LMFDB - Embedded newform 756.2.ck.a.605.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (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			605.17
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06196 + 1.36830i) q^{3} +(0.449866 + 2.55131i) q^{5} +(-2.53584 + 0.754675i) q^{7} +(-0.744465 + 2.90616i) q^{9} +O(q^{10})$	\(q+(1.06196 + 1.36830i) q^{3} +(0.449866 + 2.55131i) q^{5} +(-2.53584 + 0.754675i) q^{7} +(-0.744465 + 2.90616i) q^{9} +(3.32853 + 0.586909i) q^{11} +(-0.718420 - 0.856180i) q^{13} +(-3.01321 + 3.32495i) q^{15} -2.35421 q^{17} +0.116725i q^{19} +(-3.72559 - 2.66833i) q^{21} +(-0.0811022 - 0.0966538i) q^{23} +(-1.60836 + 0.585397i) q^{25} +(-4.76708 + 2.06759i) q^{27} +(-1.74633 + 2.08119i) q^{29} +(0.400779 - 1.10113i) q^{31} +(2.73171 + 5.17769i) q^{33} +(-3.06620 - 6.13021i) q^{35} +(-5.12795 + 8.88188i) q^{37} +(0.408570 - 1.89224i) q^{39} +(2.53395 - 2.12623i) q^{41} +(-2.39884 + 0.873106i) q^{43} +(-7.74944 - 0.591981i) q^{45} +(7.71339 - 2.80744i) q^{47} +(5.86093 - 3.82747i) q^{49} +(-2.50009 - 3.22126i) q^{51} +(-8.17694 - 4.72096i) q^{53} +8.75615i q^{55} +(-0.159715 + 0.123958i) q^{57} +(6.49318 - 5.44842i) q^{59} +(1.60136 + 4.39971i) q^{61} +(-0.305368 - 7.93138i) q^{63} +(1.86119 - 2.21808i) q^{65} +(1.57661 + 8.94138i) q^{67} +(0.0461234 - 0.213615i) q^{69} +(7.05686 - 4.07428i) q^{71} +(9.72113 - 5.61250i) q^{73} +(-2.50902 - 1.57905i) q^{75} +(-8.88353 + 1.02365i) q^{77} +(-2.45450 + 13.9202i) q^{79} +(-7.89155 - 4.32707i) q^{81} +(9.54729 + 8.01113i) q^{83} +(-1.05908 - 6.00634i) q^{85} +(-4.70223 - 0.179341i) q^{87} -0.407850 q^{89} +(2.46793 + 1.62896i) q^{91} +(1.93229 - 0.620978i) q^{93} +(-0.297803 + 0.0525107i) q^{95} +(2.76618 + 7.60002i) q^{97} +(-4.18362 + 9.23631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.06196	+	1.36830i	0.613125	+	0.789986i
$3$	1.06196	+	1.36830i	0.613125	+	0.789986i
$4$		0			0
$5$	0.449866	+	2.55131i	0.201186	+	1.14098i	0.903330	+	0.428947i	$0.141115\pi$
$5$	0.449866	+	2.55131i	0.201186	+	1.14098i	−0.702144	+	0.712035i	$0.747774\pi$
$6$		0			0
$7$	−2.53584	+	0.754675i	−0.958456	+	0.285240i
$7$	−2.53584	+	0.754675i	−0.958456	+	0.285240i
$8$		0			0
$9$	−0.744465	+	2.90616i	−0.248155	+	0.968720i
$10$		0			0
$11$	3.32853	+	0.586909i	1.00359	+	0.176960i	0.651210	−	0.758898i	$-0.274262\pi$
$11$	3.32853	+	0.586909i	1.00359	+	0.176960i	0.352379	+	0.935857i	$0.385373\pi$
$12$		0			0
$13$	−0.718420	−	0.856180i	−0.199254	−	0.237462i	0.657160	−	0.753751i	$-0.271757\pi$
$13$	−0.718420	−	0.856180i	−0.199254	−	0.237462i	−0.856414	+	0.516289i	$0.827313\pi$
$14$		0			0
$15$	−3.01321	+	3.32495i	−0.778008	+	0.858499i
$16$		0			0
$17$	−2.35421			−0.570981			−0.285490	−	0.958382i	$-0.592156\pi$
$17$	−2.35421			−0.570981			−0.285490	+	0.958382i	$0.592156\pi$
$18$		0			0
$19$			0.116725i			0.0267786i	0.999910	+	0.0133893i	$0.00426208\pi$
$19$			0.116725i			0.0267786i	−0.999910	+	0.0133893i	$0.995738\pi$
$20$		0			0
$21$	−3.72559	−	2.66833i	−0.812989	−	0.582278i
$22$		0			0
$23$	−0.0811022	−	0.0966538i	−0.0169110	−	0.0201537i	0.757523	−	0.652809i	$-0.226410\pi$
$23$	−0.0811022	−	0.0966538i	−0.0169110	−	0.0201537i	−0.774434	+	0.632655i	$0.781965\pi$
$24$		0			0
$25$	−1.60836	+	0.585397i	−0.321673	+	0.117079i
$26$		0			0
$27$	−4.76708	+	2.06759i	−0.917425	+	0.397908i
$28$		0			0
$29$	−1.74633	+	2.08119i	−0.324285	+	0.386468i	−0.903415	−	0.428767i	$-0.858948\pi$
$29$	−1.74633	+	2.08119i	−0.324285	+	0.386468i	0.579130	+	0.815235i	$0.303392\pi$
$30$		0			0
$31$	0.400779	−	1.10113i	0.0719821	−	0.197769i	−0.898484	−	0.439006i	$-0.855331\pi$
$31$	0.400779	−	1.10113i	0.0719821	−	0.197769i	0.970466	+	0.241237i	$0.0775530\pi$
$32$		0			0
$33$	2.73171	+	5.17769i	0.475530	+	0.901319i
$34$		0			0
$35$	−3.06620	−	6.13021i	−0.518282	−	1.03620i
$36$		0			0
$37$	−5.12795	+	8.88188i	−0.843031	+	1.46017i	0.0442901	+	0.999019i	$0.485897\pi$
$37$	−5.12795	+	8.88188i	−0.843031	+	1.46017i	−0.887321	+	0.461153i	$0.847436\pi$
$38$		0			0
$39$	0.408570	−	1.89224i	0.0654236	−	0.303001i
$40$		0			0
$41$	2.53395	−	2.12623i	0.395736	−	0.332062i	−0.423107	−	0.906080i	$-0.639060\pi$
$41$	2.53395	−	2.12623i	0.395736	−	0.332062i	0.818843	+	0.574018i	$0.194616\pi$
$42$		0			0
$43$	−2.39884	+	0.873106i	−0.365819	+	0.133147i	−0.518388	−	0.855146i	$-0.673468\pi$
$43$	−2.39884	+	0.873106i	−0.365819	+	0.133147i	0.152569	+	0.988293i	$0.451245\pi$
$44$		0			0
$45$	−7.74944	−	0.591981i	−1.15522	−	0.0882474i
$46$		0			0
$47$	7.71339	−	2.80744i	1.12511	−	0.409508i	0.288597	−	0.957451i	$-0.406811\pi$
$47$	7.71339	−	2.80744i	1.12511	−	0.409508i	0.836516	+	0.547943i	$0.184589\pi$
$48$		0			0
$49$	5.86093	−	3.82747i	0.837276	−	0.546781i
$50$		0			0
$51$	−2.50009	−	3.22126i	−0.350083	−	0.451067i
$52$		0			0
$53$	−8.17694	−	4.72096i	−1.12319	−	0.648473i	−0.180976	−	0.983488i	$-0.557925\pi$
$53$	−8.17694	−	4.72096i	−1.12319	−	0.648473i	−0.942213	+	0.335014i	$0.891259\pi$
$54$		0			0
$55$			8.75615i			1.18068i
$56$		0			0
$57$	−0.159715	+	0.123958i	−0.0211547	+	0.0164187i
$58$		0			0
$59$	6.49318	−	5.44842i	0.845340	−	0.709324i	−0.113419	−	0.993547i	$-0.536180\pi$
$59$	6.49318	−	5.44842i	0.845340	−	0.709324i	0.958758	+	0.284223i	$0.0917357\pi$
$60$		0			0
$61$	1.60136	+	4.39971i	0.205033	+	0.563325i	0.999003	−	0.0446321i	$-0.0142115\pi$
$61$	1.60136	+	4.39971i	0.205033	+	0.563325i	−0.793970	+	0.607957i	$0.791989\pi$
$62$		0			0
$63$	−0.305368	−	7.93138i	−0.0384728	−	0.999260i
$64$		0			0
$65$	1.86119	−	2.21808i	0.230852	−	0.275119i
$66$		0			0
$67$	1.57661	+	8.94138i	0.192613	+	1.09236i	0.915777	+	0.401687i	$0.131576\pi$
$67$	1.57661	+	8.94138i	0.192613	+	1.09236i	−0.723164	+	0.690677i	$0.757313\pi$
$68$		0			0
$69$	0.0461234	−	0.213615i	0.00555260	−	0.0257162i
$70$		0			0
$71$	7.05686	−	4.07428i	0.837495	−	0.483528i	−0.0189167	−	0.999821i	$-0.506022\pi$
$71$	7.05686	−	4.07428i	0.837495	−	0.483528i	0.856412	+	0.516293i	$0.172688\pi$
$72$		0			0
$73$	9.72113	−	5.61250i	1.13777	−	0.656893i	0.191894	−	0.981416i	$-0.438537\pi$
$73$	9.72113	−	5.61250i	1.13777	−	0.656893i	0.945878	+	0.324523i	$0.105204\pi$
$74$		0			0
$75$	−2.50902	−	1.57905i	−0.289717	−	0.182333i
$76$		0			0
$77$	−8.88353	+	1.02365i	−1.01237	+	0.116656i
$78$		0			0
$79$	−2.45450	+	13.9202i	−0.276153	+	1.56614i	0.459122	+	0.888373i	$0.348164\pi$
$79$	−2.45450	+	13.9202i	−0.276153	+	1.56614i	−0.735275	+	0.677769i	$0.762947\pi$
$80$		0			0
$81$	−7.89155	−	4.32707i	−0.876838	−	0.480785i
$82$		0			0
$83$	9.54729	+	8.01113i	1.04795	+	0.879336i	0.992877	−	0.119147i	$-0.0380159\pi$
$83$	9.54729	+	8.01113i	1.04795	+	0.879336i	0.0550746	+	0.998482i	$0.482460\pi$
$84$		0			0
$85$	−1.05908	−	6.00634i	−0.114873	−	0.651479i
