LMFDB - Embedded newform 756.2.bq.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38976 + 1.03372i) q^{3} +(3.13641 + 1.14156i) q^{5} +(-2.54733 - 0.714936i) q^{7} +(0.862856 - 2.87324i) q^{9} +O(q^{10})$	\(q+(-1.38976 + 1.03372i) q^{3} +(3.13641 + 1.14156i) q^{5} +(-2.54733 - 0.714936i) q^{7} +(0.862856 - 2.87324i) q^{9} +(4.07476 - 1.48309i) q^{11} +(-1.14376 - 6.48659i) q^{13} +(-5.53890 + 1.65567i) q^{15} +3.56357 q^{17} +1.63246 q^{19} +(4.27921 - 1.63963i) q^{21} +(-0.391926 - 2.22272i) q^{23} +(4.70369 + 3.94686i) q^{25} +(1.77095 + 4.88505i) q^{27} +(-0.118897 + 0.674299i) q^{29} +(-4.67024 + 3.91880i) q^{31} +(-4.12983 + 6.27328i) q^{33} +(-7.17332 - 5.15026i) q^{35} +(4.16600 - 7.21572i) q^{37} +(8.29485 + 7.83246i) q^{39} +(0.649477 + 3.68337i) q^{41} +(7.97341 + 6.69048i) q^{43} +(5.98624 - 8.02664i) q^{45} +(-2.60091 - 2.18242i) q^{47} +(5.97773 + 3.64235i) q^{49} +(-4.95250 + 3.68372i) q^{51} +(3.42611 - 5.93419i) q^{53} +14.4731 q^{55} +(-2.26872 + 1.68750i) q^{57} +(1.64689 + 9.33997i) q^{59} +(-1.37423 - 1.15311i) q^{61} +(-4.25215 + 6.70218i) q^{63} +(3.81753 - 21.6503i) q^{65} +(-10.7731 - 3.92108i) q^{67} +(2.84235 + 2.68390i) q^{69} +(-3.21863 - 5.57483i) q^{71} +(5.96868 + 10.3381i) q^{73} +(-10.6169 - 0.622900i) q^{75} +(-11.4400 + 0.864725i) q^{77} +(12.9215 - 4.70304i) q^{79} +(-7.51096 - 4.95838i) q^{81} +(1.48535 - 8.42382i) q^{83} +(11.1768 + 4.06803i) q^{85} +(-0.531796 - 1.06002i) q^{87} +14.1243 q^{89} +(-1.72396 + 17.3412i) q^{91} +(2.43958 - 10.2739i) q^{93} +(5.12006 + 1.86355i) q^{95} +(1.39626 + 1.17160i) q^{97} +(-0.745339 - 12.9874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.38976	+	1.03372i	−0.802377	+	0.596817i
$3$	−1.38976	+	1.03372i	−0.802377	+	0.596817i
$4$		0			0
$5$	3.13641	+	1.14156i	1.40265	+	0.510521i	0.928962	−	0.370174i	$-0.120702\pi$
$5$	3.13641	+	1.14156i	1.40265	+	0.510521i	0.473683	+	0.880695i	$0.342924\pi$
$6$		0			0
$7$	−2.54733	−	0.714936i	−0.962799	−	0.270220i
$7$	−2.54733	−	0.714936i	−0.962799	−	0.270220i
$8$		0			0
$9$	0.862856	−	2.87324i	0.287619	−	0.957745i
$10$		0			0
$11$	4.07476	−	1.48309i	1.22859	−	0.447168i	0.355473	−	0.934687i	$-0.384320\pi$
$11$	4.07476	−	1.48309i	1.22859	−	0.447168i	0.873113	+	0.487518i	$0.162098\pi$
$12$		0			0
$13$	−1.14376	−	6.48659i	−0.317222	−	1.79906i	−0.559480	−	0.828844i	$-0.688999\pi$
$13$	−1.14376	−	6.48659i	−0.317222	−	1.79906i	0.242258	−	0.970212i	$-0.422112\pi$
$14$		0			0
$15$	−5.53890	+	1.65567i	−1.43014	+	0.427492i
$16$		0			0
$17$	3.56357			0.864292			0.432146	−	0.901804i	$-0.357757\pi$
$17$	3.56357			0.864292			0.432146	+	0.901804i	$0.357757\pi$
$18$		0			0
$19$	1.63246			0.374512			0.187256	−	0.982311i	$-0.440041\pi$
$19$	1.63246			0.374512			0.187256	+	0.982311i	$0.440041\pi$
$20$		0			0
$21$	4.27921	−	1.63963i	0.933800	−	0.357796i
$22$		0			0
$23$	−0.391926	−	2.22272i	−0.0817221	−	0.463469i	−0.998016	−	0.0629624i	$-0.979945\pi$
$23$	−0.391926	−	2.22272i	−0.0817221	−	0.463469i	0.916294	−	0.400507i	$-0.131166\pi$
$24$		0			0
$25$	4.70369	+	3.94686i	0.940738	+	0.789373i
$26$		0			0
$27$	1.77095	+	4.88505i	0.340820	+	0.940129i
$28$		0			0
$29$	−0.118897	+	0.674299i	−0.0220786	+	0.125214i	−0.993855	−	0.110690i	$-0.964694\pi$
$29$	−0.118897	+	0.674299i	−0.0220786	+	0.125214i	0.971776	+	0.235904i	$0.0758051\pi$
$30$		0			0
$31$	−4.67024	+	3.91880i	−0.838800	+	0.703837i	−0.957293	−	0.289118i	$-0.906638\pi$
$31$	−4.67024	+	3.91880i	−0.838800	+	0.703837i	0.118494	+	0.992955i	$0.462193\pi$
$32$		0			0
$33$	−4.12983	+	6.27328i	−0.718911	+	1.09204i
$34$		0			0
$35$	−7.17332	−	5.15026i	−1.21251	−	0.870552i
$36$		0			0
$37$	4.16600	−	7.21572i	0.684886	−	1.18626i	−0.288586	−	0.957454i	$-0.593185\pi$
$37$	4.16600	−	7.21572i	0.684886	−	1.18626i	0.973473	−	0.228804i	$-0.0734814\pi$
$38$		0			0
$39$	8.29485	+	7.83246i	1.32824	+	1.25420i
$40$		0			0
$41$	0.649477	+	3.68337i	0.101431	+	0.575245i	0.992586	+	0.121546i	$0.0387851\pi$
$41$	0.649477	+	3.68337i	0.101431	+	0.575245i	−0.891155	+	0.453700i	$0.850104\pi$
$42$		0			0
$43$	7.97341	+	6.69048i	1.21593	+	1.02029i	0.999027	+	0.0440968i	$0.0140410\pi$
$43$	7.97341	+	6.69048i	1.21593	+	1.02029i	0.216906	+	0.976192i	$0.430403\pi$
$44$		0			0
$45$	5.98624	−	8.02664i	0.892376	−	1.19654i
$46$		0			0
$47$	−2.60091	−	2.18242i	−0.379382	−	0.318339i	0.433078	−	0.901356i	$-0.357427\pi$
$47$	−2.60091	−	2.18242i	−0.379382	−	0.318339i	−0.812460	+	0.583018i	$0.801872\pi$
$48$		0			0
$49$	5.97773	+	3.64235i	0.853962	+	0.520335i
$50$		0			0
$51$	−4.95250	+	3.68372i	−0.693488	+	0.515824i
$52$		0			0
$53$	3.42611	−	5.93419i	0.470612	−	0.815124i	−0.528823	−	0.848732i	$-0.677367\pi$
$53$	3.42611	−	5.93419i	0.470612	−	0.815124i	0.999435	+	0.0336083i	$0.0106999\pi$
$54$		0			0
$55$	14.4731			1.95156
$56$		0			0
$57$	−2.26872	+	1.68750i	−0.300500	+	0.223515i
$58$		0			0
$59$	1.64689	+	9.33997i	0.214407	+	1.21596i	0.881933	+	0.471375i	$0.156242\pi$
$59$	1.64689	+	9.33997i	0.214407	+	1.21596i	−0.667526	+	0.744586i	$0.732647\pi$
$60$		0			0
$61$	−1.37423	−	1.15311i	−0.175952	−	0.147641i	0.550559	−	0.834796i	$-0.314415\pi$
$61$	−1.37423	−	1.15311i	−0.175952	−	0.147641i	−0.726510	+	0.687155i	$0.758859\pi$
$62$		0			0
$63$	−4.25215	+	6.70218i	−0.535721	+	0.844395i
$64$		0			0
$65$	3.81753	−	21.6503i	0.473506	−	2.68539i
$66$		0			0
$67$	−10.7731	−	3.92108i	−1.31614	−	0.479037i	−0.413922	−	0.910312i	$-0.635841\pi$
$67$	−10.7731	−	3.92108i	−1.31614	−	0.479037i	−0.902220	+	0.431276i	$0.858064\pi$
$68$		0			0
$69$	2.84235	+	2.68390i	0.342178	+	0.323104i
$70$		0			0
$71$	−3.21863	−	5.57483i	−0.381981	−	0.661611i	0.609364	−	0.792890i	$-0.291425\pi$
$71$	−3.21863	−	5.57483i	−0.381981	−	0.661611i	−0.991345	+	0.131280i	$0.958091\pi$
$72$		0			0
$73$	5.96868	+	10.3381i	0.698582	+	1.20998i	0.968958	+	0.247224i	$0.0795184\pi$
$73$	5.96868	+	10.3381i	0.698582	+	1.20998i	−0.270377	+	0.962755i	$0.587148\pi$
$74$		0			0
$75$	−10.6169	−	0.622900i	−1.22594	−	0.0719263i
$76$		0			0
$77$	−11.4400	+	0.864725i	−1.30371	+	0.0985445i
$78$		0			0
$79$	12.9215	−	4.70304i	1.45378	−	0.529133i	0.510137	−	0.860093i	$-0.329595\pi$
$79$	12.9215	−	4.70304i	1.45378	−	0.529133i	0.943645	+	0.330959i	$0.107372\pi$
$80$		0			0
$81$	−7.51096	−	4.95838i	−0.834551	−	0.550931i
$82$		0			0
$83$	1.48535	−	8.42382i	0.163038	−	0.924635i	−0.788026	−	0.615642i	$-0.788897\pi$
$83$	1.48535	−	8.42382i	0.163038	−	0.924635i	0.951064	−	0.308993i	$-0.0999920\pi$
$84$		0			0
$85$	11.1768	+	4.06803i	1.21229	+	0.441239i
$86$		0			0
$87$	−0.531796	−	1.06002i	−0.0570145	−	0.113646i
$88$		0			0
$89$	14.1243			1.49718			0.748588	−	0.663036i	$-0.230732\pi$
