LMFDB - Embedded newform 720.2.by.d.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(49,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("720.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.by (of order $6$, degree $2$, not 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	720.529
Dual form			720.2.by.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67303 - 0.448288i) q^{3} +(0.358719 - 2.20711i) q^{5} +(0.776457 + 0.448288i) q^{7} +(2.59808 + 1.50000i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-2.12132 + 1.22474i) q^{13} +(-1.58957 + 3.53175i) q^{15} +0.378937i q^{17} +2.73205 q^{19} +(-1.09808 - 1.09808i) q^{21} +(-1.67303 + 0.965926i) q^{23} +(-4.74264 - 1.58346i) q^{25} +(-3.67423 - 3.67423i) q^{27} +(3.23205 - 5.59808i) q^{29} +(-1.36603 - 2.36603i) q^{31} +(-5.79555 + 5.79555i) q^{33} +(1.26795 - 1.55291i) q^{35} -4.24264i q^{37} +(4.09808 - 1.09808i) q^{39} +(-2.13397 - 3.69615i) q^{41} +(-7.91688 - 4.57081i) q^{43} +(4.24264 - 5.19615i) q^{45} +(3.79435 + 2.19067i) q^{47} +(-3.09808 - 5.36603i) q^{49} +(0.169873 - 0.633975i) q^{51} -3.86370i q^{53} +(-8.19615 - 6.69213i) q^{55} +(-4.57081 - 1.22474i) q^{57} +(-1.26795 - 2.19615i) q^{59} +(-5.33013 + 9.23205i) q^{61} +(1.34486 + 2.32937i) q^{63} +(1.94218 + 5.12132i) q^{65} +(4.45069 - 2.56961i) q^{67} +(3.23205 - 0.866025i) q^{69} -3.80385 q^{71} -8.48528i q^{73} +(7.22474 + 4.77526i) q^{75} +(3.67423 - 2.12132i) q^{77} +(-0.267949 + 0.464102i) q^{79} +(4.50000 + 7.79423i) q^{81} +(9.02150 + 5.20857i) q^{83} +(0.836355 + 0.135932i) q^{85} +(-7.91688 + 7.91688i) q^{87} +7.39230 q^{89} -2.19615 q^{91} +(1.22474 + 4.57081i) q^{93} +(0.980040 - 6.02993i) q^{95} +(8.90138 + 5.13922i) q^{97} +(12.2942 - 7.09808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{11} - 12 q^{15} + 8 q^{19} + 12 q^{21} - 4 q^{25} + 12 q^{29} - 4 q^{31} + 24 q^{35} + 12 q^{39} - 24 q^{41} - 4 q^{49} + 36 q^{51} - 24 q^{55} - 24 q^{59} - 8 q^{61} + 12 q^{69} - 72 q^{71}+ \cdots + 36 q^{99}+O(q^{100}) $ 8 * q + 12 * q^11 - 12 * q^15 + 8 * q^19 + 12 * q^21 - 4 * q^25 + 12 * q^29 - 4 * q^31 + 24 * q^35 + 12 * q^39 - 24 * q^41 - 4 * q^49 + 36 * q^51 - 24 * q^55 - 24 * q^59 - 8 * q^61 + 12 * q^69 - 72 * q^71 + 48 * q^75 - 16 * q^79 + 36 * q^81 + 16 * q^85 - 24 * q^89 + 24 * q^91 - 12 * q^95 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$		0			0
$5$	0.358719	−	2.20711i	0.160424	−	0.987048i
$5$	0.358719	−	2.20711i	0.160424	−	0.987048i
$6$		0			0
$7$	0.776457	+	0.448288i	0.293473	+	0.169437i	0.639507	−	0.768785i	$-0.279138\pi$
$7$	0.776457	+	0.448288i	0.293473	+	0.169437i	−0.346034	+	0.938222i	$0.612472\pi$
$8$		0			0
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$		0			0
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	−0.250196	−	0.968195i	$-0.580495\pi$
$11$	2.36603	−	4.09808i	0.713384	−	1.23562i	0.963580	−	0.267421i	$-0.0861715\pi$
$12$		0			0
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	−0.764444	−	0.644690i	$-0.776986\pi$
$13$	−2.12132	+	1.22474i	−0.588348	+	0.339683i	0.176096	+	0.984373i	$0.443653\pi$
$14$		0			0
$15$	−1.58957	+	3.53175i	−0.410425	+	0.911894i
$16$		0			0
$17$			0.378937i			0.0919058i	0.998944	+	0.0459529i	$0.0146324\pi$
$17$			0.378937i			0.0919058i	−0.998944	+	0.0459529i	$0.985368\pi$
$18$		0			0
$19$	2.73205			0.626775			0.313388	−	0.949625i	$-0.398536\pi$
$19$	2.73205			0.626775			0.313388	+	0.949625i	$0.398536\pi$
$20$		0			0
$21$	−1.09808	−	1.09808i	−0.239620	−	0.239620i
$22$		0			0
$23$	−1.67303	+	0.965926i	−0.348851	+	0.201409i	−0.664179	−	0.747573i	$-0.731219\pi$
$23$	−1.67303	+	0.965926i	−0.348851	+	0.201409i	0.315328	+	0.948983i	$0.397886\pi$
$24$		0			0
$25$	−4.74264	−	1.58346i	−0.948528	−	0.316693i
$26$		0			0
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$		0			0
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	−0.392617	−	0.919702i	$-0.628430\pi$
$29$	3.23205	−	5.59808i	0.600177	−	1.03954i	0.992794	−	0.119835i	$-0.0382364\pi$
$30$		0			0
$31$	−1.36603	−	2.36603i	−0.245345	−	0.424951i	0.716883	−	0.697193i	$-0.245568\pi$
$31$	−1.36603	−	2.36603i	−0.245345	−	0.424951i	−0.962229	+	0.272243i	$0.912235\pi$
$32$		0			0
$33$	−5.79555	+	5.79555i	−1.00888	+	1.00888i
$34$		0			0
$35$	1.26795	−	1.55291i	0.214323	−	0.262490i
$36$		0			0
$37$		−	4.24264i		−	0.697486i	−0.937218	−	0.348743i	$-0.886609\pi$
$37$		−	4.24264i		−	0.697486i	0.937218	−	0.348743i	$-0.113391\pi$
$38$		0			0
$39$	4.09808	−	1.09808i	0.656217	−	0.175833i
$40$		0			0
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	0.649880	−	0.760037i	$-0.274819\pi$
$41$	−2.13397	−	3.69615i	−0.333271	−	0.577242i	−0.983151	+	0.182795i	$0.941486\pi$
$42$		0			0
$43$	−7.91688	−	4.57081i	−1.20731	−	0.697042i	−0.245141	−	0.969487i	$-0.578834\pi$
$43$	−7.91688	−	4.57081i	−1.20731	−	0.697042i	−0.962171	+	0.272445i	$0.912168\pi$
$44$		0			0
$45$	4.24264	−	5.19615i	0.632456	−	0.774597i
$46$		0			0
$47$	3.79435	+	2.19067i	0.553463	+	0.319542i	0.750518	−	0.660850i	$-0.229804\pi$
$47$	3.79435	+	2.19067i	0.553463	+	0.319542i	−0.197054	+	0.980393i	$0.563138\pi$
$48$		0			0
$49$	−3.09808	−	5.36603i	−0.442582	−	0.766575i
$50$		0			0
$51$	0.169873	−	0.633975i	0.0237870	−	0.0887742i
$52$		0			0
$53$		−	3.86370i		−	0.530720i	−0.964149	−	0.265360i	$-0.914509\pi$
$53$		−	3.86370i		−	0.530720i	0.964149	−	0.265360i	$-0.0854909\pi$
$54$		0			0
$55$	−8.19615	−	6.69213i	−1.10517	−	0.902367i
$56$		0			0
$57$	−4.57081	−	1.22474i	−0.605419	−	0.162221i
$58$		0			0
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	0.771608	−	0.636098i	$-0.219453\pi$
$59$	−1.26795	−	2.19615i	−0.165073	−	0.285915i	−0.936681	+	0.350183i	$0.886119\pi$
$60$		0			0
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	0.291777	+	0.956486i	$0.405753\pi$
$61$	−5.33013	+	9.23205i	−0.682453	+	1.18204i	−0.974230	+	0.225557i	$0.927580\pi$
$62$		0			0
$63$	1.34486	+	2.32937i	0.169437	+	0.293473i
$64$		0			0
$65$	1.94218	+	5.12132i	0.240898	+	0.635222i
$66$		0			0
$67$	4.45069	−	2.56961i	0.543739	−	0.313928i	−0.202854	−	0.979209i	$-0.565022\pi$
$67$	4.45069	−	2.56961i	0.543739	−	0.313928i	0.746593	+	0.665281i	$0.231688\pi$
$68$		0			0
$69$	3.23205	−	0.866025i	0.389093	−	0.104257i
$70$		0			0
$71$	−3.80385			−0.451434			−0.225717	−	0.974193i	$-0.572472\pi$
$71$	−3.80385			−0.451434			−0.225717	+	0.974193i	$0.572472\pi$
$72$		0			0
$73$		−	8.48528i		−	0.993127i	−0.868000	−	0.496564i	$-0.834595\pi$
$73$		−	8.48528i		−	0.993127i	0.868000	−	0.496564i	$-0.165405\pi$
$74$		0			0
$75$	7.22474	+	4.77526i	0.834242	+	0.551399i
$76$		0			0
$77$	3.67423	−	2.12132i	0.418718	−	0.241747i
$78$		0			0
$79$	−0.267949	+	0.464102i	−0.0301466	+	0.0522155i	−0.880705	−	0.473665i	$-0.842931\pi$
