LMFDB - Embedded newform 1890.2.bi.a.899.8

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			899.8
Character	$\chi$	$=$	1890.899
Dual form			1890.2.bi.a.719.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.22943 - 1.86775i) q^{5} +(-0.691773 - 2.55371i) q^{7} -1.00000 q^{8} +(1.22943 + 1.86775i) q^{10} +(3.10680 - 1.79371i) q^{11} +(2.03087 + 3.51756i) q^{13} +(0.691773 + 2.55371i) q^{14} +1.00000 q^{16} +(4.57132 + 2.63925i) q^{17} +(3.13968 - 1.81269i) q^{19} +(-1.22943 - 1.86775i) q^{20} +(-3.10680 + 1.79371i) q^{22} +(-2.39862 + 4.15452i) q^{23} +(-1.97699 + 4.59255i) q^{25} +(-2.03087 - 3.51756i) q^{26} +(-0.691773 - 2.55371i) q^{28} +(6.99680 + 4.03961i) q^{29} -3.52560i q^{31} -1.00000 q^{32} +(-4.57132 - 2.63925i) q^{34} +(-3.91921 + 4.43168i) q^{35} +(-0.879847 + 0.507980i) q^{37} +(-3.13968 + 1.81269i) q^{38} +(1.22943 + 1.86775i) q^{40} +(4.80160 + 8.31661i) q^{41} +(4.43909 + 2.56291i) q^{43} +(3.10680 - 1.79371i) q^{44} +(2.39862 - 4.15452i) q^{46} -11.5014i q^{47} +(-6.04290 + 3.53318i) q^{49} +(1.97699 - 4.59255i) q^{50} +(2.03087 + 3.51756i) q^{52} +(5.71305 - 9.89529i) q^{53} +(-7.16981 - 3.59749i) q^{55} +(0.691773 + 2.55371i) q^{56} +(-6.99680 - 4.03961i) q^{58} -7.03823 q^{59} -11.2231i q^{61} +3.52560i q^{62} +1.00000 q^{64} +(4.07312 - 8.11776i) q^{65} -6.99540i q^{67} +(4.57132 + 2.63925i) q^{68} +(3.91921 - 4.43168i) q^{70} +0.828681i q^{71} +(3.51263 - 6.08405i) q^{73} +(0.879847 - 0.507980i) q^{74} +(3.13968 - 1.81269i) q^{76} +(-6.72983 - 6.69304i) q^{77} +0.0299868 q^{79} +(-1.22943 - 1.86775i) q^{80} +(-4.80160 - 8.31661i) q^{82} +(6.89727 + 3.98214i) q^{83} +(-0.690658 - 11.7829i) q^{85} +(-4.43909 - 2.56291i) q^{86} +(-3.10680 + 1.79371i) q^{88} +(0.625013 + 1.08255i) q^{89} +(7.57795 - 7.61961i) q^{91} +(-2.39862 + 4.15452i) q^{92} +11.5014i q^{94} +(-7.24569 - 3.63556i) q^{95} +(-4.69619 + 8.13404i) q^{97} +(6.04290 - 3.53318i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 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 + 12 * 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 - 12 * 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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.22943	−	1.86775i	−0.549819	−	0.835284i
$5$	−1.22943	−	1.86775i	−0.549819	−	0.835284i
$6$		0			0
$7$	−0.691773	−	2.55371i	−0.261466	−	0.965213i
$7$	−0.691773	−	2.55371i	−0.261466	−	0.965213i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.22943	+	1.86775i	0.388781	+	0.590635i
$11$	3.10680	−	1.79371i	0.936736	−	0.540825i	0.0478002	−	0.998857i	$-0.484779\pi$
$11$	3.10680	−	1.79371i	0.936736	−	0.540825i	0.888936	+	0.458032i	$0.151446\pi$
$12$		0			0
$13$	2.03087	+	3.51756i	0.563261	+	0.975597i	0.997209	+	0.0746590i	$0.0237868\pi$
$13$	2.03087	+	3.51756i	0.563261	+	0.975597i	−0.433948	+	0.900938i	$0.642880\pi$
$14$	0.691773	+	2.55371i	0.184884	+	0.682509i
$15$		0			0
$16$	1.00000			0.250000
$17$	4.57132	+	2.63925i	1.10871	+	0.640112i	0.938494	−	0.345295i	$-0.112221\pi$
$17$	4.57132	+	2.63925i	1.10871	+	0.640112i	0.170213	+	0.985407i	$0.445555\pi$
$18$		0			0
$19$	3.13968	−	1.81269i	0.720292	−	0.415861i	−0.0945683	−	0.995518i	$-0.530147\pi$
$19$	3.13968	−	1.81269i	0.720292	−	0.415861i	0.814860	+	0.579658i	$0.196814\pi$
$20$	−1.22943	−	1.86775i	−0.274909	−	0.417642i
$21$		0			0
$22$	−3.10680	+	1.79371i	−0.662372	+	0.382421i
$23$	−2.39862	+	4.15452i	−0.500146	+	0.866278i	0.499854	+	0.866110i	$0.333387\pi$
$23$	−2.39862	+	4.15452i	−0.500146	+	0.866278i	−1.00000		0.000168492i	$0.999946\pi$
$24$		0			0
$25$	−1.97699	+	4.59255i	−0.395399	+	0.918510i
$26$	−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
$31$		−	3.52560i		−	0.633216i	−0.948556	−	0.316608i	$-0.897456\pi$
$31$		−	3.52560i		−	0.633216i	0.948556	−	0.316608i	$-0.102544\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−4.57132	−	2.63925i	−0.783974	−	0.452628i
$35$	−3.91921	+	4.43168i	−0.662468	+	0.749090i
$36$		0			0
$37$	−0.879847	+	0.507980i	−0.144646	+	0.0835114i	−0.570576	−	0.821245i	$-0.693280\pi$
$37$	−0.879847	+	0.507980i	−0.144646	+	0.0835114i	0.425930	+	0.904756i	$0.359947\pi$
$38$	−3.13968	+	1.81269i	−0.509323	+	0.294058i
$39$		0			0
$40$	1.22943	+	1.86775i	0.194390	+	0.295317i
$41$	4.80160	+	8.31661i	0.749883	+	1.29884i	0.947878	+	0.318633i	$0.103224\pi$