$89$	14.1243			1.49718			0.748588	+	0.663036i	$0.230732\pi$
$90$		0			0
$91$	−1.72396	+	17.3412i	−0.180720	+	1.81785i
$92$		0			0
$93$	2.43958	−	10.2739i	0.252972	−	1.06535i
$94$		0			0
$95$	5.12006	+	1.86355i	0.525307	+	0.191196i
$96$		0			0
$97$	1.39626	+	1.17160i	0.141769	+	0.118958i	0.710914	−	0.703279i	$-0.248281\pi$
$97$	1.39626	+	1.17160i	0.141769	+	0.118958i	−0.569145	+	0.822237i	$0.692726\pi$
$98$		0			0
$99$	−0.745339	−	12.9874i	−0.0749094	−	1.30529i
$100$		0			0
$101$	−2.20493	+	12.5048i	−0.219399	+	1.24427i	0.653708	+	0.756747i	$0.273212\pi$
$101$	−2.20493	+	12.5048i	−0.219399	+	1.24427i	−0.873107	+	0.487528i	$0.837899\pi$
$102$		0			0
$103$	−6.96044	−	2.53339i	−0.685833	−	0.249623i	−0.0244828	−	0.999700i	$-0.507794\pi$
$103$	−6.96044	−	2.53339i	−0.685833	−	0.249623i	−0.661350	+	0.750078i	$0.730016\pi$
$104$		0			0
$105$	15.2931	−	0.257572i	1.49245	−	0.0251364i
$106$		0			0
$107$	−3.60917	−	6.25127i	−0.348912	−	0.604333i	0.637145	−	0.770744i	$-0.280115\pi$
$107$	−3.60917	−	6.25127i	−0.348912	−	0.604333i	−0.986056	+	0.166411i	$0.946782\pi$
$108$		0			0
$109$	−6.87105	+	11.9010i	−0.658127	+	1.13991i	0.322973	+	0.946408i	$0.395318\pi$
$109$	−6.87105	+	11.9010i	−0.658127	+	1.13991i	−0.981100	+	0.193501i	$0.938016\pi$
$110$		0			0
$111$	1.66929	+	14.3346i	0.158442	+	1.36058i
$112$		0			0
$113$	−8.07878	+	6.77890i	−0.759988	+	0.637706i	−0.938124	−	0.346300i	$-0.887438\pi$
$113$	−8.07878	+	6.77890i	−0.759988	+	0.637706i	0.178136	+	0.984006i	$0.442993\pi$
$114$		0			0
$115$	1.30813	−	7.41877i	0.121984	−	0.691804i
$116$		0			0
$117$	−19.6244	−	2.31070i	−1.81428	−	0.213624i
$118$		0			0
$119$	−9.07756	−	2.54772i	−0.832139	−	0.233549i
$120$		0			0
$121$	5.97760	−	5.01580i	0.543418	−	0.455982i
$122$		0			0
$123$	−4.71018	−	4.44761i	−0.424702	−	0.401028i
$124$		0			0
$125$	1.90287	+	3.29587i	0.170198	+	0.294791i
$126$		0			0
$127$	5.71485	−	9.89842i	0.507111	−	0.878342i	−0.492855	−	0.870112i	$-0.664047\pi$
$127$	5.71485	−	9.89842i	0.507111	−	0.878342i	0.999966	−	0.00823095i	$-0.00262002\pi$
$128$		0			0
$129$	−17.9972	−	1.05590i	−1.58456	−	0.0929671i
$130$		0			0
$131$	−2.07307	−	11.7570i	−0.181125	−	1.02721i	−0.930833	−	0.365444i	$-0.880917\pi$
$131$	−2.07307	−	11.7570i	−0.181125	−	1.02721i	0.749708	−	0.661769i	$-0.230194\pi$
$132$		0			0
$133$	−4.15840	−	1.16710i	−0.360579	−	0.101201i
$134$		0			0
$135$	−0.0221456	+	17.3432i	−0.00190599	+	1.49266i
$136$		0			0
$137$	−12.7774	−	10.7216i	−1.09165	−	0.916004i	−0.0948154	−	0.995495i	$-0.530226\pi$
$137$	−12.7774	−	10.7216i	−1.09165	−	0.916004i	−0.996836	+	0.0794910i	$0.974671\pi$
$138$		0			0
$139$	−0.810607	−	0.295037i	−0.0687548	−	0.0250247i	0.307414	−	0.951576i	$-0.400536\pi$
$139$	−0.810607	−	0.295037i	−0.0687548	−	0.0250247i	−0.376169	+	0.926551i	$0.622759\pi$
$140$		0			0
$141$	5.87064	+	0.344433i	0.494397	+	0.0290065i
$142$		0			0
$143$	−14.2807	−	24.7350i	−1.19422	−	2.06844i
$144$		0			0
$145$	−1.14266	+	1.97915i	−0.0948929	+	0.164359i
$146$		0			0
$147$	−12.0728	+	1.11731i	−0.995745	+	0.0921539i
$148$		0			0
$149$	−14.4544	+	12.1287i	−1.18415	+	0.993621i	−0.184209	+	0.982887i	$0.558972\pi$
$149$	−14.4544	+	12.1287i	−1.18415	+	0.993621i	−0.999942	+	0.0107337i	$0.996583\pi$
$150$		0			0
$151$	−12.5413	+	4.56464i	−1.02059	+	0.371465i	−0.797492	−	0.603330i	$-0.793840\pi$
$151$	−12.5413	+	4.56464i	−1.02059	+	0.371465i	−0.223101	+	0.974795i	$0.571618\pi$
$152$		0			0
$153$	3.07484	−	10.2390i	0.248586	−	0.827771i
$154$		0			0
$155$	−19.1213	+	6.95959i	−1.53586	+	0.559008i
$156$		0			0
$157$	0.593466	+	3.36571i	0.0473637	+	0.268613i	0.999288	−	0.0377192i	$-0.0120093\pi$
$157$	0.593466	+	3.36571i	0.0473637	+	0.268613i	−0.951925	+	0.306332i	$0.900898\pi$
$158$		0			0
$159$	1.37282	+	11.7887i	0.108871	+	0.934906i
$160$		0			0
$161$	−0.590740	+	5.94219i	−0.0465568	+	0.468310i
$162$		0			0
$163$	1.24825	+	2.16204i	0.0977707	+	0.169344i	0.910762	−	0.412933i	$-0.135495\pi$
$163$	1.24825	+	2.16204i	0.0977707	+	0.169344i	−0.812991	+	0.582276i	$0.802162\pi$
$164$		0			0
$165$	−20.1142	+	14.9611i	−1.56589	+	1.16472i
$166$		0			0
$167$	−9.86481	+	8.27756i	−0.763362	+	0.640537i	−0.939000	−	0.343918i	$-0.888246\pi$
$167$	−9.86481	+	8.27756i	−0.763362	+	0.640537i	0.175638	+	0.984455i	$0.443801\pi$
$168$		0			0
$169$	−28.5516	+	10.3919i	−2.19628	+	0.799380i
$170$		0			0
$171$	1.40858	−	4.69044i	0.107717	−	0.358687i
$172$		0			0
$173$	−2.98022	+	16.9017i	−0.226582	+	1.28501i	0.633055	+	0.774106i	$0.281800\pi$
$173$	−2.98022	+	16.9017i	−0.226582	+	1.28501i	−0.859638	+	0.510904i	$0.829311\pi$
$174$		0			0
$175$	−9.16007	−	13.4168i	−0.692436	−	1.01421i
$176$		0			0
$177$	−11.9437	−	11.2779i	−0.897741	−	0.847698i
$178$		0			0
$179$	13.2124			0.987538			0.493769	−	0.869593i	$-0.335619\pi$
$179$	13.2124			0.987538			0.493769	+	0.869593i	$0.335619\pi$
$180$		0			0
$181$	4.65985	−	8.07110i	0.346364	−	0.599920i	−0.639237	−	0.769010i	$-0.720750\pi$
$181$	4.65985	−	8.07110i	0.346364	−	0.599920i	0.985601	+	0.169090i	$0.0540829\pi$
$182$		0			0
$183$	3.10184	+	0.181986i	0.229294	+	0.0134528i
$184$		0			0
$185$	21.3035	−	17.8757i	1.56626	−	1.31425i
$186$		0			0
$187$	14.5207	−	5.28509i	1.06186	−	0.386484i
$188$		0			0
$189$	−1.01870	−	13.7099i	−0.0740992	−	0.997251i
$190$		0			0
$191$	8.02859	−	2.92217i	0.580928	−	0.211441i	−0.0348064	−	0.999394i	$-0.511081\pi$
$191$	8.02859	−	2.92217i	0.580928	−	0.211441i	0.615735	+	0.787953i	$0.288859\pi$
$192$		0			0
$193$	−9.08181	+	7.62055i	−0.653723	+	0.548539i	−0.908198	−	0.418541i	$-0.862542\pi$
$193$	−9.08181	+	7.62055i	−0.653723	+	0.548539i	0.254475	+	0.967079i	$0.418097\pi$
$194$		0			0
$195$	17.0748	+	34.0349i	1.22275	+	2.43729i
$196$		0			0
$197$	7.98188	−	13.8250i	0.568686	−	0.984993i	−0.428011	−	0.903774i	$-0.640785\pi$
$197$	7.98188	−	13.8250i	0.568686	−	0.984993i	0.996696	−	0.0812188i	$-0.0258813\pi$
$198$		0			0
$199$	9.60399			0.680809			0.340404	−	0.940279i	$-0.389436\pi$
$199$	9.60399			0.680809			0.340404	+	0.940279i	$0.389436\pi$
$200$		0			0
$201$	19.0253	−	5.68697i	1.34194	−	0.401128i
$202$		0			0
$203$	0.784950	−	1.63265i	0.0550927	−	0.114590i
$204$		0			0
$205$	−2.16776	+	12.2940i	−0.151403	+	0.858648i
$206$		0			0
$207$	−6.72457	−	0.791793i	−0.467390	−	0.0550334i
$208$		0			0
$209$	6.65187	−	2.42108i	0.460120	−	0.167470i
$210$		0			0
$211$	6.21005	−	5.21085i	0.427518	−	0.358730i	−0.403497	−	0.914981i	$-0.632205\pi$
$211$	6.21005	−	5.21085i	0.427518	−	0.358730i	0.831014	+	0.556251i	$0.187761\pi$
$212$		0			0
$213$	10.2359	+	4.42051i	0.701353	+	0.302888i
$214$		0			0
$215$	17.3703	+	30.0862i	1.18464	+	2.05186i
$216$		0			0
$217$	14.6983	−	6.64353i	0.997786	−	0.450992i
