LMFDB - Embedded newform 1764.2.l.f.961.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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, 2, 4]))

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

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

chi := DirichletCharacter("1764.949");

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.l (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.3
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1764.961
Dual form			1764.2.l.f.949.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29418 + 1.15113i) q^{3} +1.69963 q^{5} +(0.349814 + 2.97954i) q^{9} +O(q^{10})$	\(q+(1.29418 + 1.15113i) q^{3} +1.69963 q^{5} +(0.349814 + 2.97954i) q^{9} +2.47710 q^{11} +(0.388736 + 0.673310i) q^{13} +(2.19963 + 1.95649i) q^{15} +(1.40545 + 2.43430i) q^{17} +(-2.49381 + 4.31941i) q^{19} +0.712008 q^{23} -2.11126 q^{25} +(-2.97710 + 4.25874i) q^{27} +(-2.25526 + 3.90623i) q^{29} +(2.54944 - 4.41576i) q^{31} +(3.20582 + 2.85146i) q^{33} +(3.43818 - 5.95510i) q^{37} +(-0.271971 + 1.31887i) q^{39} +(-2.93818 - 5.08907i) q^{41} +(2.32691 - 4.03033i) q^{43} +(0.594554 + 5.06410i) q^{45} +(6.49381 + 11.2476i) q^{47} +(-0.983290 + 4.76828i) q^{51} +(-0.944368 - 1.63569i) q^{53} +4.21015 q^{55} +(-8.19963 + 2.71941i) q^{57} +(7.14400 - 12.3738i) q^{59} +(7.15452 + 12.3920i) q^{61} +(0.660706 + 1.14438i) q^{65} +(-3.99381 + 6.91748i) q^{67} +(0.921468 + 0.819611i) q^{69} -10.2632 q^{71} +(2.49381 + 4.31941i) q^{73} +(-2.73236 - 2.43033i) q^{75} +(4.60507 + 7.97622i) q^{79} +(-8.75526 + 2.08457i) q^{81} +(4.40545 - 7.63046i) q^{83} +(2.38874 + 4.13741i) q^{85} +(-7.41528 + 2.45928i) q^{87} +(4.82691 - 8.36046i) q^{89} +(8.38255 - 2.78007i) q^{93} +(-4.23855 + 7.34138i) q^{95} +(4.32072 - 7.48371i) q^{97} +(0.866524 + 7.38061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) $ 6 * q + 2 * q^3 - 2 * q^5 - 4 * q^9	$ 6 q + 2 q^{3} - 2 q^{5} - 4 q^{9} + 4 q^{11} + 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} + 28 q^{23} - 12 q^{25} - 7 q^{27} - q^{29} - 3 q^{31} + 25 q^{33} + 3 q^{37} + 18 q^{39} - 3 q^{43} + 10 q^{45} + 21 q^{47} - 13 q^{51} - 6 q^{53} - 12 q^{55} - 37 q^{57} + 31 q^{59} + 6 q^{61} - 15 q^{65} - 6 q^{67} - 5 q^{69} + 34 q^{71} - 3 q^{73} + 7 q^{75} + 9 q^{79} - 40 q^{81} + 20 q^{83} + 15 q^{85} - 16 q^{87} + 12 q^{89} + 33 q^{93} - 20 q^{95} - 9 q^{97} - 8 q^{99}+O(q^{100}) $ 6 * q + 2 * q^3 - 2 * q^5 - 4 * q^9 + 4 * q^11 + 3 * q^13 + q^15 + 2 * q^17 + 3 * q^19 + 28 * q^23 - 12 * q^25 - 7 * q^27 - q^29 - 3 * q^31 + 25 * q^33 + 3 * q^37 + 18 * q^39 - 3 * q^43 + 10 * q^45 + 21 * q^47 - 13 * q^51 - 6 * q^53 - 12 * q^55 - 37 * q^57 + 31 * q^59 + 6 * q^61 - 15 * q^65 - 6 * q^67 - 5 * q^69 + 34 * q^71 - 3 * q^73 + 7 * q^75 + 9 * q^79 - 40 * q^81 + 20 * q^83 + 15 * q^85 - 16 * q^87 + 12 * q^89 + 33 * q^93 - 20 * q^95 - 9 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.29418	+	1.15113i	0.747196	+	0.664603i
$3$	1.29418	+	1.15113i	0.747196	+	0.664603i
$4$		0			0
$5$	1.69963			0.760097			0.380048	−	0.924967i	$-0.375907\pi$
$5$	1.69963			0.760097			0.380048	+	0.924967i	$0.375907\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.349814	+	2.97954i	0.116605	+	0.993178i
$10$		0			0
$11$	2.47710			0.746874			0.373437	−	0.927656i	$-0.378179\pi$
$11$	2.47710			0.746874			0.373437	+	0.927656i	$0.378179\pi$
$12$		0			0
$13$	0.388736	+	0.673310i	0.107816	+	0.186743i	0.914885	−	0.403714i	$-0.132281\pi$
$13$	0.388736	+	0.673310i	0.107816	+	0.186743i	−0.807069	+	0.590457i	$0.798948\pi$
$14$		0			0
$15$	2.19963	+	1.95649i	0.567942	+	0.505163i
$16$		0			0
$17$	1.40545	+	2.43430i	0.340871	+	0.590405i	0.984595	−	0.174852i	$-0.0559448\pi$
$17$	1.40545	+	2.43430i	0.340871	+	0.590405i	−0.643724	+	0.765258i	$0.722611\pi$
$18$		0			0
$19$	−2.49381	+	4.31941i	−0.572119	+	0.990940i	0.424229	+	0.905555i	$0.360545\pi$
$19$	−2.49381	+	4.31941i	−0.572119	+	0.990940i	−0.996348	+	0.0853846i	$0.972788\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.712008			0.148464			0.0742320	−	0.997241i	$-0.476349\pi$
$23$	0.712008			0.148464			0.0742320	+	0.997241i	$0.476349\pi$
$24$		0			0
$25$	−2.11126			−0.422253
$26$		0			0
$27$	−2.97710	+	4.25874i	−0.572943	+	0.819595i
$28$		0			0
$29$	−2.25526	+	3.90623i	−0.418791	+	0.725368i	−0.995818	−	0.0913573i	$-0.970879\pi$
$29$	−2.25526	+	3.90623i	−0.418791	+	0.725368i	0.577027	+	0.816725i	$0.304213\pi$
$30$		0			0
$31$	2.54944	−	4.41576i	0.457893	−	0.793095i	−0.540956	−	0.841051i	$-0.681937\pi$
$31$	2.54944	−	4.41576i	0.457893	−	0.793095i	0.998849	+	0.0479563i	$0.0152708\pi$
$32$		0			0
$33$	3.20582	+	2.85146i	0.558061	+	0.496375i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.43818	−	5.95510i	0.565233	−	0.979012i	−0.431795	−	0.901972i	$-0.642120\pi$
$37$	3.43818	−	5.95510i	0.565233	−	0.979012i	0.997028	−	0.0770405i	$-0.0245471\pi$
$38$		0			0
$39$	−0.271971	+	1.31887i	−0.0435501	+	0.211188i
$40$		0			0
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	0.540035	−	0.841643i	$-0.318411\pi$
$41$	−2.93818	−	5.08907i	−0.458866	−	0.794780i	−0.998901	+	0.0468628i	$0.985078\pi$
$42$		0			0
$43$	2.32691	−	4.03033i	0.354851	−	0.614620i	−0.632241	−	0.774771i	$-0.717865\pi$
$43$	2.32691	−	4.03033i	0.354851	−	0.614620i	0.987092	+	0.160151i	$0.0511982\pi$
$44$		0			0
$45$	0.594554	+	5.06410i	0.0886309	+	0.754912i
$46$		0			0
$47$	6.49381	+	11.2476i	0.947220	+	1.64063i	0.751245	+	0.660023i	$0.229454\pi$
$47$	6.49381	+	11.2476i	0.947220	+	1.64063i	0.195975	+	0.980609i	$0.437213\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.983290	+	4.76828i	−0.137688	+	0.667693i
$52$		0			0
$53$	−0.944368	−	1.63569i	−0.129719	−	0.224680i	0.793849	−	0.608115i	$-0.208074\pi$
$53$	−0.944368	−	1.63569i	−0.129719	−	0.224680i	−0.923568	+	0.383436i	$0.874741\pi$
$54$		0			0
$55$	4.21015			0.567696
$56$		0			0
$57$	−8.19963	+	2.71941i	−1.08607	+	0.360194i
$58$		0			0
$59$	7.14400	−	12.3738i	0.930069	−	1.61093i	0.146870	−	0.989156i	$-0.453080\pi$
$59$	7.14400	−	12.3738i	0.930069	−	1.61093i	0.783199	−	0.621771i	$-0.213587\pi$
$60$		0			0
$61$	7.15452	+	12.3920i	0.916042	+	1.58663i	0.805369	+	0.592774i	$0.201967\pi$
$61$	7.15452	+	12.3920i	0.916042	+	1.58663i	0.110673	+	0.993857i	$0.464699\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.660706	+	1.14438i	0.0819505	+	0.141942i
$66$		0			0
$67$	−3.99381	+	6.91748i	−0.487922	+	0.845105i	−0.999904	−	0.0138913i	$-0.995578\pi$
$67$	−3.99381	+	6.91748i	−0.487922	+	0.845105i	0.511982	+	0.858996i	$0.328911\pi$
$68$		0			0
$69$	0.921468	+	0.819611i	0.110932	+	0.0986696i
