LMFDB - Embedded newform 1890.2.bi.b.719.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(719,1890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1890, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1890.719"); 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.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			719.11
Character	$\chi$	$=$	1890.719
Dual form			1890.2.bi.b.899.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.796362 - 2.08945i) q^{5} +(-2.55753 - 0.677517i) q^{7} +1.00000 q^{8} +(-0.796362 - 2.08945i) q^{10} +(2.46056 + 1.42061i) q^{11} +(2.51471 - 4.35560i) q^{13} +(-2.55753 - 0.677517i) q^{14} +1.00000 q^{16} +(-3.91852 + 2.26236i) q^{17} +(-3.40172 - 1.96399i) q^{19} +(-0.796362 - 2.08945i) q^{20} +(2.46056 + 1.42061i) q^{22} +(-3.21075 - 5.56118i) q^{23} +(-3.73162 + 3.32792i) q^{25} +(2.51471 - 4.35560i) q^{26} +(-2.55753 - 0.677517i) q^{28} +(-3.16363 + 1.82652i) q^{29} -2.04291i q^{31} +1.00000 q^{32} +(-3.91852 + 2.26236i) q^{34} +(0.621082 + 5.88339i) q^{35} +(-0.925584 - 0.534386i) q^{37} +(-3.40172 - 1.96399i) q^{38} +(-0.796362 - 2.08945i) q^{40} +(-2.85368 + 4.94272i) q^{41} +(6.76731 - 3.90711i) q^{43} +(2.46056 + 1.42061i) q^{44} +(-3.21075 - 5.56118i) q^{46} -2.23938i q^{47} +(6.08194 + 3.46554i) q^{49} +(-3.73162 + 3.32792i) q^{50} +(2.51471 - 4.35560i) q^{52} +(-2.88164 - 4.99115i) q^{53} +(1.00879 - 6.27254i) q^{55} +(-2.55753 - 0.677517i) q^{56} +(-3.16363 + 1.82652i) q^{58} -12.8102 q^{59} -10.4338i q^{61} -2.04291i q^{62} +1.00000 q^{64} +(-11.1034 - 1.78572i) q^{65} +5.99972i q^{67} +(-3.91852 + 2.26236i) q^{68} +(0.621082 + 5.88339i) q^{70} +7.81664i q^{71} +(-7.04158 - 12.1964i) q^{73} +(-0.925584 - 0.534386i) q^{74} +(-3.40172 - 1.96399i) q^{76} +(-5.33048 - 5.30032i) q^{77} +4.51074 q^{79} +(-0.796362 - 2.08945i) q^{80} +(-2.85368 + 4.94272i) q^{82} +(-10.9918 + 6.34613i) q^{83} +(7.84765 + 6.38590i) q^{85} +(6.76731 - 3.90711i) q^{86} +(2.46056 + 1.42061i) q^{88} +(5.33519 - 9.24081i) q^{89} +(-9.38244 + 9.43583i) q^{91} +(-3.21075 - 5.56118i) q^{92} -2.23938i q^{94} +(-1.39465 + 8.67178i) q^{95} +(-8.91744 - 15.4455i) q^{97} +(6.08194 + 3.46554i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots + 3 q^{98}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.796362	−	2.08945i	−0.356144	−	0.934431i
$5$	−0.796362	−	2.08945i	−0.356144	−	0.934431i
$6$		0			0
$7$	−2.55753	−	0.677517i	−0.966656	−	0.256077i
$7$	−2.55753	−	0.677517i	−0.966656	−	0.256077i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.796362	−	2.08945i	−0.251832	−	0.660743i
$11$	2.46056	+	1.42061i	0.741887	+	0.428329i	0.822755	−	0.568396i	$-0.192436\pi$
$11$	2.46056	+	1.42061i	0.741887	+	0.428329i	−0.0808677	+	0.996725i	$0.525769\pi$
$12$		0			0
$13$	2.51471	−	4.35560i	0.697455	−	1.20803i	−0.271892	−	0.962328i	$-0.587649\pi$
$13$	2.51471	−	4.35560i	0.697455	−	1.20803i	0.969346	−	0.245699i	$-0.0790174\pi$
$14$	−2.55753	−	0.677517i	−0.683529	−	0.181074i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.91852	+	2.26236i	−0.950381	+	0.548703i	−0.893199	−	0.449661i	$-0.851545\pi$
$17$	−3.91852	+	2.26236i	−0.950381	+	0.548703i	−0.0571816	+	0.998364i	$0.518211\pi$
$18$		0			0
$19$	−3.40172	−	1.96399i	−0.780409	−	0.450569i	0.0561661	−	0.998421i	$-0.482112\pi$
$19$	−3.40172	−	1.96399i	−0.780409	−	0.450569i	−0.836575	+	0.547852i	$0.815446\pi$
$20$	−0.796362	−	2.08945i	−0.178072	−	0.467216i
$21$		0			0
$22$	2.46056	+	1.42061i	0.524594	+	0.302874i
$23$	−3.21075	−	5.56118i	−0.669487	−	1.15959i	−0.978048	−	0.208381i	$-0.933181\pi$
$23$	−3.21075	−	5.56118i	−0.669487	−	1.15959i	0.308560	−	0.951205i	$-0.400153\pi$
$24$		0			0
$25$	−3.73162	+	3.32792i	−0.746323	+	0.665584i
$26$	2.51471	−	4.35560i	0.493175	−	0.854204i
$27$		0			0
$28$	−2.55753	−	0.677517i	−0.483328	−	0.128039i
$29$	−3.16363	+	1.82652i	−0.587472	+	0.339177i	−0.764097	−	0.645101i	$-0.776815\pi$
$29$	−3.16363	+	1.82652i	−0.587472	+	0.339177i	0.176626	+	0.984278i	$0.443482\pi$
$30$		0			0
$31$		−	2.04291i		−	0.366917i	−0.983027	−	0.183459i	$-0.941271\pi$
$31$		−	2.04291i		−	0.366917i	0.983027	−	0.183459i	$-0.0587294\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−3.91852	+	2.26236i	−0.672021	+	0.387991i
$35$	0.621082	+	5.88339i	0.104982	+	0.994474i
$36$		0			0
$37$	−0.925584	−	0.534386i	−0.152165	−	0.0878526i	0.421984	−	0.906603i	$-0.361334\pi$
$37$	−0.925584	−	0.534386i	−0.152165	−	0.0878526i	−0.574149	+	0.818751i	$0.694667\pi$
$38$	−3.40172	−	1.96399i	−0.551833	−	0.318601i
$39$		0			0
$40$	−0.796362	−	2.08945i	−0.125916	−	0.330371i
$41$	−2.85368	+	4.94272i	−0.445670	+	0.771923i	−0.998099	−	0.0616375i	$-0.980368\pi$
$41$	−2.85368	+	4.94272i	−0.445670	+	0.771923i	0.552429	+	0.833560i	$0.313701\pi$
$42$		0			0
$43$	6.76731	−	3.90711i	1.03201	−	0.595829i	0.114447	−	0.993429i	$-0.463490\pi$
$43$	6.76731	−	3.90711i	1.03201	−	0.595829i	0.917559	+	0.397601i	$0.130157\pi$
$44$	2.46056	+	1.42061i	0.370944	+	0.214164i
$45$		0			0
$46$	−3.21075	−	5.56118i	−0.473399	−	0.819951i
$47$		−	2.23938i		−	0.326647i	−0.986573	−	0.163323i	$-0.947779\pi$
$47$		−	2.23938i		−	0.326647i	0.986573	−	0.163323i	$-0.0522213\pi$
$48$		0			0
$49$	6.08194	+	3.46554i	0.868849	+	0.495078i
$50$	−3.73162	+	3.32792i	−0.527730	+	0.470639i
$51$		0			0
$52$	2.51471	−	4.35560i	0.348727	−	0.604013i
$53$	−2.88164	−	4.99115i	−0.395824	−	0.685587i	0.597382	−	0.801957i	$-0.296208\pi$
$53$	−2.88164	−	4.99115i	−0.395824	−	0.685587i	−0.993206	+	0.116370i	$0.962874\pi$
$54$		0			0
$55$	1.00879	−	6.27254i	0.136025	−	0.845789i
$56$	−2.55753	−	0.677517i	−0.341765	−	0.0905371i
$57$		0			0
$58$	−3.16363	+	1.82652i	−0.415405	+	0.239834i
$59$	−12.8102			−1.66775			−0.833875	−	0.551953i	$-0.813883\pi$
$59$	−12.8102			−1.66775			−0.833875	+	0.551953i	$0.813883\pi$
$60$		0			0
$61$		−	10.4338i		−	1.33592i	−0.744199	−	0.667958i	$-0.767169\pi$
$61$		−	10.4338i		−	1.33592i	0.744199	−	0.667958i	$-0.232831\pi$
$62$		−	2.04291i		−	0.259450i
$63$		0			0
$64$	1.00000			0.125000
$65$	−11.1034	−	1.78572i	−1.37721	−	0.221492i
$66$		0			0
$67$			5.99972i			0.732982i	0.930422	+	0.366491i	$0.119441\pi$
$67$			5.99972i			0.732982i	−0.930422	+	0.366491i	$0.880559\pi$
$68$	−3.91852	+	2.26236i	−0.475190	+	0.274351i
$69$		0			0
$70$	0.621082	+	5.88339i	0.0742335	+	0.703199i
$71$			7.81664i			0.927664i	0.885923	+	0.463832i	$0.153526\pi$
$71$			7.81664i			0.927664i	−0.885923	+	0.463832i	$0.846474\pi$
$72$		0			0
$73$	−7.04158	−	12.1964i	−0.824154	−	1.42748i	−0.902564	−	0.430556i	$-0.858318\pi$
$73$	−7.04158	−	12.1964i	−0.824154	−	1.42748i	0.0784100	−	0.996921i	$-0.475016\pi$
$74$	−0.925584	−	0.534386i	−0.107597	−	0.0621212i
$75$		0			0
$76$	−3.40172	−	1.96399i	−0.390205	−	0.225285i
$77$	−5.33048	−	5.30032i	−0.607465	−	0.604028i
$78$		0			0
$79$	4.51074			0.507498			0.253749	−	0.967270i	$-0.418336\pi$
$79$	4.51074			0.507498			0.253749	+	0.967270i	$0.418336\pi$
$80$	−0.796362	−	2.08945i	−0.0890360	−	0.233608i
$81$		0			0
$82$	−2.85368	+	4.94272i	−0.315136	+	0.545832i
$83$	−10.9918	+	6.34613i	−1.20651	+	0.696578i	−0.961995	−	0.273068i	$-0.911962\pi$
$83$	−10.9918	+	6.34613i	−1.20651	+	0.696578i	−0.244513	+	0.969646i	$0.578628\pi$
$84$		0			0
