LMFDB - Embedded newform 891.2.n.d.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			757.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	891.757
Dual form			891.2.n.d.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.604528 - 0.128496i) q^{2} +(-1.47815 + 0.658114i) q^{4} +(2.56082 + 0.544320i) q^{5} +(-0.313585 + 2.98357i) q^{7} +(-1.80902 + 1.31433i) q^{8} +1.61803 q^{10} +(1.62543 - 2.89102i) q^{11} +(1.18030 + 1.31086i) q^{13} +(0.193806 + 1.84395i) q^{14} +(1.24064 - 1.37787i) q^{16} +(0.500000 + 1.53884i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(-4.14350 + 0.880728i) q^{20} +(0.611130 - 1.95656i) q^{22} +(-1.73607 + 3.00696i) q^{23} +(1.69381 + 0.754131i) q^{25} +(0.881966 + 0.640786i) q^{26} +(-1.50000 - 4.61653i) q^{28} +(-0.467465 + 4.44764i) q^{29} +(1.90977 + 2.12101i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.500000 + 0.866025i) q^{34} +(-2.42705 + 7.46969i) q^{35} +(-0.190983 - 0.138757i) q^{37} +(-2.42094 + 2.68872i) q^{38} +(-5.34799 + 2.38108i) q^{40} +(1.24852 + 11.8788i) q^{41} +(-3.11803 - 5.40059i) q^{43} +(-0.500000 + 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(1.47815 + 0.658114i) q^{47} +(-1.95630 - 0.415823i) q^{49} +(1.12086 + 0.238246i) q^{50} +(-2.60735 - 1.16087i) q^{52} +(-2.97214 + 9.14729i) q^{53} +(5.73607 - 6.51864i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(0.288910 + 2.74879i) q^{58} +(9.43349 - 4.20006i) q^{59} +(5.25542 - 5.83674i) q^{61} +(1.42705 + 1.03681i) q^{62} +(-0.0729490 + 0.224514i) q^{64} +(2.30902 + 3.99933i) q^{65} +(4.78115 - 8.28120i) q^{67} +(-1.75181 - 1.94558i) q^{68} +(-0.507392 + 4.82751i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(2.61803 + 1.90211i) q^{73} +(-0.133284 - 0.0593421i) q^{74} +(4.73607 - 8.20311i) q^{76} +(8.11584 + 5.75615i) q^{77} +(-9.26515 + 1.96937i) q^{79} +(3.92705 - 2.85317i) q^{80} +(2.28115 + 7.02067i) q^{82} +(0.473881 - 0.526298i) q^{83} +(0.442790 + 4.21286i) q^{85} +(-2.57890 - 2.86416i) q^{86} +(0.859324 + 7.36624i) q^{88} +0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(0.587244 - 5.58726i) q^{92} +(0.978148 + 0.207912i) q^{94} +(-14.0012 + 6.23374i) q^{95} +(13.7278 - 2.91792i) q^{97} -1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 6 q^{14} - 9 q^{16} + 4 q^{17} - 20 q^{19} - 3 q^{20} + 8 q^{22} + 4 q^{23} + 6 q^{25} + 16 q^{26} - 12 q^{28} + 10 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 - 3 * q^4 + q^5 + 3 * q^7 - 10 * q^8 + 4 * q^10 - 9 * q^11 + 9 * q^13 - 6 * q^14 - 9 * q^16 + 4 * q^17 - 20 * q^19 - 3 * q^20 + 8 * q^22 + 4 * q^23 + 6 * q^25 + 16 * q^26 - 12 * q^28 + 10 * q^29 - 8 * q^31 + 18 * q^32 + 4 * q^34 - 6 * q^35 - 6 * q^37 - 10 * q^40 - 23 * q^41 - 16 * q^43 - 4 * q^44 + 26 * q^46 + 3 * q^47 + 2 * q^49 - 12 * q^50 - 7 * q^52 + 12 * q^53 + 28 * q^55 + 20 * q^59 - 3 * q^61 - 2 * q^62 - 14 * q^64 + 14 * q^65 - 2 * q^67 + q^68 + 9 * q^70 - 54 * q^71 + 12 * q^73 + 4 * q^74 + 20 * q^76 + 3 * q^77 - 5 * q^79 + 18 * q^80 - 22 * q^82 - 21 * q^83 - 7 * q^85 + 7 * q^86 + 25 * q^88 + 40 * q^89 + 6 * q^91 - 7 * q^92 - q^94 - 25 * q^95 + 33 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.604528	−	0.128496i	0.427466	−	0.0908607i	0.0108456	−	0.999941i	$-0.496548\pi$
$2$	0.604528	−	0.128496i	0.427466	−	0.0908607i	0.416621	+	0.909080i	$0.363214\pi$
$3$		0			0
$3$		0			0
$4$	−1.47815	+	0.658114i	−0.739074	+	0.329057i
$5$	2.56082	+	0.544320i	1.14524	+	0.243427i	0.741179	−	0.671307i	$-0.234267\pi$
$5$	2.56082	+	0.544320i	1.14524	+	0.243427i	0.404056	+	0.914734i	$0.367600\pi$
$6$		0			0
$7$	−0.313585	+	2.98357i	−0.118524	+	1.12768i	0.759980	+	0.649947i	$0.225209\pi$
$7$	−0.313585	+	2.98357i	−0.118524	+	1.12768i	−0.878504	+	0.477735i	$0.841458\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$		0			0
$10$	1.61803			0.511667
$11$	1.62543	−	2.89102i	0.490084	−	0.871675i
$11$	1.62543	−	2.89102i	0.490084	−	0.871675i
$12$		0			0
$13$	1.18030	+	1.31086i	0.327357	+	0.363566i	0.884247	−	0.467020i	$-0.154672\pi$
$13$	1.18030	+	1.31086i	0.327357	+	0.363566i	−0.556890	+	0.830586i	$0.688006\pi$
$14$	0.193806	+	1.84395i	0.0517969	+	0.492815i
$15$		0			0
$16$	1.24064	−	1.37787i	0.310159	−	0.344467i
$17$	0.500000	+	1.53884i	0.121268	+	0.373224i	0.993203	−	0.116398i	$-0.0371348\pi$
$17$	0.500000	+	1.53884i	0.121268	+	0.373224i	−0.871935	+	0.489622i	$0.837135\pi$
$18$		0			0
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.978810	−	0.204772i	$-0.934355\pi$
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.107719	+	0.994181i	$0.534355\pi$
$20$	−4.14350	+	0.880728i	−0.926515	+	0.196937i
$21$		0			0
$22$	0.611130	−	1.95656i	0.130293	−	0.417141i
$23$	−1.73607	+	3.00696i	−0.361995	+	0.626994i	−0.988289	−	0.152593i	$-0.951238\pi$
$23$	−1.73607	+	3.00696i	−0.361995	+	0.626994i	0.626294	+	0.779587i	$0.284571\pi$
$24$		0			0
$25$	1.69381	+	0.754131i	0.338761	+	0.150826i
$26$	0.881966	+	0.640786i	0.172968	+	0.125668i
$27$		0			0
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	−0.467465	+	4.44764i	−0.0868062	+	0.825905i	0.861331	+	0.508044i	$0.169631\pi$
$29$	−0.467465	+	4.44764i	−0.0868062	+	0.825905i	−0.948137	+	0.317861i	$0.897035\pi$
$30$		0			0
$31$	1.90977	+	2.12101i	0.343004	+	0.380945i	0.889823	−	0.456306i	$-0.150828\pi$
$31$	1.90977	+	2.12101i	0.343004	+	0.380945i	−0.546818	+	0.837251i	$0.684161\pi$
$32$	2.80902	−	4.86536i	0.496569	−	0.860082i
$33$		0			0
$34$	0.500000	+	0.866025i	0.0857493	+	0.148522i
$35$	−2.42705	+	7.46969i	−0.410246	+	1.26261i
$36$		0			0
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	0.571976	−	0.820270i	$-0.306177\pi$
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	−0.603373	+	0.797459i	$0.706177\pi$
$38$	−2.42094	+	2.68872i	−0.392728	+	0.436169i
$39$		0			0
$40$	−5.34799	+	2.38108i	−0.845591	+	0.376481i
$41$	1.24852	+	11.8788i	0.194986	+	1.85516i	0.456194	+	0.889881i	$0.349212\pi$
$41$	1.24852	+	11.8788i	0.194986	+	1.85516i	−0.261208	+	0.965283i	$0.584121\pi$
$42$		0			0
$43$	−3.11803	−	5.40059i	−0.475496	−	0.823583i	0.524110	−	0.851650i	$-0.324398\pi$
$43$	−3.11803	−	5.40059i	−0.475496	−	0.823583i	−0.999606	+	0.0280676i	$0.991065\pi$
$44$	−0.500000	+	5.34307i	−0.0753778	+	0.805498i
$45$		0			0
$46$	−0.663119	+	2.04087i	−0.0977716	+	0.300910i
$47$	1.47815	+	0.658114i	0.215610	+	0.0959958i	0.511700	−	0.859164i	$-0.329016\pi$
$47$	1.47815	+	0.658114i	0.215610	+	0.0959958i	−0.296090	+	0.955160i	$0.595683\pi$
$48$		0			0
$49$	−1.95630	−	0.415823i	−0.279471	−	0.0594033i
$50$	1.12086	+	0.238246i	0.158513	+	0.0336930i
$51$		0			0
$52$	−2.60735	−	1.16087i	−0.361575	−	0.160983i
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	0.509893	+	0.860238i	$0.329685\pi$
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	−0.918147	+	0.396240i	$0.870315\pi$
$54$		0			0
$55$	5.73607	−	6.51864i	0.773451	−	0.878973i
$56$	−3.35410	−	5.80948i	−0.448211	−	0.776324i
$57$		0			0
$58$	0.288910	+	2.74879i	0.0379357	+	0.360934i
$59$	9.43349	−	4.20006i	1.22814	−	0.546801i	0.312925	−	0.949778i	$-0.398691\pi$
$59$	9.43349	−	4.20006i	1.22814	−	0.546801i	0.915210	+	0.402977i	$0.132024\pi$
$60$		0			0
$61$	5.25542	−	5.83674i	0.672888	−	0.747317i	−0.305929	−	0.952054i	$-0.598967\pi$
$61$	5.25542	−	5.83674i	0.672888	−	0.747317i	0.978817	+	0.204737i	$0.0656338\pi$
$62$	1.42705	+	1.03681i	0.181236	+	0.131675i
$63$		0			0
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	2.30902	+	3.99933i	0.286398	+	0.496056i
$66$		0			0
$67$	4.78115	−	8.28120i	0.584111	−	1.01171i	−0.410875	−	0.911692i	$-0.634777\pi$
$67$	4.78115	−	8.28120i	0.584111	−	1.01171i	0.994986	−	0.100018i	$-0.0318900\pi$
$68$	−1.75181	−	1.94558i	−0.212438	−	0.235936i
$69$		0			0
$70$	−0.507392	+	4.82751i	−0.0606449	+	0.576998i
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	−0.999753	−	0.0222083i	$-0.992930\pi$
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	0.795764	−	0.605607i	$-0.207070\pi$
$72$		0			0
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	0.730358	−	0.683065i	$-0.239353\pi$
