LMFDB - Embedded newform 252.2.x.a.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.5
Root			$-1.71965 + 0.206851i$ of defining polynomial
Character	$\chi$	$=$	252.209
Dual form			252.2.x.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680689 - 1.59269i) q^{3} +(-2.09336 - 3.62580i) q^{5} +(1.36869 + 2.26422i) q^{7} +(-2.07332 - 2.16825i) q^{9} +O(q^{10})$	\(q+(0.680689 - 1.59269i) q^{3} +(-2.09336 - 3.62580i) q^{5} +(1.36869 + 2.26422i) q^{7} +(-2.07332 - 2.16825i) q^{9} +(-1.23222 - 0.711425i) q^{11} +(-0.850739 + 0.491174i) q^{13} +(-7.19970 + 0.866025i) q^{15} +0.370947 q^{17} -4.97471i q^{19} +(4.53785 - 0.638674i) q^{21} +(4.98775 - 2.87968i) q^{23} +(-6.26427 + 10.8500i) q^{25} +(-4.86465 + 1.82626i) q^{27} +(7.31732 + 4.22466i) q^{29} +(6.28007 - 3.62580i) q^{31} +(-1.97184 + 1.47829i) q^{33} +(5.34444 - 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 + 1.68930i) q^{39} +(-1.06981 - 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(-3.52145 + 12.0564i) q^{45} +(-4.13542 + 7.16276i) q^{47} +(-3.25337 + 6.19803i) q^{49} +(0.252500 - 0.590804i) q^{51} -4.97245i q^{53} +5.95706i q^{55} +(-7.92317 - 3.38623i) q^{57} +(-2.27883 - 3.94705i) q^{59} +(6.50416 + 3.75518i) q^{61} +(2.07166 - 7.66213i) q^{63} +(3.56180 + 2.05640i) q^{65} +(5.03205 + 8.71577i) q^{67} +(-1.19133 - 9.90411i) q^{69} +10.9555i q^{71} +9.52848i q^{73} +(13.0167 + 17.3626i) q^{75} +(-0.0757141 - 3.76374i) q^{77} +(4.25553 - 7.37079i) q^{79} +(-0.402651 + 8.99099i) q^{81} +(0.972254 - 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(11.7094 - 8.77855i) q^{87} -7.80735 q^{89} +(-2.27652 - 1.25399i) q^{91} +(-1.50000 - 12.4702i) q^{93} +(-18.0373 + 10.4138i) q^{95} +(-3.34099 - 1.92892i) q^{97} +(1.01225 + 4.14679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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
$3$	0.680689	−	1.59269i	0.392996	−	0.919540i
$3$	0.680689	−	1.59269i	0.392996	−	0.919540i
$4$		0			0
$5$	−2.09336	−	3.62580i	−0.936177	−	1.62151i	−0.772521	−	0.634989i	$-0.781005\pi$
$5$	−2.09336	−	3.62580i	−0.936177	−	1.62151i	−0.163656	−	0.986518i	$-0.552329\pi$
$6$		0			0
$7$	1.36869	+	2.26422i	0.517317	+	0.855794i
$7$	1.36869	+	2.26422i	0.517317	+	0.855794i
$8$		0			0
$9$	−2.07332	−	2.16825i	−0.691108	−	0.722751i
$10$		0			0
$11$	−1.23222	−	0.711425i	−0.371529	−	0.214503i	0.302597	−	0.953119i	$-0.402146\pi$
$11$	−1.23222	−	0.711425i	−0.371529	−	0.214503i	−0.674126	+	0.738616i	$0.735480\pi$
$12$		0			0
$13$	−0.850739	+	0.491174i	−0.235952	+	0.136227i	−0.613315	−	0.789838i	$-0.710164\pi$
$13$	−0.850739	+	0.491174i	−0.235952	+	0.136227i	0.377363	+	0.926066i	$0.376831\pi$
$14$		0			0
$15$	−7.19970	+	0.866025i	−1.85895	+	0.223607i
$16$		0			0
$17$	0.370947			0.0899679			0.0449840	−	0.998988i	$-0.485676\pi$
$17$	0.370947			0.0899679			0.0449840	+	0.998988i	$0.485676\pi$
$18$		0			0
$19$		−	4.97471i		−	1.14128i	−0.821201	−	0.570638i	$-0.806696\pi$
$19$		−	4.97471i		−	1.14128i	0.821201	−	0.570638i	$-0.193304\pi$
$20$		0			0
$21$	4.53785	−	0.638674i	0.990240	−	0.139370i
$22$		0			0
$23$	4.98775	−	2.87968i	1.04002	−	0.600455i	0.120179	−	0.992752i	$-0.461653\pi$
$23$	4.98775	−	2.87968i	1.04002	−	0.600455i	0.919838	+	0.392298i	$0.128320\pi$
$24$		0			0
$25$	−6.26427	+	10.8500i	−1.25285	+	2.17001i
$26$		0			0
$27$	−4.86465	+	1.82626i	−0.936202	+	0.351463i
$28$		0			0
$29$	7.31732	+	4.22466i	1.35879	+	0.784499i	0.989461	−	0.144798i	$-0.0462534\pi$
$29$	7.31732	+	4.22466i	1.35879	+	0.784499i	0.369332	+	0.929298i	$0.379587\pi$
$30$		0			0
$31$	6.28007	−	3.62580i	1.12793	−	0.651213i	0.184519	−	0.982829i	$-0.440927\pi$
$31$	6.28007	−	3.62580i	1.12793	−	0.651213i	0.943414	+	0.331616i	$0.107594\pi$
$32$		0			0
$33$	−1.97184	+	1.47829i	−0.343253	+	0.257338i
$34$		0			0
$35$	5.34444	−	9.70241i	0.903375	−	1.64001i
$36$		0			0
$37$	3.46445			0.569552			0.284776	−	0.958594i	$-0.408081\pi$
$37$	3.46445			0.569552			0.284776	+	0.958594i	$0.408081\pi$
$38$		0			0
$39$	0.203200	+	1.68930i	0.0325380	+	0.270504i
$40$		0			0
$41$	−1.06981	−	1.85297i	−0.167077	−	0.289386i	0.770314	−	0.637665i	$-0.220099\pi$
$41$	−1.06981	−	1.85297i	−0.167077	−	0.289386i	−0.937391	+	0.348279i	$0.886766\pi$
$42$		0			0
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	−0.540070	−	0.841620i	$-0.681602\pi$
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	0.998899	+	0.0469039i	$0.0149354\pi$
$44$		0			0
$45$	−3.52145	+	12.0564i	−0.524946	+	1.79726i
$46$		0			0
$47$	−4.13542	+	7.16276i	−0.603213	+	1.04480i	0.389118	+	0.921188i	$0.372780\pi$
$47$	−4.13542	+	7.16276i	−0.603213	+	1.04480i	−0.992331	+	0.123608i	$0.960553\pi$
$48$		0			0
$49$	−3.25337	+	6.19803i	−0.464766	+	0.885433i
$50$		0			0
$51$	0.252500	−	0.590804i	0.0353570	−	0.0827291i
$52$		0			0
$53$		−	4.97245i		−	0.683019i	−0.939878	−	0.341509i	$-0.889062\pi$
$53$		−	4.97245i		−	0.683019i	0.939878	−	0.341509i	$-0.110938\pi$
$54$		0			0
$55$			5.95706i			0.803250i
$56$		0			0
$57$	−7.92317	−	3.38623i	−1.04945	−	0.448517i
$58$		0			0
$59$	−2.27883	−	3.94705i	−0.296678	−	0.513862i	0.678696	−	0.734420i	$-0.262546\pi$
$59$	−2.27883	−	3.94705i	−0.296678	−	0.513862i	−0.975374	+	0.220558i	$0.929212\pi$
$60$		0			0
$61$	6.50416	+	3.75518i	0.832772	+	0.480801i	0.854801	−	0.518956i	$-0.173679\pi$
$61$	6.50416	+	3.75518i	0.832772	+	0.480801i	−0.0220288	+	0.999757i	$0.507013\pi$
$62$		0			0
$63$	2.07166	−	7.66213i	0.261004	−	0.965338i
$64$		0			0
$65$	3.56180	+	2.05640i	0.441786	+	0.255066i
$66$		0			0
$67$	5.03205	+	8.71577i	0.614763	+	1.06480i	0.990426	+	0.138044i	$0.0440816\pi$
$67$	5.03205	+	8.71577i	0.614763	+	1.06480i	−0.375663	+	0.926756i	$0.622585\pi$
$68$		0			0
$69$	−1.19133	−	9.90411i	−0.143419	−	1.19231i
$70$		0			0
$71$			10.9555i			1.30018i	0.759857	+	0.650090i	$0.225269\pi$
$71$			10.9555i			1.30018i	−0.759857	+	0.650090i	$0.774731\pi$
$72$		0			0
$73$			9.52848i			1.11522i	0.830102	+	0.557612i	$0.188282\pi$
$73$			9.52848i			1.11522i	−0.830102	+	0.557612i	$0.811718\pi$
$74$		0			0
$75$	13.0167	+	17.3626i	1.50304	+	2.00486i
$76$		0			0
$77$	−0.0757141	−	3.76374i	−0.00862842	−	0.428918i
$78$		0			0
$79$	4.25553	−	7.37079i	0.478784	−	0.829278i	−0.520920	−	0.853606i	$-0.674411\pi$
$79$	4.25553	−	7.37079i	0.478784	−	0.829278i	0.999704	+	0.0243272i	$0.00774434\pi$
$80$		0			0
$81$	−0.402651	+	8.99099i	−0.0447390	+	0.998999i
$82$		0			0
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	−0.807720	−	0.589566i	$-0.799299\pi$
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	0.914439	+	0.404724i	$0.132632\pi$
$84$		0			0
$85$	−0.776524	−	1.34498i	−0.0842259	−	0.145884i
$86$		0			0
$87$	11.7094	−	8.77855i	1.25538	−	0.941159i
$88$		0			0
$89$	−7.80735			−0.827578			−0.413789	−	0.910373i	$-0.635795\pi$
