LMFDB - Embedded newform 891.2.n.a.460.1

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			460.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	891.460
Dual form			891.2.n.a.676.1

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

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

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	$-0.163214\pi$
$2$	0.413545	+	0.459289i	0.292421	+	0.324766i	−0.578976	+	0.815344i	$0.696548\pi$
$3$		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	$-0.567600\pi$
$5$	1.75181	−	1.94558i	0.783432	−	0.870089i	0.994211	+	0.107445i	$0.0342668\pi$
$6$		0			0
$7$	2.74064	−	1.22021i	1.03586	−	0.461196i	0.182880	−	0.983135i	$-0.441458\pi$
$7$	2.74064	−	1.22021i	1.03586	−	0.461196i	0.852983	+	0.521939i	$0.174791\pi$
$8$	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	−0.440863	−	0.897574i	$-0.645328\pi$
$13$	−1.72539	+	0.366742i	−0.478536	+	0.101716i	−0.0376725	+	0.999290i	$0.511994\pi$
$14$	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	$-0.162865\pi$
$17$	−0.500000	−	1.53884i	−0.121268	−	0.373224i	−0.993203	+	0.116398i	$0.962865\pi$
$18$		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	$0.534355\pi$
$20$	−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	$-0.0487623\pi$
$23$	1.73607	+	3.00696i	0.361995	+	0.626994i	−0.626294	+	0.779587i	$0.715429\pi$
$24$		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	$-0.769631\pi$
$29$	−4.08550	+	1.81898i	−0.758658	+	0.337776i	−0.00931360	+	0.999957i	$0.502965\pi$
$30$		0			0
$31$	−2.79173	+	0.593401i	−0.501410	+	0.106578i	−0.451672	−	0.892184i	$-0.649172\pi$
$31$	−2.79173	+	0.593401i	−0.501410	+	0.106578i	−0.0497385	+	0.998762i	$0.515839\pi$
$32$	−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	$0.706177\pi$
$38$	−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	0.998756	+	0.0498651i	$0.0158791\pi$
$41$	10.9116	+	4.85817i	1.70411	+	0.758719i	0.705355	+	0.708854i	$0.250788\pi$
$42$		0			0
$43$	−3.11803	+	5.40059i	−0.475496	+	0.823583i	−0.999606	−	0.0280676i	$-0.991065\pi$
$43$	−3.11803	+	5.40059i	−0.475496	+	0.823583i	0.524110	+	0.851650i	$0.324398\pi$
$44$	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	0.999908	+	0.0135627i	$0.00431728\pi$
$47$	0.169131	+	1.60917i	0.0246702	+	0.234722i	−0.975238	+	0.221159i	$0.929016\pi$
$48$		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	−0.509893	−	0.860238i	$-0.670315\pi$
$53$	2.97214	−	9.14729i	0.408254	−	1.25648i	0.918147	−	0.396240i	$-0.129685\pi$
$54$		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	−0.666069	−	0.745890i	$-0.732024\pi$
$59$	1.07939	−	10.2697i	0.140524	−	1.33700i	0.806593	−	0.591107i	$-0.201309\pi$
$60$		0			0
$61$	−7.68247	−	1.63296i	−0.983640	−	0.209079i	−0.312101	−	0.950049i	$-0.601033\pi$
$61$	−7.68247	−	1.63296i	−0.983640	−	0.209079i	−0.671538	+	0.740970i	$0.734366\pi$
$62$	−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	0.994986	+	0.100018i	$0.0318900\pi$
$67$	4.78115	+	8.28120i	0.584111	+	1.01171i	−0.410875	+	0.911692i	$0.634777\pi$
$68$	−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	0.999753	+	0.0222083i	$0.00706970\pi$
$71$	1.71885	+	5.29007i	0.203990	+	0.627815i	−0.795764	+	0.605607i	$0.792930\pi$
$72$		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	$0.639353\pi$
$74$	−0.0152505	−	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	0.985402	−	0.170241i	$-0.0544546\pi$
$79$	6.33810	+	7.03917i	0.713092	+	0.791968i	−0.272311	+	0.962209i	$0.587788\pi$
$80$	−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	$-0.420958\pi$
$83$	0.692728	+	0.147244i	0.0760368	+	0.0161621i	−0.169736	+	0.985490i	$0.554292\pi$
