LMFDB - Embedded newform 756.2.ck.a.605.4

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			605.4
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63242 - 0.578955i) q^{3} +(0.649280 + 3.68225i) q^{5} +(0.647047 + 2.56541i) q^{7} +(2.32962 + 1.89020i) q^{9} +O(q^{10})$	\(q+(-1.63242 - 0.578955i) q^{3} +(0.649280 + 3.68225i) q^{5} +(0.647047 + 2.56541i) q^{7} +(2.32962 + 1.89020i) q^{9} +(0.889725 + 0.156882i) q^{11} +(-0.769375 - 0.916906i) q^{13} +(1.07196 - 6.38690i) q^{15} -7.46688 q^{17} -0.689746i q^{19} +(0.429002 - 4.56245i) q^{21} +(2.84180 + 3.38672i) q^{23} +(-8.43895 + 3.07153i) q^{25} +(-2.70859 - 4.43436i) q^{27} +(-0.230745 + 0.274991i) q^{29} +(3.43265 - 9.43113i) q^{31} +(-1.36158 - 0.771209i) q^{33} +(-9.02637 + 4.04826i) q^{35} +(-4.77757 + 8.27499i) q^{37} +(0.725101 + 1.94221i) q^{39} +(-5.79118 + 4.85938i) q^{41} +(4.12751 - 1.50229i) q^{43} +(-5.44762 + 9.80553i) q^{45} +(-4.35416 + 1.58478i) q^{47} +(-6.16266 + 3.31988i) q^{49} +(12.1891 + 4.32299i) q^{51} +(11.6009 + 6.69781i) q^{53} +3.37805i q^{55} +(-0.399332 + 1.12596i) q^{57} +(0.0113213 - 0.00949971i) q^{59} +(-1.34236 - 3.68810i) q^{61} +(-3.34177 + 7.19949i) q^{63} +(2.87674 - 3.42836i) q^{65} +(-0.323090 - 1.83233i) q^{67} +(-2.67826 - 7.17384i) q^{69} +(-9.69050 + 5.59481i) q^{71} +(-9.63739 + 5.56415i) q^{73} +(15.5542 - 0.128266i) q^{75} +(0.173225 + 2.38402i) q^{77} +(1.78156 - 10.1037i) q^{79} +(1.85428 + 8.80691i) q^{81} +(4.58220 + 3.84492i) q^{83} +(-4.84810 - 27.4949i) q^{85} +(0.535881 - 0.315311i) q^{87} +13.9206 q^{89} +(1.85442 - 2.56704i) q^{91} +(-11.0637 + 13.4083i) q^{93} +(2.53982 - 0.447839i) q^{95} +(1.53264 + 4.21088i) q^{97} +(1.77618 + 2.04723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.63242	−	0.578955i	−0.942481	−	0.334260i
$3$	−1.63242	−	0.578955i	−0.942481	−	0.334260i
$4$		0			0
$5$	0.649280	+	3.68225i	0.290367	+	1.64675i	0.685459	+	0.728111i	$0.259602\pi$
$5$	0.649280	+	3.68225i	0.290367	+	1.64675i	−0.395092	+	0.918642i	$0.629287\pi$
$6$		0			0
$7$	0.647047	+	2.56541i	0.244561	+	0.969634i
$7$	0.647047	+	2.56541i	0.244561	+	0.969634i
$8$		0			0
$9$	2.32962	+	1.89020i	0.776541	+	0.630067i
$10$		0			0
$11$	0.889725	+	0.156882i	0.268262	+	0.0473018i	0.306161	−	0.951980i	$-0.400955\pi$
$11$	0.889725	+	0.156882i	0.268262	+	0.0473018i	−0.0378990	+	0.999282i	$0.512067\pi$
$12$		0			0
$13$	−0.769375	−	0.916906i	−0.213386	−	0.254304i	0.648725	−	0.761023i	$-0.275303\pi$
$13$	−0.769375	−	0.916906i	−0.213386	−	0.254304i	−0.862111	+	0.506719i	$0.830858\pi$
$14$		0			0
$15$	1.07196	−	6.38690i	0.276778	−	1.64909i
$16$		0			0
$17$	−7.46688			−1.81098			−0.905492	−	0.424362i	$-0.860498\pi$
$17$	−7.46688			−1.81098			−0.905492	+	0.424362i	$0.860498\pi$
$18$		0			0
$19$		−	0.689746i		−	0.158239i	−0.996865	−	0.0791193i	$-0.974789\pi$
$19$		−	0.689746i		−	0.158239i	0.996865	−	0.0791193i	$-0.0252108\pi$
$20$		0			0
$21$	0.429002	−	4.56245i	0.0936159	−	0.995608i
$22$		0			0
$23$	2.84180	+	3.38672i	0.592555	+	0.706180i	0.976095	−	0.217344i	$-0.0697395\pi$
$23$	2.84180	+	3.38672i	0.592555	+	0.706180i	−0.383540	+	0.923524i	$0.625295\pi$
$24$		0			0
$25$	−8.43895	+	3.07153i	−1.68779	+	0.614305i
$26$		0			0
$27$	−2.70859	−	4.43436i	−0.521269	−	0.853392i
$28$		0			0
$29$	−0.230745	+	0.274991i	−0.0428482	+	0.0510645i	−0.787043	−	0.616898i	$-0.788389\pi$
$29$	−0.230745	+	0.274991i	−0.0428482	+	0.0510645i	0.744195	+	0.667963i	$0.232833\pi$
$30$		0			0
$31$	3.43265	−	9.43113i	0.616522	−	1.69388i	−0.0988186	−	0.995105i	$-0.531506\pi$
$31$	3.43265	−	9.43113i	0.616522	−	1.69388i	0.715341	−	0.698776i	$-0.246271\pi$
$32$		0			0
$33$	−1.36158	−	0.771209i	−0.237021	−	0.134250i
$34$		0			0
$35$	−9.02637	+	4.04826i	−1.52574	+	0.684281i
$36$		0			0
$37$	−4.77757	+	8.27499i	−0.785427	+	1.36040i	0.143316	+	0.989677i	$0.454223\pi$
$37$	−4.77757	+	8.27499i	−0.785427	+	1.36040i	−0.928743	+	0.370723i	$0.879110\pi$
$38$		0			0
$39$	0.725101	+	1.94221i	0.116109	+	0.311003i
$40$		0			0
$41$	−5.79118	+	4.85938i	−0.904430	+	0.758907i	−0.971051	−	0.238871i	$-0.923223\pi$
$41$	−5.79118	+	4.85938i	−0.904430	+	0.758907i	0.0666210	+	0.997778i	$0.478778\pi$
$42$		0			0
$43$	4.12751	−	1.50229i	0.629440	−	0.229097i	−0.00754750	−	0.999972i	$-0.502402\pi$
$43$	4.12751	−	1.50229i	0.629440	−	0.229097i	0.636988	+	0.770874i	$0.280180\pi$
$44$		0			0
$45$	−5.44762	+	9.80553i	−0.812083	+	1.46172i
$46$		0			0
$47$	−4.35416	+	1.58478i	−0.635119	+	0.231165i	−0.639458	−	0.768826i	$-0.720841\pi$
$47$	−4.35416	+	1.58478i	−0.635119	+	0.231165i	0.00433856	+	0.999991i	$0.498619\pi$
$48$		0			0
$49$	−6.16266	+	3.31988i	−0.880380	+	0.474269i
$50$		0			0
$51$	12.1891	+	4.32299i	1.70682	+	0.605339i
$52$		0			0
$53$	11.6009	+	6.69781i	1.59351	+	0.920014i	0.992698	+	0.120625i	$0.0384900\pi$
$53$	11.6009	+	6.69781i	1.59351	+	0.920014i	0.600814	+	0.799389i	$0.294843\pi$
$54$		0			0
$55$			3.37805i			0.455496i
$56$		0			0
$57$	−0.399332	+	1.12596i	−0.0528928	+	0.149137i
$58$		0			0
$59$	0.0113213	−	0.00949971i	0.00147391	−	0.00123676i	−0.642050	−	0.766662i	$-0.721916\pi$
$59$	0.0113213	−	0.00949971i	0.00147391	−	0.00123676i	0.643524	+	0.765426i	$0.277472\pi$
$60$		0			0
$61$	−1.34236	−	3.68810i	−0.171871	−	0.472213i	0.823612	−	0.567154i	$-0.191956\pi$
$61$	−1.34236	−	3.68810i	−0.171871	−	0.472213i	−0.995483	+	0.0949418i	$0.969733\pi$
$62$		0			0
$63$	−3.34177	+	7.19949i	−0.421023	+	0.907050i
$64$		0			0
$65$	2.87674	−	3.42836i	0.356815	−	0.425236i
$66$		0			0
$67$	−0.323090	−	1.83233i	−0.0394717	−	0.223855i	0.958691	−	0.284451i	$-0.0918112\pi$
$67$	−0.323090	−	1.83233i	−0.0394717	−	0.223855i	−0.998162	+	0.0605954i	$0.980700\pi$
$68$		0			0
$69$	−2.67826	−	7.17384i	−0.322425	−	0.863629i
$70$		0			0
$71$	−9.69050	+	5.59481i	−1.15005	+	0.663982i	−0.948899	−	0.315578i	$-0.897801\pi$
$71$	−9.69050	+	5.59481i	−1.15005	+	0.663982i	−0.201151	+	0.979560i	$0.564468\pi$
$72$		0			0
$73$	−9.63739	+	5.56415i	−1.12797	+	0.651234i	−0.943424	−	0.331589i	$-0.892415\pi$
$73$	−9.63739	+	5.56415i	−1.12797	+	0.651234i	−0.184547	+	0.982824i	$0.559082\pi$
$74$		0			0
$75$	15.5542	−	0.128266i	1.79605	−	0.0148108i
$76$		0			0
$77$	0.173225	+	2.38402i	0.0197409	+	0.271684i
$78$		0			0
$79$	1.78156	−	10.1037i	0.200441	−	1.13676i	−0.704014	−	0.710186i	$-0.748611\pi$
$79$	1.78156	−	10.1037i	0.200441	−	1.13676i	0.904455	−	0.426570i	$-0.140278\pi$
$80$		0			0
$81$	1.85428	+	8.80691i	0.206031	+	0.978545i
$82$		0			0
$83$	4.58220	+	3.84492i	0.502962	+	0.422035i	0.858644	−	0.512572i	$-0.171307\pi$
$83$	4.58220	+	3.84492i	0.502962	+	0.422035i	−0.355683	+	0.934607i	$0.615752\pi$
$84$		0			0
$85$	−4.84810	−	27.4949i	−0.525850	−	2.98224i
$86$		0			0
