LMFDB - Embedded newform 189.2.p.b.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(26,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.p (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	189.26
Dual form			189.2.p.b.80.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(1.22474 - 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(1.22474 - 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(3.00000 - 1.73205i) q^{10} +(-4.89898 + 2.82843i) q^{11} +3.46410i q^{13} +(2.44949 + 2.82843i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.22474 + 2.12132i) q^{17} +(1.50000 + 0.866025i) q^{19} -8.00000 q^{22} +(-6.12372 - 3.53553i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.44949 + 4.24264i) q^{26} -1.41421i q^{29} +(-4.50000 + 2.59808i) q^{31} +3.46410i q^{34} +(4.89898 - 4.24264i) q^{35} +(2.00000 - 3.46410i) q^{37} +(1.22474 + 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} +2.44949 q^{41} -7.00000 q^{43} +(-5.00000 - 8.66025i) q^{46} +(3.67423 - 6.36396i) q^{47} +(5.50000 + 4.33013i) q^{49} -1.41421i q^{50} +(-1.22474 + 0.707107i) q^{53} +13.8564i q^{55} +(2.44949 - 7.07107i) q^{56} +(1.00000 - 1.73205i) q^{58} +(7.34847 + 12.7279i) q^{59} +(-4.50000 - 2.59808i) q^{61} -7.34847 q^{62} -8.00000 q^{64} +(7.34847 + 4.24264i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(9.00000 - 1.73205i) q^{70} +2.82843i q^{71} +(10.5000 - 6.06218i) q^{73} +(4.89898 - 2.82843i) q^{74} +(-14.6969 + 2.82843i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.89898 - 8.48528i) q^{80} +(3.00000 + 1.73205i) q^{82} -9.79796 q^{83} +6.00000 q^{85} +(-8.57321 - 4.94975i) q^{86} +(8.00000 + 13.8564i) q^{88} +(-1.22474 + 2.12132i) q^{89} +(-3.00000 + 8.66025i) q^{91} +(9.00000 - 5.19615i) q^{94} +(3.67423 - 2.12132i) q^{95} -8.66025i q^{97} +(3.67423 + 9.19239i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{7}+O(q^{10}) $ 4 * q + 10 * q^7	$ 4 q + 10 q^{7} + 12 q^{10} + 8 q^{16} + 6 q^{19} - 32 q^{22} - 2 q^{25} - 18 q^{31} + 8 q^{37} - 24 q^{40} - 28 q^{43} - 20 q^{46} + 22 q^{49} + 4 q^{58} - 18 q^{61} - 32 q^{64} - 4 q^{67} + 36 q^{70} + 42 q^{73} + 8 q^{79} + 12 q^{82} + 24 q^{85} + 32 q^{88} - 12 q^{91} + 36 q^{94}+O(q^{100}) $ 4 * q + 10 * q^7 + 12 * q^10 + 8 * q^16 + 6 * q^19 - 32 * q^22 - 2 * q^25 - 18 * q^31 + 8 * q^37 - 24 * q^40 - 28 * q^43 - 20 * q^46 + 22 * q^49 + 4 * q^58 - 18 * q^61 - 32 * q^64 - 4 * q^67 + 36 * q^70 + 42 * q^73 + 8 * q^79 + 12 * q^82 + 24 * q^85 + 32 * q^88 - 12 * q^91 + 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.22474	+	0.707107i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	1.22474	+	0.707107i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	−0.450708	−	0.892672i	$-0.648828\pi$
$5$	1.22474	−	2.12132i	0.547723	−	0.948683i	0.998430	−	0.0560116i	$-0.0178384\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	3.00000	−	1.73205i	0.948683	−	0.547723i
$11$	−4.89898	+	2.82843i	−1.47710	+	0.852803i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$	−4.89898	+	2.82843i	−1.47710	+	0.852803i	−0.477432	+	0.878668i	$0.658432\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$	2.44949	+	2.82843i	0.654654	+	0.755929i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.22474	+	2.12132i	0.297044	+	0.514496i	0.975458	−	0.220184i	$-0.0706658\pi$
$17$	1.22474	+	2.12132i	0.297044	+	0.514496i	−0.678414	+	0.734680i	$0.737332\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$		0			0
$22$	−8.00000			−1.70561
$23$	−6.12372	−	3.53553i	−1.27688	−	0.737210i	−0.300610	−	0.953747i	$-0.597190\pi$
$23$	−6.12372	−	3.53553i	−1.27688	−	0.737210i	−0.976274	+	0.216537i	$0.930524\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.44949	+	4.24264i	−0.480384	+	0.832050i
$27$		0			0
$28$		0			0
$29$		−	1.41421i		−	0.262613i	−0.991342	−	0.131306i	$-0.958083\pi$
$29$		−	1.41421i		−	0.262613i	0.991342	−	0.131306i	$-0.0419172\pi$
$30$		0			0
$31$	−4.50000	+	2.59808i	−0.808224	+	0.466628i	−0.846339	−	0.532645i	$-0.821198\pi$
$31$	−4.50000	+	2.59808i	−0.808224	+	0.466628i	0.0381148	+	0.999273i	$0.487865\pi$
$32$		0			0
$33$		0			0
$34$			3.46410i			0.594089i
$35$	4.89898	−	4.24264i	0.828079	−	0.717137i
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	1.22474	+	2.12132i	0.198680	+	0.344124i
$39$		0			0
$40$	−6.00000	−	3.46410i	−0.948683	−	0.547723i
$41$	2.44949			0.382546			0.191273	−	0.981537i	$-0.438738\pi$
$41$	2.44949			0.382546			0.191273	+	0.981537i	$0.438738\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$		0			0
$45$		0			0
$46$	−5.00000	−	8.66025i	−0.737210	−	1.27688i
$47$	3.67423	−	6.36396i	0.535942	−	0.928279i	−0.463175	−	0.886267i	$-0.653290\pi$
$47$	3.67423	−	6.36396i	0.535942	−	0.928279i	0.999117	−	0.0420122i	$-0.0133768\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		−	1.41421i		−	0.200000i
$51$		0			0
$52$		0			0
$53$	−1.22474	+	0.707107i	−0.168232	+	0.0971286i	−0.581752	−	0.813366i	$-0.697632\pi$
$53$	−1.22474	+	0.707107i	−0.168232	+	0.0971286i	0.413520	+	0.910495i	$0.364299\pi$
$54$		0			0
$55$			13.8564i			1.86840i
$56$	2.44949	−	7.07107i	0.327327	−	0.944911i
$57$		0			0
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	7.34847	+	12.7279i	0.956689	+	1.65703i	0.730454	+	0.682962i	$0.239308\pi$
$59$	7.34847	+	12.7279i	0.956689	+	1.65703i	0.226235	+	0.974073i	$0.427358\pi$
$60$		0			0
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	0.183442	−	0.983030i	$-0.441276\pi$
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	−0.759608	+	0.650381i	$0.774609\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	−8.00000			−1.00000
$65$	7.34847	+	4.24264i	0.911465	+	0.526235i
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$		0			0
$69$		0			0
$70$	9.00000	−	1.73205i	1.07571	−	0.207020i
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$		0			0
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.262126	−	0.965034i	$-0.415577\pi$
$73$	10.5000	−	6.06218i	1.22893	−	0.709524i	0.966807	+	0.255510i	$0.0822432\pi$
$74$	4.89898	−	2.82843i	0.569495	−	0.328798i
$75$		0			0
$76$		0			0
$77$	−14.6969	+	2.82843i	−1.67487	+	0.322329i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	−4.89898	−	8.48528i	−0.547723	−	0.948683i
$81$		0			0
$82$	3.00000	+	1.73205i	0.331295	+	0.191273i
$83$	−9.79796			−1.07547			−0.537733	−	0.843115i	$-0.680719\pi$
$83$	−9.79796			−1.07547			−0.537733	+	0.843115i	$0.680719\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$	−8.57321	−	4.94975i	−0.924473	−	0.533745i
$87$		0			0
