LMFDB - Embedded newform 624.2.bv.g.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.649638144.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 $ x^8 - 14x^6 + 75x^4 - 170*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$2.34138 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.2.bv.g.433.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +4.20740i q^{5} +(3.07905 + 1.77769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +4.20740i q^{5} +(3.07905 + 1.77769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(4.39944 - 2.54002i) q^{11} +(-3.51537 + 0.801361i) q^{13} +(-3.64372 + 2.10370i) q^{15} +(1.62835 - 2.82038i) q^{17} +(-2.88800 - 1.66739i) q^{19} +3.55539i q^{21} +(-0.192034 - 0.332613i) q^{23} -12.7022 q^{25} -1.00000 q^{27} +(3.64372 + 6.31111i) q^{29} -6.47535i q^{31} +(4.39944 + 2.54002i) q^{33} +(-7.47947 + 12.9548i) q^{35} +(-2.70838 + 1.56369i) q^{37} +(-2.45168 - 2.64372i) q^{39} +(5.86649 - 3.38702i) q^{41} +(-2.07905 + 3.60103i) q^{43} +(-3.64372 - 2.10370i) q^{45} -5.49484i q^{47} +(2.82038 + 4.88505i) q^{49} +3.25670 q^{51} +0.613974 q^{53} +(10.6869 + 18.5102i) q^{55} -3.33477i q^{57} +(6.82333 + 3.93945i) q^{59} +(4.15614 - 7.19864i) q^{61} +(-3.07905 + 1.77769i) q^{63} +(-3.37165 - 14.7906i) q^{65} +(-1.79162 + 1.03439i) q^{67} +(0.192034 - 0.332613i) q^{69} +(-2.44677 - 1.41265i) q^{71} -3.21865i q^{73} +(-6.35112 - 11.0005i) q^{75} +18.0615 q^{77} +2.64077 q^{79} +(-0.500000 - 0.866025i) q^{81} -1.96926i q^{83} +(11.8665 + 6.85112i) q^{85} +(-3.64372 + 6.31111i) q^{87} +(-12.2630 + 7.08003i) q^{89} +(-12.2486 - 3.78181i) q^{91} +(5.60782 - 3.23768i) q^{93} +(7.01537 - 12.1510i) q^{95} +(-7.67962 - 4.43383i) q^{97} +5.08003i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51} + 4 q^{53} + 10 q^{55} + 36 q^{59} + 2 q^{61} - 28 q^{65} - 36 q^{67} - 2 q^{69} - 6 q^{71} - 2 q^{75} + 56 q^{77} + 12 q^{79} - 4 q^{81} + 24 q^{85} - 6 q^{87} - 12 q^{89} - 38 q^{91} - 6 q^{93} + 34 q^{95} - 66 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$			4.20740i			1.88161i	0.338951	+	0.940804i	$0.389928\pi$
$5$			4.20740i			1.88161i	−0.338951	+	0.940804i	$0.610072\pi$
$6$		0			0
$7$	3.07905	+	1.77769i	1.16377	+	0.671905i	0.952205	−	0.305459i	$-0.0988098\pi$
$7$	3.07905	+	1.77769i	1.16377	+	0.671905i	0.211568	+	0.977363i	$0.432143\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.39944	−	2.54002i	1.32648	−	0.765844i	0.341727	−	0.939799i	$-0.388988\pi$
$11$	4.39944	−	2.54002i	1.32648	−	0.765844i	0.984754	+	0.173956i	$0.0556549\pi$
$12$		0			0
$13$	−3.51537	+	0.801361i	−0.974988	+	0.222258i
$13$	−3.51537	+	0.801361i	−0.974988	+	0.222258i
$14$		0			0
$15$	−3.64372	+	2.10370i	−0.940804	+	0.543173i
$16$		0			0
$17$	1.62835	−	2.82038i	0.394933	−	0.684043i	−0.598160	−	0.801377i	$-0.704101\pi$
$17$	1.62835	−	2.82038i	0.394933	−	0.684043i	0.993093	+	0.117333i	$0.0374346\pi$
$18$		0			0
$19$	−2.88800	−	1.66739i	−0.662552	−	0.382525i	0.130696	−	0.991422i	$-0.458279\pi$
$19$	−2.88800	−	1.66739i	−0.662552	−	0.382525i	−0.793249	+	0.608898i	$0.791612\pi$
$20$		0			0
$21$			3.55539i			0.775849i
$22$		0			0
$23$	−0.192034	−	0.332613i	−0.0400419	−	0.0693546i	0.845310	−	0.534276i	$-0.179416\pi$
$23$	−0.192034	−	0.332613i	−0.0400419	−	0.0693546i	−0.885352	+	0.464922i	$0.846082\pi$
$24$		0			0
$25$	−12.7022			−2.54045
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	3.64372	+	6.31111i	0.676621	+	1.17194i	0.975992	+	0.217806i	$0.0698900\pi$
$29$	3.64372	+	6.31111i	0.676621	+	1.17194i	−0.299371	+	0.954137i	$0.596777\pi$
$30$		0			0
$31$		−	6.47535i		−	1.16301i	−0.813544	−	0.581504i	$-0.802465\pi$
$31$		−	6.47535i		−	1.16301i	0.813544	−	0.581504i	$-0.197535\pi$
$32$		0			0
$33$	4.39944	+	2.54002i	0.765844	+	0.442160i
$34$		0			0
$35$	−7.47947	+	12.9548i	−1.26426	+	2.18976i
$36$		0			0
$37$	−2.70838	+	1.56369i	−0.445255	+	0.257068i	−0.705824	−	0.708387i	$-0.749423\pi$
$37$	−2.70838	+	1.56369i	−0.445255	+	0.257068i	0.260569	+	0.965455i	$0.416090\pi$
$38$		0			0
$39$	−2.45168	−	2.64372i	−0.392584	−	0.423334i
$40$		0			0
$41$	5.86649	−	3.38702i	0.916192	−	0.528964i	0.0337737	−	0.999430i	$-0.489247\pi$
$41$	5.86649	−	3.38702i	0.916192	−	0.528964i	0.882418	+	0.470466i	$0.155914\pi$
$42$		0			0
$43$	−2.07905	+	3.60103i	−0.317053	+	0.549152i	−0.979872	−	0.199628i	$-0.936027\pi$
$43$	−2.07905	+	3.60103i	−0.317053	+	0.549152i	0.662819	+	0.748780i	$0.269360\pi$
$44$		0			0
$45$	−3.64372	−	2.10370i	−0.543173	−	0.313601i
$46$		0			0
$47$		−	5.49484i		−	0.801505i	−0.916186	−	0.400752i	$-0.868749\pi$
$47$		−	5.49484i		−	0.801505i	0.916186	−	0.400752i	$-0.131251\pi$
$48$		0			0
$49$	2.82038	+	4.88505i	0.402912	+	0.697864i
$50$		0			0
$51$	3.25670			0.456029
$52$		0			0
$53$	0.613974			0.0843358			0.0421679	−	0.999111i	$-0.486574\pi$
$53$	0.613974			0.0843358			0.0421679	+	0.999111i	$0.486574\pi$
$54$		0			0
$55$	10.6869	+	18.5102i	1.44102	+	2.49592i
$56$		0			0
$57$		−	3.33477i		−	0.441702i
$58$		0			0
$59$	6.82333	+	3.93945i	0.888323	+	0.512873i	0.873393	−	0.487015i	$-0.161914\pi$
$59$	6.82333	+	3.93945i	0.888323	+	0.512873i	0.0149291	+	0.999889i	$0.495248\pi$
$60$		0			0
$61$	4.15614	−	7.19864i	0.532139	−	0.921691i	−0.467157	−	0.884174i	$-0.654722\pi$
$61$	4.15614	−	7.19864i	0.532139	−	0.921691i	0.999296	−	0.0375170i	$-0.0119448\pi$
$62$		0			0
$63$	−3.07905	+	1.77769i	−0.387924	+	0.223968i
$64$		0			0
$65$	−3.37165	−	14.7906i	−0.418202	−	1.83455i
$66$		0			0
$67$	−1.79162	+	1.03439i	−0.218881	+	0.126371i	−0.605432	−	0.795897i	$-0.707000\pi$
$67$	−1.79162	+	1.03439i	−0.218881	+	0.126371i	0.386551	+	0.922268i	$0.373666\pi$
$68$		0			0
$69$	0.192034	−	0.332613i	0.0231182	−	0.0400419i
$70$		0			0
$71$	−2.44677	−	1.41265i	−0.290379	−	0.167650i	0.347734	−	0.937593i	$-0.386951\pi$
$71$	−2.44677	−	1.41265i	−0.290379	−	0.167650i	−0.638113	+	0.769943i	$0.720285\pi$
$72$		0			0
$73$		−	3.21865i		−	0.376715i	−0.982101	−	0.188357i	$-0.939684\pi$
$73$		−	3.21865i		−	0.376715i	0.982101	−	0.188357i	$-0.0603164\pi$
$74$		0			0
$75$	−6.35112	−	11.0005i	−0.733364	−	1.27022i
$76$		0			0
$77$	18.0615			2.05830
$78$		0			0
$79$	2.64077			0.297109			0.148555	−	0.988904i	$-0.452538\pi$
$79$	2.64077			0.297109			0.148555	+	0.988904i	$0.452538\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	1.96926i		−	0.216155i	−0.994142	−	0.108077i	$-0.965531\pi$
$83$		−	1.96926i		−	0.216155i	0.994142	−	0.108077i	$-0.0344694\pi$
$84$		0			0
$85$	11.8665	+	6.85112i	1.28710	+	0.743108i
