LMFDB - Embedded newform 468.2.j.a.133.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [468,2,Mod(133,468)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("468.133"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(468, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.5
Character	$\chi$	$=$	468.133
Dual form			468.2.j.a.373.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.964252 + 1.43883i) q^{3} +(-0.216950 - 0.375768i) q^{5} +(-0.791636 - 1.37115i) q^{7} +(-1.14044 - 2.77478i) q^{9} -3.28568 q^{11} +(-1.50098 - 3.27827i) q^{13} +(0.749859 + 0.0501820i) q^{15} +(0.820732 - 1.42155i) q^{17} +(0.0150406 - 0.0260511i) q^{19} +(2.73619 + 0.183111i) q^{21} +(0.0282011 - 0.0488457i) q^{23} +(2.40587 - 4.16708i) q^{25} +(5.09209 + 1.03469i) q^{27} -3.37346 q^{29} +(-2.73925 - 4.74451i) q^{31} +(3.16823 - 4.72753i) q^{33} +(-0.343491 + 0.594943i) q^{35} +(-1.81655 - 3.14636i) q^{37} +(6.16418 + 1.00143i) q^{39} +(1.81506 - 3.14378i) q^{41} +(-1.33998 - 2.32092i) q^{43} +(-0.795256 + 1.03053i) q^{45} +(-3.78962 + 6.56382i) q^{47} +(2.24662 - 3.89127i) q^{49} +(1.25397 + 2.55162i) q^{51} -4.05057 q^{53} +(0.712828 + 1.23465i) q^{55} +(0.0229801 + 0.0467606i) q^{57} -0.362821 q^{59} +(1.72774 + 2.99253i) q^{61} +(-2.90184 + 3.76033i) q^{63} +(-0.906231 + 1.27524i) q^{65} +(-1.28103 + 2.21882i) q^{67} +(0.0430875 + 0.0876760i) q^{69} +(-7.29808 + 12.6407i) q^{71} -0.162888 q^{73} +(3.67584 + 7.47974i) q^{75} +(2.60107 + 4.50518i) q^{77} +(5.70128 - 9.87490i) q^{79} +(-6.39880 + 6.32893i) q^{81} +(-5.52019 + 9.56125i) q^{83} -0.712231 q^{85} +(3.25286 - 4.85382i) q^{87} +(-6.13248 - 10.6218i) q^{89} +(-3.30678 + 4.65327i) q^{91} +(9.46785 + 0.633607i) q^{93} -0.0130522 q^{95} +(6.46904 + 11.2047i) q^{97} +(3.74712 + 9.11705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) $ 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.964252	+	1.43883i	−0.556711	+	0.830706i
$3$	−0.964252	+	1.43883i	−0.556711	+	0.830706i
$4$		0			0
$5$	−0.216950	−	0.375768i	−0.0970229	−	0.168049i	0.813428	−	0.581665i	$-0.197599\pi$
$5$	−0.216950	−	0.375768i	−0.0970229	−	0.168049i	−0.910451	+	0.413617i	$0.864265\pi$
$6$		0			0
$7$	−0.791636	−	1.37115i	−0.299210	−	0.518248i	0.676745	−	0.736217i	$-0.263390\pi$
$7$	−0.791636	−	1.37115i	−0.299210	−	0.518248i	−0.975956	+	0.217970i	$0.930057\pi$
$8$		0			0
$9$	−1.14044	−	2.77478i	−0.380146	−	0.924926i
$10$		0			0
$11$	−3.28568			−0.990671			−0.495335	−	0.868702i	$-0.664955\pi$
$11$	−3.28568			−0.990671			−0.495335	+	0.868702i	$0.664955\pi$
$12$		0			0
$13$	−1.50098	−	3.27827i	−0.416298	−	0.909228i
$13$	−1.50098	−	3.27827i	−0.416298	−	0.909228i
$14$		0			0
$15$	0.749859	+	0.0501820i	0.193613	+	0.0129569i
$16$		0			0
$17$	0.820732	−	1.42155i	0.199057	−	0.344777i	−0.749166	−	0.662382i	$-0.769545\pi$
$17$	0.820732	−	1.42155i	0.199057	−	0.344777i	0.948223	+	0.317606i	$0.102879\pi$
$18$		0			0
$19$	0.0150406	−	0.0260511i	0.00345055	−	0.00597653i	−0.864295	−	0.502985i	$-0.832235\pi$
$19$	0.0150406	−	0.0260511i	0.00345055	−	0.00597653i	0.867746	+	0.497009i	$0.165568\pi$
$20$		0			0
$21$	2.73619	+	0.183111i	0.597085	+	0.0399581i
$22$		0			0
$23$	0.0282011	−	0.0488457i	0.00588033	−	0.0101850i	−0.863070	−	0.505084i	$-0.831462\pi$
$23$	0.0282011	−	0.0488457i	0.00588033	−	0.0101850i	0.868951	+	0.494899i	$0.164795\pi$
$24$		0			0
$25$	2.40587	−	4.16708i	0.481173	−	0.833416i
$26$		0			0
$27$	5.09209	+	1.03469i	0.979974	+	0.199127i
$28$		0			0
$29$	−3.37346			−0.626436			−0.313218	−	0.949681i	$-0.601407\pi$
$29$	−3.37346			−0.626436			−0.313218	+	0.949681i	$0.601407\pi$
$30$		0			0
$31$	−2.73925	−	4.74451i	−0.491983	−	0.852140i	0.507974	−	0.861372i	$-0.330394\pi$
$31$	−2.73925	−	4.74451i	−0.491983	−	0.852140i	−0.999957	+	0.00923265i	$0.997061\pi$
$32$		0			0
$33$	3.16823	−	4.72753i	0.551517	−	0.822957i
$34$		0			0
$35$	−0.343491	+	0.594943i	−0.0580605	+	0.100564i
$36$		0			0
$37$	−1.81655	−	3.14636i	−0.298639	−	0.517258i	0.677186	−	0.735812i	$-0.263199\pi$
$37$	−1.81655	−	3.14636i	−0.298639	−	0.517258i	−0.975825	+	0.218554i	$0.929866\pi$
$38$		0			0
$39$	6.16418	+	1.00143i	0.987059	+	0.160356i
$40$		0			0
$41$	1.81506	−	3.14378i	0.283465	−	0.490976i	−0.688771	−	0.724979i	$-0.741849\pi$
$41$	1.81506	−	3.14378i	0.283465	−	0.490976i	0.972236	+	0.234004i	$0.0751827\pi$
$42$		0			0
$43$	−1.33998	−	2.32092i	−0.204345	−	0.353937i	0.745579	−	0.666418i	$-0.232173\pi$
$43$	−1.33998	−	2.32092i	−0.204345	−	0.353937i	−0.949924	+	0.312481i	$0.898840\pi$
$44$		0			0
$45$	−0.795256	+	1.03053i	−0.118550	+	0.153622i
$46$		0			0
$47$	−3.78962	+	6.56382i	−0.552773	+	0.957432i	0.445300	+	0.895382i	$0.353097\pi$
$47$	−3.78962	+	6.56382i	−0.552773	+	0.957432i	−0.998073	+	0.0620500i	$0.980236\pi$
$48$		0			0
$49$	2.24662	−	3.89127i	0.320946	−	0.555895i
$50$		0			0
$51$	1.25397	+	2.55162i	0.175591	+	0.357299i
$52$		0			0
$53$	−4.05057			−0.556388			−0.278194	−	0.960525i	$-0.589736\pi$
$53$	−4.05057			−0.556388			−0.278194	+	0.960525i	$0.589736\pi$
$54$		0			0
$55$	0.712828	+	1.23465i	0.0961178	+	0.166481i
$56$		0			0
$57$	0.0229801	+	0.0467606i	0.00304378	+	0.00619360i
$58$		0			0
$59$	−0.362821			−0.0472353			−0.0236176	−	0.999721i	$-0.507518\pi$
$59$	−0.362821			−0.0472353			−0.0236176	+	0.999721i	$0.507518\pi$
$60$		0			0
$61$	1.72774	+	2.99253i	0.221214	+	0.383154i	0.955177	−	0.296035i	$-0.0956646\pi$
$61$	1.72774	+	2.99253i	0.221214	+	0.383154i	−0.733963	+	0.679190i	$0.762331\pi$
$62$		0			0
$63$	−2.90184	+	3.76033i	−0.365597	+	0.473757i
$64$		0			0
$65$	−0.906231	+	1.27524i	−0.112404	+	0.158174i
$66$		0			0
$67$	−1.28103	+	2.21882i	−0.156503	+	0.271071i	−0.933605	−	0.358303i	$-0.883355\pi$
$67$	−1.28103	+	2.21882i	−0.156503	+	0.271071i	0.777102	+	0.629374i	$0.216689\pi$
$68$		0			0
$69$	0.0430875	+	0.0876760i	0.00518713	+	0.0105549i
$70$		0			0
$71$	−7.29808	+	12.6407i	−0.866123	+	1.50017i	−0.000195676		1.00000i	$0.500062\pi$
$71$	−7.29808	+	12.6407i	−0.866123	+	1.50017i	−0.865928	+	0.500169i	$0.833271\pi$
$72$		0			0
$73$	−0.162888			−0.0190646			−0.00953230	−	0.999955i	$-0.503034\pi$
$73$	−0.162888			−0.0190646			−0.00953230	+	0.999955i	$0.503034\pi$
$74$		0			0
$75$	3.67584	+	7.47974i	0.424450	+	0.863685i
$76$		0			0
$77$	2.60107	+	4.50518i	0.296419	+	0.513413i
$78$		0			0
$79$	5.70128	−	9.87490i	0.641444	−	1.11101i	−0.343667	−	0.939092i	$-0.611669\pi$
$79$	5.70128	−	9.87490i	0.641444	−	1.11101i	0.985111	−	0.171922i	$-0.0549976\pi$
$80$		0			0
$81$	−6.39880	+	6.32893i	−0.710978	+	0.703214i
$82$		0			0
$83$	−5.52019	+	9.56125i	−0.605920	+	1.04948i	0.385986	+	0.922505i	$0.373861\pi$
