LMFDB - Embedded newform 156.2.q.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(49,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("156.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-43})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} - 11x + 121 $ x^4 - x^3 - 10x^2 - 11x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$3.08945 - 1.20635i$ of defining polynomial
Character	$\chi$	$=$	156.49
Dual form			156.2.q.b.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} -2.41269i q^{5} +(-3.58945 - 2.07237i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(1.50000 + 3.27872i) q^{13} +(-2.08945 + 1.20635i) q^{15} +(3.08945 - 5.35109i) q^{17} +(-3.00000 - 1.73205i) q^{19} +4.14474i q^{21} +(1.00000 + 1.73205i) q^{23} -0.821092 q^{25} +1.00000 q^{27} +(4.08945 + 7.08314i) q^{29} +7.60885i q^{31} +(-3.00000 - 1.73205i) q^{33} +(-5.00000 + 8.66025i) q^{35} +(0.910546 - 0.525704i) q^{37} +(2.08945 - 2.93840i) q^{39} +(5.08945 - 2.93840i) q^{41} +(0.410546 - 0.711086i) q^{43} +(2.08945 + 1.20635i) q^{45} -10.3923i q^{47} +(5.08945 + 8.81519i) q^{49} -6.17891 q^{51} -10.1789 q^{53} +(-4.17891 - 7.23808i) q^{55} +3.46410i q^{57} +(1.17891 + 0.680643i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(3.58945 - 2.07237i) q^{63} +(7.91055 - 3.61904i) q^{65} +(3.58945 - 2.07237i) q^{67} +(1.00000 - 1.73205i) q^{69} +(-3.00000 - 1.73205i) q^{71} -11.3828i q^{73} +(0.410546 + 0.711086i) q^{75} -14.3578 q^{77} +13.1789 q^{79} +(-0.500000 - 0.866025i) q^{81} +11.7536i q^{83} +(-12.9105 - 7.45391i) q^{85} +(4.08945 - 7.08314i) q^{87} +(6.00000 - 3.46410i) q^{89} +(1.41055 - 14.8774i) q^{91} +(6.58945 - 3.80442i) q^{93} +(-4.17891 + 7.23808i) q^{95} +(-1.76836 - 1.02096i) q^{97} +3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 3 q^{7} - 2 q^{9} + 12 q^{11} + 6 q^{13} + 3 q^{15} + q^{17} - 12 q^{19} + 4 q^{23} - 26 q^{25} + 4 q^{27} + 5 q^{29} - 12 q^{33} - 20 q^{35} + 15 q^{37} - 3 q^{39} + 9 q^{41} + 13 q^{43}+ \cdots + 27 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 3 * q^7 - 2 * q^9 + 12 * q^11 + 6 * q^13 + 3 * q^15 + q^17 - 12 * q^19 + 4 * q^23 - 26 * q^25 + 4 * q^27 + 5 * q^29 - 12 * q^33 - 20 * q^35 + 15 * q^37 - 3 * q^39 + 9 * q^41 + 13 * q^43 - 3 * q^45 + 9 * q^49 - 2 * q^51 - 18 * q^53 + 6 * q^55 - 18 * q^59 - 10 * q^61 + 3 * q^63 + 43 * q^65 + 3 * q^67 + 4 * q^69 - 12 * q^71 + 13 * q^75 - 12 * q^77 + 30 * q^79 - 2 * q^81 - 63 * q^85 + 5 * q^87 + 24 * q^89 + 17 * q^91 + 15 * q^93 + 6 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$		−	2.41269i		−	1.07899i	−0.841989	−	0.539495i	$-0.818615\pi$
$5$		−	2.41269i		−	1.07899i	0.841989	−	0.539495i	$-0.181385\pi$
$6$		0			0
$7$	−3.58945	−	2.07237i	−1.35669	−	0.783283i	−0.367511	−	0.930019i	$-0.619790\pi$
$7$	−3.58945	−	2.07237i	−1.35669	−	0.783283i	−0.989176	+	0.146736i	$0.953123\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$		0			0
$13$	1.50000	+	3.27872i	0.416025	+	0.909353i
$13$	1.50000	+	3.27872i	0.416025	+	0.909353i
$14$		0			0
$15$	−2.08945	+	1.20635i	−0.539495	+	0.311477i
$16$		0			0
$17$	3.08945	−	5.35109i	0.749303	−	1.29783i	−0.198855	−	0.980029i	$-0.563722\pi$
$17$	3.08945	−	5.35109i	0.749303	−	1.29783i	0.948157	−	0.317801i	$-0.102945\pi$
$18$		0			0
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	0.114708	−	0.993399i	$-0.463407\pi$
$19$	−3.00000	−	1.73205i	−0.688247	−	0.397360i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$			4.14474i			0.904457i
$22$		0			0
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$		0			0
$25$	−0.821092			−0.164218
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	0.943161	+	0.332337i	$0.107837\pi$
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	−0.183768	+	0.982970i	$0.558830\pi$
$30$		0			0
$31$			7.60885i			1.36659i	0.730143	+	0.683295i	$0.239454\pi$
$31$			7.60885i			1.36659i	−0.730143	+	0.683295i	$0.760546\pi$
$32$		0			0
$33$	−3.00000	−	1.73205i	−0.522233	−	0.301511i
$34$		0			0
$35$	−5.00000	+	8.66025i	−0.845154	+	1.46385i
$36$		0			0
$37$	0.910546	−	0.525704i	0.149693	−	0.0864252i	−0.423283	−	0.905998i	$-0.639122\pi$
$37$	0.910546	−	0.525704i	0.149693	−	0.0864252i	0.572976	+	0.819572i	$0.305789\pi$
$38$		0			0
$39$	2.08945	−	2.93840i	0.334580	−	0.470520i
$40$		0			0
$41$	5.08945	−	2.93840i	0.794839	−	0.458901i	−0.0468242	−	0.998903i	$-0.514910\pi$
$41$	5.08945	−	2.93840i	0.794839	−	0.458901i	0.841663	+	0.540003i	$0.181577\pi$
$42$		0			0
$43$	0.410546	−	0.711086i	0.0626077	−	0.108440i	−0.833023	−	0.553239i	$-0.813392\pi$
$43$	0.410546	−	0.711086i	0.0626077	−	0.108440i	0.895630	+	0.444799i	$0.146725\pi$
$44$		0			0
$45$	2.08945	+	1.20635i	0.311477	+	0.179832i
$46$		0			0
$47$		−	10.3923i		−	1.51587i	−0.652328	−	0.757937i	$-0.726208\pi$
$47$		−	10.3923i		−	1.51587i	0.652328	−	0.757937i	$-0.273792\pi$
$48$		0			0
$49$	5.08945	+	8.81519i	0.727065	+	1.25931i
$50$		0			0
$51$	−6.17891			−0.865220
$52$		0			0
$53$	−10.1789			−1.39818			−0.699090	−	0.715033i	$-0.746411\pi$
$53$	−10.1789			−1.39818			−0.699090	+	0.715033i	$0.746411\pi$
$54$		0			0
$55$	−4.17891	−	7.23808i	−0.563484	−	0.975983i
$56$		0			0
$57$			3.46410i			0.458831i
$58$		0			0
$59$	1.17891	+	0.680643i	0.153481	+	0.0886122i	0.574773	−	0.818313i	$-0.305090\pi$
$59$	1.17891	+	0.680643i	0.153481	+	0.0886122i	−0.421293	+	0.906925i	$0.638423\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$	3.58945	−	2.07237i	0.452229	−	0.261094i
$64$		0			0
$65$	7.91055	−	3.61904i	0.981182	−	0.448887i
$66$		0			0
$67$	3.58945	−	2.07237i	0.438522	−	0.253181i	−0.264449	−	0.964400i	$-0.585190\pi$
$67$	3.58945	−	2.07237i	0.438522	−	0.253181i	0.702970	+	0.711219i	$0.251857\pi$
$68$		0			0
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$		0			0
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	0.311305	−	0.950310i	$-0.399234\pi$
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	−0.667340	+	0.744753i	$0.732567\pi$
$72$		0			0
$73$		−	11.3828i		−	1.33226i	−0.745836	−	0.666130i	$-0.767950\pi$
$73$		−	11.3828i		−	1.33226i	0.745836	−	0.666130i	$-0.232050\pi$
$74$		0			0
$75$	0.410546	+	0.711086i	0.0474057	+	0.0821092i
$76$		0			0
$77$	−14.3578			−1.63623
$78$		0			0
$79$	13.1789			1.48274			0.741372	−	0.671095i	$-0.234176\pi$
$79$	13.1789			1.48274			0.741372	+	0.671095i	$0.234176\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			11.7536i			1.29012i	0.764130	+	0.645062i	$0.223169\pi$
