LMFDB - Embedded newform 1764.2.bm.b.1685.1

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			1685.1
Root			$-1.71965 + 0.206851i$ of defining polynomial
Character	$\chi$	$=$	1764.1685
Dual form			1764.2.bm.b.1697.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71965 + 0.206851i) q^{3} +4.18671 q^{5} +(2.91443 - 0.711425i) q^{9} +O(q^{10})$	\(q+(-1.71965 + 0.206851i) q^{3} +4.18671 q^{5} +(2.91443 - 0.711425i) q^{9} +1.42285i q^{11} +(-0.850739 + 0.491174i) q^{13} +(-7.19970 + 0.866025i) q^{15} +(-0.185474 - 0.321250i) q^{17} +(4.30823 + 2.48736i) q^{19} +5.75936i q^{23} +12.5285 q^{25} +(-4.86465 + 1.82626i) q^{27} +(7.31732 + 4.22466i) q^{29} +(-6.28007 - 3.62580i) q^{31} +(-0.294318 - 2.44681i) q^{33} +(-1.73222 + 3.00030i) q^{37} +(1.36138 - 1.02063i) q^{39} +(-1.06981 - 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(12.2019 - 2.97853i) q^{45} +(-4.13542 - 7.16276i) q^{47} +(0.385401 + 0.514073i) q^{51} +(-4.30627 + 2.48623i) q^{53} +5.95706i q^{55} +(-7.92317 - 3.38623i) q^{57} +(-2.27883 + 3.94705i) q^{59} +(-6.50416 + 3.75518i) q^{61} +(-3.56180 + 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} +(-1.19133 - 9.90411i) q^{69} +10.9555i q^{71} +(8.25191 - 4.76424i) q^{73} +(-21.5448 + 2.59154i) q^{75} +(4.25553 + 7.37079i) q^{79} +(7.98775 - 4.14679i) q^{81} +(0.972254 - 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(-13.4571 - 5.75136i) q^{87} +(3.90368 - 6.76137i) q^{89} +(11.5495 + 4.93608i) q^{93} +(18.0373 + 10.4138i) q^{95} +(-3.34099 - 1.92892i) q^{97} +(1.01225 + 4.14679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

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

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	$-0.114338\pi$
$5$	4.18671			1.87235			0.936177	+	0.351529i	$0.114338\pi$
$6$		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	$0.0688130\pi$
$11$			1.42285i			0.429005i	−0.976723	+	0.214503i	$0.931187\pi$
$12$		0			0
$13$	−0.850739	+	0.491174i	−0.235952	+	0.136227i	−0.613315	−	0.789838i	$-0.710164\pi$
$13$	−0.850739	+	0.491174i	−0.235952	+	0.136227i	0.377363	+	0.926066i	$0.376831\pi$
$14$		0			0
$15$	−7.19970	+	0.866025i	−1.85895	+	0.223607i
$16$		0			0
$17$	−0.185474	−	0.321250i	−0.0449840	−	0.0779145i	0.842657	−	0.538451i	$-0.180990\pi$
$17$	−0.185474	−	0.321250i	−0.0449840	−	0.0779145i	−0.887641	+	0.460537i	$0.847657\pi$
$18$		0			0
$19$	4.30823	+	2.48736i	0.988375	+	0.570638i	0.904788	−	0.425862i	$-0.140029\pi$
$19$	4.30823	+	2.48736i	0.988375	+	0.570638i	0.0835867	+	0.996501i	$0.473362\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			5.75936i			1.20091i	0.799659	+	0.600455i	$0.205014\pi$
$23$			5.75936i			1.20091i	−0.799659	+	0.600455i	$0.794986\pi$
$24$		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	0.989461	−	0.144798i	$-0.0462534\pi$
$29$	7.31732	+	4.22466i	1.35879	+	0.784499i	0.369332	+	0.929298i	$0.379587\pi$
$30$		0			0
$31$	−6.28007	−	3.62580i	−1.12793	−	0.651213i	−0.184519	−	0.982829i	$-0.559073\pi$
$31$	−6.28007	−	3.62580i	−1.12793	−	0.651213i	−0.943414	+	0.331616i	$0.892406\pi$
$32$		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	−0.972555	−	0.232674i	$-0.925252\pi$
$37$	−1.73222	+	3.00030i	−0.284776	+	0.493246i	0.687779	+	0.725920i	$0.258586\pi$
$38$		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	$-0.220099\pi$
$41$	−1.06981	−	1.85297i	−0.167077	−	0.289386i	−0.937391	+	0.348279i	$0.886766\pi$
$42$		0			0
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	−0.540070	−	0.841620i	$-0.681602\pi$
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	0.998899	+	0.0469039i	$0.0149354\pi$
$44$		0			0
$45$	12.2019	−	2.97853i	1.81895	−	0.444013i
$46$		0			0
$47$	−4.13542	−	7.16276i	−0.603213	−	1.04480i	−0.992331	−	0.123608i	$-0.960553\pi$
$47$	−4.13542	−	7.16276i	−0.603213	−	1.04480i	0.389118	−	0.921188i	$-0.372780\pi$
