LMFDB - Embedded newform 1134.2.k.c.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.7
Root			$0.500000 - 0.0390518i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.c.971.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.860850 + 1.49104i) q^{5} +(-2.25833 - 1.37838i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.860850 + 1.49104i) q^{5} +(-2.25833 - 1.37838i) q^{7} -1.00000i q^{8} +(1.49104 + 0.860850i) q^{10} +(1.47921 + 0.854023i) q^{11} -1.28315i q^{13} +(-2.64496 - 0.0645439i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.60152 - 4.50597i) q^{17} +(2.39385 - 1.38209i) q^{19} +1.72170 q^{20} +1.70805 q^{22} +(4.71463 - 2.72199i) q^{23} +(1.01787 - 1.76301i) q^{25} +(-0.641574 - 1.11124i) q^{26} +(-2.32288 + 1.26659i) q^{28} -1.44960i q^{29} +(5.82274 + 3.36176i) q^{31} +(-0.866025 - 0.500000i) q^{32} -5.20305i q^{34} +(0.111125 - 4.55384i) q^{35} +(3.75959 + 6.51181i) q^{37} +(1.38209 - 2.39385i) q^{38} +(1.49104 - 0.860850i) q^{40} +8.96434 q^{41} -8.37200 q^{43} +(1.47921 - 0.854023i) q^{44} +(2.72199 - 4.71463i) q^{46} +(-2.61809 - 4.53466i) q^{47} +(3.20014 + 6.22568i) q^{49} -2.03575i q^{50} +(-1.11124 - 0.641574i) q^{52} +(-9.46059 - 5.46207i) q^{53} +2.94074i q^{55} +(-1.37838 + 2.25833i) q^{56} +(-0.724802 - 1.25539i) q^{58} +(2.08655 - 3.61401i) q^{59} +(-2.28575 + 1.31968i) q^{61} +6.72352 q^{62} -1.00000 q^{64} +(1.91322 - 1.10460i) q^{65} +(-4.31994 + 7.48235i) q^{67} +(-2.60152 - 4.50597i) q^{68} +(-2.18068 - 3.99930i) q^{70} +5.07491i q^{71} +(8.18155 + 4.72362i) q^{73} +(6.51181 + 3.75959i) q^{74} -2.76418i q^{76} +(-2.16339 - 3.96758i) q^{77} +(-6.73747 - 11.6696i) q^{79} +(0.860850 - 1.49104i) q^{80} +(7.76335 - 4.48217i) q^{82} -6.07609 q^{83} +8.95809 q^{85} +(-7.25036 + 4.18600i) q^{86} +(0.854023 - 1.47921i) q^{88} +(4.16679 + 7.21709i) q^{89} +(-1.76866 + 2.89778i) q^{91} -5.44399i q^{92} +(-4.53466 - 2.61809i) q^{94} +(4.12150 + 2.37955i) q^{95} +10.0571i q^{97} +(5.88425 + 3.79152i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^7	$ 16 q + 8 q^{4} + 8 q^{7} - 12 q^{11} - 12 q^{14} - 8 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} - 60 q^{35} + 4 q^{37} + 12 q^{38} + 48 q^{41} - 32 q^{43} - 12 q^{44} + 4 q^{49} - 12 q^{52} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 12 q^{61} + 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} - 36 q^{74} - 84 q^{77} + 8 q^{79} + 72 q^{83} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 36 q^{94} - 12 q^{95} - 36 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^7 - 12 * q^11 - 12 * q^14 - 8 * q^16 - 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 - 60 * q^35 + 4 * q^37 + 12 * q^38 + 48 * q^41 - 32 * q^43 - 12 * q^44 + 4 * q^49 - 12 * q^52 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 12 * q^61 + 48 * q^62 - 16 * q^64 - 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 - 36 * q^74 - 84 * q^77 + 8 * q^79 + 72 * q^83 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 36 * q^94 - 12 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.860850	+	1.49104i	0.384984	+	0.666812i	0.991767	−	0.128056i	$-0.0408736\pi$
$5$	0.860850	+	1.49104i	0.384984	+	0.666812i	−0.606783	+	0.794868i	$0.707540\pi$
$6$		0			0
$7$	−2.25833	−	1.37838i	−0.853570	−	0.520978i
$7$	−2.25833	−	1.37838i	−0.853570	−	0.520978i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.49104	+	0.860850i	0.471507	+	0.272225i
$11$	1.47921	+	0.854023i	0.445999	+	0.257498i	0.706139	−	0.708073i	$-0.250435\pi$
$11$	1.47921	+	0.854023i	0.445999	+	0.257498i	−0.260140	+	0.965571i	$0.583769\pi$
$12$		0			0
$13$		−	1.28315i		−	0.355881i	−0.984041	−	0.177941i	$-0.943056\pi$
$13$		−	1.28315i		−	0.355881i	0.984041	−	0.177941i	$-0.0569435\pi$
$14$	−2.64496	−	0.0645439i	−0.706896	−	0.0172501i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.60152	−	4.50597i	0.630962	−	1.09286i	−0.356394	−	0.934336i	$-0.615994\pi$
$17$	2.60152	−	4.50597i	0.630962	−	1.09286i	0.987355	−	0.158522i	$-0.0506729\pi$
$18$		0			0
$19$	2.39385	−	1.38209i	0.549187	−	0.317074i	−0.199607	−	0.979876i	$-0.563966\pi$
$19$	2.39385	−	1.38209i	0.549187	−	0.317074i	0.748794	+	0.662803i	$0.230633\pi$
$20$	1.72170			0.384984
$21$		0			0
$22$	1.70805			0.364157
$23$	4.71463	−	2.72199i	0.983069	−	0.567575i	0.0798736	−	0.996805i	$-0.474548\pi$
$23$	4.71463	−	2.72199i	0.983069	−	0.567575i	0.903195	+	0.429230i	$0.141215\pi$
$24$		0			0
$25$	1.01787	−	1.76301i	0.203575	−	0.352602i
$26$	−0.641574	−	1.11124i	−0.125823	−	0.217932i
$27$		0			0
$28$	−2.32288	+	1.26659i	−0.438983	+	0.239362i
$29$		−	1.44960i		−	0.269185i	−0.990901	−	0.134592i	$-0.957028\pi$
$29$		−	1.44960i		−	0.269185i	0.990901	−	0.134592i	$-0.0429725\pi$
$30$		0			0
$31$	5.82274	+	3.36176i	1.04579	+	0.603790i	0.921469	−	0.388452i	$-0.126990\pi$
$31$	5.82274	+	3.36176i	1.04579	+	0.603790i	0.124325	+	0.992242i	$0.460323\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	5.20305i		−	0.892315i
$35$	0.111125	−	4.55384i	0.0187836	−	0.769739i
$36$		0			0
$37$	3.75959	+	6.51181i	0.618073	+	1.07053i	0.989837	+	0.142207i	$0.0454198\pi$
$37$	3.75959	+	6.51181i	0.618073	+	1.07053i	−0.371764	+	0.928327i	$0.621247\pi$
$38$	1.38209	−	2.39385i	0.224205	−	0.388334i
$39$		0			0
$40$	1.49104	−	0.860850i	0.235754	−	0.136112i
$41$	8.96434			1.39999			0.699997	−	0.714145i	$-0.253184\pi$
$41$	8.96434			1.39999			0.699997	+	0.714145i	$0.253184\pi$
$42$		0			0
$43$	−8.37200			−1.27672			−0.638359	−	0.769739i	$-0.720386\pi$
$43$	−8.37200			−1.27672			−0.638359	+	0.769739i	$0.720386\pi$
$44$	1.47921	−	0.854023i	0.222999	−	0.128749i
$45$		0			0
$46$	2.72199	−	4.71463i	0.401336	−	0.695135i
$47$	−2.61809	−	4.53466i	−0.381887	−	0.661448i	0.609445	−	0.792828i	$-0.291392\pi$
$47$	−2.61809	−	4.53466i	−0.381887	−	0.661448i	−0.991332	+	0.131381i	$0.958059\pi$
$48$		0			0
$49$	3.20014	+	6.22568i	0.457164	+	0.889383i
$50$		−	2.03575i		−	0.287898i
$51$		0			0
$52$	−1.11124	−	0.641574i	−0.154101	−	0.0889703i
$53$	−9.46059	−	5.46207i	−1.29951	−	0.750273i	−0.319192	−	0.947690i	$-0.603411\pi$
$53$	−9.46059	−	5.46207i	−1.29951	−	0.750273i	−0.980320	+	0.197417i	$0.936745\pi$
$54$		0			0
$55$			2.94074i			0.396530i
$56$	−1.37838	+	2.25833i	−0.184194	+	0.301783i
$57$		0			0
$58$	−0.724802	−	1.25539i	−0.0951711	−	0.164841i
$59$	2.08655	−	3.61401i	0.271646	−	0.470504i	−0.697638	−	0.716451i	$-0.745765\pi$
$59$	2.08655	−	3.61401i	0.271646	−	0.470504i	0.969283	+	0.245946i	$0.0790987\pi$
$60$		0			0
$61$	−2.28575	+	1.31968i	−0.292660	+	0.168967i	−0.639141	−	0.769090i	$-0.720710\pi$
$61$	−2.28575	+	1.31968i	−0.292660	+	0.168967i	0.346481	+	0.938057i	$0.387377\pi$
$62$	6.72352			0.853888
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.91322	−	1.10460i	0.237306	−	0.137009i
$66$		0			0
$67$	−4.31994	+	7.48235i	−0.527764	+	0.914115i	0.471712	+	0.881753i	$0.343636\pi$
$67$	−4.31994	+	7.48235i	−0.527764	+	0.914115i	−0.999476	+	0.0323619i	$0.989697\pi$
$68$	−2.60152	−	4.50597i	−0.315481	−	0.546429i
$69$		0			0
$70$	−2.18068	−	3.99930i	−0.260641	−	0.478008i
$71$			5.07491i			0.602282i	0.953580	+	0.301141i	$0.0973674\pi$
$71$			5.07491i			0.602282i	−0.953580	+	0.301141i	$0.902633\pi$
$72$		0			0
$73$	8.18155	+	4.72362i	0.957578	+	0.552858i	0.895427	−	0.445209i	$-0.146870\pi$