$84$		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	$-0.508906\pi$
$89$	−0.527864			−0.0559535			−0.0279767	+	0.999609i	$0.508906\pi$
$90$		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	−0.998200	−	0.0599674i	$-0.980900\pi$
$97$	−9.39087	−	10.4296i	−0.953499	−	1.05897i	0.0447015	−	0.999000i	$-0.485766\pi$
$98$	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	$-0.185646\pi$
$101$	2.00739	+	2.22943i	0.199743	+	0.221837i	−0.634949	+	0.772554i	$0.718979\pi$
$102$		0			0
$103$	0.627171	−	5.96713i	0.0617970	−	0.587959i	−0.919180	−	0.393837i	$-0.871148\pi$
$103$	0.627171	−	5.96713i	0.0617970	−	0.587959i	0.980977	−	0.194122i	$-0.0621858\pi$
$104$	−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	$-0.765641\pi$
$107$	−3.42705	+	2.48990i	−0.331306	+	0.240708i	0.409679	+	0.912230i	$0.365641\pi$
$108$		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	$-0.377272\pi$
$113$	−0.646976	−	0.288052i	−0.0608624	−	0.0270977i	−0.436942	+	0.899490i	$0.643939\pi$
$114$		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	0.887255	−	0.461279i	$-0.152609\pi$
$127$	−1.14590	−	3.52671i	−0.101682	−	0.312945i	−0.988937	+	0.148333i	$0.952609\pi$
$128$	−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	$-0.267723\pi$
$131$	−3.57295	−	6.18853i	−0.312170	−	0.540694i	−0.978832	+	0.204666i	$0.934389\pi$
$132$		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	$-0.329921\pi$
$137$	7.30885	+	1.55354i	0.624437	+	0.132728i	0.115183	+	0.993344i	$0.463255\pi$
$138$		0			0
$139$	0.0892780	−	0.849423i	0.00757246	−	0.0720471i	−0.990083	−	0.140483i	$-0.955134\pi$
$139$	0.0892780	−	0.849423i	0.00757246	−	0.0720471i	0.997655	+	0.0684363i	$0.0218010\pi$
$140$	−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	$-0.977278\pi$
$149$	−10.0370	+	11.1472i	−0.822260	+	0.913212i	0.175194	+	0.984534i	$0.443945\pi$
$150$		0			0
$151$	−0.209057	−	1.98904i	−0.0170128	−	0.161866i	0.982717	−	0.185115i	$-0.0592657\pi$
$151$	−0.209057	−	1.98904i	−0.0170128	−	0.161866i	−0.999730	+	0.0232487i	$0.992599\pi$
$152$	−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	0.267079	−	0.963675i	$-0.413942\pi$
$157$	−3.38761	−	1.50826i	−0.270361	−	0.120372i	−0.537439	+	0.843302i	$0.680608\pi$
$158$	−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	−0.443282	−	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
$167$	9.81517	−	2.08628i	0.759520	−	0.161441i	0.188158	−	0.982139i	$-0.439748\pi$
$167$	9.81517	−	2.08628i	0.759520	−	0.161441i	0.571363	+	0.820698i	$0.306415\pi$
$168$		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	0.867902	+	0.496735i	$0.165468\pi$
$173$	1.60785	+	15.2977i	0.122243	+	1.16306i	−0.745659	+	0.666327i	$0.767865\pi$
$174$		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	$-0.726631\pi$
$179$	−1.80902	+	1.31433i	−0.135212	+	0.0982375i	0.518123	+	0.855306i	$0.326631\pi$
$180$		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	$-0.324958\pi$
$182$	−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	$-0.546200\pi$
$191$	6.82614	−	3.03919i	0.493922	−	0.219908i	0.638554	+	0.769577i	$0.279533\pi$
$192$		0			0
$193$	−12.4206	+	13.7945i	−0.894055	+	0.992949i	−0.999999	−	0.00142357i	$-0.999547\pi$
$193$	−12.4206	+	13.7945i	−0.894055	+	0.992949i	0.105944	+	0.994372i	$0.466214\pi$
$194$	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	$-0.834961\pi$
$197$	−24.3820			−1.73714			−0.868572	+	0.495564i	$0.834961\pi$
$198$		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	0.616321	−	0.787495i	$-0.288622\pi$
$211$	21.7838	−	4.63030i	1.49966	−	0.318763i	0.883341	+	0.468732i	$0.155289\pi$
$212$	−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	0.991764	−	0.128082i	$-0.0408819\pi$