$218$		0			0
$219$	−18.9817	−	8.19748i	−1.28266	−	0.553934i
$220$		0			0
$221$	−4.07587	−	23.1154i	−0.274172	−	1.55491i
$222$		0			0
$223$	−5.92504	+	2.15654i	−0.396770	+	0.144413i	−0.532696	−	0.846306i	$-0.678821\pi$
$223$	−5.92504	+	2.15654i	−0.396770	+	0.144413i	0.135926	+	0.990719i	$0.456599\pi$
$224$		0			0
$225$	15.3989	−	10.1092i	1.02659	−	0.673949i
$226$		0			0
$227$	−16.0716	+	5.84958i	−1.06671	+	0.388250i	−0.814945	−	0.579538i	$-0.803233\pi$
$227$	−16.0716	+	5.84958i	−1.06671	+	0.388250i	−0.251764	+	0.967789i	$0.581011\pi$
$228$		0			0
$229$	2.38053	−	1.99750i	0.157310	−	0.131999i	−0.560735	−	0.827995i	$-0.689482\pi$
$229$	2.38053	−	1.99750i	0.157310	−	0.131999i	0.718045	+	0.695996i	$0.245037\pi$
$230$		0			0
$231$	15.0050	−	13.0275i	0.987258	−	0.857149i
$232$		0			0
$233$	10.4155	−	18.0401i	0.682339	−	1.18185i	−0.291926	−	0.956441i	$-0.594296\pi$
$233$	10.4155	−	18.0401i	0.682339	−	1.18185i	0.974265	−	0.225405i	$-0.0723705\pi$
$234$		0			0
$235$	−5.66615	−	9.81406i	−0.369619	−	0.640199i
$236$		0			0
$237$	−13.0961	+	19.8933i	−0.850686	+	1.29221i
$238$		0			0
$239$	21.9863	+	8.00237i	1.42218	+	0.517631i	0.934679	−	0.355493i	$-0.115687\pi$
$239$	21.9863	+	8.00237i	1.42218	+	0.517631i	0.487499	+	0.873123i	$0.337909\pi$
$240$		0			0
$241$	−7.10784	−	5.96419i	−0.457856	−	0.384187i	0.384485	−	0.923131i	$-0.374379\pi$
$241$	−7.10784	−	5.96419i	−0.457856	−	0.384187i	−0.842342	+	0.538944i	$0.818823\pi$
$242$		0			0
$243$	15.5640	−	0.873267i	0.998430	−	0.0560201i
$244$		0			0
$245$	14.5907	+	18.2478i	0.932164	+	1.16581i
$246$		0			0
$247$	−1.86714	−	10.5891i	−0.118803	−	0.673768i
$248$		0			0
$249$	6.64358	+	13.2425i	0.421020	+	0.839210i
$250$		0			0
$251$	−7.94245	+	13.7567i	−0.501323	+	0.868317i	0.498676	+	0.866789i	$0.333820\pi$
$251$	−7.94245	+	13.7567i	−0.501323	+	0.868317i	−0.999999	+	0.00152865i	$0.999513\pi$
$252$		0			0
$253$	−4.89350	−	8.47578i	−0.307651	−	0.532868i
$254$		0			0
$255$	−19.7382	+	5.90009i	−1.23606	+	0.369478i
$256$		0			0
$257$	0.268641	−	0.225417i	0.0167574	−	0.0140611i	−0.634370	−	0.773029i	$-0.718741\pi$
$257$	0.268641	−	0.225417i	0.0167574	−	0.0140611i	0.651128	+	0.758968i	$0.274296\pi$
$258$		0			0
$259$	−15.7709	+	15.4024i	−0.979958	+	0.957057i
$260$		0			0
$261$	1.83483	+	0.923442i	0.113573	+	0.0571596i
$262$		0			0
$263$	3.34189	−	18.9528i	0.206070	−	1.16868i	−0.689678	−	0.724116i	$-0.742248\pi$
$263$	3.34189	−	18.9528i	0.206070	−	1.16868i	0.895748	−	0.444563i	$-0.146641\pi$
$264$		0			0
$265$	17.5199	−	14.7010i	1.07624	−	0.903072i
$266$		0			0
$267$	−19.6294	+	14.6006i	−1.20130	+	0.893540i
$268$		0			0
$269$	−4.21402	+	7.29890i	−0.256934	+	0.445022i	−0.965419	−	0.260704i	$-0.916045\pi$
$269$	−4.21402	+	7.29890i	−0.256934	+	0.445022i	0.708485	+	0.705726i	$0.249379\pi$
$270$		0			0
$271$	0.506123	+	0.876631i	0.0307448	+	0.0532516i	0.880988	−	0.473138i	$-0.156879\pi$
$271$	0.506123	+	0.876631i	0.0307448	+	0.0532516i	−0.850244	+	0.526389i	$0.823545\pi$
$272$		0			0
$273$	−15.5300	−	25.8821i	−0.939917	−	1.56646i
$274$		0			0
$275$	25.0199	+	9.10651i	1.50876	+	0.549143i
$276$		0			0
$277$	−2.21185	+	12.5440i	−0.132897	+	0.753698i	0.843404	+	0.537281i	$0.180548\pi$
$277$	−2.21185	+	12.5440i	−0.132897	+	0.753698i	−0.976301	+	0.216418i	$0.930563\pi$
$278$		0			0
$279$	7.22988	+	16.8001i	0.432841	+	1.00579i
$280$		0			0
$281$	−6.45895	−	5.41970i	−0.385308	−	0.323312i	0.429474	−	0.903079i	$-0.358699\pi$
$281$	−6.45895	−	5.41970i	−0.385308	−	0.323312i	−0.814782	+	0.579767i	$0.803144\pi$
$282$		0			0
$283$	17.9677	+	6.53971i	1.06807	+	0.388746i	0.815455	−	0.578821i	$-0.196487\pi$
$283$	17.9677	+	6.53971i	1.06807	+	0.388746i	0.252615	+	0.967567i	$0.418709\pi$
$284$		0			0
$285$	−9.04203	+	2.70281i	−0.535604	+	0.160101i
$286$		0			0
$287$	0.978941	−	9.84707i	0.0577851	−	0.581254i
$288$		0			0
$289$	−4.30099			−0.253000
$290$		0			0
$291$	−3.15157	−	0.184904i	−0.184749	−	0.0108393i
$292$		0			0
$293$	12.2434	+	4.45623i	0.715267	+	0.260336i	0.673915	−	0.738809i	$-0.264611\pi$
$293$	12.2434	+	4.45623i	0.715267	+	0.260336i	0.0413518	+	0.999145i	$0.486834\pi$
$294$		0			0
$295$	−5.49682	+	31.1740i	−0.320037	+	1.81502i
$296$		0			0
$297$	14.4612	+	17.2789i	0.839122	+	1.00262i
$298$		0			0
$299$	−13.9696	+	5.08452i	−0.807883	+	0.294045i
$300$		0			0
$301$	−15.5276	−	22.7433i	−0.894996	−	1.31090i
$302$		0			0
$303$	−9.86211	−	19.6579i	−0.566564	−	1.12932i
$304$		0			0
$305$	−2.99379	−	5.18540i	−0.171424	−	0.296915i
$306$		0			0
$307$	16.2977	+	28.2285i	0.930160	+	1.61108i	0.783045	+	0.621965i	$0.213665\pi$
$307$	16.2977	+	28.2285i	0.930160	+	1.61108i	0.147115	+	0.989119i	$0.453001\pi$
$308$		0			0
$309$	12.2921	−	3.67433i	0.699276	−	0.209025i
$310$		0			0
$311$	9.39813	+	3.42064i	0.532919	+	0.193967i	0.594441	−	0.804139i	$-0.297373\pi$
$311$	9.39813	+	3.42064i	0.532919	+	0.193967i	−0.0615222	+	0.998106i	$0.519595\pi$
$312$		0			0
$313$	−1.21140	+	6.87018i	−0.0684722	+	0.388325i	0.931242	+	0.364402i	$0.118727\pi$
$313$	−1.21140	+	6.87018i	−0.0684722	+	0.388325i	−0.999714	+	0.0239229i	$0.992384\pi$
$314$		0			0
$315$	−20.9874	+	16.1667i	−1.18251	+	0.910890i
$316$		0			0
$317$	−7.20467	−	6.04543i	−0.404654	−	0.339545i	0.417635	−	0.908615i	$-0.362859\pi$
$317$	−7.20467	−	6.04543i	−0.404654	−	0.339545i	−0.822289	+	0.569070i	$0.807304\pi$
$318$		0			0
$319$	0.515569	+	2.92394i	0.0288663	+	0.163709i
$320$		0			0
$321$	11.4779	+	4.95689i	0.640635	+	0.276666i
$322$		0			0
$323$	5.81738			0.323688
$324$		0			0
$325$	20.2218	−	35.0251i	1.12170	−	1.94285i
$326$		0			0
$327$	−2.75318	−	23.6422i	−0.152251	−	1.30742i
$328$		0			0
$329$	5.06507	+	7.41882i	0.279246	+	0.409013i
$330$		0			0
$331$	−4.31340	−	3.61938i	−0.237086	−	0.198939i	0.516502	−	0.856286i	$-0.327234\pi$
$331$	−4.31340	−	3.61938i	−0.237086	−	0.198939i	−0.753588	+	0.657347i	$0.771678\pi$
$332$		0			0
$333$	−17.1378	−	18.1960i	−0.939146	−	0.997136i
$334$		0			0
$335$	−29.3127	−	24.5963i	−1.60152	−	1.34384i
$336$		0			0
$337$	−2.24738	−	12.7455i	−0.122423	−	0.694293i	−0.982805	−	0.184644i	$-0.940887\pi$
$337$	−2.24738	−	12.7455i	−0.122423	−	0.694293i	0.860383	−	0.509648i	$-0.170224\pi$
$338$		0			0
$339$	4.22008	−	17.7722i	0.229203	−	0.965254i
$340$		0			0
$341$	−13.2182	+	22.8945i	−0.715804	+	1.23981i
$342$		0			0
$343$	−12.6232	−	13.5519i	−0.681588	−	0.731736i
$344$		0			0
$345$	5.85093	+	11.6625i	0.315003	+	0.627890i
$346$		0			0
$347$	−11.2347	+	9.42699i	−0.603108	+	0.506067i	−0.892443	−	0.451160i	$-0.851010\pi$
$347$	−11.2347	+	9.42699i	−0.603108	+	0.506067i	0.289335	+	0.957228i	$0.406566\pi$
$348$		0			0