$89$	−7.80735			−0.827578			−0.413789	+	0.910373i	$0.635795\pi$
$90$		0			0
$91$	−2.27652	−	1.25399i	−0.238645	−	0.131454i
$92$		0			0
$93$	−1.50000	−	12.4702i	−0.155543	−	1.29310i
$94$		0			0
$95$	−18.0373	+	10.4138i	−1.85059	+	1.06844i
$96$		0			0
$97$	−3.34099	−	1.92892i	−0.339226	−	0.195852i	0.320704	−	0.947180i	$-0.396081\pi$
$97$	−3.34099	−	1.92892i	−0.339226	−	0.195852i	−0.659930	+	0.751327i	$0.729414\pi$
$98$		0			0
$99$	1.01225	+	4.14679i	0.101735	+	0.416768i
$100$		0			0
$101$	−4.50637	+	7.80526i	−0.448401	+	0.776653i	−0.998282	−	0.0585901i	$-0.981340\pi$
$101$	−4.50637	+	7.80526i	−0.448401	+	0.776653i	0.549882	+	0.835243i	$0.314673\pi$
$102$		0			0
$103$	5.96343	−	3.44299i	0.587594	−	0.339248i	−0.176551	−	0.984291i	$-0.556494\pi$
$103$	5.96343	−	3.44299i	0.587594	−	0.339248i	0.764146	+	0.645044i	$0.223161\pi$
$104$		0			0
$105$	−11.8150	−	15.1164i	−1.15303	−	1.47521i
$106$		0			0
$107$		−	11.3630i		−	1.09850i	−0.835658	−	0.549250i	$-0.814913\pi$
$107$		−	11.3630i		−	1.09850i	0.835658	−	0.549250i	$-0.185087\pi$
$108$		0			0
$109$	−15.9930			−1.53185			−0.765926	−	0.642929i	$-0.777719\pi$
$109$	−15.9930			−1.53185			−0.765926	+	0.642929i	$0.777719\pi$
$110$		0			0
$111$	2.35821	−	5.51779i	0.223832	−	0.523726i
$112$		0			0
$113$	2.17043	−	1.25310i	0.204177	−	0.117881i	−0.394426	−	0.918928i	$-0.629056\pi$
$113$	2.17043	−	1.25310i	0.204177	−	0.117881i	0.598602	+	0.801046i	$0.295723\pi$
$114$		0			0
$115$	−20.8823	−	12.0564i	−1.94728	−	1.12426i
$116$		0			0
$117$	2.82885	+	0.826254i	0.261527	+	0.0763872i
$118$		0			0
$119$	0.507712	+	0.839905i	0.0465419	+	0.0769940i
$120$		0			0
$121$	−4.48775	−	7.77301i	−0.407977	−	0.706637i
$122$		0			0
$123$	−3.67942	+	0.442584i	−0.331762	+	0.0399065i
$124$		0			0
$125$	31.5199			2.81922
$126$		0			0
$127$	−1.91140			−0.169609			−0.0848046	−	0.996398i	$-0.527027\pi$
$127$	−1.91140			−0.169609			−0.0848046	+	0.996398i	$0.527027\pi$
$128$		0			0
$129$	−6.25197	−	8.33928i	−0.550455	−	0.734233i
$130$		0			0
$131$	−4.32591	−	7.49270i	−0.377957	−	0.654640i	0.612808	−	0.790232i	$-0.290040\pi$
$131$	−4.32591	−	7.49270i	−0.377957	−	0.654640i	−0.990765	+	0.135592i	$0.956707\pi$
$132$		0			0
$133$	11.2638	−	6.80885i	0.976698	−	0.590402i
$134$		0			0
$135$	16.8051	+	13.8152i	1.44635	+	1.18902i
$136$		0			0
$137$	10.0973	+	5.82971i	0.862675	+	0.498065i	0.864907	−	0.501932i	$-0.167377\pi$
$137$	10.0973	+	5.82971i	0.862675	+	0.498065i	−0.00223233	+	0.999998i	$0.500711\pi$
$138$		0			0
$139$	−4.82663	+	2.78666i	−0.409390	+	0.236361i	−0.690528	−	0.723306i	$-0.742622\pi$
$139$	−4.82663	+	2.78666i	−0.409390	+	0.236361i	0.281138	+	0.959667i	$0.409288\pi$
$140$		0			0
$141$	8.59312	+	11.4621i	0.723672	+	0.965280i
$142$		0			0
$143$	1.39773			0.116884
$144$		0			0
$145$		−	35.3748i		−	2.93772i
$146$		0			0
$147$	7.65702	+	9.40054i	0.631540	+	0.775343i
$148$		0			0
$149$	−13.4024	+	7.73789i	−1.09797	+	0.633913i	−0.935687	−	0.352832i	$-0.885219\pi$
$149$	−13.4024	+	7.73789i	−1.09797	+	0.633913i	−0.162282	+	0.986744i	$0.551886\pi$
$150$		0			0
$151$	8.31732	−	14.4060i	0.676854	−	1.17235i	−0.299069	−	0.954231i	$-0.596676\pi$
$151$	8.31732	−	14.4060i	0.676854	−	1.17235i	0.975923	−	0.218114i	$-0.0699905\pi$
$152$		0			0
$153$	−0.769094	−	0.804308i	−0.0621776	−	0.0650244i
$154$		0			0
$155$	−26.2928	−	15.1802i	−2.11189	−	1.21930i
$156$		0			0
$157$	14.5559	−	8.40387i	1.16169	−	0.670702i	0.209981	−	0.977705i	$-0.432660\pi$
$157$	14.5559	−	8.40387i	1.16169	−	0.670702i	0.951708	+	0.307004i	$0.0993264\pi$
$158$		0			0
$159$	−7.91958	−	3.38469i	−0.628063	−	0.268424i
$160$		0			0
$161$	13.3469	+	7.35196i	1.05188	+	0.579416i
$162$		0			0
$163$	3.51105			0.275007			0.137503	−	0.990501i	$-0.456092\pi$
$163$	3.51105			0.275007			0.137503	+	0.990501i	$0.456092\pi$
$164$		0			0
$165$	9.48775	+	4.05491i	0.738620	+	0.315674i
$166$		0			0
$167$	4.05253	+	7.01918i	0.313594	+	0.543160i	0.979138	−	0.203198i	$-0.0651336\pi$
$167$	4.05253	+	7.01918i	0.313594	+	0.543160i	−0.665544	+	0.746359i	$0.731800\pi$
$168$		0			0
$169$	−6.01750	+	10.4226i	−0.462884	+	0.801739i
$170$		0			0
$171$	−10.7864	+	10.3142i	−0.824859	+	0.788746i
$172$		0			0
$173$	−6.54844	+	11.3422i	−0.497868	+	0.862334i	−0.999997	−	0.00245951i	$-0.999217\pi$
$173$	−6.54844	+	11.3422i	−0.497868	+	0.862334i	0.502128	+	0.864793i	$0.332550\pi$
$174$		0			0
$175$	−33.1407	+	0.666682i	−2.50520	+	0.0503964i
$176$		0			0
$177$	−7.83760	+	0.942756i	−0.589110	+	0.0708619i
$178$		0			0
$179$			12.7179i			0.950578i	0.879830	+	0.475289i	$0.157656\pi$
$179$			12.7179i			0.950578i	−0.879830	+	0.475289i	$0.842344\pi$
$180$		0			0
$181$			26.5518i			1.97358i	0.161998	+	0.986791i	$0.448206\pi$
$181$			26.5518i			1.97358i	−0.161998	+	0.986791i	$0.551794\pi$
$182$		0			0
$183$	10.4081	−	7.80300i	0.769392	−	0.576814i
$184$		0			0
$185$	−7.25232	−	12.5614i	−0.533201	−	0.923532i
$186$		0			0
$187$	−0.457090	−	0.263901i	−0.0334257	−	0.0192983i
$188$		0			0
$189$	−10.7932	−	8.51504i	−0.785093	−	0.619378i
$190$		0			0
$191$	−1.09735	−	0.633555i	−0.0794014	−	0.0458424i	0.459774	−	0.888036i	$-0.347931\pi$
$191$	−1.09735	−	0.633555i	−0.0794014	−	0.0458424i	−0.539175	+	0.842194i	$0.681264\pi$
$192$		0			0
$193$	−9.31732	−	16.1381i	−0.670676	−	1.16164i	−0.977713	−	0.209947i	$-0.932671\pi$
$193$	−9.31732	−	16.1381i	−0.670676	−	1.16164i	0.307037	−	0.951697i	$-0.400662\pi$
$194$		0			0
$195$	5.69969	−	4.27307i	0.408163	−	0.306001i
$196$		0			0
$197$		−	5.94312i		−	0.423430i	−0.977331	−	0.211715i	$-0.932095\pi$
$197$		−	5.94312i		−	0.423430i	0.977331	−	0.211715i	$-0.0679049\pi$
$198$		0			0
$199$			5.62675i			0.398870i	0.979911	+	0.199435i	$0.0639106\pi$
$199$			5.62675i			0.398870i	−0.979911	+	0.199435i	$0.936089\pi$
$200$		0			0
$201$	17.3068	−	2.08177i	1.22073	−	0.146837i
$202$		0			0
$203$	0.449613	+	22.3503i	0.0315567	+	1.56868i
$204$		0			0
$205$	−4.47900	+	7.75786i	−0.312827	+	0.541832i
$206$		0			0
$207$	−16.5851	−	4.84420i	−1.15274	−	0.336695i
$208$		0			0
$209$	−3.53913	+	6.12996i	−0.244807	+	0.424018i
$210$		0			0
$211$	1.05305	+	1.82393i	0.0724948	+	0.125565i	0.899994	−	0.435902i	$-0.143571\pi$
$211$	1.05305	+	1.82393i	0.0724948	+	0.125565i	−0.827499	+	0.561467i	$0.810237\pi$
$212$		0			0
$213$	17.4487	+	7.45730i	1.19557	+	0.510966i
$214$		0			0
$215$	−25.1935			−1.71818
$216$		0			0
$217$	16.8051	+	9.25684i	1.14080	+	0.628395i
$218$		0			0
$219$	15.1759	+	6.48593i	1.02549	+	0.438279i
$220$		0			0
$221$	−0.315579	+	0.182200i	−0.0212281	+	0.0122561i
$222$		0			0
$223$	5.52351	+	3.18900i	0.369882	+	0.213551i	0.673407	−	0.739272i	$-0.264830\pi$
$223$	5.52351	+	3.18900i	0.369882	+	0.213551i	−0.303525	+	0.952823i	$0.598164\pi$
$224$		0			0