$41$	4.80160	+	8.31661i	0.749883	+	1.29884i	−0.197995	+	0.980203i	$0.563443\pi$
$42$		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
$47$		−	11.5014i		−	1.67765i	−0.544403	−	0.838824i	$-0.683244\pi$
$47$		−	11.5014i		−	1.67765i	0.544403	−	0.838824i	$-0.316756\pi$
$48$		0			0
$49$	−6.04290	+	3.53318i	−0.863272	+	0.504740i
$50$	1.97699	−	4.59255i	0.279589	−	0.649484i
$51$		0			0
$52$	2.03087	+	3.51756i	0.281631	+	0.487798i
$53$	5.71305	−	9.89529i	0.784747	−	1.35922i	−0.144403	−	0.989519i	$-0.546126\pi$
$53$	5.71305	−	9.89529i	0.784747	−	1.35922i	0.929150	−	0.369703i	$-0.120541\pi$
$54$		0			0
$55$	−7.16981	−	3.59749i	−0.966777	−	0.485085i
$56$	0.691773	+	2.55371i	0.0924420	+	0.341254i
$57$		0			0
$58$	−6.99680	−	4.03961i	−0.918725	−	0.530426i
$59$	−7.03823			−0.916299			−0.458150	−	0.888875i	$-0.651488\pi$
$59$	−7.03823			−0.916299			−0.458150	+	0.888875i	$0.651488\pi$
$60$		0			0
$61$		−	11.2231i		−	1.43696i	−0.695545	−	0.718482i	$-0.744837\pi$
$61$		−	11.2231i		−	1.43696i	0.695545	−	0.718482i	$-0.255163\pi$
$62$			3.52560i			0.447751i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.07312	−	8.11776i	0.505209	−	1.00688i
$66$		0			0
$67$		−	6.99540i		−	0.854624i	−0.904104	−	0.427312i	$-0.859461\pi$
$67$		−	6.99540i		−	0.854624i	0.904104	−	0.427312i	$-0.140539\pi$
$68$	4.57132	+	2.63925i	0.554353	+	0.320056i
$69$		0			0
$70$	3.91921	−	4.43168i	0.468436	−	0.529687i
$71$			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	$-0.698470\pi$
$73$	3.51263	−	6.08405i	0.411122	−	0.712084i	0.995013	+	0.0997484i	$0.0318038\pi$
$74$	0.879847	−	0.507980i	0.102280	−	0.0590515i
$75$		0			0
$76$	3.13968	−	1.81269i	0.360146	−	0.207930i
$77$	−6.72983	−	6.69304i	−0.766935	−	0.762742i
$78$		0			0
$79$	0.0299868			0.00337377			0.00168689	−	0.999999i	$-0.499463\pi$
$79$	0.0299868			0.00337377			0.00168689	+	0.999999i	$0.499463\pi$
$80$	−1.22943	−	1.86775i	−0.137455	−	0.208821i
$81$		0			0
$82$	−4.80160	−	8.31661i	−0.530248	−	0.918416i
$83$	6.89727	+	3.98214i	0.757074	+	0.437097i	0.828244	−	0.560368i	$-0.189340\pi$
$83$	6.89727	+	3.98214i	0.757074	+	0.437097i	−0.0711705	+	0.997464i	$0.522673\pi$
$84$		0			0
$85$	−0.690658	−	11.7829i	−0.0749124	−	1.27803i
$86$	−4.43909	−	2.56291i	−0.478679	−	0.276366i
$87$		0			0
$88$	−3.10680	+	1.79371i	−0.331186	+	0.191210i
$89$	0.625013	+	1.08255i	0.0662512	+	0.114750i	0.897248	−	0.441526i	$-0.145563\pi$
$89$	0.625013	+	1.08255i	0.0662512	+	0.114750i	−0.830997	+	0.556277i	$0.812229\pi$
$90$		0			0
$91$	7.57795	−	7.61961i	0.794385	−	0.798752i
$92$	−2.39862	+	4.15452i	−0.250073	+	0.433139i
$93$		0			0
$94$			11.5014i			1.18628i
$95$	−7.24569	−	3.63556i	−0.743392	−	0.373000i
$96$		0			0
$97$	−4.69619	+	8.13404i	−0.476826	+	0.825887i	−0.999647	−	0.0265556i	$-0.991546\pi$
$97$	−4.69619	+	8.13404i	−0.476826	+	0.825887i	0.522821	+	0.852442i	$0.324879\pi$
$98$	6.04290	−	3.53318i	0.610425	−	0.356905i
$99$		0			0
$100$	−1.97699	+	4.59255i	−0.197699	+	0.459255i
$101$	5.44619	+	9.43308i	0.541916	+	0.938626i	0.998794	+	0.0490969i	$0.0156343\pi$
$101$	5.44619	+	9.43308i	0.541916	+	0.938626i	−0.456878	+	0.889529i	$0.651032\pi$
$102$		0			0
$103$	−0.292115	+	0.505958i	−0.0287830	+	0.0498536i	−0.880058	−	0.474866i	$-0.842496\pi$
$103$	−0.292115	+	0.505958i	−0.0287830	+	0.0498536i	0.851275	+	0.524720i	$0.175830\pi$
$104$	−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	0.923607	−	0.383341i	$-0.125227\pi$
$107$	1.34287	+	2.32592i	0.129820	+	0.224855i	−0.793787	+	0.608196i	$0.791893\pi$
$108$		0			0
$109$	−0.618180	+	1.07072i	−0.0592109	+	0.102556i	−0.894111	−	0.447845i	$-0.852192\pi$
$109$	−0.618180	+	1.07072i	−0.0592109	+	0.102556i	0.834901	+	0.550401i	$0.185525\pi$
$110$	7.16981	+	3.59749i	0.683615	+	0.343007i
$111$		0			0
$112$	−0.691773	−	2.55371i	−0.0653664	−	0.241303i
$113$	−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
$115$	10.7086	−	0.627687i	0.998578	−	0.0585321i
$116$	6.99680	+	4.03961i	0.649637	+	0.375068i
$117$		0			0
$118$	7.03823			0.647921
$119$	3.57758	−	13.4996i	0.327956	−	1.23751i
$120$		0			0
$121$	0.934810	−	1.61914i	0.0849827	−	0.147194i
$122$			11.2231i			1.01609i
$123$		0			0
$124$		−	3.52560i		−	0.316608i
$125$	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	$0.929382\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−4.07312	+	8.11776i	−0.357237	+	0.711975i
