LMFDB - Embedded newform 1890.2.r.b.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.b.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 - 0.435950i) q^{5} +(-2.64572 - 0.0128895i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 - 0.435950i) q^{5} +(-2.64572 - 0.0128895i) q^{7} -1.00000 q^{8} +(-1.47412 + 1.68136i) q^{10} +4.12106i q^{11} +(1.18566 - 2.05363i) q^{13} +(-1.33402 + 2.28482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.28111 + 1.31700i) q^{17} +(0.956982 - 0.552514i) q^{19} +(0.719036 + 2.11731i) q^{20} +(3.56894 + 2.06053i) q^{22} -0.592478 q^{23} +(4.61990 + 1.91221i) q^{25} +(-1.18566 - 2.05363i) q^{26} +(1.31170 + 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} +(2.33615 - 1.34878i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.28111 - 1.31700i) q^{34} +(5.79687 + 1.18167i) q^{35} +(-6.05512 + 3.49593i) q^{37} -1.10503i q^{38} +(2.19316 + 0.435950i) q^{40} +(0.257087 - 0.445287i) q^{41} +(10.4023 - 6.00577i) q^{43} +(3.56894 - 2.06053i) q^{44} +(-0.296239 + 0.513101i) q^{46} +(3.57645 + 2.06487i) q^{47} +(6.99967 + 0.0682042i) q^{49} +(3.96597 - 3.04484i) q^{50} -2.37133 q^{52} +(4.54406 - 7.87055i) q^{53} +(1.79657 - 9.03814i) q^{55} +(2.64572 + 0.0128895i) q^{56} +2.73609i q^{58} +(3.46974 + 6.00977i) q^{59} +(3.71806 + 2.14662i) q^{61} -2.69755i q^{62} +1.00000 q^{64} +(-3.49563 + 3.98705i) q^{65} +(11.7043 - 6.75750i) q^{67} -2.63400i q^{68} +(3.92179 - 4.42940i) q^{70} +1.60164i q^{71} +(3.29147 - 5.70100i) q^{73} +6.99185i q^{74} +(-0.956982 - 0.552514i) q^{76} +(0.0531186 - 10.9032i) q^{77} +(-6.72172 + 11.6424i) q^{79} +(1.47412 - 1.68136i) q^{80} +(-0.257087 - 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(-4.42869 - 3.88283i) q^{85} -12.0115i q^{86} -4.12106i q^{88} +(-7.82648 - 13.5559i) q^{89} +(-3.16341 + 5.41805i) q^{91} +(0.296239 + 0.513101i) q^{92} +(3.57645 - 2.06487i) q^{94} +(-2.33968 + 0.794555i) q^{95} +(6.92406 + 11.9928i) q^{97} +(3.55890 - 6.02779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 18 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} + 33 q^{65} - 33 q^{67} - 6 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 - 18 * 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 + 33 * q^65 - 33 * q^67 - 6 * 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
$10$	−1.47412	+	1.68136i	−0.466159	+	0.531692i
$11$			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	−0.653439	−	0.756979i	$-0.726674\pi$
$13$	1.18566	−	2.05363i	0.328844	−	0.569575i	0.982283	+	0.187405i	$0.0600076\pi$
$14$	−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	0.750432	−	0.660948i	$-0.229846\pi$
$17$	2.28111	+	1.31700i	0.553250	+	0.319419i	−0.197182	+	0.980367i	$0.563179\pi$
$18$		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	$0.292877\pi$
$20$	0.719036	+	2.11731i	0.160781	+	0.473444i
$21$		0			0
$22$	3.56894	+	2.06053i	0.760901	+	0.439306i
$23$	−0.592478			−0.123540			−0.0617701	−	0.998090i	$-0.519675\pi$
$23$	−0.592478			−0.123540			−0.0617701	+	0.998090i	$0.519675\pi$
$24$		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
$35$	5.79687	+	1.18167i	0.979849	+	0.199739i
$36$		0			0
$37$	−6.05512	+	3.49593i	−0.995456	+	0.574727i	−0.906901	−	0.421345i	$-0.861558\pi$
$37$	−6.05512	+	3.49593i	−0.995456	+	0.574727i	−0.0885553	+	0.996071i	$0.528225\pi$
$38$		−	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	$-0.298168\pi$
$43$	10.4023	−	6.00577i	1.58634	−	0.915872i	0.993904	−	0.110251i	$-0.0351655\pi$
$44$	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	0.737622	−	0.675214i	$-0.235949\pi$
$47$	3.57645	+	2.06487i	0.521679	+	0.301192i	−0.215942	+	0.976406i	$0.569282\pi$
$48$		0			0
$49$	6.99967	+	0.0682042i	0.999953	+	0.00974346i
$50$	3.96597	−	3.04484i	0.560873	−	0.430605i
$51$		0			0
$52$	−2.37133			−0.328844
$53$	4.54406	−	7.87055i	0.624175	−	1.08110i	−0.364525	−	0.931194i	$-0.618768\pi$