$86$		0			0
$87$	−3.64372	+	6.31111i	−0.390648	+	0.676621i
$88$		0			0
$89$	−12.2630	+	7.08003i	−1.29987	+	0.750482i	−0.980382	−	0.197107i	$-0.936845\pi$
$89$	−12.2630	+	7.08003i	−1.29987	+	0.750482i	−0.319491	+	0.947589i	$0.603512\pi$
$90$		0			0
$91$	−12.2486	−	3.78181i	−1.28400	−	0.396442i
$92$		0			0
$93$	5.60782	−	3.23768i	0.581504	−	0.335731i
$94$		0			0
$95$	7.01537	−	12.1510i	0.719762	−	1.24666i
$96$		0			0
$97$	−7.67962	−	4.43383i	−0.779747	−	0.450187i	0.0565937	−	0.998397i	$-0.481976\pi$
$97$	−7.67962	−	4.43383i	−0.779747	−	0.450187i	−0.836341	+	0.548210i	$0.815309\pi$
$98$		0			0
$99$			5.08003i			0.510563i
$100$		0			0
$101$	4.72375	+	8.18178i	0.470031	+	0.814117i	0.999413	−	0.0342664i	$-0.0109095\pi$
$101$	4.72375	+	8.18178i	0.470031	+	0.814117i	−0.529382	+	0.848384i	$0.677576\pi$
$102$		0			0
$103$	−2.15811			−0.212645			−0.106322	−	0.994332i	$-0.533908\pi$
$103$	−2.15811			−0.212645			−0.106322	+	0.994332i	$0.533908\pi$
$104$		0			0
$105$	−14.9589			−1.45984
$106$		0			0
$107$	−9.35014	−	16.1949i	−0.903912	−	1.56562i	−0.822371	−	0.568952i	$-0.807349\pi$
$107$	−9.35014	−	16.1949i	−0.903912	−	1.56562i	−0.0815419	−	0.996670i	$-0.525984\pi$
$108$		0			0
$109$			14.4754i			1.38649i	0.720703	+	0.693244i	$0.243819\pi$
$109$			14.4754i			1.38649i	−0.720703	+	0.693244i	$0.756181\pi$
$110$		0			0
$111$	−2.70838	−	1.56369i	−0.257068	−	0.148418i
$112$		0			0
$113$	−1.37165	+	2.37577i	−0.129034	+	0.223494i	−0.923303	−	0.384073i	$-0.874521\pi$
$113$	−1.37165	+	2.37577i	−0.129034	+	0.223494i	0.794269	+	0.607567i	$0.207854\pi$
$114$		0			0
$115$	1.39944	−	0.807966i	0.130498	−	0.0753432i
$116$		0			0
$117$	1.06369	−	3.44508i	0.0983377	−	0.318498i
$118$		0			0
$119$	10.0276	−	5.78941i	0.919224	−	0.530714i
$120$		0			0
$121$	7.40337	−	12.8230i	0.673033	−	1.16573i
$122$		0			0
$123$	5.86649	+	3.38702i	0.528964	+	0.305397i
$124$		0			0
$125$		−	32.4064i		−	2.89852i
$126$		0			0
$127$	5.06369	+	8.77056i	0.449329	+	0.778261i	0.998342	−	0.0575524i	$-0.0183296\pi$
$127$	5.06369	+	8.77056i	0.449329	+	0.778261i	−0.549013	+	0.835814i	$0.684996\pi$
$128$		0			0
$129$	−4.15811			−0.366101
$130$		0			0
$131$	13.3430			1.16578			0.582892	−	0.812550i	$-0.301921\pi$
$131$	13.3430			1.16578			0.582892	+	0.812550i	$0.301921\pi$
$132$		0			0
$133$	−5.92820	−	10.2679i	−0.514040	−	0.890344i
$134$		0			0
$135$		−	4.20740i		−	0.362116i
$136$		0			0
$137$	10.3018	+	5.94775i	0.880143	+	0.508151i	0.870706	−	0.491805i	$-0.163663\pi$
$137$	10.3018	+	5.94775i	0.880143	+	0.508151i	0.00943756	+	0.999955i	$0.496996\pi$
$138$		0			0
$139$	6.71035	−	11.6227i	0.569165	−	0.985822i	−0.427484	−	0.904023i	$-0.640600\pi$
$139$	6.71035	−	11.6227i	0.569165	−	0.985822i	0.996649	−	0.0817995i	$-0.0260667\pi$
$140$		0			0
$141$	4.75867	−	2.74742i	0.400752	−	0.231374i
$142$		0			0
$143$	−13.4302	+	12.4546i	−1.12309	+	1.04151i
$144$		0			0
$145$	−26.5534	+	15.3306i	−2.20514	+	1.27314i
$146$		0			0
$147$	−2.82038	+	4.88505i	−0.232621	+	0.402912i
$148$		0			0
$149$	4.77305	+	2.75572i	0.391023	+	0.225757i	0.682603	−	0.730789i	$-0.260848\pi$
$149$	4.77305	+	2.75572i	0.391023	+	0.225757i	−0.291580	+	0.956546i	$0.594181\pi$
$150$		0			0
$151$		−	5.08003i		−	0.413407i	−0.978404	−	0.206704i	$-0.933726\pi$
$151$		−	5.08003i		−	0.413407i	0.978404	−	0.206704i	$-0.0662736\pi$
$152$		0			0
$153$	1.62835	+	2.82038i	0.131644	+	0.228014i
$154$		0			0
$155$	27.2444			2.18832
$156$		0			0
$157$	−12.5670			−1.00296			−0.501478	−	0.865170i	$-0.667210\pi$
$157$	−12.5670			−1.00296			−0.501478	+	0.865170i	$0.667210\pi$
$158$		0			0
$159$	0.306987	+	0.531717i	0.0243456	+	0.0421679i
$160$		0			0
$161$		−	1.36551i		−	0.107617i
$162$		0			0
$163$	−7.63660	−	4.40899i	−0.598145	−	0.345339i	0.170167	−	0.985415i	$-0.445569\pi$
$163$	−7.63660	−	4.40899i	−0.598145	−	0.345339i	−0.768311	+	0.640076i	$0.778903\pi$
$164$		0			0
$165$	−10.6869	+	18.5102i	−0.831972	+	1.44102i
$166$		0			0
$167$	12.7042	−	7.33477i	0.983081	−	0.567582i	0.0798818	−	0.996804i	$-0.474546\pi$
$167$	12.7042	−	7.33477i	0.983081	−	0.567582i	0.903199	+	0.429223i	$0.141212\pi$
$168$		0			0
$169$	11.7156	−	5.63416i	0.901203	−	0.433397i
$170$		0			0
$171$	2.88800	−	1.66739i	0.220851	−	0.127508i
$172$		0			0
$173$	−1.20740	+	2.09128i	−0.0917972	+	0.158997i	−0.908267	−	0.418390i	$-0.862594\pi$
$173$	−1.20740	+	2.09128i	−0.0917972	+	0.158997i	0.816470	+	0.577388i	$0.195928\pi$
$174$		0			0
$175$	−39.1109	−	22.5807i	−2.95651	−	1.70694i
$176$		0			0
$177$			7.87891i			0.592215i
$178$		0			0
$179$	2.67864	+	4.63954i	0.200211	+	0.346775i	0.948596	−	0.316489i	$-0.102504\pi$
$179$	2.67864	+	4.63954i	0.200211	+	0.346775i	−0.748385	+	0.663264i	$0.769171\pi$
$180$		0			0
$181$	17.6715			1.31351			0.656756	−	0.754103i	$-0.271928\pi$
$181$	17.6715			1.31351			0.656756	+	0.754103i	$0.271928\pi$
$182$		0			0
$183$	8.31227			0.614461
$184$		0			0
$185$	−6.57905	−	11.3953i	−0.483702	−	0.837796i
$186$		0			0
$187$		−	16.5441i		−	1.20983i
$188$		0			0
$189$	−3.07905	−	1.77769i	−0.223968	−	0.129308i
$190$		0			0
$191$	2.28744	−	3.96196i	0.165513	−	0.286677i	−0.771324	−	0.636442i	$-0.780405\pi$
$191$	2.28744	−	3.96196i	0.165513	−	0.286677i	0.936837	+	0.349765i	$0.113739\pi$
$192$		0			0
$193$	14.5863	−	8.42141i	1.04995	−	0.606186i	0.127312	−	0.991863i	$-0.459365\pi$
$193$	14.5863	−	8.42141i	1.04995	−	0.606186i	0.922634	+	0.385676i	$0.126032\pi$
$194$		0			0
$195$	11.1232	−	10.3152i	0.796548	−	0.738688i
$196$		0			0
$197$	−1.60770	+	0.928203i	−0.114544	+	0.0661317i	−0.556177	−	0.831064i	$-0.687732\pi$
$197$	−1.60770	+	0.928203i	−0.114544	+	0.0661317i	0.441634	+	0.897195i	$0.354399\pi$
$198$		0			0
$199$	9.49386	−	16.4438i	0.673002	−	1.16567i	−0.304047	−	0.952657i	$-0.598338\pi$
$199$	9.49386	−	16.4438i	0.673002	−	1.16567i	0.977049	−	0.213016i	$-0.0683288\pi$
$200$		0			0
$201$	−1.79162	−	1.03439i	−0.126371	−	0.0729603i
$202$		0			0
$203$			25.9096i			1.81850i
$204$		0			0
$205$	14.2506	+	24.6827i	0.995302	+	1.72391i
$206$		0			0
$207$	0.384069			0.0266946
$208$		0			0
$209$	−16.9408			−1.17182
$210$		0			0
$211$	6.12122	+	10.6023i	0.421402	+	0.729890i	0.996077	−	0.0884922i	$-0.0282048\pi$
$211$	6.12122	+	10.6023i	0.421402	+	0.729890i	−0.574675	+	0.818382i	$0.694872\pi$
$212$		0			0
$213$		−	2.82529i		−	0.193586i
$214$		0			0
$215$	−15.1510	−	8.74742i	−1.03329	−	0.596569i
$216$		0			0
$217$	11.5112	−	19.9380i	0.781430	−	1.35348i
$218$		0			0
