LMFDB - Embedded newform 252.2.x.a.41.4

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			41.4
Root			$1.71965 + 0.206851i$ of defining polynomial
Character	$\chi$	$=$	252.41
Dual form			252.2.x.a.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +O(q^{10})$	\(q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +(-1.23222 + 0.711425i) q^{11} +(0.850739 + 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} -0.370947 q^{17} -4.97471i q^{19} +(1.88532 + 4.17679i) q^{21} +(4.98775 + 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(4.86465 + 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(-6.28007 - 3.62580i) q^{31} +(1.97184 + 1.47829i) q^{33} +(-5.34444 + 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 - 1.68930i) q^{39} +(1.06981 - 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(3.52145 + 12.0564i) q^{45} +(4.13542 + 7.16276i) q^{47} +(6.99434 - 0.281520i) q^{49} +(0.252500 + 0.590804i) q^{51} +4.97245i q^{53} +5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(2.27883 - 3.94705i) q^{59} +(-6.50416 + 3.75518i) q^{61} +(5.36901 - 5.84583i) q^{63} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} +(1.19133 - 9.90411i) q^{69} -10.9555i q^{71} +9.52848i q^{73} +(-13.0167 + 17.3626i) q^{75} +(3.22164 - 1.94744i) q^{77} +(4.25553 + 7.37079i) q^{79} +(-0.402651 - 8.99099i) q^{81} +(-0.972254 - 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(-11.7094 - 8.77855i) q^{87} +7.80735 q^{89} +(-2.27652 - 1.25399i) q^{91} +(-1.50000 + 12.4702i) q^{93} +(-18.0373 - 10.4138i) q^{95} +(3.34099 - 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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
$3$	−0.680689	−	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	0.163656	−	0.986518i	$-0.447671\pi$
$5$	2.09336	−	3.62580i	0.936177	−	1.62151i	0.772521	−	0.634989i	$-0.218995\pi$
$6$		0			0
$7$	−2.64522	+	0.0532130i	−0.999798	+	0.0201126i
$7$	−2.64522	+	0.0532130i	−0.999798	+	0.0201126i
$8$		0			0
$9$	−2.07332	+	2.16825i	−0.691108	+	0.722751i
$10$		0			0
$11$	−1.23222	+	0.711425i	−0.371529	+	0.214503i	−0.674126	−	0.738616i	$-0.735480\pi$
$11$	−1.23222	+	0.711425i	−0.371529	+	0.214503i	0.302597	+	0.953119i	$0.402146\pi$
$12$		0			0
$13$	0.850739	+	0.491174i	0.235952	+	0.136227i	0.613315	−	0.789838i	$-0.289836\pi$
$13$	0.850739	+	0.491174i	0.235952	+	0.136227i	−0.377363	+	0.926066i	$0.623169\pi$
$14$		0			0
$15$	−7.19970	−	0.866025i	−1.85895	−	0.223607i
$16$		0			0
$17$	−0.370947			−0.0899679			−0.0449840	−	0.998988i	$-0.514324\pi$
$17$	−0.370947			−0.0899679			−0.0449840	+	0.998988i	$0.514324\pi$
$18$		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
$21$	1.88532	+	4.17679i	0.411411	+	0.911450i
$22$		0			0
$23$	4.98775	+	2.87968i	1.04002	+	0.600455i	0.919838	−	0.392298i	$-0.128320\pi$
$23$	4.98775	+	2.87968i	1.04002	+	0.600455i	0.120179	+	0.992752i	$0.461653\pi$
$24$		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	0.369332	−	0.929298i	$-0.379587\pi$
$29$	7.31732	−	4.22466i	1.35879	−	0.784499i	0.989461	+	0.144798i	$0.0462534\pi$
$30$		0			0
$31$	−6.28007	−	3.62580i	−1.12793	−	0.651213i	−0.184519	−	0.982829i	$-0.559073\pi$
$31$	−6.28007	−	3.62580i	−1.12793	−	0.651213i	−0.943414	+	0.331616i	$0.892406\pi$
$32$		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	$-0.779901\pi$
$41$	1.06981	−	1.85297i	0.167077	−	0.289386i	0.937391	+	0.348279i	$0.113234\pi$
$42$		0			0
$43$	3.00875	+	5.21130i	0.458830	+	0.794716i	0.998899	−	0.0469039i	$-0.0149354\pi$
$43$	3.00875	+	5.21130i	0.458830	+	0.794716i	−0.540070	+	0.841620i	$0.681602\pi$
$44$		0			0
$45$	3.52145	+	12.0564i	0.524946	+	1.79726i
$46$		0			0
$47$	4.13542	+	7.16276i	0.603213	+	1.04480i	0.992331	+	0.123608i	$0.0394466\pi$
$47$	4.13542	+	7.16276i	0.603213	+	1.04480i	−0.389118	+	0.921188i	$0.627220\pi$
$48$		0			0
$49$	6.99434	−	0.281520i	0.999191	−	0.0402171i
$50$		0			0
$51$	0.252500	+	0.590804i	0.0353570	+	0.0827291i
$52$		0			0
$53$			4.97245i			0.683019i	0.939878	+	0.341509i	$0.110938\pi$
$53$			4.97245i			0.683019i	−0.939878	+	0.341509i	$0.889062\pi$
$54$		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	$-0.737454\pi$
$59$	2.27883	−	3.94705i	0.296678	−	0.513862i	0.975374	+	0.220558i	$0.0707878\pi$
$60$		0			0
$61$	−6.50416	+	3.75518i	−0.832772	+	0.480801i	−0.854801	−	0.518956i	$-0.826321\pi$
$61$	−6.50416	+	3.75518i	−0.832772	+	0.480801i	0.0220288	+	0.999757i	$0.492987\pi$
$62$		0			0
$63$	5.36901	−	5.84583i	0.676432	−	0.736505i
$64$		0			0
$65$	3.56180	−	2.05640i	0.441786	−	0.255066i