$87$	0.535881	−	0.315311i	0.0574525	−	0.0338049i
$88$		0			0
$89$	13.9206			1.47558			0.737788	−	0.675032i	$-0.235870\pi$
$89$	13.9206			1.47558			0.737788	+	0.675032i	$0.235870\pi$
$90$		0			0
$91$	1.85442	−	2.56704i	0.194396	−	0.269099i
$92$		0			0
$93$	−11.0637	+	13.4083i	−1.14726	+	1.39037i
$94$		0			0
$95$	2.53982	−	0.447839i	0.260580	−	0.0459473i
$96$		0			0
$97$	1.53264	+	4.21088i	0.155616	+	0.427550i	0.992861	−	0.119277i	$-0.0380576\pi$
$97$	1.53264	+	4.21088i	0.155616	+	0.427550i	−0.837245	+	0.546827i	$0.815835\pi$
$98$		0			0
$99$	1.77618	+	2.04723i	0.178513	+	0.205755i
$100$		0			0
$101$	3.46818	+	2.91015i	0.345097	+	0.289571i	0.798818	−	0.601573i	$-0.205459\pi$
$101$	3.46818	+	2.91015i	0.345097	+	0.289571i	−0.453721	+	0.891144i	$0.649904\pi$
$102$		0			0
$103$	−11.5700	+	2.04010i	−1.14002	+	0.201017i	−0.711615	−	0.702570i	$-0.752036\pi$
$103$	−11.5700	+	2.04010i	−1.14002	+	0.201017i	−0.428406	+	0.903586i	$0.640925\pi$
$104$		0			0
$105$	17.0786	−	1.38262i	1.66670	−	0.134930i
$106$		0			0
$107$	−5.33302	+	3.07902i	−0.515563	+	0.297660i	−0.735117	−	0.677940i	$-0.762873\pi$
$107$	−5.33302	+	3.07902i	−0.515563	+	0.297660i	0.219555	+	0.975600i	$0.429540\pi$
$108$		0			0
$109$	2.87972	−	4.98782i	0.275827	−	0.477746i	−0.694516	−	0.719477i	$-0.744382\pi$
$109$	2.87972	−	4.98782i	0.275827	−	0.477746i	0.970343	+	0.241730i	$0.0777150\pi$
$110$		0			0
$111$	12.5899	−	10.7423i	1.19498	−	1.01961i
$112$		0			0
$113$	1.26420	−	3.47337i	0.118926	−	0.326747i	−0.865919	−	0.500185i	$-0.833265\pi$
$113$	1.26420	−	3.47337i	0.118926	−	0.326747i	0.984845	+	0.173438i	$0.0554875\pi$
$114$		0			0
$115$	−10.6256	+	12.6631i	−0.990846	+	1.18084i
$116$		0			0
$117$	−0.0592181	−	3.59032i	−0.00547471	−	0.331925i
$118$		0			0
$119$	−4.83142	−	19.1556i	−0.442896	−	1.75599i
$120$		0			0
$121$	−9.56962	−	3.48306i	−0.869966	−	0.316642i
$122$		0			0
$123$	12.2670	−	4.57974i	1.10608	−	0.412941i
$124$		0			0
$125$	−7.44173	−	12.8895i	−0.665609	−	1.15287i
$126$		0			0
$127$	7.29860	−	12.6416i	0.647646	−	1.12176i	−0.336037	−	0.941849i	$-0.609087\pi$
$127$	7.29860	−	12.6416i	0.647646	−	1.12176i	0.983683	−	0.179908i	$-0.0575799\pi$
$128$		0			0
$129$	−7.60762	+	0.0627351i	−0.669813	+	0.00552352i
$130$		0			0
$131$	−2.05501	+	1.72436i	−0.179547	+	0.150658i	−0.728132	−	0.685437i	$-0.759611\pi$
$131$	−2.05501	+	1.72436i	−0.179547	+	0.150658i	0.548585	+	0.836095i	$0.315167\pi$
$132$		0			0
$133$	1.76948	−	0.446298i	0.153434	−	0.0386989i
$134$		0			0
$135$	14.5698	−	12.8529i	1.25397	−	1.10620i
$136$		0			0
$137$	0.607400	+	1.66882i	0.0518937	+	0.142577i	0.962931	−	0.269746i	$-0.0869398\pi$
$137$	0.607400	+	1.66882i	0.0518937	+	0.142577i	−0.911038	+	0.412323i	$0.864718\pi$
$138$		0			0
$139$	7.70465	−	1.35854i	0.653500	−	0.115230i	0.162938	−	0.986636i	$-0.447903\pi$
$139$	7.70465	−	1.35854i	0.653500	−	0.115230i	0.490561	+	0.871407i	$0.336792\pi$
$140$		0			0
$141$	8.02536	−	0.0661799i	0.675857	−	0.00557335i
$142$		0			0
$143$	−0.540686	−	0.936495i	−0.0452144	−	0.0783137i
$144$		0			0
$145$	−1.16240	−	0.671114i	−0.0965324	−	0.0557330i
$146$		0			0
$147$	11.9821	−	1.85155i	0.988271	−	0.152713i
$148$		0			0
$149$	5.08102	−	13.9600i	0.416254	−	1.14365i	−0.537554	−	0.843229i	$-0.680652\pi$
$149$	5.08102	−	13.9600i	0.416254	−	1.14365i	0.953808	−	0.300418i	$-0.0971262\pi$
$150$		0			0
$151$	−2.80728	+	15.9209i	−0.228453	+	1.29562i	0.627518	+	0.778602i	$0.284071\pi$
$151$	−2.80728	+	15.9209i	−0.228453	+	1.29562i	−0.855972	+	0.517022i	$0.827040\pi$
$152$		0			0
$153$	−17.3950	−	14.1139i	−1.40630	−	1.14104i
$154$		0			0
$155$	36.9565	+	6.51644i	2.96842	+	0.523413i
$156$		0			0
$157$	0.0313116	+	0.0373157i	0.00249894	+	0.00297812i	0.767292	−	0.641297i	$-0.221603\pi$
$157$	0.0313116	+	0.0373157i	0.00249894	+	0.00297812i	−0.764794	+	0.644275i	$0.777159\pi$
$158$		0			0
$159$	−15.0599	−	17.6501i	−1.19433	−	1.39974i
$160$		0			0
$161$	−6.84955	+	9.48174i	−0.539820	+	0.747266i
$162$		0			0
$163$	−2.22231	−	3.84915i	−0.174064	−	0.301488i	0.765773	−	0.643111i	$-0.222357\pi$
$163$	−2.22231	−	3.84915i	−0.174064	−	0.301488i	−0.939837	+	0.341623i	$0.889023\pi$
$164$		0			0
$165$	1.95574	−	5.51441i	0.152254	−	0.429297i
$166$		0			0
$167$	3.33767	+	1.21481i	0.258277	+	0.0940050i	0.467913	−	0.883774i	$-0.345006\pi$
$167$	3.33767	+	1.21481i	0.258277	+	0.0940050i	−0.209637	+	0.977779i	$0.567228\pi$
$168$		0			0
$169$	2.00865	−	11.3916i	0.154511	−	0.876278i
$170$		0			0
$171$	1.30376	−	1.60685i	0.0997009	−	0.122879i
$172$		0			0
$173$	14.4798	+	12.1500i	1.10088	+	0.923749i	0.997484	−	0.0708908i	$-0.0225842\pi$
$173$	14.4798	+	12.1500i	1.10088	+	0.923749i	0.103397	+	0.994640i	$0.467029\pi$
$174$		0			0
$175$	−13.3401	−	19.6619i	−1.00842	−	1.48630i
$176$		0			0
$177$	−0.0239811	+	0.00895304i	−0.00180253	+	0.000672952i
$178$		0			0
$179$			26.7211i			1.99723i	0.0526473	+	0.998613i	$0.483234\pi$
$179$			26.7211i			1.99723i	−0.0526473	+	0.998613i	$0.516766\pi$
$180$		0			0
$181$	6.39653	+	3.69304i	0.475450	+	0.274501i	0.718519	−	0.695508i	$-0.244821\pi$
$181$	6.39653	+	3.69304i	0.475450	+	0.274501i	−0.243068	+	0.970009i	$0.578154\pi$
$182$		0			0
$183$	0.0560563	+	6.79771i	0.00414380	+	0.502501i
$184$		0			0
$185$	−33.5726	−	12.2194i	−2.46831	−	0.898390i
$186$		0			0
$187$	−6.64347	−	1.17142i	−0.485819	−	0.0856629i
$188$		0			0
$189$	9.62336	−	9.81789i	0.699996	−	0.714146i
$190$		0			0
$191$	−1.42440	−	0.251161i	−0.103066	−	0.0181733i	0.121877	−	0.992545i	$-0.461109\pi$
$191$	−1.42440	−	0.251161i	−0.103066	−	0.0181733i	−0.224943	+	0.974372i	$0.572220\pi$
$192$		0			0
$193$	16.3927	+	5.96644i	1.17997	+	0.429474i	0.856191	−	0.516659i	$-0.172825\pi$
$193$	16.3927	+	5.96644i	1.17997	+	0.429474i	0.323779	+	0.946133i	$0.395047\pi$
$194$		0			0
$195$	−6.68093	+	3.93104i	−0.478431	+	0.281508i
$196$		0			0
$197$	13.9252	+	8.03969i	0.992126	+	0.572804i	0.905909	−	0.423472i	$-0.139189\pi$
$197$	13.9252	+	8.03969i	0.992126	+	0.572804i	0.0862168	+	0.996276i	$0.472522\pi$
$198$		0			0
$199$			3.28881i			0.233138i	0.993183	+	0.116569i	$0.0371896\pi$
$199$			3.28881i			0.233138i	−0.993183	+	0.116569i	$0.962810\pi$
$200$		0			0
$201$	−0.533418	+	3.17820i	−0.0376244	+	0.224173i
$202$		0			0
$203$	−0.854767	−	0.414023i	−0.0599929	−	0.0290587i
$204$		0			0
$205$	−21.6535	−	18.1695i	−1.51235	−	1.26901i
$206$		0			0
$207$	0.218730	+	13.2613i	0.0152028	+	0.921727i
$208$		0			0
$209$	0.108209	−	0.613684i	0.00748498	−	0.0424494i
$210$		0			0
$211$	23.2958	+	8.47897i	1.60375	+	0.583717i	0.980190	−	0.198060i	$-0.0634642\pi$
$211$	23.2958	+	8.47897i	1.60375	+	0.583717i	0.623558	+	0.781777i	$0.285686\pi$
$212$		0			0
$213$	19.0581	−	3.52275i	1.30584	−	0.241375i
$214$		0			0