$73$	8.18155	+	4.72362i	0.957578	+	0.552858i	0.0621516	+	0.998067i	$0.480204\pi$
$74$	6.51181	+	3.75959i	0.756982	+	0.437044i
$75$		0			0
$76$		−	2.76418i		−	0.317074i
$77$	−2.16339	−	3.96758i	−0.246541	−	0.452148i
$78$		0			0
$79$	−6.73747	−	11.6696i	−0.758024	−	1.31294i	−0.943857	−	0.330355i	$-0.892832\pi$
$79$	−6.73747	−	11.6696i	−0.758024	−	1.31294i	0.185833	−	0.982581i	$-0.440502\pi$
$80$	0.860850	−	1.49104i	0.0962460	−	0.166703i
$81$		0			0
$82$	7.76335	−	4.48217i	0.857318	−	0.494973i
$83$	−6.07609			−0.666937			−0.333469	−	0.942761i	$-0.608219\pi$
$83$	−6.07609			−0.666937			−0.333469	+	0.942761i	$0.608219\pi$
$84$		0			0
$85$	8.95809			0.971641
$86$	−7.25036	+	4.18600i	−0.781826	+	0.451388i
$87$		0			0
$88$	0.854023	−	1.47921i	0.0910391	−	0.157684i
$89$	4.16679	+	7.21709i	0.441679	+	0.765010i	0.997814	−	0.0660818i	$-0.0210498\pi$
$89$	4.16679	+	7.21709i	0.441679	+	0.765010i	−0.556136	+	0.831092i	$0.687717\pi$
$90$		0			0
$91$	−1.76866	+	2.89778i	−0.185406	+	0.303770i
$92$		−	5.44399i		−	0.567575i
$93$		0			0
$94$	−4.53466	−	2.61809i	−0.467714	−	0.270035i
$95$	4.12150	+	2.37955i	0.422857	+	0.244136i
$96$		0			0
$97$			10.0571i			1.02115i	0.859834	+	0.510574i	$0.170567\pi$
$97$			10.0571i			1.02115i	−0.859834	+	0.510574i	$0.829433\pi$
$98$	5.88425	+	3.79152i	0.594399	+	0.383002i
$99$		0			0
$100$	−1.01787	−	1.76301i	−0.101787	−	0.176301i
$101$	7.90634	−	13.6942i	0.786710	−	1.36262i	−0.141261	−	0.989972i	$-0.545116\pi$
$101$	7.90634	−	13.6942i	0.786710	−	1.36262i	0.927972	−	0.372650i	$-0.121551\pi$
$102$		0			0
$103$	−12.5857	+	7.26634i	−1.24010	+	0.715973i	−0.969115	−	0.246609i	$-0.920684\pi$
$103$	−12.5857	+	7.26634i	−1.24010	+	0.715973i	−0.270988	+	0.962583i	$0.587350\pi$
$104$	−1.28315			−0.125823
$105$		0			0
$106$	−10.9241			−1.06105
$107$	−3.01627	+	1.74144i	−0.291594	+	0.168352i	−0.638660	−	0.769489i	$-0.720511\pi$
$107$	−3.01627	+	1.74144i	−0.291594	+	0.168352i	0.347067	+	0.937841i	$0.387178\pi$
$108$		0			0
$109$	−4.53452	+	7.85401i	−0.434328	+	0.752278i	−0.997241	−	0.0742384i	$-0.976347\pi$
$109$	−4.53452	+	7.85401i	−0.434328	+	0.752278i	0.562913	+	0.826516i	$0.309681\pi$
$110$	1.47037	+	2.54676i	0.140194	+	0.242824i
$111$		0			0
$112$	−0.0645439	+	2.64496i	−0.00609883	+	0.249926i
$113$			6.62531i			0.623257i	0.950204	+	0.311628i	$0.100874\pi$
$113$			6.62531i			0.623257i	−0.950204	+	0.311628i	$0.899126\pi$
$114$		0			0
$115$	8.11719	+	4.68646i	0.756931	+	0.437015i
$116$	−1.25539	−	0.724802i	−0.116560	−	0.0672961i
$117$		0			0
$118$		−	4.17310i		−	0.384165i
$119$	−12.0860	+	6.59010i	−1.10793	+	0.604114i
$120$		0			0
$121$	−4.04129	−	6.99972i	−0.367390	−	0.636338i
$122$	−1.31968	+	2.28575i	−0.119478	+	0.206942i
$123$		0			0
$124$	5.82274	−	3.36176i	0.522897	−	0.301895i
$125$	12.1134			1.08346
$126$		0			0
$127$	−19.4923			−1.72966			−0.864830	−	0.502065i	$-0.832574\pi$
$127$	−19.4923			−1.72966			−0.864830	+	0.502065i	$0.832574\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.10460	−	1.91322i	0.0968797	−	0.167801i
$131$	−5.31336	−	9.20301i	−0.464230	−	0.804071i	0.534936	−	0.844893i	$-0.320336\pi$
$131$	−5.31336	−	9.20301i	−0.464230	−	0.804071i	−0.999166	+	0.0408220i	$0.987002\pi$
$132$		0			0
$133$	−7.31116	−	0.178411i	−0.633958	−	0.0154702i
$134$			8.63987i			0.746371i
$135$		0			0
$136$	−4.50597	−	2.60152i	−0.386384	−	0.223079i
$137$	1.76722	+	1.02030i	0.150984	+	0.0871704i	0.573588	−	0.819144i	$-0.305551\pi$
$137$	1.76722	+	1.02030i	0.150984	+	0.0871704i	−0.422605	+	0.906314i	$0.638884\pi$
$138$		0			0
$139$		−	17.9136i		−	1.51941i	−0.650266	−	0.759707i	$-0.725342\pi$
$139$		−	17.9136i		−	1.51941i	0.650266	−	0.759707i	$-0.274658\pi$
$140$	−3.88817	−	2.37316i	−0.328611	−	0.200568i
$141$		0			0
$142$	2.53746	+	4.39500i	0.212939	+	0.368821i
$143$	1.09584	−	1.89805i	0.0916386	−	0.158723i
$144$		0			0
$145$	2.16141	−	1.24789i	0.179495	−	0.103632i
$146$	9.44724			0.781860
$147$		0			0
$148$	7.51919			0.618073
$149$	9.22227	−	5.32448i	0.755518	−	0.436198i	−0.0721664	−	0.997393i	$-0.522991\pi$
$149$	9.22227	−	5.32448i	0.755518	−	0.436198i	0.827684	+	0.561194i	$0.189658\pi$
$150$		0			0
$151$	−5.09396	+	8.82301i	−0.414541	+	0.718006i	−0.995380	−	0.0960123i	$-0.969391\pi$
$151$	−5.09396	+	8.82301i	−0.414541	+	0.718006i	0.580839	+	0.814018i	$0.302725\pi$
$152$	−1.38209	−	2.39385i	−0.112102	−	0.194167i
$153$		0			0
$154$	−3.85734	−	2.35433i	−0.310833	−	0.189718i
$155$			11.5759i			0.929797i
$156$		0			0
$157$	3.72429	+	2.15022i	0.297231	+	0.171606i	0.641198	−	0.767375i	$-0.278438\pi$
$157$	3.72429	+	2.15022i	0.297231	+	0.171606i	−0.343967	+	0.938982i	$0.611771\pi$
$158$	−11.6696	−	6.73747i	−0.928386	−	0.536004i
$159$		0			0
$160$		−	1.72170i		−	0.136112i
$161$	−14.3992	−	0.351376i	−1.13481	−	0.0276923i
$162$		0			0
$163$	−4.30789	−	7.46149i	−0.337420	−	0.584429i	0.646527	−	0.762891i	$-0.276221\pi$
$163$	−4.30789	−	7.46149i	−0.337420	−	0.584429i	−0.983947	+	0.178463i	$0.942888\pi$
$164$	4.48217	−	7.76335i	0.349999	−	0.606216i
$165$		0			0
$166$	−5.26205	+	3.03804i	−0.408414	+	0.235798i
$167$	13.9852			1.08220			0.541102	−	0.840957i	$-0.318007\pi$
$167$	13.9852			1.08220			0.541102	+	0.840957i	$0.318007\pi$
$168$		0			0
$169$	11.3535			0.873348
$170$	7.75793	−	4.47904i	0.595006	−	0.343527i
$171$		0			0
$172$	−4.18600	+	7.25036i	−0.319179	+	0.552835i
$173$	−8.01193	−	13.8771i	−0.609135	−	1.05505i	−0.991383	−	0.130994i	$-0.958183\pi$
$173$	−8.01193	−	13.8771i	−0.609135	−	1.05505i	0.382248	−	0.924060i	$-0.375150\pi$
$174$		0			0
$175$	−4.72879	+	2.57845i	−0.357463	+	0.194912i
$176$		−	1.70805i		−	0.128749i
$177$		0			0
$178$	7.21709	+	4.16679i	0.540944	+	0.312314i
$179$	3.23826	+	1.86961i	0.242039	+	0.139741i	0.616113	−	0.787658i	$-0.288706\pi$
$179$	3.23826	+	1.86961i	0.242039	+	0.139741i	−0.374075	+	0.927399i	$0.622040\pi$
$180$		0			0
$181$			1.07693i			0.0800478i	0.999199	+	0.0400239i	$0.0127434\pi$
$181$			1.07693i			0.0800478i	−0.999199	+	0.0400239i	$0.987257\pi$
$182$	−0.0828194	+	3.39388i	−0.00613898	+	0.251571i
$183$		0			0
$184$	−2.72199	−	4.71463i	−0.200668	−	0.347567i
$185$	−6.47289	+	11.2114i	−0.475897	+	0.824277i
$186$		0			0
$187$	7.69640	−	4.44352i	0.562817	−	0.324942i
$188$	−5.23617			−0.381887
$189$		0			0
$190$	4.75910			0.345261
$191$	−14.5988	+	8.42859i	−1.05633	+	0.609872i	−0.924414	−	0.381389i	$-0.875446\pi$
$191$	−14.5988	+	8.42859i	−1.05633	+	0.609872i	−0.131914	+	0.991261i	$0.542112\pi$
$192$		0			0
$193$	−7.11546	+	12.3243i	−0.512182	+	0.887125i	0.487718	+	0.873001i	$0.337829\pi$
$193$	−7.11546	+	12.3243i	−0.512182	+	0.887125i	−0.999900	+	0.0141241i	$0.995504\pi$
$194$	5.02857	+	8.70974i	0.361030	+	0.625323i
$195$		0			0
$196$	6.99167	+	0.341433i	0.499405	+	0.0243880i
$197$			19.4230i			1.38383i	0.721979	+	0.691915i	$0.243233\pi$
$197$			19.4230i			1.38383i	−0.721979	+	0.691915i	$0.756767\pi$
$198$		0			0
$199$	6.99323	+	4.03754i	0.495737	+	0.286214i	0.726951	−	0.686689i	$-0.240937\pi$
$199$	6.99323	+	4.03754i	0.495737	+	0.286214i	−0.231214	+	0.972903i	$0.574270\pi$
$200$	−1.76301	−	1.01787i	−0.124664	−	0.0719745i
$201$		0			0
$202$		−	15.8127i		−	1.11258i
$203$	−1.99810	+	3.27369i	−0.140239	+	0.229768i
$204$		0			0
$205$	7.71696	+	13.3662i	0.538976	+	0.933533i
$206$	−7.26634	+	12.5857i	−0.506270	+	0.876885i
$207$		0			0