$219$	2.78744	−	1.60933i	0.188357	−	0.108748i
$220$		0			0
$221$	−3.46410	+	11.2196i	−0.233021	+	0.754711i
$222$		0			0
$223$	−17.9341	+	10.3543i	−1.20096	+	0.693373i	−0.960768	−	0.277354i	$-0.910543\pi$
$223$	−17.9341	+	10.3543i	−1.20096	+	0.693373i	−0.240189	+	0.970726i	$0.577209\pi$
$224$		0			0
$225$	6.35112	−	11.0005i	0.423408	−	0.733364i
$226$		0			0
$227$	−7.48143	−	4.31940i	−0.496560	−	0.286689i	0.230732	−	0.973017i	$-0.425888\pi$
$227$	−7.48143	−	4.31940i	−0.496560	−	0.286689i	−0.727292	+	0.686328i	$0.759221\pi$
$228$		0			0
$229$		−	20.1111i		−	1.32898i	−0.747296	−	0.664491i	$-0.768648\pi$
$229$		−	20.1111i		−	1.32898i	0.747296	−	0.664491i	$-0.231352\pi$
$230$		0			0
$231$	9.03074	+	15.6417i	0.594179	+	1.02915i
$232$		0			0
$233$	4.41089			0.288967			0.144484	−	0.989507i	$-0.453848\pi$
$233$	4.41089			0.288967			0.144484	+	0.989507i	$0.453848\pi$
$234$		0			0
$235$	23.1190			1.50812
$236$		0			0
$237$	1.32038	+	2.28697i	0.0857681	+	0.148555i
$238$		0			0
$239$		−	3.51734i		−	0.227518i	−0.993508	−	0.113759i	$-0.963711\pi$
$239$		−	3.51734i		−	0.227518i	0.993508	−	0.113759i	$-0.0362892\pi$
$240$		0			0
$241$	−4.10782	−	2.37165i	−0.264608	−	0.152771i	0.361827	−	0.932245i	$-0.382153\pi$
$241$	−4.10782	−	2.37165i	−0.264608	−	0.152771i	−0.626435	+	0.779474i	$0.715487\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−20.5534	+	11.8665i	−1.31311	+	0.758122i
$246$		0			0
$247$	11.4886	+	3.54715i	0.731000	+	0.225700i
$248$		0			0
$249$	1.70543	−	0.984631i	0.108077	−	0.0623984i
$250$		0			0
$251$	−3.49484	+	6.05324i	−0.220592	+	0.382077i	−0.954988	−	0.296644i	$-0.904132\pi$
$251$	−3.49484	+	6.05324i	−0.220592	+	0.382077i	0.734396	+	0.678722i	$0.237466\pi$
$252$		0			0
$253$	−1.68969	−	0.975541i	−0.106230	−	0.0613317i
$254$		0			0
$255$			13.7022i			0.858068i
$256$		0			0
$257$	−2.35505	−	4.07907i	−0.146904	−	0.254445i	0.783178	−	0.621798i	$-0.213598\pi$
$257$	−2.35505	−	4.07907i	−0.146904	−	0.254445i	−0.930082	+	0.367353i	$0.880264\pi$
$258$		0			0
$259$	−11.1190			−0.690902
$260$		0			0
$261$	−7.28744			−0.451081
$262$		0			0
$263$	−2.06466	−	3.57610i	−0.127313	−	0.220512i	0.795322	−	0.606187i	$-0.207302\pi$
$263$	−2.06466	−	3.57610i	−0.127313	−	0.220512i	−0.922635	+	0.385675i	$0.873968\pi$
$264$		0			0
$265$			2.58324i			0.158687i
$266$		0			0
$267$	−12.2630	−	7.08003i	−0.750482	−	0.433291i
$268$		0			0
$269$	−8.12933	+	14.0804i	−0.495654	+	0.858498i	−0.999987	−	0.00501123i	$-0.998405\pi$
$269$	−8.12933	+	14.0804i	−0.495654	+	0.858498i	0.504334	+	0.863509i	$0.331738\pi$
$270$		0			0
$271$	−27.9875	+	16.1586i	−1.70012	+	0.981563i	−0.754491	+	0.656311i	$0.772116\pi$
$271$	−27.9875	+	16.1586i	−1.70012	+	0.981563i	−0.945627	+	0.325253i	$0.894551\pi$
$272$		0			0
$273$	−2.84915	−	12.4985i	−0.172438	−	0.756443i
$274$		0			0
$275$	−55.8827	+	32.2639i	−3.36986	+	1.94559i
$276$		0			0
$277$	−11.8684	+	20.5568i	−0.713106	+	1.23514i	0.250580	+	0.968096i	$0.419379\pi$
$277$	−11.8684	+	20.5568i	−0.713106	+	1.23514i	−0.963686	+	0.267040i	$0.913955\pi$
$278$		0			0
$279$	5.60782	+	3.23768i	0.335731	+	0.193835i
$280$		0			0
$281$			25.5812i			1.52604i	0.646373	+	0.763022i	$0.276285\pi$
$281$			25.5812i			1.52604i	−0.646373	+	0.763022i	$0.723715\pi$
$282$		0			0
$283$	5.82431	+	10.0880i	0.346220	+	0.599670i	0.985575	−	0.169242i	$-0.0541319\pi$
$283$	5.82431	+	10.0880i	0.346220	+	0.599670i	−0.639355	+	0.768912i	$0.720799\pi$
$284$		0			0
$285$	14.0307			0.831109
$286$		0			0
$287$	24.0843			1.42165
$288$		0			0
$289$	3.19696	+	5.53729i	0.188056	+	0.325723i
$290$		0			0
$291$		−	8.86766i		−	0.519831i
$292$		0			0
$293$	−8.53049	−	4.92508i	−0.498356	−	0.287726i	0.229678	−	0.973267i	$-0.426233\pi$
$293$	−8.53049	−	4.92508i	−0.498356	−	0.287726i	−0.728035	+	0.685540i	$0.759566\pi$
$294$		0			0
$295$	−16.5749	+	28.7085i	−0.965026	+	1.67147i
$296$		0			0
$297$	−4.39944	+	2.54002i	−0.255281	+	0.147387i
$298$		0			0
$299$	0.941615	+	1.01537i	0.0544550	+	0.0587203i
$300$		0			0
$301$	−12.8030	+	7.39184i	−0.737955	+	0.426059i
$302$		0			0
$303$	−4.72375	+	8.18178i	−0.271372	+	0.470031i
$304$		0			0
$305$	30.2876	+	17.4865i	1.73426	+	1.00128i
$306$		0			0
$307$		−	12.4182i		−	0.708744i	−0.935105	−	0.354372i	$-0.884695\pi$
$307$		−	12.4182i		−	0.708744i	0.935105	−	0.354372i	$-0.115305\pi$
$308$		0			0
$309$	−1.07905	−	1.86898i	−0.0613853	−	0.106322i
$310$		0			0
$311$	7.42267			0.420901			0.210450	−	0.977605i	$-0.432507\pi$
$311$	7.42267			0.420901			0.210450	+	0.977605i	$0.432507\pi$
$312$		0			0
$313$	27.9799			1.58152			0.790758	−	0.612129i	$-0.209687\pi$
$313$	27.9799			1.58152			0.790758	+	0.612129i	$0.209687\pi$
$314$		0			0
$315$	−7.47947	−	12.9548i	−0.421420	−	0.729922i
$316$		0			0
$317$		−	8.02484i		−	0.450720i	−0.974276	−	0.225360i	$-0.927644\pi$
$317$		−	8.02484i		−	0.450720i	0.974276	−	0.225360i	$-0.0723558\pi$
$318$		0			0
$319$	32.0606	+	18.5102i	1.79505	+	1.03637i
$320$		0			0
$321$	9.35014	−	16.1949i	0.521874	−	0.903912i
$322$		0			0
$323$	−9.40534	+	5.43018i	−0.523327	+	0.302143i
$324$		0			0
$325$	44.6531	−	10.1791i	2.47691	−	0.564634i
$326$		0			0
$327$	−12.5360	+	7.23768i	−0.693244	+	0.400244i
$328$		0			0
$329$	9.76814	−	16.9189i	0.538535	−	0.932770i
$330$		0			0
$331$	16.3897	+	9.46261i	0.900860	+	0.520112i	0.877479	−	0.479615i	$-0.159224\pi$
$331$	16.3897	+	9.46261i	0.900860	+	0.520112i	0.0233812	+	0.999727i	$0.492557\pi$
$332$		0			0
$333$		−	3.12737i		−	0.171379i
$334$		0			0
$335$	−4.35210	−	7.53806i	−0.237781	−	0.411848i
$336$		0			0
$337$	−13.8296			−0.753347			−0.376674	−	0.926346i	$-0.622932\pi$
$337$	−13.8296			−0.753347			−0.376674	+	0.926346i	$0.622932\pi$
$338$		0			0
$339$	−2.74330			−0.148996
$340$		0			0
$341$	−16.4475	−	28.4879i	−0.890682	−	1.54271i
$342$		0			0
$343$		−	4.83260i		−	0.260936i
$344$		0			0
$345$	1.39944	+	0.807966i	0.0753432	+	0.0434994i
$346$		0			0
$347$	−8.45464	+	14.6439i	−0.453869	+	0.786123i	−0.998622	−	0.0524726i	$-0.983290\pi$
$347$	−8.45464	+	14.6439i	−0.453869	+	0.786123i	0.544754	+	0.838596i	$0.316623\pi$
$348$		0			0
$349$	−13.6366	+	7.87309i	−0.729950	+	0.421437i	−0.818404	−	0.574643i	$-0.805141\pi$
$349$	−13.6366	+	7.87309i	−0.729950	+	0.421437i	0.0884536	+	0.996080i	$0.471808\pi$
$350$		0			0
$351$	3.51537	−	0.801361i	0.187637	−	0.0427735i
$352$		0			0
$353$	−19.0491	+	10.9980i	−1.01388	+	0.585363i	−0.912325	−	0.409467i	$-0.865715\pi$
$353$	−19.0491	+	10.9980i	−1.01388	+	0.585363i	−0.101554	+	0.994830i	$0.532381\pi$