$85$	7.84765	+	6.38590i	0.851197	+	0.692648i
$86$	6.76731	−	3.90711i	0.729738	−	0.421315i
$87$		0			0
$88$	2.46056	+	1.42061i	0.262297	+	0.151437i
$89$	5.33519	−	9.24081i	0.565529	−	0.979524i	−0.431472	−	0.902127i	$-0.642005\pi$
$89$	5.33519	−	9.24081i	0.565529	−	0.979524i	0.997000	−	0.0773979i	$-0.0246612\pi$
$90$		0			0
$91$	−9.38244	+	9.43583i	−0.983547	+	0.989144i
$92$	−3.21075	−	5.56118i	−0.334744	−	0.579793i
$93$		0			0
$94$		−	2.23938i		−	0.230974i
$95$	−1.39465	+	8.67178i	−0.143088	+	0.889706i
$96$		0			0
$97$	−8.91744	−	15.4455i	−0.905429	−	1.56825i	−0.820341	−	0.571875i	$-0.806216\pi$
$97$	−8.91744	−	15.4455i	−0.905429	−	1.56825i	−0.0850876	−	0.996373i	$-0.527117\pi$
$98$	6.08194	+	3.46554i	0.614369	+	0.350073i
$99$		0			0
$100$	−3.73162	+	3.32792i	−0.373162	+	0.332792i
$101$	5.04091	−	8.73112i	0.501590	−	0.868779i	−0.498409	−	0.866942i	$-0.666082\pi$
$101$	5.04091	−	8.73112i	0.501590	−	0.868779i	0.999998	−	0.00183643i	$-0.000584554\pi$
$102$		0			0
$103$	−1.03484	−	1.79239i	−0.101965	−	0.176609i	0.810529	−	0.585699i	$-0.199180\pi$
$103$	−1.03484	−	1.79239i	−0.101965	−	0.176609i	−0.912494	+	0.409089i	$0.865846\pi$
$104$	2.51471	−	4.35560i	0.246587	−	0.427102i
$105$		0			0
$106$	−2.88164	−	4.99115i	−0.279890	−	0.484783i
$107$	−1.27205	+	2.20325i	−0.122973	+	0.212996i	−0.920939	−	0.389707i	$-0.872576\pi$
$107$	−1.27205	+	2.20325i	−0.122973	+	0.212996i	0.797966	+	0.602703i	$0.205910\pi$
$108$		0			0
$109$	5.96532	+	10.3322i	0.571374	+	0.989649i	0.996425	+	0.0844800i	$0.0269229\pi$
$109$	5.96532	+	10.3322i	0.571374	+	0.989649i	−0.425051	+	0.905170i	$0.639744\pi$
$110$	1.00879	−	6.27254i	0.0961843	−	0.598063i
$111$		0			0
$112$	−2.55753	−	0.677517i	−0.241664	−	0.0640194i
$113$	4.09453	−	7.09194i	0.385181	−	0.667153i	−0.606613	−	0.794997i	$-0.707472\pi$
$113$	4.09453	−	7.09194i	0.385181	−	0.667153i	0.991794	+	0.127844i	$0.0408056\pi$
$114$		0			0
$115$	−9.06290	+	11.1374i	−0.845119	+	1.03857i
$116$	−3.16363	+	1.82652i	−0.293736	+	0.169588i
$117$		0			0
$118$	−12.8102			−1.17928
$119$	11.5545	−	3.13119i	1.05920	−	0.287036i
$120$		0			0
$121$	−1.46376	−	2.53530i	−0.133069	−	0.230482i
$122$		−	10.4338i		−	0.944635i
$123$		0			0
$124$		−	2.04291i		−	0.183459i
$125$	9.92524	+	5.14680i	0.887741	+	0.460344i
$126$		0			0
$127$		−	18.1709i		−	1.61240i	−0.591641	−	0.806202i	$-0.701520\pi$
$127$		−	18.1709i		−	1.61240i	0.591641	−	0.806202i	$-0.298480\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−11.1034	−	1.78572i	−0.973836	−	0.156618i
$131$	8.55442	+	14.8167i	0.747403	+	1.29454i	0.949064	+	0.315084i	$0.102033\pi$
$131$	8.55442	+	14.8167i	0.747403	+	1.29454i	−0.201661	+	0.979455i	$0.564634\pi$
$132$		0			0
$133$	7.36938	+	7.32769i	0.639007	+	0.635391i
$134$			5.99972i			0.518296i
$135$		0			0
$136$	−3.91852	+	2.26236i	−0.336010	+	0.193996i
$137$	−3.10008	+	5.36950i	−0.264858	+	0.458747i	−0.967526	−	0.252770i	$-0.918658\pi$
$137$	−3.10008	+	5.36950i	−0.264858	+	0.458747i	0.702668	+	0.711517i	$0.251992\pi$
$138$		0			0
$139$	13.0131	+	7.51311i	1.10376	+	0.637253i	0.937205	−	0.348780i	$-0.113404\pi$
$139$	13.0131	+	7.51311i	1.10376	+	0.637253i	0.166550	+	0.986033i	$0.446737\pi$
$140$	0.621082	+	5.88339i	0.0524910	+	0.497237i
$141$		0			0
$142$			7.81664i			0.655958i
$143$	12.3752	−	7.14482i	1.03487	−	0.597480i
$144$		0			0
$145$	6.33583	+	5.15568i	0.526162	+	0.428156i
$146$	−7.04158	−	12.1964i	−0.582765	−	1.00938i
$147$		0			0
$148$	−0.925584	−	0.534386i	−0.0760826	−	0.0439263i
$149$	1.97748	−	1.14170i	0.162001	−	0.0935314i	−0.416808	−	0.908995i	$-0.636851\pi$
$149$	1.97748	−	1.14170i	0.162001	−	0.0935314i	0.578809	+	0.815463i	$0.303518\pi$
$150$		0			0
$151$	−6.59525	+	11.4233i	−0.536714	+	0.929616i	0.462365	+	0.886690i	$0.347001\pi$
$151$	−6.59525	+	11.4233i	−0.536714	+	0.929616i	−0.999078	+	0.0429256i	$0.986332\pi$
$152$	−3.40172	−	1.96399i	−0.275916	−	0.159300i
$153$		0			0
$154$	−5.33048	−	5.30032i	−0.429542	−	0.427112i
$155$	−4.26856	+	1.62690i	−0.342859	+	0.130675i
$156$		0			0
$157$	17.9261			1.43066			0.715330	−	0.698786i	$-0.246276\pi$
$157$	17.9261			1.43066			0.715330	+	0.698786i	$0.246276\pi$
$158$	4.51074			0.358855
$159$		0			0
$160$	−0.796362	−	2.08945i	−0.0629579	−	0.165186i
$161$	4.44380	+	16.3982i	0.350220	+	1.29236i
$162$		0			0
$163$	3.27021	+	1.88806i	0.256143	+	0.147884i	0.622574	−	0.782561i	$-0.286087\pi$
$163$	3.27021	+	1.88806i	0.256143	+	0.147884i	−0.366431	+	0.930445i	$0.619420\pi$
$164$	−2.85368	+	4.94272i	−0.222835	+	0.385961i
$165$		0			0
$166$	−10.9918	+	6.34613i	−0.853130	+	0.492555i
$167$	20.8655	+	12.0467i	1.61462	+	0.932201i	0.988280	+	0.152651i	$0.0487811\pi$
$167$	20.8655	+	12.0467i	1.61462	+	0.932201i	0.626340	+	0.779550i	$0.284552\pi$
$168$		0			0
$169$	−6.14752	−	10.6478i	−0.472886	−	0.819062i
$170$	7.84765	+	6.38590i	0.601887	+	0.489776i
$171$		0			0
$172$	6.76731	−	3.90711i	0.516003	−	0.297914i
$173$		−	12.1734i		−	0.925523i	−0.886483	−	0.462762i	$-0.846859\pi$
$173$		−	12.1734i		−	0.925523i	0.886483	−	0.462762i	$-0.153141\pi$
$174$		0			0
$175$	11.7984	−	5.98303i	0.891879	−	0.452274i
$176$	2.46056	+	1.42061i	0.185472	+	0.107082i
$177$		0			0
$178$	5.33519	−	9.24081i	0.399889	−	0.692628i
$179$	3.16979	−	1.83008i	0.236921	−	0.136786i	−0.376840	−	0.926278i	$-0.622989\pi$
$179$	3.16979	−	1.83008i	0.236921	−	0.136786i	0.613761	+	0.789492i	$0.289656\pi$
$180$		0			0
$181$			11.5653i			0.859645i	0.902914	+	0.429822i	$0.141424\pi$
$181$			11.5653i			0.859645i	−0.902914	+	0.429822i	$0.858576\pi$
$182$	−9.38244	+	9.43583i	−0.695473	+	0.699431i
$183$		0			0
$184$	−3.21075	−	5.56118i	−0.236700	−	0.409976i
$185$	−0.379474	+	2.35953i	−0.0278995	+	0.173476i
$186$		0			0
$187$	−12.8557			−0.940101
$188$		−	2.23938i		−	0.163323i
$189$		0			0
$190$	−1.39465	+	8.67178i	−0.101179	+	0.629117i
$191$			9.43103i			0.682405i	0.939990	+	0.341203i	$0.110834\pi$
$191$			9.43103i			0.682405i	−0.939990	+	0.341203i	$0.889166\pi$
$192$		0			0
$193$			1.48521i			0.106908i	0.998570	+	0.0534540i	$0.0170230\pi$
$193$			1.48521i			0.106908i	−0.998570	+	0.0534540i	$0.982977\pi$
$194$	−8.91744	−	15.4455i	−0.640235	−	1.10892i
$195$		0			0
$196$	6.08194	+	3.46554i	0.434424	+	0.247539i
$197$	−17.6493			−1.25746			−0.628729	−	0.777624i	$-0.716425\pi$
$197$	−17.6493			−1.25746			−0.628729	+	0.777624i	$0.716425\pi$
$198$		0			0
$199$	17.8938	−	10.3310i	1.26846	−	0.732344i	0.293762	−	0.955879i	$-0.405093\pi$
$199$	17.8938	−	10.3310i	1.26846	−	0.732344i	0.974696	+	0.223534i	$0.0717595\pi$
$200$	−3.73162	+	3.32792i	−0.263865	+	0.235319i
$201$		0			0
$202$	5.04091	−	8.73112i	0.354677	−	0.614319i
$203$	9.32859	−	2.52798i	0.654739	−	0.177429i
$204$		0			0
$205$	12.6001	+	2.02643i	0.880031	+	0.141532i
$206$	−1.03484	−	1.79239i	−0.0721004	−	0.124882i
$207$		0			0
$208$	2.51471	−	4.35560i	0.174364	−	0.302007i
$209$	−5.58010	−	9.66502i	−0.385984	−	0.668544i
$210$		0			0
$211$	5.63953	−	9.76796i	0.388241	−	0.672454i	−0.603972	−	0.797006i	$-0.706416\pi$
$211$	5.63953	−	9.76796i	0.388241	−	0.672454i	0.992213	+	0.124552i	$0.0397493\pi$
$212$	−2.88164	−	4.99115i	−0.197912	−	0.342793i
$213$		0			0
$214$	−1.27205	+	2.20325i	−0.0869553	+	0.150611i
$215$	−13.5529	−	11.0285i	−0.924303	−	0.752137i
$216$		0			0
