LMFDB - Embedded newform 1764.2.j.i.1177.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(589,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("1764.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.j (of order $3$, degree $2$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1177.5
Character	$\chi$	$=$	1764.1177
Dual form			1764.2.j.i.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.899846 + 1.47996i) q^{3} +(1.19243 + 2.06535i) q^{5} +(-1.38055 - 2.66347i) q^{9} +O(q^{10})$	\(q+(-0.899846 + 1.47996i) q^{3} +(1.19243 + 2.06535i) q^{5} +(-1.38055 - 2.66347i) q^{9} +(1.12978 - 1.95684i) q^{11} +(2.37884 + 4.12027i) q^{13} +(-4.12964 - 0.0937498i) q^{15} -4.30404 q^{17} -8.59629 q^{19} +(-0.664550 - 1.15103i) q^{23} +(-0.343781 + 0.595446i) q^{25} +(5.18411 + 0.353550i) q^{27} +(-3.87886 + 6.71839i) q^{29} +(-0.405320 - 0.702036i) q^{31} +(1.87941 + 3.43288i) q^{33} -4.63226 q^{37} +(-8.23841 - 0.187026i) q^{39} +(5.00426 + 8.66764i) q^{41} +(-1.74292 + 3.01883i) q^{43} +(3.85478 - 6.02733i) q^{45} +(2.18338 - 3.78173i) q^{47} +(3.87297 - 6.36979i) q^{51} -11.6787 q^{53} +5.38874 q^{55} +(7.73534 - 12.7222i) q^{57} +(2.40463 + 4.16495i) q^{59} +(0.575967 - 0.997604i) q^{61} +(-5.67319 + 9.82626i) q^{65} +(2.06381 + 3.57463i) q^{67} +(2.30148 + 0.0522474i) q^{69} -4.41593 q^{71} -12.1118 q^{73} +(-0.571885 - 1.04459i) q^{75} +(4.23312 - 7.33198i) q^{79} +(-5.18814 + 7.35413i) q^{81} +(0.817808 - 1.41648i) q^{83} +(-5.13226 - 8.88934i) q^{85} +(-6.45255 - 11.7861i) q^{87} -6.34310 q^{89} +(1.40371 + 0.0318666i) q^{93} +(-10.2505 - 17.7543i) q^{95} +(5.98278 - 10.3625i) q^{97} +(-6.77170 - 0.307617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{9}+O(q^{10}) $ 24 * q + 8 * q^9	$ 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) $ 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.899846	+	1.47996i	−0.519526	+	0.854454i
$3$	−0.899846	+	1.47996i	−0.519526	+	0.854454i
$4$		0			0
$5$	1.19243	+	2.06535i	0.533271	+	0.923653i	0.999245	+	0.0388541i	$0.0123708\pi$
$5$	1.19243	+	2.06535i	0.533271	+	0.923653i	−0.465974	+	0.884799i	$0.654296\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.38055	−	2.66347i	−0.460185	−	0.887823i
$10$		0			0
$11$	1.12978	−	1.95684i	0.340642	−	0.590009i	−0.643910	−	0.765101i	$-0.722689\pi$
$11$	1.12978	−	1.95684i	0.340642	−	0.590009i	0.984552	+	0.175092i	$0.0560224\pi$
$12$		0			0
$13$	2.37884	+	4.12027i	0.659770	+	1.14276i	0.980675	+	0.195644i	$0.0626798\pi$
$13$	2.37884	+	4.12027i	0.659770	+	1.14276i	−0.320904	+	0.947112i	$0.603987\pi$
$14$		0			0
$15$	−4.12964	−	0.0937498i	−1.06627	−	0.0242061i
$16$		0			0
$17$	−4.30404			−1.04388			−0.521941	−	0.852982i	$-0.674792\pi$
$17$	−4.30404			−1.04388			−0.521941	+	0.852982i	$0.674792\pi$
$18$		0			0
$19$	−8.59629			−1.97212			−0.986062	−	0.166378i	$-0.946793\pi$
$19$	−8.59629			−1.97212			−0.986062	+	0.166378i	$0.946793\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.664550	−	1.15103i	−0.138568	−	0.240007i	0.788387	−	0.615180i	$-0.210917\pi$
$23$	−0.664550	−	1.15103i	−0.138568	−	0.240007i	−0.926955	+	0.375173i	$0.877583\pi$
$24$		0			0
$25$	−0.343781	+	0.595446i	−0.0687562	+	0.119089i
$26$		0			0
$27$	5.18411	+	0.353550i	0.997683	+	0.0680408i
$28$		0			0
$29$	−3.87886	+	6.71839i	−0.720287	+	1.24757i	0.240598	+	0.970625i	$0.422656\pi$
$29$	−3.87886	+	6.71839i	−0.720287	+	1.24757i	−0.960885	+	0.276948i	$0.910677\pi$
$30$		0			0
$31$	−0.405320	−	0.702036i	−0.0727977	−	0.126089i	0.827329	−	0.561718i	$-0.189859\pi$
$31$	−0.405320	−	0.702036i	−0.0727977	−	0.126089i	−0.900126	+	0.435629i	$0.856526\pi$
$32$		0			0
$33$	1.87941	+	3.43288i	0.327163	+	0.597588i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.63226			−0.761539			−0.380770	−	0.924670i	$-0.624341\pi$
$37$	−4.63226			−0.761539			−0.380770	+	0.924670i	$0.624341\pi$
$38$		0			0
$39$	−8.23841	−	0.187026i	−1.31920	−	0.0299481i
$40$		0			0
$41$	5.00426	+	8.66764i	0.781534	+	1.35366i	0.931048	+	0.364898i	$0.118896\pi$
$41$	5.00426	+	8.66764i	0.781534	+	1.35366i	−0.149513	+	0.988760i	$0.547771\pi$
$42$		0			0
$43$	−1.74292	+	3.01883i	−0.265793	+	0.460367i	−0.967771	−	0.251831i	$-0.918967\pi$
$43$	−1.74292	+	3.01883i	−0.265793	+	0.460367i	0.701978	+	0.712199i	$0.252300\pi$
$44$		0			0
$45$	3.85478	−	6.02733i	0.574637	−	0.898501i
$46$		0			0
$47$	2.18338	−	3.78173i	0.318479	−	0.551622i	−0.661692	−	0.749776i	$-0.730161\pi$
$47$	2.18338	−	3.78173i	0.318479	−	0.551622i	0.980171	+	0.198154i	$0.0634946\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.87297	−	6.36979i	0.542324	−	0.891950i
$52$		0			0
$53$	−11.6787			−1.60419			−0.802094	−	0.597197i	$-0.796281\pi$
$53$	−11.6787			−1.60419			−0.802094	+	0.597197i	$0.796281\pi$
$54$		0			0
$55$	5.38874			0.726617
$56$		0			0
$57$	7.73534	−	12.7222i	1.02457	−	1.68509i
$58$		0			0
$59$	2.40463	+	4.16495i	0.313056	+	0.542230i	0.979022	−	0.203752i	$-0.0653137\pi$
$59$	2.40463	+	4.16495i	0.313056	+	0.542230i	−0.665966	+	0.745982i	$0.731980\pi$
$60$		0			0
$61$	0.575967	−	0.997604i	0.0737450	−	0.127730i	−0.826795	−	0.562504i	$-0.809838\pi$
$61$	0.575967	−	0.997604i	0.0737450	−	0.127730i	0.900540	+	0.434774i	$0.143172\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.67319	+	9.82626i	−0.703673	+	1.21880i
$66$		0			0
$67$	2.06381	+	3.57463i	0.252135	+	0.436710i	0.964113	−	0.265491i	$-0.0855341\pi$
$67$	2.06381	+	3.57463i	0.252135	+	0.436710i	−0.711979	+	0.702201i	$0.752201\pi$
$68$		0			0
$69$	2.30148	+	0.0522474i	0.277065	+	0.00628985i
$70$		0			0
$71$	−4.41593			−0.524074			−0.262037	−	0.965058i	$-0.584394\pi$
$71$	−4.41593			−0.524074			−0.262037	+	0.965058i	$0.584394\pi$
$72$		0			0
$73$	−12.1118			−1.41758			−0.708790	−	0.705420i	$-0.750759\pi$
$73$	−12.1118			−1.41758			−0.708790	+	0.705420i	$0.750759\pi$
$74$		0			0
$75$	−0.571885	−	1.04459i	−0.0660356	−	0.120619i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.23312	−	7.33198i	0.476263	−	0.824913i	−0.523367	−	0.852108i	$-0.675324\pi$
$79$	4.23312	−	7.33198i	0.476263	−	0.824913i	0.999630	+	0.0271950i	$0.00865752\pi$
$80$		0			0
$81$	−5.18814	+	7.35413i	−0.576460	+	0.817125i
$82$		0			0
$83$	0.817808	−	1.41648i	0.0897661	−	0.155479i	−0.817646	−	0.575721i	$-0.804721\pi$
$83$	0.817808	−	1.41648i	0.0897661	−	0.155479i	0.907412	+	0.420242i	$0.138055\pi$
$84$		0			0
$85$	−5.13226	−	8.88934i	−0.556672	−	0.964184i