$88$	8.00000	+	13.8564i	0.852803	+	1.47710i
$89$	−1.22474	+	2.12132i	−0.129823	+	0.224860i	−0.923608	−	0.383339i	$-0.874774\pi$
$89$	−1.22474	+	2.12132i	−0.129823	+	0.224860i	0.793785	+	0.608198i	$0.208107\pi$
$90$		0			0
$91$	−3.00000	+	8.66025i	−0.314485	+	0.907841i
$92$		0			0
$93$		0			0
$94$	9.00000	−	5.19615i	0.928279	−	0.535942i
$95$	3.67423	−	2.12132i	0.376969	−	0.217643i
$96$		0			0
$97$		−	8.66025i		−	0.879316i	−0.898165	−	0.439658i	$-0.855100\pi$
$97$		−	8.66025i		−	0.879316i	0.898165	−	0.439658i	$-0.144900\pi$
$98$	3.67423	+	9.19239i	0.371154	+	0.928571i
$99$		0			0
$100$		0			0
$101$	−4.89898	−	8.48528i	−0.487467	−	0.844317i	0.512429	−	0.858729i	$-0.328746\pi$
$101$	−4.89898	−	8.48528i	−0.487467	−	0.844317i	−0.999896	+	0.0144123i	$0.995412\pi$
$102$		0			0
$103$	12.0000	+	6.92820i	1.18240	+	0.682656i	0.956567	−	0.291511i	$-0.0941580\pi$
$103$	12.0000	+	6.92820i	1.18240	+	0.682656i	0.225828	+	0.974167i	$0.427491\pi$
$104$	9.79796			0.960769
$105$		0			0
$106$	−2.00000			−0.194257
$107$	12.2474	+	7.07107i	1.18401	+	0.683586i	0.956938	−	0.290293i	$-0.0937528\pi$
$107$	12.2474	+	7.07107i	1.18401	+	0.683586i	0.227068	+	0.973879i	$0.427086\pi$
$108$		0			0
$109$	−8.50000	−	14.7224i	−0.814152	−	1.41015i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−8.50000	−	14.7224i	−0.814152	−	1.41015i	0.0957826	−	0.995402i	$-0.469465\pi$
$110$	−9.79796	+	16.9706i	−0.934199	+	1.61808i
$111$		0			0
$112$	8.00000	−	6.92820i	0.755929	−	0.654654i
$113$			2.82843i			0.266076i	0.991111	+	0.133038i	$0.0424732\pi$
$113$			2.82843i			0.266076i	−0.991111	+	0.133038i	$0.957527\pi$
$114$		0			0
$115$	−15.0000	+	8.66025i	−1.39876	+	0.807573i
$116$		0			0
$117$		0			0
$118$			20.7846i			1.91338i
$119$	1.22474	+	6.36396i	0.112272	+	0.583383i
$120$		0			0
$121$	10.5000	−	18.1865i	0.954545	−	1.65332i
$122$	−3.67423	−	6.36396i	−0.332650	−	0.576166i
$123$		0			0
$124$		0			0
$125$	9.79796			0.876356
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−9.79796	−	5.65685i	−0.866025	−	0.500000i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	8.57321	−	14.8492i	0.749045	−	1.29738i	−0.199236	−	0.979952i	$-0.563846\pi$
$131$	8.57321	−	14.8492i	0.749045	−	1.29738i	0.948281	−	0.317433i	$-0.102821\pi$
$132$		0			0
$133$	3.00000	+	3.46410i	0.260133	+	0.300376i
$134$		−	2.82843i		−	0.244339i
$135$		0			0
$136$	6.00000	−	3.46410i	0.514496	−	0.297044i
$137$	6.12372	−	3.53553i	0.523185	−	0.302061i	−0.215052	−	0.976603i	$-0.568992\pi$
$137$	6.12372	−	3.53553i	0.523185	−	0.302061i	0.738237	+	0.674542i	$0.235659\pi$
$138$		0			0
$139$		−	6.92820i		−	0.587643i	−0.955860	−	0.293821i	$-0.905073\pi$
$139$		−	6.92820i		−	0.587643i	0.955860	−	0.293821i	$-0.0949270\pi$
$140$		0			0
$141$		0			0
$142$	−2.00000	+	3.46410i	−0.167836	+	0.290701i
$143$	−9.79796	−	16.9706i	−0.819346	−	1.41915i
$144$		0			0
$145$	−3.00000	−	1.73205i	−0.249136	−	0.143839i
$146$	17.1464			1.41905
$147$		0			0
$148$		0			0
$149$	8.57321	+	4.94975i	0.702345	+	0.405499i	0.808220	−	0.588880i	$-0.200431\pi$
$149$	8.57321	+	4.94975i	0.702345	+	0.405499i	−0.105875	+	0.994379i	$0.533764\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	2.44949	−	4.24264i	0.198680	−	0.344124i
$153$		0			0
$154$	−20.0000	−	6.92820i	−1.61165	−	0.558291i
$155$			12.7279i			1.02233i
$156$		0			0
$157$	−9.00000	+	5.19615i	−0.718278	+	0.414698i	−0.814119	−	0.580699i	$-0.802779\pi$
$157$	−9.00000	+	5.19615i	−0.718278	+	0.414698i	0.0958404	+	0.995397i	$0.469446\pi$
$158$	4.89898	−	2.82843i	0.389742	−	0.225018i
$159$		0			0
$160$		0			0
$161$	−12.2474	−	14.1421i	−0.965234	−	1.11456i
$162$		0			0
$163$	−11.5000	+	19.9186i	−0.900750	+	1.56014i	−0.0742262	+	0.997241i	$0.523649\pi$
$163$	−11.5000	+	19.9186i	−0.900750	+	1.56014i	−0.826523	+	0.562902i	$0.809685\pi$
$164$		0			0
$165$		0			0
$166$	−12.0000	−	6.92820i	−0.931381	−	0.537733i
$167$	−4.89898			−0.379094			−0.189547	−	0.981872i	$-0.560702\pi$
$167$	−4.89898			−0.379094			−0.189547	+	0.981872i	$0.560702\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	7.34847	+	4.24264i	0.563602	+	0.325396i
$171$		0			0
$172$		0			0
$173$	−3.67423	+	6.36396i	−0.279347	+	0.483843i	−0.971223	−	0.238174i	$-0.923451\pi$
$173$	−3.67423	+	6.36396i	−0.279347	+	0.483843i	0.691876	+	0.722017i	$0.256785\pi$
$174$		0			0
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$			22.6274i			1.70561i
$177$		0			0
$178$	−3.00000	+	1.73205i	−0.224860	+	0.129823i
$179$	−8.57321	+	4.94975i	−0.640792	+	0.369961i	−0.784920	−	0.619598i	$-0.787296\pi$
$179$	−8.57321	+	4.94975i	−0.640792	+	0.369961i	0.144127	+	0.989559i	$0.453962\pi$
$180$		0			0
$181$		−	15.5885i		−	1.15868i	−0.815086	−	0.579340i	$-0.803310\pi$
$181$		−	15.5885i		−	1.15868i	0.815086	−	0.579340i	$-0.196690\pi$
$182$	−9.79796	+	8.48528i	−0.726273	+	0.628971i
$183$		0			0
$184$	−10.0000	+	17.3205i	−0.737210	+	1.27688i
$185$	−4.89898	−	8.48528i	−0.360180	−	0.623850i
$186$		0			0
$187$	−12.0000	−	6.92820i	−0.877527	−	0.506640i
$188$		0			0
$189$		0			0
$190$	6.00000			0.435286
$191$	1.22474	+	0.707107i	0.0886194	+	0.0511645i	0.543655	−	0.839309i	$-0.317040\pi$
$191$	1.22474	+	0.707107i	0.0886194	+	0.0511645i	−0.455035	+	0.890473i	$0.650373\pi$
$192$		0			0
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	6.12372	−	10.6066i	0.439658	−	0.761510i
$195$		0			0
$196$		0			0
$197$			2.82843i			0.201517i	0.994911	+	0.100759i	$0.0321270\pi$
$197$			2.82843i			0.201517i	−0.994911	+	0.100759i	$0.967873\pi$
$198$		0			0
$199$	1.50000	−	0.866025i	0.106332	−	0.0613909i	−0.445891	−	0.895087i	$-0.647113\pi$
$199$	1.50000	−	0.866025i	0.106332	−	0.0613909i	0.552223	+	0.833696i	$0.313780\pi$
$200$	−2.44949	+	1.41421i	−0.173205	+	0.100000i
$201$		0			0
$202$		−	13.8564i		−	0.974933i
$203$	1.22474	−	3.53553i	0.0859602	−	0.248146i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	9.79796	+	16.9706i	0.682656	+	1.18240i
$207$		0			0
$208$	12.0000	+	6.92820i	0.832050	+	0.480384i
$209$	−9.79796			−0.677739
$210$		0			0
$211$	−1.00000			−0.0688428			−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000			−0.0688428			−0.0344214	+	0.999407i	$0.510959\pi$
$212$		0			0
$213$		0			0
$214$	10.0000	+	17.3205i	0.683586	+	1.18401i
$215$	−8.57321	+	14.8492i	−0.584688	+	1.01271i
$216$		0			0
$217$	−13.5000	+	2.59808i	−0.916440	+	0.176369i
$218$		−	24.0416i		−	1.62830i
$219$		0			0
$220$		0			0
$221$	−7.34847	+	4.24264i	−0.494312	+	0.285391i
$222$		0			0
$223$		−	13.8564i		−	0.927894i	−0.885863	−	0.463947i	$-0.846433\pi$
