LMFDB - Embedded newform 1890.2.r.b.89.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1890,2,Mod(89,1890)] 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([1, 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("1890.89"); 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:traces = [48,24] 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			89.16
Character	$\chi$	$=$	1890.89
Dual form			1890.2.r.b.1529.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00280 - 1.99860i) q^{5} +(-2.55747 + 0.677764i) q^{7} -1.00000 q^{8} +(2.23224 - 0.130844i) q^{10} +3.58743i q^{11} +(-2.03087 - 3.51756i) q^{13} +(-1.86569 - 1.87595i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.57132 - 2.63925i) q^{17} +(3.13968 + 1.81269i) q^{19} +(1.22943 + 1.86775i) q^{20} +(-3.10680 + 1.79371i) q^{22} +4.79723 q^{23} +(-2.98877 - 4.00840i) q^{25} +(2.03087 - 3.51756i) q^{26} +(0.691773 - 2.55371i) q^{28} +(6.99680 + 4.03961i) q^{29} +(-3.05326 - 1.76280i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.57132 + 2.63925i) q^{34} +(-1.21006 + 5.79101i) q^{35} +(0.879847 + 0.507980i) q^{37} +3.62539i q^{38} +(-1.00280 + 1.99860i) q^{40} +(-4.80160 - 8.31661i) q^{41} +(4.43909 + 2.56291i) q^{43} +(-3.10680 - 1.79371i) q^{44} +(2.39862 + 4.15452i) q^{46} +(9.96048 - 5.75069i) q^{47} +(6.08127 - 3.46672i) q^{49} +(1.97699 - 4.59255i) q^{50} +4.06173 q^{52} +(5.71305 + 9.89529i) q^{53} +(7.16981 + 3.59749i) q^{55} +(2.55747 - 0.677764i) q^{56} +8.07921i q^{58} +(-3.51911 + 6.09528i) q^{59} +(9.71945 - 5.61153i) q^{61} -3.52560i q^{62} +1.00000 q^{64} +(-9.06675 + 0.531452i) q^{65} +(6.05819 + 3.49770i) q^{67} +5.27850i q^{68} +(-5.62019 + 1.84756i) q^{70} +0.828681i q^{71} +(-3.51263 - 6.08405i) q^{73} +1.01596i q^{74} +(-3.13968 + 1.81269i) q^{76} +(-2.43143 - 9.17472i) q^{77} +(-0.0149934 - 0.0259693i) q^{79} +(-2.23224 + 0.130844i) q^{80} +(4.80160 - 8.31661i) q^{82} +(-6.89727 - 3.98214i) q^{83} +(-0.690658 - 11.7829i) q^{85} +5.12582i q^{86} -3.58743i q^{88} +(-0.625013 + 1.08255i) q^{89} +(7.57795 + 7.61961i) q^{91} +(-2.39862 + 4.15452i) q^{92} +(9.96048 + 5.75069i) q^{94} +(6.77133 - 4.45717i) q^{95} +(4.69619 - 8.13404i) q^{97} +(6.04290 + 3.53318i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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
$5$	1.00280	−	1.99860i	0.448468	−	0.893799i
$5$	1.00280	−	1.99860i	0.448468	−	0.893799i
$6$		0			0
$7$	−2.55747	+	0.677764i	−0.966632	+	0.256171i
$7$	−2.55747	+	0.677764i	−0.966632	+	0.256171i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.23224	−	0.130844i	0.705895	−	0.0413764i
$11$			3.58743i			1.08165i	0.841135	+	0.540825i	$0.181888\pi$
$11$			3.58743i			1.08165i	−0.841135	+	0.540825i	$0.818112\pi$
$12$		0			0
$13$	−2.03087	−	3.51756i	−0.563261	−	0.975597i	−0.997209	−	0.0746590i	$-0.976213\pi$
$13$	−2.03087	−	3.51756i	−0.563261	−	0.975597i	0.433948	−	0.900938i	$-0.357120\pi$
$14$	−1.86569	−	1.87595i	−0.498628	−	0.501369i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.57132	−	2.63925i	1.10871	−	0.640112i	0.170213	−	0.985407i	$-0.445555\pi$
$17$	4.57132	−	2.63925i	1.10871	−	0.640112i	0.938494	+	0.345295i	$0.112221\pi$
$18$		0			0
$19$	3.13968	+	1.81269i	0.720292	+	0.415861i	0.814860	−	0.579658i	$-0.196814\pi$
$19$	3.13968	+	1.81269i	0.720292	+	0.415861i	−0.0945683	+	0.995518i	$0.530147\pi$
$20$	1.22943	+	1.86775i	0.274909	+	0.417642i
$21$		0			0
$22$	−3.10680	+	1.79371i	−0.662372	+	0.382421i
$23$	4.79723			1.00029			0.500146	−	0.865941i	$-0.333280\pi$
$23$	4.79723			1.00029			0.500146	+	0.865941i	$0.333280\pi$
$24$		0			0
$25$	−2.98877	−	4.00840i	−0.597753	−	0.801680i
$26$	2.03087	−	3.51756i	0.398286	−	0.689851i
$27$		0			0
$28$	0.691773	−	2.55371i	0.130733	−	0.482606i
$29$	6.99680	+	4.03961i	1.29927	+	0.750136i	0.980279	−	0.197620i	$-0.0633213\pi$
$29$	6.99680	+	4.03961i	1.29927	+	0.750136i	0.318995	+	0.947756i	$0.396655\pi$
$30$		0			0
$31$	−3.05326	−	1.76280i	−0.548381	−	0.316608i	0.200088	−	0.979778i	$-0.435877\pi$
$31$	−3.05326	−	1.76280i	−0.548381	−	0.316608i	−0.748469	+	0.663170i	$0.769211\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	4.57132	+	2.63925i	0.783974	+	0.452628i
$35$	−1.21006	+	5.79101i	−0.204538	+	0.978859i
$36$		0			0
$37$	0.879847	+	0.507980i	0.144646	+	0.0835114i	0.570576	−	0.821245i	$-0.306720\pi$
$37$	0.879847	+	0.507980i	0.144646	+	0.0835114i	−0.425930	+	0.904756i	$0.640053\pi$
$38$			3.62539i			0.588116i
$39$		0			0
$40$	−1.00280	+	1.99860i	−0.158557	+	0.316006i
$41$	−4.80160	−	8.31661i	−0.749883	−	1.29884i	−0.947878	−	0.318633i	$-0.896776\pi$
$41$	−4.80160	−	8.31661i	−0.749883	−	1.29884i	0.197995	−	0.980203i	$-0.436557\pi$
$42$		0			0
$43$	4.43909	+	2.56291i	0.676955	+	0.390840i	0.798707	−	0.601720i	$-0.205518\pi$
$43$	4.43909	+	2.56291i	0.676955	+	0.390840i	−0.121752	+	0.992561i	$0.538851\pi$
$44$	−3.10680	−	1.79371i	−0.468368	−	0.270412i
$45$		0			0
$46$	2.39862	+	4.15452i	0.353657	+	0.612551i
$47$	9.96048	−	5.75069i	1.45289	−	0.838824i	0.454242	−	0.890879i	$-0.349910\pi$
$47$	9.96048	−	5.75069i	1.45289	−	0.838824i	0.998644	+	0.0520545i	$0.0165770\pi$
$48$		0			0
$49$	6.08127	−	3.46672i	0.868753	−	0.495245i
$50$	1.97699	−	4.59255i	0.279589	−	0.649484i
$51$		0			0
$52$	4.06173			0.563261
$53$	5.71305	+	9.89529i	0.784747	+	1.35922i	0.929150	+	0.369703i	$0.120541\pi$
$53$	5.71305	+	9.89529i	0.784747	+	1.35922i	−0.144403	+	0.989519i	$0.546126\pi$
$54$		0			0
$55$	7.16981	+	3.59749i	0.966777	+	0.485085i
$56$	2.55747	−	0.677764i	0.341756	−	0.0905700i
$57$		0			0
$58$			8.07921i			1.06085i
$59$	−3.51911	+	6.09528i	−0.458150	+	0.793538i	−0.998863	−	0.0476683i	$-0.984821\pi$
$59$	−3.51911	+	6.09528i	−0.458150	+	0.793538i	0.540714	+	0.841207i	$0.318154\pi$
$60$		0			0
$61$	9.71945	−	5.61153i	1.24445	−	0.718482i	0.274451	−	0.961601i	$-0.411504\pi$
$61$	9.71945	−	5.61153i	1.24445	−	0.718482i	0.969997	+	0.243119i	$0.0781704\pi$
$62$		−	3.52560i		−	0.447751i
$63$		0			0
$64$	1.00000			0.125000
$65$	−9.06675	+	0.531452i	−1.12459	+	0.0659185i
$66$		0			0
$67$	6.05819	+	3.49770i	0.740126	+	0.427312i	0.822115	−	0.569321i	$-0.192794\pi$
$67$	6.05819	+	3.49770i	0.740126	+	0.427312i	−0.0819892	+	0.996633i	$0.526127\pi$
$68$			5.27850i			0.640112i
$69$		0			0
$70$	−5.62019	+	1.84756i	−0.671741	+	0.220825i
$71$			0.828681i			0.0983464i	0.998790	+	0.0491732i	$0.0156586\pi$
$71$			0.828681i			0.0983464i	−0.998790	+	0.0491732i	$0.984341\pi$
$72$		0			0
$73$	−3.51263	−	6.08405i	−0.411122	−	0.712084i	0.583891	−	0.811832i	$-0.301530\pi$
$73$	−3.51263	−	6.08405i	−0.411122	−	0.712084i	−0.995013	+	0.0997484i	$0.968196\pi$
$74$			1.01596i			0.118103i
$75$		0			0
$76$	−3.13968	+	1.81269i	−0.360146	+	0.207930i
$77$	−2.43143	−	9.17472i	−0.277087	−	1.04556i
$78$		0			0
$79$	−0.0149934	−	0.0259693i	−0.00168689	−	0.00292177i	0.865181	−	0.501460i	$-0.167204\pi$
$79$	−0.0149934	−	0.0259693i	−0.00168689	−	0.00292177i	−0.866868	+	0.498538i	$0.833870\pi$
$80$	−2.23224	+	0.130844i	−0.249572	+	0.0146288i
$81$		0			0
$82$	4.80160	−	8.31661i	0.530248	−	0.918416i
$83$	−6.89727	−	3.98214i	−0.757074	−	0.437097i	0.0711705	−	0.997464i	$-0.477327\pi$
$83$	−6.89727	−	3.98214i	−0.757074	−	0.437097i	−0.828244	+	0.560368i	$0.810660\pi$
$84$		0			0
