LMFDB - Embedded newform 1890.2.r.a.1529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(89,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 5]))

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

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

chi := DirichletCharacter("1890.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.r (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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1529.3
Character	$\chi$	$=$	1890.1529
Dual form			1890.2.r.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 + 0.435950i) q^{5} +(2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 + 0.435950i) q^{5} +(2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(0.719036 - 2.11731i) q^{10} +4.12106i q^{11} +(-1.18566 + 2.05363i) q^{13} +(-1.33402 + 2.28482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.28111 - 1.31700i) q^{17} +(0.956982 - 0.552514i) q^{19} +(1.47412 + 1.68136i) q^{20} +(-3.56894 - 2.06053i) q^{22} +0.592478 q^{23} +(4.61990 - 1.91221i) q^{25} +(-1.18566 - 2.05363i) q^{26} +(-1.31170 - 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} +(2.33615 - 1.34878i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.28111 - 1.31700i) q^{34} +(-5.80810 + 1.12513i) q^{35} +(6.05512 - 3.49593i) q^{37} +1.10503i q^{38} +(-2.19316 + 0.435950i) q^{40} +(0.257087 - 0.445287i) q^{41} +(-10.4023 + 6.00577i) q^{43} +(3.56894 - 2.06053i) q^{44} +(-0.296239 + 0.513101i) q^{46} +(-3.57645 - 2.06487i) q^{47} +(6.99967 + 0.0682042i) q^{49} +(-0.653922 + 4.95705i) q^{50} +2.37133 q^{52} +(-4.54406 + 7.87055i) q^{53} +(-1.79657 - 9.03814i) q^{55} +(2.64572 + 0.0128895i) q^{56} -2.73609i q^{58} +(3.46974 + 6.00977i) q^{59} +(3.71806 + 2.14662i) q^{61} +2.69755i q^{62} +1.00000 q^{64} +(1.70507 - 5.02083i) q^{65} +(-11.7043 + 6.75750i) q^{67} +2.63400i q^{68} +(1.92966 - 5.59253i) q^{70} +1.60164i q^{71} +(-3.29147 + 5.70100i) q^{73} +6.99185i q^{74} +(-0.956982 - 0.552514i) q^{76} +(-0.0531186 + 10.9032i) q^{77} +(-6.72172 + 11.6424i) q^{79} +(0.719036 - 2.11731i) q^{80} +(0.257087 + 0.445287i) q^{82} +(-3.80374 + 2.19609i) q^{83} +(5.57698 + 1.89394i) q^{85} -12.0115i q^{86} +4.12106i q^{88} +(-7.82648 - 13.5559i) q^{89} +(-3.16341 + 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} +(3.57645 - 2.06487i) q^{94} +(-1.85794 + 1.62895i) q^{95} +(-6.92406 - 11.9928i) q^{97} +(-3.55890 + 6.02779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8	$ 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} - 3 q^{14} - 24 q^{16} - 6 q^{22} - 6 q^{23} + 3 q^{28} + 3 q^{29} - 24 q^{32} - 12 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} - 42 q^{55} - 9 q^{61} + 48 q^{64} + 21 q^{65} + 33 q^{67} + 12 q^{70} - 18 q^{73} + 6 q^{77} - 3 q^{82} - 9 q^{83} + 33 q^{85} - 33 q^{89} + 3 q^{92} - 33 q^{95} - 24 q^{97} + 3 q^{98}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 - 3 * q^14 - 24 * q^16 - 6 * q^22 - 6 * q^23 + 3 * q^28 + 3 * q^29 - 24 * q^32 - 12 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 - 42 * q^55 - 9 * q^61 + 48 * q^64 + 21 * q^65 + 33 * q^67 + 12 * q^70 - 18 * q^73 + 6 * q^77 - 3 * q^82 - 9 * q^83 + 33 * q^85 - 33 * q^89 + 3 * q^92 - 33 * q^95 - 24 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.19316	+	0.435950i	−0.980811	+	0.194963i
$5$	−2.19316	+	0.435950i	−0.980811	+	0.194963i
$6$		0			0
$7$	2.64572	+	0.0128895i	0.999988	+	0.00487179i
$7$	2.64572	+	0.0128895i	0.999988	+	0.00487179i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.719036	−	2.11731i	0.227379	−	0.669551i
$11$			4.12106i			1.24255i	0.783594	+	0.621273i	$0.213384\pi$
$11$			4.12106i			1.24255i	−0.783594	+	0.621273i	$0.786616\pi$
$12$		0			0
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	−0.982283	−	0.187405i	$-0.939992\pi$
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	0.653439	+	0.756979i	$0.273326\pi$
$14$	−1.33402	+	2.28482i	−0.356533	+	0.610643i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.28111	−	1.31700i	−0.553250	−	0.319419i	0.197182	−	0.980367i	$-0.436821\pi$
$17$	−2.28111	−	1.31700i	−0.553250	−	0.319419i	−0.750432	+	0.660948i	$0.770154\pi$
$18$		0			0
$19$	0.956982	−	0.552514i	0.219547	−	0.126755i	−0.386194	−	0.922418i	$-0.626210\pi$
$19$	0.956982	−	0.552514i	0.219547	−	0.126755i	0.605740	+	0.795662i	$0.292877\pi$
$20$	1.47412	+	1.68136i	0.329624	+	0.375963i
$21$		0			0
$22$	−3.56894	−	2.06053i	−0.760901	−	0.439306i
$23$	0.592478			0.123540			0.0617701	−	0.998090i	$-0.480325\pi$
$23$	0.592478			0.123540			0.0617701	+	0.998090i	$0.480325\pi$
$24$		0			0
$25$	4.61990	−	1.91221i	0.923979	−	0.382443i
$26$	−1.18566	−	2.05363i	−0.232528	−	0.402750i
$27$		0			0
$28$	−1.31170	−	2.29771i	−0.247887	−	0.434226i
$29$	−2.36953	+	1.36805i	−0.440010	+	0.254040i	−0.703602	−	0.710594i	$-0.748426\pi$
$29$	−2.36953	+	1.36805i	−0.440010	+	0.254040i	0.263592	+	0.964634i	$0.415093\pi$
$30$		0			0
$31$	2.33615	−	1.34878i	0.419585	−	0.242247i	−0.275315	−	0.961354i	$-0.588782\pi$
$31$	2.33615	−	1.34878i	0.419585	−	0.242247i	0.694900	+	0.719107i	$0.255449\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.28111	−	1.31700i	0.391207	−	0.225863i
$35$	−5.80810	+	1.12513i	−0.981749	+	0.190182i
$36$		0			0
$37$	6.05512	−	3.49593i	0.995456	−	0.574727i	0.0885553	−	0.996071i	$-0.471775\pi$
$37$	6.05512	−	3.49593i	0.995456	−	0.574727i	0.906901	+	0.421345i	$0.138442\pi$
$38$			1.10503i			0.179259i
$39$		0			0
$40$	−2.19316	+	0.435950i	−0.346769	+	0.0689297i
$41$	0.257087	−	0.445287i	0.0401502	−	0.0695422i	−0.845252	−	0.534368i	$-0.820550\pi$
$41$	0.257087	−	0.445287i	0.0401502	−	0.0695422i	0.885402	+	0.464826i	$0.153883\pi$
$42$		0			0
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.592432	+	0.805620i	$0.701832\pi$
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.993904	+	0.110251i	$0.964834\pi$
$44$	3.56894	−	2.06053i	0.538038	−	0.310636i
$45$		0			0
$46$	−0.296239	+	0.513101i	−0.0436781	+	0.0756527i
$47$	−3.57645	−	2.06487i	−0.521679	−	0.301192i	0.215942	−	0.976406i	$-0.430718\pi$
$47$	−3.57645	−	2.06487i	−0.521679	−	0.301192i	−0.737622	+	0.675214i	$0.764051\pi$
$48$		0			0
$49$	6.99967	+	0.0682042i	0.999953	+	0.00974346i
$50$	−0.653922	+	4.95705i	−0.0924786	+	0.701033i
$51$		0			0
$52$	2.37133			0.328844
$53$	−4.54406	+	7.87055i	−0.624175	+	1.08110i	0.364525	+	0.931194i	$0.381232\pi$
$53$	−4.54406	+	7.87055i	−0.624175	+	1.08110i	−0.988700	+	0.149909i	$0.952102\pi$
$54$		0			0
$55$	−1.79657	−	9.03814i	−0.242250	−	1.21870i
$56$	2.64572	+	0.0128895i	0.353549	+	0.00172244i
$57$		0			0
$58$		−	2.73609i		−	0.359266i
$59$	3.46974	+	6.00977i	0.451722	+	0.782405i	0.998493	−	0.0548770i	$-0.0174767\pi$
$59$	3.46974	+	6.00977i	0.451722	+	0.782405i	−0.546771	+	0.837282i	$0.684143\pi$
$60$		0			0
$61$	3.71806	+	2.14662i	0.476048	+	0.274847i	0.718768	−	0.695250i	$-0.244706\pi$
$61$	3.71806	+	2.14662i	0.476048	+	0.274847i	−0.242720	+	0.970096i	$0.578040\pi$
$62$			2.69755i			0.342589i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.70507	−	5.02083i	0.211488	−	0.622757i
$66$		0			0
$67$	−11.7043	+	6.75750i	−1.42991	+	0.825560i	−0.997113	−	0.0759308i	$-0.975807\pi$
$67$	−11.7043	+	6.75750i	−1.42991	+	0.825560i	−0.432799	+	0.901491i	$0.642474\pi$
$68$			2.63400i			0.319419i
$69$		0			0
$70$	1.92966	−	5.59253i	0.230638	−	0.668435i
$71$			1.60164i			0.190079i	0.995473	+	0.0950396i	$0.0302978\pi$
$71$			1.60164i			0.190079i	−0.995473	+	0.0950396i	$0.969702\pi$