$86$		0			0
$87$	−6.45255	−	11.7861i	−0.691786	−	1.26360i
$88$		0			0
$89$	−6.34310			−0.672367			−0.336184	−	0.941796i	$-0.609136\pi$
$89$	−6.34310			−0.672367			−0.336184	+	0.941796i	$0.609136\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.40371	+	0.0318666i	0.145558	+	0.00330441i
$94$		0			0
$95$	−10.2505	−	17.7543i	−1.05168	−	1.82156i
$96$		0			0
$97$	5.98278	−	10.3625i	0.607459	−	1.05215i	−0.384198	−	0.923251i	$-0.625522\pi$
$97$	5.98278	−	10.3625i	0.607459	−	1.05215i	0.991658	−	0.128900i	$-0.0411445\pi$
$98$		0			0
$99$	−6.77170	−	0.307617i	−0.680581	−	0.0309166i
$100$		0			0
$101$	−5.42348	+	9.39374i	−0.539656	+	0.934712i	0.459266	+	0.888299i	$0.348112\pi$
$101$	−5.42348	+	9.39374i	−0.539656	+	0.934712i	−0.998922	+	0.0464132i	$0.985221\pi$
$102$		0			0
$103$	−9.17226	−	15.8868i	−0.903769	−	1.56537i	−0.822561	−	0.568677i	$-0.807455\pi$
$103$	−9.17226	−	15.8868i	−0.903769	−	1.56537i	−0.0812086	−	0.996697i	$-0.525878\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.83412			0.370658			0.185329	−	0.982676i	$-0.440665\pi$
$107$	3.83412			0.370658			0.185329	+	0.982676i	$0.440665\pi$
$108$		0			0
$109$	2.64496			0.253341			0.126671	−	0.991945i	$-0.459571\pi$
$109$	2.64496			0.253341			0.126671	+	0.991945i	$0.459571\pi$
$110$		0			0
$111$	4.16832	−	6.85556i	0.395640	−	0.650701i
$112$		0			0
$113$	−2.64275	−	4.57738i	−0.248609	−	0.430603i	0.714531	−	0.699604i	$-0.246640\pi$
$113$	−2.64275	−	4.57738i	−0.248609	−	0.430603i	−0.963140	+	0.269000i	$0.913307\pi$
$114$		0			0
$115$	1.58486	−	2.74506i	0.147789	−	0.255978i
$116$		0			0
$117$	7.69009	−	12.0242i	0.710949	−	1.11164i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.94719	+	5.10469i	0.267927	+	0.464062i
$122$		0			0
$123$	−17.3308	−	0.393439i	−1.56267	−	0.0354752i
$124$		0			0
$125$	10.2846			0.919880
$126$		0			0
$127$	−7.67115			−0.680704			−0.340352	−	0.940298i	$-0.610546\pi$
$127$	−7.67115			−0.680704			−0.340352	+	0.940298i	$0.610546\pi$
$128$		0			0
$129$	−2.89938	−	5.29593i	−0.255276	−	0.466281i
$130$		0			0
$131$	9.69007	+	16.7837i	0.846625	+	1.46640i	0.884202	+	0.467104i	$0.154703\pi$
$131$	9.69007	+	16.7837i	0.846625	+	1.46640i	−0.0375770	+	0.999294i	$0.511964\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	5.45149	+	11.1286i	0.469189	+	0.957796i
$136$		0			0
$137$	4.84498	−	8.39176i	0.413935	−	0.716956i	−0.581381	−	0.813631i	$-0.697487\pi$
$137$	4.84498	−	8.39176i	0.413935	−	0.716956i	0.995316	+	0.0966750i	$0.0308208\pi$
$138$		0			0
$139$	3.81197	+	6.60252i	0.323327	+	0.560018i	0.981172	−	0.193135i	$-0.0618654\pi$
$139$	3.81197	+	6.60252i	0.323327	+	0.560018i	−0.657846	+	0.753153i	$0.728532\pi$
$140$		0			0
$141$	3.63210	+	6.63429i	0.305878	+	0.558708i
$142$		0			0
$143$	10.7503			0.898981
$144$		0			0
$145$	−18.5011			−1.53643
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.54590	+	7.87372i	0.372414	+	0.645041i	0.989936	−	0.141513i	$-0.0451967\pi$
$149$	4.54590	+	7.87372i	0.372414	+	0.645041i	−0.617522	+	0.786554i	$0.711863\pi$
$150$		0			0
$151$	10.1291	−	17.5441i	0.824294	−	1.42772i	−0.0781631	−	0.996941i	$-0.524905\pi$
$151$	10.1291	−	17.5441i	0.824294	−	1.42772i	0.902457	−	0.430779i	$-0.141761\pi$
$152$		0			0
$153$	5.94195	+	11.4637i	0.480379	+	0.926783i
$154$		0			0
$155$	0.966633	−	1.67426i	0.0776418	−	0.134480i
$156$		0			0
$157$	−4.18075	−	7.24127i	−0.333660	−	0.577917i	0.649566	−	0.760305i	$-0.274951\pi$
$157$	−4.18075	−	7.24127i	−0.333660	−	0.577917i	−0.983227	+	0.182388i	$0.941617\pi$
$158$		0			0
$159$	10.5090	−	17.2839i	0.833418	−	1.37071i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−19.3839			−1.51826			−0.759132	−	0.650937i	$-0.774376\pi$
$163$	−19.3839			−1.51826			−0.759132	+	0.650937i	$0.774376\pi$
$164$		0			0
$165$	−4.84904	+	7.97511i	−0.377497	+	0.620861i
$166$		0			0
$167$	−8.84158	−	15.3141i	−0.684182	−	1.18504i	−0.973693	−	0.227864i	$-0.926826\pi$
$167$	−8.84158	−	15.3141i	−0.684182	−	1.18504i	0.289511	−	0.957175i	$-0.406507\pi$
$168$		0			0
$169$	−4.81772	+	8.34454i	−0.370594	+	0.641888i
$170$		0			0
$171$	11.8676	+	22.8960i	0.907541	+	1.75090i
$172$		0			0
$173$	−10.5928	+	18.3473i	−0.805356	+	1.39492i	0.110695	+	0.993854i	$0.464692\pi$
$173$	−10.5928	+	18.3473i	−0.805356	+	1.39492i	−0.916051	+	0.401063i	$0.868641\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.32775	−	0.189054i	−0.625952	−	0.0142102i
$178$		0			0
$179$	12.9878			0.970753			0.485376	−	0.874305i	$-0.338683\pi$
$179$	12.9878			0.970753			0.485376	+	0.874305i	$0.338683\pi$
$180$		0			0
$181$	−16.8238			−1.25050			−0.625251	−	0.780423i	$-0.715004\pi$
$181$	−16.8238			−1.25050			−0.625251	+	0.780423i	$0.715004\pi$
$182$		0			0
$183$	0.958131	+	1.75010i	0.0708271	+	0.129371i
$184$		0			0
$185$	−5.52365	−	9.56725i	−0.406107	−	0.703398i
$186$		0			0
$187$	−4.86262	+	8.42230i	−0.355590	+	0.615899i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.58561	+	7.94251i	−0.331803	+	0.574700i	−0.982865	−	0.184324i	$-0.940990\pi$
$191$	−4.58561	+	7.94251i	−0.331803	+	0.574700i	0.651062	+	0.759024i	$0.274324\pi$
$192$		0			0
$193$	12.8153	+	22.1968i	0.922466	+	1.59776i	0.795586	+	0.605840i	$0.207163\pi$
$193$	12.8153	+	22.1968i	0.922466	+	1.59776i	0.126880	+	0.991918i	$0.459504\pi$
$194$		0			0
$195$	−9.43745	−	17.2382i	−0.675830	−	1.23445i
$196$		0			0
$197$	16.1036			1.14734			0.573668	−	0.819088i	$-0.305520\pi$
$197$	16.1036			1.14734			0.573668	+	0.819088i	$0.305520\pi$
$198$		0			0
$199$	−19.2282			−1.36305			−0.681526	−	0.731794i	$-0.738683\pi$
$199$	−19.2282			−1.36305			−0.681526	+	0.731794i	$0.738683\pi$
$200$		0			0
$201$	−7.14741	−	0.162258i	−0.504140	−	0.0114448i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−11.9345	+	20.6711i	−0.833540	+	1.44373i
$206$		0			0
$207$	−2.14830	+	3.35907i	−0.149317	+	0.233472i
$208$		0			0
$209$	−9.71192	+	16.8215i	−0.671788	+	1.16357i
$210$		0			0
$211$	−12.3251	−	21.3477i	−0.848496	−	1.46964i	−0.882551	−	0.470218i	$-0.844175\pi$
$211$	−12.3251	−	21.3477i	−0.848496	−	1.46964i	0.0340549	−	0.999420i	$-0.489158\pi$
$212$		0			0
$213$	3.97365	−	6.53539i	0.272270	−	0.447797i
$214$		0			0
$215$	−8.31325			−0.566959
$216$		0			0
$217$		0			0
$218$		0			0
$219$	10.8988	−	17.9250i	0.736470	−	1.21126i
$220$		0			0
$221$	−10.2386	−	17.7338i	−0.688723	−	1.19290i
$222$		0			0