$223$	−0.0740275	−	0.704324i	−0.00495725	−	0.0471650i	−0.996721	+	0.0809165i	$0.974215\pi$
$224$	−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	$-0.323970\pi$
$227$	22.7368	−	10.1231i	1.50910	−	0.671893i	0.983840	+	0.179052i	$0.0573030\pi$
$228$		0			0
$229$	−9.78148	+	2.07912i	−0.646378	+	0.137392i	−0.519424	−	0.854517i	$-0.673853\pi$
$229$	−9.78148	+	2.07912i	−0.646378	+	0.137392i	−0.126954	+	0.991909i	$0.540520\pi$
$230$	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	$0.393493\pi$
$233$	−7.51722	+	23.1356i	−0.492470	+	1.51567i	−0.820863	+	0.571124i	$0.806507\pi$
$234$		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	$-0.393076\pi$
$239$	−2.34078	−	1.04218i	−0.151413	−	0.0674133i	−0.481044	+	0.876696i	$0.659742\pi$
$240$		0			0
$241$	11.5623	−	20.0265i	0.744794	−	1.29002i	−0.205498	−	0.978658i	$-0.565881\pi$
$241$	11.5623	−	20.0265i	0.744794	−	1.29002i	0.950291	−	0.311363i	$-0.100785\pi$
$242$	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	$-0.820846\pi$
$251$	2.40983	−	7.41669i	0.152107	−	0.468138i	0.997856	+	0.0654431i	$0.0208461\pi$
$252$		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	0.888202	+	0.459454i	$0.151955\pi$
$257$	−1.22024	+	11.6098i	−0.0761165	+	0.724200i	−0.964318	+	0.264746i	$0.914712\pi$
$258$		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	0.496633	+	0.867961i	$0.334570\pi$
$263$	−8.16312	+	14.1389i	−0.503359	+	0.871844i	−0.999992	+	0.00388355i	$0.998764\pi$
$264$		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	−0.984029	−	0.178006i	$-0.943035\pi$
$269$	−4.79837	−	14.7679i	−0.292562	−	0.900413i	0.691467	−	0.722408i	$-0.256965\pi$
$270$		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	$0.389318\pi$
$272$	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	0.908815	+	0.417199i	$0.136988\pi$
$277$	20.4502	+	22.7122i	1.22873	+	1.36465i	0.319917	+	0.947446i	$0.396345\pi$
$278$	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	$-0.440587\pi$
$281$	−0.747238	−	0.158830i	−0.0445765	−	0.00947503i	−0.230146	+	0.973156i	$0.573920\pi$
$282$		0			0
$283$	0.164749	+	0.0733508i	0.00979329	+	0.00436025i	0.411627	−	0.911352i	$-0.364961\pi$
$283$	0.164749	+	0.0733508i	0.00979329	+	0.00436025i	−0.401834	+	0.915712i	$0.631627\pi$
$284$	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	$-0.966149\pi$
$293$	0.00582517	−	0.0554228i	0.000340310	−	0.00323783i	0.994691	+	0.102909i	$0.0328152\pi$
$294$		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	$-0.389500\pi$
$311$	−2.30932	−	1.02817i	−0.130949	−	0.0583025i	−0.471165	+	0.882045i	$0.656167\pi$
$312$		0			0
$313$	−25.2683	−	5.37094i	−1.42825	−	0.303584i	−0.572045	−	0.820222i	$-0.693850\pi$
$313$	−25.2683	−	5.37094i	−1.42825	−	0.303584i	−0.856204	+	0.516638i	$0.827183\pi$
$314$	−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	$-0.0503555\pi$
$317$	12.9548	+	14.3878i	0.727615	+	0.808099i	−0.259898	+	0.965636i	$0.583689\pi$
$318$		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	0.225535	+	0.974235i	$0.427587\pi$
$331$	−13.2984	+	23.0335i	−0.730945	+	1.26603i	−0.956480	+	0.291798i	$0.905746\pi$
$332$	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	−0.993660	−	0.112429i	$-0.964137\pi$
$337$	0.0305010	−	0.290198i	0.00166150	−	0.0158081i	0.995321	+	0.0966211i	$0.0308035\pi$
$338$	−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	$-0.576632\pi$
$347$	14.0145	−	15.5646i	0.752335	−	0.835553i	0.990763	+	0.135607i	$0.0432986\pi$
$348$		0			0
$349$	1.05831	+	10.0691i	0.0566500	+	0.538989i	0.985637	+	0.168877i	$0.0540141\pi$
$349$	1.05831	+	10.0691i	0.0566500	+	0.538989i	−0.928987	+	0.370112i	$0.879319\pi$
$350$	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	$-0.923233\pi$