$72$		0			0
$73$	−3.29147	+	5.70100i	−0.385238	+	0.667252i	−0.991802	−	0.127783i	$-0.959214\pi$
$73$	−3.29147	+	5.70100i	−0.385238	+	0.667252i	0.606564	+	0.795035i	$0.292547\pi$
$74$			6.99185i			0.812786i
$75$		0			0
$76$	−0.956982	−	0.552514i	−0.109773	−	0.0633777i
$77$	−0.0531186	+	10.9032i	−0.00605342	+	1.24253i
$78$		0			0
$79$	−6.72172	+	11.6424i	−0.756253	+	1.30987i	0.188497	+	0.982074i	$0.439639\pi$
$79$	−6.72172	+	11.6424i	−0.756253	+	1.30987i	−0.944749	+	0.327794i	$0.893695\pi$
$80$	0.719036	−	2.11731i	0.0803907	−	0.236722i
$81$		0			0
$82$	0.257087	+	0.445287i	0.0283905	+	0.0491738i
$83$	−3.80374	+	2.19609i	−0.417515	+	0.241052i	−0.694013	−	0.719962i	$-0.744159\pi$
$83$	−3.80374	+	2.19609i	−0.417515	+	0.241052i	0.276499	+	0.961014i	$0.410826\pi$
$84$		0			0
$85$	5.57698	+	1.89394i	0.604908	+	0.205426i
$86$		−	12.0115i		−	1.29524i
$87$		0			0
$88$			4.12106i			0.439306i
$89$	−7.82648	−	13.5559i	−0.829605	−	1.43692i	−0.898349	−	0.439283i	$-0.855232\pi$
$89$	−7.82648	−	13.5559i	−0.829605	−	1.43692i	0.0687438	−	0.997634i	$-0.478101\pi$
$90$		0			0
$91$	−3.16341	+	5.41805i	−0.331615	+	0.567966i
$92$	−0.296239	−	0.513101i	−0.0308851	−	0.0534945i
$93$		0			0
$94$	3.57645	−	2.06487i	0.368883	−	0.212975i
$95$	−1.85794	+	1.62895i	−0.190621	+	0.167126i
$96$		0			0
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	−0.967397	−	0.253265i	$-0.918496\pi$
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	0.264365	−	0.964423i	$-0.414838\pi$
$98$	−3.55890	+	6.02779i	−0.359503	+	0.608899i
$99$		0			0
$100$	−3.96597	−	3.04484i	−0.396597	−	0.304484i
$101$	−2.70907			−0.269562			−0.134781	−	0.990875i	$-0.543033\pi$
$101$	−2.70907			−0.269562			−0.134781	+	0.990875i	$0.543033\pi$
$102$		0			0
$103$	−18.1448			−1.78786			−0.893929	−	0.448209i	$-0.852062\pi$
$103$	−18.1448			−1.78786			−0.893929	+	0.448209i	$0.852062\pi$
$104$	−1.18566	+	2.05363i	−0.116264	+	0.201375i
$105$		0			0
$106$	−4.54406	−	7.87055i	−0.441358	−	0.764455i
$107$	−4.33862	−	7.51471i	−0.419430	−	0.726475i	0.576452	−	0.817131i	$-0.304437\pi$
$107$	−4.33862	−	7.51471i	−0.419430	−	0.726475i	−0.995882	+	0.0906565i	$0.971103\pi$
$108$		0			0
$109$	−7.55567	+	13.0868i	−0.723702	+	1.25349i	0.235804	+	0.971801i	$0.424228\pi$
$109$	−7.55567	+	13.0868i	−0.723702	+	1.25349i	−0.959506	+	0.281688i	$0.909106\pi$
$110$	8.72554	+	2.96319i	0.831948	+	0.282529i
$111$		0			0
$112$	−1.33402	+	2.28482i	−0.126053	+	0.215895i
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	−0.841382	−	0.540441i	$-0.818257\pi$
$113$	0.503287	−	0.871718i	0.0473452	−	0.0820044i	0.888727	+	0.458437i	$0.151591\pi$
$114$		0			0
$115$	−1.29940	+	0.258291i	−0.121170	+	0.0240857i
$116$	2.36953	+	1.36805i	0.220005	+	0.127020i
$117$		0			0
$118$	−6.93948			−0.638831
$119$	−6.01820	−	3.51381i	−0.551687	−	0.322110i
$120$		0			0
$121$	−5.98313			−0.543921
$122$	−3.71806	+	2.14662i	−0.336617	+	0.194346i
$123$		0			0
$124$	−2.33615	−	1.34878i	−0.209792	−	0.121124i
$125$	−9.29854	+	6.20783i	−0.831687	+	0.555245i
$126$		0			0
$127$		−	3.12538i		−	0.277333i	−0.990339	−	0.138666i	$-0.955718\pi$
$127$		−	3.12538i		−	0.277333i	0.990339	−	0.138666i	$-0.0442816\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	3.49563	+	3.98705i	0.306587	+	0.349687i
$131$	21.5741			1.88494			0.942469	−	0.334294i	$-0.108498\pi$
$131$	21.5741			1.88494			0.942469	+	0.334294i	$0.108498\pi$
$132$		0			0
$133$	2.53903	−	1.44946i	0.220162	−	0.125684i
$134$		−	13.5150i		−	1.16752i
$135$		0			0
$136$	−2.28111	−	1.31700i	−0.195603	−	0.112932i
$137$	3.76795			0.321917			0.160959	−	0.986961i	$-0.448541\pi$
$137$	3.76795			0.321917			0.160959	+	0.986961i	$0.448541\pi$
$138$		0			0
$139$	−5.20651	−	3.00598i	−0.441610	−	0.254964i	0.262670	−	0.964886i	$-0.415397\pi$
$139$	−5.20651	−	3.00598i	−0.441610	−	0.254964i	−0.704280	+	0.709922i	$0.748730\pi$
$140$	3.87844	+	4.46740i	0.327788	+	0.377564i
$141$		0			0
$142$	−1.38706	−	0.800818i	−0.116399	−	0.0672032i
$143$	−8.46313	−	4.88619i	−0.707723	−	0.408604i
$144$		0			0
$145$	4.60035	−	4.03334i	0.382038	−	0.334950i
$146$	−3.29147	−	5.70100i	−0.272404	−	0.471818i
$147$		0			0
$148$	−6.05512	−	3.49593i	−0.497728	−	0.287363i
$149$			11.1918i			0.916866i	0.888729	+	0.458433i	$0.151589\pi$
$149$			11.1918i			0.916866i	−0.888729	+	0.458433i	$0.848411\pi$
$150$		0			0
$151$	−18.5494			−1.50953			−0.754763	−	0.655997i	$-0.772248\pi$
$151$	−18.5494			−1.50953			−0.754763	+	0.655997i	$0.772248\pi$
$152$	0.956982	−	0.552514i	0.0776215	−	0.0448148i
$153$		0			0
$154$	−9.41586	−	5.49759i	−0.758752	−	0.443008i
$155$	−4.53555	+	3.97652i	−0.364304	+	0.319402i
$156$		0			0
$157$	−5.83514	−	10.1068i	−0.465695	−	0.806607i	0.533538	−	0.845776i	$-0.320862\pi$
$157$	−5.83514	−	10.1068i	−0.465695	−	0.806607i	−0.999233	+	0.0391693i	$0.987529\pi$
$158$	−6.72172	−	11.6424i	−0.534751	−	0.926217i
$159$		0			0
$160$	1.47412	+	1.68136i	0.116540	+	0.132923i
$161$	1.56753	+	0.00763677i	0.123539	+	0.000601862i
$162$		0			0
$163$	10.7728	−	6.21967i	0.843789	−	0.487162i	−0.0147613	−	0.999891i	$-0.504699\pi$
$163$	10.7728	−	6.21967i	0.843789	−	0.487162i	0.858550	+	0.512729i	$0.171366\pi$
$164$	−0.514173			−0.0401502
$165$		0			0
$166$		−	4.39218i		−	0.340899i
$167$	11.4205	+	6.59363i	0.883745	+	0.510230i	0.871891	−	0.489699i	$-0.162893\pi$
$167$	11.4205	+	6.59363i	0.883745	+	0.510230i	0.0118537	+	0.999930i	$0.496227\pi$
$168$		0			0
$169$	3.68840	+	6.38850i	0.283723	+	0.491423i
$170$	−4.42869	+	3.88283i	−0.339665	+	0.297800i
$171$		0			0
$172$	10.4023	+	6.00577i	0.793168	+	0.457936i
$173$	−12.8284	−	7.40645i	−0.975321	−	0.563102i	−0.0744670	−	0.997223i	$-0.523726\pi$
$173$	−12.8284	−	7.40645i	−0.975321	−	0.563102i	−0.900854	+	0.434121i	$0.857059\pi$
$174$		0			0
$175$	12.2476	−	4.99963i	0.925831	−	0.377937i
$176$	−3.56894	−	2.06053i	−0.269019	−	0.155318i
$177$		0			0
$178$	15.6530			1.17324
$179$	20.6373	+	11.9149i	1.54250	+	0.890564i	0.998680	+	0.0513644i	$0.0163570\pi$
$179$	20.6373	+	11.9149i	1.54250	+	0.890564i	0.543823	+	0.839200i	$0.316976\pi$
$180$		0			0
$181$			11.6911i			0.868992i	0.900674	+	0.434496i	$0.143074\pi$
$181$			11.6911i			0.868992i	−0.900674	+	0.434496i	$0.856926\pi$
$182$	−3.11046	−	5.44861i	−0.230563	−	0.403878i
$183$		0			0
$184$	0.592478			0.0436781
$185$	−11.7558	+	10.3069i	−0.864304	+	0.757775i
$186$		0			0
$187$	5.42743	−	9.40058i	0.396893	−	0.687438i
$188$			4.12973i			0.301192i
$189$		0			0
$190$	−0.481736	−	2.42350i	−0.0349488	−	0.175819i
$191$	−22.5387	−	13.0127i	−1.63084	−	0.941567i	−0.983834	−	0.179085i	$-0.942686\pi$
$191$	−22.5387	−	13.0127i	−1.63084	−	0.941567i	−0.647009	−	0.762482i	$-0.723980\pi$
$192$		0			0
$193$	−15.6522	+	9.03678i	−1.12667	+	0.650482i	−0.943095	−	0.332524i	$-0.892100\pi$
$193$	−15.6522	+	9.03678i	−1.12667	+	0.650482i	−0.183573	+	0.983006i	$0.558766\pi$
$194$	13.8481			0.994238
$195$		0			0
$196$	−3.44077	−	6.09599i	−0.245769	−	0.435428i
$197$	19.0964			1.36056			0.680281	−	0.732951i	$-0.261858\pi$
$197$	19.0964			1.36056			0.680281	+	0.732951i	$0.261858\pi$
$198$		0			0
$199$	21.6198	+	12.4822i	1.53259	+	0.884840i	0.999241	+	0.0389429i	$0.0123991\pi$
$199$	21.6198	+	12.4822i	1.53259	+	0.884840i	0.533346	+	0.845897i	$0.320934\pi$
$200$	4.61990	−	1.91221i	0.326676	−	0.135214i
$201$		0			0
$202$	1.35453	−	2.34612i	0.0953046	−	0.165072i
$203$	−6.28673	+	3.58892i	−0.441242	+	0.251893i
$204$		0			0
$205$	−0.369709	+	1.08866i	−0.0258216	+	0.0760355i
$206$	9.07239	−	15.7138i	0.632103	−	1.09483i
