$149$	16.5473	+	9.55357i	1.35560	+	0.782659i	0.366577	+	0.930388i	$0.380530\pi$
$150$		0			0
$151$	−15.6251	+	9.02114i	−1.27155	+	0.734130i	−0.975280	−	0.220974i	$-0.929076\pi$
$151$	−15.6251	+	9.02114i	−1.27155	+	0.734130i	−0.296271	+	0.955104i	$0.595743\pi$
$152$		0			0
$153$	9.04619			0.731341
$154$		0			0
$155$	9.01014			0.723712
$156$		0			0
$157$	8.85894	+	15.3441i	0.707021	+	1.22460i	0.965957	+	0.258701i	$0.0832945\pi$
$157$	8.85894	+	15.3441i	0.707021	+	1.22460i	−0.258937	+	0.965894i	$0.583372\pi$
$158$		0			0
$159$	−14.9361	+	25.8702i	−1.18451	+	2.05164i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.992276	−	0.572891i	−0.0777210	−	0.0448722i	0.460636	−	0.887589i	$-0.347621\pi$
$163$	−0.992276	−	0.572891i	−0.0777210	−	0.0448722i	−0.538357	+	0.842717i	$0.680955\pi$
$164$		0			0
$165$	2.93127	+	5.07712i	0.228199	+	0.395253i
$166$		0			0
$167$			1.10532i			0.0855321i	0.999085	+	0.0427660i	$0.0136170\pi$
$167$			1.10532i			0.0855321i	−0.999085	+	0.0427660i	$0.986383\pi$
$168$		0			0
$169$	−9.47330	−	8.90262i	−0.728715	−	0.684817i
$170$		0			0
$171$	−16.9840	+	9.80572i	−1.29880	+	0.749862i
$172$		0			0
$173$	−9.30232	+	16.1121i	−0.707242	+	1.22498i	0.258634	+	0.965975i	$0.416728\pi$
$173$	−9.30232	+	16.1121i	−0.707242	+	1.22498i	−0.965876	+	0.259004i	$0.916606\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.9419	−	6.89468i	−0.897611	−	0.518236i
$178$		0			0
$179$	−4.22169	−	7.31218i	−0.315544	−	0.546538i	0.664009	−	0.747724i	$-0.268854\pi$
$179$	−4.22169	−	7.31218i	−0.315544	−	0.546538i	−0.979553	+	0.201187i	$0.935520\pi$
$180$		0			0
$181$	19.3506			1.43832			0.719159	−	0.694845i	$-0.244527\pi$
$181$	19.3506			1.43832			0.719159	+	0.694845i	$0.244527\pi$
$182$		0			0
$183$	−0.134126			−0.00991488
$184$		0			0
$185$	−13.9603	−	24.1800i	−1.02639	−	1.77775i
$186$		0			0
$187$	1.52120	+	0.878266i	0.111241	+	0.0642252i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.81802	+	10.0771i	−0.420977	+	0.729154i	−0.996035	−	0.0889586i	$-0.971646\pi$
$191$	−5.81802	+	10.0771i	−0.420977	+	0.729154i	0.575058	+	0.818113i	$0.304979\pi$
$192$		0			0
$193$	−14.5543	+	8.40291i	−1.04764	+	0.604855i	−0.921987	−	0.387220i	$-0.873435\pi$
$193$	−14.5543	+	8.40291i	−1.04764	+	0.604855i	−0.125652	+	0.992074i	$0.540102\pi$
$194$		0			0
$195$	21.6255	+	8.56677i	1.54863	+	0.613479i
$196$		0			0
$197$			6.56344i			0.467626i	0.972282	+	0.233813i	$0.0751204\pi$
$197$			6.56344i			0.467626i	−0.972282	+	0.233813i	$0.924880\pi$
$198$		0			0
$199$	−13.0736	−	22.6441i	−0.926763	−	1.60520i	−0.788701	−	0.614777i	$-0.789246\pi$
$199$	−13.0736	−	22.6441i	−0.926763	−	1.60520i	−0.138062	−	0.990424i	$-0.544087\pi$
$200$		0			0
$201$	−9.04580	−	5.22259i	−0.638041	−	0.368373i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	7.21466	−	12.4962i	0.503894	−	0.872769i
$206$		0			0
$207$	3.32088	+	5.75194i	0.230817	+	0.399787i
$208$		0			0
$209$	−3.80803			−0.263407
$210$		0			0
$211$	1.82820			0.125859			0.0629294	−	0.998018i	$-0.479956\pi$
$211$	1.82820			0.125859			0.0629294	+	0.998018i	$0.479956\pi$
$212$		0			0
$213$	−36.8114	+	21.2531i	−2.52227	+	1.45624i
$214$		0			0
$215$	−13.9442	−	8.05070i	−0.950988	−	0.549053i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	17.2070	+	9.93449i	1.16274	+	0.671310i
$220$		0			0
$221$	6.89473	−	1.01682i	0.463790	−	0.0683988i
$222$		0			0
$223$			8.98815i			0.601891i	0.953641	+	0.300946i	$0.0973023\pi$
$223$			8.98815i			0.601891i	−0.953641	+	0.300946i	$0.902698\pi$
$224$		0			0
$225$	−1.96175			−0.130783
$226$		0			0
$227$	9.04580	−	5.22259i	0.600391	−	0.346636i	−0.168805	−	0.985650i	$-0.553991\pi$
$227$	9.04580	−	5.22259i	0.600391	−	0.346636i	0.769195	+	0.639014i	$0.220657\pi$
$228$		0			0
$229$	−17.6251	−	10.1759i	−1.16470	−	0.672440i	−0.212274	−	0.977210i	$-0.568087\pi$
$229$	−17.6251	−	10.1759i	−1.16470	−	0.672440i	−0.952426	+	0.304771i	$0.901420\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.3310	+	19.6259i	−0.742320	+	1.28574i	0.209116	+	0.977891i	$0.432941\pi$
$233$	−11.3310	+	19.6259i	−0.742320	+	1.28574i	−0.951436	+	0.307846i	$0.900392\pi$
$234$		0			0
$235$	−3.68926	−	6.38998i	−0.240661	−	0.416837i
$236$		0			0
$237$	−48.0707			−3.12253
$238$		0			0
$239$		−	20.0159i		−	1.29472i	−0.762185	−	0.647360i	$-0.775873\pi$
$239$		−	20.0159i		−	1.29472i	0.762185	−	0.647360i	$-0.224127\pi$
$240$		0			0
$241$	18.9122	−	10.9190i	1.21824	−	0.703353i	0.253701	−	0.967283i	$-0.418352\pi$
$241$	18.9122	−	10.9190i	1.21824	−	0.703353i	0.964542	+	0.263929i	$0.0850186\pi$
$242$		0			0
$243$	8.55984	−	14.8261i	0.549114	−	0.951093i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.8425	+	9.38268i	−0.753520	+	0.597006i
$248$		0			0
$249$	29.0815	−	16.7902i	1.84297	−	1.06404i
$250$		0			0
$251$	−10.7713			−0.679878			−0.339939	−	0.940448i	$-0.610406\pi$
$251$	−10.7713			−0.679878			−0.339939	+	0.940448i	$0.610406\pi$
$252$		0			0
$253$			1.28966i			0.0810801i
$254$		0			0
$255$	−10.7993	+	6.23499i	−0.676279	+	0.390450i
$256$		0			0