$66$		0			0
$67$	5.03205	−	8.71577i	0.614763	−	1.06480i	−0.375663	−	0.926756i	$-0.622585\pi$
$67$	5.03205	−	8.71577i	0.614763	−	1.06480i	0.990426	−	0.138044i	$-0.0440816\pi$
$68$		0			0
$69$	1.19133	−	9.90411i	0.143419	−	1.19231i
$70$		0			0
$71$		−	10.9555i		−	1.30018i	−0.759857	−	0.650090i	$-0.774731\pi$
$71$		−	10.9555i		−	1.30018i	0.759857	−	0.650090i	$-0.225269\pi$
$72$		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
$77$	3.22164	−	1.94744i	0.367140	−	0.221932i
$78$		0			0
$79$	4.25553	+	7.37079i	0.478784	+	0.829278i	0.999704	−	0.0243272i	$-0.00774434\pi$
$79$	4.25553	+	7.37079i	0.478784	+	0.829278i	−0.520920	+	0.853606i	$0.674411\pi$
$80$		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	$-0.200701\pi$
$83$	−0.972254	−	1.68399i	−0.106719	−	0.184842i	−0.914439	+	0.404724i	$0.867368\pi$
$84$		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	$-0.364205\pi$
$89$	7.80735			0.827578			0.413789	+	0.910373i	$0.364205\pi$
$90$		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	$-0.603919\pi$
$97$	3.34099	−	1.92892i	0.339226	−	0.195852i	0.659930	+	0.751327i	$0.270586\pi$
$98$		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	$-0.0186605\pi$
$101$	4.50637	+	7.80526i	0.448401	+	0.776653i	−0.549882	+	0.835243i	$0.685327\pi$
$102$		0			0
$103$	−5.96343	−	3.44299i	−0.587594	−	0.339248i	0.176551	−	0.984291i	$-0.443506\pi$
$103$	−5.96343	−	3.44299i	−0.587594	−	0.339248i	−0.764146	+	0.645044i	$0.776839\pi$
$104$		0			0
$105$	19.0908	+	1.90771i	1.86308	+	0.186173i
$106$		0			0
$107$			11.3630i			1.09850i	0.835658	+	0.549250i	$0.185087\pi$
$107$			11.3630i			1.09850i	−0.835658	+	0.549250i	$0.814913\pi$
$108$		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	0.598602	−	0.801046i	$-0.295723\pi$
$113$	2.17043	+	1.25310i	0.204177	+	0.117881i	−0.394426	+	0.918928i	$0.629056\pi$
$114$		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
$119$	0.981235	−	0.0197392i	0.0899497	−	0.00180949i
$120$		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	$-0.709960\pi$
$131$	4.32591	−	7.49270i	0.377957	−	0.654640i	0.990765	+	0.135592i	$0.0432935\pi$
$132$		0			0
$133$	0.264719	+	13.1592i	0.0229541	+	1.14105i
$134$		0			0
$135$	16.8051	−	13.8152i	1.44635	−	1.18902i
$136$		0			0
$137$	10.0973	−	5.82971i	0.862675	−	0.498065i	−0.00223233	−	0.999998i	$-0.500711\pi$
$137$	10.0973	−	5.82971i	0.862675	−	0.498065i	0.864907	+	0.501932i	$0.167377\pi$
$138$		0			0
$139$	4.82663	+	2.78666i	0.409390	+	0.236361i	0.690528	−	0.723306i	$-0.257378\pi$
$139$	4.82663	+	2.78666i	0.409390	+	0.236361i	−0.281138	+	0.959667i	$0.590712\pi$
$140$		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
$147$	−5.20934	−	10.9482i	−0.429659	−	0.902991i
$148$		0			0
$149$	−13.4024	−	7.73789i	−1.09797	−	0.633913i	−0.162282	−	0.986744i	$-0.551886\pi$
$149$	−13.4024	−	7.73789i	−1.09797	−	0.633913i	−0.935687	+	0.352832i	$0.885219\pi$
$150$		0			0
$151$	8.31732	+	14.4060i	0.676854	+	1.17235i	0.975923	+	0.218114i	$0.0699905\pi$
$151$	8.31732	+	14.4060i	0.676854	+	1.17235i	−0.299069	+	0.954231i	$0.596676\pi$
$152$		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	$-0.567340\pi$
$157$	−14.5559	−	8.40387i	−1.16169	−	0.670702i	−0.951708	+	0.307004i	$0.900674\pi$
$158$		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	$-0.934866\pi$
$167$	−4.05253	+	7.01918i	−0.313594	+	0.543160i	0.665544	+	0.746359i	$0.268200\pi$
$168$		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	$-0.000782886\pi$
$173$	6.54844	+	11.3422i	0.497868	+	0.862334i	−0.502128	+	0.864793i	$0.667450\pi$
$174$		0			0
$175$	17.1477	+	28.3674i	1.29625	+	2.14437i
$176$		0			0
$177$	−7.83760	−	0.942756i	−0.589110	−	0.0708619i
$178$		0			0
$179$		−	12.7179i		−	0.950578i	−0.879830	−	0.475289i	$-0.842344\pi$
$179$		−	12.7179i		−	0.950578i	0.879830	−	0.475289i	$-0.157656\pi$
$180$		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
$189$	−12.9652	−	4.57198i	−0.943081	−	0.332563i
$190$		0			0
$191$	−1.09735	+	0.633555i	−0.0794014	+	0.0458424i	−0.539175	−	0.842194i	$-0.681264\pi$
$191$	−1.09735	+	0.633555i	−0.0794014	+	0.0458424i	0.459774	+	0.888036i	$0.347931\pi$
$192$		0			0
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	0.307037	+	0.951697i	$0.400662\pi$
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	−0.977713	+	0.209947i	$0.932671\pi$
$194$		0			0
$195$	−5.69969	−	4.27307i	−0.408163	−	0.306001i
$196$		0			0
$197$			5.94312i			0.423430i	0.977331	+	0.211715i	$0.0679049\pi$
$197$			5.94312i			0.423430i	−0.977331	+	0.211715i	$0.932095\pi$