$217$	−1.38411	+	5.22481i	−0.0939593	+	0.354683i
$218$	5.96532	+	10.3322i	0.404023	+	0.699788i
$219$		0			0
$220$	1.00879	−	6.27254i	0.0680126	−	0.422895i
$221$			22.7567i			1.53078i
$222$		0			0
$223$	−6.07248	−	10.5178i	−0.406643	−	0.704327i	0.587868	−	0.808957i	$-0.299968\pi$
$223$	−6.07248	−	10.5178i	−0.406643	−	0.704327i	−0.994511	+	0.104630i	$0.966634\pi$
$224$	−2.55753	−	0.677517i	−0.170882	−	0.0452685i
$225$		0			0
$226$	4.09453	−	7.09194i	0.272364	−	0.471749i
$227$	20.5863	+	11.8855i	1.36636	+	0.788868i	0.990461	−	0.137793i	$-0.0440010\pi$
$227$	20.5863	+	11.8855i	1.36636	+	0.788868i	0.375898	+	0.926661i	$0.377334\pi$
$228$		0			0
$229$	9.88508	−	5.70716i	0.653225	−	0.377139i	−0.136466	−	0.990645i	$-0.543574\pi$
$229$	9.88508	−	5.70716i	0.653225	−	0.377139i	0.789691	+	0.613505i	$0.210241\pi$
$230$	−9.06290	+	11.1374i	−0.597590	+	0.734379i
$231$		0			0
$232$	−3.16363	+	1.82652i	−0.207703	+	0.119917i
$233$	4.16132	−	7.20762i	0.272617	−	0.472187i	−0.696914	−	0.717155i	$-0.745444\pi$
$233$	4.16132	−	7.20762i	0.272617	−	0.472187i	0.969531	+	0.244968i	$0.0787775\pi$
$234$		0			0
$235$	−4.67907	+	1.78335i	−0.305229	+	0.116333i
$236$	−12.8102			−0.833875
$237$		0			0
$238$	11.5545	−	3.13119i	0.748969	−	0.202965i
$239$	6.41684	+	3.70476i	0.415071	+	0.239641i	0.692966	−	0.720970i	$-0.256304\pi$
$239$	6.41684	+	3.70476i	0.415071	+	0.239641i	−0.277895	+	0.960611i	$0.589637\pi$
$240$		0			0
$241$	−7.50748	−	4.33445i	−0.483599	−	0.279206i	0.238316	−	0.971188i	$-0.423405\pi$
$241$	−7.50748	−	4.33445i	−0.483599	−	0.279206i	−0.721915	+	0.691981i	$0.756738\pi$
$242$	−1.46376	−	2.53530i	−0.0940937	−	0.162975i
$243$		0			0
$244$		−	10.4338i		−	0.667958i
$245$	2.39766	−	15.4677i	0.153181	−	0.988198i
$246$		0			0
$247$	−17.1087	+	9.87771i	−1.08860	+	0.628503i
$248$		−	2.04291i		−	0.129725i
$249$		0			0
$250$	9.92524	+	5.14680i	0.627727	+	0.325512i
$251$	15.4449			0.974871			0.487436	−	0.873159i	$-0.337932\pi$
$251$	15.4449			0.974871			0.487436	+	0.873159i	$0.337932\pi$
$252$		0			0
$253$		−	18.2448i		−	1.14704i
$254$		−	18.1709i		−	1.14014i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.03816	+	2.90878i	−0.314272	+	0.181445i	−0.648836	−	0.760928i	$-0.724744\pi$
$257$	−5.03816	+	2.90878i	−0.314272	+	0.181445i	0.334565	+	0.942373i	$0.391411\pi$
$258$		0			0
$259$	2.00516	+	1.99381i	0.124594	+	0.123889i
$260$	−11.1034	−	1.78572i	−0.688606	−	0.110746i
$261$		0			0
$262$	8.55442	+	14.8167i	0.528494	+	0.915378i
$263$	1.08784	−	1.88419i	0.0670790	−	0.116184i	−0.830535	−	0.556966i	$-0.811965\pi$
$263$	1.08784	−	1.88419i	0.0670790	−	0.116184i	0.897614	+	0.440782i	$0.145299\pi$
$264$		0			0
$265$	−8.13393	+	9.99581i	−0.499663	+	0.614037i
$266$	7.36938	+	7.32769i	0.451846	+	0.449289i
$267$		0			0
$268$			5.99972i			0.366491i
$269$	−1.75606	−	3.04158i	−0.107069	−	0.185449i	0.807513	−	0.589850i	$-0.200813\pi$
$269$	−1.75606	−	3.04158i	−0.107069	−	0.185449i	−0.914582	+	0.404401i	$0.867480\pi$
$270$		0			0
$271$	1.39309	+	0.804303i	0.0846244	+	0.0488579i	0.541715	−	0.840562i	$-0.317775\pi$
$271$	1.39309	+	0.804303i	0.0846244	+	0.0488579i	−0.457091	+	0.889420i	$0.651109\pi$
$272$	−3.91852	+	2.26236i	−0.237595	+	0.137176i
$273$		0			0
$274$	−3.10008	+	5.36950i	−0.187283	+	0.324383i
$275$	−13.9095	+	2.88740i	−0.838777	+	0.174117i
$276$		0			0
$277$	3.87815	+	2.23905i	0.233015	+	0.134531i	0.611962	−	0.790887i	$-0.290380\pi$
$277$	3.87815	+	2.23905i	0.233015	+	0.134531i	−0.378947	+	0.925418i	$0.623714\pi$
$278$	13.0131	+	7.51311i	0.780473	+	0.450606i
$279$		0			0
$280$	0.621082	+	5.88339i	0.0371167	+	0.351600i
$281$	9.04334	−	5.22117i	0.539480	−	0.311469i	−0.205388	−	0.978681i	$-0.565846\pi$
$281$	9.04334	−	5.22117i	0.539480	−	0.311469i	0.744868	+	0.667211i	$0.232512\pi$
$282$		0			0
$283$	−18.5038			−1.09994			−0.549969	−	0.835185i	$-0.685360\pi$
$283$	−18.5038			−1.09994			−0.549969	+	0.835185i	$0.685360\pi$
$284$			7.81664i			0.463832i
$285$		0			0
$286$	12.3752	−	7.14482i	0.731761	−	0.422482i
$287$	10.6471	−	10.7077i	0.628481	−	0.632058i
$288$		0			0
$289$	1.73653	−	3.00776i	0.102149	−	0.176927i
$290$	6.33583	+	5.15568i	0.372053	+	0.302752i
$291$		0			0
$292$	−7.04158	−	12.1964i	−0.412077	−	0.713738i
$293$	0.317382	+	0.183240i	0.0185416	+	0.0107050i	0.509242	−	0.860623i	$-0.329926\pi$
$293$	0.317382	+	0.183240i	0.0185416	+	0.0107050i	−0.490701	+	0.871328i	$0.663259\pi$
$294$		0			0
$295$	10.2016	+	26.7664i	0.593959	+	1.55840i
$296$	−0.925584	−	0.534386i	−0.0537985	−	0.0310606i
$297$		0			0
$298$	1.97748	−	1.14170i	0.114552	−	0.0661367i
$299$	−32.2964			−1.86775
$300$		0			0
$301$	−19.9548	+	5.40759i	−1.15017	+	0.311688i
$302$	−6.59525	+	11.4233i	−0.379514	+	0.657337i
$303$		0			0
$304$	−3.40172	−	1.96399i	−0.195102	−	0.112642i
$305$	−21.8010	+	8.30911i	−1.24832	+	0.475778i
$306$		0			0
$307$	24.9894			1.42622			0.713110	−	0.701053i	$-0.247286\pi$
$307$	24.9894			1.42622			0.713110	+	0.701053i	$0.247286\pi$
$308$	−5.33048	−	5.30032i	−0.303732	−	0.302014i
$309$		0			0
$310$	−4.26856	+	1.62690i	−0.242438	+	0.0924015i
$311$	−24.0318			−1.36272			−0.681358	−	0.731950i	$-0.738610\pi$
$311$	−24.0318			−1.36272			−0.681358	+	0.731950i	$0.738610\pi$
$312$		0			0
$313$	−6.50477			−0.367671			−0.183836	−	0.982957i	$-0.558851\pi$
$313$	−6.50477			−0.367671			−0.183836	+	0.982957i	$0.558851\pi$
$314$	17.9261			1.01163
$315$		0			0
$316$	4.51074			0.253749
$317$	7.38882			0.414997			0.207499	−	0.978235i	$-0.433468\pi$
$317$	7.38882			0.414997			0.207499	+	0.978235i	$0.433468\pi$
$318$		0			0
$319$	−10.3791			−0.581117
$320$	−0.796362	−	2.08945i	−0.0445180	−	0.116804i
$321$		0			0
$322$	4.44380	+	16.3982i	0.247643	+	0.913838i
$323$	17.7730			0.988914
$324$		0			0
$325$	5.11117	+	24.6222i	0.283517	+	1.36579i
$326$	3.27021	+	1.88806i	0.181120	+	0.104570i
$327$		0			0
$328$	−2.85368	+	4.94272i	−0.157568	+	0.272916i
$329$	−1.51722	+	5.72727i	−0.0836468	+	0.315755i
$330$		0			0
$331$	26.3139			1.44634			0.723171	−	0.690669i	$-0.242684\pi$
$331$	26.3139			1.44634			0.723171	+	0.690669i	$0.242684\pi$
$332$	−10.9918	+	6.34613i	−0.603254	+	0.348289i
$333$		0			0
$334$	20.8655	+	12.0467i	1.14171	+	0.659166i
$335$	12.5361	−	4.77795i	0.684921	−	0.261047i
$336$		0			0
$337$	5.78970	+	3.34269i	0.315385	+	0.182088i	0.649334	−	0.760504i	$-0.275048\pi$
$337$	5.78970	+	3.34269i	0.315385	+	0.182088i	−0.333949	+	0.942591i	$0.608381\pi$
$338$	−6.14752	−	10.6478i	−0.334381	−	0.579164i
$339$		0			0
$340$	7.84765	+	6.38590i	0.425599	+	0.346324i
$341$	2.90217	−	5.02671i	0.157161	−	0.272211i
$342$		0			0
$343$	−13.2068	−	12.9839i	−0.713100	−	0.701063i
$344$	6.76731	−	3.90711i	0.364869	−	0.210657i
$345$		0			0
$346$		−	12.1734i		−	0.654444i
$347$	2.41396			0.129588			0.0647940	−	0.997899i	$-0.479361\pi$
$347$	2.41396			0.129588			0.0647940	+	0.997899i	$0.479361\pi$
$348$		0			0
$349$	−0.654664	+	0.377971i	−0.0350434	+	0.0202323i	−0.517419	−	0.855732i	$-0.673107\pi$
$349$	−0.654664	+	0.377971i	−0.0350434	+	0.0202323i	0.482376	+	0.875964i	$0.339774\pi$
$350$	11.7984	−	5.98303i	0.630654	−	0.319806i
$351$		0			0
$352$	2.46056	+	1.42061i	0.131148	+	0.0757186i
$353$	8.10821	+	4.68128i	0.431557	+	0.249159i	0.700010	−	0.714133i	$-0.253179\pi$
