LMFDB - Embedded newform 756.2.bx.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(41,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17, 9]))

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

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

chi := DirichletCharacter("756.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bx (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	756.41
Dual form			756.2.bx.a.461.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.803760 + 1.53427i) q^{3} +(-3.10123 - 2.60224i) q^{5} +(-0.828412 - 2.51271i) q^{7} +(-1.70794 - 2.46636i) q^{9} +O(q^{10})$	\(q+(-0.803760 + 1.53427i) q^{3} +(-3.10123 - 2.60224i) q^{5} +(-0.828412 - 2.51271i) q^{7} +(-1.70794 - 2.46636i) q^{9} +(2.97600 + 3.54666i) q^{11} +(1.01225 + 0.178487i) q^{13} +(6.48518 - 2.66654i) q^{15} +(-3.08179 + 5.33782i) q^{17} +(-0.572912 + 0.330771i) q^{19} +(4.52102 + 0.748614i) q^{21} +(2.58461 + 7.10116i) q^{23} +(1.97773 + 11.2163i) q^{25} +(5.15683 - 0.638074i) q^{27} +(1.26912 - 0.223781i) q^{29} +(-1.39697 - 3.83815i) q^{31} +(-7.83352 + 1.71532i) q^{33} +(-3.96959 + 9.94824i) q^{35} +(3.02730 - 5.24343i) q^{37} +(-1.08745 + 1.40960i) q^{39} +(-0.915195 + 5.19033i) q^{41} +(-0.0189843 + 0.0159297i) q^{43} +(-1.12135 + 12.0932i) q^{45} +(10.5471 + 3.83884i) q^{47} +(-5.62747 + 4.16313i) q^{49} +(-5.71262 - 9.01861i) q^{51} +4.65757i q^{53} -18.7433i q^{55} +(-0.0470069 - 1.14486i) q^{57} +(-6.13282 - 5.14605i) q^{59} +(-3.24287 + 8.90971i) q^{61} +(-4.78238 + 6.33473i) q^{63} +(-2.67475 - 3.18764i) q^{65} +(0.755393 - 4.28405i) q^{67} +(-12.9725 - 1.74214i) q^{69} +(-9.13833 - 5.27602i) q^{71} +(6.68607 - 3.86020i) q^{73} +(-18.7984 - 5.98082i) q^{75} +(6.44639 - 10.4159i) q^{77} +(2.29656 + 13.0245i) q^{79} +(-3.16587 + 8.42480i) q^{81} +(2.10826 + 11.9566i) q^{83} +(23.4477 - 8.53425i) q^{85} +(-0.676731 + 2.12704i) q^{87} +(4.16153 + 7.20798i) q^{89} +(-0.390072 - 2.69135i) q^{91} +(7.01156 + 0.941622i) q^{93} +(2.63748 + 0.465058i) q^{95} +(8.24903 + 9.83081i) q^{97} +(3.66451 - 13.3974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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
$3$	−0.803760	+	1.53427i	−0.464051	+	0.885809i
$3$	−0.803760	+	1.53427i	−0.464051	+	0.885809i
$4$		0			0
$5$	−3.10123	−	2.60224i	−1.38691	−	1.16376i	−0.966573	−	0.256392i	$-0.917466\pi$
$5$	−3.10123	−	2.60224i	−1.38691	−	1.16376i	−0.420340	−	0.907367i	$-0.638089\pi$
$6$		0			0
$7$	−0.828412	−	2.51271i	−0.313110	−	0.949717i
$7$	−0.828412	−	2.51271i	−0.313110	−	0.949717i
$8$		0			0
$9$	−1.70794	−	2.46636i	−0.569314	−	0.822120i
$10$		0			0
$11$	2.97600	+	3.54666i	0.897299	+	1.06936i	0.997231	+	0.0743650i	$0.0236930\pi$
$11$	2.97600	+	3.54666i	0.897299	+	1.06936i	−0.0999321	+	0.994994i	$0.531863\pi$
$12$		0			0
$13$	1.01225	+	0.178487i	0.280747	+	0.0495033i	0.312249	−	0.950000i	$-0.398918\pi$
$13$	1.01225	+	0.178487i	0.280747	+	0.0495033i	−0.0315016	+	0.999504i	$0.510029\pi$
$14$		0			0
$15$	6.48518	−	2.66654i	1.67447	−	0.688497i
$16$		0			0
$17$	−3.08179	+	5.33782i	−0.747445	+	1.29461i	0.201599	+	0.979468i	$0.435386\pi$
$17$	−3.08179	+	5.33782i	−0.747445	+	1.29461i	−0.949044	+	0.315144i	$0.897947\pi$
$18$		0			0
$19$	−0.572912	+	0.330771i	−0.131435	+	0.0758840i	−0.564276	−	0.825586i	$-0.690845\pi$
$19$	−0.572912	+	0.330771i	−0.131435	+	0.0758840i	0.432841	+	0.901470i	$0.357511\pi$
$20$		0			0
$21$	4.52102	+	0.748614i	0.986566	+	0.163361i
$22$		0			0
$23$	2.58461	+	7.10116i	0.538928	+	1.48069i	0.848177	+	0.529713i	$0.177700\pi$
$23$	2.58461	+	7.10116i	0.538928	+	1.48069i	−0.309249	+	0.950981i	$0.600078\pi$
$24$		0			0
$25$	1.97773	+	11.2163i	0.395546	+	2.24326i
$26$		0			0
$27$	5.15683	−	0.638074i	0.992432	−	0.122797i
$28$		0			0
$29$	1.26912	−	0.223781i	0.235670	−	0.0415550i	−0.0545655	−	0.998510i	$-0.517377\pi$
$29$	1.26912	−	0.223781i	0.235670	−	0.0415550i	0.290236	+	0.956955i	$0.406266\pi$
$30$		0			0
$31$	−1.39697	−	3.83815i	−0.250903	−	0.689351i	−0.999649	−	0.0264938i	$-0.991566\pi$
$31$	−1.39697	−	3.83815i	−0.250903	−	0.689351i	0.748746	−	0.662857i	$-0.230656\pi$
$32$		0			0
$33$	−7.83352	+	1.71532i	−1.36364	+	0.298598i
$34$		0			0
$35$	−3.96959	+	9.94824i	−0.670984	+	1.68156i
$36$		0			0
$37$	3.02730	−	5.24343i	0.497684	−	0.862015i	−0.502312	−	0.864686i	$-0.667517\pi$
$37$	3.02730	−	5.24343i	0.497684	−	0.862015i	0.999996	+	0.00267175i	$0.000850445\pi$
$38$		0			0
$39$	−1.08745	+	1.40960i	−0.174131	+	0.225716i
$40$		0			0
$41$	−0.915195	+	5.19033i	−0.142929	+	0.810593i	0.826077	+	0.563558i	$0.190568\pi$
$41$	−0.915195	+	5.19033i	−0.142929	+	0.810593i	−0.969006	+	0.247036i	$0.920543\pi$
$42$		0			0
$43$	−0.0189843	+	0.0159297i	−0.00289508	+	0.00242926i	−0.644234	−	0.764828i	$-0.722824\pi$
$43$	−0.0189843	+	0.0159297i	−0.00289508	+	0.00242926i	0.641339	+	0.767258i	$0.278379\pi$
$44$		0			0
$45$	−1.12135	+	12.0932i	−0.167161	+	1.80275i
$46$		0			0
$47$	10.5471	+	3.83884i	1.53846	+	0.559952i	0.965674	−	0.259756i	$-0.0836422\pi$
$47$	10.5471	+	3.83884i	1.53846	+	0.559952i	0.572781	+	0.819708i	$0.305864\pi$
$48$		0			0
$49$	−5.62747	+	4.16313i	−0.803924	+	0.594732i
$50$		0			0
$51$	−5.71262	−	9.01861i	−0.799926	−	1.26286i
$52$		0			0
$53$			4.65757i			0.639767i	0.947457	+	0.319883i	$0.103644\pi$
$53$			4.65757i			0.639767i	−0.947457	+	0.319883i	$0.896356\pi$
$54$		0			0
$55$		−	18.7433i		−	2.52735i
$56$		0			0
$57$	−0.0470069	−	1.14486i	−0.00622622	−	0.151640i
$58$		0			0
$59$	−6.13282	−	5.14605i	−0.798425	−	0.669958i	0.149390	−	0.988778i	$-0.452269\pi$
$59$	−6.13282	−	5.14605i	−0.798425	−	0.669958i	−0.947815	+	0.318820i	$0.896713\pi$
$60$		0			0
$61$	−3.24287	+	8.90971i	−0.415207	+	1.14077i	0.539178	+	0.842192i	$0.318735\pi$
$61$	−3.24287	+	8.90971i	−0.415207	+	1.14077i	−0.954385	+	0.298579i	$0.903487\pi$
$62$		0			0
$63$	−4.78238	+	6.33473i	−0.602523	+	0.798101i
$64$		0			0
$65$	−2.67475	−	3.18764i	−0.331762	−	0.395378i
$66$		0			0
$67$	0.755393	−	4.28405i	0.0922860	−	0.523380i	−0.903259	−	0.429095i	$-0.858833\pi$
$67$	0.755393	−	4.28405i	0.0922860	−	0.523380i	0.995545	−	0.0942846i	$-0.0300564\pi$
$68$		0			0
$69$	−12.9725	−	1.74214i	−1.56170	−	0.209730i
$70$		0			0
$71$	−9.13833	−	5.27602i	−1.08452	−	0.626148i	−0.152408	−	0.988318i	$-0.548703\pi$
$71$	−9.13833	−	5.27602i	−1.08452	−	0.626148i	−0.932112	+	0.362170i	$0.882036\pi$
$72$		0			0
$73$	6.68607	−	3.86020i	0.782545	−	0.451803i	−0.0547865	−	0.998498i	$-0.517448\pi$
$73$	6.68607	−	3.86020i	0.782545	−	0.451803i	0.837331	+	0.546696i	$0.184114\pi$
$74$		0			0
$75$	−18.7984	−	5.98082i	−2.17065	−	0.690606i
$76$		0			0
$77$	6.44639	−	10.4159i	0.734635	−	1.18701i
$78$		0			0
$79$	2.29656	+	13.0245i	0.258383	+	1.46537i	0.787236	+	0.616652i	$0.211511\pi$
$79$	2.29656	+	13.0245i	0.258383	+	1.46537i	−0.528853	+	0.848714i	$0.677378\pi$