$83$	−5.52019	+	9.56125i	−0.605920	+	1.04948i	−0.991905	+	0.126979i	$0.959472\pi$
$84$		0			0
$85$	−0.712231			−0.0772523
$86$		0			0
$87$	3.25286	−	4.85382i	0.348744	−	0.520384i
$88$		0			0
$89$	−6.13248	−	10.6218i	−0.650042	−	1.12591i	−0.983112	−	0.183004i	$-0.941418\pi$
$89$	−6.13248	−	10.6218i	−0.650042	−	1.12591i	0.333070	−	0.942902i	$-0.391915\pi$
$90$		0			0
$91$	−3.30678	+	4.65327i	−0.346645	+	0.487796i
$92$		0			0
$93$	9.46785	+	0.633607i	0.981770	+	0.0657020i
$94$		0			0
$95$	−0.0130522			−0.00133913
$96$		0			0
$97$	6.46904	+	11.2047i	0.656831	+	1.13767i	0.981431	+	0.191814i	$0.0614371\pi$
$97$	6.46904	+	11.2047i	0.656831	+	1.13767i	−0.324600	+	0.945851i	$0.605230\pi$
$98$		0			0
$99$	3.74712	+	9.11705i	0.376600	+	0.916298i
$100$		0			0
$101$	−7.63565			−0.759775			−0.379888	−	0.925033i	$-0.624037\pi$
$101$	−7.63565			−0.759775			−0.379888	+	0.925033i	$0.624037\pi$
$102$		0			0
$103$	−3.58661	−	6.21219i	−0.353399	−	0.612105i	0.633444	−	0.773789i	$-0.281641\pi$
$103$	−3.58661	−	6.21219i	−0.353399	−	0.612105i	−0.986843	+	0.161684i	$0.948307\pi$
$104$		0			0
$105$	−0.524808	−	1.06790i	−0.0512160	−	0.104216i
$106$		0			0
$107$	7.29326	+	12.6323i	0.705066	+	1.22121i	0.966668	+	0.256035i	$0.0824162\pi$
$107$	7.29326	+	12.6323i	0.705066	+	1.22121i	−0.261601	+	0.965176i	$0.584250\pi$
$108$		0			0
$109$	−16.2665			−1.55805			−0.779026	−	0.626992i	$-0.784286\pi$
$109$	−16.2665			−1.55805			−0.779026	+	0.626992i	$0.784286\pi$
$110$		0			0
$111$	6.27867	+	0.420181i	0.595945	+	0.0398818i
$112$		0			0
$113$	19.2845			1.81413			0.907066	−	0.420988i	$-0.138317\pi$
$113$	19.2845			1.81413			0.907066	+	0.420988i	$0.138317\pi$
$114$		0			0
$115$	−0.0244729			−0.00228211
$116$		0			0
$117$	−7.38470	+	7.90356i	−0.682716	+	0.730684i
$118$		0			0
$119$	−2.59889			−0.238239
$120$		0			0
$121$	−0.204282			−0.0185711
$122$		0			0
$123$	2.77317	+	5.64295i	0.250049	+	0.508808i
$124$		0			0
$125$	−4.25731			−0.380785
$126$		0			0
$127$	4.39676	+	7.61542i	0.390150	+	0.675759i	0.992469	−	0.122496i	$-0.0390899\pi$
$127$	4.39676	+	7.61542i	0.390150	+	0.675759i	−0.602319	+	0.798255i	$0.705757\pi$
$128$		0			0
$129$	4.63148	+	0.309947i	0.407779	+	0.0272893i
$130$		0			0
$131$	−9.05299	−	15.6802i	−0.790964	−	1.36999i	−0.925371	−	0.379063i	$-0.876246\pi$
$131$	−9.05299	−	15.6802i	−0.790964	−	1.36999i	0.134407	−	0.990926i	$-0.457087\pi$
$132$		0			0
$133$	−0.0476268			−0.00412976
$134$		0			0
$135$	−0.715924	−	2.13792i	−0.0616169	−	0.184003i
$136$		0			0
$137$	−2.05714	−	3.56307i	−0.175753	−	0.304414i	0.764668	−	0.644424i	$-0.222903\pi$
$137$	−2.05714	−	3.56307i	−0.175753	−	0.304414i	−0.940422	+	0.340010i	$0.889569\pi$
$138$		0			0
$139$	12.1691			1.03217			0.516084	−	0.856538i	$-0.327389\pi$
$139$	12.1691			1.03217			0.516084	+	0.856538i	$0.327389\pi$
$140$		0			0
$141$	−5.79004	−	11.7818i	−0.487610	−	0.992205i
$142$		0			0
$143$	4.93175	+	10.7714i	0.412414	+	0.900746i
$144$		0			0
$145$	0.731872	+	1.26764i	0.0607786	+	0.105272i
$146$		0			0
$147$	3.43254	+	6.98466i	0.283111	+	0.576085i
$148$		0			0
$149$	9.45044			0.774210			0.387105	−	0.922036i	$-0.373475\pi$
$149$	9.45044			0.774210			0.387105	+	0.922036i	$0.373475\pi$
$150$		0			0
$151$	5.31651	−	9.20847i	0.432651	−	0.749374i	−0.564449	−	0.825468i	$-0.690911\pi$
$151$	5.31651	−	9.20847i	0.432651	−	0.749374i	0.997101	+	0.0760934i	$0.0242447\pi$
$152$		0			0
$153$	−4.88048	−	0.656161i	−0.394564	−	0.0530475i
$154$		0			0
$155$	−1.18856	+	2.05864i	−0.0954672	+	0.165354i
$156$		0			0
$157$	−0.146130	−	0.253105i	−0.0116624	−	0.0202000i	0.860135	−	0.510066i	$-0.170379\pi$
$157$	−0.146130	−	0.253105i	−0.0116624	−	0.0202000i	−0.871798	+	0.489866i	$0.837046\pi$
$158$		0			0
$159$	3.90576	−	5.82806i	0.309747	−	0.462195i
$160$		0			0
$161$	−0.0893000			−0.00703782
$162$		0			0
$163$	7.12118	−	12.3342i	0.557774	−	0.966092i	−0.439908	−	0.898043i	$-0.644989\pi$
$163$	7.12118	−	12.3342i	0.557774	−	0.966092i	0.997682	−	0.0680496i	$-0.0216776\pi$
$164$		0			0
$165$	−2.46380	−	0.164882i	−0.191806	−	0.0128361i
$166$		0			0
$167$	7.62713	−	13.2106i	0.590205	−	1.02227i	−0.403999	−	0.914759i	$-0.632380\pi$
$167$	7.62713	−	13.2106i	0.590205	−	1.02227i	0.994204	−	0.107506i	$-0.0342864\pi$
$168$		0			0
$169$	−8.49411	+	9.84125i	−0.653393	+	0.757019i
$170$		0			0
$171$	−0.0894389	−	0.0120247i	−0.00683957	−	0.000919552i
$172$		0			0
$173$	−3.88027	−	6.72083i	−0.295012	−	0.510975i	0.679976	−	0.733235i	$-0.261990\pi$
$173$	−3.88027	−	6.72083i	−0.295012	−	0.510975i	−0.974988	+	0.222259i	$0.928657\pi$
$174$		0			0
$175$	−7.61828			−0.575888
$176$		0			0
$177$	0.349851	−	0.522036i	0.0262964	−	0.0392386i
$178$		0			0
$179$	4.40510	+	7.62986i	0.329253	+	0.570282i	0.982364	−	0.186980i	$-0.0598699\pi$
$179$	4.40510	+	7.62986i	0.329253	+	0.570282i	−0.653111	+	0.757262i	$0.726537\pi$
$180$		0			0
$181$	9.31165			0.692129			0.346065	−	0.938211i	$-0.387518\pi$
$181$	9.31165			0.692129			0.346065	+	0.938211i	$0.387518\pi$
$182$		0			0
$183$	−5.97171	−	0.399638i	−0.441441	−	0.0295421i
$184$		0			0
$185$	−0.788200	+	1.36520i	−0.0579496	+	0.100372i
$186$		0			0
$187$	−2.69667	+	4.67076i	−0.197200	+	0.341560i
$188$		0			0
$189$	−2.61236	−	7.80114i	−0.190021	−	0.567450i
$190$		0			0
$191$	−9.04730	−	15.6704i	−0.654639	−	1.13387i	−0.981984	−	0.188964i	$-0.939487\pi$
$191$	−9.04730	−	15.6704i	−0.654639	−	1.13387i	0.327345	−	0.944905i	$-0.393846\pi$
$192$		0			0
$193$	2.08885	−	3.61799i	0.150359	−	0.260429i	−0.781001	−	0.624530i	$-0.785290\pi$
$193$	2.08885	−	3.61799i	0.150359	−	0.260429i	0.931359	+	0.364101i	$0.118624\pi$
$194$		0			0
$195$	−0.961015	−	2.53356i	−0.0688197	−	0.181432i
$196$		0			0
$197$	10.8080	+	18.7200i	0.770038	+	1.33374i	0.937542	+	0.347873i	$0.113096\pi$
$197$	10.8080	+	18.7200i	0.770038	+	1.33374i	−0.167504	+	0.985871i	$0.553571\pi$
$198$		0			0
$199$	7.59202	−	13.1498i	0.538184	−	0.932162i	−0.460818	−	0.887495i	$-0.652444\pi$
$199$	7.59202	−	13.1498i	0.538184	−	0.932162i	0.999002	−	0.0446676i	$-0.0142229\pi$
$200$		0			0
$201$	−1.95725	−	3.98268i	−0.138054	−	0.280917i
$202$		0			0
$203$	2.67055	+	4.62553i	0.187436	+	0.324649i
$204$		0			0
$205$	−1.57511			−0.110010
$206$		0			0
$207$	−0.167698	−	0.0225463i	−0.0116558	−	0.00156707i
$208$		0			0
$209$	−0.0494187	+	0.0855957i	−0.00341836	+	0.00592078i
$210$		0			0
$211$	−9.96737	+	17.2640i	−0.686182	+	1.18850i	0.286881	+	0.957966i	$0.407381\pi$
$211$	−9.96737	+	17.2640i	−0.686182	+	1.18850i	−0.973064	+	0.230537i	$0.925952\pi$
$212$		0			0
$213$	−11.1505	−	22.6894i	−0.764020	−	1.55465i