$79$	−0.267949	+	0.464102i	−0.0301466	+	0.0522155i	0.850558	+	0.525880i	$0.176264\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		0			0
$83$	9.02150	+	5.20857i	0.990238	+	0.571714i	0.905346	−	0.424676i	$-0.139612\pi$
$83$	9.02150	+	5.20857i	0.990238	+	0.571714i	0.0848929	+	0.996390i	$0.472945\pi$
$84$		0			0
$85$	0.836355	+	0.135932i	0.0907155	+	0.0147439i
$86$		0			0
$87$	−7.91688	+	7.91688i	−0.848778	+	0.848778i
$88$		0			0
$89$	7.39230			0.783583			0.391791	−	0.920054i	$-0.371856\pi$
$89$	7.39230			0.783583			0.391791	+	0.920054i	$0.371856\pi$
$90$		0			0
$91$	−2.19615			−0.230219
$92$		0			0
$93$	1.22474	+	4.57081i	0.127000	+	0.473971i
$94$		0			0
$95$	0.980040	−	6.02993i	0.100550	−	0.618658i
$96$		0			0
$97$	8.90138	+	5.13922i	0.903799	+	0.521808i	0.878431	−	0.477870i	$-0.158591\pi$
$97$	8.90138	+	5.13922i	0.903799	+	0.521808i	0.0253679	+	0.999678i	$0.491924\pi$
$98$		0			0
$99$	12.2942	−	7.09808i	1.23562	−	0.713384i
$100$		0			0
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	−0.922188	−	0.386742i	$-0.873600\pi$
$101$	−1.26795	+	2.19615i	−0.126166	+	0.218525i	0.796022	+	0.605267i	$0.206934\pi$
$102$		0			0
$103$	−7.91688	+	4.57081i	−0.780073	+	0.450375i	−0.836456	−	0.548034i	$-0.815376\pi$
$103$	−7.91688	+	4.57081i	−0.780073	+	0.450375i	0.0563832	+	0.998409i	$0.482043\pi$
$104$		0			0
$105$	−2.81747	+	2.02967i	−0.274957	+	0.198076i
$106$		0			0
$107$		−	11.7298i		−	1.13396i	−0.823730	−	0.566982i	$-0.808111\pi$
$107$		−	11.7298i		−	1.13396i	0.823730	−	0.566982i	$-0.191889\pi$
$108$		0			0
$109$	4.66025			0.446371			0.223186	−	0.974776i	$-0.428354\pi$
$109$	4.66025			0.446371			0.223186	+	0.974776i	$0.428354\pi$
$110$		0			0
$111$	−1.90192	+	7.09808i	−0.180523	+	0.673720i
$112$		0			0
$113$	−2.20925	+	1.27551i	−0.207829	+	0.119990i	−0.600302	−	0.799773i	$-0.704953\pi$
$113$	−2.20925	+	1.27551i	−0.207829	+	0.119990i	0.392473	+	0.919764i	$0.371620\pi$
$114$		0			0
$115$	1.53175	+	4.03906i	0.142837	+	0.376644i
$116$		0			0
$117$	−7.34847			−0.679366
$118$		0			0
$119$	−0.169873	+	0.294229i	−0.0155722	+	0.0269719i
$120$		0			0
$121$	−5.69615	−	9.86603i	−0.517832	−	0.896911i
$122$		0			0
$123$	1.91327	+	7.14042i	0.172514	+	0.643830i
$124$		0			0
$125$	−5.19615	+	9.89949i	−0.464758	+	0.885438i
$126$		0			0
$127$			4.65874i			0.413397i	0.978405	+	0.206698i	$0.0662719\pi$
$127$			4.65874i			0.413397i	−0.978405	+	0.206698i	$0.933728\pi$
$128$		0			0
$129$	11.1962	+	11.1962i	0.985766	+	0.985766i
$130$		0			0
$131$	−0.464102	−	0.803848i	−0.0405487	−	0.0702325i	0.845039	−	0.534705i	$-0.179577\pi$
$131$	−0.464102	−	0.803848i	−0.0405487	−	0.0702325i	−0.885588	+	0.464473i	$0.846244\pi$
$132$		0			0
$133$	2.12132	+	1.22474i	0.183942	+	0.106199i
$134$		0			0
$135$	−9.42745	+	6.79141i	−0.811386	+	0.584511i
$136$		0			0
$137$	16.0740	+	9.28032i	1.37329	+	0.792871i	0.991341	−	0.131311i	$-0.0419186\pi$
$137$	16.0740	+	9.28032i	1.37329	+	0.792871i	0.381952	+	0.924182i	$0.375252\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	−5.36603	−	5.36603i	−0.451901	−	0.451901i
$142$		0			0
$143$			11.5911i			0.969297i
$144$		0			0
$145$	−11.1962	−	9.14162i	−0.929790	−	0.759170i
$146$		0			0
$147$	2.77766	+	10.3664i	0.229097	+	0.855003i
$148$		0			0
$149$	3.86603	+	6.69615i	0.316717	+	0.548570i	0.979801	−	0.199975i	$-0.0640861\pi$
$149$	3.86603	+	6.69615i	0.316717	+	0.548570i	−0.663084	+	0.748545i	$0.730753\pi$
$150$		0			0
$151$	−11.2942	+	19.5622i	−0.919111	+	1.59195i	−0.118343	+	0.992973i	$0.537758\pi$
$151$	−11.2942	+	19.5622i	−0.919111	+	1.59195i	−0.800768	+	0.598975i	$0.795575\pi$
$152$		0			0
$153$	−0.568406	+	0.984508i	−0.0459529	+	0.0795928i
$154$		0			0
$155$	−5.71209	+	2.16622i	−0.458806	+	0.173995i
$156$		0			0
$157$	−18.5235	+	10.6945i	−1.47833	+	0.853517i	−0.999700	−	0.0244975i	$-0.992201\pi$
$157$	−18.5235	+	10.6945i	−1.47833	+	0.853517i	−0.478635	+	0.878014i	$0.658868\pi$
$158$		0			0
$159$	−1.73205	+	6.46410i	−0.137361	+	0.512637i
$160$		0			0
$161$	−1.73205			−0.136505
$162$		0			0
$163$		−	18.9396i		−	1.48346i	−0.670697	−	0.741731i	$-0.734005\pi$
$163$		−	18.9396i		−	1.48346i	0.670697	−	0.741731i	$-0.265995\pi$
$164$		0			0
$165$	10.7124	+	14.8704i	0.833962	+	1.15766i
$166$		0			0
$167$	14.7291	−	8.50386i	1.13977	−	0.658049i	0.193399	−	0.981120i	$-0.438049\pi$
$167$	14.7291	−	8.50386i	1.13977	−	0.658049i	0.946375	+	0.323071i	$0.104715\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$		0			0
$171$	7.09808	+	4.09808i	0.542803	+	0.313388i
$172$		0			0
$173$	0.656339	+	0.378937i	0.0499005	+	0.0288101i	0.524743	−	0.851261i	$-0.324162\pi$
$173$	0.656339	+	0.378937i	0.0499005	+	0.0288101i	−0.474842	+	0.880071i	$0.657495\pi$
$174$		0			0
$175$	−2.97261	−	3.35556i	−0.224708	−	0.253656i
$176$		0			0
$177$	1.13681	+	4.24264i	0.0854480	+	0.318896i
$178$		0			0
$179$	24.5885			1.83783			0.918914	−	0.394458i	$-0.129068\pi$
$179$	24.5885			1.83783			0.918914	+	0.394458i	$0.129068\pi$
$180$		0			0
$181$	8.46410			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$181$	8.46410			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$182$		0			0
$183$	13.0561	−	13.0561i	0.965134	−	0.965134i
$184$		0			0
$185$	−9.36396	−	1.52192i	−0.688452	−	0.111894i
$186$		0			0
$187$	1.55291	+	0.896575i	0.113560	+	0.0655641i
$188$		0			0
$189$	−1.20577	−	4.50000i	−0.0877070	−	0.327327i
$190$		0			0
$191$	0.169873	−	0.294229i	0.0122916	−	0.0212896i	−0.859814	−	0.510607i	$-0.829421\pi$
$191$	0.169873	−	0.294229i	0.0122916	−	0.0212896i	0.872106	+	0.489317i	$0.162754\pi$
$192$		0			0
$193$	17.9551	−	10.3664i	1.29243	−	0.746187i	0.313349	−	0.949638i	$-0.398549\pi$
$193$	17.9551	−	10.3664i	1.29243	−	0.746187i	0.979085	+	0.203451i	$0.0652157\pi$
$194$		0			0
$195$	−0.953512	−	9.43879i	−0.0682824	−	0.675926i
$196$		0			0
$197$		−	20.8343i		−	1.48438i	−0.670190	−	0.742190i	$-0.733787\pi$
$197$		−	20.8343i		−	1.48438i	0.670190	−	0.742190i	$-0.266213\pi$
$198$		0			0
$199$	4.58846			0.325267			0.162634	−	0.986687i	$-0.448001\pi$
$199$	4.58846			0.325267			0.162634	+	0.986687i	$0.448001\pi$
$200$		0			0
$201$	−8.59808	+	2.30385i	−0.606462	+	0.162501i
$202$		0			0
$203$	5.01910	−	2.89778i	0.352272	−	0.203384i
$204$		0			0
$205$	−8.92330	+	3.38403i	−0.623230	+	0.236351i
$206$		0			0
$207$	−5.79555			−0.402819
$208$		0			0
$209$	6.46410	−	11.1962i	0.447131	−	0.774454i
$210$		0			0
$211$	−6.56218	−	11.3660i	−0.451759	−	0.782469i	0.546736	−	0.837305i	$-0.315870\pi$
$211$	−6.56218	−	11.3660i	−0.451759	−	0.782469i	−0.998495	+	0.0548353i	$0.982537\pi$
$212$		0			0
$213$	6.36396	+	1.70522i	0.436051	+	0.116840i
$214$		0			0
$215$	−12.9282	+	15.8338i	−0.881696	+	1.07985i
$216$		0			0
$217$		−	2.44949i		−	0.166282i
$218$		0			0
$219$	−3.80385	+	14.1962i	−0.257040	+	0.959287i