$73$	2.61803	+	1.90211i	0.306418	+	0.222625i	−0.423940	+	0.905690i	$0.639353\pi$
$74$	−0.133284	−	0.0593421i	−0.0154940	−	0.00689838i
$75$		0			0
$76$	4.73607	−	8.20311i	0.543264	−	0.940961i
$77$	8.11584	+	5.75615i	0.924885	+	0.655974i
$78$		0			0
$79$	−9.26515	+	1.96937i	−1.04241	+	0.221571i	−0.697142	−	0.716933i	$-0.745545\pi$
$79$	−9.26515	+	1.96937i	−1.04241	+	0.221571i	−0.345268	+	0.938504i	$0.612212\pi$
$80$	3.92705	−	2.85317i	0.439058	−	0.318994i
$81$		0			0
$82$	2.28115	+	7.02067i	0.251911	+	0.775303i
$83$	0.473881	−	0.526298i	0.0520152	−	0.0577687i	−0.716576	−	0.697509i	$-0.754292\pi$
$83$	0.473881	−	0.526298i	0.0520152	−	0.0577687i	0.768591	+	0.639741i	$0.220958\pi$
$84$		0			0
$85$	0.442790	+	4.21286i	0.0480273	+	0.456949i
$86$	−2.57890	−	2.86416i	−0.278090	−	0.308850i
$87$		0			0
$88$	0.859324	+	7.36624i	0.0916042	+	0.785244i
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$		0			0
$91$	−4.28115	+	3.11044i	−0.448787	+	0.326063i
$92$	0.587244	−	5.58726i	0.0612245	−	0.582512i
$93$		0			0
$94$	0.978148	+	0.207912i	0.100888	+	0.0214445i
$95$	−14.0012	+	6.23374i	−1.43649	+	0.639568i
$96$		0			0
$97$	13.7278	−	2.91792i	1.39384	−	0.296270i	0.551033	−	0.834483i	$-0.314234\pi$
$97$	13.7278	−	2.91792i	1.39384	−	0.296270i	0.842809	+	0.538213i	$0.180900\pi$
$98$	−1.23607			−0.124862
$99$		0			0
$100$	−3.00000			−0.300000
$101$	2.93444	−	0.623735i	0.291988	−	0.0620640i	−0.0595888	−	0.998223i	$-0.518979\pi$
$101$	2.93444	−	0.623735i	0.291988	−	0.0620640i	0.351577	+	0.936159i	$0.385646\pi$
$102$		0			0
$103$	−5.48127	+	2.44042i	−0.540086	+	0.240462i	−0.658603	−	0.752490i	$-0.728852\pi$
$103$	−5.48127	+	2.44042i	−0.540086	+	0.240462i	0.118518	+	0.992952i	$0.462186\pi$
$104$	−3.85808	−	0.820060i	−0.378316	−	0.0804135i
$105$		0			0
$106$	−0.621346	+	5.91171i	−0.0603504	+	0.574196i
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	−0.409679	−	0.912230i	$-0.634359\pi$
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	0.740984	+	0.671522i	$0.234359\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	2.62999	−	4.67777i	0.250760	−	0.446008i
$111$		0			0
$112$	3.72191	+	4.13360i	0.351687	+	0.390588i
$113$	−0.0740275	−	0.704324i	−0.00696392	−	0.0662573i	0.990488	−	0.137599i	$-0.0439386\pi$
$113$	−0.0740275	−	0.704324i	−0.00696392	−	0.0662573i	−0.997452	+	0.0713418i	$0.977272\pi$
$114$		0			0
$115$	−6.08251	+	6.75531i	−0.567197	+	0.629936i
$116$	−2.23607	−	6.88191i	−0.207614	−	0.638969i
$117$		0			0
$118$	5.16312	−	3.75123i	0.475304	−	0.345328i
$119$	−4.74803	+	1.00922i	−0.435251	+	0.0925155i
$120$		0			0
$121$	−5.71598	−	9.39827i	−0.519635	−	0.854389i
$122$	2.42705	−	4.20378i	0.219735	−	0.380592i
$123$		0			0
$124$	−4.21878	−	1.87832i	−0.378858	−	0.168678i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$		0			0
$127$	−1.14590	−	3.52671i	−0.101682	−	0.312945i	0.887255	−	0.461279i	$-0.152609\pi$
$127$	−1.14590	−	3.52671i	−0.101682	−	0.312945i	−0.988937	+	0.148333i	$0.952609\pi$
$128$	−1.18974	+	11.3196i	−0.105159	+	1.00052i
$129$		0			0
$130$	1.90977	+	2.12101i	0.167498	+	0.186025i
$131$	3.57295	−	6.18853i	0.312170	−	0.540694i	−0.666662	−	0.745360i	$-0.732277\pi$
$131$	3.57295	−	6.18853i	0.312170	−	0.540694i	0.978832	+	0.204666i	$0.0656108\pi$
$132$		0			0
$133$	−8.78115	−	15.2094i	−0.761423	−	1.31882i
$134$	1.82624	−	5.62058i	0.157763	−	0.485544i
$135$		0			0
$136$	−2.92705	−	2.12663i	−0.250993	−	0.182357i
$137$	4.99983	−	5.55288i	0.427165	−	0.474414i	−0.490688	−	0.871335i	$-0.663255\pi$
$137$	4.99983	−	5.55288i	0.427165	−	0.474414i	0.917853	+	0.396921i	$0.129921\pi$
$138$		0			0
$139$	−0.780261	+	0.347395i	−0.0661809	+	0.0294656i	−0.439560	−	0.898213i	$-0.644866\pi$
$139$	−0.780261	+	0.347395i	−0.0661809	+	0.0294656i	0.373379	+	0.927679i	$0.378199\pi$
$140$	−1.32837	−	12.6386i	−0.112268	−	1.06816i
$141$		0			0
$142$	−1.71885	−	2.97713i	−0.144242	−	0.249835i
$143$	5.70820	−	1.28157i	0.477344	−	0.107170i
$144$		0			0
$145$	−3.61803	+	11.1352i	−0.300461	+	0.924725i
$146$	1.82709	+	0.813473i	0.151211	+	0.0673235i
$147$		0			0
$148$	0.373619	+	0.0794152i	0.0307113	+	0.00652789i
$149$	−14.6722	−	3.11868i	−1.20199	−	0.255492i	−0.436960	−	0.899481i	$-0.643945\pi$
$149$	−14.6722	−	3.11868i	−1.20199	−	0.255492i	−0.765035	+	0.643989i	$0.777278\pi$
$150$		0			0
$151$	1.82709	+	0.813473i	0.148687	+	0.0661995i	0.479731	−	0.877416i	$-0.340734\pi$
$151$	1.82709	+	0.813473i	0.148687	+	0.0661995i	−0.331044	+	0.943615i	$0.607401\pi$
$152$	4.04508	−	12.4495i	0.328100	−	1.00979i
$153$		0			0
$154$	5.64590	+	2.43690i	0.454959	+	0.196371i
$155$	3.73607	+	6.47106i	0.300088	+	0.519768i
$156$		0			0
$157$	0.387613	+	3.68789i	0.0309349	+	0.294326i	0.999041	+	0.0437851i	$0.0139417\pi$
$157$	0.387613	+	3.68789i	0.0309349	+	0.294326i	−0.968106	+	0.250541i	$0.919392\pi$
$158$	−5.34799	+	2.38108i	−0.425463	+	0.189428i
$159$		0			0
$160$	9.84171	−	10.9303i	0.778055	−	0.864118i
$161$	−8.42705	−	6.12261i	−0.664145	−	0.482529i
$162$		0			0
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	−0.443282	−	0.896382i	$-0.646186\pi$
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	0.885503	−	0.464634i	$-0.153814\pi$
$164$	−9.66312	−	16.7370i	−0.754563	−	1.30694i
$165$		0			0
$166$	0.218847	−	0.379054i	0.0169858	−	0.0294203i
$167$	6.71435	+	7.45704i	0.519572	+	0.577043i	0.944636	−	0.328120i	$-0.106415\pi$
$167$	6.71435	+	7.45704i	0.519572	+	0.577043i	−0.425064	+	0.905163i	$0.639748\pi$
$168$		0			0
$169$	1.03363	−	9.83437i	0.0795103	−	0.756490i
$170$	0.809017	+	2.48990i	0.0620488	+	0.190966i
$171$		0			0
$172$	8.16312	+	5.93085i	0.622432	+	0.452223i
$173$	14.0521	+	6.25641i	1.06836	+	0.475666i	0.864136	−	0.503258i	$-0.167865\pi$
$173$	14.0521	+	6.25641i	1.06836	+	0.475666i	0.204227	+	0.978924i	$0.434532\pi$
$174$		0			0
$175$	−2.78115	+	4.81710i	−0.210235	+	0.364138i
$176$	−1.96688	−	5.82632i	−0.148259	−	0.439176i
$177$		0			0
$178$	0.319109	−	0.0678287i	0.0239182	−	0.00508397i
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	−0.518123	−	0.855306i	$-0.673369\pi$
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	0.653335	+	0.757069i	$0.273369\pi$
$180$		0			0
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	−0.923930	−	0.382560i	$-0.875042\pi$
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	0.522612	−	0.852571i	$-0.324958\pi$
$182$	−2.18840	+	2.43046i	−0.162215	+	0.180158i
$183$		0			0
$184$	−0.811552	−	7.72140i	−0.0598284	−	0.569229i
$185$	−0.413545	−	0.459289i	−0.0304045	−	0.0337676i
$186$		0			0
$187$	5.26153	+	1.05576i	0.384761	+	0.0772051i
$188$	−2.61803			−0.190940
$189$		0			0
$190$	−7.66312	+	5.56758i	−0.555941	+	0.403915i
$191$	0.781051	−	7.43120i	0.0565149	−	0.537703i	−0.929235	−	0.369488i	$-0.879533\pi$
$191$	0.781051	−	7.43120i	0.0565149	−	0.537703i	0.985750	−	0.168215i	$-0.0538003\pi$
$192$		0			0
$193$	18.1567	+	3.85932i	1.30695	+	0.277800i	0.808179	−	0.588936i	$-0.200453\pi$
$193$	18.1567	+	3.85932i	1.30695	+	0.277800i	0.498767	+	0.866736i	$0.333786\pi$
$194$	7.92388	−	3.52794i	0.568901	−	0.253291i
$195$		0			0
$196$	3.16535	−	0.672816i	0.226097	−	0.0480583i
$197$	24.3820			1.73714			0.868572	−	0.495564i	$-0.165039\pi$
$197$	24.3820			1.73714			0.868572	+	0.495564i	$0.165039\pi$
$198$		0			0
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$	−4.05530	+	0.861981i	−0.286753	+	0.0609512i
$201$		0			0
$202$	1.69381	−	0.754131i	0.119176	−	0.0530605i
$203$	−13.1232	−	2.78943i	−0.921070	−	0.195779i
$204$		0			0
$205$	−3.26866	+	31.0992i	−0.228293	+	2.17206i
$206$	−3.00000	+	2.17963i	−0.209020	+	0.151862i
$207$		0			0
$208$	3.27051			0.226769
$209$	2.24974	+	19.2851i	0.155618	+	1.33398i
$210$		0			0
$211$	−14.9019	−	16.5502i	−1.02589	−	1.13936i	−0.990151	−	0.140002i	$-0.955289\pi$
$211$	−14.9019	−	16.5502i	−1.02589	−	1.13936i	−0.0357366	−	0.999361i	$-0.511378\pi$
$212$	−1.62670	−	15.4771i	−0.111722	−	1.06297i
$213$		0			0
$214$	1.75181	−	1.94558i	0.119751	−	0.132997i