$86$		0			0
$87$	−4.70223	−	0.179341i	−0.504132	−	0.0192273i
$88$		0			0
$89$	−0.407850			−0.0432321			−0.0216160	−	0.999766i	$-0.506881\pi$
$89$	−0.407850			−0.0432321			−0.0216160	+	0.999766i	$0.506881\pi$
$90$		0			0
$91$	2.46793	+	1.62896i	0.258710	+	0.170761i
$92$		0			0
$93$	1.93229	−	0.620978i	0.200369	−	0.0643925i
$94$		0			0
$95$	−0.297803	+	0.0525107i	−0.0305540	+	0.00538749i
$96$		0			0
$97$	2.76618	+	7.60002i	0.280863	+	0.771665i	0.997260	+	0.0739724i	$0.0235677\pi$
$97$	2.76618	+	7.60002i	0.280863	+	0.771665i	−0.716397	+	0.697693i	$0.754210\pi$
$98$		0			0
$99$	−4.18362	+	9.23631i	−0.420470	+	0.928284i
$100$		0			0
$101$	−8.69458	−	7.29562i	−0.865143	−	0.725941i	0.0979265	−	0.995194i	$-0.468779\pi$
$101$	−8.69458	−	7.29562i	−0.865143	−	0.725941i	−0.963070	+	0.269252i	$0.913223\pi$
$102$		0			0
$103$	15.4152	−	2.71812i	1.51891	−	0.267824i	0.648903	−	0.760871i	$-0.275228\pi$
$103$	15.4152	−	2.71812i	1.51891	−	0.267824i	0.870003	+	0.493047i	$0.164117\pi$
$104$		0			0
$105$	5.13175	−	10.7055i	0.500807	−	1.04475i
$106$		0			0
$107$	−6.44745	+	3.72244i	−0.623298	+	0.359862i	−0.778152	−	0.628076i	$-0.783843\pi$
$107$	−6.44745	+	3.72244i	−0.623298	+	0.359862i	0.154854	+	0.987937i	$0.450509\pi$
$108$		0			0
$109$	−8.47513	+	14.6794i	−0.811770	+	1.40603i	0.0998542	+	0.995002i	$0.468162\pi$
$109$	−8.47513	+	14.6794i	−0.811770	+	1.40603i	−0.911624	+	0.411025i	$0.865171\pi$
$110$		0			0
$111$	−17.5987	+	2.41568i	−1.67040	+	0.229286i
$112$		0			0
$113$	0.327903	−	0.900905i	0.0308465	−	0.0847500i	−0.923313	−	0.384047i	$-0.874530\pi$
$113$	0.327903	−	0.900905i	0.0308465	−	0.0847500i	0.954160	+	0.299297i	$0.0967522\pi$
$114$		0			0
$115$	0.210109	−	0.250398i	0.0195928	−	0.0233498i
$116$		0			0
$117$	3.02303	−	1.45045i	0.279480	−	0.134094i
$118$		0			0
$119$	5.96990	−	1.77667i	0.547260	−	0.162867i
$120$		0			0
$121$	0.398017	+	0.144866i	0.0361834	+	0.0131697i
$122$		0			0
$123$	5.60028	+	1.20920i	0.504960	+	0.109030i
$124$		0			0
$125$	4.25960	+	7.37785i	0.380990	+	0.659895i
$126$		0			0
$127$	2.30393	−	3.99052i	0.204441	−	0.354102i	−0.745514	−	0.666490i	$-0.767796\pi$
$127$	2.30393	−	3.99052i	0.204441	−	0.354102i	0.949954	+	0.312389i	$0.101129\pi$
$128$		0			0
$129$	−3.74215	−	2.35511i	−0.329478	−	0.207356i
$130$		0			0
$131$	15.6483	−	13.1305i	1.36720	−	1.14721i	0.393512	−	0.919320i	$-0.371260\pi$
$131$	15.6483	−	13.1305i	1.36720	−	1.14721i	0.973686	−	0.227895i	$-0.0731843\pi$
$132$		0			0
$133$	−0.0880897	−	0.295996i	−0.00763835	−	0.0256661i
$134$		0			0
$135$	−7.41962	−	11.2322i	−0.638579	−	0.966713i
$136$		0			0
$137$	4.84629	+	13.3151i	0.414046	+	1.13758i	0.955019	+	0.296543i	$0.0958339\pi$
$137$	4.84629	+	13.3151i	0.414046	+	1.13758i	−0.540973	+	0.841040i	$0.681944\pi$
$138$		0			0
$139$	18.1091	−	3.19312i	1.53599	−	0.270837i	0.659298	−	0.751882i	$-0.270854\pi$
$139$	18.1091	−	3.19312i	1.53599	−	0.270837i	0.876696	+	0.481045i	$0.159743\pi$
$140$		0			0
$141$	12.0327	+	7.57279i	1.01334	+	0.637744i
$142$		0			0
$143$	−1.88878	−	3.27147i	−0.157948	−	0.273574i
$144$		0			0
$145$	−6.09539	−	3.51918i	−0.506195	−	0.292252i
$146$		0			0
$147$	11.4612	+	3.95485i	0.945304	+	0.326191i
$148$		0			0
$149$	6.37358	−	17.5113i	0.522144	−	1.43458i	−0.345985	−	0.938240i	$-0.612455\pi$
$149$	6.37358	−	17.5113i	0.522144	−	1.43458i	0.868129	−	0.496338i	$-0.165322\pi$
$150$		0			0
$151$	1.85223	−	10.5045i	0.150733	−	0.854847i	−0.811852	−	0.583864i	$-0.801540\pi$
$151$	1.85223	−	10.5045i	0.150733	−	0.854847i	0.962584	−	0.270983i	$-0.0873487\pi$
$152$		0			0
$153$	1.75263	−	6.84172i	0.141692	−	0.553121i
$154$		0			0
$155$	2.98963	+	0.527153i	0.240133	+	0.0423419i
$156$		0			0
$157$	3.30641	+	3.94043i	0.263881	+	0.314481i	0.881673	−	0.471860i	$-0.156417\pi$
$157$	3.30641	+	3.94043i	0.263881	+	0.314481i	−0.617793	+	0.786341i	$0.711973\pi$
$158$		0			0
$159$	−2.22395	−	16.2020i	−0.176371	−	1.28490i
$160$		0			0
$161$	0.278604	+	0.183892i	0.0219571	+	0.0144928i
$162$		0			0
$163$	1.26560	+	2.19209i	0.0991296	+	0.171697i	0.911325	−	0.411689i	$-0.135061\pi$
$163$	1.26560	+	2.19209i	0.0991296	+	0.171697i	−0.812195	+	0.583386i	$0.801727\pi$
$164$		0			0
$165$	−11.9810	+	9.29872i	−0.932720	+	0.723904i
$166$		0			0
$167$	−6.21832	−	2.26328i	−0.481188	−	0.175138i	0.0900259	−	0.995939i	$-0.471305\pi$
$167$	−6.21832	−	2.26328i	−0.481188	−	0.175138i	−0.571214	+	0.820801i	$0.693527\pi$
$168$		0			0
$169$	2.04051	−	11.5723i	0.156962	−	0.890177i
$170$		0			0
$171$	−0.339223	−	0.0868979i	−0.0259410	−	0.00664525i
$172$		0			0
$173$	−8.20343	−	6.88349i	−0.623695	−	0.523342i	0.275267	−	0.961368i	$-0.411234\pi$
$173$	−8.20343	−	6.88349i	−0.623695	−	0.523342i	−0.898963	+	0.438025i	$0.855678\pi$
$174$		0			0
$175$	3.63676	−	2.69826i	0.274914	−	0.203970i
$176$		0			0
$177$	14.3506	+	3.09855i	1.07866	+	0.232902i
$178$		0			0
$179$		−	4.62241i		−	0.345495i	−0.984966	−	0.172748i	$-0.944735\pi$
$179$		−	4.62241i		−	0.345495i	0.984966	−	0.172748i	$-0.0552645\pi$
$180$		0			0
$181$	9.48331	+	5.47519i	0.704889	+	0.406968i	0.809166	−	0.587580i	$-0.199919\pi$
$181$	9.48331	+	5.47519i	0.704889	+	0.406968i	−0.104277	+	0.994548i	$0.533253\pi$
$182$		0			0
$183$	−4.31951	+	6.86347i	−0.319307	+	0.507362i
$184$		0			0
$185$	−24.9674	−	9.08737i	−1.83564	−	0.668117i
$186$		0			0
$187$	−7.83607	−	1.38171i	−0.573030	−	0.101041i
$188$		0			0
$189$	10.5282	−	8.84067i	0.765812	−	0.643064i
$190$		0			0
$191$	19.4111	+	3.42270i	1.40454	+	0.247658i	0.824007	−	0.566579i	$-0.191733\pi$
$191$	19.4111	+	3.42270i	1.40454	+	0.247658i	0.580532	+	0.814237i	$0.302845\pi$
$192$		0			0
$193$	−20.8024	−	7.57147i	−1.49739	−	0.545006i	−0.542008	−	0.840373i	$-0.682336\pi$
$193$	−20.8024	−	7.57147i	−1.49739	−	0.545006i	−0.955384	+	0.295367i	$0.904558\pi$
$194$		0			0
$195$	5.01151	+	0.191137i	0.358882	+	0.0136876i
$196$		0			0
$197$	1.74551	+	1.00777i	0.124363	+	0.0718008i	0.560891	−	0.827890i	$-0.310459\pi$
$197$	1.74551	+	1.00777i	0.124363	+	0.0718008i	−0.436528	+	0.899691i	$0.643792\pi$
$198$		0			0
$199$		−	3.72542i		−	0.264088i	−0.991244	−	0.132044i	$-0.957846\pi$
$199$		−	3.72542i		−	0.264088i	0.991244	−	0.132044i	$-0.0421540\pi$
$200$		0			0
$201$	−10.5602	+	11.6527i	−0.744856	+	0.821917i
$202$		0			0
$203$	2.85778	−	6.59548i	0.200577	−	0.462912i
$204$		0			0
$205$	6.56463	+	5.50838i	0.458493	+	0.384722i
$206$		0			0
$207$	0.341269	−	0.163741i	0.0237199	−	0.0113808i
$208$		0			0
$209$	−0.0685072	+	0.388524i	−0.00473874	+	0.0268747i
$210$		0			0
$211$	4.81139	+	1.75120i	0.331229	+	0.120558i	0.502281	−	0.864704i	$-0.332494\pi$
$211$	4.81139	+	1.75120i	0.331229	+	0.120558i	−0.171052	+	0.985262i	$0.554717\pi$
$212$		0			0
$213$	13.0690	+	5.32913i	0.895470	+	0.365146i
