LMFDB - Embedded newform 1764.2.x.a.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("1764.293");

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.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.0856109166$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.2
Root			$-0.811340 + 1.53027i$ of defining polynomial
Character	$\chi$	$=$	1764.293
Dual form			1764.2.x.a.1469.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20245 + 1.24664i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-0.108243 - 2.99805i) q^{9} +O(q^{10})$	\(q+(-1.20245 + 1.24664i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-0.108243 - 2.99805i) q^{9} +(0.362306 - 0.209178i) q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +3.90581 q^{17} +5.91199i q^{19} +(-7.72884 - 4.46225i) q^{23} +(-1.26290 - 2.18740i) q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +(-3.05626 - 1.76453i) q^{31} +(-0.174884 + 0.703192i) q^{33} +9.09722 q^{37} +(-2.54713 + 0.732009i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(-7.27118 - 3.85514i) q^{45} +(0.885373 + 1.53351i) q^{47} +(-4.69653 + 4.86916i) q^{51} -3.92050i q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} +(2.02728 - 3.51135i) q^{59} +(-1.61459 + 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +1.90594i q^{73} +(4.24548 + 1.05585i) q^{75} +(0.433633 + 0.751074i) q^{79} +(-8.97657 + 0.649034i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-2.89801 + 11.6526i) q^{87} +9.77729 q^{89} +(5.87474 - 1.68831i) q^{93} +(14.0456 + 8.10924i) q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} + 6 q^{11} - 3 q^{13} - 3 q^{15} - 18 q^{17} - 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} - 2 q^{37} + 6 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 18 q^{51} + 15 q^{57} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 21 q^{69} + 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} - 51 q^{87} - 42 q^{89} + 48 q^{93} - 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 - 18 * q^17 - 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 - 2 * q^37 + 6 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 18 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 21 * q^69 + 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 - 51 * q^87 - 42 * q^89 + 48 * q^93 - 6 * q^95 - 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.20245	+	1.24664i	−0.694233	+	0.719750i
$3$	−1.20245	+	1.24664i	−0.694233	+	0.719750i
$4$		0			0
$5$	1.37166	−	2.37578i	0.613425	−	1.06248i	−0.377234	−	0.926118i	$-0.623125\pi$
$5$	1.37166	−	2.37578i	0.613425	−	1.06248i	0.990659	−	0.136365i	$-0.0435419\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.108243	−	2.99805i	−0.0360809	−	0.999349i
$10$		0			0
$11$	0.362306	−	0.209178i	0.109240	−	0.0630695i	−0.444385	−	0.895836i	$-0.646578\pi$
$11$	0.362306	−	0.209178i	0.109240	−	0.0630695i	0.553624	+	0.832767i	$0.313244\pi$
$12$		0			0
$13$	1.32512	+	0.765056i	0.367521	+	0.212188i	0.672375	−	0.740211i	$-0.265274\pi$
$13$	1.32512	+	0.765056i	0.367521	+	0.212188i	−0.304854	+	0.952399i	$0.598608\pi$
$14$		0			0
$15$	1.31241	+	4.56672i	0.338862	+	1.17912i
$16$		0			0
$17$	3.90581			0.947298			0.473649	−	0.880714i	$-0.342936\pi$
$17$	3.90581			0.947298			0.473649	+	0.880714i	$0.342936\pi$
$18$		0			0
$19$			5.91199i			1.35630i	0.734922	+	0.678152i	$0.237219\pi$
$19$			5.91199i			1.35630i	−0.734922	+	0.678152i	$0.762781\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.72884	−	4.46225i	−1.61157	−	0.930443i	−0.989006	−	0.147878i	$-0.952756\pi$
$23$	−7.72884	−	4.46225i	−1.61157	−	0.930443i	−0.622569	−	0.782565i	$-0.713911\pi$
$24$		0			0
$25$	−1.26290	−	2.18740i	−0.252579	−	0.437480i
$26$		0			0
$27$	3.86765	+	3.47005i	0.744330	+	0.667812i
$28$		0			0
$29$	6.00378	−	3.46629i	1.11487	−	0.643673i	0.174787	−	0.984606i	$-0.444076\pi$
$29$	6.00378	−	3.46629i	1.11487	−	0.643673i	0.940088	+	0.340933i	$0.110743\pi$
$30$		0			0
$31$	−3.05626	−	1.76453i	−0.548921	−	0.316920i	0.199766	−	0.979844i	$-0.435982\pi$
$31$	−3.05626	−	1.76453i	−0.548921	−	0.316920i	−0.748687	+	0.662924i	$0.769315\pi$
$32$		0			0
$33$	−0.174884	+	0.703192i	−0.0304434	+	0.122410i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.09722			1.49557			0.747787	−	0.663939i	$-0.231116\pi$
$37$	9.09722			1.49557			0.747787	+	0.663939i	$0.231116\pi$
$38$		0			0
$39$	−2.54713	+	0.732009i	−0.407868	+	0.117215i
$40$		0			0
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	−0.771066	−	0.636755i	$-0.780276\pi$
$41$	1.06236	−	1.84006i	0.165913	−	0.287370i	0.936979	+	0.349385i	$0.113610\pi$
$42$		0			0
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.850000	−	0.526783i	$-0.823398\pi$
$43$	−5.77846	−	10.0086i	−0.881208	−	1.52630i	−0.0312079	−	0.999513i	$-0.509935\pi$
$44$		0			0
$45$	−7.27118	−	3.85514i	−1.08392	−	0.574690i
$46$		0			0
$47$	0.885373	+	1.53351i	0.129145	+	0.223686i	0.923346	−	0.383970i	$-0.125443\pi$
$47$	0.885373	+	1.53351i	0.129145	+	0.223686i	−0.794201	+	0.607656i	$0.792110\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.69653	+	4.86916i	−0.657646	+	0.681818i
$52$		0			0
$53$		−	3.92050i		−	0.538523i	−0.963067	−	0.269261i	$-0.913220\pi$
$53$		−	3.92050i		−	0.538523i	0.963067	−	0.269261i	$-0.0867795\pi$
$54$		0			0
$55$		−	1.14768i		−	0.154753i
$56$		0			0
$57$	−7.37015	−	7.10886i	−0.976200	−	0.941591i
$58$		0			0
$59$	2.02728	−	3.51135i	0.263929	−	0.457139i	−0.703353	−	0.710840i	$-0.748315\pi$
$59$	2.02728	−	3.51135i	0.263929	−	0.457139i	0.967283	+	0.253702i	$0.0816481\pi$
$60$		0			0
$61$	−1.61459	+	0.932184i	−0.206727	+	0.119354i	−0.599789	−	0.800158i	$-0.704749\pi$
$61$	−1.61459	+	0.932184i	−0.206727	+	0.119354i	0.393062	+	0.919512i	$0.371416\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.63521	−	2.09879i	0.450893	−	0.260323i
$66$		0			0
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	−0.151974	−	0.988385i	$-0.548563\pi$
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	0.931953	−	0.362579i	$-0.118104\pi$
$68$		0			0
$69$	14.8564	−	4.26950i	1.78850	−	0.513987i
$70$		0			0
$71$		−	8.51021i		−	1.00998i	−0.863126	−	0.504988i	$-0.831497\pi$
$71$		−	8.51021i		−	1.00998i	0.863126	−	0.504988i	$-0.168503\pi$
$72$		0			0
$73$			1.90594i			0.223074i	0.993760	+	0.111537i	$0.0355773\pi$
$73$			1.90594i			0.223074i	−0.993760	+	0.111537i	$0.964423\pi$
$74$		0			0
$75$	4.24548	+	1.05585i	0.490226	+	0.121919i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	0.889388	−	0.457153i	$-0.151131\pi$
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	−0.840600	+	0.541656i	$0.817798\pi$