$354$		0			0
$355$	5.94357	−	10.2946i	0.315452	−	0.546379i
$356$		0			0
$357$	10.0276	+	5.78941i	0.530714	+	0.306408i
$358$		0			0
$359$		−	24.5606i		−	1.29626i	−0.761530	−	0.648130i	$-0.775551\pi$
$359$		−	24.5606i		−	1.29626i	0.761530	−	0.648130i	$-0.224449\pi$
$360$		0			0
$361$	−3.93964	−	6.82366i	−0.207350	−	0.359140i
$362$		0			0
$363$	14.8067			0.777152
$364$		0			0
$365$	13.5422			0.708830
$366$		0			0
$367$	4.10389	+	7.10815i	0.214221	+	0.371042i	0.953031	−	0.302871i	$-0.0979453\pi$
$367$	4.10389	+	7.10815i	0.214221	+	0.371042i	−0.738810	+	0.673914i	$0.764612\pi$
$368$		0			0
$369$			6.77404i			0.352642i
$370$		0			0
$371$	1.89046	+	1.09146i	0.0981477	+	0.0566656i
$372$		0			0
$373$	5.05950	−	8.76332i	0.261971	−	0.453747i	−0.704794	−	0.709412i	$-0.748961\pi$
$373$	5.05950	−	8.76332i	0.261971	−	0.453747i	0.966766	+	0.255664i	$0.0822941\pi$
$374$		0			0
$375$	28.0648	−	16.2032i	1.44926	−	0.836731i
$376$		0			0
$377$	−17.8665	−	19.2659i	−0.920171	−	0.992246i
$378$		0			0
$379$	−18.3263	+	10.5807i	−0.941358	+	0.543493i	−0.890386	−	0.455207i	$-0.849565\pi$
$379$	−18.3263	+	10.5807i	−0.941358	+	0.543493i	−0.0509723	+	0.998700i	$0.516232\pi$
$380$		0			0
$381$	−5.06369	+	8.77056i	−0.259420	+	0.449329i
$382$		0			0
$383$	22.6163	+	13.0575i	1.15564	+	0.667209i	0.950255	−	0.311473i	$-0.100822\pi$
$383$	22.6163	+	13.0575i	1.15564	+	0.667209i	0.205384	+	0.978681i	$0.434156\pi$
$384$		0			0
$385$			75.9919i			3.87291i
$386$		0			0
$387$	−2.07905	−	3.60103i	−0.105684	−	0.183051i
$388$		0			0
$389$	−9.18493			−0.465695			−0.232847	−	0.972513i	$-0.574804\pi$
$389$	−9.18493			−0.465695			−0.232847	+	0.972513i	$0.574804\pi$
$390$		0			0
$391$	−1.25080			−0.0632554
$392$		0			0
$393$	6.67150	+	11.5554i	0.336533	+	0.582892i
$394$		0			0
$395$			11.1108i			0.559044i
$396$		0			0
$397$	−10.2115	−	5.89560i	−0.512499	−	0.295892i	0.221361	−	0.975192i	$-0.428950\pi$
$397$	−10.2115	−	5.89560i	−0.512499	−	0.295892i	−0.733860	+	0.679300i	$0.762283\pi$
$398$		0			0
$399$	5.92820	−	10.2679i	0.296781	−	0.514040i
$400$		0			0
$401$	26.3983	−	15.2411i	1.31827	−	0.761104i	0.334820	−	0.942282i	$-0.391324\pi$
$401$	26.3983	−	15.2411i	1.31827	−	0.761104i	0.983450	+	0.181178i	$0.0579911\pi$
$402$		0			0
$403$	5.18910	+	22.7633i	0.258487	+	1.13392i
$404$		0			0
$405$	3.64372	−	2.10370i	0.181058	−	0.104534i
$406$		0			0
$407$	−7.94357	+	13.7587i	−0.393748	+	0.681992i
$408$		0			0
$409$	−14.5576	−	8.40481i	−0.719825	−	0.415591i	0.0948632	−	0.995490i	$-0.469759\pi$
$409$	−14.5576	−	8.40481i	−0.719825	−	0.415591i	−0.814688	+	0.579899i	$0.803092\pi$
$410$		0			0
$411$			11.8955i			0.586762i
$412$		0			0
$413$	14.0063	+	24.2596i	0.689204	+	1.19374i
$414$		0			0
$415$	8.28548			0.406718
$416$		0			0
$417$	13.4207			0.657215
$418$		0			0
$419$	−12.2894	−	21.2859i	−0.600376	−	1.03988i	−0.992764	−	0.120082i	$-0.961684\pi$
$419$	−12.2894	−	21.2859i	−0.600376	−	1.03988i	0.392388	−	0.919800i	$-0.371649\pi$
$420$		0			0
$421$			11.1157i			0.541748i	0.962615	+	0.270874i	$0.0873127\pi$
$421$			11.1157i			0.541748i	−0.962615	+	0.270874i	$0.912687\pi$
$422$		0			0
$423$	4.75867	+	2.74742i	0.231374	+	0.133584i
$424$		0			0
$425$	−20.6837	+	35.8252i	−1.00331	+	1.73778i
$426$		0			0
$427$	25.5939	−	14.7767i	1.23858	−	0.715093i
$428$		0			0
$429$	−17.5011	−	5.40356i	−0.844962	−	0.260886i
$430$		0			0
$431$	−31.6624	+	18.2803i	−1.52512	+	0.880531i	−0.525568	+	0.850751i	$0.676147\pi$
$431$	−31.6624	+	18.2803i	−1.52512	+	0.880531i	−0.999556	+	0.0297799i	$0.990519\pi$
$432$		0			0
$433$	−9.58827	+	16.6074i	−0.460783	+	0.798099i	−0.999000	−	0.0447068i	$-0.985765\pi$
$433$	−9.58827	+	16.6074i	−0.460783	+	0.798099i	0.538217	+	0.842806i	$0.319098\pi$
$434$		0			0
$435$	−26.5534	−	15.3306i	−1.27314	−	0.735046i
$436$		0			0
$437$			1.28078i			0.0612681i
$438$		0			0
$439$	−11.9106	−	20.6298i	−0.568463	−	0.984607i	−0.996718	−	0.0809491i	$-0.974205\pi$
$439$	−11.9106	−	20.6298i	−0.568463	−	0.984607i	0.428255	−	0.903658i	$-0.359128\pi$
$440$		0			0
$441$	−5.64077			−0.268608
$442$		0			0
$443$	−6.48020			−0.307884			−0.153942	−	0.988080i	$-0.549197\pi$
$443$	−6.48020			−0.307884			−0.153942	+	0.988080i	$0.549197\pi$
$444$		0			0
$445$	−29.7886	−	51.5953i	−1.41211	−	2.44585i
$446$		0			0
$447$			5.51144i			0.260682i
$448$		0			0
$449$	6.15811	+	3.55539i	0.290619	+	0.167789i	0.638221	−	0.769853i	$-0.279671\pi$
$449$	6.15811	+	3.55539i	0.290619	+	0.167789i	−0.347602	+	0.937642i	$0.613004\pi$
$450$		0			0
$451$	17.2062	−	29.8020i	0.810207	−	1.40332i
$452$		0			0
$453$	4.39944	−	2.54002i	0.206704	−	0.119340i
$454$		0			0
$455$	15.9116	−	51.5347i	0.745948	−	2.41599i
$456$		0			0
$457$	−1.48573	+	0.857789i	−0.0694997	+	0.0401257i	−0.534347	−	0.845265i	$-0.679442\pi$
$457$	−1.48573	+	0.857789i	−0.0694997	+	0.0401257i	0.464847	+	0.885391i	$0.346109\pi$
$458$		0			0
$459$	−1.62835	+	2.82038i	−0.0760048	+	0.131644i
$460$		0			0
$461$	−28.1570	−	16.2565i	−1.31140	−	0.757139i	−0.329075	−	0.944304i	$-0.606737\pi$
$461$	−28.1570	−	16.2565i	−1.31140	−	0.757139i	−0.982328	+	0.187165i	$0.940070\pi$
$462$		0			0
$463$			3.37282i			0.156748i	0.996924	+	0.0783741i	$0.0249728\pi$
$463$			3.37282i			0.156748i	−0.996924	+	0.0783741i	$0.975027\pi$
$464$		0			0
$465$	13.6222	+	23.5944i	0.631715	+	1.09416i
$466$		0			0
$467$	−19.3241			−0.894212			−0.447106	−	0.894481i	$-0.647545\pi$
$467$	−19.3241			−0.894212			−0.447106	+	0.894481i	$0.647545\pi$
$468$		0			0
$469$	−7.35532			−0.339637
$470$		0			0
$471$	−6.28351	−	10.8834i	−0.289529	−	0.501478i
$472$		0			0
$473$			21.1233i			0.971252i
$474$		0			0
$475$	36.6841	+	21.1796i	1.68318	+	0.971785i
$476$		0			0
$477$	−0.306987	+	0.531717i	−0.0140560	+	0.0243456i
$478$		0			0
$479$	−7.55446	+	4.36157i	−0.345172	+	0.199285i	−0.662557	−	0.749012i	$-0.730529\pi$
$479$	−7.55446	+	4.36157i	−0.345172	+	0.199285i	0.317385	+	0.948297i	$0.397195\pi$
$480$		0			0
$481$	8.26789	−	7.66732i	0.376983	−	0.349600i
$482$		0			0
$483$	1.18257	−	0.682756i	0.0538087	−	0.0310665i
$484$		0			0
$485$	18.6549	−	32.3112i	0.847076	−	1.46718i
$486$		0			0
$487$	−10.0832	−	5.82155i	−0.456914	−	0.263800i	0.253832	−	0.967248i	$-0.418309\pi$
$487$	−10.0832	−	5.82155i	−0.456914	−	0.263800i	−0.710746	+	0.703449i	$0.751642\pi$
$488$		0			0
$489$		−	8.81799i		−	0.398763i
$490$		0			0
$491$	−3.88604	−	6.73082i	−0.175375	−	0.303758i	0.764916	−	0.644130i	$-0.222780\pi$
$491$	−3.88604	−	6.73082i	−0.175375	−	0.303758i	−0.940291	+	0.340372i	$0.889447\pi$