$53$	4.54406	−	7.87055i	0.624175	−	1.08110i	0.988700	−	0.149909i	$-0.0478982\pi$
$54$		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
$65$	−3.49563	+	3.98705i	−0.433579	+	0.494533i
$66$		0			0
$67$	11.7043	−	6.75750i	1.42991	−	0.825560i	0.432799	−	0.901491i	$-0.357526\pi$
$67$	11.7043	−	6.75750i	1.42991	−	0.825560i	0.997113	+	0.0759308i	$0.0241928\pi$
$68$		−	2.63400i		−	0.319419i
$69$		0			0
$70$	3.92179	−	4.42940i	0.468743	−	0.529414i
$71$			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	−0.606564	−	0.795035i	$-0.707453\pi$
$73$	3.29147	−	5.70100i	0.385238	−	0.667252i	0.991802	+	0.127783i	$0.0407860\pi$
$74$			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	$0.893695\pi$
$80$	1.47412	−	1.68136i	0.164812	−	0.187981i
$81$		0			0
$82$	−0.257087	−	0.445287i	−0.0283905	−	0.0491738i
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	−0.276499	−	0.961014i	$-0.589174\pi$
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	0.694013	+	0.719962i	$0.255841\pi$
$84$		0			0
$85$	−4.42869	−	3.88283i	−0.480359	−	0.421152i
$86$		−	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
$95$	−2.33968	+	0.794555i	−0.240046	+	0.0815196i
$96$		0			0
$97$	6.92406	+	11.9928i	0.703032	+	1.21769i	0.967397	+	0.253265i	$0.0815044\pi$
$97$	6.92406	+	11.9928i	0.703032	+	1.21769i	−0.264365	+	0.964423i	$0.585162\pi$
$98$	3.55890	−	6.02779i	0.359503	−	0.608899i
$99$		0			0
$100$	−0.653922	−	4.95705i	−0.0653922	−	0.495705i
$101$	−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	$-0.147938\pi$
$103$	18.1448			1.78786			0.893929	+	0.448209i	$0.147938\pi$
$104$	−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	0.995882	−	0.0906565i	$-0.0288965\pi$
$107$	4.33862	+	7.51471i	0.419430	+	0.726475i	−0.576452	+	0.817131i	$0.695563\pi$
$108$		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	$0.909106\pi$
$110$	−6.92897	−	6.07495i	−0.660651	−	0.579224i
$111$		0			0
$112$	1.33402	−	2.28482i	0.126053	−	0.215895i
$113$	−0.503287	+	0.871718i	−0.0473452	+	0.0820044i	−0.888727	−	0.458437i	$-0.848409\pi$
$113$	−0.503287	+	0.871718i	−0.0473452	+	0.0820044i	0.841382	+	0.540441i	$0.181743\pi$
$114$		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	$0.0442816\pi$
$127$			3.12538i			0.277333i	−0.990339	+	0.138666i	$0.955718\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	1.70507	+	5.02083i	0.149545	+	0.440356i
$131$	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	$-0.551459\pi$
$137$	−3.76795			−0.321917			−0.160959	+	0.986961i	$0.551459\pi$
$138$		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	$0.748730\pi$
$140$	−1.87508	−	5.61107i	−0.158473	−	0.474222i
$141$		0			0
$142$	1.38706	+	0.800818i	0.116399	+	0.0672032i
$143$	8.46313	+	4.88619i	0.707723	+	0.408604i
$144$		0			0
$145$	5.79315	−	1.96735i	0.481095	−	0.163379i
$146$	−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
$155$	−5.71154	+	1.93964i	−0.458762	+	0.155795i
$156$		0			0
$157$	5.83514	+	10.1068i	0.465695	+	0.806607i	0.999233	−	0.0391693i	$-0.0124712\pi$
$157$	5.83514	+	10.1068i	0.465695	+	0.806607i	−0.533538	+	0.845776i	$0.679138\pi$
$158$	6.72172	+	11.6424i	0.534751	+	0.926217i
$159$		0			0
$160$	−0.719036	−	2.11731i	−0.0568448	−	0.167388i
$161$	1.56753	+	0.00763677i	0.123539	+	0.000601862i
$162$		0			0
$163$	−10.7728	+	6.21967i	−0.843789	+	0.487162i	−0.858550	−	0.512729i	$-0.828634\pi$
$163$	−10.7728	+	6.21967i	−0.843789	+	0.487162i	0.0147613	+	0.999891i	$0.495301\pi$
$164$	−0.514173			−0.0401502
$165$		0			0
$166$		−	4.39218i		−	0.340899i
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.0118537	−	0.999930i	$-0.503773\pi$
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.871891	+	0.489699i	$0.837107\pi$
$168$		0			0
$169$	3.68840	+	6.38850i	0.283723	+	0.491423i
$170$	−5.57698	+	1.89394i	−0.427735	+	0.145258i
$171$		0			0
$172$	−10.4023	−	6.00577i	−0.793168	−	0.457936i
$173$	12.8284	+	7.40645i	0.975321	+	0.563102i	0.900854	−	0.434121i	$-0.142941\pi$