$131$	4.64103	−	8.03850i	0.405489	−	0.702327i	−0.588890	−	0.808213i	$-0.700435\pi$
$131$	4.64103	−	8.03850i	0.405489	−	0.702327i	0.994378	+	0.105887i	$0.0337681\pi$
$132$		0			0
$133$	−6.80105	−	6.76387i	−0.589725	−	0.586502i
$134$			6.99540i			0.604310i
$135$		0			0
$136$	−4.57132	−	2.63925i	−0.391987	−	0.226314i
$137$	−0.00306228	−	0.00530403i	−0.000261628	−	0.000453154i	0.865895	−	0.500227i	$-0.166750\pi$
$137$	−0.00306228	−	0.00530403i	−0.000261628	−	0.000453154i	−0.866156	+	0.499773i	$0.833417\pi$
$138$		0			0
$139$	−7.32549	+	4.22938i	−0.621340	+	0.358731i	−0.777391	−	0.629018i	$-0.783457\pi$
$139$	−7.32549	+	4.22938i	−0.621340	+	0.358731i	0.156050	+	0.987749i	$0.450124\pi$
$140$	−3.91921	+	4.43168i	−0.331234	+	0.374545i
$141$		0			0
$142$		−	0.828681i		−	0.0695414i
$143$	12.6190	+	7.28558i	1.05525	+	0.609251i
$144$		0			0
$145$	−1.05711	−	18.0347i	−0.0877885	−	1.49770i
$146$	−3.51263	+	6.08405i	−0.290707	+	0.503519i
$147$		0			0
$148$	−0.879847	+	0.507980i	−0.0723230	+	0.0417557i
$149$	−15.0057	−	8.66353i	−1.22931	−	0.709744i	−0.262426	−	0.964952i	$-0.584523\pi$
$149$	−15.0057	−	8.66353i	−1.22931	−	0.709744i	−0.966886	+	0.255208i	$0.917856\pi$
$150$		0			0
$151$	2.82204	+	4.88791i	0.229654	+	0.397773i	0.957706	−	0.287750i	$-0.0929071\pi$
$151$	2.82204	+	4.88791i	0.229654	+	0.397773i	−0.728051	+	0.685523i	$0.759574\pi$
$152$	−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
$157$	6.48693			0.517713			0.258857	−	0.965916i	$-0.416654\pi$
$157$	6.48693			0.517713			0.258857	+	0.965916i	$0.416654\pi$
$158$	−0.0299868			−0.00238562
$159$		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	$-0.600872\pi$
$163$	4.53833	−	2.62021i	0.355469	−	0.205230i	0.667092	+	0.744976i	$0.267539\pi$
$164$	4.80160	+	8.31661i	0.374942	+	0.649418i
$165$		0			0
$166$	−6.89727	−	3.98214i	−0.535332	−	0.309074i
$167$	18.8867	−	10.9043i	1.46150	−	0.843797i	0.462418	−	0.886662i	$-0.346982\pi$
$167$	18.8867	−	10.9043i	1.46150	−	0.843797i	0.999081	+	0.0428649i	$0.0136485\pi$
$168$		0			0
$169$	−1.74884	+	3.02908i	−0.134526	+	0.233006i
$170$	0.690658	+	11.7829i	0.0529710	+	0.903704i
$171$		0			0
$172$	4.43909	+	2.56291i	0.338477	+	0.195420i
$173$			21.6843i			1.64863i	0.566133	+	0.824314i	$0.308439\pi$
$173$			21.6843i			1.64863i	−0.566133	+	0.824314i	$0.691561\pi$
$174$		0			0
$175$	13.0957	+	1.87167i	0.989940	+	0.141485i
$176$	3.10680	−	1.79371i	0.234184	−	0.135206i
$177$		0			0
$178$	−0.625013	−	1.08255i	−0.0468467	−	0.0811408i
$179$	−15.1142	−	8.72620i	−1.12969	−	0.652227i	−0.185833	−	0.982581i	$-0.559498\pi$
$179$	−15.1142	−	8.72620i	−1.12969	−	0.652227i	−0.943857	+	0.330355i	$0.892832\pi$
$180$		0			0
$181$		−	24.0491i		−	1.78755i	−0.448513	−	0.893776i	$-0.648046\pi$
$181$		−	24.0491i		−	1.78755i	0.448513	−	0.893776i	$-0.351954\pi$
$182$	−7.57795	+	7.61961i	−0.561715	+	0.564803i
$183$		0			0
$184$	2.39862	−	4.15452i	0.176828	−	0.306276i
$185$	2.03049	+	1.01881i	0.149285	+	0.0749044i
$186$		0			0
$187$	18.9362			1.38475
$188$		−	11.5014i		−	0.838824i
$189$		0			0
$190$	7.24569	+	3.63556i	0.525657	+	0.263751i
$191$			3.22636i			0.233451i	0.993164	+	0.116726i	$0.0372398\pi$
$191$			3.22636i			0.233451i	−0.993164	+	0.116726i	$0.962760\pi$
$192$		0			0
$193$			24.2271i			1.74390i	0.489593	+	0.871951i	$0.337145\pi$
$193$			24.2271i			1.74390i	−0.489593	+	0.871951i	$0.662855\pi$
$194$	4.69619	−	8.13404i	0.337167	−	0.583990i
$195$		0			0
$196$	−6.04290	+	3.53318i	−0.431636	+	0.252370i
$197$	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	−0.112797	−	0.993618i	$-0.535981\pi$
$199$	−14.5256	−	8.38638i	−1.02969	−	0.594494i	−0.916897	+	0.399124i	$0.869314\pi$
$200$	1.97699	−	4.59255i	0.139795	−	0.324742i
$201$		0			0
$202$	−5.44619	−	9.43308i	−0.383193	−	0.663709i
$203$	5.47580	−	20.6623i	0.384326	−	1.45021i
$204$		0			0
$205$	9.63012	−	19.1929i	0.672597	−	1.34049i
$206$	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	$0.781012\pi$
$212$	5.71305	−	9.89529i	0.392374	−	0.679611i
$213$		0			0
$214$	−1.34287	−	2.32592i	−0.0917967	−	0.158997i
$215$	−0.670681	−	11.4420i	−0.0457400	−	0.780341i
$216$		0			0
$217$	−9.00336	+	2.43891i	−0.611188	+	0.165564i
$218$	0.618180	−	1.07072i	0.0418684	−	0.0725182i