$80$		0			0
$81$	−3.16587	+	8.42480i	−0.351764	+	0.936089i
$82$		0			0
$83$	2.10826	+	11.9566i	0.231412	+	1.31240i	0.850040	+	0.526719i	$0.176578\pi$
$83$	2.10826	+	11.9566i	0.231412	+	1.31240i	−0.618628	+	0.785684i	$0.712311\pi$
$84$		0			0
$85$	23.4477	−	8.53425i	2.54326	−	0.925670i
$86$		0			0
$87$	−0.676731	+	2.12704i	−0.0725532	+	0.228042i
$88$		0			0
$89$	4.16153	+	7.20798i	0.441121	+	0.764045i	0.997773	−	0.0667015i	$-0.0212475\pi$
$89$	4.16153	+	7.20798i	0.441121	+	0.764045i	−0.556652	+	0.830746i	$0.687914\pi$
$90$		0			0
$91$	−0.390072	−	2.69135i	−0.0408907	−	0.282130i
$92$		0			0
$93$	7.01156	+	0.941622i	0.727065	+	0.0976416i
$94$		0			0
$95$	2.63748	+	0.465058i	0.270600	+	0.0477140i
$96$		0			0
$97$	8.24903	+	9.83081i	0.837562	+	0.998168i	0.999935	+	0.0114383i	$0.00364102\pi$
$97$	8.24903	+	9.83081i	0.837562	+	0.998168i	−0.162372	+	0.986730i	$0.551915\pi$
$98$		0			0
$99$	3.66451	−	13.3974i	0.368297	−	1.34649i
$100$		0			0
$101$	−0.805518	−	0.293185i	−0.0801521	−	0.0291730i	0.301633	−	0.953424i	$-0.402468\pi$
$101$	−0.805518	−	0.293185i	−0.0801521	−	0.0291730i	−0.381785	+	0.924251i	$0.624691\pi$
$102$		0			0
$103$	−2.67106	+	3.18324i	−0.263187	+	0.313654i	−0.881413	−	0.472346i	$-0.843407\pi$
$103$	−2.67106	+	3.18324i	−0.263187	+	0.313654i	0.618226	+	0.786000i	$0.287852\pi$
$104$		0			0
$105$	−12.0726	−	14.0864i	−1.17817	−	1.37469i
$106$		0			0
$107$		−	18.7899i		−	1.81649i	−0.418438	−	0.908246i	$-0.637422\pi$
$107$		−	18.7899i		−	1.81649i	0.418438	−	0.908246i	$-0.362578\pi$
$108$		0			0
$109$	3.04903			0.292044			0.146022	−	0.989281i	$-0.453353\pi$
$109$	3.04903			0.292044			0.146022	+	0.989281i	$0.453353\pi$
$110$		0			0
$111$	5.61160	+	8.85913i	0.532629	+	0.840872i
$112$		0			0
$113$	−8.30991	+	9.90336i	−0.781731	+	0.931630i	−0.999010	−	0.0444792i	$-0.985837\pi$
$113$	−8.30991	+	9.90336i	−0.781731	+	0.931630i	0.217280	+	0.976109i	$0.430282\pi$
$114$		0			0
$115$	10.4635	−	28.7481i	0.975723	−	2.68078i
$116$		0			0
$117$	−1.28865	−	2.80141i	−0.119135	−	0.258991i
$118$		0			0
$119$	15.9654	+	3.32175i	1.46355	+	0.304504i
$120$		0			0
$121$	−1.81209	+	10.2769i	−0.164736	+	0.934262i
$122$		0			0
$123$	−7.22775	−	5.57593i	−0.651704	−	0.502765i
$124$		0			0
$125$	12.9331	−	22.4009i	1.15678	−	2.00359i
$126$		0			0
$127$	6.23905	+	10.8064i	0.553626	+	0.958909i	0.998009	+	0.0630718i	$0.0200897\pi$
$127$	6.23905	+	10.8064i	0.553626	+	0.958909i	−0.444383	+	0.895837i	$0.646577\pi$
$128$		0			0
$129$	−0.00918161	−	0.0419307i	−0.000808396	−	0.00369179i
$130$		0			0
$131$	3.79546	−	1.38143i	0.331611	−	0.120696i	−0.170849	−	0.985297i	$-0.554651\pi$
$131$	3.79546	−	1.38143i	0.331611	−	0.120696i	0.502459	+	0.864601i	$0.332429\pi$
$132$		0			0
$133$	1.30574	+	1.16555i	0.113222	+	0.101066i
$134$		0			0
$135$	−17.6529	−	11.4405i	−1.51932	−	0.984641i
$136$		0			0
$137$	5.58588	−	0.984941i	0.477234	−	0.0841492i	0.0701432	−	0.997537i	$-0.477654\pi$
$137$	5.58588	−	0.984941i	0.477234	−	0.0841492i	0.407091	+	0.913388i	$0.366543\pi$
$138$		0			0
$139$	1.69415	+	4.65465i	0.143696	+	0.394802i	0.990573	−	0.136987i	$-0.0437420\pi$
$139$	1.69415	+	4.65465i	0.143696	+	0.394802i	−0.846877	+	0.531789i	$0.821520\pi$
$140$		0			0
$141$	−14.3671	+	13.0966i	−1.20993	+	1.10293i
$142$		0			0
$143$	2.37942	+	4.12128i	0.198977	+	0.344639i
$144$		0			0
$145$	−4.51818	−	2.60857i	−0.375214	−	0.216630i
$146$		0			0
$147$	−1.86421	−	11.9802i	−0.153757	−	0.988109i
$148$		0			0
$149$	−8.13276	−	1.43402i	−0.666262	−	0.117480i	−0.169719	−	0.985492i	$-0.554286\pi$
$149$	−8.13276	−	1.43402i	−0.666262	−	0.117480i	−0.496542	+	0.868013i	$0.665397\pi$
$150$		0			0
$151$	7.62328	−	6.39669i	0.620374	−	0.520555i	−0.277547	−	0.960712i	$-0.589522\pi$
$151$	7.62328	−	6.39669i	0.620374	−	0.520555i	0.897921	+	0.440157i	$0.145077\pi$
$152$		0			0
$153$	18.4285	−	1.51587i	1.48986	−	0.122551i
$154$		0			0
$155$	−5.65545	+	15.5382i	−0.454257	+	1.24806i
$156$		0			0
$157$	3.50631	−	4.17866i	0.279834	−	0.333494i	−0.607759	−	0.794122i	$-0.707931\pi$
$157$	3.50631	−	4.17866i	0.279834	−	0.333494i	0.887593	+	0.460628i	$0.152376\pi$
$158$		0			0
$159$	−7.14595	−	3.74357i	−0.566711	−	0.296884i
$160$		0			0
$161$	15.7021	−	12.3771i	1.23750	−	0.975450i
$162$		0			0
$163$	−15.7971			−1.23732			−0.618660	−	0.785659i	$-0.712324\pi$
$163$	−15.7971			−1.23732			−0.618660	+	0.785659i	$0.712324\pi$
$164$		0			0
$165$	28.7572	+	15.0651i	2.23875	+	1.17282i
$166$		0			0
$167$	2.81943	+	2.36578i	0.218174	+	0.183070i	0.745324	−	0.666703i	$-0.232295\pi$
$167$	2.81943	+	2.36578i	0.218174	+	0.183070i	−0.527150	+	0.849772i	$0.676739\pi$
$168$		0			0
$169$	−11.2232	−	4.08492i	−0.863324	−	0.314224i
$170$		0			0
$171$	1.79430	+	0.848070i	0.137214	+	0.0648535i
$172$		0			0
$173$	−15.9773	+	13.4065i	−1.21473	+	1.01928i	−0.215648	+	0.976471i	$0.569186\pi$
$173$	−15.9773	+	13.4065i	−1.21473	+	1.01928i	−0.999083	+	0.0428092i	$0.986369\pi$
$174$		0			0
$175$	26.5449	−	14.2612i	2.00661	−	1.07804i
$176$		0			0
$177$	12.8247	−	5.27319i	0.963965	−	0.396357i
$178$		0			0
$179$	−10.1369	−	5.85254i	−0.757668	−	0.437440i	0.0707900	−	0.997491i	$-0.477448\pi$
$179$	−10.1369	−	5.85254i	−0.757668	−	0.437440i	−0.828458	+	0.560052i	$0.810781\pi$
$180$		0			0
$181$	14.5337	−	8.39101i	1.08028	−	0.623699i	0.149307	−	0.988791i	$-0.452296\pi$
$181$	14.5337	−	8.39101i	1.08028	−	0.623699i	0.930971	+	0.365092i	$0.118963\pi$
$182$		0			0
$183$	−11.0634	−	12.1367i	−0.817828	−	0.897169i
$184$		0			0
$185$	−23.0330	+	8.38334i	−1.69342	+	0.616355i
$186$		0			0
$187$	−28.1029	+	4.95530i	−2.05509	+	0.362367i
$188$		0			0
$189$	−5.87528	−	12.4290i	−0.427363	−	0.904080i
$190$		0			0
$191$	−12.6276	+	2.22659i	−0.913704	+	0.161111i	−0.610685	−	0.791874i	$-0.709106\pi$
$191$	−12.6276	+	2.22659i	−0.913704	+	0.161111i	−0.303019	+	0.952984i	$0.597995\pi$
$192$		0			0
$193$	−8.22287	+	2.99288i	−0.591895	+	0.215432i	−0.620563	−	0.784157i	$-0.713096\pi$
$193$	−8.22287	+	2.99288i	−0.591895	+	0.215432i	0.0286678	+	0.999589i	$0.490874\pi$
$194$		0			0
$195$	7.04054	−	1.54168i	0.504184	−	0.110402i
$196$		0			0
$197$	−13.8885	+	8.01851i	−0.989513	+	0.571295i	−0.905129	−	0.425138i	$-0.860226\pi$
$197$	−13.8885	+	8.01851i	−0.989513	+	0.571295i	−0.0843842	+	0.996433i	$0.526892\pi$
$198$		0			0
$199$	−1.48429	−	0.856952i	−0.105218	−	0.0607477i	0.446467	−	0.894800i	$-0.352682\pi$
$199$	−1.48429	−	0.856952i	−0.105218	−	0.0607477i	−0.551686	+	0.834052i	$0.686015\pi$
$200$		0			0
$201$	5.96571	+	4.60232i	0.420789	+	0.324622i
$202$		0			0
$203$	−1.61365	−	3.00356i	−0.113256	−	0.210809i
$204$		0			0
$205$	16.3447	−	13.7149i	1.14157	−	0.957887i
$206$		0			0
$207$	13.0997	−	18.5029i	0.910489	−	1.28604i
$208$		0			0
$209$	−2.87812	−	1.04755i	−0.199084	−	0.0724606i
$210$		0			0