$83$			11.7536i			1.29012i	−0.764130	+	0.645062i	$0.776831\pi$
$84$		0			0
$85$	−12.9105	−	7.45391i	−1.40035	−	0.808490i
$86$		0			0
$87$	4.08945	−	7.08314i	0.438436	−	0.759393i
$88$		0			0
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$		0			0
$91$	1.41055	−	14.8774i	0.147865	−	1.55957i
$92$		0			0
$93$	6.58945	−	3.80442i	0.683295	−	0.394500i
$94$		0			0
$95$	−4.17891	+	7.23808i	−0.428747	+	0.742612i
$96$		0			0
$97$	−1.76836	−	1.02096i	−0.179550	−	0.103663i	0.407531	−	0.913191i	$-0.366390\pi$
$97$	−1.76836	−	1.02096i	−0.179550	−	0.103663i	−0.587081	+	0.809528i	$0.699723\pi$
$98$		0			0
$99$			3.46410i			0.348155i
$100$		0			0
$101$	−6.08945	−	10.5472i	−0.605923	−	1.04949i	−0.991905	−	0.126983i	$-0.959470\pi$
$101$	−6.08945	−	10.5472i	−0.605923	−	1.04949i	0.385981	−	0.922507i	$-0.373863\pi$
$102$		0			0
$103$	3.17891			0.313227			0.156614	−	0.987660i	$-0.449942\pi$
$103$	3.17891			0.313227			0.156614	+	0.987660i	$0.449942\pi$
$104$		0			0
$105$	10.0000			0.975900
$106$		0			0
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	0.999818	−	0.0190994i	$-0.00607989\pi$
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	−0.516449	+	0.856318i	$0.672747\pi$
$108$		0			0
$109$			7.60885i			0.728795i	0.931243	+	0.364398i	$0.118725\pi$
$109$			7.60885i			0.728795i	−0.931243	+	0.364398i	$0.881275\pi$
$110$		0			0
$111$	−0.910546	−	0.525704i	−0.0864252	−	0.0498976i
$112$		0			0
$113$	−6.08945	+	10.5472i	−0.572848	+	0.992201i	0.423424	+	0.905932i	$0.360828\pi$
$113$	−6.08945	+	10.5472i	−0.572848	+	0.992201i	−0.996272	+	0.0862697i	$0.972505\pi$
$114$		0			0
$115$	4.17891	−	2.41269i	0.389685	−	0.224985i
$116$		0			0
$117$	−3.58945	−	0.340322i	−0.331845	−	0.0314627i
$118$		0			0
$119$	−22.1789	+	12.8050i	−2.03314	+	1.17383i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−5.08945	−	2.93840i	−0.458901	−	0.264946i
$124$		0			0
$125$		−	10.0824i		−	0.901800i
$126$		0			0
$127$	1.41055	+	2.44314i	0.125166	+	0.216793i	0.921798	−	0.387671i	$-0.126720\pi$
$127$	1.41055	+	2.44314i	0.125166	+	0.216793i	−0.796632	+	0.604465i	$0.793387\pi$
$128$		0			0
$129$	−0.821092			−0.0722931
$130$		0			0
$131$	6.35782			0.555485			0.277743	−	0.960656i	$-0.410414\pi$
$131$	6.35782			0.555485			0.277743	+	0.960656i	$0.410414\pi$
$132$		0			0
$133$	7.17891	+	12.4342i	0.622490	+	1.07818i
$134$		0			0
$135$		−	2.41269i		−	0.207652i
$136$		0			0
$137$	−11.0895	−	6.40250i	−0.947436	−	0.547002i	−0.0551525	−	0.998478i	$-0.517564\pi$
$137$	−11.0895	−	6.40250i	−0.947436	−	0.547002i	−0.892284	+	0.451476i	$0.850898\pi$
$138$		0			0
$139$	−8.58945	+	14.8774i	−0.728548	+	1.26188i	0.228949	+	0.973438i	$0.426471\pi$
$139$	−8.58945	+	14.8774i	−0.728548	+	1.26188i	−0.957497	+	0.288444i	$0.906862\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$		0			0
$143$	10.1789	+	7.23808i	0.851203	+	0.605279i
$144$		0			0
$145$	17.0895	−	9.86660i	1.41920	−	0.819377i
$146$		0			0
$147$	5.08945	−	8.81519i	0.419771	−	0.727065i
$148$		0			0
$149$	5.08945	+	2.93840i	0.416944	+	0.240723i	0.693769	−	0.720197i	$-0.255949\pi$
$149$	5.08945	+	2.93840i	0.416944	+	0.240723i	−0.276825	+	0.960920i	$0.589282\pi$
$150$		0			0
$151$			20.0431i			1.63108i	0.578699	+	0.815541i	$0.303561\pi$
$151$			20.0431i			1.63108i	−0.578699	+	0.815541i	$0.696439\pi$
$152$		0			0
$153$	3.08945	+	5.35109i	0.249768	+	0.432610i
$154$		0			0
$155$	18.3578			1.47454
$156$		0			0
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$		0			0
$159$	5.08945	+	8.81519i	0.403620	+	0.699090i
$160$		0			0
$161$		−	8.28949i		−	0.653303i
$162$		0			0
$163$	−6.58945	−	3.80442i	−0.516126	−	0.297985i	0.219222	−	0.975675i	$-0.429648\pi$
$163$	−6.58945	−	3.80442i	−0.516126	−	0.297985i	−0.735348	+	0.677690i	$0.762981\pi$
$164$		0			0
$165$	−4.17891	+	7.23808i	−0.325328	+	0.563484i
$166$		0			0
$167$	6.00000	−	3.46410i	0.464294	−	0.268060i	−0.249554	−	0.968361i	$-0.580284\pi$
$167$	6.00000	−	3.46410i	0.464294	−	0.268060i	0.713848	+	0.700301i	$0.246951\pi$
$168$		0			0
$169$	−8.50000	+	9.83616i	−0.653846	+	0.756628i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$		0			0
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$	2.94727	+	1.70161i	0.222793	+	0.128629i
$176$		0			0
$177$		−	1.36129i		−	0.102321i
$178$		0			0
$179$	4.17891	+	7.23808i	0.312346	+	0.541000i	0.978870	−	0.204484i	$-0.0655518\pi$
$179$	4.17891	+	7.23808i	0.312346	+	0.541000i	−0.666524	+	0.745484i	$0.732218\pi$
$180$		0			0
$181$	−20.5367			−1.52648			−0.763241	−	0.646113i	$-0.776393\pi$
$181$	−20.5367			−1.52648			−0.763241	+	0.646113i	$0.776393\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$		0			0
$185$	−1.26836	−	2.19687i	−0.0932519	−	0.161517i
$186$		0			0
$187$		−	21.4044i		−	1.56524i
$188$		0			0
$189$	−3.58945	−	2.07237i	−0.261094	−	0.150743i
$190$		0			0
$191$	1.17891	−	2.04193i	0.0853028	−	0.147749i	−0.820217	−	0.572052i	$-0.806148\pi$
$191$	1.17891	−	2.04193i	0.0853028	−	0.147749i	0.905520	+	0.424303i	$0.139481\pi$
$192$		0			0
$193$	−11.6789	+	6.74282i	−0.840666	+	0.485359i	−0.857491	−	0.514500i	$-0.827978\pi$
$193$	−11.6789	+	6.74282i	−0.840666	+	0.485359i	0.0168244	+	0.999858i	$0.494644\pi$
$194$		0			0
$195$	−7.08945	−	5.04121i	−0.507686	−	0.361009i
$196$		0			0
$197$	−8.35782	+	4.82539i	−0.595470	+	0.343795i	−0.767257	−	0.641339i	$-0.778379\pi$
$197$	−8.35782	+	4.82539i	−0.595470	+	0.343795i	0.171788	+	0.985134i	$0.445046\pi$
$198$		0			0
$199$	10.7684	−	18.6514i	0.763349	−	1.32216i	−0.177766	−	0.984073i	$-0.556887\pi$
$199$	10.7684	−	18.6514i	0.763349	−	1.32216i	0.941115	−	0.338086i	$-0.109780\pi$
$200$		0			0
$201$	−3.58945	−	2.07237i	−0.253181	−	0.146174i
$202$		0			0
$203$		−	33.8995i		−	2.37928i
$204$		0			0
$205$	−7.08945	−	12.2793i	−0.495149	−	0.857623i
$206$		0			0
$207$	−2.00000			−0.139010
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	7.76836	+	13.4552i	0.534796	+	0.926294i	0.999173	+	0.0406565i	$0.0129449\pi$
$211$	7.76836	+	13.4552i	0.534796	+	0.926294i	−0.464377	+	0.885638i	$0.653722\pi$
$212$		0			0
$213$			3.46410i			0.237356i
$214$		0			0
$215$	−1.71563	−	0.990521i	−0.117005	−	0.0675530i
$216$		0			0
$217$	15.7684	−	27.3116i	1.07043	−	1.85403i
$218$		0			0
$219$	−9.85782	+	5.69141i	−0.666130	+	0.384590i
$220$		0			0
$221$	22.1789	+	2.10282i	1.49191	+	0.141451i
$222$		0			0
$223$	−13.1789	+	7.60885i	−0.882525	+	0.509526i	−0.871490	−	0.490413i	$-0.836846\pi$
$223$	−13.1789	+	7.60885i	−0.882525	+	0.509526i	−0.0110349	+	0.999939i	$0.503513\pi$