$223$	−7.41074	+	12.8358i	−0.496260	+	0.859547i	−0.999991	−	0.00431335i	$-0.998627\pi$
$223$	−7.41074	+	12.8358i	−0.496260	+	0.859547i	0.503731	+	0.863861i	$0.331960\pi$
$224$		0			0
$225$	2.06056	+	0.0936047i	0.137371	+	0.00624031i
$226$		0			0
$227$	−9.07752	+	15.7227i	−0.602496	+	1.04355i	0.389946	+	0.920838i	$0.372494\pi$
$227$	−9.07752	+	15.7227i	−0.602496	+	1.04355i	−0.992442	+	0.122716i	$0.960840\pi$
$228$		0			0
$229$	4.75346	+	8.23323i	0.314117	+	0.544067i	0.979249	−	0.202659i	$-0.0649581\pi$
$229$	4.75346	+	8.23323i	0.314117	+	0.544067i	−0.665132	+	0.746726i	$0.731625\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.3431			1.33272			0.666360	−	0.745630i	$-0.267851\pi$
$233$	20.3431			1.33272			0.666360	+	0.745630i	$0.267851\pi$
$234$		0			0
$235$	10.4141			0.679343
$236$		0			0
$237$	7.04187	+	12.8625i	0.457419	+	0.835509i
$238$		0			0
$239$	8.90544	+	15.4247i	0.576045	+	0.997739i	0.995927	+	0.0901607i	$0.0287381\pi$
$239$	8.90544	+	15.4247i	0.576045	+	0.997739i	−0.419882	+	0.907579i	$0.637929\pi$
$240$		0			0
$241$	3.14437	−	5.44620i	0.202546	−	0.350821i	−0.746802	−	0.665047i	$-0.768412\pi$
$241$	3.14437	−	5.44620i	0.202546	−	0.350821i	0.949348	+	0.314226i	$0.101745\pi$
$242$		0			0
$243$	−6.21527	−	14.2958i	−0.398710	−	0.917077i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−20.4492	−	35.4190i	−1.30115	−	2.25366i
$248$		0			0
$249$	1.36044	+	2.48494i	0.0862142	+	0.157477i
$250$		0			0
$251$	25.1868			1.58978			0.794889	−	0.606755i	$-0.207529\pi$
$251$	25.1868			1.58978			0.794889	+	0.606755i	$0.207529\pi$
$252$		0			0
$253$	−3.00318			−0.188809
$254$		0			0
$255$	17.7741	+	0.403502i	1.11306	+	0.0252683i
$256$		0			0
$257$	14.3401	+	24.8379i	0.894514	+	1.54934i	0.834405	+	0.551152i	$0.185811\pi$
$257$	14.3401	+	24.8379i	0.894514	+	1.54934i	0.0601087	+	0.998192i	$0.480855\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	23.2492	+	1.05614i	1.43909	+	0.0653732i
$262$		0			0
$263$	7.20840	−	12.4853i	0.444489	−	0.769877i	−0.553528	−	0.832831i	$-0.686719\pi$
$263$	7.20840	−	12.4853i	0.444489	−	0.769877i	0.998016	+	0.0629537i	$0.0200520\pi$
$264$		0			0
$265$	−13.9260	−	24.1205i	−0.855468	−	1.48171i
$266$		0			0
$267$	5.70782	−	9.38753i	0.349313	−	0.574507i
$268$		0			0
$269$	12.8999			0.786524			0.393262	−	0.919426i	$-0.371347\pi$
$269$	12.8999			0.786524			0.393262	+	0.919426i	$0.371347\pi$
$270$		0			0
$271$	19.4622			1.18224			0.591122	−	0.806582i	$-0.298685\pi$
$271$	19.4622			1.18224			0.591122	+	0.806582i	$0.298685\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.776794	+	1.34545i	0.0468424	+	0.0811335i
$276$		0			0
$277$	−7.95620	+	13.7805i	−0.478042	+	0.827993i	−0.999683	−	0.0251721i	$-0.991987\pi$
$277$	−7.95620	+	13.7805i	−0.478042	+	0.827993i	0.521641	+	0.853165i	$0.325320\pi$
$278$		0			0
$279$	−1.31028	+	2.04876i	−0.0784446	+	0.122656i
$280$		0			0
$281$	−13.9998	+	24.2484i	−0.835158	+	1.44654i	0.0587432	+	0.998273i	$0.481291\pi$
$281$	−13.9998	+	24.2484i	−0.835158	+	1.44654i	−0.893901	+	0.448263i	$0.852043\pi$
$282$		0			0
$283$	2.62345	+	4.54394i	0.155948	+	0.270109i	0.933404	−	0.358828i	$-0.116824\pi$
$283$	2.62345	+	4.54394i	0.155948	+	0.270109i	−0.777456	+	0.628937i	$0.783490\pi$
$284$		0			0
$285$	35.4996	+	0.805900i	2.10281	+	0.0477374i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.52473			0.0896898
$290$		0			0
$291$	9.95246	+	18.1789i	0.583423	+	1.06567i
$292$		0			0
$293$	−1.65939	−	2.87415i	−0.0969428	−	0.167910i	0.813475	−	0.581600i	$-0.197573\pi$
$293$	−1.65939	−	2.87415i	−0.0969428	−	0.167910i	−0.910418	+	0.413690i	$0.864240\pi$
$294$		0			0
$295$	−5.73471	+	9.93282i	−0.333888	+	0.578311i
$296$		0			0
$297$	6.54875	−	9.74503i	0.379997	−	0.565464i
$298$		0			0
$299$	3.16171	−	5.47625i	0.182847	−	0.316700i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−9.02205	−	16.4794i	−0.518303	−	0.946719i
$304$		0			0
$305$	2.74720			0.157304
$306$		0			0
$307$	−12.4703			−0.711715			−0.355857	−	0.934540i	$-0.615811\pi$
$307$	−12.4703			−0.711715			−0.355857	+	0.934540i	$0.615811\pi$
$308$		0			0
$309$	31.7654	+	0.721130i	1.80707	+	0.0410236i
$310$		0			0
$311$	11.3383	+	19.6385i	0.642936	+	1.11360i	0.984774	+	0.173840i	$0.0556174\pi$
$311$	11.3383	+	19.6385i	0.642936	+	1.11360i	−0.341838	+	0.939759i	$0.611049\pi$
$312$		0			0
$313$	3.16108	−	5.47515i	0.178675	−	0.309474i	−0.762752	−	0.646691i	$-0.776152\pi$
$313$	3.16108	−	5.47515i	0.178675	−	0.309474i	0.941427	+	0.337217i	$0.109486\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.79041	−	13.4934i	0.437553	−	0.757864i	−0.559947	−	0.828528i	$-0.689179\pi$
$317$	7.79041	−	13.4934i	0.437553	−	0.757864i	0.997500	+	0.0706643i	$0.0225119\pi$
$318$		0			0
$319$	8.76453	+	15.1806i	0.490719	+	0.849951i
$320$		0			0
$321$	−3.45012	+	5.67434i	−0.192567	+	0.316711i
$322$		0			0
$323$	36.9987			2.05867
$324$		0			0
$325$	−3.27119			−0.181453
$326$		0			0
$327$	−2.38006	+	3.91443i	−0.131618	+	0.216469i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.8634	−	18.8159i	0.597104	−	1.03422i	−0.396142	−	0.918189i	$-0.629651\pi$
$331$	10.8634	−	18.8159i	0.597104	−	1.03422i	0.993246	−	0.116026i	$-0.0370155\pi$
$332$		0			0
$333$	6.39509	+	12.3379i	0.350449	+	0.676112i
$334$		0			0
$335$	−4.92190	+	8.52499i	−0.268912	+	0.465770i
$336$		0			0
$337$	4.04329	+	7.00319i	0.220252	+	0.381488i	0.954884	−	0.296977i	$-0.0959786\pi$
$337$	4.04329	+	7.00319i	0.220252	+	0.381488i	−0.734632	+	0.678465i	$0.762645\pi$
$338$		0			0
$339$	9.15239	+	0.207775i	0.497090	+	0.0112848i
$340$		0			0
$341$	−1.83169			−0.0991917
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.63644	+	4.81566i	0.141941	+	0.259266i
$346$		0			0
$347$	0.466877	+	0.808654i	0.0250632	+	0.0434108i	0.878285	−	0.478138i	$-0.158688\pi$
$347$	0.466877	+	0.808654i	0.0250632	+	0.0434108i	−0.853222	+	0.521548i	$0.825355\pi$
$348$		0			0
$349$	−1.90264	+	3.29548i	−0.101846	+	0.176403i	−0.912445	−	0.409199i	$-0.865808\pi$
$349$	−1.90264	+	3.29548i	−0.101846	+	0.176403i	0.810599	+	0.585601i	$0.199142\pi$
$350$		0			0
$351$	10.8754	+	22.2009i	0.580487	+	1.18500i
$352$		0			0
$353$	6.55974	−	11.3618i	0.349140	−	0.604728i	−0.636957	−	0.770899i	$-0.719807\pi$
$353$	6.55974	−	11.3618i	0.349140	−	0.604728i	0.986097	+	0.166171i	$0.0531405\pi$
$354$		0			0
$355$	−5.26569	−	9.12043i	−0.279474	−	0.484062i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−21.5658			−1.13820			−0.569100	−	0.822268i	$-0.692708\pi$