$211$	5.37007	+	4.50603i	0.369691	+	0.310208i	0.808639	−	0.588305i	$-0.200204\pi$
$211$	5.37007	+	4.50603i	0.369691	+	0.310208i	−0.438948	+	0.898512i	$0.644649\pi$
$212$		0			0
$213$	15.4398	−	9.77997i	1.05792	−	0.670113i
$214$		0			0
$215$	0.100328			0.00684230
$216$		0			0
$217$	−8.48690	+	6.68975i	−0.576128	+	0.454130i
$218$		0			0
$219$	0.548586	+	13.3609i	0.0370700	+	0.902844i
$220$		0			0
$221$	−4.07227	+	4.85314i	−0.273930	+	0.326457i
$222$		0			0
$223$	3.64568	−	10.0164i	0.244133	−	0.670749i	−0.755741	−	0.654870i	$-0.772723\pi$
$223$	3.64568	−	10.0164i	0.244133	−	0.670749i	0.999874	−	0.0158789i	$-0.00505461\pi$
$224$		0			0
$225$	24.2855	−	24.0345i	1.61904	−	1.60230i
$226$		0			0
$227$	−2.39386	+	2.00869i	−0.158886	+	0.133321i	−0.718765	−	0.695253i	$-0.755292\pi$
$227$	−2.39386	+	2.00869i	−0.158886	+	0.133321i	0.559879	+	0.828575i	$0.310848\pi$
$228$		0			0
$229$	−8.15335	−	1.43765i	−0.538788	−	0.0950029i	−0.102369	−	0.994746i	$-0.532642\pi$
$229$	−8.15335	−	1.43765i	−0.538788	−	0.0950029i	−0.436419	+	0.899744i	$0.643753\pi$
$230$		0			0
$231$	10.7995	+	18.2624i	0.710553	+	1.20158i
$232$		0			0
$233$	23.9179	+	13.8090i	1.56691	+	0.904658i	0.996526	+	0.0832831i	$0.0265406\pi$
$233$	23.9179	+	13.8090i	1.56691	+	0.904658i	0.570388	+	0.821375i	$0.306793\pi$
$234$		0			0
$235$	−22.7195	−	39.3513i	−1.48206	−	2.56699i
$236$		0			0
$237$	−21.8289	−	6.94499i	−1.41794	−	0.451126i
$238$		0			0
$239$	−0.252963	−	0.695009i	−0.0163628	−	0.0449564i	0.931242	−	0.364400i	$-0.118726\pi$
$239$	−0.252963	−	0.695009i	−0.0163628	−	0.0449564i	−0.947605	+	0.319444i	$0.896504\pi$
$240$		0			0
$241$	−28.4165	+	5.01060i	−1.83047	+	0.322761i	−0.979344	−	0.202203i	$-0.935190\pi$
$241$	−28.4165	+	5.01060i	−1.83047	+	0.322761i	−0.851124	+	0.524964i	$0.824079\pi$
$242$		0			0
$243$	−10.3813	−	11.6288i	−0.665959	−	0.745988i
$244$		0			0
$245$	28.2855	+	1.73321i	1.80710	+	0.110731i
$246$		0			0
$247$	−0.638967	+	0.232565i	−0.0406565	+	0.0147977i
$248$		0			0
$249$	−20.0391	−	6.37556i	−1.26992	−	0.404035i
$250$		0			0
$251$	−1.91452	−	3.31605i	−0.120844	−	0.209307i	0.799257	−	0.600990i	$-0.205227\pi$
$251$	−1.91452	−	3.31605i	−0.120844	−	0.209307i	−0.920101	+	0.391682i	$0.871893\pi$
$252$		0			0
$253$	−17.4936	+	30.2998i	−1.09981	+	1.90493i
$254$		0			0
$255$	−5.75247	+	42.8344i	−0.360234	+	2.68240i
$256$		0			0
$257$	−0.402744	+	2.28408i	−0.0251225	+	0.142477i	−0.994789	−	0.101955i	$-0.967490\pi$
$257$	−0.402744	+	2.28408i	−0.0251225	+	0.142477i	0.969667	+	0.244432i	$0.0786014\pi$
$258$		0			0
$259$	−15.6831	−	3.26301i	−0.974500	−	0.202754i
$260$		0			0
$261$	−2.71951	−	2.74791i	−0.168334	−	0.170091i
$262$		0			0
$263$	7.36755	−	20.2422i	0.454302	−	1.24819i	−0.475366	−	0.879788i	$-0.657684\pi$
$263$	7.36755	−	20.2422i	0.454302	−	1.24819i	0.929668	−	0.368397i	$-0.120093\pi$
$264$		0			0
$265$	12.1201	−	14.4442i	0.744534	−	0.887301i
$266$		0			0
$267$	−14.4038	+	0.591408i	−0.881500	+	0.0361936i
$268$		0			0
$269$	−24.1630			−1.47325			−0.736623	−	0.676303i	$-0.763581\pi$
$269$	−24.1630			−1.47325			−0.736623	+	0.676303i	$0.763581\pi$
$270$		0			0
$271$		−	9.25145i		−	0.561985i	−0.959710	−	0.280993i	$-0.909336\pi$
$271$		−	9.25145i		−	0.561985i	0.959710	−	0.280993i	$-0.0906637\pi$
$272$		0			0
$273$	4.44277	+	1.56472i	0.268889	+	0.0947013i
$274$		0			0
$275$	−33.8946	+	40.3940i	−2.04392	+	2.43585i
$276$		0			0
$277$	−5.27556	−	1.92015i	−0.316978	−	0.115370i	0.178632	−	0.983916i	$-0.442833\pi$
$277$	−5.27556	−	1.92015i	−0.316978	−	0.115370i	−0.495609	+	0.868546i	$0.665055\pi$
$278$		0			0
$279$	−7.08031	+	10.0008i	−0.423887	+	0.598730i
$280$		0			0
$281$	2.00723	+	2.39212i	0.119741	+	0.142702i	0.822585	−	0.568642i	$-0.192531\pi$
$281$	2.00723	+	2.39212i	0.119741	+	0.142702i	−0.702844	+	0.711344i	$0.748087\pi$
$282$		0			0
$283$	21.4582	+	3.78366i	1.27556	+	0.224915i	0.770093	−	0.637932i	$-0.220210\pi$
$283$	21.4582	+	3.78366i	1.27556	+	0.224915i	0.505465	+	0.862847i	$0.331321\pi$
$284$		0			0
$285$	−2.83342	+	3.67280i	−0.167837	+	0.217558i
$286$		0			0
$287$	13.8000	−	2.00011i	0.814587	−	0.118063i
$288$		0			0
$289$	−10.4949	−	18.1777i	−0.617347	−	1.06928i
$290$		0			0
$291$	−21.7133	+	4.75460i	−1.27286	+	0.278719i
$292$		0			0
$293$	18.2717	−	6.65034i	1.06744	−	0.388517i	0.252222	−	0.967669i	$-0.418839\pi$
$293$	18.2717	−	6.65034i	1.06744	−	0.388517i	0.815219	+	0.579153i	$0.196616\pi$
$294$		0			0
$295$	5.62804	+	31.9182i	0.327677	+	1.85835i
$296$		0			0
$297$	17.6098	+	16.3906i	1.02182	+	0.951080i
$298$		0			0
$299$	1.34880	+	7.64945i	0.0780033	+	0.442379i
$300$		0			0
$301$	0.0557537	+	0.0345058i	0.00321359	+	0.00198888i
$302$		0			0
$303$	1.09727	−	1.00023i	0.0630363	−	0.0574616i
$304$		0			0
$305$	33.2421	−	19.1923i	1.90344	−	1.09895i
$306$		0			0
$307$	16.1729	+	9.33744i	0.923038	+	0.532916i	0.884603	−	0.466345i	$-0.154429\pi$
$307$	16.1729	+	9.33744i	0.923038	+	0.532916i	0.0384347	+	0.999261i	$0.487763\pi$
$308$		0			0
$309$	−2.73705	−	6.65667i	−0.155705	−	0.378685i
$310$		0			0
$311$	−1.33576	+	7.57549i	−0.0757442	+	0.429567i	0.923229	+	0.384251i	$0.125540\pi$
$311$	−1.33576	+	7.57549i	−0.0757442	+	0.429567i	−0.998973	+	0.0453154i	$0.985571\pi$
$312$		0			0
$313$	−7.85538	−	9.36168i	−0.444012	−	0.529153i	0.496898	−	0.867809i	$-0.334472\pi$
$313$	−7.85538	−	9.36168i	−0.444012	−	0.529153i	−0.940910	+	0.338656i	$0.890028\pi$
$314$		0			0
$315$	31.3158	−	7.20056i	1.76444	−	0.405705i
$316$		0			0
$317$	5.16733	−	14.1971i	0.290226	−	0.797390i	−0.705807	−	0.708405i	$-0.749415\pi$
$317$	5.16733	−	14.1971i	0.290226	−	0.797390i	0.996033	−	0.0889857i	$-0.0283625\pi$
$318$		0			0
$319$	4.57059	+	3.83518i	0.255904	+	0.214729i
$320$		0			0
$321$	28.8287	+	15.1026i	1.60906	+	0.842944i
$322$		0			0
$323$		−	4.07747i		−	0.226876i
$324$		0			0
$325$			11.7066i			0.649368i
$326$		0			0
$327$	−2.45069	+	4.67802i	−0.135523	+	0.258695i
$328$		0			0
$329$	0.908541	−	29.6820i	0.0500895	−	1.63642i
$330$		0			0
$331$	33.0748	+	12.0382i	1.81796	+	0.661682i	0.995708	+	0.0925533i	$0.0295028\pi$
$331$	33.0748	+	12.0382i	1.81796	+	0.661682i	0.822248	+	0.569129i	$0.192719\pi$
$332$		0			0
$333$	−18.1026	+	1.48907i	−0.992018	+	0.0816004i
$334$		0			0
$335$	−13.4908	+	11.3201i	−0.737080	+	0.618484i
$336$		0			0
$337$	−0.277303	+	1.57266i	−0.0151057	+	0.0856684i	−0.991429	−	0.130650i	$-0.958294\pi$
$337$	−0.277303	+	1.57266i	−0.0151057	+	0.0856684i	0.976323	+	0.216318i	$0.0694048\pi$
$338$		0			0
$339$	−8.51522	−	20.7095i	−0.462483	−	1.12479i
$340$		0			0
$341$	9.45522	−	16.3769i	0.512029	−	0.886860i
$342$		0			0
$343$	15.1226	+	10.6914i	0.816544	+	0.577283i
$344$		0			0
$345$	35.6971	+	39.1603i	1.92187	+	2.10832i
$346$		0			0
$347$	4.42153	+	12.1480i	0.237360	+	0.652141i	0.999986	+	0.00530153i	$0.00168754\pi$
$347$	4.42153	+	12.1480i	0.237360	+	0.652141i	−0.762626	+	0.646840i	$0.776090\pi$