$214$		0			0
$215$	−0.581418	+	1.00705i	−0.0396524	+	0.0686799i
$216$		0			0
$217$	−4.33697	+	7.51185i	−0.294413	+	0.509938i
$218$		0			0
$219$	0.157065	−	0.234367i	0.0106135	−	0.0158371i
$220$		0			0
$221$	−5.89213	−	0.556861i	−0.396348	−	0.0374585i
$222$		0			0
$223$	−19.1053			−1.27938			−0.639692	−	0.768631i	$-0.720938\pi$
$223$	−19.1053			−1.27938			−0.639692	+	0.768631i	$0.720938\pi$
$224$		0			0
$225$	−14.3065	−	1.92345i	−0.953765	−	0.128230i
$226$		0			0
$227$	−6.44350	−	11.1605i	−0.427670	−	0.740747i	0.568995	−	0.822341i	$-0.307332\pi$
$227$	−6.44350	−	11.1605i	−0.427670	−	0.740747i	−0.996666	+	0.0815941i	$0.973999\pi$
$228$		0			0
$229$	5.06389	+	8.77091i	0.334631	+	0.579598i	0.983414	−	0.181376i	$-0.0580550\pi$
$229$	5.06389	+	8.77091i	0.334631	+	0.579598i	−0.648783	+	0.760974i	$0.724722\pi$
$230$		0			0
$231$	−8.99025	−	0.601645i	−0.591515	−	0.0395853i
$232$		0			0
$233$	19.4552			1.27455			0.637275	−	0.770637i	$-0.280062\pi$
$233$	19.4552			1.27455			0.637275	+	0.770637i	$0.280062\pi$
$234$		0			0
$235$	3.28863			0.214527
$236$		0			0
$237$	8.71080	+	17.7250i	0.565827	+	1.15136i
$238$		0			0
$239$	−6.33263	−	10.9684i	−0.409623	−	0.709489i	0.585224	−	0.810872i	$-0.301007\pi$
$239$	−6.33263	−	10.9684i	−0.409623	−	0.709489i	−0.994847	+	0.101383i	$0.967673\pi$
$240$		0			0
$241$	−7.50431	−	12.9979i	−0.483395	−	0.837265i	0.516423	−	0.856334i	$-0.327263\pi$
$241$	−7.50431	−	12.9979i	−0.483395	−	0.837265i	−0.999818	+	0.0190684i	$0.993930\pi$
$242$		0			0
$243$	−2.93617	−	15.3094i	−0.188355	−	0.982101i
$244$		0			0
$245$	−1.94962			−0.124557
$246$		0			0
$247$	−0.107978	−	0.0102049i	−0.00687049	−	0.000649325i
$248$		0			0
$249$	−8.43412	−	17.1620i	−0.534491	−	1.08760i
$250$		0			0
$251$	3.90158	−	6.75773i	0.246265	−	0.426544i	−0.716221	−	0.697873i	$-0.754130\pi$
$251$	3.90158	−	6.75773i	0.246265	−	0.426544i	0.962487	+	0.271329i	$0.0874632\pi$
$252$		0			0
$253$	−0.0926598	+	0.160492i	−0.00582547	+	0.0100900i
$254$		0			0
$255$	0.686770	−	1.02478i	0.0430072	−	0.0641740i
$256$		0			0
$257$	3.72220	−	6.44703i	0.232184	−	0.402155i	−0.726266	−	0.687413i	$-0.758746\pi$
$257$	3.72220	−	6.44703i	0.232184	−	0.402155i	0.958451	+	0.285259i	$0.0920795\pi$
$258$		0			0
$259$	−2.87609	+	4.98154i	−0.178712	+	0.309538i
$260$		0			0
$261$	3.84722	+	9.36061i	0.238137	+	0.579407i
$262$		0			0
$263$	7.13493			0.439958			0.219979	−	0.975505i	$-0.429401\pi$
$263$	7.13493			0.439958			0.219979	+	0.975505i	$0.429401\pi$
$264$		0			0
$265$	0.878769	+	1.52207i	0.0539824	+	0.0935002i
$266$		0			0
$267$	21.1961	+	1.41849i	1.29718	+	0.0868100i
$268$		0			0
$269$	14.1183	−	24.4536i	0.860807	−	1.49096i	−0.0103450	−	0.999946i	$-0.503293\pi$
$269$	14.1183	−	24.4536i	0.860807	−	1.49096i	0.871152	−	0.491014i	$-0.163374\pi$
$270$		0			0
$271$	−3.82382	−	6.62305i	−0.232281	−	0.402322i	0.726198	−	0.687485i	$-0.241285\pi$
$271$	−3.82382	−	6.62305i	−0.232281	−	0.402322i	−0.958479	+	0.285164i	$0.907952\pi$
$272$		0			0
$273$	−3.50668	−	9.24481i	−0.212234	−	0.559521i
$274$		0			0
$275$	−7.90491	+	13.6917i	−0.476684	+	0.825641i
$276$		0			0
$277$	9.47813	+	16.4166i	0.569486	+	0.986378i	0.996617	+	0.0821882i	$0.0261909\pi$
$277$	9.47813	+	16.4166i	0.569486	+	0.986378i	−0.427131	+	0.904190i	$0.640476\pi$
$278$		0			0
$279$	−10.0410	+	13.0116i	−0.601141	+	0.778986i
$280$		0			0
$281$	12.7457	−	22.0763i	0.760347	−	1.31696i	−0.182325	−	0.983238i	$-0.558362\pi$
$281$	12.7457	−	22.0763i	0.760347	−	1.31696i	0.942672	−	0.333721i	$-0.108304\pi$
$282$		0			0
$283$	−4.26197	+	7.38195i	−0.253348	+	0.438811i	−0.964445	−	0.264282i	$-0.914865\pi$
$283$	−4.26197	+	7.38195i	−0.253348	+	0.438811i	0.711098	+	0.703093i	$0.248198\pi$
$284$		0			0
$285$	0.0125856	−	0.0187799i	0.000745508	−	0.00111242i
$286$		0			0
$287$	−5.74747			−0.339262
$288$		0			0
$289$	7.15280	+	12.3890i	0.420753	+	0.728765i
$290$		0			0
$291$	−22.3594	−	1.49633i	−1.31073	−	0.0877167i
$292$		0			0
$293$	−2.30817			−0.134845			−0.0674223	−	0.997725i	$-0.521477\pi$
$293$	−2.30817			−0.134845			−0.0674223	+	0.997725i	$0.521477\pi$
$294$		0			0
$295$	0.0787140	+	0.136337i	0.00458290	+	0.00793782i
$296$		0			0
$297$	−16.7310	−	3.39968i	−0.970831	−	0.197269i
$298$		0			0
$299$	−0.202459	−	0.0191342i	−0.0117085	−	0.00110656i
$300$		0			0
$301$	−2.12156	+	3.67464i	−0.122285	+	0.211803i
$302$		0			0
$303$	7.36269	−	10.9864i	0.422975	−	0.631150i
$304$		0			0
$305$	0.749665	−	1.29846i	0.0429257	−	0.0743495i
$306$		0			0
$307$	25.9276			1.47976			0.739882	−	0.672736i	$-0.234881\pi$
$307$	25.9276			1.47976			0.739882	+	0.672736i	$0.234881\pi$
$308$		0			0
$309$	12.3966	+	0.829607i	0.705220	+	0.0471947i
$310$		0			0
$311$	−16.1747	−	28.0154i	−0.917181	−	1.58860i	−0.803676	−	0.595068i	$-0.797125\pi$
$311$	−16.1747	−	28.0154i	−0.917181	−	1.58860i	−0.113506	−	0.993537i	$-0.536208\pi$
$312$		0			0
$313$	−1.84638	+	3.19803i	−0.104364	+	0.180763i	−0.913478	−	0.406888i	$-0.866614\pi$
$313$	−1.84638	+	3.19803i	−0.104364	+	0.180763i	0.809114	+	0.587651i	$0.199947\pi$
$314$		0			0
$315$	2.04257	+	0.274615i	0.115086	+	0.0154728i
$316$		0			0
$317$	6.38892	−	11.0659i	0.358837	−	0.621524i	−0.628930	−	0.777462i	$-0.716507\pi$
$317$	6.38892	−	11.0659i	0.358837	−	0.621524i	0.987767	+	0.155938i	$0.0498400\pi$
$318$		0			0
$319$	11.0841			0.620592
$320$		0			0
$321$	−25.2082	−	1.68698i	−1.40699	−	0.0941582i
$322$		0			0
$323$	−0.0246886	−	0.0427620i	−0.00137371	−	0.00237934i
$324$		0			0
$325$	−17.2720	−	1.63236i	−0.958077	−	0.0905471i
$326$		0			0
$327$	15.6850	−	23.4047i	0.867384	−	1.29428i
$328$		0			0
$329$	12.0000			0.661582
$330$		0			0
$331$	−4.05904	−	7.03047i	−0.223105	−	0.386430i	0.732644	−	0.680612i	$-0.238286\pi$
$331$	−4.05904	−	7.03047i	−0.223105	−	0.386430i	−0.955749	+	0.294182i	$0.904953\pi$
$332$		0			0
$333$	−6.65878	+	8.62875i	−0.364899	+	0.472853i
$334$		0			0
$335$	1.11168			0.0607376
$336$		0			0
$337$	17.4314	+	30.1921i	0.949551	+	1.64467i	0.746373	+	0.665528i	$0.231794\pi$
$337$	17.4314	+	30.1921i	0.949551	+	1.64467i	0.203178	+	0.979142i	$0.434873\pi$
$338$		0			0
$339$	−18.5951	+	27.7470i	−1.00995	+	1.50701i
$340$		0			0
$341$	9.00029	+	15.5890i	0.487393	+	0.844190i
$342$		0			0
$343$	−18.1969			−0.982543
$344$		0			0
$345$	0.0235980	−	0.0352122i	0.00127047	−	0.00189576i
$346$		0			0
$347$	22.1469			1.18891			0.594453	−	0.804130i	$-0.297369\pi$
$347$	22.1469			1.18891			0.594453	+	0.804130i	$0.297369\pi$
$348$		0			0
$349$	17.8426			0.955094			0.477547	−	0.878606i	$-0.341526\pi$
$349$	17.8426			0.955094			0.477547	+	0.878606i	$0.341526\pi$
$350$		0			0