$220$		0			0
$221$	−0.464102	−	0.803848i	−0.0312189	−	0.0540726i
$222$		0			0
$223$	14.4889	+	8.36516i	0.970248	+	0.560173i	0.899312	−	0.437308i	$-0.144068\pi$
$223$	14.4889	+	8.36516i	0.970248	+	0.560173i	0.0709359	+	0.997481i	$0.477401\pi$
$224$		0			0
$225$	−9.94655	−	11.2279i	−0.663103	−	0.748528i
$226$		0			0
$227$	−1.64085	−	0.947343i	−0.108907	−	0.0628774i	0.444557	−	0.895750i	$-0.353361\pi$
$227$	−1.64085	−	0.947343i	−0.108907	−	0.0628774i	−0.553464	+	0.832873i	$0.686694\pi$
$228$		0			0
$229$	9.96410	+	17.2583i	0.658446	+	1.14046i	0.981018	+	0.193917i	$0.0621194\pi$
$229$	9.96410	+	17.2583i	0.658446	+	1.14046i	−0.322571	+	0.946545i	$0.604547\pi$
$230$		0			0
$231$	−7.09808	+	1.90192i	−0.467019	+	0.125137i
$232$		0			0
$233$			7.07107i			0.463241i	0.972806	+	0.231621i	$0.0744028\pi$
$233$			7.07107i			0.463241i	−0.972806	+	0.231621i	$0.925597\pi$
$234$		0			0
$235$	6.19615	−	7.58871i	0.404192	−	0.495033i
$236$		0			0
$237$	0.656339	−	0.656339i	0.0426338	−	0.0426338i
$238$		0			0
$239$	−6.46410	−	11.1962i	−0.418128	−	0.724219i	0.577623	−	0.816304i	$-0.303980\pi$
$239$	−6.46410	−	11.1962i	−0.418128	−	0.724219i	−0.995751	+	0.0920846i	$0.970647\pi$
$240$		0			0
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	−0.949133	−	0.314875i	$-0.898037\pi$
$241$	−3.13397	+	5.42820i	−0.201877	+	0.349661i	0.747256	+	0.664536i	$0.231371\pi$
$242$		0			0
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$		0			0
$245$	−12.9547	+	4.91289i	−0.827647	+	0.313873i
$246$		0			0
$247$	−5.79555	+	3.34607i	−0.368762	+	0.212905i
$248$		0			0
$249$	−12.7583	−	12.7583i	−0.808526	−	0.808526i
$250$		0			0
$251$	−18.5885			−1.17329			−0.586647	−	0.809843i	$-0.699552\pi$
$251$	−18.5885			−1.17329			−0.586647	+	0.809843i	$0.699552\pi$
$252$		0			0
$253$			9.14162i			0.574729i
$254$		0			0
$255$	−1.33831	−	0.602347i	−0.0838084	−	0.0377204i
$256$		0			0
$257$	19.4201	−	11.2122i	1.21139	−	0.699396i	0.248328	−	0.968676i	$-0.420119\pi$
$257$	19.4201	−	11.2122i	1.21139	−	0.699396i	0.963062	+	0.269280i	$0.0867857\pi$
$258$		0			0
$259$	1.90192	−	3.29423i	0.118180	−	0.204693i
$260$		0			0
$261$	16.7942	−	9.69615i	1.03954	−	0.600177i
$262$		0			0
$263$	−6.60420	−	3.81294i	−0.407232	−	0.235116i	0.282368	−	0.959306i	$-0.408880\pi$
$263$	−6.60420	−	3.81294i	−0.407232	−	0.235116i	−0.689600	+	0.724191i	$0.742214\pi$
$264$		0			0
$265$	−8.52761	−	1.38599i	−0.523847	−	0.0851404i
$266$		0			0
$267$	−12.3676	−	3.31388i	−0.756883	−	0.202806i
$268$		0			0
$269$	−17.1962			−1.04847			−0.524234	−	0.851574i	$-0.675648\pi$
$269$	−17.1962			−1.04847			−0.524234	+	0.851574i	$0.675648\pi$
$270$		0			0
$271$	23.5167			1.42854			0.714268	−	0.699873i	$-0.246760\pi$
$271$	23.5167			1.42854			0.714268	+	0.699873i	$0.246760\pi$
$272$		0			0
$273$	3.67423	+	0.984508i	0.222375	+	0.0595851i
$274$		0			0
$275$	−17.7104	+	15.6892i	−1.06798	+	0.946094i
$276$		0			0
$277$	10.6066	+	6.12372i	0.637289	+	0.367939i	0.783569	−	0.621304i	$-0.213397\pi$
$277$	10.6066	+	6.12372i	0.637289	+	0.367939i	−0.146281	+	0.989243i	$0.546730\pi$
$278$		0			0
$279$		−	8.19615i		−	0.490691i
$280$		0			0
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	−0.514624	−	0.857416i	$-0.672068\pi$
$281$	8.13397	−	14.0885i	0.485232	−	0.840447i	0.999856	+	0.0169692i	$0.00540173\pi$
$282$		0			0
$283$	−3.88229	+	2.24144i	−0.230778	+	0.133240i	−0.610931	−	0.791684i	$-0.709205\pi$
$283$	−3.88229	+	2.24144i	−0.230778	+	0.133240i	0.380153	+	0.924924i	$0.375871\pi$
$284$		0			0
$285$	−4.34278	+	9.64893i	−0.257244	+	0.571553i
$286$		0			0
$287$		−	3.82654i		−	0.225873i
$288$		0			0
$289$	16.8564			0.991553
$290$		0			0
$291$	−12.5885	−	12.5885i	−0.737948	−	0.737948i
$292$		0			0
$293$	7.67664	−	4.43211i	0.448474	−	0.258927i	−0.258711	−	0.965955i	$-0.583298\pi$
$293$	7.67664	−	4.43211i	0.448474	−	0.258927i	0.707186	+	0.707028i	$0.249965\pi$
$294$		0			0
$295$	−5.30198	+	2.01070i	−0.308693	+	0.117067i
$296$		0			0
$297$	−23.7506	+	6.36396i	−1.37815	+	0.369274i
$298$		0			0
$299$	2.36603	−	4.09808i	0.136831	−	0.236998i
$300$		0			0
$301$	−4.09808	−	7.09808i	−0.236209	−	0.409126i
$302$		0			0
$303$	3.10583	−	3.10583i	0.178425	−	0.178425i
$304$		0			0
$305$	18.4641	+	15.0759i	1.05725	+	0.863242i
$306$		0			0
$307$			25.8719i			1.47659i	0.674478	+	0.738295i	$0.264369\pi$
$307$			25.8719i			1.47659i	−0.674478	+	0.738295i	$0.735631\pi$
$308$		0			0
$309$	15.2942	−	4.09808i	0.870058	−	0.233131i
$310$		0			0
$311$	14.0263	+	24.2942i	0.795357	+	1.37760i	0.922612	+	0.385729i	$0.126050\pi$
$311$	14.0263	+	24.2942i	0.795357	+	1.37760i	−0.127255	+	0.991870i	$0.540617\pi$
$312$		0			0
$313$	−4.81105	−	2.77766i	−0.271936	−	0.157003i	0.357831	−	0.933786i	$-0.383516\pi$
$313$	−4.81105	−	2.77766i	−0.271936	−	0.157003i	−0.629767	+	0.776784i	$0.716850\pi$
$314$		0			0
$315$	5.62360	−	2.13267i	0.316854	−	0.120162i
$316$		0			0
$317$	−30.4428	−	17.5761i	−1.70984	−	0.987174i	−0.934742	−	0.355328i	$-0.884369\pi$
$317$	−30.4428	−	17.5761i	−1.70984	−	0.987174i	−0.775094	−	0.631846i	$-0.782297\pi$
$318$		0			0
$319$	−15.2942	−	26.4904i	−0.856312	−	1.48318i
$320$		0			0
$321$	−5.25833	+	19.6244i	−0.293491	+	1.09532i
$322$		0			0
$323$			1.03528i			0.0576043i
$324$		0			0
$325$	12.0000	−	2.44949i	0.665640	−	0.135873i
$326$		0			0
$327$	−7.79676	−	2.08913i	−0.431162	−	0.115529i
$328$		0			0
$329$	1.96410	+	3.40192i	0.108284	+	0.187554i
$330$		0			0
$331$	6.19615	−	10.7321i	0.340571	−	0.589887i	−0.643968	−	0.765053i	$-0.722713\pi$
$331$	6.19615	−	10.7321i	0.340571	−	0.589887i	0.984539	+	0.175166i	$0.0560462\pi$
$332$		0			0
$333$	6.36396	−	11.0227i	0.348743	−	0.604040i
$334$		0			0
$335$	−4.07485	−	10.7449i	−0.222633	−	0.587058i
$336$		0			0
$337$	1.55291	−	0.896575i	0.0845926	−	0.0488396i	−0.457107	−	0.889412i	$-0.651114\pi$
$337$	1.55291	−	0.896575i	0.0845926	−	0.0488396i	0.541700	+	0.840572i	$0.317781\pi$
$338$		0			0
$339$	4.26795	−	1.14359i	0.231803	−	0.0621115i
$340$		0			0
$341$	−12.9282			−0.700101
$342$		0			0
$343$		−	11.8313i		−	0.638833i
$344$		0			0
$345$	−0.752011	−	7.44414i	−0.0404869	−	0.400779i
$346$		0			0
$347$	8.57321	−	4.94975i	0.460234	−	0.265716i	−0.251909	−	0.967751i	$-0.581058\pi$
$347$	8.57321	−	4.94975i	0.460234	−	0.265716i	0.712143	+	0.702035i	$0.247725\pi$
$348$		0			0
$349$	10.7679	−	18.6506i	0.576395	−	0.998346i	−0.419493	−	0.907758i	$-0.637792\pi$
$349$	10.7679	−	18.6506i	0.576395	−	0.998346i	0.995889	−	0.0905872i	$-0.0288744\pi$
$350$		0			0
$351$	12.2942	+	3.29423i	0.656217	+	0.175833i
$352$		0			0
$353$	−7.82894	−	4.52004i	−0.416693	−	0.240578i	0.276969	−	0.960879i	$-0.410670\pi$
$353$	−7.82894	−	4.52004i	−0.416693	−	0.240578i	−0.693661	+	0.720301i	$0.744004\pi$
$354$		0			0