$353$	−5.23607	+	9.06914i	−0.278688	+	0.482701i	0.692371	+	0.721542i	$0.256566\pi$
$354$		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	$-0.409354\pi$
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	−0.825938	+	0.563761i	$0.809354\pi$
$360$		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	−0.269804	−	0.962915i	$-0.586959\pi$
$367$	5.08142	−	2.26239i	0.265248	−	0.118096i	0.535052	+	0.844819i	$0.320292\pi$
$368$	−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	0.917514	−	0.397703i	$-0.130192\pi$
$373$	2.20820	+	3.82472i	0.114336	+	0.198037i	−0.803178	+	0.595739i	$0.796859\pi$
$374$	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	0.962838	−	0.270080i	$-0.0870502\pi$
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	−0.937701	+	0.347443i	$0.887050\pi$
$380$	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	$-0.325607\pi$
$383$	26.3010	−	5.59044i	1.34392	−	0.285658i	0.823045	+	0.567977i	$0.192274\pi$
$384$		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	$-0.844291\pi$
$389$	−22.1722	+	9.87171i	−1.12418	+	0.500515i	−0.241455	+	0.970412i	$0.577624\pi$
$390$		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	$-0.540832\pi$
$401$	17.4577	−	19.3888i	0.871797	−	0.968229i	0.999723	+	0.0235546i	$0.00749836\pi$
$402$		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	0.0673681	−	0.997728i	$-0.478540\pi$
$409$	10.8141	−	2.29862i	0.534725	−	0.113659i	0.467356	+	0.884069i	$0.345206\pi$
$410$	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	$-0.0345647\pi$
$419$	8.25329	+	14.2951i	0.403200	+	0.698362i	−0.590911	+	0.806737i	$0.701231\pi$
$420$		0			0
$421$	3.89583	+	37.0663i	0.189871	+	1.80650i	0.511121	+	0.859508i	$0.329230\pi$
$421$	3.89583	+	37.0663i	0.189871	+	1.80650i	−0.321250	+	0.946994i	$0.604103\pi$
$422$	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	0.00138127	−	0.999999i	$-0.499560\pi$
$431$	12.2082	−	37.5730i	0.588048	−	1.80983i	0.586667	−	0.809828i	$-0.300440\pi$
$432$		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	$0.653949\pi$
$434$	−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	−0.902626	−	0.430425i	$-0.858364\pi$
$439$	−1.64590	+	2.85078i	−0.0785544	+	0.136060i	0.824072	+	0.566485i	$0.191697\pi$
$440$	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	−0.314442	−	0.949277i	$-0.601817\pi$
$443$	−4.29869	−	40.8993i	−0.204237	−	1.94319i	0.110205	−	0.993909i	$-0.464849\pi$
$444$		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	−0.598020	−	0.801481i	$-0.704046\pi$
$449$	7.56231	−	23.2744i	0.356887	−	1.09839i	0.954907	−	0.296905i	$-0.0959544\pi$
$450$		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	0.0164144	−	0.999865i	$-0.494775\pi$
$457$	−8.02240	−	1.70521i	−0.375272	−	0.0797665i	−0.391687	+	0.920099i	$0.628108\pi$
$458$	−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	$-0.996751\pi$
$461$	−10.5451	+	18.2646i	−0.491134	+	0.850668i	0.508814	+	0.860876i	$0.330084\pi$
$462$		0			0
$463$	7.89919	+	13.6818i	0.367106	+	0.635847i	0.989112	−	0.147166i	$-0.0470152\pi$
$463$	7.89919	+	13.6818i	0.367106	+	0.635847i	−0.622005	+	0.783013i	$0.713682\pi$
$464$	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	$-0.0274643\pi$
$467$	3.01722	+	9.28605i	0.139620	+	0.429707i	−0.856660	+	0.515882i	$0.827464\pi$
$468$		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	$-0.655119\pi$
$479$	−27.4763	−	5.84027i	−1.25543	−	0.266849i	−0.787166	+	0.616742i	$0.788452\pi$
$480$		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	−0.851736	−	0.523972i	$-0.824450\pi$
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	0.235126	+	0.971965i	$0.424450\pi$