$351$	−4.25113	−	18.2463i	−0.226909	−	0.973916i
$352$		0			0
$353$	14.9858			0.797616			0.398808	−	0.917034i	$-0.369424\pi$
$353$	14.9858			0.797616			0.398808	+	0.917034i	$0.369424\pi$
$354$		0			0
$355$	6.33327			0.336135
$356$		0			0
$357$	2.50598	−	3.73934i	0.132630	−	0.197907i
$358$		0			0
$359$	2.49334			0.131594			0.0657968	−	0.997833i	$-0.479041\pi$
$359$	2.49334			0.131594			0.0657968	+	0.997833i	$0.479041\pi$
$360$		0			0
$361$	9.49955	+	16.4537i	0.499976	+	0.865984i
$362$		0			0
$363$	0.196979	−	0.293926i	0.0103387	−	0.0154271i
$364$		0			0
$365$	0.0353385	+	0.0612081i	0.00184970	+	0.00320378i
$366$		0			0
$367$	−4.38816			−0.229060			−0.114530	−	0.993420i	$-0.536536\pi$
$367$	−4.38816			−0.229060			−0.114530	+	0.993420i	$0.536536\pi$
$368$		0			0
$369$	−10.7933	−	1.45111i	−0.561874	−	0.0755418i
$370$		0			0
$371$	3.20657	+	5.55395i	0.166477	+	0.288347i
$372$		0			0
$373$	15.0702			0.780304			0.390152	−	0.920750i	$-0.372422\pi$
$373$	15.0702			0.780304			0.390152	+	0.920750i	$0.372422\pi$
$374$		0			0
$375$	4.10511	−	6.12552i	0.211987	−	0.316321i
$376$		0			0
$377$	5.06350	+	11.0591i	0.260784	+	0.569573i
$378$		0			0
$379$	−13.2405	−	22.9331i	−0.680117	−	1.17800i	−0.974945	−	0.222446i	$-0.928596\pi$
$379$	−13.2405	−	22.9331i	−0.680117	−	1.17800i	0.294828	−	0.955550i	$-0.404738\pi$
$380$		0			0
$381$	−15.1968	−	1.01700i	−0.778558	−	0.0521026i
$382$		0			0
$383$	−3.05939			−0.156327			−0.0781637	−	0.996941i	$-0.524906\pi$
$383$	−3.05939			−0.156327			−0.0781637	+	0.996941i	$0.524906\pi$
$384$		0			0
$385$	1.12860	−	1.95480i	0.0575189	−	0.0996256i
$386$		0			0
$387$	−4.91187	+	6.36502i	−0.249684	+	0.323552i
$388$		0			0
$389$	−7.58306	+	13.1342i	−0.384476	+	0.665932i	−0.991696	−	0.128601i	$-0.958951\pi$
$389$	−7.58306	+	13.1342i	−0.384476	+	0.665932i	0.607220	+	0.794534i	$0.292285\pi$
$390$		0			0
$391$	−0.0462911	−	0.0801785i	−0.00234104	−	0.00405480i
$392$		0			0
$393$	31.2905	+	2.09402i	1.57840	+	0.105629i
$394$		0			0
$395$	−4.94756			−0.248939
$396$		0			0
$397$	6.92576	−	11.9958i	0.347594	−	0.602050i	−0.638228	−	0.769848i	$-0.720332\pi$
$397$	6.92576	−	11.9958i	0.347594	−	0.602050i	0.985821	+	0.167798i	$0.0536655\pi$
$398$		0			0
$399$	0.0459242	−	0.0685266i	0.00229908	−	0.00343062i
$400$		0			0
$401$	1.31025	−	2.26942i	0.0654309	−	0.113330i	−0.831454	−	0.555593i	$-0.812491\pi$
$401$	1.31025	−	2.26942i	0.0654309	−	0.113330i	0.896885	+	0.442264i	$0.145824\pi$
$402$		0			0
$403$	−11.4422	+	16.1014i	−0.569978	+	0.802068i
$404$		0			0
$405$	3.76643	+	1.03141i	0.187155	+	0.0512510i
$406$		0			0
$407$	5.96861	+	10.3379i	0.295853	+	0.512432i
$408$		0			0
$409$	−15.7656			−0.779558			−0.389779	−	0.920909i	$-0.627449\pi$
$409$	−15.7656			−0.779558			−0.389779	+	0.920909i	$0.627449\pi$
$410$		0			0
$411$	7.11024	+	0.475831i	0.350722	+	0.0234710i
$412$		0			0
$413$	0.287222	+	0.497484i	0.0141333	+	0.0244796i
$414$		0			0
$415$	4.79042			0.235152
$416$		0			0
$417$	−11.7341	+	17.5092i	−0.574619	+	0.857428i
$418$		0			0
$419$	−4.26344	+	7.38449i	−0.208282	+	0.360756i	−0.951174	−	0.308656i	$-0.900121\pi$
$419$	−4.26344	+	7.38449i	−0.208282	+	0.360756i	0.742891	+	0.669412i	$0.233454\pi$
$420$		0			0
$421$	−7.83552	+	13.5715i	−0.381880	+	0.661436i	−0.991331	−	0.131388i	$-0.958057\pi$
$421$	−7.83552	+	13.5715i	−0.381880	+	0.661436i	0.609451	+	0.792824i	$0.291390\pi$
$422$		0			0
$423$	22.5350	+	3.02974i	1.09569	+	0.147311i
$424$		0			0
$425$	−3.94914	−	6.84012i	−0.191562	−	0.331794i
$426$		0			0
$427$	2.73548	−	4.73799i	0.132379	−	0.229288i
$428$		0			0
$429$	−20.2536	−	3.29037i	−0.977851	−	0.158860i
$430$		0			0
$431$	12.8332	+	22.2278i	0.618155	+	1.07068i	0.989822	+	0.142310i	$0.0454528\pi$
$431$	12.8332	+	22.2278i	0.618155	+	1.07068i	−0.371667	+	0.928366i	$0.621214\pi$
$432$		0			0
$433$	−18.3374	+	31.7614i	−0.881241	+	1.52635i	−0.0312791	+	0.999511i	$0.509958\pi$
$433$	−18.3374	+	31.7614i	−0.881241	+	1.52635i	−0.849962	+	0.526844i	$0.823375\pi$
$434$		0			0
$435$	−2.52962	−	0.169287i	−0.121286	−	0.00811669i
$436$		0			0
$437$	−0.000848323	−	0.00146934i	−4.05808e−5	−	7.02880e-5i
$438$		0			0
$439$	4.99493			0.238395			0.119197	−	0.992871i	$-0.461968\pi$
$439$	4.99493			0.238395			0.119197	+	0.992871i	$0.461968\pi$
$440$		0			0
$441$	−13.3595	−	1.79614i	−0.636169	−	0.0855304i
$442$		0			0
$443$	−15.1200	+	26.1886i	−0.718373	+	1.24426i	0.243271	+	0.969958i	$0.421780\pi$
$443$	−15.1200	+	26.1886i	−0.718373	+	1.24426i	−0.961644	+	0.274300i	$0.911554\pi$
$444$		0			0
$445$	−2.66088	+	4.60878i	−0.126138	+	0.218477i
$446$		0			0
$447$	−9.11260	+	13.5975i	−0.431011	+	0.643141i
$448$		0			0
$449$	−9.70002	+	16.8009i	−0.457772	+	0.792885i	−0.998843	−	0.0480922i	$-0.984686\pi$
$449$	−9.70002	+	16.8009i	−0.457772	+	0.792885i	0.541071	+	0.840977i	$0.318019\pi$
$450$		0			0
$451$	−5.96372	+	10.3295i	−0.280820	+	0.486395i
$452$		0			0
$453$	8.12292	+	16.5288i	0.381648	+	0.776591i
$454$		0			0
$455$	2.46596	+	0.233056i	0.115606	+	0.0109258i
$456$		0			0
$457$	−9.45223			−0.442156			−0.221078	−	0.975256i	$-0.570958\pi$
$457$	−9.45223			−0.442156			−0.221078	+	0.975256i	$0.570958\pi$
$458$		0			0
$459$	5.65011	−	6.38946i	0.263725	−	0.298234i
$460$		0			0
$461$	−11.5227	−	19.9580i	−0.536668	−	0.929536i	−0.999081	−	0.0428711i	$-0.986350\pi$
$461$	−11.5227	−	19.9580i	−0.536668	−	0.929536i	0.462413	−	0.886665i	$-0.346984\pi$
$462$		0			0
$463$	−10.3312	−	17.8942i	−0.480134	−	0.831616i	0.519607	−	0.854406i	$-0.326078\pi$
$463$	−10.3312	−	17.8942i	−0.480134	−	0.831616i	−0.999740	+	0.0227898i	$0.992745\pi$
$464$		0			0
$465$	−1.81596	−	3.69518i	−0.0842130	−	0.171360i
$466$		0			0
$467$	−5.84410			−0.270433			−0.135216	−	0.990816i	$-0.543173\pi$
$467$	−5.84410			−0.270433			−0.135216	+	0.990816i	$0.543173\pi$
$468$		0			0
$469$	4.05645			0.187309
$470$		0			0
$471$	0.505080	+	0.0338009i	0.0232728	+	0.00155746i
$472$		0			0
$473$	4.40276	+	7.62580i	0.202439	+	0.350635i
$474$		0			0
$475$	−0.0723714	−	0.125351i	−0.00332063	−	0.00575149i
$476$		0			0
$477$	4.61942	+	11.2394i	0.211509	+	0.514618i
$478$		0			0
$479$	9.41643			0.430248			0.215124	−	0.976587i	$-0.430985\pi$
$479$	9.41643			0.430248			0.215124	+	0.976587i	$0.430985\pi$
$480$		0			0
$481$	−7.58800	+	10.6778i	−0.345983	+	0.486864i
$482$		0			0
$483$	0.0861076	−	0.128487i	0.00391803	−	0.00584636i
$484$		0			0
$485$	2.80691	−	4.86172i	0.127455	−	0.220759i
$486$		0			0
$487$	1.94398	−	3.36708i	0.0880903	−	0.152577i	−0.818614	−	0.574345i	$-0.805257\pi$
$487$	1.94398	−	3.36708i	0.0880903	−	0.152577i	0.906704	+	0.421768i	$0.138590\pi$