$198$		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
$203$	−19.1311	+	11.5645i	−1.34274	+	0.811670i
$204$		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	−0.827499	−	0.561467i	$-0.810237\pi$
$211$	1.05305	−	1.82393i	0.0724948	−	0.125565i	0.899994	+	0.435902i	$0.143571\pi$
$212$		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	$-0.735170\pi$
$223$	−5.52351	+	3.18900i	−0.369882	+	0.213551i	0.303525	+	0.952823i	$0.401836\pi$
$224$		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	$-0.0426279\pi$
$227$	5.72365	+	9.91365i	0.379892	+	0.657992i	−0.611154	+	0.791511i	$0.709295\pi$
$228$		0			0
$229$	4.88696	+	2.82149i	0.322940	+	0.186449i	0.652702	−	0.757615i	$-0.273635\pi$
$229$	4.88696	+	2.82149i	0.322940	+	0.186449i	−0.329762	+	0.944064i	$0.606969\pi$
$230$		0			0
$231$	−5.29461	−	3.80547i	−0.348360	−	0.250382i
$232$		0			0
$233$		−	12.4463i		−	0.815385i	−0.913119	−	0.407693i	$-0.866333\pi$
$233$		−	12.4463i		−	0.815385i	0.913119	−	0.407693i	$-0.133667\pi$
$234$		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	0.609640	−	0.792678i	$-0.291314\pi$
$239$	3.52450	+	2.03487i	0.227981	+	0.131625i	−0.381659	+	0.924303i	$0.624647\pi$
$240$		0			0
$241$	−4.26195	+	2.46064i	−0.274537	+	0.158504i	−0.630947	−	0.775826i	$-0.717334\pi$
$241$	−4.26195	+	2.46064i	−0.274537	+	0.158504i	0.356411	+	0.934329i	$0.384000\pi$
$242$		0			0
$243$	−14.0458	+	6.76137i	−0.901037	+	0.433742i
$244$		0			0
$245$	13.6209	−	25.9494i	0.870207	−	1.65784i
$246$		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	$-0.453116\pi$
$251$	4.65020			0.293518			0.146759	+	0.989172i	$0.453116\pi$
$252$		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	$-0.722982\pi$
$257$	5.44701	−	9.43450i	0.339775	−	0.588508i	0.984390	+	0.175999i	$0.0563156\pi$
$258$		0			0
$259$	−9.16421	+	0.184354i	−0.569436	+	0.0114552i
$260$		0			0
$261$	−6.01105	+	24.6249i	−0.372075	+	1.52424i
$262$		0			0
$263$	15.6489	−	9.03488i	0.964951	−	0.557114i	0.0672574	−	0.997736i	$-0.478575\pi$
$263$	15.6489	−	9.03488i	0.964951	−	0.557114i	0.897693	+	0.440621i	$0.145242\pi$
$264$		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	$-0.528997\pi$
$269$	−2.98410			−0.181944			−0.0909718	+	0.995853i	$0.528997\pi$
$270$		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
$273$	−0.447615	+	4.47938i	−0.0270909	+	0.271104i
$274$		0			0
$275$	15.4380	+	8.91312i	0.930945	+	0.537481i
$276$		0			0
$277$	5.94345	+	10.2944i	0.357107	+	0.618528i	0.987476	−	0.157768i	$-0.0504297\pi$
$277$	5.94345	+	10.2944i	0.357107	+	0.618528i	−0.630369	+	0.776296i	$0.717096\pi$
$278$		0			0
$279$	20.8823	−	6.09932i	1.25019	−	0.365157i
$280$		0			0
$281$	−12.0740	+	6.97095i	−0.720277	+	0.415852i	−0.814855	−	0.579665i	$-0.803183\pi$
$281$	−12.0740	+	6.97095i	−0.720277	+	0.415852i	0.0945775	+	0.995518i	$0.469850\pi$
$282$		0			0
$283$	−2.19593	−	1.26782i	−0.130535	−	0.0753642i	0.433311	−	0.901245i	$-0.357345\pi$
$283$	−2.19593	−	1.26782i	−0.130535	−	0.0753642i	−0.563845	+	0.825880i	$0.690679\pi$
$284$		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	$-0.907550\pi$
$293$	−3.95496	+	6.85020i	−0.231052	+	0.400193i	0.727066	+	0.686567i	$0.240883\pi$
$294$		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
$301$	−8.23610	−	13.6249i	−0.474721	−	0.785327i
$302$		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	−0.134001	+	0.990981i	$0.542782\pi$
$311$	−16.3163	+	28.2607i	−0.925215	+	1.60252i	−0.791215	+	0.611539i	$0.790551\pi$
$312$		0			0
$313$	−13.6110	+	7.85832i	−0.769340	+	0.444178i	−0.832639	−	0.553816i	$-0.813171\pi$
$313$	−13.6110	+	7.85832i	−0.769340	+	0.444178i	0.0632994	+	0.997995i	$0.479838\pi$
$314$		0			0
$315$	−9.95654	−	31.7043i	−0.560988	−	1.78634i
$316$		0			0
$317$	−25.1366	+	14.5126i	−1.41181	+	0.815111i	−0.995559	−	0.0941377i	$-0.969991\pi$
$317$	−25.1366	+	14.5126i	−1.41181	+	0.815111i	−0.416254	+	0.909248i	$0.636657\pi$
$318$		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
$329$	−11.3202	−	18.7270i	−0.624105	−	1.03245i
$330$		0			0
$331$	−6.58510	−	11.4057i	−0.361950	−	0.626915i	0.626332	−	0.779556i	$-0.284555\pi$
$331$	−6.58510	−	11.4057i	−0.361950	−	0.626915i	−0.988282	+	0.152641i	$0.951222\pi$
$332$		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	−0.545502	−	0.838110i	$-0.683661\pi$
$337$	8.31732	−	14.4060i	0.453073	−	0.784746i	0.998575	+	0.0533635i	$0.0169942\pi$
$338$		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	0.948614	−	0.316437i	$-0.102487\pi$