$488$	−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	−0.758385	−	0.651807i	$-0.774011\pi$
$491$	2.63566	−	25.0767i	0.118946	−	1.13169i	0.877331	−	0.479886i	$-0.159322\pi$
$492$		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	−0.873369	−	0.487059i	$-0.838070\pi$
$499$	1.83576	−	17.4661i	0.0821799	−	0.781890i	0.955549	−	0.294831i	$-0.0952635\pi$
$500$	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	$-0.484787\pi$
$503$	22.7082	−	16.4985i	1.01251	−	0.735631i	0.964734	+	0.263227i	$0.0847870\pi$
$504$		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	$-0.542013\pi$
$509$	−21.5761	−	9.60632i	−0.956346	−	0.425793i	−0.824742	+	0.565510i	$0.808679\pi$
$510$		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	$-0.405337\pi$
$521$	−12.0000	−	8.71851i	−0.525730	−	0.381965i	−0.818758	+	0.574139i	$0.805337\pi$
$522$		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	$0.984348\pi$
$524$	−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	−0.732926	−	0.680308i	$-0.761846\pi$
$541$	6.04508	−	18.6049i	0.259899	−	0.799885i	0.992825	−	0.119577i	$-0.0381540\pi$
$542$	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	−0.930247	−	0.366933i	$-0.880408\pi$
$547$	−2.25970	−	21.4996i	−0.0966178	−	0.919257i	0.833630	−	0.552324i	$-0.186259\pi$
$548$	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	$-0.197702\pi$
$557$	12.0623	+	8.76378i	0.511096	+	0.371333i	−0.302143	+	0.953263i	$0.597702\pi$
$558$		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	$-0.626642\pi$
$563$	−8.69431	+	1.84803i	−0.366421	+	0.0778853i	0.0210214	+	0.999779i	$0.493308\pi$
$564$		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	−0.911412	−	0.411496i	$-0.865006\pi$
$569$	−2.51588	−	23.9370i	−0.105471	−	1.00349i	0.805940	−	0.591997i	$-0.201660\pi$
$570$		0			0
$571$	−17.3435	−	30.0398i	−0.725801	−	1.25712i	−0.958643	−	0.284610i	$-0.908136\pi$
$571$	−17.3435	−	30.0398i	−0.725801	−	1.25712i	0.232842	−	0.972515i	$-0.425197\pi$
$572$	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	0.996114	−	0.0880726i	$-0.0280707\pi$
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	−0.857641	+	0.514249i	$0.828071\pi$
$578$	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	$-0.343150\pi$
$587$	34.9933	−	15.5800i	1.44433	−	0.643057i	0.971271	+	0.237975i	$0.0764837\pi$
$588$		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	$-0.650763\pi$
$593$	−22.2148			−0.912252			−0.456126	+	0.889915i	$0.650763\pi$
$594$		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	$-0.712485\pi$
$599$	5.54829	−	6.16201i	0.226697	−	0.251773i	0.845753	+	0.533574i	$0.179151\pi$
$600$		0			0
$601$	30.9078	−	13.7610i	1.26076	−	0.561325i	0.335992	−	0.941865i	$-0.390929\pi$
$601$	30.9078	−	13.7610i	1.26076	−	0.561325i	0.924764	+	0.380540i	$0.124262\pi$
$602$	−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	−0.464702	−	0.885467i	$-0.653838\pi$
$607$	−13.0350	+	2.77068i	−0.529075	+	0.112458i	−0.0643739	+	0.997926i	$0.520505\pi$
$608$	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	−0.986028	−	0.166580i	$-0.946728\pi$
$613$	−28.0344	+	20.3682i	−1.13230	+	0.822664i	−0.146272	+	0.989244i	$0.546728\pi$
$614$	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	$-0.0376874\pi$
$617$	9.79180	+	16.9599i	0.394203	+	0.682779i	−0.598796	+	0.800901i	$0.704354\pi$
$618$		0			0
$619$	0.921906	+	8.77135i	0.0370545	+	0.352550i	0.997302	+	0.0734016i	$0.0233855\pi$
$619$	0.921906	+	8.77135i	0.0370545	+	0.352550i	−0.960248	+	0.279148i	$0.909948\pi$
$620$	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	−0.974084	−	0.226187i	$-0.927374\pi$
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.516125	−	0.856513i	$-0.672626\pi$