$224$		0			0
$225$	0.410546	−	0.711086i	0.0273697	−	0.0474057i
$226$		0			0
$227$	7.82109	+	4.51551i	0.519104	+	0.299705i	0.736568	−	0.676363i	$-0.236445\pi$
$227$	7.82109	+	4.51551i	0.519104	+	0.299705i	−0.217464	+	0.976068i	$0.569778\pi$
$228$		0			0
$229$			9.65078i			0.637741i	0.947798	+	0.318871i	$0.103304\pi$
$229$			9.65078i			0.637741i	−0.947798	+	0.318871i	$0.896696\pi$
$230$		0			0
$231$	7.17891	+	12.4342i	0.472337	+	0.818113i
$232$		0			0
$233$	22.7156			1.48815			0.744075	−	0.668096i	$-0.232890\pi$
$233$	22.7156			1.48815			0.744075	+	0.668096i	$0.232890\pi$
$234$		0			0
$235$	−25.0735			−1.63561
$236$		0			0
$237$	−6.58945	−	11.4133i	−0.428031	−	0.741372i
$238$		0			0
$239$		−	2.10282i		−	0.136020i	−0.997685	−	0.0680099i	$-0.978335\pi$
$239$		−	2.10282i		−	0.136020i	0.997685	−	0.0680099i	$-0.0216650\pi$
$240$		0			0
$241$	5.08945	+	2.93840i	0.327841	+	0.189279i	0.654882	−	0.755731i	$-0.272718\pi$
$241$	5.08945	+	2.93840i	0.327841	+	0.189279i	−0.327041	+	0.945010i	$0.606052\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	21.2684	−	12.2793i	1.35879	−	0.784495i
$246$		0			0
$247$	1.17891	−	12.4342i	0.0750121	−	0.791171i
$248$		0			0
$249$	10.1789	−	5.87680i	0.645062	−	0.372427i
$250$		0			0
$251$	10.3578	−	17.9403i	0.653780	−	1.13238i	−0.328419	−	0.944532i	$-0.606516\pi$
$251$	10.3578	−	17.9403i	0.653780	−	1.13238i	0.982198	−	0.187847i	$-0.0601510\pi$
$252$		0			0
$253$	6.00000	+	3.46410i	0.377217	+	0.217786i
$254$		0			0
$255$			14.9078i			0.933564i
$256$		0			0
$257$	−11.0895	−	19.2075i	−0.691741	−	1.19813i	−0.971267	−	0.237993i	$-0.923511\pi$
$257$	−11.0895	−	19.2075i	−0.691741	−	1.19813i	0.279526	−	0.960138i	$-0.409823\pi$
$258$		0			0
$259$	−4.35782			−0.270782
$260$		0			0
$261$	−8.17891			−0.506262
$262$		0			0
$263$	−16.1789	−	28.0227i	−0.997634	−	1.72795i	−0.558352	−	0.829604i	$-0.688566\pi$
$263$	−16.1789	−	28.0227i	−0.997634	−	1.72795i	−0.439282	−	0.898349i	$-0.644767\pi$
$264$		0			0
$265$			24.5586i			1.50862i
$266$		0			0
$267$	−6.00000	−	3.46410i	−0.367194	−	0.212000i
$268$		0			0
$269$	6.17891	−	10.7022i	0.376735	−	0.652524i	−0.613850	−	0.789422i	$-0.710380\pi$
$269$	6.17891	−	10.7022i	0.376735	−	0.652524i	0.990585	+	0.136899i	$0.0437135\pi$
$270$		0			0
$271$	−12.5895	+	7.26852i	−0.764755	+	0.441531i	−0.831000	−	0.556272i	$-0.812231\pi$
$271$	−12.5895	+	7.26852i	−0.764755	+	0.441531i	0.0662455	+	0.997803i	$0.478898\pi$
$272$		0			0
$273$	−13.5895	+	6.21712i	−0.822471	+	0.376277i
$274$		0			0
$275$	−2.46327	+	1.42217i	−0.148541	+	0.0857602i
$276$		0			0
$277$	0.0894542	−	0.154939i	0.00537478	−	0.00930939i	−0.863326	−	0.504647i	$-0.831622\pi$
$277$	0.0894542	−	0.154939i	0.00537478	−	0.00930939i	0.868700	+	0.495338i	$0.164956\pi$
$278$		0			0
$279$	−6.58945	−	3.80442i	−0.394500	−	0.227765i
$280$		0			0
$281$			11.4437i			0.682675i	0.939941	+	0.341337i	$0.110880\pi$
$281$			11.4437i			0.682675i	−0.939941	+	0.341337i	$0.889120\pi$
$282$		0			0
$283$	13.5895	+	23.5376i	0.807809	+	1.39917i	0.914378	+	0.404861i	$0.132680\pi$
$283$	13.5895	+	23.5376i	0.807809	+	1.39917i	−0.106569	+	0.994305i	$0.533986\pi$
$284$		0			0
$285$	8.35782			0.495074
$286$		0			0
$287$	−24.3578			−1.43780
$288$		0			0
$289$	−10.5895	−	18.3415i	−0.622909	−	1.07891i
$290$		0			0
$291$			2.04193i			0.119700i
$292$		0			0
$293$	28.4473	+	16.4240i	1.66191	+	0.959503i	0.971803	+	0.235792i	$0.0757685\pi$
$293$	28.4473	+	16.4240i	1.66191	+	0.959503i	0.690104	+	0.723710i	$0.257565\pi$
$294$		0			0
$295$	1.64218	−	2.84434i	0.0956116	−	0.165604i
$296$		0			0
$297$	3.00000	−	1.73205i	0.174078	−	0.100504i
$298$		0			0
$299$	−4.17891	+	5.87680i	−0.241673	+	0.339864i
$300$		0			0
$301$	−2.94727	+	1.70161i	−0.169878	+	0.0980790i
$302$		0			0
$303$	−6.08945	+	10.5472i	−0.349830	+	0.605923i
$304$		0			0
$305$	10.4473	+	6.03173i	0.598209	+	0.345376i
$306$		0			0
$307$			11.0729i			0.631967i	0.948765	+	0.315983i	$0.102334\pi$
$307$			11.0729i			0.631967i	−0.948765	+	0.315983i	$0.897666\pi$
$308$		0			0
$309$	−1.58945	−	2.75302i	−0.0904209	−	0.156614i
$310$		0			0
$311$	11.6422			0.660168			0.330084	−	0.943952i	$-0.392923\pi$
$311$	11.6422			0.660168			0.330084	+	0.943952i	$0.392923\pi$
$312$		0			0
$313$	27.8945			1.57669			0.788346	−	0.615232i	$-0.210938\pi$
$313$	27.8945			1.57669			0.788346	+	0.615232i	$0.210938\pi$
$314$		0			0
$315$	−5.00000	−	8.66025i	−0.281718	−	0.487950i
$316$		0			0
$317$			3.77398i			0.211968i	0.994368	+	0.105984i	$0.0337992\pi$
$317$			3.77398i			0.211968i	−0.994368	+	0.105984i	$0.966201\pi$
$318$		0			0
$319$	24.5367	+	14.1663i	1.37379	+	0.793160i
$320$		0			0
$321$	5.00000	−	8.66025i	0.279073	−	0.483368i
$322$		0			0
$323$	−18.5367	+	10.7022i	−1.03141	+	0.595485i
$324$		0			0
$325$	−1.23164	−	2.69213i	−0.0683190	−	0.149332i
$326$		0			0
$327$	6.58945	−	3.80442i	0.364398	−	0.210385i
$328$		0			0
$329$	−21.5367	+	37.3027i	−1.18736	+	2.05656i
$330$		0			0
$331$	−17.4105	−	10.0520i	−0.956970	−	0.552507i	−0.0617309	−	0.998093i	$-0.519662\pi$
$331$	−17.4105	−	10.0520i	−0.956970	−	0.552507i	−0.895239	+	0.445586i	$0.852995\pi$
$332$		0			0
$333$			1.05141i			0.0576168i
$334$		0			0
$335$	−5.00000	−	8.66025i	−0.273179	−	0.473160i
$336$		0			0
$337$	−25.3578			−1.38133			−0.690664	−	0.723176i	$-0.742682\pi$
$337$	−25.3578			−1.38133			−0.690664	+	0.723176i	$0.742682\pi$
$338$		0			0
$339$	12.1789			0.661468
$340$		0			0
$341$	13.1789	+	22.8265i	0.713678	+	1.23613i
$342$		0			0
$343$		−	13.1758i		−	0.711424i
$344$		0			0
$345$	−4.17891	−	2.41269i	−0.224985	−	0.129895i
$346$		0			0
$347$	−10.1789	+	17.6304i	−0.546432	+	0.946449i	0.452083	+	0.891976i	$0.350681\pi$
$347$	−10.1789	+	17.6304i	−0.546432	+	0.946449i	−0.998515	+	0.0544728i	$0.982652\pi$
$348$		0			0
$349$	8.94727	−	5.16571i	0.478936	−	0.276514i	−0.241037	−	0.970516i	$-0.577487\pi$
$349$	8.94727	−	5.16571i	0.478936	−	0.276514i	0.719973	+	0.694002i	$0.244154\pi$
$350$		0			0
$351$	1.50000	+	3.27872i	0.0800641	+	0.175005i
$352$		0			0
$353$	16.4473	−	9.49584i	0.875400	−	0.505412i	0.00626098	−	0.999980i	$-0.498007\pi$
$353$	16.4473	−	9.49584i	0.875400	−	0.505412i	0.869139	+	0.494568i	$0.164674\pi$
$354$		0			0
$355$	−4.17891	+	7.23808i	−0.221793	+	0.384157i
$356$		0			0
$357$	22.1789	+	12.8050i	1.17383	+	0.677712i
$358$		0			0
$359$		−	18.6818i		−	0.985987i	−0.870033	−	0.492994i	$-0.835903\pi$