$347$	21.4012	+	12.3560i	1.14888	+	0.663305i	0.200264	+	0.979742i	$0.435820\pi$
$348$		0			0
$349$	26.7994	−	15.4727i	1.43454	−	0.828232i	0.437078	−	0.899424i	$-0.356013\pi$
$349$	26.7994	−	15.4727i	1.43454	−	0.828232i	0.997463	+	0.0711915i	$0.0226802\pi$
$350$		0			0
$351$	3.24153	+	3.94306i	0.173020	+	0.210465i
$352$		0			0
$353$	−11.6758	−	20.2231i	−0.621440	−	1.07637i	−0.989218	−	0.146452i	$-0.953215\pi$
$353$	−11.6758	−	20.2231i	−0.621440	−	1.07637i	0.367778	−	0.929914i	$-0.380119\pi$
$354$		0			0
$355$	−39.7225	−	22.9338i	−2.10825	−	1.21720i
$356$		0			0
$357$	−0.699355	−	1.54937i	−0.0370138	−	0.0820012i
$358$		0			0
$359$		−	21.2351i		−	1.12075i	−0.828240	−	0.560374i	$-0.810657\pi$
$359$		−	21.2351i		−	1.12075i	0.828240	−	0.560374i	$-0.189343\pi$
$360$		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	$-0.784636\pi$
$367$	−12.0178	+	6.93846i	−0.627322	+	0.362185i	0.152392	+	0.988320i	$0.451302\pi$
$368$		0			0
$369$	1.79964	+	6.16144i	0.0936857	+	0.320752i
$370$		0			0
$371$	−0.264599	−	13.1532i	−0.0137373	−	0.682881i
$372$		0			0
$373$	16.0728	−	27.8390i	0.832221	−	1.44145i	−0.0640529	−	0.997947i	$-0.520403\pi$
$373$	16.0728	−	27.8390i	0.832221	−	1.44145i	0.896273	−	0.443502i	$-0.146264\pi$
$374$		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	$-0.846156\pi$
$383$	−0.788167	+	1.36514i	−0.0402734	+	0.0697557i	0.845186	+	0.534472i	$0.179490\pi$
$384$		0			0
$385$	−0.316993	−	15.7577i	−0.0161555	−	0.803087i
$386$		0			0
$387$	−17.5375	−	4.28100i	−0.891483	−	0.217615i
$388$		0			0
$389$	9.74447	−	5.62597i	0.494064	−	0.285248i	−0.232195	−	0.972669i	$-0.574591\pi$
$389$	9.74447	−	5.62597i	0.494064	−	0.285248i	0.726259	+	0.687421i	$0.241257\pi$
$390$		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
$399$	20.7783	−	9.37893i	1.04022	−	0.469534i
$400$		0			0
$401$	7.38032	+	4.26103i	0.368555	+	0.212786i	0.672827	−	0.739800i	$-0.265080\pi$
$401$	7.38032	+	4.26103i	0.368555	+	0.212786i	−0.304272	+	0.952585i	$0.598413\pi$
$402$		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	$-0.446397\pi$
$409$	−12.1822	−	7.03338i	−0.602370	−	0.347778i	−0.769973	+	0.638076i	$0.779731\pi$
$410$		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	−0.465048	−	0.885286i	$-0.653963\pi$
$419$	10.9339	−	18.9381i	0.534156	−	0.925185i	0.999204	−	0.0398995i	$-0.0127038\pi$
$420$		0			0
$421$	13.3616	+	23.1430i	0.651206	+	1.12792i	0.982831	+	0.184510i	$0.0590698\pi$
$421$	13.3616	+	23.1430i	0.651206	+	1.12792i	−0.331625	+	0.943411i	$0.607597\pi$
$422$		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
$427$	17.0051	−	10.2794i	0.822933	−	0.497453i
$428$		0			0
$429$	0.951422	+	2.22616i	0.0459351	+	0.107480i
$430$		0			0
$431$			19.9400i			0.960476i	0.877138	+	0.480238i	$0.159450\pi$
$431$			19.9400i			0.960476i	−0.877138	+	0.480238i	$0.840550\pi$
$432$		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	$-0.429649\pi$
$439$	24.5936	−	14.1991i	1.17379	−	0.677687i	0.954569	+	0.297989i	$0.0963158\pi$
$440$		0			0
$441$	−13.8911	+	15.7492i	−0.661482	+	0.749961i
$442$		0			0
$443$	10.6570	−	6.15281i	0.506328	−	0.292329i	−0.224995	−	0.974360i	$-0.572236\pi$
$443$	10.6570	−	6.15281i	0.506328	−	0.292329i	0.731323	+	0.682031i	$0.238903\pi$
$444$		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	$-0.674162\pi$
$449$		−	36.1924i		−	1.70803i	0.520251	−	0.854013i	$-0.325838\pi$
$450$		0			0
$451$			3.04437i			0.143354i
$452$		0			0
$453$	17.2828	−	23.0529i	0.812018	−	1.08312i
$454$		0			0
$455$	−9.31229	+	5.62917i	−0.436567	+	0.263899i
$456$		0			0
$457$	4.20892	+	7.29007i	0.196885	+	0.341015i	0.947517	−	0.319706i	$-0.103584\pi$
$457$	4.20892	+	7.29007i	0.196885	+	0.341015i	−0.750632	+	0.660721i	$0.770251\pi$
$458$		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	$-0.0277237\pi$
$461$	9.07730	+	15.7224i	0.422772	+	0.732263i	−0.573437	+	0.819249i	$0.694390\pi$
$462$		0			0
$463$	−7.64690	+	13.2448i	−0.355381	+	0.615539i	−0.987183	−	0.159591i	$-0.948982\pi$
$463$	−7.64690	+	13.2448i	−0.355381	+	0.615539i	0.631802	+	0.775130i	$0.282316\pi$
$464$		0			0
$465$	42.0745	+	31.5433i	1.95116	+	1.46279i
$466$		0			0
$467$	26.7864			1.23953			0.619763	−	0.784789i	$-0.287229\pi$
$467$	26.7864			1.23953			0.619763	+	0.784789i	$0.287229\pi$
$468$		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	−0.982549	−	0.186002i	$-0.940447\pi$
$479$	−14.2775	−	24.7294i	−0.652357	−	1.12992i	0.330193	−	0.943914i	$-0.392886\pi$
$480$		0			0
$481$	2.94734	+	1.70165i	0.134387	+	0.0775884i
$482$		0			0
$483$	−2.62430	+	26.2619i	−0.119410	+	1.19496i