$214$		0			0
$215$	−3.30672	−	5.72741i	−0.225517	−	0.390606i
$216$		0			0
$217$	−0.185313	+	3.09475i	−0.0125799	+	0.210085i
$218$		0			0
$219$	18.0030	+	7.34111i	1.21653	+	0.496066i
$220$		0			0
$221$	1.69131	+	2.01563i	0.113770	+	0.135586i
$222$		0			0
$223$	−23.3657	−	4.12001i	−1.56468	−	0.275896i	−0.676871	−	0.736101i	$-0.736665\pi$
$223$	−23.3657	−	4.12001i	−1.56468	−	0.275896i	−0.887812	+	0.460205i	$0.847776\pi$
$224$		0			0
$225$	−0.503887	−	5.10997i	−0.0335925	−	0.340665i
$226$		0			0
$227$	3.55971	−	20.1881i	0.236266	−	1.33993i	−0.603665	−	0.797238i	$-0.706294\pi$
$227$	3.55971	−	20.1881i	0.236266	−	1.33993i	0.839931	−	0.542693i	$-0.182595\pi$
$228$		0			0
$229$	−6.76544	+	18.5879i	−0.447073	+	1.22832i	0.487679	+	0.873023i	$0.337844\pi$
$229$	−6.76544	+	18.5879i	−0.447073	+	1.22832i	−0.934752	+	0.355300i	$0.884379\pi$
$230$		0			0
$231$	−10.8346	−	11.0682i	−0.712867	−	0.728235i
$232$		0			0
$233$	15.2011	+	8.77638i	0.995859	+	0.574959i	0.907020	−	0.421087i	$-0.138351\pi$
$233$	15.2011	+	8.77638i	0.995859	+	0.574959i	0.0888386	+	0.996046i	$0.471684\pi$
$234$		0			0
$235$	10.6327	+	18.4163i	0.693598	+	1.20135i
$236$		0			0
$237$	−21.6535	+	11.4242i	−1.40655	+	0.742084i
$238$		0			0
$239$	17.9853	−	3.17130i	1.16337	−	0.205134i	0.441566	−	0.897229i	$-0.354423\pi$
$239$	17.9853	−	3.17130i	1.16337	−	0.205134i	0.721807	+	0.692095i	$0.243312\pi$
$240$		0			0
$241$	−5.56206	−	15.2816i	−0.358284	−	0.984377i	−0.979625	−	0.200837i	$-0.935634\pi$
$241$	−5.56206	−	15.2816i	−0.358284	−	0.984377i	0.621341	−	0.783541i	$-0.286588\pi$
$242$		0			0
$243$	−2.45983	−	15.3932i	−0.157798	−	0.987471i
$244$		0			0
$245$	12.4017	+	13.2312i	0.792316	+	0.845312i
$246$		0			0
$247$	0.0999379	−	0.0838578i	0.00635890	−	0.00533575i
$248$		0			0
$249$	−0.822710	+	21.5710i	−0.0521371	+	1.36701i
$250$		0			0
$251$	−3.28698	+	5.69321i	−0.207472	+	0.359352i	−0.950918	−	0.309444i	$-0.899857\pi$
$251$	−3.28698	+	5.69321i	−0.207472	+	0.359352i	0.743445	+	0.668797i	$0.233190\pi$
$252$		0			0
$253$	−0.213224	−	0.369315i	−0.0134053	−	0.0232186i
$254$		0			0
$255$	7.09374	−	7.82765i	0.444227	−	0.490187i
$256$		0			0
$257$	15.3134	+	5.57362i	0.955224	+	0.347673i	0.772160	−	0.635428i	$-0.219176\pi$
$257$	15.3134	+	5.57362i	0.955224	+	0.347673i	0.183064	+	0.983101i	$0.441398\pi$
$258$		0			0
$259$	6.30072	−	26.3929i	0.391508	−	1.63998i
$260$		0			0
$261$	−4.74820	−	6.62449i	−0.293906	−	0.410046i
$262$		0			0
$263$	3.67048	−	4.37430i	0.226331	−	0.269731i	−0.640914	−	0.767613i	$-0.721444\pi$
$263$	3.67048	−	4.37430i	0.226331	−	0.269731i	0.867245	+	0.497882i	$0.165889\pi$
$264$		0			0
$265$	8.36612	−	22.9857i	0.513927	−	1.41200i
$266$		0			0
$267$	−0.433122	−	0.558060i	−0.0265067	−	0.0341527i
$268$		0			0
$269$	−12.6846	+	21.9703i	−0.773392	+	1.33955i	0.162302	+	0.986741i	$0.448108\pi$
$269$	−12.6846	+	21.9703i	−0.773392	+	1.33955i	−0.935694	+	0.352813i	$0.885225\pi$
$270$		0			0
$271$	2.95607	−	1.70669i	0.179568	−	0.103674i	−0.407521	−	0.913196i	$-0.633607\pi$
$271$	2.95607	−	1.70669i	0.179568	−	0.103674i	0.587090	+	0.809522i	$0.300274\pi$
$272$		0			0
$273$	0.391962	+	5.10676i	0.0237226	+	0.309075i
$274$		0			0
$275$	−5.69706	+	1.00455i	−0.343546	+	0.0605764i
$276$		0			0
$277$	−16.4067	−	13.7669i	−0.985784	−	0.827171i	−0.000832089	−	1.00000i	$-0.500265\pi$
$277$	−16.4067	−	13.7669i	−0.985784	−	0.827171i	−0.984952	+	0.172829i	$0.944709\pi$
$278$		0			0
$279$	2.90170	+	1.98448i	0.173720	+	0.118808i
$280$		0			0
$281$	−2.04388	−	5.61551i	−0.121928	−	0.334993i	0.863680	−	0.504040i	$-0.168153\pi$
$281$	−2.04388	−	5.61551i	−0.121928	−	0.334993i	−0.985608	+	0.169046i	$0.945931\pi$
$282$		0			0
$283$	−5.29351	+	0.933388i	−0.314666	+	0.0554842i	−0.328751	−	0.944417i	$-0.606628\pi$
$283$	−5.29351	+	0.933388i	−0.314666	+	0.0554842i	0.0140846	+	0.999901i	$0.495517\pi$
$284$		0			0
$285$	−0.388106	−	0.351718i	−0.0229894	−	0.0208340i
$286$		0			0
$287$	−4.82106	+	7.30409i	−0.284578	+	0.431147i
$288$		0			0
$289$	−11.4577			−0.673981
$290$		0			0
$291$	−7.46149	+	11.8559i	−0.437400	+	0.695005i
$292$		0			0
$293$	−4.55335	−	25.8233i	−0.266010	−	1.50862i	−0.766144	−	0.642668i	$-0.777827\pi$
$293$	−4.55335	−	25.8233i	−0.266010	−	1.50862i	0.500135	−	0.865948i	$-0.333284\pi$
$294$		0			0
$295$	16.8217	+	14.1151i	0.979397	+	0.821812i
$296$		0			0
$297$	−17.0809	+	4.08419i	−0.991132	+	0.236989i
$298$		0			0
$299$	−0.0244876	+	0.138876i	−0.00141615	+	0.00803141i
$300$		0			0
$301$	5.42415	−	4.02440i	0.312643	−	0.231962i
$302$		0			0
$303$	0.749230	−	19.6444i	0.0430421	−	1.12854i
$304$		0			0
$305$	−10.5046	+	6.06486i	−0.601494	+	0.347273i
$306$		0			0
$307$	10.1398	−	5.85419i	0.578707	−	0.334116i	−0.181913	−	0.983315i	$-0.558229\pi$
$307$	10.1398	−	5.85419i	0.578707	−	0.334116i	0.760619	+	0.649198i	$0.224895\pi$
$308$		0			0
$309$	20.0896	+	18.2060i	1.14286	+	1.03570i
$310$		0			0
$311$	−1.85672	−	10.5300i	−0.105285	−	0.597100i	−0.991106	−	0.133074i	$-0.957515\pi$
$311$	−1.85672	−	10.5300i	−0.105285	−	0.597100i	0.885821	−	0.464027i	$-0.153596\pi$
$312$		0			0
$313$	1.63919	−	1.95351i	0.0926523	−	0.110419i	−0.717726	−	0.696325i	$-0.754817\pi$
$313$	1.63919	−	1.95351i	0.0926523	−	0.110419i	0.810379	+	0.585907i	$0.199262\pi$
$314$		0			0
$315$	20.0981	−	4.34714i	1.13240	−	0.244934i
$316$		0			0
$317$	5.30604	+	14.5782i	0.298017	+	0.818795i	0.994831	+	0.101543i	$0.0323780\pi$
$317$	5.30604	+	14.5782i	0.298017	+	0.818795i	−0.696814	+	0.717252i	$0.745400\pi$
$318$		0			0
$319$	−7.03418	+	5.90237i	−0.393838	+	0.330470i
$320$		0			0
$321$	−11.9404	−	4.86892i	−0.666446	−	0.271757i
$322$		0			0
$323$		−	0.274796i		−	0.0152901i
$324$		0			0
$325$	1.65669	+	0.956488i	0.0918964	+	0.0530564i
$326$		0			0
$327$	−29.0860	+	3.99247i	−1.60846	+	0.220784i
$328$		0			0
$329$	−17.4412	+	12.9403i	−0.961563	+	0.713423i
$330$		0			0
$331$	−22.6410	+	8.24065i	−1.24446	+	0.452947i	−0.878527	−	0.477693i	$-0.841473\pi$
$331$	−22.6410	+	8.24065i	−1.24446	+	0.452947i	−0.365936	+	0.930640i	$0.619251\pi$
$332$		0			0
$333$	−21.9946	−	21.5149i	−1.20530	−	1.17901i
$334$		0			0
$335$	−22.1030	+	8.04484i	−1.20762	+	0.439537i
$336$		0			0
$337$	−10.1610	+	8.52606i	−0.553503	+	0.464444i	−0.876125	−	0.482084i	$-0.839880\pi$
$337$	−10.1610	+	8.52606i	−0.553503	+	0.464444i	0.322622	+	0.946528i	$0.395436\pi$
$338$		0			0
$339$	1.58092	−	0.508061i	0.0858641	−	0.0275941i
$340$		0			0
$341$	1.98027	−	3.42993i	0.107238	−	0.185741i
$342$		0			0
$343$	−11.9739	+	14.1289i	−0.646528	+	0.762890i
$344$		0			0
$345$	0.565747	+	0.0215773i	0.0304588	+	0.00116169i
$346$		0			0
$347$	2.30205	−	6.32484i	0.123581	−	0.339535i	−0.862440	−	0.506160i	$-0.831065\pi$