$219$		0			0
$220$	−7.16981	−	3.59749i	−0.483389	−	0.242542i
$221$			21.4399i			1.44220i
$222$		0			0
$223$	8.37432	−	14.5048i	0.560786	−	0.971310i	−0.436642	−	0.899635i	$-0.643832\pi$
$223$	8.37432	−	14.5048i	0.560786	−	0.971310i	0.997428	−	0.0716748i	$-0.0228344\pi$
$224$	0.691773	+	2.55371i	0.0462210	+	0.170627i
$225$		0			0
$226$	5.41347	+	9.37640i	0.360099	+	0.623709i
$227$	−5.49698	+	3.17368i	−0.364847	+	0.210645i	−0.671205	−	0.741272i	$-0.734223\pi$
$227$	−5.49698	+	3.17368i	−0.364847	+	0.210645i	0.306358	+	0.951916i	$0.400890\pi$
$228$		0			0
$229$	3.78920	+	2.18769i	0.250397	+	0.144567i	0.619946	−	0.784644i	$-0.287154\pi$
$229$	3.78920	+	2.18769i	0.250397	+	0.144567i	−0.369549	+	0.929211i	$0.620488\pi$
$230$	−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	−0.918284	−	0.395922i	$-0.870425\pi$
$233$	−12.2423	−	21.2043i	−0.802021	−	1.38914i	0.116263	−	0.993218i	$-0.462908\pi$
$234$		0			0
$235$	−21.4817	+	14.1402i	−1.40131	+	0.922402i
$236$	−7.03823			−0.458150
$237$		0			0
$238$	−3.57758	+	13.4996i	−0.231900	+	0.875048i
$239$	−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
$241$	1.82213	−	1.05201i	0.117374	−	0.0677659i	−0.440164	−	0.897918i	$-0.645080\pi$
$241$	1.82213	−	1.05201i	0.117374	−	0.0677659i	0.557538	+	0.830152i	$0.311746\pi$
$242$	−0.934810	+	1.61914i	−0.0600918	+	0.104082i
$243$		0			0
$244$		−	11.2231i		−	0.718482i
$245$	14.0284	+	6.94283i	0.896244	+	0.443561i
$246$		0			0
$247$	12.7525	+	7.36268i	0.811425	+	0.468476i
$248$			3.52560i			0.223876i
$249$		0			0
$250$	−11.0083	+	1.95369i	−0.696227	+	0.123562i
$251$	−19.3343			−1.22037			−0.610184	−	0.792260i	$-0.708904\pi$
$251$	−19.3343			−1.22037			−0.610184	+	0.792260i	$0.708904\pi$
$252$		0			0
$253$			17.2097i			1.08197i
$254$		−	4.95940i		−	0.311181i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−22.4822	−	12.9801i	−1.40240	−	0.809677i	−0.407762	−	0.913088i	$-0.633691\pi$
$257$	−22.4822	−	12.9801i	−1.40240	−	0.809677i	−0.994639	+	0.103412i	$0.967024\pi$
$258$		0			0
$259$	1.90589	+	1.89547i	0.118426	+	0.117779i
$260$	4.07312	−	8.11776i	0.252604	−	0.503442i
$261$		0			0
$262$	−4.64103	+	8.03850i	−0.286724	+	0.496620i
$263$	−3.89109	−	6.73957i	−0.239935	−	0.415579i	0.720760	−	0.693184i	$-0.243793\pi$
$263$	−3.89109	−	6.73957i	−0.239935	−	0.415579i	−0.960695	+	0.277605i	$0.910459\pi$
$264$		0			0
$265$	−25.5057	+	1.49503i	−1.56681	+	0.0918390i
$266$	6.80105	+	6.76387i	0.416999	+	0.414719i
$267$		0			0
$268$		−	6.99540i		−	0.427312i
$269$	9.76085	−	16.9063i	0.595129	−	1.03079i	−0.398399	−	0.917212i	$-0.630434\pi$
$269$	9.76085	−	16.9063i	0.595129	−	1.03079i	0.993529	−	0.113582i	$-0.0362325\pi$
$270$		0			0
$271$	−0.125260	+	0.0723187i	−0.00760898	+	0.00439305i	−0.503800	−	0.863821i	$-0.668065\pi$
$271$	−0.125260	+	0.0723187i	−0.00760898	+	0.00439305i	0.496191	+	0.868214i	$0.334732\pi$
$272$	4.57132	+	2.63925i	0.277177	+	0.160028i
$273$		0			0
$274$	0.00306228	+	0.00530403i	0.000184999	+	0.000320428i
$275$	2.09559	+	17.8143i	0.126369	+	1.07424i
$276$		0			0
$277$	−22.2251	+	12.8317i	−1.33538	+	0.770981i	−0.986118	−	0.166044i	$-0.946900\pi$
$277$	−22.2251	+	12.8317i	−1.33538	+	0.770981i	−0.349260	+	0.937026i	$0.613567\pi$
$278$	7.32549	−	4.22938i	0.439354	−	0.253661i
$279$		0			0
$280$	3.91921	−	4.43168i	0.234218	−	0.264843i
$281$	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
$283$	30.3966			1.80689			0.903444	−	0.428706i	$-0.141030\pi$
$283$	30.3966			1.80689			0.903444	+	0.428706i	$0.141030\pi$
$284$			0.828681i			0.0491732i
$285$		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
$290$	1.05711	+	18.0347i	0.0620758	+	1.05903i
$291$		0			0
$292$	3.51263	−	6.08405i	0.205561	−	0.356042i
$293$	24.1090	−	13.9193i	1.40846	−	0.813176i	0.413222	−	0.910630i	$-0.364403\pi$
$293$	24.1090	−	13.9193i	1.40846	−	0.813176i	0.995240	+	0.0974541i	$0.0310699\pi$
$294$		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
$299$	−19.4851			−1.12685
$300$		0			0
$301$	3.47409	−	13.1091i	0.200243	−	0.755597i
$302$	−2.82204	−	4.88791i	−0.162390	−	0.281268i
$303$		0			0
$304$	3.13968	−	1.81269i	0.180073	−	0.103965i
$305$	−20.9619	+	13.7980i	−1.20027	+	0.790070i
$306$		0			0
$307$	29.1963			1.66632			0.833162	−	0.553030i	$-0.186528\pi$
$307$	29.1963			1.66632			0.833162	+	0.553030i	$0.186528\pi$