$355$	−1.36451	+	8.39550i	−0.0724209	+	0.445587i
$356$		0			0
$357$	0.416102	−	0.416102i	0.0220225	−	0.0220225i
$358$		0			0
$359$	9.80385			0.517427			0.258714	−	0.965954i	$-0.416701\pi$
$359$	9.80385			0.517427			0.258714	+	0.965954i	$0.416701\pi$
$360$		0			0
$361$	−11.5359			−0.607153
$362$		0			0
$363$	5.10703	+	19.0597i	0.268050	+	1.00037i
$364$		0			0
$365$	−18.7279	−	3.04384i	−0.980264	−	0.159322i
$366$		0			0
$367$	21.4770	+	12.3998i	1.12109	+	0.647262i	0.941679	−	0.336512i	$-0.109247\pi$
$367$	21.4770	+	12.3998i	1.12109	+	0.647262i	0.179411	+	0.983774i	$0.442581\pi$
$368$		0			0
$369$		−	12.8038i		−	0.666542i
$370$		0			0
$371$	1.73205	−	3.00000i	0.0899236	−	0.155752i
$372$		0			0
$373$	−27.8410	+	16.0740i	−1.44155	+	0.832280i	−0.997953	−	0.0639468i	$-0.979631\pi$
$373$	−27.8410	+	16.0740i	−1.44155	+	0.832280i	−0.443597	+	0.896226i	$0.646298\pi$
$374$		0			0
$375$	13.1312	−	14.2328i	0.678090	−	0.734979i
$376$		0			0
$377$			15.8338i			0.815480i
$378$		0			0
$379$	12.5359			0.643926			0.321963	−	0.946752i	$-0.395657\pi$
$379$	12.5359			0.643926			0.321963	+	0.946752i	$0.395657\pi$
$380$		0			0
$381$	2.08846	−	7.79423i	0.106995	−	0.399310i
$382$		0			0
$383$	−17.7148	+	10.2277i	−0.905186	+	0.522609i	−0.878879	−	0.477045i	$-0.841708\pi$
$383$	−17.7148	+	10.2277i	−0.905186	+	0.522609i	−0.0263067	+	0.999654i	$0.508375\pi$
$384$		0			0
$385$	−3.36396	−	8.87039i	−0.171443	−	0.452077i
$386$		0			0
$387$	−13.7124	−	23.7506i	−0.697042	−	1.20731i
$388$		0			0
$389$	−12.0622	+	20.8923i	−0.611577	+	1.05928i	0.379398	+	0.925234i	$0.376131\pi$
$389$	−12.0622	+	20.8923i	−0.611577	+	1.05928i	−0.990975	+	0.134048i	$0.957202\pi$
$390$		0			0
$391$	−0.366025	−	0.633975i	−0.0185107	−	0.0320615i
$392$		0			0
$393$	0.416102	+	1.55291i	0.0209896	+	0.0783342i
$394$		0			0
$395$	0.928203	+	0.757875i	0.0467030	+	0.0381328i
$396$		0			0
$397$			29.3939i			1.47524i	0.675218	+	0.737618i	$0.264050\pi$
$397$			29.3939i			1.47524i	−0.675218	+	0.737618i	$0.735950\pi$
$398$		0			0
$399$	−3.00000	−	3.00000i	−0.150188	−	0.150188i
$400$		0			0
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	0.936333	+	0.351115i	$0.114197\pi$
$401$	15.4641	+	26.7846i	0.772240	+	1.33756i	−0.164092	+	0.986445i	$0.552469\pi$
$402$		0			0
$403$	5.79555	+	3.34607i	0.288697	+	0.166679i
$404$		0			0
$405$	18.8169	−	7.13604i	0.935021	−	0.354593i
$406$		0			0
$407$	−17.3867	−	10.0382i	−0.861825	−	0.497575i
$408$		0			0
$409$	−11.7321	−	20.3205i	−0.580113	−	1.00478i	−0.995465	−	0.0951241i	$-0.969675\pi$
$409$	−11.7321	−	20.3205i	−0.580113	−	1.00478i	0.415353	−	0.909660i	$-0.363658\pi$
$410$		0			0
$411$	−22.7321	−	22.7321i	−1.12129	−	1.12129i
$412$		0			0
$413$		−	2.27362i		−	0.111878i
$414$		0			0
$415$	14.7321	−	18.0430i	0.723168	−	0.885696i
$416$		0			0
$417$	−3.58630	−	13.3843i	−0.175622	−	0.655430i
$418$		0			0
$419$	8.02628	+	13.9019i	0.392109	+	0.679153i	0.992728	−	0.120383i	$-0.0384121\pi$
$419$	8.02628	+	13.9019i	0.392109	+	0.679153i	−0.600618	+	0.799536i	$0.705079\pi$
$420$		0			0
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	−0.671887	−	0.740653i	$-0.734516\pi$
$421$	6.26795	−	10.8564i	0.305481	−	0.529109i	0.977368	+	0.211545i	$0.0678494\pi$
$422$		0			0
$423$	6.57201	+	11.3831i	0.319542	+	0.553463i
$424$		0			0
$425$	0.600034	−	1.79716i	0.0291059	−	0.0871753i
$426$		0			0
$427$	−8.27723	+	4.77886i	−0.400563	+	0.231265i
$428$		0			0
$429$	5.19615	−	19.3923i	0.250873	−	0.936269i
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$		0			0
$433$		−	30.5307i		−	1.46721i	−0.679575	−	0.733606i	$-0.737836\pi$
$433$		−	30.5307i		−	1.46721i	0.679575	−	0.733606i	$-0.262164\pi$
$434$		0			0
$435$	14.6335	+	20.3133i	0.701620	+	0.973949i
$436$		0			0
$437$	−4.57081	+	2.63896i	−0.218651	+	0.126239i
$438$		0			0
$439$	−4.66025	+	8.07180i	−0.222422	+	0.385246i	−0.955543	−	0.294852i	$-0.904730\pi$
$439$	−4.66025	+	8.07180i	−0.222422	+	0.385246i	0.733121	+	0.680098i	$0.238063\pi$
$440$		0			0
$441$		−	18.5885i		−	0.885165i
$442$		0			0
$443$	−12.0394	−	6.95095i	−0.572009	−	0.330250i	0.185942	−	0.982561i	$-0.440466\pi$
$443$	−12.0394	−	6.95095i	−0.572009	−	0.330250i	−0.757951	+	0.652311i	$0.773800\pi$
$444$		0			0
$445$	2.65176	−	16.3156i	0.125706	−	0.773434i
$446$		0			0
$447$	−3.46618	−	12.9360i	−0.163945	−	0.611851i
$448$		0			0
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$	−20.1962			−0.951000
$452$		0			0
$453$	27.6651	−	27.6651i	1.29982	−	1.29982i
$454$		0			0
$455$	−0.787803	+	4.84714i	−0.0369328	+	0.227238i
$456$		0			0
$457$	29.9623	+	17.2987i	1.40158	+	0.809201i	0.994554	−	0.104218i	$-0.0332339\pi$
$457$	29.9623	+	17.2987i	1.40158	+	0.809201i	0.407022	+	0.913418i	$0.366567\pi$
$458$		0			0
$459$	1.39230	−	1.39230i	0.0649872	−	0.0649872i
$460$		0			0
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	−0.997358	−	0.0726397i	$-0.976858\pi$
$461$	−9.35641	+	16.2058i	−0.435771	+	0.754778i	0.561587	+	0.827418i	$0.310191\pi$
$462$		0			0
$463$	0.152304	−	0.0879327i	0.00707816	−	0.00408658i	−0.496457	−	0.868061i	$-0.665366\pi$
$463$	0.152304	−	0.0879327i	0.00707816	−	0.00408658i	0.503535	+	0.863975i	$0.332033\pi$
$464$		0			0
$465$	10.5276	−	1.06350i	0.488206	−	0.0493188i
$466$		0			0
$467$		−	5.75839i		−	0.266467i	−0.991085	−	0.133233i	$-0.957464\pi$
$467$		−	5.75839i		−	0.266467i	0.991085	−	0.133233i	$-0.0425359\pi$
$468$		0			0
$469$	4.60770			0.212764
$470$		0			0
$471$	35.7846	−	9.58846i	1.64887	−	0.441813i
$472$		0			0
$473$	−37.4631	+	21.6293i	−1.72255	+	0.994517i
$474$		0			0
$475$	−12.9571	−	4.32611i	−0.594514	−	0.198495i
$476$		0			0
$477$	5.79555	−	10.0382i	0.265360	−	0.459617i
$478$		0			0
$479$	−15.9282	+	27.5885i	−0.727778	+	1.26055i	0.230042	+	0.973181i	$0.426114\pi$
$479$	−15.9282	+	27.5885i	−0.727778	+	1.26055i	−0.957820	+	0.287368i	$0.907220\pi$
$480$		0			0
$481$	5.19615	+	9.00000i	0.236924	+	0.410365i
$482$		0			0
$483$	2.89778	+	0.776457i	0.131853	+	0.0353300i
$484$		0			0
$485$	14.5359	−	17.8028i	0.660041	−	0.808382i
$486$		0			0
$487$		−	1.13681i		−	0.0515139i	−0.999668	−	0.0257569i	$-0.991800\pi$
$487$		−	1.13681i		−	0.0515139i	0.999668	−	0.0257569i	$-0.00819959\pi$
$488$		0			0
$489$	−8.49038	+	31.6865i	−0.383948	+	1.43291i
$490$		0			0
$491$	−10.8564	−	18.8038i	−0.489943	−	0.848606i	0.509990	−	0.860180i	$-0.329649\pi$
$491$	−10.8564	−	18.8038i	−0.489943	−	0.848606i	−0.999933	+	0.0115744i	$0.996316\pi$
$492$		0			0
$493$	2.12132	+	1.22474i	0.0955395	+	0.0551597i
$494$		0			0
$495$	−11.2560	−	29.6809i	−0.505921	−	1.33406i
$496$		0			0
$497$	−2.95352	−	1.70522i	−0.132484	−	0.0764895i
$498$		0			0
$499$	1.92820	+	3.33975i	0.0863182	+	0.149508i	0.905952	−	0.423380i	$-0.139156\pi$
$499$	1.92820	+	3.33975i	0.0863182	+	0.149508i	−0.819634	+	0.572888i	$0.805823\pi$