$353$	8.10821	+	4.68128i	0.431557	+	0.249159i	−0.268453	+	0.963293i	$0.586512\pi$
$354$		0			0
$355$	16.3325	−	6.22487i	0.866838	−	0.330382i
$356$	5.33519	−	9.24081i	0.282764	−	0.489762i
$357$		0			0
$358$	3.16979	−	1.83008i	0.167529	−	0.0967227i
$359$	20.7136	+	11.9590i	1.09322	+	0.631172i	0.934433	−	0.356140i	$-0.115907\pi$
$359$	20.7136	+	11.9590i	1.09322	+	0.631172i	0.158790	+	0.987312i	$0.449241\pi$
$360$		0			0
$361$	−1.78551	−	3.09260i	−0.0939744	−	0.162768i
$362$			11.5653i			0.607860i
$363$		0			0
$364$	−9.38244	+	9.43583i	−0.491774	+	0.494572i
$365$	−19.8761	+	24.4258i	−1.04036	+	1.27850i
$366$		0			0
$367$	−2.63628	+	4.56616i	−0.137612	+	0.238352i	−0.926592	−	0.376067i	$-0.877276\pi$
$367$	−2.63628	+	4.56616i	−0.137612	+	0.238352i	0.788980	+	0.614419i	$0.210610\pi$
$368$	−3.21075	−	5.56118i	−0.167372	−	0.289896i
$369$		0			0
$370$	−0.379474	+	2.35953i	−0.0197279	+	0.122666i
$371$	3.98830	+	14.7174i	0.207062	+	0.764088i
$372$		0			0
$373$	−6.37029	+	3.67789i	−0.329841	+	0.190434i	−0.655770	−	0.754960i	$-0.727656\pi$
$373$	−6.37029	+	3.67789i	−0.329841	+	0.190434i	0.325930	+	0.945394i	$0.394323\pi$
$374$	−12.8557			−0.664752
$375$		0			0
$376$		−	2.23938i		−	0.115487i
$377$			18.3727i			0.946242i
$378$		0			0
$379$	−6.48462			−0.333092			−0.166546	−	0.986034i	$-0.553261\pi$
$379$	−6.48462			−0.333092			−0.166546	+	0.986034i	$0.553261\pi$
$380$	−1.39465	+	8.67178i	−0.0715441	+	0.444853i
$381$		0			0
$382$			9.43103i			0.482534i
$383$	−8.50872	+	4.91251i	−0.434775	+	0.251018i	−0.701379	−	0.712789i	$-0.747432\pi$
$383$	−8.50872	+	4.91251i	−0.434775	+	0.251018i	0.266604	+	0.963806i	$0.414099\pi$
$384$		0			0
$385$	−6.82977	+	15.3588i	−0.348077	+	0.782755i
$386$			1.48521i			0.0755953i
$387$		0			0
$388$	−8.91744	−	15.4455i	−0.452714	−	0.784124i
$389$	−7.18549	−	4.14854i	−0.364319	−	0.210340i	0.306655	−	0.951821i	$-0.400790\pi$
$389$	−7.18549	−	4.14854i	−0.364319	−	0.210340i	−0.670974	+	0.741481i	$0.734124\pi$
$390$		0			0
$391$	25.1628	+	14.5277i	1.27254	+	0.734699i
$392$	6.08194	+	3.46554i	0.307184	+	0.175036i
$393$		0			0
$394$	−17.6493			−0.889158
$395$	−3.59218	−	9.42498i	−0.180742	−	0.474222i
$396$		0			0
$397$	−6.65037	+	11.5188i	−0.333772	+	0.578111i	−0.983248	−	0.182272i	$-0.941655\pi$
$397$	−6.65037	+	11.5188i	−0.333772	+	0.578111i	0.649476	+	0.760382i	$0.274988\pi$
$398$	17.8938	−	10.3310i	0.896935	−	0.517846i
$399$		0			0
$400$	−3.73162	+	3.32792i	−0.186581	+	0.166396i
$401$	−18.0899	+	10.4442i	−0.903367	+	0.521559i	−0.878291	−	0.478126i	$-0.841316\pi$
$401$	−18.0899	+	10.4442i	−0.903367	+	0.521559i	−0.0250758	+	0.999686i	$0.507983\pi$
$402$		0			0
$403$	−8.89810	−	5.13732i	−0.443246	−	0.255908i
$404$	5.04091	−	8.73112i	0.250795	−	0.434389i
$405$		0			0
$406$	9.32859	−	2.52798i	0.462970	−	0.125461i
$407$	−1.51831	−	2.62978i	−0.0752596	−	0.130353i
$408$		0			0
$409$		−	28.3129i		−	1.39998i	−0.714151	−	0.699992i	$-0.753187\pi$
$409$		−	28.3129i		−	1.39998i	0.714151	−	0.699992i	$-0.246813\pi$
$410$	12.6001	+	2.02643i	0.622276	+	0.100078i
$411$		0			0
$412$	−1.03484	−	1.79239i	−0.0509827	−	0.0883046i
$413$	32.7626	+	8.67915i	1.61214	+	0.427073i
$414$		0			0
$415$	22.0134	+	17.9130i	1.08059	+	0.879317i
$416$	2.51471	−	4.35560i	0.123294	−	0.213551i
$417$		0			0
$418$	−5.58010	−	9.66502i	−0.272932	−	0.472732i
$419$	7.85403	−	13.6036i	0.383695	−	0.664578i	−0.607893	−	0.794019i	$-0.707985\pi$
$419$	7.85403	−	13.6036i	0.383695	−	0.664578i	0.991587	+	0.129441i	$0.0413182\pi$
$420$		0			0
$421$	−13.2658	−	22.9771i	−0.646537	−	1.11983i	−0.983944	−	0.178476i	$-0.942883\pi$
$421$	−13.2658	−	22.9771i	−0.646537	−	1.11983i	0.337408	−	0.941359i	$-0.390450\pi$
$422$	5.63953	−	9.76796i	0.274528	−	0.475497i
$423$		0			0
$424$	−2.88164	−	4.99115i	−0.139945	−	0.242391i
$425$	7.09346	−	21.4828i	0.344083	−	1.04207i
$426$		0			0
$427$	−7.06910	+	26.6849i	−0.342098	+	1.29137i
$428$	−1.27205	+	2.20325i	−0.0614867	+	0.106498i
$429$		0			0
$430$	−13.5529	−	11.0285i	−0.653581	−	0.531841i
$431$	14.0479	−	8.11059i	0.676666	−	0.390673i	−0.121932	−	0.992538i	$-0.538909\pi$
$431$	14.0479	−	8.11059i	0.676666	−	0.390673i	0.798598	+	0.601865i	$0.205576\pi$
$432$		0			0
$433$	19.7268			0.948010			0.474005	−	0.880522i	$-0.342808\pi$
$433$	19.7268			0.948010			0.474005	+	0.880522i	$0.342808\pi$
$434$	−1.38411	+	5.22481i	−0.0664392	+	0.250799i
$435$		0			0
$436$	5.96532	+	10.3322i	0.285687	+	0.494825i
$437$			25.2235i			1.20660i
$438$		0			0
$439$		−	13.1264i		−	0.626488i	−0.949673	−	0.313244i	$-0.898584\pi$
$439$		−	13.1264i		−	0.626488i	0.949673	−	0.313244i	$-0.101416\pi$
$440$	1.00879	−	6.27254i	0.0480922	−	0.299032i
$441$		0			0
$442$			22.7567i			1.08243i
$443$	8.62000			0.409548			0.204774	−	0.978809i	$-0.434354\pi$
$443$	8.62000			0.409548			0.204774	+	0.978809i	$0.434354\pi$
$444$		0			0
$445$	−23.5570	−	3.78858i	−1.11671	−	0.179596i
$446$	−6.07248	−	10.5178i	−0.287540	−	0.498034i
$447$		0			0
$448$	−2.55753	−	0.677517i	−0.120832	−	0.0320097i
$449$		−	37.2222i		−	1.75663i	−0.478086	−	0.878313i	$-0.658669\pi$
$449$		−	37.2222i		−	1.75663i	0.478086	−	0.878313i	$-0.341331\pi$
$450$		0			0
$451$	−14.0433	+	8.10791i	−0.661274	+	0.381786i
$452$	4.09453	−	7.09194i	0.192591	−	0.333577i
$453$		0			0
$454$	20.5863	+	11.8855i	0.966162	+	0.557814i
$455$	27.1875	+	12.0898i	1.27457	+	0.566780i
$456$		0			0
$457$			40.5035i			1.89467i	0.320238	+	0.947337i	$0.396237\pi$
$457$			40.5035i			1.89467i	−0.320238	+	0.947337i	$0.603763\pi$
$458$	9.88508	−	5.70716i	0.461900	−	0.266678i
$459$		0			0
$460$	−9.06290	+	11.1374i	−0.422560	+	0.519285i
$461$	−16.8755	−	29.2292i	−0.785971	−	1.36134i	−0.928417	−	0.371539i	$-0.878830\pi$
$461$	−16.8755	−	29.2292i	−0.785971	−	1.36134i	0.142446	−	0.989803i	$-0.454503\pi$
$462$		0			0
$463$	23.0998	+	13.3367i	1.07354	+	0.619809i	0.929147	−	0.369712i	$-0.120543\pi$
$463$	23.0998	+	13.3367i	1.07354	+	0.619809i	0.144394	+	0.989520i	$0.453877\pi$
$464$	−3.16363	+	1.82652i	−0.146868	+	0.0847942i
$465$		0			0
$466$	4.16132	−	7.20762i	0.192769	−	0.333886i
$467$	−4.89263	−	2.82476i	−0.226404	−	0.130714i	0.382508	−	0.923952i	$-0.375060\pi$
$467$	−4.89263	−	2.82476i	−0.226404	−	0.130714i	−0.608912	+	0.793238i	$0.708394\pi$
$468$		0			0
$469$	4.06491	−	15.3445i	0.187700	−	0.708542i
$470$	−4.67907	+	1.78335i	−0.215829	+	0.0822600i
$471$		0			0
$472$	−12.8102			−0.589639
$473$	22.2019			1.02084
$474$		0			0
$475$	19.2299	−	3.99182i	0.882329	−	0.183157i
$476$	11.5545	−	3.13119i	0.529601	−	0.143518i
$477$		0			0
$478$	6.41684	+	3.70476i	0.293499	+	0.169452i
$479$	−0.136929	+	0.237168i	−0.00625644	+	0.0108365i	−0.869137	−	0.494572i	$-0.835325\pi$
$479$	−0.136929	+	0.237168i	−0.00625644	+	0.0108365i	0.862880	+	0.505408i	$0.168658\pi$
$480$		0			0
$481$	−4.65515	+	2.68765i	−0.212257	+	0.122546i
$482$	−7.50748	−	4.33445i	−0.341956	−	0.197429i
$483$		0			0
$484$	−1.46376	−	2.53530i	−0.0665343	−	0.115241i
$485$	−25.1710	+	30.9327i	−1.14296	+	1.40458i
$486$		0			0
$487$	−12.4072	+	7.16329i	−0.562223	+	0.324600i	−0.754037	−	0.656832i	$-0.771896\pi$
$487$	−12.4072	+	7.16329i	−0.562223	+	0.324600i	0.191814	+	0.981431i	$0.438563\pi$
$488$		−	10.4338i		−	0.472317i
$489$		0			0