$173$	12.8284	+	7.40645i	0.975321	+	0.563102i	0.0744670	+	0.997223i	$0.476274\pi$
$174$		0			0
$175$	−12.1983	−	5.11873i	−0.922105	−	0.386940i
$176$	−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
$185$	14.8039	−	5.02740i	1.08840	−	0.369621i
$186$		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	0.183573	−	0.983006i	$-0.441234\pi$
$193$	15.6522	−	9.03678i	1.12667	−	0.650482i	0.943095	+	0.332524i	$0.107900\pi$
$194$	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	$-0.738142\pi$
$197$	−19.0964			−1.36056			−0.680281	+	0.732951i	$0.738142\pi$
$198$		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
$205$	−0.757955	+	0.864509i	−0.0529379	+	0.0603799i
$206$	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
$215$	−25.4321	+	8.63673i	−1.73446	+	0.589020i
$216$		0			0
$217$	−6.19818	+	3.53837i	−0.420760	+	0.240200i
$218$	7.55567	+	13.0868i	0.511735	+	0.886351i
$219$		0			0
$220$	−8.72554	+	2.96319i	−0.588276	+	0.199778i
$221$	5.40925	−	3.12303i	0.363866	−	0.210078i
$222$		0			0
$223$	−2.44383	−	4.23284i	−0.163651	−	0.283452i	0.772524	−	0.634985i	$-0.218994\pi$
$223$	−2.44383	−	4.23284i	−0.163651	−	0.283452i	−0.936175	+	0.351533i	$0.885660\pi$
$224$	−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	$-0.869690\pi$
$227$		−	11.9942i		−	0.796084i	0.917367	−	0.398042i	$-0.130310\pi$
$228$		0			0
$229$		−	10.5849i		−	0.699467i	−0.936849	−	0.349734i	$-0.886272\pi$
$229$		−	10.5849i		−	0.699467i	0.936849	−	0.349734i	$-0.113728\pi$
$230$	0.873386	−	0.996168i	0.0575894	−	0.0656853i
$231$		0			0
$232$	2.36953	−	1.36805i	0.155567	−	0.0898166i
$233$	−0.259858	−	0.450088i	−0.0170239	−	0.0294862i	0.857388	−	0.514671i	$-0.172086\pi$
$233$	−0.259858	−	0.450088i	−0.0170239	−	0.0294862i	−0.874412	+	0.485184i	$0.838752\pi$
$234$		0			0
$235$	−6.94356	−	6.08774i	−0.452948	−	0.397120i
$236$	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
$245$	−15.3217	−	3.20109i	−0.978865	−	0.204510i
$246$		0			0
$247$		−	2.62038i		−	0.166731i
$248$	−2.33615	+	1.34878i	−0.148346	+	0.0856474i
$249$		0			0
$250$	−10.0254	+	4.94886i	−0.634063	+	0.312993i
$251$	−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	$-0.904426\pi$
$257$		−	9.48293i		−	0.591529i	0.955261	−	0.295764i	$-0.0955743\pi$
$258$		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	$-0.382811\pi$
$263$	11.6732			0.719800			0.359900	+	0.932991i	$0.382811\pi$
$264$		0			0
$265$	−13.3970	+	15.2804i	−0.822972	+	0.938667i
$266$	−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	$0.214142\pi$
$277$			20.7421i			1.24627i	−0.782114	+	0.623136i	$0.785858\pi$
$278$	−5.20651	+	3.00598i	−0.312265	+	0.180287i
$279$		0			0
$280$	−5.79687	−	1.18167i	−0.346429	−	0.0706183i
$281$	−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	0.554074	−	0.832468i	$-0.313073\pi$
$283$	−7.46757	−	12.9342i	−0.443901	−	0.768859i	−0.997975	+	0.0636082i	$0.979739\pi$
$284$	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	0.754327	−	0.656499i	$-0.227963\pi$
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	−0.191382	+	0.981516i	$0.561297\pi$
$294$		0			0
$295$	−4.98974	−	14.6930i	−0.290514	−	0.855460i
$296$	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
$305$	−7.21847	−	6.32877i	−0.413329	−	0.362384i
$306$		0			0
$307$	14.1337			0.806651			0.403325	−	0.915057i	$-0.367854\pi$
$307$	14.1337			0.806651			0.403325	+	0.915057i	$0.367854\pi$
$308$	−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	$-0.652508\pi$
$313$	9.51843	−	16.4864i	0.538014	−	0.931867i	0.999011	−	0.0444656i	$-0.0141585\pi$
$314$	11.6703			0.658592
$315$		0			0
$316$	13.4434			0.756253
$317$	−7.70830	+	13.3512i	−0.432941	+	0.749876i	−0.997125	−	0.0757731i	$-0.975858\pi$
$317$	−7.70830	+	13.3512i	−0.432941	+	0.749876i	0.564184	+	0.825649i	$0.309191\pi$
$318$		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
$325$	9.40463	−	7.22032i	0.521675	−	0.400511i
$326$			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