$208$	−1.11124	+	0.641574i	−0.0770506	+	0.0444852i
$209$	4.72135			0.326583
$210$		0			0
$211$	19.9133			1.37089			0.685444	−	0.728125i	$-0.259608\pi$
$211$	19.9133			1.37089			0.685444	+	0.728125i	$0.259608\pi$
$212$	−9.46059	+	5.46207i	−0.649756	+	0.375137i
$213$		0			0
$214$	−1.74144	+	3.01627i	−0.119043	+	0.206188i
$215$	−7.20703	−	12.4829i	−0.491516	−	0.851330i
$216$		0			0
$217$	−8.51591	−	15.6179i	−0.578097	−	1.06021i
$218$			9.06903i			0.614232i
$219$		0			0
$220$	2.54676	+	1.47037i	0.171702	+	0.0991324i
$221$	−5.78183	−	3.33814i	−0.388928	−	0.224548i
$222$		0			0
$223$			21.2100i			1.42033i	0.704036	+	0.710164i	$0.251379\pi$
$223$			21.2100i			1.42033i	−0.704036	+	0.710164i	$0.748621\pi$
$224$	1.26659	+	2.32288i	0.0846273	+	0.155204i
$225$		0			0
$226$	3.31266	+	5.73769i	0.220355	+	0.381665i
$227$	−6.79579	+	11.7707i	−0.451053	+	0.781246i	−0.998452	−	0.0556258i	$-0.982285\pi$
$227$	−6.79579	+	11.7707i	−0.451053	+	0.781246i	0.547399	+	0.836872i	$0.315618\pi$
$228$		0			0
$229$	−20.8769	+	12.0533i	−1.37959	+	0.796504i	−0.992109	−	0.125376i	$-0.959986\pi$
$229$	−20.8769	+	12.0533i	−1.37959	+	0.796504i	−0.387476	+	0.921880i	$0.626653\pi$
$230$	9.37292			0.618032
$231$		0			0
$232$	−1.44960			−0.0951711
$233$	−15.9891	+	9.23129i	−1.04748	+	0.604762i	−0.921942	−	0.387327i	$-0.873398\pi$
$233$	−15.9891	+	9.23129i	−1.04748	+	0.604762i	−0.125536	+	0.992089i	$0.540065\pi$
$234$		0			0
$235$	4.50756	−	7.80732i	0.294041	−	0.509294i
$236$	−2.08655	−	3.61401i	−0.135823	−	0.235252i
$237$		0			0
$238$	−7.17177	+	11.7502i	−0.464877	+	0.761653i
$239$			23.1917i			1.50015i	0.661355	+	0.750073i	$0.269981\pi$
$239$			23.1917i			1.50015i	−0.661355	+	0.750073i	$0.730019\pi$
$240$		0			0
$241$	22.4458	+	12.9591i	1.44586	+	0.834770i	0.998231	−	0.0594484i	$-0.0189342\pi$
$241$	22.4458	+	12.9591i	1.44586	+	0.834770i	0.447632	+	0.894218i	$0.352267\pi$
$242$	−6.99972	−	4.04129i	−0.449959	−	0.259784i
$243$		0			0
$244$			2.63936i			0.168967i
$245$	−6.52787	+	10.1309i	−0.417050	+	0.647240i
$246$		0			0
$247$	−1.77343	−	3.07167i	−0.112841	−	0.195446i
$248$	3.36176	−	5.82274i	0.213472	−	0.369744i
$249$		0			0
$250$	10.4906	−	6.05672i	0.663481	−	0.383061i
$251$	17.9492			1.13295			0.566473	−	0.824081i	$-0.308308\pi$
$251$	17.9492			1.13295			0.566473	+	0.824081i	$0.308308\pi$
$252$		0			0
$253$	9.29858			0.584597
$254$	−16.8808	+	9.74614i	−1.05920	+	0.611527i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.31001	+	7.46516i	0.268851	+	0.465664i	0.968565	−	0.248759i	$-0.0800226\pi$
$257$	4.31001	+	7.46516i	0.268851	+	0.465664i	−0.699714	+	0.714423i	$0.746689\pi$
$258$		0			0
$259$	0.485318	−	19.8880i	0.0301562	−	1.23578i
$260$		−	2.20920i		−	0.137009i
$261$		0			0
$262$	−9.20301	−	5.31336i	−0.568564	−	0.328260i
$263$	16.9777	+	9.80208i	1.04689	+	0.604422i	0.921777	−	0.387720i	$-0.126737\pi$
$263$	16.9777	+	9.80208i	1.04689	+	0.604422i	0.125113	+	0.992143i	$0.460071\pi$
$264$		0			0
$265$		−	18.8081i		−	1.15537i
$266$	−6.42086	+	3.50107i	−0.393688	+	0.214665i
$267$		0			0
$268$	4.31994	+	7.48235i	0.263882	+	0.457057i
$269$	−6.95328	+	12.0434i	−0.423949	+	0.734301i	−0.996322	−	0.0856923i	$-0.972690\pi$
$269$	−6.95328	+	12.0434i	−0.423949	+	0.734301i	0.572373	+	0.819994i	$0.306023\pi$
$270$		0			0
$271$	−1.90381	+	1.09916i	−0.115648	+	0.0667694i	−0.556708	−	0.830708i	$-0.687936\pi$
$271$	−1.90381	+	1.09916i	−0.115648	+	0.0667694i	0.441060	+	0.897478i	$0.354603\pi$
$272$	−5.20305			−0.315481
$273$		0			0
$274$	2.04061			0.123278
$275$	3.01130	−	1.73857i	0.181588	−	0.104840i
$276$		0			0
$277$	0.259978	−	0.450295i	0.0156206	−	0.0270556i	−0.858109	−	0.513467i	$-0.828361\pi$
$277$	0.259978	−	0.450295i	0.0156206	−	0.0270556i	0.873730	+	0.486411i	$0.161694\pi$
$278$	−8.95681	−	15.5137i	−0.537194	−	0.930447i
$279$		0			0
$280$	−4.55384	−	0.111125i	−0.272144	−	0.00664101i
$281$			19.7706i			1.17942i	0.807616	+	0.589709i	$0.200758\pi$
$281$			19.7706i			1.17942i	−0.807616	+	0.589709i	$0.799242\pi$
$282$		0			0
$283$	−28.1815	−	16.2706i	−1.67522	−	0.967187i	−0.964641	−	0.263566i	$-0.915101\pi$
$283$	−28.1815	−	16.2706i	−1.67522	−	0.967187i	−0.710575	−	0.703621i	$-0.751565\pi$
$284$	4.39500	+	2.53746i	0.260796	+	0.150570i
$285$		0			0
$286$		−	2.19168i		−	0.129597i
$287$	−20.2445	−	12.3563i	−1.19499	−	0.729367i
$288$		0			0
$289$	−5.03584	−	8.72233i	−0.296226	−	0.513078i
$290$	1.24789	−	2.16141i	0.0732787	−	0.126922i
$291$		0			0
$292$	8.18155	−	4.72362i	0.478789	−	0.276429i
$293$	−25.5700			−1.49382			−0.746909	−	0.664927i	$-0.768463\pi$
$293$	−25.5700			−1.49382			−0.746909	+	0.664927i	$0.768463\pi$
$294$		0			0
$295$	7.18483			0.418317
$296$	6.51181	−	3.75959i	0.378491	−	0.218522i
$297$		0			0
$298$	5.32448	−	9.22227i	0.308439	−	0.534232i
$299$	−3.49272	−	6.04957i	−0.201989	−	0.349856i
$300$		0			0
$301$	18.9068	+	11.5398i	1.08977	+	0.665142i
$302$			10.1879i			0.586249i
$303$		0			0
$304$	−2.39385	−	1.38209i	−0.137297	−	0.0792684i
$305$	−3.93538	−	2.27209i	−0.225339	−	0.130100i
$306$		0			0
$307$		−	4.85183i		−	0.276909i	−0.990369	−	0.138454i	$-0.955787\pi$
$307$		−	4.85183i		−	0.276909i	0.990369	−	0.138454i	$-0.0442134\pi$
$308$	−4.51772	−	0.110244i	−0.257421	−	0.00628173i
$309$		0			0
$310$	5.78794	+	10.0250i	0.328733	+	0.569382i
$311$	−2.17193	+	3.76189i	−0.123159	+	0.213317i	−0.921012	−	0.389535i	$-0.872636\pi$
$311$	−2.17193	+	3.76189i	−0.123159	+	0.213317i	0.797853	+	0.602852i	$0.205969\pi$
$312$		0			0
$313$	19.5391	−	11.2809i	1.10442	−	0.637635i	0.167039	−	0.985950i	$-0.446579\pi$
$313$	19.5391	−	11.2809i	1.10442	−	0.637635i	0.937378	+	0.348315i	$0.113246\pi$
$314$	4.30044			0.242688
$315$		0			0
$316$	−13.4749			−0.758024
$317$	29.6293	−	17.1065i	1.66415	−	0.960795i	0.693442	−	0.720513i	$-0.256093\pi$
$317$	29.6293	−	17.1065i	1.66415	−	0.960795i	0.970703	−	0.240282i	$-0.0772399\pi$
$318$		0			0
$319$	1.23799	−	2.14427i	0.0693144	−	0.120056i
$320$	−0.860850	−	1.49104i	−0.0481230	−	0.0833515i
$321$		0			0
$322$	−12.6457	+	6.89528i	−0.704718	+	0.384259i
$323$		−	14.3822i		−	0.800245i
$324$		0			0
$325$	−2.26220	−	1.30608i	−0.125484	−	0.0724485i
$326$	−7.46149	−	4.30789i	−0.413254	−	0.238592i
$327$		0			0
$328$		−	8.96434i		−	0.494973i
$329$	−0.337963	+	13.8495i	−0.0186325	+	0.763547i
$330$		0			0
$331$	2.28003	+	3.94913i	0.125322	+	0.217064i	0.921859	−	0.387526i	$-0.126670\pi$
$331$	2.28003	+	3.94913i	0.125322	+	0.217064i	−0.796537	+	0.604590i	$0.793337\pi$
$332$	−3.03804	+	5.26205i	−0.166734	+	0.288792i
$333$		0			0
$334$	12.1115	−	6.99258i	0.662712	−	0.382617i
$335$	−14.8753			−0.812723
$336$		0			0
$337$	30.7531			1.67523			0.837613	−	0.546264i	$-0.183950\pi$
$337$	30.7531			1.67523			0.837613	+	0.546264i	$0.183950\pi$
$338$	9.83245	−	5.67676i	0.534815	−	0.308775i
$339$		0			0
$340$	4.47904	−	7.75793i	0.242910	−	0.420733i
$341$	5.74204	+	9.94550i	0.310949	+	0.538579i
$342$		0			0
$343$	1.35435	−	18.4707i	0.0731278	−	0.997323i
$344$			8.37200i			0.451388i
$345$		0			0
$346$	−13.8771	−	8.01193i	−0.746035	−	0.430724i
$347$	−20.6474	−	11.9208i	−1.10841	−	0.639940i	−0.169992	−	0.985446i	$-0.554374\pi$
$347$	−20.6474	−	11.9208i	−1.10841	−	0.639940i	−0.938417	+	0.345506i	$0.887707\pi$
$348$		0			0
$349$			3.14373i			0.168280i	0.996454	+	0.0841401i	$0.0268143\pi$
