LMFDB - Embedded newform 459.2.f.b.55.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(55,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 24 x^{18} + 253 x^{16} - 1452 x^{14} + 5148 x^{12} - 11204 x^{10} + 15124 x^{8} - 7528 x^{6} + \cdots + 5476 $ x^20 - 24x^18 + 253x^16 - 1452x^14 + 5148x^12 - 11204x^10 + 15124x^8 - 7528x^6 - 2992x^4 + 11920*x^2 + 5476
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			55.3
Root			$2.76922 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	459.55
Dual form			459.2.f.b.217.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.06212i q^{2} -2.25232 q^{4} +(-1.02072 + 1.02072i) q^{5} +(-0.0902131 - 0.0902131i) q^{7} +0.520322i q^{8} +(2.10484 + 2.10484i) q^{10} +(-4.04825 - 4.04825i) q^{11} -2.54466 q^{13} +(-0.186030 + 0.186030i) q^{14} -3.43168 q^{16} +(-3.31209 - 2.45561i) q^{17} +1.47276i q^{19} +(2.29899 - 2.29899i) q^{20} +(-8.34796 + 8.34796i) q^{22} +(-1.15144 - 1.15144i) q^{23} +2.91627i q^{25} +5.24738i q^{26} +(0.203189 + 0.203189i) q^{28} +(2.79177 - 2.79177i) q^{29} +(0.292335 - 0.292335i) q^{31} +8.11718i q^{32} +(-5.06376 + 6.82992i) q^{34} +0.184164 q^{35} +(4.00649 - 4.00649i) q^{37} +3.03701 q^{38} +(-0.531102 - 0.531102i) q^{40} +(1.33747 + 1.33747i) q^{41} -7.93369i q^{43} +(9.11797 + 9.11797i) q^{44} +(-2.37441 + 2.37441i) q^{46} +0.484421 q^{47} -6.98372i q^{49} +6.01369 q^{50} +5.73140 q^{52} +9.05465i q^{53} +8.26423 q^{55} +(0.0469399 - 0.0469399i) q^{56} +(-5.75696 - 5.75696i) q^{58} -12.0518i q^{59} +(3.04914 + 3.04914i) q^{61} +(-0.602829 - 0.602829i) q^{62} +9.87520 q^{64} +(2.59738 - 2.59738i) q^{65} +9.00823 q^{67} +(7.45991 + 5.53084i) q^{68} -0.379768i q^{70} +(-7.77062 + 7.77062i) q^{71} +(-4.93459 + 4.93459i) q^{73} +(-8.26184 - 8.26184i) q^{74} -3.31714i q^{76} +0.730409i q^{77} +(-9.85086 - 9.85086i) q^{79} +(3.50278 - 3.50278i) q^{80} +(2.75802 - 2.75802i) q^{82} +4.09960i q^{83} +(5.88720 - 0.874225i) q^{85} -16.3602 q^{86} +(2.10639 - 2.10639i) q^{88} +13.1764 q^{89} +(0.229561 + 0.229561i) q^{91} +(2.59342 + 2.59342i) q^{92} -0.998933i q^{94} +(-1.50327 - 1.50327i) q^{95} +(-2.54449 + 2.54449i) q^{97} -14.4013 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{4} + 8 q^{7} + 20 q^{10} + 32 q^{16} + 8 q^{22} + 44 q^{28} - 24 q^{31} - 28 q^{34} - 4 q^{37} - 32 q^{40} + 64 q^{46} - 8 q^{52} - 84 q^{55} + 36 q^{58} + 72 q^{64} + 36 q^{67} - 16 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) $ 20 * q - 24 * q^4 + 8 * q^7 + 20 * q^10 + 32 * q^16 + 8 * q^22 + 44 * q^28 - 24 * q^31 - 28 * q^34 - 4 * q^37 - 32 * q^40 + 64 * q^46 - 8 * q^52 - 84 * q^55 + 36 * q^58 + 72 * q^64 + 36 * q^67 - 16 * q^73 - 40 * q^79 - 36 * q^82 + 36 * q^85 - 96 * q^88 - 76 * q^91 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	2.06212i		−	1.45814i	−0.684441	−	0.729068i	$-0.739954\pi$
$2$		−	2.06212i		−	1.45814i	0.684441	−	0.729068i	$-0.260046\pi$
$3$		0			0
$3$		0			0
$4$	−2.25232			−1.12616
$5$	−1.02072	+	1.02072i	−0.456479	+	0.456479i	−0.897498	−	0.441019i	$-0.854617\pi$
$5$	−1.02072	+	1.02072i	−0.456479	+	0.456479i	0.441019	+	0.897498i	$0.354617\pi$
$6$		0			0
$7$	−0.0902131	−	0.0902131i	−0.0340973	−	0.0340973i	0.689853	−	0.723950i	$-0.257675\pi$
$7$	−0.0902131	−	0.0902131i	−0.0340973	−	0.0340973i	−0.723950	+	0.689853i	$0.757675\pi$
$8$			0.520322i			0.183962i
$9$		0			0
$10$	2.10484	+	2.10484i	0.665608	+	0.665608i
$11$	−4.04825	−	4.04825i	−1.22059	−	1.22059i	−0.967422	−	0.253171i	$-0.918527\pi$
$11$	−4.04825	−	4.04825i	−1.22059	−	1.22059i	−0.253171	−	0.967422i	$-0.581473\pi$
$12$		0			0
$13$	−2.54466			−0.705762			−0.352881	−	0.935668i	$-0.614798\pi$
$13$	−2.54466			−0.705762			−0.352881	+	0.935668i	$0.614798\pi$
$14$	−0.186030	+	0.186030i	−0.0497186	+	0.0497186i
$15$		0			0
$16$	−3.43168			−0.857921
$17$	−3.31209	−	2.45561i	−0.803301	−	0.595574i
$17$	−3.31209	−	2.45561i	−0.803301	−	0.595574i
$18$		0			0
$19$			1.47276i			0.337875i	0.985627	+	0.168937i	$0.0540335\pi$
$19$			1.47276i			0.337875i	−0.985627	+	0.168937i	$0.945966\pi$
$20$	2.29899	−	2.29899i	0.514069	−	0.514069i
$21$		0			0
$22$	−8.34796	+	8.34796i	−1.77979	+	1.77979i
$23$	−1.15144	−	1.15144i	−0.240092	−	0.240092i	0.576796	−	0.816888i	$-0.304303\pi$
$23$	−1.15144	−	1.15144i	−0.240092	−	0.240092i	−0.816888	+	0.576796i	$0.804303\pi$
$24$		0			0
$25$			2.91627i			0.583255i
$26$			5.24738i			1.02910i
$27$		0			0
$28$	0.203189	+	0.203189i	0.0383991	+	0.0383991i
$29$	2.79177	−	2.79177i	0.518419	−	0.518419i	−0.398674	−	0.917093i	$-0.630529\pi$
$29$	2.79177	−	2.79177i	0.518419	−	0.518419i	0.917093	+	0.398674i	$0.130529\pi$
$30$		0			0
$31$	0.292335	−	0.292335i	0.0525049	−	0.0525049i	−0.680367	−	0.732872i	$-0.738180\pi$
$31$	0.292335	−	0.292335i	0.0525049	−	0.0525049i	0.732872	+	0.680367i	$0.238180\pi$
$32$			8.11718i			1.43493i
$33$		0			0
$34$	−5.06376	+	6.82992i	−0.868428	+	1.17132i
$35$	0.184164			0.0311294
$36$		0			0
$37$	4.00649	−	4.00649i	0.658662	−	0.658662i	−0.296401	−	0.955064i	$-0.595787\pi$
$37$	4.00649	−	4.00649i	0.658662	−	0.658662i	0.955064	+	0.296401i	$0.0957866\pi$
$38$	3.03701			0.492667
$39$		0			0
$40$	−0.531102	−	0.531102i	−0.0839746	−	0.0839746i
$41$	1.33747	+	1.33747i	0.208878	+	0.208878i	0.803791	−	0.594912i	$-0.202813\pi$
$41$	1.33747	+	1.33747i	0.208878	+	0.208878i	−0.594912	+	0.803791i	$0.702813\pi$
$42$		0			0
$43$		−	7.93369i		−	1.20988i	−0.796272	−	0.604938i	$-0.793198\pi$
$43$		−	7.93369i		−	1.20988i	0.796272	−	0.604938i	$-0.206802\pi$
$44$	9.11797	+	9.11797i	1.37458	+	1.37458i
$45$		0			0
$46$	−2.37441	+	2.37441i	−0.350088	+	0.350088i
$47$	0.484421			0.0706601			0.0353300	−	0.999376i	$-0.488752\pi$
$47$	0.484421			0.0706601			0.0353300	+	0.999376i	$0.488752\pi$
$48$		0			0
$49$		−	6.98372i		−	0.997675i
$50$	6.01369			0.850465
$51$		0			0
$52$	5.73140			0.794802
$53$			9.05465i			1.24375i	0.783116	+	0.621876i	$0.213629\pi$
$53$			9.05465i			1.24375i	−0.783116	+	0.621876i	$0.786371\pi$
$54$		0			0
$55$	8.26423			1.11435
$56$	0.0469399	−	0.0469399i	0.00627260	−	0.00627260i
$57$		0			0
$58$	−5.75696	−	5.75696i	−0.755926	−	0.755926i
$59$		−	12.0518i		−	1.56901i	−0.620124	−	0.784504i	$-0.712918\pi$
$59$		−	12.0518i		−	1.56901i	0.620124	−	0.784504i	$-0.287082\pi$
$60$		0			0
$61$	3.04914	+	3.04914i	0.390402	+	0.390402i	0.874831	−	0.484429i	$-0.160973\pi$
$61$	3.04914	+	3.04914i	0.390402	+	0.390402i	−0.484429	+	0.874831i	$0.660973\pi$
$62$	−0.602829	−	0.602829i	−0.0765593	−	0.0765593i
$63$		0			0
$64$	9.87520			1.23440
$65$	2.59738	−	2.59738i	0.322165	−	0.322165i
$66$		0			0
$67$	9.00823			1.10053			0.550265	−	0.834990i	$-0.314527\pi$
$67$	9.00823			1.10053			0.550265	+	0.834990i	$0.314527\pi$
$68$	7.45991	+	5.53084i	0.904647	+	0.670713i
$69$		0			0
$70$		−	0.379768i		−	0.0453909i
$71$	−7.77062	+	7.77062i	−0.922203	+	0.922203i	−0.997185	−	0.0749820i	$-0.976110\pi$