$490$	2.39766	−	15.4677i	0.108315	−	0.698762i
$491$	−31.8165	−	18.3692i	−1.43586	−	0.828992i	−0.438298	−	0.898830i	$-0.644419\pi$
$491$	−31.8165	−	18.3692i	−1.43586	−	0.828992i	−0.997558	+	0.0698374i	$0.977752\pi$
$492$		0			0
$493$	8.26450	−	14.3145i	0.372214	−	0.644694i
$494$	−17.1087	+	9.87771i	−0.769756	+	0.444419i
$495$		0			0
$496$		−	2.04291i		−	0.0917294i
$497$	5.29591	−	19.9913i	0.237554	−	0.896733i
$498$		0			0
$499$	16.0396	+	27.7814i	0.718032	+	1.24367i	0.961778	+	0.273829i	$0.0882902\pi$
$499$	16.0396	+	27.7814i	0.718032	+	1.24367i	−0.243746	+	0.969839i	$0.578376\pi$
$500$	9.92524	+	5.14680i	0.443870	+	0.230172i
$501$		0			0
$502$	15.4449			0.689338
$503$		−	35.1778i		−	1.56850i	−0.620445	−	0.784250i	$-0.713048\pi$
$503$		−	35.1778i		−	1.56850i	0.620445	−	0.784250i	$-0.286952\pi$
$504$		0			0
$505$	−22.2576	−	3.57961i	−0.990452	−	0.159291i
$506$		−	18.2448i		−	0.811082i
$507$		0			0
$508$		−	18.1709i		−	0.806202i
$509$	11.7471	+	20.3465i	0.520679	+	0.901843i	0.999711	+	0.0240450i	$0.00765451\pi$
$509$	11.7471	+	20.3465i	0.520679	+	0.901843i	−0.479032	+	0.877798i	$0.659012\pi$
$510$		0			0
$511$	9.74581	+	35.9634i	0.431129	+	1.59093i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−5.03816	+	2.90878i	−0.222224	+	0.128301i
$515$	−2.92100	+	3.58963i	−0.128715	+	0.158178i
$516$		0			0
$517$	3.18127	−	5.51012i	0.139912	−	0.242335i
$518$	2.00516	+	1.99381i	0.0881015	+	0.0876030i
$519$		0			0
$520$	−11.1034	−	1.78572i	−0.486918	−	0.0783092i
$521$	0.581200	+	1.00667i	0.0254628	+	0.0441029i	0.878476	−	0.477786i	$-0.158561\pi$
$521$	0.581200	+	1.00667i	0.0254628	+	0.0441029i	−0.853013	+	0.521889i	$0.825227\pi$
$522$		0			0
$523$	−1.24452	+	2.15558i	−0.0544191	+	0.0942567i	−0.891952	−	0.452131i	$-0.850664\pi$
$523$	−1.24452	+	2.15558i	−0.0544191	+	0.0942567i	0.837533	+	0.546387i	$0.183997\pi$
$524$	8.55442	+	14.8167i	0.373701	+	0.647270i
$525$		0			0
$526$	1.08784	−	1.88419i	0.0474320	−	0.0821547i
$527$	4.62179	+	8.00518i	0.201329	+	0.348711i
$528$		0			0
$529$	−9.11781	+	15.7925i	−0.396426	+	0.686631i
$530$	−8.13393	+	9.99581i	−0.353315	+	0.434190i
$531$		0			0
$532$	7.36938	+	7.32769i	0.319503	+	0.317695i
$533$	14.3523	+	24.8590i	0.621669	+	1.07676i
$534$		0			0
$535$	5.61659	+	0.903296i	0.242827	+	0.0390529i
$536$			5.99972i			0.259148i
$537$		0			0
$538$	−1.75606	−	3.04158i	−0.0757091	−	0.131132i
$539$	10.0418	+	17.1672i	0.432532	+	0.739445i
$540$		0			0
$541$	−10.4582	+	18.1142i	−0.449634	+	0.778789i	−0.998362	−	0.0572120i	$-0.981779\pi$
$541$	−10.4582	+	18.1142i	−0.449634	+	0.778789i	0.548728	+	0.836001i	$0.315112\pi$
$542$	1.39309	+	0.804303i	0.0598385	+	0.0345478i
$543$		0			0
$544$	−3.91852	+	2.26236i	−0.168005	+	0.0969978i
$545$	16.8382	−	20.6925i	0.721268	−	0.886368i
$546$		0			0
$547$	0.150888	−	0.0871155i	0.00645152	−	0.00372479i	−0.496771	−	0.867882i	$-0.665481\pi$
$547$	0.150888	−	0.0871155i	0.00645152	−	0.00372479i	0.503222	+	0.864157i	$0.332148\pi$
$548$	−3.10008	+	5.36950i	−0.132429	+	0.229374i
$549$		0			0
$550$	−13.9095	+	2.88740i	−0.593105	+	0.123119i
$551$	14.3491			0.611291
$552$		0			0
$553$	−11.5364	−	3.05611i	−0.490576	−	0.129959i
$554$	3.87815	+	2.23905i	0.164767	+	0.0951281i
$555$		0			0
$556$	13.0131	+	7.51311i	0.551878	+	0.318627i
$557$	−10.1509	−	17.5819i	−0.430109	−	0.744971i	0.566773	−	0.823874i	$-0.308192\pi$
$557$	−10.1509	−	17.5819i	−0.430109	−	0.744971i	−0.996882	+	0.0789031i	$0.974858\pi$
$558$		0			0
$559$		−	39.3010i		−	1.66225i
$560$	0.621082	+	5.88339i	0.0262455	+	0.248619i
$561$		0			0
$562$	9.04334	−	5.22117i	0.381470	−	0.220242i
$563$		−	12.0047i		−	0.505938i	−0.967474	−	0.252969i	$-0.918593\pi$
$563$		−	12.0047i		−	0.505938i	0.967474	−	0.252969i	$-0.0814070\pi$
$564$		0			0
$565$	−18.0790	−	2.90758i	−0.760589	−	0.122323i
$566$	−18.5038			−0.777773
$567$		0			0
$568$			7.81664i			0.327979i
$569$		−	32.3222i		−	1.35502i	−0.735515	−	0.677509i	$-0.763060\pi$
$569$		−	32.3222i		−	1.35502i	0.735515	−	0.677509i	$-0.236940\pi$
$570$		0			0
$571$	−39.7878			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$571$	−39.7878			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$572$	12.3752	−	7.14482i	0.517433	−	0.298740i
$573$		0			0
$574$	10.6471	−	10.7077i	0.444403	−	0.446932i
$575$	30.4884	+	10.0671i	1.27146	+	0.419826i
$576$		0			0
$577$	5.59098	+	9.68386i	0.232756	+	0.403144i	0.958618	−	0.284695i	$-0.0918925\pi$
$577$	5.59098	+	9.68386i	0.232756	+	0.403144i	−0.725862	+	0.687840i	$0.758559\pi$
$578$	1.73653	−	3.00776i	0.0722303	−	0.125107i
$579$		0			0
$580$	6.33583	+	5.15568i	0.263081	+	0.214078i
$581$	32.4115	−	8.78328i	1.34466	−	0.364392i
$582$		0			0
$583$		−	16.3747i		−	0.678171i
$584$	−7.04158	−	12.1964i	−0.291382	−	0.504689i
$585$		0			0
$586$	0.317382	+	0.183240i	0.0131109	+	0.00756959i
$587$	−2.92497	+	1.68873i	−0.120726	+	0.0697015i	−0.559147	−	0.829068i	$-0.688871\pi$
$587$	−2.92497	+	1.68873i	−0.120726	+	0.0697015i	0.438421	+	0.898770i	$0.355538\pi$
$588$		0			0
$589$	−4.01225	+	6.94942i	−0.165322	+	0.286346i
$590$	10.2016	+	26.7664i	0.419992	+	1.10195i
$591$		0			0
$592$	−0.925584	−	0.534386i	−0.0380413	−	0.0219631i
$593$	28.6406	+	16.5357i	1.17613	+	0.679039i	0.955116	−	0.296232i	$-0.0957301\pi$
$593$	28.6406	+	16.5357i	1.17613	+	0.679039i	0.221014	+	0.975271i	$0.429063\pi$
$594$		0			0
$595$	−15.7441	−	21.6491i	−0.645443	−	0.887525i
$596$	1.97748	−	1.14170i	0.0810005	−	0.0467657i
$597$		0			0
$598$	−32.2964			−1.32070
$599$			15.0631i			0.615461i	0.951474	+	0.307730i	$0.0995695\pi$
$599$			15.0631i			0.615461i	−0.951474	+	0.307730i	$0.900431\pi$
$600$		0			0
$601$	−38.2212	+	22.0670i	−1.55908	+	0.900133i	−0.561730	+	0.827321i	$0.689864\pi$
$601$	−38.2212	+	22.0670i	−1.55908	+	0.900133i	−0.997346	+	0.0728123i	$0.976803\pi$
$602$	−19.9548	+	5.40759i	−0.813295	+	0.220397i
$603$		0			0
$604$	−6.59525	+	11.4233i	−0.268357	+	0.464808i
$605$	−4.13170	+	5.07746i	−0.167978	+	0.206428i
$606$		0			0
$607$	−9.73116	−	16.8549i	−0.394976	−	0.684118i	0.598122	−	0.801405i	$-0.295914\pi$
$607$	−9.73116	−	16.8549i	−0.394976	−	0.684118i	−0.993098	+	0.117287i	$0.962580\pi$
$608$	−3.40172	−	1.96399i	−0.137958	−	0.0796502i
$609$		0			0
$610$	−21.8010	+	8.30911i	−0.882696	+	0.336426i
$611$	−9.75383	−	5.63138i	−0.394598	−	0.227821i
$612$		0			0
$613$	26.5030	−	15.3015i	1.07045	−	0.618023i	0.142144	−	0.989846i	$-0.454600\pi$
$613$	26.5030	−	15.3015i	1.07045	−	0.618023i	0.928304	+	0.371823i	$0.121267\pi$
$614$	24.9894			1.00849
$615$		0			0
$616$	−5.33048	−	5.30032i	−0.214771	−	0.213556i
$617$	18.9195	−	32.7695i	0.761671	−	1.31925i	−0.180318	−	0.983608i	$-0.557713\pi$
$617$	18.9195	−	32.7695i	0.761671	−	1.31925i	0.941989	−	0.335644i	$-0.108954\pi$
$618$		0			0
$619$	−42.1495	−	24.3350i	−1.69413	−	0.978107i	−0.951116	−	0.308833i	$-0.900062\pi$
$619$	−42.1495	−	24.3350i	−1.69413	−	0.978107i	−0.743015	−	0.669274i	$-0.766605\pi$
$620$	−4.26856	+	1.62690i	−0.171430	+	0.0653377i
$621$		0			0
$622$	−24.0318			−0.963586
$623$	−19.9057	+	20.0190i	−0.797506	+	0.802044i
$624$		0			0
$625$	2.84990	−	24.8370i	0.113996	−	0.993481i
$626$	−6.50477			−0.259983
$627$		0			0
$628$	17.9261			0.715330
$629$	4.83590			0.192820
$630$		0			0
