LMFDB - Embedded newform 1764.2.x.b.293.7

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			293.7
Root			$-0.811340 - 1.53027i$ of defining polynomial
Character	$\chi$	$=$	1764.293
Dual form			1764.2.x.b.1469.7

$q$-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	$0.376875\pi$
$5$	−1.37166	+	2.37578i	−0.613425	+	1.06248i	−0.990659	+	0.136365i	$0.956458\pi$
$6$		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	0.304854	−	0.952399i	$-0.401392\pi$
$13$	−1.32512	−	0.765056i	−0.367521	−	0.212188i	−0.672375	+	0.740211i	$0.734726\pi$
$14$		0			0
$15$	1.31241	+	4.56672i	0.338862	+	1.17912i
$16$		0			0
$17$	−3.90581			−0.947298			−0.473649	−	0.880714i	$-0.657064\pi$
$17$	−3.90581			−0.947298			−0.473649	+	0.880714i	$0.657064\pi$
$18$		0			0
$19$		−	5.91199i		−	1.35630i	−0.734922	−	0.678152i	$-0.762781\pi$
$19$		−	5.91199i		−	1.35630i	0.734922	−	0.678152i	$-0.237219\pi$
$20$		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	0.748687	−	0.662924i	$-0.230685\pi$
$31$	3.05626	+	1.76453i	0.548921	+	0.316920i	−0.199766	+	0.979844i	$0.564018\pi$
$32$		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	−0.936979	−	0.349385i	$-0.886390\pi$
$41$	−1.06236	+	1.84006i	−0.165913	+	0.287370i	0.771066	+	0.636755i	$0.219724\pi$
$42$		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	0.794201	−	0.607656i	$-0.207890\pi$
$47$	−0.885373	−	1.53351i	−0.129145	−	0.223686i	−0.923346	+	0.383970i	$0.874557\pi$
$48$		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	−0.967283	−	0.253702i	$-0.918352\pi$
$59$	−2.02728	+	3.51135i	−0.263929	+	0.457139i	0.703353	+	0.710840i	$0.251685\pi$
$60$		0			0
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	−0.393062	−	0.919512i	$-0.628584\pi$
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	0.599789	+	0.800158i	$0.295251\pi$
$62$		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	$-0.964423\pi$
$73$		−	1.90594i		−	0.223074i	0.993760	−	0.111537i	$-0.0355773\pi$
$74$		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	0.611359	−	0.791354i	$-0.290623\pi$
$83$	−3.45880	−	5.99082i	−0.379653	−	0.657578i	−0.991012	+	0.133775i	$0.957290\pi$
$84$		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	$-0.673396\pi$
$89$	−9.77729			−1.03639			−0.518195	+	0.855262i	$0.673396\pi$
$90$		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	−0.510140	−	0.860091i	$-0.670406\pi$
$97$	−0.200411	+	0.115707i	−0.0203486	+	0.0117483i	0.489791	+	0.871840i	$0.337073\pi$
$98$		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	$0.0848587\pi$
$101$	7.14031	+	12.3674i	0.710487	+	1.23060i	−0.254187	+	0.967155i	$0.581808\pi$
$102$		0			0
$103$	−9.30617	−	5.37292i	−0.916964	−	0.529410i	−0.0342991	−	0.999412i	$-0.510920\pi$
$103$	−9.30617	−	5.37292i	−0.916964	−	0.529410i	−0.882665	+	0.470002i	$0.844253\pi$
$104$		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	$0.495514\pi$
$131$	−9.83048	+	17.0269i	−0.858893	+	1.48765i	−0.872986	+	0.487746i	$0.837819\pi$
$132$		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	−0.282062	−	0.959396i	$-0.591018\pi$
$139$	−14.7839	−	8.53549i	−1.25395	−	0.723971i	−0.971892	+	0.235425i	$0.924352\pi$
$140$		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	0.860144	−	0.510051i	$-0.170373\pi$
$157$	10.6317	+	6.13820i	0.848500	+	0.489882i	−0.0116445	+	0.999932i	$0.503707\pi$
$158$		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	$0.342718\pi$
$167$	−6.78854	+	11.7581i	−0.525313	+	0.909869i	−0.999565	+	0.0294798i	$0.990615\pi$