$359$	−21.5658			−1.13820			−0.569100	+	0.822268i	$0.692708\pi$
$360$		0			0
$361$	54.8962			2.88927
$362$		0			0
$363$	−10.2067	−	0.231710i	−0.535715	−	0.0121616i
$364$		0			0
$365$	−14.4425	−	25.0151i	−0.755954	−	1.30935i
$366$		0			0
$367$	−9.33095	+	16.1617i	−0.487072	+	0.843633i	−0.999890	−	0.0148645i	$-0.995268\pi$
$367$	−9.33095	+	16.1617i	−0.487072	+	0.843633i	0.512818	+	0.858497i	$0.328602\pi$
$368$		0			0
$369$	16.1773	−	25.2948i	0.842158	−	1.31680i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.0854	+	17.4684i	0.522201	+	0.904478i	0.999666	+	0.0258279i	$0.00822218\pi$
$373$	10.0854	+	17.4684i	0.522201	+	0.904478i	−0.477466	+	0.878650i	$0.658444\pi$
$374$		0			0
$375$	−9.25453	+	15.2207i	−0.477902	+	0.785995i
$376$		0			0
$377$	−36.9087			−1.90090
$378$		0			0
$379$	18.2436			0.937110			0.468555	−	0.883434i	$-0.344775\pi$
$379$	18.2436			0.937110			0.468555	+	0.883434i	$0.344775\pi$
$380$		0			0
$381$	6.90285	−	11.3530i	0.353644	−	0.581631i
$382$		0			0
$383$	11.4282	+	19.7942i	0.583952	+	1.01143i	0.995005	+	0.0998233i	$0.0318278\pi$
$383$	11.4282	+	19.7942i	0.583952	+	1.01143i	−0.411053	+	0.911611i	$0.634839\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.4468	+	0.474563i	0.531039	+	0.0241234i
$388$		0			0
$389$	−6.17146	+	10.6893i	−0.312905	+	0.541968i	−0.978990	−	0.203908i	$-0.934636\pi$
$389$	−6.17146	+	10.6893i	−0.312905	+	0.541968i	0.666085	+	0.745876i	$0.267969\pi$
$390$		0			0
$391$	2.86025	+	4.95410i	0.144649	+	0.250539i
$392$		0			0
$393$	−33.5587	−	0.761840i	−1.69281	−	0.0384298i
$394$		0			0
$395$	20.1908			1.01591
$396$		0			0
$397$	−26.2032			−1.31510			−0.657551	−	0.753410i	$-0.728408\pi$
$397$	−26.2032			−1.31510			−0.657551	+	0.753410i	$0.728408\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.95559	−	3.38718i	−0.0976575	−	0.169148i	0.813057	−	0.582184i	$-0.197802\pi$
$401$	−1.95559	−	3.38718i	−0.0976575	−	0.169148i	−0.910715	+	0.413036i	$0.864468\pi$
$402$		0			0
$403$	1.92838	−	3.34006i	0.0960596	−	0.166380i
$404$		0			0
$405$	−21.3753	−	1.94604i	−1.06215	−	0.0966997i
$406$		0			0
$407$	−5.23344	+	9.06459i	−0.259412	+	0.449315i
$408$		0			0
$409$	−1.05065	−	1.81978i	−0.0519513	−	0.0899823i	0.838880	−	0.544316i	$-0.183211\pi$
$409$	−1.05065	−	1.81978i	−0.0519513	−	0.0899823i	−0.890832	+	0.454334i	$0.849877\pi$
$410$		0			0
$411$	8.05971	+	14.7217i	0.397556	+	0.726166i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.90072			0.191479
$416$		0			0
$417$	−13.2016	−	0.299700i	−0.646487	−	0.0146763i
$418$		0			0
$419$	−11.7017	−	20.2679i	−0.571664	−	0.990150i	−0.996395	−	0.0848311i	$-0.972965\pi$
$419$	−11.7017	−	20.2679i	−0.571664	−	0.990150i	0.424732	−	0.905319i	$-0.360368\pi$
$420$		0			0
$421$	9.78341	−	16.9454i	0.476814	−	0.825866i	−0.522833	−	0.852435i	$-0.675125\pi$
$421$	9.78341	−	16.9454i	0.476814	−	0.825866i	0.999647	+	0.0265688i	$0.00845812\pi$
$422$		0			0
$423$	−13.0868	−	0.594492i	−0.636302	−	0.0289052i
$424$		0			0
$425$	1.47965	−	2.56282i	0.0717733	−	0.124315i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−9.67357	+	15.9099i	−0.467044	+	0.768138i
$430$		0			0
$431$	6.70877			0.323150			0.161575	−	0.986860i	$-0.448343\pi$
$431$	6.70877			0.323150			0.161575	+	0.986860i	$0.448343\pi$
$432$		0			0
$433$	9.46607			0.454910			0.227455	−	0.973789i	$-0.426959\pi$
$433$	9.46607			0.454910			0.227455	+	0.973789i	$0.426959\pi$
$434$		0			0
$435$	16.6481	−	27.3809i	0.798217	−	1.31281i
$436$		0			0
$437$	5.71267	+	9.89463i	0.273274	+	0.473324i
$438$		0			0
$439$	−3.82386	+	6.62312i	−0.182503	+	0.316104i	−0.942732	−	0.333550i	$-0.891753\pi$
$439$	−3.82386	+	6.62312i	−0.182503	+	0.316104i	0.760229	+	0.649655i	$0.225087\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.0763	+	31.3091i	−0.858833	+	1.48754i	0.0142102	+	0.999899i	$0.495477\pi$
$443$	−18.0763	+	31.3091i	−0.858833	+	1.48754i	−0.873043	+	0.487643i	$0.837857\pi$
$444$		0			0
$445$	−7.56371	−	13.1007i	−0.358554	−	0.621034i
$446$		0			0
$447$	−15.7434	−	0.357402i	−0.744637	−	0.0169045i
$448$		0			0
$449$	13.7337			0.648132			0.324066	−	0.946034i	$-0.394950\pi$
$449$	13.7337			0.648132			0.324066	+	0.946034i	$0.394950\pi$
$450$		0			0
$451$	22.6149			1.06489
$452$		0			0
$453$	16.8499	+	30.7776i	0.791679	+	1.44606i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.213109	−	0.369115i	0.00996881	−	0.0172665i	−0.860998	−	0.508608i	$-0.830160\pi$
$457$	0.213109	−	0.369115i	0.00996881	−	0.0172665i	0.870967	+	0.491342i	$0.163493\pi$
$458$		0			0
$459$	−22.3126	−	1.52169i	−1.04146	−	0.0710266i
$460$		0			0
$461$	−2.26453	+	3.92228i	−0.105470	+	0.182679i	−0.913930	−	0.405872i	$-0.866968\pi$
$461$	−2.26453	+	3.92228i	−0.105470	+	0.182679i	0.808460	+	0.588551i	$0.200301\pi$
$462$		0			0
$463$	16.5598	+	28.6825i	0.769600	+	1.33299i	0.937780	+	0.347230i	$0.112878\pi$
$463$	16.5598	+	28.6825i	0.769600	+	1.33299i	−0.168179	+	0.985756i	$0.553789\pi$
$464$		0			0
$465$	1.60801	+	2.93715i	0.0745697	+	0.136207i
$466$		0			0
$467$	−1.51332			−0.0700281			−0.0350140	−	0.999387i	$-0.511148\pi$
$467$	−1.51332			−0.0700281			−0.0350140	+	0.999387i	$0.511148\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	14.4788	+	0.328694i	0.667149	+	0.0151454i
$472$		0			0
$473$	3.93824	+	6.82123i	0.181080	+	0.313640i
$474$		0			0
$475$	2.95524	−	5.11863i	0.135596	−	0.234859i
$476$		0			0
$477$	16.1230	+	31.1058i	0.738223	+	1.42424i
$478$		0			0
$479$	−11.1463	+	19.3060i	−0.509288	+	0.882112i	0.490654	+	0.871354i	$0.336758\pi$
$479$	−11.1463	+	19.3060i	−0.509288	+	0.882112i	−0.999942	+	0.0107580i	$0.996576\pi$
$480$		0			0
$481$	−11.0194	−	19.0862i	−0.502441	−	0.870254i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	28.5362			1.29576
$486$		0			0
$487$	4.63353			0.209965			0.104983	−	0.994474i	$-0.466521\pi$
$487$	4.63353			0.209965			0.104983	+	0.994474i	$0.466521\pi$
$488$		0			0
$489$	17.4425	−	28.6874i	0.788778	−	1.29729i
$490$		0			0
$491$	−12.5858	−	21.7993i	−0.567990	−	0.983788i	−0.996765	−	0.0803766i	$-0.974388\pi$
$491$	−12.5858	−	21.7993i	−0.567990	−	0.983788i	0.428774	−	0.903412i	$-0.358946\pi$
$492$		0			0
$493$	16.6948	−	28.9162i	0.751894	−	1.30232i
$494$		0			0
$495$	−7.43944	−	14.3527i	−0.334378	−	0.645108i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.13727	+	1.96982i	0.0509114	+	0.0881811i	0.890358	−	0.455261i	$-0.150454\pi$