$257$	−8.65443	+	14.9899i	−0.539848	+	0.935045i	0.459063	+	0.888404i	$0.348185\pi$
$257$	−8.65443	+	14.9899i	−0.539848	+	0.935045i	−0.998912	+	0.0466412i	$0.985148\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	18.1468	−	31.4312i	1.12326	−	1.94555i
$262$		0			0
$263$	2.68705	+	4.65411i	0.165691	+	0.286985i	0.936900	−	0.349597i	$-0.113681\pi$
$263$	2.68705	+	4.65411i	0.165691	+	0.286985i	−0.771210	+	0.636581i	$0.780348\pi$
$264$		0			0
$265$		−	25.0931i		−	1.54146i
$266$		0			0
$267$			32.6497i			1.99813i
$268$		0			0
$269$	8.54257	+	14.7962i	0.520850	+	0.902138i	0.999706	+	0.0242449i	$0.00771816\pi$
$269$	8.54257	+	14.7962i	0.520850	+	0.902138i	−0.478856	+	0.877893i	$0.658949\pi$
$270$		0			0
$271$	15.9740	+	9.22259i	0.970351	+	0.560233i	0.899343	−	0.437243i	$-0.144045\pi$
$271$	15.9740	+	9.22259i	0.970351	+	0.560233i	0.0710081	+	0.997476i	$0.477378\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.329886	−	0.190460i	−0.0198929	−	0.0114852i
$276$		0			0
$277$	4.17882	+	7.23793i	0.251081	+	0.434885i	0.963824	−	0.266540i	$-0.0858806\pi$
$277$	4.17882	+	7.23793i	0.251081	+	0.434885i	−0.712743	+	0.701426i	$0.752547\pi$
$278$		0			0
$279$			18.1140i			1.08445i
$280$		0			0
$281$		−	9.28966i		−	0.554174i	−0.960845	−	0.277087i	$-0.910631\pi$
$281$		−	9.28966i		−	0.554174i	0.960845	−	0.277087i	$-0.0893691\pi$
$282$		0			0
$283$	−0.957136	−	1.65781i	−0.0568958	−	0.0985465i	0.836175	−	0.548463i	$-0.184787\pi$
$283$	−0.957136	−	1.65781i	−0.0568958	−	0.0985465i	−0.893070	+	0.449917i	$0.851454\pi$
$284$		0			0
$285$	13.5170	−	23.4121i	0.800676	−	1.38681i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.63188	−	11.4867i	0.390110	−	0.675691i
$290$		0			0
$291$	−15.2952	+	8.83068i	−0.896620	+	0.517664i
$292$		0			0
$293$		−	11.6473i		−	0.680443i	−0.940345	−	0.340221i	$-0.889498\pi$
$293$		−	11.6473i		−	0.680443i	0.940345	−	0.340221i	$-0.110502\pi$
$294$		0			0
$295$	11.5832			0.674402
$296$		0			0
$297$	−3.66409	+	2.11546i	−0.212612	+	0.122752i
$298$		0			0
$299$	3.17761	+	4.01067i	0.183766	+	0.231943i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−10.5442	+	18.2631i	−0.605750	+	1.04919i
$304$		0			0
$305$	0.0975728	−	0.0563337i	0.00558700	−	0.00322566i
$306$		0			0
$307$		−	5.53131i		−	0.315689i	−0.987464	−	0.157844i	$-0.949546\pi$
$307$		−	5.53131i		−	0.315689i	0.987464	−	0.157844i	$-0.0504544\pi$
$308$		0			0
$309$	−10.3233			−0.587272
$310$		0			0
$311$	9.62450	+	16.6701i	0.545755	+	0.945276i	0.998559	+	0.0536657i	$0.0170905\pi$
$311$	9.62450	+	16.6701i	0.545755	+	0.945276i	−0.452804	+	0.891610i	$0.649576\pi$
$312$		0			0
$313$	−10.4466	+	18.0940i	−0.590476	+	1.02273i	0.403692	+	0.914895i	$0.367727\pi$
$313$	−10.4466	+	18.0940i	−0.590476	+	1.02273i	−0.994168	+	0.107840i	$0.965607\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00601	+	3.46757i	0.337331	+	0.194758i	0.659091	−	0.752063i	$-0.270941\pi$
$317$	6.00601	+	3.46757i	0.337331	+	0.194758i	−0.321760	+	0.946821i	$0.604274\pi$
$318$		0			0
$319$	6.10312	−	3.52364i	0.341709	−	0.197286i
$320$		0			0
$321$	−24.7966			−1.38401
$322$		0			0
$323$		−	8.09989i		−	0.450690i
$324$		0			0
$325$	−1.49518	+	0.220507i	−0.0829378	+	0.0122315i
$326$		0			0
$327$	−0.645083	−	0.372439i	−0.0356732	−	0.0205959i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−24.8061	−	14.3218i	−1.36346	−	0.787197i	−0.373382	−	0.927678i	$-0.621802\pi$
$331$	−24.8061	−	14.3218i	−1.36346	−	0.787197i	−0.990083	+	0.140481i	$0.955135\pi$
$332$		0			0
$333$	48.6114	−	28.0658i	2.66389	−	1.53800i
$334$		0			0
$335$	8.77408			0.479379
$336$		0			0
$337$	−10.1234			−0.551457			−0.275728	−	0.961236i	$-0.588919\pi$
$337$	−10.1234			−0.551457			−0.275728	+	0.961236i	$0.588919\pi$
$338$		0			0
$339$	−16.8658	−	29.2124i	−0.916022	−	1.58660i
$340$		0			0
$341$	−1.75863	+	3.04603i	−0.0952350	+	0.164952i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−7.92892	−	4.57777i	−0.426879	−	0.246459i
$346$		0			0
$347$	3.09126	+	5.35422i	0.165948	+	0.287430i	0.936991	−	0.349352i	$-0.113598\pi$
$347$	3.09126	+	5.35422i	0.165948	+	0.287430i	−0.771044	+	0.636782i	$0.780265\pi$
$348$		0			0
$349$			18.1738i			0.972821i	0.873730	+	0.486411i	$0.161694\pi$
$349$			18.1738i			0.972821i	−0.873730	+	0.486411i	$0.838306\pi$
$350$		0			0
$351$	−6.18252	+	15.6068i	−0.329999	+	0.833031i
$352$		0			0
$353$	24.4771	−	14.1319i	1.30279	−	0.752164i	0.321905	−	0.946772i	$-0.395677\pi$
$353$	24.4771	−	14.1319i	1.30279	−	0.752164i	0.980881	+	0.194608i	$0.0623435\pi$
$354$		0			0
$355$	17.8528	−	30.9220i	0.947529	−	1.64117i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.2051	+	13.3974i	1.22472	+	0.707090i	0.965920	−	0.258841i	$-0.0833407\pi$
$359$	23.2051	+	13.3974i	1.22472	+	0.707090i	0.258797	+	0.965932i	$0.416674\pi$
$360$		0			0
$361$	−0.720024	−	1.24712i	−0.0378960	−	0.0656378i
$362$		0			0
$363$	28.1956			1.47989
$364$		0			0
$365$	−16.6902			−0.873603
$366$		0			0
$367$	−7.44659	−	12.8979i	−0.388709	−	0.673263i	0.603568	−	0.797312i	$-0.293745\pi$
$367$	−7.44659	−	12.8979i	−0.388709	−	0.673263i	−0.992276	+	0.124049i	$0.960412\pi$