$348$		0			0
$349$	−13.3627	+	2.35621i	−0.715289	+	0.126125i	−0.519437	−	0.854509i	$-0.673858\pi$
$349$	−13.3627	+	2.35621i	−0.715289	+	0.126125i	−0.195852	+	0.980633i	$0.562747\pi$
$350$		0			0
$351$	5.33387	+	0.274535i	0.284701	+	0.0146536i
$352$		0			0
$353$	2.10572	+	11.9422i	0.112076	+	0.635617i	0.988156	+	0.153451i	$0.0490387\pi$
$353$	2.10572	+	11.9422i	0.112076	+	0.635617i	−0.876080	+	0.482166i	$0.839850\pi$
$354$		0			0
$355$	14.6106	+	40.1423i	0.775450	+	2.13053i
$356$		0			0
$357$	−17.9288	+	21.8253i	−0.948893	+	1.15512i
$358$		0			0
$359$	−0.939857	+	0.542627i	−0.0496038	+	0.0286387i	−0.524597	−	0.851351i	$-0.675784\pi$
$359$	−0.939857	+	0.542627i	−0.0496038	+	0.0286387i	0.474993	+	0.879990i	$0.342451\pi$
$360$		0			0
$361$	−9.28118	+	16.0755i	−0.488483	+	0.846078i
$362$		0			0
$363$	−14.3110	−	11.0404i	−0.751132	−	0.579469i
$364$		0			0
$365$	−30.7802	−	5.42738i	−1.61111	−	0.284082i
$366$		0			0
$367$	7.39708	+	8.81550i	0.386124	+	0.460165i	0.923737	−	0.383027i	$-0.125118\pi$
$367$	7.39708	+	8.81550i	0.386124	+	0.460165i	−0.537613	+	0.843192i	$0.680674\pi$
$368$		0			0
$369$	14.3643	−	6.60758i	0.747777	−	0.343977i
$370$		0			0
$371$	11.7031	−	3.85839i	0.607597	−	0.200318i
$372$		0			0
$373$	3.96810	+	3.32963i	0.205460	+	0.172402i	0.739712	−	0.672924i	$-0.234962\pi$
$373$	3.96810	+	3.32963i	0.205460	+	0.172402i	−0.534251	+	0.845326i	$0.679406\pi$
$374$		0			0
$375$	23.9737	+	37.8478i	1.23800	+	1.95445i
$376$		0			0
$377$	1.32461			0.0682208
$378$		0			0
$379$	12.0526			0.619100			0.309550	−	0.950883i	$-0.399822\pi$
$379$	12.0526			0.619100			0.309550	+	0.950883i	$0.399822\pi$
$380$		0			0
$381$	−21.5945	+	0.886652i	−1.10632	+	0.0454245i
$382$		0			0
$383$	−2.77860	−	2.33153i	−0.141980	−	0.119135i	0.569032	−	0.822316i	$-0.307318\pi$
$383$	−2.77860	−	2.33153i	−0.141980	−	0.119135i	−0.711012	+	0.703180i	$0.751763\pi$
$384$		0			0
$385$	−47.0966	+	15.5272i	−2.40026	+	0.791339i
$386$		0			0
$387$	0.0717126	+	0.0196151i	0.00364535	+	0.000997093i
$388$		0			0
$389$	0.674280	+	0.803575i	0.0341873	+	0.0407429i	0.782867	−	0.622189i	$-0.213756\pi$
$389$	0.674280	+	0.803575i	0.0341873	+	0.0407429i	−0.748680	+	0.662932i	$0.769312\pi$
$390$		0			0
$391$	−45.8700	−	8.08811i	−2.31974	−	0.409033i
$392$		0			0
$393$	−0.931149	+	6.93358i	−0.0469703	+	0.349753i
$394$		0			0
$395$	26.7706	−	46.3681i	1.34698	−	2.33303i
$396$		0			0
$397$	−6.55070	+	3.78205i	−0.328770	+	0.189816i	−0.655295	−	0.755373i	$-0.727456\pi$
$397$	−6.55070	+	3.78205i	−0.328770	+	0.189816i	0.326525	+	0.945189i	$0.394122\pi$
$398$		0			0
$399$	−2.83776	+	1.06653i	−0.142066	+	0.0533933i
$400$		0			0
$401$	10.9897	+	30.1939i	0.548798	+	1.50781i	0.835335	+	0.549741i	$0.185273\pi$
$401$	10.9897	+	30.1939i	0.548798	+	1.50781i	−0.286538	+	0.958069i	$0.592504\pi$
$402$		0			0
$403$	−0.729023	−	4.13449i	−0.0363152	−	0.205954i
$404$		0			0
$405$	31.7415	−	17.8889i	1.57725	−	0.888906i
$406$		0			0
$407$	27.6059	−	4.86767i	1.36838	−	0.241281i
$408$		0			0
$409$	−3.10609	−	8.53392i	−0.153586	−	0.421975i	0.838907	−	0.544275i	$-0.183195\pi$
$409$	−3.10609	−	8.53392i	−0.153586	−	0.421975i	−0.992493	+	0.122300i	$0.960973\pi$
$410$		0			0
$411$	−2.97854	+	9.36188i	−0.146921	+	0.461787i
$412$		0			0
$413$	−7.85005	+	19.6731i	−0.386276	+	0.968049i
$414$		0			0
$415$	24.5756	−	42.5663i	1.20637	−	2.08950i
$416$		0			0
$417$	−8.50316	−	1.14194i	−0.416401	−	0.0559209i
$418$		0			0
$419$	2.24013	−	12.7044i	0.109438	−	0.620652i	−0.879917	−	0.475127i	$-0.842402\pi$
$419$	2.24013	−	12.7044i	0.109438	−	0.620652i	0.989355	−	0.145524i	$-0.0464869\pi$
$420$		0			0
$421$	0.352709	−	0.295958i	0.0171900	−	0.0144241i	−0.634152	−	0.773208i	$-0.718651\pi$
$421$	0.352709	−	0.295958i	0.0171900	−	0.0144241i	0.651342	+	0.758784i	$0.274206\pi$
$422$		0			0
$423$	−8.54590	−	32.5695i	−0.415516	−	1.58358i
$424$		0			0
$425$	−65.9654	−	24.0095i	−3.19979	−	1.16463i
$426$		0			0
$427$	25.0740	+	0.767492i	1.21341	+	0.0371416i
$428$		0			0
$429$	−8.23562	+	0.338147i	−0.397619	+	0.0163259i
$430$		0			0
$431$		−	20.4220i		−	0.983692i	−0.870682	−	0.491846i	$-0.836322\pi$
$431$		−	20.4220i		−	0.983692i	0.870682	−	0.491846i	$-0.163678\pi$
$432$		0			0
$433$			33.0304i			1.58734i	0.608348	+	0.793670i	$0.291832\pi$
$433$			33.0304i			1.58734i	−0.608348	+	0.793670i	$0.708168\pi$
$434$		0			0
$435$	7.63377	−	4.83542i	0.366011	−	0.231841i
$436$		0			0
$437$	−3.82961	−	3.21342i	−0.183195	−	0.153719i
$438$		0			0
$439$	−10.2339	+	28.1173i	−0.488436	+	1.34197i	0.413659	+	0.910432i	$0.364250\pi$
$439$	−10.2339	+	28.1173i	−0.488436	+	1.34197i	−0.902096	+	0.431536i	$0.857972\pi$
$440$		0			0
$441$	19.8792	+	6.76899i	0.946626	+	0.322333i
$442$		0			0
$443$	−12.8851	−	15.3558i	−0.612188	−	0.729577i	0.367518	−	0.930016i	$-0.380208\pi$
$443$	−12.8851	−	15.3558i	−0.612188	−	0.729577i	−0.979706	+	0.200439i	$0.935763\pi$
$444$		0			0
$445$	5.85105	−	33.1829i	0.277366	−	1.57302i
$446$		0			0
$447$	8.73696	−	11.3252i	0.413244	−	0.535664i
$448$		0			0
$449$	−8.29511	−	4.78919i	−0.391471	−	0.226016i	0.291327	−	0.956624i	$-0.405903\pi$
$449$	−8.29511	−	4.78919i	−0.391471	−	0.226016i	−0.682797	+	0.730608i	$0.739237\pi$
$450$		0			0
$451$	−21.1320	+	12.2006i	−0.995066	+	0.574502i
$452$		0			0
$453$	3.68694	+	16.8375i	0.173228	+	0.791097i
$454$		0			0
$455$	−5.79384	+	9.36156i	−0.271619	+	0.438877i
$456$		0			0
$457$	4.78858	+	27.1574i	0.224000	+	1.27037i	0.864587	+	0.502482i	$0.167580\pi$
$457$	4.78858	+	27.1574i	0.224000	+	1.27037i	−0.640587	+	0.767885i	$0.721309\pi$
$458$		0			0
$459$	−12.4863	+	29.4926i	−0.582813	+	1.37660i
$460$		0			0
$461$	−3.71831	−	21.0876i	−0.173179	−	0.982148i	−0.940225	−	0.340555i	$-0.889385\pi$
$461$	−3.71831	−	21.0876i	−0.173179	−	0.982148i	0.767046	−	0.641593i	$-0.221726\pi$
$462$		0			0
$463$	39.1651	−	14.2549i	1.82015	−	0.662482i	0.824888	−	0.565296i	$-0.191238\pi$
$463$	39.1651	−	14.2549i	1.82015	−	0.662482i	0.995266	−	0.0971866i	$-0.0309844\pi$
$464$		0			0
$465$	−19.2942	−	21.1660i	−0.894745	−	0.981549i
$466$		0			0
$467$	7.48605	+	12.9662i	0.346413	+	0.600005i	0.985609	−	0.169039i	$-0.0540663\pi$
$467$	7.48605	+	12.9662i	0.346413	+	0.600005i	−0.639196	+	0.769043i	$0.720733\pi$
$468$		0			0
$469$	−11.3904	+	1.65087i	−0.525958	+	0.0762301i
$470$		0			0
$471$	3.59294	+	8.73826i	0.165554	+	0.402638i
$472$		0			0
$473$	−0.112995	−	0.0199240i	−0.00519551	−	0.000916108i
$474$		0			0
$475$	−4.84308	−	5.77176i	−0.222216	−	0.264827i
$476$		0			0
$477$	11.4873	−	7.95486i	0.525965	−	0.364228i
$478$		0			0
$479$	31.1422	+	11.3348i	1.42292	+	0.517902i	0.934894	−	0.354926i	$-0.115494\pi$
$479$	31.1422	+	11.3348i	1.42292	+	0.517902i	0.488029	+	0.872828i	$0.337716\pi$
$480$		0			0
$481$	4.00025	−	4.76732i	0.182396	−	0.217371i
$482$		0			0