$215$	−5.04508	−	15.5272i	−0.344072	−	1.05894i
$216$		0			0
$217$	−6.92705	+	5.03280i	−0.470239	+	0.341649i
$218$		0			0
$219$		0			0
$220$	−4.18875	+	13.4105i	−0.282405	+	0.904135i
$221$	−1.42705	+	2.47172i	−0.0959938	+	0.166266i
$222$		0			0
$223$	0.646976	+	0.288052i	0.0433247	+	0.0192894i	0.428285	−	0.903644i	$-0.359118\pi$
$223$	0.646976	+	0.288052i	0.0433247	+	0.0192894i	−0.384960	+	0.922933i	$0.625785\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$		0			0
$226$	−0.135255	−	0.416272i	−0.00899702	−	0.0276900i
$227$	2.60156	−	24.7522i	0.172672	−	1.64286i	−0.474312	−	0.880357i	$-0.657303\pi$
$227$	2.60156	−	24.7522i	0.172672	−	1.64286i	0.646983	−	0.762504i	$-0.276030\pi$
$228$		0			0
$229$	6.69131	+	7.43145i	0.442174	+	0.491084i	0.922495	−	0.386009i	$-0.126147\pi$
$229$	6.69131	+	7.43145i	0.442174	+	0.491084i	−0.480321	+	0.877093i	$0.659480\pi$
$230$	−2.80902	+	4.86536i	−0.185221	+	0.320812i
$231$		0			0
$232$	−5.00000	−	8.66025i	−0.328266	−	0.568574i
$233$	7.51722	−	23.1356i	0.492470	−	1.51567i	−0.328394	−	0.944541i	$-0.606507\pi$
$233$	7.51722	−	23.1356i	0.492470	−	1.51567i	0.820863	−	0.571124i	$-0.193493\pi$
$234$		0			0
$235$	3.42705	+	2.48990i	0.223556	+	0.162423i
$236$	−11.1800	+	12.4166i	−0.727754	+	0.808253i
$237$		0			0
$238$	−2.74064	+	1.22021i	−0.177649	+	0.0790945i
$239$	−0.267834	−	2.54827i	−0.0173247	−	0.164834i	0.982439	−	0.186586i	$-0.0597422\pi$
$239$	−0.267834	−	2.54827i	−0.0173247	−	0.164834i	−0.999763	+	0.0217520i	$0.993076\pi$
$240$		0			0
$241$	11.5623	+	20.0265i	0.744794	+	1.29002i	0.950291	+	0.311363i	$0.100785\pi$
$241$	11.5623	+	20.0265i	0.744794	+	1.29002i	−0.205498	+	0.978658i	$0.565881\pi$
$242$	−4.66312	−	4.94704i	−0.299757	−	0.318008i
$243$		0			0
$244$	−3.92705	+	12.0862i	−0.251404	+	0.773741i
$245$	−4.78339	−	2.12970i	−0.305599	−	0.136062i
$246$		0			0
$247$	−10.1006	−	2.14695i	−0.642685	−	0.136607i
$248$	−6.24250	−	1.32689i	−0.396399	−	0.0842573i
$249$		0			0
$250$	−4.65010	−	2.07036i	−0.294098	−	0.130941i
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	−0.997856	−	0.0654431i	$-0.979154\pi$
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	0.845749	+	0.533581i	$0.179154\pi$
$252$		0			0
$253$	5.87132	+	9.90659i	0.369127	+	0.622822i
$254$	−1.14590	−	1.98475i	−0.0719000	−	0.124535i
$255$		0			0
$256$	0.685948	+	6.52636i	0.0428717	+	0.407897i
$257$	−10.6645	+	4.74815i	−0.665234	+	0.296181i	−0.711436	−	0.702751i	$-0.751955\pi$
$257$	−10.6645	+	4.74815i	−0.665234	+	0.296181i	0.0462020	+	0.998932i	$0.485288\pi$
$258$		0			0
$259$	0.473881	−	0.526298i	0.0294455	−	0.0327026i
$260$	−6.04508	−	4.39201i	−0.374900	−	0.272381i
$261$		0			0
$262$	1.36475	−	4.20025i	0.0843142	−	0.259493i
$263$	8.16312	+	14.1389i	0.503359	+	0.871844i	0.999992	+	0.00388355i	$0.00123617\pi$
$263$	8.16312	+	14.1389i	0.503359	+	0.871844i	−0.496633	+	0.867961i	$0.665430\pi$
$264$		0			0
$265$	−12.5902	+	21.8068i	−0.773408	+	1.33958i
$266$	−7.26281	−	8.06617i	−0.445312	−	0.494569i
$267$		0			0
$268$	−1.61728	+	15.3874i	−0.0987910	+	0.939934i
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	0.984029	+	0.178006i	$0.0569645\pi$
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	−0.691467	+	0.722408i	$0.743035\pi$
$270$		0			0
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.999437	+	0.0335518i	$0.0106819\pi$
$271$	22.0623	+	16.0292i	1.34019	+	0.973705i	0.340753	+	0.940153i	$0.389318\pi$
$272$	2.74064	+	1.22021i	0.166175	+	0.0739861i
$273$		0			0
$274$	2.30902	−	3.99933i	0.139493	−	0.241609i
$275$	4.93336	−	3.67104i	0.297493	−	0.221372i
$276$		0			0
$277$	−29.8944	+	6.35426i	−1.79618	+	0.381791i	−0.980470	−	0.196667i	$-0.936988\pi$
$277$	−29.8944	+	6.35426i	−1.79618	+	0.381791i	−0.815713	+	0.578457i	$0.803655\pi$
$278$	−0.427051	+	0.310271i	−0.0256128	+	0.0186088i
$279$		0			0
$280$	−5.42705	−	16.7027i	−0.324328	−	0.998180i
$281$	−0.511170	+	0.567712i	−0.0304939	+	0.0338669i	−0.758199	−	0.652023i	$-0.773920\pi$
$281$	−0.511170	+	0.567712i	−0.0304939	+	0.0338669i	0.727705	+	0.685890i	$0.240587\pi$
$282$		0			0
$283$	−0.0188507	−	0.179352i	−0.00112055	−	0.0106614i	0.993947	−	0.109858i	$-0.0350395\pi$
$283$	−0.0188507	−	0.179352i	−0.00112055	−	0.0106614i	−0.995068	+	0.0991963i	$0.968373\pi$
$284$	6.02218	+	6.68830i	0.357350	+	0.396878i
$285$		0			0
$286$	3.28609	−	1.50823i	0.194311	−	0.0891836i
$287$	−35.8328			−2.11514
$288$		0			0
$289$	11.6353	−	8.45351i	0.684427	−	0.497265i
$290$	−0.756375	+	7.19643i	−0.0444159	+	0.422589i
$291$		0			0
$292$	−5.12165	−	1.08864i	−0.299722	−	0.0637078i
$293$	0.0509101	−	0.0226667i	0.00297420	−	0.00132420i	−0.405249	−	0.914206i	$-0.632815\pi$
$293$	0.0509101	−	0.0226667i	0.00297420	−	0.00132420i	0.408223	+	0.912882i	$0.366149\pi$
$294$		0			0
$295$	26.4437	−	5.62078i	1.53961	−	0.327254i
$296$	0.527864			0.0306815
$297$		0			0
$298$	−9.27051			−0.537026
$299$	−5.99077	+	1.27338i	−0.346455	+	0.0736414i
$300$		0			0
$301$	17.0908	−	7.60931i	0.985097	−	0.438593i
$302$	1.20906	+	0.256993i	0.0695734	+	0.0147883i
$303$		0			0
$304$	−1.13456	+	10.7946i	−0.0650716	+	0.619115i
$305$	16.6353	−	12.0862i	0.952532	−	0.692055i
$306$		0			0
$307$	0.562306			0.0320925			0.0160462	−	0.999871i	$-0.494892\pi$
$307$	0.562306			0.0320925			0.0160462	+	0.999871i	$0.494892\pi$
$308$	−15.7846	−	3.16729i	−0.899411	−	0.180473i
$309$		0			0
$310$	3.09007	+	3.43187i	0.175504	+	0.194917i
$311$	−0.264234	−	2.51402i	−0.0149833	−	0.142557i	0.984473	−	0.175538i	$-0.0561665\pi$
$311$	−0.264234	−	2.51402i	−0.0149833	−	0.142557i	−0.999456	+	0.0329813i	$0.989500\pi$
$312$		0			0
$313$	17.2855	−	19.1975i	0.977036	−	1.08511i	−0.0193200	−	0.999813i	$-0.506150\pi$
$313$	17.2855	−	19.1975i	0.977036	−	1.08511i	0.996356	−	0.0852948i	$-0.0271832\pi$
$314$	0.708204	+	2.17963i	0.0399663	+	0.123004i
$315$		0			0
$316$	12.3992	−	9.00854i	0.697509	−	0.506770i
$317$	18.9376	−	4.02531i	1.06364	−	0.226084i	0.357325	−	0.933980i	$-0.383689\pi$
$317$	18.9376	−	4.02531i	1.06364	−	0.226084i	0.706317	+	0.707896i	$0.250355\pi$
$318$		0			0
$319$	12.0984	+	8.58076i	0.677379	+	0.480430i
$320$	−0.309017	+	0.535233i	−0.0172746	+	0.0299204i
$321$		0			0
$322$	−5.88113	−	2.61845i	−0.327742	−	0.145920i
$323$	−7.66312	−	5.56758i	−0.426387	−	0.309789i
$324$		0			0
$325$	1.01064	+	3.11044i	0.0560604	+	0.172536i
$326$	1.18031	−	11.2299i	0.0653716	−	0.621969i
$327$		0			0
$328$	−17.8713	−	19.8481i	−0.986776	−	1.09593i
$329$	−2.42705	+	4.20378i	−0.133808	+	0.231762i
$330$		0			0
$331$	−13.2984	−	23.0335i	−0.730945	−	1.26603i	−0.956480	−	0.291798i	$-0.905746\pi$
$331$	−13.2984	−	23.0335i	−0.730945	−	1.26603i	0.225535	−	0.974235i	$-0.427587\pi$
$332$	−0.354102	+	1.08981i	−0.0194339	+	0.0598113i
$333$		0			0
$334$	5.01722	+	3.64522i	0.274530	+	0.199458i
$335$	16.7513	−	18.6042i	0.915222	−	1.01646i
$336$		0			0
$337$	−0.266569	+	0.118684i	−0.0145209	+	0.00646514i	−0.413984	−	0.910284i	$-0.635863\pi$
$337$	−0.266569	+	0.118684i	−0.0145209	+	0.00646514i	0.399463	+	0.916749i	$0.369196\pi$
$338$	−0.638821	−	6.07798i	−0.0347473	−	0.330598i
$339$		0			0
$340$	−3.42705	−	5.93583i	−0.185858	−	0.321915i
$341$	9.23607	−	2.07363i	0.500161	−	0.112293i
$342$		0			0
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	12.7387	+	5.67165i	0.686826	+	0.305795i
$345$		0			0
$346$	9.29884	+	1.97653i	0.499909	+	0.106259i
$347$	20.4866	+	4.35456i	1.09978	+	0.233765i	0.721836	−	0.692064i	$-0.243299\pi$
$347$	20.4866	+	4.35456i	1.09978	+	0.233765i	0.377942	+	0.925829i	$0.376632\pi$
$348$		0			0
$349$	−9.24929	−	4.11805i	−0.495103	−	0.220434i	0.143967	−	0.989582i	$-0.454014\pi$
$349$	−9.24929	−	4.11805i	−0.495103	−	0.220434i	−0.639070	+	0.769148i	$0.720681\pi$
$350$	−1.06231	+	3.26944i	−0.0567826	+	0.174759i
$351$		0			0
$352$	−9.50000	−	16.0292i	−0.506352	−	0.854359i
$353$	5.23607	+	9.06914i	0.278688	+	0.482701i	0.971059	−	0.238840i	$-0.0767672\pi$
$353$	5.23607	+	9.06914i	0.278688	+	0.482701i	−0.692371	+	0.721542i	$0.743434\pi$
$354$		0			0