$349$			3.14373i			0.168280i	−0.996454	+	0.0841401i	$0.973186\pi$
$350$	−2.80603	+	4.59740i	−0.149989	+	0.245741i
$351$		0			0
$352$	−0.854023	−	1.47921i	−0.0455196	−	0.0788422i
$353$	13.8459	−	23.9818i	0.736944	−	1.27642i	−0.216921	−	0.976189i	$-0.569601\pi$
$353$	13.8459	−	23.9818i	0.736944	−	1.27642i	0.953865	−	0.300236i	$-0.0970653\pi$
$354$		0			0
$355$	−7.56688	+	4.36874i	−0.401608	+	0.231869i
$356$	8.33357			0.441679
$357$		0			0
$358$	3.73922			0.197624
$359$	18.1125	−	10.4572i	0.955940	−	0.551912i	0.0610187	−	0.998137i	$-0.480565\pi$
$359$	18.1125	−	10.4572i	0.955940	−	0.551912i	0.894921	+	0.446225i	$0.147232\pi$
$360$		0			0
$361$	−5.67965	+	9.83744i	−0.298929	+	0.517760i
$362$	0.538466	+	0.932651i	0.0283012	+	0.0490190i
$363$		0			0
$364$	1.62522	+	2.98060i	0.0851845	+	0.156226i
$365$			16.2653i			0.851366i
$366$		0			0
$367$	−1.01292	−	0.584811i	−0.0528741	−	0.0305269i	0.473330	−	0.880885i	$-0.343052\pi$
$367$	−1.01292	−	0.584811i	−0.0528741	−	0.0305269i	−0.526204	+	0.850358i	$0.676385\pi$
$368$	−4.71463	−	2.72199i	−0.245767	−	0.141894i
$369$		0			0
$370$			12.9458i			0.673019i
$371$	13.8364	+	25.3755i	0.718348	+	1.31743i
$372$		0			0
$373$	−4.85503	−	8.40915i	−0.251384	−	0.435409i	0.712523	−	0.701648i	$-0.247552\pi$
$373$	−4.85503	−	8.40915i	−0.251384	−	0.435409i	−0.963907	+	0.266239i	$0.914219\pi$
$374$	4.44352	−	7.69640i	0.229769	−	0.397971i
$375$		0			0
$376$	−4.53466	+	2.61809i	−0.233857	+	0.135017i
$377$	−1.86006			−0.0957978
$378$		0			0
$379$	−15.1452			−0.777958			−0.388979	−	0.921247i	$-0.627172\pi$
$379$	−15.1452			−0.777958			−0.388979	+	0.921247i	$0.627172\pi$
$380$	4.12150	−	2.37955i	0.211428	−	0.122068i
$381$		0			0
$382$	−8.42859	+	14.5988i	−0.431244	+	0.746937i
$383$	−15.9902	−	27.6958i	−0.817059	−	1.41519i	−0.907840	−	0.419316i	$-0.862270\pi$
$383$	−15.9902	−	27.6958i	−0.817059	−	1.41519i	0.0907815	−	0.995871i	$-0.471064\pi$
$384$		0			0
$385$	4.05346	−	6.64118i	0.206583	−	0.338466i
$386$			14.2309i			0.724335i
$387$		0			0
$388$	8.70974	+	5.02857i	0.442170	+	0.255287i
$389$	−21.6056	−	12.4740i	−1.09545	−	0.632457i	−0.160426	−	0.987048i	$-0.551287\pi$
$389$	−21.6056	−	12.4740i	−1.09545	−	0.632457i	−0.935021	+	0.354591i	$0.884620\pi$
$390$		0			0
$391$		−	28.3253i		−	1.43247i
$392$	6.22568	−	3.20014i	0.314444	−	0.161632i
$393$		0			0
$394$	9.71149	+	16.8208i	0.489258	+	0.847420i
$395$	11.5999	−	20.0916i	0.583654	−	1.01092i
$396$		0			0
$397$	0.280202	−	0.161774i	0.0140629	−	0.00811923i	−0.492952	−	0.870056i	$-0.664082\pi$
$397$	0.280202	−	0.161774i	0.0140629	−	0.00811923i	0.507015	+	0.861937i	$0.330749\pi$
$398$	8.07509			0.404768
$399$		0			0
$400$	−2.03575			−0.101787
$401$	−16.4678	+	9.50768i	−0.822362	+	0.474791i	−0.851230	−	0.524792i	$-0.824143\pi$
$401$	−16.4678	+	9.50768i	−0.822362	+	0.474791i	0.0288684	+	0.999583i	$0.490810\pi$
$402$		0			0
$403$	4.31364	−	7.47144i	0.214877	−	0.372179i
$404$	−7.90634	−	13.6942i	−0.393355	−	0.681311i
$405$		0			0
$406$	−0.0935631	+	3.83415i	−0.00464346	+	0.190286i
$407$			12.8431i			0.636609i
$408$		0			0
$409$	3.90841	+	2.25652i	0.193258	+	0.111578i	0.593507	−	0.804829i	$-0.297743\pi$
$409$	3.90841	+	2.25652i	0.193258	+	0.111578i	−0.400249	+	0.916407i	$0.631076\pi$
$410$	13.3662	+	7.71696i	0.660108	+	0.381113i
$411$		0			0
$412$			14.5327i			0.715973i
$413$	−9.69361	+	5.28559i	−0.476991	+	0.260087i
$414$		0			0
$415$	−5.23060	−	9.05967i	−0.256760	−	0.444722i
$416$	−0.641574	+	1.11124i	−0.0314558	+	0.0544830i
$417$		0			0
$418$	4.08881	−	2.36068i	0.199990	−	0.115464i
$419$	29.2149			1.42724			0.713621	−	0.700532i	$-0.247054\pi$
$419$	29.2149			1.42724			0.713621	+	0.700532i	$0.247054\pi$
$420$		0			0
$421$	−36.3361			−1.77092			−0.885458	−	0.464720i	$-0.846155\pi$
$421$	−36.3361			−1.77092			−0.885458	+	0.464720i	$0.846155\pi$
$422$	17.2454	−	9.95665i	0.839494	−	0.484682i
$423$		0			0
$424$	−5.46207	+	9.46059i	−0.265262	+	0.459447i
$425$	−5.29604	−	9.17301i	−0.256896	−	0.444957i
$426$		0			0
$427$	6.98100	+	0.170354i	0.337834	+	0.00824403i
$428$			3.48289i			0.168352i
$429$		0			0
$430$	−12.4829	−	7.20703i	−0.601981	−	0.347554i
$431$	10.4967	+	6.06028i	0.505609	+	0.291913i	0.731027	−	0.682349i	$-0.239041\pi$
$431$	10.4967	+	6.06028i	0.505609	+	0.291913i	−0.225418	+	0.974262i	$0.572375\pi$
$432$		0			0
$433$			31.4160i			1.50976i	0.655864	+	0.754879i	$0.272304\pi$
$433$			31.4160i			1.50976i	−0.655864	+	0.754879i	$0.727696\pi$
$434$	−15.1839	−	9.26755i	−0.728853	−	0.444857i
$435$		0			0
$436$	4.53452	+	7.85401i	0.217164	+	0.376139i
$437$	7.52409	−	13.0321i	0.359926	−	0.623410i
$438$		0			0
$439$	−2.80118	+	1.61726i	−0.133693	+	0.0771877i	−0.565355	−	0.824848i	$-0.691261\pi$
$439$	−2.80118	+	1.61726i	−0.133693	+	0.0771877i	0.431662	+	0.902036i	$0.357927\pi$
$440$	2.94074			0.140194
$441$		0			0
$442$	−6.67628			−0.317558
$443$	7.65097	−	4.41729i	0.363509	−	0.209872i	−0.307110	−	0.951674i	$-0.599362\pi$
$443$	7.65097	−	4.41729i	0.363509	−	0.209872i	0.670619	+	0.741802i	$0.266029\pi$
$444$		0			0
$445$	−7.17396	+	12.4257i	−0.340078	+	0.589033i
$446$	10.6050	+	18.3684i	0.502162	+	0.869770i
$447$		0			0
$448$	2.25833	+	1.37838i	0.106696	+	0.0651223i
$449$			6.83193i			0.322419i	0.986920	+	0.161209i	$0.0515395\pi$
$449$			6.83193i			0.322419i	−0.986920	+	0.161209i	$0.948461\pi$
$450$		0			0
$451$	13.2602	+	7.65575i	0.624396	+	0.360495i
$452$	5.73769	+	3.31266i	0.269878	+	0.155814i
$453$		0			0
$454$			13.5916i			0.637885i
$455$	−5.84325	−	0.142590i	−0.273936	−	0.00668473i
$456$		0			0
$457$	−9.21190	−	15.9555i	−0.430915	−	0.746366i	0.566038	−	0.824379i	$-0.308476\pi$
$457$	−9.21190	−	15.9555i	−0.430915	−	0.746366i	−0.996952	+	0.0780133i	$0.975142\pi$
$458$	−12.0533	+	20.8769i	−0.563213	+	0.975514i
$459$		0			0
$460$	8.11719	−	4.68646i	0.378466	−	0.218507i
$461$	29.9065			1.39289			0.696443	−	0.717612i	$-0.254765\pi$
$461$	29.9065			1.39289			0.696443	+	0.717612i	$0.254765\pi$
$462$		0			0
$463$	1.32509			0.0615821			0.0307911	−	0.999526i	$-0.490197\pi$
$463$	1.32509			0.0615821			0.0307911	+	0.999526i	$0.490197\pi$
$464$	−1.25539	+	0.724802i	−0.0582802	+	0.0336481i
$465$		0			0
$466$	−9.23129	+	15.9891i	−0.427631	+	0.740679i
$467$	13.6817	+	23.6973i	0.633112	+	1.09658i	0.986912	+	0.161260i	$0.0515559\pi$
$467$	13.6817	+	23.6973i	0.633112	+	1.09658i	−0.353800	+	0.935321i	$0.615111\pi$
$468$		0			0
$469$	20.0694	−	10.9431i	0.926718	−	0.505307i
$470$		−	9.01512i		−	0.415836i
$471$		0			0
$472$	−3.61401	−	2.08655i	−0.166348	−	0.0960413i
$473$	−12.3839	−	7.14987i	−0.569414	−	0.328752i
$474$		0			0
$475$		−	5.62718i		−	0.258193i
$476$	−0.335825	+	13.7619i	−0.0153925	+	0.630774i
$477$		0			0
$478$	11.5958	+	20.0846i	0.530381	+	0.918648i
$479$	−8.41054	+	14.5675i	−0.384287	+	0.665605i	−0.991670	−	0.128804i	$-0.958886\pi$
$479$	−8.41054	+	14.5675i	−0.384287	+	0.665605i	0.607383	+	0.794409i	$0.292219\pi$
$480$		0			0
$481$	8.35561	−	4.82412i	0.380983	−	0.219961i
$482$	25.9182			1.18054
$483$		0			0
$484$	−8.08258			−0.367390
$485$	−14.9956	+	8.65769i	−0.680913	+	0.393126i
$486$		0			0
$487$	0.357602	−	0.619385i	0.0162045	−	0.0280670i	−0.857809	−	0.513968i	$-0.828175\pi$
$487$	0.357602	−	0.619385i	0.0162045	−	0.0280670i	0.874014	+	0.485901i	$0.161508\pi$
$488$	1.31968	+	2.28575i	0.0597390	+	0.103471i