$488$		0			0
$489$	10.8802	+	22.1394i	0.492020	+	1.00118i
$490$		0			0
$491$	2.62024	−	4.53840i	0.118250	−	0.204815i	−0.800824	−	0.598899i	$-0.795605\pi$
$491$	2.62024	−	4.53840i	0.118250	−	0.204815i	0.919074	+	0.394084i	$0.128938\pi$
$492$		0			0
$493$	−2.76871	+	4.79554i	−0.124696	+	0.215980i
$494$		0			0
$495$	2.61296	−	3.38599i	0.117444	−	0.152189i
$496$		0			0
$497$	23.1097			1.03661
$498$		0			0
$499$	10.8182	+	18.7377i	0.484289	+	0.838813i	0.999837	−	0.0180474i	$-0.00574497\pi$
$499$	10.8182	+	18.7377i	0.484289	+	0.838813i	−0.515548	+	0.856861i	$0.672412\pi$
$500$		0			0
$501$	11.6532	+	23.7124i	0.520629	+	1.05939i
$502$		0			0
$503$	14.9763	−	25.9397i	0.667760	−	1.15659i	−0.310769	−	0.950485i	$-0.600587\pi$
$503$	14.9763	−	25.9397i	0.667760	−	1.15659i	0.978529	−	0.206108i	$-0.0660800\pi$
$504$		0			0
$505$	1.65655	+	2.86923i	0.0737156	+	0.127679i
$506$		0			0
$507$	−5.96939	−	21.7110i	−0.265110	−	0.964218i
$508$		0			0
$509$	−12.5253	+	21.6945i	−0.555176	+	0.961594i	0.442713	+	0.896663i	$0.354016\pi$
$509$	−12.5253	+	21.6945i	−0.555176	+	0.961594i	−0.997890	+	0.0649305i	$0.979317\pi$
$510$		0			0
$511$	0.128948	+	0.223345i	0.00570433	+	0.00988018i
$512$		0			0
$513$	0.103543	−	0.117092i	0.00457154	−	0.00516975i
$514$		0			0
$515$	−1.55623	+	2.69546i	−0.0685756	+	0.118776i
$516$		0			0
$517$	12.4515	−	21.5666i	0.547617	−	0.948500i
$518$		0			0
$519$	13.4117	+	0.897535i	0.588707	+	0.0393974i
$520$		0			0
$521$	−21.4586			−0.940116			−0.470058	−	0.882635i	$-0.655767\pi$
$521$	−21.4586			−0.940116			−0.470058	+	0.882635i	$0.655767\pi$
$522$		0			0
$523$	−0.790297	−	1.36883i	−0.0345573	−	0.0598550i	0.848230	−	0.529629i	$-0.177669\pi$
$523$	−0.790297	−	1.36883i	−0.0345573	−	0.0598550i	−0.882787	+	0.469774i	$0.844335\pi$
$524$		0			0
$525$	7.34594	−	10.9614i	0.320603	−	0.478394i
$526$		0			0
$527$	−8.99275			−0.391730
$528$		0			0
$529$	11.4984	+	19.9158i	0.499931	+	0.865906i
$530$		0			0
$531$	0.413775	+	1.00675i	0.0179563	+	0.0436892i
$532$		0			0
$533$	−13.0305	−	1.23151i	−0.564415	−	0.0533424i
$534$		0			0
$535$	3.16454	−	5.48115i	0.136815	−	0.236971i
$536$		0			0
$537$	−15.2257	−	1.01893i	−0.657036	−	0.0439701i
$538$		0			0
$539$	−7.38170	+	12.7855i	−0.317952	+	0.550709i
$540$		0			0
$541$	26.1156			1.12280			0.561398	−	0.827546i	$-0.310264\pi$
$541$	26.1156			1.12280			0.561398	+	0.827546i	$0.310264\pi$
$542$		0			0
$543$	−8.97877	+	13.3978i	−0.385316	+	0.574956i
$544$		0			0
$545$	3.52902	+	6.11244i	0.151167	+	0.261828i
$546$		0			0
$547$	10.4157	−	18.0406i	0.445344	−	0.771359i	−0.552732	−	0.833359i	$-0.686415\pi$
$547$	10.4157	−	18.0406i	0.445344	−	0.771359i	0.998076	+	0.0620002i	$0.0197479\pi$
$548$		0			0
$549$	6.33324	−	8.20689i	0.270296	−	0.350262i
$550$		0			0
$551$	−0.0507389	+	0.0878823i	−0.00216155	+	0.00374391i
$552$		0			0
$553$	−18.0533			−0.767706
$554$		0			0
$555$	−1.20427	−	2.45048i	−0.0511182	−	0.104017i
$556$		0			0
$557$	−19.4069	−	33.6138i	−0.822299	−	1.42426i	−0.903967	−	0.427603i	$-0.859358\pi$
$557$	−19.4069	−	33.6138i	−0.822299	−	1.42426i	0.0816680	−	0.996660i	$-0.473975\pi$
$558$		0			0
$559$	−5.59730	+	7.87648i	−0.236741	+	0.333140i
$560$		0			0
$561$	−4.12015	−	8.38382i	−0.173953	−	0.353965i
$562$		0			0
$563$	−0.804224			−0.0338940			−0.0169470	−	0.999856i	$-0.505395\pi$
$563$	−0.804224			−0.0338940			−0.0169470	+	0.999856i	$0.505395\pi$
$564$		0			0
$565$	−4.18377	−	7.24650i	−0.176012	−	0.304862i
$566$		0			0
$567$	13.7435	+	3.76353i	0.577171	+	0.158054i
$568$		0			0
$569$	19.8108			0.830514			0.415257	−	0.909704i	$-0.363692\pi$
$569$	19.8108			0.830514			0.415257	+	0.909704i	$0.363692\pi$
$570$		0			0
$571$	−18.8485	−	32.6466i	−0.788786	−	1.36622i	−0.926711	−	0.375775i	$-0.877376\pi$
$571$	−18.8485	−	32.6466i	−0.788786	−	1.36622i	0.137924	−	0.990443i	$-0.455957\pi$
$572$		0			0
$573$	31.2708	+	2.09270i	1.30636	+	0.0874239i
$574$		0			0
$575$	−0.135696	−	0.235032i	−0.00565891	−	0.00980153i
$576$		0			0
$577$	1.66499			0.0693145			0.0346573	−	0.999399i	$-0.488966\pi$
$577$	1.66499			0.0693145			0.0346573	+	0.999399i	$0.488966\pi$
$578$		0			0
$579$	3.19148	+	6.49414i	0.132634	+	0.269887i
$580$		0			0
$581$	17.4799			0.725190
$582$		0			0
$583$	13.3089			0.551197
$584$		0			0
$585$	4.57201	+	1.06026i	0.189029	+	0.0438363i
$586$		0			0
$587$	−13.7504			−0.567541			−0.283770	−	0.958892i	$-0.591585\pi$
$587$	−13.7504			−0.567541			−0.283770	+	0.958892i	$0.591585\pi$
$588$		0			0
$589$	−0.164800			−0.00679045
$590$		0			0
$591$	−37.3564	−	2.49997i	−1.53664	−	0.102835i
$592$		0			0
$593$	−48.0032			−1.97125			−0.985627	−	0.168937i	$-0.945967\pi$
$593$	−48.0032			−1.97125			−0.985627	+	0.168937i	$0.945967\pi$
$594$		0			0
$595$	0.563828	+	0.976578i	0.0231147	+	0.0400358i
$596$		0			0
$597$	11.5996	+	23.6033i	0.474740	+	0.966018i
$598$		0			0
$599$	−18.5595	−	32.1459i	−0.758319	−	1.31345i	−0.943707	−	0.330782i	$-0.892688\pi$
$599$	−18.5595	−	32.1459i	−0.758319	−	1.31345i	0.185388	−	0.982665i	$-0.440646\pi$
$600$		0			0
$601$	7.04826			0.287505			0.143752	−	0.989614i	$-0.454083\pi$
$601$	7.04826			0.287505			0.143752	+	0.989614i	$0.454083\pi$
$602$		0			0
$603$	7.61766	+	1.02416i	0.310215	+	0.0417072i
$604$		0			0
$605$	0.0443189	+	0.0767627i	0.00180182	+	0.00312085i
$606$		0			0
$607$	10.3740			0.421068			0.210534	−	0.977587i	$-0.432480\pi$
$607$	10.3740			0.421068			0.210534	+	0.977587i	$0.432480\pi$
$608$		0			0
$609$	−9.23042	−	0.617718i	−0.374036	−	0.0250312i
$610$		0			0
$611$	27.2061	+	2.57123i	1.10064	+	0.104021i
$612$		0			0
$613$	−16.7614	−	29.0316i	−0.676986	−	1.17257i	−0.975884	−	0.218289i	$-0.929952\pi$
$613$	−16.7614	−	29.0316i	−0.676986	−	1.17257i	0.298898	−	0.954285i	$-0.403381\pi$
$614$		0			0
$615$	1.51880	−	2.26631i	0.0612439	−	0.0913863i
$616$		0			0
$617$	35.1206			1.41390			0.706952	−	0.707262i	$-0.250070\pi$
$617$	35.1206			1.41390			0.706952	+	0.707262i	$0.250070\pi$
$618$		0			0
$619$	19.5529	−	33.8667i	0.785899	−	1.36122i	−0.142562	−	0.989786i	$-0.545534\pi$
$619$	19.5529	−	33.8667i	0.785899	−	1.36122i	0.928461	−	0.371431i	$-0.121133\pi$
$620$		0			0
$621$	0.194143	−	0.219547i	0.00779068	−	0.00881013i
$622$		0			0
$623$	−9.70939	+	16.8172i	−0.388999	+	0.673765i
$624$		0			0
$625$	−11.1057	−	19.2356i	−0.444228	−	0.769426i
$626$		0			0
$627$	−0.0755052	−	0.153641i	−0.00301539	−	0.00613581i
$628$		0			0
$629$	−5.96361			−0.237785
$630$		0			0
$631$	11.2857	−	19.5474i	0.449277	−	0.778170i	−0.549062	−	0.835781i	$-0.685015\pi$
$631$	11.2857	−	19.5474i	0.449277	−	0.778170i	0.998339	+	0.0576114i	$0.0183484\pi$
$632$		0			0