$632$	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	0.778240	+	0.627967i	$0.216113\pi$
$641$	3.73612	+	35.5468i	0.147568	+	1.40402i	−0.630672	+	0.776049i	$0.717221\pi$
$642$		0			0
$643$	−25.8032	+	28.6574i	−1.01758	+	1.13014i	−0.0261284	+	0.999659i	$0.508318\pi$
$643$	−25.8032	+	28.6574i	−1.01758	+	1.13014i	−0.991451	+	0.130478i	$0.958349\pi$
$644$	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	0.627655	+	0.778492i	$0.284015\pi$
$647$	−8.59017	+	26.4378i	−0.337714	+	1.03938i	−0.965369	+	0.260887i	$0.915985\pi$
$648$		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	0.0511377	−	0.998692i	$-0.483715\pi$
$653$	5.33455	−	50.7549i	0.208757	−	1.98619i	0.157619	−	0.987500i	$-0.449618\pi$
$654$		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	$-0.899860\pi$
$659$	−5.32624	+	9.22531i	−0.207481	+	0.359367i	0.743440	+	0.668803i	$0.233193\pi$
$660$		0			0
$661$	4.95492	+	8.58216i	0.192724	+	0.333808i	0.946152	−	0.323723i	$-0.104935\pi$
$661$	4.95492	+	8.58216i	0.192724	+	0.333808i	−0.753428	+	0.657530i	$0.771601\pi$
$662$	−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	0.881680	−	0.471847i	$-0.156413\pi$
$673$	8.30820	+	9.22719i	0.320258	+	0.355682i	−0.561423	+	0.827529i	$0.689746\pi$
$674$	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	$-0.349624\pi$
$677$	13.2322	+	2.81260i	0.508557	+	0.108097i	0.0535147	+	0.998567i	$0.482958\pi$
$678$		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	$-0.481040\pi$
$683$	3.11146			0.119057			0.0595283	+	0.998227i	$0.481040\pi$
$684$		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	0.308914	−	0.951090i	$-0.400034\pi$
$691$	−17.5926	−	19.5386i	−0.669256	−	0.743284i	−0.978170	+	0.207806i	$0.933368\pi$
$692$	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	$-0.764685\pi$
$701$	−8.64590	+	6.28161i	−0.326551	+	0.237253i	0.412415	+	0.910996i	$0.364685\pi$
$702$		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	−0.811534	−	0.584305i	$-0.801367\pi$
$709$	−47.6775	−	10.1342i	−1.79057	−	0.380597i	−0.979032	+	0.203708i	$0.934701\pi$
$710$	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	$-0.309401\pi$
$719$	−1.28115	−	0.930812i	−0.0477789	−	0.0347134i	−0.611418	+	0.791307i	$0.709401\pi$
$720$		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	0.240286	+	0.970702i	$0.422759\pi$
$727$	−19.4271	+	33.6486i	−0.720509	+	1.24796i	−0.960796	+	0.277257i	$0.910575\pi$
$728$	−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	−0.640937	−	0.767593i	$-0.721454\pi$
$733$	3.94158	−	37.5016i	0.145586	−	1.38515i	0.786523	−	0.617561i	$-0.211879\pi$
$734$	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	0.702458	+	0.711726i	$0.252086\pi$
$739$	−7.72542	+	23.7764i	−0.284184	+	0.874629i	−0.986642	+	0.162904i	$0.947914\pi$
$740$	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	$-0.989943\pi$
$743$	−23.5402	+	26.1441i	−0.863608	+	0.959134i	0.135893	+	0.990723i	$0.456610\pi$
$744$		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	0.595727	−	0.803187i	$-0.296864\pi$
$751$	10.8922	+	4.84952i	0.397462	+	0.176961i	−0.198265	+	0.980148i	$0.563531\pi$
$752$	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	−0.939544	−	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
$761$	−30.2136	+	6.42209i	−1.09524	+	0.232801i	−0.719894	−	0.694084i	$-0.755810\pi$
$761$	−30.2136	+	6.42209i	−1.09524	+	0.232801i	−0.375347	+	0.926885i	$0.622476\pi$
$762$		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	0.728687	−	0.684847i	$-0.240131\pi$
$769$	−6.34346	−	10.9872i	−0.228751	−	0.396208i	−0.957438	+	0.288638i	$0.906797\pi$
$770$	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	$-0.889960\pi$
