LMFDB - Embedded newform 1764.2.bm.b.1697.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

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.bm (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			1697.8
Root			$1.71965 + 0.206851i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.b.1685.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71965 + 0.206851i) q^{3} -4.18671 q^{5} +(2.91443 + 0.711425i) q^{9} +O(q^{10})$	\(q+(1.71965 + 0.206851i) q^{3} -4.18671 q^{5} +(2.91443 + 0.711425i) q^{9} -1.42285i q^{11} +(0.850739 + 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} +(0.185474 - 0.321250i) q^{17} +(-4.30823 + 2.48736i) q^{19} -5.75936i q^{23} +12.5285 q^{25} +(4.86465 + 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(6.28007 - 3.62580i) q^{31} +(0.294318 - 2.44681i) q^{33} +(-1.73222 - 3.00030i) q^{37} +(1.36138 + 1.02063i) q^{39} +(1.06981 - 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(-12.2019 - 2.97853i) q^{45} +(4.13542 - 7.16276i) q^{47} +(0.385401 - 0.514073i) q^{51} +(-4.30627 - 2.48623i) q^{53} +5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(2.27883 + 3.94705i) q^{59} +(6.50416 + 3.75518i) q^{61} +(-3.56180 - 2.05640i) q^{65} +(5.03205 + 8.71577i) q^{67} +(1.19133 - 9.90411i) q^{69} -10.9555i q^{71} +(-8.25191 - 4.76424i) q^{73} +(21.5448 + 2.59154i) q^{75} +(4.25553 - 7.37079i) q^{79} +(7.98775 + 4.14679i) q^{81} +(-0.972254 - 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(13.4571 - 5.75136i) q^{87} +(-3.90368 - 6.76137i) q^{89} +(11.5495 - 4.93608i) q^{93} +(18.0373 - 10.4138i) q^{95} +(3.34099 - 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	1.71965	+	0.206851i	0.992843	+	0.119425i
$3$	1.71965	+	0.206851i	0.992843	+	0.119425i
$4$		0			0
$5$	−4.18671			−1.87235			−0.936177	−	0.351529i	$-0.885662\pi$
$5$	−4.18671			−1.87235			−0.936177	+	0.351529i	$0.885662\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.91443	+	0.711425i	0.971475	+	0.237142i
$10$		0			0
$11$		−	1.42285i		−	0.429005i	−0.976723	−	0.214503i	$-0.931187\pi$
$11$		−	1.42285i		−	0.429005i	0.976723	−	0.214503i	$-0.0688130\pi$
$12$		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
$17$	0.185474	−	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	−0.904788	−	0.425862i	$-0.859971\pi$
$19$	−4.30823	+	2.48736i	−0.988375	+	0.570638i	−0.0835867	+	0.996501i	$0.526638\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.75936i		−	1.20091i	−0.799659	−	0.600455i	$-0.794986\pi$
$23$		−	5.75936i		−	1.20091i	0.799659	−	0.600455i	$-0.205014\pi$
$24$		0			0
$25$	12.5285			2.50571
$26$		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	$-0.440927\pi$
$31$	6.28007	−	3.62580i	1.12793	−	0.651213i	0.943414	+	0.331616i	$0.107594\pi$
$32$		0			0
$33$	0.294318	−	2.44681i	0.0512342	−	0.425935i
$34$		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
$39$	1.36138	+	1.02063i	0.217995	+	0.163431i
$40$		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
$45$	−12.2019	−	2.97853i	−1.81895	−	0.444013i
$46$		0			0
$47$	4.13542	−	7.16276i	0.603213	−	1.04480i	−0.389118	−	0.921188i	$-0.627220\pi$
$47$	4.13542	−	7.16276i	0.603213	−	1.04480i	0.992331	−	0.123608i	$-0.0394466\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.385401	−	0.514073i	0.0539670	−	0.0719846i
$52$		0			0
$53$	−4.30627	−	2.48623i	−0.591512	−	0.341509i	0.174183	−	0.984713i	$-0.444271\pi$
$53$	−4.30627	−	2.48623i	−0.591512	−	0.341509i	−0.765695	+	0.643204i	$0.777605\pi$
$54$		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	0.975374	−	0.220558i	$-0.0707878\pi$
$59$	2.27883	+	3.94705i	0.296678	+	0.513862i	−0.678696	+	0.734420i	$0.737454\pi$
$60$		0			0
$61$	6.50416	+	3.75518i	0.832772	+	0.480801i	0.854801	−	0.518956i	$-0.173679\pi$
$61$	6.50416	+	3.75518i	0.832772	+	0.480801i	−0.0220288	+	0.999757i	$0.507013\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.56180	−	2.05640i	−0.441786	−	0.255066i
$66$		0			0
$67$	5.03205	+	8.71577i	0.614763	+	1.06480i	0.990426	+	0.138044i	$0.0440816\pi$
$67$	5.03205	+	8.71577i	0.614763	+	1.06480i	−0.375663	+	0.926756i	$0.622585\pi$
$68$		0			0
$69$	1.19133	−	9.90411i	0.143419	−	1.19231i
$70$		0			0
$71$		−	10.9555i		−	1.30018i	−0.759857	−	0.650090i	$-0.774731\pi$
$71$		−	10.9555i		−	1.30018i	0.759857	−	0.650090i	$-0.225269\pi$
$72$		0			0
$73$	−8.25191	−	4.76424i	−0.965813	−	0.557612i	−0.0678555	−	0.997695i	$-0.521616\pi$
$73$	−8.25191	−	4.76424i	−0.965813	−	0.557612i	−0.897957	+	0.440083i	$0.854949\pi$
$74$		0			0