$70$		0			0
$71$	−10.2632			−1.21802			−0.609011	−	0.793162i	$-0.708433\pi$
$71$	−10.2632			−1.21802			−0.609011	+	0.793162i	$0.708433\pi$
$72$		0			0
$73$	2.49381	+	4.31941i	0.291878	+	0.505548i	0.974254	−	0.225454i	$-0.0723864\pi$
$73$	2.49381	+	4.31941i	0.291878	+	0.505548i	−0.682376	+	0.731002i	$0.739053\pi$
$74$		0			0
$75$	−2.73236	−	2.43033i	−0.315506	−	0.280631i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.60507	+	7.97622i	0.518111	+	0.897395i	0.999779	+	0.0210410i	$0.00669805\pi$
$79$	4.60507	+	7.97622i	0.518111	+	0.897395i	−0.481667	+	0.876354i	$0.659969\pi$
$80$		0			0
$81$	−8.75526	+	2.08457i	−0.972807	+	0.231619i
$82$		0			0
$83$	4.40545	−	7.63046i	0.483561	−	0.837551i	−0.516261	−	0.856431i	$-0.672677\pi$
$83$	4.40545	−	7.63046i	0.483561	−	0.837551i	0.999822	+	0.0188798i	$0.00600997\pi$
$84$		0			0
$85$	2.38874	+	4.13741i	0.259095	+	0.448765i
$86$		0			0
$87$	−7.41528	+	2.45928i	−0.795001	+	0.263662i
$88$		0			0
$89$	4.82691	−	8.36046i	0.511652	−	0.886207i	−0.488257	−	0.872700i	$-0.662367\pi$
$89$	4.82691	−	8.36046i	0.511652	−	0.886207i	0.999909	−	0.0135071i	$-0.00429956\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	8.38255	−	2.78007i	0.869230	−	0.288280i
$94$		0			0
$95$	−4.23855	+	7.34138i	−0.434866	+	0.753210i
$96$		0			0
$97$	4.32072	−	7.48371i	0.438703	−	0.759856i	−0.558887	−	0.829244i	$-0.688771\pi$
$97$	4.32072	−	7.48371i	0.438703	−	0.759856i	0.997590	+	0.0693880i	$0.0221047\pi$
$98$		0			0
$99$	0.866524	+	7.38061i	0.0870890	+	0.741779i
$100$		0			0
$101$	−2.41164			−0.239967			−0.119983	−	0.992776i	$-0.538284\pi$
$101$	−2.41164			−0.239967			−0.119983	+	0.992776i	$0.538284\pi$
$102$		0			0
$103$	4.33379			0.427021			0.213511	−	0.976941i	$-0.431510\pi$
$103$	4.33379			0.427021			0.213511	+	0.976941i	$0.431510\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.59888	+	16.6258i	−0.927959	+	1.60727i	−0.141228	+	0.989977i	$0.545105\pi$
$107$	−9.59888	+	16.6258i	−0.927959	+	1.60727i	−0.786732	+	0.617295i	$0.788228\pi$
$108$		0			0
$109$	−9.48143	−	16.4223i	−0.908156	−	1.57297i	−0.816623	−	0.577171i	$-0.804157\pi$
$109$	−9.48143	−	16.4223i	−0.908156	−	1.57297i	−0.0915329	−	0.995802i	$-0.529177\pi$
$110$		0			0
$111$	11.3047	−	3.74920i	1.07299	−	0.355859i
$112$		0			0
$113$	−6.46472	−	11.1972i	−0.608150	−	1.05335i	−0.991545	−	0.129762i	$-0.958579\pi$
$113$	−6.46472	−	11.1972i	−0.608150	−	1.05335i	0.383395	−	0.923584i	$-0.374755\pi$
$114$		0			0
$115$	1.21015			0.112847
$116$		0			0
$117$	−1.87017	+	1.39379i	−0.172897	+	0.128856i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.86398			−0.442180
$122$		0			0
$123$	2.05563	−	9.96840i	0.185350	−	0.898821i
$124$		0			0
$125$	−12.0865			−1.08105
$126$		0			0
$127$	17.6291			1.56433			0.782163	−	0.623073i	$-0.214116\pi$
$127$	17.6291			1.56433			0.782163	+	0.623073i	$0.214116\pi$
$128$		0			0
$129$	7.65087	−	2.53741i	0.673622	−	0.223407i
$130$		0			0
$131$	5.68725			0.496897			0.248449	−	0.968645i	$-0.420079\pi$
$131$	5.68725			0.496897			0.248449	+	0.968645i	$0.420079\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−5.05996	+	7.23828i	−0.435492	+	0.622972i
$136$		0			0
$137$	−19.4523			−1.66193			−0.830963	−	0.556328i	$-0.812210\pi$
$137$	−19.4523			−1.66193			−0.830963	+	0.556328i	$0.812210\pi$
$138$		0			0
$139$	−1.49381	−	2.58736i	−0.126703	−	0.219457i	0.795694	−	0.605699i	$-0.207106\pi$
$139$	−1.49381	−	2.58736i	−0.126703	−	0.219457i	−0.922397	+	0.386242i	$0.873773\pi$
$140$		0			0
$141$	−4.54325	+	22.0317i	−0.382611	+	1.85540i
$142$		0			0
$143$	0.962937	+	1.66786i	0.0805249	+	0.139473i
$144$		0			0
$145$	−3.83310	+	6.63913i	−0.318322	+	0.551350i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.09888			0.663486			0.331743	−	0.943370i	$-0.392363\pi$
$149$	8.09888			0.663486			0.331743	+	0.943370i	$0.392363\pi$
$150$		0			0
$151$	−8.86398			−0.721340			−0.360670	−	0.932693i	$-0.617452\pi$
$151$	−8.86398			−0.721340			−0.360670	+	0.932693i	$0.617452\pi$
$152$		0			0
$153$	−6.76145	+	5.03913i	−0.546631	+	0.407390i
$154$		0			0
$155$	4.33310	−	7.50516i	0.348043	−	0.602829i
$156$		0			0
$157$	−4.38255	+	7.59079i	−0.349765	+	0.605811i	−0.986208	−	0.165513i	$-0.947072\pi$
$157$	−4.38255	+	7.59079i	−0.349765	+	0.605811i	0.636442	+	0.771324i	$0.280405\pi$
$158$		0			0
$159$	0.660706	−	3.20397i	0.0523974	−	0.254092i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.993810	−	1.72133i	0.0778412	−	0.134825i	−0.824477	−	0.565895i	$-0.808531\pi$
$163$	0.993810	−	1.72133i	0.0778412	−	0.134825i	0.902318	+	0.431070i	$0.141864\pi$
$164$		0			0
$165$	5.44870	+	4.84641i	0.424181	+	0.377293i
$166$		0			0
$167$	1.31089	+	2.27053i	0.101440	+	0.175699i	0.912278	−	0.409571i	$-0.134322\pi$
$167$	1.31089	+	2.27053i	0.101440	+	0.175699i	−0.810838	+	0.585270i	$0.800988\pi$
$168$		0			0
$169$	6.19777	−	10.7349i	0.476751	−	0.825758i
$170$		0			0
$171$	−13.7422	−	5.91941i	−1.05089	−	0.452668i
$172$		0			0
$173$	−2.61491	−	4.52915i	−0.198808	−	0.344345i	0.749334	−	0.662192i	$-0.230374\pi$
$173$	−2.61491	−	4.52915i	−0.198808	−	0.344345i	−0.948142	+	0.317847i	$0.897040\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	23.4894	−	7.79026i	1.76557	−	0.585552i
$178$		0			0
$179$	2.38255	+	4.12669i	0.178080	+	0.308443i	0.941223	−	0.337786i	$-0.109678\pi$
$179$	2.38255	+	4.12669i	0.178080	+	0.308443i	−0.763143	+	0.646230i	$0.776345\pi$
$180$		0			0
$181$	10.4313			0.775352			0.387676	−	0.921796i	$-0.373278\pi$
$181$	10.4313			0.775352			0.387676	+	0.921796i	$0.373278\pi$
$182$		0			0
$183$	−5.00550	+	24.2732i	−0.370017	+	1.79433i
$184$		0			0
$185$	5.84362	−	10.1215i	0.429632	−	0.744144i
$186$		0			0
$187$	3.48143	+	6.03001i	0.254587	+	0.440958i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.66071	−	11.5367i	−0.481952	−	0.834765i	0.517834	−	0.855481i	$-0.326739\pi$
$191$	−6.66071	−	11.5367i	−0.481952	−	0.834765i	−0.999785	+	0.0207164i	$0.993405\pi$
$192$		0			0
$193$	7.32072	−	12.6799i	0.526957	−	0.912717i	−0.472549	−	0.881304i	$-0.656666\pi$
$193$	7.32072	−	12.6799i	0.526957	−	0.912717i	0.999507	−	0.0314125i	$-0.0100005\pi$
$194$		0			0
$195$	−0.462249	+	2.24159i	−0.0331023	+	0.160524i
$196$		0			0
$197$	−18.4858			−1.31706			−0.658528	−	0.752556i	$-0.728821\pi$
$197$	−18.4858			−1.31706			−0.658528	+	0.752556i	$0.728821\pi$
$198$		0			0
$199$	11.8083	+	20.4527i	0.837071	+	1.44985i	0.892333	+	0.451378i	$0.149067\pi$
$199$	11.8083	+	20.4527i	0.837071	+	1.44985i	−0.0552614	+	0.998472i	$0.517599\pi$
$200$		0			0
$201$	−13.1316	+	4.35510i	−0.926233	+	0.307185i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.99381	−	8.64953i	−0.348783	−	0.604110i
