LMFDB - Embedded newform 1764.2.w.a.1109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1764.509");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.0856109166$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1109.2
Root			$-1.71965 - 0.206851i$ of defining polynomial
Character	$\chi$	$=$	1764.1109
Dual form			1764.2.w.a.509.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03897 - 1.38584i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-0.841101 + 2.87968i) q^{9} +O(q^{10})$	\(q+(-1.03897 - 1.38584i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-0.841101 + 2.87968i) q^{9} +(1.23222 - 0.711425i) q^{11} +(0.850739 - 0.491174i) q^{13} +(-7.19970 + 0.866025i) q^{15} +(0.185474 - 0.321250i) q^{17} +(4.30823 - 2.48736i) q^{19} +(-4.98775 - 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(4.86465 - 1.82626i) q^{27} +(7.31732 + 4.22466i) q^{29} -7.25160i q^{31} +(-2.26616 - 0.968518i) q^{33} +(-1.73222 - 3.00030i) q^{37} +(-1.56458 - 0.668674i) q^{39} +(1.06981 + 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(8.68041 + 9.07785i) q^{45} -8.27085 q^{47} +(-0.637901 + 0.0767308i) q^{51} +(4.30627 + 2.48623i) q^{53} -5.95706i q^{55} +(-7.92317 - 3.38623i) q^{57} -4.55766 q^{59} +7.51035i q^{61} -4.11281i q^{65} -10.0641 q^{67} +(1.19133 + 9.90411i) q^{69} +10.9555i q^{71} +(8.25191 + 4.76424i) q^{73} +(-8.52805 + 19.9541i) q^{75} -8.51105 q^{79} +(-7.58510 - 4.84420i) q^{81} +(-0.972254 + 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(-1.74775 - 14.5299i) q^{87} +(-3.90368 - 6.76137i) q^{89} +(-10.0495 + 7.53416i) q^{93} -20.8277i q^{95} +(3.34099 + 1.92892i) q^{97} +(1.01225 + 4.14679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.03897	−	1.38584i	−0.599847	−	0.800115i
$3$	−1.03897	−	1.38584i	−0.599847	−	0.800115i
$4$		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
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.841101	+	2.87968i	−0.280367	+	0.959893i
$10$		0			0
$11$	1.23222	−	0.711425i	0.371529	−	0.214503i	−0.302597	−	0.953119i	$-0.597854\pi$
$11$	1.23222	−	0.711425i	0.371529	−	0.214503i	0.674126	+	0.738616i	$0.264520\pi$
$12$		0			0
$13$	0.850739	−	0.491174i	0.235952	−	0.136227i	−0.377363	−	0.926066i	$-0.623169\pi$
$13$	0.850739	−	0.491174i	0.235952	−	0.136227i	0.613315	+	0.789838i	$0.289836\pi$
$14$		0			0
$15$	−7.19970	+	0.866025i	−1.85895	+	0.223607i
$16$		0			0
$17$	0.185474	−	0.321250i	0.0449840	−	0.0779145i	−0.842657	−	0.538451i	$-0.819010\pi$
$17$	0.185474	−	0.321250i	0.0449840	−	0.0779145i	0.887641	+	0.460537i	$0.152343\pi$
$18$		0			0
$19$	4.30823	−	2.48736i	0.988375	−	0.570638i	0.0835867	−	0.996501i	$-0.473362\pi$
$19$	4.30823	−	2.48736i	0.988375	−	0.570638i	0.904788	+	0.425862i	$0.140029\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.98775	−	2.87968i	−1.04002	−	0.600455i	−0.120179	−	0.992752i	$-0.538347\pi$
$23$	−4.98775	−	2.87968i	−1.04002	−	0.600455i	−0.919838	+	0.392298i	$0.871680\pi$
$24$		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
$31$		−	7.25160i		−	1.30243i	−0.758895	−	0.651213i	$-0.774261\pi$
$31$		−	7.25160i		−	1.30243i	0.758895	−	0.651213i	$-0.225739\pi$
$32$		0			0
$33$	−2.26616	−	0.968518i	−0.394488	−	0.168597i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.73222	−	3.00030i	−0.284776	−	0.493246i	0.687779	−	0.725920i	$-0.258586\pi$
$37$	−1.73222	−	3.00030i	−0.284776	−	0.493246i	−0.972555	+	0.232674i	$0.925252\pi$
$38$		0			0
$39$	−1.56458	−	0.668674i	−0.250533	−	0.107074i
$40$		0			0
$41$	1.06981	+	1.85297i	0.167077	+	0.289386i	0.937391	−	0.348279i	$-0.113234\pi$
$41$	1.06981	+	1.85297i	0.167077	+	0.289386i	−0.770314	+	0.637665i	$0.779901\pi$
$42$		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
$45$	8.68041	+	9.07785i	1.29400	+	1.35325i
$46$		0			0
$47$	−8.27085			−1.20643			−0.603213	−	0.797580i	$-0.706113\pi$
$47$	−8.27085			−1.20643			−0.603213	+	0.797580i	$0.706113\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.637901	+	0.0767308i	−0.0893240	+	0.0107445i
$52$		0			0
$53$	4.30627	+	2.48623i	0.591512	+	0.341509i	0.765695	−	0.643204i	$-0.222395\pi$
$53$	4.30627	+	2.48623i	0.591512	+	0.341509i	−0.174183	+	0.984713i	$0.555729\pi$
$54$		0			0
$55$		−	5.95706i		−	0.803250i
$56$		0			0
$57$	−7.92317	−	3.38623i	−1.04945	−	0.448517i
$58$		0			0
$59$	−4.55766			−0.593357			−0.296678	−	0.954977i	$-0.595879\pi$
$59$	−4.55766			−0.593357			−0.296678	+	0.954977i	$0.595879\pi$
$60$		0			0
$61$			7.51035i			0.961602i	0.876830	+	0.480801i	$0.159654\pi$
$61$			7.51035i			0.961602i	−0.876830	+	0.480801i	$0.840346\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	4.11281i		−	0.510131i
$66$		0			0
$67$	−10.0641			−1.22953			−0.614763	−	0.788712i	$-0.710748\pi$
$67$	−10.0641			−1.22953			−0.614763	+	0.788712i	$0.710748\pi$
$68$		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
$73$	8.25191	+	4.76424i	0.965813	+	0.557612i	0.897957	−	0.440083i	$-0.145051\pi$
$73$	8.25191	+	4.76424i	0.965813	+	0.557612i	0.0678555	+	0.997695i	$0.478384\pi$
$74$		0			0