$85$	−0.690658	−	11.7829i	−0.0749124	−	1.27803i
$86$			5.12582i			0.552731i
$87$		0			0
$88$		−	3.58743i		−	0.382421i
$89$	−0.625013	+	1.08255i	−0.0662512	+	0.114750i	−0.897248	−	0.441526i	$-0.854437\pi$
$89$	−0.625013	+	1.08255i	−0.0662512	+	0.114750i	0.830997	+	0.556277i	$0.187771\pi$
$90$		0			0
$91$	7.57795	+	7.61961i	0.794385	+	0.798752i
$92$	−2.39862	+	4.15452i	−0.250073	+	0.433139i
$93$		0			0
$94$	9.96048	+	5.75069i	1.02735	+	0.593138i
$95$	6.77133	−	4.45717i	0.694723	−	0.457296i
$96$		0			0
$97$	4.69619	−	8.13404i	0.476826	−	0.825887i	−0.522821	−	0.852442i	$-0.675121\pi$
$97$	4.69619	−	8.13404i	0.476826	−	0.825887i	0.999647	+	0.0265556i	$0.00845391\pi$
$98$	6.04290	+	3.53318i	0.610425	+	0.356905i
$99$		0			0
$100$	4.96576	−	0.584148i	0.496576	−	0.0584148i
$101$	10.8924			1.08383			0.541916	−	0.840433i	$-0.317699\pi$
$101$	10.8924			1.08383			0.541916	+	0.840433i	$0.317699\pi$
$102$		0			0
$103$	−0.584230			−0.0575659			−0.0287830	−	0.999586i	$-0.509163\pi$
$103$	−0.584230			−0.0575659			−0.0287830	+	0.999586i	$0.509163\pi$
$104$	2.03087	+	3.51756i	0.199143	+	0.344926i
$105$		0			0
$106$	−5.71305	+	9.89529i	−0.554900	+	0.961115i
$107$	1.34287	−	2.32592i	0.129820	−	0.224855i	−0.793787	−	0.608196i	$-0.791893\pi$
$107$	1.34287	−	2.32592i	0.129820	−	0.224855i	0.923607	+	0.383341i	$0.125227\pi$
$108$		0			0
$109$	−0.618180	−	1.07072i	−0.0592109	−	0.102556i	0.834901	−	0.550401i	$-0.185525\pi$
$109$	−0.618180	−	1.07072i	−0.0592109	−	0.102556i	−0.894111	+	0.447845i	$0.852192\pi$
$110$	0.469392	+	8.00798i	0.0447547	+	0.763531i
$111$		0			0
$112$	1.86569	+	1.87595i	0.176292	+	0.177261i
$113$	−5.41347	−	9.37640i	−0.509256	−	0.882058i	−0.999943	−	0.0107214i	$-0.996587\pi$
$113$	−5.41347	−	9.37640i	−0.509256	−	0.882058i	0.490686	−	0.871336i	$-0.336746\pi$
$114$		0			0
$115$	4.81068	−	9.58772i	0.448599	−	0.894060i
$116$	−6.99680	+	4.03961i	−0.649637	+	0.375068i
$117$		0			0
$118$	−7.03823			−0.647921
$119$	−9.90220	+	9.84807i	−0.907733	+	0.902771i
$120$		0			0
$121$	−1.86962			−0.169965
$122$	9.71945	+	5.61153i	0.879958	+	0.508044i
$123$		0			0
$124$	3.05326	−	1.76280i	0.274191	−	0.158304i
$125$	−11.0083	+	1.95369i	−0.984614	+	0.174744i
$126$		0			0
$127$			4.95940i			0.440076i	0.975491	+	0.220038i	$0.0706181\pi$
$127$			4.95940i			0.440076i	−0.975491	+	0.220038i	$0.929382\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−4.99363	−	7.58631i	−0.437970	−	0.665364i
$131$	9.28206			0.810977			0.405489	−	0.914100i	$-0.367101\pi$
$131$	9.28206			0.810977			0.405489	+	0.914100i	$0.367101\pi$
$132$		0			0
$133$	−9.25820	−	2.50795i	−0.802788	−	0.217466i
$134$			6.99540i			0.604310i
$135$		0			0
$136$	−4.57132	+	2.63925i	−0.391987	+	0.226314i
$137$	0.00612456			0.000523257			0.000261628	−	1.00000i	$-0.499917\pi$
$137$	0.00612456			0.000523257			0.000261628		1.00000i	$0.499917\pi$
$138$		0			0
$139$	7.32549	−	4.22938i	0.621340	−	0.358731i	−0.156050	−	0.987749i	$-0.549876\pi$
$139$	7.32549	−	4.22938i	0.621340	−	0.358731i	0.777391	+	0.629018i	$0.216543\pi$
$140$	−4.41013	−	3.94345i	−0.372724	−	0.333282i
$141$		0			0
$142$	−0.717659	+	0.414341i	−0.0602246	+	0.0347707i
$143$	12.6190	−	7.28558i	1.05525	−	0.609251i
$144$		0			0
$145$	15.0900	−	9.93284i	1.25315	−	0.824878i
$146$	3.51263	−	6.08405i	0.290707	−	0.503519i
$147$		0			0
$148$	−0.879847	+	0.507980i	−0.0723230	+	0.0417557i
$149$			17.3271i			1.41949i	0.704460	+	0.709744i	$0.251189\pi$
$149$			17.3271i			1.41949i	−0.704460	+	0.709744i	$0.748811\pi$
$150$		0			0
$151$	−5.64408			−0.459308			−0.229654	−	0.973272i	$-0.573760\pi$
$151$	−5.64408			−0.459308			−0.229654	+	0.973272i	$0.573760\pi$
$152$	−3.13968	−	1.81269i	−0.254662	−	0.147029i
$153$		0			0
$154$	6.72983	−	6.69304i	0.542305	−	0.539340i
$155$	−6.58494	+	4.33448i	−0.528915	+	0.348154i
$156$		0			0
$157$	3.24346	−	5.61784i	0.258857	−	0.448353i	−0.707079	−	0.707134i	$-0.749988\pi$
$157$	3.24346	−	5.61784i	0.258857	−	0.448353i	0.965936	+	0.258782i	$0.0833210\pi$
$158$	0.0149934	−	0.0259693i	0.00119281	−	0.00206601i
$159$		0			0
$160$	−1.22943	−	1.86775i	−0.0971951	−	0.147659i
$161$	−12.2688	+	3.25139i	−0.966914	+	0.256245i
$162$		0			0
$163$	−4.53833	−	2.62021i	−0.355469	−	0.205230i	0.311622	−	0.950206i	$-0.399128\pi$
$163$	−4.53833	−	2.62021i	−0.355469	−	0.205230i	−0.667092	+	0.744976i	$0.732461\pi$
$164$	9.60319			0.749883
$165$		0			0
$166$		−	7.96428i		−	0.618148i
$167$	−18.8867	+	10.9043i	−1.46150	+	0.843797i	−0.999081	−	0.0428649i	$-0.986351\pi$
$167$	−18.8867	+	10.9043i	−1.46150	+	0.843797i	−0.462418	+	0.886662i	$0.653018\pi$
$168$		0			0
$169$	−1.74884	+	3.02908i	−0.134526	+	0.233006i
$170$	9.85893	−	6.48956i	0.756145	−	0.497726i
$171$		0			0
$172$	−4.43909	+	2.56291i	−0.338477	+	0.195420i
$173$	−18.7792	+	10.8422i	−1.42775	+	0.824314i	−0.996943	−	0.0781289i	$-0.975105\pi$
$173$	−18.7792	+	10.8422i	−1.42775	+	0.824314i	−0.430810	+	0.902443i	$0.641772\pi$
$174$		0			0
$175$	10.3604	+	8.22567i	0.783174	+	0.621802i
$176$	3.10680	−	1.79371i	0.234184	−	0.135206i
$177$		0			0
$178$	−1.25003			−0.0936934
$179$	15.1142	−	8.72620i	1.12969	−	0.652227i	0.185833	−	0.982581i	$-0.440502\pi$
$179$	15.1142	−	8.72620i	1.12969	−	0.652227i	0.943857	+	0.330355i	$0.107168\pi$
$180$		0			0
$181$			24.0491i			1.78755i	0.448513	+	0.893776i	$0.351954\pi$
$181$			24.0491i			1.78755i	−0.448513	+	0.893776i	$0.648046\pi$
$182$	−2.80980	+	10.3725i	−0.208276	+	0.768861i
$183$		0			0
$184$	−4.79723			−0.353657
$185$	1.89756	−	1.24905i	0.139511	−	0.0918323i
$186$		0			0
$187$	9.46811	+	16.3993i	0.692377	+	1.19923i
$188$			11.5014i			0.838824i
$189$		0			0
$190$	7.24569	+	3.63556i	0.525657	+	0.263751i
$191$	2.79411	−	1.61318i	0.202175	−	0.116726i	−0.395495	−	0.918468i	$-0.629427\pi$
$191$	2.79411	−	1.61318i	0.202175	−	0.116726i	0.597670	+	0.801743i	$0.296093\pi$
$192$		0			0
$193$	−20.9812	−	12.1135i	−1.51026	−	0.871951i	−0.999928	−	0.0119754i	$-0.996188\pi$
$193$	−20.9812	−	12.1135i	−1.51026	−	0.871951i	−0.510335	−	0.859976i	$-0.670479\pi$
$194$	9.39238			0.674334
$195$		0			0
$196$	−0.0383723	+	6.99989i	−0.00274088	+	0.499992i
$197$	6.89656			0.491359			0.245680	−	0.969351i	$-0.420989\pi$
$197$	6.89656			0.491359			0.245680	+	0.969351i	$0.420989\pi$
$198$		0			0
$199$	−14.5256	+	8.38638i	−1.02969	+	0.594494i	−0.916897	−	0.399124i	$-0.869314\pi$
$199$	−14.5256	+	8.38638i	−1.02969	+	0.594494i	−0.112797	+	0.993618i	$0.535981\pi$
$200$	2.98877	+	4.00840i	0.211338	+	0.283437i
$201$		0			0
$202$	5.44619	+	9.43308i	0.383193	+	0.663709i
$203$	−20.6320	−	5.58898i	−1.44808	−	0.392270i
$204$		0			0
$205$	−21.4366	+	1.25652i	−1.49720	+	0.0877589i
$206$	−0.292115	−	0.505958i	−0.0203526	−	0.0352518i
$207$		0			0
$208$	−2.03087	+	3.51756i	−0.140815	+	0.243899i
$209$	−6.50291	+	11.2634i	−0.449815	+	0.779103i
$210$		0			0
$211$	2.37689	+	4.11690i	0.163632	+	0.283419i	0.936169	−	0.351551i	$-0.114346\pi$
$211$	2.37689	+	4.11690i	0.163632	+	0.283419i	−0.772537	+	0.634970i	$0.781012\pi$
$212$	−11.4261			−0.784747
$213$		0			0
$214$	2.68574			0.183593
$215$	9.57376	−	6.30185i	0.652925	−	0.429782i
$216$		0			0
$217$	9.00336	+	2.43891i	0.611188	+	0.165564i
$218$	0.618180	−	1.07072i	0.0418684	−	0.0725182i
$219$		0			0
$220$	−6.70042	+	4.41050i	−0.451742	+	0.297356i
$221$	−18.5675	−	10.7199i	−1.24898	−	0.721101i