$347$	2.30205	−	6.32484i	0.123581	−	0.339535i	0.986020	+	0.166625i	$0.0532868\pi$
$348$		0			0
$349$	−1.49276	+	1.77900i	−0.0799055	+	0.0952277i	−0.804516	−	0.593931i	$-0.797575\pi$
$349$	−1.49276	+	1.77900i	−0.0799055	+	0.0952277i	0.724611	+	0.689159i	$0.242020\pi$
$350$		0			0
$351$	5.19500	+	2.59608i	0.277288	+	0.138568i
$352$		0			0
$353$	−10.1311	+	3.68740i	−0.539221	+	0.196261i	−0.597251	−	0.802054i	$-0.703740\pi$
$353$	−10.1311	+	3.68740i	−0.539221	+	0.196261i	0.0580297	+	0.998315i	$0.481518\pi$
$354$		0			0
$355$	13.5694	+	16.1714i	0.720190	+	0.858289i
$356$		0			0
$357$	8.77083	+	6.28183i	0.464201	+	0.332470i
$358$		0			0
$359$			27.3379i			1.44284i	0.692497	+	0.721421i	$0.256511\pi$
$359$			27.3379i			1.44284i	−0.692497	+	0.721421i	$0.743489\pi$
$360$		0			0
$361$	18.9864			0.999283
$362$		0			0
$363$	0.224460	+	0.698448i	0.0117811	+	0.0366590i
$364$		0			0
$365$	18.6924	+	22.2768i	0.978407	+	1.16602i
$366$		0			0
$367$	−28.5523	−	5.03454i	−1.49042	−	0.262801i	−0.631685	−	0.775225i	$-0.717636\pi$
$367$	−28.5523	−	5.03454i	−1.49042	−	0.262801i	−0.858732	+	0.512424i	$0.828748\pi$
$368$		0			0
$369$	4.29274	+	8.94696i	0.223471	+	0.465760i
$370$		0			0
$371$	24.2982	+	5.80064i	1.26150	+	0.301154i
$372$		0			0
$373$	−3.02012	−	17.1280i	−0.156376	−	0.886852i	−0.957517	−	0.288377i	$-0.906884\pi$
$373$	−3.02012	−	17.1280i	−0.156376	−	0.886852i	0.801141	−	0.598476i	$-0.204227\pi$
$374$		0			0
$375$	−5.57153	+	13.6634i	−0.287713	+	0.705575i
$376$		0			0
$377$	3.03647			0.156386
$378$		0			0
$379$	19.8221			1.01819			0.509097	−	0.860709i	$-0.329980\pi$
$379$	19.8221			1.01819			0.509097	+	0.860709i	$0.329980\pi$
$380$		0			0
$381$	7.90690	−	1.08534i	0.405083	−	0.0556034i
$382$		0			0
$383$	−2.13848	−	12.1279i	−0.109271	−	0.619707i	−0.989428	−	0.145024i	$-0.953674\pi$
$383$	−2.13848	−	12.1279i	−0.109271	−	0.619707i	0.880157	−	0.474683i	$-0.157437\pi$
$384$		0			0
$385$	−6.60805	−	22.2042i	−0.336778	−	1.13163i
$386$		0			0
$387$	−0.751536	−	7.62141i	−0.0382027	−	0.387418i
$388$		0			0
$389$	−10.0836	−	1.77801i	−0.511257	−	0.0901484i	−0.0879325	−	0.996126i	$-0.528026\pi$
$389$	−10.0836	−	1.77801i	−0.511257	−	0.0901484i	−0.423325	+	0.905978i	$0.639137\pi$
$390$		0			0
$391$	0.190932	+	0.227544i	0.00965584	+	0.0115074i
$392$		0			0
$393$	34.5843	+	7.46739i	1.74455	+	0.376680i
$394$		0			0
$395$	−36.6189			−1.84250
$396$		0			0
$397$			33.0450i			1.65848i	0.558892	+	0.829240i	$0.311227\pi$
$397$			33.0450i			1.65848i	−0.558892	+	0.829240i	$0.688773\pi$
$398$		0			0
$399$	0.311462	−	0.434870i	0.0155926	−	0.0217707i
$400$		0			0
$401$	1.12919	+	1.34572i	0.0563892	+	0.0672020i	0.793502	−	0.608568i	$-0.208256\pi$
$401$	1.12919	+	1.34572i	0.0563892	+	0.0672020i	−0.737113	+	0.675770i	$0.763811\pi$
$402$		0			0
$403$	−1.23070	+	0.447936i	−0.0613053	+	0.0223133i
$404$		0			0
$405$	7.48958	−	22.0804i	0.372160	−	1.09718i
$406$		0			0
$407$	−22.2814	+	26.5539i	−1.10445	+	1.31623i
$408$		0			0
$409$	3.23082	−	8.87661i	0.159754	−	0.438920i	−0.833829	−	0.552022i	$-0.813856\pi$
$409$	3.23082	−	8.87661i	0.159754	−	0.438920i	0.993583	+	0.113102i	$0.0360786\pi$
$410$		0			0
$411$	−13.0724	+	20.7713i	−0.644812	+	1.02457i
$412$		0			0
$413$	−12.3538	+	18.7165i	−0.607893	+	0.920981i
$414$		0			0
$415$	−16.1439	+	27.9621i	−0.792473	+	1.37260i
$416$		0			0
$417$	23.6004	+	21.3876i	1.15571	+	1.04736i
$418$		0			0
$419$	−5.84407	+	4.90375i	−0.285501	+	0.239564i	−0.774279	−	0.632844i	$-0.781887\pi$
$419$	−5.84407	+	4.90375i	−0.285501	+	0.239564i	0.488778	+	0.872408i	$0.337443\pi$
$420$		0			0
$421$	−7.26865	+	2.64557i	−0.354252	+	0.128937i	−0.513015	−	0.858379i	$-0.671472\pi$
$421$	−7.26865	+	2.64557i	−0.354252	+	0.128937i	0.158763	+	0.987317i	$0.449249\pi$
$422$		0			0
$423$	2.41654	+	24.5064i	0.117496	+	1.19154i
$424$		0			0
$425$	3.78643	−	1.37815i	0.183669	−	0.0668501i
$426$		0			0
$427$	−7.38114	−	9.94843i	−0.357199	−	0.481438i
$428$		0			0
$429$	2.47051	−	6.05859i	0.119277	−	0.292511i
$430$		0			0
$431$	−32.2999	−	18.6484i	−1.55583	−	0.898260i	−0.997648	−	0.0685418i	$-0.978165\pi$
$431$	−32.2999	−	18.6484i	−1.55583	−	0.898260i	−0.558183	−	0.829718i	$-0.688501\pi$
$432$		0			0
$433$			11.0883i			0.532870i	0.963853	+	0.266435i	$0.0858458\pi$
$433$			11.0883i			0.532870i	−0.963853	+	0.266435i	$0.914154\pi$
$434$		0			0
$435$	−1.65782	−	12.0775i	−0.0794862	−	0.579074i
$436$		0			0
$437$	0.0112819	−	0.00946668i	0.000539689	−	0.000452853i
$438$		0			0
$439$	9.22473	+	25.3447i	0.440272	+	1.20964i	0.939313	+	0.343060i	$0.111464\pi$
$439$	9.22473	+	25.3447i	0.440272	+	1.20964i	−0.499041	+	0.866578i	$0.666314\pi$
$440$		0			0
$441$	6.75998	+	19.8822i	0.321904	+	0.946772i
$442$		0			0
$443$	−25.6317	+	30.5467i	−1.21780	+	1.45132i	−0.363454	+	0.931612i	$0.618403\pi$
$443$	−25.6317	+	30.5467i	−1.21780	+	1.45132i	−0.854346	+	0.519705i	$0.826042\pi$
$444$		0			0
$445$	−0.183478	−	1.04055i	−0.00869768	−	0.0493270i
$446$		0			0
$447$	30.7291	−	9.87539i	1.45344	−	0.467090i
$448$		0			0
$449$	−1.95937	+	1.13124i	−0.0924682	+	0.0533865i	−0.545521	−	0.838097i	$-0.683668\pi$
$449$	−1.95937	+	1.13124i	−0.0924682	+	0.0533865i	0.453053	+	0.891484i	$0.350335\pi$
$450$		0			0
$451$	9.68222	−	5.59003i	0.455918	−	0.263224i
$452$		0			0
$453$	16.3403	−	8.62104i	0.767735	−	0.405052i
$454$		0			0
$455$	−3.04575	+	7.02929i	−0.142787	+	0.329538i
$456$		0			0
$457$	3.51406	−	19.9292i	0.164381	−	0.932250i	−0.785320	−	0.619091i	$-0.787501\pi$
$457$	3.51406	−	19.9292i	0.164381	−	0.932250i	0.949700	−	0.313160i	$-0.101388\pi$
$458$		0			0
$459$	11.2227	−	4.86755i	0.523832	−	0.227198i
$460$		0			0
$461$	8.26907	+	6.93857i	0.385129	+	0.323162i	0.814712	−	0.579866i	$-0.196895\pi$
$461$	8.26907	+	6.93857i	0.385129	+	0.323162i	−0.429583	+	0.903027i	$0.641339\pi$
$462$		0			0
$463$	−3.86641	−	21.9275i	−0.179687	−	1.01906i	−0.932593	−	0.360929i	$-0.882460\pi$
$463$	−3.86641	−	21.9275i	−0.179687	−	1.01906i	0.752906	−	0.658128i	$-0.228651\pi$
$464$		0			0
$465$	2.45358	+	4.65052i	0.113782	+	0.215663i
$466$		0			0
$467$	−1.50943			−0.0698481			−0.0349241	−	0.999390i	$-0.511119\pi$
$467$	−1.50943			−0.0698481			−0.0349241	+	0.999390i	$0.511119\pi$
$468$		0			0
$469$	−10.7459	−	21.4841i	−0.496198	−	0.992041i
$470$		0			0
$471$	−1.88038	+	8.70875i	−0.0866434	+	0.401278i
$472$		0			0
$473$	−8.49703	+	1.49826i	−0.390694	+	0.0688899i
$474$		0			0
$475$	−0.0683306	−	0.187737i	−0.00313523	−	0.00861396i
$476$		0			0
$477$	19.8073	−	20.2489i	0.906914	−	0.927134i
$478$		0			0
$479$	−9.83065	−	8.24890i	−0.449174	−	0.376902i	0.389955	−	0.920834i	$-0.372490\pi$
$479$	−9.83065	−	8.24890i	−0.449174	−	0.376902i	−0.839129	+	0.543932i	$0.816935\pi$
$480$		0			0
$481$	11.2885	−	1.99047i	0.514712	−	0.0907576i
$482$		0			0