$335$	−28.6154	+	9.71777i	−1.56343	+	0.530939i
$336$		0			0
$337$	−21.3417	−	12.3216i	−1.16256	−	0.671202i	−0.210640	−	0.977564i	$-0.567555\pi$
$337$	−21.3417	−	12.3216i	−1.16256	−	0.671202i	−0.951915	+	0.306362i	$0.900888\pi$
$338$	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	0.873262	−	0.487251i	$-0.162000\pi$
$347$	0.273072	+	0.472975i	0.0146593	+	0.0253906i	−0.858603	+	0.512642i	$0.828667\pi$
$348$		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	$0.277664\pi$
$350$	−10.5321	+	8.00467i	−0.562965	+	0.427868i
$351$		0			0
$352$	−3.56894	+	2.06053i	−0.190225	+	0.109827i
$353$			6.55439i			0.348855i	0.984670	+	0.174427i	$0.0558074\pi$
$353$			6.55439i			0.348855i	−0.984670	+	0.174427i	$0.944193\pi$
$354$		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
$365$	−9.70408	+	11.0683i	−0.507935	+	0.579341i
$366$		0			0
$367$	20.1571			1.05219			0.526096	−	0.850425i	$-0.323655\pi$
$367$	20.1571			1.05219			0.526096	+	0.850425i	$0.323655\pi$
$368$	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	$-0.952767\pi$
$373$		−	5.71061i		−	0.295684i	0.989011	−	0.147842i	$-0.0472327\pi$
$374$	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	$0.455511\pi$
$380$	1.85794	+	1.62895i	0.0953106	+	0.0835632i
$381$		0			0
$382$	−22.5387	+	13.0127i	−1.15318	+	0.665789i
$383$			33.3230i			1.70273i	0.524578	+	0.851363i	$0.324223\pi$
$383$			33.3230i			1.70273i	−0.524578	+	0.851363i	$0.675777\pi$
$384$		0			0
$385$	−4.86973	+	23.8892i	−0.248184	+	1.21751i
$386$		−	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
$395$	19.8173	−	22.6032i	0.997116	−	1.13729i
$396$		0			0
$397$	−5.42713	−	9.40006i	−0.272380	−	0.471775i	0.697091	−	0.716983i	$-0.254477\pi$
$397$	−5.42713	−	9.40006i	−0.272380	−	0.471775i	−0.969471	+	0.245207i	$0.921144\pi$
$398$	21.6198	−	12.4822i	1.08370	−	0.625676i
$399$		0			0
$400$	−3.96597	+	3.04484i	−0.198299	+	0.152242i
$401$			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	$0.256422\pi$
$410$	0.369709	+	1.08866i	0.0182586	+	0.0537652i
$411$		0			0
$412$	−9.07239	−	15.7138i	−0.446964	−	0.774165i
$413$	−9.10250	−	15.9449i	−0.447905	−	0.784596i
$414$		0			0
$415$	−9.29959	+	3.15814i	−0.456499	+	0.155027i
$416$	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
$425$	8.02010	+	10.4464i	0.389032	+	0.506723i
$426$		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	$-0.561366\pi$
$433$	−7.97362			−0.383188			−0.191594	+	0.981474i	$0.561366\pi$
$434$	−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	$-0.566607\pi$
$443$	15.6440	−	27.0962i	0.743269	−	1.28738i	0.950999	−	0.309194i	$-0.100059\pi$
$444$		0			0
$445$	11.2550	+	33.1421i	0.533540	+	1.57109i
$446$	−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
$455$	9.29985	−	10.5036i	0.435984	−	0.492414i
$456$		0			0
$457$	−23.7421	−	13.7075i	−1.11061	−	0.641209i	−0.171620	−	0.985163i	$-0.554900\pi$
$457$	−23.7421	−	13.7075i	−1.11061	−	0.641209i	−0.938986	+	0.343954i	$0.888233\pi$
$458$	−9.16676	−	5.29243i	−0.428335	−	0.247299i
$459$		0			0
$460$	−0.426013	−	1.25446i	−0.0198630	−	0.0584894i
$461$	−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	0.0590450	−	0.998255i	$-0.481194\pi$
$463$	−16.6964	−	9.63966i	−0.775947	−	0.447993i	−0.834992	+	0.550262i	$0.814528\pi$
$464$		−	2.73609i		−	0.127020i
$465$		0			0
$466$	−0.519717			−0.0240754
$467$	−11.2146	+	6.47476i	−0.518951	+	0.299616i	−0.736505	−	0.676432i	$-0.763525\pi$
$467$	−11.2146	+	6.47476i	−0.518951	+	0.299616i	0.217555	+	0.976048i	$0.430192\pi$
$468$		0			0
$469$	−31.0535	+	17.7276i	−1.43392	+	0.818584i
$470$	−8.74391	+	2.96943i	−0.403327	+	0.136970i
$471$		0			0
$472$	−3.46974	−	6.00977i	−0.159708	−	0.276622i
$473$	24.7501	+	42.8685i	1.13801	+	1.97110i
$474$		0			0
$475$	5.47768	−	0.722602i	0.251333	−	0.0331552i
$476$	−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
$485$	−9.95731	−	29.3207i	−0.452138	−	1.33139i
$486$		0			0