$308$	−6.72983	−	6.69304i	−0.383468	−	0.381371i
$309$		0			0
$310$	6.58494	−	4.33448i	0.373999	−	0.246182i
$311$	1.53984			0.0873161			0.0436580	−	0.999047i	$-0.486099\pi$
$311$	1.53984			0.0873161			0.0436580	+	0.999047i	$0.486099\pi$
$312$		0			0
$313$	9.00202			0.508824			0.254412	−	0.967096i	$-0.418118\pi$
$313$	9.00202			0.508824			0.254412	+	0.967096i	$0.418118\pi$
$314$	−6.48693			−0.366078
$315$		0			0
$316$	0.0299868			0.00168689
$317$	−17.2577			−0.969287			−0.484644	−	0.874712i	$-0.661051\pi$
$317$	−17.2577			−0.969287			−0.484644	+	0.874712i	$0.661051\pi$
$318$		0			0
$319$	28.9836			1.62277
$320$	−1.22943	−	1.86775i	−0.0687273	−	0.104410i
$321$		0			0
$322$	−12.2688	−	3.25139i	−0.683711	−	0.181193i
$323$	19.1366			1.06479
$324$		0			0
$325$	−20.1696	+	2.37265i	−1.11881	+	0.131611i
$326$	−4.53833	+	2.62021i	−0.251355	+	0.145120i
$327$		0			0
$328$	−4.80160	−	8.31661i	−0.265124	−	0.459208i
$329$	−29.3712	+	7.95634i	−1.61929	+	0.438647i
$330$		0			0
$331$	29.0182			1.59498			0.797492	−	0.603329i	$-0.206159\pi$
$331$	29.0182			1.59498			0.797492	+	0.603329i	$0.206159\pi$
$332$	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	$0.325563\pi$
$338$	1.74884	−	3.02908i	0.0951245	−	0.164760i
$339$		0			0
$340$	−0.690658	−	11.7829i	−0.0374562	−	0.639015i
$341$	−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
$346$		−	21.6843i		−	1.16576i
$347$	−34.3492			−1.84396			−0.921982	−	0.387233i	$-0.873431\pi$
$347$	−34.3492			−1.84396			−0.921982	+	0.387233i	$0.873431\pi$
$348$		0			0
$349$	−1.95233	−	1.12718i	−0.104506	−	0.0603366i	0.446836	−	0.894616i	$-0.352551\pi$
$349$	−1.95233	−	1.12718i	−0.104506	−	0.0603366i	−0.551342	+	0.834279i	$0.685884\pi$
$350$	−13.0957	−	1.87167i	−0.699994	−	0.100045i
$351$		0			0
$352$	−3.10680	+	1.79371i	−0.165593	+	0.0956052i
$353$	−5.09123	+	2.93942i	−0.270979	+	0.156450i	−0.629332	−	0.777136i	$-0.716672\pi$
$353$	−5.09123	+	2.93942i	−0.270979	+	0.156450i	0.358354	+	0.933586i	$0.383338\pi$
$354$		0			0
$355$	1.54777	−	1.01881i	0.0821472	−	0.0540727i
$356$	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	$-0.608997\pi$
$359$	5.91330	−	3.41404i	0.312092	−	0.180186i	0.647862	+	0.761758i	$0.275663\pi$
$360$		0			0
$361$	−2.92828	+	5.07193i	−0.154120	+	0.266944i
$362$			24.0491i			1.26399i
$363$		0			0
$364$	7.57795	−	7.61961i	0.397193	−	0.399376i
$365$	−15.6820	+	0.919209i	−0.820835	+	0.0481136i
$366$		0			0
$367$	−0.284464	−	0.492706i	−0.0148489	−	0.0257190i	0.858505	−	0.512804i	$-0.171393\pi$
$367$	−0.284464	−	0.492706i	−0.0148489	−	0.0257190i	−0.873354	+	0.487085i	$0.838060\pi$
$368$	−2.39862	+	4.15452i	−0.125036	+	0.216570i
$369$		0			0
$370$	−2.03049	−	1.01881i	−0.105560	−	0.0529654i
$371$	−29.2219	−	7.74419i	−1.51712	−	0.402058i
$372$		0			0
$373$	6.58348	+	3.80098i	0.340880	+	0.196807i	0.660661	−	0.750684i	$-0.270276\pi$
$373$	6.58348	+	3.80098i	0.340880	+	0.196807i	−0.319781	+	0.947491i	$0.603609\pi$
$374$	−18.9362			−0.979169
$375$		0			0
$376$			11.5014i			0.593138i
$377$			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	$0.929685\pi$
$380$	−7.24569	−	3.63556i	−0.371696	−	0.186500i
$381$		0			0
$382$		−	3.22636i		−	0.165075i
$383$	10.4289	+	6.02112i	0.532891	+	0.307665i	0.742193	−	0.670186i	$-0.233786\pi$
$383$	10.4289	+	6.02112i	0.532891	+	0.307665i	−0.209302	+	0.977851i	$0.567119\pi$
$384$		0			0
$385$	−4.22707	+	20.7983i	−0.215431	+	1.05998i
$386$		−	24.2271i		−	1.23312i
$387$		0			0
$388$	−4.69619	+	8.13404i	−0.238413	+	0.412943i
$389$	−9.93198	+	5.73423i	−0.503571	+	0.290737i	−0.730187	−	0.683247i	$-0.760567\pi$
$389$	−9.93198	+	5.73423i	−0.503571	+	0.290737i	0.226616	+	0.973984i	$0.427234\pi$
$390$		0			0
$391$	−21.9297	+	12.6611i	−1.10903	+	0.640299i
$392$	6.04290	−	3.53318i	0.305213	−	0.178452i
$393$		0			0
$394$	−6.89656			−0.347444
$395$	−0.0368667	−	0.0560078i	−0.00185496	−	0.00281806i
$396$		0			0
$397$	−1.89421	−	3.28087i	−0.0950678	−	0.164662i	0.814569	−	0.580067i	$-0.196973\pi$
$397$	−1.89421	−	3.28087i	−0.0950678	−	0.164662i	−0.909637	+	0.415404i	$0.863640\pi$
$398$	14.5256	+	8.38638i	0.728104	+	0.420371i
$399$		0			0
$400$	−1.97699	+	4.59255i	−0.0988497	+	0.229627i
$401$	−10.0319	−	5.79192i	−0.500970	−	0.289235i	0.228144	−	0.973627i	$-0.426734\pi$