$368$		0			0
$369$	25.1222	+	14.5043i	1.30781	+	0.755065i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−13.2880	+	23.0155i	−0.688026	+	1.19170i	0.284449	+	0.958691i	$0.408189\pi$
$373$	−13.2880	+	23.0155i	−0.688026	+	1.19170i	−0.972475	+	0.233005i	$0.925144\pi$
$374$		0			0
$375$	−25.5931	+	14.7762i	−1.32162	+	0.763038i
$376$		0			0
$377$	10.2980	−	25.9957i	0.530373	−	1.33885i
$378$		0			0
$379$			0.349711i			0.0179634i	0.999960	+	0.00898172i	$0.00285901\pi$
$379$			0.349711i			0.0179634i	−0.999960	+	0.00898172i	$0.997141\pi$
$380$		0			0
$381$	15.4834	+	26.8181i	0.793241	+	1.37393i
$382$		0			0
$383$	24.5923	+	14.1984i	1.25661	+	0.725504i	0.972414	−	0.233262i	$-0.0749400\pi$
$383$	24.5923	+	14.1984i	1.25661	+	0.725504i	0.284196	+	0.958766i	$0.408273\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.1851	−	28.0334i	0.822735	−	1.42502i
$388$		0			0
$389$	3.07093	+	5.31901i	0.155703	+	0.269685i	0.933315	−	0.359060i	$-0.116903\pi$
$389$	3.07093	+	5.31901i	0.155703	+	0.269685i	−0.777612	+	0.628744i	$0.783569\pi$
$390$		0			0
$391$	−2.74317			−0.138728
$392$		0			0
$393$	4.27490			0.215640
$394$		0			0
$395$	34.9701	−	20.1900i	1.75953	−	1.01587i
$396$		0			0
$397$	6.32520	+	3.65186i	0.317453	+	0.183281i	0.650257	−	0.759715i	$-0.274661\pi$
$397$	6.32520	+	3.65186i	0.317453	+	0.183281i	−0.332804	+	0.942996i	$0.607995\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.92794	+	3.42250i	0.296027	+	0.170912i	0.640657	−	0.767827i	$-0.278662\pi$
$401$	5.92794	+	3.42250i	0.296027	+	0.170912i	−0.344629	+	0.938739i	$0.611995\pi$
$402$		0			0
$403$	2.03607	+	13.8059i	0.101424	+	0.687721i
$404$		0			0
$405$			2.64789i			0.131575i
$406$		0			0
$407$	10.8993			0.540258
$408$		0			0
$409$	2.73918	−	1.58147i	0.135444	−	0.0781985i	−0.430747	−	0.902473i	$-0.641750\pi$
$409$	2.73918	−	1.58147i	0.135444	−	0.0781985i	0.566191	+	0.824274i	$0.308417\pi$
$410$		0			0
$411$	36.6172	+	21.1409i	1.80619	+	1.04281i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−14.1040	+	24.4288i	−0.692337	+	1.19916i
$416$		0			0
$417$	−13.1517	−	22.7793i	−0.644040	−	1.11551i
$418$		0			0
$419$	−27.1522			−1.32647			−0.663236	−	0.748410i	$-0.730817\pi$
$419$	−27.1522			−1.32647			−0.663236	+	0.748410i	$0.730817\pi$
$420$		0			0
$421$			26.6238i			1.29757i	0.760973	+	0.648783i	$0.224722\pi$
$421$			26.6238i			1.29757i	−0.760973	+	0.648783i	$0.775278\pi$
$422$		0			0
$423$	12.8464	−	7.41687i	0.624613	−	0.360621i
$424$		0			0
$425$	0.405119	−	0.701686i	0.0196511	−	0.0340368i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−7.11707	+	5.63878i	−0.343615	+	0.272243i
$430$		0			0
$431$	14.3299	−	8.27339i	0.690249	−	0.398515i	−0.113456	−	0.993543i	$-0.536192\pi$
$431$	14.3299	−	8.27339i	0.690249	−	0.398515i	0.803705	+	0.595028i	$0.202859\pi$
$432$		0			0
$433$	10.9994			0.528598			0.264299	−	0.964441i	$-0.414859\pi$
$433$	10.9994			0.528598			0.264299	+	0.964441i	$0.414859\pi$
$434$		0			0
$435$			50.0300i			2.39876i
$436$		0			0
$437$	5.15025	−	2.97350i	0.246370	−	0.142242i
$438$		0			0
$439$	12.8012	−	22.1723i	0.610968	−	1.05823i	−0.380109	−	0.924942i	$-0.624114\pi$
$439$	12.8012	−	22.1723i	0.610968	−	1.05823i	0.991078	−	0.133287i	$-0.0425531\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.2139	−	19.4231i	0.532789	−	0.922817i	−0.466478	−	0.884533i	$-0.654477\pi$
$443$	11.2139	−	19.4231i	0.532789	−	0.922817i	0.999267	−	0.0382843i	$-0.0121893\pi$
$444$		0			0
$445$	−13.7131	−	23.7517i	−0.650062	−	1.12594i
$446$		0			0
$447$		−	52.9513i		−	2.50451i
$448$		0			0
$449$		−	4.49918i		−	0.212329i	−0.994349	−	0.106165i	$-0.966143\pi$
$449$		−	4.49918i		−	0.212329i	0.994349	−	0.106165i	$-0.0338570\pi$
$450$		0			0
$451$	2.81636	+	4.87807i	0.132617	+	0.229700i
$452$		0			0
$453$	43.3015	+	25.0002i	2.03448	+	1.17461i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−34.7656	−	20.0719i	−1.62627	−	0.938926i	−0.985193	−	0.171446i	$-0.945156\pi$
$457$	−34.7656	−	20.0719i	−1.62627	−	0.938926i	−0.641073	−	0.767480i	$-0.721511\pi$
$458$		0			0
$459$	−4.49971	−	7.79372i	−0.210028	−	0.363780i
$460$		0			0
$461$		−	9.66748i		−	0.450259i	−0.974329	−	0.225130i	$-0.927719\pi$
$461$		−	9.66748i		−	0.450259i	0.974329	−	0.225130i	$-0.0722806\pi$
$462$		0			0
$463$		−	22.7513i		−	1.05734i	−0.848827	−	0.528671i	$-0.822690\pi$
$463$		−	22.7513i		−	1.05734i	0.848827	−	0.528671i	$-0.177310\pi$
$464$		0			0
$465$	−12.4848	−	21.6244i	−0.578971	−	1.00281i
$466$		0			0
$467$	12.4037	−	21.4839i	0.573976	−	0.994155i	−0.422176	−	0.906514i	$-0.638734\pi$
$467$	12.4037	−	21.4839i	0.573976	−	0.994155i	0.996152	−	0.0876415i	$-0.0279330\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	24.5507	−	42.5230i	1.13123	−	1.95936i
$472$		0			0
$473$	5.44335	−	3.14272i	0.250286	−	0.144502i
$474$		0			0
$475$			1.75653i			0.0805953i
$476$		0			0
$477$	50.4470			2.30981
$478$		0			0
$479$	34.9807	−	20.1961i	1.59831	−	0.922783i	0.606493	−	0.795089i	$-0.292576\pi$
$479$	34.9807	−	20.1961i	1.59831	−	0.922783i	0.991814	−	0.127694i	$-0.0407577\pi$
$480$		0			0