$71$	−7.77062	+	7.77062i	−0.922203	+	0.922203i	0.0749820	+	0.997185i	$0.476110\pi$
$72$		0			0
$73$	−4.93459	+	4.93459i	−0.577550	+	0.577550i	−0.934228	−	0.356678i	$-0.883909\pi$
$73$	−4.93459	+	4.93459i	−0.577550	+	0.577550i	0.356678	+	0.934228i	$0.383909\pi$
$74$	−8.26184	−	8.26184i	−0.960420	−	0.960420i
$75$		0			0
$76$		−	3.31714i		−	0.380502i
$77$			0.730409i			0.0832379i
$78$		0			0
$79$	−9.85086	−	9.85086i	−1.10831	−	1.10831i	−0.993373	−	0.114935i	$-0.963334\pi$
$79$	−9.85086	−	9.85086i	−1.10831	−	1.10831i	−0.114935	−	0.993373i	$-0.536666\pi$
$80$	3.50278	−	3.50278i	0.391622	−	0.391622i
$81$		0			0
$82$	2.75802	−	2.75802i	0.304573	−	0.304573i
$83$			4.09960i			0.449989i	0.974360	+	0.224995i	$0.0722364\pi$
$83$			4.09960i			0.449989i	−0.974360	+	0.224995i	$0.927764\pi$
$84$		0			0
$85$	5.88720	−	0.874225i	0.638556	−	0.0948230i
$86$	−16.3602			−1.76417
$87$		0			0
$88$	2.10639	−	2.10639i	0.224542	−	0.224542i
$89$	13.1764			1.39670			0.698349	−	0.715758i	$-0.253918\pi$
$89$	13.1764			1.39670			0.698349	+	0.715758i	$0.253918\pi$
$90$		0			0
$91$	0.229561	+	0.229561i	0.0240646	+	0.0240646i
$92$	2.59342	+	2.59342i	0.270383	+	0.270383i
$93$		0			0
$94$		−	0.998933i		−	0.103032i
$95$	−1.50327	−	1.50327i	−0.154233	−	0.154233i
$96$		0			0
$97$	−2.54449	+	2.54449i	−0.258353	+	0.258353i	−0.824384	−	0.566031i	$-0.808478\pi$
$97$	−2.54449	+	2.54449i	−0.258353	+	0.258353i	0.566031	+	0.824384i	$0.308478\pi$
$98$	−14.4013			−1.45475
$99$		0			0
$100$		−	6.56839i		−	0.656839i
$101$	−3.12471			−0.310920			−0.155460	−	0.987842i	$-0.549686\pi$
$101$	−3.12471			−0.310920			−0.155460	+	0.987842i	$0.549686\pi$
$102$		0			0
$103$	17.4113			1.71559			0.857793	−	0.513995i	$-0.171835\pi$
$103$	17.4113			1.71559			0.857793	+	0.513995i	$0.171835\pi$
$104$		−	1.32404i		−	0.129833i
$105$		0			0
$106$	18.6718			1.81356
$107$	−0.884773	+	0.884773i	−0.0855342	+	0.0855342i	−0.748579	−	0.663045i	$-0.769264\pi$
$107$	−0.884773	+	0.884773i	−0.0855342	+	0.0855342i	0.663045	+	0.748579i	$0.269264\pi$
$108$		0			0
$109$	−12.6586	−	12.6586i	−1.21247	−	1.21247i	−0.970210	−	0.242264i	$-0.922110\pi$
$109$	−12.6586	−	12.6586i	−1.21247	−	1.21247i	−0.242264	−	0.970210i	$-0.577890\pi$
$110$		−	17.0418i		−	1.62487i
$111$		0			0
$112$	0.309583	+	0.309583i	0.0292528	+	0.0292528i
$113$	−9.16805	−	9.16805i	−0.862458	−	0.862458i	0.129165	−	0.991623i	$-0.458770\pi$
$113$	−9.16805	−	9.16805i	−0.862458	−	0.862458i	−0.991623	+	0.129165i	$0.958770\pi$
$114$		0			0
$115$	2.35060			0.219194
$116$	−6.28797	+	6.28797i	−0.583824	+	0.583824i
$117$		0			0
$118$	−24.8522			−2.28783
$119$	0.0772657	+	0.520322i	0.00708294	+	0.0476979i
$120$		0			0
$121$			21.7766i			1.97969i
$122$	6.28767	−	6.28767i	0.569259	−	0.569259i
$123$		0			0
$124$	−0.658433	+	0.658433i	−0.0591291	+	0.0591291i
$125$	−8.08028	−	8.08028i	−0.722722	−	0.722722i
$126$		0			0
$127$		−	0.867311i		−	0.0769614i	−0.999259	−	0.0384807i	$-0.987748\pi$
$127$		−	0.867311i		−	0.0769614i	0.999259	−	0.0384807i	$-0.0122518\pi$
$128$		−	4.12945i		−	0.364995i
$129$		0			0
$130$	−5.35609	−	5.35609i	−0.469761	−	0.469761i
$131$	7.35720	−	7.35720i	0.642801	−	0.642801i	−0.308442	−	0.951243i	$-0.599808\pi$
$131$	7.35720	−	7.35720i	0.642801	−	0.642801i	0.951243	+	0.308442i	$0.0998076\pi$
$132$		0			0
$133$	0.132862	−	0.132862i	0.0115206	−	0.0115206i
$134$		−	18.5760i		−	1.60472i
$135$		0			0
$136$	1.27771	−	1.72336i	0.109563	−	0.147777i
$137$	−13.1508			−1.12355			−0.561773	−	0.827292i	$-0.689880\pi$
$137$	−13.1508			−1.12355			−0.561773	+	0.827292i	$0.689880\pi$
$138$		0			0
$139$	15.8126	−	15.8126i	1.34121	−	1.34121i	0.446347	−	0.894860i	$-0.352725\pi$
$139$	15.8126	−	15.8126i	1.34121	−	1.34121i	0.894860	−	0.446347i	$-0.147275\pi$
$140$	−0.414797			−0.0350568
$141$		0			0
$142$	16.0239	+	16.0239i	1.34470	+	1.34470i
$143$	10.3014	+	10.3014i	0.861447	+	0.861447i
$144$		0			0
$145$			5.69922i			0.473294i
$146$	10.1757	+	10.1757i	0.842147	+	0.842147i
$147$		0			0
$148$	−9.02391	+	9.02391i	−0.741761	+	0.741761i
$149$	14.8896			1.21981			0.609903	−	0.792476i	$-0.291208\pi$
$149$	14.8896			1.21981			0.609903	+	0.792476i	$0.291208\pi$
$150$		0			0
$151$		−	18.9574i		−	1.54273i	−0.636391	−	0.771367i	$-0.719573\pi$
$151$		−	18.9574i		−	1.54273i	0.636391	−	0.771367i	$-0.280427\pi$
$152$	−0.766311			−0.0621560
$153$		0			0
$154$	1.50619			0.121372
$155$			0.596783i			0.0479347i
$156$		0			0
$157$	17.0660			1.36201			0.681006	−	0.732278i	$-0.261543\pi$
$157$	17.0660			1.36201			0.681006	+	0.732278i	$0.261543\pi$
$158$	−20.3136	+	20.3136i	−1.61607	+	1.61607i
$159$		0			0
$160$	−8.28534	−	8.28534i	−0.655014	−	0.655014i
$161$			0.207750i			0.0163730i
$162$		0			0
$163$	−6.75433	−	6.75433i	−0.529040	−	0.529040i	0.391246	−	0.920286i	$-0.372044\pi$
$163$	−6.75433	−	6.75433i	−0.529040	−	0.529040i	−0.920286	+	0.391246i	$0.872044\pi$
$164$	−3.01242	−	3.01242i	−0.235231	−	0.235231i
$165$		0			0
$166$	8.45385			0.656146
$167$	−13.5191	+	13.5191i	−1.04614	+	1.04614i	−0.0472547	+	0.998883i	$0.515047\pi$
$167$	−13.5191	+	13.5191i	−1.04614	+	1.04614i	−0.998883	+	0.0472547i	$0.984953\pi$
$168$		0			0
$169$	−6.52471			−0.501901
$170$	−1.80275	−	12.1401i	−0.138265	−	0.931102i
$171$		0			0
$172$			17.8693i			1.36252i
$173$	9.07008	−	9.07008i	0.689585	−	0.689585i	−0.272555	−	0.962140i	$-0.587869\pi$
$173$	9.07008	−	9.07008i	0.689585	−	0.689585i	0.962140	+	0.272555i	$0.0878686\pi$
$174$		0			0
$175$	0.263086	−	0.263086i	0.0198874	−	0.0198874i
$176$	13.8923	+	13.8923i	1.04717	+	1.04717i
$177$		0			0
$178$		−	27.1713i		−	2.03658i
$179$			9.39230i			0.702013i	0.936373	+	0.351007i	$0.114161\pi$
$179$			9.39230i			0.702013i	−0.936373	+	0.351007i	$0.885839\pi$
$180$		0			0
$181$	−5.08487	−	5.08487i	−0.377955	−	0.377955i	0.492409	−	0.870364i	$-0.336117\pi$
$181$	−5.08487	−	5.08487i	−0.377955	−	0.377955i	−0.870364	+	0.492409i	$0.836117\pi$
$182$	0.473383	−	0.473383i	0.0350894	−	0.0350894i
$183$		0			0
$184$	0.599122	−	0.599122i	0.0441678	−	0.0441678i
$185$			8.17898i			0.601330i
$186$		0			0
$187$	3.46725	+	23.3491i	0.253550	+	1.70746i
$188$	−1.09107			−0.0795747
$189$		0			0
$190$	−3.09992	+	3.09992i	−0.224892	+	0.224892i
$191$	9.81454			0.710155			0.355078	−	0.934837i	$-0.384454\pi$
$191$	9.81454			0.710155			0.355078	+	0.934837i	$0.384454\pi$
$192$		0			0
$193$	−16.2443	−	16.2443i	−1.16929	−	1.16929i	−0.982377	−	0.186912i	$-0.940152\pi$
$193$	−16.2443	−	16.2443i	−1.16929	−	1.16929i	−0.186912	−	0.982377i	$-0.559848\pi$
$194$	5.24703	+	5.24703i	0.376715	+	0.376715i
$195$		0			0
$196$			15.7296i			1.12354i
$197$	10.7410	+	10.7410i	0.765267	+	0.765267i	0.977269	−	0.212002i	$-0.0679983\pi$
$197$	10.7410	+	10.7410i	0.765267	+	0.765267i	−0.212002	+	0.977269i	$0.567998\pi$
$198$		0			0
$199$	−3.64243	+	3.64243i	−0.258205	+	0.258205i	−0.824324	−	0.566119i	$-0.808444\pi$
