LMFDB - Embedded newform 891.2.n.d.676.1

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			676.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	891.676
Dual form			891.2.n.d.460.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.413545 + 0.459289i) q^{2} +(0.169131 + 1.60917i) q^{4} +(-1.75181 - 1.94558i) q^{5} +(2.74064 + 1.22021i) q^{7} +(-1.80902 - 1.31433i) q^{8} +1.61803 q^{10} +(-3.31641 - 0.0378495i) q^{11} +(-1.72539 - 0.366742i) q^{13} +(-1.69381 + 0.754131i) q^{14} +(-1.81359 + 0.385489i) q^{16} +(0.500000 - 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.83448 - 3.14801i) q^{20} +(1.38887 - 1.50754i) q^{22} +(-1.73607 + 3.00696i) q^{23} +(-0.193806 + 1.84395i) q^{25} +(0.881966 - 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(4.08550 + 1.81898i) q^{29} +(-2.79173 - 0.593401i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.500000 + 0.866025i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(3.53897 - 0.752232i) q^{38} +(0.611920 + 5.82203i) q^{40} +(-10.9116 + 4.85817i) q^{41} +(-3.11803 - 5.40059i) q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(-0.169131 + 1.60917i) q^{47} +(1.33826 + 1.48629i) q^{49} +(-0.766755 - 0.851568i) q^{50} +(0.298335 - 2.83847i) q^{52} +(-2.97214 - 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.52498 + 1.12419i) q^{58} +(-1.07939 - 10.2697i) q^{59} +(-7.68247 + 1.63296i) q^{61} +(1.42705 - 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +(2.30902 + 3.99933i) q^{65} +(4.78115 - 8.28120i) q^{67} +(2.56082 + 0.544320i) q^{68} +(4.43444 + 1.97434i) q^{70} +(-1.71885 + 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(0.0152505 - 0.145099i) q^{74} +(4.73607 - 8.20311i) q^{76} +(-9.04289 - 4.15045i) q^{77} +(6.33810 - 7.03917i) q^{79} +(3.92705 + 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.692728 + 0.147244i) q^{83} +(-3.86984 + 1.72296i) q^{85} +(3.76988 + 0.801313i) q^{86} +(5.94969 + 4.42732i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-5.13233 - 2.28506i) q^{92} +(-0.669131 - 0.743145i) q^{94} +(1.60203 + 15.2423i) q^{95} +(-9.39087 + 10.4296i) q^{97} -1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.413545	+	0.459289i	−0.292421	+	0.324766i	−0.871397	−	0.490578i	$-0.836786\pi$
$2$	−0.413545	+	0.459289i	−0.292421	+	0.324766i	0.578976	+	0.815344i	$0.303452\pi$
$3$		0			0
$3$		0			0
$4$	0.169131	+	1.60917i	0.0845653	+	0.804585i
$5$	−1.75181	−	1.94558i	−0.783432	−	0.870089i	0.210779	−	0.977534i	$-0.432400\pi$
$5$	−1.75181	−	1.94558i	−0.783432	−	0.870089i	−0.994211	+	0.107445i	$0.965733\pi$
$6$		0			0
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.852983	−	0.521939i	$-0.174791\pi$
$7$	2.74064	+	1.22021i	1.03586	+	0.461196i	0.182880	+	0.983135i	$0.441458\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$		0			0
$10$	1.61803			0.511667
$11$	−3.31641	−	0.0378495i	−0.999935	−	0.0114120i
$11$	−3.31641	−	0.0378495i	−0.999935	−	0.0114120i
$12$		0			0
$13$	−1.72539	−	0.366742i	−0.478536	−	0.101716i	−0.0376725	−	0.999290i	$-0.511994\pi$
$13$	−1.72539	−	0.366742i	−0.478536	−	0.101716i	−0.440863	+	0.897574i	$0.645328\pi$
$14$	−1.69381	+	0.754131i	−0.452689	+	0.201550i
$15$		0			0
$16$	−1.81359	+	0.385489i	−0.453396	+	0.0963724i
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	−0.871935	−	0.489622i	$-0.837135\pi$
$17$	0.500000	−	1.53884i	0.121268	−	0.373224i	0.993203	+	0.116398i	$0.0371348\pi$
$18$		0			0
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$	2.83448	−	3.14801i	0.633810	−	0.703917i
$21$		0			0
$22$	1.38887	−	1.50754i	0.296108	−	0.321408i
$23$	−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
$25$	−0.193806	+	1.84395i	−0.0387613	+	0.368789i
$26$	0.881966	−	0.640786i	0.172968	−	0.125668i
$27$		0			0
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	4.08550	+	1.81898i	0.758658	+	0.337776i	0.749345	−	0.662180i	$-0.230369\pi$
$29$	4.08550	+	1.81898i	0.758658	+	0.337776i	0.00931360	+	0.999957i	$0.497035\pi$
$30$		0			0
$31$	−2.79173	−	0.593401i	−0.501410	−	0.106578i	−0.0497385	−	0.998762i	$-0.515839\pi$
$31$	−2.79173	−	0.593401i	−0.501410	−	0.106578i	−0.451672	+	0.892184i	$0.649172\pi$
$32$	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	−0.603373	−	0.797459i	$-0.706177\pi$
$37$	−0.190983	+	0.138757i	−0.0313974	+	0.0228116i	0.571976	+	0.820270i	$0.306177\pi$
$38$	3.53897	−	0.752232i	0.574097	−	0.122028i
$39$		0			0
$40$	0.611920	+	5.82203i	0.0967531	+	0.920544i
$41$	−10.9116	+	4.85817i	−1.70411	+	0.758719i	−0.705355	+	0.708854i	$0.749212\pi$
$41$	−10.9116	+	4.85817i	−1.70411	+	0.758719i	−0.998756	+	0.0498651i	$0.984121\pi$
$42$		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
$47$	−0.169131	+	1.60917i	−0.0246702	+	0.234722i	0.975238	+	0.221159i	$0.0709839\pi$
$47$	−0.169131	+	1.60917i	−0.0246702	+	0.234722i	−0.999908	+	0.0135627i	$0.995683\pi$
$48$		0			0
$49$	1.33826	+	1.48629i	0.191180	+	0.212327i
$50$	−0.766755	−	0.851568i	−0.108436	−	0.120430i
$51$		0			0
$52$	0.298335	−	2.83847i	0.0413716	−	0.393625i
$53$	−2.97214	−	9.14729i	−0.408254	−	1.25648i	−0.918147	−	0.396240i	$-0.870315\pi$
$53$	−2.97214	−	9.14729i	−0.408254	−	1.25648i	0.509893	−	0.860238i	$-0.329685\pi$
$54$		0			0
$55$	5.73607	+	6.51864i	0.773451	+	0.878973i
$56$	−3.35410	−	5.80948i	−0.448211	−	0.776324i
$57$		0			0
$58$	−2.52498	+	1.12419i	−0.331546	+	0.147614i
$59$	−1.07939	−	10.2697i	−0.140524	−	1.33700i	−0.806593	−	0.591107i	$-0.798691\pi$
$59$	−1.07939	−	10.2697i	−0.140524	−	1.33700i	0.666069	−	0.745890i	$-0.267976\pi$
$60$		0			0
$61$	−7.68247	+	1.63296i	−0.983640	+	0.209079i	−0.671538	−	0.740970i	$-0.734366\pi$
$61$	−7.68247	+	1.63296i	−0.983640	+	0.209079i	−0.312101	+	0.950049i	$0.601033\pi$
$62$	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	$-0.0318900\pi$
$68$	2.56082	+	0.544320i	0.310545	+	0.0660085i
$69$		0			0
$70$	4.43444	+	1.97434i	0.530017	+	0.235979i
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	0.795764	+	0.605607i	$0.207070\pi$
$71$	−1.71885	+	5.29007i	−0.203990	+	0.627815i	−0.999753	+	0.0222083i	$0.992930\pi$
$72$		0			0
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	−0.423940	−	0.905690i	$-0.639353\pi$
$73$	2.61803	−	1.90211i	0.306418	−	0.222625i	0.730358	+	0.683065i	$0.239353\pi$
$74$	0.0152505	−	0.145099i	0.00177283	−	0.0168674i
$75$		0			0
$76$	4.73607	−	8.20311i	0.543264	−	0.940961i
$77$	−9.04289	−	4.15045i	−1.03053	−	0.472987i
$78$		0			0
$79$	6.33810	−	7.03917i	0.713092	−	0.791968i	−0.272311	−	0.962209i	$-0.587788\pi$
$79$	6.33810	−	7.03917i	0.713092	−	0.791968i	0.985402	+	0.170241i	$0.0544546\pi$
$80$	3.92705	+	2.85317i	0.439058	+	0.318994i
$81$		0			0
$82$	2.28115	−	7.02067i	0.251911	−	0.775303i
$83$	−0.692728	+	0.147244i	−0.0760368	+	0.0161621i	−0.245773	−	0.969327i	$-0.579042\pi$