$487$	−2.98800	−	1.72512i	−0.135399	−	0.0781727i	0.430770	−	0.902462i	$-0.358242\pi$
$487$	−2.98800	−	1.72512i	−0.135399	−	0.0781727i	−0.566169	+	0.824289i	$0.691575\pi$
$488$	−3.71806	−	2.14662i	−0.168309	−	0.0971730i
$489$		0			0
$490$	−10.4330	+	11.6684i	−0.471317	+	0.527125i
$491$	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	$0.201276\pi$
$500$	−0.726870	+	11.1567i	−0.0325066	+	0.498942i
$501$		0			0
$502$	−10.4934	+	18.1752i	−0.468345	+	0.811198i
$503$			4.41774i			0.196977i	0.995138	+	0.0984887i	$0.0314008\pi$
$503$			4.41774i			0.196977i	−0.995138	+	0.0984887i	$0.968599\pi$
$504$		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
$520$	3.49563	−	3.98705i	0.153293	−	0.174844i
$521$	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	0.859514	−	0.511111i	$-0.170766\pi$
$523$	−0.294517	−	0.510118i	−0.0128783	−	0.0223059i	−0.872393	+	0.488806i	$0.837433\pi$
$524$	−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
$530$	6.53469	+	19.2424i	0.283849	+	0.835834i
$531$		0			0
$532$	2.52478	+	1.47413i	0.109463	+	0.0639117i
$533$	−0.609637	−	1.05592i	−0.0264063	−	0.0457371i
$534$		0			0
$535$	−6.23925	−	18.3724i	−0.269746	−	0.794307i
$536$	−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
$545$	22.2760	−	25.4076i	0.954198	−	1.08834i
$546$		0			0
$547$	−7.46589	+	4.31044i	−0.319219	+	0.184301i	−0.651044	−	0.759040i	$-0.725669\pi$
$547$	−7.46589	+	4.31044i	−0.319219	+	0.184301i	0.331826	+	0.943341i	$0.392335\pi$
$548$	1.88397	+	3.26314i	0.0804793	+	0.139394i
$549$		0			0
$550$	12.5480	+	16.3440i	0.535047	+	0.696911i
$551$	−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	−0.793024	−	0.609191i	$-0.791494\pi$
$557$	3.09319	−	5.35757i	0.131063	−	0.227007i	0.924087	+	0.382183i	$0.124828\pi$
$558$		0			0
$559$		−	28.4833i		−	1.20472i
$560$	−3.92179	+	4.42940i	−0.165726	+	0.187176i
$561$		0			0
$562$			1.36041i			0.0573856i
$563$	−28.2325	+	16.3001i	−1.18986	+	0.686966i	−0.958275	−	0.285849i	$-0.907725\pi$
$563$	−28.2325	+	16.3001i	−1.18986	+	0.686966i	−0.231585	+	0.972815i	$0.574391\pi$
$564$		0			0
$565$	1.48381	−	1.69241i	0.0624245	−	0.0712002i
$566$	−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	−0.999984	−	0.00570479i	$-0.998184\pi$
$577$	−11.8915	+	20.5968i	−0.495051	+	0.857454i	0.504932	+	0.863159i	$0.331517\pi$
$578$	−10.0621			−0.418527
$579$		0			0
$580$	−4.60035	−	4.03334i	−0.191019	−	0.167475i
$581$	−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	−0.764854	−	0.644204i	$-0.777189\pi$
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	0.175470	+	0.984485i	$0.443855\pi$
$588$		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	−0.667733	−	0.744401i	$-0.732735\pi$
$593$	−8.69178	+	5.01820i	−0.356928	+	0.206073i	0.310804	+	0.950474i	$0.399402\pi$
$594$		0			0
$595$	11.6670	+	10.3300i	0.478301	+	0.423488i
$596$	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	$-0.663305\pi$
$607$	−24.1853			−0.981653			−0.490827	+	0.871257i	$0.663305\pi$
$608$	0.956982	+	0.552514i	0.0388107	+	0.0224074i
$609$		0			0
$610$	−9.09011	+	3.08700i	−0.368048	+	0.124989i
$611$	8.48095	−	4.89648i	0.343102	−	0.198090i
$612$		0			0
$613$	23.6618	+	13.6611i	0.955690	+	0.551768i	0.894844	−	0.446379i	$-0.147287\pi$
$613$	23.6618	+	13.6611i	0.955690	+	0.551768i	0.0608460	+	0.998147i	$0.480620\pi$
$614$	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	−0.666269	−	0.745712i	$-0.732110\pi$
$617$	7.76658	−	13.4521i	0.312671	−	0.541562i	0.978940	+	0.204150i	$0.0654430\pi$
$618$		0			0
$619$			21.2581i			0.854435i	0.904149	+	0.427218i	$0.140506\pi$
$619$			21.2581i			0.854435i	−0.904149	+	0.427218i	$0.859494\pi$
$620$	4.53555	+	3.97652i	0.182152	+	0.159701i
$621$		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
$640$	−1.47412	+	1.68136i	−0.0582698	+	0.0664615i
$641$			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	−0.875813	−	0.482651i	$-0.839674\pi$