$492$		0			0
$493$	23.7330			1.06888
$494$		0			0
$495$	−21.3737			−0.960679
$496$		0			0
$497$	−5.02250	−	8.69923i	−0.225290	−	0.390214i
$498$		0			0
$499$		−	20.3434i		−	0.910695i	−0.890314	−	0.455348i	$-0.849515\pi$
$499$		−	20.3434i		−	0.910695i	0.890314	−	0.455348i	$-0.150485\pi$
$500$		0			0
$501$	12.7042	+	7.33477i	0.567582	+	0.327694i
$502$		0			0
$503$	−10.5761	+	18.3183i	−0.471565	+	0.816775i	−0.999471	−	0.0325282i	$-0.989644\pi$
$503$	−10.5761	+	18.3183i	−0.471565	+	0.816775i	0.527906	+	0.849303i	$0.322977\pi$
$504$		0			0
$505$	−34.4240	+	19.8747i	−1.53185	+	0.884414i
$506$		0			0
$507$	10.7371	+	7.32896i	0.476853	+	0.325491i
$508$		0			0
$509$	−32.9785	+	19.0401i	−1.46175	+	0.843939i	−0.999092	−	0.0425997i	$-0.986436\pi$
$509$	−32.9785	+	19.0401i	−1.46175	+	0.843939i	−0.462654	+	0.886539i	$0.653103\pi$
$510$		0			0
$511$	5.72178	−	9.91041i	0.253117	−	0.438411i
$512$		0			0
$513$	2.88800	+	1.66739i	0.127508	+	0.0736169i
$514$		0			0
$515$		−	9.08003i		−	0.400114i
$516$		0			0
$517$	−13.9570	−	24.1742i	−0.613827	−	1.06318i
$518$		0			0
$519$	−2.41481			−0.105998
$520$		0			0
$521$	20.7433			0.908781			0.454390	−	0.890803i	$-0.349857\pi$
$521$	20.7433			0.908781			0.454390	+	0.890803i	$0.349857\pi$
$522$		0			0
$523$	−2.47123	−	4.28030i	−0.108060	−	0.187165i	0.806925	−	0.590655i	$-0.201130\pi$
$523$	−2.47123	−	4.28030i	−0.108060	−	0.187165i	−0.914984	+	0.403490i	$0.867797\pi$
$524$		0			0
$525$		−	45.1614i		−	1.97100i
$526$		0			0
$527$	−18.2630	−	10.5441i	−0.795548	−	0.459310i
$528$		0			0
$529$	11.4262	−	19.7908i	0.496793	−	0.860471i
$530$		0			0
$531$	−6.82333	+	3.93945i	−0.296108	+	0.170958i
$532$		0			0
$533$	−17.9087	+	16.6078i	−0.775710	+	0.719364i
$534$		0			0
$535$	68.1386	−	39.3398i	2.94589	−	1.70081i
$536$		0			0
$537$	−2.67864	+	4.63954i	−0.115592	+	0.200211i
$538$		0			0
$539$	24.8162	+	14.3276i	1.06891	+	0.617135i
$540$		0			0
$541$		−	43.7196i		−	1.87965i	−0.341650	−	0.939827i	$-0.610986\pi$
$541$		−	43.7196i		−	1.87965i	0.341650	−	0.939827i	$-0.389014\pi$
$542$		0			0
$543$	8.83575	+	15.3040i	0.379178	+	0.656756i
$544$		0			0
$545$	−60.9036			−2.60883
$546$		0			0
$547$	−39.1028			−1.67191			−0.835957	−	0.548795i	$-0.815087\pi$
$547$	−39.1028			−1.67191			−0.835957	+	0.548795i	$0.815087\pi$
$548$		0			0
$549$	4.15614	+	7.19864i	0.177380	+	0.307230i
$550$		0			0
$551$		−	24.3020i		−	1.03530i
$552$		0			0
$553$	8.13106	+	4.69447i	0.345768	+	0.199629i
$554$		0			0
$555$	6.57905	−	11.3953i	0.279265	−	0.483702i
$556$		0			0
$557$	20.7774	−	11.9958i	0.880365	−	0.508279i	0.00958646	−	0.999954i	$-0.496948\pi$
$557$	20.7774	−	11.9958i	0.880365	−	0.508279i	0.870779	+	0.491675i	$0.163615\pi$
$558$		0			0
$559$	4.42292	−	14.3250i	0.187070	−	0.605884i
$560$		0			0
$561$	14.3276	−	8.27207i	0.604913	−	0.349247i
$562$		0			0
$563$	−5.23814	+	9.07273i	−0.220761	+	0.382370i	−0.955039	−	0.296479i	$-0.904188\pi$
$563$	−5.23814	+	9.07273i	−0.220761	+	0.382370i	0.734278	+	0.678849i	$0.237521\pi$
$564$		0			0
$565$	−9.99582	−	5.77109i	−0.420527	−	0.242792i
$566$		0			0
$567$		−	3.55539i		−	0.149312i
$568$		0			0
$569$	15.3982	+	26.6705i	0.645526	+	1.11808i	0.984180	+	0.177173i	$0.0566953\pi$
$569$	15.3982	+	26.6705i	0.645526	+	1.11808i	−0.338653	+	0.940911i	$0.609971\pi$
$570$		0			0
$571$	9.52126			0.398452			0.199226	−	0.979954i	$-0.436157\pi$
$571$	9.52126			0.398452			0.199226	+	0.979954i	$0.436157\pi$
$572$		0			0
$573$	4.57487			0.191118
$574$		0			0
$575$	2.43927	+	4.22493i	0.101724	+	0.176192i
$576$		0			0
$577$		−	47.7495i		−	1.98784i	−0.110124	−	0.993918i	$-0.535125\pi$
$577$		−	47.7495i		−	1.98784i	0.110124	−	0.993918i	$-0.464875\pi$
$578$		0			0
$579$	14.5863	+	8.42141i	0.606186	+	0.349982i
$580$		0			0
$581$	3.50074	−	6.06346i	0.145235	−	0.251555i
$582$		0			0
$583$	2.70114	−	1.55950i	0.111870	−	0.0645880i
$584$		0			0
$585$	14.4948	+	4.47535i	0.599288	+	0.185033i
$586$		0			0
$587$	34.1946	−	19.7423i	1.41136	−	0.814851i	0.415846	−	0.909435i	$-0.363485\pi$
$587$	34.1946	−	19.7423i	1.41136	−	0.814851i	0.995517	+	0.0945840i	$0.0301521\pi$
$588$		0			0
$589$	−10.7969	+	18.7008i	−0.444879	+	0.770553i
$590$		0			0
$591$	−1.60770	−	0.928203i	−0.0661317	−	0.0381812i
$592$		0			0
$593$		−	20.0166i		−	0.821983i	−0.911639	−	0.410992i	$-0.865183\pi$
$593$		−	20.0166i		−	0.821983i	0.911639	−	0.410992i	$-0.134817\pi$
$594$		0			0
$595$	24.3584	+	42.1900i	0.998596	+	1.72962i
$596$		0			0
$597$	18.9877			0.777116
$598$		0			0
$599$	19.8517			0.811120			0.405560	−	0.914068i	$-0.367077\pi$
$599$	19.8517			0.811120			0.405560	+	0.914068i	$0.367077\pi$
$600$		0			0
$601$	−5.85112	−	10.1344i	−0.238672	−	0.413392i	0.721661	−	0.692246i	$-0.243379\pi$
$601$	−5.85112	−	10.1344i	−0.238672	−	0.413392i	−0.960334	+	0.278854i	$0.910045\pi$
$602$		0			0
$603$		−	2.06878i		−	0.0842473i
$604$		0			0
$605$	53.9516	+	31.1490i	2.19344	+	1.26639i
$606$		0			0
$607$	−21.5978	+	37.4084i	−0.876626	+	1.51836i	−0.0216048	+	0.999767i	$0.506878\pi$
$607$	−21.5978	+	37.4084i	−0.876626	+	1.51836i	−0.855021	+	0.518594i	$0.826456\pi$
$608$		0			0
$609$	−22.4384	+	12.9548i	−0.909250	+	0.524956i
$610$		0			0
$611$	4.40335	+	19.3164i	0.178141	+	0.781457i
$612$		0			0
$613$	−27.4025	+	15.8208i	−1.10678	+	0.638998i	−0.937993	−	0.346655i	$-0.887317\pi$
$613$	−27.4025	+	15.8208i	−1.10678	+	0.638998i	−0.168784	+	0.985653i	$0.553984\pi$
$614$		0			0
$615$	−14.2506	+	24.6827i	−0.574638	+	0.995302i
$616$		0			0
$617$	13.6855	+	7.90135i	0.550959	+	0.318096i	0.749509	−	0.661995i	$-0.230290\pi$
$617$	13.6855	+	7.90135i	0.550959	+	0.318096i	−0.198550	+	0.980091i	$0.563623\pi$
$618$		0			0
$619$		−	36.0663i		−	1.44963i	−0.688945	−	0.724814i	$-0.741926\pi$
$619$		−	36.0663i		−	1.44963i	0.688945	−	0.724814i	$-0.258074\pi$
$620$		0			0
$621$	0.192034	+	0.332613i	0.00770607	+	0.0133473i
$622$		0			0
$623$	−50.3445			−2.01701
$624$		0			0
$625$	72.8358			2.91343
$626$		0			0
$627$	−8.47038	−	14.6711i	−0.338274	−	0.585908i
$628$		0			0
$629$			10.1849i			0.406099i
$630$		0			0
$631$	−15.5073	−	8.95313i	−0.617335	−	0.356418i	0.158496	−	0.987360i	$-0.449336\pi$
$631$	−15.5073	−	8.95313i	−0.617335	−	0.356418i	−0.775831	+	0.630941i	$0.782669\pi$
$632$		0			0
$633$	−6.12122	+	10.6023i	−0.243297	+	0.421402i
$634$		0			0
$635$	−36.9013	+	21.3050i	−1.46438	+	0.845462i
$636$		0			0
$637$	−13.8294	−	14.9126i	−0.547940	−	0.590859i
$638$		0			0