$48$		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	−0.765695	−	0.643204i	$-0.777605\pi$
$53$	−4.30627	+	2.48623i	−0.591512	+	0.341509i	0.174183	+	0.984713i	$0.444271\pi$
$54$		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	$-0.929212\pi$
$59$	−2.27883	+	3.94705i	−0.296678	+	0.513862i	0.678696	+	0.734420i	$0.262546\pi$
$60$		0			0
$61$	−6.50416	+	3.75518i	−0.832772	+	0.480801i	−0.854801	−	0.518956i	$-0.826321\pi$
$61$	−6.50416	+	3.75518i	−0.832772	+	0.480801i	0.0220288	+	0.999757i	$0.492987\pi$
$62$		0			0
$63$		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	−0.375663	−	0.926756i	$-0.622585\pi$
$67$	5.03205	−	8.71577i	0.614763	−	1.06480i	0.990426	−	0.138044i	$-0.0440816\pi$
$68$		0			0
$69$	−1.19133	−	9.90411i	−0.143419	−	1.19231i
$70$		0			0
$71$			10.9555i			1.30018i	0.759857	+	0.650090i	$0.225269\pi$
$71$			10.9555i			1.30018i	−0.759857	+	0.650090i	$0.774731\pi$
$72$		0			0
$73$	8.25191	−	4.76424i	0.965813	−	0.557612i	0.0678555	−	0.997695i	$-0.478384\pi$
$73$	8.25191	−	4.76424i	0.965813	−	0.557612i	0.897957	+	0.440083i	$0.145051\pi$
$74$		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	0.999704	−	0.0243272i	$-0.00774434\pi$
$79$	4.25553	+	7.37079i	0.478784	+	0.829278i	−0.520920	+	0.853606i	$0.674411\pi$
$80$		0			0
$81$	7.98775	−	4.14679i	0.887528	−	0.460754i
$82$		0			0
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	−0.807720	−	0.589566i	$-0.799299\pi$
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	0.914439	+	0.404724i	$0.132632\pi$
$84$		0			0
$85$	−0.776524	−	1.34498i	−0.0842259	−	0.145884i
$86$		0			0
$87$	−13.4571	−	5.75136i	−1.44276	−	0.616610i
$88$		0			0
$89$	3.90368	−	6.76137i	0.413789	−	0.716703i	−0.581512	−	0.813538i	$-0.697538\pi$
$89$	3.90368	−	6.76137i	0.413789	−	0.716703i	0.995300	+	0.0968347i	$0.0308718\pi$
$90$		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	$-0.396081\pi$
$97$	−3.34099	−	1.92892i	−0.339226	−	0.195852i	−0.659930	+	0.751327i	$0.729414\pi$
$98$		0			0
$99$	1.01225	+	4.14679i	0.101735	+	0.416768i
$100$		0			0
$101$	9.01274			0.896801			0.448401	−	0.893833i	$-0.351994\pi$
$101$	9.01274			0.896801			0.448401	+	0.893833i	$0.351994\pi$
$102$		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	0.893494	−	0.449076i	$-0.148247\pi$
$107$	9.84062	+	5.68149i	0.951329	+	0.549250i	0.0578356	+	0.998326i	$0.481580\pi$
$108$		0			0
$109$	7.99650	+	13.8503i	0.765926	+	1.32662i	0.939756	+	0.341846i	$0.111052\pi$
$109$	7.99650	+	13.8503i	0.765926	+	1.32662i	−0.173830	+	0.984776i	$0.555614\pi$
$110$		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
$115$			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	$-0.376627\pi$
$131$	8.65182			0.755913			0.377957	+	0.925823i	$0.376627\pi$
$132$		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	$-0.834044\pi$
$137$		−	11.6594i		−	0.996131i	0.867139	−	0.498065i	$-0.165956\pi$
$138$		0			0
$139$	−4.82663	+	2.78666i	−0.409390	+	0.236361i	−0.690528	−	0.723306i	$-0.742622\pi$
$139$	−4.82663	+	2.78666i	−0.409390	+	0.236361i	0.281138	+	0.959667i	$0.409288\pi$
$140$		0			0
$141$	8.59312	+	11.4621i	0.723672	+	0.965280i
$142$		0			0
$143$	−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	$-0.781448\pi$
$149$		−	15.4758i		−	1.26783i	0.773405	−	0.633913i	$-0.218552\pi$
$150$		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	$-0.567340\pi$
$157$	−14.5559	−	8.40387i	−1.16169	−	0.670702i	−0.951708	+	0.307004i	$0.900674\pi$
$158$		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	−0.926551	−	0.376169i	$-0.877241\pi$
$163$	−1.75553	+	3.04066i	−0.137503	+	0.238163i	0.789048	+	0.614332i	$0.210574\pi$
$164$		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	$-0.0651336\pi$
$167$	4.05253	+	7.01918i	0.313594	+	0.543160i	−0.665544	+	0.746359i	$0.731800\pi$
$168$		0			0
$169$	−6.01750	+	10.4226i	−0.462884	+	0.801739i
$170$		0			0
$171$	14.3256	+	4.18423i	1.09550	+	0.319976i