$215$	8.21173	+	14.2231i	0.560036	+	0.970010i
$216$		0			0
$217$	26.4158	+	2.70378i	1.79322	+	0.183544i
$218$		0			0
$219$	18.9537	−	3.50344i	1.28077	−	0.236741i
$220$		0			0
$221$	5.74484	+	6.84643i	0.386439	+	0.460541i
$222$		0			0
$223$	15.8216	+	2.78978i	1.05949	+	0.186817i	0.676132	−	0.736781i	$-0.263655\pi$
$223$	15.8216	+	2.78978i	1.05949	+	0.186817i	0.383362	+	0.923598i	$0.374766\pi$
$224$		0			0
$225$	−25.4654	−	8.79581i	−1.69769	−	0.586387i
$226$		0			0
$227$	−1.48157	+	8.40237i	−0.0983349	+	0.557685i	0.895339	+	0.445385i	$0.146933\pi$
$227$	−1.48157	+	8.40237i	−0.0983349	+	0.557685i	−0.993674	+	0.112301i	$0.964178\pi$
$228$		0			0
$229$	0.302173	−	0.830212i	0.0199681	−	0.0548620i	−0.929308	−	0.369305i	$-0.879596\pi$
$229$	0.302173	−	0.830212i	0.0199681	−	0.0548620i	0.949276	+	0.314443i	$0.101818\pi$
$230$		0			0
$231$	1.09746	−	3.99202i	0.0722077	−	0.262656i
$232$		0			0
$233$	7.90471	+	4.56379i	0.517855	+	0.298984i	0.736057	−	0.676920i	$-0.236686\pi$
$233$	7.90471	+	4.56379i	0.517855	+	0.298984i	−0.218202	+	0.975904i	$0.570019\pi$
$234$		0			0
$235$	−8.66265	−	15.0041i	−0.565089	−	0.978762i
$236$		0			0
$237$	−8.75785	+	15.4621i	−0.568883	+	1.00437i
$238$		0			0
$239$	−16.4613	+	2.90258i	−1.06480	+	0.187752i	−0.678483	−	0.734616i	$-0.737362\pi$
$239$	−16.4613	+	2.90258i	−1.06480	+	0.187752i	−0.386312	+	0.922368i	$0.626251\pi$
$240$		0			0
$241$	8.58860	+	23.5970i	0.553241	+	1.52002i	0.829259	+	0.558864i	$0.188763\pi$
$241$	8.58860	+	23.5970i	0.553241	+	1.52002i	−0.276019	+	0.961152i	$0.589015\pi$
$242$		0			0
$243$	2.07183	−	15.4502i	0.132908	−	0.991128i
$244$		0			0
$245$	−16.2259	−	20.5369i	−1.03664	−	1.31206i
$246$		0			0
$247$	−0.632433	+	0.530674i	−0.0402407	+	0.0337660i
$248$		0			0
$249$	−5.25406	−	8.92944i	−0.332963	−	0.565880i
$250$		0			0
$251$	−8.73608	+	15.1313i	−0.551417	+	0.955082i	0.446756	+	0.894656i	$0.352579\pi$
$251$	−8.73608	+	15.1313i	−0.551417	+	0.955082i	−0.998173	+	0.0604258i	$0.980754\pi$
$252$		0			0
$253$	1.99710	+	3.45908i	0.125557	+	0.217470i
$254$		0			0
$255$	−8.00417	+	47.6903i	−0.501241	+	2.98648i
$256$		0			0
$257$	−21.3751	−	7.77990i	−1.33334	−	0.485297i	−0.425632	−	0.904896i	$-0.639948\pi$
$257$	−21.3751	−	7.77990i	−1.33334	−	0.485297i	−0.907709	+	0.419599i	$0.862171\pi$
$258$		0			0
$259$	−24.3201	−	6.90212i	−1.51117	−	0.428877i
$260$		0			0
$261$	−1.05734	+	0.204471i	−0.0654475	+	0.0126564i
$262$		0			0
$263$	−1.78344	+	2.12542i	−0.109972	+	0.131059i	−0.818222	−	0.574902i	$-0.805040\pi$
$263$	−1.78344	+	2.12542i	−0.109972	+	0.131059i	0.708251	+	0.705961i	$0.249485\pi$
$264$		0			0
$265$	−17.1307	+	47.0663i	−1.05233	+	2.89126i
$266$		0			0
$267$	−22.7243	−	8.05937i	−1.39070	−	0.493226i
$268$		0			0
$269$	5.69974	−	9.87224i	0.347519	−	0.601921i	−0.638289	−	0.769797i	$-0.720357\pi$
$269$	5.69974	−	9.87224i	0.347519	−	0.601921i	0.985808	+	0.167876i	$0.0536908\pi$
$270$		0			0
$271$	3.39054	−	1.95753i	0.205961	−	0.118912i	−0.393472	−	0.919337i	$-0.628726\pi$
$271$	3.39054	−	1.95753i	0.205961	−	0.118912i	0.599433	+	0.800425i	$0.295393\pi$
$272$		0			0
$273$	−4.51340	+	3.11688i	−0.273164	+	0.188642i
$274$		0			0
$275$	−7.99021	+	1.40889i	−0.481828	+	0.0849592i
$276$		0			0
$277$	4.15531	+	3.48672i	0.249669	+	0.209497i	0.759030	−	0.651056i	$-0.225674\pi$
$277$	4.15531	+	3.48672i	0.249669	+	0.209497i	−0.509361	+	0.860553i	$0.670118\pi$
$278$		0			0
$279$	25.8235	−	15.4826i	1.54601	−	0.926918i
$280$		0			0
$281$	−6.74746	−	18.5385i	−0.402520	−	1.10591i	−0.961037	−	0.276421i	$-0.910852\pi$
$281$	−6.74746	−	18.5385i	−0.402520	−	1.10591i	0.558517	−	0.829493i	$-0.311370\pi$
$282$		0			0
$283$	15.3551	−	2.70751i	0.912764	−	0.160945i	0.302506	−	0.953147i	$-0.402177\pi$
$283$	15.3551	−	2.70751i	0.912764	−	0.160945i	0.610258	+	0.792203i	$0.291066\pi$
$284$		0			0
$285$	−4.40534	−	0.739378i	−0.260950	−	0.0437970i
$286$		0			0
$287$	−16.2135	−	11.7125i	−0.957050	−	0.691368i
$288$		0			0
$289$	38.7543			2.27967
$290$		0			0
$291$	−0.0640022	−	7.76128i	−0.00375188	−	0.454974i
$292$		0			0
$293$	3.36781	+	19.0998i	0.196749	+	1.11582i	0.909905	+	0.414816i	$0.136154\pi$
$293$	3.36781	+	19.0998i	0.196749	+	1.11582i	−0.713156	+	0.701005i	$0.752735\pi$
$294$		0			0
$295$	0.0423310	+	0.0355200i	0.00246461	+	0.00206805i
$296$		0			0
$297$	−1.71423	−	4.37029i	−0.0994697	−	0.253590i
$298$		0			0
$299$	0.918896	−	5.21132i	0.0531411	−	0.301378i
$300$		0			0
$301$	6.52469	+	9.61672i	0.376077	+	0.554298i
$302$		0			0
$303$	−3.97670	−	6.75852i	−0.228455	−	0.388267i
$304$		0			0
$305$	12.7089	−	7.33751i	0.727712	−	0.420145i
$306$		0			0
$307$	15.6946	−	9.06129i	0.895739	−	0.517155i	0.0199238	−	0.999802i	$-0.493658\pi$
$307$	15.6946	−	9.06129i	0.895739	−	0.517155i	0.875815	+	0.482646i	$0.160324\pi$
$308$		0			0
$309$	20.0682	+	3.36818i	1.14164	+	0.191609i
$310$		0			0
$311$	−3.95939	−	22.4548i	−0.224516	−	1.27330i	−0.863608	−	0.504165i	$-0.831800\pi$
$311$	−3.95939	−	22.4548i	−0.224516	−	1.27330i	0.639091	−	0.769131i	$-0.279311\pi$
$312$		0			0
$313$	−16.4418	+	19.5945i	−0.929344	+	1.10755i	0.0646276	+	0.997909i	$0.479414\pi$
$313$	−16.4418	+	19.5945i	−0.929344	+	1.10755i	−0.993971	+	0.109639i	$0.965030\pi$
$314$		0			0
$315$	−28.6801	−	7.63074i	−1.61594	−	0.429944i
$316$		0			0
$317$	5.90887	+	16.2345i	0.331875	+	0.911819i	0.987624	+	0.156840i	$0.0501307\pi$
$317$	5.90887	+	16.2345i	0.331875	+	0.911819i	−0.655749	+	0.754979i	$0.727647\pi$
$318$		0			0
$319$	−0.248441	+	0.208466i	−0.0139100	+	0.0116719i
$320$		0			0
$321$	10.4884	−	1.93869i	0.585404	−	0.108207i
$322$		0			0
$323$			5.15025i			0.286568i
$324$		0			0
$325$	9.30902	+	5.37457i	0.516372	+	0.298127i
$326$		0			0
$327$	−7.58865	+	6.47501i	−0.419653	+	0.358069i
$328$		0			0
$329$	−6.88297	−	10.1448i	−0.379470	−	0.559300i
$330$		0			0
$331$	−23.3643	+	8.50391i	−1.28422	+	0.467417i	−0.891825	−	0.452380i	$-0.850575\pi$
$331$	−23.3643	+	8.50391i	−1.28422	+	0.467417i	−0.392393	+	0.919797i	$0.628353\pi$
$332$		0			0
$333$	−26.7713	+	10.2470i	−1.46706	+	0.561534i
$334$		0			0
$335$	6.53734	−	2.37940i	0.357173	−	0.130000i
$336$		0			0
$337$	−5.16317	+	4.33242i	−0.281256	+	0.236002i	−0.772492	−	0.635025i	$-0.780990\pi$
$337$	−5.16317	+	4.33242i	−0.281256	+	0.236002i	0.491236	+	0.871027i	$0.336545\pi$
$338$		0			0
$339$	−4.07465	+	4.93810i	−0.221304	+	0.268201i
$340$		0			0
$341$	4.53369	−	7.85259i	0.245513	−	0.425241i
$342$		0			0
$343$	−12.5044	−	13.6616i	−0.675173	−	0.737659i
$344$		0			0
$345$	24.6769	−	14.5199i	1.32856	−	0.781723i
$346$		0			0
$347$	9.44947	−	25.9622i	0.507274	−	1.39372i	−0.376764	−	0.926309i	$-0.622963\pi$
$347$	9.44947	−	25.9622i	0.507274	−	1.39372i	0.884038	−	0.467415i	$-0.154815\pi$
$348$		0			0