$223$		−	13.8564i		−	0.927894i	0.885863	−	0.463947i	$-0.153567\pi$
$224$		0			0
$225$		0			0
$226$	−2.00000	+	3.46410i	−0.133038	+	0.230429i
$227$	−1.22474	−	2.12132i	−0.0812892	−	0.140797i	0.822515	−	0.568744i	$-0.192570\pi$
$227$	−1.22474	−	2.12132i	−0.0812892	−	0.140797i	−0.903804	+	0.427947i	$0.859237\pi$
$228$		0			0
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	0.449619	−	0.893220i	$-0.351560\pi$
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	−0.548742	+	0.835992i	$0.684893\pi$
$230$	−24.4949			−1.61515
$231$		0			0
$232$	−4.00000			−0.262613
$233$	−13.4722	−	7.77817i	−0.882593	−	0.509565i	−0.0110803	−	0.999939i	$-0.503527\pi$
$233$	−13.4722	−	7.77817i	−0.882593	−	0.509565i	−0.871512	+	0.490373i	$0.836860\pi$
$234$		0			0
$235$	−9.00000	−	15.5885i	−0.587095	−	1.01688i
$236$		0			0
$237$		0			0
$238$	−3.00000	+	8.66025i	−0.194461	+	0.561361i
$239$		−	9.89949i		−	0.640345i	−0.947359	−	0.320173i	$-0.896259\pi$
$239$		−	9.89949i		−	0.640345i	0.947359	−	0.320173i	$-0.103741\pi$
$240$		0			0
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	−0.798484	−	0.602016i	$-0.794364\pi$
$241$	−10.5000	+	6.06218i	−0.676364	+	0.390499i	0.122119	+	0.992515i	$0.461031\pi$
$242$	25.7196	−	14.8492i	1.65332	−	0.954545i
$243$		0			0
$244$		0			0
$245$	15.9217	−	6.36396i	1.01720	−	0.406579i
$246$		0			0
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	7.34847	+	12.7279i	0.466628	+	0.808224i
$249$		0			0
$250$	12.0000	+	6.92820i	0.758947	+	0.438178i
$251$	−7.34847			−0.463831			−0.231916	−	0.972736i	$-0.574499\pi$
$251$	−7.34847			−0.463831			−0.231916	+	0.972736i	$0.574499\pi$
$252$		0			0
$253$	40.0000			2.51478
$254$	−1.22474	−	0.707107i	−0.0768473	−	0.0443678i
$255$		0			0
$256$		0			0
$257$	−9.79796	+	16.9706i	−0.611180	+	1.05859i	0.379862	+	0.925043i	$0.375971\pi$
$257$	−9.79796	+	16.9706i	−0.611180	+	1.05859i	−0.991042	+	0.133551i	$0.957362\pi$
$258$		0			0
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$		0			0
$262$	21.0000	−	12.1244i	1.29738	−	0.749045i
$263$	17.1464	−	9.89949i	1.05729	−	0.610429i	0.132612	−	0.991168i	$-0.457664\pi$
$263$	17.1464	−	9.89949i	1.05729	−	0.610429i	0.924683	+	0.380739i	$0.124330\pi$
$264$		0			0
$265$			3.46410i			0.212798i
$266$	1.22474	+	6.36396i	0.0750939	+	0.390199i
$267$		0			0
$268$		0			0
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	0.949377	+	0.314138i	$0.101715\pi$
$269$	12.2474	+	21.2132i	0.746740	+	1.29339i	−0.202637	+	0.979254i	$0.564951\pi$
$270$		0			0
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.957061	−	0.289888i	$-0.0936180\pi$
$271$	19.5000	+	11.2583i	1.18454	+	0.683895i	0.227480	+	0.973783i	$0.426951\pi$
$272$	9.79796			0.594089
$273$		0			0
$274$	10.0000			0.604122
$275$	4.89898	+	2.82843i	0.295420	+	0.170561i
$276$		0			0
$277$	12.5000	+	21.6506i	0.751052	+	1.30086i	0.947313	+	0.320309i	$0.103787\pi$
$277$	12.5000	+	21.6506i	0.751052	+	1.30086i	−0.196261	+	0.980552i	$0.562880\pi$
$278$	4.89898	−	8.48528i	0.293821	−	0.508913i
$279$		0			0
$280$	−12.0000	−	13.8564i	−0.717137	−	0.828079i
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$		0			0
$283$	−22.5000	+	12.9904i	−1.33749	+	0.772198i	−0.986434	−	0.164158i	$-0.947509\pi$
$283$	−22.5000	+	12.9904i	−1.33749	+	0.772198i	−0.351052	+	0.936356i	$0.614176\pi$
$284$		0			0
$285$		0			0
$286$		−	27.7128i		−	1.63869i
$287$	6.12372	+	2.12132i	0.361472	+	0.125218i
$288$		0			0
$289$	5.50000	−	9.52628i	0.323529	−	0.560369i
$290$	−2.44949	−	4.24264i	−0.143839	−	0.249136i
$291$		0			0
$292$		0			0
$293$	24.4949			1.43101			0.715504	−	0.698609i	$-0.246197\pi$
$293$	24.4949			1.43101			0.715504	+	0.698609i	$0.246197\pi$
$294$		0			0
$295$	36.0000			2.09600
$296$	−9.79796	−	5.65685i	−0.569495	−	0.328798i
$297$		0			0
$298$	7.00000	+	12.1244i	0.405499	+	0.702345i
$299$	12.2474	−	21.2132i	0.708288	−	1.22679i
$300$		0			0
$301$	−17.5000	−	6.06218i	−1.00868	−	0.349418i
$302$		−	15.5563i		−	0.895167i
$303$		0			0
$304$	6.00000	−	3.46410i	0.344124	−	0.198680i
$305$	−11.0227	+	6.36396i	−0.631158	+	0.364399i
$306$		0			0
$307$			5.19615i			0.296560i	0.988945	+	0.148280i	$0.0473737\pi$
$307$			5.19615i			0.296560i	−0.988945	+	0.148280i	$0.952626\pi$
$308$		0			0
$309$		0			0
$310$	−9.00000	+	15.5885i	−0.511166	+	0.885365i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	4.50000	+	2.59808i	0.254355	+	0.146852i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	4.50000	+	2.59808i	0.254355	+	0.146852i	−0.367402	+	0.930062i	$0.619753\pi$
$314$	−14.6969			−0.829396
$315$		0			0
$316$		0			0
$317$	−2.44949	−	1.41421i	−0.137577	−	0.0794301i	0.429632	−	0.903004i	$-0.358643\pi$
$317$	−2.44949	−	1.41421i	−0.137577	−	0.0794301i	−0.567209	+	0.823574i	$0.691977\pi$
$318$		0			0
$319$	4.00000	+	6.92820i	0.223957	+	0.387905i
$320$	−9.79796	+	16.9706i	−0.547723	+	0.948683i
$321$		0			0
$322$	−5.00000	−	25.9808i	−0.278639	−	1.44785i
$323$			4.24264i			0.236067i
$324$		0			0
$325$	3.00000	−	1.73205i	0.166410	−	0.0960769i
$326$	−28.1691	+	16.2635i	−1.56014	+	0.900750i
$327$		0			0
$328$		−	6.92820i		−	0.382546i
$329$	14.6969	−	12.7279i	0.810268	−	0.701713i
$330$		0			0
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$		0			0
$333$		0			0
$334$	−6.00000	−	3.46410i	−0.328305	−	0.189547i
$335$	−4.89898			−0.267660
$336$		0			0
$337$	−1.00000			−0.0544735			−0.0272367	−	0.999629i	$-0.508671\pi$
$337$	−1.00000			−0.0544735			−0.0272367	+	0.999629i	$0.508671\pi$
$338$	1.22474	+	0.707107i	0.0666173	+	0.0384615i
$339$		0			0
$340$		0			0
$341$	14.6969	−	25.4558i	0.795884	−	1.37851i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$			19.7990i			1.06749i
$345$		0			0
$346$	−9.00000	+	5.19615i	−0.483843	+	0.279347i
$347$	−26.9444	+	15.5563i	−1.44645	+	0.835109i	−0.998268	−	0.0588334i	$-0.981262\pi$
$347$	−26.9444	+	15.5563i	−1.44645	+	0.835109i	−0.448183	+	0.893942i	$0.647929\pi$
$348$		0			0
$349$			1.73205i			0.0927146i	0.998925	+	0.0463573i	$0.0147613\pi$
$349$			1.73205i			0.0927146i	−0.998925	+	0.0463573i	$0.985239\pi$
$350$	1.22474	−	3.53553i	0.0654654	−	0.188982i
$351$		0			0
$352$		0			0
$353$	17.1464	+	29.6985i	0.912612	+	1.58069i	0.810360	+	0.585932i	$0.199272\pi$
$353$	17.1464	+	29.6985i	0.912612	+	1.58069i	0.102252	+	0.994758i	$0.467395\pi$
$354$		0			0
$355$	6.00000	+	3.46410i	0.318447	+	0.183855i
$356$		0			0
$357$		0			0
$358$	−14.0000			−0.739923
$359$	−9.79796	−	5.65685i	−0.517116	−	0.298557i	0.218638	−	0.975806i	$-0.429839\pi$