$83$	−0.692728	+	0.147244i	−0.0760368	+	0.0161621i	0.169736	+	0.985490i	$0.445708\pi$
$84$		0			0
$85$	−3.86984	+	1.72296i	−0.419743	+	0.186882i
$86$	3.76988	+	0.801313i	0.406517	+	0.0864078i
$87$		0			0
$88$	5.94969	+	4.42732i	0.634239	+	0.471954i
$89$	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
$92$	−5.13233	−	2.28506i	−0.535082	−	0.238234i
$93$		0			0
$94$	−0.669131	−	0.743145i	−0.0690156	−	0.0766495i
$95$	1.60203	+	15.2423i	0.164365	+	1.56382i
$96$		0			0
$97$	−9.39087	+	10.4296i	−0.953499	+	1.05897i	0.0447015	+	0.999000i	$0.485766\pi$
$97$	−9.39087	+	10.4296i	−0.953499	+	1.05897i	−0.998200	+	0.0599674i	$0.980900\pi$
$98$	−1.23607			−0.124862
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−2.00739	+	2.22943i	−0.199743	+	0.221837i	−0.834692	−	0.550717i	$-0.814354\pi$
$101$	−2.00739	+	2.22943i	−0.199743	+	0.221837i	0.634949	+	0.772554i	$0.281021\pi$
$102$		0			0
$103$	0.627171	+	5.96713i	0.0617970	+	0.587959i	0.980977	+	0.194122i	$0.0621858\pi$
$103$	0.627171	+	5.96713i	0.0617970	+	0.587959i	−0.919180	+	0.393837i	$0.871148\pi$
$104$	2.63923	+	2.93117i	0.258798	+	0.287424i
$105$		0			0
$106$	5.43036	+	2.41775i	0.527443	+	0.234833i
$107$	3.42705	+	2.48990i	0.331306	+	0.240708i	0.740984	−	0.671522i	$-0.234359\pi$
$107$	3.42705	+	2.48990i	0.331306	+	0.240708i	−0.409679	+	0.912230i	$0.634359\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	−5.36606	−	0.0612417i	−0.511634	−	0.00583917i
$111$		0			0
$112$	−5.44076	−	1.15647i	−0.514103	−	0.109276i
$113$	0.646976	−	0.288052i	0.0608624	−	0.0270977i	−0.376080	−	0.926587i	$-0.622728\pi$
$113$	0.646976	−	0.288052i	0.0608624	−	0.0270977i	0.436942	+	0.899490i	$0.356061\pi$
$114$		0			0
$115$	8.89153	−	1.88995i	0.829139	−	0.176239i
$116$	−2.23607	+	6.88191i	−0.207614	+	0.638969i
$117$		0			0
$118$	5.16312	+	3.75123i	0.475304	+	0.345328i
$119$	3.24803	−	3.60730i	0.297746	−	0.330681i
$120$		0			0
$121$	10.9971	+	0.251049i	0.999740	+	0.0228226i
$122$	2.42705	−	4.20378i	0.219735	−	0.380592i
$123$		0			0
$124$	0.482716	−	4.59274i	0.0433492	−	0.412440i
$125$	−6.66312	+	4.84104i	−0.595967	+	0.432996i
$126$		0			0
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	−0.988937	−	0.148333i	$-0.952609\pi$
$127$	−1.14590	+	3.52671i	−0.101682	+	0.312945i	0.887255	+	0.461279i	$0.152609\pi$
$128$	10.3979	+	4.62946i	0.919057	+	0.409191i
$129$		0			0
$130$	−2.79173	−	0.593401i	−0.244851	−	0.0520447i
$131$	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
$137$	−7.30885	+	1.55354i	−0.624437	+	0.132728i	−0.509254	−	0.860616i	$-0.670079\pi$
$137$	−7.30885	+	1.55354i	−0.624437	+	0.132728i	−0.115183	+	0.993344i	$0.536745\pi$
$138$		0			0
$139$	0.0892780	+	0.849423i	0.00757246	+	0.0720471i	0.997655	−	0.0684363i	$-0.0218010\pi$
$139$	0.0892780	+	0.849423i	0.00757246	+	0.0720471i	−0.990083	+	0.140483i	$0.955134\pi$
$140$	11.6095	−	5.16889i	0.981184	−	0.436851i
$141$		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
$146$	−0.209057	+	1.98904i	−0.0173017	+	0.164614i
$147$		0			0
$148$	−0.255585	−	0.283856i	−0.0210090	−	0.0233328i
$149$	10.0370	+	11.1472i	0.822260	+	0.913212i	0.997453	−	0.0713221i	$-0.0227218\pi$
$149$	10.0370	+	11.1472i	0.822260	+	0.913212i	−0.175194	+	0.984534i	$0.556055\pi$
$150$		0			0
$151$	−0.209057	+	1.98904i	−0.0170128	+	0.161866i	−0.999730	−	0.0232487i	$-0.992599\pi$
$151$	−0.209057	+	1.98904i	−0.0170128	+	0.161866i	0.982717	+	0.185115i	$0.0592657\pi$
$152$	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
$157$	−3.38761	+	1.50826i	−0.270361	+	0.120372i	−0.537439	−	0.843302i	$-0.680608\pi$
$157$	−3.38761	+	1.50826i	−0.270361	+	0.120372i	0.267079	+	0.963675i	$0.413942\pi$
$158$	0.611920	+	5.82203i	0.0486818	+	0.463176i
$159$		0			0
$160$	−14.3868	+	3.05801i	−1.13738	+	0.241757i
$161$	−8.42705	+	6.12261i	−0.664145	+	0.482529i
$162$		0			0
$163$	5.64590	+	17.3763i	0.442221	+	1.36102i	0.885503	+	0.464634i	$0.153814\pi$
$163$	5.64590	+	17.3763i	0.442221	+	1.36102i	−0.443282	+	0.896382i	$0.646186\pi$
$164$	−9.66312	−	16.7370i	−0.754563	−	1.30694i
$165$		0			0
$166$	0.218847	−	0.379054i	0.0169858	−	0.0294203i
$167$	−9.81517	−	2.08628i	−0.759520	−	0.161441i	−0.188158	−	0.982139i	$-0.560252\pi$
$167$	−9.81517	−	2.08628i	−0.759520	−	0.161441i	−0.571363	+	0.820698i	$0.693585\pi$
$168$		0			0
$169$	−9.03363	−	4.02203i	−0.694895	−	0.309387i
$170$	0.809017	−	2.48990i	0.0620488	−	0.190966i
$171$		0			0
$172$	8.16312	−	5.93085i	0.622432	−	0.452223i
$173$	−1.60785	+	15.2977i	−0.122243	+	1.16306i	0.745659	+	0.666327i	$0.232135\pi$
$173$	−1.60785	+	15.2977i	−0.122243	+	1.16306i	−0.867902	+	0.496735i	$0.834532\pi$
$174$		0			0
$175$	−2.78115	+	4.81710i	−0.210235	+	0.364138i
$176$	6.02918	−	1.20980i	0.454467	−	0.0911919i
$177$		0			0
$178$	−0.218296	+	0.242442i	−0.0163620	+	0.0181718i
$179$	1.80902	+	1.31433i	0.135212	+	0.0982375i	0.653335	−	0.757069i	$-0.273369\pi$
$179$	1.80902	+	1.31433i	0.135212	+	0.0982375i	−0.518123	+	0.855306i	$0.673369\pi$
$180$		0			0
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	0.522612	+	0.852571i	$0.324958\pi$
$181$	−5.39919	+	16.6170i	−0.401318	+	1.23513i	−0.923930	+	0.382560i	$0.875042\pi$
$182$	3.19904	−	0.679977i	0.237129	−	0.0504033i
$183$		0			0
$184$	7.09270	−	3.15788i	0.522881	−	0.232802i
$185$	0.604528	+	0.128496i	0.0444458	+	0.00944725i
$186$		0			0
$187$	−1.71645	+	5.08450i	−0.125519	+	0.371816i
$188$	−2.61803			−0.190940
$189$		0			0
$190$	−7.66312	−	5.56758i	−0.555941	−	0.403915i
$191$	−6.82614	−	3.03919i	−0.493922	−	0.219908i	0.144632	−	0.989486i	$-0.453800\pi$
$191$	−6.82614	−	3.03919i	−0.493922	−	0.219908i	−0.638554	+	0.769577i	$0.720467\pi$
$192$		0			0
$193$	−12.4206	−	13.7945i	−0.894055	−	0.992949i	0.105944	−	0.994372i	$-0.466214\pi$
$193$	−12.4206	−	13.7945i	−0.894055	−	0.992949i	−0.999999	+	0.00142357i	$0.999547\pi$
$194$	−0.906655	−	8.62625i	−0.0650940	−	0.619328i
$195$		0			0
$196$	−2.16535	+	2.40487i	−0.154668	+	0.171776i
$197$	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	$0.701743\pi$
$200$	2.77415	−	3.08100i	0.196162	−	0.217860i
$201$		0			0
$202$	−0.193806	−	1.84395i	−0.0136362	−	0.129740i
$203$	8.97733	+	9.97033i	0.630085	+	0.699780i
$204$		0			0
$205$	28.5670	+	12.7189i	1.99521	+	0.888324i
$206$	−3.00000	−	2.17963i	−0.209020	−	0.151862i
$207$		0			0
$208$	3.27051			0.226769
$209$	15.5765	+	11.5909i	1.07745	+	0.801757i
$210$		0			0
$211$	21.7838	+	4.63030i	1.49966	+	0.318763i	0.883341	−	0.468732i	$-0.155289\pi$
$211$	21.7838	+	4.63030i	1.49966	+	0.318763i	0.616321	+	0.787495i	$0.288622\pi$
$212$	14.2169	−	6.32976i	0.976419	−	0.434730i
$213$		0			0
$214$	−2.56082	+	0.544320i	−0.175054	+	0.0372089i
$215$	−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
$220$	−9.51945	+	10.3328i	−0.641801	+	0.696638i
$221$	−1.42705	+	2.47172i	−0.0959938	+	0.166266i