$349$	17.8032	−	21.2170i	0.952981	−	1.13572i	−0.0376687	−	0.999290i	$-0.511993\pi$
$349$	17.8032	−	21.2170i	0.952981	−	1.13572i	0.990650	−	0.136429i	$-0.0435624\pi$
$350$		0			0
$351$	−1.98196	+	5.89521i	−0.105789	+	0.314663i
$352$		0			0
$353$	−13.2918	+	4.83782i	−0.707451	+	0.257491i	−0.670589	−	0.741829i	$-0.733958\pi$
$353$	−13.2918	+	4.83782i	−0.707451	+	0.257491i	−0.0368622	+	0.999320i	$0.511736\pi$
$354$		0			0
$355$	−26.8933	−	32.0502i	−1.42735	−	1.70105i
$356$		0			0
$357$	−3.20331	+	34.0673i	−0.169537	+	1.80303i
$358$		0			0
$359$			14.6085i			0.771006i	0.922707	+	0.385503i	$0.125972\pi$
$359$			14.6085i			0.771006i	−0.922707	+	0.385503i	$0.874028\pi$
$360$		0			0
$361$	18.5242			0.974961
$362$		0			0
$363$	13.6052	+	11.2262i	0.714085	+	0.589223i
$364$		0			0
$365$	−26.7460	−	31.8746i	−1.39995	−	1.66839i
$366$		0			0
$367$	−2.66648	−	0.470173i	−0.139189	−	0.0245428i	0.103619	−	0.994617i	$-0.466958\pi$
$367$	−2.66648	−	0.470173i	−0.139189	−	0.0245428i	−0.242809	+	0.970074i	$0.578069\pi$
$368$		0			0
$369$	−22.6765	+	0.374022i	−1.18049	+	0.0194708i
$370$		0			0
$371$	−9.67627	+	34.0950i	−0.502367	+	1.77012i
$372$		0			0
$373$	−5.01731	−	28.4546i	−0.259786	−	1.47332i	−0.783481	−	0.621415i	$-0.786558\pi$
$373$	−5.01731	−	28.4546i	−0.259786	−	1.47332i	0.523695	−	0.851906i	$-0.324553\pi$
$374$		0			0
$375$	4.68566	+	25.3495i	0.241966	+	1.30904i
$376$		0			0
$377$	0.429670			0.0221291
$378$		0			0
$379$	3.86950			0.198763			0.0993815	−	0.995049i	$-0.468314\pi$
$379$	3.86950			0.198763			0.0993815	+	0.995049i	$0.468314\pi$
$380$		0			0
$381$	−19.2333	+	16.4108i	−0.985352	+	0.840752i
$382$		0			0
$383$	−3.64342	−	20.6629i	−0.186170	−	1.05582i	−0.924443	−	0.381321i	$-0.875469\pi$
$383$	−3.64342	−	20.6629i	−0.186170	−	1.05582i	0.738273	−	0.674502i	$-0.235642\pi$
$384$		0			0
$385$	−8.66609	+	2.18576i	−0.441665	+	0.111396i
$386$		0			0
$387$	12.4552	+	4.30206i	0.633133	+	0.218686i
$388$		0			0
$389$	−14.0482	−	2.47708i	−0.712274	−	0.125593i	−0.194241	−	0.980954i	$-0.562224\pi$
$389$	−14.0482	−	2.47708i	−0.712274	−	0.125593i	−0.518033	+	0.855361i	$0.673336\pi$
$390$		0			0
$391$	−21.2194	−	25.2882i	−1.07311	−	1.27888i
$392$		0			0
$393$	4.35298	−	1.62513i	0.219579	−	0.0819769i
$394$		0			0
$395$	38.3611			1.93016
$396$		0			0
$397$			28.9198i			1.45144i	0.687989	+	0.725721i	$0.258494\pi$
$397$			28.9198i			1.45144i	−0.687989	+	0.725721i	$0.741506\pi$
$398$		0			0
$399$	−3.14693	−	0.295903i	−0.157544	−	0.0148137i
$400$		0			0
$401$	9.75159	+	11.6215i	0.486971	+	0.580350i	0.952444	−	0.304712i	$-0.0985603\pi$
$401$	9.75159	+	11.6215i	0.486971	+	0.580350i	−0.465473	+	0.885062i	$0.654116\pi$
$402$		0			0
$403$	−11.2885	+	4.10866i	−0.562318	+	0.204667i
$404$		0			0
$405$	−31.2253	+	12.5461i	−1.55160	+	0.623420i
$406$		0			0
$407$	−5.54892	+	6.61295i	−0.275050	+	0.327792i
$408$		0			0
$409$	7.75940	−	21.3188i	0.383678	−	1.05415i	−0.586117	−	0.810226i	$-0.699344\pi$
$409$	7.75940	−	21.3188i	0.383678	−	1.05415i	0.969795	−	0.243920i	$-0.0784335\pi$
$410$		0			0
$411$	−0.0253648	−	3.07588i	−0.00125115	−	0.151722i
$412$		0			0
$413$	0.0316961	+	0.0228971i	0.00155966	+	0.00112669i
$414$		0			0
$415$	−11.1828	+	19.3693i	−0.548944	+	0.950799i
$416$		0			0
$417$	−13.3638	−	2.24293i	−0.654427	−	0.109837i
$418$		0			0
$419$	21.2332	−	17.8168i	1.03731	−	0.870407i	0.0456084	−	0.998959i	$-0.485477\pi$
$419$	21.2332	−	17.8168i	1.03731	−	0.870407i	0.991703	+	0.128552i	$0.0410329\pi$
$420$		0			0
$421$	−10.8260	+	3.94035i	−0.527628	+	0.192041i	−0.592079	−	0.805880i	$-0.701693\pi$
$421$	−10.8260	+	3.94035i	−0.527628	+	0.192041i	0.0644509	+	0.997921i	$0.479470\pi$
$422$		0			0
$423$	−13.1391	−	4.53829i	−0.638845	−	0.220659i
$424$		0			0
$425$	63.0126	−	22.9347i	3.05656	−	1.11250i
$426$		0			0
$427$	8.59292	−	5.83007i	0.415840	−	0.282137i
$428$		0			0
$429$	0.340441	+	1.84179i	0.0164366	+	0.0889225i
$430$		0			0
$431$	0.198915	+	0.114844i	0.00958139	+	0.00553182i	0.504783	−	0.863246i	$-0.331572\pi$
$431$	0.198915	+	0.114844i	0.00958139	+	0.00553182i	−0.495202	+	0.868778i	$0.664906\pi$
$432$		0			0
$433$			27.7350i			1.33286i	0.745568	+	0.666429i	$0.232178\pi$
$433$			27.7350i			1.33286i	−0.745568	+	0.666429i	$0.767822\pi$
$434$		0			0
$435$	1.50899	+	1.76852i	0.0723506	+	0.0847942i
$436$		0			0
$437$	2.33598	−	1.96012i	0.111745	−	0.0937652i
$438$		0			0
$439$	14.1419	+	38.8545i	0.674956	+	1.85443i	0.490115	+	0.871658i	$0.336955\pi$
$439$	14.1419	+	38.8545i	0.674956	+	1.85443i	0.184841	+	0.982768i	$0.440823\pi$
$440$		0			0
$441$	−20.6319	−	3.91460i	−0.982472	−	0.186410i
$442$		0			0
$443$	11.3456	−	13.5212i	0.539045	−	0.642409i	−0.425928	−	0.904757i	$-0.640052\pi$
$443$	11.3456	−	13.5212i	0.539045	−	0.642409i	0.964973	+	0.262348i	$0.0844968\pi$
$444$		0			0
$445$	9.03834	+	51.2590i	0.428459	+	2.42991i
$446$		0			0
$447$	−16.3766	+	19.8470i	−0.774586	+	0.938729i
$448$		0			0
$449$	−2.02166	+	1.16721i	−0.0954080	+	0.0550838i	−0.546945	−	0.837169i	$-0.684209\pi$
$449$	−2.02166	+	1.16721i	−0.0954080	+	0.0550838i	0.451537	+	0.892252i	$0.350876\pi$
$450$		0			0
$451$	−5.91491	+	3.41497i	−0.278522	+	0.160805i
$452$		0			0
$453$	13.8002	−	24.3644i	0.648388	−	1.14474i
$454$		0			0
$455$	10.6565	+	5.16170i	0.499586	+	0.241984i
$456$		0			0
$457$	0.544911	−	3.09034i	0.0254899	−	0.144560i	−0.969407	−	0.245460i	$-0.921061\pi$
$457$	0.544911	−	3.09034i	0.0254899	−	0.144560i	0.994897	+	0.100900i	$0.0321721\pi$
$458$		0			0
$459$	20.2247	+	33.1108i	0.944010	+	1.54548i
$460$		0			0
$461$	9.62681	+	8.07785i	0.448365	+	0.376223i	0.838829	−	0.544395i	$-0.183241\pi$
$461$	9.62681	+	8.07785i	0.448365	+	0.376223i	−0.390464	+	0.920618i	$0.627685\pi$
$462$		0			0
$463$	2.81661	+	15.9738i	0.130899	+	0.742364i	0.977628	+	0.210340i	$0.0674573\pi$
$463$	2.81661	+	15.9738i	0.130899	+	0.742364i	−0.846729	+	0.532024i	$0.821432\pi$
$464$		0			0
$465$	−56.5561	−	32.0338i	−2.62272	−	1.48553i
$466$		0			0
$467$	−10.1387			−0.469162			−0.234581	−	0.972097i	$-0.575372\pi$
$467$	−10.1387			−0.469162			−0.234581	+	0.972097i	$0.575372\pi$
$468$		0			0
$469$	4.49163	−	2.01446i	0.207404	−	0.0930193i
$470$		0			0
$471$	−0.0295097	−	0.0790432i	−0.00135974	−	0.00364212i
$472$		0			0
$473$	3.90803	−	0.689092i	0.179692	−	0.0316845i
$474$		0			0
$475$	2.11857	+	5.82073i	0.0972068	+	0.267074i
$476$		0			0
$477$	14.3656	+	37.5315i	0.657756	+	1.71845i
$478$		0			0
$479$	19.3092	+	16.2023i	0.882259	+	0.740303i	0.966642	−	0.256130i	$-0.0824476\pi$
$479$	19.3092	+	16.2023i	0.882259	+	0.740303i	−0.0843835	+	0.996433i	$0.526892\pi$
$480$		0			0
$481$	11.2631	−	1.98599i	0.513555	−	0.0905535i
$482$		0			0
$483$	16.6709	−	11.5126i	0.758551	−	0.523843i
$484$		0			0