$483$	0.0442484	+	0.576500i	0.00201337	+	0.0262316i
$484$		0			0
$485$	−18.1456	+	10.4764i	−0.823951	+	0.475708i
$486$		0			0
$487$	−11.2032	+	19.4046i	−0.507667	+	0.879306i	0.492293	+	0.870429i	$0.336159\pi$
$487$	−11.2032	+	19.4046i	−0.507667	+	0.879306i	−0.999961	+	0.00887634i	$0.997175\pi$
$488$		0			0
$489$	−1.65540	+	4.05963i	−0.0748597	+	0.183583i
$490$		0			0
$491$	1.86210	−	5.11607i	0.0840353	−	0.230885i	−0.890557	−	0.454872i	$-0.849685\pi$
$491$	1.86210	−	5.11607i	0.0840353	−	0.230885i	0.974592	+	0.223987i	$0.0719073\pi$
$492$		0			0
$493$	4.11123	−	4.89957i	0.185161	−	0.220666i
$494$		0			0
$495$	−25.4468	−	6.51864i	−1.14375	−	0.292991i
$496$		0			0
$497$	−14.8203	+	15.6573i	−0.664781	+	0.702328i
$498$		0			0
$499$	−14.3904	−	5.23768i	−0.644203	−	0.234471i	−0.000801335	−	1.00000i	$-0.500255\pi$
$499$	−14.3904	−	5.23768i	−0.644203	−	0.234471i	−0.643401	+	0.765529i	$0.722477\pi$
$500$		0			0
$501$	−3.50679	−	10.9120i	−0.156672	−	0.487513i
$502$		0			0
$503$	−5.37147	−	9.30366i	−0.239502	−	0.414830i	0.721069	−	0.692863i	$-0.243651\pi$
$503$	−5.37147	−	9.30366i	−0.239502	−	0.414830i	−0.960572	+	0.278033i	$0.910318\pi$
$504$		0			0
$505$	14.7020	−	25.4647i	0.654232	−	1.13316i
$506$		0			0
$507$	18.0013	−	9.49735i	0.799465	−	0.421792i
$508$		0			0
$509$	10.4319	−	8.75343i	0.462387	−	0.387989i	−0.381621	−	0.924319i	$-0.624634\pi$
$509$	10.4319	−	8.75343i	0.462387	−	0.387989i	0.844008	+	0.536330i	$0.180190\pi$
$510$		0			0
$511$	−20.4156	+	21.5687i	−0.903132	+	0.954142i
$512$		0			0
$513$	−0.241340	−	0.556439i	−0.0106554	−	0.0245674i
$514$		0			0
$515$	13.8696	+	38.1063i	0.611165	+	1.67916i
$516$		0			0
$517$	27.3219	−	4.81759i	1.20162	−	0.211878i
$518$		0			0
$519$	0.706906	−	18.5347i	0.0310297	−	0.813585i
$520$		0			0
$521$	7.64859	+	13.2477i	0.335091	+	0.580394i	0.983502	−	0.180896i	$-0.0578997\pi$
$521$	7.64859	+	13.2477i	0.335091	+	0.580394i	−0.648412	+	0.761290i	$0.724566\pi$
$522$		0			0
$523$	−12.1121	−	6.99294i	−0.529626	−	0.305780i	0.211238	−	0.977435i	$-0.432250\pi$
$523$	−12.1121	−	6.99294i	−0.529626	−	0.305780i	−0.740864	+	0.671655i	$0.765584\pi$
$524$		0			0
$525$	7.55413	+	2.11071i	0.329689	+	0.0921189i
$526$		0			0
$527$	−0.943520	+	2.59230i	−0.0411004	+	0.112922i
$528$		0			0
$529$	3.99114	−	22.6349i	0.173528	−	0.984126i
$530$		0			0
$531$	11.0001	+	22.9264i	0.477362	+	0.994920i
$532$		0			0
$533$	−3.64088	−	0.641985i	−0.157704	−	0.0278074i
$534$		0			0
$535$	−12.3976	−	14.7749i	−0.535995	−	0.638774i
$536$		0			0
$537$	6.32483	−	4.90884i	0.272936	−	0.211832i
$538$		0			0
$539$	21.7546	−	9.29999i	0.937039	−	0.400579i
$540$		0			0
$541$	−16.0626	−	27.8212i	−0.690583	−	1.19613i	−0.971647	−	0.236436i	$-0.924021\pi$
$541$	−16.0626	−	27.8212i	−0.690583	−	1.19613i	0.281064	−	0.959689i	$-0.409313\pi$
$542$		0			0
$543$	2.57926	+	18.7904i	0.110686	+	0.806375i
$544$		0			0
$545$	−41.2643	−	15.0190i	−1.76757	−	0.643343i
$546$		0			0
$547$	−4.13424	+	23.4464i	−0.176767	+	1.00250i	0.759317	+	0.650721i	$0.225533\pi$
$547$	−4.13424	+	23.4464i	−0.176767	+	1.00250i	−0.936084	+	0.351776i	$0.885578\pi$
$548$		0			0
$549$	−13.9784	+	1.37839i	−0.596584	+	0.0588283i
$550$		0			0
$551$	−0.242928	−	0.203841i	−0.0103491	−	0.00868391i
$552$		0			0
$553$	−4.28100	−	37.1516i	−0.182046	−	1.57985i
$554$		0			0
$555$	−14.0802	−	43.8132i	−0.597672	−	1.85977i
$556$		0			0
$557$		−	9.33194i		−	0.395407i	−0.980262	−	0.197703i	$-0.936652\pi$
$557$		−	9.33194i		−	0.395407i	0.980262	−	0.197703i	$-0.0633483\pi$
$558$		0			0
$559$	2.47091	+	1.42658i	0.104508	+	0.0603379i
$560$		0			0
$561$	−6.43103	−	12.1894i	−0.271518	−	0.514636i
$562$		0			0
$563$	30.5263	+	11.1107i	1.28653	+	0.468259i	0.892586	−	0.450876i	$-0.148888\pi$
$563$	30.5263	+	11.1107i	1.28653	+	0.468259i	0.393943	+	0.919135i	$0.371111\pi$
$564$		0			0
$565$	2.44600	+	0.431297i	0.102904	+	0.0181448i
$566$		0			0
$567$	23.2772	+	5.01718i	0.977550	+	0.210702i
$568$		0			0
$569$	40.1659	+	7.08232i	1.68384	+	0.296906i	0.932005	−	0.362445i	$-0.118058\pi$
$569$	40.1659	+	7.08232i	1.68384	+	0.296906i	0.751835	+	0.659351i	$0.229169\pi$
$570$		0			0
$571$	31.1702	+	11.3450i	1.30443	+	0.474775i	0.898438	−	0.439101i	$-0.144703\pi$
$571$	31.1702	+	11.3450i	1.30443	+	0.474775i	0.405995	+	0.913875i	$0.366925\pi$
$572$		0			0
$573$	15.9306	+	30.1949i	0.665512	+	1.26141i
$574$		0			0
$575$	0.187023	+	0.107978i	0.00779939	+	0.00450298i
$576$		0			0
$577$		−	43.1437i		−	1.79609i	−0.439899	−	0.898047i	$-0.644986\pi$
$577$		−	43.1437i		−	1.79609i	0.439899	−	0.898047i	$-0.355014\pi$
$578$		0			0
$579$	−11.7314	−	36.5045i	−0.487542	−	1.51708i
$580$		0			0
$581$	−30.2562	−	13.1098i	−1.25524	−	0.543886i
$582$		0			0
$583$	−24.4464	−	20.5130i	−1.01247	−	0.849560i
$584$		0			0
$585$	5.06051	+	7.06021i	0.209226	+	0.291904i
$586$		0			0
$587$	7.44234	−	42.2076i	0.307178	−	1.74209i	−0.305892	−	0.952066i	$-0.598955\pi$
$587$	7.44234	−	42.2076i	0.307178	−	1.74209i	0.613070	−	0.790028i	$-0.289934\pi$
$588$		0			0
$589$	0.128530	+	0.0467811i	0.00529599	+	0.00192758i
$590$		0			0
$591$	0.474742	+	3.45859i	0.0195283	+	0.142268i
$592$		0			0
$593$	2.95663	+	5.12102i	0.121414	+	0.210295i	0.920326	−	0.391153i	$-0.127924\pi$
$593$	2.95663	+	5.12102i	0.121414	+	0.210295i	−0.798911	+	0.601449i	$0.794590\pi$
$594$		0			0
$595$	7.21849	+	14.4318i	0.295929	+	0.591647i
$596$		0			0
$597$	5.09747	−	3.95626i	0.208626	−	0.161919i
$598$		0			0
$599$	16.5465	+	19.7193i	0.676070	+	0.805709i	0.989596	−	0.143871i	$-0.0459550\pi$
$599$	16.5465	+	19.7193i	0.676070	+	0.805709i	−0.313527	+	0.949579i	$0.601511\pi$
$600$		0			0
$601$	−19.3751	−	3.41635i	−0.790325	−	0.139356i	−0.236107	−	0.971727i	$-0.575872\pi$
$601$	−19.3751	−	3.41635i	−0.790325	−	0.139356i	−0.554218	+	0.832371i	$0.686983\pi$
$602$		0			0
$603$	−27.1588	−	2.07467i	−1.10599	−	0.0844870i
$604$		0			0
$605$	−0.190546	+	1.08064i	−0.00774678	+	0.0439342i
$606$		0			0
$607$	4.38614	−	12.0508i	0.178028	−	0.489128i	−0.818296	−	0.574798i	$-0.805081\pi$
$607$	4.38614	−	12.0508i	0.178028	−	0.489128i	0.996324	+	0.0856697i	$0.0273030\pi$
$608$		0			0
$609$	12.0594	−	3.09388i	0.488672	−	0.125370i
$610$		0			0
$611$	−7.94513	−	4.58712i	−0.321425	−	0.185575i
$612$		0			0
$613$	−15.1423	−	26.2273i	−0.611594	−	1.05931i	−0.990972	−	0.134070i	$-0.957195\pi$
$613$	−15.1423	−	26.2273i	−0.611594	−	1.05931i	0.379378	−	0.925242i	$-0.376138\pi$
$614$		0			0
$615$	−0.565687	+	14.8320i	−0.0228107	+	0.598086i
$616$		0			0
$617$	−33.7970	+	5.95933i	−1.36062	+	0.239913i	−0.805863	−	0.592101i	$-0.798298\pi$
$617$	−33.7970	+	5.95933i	−1.36062	+	0.239913i	−0.554753	+	0.832015i	$0.687187\pi$
$618$		0			0
$619$	−7.36707	−	20.2409i	−0.296107	−	0.813548i	−0.995141	−	0.0984597i	$-0.968608\pi$