$349$	−0.556948	+	3.15861i	−0.0298128	+	0.169077i	−0.996079	−	0.0884689i	$-0.971803\pi$
$349$	−0.556948	+	3.15861i	−0.0298128	+	0.169077i	0.966266	+	0.257545i	$0.0829137\pi$
$350$		0			0
$351$	29.6618	−	17.0748i	1.58323	−	0.911384i
$352$		0			0
$353$	15.9471	+	13.3812i	0.848778	+	0.712209i	0.959520	−	0.281640i	$-0.0908783\pi$
$353$	15.9471	+	13.3812i	0.848778	+	0.712209i	−0.110742	+	0.993849i	$0.535323\pi$
$354$		0			0
$355$	−3.73094	−	21.1592i	−0.198018	−	1.12301i
$356$		0			0
$357$	15.2492	−	5.84292i	0.807076	−	0.309240i
$358$		0			0
$359$	−2.21241			−0.116766			−0.0583832	−	0.998294i	$-0.518595\pi$
$359$	−2.21241			−0.116766			−0.0583832	+	0.998294i	$0.518595\pi$
$360$		0			0
$361$	−16.3351			−0.859741
$362$		0			0
$363$	−3.12249	+	13.1499i	−0.163888	+	0.690190i
$364$		0			0
$365$	6.91872	+	39.2380i	0.362142	+	2.05381i
$366$		0			0
$367$	16.5967	−	6.04071i	0.866342	−	0.315323i	0.129657	−	0.991559i	$-0.458612\pi$
$367$	16.5967	−	6.04071i	0.866342	−	0.315323i	0.736685	+	0.676236i	$0.236390\pi$
$368$		0			0
$369$	11.1436	+	1.31212i	0.580112	+	0.0683060i
$370$		0			0
$371$	−12.9700	+	12.6669i	−0.673367	+	0.657631i
$372$		0			0
$373$	14.0572	+	5.11640i	0.727854	+	0.264917i	0.679256	−	0.733901i	$-0.262303\pi$
$373$	14.0572	+	5.11640i	0.727854	+	0.264917i	0.0485979	+	0.998818i	$0.484525\pi$
$374$		0			0
$375$	−6.05153	−	2.61343i	−0.312499	−	0.134957i
$376$		0			0
$377$	4.50989			0.232271
$378$		0			0
$379$	13.2785			0.682073			0.341037	−	0.940050i	$-0.389222\pi$
$379$	13.2785			0.682073			0.341037	+	0.940050i	$0.389222\pi$
$380$		0			0
$381$	2.28990	+	19.6640i	0.117315	+	1.00741i
$382$		0			0
$383$	−28.9752	−	10.5461i	−1.48056	−	0.538881i	−0.529617	−	0.848237i	$-0.677664\pi$
$383$	−28.9752	−	10.5461i	−1.48056	−	0.538881i	−0.950946	+	0.309356i	$0.899886\pi$
$384$		0			0
$385$	−36.8678	−	10.3474i	−1.87896	−	0.527351i
$386$		0			0
$387$	26.1032	−	17.1366i	1.32690	−	0.871100i
$388$		0			0
$389$	−26.7307	+	9.72919i	−1.35530	+	0.493289i	−0.914598	−	0.404364i	$-0.867493\pi$
$389$	−26.7307	+	9.72919i	−1.35530	+	0.493289i	−0.440703	+	0.897653i	$0.645271\pi$
$390$		0			0
$391$	−1.39665	−	7.92081i	−0.0706318	−	0.400573i
$392$		0			0
$393$	15.0345	+	14.1964i	0.758389	+	0.716113i
$394$		0			0
$395$	45.8959			2.30927
$396$		0			0
$397$	−21.8379			−1.09601			−0.548005	−	0.836475i	$-0.684613\pi$
$397$	−21.8379			−1.09601			−0.548005	+	0.836475i	$0.684613\pi$
$398$		0			0
$399$	6.98563	−	2.67662i	0.349719	−	0.133999i
$400$		0			0
$401$	−5.65394	−	32.0651i	−0.282344	−	1.60125i	−0.714620	−	0.699513i	$-0.753400\pi$
$401$	−5.65394	−	32.0651i	−0.282344	−	1.60125i	0.432275	−	0.901742i	$-0.357711\pi$
$402$		0			0
$403$	30.7612	+	25.8117i	1.53233	+	1.28577i
$404$		0			0
$405$	−17.8972	−	24.1257i	−0.889317	−	1.19882i
$406$		0			0
$407$	6.27387	−	35.5809i	0.310984	−	1.76368i
$408$		0			0
$409$	−23.0217	+	19.3175i	−1.13835	+	0.955187i	−0.999383	−	0.0351103i	$-0.988822\pi$
$409$	−23.0217	+	19.3175i	−1.13835	+	0.955187i	−0.138964	+	0.990297i	$0.544377\pi$
$410$		0			0
$411$	28.8406	+	1.69209i	1.42260	+	0.0834648i
$412$		0			0
$413$	2.48232	−	24.9694i	0.122147	−	1.22866i
$414$		0			0
$415$	14.2750	−	24.7250i	0.700730	−	1.21370i
$416$		0			0
$417$	1.43153	−	0.427909i	0.0701025	−	0.0209548i
$418$		0			0
$419$	−2.29781	−	13.0315i	−0.112255	−	0.636631i	−0.988073	−	0.153989i	$-0.950788\pi$
$419$	−2.29781	−	13.0315i	−0.112255	−	0.636631i	0.875817	−	0.482643i	$-0.160323\pi$
$420$		0			0
$421$	−10.0535	−	8.43585i	−0.489975	−	0.411138i	0.364042	−	0.931382i	$-0.381396\pi$
$421$	−10.0535	−	8.43585i	−0.489975	−	0.411138i	−0.854017	+	0.520244i	$0.825841\pi$
$422$		0			0
$423$	−8.51482	+	5.58991i	−0.414005	+	0.271791i
$424$		0			0
$425$	16.7619	+	14.0649i	0.813072	+	0.682248i
$426$		0			0
$427$	2.67620	+	3.91984i	0.129511	+	0.189694i
$428$		0			0
$429$	45.4157	+	19.6134i	2.19269	+	0.946942i
$430$		0			0
$431$	−9.10042	+	15.7624i	−0.438352	+	0.759248i	−0.997563	−	0.0697777i	$-0.977771\pi$
$431$	−9.10042	+	15.7624i	−0.438352	+	0.759248i	0.559211	+	0.829026i	$0.311104\pi$
$432$		0			0
$433$	−22.9654			−1.10365			−0.551824	−	0.833961i	$-0.686068\pi$
$433$	−22.9654			−1.10365			−0.551824	+	0.833961i	$0.686068\pi$
$434$		0			0
$435$	−0.457857	−	3.93173i	−0.0219526	−	0.188512i
$436$		0			0
$437$	−0.639802	−	3.62850i	−0.0306059	−	0.173575i
$438$		0			0
$439$	14.9654	+	12.5574i	0.714258	+	0.599334i	0.925790	−	0.378037i	$-0.123401\pi$
$439$	14.9654	+	12.5574i	0.714258	+	0.599334i	−0.211532	+	0.977371i	$0.567845\pi$
$440$		0			0
$441$	15.6232	−	14.0326i	0.743964	−	0.668220i
$442$		0			0
$443$	−2.62825	+	14.9055i	−0.124872	+	0.708183i	0.856512	+	0.516127i	$0.172627\pi$
$443$	−2.62825	+	14.9055i	−0.124872	+	0.708183i	−0.981384	+	0.192056i	$0.938484\pi$
$444$		0			0
$445$	44.2997	+	16.1238i	2.10001	+	0.764340i
$446$		0			0
$447$	7.55049	−	31.7977i	0.357126	−	1.50398i
$448$		0			0
$449$	14.3363	+	24.8312i	0.676573	+	1.17186i	0.976006	+	0.217742i	$0.0698691\pi$
$449$	14.3363	+	24.8312i	0.676573	+	1.17186i	−0.299433	+	0.954117i	$0.596798\pi$
$450$		0			0
$451$	8.10923	+	14.0456i	0.381849	+	0.661381i
$452$		0			0
$453$	12.7108	−	19.3079i	0.597204	−	0.907163i
$454$		0			0
$455$	−25.2030	+	52.4210i	−1.18154	+	2.45753i
$456$		0			0
$457$	−13.9728	+	5.08569i	−0.653621	+	0.237899i	−0.647480	−	0.762083i	$-0.724177\pi$
$457$	−13.9728	+	5.08569i	−0.653621	+	0.237899i	−0.00614119	+	0.999981i	$0.501955\pi$
$458$		0			0
$459$	6.31091	+	17.4082i	0.294568	+	0.812545i
$460$		0			0
$461$	−2.26251	+	12.8313i	−0.105375	+	0.597614i	0.885694	+	0.464269i	$0.153683\pi$
$461$	−2.26251	+	12.8313i	−0.105375	+	0.597614i	−0.991070	+	0.133345i	$0.957428\pi$
$462$		0			0
$463$	19.9215	+	7.25084i	0.925832	+	0.336975i	0.760556	−	0.649272i	$-0.224926\pi$
$463$	19.9215	+	7.25084i	0.925832	+	0.336975i	0.165276	+	0.986247i	$0.447149\pi$
$464$		0			0
$465$	19.3798	−	29.4382i	0.898715	−	1.36516i
$466$		0			0
$467$	1.09430			0.0506382			0.0253191	−	0.999679i	$-0.491940\pi$
$467$	1.09430			0.0506382			0.0253191	+	0.999679i	$0.491940\pi$
$468$		0			0
$469$	24.6392	+	17.6903i	1.13773	+	0.816864i
$470$		0			0
$471$	−4.30397	−	4.06405i	−0.198316	−	0.187262i
$472$		0			0
$473$	42.4123	+	15.4368i	1.95012	+	0.709785i
$474$		0			0
$475$	7.67858	+	6.44309i	0.352317	+	0.295629i
$476$		0			0
$477$	−14.0941	−	14.9644i	−0.645324	−	0.685171i
$478$		0			0
$479$	3.40598	−	19.3163i	0.155623	−	0.882584i	−0.802590	−	0.596531i	$-0.796545\pi$
$479$	3.40598	−	19.3163i	0.155623	−	0.882584i	0.958214	−	0.286053i	$-0.0923434\pi$
$480$		0			0
$481$	−51.5703	−	18.7701i	−2.35140	−	0.855841i
$482$		0			0
$483$	−5.32156	−	8.86887i	−0.242140	−	0.403548i
$484$		0			0