$483$	6.36904	+	34.0393i	0.289801	+	1.54884i
$484$		0			0
$485$		−	51.9536i		−	2.35909i
$486$		0			0
$487$	−28.0871			−1.27275			−0.636374	−	0.771380i	$-0.719567\pi$
$487$	−28.0871			−1.27275			−0.636374	+	0.771380i	$0.719567\pi$
$488$		0			0
$489$	12.6970	−	24.2369i	0.574180	−	1.09603i
$490$		0			0
$491$	19.4627	−	23.1947i	0.878339	−	1.04676i	−0.120201	−	0.992750i	$-0.538354\pi$
$491$	19.4627	−	23.1947i	0.878339	−	1.04676i	0.998540	−	0.0540139i	$-0.0172015\pi$
$492$		0			0
$493$	−2.71667	+	7.46400i	−0.122353	+	0.336162i
$494$		0			0
$495$	−46.2278	+	32.0125i	−2.07778	+	1.43885i
$496$		0			0
$497$	−5.68682	+	27.3327i	−0.255089	+	1.22604i
$498$		0			0
$499$	−3.23627	+	18.3538i	−0.144875	+	0.821629i	0.822592	+	0.568632i	$0.192527\pi$
$499$	−3.23627	+	18.3538i	−0.144875	+	0.821629i	−0.967467	+	0.252997i	$0.918584\pi$
$500$		0			0
$501$	−5.89589	+	2.42424i	−0.263409	+	0.108307i
$502$		0			0
$503$	−7.36361	+	12.7541i	−0.328327	+	0.568679i	−0.982180	−	0.187942i	$-0.939818\pi$
$503$	−7.36361	+	12.7541i	−0.328327	+	0.568679i	0.653853	+	0.756622i	$0.273152\pi$
$504$		0			0
$505$	1.73516	+	3.00539i	0.0772137	+	0.133738i
$506$		0			0
$507$	15.2881	−	13.9361i	0.678969	−	0.618924i
$508$		0			0
$509$	−15.0505	+	5.47795i	−0.667103	+	0.242806i	−0.653300	−	0.757099i	$-0.726616\pi$
$509$	−15.0505	+	5.47795i	−0.667103	+	0.242806i	−0.0138031	+	0.999905i	$0.504394\pi$
$510$		0			0
$511$	−15.2384	−	13.6023i	−0.674107	−	0.601732i
$512$		0			0
$513$	−2.74335	+	2.07129i	−0.121122	+	0.0914496i
$514$		0			0
$515$	16.5671	−	2.92123i	0.730035	−	0.128725i
$516$		0			0
$517$	17.7732	+	48.8315i	0.781665	+	2.14761i
$518$		0			0
$519$	−7.72729	−	35.2890i	−0.339190	−	1.54902i
$520$		0			0
$521$	−6.20935	−	10.7549i	−0.272037	−	0.471181i	0.697347	−	0.716734i	$-0.254364\pi$
$521$	−6.20935	−	10.7549i	−0.272037	−	0.471181i	−0.969383	+	0.245553i	$0.921031\pi$
$522$		0			0
$523$	−10.8234	−	6.24887i	−0.473272	−	0.273244i	0.244336	−	0.969691i	$-0.421430\pi$
$523$	−10.8234	−	6.24887i	−0.473272	−	0.273244i	−0.717609	+	0.696447i	$0.754763\pi$
$524$		0			0
$525$	0.544696	+	52.1895i	0.0237725	+	2.27774i
$526$		0			0
$527$	24.7925	+	4.37159i	1.07998	+	0.190429i
$528$		0			0
$529$	−26.1272	+	21.9233i	−1.13597	+	0.953188i
$530$		0			0
$531$	−2.21751	+	23.9149i	−0.0962319	+	1.03782i
$532$		0			0
$533$	−1.85281	+	5.09055i	−0.0802540	+	0.220496i
$534$		0			0
$535$	−48.8960	+	58.2719i	−2.11396	+	2.51932i
$536$		0			0
$537$	17.1270	−	10.8487i	0.739084	−	0.468154i
$538$		0			0
$539$	−31.5126	−	7.56925i	−1.35734	−	0.326031i
$540$		0			0
$541$	−32.8528			−1.41245			−0.706227	−	0.707986i	$-0.749604\pi$
$541$	−32.8528			−1.41245			−0.706227	+	0.707986i	$0.749604\pi$
$542$		0			0
$543$	1.19247	+	29.0428i	0.0511739	+	1.24635i
$544$		0			0
$545$	−9.45574	−	7.93431i	−0.405040	−	0.339868i
$546$		0			0
$547$	14.0005	+	5.09577i	0.598618	+	0.217879i	0.623516	−	0.781811i	$-0.285704\pi$
$547$	14.0005	+	5.09577i	0.598618	+	0.217879i	−0.0248975	+	0.999690i	$0.507926\pi$
$548$		0			0
$549$	27.5132	−	7.21917i	1.17423	−	0.308107i
$550$		0			0
$551$	−0.653075	+	0.547995i	−0.0278220	+	0.0233454i
$552$		0			0
$553$	30.8242	−	16.5602i	1.31078	−	0.704212i
$554$		0			0
$555$	5.65075	−	42.0770i	0.239861	−	1.78607i
$556$		0			0
$557$	6.67432	+	3.85342i	0.282800	+	0.163275i	0.634690	−	0.772767i	$-0.281128\pi$
$557$	6.67432	+	3.85342i	0.282800	+	0.163275i	−0.351890	+	0.936041i	$0.614461\pi$
$558$		0			0
$559$	−0.0220601	+	0.0127364i	−0.000933041	+	0.000538692i
$560$		0			0
$561$	14.9852	−	47.1002i	0.632677	−	1.98857i
$562$		0			0
$563$	−13.2290	+	4.81495i	−0.557535	+	0.202926i	−0.605391	−	0.795928i	$-0.706983\pi$
$563$	−13.2290	+	4.81495i	−0.557535	+	0.202926i	0.0478564	+	0.998854i	$0.484761\pi$
$564$		0			0
$565$	51.5419	−	9.08823i	2.16838	−	0.382345i
$566$		0			0
$567$	23.7918	+	0.975728i	0.999160	+	0.0409767i
$568$		0			0
$569$	−19.4187	+	3.42404i	−0.814074	+	0.143543i	−0.565159	−	0.824982i	$-0.691185\pi$
$569$	−19.4187	+	3.42404i	−0.814074	+	0.143543i	−0.248915	+	0.968525i	$0.580074\pi$
$570$		0			0
$571$	−14.4323	+	5.25292i	−0.603972	+	0.219828i	−0.625864	−	0.779933i	$-0.715253\pi$
$571$	−14.4323	+	5.25292i	−0.603972	+	0.219828i	0.0218917	+	0.999760i	$0.493031\pi$
$572$		0			0
$573$	6.73340	−	21.1638i	0.281292	−	0.884131i
$574$		0			0
$575$	−74.5369	+	43.0339i	−3.10840	+	1.79464i
$576$		0			0
$577$	17.7565	+	10.2517i	0.739213	+	0.426785i	0.821783	−	0.569800i	$-0.192979\pi$
$577$	17.7565	+	10.2517i	0.739213	+	0.426785i	−0.0825699	+	0.996585i	$0.526313\pi$
$578$		0			0
$579$	2.01734	−	15.0216i	0.0838376	−	0.624277i
$580$		0			0
$581$	28.2969	−	15.2024i	1.17395	−	0.630703i
$582$		0			0
$583$	−16.5188	+	13.8610i	−0.684141	+	0.574062i
$584$		0			0
$585$	−3.29356	+	12.0412i	−0.136172	+	0.497842i
$586$		0			0
$587$	24.3540	+	8.86414i	1.00520	+	0.365862i	0.791587	−	0.611057i	$-0.209255\pi$
$587$	24.3540	+	8.86414i	1.00520	+	0.365862i	0.213611	+	0.976919i	$0.431477\pi$
$588$		0			0
$589$	2.06989	+	1.73684i	0.0852882	+	0.0715653i
$590$		0			0
$591$	−1.13954	−	27.7536i	−0.0468743	−	1.14163i
$592$		0			0
$593$	−24.4037			−1.00214			−0.501071	−	0.865406i	$-0.667060\pi$
$593$	−24.4037			−1.00214			−0.501071	+	0.865406i	$0.667060\pi$
$594$		0			0
$595$	−40.8685	−	51.8474i	−1.67544	−	2.12554i
$596$		0			0
$597$	2.50780	−	1.58850i	0.102637	−	0.0650131i
$598$		0			0
$599$	1.01854	−	1.21385i	0.0416164	−	0.0495964i	−0.744835	−	0.667249i	$-0.767472\pi$
$599$	1.01854	−	1.21385i	0.0416164	−	0.0495964i	0.786451	+	0.617653i	$0.211916\pi$
$600$		0			0
$601$	0.505039	−	1.38758i	0.0206010	−	0.0566007i	−0.928966	−	0.370165i	$-0.879301\pi$
$601$	0.505039	−	1.38758i	0.0206010	−	0.0566007i	0.949567	+	0.313565i	$0.101523\pi$
$602$		0			0
$603$	−11.8562	+	5.45383i	−0.482821	+	0.222097i
$604$		0			0
$605$	32.3627	−	27.1555i	1.31573	−	1.10403i
$606$		0			0
$607$	10.6242	+	1.87333i	0.431222	+	0.0760361i	0.385046	−	0.922897i	$-0.374185\pi$
$607$	10.6242	+	1.87333i	0.431222	+	0.0760361i	0.0461757	+	0.998933i	$0.485297\pi$
$608$		0			0
$609$	5.90525	−	0.0616324i	0.239293	−	0.00249747i
$610$		0			0
$611$	9.99111	+	5.76837i	0.404197	+	0.233363i
$612$		0			0
$613$	−11.2338	−	19.4575i	−0.453728	−	0.785880i	0.544886	−	0.838510i	$-0.316573\pi$
$613$	−11.2338	−	19.4575i	−0.453728	−	0.785880i	−0.998614	+	0.0526300i	$0.983240\pi$
$614$		0			0
$615$	7.90500	+	36.1006i	0.318760	+	1.45572i
$616$		0			0
$617$	−13.4452	−	36.9405i	−0.541285	−	1.48717i	−0.845190	−	0.534466i	$-0.820513\pi$
$617$	−13.4452	−	36.9405i	−0.541285	−	1.48717i	0.303905	−	0.952702i	$-0.401710\pi$
$618$		0			0
$619$	20.4496	−	3.60582i	0.821940	−	0.144930i	0.253165	−	0.967423i	$-0.418529\pi$
$619$	20.4496	−	3.60582i	0.821940	−	0.144930i	0.568775	+	0.822493i	$0.307417\pi$
$620$		0			0
$621$	17.8595	+	34.9703i	0.716675	+	1.40331i
$622$		0			0