$75$	21.5448	+	2.59154i	2.48778	+	0.299246i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.25553	−	7.37079i	0.478784	−	0.829278i	−0.520920	−	0.853606i	$-0.674411\pi$
$79$	4.25553	−	7.37079i	0.478784	−	0.829278i	0.999704	+	0.0243272i	$0.00774434\pi$
$80$		0			0
$81$	7.98775	+	4.14679i	0.887528	+	0.460754i
$82$		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
$87$	13.4571	−	5.75136i	1.44276	−	0.616610i
$88$		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
$93$	11.5495	−	4.93608i	1.19763	−	0.511848i
$94$		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
$101$	−9.01274			−0.896801			−0.448401	−	0.893833i	$-0.648006\pi$
$101$	−9.01274			−0.896801			−0.448401	+	0.893833i	$0.648006\pi$
$102$		0			0
$103$			6.88598i			0.678495i	0.940697	+	0.339248i	$0.110172\pi$
$103$			6.88598i			0.678495i	−0.940697	+	0.339248i	$0.889828\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.84062	−	5.68149i	0.951329	−	0.549250i	0.0578356	−	0.998326i	$-0.481580\pi$
$107$	9.84062	−	5.68149i	0.951329	−	0.549250i	0.893494	+	0.449076i	$0.148247\pi$
$108$		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	0.598602	−	0.801046i	$-0.295723\pi$
$113$	2.17043	+	1.25310i	0.204177	+	0.117881i	−0.394426	+	0.918928i	$0.629056\pi$
$114$		0			0
$115$			24.1128i			2.24853i
$116$		0			0
$117$	2.12998	+	2.03673i	0.196917	+	0.188295i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.97550			0.815955
$122$		0			0
$123$	2.22300	−	2.96518i	0.200441	−	0.267361i
$124$		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
$129$	4.09604	+	9.58401i	0.360637	+	0.843825i
$130$		0			0
$131$	−8.65182			−0.755913			−0.377957	−	0.925823i	$-0.623373\pi$
$131$	−8.65182			−0.755913			−0.377957	+	0.925823i	$0.623373\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−20.3669	−	7.64601i	−1.75290	−	0.658064i
$136$		0			0
$137$			11.6594i			0.996131i	0.867139	+	0.498065i	$0.165956\pi$
$137$			11.6594i			0.996131i	−0.867139	+	0.498065i	$0.834044\pi$
$138$		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
$143$	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
$149$			15.4758i			1.26783i	0.773405	+	0.633913i	$0.218552\pi$
$149$			15.4758i			1.26783i	−0.773405	+	0.633913i	$0.781448\pi$
$150$		0			0
$151$	−16.6346			−1.35371			−0.676854	−	0.736117i	$-0.736657\pi$
$151$	−16.6346			−1.35371			−0.676854	+	0.736117i	$0.736657\pi$
$152$		0			0
$153$	0.769094	−	0.804308i	0.0621776	−	0.0650244i
$154$		0			0
$155$	−26.2928	+	15.1802i	−2.11189	+	1.21930i
$156$		0			0
$157$	14.5559	−	8.40387i	1.16169	−	0.670702i	0.209981	−	0.977705i	$-0.432660\pi$
$157$	14.5559	−	8.40387i	1.16169	−	0.670702i	0.951708	+	0.307004i	$0.0993264\pi$
$158$		0			0
$159$	−6.89102	−	5.16621i	−0.546493	−	0.409707i
$160$		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
$165$	−1.23222	+	10.2441i	−0.0959285	+	0.797501i
$166$		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
$171$	−14.3256	+	4.18423i	−1.09550	+	0.319976i
$172$		0			0
$173$	6.54844	−	11.3422i	0.497868	−	0.862334i	−0.502128	−	0.864793i	$-0.667450\pi$
$173$	6.54844	−	11.3422i	0.497868	−	0.862334i	0.999997	+	0.00245951i	$0.000782886\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.10235	+	7.25894i	0.233187	+	0.545615i
$178$		0			0
$179$	11.0140	+	6.35893i	0.823225	+	0.475289i	0.851527	−	0.524310i	$-0.175677\pi$
$179$	11.0140	+	6.35893i	0.823225	+	0.475289i	−0.0283026	+	0.999599i	$0.509010\pi$
$180$		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
$189$		0			0
$190$		0			0
$191$	1.09735	+	0.633555i	0.0794014	+	0.0458424i	0.539175	−	0.842194i	$-0.318736\pi$
$191$	1.09735	+	0.633555i	0.0794014	+	0.0458424i	−0.459774	+	0.888036i	$0.652069\pi$
$192$		0			0
$193$	−9.31732	−	16.1381i	−0.670676	−	1.16164i	−0.977713	−	0.209947i	$-0.932671\pi$
$193$	−9.31732	−	16.1381i	−0.670676	−	1.16164i	0.307037	−	0.951697i	$-0.400662\pi$
$194$		0			0
$195$	−5.69969	−	4.27307i	−0.408163	−	0.306001i
$196$		0			0
$197$			5.94312i			0.423430i	0.977331	+	0.211715i	$0.0679049\pi$
$197$			5.94312i			0.423430i	−0.977331	+	0.211715i	$0.932095\pi$
$198$		0			0
$199$	−4.87291	−	2.81337i	−0.345431	−	0.199435i	0.317240	−	0.948345i	$-0.397244\pi$
$199$	−4.87291	−	2.81337i	−0.345431	−	0.199435i	−0.662671	+	0.748910i	$0.730577\pi$
$200$		0			0
$201$	6.85052	+	16.0290i	0.483199	+	1.13060i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.47900	+	7.75786i	−0.312827	+	0.541832i
$206$		0			0
$207$	4.09735	−	16.7852i	0.284785	−	1.16665i
$208$		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
$213$	2.26616	−	18.8397i	0.155275	−	1.29087i
$214$		0			0
$215$	−12.5968	−	21.8182i	−0.859092	−	1.48799i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−13.2049	−	9.89976i	−0.892307	−	0.668964i