$484$		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	0.979458	−	0.201649i	$-0.0646301\pi$
$491$	28.6854	+	16.5615i	1.29455	+	0.747411i	0.315096	+	0.949060i	$0.397963\pi$
$492$		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
$497$	0.582976	+	28.9797i	0.0261500	+	1.29992i
$498$		0			0
$499$	3.27652	−	5.67511i	0.146677	−	0.254053i	−0.783320	−	0.621619i	$-0.786475\pi$
$499$	3.27652	−	5.67511i	0.146677	−	0.254053i	0.929997	+	0.367566i	$0.119809\pi$
$500$		0			0
$501$	13.9379	+	1.67654i	0.622699	+	0.0749022i
$502$		0			0
$503$	−12.4969			−0.557210			−0.278605	−	0.960406i	$-0.589872\pi$
$503$	−12.4969			−0.557210			−0.278605	+	0.960406i	$0.589872\pi$
$504$		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	$-0.880094\pi$
$509$	−3.30237	+	5.71987i	−0.146375	+	0.253529i	0.783510	+	0.621379i	$0.213427\pi$
$510$		0			0
$511$	−0.507039	−	25.2049i	−0.0224301	−	1.11500i
$512$		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	$-0.386177\pi$
$521$	15.9784			0.700026			0.350013	+	0.936745i	$0.386177\pi$
$522$		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
$525$	33.5082	−	46.6204i	1.46242	−	2.03468i
$526$		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	0.999939	+	0.0110266i	$0.00350995\pi$
$547$	11.9166	+	20.6402i	0.509519	+	0.882513i	−0.490420	+	0.871486i	$0.663157\pi$
$548$		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
$553$	−11.6490	−	19.2709i	−0.495366	−	0.819481i
$554$		0			0
$555$	−24.9430	−	3.00030i	−1.05877	−	0.127356i
$556$		0			0
$557$			42.9474i			1.81974i	0.414896	+	0.909869i	$0.363818\pi$
$557$			42.9474i			1.81974i	−0.414896	+	0.909869i	$0.636182\pi$
$558$		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	0.305312	+	0.952252i	$0.401239\pi$
$563$	−15.9454	+	27.6182i	−0.672019	+	1.16397i	−0.977331	+	0.211718i	$0.932094\pi$
$564$		0			0
$565$	9.08695	−	5.24635i	0.382291	−	0.220716i
$566$		0			0
$567$	1.54354	+	23.7617i	0.0648224	+	0.997897i
$568$		0			0
$569$	0.428895	−	0.247623i	0.0179802	−	0.0103809i	−0.490983	−	0.871169i	$-0.663362\pi$
$569$	0.428895	−	0.247623i	0.0179802	−	0.0103809i	0.508963	+	0.860788i	$0.330029\pi$
$570$		0			0
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	−0.892736	−	0.450581i	$-0.851217\pi$
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	0.836582	+	0.547841i	$0.184550\pi$
$572$		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
$581$	2.66143	+	4.40279i	0.110415	+	0.182658i
$582$		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	$-0.189272\pi$
$587$	−1.71916	−	2.97768i	−0.0709575	−	0.122902i	−0.899321	+	0.437289i	$0.855939\pi$
$588$		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	$-0.559843\pi$
$593$	−9.10251			−0.373795			−0.186898	+	0.982379i	$0.559843\pi$
$594$		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	0.630813	−	0.775935i	$-0.282722\pi$
$599$	6.71186	+	3.87510i	0.274239	+	0.158332i	−0.356573	+	0.934267i	$0.616055\pi$
$600$		0			0
$601$	22.0034	−	12.7037i	0.897536	−	0.518193i	0.0211361	−	0.999777i	$-0.493272\pi$
$601$	22.0034	−	12.7037i	0.897536	−	0.518193i	0.876400	+	0.481584i	$0.159938\pi$
$602$		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	$-0.421812\pi$
$607$	−11.7094	−	6.76042i	−0.475270	−	0.274397i	−0.718443	+	0.695586i	$0.755145\pi$
$608$		0			0
$609$	31.4410	+	22.5981i	1.27405	+	0.915720i
$610$		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	0.602939	−	0.797787i	$-0.293996\pi$
$617$	5.30333	+	3.06188i	0.213504	+	0.123267i	−0.389435	+	0.921054i	$0.627330\pi$
$618$		0			0
$619$	−4.94313	+	2.85392i	−0.198681	+	0.114709i	−0.596040	−	0.802955i	$-0.703260\pi$
$619$	−4.94313	+	2.85392i	−0.198681	+	0.114709i	0.397359	+	0.917663i	$0.369927\pi$
$620$		0			0
$621$	19.0046	+	23.1175i	0.762629	+	0.927675i
$622$		0			0
$623$	−20.6521	+	0.415453i	−0.827410	+	0.0166448i
$624$		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
$637$	6.08863	+	3.19594i	0.241240	+	0.126628i
$638$		0			0
$639$	23.7543	+	22.7143i	0.939707	+	0.898565i
$640$		0			0
$641$	13.2820	−	7.66837i	0.524607	−	0.302882i	−0.214210	−	0.976788i	$-0.568718\pi$
$641$	13.2820	−	7.66837i	0.524607	−	0.302882i	0.738818	+	0.673905i	$0.235384\pi$
$642$		0			0
$643$	11.3209	+	6.53612i	0.446453	+	0.257759i	0.706331	−	0.707882i	$-0.250349\pi$
$643$	11.3209	+	6.53612i	0.446453	+	0.257759i	−0.259878	+	0.965641i	$0.583682\pi$
$644$		0			0
$645$	−17.1490	−	40.1255i	−0.675239	−	1.57994i
$646$		0			0
$647$	−35.7066			−1.40377			−0.701885	−	0.712290i	$-0.747658\pi$