$359$		−	18.6818i		−	0.985987i	0.870033	−	0.492994i	$-0.164097\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$		0			0
$363$	−1.00000			−0.0524864
$364$		0			0
$365$	−27.4633			−1.43749
$366$		0			0
$367$	−6.41055	−	11.1034i	−0.334628	−	0.579592i	0.648785	−	0.760971i	$-0.275277\pi$
$367$	−6.41055	−	11.1034i	−0.334628	−	0.579592i	−0.983413	+	0.181379i	$0.941944\pi$
$368$		0			0
$369$			5.87680i			0.305934i
$370$		0			0
$371$	36.5367	+	21.0945i	1.89689	+	1.09517i
$372$		0			0
$373$	5.67891	−	9.83616i	0.294043	−	0.509297i	−0.680719	−	0.732545i	$-0.738333\pi$
$373$	5.67891	−	9.83616i	0.294043	−	0.509297i	0.974762	+	0.223248i	$0.0716659\pi$
$374$		0			0
$375$	−8.73164	+	5.04121i	−0.450900	+	0.260327i
$376$		0			0
$377$	−17.0895	+	24.0329i	−0.880152	+	1.23776i
$378$		0			0
$379$	−5.41055	+	3.12378i	−0.277921	+	0.160458i	−0.632482	−	0.774575i	$-0.717964\pi$
$379$	−5.41055	+	3.12378i	−0.277921	+	0.160458i	0.354561	+	0.935033i	$0.384630\pi$
$380$		0			0
$381$	1.41055	−	2.44314i	0.0722645	−	0.125166i
$382$		0			0
$383$	−16.7156	−	9.65078i	−0.854129	−	0.493132i	0.00791288	−	0.999969i	$-0.497481\pi$
$383$	−16.7156	−	9.65078i	−0.854129	−	0.493132i	−0.862042	+	0.506837i	$0.830815\pi$
$384$		0			0
$385$			34.6410i			1.76547i
$386$		0			0
$387$	0.410546	+	0.711086i	0.0208692	+	0.0361465i
$388$		0			0
$389$	−6.53673			−0.331425			−0.165713	−	0.986174i	$-0.552992\pi$
$389$	−6.53673			−0.331425			−0.165713	+	0.986174i	$0.552992\pi$
$390$		0			0
$391$	12.3578			0.624962
$392$		0			0
$393$	−3.17891	−	5.50603i	−0.160355	−	0.277743i
$394$		0			0
$395$		−	31.7967i		−	1.59986i
$396$		0			0
$397$	18.5895	+	10.7326i	0.932978	+	0.538655i	0.887752	−	0.460322i	$-0.152266\pi$
$397$	18.5895	+	10.7326i	0.932978	+	0.538655i	0.0452258	+	0.998977i	$0.485599\pi$
$398$		0			0
$399$	7.17891	−	12.4342i	0.359395	−	0.622490i
$400$		0			0
$401$	9.26836	−	5.35109i	0.462840	−	0.267221i	−0.250398	−	0.968143i	$-0.580561\pi$
$401$	9.26836	−	5.35109i	0.462840	−	0.267221i	0.713238	+	0.700922i	$0.247228\pi$
$402$		0			0
$403$	−24.9473	+	11.4133i	−1.24271	+	0.568535i
$404$		0			0
$405$	−2.08945	+	1.20635i	−0.103826	+	0.0599439i
$406$		0			0
$407$	1.82109	−	3.15422i	0.0902682	−	0.156349i
$408$		0			0
$409$	−0.857817	−	0.495261i	−0.0424163	−	0.0244891i	0.478642	−	0.878010i	$-0.341129\pi$
$409$	−0.857817	−	0.495261i	−0.0424163	−	0.0244891i	−0.521058	+	0.853521i	$0.674463\pi$
$410$		0			0
$411$			12.8050i			0.631624i
$412$		0			0
$413$	−2.82109	−	4.88627i	−0.138817	−	0.240438i
$414$		0			0
$415$	28.3578			1.39203
$416$		0			0
$417$	17.1789			0.841255
$418$		0			0
$419$	6.35782	+	11.0121i	0.310600	+	0.537974i	0.978492	−	0.206283i	$-0.0661368\pi$
$419$	6.35782	+	11.0121i	0.310600	+	0.537974i	−0.667893	+	0.744258i	$0.732803\pi$
$420$		0			0
$421$		−	32.1674i		−	1.56774i	−0.620922	−	0.783872i	$-0.713242\pi$
$421$		−	32.1674i		−	1.56774i	0.620922	−	0.783872i	$-0.286758\pi$
$422$		0			0
$423$	9.00000	+	5.19615i	0.437595	+	0.252646i
$424$		0			0
$425$	−2.53673	+	4.39374i	−0.123049	+	0.213128i
$426$		0			0
$427$	17.9473	−	10.3619i	0.868529	−	0.501446i
$428$		0			0
$429$	1.17891	−	12.4342i	0.0569182	−	0.600330i
$430$		0			0
$431$	−16.1789	+	9.34090i	−0.779311	+	0.449935i	−0.836186	−	0.548446i	$-0.815220\pi$
$431$	−16.1789	+	9.34090i	−0.779311	+	0.449935i	0.0568753	+	0.998381i	$0.481886\pi$
$432$		0			0
$433$	1.32109	−	2.28820i	0.0634876	−	0.109964i	−0.832535	−	0.553973i	$-0.813111\pi$
$433$	1.32109	−	2.28820i	0.0634876	−	0.109964i	0.896022	+	0.444009i	$0.146444\pi$
$434$		0			0
$435$	−17.0895	−	9.86660i	−0.819377	−	0.473067i
$436$		0			0
$437$		−	6.92820i		−	0.331421i
$438$		0			0
$439$	−11.9473	−	20.6933i	−0.570212	−	0.987636i	−0.996544	−	0.0830694i	$-0.973528\pi$
$439$	−11.9473	−	20.6933i	−0.570212	−	0.987636i	0.426332	−	0.904567i	$-0.359806\pi$
$440$		0			0
$441$	−10.1789			−0.484710
$442$		0			0
$443$	8.00000			0.380091			0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000			0.380091			0.190046	+	0.981775i	$0.439136\pi$
$444$		0			0
$445$	−8.35782	−	14.4762i	−0.396199	−	0.686236i
$446$		0			0
$447$		−	5.87680i		−	0.277963i
$448$		0			0
$449$	−9.53673	−	5.50603i	−0.450066	−	0.259846i	0.257792	−	0.966200i	$-0.417005\pi$
$449$	−9.53673	−	5.50603i	−0.450066	−	0.259846i	−0.707858	+	0.706355i	$0.750338\pi$
$450$		0			0
$451$	10.1789	−	17.6304i	0.479306	−	0.830182i
$452$		0			0
$453$	17.3578	−	10.0215i	0.815541	−	0.470853i
$454$		0			0
$455$	−35.8945	−	3.40322i	−1.68276	−	0.159545i
$456$		0			0
$457$	6.32109	−	3.64948i	0.295688	−	0.170716i	−0.344816	−	0.938670i	$-0.612059\pi$
$457$	6.32109	−	3.64948i	0.295688	−	0.170716i	0.640504	+	0.767955i	$0.278725\pi$
$458$		0			0
$459$	3.08945	−	5.35109i	0.144203	−	0.249768i
$460$		0			0
$461$	−21.2684	−	12.2793i	−0.990566	−	0.571904i	−0.0851228	−	0.996370i	$-0.527128\pi$
$461$	−21.2684	−	12.2793i	−0.990566	−	0.571904i	−0.905444	+	0.424467i	$0.860462\pi$
$462$		0			0
$463$			1.42217i			0.0660940i	0.999454	+	0.0330470i	$0.0105211\pi$
$463$			1.42217i			0.0660940i	−0.999454	+	0.0330470i	$0.989479\pi$
$464$		0			0
$465$	−9.17891	−	15.8983i	−0.425662	−	0.737268i
$466$		0			0
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$		0			0
$469$	−17.1789			−0.793248
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$		0			0
$473$		−	2.84434i		−	0.130783i
$474$		0			0
$475$	2.46327	+	1.42217i	0.113023	+	0.0652537i
$476$		0			0
$477$	5.08945	−	8.81519i	0.233030	−	0.403620i
$478$		0			0
$479$	−6.00000	+	3.46410i	−0.274147	+	0.158279i	−0.630771	−	0.775969i	$-0.717261\pi$
$479$	−6.00000	+	3.46410i	−0.274147	+	0.158279i	0.356624	+	0.934248i	$0.383928\pi$
$480$		0			0
$481$	3.08945	+	2.19687i	0.140867	+	0.100169i
$482$		0			0
$483$	−7.17891	+	4.14474i	−0.326652	+	0.188592i
$484$		0			0
$485$	−2.46327	+	4.26652i	−0.111852	+	0.193733i
$486$		0			0
$487$	21.0000	+	12.1244i	0.951601	+	0.549407i	0.893578	−	0.448908i	$-0.148187\pi$
$487$	21.0000	+	12.1244i	0.951601	+	0.549407i	0.0580230	+	0.998315i	$0.481520\pi$
$488$		0			0
$489$			7.60885i			0.344084i
$490$		0			0
$491$	−9.35782	−	16.2082i	−0.422312	−	0.731466i	0.573853	−	0.818958i	$-0.305448\pi$
$491$	−9.35782	−	16.2082i	−0.422312	−	0.731466i	−0.996165	+	0.0874920i	$0.972115\pi$
$492$		0			0
$493$	50.5367			2.27606
$494$		0			0
$495$	8.35782			0.375656
$496$		0			0
$497$	7.17891	+	12.4342i	0.322018	+	0.557752i
$498$		0			0
$499$			1.36129i			0.0609395i	0.999536	+	0.0304698i	$0.00970033\pi$