$222$		0			0
$223$	−0.0740275	+	0.704324i	−0.00495725	+	0.0471650i	−0.996721	−	0.0809165i	$-0.974215\pi$
$223$	−0.0740275	+	0.704324i	−0.00495725	+	0.0471650i	0.991764	+	0.128082i	$0.0408819\pi$
$224$	13.6353	−	9.90659i	0.911044	−	0.661912i
$225$		0			0
$226$	−0.135255	+	0.416272i	−0.00899702	+	0.0276900i
$227$	−22.7368	−	10.1231i	−1.50910	−	0.671893i	−0.525256	−	0.850944i	$-0.676030\pi$
$227$	−22.7368	−	10.1231i	−1.50910	−	0.671893i	−0.983840	+	0.179052i	$0.942697\pi$
$228$		0			0
$229$	−9.78148	−	2.07912i	−0.646378	−	0.137392i	−0.126954	−	0.991909i	$-0.540520\pi$
$229$	−9.78148	−	2.07912i	−0.646378	−	0.137392i	−0.519424	+	0.854517i	$0.673853\pi$
$230$	−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	0.820863	+	0.571124i	$0.193493\pi$
$233$	7.51722	+	23.1356i	0.492470	+	1.51567i	−0.328394	+	0.944541i	$0.606507\pi$
$234$		0			0
$235$	3.42705	−	2.48990i	0.223556	−	0.162423i
$236$	16.3431	−	3.47383i	1.06384	−	0.226127i
$237$		0			0
$238$	0.313585	+	2.98357i	0.0203267	+	0.193396i
$239$	2.34078	−	1.04218i	0.151413	−	0.0674133i	−0.329631	−	0.944110i	$-0.606924\pi$
$239$	2.34078	−	1.04218i	0.151413	−	0.0674133i	0.481044	+	0.876696i	$0.340258\pi$
$240$		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
$245$	0.547318	−	5.20738i	0.0349669	−	0.332688i
$246$		0			0
$247$	6.90960	+	7.67389i	0.439647	+	0.488278i
$248$	4.27037	+	4.74273i	0.271169	+	0.301163i
$249$		0			0
$250$	0.532068	−	5.06229i	0.0336509	−	0.320167i
$251$	−2.40983	−	7.41669i	−0.152107	−	0.468138i	0.845749	−	0.533581i	$-0.179154\pi$
$251$	−2.40983	−	7.41669i	−0.152107	−	0.468138i	−0.997856	+	0.0654431i	$0.979154\pi$
$252$		0			0
$253$	5.87132	−	9.90659i	0.369127	−	0.622822i
$254$	−1.14590	−	1.98475i	−0.0719000	−	0.124535i
$255$		0			0
$256$	−5.99496	+	2.66913i	−0.374685	+	0.166821i
$257$	1.22024	+	11.6098i	0.0761165	+	0.724200i	0.964318	+	0.264746i	$0.0852882\pi$
$257$	1.22024	+	11.6098i	0.0761165	+	0.724200i	−0.888202	+	0.459454i	$0.848045\pi$
$258$		0			0
$259$	−0.692728	+	0.147244i	−0.0430440	+	0.00914929i
$260$	−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
$266$	10.6169	+	2.25669i	0.650965	+	0.138367i
$267$		0			0
$268$	14.1345	+	6.29308i	0.863402	+	0.384411i
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	−0.691467	−	0.722408i	$-0.743035\pi$
$269$	4.79837	−	14.7679i	0.292562	−	0.900413i	0.984029	−	0.178006i	$-0.0569645\pi$
$270$		0			0
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.340753	−	0.940153i	$-0.389318\pi$
$271$	22.0623	−	16.0292i	1.34019	−	0.973705i	0.999437	−	0.0335518i	$-0.0106819\pi$
$272$	−0.313585	+	2.98357i	−0.0190139	+	0.180905i
$273$		0			0
$274$	2.30902	−	3.99933i	0.139493	−	0.241609i
$275$	0.712534	−	6.10794i	0.0429674	−	0.368323i
$276$		0			0
$277$	20.4502	−	22.7122i	1.22873	−	1.36465i	0.319917	−	0.947446i	$-0.396345\pi$
$277$	20.4502	−	22.7122i	1.22873	−	1.36465i	0.908815	−	0.417199i	$-0.136988\pi$
$278$	−0.427051	−	0.310271i	−0.0256128	−	0.0186088i
$279$		0			0
$280$	−5.42705	+	16.7027i	−0.324328	+	0.998180i
$281$	0.747238	−	0.158830i	0.0445765	−	0.00947503i	−0.185569	−	0.982631i	$-0.559413\pi$
$281$	0.747238	−	0.158830i	0.0445765	−	0.00947503i	0.230146	+	0.973156i	$0.426080\pi$
$282$		0			0
$283$	0.164749	−	0.0733508i	0.00979329	−	0.00436025i	−0.401834	−	0.915712i	$-0.631627\pi$
$283$	0.164749	−	0.0733508i	0.00979329	−	0.00436025i	0.411627	+	0.911352i	$0.364961\pi$
$284$	−8.80333	−	1.87121i	−0.522381	−	0.111036i
$285$		0			0
$286$	−2.94921	+	2.09173i	−0.174391	+	0.123686i
$287$	−35.8328			−2.11514
$288$		0			0
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$	6.61048	+	2.94317i	0.388181	+	0.172829i
$291$		0			0
$292$	3.50361	+	3.89116i	0.205033	+	0.227713i
$293$	−0.00582517	−	0.0554228i	−0.000340310	−	0.00323783i	0.994350	−	0.106147i	$-0.0338515\pi$
$293$	−0.00582517	−	0.0554228i	−0.000340310	−	0.00323783i	−0.994691	+	0.102909i	$0.967185\pi$
$294$		0			0
$295$	−18.0896	+	20.0905i	−1.05322	+	1.16971i
$296$	0.527864			0.0306815
$297$		0			0
$298$	−9.27051			−0.537026
$299$	4.09817	−	4.55147i	0.237003	−	0.263219i
$300$		0			0
$301$	−1.95554	−	18.6057i	−0.112715	−	1.07242i
$302$	−0.827091	−	0.918578i	−0.0475937	−	0.0528582i
$303$		0			0
$304$	9.91572	+	4.41476i	0.568705	+	0.253204i
$305$	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	$0.494892\pi$
$308$	5.14935	−	15.2535i	0.293411	−	0.869149i
$309$		0			0
$310$	−4.51712	−	0.960143i	−0.256555	−	0.0545325i
$311$	2.30932	−	1.02817i	0.130949	−	0.0583025i	−0.340216	−	0.940347i	$-0.610500\pi$
$311$	2.30932	−	1.02817i	0.130949	−	0.0583025i	0.471165	+	0.882045i	$0.343833\pi$
$312$		0			0
$313$	−25.2683	+	5.37094i	−1.42825	+	0.303584i	−0.856204	−	0.516638i	$-0.827183\pi$
$313$	−25.2683	+	5.37094i	−1.42825	+	0.303584i	−0.572045	+	0.820222i	$0.693850\pi$
$314$	0.708204	−	2.17963i	0.0399663	−	0.123004i
$315$		0			0
$316$	12.3992	+	9.00854i	0.697509	+	0.506770i
$317$	−12.9548	+	14.3878i	−0.727615	+	0.808099i	−0.987513	−	0.157537i	$-0.949645\pi$
$317$	−12.9548	+	14.3878i	−0.727615	+	0.808099i	0.259898	+	0.965636i	$0.416311\pi$
$318$		0			0
$319$	−13.4803	−	6.18712i	−0.754754	−	0.346412i
$320$	−0.309017	+	0.535233i	−0.0172746	+	0.0299204i
$321$		0			0
$322$	0.672922	−	6.40243i	0.0375005	−	0.356793i
$323$	−7.66312	+	5.56758i	−0.426387	+	0.309789i
$324$		0			0
$325$	1.01064	−	3.11044i	0.0560604	−	0.172536i
$326$	−10.3156	−	4.59279i	−0.571327	−	0.254371i
$327$		0			0
$328$	26.1246	+	5.55295i	1.44249	+	0.306610i
$329$	−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
$335$	−24.4874	+	5.20495i	−1.33789	+	0.284377i
$336$		0			0
$337$	0.0305010	+	0.290198i	0.00166150	+	0.0158081i	0.995321	−	0.0966211i	$-0.0308035\pi$
$337$	0.0305010	+	0.290198i	0.00166150	+	0.0158081i	−0.993660	+	0.112429i	$0.964137\pi$
$338$	5.58309	−	2.48575i	0.303680	−	0.135207i
$339$		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
$344$	−1.45757	+	13.8679i	−0.0785871	+	0.747706i
$345$		0			0
$346$	−6.36114	−	7.06476i	−0.341977	−	0.379804i
$347$	−14.0145	−	15.5646i	−0.752335	−	0.835553i	0.238427	−	0.971160i	$-0.423368\pi$
$347$	−14.0145	−	15.5646i	−0.752335	−	0.835553i	−0.990763	+	0.135607i	$0.956701\pi$
$348$		0			0
$349$	1.05831	−	10.0691i	0.0566500	−	0.538989i	−0.928987	−	0.370112i	$-0.879319\pi$
$349$	1.05831	−	10.0691i	0.0566500	−	0.538989i	0.985637	−	0.168877i	$-0.0540141\pi$
$350$	−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
$355$	13.3033	−	5.92302i	0.706067	−	0.314361i
$356$	0.0892780	+	0.849423i	0.00473172	+	0.0450193i
$357$		0			0
$358$	−1.35177	+	0.287327i	−0.0714431	+	0.0151857i
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	−0.280940	−	0.959725i	$-0.590646\pi$
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	0.825938	+	0.563761i	$0.190646\pi$
$360$		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