$489$		0			0
$490$	−0.587845	+	12.0376i	−0.0265561	+	0.543801i
$491$		−	5.36907i		−	0.242303i	−0.992634	−	0.121151i	$-0.961341\pi$
$491$		−	5.36907i		−	0.242303i	0.992634	−	0.121151i	$-0.0386586\pi$
$492$		0			0
$493$	−6.53187	−	3.77118i	−0.294181	−	0.169845i
$494$	−3.07167	−	1.77343i	−0.138201	−	0.0797903i
$495$		0			0
$496$		−	6.72352i		−	0.301895i
$497$	6.99515	−	11.4609i	0.313776	−	0.514089i
$498$		0			0
$499$	−12.0464	−	20.8649i	−0.539269	−	0.934041i	−0.998944	−	0.0459536i	$-0.985367\pi$
$499$	−12.0464	−	20.8649i	−0.539269	−	0.934041i	0.459675	−	0.888087i	$-0.347966\pi$
$500$	6.05672	−	10.4906i	0.270865	−	0.469152i
$501$		0			0
$502$	15.5445	−	8.97461i	0.693784	−	0.400557i
$503$	26.8386			1.19667			0.598336	−	0.801245i	$-0.295829\pi$
$503$	26.8386			1.19667			0.598336	+	0.801245i	$0.295829\pi$
$504$		0			0
$505$	27.2247			1.21148
$506$	8.05281	−	4.64929i	0.357991	−	0.206686i
$507$		0			0
$508$	−9.74614	+	16.8808i	−0.432415	+	0.748965i
$509$	−20.1952	−	34.9791i	−0.895137	−	1.55042i	−0.833634	−	0.552317i	$-0.813744\pi$
$509$	−20.1952	−	34.9791i	−0.895137	−	1.55042i	−0.0615030	−	0.998107i	$-0.519589\pi$
$510$		0			0
$511$	−11.9657	−	21.9448i	−0.529333	−	0.970781i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	7.46516	+	4.31001i	0.329274	+	0.190107i
$515$	−21.6687	−	12.5105i	−0.954839	−	0.551277i
$516$		0			0
$517$		−	8.94362i		−	0.393340i
$518$	−9.52369	−	17.4661i	−0.418447	−	0.767419i
$519$		0			0
$520$	−1.10460	−	1.91322i	−0.0484399	−	0.0839003i
$521$	15.1983	−	26.3243i	0.665852	−	1.15329i	−0.313202	−	0.949686i	$-0.601402\pi$
$521$	15.1983	−	26.3243i	0.665852	−	1.15329i	0.979054	−	0.203602i	$-0.0652649\pi$
$522$		0			0
$523$	−5.53367	+	3.19487i	−0.241971	+	0.139702i	−0.616082	−	0.787682i	$-0.711281\pi$
$523$	−5.53367	+	3.19487i	−0.241971	+	0.139702i	0.374112	+	0.927384i	$0.377948\pi$
$524$	−10.6267			−0.464230
$525$		0			0
$526$	19.6042			0.854782
$527$	30.2960	−	17.4914i	1.31971	−	0.761937i
$528$		0			0
$529$	3.31851	−	5.74782i	0.144283	−	0.249905i
$530$	−9.40405	−	16.2883i	−0.408486	−	0.707518i
$531$		0			0
$532$	−3.81009	+	6.24245i	−0.165188	+	0.270644i
$533$		−	11.5026i		−	0.498232i
$534$		0			0
$535$	−5.19311	−	2.99825i	−0.224518	−	0.129625i
$536$	7.48235	+	4.31994i	0.323188	+	0.186593i
$537$		0			0
$538$			13.9066i			0.599555i
$539$	−0.583182	+	11.9421i	−0.0251194	+	0.514382i
$540$		0			0
$541$	−0.909263	−	1.57489i	−0.0390923	−	0.0677098i	0.845817	−	0.533473i	$-0.179113\pi$
$541$	−0.909263	−	1.57489i	−0.0390923	−	0.0677098i	−0.884910	+	0.465763i	$0.845780\pi$
$542$	−1.09916	+	1.90381i	−0.0472131	+	0.0817755i
$543$		0			0
$544$	−4.50597	+	2.60152i	−0.193192	+	0.111539i
$545$	−15.6142			−0.668837
$546$		0			0
$547$	−43.7214			−1.86939			−0.934695	−	0.355450i	$-0.884327\pi$
$547$	−43.7214			−1.86939			−0.934695	+	0.355450i	$0.884327\pi$
$548$	1.76722	−	1.02030i	0.0754918	−	0.0435852i
$549$		0			0
$550$	1.73857	−	3.01130i	0.0741331	−	0.128402i
$551$	−2.00348	−	3.47014i	−0.0853513	−	0.147833i
$552$		0			0
$553$	−0.869725	+	35.6407i	−0.0369845	+	1.51560i
$554$		−	0.519956i		−	0.0220908i
$555$		0			0
$556$	−15.5137	−	8.95681i	−0.657926	−	0.379854i
$557$	22.5591	+	13.0245i	0.955859	+	0.551865i	0.894896	−	0.446275i	$-0.147250\pi$
$557$	22.5591	+	13.0245i	0.955859	+	0.551865i	0.0609627	+	0.998140i	$0.480583\pi$
$558$		0			0
$559$			10.7425i			0.454360i
$560$	−3.99930	+	2.18068i	−0.169001	+	0.0921506i
$561$		0			0
$562$	9.88532	+	17.1219i	0.416987	+	0.722243i
$563$	−2.00985	+	3.48116i	−0.0847051	+	0.146713i	−0.905265	−	0.424846i	$-0.860328\pi$
$563$	−2.00985	+	3.48116i	−0.0847051	+	0.146713i	0.820560	+	0.571560i	$0.193661\pi$
$564$		0			0
$565$	−9.87858	+	5.70340i	−0.415595	+	0.239944i
$566$	−32.5412			−1.36781
$567$		0			0
$568$	5.07491			0.212939
$569$	−2.17982	+	1.25852i	−0.0913826	+	0.0527598i	−0.544995	−	0.838439i	$-0.683468\pi$
$569$	−2.17982	+	1.25852i	−0.0913826	+	0.0527598i	0.453612	+	0.891199i	$0.350135\pi$
$570$		0			0
$571$	1.44662	−	2.50561i	0.0605390	−	0.104857i	−0.834167	−	0.551511i	$-0.814051\pi$
$571$	1.44662	−	2.50561i	0.0605390	−	0.104857i	0.894706	+	0.446655i	$0.147385\pi$
$572$	−1.09584	−	1.89805i	−0.0458193	−	0.0793613i
$573$		0			0
$574$	−23.7104	−	0.578594i	−0.989651	−	0.0241500i
$575$		−	11.0826i		−	0.462176i
$576$		0			0
$577$	2.76783	+	1.59801i	0.115226	+	0.0665258i	0.556505	−	0.830844i	$-0.312142\pi$
$577$	2.76783	+	1.59801i	0.115226	+	0.0665258i	−0.441279	+	0.897370i	$0.645475\pi$
$578$	−8.72233	−	5.03584i	−0.362801	−	0.209463i
$579$		0			0
$580$		−	2.49578i		−	0.103632i
$581$	13.7218	+	8.37515i	0.569278	+	0.347460i
$582$		0			0
$583$	−9.32947	−	16.1591i	−0.386387	−	0.669242i
$584$	4.72362	−	8.18155i	0.195465	−	0.338555i
$585$		0			0
$586$	−22.1443	+	12.7850i	−0.914772	+	0.528144i
$587$	27.5816			1.13841			0.569207	−	0.822194i	$-0.307250\pi$
$587$	27.5816			1.13841			0.569207	+	0.822194i	$0.307250\pi$
$588$		0			0
$589$	18.5850			0.765783
$590$	6.22225	−	3.59242i	0.256166	−	0.147897i
$591$		0			0
$592$	3.75959	−	6.51181i	0.154518	−	0.267634i
$593$	−15.1199	−	26.1884i	−0.620899	−	1.07543i	−0.989319	−	0.145769i	$-0.953434\pi$
$593$	−15.1199	−	26.1884i	−0.620899	−	1.07543i	0.368420	−	0.929660i	$-0.379899\pi$
$594$		0			0
$595$	−20.2303	−	12.3476i	−0.829363	−	0.506204i
$596$		−	10.6490i		−	0.436198i
$597$		0			0
$598$	−6.04957	−	3.49272i	−0.247385	−	0.142828i
$599$	−2.87629	−	1.66063i	−0.117522	−	0.0678515i	0.440087	−	0.897955i	$-0.354948\pi$
$599$	−2.87629	−	1.66063i	−0.117522	−	0.0678515i	−0.557609	+	0.830104i	$0.688281\pi$
$600$		0			0
$601$		−	10.0946i		−	0.411766i	−0.978577	−	0.205883i	$-0.933993\pi$
$601$		−	10.0946i		−	0.411766i	0.978577	−	0.205883i	$-0.0660067\pi$
$602$	22.1436	+	0.540361i	0.902507	+	0.0220235i
$603$		0			0
$604$	5.09396	+	8.82301i	0.207270	+	0.359003i
$605$	6.95789	−	12.0514i	0.282879	−	0.489960i
$606$		0			0
$607$	−18.1038	+	10.4523i	−0.734812	+	0.424244i	−0.820180	−	0.572106i	$-0.806127\pi$
$607$	−18.1038	+	10.4523i	−0.734812	+	0.424244i	0.0853682	+	0.996349i	$0.472793\pi$
$608$	−2.76418			−0.112102
$609$		0			0
$610$	−4.54418			−0.183989
$611$	−5.81864	+	3.35939i	−0.235397	+	0.135907i
$612$		0			0
$613$	2.11525	−	3.66372i	0.0854341	−	0.147976i	−0.820142	−	0.572160i	$-0.806106\pi$
$613$	2.11525	−	3.66372i	0.0854341	−	0.147976i	0.905576	+	0.424184i	$0.139439\pi$
$614$	−2.42592	−	4.20181i	−0.0979020	−	0.169571i
$615$		0			0
$616$	−3.96758	+	2.16339i	−0.159858	+	0.0871653i
$617$		−	6.22012i		−	0.250412i	−0.992131	−	0.125206i	$-0.960041\pi$
$617$		−	6.22012i		−	0.250412i	0.992131	−	0.125206i	$-0.0399593\pi$
$618$		0			0
$619$	−23.7546	−	13.7148i	−0.954780	−	0.551242i	−0.0602173	−	0.998185i	$-0.519179\pi$
$619$	−23.7546	−	13.7148i	−0.954780	−	0.551242i	−0.894562	+	0.446943i	$0.852513\pi$
$620$	10.0250	+	5.78794i	0.402614	+	0.232449i
$621$		0			0
$622$			4.34386i			0.174173i
$623$	0.537881	−	22.0420i	0.0215498	−	0.883094i
$624$		0			0
$625$	5.33850	+	9.24655i	0.213540	+	0.369862i
$626$	11.2809	−	19.5391i	0.450876	−	0.780941i
$627$		0			0
$628$	3.72429	−	2.15022i	0.148616	−	0.0858032i
$629$	39.1227			1.55992
$630$		0			0
$631$	−15.0610			−0.599570			−0.299785	−	0.954007i	$-0.596915\pi$
$631$	−15.0610			−0.599570			−0.299785	+	0.954007i	$0.596915\pi$
$632$	−11.6696	+	6.73747i	−0.464193	+	0.268002i