$206$		0			0
$207$	0.249070	+	2.12145i	0.0173116	+	0.147451i
$208$		0			0
$209$	−6.17742	+	10.6996i	−0.427301	+	0.740107i
$210$		0			0
$211$	7.27747	+	12.6050i	0.501002	+	0.867761i	0.999999	+	0.00115718i	$0.000368342\pi$
$211$	7.27747	+	12.6050i	0.501002	+	0.867761i	−0.498998	+	0.866603i	$0.666298\pi$
$212$		0			0
$213$	−13.2825	−	11.8143i	−0.910101	−	0.809501i
$214$		0			0
$215$	3.95489	−	6.85007i	0.269721	−	0.467171i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.74474	+	8.46079i	−0.117899	+	0.571727i
$220$		0			0
$221$	−1.09269	+	1.89260i	−0.0735026	+	0.127310i
$222$		0			0
$223$	4.72253	−	8.17966i	0.316244	−	0.547750i	−0.663457	−	0.748214i	$-0.730912\pi$
$223$	4.72253	−	8.17966i	0.316244	−	0.547750i	0.979701	+	0.200464i	$0.0642449\pi$
$224$		0			0
$225$	−0.738550	−	6.29059i	−0.0492367	−	0.419372i
$226$		0			0
$227$	−19.1113			−1.26846			−0.634230	−	0.773145i	$-0.718683\pi$
$227$	−19.1113			−1.26846			−0.634230	+	0.773145i	$0.718683\pi$
$228$		0			0
$229$	−11.4451			−0.756311			−0.378155	−	0.925742i	$-0.623441\pi$
$229$	−11.4451			−0.756311			−0.378155	+	0.925742i	$0.623441\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.595243	−	1.03099i	0.0389956	−	0.0675424i	−0.845869	−	0.533391i	$-0.820917\pi$
$233$	0.595243	−	1.03099i	0.0389956	−	0.0675424i	0.884865	+	0.465848i	$0.154251\pi$
$234$		0			0
$235$	11.0371	+	19.1168i	0.719979	+	1.24704i
$236$		0			0
$237$	−3.22184	+	15.6237i	−0.209281	+	1.01487i
$238$		0			0
$239$	−12.1414	−	21.0296i	−0.785365	−	1.36029i	−0.928781	−	0.370630i	$-0.879142\pi$
$239$	−12.1414	−	21.0296i	−0.785365	−	1.36029i	0.143416	−	0.989663i	$-0.454191\pi$
$240$		0			0
$241$	21.4189			1.37971			0.689857	−	0.723946i	$-0.257673\pi$
$241$	21.4189			1.37971			0.689857	+	0.723946i	$0.257673\pi$
$242$		0			0
$243$	−13.7305	−	7.38061i	−0.880812	−	0.473466i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.87773			−0.246734
$248$		0			0
$249$	14.4851	−	4.80397i	0.917954	−	0.304439i
$250$		0			0
$251$	2.67996			0.169158			0.0845789	−	0.996417i	$-0.473045\pi$
$251$	2.67996			0.169158			0.0845789	+	0.996417i	$0.473045\pi$
$252$		0			0
$253$	1.76371			0.110884
$254$		0			0
$255$	−1.67123	+	8.10430i	−0.104656	+	0.507511i
$256$		0			0
$257$	11.0851			0.691471			0.345736	−	0.938332i	$-0.387629\pi$
$257$	11.0851			0.691471			0.345736	+	0.938332i	$0.387629\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−12.4277	−	5.35317i	−0.769253	−	0.331353i
$262$		0			0
$263$	13.4079			0.826768			0.413384	−	0.910557i	$-0.364347\pi$
$263$	13.4079			0.826768			0.413384	+	0.910557i	$0.364347\pi$
$264$		0			0
$265$	−1.60507	−	2.78007i	−0.0985989	−	0.170778i
$266$		0			0
$267$	15.8709	−	5.26357i	0.971281	−	0.322125i
$268$		0			0
$269$	2.04511	+	3.54224i	0.124693	+	0.215974i	0.921613	−	0.388111i	$-0.126872\pi$
$269$	2.04511	+	3.54224i	0.124693	+	0.215974i	−0.796920	+	0.604085i	$0.793539\pi$
$270$		0			0
$271$	3.06182	−	5.30323i	0.185992	−	0.322148i	−0.757918	−	0.652350i	$-0.773783\pi$
$271$	3.06182	−	5.30323i	0.185992	−	0.322148i	0.943910	+	0.330201i	$0.107117\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.22981			−0.315370
$276$		0			0
$277$	15.7651			0.947233			0.473616	−	0.880731i	$-0.342948\pi$
$277$	15.7651			0.947233			0.473616	+	0.880731i	$0.342948\pi$
$278$		0			0
$279$	14.0488	+	6.05146i	0.841077	+	0.362291i
$280$		0			0
$281$	10.5946	−	18.3503i	0.632018	−	1.09469i	−0.355120	−	0.934821i	$-0.615560\pi$
$281$	10.5946	−	18.3503i	0.632018	−	1.09469i	0.987139	−	0.159867i	$-0.0511065\pi$
$282$		0			0
$283$	3.43818	−	5.95510i	0.204378	−	0.353994i	−0.745556	−	0.666443i	$-0.767816\pi$
$283$	3.43818	−	5.95510i	0.204378	−	0.353994i	0.949935	+	0.312449i	$0.101149\pi$
$284$		0			0
$285$	−13.9363	+	4.62198i	−0.825516	+	0.273782i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.54944	−	7.87987i	0.267614	−	0.463521i
$290$		0			0
$291$	14.2065	−	4.71159i	0.832800	−	0.276198i
$292$		0			0
$293$	−13.7534	−	23.8216i	−0.803482	−	1.39167i	−0.917311	−	0.398172i	$-0.869645\pi$
$293$	−13.7534	−	23.8216i	−0.803482	−	1.39167i	0.113829	−	0.993500i	$-0.463689\pi$
$294$		0			0
$295$	12.1421	−	21.0308i	0.706943	−	1.22446i
$296$		0			0
$297$	−7.37457	+	10.5493i	−0.427916	+	0.612134i
$298$		0			0
$299$	0.276783	+	0.479402i	0.0160068	+	0.0277245i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.12110	−	2.77610i	−0.179302	−	0.159483i
$304$		0			0
$305$	12.1600	+	21.0618i	0.696281	+	1.20599i
$306$		0			0
$307$	21.5178			1.22809			0.614043	−	0.789273i	$-0.289542\pi$
$307$	21.5178			1.22809			0.614043	+	0.789273i	$0.289542\pi$
$308$		0			0
$309$	5.60872	+	4.98874i	0.319069	+	0.283800i
$310$		0			0
$311$	9.19275	−	15.9223i	0.521273	−	0.902871i	−0.478421	−	0.878131i	$-0.658791\pi$
$311$	9.19275	−	15.9223i	0.521273	−	0.902871i	0.999694	−	0.0247407i	$-0.00787601\pi$
$312$		0			0
$313$	−0.000688709	−	0.00119288i	−3.89281e−5	−	6.74255e-5i	0.866006	−	0.500034i	$-0.166679\pi$
$313$	−0.000688709	−	0.00119288i	−3.89281e−5	−	6.74255e-5i	−0.866045	+	0.499966i	$0.833346\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.04944	−	12.2100i	−0.395936	−	0.685781i	0.597284	−	0.802030i	$-0.296247\pi$
$317$	−7.04944	−	12.2100i	−0.395936	−	0.685781i	−0.993220	+	0.116248i	$0.962913\pi$
$318$		0			0
$319$	−5.58650	+	9.67611i	−0.312784	+	0.541758i
$320$		0			0
$321$	−31.5611	+	10.4672i	−1.76157	+	0.584223i
$322$		0			0
$323$	−14.0197			−0.780075
$324$		0			0
$325$	−0.820724	−	1.42154i	−0.0455256	−	0.0788526i
$326$		0			0
$327$	6.63348	−	32.1678i	0.366832	−	1.77888i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.98143	−	12.0922i	−0.383734	−	0.664647i	0.607859	−	0.794045i	$-0.292029\pi$
$331$	−6.98143	−	12.0922i	−0.383734	−	0.664647i	−0.991593	+	0.129398i	$0.958695\pi$
$332$		0			0
$333$	18.9462	+	8.16100i	1.03824	+	0.447220i
$334$		0			0
$335$	−6.78799	+	11.7571i	−0.370868	+	0.642362i
$336$		0			0
$337$	−12.0982	−	20.9547i	−0.659031	−	1.14147i	−0.980867	−	0.194679i	$-0.937633\pi$
$337$	−12.0982	−	20.9547i	−0.659031	−	1.14147i	0.321836	−	0.946795i	$-0.395700\pi$
$338$		0			0
$339$	4.52290	−	21.9330i	0.245650	−	1.19123i
$340$		0			0
$341$	6.31522	−	10.9383i	0.341988	−	0.592341i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.56615	+	1.39303i	0.0843188	+	0.0749985i
$346$		0			0
$347$	16.3578	−	28.3325i	0.878132	−	1.52097i	0.0247435	−	0.999694i	$-0.492123\pi$
$347$	16.3578	−	28.3325i	0.878132	−	1.52097i	0.853389	−	0.521275i	$-0.174544\pi$
$348$		0			0
$349$	−11.8887	+	20.5919i	−0.636389	+	1.10226i	0.349830	+	0.936813i	$0.386240\pi$