$168$		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	$-0.948957\pi$
$173$	−8.31085	−	14.3948i	−0.631862	−	1.09442i	0.355308	−	0.934749i	$-0.384376\pi$
$174$		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	$0.236735\pi$
$181$			18.2171i			1.35407i	−0.735952	+	0.677034i	$0.763265\pi$
$182$		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	$0.0715966\pi$
$199$			6.29261i			0.446071i	−0.974810	+	0.223036i	$0.928403\pi$
$200$		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	0.394571	−	0.918866i	$-0.370893\pi$
$223$	20.7215	−	11.9636i	1.38762	−	0.801141i	0.993046	+	0.117725i	$0.0375600\pi$
$224$		0			0
$225$	−6.42123	+	4.02299i	−0.428082	+	0.268200i
$226$		0			0
$227$	1.86609	+	3.23216i	0.123857	+	0.214526i	0.921285	−	0.388887i	$-0.127140\pi$
$227$	1.86609	+	3.23216i	0.123857	+	0.214526i	−0.797429	+	0.603413i	$0.793807\pi$
$228$		0			0
$229$	18.2455	+	10.5341i	1.20570	+	0.696111i	0.961817	−	0.273694i	$-0.0882457\pi$
$229$	18.2455	+	10.5341i	1.20570	+	0.696111i	0.243882	+	0.969805i	$0.421579\pi$
$230$		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	−0.582442	−	0.812872i	$-0.697903\pi$
$241$	−2.63438	+	1.52096i	−0.169695	+	0.0979737i	0.412747	+	0.910846i	$0.364569\pi$
$242$		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	$-0.436075\pi$
$251$	6.32067			0.398957			0.199478	+	0.979902i	$0.436075\pi$
$252$		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	$-0.556383\pi$
$257$	12.2538	−	21.2242i	0.764372	−	1.32393i	0.940578	−	0.339577i	$-0.110284\pi$
$258$		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	$-0.402507\pi$
$269$	9.89049			0.603034			0.301517	+	0.953461i	$0.402507\pi$
$270$		0			0
$271$		−	5.89481i		−	0.358084i	−0.983841	−	0.179042i	$-0.942700\pi$
$271$		−	5.89481i		−	0.358084i	0.983841	−	0.179042i	$-0.0572998\pi$
$272$		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	0.734052	−	0.679093i	$-0.237627\pi$
$283$	8.62942	+	4.98220i	0.512966	+	0.296161i	−0.221086	+	0.975254i	$0.570960\pi$
$284$		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	−0.596604	−	0.802536i	$-0.703484\pi$
$293$	6.79065	−	11.7618i	0.396714	−	0.687129i	0.993318	+	0.115406i	$0.0368171\pi$
$294$		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	$-0.838932\pi$
$307$		−	16.9849i		−	0.969381i	0.874686	−	0.484691i	$-0.161068\pi$
$308$		0			0
$309$	−17.8883	+	5.14083i	−1.01763	+	0.292452i
$310$		0			0
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	−0.865983	−	0.500073i	$-0.833306\pi$
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	0.866068	+	0.499927i	$0.166640\pi$
$312$		0			0
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	−0.169032	−	0.985611i	$-0.554064\pi$
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	0.769048	+	0.639191i	$0.220731\pi$
$314$		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	−0.499634	−	0.866237i	$-0.666532\pi$
$349$	0.0136817	−	0.00789914i	0.000732365	−	0.000422831i	0.500366	+	0.865814i	$0.333199\pi$
$350$		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	$-0.800403\pi$
$353$	−17.1543	−	29.7121i	−0.913029	−	1.58141i	−0.103268	−	0.994654i	$-0.532930\pi$
$354$		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	−0.00353959	−	0.999994i	$-0.501127\pi$
$367$	16.4888	−	9.51984i	0.860711	−	0.496931i	0.864250	+	0.503062i	$0.167793\pi$
$368$		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	$0.591240\pi$
$383$	−19.0235	+	32.9497i	−0.972056	+	1.68365i	−0.689327	+	0.724451i	$0.742094\pi$