$773$	−25.2812	+	18.3678i	−0.909300	+	0.660645i	0.0315378	+	0.999503i	$0.489960\pi$
$774$		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	−0.853275	−	0.521461i	$-0.825387\pi$
$787$	−6.88656	+	7.64829i	−0.245479	+	0.272632i	0.607796	+	0.794093i	$0.292054\pi$
$788$	−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	$-0.827723\pi$
$797$	−7.20248	+	7.99916i	−0.255125	+	0.283345i	0.601953	+	0.798531i	$0.294389\pi$
$798$		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	$-0.154395\pi$
$809$	−2.98936	−	9.20029i	−0.105100	−	0.323465i	−0.989754	+	0.142783i	$0.954395\pi$
$810$		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	$0.318214\pi$
$812$	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	$-0.882508\pi$
$821$	−36.9222	+	16.4388i	−1.28859	+	0.573719i	−0.355946	+	0.934506i	$0.615841\pi$
$822$		0			0
$823$	34.6970	−	7.37507i	1.20946	−	0.257079i	0.441314	−	0.897353i	$-0.354512\pi$
$823$	34.6970	−	7.37507i	1.20946	−	0.257079i	0.768147	+	0.640274i	$0.221179\pi$
$824$	−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	$0.474819\pi$
$827$	−16.4164	+	50.5245i	−0.570854	+	1.75691i	−0.649880	+	0.760037i	$0.725181\pi$
$828$		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	$0.799374\pi$
$830$	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	−0.835614	−	0.549318i	$-0.814888\pi$
$839$	−3.83705	−	36.5071i	−0.132470	−	1.26037i	0.703144	−	0.711048i	$-0.251779\pi$
$840$		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	0.371399	−	0.928473i	$-0.378878\pi$
$853$	9.72697	+	2.06753i	0.333045	+	0.0707909i	−0.0383541	+	0.999264i	$0.512211\pi$
$854$	−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	−0.0942157	−	0.995552i	$-0.530034\pi$
$857$	23.8607	−	41.3279i	0.815065	−	1.41173i	0.909281	−	0.416183i	$-0.136632\pi$
$858$		0			0
$859$	−3.55573	−	6.15870i	−0.121320	−	0.210132i	0.798969	−	0.601373i	$-0.205379\pi$
$859$	−3.55573	−	6.15870i	−0.121320	−	0.210132i	−0.920288	+	0.391241i	$0.872046\pi$
$860$	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	$-0.164856\pi$
$863$	−3.67376	−	11.3067i	−0.125056	−	0.384884i	−0.993911	+	0.110183i	$0.964856\pi$
$864$		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	0.503310	−	0.864106i	$-0.332115\pi$
$877$	5.86168	+	2.60979i	0.197935	+	0.0881263i	−0.305375	+	0.952232i	$0.598782\pi$
$878$	−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	$-0.575285\pi$
$881$	−13.9098			−0.468634			−0.234317	+	0.972160i	$0.575285\pi$
$882$		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	$0.356990\pi$
$884$	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	$-0.950628\pi$
$887$	0.313585	−	2.98357i	0.0105292	−	0.100178i	0.998524	+	0.0543066i	$0.0172948\pi$
$888$		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	0.843615	−	0.536948i	$-0.180423\pi$
$907$	42.0395	+	8.93578i	1.39590	+	0.296708i	0.552284	+	0.833656i	$0.313756\pi$
$908$	−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	$-0.330022\pi$
$911$	−12.0816	−	13.4180i	−0.400283	−	0.444559i	−0.909265	+	0.416218i	$0.863355\pi$
$912$		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	0.840955	+	0.541106i	$0.181994\pi$
$919$	14.5106	+	44.6592i	0.478662	+	1.47317i	−0.362293	+	0.932064i	$0.618006\pi$
$920$	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	$-0.614727\pi$
$929$	−32.1699	−	6.83791i	−1.05546	−	0.224345i	−0.702785	+	0.711402i	$0.748061\pi$
$930$		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	−0.999215	−	0.0396173i	$-0.987386\pi$
$937$	−5.12868	+	15.7844i	−0.167547	+	0.515655i	0.831668	+	0.555273i	$0.187386\pi$
$938$	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	−0.0231321	−	0.999732i	$-0.507364\pi$
$941$	29.8641	−	33.1674i	0.973542	−	1.08123i	0.996674	−	0.0814951i	$-0.0259695\pi$