$75$	−8.52805	+	19.9541i	−0.984734	+	2.30410i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−8.51105			−0.957568			−0.478784	−	0.877933i	$-0.658922\pi$
$79$	−8.51105			−0.957568			−0.478784	+	0.877933i	$0.658922\pi$
$80$		0			0
$81$	−7.58510	−	4.84420i	−0.842789	−	0.538244i
$82$		0			0
$83$	−0.972254	+	1.68399i	−0.106719	+	0.184842i	−0.914439	−	0.404724i	$-0.867368\pi$
$83$	−0.972254	+	1.68399i	−0.106719	+	0.184842i	0.807720	+	0.589566i	$0.200701\pi$
$84$		0			0
$85$	−0.776524	−	1.34498i	−0.0842259	−	0.145884i
$86$		0			0
$87$	−1.74775	−	14.5299i	−0.187378	−	1.55777i
$88$		0			0
$89$	−3.90368	−	6.76137i	−0.413789	−	0.716703i	0.581512	−	0.813538i	$-0.302462\pi$
$89$	−3.90368	−	6.76137i	−0.413789	−	0.716703i	−0.995300	+	0.0968347i	$0.969128\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.0495	+	7.53416i	−1.04209	+	0.781256i
$94$		0			0
$95$		−	20.8277i		−	2.13687i
$96$		0			0
$97$	3.34099	+	1.92892i	0.339226	+	0.195852i	0.659930	−	0.751327i	$-0.270586\pi$
$97$	3.34099	+	1.92892i	0.339226	+	0.195852i	−0.320704	+	0.947180i	$0.603919\pi$
$98$		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	0.764146	−	0.645044i	$-0.223161\pi$
$103$	5.96343	+	3.44299i	0.587594	+	0.339248i	−0.176551	+	0.984291i	$0.556494\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.84062	+	5.68149i	−0.951329	+	0.549250i	−0.893494	−	0.449076i	$-0.851753\pi$
$107$	−9.84062	+	5.68149i	−0.951329	+	0.549250i	−0.0578356	+	0.998326i	$0.518420\pi$
$108$		0			0
$109$	7.99650	−	13.8503i	0.765926	−	1.32662i	−0.173830	−	0.984776i	$-0.555614\pi$
$109$	7.99650	−	13.8503i	0.765926	−	1.32662i	0.939756	−	0.341846i	$-0.111052\pi$
$110$		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
$117$	0.698867	+	2.86298i	0.0646103	+	0.264683i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.48775	+	7.77301i	−0.407977	+	0.706637i
$122$		0			0
$123$	1.45642	−	3.40776i	0.131321	−	0.307268i
$124$		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
$129$	−10.3480	+	1.24473i	−0.911092	+	0.109592i
$130$		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			0
$134$		0			0
$135$	3.56180	−	21.4612i	0.306551	−	1.84709i
$136$		0			0
$137$	−10.0973	+	5.82971i	−0.862675	+	0.498065i	−0.864907	−	0.501932i	$-0.832623\pi$
$137$	−10.0973	+	5.82971i	−0.862675	+	0.498065i	0.00223233	+	0.999998i	$0.499289\pi$
$138$		0			0
$139$	4.82663	−	2.78666i	0.409390	−	0.236361i	−0.281138	−	0.959667i	$-0.590712\pi$
$139$	4.82663	−	2.78666i	0.409390	−	0.236361i	0.690528	+	0.723306i	$0.257378\pi$
$140$		0			0
$141$	8.59312	+	11.4621i	0.723672	+	0.965280i
$142$		0			0
$143$	0.698867	−	1.21047i	0.0584422	−	0.101225i
$144$		0			0
$145$	30.6355	−	17.6874i	2.54414	−	1.46886i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.4024	+	7.73789i	1.09797	+	0.633913i	0.935687	−	0.352832i	$-0.114781\pi$
$149$	13.4024	+	7.73789i	1.09797	+	0.633913i	0.162282	+	0.986744i	$0.448114\pi$
$150$		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
$157$		−	16.8077i		−	1.34140i	−0.741727	−	0.670702i	$-0.765993\pi$
$157$		−	16.8077i		−	1.34140i	0.741727	−	0.670702i	$-0.234007\pi$
$158$		0			0
$159$	−1.02856	−	8.55090i	−0.0815699	−	0.678131i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.75553	−	3.04066i	−0.137503	−	0.238163i	0.789048	−	0.614332i	$-0.210574\pi$
$163$	−1.75553	−	3.04066i	−0.137503	−	0.238163i	−0.926551	+	0.376169i	$0.877241\pi$
$164$		0			0
$165$	−8.25553	+	6.18918i	−0.642692	+	0.481827i
$166$		0			0
$167$	−4.05253	−	7.01918i	−0.313594	−	0.543160i	0.665544	−	0.746359i	$-0.268200\pi$
$167$	−4.05253	−	7.01918i	−0.313594	−	0.543160i	−0.979138	+	0.203198i	$0.934866\pi$
$168$		0			0
$169$	−6.01750	+	10.4226i	−0.462884	+	0.801739i
$170$		0			0
$171$	3.53913	+	14.4984i	0.270644	+	1.10872i
$172$		0			0
$173$	−13.0969			−0.995737			−0.497868	−	0.867253i	$-0.665884\pi$
$173$	−13.0969			−0.995737			−0.497868	+	0.867253i	$0.665884\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.73525	+	6.31618i	0.355923	+	0.474753i
$178$		0			0
$179$	−11.0140	−	6.35893i	−0.823225	−	0.475289i	0.0283026	−	0.999599i	$-0.490990\pi$
$179$	−11.0140	−	6.35893i	−0.823225	−	0.475289i	−0.851527	+	0.524310i	$0.824323\pi$
$180$		0			0
$181$		−	26.5518i		−	1.97358i	−0.161998	−	0.986791i	$-0.551794\pi$
$181$		−	26.5518i		−	1.97358i	0.161998	−	0.986791i	$-0.448206\pi$
$182$		0			0
$183$	10.4081	−	7.80300i	0.769392	−	0.576814i
$184$		0			0
$185$	−14.5046			−1.06640
$186$		0			0
$187$		−	0.527802i		−	0.0385967i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			1.26711i			0.0916848i	0.998949	+	0.0458424i	$0.0145972\pi$
$191$			1.26711i			0.0916848i	−0.998949	+	0.0458424i	$0.985403\pi$
$192$		0			0
$193$	18.6346			1.34135			0.670676	−	0.741751i	$-0.266004\pi$
$193$	18.6346			1.34135			0.670676	+	0.741751i	$0.266004\pi$
$194$		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
$199$	4.87291	+	2.81337i	0.345431	+	0.199435i	0.662671	−	0.748910i	$-0.269423\pi$
$199$	4.87291	+	2.81337i	0.345431	+	0.199435i	−0.317240	+	0.948345i	$0.602756\pi$
$200$		0			0