$623$	14.6641	−	16.4279i	0.587506	−	0.658171i
$624$		0			0
$625$	−44.8889	+	16.3382i	−1.79556	+	0.653529i
$626$		0			0
$627$	3.92054	−	3.57382i	0.156571	−	0.142725i
$628$		0			0
$629$	18.6590	+	32.3183i	0.743983	+	1.28862i
$630$		0			0
$631$	17.0835	−	29.5895i	0.680083	−	1.17794i	−0.294873	−	0.955537i	$-0.595277\pi$
$631$	17.0835	−	29.5895i	0.680083	−	1.17794i	0.974955	−	0.222401i	$-0.0713895\pi$
$632$		0			0
$633$	−11.2297	+	4.61736i	−0.446340	+	0.183523i
$634$		0			0
$635$	8.77201	−	49.7485i	0.348107	−	1.97421i
$636$		0			0
$637$	−6.43945	+	3.20969i	−0.255140	+	0.127172i
$638$		0			0
$639$	2.59517	+	31.5495i	0.102663	+	1.24808i
$640$		0			0
$641$	−2.22136	+	6.10314i	−0.0877385	+	0.241059i	−0.975800	−	0.218665i	$-0.929830\pi$
$641$	−2.22136	+	6.10314i	−0.0877385	+	0.241059i	0.888061	+	0.459725i	$0.152052\pi$
$642$		0			0
$643$	17.2666	−	20.5776i	0.680930	−	0.811501i	−0.309297	−	0.950965i	$-0.600094\pi$
$643$	17.2666	−	20.5776i	0.680930	−	0.811501i	0.990227	+	0.139465i	$0.0445382\pi$
$644$		0			0
$645$	−0.0806394	+	0.153929i	−0.00317517	+	0.00606097i
$646$		0			0
$647$	11.7625			0.462430			0.231215	−	0.972903i	$-0.425730\pi$
$647$	11.7625			0.462430			0.231215	+	0.972903i	$0.425730\pi$
$648$		0			0
$649$		−	37.0657i		−	1.45496i
$650$		0			0
$651$	−3.44244	−	18.3981i	−0.134920	−	0.721079i
$652$		0			0
$653$	16.4947	−	19.6577i	0.645489	−	0.769264i	−0.339737	−	0.940520i	$-0.610338\pi$
$653$	16.4947	−	19.6577i	0.645489	−	0.769264i	0.985227	+	0.171256i	$0.0547826\pi$
$654$		0			0
$655$	−15.3654	−	5.59255i	−0.600377	−	0.218519i
$656$		0			0
$657$	−20.9401	−	9.89726i	−0.816950	−	0.386129i
$658$		0			0
$659$	27.6717	+	32.9778i	1.07794	+	1.28463i	0.956404	+	0.292046i	$0.0943361\pi$
$659$	27.6717	+	32.9778i	1.07794	+	1.28463i	0.121531	+	0.992588i	$0.461219\pi$
$660$		0			0
$661$	−17.6874	−	3.11877i	−0.687961	−	0.121306i	−0.181269	−	0.983434i	$-0.558021\pi$
$661$	−17.6874	−	3.11877i	−0.687961	−	0.121306i	−0.506691	+	0.862128i	$0.669132\pi$
$662$		0			0
$663$	−4.17288	−	10.1487i	−0.162061	−	0.394143i
$664$		0			0
$665$	−1.01636	−	7.01249i	−0.0394127	−	0.271933i
$666$		0			0
$667$	4.86929	+	8.43386i	0.188540	+	0.326560i
$668$		0			0
$669$	12.4376	+	13.6442i	0.480866	+	0.527517i
$670$		0			0
$671$	−41.2505	+	15.0140i	−1.59246	+	0.579608i
$672$		0			0
$673$	−4.14578	−	23.5119i	−0.159808	−	0.906317i	−0.954257	−	0.298987i	$-0.903351\pi$
$673$	−4.14578	−	23.5119i	−0.159808	−	0.906317i	0.794449	−	0.607331i	$-0.207760\pi$
$674$		0			0
$675$	17.3556	+	56.5785i	0.668019	+	2.17771i
$676$		0			0
$677$	2.31306	+	13.1180i	0.0888982	+	0.504167i	0.996447	+	0.0842205i	$0.0268400\pi$
$677$	2.31306	+	13.1180i	0.0888982	+	0.504167i	−0.907549	+	0.419946i	$0.862049\pi$
$678$		0			0
$679$	17.8684	−	28.8714i	0.685727	−	1.10798i
$680$		0			0
$681$	−1.15777	−	5.28733i	−0.0443660	−	0.202611i
$682$		0			0
$683$	−4.92769	+	2.84500i	−0.188553	+	0.108861i	−0.591305	−	0.806448i	$-0.701387\pi$
$683$	−4.92769	+	2.84500i	−0.188553	+	0.108861i	0.402752	+	0.915309i	$0.368054\pi$
$684$		0			0
$685$	−19.8862	−	11.4813i	−0.759811	−	0.438677i
$686$		0			0
$687$	8.75907	−	11.3539i	0.334179	−	0.433177i
$688$		0			0
$689$	−0.831314	+	4.71462i	−0.0316705	+	0.179613i
$690$		0			0
$691$	−9.04506	−	10.7795i	−0.344090	−	0.410071i	0.566050	−	0.824371i	$-0.308471\pi$
$691$	−9.04506	−	10.7795i	−0.344090	−	0.410071i	−0.910140	+	0.414300i	$0.864026\pi$
$692$		0			0
$693$	−36.6995	+	1.89069i	−1.39410	+	0.0718214i
$694$		0			0
$695$	6.85856	−	18.8437i	0.260160	−	0.714784i
$696$		0			0
$697$	−24.8846	−	20.8807i	−0.942572	−	0.790912i
$698$		0			0
$699$	−40.4109	+	25.5973i	−1.52848	+	0.968179i
$700$		0			0
$701$			3.91747i			0.147961i	0.997260	+	0.0739804i	$0.0235702\pi$
$701$			3.91747i			0.147961i	−0.997260	+	0.0739804i	$0.976430\pi$
$702$		0			0
$703$			4.00536i			0.151065i
$704$		0			0
$705$	78.6363	−	3.22874i	2.96161	−	0.121601i
$706$		0			0
$707$	−0.0693883	+	2.26691i	−0.00260961	+	0.0852561i
$708$		0			0
$709$	31.7056	+	11.5399i	1.19073	+	0.433390i	0.859979	−	0.510329i	$-0.170476\pi$
$709$	31.7056	+	11.5399i	1.19073	+	0.433390i	0.330749	+	0.943719i	$0.392699\pi$
$710$		0			0
$711$	28.2006	−	27.9092i	1.05761	−	1.04667i
$712$		0			0
$713$	23.6447	−	19.8402i	0.885499	−	0.743022i
$714$		0			0
$715$	3.34543	−	18.9729i	0.125112	−	0.709545i
$716$		0			0
$717$	1.26965	+	0.170508i	0.0474159	+	0.00636775i
$718$		0			0
$719$	2.83359	−	4.90792i	0.105675	−	0.183035i	−0.808339	−	0.588718i	$-0.799633\pi$
$719$	2.83359	−	4.90792i	0.105675	−	0.183035i	0.914014	+	0.405683i	$0.132966\pi$
$720$		0			0
$721$	10.2113	+	4.07456i	0.380289	+	0.151745i
$722$		0			0
$723$	15.1525	−	47.6258i	0.563526	−	1.77122i
$724$		0			0
$725$	5.01997	+	13.7923i	0.186437	+	0.512232i
$726$		0			0
$727$	12.2640	−	2.16248i	0.454848	−	0.0802020i	0.0584696	−	0.998289i	$-0.481378\pi$
$727$	12.2640	−	2.16248i	0.454848	−	0.0802020i	0.396378	+	0.918087i	$0.370267\pi$
$728$		0			0
$729$	26.1857	−	6.58088i	0.969842	−	0.243736i
$730$		0			0
$731$	−0.0265243	−	0.150427i	−0.000981038	−	0.00556375i
$732$		0			0
$733$	−7.54590	−	20.7322i	−0.278714	−	0.765761i	−0.997509	−	0.0705387i	$-0.977528\pi$
$733$	−7.54590	−	20.7322i	−0.278714	−	0.765761i	0.718795	−	0.695222i	$-0.244694\pi$
$734$		0			0
$735$	−25.3940	+	42.0044i	−0.936671	+	1.54936i
$736$		0			0
$737$	17.4421	−	10.0702i	0.642489	−	0.370941i
$738$		0			0
$739$	−7.58135	+	13.1313i	−0.278885	+	0.483042i	−0.971108	−	0.238641i	$-0.923298\pi$
$739$	−7.58135	+	13.1313i	−0.278885	+	0.483042i	0.692223	+	0.721683i	$0.256631\pi$
$740$		0			0
$741$	0.156759	−	1.16727i	0.00575870	−	0.0428808i
$742$		0			0
$743$	−9.78300	−	1.72501i	−0.358904	−	0.0632844i	−0.00871090	−	0.999962i	$-0.502773\pi$
$743$	−9.78300	−	1.72501i	−0.358904	−	0.0632844i	−0.350193	+	0.936678i	$0.613884\pi$
$744$		0			0
$745$	21.4899	+	25.6107i	0.787329	+	0.938302i
$746$		0			0
$747$	25.8884	−	25.6208i	0.947207	−	0.937417i
$748$		0			0
$749$	−47.2137	+	15.5658i	−1.72515	+	0.568762i
$750$		0			0
$751$	−10.6006	−	8.89495i	−0.386821	−	0.324581i	0.428552	−	0.903517i	$-0.359024\pi$
$751$	−10.6006	−	8.89495i	−0.386821	−	0.324581i	−0.815373	+	0.578936i	$0.803468\pi$
$752$		0			0
$753$	6.62652	−	0.272079i	0.241484	−	0.00991512i
$754$		0			0
$755$	−40.2873			−1.46621
$756$		0			0
$757$	45.3818			1.64943			0.824715	−	0.565549i	$-0.191336\pi$
$757$	45.3818			1.64943			0.824715	+	0.565549i	$0.191336\pi$
$758$		0			0
$759$	−32.4273	−	51.1936i	−1.17704	−	1.85821i
$760$		0			0
$761$	−8.74236	−	7.33571i	−0.316910	−	0.265919i	0.470431	−	0.882437i	$-0.344099\pi$
$761$	−8.74236	−	7.33571i	−0.316910	−	0.265919i	−0.787341	+	0.616517i	$0.788543\pi$
$762$		0			0
$763$	−2.52585	−	7.66134i	−0.0914420	−	0.277359i
$764$		0			0
$765$	−61.0958	−	43.2544i	−2.20892	−	1.56387i
$766$		0			0
$767$	−5.28943	−	6.30370i	−0.190990	−	0.227613i