$499$	1.13727	+	1.96982i	0.0509114	+	0.0881811i	−0.839447	+	0.543442i	$0.817121\pi$
$500$		0			0
$501$	30.6203	+	0.695132i	1.36801	+	0.0310562i
$502$		0			0
$503$	−8.94793			−0.398968			−0.199484	−	0.979901i	$-0.563927\pi$
$503$	−8.94793			−0.398968			−0.199484	+	0.979901i	$0.563927\pi$
$504$		0			0
$505$	−25.8685			−1.15113
$506$		0			0
$507$	−8.01437	−	14.6388i	−0.355930	−	0.650133i
$508$		0			0
$509$	16.6343	+	28.8115i	0.737304	+	1.27705i	0.953705	+	0.300743i	$0.0972346\pi$
$509$	16.6343	+	28.8115i	0.737304	+	1.27705i	−0.216402	+	0.976304i	$0.569432\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−44.5641	−	3.03922i	−1.96755	−	0.134185i
$514$		0			0
$515$	21.8746	−	37.8878i	0.963908	−	1.66954i
$516$		0			0
$517$	−4.93349	−	8.54505i	−0.216975	−	0.375811i
$518$		0			0
$519$	−17.6213	−	32.1866i	−0.773490	−	1.41284i
$520$		0			0
$521$	−15.1479			−0.663642			−0.331821	−	0.943342i	$-0.607663\pi$
$521$	−15.1479			−0.663642			−0.331821	+	0.943342i	$0.607663\pi$
$522$		0			0
$523$	−10.4790			−0.458217			−0.229108	−	0.973401i	$-0.573581\pi$
$523$	−10.4790			−0.458217			−0.229108	+	0.973401i	$0.573581\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.74451	+	3.02159i	0.0759922	+	0.131622i
$528$		0			0
$529$	10.6167	−	18.3887i	0.461598	−	0.799511i
$530$		0			0
$531$	7.77348	−	12.1546i	0.337340	−	0.527465i
$532$		0			0
$533$	−23.8086	+	41.2378i	−1.03127	+	1.78621i
$534$		0			0
$535$	4.57192	+	7.91880i	0.197661	+	0.342360i
$536$		0			0
$537$	−11.6870	+	19.2214i	−0.504332	+	0.829464i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.87748			0.209699			0.104850	−	0.994488i	$-0.466564\pi$
$541$	4.87748			0.209699			0.104850	+	0.994488i	$0.466564\pi$
$542$		0			0
$543$	15.1388	−	24.8985i	0.649669	−	1.06850i
$544$		0			0
$545$	3.15393	+	5.46277i	0.135100	+	0.234000i
$546$		0			0
$547$	9.62179	−	16.6654i	0.411398	−	0.712562i	−0.583645	−	0.812009i	$-0.698374\pi$
$547$	9.62179	−	16.6654i	0.411398	−	0.712562i	0.995043	+	0.0994468i	$0.0317073\pi$
$548$		0			0
$549$	−3.45224	−	0.156824i	−0.147338	−	0.00669310i
$550$		0			0
$551$	33.3438	−	57.7532i	1.42049	−	2.46037i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	19.1296	+	0.434274i	0.812005	+	0.0184339i
$556$		0			0
$557$	14.6478			0.620646			0.310323	−	0.950631i	$-0.399563\pi$
$557$	14.6478			0.620646			0.310323	+	0.950631i	$0.399563\pi$
$558$		0			0
$559$	−16.5845			−0.701450
$560$		0			0
$561$	−8.08905	−	14.7752i	−0.341520	−	0.623811i
$562$		0			0
$563$	−1.85335	−	3.21010i	−0.0781095	−	0.135290i	0.824325	−	0.566117i	$-0.191555\pi$
$563$	−1.85335	−	3.21010i	−0.0781095	−	0.135290i	−0.902434	+	0.430828i	$0.858222\pi$
$564$		0			0
$565$	6.30259	−	10.9164i	0.265152	−	0.459257i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.1768	+	26.2871i	−0.636246	+	1.10201i	0.350004	+	0.936748i	$0.386180\pi$
$569$	−15.1768	+	26.2871i	−0.636246	+	1.10201i	−0.986250	+	0.165262i	$0.947153\pi$
$570$		0			0
$571$	5.88458	+	10.1924i	0.246262	+	0.426539i	0.962486	−	0.271332i	$-0.0874642\pi$
$571$	5.88458	+	10.1924i	0.246262	+	0.426539i	−0.716224	+	0.697871i	$0.754131\pi$
$572$		0			0
$573$	−7.62825	−	13.9336i	−0.318675	−	0.582083i
$574$		0			0
$575$	0.913839			0.0381097
$576$		0			0
$577$	−3.59281			−0.149570			−0.0747852	−	0.997200i	$-0.523827\pi$
$577$	−3.59281			−0.149570			−0.0747852	+	0.997200i	$0.523827\pi$
$578$		0			0
$579$	−44.3821	−	1.00755i	−1.84446	−	0.0418723i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−13.1943	+	22.8533i	−0.546454	+	0.946485i
$584$		0			0
$585$	34.0041	+	1.54470i	1.40590	+	0.0638654i
$586$		0			0
$587$	−4.62298	+	8.00724i	−0.190811	+	0.330494i	−0.945519	−	0.325566i	$-0.894445\pi$
$587$	−4.62298	+	8.00724i	−0.190811	+	0.330494i	0.754708	+	0.656060i	$0.227778\pi$
$588$		0			0
$589$	3.48425	+	6.03490i	0.143566	+	0.248664i
$590$		0			0
$591$	−14.4908	+	23.8327i	−0.596071	+	0.980346i
$592$		0			0
$593$	−34.0793			−1.39947			−0.699735	−	0.714403i	$-0.746698\pi$
$593$	−34.0793			−1.39947			−0.699735	+	0.714403i	$0.746698\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	17.3024	−	28.4570i	0.708142	−	1.16467i
$598$		0			0
$599$	3.51340	+	6.08539i	0.143554	+	0.248642i	0.928832	−	0.370500i	$-0.120814\pi$
$599$	3.51340	+	6.08539i	0.143554	+	0.248642i	−0.785279	+	0.619142i	$0.787480\pi$
$600$		0			0
$601$	2.31218	−	4.00481i	0.0943158	−	0.163360i	−0.815007	−	0.579451i	$-0.803267\pi$
$601$	2.31218	−	4.00481i	0.0943158	−	0.163360i	0.909323	+	0.416091i	$0.136600\pi$
$602$		0			0
$603$	6.67171	−	10.4319i	0.271693	−	0.424818i
$604$		0			0
$605$	−7.02864	+	12.1740i	−0.285755	+	0.494942i
$606$		0			0
$607$	10.1041	+	17.5007i	0.410111	+	0.710333i	0.994901	−	0.100852i	$-0.0321567\pi$
$607$	10.1041	+	17.5007i	0.410111	+	0.710333i	−0.584791	+	0.811184i	$0.698823\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.7756			0.840493
$612$		0			0
$613$	−17.8207			−0.719773			−0.359887	−	0.932996i	$-0.617185\pi$
$613$	−17.8207			−0.719773			−0.359887	+	0.932996i	$0.617185\pi$
$614$		0			0
$615$	−19.8532	−	36.2633i	−0.800558	−	1.46228i
$616$		0			0
$617$	15.0671	+	26.0969i	0.606577	+	1.05062i	0.991800	+	0.127799i	$0.0407913\pi$
$617$	15.0671	+	26.0969i	0.606577	+	1.05062i	−0.385223	+	0.922824i	$0.625875\pi$
$618$		0			0
$619$	−15.9558	+	27.6363i	−0.641318	+	1.11080i	0.343821	+	0.939035i	$0.388279\pi$
$619$	−15.9558	+	27.6363i	−0.641318	+	1.11080i	−0.985139	+	0.171760i	$0.945055\pi$
$620$		0			0
$621$	−3.03815	−	6.20204i	−0.121917	−	0.248879i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	13.9825	+	24.2185i	0.559301	+	0.968738i
$626$		0			0
$627$	−16.1559	−	29.5100i	−0.645206	−	1.17852i
$628$		0			0
$629$	19.9374			0.794957
$630$		0			0
$631$	−10.1430			−0.403788			−0.201894	−	0.979407i	$-0.564710\pi$
$631$	−10.1430			−0.403788			−0.201894	+	0.979407i	$0.564710\pi$
$632$		0			0
$633$	42.6844	+	0.969009i	1.69655	+	0.0385147i
$634$		0			0
$635$	−9.14731	−	15.8436i	−0.363000	−	0.628734i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.09643	+	11.7617i	0.241171	+	0.465285i
$640$		0			0
$641$	−21.9256	+	37.9762i	−0.866009	+	1.49997i	3.28428e−5		1.00000i	$0.499990\pi$
$641$	−21.9256	+	37.9762i	−0.866009	+	1.49997i	−0.866042	+	0.499972i	$0.833344\pi$
$642$		0			0
$643$	−1.10737	−	1.91802i	−0.0436704	−	0.0756394i	0.843364	−	0.537343i	$-0.180572\pi$