$359$	−9.79796	−	5.65685i	−0.517116	−	0.298557i	−0.735754	+	0.677249i	$0.763172\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$	11.0227	−	19.0919i	0.579340	−	1.00345i
$363$		0			0
$364$		0			0
$365$		−	29.6985i		−	1.55449i
$366$		0			0
$367$	7.50000	−	4.33013i	0.391497	−	0.226031i	−0.291312	−	0.956628i	$-0.594092\pi$
$367$	7.50000	−	4.33013i	0.391497	−	0.226031i	0.682808	+	0.730597i	$0.260758\pi$
$368$	−24.4949	+	14.1421i	−1.27688	+	0.737210i
$369$		0			0
$370$		−	13.8564i		−	0.720360i
$371$	−3.67423	+	0.707107i	−0.190757	+	0.0367112i
$372$		0			0
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$	−9.79796	−	16.9706i	−0.506640	−	0.877527i
$375$		0			0
$376$	−18.0000	−	10.3923i	−0.928279	−	0.535942i
$377$	4.89898			0.252310
$378$		0			0
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$		0			0
$381$		0			0
$382$	1.00000	+	1.73205i	0.0511645	+	0.0886194i
$383$	−17.1464	+	29.6985i	−0.876142	+	1.51752i	−0.0205998	+	0.999788i	$0.506558\pi$
$383$	−17.1464	+	29.6985i	−0.876142	+	1.51752i	−0.855542	+	0.517734i	$0.826776\pi$
$384$		0			0
$385$	−12.0000	+	34.6410i	−0.611577	+	1.76547i
$386$			5.65685i			0.287926i
$387$		0			0
$388$		0			0
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.955978	−	0.293437i	$-0.905201\pi$
$389$	−23.2702	+	13.4350i	−1.17984	+	0.681183i	−0.223865	+	0.974620i	$0.571868\pi$
$390$		0			0
$391$		−	17.3205i		−	0.875936i
$392$	12.2474	−	15.5563i	0.618590	−	0.785714i
$393$		0			0
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$	−4.89898	−	8.48528i	−0.246494	−	0.426941i
$396$		0			0
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	0.0250943	−	0.999685i	$-0.492011\pi$
$397$	−16.5000	−	9.52628i	−0.828111	−	0.478110i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	2.44949			0.122782
$399$		0			0
$400$	−4.00000			−0.200000
$401$	19.5959	+	11.3137i	0.978573	+	0.564980i	0.901839	−	0.432072i	$-0.142217\pi$
$401$	19.5959	+	11.3137i	0.978573	+	0.564980i	0.0767343	+	0.997052i	$0.475551\pi$
$402$		0			0
$403$	−9.00000	−	15.5885i	−0.448322	−	0.776516i
$404$		0			0
$405$		0			0
$406$	4.00000	−	3.46410i	0.198517	−	0.171920i
$407$			22.6274i			1.12160i
$408$		0			0
$409$	−9.00000	+	5.19615i	−0.445021	+	0.256933i	−0.705725	−	0.708486i	$-0.749379\pi$
$409$	−9.00000	+	5.19615i	−0.445021	+	0.256933i	0.260704	+	0.965419i	$0.416045\pi$
$410$	7.34847	−	4.24264i	0.362915	−	0.209529i
$411$		0			0
$412$		0			0
$413$	7.34847	+	38.1838i	0.361595	+	1.87890i
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$		0			0
$417$		0			0
$418$	−12.0000	−	6.92820i	−0.586939	−	0.338869i
$419$	2.44949			0.119665			0.0598327	−	0.998208i	$-0.480943\pi$
$419$	2.44949			0.119665			0.0598327	+	0.998208i	$0.480943\pi$
$420$		0			0
$421$	11.0000			0.536107			0.268054	−	0.963404i	$-0.413620\pi$
$421$	11.0000			0.536107			0.268054	+	0.963404i	$0.413620\pi$
$422$	−1.22474	−	0.707107i	−0.0596196	−	0.0344214i
$423$		0			0
$424$	2.00000	+	3.46410i	0.0971286	+	0.168232i
$425$	1.22474	−	2.12132i	0.0594089	−	0.102899i
$426$		0			0
$427$	−9.00000	−	10.3923i	−0.435541	−	0.502919i
$428$		0			0
$429$		0			0
$430$	−21.0000	+	12.1244i	−1.01271	+	0.584688i
$431$	24.4949	−	14.1421i	1.17988	−	0.681203i	0.223891	−	0.974614i	$-0.428124\pi$
$431$	24.4949	−	14.1421i	1.17988	−	0.681203i	0.955986	+	0.293411i	$0.0947906\pi$
$432$		0			0
$433$			5.19615i			0.249711i	0.992175	+	0.124856i	$0.0398468\pi$
$433$			5.19615i			0.249711i	−0.992175	+	0.124856i	$0.960153\pi$
$434$	−18.3712	−	6.36396i	−0.881845	−	0.305480i
$435$		0			0
$436$		0			0
$437$	−6.12372	−	10.6066i	−0.292937	−	0.507383i
$438$		0			0
$439$	18.0000	+	10.3923i	0.859093	+	0.495998i	0.863708	−	0.503992i	$-0.168136\pi$
$439$	18.0000	+	10.3923i	0.859093	+	0.495998i	−0.00461537	+	0.999989i	$0.501469\pi$
$440$	39.1918			1.86840
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−13.4722	−	7.77817i	−0.640083	−	0.369552i	0.144563	−	0.989496i	$-0.453822\pi$
$443$	−13.4722	−	7.77817i	−0.640083	−	0.369552i	−0.784647	+	0.619943i	$0.787156\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	9.79796	−	16.9706i	0.463947	−	0.803579i
$447$		0			0
$448$	−20.0000	−	6.92820i	−0.944911	−	0.327327i
$449$		−	35.3553i		−	1.66852i	−0.551370	−	0.834261i	$-0.685895\pi$
$449$		−	35.3553i		−	1.66852i	0.551370	−	0.834261i	$-0.314105\pi$
$450$		0			0
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$		0			0
$453$		0			0
$454$		−	3.46410i		−	0.162578i
$455$	14.6969	+	16.9706i	0.689003	+	0.795592i
$456$		0			0
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	−0.918556	−	0.395292i	$-0.870643\pi$
$457$	−2.50000	+	4.33013i	−0.116945	+	0.202555i	0.801611	+	0.597847i	$0.203977\pi$
$458$	−1.22474	−	2.12132i	−0.0572286	−	0.0991228i
$459$		0			0
$460$		0			0
$461$	−24.4949			−1.14084			−0.570421	−	0.821353i	$-0.693220\pi$
$461$	−24.4949			−1.14084			−0.570421	+	0.821353i	$0.693220\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$	−4.89898	−	2.82843i	−0.227429	−	0.131306i
$465$		0			0
$466$	−11.0000	−	19.0526i	−0.509565	−	0.882593i
$467$	2.44949	−	4.24264i	0.113349	−	0.196326i	−0.803770	−	0.594941i	$-0.797176\pi$
$467$	2.44949	−	4.24264i	0.113349	−	0.196326i	0.917119	+	0.398615i	$0.130509\pi$
$468$		0			0
$469$	−1.00000	−	5.19615i	−0.0461757	−	0.239936i
$470$		−	25.4558i		−	1.17419i
$471$		0			0
$472$	36.0000	−	20.7846i	1.65703	−	0.956689i
$473$	34.2929	−	19.7990i	1.57679	−	0.910359i
$474$		0			0
$475$		−	1.73205i		−	0.0794719i
$476$		0			0
$477$		0			0
$478$	7.00000	−	12.1244i	0.320173	−	0.554555i
$479$	−1.22474	−	2.12132i	−0.0559600	−	0.0969256i	0.836688	−	0.547679i	$-0.184489\pi$
$479$	−1.22474	−	2.12132i	−0.0559600	−	0.0969256i	−0.892648	+	0.450754i	$0.851155\pi$
$480$		0			0
$481$	12.0000	+	6.92820i	0.547153	+	0.315899i
$482$	−17.1464			−0.780998
$483$		0			0
$484$		0			0
$485$	−18.3712	−	10.6066i	−0.834192	−	0.481621i
$486$		0			0
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	0.974879	−	0.222737i	$-0.0714992\pi$
$487$	6.50000	+	11.2583i	0.294543	+	0.510164i	−0.680335	+	0.732901i	$0.738166\pi$
$488$	−7.34847	+	12.7279i	−0.332650	+	0.576166i
$489$		0			0
$490$	24.0000	+	3.46410i	1.08421	+	0.156492i
$491$		−	5.65685i		−	0.255290i	−0.991820	−	0.127645i	$-0.959258\pi$
$491$		−	5.65685i		−	0.255290i	0.991820	−	0.127645i	$-0.0407419\pi$
$492$		0			0
$493$	3.00000	−	1.73205i	0.135113	−	0.0780076i
$494$	−7.34847	+	4.24264i	−0.330623	+	0.190885i
$495$		0			0
$496$			20.7846i			0.933257i
$497$	−2.44949	+	7.07107i	−0.109875	+	0.317181i
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$		0			0
$501$		0			0