$499$			1.36129i			0.0609395i	−0.999536	+	0.0304698i	$0.990300\pi$
$500$		0			0
$501$	−6.00000	−	3.46410i	−0.268060	−	0.154765i
$502$		0			0
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$		0			0
$505$	−25.4473	+	14.6920i	−1.13239	+	0.653785i
$506$		0			0
$507$	12.7684	+	2.44314i	0.567063	+	0.108504i
$508$		0			0
$509$	−12.2684	+	7.08314i	−0.543786	+	0.313955i	−0.746612	−	0.665260i	$-0.768321\pi$
$509$	−12.2684	+	7.08314i	−0.543786	+	0.313955i	0.202826	+	0.979215i	$0.434987\pi$
$510$		0			0
$511$	−23.5895	+	40.8581i	−1.04354	+	1.80746i
$512$		0			0
$513$	−3.00000	−	1.73205i	−0.132453	−	0.0764719i
$514$		0			0
$515$		−	7.66973i		−	0.337969i
$516$		0			0
$517$	−18.0000	−	31.1769i	−0.791639	−	1.37116i
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	−38.8945			−1.70400			−0.852000	−	0.523541i	$-0.824611\pi$
$521$	−38.8945			−1.70400			−0.852000	+	0.523541i	$0.824611\pi$
$522$		0			0
$523$	−12.1789	−	21.0945i	−0.532546	−	0.922398i	−0.999278	−	0.0379984i	$-0.987902\pi$
$523$	−12.1789	−	21.0945i	−0.532546	−	0.922398i	0.466731	−	0.884399i	$-0.345432\pi$
$524$		0			0
$525$		−	3.40322i		−	0.148528i
$526$		0			0
$527$	40.7156	+	23.5072i	1.77360	+	1.02399i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−1.17891	+	0.680643i	−0.0511603	+	0.0295374i
$532$		0			0
$533$	17.2684	+	12.2793i	0.747976	+	0.531875i
$534$		0			0
$535$	20.8945	−	12.0635i	0.903350	−	0.521549i
$536$		0			0
$537$	4.17891	−	7.23808i	0.180333	−	0.312346i
$538$		0			0
$539$	30.5367	+	17.6304i	1.31531	+	0.759395i
$540$		0			0
$541$		−	3.09334i		−	0.132993i	−0.997787	−	0.0664965i	$-0.978818\pi$
$541$		−	3.09334i		−	0.132993i	0.997787	−	0.0664965i	$-0.0211821\pi$
$542$		0			0
$543$	10.2684	+	17.7853i	0.440658	+	0.763241i
$544$		0			0
$545$	18.3578			0.786362
$546$		0			0
$547$	13.5367			0.578789			0.289394	−	0.957210i	$-0.406546\pi$
$547$	13.5367			0.578789			0.289394	+	0.957210i	$0.406546\pi$
$548$		0			0
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$		0			0
$551$		−	28.3326i		−	1.20701i
$552$		0			0
$553$	−47.3051	−	27.3116i	−2.01162	−	1.16141i
$554$		0			0
$555$	−1.26836	+	2.19687i	−0.0538390	+	0.0932519i
$556$		0			0
$557$	−27.8051	+	16.0533i	−1.17814	+	0.680199i	−0.955583	−	0.294721i	$-0.904773\pi$
$557$	−27.8051	+	16.0533i	−1.17814	+	0.680199i	−0.222556	+	0.974920i	$0.571440\pi$
$558$		0			0
$559$	2.94727	+	0.279435i	0.124656	+	0.0118188i
$560$		0			0
$561$	−18.5367	+	10.7022i	−0.782621	+	0.451847i
$562$		0			0
$563$	9.17891	−	15.8983i	0.386845	−	0.670035i	−0.605178	−	0.796090i	$-0.706898\pi$
$563$	9.17891	−	15.8983i	0.386845	−	0.670035i	0.992023	+	0.126055i	$0.0402316\pi$
$564$		0			0
$565$	25.4473	+	14.6920i	1.07057	+	0.618097i
$566$		0			0
$567$			4.14474i			0.174063i
$568$		0			0
$569$	15.3578	+	26.6005i	0.643833	+	1.11515i	0.984570	+	0.174993i	$0.0559903\pi$
$569$	15.3578	+	26.6005i	0.643833	+	1.11515i	−0.340737	+	0.940159i	$0.610676\pi$
$570$		0			0
$571$	−7.64218			−0.319815			−0.159908	−	0.987132i	$-0.551120\pi$
$571$	−7.64218			−0.319815			−0.159908	+	0.987132i	$0.551120\pi$
$572$		0			0
$573$	−2.35782			−0.0984992
$574$		0			0
$575$	−0.821092	−	1.42217i	−0.0342419	−	0.0593087i
$576$		0			0
$577$			43.2404i			1.80012i	0.435765	+	0.900060i	$0.356478\pi$
$577$			43.2404i			1.80012i	−0.435765	+	0.900060i	$0.643522\pi$
$578$		0			0
$579$	11.6789	+	6.74282i	0.485359	+	0.280222i
$580$		0			0
$581$	24.3578	−	42.1890i	1.01053	−	1.75029i
$582$		0			0
$583$	−30.5367	+	17.6304i	−1.26470	+	0.730176i
$584$		0			0
$585$	−0.821092	+	8.66025i	−0.0339480	+	0.358057i
$586$		0			0
$587$	−19.1789	+	11.0729i	−0.791598	+	0.457029i	−0.840525	−	0.541773i	$-0.817753\pi$
$587$	−19.1789	+	11.0729i	−0.791598	+	0.457029i	0.0489266	+	0.998802i	$0.484420\pi$
$588$		0			0
$589$	13.1789	−	22.8265i	0.543027	−	0.940551i
$590$		0			0
$591$	8.35782	+	4.82539i	0.343795	+	0.198490i
$592$		0			0
$593$			32.8481i			1.34891i	0.738316	+	0.674454i	$0.235621\pi$
$593$			32.8481i			1.34891i	−0.738316	+	0.674454i	$0.764379\pi$
$594$		0			0
$595$	30.8945	+	53.5109i	1.26655	+	2.19373i
$596$		0			0
$597$	−21.5367			−0.881439
$598$		0			0
$599$	9.64218			0.393969			0.196984	−	0.980407i	$-0.436885\pi$
$599$	9.64218			0.393969			0.196984	+	0.980407i	$0.436885\pi$
$600$		0			0
$601$	0.0894542	+	0.154939i	0.00364891	+	0.00632010i	0.867844	−	0.496837i	$-0.165505\pi$
$601$	0.0894542	+	0.154939i	0.00364891	+	0.00632010i	−0.864195	+	0.503157i	$0.832172\pi$
$602$		0			0
$603$			4.14474i			0.168787i
$604$		0			0
$605$	−2.08945	−	1.20635i	−0.0849484	−	0.0490450i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$	−29.3578	+	16.9497i	−1.18964	+	0.686838i
$610$		0			0
$611$	34.0735	−	15.5885i	1.37846	−	0.630641i
$612$		0			0
$613$	−2.14218	+	1.23679i	−0.0865220	+	0.0499535i	−0.542637	−	0.839967i	$-0.682574\pi$
$613$	−2.14218	+	1.23679i	−0.0865220	+	0.0499535i	0.456115	+	0.889921i	$0.349241\pi$
$614$		0			0
$615$	−7.08945	+	12.2793i	−0.285874	+	0.495149i
$616$		0			0
$617$	2.08945	+	1.20635i	0.0841183	+	0.0485657i	0.541469	−	0.840721i	$-0.317868\pi$
$617$	2.08945	+	1.20635i	0.0841183	+	0.0485657i	−0.457351	+	0.889286i	$0.651202\pi$
$618$		0			0
$619$		−	10.3314i		−	0.415255i	−0.978208	−	0.207627i	$-0.933426\pi$
$619$		−	10.3314i		−	0.415255i	0.978208	−	0.207627i	$-0.0665742\pi$
$620$		0			0
$621$	1.00000	+	1.73205i	0.0401286	+	0.0695048i
$622$		0			0
$623$	−28.7156			−1.15047
$624$		0			0
$625$	−28.4313			−1.13725
$626$		0			0
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$		0			0
$629$		−	6.49655i		−	0.259034i
$630$		0			0
$631$	5.41055	+	3.12378i	0.215390	+	0.124356i	0.603814	−	0.797125i	$-0.293647\pi$
$631$	5.41055	+	3.12378i	0.215390	+	0.124356i	−0.388424	+	0.921481i	$0.626980\pi$
$632$		0			0
$633$	7.76836	−	13.4552i	0.308765	−	0.534796i
$634$		0			0
$635$	5.89454	−	3.40322i	0.233918	−	0.135052i
$636$		0			0
$637$	−21.2684	+	29.9097i	−0.842683	+	1.18506i
$638$		0			0
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$		0			0
$641$	0.268363	−	0.464818i	0.0105997	−	0.0183592i	−0.860677	−	0.509152i	$-0.829959\pi$
$641$	0.268363	−	0.464818i	0.0105997	−	0.0183592i	0.871277	+	0.490792i	$0.163293\pi$
$642$		0			0
$643$	−13.7684	−	7.94917i	−0.542971	−	0.313485i	0.203311	−	0.979114i	$-0.434830\pi$
$643$	−13.7684	−	7.94917i	−0.542971	−	0.313485i	−0.746282	+	0.665630i	$0.768163\pi$
$644$		0			0
$645$			1.98104i			0.0780035i
$646$		0			0
$647$	−6.82109	−	11.8145i	−0.268165	−	0.464475i	0.700223	−	0.713924i	$-0.253084\pi$