$942$		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	$-0.737093\pi$
$947$	9.16312	−	15.8710i	0.297761	−	0.515738i	0.975623	+	0.219451i	$0.0704267\pi$
$948$		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	$-0.0901440\pi$
$953$	30.5967	+	22.2298i	0.991126	+	0.720095i	0.0309585	+	0.999521i	$0.490144\pi$
$954$		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	0.997686	+	0.0679948i	$0.0216601\pi$
$967$	17.3435	+	30.0398i	0.557728	+	0.966013i	−0.439958	+	0.898019i	$0.645007\pi$
$968$	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	$-0.492708\pi$
$971$	30.5623	−	22.2048i	0.980791	−	0.712586i	0.957885	+	0.287151i	$0.0927082\pi$
$972$		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	$-0.590311\pi$
$977$	−4.53794	+	0.964569i	−0.145182	+	0.0308593i	0.134748	+	0.990880i	$0.456978\pi$
$978$		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	$-0.489924\pi$
$983$	24.9443	−	11.1059i	0.795600	−	0.354224i	0.763950	+	0.645275i	$0.223257\pi$
$984$		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	−0.585806	−	0.810451i	$-0.699222\pi$
$997$	−11.8566	+	5.27892i	−0.375504	+	0.167185i	0.210302	+	0.977636i	$0.432555\pi$
$998$	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.a.460.1		8
3.2	odd	2		891.2.n.d.460.1		8
9.2	odd	6		33.2.e.a.31.1	yes	4
9.4	even	3	inner	891.2.n.a.757.1		8
9.5	odd	6		891.2.n.d.757.1		8
9.7	even	3		99.2.f.b.64.1		4
11.5	even	5	inner	891.2.n.a.379.1		8
33.5	odd	10		891.2.n.d.379.1		8
36.11	even	6		528.2.y.f.97.1		4
45.2	even	12		825.2.bx.b.724.1		8
45.29	odd	6		825.2.n.f.526.1		4
45.38	even	12		825.2.bx.b.724.2		8
99.2	even	30		363.2.e.c.124.1		4
99.5	odd	30		891.2.n.d.676.1		8
99.7	odd	30		1089.2.a.s.1.1		2
99.16	even	15		99.2.f.b.82.1		4
99.20	odd	30		363.2.e.h.124.1		4
99.29	even	30		363.2.a.e.1.2		2
99.38	odd	30		33.2.e.a.16.1	✓	4
99.47	odd	30		363.2.e.h.202.1		4
99.49	even	15	inner	891.2.n.a.676.1		8
99.65	even	6		363.2.e.j.130.1		4
99.70	even	15		1089.2.a.m.1.2		2
99.74	even	30		363.2.e.c.202.1		4
99.83	even	30		363.2.e.j.148.1		4
99.92	odd	30		363.2.a.h.1.1		2
396.191	even	30		5808.2.a.bl.1.1		2
396.227	odd	30		5808.2.a.bm.1.1		2
396.335	even	30		528.2.y.f.49.1		4
495.29	even	30		9075.2.a.bv.1.1		2
495.38	even	60		825.2.bx.b.49.1		8
495.137	even	60		825.2.bx.b.49.2		8
495.389	odd	30		9075.2.a.x.1.2		2
495.434	odd	30		825.2.n.f.676.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	99.38	odd	30
33.2.e.a.31.1	yes	4	9.2	odd	6
99.2.f.b.64.1		4	9.7	even	3
99.2.f.b.82.1		4	99.16	even	15
363.2.a.e.1.2		2	99.29	even	30
363.2.a.h.1.1		2	99.92	odd	30
363.2.e.c.124.1		4	99.2	even	30
363.2.e.c.202.1		4	99.74	even	30
363.2.e.h.124.1		4	99.20	odd	30
363.2.e.h.202.1		4	99.47	odd	30
363.2.e.j.130.1		4	99.65	even	6
363.2.e.j.148.1		4	99.83	even	30
528.2.y.f.49.1		4	396.335	even	30
528.2.y.f.97.1		4	36.11	even	6
825.2.n.f.526.1		4	45.29	odd	6
825.2.n.f.676.1		4	495.434	odd	30
825.2.bx.b.49.1		8	495.38	even	60
825.2.bx.b.49.2		8	495.137	even	60
825.2.bx.b.724.1		8	45.2	even	12
825.2.bx.b.724.2		8	45.38	even	12
891.2.n.a.379.1		8	11.5	even	5	inner
891.2.n.a.460.1		8	1.1	even	1	trivial
891.2.n.a.676.1		8	99.49	even	15	inner
891.2.n.a.757.1		8	9.4	even	3	inner
891.2.n.d.379.1		8	33.5	odd	10
891.2.n.d.460.1		8	3.2	odd	2
891.2.n.d.676.1		8	99.5	odd	30
891.2.n.d.757.1		8	9.5	odd	6
1089.2.a.m.1.2		2	99.70	even	15
1089.2.a.s.1.1		2	99.7	odd	30
5808.2.a.bl.1.1		2	396.191	even	30
5808.2.a.bm.1.1		2	396.227	odd	30
9075.2.a.x.1.2		2	495.389	odd	30
9075.2.a.bv.1.1		2	495.29	even	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)

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

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