$222$		0			0
$223$	−8.37432	+	14.5048i	−0.560786	+	0.971310i	0.436642	+	0.899635i	$0.356168\pi$
$223$	−8.37432	+	14.5048i	−0.560786	+	0.971310i	−0.997428	+	0.0716748i	$0.977166\pi$
$224$	−0.691773	+	2.55371i	−0.0462210	+	0.170627i
$225$		0			0
$226$	5.41347	−	9.37640i	0.360099	−	0.623709i
$227$			6.34736i			0.421289i	0.977563	+	0.210645i	$0.0675563\pi$
$227$			6.34736i			0.421289i	−0.977563	+	0.210645i	$0.932444\pi$
$228$		0			0
$229$			4.37539i			0.289134i	0.989495	+	0.144567i	$0.0461789\pi$
$229$			4.37539i			0.289134i	−0.989495	+	0.144567i	$0.953821\pi$
$230$	10.7086	−	0.627687i	0.706101	−	0.0413884i
$231$		0			0
$232$	−6.99680	−	4.03961i	−0.459363	−	0.265213i
$233$	−12.2423	+	21.2043i	−0.802021	+	1.38914i	0.116263	+	0.993218i	$0.462908\pi$
$233$	−12.2423	+	21.2043i	−0.802021	+	1.38914i	−0.918284	+	0.395922i	$0.870425\pi$
$234$		0			0
$235$	−1.50488	−	25.6738i	−0.0981676	−	1.67477i
$236$	−3.51911	−	6.09528i	−0.229075	−	0.396769i
$237$		0			0
$238$	−13.4798	−	3.65152i	−0.873764	−	0.236693i
$239$	−2.10722	+	1.21660i	−0.136305	+	0.0786956i	−0.566602	−	0.823992i	$-0.691742\pi$
$239$	−2.10722	+	1.21660i	−0.136305	+	0.0786956i	0.430297	+	0.902687i	$0.358409\pi$
$240$		0			0
$241$		−	2.10402i		−	0.135532i	−0.997701	−	0.0677659i	$-0.978413\pi$
$241$		−	2.10402i		−	0.135532i	0.997701	−	0.0677659i	$-0.0215871\pi$
$242$	−0.934810	−	1.61914i	−0.0600918	−	0.104082i
$243$		0			0
$244$			11.2231i			0.718482i
$245$	−0.830235	−	15.6304i	−0.0530418	−	0.998592i
$246$		0			0
$247$		−	14.7254i		−	0.936953i
$248$	3.05326	+	1.76280i	0.193882	+	0.111938i
$249$		0			0
$250$	−7.19611	−	8.55664i	−0.455122	−	0.541169i
$251$	19.3343			1.22037			0.610184	−	0.792260i	$-0.291096\pi$
$251$	19.3343			1.22037			0.610184	+	0.792260i	$0.291096\pi$
$252$		0			0
$253$			17.2097i			1.08197i
$254$	−4.29497	+	2.47970i	−0.269490	+	0.155590i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	25.9602i		−	1.61935i	−0.586876	−	0.809677i	$-0.699643\pi$
$257$		−	25.9602i		−	1.61935i	0.586876	−	0.809677i	$-0.300357\pi$
$258$		0			0
$259$	−2.59447	−	0.702814i	−0.161213	−	0.0436707i
$260$	4.07312	−	8.11776i	0.252604	−	0.503442i
$261$		0			0
$262$	4.64103	+	8.03850i	0.286724	+	0.496620i
$263$	7.78218			0.479870			0.239935	−	0.970789i	$-0.422874\pi$
$263$	7.78218			0.479870			0.239935	+	0.970789i	$0.422874\pi$
$264$		0			0
$265$	25.5057	−	1.49503i	1.56681	−	0.0918390i
$266$	−2.45716	−	9.27181i	−0.150658	−	0.568491i
$267$		0			0
$268$	−6.05819	+	3.49770i	−0.370063	+	0.213656i
$269$	−9.76085	−	16.9063i	−0.595129	−	1.03079i	−0.993529	−	0.113582i	$-0.963767\pi$
$269$	−9.76085	−	16.9063i	−0.595129	−	1.03079i	0.398399	−	0.917212i	$-0.369566\pi$
$270$		0			0
$271$	−0.125260	−	0.0723187i	−0.00760898	−	0.00439305i	0.496191	−	0.868214i	$-0.334732\pi$
$271$	−0.125260	−	0.0723187i	−0.00760898	−	0.00439305i	−0.503800	+	0.863821i	$0.668065\pi$
$272$	−4.57132	−	2.63925i	−0.277177	−	0.160028i
$273$		0			0
$274$	0.00306228	+	0.00530403i	0.000184999	+	0.000320428i
$275$	14.3798	−	10.7220i	0.867137	−	0.646560i
$276$		0			0
$277$		−	25.6634i		−	1.54196i	−0.636858	−	0.770981i	$-0.719766\pi$
$277$		−	25.6634i		−	1.54196i	0.636858	−	0.770981i	$-0.280234\pi$
$278$	7.32549	+	4.22938i	0.439354	+	0.253661i
$279$		0			0
$280$	1.21006	−	5.79101i	0.0723151	−	0.346079i
$281$	16.2907	+	9.40542i	0.971819	+	0.561080i	0.899790	−	0.436322i	$-0.143719\pi$
$281$	16.2907	+	9.40542i	0.971819	+	0.561080i	0.0720288	+	0.997403i	$0.477053\pi$
$282$		0			0
$283$	15.1983	−	26.3242i	0.903444	−	1.56481i	0.0804519	−	0.996758i	$-0.474364\pi$
$283$	15.1983	−	26.3242i	0.903444	−	1.56481i	0.822992	−	0.568053i	$-0.192303\pi$
$284$	−0.717659	−	0.414341i	−0.0425852	−	0.0245866i
$285$		0			0
$286$	12.6190	+	7.28558i	0.746177	+	0.430806i
$287$	17.9166	+	18.0151i	1.05758	+	1.06340i
$288$		0			0
$289$	5.43128	−	9.40726i	0.319487	−	0.553368i
$290$	16.1471	+	8.10187i	0.948189	+	0.475758i
$291$		0			0
$292$	7.02525			0.411122
$293$	−24.1090	+	13.9193i	−1.40846	+	0.813176i	−0.995240	−	0.0974541i	$-0.968930\pi$
$293$	−24.1090	+	13.9193i	−1.40846	+	0.813176i	−0.413222	+	0.910630i	$0.635597\pi$
$294$		0			0
$295$	8.65302	+	13.1457i	0.503799	+	0.765370i
$296$	−0.879847	−	0.507980i	−0.0511401	−	0.0295257i
$297$		0			0
$298$	−15.0057	+	8.66353i	−0.869255	+	0.501865i
$299$	−9.74254	−	16.8746i	−0.563426	−	0.975882i
$300$		0			0
$301$	−13.0899	−	3.54590i	−0.754488	−	0.204382i
$302$	−2.82204	−	4.88791i	−0.162390	−	0.281268i
$303$		0			0
$304$		−	3.62539i		−	0.207930i
$305$	−1.46846	−	25.0525i	−0.0840840	−	1.43450i
$306$		0			0
$307$	−29.1963			−1.66632			−0.833162	−	0.553030i	$-0.813472\pi$
$307$	−29.1963			−1.66632			−0.833162	+	0.553030i	$0.813472\pi$
$308$	9.16125	+	2.48168i	0.522011	+	0.141407i
$309$		0			0
$310$	−7.04624	−	3.53548i	−0.400200	−	0.200802i
$311$	0.769918	−	1.33354i	0.0436580	−	0.0756179i	−0.843371	−	0.537332i	$-0.819432\pi$
$311$	0.769918	−	1.33354i	0.0436580	−	0.0756179i	0.887029	+	0.461714i	$0.152765\pi$
$312$		0			0
$313$	4.50101	+	7.79598i	0.254412	+	0.440655i	0.964736	−	0.263221i	$-0.0847847\pi$
$313$	4.50101	+	7.79598i	0.254412	+	0.440655i	−0.710324	+	0.703875i	$0.751451\pi$
$314$	6.48693			0.366078
$315$		0			0
$316$	0.0299868			0.00168689
$317$	8.62883	+	14.9456i	0.484644	+	0.839427i	0.999844	−	0.0176421i	$-0.00561596\pi$
$317$	8.62883	+	14.9456i	0.484644	+	0.839427i	−0.515201	+	0.857070i	$0.672283\pi$
$318$		0			0
$319$	−14.4918	+	25.1005i	−0.811384	+	1.40536i
$320$	1.00280	−	1.99860i	0.0560585	−	0.111725i
$321$		0			0
$322$	−8.95016	−	8.99936i	−0.498773	−	0.501515i
$323$	19.1366			1.06479
$324$		0			0
$325$	−8.03002	+	18.6537i	−0.445425	+	1.03472i
$326$		−	5.24041i		−	0.290240i
$327$		0			0
$328$	4.80160	+	8.31661i	0.265124	+	0.459208i
$329$	−21.5760	+	21.4580i	−1.18952	+	1.18302i
$330$		0			0
$331$	−14.5091	−	25.1305i	−0.797492	−	1.38130i	−0.921244	−	0.388984i	$-0.872826\pi$
$331$	−14.5091	−	25.1305i	−0.797492	−	1.38130i	0.123752	−	0.992313i	$-0.460507\pi$
$332$	6.89727	−	3.98214i	0.378537	−	0.218548i
$333$		0			0
$334$	−18.8867	−	10.9043i	−1.03344	−	0.596655i
$335$	13.0657	−	8.60037i	0.713854	−	0.469888i
$336$		0			0
$337$	0.776124	−	0.448095i	0.0422782	−	0.0244093i	−0.478712	−	0.877972i	$-0.658896\pi$
$337$	0.776124	−	0.448095i	0.0422782	−	0.0244093i	0.520990	+	0.853563i	$0.325563\pi$
$338$	−3.49768			−0.190249
$339$		0			0
$340$	10.5496	+	5.29330i	0.572132	+	0.287070i
$341$	6.32391	−	10.9533i	0.342459	−	0.593156i
$342$		0			0
$343$	−13.2030	+	12.9877i	−0.712897	+	0.701269i
$344$	−4.43909	−	2.56291i	−0.239340	−	0.138183i
$345$		0			0
$346$	−18.7792	−	10.8422i	−1.00957	−	0.582878i
$347$	17.1746	−	29.7473i	0.921982	−	1.59692i	0.125637	−	0.992076i	$-0.459902\pi$
$347$	17.1746	−	29.7473i	0.921982	−	1.59692i	0.796345	−	0.604843i	$-0.206764\pi$
$348$		0			0
$349$	1.95233	+	1.12718i	0.104506	+	0.0603366i	0.551342	−	0.834279i	$-0.314116\pi$
$349$	1.95233	+	1.12718i	0.104506	+	0.0603366i	−0.446836	+	0.894616i	$0.647449\pi$
$350$	−1.94343	+	13.0852i	−0.103881	+	0.699435i
$351$		0			0
$352$	3.10680	+	1.79371i	0.165593	+	0.0956052i
$353$			5.87884i			0.312899i	0.987686	+	0.156450i	$0.0500049\pi$
$353$			5.87884i			0.312899i	−0.987686	+	0.156450i	$0.949995\pi$
$354$		0			0
$355$	1.65620	+	0.831005i	0.0879019	+	0.0441052i