$220$		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
$227$	−11.4473			−0.759783			−0.379892	−	0.925031i	$-0.624039\pi$
$227$	−11.4473			−0.759783			−0.379892	+	0.925031i	$0.624039\pi$
$228$		0			0
$229$		−	5.64298i		−	0.372899i	−0.982465	−	0.186449i	$-0.940302\pi$
$229$		−	5.64298i		−	0.372899i	0.982465	−	0.186449i	$-0.0596980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.7788	+	6.22316i	−0.706145	+	0.407693i	−0.809632	−	0.586938i	$-0.800333\pi$
$233$	−10.7788	+	6.22316i	−0.706145	+	0.407693i	0.103487	+	0.994631i	$0.467000\pi$
$234$		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	0.609640	−	0.792678i	$-0.291314\pi$
$239$	3.52450	+	2.03487i	0.227981	+	0.131625i	−0.381659	+	0.924303i	$0.624647\pi$
$240$		0			0
$241$		−	4.92128i		−	0.317007i	−0.987358	−	0.158504i	$-0.949333\pi$
$241$		−	4.92128i		−	0.317007i	0.987358	−	0.158504i	$-0.0506670\pi$
$242$		0			0
$243$	12.8784	+	8.78332i	0.826150	+	0.563450i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.88690			−0.310946
$248$		0			0
$249$	−1.32360	−	3.09700i	−0.0838801	−	0.196264i
$250$		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
$255$	−1.61356	+	2.15228i	−0.101045	+	0.134781i
$256$		0			0
$257$	−10.8940			−0.679551			−0.339775	−	0.940507i	$-0.610351\pi$
$257$	−10.8940			−0.679551			−0.339775	+	0.940507i	$0.610351\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	24.3313	−	7.10673i	1.50607	−	0.439895i
$262$		0			0
$263$			18.0698i			1.11423i	0.830436	+	0.557114i	$0.188092\pi$
$263$			18.0698i			1.11423i	−0.830436	+	0.557114i	$0.811908\pi$
$264$		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	−0.747125	−	0.664683i	$-0.768566\pi$
$271$	−8.97274	+	5.18041i	−0.545055	+	0.314688i	0.202070	+	0.979371i	$0.435233\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	17.8262i		−	1.07496i
$276$		0			0
$277$	−11.8869			−0.714215			−0.357107	−	0.934063i	$-0.616237\pi$
$277$	−11.8869			−0.714215			−0.357107	+	0.934063i	$0.616237\pi$
$278$		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	$-0.642655\pi$
$283$	2.19593	−	1.26782i	0.130535	−	0.0753642i	0.563845	+	0.825880i	$0.309321\pi$
$284$		0			0
$285$	33.1720	−	14.1772i	1.96494	−	0.839783i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.43120	+	14.6033i	0.495953	+	0.859016i
$290$		0			0
$291$	6.14434	−	2.62599i	0.360188	−	0.153938i
$292$		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
$297$	2.59849	−	6.92166i	0.150780	−	0.401635i
$298$		0			0
$299$	2.82885	−	4.89971i	0.163596	−	0.283357i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−15.4988	−	1.86429i	−0.890383	−	0.107101i
$304$		0			0
$305$	−27.2310	−	15.7218i	−1.55924	−	0.900230i
$306$		0			0
$307$		−	13.9676i		−	0.797170i	−0.917131	−	0.398585i	$-0.869501\pi$
$307$		−	13.9676i		−	0.797170i	0.917131	−	0.398585i	$-0.130499\pi$
$308$		0			0
$309$	−1.42437	+	11.8415i	−0.0810296	+	0.673640i
$310$		0			0
$311$	−16.3163	−	28.2607i	−0.925215	−	1.60252i	−0.791215	−	0.611539i	$-0.790551\pi$
$311$	−16.3163	−	28.2607i	−0.925215	−	1.60252i	−0.134001	−	0.990981i	$-0.542782\pi$
$312$		0			0
$313$	13.6110	+	7.85832i	0.769340	+	0.444178i	0.832639	−	0.553816i	$-0.186829\pi$
$313$	13.6110	+	7.85832i	0.769340	+	0.444178i	−0.0632994	+	0.997995i	$0.520162\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.1366	+	14.5126i	1.41181	+	0.815111i	0.995559	−	0.0941377i	$-0.0300094\pi$
$317$	25.1366	+	14.5126i	1.41181	+	0.815111i	0.416254	+	0.909248i	$0.363343\pi$
$318$		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
$325$	10.6585	+	6.15370i	0.591228	+	0.341346i
$326$		0			0
$327$	16.6162	−	22.1637i	0.918876	−	1.22566i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.58510	+	11.4057i	−0.361950	+	0.626915i	−0.988282	−	0.152641i	$-0.951222\pi$
$331$	−6.58510	+	11.4057i	−0.361950	+	0.626915i	0.626332	+	0.779556i	$0.284555\pi$
$332$		0			0
$333$	−2.91395	−	9.97650i	−0.159683	−	0.546709i
$334$		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
$339$	3.47318	+	2.60385i	0.188637	+	0.141422i
$340$		0			0
$341$	−5.15896	−	8.93559i	−0.279374	−	0.483889i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4.98775	+	41.4656i	−0.268531	+	2.23243i
$346$		0			0
$347$	−21.4012	+	12.3560i	−1.14888	+	0.663305i	−0.948614	−	0.316437i	$-0.897513\pi$
$347$	−21.4012	+	12.3560i	−1.14888	+	0.663305i	−0.200264	+	0.979742i	$0.564180\pi$
$348$		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
$353$	23.3516			1.24288			0.621440	−	0.783462i	$-0.286548\pi$
$353$	23.3516			1.24288			0.621440	+	0.783462i	$0.286548\pi$