$647$	−35.7066			−1.40377			−0.701885	+	0.712290i	$0.747658\pi$
$648$		0			0
$649$			6.48486i			0.254553i
$650$		0			0
$651$	3.30425	−	33.0663i	0.129504	−	1.29597i
$652$		0			0
$653$	−23.6131	−	13.6330i	−0.924051	−	0.533501i	−0.0391261	−	0.999234i	$-0.512457\pi$
$653$	−23.6131	−	13.6330i	−0.924051	−	0.533501i	−0.884925	+	0.465733i	$0.845791\pi$
$654$		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	−0.759613	−	0.650375i	$-0.774612\pi$
$659$	−14.7911	+	8.53963i	−0.576179	+	0.332657i	0.183435	+	0.983032i	$0.441278\pi$
$660$		0			0
$661$	40.6657	+	23.4784i	1.58171	+	0.913203i	0.994609	+	0.103692i	$0.0330657\pi$
$661$	40.6657	+	23.4784i	1.58171	+	0.913203i	0.587105	+	0.809511i	$0.300268\pi$
$662$		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	0.975943	−	0.218026i	$-0.0699616\pi$
$673$	7.76077	+	13.4421i	0.299156	+	0.518153i	−0.676787	+	0.736179i	$0.736628\pi$
$674$		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	$-0.0532143\pi$
$677$	9.07869	+	15.7248i	0.348922	+	0.604351i	−0.637136	+	0.770751i	$0.719881\pi$
$678$		0			0
$679$	−8.73499	+	5.28019i	−0.335218	+	0.202635i
$680$		0			0
$681$	11.8933	−	15.8641i	0.455754	−	0.607914i
$682$		0			0
$683$		−	20.1917i		−	0.772615i	−0.922370	−	0.386308i	$-0.873750\pi$
$683$		−	20.1917i		−	0.772615i	0.922370	−	0.386308i	$-0.126250\pi$
$684$		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	$-0.666180\pi$
$691$	0.0695792	−	0.0401716i	0.00264692	−	0.00152820i	0.501323	+	0.865260i	$0.332847\pi$
$692$		0			0
$693$	−2.45696	+	11.0230i	−0.0933321	+	0.418730i
$694$		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	$-0.768951\pi$
$701$		−	35.1490i		−	1.32756i	0.747928	−	0.663780i	$-0.231049\pi$
$702$		0			0
$703$		−	17.2346i		−	0.650016i
$704$		0			0
$705$	−23.5707	−	55.1511i	−0.887722	−	2.07711i
$706$		0			0
$707$	−12.3357	−	20.4068i	−0.463930	−	0.767477i
$708$		0			0
$709$	−0.782968	−	1.35614i	−0.0294050	−	0.0509309i	0.850948	−	0.525249i	$-0.176028\pi$
$709$	−0.782968	−	1.35614i	−0.0294050	−	0.0509309i	−0.880353	+	0.474318i	$0.842695\pi$
$710$		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	$-0.660291\pi$
$719$	−25.8787			−0.965112			−0.482556	+	0.875865i	$0.660291\pi$
$720$		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	$-0.673419\pi$
$727$	−0.990545	+	0.571891i	−0.0367373	+	0.0212103i	0.481519	+	0.876436i	$0.340085\pi$
$728$		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	$-0.192023\pi$
$733$	20.1408	+	11.6283i	0.743916	+	0.429500i	−0.0795755	+	0.996829i	$0.525356\pi$
$734$		0			0
$735$	−50.6009	−	4.03042i	−1.86644	−	0.148664i
$736$		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	0.613447	−	0.789736i	$-0.289783\pi$
$743$	6.43940	+	3.71779i	0.236239	+	0.136392i	−0.377208	+	0.926129i	$0.623116\pi$
$744$		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
$749$	−0.604658	−	30.0575i	−0.0220937	−	1.09828i
$750$		0			0
$751$	−3.67798	+	6.37044i	−0.134211	+	0.232461i	−0.925296	−	0.379246i	$-0.876183\pi$
$751$	−3.67798	+	6.37044i	−0.134211	+	0.232461i	0.791085	+	0.611707i	$0.209517\pi$
$752$		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	0.140217	+	0.990121i	$0.455220\pi$
$761$	−21.7203	+	37.6207i	−0.787362	+	1.36375i	−0.927578	+	0.373629i	$0.878113\pi$
$762$		0			0
$763$	42.3049	−	0.851035i	1.53154	−	0.0308095i
$764$		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	$-0.204966\pi$
$769$	18.8491	+	10.8825i	0.679716	+	0.392434i	−0.120032	+	0.992770i	$0.538300\pi$
$770$		0			0
$771$	−18.7340	−	2.25344i	−0.674687	−	0.0811557i
$772$		0			0
$773$	14.5147			0.522056			0.261028	−	0.965331i	$-0.415938\pi$
$773$	14.5147			0.522056			0.261028	+	0.965331i	$0.415938\pi$
$774$		0			0
$775$			90.8520i			3.26350i
$776$		0			0
$777$	6.53160	+	14.4703i	0.234320	+	0.519118i
$778$		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	$-0.408913\pi$
$787$	−11.4291	−	6.59861i	−0.407405	−	0.235215i	−0.689674	+	0.724120i	$0.742246\pi$
$788$		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	0.0321352	−	0.999484i	$-0.489769\pi$
$797$	24.8899	−	43.1106i	0.881646	−	1.52706i	0.849511	−	0.527572i	$-0.176897\pi$
$798$		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
$805$	−54.5966	+	33.0029i	−1.92428	+	1.16320i
$806$		0			0
$807$	2.03124	+	4.75274i	0.0715032	+	0.167305i
$808$		0			0
$809$		−	28.1889i		−	0.991068i	−0.868589	−	0.495534i	$-0.834972\pi$
$809$		−	28.1889i		−	0.991068i	0.868589	−	0.495534i	$-0.165028\pi$
$810$		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
$819$	7.43895	−	2.33615i	0.259938	−	0.0816317i