$485$	3.04180	+	5.26855i	0.138121	+	0.239232i
$486$		0			0
$487$	4.01523	−	6.95458i	0.181947	−	0.315142i	−0.760596	−	0.649225i	$-0.775093\pi$
$487$	4.01523	−	6.95458i	0.181947	−	0.315142i	0.942544	+	0.334083i	$0.108427\pi$
$488$		0			0
$489$	−3.96970	−	1.71437i	−0.179516	−	0.0775264i
$490$		0			0
$491$	3.82295	−	3.20783i	0.172527	−	0.144767i	−0.552436	−	0.833556i	$-0.686301\pi$
$491$	3.82295	−	3.20783i	0.172527	−	0.144767i	0.724963	+	0.688788i	$0.241857\pi$
$492$		0			0
$493$	−0.423698	+	2.40291i	−0.0190824	+	0.108222i
$494$		0			0
$495$	12.4882	−	41.5847i	0.561305	−	1.86910i
$496$		0			0
$497$	4.21325	+	16.5020i	0.188990	+	0.740217i
$498$		0			0
$499$	−16.3452	+	13.7153i	−0.731712	+	0.613979i	−0.930598	−	0.366043i	$-0.880712\pi$
$499$	−16.3452	+	13.7153i	−0.731712	+	0.613979i	0.198886	+	0.980023i	$0.436268\pi$
$500$		0			0
$501$	5.15304	−	21.7012i	0.230221	−	0.969539i
$502$		0			0
$503$	−2.46959	−	4.27746i	−0.110114	−	0.190723i	0.805702	−	0.592321i	$-0.201788\pi$
$503$	−2.46959	−	4.27746i	−0.110114	−	0.190723i	−0.915816	+	0.401598i	$0.868455\pi$
$504$		0			0
$505$	−21.1906	+	36.7031i	−0.942968	+	1.63327i
$506$		0			0
$507$	28.9375	−	43.9566i	1.28516	−	1.95218i
$508$		0			0
$509$	2.06552	+	11.7141i	0.0915526	+	0.519220i	0.995749	+	0.0921043i	$0.0293593\pi$
$509$	2.06552	+	11.7141i	0.0915526	+	0.519220i	−0.904197	+	0.427116i	$0.859530\pi$
$510$		0			0
$511$	−7.81313	−	30.6016i	−0.345633	−	1.35374i
$512$		0			0
$513$	2.89101	+	7.97465i	0.127641	+	0.352089i
$514$		0			0
$515$	−18.9388	−	15.8915i	−0.834542	−	0.700264i
$516$		0			0
$517$	−13.8348	−	5.03545i	−0.608454	−	0.221459i
$518$		0			0
$519$	−13.3298	−	26.5700i	−0.585112	−	1.16629i
$520$		0			0
$521$	−15.1983	−	26.3242i	−0.665850	−	1.15329i	−0.979054	−	0.203600i	$-0.934736\pi$
$521$	−15.1983	−	26.3242i	−0.665850	−	1.15329i	0.313204	−	0.949686i	$-0.398598\pi$
$522$		0			0
$523$	−10.5158	+	18.2139i	−0.459824	+	0.796439i	−0.998951	−	0.0457857i	$-0.985421\pi$
$523$	−10.5158	+	18.2139i	−0.459824	+	0.796439i	0.539127	+	0.842224i	$0.318754\pi$
$524$		0			0
$525$	26.5994	+	9.17715i	1.16089	+	0.400524i
$526$		0			0
$527$	−16.6427	+	13.9649i	−0.724968	+	0.608320i
$528$		0			0
$529$	16.8261	−	6.12418i	0.731567	−	0.266269i
$530$		0			0
$531$	28.2570	+	3.32715i	1.22625	+	0.144386i
$532$		0			0
$533$	23.1496	−	8.42578i	1.00272	−	0.364961i
$534$		0			0
$535$	−4.18364	−	23.7266i	−0.180875	−	1.02579i
$536$		0			0
$537$	−18.3620	+	13.6578i	−0.792378	+	0.589379i
$538$		0			0
$539$	29.7597	+	5.97616i	1.28184	+	0.257411i
$540$		0			0
$541$	4.88029	+	8.45291i	0.209820	+	0.363419i	0.951658	−	0.307161i	$-0.0993789\pi$
$541$	4.88029	+	8.45291i	0.209820	+	0.363419i	−0.741838	+	0.670579i	$0.766046\pi$
$542$		0			0
$543$	1.86717	+	16.0338i	0.0801279	+	0.688078i
$544$		0			0
$545$	−35.1361	+	29.4827i	−1.50507	+	1.26290i
$546$		0			0
$547$	−40.4855	+	14.7355i	−1.73104	+	0.630046i	−0.998704	−	0.0509020i	$-0.983790\pi$
$547$	−40.4855	+	14.7355i	−1.73104	+	0.630046i	−0.732332	+	0.680948i	$0.761568\pi$
$548$		0			0
$549$	−4.49893	+	2.95351i	−0.192010	+	0.126053i
$550$		0			0
$551$	−0.194095	+	1.10077i	−0.00826871	+	0.0468942i
$552$		0			0
$553$	−36.2776	+	2.74214i	−1.54268	+	0.116608i
$554$		0			0
$555$	−11.1282	+	46.8647i	−0.472366	+	1.98930i
$556$		0			0
$557$	43.3845			1.83826			0.919130	−	0.393955i	$-0.128893\pi$
$557$	43.3845			1.83826			0.919130	+	0.393955i	$0.128893\pi$
$558$		0			0
$559$	34.2787	−	59.3725i	1.44984	−	2.51119i
$560$		0			0
$561$	−14.7169	+	22.3553i	−0.621349	+	0.943840i
$562$		0			0
$563$	−23.6821	+	19.8716i	−0.998080	+	0.837489i	−0.986717	−	0.162447i	$-0.948061\pi$
$563$	−23.6821	+	19.8716i	−0.998080	+	0.837489i	−0.0113628	+	0.999935i	$0.503617\pi$
$564$		0			0
$565$	−33.0769	+	12.0390i	−1.39156	+	0.506485i
$566$		0			0
$567$	15.5879	+	18.0004i	0.654632	+	0.755948i
$568$		0			0
$569$	20.6085	−	7.50090i	0.863955	−	0.314454i	0.128238	−	0.991743i	$-0.459068\pi$
$569$	20.6085	−	7.50090i	0.863955	−	0.314454i	0.735717	+	0.677289i	$0.236846\pi$
$570$		0			0
$571$	−17.0034	+	14.2676i	−0.711571	+	0.597079i	−0.925039	−	0.379871i	$-0.875968\pi$
$571$	−17.0034	+	14.2676i	−0.711571	+	0.597079i	0.213469	+	0.976950i	$0.431524\pi$
$572$		0			0
$573$	−8.13710	+	12.3604i	−0.339932	+	0.516363i
$574$		0			0
$575$	6.92928	−	12.0019i	0.288971	−	0.500512i
$576$		0			0
$577$	−8.33610			−0.347036			−0.173518	−	0.984831i	$-0.555514\pi$
$577$	−8.33610			−0.347036			−0.173518	+	0.984831i	$0.555514\pi$
$578$		0			0
$579$	4.74403	−	19.9787i	0.197155	−	0.830288i
$580$		0			0
$581$	−9.80616	+	20.3963i	−0.406828	+	0.846181i
$582$		0			0
$583$	5.15961	−	29.2616i	0.213689	−	1.21189i
$584$		0			0
$585$	−58.9123	−	29.6497i	−2.43573	−	1.22586i
$586$		0			0
$587$	−33.0226	+	12.0192i	−1.36299	+	0.496087i	−0.916977	−	0.398941i	$-0.869378\pi$
$587$	−33.0226	+	12.0192i	−1.36299	+	0.496087i	−0.446011	+	0.895028i	$0.647156\pi$
$588$		0			0
$589$	−7.62397	+	6.39727i	−0.314140	+	0.263595i
$590$		0			0
$591$	3.19829	+	27.4645i	0.131560	+	1.12974i
$592$		0			0
$593$	19.4158	+	33.6292i	0.797313	+	1.38099i	0.921360	+	0.388710i	$0.127079\pi$
$593$	19.4158	+	33.6292i	0.797313	+	1.38099i	−0.124047	+	0.992276i	$0.539587\pi$
$594$		0			0
$595$	−25.5626	−	18.3533i	−1.04796	−	0.752411i
$596$		0			0
$597$	−13.3472	+	9.92782i	−0.546266	+	0.406318i
$598$		0			0
$599$	4.87684	+	27.6579i	0.199262	+	1.13007i	0.906217	+	0.422814i	$0.138957\pi$
$599$	4.87684	+	27.6579i	0.199262	+	1.13007i	−0.706954	+	0.707259i	$0.749931\pi$
$600$		0			0
$601$	28.6781	−	10.4380i	1.16981	−	0.425774i	0.317215	−	0.948354i	$-0.397252\pi$
$601$	28.6781	−	10.4380i	1.16981	−	0.425774i	0.852591	+	0.522579i	$0.175030\pi$
$602$		0			0
$603$	−20.5618	+	27.5703i	−0.837342	+	1.12275i
$604$		0			0
$605$	24.4740	−	8.90782i	0.995011	−	0.362154i
$606$		0			0
$607$	−34.3805	+	28.8486i	−1.39546	+	1.17093i	−0.432388	+	0.901688i	$0.642329\pi$
$607$	−34.3805	+	28.8486i	−1.39546	+	1.17093i	−0.963073	+	0.269242i	$0.913227\pi$
$608$		0			0
$609$	0.596813	+	3.08041i	0.0241841	+	0.124825i
$610$		0			0
$611$	−11.1817	+	19.3672i	−0.452361	+	0.783513i
$612$		0			0
$613$	12.4779	+	21.6123i	0.503976	+	0.872912i	0.999989	+	0.00459715i	$0.00146332\pi$
$613$	12.4779	+	21.6123i	0.503976	+	0.872912i	−0.496013	+	0.868315i	$0.665203\pi$
$614$		0			0
$615$	−9.69583	−	19.3265i	−0.390974	−	0.779320i
$616$		0			0
$617$	41.0150	+	14.9282i	1.65120	+	0.600988i	0.988944	−	0.148290i	$-0.0473769\pi$
$617$	41.0150	+	14.9282i	1.65120	+	0.600988i	0.662256	+	0.749278i	$0.269599\pi$
$618$		0			0
$619$	10.6056	+	8.89914i	0.426274	+	0.357687i	0.830544	−	0.556953i	$-0.188030\pi$
$619$	10.6056	+	8.89914i	0.426274	+	0.357687i	−0.404270	+	0.914640i	$0.632474\pi$