$500$		0			0
$501$	−28.4545	+	7.62436i	−1.27125	+	0.340631i
$502$		0			0
$503$		−	29.3567i		−	1.30895i	−0.756083	−	0.654476i	$-0.772889\pi$
$503$		−	29.3567i		−	1.30895i	0.756083	−	0.654476i	$-0.227111\pi$
$504$		0			0
$505$	4.39230	+	3.58630i	0.195455	+	0.159588i
$506$		0			0
$507$	8.57321	−	8.57321i	0.380750	−	0.380750i
$508$		0			0
$509$	−5.42820	−	9.40192i	−0.240601	−	0.416733i	0.720285	−	0.693679i	$-0.244011\pi$
$509$	−5.42820	−	9.40192i	−0.240601	−	0.416733i	−0.960886	+	0.276946i	$0.910678\pi$
$510$		0			0
$511$	3.80385	−	6.58846i	0.168272	−	0.291456i
$512$		0			0
$513$	−10.0382	−	10.0382i	−0.443197	−	0.443197i
$514$		0			0
$515$	7.24833	+	19.1130i	0.319400	+	0.842221i
$516$		0			0
$517$	17.9551	−	10.3664i	0.789663	−	0.455912i
$518$		0			0
$519$	−0.928203	−	0.928203i	−0.0407436	−	0.0407436i
$520$		0			0
$521$	1.39230			0.0609980			0.0304990	−	0.999535i	$-0.490290\pi$
$521$	1.39230			0.0609980			0.0304990	+	0.999535i	$0.490290\pi$
$522$		0			0
$523$			30.9468i			1.35321i	0.736347	+	0.676604i	$0.236549\pi$
$523$			30.9468i			1.35321i	−0.736347	+	0.676604i	$0.763451\pi$
$524$		0			0
$525$	3.46902	+	6.94655i	0.151400	+	0.303172i
$526$		0			0
$527$	0.896575	−	0.517638i	0.0390554	−	0.0225487i
$528$		0			0
$529$	−9.63397	+	16.6865i	−0.418868	+	0.725501i
$530$		0			0
$531$		−	7.60770i		−	0.330146i
$532$		0			0
$533$	9.05369	+	5.22715i	0.392159	+	0.226413i
$534$		0			0
$535$	−25.8889	−	4.20771i	−1.11928	−	0.181915i
$536$		0			0
$537$	−41.1373	−	11.0227i	−1.77521	−	0.475665i
$538$		0			0
$539$	−29.3205			−1.26292
$540$		0			0
$541$	21.3923			0.919727			0.459864	−	0.887990i	$-0.347898\pi$
$541$	21.3923			0.919727			0.459864	+	0.887990i	$0.347898\pi$
$542$		0			0
$543$	−14.1607	−	3.79435i	−0.607695	−	0.162831i
$544$		0			0
$545$	1.67172	−	10.2857i	0.0716088	−	0.440590i
$546$		0			0
$547$	26.2323	+	15.1452i	1.12161	+	0.647563i	0.941812	−	0.336140i	$-0.109122\pi$
$547$	26.2323	+	15.1452i	1.12161	+	0.647563i	0.179800	+	0.983703i	$0.442455\pi$
$548$		0			0
$549$	−27.6962	+	15.9904i	−1.18204	+	0.682453i
$550$		0			0
$551$	8.83013	−	15.2942i	0.376176	−	0.651556i
$552$		0			0
$553$	−0.416102	+	0.240237i	−0.0176945	+	0.0102159i
$554$		0			0
$555$	14.9840	+	6.74397i	0.636033	+	0.286265i
$556$		0			0
$557$		−	31.1127i		−	1.31829i	−0.752017	−	0.659144i	$-0.770919\pi$
$557$		−	31.1127i		−	1.31829i	0.752017	−	0.659144i	$-0.229081\pi$
$558$		0			0
$559$	22.3923			0.947094
$560$		0			0
$561$	−2.19615	−	2.19615i	−0.0927216	−	0.0927216i
$562$		0			0
$563$	−23.8707	+	13.7818i	−1.00603	+	0.580833i	−0.910027	−	0.414548i	$-0.863940\pi$
$563$	−23.8707	+	13.7818i	−1.00603	+	0.580833i	−0.0960045	+	0.995381i	$0.530606\pi$
$564$		0			0
$565$	2.02269	+	5.33361i	0.0850952	+	0.224387i
$566$		0			0
$567$			8.06918i			0.338874i
$568$		0			0
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	−0.916385	−	0.400299i	$-0.868906\pi$
$569$	−2.66025	+	4.60770i	−0.111524	+	0.193165i	0.804861	+	0.593463i	$0.202240\pi$
$570$		0			0
$571$	2.73205	+	4.73205i	0.114333	+	0.198030i	0.917513	−	0.397706i	$-0.130194\pi$
$571$	2.73205	+	4.73205i	0.114333	+	0.198030i	−0.803180	+	0.595736i	$0.796860\pi$
$572$		0			0
$573$	−0.416102	+	0.416102i	−0.0173829	+	0.0173829i
$574$		0			0
$575$	9.46410	−	1.93185i	0.394680	−	0.0805638i
$576$		0			0
$577$			28.5617i			1.18904i	0.804082	+	0.594519i	$0.202657\pi$
$577$			28.5617i			1.18904i	−0.804082	+	0.594519i	$0.797343\pi$
$578$		0			0
$579$	−34.6865	+	9.29423i	−1.44152	+	0.386255i
$580$		0			0
$581$	4.66987	+	8.08846i	0.193739	+	0.335566i
$582$		0			0
$583$	−15.8338	−	9.14162i	−0.655767	−	0.378607i
$584$		0			0
$585$	−2.63604	+	16.2189i	−0.108987	+	0.670567i
$586$		0			0
$587$	19.0597	+	11.0041i	0.786678	+	0.454189i	0.838792	−	0.544452i	$-0.183263\pi$
$587$	19.0597	+	11.0041i	0.786678	+	0.454189i	−0.0521138	+	0.998641i	$0.516596\pi$
$588$		0			0
$589$	−3.73205	−	6.46410i	−0.153776	−	0.266349i
$590$		0			0
$591$	−9.33975	+	34.8564i	−0.384186	+	1.43380i
$592$		0			0
$593$			28.9406i			1.18845i	0.804299	+	0.594224i	$0.202541\pi$
$593$			28.9406i			1.18845i	−0.804299	+	0.594224i	$0.797459\pi$
$594$		0			0
$595$	0.588457	+	0.480473i	0.0241244	+	0.0196975i
$596$		0			0
$597$	−7.67664	−	2.05695i	−0.314184	−	0.0841853i
$598$		0			0
$599$	−16.8564	−	29.1962i	−0.688734	−	1.19292i	−0.972248	−	0.233954i	$-0.924833\pi$
$599$	−16.8564	−	29.1962i	−0.688734	−	1.19292i	0.283514	−	0.958968i	$-0.408500\pi$
$600$		0			0
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	−0.640143	−	0.768256i	$-0.721125\pi$
$601$	8.46410	−	14.6603i	0.345258	−	0.598004i	0.985401	+	0.170252i	$0.0544581\pi$
$602$		0			0
$603$	15.4176			0.627855
$604$		0			0
$605$	−23.8187	+	9.03288i	−0.968368	+	0.367239i
$606$		0			0
$607$	−7.55652	+	4.36276i	−0.306710	+	0.177079i	−0.645453	−	0.763800i	$-0.723331\pi$
$607$	−7.55652	+	4.36276i	−0.306710	+	0.177079i	0.338743	+	0.940879i	$0.389998\pi$
$608$		0			0
$609$	−9.69615	+	2.59808i	−0.392908	+	0.105279i
$610$		0			0
$611$	−10.7321			−0.434172
$612$		0			0
$613$			24.3190i			0.982236i	0.871093	+	0.491118i	$0.163412\pi$
$613$			24.3190i			0.982236i	−0.871093	+	0.491118i	$0.836588\pi$
$614$		0			0
$615$	16.4460	−	1.66138i	0.663166	−	0.0669934i
$616$		0			0
$617$	11.3509	−	6.55343i	0.456969	−	0.263831i	−0.253800	−	0.967257i	$-0.581680\pi$
$617$	11.3509	−	6.55343i	0.456969	−	0.263831i	0.710769	+	0.703426i	$0.248347\pi$
$618$		0			0
$619$	−9.90192	+	17.1506i	−0.397992	+	0.689342i	−0.993478	−	0.114023i	$-0.963626\pi$
$619$	−9.90192	+	17.1506i	−0.397992	+	0.689342i	0.595486	+	0.803366i	$0.296959\pi$
$620$		0			0
$621$	9.69615	+	2.59808i	0.389093	+	0.104257i
$622$		0			0
$623$	5.73981	+	3.31388i	0.229961	+	0.132768i
$624$		0			0
$625$	19.9853	+	15.0196i	0.799411	+	0.600784i
$626$		0			0
$627$	−15.8338	+	15.8338i	−0.632339	+	0.632339i
$628$		0			0
$629$	1.60770			0.0641030
$630$		0			0
$631$	33.3205			1.32647			0.663234	−	0.748412i	$-0.269183\pi$
$631$	33.3205			1.32647			0.663234	+	0.748412i	$0.269183\pi$
$632$		0			0
$633$	5.88349	+	21.9575i	0.233848	+	0.872731i
$634$		0			0
$635$	10.2823	+	1.67118i	0.408042	+	0.0663188i
$636$		0			0
$637$	13.1440	+	7.58871i	0.520785	+	0.300675i
$638$		0			0
$639$	−9.88269	−	5.70577i	−0.390953	−	0.225717i
$640$		0			0
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	−0.505223	−	0.862989i	$-0.668590\pi$
$641$	12.5263	−	21.6962i	0.494758	−	0.856946i	0.999982	+	0.00604207i	$0.00192326\pi$
$642$		0			0
$643$	21.8374	−	12.6078i	0.861181	−	0.497203i	−0.00322641	−	0.999995i	$-0.501027\pi$
$643$	21.8374	−	12.6078i	0.861181	−	0.497203i	0.864408	+	0.502792i	$0.167694\pi$
$644$		0			0
$645$	28.7274	−	20.6948i	1.13114	−	0.814858i
$646$		0			0
$647$		−	12.3861i		−	0.486950i	−0.969907	−	0.243475i	$-0.921713\pi$