$401$	−10.0319	−	5.79192i	−0.500970	−	0.289235i	−0.729114	+	0.684392i	$0.760068\pi$
$402$		0			0
$403$	12.4015	−	7.16002i	0.617764	−	0.356666i
$404$	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
$409$			30.2706i			1.49679i	0.663256	+	0.748393i	$0.269174\pi$
$409$			30.2706i			1.49679i	−0.663256	+	0.748393i	$0.730826\pi$
$410$	−9.63012	+	19.1929i	−0.475598	+	0.947869i
$411$		0			0
$412$	−0.292115	+	0.505958i	−0.0143915	+	0.0249268i
$413$	4.86886	+	17.9736i	0.239581	+	0.884424i
$414$		0			0
$415$	−1.04207	−	17.7782i	−0.0511534	−	0.872695i
$416$	−2.03087	−	3.51756i	−0.0995715	−	0.172463i
$417$		0			0
$418$	−6.50291	+	11.2634i	−0.318067	+	0.550909i
$419$	10.7319	+	18.5882i	0.524287	+	0.908091i	0.999600	+	0.0282749i	$0.00900138\pi$
$419$	10.7319	+	18.5882i	0.524287	+	0.908091i	−0.475313	+	0.879817i	$0.657665\pi$
$420$		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
$425$	−21.1583	+	15.7762i	−1.02633	+	0.765258i
$426$		0			0
$427$	−28.6605	+	7.76380i	−1.38698	+	0.375717i
$428$	1.34287	+	2.32592i	0.0649101	+	0.112428i
$429$		0			0
$430$	0.670681	+	11.4420i	0.0323431	+	0.551784i
$431$	1.05463	+	0.608890i	0.0507997	+	0.0293292i	0.525185	−	0.850988i	$-0.323996\pi$
$431$	1.05463	+	0.608890i	0.0507997	+	0.0293292i	−0.474385	+	0.880317i	$0.657330\pi$
$432$		0			0
$433$	6.29897			0.302709			0.151355	−	0.988480i	$-0.451636\pi$
$433$	6.29897			0.302709			0.151355	+	0.988480i	$0.451636\pi$
$434$	9.00336	−	2.43891i	0.432175	−	0.117072i
$435$		0			0
$436$	−0.618180	+	1.07072i	−0.0296054	+	0.0512781i
$437$			17.3918i			0.831964i
$438$		0			0
$439$		−	36.3857i		−	1.73659i	−0.496046	−	0.868296i	$-0.665215\pi$
$439$		−	36.3857i		−	1.73659i	0.496046	−	0.868296i	$-0.334785\pi$
$440$	7.16981	+	3.59749i	0.341807	+	0.171503i
$441$		0			0
$442$		−	21.4399i		−	1.01979i
$443$	11.5534			0.548917			0.274459	−	0.961599i	$-0.411501\pi$
$443$	11.5534			0.548917			0.274459	+	0.961599i	$0.411501\pi$
$444$		0			0
$445$	1.25353	−	2.49830i	0.0594231	−	0.118431i
$446$	−8.37432	+	14.5048i	−0.396536	+	0.686820i
$447$		0			0
$448$	−0.691773	−	2.55371i	−0.0326832	−	0.120652i
$449$		−	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
$452$	−5.41347	−	9.37640i	−0.254628	−	0.441029i
$453$		0			0
$454$	5.49698	−	3.17368i	0.257986	−	0.148948i
$455$	−23.5481	−	4.78594i	−1.10395	−	0.224369i
$456$		0			0
$457$		−	3.77155i		−	0.176426i	−0.996102	−	0.0882129i	$-0.971884\pi$
$457$		−	3.77155i		−	0.176426i	0.996102	−	0.0882129i	$-0.0281156\pi$
$458$	−3.78920	−	2.18769i	−0.177058	−	0.102224i
$459$		0			0
$460$	10.7086	−	0.627687i	0.499289	−	0.0292661i
$461$	1.39131	−	2.40982i	0.0647998	−	0.112237i	−0.831805	−	0.555067i	$-0.812692\pi$
$461$	1.39131	−	2.40982i	0.0647998	−	0.112237i	0.896605	+	0.442831i	$0.146026\pi$
$462$		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	$0.415633\pi$
$464$	6.99680	+	4.03961i	0.324818	+	0.187534i
$465$		0			0
$466$	12.2423	+	21.2043i	0.567114	+	0.982271i
$467$	−16.4814	+	9.51552i	−0.762667	+	0.440326i	−0.830252	−	0.557388i	$-0.811804\pi$
$467$	−16.4814	+	9.51552i	−0.762667	+	0.440326i	0.0675856	+	0.997713i	$0.478470\pi$
$468$		0			0
$469$	−17.8642	+	4.83923i	−0.824894	+	0.223455i
$470$	21.4817	−	14.1402i	0.990878	−	0.652237i
$471$		0			0
$472$	7.03823			0.323961
$473$	18.3885			0.845504
$474$		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
$479$	−0.146168	−	0.253170i	−0.00667858	−	0.0115676i	0.862667	−	0.505773i	$-0.168793\pi$
$479$	−0.146168	−	0.253170i	−0.00667858	−	0.0115676i	−0.869345	+	0.494205i	$0.835459\pi$
$480$		0			0
$481$	−3.57371	−	2.06328i	−0.162947	−	0.0940775i
$482$	−1.82213	+	1.05201i	−0.0829960	+	0.0479177i
$483$		0			0
$484$	0.934810	−	1.61914i	0.0424913	−	0.0735972i
$485$	20.9660	−	1.22893i	0.952018	−	0.0558030i
$486$		0			0
$487$	−17.4211	−	10.0581i	−0.789425	−	0.455775i	0.0503353	−	0.998732i	$-0.483971\pi$
$487$	−17.4211	−	10.0581i	−0.789425	−	0.455775i	−0.839760	+	0.542958i	$0.817304\pi$
$488$			11.2231i			0.508044i
$489$		0			0
$490$	−14.0284	−	6.94283i	−0.633740	−	0.313645i
$491$	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
$493$	21.3231	+	36.9326i	0.960343	+	1.66336i
$494$	−12.7525	−	7.36268i	−0.573764	−	0.331263i
$495$		0			0
$496$		−	3.52560i		−	0.158304i
$497$	2.11621	−	0.573259i	0.0949252	−	0.0257142i
$498$		0			0