$485$	−14.5104	+	8.37760i	−0.658884	+	0.380407i
$486$		0			0
$487$	−4.27727	+	7.40844i	−0.193821	+	0.335709i	−0.946514	−	0.322664i	$-0.895422\pi$
$487$	−4.27727	+	7.40844i	−0.193821	+	0.335709i	0.752692	+	0.658373i	$0.228755\pi$
$488$		0			0
$489$	1.39927	+	7.57006i	0.0632770	+	0.342330i
$490$		0			0
$491$	11.2025	−	30.7785i	0.505560	−	1.38902i	−0.380213	−	0.924899i	$-0.624149\pi$
$491$	11.2025	−	30.7785i	0.505560	−	1.38902i	0.885774	−	0.464117i	$-0.153628\pi$
$492$		0			0
$493$	1.72294	−	2.05333i	0.0775975	−	0.0924771i
$494$		0			0
$495$	−6.38519	+	7.86958i	−0.286993	+	0.353711i
$496$		0			0
$497$	−20.6232	−	21.2400i	−0.925076	−	0.952744i
$498$		0			0
$499$	12.7319	+	4.63403i	0.569958	+	0.207448i	0.610892	−	0.791714i	$-0.290811\pi$
$499$	12.7319	+	4.63403i	0.569958	+	0.207448i	−0.0409339	+	0.999162i	$0.513033\pi$
$500$		0			0
$501$	−4.74517	−	3.91545i	−0.211999	−	0.174929i
$502$		0			0
$503$	−19.3212	−	33.4653i	−0.861490	−	1.49215i	−0.870490	−	0.492186i	$-0.836198\pi$
$503$	−19.3212	−	33.4653i	−0.861490	−	1.49215i	0.00899970	−	0.999960i	$-0.497135\pi$
$504$		0			0
$505$	−8.46408	+	14.6602i	−0.376647	+	0.652371i
$506$		0			0
$507$	−9.87420	+	17.4330i	−0.438528	+	0.774228i
$508$		0			0
$509$	−0.0630183	+	0.0528786i	−0.00279324	+	0.00234380i	−0.644183	−	0.764871i	$-0.722803\pi$
$509$	−0.0630183	+	0.0528786i	−0.00279324	+	0.00234380i	0.641390	+	0.767215i	$0.278358\pi$
$510$		0			0
$511$	−20.5102	−	21.1236i	−0.907316	−	0.934453i
$512$		0			0
$513$	−3.05858	+	1.86824i	−0.135040	+	0.0824849i
$514$		0			0
$515$	−15.0243	−	41.2789i	−0.662049	−	1.81897i
$516$		0			0
$517$	−4.12263	+	0.726931i	−0.181313	+	0.0319704i
$518$		0			0
$519$	−16.6029	−	28.2172i	−0.728788	−	1.23860i
$520$		0			0
$521$	−1.02550	−	1.77622i	−0.0449281	−	0.0778177i	0.842687	−	0.538404i	$-0.180973\pi$
$521$	−1.02550	−	1.77622i	−0.0449281	−	0.0778177i	−0.887615	+	0.460586i	$0.847639\pi$
$522$		0			0
$523$	0.666771	+	0.384961i	0.0291559	+	0.0168332i	0.514507	−	0.857486i	$-0.327975\pi$
$523$	0.666771	+	0.384961i	0.0291559	+	0.0168332i	−0.485351	+	0.874319i	$0.661308\pi$
$524$		0			0
$525$	10.3934	+	39.8200i	0.453603	+	1.73789i
$526$		0			0
$527$	−25.6312	+	70.4211i	−1.11651	+	3.06759i
$528$		0			0
$529$	0.599836	−	3.40184i	0.0260798	−	0.147906i
$530$		0			0
$531$	0.0443308		0.000731184i	0.00192379		3.17307e-5i
$532$		0			0
$533$	8.91118	+	1.57128i	0.385986	+	0.0680598i
$534$		0			0
$535$	−14.8004	−	17.6384i	−0.639875	−	0.762574i
$536$		0			0
$537$	15.4703	−	43.6201i	0.667592	−	1.88235i
$538$		0			0
$539$	−6.00390	+	1.98697i	−0.258606	+	0.0855847i
$540$		0			0
$541$	−11.6715	−	20.2156i	−0.501796	−	0.869136i	−0.999998	−	0.00207506i	$-0.999339\pi$
$541$	−11.6715	−	20.2156i	−0.501796	−	0.869136i	0.498202	−	0.867061i	$-0.333994\pi$
$542$		0			0
$543$	−8.30375	−	9.73191i	−0.356348	−	0.417636i
$544$		0			0
$545$	20.2361	+	7.36535i	0.866821	+	0.315497i
$546$		0			0
$547$	−5.13973	+	29.1488i	−0.219759	+	1.24631i	0.652696	+	0.757620i	$0.273638\pi$
$547$	−5.13973	+	29.1488i	−0.219759	+	1.24631i	−0.872455	+	0.488695i	$0.837473\pi$
$548$		0			0
$549$	3.84406	−	11.1292i	0.164060	−	0.474983i
$550$		0			0
$551$	0.189674	+	0.159155i	0.00808038	+	0.00678025i
$552$		0			0
$553$	27.0729	−	1.96715i	1.15126	−	0.0836515i
$554$		0			0
$555$	47.7302	+	39.3843i	2.02604	+	1.67177i
$556$		0			0
$557$			24.7683i			1.04947i	0.851266	+	0.524734i	$0.175835\pi$
$557$			24.7683i			1.04947i	−0.851266	+	0.524734i	$0.824165\pi$
$558$		0			0
$559$	−4.55307	−	2.62872i	−0.192574	−	0.111183i
$560$		0			0
$561$	10.1668	+	5.75853i	0.429241	+	0.243125i
$562$		0			0
$563$	−17.2769	−	6.28829i	−0.728136	−	0.265020i	−0.0487606	−	0.998810i	$-0.515527\pi$
$563$	−17.2769	−	6.28829i	−0.728136	−	0.265020i	−0.679376	+	0.733791i	$0.737749\pi$
$564$		0			0
$565$	13.6107	+	2.39993i	0.572605	+	0.100966i
$566$		0			0
$567$	−21.3935	+	10.4555i	−0.898444	+	0.439089i
$568$		0			0
$569$	−16.9229	−	2.98396i	−0.709444	−	0.125094i	−0.192729	−	0.981252i	$-0.561734\pi$
$569$	−16.9229	−	2.98396i	−0.709444	−	0.125094i	−0.516714	+	0.856158i	$0.672845\pi$
$570$		0			0
$571$	−0.968221	−	0.352404i	−0.0405188	−	0.0147476i	0.321681	−	0.946848i	$-0.395752\pi$
$571$	−0.968221	−	0.352404i	−0.0405188	−	0.0147476i	−0.362200	+	0.932100i	$0.617974\pi$
$572$		0			0
$573$	2.17982	+	1.23467i	0.0910633	+	0.0515789i
$574$		0			0
$575$	−34.3842	−	19.8517i	−1.43392	−	0.827873i
$576$		0			0
$577$			39.7208i			1.65360i	0.562498	+	0.826798i	$0.309840\pi$
$577$			39.7208i			1.65360i	−0.562498	+	0.826798i	$0.690160\pi$
$578$		0			0
$579$	−23.3055	−	19.2304i	−0.968543	−	0.799187i
$580$		0			0
$581$	−6.89891	+	14.2431i	−0.286215	+	0.590902i
$582$		0			0
$583$	9.27087	+	7.77919i	0.383960	+	0.322181i
$584$		0			0
$585$	13.1820	−	2.54918i	0.545009	−	0.105396i
$586$		0			0
$587$	1.61600	−	9.16478i	0.0666994	−	0.378271i	−0.933125	−	0.359551i	$-0.882930\pi$
$587$	1.61600	−	9.16478i	0.0666994	−	0.378271i	0.999825	−	0.0187199i	$-0.00595907\pi$
$588$		0			0
$589$	−6.50509	−	2.36766i	−0.268037	−	0.0975577i
$590$		0			0
$591$	−18.0771	−	21.1862i	−0.743594	−	0.871485i
$592$		0			0
$593$	−5.72573	−	9.91725i	−0.235127	−	0.407253i	0.724182	−	0.689609i	$-0.242217\pi$
$593$	−5.72573	−	9.91725i	−0.235127	−	0.407253i	−0.959310	+	0.282356i	$0.908884\pi$
$594$		0			0
$595$	67.3989	−	30.2279i	2.76308	−	1.23922i
$596$		0			0
$597$	1.90407	−	5.36874i	0.0779286	−	0.219728i
$598$		0			0
$599$	−3.34805	−	3.99005i	−0.136798	−	0.163029i	0.693296	−	0.720653i	$-0.256158\pi$
$599$	−3.34805	−	3.99005i	−0.136798	−	0.163029i	−0.830094	+	0.557624i	$0.811713\pi$
$600$		0			0
$601$	5.98265	+	1.05490i	0.244037	+	0.0430304i	0.294329	−	0.955704i	$-0.404904\pi$
$601$	5.98265	+	1.05490i	0.244037	+	0.0430304i	−0.0502914	+	0.998735i	$0.516015\pi$
$602$		0			0
$603$	2.71080	−	4.87935i	0.110392	−	0.198703i
$604$		0			0
$605$	6.61213	−	37.4992i	0.268821	−	1.52456i
$606$		0			0
$607$	−0.0760370	+	0.208910i	−0.00308625	+	0.00847940i	−0.941226	−	0.337777i	$-0.890325\pi$
$607$	−0.0760370	+	0.208910i	−0.00308625	+	0.00847940i	0.938140	+	0.346256i	$0.112547\pi$
$608$		0			0
$609$	1.15564	+	1.17073i	0.0468290	+	0.0474405i
$610$		0			0
$611$	4.80308	+	2.77306i	0.194312	+	0.112186i
$612$		0			0
$613$	−14.4222	−	24.9801i	−0.582509	−	1.00894i	−0.995181	−	0.0980556i	$-0.968738\pi$
$613$	−14.4222	−	24.9801i	−0.582509	−	1.00894i	0.412672	−	0.910880i	$-0.364596\pi$
$614$		0			0
$615$	24.8285	+	42.1967i	1.00118	+	1.70154i
$616$		0			0
$617$	9.68410	−	1.70757i	0.389867	−	0.0687441i	0.0247213	−	0.999694i	$-0.492130\pi$
$617$	9.68410	−	1.70757i	0.389867	−	0.0687441i	0.365146	+	0.930950i	$0.381019\pi$
$618$		0			0
$619$	0.486578	+	1.33686i	0.0195572	+	0.0537330i	0.949087	−	0.315014i	$-0.102009\pi$