$355$	−1.52218	−	14.4825i	−0.0807887	−	0.768653i
$356$	−0.780261	+	0.347395i	−0.0413537	+	0.0184119i
$357$		0			0
$358$	0.924716	−	1.02700i	0.0488727	−	0.0542787i
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	0.825938	−	0.563761i	$-0.190646\pi$
$359$	10.3262	+	7.50245i	0.544998	+	0.395964i	−0.280940	+	0.959725i	$0.590646\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	−5.39919	−	9.35167i	−0.283775	−	0.491513i
$363$		0			0
$364$	4.28115	−	7.41517i	0.224393	−	0.388661i
$365$	5.66897	+	6.29602i	0.296727	+	0.329549i
$366$		0			0
$367$	−0.581419	+	5.53184i	−0.0303498	+	0.288759i	0.968811	+	0.247801i	$0.0797079\pi$
$367$	−0.581419	+	5.53184i	−0.0303498	+	0.288759i	−0.999161	+	0.0409586i	$0.986959\pi$
$368$	1.98936	+	6.12261i	0.103702	+	0.319163i
$369$		0			0
$370$	−0.309017	−	0.224514i	−0.0160650	−	0.0116719i
$371$	−26.3595	−	11.7360i	−1.36852	−	0.609304i
$372$		0			0
$373$	2.20820	−	3.82472i	0.114336	−	0.198037i	−0.803178	−	0.595739i	$-0.796859\pi$
$373$	2.20820	−	3.82472i	0.114336	−	0.198037i	0.917514	+	0.397703i	$0.130192\pi$
$374$	3.31641	−	0.0378495i	0.171487	−	0.00195715i
$375$		0			0
$376$	−3.53897	+	0.752232i	−0.182509	+	0.0387934i
$377$	−6.38197	+	4.63677i	−0.328688	+	0.238806i
$378$		0			0
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	0.962838	−	0.270080i	$-0.0870502\pi$
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	−0.937701	+	0.347443i	$0.887050\pi$
$380$	16.5934	−	18.4288i	0.851221	−	0.945377i
$381$		0			0
$382$	−0.482716	−	4.59274i	−0.0246979	−	0.234985i
$383$	17.9919	+	19.9821i	0.919346	+	1.02104i	0.999705	+	0.0242708i	$0.00772639\pi$
$383$	17.9919	+	19.9821i	0.919346	+	1.02104i	−0.0803598	+	0.996766i	$0.525607\pi$
$384$		0			0
$385$	17.6500	+	19.1581i	0.899529	+	0.976386i
$386$	11.4721			0.583916
$387$		0			0
$388$	−18.3713	+	13.3475i	−0.932663	+	0.677619i
$389$	−2.53696	+	24.1376i	−0.128629	+	1.22382i	0.719674	+	0.694312i	$0.244291\pi$
$389$	−2.53696	+	24.1376i	−0.128629	+	1.22382i	−0.848303	+	0.529511i	$0.822376\pi$
$390$		0			0
$391$	−5.49527	−	1.16805i	−0.277908	−	0.0590711i
$392$	4.08550	−	1.81898i	0.206349	−	0.0918724i
$393$		0			0
$394$	14.7396	−	3.13300i	0.742570	−	0.157838i
$395$	−24.7984			−1.24774
$396$		0			0
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$	−10.1006	+	2.14695i	−0.506297	+	0.107617i
$399$		0			0
$400$	3.14049	−	1.39824i	0.157024	−	0.0699118i
$401$	25.5200	+	5.42445i	1.27441	+	0.270884i	0.794947	−	0.606678i	$-0.207498\pi$
$401$	25.5200	+	5.42445i	1.27441	+	0.270884i	0.479462	+	0.877562i	$0.340832\pi$
$402$		0			0
$403$	−0.526242	+	5.00686i	−0.0262140	+	0.249410i
$404$	−3.92705	+	2.85317i	−0.195378	+	0.141950i
$405$		0			0
$406$	−8.29180			−0.411515
$407$	−0.711579	+	0.326596i	−0.0352716	+	0.0161888i
$408$		0			0
$409$	−7.39773	−	8.21601i	−0.365794	−	0.406255i	0.531948	−	0.846777i	$-0.321460\pi$
$409$	−7.39773	−	8.21601i	−0.365794	−	0.406255i	−0.897742	+	0.440522i	$0.854794\pi$
$410$	2.02014	+	19.2204i	0.0997677	+	0.949226i
$411$		0			0
$412$	6.49606	−	7.21460i	0.320038	−	0.355438i
$413$	9.57295	+	29.4625i	0.471054	+	1.44976i
$414$		0			0
$415$	1.50000	−	1.08981i	0.0736321	−	0.0534969i
$416$	9.69328	−	2.06037i	0.475252	−	0.101018i
$417$		0			0
$418$	3.83810	+	11.3693i	0.187727	+	0.556090i
$419$	−8.25329	+	14.2951i	−0.403200	+	0.698362i	−0.994110	−	0.108375i	$-0.965435\pi$
$419$	−8.25329	+	14.2951i	−0.403200	+	0.698362i	0.590911	+	0.806737i	$0.298769\pi$
$420$		0			0
$421$	−34.0483	−	15.1593i	−1.65941	−	0.738818i	−0.659496	−	0.751708i	$-0.729230\pi$
$421$	−34.0483	−	15.1593i	−1.65941	−	0.738818i	−0.999917	+	0.0128899i	$0.995897\pi$
$422$	−11.1353	−	8.09024i	−0.542056	−	0.393827i
$423$		0			0
$424$	−6.64590	−	20.4540i	−0.322753	−	0.993333i
$425$	−0.313585	+	2.98357i	−0.0152111	+	0.144724i
$426$		0			0
$427$	15.7663	+	17.5102i	0.762983	+	0.847378i
$428$	−3.42705	+	5.93583i	−0.165653	+	0.286919i
$429$		0			0
$430$	−5.04508	−	8.73834i	−0.243296	−	0.421400i
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.00138127	+	0.999999i	$0.500440\pi$
$431$	−12.2082	+	37.5730i	−0.588048	+	1.80983i	−0.586667	+	0.809828i	$0.699560\pi$
$432$		0			0
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$	−3.54090	+	3.93257i	−0.169969	+	0.188769i
$435$		0			0
$436$		0			0
$437$	−2.12467	−	20.2149i	−0.101637	−	0.967009i
$438$		0			0
$439$	−1.64590	−	2.85078i	−0.0785544	−	0.136060i	0.824072	−	0.566485i	$-0.191697\pi$
$439$	−1.64590	−	2.85078i	−0.0785544	−	0.136060i	−0.902626	+	0.430425i	$0.858364\pi$
$440$	−1.80902	+	19.3314i	−0.0862415	+	0.921588i
$441$		0			0
$442$	−0.545085	+	1.67760i	−0.0259270	+	0.0797952i
$443$	−37.5692	−	16.7269i	−1.78497	−	0.794718i	−0.979319	−	0.202324i	$-0.935151\pi$
$443$	−37.5692	−	16.7269i	−1.78497	−	0.794718i	−0.805648	−	0.592395i	$-0.798183\pi$
$444$		0			0
$445$	1.35177	+	0.287327i	0.0640799	+	0.0136206i
$446$	0.428129	+	0.0910017i	0.0202725	+	0.00430906i
$447$		0			0
$448$	−0.646976	−	0.288052i	−0.0305668	−	0.0136092i
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	0.598020	+	0.801481i	$0.295954\pi$
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	−0.954907	+	0.296905i	$0.904046\pi$
$450$		0			0
$451$	36.3713	+	15.6987i	1.71266	+	0.739222i
$452$	0.572949	+	0.992377i	0.0269493	+	0.0466775i
$453$		0			0
$454$	−1.60785	−	15.2977i	−0.0754603	−	0.717957i
$455$	−12.6564	+	5.63497i	−0.593339	+	0.264172i
$456$		0			0
$457$	5.48796	−	6.09500i	0.256716	−	0.285112i	−0.600986	−	0.799260i	$-0.705225\pi$
$457$	5.48796	−	6.09500i	0.256716	−	0.285112i	0.857702	+	0.514148i	$0.171892\pi$
$458$	5.00000	+	3.63271i	0.233635	+	0.169746i
$459$		0			0
$460$	4.54508	−	13.9883i	0.211916	−	0.652209i
$461$	10.5451	+	18.2646i	0.491134	+	0.850668i	0.999948	−	0.0102080i	$-0.00324936\pi$
$461$	10.5451	+	18.2646i	0.491134	+	0.850668i	−0.508814	+	0.860876i	$0.669916\pi$
$462$		0			0
$463$	7.89919	−	13.6818i	0.367106	−	0.635847i	−0.622005	−	0.783013i	$-0.713682\pi$
$463$	7.89919	−	13.6818i	0.367106	−	0.635847i	0.989112	+	0.147166i	$0.0470152\pi$
$464$	5.54829	+	6.16201i	0.257573	+	0.286064i
$465$		0			0
$466$	1.57153	−	14.9521i	0.0727996	−	0.692642i
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	0.856660	−	0.515882i	$-0.172536\pi$
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	−0.996280	+	0.0861747i	$0.972536\pi$
$468$		0			0
$469$	23.2082	+	16.8617i	1.07166	+	0.778603i
$470$	2.39169	+	1.06485i	0.110321	+	0.0491179i
$471$		0			0
$472$	−11.5451	+	19.9967i	−0.531406	+	0.920422i
$473$	−20.6814	+	0.236032i	−0.950930	+	0.0108528i
$474$		0			0
$475$	−10.6169	+	2.25669i	−0.487137	+	0.103544i
$476$	6.35410	−	4.61653i	0.291240	−	0.211598i
$477$		0			0
$478$	−0.489357	−	1.50609i	−0.0223827	−	0.0688868i
$479$	−18.7960	+	20.8751i	−0.858811	+	0.953806i	−0.999342	−	0.0362702i	$-0.988452\pi$
$479$	−18.7960	+	20.8751i	−0.858811	+	0.953806i	0.140531	+	0.990076i	$0.455119\pi$
$480$		0			0
$481$	−0.0435265	−	0.414127i	−0.00198464	−	0.0188826i
$482$	9.56308	+	10.6209i	0.435586	+	0.483768i
$483$		0			0
$484$	14.6342	+	10.1303i	0.665191	+	0.460467i
$485$	36.7426			1.66840
$486$		0			0
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	−0.851736	−	0.523972i	$-0.824450\pi$
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	0.235126	+	0.971965i	$0.424450\pi$
$488$	−1.83576	+	17.4661i	−0.0831010	+	0.790653i
$489$		0			0
$490$	−3.16535	−	0.672816i	−0.142996	−	0.0303947i
$491$	23.0348	−	10.2558i	1.03955	−	0.462837i	0.185289	−	0.982684i	$-0.440678\pi$
$491$	23.0348	−	10.2558i	1.03955	−	0.462837i	0.854259	+	0.519847i	$0.174011\pi$
$492$		0			0
$493$	−7.07794	+	1.50446i	−0.318774	+	0.0677576i
$494$	−6.38197			−0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	16.3223	−	3.46941i	0.732154	−	0.155624i
$498$		0			0
$499$	−16.0440	+	7.14323i	−0.718227	+	0.319775i	−0.733106	−	0.680114i	$-0.761930\pi$
$499$	−16.0440	+	7.14323i	−0.718227	+	0.319775i	0.0148796	+	0.999889i	$0.495263\pi$
$500$	13.0350	+	2.77068i	0.582944	+	0.123909i
$501$		0			0
$502$	−0.503792	+	4.79326i	−0.0224853	+	0.213934i