$199$	−3.64243	+	3.64243i	−0.258205	+	0.258205i	0.566119	+	0.824324i	$0.308444\pi$
$200$	−1.51740			−0.107297
$201$		0			0
$202$			6.44351i			0.453364i
$203$	−0.503708			−0.0353534
$204$		0			0
$205$	−2.73036			−0.190697
$206$		−	35.9041i		−	2.50156i
$207$		0			0
$208$	8.73247			0.605488
$209$	5.96210	−	5.96210i	0.412407	−	0.412407i
$210$		0			0
$211$	1.75494	+	1.75494i	0.120815	+	0.120815i	0.764929	−	0.644114i	$-0.222774\pi$
$211$	1.75494	+	1.75494i	0.120815	+	0.120815i	−0.644114	+	0.764929i	$0.722774\pi$
$212$		−	20.3940i		−	1.40067i
$213$		0			0
$214$	1.82450	+	1.82450i	0.124721	+	0.124721i
$215$	8.09806	+	8.09806i	0.552283	+	0.552283i
$216$		0			0
$217$	−0.0527449			−0.00358055
$218$	−26.1035	+	26.1035i	−1.76795	+	1.76795i
$219$		0			0
$220$	−18.6137			−1.25494
$221$	8.42815	+	6.24870i	0.566939	+	0.420333i
$222$		0			0
$223$		−	0.793309i		−	0.0531239i	−0.999647	−	0.0265620i	$-0.991544\pi$
$223$		−	0.793309i		−	0.0531239i	0.999647	−	0.0265620i	$-0.00845593\pi$
$224$	0.732275	−	0.732275i	0.0489272	−	0.0489272i
$225$		0			0
$226$	−18.9056	+	18.9056i	−1.25758	+	1.25758i
$227$	3.14153	+	3.14153i	0.208511	+	0.208511i	0.803634	−	0.595124i	$-0.202897\pi$
$227$	3.14153	+	3.14153i	0.208511	+	0.208511i	−0.595124	+	0.803634i	$0.702897\pi$
$228$		0			0
$229$			28.4102i			1.87740i	0.344733	+	0.938701i	$0.387969\pi$
$229$			28.4102i			1.87740i	−0.344733	+	0.938701i	$0.612031\pi$
$230$		−	4.84720i		−	0.319615i
$231$		0			0
$232$	1.45262	+	1.45262i	0.0953693	+	0.0953693i
$233$	−16.4010	+	16.4010i	−1.07447	+	1.07447i	−0.0774719	+	0.996995i	$0.524685\pi$
$233$	−16.4010	+	16.4010i	−1.07447	+	1.07447i	−0.996995	+	0.0774719i	$0.975315\pi$
$234$		0			0
$235$	−0.494457	+	0.494457i	−0.0322548	+	0.0322548i
$236$			27.1445i			1.76696i
$237$		0			0
$238$	1.07297	−	0.159331i	0.0695500	−	0.0103279i
$239$	6.48768			0.419653			0.209827	−	0.977739i	$-0.432710\pi$
$239$	6.48768			0.419653			0.209827	+	0.977739i	$0.432710\pi$
$240$		0			0
$241$	−19.2617	+	19.2617i	−1.24076	+	1.24076i	−0.281067	+	0.959688i	$0.590688\pi$
$241$	−19.2617	+	19.2617i	−1.24076	+	1.24076i	−0.959688	+	0.281067i	$0.909312\pi$
$242$	44.9059			2.88666
$243$		0			0
$244$	−6.86764	−	6.86764i	−0.439656	−	0.439656i
$245$	7.12841	+	7.12841i	0.455417	+	0.455417i
$246$		0			0
$247$		−	3.74768i		−	0.238459i
$248$	0.152108	+	0.152108i	0.00965890	+	0.00965890i
$249$		0			0
$250$	−16.6625	+	16.6625i	−1.05383	+	1.05383i
$251$	−10.8217			−0.683062			−0.341531	−	0.939871i	$-0.610945\pi$
$251$	−10.8217			−0.683062			−0.341531	+	0.939871i	$0.610945\pi$
$252$		0			0
$253$			9.32265i			0.586110i
$254$	−1.78850			−0.112220
$255$		0			0
$256$	11.2350			0.702186
$257$		−	0.736456i		−	0.0459388i	−0.999736	−	0.0229694i	$-0.992688\pi$
$257$		−	0.736456i		−	0.0459388i	0.999736	−	0.0229694i	$-0.00731204\pi$
$258$		0			0
$259$	−0.722875			−0.0449172
$260$	−5.85014	+	5.85014i	−0.362810	+	0.362810i
$261$		0			0
$262$	−15.1714	−	15.1714i	−0.937292	−	0.937292i
$263$			21.9569i			1.35392i	0.736020	+	0.676959i	$0.236703\pi$
$263$			21.9569i			1.35392i	−0.736020	+	0.676959i	$0.763297\pi$
$264$		0			0
$265$	−9.24224	−	9.24224i	−0.567746	−	0.567746i
$266$	−0.273977	−	0.273977i	−0.0167986	−	0.0167986i
$267$		0			0
$268$	−20.2895			−1.23938
$269$	6.47638	−	6.47638i	0.394872	−	0.394872i	−0.481548	−	0.876420i	$-0.659925\pi$
$269$	6.47638	−	6.47638i	0.394872	−	0.394872i	0.876420	+	0.481548i	$0.159925\pi$
$270$		0			0
$271$	17.4194			1.05815			0.529077	−	0.848574i	$-0.322538\pi$
$271$	17.4194			1.05815			0.529077	+	0.848574i	$0.322538\pi$
$272$	11.3661	+	8.42689i	0.689168	+	0.510955i
$273$		0			0
$274$			27.1184i			1.63828i
$275$	11.8058	−	11.8058i	0.711916	−	0.711916i
$276$		0			0
$277$	−6.19695	+	6.19695i	−0.372339	+	0.372339i	−0.868328	−	0.495990i	$-0.834805\pi$
$277$	−6.19695	+	6.19695i	−0.372339	+	0.372339i	0.495990	+	0.868328i	$0.334805\pi$
$278$	−32.6074	−	32.6074i	−1.95566	−	1.95566i
$279$		0			0
$280$			0.0958247i			0.00572662i
$281$		−	3.29450i		−	0.196534i	−0.995160	−	0.0982668i	$-0.968670\pi$
$281$		−	3.29450i		−	0.196534i	0.995160	−	0.0982668i	$-0.0313298\pi$
$282$		0			0
$283$	−10.4511	−	10.4511i	−0.621256	−	0.621256i	0.324597	−	0.945853i	$-0.394771\pi$
$283$	−10.4511	−	10.4511i	−0.621256	−	0.621256i	−0.945853	+	0.324597i	$0.894771\pi$
$284$	17.5020	−	17.5020i	1.03855	−	1.03855i
$285$		0			0
$286$	21.2427	−	21.2427i	1.25611	−	1.25611i
$287$		−	0.241315i		−	0.0142444i
$288$		0			0
$289$	4.93993	+	16.2664i	0.290584	+	0.956849i
$290$	11.7525			0.690128
$291$		0			0
$292$	11.1143	−	11.1143i	0.650415	−	0.650415i
$293$	−20.3034			−1.18614			−0.593068	−	0.805152i	$-0.702083\pi$
$293$	−20.3034			−1.18614			−0.593068	+	0.805152i	$0.702083\pi$
$294$		0			0
$295$	12.3015	+	12.3015i	0.716219	+	0.716219i
$296$	2.08466	+	2.08466i	0.121169	+	0.121169i
$297$		0			0
$298$		−	30.7041i		−	1.77864i
$299$	2.93003	+	2.93003i	0.169448	+	0.169448i
$300$		0			0
$301$	−0.715723	+	0.715723i	−0.0412536	+	0.0412536i
$302$	−39.0924			−2.24952
$303$		0			0
$304$		−	5.05405i		−	0.289870i
$305$	−6.22461			−0.356420
$306$		0			0
$307$	1.64581			0.0939312			0.0469656	−	0.998897i	$-0.485045\pi$
$307$	1.64581			0.0939312			0.0469656	+	0.998897i	$0.485045\pi$
$308$		−	1.64512i		−	0.0937394i
$309$		0			0
$310$	1.23064			0.0698954
$311$	22.2091	−	22.2091i	1.25936	−	1.25936i	0.307967	−	0.951397i	$-0.400351\pi$
$311$	22.2091	−	22.2091i	1.25936	−	1.25936i	0.951397	−	0.307967i	$-0.0996487\pi$
$312$		0			0
$313$	−8.60958	−	8.60958i	−0.486642	−	0.486642i	0.420603	−	0.907245i	$-0.361819\pi$
$313$	−8.60958	−	8.60958i	−0.486642	−	0.486642i	−0.907245	+	0.420603i	$0.861819\pi$
$314$		−	35.1920i		−	1.98600i
$315$		0			0
$316$	22.1873	+	22.1873i	1.24814	+	1.24814i
$317$	−2.15686	−	2.15686i	−0.121142	−	0.121142i	0.643937	−	0.765079i	$-0.277300\pi$
$317$	−2.15686	−	2.15686i	−0.121142	−	0.121142i	−0.765079	+	0.643937i	$0.777300\pi$
$318$		0			0
$319$	−22.6036			−1.26556
$320$	−10.0798	+	10.0798i	−0.563477	+	0.563477i
$321$		0			0
$322$	0.428405			0.0238741
$323$	3.61653	−	4.87792i	0.201229	−	0.271415i
$324$		0			0
$325$		−	7.42092i		−	0.411639i
$326$	−13.9282	+	13.9282i	−0.771413	+	0.771413i
$327$		0			0
$328$	−0.695917	+	0.695917i	−0.0384256	+	0.0384256i
$329$	−0.0437011	−	0.0437011i	−0.00240932	−	0.00240932i
$330$		0			0
$331$		−	11.9151i		−	0.654915i	−0.944866	−	0.327457i	$-0.893808\pi$
$331$		−	11.9151i		−	0.654915i	0.944866	−	0.327457i	$-0.106192\pi$
$332$		−	9.23362i		−	0.506761i
$333$		0			0
$334$	27.8779	+	27.8779i	1.52541	+	1.52541i
$335$	−9.19486	+	9.19486i	−0.502369	+	0.502369i
$336$		0			0
$337$	−19.9529	+	19.9529i	−1.08690	+	1.08690i	−0.0910557	+	0.995846i	$0.529024\pi$
$337$	−19.9529	+	19.9529i	−1.08690	+	1.08690i	−0.995846	+	0.0910557i	$0.970976\pi$
$338$			13.4547i			0.731840i
$339$		0			0
$340$	−13.2599	+	1.96904i	−0.719118	+	0.106786i