$365$	−8.28700	−	1.76146i	−0.433761	−	0.0921988i
$366$		0			0
$367$	5.08142	+	2.26239i	0.265248	+	0.118096i	0.535052	−	0.844819i	$-0.320292\pi$
$367$	5.08142	+	2.26239i	0.265248	+	0.118096i	−0.269804	+	0.962915i	$0.586959\pi$
$368$	1.98936	−	6.12261i	0.103702	−	0.319163i
$369$		0			0
$370$	−0.309017	+	0.224514i	−0.0160650	+	0.0116719i
$371$	3.01607	−	28.6960i	0.156587	−	1.48982i
$372$		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	$0.130192\pi$
$374$	−1.62543	−	2.89102i	−0.0840488	−	0.149491i
$375$		0			0
$376$	2.42094	−	2.68872i	0.124850	−	0.138660i
$377$	−6.38197	−	4.63677i	−0.328688	−	0.238806i
$378$		0			0
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	−0.937701	−	0.347443i	$-0.887050\pi$
$379$	0.489357	−	1.50609i	0.0251366	−	0.0773624i	0.962838	+	0.270080i	$0.0870502\pi$
$380$	−24.2565	+	5.15587i	−1.24433	+	0.264491i
$381$		0			0
$382$	4.21878	−	1.87832i	0.215852	−	0.0961034i
$383$	−26.3010	−	5.59044i	−1.34392	−	0.285658i	−0.520872	−	0.853635i	$-0.674393\pi$
$383$	−26.3010	−	5.59044i	−1.34392	−	0.285658i	−0.823045	+	0.567977i	$0.807726\pi$
$384$		0			0
$385$	7.76637	+	24.8644i	0.395811	+	1.26721i
$386$	11.4721			0.583916
$387$		0			0
$388$	−18.3713	−	13.3475i	−0.932663	−	0.677619i
$389$	22.1722	+	9.87171i	1.12418	+	0.500515i	0.882721	−	0.469897i	$-0.155709\pi$
$389$	22.1722	+	9.87171i	1.12418	+	0.500515i	0.241455	+	0.970412i	$0.422376\pi$
$390$		0			0
$391$	3.75920	+	4.17501i	0.190111	+	0.211139i
$392$	−0.467465	−	4.44764i	−0.0236106	−	0.224640i
$393$		0			0
$394$	−10.0831	+	11.1984i	−0.507977	+	0.564165i
$395$	−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	$0.923628\pi$
$398$	6.90960	−	7.67389i	0.346347	−	0.384657i
$399$		0			0
$400$	−0.359337	−	3.41886i	−0.0179668	−	0.170943i
$401$	−17.4577	−	19.3888i	−0.871797	−	0.968229i	0.127925	−	0.991784i	$-0.459168\pi$
$401$	−17.4577	−	19.3888i	−0.871797	−	0.968229i	−0.999723	+	0.0235546i	$0.992502\pi$
$402$		0			0
$403$	4.59919	+	2.04769i	0.229102	+	0.102003i
$404$	−3.92705	−	2.85317i	−0.195378	−	0.141950i
$405$		0			0
$406$	−8.29180			−0.411515
$407$	0.638630	−	0.452947i	0.0316557	−	0.0224518i
$408$		0			0
$409$	10.8141	+	2.29862i	0.534725	+	0.113659i	0.467356	−	0.884069i	$-0.345206\pi$
$409$	10.8141	+	2.29862i	0.534725	+	0.113659i	0.0673681	+	0.997728i	$0.478540\pi$
$410$	−17.6554	+	7.86069i	−0.871938	+	0.388212i
$411$		0			0
$412$	−9.49606	+	2.01845i	−0.467837	+	0.0994418i
$413$	9.57295	−	29.4625i	0.471054	−	1.44976i
$414$		0			0
$415$	1.50000	+	1.08981i	0.0736321	+	0.0534969i
$416$	−6.63097	+	7.36444i	−0.325110	+	0.361071i
$417$		0			0
$418$	−11.7651	+	2.36076i	−0.575452	+	0.115469i
$419$	−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
$421$	3.89583	−	37.0663i	0.189871	−	1.80650i	−0.321250	−	0.946994i	$-0.604103\pi$
$421$	3.89583	−	37.0663i	0.189871	−	1.80650i	0.511121	−	0.859508i	$-0.329230\pi$
$422$	−11.1353	+	8.09024i	−0.542056	+	0.393827i
$423$		0			0
$424$	−6.64590	+	20.4540i	−0.322753	+	0.993333i
$425$	2.74064	+	1.22021i	0.132940	+	0.0591889i
$426$		0			0
$427$	−23.0474	−	4.89888i	−1.11534	−	0.237073i
$428$	−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	−0.586667	−	0.809828i	$-0.699560\pi$
$431$	−12.2082	−	37.5730i	−0.588048	−	1.80983i	−0.00138127	−	0.999999i	$-0.500440\pi$
$432$		0			0
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	−0.465008	−	0.885307i	$-0.653949\pi$
$433$	4.85410	−	3.52671i	0.233273	−	0.169483i	0.698281	+	0.715824i	$0.253949\pi$
$434$	5.17616	−	1.10023i	0.248464	−	0.0528126i
$435$		0			0
$436$		0			0
$437$	18.5689	−	8.26743i	0.888273	−	0.395485i
$438$		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
$443$	4.29869	−	40.8993i	0.204237	−	1.94319i	−0.110205	−	0.993909i	$-0.535151\pi$
$443$	4.29869	−	40.8993i	0.204237	−	1.94319i	0.314442	−	0.949277i	$-0.398183\pi$
$444$		0			0
$445$	−0.924716	−	1.02700i	−0.0438357	−	0.0486845i
$446$	−0.292875	−	0.325270i	−0.0138680	−	0.0154020i
$447$		0			0
$448$	0.0740275	−	0.704324i	0.00349747	−	0.0332762i
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	−0.954907	−	0.296905i	$-0.904046\pi$
$449$	−7.56231	−	23.2744i	−0.356887	−	1.09839i	0.598020	−	0.801481i	$-0.295954\pi$
$450$		0			0
$451$	36.3713	−	15.6987i	1.71266	−	0.739222i
$452$	0.572949	+	0.992377i	0.0269493	+	0.0466775i
$453$		0			0
$454$	14.0521	−	6.25641i	0.659499	−	0.293628i
$455$	1.44815	+	13.7782i	0.0678902	+	0.645932i
$456$		0			0
$457$	−8.02240	+	1.70521i	−0.375272	+	0.0797665i	−0.391687	−	0.920099i	$-0.628108\pi$
$457$	−8.02240	+	1.70521i	−0.375272	+	0.0797665i	0.0164144	+	0.999865i	$0.494775\pi$
$458$	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	$0.0470152\pi$
$464$	−8.11060	−	1.72396i	−0.376525	−	0.0800329i
$465$		0			0
$466$	−13.7346	−	6.11506i	−0.636245	−	0.283275i
$467$	−3.01722	+	9.28605i	−0.139620	+	0.429707i	−0.996280	−	0.0861747i	$-0.972536\pi$
$467$	−3.01722	+	9.28605i	−0.139620	+	0.429707i	0.856660	+	0.515882i	$0.172536\pi$
$468$		0			0
$469$	23.2082	−	16.8617i	1.07166	−	0.778603i
$470$	−0.273659	+	2.60369i	−0.0126230	+	0.120099i
$471$		0			0
$472$	−11.5451	+	19.9967i	−0.531406	+	0.920422i
$473$	10.1363	+	18.0286i	0.466066	+	0.828956i
$474$		0			0
$475$	7.26281	−	8.06617i	0.333241	−	0.370101i
$476$	6.35410	+	4.61653i	0.291240	+	0.211598i
$477$		0			0
$478$	−0.489357	+	1.50609i	−0.0223827	+	0.0688868i
$479$	27.4763	−	5.84027i	1.25543	−	0.266849i	0.468260	−	0.883591i	$-0.344881\pi$
$479$	27.4763	−	5.84027i	1.25543	−	0.266849i	0.787166	+	0.616742i	$0.211548\pi$
$480$		0			0
$481$	0.380408	−	0.169368i	0.0173451	−	0.00772253i
$482$	−13.9795	−	2.97143i	−0.636748	−	0.135345i
$483$		0			0
$484$	1.45597	+	17.7387i	0.0661806	+	0.806306i
$485$	36.7426			1.66840
$486$		0			0
$487$	−13.6074	−	9.88635i	−0.616610	−	0.447993i	0.235126	−	0.971965i	$-0.424450\pi$
$487$	−13.6074	−	9.88635i	−0.616610	−	0.447993i	−0.851736	+	0.523972i	$0.824450\pi$
$488$	16.0440	+	7.14323i	0.726276	+	0.323359i
$489$		0			0
$490$	2.16535	+	2.40487i	0.0978206	+	0.108641i
$491$	−2.63566	−	25.0767i	−0.118946	−	1.13169i	−0.877331	−	0.479886i	$-0.840678\pi$
$491$	−2.63566	−	25.0767i	−0.118946	−	1.13169i	0.758385	−	0.651807i	$-0.225989\pi$
$492$		0			0
$493$	4.84187	−	5.37745i	0.218067	−	0.242188i
$494$	−6.38197			−0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	−11.1657	+	12.4008i	−0.500851	+	0.556252i
$498$		0			0
$499$	1.83576	+	17.4661i	0.0821799	+	0.781890i	0.955549	+	0.294831i	$0.0952635\pi$
$499$	1.83576	+	17.4661i	0.0821799	+	0.781890i	−0.873369	+	0.487059i	$0.838070\pi$
$500$	−8.91699	−	9.90332i	−0.398780	−	0.442890i
$501$		0			0
$502$	4.40298	+	1.96033i	0.196515	+	0.0874939i
$503$	−22.7082	−	16.4985i	−1.01251	−	0.735631i	−0.0477750	−	0.998858i	$-0.515213\pi$
$503$	−22.7082	−	16.4985i	−1.01251	−	0.735631i	−0.964734	+	0.263227i	$0.915213\pi$