$201$	10.4563	+	13.9472i	0.737527	+	0.983761i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	8.95800			0.625654
$206$		0			0
$207$	12.4877	−	11.9410i	0.867959	−	0.829958i
$208$		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
$213$	15.1826	−	11.3824i	1.04029	−	0.779909i
$214$		0			0
$215$	−12.5968	−	21.8182i	−0.859092	−	1.48799i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.97098	−	16.3857i	−0.133186	−	1.10724i
$220$		0			0
$221$		−	0.364399i		−	0.0245121i
$222$		0			0
$223$	−5.52351	−	3.18900i	−0.369882	−	0.213551i	0.303525	−	0.952823i	$-0.401836\pi$
$223$	−5.52351	−	3.18900i	−0.369882	−	0.213551i	−0.673407	+	0.739272i	$0.735170\pi$
$224$		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	0.329762	−	0.944064i	$-0.393031\pi$
$229$	−4.88696	−	2.82149i	−0.322940	−	0.186449i	−0.652702	+	0.757615i	$0.726365\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.7788	−	6.22316i	0.706145	−	0.407693i	−0.103487	−	0.994631i	$-0.533000\pi$
$233$	10.7788	−	6.22316i	0.706145	−	0.407693i	0.809632	+	0.586938i	$0.199667\pi$
$234$		0			0
$235$	−17.3138	+	29.9884i	−1.12943	+	1.95623i
$236$		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	−0.356411	−	0.934329i	$-0.616000\pi$
$241$	4.26195	−	2.46064i	0.274537	−	0.158504i	0.630947	+	0.775826i	$0.282666\pi$
$242$		0			0
$243$	1.16737	+	15.5447i	0.0748871	+	0.997192i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.44345	−	4.23218i	0.155473	−	0.269287i
$248$		0			0
$249$	3.34388	−	0.402223i	0.211910	−	0.0254899i
$250$		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
$255$	−1.05714	+	2.47353i	−0.0662009	+	0.154898i
$256$		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
$259$		0			0
$260$		0			0
$261$	−18.3203	+	17.5182i	−1.13400	+	1.08435i
$262$		0			0
$263$	−15.6489	+	9.03488i	−0.964951	+	0.557114i	−0.897693	−	0.440621i	$-0.854758\pi$
$263$	−15.6489	+	9.03488i	−0.964951	+	0.557114i	−0.0672574	+	0.997736i	$0.521425\pi$
$264$		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
$269$	1.49205	−	2.58430i	0.0909718	−	0.157568i	−0.816948	−	0.576711i	$-0.804336\pi$
$269$	1.49205	−	2.58430i	0.0909718	−	0.157568i	0.907920	+	0.419143i	$0.137669\pi$
$270$		0			0
$271$	8.97274	−	5.18041i	0.545055	−	0.314688i	−0.202070	−	0.979371i	$-0.564767\pi$
$271$	8.97274	−	5.18041i	0.545055	−	0.314688i	0.747125	+	0.664683i	$0.231434\pi$
$272$		0			0
$273$		0			0
$274$		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	0.0945775	−	0.995518i	$-0.469850\pi$
$281$	−12.0740	−	6.97095i	−0.720277	−	0.415852i	−0.814855	+	0.579665i	$0.803183\pi$
$282$		0			0
$283$		−	2.53564i		−	0.150728i	−0.997156	−	0.0753642i	$-0.975988\pi$
$283$		−	2.53564i		−	0.150728i	0.997156	−	0.0753642i	$-0.0240119\pi$
$284$		0			0
$285$	−28.8638	+	21.6392i	−1.70974	+	1.28180i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.43120	+	14.6033i	0.495953	+	0.859016i
$290$		0			0
$291$	−0.797998	−	6.63415i	−0.0467795	−	0.388901i
$292$		0			0
$293$	−3.95496	−	6.85020i	−0.231052	−	0.400193i	0.727066	−	0.686567i	$-0.240883\pi$
$293$	−3.95496	−	6.85020i	−0.231052	−	0.400193i	−0.958118	+	0.286374i	$0.907550\pi$
$294$		0			0
$295$	−9.54080	+	16.5251i	−0.555487	+	0.962131i
$296$		0			0
$297$	4.69509	−	5.71119i	0.272437	−	0.331397i
$298$		0			0
$299$	−5.65769			−0.327193
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.13487	−	14.3545i	0.352439	−	0.824645i
$304$		0			0
$305$	27.2310	+	15.7218i	1.55924	+	0.900230i
$306$		0			0
$307$			13.9676i			0.797170i	0.917131	+	0.398585i	$0.130499\pi$
$307$			13.9676i			0.797170i	−0.917131	+	0.398585i	$0.869501\pi$
$308$		0			0
$309$	−1.42437	−	11.8415i	−0.0810296	−	0.673640i
$310$		0			0
$311$	32.6327			1.85043			0.925215	−	0.379443i	$-0.123884\pi$
$311$	32.6327			1.85043			0.925215	+	0.379443i	$0.123884\pi$
$312$		0			0
$313$			15.7166i			0.888357i	0.895938	+	0.444178i	$0.146504\pi$
$313$			15.7166i			0.888357i	−0.895938	+	0.444178i	$0.853496\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			29.0253i			1.63022i	0.579305	+	0.815111i	$0.303324\pi$
$317$			29.0253i			1.63022i	−0.579305	+	0.815111i	$0.696676\pi$
$318$		0			0
$319$	12.0221			0.673109
$320$		0			0
$321$	18.0977	+	7.73465i	1.01012	+	0.431706i
$322$		0			0
$323$		−	1.84535i		−	0.102678i
$324$		0			0
$325$	−10.6585	−	6.15370i	−0.591228	−	0.341346i
$326$		0			0
$327$	−27.5024	+	3.30817i	−1.52089	+	0.182942i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	13.1702			0.723900			0.361950	−	0.932198i	$-0.382111\pi$
$331$	13.1702			0.723900			0.361950	+	0.932198i	$0.382111\pi$
$332$		0			0
$333$	10.0969	−	2.46469i	0.553305	−	0.135064i
$334$		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
$339$	−3.99159	−	1.70594i	−0.216793	−	0.0926539i
$340$		0			0
$341$	−5.15896	−	8.93559i	−0.279374	−	0.483889i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	38.4042	+	16.4133i	2.06761	+	0.883662i
$346$		0			0
$347$			24.7120i			1.32661i	0.748349	+	0.663305i	$0.230847\pi$
$347$			24.7120i			1.32661i	−0.748349	+	0.663305i	$0.769153\pi$
$348$		0			0
$349$	26.7994	+	15.4727i	1.43454	+	0.828232i	0.997463	−	0.0711915i	$-0.0226802\pi$