$633$		0			0
$634$	17.1065	−	29.6293i	0.679384	−	1.17673i
$635$	−16.7799	−	29.0637i	−0.665891	−	1.15336i
$636$		0			0
$637$	7.98847	−	4.10626i	0.316515	−	0.162696i
$638$		−	2.47599i		−	0.0980253i
$639$		0			0
$640$	−1.49104	−	0.860850i	−0.0589384	−	0.0340281i
$641$	21.2390	+	12.2623i	0.838890	+	0.484333i	0.856887	−	0.515505i	$-0.172396\pi$
$641$	21.2390	+	12.2623i	0.838890	+	0.484333i	−0.0179970	+	0.999838i	$0.505729\pi$
$642$		0			0
$643$			44.1029i			1.73925i	0.493714	+	0.869625i	$0.335639\pi$
$643$			44.1029i			1.73925i	−0.493714	+	0.869625i	$0.664361\pi$
$644$	−7.50388	+	12.2943i	−0.295694	+	0.484465i
$645$		0			0
$646$	−7.19108	−	12.4553i	−0.282929	−	0.490048i
$647$	3.67645	−	6.36779i	0.144536	−	0.250344i	−0.784664	−	0.619922i	$-0.787164\pi$
$647$	3.67645	−	6.36779i	0.144536	−	0.250344i	0.929200	+	0.369578i	$0.120498\pi$
$648$		0			0
$649$	6.17290	−	3.56393i	0.242308	−	0.139896i
$650$	−2.61217			−0.102458
$651$		0			0
$652$	−8.61578			−0.337420
$653$	−4.37627	+	2.52664i	−0.171257	+	0.0988750i	−0.583178	−	0.812344i	$-0.698191\pi$
$653$	−4.37627	+	2.52664i	−0.171257	+	0.0988750i	0.411922	+	0.911219i	$0.364858\pi$
$654$		0			0
$655$	9.14801	−	15.8448i	0.357442	−	0.619109i
$656$	−4.48217	−	7.76335i	−0.174999	−	0.303108i
$657$		0			0
$658$	6.63206	+	12.1630i	0.258545	+	0.474163i
$659$		−	2.83130i		−	0.110292i	−0.998478	−	0.0551460i	$-0.982438\pi$
$659$		−	2.83130i		−	0.110292i	0.998478	−	0.0551460i	$-0.0175624\pi$
$660$		0			0
$661$	25.5374	+	14.7440i	0.993290	+	0.573476i	0.906256	−	0.422729i	$-0.138928\pi$
$661$	25.5374	+	14.7440i	0.993290	+	0.573476i	0.0870338	+	0.996205i	$0.472261\pi$
$662$	3.94913	+	2.28003i	0.153487	+	0.0886159i
$663$		0			0
$664$			6.07609i			0.235798i
$665$	−6.02780	−	11.0548i	−0.233748	−	0.428687i
$666$		0			0
$667$	−3.94581	−	6.83435i	−0.152782	−	0.264627i
$668$	6.99258	−	12.1115i	0.270551	−	0.468608i
$669$		0			0
$670$	−12.8824	+	7.43764i	−0.497689	+	0.287341i
$671$	−4.50814			−0.174035
$672$		0			0
$673$	29.2177			1.12626			0.563130	−	0.826368i	$-0.309597\pi$
$673$	29.2177			1.12626			0.563130	+	0.826368i	$0.309597\pi$
$674$	26.6329	−	15.3765i	1.02586	−	0.592282i
$675$		0			0
$676$	5.67676	−	9.83245i	0.218337	−	0.378171i
$677$	−11.4401	−	19.8149i	−0.439680	−	0.761548i	0.557985	−	0.829851i	$-0.311575\pi$
$677$	−11.4401	−	19.8149i	−0.439680	−	0.761548i	−0.997665	+	0.0683033i	$0.978241\pi$
$678$		0			0
$679$	13.8625	−	22.7124i	0.531996	−	0.871621i
$680$		−	8.95809i		−	0.343527i
$681$		0			0
$682$	9.94550	+	5.74204i	0.380833	+	0.219874i
$683$	−13.0677	−	7.54464i	−0.500021	−	0.288688i	0.228701	−	0.973497i	$-0.426552\pi$
$683$	−13.0677	−	7.54464i	−0.500021	−	0.288688i	−0.728722	+	0.684809i	$0.759886\pi$
$684$		0			0
$685$			3.51331i			0.134237i
$686$	−8.06244	−	16.6732i	−0.307825	−	0.636587i
$687$		0			0
$688$	4.18600	+	7.25036i	0.159590	+	0.276417i
$689$	−7.00865	+	12.1393i	−0.267008	+	0.462472i
$690$		0			0
$691$	−24.1708	+	13.9550i	−0.919499	+	0.530873i	−0.883475	−	0.468478i	$-0.844803\pi$
$691$	−24.1708	+	13.9550i	−0.919499	+	0.530873i	−0.0360240	+	0.999351i	$0.511469\pi$
$692$	−16.0239			−0.609135
$693$		0			0
$694$	−23.8415			−0.905012
$695$	26.7099	−	15.4210i	1.01316	−	0.584950i
$696$		0			0
$697$	23.3209	−	40.3930i	0.883343	−	1.53000i
$698$	1.57187	+	2.72255i	0.0594960	+	0.103050i
$699$		0			0
$700$	−0.131395	+	5.38448i	−0.00496627	+	0.203514i
$701$			27.9911i			1.05721i	0.848868	+	0.528605i	$0.177285\pi$
$701$			27.9911i			1.05721i	−0.848868	+	0.528605i	$0.822715\pi$
$702$		0			0
$703$	17.9998	+	10.3922i	0.678876	+	0.391949i
$704$	−1.47921	−	0.854023i	−0.0557499	−	0.0321872i
$705$		0			0
$706$		−	27.6919i		−	1.04220i
$707$	−36.7309	+	20.0281i	−1.38141	+	0.753235i
$708$		0			0
$709$	−11.5397	−	19.9873i	−0.433382	−	0.750640i	0.563780	−	0.825925i	$-0.309347\pi$
$709$	−11.5397	−	19.9873i	−0.433382	−	0.750640i	−0.997162	+	0.0752852i	$0.976013\pi$
$710$	−4.36874	+	7.56688i	−0.163956	+	0.283980i
$711$		0			0
$712$	7.21709	−	4.16679i	0.270472	−	0.156157i
$713$	36.6028			1.37078
$714$		0			0
$715$	3.77341			0.141118
$716$	3.23826	−	1.86961i	0.121019	−	0.0698705i
$717$		0			0
$718$	10.4572	−	18.1125i	0.390261	−	0.675951i
$719$	9.45610	+	16.3784i	0.352653	+	0.610813i	0.986713	−	0.162471i	$-0.0519463\pi$
$719$	9.45610	+	16.3784i	0.352653	+	0.610813i	−0.634061	+	0.773283i	$0.718613\pi$
$720$		0			0
$721$	38.4384	+	0.937996i	1.43152	+	0.0349328i
$722$			11.3593i			0.422749i
$723$		0			0
$724$	0.932651	+	0.538466i	0.0346617	+	0.0200119i
$725$	−2.55566	−	1.47551i	−0.0949150	−	0.0547992i
$726$		0			0
$727$			5.34127i			0.198097i	0.995083	+	0.0990484i	$0.0315799\pi$
$727$			5.34127i			0.198097i	−0.995083	+	0.0990484i	$0.968420\pi$
$728$	2.89778	+	1.76866i	0.107399	+	0.0655511i
$729$		0			0
$730$	8.13266	+	14.0862i	0.301003	+	0.521353i
$731$	−21.7799	+	37.7240i	−0.805560	+	1.39527i
$732$		0			0
$733$	−44.6896	+	25.8016i	−1.65065	+	0.953003i	−0.673844	+	0.738874i	$0.735358\pi$
$733$	−44.6896	+	25.8016i	−1.65065	+	0.953003i	−0.976805	+	0.214129i	$0.931309\pi$
$734$	−1.16962			−0.0431715
$735$		0			0
$736$	−5.44399			−0.200668
$737$	−12.7802	+	7.37865i	−0.470765	+	0.271796i
$738$		0			0
$739$	18.0639	−	31.2875i	0.664490	−	1.15093i	−0.314933	−	0.949114i	$-0.601982\pi$
$739$	18.0639	−	31.2875i	0.664490	−	1.15093i	0.979423	−	0.201817i	$-0.0646847\pi$
$740$	6.47289	+	11.2114i	0.237948	+	0.412139i
$741$		0			0
$742$	24.6704	+	15.0576i	0.905678	+	0.552782i
$743$			3.88507i			0.142529i	0.997457	+	0.0712647i	$0.0227035\pi$
$743$			3.88507i			0.142529i	−0.997457	+	0.0712647i	$0.977296\pi$
$744$		0			0
$745$	15.8780	+	9.16716i	0.581724	+	0.335859i
$746$	−8.40915	−	4.85503i	−0.307881	−	0.177755i
$747$		0			0
$748$		−	8.88704i		−	0.324942i
$749$	9.21212	+	0.224799i	0.336603	+	0.00821399i
$750$		0			0
$751$	−1.55761	−	2.69786i	−0.0568380	−	0.0984463i	0.836206	−	0.548415i	$-0.184769\pi$
$751$	−1.55761	−	2.69786i	−0.0568380	−	0.0984463i	−0.893044	+	0.449969i	$0.851435\pi$
$752$	−2.61809	+	4.53466i	−0.0954718	+	0.165362i
$753$		0			0
$754$	−1.61086	+	0.930028i	−0.0586639	+	0.0338696i
$755$	−17.5406			−0.638366
$756$		0			0
$757$	−1.55505			−0.0565193			−0.0282597	−	0.999601i	$-0.508997\pi$
$757$	−1.55505			−0.0565193			−0.0282597	+	0.999601i	$0.508997\pi$
$758$	−13.1161	+	7.57261i	−0.476400	+	0.275050i
$759$		0			0
$760$	2.37955	−	4.12150i	0.0863153	−	0.149502i
$761$	24.4514	+	42.3511i	0.886364	+	1.53523i	0.844142	+	0.536119i	$0.180110\pi$
$761$	24.4514	+	42.3511i	0.886364	+	1.53523i	0.0422217	+	0.999108i	$0.486556\pi$
$762$		0			0
$763$	21.0663	−	11.4867i	0.762650	−	0.415847i
$764$			16.8572i			0.609872i
$765$		0			0
$766$	−27.6958	−	15.9902i	−1.00069	−	0.577748i
$767$	−4.63732	−	2.67736i	−0.167444	−	0.0966737i
$768$		0			0
$769$		−	19.3089i		−	0.696298i	−0.937439	−	0.348149i	$-0.886810\pi$
$769$		−	19.3089i		−	0.696298i	0.937439	−	0.348149i	$-0.113190\pi$
$770$	0.189807	−	7.77816i	0.00684017	−	0.280305i
$771$		0			0
$772$	7.11546	+	12.3243i	0.256091	+	0.443563i
$773$	21.5416	−	37.3112i	0.774798	−	1.34199i	−0.160110	−	0.987099i	$-0.551185\pi$
$773$	21.5416	−	37.3112i	0.774798	−	1.34199i	0.934908	−	0.354890i	$-0.115482\pi$
$774$		0			0
$775$	11.8536	−	6.84369i	0.425795	−	0.245833i
$776$	10.0571			0.361030
$777$		0			0
$778$	−24.9480			−0.894429