$647$	−6.82109	−	11.8145i	−0.268165	−	0.464475i	−0.968388	+	0.249449i	$0.919750\pi$
$648$		0			0
$649$	4.71563			0.185105
$650$		0			0
$651$	−31.5367			−1.23602
$652$		0			0
$653$	−0.178908	−	0.309878i	−0.00700122	−	0.0121265i	0.862504	−	0.506051i	$-0.168895\pi$
$653$	−0.178908	−	0.309878i	−0.00700122	−	0.0121265i	−0.869505	+	0.493925i	$0.835562\pi$
$654$		0			0
$655$		−	15.3395i		−	0.599363i
$656$		0			0
$657$	9.85782	+	5.69141i	0.384590	+	0.222043i
$658$		0			0
$659$	4.35782	−	7.54796i	0.169756	−	0.294027i	−0.768578	−	0.639756i	$-0.779035\pi$
$659$	4.35782	−	7.54796i	0.169756	−	0.294027i	0.938334	+	0.345730i	$0.112369\pi$
$660$		0			0
$661$	11.1422	−	6.43294i	0.433381	−	0.250212i	−0.267405	−	0.963584i	$-0.586166\pi$
$661$	11.1422	−	6.43294i	0.433381	−	0.250212i	0.700786	+	0.713372i	$0.252833\pi$
$662$		0			0
$663$	−9.26836	−	20.2589i	−0.359953	−	0.786791i
$664$		0			0
$665$	30.0000	−	17.3205i	1.16335	−	0.671660i
$666$		0			0
$667$	−8.17891	+	14.1663i	−0.316689	+	0.548521i
$668$		0			0
$669$	13.1789	+	7.60885i	0.509526	+	0.294175i
$670$		0			0
$671$			17.3205i			0.668651i
$672$		0			0
$673$	2.67891	+	4.64001i	0.103264	+	0.178859i	0.913028	−	0.407897i	$-0.133738\pi$
$673$	2.67891	+	4.64001i	0.103264	+	0.178859i	−0.809763	+	0.586757i	$0.800405\pi$
$674$		0			0
$675$	−0.821092			−0.0316038
$676$		0			0
$677$	−3.64218			−0.139980			−0.0699902	−	0.997548i	$-0.522297\pi$
$677$	−3.64218			−0.139980			−0.0699902	+	0.997548i	$0.522297\pi$
$678$		0			0
$679$	4.23164	+	7.32941i	0.162395	+	0.281277i
$680$		0			0
$681$		−	9.03102i		−	0.346069i
$682$		0			0
$683$	−15.5367	−	8.97013i	−0.594496	−	0.343233i	0.172377	−	0.985031i	$-0.444855\pi$
$683$	−15.5367	−	8.97013i	−0.594496	−	0.343233i	−0.766873	+	0.641798i	$0.778189\pi$
$684$		0			0
$685$	−15.4473	+	26.7555i	−0.590210	+	1.02227i
$686$		0			0
$687$	8.35782	−	4.82539i	0.318871	−	0.184100i
$688$		0			0
$689$	−15.2684	−	33.3738i	−0.581678	−	1.27144i
$690$		0			0
$691$	−7.12618	+	4.11430i	−0.271093	+	0.156515i	−0.629384	−	0.777094i	$-0.716693\pi$
$691$	−7.12618	+	4.11430i	−0.271093	+	0.156515i	0.358291	+	0.933610i	$0.383359\pi$
$692$		0			0
$693$	7.17891	−	12.4342i	0.272704	−	0.472337i
$694$		0			0
$695$	35.8945	+	20.7237i	1.36156	+	0.786096i
$696$		0			0
$697$		−	36.3122i		−	1.37542i
$698$		0			0
$699$	−11.3578	−	19.6723i	−0.429592	−	0.744075i
$700$		0			0
$701$	48.3578			1.82645			0.913225	−	0.407456i	$-0.133584\pi$
$701$	48.3578			1.82645			0.913225	+	0.407456i	$0.133584\pi$
$702$		0			0
$703$	−3.64218			−0.137368
$704$		0			0
$705$	12.5367	+	21.7142i	0.472160	+	0.817806i
$706$		0			0
$707$			50.4785i			1.89844i
$708$		0			0
$709$	25.5000	+	14.7224i	0.957673	+	0.552913i	0.895456	−	0.445150i	$-0.146850\pi$
$709$	25.5000	+	14.7224i	0.957673	+	0.552913i	0.0622167	+	0.998063i	$0.480183\pi$
$710$		0			0
$711$	−6.58945	+	11.4133i	−0.247124	+	0.428031i
$712$		0			0
$713$	−13.1789	+	7.60885i	−0.493554	+	0.284954i
$714$		0			0
$715$	17.4633	−	24.5586i	0.653089	−	0.918439i
$716$		0			0
$717$	−1.82109	+	1.05141i	−0.0680099	+	0.0392655i
$718$		0			0
$719$	15.1789	−	26.2906i	0.566078	−	0.980475i	−0.430871	−	0.902414i	$-0.641794\pi$
$719$	15.1789	−	26.2906i	0.566078	−	0.980475i	0.996949	−	0.0780618i	$-0.0248731\pi$
$720$		0			0
$721$	−11.4105	−	6.58788i	−0.424951	−	0.245346i
$722$		0			0
$723$		−	5.87680i		−	0.218560i
$724$		0			0
$725$	−3.35782	−	5.81591i	−0.124706	−	0.215997i
$726$		0			0
$727$	17.5367			0.650401			0.325201	−	0.945645i	$-0.394568\pi$
$727$	17.5367			0.650401			0.325201	+	0.945645i	$0.394568\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.53673	−	4.39374i	−0.0938242	−	0.162508i
$732$		0			0
$733$		−	10.6413i		−	0.393045i	−0.980499	−	0.196523i	$-0.937035\pi$
$733$		−	10.6413i		−	0.393045i	0.980499	−	0.196523i	$-0.0629649\pi$
$734$		0			0
$735$	−21.2684	−	12.2793i	−0.784495	−	0.452929i
$736$		0			0
$737$	7.17891	−	12.4342i	0.264438	−	0.458021i
$738$		0			0
$739$	−13.1789	+	7.60885i	−0.484794	+	0.279896i	−0.722412	−	0.691463i	$-0.756967\pi$
$739$	−13.1789	+	7.60885i	−0.484794	+	0.279896i	0.237618	+	0.971359i	$0.423633\pi$
$740$		0			0
$741$	−11.3578	+	5.19615i	−0.417240	+	0.190885i
$742$		0			0
$743$	−1.17891	+	0.680643i	−0.0432500	+	0.0249704i	−0.521469	−	0.853270i	$-0.674616\pi$
$743$	−1.17891	+	0.680643i	−0.0432500	+	0.0249704i	0.478219	+	0.878241i	$0.341282\pi$
$744$		0			0
$745$	7.08945	−	12.2793i	0.259738	−	0.449879i
$746$		0			0
$747$	−10.1789	−	5.87680i	−0.372427	−	0.215021i
$748$		0			0
$749$		−	41.4474i		−	1.51446i
$750$		0			0
$751$	9.82109	+	17.0106i	0.358377	+	0.620727i	0.987690	−	0.156425i	$-0.0499970\pi$
$751$	9.82109	+	17.0106i	0.358377	+	0.620727i	−0.629313	+	0.777152i	$0.716664\pi$
$752$		0			0
$753$	−20.7156			−0.754920
$754$		0			0
$755$	48.3578			1.75992
$756$		0			0
$757$	19.3578	+	33.5287i	0.703572	+	1.21862i	0.967204	+	0.253999i	$0.0817460\pi$
$757$	19.3578	+	33.5287i	0.703572	+	1.21862i	−0.263633	+	0.964623i	$0.584921\pi$
$758$		0			0
$759$		−	6.92820i		−	0.251478i
$760$		0			0
$761$	−42.0000	−	24.2487i	−1.52250	−	0.879015i	−0.999646	−	0.0265919i	$-0.991535\pi$
$761$	−42.0000	−	24.2487i	−1.52250	−	0.879015i	−0.522852	−	0.852423i	$-0.675132\pi$
$762$		0			0
$763$	15.7684	−	27.3116i	0.570853	−	0.988746i
$764$		0			0
$765$	12.9105	−	7.45391i	0.466782	−	0.269497i
$766$		0			0
$767$	−0.463275	+	4.88627i	−0.0167279	+	0.176433i
$768$		0			0
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	−0.604266	−	0.796782i	$-0.706534\pi$
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	0.387901	+	0.921701i	$0.373200\pi$
$770$		0			0
$771$	−11.0895	+	19.2075i	−0.399377	+	0.691741i
$772$		0			0
$773$	−27.5367	−	15.8983i	−0.990427	−	0.571823i	−0.0850252	−	0.996379i	$-0.527097\pi$
$773$	−27.5367	−	15.8983i	−0.990427	−	0.571823i	−0.905402	+	0.424555i	$0.860430\pi$
$774$		0			0
$775$		−	6.24756i		−	0.224419i
$776$		0			0
$777$	2.17891	+	3.77398i	0.0781679	+	0.135391i
$778$		0			0
$779$	−20.3578			−0.729394
$780$		0			0
$781$	−12.0000			−0.429394
$782$		0			0
$783$	4.08945	+	7.08314i	0.146145	+	0.253131i
$784$		0			0
$785$		−	16.8889i		−	0.602789i
$786$		0			0
$787$	−29.4105	−	16.9802i	−1.04837	−	0.605278i	−0.126179	−	0.992007i	$-0.540271\pi$
$787$	−29.4105	−	16.9802i	−1.04837	−	0.605278i	−0.922193	+	0.386729i	$0.873605\pi$
$788$		0			0
$789$	−16.1789	+	28.0227i	−0.575984	+	0.997634i
$790$		0			0
$791$	43.7156	−	25.2392i	1.55435	−	0.897404i