$354$		0			0
$355$			45.8676i			2.43440i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.3902	+	10.6176i	−0.970596	+	0.560374i	−0.899418	−	0.437090i	$-0.856009\pi$
$359$	−18.3902	+	10.6176i	−0.970596	+	0.560374i	−0.0711782	+	0.997464i	$0.522676\pi$
$360$		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
$367$		−	13.8769i		−	0.724370i	−0.932106	−	0.362185i	$-0.882031\pi$
$367$		−	13.8769i		−	0.724370i	0.932106	−	0.362185i	$-0.117969\pi$
$368$		0			0
$369$	4.43614	−	4.63926i	0.230936	−	0.241510i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−32.1457			−1.66444			−0.832221	−	0.554445i	$-0.812931\pi$
$373$	−32.1457			−1.66444			−0.832221	+	0.554445i	$0.812931\pi$
$374$		0			0
$375$	−54.2033	−	6.51991i	−2.79904	−	0.336687i
$376$		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
$381$	−3.28695	−	0.395375i	−0.168395	−	0.0202557i
$382$		0			0
$383$	1.57633			0.0805469			0.0402734	−	0.999189i	$-0.487177\pi$
$383$	1.57633			0.0805469			0.0402734	+	0.999189i	$0.487177\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.06132	+	17.3285i	0.257281	+	0.880855i
$388$		0			0
$389$			11.2519i			0.570496i	0.958454	+	0.285248i	$0.0920760\pi$
$389$			11.2519i			0.570496i	−0.958454	+	0.285248i	$0.907924\pi$
$390$		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	−0.486181	−	0.873858i	$-0.661611\pi$
$397$	0.548160	−	0.316480i	0.0275114	−	0.0158837i	0.513693	+	0.857974i	$0.328277\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	8.52206i		−	0.425571i	−0.977099	−	0.212786i	$-0.931746\pi$
$401$		−	8.52206i		−	0.425571i	0.977099	−	0.212786i	$-0.0682536\pi$
$402$		0			0
$403$	7.12359			0.354851
$404$		0			0
$405$	−33.4424	−	17.3614i	−1.66177	−	0.862695i
$406$		0			0
$407$	−4.26897	+	2.46469i	−0.211605	+	0.122170i
$408$		0			0
$409$	12.1822	−	7.03338i	0.602370	−	0.347778i	−0.167603	−	0.985855i	$-0.553603\pi$
$409$	12.1822	−	7.03338i	0.602370	−	0.347778i	0.769973	+	0.638076i	$0.220269\pi$
$410$		0			0
$411$	−2.41176	+	20.0502i	−0.118963	+	0.989002i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.07054	+	7.05039i	0.199815	+	0.346090i
$416$		0			0
$417$	7.72372	+	5.79049i	0.378232	+	0.283561i
$418$		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
$423$	17.1481	−	17.9333i	0.833771	−	0.871947i
$424$		0			0
$425$	2.32371	−	4.02479i	0.112717	−	0.195231i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	1.45220	−	1.93703i	0.0701127	−	0.0935209i
$430$		0			0
$431$	−17.2686	−	9.97000i	−0.831797	−	0.480238i	0.0226706	−	0.999743i	$-0.492783\pi$
$431$	−17.2686	−	9.97000i	−0.831797	−	0.480238i	−0.854468	+	0.519505i	$0.826116\pi$
$432$		0			0
$433$			20.2826i			0.974719i	0.873201	+	0.487359i	$0.162040\pi$
$433$			20.2826i			0.974719i	−0.873201	+	0.487359i	$0.837960\pi$
$434$		0			0
$435$	−56.3412	+	24.0793i	−2.70135	+	1.15451i
$436$		0			0
$437$	14.3256	+	24.8126i	0.685285	+	1.18695i
$438$		0			0
$439$	−24.5936	−	14.1991i	−1.17379	−	0.677687i	−0.219219	−	0.975676i	$-0.570351\pi$
$439$	−24.5936	−	14.1991i	−1.17379	−	0.677687i	−0.954569	+	0.297989i	$0.903684\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.6570	−	6.15281i	−0.506328	−	0.292329i	0.224995	−	0.974360i	$-0.427764\pi$
$443$	−10.6570	−	6.15281i	−0.506328	−	0.292329i	−0.731323	+	0.682031i	$0.761097\pi$
$444$		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
$451$	−2.63650	−	1.52218i	−0.124148	−	0.0716769i
$452$		0			0
$453$	−28.6058	−	3.44089i	−1.34402	−	0.161667i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.20892	−	7.29007i	0.196885	−	0.341015i	−0.750632	−	0.660721i	$-0.770251\pi$
$457$	4.20892	−	7.29007i	0.196885	−	0.341015i	0.947517	+	0.319706i	$0.103584\pi$
$458$		0			0
$459$	1.48895	−	1.22404i	0.0694981	−	0.0571335i
$460$		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
$465$	−48.3546	+	20.6660i	−2.24239	+	0.958361i
$466$		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
$471$	26.7695	−	11.4408i	1.23347	−	0.527166i
$472$		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
$479$	28.5551			1.30471			0.652357	−	0.757912i	$-0.273780\pi$
$479$	28.5551			1.30471			0.652357	+	0.757912i	$0.273780\pi$
$480$		0			0
$481$		−	3.40329i		−	0.155177i
$482$		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	0.979458	−	0.201649i	$-0.0646301\pi$
$491$	28.6854	+	16.5615i	1.29455	+	0.747411i	0.315096	+	0.949060i	$0.397963\pi$
$492$		0			0
$493$		−	3.13425i		−	0.141160i
$494$		0			0
$495$	−4.23800	+	17.3614i	−0.190484	+	0.780337i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.55305			−0.293355			−0.146677	−	0.989184i	$-0.546858\pi$