$80$		0			0
$81$	−8.97657	+	0.649034i	−0.997396	+	0.0721149i
$82$		0			0
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	0.991012	−	0.133775i	$-0.0427100\pi$
$83$	3.45880	+	5.99082i	0.379653	+	0.657578i	−0.611359	+	0.791354i	$0.709377\pi$
$84$		0			0
$85$	5.35744	−	9.27936i	0.581096	−	1.00649i
$86$		0			0
$87$	−2.89801	+	11.6526i	−0.310699	+	1.24929i
$88$		0			0
$89$	9.77729			1.03639			0.518195	−	0.855262i	$-0.326604\pi$
$89$	9.77729			1.03639			0.518195	+	0.855262i	$0.326604\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.87474	−	1.68831i	0.609182	−	0.175070i
$94$		0			0
$95$	14.0456	+	8.10924i	1.44105	+	0.831990i
$96$		0			0
$97$	0.200411	−	0.115707i	0.0203486	−	0.0117483i	−0.489791	−	0.871840i	$-0.662927\pi$
$97$	0.200411	−	0.115707i	0.0203486	−	0.0117483i	0.510140	+	0.860091i	$0.329594\pi$
$98$		0			0
$99$	−0.666342	−	1.06357i	−0.0669699	−	0.106893i
$100$		0			0
$101$	−7.14031	−	12.3674i	−0.710487	−	1.23060i	−0.964674	−	0.263445i	$-0.915141\pi$
$101$	−7.14031	−	12.3674i	−0.710487	−	1.23060i	0.254187	−	0.967155i	$-0.418192\pi$
$102$		0			0
$103$	9.30617	+	5.37292i	0.916964	+	0.529410i	0.882665	−	0.470002i	$-0.155747\pi$
$103$	9.30617	+	5.37292i	0.916964	+	0.529410i	0.0342991	+	0.999412i	$0.489080\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			6.35702i			0.614556i	0.951620	+	0.307278i	$0.0994181\pi$
$107$			6.35702i			0.614556i	−0.951620	+	0.307278i	$0.900582\pi$
$108$		0			0
$109$	−5.16072			−0.494308			−0.247154	−	0.968976i	$-0.579495\pi$
$109$	−5.16072			−0.494308			−0.247154	+	0.968976i	$0.579495\pi$
$110$		0			0
$111$	−10.9389	+	11.3410i	−1.03828	+	1.07644i
$112$		0			0
$113$	9.19186	+	5.30692i	0.864697	+	0.499233i	0.865582	−	0.500766i	$-0.166948\pi$
$113$	9.19186	+	5.30692i	0.864697	+	0.499233i	−0.000885276		1.00000i	$0.500282\pi$
$114$		0			0
$115$	−21.2027	+	12.2414i	−1.97716	+	1.14151i
$116$		0			0
$117$	2.15024	−	4.05557i	0.198790	−	0.374938i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.41249	+	9.37471i	−0.492044	+	0.852246i
$122$		0			0
$123$	1.01647	+	3.53697i	0.0916521	+	0.318917i
$124$		0			0
$125$	6.78753			0.607096
$126$		0			0
$127$	10.2909			0.913169			0.456584	−	0.889680i	$-0.349073\pi$
$127$	10.2909			0.913169			0.456584	+	0.889680i	$0.349073\pi$
$128$		0			0
$129$	19.4255	+	4.83111i	1.71032	+	0.425356i
$130$		0			0
$131$	9.83048	−	17.0269i	0.858893	−	1.48765i	−0.0140928	−	0.999901i	$-0.504486\pi$
$131$	9.83048	−	17.0269i	0.858893	−	1.48765i	0.872986	−	0.487746i	$-0.162181\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	13.5492	−	4.42898i	1.16613	−	0.381186i
$136$		0			0
$137$	4.66411	−	2.69282i	0.398481	−	0.230063i	−0.287347	−	0.957827i	$-0.592773\pi$
$137$	4.66411	−	2.69282i	0.398481	−	0.230063i	0.685829	+	0.727763i	$0.259440\pi$
$138$		0			0
$139$	14.7839	+	8.53549i	1.25395	+	0.723971i	0.971892	−	0.235425i	$-0.0756484\pi$
$139$	14.7839	+	8.53549i	1.25395	+	0.723971i	0.282062	+	0.959396i	$0.408982\pi$
$140$		0			0
$141$	−2.97636	−	0.740221i	−0.250655	−	0.0623379i
$142$		0			0
$143$	0.640131			0.0535304
$144$		0			0
$145$		−	19.0182i		−	1.57938i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.31162	−	5.37607i	−0.762838	−	0.440425i	0.0674758	−	0.997721i	$-0.478505\pi$
$149$	−9.31162	−	5.37607i	−0.762838	−	0.440425i	−0.830314	+	0.557296i	$0.811839\pi$
$150$		0			0
$151$	−3.78223	−	6.55102i	−0.307794	−	0.533115i	0.670086	−	0.742284i	$-0.266257\pi$
$151$	−3.78223	−	6.55102i	−0.307794	−	0.533115i	−0.977879	+	0.209169i	$0.932924\pi$
$152$		0			0
$153$	−0.422776	−	11.7098i	−0.0341794	−	0.946682i
$154$		0			0
$155$	−8.38430	+	4.84068i	−0.673443	+	0.388812i
$156$		0			0
$157$	−10.6317	−	6.13820i	−0.848500	−	0.489882i	0.0116445	−	0.999932i	$-0.496293\pi$
$157$	−10.6317	−	6.13820i	−0.848500	−	0.489882i	−0.860144	+	0.510051i	$0.829627\pi$
$158$		0			0
$159$	4.88747	+	4.71420i	0.387602	+	0.373860i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−11.8349			−0.926981			−0.463490	−	0.886102i	$-0.653403\pi$
$163$	−11.8349			−0.926981			−0.463490	+	0.886102i	$0.653403\pi$
$164$		0			0
$165$	1.43075	+	1.38003i	0.111384	+	0.107435i
$166$		0			0
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	−0.474252	−	0.880389i	$-0.657282\pi$
$167$	6.78854	−	11.7581i	0.525313	−	0.909869i	0.999565	−	0.0294798i	$-0.00938508\pi$
$168$		0			0
$169$	−5.32938	−	9.23075i	−0.409952	−	0.710058i
$170$		0			0
$171$	17.7244	−	0.639931i	1.35542	−	0.0489367i
$172$		0			0
$173$	8.31085	+	14.3948i	0.631862	+	1.09442i	0.987171	+	0.159668i	$0.0510425\pi$
$173$	8.31085	+	14.3948i	0.631862	+	1.09442i	−0.355308	+	0.934749i	$0.615624\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.93971	+	6.74951i	0.145797	+	0.507324i
$178$		0			0
$179$			17.0988i			1.27803i	0.769195	+	0.639014i	$0.220657\pi$
$179$			17.0988i			1.27803i	−0.769195	+	0.639014i	$0.779343\pi$
$180$		0			0
$181$		−	18.2171i		−	1.35407i	−0.735952	−	0.677034i	$-0.763265\pi$
$181$		−	18.2171i		−	1.35407i	0.735952	−	0.677034i	$-0.236735\pi$
$182$		0			0
$183$	0.779357	−	3.13372i	0.0576117	−	0.231651i
$184$		0			0
$185$	12.4783	−	21.6130i	0.917422	−	1.58902i
$186$		0			0
$187$	1.41510	−	0.817009i	0.103482	−	0.0597456i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.332826	−	0.942988i	$-0.391998\pi$
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.983065	+	0.183258i	$0.0586644\pi$
$192$		0			0
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	−0.712780	−	0.701388i	$-0.752564\pi$
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	0.963810	+	0.266592i	$0.0858975\pi$
$194$		0			0
$195$	−1.75471	+	7.05550i	−0.125657	+	0.505255i
$196$		0			0
$197$			16.0756i			1.14534i	0.819786	+	0.572670i	$0.194092\pi$
$197$			16.0756i			1.14534i	−0.819786	+	0.572670i	$0.805908\pi$
$198$		0			0
$199$		−	6.29261i		−	0.446071i	−0.974810	−	0.223036i	$-0.928403\pi$
$199$		−	6.29261i		−	0.446071i	0.974810	−	0.223036i	$-0.0715966\pi$
$200$		0			0
$201$	6.10862	+	21.2559i	0.430869	+	1.49927i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.91440	−	5.04788i	−0.203550	−	0.352559i
$206$		0			0
$207$	−12.5414	+	23.6544i	−0.871690	+	1.64410i
$208$		0			0
$209$	1.23666	+	2.14195i	0.0855414	+	0.148162i
$210$		0			0
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	−0.907244	−	0.420605i	$-0.861818\pi$
$211$	−1.29814	+	2.24844i	−0.0893674	+	0.154789i	0.817876	+	0.575394i	$0.195151\pi$
$212$		0			0
$213$	10.6092	+	10.2331i	0.726931	+	0.701159i
$214$		0			0
$215$	−31.7043			−2.16222
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.37603	−	2.29179i	−0.160557	−	0.154865i
$220$		0			0