$647$		−	12.3861i		−	0.486950i	0.969907	−	0.243475i	$-0.0782873\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$		0			0
$651$	−1.09808	+	4.09808i	−0.0430370	+	0.160616i
$652$		0			0
$653$	−0.392541	+	0.226633i	−0.0153613	+	0.00886885i	−0.507661	−	0.861557i	$-0.669490\pi$
$653$	−0.392541	+	0.226633i	−0.0153613	+	0.00886885i	0.492300	+	0.870426i	$0.336156\pi$
$654$		0			0
$655$	−1.94066	+	0.735966i	−0.0758279	+	0.0287566i
$656$		0			0
$657$	12.7279	−	22.0454i	0.496564	−	0.860073i
$658$		0			0
$659$	−18.1244	+	31.3923i	−0.706025	+	1.22287i	0.260296	+	0.965529i	$0.416180\pi$
$659$	−18.1244	+	31.3923i	−0.706025	+	1.22287i	−0.966320	+	0.257342i	$0.917153\pi$
$660$		0			0
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	0.993015	+	0.117992i	$0.0376457\pi$
$661$	15.3923	+	26.6603i	0.598691	+	1.03696i	−0.394323	+	0.918972i	$0.629021\pi$
$662$		0			0
$663$	0.416102	+	1.55291i	0.0161601	+	0.0603102i
$664$		0			0
$665$	3.46410	−	4.24264i	0.134332	−	0.164523i
$666$		0			0
$667$			12.4877i			0.483525i
$668$		0			0
$669$	−20.4904	−	20.4904i	−0.792204	−	0.792204i
$670$		0			0
$671$	25.2224	+	43.6865i	0.973701	+	1.68650i
$672$		0			0
$673$	−1.40061	−	0.808643i	−0.0539896	−	0.0311709i	0.472762	−	0.881190i	$-0.343257\pi$
$673$	−1.40061	−	0.808643i	−0.0539896	−	0.0311709i	−0.526752	+	0.850019i	$0.676590\pi$
$674$		0			0
$675$	11.6076	+	23.2436i	0.446775	+	0.894646i
$676$		0			0
$677$	28.6496	+	16.5409i	1.10109	+	0.635717i	0.936508	−	0.350646i	$-0.114038\pi$
$677$	28.6496	+	16.5409i	1.10109	+	0.635717i	0.164586	+	0.986363i	$0.447371\pi$
$678$		0			0
$679$	4.60770	+	7.98076i	0.176827	+	0.306274i
$680$		0			0
$681$	2.32051	+	2.32051i	0.0889221	+	0.0889221i
$682$		0			0
$683$			19.6975i			0.753702i	0.926274	+	0.376851i	$0.122993\pi$
$683$			19.6975i			0.753702i	−0.926274	+	0.376851i	$0.877007\pi$
$684$		0			0
$685$	26.2487	−	32.1480i	1.00291	−	1.22831i
$686$		0			0
$687$	−8.93357	−	33.3405i	−0.340837	−	1.27202i
$688$		0			0
$689$	4.73205	+	8.19615i	0.180277	+	0.312249i
$690$		0			0
$691$	10.1244	−	17.5359i	0.385149	−	0.667097i	−0.606641	−	0.794976i	$-0.707484\pi$
$691$	10.1244	−	17.5359i	0.385149	−	0.667097i	0.991790	+	0.127879i	$0.0408168\pi$
$692$		0			0
$693$	12.7279			0.483494
$694$		0			0
$695$	16.7262	−	6.34315i	0.634459	−	0.240609i
$696$		0			0
$697$	1.40061	−	0.808643i	0.0530519	−	0.0306295i
$698$		0			0
$699$	3.16987	−	11.8301i	0.119896	−	0.447456i
$700$		0			0
$701$	−23.1962			−0.876107			−0.438053	−	0.898949i	$-0.644332\pi$
$701$	−23.1962			−0.876107			−0.438053	+	0.898949i	$0.644332\pi$
$702$		0			0
$703$		−	11.5911i		−	0.437167i
$704$		0			0
$705$	−13.7683	+	9.91849i	−0.518544	+	0.373552i
$706$		0			0
$707$	−1.96902	+	1.13681i	−0.0740525	+	0.0427542i
$708$		0			0
$709$	−15.8923	+	27.5263i	−0.596848	+	1.03377i	0.396435	+	0.918063i	$0.370247\pi$
$709$	−15.8923	+	27.5263i	−0.596848	+	1.03377i	−0.993283	+	0.115708i	$0.963086\pi$
$710$		0			0
$711$	−1.39230	+	0.803848i	−0.0522155	+	0.0301466i
$712$		0			0
$713$	4.57081	+	2.63896i	0.171178	+	0.0988298i
$714$		0			0
$715$	25.5828	+	4.15796i	0.956743	+	0.155499i
$716$		0			0
$717$	5.79555	+	21.6293i	0.216439	+	0.807761i
$718$		0			0
$719$	19.6077			0.731244			0.365622	−	0.930763i	$-0.380856\pi$
$719$	19.6077			0.731244			0.365622	+	0.930763i	$0.380856\pi$
$720$		0			0
$721$	−8.19615			−0.305241
$722$		0			0
$723$	7.67664	−	7.67664i	0.285497	−	0.285497i
$724$		0			0
$725$	−24.1928	+	21.4318i	−0.898498	+	0.795958i
$726$		0			0
$727$	24.5271	+	14.1607i	0.909659	+	0.525192i	0.880321	−	0.474378i	$-0.157327\pi$
$727$	24.5271	+	14.1607i	0.909659	+	0.525192i	0.0293377	+	0.999570i	$0.490660\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	1.73205	−	3.00000i	0.0640622	−	0.110959i
$732$		0			0
$733$	−35.9101	+	20.7327i	−1.32637	+	0.765781i	−0.984736	−	0.174052i	$-0.944314\pi$
$733$	−35.9101	+	20.7327i	−1.32637	+	0.765781i	−0.341635	+	0.939833i	$0.610981\pi$
$734$		0			0
$735$	23.8761	−	2.41197i	0.880682	−	0.0889670i
$736$		0			0
$737$		−	24.3190i		−	0.895803i
$738$		0			0
$739$	−45.8564			−1.68686			−0.843428	−	0.537243i	$-0.819466\pi$
$739$	−45.8564			−1.68686			−0.843428	+	0.537243i	$0.819466\pi$
$740$		0			0
$741$	11.1962	−	3.00000i	0.411301	−	0.110208i
$742$		0			0
$743$	21.9253	−	12.6586i	0.804361	−	0.464398i	−0.0406329	−	0.999174i	$-0.512937\pi$
$743$	21.9253	−	12.6586i	0.804361	−	0.464398i	0.844994	+	0.534776i	$0.179604\pi$
$744$		0			0
$745$	16.1659	−	6.13069i	0.592274	−	0.224611i
$746$		0			0
$747$	15.6257	+	27.0645i	0.571714	+	0.990238i
$748$		0			0
$749$	5.25833	−	9.10770i	0.192135	−	0.332788i
$750$		0			0
$751$	17.2224	+	29.8301i	0.628455	+	1.08852i	0.987862	+	0.155336i	$0.0496459\pi$
$751$	17.2224	+	29.8301i	0.628455	+	1.08852i	−0.359406	+	0.933181i	$0.617021\pi$
$752$		0			0
$753$	31.0991	+	8.33298i	1.13331	+	0.303671i
$754$		0			0
$755$	39.1244	+	31.9449i	1.42388	+	1.16259i
$756$		0			0
$757$			7.34847i			0.267085i	0.991043	+	0.133542i	$0.0426352\pi$
$757$			7.34847i			0.267085i	−0.991043	+	0.133542i	$0.957365\pi$
$758$		0			0
$759$	4.09808	−	15.2942i	0.148751	−	0.555145i
$760$		0			0
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	0.846639	−	0.532168i	$-0.178622\pi$
$761$	−1.03590	−	1.79423i	−0.0375513	−	0.0650407i	−0.884190	+	0.467127i	$0.845289\pi$
$762$		0			0
$763$	3.61849	+	2.08913i	0.130998	+	0.0756318i
$764$		0			0
$765$	1.96902	+	1.60770i	0.0711899	+	0.0581263i
$766$		0			0
$767$	5.37945	+	3.10583i	0.194241	+	0.112145i
$768$		0			0
$769$	−13.8205	−	23.9378i	−0.498380	−	0.863220i	0.501618	−	0.865089i	$-0.332738\pi$
$769$	−13.8205	−	23.9378i	−0.498380	−	0.863220i	−0.999998	+	0.00186930i	$0.999405\pi$
$770$		0			0
$771$	−37.5167	+	10.0526i	−1.35113	+	0.362034i
$772$		0			0
$773$			7.72741i			0.277935i	0.990297	+	0.138968i	$0.0443784\pi$
$773$			7.72741i			0.277935i	−0.990297	+	0.138968i	$0.955622\pi$
$774$		0			0
$775$	2.73205	+	13.3843i	0.0981382	+	0.480777i
$776$		0			0
$777$	−4.65874	+	4.65874i	−0.167131	+	0.167131i
$778$		0			0
$779$	−5.83013	−	10.0981i	−0.208886	−	0.361801i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$		0			0
$783$	−32.4440	+	8.69333i	−1.15945	+	0.310674i
$784$		0			0
$785$	16.9592	+	44.7196i	0.605302	+	1.59611i
$786$		0			0
$787$	14.1285	−	8.15711i	0.503628	−	0.290770i	−0.226583	−	0.973992i	$-0.572755\pi$
$787$	14.1285	−	8.15711i	0.503628	−	0.290770i	0.730210	+	0.683222i	$0.239422\pi$
$788$		0			0
$789$	9.33975	+	9.33975i	0.332504	+	0.332504i
$790$		0			0
$791$	−2.28719			−0.0813230
$792$		0			0
$793$		−	26.1122i		−	0.927271i
$794$		0			0
$795$	13.6456	+	6.14162i	0.483961	+	0.217821i
$796$		0			0
$797$	13.7768	−	7.95404i	0.487999	−	0.281747i	−0.235745	−	0.971815i	$-0.575753\pi$