$504$		0			0
$505$	7.85410			0.349503
$506$	2.12193	+	6.79346i	0.0943312	+	0.302006i
$507$		0			0
$508$	−5.86889	−	1.24747i	−0.260390	−	0.0553475i
$509$	21.5761	−	9.60632i	0.956346	−	0.425793i	0.131604	−	0.991302i	$-0.457987\pi$
$509$	21.5761	−	9.60632i	0.956346	−	0.425793i	0.824742	+	0.565510i	$0.191321\pi$
$510$		0			0
$511$	9.49606	−	2.01845i	0.420081	−	0.0892909i
$512$	−5.78115	+	17.7926i	−0.255493	+	0.786327i
$513$		0			0
$514$	−5.83688	−	4.24074i	−0.257454	−	0.187051i
$515$	10.5108	−	11.6735i	0.463163	−	0.514395i
$516$		0			0
$517$	0.621812	−	5.33026i	0.0273473	−	0.234425i
$518$	0.218847	−	0.379054i	0.00961559	−	0.0166547i
$519$		0			0
$520$	1.07939	−	10.2697i	0.0473342	−	0.450355i
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	−0.293028	−	0.956104i	$-0.594663\pi$
$521$	12.0000	−	8.71851i	0.525730	−	0.381965i	0.818758	+	0.574139i	$0.194663\pi$
$522$		0			0
$523$	−3.70163	+	11.3924i	−0.161861	+	0.498156i	−0.998791	−	0.0491529i	$-0.984348\pi$
$523$	−3.70163	+	11.3924i	−0.161861	+	0.498156i	0.836930	+	0.547309i	$0.184348\pi$
$524$	10.5627	+	4.70281i	0.461433	+	0.205443i
$525$		0			0
$526$	−9.86968	−	2.09786i	−0.430338	−	0.0914712i
$527$	−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
$533$	20.6085	−	4.38047i	0.892652	−	0.189739i
$534$		0			0
$535$	−1.15924	−	11.0294i	−0.0501182	−	0.476843i
$536$	−19.5334	+	8.69683i	−0.843714	+	0.375646i
$537$		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	0.992825	+	0.119577i	$0.0381540\pi$
$541$	6.04508	+	18.6049i	0.259899	+	0.799885i	−0.732926	+	0.680308i	$0.761846\pi$
$542$	−1.76173	+	16.7618i	−0.0756729	+	0.719980i
$543$		0			0
$544$	−6.08251	−	6.75531i	−0.260786	−	0.289632i
$545$		0			0
$546$		0			0
$547$	−2.25970	+	21.4996i	−0.0966178	+	0.919257i	0.833630	+	0.552324i	$0.186259\pi$
$547$	−2.25970	+	21.4996i	−0.0966178	+	0.919257i	−0.930247	+	0.366933i	$0.880408\pi$
$548$	−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
$553$	25.9597	−	11.5580i	1.10392	−	0.491496i
$554$	1.97439	+	18.7851i	0.0838838	+	0.798101i
$555$		0			0
$556$	−1.35177	+	0.287327i	−0.0573277	+	0.0121854i
$557$	−12.0623	+	8.76378i	−0.511096	+	0.371333i	−0.813239	−	0.581929i	$-0.802298\pi$
$557$	−12.0623	+	8.76378i	−0.511096	+	0.371333i	0.302143	+	0.953263i	$0.402298\pi$
$558$		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
$563$	8.69431	+	1.84803i	0.366421	+	0.0778853i	0.387443	−	0.921894i	$-0.373358\pi$
$563$	8.69431	+	1.84803i	0.366421	+	0.0778853i	−0.0210214	+	0.999779i	$0.506692\pi$
$564$		0			0
$565$	−1.69381	−	0.754131i	−0.0712590	−	0.0317265i
$566$	−0.0344419	+	0.106001i	−0.00144770	+	0.00445556i
$567$		0			0
$568$	10.0623	−	7.31069i	0.422205	−	0.306750i
$569$	2.51588	−	23.9370i	0.105471	−	1.00349i	−0.805940	−	0.591997i	$-0.798340\pi$
$569$	2.51588	−	23.9370i	0.105471	−	1.00349i	0.911412	−	0.411496i	$-0.134994\pi$
$570$		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	$0.908136\pi$
$572$	−1.09683	+	9.40222i	−0.0458610	+	0.393127i
$573$		0			0
$574$	14.8185	−	16.4576i	0.618512	−	0.686927i
$575$	−5.20820	−	3.78398i	−0.217197	−	0.157803i
$576$		0			0
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	−0.857641	−	0.514249i	$-0.828071\pi$
$577$	3.32624	−	10.2371i	0.138473	−	0.426176i	0.996114	+	0.0880726i	$0.0280707\pi$
$578$	−8.69431	+	1.84803i	−0.361636	+	0.0768680i
$579$		0			0
$580$	17.3065	−	7.70533i	0.718611	−	0.319946i
$581$	−2.07818	−	0.441732i	−0.0862176	−	0.0183261i
$582$		0			0
$583$	9.51060	+	30.4487i	0.393889	+	1.26105i
$584$	−7.23607			−0.299431
$585$		0			0
$586$	0.0278640	+	0.0202444i	0.00115105	+	0.000836289i
$587$	−34.9933	−	15.5800i	−1.44433	−	0.643057i	−0.473057	−	0.881032i	$-0.656850\pi$
$587$	−34.9933	−	15.5800i	−1.44433	−	0.643057i	−0.971271	+	0.237975i	$0.923516\pi$
$588$		0			0
$589$	11.1800	+	12.4166i	0.460663	+	0.511618i
$590$	−1.74648	−	16.6167i	−0.0719016	−	0.684098i
$591$		0			0
$592$	0.292875	−	0.325270i	0.0120371	−	0.0133685i
$593$	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
$596$	−16.2401	+	18.0365i	−0.665222	+	0.738804i
$597$		0			0
$598$	0.395663	+	3.76448i	0.0161799	+	0.153941i
$599$	−5.54829	−	6.16201i	−0.226697	−	0.251773i	0.619056	−	0.785347i	$-0.287515\pi$
$599$	−5.54829	−	6.16201i	−0.226697	−	0.251773i	−0.845753	+	0.533574i	$0.820849\pi$
$600$		0			0
$601$	30.9078	+	13.7610i	1.26076	+	0.561325i	0.924764	−	0.380540i	$-0.124262\pi$
$601$	30.9078	+	13.7610i	1.26076	+	0.561325i	0.335992	+	0.941865i	$0.390929\pi$
$602$	9.35410	+	6.79615i	0.381245	+	0.276991i
$603$		0			0
$604$	−3.23607			−0.131674
$605$	−18.7764	−	21.8356i	−0.763370	−	0.887742i
$606$		0			0
$607$	−13.0350	−	2.77068i	−0.529075	−	0.112458i	−0.0643739	−	0.997926i	$-0.520505\pi$
$607$	−13.0350	−	2.77068i	−0.529075	−	0.112458i	−0.464702	+	0.885467i	$0.653838\pi$
$608$	−30.0452	+	13.3770i	−1.21849	+	0.542508i
$609$		0			0
$610$	−12.4305	+	2.64218i	−0.503296	+	0.106979i
$611$	0.881966	−	2.71441i	0.0356805	−	0.109813i
$612$		0			0
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.146272	−	0.989244i	$-0.546728\pi$
$613$	−28.0344	−	20.3682i	−1.13230	−	0.822664i	−0.986028	+	0.166580i	$0.946728\pi$
$614$	−0.232539	+	0.258261i	−0.00938451	+	0.0104226i
$615$		0			0
$616$	10.9037	+	19.3935i	0.439322	+	0.781388i
$617$	−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
$619$	0.921906	−	8.77135i	0.0370545	−	0.352550i	−0.960248	−	0.279148i	$-0.909948\pi$
$619$	0.921906	−	8.77135i	0.0370545	−	0.352550i	0.997302	−	0.0734016i	$-0.0233855\pi$
$620$	−9.78115	+	7.10642i	−0.392821	+	0.285401i
$621$		0			0
$622$	−0.482779	+	1.48584i	−0.0193577	+	0.0595768i
$623$	1.44668	+	0.644105i	0.0579601	+	0.0258055i
$624$		0			0
$625$	30.1590	+	6.41050i	1.20636	+	0.256420i
$626$	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	−0.516125	+	0.856513i	$0.672626\pi$
$631$	−37.4336	+	27.1971i	−1.49021	+	1.08270i	−0.974084	+	0.226187i	$0.927374\pi$
$632$	−20.7175	+	4.40364i	−0.824098	+	0.175167i
$633$		0			0
$634$	−1.25074	−	11.9000i	−0.0496733	−	0.472610i
$635$	8.86889	−	3.94868i	0.351951	−	0.156699i
$636$		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
$641$	−3.73612	+	35.5468i	−0.147568	+	1.40402i	0.630672	+	0.776049i	$0.282779\pi$
$641$	−3.73612	+	35.5468i	−0.147568	+	1.40402i	−0.778240	+	0.627967i	$0.783887\pi$
$642$		0			0
$643$	−25.8032	−	28.6574i	−1.01758	−	1.13014i	−0.991451	−	0.130478i	$-0.958349\pi$
$643$	−25.8032	−	28.6574i	−1.01758	−	1.13014i	−0.0261284	−	0.999659i	$-0.508318\pi$
$644$	−11.2776	−	12.5250i	−0.444400	−	0.493556i
$645$		0			0
$646$	0.611920	−	5.82203i	0.0240757	−	0.229065i
$647$	8.59017	+	26.4378i	0.337714	+	1.03938i	0.965369	+	0.260887i	$0.0840149\pi$
$647$	8.59017	+	26.4378i	0.337714	+	1.03938i	−0.627655	+	0.778492i	$0.715985\pi$
$648$		0			0
$649$	3.19098	+	34.0993i	0.125257	+	1.33851i