$341$	−2.36689			−0.128174
$342$		0			0
$343$	−1.26151	+	1.26151i	−0.0681154	+	0.0681154i
$344$	4.12808			0.222571
$345$		0			0
$346$	−18.7036	−	18.7036i	−1.00551	−	1.00551i
$347$	−23.6969	−	23.6969i	−1.27212	−	1.27212i	−0.944975	−	0.327144i	$-0.893914\pi$
$347$	−23.6969	−	23.6969i	−1.27212	−	1.27212i	−0.327144	−	0.944975i	$-0.606086\pi$
$348$		0			0
$349$		−	15.8690i		−	0.849446i	−0.905323	−	0.424723i	$-0.860372\pi$
$349$		−	15.8690i		−	0.849446i	0.905323	−	0.424723i	$-0.139628\pi$
$350$	−0.542514	−	0.542514i	−0.0289986	−	0.0289986i
$351$		0			0
$352$	32.8603	−	32.8603i	1.75146	−	1.75146i
$353$	−22.6893			−1.20763			−0.603816	−	0.797124i	$-0.706354\pi$
$353$	−22.6893			−1.20763			−0.603816	+	0.797124i	$0.706354\pi$
$354$		0			0
$355$		−	15.8632i		−	0.841932i
$356$	−29.6776			−1.57291
$357$		0			0
$358$	19.3680			1.02363
$359$		−	32.5288i		−	1.71680i	−0.512978	−	0.858402i	$-0.671458\pi$
$359$		−	32.5288i		−	1.71680i	0.512978	−	0.858402i	$-0.328542\pi$
$360$		0			0
$361$	16.8310			0.885841
$362$	−10.4856	+	10.4856i	−0.551111	+	0.551111i
$363$		0			0
$364$	−0.517047	−	0.517047i	−0.0271006	−	0.0271006i
$365$		−	10.0736i		−	0.527278i
$366$		0			0
$367$	17.7443	+	17.7443i	0.926242	+	0.926242i	0.997461	−	0.0712184i	$-0.0226887\pi$
$367$	17.7443	+	17.7443i	0.926242	+	0.926242i	−0.0712184	+	0.997461i	$0.522689\pi$
$368$	3.95139	+	3.95139i	0.205980	+	0.205980i
$369$		0			0
$370$	16.8660			0.876822
$371$	0.816848	−	0.816848i	0.0424086	−	0.0424086i
$372$		0			0
$373$	8.90157			0.460906			0.230453	−	0.973083i	$-0.425979\pi$
$373$	8.90157			0.460906			0.230453	+	0.973083i	$0.425979\pi$
$374$	48.1486	−	7.14986i	2.48970	−	0.369711i
$375$		0			0
$376$			0.252055i			0.0129988i
$377$	−7.10411	+	7.10411i	−0.365880	+	0.365880i
$378$		0			0
$379$	6.06211	−	6.06211i	0.311390	−	0.311390i	−0.534058	−	0.845448i	$-0.679334\pi$
$379$	6.06211	−	6.06211i	0.311390	−	0.311390i	0.845448	+	0.534058i	$0.179334\pi$
$380$	3.38586	+	3.38586i	0.173691	+	0.173691i
$381$		0			0
$382$		−	20.2387i		−	1.03550i
$383$		−	26.5050i		−	1.35434i	−0.735826	−	0.677170i	$-0.763206\pi$
$383$		−	26.5050i		−	1.35434i	0.735826	−	0.677170i	$-0.236794\pi$
$384$		0			0
$385$	−0.745541	−	0.745541i	−0.0379963	−	0.0379963i
$386$	−33.4976	+	33.4976i	−1.70498	+	1.70498i
$387$		0			0
$388$	5.73101	−	5.73101i	0.290948	−	0.290948i
$389$			15.4897i			0.785361i	0.919675	+	0.392681i	$0.128452\pi$
$389$			15.4897i			0.785361i	−0.919675	+	0.392681i	$0.871548\pi$
$390$		0			0
$391$	0.986189	+	6.64119i	0.0498737	+	0.335859i
$392$	3.63379			0.183534
$393$		0			0
$394$	22.1493	−	22.1493i	1.11586	−	1.11586i
$395$	20.1099			1.01184
$396$		0			0
$397$	−0.809534	−	0.809534i	−0.0406293	−	0.0406293i	0.686500	−	0.727130i	$-0.259146\pi$
$397$	−0.809534	−	0.809534i	−0.0406293	−	0.0406293i	−0.727130	+	0.686500i	$0.759146\pi$
$398$	7.51111	+	7.51111i	0.376498	+	0.376498i
$399$		0			0
$400$		−	10.0077i		−	0.500386i
$401$	10.7774	+	10.7774i	0.538197	+	0.538197i	0.922999	−	0.384802i	$-0.125730\pi$
$401$	10.7774	+	10.7774i	0.538197	+	0.538197i	−0.384802	+	0.922999i	$0.625730\pi$
$402$		0			0
$403$	−0.743893	+	0.743893i	−0.0370560	+	0.0370560i
$404$	7.03786			0.350146
$405$		0			0
$406$			1.03871i			0.0515501i
$407$	−32.4385			−1.60792
$408$		0			0
$409$	−20.8505			−1.03099			−0.515495	−	0.856893i	$-0.672392\pi$
$409$	−20.8505			−1.03099			−0.515495	+	0.856893i	$0.672392\pi$
$410$			5.63033i			0.278062i
$411$		0			0
$412$	−39.2159			−1.93203
$413$	−1.08723	+	1.08723i	−0.0534990	+	0.0534990i
$414$		0			0
$415$	−4.18453	−	4.18453i	−0.205410	−	0.205410i
$416$		−	20.6554i		−	1.01272i
$417$		0			0
$418$	−12.2945	−	12.2945i	−0.601346	−	0.601346i
$419$	−1.12177	−	1.12177i	−0.0548022	−	0.0548022i	0.679175	−	0.733977i	$-0.262338\pi$
$419$	−1.12177	−	1.12177i	−0.0548022	−	0.0548022i	−0.733977	+	0.679175i	$0.762338\pi$
$420$		0			0
$421$	−6.69178			−0.326138			−0.163069	−	0.986615i	$-0.552139\pi$
$421$	−6.69178			−0.326138			−0.163069	+	0.986615i	$0.552139\pi$
$422$	3.61888	−	3.61888i	0.176164	−	0.176164i
$423$		0			0
$424$	−4.71134			−0.228803
$425$	7.16124	−	9.65897i	0.347371	−	0.468529i
$426$		0			0
$427$		−	0.550144i		−	0.0266233i
$428$	1.99279	−	1.99279i	0.0963254	−	0.0963254i
$429$		0			0
$430$	16.6991	−	16.6991i	0.805304	−	0.805304i
$431$	−14.4450	−	14.4450i	−0.695790	−	0.695790i	0.267710	−	0.963500i	$-0.413733\pi$
$431$	−14.4450	−	14.4450i	−0.695790	−	0.695790i	−0.963500	+	0.267710i	$0.913733\pi$
$432$		0			0
$433$			37.9714i			1.82479i	0.409310	+	0.912395i	$0.365769\pi$
$433$			37.9714i			1.82479i	−0.409310	+	0.912395i	$0.634231\pi$
$434$			0.108766i			0.00522094i
$435$		0			0
$436$	28.5113	+	28.5113i	1.36544	+	1.36544i
$437$	1.69580	−	1.69580i	0.0811211	−	0.0811211i
$438$		0			0
$439$	13.3099	−	13.3099i	0.635248	−	0.635248i	−0.314131	−	0.949380i	$-0.601713\pi$
$439$	13.3099	−	13.3099i	0.635248	−	0.635248i	0.949380	+	0.314131i	$0.101713\pi$
$440$			4.30006i			0.204998i
$441$		0			0
$442$	12.8855	−	17.3798i	0.612903	−	0.826674i
$443$	29.2336			1.38893			0.694465	−	0.719526i	$-0.255641\pi$
$443$	29.2336			1.38893			0.694465	+	0.719526i	$0.255641\pi$
$444$		0			0
$445$	−13.4494	+	13.4494i	−0.637563	+	0.637563i
$446$	−1.63590			−0.0774619
$447$		0			0
$448$	−0.890872	−	0.890872i	−0.0420897	−	0.0420897i
$449$	6.04935	+	6.04935i	0.285487	+	0.285487i	0.835292	−	0.549806i	$-0.185298\pi$
$449$	6.04935	+	6.04935i	0.285487	+	0.285487i	−0.549806	+	0.835292i	$0.685298\pi$
$450$		0			0
$451$		−	10.8288i		−	0.509910i
$452$	20.6494	+	20.6494i	0.971267	+	0.971267i
$453$		0			0
$454$	6.47820	−	6.47820i	0.304037	−	0.304037i
$455$	−0.468635			−0.0219699
$456$		0			0
$457$			17.8952i			0.837101i	0.908194	+	0.418550i	$0.137462\pi$
$457$			17.8952i			0.837101i	−0.908194	+	0.418550i	$0.862538\pi$
$458$	58.5852			2.73751
$459$		0			0
$460$	−5.29430			−0.246848
$461$		−	30.3494i		−	1.41351i	−0.707457	−	0.706756i	$-0.750158\pi$
$461$		−	30.3494i		−	1.41351i	0.707457	−	0.706756i	$-0.249842\pi$
$462$		0			0
$463$	−10.8211			−0.502901			−0.251451	−	0.967870i	$-0.580908\pi$
$463$	−10.8211			−0.502901			−0.251451	+	0.967870i	$0.580908\pi$
$464$	−9.58048	+	9.58048i	−0.444762	+	0.444762i
$465$		0			0
$466$	33.8208	+	33.8208i	1.56672	+	1.56672i
$467$			33.7498i			1.56175i	0.624686	+	0.780876i	$0.285227\pi$
$467$			33.7498i			1.56175i	−0.624686	+	0.780876i	$0.714773\pi$
$468$		0			0
$469$	−0.812660	−	0.812660i	−0.0375252	−	0.0375252i
$470$	1.01963	+	1.01963i	0.0470319	+	0.0470319i
$471$		0			0
$472$	6.27081			0.288638
$473$	−32.1176	+	32.1176i	−1.47677	+	1.47677i
$474$		0			0
$475$	−4.29497			−0.197067
$476$	−0.174028	−	1.17193i	−0.00797654	−	0.0537155i
$477$		0			0
$478$		−	13.3783i		−	0.611911i
$479$	20.4587	−	20.4587i	0.934781	−	0.934781i	−0.0632185	−	0.998000i	$-0.520136\pi$
$479$	20.4587	−	20.4587i	0.934781	−	0.934781i	0.998000	+	0.0632185i	$0.0201365\pi$