$349$	−11.8887	+	20.5919i	−0.636389	+	1.10226i	−0.986219	+	0.165445i	$0.947094\pi$
$350$		0			0
$351$	−4.02476	−	0.348986i	−0.214826	−	0.0186275i
$352$		0			0
$353$	−20.0617			−1.06778			−0.533889	−	0.845554i	$-0.679270\pi$
$353$	−20.0617			−1.06778			−0.533889	+	0.845554i	$0.679270\pi$
$354$		0			0
$355$	−17.4437			−0.925814
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.15087	+	7.18953i	−0.219075	+	0.379449i	−0.954525	−	0.298130i	$-0.903637\pi$
$359$	−4.15087	+	7.18953i	−0.219075	+	0.379449i	0.735451	+	0.677578i	$0.236971\pi$
$360$		0			0
$361$	−2.93818	−	5.08907i	−0.154641	−	0.267846i
$362$		0			0
$363$	−6.29487	−	5.59905i	−0.330395	−	0.293874i
$364$		0			0
$365$	4.23855	+	7.34138i	0.221856	+	0.384266i
$366$		0			0
$367$	−11.5439			−0.602589			−0.301294	−	0.953531i	$-0.597419\pi$
$367$	−11.5439			−0.602589			−0.301294	+	0.953531i	$0.597419\pi$
$368$		0			0
$369$	14.1353	−	10.5346i	0.735852	−	0.548411i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.85160			0.147650			0.0738250	−	0.997271i	$-0.476479\pi$
$373$	2.85160			0.147650			0.0738250	+	0.997271i	$0.476479\pi$
$374$		0			0
$375$	−15.6421	−	13.9131i	−0.807756	−	0.718469i
$376$		0			0
$377$	−3.50680			−0.180609
$378$		0			0
$379$	35.9519			1.84672			0.923361	−	0.383932i	$-0.125430\pi$
$379$	35.9519			1.84672			0.923361	+	0.383932i	$0.125430\pi$
$380$		0			0
$381$	22.8152	+	20.2933i	1.16886	+	1.03966i
$382$		0			0
$383$	1.83056			0.0935370			0.0467685	−	0.998906i	$-0.485108\pi$
$383$	1.83056			0.0935370			0.0467685	+	0.998906i	$0.485108\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	12.8225	+	5.52325i	0.651805	+	0.280763i
$388$		0			0
$389$	−11.3906			−0.577526			−0.288763	−	0.957401i	$-0.593244\pi$
$389$	−11.3906			−0.577526			−0.288763	+	0.957401i	$0.593244\pi$
$390$		0			0
$391$	1.00069	+	1.73324i	0.0506070	+	0.0876539i
$392$		0			0
$393$	7.36033	+	6.54674i	0.371280	+	0.330240i
$394$		0			0
$395$	7.82691	+	13.5566i	0.393815	+	0.682107i
$396$		0			0
$397$	−5.21565	+	9.03377i	−0.261766	+	0.453392i	−0.966711	−	0.255870i	$-0.917638\pi$
$397$	−5.21565	+	9.03377i	−0.261766	+	0.453392i	0.704945	+	0.709262i	$0.250972\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−34.0741			−1.70158			−0.850790	−	0.525505i	$-0.823876\pi$
$401$	−34.0741			−1.70158			−0.850790	+	0.525505i	$0.823876\pi$
$402$		0			0
$403$	3.96424			0.197473
$404$		0			0
$405$	−14.8807	+	3.54299i	−0.739427	+	0.176053i
$406$		0			0
$407$	8.51671	−	14.7514i	0.422158	−	0.731199i
$408$		0			0
$409$	1.98762	−	3.44266i	0.0982815	−	0.170229i	−0.812692	−	0.582694i	$-0.801999\pi$
$409$	1.98762	−	3.44266i	0.0982815	−	0.170229i	0.910973	+	0.412465i	$0.135332\pi$
$410$		0			0
$411$	−25.1749	−	22.3921i	−1.24178	−	1.10452i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7.48762	−	12.9689i	0.367553	−	0.636620i
$416$		0			0
$417$	1.04511	−	5.06807i	0.0511793	−	0.248185i
$418$		0			0
$419$	−4.72184	−	8.17847i	−0.230677	−	0.399544i	0.727331	−	0.686287i	$-0.240761\pi$
$419$	−4.72184	−	8.17847i	−0.230677	−	0.399544i	−0.958008	+	0.286743i	$0.907427\pi$
$420$		0			0
$421$	3.16002	−	5.47331i	0.154010	−	0.266753i	−0.778688	−	0.627411i	$-0.784115\pi$
$421$	3.16002	−	5.47331i	0.154010	−	0.266753i	0.932698	+	0.360658i	$0.117448\pi$
$422$		0			0
$423$	−31.2410	+	23.2831i	−1.51899	+	1.13206i
$424$		0			0
$425$	−2.96727	−	5.13946i	−0.143934	−	0.249300i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.673698	+	3.26697i	−0.0325265	+	0.157731i
$430$		0			0
$431$	13.8770	+	24.0357i	0.668434	+	1.15776i	0.978342	+	0.206995i	$0.0663683\pi$
$431$	13.8770	+	24.0357i	0.668434	+	1.15776i	−0.309908	+	0.950766i	$0.600298\pi$
$432$		0			0
$433$	−11.2473			−0.540510			−0.270255	−	0.962789i	$-0.587108\pi$
$433$	−11.2473			−0.540510			−0.270255	+	0.962789i	$0.587108\pi$
$434$		0			0
$435$	−12.6032	+	4.17985i	−0.604278	+	0.200409i
$436$		0			0
$437$	−1.77561	+	3.07545i	−0.0849391	+	0.147119i
$438$		0			0
$439$	−7.54325	−	13.0653i	−0.360020	−	0.623573i	0.627944	−	0.778259i	$-0.283897\pi$
$439$	−7.54325	−	13.0653i	−0.360020	−	0.623573i	−0.987964	+	0.154686i	$0.950563\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.96658	−	6.87032i	−0.188458	−	0.326419i	0.756278	−	0.654250i	$-0.227016\pi$
$443$	−3.96658	−	6.87032i	−0.188458	−	0.326419i	−0.944736	+	0.327831i	$0.893682\pi$
$444$		0			0
$445$	8.20396	−	14.2097i	0.388905	−	0.673603i
$446$		0			0
$447$	10.4814	+	9.32284i	0.495755	+	0.440955i
$448$		0			0
$449$	−32.5636			−1.53677			−0.768386	−	0.639987i	$-0.778940\pi$
$449$	−32.5636			−1.53677			−0.768386	+	0.639987i	$0.778940\pi$
$450$		0			0
$451$	−7.27816	−	12.6061i	−0.342715	−	0.593600i
$452$		0			0
$453$	−11.4716	−	10.2036i	−0.538983	−	0.479405i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.70396	−	9.87955i	−0.266820	−	0.462146i	0.701219	−	0.712946i	$-0.252640\pi$
$457$	−5.70396	−	9.87955i	−0.266820	−	0.462146i	−0.968039	+	0.250800i	$0.919306\pi$
$458$		0			0
$459$	−14.5512	−	1.26174i	−0.679193	−	0.0588927i
$460$		0			0
$461$	2.45853	−	4.25830i	0.114505	−	0.198329i	−0.803077	−	0.595876i	$-0.796805\pi$
$461$	2.45853	−	4.25830i	0.114505	−	0.198329i	0.917582	+	0.397547i	$0.130138\pi$
$462$		0			0
$463$	−7.59957	−	13.1628i	−0.353182	−	0.611729i	0.633623	−	0.773642i	$-0.281567\pi$
$463$	−7.59957	−	13.1628i	−0.353182	−	0.611729i	−0.986805	+	0.161913i	$0.948234\pi$
$464$		0			0
$465$	14.2472	−	4.72509i	0.660699	−	0.219121i
$466$		0			0
$467$	11.8905	−	20.5950i	0.550228	−	0.953022i	−0.448030	−	0.894018i	$-0.647874\pi$
$467$	11.8905	−	20.5950i	0.550228	−	0.953022i	0.998258	−	0.0590037i	$-0.0187924\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−14.4098	+	4.77900i	−0.663967	+	0.220205i
$472$		0			0
$473$	5.76400	−	9.98354i	0.265029	−	0.459044i
$474$		0			0
$475$	5.26509	−	9.11941i	0.241579	−	0.418427i
$476$		0			0
$477$	4.54325	−	3.38597i	0.208021	−	0.155033i
$478$		0			0
$479$	−6.05818			−0.276805			−0.138403	−	0.990376i	$-0.544197\pi$
$479$	−6.05818			−0.276805			−0.138403	+	0.990376i	$0.544197\pi$
$480$		0			0
$481$	5.34617			0.243764
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.34362	−	12.7195i	0.333457	−	0.577564i
$486$		0			0
$487$	−0.568012	−	0.983825i	−0.0257391	−	0.0445814i	0.852869	−	0.522125i	$-0.174861\pi$
$487$	−0.568012	−	0.983825i	−0.0257391	−	0.0445814i	−0.878608	+	0.477544i	$0.841527\pi$
$488$		0			0
$489$	3.26764	−	1.08371i	0.147768	−	0.0490072i
$490$		0			0
$491$	16.4382	+	28.4718i	0.741845	+	1.28491i	0.951655	+	0.307170i	$0.0993821\pi$
$491$	16.4382	+	28.4718i	0.741845	+	1.28491i	−0.209810	+	0.977742i	$0.567285\pi$
$492$		0			0
$493$	−12.6786			−0.571015