$349$	26.7994	+	15.4727i	1.43454	+	0.828232i	0.437078	+	0.899424i	$0.356013\pi$
$350$		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			0
$358$		0			0
$359$	18.3902	−	10.6176i	0.970596	−	0.560374i	0.0711782	−	0.997464i	$-0.477324\pi$
$359$	18.3902	−	10.6176i	0.970596	−	0.560374i	0.899418	+	0.437090i	$0.143991\pi$
$360$		0			0
$361$	2.87387	−	4.97769i	0.151256	−	0.261984i
$362$		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	−0.152392	−	0.988320i	$-0.548698\pi$
$367$	12.0178	−	6.93846i	0.627322	−	0.362185i	0.779714	+	0.626135i	$0.215364\pi$
$368$		0			0
$369$	−6.23579	+	1.52218i	−0.324622	+	0.0792417i
$370$		0			0
$371$		0			0
$372$		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
$375$	32.7480	+	43.6815i	1.69110	+	2.25570i
$376$		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
$381$	1.98588	+	2.64889i	0.101740	+	0.135707i
$382$		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			0
$386$		0			0
$387$	12.4762	+	13.0475i	0.634202	+	0.663240i
$388$		0			0
$389$	−9.74447	+	5.62597i	−0.494064	+	0.285248i	−0.726259	−	0.687421i	$-0.758743\pi$
$389$	−9.74447	+	5.62597i	−0.494064	+	0.285248i	0.232195	+	0.972669i	$0.425409\pi$
$390$		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
$395$	−17.8167	+	30.8594i	−0.896453	+	1.55270i
$396$		0			0
$397$	−0.548160	+	0.316480i	−0.0275114	+	0.0158837i	−0.513693	−	0.857974i	$-0.671723\pi$
$397$	−0.548160	+	0.316480i	−0.0275114	+	0.0158837i	0.486181	+	0.873858i	$0.338389\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.38032	−	4.26103i	−0.368555	−	0.212786i	0.304272	−	0.952585i	$-0.401587\pi$
$401$	−7.38032	−	4.26103i	−0.368555	−	0.212786i	−0.672827	+	0.739800i	$0.734920\pi$
$402$		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
$409$		−	14.0668i		−	0.695557i	−0.937577	−	0.347778i	$-0.886936\pi$
$409$		−	14.0668i		−	0.695557i	0.937577	−	0.347778i	$-0.113064\pi$
$410$		0			0
$411$	18.5698	+	7.93644i	0.915982	+	0.391476i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.07054	+	7.05039i	0.199815	+	0.346090i
$416$		0			0
$417$	−8.87657	−	3.79370i	−0.434687	−	0.185778i
$418$		0			0
$419$	10.9339	+	18.9381i	0.534156	+	0.925185i	0.999204	+	0.0398995i	$0.0127038\pi$
$419$	10.9339	+	18.9381i	0.534156	+	0.925185i	−0.465048	+	0.885286i	$0.653963\pi$
$420$		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
$423$	6.95662	−	23.8174i	0.338242	−	1.15804i
$424$		0			0
$425$	−4.64743			−0.225433
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.40362	+	0.289123i	−0.116048	+	0.0139590i
$430$		0			0
$431$	17.2686	+	9.97000i	0.831797	+	0.480238i	0.854468	−	0.519505i	$-0.173884\pi$
$431$	17.2686	+	9.97000i	0.831797	+	0.480238i	−0.0226706	+	0.999743i	$0.507217\pi$
$432$		0			0
$433$		−	20.2826i		−	0.974719i	−0.873201	−	0.487359i	$-0.837960\pi$
$433$		−	20.2826i		−	0.974719i	0.873201	−	0.487359i	$-0.162040\pi$
$434$		0			0
$435$	−56.3412	−	24.0793i	−2.70135	−	1.15451i
$436$		0			0
$437$	−28.6511			−1.37057
$438$		0			0
$439$		−	28.3982i		−	1.35537i	−0.735350	−	0.677687i	$-0.762982\pi$
$439$		−	28.3982i		−	1.35537i	0.735350	−	0.677687i	$-0.237018\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	12.3056i		−	0.584658i	−0.956318	−	0.292329i	$-0.905570\pi$
$443$		−	12.3056i		−	0.584658i	0.956318	−	0.292329i	$-0.0944302\pi$
$444$		0			0
$445$	−32.6871			−1.54952
$446$		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
$451$	2.63650	+	1.52218i	0.124148	+	0.0716769i
$452$		0			0
$453$	11.3230	−	26.4938i	0.532002	−	1.24479i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.41784			−0.393770			−0.196885	−	0.980427i	$-0.563083\pi$
$457$	−8.41784			−0.393770			−0.196885	+	0.980427i	$0.563083\pi$
$458$		0			0
$459$	0.315579	−	1.90149i	0.0147300	−	0.0887539i
$460$		0			0
$461$	9.07730	−	15.7224i	0.422772	−	0.732263i	−0.573437	−	0.819249i	$-0.694390\pi$
$461$	9.07730	−	15.7224i	0.422772	−	0.732263i	0.996209	+	0.0869865i	$0.0277237\pi$
$462$		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
$465$	6.28007	+	52.2093i	0.291231	+	2.42115i
$466$		0			0
$467$	−13.3932	−	23.1977i	−0.619763	−	1.07346i	−0.989529	−	0.144336i	$-0.953896\pi$
$467$	−13.3932	−	23.1977i	−0.619763	−	1.07346i	0.369766	−	0.929125i	$-0.379438\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−23.2928	+	17.4627i	−1.07328	+	0.804637i
$472$		0			0
$473$		−	8.56199i		−	0.393681i
$474$		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
$483$		0			0
$484$		0			0
$485$	13.9877	−	8.07583i	0.635151	−	0.366705i
$486$		0			0
$487$	6.57635	−	11.3906i	0.298003	−	0.516156i	−0.677676	−	0.735361i	$-0.737013\pi$
$487$	6.57635	−	11.3906i	0.298003	−	0.516156i	0.975679	+	0.219204i	$0.0703462\pi$
$488$		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
$495$	17.1544	+	5.01049i	0.771034	+	0.225205i
$496$		0			0
$497$		0			0
$498$		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
$501$	−5.51702	+	12.9088i	−0.246482	+	0.576724i
$502$		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
$507$	20.6960	−	2.48945i	0.919143	−	0.110560i