$356$	−0.625013	−	1.08255i	−0.0331256	−	0.0573752i
$357$		0			0
$358$	15.1142	+	8.72620i	0.798811	+	0.461194i
$359$	−5.91330	−	3.41404i	−0.312092	−	0.180186i	0.335770	−	0.941944i	$-0.391003\pi$
$359$	−5.91330	−	3.41404i	−0.312092	−	0.180186i	−0.647862	+	0.761758i	$0.724337\pi$
$360$		0			0
$361$	−2.92828	−	5.07193i	−0.154120	−	0.266944i
$362$	−20.8271	+	12.0245i	−1.09465	+	0.631995i
$363$		0			0
$364$	−10.3878	+	2.75290i	−0.544466	+	0.144291i
$365$	−15.6820	+	0.919209i	−0.820835	+	0.0481136i
$366$		0			0
$367$	−0.568928			−0.0296978			−0.0148489	−	0.999890i	$-0.504727\pi$
$367$	−0.568928			−0.0296978			−0.0148489	+	0.999890i	$0.504727\pi$
$368$	−2.39862	−	4.15452i	−0.125036	−	0.216570i
$369$		0			0
$370$	2.03049	+	1.01881i	0.105560	+	0.0529654i
$371$	−21.3176	−	21.4348i	−1.10675	−	1.11284i
$372$		0			0
$373$		−	7.60195i		−	0.393614i	−0.980442	−	0.196807i	$-0.936943\pi$
$373$		−	7.60195i		−	0.393614i	0.980442	−	0.196807i	$-0.0630573\pi$
$374$	−9.46811	+	16.3993i	−0.489584	+	0.847985i
$375$		0			0
$376$	−9.96048	+	5.75069i	−0.513673	+	0.296569i
$377$		−	32.8156i		−	1.69009i
$378$		0			0
$379$	−37.9897			−1.95140			−0.975700	−	0.219109i	$-0.929685\pi$
$379$	−37.9897			−1.95140			−0.975700	+	0.219109i	$0.929685\pi$
$380$	0.474359	+	8.09273i	0.0243341	+	0.415148i
$381$		0			0
$382$	2.79411	+	1.61318i	0.142959	+	0.0825375i
$383$			12.0422i			0.615329i	0.951495	+	0.307665i	$0.0995475\pi$
$383$			12.0422i			0.615329i	−0.951495	+	0.307665i	$0.900452\pi$
$384$		0			0
$385$	−20.7748	−	4.34101i	−1.05878	−	0.221239i
$386$		−	24.2271i		−	1.23312i
$387$		0			0
$388$	4.69619	+	8.13404i	0.238413	+	0.412943i
$389$		−	11.4685i		−	0.581474i	−0.956803	−	0.290737i	$-0.906100\pi$
$389$		−	11.4685i		−	0.581474i	0.956803	−	0.290737i	$-0.0939005\pi$
$390$		0			0
$391$	21.9297	−	12.6611i	1.10903	−	0.640299i
$392$	−6.08127	+	3.46672i	−0.307151	+	0.175096i
$393$		0			0
$394$	3.44828	+	5.97260i	0.173722	+	0.300895i
$395$	−0.0669375	+	0.00392358i	−0.00336799	+	0.000197416i
$396$		0			0
$397$	1.89421	−	3.28087i	0.0950678	−	0.164662i	−0.814569	−	0.580067i	$-0.803027\pi$
$397$	1.89421	−	3.28087i	0.0950678	−	0.164662i	0.909637	+	0.415404i	$0.136360\pi$
$398$	−14.5256	−	8.38638i	−0.728104	−	0.420371i
$399$		0			0
$400$	−1.97699	+	4.59255i	−0.0988497	+	0.229627i
$401$			11.5838i			0.578470i	0.957258	+	0.289235i	$0.0934009\pi$
$401$			11.5838i			0.578470i	−0.957258	+	0.289235i	$0.906599\pi$
$402$		0			0
$403$			14.3200i			0.713332i
$404$	−5.44619	+	9.43308i	−0.270958	+	0.469313i
$405$		0			0
$406$	−5.47580	−	20.6623i	−0.271759	−	1.02545i
$407$	−1.82234	+	3.15639i	−0.0903301	+	0.156456i
$408$		0			0
$409$	26.2151	+	15.1353i	1.29625	+	0.748393i	0.979755	−	0.200200i	$-0.0641591\pi$
$409$	26.2151	+	15.1353i	1.29625	+	0.748393i	0.316500	+	0.948593i	$0.397492\pi$
$410$	−11.8065	−	17.9364i	−0.583080	−	0.885815i
$411$		0			0
$412$	0.292115	−	0.505958i	0.0143915	−	0.0249268i
$413$	4.86886	−	17.9736i	0.239581	−	0.884424i
$414$		0			0
$415$	−14.8753	+	9.79154i	−0.730200	+	0.480648i
$416$	−4.06173			−0.199143
$417$		0			0
$418$	−13.0058			−0.636135
$419$	−10.7319	−	18.5882i	−0.524287	−	0.908091i	−0.999600	−	0.0282749i	$-0.990999\pi$
$419$	−10.7319	−	18.5882i	−0.524287	−	0.908091i	0.475313	−	0.879817i	$-0.342335\pi$
$420$		0			0
$421$	−12.8685	+	22.2889i	−0.627173	+	1.08630i	0.360943	+	0.932588i	$0.382455\pi$
$421$	−12.8685	+	22.2889i	−0.627173	+	1.08630i	−0.988116	+	0.153708i	$0.950878\pi$
$422$	−2.37689	+	4.11690i	−0.115705	+	0.200408i
$423$		0			0
$424$	−5.71305	−	9.89529i	−0.277450	−	0.480558i
$425$	−24.2418	−	10.4356i	−1.17590	−	0.506199i
$426$		0			0
$427$	−21.0539	+	20.9388i	−1.01887	+	1.01330i
$428$	1.34287	+	2.32592i	0.0649101	+	0.112428i
$429$		0			0
$430$	10.2444	+	5.14020i	0.494031	+	0.247882i
$431$	−1.05463	+	0.608890i	−0.0507997	+	0.0293292i	−0.525185	−	0.850988i	$-0.676004\pi$
$431$	−1.05463	+	0.608890i	−0.0507997	+	0.0293292i	0.474385	+	0.880317i	$0.342670\pi$
$432$		0			0
$433$	−6.29897			−0.302709			−0.151355	−	0.988480i	$-0.548364\pi$
$433$	−6.29897			−0.302709			−0.151355	+	0.988480i	$0.548364\pi$
$434$	2.38952	+	9.01660i	0.114701	+	0.432811i
$435$		0			0
$436$	1.23636			0.0592109
$437$	15.0618	+	8.69591i	0.720502	+	0.415982i
$438$		0			0
$439$	31.5109	−	18.1928i	1.50393	−	0.868296i	0.503944	−	0.863736i	$-0.331882\pi$
$439$	31.5109	−	18.1928i	1.50393	−	0.868296i	0.999990	−	0.00456010i	$-0.00145153\pi$
$440$	−7.16981	−	3.59749i	−0.341807	−	0.171503i
$441$		0			0
$442$		−	21.4399i		−	1.01979i
$443$	−5.77669	−	10.0055i	−0.274459	−	0.475376i	0.695540	−	0.718488i	$-0.255165\pi$
$443$	−5.77669	−	10.0055i	−0.274459	−	0.475376i	−0.969998	+	0.243111i	$0.921832\pi$
$444$		0			0
$445$	1.53682	+	2.33474i	0.0728523	+	0.110677i
$446$	−16.7486			−0.793072
$447$		0			0
$448$	−2.55747	+	0.677764i	−0.120829	+	0.0320213i
$449$		−	8.35607i		−	0.394347i	−0.980369	−	0.197174i	$-0.936824\pi$
$449$		−	8.35607i		−	0.394347i	0.980369	−	0.197174i	$-0.0631763\pi$
$450$		0			0
$451$	29.8352	−	17.2254i	1.40489	−	0.811111i
$452$	10.8269			0.509256
$453$		0			0
$454$	−5.49698	+	3.17368i	−0.257986	+	0.148948i
$455$	22.8277	−	7.50428i	1.07018	−	0.351806i
$456$		0			0
$457$	−3.26626	+	1.88578i	−0.152789	+	0.0882129i	−0.574445	−	0.818543i	$-0.694782\pi$
$457$	−3.26626	+	1.88578i	−0.152789	+	0.0882129i	0.421656	+	0.906756i	$0.361449\pi$
$458$	−3.78920	+	2.18769i	−0.177058	+	0.102224i
$459$		0			0
$460$	5.89787	+	8.96004i	0.274990	+	0.417764i
$461$	−1.39131	+	2.40982i	−0.0647998	+	0.112237i	−0.896605	−	0.442831i	$-0.853974\pi$
$461$	−1.39131	+	2.40982i	−0.0647998	+	0.112237i	0.831805	+	0.555067i	$0.187308\pi$
$462$		0			0
$463$	−9.52910	+	5.50163i	−0.442855	+	0.255682i	−0.704808	−	0.709398i	$-0.748967\pi$
$463$	−9.52910	+	5.50163i	−0.442855	+	0.255682i	0.261953	+	0.965081i	$0.415633\pi$
$464$		−	8.07921i		−	0.375068i
$465$		0			0
$466$	−24.4846			−1.13423
$467$	−16.4814	−	9.51552i	−0.762667	−	0.440326i	0.0675856	−	0.997713i	$-0.478470\pi$
$467$	−16.4814	−	9.51552i	−0.762667	−	0.440326i	−0.830252	+	0.557388i	$0.811804\pi$
$468$		0			0
$469$	−17.8642	−	4.83923i	−0.824894	−	0.223455i
$470$	21.4817	−	14.1402i	0.990878	−	0.652237i
$471$		0			0
$472$	3.51911	−	6.09528i	0.161980	−	0.280558i
$473$	−9.19425	+	15.9249i	−0.422752	+	0.732228i
$474$		0			0
$475$	−2.11776	−	18.0028i	−0.0971696	−	0.826026i
$476$	−3.57758	−	13.4996i	−0.163978	−	0.618753i
$477$		0			0
$478$	−2.10722	−	1.21660i	−0.0963820	−	0.0556462i
$479$	−0.292336			−0.0133572			−0.00667858	−	0.999978i	$-0.502126\pi$
$479$	−0.292336			−0.0133572			−0.00667858	+	0.999978i	$0.502126\pi$
$480$		0			0
$481$		−	4.12656i		−	0.188155i
$482$	1.82213	−	1.05201i	0.0829960	−	0.0479177i
$483$		0			0
$484$	0.934810	−	1.61914i	0.0424913	−	0.0735972i
$485$	−11.5473	−	17.5426i	−0.524336	−	0.796570i
$486$		0			0
$487$	17.4211	−	10.0581i	0.789425	−	0.455775i	−0.0503353	−	0.998732i	$-0.516029\pi$
$487$	17.4211	−	10.0581i	0.789425	−	0.455775i	0.839760	+	0.542958i	$0.182696\pi$
$488$	−9.71945	+	5.61153i	−0.439979	+	0.254022i
$489$		0			0
$490$	13.1212	−	8.53423i	0.592757	−	0.385537i
$491$	0.00977625	−	0.00564432i	0.000441196	−	0.000254725i	−0.499779	−	0.866153i	$-0.666586\pi$
$491$	0.00977625	−	0.00564432i	0.000441196	−	0.000254725i	0.500221	+	0.865898i	$0.333252\pi$