$172$		0			0
$173$	−6.54844	−	11.3422i	−0.497868	−	0.862334i	0.502128	−	0.864793i	$-0.332550\pi$
$173$	−6.54844	−	11.3422i	−0.497868	−	0.862334i	−0.999997	+	0.00245951i	$0.999217\pi$
$174$		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	−0.0283026	−	0.999599i	$-0.509010\pi$
$179$	11.0140	−	6.35893i	0.823225	−	0.475289i	0.851527	+	0.524310i	$0.175677\pi$
$180$		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	−0.459774	−	0.888036i	$-0.652069\pi$
$191$	1.09735	−	0.633555i	0.0794014	−	0.0458424i	0.539175	+	0.842194i	$0.318736\pi$
$192$		0			0
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	0.307037	+	0.951697i	$0.400662\pi$
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	−0.977713	+	0.209947i	$0.932671\pi$
$194$		0			0
$195$	5.69969	−	4.27307i	0.408163	−	0.306001i
$196$		0			0
$197$		−	5.94312i		−	0.423430i	−0.977331	−	0.211715i	$-0.932095\pi$
$197$		−	5.94312i		−	0.423430i	0.977331	−	0.211715i	$-0.0679049\pi$
$198$		0			0
$199$	4.87291	−	2.81337i	0.345431	−	0.199435i	−0.317240	−	0.948345i	$-0.602756\pi$
$199$	4.87291	−	2.81337i	0.345431	−	0.199435i	0.662671	+	0.748910i	$0.269423\pi$
$200$		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	0.899994	−	0.435902i	$-0.143571\pi$
$211$	1.05305	+	1.82393i	0.0724948	+	0.125565i	−0.827499	+	0.561467i	$0.810237\pi$
$212$		0			0
$213$	−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	$-0.264830\pi$
$223$	5.52351	+	3.18900i	0.369882	+	0.213551i	−0.303525	+	0.952823i	$0.598164\pi$
$224$		0			0
$225$	36.5135	−	8.91312i	2.43423	−	0.594208i
$226$		0			0
$227$	11.4473			0.759783			0.379892	−	0.925031i	$-0.375961\pi$
$227$	11.4473			0.759783			0.379892	+	0.925031i	$0.375961\pi$
$228$		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	0.103487	−	0.994631i	$-0.467000\pi$
$233$	−10.7788	−	6.22316i	−0.706145	−	0.407693i	−0.809632	+	0.586938i	$0.800333\pi$
$234$		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
$241$		−	4.92128i		−	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	$-0.546884\pi$
$251$	−4.65020			−0.293518			−0.146759	+	0.989172i	$0.546884\pi$
$252$		0			0
$253$	−8.19470			−0.515196
$254$		0			0
$255$	1.61356	+	2.15228i	0.101045	+	0.134781i
$256$		0			0
$257$	10.8940			0.679551			0.339775	−	0.940507i	$-0.389649\pi$
$257$	10.8940			0.679551			0.339775	+	0.940507i	$0.389649\pi$
$258$		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	$-0.811908\pi$
$263$		−	18.0698i		−	1.11423i	0.830436	−	0.557114i	$-0.188092\pi$
$264$		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	$-0.195664\pi$
$269$	−1.49205	−	2.58430i	−0.0909718	−	0.157568i	−0.907920	+	0.419143i	$0.862331\pi$
$270$		0			0
$271$	8.97274	+	5.18041i	0.545055	+	0.314688i	0.747125	−	0.664683i	$-0.231434\pi$
$271$	8.97274	+	5.18041i	0.545055	+	0.314688i	−0.202070	+	0.979371i	$0.564767\pi$
$272$		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	0.0945775	−	0.995518i	$-0.469850\pi$
$281$	−12.0740	−	6.97095i	−0.720277	−	0.415852i	−0.814855	+	0.579665i	$0.803183\pi$
$282$		0			0
$283$	−2.19593	−	1.26782i	−0.130535	−	0.0753642i	0.433311	−	0.901245i	$-0.357345\pi$
$283$	−2.19593	−	1.26782i	−0.130535	−	0.0753642i	−0.563845	+	0.825880i	$0.690679\pi$
$284$		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	$-0.0924501\pi$
$293$	3.95496	+	6.85020i	0.231052	+	0.400193i	−0.727066	+	0.686567i	$0.759117\pi$
$294$		0			0
$295$	−9.54080	+	16.5251i	−0.555487	+	0.962131i
$296$		0			0
$297$	−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	0.134001	−	0.990981i	$-0.457218\pi$
$311$	16.3163	−	28.2607i	0.925215	−	1.60252i	0.791215	−	0.611539i	$-0.209449\pi$
$312$		0			0
$313$	−13.6110	+	7.85832i	−0.769340	+	0.444178i	−0.832639	−	0.553816i	$-0.813171\pi$
$313$	−13.6110	+	7.85832i	−0.769340	+	0.444178i	0.0632994	+	0.997995i	$0.479838\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	25.1366	−	14.5126i	1.41181	−	0.815111i	0.416254	−	0.909248i	$-0.363343\pi$