$508$		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			0
$512$		0			0
$513$	16.4154	−	19.9680i	0.724760	−	0.881610i
$514$		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
$521$	−7.98920	+	13.8377i	−0.350013	+	0.606241i	−0.986251	−	0.165252i	$-0.947156\pi$
$521$	−7.98920	+	13.8377i	−0.350013	+	0.606241i	0.636238	+	0.771493i	$0.280490\pi$
$522$		0			0
$523$	−10.1857	+	5.88074i	−0.445391	+	0.257147i	−0.705882	−	0.708330i	$-0.749449\pi$
$523$	−10.1857	+	5.88074i	−0.445391	+	0.257147i	0.260491	+	0.965476i	$0.416116\pi$
$524$		0			0
$525$		0			0
$526$		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
$535$			47.5735i			2.05678i
$536$		0			0
$537$	2.63070	+	21.8703i	0.113523	+	0.943775i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.205980	+	0.356768i	0.00885576	+	0.0153386i	0.870419	−	0.492311i	$-0.163848\pi$
$541$	0.205980	+	0.356768i	0.00885576	+	0.0153386i	−0.861564	+	0.507650i	$0.830514\pi$
$542$		0			0
$543$	−36.7966	+	27.5864i	−1.57909	+	1.18385i
$544$		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
$549$	−21.6274	−	6.31696i	−0.923035	−	0.269601i
$550$		0			0
$551$	42.0329			1.79066
$552$		0			0
$553$		0			0
$554$		0			0
$555$	15.0698	+	20.1011i	0.639678	+	0.853244i
$556$		0			0
$557$	37.1935	+	21.4737i	1.57594	+	0.909869i	0.995418	+	0.0956241i	$0.0304847\pi$
$557$	37.1935	+	21.4737i	1.57594	+	0.909869i	0.580522	+	0.814245i	$0.302849\pi$
$558$		0			0
$559$		−	5.91128i		−	0.250020i
$560$		0			0
$561$	−0.731449	+	0.548368i	−0.0308818	+	0.0231521i
$562$		0			0
$563$	31.8908			1.34404			0.672019	−	0.740534i	$-0.265428\pi$
$563$	31.8908			1.34404			0.672019	+	0.740534i	$0.265428\pi$
$564$		0			0
$565$		−	10.4927i		−	0.441432i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	0.495245i		−	0.0207618i	−0.999946	−	0.0103809i	$-0.996696\pi$
$569$		−	0.495245i		−	0.0207618i	0.999946	−	0.0103809i	$-0.00330440\pi$
$570$		0			0
$571$	2.68365			0.112307			0.0561535	−	0.998422i	$-0.482116\pi$
$571$	2.68365			0.112307			0.0561535	+	0.998422i	$0.482116\pi$
$572$		0			0
$573$	1.75601	−	1.31648i	0.0733584	−	0.0549969i
$574$		0			0
$575$			72.1564i			3.00913i
$576$		0			0
$577$	−36.3955	−	21.0130i	−1.51517	−	0.874781i	−0.999842	−	0.0177861i	$-0.994338\pi$
$577$	−36.3955	−	21.0130i	−1.51517	−	0.874781i	−0.515324	−	0.856995i	$-0.672328\pi$
$578$		0			0
$579$	−19.3608	−	25.8246i	−0.804606	−	1.07323i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7.07505			0.293019
$584$		0			0
$585$	11.8436	+	3.45929i	0.489671	+	0.143024i
$586$		0			0
$587$	−1.71916	+	2.97768i	−0.0709575	+	0.122902i	−0.899321	−	0.437289i	$-0.855939\pi$
$587$	−1.71916	+	2.97768i	−0.0709575	+	0.122902i	0.828364	+	0.560191i	$0.189272\pi$
$588$		0			0
$589$	−18.0373	−	31.2415i	−0.743214	−	1.28728i
$590$		0			0
$591$	−8.23621	+	6.17470i	−0.338793	+	0.253993i
$592$		0			0
$593$	4.55126	+	7.88301i	0.186898	+	0.323716i	0.944214	−	0.329332i	$-0.106823\pi$
$593$	4.55126	+	7.88301i	0.186898	+	0.323716i	−0.757317	+	0.653048i	$0.773490\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.16390	−	9.67606i	−0.0476352	−	0.396015i
$598$		0			0
$599$			7.75019i			0.316664i	0.987386	+	0.158332i	$0.0506117\pi$
$599$			7.75019i			0.316664i	−0.987386	+	0.158332i	$0.949388\pi$
$600$		0			0
$601$	22.0034	+	12.7037i	0.897536	+	0.518193i	0.876400	−	0.481584i	$-0.159938\pi$
$601$	22.0034	+	12.7037i	0.897536	+	0.518193i	0.0211361	+	0.999777i	$0.493272\pi$
$602$		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	0.718443	−	0.695586i	$-0.244855\pi$
$607$	11.7094	+	6.76042i	0.475270	+	0.274397i	−0.243173	+	0.969983i	$0.578188\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.03633	+	4.06243i	−0.284659	+	0.164348i
$612$		0			0
$613$	−2.41817	+	4.18840i	−0.0976691	+	0.169168i	−0.910719	−	0.413026i	$-0.864472\pi$
$613$	−2.41817	+	4.18840i	−0.0976691	+	0.169168i	0.813050	+	0.582193i	$0.197805\pi$
$614$		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	−0.397359	−	0.917663i	$-0.630073\pi$
$619$	4.94313	−	2.85392i	0.198681	−	0.114709i	0.596040	+	0.802955i	$0.296740\pi$
$620$		0			0
$621$	−29.5227	−	4.89971i	−1.18470	−	0.196618i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−34.6609	+	60.0344i	−1.38644	+	2.40138i
$626$		0			0
$627$	−12.1722	+	1.46415i	−0.486110	+	0.0584724i
$628$		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
$633$	1.43360	−	3.35436i	0.0569804	−	0.133324i
$634$		0			0
$635$	−4.00124	+	6.93035i	−0.158784	+	0.275022i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−31.5483	−	9.21469i	−1.24803	−	0.364527i
$640$		0			0
$641$	−13.2820	+	7.66837i	−0.524607	+	0.302882i	−0.738818	−	0.673905i	$-0.764616\pi$
$641$	−13.2820	+	7.66837i	−0.524607	+	0.302882i	0.214210	+	0.976788i	$0.431282\pi$
$642$		0			0
$643$	11.3209	−	6.53612i	0.446453	−	0.257759i	−0.259878	−	0.965641i	$-0.583682\pi$
$643$	11.3209	−	6.53612i	0.446453	−	0.257759i	0.706331	+	0.707882i	$0.250349\pi$
$644$		0			0
$645$	−17.1490	+	40.1255i	−0.675239	+	1.57994i
$646$		0			0
$647$	17.8533	−	30.9228i	0.701885	−	1.21570i	−0.265919	−	0.963995i	$-0.585675\pi$