$499$	−5.43038	+	9.40569i	−0.243097	+	0.421057i	−0.961595	−	0.274473i	$-0.911497\pi$
$499$	−5.43038	+	9.40569i	−0.243097	+	0.421057i	0.718498	+	0.695529i	$0.244830\pi$
$500$	11.0083	−	1.95369i	0.492307	−	0.0873718i
$501$		0			0
$502$	19.3343			0.862930
$503$		−	32.7910i		−	1.46208i	−0.682335	−	0.731040i	$-0.739035\pi$
$503$		−	32.7910i		−	1.46208i	0.682335	−	0.731040i	$-0.260965\pi$
$504$		0			0
$505$	10.9229	−	21.7695i	0.486064	−	0.968728i
$506$		−	17.2097i		−	0.765065i
$507$		0			0
$508$			4.95940i			0.220038i
$509$	5.90279	−	10.2239i	0.261637	−	0.453168i	−0.705040	−	0.709167i	$-0.749071\pi$
$509$	5.90279	−	10.2239i	0.261637	−	0.453168i	0.966677	+	0.255999i	$0.0824045\pi$
$510$		0			0
$511$	−17.9668	−	4.76146i	−0.794806	−	0.210635i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	22.4822	+	12.9801i	0.991647	+	0.572528i
$515$	1.30414	−	0.0764428i	0.0574673	−	0.00336847i
$516$		0			0
$517$	−20.6302	−	35.7325i	−0.907313	−	1.57151i
$518$	−1.90589	−	1.89547i	−0.0837400	−	0.0832822i
$519$		0			0
$520$	−4.07312	+	8.11776i	−0.178618	+	0.355987i
$521$	−8.58074	+	14.8623i	−0.375929	+	0.651128i	−0.990466	−	0.137760i	$-0.956010\pi$
$521$	−8.58074	+	14.8623i	−0.375929	+	0.651128i	0.614537	+	0.788888i	$0.289343\pi$
$522$		0			0
$523$	19.0538	+	33.0022i	0.833166	+	1.44309i	0.895515	+	0.445031i	$0.146807\pi$
$523$	19.0538	+	33.0022i	0.833166	+	1.44309i	−0.0623491	+	0.998054i	$0.519859\pi$
$524$	4.64103	−	8.03850i	0.202744	−	0.351163i
$525$		0			0
$526$	3.89109	+	6.73957i	0.169660	+	0.293859i
$527$	9.30493	−	16.1166i	0.405329	−	0.702051i
$528$		0			0
$529$	−0.00671290	−	0.0116271i	−0.000291865	−	0.000505525i
$530$	25.5057	−	1.49503i	1.10790	−	0.0649400i
$531$		0			0
$532$	−6.80105	−	6.76387i	−0.294863	−	0.293251i
$533$	−19.5028	+	33.7799i	−0.844760	+	1.46317i
$534$		0			0
$535$	2.69327	−	5.36771i	0.116440	−	0.232066i
$536$			6.99540i			0.302155i
$537$		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	0.999994	−	0.00349884i	$-0.00111372\pi$
$541$	11.5592	+	20.0210i	0.496967	+	0.860772i	−0.503027	+	0.864271i	$0.667780\pi$
$542$	0.125260	−	0.0723187i	0.00538036	−	0.00310635i
$543$		0			0
$544$	−4.57132	−	2.63925i	−0.195994	−	0.113157i
$545$	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
$550$	−2.09559	−	17.8143i	−0.0893561	−	0.759604i
$551$	29.2903			1.24781
$552$		0			0
$553$	−0.0207440	−	0.0765776i	−0.000882126	−	0.00325641i
$554$	22.2251	−	12.8317i	0.944255	−	0.545166i
$555$		0			0
$556$	−7.32549	+	4.22938i	−0.310670	+	0.179365i
$557$	−22.4182	+	38.8295i	−0.949891	+	1.64526i	−0.204242	+	0.978920i	$0.565473\pi$
$557$	−22.4182	+	38.8295i	−0.949891	+	1.64526i	−0.745649	+	0.666339i	$0.767860\pi$
$558$		0			0
$559$			20.8197i			0.880580i
$560$	−3.91921	+	4.43168i	−0.165617	+	0.187273i
$561$		0			0
$562$	−16.2907	−	9.40542i	−0.687180	−	0.396744i
$563$			24.6532i			1.03901i	0.854468	+	0.519504i	$0.173883\pi$
$563$			24.6532i			1.03901i	−0.854468	+	0.519504i	$0.826117\pi$
$564$		0			0
$565$	−10.8573	+	21.6387i	−0.456770	+	0.910345i
$566$	−30.3966			−1.27766
$567$		0			0
$568$		−	0.828681i		−	0.0347707i
$569$			37.5376i			1.57366i	0.617171	+	0.786829i	$0.288279\pi$
$569$			37.5376i			1.57366i	−0.617171	+	0.786829i	$0.711721\pi$
$570$		0			0
$571$	−9.36824			−0.392049			−0.196024	−	0.980599i	$-0.562803\pi$
$571$	−9.36824			−0.392049			−0.196024	+	0.980599i	$0.562803\pi$
$572$	12.6190	+	7.28558i	0.527627	+	0.304626i
$573$		0			0
$574$	−17.9166	+	18.0151i	−0.747825	+	0.751936i
$575$	−14.3378	−	19.2292i	−0.597928	−	0.801914i
$576$		0			0
$577$	3.63671	−	6.29897i	0.151398	−	0.262230i	−0.780343	−	0.625351i	$-0.784956\pi$
$577$	3.63671	−	6.29897i	0.151398	−	0.262230i	0.931742	+	0.363122i	$0.118289\pi$
$578$	−5.43128	−	9.40726i	−0.225912	−	0.391290i
$579$		0			0
$580$	−1.05711	−	18.0347i	−0.0438942	−	0.748851i
$581$	5.39790	−	20.3684i	0.223943	−	0.845023i
$582$		0			0
$583$		−	40.9903i		−	1.69764i
$584$	−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	0.456367	−	0.889792i	$-0.349150\pi$
$587$	−2.08437	−	1.20341i	−0.0860313	−	0.0496702i	−0.542398	+	0.840121i	$0.682484\pi$
$588$		0			0
$589$	−6.39083	−	11.0692i	−0.263330	−	0.456100i
$590$	−8.65302	−	13.1457i	−0.356239	−	0.541198i
$591$		0			0
$592$	−0.879847	+	0.507980i	−0.0361615	+	0.0208779i