$619$	−7.36707	−	20.2409i	−0.296107	−	0.813548i	0.699034	−	0.715089i	$-0.253614\pi$
$620$		0			0
$621$	0.586461	+	0.293070i	0.0235339	+	0.0117605i
$622$		0			0
$623$	1.03424	−	0.307795i	0.0414360	−	0.0123315i
$624$		0			0
$625$	−23.4627	+	19.6876i	−0.938509	+	0.787502i
$626$		0			0
$627$	−0.604367	+	0.318860i	−0.0241361	+	0.0127340i
$628$		0			0
$629$	12.0723	−	20.9098i	0.481354	−	0.833730i
$630$		0			0
$631$	9.15885	+	15.8636i	0.364608	+	0.631520i	0.988713	−	0.149821i	$-0.0478697\pi$
$631$	9.15885	+	15.8636i	0.364608	+	0.631520i	−0.624105	+	0.781340i	$0.714536\pi$
$632$		0			0
$633$	2.71336	+	8.44311i	0.107846	+	0.335583i
$634$		0			0
$635$	11.2175	+	4.08285i	0.445154	+	0.162023i
$636$		0			0
$637$	−7.48761	−	2.26828i	−0.296670	−	0.0898726i
$638$		0			0
$639$	6.58693	+	23.5415i	0.260575	+	0.931289i
$640$		0			0
$641$	26.4237	−	31.4905i	1.04367	−	1.24380i	0.0745514	−	0.997217i	$-0.476248\pi$
$641$	26.4237	−	31.4905i	1.04367	−	1.24380i	0.969121	−	0.246584i	$-0.0793080\pi$
$642$		0			0
$643$	14.5325	−	39.9277i	0.573105	−	1.57459i	−0.226464	−	0.974020i	$-0.572716\pi$
$643$	14.5325	−	39.9277i	0.573105	−	1.57459i	0.799569	−	0.600574i	$-0.205061\pi$
$644$		0			0
$645$	4.32517	−	10.6069i	0.170303	−	0.417645i
$646$		0			0
$647$	2.03413	−	3.52322i	0.0799700	−	0.138512i	−0.823267	−	0.567655i	$-0.807851\pi$
$647$	2.03413	−	3.52322i	0.0799700	−	0.138512i	0.903237	+	0.429143i	$0.141184\pi$
$648$		0			0
$649$	24.8104	−	14.3243i	0.973895	−	0.562279i
$650$		0			0
$651$	−4.43133	+	3.03295i	−0.173677	+	0.118871i
$652$		0			0
$653$	30.6601	−	5.40620i	1.19982	−	0.211561i	0.462201	−	0.886775i	$-0.347060\pi$
$653$	30.6601	−	5.40620i	1.19982	−	0.211561i	0.737622	+	0.675214i	$0.235949\pi$
$654$		0			0
$655$	40.5396	+	34.0168i	1.58401	+	1.32914i
$656$		0			0
$657$	9.07378	+	32.4295i	0.354002	+	1.26519i
$658$		0			0
$659$	−8.48007	−	23.2988i	−0.330337	−	0.907593i	−0.988024	−	0.154302i	$-0.950687\pi$
$659$	−8.48007	−	23.2988i	−0.330337	−	0.907593i	0.657687	−	0.753291i	$-0.271535\pi$
$660$		0			0
$661$	30.1409	−	5.31465i	1.17234	−	0.206716i	0.446634	−	0.894717i	$-0.352623\pi$
$661$	30.1409	−	5.31465i	1.17234	−	0.206716i	0.725710	+	0.688001i	$0.241511\pi$
$662$		0			0
$663$	−0.961862	+	4.45474i	−0.0373556	+	0.173008i
$664$		0			0
$665$	0.715551	−	0.357903i	0.0277479	−	0.0138789i
$666$		0			0
$667$	0.342786			0.0132727
$668$		0			0
$669$	−19.1762	−	36.3465i	−0.741393	−	1.40524i
$670$		0			0
$671$	2.74795	+	15.5844i	0.106083	+	0.601629i
$672$		0			0
$673$	4.44436	+	3.72926i	0.171317	+	0.143752i	0.724415	−	0.689364i	$-0.242110\pi$
$673$	4.44436	+	3.72926i	0.171317	+	0.143752i	−0.553098	+	0.833116i	$0.686554\pi$
$674$		0			0
$675$	6.45684	−	6.11608i	0.248524	−	0.235408i
$676$		0			0
$677$	−6.28158	+	35.6246i	−0.241421	+	1.36917i	0.587239	+	0.809413i	$0.300215\pi$
$677$	−6.28158	+	35.6246i	−0.241421	+	1.36917i	−0.828660	+	0.559752i	$0.810896\pi$
$678$		0			0
$679$	−12.7501	−	17.1848i	−0.489305	−	0.659493i
$680$		0			0
$681$	31.4036	−	16.5683i	1.20339	−	0.634899i
$682$		0			0
$683$	−23.1494	+	13.3653i	−0.885788	+	0.511410i	−0.872562	−	0.488503i	$-0.837543\pi$
$683$	−23.1494	+	13.3653i	−0.885788	+	0.511410i	−0.0132254	+	0.999913i	$0.504210\pi$
$684$		0			0
$685$	−31.7908	+	18.3544i	−1.21466	+	0.701286i
$686$		0			0
$687$	−32.6184	+	10.4826i	−1.24447	+	0.399935i
$688$		0			0
$689$	1.83249	+	10.3926i	0.0698122	+	0.395925i
$690$		0			0
$691$	−16.7330	+	19.9416i	−0.636553	+	0.758615i	−0.983822	−	0.179151i	$-0.942665\pi$
$691$	−16.7330	+	19.9416i	−0.636553	+	0.758615i	0.347268	+	0.937766i	$0.387109\pi$
$692$		0			0
$693$	3.63857	−	26.5790i	0.138218	−	1.00965i
$694$		0			0
$695$	16.2933	+	44.7655i	0.618041	+	1.69805i
$696$		0			0
$697$	−5.96545	+	5.00561i	−0.225958	+	0.189601i
$698$		0			0
$699$	4.13438	+	30.1198i	0.156377	+	1.13924i
$700$		0			0
$701$		−	22.3146i		−	0.842809i	−0.906873	−	0.421405i	$-0.861537\pi$
$701$		−	22.3146i		−	0.842809i	0.906873	−	0.421405i	$-0.138463\pi$
$702$		0			0
$703$	−1.03674	−	0.598562i	−0.0391014	−	0.0225752i
$704$		0			0
$705$	−13.9074	+	34.1061i	−0.523785	+	1.28451i
$706$		0			0
$707$	27.5539	+	11.9389i	1.03627	+	0.449009i
$708$		0			0
$709$	5.43860	−	1.97949i	0.204251	−	0.0743412i	−0.237869	−	0.971297i	$-0.576449\pi$
$709$	5.43860	−	1.97949i	0.204251	−	0.0743412i	0.442120	+	0.896956i	$0.354227\pi$
$710$		0			0
$711$	−38.6270	−	17.4963i	−1.44862	−	0.656161i
$712$		0			0
$713$	−0.138933	+	0.0505674i	−0.00520307	+	0.00189376i
$714$		0			0
$715$	7.49684	−	6.29060i	0.280366	−	0.235255i
$716$		0			0
$717$	23.4390	+	21.2414i	0.875346	+	0.793275i
$718$		0			0
$719$	26.2658	−	45.4937i	0.979548	−	1.69663i	0.315522	−	0.948918i	$-0.397820\pi$
$719$	26.2658	−	45.4937i	0.979548	−	1.69663i	0.664026	−	0.747709i	$-0.268846\pi$
$720$		0			0
$721$	−37.0392	+	18.5262i	−1.37941	+	0.689951i
$722$		0			0
$723$	15.0031	−	23.8391i	0.557971	−	0.886586i
$724$		0			0
$725$	1.59041	−	4.36961i	0.0590663	−	0.162283i
$726$		0			0
$727$	−12.3912	+	14.7672i	−0.459563	+	0.547686i	−0.945207	−	0.326471i	$-0.894141\pi$
$727$	−12.3912	+	14.7672i	−0.459563	+	0.547686i	0.485645	+	0.874156i	$0.338585\pi$
$728$		0			0
$729$	18.4501	−	19.7128i	0.683338	−	0.730102i
$730$		0			0
$731$	5.64738	−	2.05548i	0.208876	−	0.0760246i
$732$		0			0
$733$	25.2536	+	30.0960i	0.932762	+	1.11162i	0.993541	+	0.113471i	$0.0361968\pi$
$733$	25.2536	+	30.0960i	0.932762	+	1.11162i	−0.0607798	+	0.998151i	$0.519359\pi$
$734$		0			0
$735$	−4.93407	+	31.0203i	−0.181996	+	1.14420i
$736$		0			0
$737$			30.6870i			1.13037i
$738$		0			0
$739$	13.0679			0.480710			0.240355	−	0.970685i	$-0.422736\pi$
$739$	13.0679			0.480710			0.240355	+	0.970685i	$0.422736\pi$
$740$		0			0
$741$	0.220873	+	0.0476905i	0.00811396	+	0.00175196i
$742$		0			0
$743$	−3.14402	−	3.74690i	−0.115343	−	0.137460i	0.705284	−	0.708925i	$-0.250820\pi$
$743$	−3.14402	−	3.74690i	−0.115343	−	0.137460i	−0.820626	+	0.571465i	$0.806375\pi$
$744$		0			0
$745$	47.5440	+	8.38329i	1.74188	+	0.307140i
$746$		0			0
$747$	−30.3892	+	21.7820i	−1.11188	+	0.796960i
$748$		0			0
$749$	13.5404	−	14.3052i	0.494757	−	0.522701i
$750$		0			0
$751$	3.51062	+	19.9097i	0.128104	+	0.726516i	0.979415	+	0.201855i	$0.0646969\pi$
$751$	3.51062	+	19.9097i	0.128104	+	0.726516i	−0.851311	+	0.524661i	$0.824192\pi$
$752$		0			0
$753$	−11.2806	+	1.54843i	−0.411090	+	0.0564280i
$754$		0			0
$755$	27.6336			1.00569
$756$		0			0
$757$	−38.4613			−1.39790			−0.698950	−	0.715171i	$-0.746349\pi$
$757$	−38.4613			−1.39790			−0.698950	+	0.715171i	$0.746349\pi$
$758$		0			0
$759$	0.278895	−	0.683952i	0.0101233	−	0.0248259i
$760$		0			0
$761$	−6.92697	−	39.2848i	−0.251102	−	1.42407i	−0.805883	−	0.592075i	$-0.798309\pi$