$650$	1.01064	+	1.75049i	0.0396407	+	0.0686597i
$651$		0			0
$652$	−27.0065	+	12.0241i	−1.05766	+	0.470899i
$653$	−5.33455	−	50.7549i	−0.208757	−	1.98619i	−0.157619	−	0.987500i	$-0.550382\pi$
$653$	−5.33455	−	50.7549i	−0.208757	−	1.98619i	−0.0511377	−	0.998692i	$-0.516285\pi$
$654$		0			0
$655$	−18.2994	+	3.88965i	−0.715016	+	0.151981i
$656$	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	$0.104935\pi$
$662$	16.0785	+	3.41759i	0.624908	+	0.132828i
$663$		0			0
$664$	1.44668	+	0.644105i	0.0561422	+	0.0249961i
$665$	−14.2082	+	43.7284i	−0.550971	+	1.69571i
$666$		0			0
$667$	−12.5623	+	9.12705i	−0.486414	+	0.353401i
$668$	1.69713	−	16.1471i	0.0656640	−	0.624751i
$669$		0			0
$670$	7.73607	−	13.3993i	0.298870	−	0.517659i
$671$	25.5400	−	5.12478i	0.985962	−	0.197840i
$672$		0			0
$673$	8.30820	−	9.22719i	0.320258	−	0.355682i	−0.561423	−	0.827529i	$-0.689746\pi$
$673$	8.30820	−	9.22719i	0.320258	−	0.355682i	0.881680	+	0.471847i	$0.156413\pi$
$674$	−0.145898	−	0.106001i	−0.00561978	−	0.00408301i
$675$		0			0
$676$	4.94427	−	15.2169i	0.190164	−	0.585266i
$677$	−13.2322	+	2.81260i	−0.508557	+	0.108097i	−0.455042	−	0.890470i	$-0.650376\pi$
$677$	−13.2322	+	2.81260i	−0.508557	+	0.108097i	−0.0535147	+	0.998567i	$0.517042\pi$
$678$		0			0
$679$	−38.4633	+	17.1250i	−1.47609	+	0.657196i
$680$	9.26515	+	1.96937i	0.355302	+	0.0755218i
$681$		0			0
$682$	−4.77193	+	3.38448i	−0.182727	+	0.129599i
$683$	−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
$686$	8.46903	+	3.77066i	0.323349	+	0.143964i
$687$		0			0
$688$	7.73669	+	8.59247i	0.294959	+	0.327585i
$689$	1.77338	+	16.8726i	0.0675605	+	0.642796i
$690$		0			0
$691$	−17.5926	+	19.5386i	−0.669256	+	0.743284i	−0.978170	−	0.207806i	$-0.933368\pi$
$691$	−17.5926	+	19.5386i	−0.669256	+	0.743284i	0.308914	+	0.951090i	$0.400034\pi$
$692$	−24.8885			−0.946120
$693$		0			0
$694$	12.9443			0.491358
$695$	1.49622	−	1.66172i	0.0567549	−	0.0630327i
$696$		0			0
$697$	2.02014	+	19.2204i	0.0765183	+	0.728023i
$698$	4.18699	+	4.65012i	0.158480	+	0.176010i
$699$		0			0
$700$	−8.22191	−	3.66063i	−0.310759	−	0.138359i
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	0.738966	−	0.673743i	$-0.235315\pi$
$701$	8.64590	+	6.28161i	0.326551	+	0.237253i	−0.412415	+	0.910996i	$0.635315\pi$
$702$		0			0
$703$	1.38197			0.0521218
$704$	0.233431	+	0.747341i	0.00879776	+	0.0281665i
$705$		0			0
$706$	−6.33070	−	1.34563i	−0.238259	−	0.0506436i
$707$	−8.22191	+	3.66063i	−0.309217	+	0.137672i
$708$		0			0
$709$	−47.6775	+	10.1342i	−1.79057	+	0.380597i	−0.979032	−	0.203708i	$-0.934701\pi$
$709$	−47.6775	+	10.1342i	−1.79057	+	0.380597i	−0.811534	+	0.584305i	$0.801367\pi$
$710$	−2.78115	+	8.55951i	−0.104375	+	0.321233i
$711$		0			0
$712$	−0.954915	−	0.693786i	−0.0357870	−	0.0260007i
$713$	6.63097	−	7.36444i	0.248332	−	0.275800i
$714$		0			0
$715$	−7.50627	−	13.3508i	−0.280719	−	0.499293i
$716$	−1.80902	+	3.13331i	−0.0676061	+	0.117097i
$717$		0			0
$718$	−0.824577	+	7.84533i	−0.0307730	+	0.292785i
$719$	1.28115	−	0.930812i	0.0477789	−	0.0347134i	−0.563639	−	0.826021i	$-0.690599\pi$
$719$	1.28115	−	0.930812i	0.0477789	−	0.0347134i	0.611418	+	0.791307i	$0.290599\pi$
$720$		0			0
$721$	−5.56231	+	17.1190i	−0.207151	+	0.637546i
$722$	−8.62176	−	3.83866i	−0.320869	−	0.142860i
$723$		0			0
$724$	−27.6527	−	5.87777i	−1.02771	−	0.218446i
$725$	−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
$731$	−9.86968	+	2.09786i	−0.365043	+	0.0775923i
$732$		0			0
$733$	3.94158	+	37.5016i	0.145586	+	1.38515i	0.786523	+	0.617561i	$0.211879\pi$
$733$	3.94158	+	37.5016i	0.145586	+	1.38515i	−0.640937	+	0.767593i	$0.721454\pi$
$734$	−3.14049	+	1.39824i	−0.115918	+	0.0516098i
$735$		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	−0.986642	−	0.162904i	$-0.947914\pi$
$739$	−7.72542	−	23.7764i	−0.284184	−	0.874629i	0.702458	−	0.711726i	$-0.252086\pi$
$740$	−0.104528	+	0.994522i	−0.00384254	+	0.0365594i
$741$		0			0
$742$	11.9325	+	13.2524i	0.438055	+	0.486510i
$743$	23.5402	+	26.1441i	0.863608	+	0.959134i	0.999501	−	0.0315899i	$-0.0100571\pi$
$743$	23.5402	+	26.1441i	0.863608	+	0.959134i	−0.135893	+	0.990723i	$0.543390\pi$
$744$		0			0
$745$	4.10489	−	39.0554i	0.150391	−	1.43088i
$746$	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
$751$	10.8922	−	4.84952i	0.397462	−	0.176961i	−0.198265	−	0.980148i	$-0.563531\pi$
$751$	10.8922	−	4.84952i	0.397462	−	0.176961i	0.595727	+	0.803187i	$0.296864\pi$
$752$	−0.313585	−	2.98357i	−0.0114353	−	0.108799i
$753$		0			0
$754$	4.76885	−	1.01365i	0.173671	−	0.0369150i
$755$	4.23607	−	3.07768i	0.154166	−	0.112008i
$756$		0			0
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	0.961381	−	0.275220i	$-0.0887509\pi$
$757$	0.600813	+	1.84911i	0.0218369	+	0.0672071i	−0.939544	+	0.342428i	$0.888751\pi$
$758$	0.489357	+	0.847591i	0.0177742	+	0.0307859i
$759$		0			0
$760$	17.1353	−	29.6791i	0.621561	−	1.07658i
$761$	30.2136	+	6.42209i	1.09524	+	0.232801i	0.719894	−	0.694084i	$-0.244190\pi$
$761$	30.2136	+	6.42209i	1.09524	+	0.232801i	0.375347	+	0.926885i	$0.377524\pi$
$762$		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
$767$	−1.90396	+	18.1150i	−0.0687481	+	0.654095i
$768$		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	$0.240131\pi$
$770$	−14.6317	−	6.71556i	−0.527290	−	0.242012i
$771$		0			0
$772$	20.0970	−	22.3199i	0.723306	−	0.803312i
$773$	25.2812	+	18.3678i	0.909300	+	0.660645i	0.940838	−	0.338858i	$-0.110040\pi$
$773$	25.2812	+	18.3678i	0.909300	+	0.660645i	−0.0315378	+	0.999503i	$0.510040\pi$
$774$		0			0
$775$	1.63525	−	5.03280i	0.0587401	−	0.180783i
$776$	30.6962	−	6.52468i	1.10193	−	0.234222i
$777$		0			0
$778$	−13.7032	+	6.10105i	−0.491283	+	0.218733i
$779$	68.3950	+	14.5378i	2.45051	+	0.520871i
$780$		0			0
$781$	5.90063	−	17.4790i	0.211141	−	0.625447i
$782$	−3.47214			−0.124163
$783$		0			0
$784$	−3.00000	−	2.17963i	−0.107143	−	0.0778438i
$785$	8.86889	+	3.94868i	0.316544	+	0.140935i
$786$		0			0
$787$	−6.88656	−	7.64829i	−0.245479	−	0.272632i	0.607796	−	0.794093i	$-0.292054\pi$
$787$	−6.88656	−	7.64829i	−0.245479	−	0.272632i	−0.853275	+	0.521461i	$0.825387\pi$
$788$	4.12374	+	39.2347i	0.146902	+	1.39768i
$789$		0			0
$790$	10.2553	−	11.3896i	0.364866	−	0.405224i
$791$	2.12461			0.0755425
$792$		0			0
$793$	13.8541			0.491974
$794$	16.0076	−	17.7782i	0.568089	−	0.630926i
$795$		0			0
$796$	−2.82587	−	26.8863i	−0.100160	−	0.952961i
$797$	7.20248	+	7.99916i	0.255125	+	0.283345i	0.857078	−	0.515186i	$-0.172277\pi$
$797$	7.20248	+	7.99916i	0.255125	+	0.283345i	−0.601953	+	0.798531i	$0.705611\pi$
$798$		0			0
$799$	2.39169	+	1.06485i	0.0846120	+	0.0376717i
$800$	8.42705	+	6.12261i	0.297941	+	0.216467i
$801$		0			0
$802$	16.1246			0.569380
$803$	−8.75446	+	6.20909i	−0.308938	+	0.219114i