$221$	5.17565	+	2.98816i	0.348152	+	0.201006i
$222$		0			0
$223$	−20.7215	+	11.9636i	−1.38762	+	0.801141i	−0.993046	−	0.117725i	$-0.962440\pi$
$223$	−20.7215	+	11.9636i	−1.38762	+	0.801141i	−0.394571	+	0.918866i	$0.629107\pi$
$224$		0			0
$225$	−6.42123	+	4.02299i	−0.428082	+	0.268200i
$226$		0			0
$227$	−1.86609	−	3.23216i	−0.123857	−	0.214526i	0.797429	−	0.603413i	$-0.206193\pi$
$227$	−1.86609	−	3.23216i	−0.123857	−	0.214526i	−0.921285	+	0.388887i	$0.872860\pi$
$228$		0			0
$229$	−18.2455	−	10.5341i	−1.20570	−	0.696111i	−0.243882	−	0.969805i	$-0.578421\pi$
$229$	−18.2455	−	10.5341i	−1.20570	−	0.696111i	−0.961817	+	0.273694i	$0.911754\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			12.7643i			0.836217i	0.908397	+	0.418109i	$0.137307\pi$
$233$			12.7643i			0.836217i	−0.908397	+	0.418109i	$0.862693\pi$
$234$		0			0
$235$	4.85772			0.316883
$236$		0			0
$237$	−1.45774	−	0.362541i	−0.0946905	−	0.0235496i
$238$		0			0
$239$	11.0521	+	6.38091i	0.714899	+	0.412747i	0.812872	−	0.582442i	$-0.197903\pi$
$239$	11.0521	+	6.38091i	0.714899	+	0.412747i	−0.0979736	+	0.995189i	$0.531236\pi$
$240$		0			0
$241$	2.63438	−	1.52096i	0.169695	−	0.0979737i	−0.412747	−	0.910846i	$-0.635431\pi$
$241$	2.63438	−	1.52096i	0.169695	−	0.0979737i	0.582442	+	0.812872i	$0.302097\pi$
$242$		0			0
$243$	9.98473	−	11.9710i	0.640521	−	0.767941i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.52301	+	7.83408i	−0.287792	+	0.498470i
$248$		0			0
$249$	−11.6275	−	2.89175i	−0.736860	−	0.183257i
$250$		0			0
$251$	−6.32067			−0.398957			−0.199478	−	0.979902i	$-0.563925\pi$
$251$	−6.32067			−0.398957			−0.199478	+	0.979902i	$0.563925\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$	5.12602	+	17.8368i	0.321004	+	1.11698i
$256$		0			0
$257$	−12.2538	+	21.2242i	−0.764372	+	1.32393i	0.176206	+	0.984353i	$0.443617\pi$
$257$	−12.2538	+	21.2242i	−0.764372	+	1.32393i	−0.940578	+	0.339577i	$0.889716\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−11.0420	−	17.6244i	−0.683480	−	1.09092i
$262$		0			0
$263$	21.1163	−	12.1915i	1.30208	−	0.751759i	0.321323	−	0.946970i	$-0.395872\pi$
$263$	21.1163	−	12.1915i	1.30208	−	0.751759i	0.980761	+	0.195211i	$0.0625390\pi$
$264$		0			0
$265$	−9.31427	−	5.37760i	−0.572171	−	0.330343i
$266$		0			0
$267$	−11.7567	+	12.1888i	−0.719496	+	0.745942i
$268$		0			0
$269$	−9.89049			−0.603034			−0.301517	−	0.953461i	$-0.597493\pi$
$269$	−9.89049			−0.603034			−0.301517	+	0.953461i	$0.597493\pi$
$270$		0			0
$271$			5.89481i			0.358084i	0.983841	+	0.179042i	$0.0572998\pi$
$271$			5.89481i			0.358084i	−0.983841	+	0.179042i	$0.942700\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.915111	−	0.528340i	−0.0551833	−	0.0318601i
$276$		0			0
$277$	−11.6469	−	20.1731i	−0.699796	−	1.21208i	−0.968537	−	0.248870i	$-0.919941\pi$
$277$	−11.6469	−	20.1731i	−0.699796	−	1.21208i	0.268741	−	0.963213i	$-0.413392\pi$
$278$		0			0
$279$	−4.95933	+	9.35381i	−0.296908	+	0.559998i
$280$		0			0
$281$	21.7962	−	12.5840i	1.30025	−	0.750700i	0.319803	−	0.947484i	$-0.396383\pi$
$281$	21.7962	−	12.5840i	1.30025	−	0.750700i	0.980447	+	0.196784i	$0.0630499\pi$
$282$		0			0
$283$	−8.62942	−	4.98220i	−0.512966	−	0.296161i	0.221086	−	0.975254i	$-0.429040\pi$
$283$	−8.62942	−	4.98220i	−0.512966	−	0.296161i	−0.734052	+	0.679093i	$0.762373\pi$
$284$		0			0
$285$	−26.9984	+	7.75895i	−1.59925	+	0.459601i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.74463			−0.102626
$290$		0			0
$291$	−0.0967377	+	0.388973i	−0.00567086	+	0.0228020i
$292$		0			0
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	−0.993318	−	0.115406i	$-0.963183\pi$
$293$	−6.79065	+	11.7618i	−0.396714	+	0.687129i	0.596604	+	0.802536i	$0.296516\pi$
$294$		0			0
$295$	−5.56147	−	9.63275i	−0.323801	−	0.560841i
$296$		0			0
$297$	2.12713	+	0.448195i	0.123429	+	0.0260069i
$298$		0			0
$299$	−6.82774	−	11.8260i	−0.394858	−	0.683915i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	24.0036	+	5.96969i	1.37897	+	0.342950i
$304$		0			0
$305$			5.11455i			0.292858i
$306$		0			0
$307$			16.9849i			0.969381i	0.874686	+	0.484691i	$0.161068\pi$
$307$			16.9849i			0.969381i	−0.874686	+	0.484691i	$0.838932\pi$
$308$		0			0
$309$	−17.8883	+	5.14083i	−1.01763	+	0.292452i
$310$		0			0
$311$	−0.00148940	+	0.00257972i	−8.44563e−5	+	0.000146283i	−0.866068	−	0.499927i	$-0.833360\pi$
$311$	−0.00148940	+	0.00257972i	−8.44563e−5	+	0.000146283i	0.865983	+	0.500073i	$0.166694\pi$
$312$		0			0
$313$	−10.6154	+	6.12878i	−0.600015	+	0.346419i	−0.769048	−	0.639191i	$-0.779269\pi$
$313$	−10.6154	+	6.12878i	−0.600015	+	0.346419i	0.169032	+	0.985611i	$0.445936\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.942256	−	0.334894i	$-0.891300\pi$
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.181102	+	0.983464i	$0.557966\pi$
$318$		0			0
$319$	1.45014	−	2.51172i	0.0811922	−	0.140629i
$320$		0			0
$321$	−7.92494	−	7.64397i	−0.442327	−	0.426645i
$322$		0			0
$323$			23.0911i			1.28482i
$324$		0			0
$325$		−	3.86475i		−	0.214378i
$326$		0			0
$327$	6.20550	−	6.43358i	0.343165	−	0.355778i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	0.909670	−	0.415331i	$-0.136334\pi$
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	−0.814522	+	0.580132i	$0.803001\pi$
$332$		0			0
$333$	−0.984708	−	27.2739i	−0.0539617	−	1.49460i
$334$		0			0
$335$	−17.5145	−	30.3359i	−0.956917	−	1.65743i
$336$		0			0
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	−0.999995	−	0.00305455i	$-0.999028\pi$
$337$	−9.13018	+	15.8139i	−0.497352	+	0.861440i	0.502643	+	0.864494i	$0.332361\pi$
$338$		0			0
$339$	−17.6686	+	5.07768i	−0.959625	+	0.275782i
$340$		0			0
$341$	−1.47640			−0.0799518
$342$		0			0
$343$		0			0
$344$		0			0
$345$	10.2345	−	41.1518i	0.551005	−	2.21554i
$346$		0			0
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	0.618950	−	0.785431i	$-0.287558\pi$
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	−0.370728	+	0.928741i	$0.620892\pi$
$348$		0			0
$349$	−0.0136817	+	0.00789914i	−0.000732365	+	0.000422831i	−0.500366	−	0.865814i	$-0.666801\pi$
$349$	−0.0136817	+	0.00789914i	−0.000732365	+	0.000422831i	0.499634	+	0.866237i	$0.333468\pi$
$350$		0			0
$351$	2.47030	+	7.55719i	0.131855	+	0.403373i
$352$		0			0
$353$	17.1543	+	29.7121i	0.913029	+	1.58141i	0.809761	+	0.586760i	$0.199597\pi$
$353$	17.1543	+	29.7121i	0.913029	+	1.58141i	0.103268	+	0.994654i	$0.467070\pi$
$354$		0			0
$355$	−20.2184	−	11.6731i	−1.07308	−	0.619544i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			6.26718i			0.330769i	0.986229	+	0.165385i	$0.0528865\pi$
$359$			6.26718i			0.330769i	−0.986229	+	0.165385i	$0.947113\pi$