$494$		0			0
$495$	1.47277	+	12.5443i	0.0661961	+	0.563824i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	26.1978			1.17277			0.586387	−	0.810031i	$-0.300550\pi$
$499$	26.1978			1.17277			0.586387	+	0.810031i	$0.300550\pi$
$500$		0			0
$501$	−0.917137	+	4.44749i	−0.0409747	+	0.198699i
$502$		0			0
$503$	25.8516			1.15267			0.576333	−	0.817215i	$-0.304483\pi$
$503$	25.8516			1.15267			0.576333	+	0.817215i	$0.304483\pi$
$504$		0			0
$505$	−4.09888			−0.182398
$506$		0			0
$507$	20.3782	−	6.75843i	0.905028	−	0.300153i
$508$		0			0
$509$	−35.1716			−1.55896			−0.779478	−	0.626430i	$-0.784515\pi$
$509$	−35.1716			−1.55896			−0.779478	+	0.626430i	$0.784515\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−10.9709	−	23.4798i	−0.484378	−	1.03666i
$514$		0			0
$515$	7.36584			0.324578
$516$		0			0
$517$	16.0858	+	27.8615i	0.707453	+	1.22535i
$518$		0			0
$519$	1.82946	−	8.87163i	0.0803045	−	0.389421i
$520$		0			0
$521$	−8.93130	−	15.4695i	−0.391287	−	0.677730i	0.601332	−	0.798999i	$-0.294637\pi$
$521$	−8.93130	−	15.4695i	−0.391287	−	0.677730i	−0.992620	+	0.121270i	$0.961303\pi$
$522$		0			0
$523$	−11.4320	+	19.8008i	−0.499886	+	0.865828i	−1.00000		0.000131698i	$-0.999958\pi$
$523$	−11.4320	+	19.8008i	−0.499886	+	0.865828i	0.500114	+	0.865960i	$0.333291\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.3324			0.624330
$528$		0			0
$529$	−22.4930			−0.977958
$530$		0			0
$531$	39.3671	+	16.9573i	1.70839	+	0.735883i
$532$		0			0
$533$	2.28435	−	3.95661i	0.0989462	−	0.171380i
$534$		0			0
$535$	−16.3145	+	28.2576i	−0.705339	+	1.22168i
$536$		0			0
$537$	−1.66690	+	8.08330i	−0.0719319	+	0.348820i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.1538	+	19.3190i	−0.479541	+	0.830589i	−0.999725	−	0.0234656i	$-0.992530\pi$
$541$	−11.1538	+	19.3190i	−0.479541	+	0.830589i	0.520184	+	0.854054i	$0.325863\pi$
$542$		0			0
$543$	13.5000	+	12.0077i	0.579340	+	0.515302i
$544$		0			0
$545$	−16.1149	−	27.9118i	−0.690287	−	1.19561i
$546$		0			0
$547$	−10.8083	+	18.7206i	−0.462131	+	0.800435i	−0.999067	−	0.0431882i	$-0.986249\pi$
$547$	−10.8083	+	18.7206i	−0.462131	+	0.800435i	0.536936	+	0.843623i	$0.319582\pi$
$548$		0			0
$549$	−34.4196	+	25.6520i	−1.46899	+	1.09480i
$550$		0			0
$551$	−11.2484	−	19.4828i	−0.479197	−	0.829994i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	19.2138	−	6.37225i	0.815580	−	0.270487i
$556$		0			0
$557$	−1.58768	−	2.74993i	−0.0672720	−	0.116518i	0.830428	−	0.557127i	$-0.188096\pi$
$557$	−1.58768	−	2.74993i	−0.0672720	−	0.116518i	−0.897700	+	0.440608i	$0.854763\pi$
$558$		0			0
$559$	3.61822			0.153034
$560$		0			0
$561$	−2.43571	+	11.8115i	−0.102836	+	0.498682i
$562$		0			0
$563$	21.8814	−	37.8997i	0.922190	−	1.59728i	0.126171	−	0.992009i	$-0.459731\pi$
$563$	21.8814	−	37.8997i	0.922190	−	1.59728i	0.796019	−	0.605271i	$-0.206935\pi$
$564$		0			0
$565$	−10.9876	−	19.0311i	−0.462253	−	0.800645i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.9313	+	20.6656i	0.500186	+	0.866348i	1.00000		0.000214897i	$6.84039e-5\pi$
$569$	11.9313	+	20.6656i	0.500186	+	0.866348i	−0.499814	+	0.866133i	$0.666598\pi$
$570$		0			0
$571$	−5.11058	+	8.85178i	−0.213871	+	0.370435i	−0.952923	−	0.303213i	$-0.901941\pi$
$571$	−5.11058	+	8.85178i	−0.213871	+	0.370435i	0.739052	+	0.673649i	$0.235274\pi$
$572$		0			0
$573$	4.66002	−	22.5979i	0.194675	−	0.944040i
$574$		0			0
$575$	−1.50324			−0.0626893
$576$		0			0
$577$	−18.0185	−	31.2089i	−0.750120	−	1.29925i	−0.947764	−	0.318972i	$-0.896663\pi$
$577$	−18.0185	−	31.2089i	−0.750120	−	1.29925i	0.197645	−	0.980274i	$-0.436671\pi$
$578$		0			0
$579$	24.0705	−	7.98297i	1.00034	−	0.331761i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.33929	−	4.05178i	−0.0968836	−	0.167807i
$584$		0			0
$585$	−3.17859	+	2.36892i	−0.131418	+	0.0979427i
$586$		0			0
$587$	−10.5142	+	18.2111i	−0.433966	+	0.751651i	−0.997211	−	0.0746391i	$-0.976220\pi$
$587$	−10.5142	+	18.2111i	−0.433966	+	0.751651i	0.563245	+	0.826290i	$0.309553\pi$
$588$		0			0
$589$	12.7156	+	22.0242i	0.523939	+	0.907489i
$590$		0			0
$591$	−23.9239	−	21.2795i	−0.984099	−	0.875320i
$592$		0			0
$593$	−12.5803	+	21.7897i	−0.516612	+	0.894798i	0.483202	+	0.875509i	$0.339474\pi$
$593$	−12.5803	+	21.7897i	−0.516612	+	0.894798i	−0.999814	+	0.0192889i	$0.993860\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.26145	+	40.0624i	−0.338119	+	1.63964i
$598$		0			0
$599$	1.11126	−	1.92477i	0.0454050	−	0.0786438i	−0.842430	−	0.538806i	$-0.818875\pi$
$599$	1.11126	−	1.92477i	0.0454050	−	0.0786438i	0.887835	+	0.460162i	$0.152209\pi$
$600$		0			0
$601$	14.0494	−	24.3343i	0.573089	−	0.992619i	−0.423158	−	0.906056i	$-0.639078\pi$
$601$	14.0494	−	24.3343i	0.573089	−	0.992619i	0.996246	−	0.0865627i	$-0.0275883\pi$
$602$		0			0
$603$	−22.0080	−	9.47987i	−0.896234	−	0.386050i
$604$		0			0
$605$	−8.26695			−0.336099
$606$		0			0
$607$	6.53018			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$607$	6.53018			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.04875	+	8.74470i	−0.204251	+	0.353773i
$612$		0			0
$613$	−5.36398	−	9.29068i	−0.216649	−	0.375247i	0.737132	−	0.675748i	$-0.236179\pi$
$613$	−5.36398	−	9.29068i	−0.216649	−	0.375247i	−0.953781	+	0.300501i	$0.902846\pi$
$614$		0			0
$615$	3.49381	−	16.9426i	0.140884	−	0.683191i
$616$		0			0
$617$	15.5265	+	26.8928i	0.625075	+	1.08266i	0.988526	+	0.151049i	$0.0482650\pi$
$617$	15.5265	+	26.8928i	0.625075	+	1.08266i	−0.363451	+	0.931613i	$0.618402\pi$
$618$		0			0
$619$	1.44643			0.0581371			0.0290685	−	0.999577i	$-0.490746\pi$
$619$	1.44643			0.0581371			0.0290685	+	0.999577i	$0.490746\pi$
$620$		0			0
$621$	−2.11972	+	3.03226i	−0.0850614	+	0.121680i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−9.98624			−0.399450
$626$		0			0
$627$	−20.3113	+	6.73624i	−0.811155	+	0.269019i
$628$		0			0
$629$	19.3287			0.770686
$630$		0			0
$631$	0.0741250			0.00295087			0.00147544	−	0.999999i	$-0.499530\pi$
$631$	0.0741250			0.00295087			0.00147544	+	0.999999i	$0.499530\pi$
$632$		0			0
$633$	−5.09152	+	24.6904i	−0.202370	+	0.981355i
$634$		0			0
$635$	29.9629			1.18904
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.59022	−	30.5797i	−0.142027	−	1.20971i
$640$		0			0
$641$	−47.0407			−1.85800			−0.928998	−	0.370085i	$-0.879329\pi$
$641$	−47.0407			−1.85800			−0.928998	+	0.370085i	$0.879329\pi$
$642$		0			0
$643$	−16.8647	−	29.2105i	−0.665077	−	1.15195i	−0.979264	−	0.202587i	$-0.935065\pi$
$643$	−16.8647	−	29.2105i	−0.665077	−	1.15195i	0.314187	−	0.949361i	$-0.398268\pi$
$644$		0			0
$645$	13.0036	−	4.31266i	0.512018	−	0.169811i