$620$		0			0
$621$	10.1640	−	5.85091i	0.407868	−	0.234789i
$622$		0			0
$623$	−35.9793	−	10.0980i	−1.44148	−	0.404567i
$624$		0			0
$625$	−3.12545	−	17.7253i	−0.125018	−	0.709012i
$626$		0			0
$627$	−6.74178	+	10.2409i	−0.269241	+	0.408981i
$628$		0			0
$629$	14.8458	−	25.7137i	0.591941	−	1.02527i
$630$		0			0
$631$	5.46367	+	9.46335i	0.217505	+	0.376730i	0.954045	−	0.299665i	$-0.0968748\pi$
$631$	5.46367	+	9.46335i	0.217505	+	0.376730i	−0.736539	+	0.676395i	$0.763541\pi$
$632$		0			0
$633$	−3.24392	+	13.6613i	−0.128934	+	0.542986i
$634$		0			0
$635$	29.2238	−	24.5216i	1.15971	−	0.973112i
$636$		0			0
$637$	16.7893	−	42.9411i	0.665217	−	1.70139i
$638$		0			0
$639$	−18.7950	+	4.43760i	−0.743519	+	0.175549i
$640$		0			0
$641$	−1.34946	+	7.65319i	−0.0533006	+	0.302283i	−0.999791	−	0.0204496i	$-0.993490\pi$
$641$	−1.34946	+	7.65319i	−0.0533006	+	0.302283i	0.946490	+	0.322732i	$0.104601\pi$
$642$		0			0
$643$	13.5792	−	11.3943i	0.535512	−	0.449348i	−0.334488	−	0.942400i	$-0.608563\pi$
$643$	13.5792	−	11.3943i	0.535512	−	0.449348i	0.870000	+	0.493052i	$0.164119\pi$
$644$		0			0
$645$	−55.2412	−	23.8566i	−2.17512	−	0.939353i
$646$		0			0
$647$	1.33378	−	2.31017i	0.0524363	−	0.0908223i	−0.838616	−	0.544723i	$-0.816635\pi$
$647$	1.33378	−	2.31017i	0.0524363	−	0.0908223i	0.891052	+	0.453901i	$0.149968\pi$
$648$		0			0
$649$	20.5627	+	35.6156i	0.807156	+	1.39804i
$650$		0			0
$651$	−13.5596	+	24.4268i	−0.531441	+	0.957362i
$652$		0			0
$653$	−13.4186	−	4.88396i	−0.525109	−	0.191124i	0.0658439	−	0.997830i	$-0.479026\pi$
$653$	−13.4186	−	4.88396i	−0.525109	−	0.191124i	−0.590953	+	0.806706i	$0.701248\pi$
$654$		0			0
$655$	6.91929	−	39.2413i	0.270359	−	1.53328i
$656$		0			0
$657$	34.8538	−	8.22917i	1.35978	−	0.321051i
$658$		0			0
$659$	13.9405	+	11.6974i	0.543043	+	0.455667i	0.872577	−	0.488477i	$-0.162447\pi$
$659$	13.9405	+	11.6974i	0.543043	+	0.455667i	−0.329534	+	0.944144i	$0.606892\pi$
$660$		0			0
$661$	−29.9448	−	10.8990i	−1.16472	−	0.423922i	−0.313936	−	0.949444i	$-0.601648\pi$
$661$	−29.9448	−	10.8990i	−1.16472	−	0.423922i	−0.850780	+	0.525522i	$0.823870\pi$
$662$		0			0
$663$	29.5592	+	27.9115i	1.14799	+	1.08399i
$664$		0			0
$665$	−11.7101	−	8.40758i	−0.454100	−	0.326032i
$666$		0			0
$667$	1.54538			0.0598372
$668$		0			0
$669$	6.00513	−	9.12189i	0.232172	−	0.352673i
$670$		0			0
$671$	−7.30981	−	2.66055i	−0.282192	−	0.102710i
$672$		0			0
$673$	−2.03959	+	11.5671i	−0.0786204	+	0.445879i	0.919931	+	0.392080i	$0.128244\pi$
$673$	−2.03959	+	11.5671i	−0.0786204	+	0.445879i	−0.998552	+	0.0537992i	$0.982867\pi$
$674$		0			0
$675$	−10.9506	+	29.9675i	−0.421490	+	1.15345i
$676$		0			0
$677$	−20.1397	+	7.33025i	−0.774032	+	0.281725i	−0.698682	−	0.715433i	$-0.746230\pi$
$677$	−20.1397	+	7.33025i	−0.774032	+	0.281725i	−0.0753501	+	0.997157i	$0.524007\pi$
$678$		0			0
$679$	−2.71911	−	3.98269i	−0.104350	−	0.152842i
$680$		0			0
$681$	16.2888	−	24.7430i	0.624189	−	0.948153i
$682$		0			0
$683$	−15.0155	−	26.0077i	−0.574554	−	0.995156i	−0.996090	−	0.0883447i	$-0.971842\pi$
$683$	−15.0155	−	26.0077i	−0.574554	−	0.995156i	0.421536	−	0.906812i	$-0.361491\pi$
$684$		0			0
$685$	−27.8360	−	48.2134i	−1.06356	−	1.84214i
$686$		0			0
$687$	−1.24351	+	5.23684i	−0.0474428	+	0.199798i
$688$		0			0
$689$	−42.4113	−	15.4364i	−1.61574	−	0.588082i
$690$		0			0
$691$	4.13267	−	23.4375i	0.157214	−	0.891606i	−0.799519	−	0.600640i	$-0.794912\pi$
$691$	4.13267	−	23.4375i	0.157214	−	0.891606i	0.956733	−	0.290966i	$-0.0939766\pi$
$692$		0			0
$693$	−7.38655	+	33.6161i	−0.280592	+	1.27697i
$694$		0			0
$695$	−2.20559	−	1.85071i	−0.0836630	−	0.0702016i
$696$		0			0
$697$	2.31445	+	13.1259i	0.0876662	+	0.497180i
$698$		0			0
$699$	4.17340	+	35.8380i	0.157853	+	1.35552i
$700$		0			0
$701$	−28.3379			−1.07031			−0.535154	−	0.844754i	$-0.679747\pi$
$701$	−28.3379			−1.07031			−0.535154	+	0.844754i	$0.679747\pi$
$702$		0			0
$703$	6.80082	−	11.7794i	0.256498	−	0.444267i
$704$		0			0
$705$	18.0196	+	7.78197i	0.678656	+	0.293086i
$706$		0			0
$707$	14.5568	−	30.2774i	0.547466	−	1.13870i
$708$		0			0
$709$	12.4284	+	10.4287i	0.466758	+	0.391656i	0.845610	−	0.533801i	$-0.179237\pi$
$709$	12.4284	+	10.4287i	0.466758	+	0.391656i	−0.378853	+	0.925457i	$0.623681\pi$
$710$		0			0
$711$	−2.36355	−	41.1846i	−0.0886401	−	1.54454i
$712$		0			0
$713$	10.5408	+	8.84476i	0.394755	+	0.331239i
$714$		0			0
$715$	−16.5538	−	93.8813i	−0.619077	−	3.51096i
$716$		0			0
$717$	−38.8279	+	11.6063i	−1.45005	+	0.433445i
$718$		0			0
$719$	17.8401	−	30.8999i	0.665323	−	1.15237i	−0.313875	−	0.949464i	$-0.601627\pi$
$719$	17.8401	−	30.8999i	0.665323	−	1.15237i	0.979198	−	0.202908i	$-0.0650393\pi$
$720$		0			0
$721$	15.9193	+	11.4296i	0.592866	+	0.425662i
$722$		0			0
$723$	16.0435	+	0.941278i	0.596663	+	0.0350065i
$724$		0			0
$725$	−3.22062	+	2.70242i	−0.119611	+	0.100365i
$726$		0			0
$727$	−2.31724	+	13.1417i	−0.0859417	+	0.487400i	0.911208	+	0.411947i	$0.135151\pi$
$727$	−2.31724	+	13.1417i	−0.0859417	+	0.487400i	−0.997149	+	0.0754524i	$0.975960\pi$
$728$		0			0
$729$	−20.7275	+	17.3024i	−0.767683	+	0.640829i
$730$		0			0
$731$	28.4138	+	23.8420i	1.05092	+	0.881828i
$732$		0			0
$733$	−1.39210	−	7.89501i	−0.0514185	−	0.291609i	0.948245	−	0.317539i	$-0.102856\pi$
$733$	−1.39210	−	7.89501i	−0.0514185	−	0.291609i	−0.999664	+	0.0259301i	$0.991745\pi$
$734$		0			0
$735$	−39.1406	−	10.2775i	−1.44372	−	0.379090i
$736$		0			0
$737$	−49.7130			−1.83120
$738$		0			0
$739$	6.01554			0.221285			0.110643	−	0.993860i	$-0.464709\pi$
$739$	6.01554			0.221285			0.110643	+	0.993860i	$0.464709\pi$
$740$		0			0
$741$	13.5410	+	12.7862i	0.497441	+	0.469712i
$742$		0			0
$743$	−4.37820	−	24.8300i	−0.160621	−	0.910926i	−0.953466	−	0.301502i	$-0.902512\pi$
$743$	−4.37820	−	24.8300i	−0.160621	−	0.910926i	0.792845	−	0.609424i	$-0.208599\pi$
$744$		0			0
$745$	−59.1806	+	21.5400i	−2.16821	+	0.789163i
$746$		0			0
$747$	−22.9220	−	11.5363i	−0.838672	−	0.422091i
$748$		0			0
$749$	4.72448	+	18.5043i	0.172629	+	0.676134i
$750$		0			0
$751$	42.7174	+	15.5479i	1.55878	+	0.567350i	0.970457	−	0.241274i	$-0.0775654\pi$
$751$	42.7174	+	15.5479i	1.55878	+	0.567350i	0.588325	+	0.808625i	$0.299788\pi$
$752$		0			0
$753$	−3.18249	−	27.3288i	−0.115976	−	0.995916i
$754$		0			0
$755$	−44.5453			−1.62117
$756$		0			0
$757$	20.6389			0.750135			0.375067	−	0.926998i	$-0.377620\pi$
$757$	20.6389			0.750135			0.375067	+	0.926998i	$0.377620\pi$
$758$		0			0
$759$	15.5623	+	6.72080i	0.564877	+	0.243949i
$760$		0			0
$761$	8.55501	+	3.11377i	0.310119	+	0.112874i	0.492391	−	0.870374i	$-0.336123\pi$