$797$	13.7768	−	7.95404i	0.487999	−	0.281747i	0.723744	+	0.690068i	$0.242420\pi$
$798$		0			0
$799$	−0.830127	+	1.43782i	−0.0293678	+	0.0508665i
$800$		0			0
$801$	19.2058	+	11.0885i	0.678603	+	0.391791i
$802$		0			0
$803$	−34.7733	−	20.0764i	−1.22712	−	0.708480i
$804$		0			0
$805$	−0.621320	+	3.82282i	−0.0218987	+	0.134737i
$806$		0			0
$807$	28.7697	+	7.70882i	1.01274	+	0.271363i
$808$		0			0
$809$	−37.1769			−1.30707			−0.653535	−	0.756896i	$-0.726715\pi$
$809$	−37.1769			−1.30707			−0.653535	+	0.756896i	$0.726715\pi$
$810$		0			0
$811$	−43.5692			−1.52992			−0.764961	−	0.644076i	$-0.777242\pi$
$811$	−43.5692			−1.52992			−0.764961	+	0.644076i	$0.777242\pi$
$812$		0			0
$813$	−39.3441	−	10.5422i	−1.37986	−	0.369732i
$814$		0			0
$815$	−41.8017	−	6.79400i	−1.46425	−	0.237983i
$816$		0			0
$817$	−21.6293	−	12.4877i	−0.756714	−	0.436889i
$818$		0			0
$819$	−5.70577	−	3.29423i	−0.199376	−	0.115110i
$820$		0			0
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	−0.486055	−	0.873928i	$-0.661565\pi$
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	0.999872	−	0.0160280i	$-0.00510208\pi$
$822$		0			0
$823$	1.76097	−	1.01669i	0.0613834	−	0.0354397i	−0.468994	−	0.883201i	$-0.655383\pi$
$823$	1.76097	−	1.01669i	0.0613834	−	0.0354397i	0.530378	+	0.847762i	$0.322050\pi$
$824$		0			0
$825$	36.6633	−	18.3092i	1.27645	−	0.637444i
$826$		0			0
$827$		−	11.5539i		−	0.401770i	−0.979615	−	0.200885i	$-0.935618\pi$
$827$		−	11.5539i		−	0.401770i	0.979615	−	0.200885i	$-0.0643818\pi$
$828$		0			0
$829$	−31.5885			−1.09711			−0.548556	−	0.836114i	$-0.684822\pi$
$829$	−31.5885			−1.09711			−0.548556	+	0.836114i	$0.684822\pi$
$830$		0			0
$831$	−15.0000	−	15.0000i	−0.520344	−	0.520344i
$832$		0			0
$833$	2.03339	−	1.17398i	0.0704527	−	0.0406759i
$834$		0			0
$835$	−13.4853	−	35.5593i	−0.466678	−	1.23058i
$836$		0			0
$837$	−3.67423	+	13.7124i	−0.127000	+	0.473971i
$838$		0			0
$839$	−0.633975	+	1.09808i	−0.0218872	+	0.0379098i	−0.876762	−	0.480925i	$-0.840301\pi$
$839$	−0.633975	+	1.09808i	−0.0218872	+	0.0379098i	0.854874	+	0.518835i	$0.173634\pi$
$840$		0			0
$841$	−6.39230	−	11.0718i	−0.220424	−	0.381786i
$842$		0			0
$843$	−19.9241	+	19.9241i	−0.686222	+	0.686222i
$844$		0			0
$845$	12.1244	+	9.89949i	0.417091	+	0.340553i
$846$		0			0
$847$		−	10.2141i		−	0.350959i
$848$		0			0
$849$	7.50000	−	2.00962i	0.257399	−	0.0689699i
$850$		0			0
$851$	4.09808	+	7.09808i	0.140480	+	0.243319i
$852$		0			0
$853$	−30.2669	−	17.4746i	−1.03632	−	0.598319i	−0.117530	−	0.993069i	$-0.537498\pi$
$853$	−30.2669	−	17.4746i	−1.03632	−	0.598319i	−0.918788	+	0.394750i	$0.870831\pi$
$854$		0			0
$855$	11.5911	−	14.1962i	0.396408	−	0.485498i
$856$		0			0
$857$	−7.67664	−	4.43211i	−0.262229	−	0.151398i	0.363122	−	0.931742i	$-0.381711\pi$
$857$	−7.67664	−	4.43211i	−0.262229	−	0.151398i	−0.625351	+	0.780344i	$0.715044\pi$
$858$		0			0
$859$	11.2224	+	19.4378i	0.382904	+	0.663210i	0.991476	−	0.130289i	$-0.0415905\pi$
$859$	11.2224	+	19.4378i	0.382904	+	0.663210i	−0.608572	+	0.793499i	$0.708257\pi$
$860$		0			0
$861$	−1.71539	+	6.40192i	−0.0584603	+	0.218177i
$862$		0			0
$863$			13.0697i			0.444898i	0.974944	+	0.222449i	$0.0714050\pi$
$863$			13.0697i			0.444898i	−0.974944	+	0.222449i	$0.928595\pi$
$864$		0			0
$865$	1.07180	−	1.31268i	0.0364422	−	0.0446324i
$866$		0			0
$867$	−28.2013	−	7.55652i	−0.957767	−	0.256633i
$868$		0			0
$869$	1.26795	+	2.19615i	0.0430122	+	0.0744994i
$870$		0			0
$871$	−6.29423	+	10.9019i	−0.213272	+	0.369398i
$872$		0			0
$873$	15.4176	+	26.7042i	0.521808	+	0.903799i
$874$		0			0
$875$	−8.47241	+	5.35716i	−0.286420	+	0.181105i
$876$		0			0
$877$	−4.09034	+	2.36156i	−0.138121	+	0.0797441i	−0.567468	−	0.823395i	$-0.692077\pi$
$877$	−4.09034	+	2.36156i	−0.138121	+	0.0797441i	0.429347	+	0.903139i	$0.358744\pi$
$878$		0			0
$879$	−14.8301	+	3.97372i	−0.500208	+	0.134030i
$880$		0			0
$881$	−8.41154			−0.283392			−0.141696	−	0.989910i	$-0.545256\pi$
$881$	−8.41154			−0.283392			−0.141696	+	0.989910i	$0.545256\pi$
$882$		0			0
$883$			17.6913i			0.595359i	0.954666	+	0.297679i	$0.0962126\pi$
$883$			17.6913i			0.595359i	−0.954666	+	0.297679i	$0.903787\pi$
$884$		0			0
$885$	9.77176	−	0.987148i	0.328474	−	0.0331826i
$886$		0			0
$887$	24.4070	−	14.0914i	0.819506	−	0.473142i	−0.0307403	−	0.999527i	$-0.509786\pi$
$887$	24.4070	−	14.0914i	0.819506	−	0.473142i	0.850246	+	0.526386i	$0.176453\pi$
$888$		0			0
$889$	−2.08846	+	3.61731i	−0.0700446	+	0.121321i
$890$		0			0
$891$	42.5885			1.42677
$892$		0			0
$893$	10.3664	+	5.98502i	0.346897	+	0.200281i
$894$		0			0
$895$	8.82036	−	54.2694i	0.294832	−	1.81402i
$896$		0			0
$897$	−5.79555	+	5.79555i	−0.193508	+	0.193508i
$898$		0			0
$899$	−17.6603			−0.589002
$900$		0			0
$901$	1.46410			0.0487763
$902$		0			0
$903$	3.67423	+	13.7124i	0.122271	+	0.456321i
$904$		0			0
$905$	3.03624	−	18.6812i	0.100928	−	0.620983i
$906$		0			0
$907$	−43.0506	−	24.8553i	−1.42947	−	0.825305i	−0.432392	−	0.901686i	$-0.642330\pi$
$907$	−43.0506	−	24.8553i	−1.42947	−	0.825305i	−0.997079	+	0.0763808i	$0.975664\pi$
$908$		0			0
$909$	−6.58846	+	3.80385i	−0.218525	+	0.126166i
$910$		0			0
$911$	11.0718	−	19.1769i	0.366825	−	0.635360i	−0.622242	−	0.782825i	$-0.713778\pi$
$911$	11.0718	−	19.1769i	0.366825	−	0.635360i	0.989067	+	0.147465i	$0.0471114\pi$
$912$		0			0
$913$	42.6902	−	24.6472i	1.41284	−	0.815703i
$914$		0			0
$915$	−24.1327	−	33.4997i	−0.797803	−	1.10746i
$916$		0			0
$917$		−	0.832204i		−	0.0274818i
$918$		0			0
$919$	−15.1769			−0.500640			−0.250320	−	0.968163i	$-0.580536\pi$
$919$	−15.1769			−0.500640			−0.250320	+	0.968163i	$0.580536\pi$
$920$		0			0
$921$	11.5981	−	43.2846i	0.382170	−	1.42628i
$922$		0			0
$923$	8.06918	−	4.65874i	0.265600	−	0.153344i
$924$		0			0
$925$	−6.71807	+	20.1213i	−0.220889	+	0.661585i
$926$		0			0
$927$	−27.4249			−0.900751
$928$		0			0
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	−0.836213	−	0.548405i	$-0.815235\pi$
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	0.893039	+	0.449979i	$0.148568\pi$
$930$		0			0
$931$	−8.46410	−	14.6603i	−0.277400	−	0.480470i
$932$		0			0
$933$	−12.5756	−	46.9328i	−0.411707	−	1.53651i
$934$		0			0
$935$	2.53590	−	3.10583i	0.0829327	−	0.101571i
$936$		0			0
$937$		−	13.8647i		−	0.452941i	−0.974018	−	0.226471i	$-0.927281\pi$
$937$		−	13.8647i		−	0.452941i	0.974018	−	0.226471i	$-0.0727187\pi$
$938$		0			0
$939$	6.80385	+	6.80385i	0.222035	+	0.222035i
$940$		0			0
$941$	4.16025	+	7.20577i	0.135620	+	0.234901i	0.925834	−	0.377930i	$-0.123364\pi$
$941$	4.16025	+	7.20577i	0.135620	+	0.234901i	−0.790214	+	0.612831i	$0.790031\pi$
$942$		0			0
$943$	7.14042	+	4.12252i	0.232524	+	0.134248i
$944$		0			0
$945$	−10.3645	+	1.04703i	−0.337158	+	0.0340598i
$946$		0			0