$639$	2.44677	−	1.41265i	0.0967929	−	0.0558834i
$640$		0			0
$641$	17.3551	−	30.0598i	0.685483	−	1.18729i	−0.287801	−	0.957690i	$-0.592924\pi$
$641$	17.3551	−	30.0598i	0.685483	−	1.18729i	0.973285	−	0.229602i	$-0.0737424\pi$
$642$		0			0
$643$	−39.4414	−	22.7715i	−1.55542	−	0.898020i	−0.997685	−	0.0679979i	$-0.978339\pi$
$643$	−39.4414	−	22.7715i	−1.55542	−	0.898020i	−0.557731	−	0.830022i	$-0.688328\pi$
$644$		0			0
$645$		−	17.4948i		−	0.688859i
$646$		0			0
$647$	8.93016	+	15.4675i	0.351081	+	0.608090i	0.986439	−	0.164128i	$-0.0524809\pi$
$647$	8.93016	+	15.4675i	0.351081	+	0.608090i	−0.635358	+	0.772218i	$0.719148\pi$
$648$		0			0
$649$	40.0251			1.57112
$650$		0			0
$651$	23.0224			0.902318
$652$		0			0
$653$	18.8378	+	32.6281i	0.737182	+	1.27684i	0.953759	+	0.300571i	$0.0971773\pi$
$653$	18.8378	+	32.6281i	0.737182	+	1.27684i	−0.216577	+	0.976265i	$0.569489\pi$
$654$		0			0
$655$			56.1394i			2.19355i
$656$		0			0
$657$	2.78744	+	1.60933i	0.108748	+	0.0627858i
$658$		0			0
$659$	17.3737	−	30.0922i	0.676785	−	1.17223i	−0.299159	−	0.954203i	$-0.596706\pi$
$659$	17.3737	−	30.0922i	0.676785	−	1.17223i	0.975944	−	0.218023i	$-0.0699607\pi$
$660$		0			0
$661$	34.0551	−	19.6617i	1.32459	−	0.764752i	0.340132	−	0.940378i	$-0.389528\pi$
$661$	34.0551	−	19.6617i	1.32459	−	0.764752i	0.984457	+	0.175626i	$0.0561948\pi$
$662$		0			0
$663$	−11.4485	+	2.60979i	−0.444623	+	0.101356i
$664$		0			0
$665$	43.2014	−	24.9423i	1.67528	−	0.967223i
$666$		0			0
$667$	1.39944	−	2.42390i	0.0541864	−	0.0938537i
$668$		0			0
$669$	−17.9341	−	10.3543i	−0.693373	−	0.400319i
$670$		0			0
$671$		−	42.2266i		−	1.63014i
$672$		0			0
$673$	5.57180	+	9.65064i	0.214777	+	0.372005i	0.953204	−	0.302329i	$-0.0977642\pi$
$673$	5.57180	+	9.65064i	0.214777	+	0.372005i	−0.738427	+	0.674334i	$0.764431\pi$
$674$		0			0
$675$	12.7022			0.488910
$676$		0			0
$677$	−12.3037			−0.472868			−0.236434	−	0.971648i	$-0.575979\pi$
$677$	−12.3037			−0.472868			−0.236434	+	0.971648i	$0.575979\pi$
$678$		0			0
$679$	−15.7640	−	27.3040i	−0.604966	−	1.04783i
$680$		0			0
$681$		−	8.63881i		−	0.331040i
$682$		0			0
$683$	15.1885	+	8.76907i	0.581171	+	0.335539i	0.761598	−	0.648049i	$-0.224415\pi$
$683$	15.1885	+	8.76907i	0.581171	+	0.335539i	−0.180428	+	0.983588i	$0.557748\pi$
$684$		0			0
$685$	−25.0246	+	43.3439i	−0.956141	+	1.65608i
$686$		0			0
$687$	17.4168	−	10.0556i	0.664491	−	0.383644i
$688$		0			0
$689$	−2.15834	+	0.492015i	−0.0822264	+	0.0187443i
$690$		0			0
$691$	11.3606	−	6.55904i	0.432177	−	0.249518i	−0.268097	−	0.963392i	$-0.586395\pi$
$691$	11.3606	−	6.55904i	0.432177	−	0.249518i	0.700274	+	0.713874i	$0.253061\pi$
$692$		0			0
$693$	−9.03074	+	15.6417i	−0.343049	+	0.594179i
$694$		0			0
$695$	48.9013	+	28.2332i	1.85493	+	1.07095i
$696$		0			0
$697$		−	22.0610i		−	0.835620i
$698$		0			0
$699$	2.20545	+	3.81994i	0.0834176	+	0.144484i
$700$		0			0
$701$	0.768137			0.0290121			0.0145061	−	0.999895i	$-0.495382\pi$
$701$	0.768137			0.0290121			0.0145061	+	0.999895i	$0.495382\pi$
$702$		0			0
$703$	10.4291			0.393340
$704$		0			0
$705$	11.5595	+	20.0216i	0.435356	+	0.754059i
$706$		0			0
$707$			33.5895i			1.26326i
$708$		0			0
$709$	−27.7905	−	16.0449i	−1.04369	−	0.602577i	−0.122817	−	0.992429i	$-0.539193\pi$
$709$	−27.7905	−	16.0449i	−1.04369	−	0.602577i	−0.920877	+	0.389852i	$0.872526\pi$
$710$		0			0
$711$	−1.32038	+	2.28697i	−0.0495182	+	0.0857681i
$712$		0			0
$713$	−2.15379	+	1.24349i	−0.0806600	+	0.0465691i
$714$		0			0
$715$	−52.4017	−	56.5062i	−1.95971	−	2.11321i
$716$		0			0
$717$	3.04611	−	1.75867i	0.113759	−	0.0656788i
$718$		0			0
$719$	5.48856	−	9.50647i	0.204689	−	0.354531i	−0.745345	−	0.666679i	$-0.767715\pi$
$719$	5.48856	−	9.50647i	0.204689	−	0.354531i	0.950034	+	0.312148i	$0.101048\pi$
$720$		0			0
$721$	−6.64493	−	3.83645i	−0.247470	−	0.142877i
$722$		0			0
$723$		−	4.74330i		−	0.176405i
$724$		0			0
$725$	−46.2834	−	80.1652i	−1.71892	−	2.97726i
$726$		0			0
$727$	40.9056			1.51710			0.758552	−	0.651612i	$-0.225907\pi$
$727$	40.9056			1.51710			0.758552	+	0.651612i	$0.225907\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.77085	+	11.7275i	0.250429	+	0.433756i
$732$		0			0
$733$		−	6.18829i		−	0.228570i	−0.993448	−	0.114285i	$-0.963542\pi$
$733$		−	6.18829i		−	0.228570i	0.993448	−	0.114285i	$-0.0364577\pi$
$734$		0			0
$735$	−20.5534	−	11.8665i	−0.758122	−	0.437702i
$736$		0			0
$737$	−5.25474	+	9.10148i	−0.193561	+	0.335257i
$738$		0			0
$739$	−46.2014	+	26.6744i	−1.69955	+	0.981233i	−0.753361	+	0.657607i	$0.771569\pi$
$739$	−46.2014	+	26.6744i	−1.69955	+	0.981233i	−0.946185	+	0.323626i	$0.895098\pi$
$740$		0			0
$741$	2.67236	+	11.7230i	0.0981716	+	0.430654i
$742$		0			0
$743$	−38.6012	+	22.2864i	−1.41614	+	0.817609i	−0.995957	−	0.0898302i	$-0.971368\pi$
$743$	−38.6012	+	22.2864i	−1.41614	+	0.817609i	−0.420183	+	0.907439i	$0.638034\pi$
$744$		0			0
$745$	−11.5944	+	20.0821i	−0.424787	+	0.735752i
$746$		0			0
$747$	1.70543	+	0.984631i	0.0623984	+	0.0360258i
$748$		0			0
$749$		−	66.4867i		−	2.42937i
$750$		0			0
$751$	0.754726	+	1.30722i	0.0275403	+	0.0477012i	0.879467	−	0.475960i	$-0.157899\pi$
$751$	0.754726	+	1.30722i	0.0275403	+	0.0477012i	−0.851927	+	0.523661i	$0.824566\pi$
$752$		0			0
$753$	−6.98968			−0.254718
$754$		0			0
$755$	21.3737			0.777870
$756$		0			0
$757$	25.9897	+	45.0154i	0.944611	+	1.63611i	0.756528	+	0.653961i	$0.226894\pi$
$757$	25.9897	+	45.0154i	0.944611	+	1.63611i	0.188083	+	0.982153i	$0.439773\pi$
$758$		0			0
$759$		−	1.95108i		−	0.0708198i
$760$		0			0
$761$	−9.24010	−	5.33477i	−0.334953	−	0.193385i	0.323085	−	0.946370i	$-0.395280\pi$
$761$	−9.24010	−	5.33477i	−0.334953	−	0.193385i	−0.658038	+	0.752985i	$0.728613\pi$
$762$		0			0
$763$	−25.7327	+	44.5704i	−0.931587	+	1.61356i
$764$		0			0
$765$	−11.8665	+	6.85112i	−0.429034	+	0.247703i
$766$		0			0
$767$	−27.1435	−	8.38068i	−0.980094	−	0.302609i
$768$		0			0
$769$	5.20703	−	3.00628i	0.187770	−	0.108409i	−0.403168	−	0.915126i	$-0.632091\pi$
$769$	5.20703	−	3.00628i	0.187770	−	0.108409i	0.590938	+	0.806717i	$0.298758\pi$
$770$		0			0
$771$	2.35505	−	4.07907i	0.0848151	−	0.146904i
$772$		0			0
$773$	−34.5464	−	19.9454i	−1.24255	−	0.717385i	−0.272935	−	0.962033i	$-0.587994\pi$
$773$	−34.5464	−	19.9454i	−1.24255	−	0.717385i	−0.969612	+	0.244648i	$0.921328\pi$
$774$		0			0
$775$			82.2515i			2.95456i
$776$		0			0
$777$	−5.55950	−	9.62934i	−0.199446	−	0.345451i
$778$		0			0
$779$	−22.5899			−0.809367
$780$		0			0