$499$	−6.55305			−0.293355			−0.146677	+	0.989184i	$0.546858\pi$
$500$		0			0
$501$	−8.42087	+	11.2323i	−0.376217	+	0.501822i
$502$		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
$507$	−8.19209	−	19.1680i	−0.363823	−	0.851281i
$508$		0			0
$509$	6.60474			0.292750			0.146375	−	0.989229i	$-0.453239\pi$
$509$	6.60474			0.292750			0.146375	+	0.989229i	$0.453239\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−25.5005	+	4.23218i	−1.12588	+	0.186855i
$514$		0			0
$515$		−	28.8296i		−	1.27038i
$516$		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	−0.260491	−	0.965476i	$-0.583884\pi$
$523$	10.1857	−	5.88074i	0.445391	−	0.257147i	0.705882	+	0.708330i	$0.250551\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.68996i		−	0.117176i
$528$		0			0
$529$	−10.1702			−0.442183
$530$		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
$537$	17.6249	+	13.2134i	0.760571	+	0.570201i
$538$		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
$543$	−5.49227	+	45.6600i	−0.235696	+	1.95946i
$544$		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
$549$	16.2844	+	15.5714i	0.694999	+	0.664571i
$550$		0			0
$551$	−21.0165	+	36.4016i	−0.895331	+	1.55076i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	9.87315	+	23.1014i	0.419092	+	0.980600i
$556$		0			0
$557$	−37.1935	−	21.4737i	−1.57594	−	0.909869i	−0.995418	−	0.0956241i	$-0.969515\pi$
$557$	−37.1935	−	21.4737i	−1.57594	−	0.909869i	−0.580522	−	0.814245i	$-0.697151\pi$
$558$		0			0
$559$			5.91128i			0.250020i
$560$		0			0
$561$	−0.731449	−	0.548368i	−0.0308818	−	0.0231521i
$562$		0			0
$563$	−15.9454	−	27.6182i	−0.672019	−	1.16397i	−0.977331	−	0.211718i	$-0.932094\pi$
$563$	−15.9454	−	27.6182i	−0.672019	−	1.16397i	0.305312	−	0.952252i	$-0.401239\pi$
$564$		0			0
$565$	−9.08695	−	5.24635i	−0.382291	−	0.220716i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.428895	−	0.247623i	−0.0179802	−	0.0103809i	0.490983	−	0.871169i	$-0.336638\pi$
$569$	−0.428895	−	0.247623i	−0.0179802	−	0.0103809i	−0.508963	+	0.860788i	$0.669971\pi$
$570$		0			0
$571$	−1.34182	−	2.32411i	−0.0561535	−	0.0972608i	0.836582	−	0.547841i	$-0.184550\pi$
$571$	−1.34182	−	2.32411i	−0.0561535	−	0.0972608i	−0.892736	+	0.450581i	$0.851217\pi$
$572$		0			0
$573$	1.75601	+	1.31648i	0.0733584	+	0.0549969i
$574$		0			0
$575$		−	72.1564i		−	3.00913i
$576$		0			0
$577$	36.3955	+	21.0130i	1.51517	+	0.874781i	0.999842	+	0.0177861i	$0.00566180\pi$
$577$	36.3955	+	21.0130i	1.51517	+	0.874781i	0.515324	+	0.856995i	$0.327672\pi$
$578$		0			0
$579$	−12.6844	−	29.6792i	−0.527146	−	1.23343i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.53753	+	6.12717i	−0.146509	+	0.253762i
$584$		0			0
$585$	−8.91761	−	8.52719i	−0.368698	−	0.352556i
$586$		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
$591$	−1.22934	+	10.2201i	−0.0505683	+	0.420400i
$592$		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
$597$	−7.79777	−	5.84600i	−0.319141	−	0.239261i
$598$		0			0
$599$	−6.71186	+	3.87510i	−0.274239	+	0.158332i	−0.630813	−	0.775935i	$-0.717278\pi$
$599$	−6.71186	+	3.87510i	−0.274239	+	0.158332i	0.356573	+	0.934267i	$0.383945\pi$
$600$		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
$605$	−37.5778			−1.52776
$606$		0			0
$607$			13.5208i			0.548794i	0.961616	+	0.274397i	$0.0884783\pi$
$607$			13.5208i			0.548794i	−0.961616	+	0.274397i	$0.911522\pi$
$608$		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	0.602939	−	0.797787i	$-0.293996\pi$
$617$	5.30333	+	3.06188i	0.213504	+	0.123267i	−0.389435	+	0.921054i	$0.627330\pi$
$618$		0			0
$619$		−	5.70784i		−	0.229417i	−0.993399	−	0.114709i	$-0.963407\pi$
$619$		−	5.70784i		−	0.229417i	0.993399	−	0.114709i	$-0.0365935\pi$
$620$		0			0
$621$	10.5181	−	28.0172i	0.422075	−	1.12429i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	69.3218			2.77287
$626$		0			0
$627$	4.81810	+	11.2735i	0.192416	+	0.450220i
$628$		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
$633$	2.18816	−	2.91871i	0.0869716	−	0.116008i
$634$		0			0
$635$	8.00247			0.317569
$636$		0			0
$637$		0			0
$638$		0			0
$639$	7.79402	−	31.9290i	0.308327	−	1.26309i
$640$		0			0
$641$			15.3367i			0.605764i	0.953028	+	0.302882i	$0.0979489\pi$
$641$			15.3367i			0.605764i	−0.953028	+	0.302882i	$0.902051\pi$
$642$		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
$647$	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
$653$			27.2660i			1.06700i	0.845799	+	0.533501i	$0.179124\pi$
$653$			27.2660i			1.06700i	−0.845799	+	0.533501i	$0.820876\pi$
$654$		0			0