$631$	40.7671			1.62291			0.811456	−	0.584414i	$-0.198675\pi$
$631$	40.7671			1.62291			0.811456	+	0.584414i	$0.198675\pi$
$632$	4.51074			0.179428
$633$		0			0
$634$	7.38882			0.293447
$635$	−37.9671	+	14.4706i	−1.50668	+	0.574248i
$636$		0			0
$637$	30.3888	−	17.7757i	1.20405	−	0.704298i
$638$	−10.3791			−0.410912
$639$		0			0
$640$	−0.796362	−	2.08945i	−0.0314790	−	0.0825928i
$641$	16.8354	+	9.71990i	0.664957	+	0.383913i	0.794163	−	0.607705i	$-0.207910\pi$
$641$	16.8354	+	9.71990i	0.664957	+	0.383913i	−0.129206	+	0.991618i	$0.541243\pi$
$642$		0			0
$643$	−3.29651	+	5.70972i	−0.130002	+	0.225169i	−0.923677	−	0.383172i	$-0.874832\pi$
$643$	−3.29651	+	5.70972i	−0.130002	+	0.225169i	0.793675	+	0.608342i	$0.208165\pi$
$644$	4.44380	+	16.3982i	0.175110	+	0.646181i
$645$		0			0
$646$	17.7730			0.699268
$647$	−34.2506	+	19.7746i	−1.34653	+	0.777419i	−0.987756	−	0.156006i	$-0.950138\pi$
$647$	−34.2506	+	19.7746i	−1.34653	+	0.777419i	−0.358773	+	0.933425i	$0.616805\pi$
$648$		0			0
$649$	−31.5204	−	18.1983i	−1.23728	−	0.714346i
$650$	5.11117	+	24.6222i	0.200477	+	0.965761i
$651$		0			0
$652$	3.27021	+	1.88806i	0.128071	+	0.0739421i
$653$	−10.3809	−	17.9803i	−0.406236	−	0.703622i	0.588228	−	0.808695i	$-0.299826\pi$
$653$	−10.3809	−	17.9803i	−0.406236	−	0.703622i	−0.994464	+	0.105073i	$0.966492\pi$
$654$		0			0
$655$	24.1463	−	29.6735i	0.943475	−	1.15944i
$656$	−2.85368	+	4.94272i	−0.111417	+	0.192981i
$657$		0			0
$658$	−1.51722	+	5.72727i	−0.0591472	+	0.223272i
$659$	−4.81761	+	2.78145i	−0.187667	+	0.108350i	−0.590890	−	0.806752i	$-0.701223\pi$
$659$	−4.81761	+	2.78145i	−0.187667	+	0.108350i	0.403223	+	0.915102i	$0.367890\pi$
$660$		0			0
$661$		−	43.2382i		−	1.68177i	−0.541214	−	0.840885i	$-0.682035\pi$
$661$		−	43.2382i		−	1.68177i	0.541214	−	0.840885i	$-0.317965\pi$
$662$	26.3139			1.02272
$663$		0			0
$664$	−10.9918	+	6.34613i	−0.426565	+	0.246277i
$665$	9.44215	−	21.2335i	0.366151	−	0.823398i
$666$		0			0
$667$	20.3152	+	11.7290i	0.786609	+	0.454149i
$668$	20.8655	+	12.0467i	0.807310	+	0.466101i
$669$		0			0
$670$	12.5361	−	4.77795i	0.484312	−	0.184588i
$671$	14.8224	−	25.6731i	0.572211	−	0.991099i
$672$		0			0
$673$	−11.8398	+	6.83568i	−0.456389	+	0.263496i	−0.710525	−	0.703672i	$-0.751542\pi$
$673$	−11.8398	+	6.83568i	−0.456389	+	0.263496i	0.254136	+	0.967169i	$0.418209\pi$
$674$	5.78970	+	3.34269i	0.223011	+	0.128755i
$675$		0			0
$676$	−6.14752	−	10.6478i	−0.236443	−	0.409531i
$677$			8.29461i			0.318788i	0.987215	+	0.159394i	$0.0509540\pi$
$677$			8.29461i			0.318788i	−0.987215	+	0.159394i	$0.949046\pi$
$678$		0			0
$679$	12.3421	+	45.5440i	0.473645	+	1.74782i
$680$	7.84765	+	6.38590i	0.300944	+	0.244888i
$681$		0			0
$682$	2.90217	−	5.02671i	0.111130	−	0.192483i
$683$	−20.1186	−	34.8465i	−0.769817	−	1.33336i	−0.937662	−	0.347549i	$-0.887014\pi$
$683$	−20.1186	−	34.8465i	−0.769817	−	1.33336i	0.167845	−	0.985813i	$-0.446319\pi$
$684$		0			0
$685$	13.6881	+	2.20141i	0.522995	+	0.0841114i
$686$	−13.2068	−	12.9839i	−0.504238	−	0.495726i
$687$		0			0
$688$	6.76731	−	3.90711i	0.258001	−	0.148957i
$689$	−28.9859			−1.10428
$690$		0			0
$691$			7.62789i			0.290179i	0.989419	+	0.145089i	$0.0463470\pi$
$691$			7.62789i			0.290179i	−0.989419	+	0.145089i	$0.953653\pi$
$692$		−	12.1734i		−	0.462762i
$693$		0			0
$694$	2.41396			0.0916325
$695$	5.33515	−	33.1734i	0.202374	−	1.25834i
$696$		0			0
$697$		−	25.8242i		−	0.978160i
$698$	−0.654664	+	0.377971i	−0.0247794	+	0.0143064i
$699$		0			0
$700$	11.7984	−	5.98303i	0.445939	−	0.226137i
$701$		−	31.4440i		−	1.18762i	−0.804604	−	0.593812i	$-0.797622\pi$
$701$		−	31.4440i		−	1.18762i	0.804604	−	0.593812i	$-0.202378\pi$
$702$		0			0
$703$	2.09906	+	3.63567i	0.0791674	+	0.137122i
$704$	2.46056	+	1.42061i	0.0927359	+	0.0535411i
$705$		0			0
$706$	8.10821	+	4.68128i	0.305157	+	0.176182i
$707$	−18.8078	+	18.9148i	−0.707339	+	0.711364i
$708$		0			0
$709$	−20.1317			−0.756061			−0.378030	−	0.925793i	$-0.623398\pi$
$709$	−20.1317			−0.756061			−0.378030	+	0.925793i	$0.623398\pi$
$710$	16.3325	−	6.22487i	0.612947	−	0.233615i
$711$		0			0
$712$	5.33519	−	9.24081i	0.199945	−	0.346314i
$713$	−11.3610	+	6.55927i	−0.425472	+	0.245647i
$714$		0			0
$715$	−24.7839	−	20.1675i	−0.926865	−	0.754222i
$716$	3.16979	−	1.83008i	0.118461	−	0.0683932i
$717$		0			0
$718$	20.7136	+	11.9590i	0.773025	+	0.446306i
$719$	−12.4736	+	21.6049i	−0.465187	+	0.805728i	−0.999210	−	0.0397421i	$-0.987346\pi$
$719$	−12.4736	+	21.6049i	−0.465187	+	0.805728i	0.534023	+	0.845470i	$0.320680\pi$
$720$		0			0
$721$	1.43225	+	5.28521i	0.0533398	+	0.196831i
$722$	−1.78551	−	3.09260i	−0.0664499	−	0.115095i
$723$		0			0
$724$			11.5653i			0.429822i
$725$	5.72693	−	17.3442i	0.212693	−	0.644147i
$726$		0			0
$727$	0.756579	+	1.31043i	0.0280600	+	0.0486013i	0.879714	−	0.475502i	$-0.157734\pi$
$727$	0.756579	+	1.31043i	0.0280600	+	0.0486013i	−0.851654	+	0.524104i	$0.824400\pi$
$728$	−9.38244	+	9.43583i	−0.347736	+	0.349715i
$729$		0			0
$730$	−19.8761	+	24.4258i	−0.735646	+	0.904038i
$731$	−17.6786	+	30.6202i	−0.653866	+	1.13253i
$732$		0			0
$733$	4.96247	+	8.59526i	0.183293	+	0.317473i	0.943000	−	0.332793i	$-0.107991\pi$
$733$	4.96247	+	8.59526i	0.183293	+	0.317473i	−0.759707	+	0.650266i	$0.774658\pi$
$734$	−2.63628	+	4.56616i	−0.0973067	+	0.168540i
$735$		0			0
$736$	−3.21075	−	5.56118i	−0.118350	−	0.204988i
$737$	−8.52323	+	14.7627i	−0.313957	+	0.543790i
$738$		0			0
$739$	7.69829	+	13.3338i	0.283186	+	0.490493i	0.972168	−	0.234286i	$-0.0752752\pi$
$739$	7.69829	+	13.3338i	0.283186	+	0.490493i	−0.688981	+	0.724779i	$0.741942\pi$
$740$	−0.379474	+	2.35953i	−0.0139498	+	0.0867380i
$741$		0			0
$742$	3.98830	+	14.7174i	0.146415	+	0.540292i
$743$	22.7782	−	39.4530i	0.835651	−	1.44739i	−0.0578475	−	0.998325i	$-0.518424\pi$
$743$	22.7782	−	39.4530i	0.835651	−	1.44739i	0.893499	−	0.449065i	$-0.148243\pi$
$744$		0			0
$745$	−3.96030	−	3.22264i	−0.145094	−	0.118068i
$746$	−6.37029	+	3.67789i	−0.233233	+	0.134657i
$747$		0			0
$748$	−12.8557			−0.470050
$749$	4.74604	−	4.77305i	0.173417	−	0.174403i
$750$		0			0
$751$	−0.490251	−	0.849139i	−0.0178895	−	0.0309855i	0.856942	−	0.515413i	$-0.172361\pi$
$751$	−0.490251	−	0.849139i	−0.0178895	−	0.0309855i	−0.874832	+	0.484427i	$0.839028\pi$
$752$		−	2.23938i		−	0.0816616i
$753$		0			0
$754$			18.3727i			0.669094i
$755$	29.1207	+	4.68337i	1.05981	+	0.170445i
$756$		0			0
$757$		−	16.9068i		−	0.614489i	−0.951631	−	0.307245i	$-0.900593\pi$
$757$		−	16.9068i		−	0.614489i	0.951631	−	0.307245i	$-0.0994070\pi$
$758$	−6.48462			−0.235532
$759$		0			0
$760$	−1.39465	+	8.67178i	−0.0505893	+	0.314559i
$761$	−16.0830	−	27.8566i	−0.583010	−	1.00980i	−0.995120	−	0.0986685i	$-0.968542\pi$
$761$	−16.0830	−	27.8566i	−0.583010	−	1.00980i	0.412111	−	0.911134i	$-0.364792\pi$
$762$		0			0
$763$	−8.25623	−	30.4667i	−0.298896	−	1.10297i
$764$			9.43103i			0.341203i
$765$		0			0
$766$	−8.50872	+	4.91251i	−0.307432	+	0.177496i
$767$	−32.2140	+	55.7963i	−1.16318	+	2.01469i
$768$		0			0
$769$	44.2257	+	25.5337i	1.59482	+	0.920770i	0.992463	+	0.122545i	$0.0391054\pi$
$769$	44.2257	+	25.5337i	1.59482	+	0.920770i	0.602358	+	0.798226i	$0.294228\pi$
$770$	−6.82977	+	15.3588i	−0.246128	+	0.553491i
$771$		0			0