$761$	−6.92697	−	39.2848i	−0.251102	−	1.42407i	0.554780	−	0.831997i	$-0.312802\pi$
$762$		0			0
$763$	10.4134	−	43.6204i	0.376990	−	1.57916i
$764$		0			0
$765$	18.2438	+	1.39365i	0.659607	+	0.0503875i
$766$		0			0
$767$	−9.32966	−	1.64507i	−0.336874	−	0.0594000i
$768$		0			0
$769$	−12.0209	−	14.3260i	−0.433486	−	0.516609i	0.504438	−	0.863448i	$-0.331700\pi$
$769$	−12.0209	−	14.3260i	−0.433486	−	0.516609i	−0.937925	+	0.346839i	$0.887255\pi$
$770$		0			0
$771$	8.63592	+	26.8723i	0.311015	+	0.967780i
$772$		0			0
$773$	−8.57951			−0.308583			−0.154292	−	0.988025i	$-0.549310\pi$
$773$	−8.57951			−0.308583			−0.154292	+	0.988025i	$0.549310\pi$
$774$		0			0
$775$			2.00564i			0.0720446i
$776$		0			0
$777$	42.8045	−	19.4071i	1.53560	−	0.696226i
$778$		0			0
$779$	0.248185	+	0.295776i	0.00889216	+	0.0105973i
$780$		0			0
$781$	25.8802	−	9.41962i	0.926066	−	0.337061i
$782$		0			0
$783$	4.02183	−	13.5319i	0.143729	−	0.483591i
$784$		0			0
$785$	−8.56584	+	10.2084i	−0.305728	+	0.364352i
$786$		0			0
$787$	−3.88872	+	10.6842i	−0.138618	+	0.380849i	−0.989505	−	0.144499i	$-0.953843\pi$
$787$	−3.88872	+	10.6842i	−0.138618	+	0.380849i	0.850887	+	0.525349i	$0.176065\pi$
$788$		0			0
$789$	9.88325	+	0.376943i	0.351853	+	0.0134195i
$790$		0			0
$791$	−0.151616	+	2.53201i	−0.00539086	+	0.0900278i
$792$		0			0
$793$	2.61649	−	4.53189i	0.0929143	−	0.160932i
$794$		0			0
$795$	40.3358	−	12.9627i	1.43056	−	0.459739i
$796$		0			0
$797$	11.9873	−	10.0585i	0.424611	−	0.356291i	−0.405303	−	0.914183i	$-0.632834\pi$
$797$	11.9873	−	10.0585i	0.424611	−	0.356291i	0.829914	+	0.557891i	$0.188389\pi$
$798$		0			0
$799$	−18.1590	+	6.60932i	−0.642418	+	0.233821i
$800$		0			0
$801$	0.303630	−	1.18528i	0.0107282	−	0.0418798i
$802$		0			0
$803$	35.6511	−	12.9759i	1.25810	−	0.457911i
$804$		0			0
$805$	−0.343833	+	0.793534i	−0.0121185	+	0.0279684i
$806$		0			0
$807$	−43.5325	+	5.97545i	−1.53242	+	0.210346i
$808$		0			0
$809$	−10.4983	−	6.06119i	−0.369100	−	0.213100i	0.303965	−	0.952683i	$-0.401689\pi$
$809$	−10.4983	−	6.06119i	−0.369100	−	0.213100i	−0.673065	+	0.739583i	$0.735023\pi$
$810$		0			0
$811$			31.5450i			1.10770i	0.832618	+	0.553848i	$0.186841\pi$
$811$			31.5450i			1.10770i	−0.832618	+	0.553848i	$0.813159\pi$
$812$		0			0
$813$	5.47449	+	2.23233i	0.191999	+	0.0782914i
$814$		0			0
$815$	−5.02335	+	4.21509i	−0.175960	+	0.147648i
$816$		0			0
$817$	−0.101914	−	0.280005i	−0.00356550	−	0.00979614i
$818$		0			0
$819$	−6.57130	+	5.95951i	−0.229620	+	0.208242i
$820$		0			0
$821$	32.2286	−	38.4086i	1.12479	−	1.34047i	0.191434	−	0.981505i	$-0.438686\pi$
$821$	32.2286	−	38.4086i	1.12479	−	1.34047i	0.933352	−	0.358962i	$-0.116869\pi$
$822$		0			0
$823$	−2.25211	−	12.7724i	−0.0785038	−	0.445217i	−0.998570	−	0.0534548i	$-0.982977\pi$
$823$	−2.25211	−	12.7724i	−0.0785038	−	0.445217i	0.920066	−	0.391762i	$-0.128134\pi$
$824$		0			0
$825$	−7.42459	−	6.72847i	−0.258491	−	0.234255i
$826$		0			0
$827$	−12.4941	+	7.21346i	−0.434462	+	0.250837i	−0.701246	−	0.712920i	$-0.747372\pi$
$827$	−12.4941	+	7.21346i	−0.434462	+	0.250837i	0.266784	+	0.963756i	$0.414039\pi$
$828$		0			0
$829$	26.7205	−	15.4271i	0.928043	−	0.535806i	0.0418506	−	0.999124i	$-0.486675\pi$
$829$	26.7205	−	15.4271i	0.928043	−	0.535806i	0.886192	+	0.463318i	$0.153341\pi$
$830$		0			0
$831$	1.41380	−	37.0692i	0.0490442	−	1.28591i
$832$		0			0
$833$	−13.7979	+	9.01067i	−0.478068	+	0.312201i
$834$		0			0
$835$	2.97694	−	16.8831i	0.103021	−	0.584262i
$836$		0			0
$837$	0.366144	+	6.07784i	0.0126558	+	0.210081i
$838$		0			0
$839$	−30.0808	−	25.2408i	−1.03850	−	0.871409i	−0.0466664	−	0.998911i	$-0.514860\pi$
$839$	−30.0808	−	25.2408i	−1.03850	−	0.871409i	−0.991838	+	0.127502i	$0.959304\pi$
$840$		0			0
$841$	3.75409	+	21.2905i	0.129452	+	0.734156i
$842$		0			0
$843$	5.51315	−	8.76010i	0.189883	−	0.301714i
$844$		0			0
$845$	30.4426			1.04726
$846$		0			0
$847$	−1.11863	−	0.0669837i	−0.0384367	−	0.00230159i
$848$		0			0
$849$	−6.89867	−	6.25186i	−0.236762	−	0.214563i
$850$		0			0
$851$	1.27436	−	0.224703i	0.0436843	−	0.00770273i
$852$		0			0
$853$	15.8578	+	43.5689i	0.542960	+	1.49177i	0.843037	+	0.537856i	$0.180766\pi$
$853$	15.8578	+	43.5689i	0.542960	+	1.49177i	−0.300077	+	0.953915i	$0.597012\pi$
$854$		0			0
$855$	0.0690992	−	0.904556i	0.00236314	−	0.0309352i
$856$		0			0
$857$	6.03029	+	5.06001i	0.205991	+	0.172847i	0.739947	−	0.672666i	$-0.234851\pi$
$857$	6.03029	+	5.06001i	0.205991	+	0.172847i	−0.533956	+	0.845512i	$0.679295\pi$
$858$		0			0
$859$	−50.8696	+	8.96968i	−1.73565	+	0.306041i	−0.949911	−	0.312521i	$-0.898827\pi$
$859$	−50.8696	+	8.96968i	−1.73565	+	0.306041i	−0.785736	+	0.618562i	$0.787716\pi$
$860$		0			0
$861$	−15.1139	+	1.16005i	−0.515082	+	0.0395343i
$862$		0			0
$863$	36.0622	−	20.8205i	1.22757	−	0.708738i	0.261050	−	0.965325i	$-0.415931\pi$
$863$	36.0622	−	20.8205i	1.22757	−	0.708738i	0.966521	+	0.256587i	$0.0825980\pi$
$864$		0			0
$865$	13.8715	−	24.0262i	0.471646	−	0.816915i
$866$		0			0
$867$	−12.1676	−	15.6775i	−0.413235	−	0.532435i
$868$		0			0
$869$	−16.3398	+	44.8931i	−0.554288	+	1.52289i
$870$		0			0
$871$	6.52276	−	7.77353i	0.221015	−	0.263396i
$872$		0			0
$873$	−24.1462	+	2.38102i	−0.817225	+	0.0805854i
$874$		0			0
$875$	−16.3695	−	15.4944i	−0.553391	−	0.523806i
$876$		0			0
$877$	20.6069	+	7.50031i	0.695846	+	0.253267i	0.665636	−	0.746276i	$-0.268160\pi$
$877$	20.6069	+	7.50031i	0.695846	+	0.253267i	0.0302100	+	0.999544i	$0.490382\pi$
$878$		0			0
$879$	30.4985	−	33.6538i	1.02869	−	1.13511i
$880$		0			0
$881$	12.4755	+	21.6082i	0.420311	+	0.727999i	0.995970	−	0.0896905i	$-0.0285878\pi$
$881$	12.4755	+	21.6082i	0.420311	+	0.727999i	−0.575659	+	0.817690i	$0.695254\pi$
$882$		0			0
$883$	21.2389	−	36.7869i	0.714746	−	1.23798i	−0.248312	−	0.968680i	$-0.579876\pi$
$883$	21.2389	−	36.7869i	0.714746	−	1.23798i	0.963057	−	0.269296i	$-0.0867910\pi$
$884$		0			0
$885$	−1.44956	+	38.0068i	−0.0487264	+	1.27758i
$886$		0			0
$887$	−17.3786	+	14.5823i	−0.583515	+	0.489627i	−0.886099	−	0.463495i	$-0.846595\pi$
$887$	−17.3786	+	14.5823i	−0.583515	+	0.489627i	0.302584	+	0.953123i	$0.402151\pi$
$888$		0			0
$889$	−2.83084	+	11.8580i	−0.0949432	+	0.397705i
$890$		0			0
$891$	−23.7276	−	19.0344i	−0.794906	−	0.637676i
$892$		0			0
$893$	0.327700	+	0.900348i	0.0109661	+	0.0301290i
$894$		0			0
$895$	11.7932	−	2.07946i	0.394204	−	0.0695088i
$896$		0			0
$897$	−0.216028	+	0.113975i	−0.00721298	+	0.00380552i
$898$		0			0
$899$	1.59178	+	2.75704i	0.0530887	+	0.0919524i
$900$		0			0
$901$	19.2503	+	11.1141i	0.641319	+	0.370266i
$902$		0			0
$903$	11.2668	+	3.14807i	0.374936	+	0.104761i
$904$		0			0
$905$	−9.70273	+	26.6580i	−0.322530	+	0.886143i