$207$		0			0
$208$	−1.18566	−	2.05363i	−0.0822110	−	0.142394i
$209$	2.27694	+	3.94378i	0.157499	+	0.272797i
$210$		0			0
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	−0.998718	−	0.0506149i	$-0.983882\pi$
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	0.543193	+	0.839608i	$0.317215\pi$
$212$	9.08813			0.624175
$213$		0			0
$214$	8.67724			0.593164
$215$	20.1957	−	17.7065i	1.37733	−	1.20757i
$216$		0			0
$217$	6.19818	−	3.53837i	0.420760	−	0.240200i
$218$	−7.55567	−	13.0868i	−0.511735	−	0.886351i
$219$		0			0
$220$	−6.92897	+	6.07495i	−0.467151	+	0.409573i
$221$	5.40925	−	3.12303i	0.363866	−	0.210078i
$222$		0			0
$223$	2.44383	+	4.23284i	0.163651	+	0.283452i	0.936175	−	0.351533i	$-0.114340\pi$
$223$	2.44383	+	4.23284i	0.163651	+	0.283452i	−0.772524	+	0.634985i	$0.781006\pi$
$224$	−1.31170	−	2.29771i	−0.0876415	−	0.153522i
$225$		0			0
$226$	0.503287	+	0.871718i	0.0334781	+	0.0579858i
$227$			11.9942i			0.796084i	0.917367	+	0.398042i	$0.130310\pi$
$227$			11.9942i			0.796084i	−0.917367	+	0.398042i	$0.869690\pi$
$228$		0			0
$229$		−	10.5849i		−	0.699467i	−0.936849	−	0.349734i	$-0.886272\pi$
$229$		−	10.5849i		−	0.699467i	0.936849	−	0.349734i	$-0.113728\pi$
$230$	0.426013	−	1.25446i	0.0280905	−	0.0827165i
$231$		0			0
$232$	−2.36953	+	1.36805i	−0.155567	+	0.0898166i
$233$	0.259858	+	0.450088i	0.0170239	+	0.0294862i	0.874412	−	0.485184i	$-0.161248\pi$
$233$	0.259858	+	0.450088i	0.0170239	+	0.0294862i	−0.857388	+	0.514671i	$0.827914\pi$
$234$		0			0
$235$	8.74391	+	2.96943i	0.570390	+	0.193704i
$236$	3.46974	−	6.00977i	0.225861	−	0.391202i
$237$		0			0
$238$	6.05215	−	3.45501i	0.392302	−	0.223955i
$239$	2.39886	+	1.38498i	0.155169	+	0.0895869i	0.575574	−	0.817750i	$-0.304779\pi$
$239$	2.39886	+	1.38498i	0.155169	+	0.0895869i	−0.420405	+	0.907337i	$0.638112\pi$
$240$		0			0
$241$			20.2007i			1.30124i	0.759403	+	0.650621i	$0.225491\pi$
$241$			20.2007i			1.30124i	−0.759403	+	0.650621i	$0.774509\pi$
$242$	2.99156	−	5.18154i	0.192305	−	0.333082i
$243$		0			0
$244$		−	4.29324i		−	0.274847i
$245$	−15.3811	+	2.90192i	−0.982664	+	0.185397i
$246$		0			0
$247$			2.62038i			0.166731i
$248$	2.33615	−	1.34878i	0.148346	−	0.0856474i
$249$		0			0
$250$	−0.726870	−	11.1567i	−0.0459713	−	0.705611i
$251$	−20.9869			−1.32468			−0.662340	−	0.749203i	$-0.730437\pi$
$251$	−20.9869			−1.32468			−0.662340	+	0.749203i	$0.730437\pi$
$252$		0			0
$253$			2.44164i			0.153504i
$254$	2.70666	+	1.56269i	0.169831	+	0.0980519i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$			9.48293i			0.591529i	0.955261	+	0.295764i	$0.0955743\pi$
$257$			9.48293i			0.591529i	−0.955261	+	0.295764i	$0.904426\pi$
$258$		0			0
$259$	16.0652	−	9.17119i	0.998244	−	0.569870i
$260$	−5.20070	+	1.03378i	−0.322534	+	0.0641123i
$261$		0			0
$262$	−10.7870	+	18.6837i	−0.666426	+	1.15428i
$263$	−11.6732			−0.719800			−0.359900	−	0.932991i	$-0.617189\pi$
$263$	−11.6732			−0.719800			−0.359900	+	0.932991i	$0.617189\pi$
$264$		0			0
$265$	6.53469	−	19.2424i	0.401423	−	1.18205i
$266$	−0.0142433	+	2.92359i	−0.000873312	+	0.179257i
$267$		0			0
$268$	11.7043	+	6.75750i	0.714956	+	0.412780i
$269$	8.14330	−	14.1046i	0.496506	−	0.859973i	−0.503486	−	0.864003i	$-0.667950\pi$
$269$	8.14330	−	14.1046i	0.496506	−	0.859973i	0.999992	+	0.00403039i	$0.00128292\pi$
$270$		0			0
$271$	21.8041	−	12.5886i	1.32450	−	0.764703i	0.340060	−	0.940404i	$-0.389553\pi$
$271$	21.8041	−	12.5886i	1.32450	−	0.764703i	0.984444	+	0.175701i	$0.0562192\pi$
$272$	2.28111	−	1.31700i	0.138312	−	0.0798547i
$273$		0			0
$274$	−1.88397	+	3.26314i	−0.113815	+	0.197133i
$275$	7.88035	+	19.0389i	0.475203	+	1.14809i
$276$		0			0
$277$		−	20.7421i		−	1.24627i	−0.782114	−	0.623136i	$-0.785858\pi$
$277$		−	20.7421i		−	1.24627i	0.782114	−	0.623136i	$-0.214142\pi$
$278$	5.20651	−	3.00598i	0.312265	−	0.180287i
$279$		0			0
$280$	−5.80810	+	1.12513i	−0.347101	+	0.0672395i
$281$	−1.17815	+	0.680206i	−0.0702827	+	0.0405777i	−0.534730	−	0.845023i	$-0.679587\pi$
$281$	−1.17815	+	0.680206i	−0.0702827	+	0.0405777i	0.464447	+	0.885601i	$0.346253\pi$
$282$		0			0
$283$	7.46757	+	12.9342i	0.443901	+	0.768859i	0.997975	−	0.0636082i	$-0.0202608\pi$
$283$	7.46757	+	12.9342i	0.443901	+	0.768859i	−0.554074	+	0.832468i	$0.686927\pi$
$284$	1.38706	−	0.800818i	0.0823067	−	0.0475198i
$285$		0			0
$286$	8.46313	−	4.88619i	0.500435	−	0.288927i
$287$	0.685919	−	1.17479i	0.0404885	−	0.0693458i
$288$		0			0
$289$	−5.03103	−	8.71400i	−0.295943	−	0.512589i
$290$	1.19280	+	6.00069i	0.0700435	+	0.352372i
$291$		0			0
$292$	6.58295			0.385238
$293$	−9.63607	−	5.56339i	−0.562945	−	0.325016i	0.191382	−	0.981516i	$-0.438703\pi$
$293$	−9.63607	−	5.56339i	−0.562945	−	0.325016i	−0.754327	+	0.656499i	$0.772037\pi$
$294$		0			0
$295$	−10.2296	−	11.6677i	−0.595593	−	0.679322i
$296$	6.05512	−	3.49593i	0.351947	−	0.203197i
$297$		0			0
$298$	−9.69236	−	5.59589i	−0.561464	−	0.324161i
$299$	−0.702480	+	1.21673i	−0.0406255	+	0.0703654i
$300$		0			0
$301$	−27.5990	+	15.7555i	−1.59078	+	0.908132i
$302$	9.27469	−	16.0642i	0.533698	−	0.924392i
$303$		0			0
$304$			1.10503i			0.0633777i
$305$	−9.09011	−	3.08700i	−0.520498	−	0.176761i
$306$		0			0
$307$	−14.1337			−0.806651			−0.403325	−	0.915057i	$-0.632146\pi$
$307$	−14.1337			−0.806651			−0.403325	+	0.915057i	$0.632146\pi$
$308$	9.46898	−	5.40558i	0.539545	−	0.308012i
$309$		0			0
$310$	−1.17600	−	5.91616i	−0.0667921	−	0.336015i
$311$	2.93752	+	5.08794i	0.166572	+	0.288510i	0.937212	−	0.348760i	$-0.113397\pi$
$311$	2.93752	+	5.08794i	0.166572	+	0.288510i	−0.770641	+	0.637270i	$0.780064\pi$
$312$		0			0
$313$	−9.51843	+	16.4864i	−0.538014	+	0.931867i	0.460997	+	0.887402i	$0.347492\pi$
$313$	−9.51843	+	16.4864i	−0.538014	+	0.931867i	−0.999011	+	0.0444656i	$0.985842\pi$
$314$	11.6703			0.658592
$315$		0			0
$316$	13.4434			0.756253
$317$	7.70830	−	13.3512i	0.432941	−	0.749876i	−0.564184	−	0.825649i	$-0.690809\pi$
$317$	7.70830	−	13.3512i	0.432941	−	0.749876i	0.997125	+	0.0757731i	$0.0241425\pi$
$318$		0			0
$319$	−5.63780	−	9.76495i	−0.315656	−	0.546732i
$320$	−2.19316	+	0.435950i	−0.122601	+	0.0243703i
$321$		0			0
$322$	−0.790380	+	1.35370i	−0.0440461	+	0.0754390i
$323$	−2.91064			−0.161952
$324$		0			0
$325$	−1.55066	+	11.7548i	−0.0860154	+	0.652039i
$326$			12.4393i			0.688951i
$327$		0			0
$328$	0.257087	−	0.445287i	0.0141952	−	0.0245869i
$329$	−9.43568	−	5.50916i	−0.520206	−	0.303730i
$330$		0			0
$331$	15.4650	−	26.7862i	0.850033	−	1.47230i	−0.0311447	−	0.999515i	$-0.509915\pi$
$331$	15.4650	−	26.7862i	0.850033	−	1.47230i	0.881178	−	0.472785i	$-0.156751\pi$
$332$	3.80374	+	2.19609i	0.208757	+	0.120526i
$333$		0			0
$334$	−11.4205	+	6.59363i	−0.624902	+	0.360787i
$335$	22.7235	−	19.9228i	1.24152	−	1.08850i
$336$		0			0
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.951915	−	0.306362i	$-0.0991119\pi$
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.210640	+	0.977564i	$0.432445\pi$
$338$	−7.37680			−0.401245
$339$		0			0
$340$	−1.14829	−	5.77677i	−0.0622747	−	0.313289i
$341$	5.55839	+	9.62741i	0.301003	+	0.521353i
$342$		0			0
$343$	18.5183	+	0.270672i	0.999893	+	0.0146149i
$344$	−10.4023	+	6.00577i	−0.560854	+	0.323809i
$345$		0			0
$346$	12.8284	−	7.40645i	0.689656	−	0.398173i
$347$	−0.273072	−	0.472975i	−0.0146593	−	0.0253906i	0.858603	−	0.512642i	$-0.171333\pi$
$347$	−0.273072	−	0.472975i	−0.0146593	−	0.0253906i	−0.873262	+	0.487251i	$0.838000\pi$
$348$		0			0