$360$		0			0
$361$	−15.9517			−0.839561
$362$		0			0
$363$	−5.17869	−	18.0200i	−0.271811	−	0.945807i
$364$		0			0
$365$	4.52811	+	2.61430i	0.237012	+	0.136839i
$366$		0			0
$367$	−16.4888	+	9.51984i	−0.860711	+	0.496931i	−0.864250	−	0.503062i	$-0.832207\pi$
$367$	−16.4888	+	9.51984i	−0.860711	+	0.496931i	0.00353959	+	0.999994i	$0.498873\pi$
$368$		0			0
$369$	−5.63159	−	2.98584i	−0.293169	−	0.155436i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.41901	+	9.38600i	−0.280586	+	0.485989i	−0.971529	−	0.236920i	$-0.923862\pi$
$373$	−5.41901	+	9.38600i	−0.280586	+	0.485989i	0.690943	+	0.722909i	$0.257195\pi$
$374$		0			0
$375$	−8.16165	+	8.46164i	−0.421466	+	0.436957i
$376$		0			0
$377$	10.6076			0.546320
$378$		0			0
$379$	0.700312			0.0359726			0.0179863	−	0.999838i	$-0.494274\pi$
$379$	0.700312			0.0359726			0.0179863	+	0.999838i	$0.494274\pi$
$380$		0			0
$381$	−12.3742	+	12.8291i	−0.633952	+	0.657253i
$382$		0			0
$383$	19.0235	−	32.9497i	0.972056	−	1.68365i	0.282729	−	0.959200i	$-0.408760\pi$
$383$	19.0235	−	32.9497i	0.972056	−	1.68365i	0.689327	−	0.724451i	$-0.257906\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−29.3808	+	18.4075i	−1.49351	+	0.935704i
$388$		0			0
$389$	−16.6958	+	9.63934i	−0.846512	+	0.488734i	−0.859473	−	0.511182i	$-0.829208\pi$
$389$	−16.6958	+	9.63934i	−0.846512	+	0.488734i	0.0129603	+	0.999916i	$0.495875\pi$
$390$		0			0
$391$	−30.1874	−	17.4287i	−1.52664	−	0.881407i
$392$		0			0
$393$	9.40584	+	32.7290i	0.474462	+	1.65096i
$394$		0			0
$395$	2.37919			0.119710
$396$		0			0
$397$			20.0468i			1.00612i	0.864252	+	0.503059i	$0.167792\pi$
$397$			20.0468i			1.00612i	−0.864252	+	0.503059i	$0.832208\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−26.4232	−	15.2554i	−1.31951	−	0.761820i	−0.335861	−	0.941912i	$-0.609027\pi$
$401$	−26.4232	−	15.2554i	−1.31951	−	0.761820i	−0.983650	+	0.180092i	$0.942360\pi$
$402$		0			0
$403$	−2.69993	−	4.67642i	−0.134493	−	0.232949i
$404$		0			0
$405$	−10.7708	+	22.2166i	−0.535207	+	1.10395i
$406$		0			0
$407$	3.29598	−	1.90294i	0.163376	−	0.0943250i
$408$		0			0
$409$	−0.150631	−	0.0869667i	−0.00744821	−	0.00430023i	0.496271	−	0.868168i	$-0.334702\pi$
$409$	−0.150631	−	0.0869667i	−0.00744821	−	0.00430023i	−0.503719	+	0.863867i	$0.668035\pi$
$410$		0			0
$411$	−2.25135	+	9.05246i	−0.111051	+	0.446525i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	18.9772			0.931554
$416$		0			0
$417$	−28.4176	+	8.16679i	−1.39161	+	0.399929i
$418$		0			0
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	0.285387	+	0.958412i	$0.407878\pi$
$419$	−14.0690	+	24.3682i	−0.687316	+	1.19047i	−0.972703	+	0.232054i	$0.925455\pi$
$420$		0			0
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	0.825468	−	0.564449i	$-0.190911\pi$
$421$	−1.56130	−	2.70424i	−0.0760929	−	0.131797i	−0.901561	+	0.432652i	$0.857578\pi$
$422$		0			0
$423$	4.50170	−	2.82038i	0.218880	−	0.137132i
$424$		0			0
$425$	−4.93264	−	8.54358i	−0.239268	−	0.414424i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.769723	+	0.798015i	−0.0371626	+	0.0385285i
$430$		0			0
$431$			9.91744i			0.477706i	0.971056	+	0.238853i	$0.0767715\pi$
$431$			9.91744i			0.477706i	−0.971056	+	0.238853i	$0.923229\pi$
$432$		0			0
$433$			17.1274i			0.823092i	0.911389	+	0.411546i	$0.135011\pi$
$433$			17.1274i			0.823092i	−0.911389	+	0.411546i	$0.864989\pi$
$434$		0			0
$435$	23.7090	+	22.8684i	1.13676	+	1.09646i
$436$		0			0
$437$	26.3808	−	45.6929i	1.26196	−	2.18579i
$438$		0			0
$439$	−18.5795	+	10.7269i	−0.886750	+	0.511965i	−0.872878	−	0.487938i	$-0.837749\pi$
$439$	−18.5795	+	10.7269i	−0.886750	+	0.511965i	−0.0138721	+	0.999904i	$0.504416\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	−0.354721	−	0.934972i	$-0.615424\pi$
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	0.632349	+	0.774683i	$0.282091\pi$
$444$		0			0
$445$	13.4111	−	23.2287i	0.635747	−	1.10115i
$446$		0			0
$447$	17.8988	−	5.14384i	0.846583	−	0.243295i
$448$		0			0
$449$			5.81624i			0.274485i	0.990537	+	0.137243i	$0.0438240\pi$
$449$			5.81624i			0.274485i	−0.990537	+	0.137243i	$0.956176\pi$
$450$		0			0
$451$		−	0.888889i		−	0.0418562i
$452$		0			0
$453$	12.7147	+	3.16216i	0.597390	+	0.148571i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	0.931386	+	0.364032i	$0.118600\pi$
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	−0.150432	+	0.988620i	$0.548066\pi$
$458$		0			0
$459$	15.1063	+	13.5534i	0.705103	+	0.632617i
$460$		0			0
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	−0.869657	−	0.493656i	$-0.835660\pi$
$461$	−18.5154	−	32.0696i	−0.862347	−	1.49363i	0.00730959	−	0.999973i	$-0.497673\pi$
$462$		0			0
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	−0.509097	−	0.860709i	$-0.670020\pi$
$463$	10.5618	−	18.2935i	0.490848	−	0.850173i	0.999944	+	0.0105362i	$0.00335383\pi$
$464$		0			0
$465$	4.04707	−	16.2729i	0.187678	−	0.754637i
$466$		0			0
$467$	−18.6094			−0.861141			−0.430570	−	0.902557i	$-0.641688\pi$
$467$	−18.6094			−0.861141			−0.430570	+	0.902557i	$0.641688\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	20.4362	−	5.87305i	0.941649	−	0.270616i
$472$		0			0
$473$	−4.18715	−	2.41745i	−0.192525	−	0.111155i
$474$		0			0
$475$	12.9319	−	7.46624i	0.593356	−	0.342574i
$476$		0			0
$477$	−11.7539	+	0.424366i	−0.538172	+	0.0194304i
$478$		0			0
$479$	7.16703	+	12.4137i	0.327470	+	0.567194i	0.982009	−	0.188834i	$-0.0604707\pi$
$479$	7.16703	+	12.4137i	0.327470	+	0.567194i	−0.654539	+	0.756028i	$0.727137\pi$
$480$		0			0
$481$	12.0549	+	6.95988i	0.549655	+	0.317343i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	0.634844i		−	0.0288268i
$486$		0			0
$487$	11.2966			0.511897			0.255949	−	0.966690i	$-0.417612\pi$
$487$	11.2966			0.511897			0.255949	+	0.966690i	$0.417612\pi$
$488$		0			0
$489$	14.2308	−	14.7539i	0.643541	−	0.667195i
$490$		0			0
$491$	−8.84097	−	5.10434i	−0.398988	−	0.230356i	0.287059	−	0.957913i	$-0.407322\pi$
$491$	−8.84097	−	5.10434i	−0.398988	−	0.230356i	−0.686047	+	0.727557i	$0.740656\pi$
$492$		0			0
$493$	23.4496	−	13.5387i	1.05612	−	0.609751i
$494$		0			0
$495$	−3.44080	+	0.124228i	−0.154653	+	0.00558365i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.56672	−	16.5701i	0.428265	−	0.741777i	−0.568454	−	0.822715i	$-0.692458\pi$
$499$	9.56672	−	16.5701i	0.428265	−	0.741777i	0.996719	+	0.0809379i	$0.0257915\pi$
$500$		0			0
$501$	6.49530	+	22.6014i	0.290189	+	1.00976i
$502$		0			0
$503$	0.268917			0.0119904			0.00599520	−	0.999982i	$-0.498092\pi$