$225$	36.5135	−	8.91312i	2.43423	−	0.594208i
$226$		0			0
$227$	−5.72365	+	9.91365i	−0.379892	+	0.657992i	−0.991046	−	0.133520i	$-0.957372\pi$
$227$	−5.72365	+	9.91365i	−0.379892	+	0.657992i	0.611154	+	0.791511i	$0.290705\pi$
$228$		0			0
$229$	−4.88696	+	2.82149i	−0.322940	+	0.186449i	−0.652702	−	0.757615i	$-0.726365\pi$
$229$	−4.88696	+	2.82149i	−0.322940	+	0.186449i	0.329762	+	0.944064i	$0.393031\pi$
$230$		0			0
$231$	−6.04602	−	2.44135i	−0.397799	−	0.160629i
$232$		0			0
$233$			12.4463i			0.815385i	0.913119	+	0.407693i	$0.133667\pi$
$233$			12.4463i			0.815385i	−0.913119	+	0.407693i	$0.866333\pi$
$234$		0			0
$235$	34.6276			2.25886
$236$		0			0
$237$	−8.84269	−	11.7950i	−0.574394	−	0.766164i
$238$		0			0
$239$	3.52450	−	2.03487i	0.227981	−	0.131625i	−0.381659	−	0.924303i	$-0.624647\pi$
$239$	3.52450	−	2.03487i	0.227981	−	0.131625i	0.609640	+	0.792678i	$0.291314\pi$
$240$		0			0
$241$	4.26195	+	2.46064i	0.274537	+	0.158504i	0.630947	−	0.775826i	$-0.282666\pi$
$241$	4.26195	+	2.46064i	0.274537	+	0.158504i	−0.356411	+	0.934329i	$0.616000\pi$
$242$		0			0
$243$	14.0458	+	6.76137i	0.901037	+	0.433742i
$244$		0			0
$245$	29.2833	−	1.17864i	1.87084	−	0.0753007i
$246$		0			0
$247$	2.44345	+	4.23218i	0.155473	+	0.269287i
$248$		0			0
$249$	−2.02028	−	2.69477i	−0.128030	−	0.170774i
$250$		0			0
$251$	−4.65020			−0.293518			−0.146759	−	0.989172i	$-0.546884\pi$
$251$	−4.65020			−0.293518			−0.146759	+	0.989172i	$0.546884\pi$
$252$		0			0
$253$	−8.19470			−0.515196
$254$		0			0
$255$	−2.67071	+	0.321250i	−0.167246	+	0.0201174i
$256$		0			0
$257$	−5.44701	−	9.43450i	−0.339775	−	0.588508i	0.644615	−	0.764507i	$-0.277018\pi$
$257$	−5.44701	−	9.43450i	−0.339775	−	0.588508i	−0.984390	+	0.175999i	$0.943684\pi$
$258$		0			0
$259$	4.74176	+	7.84426i	0.294639	+	0.487419i
$260$		0			0
$261$	−6.01105	−	24.6249i	−0.372075	−	1.52424i
$262$		0			0
$263$	15.6489	+	9.03488i	0.964951	+	0.557114i	0.897693	−	0.440621i	$-0.145242\pi$
$263$	15.6489	+	9.03488i	0.964951	+	0.557114i	0.0672574	+	0.997736i	$0.478575\pi$
$264$		0			0
$265$	−18.0291	+	10.4091i	−1.10752	+	0.639427i
$266$		0			0
$267$	−5.31438	+	12.4347i	−0.325235	+	0.760991i
$268$		0			0
$269$	2.98410			0.181944			0.0909718	−	0.995853i	$-0.471003\pi$
$269$	2.98410			0.181944			0.0909718	+	0.995853i	$0.471003\pi$
$270$		0			0
$271$		−	10.3608i		−	0.629375i	−0.949195	−	0.314688i	$-0.898100\pi$
$271$		−	10.3608i		−	0.629375i	0.949195	−	0.314688i	$-0.101900\pi$
$272$		0			0
$273$	−3.54683	+	2.77222i	−0.214664	+	0.167782i
$274$		0			0
$275$	15.4380	−	8.91312i	0.930945	−	0.537481i
$276$		0			0
$277$	5.94345	−	10.2944i	0.357107	−	0.618528i	−0.630369	−	0.776296i	$-0.717096\pi$
$277$	5.94345	−	10.2944i	0.357107	−	0.618528i	0.987476	+	0.157768i	$0.0504297\pi$
$278$		0			0
$279$	−20.8823	−	6.09932i	−1.25019	−	0.365157i
$280$		0			0
$281$	−12.0740	−	6.97095i	−0.720277	−	0.415852i	0.0945775	−	0.995518i	$-0.469850\pi$
$281$	−12.0740	−	6.97095i	−0.720277	−	0.415852i	−0.814855	+	0.579665i	$0.803183\pi$
$282$		0			0
$283$	2.19593	−	1.26782i	0.130535	−	0.0753642i	−0.433311	−	0.901245i	$-0.642655\pi$
$283$	2.19593	−	1.26782i	0.130535	−	0.0753642i	0.563845	+	0.825880i	$0.309321\pi$
$284$		0			0
$285$	4.30823	+	35.8164i	0.255197	+	2.12158i
$286$		0			0
$287$	2.73129	−	4.95844i	0.161223	−	0.292687i
$288$		0			0
$289$	−16.8624			−0.991906
$290$		0			0
$291$	−5.34635	+	4.00816i	−0.313408	+	0.234963i
$292$		0			0
$293$	3.95496	+	6.85020i	0.231052	+	0.400193i	0.958118	−	0.286374i	$-0.0924501\pi$
$293$	3.95496	+	6.85020i	0.231052	+	0.400193i	−0.727066	+	0.686567i	$0.759117\pi$
$294$		0			0
$295$	−9.54080	+	16.5251i	−0.555487	+	0.962131i
$296$		0			0
$297$	7.29358	+	1.21047i	0.423216	+	0.0702388i
$298$		0			0
$299$	−2.82885	+	4.89971i	−0.163596	+	0.283357i
$300$		0			0
$301$	15.9176	−	0.320209i	0.917474	−	0.0184565i
$302$		0			0
$303$	9.36393	+	12.4902i	0.537944	+	0.717544i
$304$		0			0
$305$		−	31.4437i		−	1.80046i
$306$		0			0
$307$		−	13.9676i		−	0.797170i	−0.917131	−	0.398585i	$-0.869501\pi$
$307$		−	13.9676i		−	0.797170i	0.917131	−	0.398585i	$-0.130499\pi$
$308$		0			0
$309$	−1.42437	−	11.8415i	−0.0810296	−	0.673640i
$310$		0			0
$311$	16.3163	+	28.2607i	0.925215	+	1.60252i	0.791215	+	0.611539i	$0.209449\pi$
$311$	16.3163	+	28.2607i	0.925215	+	1.60252i	0.134001	+	0.990981i	$0.457218\pi$
$312$		0			0
$313$	13.6110	+	7.85832i	0.769340	+	0.444178i	0.832639	−	0.553816i	$-0.186829\pi$
$313$	13.6110	+	7.85832i	0.769340	+	0.444178i	−0.0632994	+	0.997995i	$0.520162\pi$
$314$		0			0
$315$	−32.1181	+	8.52815i	−1.80965	+	0.480507i
$316$		0			0
$317$	−25.1366	−	14.5126i	−1.41181	−	0.815111i	−0.416254	−	0.909248i	$-0.636657\pi$
$317$	−25.1366	−	14.5126i	−1.41181	−	0.815111i	−0.995559	+	0.0941377i	$0.969991\pi$
$318$		0			0
$319$	−6.01105	−	10.4114i	−0.336554	−	0.582929i
$320$		0			0
$321$	−18.0977	−	7.73465i	−1.01012	−	0.431706i
$322$		0			0
$323$		−	1.84535i		−	0.102678i
$324$		0			0
$325$		−	12.3074i		−	0.682692i
$326$		0			0
$327$	−10.8863	+	25.4719i	−0.602011	+	1.40860i
$328$		0			0
$329$	−21.8782	+	0.440117i	−1.20618	+	0.0242644i
$330$		0			0
$331$	−6.58510	+	11.4057i	−0.361950	+	0.626915i	−0.988282	−	0.152641i	$-0.951222\pi$
$331$	−6.58510	+	11.4057i	−0.361950	+	0.626915i	0.626332	+	0.779556i	$0.284555\pi$
$332$		0			0
$333$	−7.18292	−	7.51180i	−0.393622	−	0.411644i
$334$		0			0
$335$	21.0677	−	36.4904i	1.15105	−	1.99368i
$336$		0			0
$337$	8.31732	+	14.4060i	0.453073	+	0.784746i	0.998575	−	0.0533635i	$-0.0169942\pi$
$337$	8.31732	+	14.4060i	0.453073	+	0.784746i	−0.545502	+	0.838110i	$0.683661\pi$
$338$		0			0
$339$	−0.518409	−	4.30979i	−0.0281561	−	0.234076i
$340$		0			0
$341$	−10.3179			−0.558747
$342$		0			0
$343$	−18.4866	+	1.11687i	−0.998180	+	0.0603053i
$344$		0			0
$345$	−33.4164	+	25.0523i	−1.79908	+	1.34877i
$346$		0			0
$347$	21.4012	−	12.3560i	1.14888	−	0.663305i	0.200264	−	0.979742i	$-0.435820\pi$
$347$	21.4012	−	12.3560i	1.14888	−	0.663305i	0.948614	+	0.316437i	$0.102487\pi$
$348$		0			0
$349$	−26.7994	−	15.4727i	−1.43454	−	0.828232i	−0.437078	−	0.899424i	$-0.643987\pi$
$349$	−26.7994	−	15.4727i	−1.43454	−	0.828232i	−0.997463	+	0.0711915i	$0.977320\pi$
$350$		0			0
$351$	3.24153	−	3.94306i	0.173020	−	0.210465i
$352$		0			0
$353$	11.6758	−	20.2231i	0.621440	−	1.07637i	−0.367778	−	0.929914i	$-0.619881\pi$
$353$	11.6758	−	20.2231i	0.621440	−	1.07637i	0.989218	−	0.146452i	$-0.0467853\pi$
$354$		0			0
$355$	39.7225	−	22.9338i	2.10825	−	1.21720i
$356$		0			0
$357$	1.68330	−	0.236914i	0.0890898	−	0.0125388i
$358$		0			0
$359$			21.2351i			1.12075i	0.828240	+	0.560374i	$0.189343\pi$
$359$			21.2351i			1.12075i	−0.828240	+	0.560374i	$0.810657\pi$
$360$		0			0
$361$	−5.74775			−0.302513
$362$		0			0