$317$	25.1366	−	14.5126i	1.41181	−	0.815111i	0.995559	+	0.0941377i	$0.0300094\pi$
$318$		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	0.626332	−	0.779556i	$-0.284555\pi$
$331$	−6.58510	−	11.4057i	−0.361950	−	0.626915i	−0.988282	+	0.152641i	$0.951222\pi$
$332$		0			0
$333$	−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	0.998575	−	0.0533635i	$-0.0169942\pi$
$337$	8.31732	+	14.4060i	0.453073	+	0.784746i	−0.545502	+	0.838110i	$0.683661\pi$
$338$		0			0
$339$	−3.47318	+	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	−0.200264	−	0.979742i	$-0.564180\pi$
$347$	−21.4012	−	12.3560i	−1.14888	−	0.663305i	−0.948614	+	0.316437i	$0.897513\pi$
$348$		0			0
$349$	−26.7994	−	15.4727i	−1.43454	−	0.828232i	−0.437078	−	0.899424i	$-0.643987\pi$
$349$	−26.7994	−	15.4727i	−1.43454	−	0.828232i	−0.997463	+	0.0711915i	$0.977320\pi$
$350$		0			0
$351$	3.24153	−	3.94306i	0.173020	−	0.210465i
$352$		0			0
$353$	−23.3516			−1.24288			−0.621440	−	0.783462i	$-0.713452\pi$
$353$	−23.3516			−1.24288			−0.621440	+	0.783462i	$0.713452\pi$
$354$		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	−0.0711782	−	0.997464i	$-0.522676\pi$
$359$	−18.3902	−	10.6176i	−0.970596	−	0.560374i	−0.899418	+	0.437090i	$0.856009\pi$
$360$		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	$-0.512823\pi$
$383$	−1.57633			−0.0805469			−0.0402734	+	0.999189i	$0.512823\pi$
$384$		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	$-0.907924\pi$
$389$		−	11.2519i		−	0.570496i	0.958454	−	0.285248i	$-0.0920760\pi$
$390$		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	$-0.338389\pi$
$397$	−0.548160	−	0.316480i	−0.0275114	−	0.0158837i	−0.513693	+	0.857974i	$0.671723\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			8.52206i			0.425571i	0.977099	+	0.212786i	$0.0682536\pi$
$401$			8.52206i			0.425571i	−0.977099	+	0.212786i	$0.931746\pi$
$402$		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	$-0.446397\pi$
$409$	−12.1822	−	7.03338i	−0.602370	−	0.347778i	−0.769973	+	0.638076i	$0.779731\pi$
$410$		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	−0.999204	−	0.0398995i	$-0.987296\pi$
$419$	−10.9339	−	18.9381i	−0.534156	−	0.925185i	0.465048	−	0.885286i	$-0.346037\pi$
$420$		0			0
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	−0.331625	−	0.943411i	$-0.607597\pi$
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	0.982831	−	0.184510i	$-0.0590698\pi$
$422$		0			0
$423$	−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	−0.854468	−	0.519505i	$-0.826116\pi$
$431$	−17.2686	+	9.97000i	−0.831797	+	0.480238i	0.0226706	+	0.999743i	$0.492783\pi$
$432$		0			0
$433$			20.2826i			0.974719i	0.873201	+	0.487359i	$0.162040\pi$
$433$			20.2826i			0.974719i	−0.873201	+	0.487359i	$0.837960\pi$
$434$		0			0
$435$	−56.3412	−	24.0793i	−2.70135	−	1.15451i
$436$		0			0
$437$	−14.3256	+	24.8126i	−0.685285	+	1.18695i
$438$		0			0
$439$	24.5936	−	14.1991i	1.17379	−	0.677687i	0.219219	−	0.975676i	$-0.429649\pi$
$439$	24.5936	−	14.1991i	1.17379	−	0.677687i	0.954569	+	0.297989i	$0.0963158\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.6570	+	6.15281i	−0.506328	+	0.292329i	−0.731323	−	0.682031i	$-0.761097\pi$
$443$	−10.6570	+	6.15281i	−0.506328	+	0.292329i	0.224995	+	0.974360i	$0.427764\pi$
$444$		0			0
$445$	16.3436	−	28.3079i	0.774759	−	1.34192i
$446$		0			0
$447$	3.20118	+	26.6130i	0.151411	+	1.25875i
$448$		0			0
$449$			36.1924i			1.70803i	0.520251	+	0.854013i	$0.325838\pi$
$449$			36.1924i			1.70803i	−0.520251	+	0.854013i	$0.674162\pi$
$450$		0			0
$451$	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	0.947517	−	0.319706i	$-0.103584\pi$
$457$	4.20892	+	7.29007i	0.196885	+	0.341015i	−0.750632	+	0.660721i	$0.770251\pi$
$458$		0			0
$459$	1.48895	+	1.22404i	0.0694981	+	0.0571335i
$460$		0			0
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	−0.996209	−	0.0869865i	$-0.972276\pi$