$820$		0			0
$821$	−46.9123	+	27.0848i	−1.63725	+	0.945267i	−0.655475	+	0.755217i	$0.727532\pi$
$821$	−46.9123	+	27.0848i	−1.63725	+	0.945267i	−0.981774	+	0.190050i	$0.939135\pi$
$822$		0			0
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	−0.999996	−	0.00299479i	$-0.999047\pi$
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	0.502591	+	0.864524i	$0.332380\pi$
$824$		0			0
$825$	3.68738	−	30.6550i	0.128378	−	1.06727i
$826$		0			0
$827$			37.2062i			1.29379i	0.762581	+	0.646893i	$0.223932\pi$
$827$			37.2062i			1.29379i	−0.762581	+	0.646893i	$0.776068\pi$
$828$		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
$833$	−2.59453	+	0.104429i	−0.0898951	+	0.00361825i
$834$		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	0.719787	+	0.694195i	$0.244240\pi$
$839$	27.8383	+	48.2173i	0.961084	+	1.66465i	0.241297	+	0.970451i	$0.422427\pi$
$840$		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	$-0.562521\pi$
$853$	16.2574	−	9.38622i	0.556643	−	0.321378i	0.751797	+	0.659395i	$0.229187\pi$
$854$		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	$-0.299341\pi$
$857$	−11.8516	−	20.5276i	−0.404844	−	0.701210i	−0.994303	+	0.106588i	$0.966007\pi$
$858$		0			0
$859$	14.5237	+	8.38527i	0.495543	+	0.286102i	0.726871	−	0.686774i	$-0.240974\pi$
$859$	14.5237	+	8.38527i	0.495543	+	0.286102i	−0.231328	+	0.972876i	$0.574307\pi$
$860$		0			0
$861$	9.75642	+	0.974938i	0.332498	+	0.0332258i
$862$		0			0
$863$		−	33.7443i		−	1.14867i	−0.818620	−	0.574335i	$-0.805261\pi$
$863$		−	33.7443i		−	1.14867i	0.818620	−	0.574335i	$-0.194739\pi$
$864$		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
$875$	83.3768	−	1.67727i	2.81865	−	0.0567019i
$876$		0			0
$877$	19.7087	−	34.1365i	0.665515	−	1.15271i	−0.313630	−	0.949545i	$-0.601545\pi$
$877$	19.7087	−	34.1365i	0.665515	−	1.15271i	0.979145	−	0.203161i	$-0.0651215\pi$
$878$		0			0
$879$	13.6023	+	1.63618i	0.458796	+	0.0551869i
$880$		0			0
$881$	−26.2496			−0.884372			−0.442186	−	0.896923i	$-0.645797\pi$
$881$	−26.2496			−0.884372			−0.442186	+	0.896923i	$0.645797\pi$
$882$		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	$-0.863721\pi$
$887$	−2.83888	+	4.91708i	−0.0953202	+	0.165099i	0.814422	+	0.580273i	$0.197054\pi$
$888$		0			0
$889$	5.05606	−	0.101711i	0.169575	−	0.00341129i
$890$		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
$903$	−16.0941	+	22.3919i	−0.535577	+	0.745155i
$904$		0			0
$905$	96.2716	+	55.5824i	3.20018	+	1.84762i
$906$		0			0
$907$	−7.32741	−	12.6914i	−0.243303	−	0.421412i	0.718350	−	0.695681i	$-0.244897\pi$
$907$	−7.32741	−	12.6914i	−0.243303	−	0.421412i	−0.961653	+	0.274269i	$0.911564\pi$
$908$		0			0
$909$	−26.2670	−	6.41189i	−0.871220	−	0.212669i
$910$		0			0
$911$	7.19133	−	4.15192i	0.238260	−	0.137559i	−0.376117	−	0.926572i	$-0.622741\pi$
$911$	7.19133	−	4.15192i	0.238260	−	0.137559i	0.614377	+	0.789013i	$0.289408\pi$
$912$		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	$-0.207981\pi$
$929$	−3.94493	−	6.83283i	−0.129429	−	0.224178i	−0.923456	+	0.383705i	$0.874648\pi$
$930$		0			0
$931$	−1.40048	−	34.7948i	−0.0458989	−	1.14035i
$932$		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	$-0.792079\pi$
$941$	3.96461	−	6.86691i	0.129243	−	0.223855i	0.923383	+	0.383879i	$0.125412\pi$
$942$		0			0
$943$	10.6719	−	6.16144i	0.347526	−	0.200644i
$944$		0			0
$945$	−43.7179	+	37.4385i	−1.42214	+	1.21787i
$946$		0			0
$947$	−26.8152	+	15.4817i	−0.871375	+	0.503089i	−0.867805	−	0.496905i	$-0.834470\pi$
$947$	−26.8152	+	15.4817i	−0.871375	+	0.503089i	−0.00357041	+	0.999994i	$0.501136\pi$
$948$		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	$0.186305\pi$
$953$			34.1087i			1.10489i	−0.833549	+	0.552445i	$0.813695\pi$
$954$		0			0
$955$			5.30502i			0.171666i
$956$		0			0
$957$	20.6739	+	2.48678i	0.668291	+	0.0803863i
$958$		0			0
$959$	−26.3995	+	15.9581i	−0.852483	+	0.515315i
$960$		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	0.163177	−	0.986597i	$-0.447826\pi$
$967$	29.1066	−	50.4142i	0.936007	−	1.62121i	0.772829	−	0.634614i	$-0.218841\pi$
$968$		0			0
$969$	2.93908	−	1.25611i	0.0944168	−	0.0403522i
$970$		0			0
$971$	−9.83792			−0.315714			−0.157857	−	0.987462i	$-0.550458\pi$
$971$	−9.83792			−0.315714			−0.157857	+	0.987462i	$0.550458\pi$
$972$		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	−0.0424567	−	0.999098i	$-0.513518\pi$
$977$	−29.0356	−	16.7637i	−0.928930	−	0.536318i	−0.886473	+	0.462781i	$0.846852\pi$
$978$		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	0.935908	+	0.352243i	$0.114581\pi$