$502$	−9.00000	−	5.19615i	−0.401690	−	0.231916i
$503$	22.0454			0.982956			0.491478	−	0.870890i	$-0.336457\pi$
$503$	22.0454			0.982956			0.491478	+	0.870890i	$0.336457\pi$
$504$		0			0
$505$	−24.0000			−1.06799
$506$	48.9898	+	28.2843i	2.17786	+	1.25739i
$507$		0			0
$508$		0			0
$509$	−9.79796	+	16.9706i	−0.434287	+	0.752207i	−0.997237	−	0.0742838i	$-0.976333\pi$
$509$	−9.79796	+	16.9706i	−0.434287	+	0.752207i	0.562950	+	0.826491i	$0.309666\pi$
$510$		0			0
$511$	31.5000	−	6.06218i	1.39348	−	0.268175i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−24.0000	+	13.8564i	−1.05859	+	0.611180i
$515$	29.3939	−	16.9706i	1.29525	−	0.747812i
$516$		0			0
$517$			41.5692i			1.82821i
$518$	14.6969	−	2.82843i	0.645746	−	0.124274i
$519$		0			0
$520$	12.0000	−	20.7846i	0.526235	−	0.911465i
$521$	12.2474	+	21.2132i	0.536570	+	0.929367i	0.999086	+	0.0427559i	$0.0136138\pi$
$521$	12.2474	+	21.2132i	0.536570	+	0.929367i	−0.462515	+	0.886611i	$0.653053\pi$
$522$		0			0
$523$	−3.00000	−	1.73205i	−0.131181	−	0.0757373i	0.432973	−	0.901407i	$-0.357464\pi$
$523$	−3.00000	−	1.73205i	−0.131181	−	0.0757373i	−0.564154	+	0.825669i	$0.690798\pi$
$524$		0			0
$525$		0			0
$526$	28.0000			1.22086
$527$	−11.0227	−	6.36396i	−0.480157	−	0.277218i
$528$		0			0
$529$	13.5000	+	23.3827i	0.586957	+	1.01664i
$530$	−2.44949	+	4.24264i	−0.106399	+	0.184289i
$531$		0			0
$532$		0			0
$533$			8.48528i			0.367538i
$534$		0			0
$535$	30.0000	−	17.3205i	1.29701	−	0.748831i
$536$	−4.89898	+	2.82843i	−0.211604	+	0.122169i
$537$		0			0
$538$			34.6410i			1.49348i
$539$	−39.1918	−	5.65685i	−1.68811	−	0.243658i
$540$		0			0
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	−0.691793	−	0.722096i	$-0.743179\pi$
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	0.971250	+	0.238062i	$0.0765123\pi$
$542$	15.9217	+	27.5772i	0.683895	+	1.18454i
$543$		0			0
$544$		0			0
$545$	−41.6413			−1.78372
$546$		0			0
$547$	−25.0000			−1.06892			−0.534461	−	0.845193i	$-0.679486\pi$
$547$	−25.0000			−1.06892			−0.534461	+	0.845193i	$0.679486\pi$
$548$		0			0
$549$		0			0
$550$	4.00000	+	6.92820i	0.170561	+	0.295420i
$551$	1.22474	−	2.12132i	0.0521759	−	0.0903713i
$552$		0			0
$553$	8.00000	−	6.92820i	0.340195	−	0.294617i
$554$			35.3553i			1.50210i
$555$		0			0
$556$		0			0
$557$	−1.22474	+	0.707107i	−0.0518941	+	0.0299611i	−0.525723	−	0.850656i	$-0.676205\pi$
$557$	−1.22474	+	0.707107i	−0.0518941	+	0.0299611i	0.473828	+	0.880617i	$0.342872\pi$
$558$		0			0
$559$		−	24.2487i		−	1.02561i
$560$	−4.89898	−	25.4558i	−0.207020	−	1.07571i
$561$		0			0
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	−11.0227	−	19.0919i	−0.464552	−	0.804627i	0.534630	−	0.845087i	$-0.320451\pi$
$563$	−11.0227	−	19.0919i	−0.464552	−	0.804627i	−0.999181	+	0.0404596i	$0.987118\pi$
$564$		0			0
$565$	6.00000	+	3.46410i	0.252422	+	0.145736i
$566$	−36.7423			−1.54440
$567$		0			0
$568$	8.00000			0.335673
$569$	−31.8434	−	18.3848i	−1.33494	−	0.770730i	−0.348891	−	0.937163i	$-0.613442\pi$
$569$	−31.8434	−	18.3848i	−1.33494	−	0.770730i	−0.986053	+	0.166434i	$0.946775\pi$
$570$		0			0
$571$	−20.5000	−	35.5070i	−0.857898	−	1.48592i	−0.873930	−	0.486052i	$-0.838437\pi$
$571$	−20.5000	−	35.5070i	−0.857898	−	1.48592i	0.0160316	−	0.999871i	$-0.494897\pi$
$572$		0			0
$573$		0			0
$574$	6.00000	+	6.92820i	0.250435	+	0.289178i
$575$			7.07107i			0.294884i
$576$		0			0
$577$	−3.00000	+	1.73205i	−0.124892	+	0.0721062i	−0.561144	−	0.827718i	$-0.689639\pi$
$577$	−3.00000	+	1.73205i	−0.124892	+	0.0721062i	0.436253	+	0.899824i	$0.356305\pi$
$578$	13.4722	−	7.77817i	0.560369	−	0.323529i
$579$		0			0
$580$		0			0
$581$	−24.4949	−	8.48528i	−1.01622	−	0.352029i
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−17.1464	−	29.6985i	−0.709524	−	1.22893i
$585$		0			0
$586$	30.0000	+	17.3205i	1.23929	+	0.715504i
$587$	26.9444			1.11211			0.556057	−	0.831144i	$-0.312314\pi$
$587$	26.9444			1.11211			0.556057	+	0.831144i	$0.312314\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$	44.0908	+	25.4558i	1.81519	+	1.04800i
$591$		0			0
$592$	−8.00000	−	13.8564i	−0.328798	−	0.569495i
$593$	−4.89898	+	8.48528i	−0.201177	+	0.348449i	−0.948908	−	0.315553i	$-0.897810\pi$
$593$	−4.89898	+	8.48528i	−0.201177	+	0.348449i	0.747731	+	0.664002i	$0.231143\pi$
$594$		0			0
$595$	15.0000	+	5.19615i	0.614940	+	0.213021i
$596$		0			0
$597$		0			0
$598$	30.0000	−	17.3205i	1.22679	−	0.708288i
$599$	6.12372	−	3.53553i	0.250209	−	0.144458i	−0.369651	−	0.929171i	$-0.620523\pi$
$599$	6.12372	−	3.53553i	0.250209	−	0.144458i	0.619860	+	0.784713i	$0.287189\pi$
$600$		0			0
$601$			22.5167i			0.918474i	0.888314	+	0.459237i	$0.151877\pi$
$601$			22.5167i			0.918474i	−0.888314	+	0.459237i	$0.848123\pi$
$602$	−17.1464	−	19.7990i	−0.698836	−	0.806947i
$603$		0			0
$604$		0			0
$605$	−25.7196	−	44.5477i	−1.04565	−	1.81112i
$606$		0			0
$607$	25.5000	+	14.7224i	1.03501	+	0.597565i	0.918417	−	0.395614i	$-0.129468\pi$
$607$	25.5000	+	14.7224i	1.03501	+	0.597565i	0.116596	+	0.993179i	$0.462802\pi$
$608$		0			0
$609$		0			0
$610$	−18.0000			−0.728799
$611$	22.0454	+	12.7279i	0.891862	+	0.514917i
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	−3.67423	+	6.36396i	−0.148280	+	0.256829i
$615$		0			0
$616$	8.00000	+	41.5692i	0.322329	+	1.67487i
$617$			45.2548i			1.82189i	0.412527	+	0.910946i	$0.364646\pi$
$617$			45.2548i			1.82189i	−0.412527	+	0.910946i	$0.635354\pi$
$618$		0			0
$619$	30.0000	−	17.3205i	1.20580	−	0.696170i	0.243962	−	0.969785i	$-0.421553\pi$
$619$	30.0000	−	17.3205i	1.20580	−	0.696170i	0.961839	+	0.273615i	$0.0882193\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.89898	+	4.24264i	−0.196273	+	0.169978i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	3.67423	+	6.36396i	0.146852	+	0.254355i
$627$		0			0
$628$		0			0
$629$	9.79796			0.390670
$630$		0			0
$631$	11.0000			0.437903			0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000			0.437903			0.218952	+	0.975736i	$0.429736\pi$
$632$	−9.79796	−	5.65685i	−0.389742	−	0.225018i
$633$		0			0
$634$	−2.00000	−	3.46410i	−0.0794301	−	0.137577i
$635$	−1.22474	+	2.12132i	−0.0486025	+	0.0841820i
$636$		0			0
$637$	−15.0000	+	19.0526i	−0.594322	+	0.754890i
$638$			11.3137i			0.447914i
$639$		0			0
$640$	−24.0000	+	13.8564i	−0.948683	+	0.547723i
$641$	6.12372	−	3.53553i	0.241873	−	0.139645i	−0.374165	−	0.927362i	$-0.622070\pi$
$641$	6.12372	−	3.53553i	0.241873	−	0.139645i	0.616037	+	0.787717i	$0.288737\pi$
$642$		0			0