$779$	21.4593	−	12.3895i	0.768860	−	0.443901i
$780$		0			0
$781$	−4.33409	+	7.50687i	−0.155086	+	0.268617i
$782$	−14.1627	−	24.5304i	−0.506456	−	0.877207i
$783$		0			0
$784$	3.79152	−	5.88425i	0.135412	−	0.210152i
$785$			7.40408i			0.264263i
$786$		0			0
$787$	−5.16193	−	2.98024i	−0.184003	−	0.106234i	0.405169	−	0.914242i	$-0.367213\pi$
$787$	−5.16193	−	2.98024i	−0.184003	−	0.106234i	−0.589172	+	0.808008i	$0.700546\pi$
$788$	16.8208	+	9.71149i	0.599216	+	0.345958i
$789$		0			0
$790$		−	23.1998i		−	0.825412i
$791$	9.13219	−	14.9622i	0.324703	−	0.531993i
$792$		0			0
$793$	1.69334	+	2.93296i	0.0601324	+	0.104152i
$794$	0.161774	−	0.280202i	0.00574116	−	0.00994398i
$795$		0			0
$796$	6.99323	−	4.03754i	0.247868	−	0.143107i
$797$	2.12036			0.0751068			0.0375534	−	0.999295i	$-0.488044\pi$
$797$	2.12036			0.0751068			0.0375534	+	0.999295i	$0.488044\pi$
$798$		0			0
$799$	−27.2440			−0.963825
$800$	−1.76301	+	1.01787i	−0.0623318	+	0.0359873i
$801$		0			0
$802$	−9.50768	+	16.4678i	−0.335728	+	0.581498i
$803$	8.06816	+	13.9745i	0.284719	+	0.493148i
$804$		0			0
$805$	−11.8716	−	21.7721i	−0.418419	−	0.767367i
$806$		−	8.62727i		−	0.303883i
$807$		0			0
$808$	−13.6942	−	7.90634i	−0.481760	−	0.278144i
$809$	−31.7884	−	18.3530i	−1.11762	−	0.645258i	−0.176828	−	0.984242i	$-0.556584\pi$
$809$	−31.7884	−	18.3530i	−1.11762	−	0.645258i	−0.940792	+	0.338983i	$0.889917\pi$
$810$		0			0
$811$			46.1908i			1.62198i	0.585060	+	0.810990i	$0.301071\pi$
$811$			46.1908i			1.62198i	−0.585060	+	0.810990i	$0.698929\pi$
$812$	1.83605	+	3.36725i	0.0644326	+	0.118167i
$813$		0			0
$814$	6.42156	+	11.1225i	0.225075	+	0.389842i
$815$	7.41690	−	12.8464i	0.259803	−	0.449991i
$816$		0			0
$817$	−20.0413	+	11.5709i	−0.701157	+	0.404813i
$818$	4.51304			0.157795
$819$		0			0
$820$	15.4339			0.538976
$821$	−0.193084	+	0.111477i	−0.00673867	+	0.00389057i	−0.503366	−	0.864074i	$-0.667905\pi$
$821$	−0.193084	+	0.111477i	−0.00673867	+	0.00389057i	0.496627	+	0.867964i	$0.334572\pi$
$822$		0			0
$823$	−12.5354	+	21.7119i	−0.436956	+	0.756829i	−0.997453	−	0.0713268i	$-0.977277\pi$
$823$	−12.5354	+	21.7119i	−0.436956	+	0.756829i	0.560497	+	0.828156i	$0.310610\pi$
$824$	7.26634	+	12.5857i	0.253135	+	0.438442i
$825$		0			0
$826$	−5.75212	+	9.42426i	−0.200142	+	0.327912i
$827$		−	25.6351i		−	0.891421i	−0.895177	−	0.445711i	$-0.852951\pi$
$827$		−	25.6351i		−	0.891421i	0.895177	−	0.445711i	$-0.147049\pi$
$828$		0			0
$829$	−5.72963	−	3.30800i	−0.198998	−	0.114892i	0.397190	−	0.917736i	$-0.369985\pi$
$829$	−5.72963	−	3.30800i	−0.198998	−	0.114892i	−0.596188	+	0.802845i	$0.703319\pi$
$830$	−9.05967	−	5.23060i	−0.314466	−	0.181557i
$831$		0			0
$832$			1.28315i			0.0444852i
$833$	36.3780	+	1.77649i	1.26042	+	0.0615517i
$834$		0			0
$835$	12.0391	+	20.8524i	0.416631	+	0.721626i
$836$	2.36068	−	4.08881i	0.0816457	−	0.141414i
$837$		0			0
$838$	25.3009	−	14.6075i	0.874004	−	0.504607i
$839$	−11.4826			−0.396424			−0.198212	−	0.980159i	$-0.563513\pi$
$839$	−11.4826			−0.396424			−0.198212	+	0.980159i	$0.563513\pi$
$840$		0			0
$841$	26.8987			0.927540
$842$	−31.4680	+	18.1681i	−1.08446	+	0.626113i
$843$		0			0
$844$	9.95665	−	17.2454i	0.342722	−	0.593612i
$845$	9.77369	+	16.9285i	0.336225	+	0.582359i
$846$		0			0
$847$	−0.521681	+	21.3781i	−0.0179252	+	0.734561i
$848$			10.9241i			0.375137i
$849$		0			0
$850$	−9.17301	−	5.29604i	−0.314632	−	0.181653i
$851$	35.4502	+	20.4672i	1.21522	+	0.701606i
$852$		0			0
$853$			18.0012i			0.616351i	0.951330	+	0.308175i	$0.0997184\pi$
$853$			18.0012i			0.616351i	−0.951330	+	0.308175i	$0.900282\pi$
$854$	6.13090	−	3.34297i	0.209795	−	0.114394i
$855$		0			0
$856$	1.74144	+	3.01627i	0.0595213	+	0.103094i
$857$	−19.4641	+	33.7129i	−0.664882	+	1.15161i	0.314435	+	0.949279i	$0.398185\pi$
$857$	−19.4641	+	33.7129i	−0.664882	+	1.15161i	−0.979317	+	0.202331i	$0.935148\pi$
$858$		0			0
$859$	31.5963	−	18.2421i	1.07805	−	0.622414i	0.147682	−	0.989035i	$-0.452819\pi$
$859$	31.5963	−	18.2421i	1.07805	−	0.622414i	0.930370	+	0.366621i	$0.119485\pi$
$860$	−14.4141			−0.491516
$861$		0			0
$862$	12.1206			0.412828
$863$	−32.9539	+	19.0259i	−1.12176	+	0.647650i	−0.941850	−	0.336033i	$-0.890915\pi$
$863$	−32.9539	+	19.0259i	−1.12176	+	0.647650i	−0.179912	+	0.983683i	$0.557581\pi$
$864$		0			0
$865$	13.7941	−	23.8921i	0.469015	−	0.812357i
$866$	15.7080	+	27.2071i	0.533780	+	0.924534i
$867$		0			0
$868$	−17.7835	−	0.433962i	−0.603610	−	0.0147296i
$869$		−	23.0158i		−	0.780757i
$870$		0			0
$871$	9.60097	+	5.54312i	0.325316	+	0.187822i
$872$	7.85401	+	4.53452i	0.265970	+	0.153558i
$873$		0			0
$874$		−	15.0482i		−	0.509012i
$875$	−27.3562	−	16.6969i	−0.924809	−	0.564459i
$876$		0			0
$877$	−7.00470	−	12.1325i	−0.236532	−	0.409685i	0.723185	−	0.690655i	$-0.242677\pi$
$877$	−7.00470	−	12.1325i	−0.236532	−	0.409685i	−0.959717	+	0.280969i	$0.909344\pi$
$878$	−1.61726	+	2.80118i	−0.0545799	+	0.0945352i
$879$		0			0
$880$	2.54676	−	1.47037i	0.0858512	−	0.0495662i
$881$	−12.6046			−0.424659			−0.212330	−	0.977198i	$-0.568105\pi$
$881$	−12.6046			−0.424659			−0.212330	+	0.977198i	$0.568105\pi$
$882$		0			0
$883$	7.76793			0.261412			0.130706	−	0.991421i	$-0.458276\pi$
$883$	7.76793			0.261412			0.130706	+	0.991421i	$0.458276\pi$
$884$	−5.78183	+	3.33814i	−0.194464	+	0.112274i
$885$		0			0
$886$	4.41729	−	7.65097i	0.148402	−	0.257039i
$887$	−4.55420	−	7.88810i	−0.152915	−	0.264857i	0.779383	−	0.626548i	$-0.215533\pi$
$887$	−4.55420	−	7.88810i	−0.152915	−	0.264857i	−0.932298	+	0.361691i	$0.882199\pi$
$888$		0			0
$889$	44.0201	+	26.8677i	1.47639	+	0.901115i
$890$			14.3479i			0.480943i
$891$		0			0
$892$	18.3684	+	10.6050i	0.615020	+	0.355082i
$893$	−12.5346	−	7.23687i	−0.419455	−	0.242173i
$894$		0			0
$895$			6.43781i			0.215192i
$896$	2.64496	+	0.0645439i	0.0883620	+	0.00215626i
$897$		0			0
$898$	3.41597	+	5.91663i	0.113992	+	0.197440i
$899$	4.87322	−	8.44066i	0.162531	−	0.281512i
$900$		0			0
$901$	−49.2239	+	28.4194i	−1.63988	+	0.946788i
$902$	15.3115			0.509817
$903$		0			0
$904$	6.62531			0.220355
$905$	−1.60575	+	0.927078i	−0.0533768	+	0.0308171i
$906$		0			0
$907$	−1.18365	+	2.05014i	−0.0393023	+	0.0680737i	−0.885007	−	0.465577i	$-0.845847\pi$
$907$	−1.18365	+	2.05014i	−0.0393023	+	0.0680737i	0.845705	+	0.533651i	$0.179180\pi$
$908$	6.79579	+	11.7707i	0.225526	+	0.390623i
$909$		0			0
$910$	−5.13170	+	2.79814i	−0.170114	+	0.0927573i
$911$			6.15544i			0.203939i	0.994788	+	0.101969i	$0.0325144\pi$
$911$			6.15544i			0.203939i	−0.994788	+	0.101969i	$0.967486\pi$
$912$		0			0
$913$	−8.98782	−	5.18912i	−0.297453	−	0.171735i
$914$	−15.9555	−	9.21190i	−0.527760	−	0.304703i
$915$		0			0
$916$			24.1066i			0.796504i
$917$	−0.685890	+	28.1073i	−0.0226501	+	0.928184i
$918$		0			0
$919$	−14.2826	−	24.7382i	−0.471140	−	0.816038i	0.528315	−	0.849048i	$-0.322824\pi$
$919$	−14.2826	−	24.7382i	−0.471140	−	0.816038i	−0.999455	+	0.0330102i	$0.989491\pi$
$920$	4.68646	−	8.11719i	0.154508	−	0.267616i
$921$		0			0
$922$	25.8998	−	14.9533i	0.852965	−	0.492460i
$923$	6.51187			0.214341
$924$		0			0
$925$	15.3072			0.503296
$926$	1.14756	−	0.662545i	0.0377112	−	0.0217726i
$927$		0			0
$928$	−0.724802	+	1.25539i	−0.0237928	+	0.0412103i
$929$	3.84812	+	6.66515i	0.126253	+	0.218676i	0.922222	−	0.386661i	$-0.126372\pi$