$646$		0			0
$647$	22.4814	+	38.9390i	0.883836	+	1.53085i	0.847042	+	0.531526i	$0.178381\pi$
$647$	22.4814	+	38.9390i	0.883836	+	1.53085i	0.0367945	+	0.999323i	$0.488285\pi$
$648$		0			0
$649$	17.6964	−	30.6510i	0.694644	−	1.20316i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	41.7156			1.63246			0.816228	−	0.577730i	$-0.196061\pi$
$653$	41.7156			1.63246			0.816228	+	0.577730i	$0.196061\pi$
$654$		0			0
$655$	9.66621			0.377690
$656$		0			0
$657$	−11.9975	+	8.94138i	−0.468065	+	0.348837i
$658$		0			0
$659$	10.5259	−	18.2313i	0.410029	−	0.710191i	−0.584863	−	0.811132i	$-0.698852\pi$
$659$	10.5259	−	18.2313i	0.410029	−	0.710191i	0.994892	+	0.100941i	$0.0321852\pi$
$660$		0			0
$661$	11.2218	−	19.4368i	0.436479	−	0.756004i	−0.560936	−	0.827859i	$-0.689559\pi$
$661$	11.2218	−	19.4368i	0.436479	−	0.756004i	0.997415	+	0.0718553i	$0.0228920\pi$
$662$		0			0
$663$	−3.59277	+	1.19154i	−0.139532	+	0.0462757i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.60576	+	2.78126i	−0.0621754	+	0.107691i
$668$		0			0
$669$	15.5276	−	5.14974i	0.600333	−	0.199100i
$670$		0			0
$671$	17.7225	+	30.6962i	0.684168	+	1.18501i
$672$		0			0
$673$	5.83929	−	10.1140i	0.225088	−	0.389864i	−0.731258	−	0.682101i	$-0.761066\pi$
$673$	5.83929	−	10.1140i	0.225088	−	0.389864i	0.956346	+	0.292237i	$0.0943996\pi$
$674$		0			0
$675$	6.28544	−	8.99133i	0.241927	−	0.346076i
$676$		0			0
$677$	5.23422	+	9.06593i	0.201167	+	0.348432i	0.948905	−	0.315562i	$-0.102193\pi$
$677$	5.23422	+	9.06593i	0.201167	+	0.348432i	−0.747737	+	0.663995i	$0.768860\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−24.7335	−	21.9995i	−0.947788	−	0.843022i
$682$		0			0
$683$	−16.4079	−	28.4193i	−0.627832	−	1.08744i	−0.987986	−	0.154543i	$-0.950609\pi$
$683$	−16.4079	−	28.4193i	−0.627832	−	1.08744i	0.360154	−	0.932893i	$-0.382724\pi$
$684$		0			0
$685$	−33.0617			−1.26322
$686$		0			0
$687$	−14.8120	−	13.1747i	−0.565113	−	0.502647i
$688$		0			0
$689$	0.734219	−	1.27171i	0.0279715	−	0.0484481i
$690$		0			0
$691$	2.95056	+	5.11052i	0.112245	+	0.194413i	0.916675	−	0.399634i	$-0.130863\pi$
$691$	2.95056	+	5.11052i	0.112245	+	0.194413i	−0.804430	+	0.594047i	$0.797529\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.53892	−	4.39754i	−0.0963068	−	0.166808i
$696$		0			0
$697$	8.25890	−	14.3048i	0.312828	−	0.541834i
$698$		0			0
$699$	1.95715	−	0.649089i	0.0740263	−	0.0245508i
$700$		0			0
$701$	−12.3782			−0.467519			−0.233759	−	0.972294i	$-0.575103\pi$
$701$	−12.3782			−0.467519			−0.233759	+	0.972294i	$0.575103\pi$
$702$		0			0
$703$	17.1483	+	29.7018i	0.646761	+	1.12022i
$704$		0			0
$705$	−7.72184	+	37.4456i	−0.290821	+	1.41028i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.64145	+	11.5033i	0.249425	+	0.432016i	0.963366	−	0.268189i	$-0.0864251\pi$
$709$	6.64145	+	11.5033i	0.249425	+	0.432016i	−0.713942	+	0.700205i	$0.753092\pi$
$710$		0			0
$711$	−22.1545	+	16.5112i	−0.830859	+	0.619217i
$712$		0			0
$713$	1.81522	−	3.14406i	0.0679806	−	0.117746i
$714$		0			0
$715$	1.63664	+	2.83474i	0.0612067	+	0.106013i
$716$		0			0
$717$	8.49450	−	41.1925i	0.317233	−	1.53836i
$718$		0			0
$719$	−12.1847	+	21.1045i	−0.454413	+	0.787066i	−0.998654	−	0.0518628i	$-0.983484\pi$
$719$	−12.1847	+	21.1045i	−0.454413	+	0.787066i	0.544242	+	0.838929i	$0.316817\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	27.7200	+	24.6559i	1.03092	+	0.916963i
$724$		0			0
$725$	4.76145	−	8.24707i	0.176836	−	0.306289i
$726$		0			0
$727$	−7.99450	+	13.8469i	−0.296500	+	0.513552i	−0.975333	−	0.220740i	$-0.929153\pi$
$727$	−7.99450	+	13.8469i	−0.296500	+	0.513552i	0.678833	+	0.734293i	$0.262486\pi$
$728$		0			0
$729$	−9.27375	−	25.3574i	−0.343472	−	0.939163i
$730$		0			0
$731$	13.0814			0.483833
$732$		0			0
$733$	42.2829			1.56175			0.780877	−	0.624685i	$-0.214772\pi$
$733$	42.2829			1.56175			0.780877	+	0.624685i	$0.214772\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.89307	+	17.1353i	−0.364416	+	0.631187i
$738$		0			0
$739$	1.54325	+	2.67299i	0.0567695	+	0.0983276i	0.893014	−	0.450030i	$-0.148587\pi$
$739$	1.54325	+	2.67299i	0.0567695	+	0.0983276i	−0.836244	+	0.548357i	$0.815253\pi$
$740$		0			0
$741$	−5.01849	−	4.46376i	−0.184359	−	0.163980i
$742$		0			0
$743$	−3.31522	−	5.74213i	−0.121624	−	0.210658i	0.798784	−	0.601617i	$-0.205477\pi$
$743$	−3.31522	−	5.74213i	−0.121624	−	0.210658i	−0.920408	+	0.390959i	$0.872143\pi$
$744$		0			0
$745$	13.7651			0.504314
$746$		0			0
$747$	24.2763	+	10.4569i	0.888223	+	0.382599i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−42.7403			−1.55962			−0.779808	−	0.626018i	$-0.784684\pi$
$751$	−42.7403			−1.55962			−0.779808	+	0.626018i	$0.784684\pi$
$752$		0			0
$753$	3.46836	+	3.08498i	0.126394	+	0.112423i
$754$		0			0
$755$	−15.0655			−0.548288
$756$		0			0
$757$	−31.0232			−1.12756			−0.563779	−	0.825926i	$-0.690653\pi$
$757$	−31.0232			−1.12756			−0.563779	+	0.825926i	$0.690653\pi$
$758$		0			0
$759$	2.28257	+	2.03026i	0.0828520	+	0.0736937i
$760$		0			0
$761$	−23.6364			−0.856817			−0.428409	−	0.903585i	$-0.640926\pi$
$761$	−23.6364			−0.856817			−0.428409	+	0.903585i	$0.640926\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−11.4920	+	8.56465i	−0.415492	+	0.309655i
$766$		0			0
$767$	11.1085			0.401105
$768$		0			0
$769$	−1.73422	−	3.00376i	−0.0625375	−	0.108318i	0.833061	−	0.553180i	$-0.186586\pi$
$769$	−1.73422	−	3.00376i	−0.0625375	−	0.108318i	−0.895599	+	0.444862i	$0.853253\pi$
$770$		0			0
$771$	14.3462	+	12.7604i	0.516665	+	0.459554i
$772$		0			0
$773$	17.2985	+	29.9619i	0.622184	+	1.07765i	0.989078	+	0.147392i	$0.0470879\pi$
$773$	17.2985	+	29.9619i	0.622184	+	1.07765i	−0.366894	+	0.930263i	$0.619579\pi$
$774$		0			0
$775$	−5.38255	+	9.32284i	−0.193347	+	0.334886i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	29.3090			1.05011
$780$		0			0
$781$	−25.4231			−0.909708
$782$		0			0
$783$	−9.92147	−	21.2338i	−0.354564	−	0.758834i
$784$		0			0
$785$	−7.44870	+	12.9015i	−0.265855	+	0.460475i
$786$		0			0
$787$	−6.07963	+	10.5302i	−0.216715	+	0.375362i	−0.953802	−	0.300437i	$-0.902868\pi$
$787$	−6.07963	+	10.5302i	−0.216715	+	0.375362i	0.737087	+	0.675798i	$0.236201\pi$
$788$		0			0
$789$	17.3523	+	15.4342i	0.617758	+	0.549473i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.56243	+	9.63442i	−0.197528	+	0.342128i
$794$		0			0
$795$	1.12296	−	5.44556i	0.0398271	−	0.193134i
$796$		0			0
$797$	2.89493	+	5.01416i	0.102544	+	0.177611i	0.912732	−	0.408559i	$-0.133969\pi$
$797$	2.89493	+	5.01416i	0.102544	+	0.177611i	−0.810188	+	0.586170i	$0.800635\pi$
$798$		0			0