$643$		−	22.5167i		−	0.887970i	−0.896034	−	0.443985i	$-0.853564\pi$
$643$		−	22.5167i		−	0.887970i	0.896034	−	0.443985i	$-0.146436\pi$
$644$		0			0
$645$		0			0
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	12.2474	+	21.2132i	0.481497	+	0.833977i	0.999775	−	0.0212354i	$-0.00675993\pi$
$647$	12.2474	+	21.2132i	0.481497	+	0.833977i	−0.518278	+	0.855212i	$0.673427\pi$
$648$		0			0
$649$	−72.0000	−	41.5692i	−2.82625	−	1.63173i
$650$	4.89898			0.192154
$651$		0			0
$652$		0			0
$653$	−13.4722	−	7.77817i	−0.527208	−	0.304383i	0.212671	−	0.977124i	$-0.431784\pi$
$653$	−13.4722	−	7.77817i	−0.527208	−	0.304383i	−0.739879	+	0.672740i	$0.765117\pi$
$654$		0			0
$655$	−21.0000	−	36.3731i	−0.820538	−	1.42121i
$656$	4.89898	−	8.48528i	0.191273	−	0.331295i
$657$		0			0
$658$	27.0000	−	5.19615i	1.05257	−	0.202567i
$659$			7.07107i			0.275450i	0.990471	+	0.137725i	$0.0439790\pi$
$659$			7.07107i			0.275450i	−0.990471	+	0.137725i	$0.956021\pi$
$660$		0			0
$661$	−40.5000	+	23.3827i	−1.57527	+	0.909481i	−0.579761	+	0.814787i	$0.696854\pi$
$661$	−40.5000	+	23.3827i	−1.57527	+	0.909481i	−0.995506	+	0.0946945i	$0.969813\pi$
$662$	−20.8207	+	12.0208i	−0.809218	+	0.467202i
$663$		0			0
$664$			27.7128i			1.07547i
$665$	11.0227	−	2.12132i	0.427442	−	0.0822613i
$666$		0			0
$667$	−5.00000	+	8.66025i	−0.193601	+	0.335326i
$668$		0			0
$669$		0			0
$670$	−6.00000	−	3.46410i	−0.231800	−	0.133830i
$671$	29.3939			1.13474
$672$		0			0
$673$	−25.0000			−0.963679			−0.481840	−	0.876259i	$-0.660031\pi$
$673$	−25.0000			−0.963679			−0.481840	+	0.876259i	$0.660031\pi$
$674$	−1.22474	−	0.707107i	−0.0471754	−	0.0272367i
$675$		0			0
$676$		0			0
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	−0.689557	−	0.724232i	$-0.742195\pi$
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	0.971981	+	0.235058i	$0.0755280\pi$
$678$		0			0
$679$	7.50000	−	21.6506i	0.287824	−	0.830875i
$680$		−	16.9706i		−	0.650791i
$681$		0			0
$682$	36.0000	−	20.7846i	1.37851	−	0.795884i
$683$	31.8434	−	18.3848i	1.21845	−	0.703474i	0.253866	−	0.967239i	$-0.418298\pi$
$683$	31.8434	−	18.3848i	1.21845	−	0.703474i	0.964587	+	0.263766i	$0.0849645\pi$
$684$		0			0
$685$		−	17.3205i		−	0.661783i
$686$	1.22474	+	26.1630i	0.0467610	+	0.998906i
$687$		0			0
$688$	−14.0000	+	24.2487i	−0.533745	+	0.924473i
$689$	−2.44949	−	4.24264i	−0.0933181	−	0.161632i
$690$		0			0
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	0.411958	−	0.911203i	$-0.364845\pi$
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	−0.583146	+	0.812367i	$0.698178\pi$
$692$		0			0
$693$		0			0
$694$	−44.0000			−1.67022
$695$	−14.6969	−	8.48528i	−0.557487	−	0.321865i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	−1.22474	+	2.12132i	−0.0463573	+	0.0802932i
$699$		0			0
$700$		0			0
$701$			15.5563i			0.587555i	0.955874	+	0.293778i	$0.0949125\pi$
$701$			15.5563i			0.587555i	−0.955874	+	0.293778i	$0.905087\pi$
$702$		0			0
$703$	6.00000	−	3.46410i	0.226294	−	0.130651i
$704$	39.1918	−	22.6274i	1.47710	−	0.852803i
$705$		0			0
$706$			48.4974i			1.82522i
$707$	−4.89898	−	25.4558i	−0.184245	−	0.957366i
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$	4.89898	+	8.48528i	0.183855	+	0.318447i
$711$		0			0
$712$	6.00000	+	3.46410i	0.224860	+	0.129823i
$713$	36.7423			1.37601
$714$		0			0
$715$	−48.0000			−1.79510
$716$		0			0
$717$		0			0
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	−0.998787	−	0.0492373i	$-0.984321\pi$
$719$	−12.2474	+	21.2132i	−0.456753	+	0.791119i	0.542034	+	0.840356i	$0.317654\pi$
$720$		0			0
$721$	24.0000	+	27.7128i	0.893807	+	1.03208i
$722$		−	22.6274i		−	0.842105i
$723$		0			0
$724$		0			0
$725$	−1.22474	+	0.707107i	−0.0454859	+	0.0262613i
$726$		0			0
$727$			32.9090i			1.22053i	0.792199	+	0.610263i	$0.208936\pi$
$727$			32.9090i			1.22053i	−0.792199	+	0.610263i	$0.791064\pi$
$728$	24.4949	+	8.48528i	0.907841	+	0.314485i
$729$		0			0
$730$	21.0000	−	36.3731i	0.777245	−	1.34623i
$731$	−8.57321	−	14.8492i	−0.317092	−	0.549219i
$732$		0			0
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.392337	−	0.919822i	$-0.628333\pi$
$733$	−37.5000	−	21.6506i	−1.38509	−	0.799684i	−0.992757	+	0.120137i	$0.961667\pi$
$734$	12.2474			0.452062
$735$		0			0
$736$		0			0
$737$	9.79796	+	5.65685i	0.360912	+	0.208373i
$738$		0			0
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	0.816373	−	0.577524i	$-0.195981\pi$
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	−0.908337	+	0.418238i	$0.862648\pi$
$740$		0			0
$741$		0			0
$742$	−5.00000	−	1.73205i	−0.183556	−	0.0635856i
$743$		−	35.3553i		−	1.29706i	−0.761188	−	0.648531i	$-0.775384\pi$
$743$		−	35.3553i		−	1.29706i	0.761188	−	0.648531i	$-0.224616\pi$
$744$		0			0
$745$	21.0000	−	12.1244i	0.769380	−	0.444202i
$746$	1.22474	−	0.707107i	0.0448411	−	0.0258890i
$747$		0			0
$748$		0			0
$749$	24.4949	+	28.2843i	0.895024	+	1.03348i
$750$		0			0
$751$	18.5000	−	32.0429i	0.675075	−	1.16926i	−0.301373	−	0.953506i	$-0.597445\pi$
$751$	18.5000	−	32.0429i	0.675075	−	1.16926i	0.976447	−	0.215757i	$-0.0692219\pi$
$752$	−14.6969	−	25.4558i	−0.535942	−	0.928279i
$753$		0			0
$754$	6.00000	+	3.46410i	0.218507	+	0.126155i
$755$	−26.9444			−0.980607
$756$		0			0
$757$	−7.00000			−0.254419			−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000			−0.254419			−0.127210	+	0.991876i	$0.540602\pi$
$758$	−12.2474	−	7.07107i	−0.444847	−	0.256833i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	4.89898	−	8.48528i	0.177588	−	0.307591i	−0.763466	−	0.645848i	$-0.776504\pi$
$761$	4.89898	−	8.48528i	0.177588	−	0.307591i	0.941054	+	0.338257i	$0.109837\pi$
$762$		0			0
$763$	−8.50000	−	44.1673i	−0.307721	−	1.59896i
$764$		0			0
$765$		0			0
$766$	−42.0000	+	24.2487i	−1.51752	+	0.876142i
$767$	−44.0908	+	25.4558i	−1.59203	+	0.919157i
$768$		0			0
$769$			50.2295i			1.81132i	0.424003	+	0.905661i	$0.360624\pi$
$769$			50.2295i			1.81132i	−0.424003	+	0.905661i	$0.639376\pi$
$770$	−39.1918	+	33.9411i	−1.41238	+	1.22315i
$771$		0			0
$772$		0			0
$773$	−20.8207	−	36.0624i	−0.748867	−	1.29708i	−0.948366	−	0.317178i	$-0.897265\pi$
$773$	−20.8207	−	36.0624i	−0.748867	−	1.29708i	0.199499	−	0.979898i	$-0.436069\pi$
$774$		0			0
$775$	4.50000	+	2.59808i	0.161645	+	0.0933257i
$776$	−24.4949			−0.879316
$777$		0			0
$778$	−38.0000			−1.36237
$779$	3.67423	+	2.12132i	0.131643	+	0.0760042i
$780$		0			0
$781$	−8.00000	−	13.8564i	−0.286263	−	0.495821i
$782$	12.2474	−	21.2132i	0.437968	−	0.758583i
$783$		0			0
$784$	26.0000	−	10.3923i	0.928571	−	0.371154i