$647$	17.8533	−	30.9228i	0.701885	−	1.21570i	0.967804	−	0.251705i	$-0.0809913\pi$
$648$		0			0
$649$	−5.61605	+	3.24243i	−0.220449	+	0.127277i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	23.6131	+	13.6330i	0.924051	+	0.533501i	0.884925	−	0.465733i	$-0.154209\pi$
$653$	23.6131	+	13.6330i	0.924051	+	0.533501i	0.0391261	+	0.999234i	$0.487543\pi$
$654$		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
$661$			46.9568i			1.82641i	0.407505	+	0.913203i	$0.366399\pi$
$661$			46.9568i			1.82641i	−0.407505	+	0.913203i	$0.633601\pi$
$662$		0			0
$663$	−0.504999	+	0.378598i	−0.0196125	+	0.0147035i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.3313	−	42.1431i	−0.942112	−	1.63179i
$668$		0			0
$669$	1.31930	+	10.9680i	0.0510069	+	0.424046i
$670$		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
$675$	−50.2884	−	41.3414i	−1.93560	−	1.59123i
$676$		0			0
$677$	−18.1574			−0.697845			−0.348922	−	0.937152i	$-0.613452\pi$
$677$	−18.1574			−0.697845			−0.348922	+	0.937152i	$0.613452\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.79205	−	18.2320i	0.298592	−	0.698651i
$682$		0			0
$683$	−17.4866	−	10.0959i	−0.669104	−	0.386308i	0.126633	−	0.991950i	$-0.459583\pi$
$683$	−17.4866	−	10.0959i	−0.669104	−	0.386308i	−0.795737	+	0.605642i	$0.792916\pi$
$684$		0			0
$685$			48.8146i			1.86511i
$686$		0			0
$687$	1.16726	+	9.70398i	0.0445336	+	0.370230i
$688$		0			0
$689$	4.88468			0.186092
$690$		0			0
$691$		−	0.0803432i		−	0.00305640i	−0.999999	−	0.00152820i	$-0.999514\pi$
$691$		−	0.0803432i		−	0.00305640i	0.999999	−	0.00152820i	$-0.000486441\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	23.3339i		−	0.885104i
$696$		0			0
$697$	0.793689			0.0300631
$698$		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
$703$	−14.9256	−	8.61731i	−0.562930	−	0.325008i
$704$		0			0
$705$	59.5476	−	7.16276i	2.24269	−	0.269765i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.56594			0.0588100			0.0294050	−	0.999568i	$-0.490639\pi$
$709$	1.56594			0.0588100			0.0294050	+	0.999568i	$0.490639\pi$
$710$		0			0
$711$	7.15865	−	24.5091i	0.268470	−	0.919163i
$712$		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
$717$	−6.48184	−	2.77023i	−0.242069	−	0.103456i
$718$		0			0
$719$	12.9393	+	22.4116i	0.482556	+	0.835811i	0.999799	−	0.0200268i	$-0.00637517\pi$
$719$	12.9393	+	22.4116i	0.482556	+	0.835811i	−0.517243	+	0.855838i	$0.673042\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.83807	−	3.34986i	−0.291501	−	0.124583i
$724$		0			0
$725$		−	105.858i		−	3.93146i
$726$		0			0
$727$	−0.990545	−	0.571891i	−0.0367373	−	0.0212103i	0.481519	−	0.876436i	$-0.340085\pi$
$727$	−0.990545	−	0.571891i	−0.0367373	−	0.0212103i	−0.518256	+	0.855225i	$0.673419\pi$
$728$		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	0.0795755	−	0.996829i	$-0.474644\pi$
$733$	−20.1408	−	11.6283i	−0.743916	−	0.429500i	−0.823491	+	0.567329i	$0.807977\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.4012	+	7.15985i	−0.456805	+	0.263736i
$738$		0			0
$739$	18.0758	−	31.3082i	0.664929	−	1.15169i	−0.314376	−	0.949299i	$-0.601795\pi$
$739$	18.0758	−	31.3082i	0.664929	−	1.15169i	0.979305	−	0.202392i	$-0.0648714\pi$
$740$		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
$747$	−4.03159	−	4.21619i	−0.147508	−	0.154262i
$748$		0			0
$749$		0			0
$750$		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
$753$	−4.83140	−	6.44443i	−0.176066	−	0.234848i
$754$		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
$759$	8.51401	+	11.3565i	0.309039	+	0.412216i
$760$		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
$763$		0			0
$764$		0			0
$765$	4.52624	−	1.10488i	0.163647	−	0.0399469i
$766$		0			0
$767$	−3.87738	+	2.23860i	−0.140004	+	0.0808313i
$768$		0			0
$769$	18.8491	−	10.8825i	0.679716	−	0.392434i	−0.120032	−	0.992770i	$-0.538300\pi$
$769$	18.8491	−	10.8825i	0.679716	−	0.392434i	0.799748	+	0.600336i	$0.204966\pi$
$770$		0			0
$771$	−18.7340	+	2.25344i	−0.674687	+	0.0811557i
$772$		0			0
$773$	−7.25734	+	12.5701i	−0.261028	+	0.452114i	−0.966515	−	0.256609i	$-0.917395\pi$
$773$	−7.25734	+	12.5701i	−0.261028	+	0.452114i	0.705487	+	0.708723i	$0.250728\pi$
$774$		0			0
$775$	−78.6801	+	45.4260i	−2.82627	+	1.63175i
$776$		0			0
$777$		0			0
$778$		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
$787$		−	13.1972i		−	0.470430i	−0.971943	−	0.235215i	$-0.924421\pi$
$787$		−	13.1972i		−	0.470430i	0.971943	−	0.235215i	$-0.0755795\pi$
$788$		0			0
$789$	28.7795	+	12.2999i	1.02458	+	0.437888i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.68889	+	6.38935i	0.130996	+	0.226892i
$794$		0			0
$795$	−33.1570	−	14.1707i	−1.17596	−	0.502584i
$796$		0			0
$797$	24.8899	+	43.1106i	0.881646	+	1.52706i	0.849511	+	0.527572i	$0.176897\pi$
$797$	24.8899	+	43.1106i	0.881646	+	1.52706i	0.0321352	+	0.999484i	$0.489769\pi$
$798$		0			0
$799$	−1.53402	+	2.65701i	−0.0542698	+	0.0939981i
$800$		0			0
$801$	22.7539	−	5.55434i	0.803971	−	0.196253i
$802$		0			0
$803$	13.5576			0.478437