$349$	5.63017	−	3.25058i	0.301376	−	0.174000i	−0.341685	−	0.939815i	$-0.610997\pi$
$349$	5.63017	−	3.25058i	0.301376	−	0.174000i	0.643061	+	0.765815i	$0.277664\pi$
$350$	−1.79399	+	13.1065i	−0.0958927	+	0.700574i
$351$		0			0
$352$	3.56894	−	2.06053i	0.190225	−	0.109827i
$353$		−	6.55439i		−	0.348855i	−0.984670	−	0.174427i	$-0.944193\pi$
$353$		−	6.55439i		−	0.348855i	0.984670	−	0.174427i	$-0.0558074\pi$
$354$		0			0
$355$	−0.698233	−	3.51264i	−0.0370583	−	0.186432i
$356$	−7.82648	+	13.5559i	−0.414802	+	0.718459i
$357$		0			0
$358$	−20.6373	+	11.9149i	−1.09071	+	0.629724i
$359$	−3.55244	+	2.05100i	−0.187490	+	0.108248i	−0.590807	−	0.806813i	$-0.701191\pi$
$359$	−3.55244	+	2.05100i	−0.187490	+	0.108248i	0.403317	+	0.915060i	$0.367857\pi$
$360$		0			0
$361$	−8.88946	+	15.3970i	−0.467866	+	0.810368i
$362$	−10.1248	−	5.84555i	−0.532147	−	0.307235i
$363$		0			0
$364$	6.27387	+	0.0305653i	0.328840	+	0.00160206i
$365$	4.73338	−	13.9381i	0.247756	−	0.729555i
$366$		0			0
$367$	−20.1571			−1.05219			−0.526096	−	0.850425i	$-0.676345\pi$
$367$	−20.1571			−1.05219			−0.526096	+	0.850425i	$0.676345\pi$
$368$	−0.296239	+	0.513101i	−0.0154425	+	0.0267473i
$369$		0			0
$370$	−3.04810	−	15.3342i	−0.158463	−	0.797190i
$371$	−12.1238	+	20.7647i	−0.629435	+	1.07805i
$372$		0			0
$373$			5.71061i			0.295684i	0.989011	+	0.147842i	$0.0472327\pi$
$373$			5.71061i			0.295684i	−0.989011	+	0.147842i	$0.952767\pi$
$374$	5.42743	+	9.40058i	0.280646	+	0.486092i
$375$		0			0
$376$	−3.57645	−	2.06487i	−0.184442	−	0.106487i
$377$		−	6.48817i		−	0.334158i
$378$		0			0
$379$	5.42424			0.278624			0.139312	−	0.990249i	$-0.455511\pi$
$379$	5.42424			0.278624			0.139312	+	0.990249i	$0.455511\pi$
$380$	2.33968	+	0.794555i	0.120023	+	0.0407598i
$381$		0			0
$382$	22.5387	−	13.0127i	1.15318	−	0.665789i
$383$		−	33.3230i		−	1.70273i	−0.524578	−	0.851363i	$-0.675777\pi$
$383$		−	33.3230i		−	1.70273i	0.524578	−	0.851363i	$-0.324223\pi$
$384$		0			0
$385$	−4.63673	−	23.9355i	−0.236310	−	1.21987i
$386$		−	18.0736i		−	0.919920i
$387$		0			0
$388$	−6.92406	+	11.9928i	−0.351516	+	0.608844i
$389$			29.2794i			1.48453i	0.670109	+	0.742263i	$0.266247\pi$
$389$			29.2794i			1.48453i	−0.670109	+	0.742263i	$0.733753\pi$
$390$		0			0
$391$	−1.35151	−	0.780293i	−0.0683486	−	0.0394611i
$392$	6.99967	+	0.0682042i	0.353537	+	0.00344483i
$393$		0			0
$394$	−9.54821	+	16.5380i	−0.481032	+	0.833171i
$395$	9.66632	−	28.4639i	0.486365	−	1.43217i
$396$		0			0
$397$	5.42713	+	9.40006i	0.272380	+	0.471775i	0.969471	−	0.245207i	$-0.0788560\pi$
$397$	5.42713	+	9.40006i	0.272380	+	0.471775i	−0.697091	+	0.716983i	$0.745523\pi$
$398$	−21.6198	+	12.4822i	−1.08370	+	0.625676i
$399$		0			0
$400$	−0.653922	+	4.95705i	−0.0326961	+	0.247853i
$401$			18.2813i			0.912925i	0.889743	+	0.456463i	$0.150884\pi$
$401$			18.2813i			0.912925i	−0.889743	+	0.456463i	$0.849116\pi$
$402$		0			0
$403$			6.39678i			0.318646i
$404$	1.35453	+	2.34612i	0.0673905	+	0.116724i
$405$		0			0
$406$	0.0352670	−	7.23893i	0.00175027	−	0.359262i
$407$	14.4069	+	24.9535i	0.714124	+	1.23690i
$408$		0			0
$409$	8.38163	−	4.83914i	0.414445	−	0.239280i	−0.278253	−	0.960508i	$-0.589755\pi$
$409$	8.38163	−	4.83914i	0.414445	−	0.239280i	0.692698	+	0.721228i	$0.256422\pi$
$410$	−0.757955	−	0.864509i	−0.0374327	−	0.0426951i
$411$		0			0
$412$	9.07239	+	15.7138i	0.446964	+	0.774165i
$413$	9.10250	+	15.9449i	0.447905	+	0.784596i
$414$		0			0
$415$	7.38482	−	6.47461i	0.362507	−	0.317826i
$416$	2.37133			0.116264
$417$		0			0
$418$	−4.55388			−0.222738
$419$	5.02659	−	8.70630i	0.245565	−	0.425331i	−0.716725	−	0.697355i	$-0.754360\pi$
$419$	5.02659	−	8.70630i	0.245565	−	0.425331i	0.962290	+	0.272025i	$0.0876932\pi$
$420$		0			0
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	0.658485	−	0.752594i	$-0.271197\pi$
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	−0.981008	+	0.193968i	$0.937864\pi$
$422$	−6.61689	−	11.4608i	−0.322105	−	0.557902i
$423$		0			0
$424$	−4.54406	+	7.87055i	−0.220679	+	0.382228i
$425$	−13.0569	−	1.72243i	−0.633351	−	0.0835500i
$426$		0			0
$427$	9.80927	+	5.72728i	0.474704	+	0.277163i
$428$	−4.33862	+	7.51471i	−0.209715	+	0.363237i
$429$		0			0
$430$	5.23643	+	26.3432i	0.252523	+	1.27038i
$431$	4.44716	+	2.56757i	0.214212	+	0.123675i	0.603267	−	0.797539i	$-0.293865\pi$
$431$	4.44716	+	2.56757i	0.214212	+	0.123675i	−0.389055	+	0.921214i	$0.627199\pi$
$432$		0			0
$433$	7.97362			0.383188			0.191594	−	0.981474i	$-0.438634\pi$
$433$	7.97362			0.383188			0.191594	+	0.981474i	$0.438634\pi$
$434$	−0.0347702	+	7.13697i	−0.00166902	+	0.342585i
$435$		0			0
$436$	15.1113			0.723702
$437$	0.566991	−	0.327352i	0.0271229	−	0.0156594i
$438$		0			0
$439$	22.3502	+	12.9039i	1.06672	+	0.615869i	0.927282	−	0.374362i	$-0.122138\pi$
$439$	22.3502	+	12.9039i	1.06672	+	0.615869i	0.139434	+	0.990231i	$0.455472\pi$
$440$	−1.79657	−	9.03814i	−0.0856483	−	0.430876i
$441$		0			0
$442$			6.24607i			0.297095i
$443$	−15.6440	+	27.0962i	−0.743269	+	1.28738i	0.207729	+	0.978186i	$0.433393\pi$
$443$	−15.6440	+	27.0962i	−0.743269	+	1.28738i	−0.950999	+	0.309194i	$0.899941\pi$
$444$		0			0
$445$	23.0744	+	26.3182i	1.09383	+	1.24760i
$446$	−4.88766			−0.231437
$447$		0			0
$448$	2.64572	+	0.0128895i	0.124999	+	0.000608974i
$449$		−	6.93666i		−	0.327361i	−0.986513	−	0.163681i	$-0.947663\pi$
$449$		−	6.93666i		−	0.327361i	0.986513	−	0.163681i	$-0.0523366\pi$
$450$		0			0
$451$	1.83506	+	1.05947i	0.0864094	+	0.0498885i
$452$	−1.00657			−0.0473452
$453$		0			0
$454$	−10.3873	−	5.99711i	−0.487500	−	0.281458i
$455$	4.57586	−	13.2617i	0.214519	−	0.621719i
$456$		0			0
$457$	23.7421	+	13.7075i	1.11061	+	0.641209i	0.938986	−	0.343954i	$-0.111767\pi$
$457$	23.7421	+	13.7075i	1.11061	+	0.641209i	0.171620	+	0.985163i	$0.445100\pi$
$458$	9.16676	+	5.29243i	0.428335	+	0.247299i
$459$		0			0
$460$	0.873386	+	0.996168i	0.0407218	+	0.0464466i
$461$	−9.16139	−	15.8680i	−0.426689	−	0.739046i	0.569888	−	0.821722i	$-0.306987\pi$
$461$	−9.16139	−	15.8680i	−0.426689	−	0.739046i	−0.996576	+	0.0826762i	$0.973653\pi$
$462$		0			0
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	0.834992	−	0.550262i	$-0.185472\pi$
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	−0.0590450	+	0.998255i	$0.518806\pi$
$464$		−	2.73609i		−	0.127020i
$465$		0			0
$466$	−0.519717			−0.0240754
$467$	11.2146	−	6.47476i	0.518951	−	0.299616i	−0.217555	−	0.976048i	$-0.569808\pi$
$467$	11.2146	−	6.47476i	0.518951	−	0.299616i	0.736505	+	0.676432i	$0.236475\pi$
$468$		0			0
$469$	−31.0535	+	17.7276i	−1.43392	+	0.818584i
$470$	−6.94356	+	6.08774i	−0.320282	+	0.280806i
$471$		0			0
$472$	3.46974	+	6.00977i	0.159708	+	0.276622i
$473$	−24.7501	−	42.8685i	−1.13801	−	1.97110i
$474$		0			0
$475$	3.36463	−	4.38251i	0.154380	−	0.201083i
$476$	−0.0339510	+	6.96882i	−0.00155614	+	0.319415i
$477$		0			0
$478$	−2.39886	+	1.38498i	−0.109721	+	0.0633475i
$479$	27.0757			1.23712			0.618560	−	0.785738i	$-0.287716\pi$
$479$	27.0757			1.23712			0.618560	+	0.785738i	$0.287716\pi$
$480$		0			0
$481$			16.5800i			0.755982i
$482$	−17.4943	−	10.1004i	−0.796845	−	0.460059i
$483$		0			0
$484$	2.99156	+	5.18154i	0.135980	+	0.235524i
$485$	20.4138	+	23.2836i	0.926945	+	1.05726i
$486$		0			0
$487$	2.98800	+	1.72512i	0.135399	+	0.0781727i	0.566169	−	0.824289i	$-0.308425\pi$
$487$	2.98800	+	1.72512i	0.135399	+	0.0781727i	−0.430770	+	0.902462i	$0.641758\pi$
$488$	3.71806	+	2.14662i	0.168309	+	0.0971730i
$489$		0			0