$799$	−18.2534	+	31.6158i	−0.645759	+	1.11849i
$800$		0			0
$801$	26.5988	+	11.4574i	0.939823	+	0.404826i
$802$		0			0
$803$	6.17742	+	10.6996i	0.217996	+	0.377581i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.43082	+	6.93848i	−0.0503672	+	0.244246i
$808$		0			0
$809$	24.5908	+	42.5926i	0.864568	+	1.49748i	0.867476	+	0.497479i	$0.165741\pi$
$809$	24.5908	+	42.5926i	0.864568	+	1.49748i	−0.00290803	+	0.999996i	$0.500926\pi$
$810$		0			0
$811$	−40.7266			−1.43010			−0.715052	−	0.699072i	$-0.753597\pi$
$811$	−40.7266			−1.43010			−0.715052	+	0.699072i	$0.753597\pi$
$812$		0			0
$813$	10.0672	−	3.33880i	0.353074	−	0.117097i
$814$		0			0
$815$	1.68911	−	2.92562i	0.0591669	−	0.102480i
$816$		0			0
$817$	11.6058	+	20.1018i	0.406034	+	0.703272i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.54689	−	13.0716i	−0.263388	−	0.456202i	0.703752	−	0.710446i	$-0.251507\pi$
$821$	−7.54689	−	13.0716i	−0.263388	−	0.456202i	−0.967140	+	0.254244i	$0.918173\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$		0			0
$825$	−6.76833	−	6.02018i	−0.235643	−	0.209596i
$826$		0			0
$827$	35.2348			1.22523			0.612616	−	0.790381i	$-0.290117\pi$
$827$	35.2348			1.22523			0.612616	+	0.790381i	$0.290117\pi$
$828$		0			0
$829$	−1.61745	−	2.80151i	−0.0561765	−	0.0973006i	0.836570	−	0.547861i	$-0.184558\pi$
$829$	−1.61745	−	2.80151i	−0.0561765	−	0.0973006i	−0.892746	+	0.450560i	$0.851224\pi$
$830$		0			0
$831$	20.4029	+	18.1476i	0.707769	+	0.629534i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.22803	+	3.85906i	0.0771041	+	0.133548i
$836$		0			0
$837$	11.2156	+	24.0036i	0.387670	+	0.829685i
$838$		0			0
$839$	−15.5197	+	26.8808i	−0.535798	+	0.928030i	0.463326	+	0.886188i	$0.346656\pi$
$839$	−15.5197	+	26.8808i	−0.535798	+	0.928030i	−0.999124	+	0.0418419i	$0.986677\pi$
$840$		0			0
$841$	4.32760	+	7.49563i	0.149228	+	0.258470i
$842$		0			0
$843$	34.8348	−	11.5530i	1.19977	−	0.397905i
$844$		0			0
$845$	10.5339	−	18.2453i	0.362377	−	0.627656i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.3047	−	3.74920i	0.387976	−	0.128672i
$850$		0			0
$851$	2.44801	−	4.24008i	0.0839167	−	0.145348i
$852$		0			0
$853$	−8.03637	+	13.9194i	−0.275160	+	0.476591i	−0.970176	−	0.242403i	$-0.922064\pi$
$853$	−8.03637	+	13.9194i	−0.275160	+	0.476591i	0.695015	+	0.718995i	$0.255398\pi$
$854$		0			0
$855$	−23.3566	−	10.0608i	−0.798779	−	0.344072i
$856$		0			0
$857$	−19.2212			−0.656582			−0.328291	−	0.944577i	$-0.606473\pi$
$857$	−19.2212			−0.656582			−0.328291	+	0.944577i	$0.606473\pi$
$858$		0			0
$859$	14.8022			0.505046			0.252523	−	0.967591i	$-0.418740\pi$
$859$	14.8022			0.505046			0.252523	+	0.967591i	$0.418740\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.38441	+	12.7902i	−0.251368	+	0.435382i	−0.963903	−	0.266255i	$-0.914214\pi$
$863$	−7.38441	+	12.7902i	−0.251368	+	0.435382i	0.712535	+	0.701637i	$0.247547\pi$
$864$		0			0
$865$	−4.44437	−	7.69787i	−0.151113	−	0.261735i
$866$		0			0
$867$	14.9585	−	4.96099i	0.508018	−	0.168484i
$868$		0			0
$869$	11.4072	+	19.7579i	0.386964	+	0.670241i
$870$		0			0
$871$	−6.21015			−0.210423
$872$		0			0
$873$	23.8094	+	10.2558i	0.805827	+	0.347108i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	52.3832			1.76885			0.884427	−	0.466679i	$-0.154550\pi$
$877$	52.3832			1.76885			0.884427	+	0.466679i	$0.154550\pi$
$878$		0			0
$879$	9.62227	−	46.6614i	0.324551	−	1.57385i
$880$		0			0
$881$	31.3214			1.05525			0.527623	−	0.849479i	$-0.323084\pi$
$881$	31.3214			1.05525			0.527623	+	0.849479i	$0.323084\pi$
$882$		0			0
$883$	−43.0494			−1.44873			−0.724363	−	0.689419i	$-0.757866\pi$
$883$	−43.0494			−1.44873			−0.724363	+	0.689419i	$0.757866\pi$
$884$		0			0
$885$	39.9233	−	13.2405i	1.34201	−	0.445076i
$886$		0			0
$887$	14.9766			0.502866			0.251433	−	0.967875i	$-0.419098\pi$
$887$	14.9766			0.502866			0.251433	+	0.967875i	$0.419098\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−21.6877	+	5.16368i	−0.726564	+	0.172990i
$892$		0			0
$893$	−64.7773			−2.16769
$894$		0			0
$895$	4.04944	+	7.01384i	0.135358	+	0.234447i
$896$		0			0
$897$	−0.193645	+	0.939046i	−0.00646562	+	0.0313538i
$898$		0			0
$899$	11.4993	+	19.9174i	0.383524	+	0.664282i
$900$		0			0
$901$	2.65452	−	4.59776i	0.0884348	−	0.153174i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	17.7293			0.589343
$906$		0			0
$907$	30.4559			1.01127			0.505636	−	0.862747i	$-0.331258\pi$
$907$	30.4559			1.01127			0.505636	+	0.862747i	$0.331258\pi$
$908$		0			0
$909$	−0.843624	−	7.18555i	−0.0279812	−	0.238330i
$910$		0			0
$911$	9.97593	−	17.2788i	0.330517	−	0.572473i	−0.652096	−	0.758136i	$-0.726110\pi$
$911$	9.97593	−	17.2788i	0.330517	−	0.572473i	0.982613	+	0.185664i	$0.0594435\pi$
$912$		0			0
$913$	10.9127	−	18.9014i	0.361159	−	0.625545i
$914$		0			0
$915$	−8.50749	+	41.2555i	−0.281249	+	1.36386i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−22.8145	+	39.5159i	−0.752582	+	1.30351i	0.193985	+	0.981004i	$0.437859\pi$
$919$	−22.8145	+	39.5159i	−0.752582	+	1.30351i	−0.946567	+	0.322506i	$0.895475\pi$
$920$		0			0
$921$	27.8480	+	24.7697i	0.917621	+	0.816190i
$922$		0			0
$923$	−3.98969	−	6.91034i	−0.131322	−	0.227457i
$924$		0			0
$925$	−7.25890	+	12.5728i	−0.238671	+	0.413391i
$926$		0			0
$927$	1.51602	+	12.9127i	0.0497927	+	0.424108i
$928$		0			0
$929$	28.1861	+	48.8197i	0.924755	+	1.60172i	0.791954	+	0.610580i	$0.209064\pi$
$929$	28.1861	+	48.8197i	0.924755	+	1.60172i	0.132801	+	0.991143i	$0.457603\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	30.2257	−	10.0243i	0.989545	−	0.328182i
$934$		0			0
$935$	5.91714	+	10.2488i	0.193511	+	0.335171i
$936$		0			0
$937$	36.8530			1.20393			0.601967	−	0.798521i	$-0.294384\pi$
$937$	36.8530			1.20393			0.601967	+	0.798521i	$0.294384\pi$
$938$		0			0
$939$	0.000481840	−	0.00233659i	1.57243e−5	−	7.62519e-5i
$940$		0			0
$941$	−4.38000	+	7.58638i	−0.142784	+	0.247309i	−0.928544	−	0.371223i	$-0.878939\pi$
$941$	−4.38000	+	7.58638i	−0.142784	+	0.247309i	0.785760	+	0.618531i	$0.212272\pi$
$942$		0			0
$943$	−2.09201	−	3.62346i	−0.0681251	−	0.117996i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.3226	−	23.0754i	−0.432926	−	0.749849i	0.564198	−	0.825640i	$-0.309185\pi$
$947$	−13.3226	−	23.0754i	−0.432926	−	0.749849i	−0.997124	+	0.0757901i	$0.975852\pi$
$948$		0			0
$949$	−1.93887	+	3.35822i	−0.0629383	+	0.109012i
$950$		0			0
$951$	4.93199	−	23.9168i	0.159931	−	0.775554i
$952$		0			0
$953$	24.3039			0.787282			0.393641	−	0.919264i	$-0.371215\pi$
$953$	24.3039			0.787282			0.393641	+	0.919264i	$0.371215\pi$
$954$		0			0