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	0.573437	+	0.819249i	$0.305610\pi$
$462$		0			0
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	0.631802	−	0.775130i	$-0.282316\pi$
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	−0.987183	+	0.159591i	$0.948982\pi$
$464$		0			0
$465$	48.3546	+	20.6660i	2.24239	+	0.958361i
$466$		0			0
$467$	13.3932	−	23.1977i	0.619763	−	1.07346i	−0.369766	−	0.929125i	$-0.620562\pi$
$467$	13.3932	−	23.1977i	0.619763	−	1.07346i	0.989529	−	0.144336i	$-0.0461045\pi$
$468$		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	$-0.726220\pi$
$479$	−28.5551			−1.30471			−0.652357	+	0.757912i	$0.726220\pi$
$480$		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	0.975679	−	0.219204i	$-0.0703462\pi$
$487$	6.57635	+	11.3906i	0.298003	+	0.516156i	−0.677676	+	0.735361i	$0.737013\pi$
$488$		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
$493$		−	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	$-0.410128\pi$
$503$	12.4969			0.557210			0.278605	+	0.960406i	$0.410128\pi$
$504$		0			0
$505$	37.7337			1.67913
$506$		0			0
$507$	8.19209	−	19.1680i	0.363823	−	0.851281i
$508$		0			0
$509$	−6.60474			−0.292750			−0.146375	−	0.989229i	$-0.546761\pi$
$509$	−6.60474			−0.292750			−0.146375	+	0.989229i	$0.546761\pi$
$510$		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	$-0.0528438\pi$
$521$	7.98920	+	13.8377i	0.350013	+	0.606241i	−0.636238	+	0.771493i	$0.719510\pi$
$522$		0			0
$523$	−10.1857	−	5.88074i	−0.445391	−	0.257147i	0.260491	−	0.965476i	$-0.416116\pi$
$523$	−10.1857	−	5.88074i	−0.445391	−	0.257147i	−0.705882	+	0.708330i	$0.749449\pi$
$524$		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	−0.861564	−	0.507650i	$-0.830514\pi$
$541$	0.205980	−	0.356768i	0.00885576	−	0.0153386i	0.870419	+	0.492311i	$0.163848\pi$
$542$		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	−0.490420	−	0.871486i	$-0.663157\pi$
$547$	11.9166	−	20.6402i	0.509519	−	0.882513i	0.999939	−	0.0110266i	$-0.00350995\pi$
$548$		0			0
$549$	−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	−0.580522	+	0.814245i	$0.697151\pi$
$557$	−37.1935	+	21.4737i	−1.57594	+	0.909869i	−0.995418	+	0.0956241i	$0.969515\pi$
$558$		0			0
$559$			5.91128i			0.250020i
$560$		0			0
$561$	−0.731449	+	0.548368i	−0.0308818	+	0.0231521i
$562$		0			0
$563$	15.9454	−	27.6182i	0.672019	−	1.16397i	−0.305312	−	0.952252i	$-0.598761\pi$
$563$	15.9454	−	27.6182i	0.672019	−	1.16397i	0.977331	−	0.211718i	$-0.0679058\pi$
$564$		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	−0.508963	−	0.860788i	$-0.669971\pi$
$569$	−0.428895	+	0.247623i	−0.0179802	+	0.0103809i	0.490983	+	0.871169i	$0.336638\pi$
$570$		0			0
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	−0.892736	−	0.450581i	$-0.851217\pi$
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	0.836582	+	0.547841i	$0.184550\pi$
$572$		0			0
$573$	−1.75601	+	1.31648i	−0.0733584	+	0.0549969i
$574$		0			0
$575$			72.1564i			3.00913i
$576$		0			0
$577$	−36.3955	+	21.0130i	−1.51517	+	0.874781i	−0.515324	+	0.856995i	$0.672328\pi$
$577$	−36.3955	+	21.0130i	−1.51517	+	0.874781i	−0.999842	+	0.0177861i	$0.994338\pi$
$578$		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	$-0.810728\pi$
$587$	1.71916	−	2.97768i	0.0709575	−	0.122902i	0.899321	+	0.437289i	$0.144061\pi$
$588$		0			0
$589$	−18.0373	−	31.2415i	−0.743214	−	1.28728i
$590$		0			0
$591$	1.22934	+	10.2201i	0.0505683	+	0.420400i
$592$		0			0
$593$	−4.55126	+	7.88301i	−0.186898	+	0.323716i	−0.944214	−	0.329332i	$-0.893177\pi$
$593$	−4.55126	+	7.88301i	−0.186898	+	0.323716i	0.757317	+	0.653048i	$0.226510\pi$
$594$		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	0.356573	−	0.934267i	$-0.383945\pi$
$599$	−6.71186	−	3.87510i	−0.274239	−	0.158332i	−0.630813	+	0.775935i	$0.717278\pi$
$600$		0			0