$503$	−22.7082	+	16.4985i	−1.01251	+	0.735631i	−0.964734	−	0.263227i	$-0.915213\pi$
$503$	−22.7082	+	16.4985i	−1.01251	+	0.735631i	−0.0477750	+	0.998858i	$0.515213\pi$
$504$		0			0
$505$	7.85410			0.349503
$506$	4.82234	+	5.23437i	0.214379	+	0.232696i
$507$		0			0
$508$	4.01478	+	4.45887i	0.178127	+	0.197830i
$509$	−2.46876	−	23.4887i	−0.109426	−	1.04112i	−0.902117	−	0.431492i	$-0.857987\pi$
$509$	−2.46876	−	23.4887i	−0.109426	−	1.04112i	0.792691	−	0.609624i	$-0.208679\pi$
$510$		0			0
$511$	−6.49606	+	7.21460i	−0.287369	+	0.319155i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$		0			0
$514$	−5.83688	+	4.24074i	−0.257454	+	0.187051i
$515$	−15.3649	+	3.26592i	−0.677060	+	0.143914i
$516$		0			0
$517$	4.30524	−	3.20364i	0.189344	−	0.140896i
$518$	0.218847	−	0.379054i	0.00961559	−	0.0166547i
$519$		0			0
$520$	−9.43349	−	4.20006i	−0.413686	−	0.184185i
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	0.818758	−	0.574139i	$-0.194663\pi$
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	−0.293028	+	0.956104i	$0.594663\pi$
$522$		0			0
$523$	−3.70163	−	11.3924i	−0.161861	−	0.498156i	0.836930	−	0.547309i	$-0.184348\pi$
$523$	−3.70163	−	11.3924i	−0.161861	−	0.498156i	−0.998791	+	0.0491529i	$0.984348\pi$
$524$	−1.20859	+	11.4990i	−0.0527975	+	0.502335i
$525$		0			0
$526$	6.75164	+	7.49846i	0.294386	+	0.326948i
$527$	−2.30902	+	3.99933i	−0.100582	+	0.174214i
$528$		0			0
$529$	5.47214	+	9.47802i	0.237919	+	0.412088i
$530$	−4.80902	+	14.8006i	−0.208890	+	0.642898i
$531$		0			0
$532$	22.9894	+	16.7027i	0.996715	+	0.724156i
$533$	−14.0978	+	15.6572i	−0.610645	+	0.678190i
$534$		0			0
$535$	10.1314	−	4.51078i	0.438018	−	0.195018i
$536$	2.23502	+	21.2648i	0.0965383	+	0.918501i
$537$		0			0
$538$	4.79837	+	8.31103i	0.206873	+	0.358314i
$539$	−4.38197	+	4.97980i	−0.188745	+	0.214495i
$540$		0			0
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	−0.732926	−	0.680308i	$-0.761846\pi$
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	0.992825	−	0.119577i	$-0.0381540\pi$
$542$	15.3970	+	6.85518i	0.661357	+	0.294455i
$543$		0			0
$544$	8.89153	+	1.88995i	0.381221	+	0.0810310i
$545$		0			0
$546$		0			0
$547$	19.7491	+	8.79285i	0.844409	+	0.375955i	0.782897	−	0.622151i	$-0.213741\pi$
$547$	19.7491	+	8.79285i	0.844409	+	0.375955i	0.0615117	+	0.998106i	$0.480408\pi$
$548$	−3.73607	+	11.4984i	−0.159597	+	0.491189i
$549$		0			0
$550$	2.51064	−	2.85317i	0.107054	−	0.121660i
$551$	−13.0902	−	22.6728i	−0.557660	−	0.965895i
$552$		0			0
$553$	−2.97032	−	28.2607i	−0.126311	−	1.20177i
$554$	−17.2555	+	7.68266i	−0.733118	+	0.326405i
$555$		0			0
$556$	0.924716	−	1.02700i	0.0392167	−	0.0435545i
$557$	−12.0623	−	8.76378i	−0.511096	−	0.371333i	0.302143	−	0.953263i	$-0.402298\pi$
$557$	−12.0623	−	8.76378i	−0.511096	−	0.371333i	−0.813239	+	0.581929i	$0.802298\pi$
$558$		0			0
$559$	3.39919	−	10.4616i	0.143770	−	0.442479i
$560$	7.28115	+	12.6113i	0.307685	+	0.532926i
$561$		0			0
$562$	−0.236068	+	0.408882i	−0.00995793	+	0.0172476i
$563$	−5.94760	−	6.60548i	−0.250661	−	0.278388i	0.604662	−	0.796482i	$-0.293308\pi$
$563$	−5.94760	−	6.60548i	−0.250661	−	0.278388i	−0.855323	+	0.518095i	$0.826642\pi$
$564$		0			0
$565$	0.193806	−	1.84395i	0.00815350	−	0.0775753i
$566$	−0.0344419	−	0.106001i	−0.00144770	−	0.00445556i
$567$		0			0
$568$	10.0623	+	7.31069i	0.422205	+	0.306750i
$569$	−21.9880	−	9.78970i	−0.921786	−	0.410405i	−0.109714	−	0.993963i	$-0.534994\pi$
$569$	−21.9880	−	9.78970i	−0.921786	−	0.410405i	−0.812072	+	0.583558i	$0.801660\pi$
$570$		0			0
$571$	−17.3435	+	30.0398i	−0.725801	+	1.25712i	0.232842	+	0.972515i	$0.425197\pi$
$571$	−17.3435	+	30.0398i	−0.725801	+	1.25712i	−0.958643	+	0.284610i	$0.908136\pi$
$572$	−7.59415	+	5.65100i	−0.317527	+	0.236280i
$573$		0			0
$574$	−21.6620	+	4.60439i	−0.904153	+	0.192184i
$575$	−5.20820	+	3.78398i	−0.217197	+	0.157803i
$576$		0			0
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	0.996114	−	0.0880726i	$-0.0280707\pi$
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	−0.857641	+	0.514249i	$0.828071\pi$
$578$	5.94760	−	6.60548i	0.247387	−	0.274752i
$579$		0			0
$580$	−1.98022	−	18.8405i	−0.0822240	−	0.782309i
$581$	1.42164	+	1.57889i	0.0589797	+	0.0655036i
$582$		0			0
$583$	21.6140	+	23.4607i	0.895161	+	0.971645i
$584$	−7.23607			−0.299431
$585$		0			0
$586$	0.0278640	−	0.0202444i	0.00115105	−	0.000836289i
$587$	4.00396	−	38.0951i	0.165261	−	1.57235i	−0.526467	−	0.850196i	$-0.676484\pi$
$587$	4.00396	−	38.0951i	0.165261	−	1.57235i	0.691728	−	0.722158i	$-0.256850\pi$
$588$		0			0
$589$	−16.3431	−	3.47383i	−0.673405	−	0.143137i
$590$	15.2637	−	6.79584i	0.628397	−	0.279780i
$591$		0			0
$592$	−0.428129	+	0.0910017i	−0.0175960	+	0.00374015i
$593$	22.2148			0.912252			0.456126	−	0.889915i	$-0.349237\pi$
$593$	22.2148			0.912252			0.456126	+	0.889915i	$0.349237\pi$
$594$		0			0
$595$	−12.7082			−0.520986
$596$	23.7401	−	5.04612i	0.972434	−	0.206697i
$597$		0			0
$598$	−3.45797	+	1.53959i	−0.141407	+	0.0629584i
$599$	8.11060	+	1.72396i	0.331390	+	0.0704392i	0.370602	−	0.928792i	$-0.379151\pi$
$599$	8.11060	+	1.72396i	0.331390	+	0.0704392i	−0.0392119	+	0.999231i	$0.512485\pi$
$600$		0			0
$601$	−3.53649	+	33.6475i	−0.144257	+	1.37251i	0.647683	+	0.761910i	$0.275738\pi$
$601$	−3.53649	+	33.6475i	−0.144257	+	1.37251i	−0.791940	+	0.610599i	$0.790929\pi$
$602$	9.35410	−	6.79615i	0.381245	−	0.276991i
$603$		0			0
$604$	−3.23607			−0.131674
$605$	−9.52195	−	27.1786i	−0.387122	−	1.10497i
$606$		0			0
$607$	8.91699	+	9.90332i	0.361930	+	0.401964i	0.896416	−	0.443213i	$-0.146162\pi$
$607$	8.91699	+	9.90332i	0.361930	+	0.401964i	−0.534486	+	0.845177i	$0.679495\pi$
$608$	3.43779	+	32.7084i	0.139421	+	1.32650i
$609$		0			0
$610$	8.50345	−	9.44404i	0.344295	−	0.382378i
$611$	0.881966	+	2.71441i	0.0356805	+	0.109813i
$612$		0			0
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.986028	−	0.166580i	$-0.946728\pi$
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.146272	+	0.989244i	$0.546728\pi$
$614$	0.339930	−	0.0722543i	0.0137185	−	0.00291595i
$615$		0			0
$616$	−22.2471	+	0.253902i	−0.896363	+	0.0102300i
$617$	−9.79180	+	16.9599i	−0.394203	+	0.682779i	−0.992999	−	0.118122i	$-0.962313\pi$
$617$	−9.79180	+	16.9599i	−0.394203	+	0.682779i	0.598796	+	0.800901i	$0.295646\pi$
$618$		0			0
$619$	−8.05716	−	3.58728i	−0.323845	−	0.144185i	0.238374	−	0.971173i	$-0.423386\pi$
$619$	−8.05716	−	3.58728i	−0.323845	−	0.144185i	−0.562219	+	0.826988i	$0.690052\pi$
$620$	−9.78115	−	7.10642i	−0.392821	−	0.285401i
$621$		0			0
$622$	−0.482779	−	1.48584i	−0.0193577	−	0.0595768i
$623$	−0.165530	+	1.57492i	−0.00663184	+	0.0630977i
$624$		0			0
$625$	−20.6312	−	22.9132i	−0.825247	−	0.916530i
$626$	7.98278	−	13.8266i	0.319056	−	0.552621i
$627$		0			0
$628$	−3.00000	−	5.19615i	−0.119713	−	0.207349i
$629$	0.118034	−	0.363271i	0.00470632	−	0.0144846i
$630$		0			0
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.974084	−	0.226187i	$-0.927374\pi$
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.516125	−	0.856513i	$-0.672626\pi$
$632$	14.1724	−	15.7401i	0.563748	−	0.626106i
$633$		0			0
$634$	10.9311	−	4.86683i	0.434129	−	0.193287i
$635$	−1.01478	−	9.65502i	−0.0402705	−	0.383148i
$636$		0			0
$637$	−1.76393	−	3.05522i	−0.0698895	−	0.121052i
$638$	8.41641	+	3.63271i	0.333209	+	0.143820i
$639$		0			0
$640$	−9.20820	+	28.3399i	−0.363986	+	1.12023i
$641$	32.6525	+	14.5378i	1.28970	+	0.574210i	0.932955	−	0.359993i	$-0.117221\pi$
$641$	32.6525	+	14.5378i	1.28970	+	0.574210i	0.356742	+	0.934203i	$0.383887\pi$
$642$		0			0
$643$	37.7196	+	8.01755i	1.48752	+	0.316181i	0.878794	−	0.477201i	$-0.158349\pi$
$643$	37.7196	+	8.01755i	1.48752	+	0.316181i	0.608723	+	0.793383i	$0.291682\pi$
$644$	16.4858	+	3.50416i	0.649632	+	0.138083i
$645$		0			0
$646$	−5.34799	−	2.38108i	−0.210414	−	0.0936823i
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	−0.627655	−	0.778492i	$-0.715985\pi$