$785$			25.4558i			0.908558i
$786$		0			0
$787$	−22.5000	+	12.9904i	−0.802038	+	0.463057i	−0.844183	−	0.536054i	$-0.819914\pi$
$787$	−22.5000	+	12.9904i	−0.802038	+	0.463057i	0.0421450	+	0.999112i	$0.486581\pi$
$788$		0			0
$789$		0			0
$790$		−	13.8564i		−	0.492989i
$791$	−2.44949	+	7.07107i	−0.0870938	+	0.251418i
$792$		0			0
$793$	9.00000	−	15.5885i	0.319599	−	0.553562i
$794$	−13.4722	−	23.3345i	−0.478110	−	0.828111i
$795$		0			0
$796$		0			0
$797$	39.1918			1.38825			0.694123	−	0.719856i	$-0.255792\pi$
$797$	39.1918			1.38825			0.694123	+	0.719856i	$0.255792\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$		0			0
$801$		0			0
$802$	16.0000	+	27.7128i	0.564980	+	0.978573i
$803$	−34.2929	+	59.3970i	−1.21017	+	2.09607i
$804$		0			0
$805$	−45.0000	+	8.66025i	−1.58604	+	0.305234i
$806$		−	25.4558i		−	0.896644i
$807$		0			0
$808$	−24.0000	+	13.8564i	−0.844317	+	0.487467i
$809$	9.79796	−	5.65685i	0.344478	−	0.198884i	−0.317773	−	0.948167i	$-0.602935\pi$
$809$	9.79796	−	5.65685i	0.344478	−	0.198884i	0.662250	+	0.749283i	$0.269602\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$	−16.0000	+	27.7128i	−0.560800	+	0.971334i
$815$	28.1691	+	48.7904i	0.986722	+	1.70905i
$816$		0			0
$817$	−10.5000	−	6.06218i	−0.367348	−	0.212089i
$818$	−14.6969			−0.513866
$819$		0			0
$820$		0			0
$821$	34.2929	+	19.7990i	1.19683	+	0.690990i	0.959847	−	0.280525i	$-0.0905084\pi$
$821$	34.2929	+	19.7990i	1.19683	+	0.690990i	0.236982	+	0.971514i	$0.423842\pi$
$822$		0			0
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	0.592966	−	0.805228i	$-0.297957\pi$
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	−0.993831	+	0.110910i	$0.964624\pi$
$824$	19.5959	−	33.9411i	0.682656	−	1.18240i
$825$		0			0
$826$	−18.0000	+	51.9615i	−0.626300	+	1.80797i
$827$		−	22.6274i		−	0.786832i	−0.919360	−	0.393416i	$-0.871293\pi$
$827$		−	22.6274i		−	0.786832i	0.919360	−	0.393416i	$-0.128707\pi$
$828$		0			0
$829$	28.5000	−	16.4545i	0.989846	−	0.571488i	0.0846177	−	0.996413i	$-0.473033\pi$
$829$	28.5000	−	16.4545i	0.989846	−	0.571488i	0.905228	+	0.424926i	$0.139700\pi$
$830$	−29.3939	+	16.9706i	−1.02028	+	0.589057i
$831$		0			0
$832$		−	27.7128i		−	0.960769i
$833$	−2.44949	+	16.9706i	−0.0848698	+	0.587995i
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$		0			0
$838$	3.00000	+	1.73205i	0.103633	+	0.0598327i
$839$	−24.4949			−0.845658			−0.422829	−	0.906210i	$-0.638963\pi$
$839$	−24.4949			−0.845658			−0.422829	+	0.906210i	$0.638963\pi$
$840$		0			0
$841$	27.0000			0.931034
$842$	13.4722	+	7.77817i	0.464282	+	0.268054i
$843$		0			0
$844$		0			0
$845$	1.22474	−	2.12132i	0.0421325	−	0.0729756i
$846$		0			0
$847$	42.0000	−	36.3731i	1.44314	−	1.24979i
$848$			5.65685i			0.194257i
$849$		0			0
$850$	3.00000	−	1.73205i	0.102899	−	0.0594089i
$851$	−24.4949	+	14.1421i	−0.839674	+	0.484786i
$852$		0			0
$853$		−	8.66025i		−	0.296521i	−0.988948	−	0.148261i	$-0.952633\pi$
$853$		−	8.66025i		−	0.296521i	0.988948	−	0.148261i	$-0.0473675\pi$
$854$	−3.67423	−	19.0919i	−0.125730	−	0.653311i
$855$		0			0
$856$	20.0000	−	34.6410i	0.683586	−	1.18401i
$857$	2.44949	+	4.24264i	0.0836730	+	0.144926i	0.904825	−	0.425784i	$-0.140002\pi$
$857$	2.44949	+	4.24264i	0.0836730	+	0.144926i	−0.821152	+	0.570710i	$0.806668\pi$
$858$		0			0
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.999839	−	0.0179638i	$-0.00571836\pi$
$859$	43.5000	+	25.1147i	1.48420	+	0.856904i	0.484362	+	0.874868i	$0.339052\pi$
$860$		0			0
$861$		0			0
$862$	40.0000			1.36241
$863$	1.22474	+	0.707107i	0.0416908	+	0.0240702i	0.520701	−	0.853739i	$-0.325671\pi$
$863$	1.22474	+	0.707107i	0.0416908	+	0.0240702i	−0.479010	+	0.877810i	$0.659004\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	−3.67423	+	6.36396i	−0.124856	+	0.216256i
$867$		0			0
$868$		0			0
$869$			22.6274i			0.767583i
$870$		0			0
$871$	6.00000	−	3.46410i	0.203302	−	0.117377i
$872$	−41.6413	+	24.0416i	−1.41015	+	0.814152i
$873$		0			0
$874$		−	17.3205i		−	0.585875i
$875$	24.4949	+	8.48528i	0.828079	+	0.286855i
$876$		0			0
$877$	−17.5000	+	30.3109i	−0.590933	+	1.02353i	0.403174	+	0.915123i	$0.367907\pi$
$877$	−17.5000	+	30.3109i	−0.590933	+	1.02353i	−0.994107	+	0.108403i	$0.965426\pi$
$878$	14.6969	+	25.4558i	0.495998	+	0.859093i
$879$		0			0
$880$	48.0000	+	27.7128i	1.61808	+	0.934199i
$881$	−36.7423			−1.23788			−0.618941	−	0.785438i	$-0.712438\pi$
$881$	−36.7423			−1.23788			−0.618941	+	0.785438i	$0.712438\pi$
$882$		0			0
$883$	−37.0000			−1.24515			−0.622575	−	0.782560i	$-0.713913\pi$
$883$	−37.0000			−1.24515			−0.622575	+	0.782560i	$0.713913\pi$
$884$		0			0
$885$		0			0
$886$	−11.0000	−	19.0526i	−0.369552	−	0.640083i
$887$	26.9444	−	46.6690i	0.904704	−	1.56699i	0.0833899	−	0.996517i	$-0.473425\pi$
$887$	26.9444	−	46.6690i	0.904704	−	1.56699i	0.821314	−	0.570476i	$-0.193241\pi$
$888$		0			0
$889$	−2.50000	−	0.866025i	−0.0838473	−	0.0290456i
$890$			8.48528i			0.284427i
$891$		0			0
$892$		0			0
$893$	11.0227	−	6.36396i	0.368861	−	0.212962i
$894$		0			0
$895$			24.2487i			0.810545i
$896$	−19.5959	−	22.6274i	−0.654654	−	0.755929i
$897$		0			0
$898$	25.0000	−	43.3013i	0.834261	−	1.44498i
$899$	3.67423	+	6.36396i	0.122543	+	0.212250i
$900$		0			0
$901$	−3.00000	−	1.73205i	−0.0999445	−	0.0577030i
$902$	−19.5959			−0.652473
$903$		0			0
$904$	8.00000			0.266076
$905$	−33.0681	−	19.0919i	−1.09922	−	0.634636i
$906$		0			0
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$		0			0
$909$		0			0
$910$	6.00000	+	31.1769i	0.198898	+	1.03350i
$911$		−	52.3259i		−	1.73363i	−0.498626	−	0.866817i	$-0.666162\pi$
$911$		−	52.3259i		−	1.73363i	0.498626	−	0.866817i	$-0.333838\pi$
$912$		0			0
$913$	48.0000	−	27.7128i	1.58857	−	0.917160i
$914$	−6.12372	+	3.53553i	−0.202555	+	0.116945i
$915$		0			0
$916$		0			0
$917$	34.2929	−	29.6985i	1.13245	−	0.980730i
$918$		0			0
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	−0.904309	−	0.426878i	$-0.859613\pi$
$919$	−2.50000	+	4.33013i	−0.0824674	+	0.142838i	0.821842	+	0.569716i	$0.192947\pi$
$920$	24.4949	+	42.4264i	0.807573	+	1.39876i
$921$		0			0
$922$	−30.0000	−	17.3205i	−0.987997	−	0.570421i
$923$	−9.79796			−0.322504
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−1.22474	−	0.707107i	−0.0402476	−	0.0232370i
$927$		0			0
$928$		0			0
$929$	11.0227	−	19.0919i	0.361643	−	0.626384i	−0.626588	−	0.779350i	$-0.715549\pi$
$929$	11.0227	−	19.0919i	0.361643	−	0.626384i	0.988231	+	0.152966i	$0.0488825\pi$
$930$		0			0
$931$	4.50000	+	11.2583i	0.147482	+	0.368977i