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.13162	+	0.617264i	−0.180642	+	0.0217287i
$808$		0			0
$809$	−24.4123	−	14.0944i	−0.858290	−	0.495534i	0.00514934	−	0.999987i	$-0.498361\pi$
$809$	−24.4123	−	14.0944i	−0.858290	−	0.495534i	−0.863439	+	0.504453i	$0.831694\pi$
$810$		0			0
$811$			33.5981i			1.17979i	0.807480	+	0.589894i	$0.200831\pi$
$811$			33.5981i			1.17979i	−0.807480	+	0.589894i	$0.799169\pi$
$812$		0			0
$813$	−16.5016	−	7.05250i	−0.578736	−	0.247342i
$814$		0			0
$815$	−14.6998			−0.514910
$816$		0			0
$817$		−	29.9353i		−	1.04730i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			54.1696i			1.89053i	0.326299	+	0.945267i	$0.394198\pi$
$821$			54.1696i			1.89053i	−0.326299	+	0.945267i	$0.605802\pi$
$822$		0			0
$823$	28.5390			0.994808			0.497404	−	0.867519i	$-0.334287\pi$
$823$	28.5390			0.994808			0.497404	+	0.867519i	$0.334287\pi$
$824$		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
$829$	−1.92557	−	1.11173i	−0.0668777	−	0.0386119i	0.466188	−	0.884686i	$-0.345627\pi$
$829$	−1.92557	−	1.11173i	−0.0668777	−	0.0386119i	−0.533066	+	0.846074i	$0.678960\pi$
$830$		0			0
$831$	8.09128	−	18.9321i	0.280684	−	0.656749i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−33.9335			−1.17432
$836$		0			0
$837$	−13.2433	−	35.2765i	−0.457755	−	1.21933i
$838$		0			0
$839$	27.8383	−	48.2173i	0.961084	−	1.66465i	0.241297	−	0.970451i	$-0.422427\pi$
$839$	27.8383	−	48.2173i	0.961084	−	1.66465i	0.719787	−	0.694195i	$-0.244240\pi$
$840$		0			0
$841$	21.1955	+	36.7116i	0.730878	+	1.26592i
$842$		0			0
$843$	2.88390	+	23.9753i	0.0993267	+	0.825752i
$844$		0			0
$845$	25.1935	+	43.6364i	0.866683	+	1.50114i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.51399	+	2.63445i	−0.120600	+	0.0904140i
$850$		0			0
$851$			19.9530i			0.683980i
$852$		0			0
$853$	16.2574	+	9.38622i	0.556643	+	0.321378i	0.751797	−	0.659395i	$-0.229187\pi$
$853$	16.2574	+	9.38622i	0.556643	+	0.321378i	−0.195154	+	0.980773i	$0.562521\pi$
$854$		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	0.231328	−	0.972876i	$-0.425693\pi$
$859$	−14.5237	−	8.38527i	−0.495543	−	0.286102i	−0.726871	+	0.686774i	$0.759026\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.2235	−	16.8722i	0.994778	−	0.574335i	0.0880791	−	0.996113i	$-0.471927\pi$
$863$	29.2235	−	16.8722i	0.994778	−	0.574335i	0.906699	+	0.421778i	$0.138594\pi$
$864$		0			0
$865$	−27.4164	+	47.4866i	−0.932186	+	1.61459i
$866$		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
$873$	−8.36478	+	7.99855i	−0.283105	+	0.270710i
$874$		0			0
$875$		0			0
$876$		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
$879$	−5.38420	+	12.5981i	−0.181605	+	0.424922i
$880$		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
$885$	32.8138	−	3.94705i	1.10302	−	0.132679i
$886$		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
$889$		0			0
$890$		0			0
$891$	−12.7928	−	0.572912i	−0.428576	−	0.0191933i
$892$		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
$899$	30.6355	−	53.0623i	1.02175	−	1.76973i
$900$		0			0
$901$	1.59740	−	0.922259i	0.0532171	−	0.0307249i
$902$		0			0
$903$		0			0
$904$		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	0.614377	−	0.789013i	$-0.289408\pi$
$911$	7.19133	+	4.15192i	0.238260	+	0.137559i	−0.376117	+	0.926572i	$0.622741\pi$
$912$		0			0
$913$			2.76674i			0.0915658i
$914$		0			0
$915$	−6.50416	−	54.0723i	−0.215021	−	1.78757i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.5554	+	32.1388i	0.612085	+	1.06016i	0.990889	+	0.134685i	$0.0430021\pi$
$919$	18.5554	+	32.1388i	0.612085	+	1.06016i	−0.378804	+	0.925477i	$0.623665\pi$
$920$		0			0
$921$	19.3568	−	14.5118i	0.637828	−	0.478180i
$922$		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
$927$	−14.9305	+	14.2769i	−0.490383	+	0.468914i
$928$		0			0
$929$	7.88987			0.258858			0.129429	−	0.991589i	$-0.458686\pi$
$929$	7.88987			0.258858			0.129429	+	0.991589i	$0.458686\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−33.9042	−	45.2237i	−1.10998	−	1.48056i
$934$		0			0
$935$	−1.91370	−	1.10488i	−0.0625848	−	0.0361333i
$936$		0			0
$937$		−	13.2688i		−	0.433472i	−0.976230	−	0.216736i	$-0.930459\pi$
$937$		−	13.2688i		−	0.433472i	0.976230	−	0.216736i	$-0.0695411\pi$
$938$		0			0
$939$	21.7807	−	16.3290i	0.710787	−	0.532878i
$940$		0			0
$941$	−7.92922			−0.258485			−0.129243	−	0.991613i	$-0.541255\pi$
$941$	−7.92922			−0.258485			−0.129243	+	0.991613i	$0.541255\pi$
$942$		0			0
$943$		−	12.3229i		−	0.401288i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			30.9635i			1.00618i	0.864235	+	0.503089i	$0.167803\pi$
$947$			30.9635i			1.00618i	−0.864235	+	0.503089i	$0.832197\pi$
$948$		0			0
$949$	9.36029			0.303848
$950$		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
$955$	4.59428	+	2.65251i	0.148668	+	0.0858332i
$956$		0			0
$957$	−12.4906	−	16.6607i	−0.403762	−	0.538564i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−21.5856			−0.696311
$962$		0			0
$963$	−8.08390	−	33.1165i	−0.260500	−	1.06717i
$964$		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