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	0.965369	−	0.260887i	$-0.0840149\pi$
$648$		0			0
$649$	3.19098	−	34.0993i	0.125257	−	1.33851i
$650$	1.01064	+	1.75049i	0.0396407	+	0.0686597i
$651$		0			0
$652$	3.09010	+	29.4004i	0.121018	+	1.15141i
$653$	46.6223	−	20.7576i	1.82447	−	0.812307i	0.890461	−	0.455059i	$-0.150382\pi$
$653$	46.6223	−	20.7576i	1.82447	−	0.812307i	0.934010	−	0.357248i	$-0.116285\pi$
$654$		0			0
$655$	12.5182	−	13.9029i	0.489128	−	0.543231i
$656$	17.9164	+	13.0170i	0.699518	+	0.508230i
$657$		0			0
$658$	−0.927051	+	2.85317i	−0.0361402	+	0.111228i
$659$	5.32624	+	9.22531i	0.207481	+	0.359367i	0.950920	−	0.309436i	$-0.100140\pi$
$659$	5.32624	+	9.22531i	0.207481	+	0.359367i	−0.743440	+	0.668803i	$0.766807\pi$
$660$		0			0
$661$	4.95492	−	8.58216i	0.192724	−	0.333808i	−0.753428	−	0.657530i	$-0.771601\pi$
$661$	4.95492	−	8.58216i	0.192724	−	0.333808i	0.946152	+	0.323723i	$0.104935\pi$
$662$	−10.9990	−	12.2156i	−0.427487	−	0.474772i
$663$		0			0
$664$	−0.165530	+	1.57492i	−0.00642383	+	0.0611186i
$665$	−14.2082	−	43.7284i	−0.550971	−	1.69571i
$666$		0			0
$667$	−12.5623	−	9.12705i	−0.486414	−	0.353401i
$668$	−14.8324	−	6.60380i	−0.573882	−	0.255509i
$669$		0			0
$670$	7.73607	−	13.3993i	0.298870	−	0.517659i
$671$	−8.33182	−	24.6807i	−0.321646	−	0.952788i
$672$		0			0
$673$	−12.1451	+	2.58152i	−0.468158	+	0.0995101i	−0.435950	−	0.899971i	$-0.643587\pi$
$673$	−12.1451	+	2.58152i	−0.468158	+	0.0995101i	−0.0322087	+	0.999481i	$0.510254\pi$
$674$	−0.145898	+	0.106001i	−0.00561978	+	0.00408301i
$675$		0			0
$676$	4.94427	+	15.2169i	0.190164	+	0.585266i
$677$	9.05191	−	10.0532i	0.347893	−	0.386374i	−0.543649	−	0.839313i	$-0.682958\pi$
$677$	9.05191	−	10.0532i	0.347893	−	0.386374i	0.891542	+	0.452938i	$0.149624\pi$
$678$		0			0
$679$	4.40100	+	41.8727i	0.168895	+	1.60693i
$680$	−6.33810	−	7.03917i	−0.243055	−	0.269940i
$681$		0			0
$682$	5.31701	−	2.44037i	0.203599	−	0.0934465i
$683$	−3.11146			−0.119057			−0.0595283	−	0.998227i	$-0.518960\pi$
$683$	−3.11146			−0.119057			−0.0595283	+	0.998227i	$0.518960\pi$
$684$		0			0
$685$	15.8262	−	11.4984i	0.604689	−	0.439333i
$686$	−0.969032	+	9.21973i	−0.0369978	+	0.352011i
$687$		0			0
$688$	−11.3096	−	2.40394i	−0.431176	−	0.0916493i
$689$	−15.4988	+	6.90051i	−0.590458	+	0.262889i
$690$		0			0
$691$	25.7173	−	5.46637i	0.978331	−	0.207951i	0.309120	−	0.951023i	$-0.399966\pi$
$691$	25.7173	−	5.46637i	0.978331	−	0.207951i	0.669211	+	0.743073i	$0.266632\pi$
$692$	−24.8885			−0.946120
$693$		0			0
$694$	12.9443			0.491358
$695$	−2.18720	+	0.464905i	−0.0829654	+	0.0176348i
$696$		0			0
$697$	−17.6554	+	7.86069i	−0.668746	+	0.297745i
$698$	−6.12062	−	1.30098i	−0.231669	−	0.0492427i
$699$		0			0
$700$	0.940756	−	8.95070i	0.0355572	−	0.338305i
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	−0.412415	−	0.910996i	$-0.635315\pi$
$701$	8.64590	−	6.28161i	0.326551	−	0.237253i	0.738966	+	0.673743i	$0.235315\pi$
$702$		0			0
$703$	1.38197			0.0521218
$704$	0.530501	+	0.575828i	0.0199940	+	0.0217023i
$705$		0			0
$706$	4.33070	+	4.80973i	0.162988	+	0.181017i
$707$	0.940756	+	8.95070i	0.0353808	+	0.336626i
$708$		0			0
$709$	32.6152	−	36.2228i	1.22489	−	1.36038i	0.313100	−	0.949720i	$-0.398633\pi$
$709$	32.6152	−	36.2228i	1.22489	−	1.36038i	0.911790	−	0.410657i	$-0.134701\pi$
$710$	−2.78115	−	8.55951i	−0.104375	−	0.321233i
$711$		0			0
$712$	−0.954915	+	0.693786i	−0.0357870	+	0.0260007i
$713$	−9.69328	+	2.06037i	−0.363016	+	0.0771614i
$714$		0			0
$715$	15.3153	−	0.174790i	0.572759	−	0.00653678i
$716$	−1.80902	+	3.13331i	−0.0676061	+	0.117097i
$717$		0			0
$718$	7.20654	+	3.20856i	0.268946	+	0.119742i
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	0.611418	−	0.791307i	$-0.290599\pi$
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	−0.563639	+	0.826021i	$0.690599\pi$
$720$		0			0
$721$	−5.56231	−	17.1190i	−0.207151	−	0.637546i
$722$	0.986508	−	9.38599i	0.0367140	−	0.349311i
$723$		0			0
$724$	18.9167	+	21.0091i	0.703032	+	0.780796i
$725$	−4.14590	+	7.18091i	−0.153975	+	0.266692i
$726$		0			0
$727$	−19.4271	−	33.6486i	−0.720509	−	1.24796i	−0.960796	−	0.277257i	$-0.910575\pi$
$727$	−19.4271	−	33.6486i	−0.720509	−	1.24796i	0.240286	−	0.970702i	$-0.422759\pi$
$728$	3.65654	−	11.2537i	0.135520	−	0.417089i
$729$		0			0
$730$	4.23607	+	3.07768i	0.156784	+	0.113910i
$731$	6.75164	−	7.49846i	0.249718	−	0.277340i
$732$		0			0
$733$	−34.4482	+	15.3373i	−1.27237	+	0.566496i	−0.928085	−	0.372368i	$-0.878546\pi$
$733$	−34.4482	+	15.3373i	−1.27237	+	0.566496i	−0.344287	+	0.938865i	$0.611879\pi$
$734$	0.359337	+	3.41886i	0.0132634	+	0.126193i
$735$		0			0
$736$	9.75329	+	16.8932i	0.359511	+	0.622691i
$737$	−16.1697	−	27.2829i	−0.595618	−	1.00498i
$738$		0			0
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	0.702458	+	0.711726i	$0.252086\pi$
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	−0.986642	+	0.162904i	$0.947914\pi$
$740$	0.913545	+	0.406737i	0.0335826	+	0.0149519i
$741$		0			0
$742$	−17.4431	−	3.70765i	−0.640357	−	0.136112i
$743$	−34.4116	−	7.31440i	−1.26244	−	0.268339i	−0.472393	−	0.881388i	$-0.656610\pi$
$743$	−34.4116	−	7.31440i	−1.26244	−	0.268339i	−0.790045	+	0.613049i	$0.789943\pi$
$744$		0			0
$745$	−35.8754	−	15.9728i	−1.31437	−	0.585196i
$746$	0.843459	−	2.59590i	0.0308812	−	0.0950426i
$747$		0			0
$748$	−8.47214	+	1.90211i	−0.309772	+	0.0695481i
$749$	6.35410	+	11.0056i	0.232174	+	0.402137i
$750$		0			0
$751$	−1.24629	−	11.8577i	−0.0454778	−	0.432693i	−0.993444	−	0.114321i	$-0.963531\pi$
$751$	−1.24629	−	11.8577i	−0.0454778	−	0.432693i	0.947966	−	0.318371i	$-0.103136\pi$
$752$	2.74064	−	1.22021i	0.0999407	−	0.0444965i
$753$		0			0
$754$	−3.26227	+	3.62312i	−0.118805	+	0.131946i
$755$	4.23607	+	3.07768i	0.154166	+	0.112008i
$756$		0			0
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	−0.939544	−	0.342428i	$-0.888751\pi$
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	0.961381	+	0.275220i	$0.0887509\pi$
$758$	0.489357	+	0.847591i	0.0177742	+	0.0307859i
$759$		0			0
$760$	17.1353	−	29.6791i	0.621561	−	1.07658i
$761$	−20.6685	−	22.9547i	−0.749231	−	0.832106i	0.241147	−	0.970489i	$-0.422476\pi$
$761$	−20.6685	−	22.9547i	−0.749231	−	0.832106i	−0.990379	+	0.138383i	$0.955810\pi$
$762$		0			0
$763$		0			0
$764$	3.73607	+	11.4984i	0.135166	+	0.415999i
$765$		0			0
$766$	13.4443	+	9.76784i	0.485761	+	0.352926i
$767$	16.6400	+	7.40862i	0.600837	+	0.267510i
$768$		0			0
$769$	−6.34346	+	10.9872i	−0.228751	+	0.396208i	−0.957438	−	0.288638i	$-0.906797\pi$
$769$	−6.34346	+	10.9872i	−0.228751	+	0.396208i	0.728687	+	0.684847i	$0.240131\pi$
$770$	13.1317	+	9.31364i	0.473234	+	0.335640i
$771$		0			0
$772$	−29.3781	+	6.24451i	−1.05734	+	0.224745i
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	−0.0315378	−	0.999503i	$-0.510040\pi$
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	0.940838	+	0.338858i	$0.110040\pi$
$774$		0			0
$775$	1.63525	+	5.03280i	0.0587401	+	0.180783i
$776$	−20.9986	+	23.3213i	−0.753807	+	0.837188i
$777$		0			0
$778$	1.56793	+	14.9178i	0.0562129	+	0.534830i
$779$	−46.7876	−	51.9629i	−1.67634	−	1.86176i
$780$		0			0
$781$	−18.0875	−	3.62939i	−0.647223	−	0.129870i
$782$	−3.47214			−0.124163
$783$		0			0
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$	−1.01478	+	9.65502i	−0.0362192	+	0.344602i
$786$		0			0
$787$	10.0669	+	2.13978i	0.358846	+	0.0762751i	0.383807	−	0.923413i	$-0.374613\pi$
$787$	10.0669	+	2.13978i	0.358846	+	0.0762751i	−0.0249609	+	0.999688i	$0.507946\pi$
$788$	−36.0401	+	16.0461i	−1.28388	+	0.571619i
$789$		0			0
$790$	−14.9913	+	3.18650i	−0.533367	+	0.113371i
$791$	2.12461			0.0755425
$792$		0			0
$793$	13.8541			0.491974
$794$	−23.4002	+	4.97387i	−0.830442	+	0.176516i
$795$		0			0
$796$	24.6972	−	10.9959i	0.875369	−	0.389739i
$797$	−10.5287	−	2.23795i	−0.372946	−	0.0792722i	0.0176255	−	0.999845i	$-0.494389\pi$
$797$	−10.5287	−	2.23795i	−0.372946	−	0.0792722i	−0.390572	+	0.920572i	$0.627723\pi$
$798$		0			0