$768$		0			0
$769$	−23.2518	−	4.09993i	−0.838483	−	0.147847i	−0.262114	−	0.965037i	$-0.584420\pi$
$769$	−23.2518	−	4.09993i	−0.838483	−	0.147847i	−0.576369	+	0.817190i	$0.695531\pi$
$770$		0			0
$771$	−3.18067	−	2.45376i	−0.114549	−	0.0883702i
$772$		0			0
$773$	0.943664	−	1.63447i	0.0339412	−	0.0587879i	−0.848556	−	0.529106i	$-0.822527\pi$
$773$	0.943664	−	1.63447i	0.0339412	−	0.0587879i	0.882497	+	0.470318i	$0.155861\pi$
$774$		0			0
$775$	40.2869	−	23.2596i	1.44715	−	0.835511i
$776$		0			0
$777$	17.6118	−	21.4394i	0.631818	−	0.769133i
$778$		0			0
$779$	−1.19248	−	3.27632i	−0.0427251	−	0.117386i
$780$		0			0
$781$	−8.48345	−	48.1120i	−0.303562	−	1.72158i
$782$		0			0
$783$	6.40186	−	1.96379i	0.228784	−	0.0701802i
$784$		0			0
$785$	−21.7478	+	3.83472i	−0.776212	+	0.136867i
$786$		0			0
$787$	−17.8609	−	49.0725i	−0.636673	−	1.74925i	−0.661931	−	0.749565i	$-0.730263\pi$
$787$	−17.8609	−	49.0725i	−0.636673	−	1.74925i	0.0252580	−	0.999681i	$-0.491959\pi$
$788$		0			0
$789$	25.1351	+	27.5736i	0.894834	+	0.981646i
$790$		0			0
$791$	31.7684	+	12.6764i	1.12955	+	0.450720i
$792$		0			0
$793$	−4.87285	+	8.44002i	−0.173040	+	0.299714i
$794$		0			0
$795$	12.4196	+	30.2052i	0.440477	+	1.07127i
$796$		0			0
$797$	2.91356	−	16.5236i	0.103204	−	0.585297i	−0.888719	−	0.458452i	$-0.848404\pi$
$797$	2.91356	−	16.5236i	0.103204	−	0.585297i	0.991923	−	0.126845i	$-0.0404850\pi$
$798$		0			0
$799$	−52.9951	+	44.4681i	−1.87483	+	1.57317i
$800$		0			0
$801$	10.6698	−	22.5746i	0.377000	−	0.797636i
$802$		0			0
$803$	33.5886	+	12.2253i	1.18532	+	0.431420i
$804$		0			0
$805$	−80.9039	−	2.47640i	−2.85149	−	0.0872815i
$806$		0			0
$807$	19.4213	−	37.0725i	0.683661	−	1.30501i
$808$		0			0
$809$		−	47.3759i		−	1.66565i	−0.553539	−	0.832823i	$-0.686723\pi$
$809$		−	47.3759i		−	1.66565i	0.553539	−	0.832823i	$-0.313277\pi$
$810$		0			0
$811$			6.90776i			0.242564i	0.992618	+	0.121282i	$0.0387005\pi$
$811$			6.90776i			0.242564i	−0.992618	+	0.121282i	$0.961299\pi$
$812$		0			0
$813$	14.1942	+	7.43594i	0.497812	+	0.260790i
$814$		0			0
$815$	48.9903	+	41.1078i	1.71606	+	1.43994i
$816$		0			0
$817$	0.00560725	−	0.0154058i	0.000196173	−	0.000538980i
$818$		0			0
$819$	−5.97162	+	5.55873i	−0.208665	+	0.194238i
$820$		0			0
$821$	20.0394	+	23.8820i	0.699378	+	0.833487i	0.992456	−	0.122602i	$-0.0391239\pi$
$821$	20.0394	+	23.8820i	0.699378	+	0.833487i	−0.293078	+	0.956089i	$0.594679\pi$
$822$		0			0
$823$	−7.49025	+	42.4793i	−0.261094	+	1.48074i	0.518839	+	0.854872i	$0.326364\pi$
$823$	−7.49025	+	42.4793i	−0.261094	+	1.48074i	−0.779933	+	0.625864i	$0.784747\pi$
$824$		0			0
$825$	−34.7321	−	84.4704i	−1.20921	−	2.94088i
$826$		0			0
$827$	−35.8895	−	20.7208i	−1.24800	−	0.720534i	−0.277290	−	0.960786i	$-0.589436\pi$
$827$	−35.8895	−	20.7208i	−1.24800	−	0.720534i	−0.970710	+	0.240253i	$0.922770\pi$
$828$		0			0
$829$	−15.7101	+	9.07025i	−0.545636	+	0.315023i	−0.747360	−	0.664419i	$-0.768679\pi$
$829$	−15.7101	+	9.07025i	−0.545636	+	0.315023i	0.201724	+	0.979442i	$0.435346\pi$
$830$		0			0
$831$	7.18629	−	6.55077i	0.249290	−	0.227244i
$832$		0			0
$833$	−4.87934	−	42.8683i	−0.169059	−	1.48530i
$834$		0			0
$835$	−2.58737	−	14.6737i	−0.0895395	−	0.507804i
$836$		0			0
$837$	−9.65296	−	18.9013i	−0.333655	−	0.653324i
$838$		0			0
$839$	−0.840845	−	4.76867i	−0.0290292	−	0.164633i	0.966847	−	0.255357i	$-0.0821929\pi$
$839$	−0.840845	−	4.76867i	−0.0290292	−	0.164633i	−0.995876	+	0.0907242i	$0.971082\pi$
$840$		0			0
$841$	−25.6905	+	9.35057i	−0.885879	+	0.322434i
$842$		0			0
$843$	−5.28347	+	1.15693i	−0.181972	+	0.0398467i
$844$		0			0
$845$	24.1759	+	41.8738i	0.831675	+	1.44050i
$846$		0			0
$847$	27.3240	−	3.96023i	0.938865	−	0.136075i
$848$		0			0
$849$	−23.0524	+	29.8814i	−0.791155	+	1.02553i
$850$		0			0
$851$	45.0588	+	7.94508i	1.54460	+	0.272354i
$852$		0			0
$853$	−11.2460	−	13.4025i	−0.385056	−	0.458892i	0.538347	−	0.842723i	$-0.319049\pi$
$853$	−11.2460	−	13.4025i	−0.385056	−	0.458892i	−0.923403	+	0.383831i	$0.874604\pi$
$854$		0			0
$855$	−3.35766	−	7.29926i	−0.114829	−	0.249630i
$856$		0			0
$857$	18.9752	+	6.90641i	0.648181	+	0.235918i	0.645125	−	0.764077i	$-0.276805\pi$
$857$	18.9752	+	6.90641i	0.648181	+	0.235918i	0.00305543	+	0.999995i	$0.499027\pi$
$858$		0			0
$859$	26.1910	−	31.2132i	0.893626	−	1.06498i	−0.103893	−	0.994588i	$-0.533130\pi$
$859$	26.1910	−	31.2132i	0.893626	−	1.06498i	0.997519	−	0.0703937i	$-0.0224255\pi$
$860$		0			0
$861$	−8.02317	+	22.7804i	−0.273429	+	0.776355i
$862$		0			0
$863$			40.9808i			1.39500i	0.716583	+	0.697501i	$0.245705\pi$
$863$			40.9808i			1.39500i	−0.716583	+	0.697501i	$0.754295\pi$
$864$		0			0
$865$	84.4364			2.87092
$866$		0			0
$867$	36.3248	−	1.49146i	1.23365	−	0.0506528i
$868$		0			0
$869$	−39.3588	+	46.9060i	−1.33515	+	1.59118i
$870$		0			0
$871$	1.52929	−	4.20169i	0.0518180	−	0.142369i
$872$		0			0
$873$	10.1575	−	37.1355i	0.343778	−	1.25685i
$874$		0			0
$875$	−67.0009	−	13.9401i	−2.26504	−	0.471263i
$876$		0			0
$877$	−0.504033	+	2.85852i	−0.0170200	+	0.0965252i	−0.992134	−	0.125177i	$-0.960050\pi$
$877$	−0.504033	+	2.85852i	−0.0170200	+	0.0965252i	0.975114	+	0.221702i	$0.0711613\pi$
$878$		0			0
$879$	−4.48263	+	33.3788i	−0.151195	+	1.12584i
$880$		0			0
$881$	17.2219	−	29.8293i	0.580222	−	1.00497i	−0.415231	−	0.909716i	$-0.636299\pi$
$881$	17.2219	−	29.8293i	0.580222	−	1.00497i	0.995453	−	0.0952573i	$-0.0303674\pi$
$882$		0			0
$883$	24.0492	+	41.6545i	0.809320	+	1.40178i	0.913335	+	0.407208i	$0.133498\pi$
$883$	24.0492	+	41.6545i	0.809320	+	1.40178i	−0.104015	+	0.994576i	$0.533169\pi$
$884$		0			0
$885$	−53.4945	−	17.0196i	−1.79820	−	0.572109i
$886$		0			0
$887$	−23.6967	+	8.62489i	−0.795657	+	0.289596i	−0.707686	−	0.706527i	$-0.750261\pi$
$887$	−23.6967	+	8.62489i	−0.795657	+	0.289596i	−0.0879716	+	0.996123i	$0.528038\pi$
$888$		0			0
$889$	21.9848	−	24.6291i	0.737346	−	0.826032i
$890$		0			0
$891$	−39.3016	+	13.8440i	−1.31665	+	0.463790i
$892$		0			0
$893$	−7.31234	+	1.28936i	−0.244698	+	0.0431469i
$894$		0			0
$895$	16.2071	+	44.5288i	0.541745	+	1.48843i
$896$		0			0
$897$	−12.8204	−	4.07889i	−0.428061	−	0.136190i
$898$		0			0
$899$	−2.63183	−	4.55846i	−0.0877765	−	0.152033i
$900$		0			0
$901$	−24.8613	−	14.3537i	−0.828250	−	0.478190i
$902$		0			0
$903$	−0.0977536	+	0.0578066i	−0.00325304	+	0.00192368i
$904$		0			0
$905$	−66.9077	−	11.7976i	−2.22409	−	0.392166i
$906$		0			0
$907$	10.8964	−	9.14315i	0.361808	−	0.303593i	−0.443703	−	0.896174i	$-0.646335\pi$
$907$	10.8964	−	9.14315i	0.361808	−	0.303593i	0.805511	+	0.592581i	$0.201891\pi$
$908$		0			0
$909$	0.652679	+	2.48744i	0.0216480	+	0.0825032i
$910$		0			0
$911$	−12.1984	+	33.5149i	−0.404152	+	1.11040i	0.556064	+	0.831140i	$0.312311\pi$
$911$	−12.1984	+	33.5149i	−0.404152	+	1.11040i	−0.960216	+	0.279259i	$0.909911\pi$