$655$	36.2227			1.41534
$656$		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	−0.587105	+	0.809511i	$0.699732\pi$
$661$	−40.6657	+	23.4784i	−1.58171	+	0.913203i	−0.994609	+	0.103692i	$0.966934\pi$
$662$		0			0
$663$	0.580375	−	0.248043i	0.0225399	−	0.00963318i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.3313	−	42.1431i	−0.942112	−	1.63179i
$668$		0			0
$669$	−10.1582	+	4.34143i	−0.392738	+	0.167850i
$670$		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
$675$	60.9470	+	22.8803i	2.34585	+	0.880665i
$676$		0			0
$677$	9.07869	−	15.7248i	0.348922	−	0.604351i	−0.637136	−	0.770751i	$-0.719881\pi$
$677$	9.07869	−	15.7248i	0.348922	−	0.604351i	0.986058	+	0.166400i	$0.0532143\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−19.6854	−	2.36788i	−0.754346	−	0.0907375i
$682$		0			0
$683$	17.4866	+	10.0959i	0.669104	+	0.386308i	0.795737	−	0.605642i	$-0.207084\pi$
$683$	17.4866	+	10.0959i	0.669104	+	0.386308i	−0.126633	+	0.991950i	$0.540417\pi$
$684$		0			0
$685$		−	48.8146i		−	1.86511i
$686$		0			0
$687$	1.16726	−	9.70398i	0.0445336	−	0.370230i
$688$		0			0
$689$	−2.44234	−	4.23026i	−0.0930458	−	0.161160i
$690$		0			0
$691$	−0.0695792	−	0.0401716i	−0.00264692	−	0.00152820i	0.498676	−	0.866788i	$-0.333820\pi$
$691$	−0.0695792	−	0.0401716i	−0.00264692	−	0.00152820i	−0.501323	+	0.865260i	$0.667153\pi$
$692$		0			0
$693$		0			0
$694$		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
$703$	14.9256	+	8.61731i	0.562930	+	0.325008i
$704$		0			0
$705$	−35.9769	+	47.9883i	−1.35497	+	1.80735i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.782968	+	1.35614i	−0.0294050	+	0.0509309i	−0.880353	−	0.474318i	$-0.842695\pi$
$709$	−0.782968	+	1.35614i	−0.0294050	+	0.0509309i	0.850948	+	0.525249i	$0.176028\pi$
$710$		0			0
$711$	17.6462	−	18.4541i	0.661783	−	0.692084i
$712$		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
$717$	5.64001	+	4.22832i	0.210630	+	0.157910i
$718$		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
$723$	1.01797	−	8.46290i	0.0378588	−	0.314739i
$724$		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
$731$	2.23217			0.0825599
$732$		0			0
$733$		−	23.2565i		−	0.859000i	−0.903067	−	0.429500i	$-0.858690\pi$
$733$		−	23.2565i		−	0.859000i	0.903067	−	0.429500i	$-0.141310\pi$
$734$		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	0.613447	−	0.789736i	$-0.289783\pi$
$743$	6.43940	+	3.71779i	0.236239	+	0.136392i	−0.377208	+	0.926129i	$0.623116\pi$
$744$		0			0
$745$		−	64.7926i		−	2.37382i
$746$		0			0
$747$	−1.63553	−	5.59956i	−0.0598408	−	0.204877i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.35595			0.268423			0.134211	−	0.990953i	$-0.457150\pi$
$751$	7.35595			0.268423			0.134211	+	0.990953i	$0.457150\pi$
$752$		0			0
$753$	7.99674	+	0.961899i	0.291418	+	0.0350536i
$754$		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
$759$	−14.0921	−	1.69508i	−0.511509	−	0.0615276i
$760$		0			0
$761$	43.4407			1.57472			0.787362	−	0.616492i	$-0.211447\pi$
$761$	43.4407			1.57472			0.787362	+	0.616492i	$0.211447\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.21997	+	3.36740i	−0.116418	+	0.121749i
$766$		0			0
$767$			4.47721i			0.161663i
$768$		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
$773$	−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
$779$			10.6440i			0.381362i
$780$		0			0
$781$	−15.5880			−0.557784
$782$		0			0
$783$	43.3115	−	7.18816i	1.54783	−	0.256884i
$784$		0			0
$785$	−60.9415	+	35.1846i	−2.17509	+	1.25579i
$786$		0			0
$787$	11.4291	−	6.59861i	0.407405	−	0.235215i	−0.282269	−	0.959335i	$-0.591087\pi$
$787$	11.4291	−	6.59861i	0.407405	−	0.235215i	0.689674	+	0.724120i	$0.257754\pi$
$788$		0			0
$789$	−3.73775	+	31.0737i	−0.133067	+	1.10625i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.68889	+	6.38935i	0.130996	+	0.226892i
$794$		0			0
$795$	28.8507	+	21.6294i	1.02323	+	0.767116i
$796$		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
$801$	−6.56677	−	22.4827i	−0.232025	−	0.794386i
$802$		0			0
$803$	−6.77880	+	11.7412i	−0.239219	+	0.414339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.10038	−	4.13548i	0.109138	−	0.145576i
$808$		0			0
$809$	24.4123	+	14.0944i	0.858290	+	0.495534i	0.863439	−	0.504453i	$-0.168306\pi$
$809$	24.4123	+	14.0944i	0.858290	+	0.495534i	−0.00514934	+	0.999987i	$0.501639\pi$
$810$		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
$819$		0			0
$820$		0			0
$821$	46.9123	+	27.0848i	1.63725	+	0.945267i	0.981774	+	0.190050i	$0.0608650\pi$
$821$	46.9123	+	27.0848i	1.63725	+	0.945267i	0.655475	+	0.755217i	$0.272468\pi$