$492$		0			0
$493$	42.6461			1.92069
$494$	12.7525	−	7.36268i	0.573764	−	0.331263i
$495$		0			0
$496$			3.52560i			0.158304i
$497$	−0.561650	−	2.11933i	−0.0251935	−	0.0950647i
$498$		0			0
$499$	10.8608			0.486194			0.243097	−	0.970002i	$-0.421837\pi$
$499$	10.8608			0.486194			0.243097	+	0.970002i	$0.421837\pi$
$500$	3.81221	−	10.5103i	0.170487	−	0.470036i
$501$		0			0
$502$	9.66713	+	16.7440i	0.431465	+	0.747320i
$503$			32.7910i			1.46208i	0.682335	+	0.731040i	$0.260965\pi$
$503$			32.7910i			1.46208i	−0.682335	+	0.731040i	$0.739035\pi$
$504$		0			0
$505$	10.9229	−	21.7695i	0.486064	−	0.968728i
$506$	−14.9040	+	8.60485i	−0.662566	+	0.382532i
$507$		0			0
$508$	−4.29497	−	2.47970i	−0.190558	−	0.110019i
$509$	11.8056			0.523273			0.261637	−	0.965166i	$-0.415738\pi$
$509$	11.8056			0.523273			0.261637	+	0.965166i	$0.415738\pi$
$510$		0			0
$511$	13.1070	+	13.1790i	0.579818	+	0.583005i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	22.4822	−	12.9801i	0.991647	−	0.572528i
$515$	−0.585869	+	1.16764i	−0.0258165	+	0.0514524i
$516$		0			0
$517$	20.6302	+	35.7325i	0.907313	+	1.57151i
$518$	−0.688581	−	2.59828i	−0.0302545	−	0.114162i
$519$		0			0
$520$	9.06675	−	0.531452i	0.397603	−	0.0233057i
$521$	8.58074	+	14.8623i	0.375929	+	0.651128i	0.990466	−	0.137760i	$-0.0439904\pi$
$521$	8.58074	+	14.8623i	0.375929	+	0.651128i	−0.614537	+	0.788888i	$0.710657\pi$
$522$		0			0
$523$	−19.0538	+	33.0022i	−0.833166	+	1.44309i	0.0623491	+	0.998054i	$0.480141\pi$
$523$	−19.0538	+	33.0022i	−0.833166	+	1.44309i	−0.895515	+	0.445031i	$0.853193\pi$
$524$	−4.64103	+	8.03850i	−0.202744	+	0.351163i
$525$		0			0
$526$	3.89109	+	6.73957i	0.169660	+	0.293859i
$527$	−18.6099			−0.810659
$528$		0			0
$529$	0.0134258			0.000583730
$530$	14.0476	+	21.3411i	0.610189	+	0.926998i
$531$		0			0
$532$	6.80105	−	6.76387i	0.294863	−	0.293251i
$533$	−19.5028	+	33.7799i	−0.844760	+	1.46317i
$534$		0			0
$535$	−3.30194	−	5.01630i	−0.142755	−	0.216873i
$536$	−6.05819	−	3.49770i	−0.261674	−	0.151078i
$537$		0			0
$538$	9.76085	−	16.9063i	0.420820	−	0.728882i
$539$	12.4366	+	21.8161i	0.535682	+	0.939686i
$540$		0			0
$541$	11.5592	−	20.0210i	0.496967	−	0.860772i	−0.503027	−	0.864271i	$-0.667780\pi$
$541$	11.5592	−	20.0210i	0.496967	−	0.860772i	0.999994	+	0.00349884i	$0.00111372\pi$
$542$		−	0.144637i		−	0.00621271i
$543$		0			0
$544$		−	5.27850i		−	0.226314i
$545$	−2.75985	+	0.161770i	−0.118219	+	0.00692945i
$546$		0			0
$547$	0.301039	+	0.173805i	0.0128715	+	0.00743136i	0.506422	−	0.862286i	$-0.330968\pi$
$547$	0.301039	+	0.173805i	0.0128715	+	0.00743136i	−0.493550	+	0.869717i	$0.664301\pi$
$548$	−0.00306228	+	0.00530403i	−0.000130814	+	0.000226577i
$549$		0			0
$550$	16.4754	+	7.09232i	0.702514	+	0.302417i
$551$	14.6451	+	25.3661i	0.623904	+	1.08063i
$552$		0			0
$553$	0.0559461	+	0.0562536i	0.00237907	+	0.00239215i
$554$	22.2251	−	12.8317i	0.944255	−	0.545166i
$555$		0			0
$556$			8.45875i			0.358731i
$557$	−22.4182	−	38.8295i	−0.949891	−	1.64526i	−0.745649	−	0.666339i	$-0.767860\pi$
$557$	−22.4182	−	38.8295i	−0.949891	−	1.64526i	−0.204242	−	0.978920i	$-0.565473\pi$
$558$		0			0
$559$		−	20.8197i		−	0.880580i
$560$	5.62019	−	1.84756i	0.237496	−	0.0780735i
$561$		0			0
$562$			18.8108i			0.793487i
$563$	21.3503	+	12.3266i	0.899808	+	0.519504i	0.877138	−	0.480239i	$-0.159450\pi$
$563$	21.3503	+	12.3266i	0.899808	+	0.519504i	0.0226699	+	0.999743i	$0.492783\pi$
$564$		0			0
$565$	−24.1683	+	1.41663i	−1.01677	+	0.0595983i
$566$	30.3966			1.27766
$567$		0			0
$568$		−	0.828681i		−	0.0347707i
$569$	32.5085	−	18.7688i	1.36283	−	0.786829i	0.372829	−	0.927900i	$-0.378388\pi$
$569$	32.5085	−	18.7688i	1.36283	−	0.786829i	0.989999	+	0.141071i	$0.0450546\pi$
$570$		0			0
$571$	4.68412	−	8.11314i	0.196024	−	0.339524i	−0.751211	−	0.660062i	$-0.770530\pi$
$571$	4.68412	−	8.11314i	0.196024	−	0.339524i	0.947236	+	0.320537i	$0.103864\pi$
$572$			14.5712i			0.609251i
$573$		0			0
$574$	−6.64323	+	24.5238i	−0.277283	+	1.02360i
$575$	−14.3378	−	19.2292i	−0.597928	−	0.801914i
$576$		0			0
$577$	−3.63671	−	6.29897i	−0.151398	−	0.262230i	0.780343	−	0.625351i	$-0.215044\pi$
$577$	−3.63671	−	6.29897i	−0.151398	−	0.262230i	−0.931742	+	0.363122i	$0.881711\pi$
$578$	10.8626			0.451823
$579$		0			0
$580$	1.05711	+	18.0347i	0.0438942	+	0.748851i
$581$	20.3385	+	5.50947i	0.843783	+	0.228571i
$582$		0			0
$583$	−35.4986	+	20.4951i	−1.47020	+	0.848821i
$584$	3.51263	+	6.08405i	0.145353	+	0.251760i
$585$		0			0
$586$	−24.1090	−	13.9193i	−0.995933	−	0.575002i
$587$	2.08437	+	1.20341i	0.0860313	+	0.0496702i	0.542398	−	0.840121i	$-0.317516\pi$
$587$	2.08437	+	1.20341i	0.0860313	+	0.0496702i	−0.456367	+	0.889792i	$0.650850\pi$
$588$		0			0
$589$	−6.39083	−	11.0692i	−0.263330	−	0.456100i
$590$	−7.05797	+	14.0666i	−0.290572	+	0.579112i
$591$		0			0
$592$		−	1.01596i		−	0.0417557i
$593$	33.2409	+	19.1916i	1.36504	+	0.788106i	0.990290	−	0.139019i	$-0.0443950\pi$
$593$	33.2409	+	19.1916i	1.36504	+	0.788106i	0.374751	+	0.927126i	$0.377728\pi$
$594$		0			0
$595$	9.75233	+	29.6662i	0.399807	+	1.21619i
$596$	−15.0057	−	8.66353i	−0.614656	−	0.354872i
$597$		0			0
$598$	9.74254	−	16.8746i	0.398402	−	0.690053i
$599$	−15.8468	−	9.14917i	−0.647484	−	0.373825i	0.140008	−	0.990150i	$-0.455287\pi$
$599$	−15.8468	−	9.14917i	−0.647484	−	0.373825i	−0.787491	+	0.616326i	$0.788621\pi$
$600$		0			0
$601$	−20.5159	−	11.8449i	−0.836862	−	0.483163i	0.0193342	−	0.999813i	$-0.493845\pi$
$601$	−20.5159	−	11.8449i	−0.836862	−	0.483163i	−0.856196	+	0.516650i	$0.827179\pi$
$602$	−3.47409	−	13.1091i	−0.141594	−	0.534288i
$603$		0			0
$604$	2.82204	−	4.88791i	0.114827	−	0.198886i
$605$	−1.87486	+	3.73661i	−0.0762240	+	0.151915i
$606$		0			0
$607$	2.40225			0.0975043			0.0487522	−	0.998811i	$-0.484476\pi$
$607$	2.40225			0.0975043			0.0487522	+	0.998811i	$0.484476\pi$
$608$	3.13968	−	1.81269i	0.127331	−	0.0735145i
$609$		0			0
$610$	20.9619	−	13.7980i	0.848722	−	0.558664i
$611$	−40.4568	−	23.3578i	−1.63671	−	0.944954i
$612$		0			0
$613$	32.4221	−	18.7189i	1.30951	−	0.756049i	0.327500	−	0.944851i	$-0.393794\pi$
$613$	32.4221	−	18.7189i	1.30951	−	0.756049i	0.982015	+	0.188803i	$0.0604606\pi$
$614$	−14.5982	−	25.2848i	−0.589134	−	1.02041i
$615$		0			0
$616$	2.43143	+	9.17472i	0.0979650	+	0.369660i
$617$	19.7702	+	34.2430i	0.795918	+	1.37857i	0.922255	+	0.386582i	$0.126345\pi$
$617$	19.7702	+	34.2430i	0.795918	+	1.37857i	−0.126337	+	0.991987i	$0.540322\pi$
$618$		0			0
$619$		−	5.49230i		−	0.220754i	−0.993890	−	0.110377i	$-0.964794\pi$
$619$		−	5.49230i		−	0.220754i	0.993890	−	0.110377i	$-0.0352059\pi$
$620$	−0.461302	−	7.86997i	−0.0185263	−	0.316065i
$621$		0			0
$622$	1.53984			0.0617418
$623$	0.864734	−	3.19221i	0.0346448	−	0.127893i
$624$		0			0
$625$	−7.13455	+	23.9603i	−0.285382	+	0.958414i
$626$	−4.50101	+	7.79598i	−0.179896	+	0.311590i
$627$		0			0
$628$	3.24346	+	5.61784i	0.129428	+	0.224176i
$629$	5.36275			0.213827
$630$		0			0
$631$	−9.72111			−0.386991			−0.193496	−	0.981101i	$-0.561983\pi$
$631$	−9.72111			−0.386991			−0.193496	+	0.981101i	$0.561983\pi$
$632$	0.0149934	+	0.0259693i	0.000596405	+	0.00103300i
$633$		0			0
$634$	−8.62883	+	14.9456i	−0.342695	+	0.593565i