$619$	0.486578	+	1.33686i	0.0195572	+	0.0537330i	−0.929530	+	0.368747i	$0.879787\pi$
$620$		0			0
$621$	7.32066	−	21.7748i	0.293768	−	0.873792i
$622$		0			0
$623$	9.00725	+	35.7119i	0.360868	+	1.43077i
$624$		0			0
$625$	8.23300	−	6.90830i	0.329320	−	0.276332i
$626$		0			0
$627$	−0.531939	+	0.939145i	−0.0212436	+	0.0375059i
$628$		0			0
$629$	35.6735	−	61.7884i	1.42240	−	2.46366i
$630$		0			0
$631$	13.6519	+	23.6458i	0.543473	+	0.941323i	0.998701	+	0.0509480i	$0.0162243\pi$
$631$	13.6519	+	23.6458i	0.543473	+	0.941323i	−0.455228	+	0.890375i	$0.650442\pi$
$632$		0			0
$633$	−33.1197	−	27.3285i	−1.31639	−	1.08621i
$634$		0			0
$635$	51.2882	+	18.6674i	2.03531	+	0.740793i
$636$		0			0
$637$	7.78542	+	3.09635i	0.308469	+	0.122682i
$638$		0			0
$639$	−33.1505	−	5.28319i	−1.31141	−	0.209000i
$640$		0			0
$641$	2.18677	−	2.60610i	0.0863724	−	0.102935i	−0.721127	−	0.692803i	$-0.756376\pi$
$641$	2.18677	−	2.60610i	0.0863724	−	0.102935i	0.807500	+	0.589868i	$0.200820\pi$
$642$		0			0
$643$	−0.422932	+	1.16200i	−0.0166788	+	0.0458247i	−0.947753	−	0.319006i	$-0.896651\pi$
$643$	−0.422932	+	1.16200i	−0.0166788	+	0.0458247i	0.931074	+	0.364831i	$0.118873\pi$
$644$		0			0
$645$	−5.17048	−	27.9724i	−0.203588	−	1.10141i
$646$		0			0
$647$	−0.766333	+	1.32733i	−0.0301277	+	0.0521827i	−0.880696	−	0.473682i	$-0.842925\pi$
$647$	−0.766333	+	1.32733i	−0.0301277	+	0.0521827i	0.850568	+	0.525864i	$0.176258\pi$
$648$		0			0
$649$	0.0115632	−	0.00667601i	0.000453895	−	0.000262056i
$650$		0			0
$651$	−41.5565	−	19.7073i	−1.62873	−	0.772389i
$652$		0			0
$653$	−29.9964	+	5.28917i	−1.17385	+	0.206981i	−0.726364	−	0.687310i	$-0.758791\pi$
$653$	−29.9964	+	5.28917i	−1.17385	+	0.206981i	−0.447485	+	0.894291i	$0.647680\pi$
$654$		0			0
$655$	−7.68380	−	6.44747i	−0.300231	−	0.251924i
$656$		0			0
$657$	−32.9688	−	5.25423i	−1.28624	−	0.204987i
$658$		0			0
$659$	−8.70108	−	23.9060i	−0.338946	−	0.931246i	−0.985694	−	0.168543i	$-0.946094\pi$
$659$	−8.70108	−	23.9060i	−0.338946	−	0.931246i	0.646748	−	0.762703i	$-0.276128\pi$
$660$		0			0
$661$	30.7559	−	5.42310i	1.19627	−	0.210934i	0.460183	−	0.887824i	$-0.347784\pi$
$661$	30.7559	−	5.42310i	1.19627	−	0.210934i	0.736084	+	0.676890i	$0.236673\pi$
$662$		0			0
$663$	−5.41424	−	14.5023i	−0.210272	−	0.563222i
$664$		0			0
$665$	2.79227	+	6.22591i	0.108280	+	0.241430i
$666$		0			0
$667$	−1.58705			−0.0614507
$668$		0			0
$669$	−24.2125	−	13.7141i	−0.936108	−	0.530218i
$670$		0			0
$671$	−0.615731	−	3.49198i	−0.0237700	−	0.134807i
$672$		0			0
$673$	21.3263	+	17.8949i	0.822068	+	0.689797i	0.953455	−	0.301534i	$-0.0974988\pi$
$673$	21.3263	+	17.8949i	0.822068	+	0.689797i	−0.131388	+	0.991331i	$0.541943\pi$
$674$		0			0
$675$	36.4779	+	29.1018i	1.40404	+	1.12013i
$676$		0			0
$677$	3.13907	−	17.8025i	0.120644	−	0.684207i	−0.863156	−	0.504938i	$-0.831515\pi$
$677$	3.13907	−	17.8025i	0.120644	−	0.684207i	0.983800	−	0.179270i	$-0.0573734\pi$
$678$		0			0
$679$	−9.81096	+	6.65648i	−0.376510	+	0.255452i
$680$		0			0
$681$	7.28314	−	12.8585i	0.279091	−	0.492738i
$682$		0			0
$683$	−7.54357	+	4.35528i	−0.288647	+	0.166650i	−0.637331	−	0.770590i	$-0.719962\pi$
$683$	−7.54357	+	4.35528i	−0.288647	+	0.166650i	0.348685	+	0.937240i	$0.386628\pi$
$684$		0			0
$685$	−5.75064	+	3.32013i	−0.219721	+	0.126856i
$686$		0			0
$687$	−0.973930	+	1.18032i	−0.0371577	+	0.0450318i
$688$		0			0
$689$	−2.78422	−	15.7901i	−0.106070	−	0.601555i
$690$		0			0
$691$	28.1894	−	33.5948i	1.07238	−	1.27801i	0.113698	−	0.993515i	$-0.463730\pi$
$691$	28.1894	−	33.5948i	1.07238	−	1.27801i	0.958678	−	0.284493i	$-0.0918252\pi$
$692$		0			0
$693$	−4.10272	+	5.88130i	−0.155850	+	0.223412i
$694$		0			0
$695$	10.0049	+	27.4884i	0.379509	+	1.04269i
$696$		0			0
$697$	43.2421	−	36.2844i	1.63791	−	1.37437i
$698$		0			0
$699$	−10.2616	−	12.0265i	−0.388130	−	0.454884i
$700$		0			0
$701$			24.2340i			0.915305i	0.889131	+	0.457652i	$0.151310\pi$
$701$			24.2340i			0.915305i	−0.889131	+	0.457652i	$0.848690\pi$
$702$		0			0
$703$	5.70765	+	3.29531i	0.215268	+	0.124285i
$704$		0			0
$705$	5.45440	+	29.5084i	0.205425	+	1.11135i
$706$		0			0
$707$	−5.22165	+	10.7803i	−0.196380	+	0.405435i
$708$		0			0
$709$	−0.630968	+	0.229653i	−0.0236965	+	0.00862481i	−0.353841	−	0.935306i	$-0.615125\pi$
$709$	−0.630968	+	0.229653i	−0.0236965	+	0.00862481i	0.330145	+	0.943930i	$0.392902\pi$
$710$		0			0
$711$	23.2484	−	20.1703i	0.871882	−	0.756446i
$712$		0			0
$713$	41.6955	−	15.1759i	1.56151	−	0.568343i
$714$		0			0
$715$	3.09735	−	2.59899i	0.115834	−	0.0971967i
$716$		0			0
$717$	28.5524	+	4.79213i	1.06631	+	0.178965i
$718$		0			0
$719$	−9.38852	+	16.2614i	−0.350133	+	0.606448i	−0.986272	−	0.165126i	$-0.947197\pi$
$719$	−9.38852	+	16.2614i	−0.350133	+	0.606448i	0.636140	+	0.771574i	$0.280530\pi$
$720$		0			0
$721$	−12.7200	−	28.3616i	−0.473717	−	1.05624i
$722$		0			0
$723$	−0.358656	−	43.4927i	−0.0133386	−	1.61751i
$724$		0			0
$725$	1.10260	−	3.02937i	0.0409496	−	0.112508i
$726$		0			0
$727$	−0.400021	+	0.476727i	−0.0148360	+	0.0176808i	−0.773411	−	0.633904i	$-0.781451\pi$
$727$	−0.400021	+	0.476727i	−0.0148360	+	0.0176808i	0.758575	+	0.651585i	$0.225896\pi$
$728$		0			0
$729$	−12.3270	+	24.0217i	−0.456557	+	0.889694i
$730$		0			0
$731$	−30.8197	+	11.2174i	−1.13991	+	0.414892i
$732$		0			0
$733$	23.4542	+	27.9516i	0.866301	+	1.03242i	0.999148	+	0.0412808i	$0.0131438\pi$
$733$	23.4542	+	27.9516i	0.866301	+	1.03242i	−0.132846	+	0.991137i	$0.542412\pi$
$734$		0			0
$735$	14.5976	+	42.9191i	0.538442	+	1.58309i
$736$		0			0
$737$		−	1.68096i		−	0.0619189i
$738$		0			0
$739$	42.8175			1.57507			0.787533	−	0.616272i	$-0.211358\pi$
$739$	42.8175			1.57507			0.787533	+	0.616272i	$0.211358\pi$
$740$		0			0
$741$	1.33963	−	0.500135i	0.0492127	−	0.0183729i
$742$		0			0
$743$	−8.05809	−	9.60326i	−0.295623	−	0.352309i	0.597704	−	0.801717i	$-0.296080\pi$
$743$	−8.05809	−	9.60326i	−0.295623	−	0.352309i	−0.893327	+	0.449407i	$0.851635\pi$
$744$		0			0
$745$	54.7032	+	9.64565i	2.00417	+	0.353389i
$746$		0			0
$747$	3.40712	+	17.6185i	0.124660	+	0.644627i
$748$		0			0
$749$	−11.3497	−	11.6891i	−0.414708	−	0.427111i
$750$		0			0
$751$	−8.85692	−	50.2301i	−0.323193	−	1.83292i	−0.522077	−	0.852898i	$-0.674843\pi$
$751$	−8.85692	−	50.2301i	−0.323193	−	1.83292i	0.198884	−	0.980023i	$-0.436268\pi$
$752$		0			0
$753$	23.0214	−	19.6430i	0.838945	−	0.715830i
$754$		0			0
$755$	−60.4475			−2.19991
$756$		0			0
$757$	−46.4934			−1.68983			−0.844916	−	0.534899i	$-0.820350\pi$
$757$	−46.4934			−1.68983			−0.844916	+	0.534899i	$0.820350\pi$
$758$		0			0
$759$	−1.25746	−	6.80291i	−0.0456431	−	0.246930i
$760$		0			0
$761$	4.42847	+	25.1151i	0.160532	+	0.910423i	0.953552	+	0.301227i	$0.0973963\pi$