$481$	33.8954	−	26.8550i	1.54550	−	1.22448i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.41787	−	12.8481i	0.336828	−	0.583404i
$486$		0			0
$487$	−9.16196	+	5.28966i	−0.415168	+	0.239697i	−0.693008	−	0.720930i	$-0.743715\pi$
$487$	−9.16196	+	5.28966i	−0.415168	+	0.239697i	0.277840	+	0.960627i	$0.410382\pi$
$488$		0			0
$489$			3.17529i			0.143591i
$490$		0			0
$491$	−13.8186			−0.623623			−0.311812	−	0.950144i	$-0.600936\pi$
$491$	−13.8186			−0.623623			−0.311812	+	0.950144i	$0.600936\pi$
$492$		0			0
$493$	7.49498	+	12.9817i	0.337557	+	0.584666i
$494$		0			0
$495$	4.95020	−	8.57401i	0.222495	−	0.385373i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−11.1169	−	6.41832i	−0.497659	−	0.287324i	0.230087	−	0.973170i	$-0.426099\pi$
$499$	−11.1169	−	6.41832i	−0.497659	−	0.287324i	−0.727746	+	0.685846i	$0.759432\pi$
$500$		0			0
$501$	2.65277	−	1.53158i	0.118517	−	0.0684258i
$502$		0			0
$503$	−19.3882			−0.864475			−0.432238	−	0.901760i	$-0.642276\pi$
$503$	−19.3882			−0.864475			−0.432238	+	0.901760i	$0.642276\pi$
$504$		0			0
$505$		−	17.7146i		−	0.788287i
$506$		0			0
$507$	−8.23971	+	35.0718i	−0.365938	+	1.55759i
$508$		0			0
$509$	−7.99675	−	4.61693i	−0.354450	−	0.204642i	0.312194	−	0.950019i	$-0.398936\pi$
$509$	−7.99675	−	4.61693i	−0.354450	−	0.204642i	−0.666643	+	0.745377i	$0.732270\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	16.8962	+	9.75502i	0.745985	+	0.430695i
$514$		0			0
$515$	7.50991	−	4.33585i	0.330926	−	0.191060i
$516$		0			0
$517$	2.88032			0.126676
$518$		0			0
$519$	51.5587			2.26318
$520$		0			0
$521$	−19.7951	−	34.2861i	−0.867239	−	1.50210i	−0.864807	−	0.502104i	$-0.832559\pi$
$521$	−19.7951	−	34.2861i	−0.867239	−	1.50210i	−0.00243169	−	0.999997i	$-0.500774\pi$
$522$		0			0
$523$	−15.1960	+	26.3202i	−0.664474	+	1.15090i	0.314953	+	0.949107i	$0.398011\pi$
$523$	−15.1960	+	26.3202i	−0.664474	+	1.15090i	−0.979428	+	0.201796i	$0.935322\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.47908	−	3.74070i	−0.282233	−	0.162947i
$528$		0			0
$529$	10.4930	+	18.1744i	0.456216	+	0.790190i
$530$		0			0
$531$			23.2869i			1.01056i
$532$		0			0
$533$	20.7777	+	8.23092i	0.899982	+	0.356521i
$534$		0			0
$535$	18.0388	−	10.4147i	0.779886	−	0.450267i
$536$		0			0
$537$	−11.6995	+	20.2641i	−0.504871	+	0.874462i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	16.6528	+	9.61451i	0.715961	+	0.413360i	0.813264	−	0.581895i	$-0.197688\pi$
$541$	16.6528	+	9.61451i	0.715961	+	0.413360i	−0.0973035	+	0.995255i	$0.531022\pi$
$542$		0			0
$543$	−26.8130	−	46.4415i	−1.15066	−	1.99300i
$544$		0			0
$545$	0.625706			0.0268023
$546$		0			0
$547$	−8.33845			−0.356526			−0.178263	−	0.983983i	$-0.557048\pi$
$547$	−8.33845			−0.356526			−0.178263	+	0.983983i	$0.557048\pi$
$548$		0			0
$549$	0.113253	+	0.196160i	0.00483352	+	0.00837190i
$550$		0			0
$551$	−28.1433	−	16.2486i	−1.19895	−	0.692212i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−38.6881	+	67.0098i	−1.64222	+	2.84441i
$556$		0			0
$557$	32.2699	−	18.6310i	1.36732	−	0.789422i	0.376735	−	0.926321i	$-0.377047\pi$
$557$	32.2699	−	18.6310i	1.36732	−	0.789422i	0.990585	+	0.136899i	$0.0437135\pi$
$558$		0			0
$559$	9.18473	−	23.1855i	0.388473	−	0.980640i
$560$		0			0
$561$		−	4.86785i		−	0.205521i
$562$		0			0
$563$	4.51376	+	7.81807i	0.190232	+	0.329492i	0.945327	−	0.326123i	$-0.105743\pi$
$563$	4.51376	+	7.81807i	0.190232	+	0.329492i	−0.755095	+	0.655616i	$0.772409\pi$
$564$		0			0
$565$	24.5387	+	14.1674i	1.03235	+	0.596028i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	19.4280	−	33.6503i	0.814465	−	1.41069i	−0.0952467	−	0.995454i	$-0.530364\pi$
$569$	19.4280	−	33.6503i	0.814465	−	1.41069i	0.909712	−	0.415241i	$-0.136303\pi$
$570$		0			0
$571$	6.72546	+	11.6488i	0.281452	+	0.487489i	0.971743	−	0.236043i	$-0.0758508\pi$
$571$	6.72546	+	11.6488i	0.281452	+	0.487489i	−0.690291	+	0.723532i	$0.742517\pi$
$572$		0			0
$573$	32.2468			1.34713
$574$		0			0
$575$	0.594881			0.0248083
$576$		0			0
$577$	−9.97375	+	5.75835i	−0.415213	+	0.239723i	−0.693027	−	0.720912i	$-0.743723\pi$
$577$	−9.97375	+	5.75835i	−0.415213	+	0.239723i	0.277814	+	0.960635i	$0.410390\pi$
$578$		0			0
$579$	40.3340	+	23.2869i	1.67623	+	0.967769i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	8.48314	+	4.89774i	0.351336	+	0.202844i
$584$		0			0
$585$	−5.73115	−	38.8610i	−0.236954	−	1.60670i
$586$		0			0
$587$		−	46.4498i		−	1.91719i	−0.284776	−	0.958594i	$-0.591919\pi$
$587$		−	46.4498i		−	1.91719i	0.284776	−	0.958594i	$-0.408081\pi$
$588$		0			0
$589$	16.2191			0.668296
$590$		0			0
$591$	15.7523	−	9.09459i	0.647963	−	0.374101i
$592$		0			0
$593$	−7.37025	−	4.25522i	−0.302660	−	0.174741i	0.340977	−	0.940072i	$-0.389242\pi$
$593$	−7.37025	−	4.25522i	−0.302660	−	0.174741i	−0.643637	+	0.765331i	$0.722575\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−36.2307	+	62.7534i	−1.48282	+	2.56832i
$598$		0			0
$599$	−8.99758	−	15.5843i	−0.367631	−	0.636756i	0.621563	−	0.783364i	$-0.286498\pi$
$599$	−8.99758	−	15.5843i	−0.367631	−	0.636756i	−0.989195	+	0.146608i	$0.953164\pi$