$643$	−1.10737	−	1.91802i	−0.0436704	−	0.0756394i	−0.887034	+	0.461703i	$0.847238\pi$
$644$		0			0
$645$	7.48065	−	12.3033i	0.294550	−	0.484441i
$646$		0			0
$647$	−20.9266			−0.822710			−0.411355	−	0.911475i	$-0.634944\pi$
$647$	−20.9266			−0.822710			−0.411355	+	0.911475i	$0.634944\pi$
$648$		0			0
$649$	10.8668			0.426560
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.01442	−	6.95317i	−0.157096	−	0.272099i	0.776724	−	0.629841i	$-0.216880\pi$
$653$	−4.01442	−	6.95317i	−0.157096	−	0.272099i	−0.933820	+	0.357742i	$0.883547\pi$
$654$		0			0
$655$	−23.1095	+	40.0268i	−0.902962	+	1.56398i
$656$		0			0
$657$	16.7210	+	32.2594i	0.652348	+	1.25856i
$658$		0			0
$659$	9.25793	−	16.0352i	0.360638	−	0.624643i	−0.627428	−	0.778675i	$-0.715892\pi$
$659$	9.25793	−	16.0352i	0.360638	−	0.624643i	0.988066	+	0.154031i	$0.0492257\pi$
$660$		0			0
$661$	−10.4273	−	18.0606i	−0.405574	−	0.702474i	0.588814	−	0.808268i	$-0.299595\pi$
$661$	−10.4273	−	18.0606i	−0.405574	−	0.702474i	−0.994388	+	0.105794i	$0.966262\pi$
$662$		0			0
$663$	35.4584	+	0.804966i	1.37709	+	0.0312623i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.3108			0.399236
$668$		0			0
$669$	−12.3279	−	22.5178i	−0.476624	−	0.870589i
$670$		0			0
$671$	−1.30143	−	2.25415i	−0.0502412	−	0.0870204i
$672$		0			0
$673$	11.4484	−	19.8292i	0.441303	−	0.764360i	−0.556483	−	0.830859i	$-0.687850\pi$
$673$	11.4484	−	19.8292i	0.441303	−	0.764360i	0.997786	+	0.0664992i	$0.0211830\pi$
$674$		0			0
$675$	−1.99272	+	2.96531i	−0.0766998	+	0.114135i
$676$		0			0
$677$	23.3119	−	40.3774i	0.895948	−	1.55183i	0.0633218	−	0.997993i	$-0.479831\pi$
$677$	23.3119	−	40.3774i	0.895948	−	1.55183i	0.832627	−	0.553835i	$-0.186836\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−15.1006	−	27.5824i	−0.578656	−	1.05696i
$682$		0			0
$683$	−36.6203			−1.40124			−0.700618	−	0.713536i	$-0.747092\pi$
$683$	−36.6203			−1.40124			−0.700618	+	0.713536i	$0.747092\pi$
$684$		0			0
$685$	23.1092			0.882958
$686$		0			0
$687$	−16.4622	−	0.373720i	−0.628073	−	0.0142583i
$688$		0			0
$689$	−27.7816	−	48.1192i	−1.05840	−	1.83320i
$690$		0			0
$691$	−13.2586	+	22.9645i	−0.504380	+	0.873611i	0.495607	+	0.868547i	$0.334945\pi$
$691$	−13.2586	+	22.9645i	−0.504380	+	0.873611i	−0.999987	+	0.00506472i	$0.998388\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.09101	+	15.7461i	−0.344842	+	0.597283i
$696$		0			0
$697$	−21.5385	−	37.3058i	−0.815830	−	1.41306i
$698$		0			0
$699$	−18.3057	+	30.1069i	−0.692383	+	1.13875i
$700$		0			0
$701$	−29.9931			−1.13282			−0.566411	−	0.824123i	$-0.691669\pi$
$701$	−29.9931			−1.13282			−0.566411	+	0.824123i	$0.691669\pi$
$702$		0			0
$703$	39.8203			1.50185
$704$		0			0
$705$	−9.37111	+	15.4125i	−0.352937	+	0.580468i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.48805	+	9.50558i	−0.206108	+	0.356990i	−0.950485	−	0.310770i	$-0.899413\pi$
$709$	−5.48805	+	9.50558i	−0.206108	+	0.356990i	0.744377	+	0.667759i	$0.232746\pi$
$710$		0			0
$711$	−25.3726	−	1.15259i	−0.951546	−	0.0432257i
$712$		0			0
$713$	−0.538712	+	0.933076i	−0.0201749	+	0.0349440i
$714$		0			0
$715$	12.8189	+	22.2030i	0.479401	+	0.830346i
$716$		0			0
$717$	−30.8414	−	0.700152i	−1.15179	−	0.0261477i
$718$		0			0
$719$	−13.1042			−0.488705			−0.244352	−	0.969687i	$-0.578575\pi$
$719$	−13.1042			−0.488705			−0.244352	+	0.969687i	$0.578575\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.23071	+	9.55427i	0.194532	+	0.355327i
$724$		0			0
$725$	−2.66696	−	4.61931i	−0.0990483	−	0.171557i
$726$		0			0
$727$	−8.96026	+	15.5196i	−0.332318	+	0.575591i	−0.982966	−	0.183788i	$-0.941164\pi$
$727$	−8.96026	+	15.5196i	−0.332318	+	0.575591i	0.650648	+	0.759379i	$0.274497\pi$
$728$		0			0
$729$	26.7500	+	3.66569i	0.990741	+	0.135766i
$730$		0			0
$731$	7.50160	−	12.9932i	0.277457	−	0.480569i
$732$		0			0
$733$	−2.95660	−	5.12098i	−0.109204	−	0.189148i	0.806244	−	0.591583i	$-0.201497\pi$
$733$	−2.95660	−	5.12098i	−0.109204	−	0.189148i	−0.915448	+	0.402436i	$0.868164\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.32662			0.343550
$738$		0			0
$739$	−29.1774			−1.07331			−0.536653	−	0.843803i	$-0.680312\pi$
$739$	−29.1774			−1.07331			−0.536653	+	0.843803i	$0.680312\pi$
$740$		0			0
$741$	70.8197	+	1.60773i	2.60163	+	0.0590614i
$742$		0			0
$743$	−18.8512	−	32.6513i	−0.691584	−	1.19786i	−0.971319	−	0.237781i	$-0.923580\pi$
$743$	−18.8512	−	32.6513i	−0.691584	−	1.19786i	0.279735	−	0.960077i	$-0.409753\pi$
$744$		0			0
$745$	−10.8413	+	18.7777i	−0.397196	+	0.687963i
$746$		0			0
$747$	−4.90179	−	0.222673i	−0.179347	−	0.00814717i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.3277	−	35.2085i	−0.741767	−	1.28478i	−0.951690	−	0.307060i	$-0.900655\pi$
$751$	−20.3277	−	35.2085i	−0.741767	−	1.28478i	0.209923	−	0.977718i	$-0.432679\pi$
$752$		0			0
$753$	−22.6643	+	37.2755i	−0.825932	+	1.35839i
$754$		0			0
$755$	48.3130			1.75829
$756$		0			0
$757$	17.6704			0.642241			0.321120	−	0.947038i	$-0.395941\pi$
$757$	17.6704			0.642241			0.321120	+	0.947038i	$0.395941\pi$
$758$		0			0
$759$	2.70240	−	4.44459i	0.0980910	−	0.161328i
$760$		0			0
$761$	0.644183	+	1.11576i	0.0233516	+	0.0404462i	0.877465	−	0.479641i	$-0.159233\pi$
$761$	0.644183	+	1.11576i	0.0233516	+	0.0404462i	−0.854113	+	0.520087i	$0.825900\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−16.5911	+	25.9418i	−0.599853	+	0.937929i
$766$		0			0
$767$	−11.4405	+	19.8154i	−0.413091	+	0.715494i
$768$		0			0
$769$	4.19275	+	7.26205i	0.151194	+	0.261876i	0.931667	−	0.363314i	$-0.118355\pi$
$769$	4.19275	+	7.26205i	0.151194	+	0.261876i	−0.780472	+	0.625190i	$0.785021\pi$
$770$		0			0
$771$	−49.6629	−	1.12743i	−1.78857	−	0.0406035i
$772$		0			0
$773$	50.3060			1.80938			0.904691	−	0.426068i	$-0.140102\pi$
$773$	50.3060			1.80938			0.904691	+	0.426068i	$0.140102\pi$
$774$		0			0
$775$	0.557366			0.0200212
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−43.0181	−	74.5095i	−1.54128	−	2.66958i
$780$		0			0
$781$	−4.98903	+	8.64125i	−0.178521	+	0.309208i
$782$		0			0
$783$	−22.4837	+	33.4575i	−0.803503	+	1.19567i
$784$		0			0
$785$	9.97051	−	17.2694i	0.355863	−	0.616373i
$786$		0			0
$787$	−11.1922	−	19.3855i	−0.398960	−	0.691020i	0.594638	−	0.803994i	$-0.297296\pi$
$787$	−11.1922	−	19.3855i	−0.398960	−	0.691020i	−0.993598	+	0.112974i	$0.963962\pi$