$635$	9.91184	+	4.97331i	0.393339	+	0.197360i
$636$		0			0
$637$	−24.5447	−	14.3508i	−0.972495	−	0.568601i
$638$	−28.9836			−1.14747
$639$		0			0
$640$	2.23224	−	0.130844i	0.0882369	−	0.00517205i
$641$			32.2864i			1.27524i	0.770352	+	0.637619i	$0.220080\pi$
$641$			32.2864i			1.27524i	−0.770352	+	0.637619i	$0.779920\pi$
$642$		0			0
$643$	14.1941	+	24.5848i	0.559759	+	0.969532i	0.997516	+	0.0704382i	$0.0224398\pi$
$643$	14.1941	+	24.5848i	0.559759	+	0.969532i	−0.437757	+	0.899093i	$0.644227\pi$
$644$	3.31859	−	12.2508i	0.130771	−	0.482747i
$645$		0			0
$646$	9.56831	+	16.5728i	0.376460	+	0.652048i
$647$	3.35941	−	1.93956i	0.132072	−	0.0762519i	−0.432508	−	0.901630i	$-0.642371\pi$
$647$	3.35941	−	1.93956i	0.132072	−	0.0762519i	0.564580	+	0.825378i	$0.309038\pi$
$648$		0			0
$649$	−21.8664	−	12.6246i	−0.858330	−	0.495557i
$650$	−20.1696	+	2.37265i	−0.791117	+	0.0930631i
$651$		0			0
$652$	4.53833	−	2.62021i	0.177735	−	0.102615i
$653$	−21.1893			−0.829203			−0.414602	−	0.910003i	$-0.636079\pi$
$653$	−21.1893			−0.829203			−0.414602	+	0.910003i	$0.636079\pi$
$654$		0			0
$655$	9.30809	−	18.5511i	0.363697	−	0.724850i
$656$	−4.80160	+	8.31661i	−0.187471	+	0.324709i
$657$		0			0
$658$	−29.3712	−	7.95634i	−1.14501	−	0.310170i
$659$	−3.78622	−	2.18598i	−0.147490	−	0.0851535i	0.424439	−	0.905457i	$-0.360471\pi$
$659$	−3.78622	−	2.18598i	−0.147490	−	0.0851535i	−0.571929	+	0.820303i	$0.693805\pi$
$660$		0			0
$661$	−18.8326	−	10.8730i	−0.732502	−	0.422910i	0.0868348	−	0.996223i	$-0.472325\pi$
$661$	−18.8326	−	10.8730i	−0.732502	−	0.422910i	−0.819337	+	0.573313i	$0.805658\pi$
$662$	14.5091	−	25.1305i	0.563912	−	0.976725i
$663$		0			0
$664$	6.89727	+	3.98214i	0.267666	+	0.154537i
$665$	−14.2965	+	15.9884i	−0.554396	+	0.620004i
$666$		0			0
$667$	33.5653	+	19.3789i	1.29965	+	0.750355i
$668$		−	21.8085i		−	0.843797i
$669$		0			0
$670$	13.9810	+	7.01502i	0.540132	+	0.271014i
$671$	20.1309	+	34.8678i	0.777146	+	1.34606i
$672$		0			0
$673$	−33.8278	−	19.5305i	−1.30397	−	0.752845i	−0.322884	−	0.946439i	$-0.604652\pi$
$673$	−33.8278	−	19.5305i	−1.30397	−	0.752845i	−0.981082	+	0.193594i	$0.937986\pi$
$674$	0.776124	+	0.448095i	0.0298952	+	0.0172600i
$675$		0			0
$676$	−1.74884	−	3.02908i	−0.0672632	−	0.116503i
$677$	−9.30687	+	5.37333i	−0.357692	+	0.206514i	−0.668068	−	0.744100i	$-0.732878\pi$
$677$	−9.30687	+	5.37333i	−0.357692	+	0.206514i	0.310376	+	0.950614i	$0.399545\pi$
$678$		0			0
$679$	−6.49739	+	23.9854i	−0.249347	+	0.920477i
$680$	0.690658	+	11.7829i	0.0264855	+	0.451852i
$681$		0			0
$682$	12.6478			0.484310
$683$	6.84384	+	11.8539i	0.261872	+	0.453576i	0.966739	−	0.255763i	$-0.0823267\pi$
$683$	6.84384	+	11.8539i	0.261872	+	0.453576i	−0.704867	+	0.709339i	$0.748993\pi$
$684$		0			0
$685$	0.00614174	−	0.0122405i	0.000234664	−	0.000467686i
$686$	−17.8492	−	4.94033i	−0.681485	−	0.188623i
$687$		0			0
$688$		−	5.12582i		−	0.195420i
$689$	23.2049	−	40.1920i	0.884035	−	1.53119i
$690$		0			0
$691$	24.3356	−	14.0502i	0.925769	−	0.534493i	0.0402982	−	0.999188i	$-0.487169\pi$
$691$	24.3356	−	14.0502i	0.925769	−	0.534493i	0.885471	+	0.464695i	$0.153836\pi$
$692$		−	21.6843i		−	0.824314i
$693$		0			0
$694$	34.3492			1.30388
$695$	−1.10677	−	18.8819i	−0.0419823	−	0.716233i
$696$		0			0
$697$	−43.8992	−	25.3452i	−1.66280	−	0.960019i
$698$			2.25436i			0.0853288i
$699$		0			0
$700$	−12.3039	+	4.85955i	−0.465042	+	0.183674i
$701$			47.4955i			1.79388i	0.442151	+	0.896941i	$0.354216\pi$
$701$			47.4955i			1.79388i	−0.442151	+	0.896941i	$0.645784\pi$
$702$		0			0
$703$	1.84163	+	3.18979i	0.0694582	+	0.120305i
$704$			3.58743i			0.135206i
$705$		0			0
$706$	−5.09123	+	2.93942i	−0.191611	+	0.110627i
$707$	−27.8569	+	7.38246i	−1.04767	+	0.277646i
$708$		0			0
$709$	16.2728	+	28.1853i	0.611137	+	1.05852i	0.991049	+	0.133498i	$0.0426209\pi$
$709$	16.2728	+	28.1853i	0.611137	+	1.05852i	−0.379912	+	0.925023i	$0.624046\pi$
$710$	0.108428	+	1.84981i	0.00406922	+	0.0694222i
$711$		0			0
$712$	0.625013	−	1.08255i	0.0234233	−	0.0405704i
$713$	−14.6472	−	8.45655i	−0.548541	−	0.316700i
$714$		0			0
$715$	−1.90654	−	32.5263i	−0.0713007	−	1.21641i
$716$			17.4524i			0.652227i
$717$		0			0
$718$		−	6.82808i		−	0.254822i
$719$	1.35013	−	2.33850i	0.0503515	−	0.0872114i	−0.839751	−	0.542971i	$-0.817299\pi$
$719$	1.35013	−	2.33850i	0.0503515	−	0.0872114i	0.890103	+	0.455760i	$0.150633\pi$
$720$		0			0
$721$	1.49415	−	0.395970i	0.0556450	−	0.0147467i
$722$	2.92828	−	5.07193i	0.108979	−	0.188758i
$723$		0			0
$724$	−20.8271	−	12.0245i	−0.774033	−	0.446888i
$725$	−4.71945	−	40.1194i	−0.175276	−	1.49000i
$726$		0			0
$727$	−13.0226	+	22.5558i	−0.482982	+	0.836549i	−0.999809	−	0.0195409i	$-0.993780\pi$
$727$	−13.0226	+	22.5558i	−0.482982	+	0.836549i	0.516827	+	0.856090i	$0.327113\pi$
$728$	−7.57795	−	7.61961i	−0.280858	−	0.282401i
$729$		0			0
$730$	−8.63707	−	13.1214i	−0.319672	−	0.485646i
$731$	27.0566			1.00073
$732$		0			0
$733$	−19.4544			−0.718564			−0.359282	−	0.933229i	$-0.616978\pi$
$733$	−19.4544			−0.718564			−0.359282	+	0.933229i	$0.616978\pi$
$734$	−0.284464	−	0.492706i	−0.0104998	−	0.0181861i
$735$		0			0
$736$	2.39862	−	4.15452i	0.0884141	−	0.153138i
$737$	−12.5477	+	21.7333i	−0.462202	+	0.800557i
$738$		0			0
$739$	5.50909	+	9.54203i	0.202655	+	0.351009i	0.949383	−	0.314120i	$-0.101710\pi$
$739$	5.50909	+	9.54203i	0.202655	+	0.351009i	−0.746728	+	0.665130i	$0.768376\pi$
$740$	0.132932	+	2.26786i	0.00488667	+	0.0833683i
$741$		0			0
$742$	7.90426	−	29.1790i	0.290175	−	1.07119i
$743$	7.57857	+	13.1265i	0.278031	+	0.481563i	0.970895	−	0.239504i	$-0.0769850\pi$
$743$	7.57857	+	13.1265i	0.278031	+	0.481563i	−0.692865	+	0.721068i	$0.743652\pi$
$744$		0			0
$745$	34.6298	+	17.3756i	1.26874	+	0.636594i
$746$	6.58348	−	3.80098i	0.241039	−	0.139164i
$747$		0			0
$748$	−18.9362			−0.692377
$749$	−1.85792	+	6.85861i	−0.0678870	+	0.250608i
$750$		0			0
$751$	15.5951			0.569072			0.284536	−	0.958665i	$-0.408160\pi$
$751$	15.5951			0.569072			0.284536	+	0.958665i	$0.408160\pi$
$752$	−9.96048	−	5.75069i	−0.363221	−	0.209706i
$753$		0			0
$754$	28.4192	−	16.4078i	1.03496	−	0.597537i
$755$	−5.65990	+	11.2802i	−0.205985	+	0.410529i
$756$		0			0
$757$			2.00202i			0.0727648i	0.999338	+	0.0363824i	$0.0115834\pi$
$757$			2.00202i			0.0727648i	−0.999338	+	0.0363824i	$0.988417\pi$
$758$	−18.9949	−	32.9001i	−0.689924	−	1.19498i
$759$		0			0
$760$	−6.77133	+	4.45717i	−0.245622	+	0.161679i
$761$	16.9221			0.613424			0.306712	−	0.951802i	$-0.400771\pi$
$761$	16.9221			0.613424			0.306712	+	0.951802i	$0.400771\pi$
$762$		0			0
$763$	2.30667	+	2.31935i	0.0835070	+	0.0839660i
$764$			3.22636i			0.116726i
$765$		0			0
$766$	−10.4289	+	6.02112i	−0.376811	+	0.217552i
$767$	28.5874			1.03223
$768$		0			0
$769$	−10.5316	+	6.08042i	−0.379779	+	0.219265i	−0.677722	−	0.735318i	$-0.737033\pi$
$769$	−10.5316	+	6.08042i	−0.379779	+	0.219265i	0.297943	+	0.954584i	$0.403699\pi$
$770$	−6.62797	−	20.1620i	−0.238856	−	0.726588i
$771$		0			0
$772$	20.9812	−	12.1135i	0.755132	−	0.435975i
$773$	−19.6768	+	11.3604i	−0.707726	+	0.408606i	−0.810219	−	0.586128i	$-0.800652\pi$
$773$	−19.6768	+	11.3604i	−0.707726	+	0.408606i	0.102492	+	0.994734i	$0.467318\pi$
$774$		0			0
$775$	2.05947	+	17.5073i	0.0739783	+	0.628880i