$643$	−0.505064	+	0.874797i	−0.0199178	+	0.0344986i	0.855895	+	0.517150i	$0.173007\pi$
$644$	−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	0.233611	−	0.972330i	$-0.424946\pi$
$647$	−12.5056	−	7.22013i	−0.491647	−	0.283852i	−0.725257	+	0.688478i	$0.758279\pi$
$648$		0			0
$649$	−24.7666	+	14.2990i	−0.972174	+	0.561285i
$650$	−1.55066	−	11.7548i	−0.0608220	−	0.461061i
$651$		0			0
$652$	10.7728	+	6.21967i	0.421895	+	0.243581i
$653$	−44.2235			−1.73060			−0.865299	−	0.501256i	$-0.832871\pi$
$653$	−44.2235			−1.73060			−0.865299	+	0.501256i	$0.832871\pi$
$654$		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
$665$	6.20038	−	2.07201i	0.240441	−	0.0803492i
$666$		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	−0.797132	−	0.603805i	$-0.793651\pi$
$673$	−17.4536	+	10.0769i	−0.672788	+	0.388434i	0.124344	+	0.992239i	$0.460317\pi$
$674$	−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	0.888076	−	0.459697i	$-0.152042\pi$
$677$	24.3021	+	14.0308i	0.934004	+	0.539248i	0.0459284	+	0.998945i	$0.485375\pi$
$678$		0			0
$679$	−18.1646	−	31.8189i	−0.697092	−	1.22110i
$680$	4.42869	+	3.88283i	0.169832	+	0.148900i
$681$		0			0
$682$	11.1168			0.425683
$683$	14.7248	−	25.5040i	0.563428	−	0.975885i	−0.433767	−	0.901025i	$-0.642816\pi$
$683$	14.7248	−	25.5040i	0.563428	−	0.975885i	0.997194	−	0.0748598i	$-0.0238509\pi$
$684$		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
$695$	10.1082	+	8.86236i	0.383427	+	0.336169i
$696$		0			0
$697$	1.17288	−	0.677165i	0.0444262	−	0.0256495i
$698$		−	6.50116i		−	0.246073i
$699$		0			0
$700$	1.66620	+	13.1234i	0.0629765	+	0.496018i
$701$			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	$0.160563\pi$
$710$	−2.69292	−	2.36101i	−0.101064	−	0.0886071i
$711$		0			0
$712$	7.82648	+	13.5559i	0.293310	+	0.508027i
$713$	−1.38412	+	0.799121i	−0.0518356	+	0.0299273i
$714$		0			0
$715$	−16.4309	−	14.4057i	−0.614479	−	0.538742i
$716$		−	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
$725$	−13.5630	+	1.78919i	−0.503716	+	0.0664489i
$726$		0			0
$727$	7.79834	+	13.5071i	0.289224	+	0.500951i	0.973625	−	0.228155i	$-0.0732693\pi$
$727$	7.79834	+	13.5071i	0.289224	+	0.500951i	−0.684400	+	0.729106i	$0.739936\pi$
$728$	3.16341	−	5.41805i	0.117244	−	0.200806i
$729$		0			0
$730$	4.73338	+	13.9381i	0.175190	+	0.515873i
$731$	31.6384			1.17019
$732$		0			0
$733$	44.6299			1.64844			0.824222	−	0.566267i	$-0.191613\pi$
$733$	44.6299			1.64844			0.824222	+	0.566267i	$0.191613\pi$
$734$	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	$0.985107\pi$
$740$	−11.7558	−	10.3069i	−0.432152	−	0.378887i
$741$		0			0
$742$	11.9209	+	20.8818i	0.437629	+	0.766596i
$743$	20.1964	−	34.9813i	0.740936	−	1.28334i	−0.211134	−	0.977457i	$-0.567716\pi$
$743$	20.1964	−	34.9813i	0.740936	−	1.28334i	0.952070	−	0.305881i	$-0.0989510\pi$
$744$		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	$-0.917813\pi$
$757$		−	14.0506i		−	0.510679i	0.966851	−	0.255339i	$-0.0821872\pi$
$758$	2.71212	−	4.69753i	0.0985086	−	0.170622i
$759$		0			0
$760$	2.33968	−	0.794555i	0.0848692	−	0.0288215i
$761$	−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	$0.777882\pi$
$770$	18.2538	+	16.1619i	0.657822	+	0.582435i
$771$		0			0
$772$	−15.6522	−	9.03678i	−0.563334	−	0.325241i
$773$	28.9315	+	16.7036i	1.04060	+	0.600788i	0.920002	−	0.391914i	$-0.128187\pi$
$773$	28.9315	+	16.7036i	1.04060	+	0.600788i	0.120593	+	0.992702i	$0.461520\pi$
$774$		0			0
$775$	13.3719	−	1.76399i	0.480333	−	0.0633644i
$776$	−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
$785$	−8.39135	−	24.7096i	−0.299500	−	0.881922i
$786$		0			0
$787$	0.436343	+	0.755767i	0.0155539	+	0.0269402i	0.873698	−	0.486469i	$-0.161715\pi$
$787$	0.436343	+	0.755767i	0.0155539	+	0.0269402i	−0.858144	+	0.513410i	$0.828382\pi$
$788$	9.54821	+	16.5380i	0.340141	+	0.589141i
$789$		0			0
$790$	−9.66632	−	28.4639i	−0.343912	−	1.01270i
$791$	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	−0.0112647	−	0.999937i	$-0.503586\pi$