$601$	−22.0034	−	12.7037i	−0.897536	−	0.518193i	−0.0211361	−	0.999777i	$-0.506728\pi$
$601$	−22.0034	−	12.7037i	−0.897536	−	0.518193i	−0.876400	+	0.481584i	$0.840062\pi$
$602$		0			0
$603$	8.46492	−	28.9814i	0.344718	−	1.18021i
$604$		0			0
$605$	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	0.813050	−	0.582193i	$-0.197805\pi$
$613$	−2.41817	−	4.18840i	−0.0976691	−	0.169168i	−0.910719	+	0.413026i	$0.864472\pi$
$614$		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
$619$		−	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	$-0.902051\pi$
$641$		−	15.3367i		−	0.605764i	0.953028	−	0.302882i	$-0.0979489\pi$
$642$		0			0
$643$	−11.3209	+	6.53612i	−0.446453	+	0.257759i	−0.706331	−	0.707882i	$-0.749651\pi$
$643$	−11.3209	+	6.53612i	−0.446453	+	0.257759i	0.259878	+	0.965641i	$0.416318\pi$
$644$		0			0
$645$	−17.1490	+	40.1255i	−0.675239	+	1.57994i
$646$		0			0
$647$	−17.8533	−	30.9228i	−0.701885	−	1.21570i	−0.967804	−	0.251705i	$-0.919009\pi$
$647$	−17.8533	−	30.9228i	−0.701885	−	1.21570i	0.265919	−	0.963995i	$-0.414325\pi$
$648$		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	$-0.820876\pi$
$653$		−	27.2660i		−	1.06700i	0.845799	−	0.533501i	$-0.179124\pi$
$654$		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	0.183435	−	0.983032i	$-0.441278\pi$
$659$	−14.7911	−	8.53963i	−0.576179	−	0.332657i	−0.759613	+	0.650375i	$0.774612\pi$
$660$		0			0
$661$	40.6657	+	23.4784i	1.58171	+	0.913203i	0.994609	+	0.103692i	$0.0330657\pi$
$661$	40.6657	+	23.4784i	1.58171	+	0.913203i	0.587105	+	0.809511i	$0.300268\pi$
$662$		0			0
$663$	−0.580375	−	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	−0.676787	−	0.736179i	$-0.736628\pi$
$673$	7.76077	−	13.4421i	0.299156	−	0.518153i	0.975943	+	0.218026i	$0.0699616\pi$
$674$		0			0
$675$	−60.9470	+	22.8803i	−2.34585	+	0.880665i
$676$		0			0
$677$	−9.07869	−	15.7248i	−0.348922	−	0.604351i	0.637136	−	0.770751i	$-0.280119\pi$
$677$	−9.07869	−	15.7248i	−0.348922	−	0.604351i	−0.986058	+	0.166400i	$0.946786\pi$
$678$		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	−0.126633	−	0.991950i	$-0.540417\pi$
$683$	17.4866	−	10.0959i	0.669104	−	0.386308i	0.795737	+	0.605642i	$0.207084\pi$
$684$		0			0
$685$		−	48.8146i		−	1.86511i
$686$		0			0
$687$	1.16726	+	9.70398i	0.0445336	+	0.370230i
$688$		0			0
$689$	2.44234	−	4.23026i	0.0930458	−	0.161160i
$690$		0			0
$691$	0.0695792	−	0.0401716i	0.00264692	−	0.00152820i	−0.498676	−	0.866788i	$-0.666180\pi$
$691$	0.0695792	−	0.0401716i	0.00264692	−	0.00152820i	0.501323	+	0.865260i	$0.332847\pi$
$692$		0			0
$693$		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	$0.231049\pi$
$701$			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
$705$	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	0.850948	−	0.525249i	$-0.176028\pi$
$709$	−0.782968	−	1.35614i	−0.0294050	−	0.0509309i	−0.880353	+	0.474318i	$0.842695\pi$
$710$		0			0
$711$	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	$-0.993625\pi$
$719$	−12.9393	+	22.4116i	−0.482556	+	0.835811i	0.517243	+	0.855838i	$0.326958\pi$
$720$		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	$-0.326581\pi$
$727$	0.990545	+	0.571891i	0.0367373	+	0.0212103i	−0.481519	+	0.876436i	$0.659915\pi$
$728$		0			0
$729$	20.3296	−	17.7682i	0.752947	−	0.658081i
$730$		0			0
$731$	−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	0.979305	+	0.202392i	$0.0648714\pi$
$739$	18.0758	+	31.3082i	0.664929	+	1.15169i	−0.314376	+	0.949299i	$0.601795\pi$
$740$		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
$745$		−	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	$-0.788553\pi$
$761$	−43.4407			−1.57472			−0.787362	+	0.616492i	$0.788553\pi$
$762$		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	$-0.795034\pi$
$769$	−18.8491	+	10.8825i	−0.679716	+	0.392434i	0.120032	+	0.992770i	$0.461700\pi$
$770$		0			0
$771$	−18.7340	+	2.25344i	−0.674687	+	0.0811557i