$363$	−15.4348	+	1.85659i	−0.810115	+	0.0974458i
$364$		0			0
$365$	34.5483	−	19.9465i	1.80834	−	1.04405i
$366$		0			0
$367$	12.0178	+	6.93846i	0.627322	+	0.362185i	0.779714	−	0.626135i	$-0.215364\pi$
$367$	12.0178	+	6.93846i	0.627322	+	0.362185i	−0.152392	+	0.988320i	$0.548698\pi$
$368$		0			0
$369$	−1.79964	+	6.16144i	−0.0936857	+	0.320752i
$370$		0			0
$371$	11.2587	−	6.80576i	0.584523	−	0.353337i
$372$		0			0
$373$	16.0728	+	27.8390i	0.832221	+	1.44145i	0.896273	+	0.443502i	$0.146264\pi$
$373$	16.0728	+	27.8390i	0.832221	+	1.44145i	−0.0640529	+	0.997947i	$0.520403\pi$
$374$		0			0
$375$	21.4552	−	50.2014i	1.10794	−	2.59239i
$376$		0			0
$377$	−8.30017			−0.427481
$378$		0			0
$379$	1.95340			0.100339			0.0501696	−	0.998741i	$-0.484024\pi$
$379$	1.95340			0.100339			0.0501696	+	0.998741i	$0.484024\pi$
$380$		0			0
$381$	−1.30107	+	3.04427i	−0.0666558	+	0.155962i
$382$		0			0
$383$	0.788167	+	1.36514i	0.0402734	+	0.0697557i	0.885460	−	0.464717i	$-0.153844\pi$
$383$	0.788167	+	1.36514i	0.0402734	+	0.0697557i	−0.845186	+	0.534472i	$0.820510\pi$
$384$		0			0
$385$	−13.4881	+	8.15338i	−0.687416	+	0.415535i
$386$		0			0
$387$	−17.5375	+	4.28100i	−0.891483	+	0.217615i
$388$		0			0
$389$	9.74447	+	5.62597i	0.494064	+	0.285248i	0.726259	−	0.687421i	$-0.241257\pi$
$389$	9.74447	+	5.62597i	0.494064	+	0.285248i	−0.232195	+	0.972669i	$0.574591\pi$
$390$		0			0
$391$	1.85019	−	1.06821i	0.0935682	−	0.0540216i
$392$		0			0
$393$	−14.8782	+	1.78964i	−0.750503	+	0.0902753i
$394$		0			0
$395$	−35.6333			−1.79291
$396$		0			0
$397$			0.632961i			0.0317674i	0.999874	+	0.0158837i	$0.00505615\pi$
$397$			0.632961i			0.0317674i	−0.999874	+	0.0158837i	$0.994944\pi$
$398$		0			0
$399$	−3.17722	−	22.5745i	−0.159060	−	1.13014i
$400$		0			0
$401$	7.38032	−	4.26103i	0.368555	−	0.212786i	−0.304272	−	0.952585i	$-0.598413\pi$
$401$	7.38032	−	4.26103i	0.368555	−	0.212786i	0.672827	+	0.739800i	$0.265080\pi$
$402$		0			0
$403$	−3.56180	+	6.16921i	−0.177426	+	0.307310i
$404$		0			0
$405$	33.4424	−	17.3614i	1.66177	−	0.862695i
$406$		0			0
$407$	−4.26897	−	2.46469i	−0.211605	−	0.122170i
$408$		0			0
$409$	12.1822	−	7.03338i	0.602370	−	0.347778i	−0.167603	−	0.985855i	$-0.553603\pi$
$409$	12.1822	−	7.03338i	0.602370	−	0.347778i	0.769973	+	0.638076i	$0.220269\pi$
$410$		0			0
$411$	16.1581	−	12.1137i	0.797019	−	0.597526i
$412$		0			0
$413$	5.81796	−	10.5621i	0.286283	−	0.519725i
$414$		0			0
$415$	−8.14109			−0.399630
$416$		0			0
$417$	1.15285	+	9.58418i	0.0564551	+	0.469339i
$418$		0			0
$419$	−10.9339	−	18.9381i	−0.534156	−	0.925185i	−0.999204	−	0.0398995i	$-0.987296\pi$
$419$	−10.9339	−	18.9381i	−0.534156	−	0.925185i	0.465048	−	0.885286i	$-0.346037\pi$
$420$		0			0
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	−0.331625	−	0.943411i	$-0.607597\pi$
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	0.982831	−	0.184510i	$-0.0590698\pi$
$422$		0			0
$423$	24.1048	−	5.88408i	1.17201	−	0.286094i
$424$		0			0
$425$	−2.32371	+	4.02479i	−0.112717	+	0.195231i
$426$		0			0
$427$	0.399648	+	19.8665i	0.0193403	+	0.961408i
$428$		0			0
$429$	0.951422	−	2.22616i	0.0459351	−	0.107480i
$430$		0			0
$431$		−	19.9400i		−	0.960476i	−0.877138	−	0.480238i	$-0.840550\pi$
$431$		−	19.9400i		−	0.960476i	0.877138	−	0.480238i	$-0.159450\pi$
$432$		0			0
$433$			20.2826i			0.974719i	0.873201	+	0.487359i	$0.162040\pi$
$433$			20.2826i			0.974719i	−0.873201	+	0.487359i	$0.837960\pi$
$434$		0			0
$435$	−56.3412	−	24.0793i	−2.70135	−	1.15451i
$436$		0			0
$437$	−14.3256	−	24.8126i	−0.685285	−	1.18695i
$438$		0			0
$439$	−24.5936	−	14.1991i	−1.17379	−	0.677687i	−0.219219	−	0.975676i	$-0.570351\pi$
$439$	−24.5936	−	14.1991i	−1.17379	−	0.677687i	−0.954569	+	0.297989i	$0.903684\pi$
$440$		0			0
$441$	20.1842	−	5.79641i	0.961152	−	0.276020i
$442$		0			0
$443$	10.6570	+	6.15281i	0.506328	+	0.292329i	0.731323	−	0.682031i	$-0.238903\pi$
$443$	10.6570	+	6.15281i	0.506328	+	0.292329i	−0.224995	+	0.974360i	$0.572236\pi$
$444$		0			0
$445$	16.3436	+	28.3079i	0.774759	+	1.34192i
$446$		0			0
$447$	3.20118	+	26.6130i	0.151411	+	1.25875i
$448$		0			0
$449$			36.1924i			1.70803i	0.520251	+	0.854013i	$0.325838\pi$
$449$			36.1924i			1.70803i	−0.520251	+	0.854013i	$0.674162\pi$
$450$		0			0
$451$			3.04437i			0.143354i
$452$		0			0
$453$	−17.2828	−	23.0529i	−0.812018	−	1.08312i
$454$		0			0
$455$	0.218855	+	10.8793i	0.0102601	+	0.510028i
$456$		0			0
$457$	4.20892	−	7.29007i	0.196885	−	0.341015i	−0.750632	−	0.660721i	$-0.770251\pi$
$457$	4.20892	−	7.29007i	0.196885	−	0.341015i	0.947517	+	0.319706i	$0.103584\pi$
$458$		0			0
$459$	−1.80453	+	0.677445i	−0.0842281	+	0.0316204i
$460$		0			0
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	−0.996209	−	0.0869865i	$-0.972276\pi$
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	0.573437	+	0.819249i	$0.305610\pi$
$462$		0			0
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	0.631802	−	0.775130i	$-0.282316\pi$
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	−0.987183	+	0.159591i	$0.948982\pi$
$464$		0			0
$465$	−42.0745	+	31.5433i	−1.95116	+	1.46279i
$466$		0			0
$467$	−26.7864			−1.23953			−0.619763	−	0.784789i	$-0.712771\pi$
$467$	−26.7864			−1.23953			−0.619763	+	0.784789i	$0.712771\pi$
$468$		0			0
$469$	−12.8471	+	23.3229i	−0.593223	+	1.07695i
$470$		0			0
$471$	−3.47670	−	28.9035i	−0.160198	−	1.33180i
$472$		0			0
$473$	−7.41490	+	4.28100i	−0.340938	+	0.196840i
$474$		0			0
$475$	53.9758	+	31.1630i	2.47658	+	1.42985i
$476$		0			0
$477$	−10.7815	+	10.3095i	−0.493653	+	0.472040i
$478$		0			0
$479$	14.2775	−	24.7294i	0.652357	−	1.12992i	−0.330193	−	0.943914i	$-0.607114\pi$
$479$	14.2775	−	24.7294i	0.652357	−	1.12992i	0.982549	−	0.186002i	$-0.0595529\pi$
$480$		0			0
$481$	−2.94734	+	1.70165i	−0.134387	+	0.0775884i
$482$		0			0
$483$	20.7945	−	16.2531i	0.946182	−	0.739542i
$484$		0			0
$485$			16.1517i			0.733409i
$486$		0			0
$487$	−13.1527			−0.596006			−0.298003	−	0.954565i	$-0.596321\pi$
$487$	−13.1527			−0.596006			−0.298003	+	0.954565i	$0.596321\pi$
$488$		0			0
$489$	2.38994	−	5.59202i	0.108077	−	0.252880i
$490$		0			0
$491$	28.6854	−	16.5615i	1.29455	−	0.747411i	0.315096	−	0.949060i	$-0.397963\pi$
$491$	28.6854	−	16.5615i	1.29455	−	0.747411i	0.979458	+	0.201649i	$0.0646301\pi$
$492$		0			0
$493$	2.71434	+	1.56712i	0.122248	+	0.0705798i
$494$		0			0
$495$	12.9164	−	12.3509i	0.580550	−	0.555132i
$496$		0			0
$497$	−24.8057	+	14.9947i	−1.11269	+	0.672605i
$498$		0			0
$499$	3.27652	+	5.67511i	0.146677	+	0.254053i	0.929997	−	0.367566i	$-0.119809\pi$
$499$	3.27652	+	5.67511i	0.146677	+	0.254053i	−0.783320	+	0.621619i	$0.786475\pi$
$500$		0			0
$501$	13.9379	−	1.67654i	0.622699	−	0.0749022i
$502$		0			0