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.871603	+	0.490213i	$0.836919\pi$
$798$		0			0
$799$	5.43885	+	9.42037i	0.192413	+	0.333269i
$800$	0.653922	+	4.95705i	0.0231196	+	0.175258i
$801$		0			0
$802$	15.8321	+	9.14066i	0.559050	+	0.322768i
$803$	23.4942	+	13.5644i	0.829091	+	0.478676i
$804$		0			0
$805$	−3.43452	−	0.700114i	−0.121051	−	0.0246758i
$806$	−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
$815$	26.3379	−	8.94433i	0.922576	−	0.313306i
$816$		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	−0.924520	−	0.381133i	$-0.875534\pi$
$823$	−30.3149	+	17.5023i	−1.05671	+	0.610092i	−0.132190	+	0.991224i	$0.542201\pi$
$824$	−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	$-0.293334\pi$
$827$	34.7736			1.20919			0.604597	+	0.796531i	$0.293334\pi$
$828$		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
$835$	22.1725	+	19.4396i	0.767311	+	0.672737i
$836$	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
$845$	−5.30419	−	15.6190i	−0.182470	−	0.537308i
$846$		0			0
$847$	15.8297	+	0.0771197i	0.543914	+	0.00264987i
$848$	4.54406	+	7.87055i	0.156044	+	0.270276i
$849$		0			0
$850$	13.0569	−	1.72243i	0.447847	−	0.0590788i
$851$	3.58753	−	2.07126i	0.122979	−	0.0710019i
$852$		0			0
$853$	−12.6526	−	21.9150i	−0.433217	−	0.750355i	0.563931	−	0.825822i	$-0.309288\pi$
$853$	−12.6526	−	21.9150i	−0.433217	−	0.750355i	−0.997148	+	0.0754673i	$0.975955\pi$
$854$	−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	$-0.917531\pi$
$857$		−	15.0001i		−	0.512393i	0.966625	−	0.256196i	$-0.0824693\pi$
$858$		0			0
$859$		−	35.2896i		−	1.20406i	−0.798472	−	0.602032i	$-0.794358\pi$
$859$		−	35.2896i		−	1.20406i	0.798472	−	0.602032i	$-0.205642\pi$
$860$	20.1957	+	17.7065i	0.688667	+	0.603786i
$861$		0			0
$862$	4.44716	−	2.56757i	0.151471	−	0.0874517i
$863$	−8.04268	−	13.9303i	−0.273776	−	0.474194i	0.696050	−	0.717994i	$-0.254939\pi$
$863$	−8.04268	−	13.9303i	−0.273776	−	0.474194i	−0.969826	+	0.243800i	$0.921606\pi$
$864$		0			0
$865$	−24.9058	−	21.8360i	−0.846822	−	0.742448i
$866$	−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
$875$	24.5213	+	16.5440i	0.828972	+	0.559291i
$876$		0			0
$877$		−	27.8272i		−	0.939657i	−0.882758	−	0.469829i	$-0.844316\pi$
$877$		−	27.8272i		−	0.939657i	0.882758	−	0.469829i	$-0.155684\pi$
$878$	22.3502	−	12.9039i	0.754282	−	0.435485i
$879$		0			0
$880$	6.92897	+	6.07495i	0.233576	+	0.204786i
$881$	−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	$0.155812\pi$
$883$			27.9433i			0.940367i	−0.882569	+	0.470184i	$0.844188\pi$
$884$	−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	$-0.649003\pi$
$887$		−	53.1573i		−	1.78485i	0.451198	−	0.892424i	$-0.350997\pi$
$888$		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
$895$	−40.0665	−	35.1282i	−1.33928	−	1.17421i
$896$	−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	$-0.914108\pi$
$907$		−	16.0566i		−	0.533149i	0.963814	−	0.266575i	$-0.0858919\pi$
$908$	−10.3873	+	5.99711i	−0.344714	+	0.199021i
$909$		0			0
$910$	−4.44642	−	13.3057i	−0.147398	−	0.441079i
$911$	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
$925$	−34.6590	+	4.57213i	−1.13958	+	0.150331i
$926$	−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
$935$	16.0014	−	18.2509i	0.523301	−	0.596868i
$936$		0			0
$937$	−33.6125			−1.09807			−0.549036	−	0.835799i	$-0.685005\pi$
$937$	−33.6125			−1.09807			−0.549036	+	0.835799i	$0.685005\pi$
$938$	−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	−0.886563	−	0.462608i	$-0.846914\pi$
$947$	−1.31252	+	2.27335i	−0.0426512	+	0.0738740i	0.843912	+	0.536482i	$0.180247\pi$
$948$		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	$-0.420943\pi$
$953$	15.1772			0.491637			0.245818	+	0.969316i	$0.420943\pi$
$954$		0			0
$955$	43.7581	+	38.3647i	1.41598	+	1.24145i
$956$		−	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