$600$		0			0
$601$	−10.0809			−0.411210			−0.205605	−	0.978635i	$-0.565916\pi$
$601$	−10.0809			−0.411210			−0.205605	+	0.978635i	$0.565916\pi$
$602$		0			0
$603$			17.6394i			0.718331i
$604$		0			0
$605$	−20.5115	+	11.8423i	−0.833911	+	0.481459i
$606$		0			0
$607$	−19.9119	+	34.4885i	−0.808201	+	1.39985i	0.105908	+	0.994376i	$0.466225\pi$
$607$	−19.9119	+	34.4885i	−0.808201	+	1.39985i	−0.914109	+	0.405469i	$0.867108\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.95745	−	7.09689i	0.362379	−	0.287109i
$612$		0			0
$613$	5.31613	−	3.06927i	0.214717	−	0.123967i	−0.388785	−	0.921329i	$-0.627105\pi$
$613$	5.31613	−	3.06927i	0.214717	−	0.123967i	0.603502	+	0.797362i	$0.293772\pi$
$614$		0			0
$615$	−39.9878			−1.61246
$616$		0			0
$617$		−	28.3968i		−	1.14321i	−0.820528	−	0.571606i	$-0.806321\pi$
$617$		−	28.3968i		−	1.14321i	0.820528	−	0.571606i	$-0.193679\pi$
$618$		0			0
$619$	−8.61834	+	4.97580i	−0.346400	+	0.199994i	−0.663099	−	0.748532i	$-0.730759\pi$
$619$	−8.61834	+	4.97580i	−0.346400	+	0.199994i	0.316698	+	0.948526i	$0.397426\pi$
$620$		0			0
$621$	3.30371	−	5.72220i	0.132573	−	0.229624i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	13.4601	−	23.3135i	0.538403	−	0.932542i
$626$		0			0
$627$	5.27657	+	9.13928i	0.210726	+	0.364988i
$628$		0			0
$629$			23.1834i			0.924383i
$630$		0			0
$631$			46.4171i			1.84783i	0.382592	+	0.923917i	$0.375031\pi$
$631$			46.4171i			1.84783i	−0.382592	+	0.923917i	$0.624969\pi$
$632$		0			0
$633$	−2.53324	−	4.38770i	−0.100687	−	0.174395i
$634$		0			0
$635$	−22.5275	−	13.0063i	−0.893978	−	0.516138i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	62.1654	+	35.8912i	2.45923	+	1.41984i
$640$		0			0
$641$	9.60261	+	16.6322i	0.379280	+	0.656932i	0.990958	−	0.134175i	$-0.0428383\pi$
$641$	9.60261	+	16.6322i	0.379280	+	0.656932i	−0.611678	+	0.791107i	$0.709505\pi$
$642$		0			0
$643$		−	7.98776i		−	0.315006i	−0.987518	−	0.157503i	$-0.949656\pi$
$643$		−	7.98776i		−	0.315006i	0.987518	−	0.157503i	$-0.0503445\pi$
$644$		0			0
$645$			44.6216i			1.75697i
$646$		0			0
$647$	−11.2827	−	19.5423i	−0.443570	−	0.768285i	0.554382	−	0.832263i	$-0.312955\pi$
$647$	−11.2827	−	19.5423i	−0.443570	−	0.768285i	−0.997951	+	0.0639773i	$0.979621\pi$
$648$		0			0
$649$	−2.26085	+	3.91591i	−0.0887461	+	0.153713i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.8723	−	22.2955i	0.503732	−	0.872489i	−0.496259	−	0.868175i	$-0.665293\pi$
$653$	12.8723	−	22.2955i	0.503732	−	0.872489i	0.999991	−	0.00431465i	$-0.00137340\pi$
$654$		0			0
$655$	−3.10987	+	1.79548i	−0.121513	+	0.0701554i
$656$		0			0
$657$		−	33.5538i		−	1.30906i
$658$		0			0
$659$	−43.3529			−1.68879			−0.844396	−	0.535720i	$-0.820040\pi$
$659$	−43.3529			−1.68879			−0.844396	+	0.535720i	$0.820040\pi$
$660$		0			0
$661$	−4.73653	+	2.73464i	−0.184230	+	0.106365i	−0.589278	−	0.807930i	$-0.700588\pi$
$661$	−4.73653	+	2.73464i	−0.184230	+	0.106365i	0.405049	+	0.914295i	$0.367255\pi$
$662$		0			0
$663$	−11.9940	−	15.1384i	−0.465809	−	0.587927i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.50286	+	9.53124i	−0.213072	+	0.369051i
$668$		0			0
$669$	21.5716	−	12.4544i	0.834006	−	0.481514i
$670$		0			0
$671$			0.0439815i			0.00169789i
$672$		0			0
$673$	7.17601			0.276615			0.138307	−	0.990389i	$-0.455834\pi$
$673$	7.17601			0.276615			0.138307	+	0.990389i	$0.455834\pi$
$674$		0			0
$675$	0.975801	+	1.69014i	0.0375586	+	0.0650534i
$676$		0			0
$677$	−0.304524	+	0.527451i	−0.0117038	+	0.0202716i	−0.871818	−	0.489830i	$-0.837059\pi$
$677$	−0.304524	+	0.527451i	−0.0117038	+	0.0202716i	0.860114	+	0.510102i	$0.170392\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−25.0685	−	14.4733i	−0.960627	−	0.554618i
$682$		0			0
$683$	−29.6841	+	17.1381i	−1.13583	+	0.655773i	−0.945395	−	0.325926i	$-0.894324\pi$
$683$	−29.6841	+	17.1381i	−1.13583	+	0.655773i	−0.190437	+	0.981699i	$0.560991\pi$
$684$		0			0
$685$	−35.5173			−1.35704
$686$		0			0
$687$			56.4004i			2.15181i
$688$		0			0
$689$	38.4492	−	5.67041i	1.46480	−	0.216025i
$690$		0			0
$691$	18.5372	+	10.7025i	0.705189	+	0.407141i	0.809277	−	0.587427i	$-0.199859\pi$
$691$	18.5372	+	10.7025i	0.705189	+	0.407141i	−0.104088	+	0.994568i	$0.533192\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.1349	+	11.0475i	0.725829	+	0.419057i
$696$		0			0
$697$	−10.3759	+	5.99055i	−0.393017	+	0.226908i
$698$		0			0
$699$	62.8030			2.37543
$700$		0			0
$701$	−34.1562			−1.29006			−0.645031	−	0.764156i	$-0.723156\pi$
$701$	−34.1562			−1.29006			−0.645031	+	0.764156i	$0.723156\pi$
$702$		0			0
$703$	−25.1299	−	43.5263i	−0.947793	−	1.64163i
$704$		0			0
$705$	−10.2240	+	17.7085i	−0.385058	+	0.666940i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	21.3278	+	12.3136i	0.800981	+	0.462447i	0.843814	−	0.536636i	$-0.180305\pi$
$709$	21.3278	+	12.3136i	0.800981	+	0.462447i	−0.0428331	+	0.999082i	$0.513638\pi$
$710$		0			0
$711$	40.5898	+	70.3036i	1.52224	+	2.63659i
$712$		0			0
$713$		−	5.49289i		−	0.205710i
$714$		0			0