$503$	12.4969			0.557210			0.278605	−	0.960406i	$-0.410128\pi$
$503$	12.4969			0.557210			0.278605	+	0.960406i	$0.410128\pi$
$504$		0			0
$505$	37.7337			1.67913
$506$		0			0
$507$	12.5039	+	16.6786i	0.555320	+	0.740721i
$508$		0			0
$509$	3.30237	+	5.71987i	0.146375	+	0.253529i	0.929885	−	0.367850i	$-0.119906\pi$
$509$	3.30237	+	5.71987i	0.146375	+	0.253529i	−0.783510	+	0.621379i	$0.786573\pi$
$510$		0			0
$511$	−21.5746	+	13.0416i	−0.954402	+	0.576924i
$512$		0			0
$513$	9.08510	+	24.2002i	0.401117	+	1.06847i
$514$		0			0
$515$	−24.9672	−	14.4148i	−1.10018	−	0.635192i
$516$		0			0
$517$	10.1915	−	5.88408i	0.448223	−	0.258782i
$518$		0			0
$519$	13.6072	+	18.1502i	0.597290	+	0.796704i
$520$		0			0
$521$	−15.9784			−0.700026			−0.350013	−	0.936745i	$-0.613823\pi$
$521$	−15.9784			−0.700026			−0.350013	+	0.936745i	$0.613823\pi$
$522$		0			0
$523$			11.7615i			0.514293i	0.966372	+	0.257147i	$0.0827824\pi$
$523$			11.7615i			0.514293i	−0.966372	+	0.257147i	$0.917218\pi$
$524$		0			0
$525$	−21.4967	+	53.2367i	−0.938193	+	2.32344i
$526$		0			0
$527$	2.32957	−	1.34498i	0.101478	−	0.0585882i
$528$		0			0
$529$	5.08510	−	8.80765i	0.221091	−	0.382941i
$530$		0			0
$531$	−3.83345	+	13.1246i	−0.166358	+	0.569559i
$532$		0			0
$533$	1.82026	+	1.05093i	0.0788444	+	0.0455208i
$534$		0			0
$535$	−41.1999	+	23.7867i	−1.78122	+	1.02839i
$536$		0			0
$537$	20.2556	+	8.65691i	0.874094	+	0.373573i
$538$		0			0
$539$	8.41831	−	5.32284i	0.362602	−	0.229271i
$540$		0			0
$541$	−0.411960			−0.0177115			−0.00885576	−	0.999961i	$-0.502819\pi$
$541$	−0.411960			−0.0177115			−0.00885576	+	0.999961i	$0.502819\pi$
$542$		0			0
$543$	42.2888	+	18.0735i	1.81479	+	0.775610i
$544$		0			0
$545$	33.4790	+	57.9874i	1.43408	+	2.48391i
$546$		0			0
$547$	11.9166	−	20.6402i	0.509519	−	0.882513i	−0.490420	−	0.871486i	$-0.663157\pi$
$547$	11.9166	−	20.6402i	0.509519	−	0.882513i	0.999939	−	0.0110266i	$-0.00350995\pi$
$548$		0			0
$549$	−5.34305	−	21.8884i	−0.228036	−	0.934173i
$550$		0			0
$551$	21.0165	−	36.4016i	0.895331	−	1.55076i
$552$		0			0
$553$	22.5136	−	0.452899i	0.957374	−	0.0192592i
$554$		0			0
$555$	−24.9430	+	3.00030i	−1.05877	+	0.127356i
$556$		0			0
$557$		−	42.9474i		−	1.81974i	−0.414896	−	0.909869i	$-0.636182\pi$
$557$		−	42.9474i		−	1.81974i	0.414896	−	0.909869i	$-0.363818\pi$
$558$		0			0
$559$			5.91128i			0.250020i
$560$		0			0
$561$	−0.731449	+	0.548368i	−0.0308818	+	0.0231521i
$562$		0			0
$563$	15.9454	+	27.6182i	0.672019	+	1.16397i	0.977331	+	0.211718i	$0.0679058\pi$
$563$	15.9454	+	27.6182i	0.672019	+	1.16397i	−0.305312	+	0.952252i	$0.598761\pi$
$564$		0			0
$565$	−9.08695	−	5.24635i	−0.382291	−	0.220716i
$566$		0			0
$567$	−20.9087	+	11.3942i	−0.878081	+	0.478512i
$568$		0			0
$569$	0.428895	+	0.247623i	0.0179802	+	0.0103809i	0.508963	−	0.860788i	$-0.330029\pi$
$569$	0.428895	+	0.247623i	0.0179802	+	0.0103809i	−0.490983	+	0.871169i	$0.663362\pi$
$570$		0			0
$571$	−1.34182	−	2.32411i	−0.0561535	−	0.0972608i	0.836582	−	0.547841i	$-0.184550\pi$
$571$	−1.34182	−	2.32411i	−0.0561535	−	0.0972608i	−0.892736	+	0.450581i	$0.851217\pi$
$572$		0			0
$573$	−1.75601	+	1.31648i	−0.0733584	+	0.0549969i
$574$		0			0
$575$			72.1564i			3.00913i
$576$		0			0
$577$		−	42.0259i		−	1.74956i	−0.484518	−	0.874781i	$-0.661005\pi$
$577$		−	42.0259i		−	1.74956i	0.484518	−	0.874781i	$-0.338995\pi$
$578$		0			0
$579$	−32.0452	+	3.85460i	−1.33175	+	0.160192i
$580$		0			0
$581$	5.14364	−	0.103473i	0.213394	−	0.00429279i
$582$		0			0
$583$	−3.53753	+	6.12717i	−0.146509	+	0.253762i
$584$		0			0
$585$	−2.92595	−	11.9865i	−0.120973	−	0.495580i
$586$		0			0
$587$	1.71916	−	2.97768i	0.0709575	−	0.122902i	−0.828364	−	0.560191i	$-0.810728\pi$
$587$	1.71916	−	2.97768i	0.0709575	−	0.122902i	0.899321	+	0.437289i	$0.144061\pi$
$588$		0			0
$589$	−18.0373	−	31.2415i	−0.743214	−	1.28728i
$590$		0			0
$591$	−9.46555	−	4.04542i	−0.389361	−	0.166406i
$592$		0			0
$593$	9.10251			0.373795			0.186898	−	0.982379i	$-0.440157\pi$
$593$	9.10251			0.373795			0.186898	+	0.982379i	$0.440157\pi$
$594$		0			0
$595$	1.98250	−	3.59908i	0.0812747	−	0.147548i
$596$		0			0
$597$	8.96167	+	3.83007i	0.366777	+	0.156754i
$598$		0			0
$599$	6.71186	−	3.87510i	0.274239	−	0.158332i	−0.356573	−	0.934267i	$-0.616055\pi$
$599$	6.71186	−	3.87510i	0.274239	−	0.158332i	0.630813	+	0.775935i	$0.282722\pi$
$600$		0			0
$601$	−22.0034	−	12.7037i	−0.897536	−	0.518193i	−0.0211361	−	0.999777i	$-0.506728\pi$
$601$	−22.0034	−	12.7037i	−0.897536	−	0.518193i	−0.876400	+	0.481584i	$0.840062\pi$
$602$		0			0
$603$	8.46492	−	28.9814i	0.344718	−	1.18021i
$604$		0			0
$605$	−18.7889	+	32.5433i	−0.763878	+	1.32308i
$606$		0			0
$607$	11.7094	−	6.76042i	0.475270	−	0.274397i	−0.243173	−	0.969983i	$-0.578188\pi$
$607$	11.7094	−	6.76042i	0.475270	−	0.274397i	0.718443	+	0.695586i	$0.244855\pi$
$608$		0			0
$609$	35.9031	+	14.4975i	1.45487	+	0.587468i
$610$		0			0
$611$		−	8.12485i		−	0.328696i
$612$		0			0
$613$	4.83635			0.195338			0.0976691	−	0.995219i	$-0.468861\pi$
$613$	4.83635			0.195338			0.0976691	+	0.995219i	$0.468861\pi$
$614$		0			0
$615$	9.30706	+	12.4144i	0.375297	+	0.500595i
$616$		0			0
$617$	5.30333	−	3.06188i	0.213504	−	0.123267i	−0.389435	−	0.921054i	$-0.627330\pi$
$617$	5.30333	−	3.06188i	0.213504	−	0.123267i	0.602939	+	0.797787i	$0.293996\pi$
$618$		0			0
$619$	4.94313	+	2.85392i	0.198681	+	0.114709i	0.596040	−	0.802955i	$-0.296740\pi$
$619$	4.94313	+	2.85392i	0.198681	+	0.114709i	−0.397359	+	0.917663i	$0.630073\pi$
$620$		0			0
$621$	−19.0046	+	23.1175i	−0.762629	+	0.927675i
$622$		0			0
$623$	−10.6859	−	17.6775i	−0.428120	−	0.708236i
$624$		0			0
$625$	−34.6609	−	60.0344i	−1.38644	−	2.40138i
$626$		0			0
$627$	7.35407	+	9.80934i	0.293693	+	0.391747i
$628$		0			0
$629$	1.28513			0.0512414
$630$		0			0
$631$	−19.0525			−0.758468			−0.379234	−	0.925301i	$-0.623812\pi$
$631$	−19.0525			−0.758468			−0.379234	+	0.925301i	$0.623812\pi$
$632$		0			0
$633$	3.62176	−	0.435648i	0.143952	−	0.0173155i
$634$		0			0
$635$	4.00124	+	6.93035i	0.158784	+	0.275022i
$636$		0			0
$637$	−0.276550	−	6.87087i	−0.0109573	−	0.272234i
$638$		0			0
$639$	23.7543	−	22.7143i	0.939707	−	0.898565i
$640$		0			0
$641$	13.2820	+	7.66837i	0.524607	+	0.302882i	0.738818	−	0.673905i	$-0.235384\pi$
$641$	13.2820	+	7.66837i	0.524607	+	0.302882i	−0.214210	+	0.976788i	$0.568718\pi$
$642$		0			0
$643$	−11.3209	+	6.53612i	−0.446453	+	0.257759i	−0.706331	−	0.707882i	$-0.749651\pi$
$643$	−11.3209	+	6.53612i	−0.446453	+	0.257759i	0.259878	+	0.965641i	$0.416318\pi$
$644$		0			0
$645$	−17.1490	+	40.1255i	−0.675239	+	1.57994i
$646$		0			0
$647$	35.7066			1.40377			0.701885	−	0.712290i	$-0.252342\pi$
$647$	35.7066			1.40377			0.701885	+	0.712290i	$0.252342\pi$