$633$	−15.2288	−	30.9881i	−0.605292	−	1.23167i
$634$		0			0
$635$	1.90775	−	3.30433i	0.0757069	−	0.131128i
$636$		0			0
$637$	−16.1288	−	1.52432i	−0.639045	−	0.0603957i
$638$		0			0
$639$	43.3980	+	5.83469i	1.71680	+	0.230817i
$640$		0			0
$641$	5.60461	+	9.70746i	0.221369	+	0.383422i	0.955224	−	0.295884i	$-0.0956143\pi$
$641$	5.60461	+	9.70746i	0.221369	+	0.383422i	−0.733855	+	0.679306i	$0.762281\pi$
$642$		0			0
$643$	2.98337			0.117653			0.0588264	−	0.998268i	$-0.481264\pi$
$643$	2.98337			0.117653			0.0588264	+	0.998268i	$0.481264\pi$
$644$		0			0
$645$	−0.888329	−	1.80760i	−0.0349779	−	0.0711743i
$646$		0			0
$647$	−19.2748	−	33.3850i	−0.757772	−	1.31250i	−0.943984	−	0.329990i	$-0.892955\pi$
$647$	−19.2748	−	33.3850i	−0.757772	−	1.31250i	0.186212	−	0.982510i	$-0.440379\pi$
$648$		0			0
$649$	1.19212			0.0467946
$650$		0			0
$651$	−6.62632	−	13.4835i	−0.259706	−	0.528459i
$652$		0			0
$653$	−25.0269	+	43.3478i	−0.979377	+	1.69633i	−0.314716	+	0.949186i	$0.601909\pi$
$653$	−25.0269	+	43.3478i	−0.979377	+	1.69633i	−0.664661	+	0.747145i	$0.731424\pi$
$654$		0			0
$655$	−3.92809	+	6.80365i	−0.153483	+	0.265841i
$656$		0			0
$657$	0.185764	+	0.451978i	0.00724733	+	0.0176334i
$658$		0			0
$659$	−1.65831	−	2.87228i	−0.0645985	−	0.111888i	0.831917	−	0.554900i	$-0.187243\pi$
$659$	−1.65831	−	2.87228i	−0.0645985	−	0.111888i	−0.896516	+	0.443012i	$0.853910\pi$
$660$		0			0
$661$	5.56081	−	9.63160i	0.216290	−	0.374626i	−0.737381	−	0.675478i	$-0.763938\pi$
$661$	5.56081	−	9.63160i	0.216290	−	0.374626i	0.953671	+	0.300852i	$0.0972709\pi$
$662$		0			0
$663$	6.48272	−	7.94079i	0.251768	−	0.308395i
$664$		0			0
$665$	0.0103326	+	0.0178966i	0.000400682	+	0.000694001i
$666$		0			0
$667$	−0.0951352	+	0.164779i	−0.00368365	+	0.00638027i
$668$		0			0
$669$	18.4223	−	27.4892i	0.712247	−	1.06279i
$670$		0			0
$671$	−5.67680	−	9.83251i	−0.219151	−	0.379580i
$672$		0			0
$673$	32.4363			1.25033			0.625163	−	0.780494i	$-0.285032\pi$
$673$	32.4363			1.25033			0.625163	+	0.780494i	$0.285032\pi$
$674$		0			0
$675$	16.5625	−	18.7298i	0.637493	−	0.720912i
$676$		0			0
$677$	−12.6356	+	21.8854i	−0.485624	+	0.841126i	−0.999864	−	0.0165208i	$-0.994741\pi$
$677$	−12.6356	+	21.8854i	−0.485624	+	0.841126i	0.514239	+	0.857647i	$0.328074\pi$
$678$		0			0
$679$	10.2423	−	17.7401i	0.393062	−	0.680803i
$680$		0			0
$681$	22.2711	+	1.49043i	0.853432	+	0.0571133i
$682$		0			0
$683$	0.343395	−	0.594778i	0.0131397	−	0.0227585i	−0.859381	−	0.511336i	$-0.829151\pi$
$683$	0.343395	−	0.594778i	0.0131397	−	0.0227585i	0.872520	+	0.488578i	$0.162484\pi$
$684$		0			0
$685$	−0.892592	+	1.54601i	−0.0341042	+	0.0590702i
$686$		0			0
$687$	−17.5027	−	1.17131i	−0.667769	−	0.0446884i
$688$		0			0
$689$	6.07983	+	13.2788i	0.231623	+	0.505884i
$690$		0			0
$691$	−44.4463			−1.69082			−0.845409	−	0.534119i	$-0.820643\pi$
$691$	−44.4463			−1.69082			−0.845409	+	0.534119i	$0.820643\pi$
$692$		0			0
$693$	9.53452	−	12.3553i	0.362187	−	0.469338i
$694$		0			0
$695$	−2.64008	−	4.57275i	−0.100144	−	0.173454i
$696$		0			0
$697$	−2.97936	−	5.16040i	−0.112851	−	0.195464i
$698$		0			0
$699$	−18.7597	+	27.9926i	−0.709556	+	1.05878i
$700$		0			0
$701$	−5.00391			−0.188995			−0.0944975	−	0.995525i	$-0.530124\pi$
$701$	−5.00391			−0.188995			−0.0944975	+	0.995525i	$0.530124\pi$
$702$		0			0
$703$	−0.109288			−0.00412188
$704$		0			0
$705$	−3.17107	+	4.73177i	−0.119429	+	0.178209i
$706$		0			0
$707$	6.04466	+	10.4697i	0.227333	+	0.393752i
$708$		0			0
$709$	−22.0166	−	38.1339i	−0.826852	−	1.43215i	−0.900495	−	0.434866i	$-0.856796\pi$
$709$	−22.0166	−	38.1339i	−0.826852	−	1.43215i	0.0736428	−	0.997285i	$-0.476538\pi$
$710$		0			0
$711$	−33.9026	−	4.55807i	−1.27145	−	0.170941i
$712$		0			0
$713$	−0.308999			−0.0115721
$714$		0			0
$715$	2.97759	−	4.19004i	0.111356	−	0.156699i
$716$		0			0
$717$	21.8879	+	1.46478i	0.817419	+	0.0547032i
$718$		0			0
$719$	16.8809	−	29.2385i	0.629551	−	1.09041i	−0.358091	−	0.933687i	$-0.616572\pi$
$719$	16.8809	−	29.2385i	0.629551	−	1.09041i	0.987642	−	0.156727i	$-0.0500943\pi$
$720$		0			0
$721$	−5.67858	+	9.83558i	−0.211481	+	0.366296i
$722$		0			0
$723$	25.9377	+	1.73580i	0.964633	+	0.0645551i
$724$		0			0
$725$	−8.11609	+	14.0575i	−0.301424	+	0.522082i
$726$		0			0
$727$	19.1552	−	33.1778i	0.710427	−	1.23050i	−0.254270	−	0.967133i	$-0.581835\pi$
$727$	19.1552	−	33.1778i	0.710427	−	1.23050i	0.964697	−	0.263362i	$-0.0848313\pi$
$728$		0			0
$729$	24.8588	+	10.5375i	0.920697	+	0.390278i
$730$		0			0
$731$	−4.39907			−0.162705
$732$		0			0
$733$	−24.2010	−	41.9174i	−0.893885	−	1.54825i	−0.835179	−	0.549978i	$-0.814636\pi$
$733$	−24.2010	−	41.9174i	−0.893885	−	1.54825i	−0.0587059	−	0.998275i	$-0.518697\pi$
$734$		0			0
$735$	1.87992	−	2.80516i	0.0693420	−	0.103470i
$736$		0			0
$737$	4.20907	−	7.29033i	0.155043	−	0.268543i
$738$		0			0
$739$	20.1732	+	34.9409i	0.742082	+	1.28532i	0.951546	+	0.307507i	$0.0994946\pi$
$739$	20.1732	+	34.9409i	0.742082	+	1.28532i	−0.209464	+	0.977816i	$0.567172\pi$
$740$		0			0
$741$	0.118801	−	0.145522i	0.00436427	−	0.00534587i
$742$		0			0
$743$	−22.8084	+	39.5053i	−0.836758	+	1.44931i	0.0558331	+	0.998440i	$0.482219\pi$
$743$	−22.8084	+	39.5053i	−0.836758	+	1.44931i	−0.892591	+	0.450867i	$0.851115\pi$
$744$		0			0
$745$	−2.05027	−	3.55117i	−0.0751161	−	0.130105i
$746$		0			0
$747$	32.8258	+	4.41330i	1.20103	+	0.161474i
$748$		0			0
$749$	11.5472	−	20.0004i	0.421926	−	0.730798i
$750$		0			0
$751$	−21.0467	+	36.4540i	−0.768007	+	1.33023i	0.170636	+	0.985334i	$0.445418\pi$
$751$	−21.0467	+	36.4540i	−0.768007	+	1.33023i	−0.938642	+	0.344892i	$0.887915\pi$
$752$		0			0
$753$	5.96109	+	12.1298i	0.217234	+	0.442036i
$754$		0			0
$755$	−4.61366			−0.167908
$756$		0			0
$757$	−15.6559	−	27.1168i	−0.569024	−	0.985578i	−0.996663	−	0.0816283i	$-0.973988\pi$
$757$	−15.6559	−	27.1168i	−0.569024	−	0.985578i	0.427639	−	0.903949i	$-0.359345\pi$
$758$		0			0
$759$	−0.141572	−	0.288075i	−0.00513874	−	0.0104565i
$760$		0			0
$761$	−51.3570			−1.86169			−0.930845	−	0.365414i	$-0.880927\pi$
$761$	−51.3570			−1.86169			−0.930845	+	0.365414i	$0.880927\pi$
$762$		0			0
$763$	12.8772	+	22.3039i	0.466185	+	0.807456i
$764$		0			0
$765$	0.812255	+	1.97628i	0.0293671	+	0.0714527i
$766$		0			0
$767$	0.544588	+	1.18943i	0.0196639	+	0.0429477i
$768$		0			0
$769$	−10.8919	+	18.8653i	−0.392772	+	0.680301i	−0.992814	−	0.119667i	$-0.961817\pi$
$769$	−10.8919	+	18.8653i	−0.392772	+	0.680301i	0.600042	+	0.799969i	$0.295151\pi$
$770$		0			0
$771$	5.68702	+	11.5721i	0.204813	+	0.416761i
$772$		0			0