$955$	−11.3207	−	19.6081i	−0.366330	−	0.634502i
$956$		0			0
$957$	−18.3684	+	6.09187i	−0.593766	+	0.196922i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.50069	+	4.33132i	0.0806674	+	0.139720i
$962$		0			0
$963$	−52.8948	−	22.7843i	−1.70451	−	0.734214i
$964$		0			0
$965$	12.4425	−	21.5511i	0.400539	−	0.693753i
$966$		0			0
$967$	5.22872	+	9.05641i	0.168144	+	0.291234i	0.937767	−	0.347264i	$-0.112889\pi$
$967$	5.22872	+	9.05641i	0.168144	+	0.291234i	−0.769623	+	0.638498i	$0.779556\pi$
$968$		0			0
$969$	−18.1440	−	16.1384i	−0.582869	−	0.518440i
$970$		0			0
$971$	−20.8578	+	36.1267i	−0.669358	+	1.15936i	0.308726	+	0.951151i	$0.400098\pi$
$971$	−20.8578	+	36.1267i	−0.669358	+	1.15936i	−0.978084	+	0.208211i	$0.933236\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.574202	−	2.78448i	0.0183892	−	0.0891748i
$976$		0			0
$977$	−2.94506	+	5.10099i	−0.0942207	+	0.163195i	−0.909283	−	0.416178i	$-0.863369\pi$
$977$	−2.94506	+	5.10099i	−0.0942207	+	0.163195i	0.815062	+	0.579373i	$0.196703\pi$
$978$		0			0
$979$	11.9567	−	20.7097i	0.382139	−	0.661885i
$980$		0			0
$981$	45.6141	−	33.9950i	1.45635	−	1.08538i
$982$		0			0
$983$	−41.8392			−1.33446			−0.667232	−	0.744850i	$-0.732521\pi$
$983$	−41.8392			−1.33446			−0.667232	+	0.744850i	$0.732521\pi$
$984$		0			0
$985$	−31.4189			−1.00109
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.65678	−	2.86963i	0.0526826	−	0.0912489i
$990$		0			0
$991$	27.3578	+	47.3851i	0.869049	+	1.50524i	0.862970	+	0.505255i	$0.168602\pi$
$991$	27.3578	+	47.3851i	0.869049	+	1.50524i	0.00607865	+	0.999982i	$0.498065\pi$
$992$		0			0
$993$	4.88441	−	23.6860i	0.155002	−	0.751653i
$994$		0			0
$995$	20.0698	+	34.7619i	0.636255	+	1.10203i
$996$		0			0
$997$	18.0495			0.571634			0.285817	−	0.958284i	$-0.407735\pi$
$997$	18.0495			0.571634			0.285817	+	0.958284i	$0.407735\pi$
$998$		0			0
$999$	15.1254	+	32.3712i	0.478547	+	1.02418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.f.961.3		6
3.2	odd	2		5292.2.l.f.3313.1		6
7.2	even	3		1764.2.j.e.1177.1		6
7.3	odd	6		1764.2.i.g.1537.1		6
7.4	even	3		1764.2.i.d.1537.3		6
7.5	odd	6		252.2.j.a.169.3	yes	6
7.6	odd	2		1764.2.l.e.961.1		6
9.4	even	3		1764.2.i.d.373.3		6
9.5	odd	6		5292.2.i.e.1549.3		6
21.2	odd	6		5292.2.j.d.3529.3		6
21.5	even	6		756.2.j.b.505.1		6
21.11	odd	6		5292.2.i.e.2125.3		6
21.17	even	6		5292.2.i.f.2125.1		6
21.20	even	2		5292.2.l.e.3313.3		6
28.19	even	6		1008.2.r.j.673.1		6
63.4	even	3	inner	1764.2.l.f.949.3		6
63.5	even	6		756.2.j.b.253.1		6
63.13	odd	6		1764.2.i.g.373.1		6
63.23	odd	6		5292.2.j.d.1765.3		6
63.31	odd	6		1764.2.l.e.949.1		6
63.32	odd	6		5292.2.l.f.361.1		6
63.40	odd	6		252.2.j.a.85.3	✓	6
63.41	even	6		5292.2.i.f.1549.1		6
63.47	even	6		2268.2.a.h.1.3		3
63.58	even	3		1764.2.j.e.589.1		6
63.59	even	6		5292.2.l.e.361.3		6
63.61	odd	6		2268.2.a.i.1.1		3
84.47	odd	6		3024.2.r.j.2017.1		6
252.47	odd	6		9072.2.a.bv.1.3		3
252.103	even	6		1008.2.r.j.337.1		6
252.131	odd	6		3024.2.r.j.1009.1		6
252.187	even	6		9072.2.a.by.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.3	✓	6	63.40	odd	6
252.2.j.a.169.3	yes	6	7.5	odd	6
756.2.j.b.253.1		6	63.5	even	6
756.2.j.b.505.1		6	21.5	even	6
1008.2.r.j.337.1		6	252.103	even	6
1008.2.r.j.673.1		6	28.19	even	6
1764.2.i.d.373.3		6	9.4	even	3
1764.2.i.d.1537.3		6	7.4	even	3
1764.2.i.g.373.1		6	63.13	odd	6
1764.2.i.g.1537.1		6	7.3	odd	6
1764.2.j.e.589.1		6	63.58	even	3
1764.2.j.e.1177.1		6	7.2	even	3
1764.2.l.e.949.1		6	63.31	odd	6
1764.2.l.e.961.1		6	7.6	odd	2
1764.2.l.f.949.3		6	63.4	even	3	inner
1764.2.l.f.961.3		6	1.1	even	1	trivial
2268.2.a.h.1.3		3	63.47	even	6
2268.2.a.i.1.1		3	63.61	odd	6
3024.2.r.j.1009.1		6	252.131	odd	6
3024.2.r.j.2017.1		6	84.47	odd	6
5292.2.i.e.1549.3		6	9.5	odd	6
5292.2.i.e.2125.3		6	21.11	odd	6
5292.2.i.f.1549.1		6	63.41	even	6
5292.2.i.f.2125.1		6	21.17	even	6
5292.2.j.d.1765.3		6	63.23	odd	6
5292.2.j.d.3529.3		6	21.2	odd	6
5292.2.l.e.361.3		6	63.59	even	6
5292.2.l.e.3313.3		6	21.20	even	2
5292.2.l.f.361.1		6	63.32	odd	6
5292.2.l.f.3313.1		6	3.2	odd	2
9072.2.a.bv.1.3		3	252.47	odd	6
9072.2.a.by.1.1		3	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.29418 + 1.15113i) q^{3} +1.69963 q^{5} +(0.349814 + 2.97954i) q^{9} +O(q^{10})\)	\(q+(1.29418 + 1.15113i) q^{3} +1.69963 q^{5} +(0.349814 + 2.97954i) q^{9} +2.47710 q^{11} +(0.388736 + 0.673310i) q^{13} +(2.19963 + 1.95649i) q^{15} +(1.40545 + 2.43430i) q^{17} +(-2.49381 + 4.31941i) q^{19} +0.712008 q^{23} -2.11126 q^{25} +(-2.97710 + 4.25874i) q^{27} +(-2.25526 + 3.90623i) q^{29} +(2.54944 - 4.41576i) q^{31} +(3.20582 + 2.85146i) q^{33} +(3.43818 - 5.95510i) q^{37} +(-0.271971 + 1.31887i) q^{39} +(-2.93818 - 5.08907i) q^{41} +(2.32691 - 4.03033i) q^{43} +(0.594554 + 5.06410i) q^{45} +(6.49381 + 11.2476i) q^{47} +(-0.983290 + 4.76828i) q^{51} +(-0.944368 - 1.63569i) q^{53} +4.21015 q^{55} +(-8.19963 + 2.71941i) q^{57} +(7.14400 - 12.3738i) q^{59} +(7.15452 + 12.3920i) q^{61} +(0.660706 + 1.14438i) q^{65} +(-3.99381 + 6.91748i) q^{67} +(0.921468 + 0.819611i) q^{69} -10.2632 q^{71} +(2.49381 + 4.31941i) q^{73} +(-2.73236 - 2.43033i) q^{75} +(4.60507 + 7.97622i) q^{79} +(-8.75526 + 2.08457i) q^{81} +(4.40545 - 7.63046i) q^{83} +(2.38874 + 4.13741i) q^{85} +(-7.41528 + 2.45928i) q^{87} +(4.82691 - 8.36046i) q^{89} +(8.38255 - 2.78007i) q^{93} +(-4.23855 + 7.34138i) q^{95} +(4.32072 - 7.48371i) q^{97} +(0.866524 + 7.38061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{3} - 2 q^{5} - 4 q^{9}+O(q^{10}) \) 6 * q + 2 * q^3 - 2 * q^5 - 4 * q^9	\( 6 q + 2 q^{3} - 2 q^{5} - 4 q^{9} + 4 q^{11} + 3 q^{13} + q^{15} + 2 q^{17} + 3 q^{19} + 28 q^{23} - 12 q^{25} - 7 q^{27} - q^{29} - 3 q^{31} + 25 q^{33} + 3 q^{37} + 18 q^{39} - 3 q^{43} + 10 q^{45} + 21 q^{47} - 13 q^{51} - 6 q^{53} - 12 q^{55} - 37 q^{57} + 31 q^{59} + 6 q^{61} - 15 q^{65} - 6 q^{67} - 5 q^{69} + 34 q^{71} - 3 q^{73} + 7 q^{75} + 9 q^{79} - 40 q^{81} + 20 q^{83} + 15 q^{85} - 16 q^{87} + 12 q^{89} + 33 q^{93} - 20 q^{95} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 6 * q + 2 * q^3 - 2 * q^5 - 4 * q^9 + 4 * q^11 + 3 * q^13 + q^15 + 2 * q^17 + 3 * q^19 + 28 * q^23 - 12 * q^25 - 7 * q^27 - q^29 - 3 * q^31 + 25 * q^33 + 3 * q^37 + 18 * q^39 - 3 * q^43 + 10 * q^45 + 21 * q^47 - 13 * q^51 - 6 * q^53 - 12 * q^55 - 37 * q^57 + 31 * q^59 + 6 * q^61 - 15 * q^65 - 6 * q^67 - 5 * q^69 + 34 * q^71 - 3 * q^73 + 7 * q^75 + 9 * q^79 - 40 * q^81 + 20 * q^83 + 15 * q^85 - 16 * q^87 + 12 * q^89 + 33 * q^93 - 20 * q^95 - 9 * q^97 - 8 * q^99

Introduction

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