$648$		0			0
$649$			6.48486i			0.254553i
$650$		0			0
$651$	26.1823	−	20.4642i	1.02617	−	0.802057i
$652$		0			0
$653$	−23.6131	+	13.6330i	−0.924051	+	0.533501i	−0.884925	−	0.465733i	$-0.845791\pi$
$653$	−23.6131	+	13.6330i	−0.924051	+	0.533501i	−0.0391261	+	0.999234i	$0.512457\pi$
$654$		0			0
$655$	−18.1113	+	31.3698i	−0.707669	+	1.22572i
$656$		0			0
$657$	20.6602	−	19.7556i	0.806030	−	0.770741i
$658$		0			0
$659$	−14.7911	−	8.53963i	−0.576179	−	0.332657i	0.183435	−	0.983032i	$-0.441278\pi$
$659$	−14.7911	−	8.53963i	−0.576179	−	0.332657i	−0.759613	+	0.650375i	$0.774612\pi$
$660$		0			0
$661$	−40.6657	+	23.4784i	−1.58171	+	0.913203i	−0.587105	+	0.809511i	$0.699732\pi$
$661$	−40.6657	+	23.4784i	−1.58171	+	0.913203i	−0.994609	+	0.103692i	$0.966934\pi$
$662$		0			0
$663$	0.0753764	+	0.626641i	0.00292738	+	0.0243367i
$664$		0			0
$665$	−48.2667	−	26.5870i	−1.87170	−	1.03100i
$666$		0			0
$667$	48.6626			1.88422
$668$		0			0
$669$	8.83888	−	6.62652i	0.341731	−	0.256196i
$670$		0			0
$671$	−5.34305	−	9.25444i	−0.206266	−	0.357264i
$672$		0			0
$673$	7.76077	−	13.4421i	0.299156	−	0.518153i	−0.676787	−	0.736179i	$-0.736628\pi$
$673$	7.76077	−	13.4421i	0.299156	−	0.518153i	0.975943	+	0.218026i	$0.0699616\pi$
$674$		0			0
$675$	10.6585	−	64.2218i	0.410247	−	2.47190i
$676$		0			0
$677$	−9.07869	+	15.7248i	−0.348922	+	0.604351i	−0.986058	−	0.166400i	$-0.946786\pi$
$677$	−9.07869	+	15.7248i	−0.348922	+	0.604351i	0.637136	+	0.770751i	$0.280119\pi$
$678$		0			0
$679$	−0.205287	−	10.2048i	−0.00787820	−	0.391625i
$680$		0			0
$681$	11.8933	+	15.8641i	0.455754	+	0.607914i
$682$		0			0
$683$			20.1917i			0.772615i	0.922370	+	0.386308i	$0.126250\pi$
$683$			20.1917i			0.772615i	−0.922370	+	0.386308i	$0.873750\pi$
$684$		0			0
$685$		−	48.8146i		−	1.86511i
$686$		0			0
$687$	1.16726	+	9.70398i	0.0445336	+	0.370230i
$688$		0			0
$689$	2.44234	+	4.23026i	0.0930458	+	0.161160i
$690$		0			0
$691$	−0.0695792	−	0.0401716i	−0.00264692	−	0.00152820i	0.498676	−	0.866788i	$-0.333820\pi$
$691$	−0.0695792	−	0.0401716i	−0.00264692	−	0.00152820i	−0.501323	+	0.865260i	$0.667153\pi$
$692$		0			0
$693$	−8.00377	+	7.96763i	−0.304038	+	0.302665i
$694$		0			0
$695$	20.2077	+	11.6669i	0.766523	+	0.442552i
$696$		0			0
$697$	−0.396844	−	0.687355i	−0.0150316	−	0.0260354i
$698$		0			0
$699$	19.8231	+	8.47207i	0.749780	+	0.320443i
$700$		0			0
$701$			35.1490i			1.32756i	0.747928	+	0.663780i	$0.231049\pi$
$701$			35.1490i			1.32756i	−0.747928	+	0.663780i	$0.768951\pi$
$702$		0			0
$703$		−	17.2346i		−	0.650016i
$704$		0			0
$705$	23.5707	−	55.1511i	0.887722	−	2.07711i
$706$		0			0
$707$	−23.8406	+	0.479595i	−0.896620	+	0.0180370i
$708$		0			0
$709$	−0.782968	+	1.35614i	−0.0294050	+	0.0509309i	−0.880353	−	0.474318i	$-0.842695\pi$
$709$	−0.782968	+	1.35614i	−0.0294050	+	0.0509309i	0.850948	+	0.525249i	$0.176028\pi$
$710$		0			0
$711$	−24.8048	+	6.05497i	−0.930254	+	0.227079i
$712$		0			0
$713$	20.8823	−	36.1691i	0.782047	−	1.35455i
$714$		0			0
$715$	−2.92595	−	5.06790i	−0.109424	−	0.189529i
$716$		0			0
$717$	−0.841830	−	6.99855i	−0.0314387	−	0.261366i
$718$		0			0
$719$	25.8787			0.965112			0.482556	−	0.875865i	$-0.339709\pi$
$719$	25.8787			0.965112			0.482556	+	0.875865i	$0.339709\pi$
$720$		0			0
$721$	15.9578	+	8.79012i	0.594299	+	0.327361i
$722$		0			0
$723$	6.82010	−	5.11304i	0.253642	−	0.190156i
$724$		0			0
$725$	−91.6754	+	52.9288i	−3.40474	+	1.96573i
$726$		0			0
$727$	0.990545	+	0.571891i	0.0367373	+	0.0212103i	0.518256	−	0.855225i	$-0.326581\pi$
$727$	0.990545	+	0.571891i	0.0367373	+	0.0212103i	−0.481519	+	0.876436i	$0.659915\pi$
$728$		0			0
$729$	20.3296	−	17.7682i	0.752947	−	0.658081i
$730$		0			0
$731$	1.11609	−	1.93312i	0.0412800	−	0.0714990i
$732$		0			0
$733$	−20.1408	+	11.6283i	−0.743916	+	0.429500i	−0.823491	−	0.567329i	$-0.807977\pi$
$733$	−20.1408	+	11.6283i	−0.743916	+	0.429500i	0.0795755	+	0.996829i	$0.474644\pi$
$734$		0			0
$735$	18.0556	−	47.4415i	0.665990	−	1.74990i
$736$		0			0
$737$		−	14.3197i		−	0.527473i
$738$		0			0
$739$	−36.1516			−1.32986			−0.664929	−	0.746907i	$-0.731538\pi$
$739$	−36.1516			−1.32986			−0.664929	+	0.746907i	$0.731538\pi$
$740$		0			0
$741$	8.40378	−	1.01086i	0.308721	−	0.0371349i
$742$		0			0
$743$	6.43940	−	3.71779i	0.236239	−	0.136392i	−0.377208	−	0.926129i	$-0.623116\pi$
$743$	6.43940	−	3.71779i	0.236239	−	0.136392i	0.613447	+	0.789736i	$0.289783\pi$
$744$		0			0
$745$	56.1121	+	32.3963i	2.05579	+	1.18691i
$746$		0			0
$747$	−5.66712	+	1.38337i	−0.207349	+	0.0506149i
$748$		0			0
$749$	25.7283	−	15.5524i	0.940090	−	0.568273i
$750$		0			0
$751$	−3.67798	−	6.37044i	−0.134211	−	0.232461i	0.791085	−	0.611707i	$-0.209517\pi$
$751$	−3.67798	−	6.37044i	−0.134211	−	0.232461i	−0.925296	+	0.379246i	$0.876183\pi$
$752$		0			0
$753$	−3.16534	+	7.40633i	−0.115352	+	0.269902i
$754$		0			0
$755$	−69.6445			−2.53462
$756$		0			0
$757$	7.65326			0.278163			0.139081	−	0.990281i	$-0.455585\pi$
$757$	7.65326			0.278163			0.139081	+	0.990281i	$0.455585\pi$
$758$		0			0
$759$	−5.57804	+	13.0516i	−0.202470	+	0.473744i
$760$		0			0
$761$	21.7203	+	37.6207i	0.787362	+	1.36375i	0.927578	+	0.373629i	$0.121887\pi$
$761$	21.7203	+	37.6207i	0.787362	+	1.36375i	−0.140217	+	0.990121i	$0.544780\pi$
$762$		0			0
$763$	−21.8895	−	36.2116i	−0.792452	−	1.31095i
$764$		0			0
$765$	−1.30627	+	4.47228i	−0.0472283	+	0.161696i
$766$		0			0
$767$	3.87738	+	2.23860i	0.140004	+	0.0808313i
$768$		0			0
$769$	−18.8491	+	10.8825i	−0.679716	+	0.392434i	−0.799748	−	0.600336i	$-0.795034\pi$
$769$	−18.8491	+	10.8825i	−0.679716	+	0.392434i	0.120032	+	0.992770i	$0.461700\pi$
$770$		0			0
$771$	−18.7340	+	2.25344i	−0.674687	+	0.0811557i
$772$		0			0
$773$	−14.5147			−0.522056			−0.261028	−	0.965331i	$-0.584062\pi$
$773$	−14.5147			−0.522056			−0.261028	+	0.965331i	$0.584062\pi$
$774$		0			0
$775$			90.8520i			3.26350i
$776$		0			0
$777$	15.7211	−	2.21265i	0.563993	−	0.0793784i
$778$		0			0
$779$	−9.21800	+	5.32202i	−0.330269	+	0.190681i
$780$		0			0
$781$	7.79402	−	13.4996i	0.278892	−	0.483055i
$782$		0			0
$783$	−43.3115	−	7.18816i	−1.54783	−	0.256884i
$784$		0			0
$785$	−60.9415	−	35.1846i	−2.17509	−	1.25579i
$786$		0			0
$787$	11.4291	−	6.59861i	0.407405	−	0.235215i	−0.282269	−	0.959335i	$-0.591087\pi$
$787$	11.4291	−	6.59861i	0.407405	−	0.235215i	0.689674	+	0.724120i	$0.257754\pi$
$788$		0			0
$789$	25.0418	−	18.7739i	0.891511	−	0.668367i
$790$		0			0
$791$	5.80793	+	3.19922i	0.206506	+	0.113751i
$792$		0			0
$793$	−7.37778			−0.261993
$794$		0			0
$795$	4.30627	+	35.8002i	0.152728	+	1.26970i
$796$		0			0
$797$	−24.8899	−	43.1106i	−0.881646	−	1.52706i	−0.849511	−	0.527572i	$-0.823103\pi$