$384$		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	$-0.832208\pi$
$397$		−	20.0468i		−	1.00612i	0.864252	−	0.503059i	$-0.167792\pi$
$398$		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	0.503719	−	0.863867i	$-0.331965\pi$
$409$	0.150631	+	0.0869667i	0.00744821	+	0.00430023i	−0.496271	+	0.868168i	$0.665298\pi$
$410$		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	$-0.592122\pi$
$419$	14.0690	−	24.3682i	0.687316	−	1.19047i	0.972703	−	0.232054i	$-0.0745445\pi$
$420$		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	$-0.864989\pi$
$433$		−	17.1274i		−	0.823092i	0.911389	−	0.411546i	$-0.135011\pi$
$434$		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	0.0138721	−	0.999904i	$-0.495584\pi$
$439$	18.5795	−	10.7269i	0.886750	−	0.511965i	0.872878	+	0.487938i	$0.162251\pi$
$440$		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	$0.164340\pi$
$461$	18.5154	+	32.0696i	0.862347	+	1.49363i	−0.00730959	+	0.999973i	$0.502327\pi$
$462$		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	$-0.358312\pi$
$467$	18.6094			0.861141			0.430570	+	0.902557i	$0.358312\pi$
$468$		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	0.654539	−	0.756028i	$-0.272863\pi$
$479$	−7.16703	−	12.4137i	−0.327470	−	0.567194i	−0.982009	+	0.188834i	$0.939529\pi$
$480$		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	$-0.501908\pi$
$503$	−0.268917			−0.0119904			−0.00599520	+	0.999982i	$0.501908\pi$
$504$		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	−0.999853	−	0.0171449i	$-0.994542\pi$
$509$	−10.9439	+	18.9553i	−0.485079	+	0.840181i	0.514774	+	0.857326i	$0.327876\pi$
$510$		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	$-0.488059\pi$
$521$	1.71215			0.0750105			0.0375053	+	0.999296i	$0.488059\pi$
$522$		0			0
$523$			8.27136i			0.361681i	0.983512	+	0.180841i	$0.0578818\pi$
$523$			8.27136i			0.361681i	−0.983512	+	0.180841i	$0.942118\pi$
$524$		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	−0.986068	−	0.166345i	$-0.946804\pi$
$563$	−8.28035	+	14.3420i	−0.348975	+	0.604443i	0.637093	+	0.770787i	$0.280137\pi$
$564$		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	$-0.879539\pi$
$577$		−	17.7499i		−	0.738939i	0.929243	−	0.369470i	$-0.120461\pi$
$578$		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	0.760508	−	0.649329i	$-0.224950\pi$
$587$	−4.41148	−	7.64091i	−0.182081	−	0.315374i	−0.942589	+	0.333955i	$0.891617\pi$
$588$		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	$-0.444181\pi$
$593$	8.49698			0.348929			0.174465	+	0.984663i	$0.444181\pi$
$594$		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	−0.619981	−	0.784617i	$-0.712860\pi$
$601$	−6.14043	+	3.54518i	−0.250473	+	0.144611i	0.369508	+	0.929228i	$0.379526\pi$
$602$		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	−0.235500	−	0.971874i	$-0.575673\pi$
$607$	−29.4396	−	16.9970i	−1.19492	−	0.689886i	−0.959418	+	0.281988i	$0.909006\pi$
$608$		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	−0.651708	−	0.758470i	$-0.725947\pi$
$619$	−7.97914	+	4.60676i	−0.320709	+	0.185161i	0.331000	+	0.943631i	$0.392614\pi$
$620$		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	0.539134	−	0.842220i	$-0.318752\pi$
$643$	2.01129	+	1.16122i	0.0793177	+	0.0457941i	−0.459817	+	0.888014i	$0.652085\pi$
$644$		0			0
$645$	38.1228	−	39.5240i	1.50108	−	1.55626i
$646$		0			0
$647$	25.8620			1.01674			0.508370	−	0.861139i	$-0.330248\pi$
$647$	25.8620			1.01674			0.508370	+	0.861139i	$0.330248\pi$