$932$		0			0
$933$		0			0
$934$	6.00000	−	3.46410i	0.196326	−	0.113349i
$935$	−29.3939	+	16.9706i	−0.961283	+	0.554997i
$936$		0			0
$937$			10.3923i			0.339502i	0.985487	+	0.169751i	$0.0542963\pi$
$937$			10.3923i			0.339502i	−0.985487	+	0.169751i	$0.945704\pi$
$938$	2.44949	−	7.07107i	0.0799787	−	0.230879i
$939$		0			0
$940$		0			0
$941$	7.34847	+	12.7279i	0.239553	+	0.414918i	0.960586	−	0.277982i	$-0.0896657\pi$
$941$	7.34847	+	12.7279i	0.239553	+	0.414918i	−0.721033	+	0.692901i	$0.756332\pi$
$942$		0			0
$943$	−15.0000	−	8.66025i	−0.488467	−	0.282017i
$944$	58.7878			1.91338
$945$		0			0
$946$	56.0000			1.82072
$947$	8.57321	+	4.94975i	0.278592	+	0.160845i	0.632786	−	0.774327i	$-0.281911\pi$
$947$	8.57321	+	4.94975i	0.278592	+	0.160845i	−0.354194	+	0.935172i	$0.615245\pi$
$948$		0			0
$949$	21.0000	+	36.3731i	0.681689	+	1.18072i
$950$	1.22474	−	2.12132i	0.0397360	−	0.0688247i
$951$		0			0
$952$	18.0000	−	3.46410i	0.583383	−	0.112272i
$953$		−	18.3848i		−	0.595541i	−0.954637	−	0.297771i	$-0.903757\pi$
$953$		−	18.3848i		−	0.595541i	0.954637	−	0.297771i	$-0.0962431\pi$
$954$		0			0
$955$	3.00000	−	1.73205i	0.0970777	−	0.0560478i
$956$		0			0
$957$		0			0
$958$		−	3.46410i		−	0.111920i
$959$	18.3712	−	3.53553i	0.593236	−	0.114168i
$960$		0			0
$961$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i
$962$	9.79796	+	16.9706i	0.315899	+	0.547153i
$963$		0			0
$964$		0			0
$965$	9.79796			0.315407
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$	−51.4393	−	29.6985i	−1.65332	−	0.954545i
$969$		0			0
$970$	−15.0000	−	25.9808i	−0.481621	−	0.834192i
$971$	6.12372	−	10.6066i	0.196520	−	0.340382i	−0.750878	−	0.660441i	$-0.770369\pi$
$971$	6.12372	−	10.6066i	0.196520	−	0.340382i	0.947398	+	0.320059i	$0.103703\pi$
$972$		0			0
$973$	6.00000	−	17.3205i	0.192351	−	0.555270i
$974$			18.3848i			0.589086i
$975$		0			0
$976$	−18.0000	+	10.3923i	−0.576166	+	0.332650i
$977$	31.8434	−	18.3848i	1.01876	−	0.588181i	0.105015	−	0.994471i	$-0.466511\pi$
$977$	31.8434	−	18.3848i	1.01876	−	0.588181i	0.913744	+	0.406290i	$0.133178\pi$
$978$		0			0
$979$		−	13.8564i		−	0.442853i
$980$		0			0
$981$		0			0
$982$	4.00000	−	6.92820i	0.127645	−	0.221088i
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	0.902442	−	0.430812i	$-0.141773\pi$
$983$	2.44949	+	4.24264i	0.0781266	+	0.135319i	−0.824315	+	0.566131i	$0.808439\pi$
$984$		0			0
$985$	6.00000	+	3.46410i	0.191176	+	0.110375i
$986$	4.89898			0.156015
$987$		0			0
$988$		0			0
$989$	42.8661	+	24.7487i	1.36306	+	0.786964i
$990$		0			0
$991$	29.0000	+	50.2295i	0.921215	+	1.59559i	0.797537	+	0.603269i	$0.206136\pi$
$991$	29.0000	+	50.2295i	0.921215	+	1.59559i	0.123678	+	0.992322i	$0.460531\pi$
$992$		0			0
$993$		0			0
$994$	−8.00000	+	6.92820i	−0.253745	+	0.219749i
$995$		−	4.24264i		−	0.134501i
$996$		0			0
$997$	34.5000	−	19.9186i	1.09263	−	0.630828i	0.158352	−	0.987383i	$-0.449382\pi$
$997$	34.5000	−	19.9186i	1.09263	−	0.630828i	0.934274	+	0.356555i	$0.116049\pi$
$998$	30.6186	−	17.6777i	0.969216	−	0.559577i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.p.b.26.2	yes	4
3.2	odd	2	inner	189.2.p.b.26.1	✓	4
7.2	even	3		1323.2.c.c.1322.1		4
7.3	odd	6	inner	189.2.p.b.80.1	yes	4
7.5	odd	6		1323.2.c.c.1322.2		4
9.2	odd	6		567.2.i.e.215.2		4
9.4	even	3		567.2.s.c.26.1		4
9.5	odd	6		567.2.s.c.26.2		4
9.7	even	3		567.2.i.e.215.1		4
21.2	odd	6		1323.2.c.c.1322.4		4
21.5	even	6		1323.2.c.c.1322.3		4
21.17	even	6	inner	189.2.p.b.80.2	yes	4
63.31	odd	6		567.2.i.e.269.1		4
63.38	even	6		567.2.s.c.458.1		4
63.52	odd	6		567.2.s.c.458.2		4
63.59	even	6		567.2.i.e.269.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.b.26.1	✓	4	3.2	odd	2	inner
189.2.p.b.26.2	yes	4	1.1	even	1	trivial
189.2.p.b.80.1	yes	4	7.3	odd	6	inner
189.2.p.b.80.2	yes	4	21.17	even	6	inner
567.2.i.e.215.1		4	9.7	even	3
567.2.i.e.215.2		4	9.2	odd	6
567.2.i.e.269.1		4	63.31	odd	6
567.2.i.e.269.2		4	63.59	even	6
567.2.s.c.26.1		4	9.4	even	3
567.2.s.c.26.2		4	9.5	odd	6
567.2.s.c.458.1		4	63.38	even	6
567.2.s.c.458.2		4	63.52	odd	6
1323.2.c.c.1322.1		4	7.2	even	3
1323.2.c.c.1322.2		4	7.5	odd	6
1323.2.c.c.1322.3		4	21.5	even	6
1323.2.c.c.1322.4		4	21.2	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.22474 - 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.22474 - 2.12132i) q^{5} +(2.50000 + 0.866025i) q^{7} -2.82843i q^{8} +(3.00000 - 1.73205i) q^{10} +(-4.89898 + 2.82843i) q^{11} +3.46410i q^{13} +(2.44949 + 2.82843i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.22474 + 2.12132i) q^{17} +(1.50000 + 0.866025i) q^{19} -8.00000 q^{22} +(-6.12372 - 3.53553i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.44949 + 4.24264i) q^{26} -1.41421i q^{29} +(-4.50000 + 2.59808i) q^{31} +3.46410i q^{34} +(4.89898 - 4.24264i) q^{35} +(2.00000 - 3.46410i) q^{37} +(1.22474 + 2.12132i) q^{38} +(-6.00000 - 3.46410i) q^{40} +2.44949 q^{41} -7.00000 q^{43} +(-5.00000 - 8.66025i) q^{46} +(3.67423 - 6.36396i) q^{47} +(5.50000 + 4.33013i) q^{49} -1.41421i q^{50} +(-1.22474 + 0.707107i) q^{53} +13.8564i q^{55} +(2.44949 - 7.07107i) q^{56} +(1.00000 - 1.73205i) q^{58} +(7.34847 + 12.7279i) q^{59} +(-4.50000 - 2.59808i) q^{61} -7.34847 q^{62} -8.00000 q^{64} +(7.34847 + 4.24264i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(9.00000 - 1.73205i) q^{70} +2.82843i q^{71} +(10.5000 - 6.06218i) q^{73} +(4.89898 - 2.82843i) q^{74} +(-14.6969 + 2.82843i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-4.89898 - 8.48528i) q^{80} +(3.00000 + 1.73205i) q^{82} -9.79796 q^{83} +6.00000 q^{85} +(-8.57321 - 4.94975i) q^{86} +(8.00000 + 13.8564i) q^{88} +(-1.22474 + 2.12132i) q^{89} +(-3.00000 + 8.66025i) q^{91} +(9.00000 - 5.19615i) q^{94} +(3.67423 - 2.12132i) q^{95} -8.66025i q^{97} +(3.67423 + 9.19239i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{7}+O(q^{10}) \) 4 * q + 10 * q^7	\( 4 q + 10 q^{7} + 12 q^{10} + 8 q^{16} + 6 q^{19} - 32 q^{22} - 2 q^{25} - 18 q^{31} + 8 q^{37} - 24 q^{40} - 28 q^{43} - 20 q^{46} + 22 q^{49} + 4 q^{58} - 18 q^{61} - 32 q^{64} - 4 q^{67} + 36 q^{70} + 42 q^{73} + 8 q^{79} + 12 q^{82} + 24 q^{85} + 32 q^{88} - 12 q^{91} + 36 q^{94}+O(q^{100}) \) 4 * q + 10 * q^7 + 12 * q^10 + 8 * q^16 + 6 * q^19 - 32 * q^22 - 2 * q^25 - 18 * q^31 + 8 * q^37 - 24 * q^40 - 28 * q^43 - 20 * q^46 + 22 * q^49 + 4 * q^58 - 18 * q^61 - 32 * q^64 - 4 * q^67 + 36 * q^70 + 42 * q^73 + 8 * q^79 + 12 * q^82 + 24 * q^85 + 32 * q^88 - 12 * q^91 + 36 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more