$761$	4.42847	+	25.1151i	0.160532	+	0.910423i	−0.793020	+	0.609195i	$0.791493\pi$
$762$		0			0
$763$	14.6591	+	4.16031i	0.530695	+	0.150613i
$764$		0			0
$765$	40.6767	−	73.2167i	1.47067	−	2.64716i
$766$		0			0
$767$	−0.0174207	−	0.00307174i	−0.000629025	−	0.000110914i
$768$		0			0
$769$	−17.0032	−	20.2637i	−0.613153	−	0.730727i	0.366724	−	0.930330i	$-0.380479\pi$
$769$	−17.0032	−	20.2637i	−0.613153	−	0.730727i	−0.979877	+	0.199603i	$0.936035\pi$
$770$		0			0
$771$	30.3890	+	25.0753i	1.09443	+	0.903065i
$772$		0			0
$773$	−35.6277			−1.28144			−0.640719	−	0.767776i	$-0.721364\pi$
$773$	−35.6277			−1.28144			−0.640719	+	0.767776i	$0.721364\pi$
$774$		0			0
$775$			90.1323i			3.23765i
$776$		0			0
$777$	35.7047	+	25.3474i	1.28090	+	0.909333i
$778$		0			0
$779$	3.35174	+	3.99444i	0.120088	+	0.143116i
$780$		0			0
$781$	−9.49960	+	3.45757i	−0.339922	+	0.123722i
$782$		0			0
$783$	1.84440	+	0.278366i	0.0659135	+	0.00994800i
$784$		0			0
$785$	−0.117076	+	0.139526i	−0.00417862	+	0.00497988i
$786$		0			0
$787$	0.831887	−	2.28559i	0.0296536	−	0.0814725i	−0.923982	−	0.382435i	$-0.875086\pi$
$787$	0.831887	−	2.28559i	0.0296536	−	0.0814725i	0.953636	+	0.300962i	$0.0973079\pi$
$788$		0			0
$789$	4.14186	−	2.43706i	0.147454	−	0.0867617i
$790$		0			0
$791$	9.72863	+	0.995769i	0.345910	+	0.0354055i
$792$		0			0
$793$	−2.34886	+	4.06835i	−0.0834105	+	0.144471i
$794$		0			0
$795$	55.2139	−	66.9143i	1.95824	−	2.37321i
$796$		0			0
$797$	28.5314	−	23.9407i	1.01063	−	0.848022i	0.0222113	−	0.999753i	$-0.492929\pi$
$797$	28.5314	−	23.9407i	1.01063	−	0.848022i	0.988422	+	0.151731i	$0.0484849\pi$
$798$		0			0
$799$	32.5120	−	11.8334i	1.15019	−	0.418636i
$800$		0			0
$801$	32.4296	+	26.3126i	1.14585	+	0.929712i
$802$		0			0
$803$	−9.44754	+	3.43862i	−0.333396	+	0.121346i
$804$		0			0
$805$	−39.3614	−	19.0655i	−1.38731	−	0.671970i
$806$		0			0
$807$	−15.0200	+	12.8158i	−0.528728	+	0.451138i
$808$		0			0
$809$	24.4889	+	14.1387i	0.860983	+	0.497089i	0.864341	−	0.502906i	$-0.167736\pi$
$809$	24.4889	+	14.1387i	0.860983	+	0.497089i	−0.00335854	+	0.999994i	$0.501069\pi$
$810$		0			0
$811$		−	31.7458i		−	1.11475i	−0.830262	−	0.557373i	$-0.811809\pi$
$811$		−	31.7458i		−	1.11475i	0.830262	−	0.557373i	$-0.188191\pi$
$812$		0			0
$813$	−6.66813	+	1.23255i	−0.233861	+	0.0432274i
$814$		0			0
$815$	12.7306	−	10.6823i	0.445934	−	0.374183i
$816$		0			0
$817$	−1.03620	−	2.84694i	−0.0362521	−	0.0996018i
$818$		0			0
$819$	9.17232	−	2.47502i	0.320507	−	0.0864843i
$820$		0			0
$821$	5.21706	−	6.21745i	0.182077	−	0.216990i	−0.667284	−	0.744803i	$-0.732543\pi$
$821$	5.21706	−	6.21745i	0.182077	−	0.216990i	0.849361	+	0.527813i	$0.176988\pi$
$822$		0			0
$823$	−2.81536	−	15.9667i	−0.0981374	−	0.556565i	−0.993741	−	0.111711i	$-0.964367\pi$
$823$	−2.81536	−	15.9667i	−0.0981374	−	0.556565i	0.895603	−	0.444854i	$-0.146744\pi$
$824$		0			0
$825$	13.8591	+	2.32606i	0.482512	+	0.0809831i
$826$		0			0
$827$	16.0434	−	9.26264i	0.557882	−	0.322093i	−0.194413	−	0.980920i	$-0.562280\pi$
$827$	16.0434	−	9.26264i	0.557882	−	0.322093i	0.752295	+	0.658826i	$0.228947\pi$
$828$		0			0
$829$	35.8609	−	20.7043i	1.24550	−	0.719091i	0.275293	−	0.961360i	$-0.411225\pi$
$829$	35.8609	−	20.7043i	1.24550	−	0.719091i	0.970209	+	0.242269i	$0.0778917\pi$
$830$		0			0
$831$	−4.76458	−	8.09755i	−0.165282	−	0.280901i
$832$		0			0
$833$	46.0159	−	24.7892i	1.59436	−	0.858893i
$834$		0			0
$835$	−2.30616	+	13.0789i	−0.0798080	+	0.452614i
$836$		0			0
$837$	−51.1187	+	10.3235i	−1.76692	+	0.356832i
$838$		0			0
$839$	−10.1062	−	8.48015i	−0.348906	−	0.292767i	0.451444	−	0.892299i	$-0.350909\pi$
$839$	−10.1062	−	8.48015i	−0.348906	−	0.292767i	−0.800351	+	0.599532i	$0.795353\pi$
$840$		0			0
$841$	5.01342	+	28.4325i	0.172877	+	0.980432i
$842$		0			0
$843$	0.281771	+	34.1692i	0.00970471	+	1.17685i
$844$		0			0
$845$	43.2510			1.48788
$846$		0			0
$847$	2.74348	−	26.8037i	0.0942671	−	0.920986i
$848$		0			0
$849$	−26.6335	−	4.47008i	−0.914060	−	0.153413i
$850$		0			0
$851$	−41.6020	+	7.33555i	−1.42610	+	0.251459i
$852$		0			0
$853$	−0.0480517	−	0.132021i	−0.00164526	−	0.00452031i	0.938867	−	0.344279i	$-0.111877\pi$
$853$	−0.0480517	−	0.132021i	−0.00164526	−	0.00452031i	−0.940513	+	0.339759i	$0.889654\pi$
$854$		0			0
$855$	6.76333	+	3.75747i	0.231301	+	0.128503i
$856$		0			0
$857$	10.9549	+	9.19226i	0.374213	+	0.314002i	0.810425	−	0.585842i	$-0.199236\pi$
$857$	10.9549	+	9.19226i	0.374213	+	0.314002i	−0.436213	+	0.899844i	$0.643680\pi$
$858$		0			0
$859$	−46.2811	+	8.16061i	−1.57909	+	0.278436i	−0.893334	−	0.449394i	$-0.851640\pi$
$859$	−46.2811	+	8.16061i	−1.57909	+	0.278436i	−0.685757	+	0.727831i	$0.740529\pi$
$860$		0			0
$861$	19.6862	+	28.5067i	0.670905	+	0.971504i
$862$		0			0
$863$	−21.8142	+	12.5945i	−0.742566	+	0.428720i	−0.823001	−	0.568039i	$-0.807702\pi$
$863$	−21.8142	+	12.5945i	−0.742566	+	0.428720i	0.0804358	+	0.996760i	$0.474369\pi$
$864$		0			0
$865$	−35.3380	+	61.2072i	−1.20153	+	2.08111i
$866$		0			0
$867$	−63.2635	−	22.4370i	−2.14854	−	0.762001i
$868$		0			0
$869$	3.17019	−	8.71002i	0.107541	−	0.295467i
$870$		0			0
$871$	−1.43150	+	1.70600i	−0.0485045	+	0.0578055i
$872$		0			0
$873$	−4.38895	+	12.7068i	−0.148543	+	0.430059i
$874$		0			0
$875$	28.2516	−	27.4312i	0.955079	−	0.927343i
$876$		0			0
$877$	31.1326	+	11.3313i	1.05127	+	0.382632i	0.809143	−	0.587612i	$-0.199932\pi$
$877$	31.1326	+	11.3313i	1.05127	+	0.382632i	0.242129	+	0.970244i	$0.422154\pi$
$878$		0			0
$879$	5.56022	−	33.1288i	0.187542	−	1.11741i
$880$		0			0
$881$	15.5928	+	27.0075i	0.525334	+	0.909906i	0.999565	+	0.0295048i	$0.00939304\pi$
$881$	15.5928	+	27.0075i	0.525334	+	0.909906i	−0.474230	+	0.880401i	$0.657274\pi$
$882$		0			0
$883$	−6.90147	+	11.9537i	−0.232253	+	0.402274i	−0.958471	−	0.285191i	$-0.907943\pi$
$883$	−6.90147	+	11.9537i	−0.232253	+	0.402274i	0.726218	+	0.687465i	$0.241276\pi$
$884$		0			0
$885$	−0.0485378	−	0.0824914i	−0.00163158	−	0.00277292i
$886$		0			0
$887$	−26.9343	+	22.6006i	−0.904366	+	0.758853i	−0.971039	−	0.238921i	$-0.923206\pi$
$887$	−26.9343	+	22.6006i	−0.904366	+	0.758853i	0.0666726	+	0.997775i	$0.478762\pi$
$888$		0			0
$889$	37.1533	+	10.5442i	1.24608	+	0.353643i
$890$		0			0
$891$	0.268151	+	8.12663i	0.00898341	+	0.272252i
$892$		0			0
$893$	1.09310	+	3.00327i	0.0365792	+	0.100500i
$894$		0			0
$895$	−98.3937	+	17.3495i	−3.28894	+	0.579929i
$896$		0			0
$897$	−4.51715	+	7.97509i	−0.150823	+	0.266280i
$898$		0			0
$899$	1.80141	+	3.12013i	0.0600804	+	0.104062i
$900$		0			0
$901$	−86.6229	−	50.0117i	−2.88583	−	1.66613i
$902$		0			0
$903$	−5.08342	−	19.4761i	−0.169166	−	0.648123i
$904$		0			0