$490$	5.17742	−	14.7714i	0.233892	−	0.667304i
$491$	36.9916	+	21.3571i	1.66941	+	0.963833i	0.967958	+	0.251113i	$0.0807967\pi$
$491$	36.9916	+	21.3571i	1.66941	+	0.963833i	0.701449	+	0.712719i	$0.252537\pi$
$492$		0			0
$493$	7.20685			0.324580
$494$	−2.26932	−	1.31019i	−0.102101	−	0.0589483i
$495$		0			0
$496$			2.69755i			0.121124i
$497$	−0.0206444	+	4.23748i	−0.000926026	+	0.190077i
$498$		0			0
$499$	36.0386			1.61331			0.806654	−	0.591024i	$-0.201276\pi$
$499$	36.0386			1.61331			0.806654	+	0.591024i	$0.201276\pi$
$500$	10.0254	+	4.94886i	0.448350	+	0.221320i
$501$		0			0
$502$	10.4934	−	18.1752i	0.468345	−	0.811198i
$503$		−	4.41774i		−	0.196977i	−0.995138	−	0.0984887i	$-0.968599\pi$
$503$		−	4.41774i		−	0.196977i	0.995138	−	0.0984887i	$-0.0314008\pi$
$504$		0			0
$505$	5.94141	−	1.18102i	0.264389	−	0.0525545i
$506$	−2.11452	−	1.22082i	−0.0940019	−	0.0542720i
$507$		0			0
$508$	−2.70666	+	1.56269i	−0.120089	+	0.0693332i
$509$	−24.2045			−1.07284			−0.536422	−	0.843950i	$-0.680225\pi$
$509$	−24.2045			−1.07284			−0.536422	+	0.843950i	$0.680225\pi$
$510$		0			0
$511$	−8.78180	+	15.0408i	−0.388484	+	0.665367i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.21246	−	4.74146i	−0.362236	−	0.209137i
$515$	39.7944	−	7.91021i	1.75355	−	0.348565i
$516$		0			0
$517$	8.50944	−	14.7388i	0.374245	−	0.648211i
$518$	−0.0901218	+	18.4985i	−0.00395972	+	0.812777i
$519$		0			0
$520$	1.70507	−	5.02083i	0.0747723	−	0.220178i
$521$	7.58138	−	13.1313i	0.332146	−	0.575294i	−0.650786	−	0.759261i	$-0.725561\pi$
$521$	7.58138	−	13.1313i	0.332146	−	0.575294i	0.982932	+	0.183967i	$0.0588940\pi$
$522$		0			0
$523$	0.294517	+	0.510118i	0.0128783	+	0.0223059i	0.872393	−	0.488806i	$-0.162567\pi$
$523$	0.294517	+	0.510118i	0.0128783	+	0.0223059i	−0.859514	+	0.511111i	$0.829234\pi$
$524$	−10.7870	−	18.6837i	−0.471234	−	0.816202i
$525$		0			0
$526$	5.83660	−	10.1093i	0.254488	−	0.440786i
$527$	−7.10534			−0.309514
$528$		0			0
$529$	−22.6490			−0.984738
$530$	13.3970	+	15.2804i	0.581929	+	0.663738i
$531$		0			0
$532$	−2.52478	−	1.47413i	−0.109463	−	0.0639117i
$533$	0.609637	+	1.05592i	0.0264063	+	0.0457371i
$534$		0			0
$535$	12.7913	+	14.5895i	0.553017	+	0.630761i
$536$	−11.7043	+	6.75750i	−0.505550	+	0.291879i
$537$		0			0
$538$	8.14330	+	14.1046i	0.351082	+	0.608093i
$539$	−0.281074	+	28.8460i	−0.0121067	+	1.24249i
$540$		0			0
$541$	−21.2555	−	36.8156i	−0.913846	−	1.58283i	−0.808582	−	0.588384i	$-0.799764\pi$
$541$	−21.2555	−	36.8156i	−0.913846	−	1.58283i	−0.105264	−	0.994444i	$-0.533569\pi$
$542$			25.1772i			1.08145i
$543$		0			0
$544$			2.63400i			0.112932i
$545$	10.8656	−	31.9954i	0.465431	−	1.37053i
$546$		0			0
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	−0.331826	−	0.943341i	$-0.607665\pi$
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	0.651044	+	0.759040i	$0.274331\pi$
$548$	−1.88397	−	3.26314i	−0.0804793	−	0.139394i
$549$		0			0
$550$	−20.4283	−	2.69485i	−0.871066	−	0.114909i
$551$	−1.51173	+	2.61839i	−0.0644018	+	0.111547i
$552$		0			0
$553$	−17.9339	+	30.7158i	−0.762625	+	1.30617i
$554$	17.9632	+	10.3710i	0.763182	+	0.440623i
$555$		0			0
$556$			6.01195i			0.254964i
$557$	−3.09319	+	5.35757i	−0.131063	+	0.227007i	−0.924087	−	0.382183i	$-0.875172\pi$
$557$	−3.09319	+	5.35757i	−0.131063	+	0.227007i	0.793024	+	0.609191i	$0.208506\pi$
$558$		0			0
$559$		−	28.4833i		−	1.20472i
$560$	1.92966	−	5.59253i	0.0815430	−	0.236328i
$561$		0			0
$562$		−	1.36041i		−	0.0573856i
$563$	28.2325	−	16.3001i	1.18986	−	0.686966i	0.231585	−	0.972815i	$-0.425609\pi$
$563$	28.2325	−	16.3001i	1.18986	−	0.686966i	0.958275	+	0.285849i	$0.0922755\pi$
$564$		0			0
$565$	−0.723763	+	2.13122i	−0.0304489	+	0.0896613i
$566$	−14.9351			−0.627771
$567$		0			0
$568$			1.60164i			0.0672032i
$569$	−5.68792	−	3.28392i	−0.238450	−	0.137669i	0.376014	−	0.926614i	$-0.377294\pi$
$569$	−5.68792	−	3.28392i	−0.238450	−	0.137669i	−0.614464	+	0.788945i	$0.710628\pi$
$570$		0			0
$571$	8.99355	+	15.5773i	0.376369	+	0.651889i	0.990531	−	0.137290i	$-0.0438393\pi$
$571$	8.99355	+	15.5773i	0.376369	+	0.651889i	−0.614162	+	0.789180i	$0.710506\pi$
$572$			9.77238i			0.408604i
$573$		0			0
$574$	0.674440	+	1.18142i	0.0281506	+	0.0493115i
$575$	2.73719	−	1.13295i	0.114149	−	0.0472471i
$576$		0			0
$577$	11.8915	−	20.5968i	0.495051	−	0.857454i	−0.504932	−	0.863159i	$-0.668483\pi$
$577$	11.8915	−	20.5968i	0.495051	−	0.857454i	0.999984	+	0.00570479i	$0.00181590\pi$
$578$	10.0621			0.418527
$579$		0			0
$580$	−5.79315	−	1.96735i	−0.240547	−	0.0816897i
$581$	−10.0919	+	5.76121i	−0.418684	+	0.239015i
$582$		0			0
$583$	−32.4350	−	18.7264i	−1.34332	−	0.775566i
$584$	−3.29147	+	5.70100i	−0.136202	+	0.235909i
$585$		0			0
$586$	9.63607	−	5.56339i	0.398062	−	0.229821i
$587$	14.2796	−	8.24435i	0.589384	−	0.340281i	−0.175470	−	0.984485i	$-0.556145\pi$
$587$	14.2796	−	8.24435i	0.589384	−	0.340281i	0.764854	+	0.644204i	$0.222811\pi$
$588$		0			0
$589$	1.49043	−	2.58151i	0.0614123	−	0.106369i
$590$	15.2194	−	3.02526i	0.626572	−	0.124548i
$591$		0			0
$592$			6.99185i			0.287363i
$593$	8.69178	−	5.01820i	0.356928	−	0.206073i	−0.310804	−	0.950474i	$-0.600598\pi$
$593$	8.69178	−	5.01820i	0.356928	−	0.206073i	0.667733	+	0.744401i	$0.267265\pi$
$594$		0			0
$595$	14.7307	+	5.08272i	0.603900	+	0.208371i
$596$	9.69236	−	5.59589i	0.397015	−	0.229217i
$597$		0			0
$598$	−0.702480	−	1.21673i	−0.0287266	−	0.0497559i
$599$	30.4424	−	17.5759i	1.24384	−	0.718134i	0.273970	−	0.961738i	$-0.411663\pi$
$599$	30.4424	−	17.5759i	1.24384	−	0.718134i	0.969875	+	0.243605i	$0.0783299\pi$
$600$		0			0
$601$	32.5093	−	18.7692i	1.32608	−	0.765613i	0.341390	−	0.939922i	$-0.389102\pi$
$601$	32.5093	−	18.7692i	1.32608	−	0.765613i	0.984691	+	0.174309i	$0.0557691\pi$
$602$	0.154823	−	31.7792i	0.00631013	−	1.29522i
$603$		0			0
$604$	9.27469	+	16.0642i	0.377382	+	0.653644i
$605$	13.1219	−	2.60834i	0.533483	−	0.106044i
$606$		0			0
$607$	24.1853			0.981653			0.490827	−	0.871257i	$-0.336695\pi$
$607$	24.1853			0.981653			0.490827	+	0.871257i	$0.336695\pi$
$608$	−0.956982	−	0.552514i	−0.0388107	−	0.0224074i
$609$		0			0
$610$	7.21847	−	6.32877i	0.292267	−	0.256244i
$611$	8.48095	−	4.89648i	0.343102	−	0.198090i
$612$		0			0
$613$	−23.6618	−	13.6611i	−0.955690	−	0.551768i	−0.0608460	−	0.998147i	$-0.519380\pi$
$613$	−23.6618	−	13.6611i	−0.955690	−	0.551768i	−0.894844	+	0.446379i	$0.852713\pi$
$614$	7.06683	−	12.2401i	0.285194	−	0.493971i
$615$		0			0
$616$	−0.0531186	+	10.9032i	−0.00214021	+	0.439301i
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	−0.978940	−	0.204150i	$-0.934557\pi$
$617$	−7.76658	+	13.4521i	−0.312671	+	0.541562i	0.666269	+	0.745712i	$0.267890\pi$
$618$		0			0
$619$			21.2581i			0.854435i	0.904149	+	0.427218i	$0.140506\pi$
$619$			21.2581i			0.854435i	−0.904149	+	0.427218i	$0.859494\pi$
$620$	5.71154	+	1.93964i	0.229381	+	0.0778977i
$621$		0			0
$622$	−5.87504			−0.235568
$623$	−20.5319	−	35.9659i	−0.822595	−	1.44094i
$624$		0			0
$625$	17.6869	−	17.6685i	0.707475	−	0.706738i
$626$	−9.51843	−	16.4864i	−0.380433	−	0.658930i
$627$		0			0
$628$	−5.83514	+	10.1068i	−0.232847	+	0.403303i
$629$	−18.4165			−0.734314
$630$		0			0
$631$	22.0357			0.877226			0.438613	−	0.898676i	$-0.355470\pi$
$631$	22.0357			0.877226			0.438613	+	0.898676i	$0.355470\pi$
$632$	−6.72172	+	11.6424i	−0.267376	+	0.463108i
$633$		0			0
$634$	7.70830	+	13.3512i	0.306136	+	0.530242i
$635$	1.36251	+	6.85446i	0.0540695	+	0.272011i