$792$		0			0
$793$	−17.9473	−	1.70161i	−0.637326	−	0.0604259i
$794$		0			0
$795$	21.2684	−	12.2793i	0.754311	−	0.435502i
$796$		0			0
$797$	−8.53673	+	14.7860i	−0.302386	+	0.523748i	−0.976676	−	0.214718i	$-0.931117\pi$
$797$	−8.53673	+	14.7860i	−0.302386	+	0.523748i	0.674290	+	0.738467i	$0.264450\pi$
$798$		0			0
$799$	−55.6102	−	32.1065i	−1.96735	−	1.13585i
$800$		0			0
$801$			6.92820i			0.244796i
$802$		0			0
$803$	−19.7156	−	34.1485i	−0.695750	−	1.20507i
$804$		0			0
$805$	−20.0000			−0.704907
$806$		0			0
$807$	−12.3578			−0.435016
$808$		0			0
$809$	−23.2684	−	40.3020i	−0.818072	−	1.41694i	−0.907101	−	0.420913i	$-0.861710\pi$
$809$	−23.2684	−	40.3020i	−0.818072	−	1.41694i	0.0890288	−	0.996029i	$-0.471624\pi$
$810$		0			0
$811$			0.680643i			0.0239006i	0.999929	+	0.0119503i	$0.00380399\pi$
$811$			0.680643i			0.0239006i	−0.999929	+	0.0119503i	$0.996196\pi$
$812$		0			0
$813$	12.5895	+	7.26852i	0.441531	+	0.254918i
$814$		0			0
$815$	−9.17891	+	15.8983i	−0.321523	+	0.556894i
$816$		0			0
$817$	−2.46327	+	1.42217i	−0.0861791	+	0.0497555i
$818$		0			0
$819$	12.1789	+	8.66025i	0.425565	+	0.302614i
$820$		0			0
$821$	27.5367	−	15.8983i	0.961038	−	0.554856i	0.0645459	−	0.997915i	$-0.479440\pi$
$821$	27.5367	−	15.8983i	0.961038	−	0.554856i	0.896492	+	0.443059i	$0.146107\pi$
$822$		0			0
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$		0			0
$825$	2.46327	+	1.42217i	0.0857602	+	0.0495137i
$826$		0			0
$827$			35.8805i			1.24769i	0.781549	+	0.623844i	$0.214430\pi$
$827$			35.8805i			1.24769i	−0.781549	+	0.623844i	$0.785570\pi$
$828$		0			0
$829$	−11.6789	−	20.2285i	−0.405625	−	0.702564i	0.588769	−	0.808302i	$-0.299613\pi$
$829$	−11.6789	−	20.2285i	−0.405625	−	0.702564i	−0.994394	+	0.105738i	$0.966280\pi$
$830$		0			0
$831$	−0.178908			−0.00620626
$832$		0			0
$833$	62.8945			2.17917
$834$		0			0
$835$	−8.35782	−	14.4762i	−0.289234	−	0.500968i
$836$		0			0
$837$			7.60885i			0.263000i
$838$		0			0
$839$	−13.1789	−	7.60885i	−0.454986	−	0.262687i	0.254947	−	0.966955i	$-0.417942\pi$
$839$	−13.1789	−	7.60885i	−0.454986	−	0.262687i	−0.709934	+	0.704268i	$0.751275\pi$
$840$		0			0
$841$	−18.9473	+	32.8176i	−0.653354	+	1.13164i
$842$		0			0
$843$	9.91055	−	5.72186i	0.341337	−	0.197071i
$844$		0			0
$845$	23.7316	+	20.5079i	0.816393	+	0.705493i
$846$		0			0
$847$	−3.58945	+	2.07237i	−0.123335	+	0.0712076i
$848$		0			0
$849$	13.5895	−	23.5376i	0.466389	−	0.807809i
$850$		0			0
$851$	1.82109	+	1.05141i	0.0624262	+	0.0360418i
$852$		0			0
$853$		−	24.6195i		−	0.842955i	−0.906839	−	0.421477i	$-0.861512\pi$
$853$		−	24.6195i		−	0.842955i	0.906839	−	0.421477i	$-0.138488\pi$
$854$		0			0
$855$	−4.17891	−	7.23808i	−0.142916	−	0.247537i
$856$		0			0
$857$	−20.1789			−0.689298			−0.344649	−	0.938732i	$-0.612002\pi$
$857$	−20.1789			−0.689298			−0.344649	+	0.938732i	$0.612002\pi$
$858$		0			0
$859$	54.2524			1.85107			0.925533	−	0.378666i	$-0.123617\pi$
$859$	54.2524			1.85107			0.925533	+	0.378666i	$0.123617\pi$
$860$		0			0
$861$	12.1789	+	21.0945i	0.415056	+	0.718898i
$862$		0			0
$863$			20.0431i			0.682274i	0.940014	+	0.341137i	$0.110812\pi$
$863$			20.0431i			0.682274i	−0.940014	+	0.341137i	$0.889188\pi$
$864$		0			0
$865$	37.6102	+	21.7142i	1.27878	+	0.738306i
$866$		0			0
$867$	−10.5895	+	18.3415i	−0.359637	+	0.622909i
$868$		0			0
$869$	39.5367	−	22.8265i	1.34119	−	0.774337i
$870$		0			0
$871$	12.1789	+	8.66025i	0.412667	+	0.293442i
$872$		0			0
$873$	1.76836	−	1.02096i	0.0598500	−	0.0345544i
$874$		0			0
$875$	−20.8945	+	36.1904i	−0.706364	+	1.22346i
$876$		0			0
$877$	11.0895	+	6.40250i	0.374464	+	0.216197i	0.675407	−	0.737445i	$-0.263968\pi$
$877$	11.0895	+	6.40250i	0.374464	+	0.216197i	−0.300943	+	0.953642i	$0.597301\pi$
$878$		0			0
$879$		−	32.8481i		−	1.10794i
$880$		0			0
$881$	18.9105	+	32.7540i	0.637112	+	1.10351i	0.986063	+	0.166370i	$0.0532047\pi$
$881$	18.9105	+	32.7540i	0.637112	+	1.10351i	−0.348951	+	0.937141i	$0.613462\pi$
$882$		0			0
$883$	−17.8945			−0.602199			−0.301100	−	0.953593i	$-0.597354\pi$
$883$	−17.8945			−0.602199			−0.301100	+	0.953593i	$0.597354\pi$
$884$		0			0
$885$	−3.28437			−0.110403
$886$		0			0
$887$	−10.8211	−	18.7427i	−0.363337	−	0.629318i	0.625171	−	0.780488i	$-0.285029\pi$
$887$	−10.8211	−	18.7427i	−0.363337	−	0.629318i	−0.988508	+	0.151170i	$0.951696\pi$
$888$		0			0
$889$		−	11.6927i		−	0.392161i
$890$		0			0
$891$	−3.00000	−	1.73205i	−0.100504	−	0.0580259i
$892$		0			0
$893$	−18.0000	+	31.1769i	−0.602347	+	1.04330i
$894$		0			0
$895$	17.4633	−	10.0824i	0.583733	−	0.337018i
$896$		0			0
$897$	7.17891	+	0.680643i	0.239697	+	0.0227260i
$898$		0			0
$899$	−53.8945	+	31.1160i	−1.79748	+	1.03778i
$900$		0			0
$901$	−31.4473	+	54.4683i	−1.04766	+	1.81460i
$902$		0			0
$903$	2.94727	+	1.70161i	0.0980790	+	0.0566260i
$904$		0			0
$905$			49.5488i			1.64706i
$906$		0			0
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$		0			0
$909$	12.1789			0.403949
$910$		0			0
$911$	4.71563			0.156236			0.0781180	−	0.996944i	$-0.475109\pi$
$911$	4.71563			0.156236			0.0781180	+	0.996944i	$0.475109\pi$
$912$		0			0
$913$	20.3578	+	35.2608i	0.673745	+	1.16696i
$914$		0			0
$915$		−	12.0635i		−	0.398806i
$916$		0			0
$917$	−22.8211	−	13.1758i	−0.753619	−	0.435102i
$918$		0			0
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$		0			0
$921$	9.58945	−	5.53647i	0.315983	−	0.182433i
$922$		0			0
$923$	1.17891	−	12.4342i	0.0388042	−	0.409278i
$924$		0			0
$925$	−0.747642	+	0.431651i	−0.0245823	+	0.0141926i
$926$		0			0
$927$	−1.58945	+	2.75302i	−0.0522045	+	0.0904209i
$928$		0			0
$929$	−27.2684	−	15.7434i	−0.894646	−	0.516524i	−0.0191866	−	0.999816i	$-0.506108\pi$
$929$	−27.2684	−	15.7434i	−0.894646	−	0.516524i	−0.875459	+	0.483292i	$0.839441\pi$
$930$		0			0
$931$		−	35.2608i		−	1.15563i
$932$		0			0
$933$	−5.82109	−	10.0824i	−0.190574	−	0.330084i
$934$		0			0
$935$	−51.6422			−1.68888
$936$		0			0
$937$	48.8945			1.59732			0.798658	−	0.601786i	$-0.205544\pi$
$937$	48.8945			1.59732			0.798658	+	0.601786i	$0.205544\pi$
$938$		0			0
$939$	−13.9473	−	24.1574i	−0.455152	−	0.788346i
$940$		0			0
$941$			37.2418i			1.21405i	0.794683	+	0.607024i	$0.207637\pi$
$941$			37.2418i			1.21405i	−0.794683	+	0.607024i	$0.792363\pi$
$942$		0			0
$943$	10.1789	+	5.87680i	0.331471	+	0.191375i
$944$		0			0
$945$	−5.00000	+	8.66025i	−0.162650	+	0.281718i
$946$		0			0
$947$	−26.3578	+	15.2177i	−0.856514	+	0.494509i	−0.862843	−	0.505471i	$-0.831319\pi$