$906$		0			0
$907$	−1.61111	+	9.13705i	−0.0534960	+	0.303391i	−0.999802	−	0.0198803i	$-0.993671\pi$
$907$	−1.61111	+	9.13705i	−0.0534960	+	0.303391i	0.946306	+	0.323271i	$0.104783\pi$
$908$		0			0
$909$	27.6751	−	19.8365i	0.917924	−	0.657936i
$910$		0			0
$911$	−30.4364	−	5.36675i	−1.00840	−	0.177808i	−0.355037	−	0.934852i	$-0.615532\pi$
$911$	−30.4364	−	5.36675i	−1.00840	−	0.177808i	−0.653364	+	0.757044i	$0.726643\pi$
$912$		0			0
$913$	27.0766	+	32.2687i	0.896105	+	1.06794i
$914$		0			0
$915$	−19.4541	−	7.93279i	−0.643132	−	0.262250i
$916$		0			0
$917$	−29.7723	+	45.1061i	−0.983166	+	1.48953i
$918$		0			0
$919$	−25.6490	−	44.4254i	−0.846083	−	1.46546i	−0.884677	−	0.466204i	$-0.845621\pi$
$919$	−25.6490	−	44.4254i	−0.846083	−	1.46546i	0.0385944	−	0.999255i	$-0.487712\pi$
$920$		0			0
$921$	18.7783	+	7.65724i	0.618767	+	0.252315i
$922$		0			0
$923$	−8.55811	−	3.11490i	−0.281694	−	0.102528i
$924$		0			0
$925$	3.04820	−	17.2872i	0.100224	−	0.568399i
$926$		0			0
$927$	−3.57679	+	46.8226i	−0.117477	+	1.53786i
$928$		0			0
$929$	−39.6793	−	33.2949i	−1.30184	−	1.09237i	−0.989825	−	0.142291i	$-0.954553\pi$
$929$	−39.6793	−	33.2949i	−1.30184	−	1.09237i	−0.312010	−	0.950079i	$-0.601002\pi$
$930$		0			0
$931$	0.446762	+	0.684119i	0.0146420	+	0.0224211i
$932$		0			0
$933$	12.4364	−	13.7230i	0.407148	−	0.449271i
$934$		0			0
$935$		−	20.6139i		−	0.674145i
$936$		0			0
$937$	2.50743	+	1.44766i	0.0819140	+	0.0472931i	0.540398	−	0.841410i	$-0.318274\pi$
$937$	2.50743	+	1.44766i	0.0819140	+	0.0472931i	−0.458484	+	0.888703i	$0.651607\pi$
$938$		0			0
$939$	4.41373	+	0.168338i	0.144037	+	0.00549349i
$940$		0			0
$941$	−35.1125	−	12.7799i	−1.14463	−	0.416613i	−0.301050	−	0.953608i	$-0.597337\pi$
$941$	−35.1125	−	12.7799i	−1.14463	−	0.416613i	−0.843585	+	0.536995i	$0.819559\pi$
$942$		0			0
$943$	−0.411017	−	0.0724734i	−0.0133846	−	0.00236006i
$944$		0			0
$945$	27.2916	+	22.8836i	0.887796	+	0.744403i
$946$		0			0
$947$	28.0144	+	4.93969i	0.910344	+	0.160518i	0.609160	−	0.793048i	$-0.291507\pi$
$947$	28.0144	+	4.93969i	0.910344	+	0.160518i	0.301185	+	0.953566i	$0.402618\pi$
$948$		0			0
$949$	−11.7892	−	4.29090i	−0.382692	−	0.139289i
$950$		0			0
$951$	−14.3125	+	22.7418i	−0.464114	+	0.737453i
$952$		0			0
$953$	−40.2768	−	23.2538i	−1.30469	−	0.753264i	−0.323487	−	0.946233i	$-0.604855\pi$
$953$	−40.2768	−	23.2538i	−1.30469	−	0.753264i	−0.981205	+	0.192968i	$0.938189\pi$
$954$		0			0
$955$			51.0636i			1.65238i
$956$		0			0
$957$	−15.5462	−	3.35672i	−0.502538	−	0.108507i
$958$		0			0
$959$	−22.3379	−	30.1075i	−0.721330	−	0.972221i
$960$		0			0
$961$	22.6955	+	19.0438i	0.732113	+	0.614316i
$962$		0			0
$963$	−6.01810	−	21.5085i	−0.193931	−	0.693103i
$964$		0			0
$965$	9.95889	−	56.4797i	0.320588	−	1.81815i
$966$		0			0
$967$	−51.4456	−	18.7247i	−1.65438	−	0.602145i	−0.664914	−	0.746920i	$-0.731532\pi$
$967$	−51.4456	−	18.7247i	−1.65438	−	0.602145i	−0.989465	+	0.144775i	$0.953754\pi$
$968$		0			0
$969$	0.376003	−	0.291824i	0.0120789	−	0.00937474i
$970$		0			0
$971$	−8.88338	−	15.3865i	−0.285081	−	0.493775i	0.687548	−	0.726139i	$-0.258687\pi$
$971$	−8.88338	−	15.3865i	−0.285081	−	0.493775i	−0.972629	+	0.232364i	$0.925354\pi$
$972$		0			0
$973$	−43.5119	+	21.7637i	−1.39493	+	0.697713i
$974$		0			0
$975$	0.450583	+	3.28259i	0.0144302	+	0.105127i
$976$		0			0
$977$	19.0696	+	22.7262i	0.610090	+	0.727077i	0.979333	−	0.202256i	$-0.0648273\pi$
$977$	19.0696	+	22.7262i	0.610090	+	0.727077i	−0.369243	+	0.929333i	$0.620383\pi$
$978$		0			0
$979$	−1.35754	−	0.239371i	−0.0433872	−	0.00765034i
$980$		0			0
$981$	−36.3511	−	35.5583i	−1.16060	−	1.13529i
$982$		0			0
$983$	−5.87362	+	33.3109i	−0.187339	+	1.06245i	0.735573	+	0.677445i	$0.236913\pi$
$983$	−5.87362	+	33.3109i	−0.187339	+	1.06245i	−0.922913	+	0.385009i	$0.874198\pi$
$984$		0			0
$985$	−1.78590	+	4.90671i	−0.0569034	+	0.156341i
$986$		0			0
$987$	−36.2281	−	10.1225i	−1.15315	−	0.322204i
$988$		0			0
$989$	0.278940	+	0.161046i	0.00886977	+	0.00512097i
$990$		0			0
$991$	−5.57737	−	9.66029i	−0.177171	−	0.306869i	0.763739	−	0.645525i	$-0.223361\pi$
$991$	−5.57737	−	9.66029i	−0.177171	−	0.306869i	−0.940910	+	0.338655i	$0.890028\pi$
$992$		0			0
$993$	−35.3196	−	22.2283i	−1.12083	−	0.705394i
$994$		0			0
$995$	9.50471	−	1.67594i	0.301320	−	0.0531308i
$996$		0			0
$997$	−5.82149	−	15.9944i	−0.184368	−	0.506548i	0.812733	−	0.582637i	$-0.197979\pi$
$997$	−5.82149	−	15.9944i	−0.184368	−	0.506548i	−0.997101	+	0.0760887i	$0.975757\pi$
$998$		0			0
$999$	6.08128	−	52.9432i	0.192403	−	1.67505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.17	yes	144
7.5	odd	6		756.2.ca.a.173.23	✓	144
27.5	odd	18		756.2.ca.a.437.23	yes	144
189.5	even	18	inner	756.2.ck.a.5.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.23	✓	144	7.5	odd	6
756.2.ca.a.437.23	yes	144	27.5	odd	18
756.2.ck.a.5.17	yes	144	189.5	even	18	inner
756.2.ck.a.605.17	yes	144	1.1	even	1	trivial

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.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06196 + 1.36830i) q^{3} +(0.449866 + 2.55131i) q^{5} +(-2.53584 + 0.754675i) q^{7} +(-0.744465 + 2.90616i) q^{9} +O(q^{10})\)	\(q+(1.06196 + 1.36830i) q^{3} +(0.449866 + 2.55131i) q^{5} +(-2.53584 + 0.754675i) q^{7} +(-0.744465 + 2.90616i) q^{9} +(3.32853 + 0.586909i) q^{11} +(-0.718420 - 0.856180i) q^{13} +(-3.01321 + 3.32495i) q^{15} -2.35421 q^{17} +0.116725i q^{19} +(-3.72559 - 2.66833i) q^{21} +(-0.0811022 - 0.0966538i) q^{23} +(-1.60836 + 0.585397i) q^{25} +(-4.76708 + 2.06759i) q^{27} +(-1.74633 + 2.08119i) q^{29} +(0.400779 - 1.10113i) q^{31} +(2.73171 + 5.17769i) q^{33} +(-3.06620 - 6.13021i) q^{35} +(-5.12795 + 8.88188i) q^{37} +(0.408570 - 1.89224i) q^{39} +(2.53395 - 2.12623i) q^{41} +(-2.39884 + 0.873106i) q^{43} +(-7.74944 - 0.591981i) q^{45} +(7.71339 - 2.80744i) q^{47} +(5.86093 - 3.82747i) q^{49} +(-2.50009 - 3.22126i) q^{51} +(-8.17694 - 4.72096i) q^{53} +8.75615i q^{55} +(-0.159715 + 0.123958i) q^{57} +(6.49318 - 5.44842i) q^{59} +(1.60136 + 4.39971i) q^{61} +(-0.305368 - 7.93138i) q^{63} +(1.86119 - 2.21808i) q^{65} +(1.57661 + 8.94138i) q^{67} +(0.0461234 - 0.213615i) q^{69} +(7.05686 - 4.07428i) q^{71} +(9.72113 - 5.61250i) q^{73} +(-2.50902 - 1.57905i) q^{75} +(-8.88353 + 1.02365i) q^{77} +(-2.45450 + 13.9202i) q^{79} +(-7.89155 - 4.32707i) q^{81} +(9.54729 + 8.01113i) q^{83} +(-1.05908 - 6.00634i) q^{85} +(-4.70223 - 0.179341i) q^{87} -0.407850 q^{89} +(2.46793 + 1.62896i) q^{91} +(1.93229 - 0.620978i) q^{93} +(-0.297803 + 0.0525107i) q^{95} +(2.76618 + 7.60002i) q^{97} +(-4.18362 + 9.23631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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