$969$	−2.55737	+	1.91726i	−0.0821544	+	0.0615913i
$970$		0			0
$971$	4.91896	+	8.51988i	0.157857	+	0.273416i	0.934096	−	0.357023i	$-0.116208\pi$
$971$	4.91896	+	8.51988i	0.157857	+	0.273416i	−0.776239	+	0.630439i	$0.782875\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.54580	+	21.1645i	0.0815308	+	0.677806i
$976$		0			0
$977$		−	33.5274i		−	1.07264i	−0.844016	−	0.536318i	$-0.819815\pi$
$977$		−	33.5274i		−	1.07264i	0.844016	−	0.536318i	$-0.180185\pi$
$978$		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
$987$		0			0
$988$		0			0
$989$	−30.0138	+	17.3285i	−0.954382	+	0.551013i
$990$		0			0
$991$	26.5005	−	45.9003i	0.841818	−	1.45807i	−0.0465389	−	0.998916i	$-0.514819\pi$
$991$	26.5005	−	45.9003i	0.841818	−	1.45807i	0.888357	−	0.459154i	$-0.151848\pi$
$992$		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	−0.615115	−	0.788437i	$-0.710890\pi$
$997$	−7.57384	+	4.37276i	−0.239866	+	0.138487i	0.375249	+	0.926924i	$0.377557\pi$
$998$		0			0
$999$	−13.9060	−	11.4319i	−0.439966	−	0.361690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.a.1109.2		16
3.2	odd	2		5292.2.w.a.521.1		16
7.2	even	3		1764.2.bm.b.1685.8		16
7.3	odd	6		252.2.x.a.209.5	yes	16
7.4	even	3		252.2.x.a.209.4	yes	16
7.5	odd	6		1764.2.bm.b.1685.1		16
7.6	odd	2	inner	1764.2.w.a.1109.7		16
9.4	even	3		5292.2.bm.b.2285.1		16
9.5	odd	6		1764.2.bm.b.1697.1		16
21.2	odd	6		5292.2.bm.b.4625.8		16
21.5	even	6		5292.2.bm.b.4625.1		16
21.11	odd	6		756.2.x.a.629.1		16
21.17	even	6		756.2.x.a.629.8		16
21.20	even	2		5292.2.w.a.521.8		16
28.3	even	6		1008.2.cc.c.209.4		16
28.11	odd	6		1008.2.cc.c.209.5		16
63.4	even	3		756.2.x.a.125.8		16
63.5	even	6	inner	1764.2.w.a.509.2		16
63.11	odd	6		2268.2.f.b.1133.16		16
63.13	odd	6		5292.2.bm.b.2285.8		16
63.23	odd	6	inner	1764.2.w.a.509.7		16
63.25	even	3		2268.2.f.b.1133.2		16
63.31	odd	6		756.2.x.a.125.1		16
63.32	odd	6		252.2.x.a.41.5	yes	16
63.38	even	6		2268.2.f.b.1133.1		16
63.40	odd	6		5292.2.w.a.1097.1		16
63.41	even	6		1764.2.bm.b.1697.8		16
63.52	odd	6		2268.2.f.b.1133.15		16
63.58	even	3		5292.2.w.a.1097.8		16
63.59	even	6		252.2.x.a.41.4	✓	16
84.11	even	6		3024.2.cc.c.2897.1		16
84.59	odd	6		3024.2.cc.c.2897.8		16
252.31	even	6		3024.2.cc.c.881.1		16
252.59	odd	6		1008.2.cc.c.545.5		16
252.67	odd	6		3024.2.cc.c.881.8		16
252.95	even	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	63.59	even	6
252.2.x.a.41.5	yes	16	63.32	odd	6
252.2.x.a.209.4	yes	16	7.4	even	3
252.2.x.a.209.5	yes	16	7.3	odd	6
756.2.x.a.125.1		16	63.31	odd	6
756.2.x.a.125.8		16	63.4	even	3
756.2.x.a.629.1		16	21.11	odd	6
756.2.x.a.629.8		16	21.17	even	6
1008.2.cc.c.209.4		16	28.3	even	6
1008.2.cc.c.209.5		16	28.11	odd	6
1008.2.cc.c.545.4		16	252.95	even	6
1008.2.cc.c.545.5		16	252.59	odd	6
1764.2.w.a.509.2		16	63.5	even	6	inner
1764.2.w.a.509.7		16	63.23	odd	6	inner
1764.2.w.a.1109.2		16	1.1	even	1	trivial
1764.2.w.a.1109.7		16	7.6	odd	2	inner
1764.2.bm.b.1685.1		16	7.5	odd	6
1764.2.bm.b.1685.8		16	7.2	even	3
1764.2.bm.b.1697.1		16	9.5	odd	6
1764.2.bm.b.1697.8		16	63.41	even	6
2268.2.f.b.1133.1		16	63.38	even	6
2268.2.f.b.1133.2		16	63.25	even	3
2268.2.f.b.1133.15		16	63.52	odd	6
2268.2.f.b.1133.16		16	63.11	odd	6
3024.2.cc.c.881.1		16	252.31	even	6
3024.2.cc.c.881.8		16	252.67	odd	6
3024.2.cc.c.2897.1		16	84.11	even	6
3024.2.cc.c.2897.8		16	84.59	odd	6
5292.2.w.a.521.1		16	3.2	odd	2
5292.2.w.a.521.8		16	21.20	even	2
5292.2.w.a.1097.1		16	63.40	odd	6
5292.2.w.a.1097.8		16	63.58	even	3
5292.2.bm.b.2285.1		16	9.4	even	3
5292.2.bm.b.2285.8		16	63.13	odd	6
5292.2.bm.b.4625.1		16	21.5	even	6
5292.2.bm.b.4625.8		16	21.2	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03897 - 1.38584i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-0.841101 + 2.87968i) q^{9} +O(q^{10})\)	\(q+(-1.03897 - 1.38584i) q^{3} +(2.09336 - 3.62580i) q^{5} +(-0.841101 + 2.87968i) q^{9} +(1.23222 - 0.711425i) q^{11} +(0.850739 - 0.491174i) q^{13} +(-7.19970 + 0.866025i) q^{15} +(0.185474 - 0.321250i) q^{17} +(4.30823 - 2.48736i) q^{19} +(-4.98775 - 2.87968i) q^{23} +(-6.26427 - 10.8500i) q^{25} +(4.86465 - 1.82626i) q^{27} +(7.31732 + 4.22466i) q^{29} -7.25160i q^{31} +(-2.26616 - 0.968518i) q^{33} +(-1.73222 - 3.00030i) q^{37} +(-1.56458 - 0.668674i) q^{39} +(1.06981 + 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(8.68041 + 9.07785i) q^{45} -8.27085 q^{47} +(-0.637901 + 0.0767308i) q^{51} +(4.30627 + 2.48623i) q^{53} -5.95706i q^{55} +(-7.92317 - 3.38623i) q^{57} -4.55766 q^{59} +7.51035i q^{61} -4.11281i q^{65} -10.0641 q^{67} +(1.19133 + 9.90411i) q^{69} +10.9555i q^{71} +(8.25191 + 4.76424i) q^{73} +(-8.52805 + 19.9541i) q^{75} -8.51105 q^{79} +(-7.58510 - 4.84420i) q^{81} +(-0.972254 + 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(-1.74775 - 14.5299i) q^{87} +(-3.90368 - 6.76137i) q^{89} +(-10.0495 + 7.53416i) q^{93} -20.8277i q^{95} +(3.34099 + 1.92892i) q^{97} +(1.01225 + 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Introduction

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