$772$		0			0
$773$	7.25734	+	12.5701i	0.261028	+	0.452114i	0.966515	−	0.256609i	$-0.0826051\pi$
$773$	7.25734	+	12.5701i	0.261028	+	0.452114i	−0.705487	+	0.708723i	$0.749272\pi$
$774$		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	$-0.408913\pi$
$787$	−11.4291	−	6.59861i	−0.407405	−	0.235215i	−0.689674	+	0.724120i	$0.742246\pi$
$788$		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	−0.849511	−	0.527572i	$-0.823103\pi$
$797$	−24.8899	−	43.1106i	−0.881646	−	1.52706i	−0.0321352	−	0.999484i	$-0.510231\pi$
$798$		0			0
$799$	−1.53402	+	2.65701i	−0.0542698	+	0.0939981i
$800$		0			0
$801$	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	−0.00514934	−	0.999987i	$-0.501639\pi$
$809$	24.4123	−	14.0944i	0.858290	−	0.495534i	0.863439	+	0.504453i	$0.168306\pi$
$810$		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	0.655475	−	0.755217i	$-0.272468\pi$
$821$	46.9123	−	27.0848i	1.63725	−	0.945267i	0.981774	−	0.190050i	$-0.0608650\pi$
$822$		0			0
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	−0.999996	−	0.00299479i	$-0.999047\pi$
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	0.502591	+	0.864524i	$0.332380\pi$
$824$		0			0
$825$	−3.68738	−	30.6550i	−0.128378	−	1.06727i
$826$		0			0
$827$		−	37.2062i		−	1.29379i	−0.762581	−	0.646893i	$-0.776068\pi$
$827$		−	37.2062i		−	1.29379i	0.762581	−	0.646893i	$-0.223932\pi$
$828$		0			0
$829$	−1.92557	+	1.11173i	−0.0668777	+	0.0386119i	−0.533066	−	0.846074i	$-0.678960\pi$
$829$	−1.92557	+	1.11173i	−0.0668777	+	0.0386119i	0.466188	+	0.884686i	$0.345627\pi$
$830$		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	−0.241297	+	0.970451i	$0.577573\pi$
$839$	−27.8383	+	48.2173i	−0.961084	+	1.66465i	−0.719787	+	0.694195i	$0.755760\pi$
$840$		0			0
$841$	21.1955	+	36.7116i	0.730878	+	1.26592i
$842$		0			0
$843$	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	$-0.437479\pi$
$853$	−16.2574	−	9.38622i	−0.556643	−	0.321378i	−0.751797	+	0.659395i	$0.770813\pi$
$854$		0			0
$855$	59.9770	+	17.5182i	2.05117	+	0.599109i
$856$		0			0
$857$	−23.7032			−0.809687			−0.404844	−	0.914386i	$-0.632674\pi$
$857$	−23.7032			−0.809687			−0.404844	+	0.914386i	$0.632674\pi$
$858$		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	−0.0880791	−	0.996113i	$-0.528073\pi$
$863$	−29.2235	−	16.8722i	−0.994778	−	0.574335i	−0.906699	+	0.421778i	$0.861406\pi$
$864$		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	$-0.354203\pi$
$881$	26.2496			0.884372			0.442186	+	0.896923i	$0.354203\pi$
$882$		0			0
$883$	−43.5087			−1.46418			−0.732091	−	0.681206i	$-0.761456\pi$
$883$	−43.5087			−1.46418			−0.732091	+	0.681206i	$0.761456\pi$
$884$		0			0
$885$	12.9886	−	30.3911i	0.436608	−	1.02158i
$886$		0			0
$887$	−5.67776			−0.190640			−0.0953202	−	0.995447i	$-0.530387\pi$
$887$	−5.67776			−0.190640			−0.0953202	+	0.995447i	$0.530387\pi$
$888$		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	0.614377	−	0.789013i	$-0.289408\pi$
$911$	7.19133	+	4.15192i	0.238260	+	0.137559i	−0.376117	+	0.926572i	$0.622741\pi$
$912$		0			0
$913$	2.39607	+	1.38337i	0.0792983	+	0.0457829i
$914$		0			0
$915$	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	−0.378804	−	0.925477i	$-0.623665\pi$
$919$	18.5554	−	32.1388i	0.612085	−	1.06016i	0.990889	−	0.134685i	$-0.0430021\pi$
$920$		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	$-0.125352\pi$
$929$	3.94493	+	6.83283i	0.129429	+	0.224178i	−0.794026	+	0.607883i	$0.792019\pi$
$930$		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	$-0.874588\pi$
$941$	−3.96461	+	6.86691i	−0.129243	+	0.223855i	0.794141	+	0.607734i	$0.207921\pi$
$942$		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	0.00357041	−	0.999994i	$-0.498864\pi$
$947$	26.8152	−	15.4817i	0.871375	−	0.503089i	0.867805	+	0.496905i	$0.165530\pi$
$948$		0			0
$949$	−4.68014	+	8.10625i	−0.151924	+	0.263140i