$776$	−4.69619	+	8.13404i	−0.168583	+	0.291995i
$777$		0			0
$778$	9.93198	−	5.73423i	0.356079	−	0.205582i
$779$		−	34.8153i		−	1.24739i
$780$		0			0
$781$	−2.97283			−0.106376
$782$	21.9297	+	12.6611i	0.784203	+	0.452760i
$783$		0			0
$784$	−6.04290	−	3.53318i	−0.215818	−	0.126185i
$785$	−7.97524	−	12.1160i	−0.284648	−	0.432437i
$786$		0			0
$787$	−14.1585	+	24.5232i	−0.504695	+	0.874157i	0.495291	+	0.868727i	$0.335062\pi$
$787$	−14.1585	+	24.5232i	−0.504695	+	0.874157i	−0.999985	+	0.00542948i	$0.998272\pi$
$788$	−3.44828	+	5.97260i	−0.122840	+	0.212765i
$789$		0			0
$790$	−0.0368667	−	0.0560078i	−0.00131166	−	0.00199267i
$791$	20.1997	+	20.3108i	0.718220	+	0.722168i
$792$		0			0
$793$	−39.4778	−	22.7925i	−1.40190	−	0.809387i
$794$	3.78842			0.134446
$795$		0			0
$796$		−	16.7728i		−	0.594494i
$797$	−2.25578	+	1.30238i	−0.0799040	+	0.0461326i	−0.539420	−	0.842037i	$-0.681356\pi$
$797$	−2.25578	+	1.30238i	−0.0799040	+	0.0461326i	0.459516	+	0.888170i	$0.348023\pi$
$798$		0			0
$799$	30.3550	−	52.5764i	1.07388	−	1.86002i
$800$	−4.96576	+	0.584148i	−0.175566	+	0.0206527i
$801$		0			0
$802$	−10.0319	+	5.79192i	−0.354239	+	0.204520i
$803$	21.8261	−	12.6013i	0.770225	−	0.444690i
$804$		0			0
$805$	−5.80496	+	27.7808i	−0.204598	+	0.979144i
$806$	−12.4015	+	7.16002i	−0.436825	+	0.252201i
$807$		0			0
$808$	−10.8924			−0.383193
$809$	−21.2398	+	12.2628i	−0.746751	+	0.431137i	−0.824519	−	0.565835i	$-0.808554\pi$
$809$	−21.2398	+	12.2628i	−0.746751	+	0.431137i	0.0777677	+	0.996972i	$0.475221\pi$
$810$		0			0
$811$		−	9.73361i		−	0.341793i	−0.985289	−	0.170897i	$-0.945334\pi$
$811$		−	9.73361i		−	0.341793i	0.985289	−	0.170897i	$-0.0546664\pi$
$812$	15.1562	−	15.0733i	0.531878	−	0.528971i
$813$		0			0
$814$	−3.64468			−0.127746
$815$	−9.78779	+	6.44273i	−0.342851	+	0.225679i
$816$		0			0
$817$	9.29155	+	16.0934i	0.325070	+	0.563038i
$818$			30.2706i			1.05839i
$819$		0			0
$820$	9.63012	−	19.1929i	0.336298	−	0.670245i
$821$	1.76920	−	1.02145i	0.0617456	−	0.0356488i	−0.468809	−	0.883299i	$-0.655317\pi$
$821$	1.76920	−	1.02145i	0.0617456	−	0.0356488i	0.530555	+	0.847651i	$0.321984\pi$
$822$		0			0
$823$	−11.3113	−	6.53059i	−0.394287	−	0.227642i	0.289729	−	0.957109i	$-0.406435\pi$
$823$	−11.3113	−	6.53059i	−0.394287	−	0.227642i	−0.684016	+	0.729467i	$0.739768\pi$
$824$	0.584230			0.0203526
$825$		0			0
$826$	18.0000	−	4.77026i	0.626301	−	0.165978i
$827$	18.5995			0.646767			0.323384	−	0.946268i	$-0.395180\pi$
$827$	18.5995			0.646767			0.323384	+	0.946268i	$0.395180\pi$
$828$		0			0
$829$	−26.4337	+	15.2615i	−0.918080	+	0.530053i	−0.883022	−	0.469332i	$-0.844495\pi$
$829$	−26.4337	+	15.2615i	−0.918080	+	0.530053i	−0.0350576	+	0.999385i	$0.511161\pi$
$830$	−15.9174	−	7.98661i	−0.552500	−	0.277219i
$831$		0			0
$832$	−2.03087	−	3.51756i	−0.0704076	−	0.121950i
$833$	18.6499	−	31.8975i	0.646180	−	1.10518i
$834$		0			0
$835$	2.85350	+	48.6818i	0.0987496	+	1.68470i
$836$	−6.50291	−	11.2634i	−0.224908	−	0.389552i
$837$		0			0
$838$	10.7319	−	18.5882i	0.370727	−	0.642118i
$839$	−6.88932	+	11.9327i	−0.237846	+	0.411961i	−0.960096	−	0.279671i	$-0.909775\pi$
$839$	−6.88932	+	11.9327i	−0.237846	+	0.411961i	0.722250	+	0.691632i	$0.243108\pi$
$840$		0			0
$841$	18.1368	+	31.4139i	0.625408	+	1.08324i
$842$	−25.7370			−0.886957
$843$		0			0
$844$	−4.75379			−0.163632
$845$	4.30017	+	6.53281i	0.147930	+	0.224735i
$846$		0			0
$847$	4.78149	−	1.26716i	0.164294	−	0.0435401i
$848$	5.71305	−	9.89529i	0.196187	−	0.339806i
$849$		0			0
$850$	−3.08342	−	26.2118i	−0.105761	−	0.899056i
$851$	4.22083	+	2.43690i	0.144688	+	0.0835358i
$852$		0			0
$853$	2.66904	−	4.62291i	0.0913862	−	0.158286i	−0.816708	−	0.577051i	$-0.804204\pi$
$853$	2.66904	−	4.62291i	0.0913862	−	0.158286i	0.908095	+	0.418765i	$0.137537\pi$
$854$	−28.6605	−	7.76380i	−0.980741	−	0.265672i
$855$		0			0
$856$	−1.34287	+	2.32592i	−0.0458984	+	0.0794983i
$857$			37.1702i			1.26971i	0.772631	+	0.634856i	$0.218940\pi$
$857$			37.1702i			1.26971i	−0.772631	+	0.634856i	$0.781060\pi$
$858$		0			0
$859$			38.9189i			1.32790i	0.747778	+	0.663949i	$0.231121\pi$
$859$			38.9189i			1.32790i	−0.747778	+	0.663949i	$0.768879\pi$
$860$	0.670681	+	11.4420i	0.0228700	+	0.390170i
$861$		0			0
$862$	−1.05463	−	0.608890i	−0.0359208	−	0.0207389i
$863$	−2.48936	+	4.31171i	−0.0847390	+	0.146772i	−0.905280	−	0.424816i	$-0.860339\pi$
$863$	−2.48936	+	4.31171i	−0.0847390	+	0.146772i	0.820541	+	0.571588i	$0.193672\pi$
$864$		0			0
$865$	2.83725	+	48.4045i	0.0964695	+	1.64580i
$866$	−3.14949	−	5.45507i	−0.107024	−	0.185371i
$867$		0			0
$868$	−6.61384	+	6.57769i	−0.224488	+	0.223261i
$869$	0.0931629	−	0.0537876i	0.00316034	−	0.00182462i
$870$		0			0
$871$		−	28.4134i		−	0.962753i
$872$	0.618180	+	1.07072i	0.0209342	+	0.0362591i
$873$		0			0
$874$			17.3918i			0.588287i
$875$	26.8293	−	12.4575i	0.906995	−	0.421142i
$876$		0			0
$877$		−	45.8645i		−	1.54873i	−0.632737	−	0.774367i	$-0.718068\pi$
$877$		−	45.8645i		−	1.54873i	0.632737	−	0.774367i	$-0.281932\pi$
$878$	31.5109	+	18.1928i	1.06344	+	0.613978i
$879$		0			0
$880$	−0.469392	−	8.00798i	−0.0158232	−	0.269949i
$881$	4.17555			0.140678			0.0703390	−	0.997523i	$-0.477592\pi$
$881$	4.17555			0.140678			0.0703390	+	0.997523i	$0.477592\pi$
$882$		0			0
$883$			9.11973i			0.306903i	0.988156	+	0.153452i	$0.0490390\pi$
$883$			9.11973i			0.306903i	−0.988156	+	0.153452i	$0.950961\pi$
$884$	18.5675	−	10.7199i	0.624492	−	0.360550i
$885$		0			0
$886$	5.77669	−	10.0055i	0.194072	−	0.336142i
$887$		−	7.55966i		−	0.253828i	−0.991914	−	0.126914i	$-0.959493\pi$
$887$		−	7.55966i		−	0.253828i	0.991914	−	0.126914i	$-0.0405073\pi$
$888$		0			0
$889$	−3.36130	−	12.6835i	−0.112734	−	0.425391i
$890$	−1.25353	+	2.49830i	−0.0420185	+	0.0837430i
$891$		0			0
$892$	−8.37432	−	14.5048i	−0.280393	−	0.485655i
$893$	41.6970			1.39534
$894$		0			0
$895$	−2.28353	−	38.9579i	−0.0763301	−	1.30222i
$896$	−1.86569	−	1.87595i	−0.0623285	−	0.0626711i
$897$		0			0
$898$	7.23657	−	4.17804i	0.241488	−	0.139423i
$899$	−14.2420	−	24.6679i	−0.474998	−	0.822721i
$900$		0			0
$901$	52.2323	+	30.1563i	1.74011	+	1.00465i
$902$	29.8352	+	17.2254i	0.993404	+	0.573542i
$903$		0			0
$904$	5.41347	+	9.37640i	0.180049	+	0.311854i
$905$	48.0643	+	24.1165i	1.59771	+	0.801660i
$906$		0			0
$907$			16.8607i			0.559852i	0.960022	+	0.279926i	$0.0903099\pi$
$907$			16.8607i			0.559852i	−0.960022	+	0.279926i	$0.909690\pi$
$908$	−5.49698	−	3.17368i	−0.182424	−	0.105322i
$909$		0			0
$910$	17.9128	+	16.0172i	0.593802	+	0.530966i
$911$	4.64902	+	2.68411i	0.154029	+	0.0889286i	0.575033	−	0.818130i	$-0.304989\pi$
$911$	4.64902	+	2.68411i	0.154029	+	0.0889286i	−0.421005	+	0.907059i	$0.638322\pi$
$912$		0			0
$913$	14.2856	−	24.7434i	0.472785	−	0.818888i
$914$	−3.26626	−	1.88578i	−0.108038	−	0.0623759i
$915$		0			0
$916$	−3.78920	−	2.18769i	−0.125199	−	0.0722834i
$917$	−23.7386	+	6.29104i	−0.783916	+	0.207748i
$918$		0			0
$919$	−8.65286	+	14.9872i	−0.285432	+	0.494382i	−0.972714	−	0.232009i	$-0.925470\pi$
$919$	−8.65286	+	14.9872i	−0.285432	+	0.494382i	0.687282	+	0.726390i	$0.258804\pi$
$920$	−4.81068	+	9.58772i	−0.158604	+	0.316098i
$921$		0			0
$922$	−2.78262			−0.0916408
$923$	2.91494	−	1.68294i	0.0959464	−	0.0553947i
$924$		0			0