$788$		0			0
$789$	11.9913	+	21.9030i	0.426901	+	0.779767i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.48052			0.194619
$794$		0			0
$795$	48.2287	+	1.09487i	1.71049	+	0.0388311i
$796$		0			0
$797$	−0.706182	−	1.22314i	−0.0250143	−	0.0433260i	0.853247	−	0.521507i	$-0.174630\pi$
$797$	−0.706182	−	1.22314i	−0.0250143	−	0.0433260i	−0.878262	+	0.478181i	$0.841296\pi$
$798$		0			0
$799$	−9.39736	+	16.2767i	−0.332455	+	0.575828i
$800$		0			0
$801$	8.75699	+	16.8947i	0.309413	+	0.596943i
$802$		0			0
$803$	−13.6837	+	23.7008i	−0.482887	+	0.836384i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.6080	+	19.0914i	−0.408620	+	0.672049i
$808$		0			0
$809$	20.0848			0.706142			0.353071	−	0.935596i	$-0.385137\pi$
$809$	20.0848			0.706142			0.353071	+	0.935596i	$0.385137\pi$
$810$		0			0
$811$	55.7821			1.95878			0.979388	−	0.201988i	$-0.0647401\pi$
$811$	55.7821			1.95878			0.979388	+	0.201988i	$0.0647401\pi$
$812$		0			0
$813$	−17.5130	+	28.8033i	−0.614207	+	1.01017i
$814$		0			0
$815$	−23.1140	−	40.0345i	−0.809646	−	1.40235i
$816$		0			0
$817$	14.9827	−	25.9507i	0.524177	−	0.907901i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.4346	−	42.3219i	0.852772	−	1.47704i	−0.0259249	−	0.999664i	$-0.508253\pi$
$821$	24.4346	−	42.3219i	0.852772	−	1.47704i	0.878697	−	0.477380i	$-0.158414\pi$
$822$		0			0
$823$	0.266319	+	0.461277i	0.00928328	+	0.0160791i	0.870630	−	0.491939i	$-0.163712\pi$
$823$	0.266319	+	0.461277i	0.00928328	+	0.0160791i	−0.861346	+	0.508018i	$0.830378\pi$
$824$		0			0
$825$	−2.69020	−	0.0610721i	−0.0936607	−	0.00212626i
$826$		0			0
$827$	10.1951			0.354518			0.177259	−	0.984164i	$-0.443277\pi$
$827$	10.1951			0.354518			0.177259	+	0.984164i	$0.443277\pi$
$828$		0			0
$829$	21.2692			0.738711			0.369355	−	0.929288i	$-0.379579\pi$
$829$	21.2692			0.738711			0.369355	+	0.929288i	$0.379579\pi$
$830$		0			0
$831$	−13.2353	−	24.1752i	−0.459127	−	0.838629i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	21.0859	−	36.5219i	0.729709	−	1.26389i
$836$		0			0
$837$	−1.85302	−	3.78273i	−0.0640498	−	0.130750i
$838$		0			0
$839$	9.47717	−	16.4149i	0.327188	−	0.566707i	−0.654765	−	0.755833i	$-0.727232\pi$
$839$	9.47717	−	16.4149i	0.327188	−	0.566707i	0.981953	+	0.189126i	$0.0605655\pi$
$840$		0			0
$841$	−15.5912	−	27.0047i	−0.537626	−	0.931196i
$842$		0			0
$843$	−23.2889	−	42.5389i	−0.802113	−	1.46512i
$844$		0			0
$845$	−22.9792			−0.790509
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−9.08555	−	0.206257i	−0.311815	−	0.00707873i
$850$		0			0
$851$	3.07837	+	5.33190i	0.105525	+	0.182775i
$852$		0			0
$853$	−2.75811	+	4.77718i	−0.0944358	+	0.163568i	−0.909373	−	0.415982i	$-0.863438\pi$
$853$	−2.75811	+	4.77718i	−0.0944358	+	0.163568i	0.814937	+	0.579549i	$0.196771\pi$
$854$		0			0
$855$	−33.1368	+	51.8127i	−1.13326	+	1.77196i
$856$		0			0
$857$	−7.92471	+	13.7260i	−0.270703	+	0.468871i	−0.969042	−	0.246896i	$-0.920589\pi$
$857$	−7.92471	+	13.7260i	−0.270703	+	0.468871i	0.698339	+	0.715767i	$0.253923\pi$
$858$		0			0
$859$	10.7004	+	18.5337i	0.365095	+	0.632362i	0.988791	−	0.149304i	$-0.0477033\pi$
$859$	10.7004	+	18.5337i	0.365095	+	0.632362i	−0.623697	+	0.781666i	$0.714370\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.03720			−0.137428			−0.0687140	−	0.997636i	$-0.521890\pi$
$863$	−4.03720			−0.137428			−0.0687140	+	0.997636i	$0.521890\pi$
$864$		0			0
$865$	−50.5247			−1.71789
$866$		0			0
$867$	−1.37202	+	2.25653i	−0.0465962	+	0.0766358i
$868$		0			0
$869$	−9.56500	−	16.5671i	−0.324470	−	0.561999i
$870$		0			0
$871$	−9.81894	+	17.0069i	−0.332702	+	0.576257i
$872$		0			0
$873$	−35.8597	−	1.62899i	−1.21367	−	0.0551330i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.6905	+	21.9806i	0.428529	+	0.742233i	0.996743	−	0.0806475i	$-0.0256988\pi$
$877$	12.6905	+	21.9806i	0.428529	+	0.742233i	−0.568214	+	0.822881i	$0.692365\pi$
$878$		0			0
$879$	5.74683	+	0.130463i	0.193836	+	0.00440040i
$880$		0			0
$881$	−18.7755			−0.632561			−0.316281	−	0.948666i	$-0.602434\pi$
$881$	−18.7755			−0.632561			−0.316281	+	0.948666i	$0.602434\pi$
$882$		0			0
$883$	8.52167			0.286777			0.143388	−	0.989666i	$-0.454200\pi$
$883$	8.52167			0.286777			0.143388	+	0.989666i	$0.454200\pi$
$884$		0			0
$885$	−9.53980	−	17.4251i	−0.320677	−	0.585740i
$886$		0			0
$887$	5.05040	+	8.74755i	0.169576	+	0.293714i	0.938271	−	0.345902i	$-0.112427\pi$
$887$	5.05040	+	8.74755i	0.169576	+	0.293714i	−0.768695	+	0.639616i	$0.779094\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	8.52937	+	18.4609i	0.285745	+	0.618463i
$892$		0			0
$893$	−18.7690	+	32.5089i	−0.628080	+	1.08787i
$894$		0			0
$895$	15.4870	+	26.8243i	0.517674	+	0.896638i
$896$		0			0
$897$	5.25956	+	9.60698i	0.175612	+	0.320768i
$898$		0			0
$899$	6.28873			0.209741
$900$		0			0
$901$	50.2654			1.67458
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−20.0612	−	34.7470i	−0.666857	−	1.15503i
$906$		0			0
$907$	10.6088	−	18.3750i	0.352260	−	0.610131i	−0.634385	−	0.773017i	$-0.718747\pi$
$907$	10.6088	−	18.3750i	0.352260	−	0.610131i	0.986645	+	0.162885i	$0.0520801\pi$
$908$		0			0
$909$	32.5073	+	1.47670i	1.07820	+	0.0489792i
$910$		0			0
$911$	−4.46609	+	7.73550i	−0.147968	+	0.256289i	−0.930476	−	0.366352i	$-0.880607\pi$
$911$	−4.46609	+	7.73550i	−0.147968	+	0.256289i	0.782508	+	0.622640i	$0.213940\pi$
$912$		0			0
$913$	−1.84789	−	3.20063i	−0.0611561	−	0.105925i
$914$		0			0
$915$	−2.47206	+	4.06574i	−0.0817237	+	0.134409i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	34.9129			1.15167			0.575834	−	0.817566i	$-0.304677\pi$
$919$	34.9129			1.15167			0.575834	+	0.817566i	$0.304677\pi$
$920$		0			0
$921$	11.2213	−	18.4555i	0.369755	−	0.608128i
$922$		0			0
$923$	−10.5048	−	18.1948i	−0.345769	−	0.598889i
$924$		0			0
$925$	1.59248	−	2.75826i	0.0523605	−	0.0906911i
$926$		0			0
$927$	−29.6513	+	46.3626i	−0.973875	+	1.52275i
$928$		0			0
$929$	−5.51692	+	9.55559i	−0.181004	+	0.313509i	−0.942223	−	0.334987i	$-0.891268\pi$
$929$	−5.51692	+	9.55559i	−0.181004	+	0.313509i	0.761218	+	0.648496i	$0.224601\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−39.2669	−	0.891426i	−1.28554	−	0.0291840i
$934$		0			0
$935$	−23.1933			−0.758503
$936$		0			0
$937$	13.6426			0.445686			0.222843	−	0.974854i	$-0.428466\pi$
$937$	13.6426			0.445686			0.222843	+	0.974854i	$0.428466\pi$
$938$		0			0