$480$		0			0
$481$	−10.1951	+	10.1951i	−0.464859	+	0.464859i
$482$	39.7199	+	39.7199i	1.80919	+	1.80919i
$483$		0			0
$484$		−	49.0480i		−	2.22945i
$485$		−	5.19440i		−	0.235866i
$486$		0			0
$487$	−19.8381	−	19.8381i	−0.898952	−	0.898952i	0.0963916	−	0.995343i	$-0.469270\pi$
$487$	−19.8381	−	19.8381i	−0.898952	−	0.898952i	−0.995343	+	0.0963916i	$0.969270\pi$
$488$	−1.58653	+	1.58653i	−0.0718190	+	0.0718190i
$489$		0			0
$490$	14.6996	−	14.6996i	0.664060	−	0.664060i
$491$			20.1762i			0.910541i	0.890353	+	0.455271i	$0.150457\pi$
$491$			20.1762i			0.910541i	−0.890353	+	0.455271i	$0.849543\pi$
$492$		0			0
$493$	−16.1021	+	2.39110i	−0.725203	+	0.107690i
$494$	−7.72814			−0.347706
$495$		0			0
$496$	−1.00320	+	1.00320i	−0.0450451	+	0.0450451i
$497$	1.40202			0.0628893
$498$		0			0
$499$	21.2044	+	21.2044i	0.949240	+	0.949240i	0.998772	−	0.0495328i	$-0.0157732\pi$
$499$	21.2044	+	21.2044i	0.949240	+	0.949240i	−0.0495328	+	0.998772i	$0.515773\pi$
$500$	18.1994	+	18.1994i	0.813902	+	0.813902i
$501$		0			0
$502$			22.3157i			0.995997i
$503$	0.769116	+	0.769116i	0.0342932	+	0.0342932i	0.724045	−	0.689752i	$-0.242281\pi$
$503$	0.769116	+	0.769116i	0.0342932	+	0.0342932i	−0.689752	+	0.724045i	$0.742281\pi$
$504$		0			0
$505$	3.18944	−	3.18944i	0.141928	−	0.141928i
$506$	19.2244			0.854629
$507$		0			0
$508$			1.95347i			0.0866710i
$509$	−14.0982			−0.624892			−0.312446	−	0.949935i	$-0.601148\pi$
$509$	−14.0982			−0.624892			−0.312446	+	0.949935i	$0.601148\pi$
$510$		0			0
$511$	0.890328			0.0393858
$512$		−	31.4267i		−	1.38888i
$513$		0			0
$514$	−1.51866			−0.0669851
$515$	−17.7720	+	17.7720i	−0.783129	+	0.783129i
$516$		0			0
$517$	−1.96106	−	1.96106i	−0.0862472	−	0.0862472i
$518$			1.49065i			0.0654955i
$519$		0			0
$520$	1.35147	+	1.35147i	0.0592660	+	0.0592660i
$521$	0.367293	+	0.367293i	0.0160914	+	0.0160914i	0.715107	−	0.699015i	$-0.246378\pi$
$521$	0.367293	+	0.367293i	0.0160914	+	0.0160914i	−0.699015	+	0.715107i	$0.746378\pi$
$522$		0			0
$523$	−1.99821			−0.0873757			−0.0436879	−	0.999045i	$-0.513911\pi$
$523$	−1.99821			−0.0873757			−0.0436879	+	0.999045i	$0.513911\pi$
$524$	−16.5708	+	16.5708i	−0.723898	+	0.723898i
$525$		0			0
$526$	45.2776			1.97420
$527$	−1.68610	+	0.250379i	−0.0734478	+	0.0109067i
$528$		0			0
$529$		−	20.3484i		−	0.884711i
$530$	−19.0586	+	19.0586i	−0.827852	+	0.827852i
$531$		0			0
$532$	−0.299249	+	0.299249i	−0.0129741	+	0.0129741i
$533$	−3.40341	−	3.40341i	−0.147418	−	0.147418i
$534$		0			0
$535$		−	1.80621i		−	0.0780891i
$536$			4.68718i			0.202456i
$537$		0			0
$538$	−13.3550	−	13.3550i	−0.575777	−	0.575777i
$539$	−28.2718	+	28.2718i	−1.21775	+	1.21775i
$540$		0			0
$541$	2.85327	−	2.85327i	0.122672	−	0.122672i	−0.643106	−	0.765777i	$-0.722354\pi$
$541$	2.85327	−	2.85327i	0.122672	−	0.122672i	0.765777	+	0.643106i	$0.222354\pi$
$542$		−	35.9209i		−	1.54293i
$543$		0			0
$544$	19.9326	−	26.8848i	0.854605	−	1.15268i
$545$	25.8417			1.10694
$546$		0			0
$547$	1.74440	−	1.74440i	0.0745851	−	0.0745851i	−0.668830	−	0.743415i	$-0.733205\pi$
$547$	1.74440	−	1.74440i	0.0745851	−	0.0745851i	0.743415	+	0.668830i	$0.233205\pi$
$548$	29.6198			1.26529
$549$		0			0
$550$	−24.3449	−	24.3449i	−1.03807	−	1.03807i
$551$	4.11161	+	4.11161i	0.175161	+	0.175161i
$552$		0			0
$553$			1.77735i			0.0755807i
$554$	12.7788	+	12.7788i	0.542921	+	0.542921i
$555$		0			0
$556$	−35.6151	+	35.6151i	−1.51042	+	1.51042i
$557$	13.9487			0.591024			0.295512	−	0.955339i	$-0.404510\pi$
$557$	13.9487			0.591024			0.295512	+	0.955339i	$0.404510\pi$
$558$		0			0
$559$			20.1885i			0.853885i
$560$	−0.631993			−0.0267066
$561$		0			0
$562$	−6.79365			−0.286573
$563$		−	2.16638i		−	0.0913019i	−0.998957	−	0.0456510i	$-0.985464\pi$
$563$		−	2.16638i		−	0.0913019i	0.998957	−	0.0456510i	$-0.0145362\pi$
$564$		0			0
$565$	18.7160			0.787387
$566$	−21.5515	+	21.5515i	−0.905876	+	0.905876i
$567$		0			0
$568$	−4.04323	−	4.04323i	−0.169650	−	0.169650i
$569$		−	13.9324i		−	0.584078i	−0.956406	−	0.292039i	$-0.905666\pi$
$569$		−	13.9324i		−	0.584078i	0.956406	−	0.292039i	$-0.0943336\pi$
$570$		0			0
$571$	−3.68120	−	3.68120i	−0.154053	−	0.154053i	0.625872	−	0.779926i	$-0.284743\pi$
$571$	−3.68120	−	3.68120i	−0.154053	−	0.154053i	−0.779926	+	0.625872i	$0.784743\pi$
$572$	−23.2021	−	23.2021i	−0.970129	−	0.970129i
$573$		0			0
$574$	−0.497620			−0.0207702
$575$	3.35792	−	3.35792i	0.140035	−	0.140035i
$576$		0			0
$577$	1.33032			0.0553821			0.0276911	−	0.999617i	$-0.491185\pi$
$577$	1.33032			0.0553821			0.0276911	+	0.999617i	$0.491185\pi$
$578$	33.5433	−	10.1867i	1.39522	−	0.423711i
$579$		0			0
$580$		−	12.8365i		−	0.533006i
$581$	0.369837	−	0.369837i	0.0153434	−	0.0153434i
$582$		0			0
$583$	36.6555	−	36.6555i	1.51811	−	1.51811i
$584$	−2.56758	−	2.56758i	−0.106247	−	0.106247i
$585$		0			0
$586$			41.8679i			1.72955i
$587$		−	10.1422i		−	0.418615i	−0.977850	−	0.209308i	$-0.932879\pi$
$587$		−	10.1422i		−	0.418615i	0.977850	−	0.209308i	$-0.0671210\pi$
$588$		0			0
$589$	0.430540	+	0.430540i	0.0177401	+	0.0177401i
$590$	25.3670	−	25.3670i	1.04434	−	1.04434i
$591$		0			0
$592$	−13.7490	+	13.7490i	−0.565080	+	0.565080i
$593$		−	23.8630i		−	0.979937i	−0.871740	−	0.489968i	$-0.837008\pi$
$593$		−	23.8630i		−	0.979937i	0.871740	−	0.489968i	$-0.162992\pi$
$594$		0			0
$595$	−0.609968	−	0.452236i	−0.0250063	−	0.0185398i
$596$	−33.5363			−1.37370
$597$		0			0
$598$	6.04206	−	6.04206i	0.247078	−	0.247078i
$599$	−23.4361			−0.957574			−0.478787	−	0.877931i	$-0.658923\pi$
$599$	−23.4361			−0.957574			−0.478787	+	0.877931i	$0.658923\pi$
$600$		0			0
$601$	9.31984	+	9.31984i	0.380164	+	0.380164i	0.871161	−	0.490997i	$-0.163367\pi$
$601$	9.31984	+	9.31984i	0.380164	+	0.380164i	−0.490997	+	0.871161i	$0.663367\pi$
$602$	1.47590	+	1.47590i	0.0601533	+	0.0601533i
$603$		0			0
$604$			42.6983i			1.73737i
$605$	−22.2278	−	22.2278i	−0.903687	−	0.903687i
$606$		0			0
$607$	18.3106	−	18.3106i	0.743202	−	0.743202i	−0.229990	−	0.973193i	$-0.573869\pi$
$607$	18.3106	−	18.3106i	0.743202	−	0.743202i	0.973193	+	0.229990i	$0.0738695\pi$
$608$	−11.9547			−0.484826
$609$		0			0
$610$			12.8359i			0.519709i
$611$	−1.23269			−0.0498692
$612$		0			0
$613$	−32.9459			−1.33067			−0.665337	−	0.746543i	$-0.731712\pi$
$613$	−32.9459			−1.33067			−0.665337	+	0.746543i	$0.731712\pi$
$614$		−	3.39385i		−	0.136964i
$615$		0			0
$616$	−0.380048			−0.0153126
$617$	2.56378	−	2.56378i	0.103214	−	0.103214i	−0.653614	−	0.756828i	$-0.726748\pi$
$617$	2.56378	−	2.56378i	0.103214	−	0.103214i	0.756828	+	0.653614i	$0.226748\pi$
$618$		0			0
$619$	27.3667	+	27.3667i	1.09996	+	1.09996i	0.994414	+	0.105548i	$0.0336596\pi$
$619$	27.3667	+	27.3667i	1.09996	+	1.09996i	0.105548	+	0.994414i	$0.466340\pi$
$620$		−	1.34415i		−	0.0539823i
$621$		0			0
$622$	−45.7978	−	45.7978i	−1.83632	−	1.83632i