$905$	−9.44556	+	25.9515i	−0.313981	+	0.862655i
$906$		0			0
$907$	−5.33531	+	30.2580i	−0.177156	+	1.00470i	0.758470	+	0.651708i	$0.225947\pi$
$907$	−5.33531	+	30.2580i	−0.177156	+	1.00470i	−0.935626	+	0.352993i	$0.885164\pi$
$908$		0			0
$909$	2.57879	+	13.3351i	0.0855329	+	0.442298i
$910$		0			0
$911$	24.1059	+	4.25052i	0.798664	+	0.140826i	0.558064	−	0.829798i	$-0.311545\pi$
$911$	24.1059	+	4.25052i	0.798664	+	0.140826i	0.240601	+	0.970624i	$0.422656\pi$
$912$		0			0
$913$	3.47370	+	4.13979i	0.114963	+	0.137007i
$914$		0			0
$915$	−24.9945	+	4.62003i	−0.826292	+	0.152734i
$916$		0			0
$917$	−5.75338	−	4.15621i	−0.189993	−	0.137250i
$918$		0			0
$919$	−24.4426	−	42.3359i	−0.806288	−	1.39653i	−0.915418	−	0.402505i	$-0.868140\pi$
$919$	−24.4426	−	42.3359i	−0.806288	−	1.39653i	0.109130	−	0.994028i	$-0.465194\pi$
$920$		0			0
$921$	−30.8664	+	5.70540i	−1.01708	+	0.187999i
$922$		0			0
$923$	12.5855	+	4.58076i	0.414258	+	0.150778i
$924$		0			0
$925$	14.9008	−	84.5066i	0.489935	−	2.77856i
$926$		0			0
$927$	−30.8098	−	17.1169i	−1.01193	−	0.562192i
$928$		0			0
$929$	−21.3175	−	17.8875i	−0.699404	−	0.586870i	0.222200	−	0.975001i	$-0.428676\pi$
$929$	−21.3175	−	17.8875i	−0.699404	−	0.586870i	−0.921604	+	0.388131i	$0.873121\pi$
$930$		0			0
$931$	2.28988	+	4.25067i	0.0750476	+	0.139310i
$932$		0			0
$933$	−6.53692	+	38.9481i	−0.214009	+	1.27510i
$934$		0			0
$935$		−	25.2235i		−	0.824897i
$936$		0			0
$937$	−29.1474	−	16.8282i	−0.952202	−	0.549754i	−0.0584380	−	0.998291i	$-0.518612\pi$
$937$	−29.1474	−	16.8282i	−0.952202	−	0.549754i	−0.893764	+	0.448537i	$0.851945\pi$
$938$		0			0
$939$	38.1843	−	22.4676i	1.24610	−	0.733202i
$940$		0			0
$941$	19.8407	+	7.22141i	0.646787	+	0.235411i	0.644522	−	0.764586i	$-0.277057\pi$
$941$	19.8407	+	7.22141i	0.646787	+	0.235411i	0.00226561	+	0.999997i	$0.499279\pi$
$942$		0			0
$943$	−32.9147	−	5.80375i	−1.07185	−	0.188996i
$944$		0			0
$945$	42.4002	+	29.0611i	1.37928	+	0.945357i
$946$		0			0
$947$	−14.9956	−	2.64414i	−0.487293	−	0.0859228i	−0.0753965	−	0.997154i	$-0.524022\pi$
$947$	−14.9956	−	2.64414i	−0.487293	−	0.0859228i	−0.411896	+	0.911231i	$0.635133\pi$
$948$		0			0
$949$	12.5166	+	4.55566i	0.406305	+	0.147883i
$950$		0			0
$951$	−0.246752	−	29.9225i	−0.00800147	−	0.970305i
$952$		0			0
$953$	−24.0655	−	13.8942i	−0.779559	−	0.450078i	0.0567152	−	0.998390i	$-0.481937\pi$
$953$	−24.0655	−	13.8942i	−0.779559	−	0.450078i	−0.836274	+	0.548312i	$0.815271\pi$
$954$		0			0
$955$		−	5.40808i		−	0.175001i
$956$		0			0
$957$	0.526253	−	0.196470i	0.0170114	−	0.00635097i
$958$		0			0
$959$	−3.88819	+	2.63803i	−0.125556	+	0.0851866i
$960$		0			0
$961$	−53.4158	−	44.8211i	−1.72309	−	1.44584i
$962$		0			0
$963$	−18.2439	−	2.90752i	−0.587901	−	0.0936936i
$964$		0			0
$965$	−11.3265	+	64.2358i	−0.364613	+	2.06782i
$966$		0			0
$967$	19.6090	+	7.13710i	0.630584	+	0.229514i	0.637485	−	0.770462i	$-0.279975\pi$
$967$	19.6090	+	7.13710i	0.630584	+	0.229514i	−0.00690149	+	0.999976i	$0.502197\pi$
$968$		0			0
$969$	2.98176	−	8.40740i	0.0957881	−	0.270085i
$970$		0			0
$971$	13.5782	+	23.5181i	0.435745	+	0.754733i	0.997356	−	0.0726684i	$-0.0231515\pi$
$971$	13.5782	+	23.5181i	0.435745	+	0.754733i	−0.561611	+	0.827402i	$0.689818\pi$
$972$		0			0
$973$	8.47047	+	18.8865i	0.271551	+	0.605475i
$974$		0			0
$975$	−12.0846	−	14.1631i	−0.387018	−	0.453581i
$976$		0			0
$977$	−11.8599	−	14.1341i	−0.379433	−	0.452190i	0.542202	−	0.840248i	$-0.317591\pi$
$977$	−11.8599	−	14.1341i	−0.379433	−	0.452190i	−0.921635	+	0.388058i	$0.873146\pi$
$978$		0			0
$979$	12.3855	+	2.18389i	0.395841	+	0.0697975i
$980$		0			0
$981$	16.1366	−	6.17649i	0.515203	−	0.197200i
$982$		0			0
$983$	6.35199	−	36.0239i	0.202597	−	1.14899i	−0.698579	−	0.715533i	$-0.746184\pi$
$983$	6.35199	−	36.0239i	0.202597	−	1.14899i	0.901176	−	0.433453i	$-0.142705\pi$
$984$		0			0
$985$	−20.5628	+	56.4959i	−0.655186	+	1.80011i
$986$		0			0
$987$	5.36256	+	20.5455i	0.170692	+	0.653971i
$988$		0			0
$989$	16.8174	+	9.70953i	0.534762	+	0.308745i
$990$		0			0
$991$	−1.18639	−	2.05490i	−0.0376871	−	0.0652759i	0.846567	−	0.532283i	$-0.178666\pi$
$991$	−1.18639	−	2.05490i	−0.0376871	−	0.0652759i	−0.884254	+	0.467007i	$0.845332\pi$
$992$		0			0
$993$	43.0639	−	0.355120i	1.36659	−	0.0112694i
$994$		0			0
$995$	−12.1102	+	2.13536i	−0.383920	+	0.0676955i
$996$		0			0
$997$	4.75213	+	13.0564i	0.150502	+	0.413500i	0.991917	−	0.126889i	$-0.0404993\pi$
$997$	4.75213	+	13.0564i	0.150502	+	0.413500i	−0.841415	+	0.540389i	$0.818277\pi$
$998$		0			0
$999$	49.6348	−	1.22814i	1.57037	−	0.0388566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.4	yes	144
7.5	odd	6		756.2.ca.a.173.5	✓	144
27.5	odd	18		756.2.ca.a.437.5	yes	144
189.5	even	18	inner	756.2.ck.a.5.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.5	✓	144	7.5	odd	6
756.2.ca.a.437.5	yes	144	27.5	odd	18
756.2.ck.a.5.4	yes	144	189.5	even	18	inner
756.2.ck.a.605.4	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)

\(f(q)\)	\(=\)	\(q+(-1.63242 - 0.578955i) q^{3} +(0.649280 + 3.68225i) q^{5} +(0.647047 + 2.56541i) q^{7} +(2.32962 + 1.89020i) q^{9} +O(q^{10})\)	\(q+(-1.63242 - 0.578955i) q^{3} +(0.649280 + 3.68225i) q^{5} +(0.647047 + 2.56541i) q^{7} +(2.32962 + 1.89020i) q^{9} +(0.889725 + 0.156882i) q^{11} +(-0.769375 - 0.916906i) q^{13} +(1.07196 - 6.38690i) q^{15} -7.46688 q^{17} -0.689746i q^{19} +(0.429002 - 4.56245i) q^{21} +(2.84180 + 3.38672i) q^{23} +(-8.43895 + 3.07153i) q^{25} +(-2.70859 - 4.43436i) q^{27} +(-0.230745 + 0.274991i) q^{29} +(3.43265 - 9.43113i) q^{31} +(-1.36158 - 0.771209i) q^{33} +(-9.02637 + 4.04826i) q^{35} +(-4.77757 + 8.27499i) q^{37} +(0.725101 + 1.94221i) q^{39} +(-5.79118 + 4.85938i) q^{41} +(4.12751 - 1.50229i) q^{43} +(-5.44762 + 9.80553i) q^{45} +(-4.35416 + 1.58478i) q^{47} +(-6.16266 + 3.31988i) q^{49} +(12.1891 + 4.32299i) q^{51} +(11.6009 + 6.69781i) q^{53} +3.37805i q^{55} +(-0.399332 + 1.12596i) q^{57} +(0.0113213 - 0.00949971i) q^{59} +(-1.34236 - 3.68810i) q^{61} +(-3.34177 + 7.19949i) q^{63} +(2.87674 - 3.42836i) q^{65} +(-0.323090 - 1.83233i) q^{67} +(-2.67826 - 7.17384i) q^{69} +(-9.69050 + 5.59481i) q^{71} +(-9.63739 + 5.56415i) q^{73} +(15.5542 - 0.128266i) q^{75} +(0.173225 + 2.38402i) q^{77} +(1.78156 - 10.1037i) q^{79} +(1.85428 + 8.80691i) q^{81} +(4.58220 + 3.84492i) q^{83} +(-4.84810 - 27.4949i) q^{85} +(0.535881 - 0.315311i) q^{87} +13.9206 q^{89} +(1.85442 - 2.56704i) q^{91} +(-11.0637 + 13.4083i) q^{93} +(2.53982 - 0.447839i) q^{95} +(1.53264 + 4.21088i) q^{97} +(1.77618 + 2.04723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 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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