$636$		0			0
$637$	−8.43932	+	14.2939i	−0.334378	+	0.566343i
$638$	11.2756			0.446405
$639$		0			0
$640$	0.719036	−	2.11731i	0.0284224	−	0.0836939i
$641$			25.6700i			1.01390i	0.861975	+	0.506951i	$0.169228\pi$
$641$			25.6700i			1.01390i	−0.861975	+	0.506951i	$0.830772\pi$
$642$		0			0
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	−0.855895	−	0.517150i	$-0.826993\pi$
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	0.875813	+	0.482651i	$0.160326\pi$
$644$	−0.777152	−	1.36134i	−0.0306241	−	0.0536443i
$645$		0			0
$646$	1.45532	−	2.52069i	0.0572587	−	0.0991750i
$647$	12.5056	+	7.22013i	0.491647	+	0.283852i	0.725257	−	0.688478i	$-0.241721\pi$
$647$	12.5056	+	7.22013i	0.491647	+	0.283852i	−0.233611	+	0.972330i	$0.575054\pi$
$648$		0			0
$649$	−24.7666	+	14.2990i	−0.972174	+	0.561285i
$650$	−9.40463	−	7.22032i	−0.368880	−	0.283204i
$651$		0			0
$652$	−10.7728	−	6.21967i	−0.421895	−	0.243581i
$653$	44.2235			1.73060			0.865299	−	0.501256i	$-0.167129\pi$
$653$	44.2235			1.73060			0.865299	+	0.501256i	$0.167129\pi$
$654$		0			0
$655$	−47.3154	+	9.40522i	−1.84877	+	0.367492i
$656$	0.257087	+	0.445287i	0.0100376	+	0.0173855i
$657$		0			0
$658$	9.48891	−	5.41696i	0.369916	−	0.211175i
$659$	24.1702	−	13.9547i	0.941539	−	0.543598i	0.0510965	−	0.998694i	$-0.483728\pi$
$659$	24.1702	−	13.9547i	0.941539	−	0.543598i	0.890442	+	0.455096i	$0.150395\pi$
$660$		0			0
$661$	−0.0371085	+	0.0214246i	−0.00144335	+	0.000833320i	−0.500722	−	0.865608i	$-0.666932\pi$
$661$	−0.0371085	+	0.0214246i	−0.00144335	+	0.000833320i	0.499278	+	0.866442i	$0.333599\pi$
$662$	15.4650	+	26.7862i	0.601064	+	1.04107i
$663$		0			0
$664$	−3.80374	+	2.19609i	−0.147614	+	0.0852248i
$665$	−4.93660	+	4.28579i	−0.191433	+	0.166196i
$666$		0			0
$667$	−1.40389	+	0.810538i	−0.0543589	+	0.0313841i
$668$		−	13.1873i		−	0.510230i
$669$		0			0
$670$	5.89186	+	29.6405i	0.227622	+	1.14511i
$671$	−8.84635	+	15.3223i	−0.341510	+	0.591512i
$672$		0			0
$673$	17.4536	−	10.0769i	0.672788	−	0.388434i	−0.124344	−	0.992239i	$-0.539683\pi$
$673$	17.4536	−	10.0769i	0.672788	−	0.388434i	0.797132	+	0.603805i	$0.206349\pi$
$674$	−21.3417	+	12.3216i	−0.822051	+	0.474611i
$675$		0			0
$676$	3.68840	−	6.38850i	0.141862	−	0.245711i
$677$	−24.3021	−	14.0308i	−0.934004	−	0.539248i	−0.0459284	−	0.998945i	$-0.514625\pi$
$677$	−24.3021	−	14.0308i	−0.934004	−	0.539248i	−0.888076	+	0.459697i	$0.847958\pi$
$678$		0			0
$679$	−18.1646	−	31.8189i	−0.697092	−	1.22110i
$680$	5.57698	+	1.89394i	0.213867	+	0.0726292i
$681$		0			0
$682$	−11.1168			−0.425683
$683$	−14.7248	+	25.5040i	−0.563428	+	0.975885i	0.433767	+	0.901025i	$0.357184\pi$
$683$	−14.7248	+	25.5040i	−0.563428	+	0.975885i	−0.997194	+	0.0748598i	$0.976149\pi$
$684$		0			0
$685$	−8.26371	+	1.64263i	−0.315740	+	0.0627618i
$686$	−9.49355	+	15.9020i	−0.362465	+	0.607140i
$687$		0			0
$688$		−	12.0115i		−	0.457936i
$689$	−10.7755	−	18.6637i	−0.410513	−	0.711029i
$690$		0			0
$691$	6.03382	+	3.48363i	0.229537	+	0.132523i	0.610359	−	0.792125i	$-0.291025\pi$
$691$	6.03382	+	3.48363i	0.229537	+	0.132523i	−0.380821	+	0.924649i	$0.624359\pi$
$692$			14.8129i			0.563102i
$693$		0			0
$694$	0.546144			0.0207313
$695$	12.7292	+	4.32281i	0.482844	+	0.163974i
$696$		0			0
$697$	−1.17288	+	0.677165i	−0.0444262	+	0.0256495i
$698$			6.50116i			0.246073i
$699$		0			0
$700$	−10.4536	−	8.10691i	−0.395109	−	0.306413i
$701$			17.0338i			0.643357i	0.946849	+	0.321678i	$0.104247\pi$
$701$			17.0338i			0.643357i	−0.946849	+	0.321678i	$0.895753\pi$
$702$		0			0
$703$	3.86309	−	6.69107i	0.145699	−	0.252359i
$704$			4.12106i			0.155318i
$705$		0			0
$706$	5.67627	+	3.27719i	0.213629	+	0.123339i
$707$	−7.16743	−	0.0349186i	−0.269559	−	0.00131325i
$708$		0			0
$709$	0.510534	−	0.884271i	0.0191735	−	0.0332095i	−0.856279	−	0.516513i	$-0.827230\pi$
$709$	0.510534	−	0.884271i	0.0191735	−	0.0332095i	0.875453	+	0.483303i	$0.160563\pi$
$710$	3.39115	+	1.15163i	0.127268	+	0.0432201i
$711$		0			0
$712$	−7.82648	−	13.5559i	−0.293310	−	0.508027i
$713$	1.38412	−	0.799121i	0.0518356	−	0.0299273i
$714$		0			0
$715$	20.6911	+	7.02670i	0.773804	+	0.262784i
$716$		−	23.8299i		−	0.890564i
$717$		0			0
$718$		−	4.10200i		−	0.153085i
$719$	−20.6417	−	35.7524i	−0.769804	−	1.33334i	−0.937669	−	0.347530i	$-0.887020\pi$
$719$	−20.6417	−	35.7524i	−0.769804	−	1.33334i	0.167865	−	0.985810i	$-0.446313\pi$
$720$		0			0
$721$	−48.0060	−	0.233878i	−1.78784	−	0.00871006i
$722$	−8.88946	−	15.3970i	−0.330831	−	0.573017i
$723$		0			0
$724$	10.1248	−	5.84555i	0.376285	−	0.217248i
$725$	−8.33096	+	10.8513i	−0.309404	+	0.403006i
$726$		0			0
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	0.684400	−	0.729106i	$-0.260064\pi$
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	−0.973625	+	0.228155i	$0.926731\pi$
$728$	−3.16341	+	5.41805i	−0.117244	+	0.200806i
$729$		0			0
$730$	9.70408	+	11.0683i	0.359164	+	0.409656i
$731$	31.6384			1.17019
$732$		0			0
$733$	−44.6299			−1.64844			−0.824222	−	0.566267i	$-0.808387\pi$
$733$	−44.6299			−1.64844			−0.824222	+	0.566267i	$0.808387\pi$
$734$	10.0785	−	17.4565i	0.372006	−	0.644333i
$735$		0			0
$736$	−0.296239	−	0.513101i	−0.0109195	−	0.0189132i
$737$	−27.8480	−	48.2342i	−1.02580	−	1.77673i
$738$		0			0
$739$	−14.6785	+	25.4239i	−0.539957	+	0.935233i	0.458949	+	0.888463i	$0.348226\pi$
$739$	−14.6785	+	25.4239i	−0.539957	+	0.935233i	−0.998906	+	0.0467704i	$0.985107\pi$
$740$	14.8039	+	5.02740i	0.544202	+	0.184811i
$741$		0			0
$742$	−11.9209	−	20.8818i	−0.437629	−	0.766596i
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	0.211134	+	0.977457i	$0.432284\pi$
$743$	−20.1964	+	34.9813i	−0.740936	+	1.28334i	−0.952070	+	0.305881i	$0.901049\pi$
$744$		0			0
$745$	−4.87905	−	24.5454i	−0.178755	−	0.899272i
$746$	−4.94553	−	2.85530i	−0.181069	−	0.104540i
$747$		0			0
$748$	−10.8549			−0.396893
$749$	−11.3819	−	19.9377i	−0.415886	−	0.728509i
$750$		0			0
$751$	−21.8635			−0.797811			−0.398905	−	0.916992i	$-0.630610\pi$
$751$	−21.8635			−0.797811			−0.398905	+	0.916992i	$0.630610\pi$
$752$	3.57645	−	2.06487i	0.130420	−	0.0752979i
$753$		0			0
$754$	5.61892	+	3.24409i	0.204629	+	0.118143i
$755$	40.6817	−	8.08659i	1.48056	−	0.294301i
$756$		0			0
$757$			14.0506i			0.510679i	0.966851	+	0.255339i	$0.0821872\pi$
$757$			14.0506i			0.510679i	−0.966851	+	0.255339i	$0.917813\pi$
$758$	−2.71212	+	4.69753i	−0.0985086	+	0.170622i
$759$		0			0
$760$	−1.85794	+	1.62895i	−0.0673947	+	0.0590881i
$761$	−39.1837			−1.42041			−0.710204	−	0.703996i	$-0.751397\pi$
$761$	−39.1837			−1.42041			−0.710204	+	0.703996i	$0.751397\pi$
$762$		0			0
$763$	−20.1589	+	34.5266i	−0.729800	+	1.24995i
$764$			26.0254i			0.941567i
$765$		0			0
$766$	28.8586	+	16.6615i	1.04270	+	0.602004i
$767$	−16.4558			−0.594184
$768$		0			0
$769$	−16.4424	−	9.49301i	−0.592927	−	0.342327i	0.173327	−	0.984864i	$-0.444548\pi$
$769$	−16.4424	−	9.49301i	−0.592927	−	0.342327i	−0.766254	+	0.642538i	$0.777882\pi$
$770$	23.0472	+	7.95224i	0.830562	+	0.286579i
$771$		0			0
$772$	15.6522	+	9.03678i	0.563334	+	0.325241i
$773$	−28.9315	−	16.7036i	−1.04060	−	0.600788i	−0.120593	−	0.992702i	$-0.538480\pi$
$773$	−28.9315	−	16.7036i	−1.04060	−	0.600788i	−0.920002	+	0.391914i	$0.871813\pi$
$774$		0			0
$775$	8.21362	−	10.6984i	0.295042	−	0.384299i
$776$	−6.92406	−	11.9928i	−0.248559	−	0.430518i
$777$		0			0
$778$	−25.3567	−	14.6397i	−0.909082	−	0.524859i
$779$		−	0.568176i		−	0.0203570i
$780$		0			0
$781$	−6.60044			−0.236182