$797$	−24.8899	−	43.1106i	−0.881646	−	1.52706i	−0.0321352	−	0.999484i	$-0.510231\pi$
$798$		0			0
$799$	−1.53402	+	2.65701i	−0.0542698	+	0.0939981i
$800$		0			0
$801$	16.1872	+	16.9283i	0.571946	+	0.598133i
$802$		0			0
$803$	6.77880	−	11.7412i	0.239219	−	0.414339i
$804$		0			0
$805$	−1.28311	−	63.7835i	−0.0452238	−	2.24807i
$806$		0			0
$807$	2.03124	−	4.75274i	0.0715032	−	0.167305i
$808$		0			0
$809$			28.1889i			0.991068i	0.868589	+	0.495534i	$0.165028\pi$
$809$			28.1889i			0.991068i	−0.868589	+	0.495534i	$0.834972\pi$
$810$		0			0
$811$		−	33.5981i		−	1.17979i	−0.807480	−	0.589894i	$-0.799169\pi$
$811$		−	33.5981i		−	1.17979i	0.807480	−	0.589894i	$-0.200831\pi$
$812$		0			0
$813$	−16.5016	−	7.05250i	−0.578736	−	0.247342i
$814$		0			0
$815$	−7.34988	−	12.7304i	−0.257455	−	0.445925i
$816$		0			0
$817$	−25.9247	−	14.9677i	−0.906992	−	0.523652i
$818$		0			0
$819$	2.00100	+	7.53601i	0.0699207	+	0.263330i
$820$		0			0
$821$	−46.9123	−	27.0848i	−1.63725	−	0.945267i	−0.981774	−	0.190050i	$-0.939135\pi$
$821$	−46.9123	−	27.0848i	−1.63725	−	0.945267i	−0.655475	−	0.755217i	$-0.727532\pi$
$822$		0			0
$823$	−14.2695	−	24.7155i	−0.497404	−	0.861529i	0.502591	−	0.864524i	$-0.332380\pi$
$823$	−14.2695	−	24.7155i	−0.497404	−	0.861529i	−0.999996	+	0.00299479i	$0.999047\pi$
$824$		0			0
$825$	−3.68738	−	30.6550i	−0.128378	−	1.06727i
$826$		0			0
$827$		−	37.2062i		−	1.29379i	−0.762581	−	0.646893i	$-0.776068\pi$
$827$		−	37.2062i		−	1.29379i	0.762581	−	0.646893i	$-0.223932\pi$
$828$		0			0
$829$		−	2.22345i		−	0.0772238i	−0.999254	−	0.0386119i	$-0.987706\pi$
$829$		−	2.22345i		−	0.0772238i	0.999254	−	0.0386119i	$-0.0122936\pi$
$830$		0			0
$831$	−12.3501	−	16.4733i	−0.428419	−	0.571454i
$832$		0			0
$833$	−1.20683	+	2.29914i	−0.0418141	+	0.0796606i
$834$		0			0
$835$	16.9668	−	29.3873i	0.587159	−	1.01699i
$836$		0			0
$837$	−23.9287	+	29.1072i	−0.827096	+	1.00609i
$838$		0			0
$839$	−27.8383	+	48.2173i	−0.961084	+	1.66465i	−0.241297	+	0.970451i	$0.577573\pi$
$839$	−27.8383	+	48.2173i	−0.961084	+	1.66465i	−0.719787	+	0.694195i	$0.755760\pi$
$840$		0			0
$841$	21.1955	+	36.7116i	0.730878	+	1.26592i
$842$		0			0
$843$	−19.3212	+	14.4852i	−0.665459	+	0.498896i
$844$		0			0
$845$	50.3870			1.73337
$846$		0			0
$847$	11.4574	−	20.8001i	0.393682	−	0.714700i
$848$		0			0
$849$	−0.524500	−	4.36043i	−0.0180008	−	0.149650i
$850$		0			0
$851$	17.2798	−	9.97650i	0.592344	−	0.341990i
$852$		0			0
$853$	−16.2574	−	9.38622i	−0.556643	−	0.321378i	0.195154	−	0.980773i	$-0.437479\pi$
$853$	−16.2574	−	9.38622i	−0.556643	−	0.321378i	−0.751797	+	0.659395i	$0.770813\pi$
$854$		0			0
$855$	59.9770	+	17.5182i	2.05117	+	0.599109i
$856$		0			0
$857$	11.8516	−	20.5276i	0.404844	−	0.701210i	−0.589460	−	0.807798i	$-0.700659\pi$
$857$	11.8516	−	20.5276i	0.404844	−	0.701210i	0.994303	+	0.106588i	$0.0339926\pi$
$858$		0			0
$859$	−14.5237	+	8.38527i	−0.495543	+	0.286102i	−0.726871	−	0.686774i	$-0.759026\pi$
$859$	−14.5237	+	8.38527i	−0.495543	+	0.286102i	0.231328	+	0.972876i	$0.425693\pi$
$860$		0			0
$861$	−6.03810	−	7.72525i	−0.205778	−	0.263276i
$862$		0			0
$863$			33.7443i			1.14867i	0.818620	+	0.574335i	$0.194739\pi$
$863$			33.7443i			1.14867i	−0.818620	+	0.574335i	$0.805261\pi$
$864$		0			0
$865$	54.8328			1.86437
$866$		0			0
$867$	−11.4781	+	26.8566i	−0.389815	+	0.912097i
$868$		0			0
$869$	−10.4875	+	6.05497i	−0.355765	+	0.205401i
$870$		0			0
$871$	−8.56192	−	4.94323i	−0.290110	−	0.167495i
$872$		0			0
$873$	2.74456	+	11.2434i	0.0928894	+	0.380531i
$874$		0			0
$875$	43.1410	+	71.3678i	1.45843	+	2.41267i
$876$		0			0
$877$	19.7087	+	34.1365i	0.665515	+	1.15271i	0.979145	+	0.203161i	$0.0651215\pi$
$877$	19.7087	+	34.1365i	0.665515	+	1.15271i	−0.313630	+	0.949545i	$0.601545\pi$
$878$		0			0
$879$	13.6023	−	1.63618i	0.458796	−	0.0551869i
$880$		0			0
$881$	26.2496			0.884372			0.442186	−	0.896923i	$-0.354203\pi$
$881$	26.2496			0.884372			0.442186	+	0.896923i	$0.354203\pi$
$882$		0			0
$883$	−43.5087			−1.46418			−0.732091	−	0.681206i	$-0.761456\pi$
$883$	−43.5087			−1.46418			−0.732091	+	0.681206i	$0.761456\pi$
$884$		0			0
$885$	19.8251	+	26.4440i	0.666414	+	0.888906i
$886$		0			0
$887$	2.83888	+	4.91708i	0.0953202	+	0.165099i	0.909742	−	0.415174i	$-0.136279\pi$
$887$	2.83888	+	4.91708i	0.0953202	+	0.165099i	−0.814422	+	0.580273i	$0.802946\pi$
$888$		0			0
$889$	−2.61612	−	4.32782i	−0.0877417	−	0.145151i
$890$		0			0
$891$	6.89257	−	10.7925i	0.230910	−	0.361561i
$892$		0			0
$893$	35.6327	+	20.5725i	1.19240	+	0.688434i
$894$		0			0
$895$	46.1124	−	26.6230i	1.54137	−	0.889909i
$896$		0			0
$897$	5.87815	+	7.84066i	0.196266	+	0.261792i
$898$		0			0
$899$	61.2710			2.04350
$900$		0			0
$901$		−	1.84452i		−	0.0614498i
$902$		0			0
$903$	10.3249	−	25.5697i	0.343592	−	0.850907i
$904$		0			0
$905$	96.2716	−	55.5824i	3.20018	−	1.84762i
$906$		0			0
$907$	−7.32741	+	12.6914i	−0.243303	+	0.421412i	−0.961653	−	0.274269i	$-0.911564\pi$
$907$	−7.32741	+	12.6914i	−0.243303	+	0.421412i	0.718350	+	0.695681i	$0.244897\pi$
$908$		0			0
$909$	26.2670	−	6.41189i	0.871220	−	0.212669i
$910$		0			0
$911$	7.19133	+	4.15192i	0.238260	+	0.137559i	0.614377	−	0.789013i	$-0.289408\pi$
$911$	7.19133	+	4.15192i	0.238260	+	0.137559i	−0.376117	+	0.926572i	$0.622741\pi$
$912$		0			0
$913$	−2.39607	+	1.38337i	−0.0792983	+	0.0457829i
$914$		0			0
$915$	−50.0800	−	21.4034i	−1.65560	−	0.707574i
$916$		0			0
$917$	11.0443	−	20.0500i	0.364714	−	0.662109i
$918$		0			0
$919$	−37.1107			−1.22417			−0.612085	−	0.790792i	$-0.709669\pi$
$919$	−37.1107			−1.22417			−0.612085	+	0.790792i	$0.709669\pi$
$920$		0			0
$921$	−22.2460	−	9.50756i	−0.733030	−	0.313285i
$922$		0			0
$923$	−5.38106	−	9.32027i	−0.177120	−	0.306781i
$924$		0			0
$925$	−21.7022	+	37.5894i	−0.713566	+	1.23593i
$926$		0			0
$927$	−19.8294	−	5.79180i	−0.651283	−	0.190228i
$928$		0			0
$929$	3.94493	−	6.83283i	0.129429	−	0.224178i	−0.794026	−	0.607883i	$-0.792019\pi$
$929$	3.94493	−	6.83283i	0.129429	−	0.224178i	0.923456	+	0.383705i	$0.125352\pi$
$930$		0			0
$931$	30.8334	+	16.1846i	1.01052	+	0.530427i
$932$		0			0
$933$	56.1170	−	6.75011i	1.83719	−	0.220989i
$934$		0			0
$935$			2.20975i			0.0722667i
$936$		0			0
$937$			13.2688i			0.433472i	0.976230	+	0.216736i	$0.0695411\pi$
$937$			13.2688i			0.433472i	−0.976230	+	0.216736i	$0.930459\pi$
$938$		0			0
$939$	21.7807	−	16.3290i	0.710787	−	0.532878i
$940$		0			0
$941$	−3.96461	−	6.86691i	−0.129243	−	0.223855i	0.794141	−	0.607734i	$-0.207921\pi$
$941$	−3.96461	−	6.86691i	−0.129243	−	0.223855i	−0.923383	+	0.383879i	$0.874588\pi$
$942$		0			0
$943$	−10.6719	−	6.16144i	−0.347526	−	0.200644i
$944$		0			0
$945$	−8.27970	+	56.9591i	−0.269339	+	1.85288i
$946$		0			0