$761$	8.55501	+	3.11377i	0.310119	+	0.112874i	−0.182272	+	0.983248i	$0.558345\pi$
$762$		0			0
$763$	26.0112	−	25.4034i	0.941670	−	0.919664i
$764$		0			0
$765$	21.3324	−	28.6035i	0.771273	−	1.03416i
$766$		0			0
$767$	58.7009	−	21.3654i	2.11957	−	0.771459i
$768$		0			0
$769$	3.13207	+	17.7629i	0.112945	+	0.640545i	0.987747	+	0.156064i	$0.0498806\pi$
$769$	3.13207	+	17.7629i	0.112945	+	0.640545i	−0.874802	+	0.484481i	$0.839008\pi$
$770$		0			0
$771$	−0.140329	+	0.590973i	−0.00505383	+	0.0212834i
$772$		0			0
$773$	−48.1257			−1.73096			−0.865480	−	0.500944i	$-0.832986\pi$
$773$	−48.1257			−1.73096			−0.865480	+	0.500944i	$0.832986\pi$
$774$		0			0
$775$	−37.4343			−1.34468
$776$		0			0
$777$	5.99608	−	37.7083i	0.215108	−	1.35278i
$778$		0			0
$779$	1.06024	+	6.01295i	0.0379872	+	0.215436i
$780$		0			0
$781$	−21.3831	−	17.9426i	−0.765148	−	0.642035i
$782$		0			0
$783$	−3.50454	+	0.613333i	−0.125242	+	0.0219187i
$784$		0			0
$785$	−1.98081	+	11.2337i	−0.0706981	+	0.400949i
$786$		0			0
$787$	−40.6422	+	34.1029i	−1.44874	+	1.21564i	−0.515243	+	0.857044i	$0.672298\pi$
$787$	−40.6422	+	34.1029i	−1.44874	+	1.21564i	−0.933495	+	0.358591i	$0.883257\pi$
$788$		0			0
$789$	14.9474	+	29.7944i	0.532142	+	1.06071i
$790$		0			0
$791$	25.4258	−	11.4923i	0.904036	−	0.408618i
$792$		0			0
$793$	−5.90799	+	10.2329i	−0.209799	+	0.363382i
$794$		0			0
$795$	−9.15181	+	38.5414i	−0.324581	+	1.36692i
$796$		0			0
$797$	−4.93435	−	27.9841i	−0.174784	−	0.991248i	−0.938393	−	0.345570i	$-0.887686\pi$
$797$	−4.93435	−	27.9841i	−0.174784	−	0.991248i	0.763609	−	0.645679i	$-0.223425\pi$
$798$		0			0
$799$	−9.26851	−	7.77720i	−0.327896	−	0.275138i
$800$		0			0
$801$	12.1873	−	40.5825i	0.430616	−	1.43391i
$802$		0			0
$803$	39.6532	+	33.2730i	1.39933	+	1.17418i
$804$		0			0
$805$	−8.63617	+	17.9628i	−0.304385	+	0.633105i
$806$		0			0
$807$	−1.68853	−	14.4998i	−0.0594391	−	0.510418i
$808$		0			0
$809$	−15.3012	+	26.5025i	−0.537962	+	0.931777i	0.461052	+	0.887373i	$0.347472\pi$
$809$	−15.3012	+	26.5025i	−0.537962	+	0.931777i	−0.999014	+	0.0444037i	$0.985861\pi$
$810$		0			0
$811$	−5.62868			−0.197650			−0.0988248	−	0.995105i	$-0.531508\pi$
$811$	−5.62868			−0.197650			−0.0988248	+	0.995105i	$0.531508\pi$
$812$		0			0
$813$	−1.60958	−	0.695117i	−0.0564504	−	0.0243788i
$814$		0			0
$815$	1.44694	+	8.20599i	0.0506840	+	0.287443i
$816$		0			0
$817$	13.0163	+	10.9219i	0.455381	+	0.382110i
$818$		0			0
$819$	48.3377	+	19.9163i	1.68906	+	0.695931i
$820$		0			0
$821$	0.669212	−	3.79529i	0.0233556	−	0.132456i	−0.970900	−	0.239483i	$-0.923022\pi$
$821$	0.669212	−	3.79529i	0.0233556	−	0.132456i	0.994256	+	0.107027i	$0.0341331\pi$
$822$		0			0
$823$	32.7909	+	11.9349i	1.14302	+	0.416025i	0.843003	−	0.537908i	$-0.180785\pi$
$823$	32.7909	+	11.9349i	1.14302	+	0.416025i	0.300017	+	0.953934i	$0.403008\pi$
$824$		0			0
$825$	−44.1852	+	13.2077i	−1.53833	+	0.459833i
$826$		0			0
$827$	−7.22831	−	12.5198i	−0.251353	−	0.435356i	0.712545	−	0.701626i	$-0.247542\pi$
$827$	−7.22831	−	12.5198i	−0.251353	−	0.435356i	−0.963899	+	0.266270i	$0.914209\pi$
$828$		0			0
$829$	14.1038	+	24.4285i	0.489845	+	0.848436i	0.999932	−	0.0116870i	$-0.00372017\pi$
$829$	14.1038	+	24.4285i	0.489845	+	0.848436i	−0.510087	+	0.860123i	$0.670387\pi$
$830$		0			0
$831$	−9.89305	−	19.7196i	−0.343186	−	0.684066i
$832$		0			0
$833$	21.3021	+	12.9797i	0.738072	+	0.449722i
$834$		0			0
$835$	−40.3894	+	14.7005i	−1.39773	+	0.508733i
$836$		0			0
$837$	−27.4143	−	15.8744i	−0.947577	−	0.548698i
$838$		0			0
$839$	5.94255	−	33.7019i	0.205160	−	1.16352i	−0.692029	−	0.721870i	$-0.743283\pi$
$839$	5.94255	−	33.7019i	0.205160	−	1.16352i	0.897188	−	0.441648i	$-0.145606\pi$
$840$		0			0
$841$	26.8105	+	9.75824i	0.924502	+	0.336491i
$842$		0			0
$843$	14.5788	+	0.855346i	0.502121	+	0.0294597i
$844$		0			0
$845$	−101.413			−3.48870
$846$		0			0
$847$	−18.8129	+	8.50328i	−0.646417	+	0.292176i
$848$		0			0
$849$	−31.7310	+	9.48492i	−1.08901	+	0.325522i
$850$		0			0
$851$	−17.6713	−	6.43183i	−0.605764	−	0.220480i
$852$		0			0
$853$	9.74177	+	8.17432i	0.333552	+	0.279883i	0.794145	−	0.607728i	$-0.207919\pi$
$853$	9.74177	+	8.17432i	0.333552	+	0.279883i	−0.460593	+	0.887611i	$0.652363\pi$
$854$		0			0
$855$	9.77229	−	13.1032i	0.334205	−	0.448119i
$856$		0			0
$857$	1.55781	−	8.83475i	0.0532136	−	0.301789i	−0.946572	−	0.322492i	$-0.895479\pi$
$857$	1.55781	−	8.83475i	0.0532136	−	0.301789i	0.999786	+	0.0207030i	$0.00659043\pi$
$858$		0			0
$859$	−37.5963	−	13.6839i	−1.28277	−	0.466890i	−0.391423	−	0.920211i	$-0.628017\pi$
$859$	−37.5963	−	13.6839i	−1.28277	−	0.466890i	−0.891348	+	0.453321i	$0.850239\pi$
$860$		0			0
$861$	8.81860	+	14.6970i	0.300537	+	0.500872i
$862$		0			0
$863$	2.66406	+	4.61428i	0.0906855	+	0.157072i	0.907800	−	0.419404i	$-0.137761\pi$
$863$	2.66406	+	4.61428i	0.0906855	+	0.157072i	−0.817114	+	0.576476i	$0.804428\pi$
$864$		0			0
$865$	−28.6415	+	49.6085i	−0.973839	+	1.68674i
$866$		0			0
$867$	5.97734	−	4.44601i	0.203001	−	0.150995i
$868$		0			0
$869$	45.6769	−	38.3275i	1.54948	−	1.30017i
$870$		0			0
$871$	−13.1126	+	74.3653i	−0.444304	+	2.51977i
$872$		0			0
$873$	4.57107	−	3.00087i	0.154707	−	0.101564i
$874$		0			0
$875$	−2.49090	−	9.75608i	−0.0842077	−	0.329816i
$876$		0			0
$877$	−6.36608	+	5.34178i	−0.214967	+	0.180379i	−0.743913	−	0.668277i	$-0.767032\pi$
$877$	−6.36608	+	5.34178i	−0.214967	+	0.180379i	0.528945	+	0.848656i	$0.322588\pi$
$878$		0			0
$879$	−21.6218	+	6.46313i	−0.729287	+	0.217996i
$880$		0			0
$881$	8.41250	+	14.5709i	0.283424	+	0.490905i	0.972226	−	0.234045i	$-0.0751962\pi$
$881$	8.41250	+	14.5709i	0.283424	+	0.490905i	−0.688801	+	0.724950i	$0.741863\pi$
$882$		0			0
$883$	−0.862472	+	1.49384i	−0.0290245	+	0.0502719i	−0.880173	−	0.474653i	$-0.842573\pi$
$883$	−0.862472	+	1.49384i	−0.0290245	+	0.0502719i	0.851148	+	0.524925i	$0.175907\pi$
$884$		0			0
$885$	−24.5859	−	49.0065i	−0.826445	−	1.64734i
$886$		0			0
$887$	−3.60473	−	20.4435i	−0.121035	−	0.686424i	−0.983584	−	0.180451i	$-0.942244\pi$
$887$	−3.60473	−	20.4435i	−0.121035	−	0.686424i	0.862549	−	0.505974i	$-0.168867\pi$
$888$		0			0
$889$	−21.6343	+	21.1287i	−0.725592	+	0.708635i
$890$		0			0
$891$	−37.9590	−	9.06474i	−1.27168	−	0.303680i
$892$		0			0
$893$	−4.24588	−	3.56271i	−0.142083	−	0.119222i
$894$		0			0
$895$	41.4394	+	15.0827i	1.38517	+	0.504159i
$896$		0			0
$897$	14.1584	−	21.5069i	0.472736	−	0.718094i
$898$		0			0
$899$	−2.08716	−	3.61507i	−0.0696107	−	0.120569i
$900$		0			0
$901$	12.2092	−	21.1469i	0.406746	−	0.704505i
$902$		0			0
$903$	45.0898	+	15.5566i	1.50049	+	0.517690i
$904$		0			0
$905$	23.8288	−	19.9948i	0.792097	−	0.664649i