$715$	2.80915	−	7.09126i	0.105056	−	0.265198i
$716$		0			0
$717$	−48.0382	+	27.7348i	−1.79402	+	1.03578i
$718$		0			0
$719$	9.30452	−	16.1159i	0.347000	−	0.601022i	−0.638715	−	0.769444i	$-0.720534\pi$
$719$	9.30452	−	16.1159i	0.347000	−	0.601022i	0.985715	+	0.168422i	$0.0538670\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−52.4112	−	30.2596i	−1.94919	−	1.12537i
$724$		0			0
$725$	−1.62535	−	2.81519i	−0.0603641	−	0.104554i
$726$		0			0
$727$	−29.3061			−1.08690			−0.543451	−	0.839441i	$-0.682883\pi$
$727$	−29.3061			−1.08690			−0.543451	+	0.839441i	$0.682883\pi$
$728$		0			0
$729$	−44.0312			−1.63078
$730$		0			0
$731$	6.68475	+	11.5783i	0.247244	+	0.428240i
$732$		0			0
$733$	−13.1519	−	7.59327i	−0.485778	−	0.280464i	0.237043	−	0.971499i	$-0.423822\pi$
$733$	−13.1519	−	7.59327i	−0.485778	−	0.280464i	−0.722821	+	0.691035i	$0.757155\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.71255	+	2.96623i	−0.0630826	+	0.109262i
$738$		0			0
$739$	13.7292	−	7.92655i	0.505036	−	0.291583i	−0.225755	−	0.974184i	$-0.572485\pi$
$739$	13.7292	−	7.92655i	0.505036	−	0.291583i	0.730791	+	0.682601i	$0.239151\pi$
$740$		0			0
$741$	38.9279	+	15.4210i	1.43005	+	0.566504i
$742$		0			0
$743$			17.0404i			0.625151i	0.949893	+	0.312575i	$0.101192\pi$
$743$			17.0404i			0.625151i	−0.949893	+	0.312575i	$0.898808\pi$
$744$		0			0
$745$	22.2399	+	38.5206i	0.814805	+	1.41128i
$746$		0			0
$747$	−49.1116	−	28.3546i	−1.79690	−	1.03744i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.09829	−	10.5625i	0.222530	−	0.385433i	−0.733046	−	0.680179i	$-0.761902\pi$
$751$	6.09829	−	10.5625i	0.222530	−	0.385433i	0.955575	+	0.294747i	$0.0952352\pi$
$752$		0			0
$753$	14.9252	+	25.8511i	0.543903	+	0.942067i
$754$		0			0
$755$	−42.0008			−1.52857
$756$		0			0
$757$	8.90080			0.323505			0.161753	−	0.986831i	$-0.448285\pi$
$757$	8.90080			0.323505			0.161753	+	0.986831i	$0.448285\pi$
$758$		0			0
$759$	3.09518	−	1.78700i	0.112348	−	0.0648641i
$760$		0			0
$761$	−21.2435	−	12.2650i	−0.770078	−	0.444605i	0.0628244	−	0.998025i	$-0.479989\pi$
$761$	−21.2435	−	12.2650i	−0.770078	−	0.444605i	−0.832902	+	0.553420i	$0.813323\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	18.2374	+	10.5294i	0.659375	+	0.380690i
$766$		0			0
$767$	2.61752	+	17.7485i	0.0945132	+	0.640862i
$768$		0			0
$769$			31.7896i			1.14636i	0.819429	+	0.573180i	$0.194291\pi$
$769$			31.7896i			1.14636i	−0.819429	+	0.573180i	$0.805709\pi$
$770$		0			0
$771$	47.9678			1.72752
$772$		0			0
$773$	−2.85229	+	1.64677i	−0.102590	+	0.0592302i	−0.550417	−	0.834890i	$-0.685531\pi$
$773$	−2.85229	+	1.64677i	−0.102590	+	0.0592302i	0.447827	+	0.894120i	$0.352198\pi$
$774$		0			0
$775$	1.40505	+	0.811203i	0.0504707	+	0.0291393i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.9871	−	22.4943i	0.465310	−	0.805940i
$780$		0			0
$781$	6.96914	+	12.0709i	0.249375	+	0.431931i
$782$		0			0
$783$	−36.1060			−1.29032
$784$		0			0
$785$			41.2457i			1.47212i
$786$		0			0
$787$	−10.2421	+	5.91325i	−0.365090	+	0.210785i	−0.671311	−	0.741176i	$-0.734269\pi$
$787$	−10.2421	+	5.91325i	−0.365090	+	0.210785i	0.306221	+	0.951960i	$0.400935\pi$
$788$		0			0
$789$	7.44659	−	12.8979i	0.265105	−	0.459176i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.108367	+	0.136777i	0.00384822	+	0.00485710i
$794$		0			0
$795$	−60.2235	+	34.7700i	−2.13591	+	1.23317i
$796$		0			0
$797$	24.5512			0.869648			0.434824	−	0.900515i	$-0.356811\pi$
$797$	24.5512			0.869648			0.434824	+	0.900515i	$0.356811\pi$
$798$		0			0
$799$			6.12661i			0.216744i
$800$		0			0
$801$	47.7504	−	27.5687i	1.68718	−	0.974091i
$802$		0			0
$803$	3.25764	−	5.64239i	0.114960	−	0.199116i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	23.6739	−	41.0044i	0.833361	−	1.44342i
$808$		0			0
$809$	−10.0979	−	17.4901i	−0.355023	−	0.614918i	0.632099	−	0.774888i	$-0.282194\pi$
$809$	−10.0979	−	17.4901i	−0.355023	−	0.614918i	−0.987122	+	0.159970i	$0.948860\pi$
$810$		0			0
$811$			42.1330i			1.47949i	0.672888	+	0.739744i	$0.265053\pi$
$811$			42.1330i			1.47949i	−0.672888	+	0.739744i	$0.734947\pi$
$812$		0			0
$813$		−	51.1169i		−	1.79275i
$814$		0			0
$815$	−1.33364	−	2.30993i	−0.0467153	−	0.0809133i
$816$		0			0
$817$	−25.1009	−	14.4920i	−0.878170	−	0.507012i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	36.2745	+	20.9431i	1.26599	+	0.730919i	0.974226	−	0.225572i	$-0.0724252\pi$
$821$	36.2745	+	20.9431i	1.26599	+	0.730919i	0.291762	+	0.956491i	$0.405759\pi$
$822$		0			0
$823$	−10.9658	−	18.9933i	−0.382244	−	0.662066i	0.609139	−	0.793064i	$-0.291515\pi$
$823$	−10.9658	−	18.9933i	−0.382244	−	0.662066i	−0.991383	+	0.130998i	$0.958182\pi$
$824$		0			0
$825$			1.05564i			0.0367525i
$826$		0			0
$827$			35.5193i			1.23513i	0.786522	+	0.617563i	$0.211880\pi$
$827$			35.5193i			1.23513i	−0.786522	+	0.617563i	$0.788120\pi$
$828$		0			0
$829$	−6.93654	−	12.0144i	−0.240916	−	0.417279i	0.720059	−	0.693912i	$-0.244115\pi$
$829$	−6.93654	−	12.0144i	−0.240916	−	0.417279i	−0.960975	+	0.276634i	$0.910781\pi$
$830$		0			0