$782$	1.35151	−	0.780293i	0.0483298	−	0.0279032i
$783$		0			0
$784$	−3.55890	+	6.02779i	−0.127104	+	0.215278i
$785$	17.2034	+	19.6219i	0.614017	+	0.700336i
$786$		0			0
$787$	−0.436343	−	0.755767i	−0.0155539	−	0.0269402i	0.858144	−	0.513410i	$-0.171618\pi$
$787$	−0.436343	−	0.755767i	−0.0155539	−	0.0269402i	−0.873698	+	0.486469i	$0.838285\pi$
$788$	−9.54821	−	16.5380i	−0.340141	−	0.589141i
$789$		0			0
$790$	19.8173	+	22.6032i	0.705067	+	0.804187i
$791$	1.34279	−	2.29984i	0.0477442	−	0.0817727i
$792$		0			0
$793$	−8.81673	+	5.09034i	−0.313091	+	0.180763i
$794$	−10.8543			−0.385203
$795$		0			0
$796$		−	24.9644i		−	0.884840i
$797$	24.9244	+	14.3901i	0.882867	+	0.509724i	0.871603	−	0.490213i	$-0.163081\pi$
$797$	24.9244	+	14.3901i	0.882867	+	0.509724i	0.0112647	+	0.999937i	$0.496414\pi$
$798$		0			0
$799$	5.43885	+	9.42037i	0.192413	+	0.333269i
$800$	−3.96597	−	3.04484i	−0.140218	−	0.107651i
$801$		0			0
$802$	−15.8321	−	9.14066i	−0.559050	−	0.322768i
$803$	−23.4942	−	13.5644i	−0.829091	−	0.478676i
$804$		0			0
$805$	−3.44118	+	0.666616i	−0.121286	+	0.0234951i
$806$	−5.53978	−	3.19839i	−0.195130	−	0.112659i
$807$		0			0
$808$	−2.70907			−0.0953046
$809$	3.58630	+	2.07055i	0.126088	+	0.0727967i	0.561717	−	0.827329i	$-0.310141\pi$
$809$	3.58630	+	2.07055i	0.126088	+	0.0727967i	−0.435630	+	0.900126i	$0.643474\pi$
$810$		0			0
$811$		−	17.4383i		−	0.612342i	−0.951977	−	0.306171i	$-0.900952\pi$
$811$		−	17.4383i		−	0.612342i	0.951977	−	0.306171i	$-0.0990479\pi$
$812$	6.25147	+	3.65001i	0.219383	+	0.128090i
$813$		0			0
$814$	−28.8138			−1.00992
$815$	−20.9150	+	18.3371i	−0.732619	+	0.642321i
$816$		0			0
$817$	−6.63654	+	11.4948i	−0.232183	+	0.402153i
$818$			9.67827i			0.338393i
$819$		0			0
$820$	1.12766	−	0.224154i	0.0393797	−	0.00782779i
$821$	26.6695	+	15.3976i	0.930771	+	0.537381i	0.887055	−	0.461663i	$-0.152747\pi$
$821$	26.6695	+	15.3976i	0.930771	+	0.537381i	0.0437160	+	0.999044i	$0.486080\pi$
$822$		0			0
$823$	30.3149	−	17.5023i	1.05671	−	0.610092i	0.132190	−	0.991224i	$-0.457799\pi$
$823$	30.3149	−	17.5023i	1.05671	−	0.610092i	0.924520	+	0.381133i	$0.124466\pi$
$824$	−18.1448			−0.632103
$825$		0			0
$826$	−18.3599	−	0.0894467i	−0.638823	−	0.00311225i
$827$	−34.7736			−1.20919			−0.604597	−	0.796531i	$-0.706666\pi$
$827$	−34.7736			−1.20919			−0.604597	+	0.796531i	$0.706666\pi$
$828$		0			0
$829$	−7.21777	−	4.16718i	−0.250683	−	0.144732i	0.369394	−	0.929273i	$-0.379565\pi$
$829$	−7.21777	−	4.16718i	−0.250683	−	0.144732i	−0.620077	+	0.784541i	$0.712899\pi$
$830$	1.91477	+	9.63275i	0.0664626	+	0.334358i
$831$		0			0
$832$	−1.18566	+	2.05363i	−0.0411055	+	0.0711968i
$833$	−15.8772	−	9.37413i	−0.550111	−	0.324794i
$834$		0			0
$835$	−27.9215	−	9.48212i	−0.966262	−	0.328142i
$836$	2.27694	−	3.94378i	0.0787496	−	0.136398i
$837$		0			0
$838$	5.02659	+	8.70630i	0.173641	+	0.300754i
$839$	−15.4855	−	26.8216i	−0.534618	−	0.925985i	−0.999182	−	0.0404455i	$-0.987122\pi$
$839$	−15.4855	−	26.8216i	−0.534618	−	0.925985i	0.464564	−	0.885540i	$-0.346211\pi$
$840$		0			0
$841$	−10.7569	+	18.6315i	−0.370928	+	0.642465i
$842$	13.2352			0.456116
$843$		0			0
$844$	13.2338			0.455525
$845$	−10.8743	−	12.4030i	−0.374088	−	0.426677i
$846$		0			0
$847$	−15.8297	−	0.0771197i	−0.543914	−	0.00264987i
$848$	−4.54406	−	7.87055i	−0.156044	−	0.270276i
$849$		0			0
$850$	8.02010	−	10.4464i	0.275087	−	0.358307i
$851$	3.58753	−	2.07126i	0.122979	−	0.0710019i
$852$		0			0
$853$	12.6526	+	21.9150i	0.433217	+	0.750355i	0.997148	−	0.0754673i	$-0.0240449\pi$
$853$	12.6526	+	21.9150i	0.433217	+	0.750355i	−0.563931	+	0.825822i	$0.690712\pi$
$854$	−9.86461	+	5.63143i	−0.337560	+	0.192704i
$855$		0			0
$856$	−4.33862	−	7.51471i	−0.148291	−	0.256848i
$857$			15.0001i			0.512393i	0.966625	+	0.256196i	$0.0824693\pi$
$857$			15.0001i			0.512393i	−0.966625	+	0.256196i	$0.917531\pi$
$858$		0			0
$859$		−	35.2896i		−	1.20406i	−0.798472	−	0.602032i	$-0.794358\pi$
$859$		−	35.2896i		−	1.20406i	0.798472	−	0.602032i	$-0.205642\pi$
$860$	−25.4321	−	8.63673i	−0.867228	−	0.294510i
$861$		0			0
$862$	−4.44716	+	2.56757i	−0.151471	+	0.0874517i
$863$	8.04268	+	13.9303i	0.273776	+	0.474194i	0.969826	−	0.243800i	$-0.0783940\pi$
$863$	8.04268	+	13.9303i	0.273776	+	0.474194i	−0.696050	+	0.717994i	$0.745061\pi$
$864$		0			0
$865$	31.3635	+	10.6510i	1.06639	+	0.362145i
$866$	−3.98681	+	6.90536i	−0.135477	+	0.234654i
$867$		0			0
$868$	−6.16341	−	3.59860i	−0.209200	−	0.122144i
$869$	−47.9789	−	27.7006i	−1.62757	−	0.939679i
$870$		0			0
$871$		−	32.0485i		−	1.08592i
$872$	−7.55567	+	13.0868i	−0.255867	+	0.443175i
$873$		0			0
$874$			0.654705i			0.0221457i
$875$	−24.6813	+	16.3043i	−0.834382	+	0.551187i
$876$		0			0
$877$			27.8272i			0.939657i	0.882758	+	0.469829i	$0.155684\pi$
$877$			27.8272i			0.939657i	−0.882758	+	0.469829i	$0.844316\pi$
$878$	−22.3502	+	12.9039i	−0.754282	+	0.435485i
$879$		0			0
$880$	8.72554	+	2.96319i	0.294138	+	0.0998891i
$881$	−36.4477			−1.22795			−0.613977	−	0.789324i	$-0.710431\pi$
$881$	−36.4477			−1.22795			−0.613977	+	0.789324i	$0.710431\pi$
$882$		0			0
$883$		−	27.9433i		−	0.940367i	−0.882569	−	0.470184i	$-0.844188\pi$
$883$		−	27.9433i		−	0.940367i	0.882569	−	0.470184i	$-0.155812\pi$
$884$	−5.40925	−	3.12303i	−0.181933	−	0.105039i
$885$		0			0
$886$	−15.6440	−	27.0962i	−0.525571	−	0.910316i
$887$			53.1573i			1.78485i	0.451198	+	0.892424i	$0.350997\pi$
$887$			53.1573i			1.78485i	−0.451198	+	0.892424i	$0.649003\pi$
$888$		0			0
$889$	0.0402847	−	8.26888i	0.00135111	−	0.277329i
$890$	−34.3294	+	6.82390i	−1.15072	+	0.228738i
$891$		0			0
$892$	2.44383	−	4.23284i	0.0818255	−	0.141726i
$893$	−4.56347			−0.152711
$894$		0			0
$895$	−50.4552	−	17.1345i	−1.68653	−	0.572745i
$896$	−1.33402	+	2.28482i	−0.0445666	+	0.0763303i
$897$		0			0
$898$	6.00732	+	3.46833i	0.200467	+	0.115740i
$899$	−3.69038	+	6.39192i	−0.123081	+	0.213182i
$900$		0			0
$901$	20.7310	−	11.9690i	0.690650	−	0.398747i
$902$	−1.83506	+	1.05947i	−0.0611006	+	0.0352765i
$903$		0			0
$904$	0.503287	−	0.871718i	0.0167391	−	0.0289929i
$905$	−5.09673	−	25.6404i	−0.169421	−	0.852317i
$906$		0			0
$907$			16.0566i			0.533149i	0.963814	+	0.266575i	$0.0858919\pi$
$907$			16.0566i			0.533149i	−0.963814	+	0.266575i	$0.914108\pi$
$908$	10.3873	−	5.99711i	0.344714	−	0.199021i
$909$		0			0
$910$	9.19707	+	10.5937i	0.304880	+	0.351177i
$911$	36.7577	−	21.2220i	1.21784	−	0.703118i	0.253381	−	0.967367i	$-0.418457\pi$
$911$	36.7577	−	21.2220i	1.21784	−	0.703118i	0.964455	+	0.264249i	$0.0851240\pi$
$912$		0			0
$913$	−9.05021	−	15.6754i	−0.299518	−	0.518781i
$914$	−23.7421	+	13.7075i	−0.785317	+	0.453403i
$915$		0			0
$916$	−9.16676	+	5.29243i	−0.302878	+	0.174867i
$917$	57.0790	+	0.278080i	1.88492	+	0.00918302i
$918$		0			0
$919$	−11.3435	−	19.6475i	−0.374188	−	0.648112i	0.616017	−	0.787732i	$-0.288745\pi$
$919$	−11.3435	−	19.6475i	−0.374188	−	0.648112i	−0.990205	+	0.139621i	$0.955412\pi$
$920$	−1.29940	+	0.258291i	−0.0428399	+	0.00851559i
$921$		0			0
$922$	18.3228			0.603429
$923$	−3.28917	−	1.89900i	−0.108264	−	0.0625064i
$924$		0			0
$925$	21.2891	−	27.7295i	0.699980	−	0.911740i
$926$	−16.6964	+	9.63966i	−0.548677	+	0.316779i
$927$		0			0
$928$	2.36953	+	1.36805i	0.0777835	+	0.0449083i
$929$	2.82041	−	4.88508i	0.0925345	−	0.160274i	−0.816042	−	0.577992i	$-0.803836\pi$
$929$	2.82041	−	4.88508i	0.0925345	−	0.160274i	0.908577	+	0.417718i	$0.137170\pi$
$930$		0			0
$931$	6.73624	−	3.80214i	0.220771	−	0.124610i