$503$	0.268917			0.0119904			0.00599520	+	0.999982i	$0.498092\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$	17.9158	+	4.45565i	0.795667	+	0.197883i
$508$		0			0
$509$	10.9439	−	18.9553i	0.485079	−	0.840181i	−0.514774	−	0.857326i	$-0.672124\pi$
$509$	10.9439	−	18.9553i	0.485079	−	0.840181i	0.999853	+	0.0171449i	$0.00545767\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−20.5149	+	22.8655i	−0.905756	+	1.00954i
$514$		0			0
$515$	25.5298	−	14.7396i	1.12498	−	0.649506i
$516$		0			0
$517$	0.641553	+	0.370401i	0.0282155	+	0.0162902i
$518$		0			0
$519$	−27.9386	−	6.94833i	−1.22637	−	0.304998i
$520$		0			0
$521$	−1.71215			−0.0750105			−0.0375053	−	0.999296i	$-0.511941\pi$
$521$	−1.71215			−0.0750105			−0.0375053	+	0.999296i	$0.511941\pi$
$522$		0			0
$523$		−	8.27136i		−	0.361681i	−0.983512	−	0.180841i	$-0.942118\pi$
$523$		−	8.27136i		−	0.361681i	0.983512	−	0.180841i	$-0.0578818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.9372	−	6.89193i	−0.519992	−	0.300217i
$528$		0			0
$529$	28.3233	+	49.0574i	1.23145	+	2.13293i
$530$		0			0
$531$	−10.7466	−	5.69780i	−0.466364	−	0.247263i
$532$		0			0
$533$	2.81550	−	1.62553i	0.121953	−	0.0704096i
$534$		0			0
$535$	15.1029	+	8.71966i	0.652955	+	0.376984i
$536$		0			0
$537$	−21.3162	−	20.5605i	−0.919861	−	0.887249i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	20.3993			0.877036			0.438518	−	0.898722i	$-0.355503\pi$
$541$	20.3993			0.877036			0.438518	+	0.898722i	$0.355503\pi$
$542$		0			0
$543$	22.7103	+	21.9051i	0.974591	+	0.940039i
$544$		0			0
$545$	−7.07875	+	12.2608i	−0.303220	+	0.525193i
$546$		0			0
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	0.912304	+	0.409513i	$0.134301\pi$
$547$	18.9630	+	32.8449i	0.810801	+	1.40435i	−0.101503	+	0.994835i	$0.532365\pi$
$548$		0			0
$549$	2.96950	+	4.73971i	0.126735	+	0.202286i
$550$		0			0
$551$	20.4927	+	35.4943i	0.873017	+	1.51211i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	11.9393	+	41.5445i	0.506794	+	1.76347i
$556$		0			0
$557$			16.8493i			0.713926i	0.934119	+	0.356963i	$0.116188\pi$
$557$			16.8493i			0.713926i	−0.934119	+	0.356963i	$0.883812\pi$
$558$		0			0
$559$		−	17.6834i		−	0.747928i
$560$		0			0
$561$	−0.683064	+	2.74654i	−0.0288390	+	0.115959i
$562$		0			0
$563$	8.28035	−	14.3420i	0.348975	−	0.604443i	−0.637093	−	0.770787i	$-0.719863\pi$
$563$	8.28035	−	14.3420i	0.348975	−	0.604443i	0.986068	+	0.166345i	$0.0531965\pi$
$564$		0			0
$565$	25.2162	−	14.5586i	1.06085	−	0.612484i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	−0.380296	−	0.924865i	$-0.624178\pi$
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	0.610808	+	0.791779i	$0.290845\pi$
$570$		0			0
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.227585	+	0.973758i	$0.573083\pi$
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.729507	+	0.683973i	$0.760250\pi$
$572$		0			0
$573$	−8.77831	+	35.2967i	−0.366719	+	1.47454i
$574$		0			0
$575$			22.5414i			0.940043i
$576$		0			0
$577$			17.7499i			0.738939i	0.929243	+	0.369470i	$0.120461\pi$
$577$			17.7499i			0.738939i	−0.929243	+	0.369470i	$0.879539\pi$
$578$		0			0
$579$	3.33677	+	11.6108i	0.138671	+	0.482528i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.820082	−	1.42042i	−0.0339643	−	0.0588280i
$584$		0			0
$585$	−6.68576	−	10.6714i	−0.276422	−	0.441207i
$586$		0			0
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	0.942589	−	0.333955i	$-0.108383\pi$
$587$	4.41148	+	7.64091i	0.182081	+	0.315374i	−0.760508	+	0.649329i	$0.775050\pi$
$588$		0			0
$589$	10.4319	−	18.0686i	0.429839	−	0.744503i
$590$		0			0
$591$	−20.0406	−	19.3301i	−0.824359	−	0.795133i
$592$		0			0
$593$	−8.49698			−0.348929			−0.174465	−	0.984663i	$-0.555819\pi$
$593$	−8.49698			−0.348929			−0.174465	+	0.984663i	$0.555819\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.84464	+	7.56652i	0.321060	+	0.309677i
$598$		0			0
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	0.564174	−	0.825656i	$-0.309195\pi$
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	−0.432952	+	0.901417i	$0.642528\pi$
$600$		0			0
$601$	6.14043	−	3.54518i	0.250473	−	0.144611i	−0.369508	−	0.929228i	$-0.620474\pi$
$601$	6.14043	−	3.54518i	0.250473	−	0.144611i	0.619981	+	0.784617i	$0.287140\pi$
$602$		0			0
$603$	−33.8438	−	17.9438i	−1.37823	−	0.730727i
$604$		0			0
$605$	14.8482	+	25.7178i	0.603664	+	1.04558i
$606$		0			0
$607$	29.4396	+	16.9970i	1.19492	+	0.689886i	0.959418	−	0.281988i	$-0.0909939\pi$
$607$	29.4396	+	16.9970i	1.19492	+	0.689886i	0.235500	+	0.971874i	$0.424327\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			2.70944i			0.109612i
$612$		0			0
$613$	23.3523			0.943190			0.471595	−	0.881815i	$-0.343678\pi$
$613$	23.3523			0.943190			0.471595	+	0.881815i	$0.343678\pi$
$614$		0			0
$615$	9.79732	+	2.43659i	0.395066	+	0.0982530i
$616$		0			0
$617$	−39.0817	−	22.5638i	−1.57337	−	0.908386i	−0.995752	−	0.0920787i	$-0.970649\pi$
$617$	−39.0817	−	22.5638i	−1.57337	−	0.908386i	−0.577618	−	0.816307i	$-0.696018\pi$
$618$		0			0
$619$	7.97914	−	4.60676i	0.320709	−	0.185161i	−0.331000	−	0.943631i	$-0.607386\pi$
$619$	7.97914	−	4.60676i	0.320709	−	0.185161i	0.651708	+	0.758470i	$0.274053\pi$
$620$		0			0
$621$	−14.4082	−	44.0779i	−0.578183	−	1.76879i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.6247	−	27.0627i	0.624987	−	1.08251i
$626$		0			0
$627$	−4.15727	−	1.03391i	−0.166025	−	0.0412905i
$628$		0			0
$629$	35.5320			1.41675
$630$		0			0
$631$	17.6136			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$631$	17.6136			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$632$		0			0
$633$	−1.24206	−	4.32194i	−0.0493675	−	0.171782i
$634$		0			0
$635$	14.1156	−	24.4489i	0.560160	−	0.970226i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−25.5140	+	0.921169i	−1.00932	+	0.0364409i
$640$		0			0
$641$	−16.5759	+	9.57009i	−0.654708	+	0.377996i	−0.790258	−	0.612775i	$-0.790053\pi$
$641$	−16.5759	+	9.57009i	−0.654708	+	0.377996i	0.135550	+	0.990771i	$0.456720\pi$
$642$		0			0
$643$	−2.01129	−	1.16122i	−0.0793177	−	0.0457941i	0.459817	−	0.888014i	$-0.347915\pi$
$643$	−2.01129	−	1.16122i	−0.0793177	−	0.0457941i	−0.539134	+	0.842220i	$0.681248\pi$
$644$		0			0
$645$	38.1228	−	39.5240i	1.50108	−	1.55626i
$646$		0			0
$647$	−25.8620			−1.01674			−0.508370	−	0.861139i	$-0.669752\pi$
$647$	−25.8620			−1.01674			−0.508370	+	0.861139i	$0.669752\pi$
$648$		0			0
$649$		−	1.69625i		−	0.0665835i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.1140	+	11.6128i	0.787123	+	0.454446i	0.838949	−	0.544211i	$-0.183171\pi$
$653$	20.1140	+	11.6128i	0.787123	+	0.454446i	−0.0518258	+	0.998656i	$0.516504\pi$