$929$	3.84812	+	6.66515i	0.126253	+	0.218676i	−0.795969	+	0.605337i	$0.793038\pi$
$930$		0			0
$931$	16.2651	+	10.4805i	0.533068	+	0.343483i
$932$			18.4626i			0.604762i
$933$		0			0
$934$	23.6973	+	13.6817i	0.775400	+	0.447677i
$935$	13.2509	+	7.65041i	0.433351	+	0.250195i
$936$		0			0
$937$		−	28.1750i		−	0.920436i	−0.887806	−	0.460218i	$-0.847771\pi$
$937$		−	28.1750i		−	0.920436i	0.887806	−	0.460218i	$-0.152229\pi$
$938$	11.9090	−	19.5117i	0.388843	−	0.637080i
$939$		0			0
$940$	−4.50756	−	7.80732i	−0.147020	−	0.254647i
$941$	−19.2950	+	33.4199i	−0.628999	+	1.08946i	0.358754	+	0.933432i	$0.383202\pi$
$941$	−19.2950	+	33.4199i	−0.628999	+	1.08946i	−0.987753	+	0.156026i	$0.950132\pi$
$942$		0			0
$943$	42.2636	−	24.4009i	1.37629	−	0.794602i
$944$	−4.17310			−0.135823
$945$		0			0
$946$	−14.2997			−0.464925
$947$	−19.3980	+	11.1995i	−0.630351	+	0.363933i	−0.780888	−	0.624671i	$-0.785233\pi$
$947$	−19.3980	+	11.1995i	−0.630351	+	0.363933i	0.150537	+	0.988604i	$0.451900\pi$
$948$		0			0
$949$	6.06111	−	10.4981i	0.196752	−	0.340784i
$950$	−2.81359	−	4.87328i	−0.0912849	−	0.158110i
$951$		0			0
$952$	6.59010	+	12.0860i	0.213586	+	0.391711i
$953$		−	38.8771i		−	1.25935i	−0.776858	−	0.629676i	$-0.783188\pi$
$953$		−	38.8771i		−	1.25935i	0.776858	−	0.629676i	$-0.216812\pi$
$954$		0			0
$955$	−25.1347	−	14.5115i	−0.813339	−	0.469582i
$956$	20.0846	+	11.5958i	0.649582	+	0.375036i
$957$		0			0
$958$			16.8211i			0.543464i
$959$	−2.58460	−	4.74008i	−0.0834612	−	0.153065i
$960$		0			0
$961$	7.10284	+	12.3025i	0.229124	+	0.396854i
$962$	4.82412	−	8.35561i	0.155536	−	0.269396i
$963$		0			0
$964$	22.4458	−	12.9591i	0.722932	−	0.417385i
$965$	−24.5014			−0.788727
$966$		0			0
$967$	−20.5790			−0.661777			−0.330889	−	0.943670i	$-0.607348\pi$
$967$	−20.5790			−0.661777			−0.330889	+	0.943670i	$0.607348\pi$
$968$	−6.99972	+	4.04129i	−0.224980	+	0.129892i
$969$		0			0
$970$	−8.65769	+	14.9956i	−0.277982	+	0.481479i
$971$	1.02171	+	1.76966i	0.0327884	+	0.0567912i	0.881954	−	0.471336i	$-0.156228\pi$
$971$	1.02171	+	1.76966i	0.0327884	+	0.0567912i	−0.849166	+	0.528127i	$0.822895\pi$
$972$		0			0
$973$	−24.6918	+	40.4550i	−0.791581	+	1.29693i
$974$		−	0.715204i		−	0.0229166i
$975$		0			0
$976$	2.28575	+	1.31968i	0.0731651	+	0.0422419i
$977$	40.0652	+	23.1317i	1.28180	+	0.740048i	0.977177	−	0.212425i	$-0.0681361\pi$
$977$	40.0652	+	23.1317i	1.28180	+	0.740048i	0.304623	+	0.952473i	$0.401469\pi$
$978$		0			0
$979$			14.2341i			0.454925i
$980$	5.50969	+	10.7188i	0.176001	+	0.342398i
$981$		0			0
$982$	−2.68453	−	4.64975i	−0.0856669	−	0.148379i
$983$	−9.65581	+	16.7244i	−0.307972	+	0.533424i	−0.977919	−	0.208986i	$-0.932984\pi$
$983$	−9.65581	+	16.7244i	−0.307972	+	0.533424i	0.669946	+	0.742410i	$0.266317\pi$
$984$		0			0
$985$	−28.9604	+	16.7203i	−0.922754	+	0.532753i
$986$	−7.54235			−0.240197
$987$		0			0
$988$	−3.54686			−0.112841
$989$	−39.4709	+	22.7885i	−1.25510	+	0.724633i
$990$		0			0
$991$	0.313252	−	0.542568i	0.00995077	−	0.0172352i	−0.861007	−	0.508593i	$-0.830166\pi$
$991$	0.313252	−	0.542568i	0.00995077	−	0.0172352i	0.870958	+	0.491358i	$0.163499\pi$
$992$	−3.36176	−	5.82274i	−0.106736	−	0.184872i
$993$		0			0
$994$	0.327555	−	13.4230i	0.0103894	−	0.425751i
$995$			13.9029i			0.440751i
$996$		0			0
$997$	22.6691	+	13.0880i	0.717939	+	0.414502i	0.813994	−	0.580874i	$-0.197289\pi$
$997$	22.6691	+	13.0880i	0.717939	+	0.414502i	−0.0960546	+	0.995376i	$0.530622\pi$
$998$	−20.8649	−	12.0464i	−0.660467	−	0.381321i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.c.647.7	✓	16
3.2	odd	2		1134.2.k.d.647.2	yes	16
7.5	odd	6		1134.2.k.d.971.2	yes	16
9.2	odd	6		1134.2.t.g.1025.7		16
9.4	even	3		1134.2.l.h.269.7		16
9.5	odd	6		1134.2.l.g.269.2		16
9.7	even	3		1134.2.t.h.1025.2		16
21.5	even	6	inner	1134.2.k.c.971.7	yes	16
63.5	even	6		1134.2.t.h.593.2		16
63.40	odd	6		1134.2.t.g.593.7		16
63.47	even	6		1134.2.l.h.215.3		16
63.61	odd	6		1134.2.l.g.215.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.7	✓	16	1.1	even	1	trivial
1134.2.k.c.971.7	yes	16	21.5	even	6	inner
1134.2.k.d.647.2	yes	16	3.2	odd	2
1134.2.k.d.971.2	yes	16	7.5	odd	6
1134.2.l.g.215.6		16	63.61	odd	6
1134.2.l.g.269.2		16	9.5	odd	6
1134.2.l.h.215.3		16	63.47	even	6
1134.2.l.h.269.7		16	9.4	even	3
1134.2.t.g.593.7		16	63.40	odd	6
1134.2.t.g.1025.7		16	9.2	odd	6
1134.2.t.h.593.2		16	63.5	even	6
1134.2.t.h.1025.2		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.860850 + 1.49104i) q^{5} +(-2.25833 - 1.37838i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.860850 + 1.49104i) q^{5} +(-2.25833 - 1.37838i) q^{7} -1.00000i q^{8} +(1.49104 + 0.860850i) q^{10} +(1.47921 + 0.854023i) q^{11} -1.28315i q^{13} +(-2.64496 - 0.0645439i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.60152 - 4.50597i) q^{17} +(2.39385 - 1.38209i) q^{19} +1.72170 q^{20} +1.70805 q^{22} +(4.71463 - 2.72199i) q^{23} +(1.01787 - 1.76301i) q^{25} +(-0.641574 - 1.11124i) q^{26} +(-2.32288 + 1.26659i) q^{28} -1.44960i q^{29} +(5.82274 + 3.36176i) q^{31} +(-0.866025 - 0.500000i) q^{32} -5.20305i q^{34} +(0.111125 - 4.55384i) q^{35} +(3.75959 + 6.51181i) q^{37} +(1.38209 - 2.39385i) q^{38} +(1.49104 - 0.860850i) q^{40} +8.96434 q^{41} -8.37200 q^{43} +(1.47921 - 0.854023i) q^{44} +(2.72199 - 4.71463i) q^{46} +(-2.61809 - 4.53466i) q^{47} +(3.20014 + 6.22568i) q^{49} -2.03575i q^{50} +(-1.11124 - 0.641574i) q^{52} +(-9.46059 - 5.46207i) q^{53} +2.94074i q^{55} +(-1.37838 + 2.25833i) q^{56} +(-0.724802 - 1.25539i) q^{58} +(2.08655 - 3.61401i) q^{59} +(-2.28575 + 1.31968i) q^{61} +6.72352 q^{62} -1.00000 q^{64} +(1.91322 - 1.10460i) q^{65} +(-4.31994 + 7.48235i) q^{67} +(-2.60152 - 4.50597i) q^{68} +(-2.18068 - 3.99930i) q^{70} +5.07491i q^{71} +(8.18155 + 4.72362i) q^{73} +(6.51181 + 3.75959i) q^{74} -2.76418i q^{76} +(-2.16339 - 3.96758i) q^{77} +(-6.73747 - 11.6696i) q^{79} +(0.860850 - 1.49104i) q^{80} +(7.76335 - 4.48217i) q^{82} -6.07609 q^{83} +8.95809 q^{85} +(-7.25036 + 4.18600i) q^{86} +(0.854023 - 1.47921i) q^{88} +(4.16679 + 7.21709i) q^{89} +(-1.76866 + 2.89778i) q^{91} -5.44399i q^{92} +(-4.53466 - 2.61809i) q^{94} +(4.12150 + 2.37955i) q^{95} +10.0571i q^{97} +(5.88425 + 3.79152i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^7	\( 16 q + 8 q^{4} + 8 q^{7} - 12 q^{11} - 12 q^{14} - 8 q^{16} - 12 q^{23} - 8 q^{25} + 4 q^{28} + 12 q^{31} - 60 q^{35} + 4 q^{37} + 12 q^{38} + 48 q^{41} - 32 q^{43} - 12 q^{44} + 4 q^{49} - 12 q^{52} - 12 q^{56} - 12 q^{58} + 24 q^{59} - 12 q^{61} + 48 q^{62} - 16 q^{64} - 48 q^{65} - 4 q^{67} - 24 q^{70} + 36 q^{73} - 36 q^{74} - 84 q^{77} + 8 q^{79} + 72 q^{83} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 36 q^{94} - 12 q^{95} - 36 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^7 - 12 * q^11 - 12 * q^14 - 8 * q^16 - 12 * q^23 - 8 * q^25 + 4 * q^28 + 12 * q^31 - 60 * q^35 + 4 * q^37 + 12 * q^38 + 48 * q^41 - 32 * q^43 - 12 * q^44 + 4 * q^49 - 12 * q^52 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 12 * q^61 + 48 * q^62 - 16 * q^64 - 48 * q^65 - 4 * q^67 - 24 * q^70 + 36 * q^73 - 36 * q^74 - 84 * q^77 + 8 * q^79 + 72 * q^83 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 36 * q^94 - 12 * q^95 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more