$925$	−0.593471	−	5.04501i	−0.0195132	−	0.165879i
$926$	−9.52910	−	5.50163i	−0.313146	−	0.180795i
$927$		0			0
$928$	6.99680	−	4.03961i	0.229681	−	0.132607i
$929$	−5.35042	−	9.26720i	−0.175542	−	0.304047i	0.764807	−	0.644260i	$-0.222834\pi$
$929$	−5.35042	−	9.26720i	−0.175542	−	0.304047i	−0.940349	+	0.340213i	$0.889501\pi$
$930$		0			0
$931$	25.3773	+	0.139114i	0.831709	+	0.00455929i
$932$	−12.2423	−	21.2043i	−0.401010	−	0.694570i
$933$		0			0
$934$		−	19.0310i		−	0.622715i
$935$	42.2701	−	2.47768i	1.38238	−	0.0810289i
$936$		0			0
$937$	12.8760			0.420639			0.210320	−	0.977633i	$-0.432550\pi$
$937$	12.8760			0.420639			0.210320	+	0.977633i	$0.432550\pi$
$938$	−4.74123	−	17.8905i	−0.154807	−	0.584145i
$939$		0			0
$940$	22.9866	+	11.5336i	0.749740	+	0.376186i
$941$	16.8924	−	29.2584i	0.550675	−	0.953797i	−0.447551	−	0.894258i	$-0.647704\pi$
$941$	16.8924	−	29.2584i	0.550675	−	0.953797i	0.998226	−	0.0595386i	$-0.0189629\pi$
$942$		0			0
$943$	−23.0344	−	39.8967i	−0.750102	−	1.29921i
$944$	7.03823			0.229075
$945$		0			0
$946$	−18.3885			−0.597862
$947$	−10.5933	−	18.3481i	−0.344236	−	0.596235i	0.640978	−	0.767559i	$-0.278529\pi$
$947$	−10.5933	−	18.3481i	−0.344236	−	0.596235i	−0.985215	+	0.171324i	$0.945195\pi$
$948$		0			0
$949$	−14.2674	+	24.7118i	−0.463138	+	0.802178i
$950$	14.5320	−	10.8354i	0.471481	−	0.351548i
$951$		0			0
$952$	9.90220	−	9.84807i	0.320932	−	0.319178i
$953$	15.9394			0.516328			0.258164	−	0.966101i	$-0.416883\pi$
$953$	15.9394			0.516328			0.258164	+	0.966101i	$0.416883\pi$
$954$		0			0
$955$	−0.422149	−	7.20200i	−0.0136604	−	0.233051i
$956$		−	2.43321i		−	0.0786956i
$957$		0			0
$958$	−0.146168	−	0.253170i	−0.00472247	−	0.00817956i
$959$	−0.0156634	+	0.00415101i	−0.000505797	+	0.000134043i
$960$		0			0
$961$	−9.28508	−	16.0822i	−0.299519	−	0.518782i
$962$	3.57371	−	2.06328i	0.115221	−	0.0665228i
$963$		0			0
$964$	1.82213	+	1.05201i	0.0586870	+	0.0338830i
$965$	−45.2501	+	29.7855i	−1.45665	+	0.958830i
$966$		0			0
$967$	48.1802	−	27.8169i	1.54937	−	0.894530i	0.551182	−	0.834385i	$-0.314177\pi$
$967$	48.1802	−	27.8169i	1.54937	−	0.894530i	0.998190	−	0.0601450i	$-0.0191563\pi$
$968$	1.86962			0.0600918
$969$		0			0
$970$	9.41872	−	18.7716i	0.302417	−	0.602719i
$971$	−28.9188	+	50.0888i	−0.928047	+	1.60743i	−0.141462	+	0.989944i	$0.545180\pi$
$971$	−28.9188	+	50.0888i	−0.928047	+	1.60743i	−0.786586	+	0.617481i	$0.788153\pi$
$972$		0			0
$973$	−15.8682	+	15.7814i	−0.508711	+	0.505930i
$974$	17.4211	+	10.0581i	0.558208	+	0.322281i
$975$		0			0
$976$	−9.71945	−	5.61153i	−0.311112	−	0.179621i
$977$	−19.5402	+	33.8446i	−0.625146	+	1.08278i	0.363366	+	0.931646i	$0.381627\pi$
$977$	−19.5402	+	33.8446i	−0.625146	+	1.08278i	−0.988513	+	0.151139i	$0.951706\pi$
$978$		0			0
$979$	−3.88358	−	2.24219i	−0.124120	−	0.0716606i
$980$	13.9515	+	7.09622i	0.445664	+	0.226680i
$981$		0			0
$982$	0.00977625	+	0.00564432i	0.000311973	+	0.000180118i
$983$			15.9657i			0.509228i	0.967043	+	0.254614i	$0.0819485\pi$
$983$			15.9657i			0.509228i	−0.967043	+	0.254614i	$0.918052\pi$
$984$		0			0
$985$	6.91590	−	13.7834i	0.220359	−	0.439177i
$986$	21.3231	+	36.9326i	0.679065	+	1.17617i
$987$		0			0
$988$	12.7525	+	7.36268i	0.405712	+	0.234238i
$989$	21.2953	+	12.2949i	0.677153	+	0.390954i
$990$		0			0
$991$	16.1342	+	27.9452i	0.512519	+	0.887709i	0.999895	+	0.0145163i	$0.00462085\pi$
$991$	16.1342	+	27.9452i	0.512519	+	0.887709i	−0.487376	+	0.873192i	$0.662046\pi$
$992$	−3.05326	+	1.76280i	−0.0969410	+	0.0559689i
$993$		0			0
$994$	1.55456	−	1.54607i	0.0493078	−	0.0490382i
$995$	2.19461	+	37.4407i	0.0695737	+	1.18695i
$996$		0			0
$997$	−39.7139			−1.25775			−0.628877	−	0.777505i	$-0.716485\pi$
$997$	−39.7139			−1.25775			−0.628877	+	0.777505i	$0.716485\pi$
$998$	5.43038	+	9.40569i	0.171896	+	0.297732i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.r.b.89.16		48
3.2	odd	2		630.2.r.a.299.17	yes	48
5.4	even	2		1890.2.r.a.89.16		48
7.3	odd	6		1890.2.bi.a.899.8		48
9.4	even	3		630.2.bi.a.509.1	yes	48
9.5	odd	6		1890.2.bi.b.719.24		48
15.14	odd	2		630.2.r.b.299.8	yes	48
21.17	even	6		630.2.bi.b.479.24	yes	48
35.24	odd	6		1890.2.bi.b.899.24		48
45.4	even	6		630.2.bi.b.509.24	yes	48
45.14	odd	6		1890.2.bi.a.719.8		48
63.31	odd	6		630.2.r.b.59.8	yes	48
63.59	even	6		1890.2.r.a.1529.16		48
105.59	even	6		630.2.bi.a.479.1	yes	48
315.59	even	6	inner	1890.2.r.b.1529.16		48
315.94	odd	6		630.2.r.a.59.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.17	✓	48	315.94	odd	6
630.2.r.a.299.17	yes	48	3.2	odd	2
630.2.r.b.59.8	yes	48	63.31	odd	6
630.2.r.b.299.8	yes	48	15.14	odd	2
630.2.bi.a.479.1	yes	48	105.59	even	6
630.2.bi.a.509.1	yes	48	9.4	even	3
630.2.bi.b.479.24	yes	48	21.17	even	6
630.2.bi.b.509.24	yes	48	45.4	even	6
1890.2.r.a.89.16		48	5.4	even	2
1890.2.r.a.1529.16		48	63.59	even	6
1890.2.r.b.89.16		48	1.1	even	1	trivial
1890.2.r.b.1529.16		48	315.59	even	6	inner
1890.2.bi.a.719.8		48	45.14	odd	6
1890.2.bi.a.899.8		48	7.3	odd	6
1890.2.bi.b.719.24		48	9.5	odd	6
1890.2.bi.b.899.24		48	35.24	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 $\F_{q}$
Belyi maps

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00280 - 1.99860i) q^{5} +(-2.55747 + 0.677764i) q^{7} -1.00000 q^{8} +(2.23224 - 0.130844i) q^{10} +3.58743i q^{11} +(-2.03087 - 3.51756i) q^{13} +(-1.86569 - 1.87595i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(4.57132 - 2.63925i) q^{17} +(3.13968 + 1.81269i) q^{19} +(1.22943 + 1.86775i) q^{20} +(-3.10680 + 1.79371i) q^{22} +4.79723 q^{23} +(-2.98877 - 4.00840i) q^{25} +(2.03087 - 3.51756i) q^{26} +(0.691773 - 2.55371i) q^{28} +(6.99680 + 4.03961i) q^{29} +(-3.05326 - 1.76280i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.57132 + 2.63925i) q^{34} +(-1.21006 + 5.79101i) q^{35} +(0.879847 + 0.507980i) q^{37} +3.62539i q^{38} +(-1.00280 + 1.99860i) q^{40} +(-4.80160 - 8.31661i) q^{41} +(4.43909 + 2.56291i) q^{43} +(-3.10680 - 1.79371i) q^{44} +(2.39862 + 4.15452i) q^{46} +(9.96048 - 5.75069i) q^{47} +(6.08127 - 3.46672i) q^{49} +(1.97699 - 4.59255i) q^{50} +4.06173 q^{52} +(5.71305 + 9.89529i) q^{53} +(7.16981 + 3.59749i) q^{55} +(2.55747 - 0.677764i) q^{56} +8.07921i q^{58} +(-3.51911 + 6.09528i) q^{59} +(9.71945 - 5.61153i) q^{61} -3.52560i q^{62} +1.00000 q^{64} +(-9.06675 + 0.531452i) q^{65} +(6.05819 + 3.49770i) q^{67} +5.27850i q^{68} +(-5.62019 + 1.84756i) q^{70} +0.828681i q^{71} +(-3.51263 - 6.08405i) q^{73} +1.01596i q^{74} +(-3.13968 + 1.81269i) q^{76} +(-2.43143 - 9.17472i) q^{77} +(-0.0149934 - 0.0259693i) q^{79} +(-2.23224 + 0.130844i) q^{80} +(4.80160 - 8.31661i) q^{82} +(-6.89727 - 3.98214i) q^{83} +(-0.690658 - 11.7829i) q^{85} +5.12582i q^{86} -3.58743i q^{88} +(-0.625013 + 1.08255i) q^{89} +(7.57795 + 7.61961i) q^{91} +(-2.39862 + 4.15452i) q^{92} +(9.96048 + 5.75069i) q^{94} +(6.77133 - 4.45717i) q^{95} +(4.69619 - 8.13404i) q^{97} +(6.04290 + 3.53318i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} - 3 q^{14} - 24 q^{16} + 6 q^{22} + 6 q^{23} - 3 q^{28} + 3 q^{29} + 24 q^{32} - 18 q^{35} - 3 q^{41} + 6 q^{44} + 3 q^{46} - 6 q^{49} + 18 q^{50} + 42 q^{55} - 9 q^{61}+ \cdots - 3 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

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