$648$		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	0.774753	−	0.632264i	$-0.217874\pi$
$661$	15.8006	+	9.12248i	0.614572	+	0.354823i	−0.160181	+	0.987088i	$0.551208\pi$
$662$		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	$-0.943774\pi$
$677$	−16.7668	−	29.0409i	−0.644400	−	1.11613i	0.340040	−	0.940411i	$-0.389559\pi$
$678$		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	0.00256453	−	0.999997i	$-0.499184\pi$
$691$	22.8662	−	13.2018i	0.869869	−	0.502219i	0.867305	+	0.497777i	$0.165850\pi$
$692$		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	$-0.642553\pi$
$719$	−23.2223			−0.866045			−0.433023	+	0.901383i	$0.642553\pi$
$720$		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	−0.545822	−	0.837901i	$-0.683783\pi$
$727$	−2.50999	+	1.44914i	−0.0930903	+	0.0537457i	0.452732	+	0.891647i	$0.350449\pi$
$728$		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	0.677950	−	0.735108i	$-0.262869\pi$
$733$	10.2963	+	5.94457i	0.380302	+	0.219568i	−0.297647	+	0.954676i	$0.596202\pi$
$734$		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	−0.836236	−	0.548369i	$-0.815249\pi$
$761$	1.56644	−	2.71316i	0.0567835	−	0.0983520i	0.893020	+	0.450017i	$0.148582\pi$
$762$		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	0.396871	−	0.917874i	$-0.370096\pi$
$769$	−5.53497	−	3.19562i	−0.199596	−	0.115237i	−0.596467	+	0.802637i	$0.703429\pi$
$770$		0			0
$771$	−11.7245	−	40.7971i	−0.422247	−	1.46927i
$772$		0			0
$773$	47.9558			1.72485			0.862425	−	0.506185i	$-0.168945\pi$
$773$	47.9558			1.72485			0.862425	+	0.506185i	$0.168945\pi$
$774$		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	0.403855	−	0.914823i	$-0.367670\pi$
$787$	−5.23136	−	3.02033i	−0.186478	−	0.107663i	−0.590333	+	0.807160i	$0.701003\pi$
$788$		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	−0.879551	−	0.475804i	$-0.842157\pi$
$797$	−0.782501	+	1.35533i	−0.0277176	+	0.0480083i	0.851834	+	0.523812i	$0.175491\pi$
$798$		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	$-0.839443\pi$
$811$		−	27.5261i		−	0.966571i	0.875463	−	0.483285i	$-0.160557\pi$
$812$		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	$0.168240\pi$
$829$			29.0385i			1.00855i	−0.863543	+	0.504275i	$0.831760\pi$
$830$		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	0.723367	−	0.690463i	$-0.242593\pi$
$839$	−6.84383	−	11.8539i	−0.236275	−	0.409241i	−0.959642	+	0.281223i	$0.909260\pi$
$840$		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	−0.993013	−	0.118006i	$-0.962350\pi$
$853$	−40.5184	+	23.3933i	−1.38732	+	0.800972i	−0.394310	+	0.918977i	$0.629017\pi$
$854$		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	$-0.983931\pi$
$857$	−15.8980	−	27.5361i	−0.543065	−	0.940616i	0.455661	−	0.890153i	$-0.349403\pi$
$858$		0			0
$859$	21.9005	+	12.6442i	0.747235	+	0.431416i	0.824694	−	0.565579i	$-0.191347\pi$
$859$	21.9005	+	12.6442i	0.747235	+	0.431416i	−0.0774592	+	0.996996i	$0.524681\pi$
$860$		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	$-0.571223\pi$
$881$	−13.1721			−0.443780			−0.221890	+	0.975072i	$0.571223\pi$
$882$		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	$-0.643864\pi$
$887$	16.6991	−	28.9238i	0.560703	−	0.971165i	0.997435	−	0.0715740i	$-0.0228022\pi$
$888$		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	0.587184	−	0.809453i	$-0.300237\pi$
$929$	−12.4178	−	21.5083i	−0.407415	−	0.705664i	−0.994599	+	0.103789i	$0.966903\pi$