$772$			1.48521i			0.0534540i
$773$	−21.9215	+	12.6564i	−0.788463	+	0.455219i	−0.839421	−	0.543482i	$-0.817106\pi$
$773$	−21.9215	+	12.6564i	−0.788463	+	0.455219i	0.0509584	+	0.998701i	$0.483772\pi$
$774$		0			0
$775$	6.79864	+	7.62335i	0.244214	+	0.273839i
$776$	−8.91744	−	15.4455i	−0.320117	−	0.554459i
$777$		0			0
$778$	−7.18549	−	4.14854i	−0.257612	−	0.148733i
$779$	19.4149	−	11.2092i	0.695609	−	0.401610i
$780$		0			0
$781$	−11.1044	+	19.2333i	−0.397345	+	0.688223i
$782$	25.1628	+	14.5277i	0.899819	+	0.519511i
$783$		0			0
$784$	6.08194	+	3.46554i	0.217212	+	0.123769i
$785$	−14.2757	−	37.4558i	−0.509521	−	1.33685i
$786$		0			0
$787$	25.7571			0.918141			0.459071	−	0.888400i	$-0.348182\pi$
$787$	25.7571			0.918141			0.459071	+	0.888400i	$0.348182\pi$
$788$	−17.6493			−0.628729
$789$		0			0
$790$	−3.59218	−	9.42498i	−0.127804	−	0.335326i
$791$	−15.2768	+	15.3637i	−0.543181	+	0.546272i
$792$		0			0
$793$	−45.4456	−	26.2380i	−1.61382	−	0.931740i
$794$	−6.65037	+	11.5188i	−0.236013	+	0.408786i
$795$		0			0
$796$	17.8938	−	10.3310i	0.634229	−	0.366172i
$797$	−42.2492	−	24.3926i	−1.49655	−	0.864031i	−0.496553	−	0.868006i	$-0.665401\pi$
$797$	−42.2492	−	24.3926i	−1.49655	−	0.864031i	−0.999992	+	0.00397561i	$0.998735\pi$
$798$		0			0
$799$	5.06627	+	8.77504i	0.179232	+	0.310439i
$800$	−3.73162	+	3.32792i	−0.131933	+	0.117660i
$801$		0			0
$802$	−18.0899	+	10.4442i	−0.638777	+	0.368798i
$803$		−	40.0132i		−	1.41204i
$804$		0			0
$805$	30.7244	−	22.3440i	1.08289	−	0.787523i
$806$	−8.89810	−	5.13732i	−0.313422	−	0.180954i
$807$		0			0
$808$	5.04091	−	8.73112i	0.177339	−	0.307160i
$809$	−19.3683	+	11.1823i	−0.680953	+	0.393148i	−0.800214	−	0.599715i	$-0.795281\pi$
$809$	−19.3683	+	11.1823i	−0.680953	+	0.393148i	0.119261	+	0.992863i	$0.461947\pi$
$810$		0			0
$811$		−	0.819585i		−	0.0287795i	−0.999896	−	0.0143898i	$-0.995419\pi$
$811$		−	0.819585i		−	0.0287795i	0.999896	−	0.0143898i	$-0.00458056\pi$
$812$	9.32859	−	2.52798i	0.327369	−	0.0887146i
$813$		0			0
$814$	−1.51831	−	2.62978i	−0.0532166	−	0.0921738i
$815$	1.34073	−	8.33653i	0.0469638	−	0.292016i
$816$		0			0
$817$	−30.6940			−1.07385
$818$		−	28.3129i		−	0.989938i
$819$		0			0
$820$	12.6001	+	2.02643i	0.440016	+	0.0707661i
$821$			53.8484i			1.87932i	0.342108	+	0.939661i	$0.388859\pi$
$821$			53.8484i			1.87932i	−0.342108	+	0.939661i	$0.611141\pi$
$822$		0			0
$823$			44.7612i			1.56028i	0.625608	+	0.780138i	$0.284851\pi$
$823$			44.7612i			1.56028i	−0.625608	+	0.780138i	$0.715149\pi$
$824$	−1.03484	−	1.79239i	−0.0360502	−	0.0624408i
$825$		0			0
$826$	32.7626	+	8.67915i	1.13996	+	0.301986i
$827$	−14.5517			−0.506014			−0.253007	−	0.967464i	$-0.581420\pi$
$827$	−14.5517			−0.506014			−0.253007	+	0.967464i	$0.581420\pi$
$828$		0			0
$829$	29.5474	−	17.0592i	1.02623	−	0.592491i	0.110324	−	0.993896i	$-0.464811\pi$
$829$	29.5474	−	17.0592i	1.02623	−	0.592491i	0.915901	+	0.401404i	$0.131478\pi$
$830$	22.0134	+	17.9130i	0.764096	+	0.621771i
$831$		0			0
$832$	2.51471	−	4.35560i	0.0871818	−	0.151003i
$833$	−31.6725	+	0.179725i	−1.09739	+	0.00622710i
$834$		0			0
$835$	8.55450	−	53.1910i	0.296041	−	1.84075i
$836$	−5.58010	−	9.66502i	−0.192992	−	0.334272i
$837$		0			0
$838$	7.85403	−	13.6036i	0.271313	−	0.469928i
$839$	23.2722	+	40.3087i	0.803446	+	1.39161i	0.917335	+	0.398116i	$0.130336\pi$
$839$	23.2722	+	40.3087i	0.803446	+	1.39161i	−0.113889	+	0.993493i	$0.536331\pi$
$840$		0			0
$841$	−7.82763	+	13.5578i	−0.269918	+	0.467512i
$842$	−13.2658	−	22.9771i	−0.457171	−	0.791843i
$843$		0			0
$844$	5.63953	−	9.76796i	0.194121	−	0.336227i
$845$	−17.3524	+	21.3244i	−0.596942	+	0.733583i
$846$		0			0
$847$	2.02589	+	7.47583i	0.0696105	+	0.256872i
$848$	−2.88164	−	4.99115i	−0.0989559	−	0.171397i
$849$		0			0
$850$	7.09346	−	21.4828i	0.243304	−	0.736853i
$851$			6.86312i			0.235265i
$852$		0			0
$853$	19.2187	+	33.2878i	0.658037	+	1.13975i	0.981123	+	0.193384i	$0.0619462\pi$
$853$	19.2187	+	33.2878i	0.658037	+	1.13975i	−0.323086	+	0.946369i	$0.604720\pi$
$854$	−7.06910	+	26.6849i	−0.241900	+	0.913137i
$855$		0			0
$856$	−1.27205	+	2.20325i	−0.0434777	+	0.0753055i
$857$	−23.5713	−	13.6089i	−0.805180	−	0.464871i	0.0400992	−	0.999196i	$-0.487233\pi$
$857$	−23.5713	−	13.6089i	−0.805180	−	0.464871i	−0.845279	+	0.534325i	$0.820566\pi$
$858$		0			0
$859$	−27.7376	+	16.0143i	−0.946395	+	0.546402i	−0.891959	−	0.452116i	$-0.850669\pi$
$859$	−27.7376	+	16.0143i	−0.946395	+	0.546402i	−0.0544359	+	0.998517i	$0.517336\pi$
$860$	−13.5529	−	11.0285i	−0.462152	−	0.376069i
$861$		0			0
$862$	14.0479	−	8.11059i	0.478475	−	0.276248i
$863$	−14.0979	+	24.4183i	−0.479898	+	0.831208i	−0.999734	−	0.0230584i	$-0.992660\pi$
$863$	−14.0979	+	24.4183i	−0.479898	+	0.831208i	0.519836	+	0.854266i	$0.325993\pi$
$864$		0			0
$865$	−25.4356	+	9.69440i	−0.864838	+	0.329620i
$866$	19.7268			0.670344
$867$		0			0
$868$	−1.38411	+	5.22481i	−0.0469796	+	0.177342i
$869$	11.0990	+	6.40799i	0.376507	+	0.217376i
$870$		0			0
$871$	26.1324	+	15.0875i	0.885462	+	0.511222i
$872$	5.96532	+	10.3322i	0.202011	+	0.349894i
$873$		0			0
$874$			25.2235i			0.853196i
$875$	−21.8971	−	19.8876i	−0.740256	−	0.672325i
$876$		0			0
$877$	−20.2119	+	11.6694i	−0.682508	+	0.394046i	−0.800799	−	0.598933i	$-0.795592\pi$
$877$	−20.2119	+	11.6694i	−0.682508	+	0.394046i	0.118291	+	0.992979i	$0.462258\pi$
$878$		−	13.1264i		−	0.442994i
$879$		0			0
$880$	1.00879	−	6.27254i	0.0340063	−	0.211447i
$881$	−18.3044			−0.616690			−0.308345	−	0.951275i	$-0.599775\pi$
$881$	−18.3044			−0.616690			−0.308345	+	0.951275i	$0.599775\pi$
$882$		0			0
$883$		−	7.38295i		−	0.248456i	−0.992254	−	0.124228i	$-0.960355\pi$
$883$		−	7.38295i		−	0.248456i	0.992254	−	0.124228i	$-0.0396454\pi$
$884$			22.7567i			0.765390i
$885$		0			0
$886$	8.62000			0.289595
$887$	9.64775	−	5.57013i	0.323940	−	0.187027i	−0.329207	−	0.944258i	$-0.606782\pi$
$887$	9.64775	−	5.57013i	0.323940	−	0.187027i	0.653147	+	0.757231i	$0.273448\pi$
$888$		0			0
$889$	−12.3111	+	46.4726i	−0.412900	+	1.55864i
$890$	−23.5570	−	3.78858i	−0.789632	−	0.126994i
$891$		0			0
$892$	−6.07248	−	10.5178i	−0.203322	−	0.352164i
$893$	−4.39810	+	7.61774i	−0.147177	+	0.254918i
$894$		0			0
$895$	−6.34816	−	5.16572i	−0.212196	−	0.172671i
$896$	−2.55753	−	0.677517i	−0.0854411	−	0.0226343i
$897$		0			0
$898$		−	37.2222i		−	1.24212i
$899$	3.73142	+	6.46301i	0.124450	+	0.215554i
$900$		0			0
$901$	22.5835	+	13.0386i	0.752366	+	0.434379i
$902$	−14.0433	+	8.10791i	−0.467591	+	0.269964i
$903$		0			0
$904$	4.09453	−	7.09194i	0.136182	−	0.235874i
$905$	24.1652	−	9.21019i	0.803279	−	0.306157i
$906$		0			0
$907$	−21.6780	−	12.5158i	−0.719806	−	0.415580i	0.0948756	−	0.995489i	$-0.469755\pi$
$907$	−21.6780	−	12.5158i	−0.719806	−	0.415580i	−0.814681	+	0.579909i	$0.803088\pi$
$908$	20.5863	+	11.8855i	0.683180	+	0.394434i
$909$		0			0
$910$	27.1875	+	12.0898i	0.901258	+	0.400774i
$911$	−10.1366	+	5.85238i	−0.335841	+	0.193898i	−0.658431	−	0.752641i	$-0.728780\pi$
$911$	−10.1366	+	5.85238i	−0.335841	+	0.193898i	0.322590	+	0.946539i	$0.395446\pi$
$912$		0			0
$913$	−36.0614			−1.19346
$914$			40.5035i			1.33974i
$915$		0			0
$916$	9.88508	−	5.70716i	0.326612	−	0.188570i