$947$	−26.3578	+	15.2177i	−0.856514	+	0.494509i	0.00632940	+	0.999980i	$0.497985\pi$
$948$		0			0
$949$	37.3211	−	17.0742i	1.21149	−	0.554253i
$950$		0			0
$951$	3.26836	−	1.88699i	0.105984	−	0.0611898i
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$		0			0
$955$	−4.92655	−	2.84434i	−0.159419	−	0.0920408i
$956$		0			0
$957$		−	28.3326i		−	0.915862i
$958$		0			0
$959$	26.5367	+	45.9630i	0.856916	+	1.48422i
$960$		0			0
$961$	−26.8945			−0.867566
$962$		0			0
$963$	−10.0000			−0.322245
$964$		0			0
$965$	16.2684	+	28.1776i	0.523697	+	0.907070i
$966$		0			0
$967$			35.3825i			1.13783i	0.822398	+	0.568913i	$0.192636\pi$
$967$			35.3825i			1.13783i	−0.822398	+	0.568913i	$0.807364\pi$
$968$		0			0
$969$	18.5367	+	10.7022i	0.595485	+	0.343804i
$970$		0			0
$971$	−2.35782	+	4.08386i	−0.0756659	+	0.131057i	−0.901376	−	0.433038i	$-0.857442\pi$
$971$	−2.35782	+	4.08386i	−0.0756659	+	0.131057i	0.825710	+	0.564095i	$0.190775\pi$
$972$		0			0
$973$	61.6629	−	35.6011i	1.97682	−	1.14132i
$974$		0			0
$975$	−1.71563	+	2.41269i	−0.0549442	+	0.0772680i
$976$		0			0
$977$	14.7316	−	8.50531i	0.471307	−	0.272109i	−0.245480	−	0.969402i	$-0.578945\pi$
$977$	14.7316	−	8.50531i	0.471307	−	0.272109i	0.716787	+	0.697293i	$0.245612\pi$
$978$		0			0
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$		0			0
$981$	−6.58945	−	3.80442i	−0.210385	−	0.121466i
$982$		0			0
$983$			24.8685i			0.793181i	0.917996	+	0.396590i	$0.129807\pi$
$983$			24.8685i			0.793181i	−0.917996	+	0.396590i	$0.870193\pi$
$984$		0			0
$985$	11.6422	+	20.1649i	0.370951	+	0.642506i
$986$		0			0
$987$	43.0735			1.37104
$988$		0			0
$989$	1.64218			0.0522184
$990$		0			0
$991$	22.5367	+	39.0348i	0.715903	+	1.23998i	0.962610	+	0.270890i	$0.0873179\pi$
$991$	22.5367	+	39.0348i	0.715903	+	1.23998i	−0.246708	+	0.969090i	$0.579349\pi$
$992$		0			0
$993$			20.1040i			0.637980i
$994$		0			0
$995$	−45.0000	−	25.9808i	−1.42660	−	0.823646i
$996$		0			0
$997$	−17.6789	+	30.6208i	−0.559897	+	0.969769i	0.437608	+	0.899166i	$0.355826\pi$
$997$	−17.6789	+	30.6208i	−0.559897	+	0.969769i	−0.997504	+	0.0706035i	$0.977507\pi$
$998$		0			0
$999$	0.910546	−	0.525704i	0.0288084	−	0.0166325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.q.b.49.1	✓	4
3.2	odd	2		468.2.t.d.361.2		4
4.3	odd	2		624.2.bv.f.49.1		4
5.2	odd	4		3900.2.bw.j.49.2		8
5.3	odd	4		3900.2.bw.j.49.3		8
5.4	even	2		3900.2.cd.i.2701.2		4
12.11	even	2		1872.2.by.j.1297.2		4
13.2	odd	12		2028.2.a.m.1.2		4
13.3	even	3		2028.2.b.e.337.2		4
13.4	even	6	inner	156.2.q.b.121.2	yes	4
13.5	odd	4		2028.2.i.n.2005.2		8
13.6	odd	12		2028.2.i.n.529.2		8
13.7	odd	12		2028.2.i.n.529.3		8
13.8	odd	4		2028.2.i.n.2005.3		8
13.9	even	3		2028.2.q.f.1837.1		4
13.10	even	6		2028.2.b.e.337.3		4
13.11	odd	12		2028.2.a.m.1.3		4
13.12	even	2		2028.2.q.f.361.2		4
39.2	even	12		6084.2.a.bd.1.3		4
39.11	even	12		6084.2.a.bd.1.2		4
39.17	odd	6		468.2.t.d.433.1		4
39.23	odd	6		6084.2.b.o.4393.2		4
39.29	odd	6		6084.2.b.o.4393.3		4
52.11	even	12		8112.2.a.cr.1.3		4
52.15	even	12		8112.2.a.cr.1.2		4
52.43	odd	6		624.2.bv.f.433.2		4
65.4	even	6		3900.2.cd.i.901.2		4
65.17	odd	12		3900.2.bw.j.2149.3		8
65.43	odd	12		3900.2.bw.j.2149.2		8
156.95	even	6		1872.2.by.j.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.q.b.49.1	✓	4	1.1	even	1	trivial
156.2.q.b.121.2	yes	4	13.4	even	6	inner
468.2.t.d.361.2		4	3.2	odd	2
468.2.t.d.433.1		4	39.17	odd	6
624.2.bv.f.49.1		4	4.3	odd	2
624.2.bv.f.433.2		4	52.43	odd	6
1872.2.by.j.433.1		4	156.95	even	6
1872.2.by.j.1297.2		4	12.11	even	2
2028.2.a.m.1.2		4	13.2	odd	12
2028.2.a.m.1.3		4	13.11	odd	12
2028.2.b.e.337.2		4	13.3	even	3
2028.2.b.e.337.3		4	13.10	even	6
2028.2.i.n.529.2		8	13.6	odd	12
2028.2.i.n.529.3		8	13.7	odd	12
2028.2.i.n.2005.2		8	13.5	odd	4
2028.2.i.n.2005.3		8	13.8	odd	4
2028.2.q.f.361.2		4	13.12	even	2
2028.2.q.f.1837.1		4	13.9	even	3
3900.2.bw.j.49.2		8	5.2	odd	4
3900.2.bw.j.49.3		8	5.3	odd	4
3900.2.bw.j.2149.2		8	65.43	odd	12
3900.2.bw.j.2149.3		8	65.17	odd	12
3900.2.cd.i.901.2		4	65.4	even	6
3900.2.cd.i.2701.2		4	5.4	even	2
6084.2.a.bd.1.2		4	39.11	even	12
6084.2.a.bd.1.3		4	39.2	even	12
6084.2.b.o.4393.2		4	39.23	odd	6
6084.2.b.o.4393.3		4	39.29	odd	6
8112.2.a.cr.1.2		4	52.15	even	12
8112.2.a.cr.1.3		4	52.11	even	12

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} -2.41269i q^{5} +(-3.58945 - 2.07237i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(1.50000 + 3.27872i) q^{13} +(-2.08945 + 1.20635i) q^{15} +(3.08945 - 5.35109i) q^{17} +(-3.00000 - 1.73205i) q^{19} +4.14474i q^{21} +(1.00000 + 1.73205i) q^{23} -0.821092 q^{25} +1.00000 q^{27} +(4.08945 + 7.08314i) q^{29} +7.60885i q^{31} +(-3.00000 - 1.73205i) q^{33} +(-5.00000 + 8.66025i) q^{35} +(0.910546 - 0.525704i) q^{37} +(2.08945 - 2.93840i) q^{39} +(5.08945 - 2.93840i) q^{41} +(0.410546 - 0.711086i) q^{43} +(2.08945 + 1.20635i) q^{45} -10.3923i q^{47} +(5.08945 + 8.81519i) q^{49} -6.17891 q^{51} -10.1789 q^{53} +(-4.17891 - 7.23808i) q^{55} +3.46410i q^{57} +(1.17891 + 0.680643i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(3.58945 - 2.07237i) q^{63} +(7.91055 - 3.61904i) q^{65} +(3.58945 - 2.07237i) q^{67} +(1.00000 - 1.73205i) q^{69} +(-3.00000 - 1.73205i) q^{71} -11.3828i q^{73} +(0.410546 + 0.711086i) q^{75} -14.3578 q^{77} +13.1789 q^{79} +(-0.500000 - 0.866025i) q^{81} +11.7536i q^{83} +(-12.9105 - 7.45391i) q^{85} +(4.08945 - 7.08314i) q^{87} +(6.00000 - 3.46410i) q^{89} +(1.41055 - 14.8774i) q^{91} +(6.58945 - 3.80442i) q^{93} +(-4.17891 + 7.23808i) q^{95} +(-1.76836 - 1.02096i) q^{97} +3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 3 q^{7} - 2 q^{9} + 12 q^{11} + 6 q^{13} + 3 q^{15} + q^{17} - 12 q^{19} + 4 q^{23} - 26 q^{25} + 4 q^{27} + 5 q^{29} - 12 q^{33} - 20 q^{35} + 15 q^{37} - 3 q^{39} + 9 q^{41} + 13 q^{43}+ \cdots + 27 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 3 * q^7 - 2 * q^9 + 12 * q^11 + 6 * q^13 + 3 * q^15 + q^17 - 12 * q^19 + 4 * q^23 - 26 * q^25 + 4 * q^27 + 5 * q^29 - 12 * q^33 - 20 * q^35 + 15 * q^37 - 3 * q^39 + 9 * q^41 + 13 * q^43 - 3 * q^45 + 9 * q^49 - 2 * q^51 - 18 * q^53 + 6 * q^55 - 18 * q^59 - 10 * q^61 + 3 * q^63 + 43 * q^65 + 3 * q^67 + 4 * q^69 - 12 * q^71 + 13 * q^75 - 12 * q^77 + 30 * q^79 - 2 * q^81 - 63 * q^85 + 5 * q^87 + 24 * q^89 + 17 * q^91 + 15 * q^93 + 6 * q^95 + 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more