$804$		0			0
$805$	26.6746	+	5.66986i	0.940156	+	0.199836i
$806$	−2.84246	+	1.26554i	−0.100121	+	0.0445769i
$807$		0			0
$808$	6.56161	−	1.39471i	0.230837	−	0.0490659i
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	−0.884654	−	0.466249i	$-0.845605\pi$
$809$	2.98936	−	9.20029i	0.105100	−	0.323465i	0.989754	+	0.142783i	$0.0456052\pi$
$810$		0			0
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	0.540555	−	0.841309i	$-0.318214\pi$
$811$	−2.63525	−	1.91462i	−0.0925363	−	0.0672316i	−0.633091	+	0.774077i	$0.718214\pi$
$812$	−14.5256	+	16.1323i	−0.509749	+	0.566134i
$813$		0			0
$814$	−0.0560688	+	0.480630i	−0.00196521	+	0.0168461i
$815$	23.9164	−	41.4244i	0.837755	−	1.45103i
$816$		0			0
$817$	−3.81598	+	36.3066i	−0.133504	+	1.27021i
$818$	−5.52786	+	4.01623i	−0.193277	+	0.140424i
$819$		0			0
$820$	−15.6353	+	48.1204i	−0.546007	+	1.68044i
$821$	36.9222	+	16.4388i	1.28859	+	0.573719i	0.932648	−	0.360787i	$-0.117492\pi$
$821$	36.9222	+	16.4388i	1.28859	+	0.573719i	0.355946	+	0.934506i	$0.384159\pi$
$822$		0			0
$823$	34.6970	+	7.37507i	1.20946	+	0.257079i	0.768147	−	0.640274i	$-0.221179\pi$
$823$	34.6970	+	7.37507i	1.20946	+	0.257079i	0.441314	+	0.897353i	$0.354512\pi$
$824$	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	0.649880	+	0.760037i	$0.274819\pi$
$827$	16.4164	+	50.5245i	0.570854	+	1.75691i	−0.0790257	+	0.996873i	$0.525181\pi$
$828$		0			0
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	−0.807859	−	0.589375i	$-0.799374\pi$
$829$	−14.3090	+	10.3961i	−0.496973	+	0.361072i	0.310887	+	0.950447i	$0.399374\pi$
$830$	−1.12086	+	0.238246i	−0.0389055	+	0.00826963i
$831$		0			0
$832$	0.0435265	+	0.414127i	0.00150901	+	0.0143573i
$833$	2.95630	−	1.31623i	0.102430	−	0.0456046i
$834$		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
$839$	3.83705	−	36.5071i	0.132470	−	1.26037i	−0.703144	−	0.711048i	$-0.748221\pi$
$839$	3.83705	−	36.5071i	0.132470	−	1.26037i	0.835614	−	0.549318i	$-0.185112\pi$
$840$		0			0
$841$	−6.02218	−	6.68830i	−0.207661	−	0.230631i
$842$	15.4131	+	17.1179i	0.531169	+	0.589923i
$843$		0			0
$844$	−3.76662	+	35.8370i	−0.129653	+	1.23356i
$845$	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
$850$	−1.69381	+	0.754131i	−0.0580971	+	0.0258665i
$851$	−0.0856778	−	0.815170i	−0.00293700	−	0.0279437i
$852$		0			0
$853$	9.72697	−	2.06753i	0.333045	−	0.0707909i	−0.0383541	−	0.999264i	$-0.512211\pi$
$853$	9.72697	−	2.06753i	0.333045	−	0.0707909i	0.371399	+	0.928473i	$0.378878\pi$
$854$	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	$0.205379\pi$
$860$	−25.8391	−	5.49228i	−0.881108	−	0.187285i
$861$		0			0
$862$	22.3055	+	9.93105i	0.759728	+	0.338253i
$863$	3.67376	−	11.3067i	0.125056	−	0.384884i	−0.868855	−	0.495067i	$-0.835144\pi$
$863$	3.67376	−	11.3067i	0.125056	−	0.384884i	0.993911	+	0.110183i	$0.0351436\pi$
$864$		0			0
$865$	32.5795	−	23.6704i	1.10774	−	0.804818i
$866$	−0.387613	+	3.68789i	−0.0131716	+	0.125320i
$867$		0			0
$868$	6.92705	−	11.9980i	0.235119	−	0.407239i
$869$	−21.2861	+	23.1049i	−0.722083	+	0.783779i
$870$		0			0
$871$	−11.2864	+	12.5348i	−0.382425	+	0.424726i
$872$		0			0
$873$		0			0
$874$	−3.88197	+	11.9475i	−0.131309	+	0.404129i
$875$	−24.1683	+	5.13712i	−0.817037	+	0.173667i
$876$		0			0
$877$	5.86168	−	2.60979i	0.197935	−	0.0881263i	−0.305375	−	0.952232i	$-0.598782\pi$
$877$	5.86168	−	2.60979i	0.197935	−	0.0881263i	0.503310	+	0.864106i	$0.332115\pi$
$878$	1.98998	+	0.422984i	0.0671587	+	0.0142750i
$879$		0			0
$880$	−12.9157	−	9.61091i	−0.435389	−	0.323984i
$881$	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	0.434318	−	0.900760i	$-0.356990\pi$
$883$	−8.56231	−	6.22088i	−0.288145	−	0.209349i	−0.722462	+	0.691411i	$0.756990\pi$
$884$	−4.21878	−	1.87832i	−0.141893	−	0.0631749i
$885$		0			0
$886$	17.0069	+	18.8881i	0.571358	+	0.634557i
$887$	−0.313585	−	2.98357i	−0.0105292	−	0.100178i	0.987995	−	0.154485i	$-0.0493718\pi$
$887$	−0.313585	−	2.98357i	−0.0105292	−	0.100178i	−0.998524	+	0.0543066i	$0.982705\pi$
$888$		0			0
$889$	−7.44382	+	8.26720i	−0.249658	+	0.277273i
$890$	0.854102			0.0286296
$891$		0			0
$892$	−1.14590			−0.0383675
$893$	6.33810	−	7.03917i	0.212096	−	0.235557i
$894$		0			0
$895$	−0.611920	−	5.82203i	−0.0204542	−	0.194609i
$896$	22.8481	+	25.3753i	0.763300	+	0.847731i
$897$		0			0
$898$	13.8170	+	6.15173i	0.461080	+	0.205286i
$899$	−10.3262	−	7.50245i	−0.344399	−	0.250221i
$900$		0			0
$901$	−15.5623			−0.518456
$902$	−7.83096	+	23.1971i	−0.260743	+	0.772378i
$903$		0			0
$904$	−1.54899	−	0.329247i	−0.0515185	−	0.0109506i
$905$	41.7880	−	18.6052i	1.38908	−	0.618458i
$906$		0			0
$907$	42.0395	−	8.93578i	1.39590	−	0.296708i	0.552284	−	0.833656i	$-0.313756\pi$
$907$	42.0395	−	8.93578i	1.39590	−	0.296708i	0.843615	+	0.536948i	$0.180423\pi$
$908$	12.4443	−	38.2995i	0.412978	−	1.27101i
$909$		0			0
$910$	−6.92705	−	5.03280i	−0.229630	−	0.166836i
$911$	12.0816	−	13.4180i	0.400283	−	0.444559i	−0.508982	−	0.860777i	$-0.669978\pi$
$911$	12.0816	−	13.4180i	0.400283	−	0.444559i	0.909265	+	0.416218i	$0.136645\pi$
$912$		0			0
$913$	2.30294	−	0.462102i	0.0762163	−	0.0152933i
$914$	2.53444	−	4.38978i	0.0838319	−	0.145201i
$915$		0			0
$916$	1.69131	−	16.0917i	0.0558823	−	0.531685i
$917$	17.3435	−	12.6008i	0.572731	−	0.416114i
$918$		0			0
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	−0.362293	−	0.932064i	$-0.618006\pi$
$919$	14.5106	−	44.6592i	0.478662	−	1.47317i	0.840955	−	0.541106i	$-0.181994\pi$
$920$	−18.5689	−	8.26743i	−0.612200	−	0.272569i
$921$		0			0
$922$	−12.7496	−	2.71001i	−0.419886	−	0.0892495i
$923$	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
$929$	32.1699	−	6.83791i	1.05546	−	0.224345i	0.352673	−	0.935747i	$-0.385273\pi$
$929$	32.1699	−	6.83791i	1.05546	−	0.224345i	0.702785	+	0.711402i	$0.251939\pi$
$930$		0			0
$931$	−1.22384	−	11.6441i	−0.0401098	−	0.381619i
$932$	−35.9578	+	16.0094i	−1.17784	+	0.524406i
$933$		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	0.831668	−	0.555273i	$-0.187386\pi$
$937$	−5.12868	−	15.7844i	−0.167547	−	0.515655i	−0.999215	+	0.0396173i	$0.987386\pi$
$938$	−1.85324	+	17.6324i	−0.0605103	+	0.575717i
$939$		0			0
$940$	4.58629	+	5.09359i	0.149588	+	0.166135i
$941$	−29.8641	−	33.1674i	−0.973542	−	1.08123i	−0.996674	−	0.0814951i	$-0.974030\pi$
$941$	−29.8641	−	33.1674i	−0.973542	−	1.08123i	0.0231321	−	0.999732i	$-0.492636\pi$
$942$		0			0
$943$	4.33502	−	41.2449i	0.141168	−	1.34312i
$944$	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
$949$	−5.21470	+	2.32174i	−0.169276	+	0.0753667i
$950$	0.701198	+	6.67146i	0.0227499	+	0.216451i
$951$		0			0
$952$	−10.6169	+	2.25669i	−0.344096	+	0.0731399i
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.960167	−	0.279426i	$-0.909856\pi$