$773$	−9.64820	+	16.7112i	−0.347022	+	0.601059i	−0.985719	−	0.168399i	$-0.946140\pi$
$773$	−9.64820	+	16.7112i	−0.347022	+	0.601059i	0.638697	+	0.769458i	$0.279474\pi$
$774$		0			0
$775$	−26.3610			−0.946916
$776$		0			0
$777$	−4.39429	−	8.94165i	−0.157644	−	0.320780i
$778$		0			0
$779$	−0.0545992	−	0.0945687i	−0.00195622	−	0.00338827i
$780$		0			0
$781$	23.9792	−	41.5332i	0.858043	−	1.48617i
$782$		0			0
$783$	−17.1780	−	3.49050i	−0.613891	−	0.124740i
$784$		0			0
$785$	−0.0634058	+	0.109822i	−0.00226305	+	0.00391972i
$786$		0			0
$787$	−10.4299			−0.371785			−0.185893	−	0.982570i	$-0.559518\pi$
$787$	−10.4299			−0.371785			−0.185893	+	0.982570i	$0.559518\pi$
$788$		0			0
$789$	−6.87986	+	10.2659i	−0.244930	+	0.365476i
$790$		0			0
$791$	−15.2663	−	26.4420i	−0.542807	−	0.940170i
$792$		0			0
$793$	7.21702	−	10.1557i	0.256284	−	0.360641i
$794$		0			0
$795$	−3.03735	−	0.203266i	−0.107724	−	0.00720908i
$796$		0			0
$797$	−0.852516			−0.0301977			−0.0150988	−	0.999886i	$-0.504806\pi$
$797$	−0.852516			−0.0301977			−0.0150988	+	0.999886i	$0.504806\pi$
$798$		0			0
$799$	6.22053	+	10.7743i	0.220067	+	0.381167i
$800$		0			0
$801$	−22.4794	+	29.1298i	−0.794269	+	1.02925i
$802$		0			0
$803$	0.535199			0.0188867
$804$		0			0
$805$	0.0193736	+	0.0335561i	0.000682830	+	0.00118270i
$806$		0			0
$807$	21.5709	+	43.8931i	0.759330	+	1.54511i
$808$		0			0
$809$	−22.8597	−	39.5942i	−0.803704	−	1.39206i	−0.917162	−	0.398514i	$-0.869526\pi$
$809$	−22.8597	−	39.5942i	−0.803704	−	1.39206i	0.113458	−	0.993543i	$-0.463807\pi$
$810$		0			0
$811$	14.7191			0.516857			0.258429	−	0.966030i	$-0.416795\pi$
$811$	14.7191			0.516857			0.258429	+	0.966030i	$0.416795\pi$
$812$		0			0
$813$	13.2165	+	0.884476i	0.463524	+	0.0310199i
$814$		0			0
$815$	−6.17975			−0.216467
$816$		0			0
$817$	−0.0806166			−0.00282042
$818$		0			0
$819$	16.6830	+	3.86882i	0.582951	+	0.135187i
$820$		0			0
$821$	12.6029			0.439843			0.219922	−	0.975518i	$-0.429420\pi$
$821$	12.6029			0.439843			0.219922	+	0.975518i	$0.429420\pi$
$822$		0			0
$823$	−2.12581			−0.0741012			−0.0370506	−	0.999313i	$-0.511796\pi$
$823$	−2.12581			−0.0741012			−0.0370506	+	0.999313i	$0.511796\pi$
$824$		0			0
$825$	−12.0777	−	24.5760i	−0.420490	−	0.855628i
$826$		0			0
$827$	−30.0089			−1.04351			−0.521756	−	0.853095i	$-0.674723\pi$
$827$	−30.0089			−1.04351			−0.521756	+	0.853095i	$0.674723\pi$
$828$		0			0
$829$	−19.6435	−	34.0235i	−0.682246	−	1.18168i	−0.974294	−	0.225281i	$-0.927670\pi$
$829$	−19.6435	−	34.0235i	−0.682246	−	1.18168i	0.292048	−	0.956404i	$-0.405663\pi$
$830$		0			0
$831$	−32.7599	−	2.19236i	−1.13643	−	0.0760520i
$832$		0			0
$833$	−3.68775	−	6.38738i	−0.127773	−	0.221310i
$834$		0			0
$835$	−6.61882			−0.229054
$836$		0			0
$837$	−9.03937	−	26.9938i	−0.312446	−	0.933041i
$838$		0			0
$839$	26.4687	+	45.8452i	0.913802	+	1.58275i	0.808646	+	0.588296i	$0.200201\pi$
$839$	26.4687	+	45.8452i	0.913802	+	1.58275i	0.105156	+	0.994456i	$0.466466\pi$
$840$		0			0
$841$	−17.6198			−0.607578
$842$		0			0
$843$	19.4738	+	39.6259i	0.670713	+	1.36479i
$844$		0			0
$845$	5.54082	+	1.05676i	0.190610	+	0.0363535i
$846$		0			0
$847$	0.161717	+	0.280102i	0.00555666	+	0.00962442i
$848$		0			0
$849$	−6.51173	−	13.2503i	−0.223482	−	0.454749i
$850$		0			0
$851$	−0.204915			−0.00702438
$852$		0			0
$853$	−2.51731	+	4.36011i	−0.0861911	+	0.149287i	−0.905898	−	0.423496i	$-0.860803\pi$
$853$	−2.51731	+	4.36011i	−0.0861911	+	0.149287i	0.819707	+	0.572783i	$0.194136\pi$
$854$		0			0
$855$	0.0148853	+	0.0362170i	0.000509065	+	0.00123860i
$856$		0			0
$857$	1.95321	−	3.38305i	0.0667203	−	0.115563i	−0.830736	−	0.556667i	$-0.812080\pi$
$857$	1.95321	−	3.38305i	0.0667203	−	0.115563i	0.897456	+	0.441104i	$0.145413\pi$
$858$		0			0
$859$	−0.493148	−	0.854157i	−0.0168260	−	0.0291435i	0.857490	−	0.514501i	$-0.172023\pi$
$859$	−0.493148	−	0.854157i	−0.0168260	−	0.0291435i	−0.874316	+	0.485357i	$0.838689\pi$
$860$		0			0
$861$	5.54201	−	8.26961i	0.188871	−	0.281828i
$862$		0			0
$863$	44.2030			1.50469			0.752345	−	0.658770i	$-0.228923\pi$
$863$	44.2030			1.50469			0.752345	+	0.658770i	$0.228923\pi$
$864$		0			0
$865$	−1.68365	+	2.91617i	−0.0572458	+	0.0991526i
$866$		0			0
$867$	−24.7227	−	1.65449i	−0.839627	−	0.0561895i
$868$		0			0
$869$	−18.7326	+	32.4458i	−0.635460	+	1.10065i
$870$		0			0
$871$	9.19669	+	0.869172i	0.311618	+	0.0294508i
$872$		0			0
$873$	23.7130	−	30.7284i	0.802565	−	1.04000i
$874$		0			0
$875$	3.37024	+	5.83742i	0.113935	+	0.197341i
$876$		0			0
$877$	39.7236			1.34137			0.670685	−	0.741743i	$-0.266000\pi$
$877$	39.7236			1.34137			0.670685	+	0.741743i	$0.266000\pi$
$878$		0			0
$879$	2.22566	−	3.32105i	0.0750695	−	0.112016i
$880$		0			0
$881$	−21.1534	−	36.6387i	−0.712675	−	1.23439i	−0.963849	−	0.266448i	$-0.914150\pi$
$881$	−21.1534	−	36.6387i	−0.712675	−	1.23439i	0.251174	−	0.967942i	$-0.419183\pi$
$882$		0			0
$883$	−32.9536			−1.10898			−0.554488	−	0.832192i	$-0.687086\pi$
$883$	−32.9536			−1.10898			−0.554488	+	0.832192i	$0.687086\pi$
$884$		0			0
$885$	−0.272065	−	0.0182071i	−0.00914535	−	0.000612025i
$886$		0			0
$887$	−5.45287	+	9.44465i	−0.183090	+	0.317120i	−0.942931	−	0.332988i	$-0.891943\pi$
$887$	−5.45287	+	9.44465i	−0.183090	+	0.317120i	0.759842	+	0.650108i	$0.225276\pi$
$888$		0			0
$889$	6.96127	−	12.0573i	0.233474	−	0.404388i
$890$		0			0
$891$	21.0244	−	20.7949i	0.704345	−	0.696654i
$892$		0			0
$893$	0.113996	+	0.197448i	0.00381475	+	0.00660733i
$894$		0			0
$895$	1.91137	−	3.31059i	0.0638901	−	0.110661i
$896$		0			0
$897$	0.222752	−	0.272853i	0.00743747	−	0.00911028i
$898$		0			0
$899$	9.24074	+	16.0054i	0.308196	+	0.533811i
$900$		0			0
$901$	−3.32443	+	5.75808i	−0.110753	+	0.191830i
$902$		0			0
$903$	−3.24146	−	6.59583i	−0.107869	−	0.219496i
$904$		0			0
$905$	−2.02016	−	3.49902i	−0.0671524	−	0.116311i
$906$		0			0
$907$	18.7810			0.623612			0.311806	−	0.950146i	$-0.399066\pi$
$907$	18.7810			0.623612			0.311806	+	0.950146i	$0.399066\pi$
$908$		0			0
$909$	8.70798	+	21.1872i	0.288826	+	0.702736i
$910$		0			0
$911$	−3.88256	+	6.72478i	−0.128635	+	0.222802i	−0.923148	−	0.384445i	$-0.874393\pi$
$911$	−3.88256	+	6.72478i	−0.128635	+	0.222802i	0.794513	+	0.607247i	$0.207726\pi$
$912$		0			0
$913$	18.1376	−	31.4153i	0.600267	−	1.03969i
$914$		0			0
$915$	1.14539	+	2.33068i	0.0378654	+	0.0770498i
$916$		0			0
$917$	−14.3334	+	24.8261i	−0.473329	+	0.819830i
$918$		0			0
$919$	−20.9504	+	36.2872i	−0.691090	+	1.19700i	0.280391	+	0.959886i	$0.409536\pi$
$919$	−20.9504	+	36.2872i	−0.691090	+	1.19700i	−0.971481	+	0.237118i	$0.923797\pi$