$623$	−1.18869	−	1.18869i	−0.0476237	−	0.0476237i
$624$		0			0
$625$	1.91399			0.0765594
$626$	−17.7540	+	17.7540i	−0.709591	+	0.709591i
$627$		0			0
$628$	−38.4381			−1.53385
$629$	−23.1082	+	3.43148i	−0.921386	+	0.136822i
$630$		0			0
$631$		−	20.0655i		−	0.798793i	−0.916778	−	0.399396i	$-0.869220\pi$
$631$		−	20.0655i		−	0.798793i	0.916778	−	0.399396i	$-0.130780\pi$
$632$	5.12562	−	5.12562i	0.203886	−	0.203886i
$633$		0			0
$634$	−4.44771	+	4.44771i	−0.176641	+	0.176641i
$635$	0.885279	+	0.885279i	0.0351312	+	0.0351312i
$636$		0			0
$637$			17.7712i			0.704120i
$638$			46.6112i			1.84535i
$639$		0			0
$640$	4.21500	+	4.21500i	0.166613	+	0.166613i
$641$	28.7660	−	28.7660i	1.13619	−	1.13619i	0.147059	−	0.989128i	$-0.453019\pi$
$641$	28.7660	−	28.7660i	1.13619	−	1.13619i	0.989128	−	0.147059i	$-0.0469808\pi$
$642$		0			0
$643$	−18.8864	+	18.8864i	−0.744808	+	0.744808i	−0.973499	−	0.228691i	$-0.926555\pi$
$643$	−18.8864	+	18.8864i	−0.744808	+	0.744808i	0.228691	+	0.973499i	$0.426555\pi$
$644$		−	0.467921i		−	0.0184387i
$645$		0			0
$646$	−10.0588	−	7.45771i	−0.395760	−	0.293420i
$647$	1.47428			0.0579601			0.0289800	−	0.999580i	$-0.490774\pi$
$647$	1.47428			0.0579601			0.0289800	+	0.999580i	$0.490774\pi$
$648$		0			0
$649$	−48.7886	+	48.7886i	−1.91512	+	1.91512i
$650$	−15.3028			−0.600225
$651$		0			0
$652$	15.2130	+	15.2130i	0.595785	+	0.595785i
$653$	1.38168	+	1.38168i	0.0540695	+	0.0540695i	0.733625	−	0.679555i	$-0.237827\pi$
$653$	1.38168	+	1.38168i	0.0540695	+	0.0540695i	−0.679555	+	0.733625i	$0.737827\pi$
$654$		0			0
$655$			15.0192i			0.586850i
$656$	−4.58978	−	4.58978i	−0.179201	−	0.179201i
$657$		0			0
$658$	−0.0901168	+	0.0901168i	−0.00351312	+	0.00351312i
$659$	−33.4094			−1.30145			−0.650723	−	0.759315i	$-0.725534\pi$
$659$	−33.4094			−1.30145			−0.650723	+	0.759315i	$0.725534\pi$
$660$		0			0
$661$		−	23.3283i		−	0.907366i	−0.891163	−	0.453683i	$-0.850110\pi$
$661$		−	23.3283i		−	0.907366i	0.891163	−	0.453683i	$-0.149890\pi$
$662$	−24.5704			−0.954955
$663$		0			0
$664$	−2.13311			−0.0827808
$665$			0.271230i			0.0105178i
$666$		0			0
$667$	−6.42913			−0.248937
$668$	30.4493	−	30.4493i	1.17812	−	1.17812i
$669$		0			0
$670$	18.9609	+	18.9609i	0.732522	+	0.732522i
$671$		−	24.6873i		−	0.953043i
$672$		0			0
$673$	−6.04536	−	6.04536i	−0.233032	−	0.233032i	0.580925	−	0.813957i	$-0.302691\pi$
$673$	−6.04536	−	6.04536i	−0.233032	−	0.233032i	−0.813957	+	0.580925i	$0.802691\pi$
$674$	41.1451	+	41.1451i	1.58485	+	1.58485i
$675$		0			0
$676$	14.6958			0.565222
$677$	13.5147	−	13.5147i	0.519414	−	0.519414i	−0.397980	−	0.917394i	$-0.630289\pi$
$677$	13.5147	−	13.5147i	0.519414	−	0.519414i	0.917394	+	0.397980i	$0.130289\pi$
$678$		0			0
$679$	0.459092			0.0176183
$680$	0.454879	+	3.06324i	0.0174438	+	0.117470i
$681$		0			0
$682$			4.88080i			0.186895i
$683$	−0.0475261	+	0.0475261i	−0.00181854	+	0.00181854i	−0.708015	−	0.706197i	$-0.750409\pi$
$683$	−0.0475261	+	0.0475261i	−0.00181854	+	0.00181854i	0.706197	+	0.708015i	$0.250409\pi$
$684$		0			0
$685$	13.4232	−	13.4232i	0.512874	−	0.512874i
$686$	2.60139	+	2.60139i	0.0993215	+	0.0993215i
$687$		0			0
$688$			27.2259i			1.03798i
$689$		−	23.0410i		−	0.877793i
$690$		0			0
$691$	0.107807	+	0.107807i	0.00410116	+	0.00410116i	0.709154	−	0.705053i	$-0.249077\pi$
$691$	0.107807	+	0.107807i	0.00410116	+	0.00410116i	−0.705053	+	0.709154i	$0.749077\pi$
$692$	−20.4288	+	20.4288i	−0.776585	+	0.776585i
$693$		0			0
$694$	−48.8658	+	48.8658i	−1.85492	+	1.85492i
$695$			32.2804i			1.22446i
$696$		0			0
$697$	−1.14552	−	7.71415i	−0.0433897	−	0.292194i
$698$	−32.7236			−1.23861
$699$		0			0
$700$	−0.592555	+	0.592555i	−0.0223965	+	0.0223965i
$701$	28.8361			1.08912			0.544562	−	0.838721i	$-0.316696\pi$
$701$	28.8361			1.08912			0.544562	+	0.838721i	$0.316696\pi$
$702$		0			0
$703$	5.90060	+	5.90060i	0.222545	+	0.222545i
$704$	−39.9772	−	39.9772i	−1.50670	−	1.50670i
$705$		0			0
$706$			46.7881i			1.76089i
$707$	0.281889	+	0.281889i	0.0106015	+	0.0106015i
$708$		0			0
$709$	17.5343	−	17.5343i	0.658515	−	0.658515i	−0.296513	−	0.955029i	$-0.595824\pi$
$709$	17.5343	−	17.5343i	0.658515	−	0.658515i	0.955029	+	0.296513i	$0.0958240\pi$
$710$	−32.7118			−1.22765
$711$		0			0
$712$			6.85599i			0.256939i
$713$	−0.673214			−0.0252121
$714$		0			0
$715$	−21.0297			−0.786464
$716$		−	21.1545i		−	0.790581i
$717$		0			0
$718$	−67.0781			−2.50333
$719$	6.83397	−	6.83397i	0.254864	−	0.254864i	−0.568097	−	0.822961i	$-0.692320\pi$
$719$	6.83397	−	6.83397i	0.254864	−	0.254864i	0.822961	+	0.568097i	$0.192320\pi$
$720$		0			0
$721$	−1.57073	−	1.57073i	−0.0584969	−	0.0584969i
$722$		−	34.7074i		−	1.29168i
$723$		0			0
$724$	11.4528	+	11.4528i	0.425639	+	0.425639i
$725$	8.14157	+	8.14157i	0.302370	+	0.302370i
$726$		0			0
$727$	−32.5242			−1.20626			−0.603129	−	0.797644i	$-0.706080\pi$
$727$	−32.5242			−1.20626			−0.603129	+	0.797644i	$0.706080\pi$
$728$	−0.119446	+	0.119446i	−0.00442696	+	0.00442696i
$729$		0			0
$730$	−20.7730			−0.768844
$731$	−19.4821	+	26.2771i	−0.720571	+	0.971895i
$732$		0			0
$733$		−	33.0498i		−	1.22072i	−0.792123	−	0.610361i	$-0.791024\pi$
$733$		−	33.0498i		−	1.22072i	0.792123	−	0.610361i	$-0.208976\pi$
$734$	36.5907	−	36.5907i	1.35059	−	1.35059i
$735$		0			0
$736$	9.34647	−	9.34647i	0.344515	−	0.344515i
$737$	−36.4675	−	36.4675i	−1.34330	−	1.34330i
$738$		0			0
$739$			3.87288i			0.142466i	0.997460	+	0.0712330i	$0.0226934\pi$
$739$			3.87288i			0.142466i	−0.997460	+	0.0712330i	$0.977307\pi$
$740$		−	18.4217i		−	0.677196i
$741$		0			0
$742$	−1.68444	−	1.68444i	−0.0618376	−	0.0618376i
$743$	16.1760	−	16.1760i	0.593441	−	0.593441i	−0.345118	−	0.938559i	$-0.612161\pi$
$743$	16.1760	−	16.1760i	0.593441	−	0.593441i	0.938559	+	0.345118i	$0.112161\pi$
$744$		0			0
$745$	−15.1981	+	15.1981i	−0.556815	+	0.556815i
$746$		−	18.3561i		−	0.672063i
$747$		0			0
$748$	−7.80936	−	52.5897i	−0.285539	−	1.92287i
$749$	0.159636			0.00583297
$750$		0			0
$751$	−33.9294	+	33.9294i	−1.23810	+	1.23810i	−0.277324	+	0.960776i	$0.589448\pi$
$751$	−33.9294	+	33.9294i	−1.23810	+	1.23810i	−0.960776	+	0.277324i	$0.910552\pi$
$752$	−1.66238			−0.0606208
$753$		0			0
$754$	14.6495	+	14.6495i	0.533503	+	0.533503i
$755$	19.3502	+	19.3502i	0.704225	+	0.704225i
$756$		0			0
$757$		−	7.24009i		−	0.263146i	−0.991307	−	0.131573i	$-0.957997\pi$
$757$		−	7.24009i		−	0.263146i	0.991307	−	0.131573i	$-0.0420027\pi$
$758$	−12.5008	−	12.5008i	−0.454048	−	0.454048i
$759$		0			0
$760$	0.782186	−	0.782186i	0.0283729	−	0.0283729i
$761$	23.8187			0.863426			0.431713	−	0.902011i	$-0.357909\pi$
$761$	23.8187			0.863426			0.431713	+	0.902011i	$0.357909\pi$
$762$		0			0
$763$			2.28394i			0.0826843i
$764$	−22.1055			−0.799750
$765$		0			0
$766$	−54.6563			−1.97481
$767$			30.6677i			1.10735i
$768$		0			0