$953$	−30.5967	+	22.2298i	−0.991126	+	0.720095i	−0.0309585	+	0.999521i	$0.509856\pi$
$954$		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
$959$	−21.9266	−	4.66063i	−0.708045	−	0.150500i
$960$		0			0
$961$	−20.8783	−	9.29560i	−0.673492	−	0.299858i
$962$	−0.0795268	+	0.244758i	−0.00256405	+	0.00789133i
$963$		0			0
$964$	−30.2705	+	21.9928i	−0.974947	+	0.708341i
$965$	−5.07974	+	48.3305i	−0.163523	+	1.55581i
$966$		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	$-0.0216601\pi$
$968$	−19.5640	−	14.9080i	−0.628812	−	0.479161i
$969$		0			0
$970$	−15.1948	+	16.8755i	−0.487874	+	0.541839i
$971$	−30.5623	−	22.2048i	−0.980791	−	0.712586i	−0.0229058	−	0.999738i	$-0.507292\pi$
$971$	−30.5623	−	22.2048i	−0.980791	−	0.712586i	−0.957885	+	0.287151i	$0.907292\pi$
$972$		0			0
$973$	−0.791796	+	2.43690i	−0.0253838	+	0.0781234i
$974$	10.1680	−	2.16127i	0.325803	−	0.0692515i
$975$		0			0
$976$	13.3033	−	5.92302i	0.425829	−	0.189591i
$977$	4.53794	+	0.964569i	0.145182	+	0.0308593i	0.279929	−	0.960021i	$-0.409689\pi$
$977$	4.53794	+	0.964569i	0.145182	+	0.0308593i	−0.134748	+	0.990880i	$0.543022\pi$
$978$		0			0
$979$	−1.75061	−	0.0199794i	−0.0559498	−	0.000638544i
$980$	8.47214			0.270632
$981$		0			0
$982$	12.6074	+	9.15981i	0.402318	+	0.292301i
$983$	−24.9443	−	11.1059i	−0.795600	−	0.354224i	−0.0316497	−	0.999499i	$-0.510076\pi$
$983$	−24.9443	−	11.1059i	−0.795600	−	0.354224i	−0.763950	+	0.645275i	$0.776743\pi$
$984$		0			0
$985$	−42.7125	−	47.4370i	−1.36093	−	1.51147i
$986$	0.467465	+	4.44764i	0.0148871	+	0.141642i
$987$		0			0
$988$	−11.1800	+	12.4166i	−0.355682	+	0.395025i
$989$	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	$0.390304\pi$
$992$	−10.7291	+	11.9159i	−0.340650	+	0.378331i
$993$		0			0
$994$	−1.07801	−	10.2566i	−0.0341924	−	0.325319i
$995$	29.2695	+	32.5071i	0.927907	+	1.03055i
$996$		0			0
$997$	−11.8566	−	5.27892i	−0.375504	−	0.167185i	0.210302	−	0.977636i	$-0.432555\pi$
$997$	−11.8566	−	5.27892i	−0.375504	−	0.167185i	−0.585806	+	0.810451i	$0.699222\pi$
$998$	−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.676.1		8
3.2	odd	2		891.2.n.a.676.1		8
9.2	odd	6		891.2.n.a.379.1		8
9.4	even	3		33.2.e.a.16.1	✓	4
9.5	odd	6		99.2.f.b.82.1		4
9.7	even	3	inner	891.2.n.d.379.1		8
11.9	even	5	inner	891.2.n.d.757.1		8
33.20	odd	10		891.2.n.a.757.1		8
36.31	odd	6		528.2.y.f.49.1		4
45.4	even	6		825.2.n.f.676.1		4
45.13	odd	12		825.2.bx.b.49.1		8
45.22	odd	12		825.2.bx.b.49.2		8
99.4	even	15		363.2.e.h.124.1		4
99.13	odd	30		363.2.e.j.130.1		4
99.14	odd	30		1089.2.a.m.1.2		2
99.20	odd	30		891.2.n.a.460.1		8
99.31	even	15		33.2.e.a.31.1	yes	4
99.40	odd	30		363.2.e.c.124.1		4
99.41	even	30		1089.2.a.s.1.1		2
99.49	even	15		363.2.e.h.202.1		4
99.58	even	15		363.2.a.h.1.1		2
99.76	odd	6		363.2.e.j.148.1		4
99.85	odd	30		363.2.a.e.1.2		2
99.86	odd	30		99.2.f.b.64.1		4
99.94	odd	30		363.2.e.c.202.1		4
99.97	even	15	inner	891.2.n.d.460.1		8
396.31	odd	30		528.2.y.f.97.1		4
396.283	even	30		5808.2.a.bm.1.1		2
396.355	odd	30		5808.2.a.bl.1.1		2
495.184	odd	30		9075.2.a.bv.1.1		2
495.229	even	30		825.2.n.f.526.1		4
495.328	odd	60		825.2.bx.b.724.2		8
495.427	odd	60		825.2.bx.b.724.1		8
495.454	even	30		9075.2.a.x.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	9.4	even	3
33.2.e.a.31.1	yes	4	99.31	even	15
99.2.f.b.64.1		4	99.86	odd	30
99.2.f.b.82.1		4	9.5	odd	6
363.2.a.e.1.2		2	99.85	odd	30
363.2.a.h.1.1		2	99.58	even	15
363.2.e.c.124.1		4	99.40	odd	30
363.2.e.c.202.1		4	99.94	odd	30
363.2.e.h.124.1		4	99.4	even	15
363.2.e.h.202.1		4	99.49	even	15
363.2.e.j.130.1		4	99.13	odd	30
363.2.e.j.148.1		4	99.76	odd	6
528.2.y.f.49.1		4	36.31	odd	6
528.2.y.f.97.1		4	396.31	odd	30
825.2.n.f.526.1		4	495.229	even	30
825.2.n.f.676.1		4	45.4	even	6
825.2.bx.b.49.1		8	45.13	odd	12
825.2.bx.b.49.2		8	45.22	odd	12
825.2.bx.b.724.1		8	495.427	odd	60
825.2.bx.b.724.2		8	495.328	odd	60
891.2.n.a.379.1		8	9.2	odd	6
891.2.n.a.460.1		8	99.20	odd	30
891.2.n.a.676.1		8	3.2	odd	2
891.2.n.a.757.1		8	33.20	odd	10
891.2.n.d.379.1		8	9.7	even	3	inner
891.2.n.d.460.1		8	99.97	even	15	inner
891.2.n.d.676.1		8	1.1	even	1	trivial
891.2.n.d.757.1		8	11.9	even	5	inner
1089.2.a.m.1.2		2	99.14	odd	30
1089.2.a.s.1.1		2	99.41	even	30
5808.2.a.bl.1.1		2	396.355	odd	30
5808.2.a.bm.1.1		2	396.283	even	30
9075.2.a.x.1.2		2	495.454	even	30
9075.2.a.bv.1.1		2	495.184	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.413545 + 0.459289i) q^{2} +(0.169131 + 1.60917i) q^{4} +(-1.75181 - 1.94558i) q^{5} +(2.74064 + 1.22021i) q^{7} +(-1.80902 - 1.31433i) q^{8} +1.61803 q^{10} +(-3.31641 - 0.0378495i) q^{11} +(-1.72539 - 0.366742i) q^{13} +(-1.69381 + 0.754131i) q^{14} +(-1.81359 + 0.385489i) q^{16} +(0.500000 - 1.53884i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.83448 - 3.14801i) q^{20} +(1.38887 - 1.50754i) q^{22} +(-1.73607 + 3.00696i) q^{23} +(-0.193806 + 1.84395i) q^{25} +(0.881966 - 0.640786i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(4.08550 + 1.81898i) q^{29} +(-2.79173 - 0.593401i) q^{31} +(2.80902 - 4.86536i) q^{32} +(0.500000 + 0.866025i) q^{34} +(-2.42705 - 7.46969i) q^{35} +(-0.190983 + 0.138757i) q^{37} +(3.53897 - 0.752232i) q^{38} +(0.611920 + 5.82203i) q^{40} +(-10.9116 + 4.85817i) q^{41} +(-3.11803 - 5.40059i) q^{43} +(-0.500000 - 5.34307i) q^{44} +(-0.663119 - 2.04087i) q^{46} +(-0.169131 + 1.60917i) q^{47} +(1.33826 + 1.48629i) q^{49} +(-0.766755 - 0.851568i) q^{50} +(0.298335 - 2.83847i) q^{52} +(-2.97214 - 9.14729i) q^{53} +(5.73607 + 6.51864i) q^{55} +(-3.35410 - 5.80948i) q^{56} +(-2.52498 + 1.12419i) q^{58} +(-1.07939 - 10.2697i) q^{59} +(-7.68247 + 1.63296i) q^{61} +(1.42705 - 1.03681i) q^{62} +(-0.0729490 - 0.224514i) q^{64} +(2.30902 + 3.99933i) q^{65} +(4.78115 - 8.28120i) q^{67} +(2.56082 + 0.544320i) q^{68} +(4.43444 + 1.97434i) q^{70} +(-1.71885 + 5.29007i) q^{71} +(2.61803 - 1.90211i) q^{73} +(0.0152505 - 0.145099i) q^{74} +(4.73607 - 8.20311i) q^{76} +(-9.04289 - 4.15045i) q^{77} +(6.33810 - 7.03917i) q^{79} +(3.92705 + 2.85317i) q^{80} +(2.28115 - 7.02067i) q^{82} +(-0.692728 + 0.147244i) q^{83} +(-3.86984 + 1.72296i) q^{85} +(3.76988 + 0.801313i) q^{86} +(5.94969 + 4.42732i) q^{88} +0.527864 q^{89} +(-4.28115 - 3.11044i) q^{91} +(-5.13233 - 2.28506i) q^{92} +(-0.669131 - 0.743145i) q^{94} +(1.60203 + 15.2423i) q^{95} +(-9.39087 + 10.4296i) q^{97} -1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 3 q^{4} + q^{5} + 3 q^{7} - 10 q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 6 q^{14} - 9 q^{16} + 4 q^{17} - 20 q^{19} - 3 q^{20} + 8 q^{22} + 4 q^{23} + 6 q^{25} + 16 q^{26} - 12 q^{28} + 10 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) \) 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

Introduction

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