$831$	11.5807	−	20.0584i	0.401730	−	0.695818i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.28654	+	2.22835i	−0.0445226	+	0.0771154i
$836$		0			0
$837$	15.6060	−	9.01014i	0.539423	−	0.311436i
$838$		0			0
$839$			3.89096i			0.134331i	0.997742	+	0.0671655i	$0.0213955\pi$
$839$			3.89096i			0.134331i	−0.997742	+	0.0671655i	$0.978604\pi$
$840$		0			0
$841$	31.1404			1.07381
$842$		0			0
$843$	−22.2952	+	12.8721i	−0.767888	+	0.443340i
$844$		0			0
$845$	−8.73621	−	28.9745i	−0.300535	−	0.996752i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.65250	+	4.59426i	−0.0910335	+	0.157675i
$850$		0			0
$851$	−14.7410	+	8.51070i	−0.505314	+	0.291743i
$852$		0			0
$853$			22.8271i			0.781585i	0.920479	+	0.390792i	$0.127799\pi$
$853$			22.8271i			0.781585i	−0.920479	+	0.390792i	$0.872201\pi$
$854$		0			0
$855$	−45.6537			−1.56132
$856$		0			0
$857$	−12.3820	−	21.4463i	−0.422962	−	0.732592i	0.573265	−	0.819370i	$-0.305676\pi$
$857$	−12.3820	−	21.4463i	−0.422962	−	0.732592i	−0.996228	+	0.0867775i	$0.972343\pi$
$858$		0			0
$859$	−18.5156	+	32.0699i	−0.631743	+	1.09421i	0.355452	+	0.934695i	$0.384327\pi$
$859$	−18.5156	+	32.0699i	−0.631743	+	1.09421i	−0.987195	+	0.159517i	$0.949006\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	23.2516	+	13.4243i	0.791494	+	0.456969i	0.840488	−	0.541830i	$-0.182268\pi$
$863$	23.2516	+	13.4243i	0.791494	+	0.456969i	−0.0489945	+	0.998799i	$0.515602\pi$
$864$		0			0
$865$	−37.5075	+	21.6550i	−1.27529	+	0.736291i
$866$		0			0
$867$	−36.7577			−1.24836
$868$		0			0
$869$			15.7630i			0.534722i
$870$		0			0
$871$	1.98272	+	13.4442i	0.0671820	+	0.455539i
$872$		0			0
$873$	25.8298	+	14.9129i	0.874207	+	0.504724i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.45539	−	4.30437i	−0.251751	−	0.145348i	0.368815	−	0.929503i	$-0.379764\pi$
$877$	−7.45539	−	4.30437i	−0.251751	−	0.145348i	−0.620566	+	0.784155i	$0.713097\pi$
$878$		0			0
$879$	−27.9536	+	16.1390i	−0.942851	+	0.544355i
$880$		0			0
$881$	0.0606391			0.00204298			0.00102149	−	0.999999i	$-0.499675\pi$
$881$	0.0606391			0.00204298			0.00102149	+	0.999999i	$0.499675\pi$
$882$		0			0
$883$	27.3929			0.921844			0.460922	−	0.887441i	$-0.347519\pi$
$883$	27.3929			0.921844			0.460922	+	0.887441i	$0.347519\pi$
$884$		0			0
$885$	−16.0502	−	27.7998i	−0.539522	−	0.934480i
$886$		0			0
$887$	−7.76296	+	13.4458i	−0.260655	+	0.451467i	−0.966416	−	0.256983i	$-0.917272\pi$
$887$	−7.76296	+	13.4458i	−0.260655	+	0.451467i	0.705761	+	0.708450i	$0.250605\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.895164	−	0.516823i	−0.0299891	−	0.0173142i
$892$		0			0
$893$	−6.64101	−	11.5026i	−0.222233	−	0.384919i
$894$		0			0
$895$		−	19.6554i		−	0.657009i
$896$		0			0
$897$	5.22259	−	13.1836i	0.174377	−	0.440189i
$898$		0			0
$899$	−25.9943	+	15.0078i	−0.866960	+	0.500539i
$900$		0			0
$901$	−10.4178	+	18.0441i	−0.347066	+	0.601137i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	39.0114	+	22.5232i	1.29678	+	0.748698i
$906$		0			0
$907$	10.2714	+	17.7905i	0.341055	+	0.590724i	0.984629	−	0.174660i	$-0.0558825\pi$
$907$	10.2714	+	17.7905i	0.341055	+	0.590724i	−0.643574	+	0.765384i	$0.722549\pi$
$908$		0			0
$909$	35.6133			1.18122
$910$		0			0
$911$	−26.9607			−0.893246			−0.446623	−	0.894722i	$-0.647374\pi$
$911$	−26.9607			−0.893246			−0.446623	+	0.894722i	$0.647374\pi$
$912$		0			0
$913$	−5.50571	−	9.53618i	−0.182213	−	0.315601i
$914$		0			0
$915$	−0.270402	−	0.156117i	−0.00893922	−	0.00516106i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−25.2039	+	43.6545i	−0.831401	+	1.44003i	0.0655265	+	0.997851i	$0.479127\pi$
$919$	−25.2039	+	43.6545i	−0.831401	+	1.44003i	−0.896927	+	0.442178i	$0.854206\pi$
$920$		0			0
$921$	−13.2752	+	7.66442i	−0.437431	+	0.252551i
$922$		0			0
$923$	51.4149	+	20.3676i	1.69234	+	0.670407i
$924$		0			0
$925$		−	5.02753i		−	0.165304i
$926$		0			0
$927$	8.71677	+	15.0979i	0.286296	+	0.495880i
$928$		0			0
$929$	−1.24809	−	0.720583i	−0.0409484	−	0.0236415i	0.479386	−	0.877604i	$-0.340859\pi$
$929$	−1.24809	−	0.720583i	−0.0409484	−	0.0236415i	−0.520334	+	0.853963i	$0.674193\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	26.6722	−	46.1977i	0.873210	−	1.51244i
$934$		0			0
$935$	2.04453	+	3.54122i	0.0668632	+	0.115810i
$936$		0			0
$937$	−5.55565			−0.181495			−0.0907475	−	0.995874i	$-0.528926\pi$
$937$	−5.55565			−0.181495			−0.0907475	+	0.995874i	$0.528926\pi$
$938$		0			0
$939$	57.9009			1.88953
$940$		0			0
$941$	18.2844	−	10.5565i	0.596056	−	0.344133i	−0.171432	−	0.985196i	$-0.554840\pi$
$941$	18.2844	−	10.5565i	0.596056	−	0.344133i	0.767488	+	0.641063i	$0.221506\pi$
$942$		0			0
$943$	−7.61808	−	4.39830i	−0.248079	−	0.143228i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.2427	−	27.2756i	−1.53518	−	0.886338i	−0.999111	−	0.0421655i	$-0.986574\pi$
$947$	−47.2427	−	27.2756i	−1.53518	−	0.886338i	−0.536072	−	0.844172i	$-0.680092\pi$
$948$		0			0
$949$	−3.77156	−	25.5737i	−0.122430	−	0.830157i
$950$		0			0
$951$		−	19.2193i		−	0.623227i
$952$		0			0
$953$	4.78814			0.155103			0.0775515	−	0.996988i	$-0.475290\pi$