$769$	−6.92589			−0.249754			−0.124877	−	0.992172i	$-0.539854\pi$
$769$	−6.92589			−0.249754			−0.124877	+	0.992172i	$0.539854\pi$
$770$	−1.53739	+	1.53739i	−0.0554038	+	0.0554038i
$771$		0			0
$772$	36.5874	+	36.5874i	1.31681	+	1.31681i
$773$			8.04876i			0.289494i	0.989469	+	0.144747i	$0.0462368\pi$
$773$			8.04876i			0.289494i	−0.989469	+	0.144747i	$0.953763\pi$
$774$		0			0
$775$	0.852529	+	0.852529i	0.0306237	+	0.0306237i
$776$	−1.32395	−	1.32395i	−0.0475272	−	0.0475272i
$777$		0			0
$778$	31.9417			1.14516
$779$	−1.96978	+	1.96978i	−0.0705746	+	0.0705746i
$780$		0			0
$781$	62.9148			2.25127
$782$	13.6949	−	2.03364i	0.489729	−	0.0727227i
$783$		0			0
$784$			23.9659i			0.855926i
$785$	−17.4195	+	17.4195i	−0.621729	+	0.621729i
$786$		0			0
$787$	27.3494	−	27.3494i	0.974902	−	0.974902i	−0.0247902	−	0.999693i	$-0.507892\pi$
$787$	27.3494	−	27.3494i	0.974902	−	0.974902i	0.999693	+	0.0247902i	$0.00789177\pi$
$788$	−24.1923	−	24.1923i	−0.861815	−	0.861815i
$789$		0			0
$790$		−	41.4689i		−	1.47540i
$791$			1.65416i			0.0588150i
$792$		0			0
$793$	−7.75901	−	7.75901i	−0.275531	−	0.275531i
$794$	−1.66935	+	1.66935i	−0.0592431	+	0.0592431i
$795$		0			0
$796$	8.20392	−	8.20392i	0.290780	−	0.290780i
$797$			50.6758i			1.79503i	0.440985	+	0.897514i	$0.354629\pi$
$797$			50.6758i			1.79503i	−0.440985	+	0.897514i	$0.645371\pi$
$798$		0			0
$799$	−1.60445	−	1.18955i	−0.0567613	−	0.0420833i
$800$	−23.6719			−0.836928
$801$		0			0
$802$	22.2242	−	22.2242i	0.784765	−	0.784765i
$803$	39.9529			1.40991
$804$		0			0
$805$	−0.212054	−	0.212054i	−0.00747393	−	0.00747393i
$806$	1.53399	+	1.53399i	0.0540326	+	0.0540326i
$807$		0			0
$808$		−	1.62586i		−	0.0571974i
$809$	24.5798	+	24.5798i	0.864180	+	0.864180i	0.991821	−	0.127640i	$-0.0407403\pi$
$809$	24.5798	+	24.5798i	0.864180	+	0.864180i	−0.127640	+	0.991821i	$0.540740\pi$
$810$		0			0
$811$	16.4508	−	16.4508i	0.577666	−	0.577666i	−0.356594	−	0.934259i	$-0.616062\pi$
$811$	16.4508	−	16.4508i	0.577666	−	0.577666i	0.934259	+	0.356594i	$0.116062\pi$
$812$	1.13451			0.0398137
$813$		0			0
$814$			66.8919i			2.34456i
$815$	13.7885			0.482991
$816$		0			0
$817$	11.6844			0.408787
$818$			42.9961i			1.50332i
$819$		0			0
$820$	6.14966			0.214756
$821$	7.00533	−	7.00533i	0.244488	−	0.244488i	−0.574216	−	0.818704i	$-0.694693\pi$
$821$	7.00533	−	7.00533i	0.244488	−	0.244488i	0.818704	+	0.574216i	$0.194693\pi$
$822$		0			0
$823$	2.71584	+	2.71584i	0.0946683	+	0.0946683i	0.752855	−	0.658187i	$-0.228676\pi$
$823$	2.71584	+	2.71584i	0.0946683	+	0.0946683i	−0.658187	+	0.752855i	$0.728676\pi$
$824$			9.05949i			0.315602i
$825$		0			0
$826$	2.24199	+	2.24199i	0.0780088	+	0.0780088i
$827$	8.60917	+	8.60917i	0.299370	+	0.299370i	0.840767	−	0.541397i	$-0.182104\pi$
$827$	8.60917	+	8.60917i	0.299370	+	0.299370i	−0.541397	+	0.840767i	$0.682104\pi$
$828$		0			0
$829$	40.9472			1.42216			0.711078	−	0.703113i	$-0.248207\pi$
$829$	40.9472			1.42216			0.711078	+	0.703113i	$0.248207\pi$
$830$	−8.62899	+	8.62899i	−0.299516	+	0.299516i
$831$		0			0
$832$	−25.1290			−0.871192
$833$	−17.1493	+	23.1307i	−0.594189	+	0.801433i
$834$		0			0
$835$		−	27.5983i		−	0.955079i
$836$	−13.4286	+	13.4286i	−0.464437	+	0.464437i
$837$		0			0
$838$	−2.31323	+	2.31323i	−0.0799091	+	0.0799091i
$839$	6.58295	+	6.58295i	0.227269	+	0.227269i	0.811551	−	0.584282i	$-0.198624\pi$
$839$	6.58295	+	6.58295i	0.227269	+	0.227269i	−0.584282	+	0.811551i	$0.698624\pi$
$840$		0			0
$841$			13.4120i			0.462484i
$842$			13.7992i			0.475553i
$843$		0			0
$844$	−3.95268	−	3.95268i	−0.136057	−	0.136057i
$845$	6.65988	−	6.65988i	0.229107	−	0.229107i
$846$		0			0
$847$	1.96453	−	1.96453i	0.0675022	−	0.0675022i
$848$		−	31.0727i		−	1.06704i
$849$		0			0
$850$	−19.9179	−	14.7673i	−0.683179	−	0.506514i
$851$	−9.22648			−0.316280
$852$		0			0
$853$	18.4822	−	18.4822i	0.632817	−	0.632817i	−0.315956	−	0.948774i	$-0.602325\pi$
$853$	18.4822	−	18.4822i	0.632817	−	0.632817i	0.948774	+	0.315956i	$0.102325\pi$
$854$	−1.13446			−0.0388204
$855$		0			0
$856$	−0.460367	−	0.460367i	−0.0157350	−	0.0157350i
$857$	32.0279	+	32.0279i	1.09405	+	1.09405i	0.995091	+	0.0989597i	$0.0315515\pi$
$857$	32.0279	+	32.0279i	1.09405	+	1.09405i	0.0989597	+	0.995091i	$0.468448\pi$
$858$		0			0
$859$		−	26.0657i		−	0.889351i	−0.895692	−	0.444675i	$-0.853319\pi$
$859$		−	26.0657i		−	0.889351i	0.895692	−	0.444675i	$-0.146681\pi$
$860$	−18.2395	−	18.2395i	−0.621960	−	0.621960i
$861$		0			0
$862$	−29.7872	+	29.7872i	−1.01456	+	1.01456i
$863$	−7.52107			−0.256020			−0.128010	−	0.991773i	$-0.540859\pi$
$863$	−7.52107			−0.256020			−0.128010	+	0.991773i	$0.540859\pi$
$864$		0			0
$865$			18.5160i			0.629562i
$866$	78.3015			2.66079
$867$		0			0
$868$	0.118799			0.00403229
$869$			79.7574i			2.70559i
$870$		0			0
$871$	−22.9229			−0.776712
$872$	6.58656	−	6.58656i	0.223049	−	0.223049i
$873$		0			0
$874$	−3.49694	−	3.49694i	−0.118286	−	0.118286i
$875$			1.45789i			0.0492858i
$876$		0			0
$877$	7.31144	+	7.31144i	0.246890	+	0.246890i	0.819693	−	0.572803i	$-0.194144\pi$
$877$	7.31144	+	7.31144i	0.246890	+	0.246890i	−0.572803	+	0.819693i	$0.694144\pi$
$878$	−27.4466	−	27.4466i	−0.926279	−	0.926279i
$879$		0			0
$880$	−28.3602			−0.956023
$881$	21.0197	−	21.0197i	0.708170	−	0.708170i	−0.257980	−	0.966150i	$-0.583057\pi$
$881$	21.0197	−	21.0197i	0.708170	−	0.708170i	0.966150	+	0.257980i	$0.0830569\pi$
$882$		0			0
$883$	33.0395			1.11187			0.555933	−	0.831227i	$-0.312361\pi$
$883$	33.0395			1.11187			0.555933	+	0.831227i	$0.312361\pi$
$884$	−18.9829	−	14.0741i	−0.638465	−	0.473363i
$885$		0			0
$886$		−	60.2831i		−	2.02525i
$887$	8.11716	−	8.11716i	0.272548	−	0.272548i	−0.557577	−	0.830125i	$-0.688269\pi$
$887$	8.11716	−	8.11716i	0.272548	−	0.272548i	0.830125	+	0.557577i	$0.188269\pi$
$888$		0			0
$889$	−0.0782427	+	0.0782427i	−0.00262418	+	0.00262418i
$890$	27.7342	+	27.7342i	0.929653	+	0.929653i
$891$		0			0
$892$			1.78679i			0.0598262i
$893$			0.713437i			0.0238742i
$894$		0			0
$895$	−9.58688	−	9.58688i	−0.320454	−	0.320454i
$896$	−0.372530	+	0.372530i	−0.0124454	+	0.0124454i
$897$		0			0
$898$	12.4745	−	12.4745i	0.416278	−	0.416278i
$899$		−	1.63227i		−	0.0544391i
$900$		0			0
$901$	22.2347	−	29.9899i	0.740746	−	0.999107i
$902$	−22.3303			−0.743519
$903$		0			0
$904$	4.77034	−	4.77034i	0.158659	−	0.158659i
$905$	10.3804			0.345057
$906$		0			0
$907$	11.6274	+	11.6274i	0.386083	+	0.386083i	0.873288	−	0.487205i	$-0.161984\pi$
$907$	11.6274	+	11.6274i	0.386083	+	0.386083i	−0.487205	+	0.873288i	$0.661984\pi$
$908$	−7.07574	−	7.07574i	−0.234817	−	0.234817i
$909$		0			0
$910$			0.966379i			0.0320352i
$911$	8.45098	+	8.45098i	0.279993	+	0.279993i	0.833106	−	0.553113i	$-0.186560\pi$
$911$	8.45098	+	8.45098i	0.279993	+	0.279993i	−0.553113	+	0.833106i	$0.686560\pi$
$912$		0			0
$913$	16.5962	−	16.5962i	0.549253	−	0.549253i