$781$	−14.3526			−0.513576
$782$		0			0
$783$	−3.64372	−	6.31111i	−0.130216	−	0.225540i
$784$		0			0
$785$		−	52.8745i		−	1.88717i
$786$		0			0
$787$	−3.03295	−	1.75107i	−0.108113	−	0.0624190i	0.444969	−	0.895546i	$-0.353215\pi$
$787$	−3.03295	−	1.75107i	−0.108113	−	0.0624190i	−0.553081	+	0.833127i	$0.686548\pi$
$788$		0			0
$789$	2.06466	−	3.57610i	0.0735040	−	0.127313i
$790$		0			0
$791$	−8.44677	+	4.87675i	−0.300333	+	0.173397i
$792$		0			0
$793$	−8.84164	+	28.6364i	−0.313976	+	1.01691i
$794$		0			0
$795$	−2.23715	+	1.29162i	−0.0793435	+	0.0458090i
$796$		0			0
$797$	−12.1435	+	21.0331i	−0.430144	+	0.745031i	−0.996885	−	0.0788649i	$-0.974870\pi$
$797$	−12.1435	+	21.0331i	−0.430144	+	0.745031i	0.566742	+	0.823896i	$0.308204\pi$
$798$		0			0
$799$	−15.4976	−	8.94752i	−0.548264	−	0.316540i
$800$		0			0
$801$		−	14.1601i		−	0.500321i
$802$		0			0
$803$	−8.17544	−	14.1603i	−0.288505	−	0.499705i
$804$		0			0
$805$	5.74526			0.202494
$806$		0			0
$807$	−16.2587			−0.572332
$808$		0			0
$809$	9.56441	+	16.5660i	0.336267	+	0.582431i	0.983727	−	0.179668i	$-0.0575023\pi$
$809$	9.56441	+	16.5660i	0.336267	+	0.582431i	−0.647461	+	0.762099i	$0.724169\pi$
$810$		0			0
$811$		−	55.1857i		−	1.93783i	−0.247387	−	0.968917i	$-0.579572\pi$
$811$		−	55.1857i		−	1.93783i	0.247387	−	0.968917i	$-0.420428\pi$
$812$		0			0
$813$	−27.9875	−	16.1586i	−0.981563	−	0.566706i
$814$		0			0
$815$	18.5504	−	32.1303i	0.649793	−	1.12547i
$816$		0			0
$817$	12.0086	−	6.93318i	0.420128	−	0.242561i
$818$		0			0
$819$	9.39944	−	8.71668i	0.328443	−	0.304586i
$820$		0			0
$821$	−20.2098	+	11.6681i	−0.705326	+	0.407220i	−0.809328	−	0.587357i	$-0.800168\pi$
$821$	−20.2098	+	11.6681i	−0.705326	+	0.407220i	0.104002	+	0.994577i	$0.466835\pi$
$822$		0			0
$823$	1.02679	−	1.77846i	0.0357918	−	0.0619931i	−0.847575	−	0.530676i	$-0.821938\pi$
$823$	1.02679	−	1.77846i	0.0357918	−	0.0619931i	0.883366	+	0.468683i	$0.155271\pi$
$824$		0			0
$825$	−55.8827	−	32.2639i	−1.94559	−	1.12329i
$826$		0			0
$827$			5.96289i			0.207350i	0.994611	+	0.103675i	$0.0330602\pi$
$827$			5.96289i			0.207350i	−0.994611	+	0.103675i	$0.966940\pi$
$828$		0			0
$829$	7.28155	+	12.6120i	0.252899	+	0.438033i	0.964323	−	0.264730i	$-0.0852827\pi$
$829$	7.28155	+	12.6120i	0.252899	+	0.438033i	−0.711424	+	0.702763i	$0.751949\pi$
$830$		0			0
$831$	−23.7369			−0.823424
$832$		0			0
$833$	18.3703			0.636492
$834$		0			0
$835$	30.8604	+	53.4517i	1.06797	+	1.84977i
$836$		0			0
$837$			6.47535i			0.223821i
$838$		0			0
$839$	42.4990	+	24.5368i	1.46723	+	0.847105i	0.999327	−	0.0366748i	$-0.0116766\pi$
$839$	42.4990	+	24.5368i	1.46723	+	0.847105i	0.467902	+	0.883780i	$0.345010\pi$
$840$		0			0
$841$	−12.0534	+	20.8770i	−0.415633	+	0.719898i
$842$		0			0
$843$	−22.1539	+	12.7906i	−0.763022	+	0.440531i
$844$		0			0
$845$	23.7052	+	49.2924i	0.815483	+	1.69571i
$846$		0			0
$847$	45.5907	−	26.3218i	1.56652	−	0.904429i
$848$		0			0
$849$	−5.82431	+	10.0880i	−0.199890	+	0.346220i
$850$		0			0
$851$	1.04020	+	0.600562i	0.0356578	+	0.0205870i
$852$		0			0
$853$			54.6929i			1.87265i	0.351138	+	0.936324i	$0.385795\pi$
$853$			54.6929i			1.87265i	−0.351138	+	0.936324i	$0.614205\pi$
$854$		0			0
$855$	7.01537	+	12.1510i	0.239921	+	0.415555i
$856$		0			0
$857$	23.2811			0.795266			0.397633	−	0.917545i	$-0.369832\pi$
$857$	23.2811			0.795266			0.397633	+	0.917545i	$0.369832\pi$
$858$		0			0
$859$	−43.4229			−1.48157			−0.740785	−	0.671742i	$-0.765546\pi$
$859$	−43.4229			−1.48157			−0.740785	+	0.671742i	$0.765546\pi$
$860$		0			0
$861$	12.0422	+	20.8576i	0.410396	+	0.710826i
$862$		0			0
$863$			7.28977i			0.248147i	0.992273	+	0.124073i	$0.0395958\pi$
$863$			7.28977i			0.248147i	−0.992273	+	0.124073i	$0.960404\pi$
$864$		0			0
$865$	−8.79888	−	5.08003i	−0.299171	−	0.172726i
$866$		0			0
$867$	−3.19696	+	5.53729i	−0.108574	+	0.188056i
$868$		0			0
$869$	11.6179	−	6.70759i	0.394110	−	0.227539i
$870$		0			0
$871$	5.46928	−	5.07200i	0.185319	−	0.171858i
$872$		0			0
$873$	7.67962	−	4.43383i	0.259916	−	0.150062i
$874$		0			0
$875$	57.6087	−	99.7812i	1.94753	−	3.37322i
$876$		0			0
$877$	28.7922	+	16.6232i	0.972245	+	0.561326i	0.899920	−	0.436055i	$-0.143625\pi$
$877$	28.7922	+	16.6232i	0.972245	+	0.561326i	0.0723248	+	0.997381i	$0.476958\pi$
$878$		0			0
$879$		−	9.85016i		−	0.332238i
$880$		0			0
$881$	8.09441	+	14.0199i	0.272708	+	0.472343i	0.969554	−	0.244877i	$-0.0787475\pi$
$881$	8.09441	+	14.0199i	0.272708	+	0.472343i	−0.696847	+	0.717220i	$0.745414\pi$
$882$		0			0
$883$	−20.0492			−0.674708			−0.337354	−	0.941378i	$-0.609532\pi$
$883$	−20.0492			−0.674708			−0.337354	+	0.941378i	$0.609532\pi$
$884$		0			0
$885$	−33.1497			−1.11432
$886$		0			0
$887$	−27.1560	−	47.0356i	−0.911810	−	1.57930i	−0.811506	−	0.584345i	$-0.801352\pi$
$887$	−27.1560	−	47.0356i	−0.911810	−	1.57930i	−0.100304	−	0.994957i	$-0.531982\pi$
$888$		0			0
$889$			36.0067i			1.20763i
$890$		0			0
$891$	−4.39944	−	2.54002i	−0.147387	−	0.0850938i
$892$		0			0
$893$	−9.16202	+	15.8691i	−0.306595	+	0.531039i
$894$		0			0
$895$	−19.5204	+	11.2701i	−0.652495	+	0.376718i
$896$		0			0
$897$	−0.408528	+	1.32315i	−0.0136404	+	0.0441786i
$898$		0			0
$899$	40.8666	−	23.5944i	1.36298	−	0.786916i
$900$		0			0
$901$	0.999764	−	1.73164i	0.0333070	−	0.0576893i
$902$		0			0
$903$	−12.8030	−	7.39184i	−0.426059	−	0.245985i
$904$		0			0
$905$			74.3511i			2.47152i
$906$		0			0
$907$	25.9486	+	44.9443i	0.861610	+	1.49235i	0.870374	+	0.492390i	$0.163877\pi$
$907$	25.9486	+	44.9443i	0.861610	+	1.49235i	−0.00876464	+	0.999962i	$0.502790\pi$
$908$		0			0
$909$	−9.44750			−0.313354
$910$		0			0
$911$	−17.0433			−0.564669			−0.282334	−	0.959316i	$-0.591109\pi$
$911$	−17.0433			−0.564669			−0.282334	+	0.959316i	$0.591109\pi$
$912$		0			0
$913$	−5.00196	−	8.66364i	−0.165541	−	0.286725i
$914$		0			0
$915$			34.9731i			1.15617i
$916$		0			0
$917$	41.0839	+	23.7198i	1.35671	+	0.783296i
$918$		0			0
$919$	−8.03465	+	13.9164i	−0.265039	+	0.459061i	−0.967574	−	0.252589i	$-0.918718\pi$
$919$	−8.03465	+	13.9164i	−0.265039	+	0.459061i	0.702535	+	0.711649i	$0.252051\pi$
$920$		0			0
$921$	10.7545	−	6.20910i	0.354372	−	0.204597i
$922$		0			0
$923$	9.73336	+	3.00522i	0.320377	+	0.0989181i
$924$		0			0
$925$	34.4025	−	19.8623i	1.13115	−	0.653069i
$926$		0			0
$927$	1.07905	−	1.86898i	0.0354408	−	0.0613853i
$928$		0			0
$929$	9.87485	+	5.70125i	0.323983	+	0.187052i	0.653167	−	0.757214i	$-0.273440\pi$