$912$		0			0
$913$	−36.1317	+	43.0601i	−1.19578	+	1.42508i
$914$		0			0
$915$	2.72748	+	66.4282i	0.0901679	+	2.19605i
$916$		0			0
$917$	−6.61535	−	8.39250i	−0.218458	−	0.277145i
$918$		0			0
$919$	20.7729			0.685234			0.342617	−	0.939475i	$-0.388687\pi$
$919$	20.7729			0.685234			0.342617	+	0.939475i	$0.388687\pi$
$920$		0			0
$921$	−27.3253	+	17.3085i	−0.900398	+	0.570335i
$922$		0			0
$923$	−8.30855	−	6.97170i	−0.273479	−	0.229476i
$924$		0			0
$925$	64.7989	+	23.5849i	2.13058	+	0.775466i
$926$		0			0
$927$	12.4130	+	1.15100i	0.407697	+	0.0378038i
$928$		0			0
$929$	6.67675	−	5.60246i	0.219057	−	0.183811i	−0.526655	−	0.850079i	$-0.676554\pi$
$929$	6.67675	−	5.60246i	0.219057	−	0.183811i	0.745712	+	0.666268i	$0.232109\pi$
$930$		0			0
$931$	1.84700	−	4.24650i	0.0605330	−	0.139174i
$932$		0			0
$933$	−10.5492	−	8.13829i	−0.345365	−	0.266436i
$934$		0			0
$935$	100.048	+	57.7630i	3.27193	+	1.88905i
$936$		0			0
$937$	−24.4284	+	14.1037i	−0.798040	+	0.460749i	−0.842785	−	0.538250i	$-0.819086\pi$
$937$	−24.4284	+	14.1037i	−0.798040	+	0.460749i	0.0447454	+	0.998998i	$0.485752\pi$
$938$		0			0
$939$	20.6771	−	4.52770i	0.674773	−	0.147756i
$940$		0			0
$941$	44.0689	−	16.0398i	1.43661	−	0.522882i	0.497788	−	0.867299i	$-0.334146\pi$
$941$	44.0689	−	16.0398i	1.43661	−	0.522882i	0.938817	+	0.344417i	$0.111923\pi$
$942$		0			0
$943$	−39.2228	+	6.91603i	−1.27727	+	0.225217i
$944$		0			0
$945$	−14.1228	+	53.8342i	−0.459414	+	1.75123i
$946$		0			0
$947$	−41.6131	+	7.33752i	−1.35225	+	0.238437i	−0.802379	−	0.596815i	$-0.796432\pi$
$947$	−41.6131	+	7.33752i	−1.35225	+	0.238437i	−0.549866	+	0.835253i	$0.685321\pi$
$948$		0			0
$949$	7.45695	−	2.71411i	0.242063	−	0.0881037i
$950$		0			0
$951$	17.6289	+	19.3391i	0.571655	+	0.627115i
$952$		0			0
$953$	1.27681	−	0.737169i	0.0413600	−	0.0238792i	−0.479177	−	0.877718i	$-0.659065\pi$
$953$	1.27681	−	0.737169i	0.0413600	−	0.0238792i	0.520537	+	0.853839i	$0.325732\pi$
$954$		0			0
$955$	44.9554	+	25.9550i	1.45472	+	0.839884i
$956$		0			0
$957$	−9.55784	+	3.92994i	−0.308961	+	0.127037i
$958$		0			0
$959$	−7.10229	−	13.2198i	−0.229345	−	0.426889i
$960$		0			0
$961$	10.9675	−	9.20286i	0.353792	−	0.296867i
$962$		0			0
$963$	−46.3427	+	32.0921i	−1.49337	+	1.03415i
$964$		0			0
$965$	33.2892	+	12.1163i	1.07162	+	0.390037i
$966$		0			0
$967$	22.0801	+	18.5274i	0.710048	+	0.595801i	0.924613	−	0.380909i	$-0.124389\pi$
$967$	22.0801	+	18.5274i	0.710048	+	0.595801i	−0.214565	+	0.976710i	$0.568833\pi$
$968$		0			0
$969$	6.25592	+	3.27730i	0.200969	+	0.105282i
$970$		0			0
$971$	9.63311			0.309141			0.154571	−	0.987982i	$-0.450601\pi$
$971$	9.63311			0.309141			0.154571	+	0.987982i	$0.450601\pi$
$972$		0			0
$973$	10.2923	−	8.11289i	0.329957	−	0.260087i
$974$		0			0
$975$	−17.9611	−	9.40933i	−0.575216	−	0.301340i
$976$		0			0
$977$	30.8435	−	36.7578i	0.986771	−	1.17599i	0.00237858	−	0.999997i	$-0.499243\pi$
$977$	30.8435	−	36.7578i	0.986771	−	1.17599i	0.984392	−	0.175990i	$-0.0563127\pi$
$978$		0			0
$979$	−13.1796	+	36.2105i	−0.421220	+	1.15729i
$980$		0			0
$981$	−5.20756	−	7.52000i	−0.166265	−	0.240095i
$982$		0			0
$983$	14.2939	−	11.9940i	0.455904	−	0.382549i	−0.385717	−	0.922617i	$-0.626046\pi$
$983$	14.2939	−	11.9940i	0.455904	−	0.382549i	0.841621	+	0.540068i	$0.181601\pi$
$984$		0			0
$985$	63.9375	+	11.2739i	2.03722	+	0.359217i
$986$		0			0
$987$	44.8099	+	25.2512i	1.42631	+	0.803753i
$988$		0			0
$989$	−0.162187	−	0.0936385i	−0.00515723	−	0.00297753i
$990$		0			0
$991$	−3.00254	−	5.20055i	−0.0953787	−	0.165201i	0.814388	−	0.580321i	$-0.197073\pi$
$991$	−3.00254	−	5.20055i	−0.0953787	−	0.165201i	−0.909767	+	0.415120i	$0.863740\pi$
$992$		0			0
$993$	−45.0541	+	41.0697i	−1.42975	+	1.30331i
$994$		0			0
$995$	2.37311	+	6.52008i	0.0752328	+	0.206700i
$996$		0			0
$997$	46.9380	−	8.27643i	1.48654	−	0.262117i	0.629352	−	0.777120i	$-0.283320\pi$
$997$	46.9380	−	8.27643i	1.48654	−	0.262117i	0.857188	+	0.515003i	$0.172209\pi$
$998$		0			0
$999$	12.2655	−	28.9711i	0.388065	−	0.916605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bx.a.41.8	✓	144
7.6	odd	2	inner	756.2.bx.a.41.17	yes	144
27.2	odd	18	inner	756.2.bx.a.461.17	yes	144
189.83	even	18	inner	756.2.bx.a.461.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bx.a.41.8	✓	144	1.1	even	1	trivial
756.2.bx.a.41.17	yes	144	7.6	odd	2	inner
756.2.bx.a.461.8	yes	144	189.83	even	18	inner
756.2.bx.a.461.17	yes	144	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bx (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.803760 + 1.53427i) q^{3} +(-3.10123 - 2.60224i) q^{5} +(-0.828412 - 2.51271i) q^{7} +(-1.70794 - 2.46636i) q^{9} +O(q^{10})\)	\(q+(-0.803760 + 1.53427i) q^{3} +(-3.10123 - 2.60224i) q^{5} +(-0.828412 - 2.51271i) q^{7} +(-1.70794 - 2.46636i) q^{9} +(2.97600 + 3.54666i) q^{11} +(1.01225 + 0.178487i) q^{13} +(6.48518 - 2.66654i) q^{15} +(-3.08179 + 5.33782i) q^{17} +(-0.572912 + 0.330771i) q^{19} +(4.52102 + 0.748614i) q^{21} +(2.58461 + 7.10116i) q^{23} +(1.97773 + 11.2163i) q^{25} +(5.15683 - 0.638074i) q^{27} +(1.26912 - 0.223781i) q^{29} +(-1.39697 - 3.83815i) q^{31} +(-7.83352 + 1.71532i) q^{33} +(-3.96959 + 9.94824i) q^{35} +(3.02730 - 5.24343i) q^{37} +(-1.08745 + 1.40960i) q^{39} +(-0.915195 + 5.19033i) q^{41} +(-0.0189843 + 0.0159297i) q^{43} +(-1.12135 + 12.0932i) q^{45} +(10.5471 + 3.83884i) q^{47} +(-5.62747 + 4.16313i) q^{49} +(-5.71262 - 9.01861i) q^{51} +4.65757i q^{53} -18.7433i q^{55} +(-0.0470069 - 1.14486i) q^{57} +(-6.13282 - 5.14605i) q^{59} +(-3.24287 + 8.90971i) q^{61} +(-4.78238 + 6.33473i) q^{63} +(-2.67475 - 3.18764i) q^{65} +(0.755393 - 4.28405i) q^{67} +(-12.9725 - 1.74214i) q^{69} +(-9.13833 - 5.27602i) q^{71} +(6.68607 - 3.86020i) q^{73} +(-18.7984 - 5.98082i) q^{75} +(6.44639 - 10.4159i) q^{77} +(2.29656 + 13.0245i) q^{79} +(-3.16587 + 8.42480i) q^{81} +(2.10826 + 11.9566i) q^{83} +(23.4477 - 8.53425i) q^{85} +(-0.676731 + 2.12704i) q^{87} +(4.16153 + 7.20798i) q^{89} +(-0.390072 - 2.69135i) q^{91} +(7.01156 + 0.941622i) q^{93} +(2.63748 + 0.465058i) q^{95} +(8.24903 + 9.83081i) q^{97} +(3.66451 - 13.3974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} - 30 q^{21} + 48 q^{23} + 12 q^{29} - 27 q^{35} - 42 q^{39} + 18 q^{49} + 18 q^{51} + 30 q^{57} - 15 q^{63} + 42 q^{65} + 36 q^{71} - 51 q^{77} + 36 q^{79} + 18 q^{81} + 36 q^{85} + 9 q^{91} + 96 q^{93} - 48 q^{95} + 36 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 - 30 * q^21 + 48 * q^23 + 12 * q^29 - 27 * q^35 - 42 * q^39 + 18 * q^49 + 18 * q^51 + 30 * q^57 - 15 * q^63 + 42 * q^65 + 36 * q^71 - 51 * q^77 + 36 * q^79 + 18 * q^81 + 36 * q^85 + 9 * q^91 + 96 * q^93 - 48 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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