$930$		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	$-0.849352\pi$
$937$		−	27.9046i		−	0.911605i	0.890081	−	0.455802i	$-0.150648\pi$
$938$		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	$-0.506370\pi$
$941$	26.2537	−	45.4728i	0.855847	−	1.48237i	0.875857	−	0.482571i	$-0.160297\pi$
$942$		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	$-0.140948\pi$
$971$	56.3111			1.80711			0.903555	+	0.428472i	$0.140948\pi$
$972$		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	$-0.959115\pi$
$983$	−19.0252	−	32.9527i	−0.606811	−	1.05103i	0.384952	−	0.922937i	$-0.374218\pi$
$984$		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	−0.994239	−	0.107189i	$-0.965815\pi$
$997$	−44.1590	+	25.4952i	−1.39853	+	0.807441i	−0.404290	+	0.914631i	$0.632482\pi$
$998$		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.b.293.7		16
3.2	odd	2		5292.2.x.b.881.7		16
7.2	even	3		252.2.bm.a.185.5	yes	16
7.3	odd	6		252.2.w.a.5.7	✓	16
7.4	even	3		1764.2.w.b.509.2		16
7.5	odd	6		1764.2.bm.a.1697.4		16
7.6	odd	2		1764.2.x.a.293.2		16
9.2	odd	6		1764.2.x.a.1469.2		16
9.7	even	3		5292.2.x.a.4409.2		16
21.2	odd	6		756.2.bm.a.17.2		16
21.5	even	6		5292.2.bm.a.2285.7		16
21.11	odd	6		5292.2.w.b.1097.7		16
21.17	even	6		756.2.w.a.341.2		16
21.20	even	2		5292.2.x.a.881.2		16
28.3	even	6		1008.2.ca.d.257.2		16
28.23	odd	6		1008.2.df.d.689.4		16
63.2	odd	6		252.2.w.a.101.7	yes	16
63.11	odd	6		1764.2.bm.a.1685.4		16
63.16	even	3		756.2.w.a.521.2		16
63.20	even	6	inner	1764.2.x.b.1469.7		16
63.23	odd	6		2268.2.t.b.1781.7		16
63.25	even	3		5292.2.bm.a.4625.7		16
63.31	odd	6		2268.2.t.b.2105.7		16
63.34	odd	6		5292.2.x.b.4409.7		16
63.38	even	6		252.2.bm.a.173.5	yes	16
63.47	even	6		1764.2.w.b.1109.2		16
63.52	odd	6		756.2.bm.a.89.2		16
63.58	even	3		2268.2.t.a.1781.2		16
63.59	even	6		2268.2.t.a.2105.2		16
63.61	odd	6		5292.2.w.b.521.7		16
84.23	even	6		3024.2.df.d.17.2		16
84.59	odd	6		3024.2.ca.d.2609.2		16
252.79	odd	6		3024.2.ca.d.2033.2		16
252.115	even	6		3024.2.df.d.1601.2		16
252.191	even	6		1008.2.ca.d.353.2		16
252.227	odd	6		1008.2.df.d.929.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	7.3	odd	6
252.2.w.a.101.7	yes	16	63.2	odd	6
252.2.bm.a.173.5	yes	16	63.38	even	6
252.2.bm.a.185.5	yes	16	7.2	even	3
756.2.w.a.341.2		16	21.17	even	6
756.2.w.a.521.2		16	63.16	even	3
756.2.bm.a.17.2		16	21.2	odd	6
756.2.bm.a.89.2		16	63.52	odd	6
1008.2.ca.d.257.2		16	28.3	even	6
1008.2.ca.d.353.2		16	252.191	even	6
1008.2.df.d.689.4		16	28.23	odd	6
1008.2.df.d.929.4		16	252.227	odd	6
1764.2.w.b.509.2		16	7.4	even	3
1764.2.w.b.1109.2		16	63.47	even	6
1764.2.x.a.293.2		16	7.6	odd	2
1764.2.x.a.1469.2		16	9.2	odd	6
1764.2.x.b.293.7		16	1.1	even	1	trivial
1764.2.x.b.1469.7		16	63.20	even	6	inner
1764.2.bm.a.1685.4		16	63.11	odd	6
1764.2.bm.a.1697.4		16	7.5	odd	6
2268.2.t.a.1781.2		16	63.58	even	3
2268.2.t.a.2105.2		16	63.59	even	6
2268.2.t.b.1781.7		16	63.23	odd	6
2268.2.t.b.2105.7		16	63.31	odd	6
3024.2.ca.d.2033.2		16	252.79	odd	6
3024.2.ca.d.2609.2		16	84.59	odd	6
3024.2.df.d.17.2		16	84.23	even	6
3024.2.df.d.1601.2		16	252.115	even	6
5292.2.w.b.521.7		16	63.61	odd	6
5292.2.w.b.1097.7		16	21.11	odd	6
5292.2.x.a.881.2		16	21.20	even	2
5292.2.x.a.4409.2		16	9.7	even	3
5292.2.x.b.881.7		16	3.2	odd	2
5292.2.x.b.4409.7		16	63.34	odd	6
5292.2.bm.a.2285.7		16	21.5	even	6
5292.2.bm.a.4625.7		16	63.25	even	3

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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