$939$	5.25851	+	9.60506i	0.171605	+	0.313449i
$940$		0			0
$941$	12.0278	+	20.8328i	0.392095	+	0.679129i	0.992726	−	0.120398i	$-0.0384170\pi$
$941$	12.0278	+	20.8328i	0.392095	+	0.679129i	−0.600630	+	0.799527i	$0.705084\pi$
$942$		0			0
$943$	6.65117	−	11.5202i	0.216592	−	0.375148i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.69602	+	11.5978i	−0.217591	+	0.376879i	−0.954071	−	0.299580i	$-0.903153\pi$
$947$	−6.69602	+	11.5978i	−0.217591	+	0.376879i	0.736480	+	0.676460i	$0.236487\pi$
$948$		0			0
$949$	−28.8120	−	49.9038i	−0.935277	−	1.61995i
$950$		0			0
$951$	12.9595	+	23.6715i	0.420240	+	0.767600i
$952$		0			0
$953$	36.3444			1.17731			0.588655	−	0.808384i	$-0.299658\pi$
$953$	36.3444			1.17731			0.588655	+	0.808384i	$0.299658\pi$
$954$		0			0
$955$	−21.8721			−0.707764
$956$		0			0
$957$	−30.3534	−	0.689074i	−0.981186	−	0.0222746i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1714	−	26.2777i	0.489401	−	0.847667i
$962$		0			0
$963$	−5.29321	−	10.2121i	−0.170571	−	0.329079i
$964$		0			0
$965$	−30.5627	+	52.9362i	−0.983849	+	1.70408i
$966$		0			0
$967$	4.82455	+	8.35637i	0.155147	+	0.268723i	0.933113	−	0.359584i	$-0.117082\pi$
$967$	4.82455	+	8.35637i	0.155147	+	0.268723i	−0.777965	+	0.628307i	$0.783748\pi$
$968$		0			0
$969$	−33.2932	+	54.7566i	−1.06953	+	1.75904i
$970$		0			0
$971$	−43.3775			−1.39205			−0.696025	−	0.718017i	$-0.745050\pi$
$971$	−43.3775			−1.39205			−0.696025	+	0.718017i	$0.745050\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.94357	−	4.84123i	0.0942697	−	0.155043i
$976$		0			0
$977$	−2.60004	−	4.50340i	−0.0831826	−	0.144076i	0.821433	−	0.570305i	$-0.193175\pi$
$977$	−2.60004	−	4.50340i	−0.0831826	−	0.144076i	−0.904615	+	0.426229i	$0.859842\pi$
$978$		0			0
$979$	−7.16631	+	12.4124i	−0.229036	+	0.396703i
$980$		0			0
$981$	−3.65151	−	7.04478i	−0.116584	−	0.224922i
$982$		0			0
$983$	11.6349	−	20.1522i	0.371095	−	0.642755i	−0.618639	−	0.785675i	$-0.712316\pi$
$983$	11.6349	−	20.1522i	0.371095	−	0.642755i	0.989734	+	0.142920i	$0.0456491\pi$
$984$		0			0
$985$	19.2025	+	33.2596i	0.611841	+	1.05974i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.63304			0.147322
$990$		0			0
$991$	−39.0382			−1.24009			−0.620044	−	0.784567i	$-0.712885\pi$
$991$	−39.0382			−1.24009			−0.620044	+	0.784567i	$0.712885\pi$
$992$		0			0
$993$	18.0714	+	33.0087i	0.573478	+	1.04750i
$994$		0			0
$995$	−22.9283	−	39.7130i	−0.726877	−	1.25899i
$996$		0			0
$997$	−12.0905	+	20.9413i	−0.382909	+	0.663218i	−0.991477	−	0.130284i	$-0.958411\pi$
$997$	−12.0905	+	20.9413i	−0.382909	+	0.663218i	0.608568	+	0.793502i	$0.291744\pi$
$998$		0			0
$999$	−24.0142	−	1.63774i	−0.759775	−	0.0518157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.j.i.1177.5	yes	24
3.2	odd	2		5292.2.j.i.3529.3		24
7.2	even	3		1764.2.i.j.1537.5		24
7.3	odd	6		1764.2.l.j.961.1		24
7.4	even	3		1764.2.l.j.961.12		24
7.5	odd	6		1764.2.i.j.1537.8		24
7.6	odd	2	inner	1764.2.j.i.1177.8	yes	24
9.4	even	3	inner	1764.2.j.i.589.5	✓	24
9.5	odd	6		5292.2.j.i.1765.3		24
21.2	odd	6		5292.2.i.j.2125.3		24
21.5	even	6		5292.2.i.j.2125.10		24
21.11	odd	6		5292.2.l.j.3313.10		24
21.17	even	6		5292.2.l.j.3313.3		24
21.20	even	2		5292.2.j.i.3529.10		24
63.4	even	3		1764.2.i.j.373.5		24
63.5	even	6		5292.2.l.j.361.3		24
63.13	odd	6	inner	1764.2.j.i.589.8	yes	24
63.23	odd	6		5292.2.l.j.361.10		24
63.31	odd	6		1764.2.i.j.373.8		24
63.32	odd	6		5292.2.i.j.1549.3		24
63.40	odd	6		1764.2.l.j.949.1		24
63.41	even	6		5292.2.j.i.1765.10		24
63.58	even	3		1764.2.l.j.949.12		24
63.59	even	6		5292.2.i.j.1549.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.5		24	63.4	even	3
1764.2.i.j.373.8		24	63.31	odd	6
1764.2.i.j.1537.5		24	7.2	even	3
1764.2.i.j.1537.8		24	7.5	odd	6
1764.2.j.i.589.5	✓	24	9.4	even	3	inner
1764.2.j.i.589.8	yes	24	63.13	odd	6	inner
1764.2.j.i.1177.5	yes	24	1.1	even	1	trivial
1764.2.j.i.1177.8	yes	24	7.6	odd	2	inner
1764.2.l.j.949.1		24	63.40	odd	6
1764.2.l.j.949.12		24	63.58	even	3
1764.2.l.j.961.1		24	7.3	odd	6
1764.2.l.j.961.12		24	7.4	even	3
5292.2.i.j.1549.3		24	63.32	odd	6
5292.2.i.j.1549.10		24	63.59	even	6
5292.2.i.j.2125.3		24	21.2	odd	6
5292.2.i.j.2125.10		24	21.5	even	6
5292.2.j.i.1765.3		24	9.5	odd	6
5292.2.j.i.1765.10		24	63.41	even	6
5292.2.j.i.3529.3		24	3.2	odd	2
5292.2.j.i.3529.10		24	21.20	even	2
5292.2.l.j.361.3		24	63.5	even	6
5292.2.l.j.361.10		24	63.23	odd	6
5292.2.l.j.3313.3		24	21.17	even	6
5292.2.l.j.3313.10		24	21.11	odd	6

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.899846 + 1.47996i) q^{3} +(1.19243 + 2.06535i) q^{5} +(-1.38055 - 2.66347i) q^{9} +O(q^{10})\)	\(q+(-0.899846 + 1.47996i) q^{3} +(1.19243 + 2.06535i) q^{5} +(-1.38055 - 2.66347i) q^{9} +(1.12978 - 1.95684i) q^{11} +(2.37884 + 4.12027i) q^{13} +(-4.12964 - 0.0937498i) q^{15} -4.30404 q^{17} -8.59629 q^{19} +(-0.664550 - 1.15103i) q^{23} +(-0.343781 + 0.595446i) q^{25} +(5.18411 + 0.353550i) q^{27} +(-3.87886 + 6.71839i) q^{29} +(-0.405320 - 0.702036i) q^{31} +(1.87941 + 3.43288i) q^{33} -4.63226 q^{37} +(-8.23841 - 0.187026i) q^{39} +(5.00426 + 8.66764i) q^{41} +(-1.74292 + 3.01883i) q^{43} +(3.85478 - 6.02733i) q^{45} +(2.18338 - 3.78173i) q^{47} +(3.87297 - 6.36979i) q^{51} -11.6787 q^{53} +5.38874 q^{55} +(7.73534 - 12.7222i) q^{57} +(2.40463 + 4.16495i) q^{59} +(0.575967 - 0.997604i) q^{61} +(-5.67319 + 9.82626i) q^{65} +(2.06381 + 3.57463i) q^{67} +(2.30148 + 0.0522474i) q^{69} -4.41593 q^{71} -12.1118 q^{73} +(-0.571885 - 1.04459i) q^{75} +(4.23312 - 7.33198i) q^{79} +(-5.18814 + 7.35413i) q^{81} +(0.817808 - 1.41648i) q^{83} +(-5.13226 - 8.88934i) q^{85} +(-6.45255 - 11.7861i) q^{87} -6.34310 q^{89} +(1.40371 + 0.0318666i) q^{93} +(-10.2505 - 17.7543i) q^{95} +(5.98278 - 10.3625i) q^{97} +(-6.77170 - 0.307617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{9}+O(q^{10}) \) 24 * q + 8 * q^9	\( 24 q + 8 q^{9} - 4 q^{11} - 28 q^{15} - 8 q^{23} - 12 q^{25} - 32 q^{29} + 24 q^{37} - 40 q^{51} + 32 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} + 16 q^{81} + 12 q^{85} + 48 q^{93} + 32 q^{95} - 4 q^{99}+O(q^{100}) \) 24 * q + 8 * q^9 - 4 * q^11 - 28 * q^15 - 8 * q^23 - 12 * q^25 - 32 * q^29 + 24 * q^37 - 40 * q^51 + 32 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 + 16 * q^81 + 12 * q^85 + 48 * q^93 + 32 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more