$654$		0			0
$655$	−26.9681	−	46.7102i	−1.05373	−	1.82512i
$656$		0			0
$657$	5.71410	−	0.206305i	0.222928	−	0.00804871i
$658$		0			0
$659$	13.7002	−	7.90981i	0.533684	−	0.308122i	−0.208832	−	0.977952i	$-0.566966\pi$
$659$	13.7002	−	7.90981i	0.533684	−	0.308122i	0.742515	+	0.669829i	$0.233633\pi$
$660$		0			0
$661$	−15.8006	−	9.12248i	−0.614572	−	0.354823i	0.160181	−	0.987088i	$-0.448792\pi$
$661$	−15.8006	−	9.12248i	−0.614572	−	0.354823i	−0.774753	+	0.632264i	$0.782126\pi$
$662$		0			0
$663$	−9.94863	+	2.85909i	−0.386373	+	0.111038i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−61.8697			−2.39560
$668$		0			0
$669$	10.0022	−	40.2180i	0.386708	−	1.55492i
$670$		0			0
$671$	−0.389984	+	0.675472i	−0.0150552	+	0.0260763i
$672$		0			0
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	0.997842	+	0.0656633i	$0.0209163\pi$
$673$	14.4184	+	24.9733i	0.555787	+	0.962651i	−0.442055	+	0.896988i	$0.645750\pi$
$674$		0			0
$675$	2.70595	−	12.8424i	0.104152	−	0.494305i
$676$		0			0
$677$	16.7668	+	29.0409i	0.644400	+	1.11613i	0.984440	+	0.175722i	$0.0562261\pi$
$677$	16.7668	+	29.0409i	0.644400	+	1.11613i	−0.340040	+	0.940411i	$0.610441\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.27323	+	1.56015i	0.240391	+	0.0597852i
$682$		0			0
$683$		−	22.0481i		−	0.843649i	−0.906678	−	0.421824i	$-0.861390\pi$
$683$		−	22.0481i		−	0.843649i	0.906678	−	0.421824i	$-0.138610\pi$
$684$		0			0
$685$		−	14.7745i		−	0.564506i
$686$		0			0
$687$	35.0715	−	10.0790i	1.33806	−	0.384539i
$688$		0			0
$689$	2.99941	−	5.19512i	0.114268	−	0.197918i
$690$		0			0
$691$	−22.8662	+	13.2018i	−0.869869	+	0.502219i	−0.867305	−	0.497777i	$-0.834150\pi$
$691$	−22.8662	+	13.2018i	−0.869869	+	0.502219i	−0.00256453	+	0.999997i	$0.500816\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	40.5569	−	23.4156i	1.53841	−	0.888203i
$696$		0			0
$697$	4.14938	−	7.18694i	0.157169	−	0.272225i
$698$		0			0
$699$	−15.9125	−	15.3484i	−0.601868	−	0.580530i
$700$		0			0
$701$		−	20.5140i		−	0.774804i	−0.921911	−	0.387402i	$-0.873373\pi$
$701$		−	20.5140i		−	0.774804i	0.921911	−	0.387402i	$-0.126627\pi$
$702$		0			0
$703$			53.7827i			2.02845i
$704$		0			0
$705$	−5.84115	+	6.05585i	−0.219991	+	0.228076i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	0.918804	−	0.394714i	$-0.129156\pi$
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	−0.801234	+	0.598351i	$0.795823\pi$
$710$		0			0
$711$	2.20482	−	1.38135i	0.0826871	−	0.0518047i
$712$		0			0
$713$	15.7476	+	27.2756i	0.589751	+	1.02148i
$714$		0			0
$715$	0.878041	−	1.52081i	0.0328369	−	0.0568751i
$716$		0			0
$717$	−21.2442	+	6.10528i	−0.793381	+	0.228006i
$718$		0			0
$719$	23.2223			0.866045			0.433023	−	0.901383i	$-0.357447\pi$
$719$	23.2223			0.866045			0.433023	+	0.901383i	$0.357447\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.27161	+	5.11301i	−0.0472916	+	0.190155i
$724$		0			0
$725$	−15.1643	−	8.75512i	−0.563189	−	0.325157i
$726$		0			0
$727$	2.50999	−	1.44914i	0.0930903	−	0.0537457i	−0.452732	−	0.891647i	$-0.649551\pi$
$727$	2.50999	−	1.44914i	0.0930903	−	0.0537457i	0.545822	+	0.837901i	$0.316217\pi$
$728$		0			0
$729$	2.91748	+	26.8419i	0.108055	+	0.994145i
$730$		0			0
$731$	−22.5696	−	39.0917i	−0.834767	−	1.44586i
$732$		0			0
$733$	−10.2963	−	5.94457i	−0.380302	−	0.219568i	0.297647	−	0.954676i	$-0.403798\pi$
$733$	−10.2963	−	5.94457i	−0.380302	−	0.219568i	−0.677950	+	0.735108i	$0.737131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.34190i		−	0.196772i
$738$		0			0
$739$	−34.4509			−1.26730			−0.633648	−	0.773621i	$-0.718443\pi$
$739$	−34.4509			−1.26730			−0.633648	+	0.773621i	$0.718443\pi$
$740$		0			0
$741$	−4.32763	−	15.0586i	−0.158979	−	0.553193i
$742$		0			0
$743$	−2.44069	−	1.40913i	−0.0895401	−	0.0516960i	0.454561	−	0.890715i	$-0.349796\pi$
$743$	−2.44069	−	1.40913i	−0.0895401	−	0.0516960i	−0.544101	+	0.839019i	$0.683129\pi$
$744$		0			0
$745$	−25.5447	+	14.7483i	−0.935887	+	0.540335i
$746$		0			0
$747$	17.5864	−	11.0181i	0.643452	−	0.403132i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.86045	+	6.68649i	−0.140870	+	0.243993i	−0.927824	−	0.373017i	$-0.878323\pi$
$751$	−3.86045	+	6.68649i	−0.140870	+	0.243993i	0.786955	+	0.617011i	$0.211657\pi$
$752$		0			0
$753$	7.60026	−	7.87962i	0.276969	−	0.287149i
$754$		0			0
$755$	−20.7517			−0.755233
$756$		0			0
$757$	1.17924			0.0428603			0.0214302	−	0.999770i	$-0.493178\pi$
$757$	1.17924			0.0428603			0.0214302	+	0.999770i	$0.493178\pi$
$758$		0			0
$759$	4.48947	−	4.65449i	0.162957	−	0.168947i
$760$		0			0
$761$	−1.56644	+	2.71316i	−0.0567835	+	0.0983520i	−0.893020	−	0.450017i	$-0.851418\pi$
$761$	−1.56644	+	2.71316i	−0.0567835	+	0.0983520i	0.836236	+	0.548369i	$0.184751\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−28.3999	−	15.0574i	−1.02680	−	0.544403i
$766$		0			0
$767$	5.37276	−	3.10196i	0.193999	−	0.112005i
$768$		0			0
$769$	5.53497	+	3.19562i	0.199596	+	0.115237i	0.596467	−	0.802637i	$-0.296571\pi$
$769$	5.53497	+	3.19562i	0.199596	+	0.115237i	−0.396871	+	0.917874i	$0.629904\pi$
$770$		0			0
$771$	−11.7245	−	40.7971i	−0.422247	−	1.46927i
$772$		0			0
$773$	−47.9558			−1.72485			−0.862425	−	0.506185i	$-0.831055\pi$
$773$	−47.9558			−1.72485			−0.862425	+	0.506185i	$0.831055\pi$
$774$		0			0
$775$			8.91369i			0.320189i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.8784	+	6.28067i	0.389761	+	0.225028i
$780$		0			0
$781$	−1.78015	−	3.08331i	−0.0636987	−	0.110329i
$782$		0			0
$783$	35.2487	+	7.42705i	1.25969	+	0.265421i
$784$		0			0
$785$	−29.1661	+	16.8390i	−1.04098	+	0.601011i
$786$		0			0
$787$	5.23136	+	3.02033i	0.186478	+	0.107663i	0.590333	−	0.807160i	$-0.298997\pi$
$787$	5.23136	+	3.02033i	0.186478	+	0.107663i	−0.403855	+	0.914823i	$0.632330\pi$
$788$		0			0
$789$	−10.1928	+	40.9841i	−0.362872	+	1.45907i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.85269			−0.101302
$794$		0			0
$795$	17.9039	−	5.14530i	0.634985	−	0.182485i
$796$		0			0
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	−0.851834	−	0.523812i	$-0.824509\pi$
$797$	0.782501	−	1.35533i	0.0277176	−	0.0480083i	0.879551	+	0.475804i	$0.157843\pi$
$798$		0			0
$799$	3.45810	+	5.98961i	0.122339	+	0.211897i
$800$		0			0
$801$	−1.05832	−	29.3128i	−0.0373939	−	1.03572i
$802$		0			0
$803$	0.398681	+	0.690535i	0.0140691	+	0.0243685i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.8928	−	12.3299i	0.418646	−	0.434034i
$808$		0			0
$809$		−	17.7184i		−	0.622944i	−0.950255	−	0.311472i	$-0.899178\pi$
$809$		−	17.7184i		−	0.622944i	0.950255	−	0.311472i	$-0.100822\pi$