$983$	24.2359	+	41.9779i	0.773006	+	1.33889i	−0.162902	+	0.986642i	$0.552086\pi$
$984$		0			0
$985$	21.5486	+	12.4411i	0.686594	+	0.396405i
$986$		0			0
$987$	−22.1207	+	30.7769i	−0.704111	+	0.979640i
$988$		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	$-0.622443\pi$
$997$	7.57384	−	4.37276i	0.239866	−	0.138487i	0.615115	+	0.788437i	$0.289110\pi$
$998$		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.41.4	✓	16
3.2	odd	2		756.2.x.a.125.1		16
4.3	odd	2		1008.2.cc.c.545.5		16
7.2	even	3		1764.2.bm.b.1697.8		16
7.3	odd	6		1764.2.w.a.509.7		16
7.4	even	3		1764.2.w.a.509.2		16
7.5	odd	6		1764.2.bm.b.1697.1		16
7.6	odd	2	inner	252.2.x.a.41.5	yes	16
9.2	odd	6	inner	252.2.x.a.209.5	yes	16
9.4	even	3		2268.2.f.b.1133.1		16
9.5	odd	6		2268.2.f.b.1133.15		16
9.7	even	3		756.2.x.a.629.8		16
12.11	even	2		3024.2.cc.c.881.1		16
21.2	odd	6		5292.2.bm.b.2285.8		16
21.5	even	6		5292.2.bm.b.2285.1		16
21.11	odd	6		5292.2.w.a.1097.1		16
21.17	even	6		5292.2.w.a.1097.8		16
21.20	even	2		756.2.x.a.125.8		16
28.27	even	2		1008.2.cc.c.545.4		16
36.7	odd	6		3024.2.cc.c.2897.8		16
36.11	even	6		1008.2.cc.c.209.4		16
63.2	odd	6		1764.2.w.a.1109.7		16
63.11	odd	6		1764.2.bm.b.1685.1		16
63.13	odd	6		2268.2.f.b.1133.16		16
63.16	even	3		5292.2.w.a.521.8		16
63.20	even	6	inner	252.2.x.a.209.4	yes	16
63.25	even	3		5292.2.bm.b.4625.1		16
63.34	odd	6		756.2.x.a.629.1		16
63.38	even	6		1764.2.bm.b.1685.8		16
63.41	even	6		2268.2.f.b.1133.2		16
63.47	even	6		1764.2.w.a.1109.2		16
63.52	odd	6		5292.2.bm.b.4625.8		16
63.61	odd	6		5292.2.w.a.521.1		16
84.83	odd	2		3024.2.cc.c.881.8		16
252.83	odd	6		1008.2.cc.c.209.5		16
252.223	even	6		3024.2.cc.c.2897.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.4	✓	16	1.1	even	1	trivial
252.2.x.a.41.5	yes	16	7.6	odd	2	inner
252.2.x.a.209.4	yes	16	63.20	even	6	inner
252.2.x.a.209.5	yes	16	9.2	odd	6	inner
756.2.x.a.125.1		16	3.2	odd	2
756.2.x.a.125.8		16	21.20	even	2
756.2.x.a.629.1		16	63.34	odd	6
756.2.x.a.629.8		16	9.7	even	3
1008.2.cc.c.209.4		16	36.11	even	6
1008.2.cc.c.209.5		16	252.83	odd	6
1008.2.cc.c.545.4		16	28.27	even	2
1008.2.cc.c.545.5		16	4.3	odd	2
1764.2.w.a.509.2		16	7.4	even	3
1764.2.w.a.509.7		16	7.3	odd	6
1764.2.w.a.1109.2		16	63.47	even	6
1764.2.w.a.1109.7		16	63.2	odd	6
1764.2.bm.b.1685.1		16	63.11	odd	6
1764.2.bm.b.1685.8		16	63.38	even	6
1764.2.bm.b.1697.1		16	7.5	odd	6
1764.2.bm.b.1697.8		16	7.2	even	3
2268.2.f.b.1133.1		16	9.4	even	3
2268.2.f.b.1133.2		16	63.41	even	6
2268.2.f.b.1133.15		16	9.5	odd	6
2268.2.f.b.1133.16		16	63.13	odd	6
3024.2.cc.c.881.1		16	12.11	even	2
3024.2.cc.c.881.8		16	84.83	odd	2
3024.2.cc.c.2897.1		16	252.223	even	6
3024.2.cc.c.2897.8		16	36.7	odd	6
5292.2.w.a.521.1		16	63.61	odd	6
5292.2.w.a.521.8		16	63.16	even	3
5292.2.w.a.1097.1		16	21.11	odd	6
5292.2.w.a.1097.8		16	21.17	even	6
5292.2.bm.b.2285.1		16	21.5	even	6
5292.2.bm.b.2285.8		16	21.2	odd	6
5292.2.bm.b.4625.1		16	63.25	even	3
5292.2.bm.b.4625.8		16	63.52	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +O(q^{10})\)	\(q+(-0.680689 - 1.59269i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-2.64522 + 0.0532130i) q^{7} +(-2.07332 + 2.16825i) q^{9} +(-1.23222 + 0.711425i) q^{11} +(0.850739 + 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} -0.370947 q^{17} -4.97471i q^{19} +(1.88532 + 4.17679i) q^{21} +(4.98775 + 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(4.86465 + 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(-6.28007 - 3.62580i) q^{31} +(1.97184 + 1.47829i) q^{33} +(-5.34444 + 9.70241i) q^{35} +3.46445 q^{37} +(0.203200 - 1.68930i) q^{39} +(1.06981 - 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(3.52145 + 12.0564i) q^{45} +(4.13542 + 7.16276i) q^{47} +(6.99434 - 0.281520i) q^{49} +(0.252500 + 0.590804i) q^{51} +4.97245i q^{53} +5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(2.27883 - 3.94705i) q^{59} +(-6.50416 + 3.75518i) q^{61} +(5.36901 - 5.84583i) q^{63} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} +(1.19133 - 9.90411i) q^{69} -10.9555i q^{71} +9.52848i q^{73} +(-13.0167 + 17.3626i) q^{75} +(3.22164 - 1.94744i) q^{77} +(4.25553 + 7.37079i) q^{79} +(-0.402651 - 8.99099i) q^{81} +(-0.972254 - 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(-11.7094 - 8.77855i) q^{87} +7.80735 q^{89} +(-2.27652 - 1.25399i) q^{91} +(-1.50000 + 12.4702i) q^{93} +(-18.0373 - 10.4138i) q^{95} +(3.34099 - 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more