$947$	−26.8152	−	15.4817i	−0.871375	−	0.503089i	−0.00357041	−	0.999994i	$-0.501136\pi$
$947$	−26.8152	−	15.4817i	−0.871375	−	0.503089i	−0.867805	+	0.496905i	$0.834470\pi$
$948$		0			0
$949$	−4.68014	−	8.10625i	−0.151924	−	0.263140i
$950$		0			0
$951$	−40.2244	+	30.1563i	−1.30436	+	0.977884i
$952$		0			0
$953$		−	34.1087i		−	1.10489i	−0.833549	−	0.552445i	$-0.813695\pi$
$953$		−	34.1087i		−	1.10489i	0.833549	−	0.552445i	$-0.186305\pi$
$954$		0			0
$955$			5.30502i			0.171666i
$956$		0			0
$957$	−20.6739	+	2.48678i	−0.668291	+	0.0803863i
$958$		0			0
$959$	0.620432	+	30.8417i	0.0200348	+	0.995929i
$960$		0			0
$961$	10.7928	−	18.6937i	0.348156	−	0.603023i
$962$		0			0
$963$	−24.6378	+	23.5591i	−0.793943	+	0.759183i
$964$		0			0
$965$	−39.0089	+	67.5655i	−1.25574	+	2.17501i
$966$		0			0
$967$	29.1066	+	50.4142i	0.936007	+	1.62121i	0.772829	+	0.634614i	$0.218841\pi$
$967$	29.1066	+	50.4142i	0.936007	+	1.62121i	0.163177	+	0.986597i	$0.447826\pi$
$968$		0			0
$969$	−2.93908	−	1.25611i	−0.0944168	−	0.0403522i
$970$		0			0
$971$	9.83792			0.315714			0.157857	−	0.987462i	$-0.449542\pi$
$971$	9.83792			0.315714			0.157857	+	0.987462i	$0.449542\pi$
$972$		0			0
$973$	−12.9158	−	7.11447i	−0.414061	−	0.228080i
$974$		0			0
$975$	−19.6019	−	8.37751i	−0.627762	−	0.268295i
$976$		0			0
$977$	−29.0356	+	16.7637i	−0.928930	+	0.536318i	−0.886473	−	0.462781i	$-0.846852\pi$
$977$	−29.0356	+	16.7637i	−0.928930	+	0.536318i	−0.0424567	+	0.999098i	$0.513518\pi$
$978$		0			0
$979$	9.62041	+	5.55434i	0.307470	+	0.177518i
$980$		0			0
$981$	33.1587	+	34.6769i	1.05867	+	1.10715i
$982$		0			0
$983$	−24.2359	+	41.9779i	−0.773006	+	1.33889i	0.162902	+	0.986642i	$0.447914\pi$
$983$	−24.2359	+	41.9779i	−0.773006	+	1.33889i	−0.935908	+	0.352243i	$0.885419\pi$
$984$		0			0
$985$	−21.5486	+	12.4411i	−0.686594	+	0.396405i
$986$		0			0
$987$	−14.1913	+	35.1447i	−0.451713	+	1.11867i
$988$		0			0
$989$		−	34.6569i		−	1.10203i
$990$		0			0
$991$	−53.0011			−1.68364			−0.841818	−	0.539762i	$-0.818514\pi$
$991$	−53.0011			−1.68364			−0.841818	+	0.539762i	$0.818514\pi$
$992$		0			0
$993$	13.6834	+	18.2518i	0.434229	+	0.579203i
$994$		0			0
$995$	20.4015	−	11.7788i	0.646770	−	0.373413i
$996$		0			0
$997$	−7.57384	−	4.37276i	−0.239866	−	0.138487i	0.375249	−	0.926924i	$-0.377557\pi$
$997$	−7.57384	−	4.37276i	−0.239866	−	0.138487i	−0.615115	+	0.788437i	$0.710890\pi$
$998$		0			0
$999$	−16.8533	+	6.32697i	−0.533215	+	0.200176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.x.a.209.5	yes	16
3.2	odd	2		756.2.x.a.629.8		16
4.3	odd	2		1008.2.cc.c.209.4		16
7.2	even	3		1764.2.w.a.1109.7		16
7.3	odd	6		1764.2.bm.b.1685.8		16
7.4	even	3		1764.2.bm.b.1685.1		16
7.5	odd	6		1764.2.w.a.1109.2		16
7.6	odd	2	inner	252.2.x.a.209.4	yes	16
9.2	odd	6		2268.2.f.b.1133.1		16
9.4	even	3		756.2.x.a.125.1		16
9.5	odd	6	inner	252.2.x.a.41.4	✓	16
9.7	even	3		2268.2.f.b.1133.15		16
12.11	even	2		3024.2.cc.c.2897.8		16
21.2	odd	6		5292.2.w.a.521.8		16
21.5	even	6		5292.2.w.a.521.1		16
21.11	odd	6		5292.2.bm.b.4625.1		16
21.17	even	6		5292.2.bm.b.4625.8		16
21.20	even	2		756.2.x.a.629.1		16
28.27	even	2		1008.2.cc.c.209.5		16
36.23	even	6		1008.2.cc.c.545.5		16
36.31	odd	6		3024.2.cc.c.881.1		16
63.4	even	3		5292.2.w.a.1097.1		16
63.5	even	6		1764.2.bm.b.1697.1		16
63.13	odd	6		756.2.x.a.125.8		16
63.20	even	6		2268.2.f.b.1133.16		16
63.23	odd	6		1764.2.bm.b.1697.8		16
63.31	odd	6		5292.2.w.a.1097.8		16
63.32	odd	6		1764.2.w.a.509.2		16
63.34	odd	6		2268.2.f.b.1133.2		16
63.40	odd	6		5292.2.bm.b.2285.1		16
63.41	even	6	inner	252.2.x.a.41.5	yes	16
63.58	even	3		5292.2.bm.b.2285.8		16
63.59	even	6		1764.2.w.a.509.7		16
84.83	odd	2		3024.2.cc.c.2897.1		16
252.139	even	6		3024.2.cc.c.881.8		16
252.167	odd	6		1008.2.cc.c.545.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.4	✓	16	9.5	odd	6	inner
252.2.x.a.41.5	yes	16	63.41	even	6	inner
252.2.x.a.209.4	yes	16	7.6	odd	2	inner
252.2.x.a.209.5	yes	16	1.1	even	1	trivial
756.2.x.a.125.1		16	9.4	even	3
756.2.x.a.125.8		16	63.13	odd	6
756.2.x.a.629.1		16	21.20	even	2
756.2.x.a.629.8		16	3.2	odd	2
1008.2.cc.c.209.4		16	4.3	odd	2
1008.2.cc.c.209.5		16	28.27	even	2
1008.2.cc.c.545.4		16	252.167	odd	6
1008.2.cc.c.545.5		16	36.23	even	6
1764.2.w.a.509.2		16	63.32	odd	6
1764.2.w.a.509.7		16	63.59	even	6
1764.2.w.a.1109.2		16	7.5	odd	6
1764.2.w.a.1109.7		16	7.2	even	3
1764.2.bm.b.1685.1		16	7.4	even	3
1764.2.bm.b.1685.8		16	7.3	odd	6
1764.2.bm.b.1697.1		16	63.5	even	6
1764.2.bm.b.1697.8		16	63.23	odd	6
2268.2.f.b.1133.1		16	9.2	odd	6
2268.2.f.b.1133.2		16	63.34	odd	6
2268.2.f.b.1133.15		16	9.7	even	3
2268.2.f.b.1133.16		16	63.20	even	6
3024.2.cc.c.881.1		16	36.31	odd	6
3024.2.cc.c.881.8		16	252.139	even	6
3024.2.cc.c.2897.1		16	84.83	odd	2
3024.2.cc.c.2897.8		16	12.11	even	2
5292.2.w.a.521.1		16	21.5	even	6
5292.2.w.a.521.8		16	21.2	odd	6
5292.2.w.a.1097.1		16	63.4	even	3
5292.2.w.a.1097.8		16	63.31	odd	6
5292.2.bm.b.2285.1		16	63.40	odd	6
5292.2.bm.b.2285.8		16	63.58	even	3
5292.2.bm.b.4625.1		16	21.11	odd	6
5292.2.bm.b.4625.8		16	21.17	even	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.680689 - 1.59269i) q^{3} +(-2.09336 - 3.62580i) q^{5} +(1.36869 + 2.26422i) q^{7} +(-2.07332 - 2.16825i) q^{9} +O(q^{10})\)	\(q+(0.680689 - 1.59269i) q^{3} +(-2.09336 - 3.62580i) q^{5} +(1.36869 + 2.26422i) q^{7} +(-2.07332 - 2.16825i) q^{9} +(-1.23222 - 0.711425i) q^{11} +(-0.850739 + 0.491174i) q^{13} +(-7.19970 + 0.866025i) q^{15} +0.370947 q^{17} -4.97471i q^{19} +(4.53785 - 0.638674i) q^{21} +(4.98775 - 2.87968i) q^{23} +(-6.26427 + 10.8500i) q^{25} +(-4.86465 + 1.82626i) q^{27} +(7.31732 + 4.22466i) q^{29} +(6.28007 - 3.62580i) q^{31} +(-1.97184 + 1.47829i) q^{33} +(5.34444 - 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 + 1.68930i) q^{39} +(-1.06981 - 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(-3.52145 + 12.0564i) q^{45} +(-4.13542 + 7.16276i) q^{47} +(-3.25337 + 6.19803i) q^{49} +(0.252500 - 0.590804i) q^{51} -4.97245i q^{53} +5.95706i q^{55} +(-7.92317 - 3.38623i) q^{57} +(-2.27883 - 3.94705i) q^{59} +(6.50416 + 3.75518i) q^{61} +(2.07166 - 7.66213i) q^{63} +(3.56180 + 2.05640i) q^{65} +(5.03205 + 8.71577i) q^{67} +(-1.19133 - 9.90411i) q^{69} +10.9555i q^{71} +9.52848i q^{73} +(13.0167 + 17.3626i) q^{75} +(-0.0757141 - 3.76374i) q^{77} +(4.25553 - 7.37079i) q^{79} +(-0.402651 + 8.99099i) q^{81} +(0.972254 - 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(11.7094 - 8.77855i) q^{87} -7.80735 q^{89} +(-2.27652 - 1.25399i) q^{91} +(-1.50000 - 12.4702i) q^{93} +(-18.0373 + 10.4138i) q^{95} +(-3.34099 - 1.92892i) q^{97} +(1.01225 + 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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