$917$	−11.8396	−	43.6899i	−0.390979	−	1.44277i
$918$		0			0
$919$	15.3085	−	26.5152i	0.504982	−	0.874655i	−0.495001	−	0.868892i	$-0.664832\pi$
$919$	15.3085	−	26.5152i	0.504982	−	0.874655i	0.999983	−	0.00576276i	$-0.00183435\pi$
$920$	−9.06290	+	11.1374i	−0.298795	+	0.367190i
$921$		0			0
$922$	−16.8755	−	29.2292i	−0.555765	−	0.962614i
$923$	34.0462	+	19.6566i	1.12064	+	0.647004i
$924$		0			0
$925$	5.23232	−	1.08615i	0.172038	−	0.0357123i
$926$	23.0998	+	13.3367i	0.759108	+	0.438271i
$927$		0			0
$928$	−3.16363	+	1.82652i	−0.103851	+	0.0599586i
$929$	−13.3528			−0.438093			−0.219046	−	0.975714i	$-0.570295\pi$
$929$	−13.3528			−0.438093			−0.219046	+	0.975714i	$0.570295\pi$
$930$		0			0
$931$	−13.8828	−	23.7337i	−0.454991	−	0.777840i
$932$	4.16132	−	7.20762i	0.136309	−	0.236093i
$933$		0			0
$934$	−4.89263	−	2.82476i	−0.160092	−	0.0924289i
$935$	10.2378	+	26.8613i	0.334811	+	0.878459i
$936$		0			0
$937$	−32.6519			−1.06669			−0.533345	−	0.845898i	$-0.679065\pi$
$937$	−32.6519			−1.06669			−0.533345	+	0.845898i	$0.679065\pi$
$938$	4.06491	−	15.3445i	0.132724	−	0.501015i
$939$		0			0
$940$	−4.67907	+	1.78335i	−0.152614	+	0.0581666i
$941$	−35.8078			−1.16730			−0.583650	−	0.812006i	$-0.698376\pi$
$941$	−35.8078			−1.16730			−0.583650	+	0.812006i	$0.698376\pi$
$942$		0			0
$943$	36.6498			1.19348
$944$	−12.8102			−0.416937
$945$		0			0
$946$	22.2019			0.721845
$947$	34.3826			1.11729			0.558643	−	0.829408i	$-0.311322\pi$
$947$	34.3826			1.11729			0.558643	+	0.829408i	$0.311322\pi$
$948$		0			0
$949$	−70.8300			−2.29924
$950$	19.2299	−	3.99182i	0.623901	−	0.129512i
$951$		0			0
$952$	11.5545	−	3.13119i	0.374484	−	0.101482i
$953$	44.0113			1.42566			0.712832	−	0.701334i	$-0.247412\pi$
$953$	44.0113			1.42566			0.712832	+	0.701334i	$0.247412\pi$
$954$		0			0
$955$	19.7057	−	7.51051i	0.637661	−	0.243035i
$956$	6.41684	+	3.70476i	0.207535	+	0.119821i
$957$		0			0
$958$	−0.136929	+	0.237168i	−0.00442397	+	0.00766254i
$959$	11.5665	−	11.6323i	0.373501	−	0.375627i
$960$		0			0
$961$	26.8265			0.865372
$962$	−4.65515	+	2.68765i	−0.150088	+	0.0866534i
$963$		0			0
$964$	−7.50748	−	4.33445i	−0.241800	−	0.139603i
$965$	3.10328	−	1.18277i	0.0998981	−	0.0380746i
$966$		0			0
$967$	−6.03415	−	3.48382i	−0.194045	−	0.112032i	0.399830	−	0.916589i	$-0.369069\pi$
$967$	−6.03415	−	3.48382i	−0.194045	−	0.112032i	−0.593875	+	0.804557i	$0.702403\pi$
$968$	−1.46376	−	2.53530i	−0.0470469	−	0.0814876i
$969$		0			0
$970$	−25.1710	+	30.9327i	−0.808193	+	0.993190i
$971$	12.3672	−	21.4206i	0.396883	−	0.687421i	−0.596457	−	0.802645i	$-0.703425\pi$
$971$	12.3672	−	21.4206i	0.396883	−	0.687421i	0.993340	+	0.115224i	$0.0367586\pi$
$972$		0			0
$973$	−28.1911	−	28.0316i	−0.903766	−	0.898652i
$974$	−12.4072	+	7.16329i	−0.397552	+	0.229527i
$975$		0			0
$976$		−	10.4338i		−	0.333979i
$977$	45.1109			1.44323			0.721613	−	0.692296i	$-0.243401\pi$
$977$	45.1109			1.44323			0.721613	+	0.692296i	$0.243401\pi$
$978$		0			0
$979$	26.2551	−	15.1584i	0.839117	−	0.484465i
$980$	2.39766	−	15.4677i	0.0765905	−	0.494099i
$981$		0			0
$982$	−31.8165	−	18.3692i	−1.01530	−	0.586186i
$983$	−31.8263	−	18.3749i	−1.01510	−	0.586068i	−0.102419	−	0.994741i	$-0.532658\pi$
$983$	−31.8263	−	18.3749i	−1.01510	−	0.586068i	−0.912681	+	0.408673i	$0.865992\pi$
$984$		0			0
$985$	14.0552	+	36.8773i	0.447836	+	1.17501i
$986$	8.26450	−	14.3145i	0.263195	−	0.455868i
$987$		0			0
$988$	−17.1087	+	9.87771i	−0.544300	+	0.314252i
$989$	−43.4563	−	25.0895i	−1.38183	−	0.797800i
$990$		0			0
$991$	5.67076	+	9.82205i	0.180138	+	0.312008i	0.941927	−	0.335817i	$-0.109012\pi$
$991$	5.67076	+	9.82205i	0.180138	+	0.312008i	−0.761790	+	0.647825i	$0.775679\pi$
$992$		−	2.04291i		−	0.0648624i
$993$		0			0
$994$	5.29591	−	19.9913i	0.167976	−	0.634086i
$995$	−35.8360	−	29.1610i	−1.13608	−	0.924466i
$996$		0			0
$997$	4.30265	−	7.45242i	0.136266	−	0.236020i	−0.789814	−	0.613346i	$-0.789823\pi$
$997$	4.30265	−	7.45242i	0.136266	−	0.236020i	0.926081	+	0.377326i	$0.123156\pi$
$998$	16.0396	+	27.7814i	0.507725	+	0.879406i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.b.719.11		48
3.2	odd	2		630.2.bi.a.509.5	yes	48
5.4	even	2		1890.2.bi.a.719.6		48
7.3	odd	6		1890.2.r.a.1529.2		48
9.2	odd	6		1890.2.r.b.89.2		48
9.7	even	3		630.2.r.a.299.20	yes	48
15.14	odd	2		630.2.bi.b.509.20	yes	48
21.17	even	6		630.2.r.b.59.5	yes	48
35.24	odd	6		1890.2.r.b.1529.2		48
45.29	odd	6		1890.2.r.a.89.2		48
45.34	even	6		630.2.r.b.299.5	yes	48
63.38	even	6		1890.2.bi.a.899.6		48
63.52	odd	6		630.2.bi.b.479.20	yes	48
105.59	even	6		630.2.r.a.59.20	✓	48
315.164	even	6	inner	1890.2.bi.b.899.11		48
315.304	odd	6		630.2.bi.a.479.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.20	✓	48	105.59	even	6
630.2.r.a.299.20	yes	48	9.7	even	3
630.2.r.b.59.5	yes	48	21.17	even	6
630.2.r.b.299.5	yes	48	45.34	even	6
630.2.bi.a.479.5	yes	48	315.304	odd	6
630.2.bi.a.509.5	yes	48	3.2	odd	2
630.2.bi.b.479.20	yes	48	63.52	odd	6
630.2.bi.b.509.20	yes	48	15.14	odd	2
1890.2.r.a.89.2		48	45.29	odd	6
1890.2.r.a.1529.2		48	7.3	odd	6
1890.2.r.b.89.2		48	9.2	odd	6
1890.2.r.b.1529.2		48	35.24	odd	6
1890.2.bi.a.719.6		48	5.4	even	2
1890.2.bi.a.899.6		48	63.38	even	6
1890.2.bi.b.719.11		48	1.1	even	1	trivial
1890.2.bi.b.899.11		48	315.164	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.796362 - 2.08945i) q^{5} +(-2.55753 - 0.677517i) q^{7} +1.00000 q^{8} +(-0.796362 - 2.08945i) q^{10} +(2.46056 + 1.42061i) q^{11} +(2.51471 - 4.35560i) q^{13} +(-2.55753 - 0.677517i) q^{14} +1.00000 q^{16} +(-3.91852 + 2.26236i) q^{17} +(-3.40172 - 1.96399i) q^{19} +(-0.796362 - 2.08945i) q^{20} +(2.46056 + 1.42061i) q^{22} +(-3.21075 - 5.56118i) q^{23} +(-3.73162 + 3.32792i) q^{25} +(2.51471 - 4.35560i) q^{26} +(-2.55753 - 0.677517i) q^{28} +(-3.16363 + 1.82652i) q^{29} -2.04291i q^{31} +1.00000 q^{32} +(-3.91852 + 2.26236i) q^{34} +(0.621082 + 5.88339i) q^{35} +(-0.925584 - 0.534386i) q^{37} +(-3.40172 - 1.96399i) q^{38} +(-0.796362 - 2.08945i) q^{40} +(-2.85368 + 4.94272i) q^{41} +(6.76731 - 3.90711i) q^{43} +(2.46056 + 1.42061i) q^{44} +(-3.21075 - 5.56118i) q^{46} -2.23938i q^{47} +(6.08194 + 3.46554i) q^{49} +(-3.73162 + 3.32792i) q^{50} +(2.51471 - 4.35560i) q^{52} +(-2.88164 - 4.99115i) q^{53} +(1.00879 - 6.27254i) q^{55} +(-2.55753 - 0.677517i) q^{56} +(-3.16363 + 1.82652i) q^{58} -12.8102 q^{59} -10.4338i q^{61} -2.04291i q^{62} +1.00000 q^{64} +(-11.1034 - 1.78572i) q^{65} +5.99972i q^{67} +(-3.91852 + 2.26236i) q^{68} +(0.621082 + 5.88339i) q^{70} +7.81664i q^{71} +(-7.04158 - 12.1964i) q^{73} +(-0.925584 - 0.534386i) q^{74} +(-3.40172 - 1.96399i) q^{76} +(-5.33048 - 5.30032i) q^{77} +4.51074 q^{79} +(-0.796362 - 2.08945i) q^{80} +(-2.85368 + 4.94272i) q^{82} +(-10.9918 + 6.34613i) q^{83} +(7.84765 + 6.38590i) q^{85} +(6.76731 - 3.90711i) q^{86} +(2.46056 + 1.42061i) q^{88} +(5.33519 - 9.24081i) q^{89} +(-9.38244 + 9.43583i) q^{91} +(-3.21075 - 5.56118i) q^{92} -2.23938i q^{94} +(-1.39465 + 8.67178i) q^{95} +(-8.91744 - 15.4455i) q^{97} +(6.08194 + 3.46554i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots + 3 q^{98}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

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