$950$		0			0
$951$	−40.2244	+	30.1563i	−1.30436	+	0.977884i
$952$		0			0
$953$		−	34.1087i		−	1.10489i	−0.833549	−	0.552445i	$-0.813695\pi$
$953$		−	34.1087i		−	1.10489i	0.833549	−	0.552445i	$-0.186305\pi$
$954$		0			0
$955$	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	0.772829	+	0.634614i	$0.218841\pi$
$967$	29.1066	+	50.4142i	0.936007	+	1.62121i	0.163177	+	0.986597i	$0.447826\pi$
$968$		0			0
$969$	0.381714	+	3.17337i	0.0122624	+	0.101943i
$970$		0			0
$971$	−4.91896	+	8.51988i	−0.157857	+	0.273416i	−0.934096	−	0.357023i	$-0.883792\pi$
$971$	−4.91896	+	8.51988i	−0.157857	+	0.273416i	0.776239	+	0.630439i	$0.217125\pi$
$972$		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	0.886473	−	0.462781i	$-0.153148\pi$
$977$	29.0356	+	16.7637i	0.928930	+	0.536318i	0.0424567	+	0.999098i	$0.486482\pi$
$978$		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	$-0.218752\pi$
$983$	48.4718			1.54601			0.773006	+	0.634399i	$0.218752\pi$
$984$		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	0.888357	+	0.459154i	$0.151848\pi$
$991$	26.5005	+	45.9003i	0.841818	+	1.45807i	−0.0465389	+	0.998916i	$0.514819\pi$
$992$		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.1685.1		16
3.2	odd	2		5292.2.bm.b.4625.1		16
7.2	even	3		252.2.x.a.209.5	yes	16
7.3	odd	6		1764.2.w.a.1109.2		16
7.4	even	3		1764.2.w.a.1109.7		16
7.5	odd	6		252.2.x.a.209.4	yes	16
7.6	odd	2	inner	1764.2.bm.b.1685.8		16
9.4	even	3		5292.2.w.a.1097.1		16
9.5	odd	6		1764.2.w.a.509.2		16
21.2	odd	6		756.2.x.a.629.8		16
21.5	even	6		756.2.x.a.629.1		16
21.11	odd	6		5292.2.w.a.521.8		16
21.17	even	6		5292.2.w.a.521.1		16
21.20	even	2		5292.2.bm.b.4625.8		16
28.19	even	6		1008.2.cc.c.209.5		16
28.23	odd	6		1008.2.cc.c.209.4		16
63.2	odd	6		2268.2.f.b.1133.1		16
63.4	even	3		5292.2.bm.b.2285.8		16
63.5	even	6		252.2.x.a.41.5	yes	16
63.13	odd	6		5292.2.w.a.1097.8		16
63.16	even	3		2268.2.f.b.1133.15		16
63.23	odd	6		252.2.x.a.41.4	✓	16
63.31	odd	6		5292.2.bm.b.2285.1		16
63.32	odd	6	inner	1764.2.bm.b.1697.8		16
63.40	odd	6		756.2.x.a.125.8		16
63.41	even	6		1764.2.w.a.509.7		16
63.47	even	6		2268.2.f.b.1133.16		16
63.58	even	3		756.2.x.a.125.1		16
63.59	even	6	inner	1764.2.bm.b.1697.1		16
63.61	odd	6		2268.2.f.b.1133.2		16
84.23	even	6		3024.2.cc.c.2897.8		16
84.47	odd	6		3024.2.cc.c.2897.1		16
252.23	even	6		1008.2.cc.c.545.5		16
252.103	even	6		3024.2.cc.c.881.8		16
252.131	odd	6		1008.2.cc.c.545.4		16
252.247	odd	6		3024.2.cc.c.881.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.4	✓	16	63.23	odd	6
252.2.x.a.41.5	yes	16	63.5	even	6
252.2.x.a.209.4	yes	16	7.5	odd	6
252.2.x.a.209.5	yes	16	7.2	even	3
756.2.x.a.125.1		16	63.58	even	3
756.2.x.a.125.8		16	63.40	odd	6
756.2.x.a.629.1		16	21.5	even	6
756.2.x.a.629.8		16	21.2	odd	6
1008.2.cc.c.209.4		16	28.23	odd	6
1008.2.cc.c.209.5		16	28.19	even	6
1008.2.cc.c.545.4		16	252.131	odd	6
1008.2.cc.c.545.5		16	252.23	even	6
1764.2.w.a.509.2		16	9.5	odd	6
1764.2.w.a.509.7		16	63.41	even	6
1764.2.w.a.1109.2		16	7.3	odd	6
1764.2.w.a.1109.7		16	7.4	even	3
1764.2.bm.b.1685.1		16	1.1	even	1	trivial
1764.2.bm.b.1685.8		16	7.6	odd	2	inner
1764.2.bm.b.1697.1		16	63.59	even	6	inner
1764.2.bm.b.1697.8		16	63.32	odd	6	inner
2268.2.f.b.1133.1		16	63.2	odd	6
2268.2.f.b.1133.2		16	63.61	odd	6
2268.2.f.b.1133.15		16	63.16	even	3
2268.2.f.b.1133.16		16	63.47	even	6
3024.2.cc.c.881.1		16	252.247	odd	6
3024.2.cc.c.881.8		16	252.103	even	6
3024.2.cc.c.2897.1		16	84.47	odd	6
3024.2.cc.c.2897.8		16	84.23	even	6
5292.2.w.a.521.1		16	21.17	even	6
5292.2.w.a.521.8		16	21.11	odd	6
5292.2.w.a.1097.1		16	9.4	even	3
5292.2.w.a.1097.8		16	63.13	odd	6
5292.2.bm.b.2285.1		16	63.31	odd	6
5292.2.bm.b.2285.8		16	63.4	even	3
5292.2.bm.b.4625.1		16	3.2	odd	2
5292.2.bm.b.4625.8		16	21.20	even	2

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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