$914$	36.9019			1.22061
$915$		0			0
$916$		−	63.9891i		−	2.11426i
$917$	−1.32743			−0.0438356
$918$		0			0
$919$	43.9032			1.44823			0.724116	−	0.689678i	$-0.242248\pi$
$919$	43.9032			1.44823			0.724116	+	0.689678i	$0.242248\pi$
$920$			1.22307i			0.0403233i
$921$		0			0
$922$	−62.5840			−2.06109
$923$	19.7736	−	19.7736i	0.650855	−	0.650855i
$924$		0			0
$925$	11.6840	+	11.6840i	0.384168	+	0.384168i
$926$			22.3145i			0.733299i
$927$		0			0
$928$	22.6613	+	22.6613i	0.743894	+	0.743894i
$929$	−10.7494	−	10.7494i	−0.352676	−	0.352676i	0.508428	−	0.861104i	$-0.330227\pi$
$929$	−10.7494	−	10.7494i	−0.352676	−	0.352676i	−0.861104	+	0.508428i	$0.830227\pi$
$930$		0			0
$931$	10.2854			0.337089
$932$	36.9404	−	36.9404i	1.21002	−	1.21002i
$933$		0			0
$934$	69.5959			2.27725
$935$	−27.3719	−	20.2937i	−0.895157	−	0.663677i
$936$		0			0
$937$		−	44.2687i		−	1.44620i	−0.690745	−	0.723098i	$-0.742717\pi$
$937$		−	44.2687i		−	1.44620i	0.690745	−	0.723098i	$-0.257283\pi$
$938$	−1.67580	+	1.67580i	−0.0547168	+	0.0547168i
$939$		0			0
$940$	1.11368	−	1.11368i	0.0363242	−	0.0363242i
$941$	6.44173	+	6.44173i	0.209994	+	0.209994i	0.804265	−	0.594271i	$-0.202559\pi$
$941$	6.44173	+	6.44173i	0.209994	+	0.209994i	−0.594271	+	0.804265i	$0.702559\pi$
$942$		0			0
$943$		−	3.08005i		−	0.100300i
$944$			41.3579i			1.34608i
$945$		0			0
$946$	66.2301	+	66.2301i	2.15333	+	2.15333i
$947$	19.9417	−	19.9417i	0.648017	−	0.648017i	−0.304496	−	0.952514i	$-0.598488\pi$
$947$	19.9417	−	19.9417i	0.648017	−	0.648017i	0.952514	+	0.304496i	$0.0984881\pi$
$948$		0			0
$949$	12.5568	−	12.5568i	0.407612	−	0.407612i
$950$			8.85674i			0.287350i
$951$		0			0
$952$	−0.270735	+	0.0402031i	−0.00877459	+	0.00130299i
$953$	29.0372			0.940607			0.470304	−	0.882505i	$-0.344144\pi$
$953$	29.0372			0.940607			0.470304	+	0.882505i	$0.344144\pi$
$954$		0			0
$955$	−10.0179	+	10.0179i	−0.324171	+	0.324171i
$956$	−14.6124			−0.472597
$957$		0			0
$958$	−42.1882	−	42.1882i	−1.36304	−	1.36304i
$959$	1.18637	+	1.18637i	0.0383099	+	0.0383099i
$960$		0			0
$961$			30.8291i			0.994486i
$962$	21.0236	+	21.0236i	0.677827	+	0.677827i
$963$		0			0
$964$	43.3836	−	43.3836i	1.39729	−	1.39729i
$965$	33.1616			1.06751
$966$		0			0
$967$			40.3570i			1.29779i	0.760876	+	0.648897i	$0.224769\pi$
$967$			40.3570i			1.29779i	−0.760876	+	0.648897i	$0.775231\pi$
$968$	−11.3309			−0.364187
$969$		0			0
$970$	−10.7115			−0.343924
$971$		−	18.1373i		−	0.582053i	−0.956715	−	0.291026i	$-0.906003\pi$
$971$		−	18.1373i		−	0.582053i	0.956715	−	0.291026i	$-0.0939968\pi$
$972$		0			0
$973$	−2.85300			−0.0914631
$974$	−40.9086	+	40.9086i	−1.31079	+	1.31079i
$975$		0			0
$976$	−10.4637	−	10.4637i	−0.334934	−	0.334934i
$977$			41.5209i			1.32837i	0.747568	+	0.664185i	$0.231221\pi$
$977$			41.5209i			1.32837i	−0.747568	+	0.664185i	$0.768779\pi$
$978$		0			0
$979$	−53.3414	−	53.3414i	−1.70480	−	1.70480i
$980$	−16.0555	−	16.0555i	−0.512874	−	0.512874i
$981$		0			0
$982$	41.6058			1.32769
$983$	4.53864	−	4.53864i	0.144760	−	0.144760i	−0.631013	−	0.775773i	$-0.717360\pi$
$983$	4.53864	−	4.53864i	0.144760	−	0.144760i	0.775773	+	0.631013i	$0.217360\pi$
$984$		0			0
$985$	−21.9271			−0.698656
$986$	4.93072	+	33.2044i	0.157026	+	1.05744i
$987$		0			0
$988$			8.44098i			0.268543i
$989$	−9.13520	+	9.13520i	−0.290482	+	0.290482i
$990$		0			0
$991$	−9.57741	+	9.57741i	−0.304236	+	0.304236i	−0.842669	−	0.538432i	$-0.819017\pi$
$991$	−9.57741	+	9.57741i	−0.304236	+	0.304236i	0.538432	+	0.842669i	$0.319017\pi$
$992$	2.37293	+	2.37293i	0.0753408	+	0.0753408i
$993$		0			0
$994$		−	2.89113i		−	0.0917012i
$995$		−	7.43577i		−	0.235730i
$996$		0			0
$997$	6.37223	+	6.37223i	0.201810	+	0.201810i	0.800775	−	0.598965i	$-0.204421\pi$
$997$	6.37223	+	6.37223i	0.201810	+	0.201810i	−0.598965	+	0.800775i	$0.704421\pi$
$998$	43.7260	−	43.7260i	1.38412	−	1.38412i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.f.b.55.3	✓	20
3.2	odd	2	inner	459.2.f.b.55.8	yes	20
17.8	even	8		7803.2.a.br.1.3		10
17.9	even	8		7803.2.a.bs.1.3		10
17.13	even	4	inner	459.2.f.b.217.8	yes	20
51.8	odd	8		7803.2.a.bs.1.8		10
51.26	odd	8		7803.2.a.br.1.8		10
51.47	odd	4	inner	459.2.f.b.217.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.f.b.55.3	✓	20	1.1	even	1	trivial
459.2.f.b.55.8	yes	20	3.2	odd	2	inner
459.2.f.b.217.3	yes	20	51.47	odd	4	inner
459.2.f.b.217.8	yes	20	17.13	even	4	inner
7803.2.a.br.1.3		10	17.8	even	8
7803.2.a.br.1.8		10	51.26	odd	8
7803.2.a.bs.1.3		10	17.9	even	8
7803.2.a.bs.1.8		10	51.8	odd	8

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.06212i q^{2} -2.25232 q^{4} +(-1.02072 + 1.02072i) q^{5} +(-0.0902131 - 0.0902131i) q^{7} +0.520322i q^{8} +(2.10484 + 2.10484i) q^{10} +(-4.04825 - 4.04825i) q^{11} -2.54466 q^{13} +(-0.186030 + 0.186030i) q^{14} -3.43168 q^{16} +(-3.31209 - 2.45561i) q^{17} +1.47276i q^{19} +(2.29899 - 2.29899i) q^{20} +(-8.34796 + 8.34796i) q^{22} +(-1.15144 - 1.15144i) q^{23} +2.91627i q^{25} +5.24738i q^{26} +(0.203189 + 0.203189i) q^{28} +(2.79177 - 2.79177i) q^{29} +(0.292335 - 0.292335i) q^{31} +8.11718i q^{32} +(-5.06376 + 6.82992i) q^{34} +0.184164 q^{35} +(4.00649 - 4.00649i) q^{37} +3.03701 q^{38} +(-0.531102 - 0.531102i) q^{40} +(1.33747 + 1.33747i) q^{41} -7.93369i q^{43} +(9.11797 + 9.11797i) q^{44} +(-2.37441 + 2.37441i) q^{46} +0.484421 q^{47} -6.98372i q^{49} +6.01369 q^{50} +5.73140 q^{52} +9.05465i q^{53} +8.26423 q^{55} +(0.0469399 - 0.0469399i) q^{56} +(-5.75696 - 5.75696i) q^{58} -12.0518i q^{59} +(3.04914 + 3.04914i) q^{61} +(-0.602829 - 0.602829i) q^{62} +9.87520 q^{64} +(2.59738 - 2.59738i) q^{65} +9.00823 q^{67} +(7.45991 + 5.53084i) q^{68} -0.379768i q^{70} +(-7.77062 + 7.77062i) q^{71} +(-4.93459 + 4.93459i) q^{73} +(-8.26184 - 8.26184i) q^{74} -3.31714i q^{76} +0.730409i q^{77} +(-9.85086 - 9.85086i) q^{79} +(3.50278 - 3.50278i) q^{80} +(2.75802 - 2.75802i) q^{82} +4.09960i q^{83} +(5.88720 - 0.874225i) q^{85} -16.3602 q^{86} +(2.10639 - 2.10639i) q^{88} +13.1764 q^{89} +(0.229561 + 0.229561i) q^{91} +(2.59342 + 2.59342i) q^{92} -0.998933i q^{94} +(-1.50327 - 1.50327i) q^{95} +(-2.54449 + 2.54449i) q^{97} -14.4013 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{4} + 8 q^{7} + 20 q^{10} + 32 q^{16} + 8 q^{22} + 44 q^{28} - 24 q^{31} - 28 q^{34} - 4 q^{37} - 32 q^{40} + 64 q^{46} - 8 q^{52} - 84 q^{55} + 36 q^{58} + 72 q^{64} + 36 q^{67} - 16 q^{73}+ \cdots - 32 q^{97}+O(q^{100}) \) 20 * q - 24 * q^4 + 8 * q^7 + 20 * q^10 + 32 * q^16 + 8 * q^22 + 44 * q^28 - 24 * q^31 - 28 * q^34 - 4 * q^37 - 32 * q^40 + 64 * q^46 - 8 * q^52 - 84 * q^55 + 36 * q^58 + 72 * q^64 + 36 * q^67 - 16 * q^73 - 40 * q^79 - 36 * q^82 + 36 * q^85 - 96 * q^88 - 76 * q^91 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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