$932$	0.259858	−	0.450088i	0.00851194	−	0.0147431i
$933$		0			0
$934$			12.9495i			0.423721i
$935$	−7.80503	+	22.9830i	−0.255252	+	0.751626i
$936$		0			0
$937$	33.6125			1.09807			0.549036	−	0.835799i	$-0.314995\pi$
$937$	33.6125			1.09807			0.549036	+	0.835799i	$0.314995\pi$
$938$	0.174202	−	35.7569i	0.00568790	−	1.16750i
$939$		0			0
$940$	−1.80036	−	9.05716i	−0.0587211	−	0.295412i
$941$	−0.116632	−	0.202012i	−0.00380208	−	0.00658540i	0.864118	−	0.503289i	$-0.167877\pi$
$941$	−0.116632	−	0.202012i	−0.00380208	−	0.00658540i	−0.867920	+	0.496704i	$0.834544\pi$
$942$		0			0
$943$	0.152318	−	0.263823i	0.00496017	−	0.00859126i
$944$	−6.93948			−0.225861
$945$		0			0
$946$	49.5003			1.60939
$947$	1.31252	−	2.27335i	0.0426512	−	0.0738740i	−0.843912	−	0.536482i	$-0.819753\pi$
$947$	1.31252	−	2.27335i	0.0426512	−	0.0738740i	0.886563	+	0.462608i	$0.153086\pi$
$948$		0			0
$949$	−7.80517	−	13.5189i	−0.253366	−	0.438844i
$950$	2.11305	+	5.10511i	0.0685563	+	0.165632i
$951$		0			0
$952$	−6.01820	−	3.51381i	−0.195051	−	0.113883i
$953$	−15.1772			−0.491637			−0.245818	−	0.969316i	$-0.579057\pi$
$953$	−15.1772			−0.491637			−0.245818	+	0.969316i	$0.579057\pi$
$954$		0			0
$955$	55.1038	+	18.7132i	1.78312	+	0.605546i
$956$		−	2.76996i		−	0.0895869i
$957$		0			0
$958$	−13.5378	+	23.4482i	−0.437388	+	0.757578i
$959$	9.96893	+	0.0485671i	0.321914	+	0.00156831i
$960$		0			0
$961$	−11.8616	+	20.5449i	−0.382632	+	0.662739i
$962$	−14.3587	−	8.28999i	−0.462942	−	0.267280i
$963$		0			0
$964$	17.4943	−	10.1004i	0.563454	−	0.325310i
$965$	30.3881	−	26.6427i	0.978228	−	0.857658i
$966$		0			0
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	0.309797	−	0.950803i	$-0.399739\pi$
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	−0.668521	+	0.743693i	$0.733072\pi$
$968$	−5.98313			−0.192305
$969$		0			0
$970$	−30.3712	+	6.03709i	−0.975159	+	0.193839i
$971$	14.3294	+	24.8192i	0.459851	+	0.796486i	0.998953	−	0.0457549i	$-0.0145693\pi$
$971$	14.3294	+	24.8192i	0.459851	+	0.796486i	−0.539101	+	0.842241i	$0.681236\pi$
$972$		0			0
$973$	−13.7362	−	8.02008i	−0.440363	−	0.257112i
$974$	−2.98800	+	1.72512i	−0.0957416	+	0.0552765i
$975$		0			0
$976$	−3.71806	+	2.14662i	−0.119012	+	0.0687117i
$977$	−7.08037	−	12.2636i	−0.226521	−	0.392346i	0.730254	−	0.683176i	$-0.239402\pi$
$977$	−7.08037	−	12.2636i	−0.226521	−	0.392346i	−0.956775	+	0.290830i	$0.906069\pi$
$978$		0			0
$979$	55.8645	−	32.2534i	1.78544	−	1.03082i
$980$	10.2037	+	11.8695i	0.325945	+	0.379157i
$981$		0			0
$982$	−36.9916	+	21.3571i	−1.18045	+	0.681533i
$983$			39.5519i			1.26151i	0.775982	+	0.630755i	$0.217255\pi$
$983$			39.5519i			1.26151i	−0.775982	+	0.630755i	$0.782745\pi$
$984$		0			0
$985$	−41.8815	+	8.32507i	−1.33445	+	0.265259i
$986$	−3.60343	+	6.24132i	−0.114757	+	0.198764i
$987$		0			0
$988$	2.26932	−	1.31019i	0.0721966	−	0.0416827i
$989$	−6.16314	+	3.55829i	−0.195976	+	0.113147i
$990$		0			0
$991$	10.3535	−	17.9329i	0.328891	−	0.569656i	−0.653401	−	0.757012i	$-0.726658\pi$
$991$	10.3535	−	17.9329i	0.328891	−	0.569656i	0.982292	+	0.187356i	$0.0599917\pi$
$992$	−2.33615	−	1.34878i	−0.0741728	−	0.0428237i
$993$		0			0
$994$	−3.65944	−	2.13662i	−0.116070	−	0.0677694i
$995$	−52.8573	−	17.9503i	−1.67569	−	0.569063i
$996$		0			0
$997$	−49.7520			−1.57566			−0.787831	−	0.615892i	$-0.788796\pi$
$997$	−49.7520			−1.57566			−0.787831	+	0.615892i	$0.788796\pi$
$998$	−18.0193	+	31.2103i	−0.570391	+	0.987946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.r.a.1529.3		48
3.2	odd	2		630.2.r.b.59.9	yes	48
5.4	even	2		1890.2.r.b.1529.3		48
7.5	odd	6		1890.2.bi.b.719.8		48
9.2	odd	6		1890.2.bi.a.899.9		48
9.7	even	3		630.2.bi.b.479.9	yes	48
15.14	odd	2		630.2.r.a.59.16	✓	48
21.5	even	6		630.2.bi.a.509.16	yes	48
35.19	odd	6		1890.2.bi.a.719.9		48
45.29	odd	6		1890.2.bi.b.899.8		48
45.34	even	6		630.2.bi.a.479.16	yes	48
63.47	even	6		1890.2.r.b.89.3		48
63.61	odd	6		630.2.r.a.299.16	yes	48
105.89	even	6		630.2.bi.b.509.9	yes	48
315.124	odd	6		630.2.r.b.299.9	yes	48
315.299	even	6	inner	1890.2.r.a.89.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.16	✓	48	15.14	odd	2
630.2.r.a.299.16	yes	48	63.61	odd	6
630.2.r.b.59.9	yes	48	3.2	odd	2
630.2.r.b.299.9	yes	48	315.124	odd	6
630.2.bi.a.479.16	yes	48	45.34	even	6
630.2.bi.a.509.16	yes	48	21.5	even	6
630.2.bi.b.479.9	yes	48	9.7	even	3
630.2.bi.b.509.9	yes	48	105.89	even	6
1890.2.r.a.89.3		48	315.299	even	6	inner
1890.2.r.a.1529.3		48	1.1	even	1	trivial
1890.2.r.b.89.3		48	63.47	even	6
1890.2.r.b.1529.3		48	5.4	even	2
1890.2.bi.a.719.9		48	35.19	odd	6
1890.2.bi.a.899.9		48	9.2	odd	6
1890.2.bi.b.719.8		48	7.5	odd	6
1890.2.bi.b.899.8		48	45.29	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 + 0.435950i) q^{5} +(2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 + 0.435950i) q^{5} +(2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(0.719036 - 2.11731i) q^{10} +4.12106i q^{11} +(-1.18566 + 2.05363i) q^{13} +(-1.33402 + 2.28482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.28111 - 1.31700i) q^{17} +(0.956982 - 0.552514i) q^{19} +(1.47412 + 1.68136i) q^{20} +(-3.56894 - 2.06053i) q^{22} +0.592478 q^{23} +(4.61990 - 1.91221i) q^{25} +(-1.18566 - 2.05363i) q^{26} +(-1.31170 - 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} +(2.33615 - 1.34878i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.28111 - 1.31700i) q^{34} +(-5.80810 + 1.12513i) q^{35} +(6.05512 - 3.49593i) q^{37} +1.10503i q^{38} +(-2.19316 + 0.435950i) q^{40} +(0.257087 - 0.445287i) q^{41} +(-10.4023 + 6.00577i) q^{43} +(3.56894 - 2.06053i) q^{44} +(-0.296239 + 0.513101i) q^{46} +(-3.57645 - 2.06487i) q^{47} +(6.99967 + 0.0682042i) q^{49} +(-0.653922 + 4.95705i) q^{50} +2.37133 q^{52} +(-4.54406 + 7.87055i) q^{53} +(-1.79657 - 9.03814i) q^{55} +(2.64572 + 0.0128895i) q^{56} -2.73609i q^{58} +(3.46974 + 6.00977i) q^{59} +(3.71806 + 2.14662i) q^{61} +2.69755i q^{62} +1.00000 q^{64} +(1.70507 - 5.02083i) q^{65} +(-11.7043 + 6.75750i) q^{67} +2.63400i q^{68} +(1.92966 - 5.59253i) q^{70} +1.60164i q^{71} +(-3.29147 + 5.70100i) q^{73} +6.99185i q^{74} +(-0.956982 - 0.552514i) q^{76} +(-0.0531186 + 10.9032i) q^{77} +(-6.72172 + 11.6424i) q^{79} +(0.719036 - 2.11731i) q^{80} +(0.257087 + 0.445287i) q^{82} +(-3.80374 + 2.19609i) q^{83} +(5.57698 + 1.89394i) q^{85} -12.0115i q^{86} +4.12106i q^{88} +(-7.82648 - 13.5559i) q^{89} +(-3.16341 + 5.41805i) q^{91} +(-0.296239 - 0.513101i) q^{92} +(3.57645 - 2.06487i) q^{94} +(-1.85794 + 1.62895i) q^{95} +(-6.92406 - 11.9928i) q^{97} +(-3.55890 + 6.02779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8	\( 48 q - 24 q^{2} - 24 q^{4} + 48 q^{8} - 3 q^{14} - 24 q^{16} - 6 q^{22} - 6 q^{23} + 3 q^{28} + 3 q^{29} - 24 q^{32} - 12 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} - 42 q^{55} - 9 q^{61} + 48 q^{64} + 21 q^{65} + 33 q^{67} + 12 q^{70} - 18 q^{73} + 6 q^{77} - 3 q^{82} - 9 q^{83} + 33 q^{85} - 33 q^{89} + 3 q^{92} - 33 q^{95} - 24 q^{97} + 3 q^{98}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 + 48 * q^8 - 3 * q^14 - 24 * q^16 - 6 * q^22 - 6 * q^23 + 3 * q^28 + 3 * q^29 - 24 * q^32 - 12 * q^35 - 3 * q^41 + 6 * q^44 + 3 * q^46 - 6 * q^49 + 18 * q^50 - 42 * q^55 - 9 * q^61 + 48 * q^64 + 21 * q^65 + 33 * q^67 + 12 * q^70 - 18 * q^73 + 6 * q^77 - 3 * q^82 - 9 * q^83 + 33 * q^85 - 33 * q^89 + 3 * q^92 - 33 * q^95 - 24 * q^97 + 3 * q^98

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