$799$	−0.273659	+	2.60369i	−0.00968136	+	0.0921120i
$800$	8.42705	−	6.12261i	0.297941	−	0.216467i
$801$		0			0
$802$	16.1246			0.569380
$803$	9.75446	−	4.47704i	0.344228	−	0.157991i
$804$		0			0
$805$	−18.2475	−	20.2659i	−0.643141	−	0.714280i
$806$	0.325236	+	3.09441i	0.0114559	+	0.108996i
$807$		0			0
$808$	−4.48866	+	4.98517i	−0.157911	+	0.175378i
$809$	2.98936	+	9.20029i	0.105100	+	0.323465i	0.989754	−	0.142783i	$-0.0456052\pi$
$809$	2.98936	+	9.20029i	0.105100	+	0.323465i	−0.884654	+	0.466249i	$0.845605\pi$
$810$		0			0
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	−0.633091	−	0.774077i	$-0.718214\pi$
$811$	−2.63525	+	1.91462i	−0.0925363	+	0.0672316i	0.540555	+	0.841309i	$0.318214\pi$
$812$	21.2338	−	4.51339i	0.745161	−	0.158389i
$813$		0			0
$814$	−0.388203	+	0.288872i	−0.0136065	+	0.0101250i
$815$	23.9164	−	41.4244i	0.837755	−	1.45103i
$816$		0			0
$817$	33.3504	+	14.8486i	1.16678	+	0.519485i
$818$	−5.52786	−	4.01623i	−0.193277	−	0.140424i
$819$		0			0
$820$	−15.6353	−	48.1204i	−0.546007	−	1.68044i
$821$	−4.22467	+	40.1950i	−0.147442	+	1.40282i	0.631333	+	0.775512i	$0.282508\pi$
$821$	−4.22467	+	40.1950i	−0.147442	+	1.40282i	−0.778775	+	0.627303i	$0.784159\pi$
$822$		0			0
$823$	−23.7355	−	26.3609i	−0.827367	−	0.918884i	0.170420	−	0.985372i	$-0.445488\pi$
$823$	−23.7355	−	26.3609i	−0.827367	−	0.918884i	−0.997787	+	0.0664871i	$0.978821\pi$
$824$	6.70820	−	11.6190i	0.233691	−	0.404765i
$825$		0			0
$826$	9.57295	+	16.5808i	0.333085	+	0.576921i
$827$	16.4164	−	50.5245i	0.570854	−	1.75691i	−0.0790257	−	0.996873i	$-0.525181\pi$
$827$	16.4164	−	50.5245i	0.570854	−	1.75691i	0.649880	−	0.760037i	$-0.274819\pi$
$828$		0			0
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	0.310887	−	0.950447i	$-0.399374\pi$
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	−0.807859	+	0.589375i	$0.799374\pi$
$830$	0.766755	−	0.851568i	0.0266145	−	0.0295584i
$831$		0			0
$832$	−0.380408	+	0.169368i	−0.0131883	+	0.00587179i
$833$	−0.338261	−	3.21834i	−0.0117201	−	0.111509i
$834$		0			0
$835$	13.1353	+	22.7509i	0.454564	+	0.787328i
$836$	−16.0172	−	27.0256i	−0.553967	−	0.934700i
$837$		0			0
$838$	−3.15248	+	9.70232i	−0.108900	+	0.335161i
$839$	−33.5346	−	14.9306i	−1.15774	−	0.515461i	−0.264213	−	0.964464i	$-0.585112\pi$
$839$	−33.5346	−	14.9306i	−1.15774	−	0.515461i	−0.893530	+	0.449004i	$0.851779\pi$
$840$		0			0
$841$	8.80333	+	1.87121i	0.303563	+	0.0645243i
$842$	−22.5311	−	4.78913i	−0.776472	−	0.165044i
$843$		0			0
$844$	32.9191	+	14.6565i	1.13312	+	0.504498i
$845$	8.00000	−	24.6215i	0.275208	−	0.847004i
$846$		0			0
$847$	29.8328	−	14.1068i	1.02507	−	0.484717i
$848$	8.91641	+	15.4437i	0.306191	+	0.530338i
$849$		0			0
$850$	0.193806	+	1.84395i	0.00664751	+	0.0632468i
$851$	0.748797	−	0.333386i	0.0256684	−	0.0114283i
$852$		0			0
$853$	−6.65402	+	7.39003i	−0.227829	+	0.253030i	−0.846211	−	0.532848i	$-0.821122\pi$
$853$	−6.65402	+	7.39003i	−0.227829	+	0.253030i	0.618382	+	0.785878i	$0.287789\pi$
$854$	11.7812	+	8.55951i	0.403143	+	0.292900i
$855$		0			0
$856$	−2.92705	+	9.00854i	−0.100045	+	0.307905i
$857$	−23.8607	−	41.3279i	−0.815065	−	1.41173i	−0.909281	−	0.416183i	$-0.863368\pi$
$857$	−23.8607	−	41.3279i	−0.815065	−	1.41173i	0.0942157	−	0.995552i	$-0.469966\pi$
$858$		0			0
$859$	−3.55573	+	6.15870i	−0.121320	+	0.210132i	−0.920288	−	0.391241i	$-0.872046\pi$
$859$	−3.55573	+	6.15870i	−0.121320	+	0.210132i	0.798969	+	0.601373i	$0.205379\pi$
$860$	17.6760	+	19.6312i	0.602748	+	0.669419i
$861$		0			0
$862$	−2.55221	+	24.2827i	−0.0869286	+	0.827070i
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	0.993911	−	0.110183i	$-0.0351436\pi$
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	−0.868855	+	0.495067i	$0.835144\pi$
$864$		0			0
$865$	32.5795	+	23.6704i	1.10774	+	0.804818i
$866$	3.38761	+	1.50826i	0.115116	+	0.0512528i
$867$		0			0
$868$	6.92705	−	11.9980i	0.235119	−	0.407239i
$869$	−9.36633	+	29.9868i	−0.317731	+	1.01723i
$870$		0			0
$871$	16.4987	−	3.50690i	0.559036	−	0.118827i
$872$		0			0
$873$		0			0
$874$	−3.88197	−	11.9475i	−0.131309	−	0.404129i
$875$	16.5330	−	18.3618i	0.558918	−	0.620741i
$876$		0			0
$877$	−0.670697	−	6.38126i	−0.0226478	−	0.215480i	−0.999993	−	0.00382661i	$-0.998782\pi$
$877$	−0.670697	−	6.38126i	−0.0226478	−	0.215480i	0.977345	−	0.211653i	$-0.0678847\pi$
$878$	−1.36131	−	1.51188i	−0.0459419	−	0.0510236i
$879$		0			0
$880$	−1.86544	−	15.9908i	−0.0628839	−	0.539050i
$881$	13.9098			0.468634			0.234317	−	0.972160i	$-0.424715\pi$
$881$	13.9098			0.468634			0.234317	+	0.972160i	$0.424715\pi$
$882$		0			0
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	−0.722462	−	0.691411i	$-0.756990\pi$
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	0.434318	+	0.900760i	$0.356990\pi$
$884$	0.482716	−	4.59274i	0.0162355	−	0.154470i
$885$		0			0
$886$	−24.8610	−	5.28437i	−0.835222	−	0.177532i
$887$	2.74064	−	1.22021i	0.0920216	−	0.0409706i	−0.360210	−	0.932871i	$-0.617295\pi$
$887$	2.74064	−	1.22021i	0.0920216	−	0.0409706i	0.452231	+	0.891901i	$0.350628\pi$
$888$		0			0
$889$	10.8815	−	2.31294i	0.364954	−	0.0775734i
$890$	0.854102			0.0286296
$891$		0			0
$892$	−1.14590			−0.0383675
$893$	−9.26515	+	1.96937i	−0.310046	+	0.0659024i
$894$		0			0
$895$	5.34799	−	2.38108i	0.178764	−	0.0795907i
$896$	−33.3997	−	7.09933i	−1.11581	−	0.237172i
$897$		0			0
$898$	−1.58095	+	15.0418i	−0.0527571	+	0.501950i
$899$	−10.3262	+	7.50245i	−0.344399	+	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$	24.0047	+	4.81672i	0.799270	+	0.160379i
$903$		0			0
$904$	1.05963	+	1.17684i	0.0352428	+	0.0391411i
$905$	−4.78141	−	45.4921i	−0.158939	−	1.51221i
$906$		0			0
$907$	−28.7584	+	31.9394i	−0.954906	+	1.06053i	0.0432032	+	0.999066i	$0.486244\pi$
$907$	−28.7584	+	31.9394i	−0.954906	+	1.06053i	−0.998109	+	0.0614644i	$0.980423\pi$
$908$	12.4443	+	38.2995i	0.412978	+	1.27101i
$909$		0			0
$910$	−6.92705	+	5.03280i	−0.229630	+	0.166836i
$911$	−17.6612	+	3.75400i	−0.585141	+	0.124375i	−0.490964	−	0.871180i	$-0.663355\pi$
$911$	−17.6612	+	3.75400i	−0.585141	+	0.124375i	−0.0941768	+	0.995555i	$0.530022\pi$
$912$		0			0
$913$	−0.751279	−	2.22546i	−0.0248637	−	0.0736519i
$914$	2.53444	−	4.38978i	0.0838319	−	0.145201i
$915$		0			0
$916$	−14.7815	−	6.58114i	−0.488394	−	0.217447i
$917$	17.3435	+	12.6008i	0.572731	+	0.416114i
$918$		0			0
$919$	14.5106	+	44.6592i	0.478662	+	1.47317i	0.840955	+	0.541106i	$0.181994\pi$
$919$	14.5106	+	44.6592i	0.478662	+	1.47317i	−0.362293	+	0.932064i	$0.618006\pi$
$920$	2.12467	−	20.2149i	0.0700483	−	0.666465i
$921$		0			0
$922$	8.72174	+	9.68648i	0.287235	+	0.319007i
$923$	4.90576	−	8.49703i	0.161475	−	0.279683i
$924$		0			0
$925$	−0.218847	−	0.379054i	−0.00719565	−	0.0124632i
$926$	3.01722	−	9.28605i	0.0991520	−	0.305159i
$927$		0			0
$928$	20.3262	+	14.7679i	0.667241	+	0.484779i
$929$	−22.0067	+	24.4410i	−0.722017	+	0.801882i	−0.986717	−	0.162449i	$-0.948061\pi$
$929$	−22.0067	+	24.4410i	−0.722017	+	0.801882i	0.264699	+	0.964331i	$0.414727\pi$
$930$		0			0
$931$	10.6960	−	4.76216i	0.350546	−	0.156073i
$932$	4.11431	+	39.1451i	0.134769	+	1.28224i
$933$		0			0
$934$	−3.01722	−	5.22598i	−0.0987265	−	0.170999i
$935$	12.8992	+	5.56758i	0.421849	+	0.182079i
$936$		0			0
$937$	−5.12868	+	15.7844i	−0.167547	+	0.515655i	−0.999215	−	0.0396173i	$-0.987386\pi$
$937$	−5.12868	+	15.7844i	−0.167547	+	0.515655i	0.831668	+	0.555273i	$0.187386\pi$
$938$	16.1967	+	7.21123i	0.528841	+	0.235455i
$939$		0			0
$940$	−6.70432	−	1.42505i	−0.218671	−	0.0464799i
$941$	43.6559	+	9.27935i	1.42314	+	0.302498i	0.854228	−	0.519899i	$-0.174030\pi$
$941$	43.6559	+	9.27935i	1.42314	+	0.302498i	0.568914	+	0.822397i	$0.307364\pi$
$942$		0			0
$943$	−37.8867	−	16.8682i	−1.23376	−	0.549305i
$944$	5.91641	−	18.2088i	0.192563	−	0.592647i
$945$		0			0
$946$	−12.4721	+	2.80017i	−0.405504	+	0.0910413i
$947$	−9.16312	−	15.8710i	−0.297761	−	0.515738i	0.677862	−	0.735189i	$-0.262907\pi$
$947$	−9.16312	−	15.8710i	−0.297761	−	0.515738i	−0.975623	+	0.219451i	$0.929573\pi$