$953$	4.78814			0.155103			0.0775515	+	0.996988i	$0.475290\pi$
$954$		0			0
$955$	−23.4586	+	13.5438i	−0.759103	+	0.438268i
$956$		0			0
$957$	−16.9135	−	9.76501i	−0.546736	−	0.315658i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−8.00968	+	13.8732i	−0.258377	+	0.447522i
$962$		0			0
$963$	20.9377	+	36.2652i	0.674708	+	1.16863i
$964$		0			0
$965$	−39.1225			−1.25940
$966$		0			0
$967$			15.9411i			0.512630i	0.966593	+	0.256315i	$0.0825085\pi$
$967$			15.9411i			0.512630i	−0.966593	+	0.256315i	$0.917492\pi$
$968$		0			0
$969$	−19.4398	+	11.2236i	−0.624496	+	0.360553i
$970$		0			0
$971$	−3.71716	+	6.43831i	−0.119289	+	0.206615i	−0.919486	−	0.393122i	$-0.871395\pi$
$971$	−3.71716	+	6.43831i	−0.119289	+	0.206615i	0.800197	+	0.599737i	$0.204728\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.60100	+	3.28290i	0.0832988	+	0.105137i
$976$		0			0
$977$	−11.1034	+	6.41058i	−0.355231	+	0.205093i	−0.666987	−	0.745070i	$-0.732416\pi$
$977$	−11.1034	+	6.41058i	−0.355231	+	0.205093i	0.311756	+	0.950162i	$0.399083\pi$
$978$		0			0
$979$	10.7062			0.342173
$980$		0			0
$981$			1.25792i			0.0401622i
$982$		0			0
$983$	21.0334	−	12.1436i	0.670861	−	0.387322i	−0.125542	−	0.992088i	$-0.540067\pi$
$983$	21.0334	−	12.1436i	0.670861	−	0.387322i	0.796403	+	0.604767i	$0.206734\pi$
$984$		0			0
$985$	−7.63956	+	13.2321i	−0.243417	+	0.421610i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.90798	+	8.50087i	−0.156065	+	0.270312i
$990$		0			0
$991$	11.9867	+	20.7615i	0.380769	+	0.659512i	0.991172	−	0.132579i	$-0.0423258\pi$
$991$	11.9867	+	20.7615i	0.380769	+	0.659512i	−0.610403	+	0.792091i	$0.708992\pi$
$992$		0			0
$993$			79.3795i			2.51903i
$994$		0			0
$995$		−	60.8684i		−	1.92966i
$996$		0			0
$997$	11.6638	+	20.2022i	0.369395	+	0.639811i	0.989471	−	0.144731i	$-0.0462316\pi$
$997$	11.6638	+	20.2022i	0.369395	+	0.639811i	−0.620076	+	0.784542i	$0.712898\pi$
$998$		0			0
$999$	−48.3601	−	27.9207i	−1.53004	−	0.883372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.y.f.961.2		16
7.2	even	3		364.2.g.a.337.7	✓	8
7.3	odd	6		2548.2.y.e.753.8		16
7.4	even	3	inner	2548.2.y.f.753.1		16
7.5	odd	6		2548.2.g.g.2157.2		8
7.6	odd	2		2548.2.y.e.961.7		16
13.12	even	2	inner	2548.2.y.f.961.1		16
21.2	odd	6		3276.2.e.f.2521.6		8
28.23	odd	6		1456.2.k.d.337.1		8
91.12	odd	6		2548.2.g.g.2157.1		8
91.25	even	6	inner	2548.2.y.f.753.2		16
91.38	odd	6		2548.2.y.e.753.7		16
91.44	odd	12		4732.2.a.o.1.4		4
91.51	even	6		364.2.g.a.337.8	yes	8
91.86	odd	12		4732.2.a.p.1.4		4
91.90	odd	2		2548.2.y.e.961.8		16
273.233	odd	6		3276.2.e.f.2521.3		8
364.51	odd	6		1456.2.k.d.337.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.g.a.337.7	✓	8	7.2	even	3
364.2.g.a.337.8	yes	8	91.51	even	6
1456.2.k.d.337.1		8	28.23	odd	6
1456.2.k.d.337.2		8	364.51	odd	6
2548.2.g.g.2157.1		8	91.12	odd	6
2548.2.g.g.2157.2		8	7.5	odd	6
2548.2.y.e.753.7		16	91.38	odd	6
2548.2.y.e.753.8		16	7.3	odd	6
2548.2.y.e.961.7		16	7.6	odd	2
2548.2.y.e.961.8		16	91.90	odd	2
2548.2.y.f.753.1		16	7.4	even	3	inner
2548.2.y.f.753.2		16	91.25	even	6	inner
2548.2.y.f.961.1		16	13.12	even	2	inner
2548.2.y.f.961.2		16	1.1	even	1	trivial
3276.2.e.f.2521.3		8	273.233	odd	6
3276.2.e.f.2521.6		8	21.2	odd	6
4732.2.a.o.1.4		4	91.44	odd	12
4732.2.a.p.1.4		4	91.86	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38564 - 2.40000i) q^{3} +(2.01603 + 1.16396i) q^{5} +(-2.34001 + 4.05302i) q^{9} +(-0.786990 + 0.454369i) q^{11} +(-1.32791 + 3.35211i) q^{13} -6.45131i q^{15} +(-0.966468 - 1.67397i) q^{17} +(3.62904 + 2.09523i) q^{19} +(0.709587 - 1.22904i) q^{23} +(0.209587 + 0.363016i) q^{25} +4.65582 q^{27} -7.75502 q^{29} +(3.35194 - 1.93524i) q^{31} +(2.18097 + 1.25919i) q^{33} +(-10.3870 - 5.99694i) q^{37} +(9.88509 - 1.45784i) q^{39} -6.19839i q^{41} -6.91667 q^{43} +(-9.43507 + 5.44734i) q^{45} +(-2.74494 - 1.58479i) q^{47} +(-2.67836 + 4.63906i) q^{51} +(-5.38961 - 9.33508i) q^{53} -2.11546 q^{55} -11.6130i q^{57} +(4.30917 - 2.48790i) q^{59} +(0.0241992 - 0.0419143i) q^{61} +(-6.57882 + 5.21233i) q^{65} +(3.26412 - 1.88454i) q^{67} -3.93294 q^{69} -15.3381i q^{71} +(-6.20904 + 3.58479i) q^{73} +(0.580826 - 1.00602i) q^{75} +(8.67300 - 15.0221i) q^{79} +(0.568726 + 0.985063i) q^{81} +12.1173i q^{83} -4.49971i q^{85} +(10.7457 + 18.6121i) q^{87} +(-10.2030 - 5.89071i) q^{89} +(-9.28917 - 5.36311i) q^{93} +(4.87751 + 8.44810i) q^{95} -6.37298i q^{97} -4.25291i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} + 4 q^{13} - 4 q^{17} + 6 q^{23} - 2 q^{25} + 24 q^{27} - 4 q^{29} - 12 q^{43} + 8 q^{51} - 22 q^{53} - 40 q^{55} - 8 q^{61} + 6 q^{65} - 40 q^{69} + 20 q^{75} + 26 q^{79} + 24 q^{81} + 32 q^{87}+ \cdots + 18 q^{95}+O(q^{100}) \) 16 * q - 8 * q^9 + 4 * q^13 - 4 * q^17 + 6 * q^23 - 2 * q^25 + 24 * q^27 - 4 * q^29 - 12 * q^43 + 8 * q^51 - 22 * q^53 - 40 * q^55 - 8 * q^61 + 6 * q^65 - 40 * q^69 + 20 * q^75 + 26 * q^79 + 24 * q^81 + 32 * q^87 + 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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