$822$		0			0
$823$	−14.2695	−	24.7155i	−0.497404	−	0.861529i	0.502591	−	0.864524i	$-0.332380\pi$
$823$	−14.2695	−	24.7155i	−0.497404	−	0.861529i	−0.999996	+	0.00299479i	$0.999047\pi$
$824$		0			0
$825$	3.68738	−	30.6550i	0.128378	−	1.06727i
$826$		0			0
$827$			37.2062i			1.29379i	0.762581	+	0.646893i	$0.223932\pi$
$827$			37.2062i			1.29379i	−0.762581	+	0.646893i	$0.776068\pi$
$828$		0			0
$829$	1.92557	+	1.11173i	0.0668777	+	0.0386119i	0.533066	−	0.846074i	$-0.321040\pi$
$829$	1.92557	+	1.11173i	0.0668777	+	0.0386119i	−0.466188	+	0.884686i	$0.654373\pi$
$830$		0			0
$831$	−20.4414	−	2.45882i	−0.709103	−	0.0852954i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	16.9668	−	29.3873i	0.587159	−	1.01699i
$836$		0			0
$837$	37.1719	−	6.16921i	1.28485	−	0.213239i
$838$		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
$843$	−22.2051	+	9.49011i	−0.764786	+	0.326857i
$844$		0			0
$845$	25.1935	+	43.6364i	0.866683	+	1.50114i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.03849	−	1.72598i	0.138601	−	0.0592356i
$850$		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
$857$	23.7032			0.809687			0.404844	−	0.914386i	$-0.367326\pi$
$857$	23.7032			0.809687			0.404844	+	0.914386i	$0.367326\pi$
$858$		0			0
$859$		−	16.7705i		−	0.572203i	−0.958199	−	0.286102i	$-0.907640\pi$
$859$		−	16.7705i		−	0.572203i	0.958199	−	0.286102i	$-0.0923595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−29.2235	+	16.8722i	−0.994778	+	0.574335i	−0.906699	−	0.421778i	$-0.861406\pi$
$863$	−29.2235	+	16.8722i	−0.994778	+	0.574335i	−0.0880791	+	0.996113i	$0.528073\pi$
$864$		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
$871$			9.88645i			0.334990i
$872$		0			0
$873$	11.1093	−	3.24483i	0.375994	−	0.109821i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.4174			−1.33103			−0.665515	−	0.746384i	$-0.731788\pi$
$877$	−39.4174			−1.33103			−0.665515	+	0.746384i	$0.731788\pi$
$878$		0			0
$879$	−8.21815	+	10.9619i	−0.277191	+	0.369735i
$880$		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
$885$	−12.9886	−	30.3911i	−0.436608	−	1.02158i
$886$		0			0
$887$	5.67776			0.190640			0.0953202	−	0.995447i	$-0.469613\pi$
$887$	5.67776			0.190640			0.0953202	+	0.995447i	$0.469613\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.90026	−	11.3654i	0.197666	−	0.380754i
$892$		0			0
$893$			41.1451i			1.37687i
$894$		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
$905$		−	111.165i		−	3.69524i
$906$		0			0
$907$	14.6548			0.486605			0.243303	−	0.969950i	$-0.421769\pi$
$907$	14.6548			0.486605			0.243303	+	0.969950i	$0.421769\pi$
$908$		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
$915$	−43.5759	−	32.6689i	−1.44057	−	1.08000i
$916$		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
$921$	2.88920	−	24.0194i	0.0952025	−	0.791465i
$922$		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
$927$	−4.89885	+	20.0687i	−0.160899	+	0.659141i
$928$		0			0
$929$	−3.94493	+	6.83283i	−0.129429	+	0.224178i	−0.923456	−	0.383705i	$-0.874648\pi$
$929$	−3.94493	+	6.83283i	−0.129429	+	0.224178i	0.794026	+	0.607883i	$0.207981\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−22.2127	−	51.9738i	−0.727212	−	1.70155i
$934$		0			0
$935$	1.91370	+	1.10488i	0.0625848	+	0.0361333i
$936$		0			0
$937$			13.2688i			0.433472i	0.976230	+	0.216736i	$0.0695411\pi$
$937$			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	0.923383	−	0.383879i	$-0.125412\pi$
$941$	3.96461	+	6.86691i	0.129243	+	0.223855i	−0.794141	+	0.607734i	$0.792079\pi$
$942$		0			0
$943$	−10.6719	−	6.16144i	−0.347526	−	0.200644i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.8152	+	15.4817i	0.871375	+	0.503089i	0.867805	−	0.496905i	$-0.165530\pi$
$947$	26.8152	+	15.4817i	0.871375	+	0.503089i	0.00357041	+	0.999994i	$0.498864\pi$
$948$		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
$955$	−4.59428	−	2.65251i	−0.148668	−	0.0858332i
$956$		0			0
$957$	−8.18332	−	19.1475i	−0.264529	−	0.618950i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	10.7928	−	18.6937i	0.348156	−	0.603023i
$962$		0			0
$963$	32.7217	−	9.55741i	1.05444	−	0.307983i
$964$		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
$969$	−0.381714	+	3.17337i	−0.0122624	+	0.101943i
$970$		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
$975$	17.0561	+	12.7870i	0.546232	+	0.409511i
$976$		0			0
$977$	29.0356	−	16.7637i	0.928930	−	0.536318i	0.0424567	−	0.999098i	$-0.486482\pi$
$977$	29.0356	−	16.7637i	0.928930	−	0.536318i	0.886473	+	0.462781i	$0.153148\pi$
$978$		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