$920$		0			0
$921$	−25.0007	+	37.3053i	−0.823801	+	1.22925i
$922$		0			0
$923$	52.3938	+	4.95170i	1.72456	+	0.162987i
$924$		0			0
$925$	−17.4815			−0.574788
$926$		0			0
$927$	−13.1471	+	17.0367i	−0.431809	+	0.559557i
$928$		0			0
$929$	20.8258	+	36.0714i	0.683273	+	1.18346i	0.973976	+	0.226651i	$0.0727775\pi$
$929$	20.8258	+	36.0714i	0.683273	+	1.18346i	−0.290703	+	0.956813i	$0.593889\pi$
$930$		0			0
$931$	−0.0675812	−	0.117054i	−0.00221488	−	0.00383629i
$932$		0			0
$933$	55.9057	+	3.74132i	1.83027	+	0.122485i
$934$		0			0
$935$	2.34017			0.0765316
$936$		0			0
$937$	46.9101			1.53249			0.766244	−	0.642550i	$-0.222124\pi$
$937$	46.9101			1.53249			0.766244	+	0.642550i	$0.222124\pi$
$938$		0			0
$939$	−2.82103	−	5.74032i	−0.0920607	−	0.187328i
$940$		0			0
$941$	1.71346	+	2.96780i	0.0558571	+	0.0967474i	0.892602	−	0.450846i	$-0.148878\pi$
$941$	1.71346	+	2.96780i	0.0558571	+	0.0967474i	−0.836745	+	0.547593i	$0.815544\pi$
$942$		0			0
$943$	−0.102373	−	0.177316i	−0.00333373	−	0.00577420i
$944$		0			0
$945$	−2.36467	+	2.67410i	−0.0769227	+	0.0869884i
$946$		0			0
$947$	21.0542			0.684170			0.342085	−	0.939669i	$-0.388867\pi$
$947$	21.0542			0.684170			0.342085	+	0.939669i	$0.388867\pi$
$948$		0			0
$949$	0.244492	+	0.533991i	0.00793655	+	0.0173341i
$950$		0			0
$951$	9.76142	+	19.8629i	0.316536	+	0.644098i
$952$		0			0
$953$	5.77633	−	10.0049i	0.187114	−	0.324090i	−0.757173	−	0.653214i	$-0.773420\pi$
$953$	5.77633	−	10.0049i	0.187114	−	0.324090i	0.944287	+	0.329124i	$0.106753\pi$
$954$		0			0
$955$	−3.92562	+	6.79937i	−0.127030	+	0.220022i
$956$		0			0
$957$	−10.6879	+	15.9481i	−0.345490	+	0.515530i
$958$		0			0
$959$	−3.25701	+	5.64131i	−0.105174	+	0.182167i
$960$		0			0
$961$	0.493070	−	0.854023i	0.0159055	−	0.0275491i
$962$		0			0
$963$	26.7343	−	34.6436i	0.861502	−	1.11637i
$964$		0			0
$965$	−1.81270			−0.0583529
$966$		0			0
$967$	9.28441	+	16.0811i	0.298567	+	0.517133i	0.975808	−	0.218628i	$-0.0701582\pi$
$967$	9.28441	+	16.0811i	0.298567	+	0.517133i	−0.677242	+	0.735761i	$0.736825\pi$
$968$		0			0
$969$	0.0853330	+	0.00571065i	0.00274129	+	0.000183453i
$970$		0			0
$971$	−9.28362	+	16.0797i	−0.297926	+	0.516022i	−0.975661	−	0.219283i	$-0.929628\pi$
$971$	−9.28362	+	16.0797i	−0.297926	+	0.516022i	0.677736	+	0.735306i	$0.262961\pi$
$972$		0			0
$973$	−9.63348	−	16.6857i	−0.308835	−	0.534918i
$974$		0			0
$975$	19.0032	−	23.2774i	0.608590	−	0.745472i
$976$		0			0
$977$	23.9560	−	41.4930i	0.766421	−	1.32748i	−0.173071	−	0.984909i	$-0.555369\pi$
$977$	23.9560	−	41.4930i	0.766421	−	1.32748i	0.939492	−	0.342571i	$-0.111298\pi$
$978$		0			0
$979$	20.1494	+	34.8998i	0.643978	+	1.11540i
$980$		0			0
$981$	18.5510	+	45.1360i	0.592287	+	1.44108i
$982$		0			0
$983$	−28.1105	+	48.6888i	−0.896586	+	1.55293i	−0.0647561	+	0.997901i	$0.520627\pi$
$983$	−28.1105	+	48.6888i	−0.896586	+	1.55293i	−0.831830	+	0.555031i	$0.812706\pi$
$984$		0			0
$985$	4.68958	−	8.12260i	0.149423	−	0.258808i
$986$		0			0
$987$	−11.5710	+	17.2659i	−0.368310	+	0.549580i
$988$		0			0
$989$	−0.151156			−0.00480647
$990$		0			0
$991$	0.830293	+	1.43811i	0.0263751	+	0.0456831i	0.878912	−	0.476985i	$-0.158270\pi$
$991$	0.830293	+	1.43811i	0.0263751	+	0.0456831i	−0.852537	+	0.522668i	$0.824937\pi$
$992$		0			0
$993$	14.0296	+	0.938885i	0.445215	+	0.0297946i
$994$		0			0
$995$	−6.58835			−0.208865
$996$		0			0
$997$	27.4394	+	47.5265i	0.869016	+	1.50518i	0.863004	+	0.505197i	$0.168580\pi$
$997$	27.4394	+	47.5265i	0.869016	+	1.50518i	0.00601173	+	0.999982i	$0.498086\pi$
$998$		0			0
$999$	−5.99453	−	17.9011i	−0.189658	−	0.566366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.j.a.133.5	✓	28
3.2	odd	2		1404.2.j.a.289.8		28
9.4	even	3		468.2.k.a.445.14	yes	28
9.5	odd	6		1404.2.k.a.1225.8		28
13.9	even	3		468.2.k.a.61.14	yes	28
39.35	odd	6		1404.2.k.a.1153.8		28
117.22	even	3	inner	468.2.j.a.373.5	yes	28
117.113	odd	6		1404.2.j.a.685.8		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.j.a.133.5	✓	28	1.1	even	1	trivial
468.2.j.a.373.5	yes	28	117.22	even	3	inner
468.2.k.a.61.14	yes	28	13.9	even	3
468.2.k.a.445.14	yes	28	9.4	even	3
1404.2.j.a.289.8		28	3.2	odd	2
1404.2.j.a.685.8		28	117.113	odd	6
1404.2.k.a.1153.8		28	39.35	odd	6
1404.2.k.a.1225.8		28	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.964252 + 1.43883i) q^{3} +(-0.216950 - 0.375768i) q^{5} +(-0.791636 - 1.37115i) q^{7} +(-1.14044 - 2.77478i) q^{9} -3.28568 q^{11} +(-1.50098 - 3.27827i) q^{13} +(0.749859 + 0.0501820i) q^{15} +(0.820732 - 1.42155i) q^{17} +(0.0150406 - 0.0260511i) q^{19} +(2.73619 + 0.183111i) q^{21} +(0.0282011 - 0.0488457i) q^{23} +(2.40587 - 4.16708i) q^{25} +(5.09209 + 1.03469i) q^{27} -3.37346 q^{29} +(-2.73925 - 4.74451i) q^{31} +(3.16823 - 4.72753i) q^{33} +(-0.343491 + 0.594943i) q^{35} +(-1.81655 - 3.14636i) q^{37} +(6.16418 + 1.00143i) q^{39} +(1.81506 - 3.14378i) q^{41} +(-1.33998 - 2.32092i) q^{43} +(-0.795256 + 1.03053i) q^{45} +(-3.78962 + 6.56382i) q^{47} +(2.24662 - 3.89127i) q^{49} +(1.25397 + 2.55162i) q^{51} -4.05057 q^{53} +(0.712828 + 1.23465i) q^{55} +(0.0229801 + 0.0467606i) q^{57} -0.362821 q^{59} +(1.72774 + 2.99253i) q^{61} +(-2.90184 + 3.76033i) q^{63} +(-0.906231 + 1.27524i) q^{65} +(-1.28103 + 2.21882i) q^{67} +(0.0430875 + 0.0876760i) q^{69} +(-7.29808 + 12.6407i) q^{71} -0.162888 q^{73} +(3.67584 + 7.47974i) q^{75} +(2.60107 + 4.50518i) q^{77} +(5.70128 - 9.87490i) q^{79} +(-6.39880 + 6.32893i) q^{81} +(-5.52019 + 9.56125i) q^{83} -0.712231 q^{85} +(3.25286 - 4.85382i) q^{87} +(-6.13248 - 10.6218i) q^{89} +(-3.30678 + 4.65327i) q^{91} +(9.46785 + 0.633607i) q^{93} -0.0130522 q^{95} +(6.46904 + 11.2047i) q^{97} +(3.74712 + 9.11705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{7} - 2 q^{9} + 8 q^{11} + q^{13} - 10 q^{15} - 8 q^{17} - q^{19} + 14 q^{21} - 4 q^{23} - 14 q^{25} + 26 q^{29} + 2 q^{31} + 8 q^{33} + 3 q^{35} - q^{37} - 12 q^{39} + 4 q^{41} + 2 q^{43}+ \cdots - 29 q^{99}+O(q^{100}) \) 28 * q + 2 * q^7 - 2 * q^9 + 8 * q^11 + q^13 - 10 * q^15 - 8 * q^17 - q^19 + 14 * q^21 - 4 * q^23 - 14 * q^25 + 26 * q^29 + 2 * q^31 + 8 * q^33 + 3 * q^35 - q^37 - 12 * q^39 + 4 * q^41 + 2 * q^43 + q^45 + 11 * q^47 - 12 * q^49 + 5 * q^51 + 52 * q^53 - q^57 + 16 * q^59 - 7 * q^61 - 24 * q^63 - 31 * q^65 - 7 * q^67 + 24 * q^69 - 12 * q^71 + 14 * q^73 + 16 * q^75 - 28 * q^77 + 5 * q^79 - 50 * q^81 + 9 * q^83 - 36 * q^85 - 21 * q^87 - 11 * q^89 - q^91 - 33 * q^93 - 56 * q^95 - 25 * q^97 - 29 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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