$906$		0			0
$907$	51.6276	−	18.7909i	1.71427	−	0.623942i	0.716949	−	0.697125i	$-0.245538\pi$
$907$	51.6276	−	18.7909i	1.71427	−	0.623942i	0.997319	+	0.0731827i	$0.0233156\pi$
$908$		0			0
$909$	34.0267	+	17.1251i	1.12859	+	0.568005i
$910$		0			0
$911$	−25.5168	+	9.28735i	−0.845409	+	0.307704i	−0.728167	−	0.685400i	$-0.759627\pi$
$911$	−25.5168	+	9.28735i	−0.845409	+	0.307704i	−0.117242	+	0.993103i	$0.537405\pi$
$912$		0			0
$913$	−6.44086	−	36.5279i	−0.213161	−	1.20890i
$914$		0			0
$915$	9.52089	+	4.11172i	0.314751	+	0.135929i
$916$		0			0
$917$	−3.12469	+	31.4310i	−0.103186	+	1.03794i
$918$		0			0
$919$	14.9455	+	25.8864i	0.493006	+	0.853912i	0.999968	−	0.00805677i	$-0.00256458\pi$
$919$	14.9455	+	25.8864i	0.493006	+	0.853912i	−0.506961	+	0.861969i	$0.669231\pi$
$920$		0			0
$921$	−51.8302	−	22.3835i	−1.70786	−	0.737562i
$922$		0			0
$923$	−32.4803	+	27.2542i	−1.06910	+	0.897083i
$924$		0			0
$925$	48.0750	−	17.4979i	1.58070	−	0.575327i
$926$		0			0
$927$	−13.2849	+	17.8130i	−0.436333	+	0.585057i
$928$		0			0
$929$	9.78973	−	55.5203i	0.321191	−	1.82156i	−0.214004	−	0.976833i	$-0.568650\pi$
$929$	9.78973	−	55.5203i	0.321191	−	1.82156i	0.535194	−	0.844729i	$-0.320238\pi$
$930$		0			0
$931$	9.75841	+	5.94598i	0.319819	+	0.194872i
$932$		0			0
$933$	−16.5971	+	4.96115i	−0.543365	+	0.162421i
$934$		0			0
$935$	51.5760			1.68672
$936$		0			0
$937$	−23.1328	+	40.0672i	−0.755717	+	1.30894i	0.189301	+	0.981919i	$0.439378\pi$
$937$	−23.1328	+	40.0672i	−0.755717	+	1.30894i	−0.945017	+	0.327020i	$0.893955\pi$
$938$		0			0
$939$	−5.41827	−	10.8001i	−0.176819	−	0.352449i
$940$		0			0
$941$	−15.6730	+	13.1512i	−0.510926	+	0.428718i	−0.861455	−	0.507834i	$-0.830446\pi$
$941$	−15.6730	+	13.1512i	−0.510926	+	0.428718i	0.350529	+	0.936552i	$0.386002\pi$
$942$		0			0
$943$	7.93255	−	2.88721i	0.258319	−	0.0940205i
$944$		0			0
$945$	12.4557	−	44.1629i	0.405183	−	1.43662i
$946$		0			0
$947$	−19.9055	+	7.24500i	−0.646841	+	0.235431i	−0.644545	−	0.764567i	$-0.722953\pi$
$947$	−19.9055	+	7.24500i	−0.646841	+	0.235431i	−0.00229588	+	0.999997i	$0.500731\pi$
$948$		0			0
$949$	60.2320	−	50.5406i	1.95521	−	1.64062i
$950$		0			0
$951$	16.2620	+	0.954100i	0.527332	+	0.0309388i
$952$		0			0
$953$	−9.38049	+	16.2475i	−0.303864	+	0.526308i	−0.977008	−	0.213204i	$-0.931610\pi$
$953$	−9.38049	+	16.2475i	−0.303864	+	0.526308i	0.673144	+	0.739512i	$0.264944\pi$
$954$		0			0
$955$	28.5168			0.922782
$956$		0			0
$957$	−3.73904	−	3.53061i	−0.120866	−	0.114129i
$958$		0			0
$959$	24.8831	+	36.4463i	0.803517	+	1.17691i
$960$		0			0
$961$	1.07108	−	6.07439i	0.0345509	−	0.195948i
$962$		0			0
$963$	−21.0755	+	4.97605i	−0.679150	+	0.160351i
$964$		0			0
$965$	−37.1836	+	13.5337i	−1.19698	+	0.435666i
$966$		0			0
$967$	−33.0935	+	27.7688i	−1.06422	+	0.892984i	−0.994516	−	0.104584i	$-0.966649\pi$
$967$	−33.0935	+	27.7688i	−1.06422	+	0.892984i	−0.0697007	+	0.997568i	$0.522204\pi$
$968$		0			0
$969$	−8.08475	+	6.01352i	−0.259720	+	0.193182i
$970$		0			0
$971$	3.25634	+	5.64015i	0.104501	+	0.181001i	0.913534	−	0.406762i	$-0.133342\pi$
$971$	3.25634	+	5.64015i	0.104501	+	0.181001i	−0.809033	+	0.587763i	$0.800009\pi$
$972$		0			0
$973$	1.85395	+	1.33109i	0.0594349	+	0.0426727i
$974$		0			0
$975$	8.10273	+	69.5801i	0.259495	+	2.22835i
$976$		0			0
$977$	−2.42002	−	13.7246i	−0.0774233	−	0.439089i	−0.998736	−	0.0502665i	$-0.983993\pi$
$977$	−2.42002	−	13.7246i	−0.0774233	−	0.439089i	0.921313	−	0.388823i	$-0.127118\pi$
$978$		0			0
$979$	57.5532	−	20.9477i	1.83941	−	0.669490i
$980$		0			0
$981$	28.2657	+	30.0110i	0.902453	+	0.958177i
$982$		0			0
$983$	6.26459	−	2.28012i	0.199809	−	0.0727247i	−0.240177	−	0.970729i	$-0.577205\pi$
$983$	6.26459	−	2.28012i	0.199809	−	0.0727247i	0.439986	+	0.898004i	$0.354983\pi$
$984$		0			0
$985$	40.8166	−	34.2492i	1.30052	−	1.09127i
$986$		0			0
$987$	−14.7082	−	5.07451i	−0.468167	−	0.161524i
$988$		0			0
$989$	11.7461	−	20.3448i	0.373504	−	0.646928i
$990$		0			0
$991$	−11.5633	−	20.0283i	−0.367322	−	0.636220i	0.621824	−	0.783157i	$-0.286392\pi$
$991$	−11.5633	−	20.0283i	−0.367322	−	0.636220i	−0.989146	+	0.146937i	$0.953058\pi$
$992$		0			0
$993$	9.73600	+	0.571216i	0.308963	+	0.0181270i
$994$		0			0
$995$	30.1221	+	10.9635i	0.954933	+	0.347567i
$996$		0			0
$997$	−3.22249	−	2.70399i	−0.102057	−	0.0856361i	0.590331	−	0.807161i	$-0.298997\pi$
$997$	−3.22249	−	2.70399i	−0.102057	−	0.0856361i	−0.692388	+	0.721525i	$0.743442\pi$
$998$		0			0
$999$	42.6270	+	7.57242i	1.34866	+	0.239581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.5	yes	144
7.2	even	3		756.2.bp.a.457.12	yes	144
27.13	even	9		756.2.bp.a.445.12	✓	144
189.121	even	9	inner	756.2.bq.a.121.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.12	✓	144	27.13	even	9
756.2.bp.a.457.12	yes	144	7.2	even	3
756.2.bq.a.25.5	yes	144	1.1	even	1	trivial
756.2.bq.a.121.5	yes	144	189.121	even	9	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.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38976 + 1.03372i) q^{3} +(3.13641 + 1.14156i) q^{5} +(-2.54733 - 0.714936i) q^{7} +(0.862856 - 2.87324i) q^{9} +O(q^{10})\)	\(q+(-1.38976 + 1.03372i) q^{3} +(3.13641 + 1.14156i) q^{5} +(-2.54733 - 0.714936i) q^{7} +(0.862856 - 2.87324i) q^{9} +(4.07476 - 1.48309i) q^{11} +(-1.14376 - 6.48659i) q^{13} +(-5.53890 + 1.65567i) q^{15} +3.56357 q^{17} +1.63246 q^{19} +(4.27921 - 1.63963i) q^{21} +(-0.391926 - 2.22272i) q^{23} +(4.70369 + 3.94686i) q^{25} +(1.77095 + 4.88505i) q^{27} +(-0.118897 + 0.674299i) q^{29} +(-4.67024 + 3.91880i) q^{31} +(-4.12983 + 6.27328i) q^{33} +(-7.17332 - 5.15026i) q^{35} +(4.16600 - 7.21572i) q^{37} +(8.29485 + 7.83246i) q^{39} +(0.649477 + 3.68337i) q^{41} +(7.97341 + 6.69048i) q^{43} +(5.98624 - 8.02664i) q^{45} +(-2.60091 - 2.18242i) q^{47} +(5.97773 + 3.64235i) q^{49} +(-4.95250 + 3.68372i) q^{51} +(3.42611 - 5.93419i) q^{53} +14.4731 q^{55} +(-2.26872 + 1.68750i) q^{57} +(1.64689 + 9.33997i) q^{59} +(-1.37423 - 1.15311i) q^{61} +(-4.25215 + 6.70218i) q^{63} +(3.81753 - 21.6503i) q^{65} +(-10.7731 - 3.92108i) q^{67} +(2.84235 + 2.68390i) q^{69} +(-3.21863 - 5.57483i) q^{71} +(5.96868 + 10.3381i) q^{73} +(-10.6169 - 0.622900i) q^{75} +(-11.4400 + 0.864725i) q^{77} +(12.9215 - 4.70304i) q^{79} +(-7.51096 - 4.95838i) q^{81} +(1.48535 - 8.42382i) q^{83} +(11.1768 + 4.06803i) q^{85} +(-0.531796 - 1.06002i) q^{87} +14.1243 q^{89} +(-1.72396 + 17.3412i) q^{91} +(2.43958 - 10.2739i) q^{93} +(5.12006 + 1.86355i) q^{95} +(1.39626 + 1.17160i) q^{97} +(-0.745339 - 12.9874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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