$965$	−38.2673	+	12.9956i	−1.23187	+	0.418342i
$966$		0			0
$967$	11.1551	+	6.44040i	0.358724	+	0.207109i	0.668521	−	0.743693i	$-0.266928\pi$
$967$	11.1551	+	6.44040i	0.358724	+	0.207109i	−0.309797	+	0.950803i	$0.600261\pi$
$968$	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	0.956775	−	0.290830i	$-0.0939315\pi$
$977$	7.08037	+	12.2636i	0.226521	+	0.392346i	−0.730254	+	0.683176i	$0.760598\pi$
$978$		0			0
$979$	55.8645	−	32.2534i	1.78544	−	1.03082i
$980$	4.88861	+	14.8695i	0.156161	+	0.474988i
$981$		0			0
$982$	36.9916	−	21.3571i	1.18045	−	0.681533i
$983$		−	39.5519i		−	1.26151i	−0.775982	−	0.630755i	$-0.782745\pi$
$983$		−	39.5519i		−	1.26151i	0.775982	−	0.630755i	$-0.217255\pi$
$984$		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
$995$	−41.9741	−	36.8006i	−1.33067	−	1.16666i
$996$		0			0
$997$	49.7520			1.57566			0.787831	−	0.615892i	$-0.211204\pi$
$997$	49.7520			1.57566			0.787831	+	0.615892i	$0.211204\pi$
$998$	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.b.1529.3		48
3.2	odd	2		630.2.r.a.59.16	✓	48
5.4	even	2		1890.2.r.a.1529.3		48
7.5	odd	6		1890.2.bi.a.719.9		48
9.2	odd	6		1890.2.bi.b.899.8		48
9.7	even	3		630.2.bi.a.479.16	yes	48
15.14	odd	2		630.2.r.b.59.9	yes	48
21.5	even	6		630.2.bi.b.509.9	yes	48
35.19	odd	6		1890.2.bi.b.719.8		48
45.29	odd	6		1890.2.bi.a.899.9		48
45.34	even	6		630.2.bi.b.479.9	yes	48
63.47	even	6		1890.2.r.a.89.3		48
63.61	odd	6		630.2.r.b.299.9	yes	48
105.89	even	6		630.2.bi.a.509.16	yes	48
315.124	odd	6		630.2.r.a.299.16	yes	48
315.299	even	6	inner	1890.2.r.b.89.3		48

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 - 0.435950i) q^{5} +(-2.64572 - 0.0128895i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.19316 - 0.435950i) q^{5} +(-2.64572 - 0.0128895i) q^{7} -1.00000 q^{8} +(-1.47412 + 1.68136i) q^{10} +4.12106i q^{11} +(1.18566 - 2.05363i) q^{13} +(-1.33402 + 2.28482i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.28111 + 1.31700i) q^{17} +(0.956982 - 0.552514i) q^{19} +(0.719036 + 2.11731i) q^{20} +(3.56894 + 2.06053i) q^{22} -0.592478 q^{23} +(4.61990 + 1.91221i) q^{25} +(-1.18566 - 2.05363i) q^{26} +(1.31170 + 2.29771i) q^{28} +(-2.36953 + 1.36805i) q^{29} +(2.33615 - 1.34878i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.28111 - 1.31700i) q^{34} +(5.79687 + 1.18167i) q^{35} +(-6.05512 + 3.49593i) q^{37} -1.10503i q^{38} +(2.19316 + 0.435950i) q^{40} +(0.257087 - 0.445287i) q^{41} +(10.4023 - 6.00577i) q^{43} +(3.56894 - 2.06053i) q^{44} +(-0.296239 + 0.513101i) q^{46} +(3.57645 + 2.06487i) q^{47} +(6.99967 + 0.0682042i) q^{49} +(3.96597 - 3.04484i) q^{50} -2.37133 q^{52} +(4.54406 - 7.87055i) q^{53} +(1.79657 - 9.03814i) q^{55} +(2.64572 + 0.0128895i) q^{56} +2.73609i q^{58} +(3.46974 + 6.00977i) q^{59} +(3.71806 + 2.14662i) q^{61} -2.69755i q^{62} +1.00000 q^{64} +(-3.49563 + 3.98705i) q^{65} +(11.7043 - 6.75750i) q^{67} -2.63400i q^{68} +(3.92179 - 4.42940i) q^{70} +1.60164i q^{71} +(3.29147 - 5.70100i) q^{73} +6.99185i q^{74} +(-0.956982 - 0.552514i) q^{76} +(0.0531186 - 10.9032i) q^{77} +(-6.72172 + 11.6424i) q^{79} +(1.47412 - 1.68136i) q^{80} +(-0.257087 - 0.445287i) q^{82} +(3.80374 - 2.19609i) q^{83} +(-4.42869 - 3.88283i) q^{85} -12.0115i q^{86} -4.12106i q^{88} +(-7.82648 - 13.5559i) q^{89} +(-3.16341 + 5.41805i) q^{91} +(0.296239 + 0.513101i) q^{92} +(3.57645 - 2.06487i) q^{94} +(-2.33968 + 0.794555i) q^{95} +(6.92406 + 11.9928i) q^{97} +(3.55890 - 6.02779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61} + 48 q^{64} + 33 q^{65} - 33 q^{67} - 6 q^{70} + 18 q^{73} - 6 q^{77} + 3 q^{82} + 9 q^{83} - 33 q^{85} - 33 q^{89} - 3 q^{92} - 33 q^{95} + 24 q^{97} - 3 q^{98}+O(q^{100}) \) 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 - 18 * 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 + 33 * q^65 - 33 * q^67 - 6 * 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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