$929$	9.87485	+	5.70125i	0.323983	+	0.187052i	−0.329183	+	0.944266i	$0.606773\pi$
$930$		0			0
$931$		−	18.8107i		−	0.616495i
$932$		0			0
$933$	3.71133	+	6.42822i	0.121504	+	0.210450i
$934$		0			0
$935$	69.6078			2.27642
$936$		0			0
$937$	−33.8213			−1.10489			−0.552447	−	0.833548i	$-0.686306\pi$
$937$	−33.8213			−1.10489			−0.552447	+	0.833548i	$0.686306\pi$
$938$		0			0
$939$	13.9899	+	24.2313i	0.456544	+	0.790758i
$940$		0			0
$941$		−	48.0429i		−	1.56615i	−0.621925	−	0.783077i	$-0.713649\pi$
$941$		−	48.0429i		−	1.56615i	0.621925	−	0.783077i	$-0.286351\pi$
$942$		0			0
$943$	−2.25313	−	1.30085i	−0.0733722	−	0.0423614i
$944$		0			0
$945$	7.47947	−	12.9548i	0.243307	−	0.421420i
$946$		0			0
$947$	10.4598	−	6.03897i	0.339898	−	0.196240i	−0.320329	−	0.947306i	$-0.603793\pi$
$947$	10.4598	−	6.03897i	0.339898	−	0.196240i	0.660227	+	0.751066i	$0.270460\pi$
$948$		0			0
$949$	2.57931	+	11.3148i	0.0837278	+	0.367293i
$950$		0			0
$951$	6.94971	−	4.01242i	0.225360	−	0.130112i
$952$		0			0
$953$	7.71256	−	13.3586i	0.249834	−	0.432726i	−0.713645	−	0.700507i	$-0.752957\pi$
$953$	7.71256	−	13.3586i	0.249834	−	0.432726i	0.963480	+	0.267781i	$0.0862905\pi$
$954$		0			0
$955$	16.6695	+	9.62417i	0.539414	+	0.311431i
$956$		0			0
$957$			37.0204i			1.19670i
$958$		0			0
$959$	21.1466	+	36.6269i	0.682858	+	1.18274i
$960$		0			0
$961$	−10.9302			−0.352587
$962$		0			0
$963$	18.7003			0.602608
$964$		0			0
$965$	35.4323	+	61.3705i	1.14061	+	1.97559i
$966$		0			0
$967$		−	49.7289i		−	1.59917i	−0.600550	−	0.799587i	$-0.705052\pi$
$967$		−	49.7289i		−	1.59917i	0.600550	−	0.799587i	$-0.294948\pi$
$968$		0			0
$969$	−9.40534	−	5.43018i	−0.302143	−	0.174442i
$970$		0			0
$971$	−15.4948	+	26.8378i	−0.497253	+	0.861268i	−0.999995	−	0.00316898i	$-0.998991\pi$
$971$	−15.4948	+	26.8378i	−0.497253	+	0.861268i	0.502742	+	0.864437i	$0.332325\pi$
$972$		0			0
$973$	41.3231	−	23.8579i	1.32476	−	0.764849i
$974$		0			0
$975$	31.1419	+	33.5812i	0.997339	+	1.07546i
$976$		0			0
$977$	−19.8117	+	11.4383i	−0.633831	+	0.365943i	−0.782234	−	0.622984i	$-0.785920\pi$
$977$	−19.8117	+	11.4383i	−0.633831	+	0.365943i	0.148403	+	0.988927i	$0.452587\pi$
$978$		0			0
$979$	−35.9668	+	62.2963i	−1.14950	+	1.99100i
$980$		0			0
$981$	−12.5360	−	7.23768i	−0.400244	−	0.231081i
$982$		0			0
$983$			28.0019i			0.893121i	0.894754	+	0.446560i	$0.147351\pi$
$983$			28.0019i			0.893121i	−0.894754	+	0.446560i	$0.852649\pi$
$984$		0			0
$985$	−3.90533	−	6.76422i	−0.124434	−	0.215526i
$986$		0			0
$987$	19.5363			0.621846
$988$		0			0
$989$	1.59700			0.0507816
$990$		0			0
$991$	−8.14274	−	14.1036i	−0.258663	−	0.448017i	0.707221	−	0.706992i	$-0.249948\pi$
$991$	−8.14274	−	14.1036i	−0.258663	−	0.448017i	−0.965884	+	0.258975i	$0.916615\pi$
$992$		0			0
$993$			18.9252i			0.600574i
$994$		0			0
$995$	69.1859	+	39.9445i	2.19334	+	1.26633i
$996$		0			0
$997$	−23.1517	+	40.1000i	−0.733222	+	1.26998i	0.222277	+	0.974984i	$0.428651\pi$
$997$	−23.1517	+	40.1000i	−0.733222	+	1.26998i	−0.955499	+	0.294995i	$0.904682\pi$
$998$		0			0
$999$	2.70838	−	1.56369i	0.0856894	−	0.0494728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.g.49.4		8
3.2	odd	2		1872.2.by.m.1297.1		8
4.3	odd	2		312.2.bf.b.49.4	✓	8
12.11	even	2		936.2.bi.c.361.1		8
13.2	odd	12		8112.2.a.cs.1.4		4
13.4	even	6	inner	624.2.bv.g.433.1		8
13.11	odd	12		8112.2.a.cq.1.1		4
39.17	odd	6		1872.2.by.m.433.4		8
52.3	odd	6		4056.2.c.p.337.8		8
52.11	even	12		4056.2.a.bd.1.1		4
52.15	even	12		4056.2.a.be.1.4		4
52.23	odd	6		4056.2.c.p.337.1		8
52.43	odd	6		312.2.bf.b.121.1	yes	8
156.95	even	6		936.2.bi.c.433.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.b.49.4	✓	8	4.3	odd	2
312.2.bf.b.121.1	yes	8	52.43	odd	6
624.2.bv.g.49.4		8	1.1	even	1	trivial
624.2.bv.g.433.1		8	13.4	even	6	inner
936.2.bi.c.361.1		8	12.11	even	2
936.2.bi.c.433.4		8	156.95	even	6
1872.2.by.m.433.4		8	39.17	odd	6
1872.2.by.m.1297.1		8	3.2	odd	2
4056.2.a.bd.1.1		4	52.11	even	12
4056.2.a.be.1.4		4	52.15	even	12
4056.2.c.p.337.1		8	52.23	odd	6
4056.2.c.p.337.8		8	52.3	odd	6
8112.2.a.cq.1.1		4	13.11	odd	12
8112.2.a.cs.1.4		4	13.2	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +4.20740i q^{5} +(3.07905 + 1.77769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +4.20740i q^{5} +(3.07905 + 1.77769i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(4.39944 - 2.54002i) q^{11} +(-3.51537 + 0.801361i) q^{13} +(-3.64372 + 2.10370i) q^{15} +(1.62835 - 2.82038i) q^{17} +(-2.88800 - 1.66739i) q^{19} +3.55539i q^{21} +(-0.192034 - 0.332613i) q^{23} -12.7022 q^{25} -1.00000 q^{27} +(3.64372 + 6.31111i) q^{29} -6.47535i q^{31} +(4.39944 + 2.54002i) q^{33} +(-7.47947 + 12.9548i) q^{35} +(-2.70838 + 1.56369i) q^{37} +(-2.45168 - 2.64372i) q^{39} +(5.86649 - 3.38702i) q^{41} +(-2.07905 + 3.60103i) q^{43} +(-3.64372 - 2.10370i) q^{45} -5.49484i q^{47} +(2.82038 + 4.88505i) q^{49} +3.25670 q^{51} +0.613974 q^{53} +(10.6869 + 18.5102i) q^{55} -3.33477i q^{57} +(6.82333 + 3.93945i) q^{59} +(4.15614 - 7.19864i) q^{61} +(-3.07905 + 1.77769i) q^{63} +(-3.37165 - 14.7906i) q^{65} +(-1.79162 + 1.03439i) q^{67} +(0.192034 - 0.332613i) q^{69} +(-2.44677 - 1.41265i) q^{71} -3.21865i q^{73} +(-6.35112 - 11.0005i) q^{75} +18.0615 q^{77} +2.64077 q^{79} +(-0.500000 - 0.866025i) q^{81} -1.96926i q^{83} +(11.8665 + 6.85112i) q^{85} +(-3.64372 + 6.31111i) q^{87} +(-12.2630 + 7.08003i) q^{89} +(-12.2486 - 3.78181i) q^{91} +(5.60782 - 3.23768i) q^{93} +(7.01537 - 12.1510i) q^{95} +(-7.67962 - 4.43383i) q^{97} +5.08003i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} + 12 q^{17} - 6 q^{19} + 2 q^{23} - 4 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{33} - 10 q^{35} - 24 q^{41} + 8 q^{43} - 6 q^{45} + 18 q^{49} + 24 q^{51} + 4 q^{53} + 10 q^{55} + 36 q^{59} + 2 q^{61} - 28 q^{65} - 36 q^{67} - 2 q^{69} - 6 q^{71} - 2 q^{75} + 56 q^{77} + 12 q^{79} - 4 q^{81} + 24 q^{85} - 6 q^{87} - 12 q^{89} - 38 q^{91} - 6 q^{93} + 34 q^{95} - 66 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 + 12 * q^17 - 6 * q^19 + 2 * q^23 - 4 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^33 - 10 * q^35 - 24 * q^41 + 8 * q^43 - 6 * q^45 + 18 * q^49 + 24 * q^51 + 4 * q^53 + 10 * q^55 + 36 * q^59 + 2 * q^61 - 28 * q^65 - 36 * q^67 - 2 * q^69 - 6 * q^71 - 2 * q^75 + 56 * q^77 + 12 * q^79 - 4 * q^81 + 24 * q^85 - 6 * q^87 - 12 * q^89 - 38 * q^91 - 6 * q^93 + 34 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more