$983$	−48.4718			−1.54601			−0.773006	−	0.634399i	$-0.781248\pi$
$983$	−48.4718			−1.54601			−0.773006	+	0.634399i	$0.781248\pi$
$984$		0			0
$985$		−	24.8821i		−	0.792811i
$986$		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
$997$			8.74551i			0.276973i	0.990364	+	0.138487i	$0.0442238\pi$
$997$			8.74551i			0.276973i	−0.990364	+	0.138487i	$0.955776\pi$
$998$		0			0
$999$	−2.94734	−	17.7589i	−0.0932497	−	0.561866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.b.1697.8		16
3.2	odd	2		5292.2.bm.b.2285.8		16
7.2	even	3		1764.2.w.a.509.2		16
7.3	odd	6		252.2.x.a.41.5	yes	16
7.4	even	3		252.2.x.a.41.4	✓	16
7.5	odd	6		1764.2.w.a.509.7		16
7.6	odd	2	inner	1764.2.bm.b.1697.1		16
9.2	odd	6		1764.2.w.a.1109.7		16
9.7	even	3		5292.2.w.a.521.8		16
21.2	odd	6		5292.2.w.a.1097.1		16
21.5	even	6		5292.2.w.a.1097.8		16
21.11	odd	6		756.2.x.a.125.1		16
21.17	even	6		756.2.x.a.125.8		16
21.20	even	2		5292.2.bm.b.2285.1		16
28.3	even	6		1008.2.cc.c.545.4		16
28.11	odd	6		1008.2.cc.c.545.5		16
63.2	odd	6	inner	1764.2.bm.b.1685.1		16
63.4	even	3		2268.2.f.b.1133.1		16
63.11	odd	6		252.2.x.a.209.5	yes	16
63.16	even	3		5292.2.bm.b.4625.1		16
63.20	even	6		1764.2.w.a.1109.2		16
63.25	even	3		756.2.x.a.629.8		16
63.31	odd	6		2268.2.f.b.1133.16		16
63.32	odd	6		2268.2.f.b.1133.15		16
63.34	odd	6		5292.2.w.a.521.1		16
63.38	even	6		252.2.x.a.209.4	yes	16
63.47	even	6	inner	1764.2.bm.b.1685.8		16
63.52	odd	6		756.2.x.a.629.1		16
63.59	even	6		2268.2.f.b.1133.2		16
63.61	odd	6		5292.2.bm.b.4625.8		16
84.11	even	6		3024.2.cc.c.881.1		16
84.59	odd	6		3024.2.cc.c.881.8		16
252.11	even	6		1008.2.cc.c.209.4		16
252.115	even	6		3024.2.cc.c.2897.1		16
252.151	odd	6		3024.2.cc.c.2897.8		16
252.227	odd	6		1008.2.cc.c.209.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.4	✓	16	7.4	even	3
252.2.x.a.41.5	yes	16	7.3	odd	6
252.2.x.a.209.4	yes	16	63.38	even	6
252.2.x.a.209.5	yes	16	63.11	odd	6
756.2.x.a.125.1		16	21.11	odd	6
756.2.x.a.125.8		16	21.17	even	6
756.2.x.a.629.1		16	63.52	odd	6
756.2.x.a.629.8		16	63.25	even	3
1008.2.cc.c.209.4		16	252.11	even	6
1008.2.cc.c.209.5		16	252.227	odd	6
1008.2.cc.c.545.4		16	28.3	even	6
1008.2.cc.c.545.5		16	28.11	odd	6
1764.2.w.a.509.2		16	7.2	even	3
1764.2.w.a.509.7		16	7.5	odd	6
1764.2.w.a.1109.2		16	63.20	even	6
1764.2.w.a.1109.7		16	9.2	odd	6
1764.2.bm.b.1685.1		16	63.2	odd	6	inner
1764.2.bm.b.1685.8		16	63.47	even	6	inner
1764.2.bm.b.1697.1		16	7.6	odd	2	inner
1764.2.bm.b.1697.8		16	1.1	even	1	trivial
2268.2.f.b.1133.1		16	63.4	even	3
2268.2.f.b.1133.2		16	63.59	even	6
2268.2.f.b.1133.15		16	63.32	odd	6
2268.2.f.b.1133.16		16	63.31	odd	6
3024.2.cc.c.881.1		16	84.11	even	6
3024.2.cc.c.881.8		16	84.59	odd	6
3024.2.cc.c.2897.1		16	252.115	even	6
3024.2.cc.c.2897.8		16	252.151	odd	6
5292.2.w.a.521.1		16	63.34	odd	6
5292.2.w.a.521.8		16	9.7	even	3
5292.2.w.a.1097.1		16	21.2	odd	6
5292.2.w.a.1097.8		16	21.5	even	6
5292.2.bm.b.2285.1		16	21.20	even	2
5292.2.bm.b.2285.8		16	3.2	odd	2
5292.2.bm.b.4625.1		16	63.16	even	3
5292.2.bm.b.4625.8		16	63.61	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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71965 + 0.206851i) q^{3} -4.18671 q^{5} +(2.91443 + 0.711425i) q^{9} +O(q^{10})\)	\(q+(1.71965 + 0.206851i) q^{3} -4.18671 q^{5} +(2.91443 + 0.711425i) q^{9} -1.42285i q^{11} +(0.850739 + 0.491174i) q^{13} +(-7.19970 - 0.866025i) q^{15} +(0.185474 - 0.321250i) q^{17} +(-4.30823 + 2.48736i) q^{19} -5.75936i q^{23} +12.5285 q^{25} +(4.86465 + 1.82626i) q^{27} +(7.31732 - 4.22466i) q^{29} +(6.28007 - 3.62580i) q^{31} +(0.294318 - 2.44681i) q^{33} +(-1.73222 - 3.00030i) q^{37} +(1.36138 + 1.02063i) q^{39} +(1.06981 - 1.85297i) q^{41} +(3.00875 + 5.21130i) q^{43} +(-12.2019 - 2.97853i) q^{45} +(4.13542 - 7.16276i) q^{47} +(0.385401 - 0.514073i) q^{51} +(-4.30627 - 2.48623i) q^{53} +5.95706i q^{55} +(-7.92317 + 3.38623i) q^{57} +(2.27883 + 3.94705i) q^{59} +(6.50416 + 3.75518i) q^{61} +(-3.56180 - 2.05640i) q^{65} +(5.03205 + 8.71577i) q^{67} +(1.19133 - 9.90411i) q^{69} -10.9555i q^{71} +(-8.25191 - 4.76424i) q^{73} +(21.5448 + 2.59154i) q^{75} +(4.25553 - 7.37079i) q^{79} +(7.98775 + 4.14679i) q^{81} +(-0.972254 - 1.68399i) q^{83} +(-0.776524 + 1.34498i) q^{85} +(13.4571 - 5.75136i) q^{87} +(-3.90368 - 6.76137i) q^{89} +(11.5495 - 4.93608i) q^{93} +(18.0373 - 10.4138i) q^{95} +(3.34099 - 1.92892i) q^{97} +(1.01225 - 4.14679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Introduction

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