$947$	−2.00120	−	1.15539i	−0.0650303	−	0.0375453i	0.467132	−	0.884187i	$-0.345287\pi$
$947$	−2.00120	−	1.15539i	−0.0650303	−	0.0375453i	−0.532163	+	0.846642i	$0.678621\pi$
$948$		0			0
$949$	10.3923	+	18.0000i	0.337348	+	0.584305i
$950$		0			0
$951$	43.0526	+	43.0526i	1.39607	+	1.39607i
$952$		0			0
$953$		−	37.0197i		−	1.19919i	−0.800305	−	0.599594i	$-0.795329\pi$
$953$		−	37.0197i		−	1.19919i	0.800305	−	0.599594i	$-0.204671\pi$
$954$		0			0
$955$	−0.588457	−	0.480473i	−0.0190420	−	0.0155478i
$956$		0			0
$957$	13.7124	+	51.1755i	0.443260	+	1.65427i
$958$		0			0
$959$	8.32051	+	14.4115i	0.268683	+	0.465373i
$960$		0			0
$961$	11.7679	−	20.3827i	0.379611	−	0.657506i
$962$		0			0
$963$	17.5947	−	30.4749i	0.566982	−	0.982041i
$964$		0			0
$965$	−16.4388	−	43.3474i	−0.529185	−	1.39540i
$966$		0			0
$967$	−30.0588	+	17.3545i	−0.966627	+	0.558082i	−0.898206	−	0.439574i	$-0.855129\pi$
$967$	−30.0588	+	17.3545i	−0.966627	+	0.558082i	−0.0684208	+	0.997657i	$0.521796\pi$
$968$		0			0
$969$	0.464102	−	1.73205i	0.0149091	−	0.0556415i
$970$		0			0
$971$	−27.8038			−0.892268			−0.446134	−	0.894966i	$-0.647200\pi$
$971$	−27.8038			−0.892268			−0.446134	+	0.894966i	$0.647200\pi$
$972$		0			0
$973$			7.17260i			0.229943i
$974$		0			0
$975$	−21.1745	−	1.28138i	−0.678126	−	0.0410369i
$976$		0			0
$977$	13.4722	−	7.77817i	0.431014	−	0.248846i	−0.268765	−	0.963206i	$-0.586615\pi$
$977$	13.4722	−	7.77817i	0.431014	−	0.248846i	0.699778	+	0.714360i	$0.253282\pi$
$978$		0			0
$979$	17.4904	−	30.2942i	0.558995	−	0.968208i
$980$		0			0
$981$	12.1077	+	6.99038i	0.386569	+	0.223186i
$982$		0			0
$983$	31.0669	+	17.9365i	0.990881	+	0.572085i	0.905537	−	0.424266i	$-0.139468\pi$
$983$	31.0669	+	17.9365i	0.990881	+	0.572085i	0.0853431	+	0.996352i	$0.472801\pi$
$984$		0			0
$985$	−45.9834	−	7.47366i	−1.46515	−	0.238131i
$986$		0			0
$987$	−1.76097	−	6.57201i	−0.0560521	−	0.209189i
$988$		0			0
$989$	17.6603			0.561563
$990$		0			0
$991$	−25.0718			−0.796432			−0.398216	−	0.917292i	$-0.630371\pi$
$991$	−25.0718			−0.796432			−0.398216	+	0.917292i	$0.630371\pi$
$992$		0			0
$993$	−15.1774	+	15.1774i	−0.481641	+	0.481641i
$994$		0			0
$995$	1.64597	−	10.1272i	0.0521807	−	0.321054i
$996$		0			0
$997$	−13.1440	−	7.58871i	−0.416275	−	0.240337i	0.277207	−	0.960810i	$-0.410591\pi$
$997$	−13.1440	−	7.58871i	−0.416275	−	0.240337i	−0.693483	+	0.720473i	$0.743925\pi$
$998$		0			0
$999$	−15.5885	+	15.5885i	−0.493197	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.by.d.529.1		8
3.2	odd	2		2160.2.by.c.289.2		8
4.3	odd	2		45.2.j.a.34.1	yes	8
5.4	even	2	inner	720.2.by.d.529.4		8
9.4	even	3	inner	720.2.by.d.49.4		8
9.5	odd	6		2160.2.by.c.1009.4		8
12.11	even	2		135.2.j.a.19.4		8
15.14	odd	2		2160.2.by.c.289.4		8
20.3	even	4		225.2.e.d.151.1		8
20.7	even	4		225.2.e.d.151.4		8
20.19	odd	2		45.2.j.a.34.4	yes	8
36.7	odd	6		405.2.b.d.244.4		4
36.11	even	6		405.2.b.c.244.1		4
36.23	even	6		135.2.j.a.64.1		8
36.31	odd	6		45.2.j.a.4.4	yes	8
45.4	even	6	inner	720.2.by.d.49.1		8
45.14	odd	6		2160.2.by.c.1009.2		8
60.23	odd	4		675.2.e.d.451.4		8
60.47	odd	4		675.2.e.d.451.1		8
60.59	even	2		135.2.j.a.19.1		8
180.7	even	12		2025.2.a.t.1.1		4
180.23	odd	12		675.2.e.d.226.4		8
180.43	even	12		2025.2.a.t.1.4		4
180.47	odd	12		2025.2.a.r.1.4		4
180.59	even	6		135.2.j.a.64.4		8
180.67	even	12		225.2.e.d.76.4		8
180.79	odd	6		405.2.b.d.244.1		4
180.83	odd	12		2025.2.a.r.1.1		4
180.103	even	12		225.2.e.d.76.1		8
180.119	even	6		405.2.b.c.244.4		4
180.139	odd	6		45.2.j.a.4.1	✓	8
180.167	odd	12		675.2.e.d.226.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	180.139	odd	6
45.2.j.a.4.4	yes	8	36.31	odd	6
45.2.j.a.34.1	yes	8	4.3	odd	2
45.2.j.a.34.4	yes	8	20.19	odd	2
135.2.j.a.19.1		8	60.59	even	2
135.2.j.a.19.4		8	12.11	even	2
135.2.j.a.64.1		8	36.23	even	6
135.2.j.a.64.4		8	180.59	even	6
225.2.e.d.76.1		8	180.103	even	12
225.2.e.d.76.4		8	180.67	even	12
225.2.e.d.151.1		8	20.3	even	4
225.2.e.d.151.4		8	20.7	even	4
405.2.b.c.244.1		4	36.11	even	6
405.2.b.c.244.4		4	180.119	even	6
405.2.b.d.244.1		4	180.79	odd	6
405.2.b.d.244.4		4	36.7	odd	6
675.2.e.d.226.1		8	180.167	odd	12
675.2.e.d.226.4		8	180.23	odd	12
675.2.e.d.451.1		8	60.47	odd	4
675.2.e.d.451.4		8	60.23	odd	4
720.2.by.d.49.1		8	45.4	even	6	inner
720.2.by.d.49.4		8	9.4	even	3	inner
720.2.by.d.529.1		8	1.1	even	1	trivial
720.2.by.d.529.4		8	5.4	even	2	inner
2025.2.a.r.1.1		4	180.83	odd	12
2025.2.a.r.1.4		4	180.47	odd	12
2025.2.a.t.1.1		4	180.7	even	12
2025.2.a.t.1.4		4	180.43	even	12
2160.2.by.c.289.2		8	3.2	odd	2
2160.2.by.c.289.4		8	15.14	odd	2
2160.2.by.c.1009.2		8	45.14	odd	6
2160.2.by.c.1009.4		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67303 - 0.448288i) q^{3} +(0.358719 - 2.20711i) q^{5} +(0.776457 + 0.448288i) q^{7} +(2.59808 + 1.50000i) q^{9} +(2.36603 - 4.09808i) q^{11} +(-2.12132 + 1.22474i) q^{13} +(-1.58957 + 3.53175i) q^{15} +0.378937i q^{17} +2.73205 q^{19} +(-1.09808 - 1.09808i) q^{21} +(-1.67303 + 0.965926i) q^{23} +(-4.74264 - 1.58346i) q^{25} +(-3.67423 - 3.67423i) q^{27} +(3.23205 - 5.59808i) q^{29} +(-1.36603 - 2.36603i) q^{31} +(-5.79555 + 5.79555i) q^{33} +(1.26795 - 1.55291i) q^{35} -4.24264i q^{37} +(4.09808 - 1.09808i) q^{39} +(-2.13397 - 3.69615i) q^{41} +(-7.91688 - 4.57081i) q^{43} +(4.24264 - 5.19615i) q^{45} +(3.79435 + 2.19067i) q^{47} +(-3.09808 - 5.36603i) q^{49} +(0.169873 - 0.633975i) q^{51} -3.86370i q^{53} +(-8.19615 - 6.69213i) q^{55} +(-4.57081 - 1.22474i) q^{57} +(-1.26795 - 2.19615i) q^{59} +(-5.33013 + 9.23205i) q^{61} +(1.34486 + 2.32937i) q^{63} +(1.94218 + 5.12132i) q^{65} +(4.45069 - 2.56961i) q^{67} +(3.23205 - 0.866025i) q^{69} -3.80385 q^{71} -8.48528i q^{73} +(7.22474 + 4.77526i) q^{75} +(3.67423 - 2.12132i) q^{77} +(-0.267949 + 0.464102i) q^{79} +(4.50000 + 7.79423i) q^{81} +(9.02150 + 5.20857i) q^{83} +(0.836355 + 0.135932i) q^{85} +(-7.91688 + 7.91688i) q^{87} +7.39230 q^{89} -2.19615 q^{91} +(1.22474 + 4.57081i) q^{93} +(0.980040 - 6.02993i) q^{95} +(8.90138 + 5.13922i) q^{97} +(12.2942 - 7.09808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{11} - 12 q^{15} + 8 q^{19} + 12 q^{21} - 4 q^{25} + 12 q^{29} - 4 q^{31} + 24 q^{35} + 12 q^{39} - 24 q^{41} - 4 q^{49} + 36 q^{51} - 24 q^{55} - 24 q^{59} - 8 q^{61} + 12 q^{69} - 72 q^{71}+ \cdots + 36 q^{99}+O(q^{100}) \) 8 * q + 12 * q^11 - 12 * q^15 + 8 * q^19 + 12 * q^21 - 4 * q^25 + 12 * q^29 - 4 * q^31 + 24 * q^35 + 12 * q^39 - 24 * q^41 - 4 * q^49 + 36 * q^51 - 24 * q^55 - 24 * q^59 - 8 * q^61 + 12 * q^69 - 72 * q^71 + 48 * q^75 - 16 * q^79 + 36 * q^81 + 16 * q^85 - 24 * q^89 + 24 * q^91 - 12 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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