$948$		0			0
$949$	0.596670	+	5.67693i	0.0193687	+	0.184281i
$950$	−6.12825	+	2.72847i	−0.198827	+	0.0885233i
$951$		0			0
$952$	7.26281	−	8.06617i	0.235389	−	0.261426i
$953$	−30.5967	−	22.2298i	−0.991126	−	0.720095i	−0.0309585	−	0.999521i	$-0.509856\pi$
$953$	−30.5967	−	22.2298i	−0.991126	−	0.720095i	−0.960167	+	0.279426i	$0.909856\pi$
$954$		0			0
$955$	6.04508	−	18.6049i	0.195614	−	0.602039i
$956$	2.07295	+	3.59045i	0.0670440	+	0.116124i
$957$		0			0
$958$	−8.68034	+	15.0348i	−0.280449	+	0.485752i
$959$	14.9995	+	16.6586i	0.484359	+	0.537935i
$960$		0			0
$961$	2.38890	−	22.7289i	0.0770614	−	0.733190i
$962$	−0.0795268	−	0.244758i	−0.00256405	−	0.00789133i
$963$		0			0
$964$	−30.2705	−	21.9928i	−0.974947	−	0.708341i
$965$	44.3953	+	19.7661i	1.42914	+	0.636293i
$966$		0			0
$967$	17.3435	−	30.0398i	0.557728	−	0.966013i	−0.439958	−	0.898019i	$-0.645007\pi$
$967$	17.3435	−	30.0398i	0.557728	−	0.966013i	0.997686	−	0.0679948i	$-0.0216601\pi$
$968$	22.6927	+	9.48896i	0.729372	+	0.304987i
$969$		0			0
$970$	22.2120	−	4.72130i	0.713184	−	0.151592i
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.957885	−	0.287151i	$-0.907292\pi$
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.0229058	+	0.999738i	$0.507292\pi$
$972$		0			0
$973$	−0.791796	−	2.43690i	−0.0253838	−	0.0781234i
$974$	−6.95569	+	7.72508i	−0.222875	+	0.247528i
$975$		0			0
$976$	−1.52218	−	14.4825i	−0.0487236	−	0.463575i
$977$	−3.10431	−	3.44769i	−0.0993157	−	0.110301i	0.691438	−	0.722436i	$-0.256978\pi$
$977$	−3.10431	−	3.44769i	−0.0993157	−	0.110301i	−0.790753	+	0.612135i	$0.790311\pi$
$978$		0			0
$979$	0.858004	−	1.52606i	0.0274219	−	0.0487732i
$980$	8.47214			0.270632
$981$		0			0
$982$	12.6074	−	9.15981i	0.402318	−	0.292301i
$983$	2.85414	−	27.1554i	0.0910331	−	0.866122i	−0.849767	−	0.527159i	$-0.823257\pi$
$983$	2.85414	−	27.1554i	0.0910331	−	0.866122i	0.940800	−	0.338963i	$-0.110076\pi$
$984$		0			0
$985$	62.4379	+	13.2716i	1.98944	+	0.422868i
$986$	−4.08550	+	1.81898i	−0.130109	+	0.0579282i
$987$		0			0
$988$	16.3431	−	3.47383i	0.519943	−	0.110517i
$989$	21.6525			0.688509
$990$		0			0
$991$	21.2705			0.675680			0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705			0.675680			0.337840	+	0.941204i	$0.390304\pi$
$992$	15.6841	−	3.33375i	0.497969	−	0.105847i
$993$		0			0
$994$	9.42147	−	4.19471i	0.298831	−	0.133048i
$995$	−42.7868	−	9.09461i	−1.35643	−	0.288318i
$996$		0			0
$997$	1.35665	−	12.9076i	0.0429654	−	0.408788i	−0.951809	−	0.306691i	$-0.900778\pi$
$997$	1.35665	−	12.9076i	0.0429654	−	0.408788i	0.994774	−	0.102097i	$-0.0325552\pi$
$998$	−8.78115	+	6.37988i	−0.277963	+	0.201952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.d.757.1		8
3.2	odd	2		891.2.n.a.757.1		8
9.2	odd	6		891.2.n.a.460.1		8
9.4	even	3		33.2.e.a.31.1	yes	4
9.5	odd	6		99.2.f.b.64.1		4
9.7	even	3	inner	891.2.n.d.460.1		8
11.5	even	5	inner	891.2.n.d.676.1		8
33.5	odd	10		891.2.n.a.676.1		8
36.31	odd	6		528.2.y.f.97.1		4
45.4	even	6		825.2.n.f.526.1		4
45.13	odd	12		825.2.bx.b.724.2		8
45.22	odd	12		825.2.bx.b.724.1		8
99.4	even	15		363.2.a.h.1.1		2
99.5	odd	30		99.2.f.b.82.1		4
99.13	odd	30		363.2.e.c.124.1		4
99.16	even	15	inner	891.2.n.d.379.1		8
99.31	even	15		363.2.e.h.124.1		4
99.38	odd	30		891.2.n.a.379.1		8
99.40	odd	30		363.2.a.e.1.2		2
99.49	even	15		33.2.e.a.16.1	✓	4
99.58	even	15		363.2.e.h.202.1		4
99.59	odd	30		1089.2.a.m.1.2		2
99.76	odd	6		363.2.e.j.130.1		4
99.85	odd	30		363.2.e.c.202.1		4
99.94	odd	30		363.2.e.j.148.1		4
99.95	even	30		1089.2.a.s.1.1		2
396.103	odd	30		5808.2.a.bl.1.1		2
396.139	even	30		5808.2.a.bm.1.1		2
396.247	odd	30		528.2.y.f.49.1		4
495.4	even	30		9075.2.a.x.1.2		2
495.49	even	30		825.2.n.f.676.1		4
495.139	odd	30		9075.2.a.bv.1.1		2
495.148	odd	60		825.2.bx.b.49.1		8
495.247	odd	60		825.2.bx.b.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	99.49	even	15
33.2.e.a.31.1	yes	4	9.4	even	3
99.2.f.b.64.1		4	9.5	odd	6
99.2.f.b.82.1		4	99.5	odd	30
363.2.a.e.1.2		2	99.40	odd	30
363.2.a.h.1.1		2	99.4	even	15
363.2.e.c.124.1		4	99.13	odd	30
363.2.e.c.202.1		4	99.85	odd	30
363.2.e.h.124.1		4	99.31	even	15
363.2.e.h.202.1		4	99.58	even	15
363.2.e.j.130.1		4	99.76	odd	6
363.2.e.j.148.1		4	99.94	odd	30
528.2.y.f.49.1		4	396.247	odd	30
528.2.y.f.97.1		4	36.31	odd	6
825.2.n.f.526.1		4	45.4	even	6
825.2.n.f.676.1		4	495.49	even	30
825.2.bx.b.49.1		8	495.148	odd	60
825.2.bx.b.49.2		8	495.247	odd	60
825.2.bx.b.724.1		8	45.22	odd	12
825.2.bx.b.724.2		8	45.13	odd	12
891.2.n.a.379.1		8	99.38	odd	30
891.2.n.a.460.1		8	9.2	odd	6
891.2.n.a.676.1		8	33.5	odd	10
891.2.n.a.757.1		8	3.2	odd	2
891.2.n.d.379.1		8	99.16	even	15	inner
891.2.n.d.460.1		8	9.7	even	3	inner
891.2.n.d.676.1		8	11.5	even	5	inner
891.2.n.d.757.1		8	1.1	even	1	trivial
1089.2.a.m.1.2		2	99.59	odd	30
1089.2.a.s.1.1		2	99.95	even	30
5808.2.a.bl.1.1		2	396.103	odd	30
5808.2.a.bm.1.1		2	396.139	even	30
9075.2.a.x.1.2		2	495.4	even	30
9075.2.a.bv.1.1		2	495.139	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.604528 - 0.128496i) q^{2} +(-1.47815 + 0.658114i) q^{4} +(2.56082 + 0.544320i) q^{5} +(-0.313585 + 2.98357i) q^{7} +(-1.80902 + 1.31433i) q^{8} +1.61803 q^{10} +(1.62543 - 2.89102i) q^{11} +(1.18030 + 1.31086i) q^{13} +(0.193806 + 1.84395i) q^{14} +(1.24064 - 1.37787i) q^{16} +(0.500000 + 1.53884i) q^{17} +(-4.73607 + 3.44095i) q^{19} +(-4.14350 + 0.880728i) q^{20} +(0.611130 - 1.95656i) q^{22} +(-1.73607 + 3.00696i) q^{23} +(1.69381 + 0.754131i) q^{25} +(0.881966 + 0.640786i) q^{26} +(-1.50000 - 4.61653i) q^{28} +(-0.467465 + 4.44764i) q^{29} +(1.90977 + 2.12101i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.500000 + 0.866025i) q^{34} +(-2.42705 + 7.46969i) q^{35} +(-0.190983 - 0.138757i) q^{37} +(-2.42094 + 2.68872i) q^{38} +(-5.34799 + 2.38108i) q^{40} +(1.24852 + 11.8788i) q^{41} +(-3.11803 - 5.40059i) q^{43} +(-0.500000 + 5.34307i) q^{44} +(-0.663119 + 2.04087i) q^{46} +(1.47815 + 0.658114i) q^{47} +(-1.95630 - 0.415823i) q^{49} +(1.12086 + 0.238246i) q^{50} +(-2.60735 - 1.16087i) q^{52} +(-2.97214 + 9.14729i) q^{53} +(5.73607 - 6.51864i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(0.288910 + 2.74879i) q^{58} +(9.43349 - 4.20006i) q^{59} +(5.25542 - 5.83674i) q^{61} +(1.42705 + 1.03681i) q^{62} +(-0.0729490 + 0.224514i) q^{64} +(2.30902 + 3.99933i) q^{65} +(4.78115 - 8.28120i) q^{67} +(-1.75181 - 1.94558i) q^{68} +(-0.507392 + 4.82751i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(2.61803 + 1.90211i) q^{73} +(-0.133284 - 0.0593421i) q^{74} +(4.73607 - 8.20311i) q^{76} +(8.11584 + 5.75615i) q^{77} +(-9.26515 + 1.96937i) q^{79} +(3.92705 - 2.85317i) q^{80} +(2.28115 + 7.02067i) q^{82} +(0.473881 - 0.526298i) q^{83} +(0.442790 + 4.21286i) q^{85} +(-2.57890 - 2.86416i) q^{86} +(0.859324 + 7.36624i) q^{88} +0.527864 q^{89} +(-4.28115 + 3.11044i) q^{91} +(0.587244 - 5.58726i) q^{92} +(0.978148 + 0.207912i) q^{94} +(-14.0012 + 6.23374i) q^{95} +(13.7278 - 2.91792i) q^{97} -1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 6 q^{14} - 9 q^{16} + 4 q^{17} - 20 q^{19} - 3 q^{20} + 8 q^{22} + 4 q^{23} + 6 q^{25} + 16 q^{26} - 12 q^{28} + 10 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 - 3 * q^4 + q^5 + 3 * q^7 - 10 * q^8 + 4 * q^10 - 9 * q^11 + 9 * q^13 - 6 * q^14 - 9 * q^16 + 4 * q^17 - 20 * q^19 - 3 * q^20 + 8 * q^22 + 4 * q^23 + 6 * q^25 + 16 * q^26 - 12 * q^28 + 10 * q^29 - 8 * q^31 + 18 * q^32 + 4 * q^34 - 6 * q^35 - 6 * q^37 - 10 * q^40 - 23 * q^41 - 16 * q^43 - 4 * q^44 + 26 * q^46 + 3 * q^47 + 2 * q^49 - 12 * q^50 - 7 * q^52 + 12 * q^53 + 28 * q^55 + 20 * q^59 - 3 * q^61 - 2 * q^62 - 14 * q^64 + 14 * q^65 - 2 * q^67 + q^68 + 9 * q^70 - 54 * q^71 + 12 * q^73 + 4 * q^74 + 20 * q^76 + 3 * q^77 - 5 * q^79 + 18 * q^80 - 22 * q^82 - 21 * q^83 - 7 * q^85 + 7 * q^86 + 25 * q^88 + 40 * q^89 + 6 * q^91 - 7 * q^92 - q^94 - 25 * q^95 + 33 * q^97 + 8 * q^98

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