$810$		0			0
$811$			27.5261i			0.966571i	0.875463	+	0.483285i	$0.160557\pi$
$811$			27.5261i			0.966571i	−0.875463	+	0.483285i	$0.839443\pi$
$812$		0			0
$813$	−7.34872	−	7.08819i	−0.257731	−	0.248594i
$814$		0			0
$815$	−16.2334	+	28.1171i	−0.568633	+	0.984901i
$816$		0			0
$817$	59.1707	−	34.1622i	2.07012	−	1.19519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	−0.844834	−	0.535028i	$-0.820301\pi$
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	0.0409311	+	0.999162i	$0.486968\pi$
$822$		0			0
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	−0.996045	−	0.0888537i	$-0.971680\pi$
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	0.574972	+	0.818173i	$0.305013\pi$
$824$		0			0
$825$	1.75902	−	0.505518i	0.0612414	−	0.0175999i
$826$		0			0
$827$		−	9.64923i		−	0.335537i	−0.985826	−	0.167768i	$-0.946344\pi$
$827$		−	9.64923i		−	0.335537i	0.985826	−	0.167768i	$-0.0536561\pi$
$828$		0			0
$829$		−	29.0385i		−	1.00855i	−0.863543	−	0.504275i	$-0.831760\pi$
$829$		−	29.0385i		−	1.00855i	0.863543	−	0.504275i	$-0.168240\pi$
$830$		0			0
$831$	39.1535	+	9.73747i	1.35822	+	0.337789i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−18.6231	−	32.2562i	−0.644480	−	1.11627i
$836$		0			0
$837$	−5.69754	−	17.4300i	−0.196936	−	0.602468i
$838$		0			0
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	0.959642	−	0.281223i	$-0.0907400\pi$
$839$	6.84383	+	11.8539i	0.236275	+	0.409241i	−0.723367	+	0.690463i	$0.757407\pi$
$840$		0			0
$841$	9.53027	−	16.5069i	0.328630	−	0.569204i
$842$		0			0
$843$	−10.5209	+	42.3037i	−0.362360	+	1.45702i
$844$		0			0
$845$	−29.2404			−1.00590
$846$		0			0
$847$		0			0
$848$		0			0
$849$	16.5874	−	4.76698i	0.569279	−	0.163602i
$850$		0			0
$851$	−70.3110	−	40.5941i	−2.41023	−	1.39155i
$852$		0			0
$853$	40.5184	−	23.3933i	1.38732	−	0.800972i	0.394310	−	0.918977i	$-0.370983\pi$
$853$	40.5184	−	23.3933i	1.38732	−	0.800972i	0.993013	+	0.118006i	$0.0376501\pi$
$854$		0			0
$855$	22.7915	−	42.9872i	0.779454	−	1.47013i
$856$		0			0
$857$	15.8980	+	27.5361i	0.543065	+	0.940616i	0.998726	+	0.0504623i	$0.0160695\pi$
$857$	15.8980	+	27.5361i	0.543065	+	0.940616i	−0.455661	+	0.890153i	$0.650597\pi$
$858$		0			0
$859$	−21.9005	−	12.6442i	−0.747235	−	0.431416i	0.0774592	−	0.996996i	$-0.475319\pi$
$859$	−21.9005	−	12.6442i	−0.747235	−	0.431416i	−0.824694	+	0.565579i	$0.808653\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	18.4189i		−	0.626987i	−0.949590	−	0.313494i	$-0.898501\pi$
$863$		−	18.4189i		−	0.626987i	0.949590	−	0.313494i	$-0.101499\pi$
$864$		0			0
$865$	45.5986			1.55040
$866$		0			0
$867$	2.09783	−	2.17494i	0.0712461	−	0.0738648i
$868$		0			0
$869$	0.314216	+	0.181413i	0.0106590	+	0.00615400i
$870$		0			0
$871$	16.9202	−	9.76886i	0.573318	−	0.331005i
$872$		0			0
$873$	−0.368589	−	0.588317i	−0.0124748	−	0.0199115i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.44695	−	7.70234i	0.150163	−	0.260089i	−0.781124	−	0.624375i	$-0.785354\pi$
$877$	4.44695	−	7.70234i	0.150163	−	0.260089i	0.931287	+	0.364286i	$0.118687\pi$
$878$		0			0
$879$	−6.49732	−	22.6084i	−0.219149	−	0.762563i
$880$		0			0
$881$	13.1721			0.443780			0.221890	−	0.975072i	$-0.428777\pi$
$881$	13.1721			0.443780			0.221890	+	0.975072i	$0.428777\pi$
$882$		0			0
$883$	12.6729			0.426477			0.213239	−	0.977000i	$-0.431599\pi$
$883$	12.6729			0.426477			0.213239	+	0.977000i	$0.431599\pi$
$884$		0			0
$885$	18.6960	+	4.64970i	0.628459	+	0.156298i
$886$		0			0
$887$	−16.6991	+	28.9238i	−0.560703	+	0.971165i	0.436733	+	0.899591i	$0.356136\pi$
$887$	−16.6991	+	28.9238i	−0.560703	+	0.971165i	−0.997435	+	0.0715740i	$0.977198\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.11650	+	2.11285i	−0.104407	+	0.0707830i
$892$		0			0
$893$	−9.06611	+	5.23432i	−0.303386	+	0.175160i
$894$		0			0
$895$	40.6231	+	23.4538i	1.35788	+	0.783974i
$896$		0			0
$897$	22.9528	+	5.70837i	0.766372	+	0.190597i
$898$		0			0
$899$	−24.4655			−0.815970
$900$		0			0
$901$		−	15.3128i		−	0.510142i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−43.2799	−	24.9877i	−1.43867	−	0.830618i
$906$		0			0
$907$	14.6563	+	25.3855i	0.486655	+	0.842912i	0.999882	−	0.0153411i	$-0.00488340\pi$
$907$	14.6563	+	25.3855i	0.486655	+	0.842912i	−0.513227	+	0.858253i	$0.671550\pi$
$908$		0			0
$909$	−36.3051	+	22.7457i	−1.20416	+	0.754426i
$910$		0			0
$911$	1.72555	−	0.996246i	0.0571700	−	0.0330071i	−0.471143	−	0.882057i	$-0.656158\pi$
$911$	1.72555	−	0.996246i	0.0571700	−	0.0330071i	0.528313	+	0.849050i	$0.322825\pi$
$912$		0			0
$913$	2.50629	+	1.44701i	0.0829462	+	0.0478890i
$914$		0			0
$915$	−6.37603	−	6.14998i	−0.210785	−	0.203312i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.79536			0.0592233			0.0296117	−	0.999561i	$-0.490573\pi$
$919$	1.79536			0.0592233			0.0296117	+	0.999561i	$0.490573\pi$
$920$		0			0
$921$	−21.1742	−	20.4235i	−0.697712	−	0.672976i
$922$		0			0
$923$	6.51079	−	11.2770i	0.214305	−	0.371188i
$924$		0			0
$925$	−11.4889	−	19.8993i	−0.377751	−	0.654284i
$926$		0			0
$927$	15.1009	−	28.4819i	0.495980	−	0.935469i
$928$		0			0
$929$	12.4178	+	21.5083i	0.407415	+	0.705664i	0.994599	−	0.103789i	$-0.0330968\pi$
$929$	12.4178	+	21.5083i	0.407415	+	0.705664i	−0.587184	+	0.809453i	$0.699763\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.00142507	−	0.00495873i	−4.66546e−5	−	0.000162342i
$934$		0			0
$935$		−	4.48263i		−	0.146598i
$936$		0			0
$937$			27.9046i			0.911605i	0.890081	+	0.455802i	$0.150648\pi$
$937$			27.9046i			0.911605i	−0.890081	+	0.455802i	$0.849352\pi$
$938$		0			0
$939$	5.12400	−	20.6031i	0.167215	−	0.672357i
$940$		0			0
$941$	−26.2537	+	45.4728i	−0.855847	+	1.48237i	0.0200094	+	0.999800i	$0.493630\pi$
$941$	−26.2537	+	45.4728i	−0.855847	+	1.48237i	−0.875857	+	0.482571i	$0.839703\pi$
$942$		0			0
$943$	−16.4216	+	9.48104i	−0.534762	+	0.308745i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.250377	−	0.968148i	$-0.419445\pi$
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.963630	+	0.267241i	$0.0861121\pi$
$948$		0			0
$949$	−1.45815	+	2.52559i	−0.0473336	+	0.0819843i
$950$		0			0
$951$	9.65433	−	38.8191i	0.313063	−	1.25880i
$952$		0			0
$953$		−	59.9829i		−	1.94304i	−0.236965	−	0.971518i	$-0.576153\pi$
$953$		−	59.9829i		−	1.94304i	0.236965	−	0.971518i	$-0.423847\pi$
$954$		0			0
$955$		−	57.6079i		−	1.86415i
$956$		0			0
$957$	1.38750	+	4.82801i	0.0448515	+	0.156067i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.27285	−	16.0610i	−0.299124	−	0.518098i
$962$		0			0
$963$	19.0586	−	0.688101i	0.614156	−	0.0221737i
$964$		0			0
$965$	−9.56709	−	16.5707i	−0.307975	−	0.533429i
$966$		0			0
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	0.0184029	+	0.999831i	$0.494142\pi$
$967$	−26.6398	+	46.1414i	−0.856677	+	1.48381i	−0.875080	+	0.483978i	$0.839191\pi$
$968$		0			0
$969$	−28.7864	−	27.7659i	−0.924753	−	0.891968i
$970$		0			0
$971$	−56.3111			−1.80711			−0.903555	−	0.428472i	$-0.859052\pi$
$971$	−56.3111			−1.80711			−0.903555	+	0.428472i	$0.859052\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	4.81796	+	4.64715i	0.154298	+	0.148828i
$976$		0			0
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	0.815582	−	0.578642i	$-0.196417\pi$
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	−0.0933275	+	0.995635i	$0.529750\pi$
$978$		0			0
$979$	3.54237	−	2.04519i	0.113215	−	0.0653646i
$980$		0			0
$981$	0.558611	+	15.4721i	0.0178351	+	0.493986i
$982$		0			0
$983$	19.0252	+	32.9527i	0.606811	+	1.05103i	0.991763	+	0.128090i	$0.0408848\pi$
$983$	19.0252	+	32.9527i	0.606811	+	1.05103i	−0.384952	+	0.922937i	$0.625782\pi$
$984$		0			0
$985$	38.1922	+	22.0503i	1.21690	+	0.702580i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			103.140i			3.27965i
$990$		0			0
$991$	11.3752			0.361344			0.180672	−	0.983543i	$-0.442173\pi$
$991$	11.3752			0.361344			0.180672	+	0.983543i	$0.442173\pi$
$992$		0			0
$993$	−5.81931	−	1.44726i	−0.184670	−	0.0459276i
$994$		0			0
$995$	−14.9499	−	8.63131i	−0.473943	−	0.273631i
$996$		0			0
$997$	44.1590	−	25.4952i	1.39853	−	0.807441i	0.404290	−	0.914631i	$-0.367518\pi$
$997$	44.1590	−	25.4952i	1.39853	−	0.807441i	0.994239	+	0.107189i	$0.0341851\pi$
$998$		0			0
$999$	35.1849	+	31.5678i	1.11320	+	0.998762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.a.293.2		16
3.2	odd	2		5292.2.x.a.881.2		16
7.2	even	3		1764.2.bm.a.1697.4		16
7.3	odd	6		1764.2.w.b.509.2		16
7.4	even	3		252.2.w.a.5.7	✓	16
7.5	odd	6		252.2.bm.a.185.5	yes	16
7.6	odd	2		1764.2.x.b.293.7		16
9.2	odd	6		1764.2.x.b.1469.7		16
9.7	even	3		5292.2.x.b.4409.7		16
21.2	odd	6		5292.2.bm.a.2285.7		16
21.5	even	6		756.2.bm.a.17.2		16
21.11	odd	6		756.2.w.a.341.2		16
21.17	even	6		5292.2.w.b.1097.7		16
21.20	even	2		5292.2.x.b.881.7		16
28.11	odd	6		1008.2.ca.d.257.2		16
28.19	even	6		1008.2.df.d.689.4		16
63.2	odd	6		1764.2.w.b.1109.2		16
63.4	even	3		2268.2.t.b.2105.7		16
63.5	even	6		2268.2.t.b.1781.7		16
63.11	odd	6		252.2.bm.a.173.5	yes	16
63.16	even	3		5292.2.w.b.521.7		16
63.20	even	6	inner	1764.2.x.a.1469.2		16
63.25	even	3		756.2.bm.a.89.2		16
63.32	odd	6		2268.2.t.a.2105.2		16
63.34	odd	6		5292.2.x.a.4409.2		16
63.38	even	6		1764.2.bm.a.1685.4		16
63.40	odd	6		2268.2.t.a.1781.2		16
63.47	even	6		252.2.w.a.101.7	yes	16
63.52	odd	6		5292.2.bm.a.4625.7		16
63.61	odd	6		756.2.w.a.521.2		16
84.11	even	6		3024.2.ca.d.2609.2		16
84.47	odd	6		3024.2.df.d.17.2		16
252.11	even	6		1008.2.df.d.929.4		16
252.47	odd	6		1008.2.ca.d.353.2		16
252.151	odd	6		3024.2.df.d.1601.2		16
252.187	even	6		3024.2.ca.d.2033.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	7.4	even	3
252.2.w.a.101.7	yes	16	63.47	even	6
252.2.bm.a.173.5	yes	16	63.11	odd	6
252.2.bm.a.185.5	yes	16	7.5	odd	6
756.2.w.a.341.2		16	21.11	odd	6
756.2.w.a.521.2		16	63.61	odd	6
756.2.bm.a.17.2		16	21.5	even	6
756.2.bm.a.89.2		16	63.25	even	3
1008.2.ca.d.257.2		16	28.11	odd	6
1008.2.ca.d.353.2		16	252.47	odd	6
1008.2.df.d.689.4		16	28.19	even	6
1008.2.df.d.929.4		16	252.11	even	6
1764.2.w.b.509.2		16	7.3	odd	6
1764.2.w.b.1109.2		16	63.2	odd	6
1764.2.x.a.293.2		16	1.1	even	1	trivial
1764.2.x.a.1469.2		16	63.20	even	6	inner
1764.2.x.b.293.7		16	7.6	odd	2
1764.2.x.b.1469.7		16	9.2	odd	6
1764.2.bm.a.1685.4		16	63.38	even	6
1764.2.bm.a.1697.4		16	7.2	even	3
2268.2.t.a.1781.2		16	63.40	odd	6
2268.2.t.a.2105.2		16	63.32	odd	6
2268.2.t.b.1781.7		16	63.5	even	6
2268.2.t.b.2105.7		16	63.4	even	3
3024.2.ca.d.2033.2		16	252.187	even	6
3024.2.ca.d.2609.2		16	84.11	even	6
3024.2.df.d.17.2		16	84.47	odd	6
3024.2.df.d.1601.2		16	252.151	odd	6
5292.2.w.b.521.7		16	63.16	even	3
5292.2.w.b.1097.7		16	21.17	even	6
5292.2.x.a.881.2		16	3.2	odd	2
5292.2.x.a.4409.2		16	63.34	odd	6
5292.2.x.b.881.7		16	21.20	even	2
5292.2.x.b.4409.7		16	9.7	even	3
5292.2.bm.a.2285.7		16	21.2	odd	6
5292.2.bm.a.4625.7		16	63.52	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20245 + 1.24664i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-0.108243 - 2.99805i) q^{9} +O(q^{10})\)	\(q+(-1.20245 + 1.24664i) q^{3} +(1.37166 - 2.37578i) q^{5} +(-0.108243 - 2.99805i) q^{9} +(0.362306 - 0.209178i) q^{11} +(1.32512 + 0.765056i) q^{13} +(1.31241 + 4.56672i) q^{15} +3.90581 q^{17} +5.91199i q^{19} +(-7.72884 - 4.46225i) q^{23} +(-1.26290 - 2.18740i) q^{25} +(3.86765 + 3.47005i) q^{27} +(6.00378 - 3.46629i) q^{29} +(-3.05626 - 1.76453i) q^{31} +(-0.174884 + 0.703192i) q^{33} +9.09722 q^{37} +(-2.54713 + 0.732009i) q^{39} +(1.06236 - 1.84006i) q^{41} +(-5.77846 - 10.0086i) q^{43} +(-7.27118 - 3.85514i) q^{45} +(0.885373 + 1.53351i) q^{47} +(-4.69653 + 4.86916i) q^{51} -3.92050i q^{53} -1.14768i q^{55} +(-7.37015 - 7.10886i) q^{57} +(2.02728 - 3.51135i) q^{59} +(-1.61459 + 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} +(14.8564 - 4.26950i) q^{69} -8.51021i q^{71} +1.90594i q^{73} +(4.24548 + 1.05585i) q^{75} +(0.433633 + 0.751074i) q^{79} +(-8.97657 + 0.649034i) q^{81} +(3.45880 + 5.99082i) q^{83} +(5.35744 - 9.27936i) q^{85} +(-2.89801 + 11.6526i) q^{87} +9.77729 q^{89} +(5.87474 - 1.68831i) q^{93} +(14.0456 + 8.10924i) q^{95} +(0.200411 - 0.115707i) q^{97} +(-0.666342 - 1.06357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 6 q^{11} - 3 q^{13} - 3 q^{15} - 18 q^{17} - 21 q^{23} - 8 q^{25} + 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} - 2 q^{37} + 6 q^{39} - 6 q^{41} - 2 q^{43} + 15 q^{45} + 18 q^{47} + 18 q^{51} + 15 q^{57} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 21 q^{69} + 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} - 51 q^{87} - 42 q^{89} + 48 q^{93} - 6 q^{95} - 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 6 * q^11 - 3 * q^13 - 3 * q^15 - 18 * q^17 - 21 * q^23 - 8 * q^25 + 9 * q^27 + 6 * q^29 + 6 * q^31 - 27 * q^33 - 2 * q^37 + 6 * q^39 - 6 * q^41 - 2 * q^43 + 15 * q^45 + 18 * q^47 + 18 * q^51 + 15 * q^57 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 21 * q^69 + 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 - 51 * q^87 - 42 * q^89 + 48 * q^93 - 6 * q^95 - 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

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Database

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