$593$	33.2409	−	19.1916i	1.36504	−	0.788106i	0.374751	−	0.927126i	$-0.377728\pi$
$593$	33.2409	−	19.1916i	1.36504	−	0.788106i	0.990290	+	0.139019i	$0.0443950\pi$
$594$		0			0
$595$	−29.6123	+	9.91481i	−1.21398	+	0.406467i
$596$	−15.0057	−	8.66353i	−0.614656	−	0.354872i
$597$		0			0
$598$	19.4851			0.796804
$599$			18.2983i			0.747650i	0.927499	+	0.373825i	$0.121954\pi$
$599$			18.2983i			0.747650i	−0.927499	+	0.373825i	$0.878046\pi$
$600$		0			0
$601$	20.5159	+	11.8449i	0.836862	+	0.483163i	0.856196	−	0.516650i	$-0.172821\pi$
$601$	20.5159	+	11.8449i	0.836862	+	0.483163i	−0.0193342	+	0.999813i	$0.506155\pi$
$602$	−3.47409	+	13.1091i	−0.141594	+	0.534288i
$603$		0			0
$604$	2.82204	+	4.88791i	0.114827	+	0.198886i
$605$	−4.17343	+	0.244628i	−0.169674	+	0.00994553i
$606$		0			0
$607$	1.20113	−	2.08041i	0.0487522	−	0.0844412i	−0.840620	−	0.541626i	$-0.817809\pi$
$607$	1.20113	−	2.08041i	0.0487522	−	0.0844412i	0.889372	+	0.457185i	$0.151142\pi$
$608$	−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	$-0.606206\pi$
$613$	−32.4221	−	18.7189i	−1.30951	−	0.756049i	−0.982015	+	0.188803i	$0.939539\pi$
$614$	−29.1963			−1.17827
$615$		0			0
$616$	6.72983	+	6.69304i	0.271152	+	0.269670i
$617$	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
$619$	4.75647	−	2.74615i	0.191179	−	0.110377i	−0.401356	−	0.915922i	$-0.631461\pi$
$619$	4.75647	−	2.74615i	0.191179	−	0.110377i	0.592534	+	0.805545i	$0.298127\pi$
$620$	−6.58494	+	4.33448i	−0.264458	+	0.174077i
$621$		0			0
$622$	−1.53984			−0.0617418
$623$	2.33216	−	2.34498i	0.0934362	−	0.0939498i
$624$		0			0
$625$	−17.1830	−	18.1589i	−0.687320	−	0.726355i
$626$	−9.00202			−0.359793
$627$		0			0
$628$	6.48693			0.258857
$629$	−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	$0.561983\pi$
$632$	−0.0299868			−0.00119281
$633$		0			0
$634$	17.2577			0.685390
$635$	9.26293	−	6.09725i	0.367588	−	0.241962i
$636$		0			0
$637$	−24.7005	−	14.0809i	−0.978670	−	0.557905i
$638$	−28.9836			−1.14747
$639$		0			0
$640$	1.22943	+	1.86775i	0.0485976	+	0.0738294i
$641$	27.9609	−	16.1432i	1.10439	−	0.637619i	0.167018	−	0.985954i	$-0.446586\pi$
$641$	27.9609	−	16.1432i	1.10439	−	0.637619i	0.937370	+	0.348335i	$0.113253\pi$
$642$		0			0
$643$	−14.1941	−	24.5848i	−0.559759	−	0.969532i	−0.997516	−	0.0704382i	$-0.977560\pi$
$643$	−14.1941	−	24.5848i	−0.559759	−	0.969532i	0.437757	−	0.899093i	$-0.355773\pi$
$644$	12.2688	+	3.25139i	0.483457	+	0.128123i
$645$		0			0
$646$	−19.1366			−0.752920
$647$	3.35941	+	1.93956i	0.132072	+	0.0762519i	0.564580	−	0.825378i	$-0.309038\pi$
$647$	3.35941	+	1.93956i	0.132072	+	0.0762519i	−0.432508	+	0.901630i	$0.642371\pi$
$648$		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
$653$	10.5947	−	18.3505i	0.414602	−	0.718111i	−0.580785	−	0.814057i	$-0.697254\pi$
$653$	10.5947	−	18.3505i	0.414602	−	0.718111i	0.995387	+	0.0959461i	$0.0305876\pi$
$654$		0			0
$655$	−20.7197	+	1.21450i	−0.809587	+	0.0474543i
$656$	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
$661$		−	21.7460i		−	0.845820i	−0.906172	−	0.422910i	$-0.861009\pi$
$661$		−	21.7460i		−	0.845820i	0.906172	−	0.422910i	$-0.138991\pi$
$662$	−29.0182			−1.12782
$663$		0			0
$664$	−6.89727	−	3.98214i	−0.267666	−	0.154537i
$665$	−4.27180	+	21.0184i	−0.165653	+	0.815058i
$666$		0			0
$667$	−33.5653	+	19.3789i	−1.29965	+	0.750355i
$668$	18.8867	−	10.9043i	0.730750	−	0.421898i
$669$		0			0
$670$	13.0657	−	8.60037i	0.504771	−	0.332261i
$671$	−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
$677$			10.7467i			0.413027i	0.978444	+	0.206514i	$0.0662118\pi$
$677$			10.7467i			0.413027i	−0.978444	+	0.206514i	$0.933788\pi$
$678$		0			0
$679$	24.0207	+	6.36581i	0.921830	+	0.244298i
$680$	0.690658	+	11.7829i	0.0264855	+	0.451852i
$681$		0			0
$682$	6.32391	+	10.9533i	0.242155	+	0.419425i
$683$	6.84384	−	11.8539i	0.261872	−	0.453576i	−0.704867	−	0.709339i	$-0.748993\pi$
$683$	6.84384	−	11.8539i	0.261872	−	0.453576i	0.966739	+	0.255763i	$0.0823267\pi$
$684$		0			0
$685$	−0.00614174	+	0.0122405i	−0.000234664	+	0.000467686i
$686$	−13.2030	−	12.9877i	−0.504094	−	0.495872i
$687$		0			0
$688$	4.43909	+	2.56291i	0.169239	+	0.0977100i
$689$	46.4098			1.76807
$690$		0			0
$691$		−	28.1003i		−	1.06899i	−0.845173	−	0.534493i	$-0.820503\pi$
$691$		−	28.1003i		−	1.06899i	0.845173	−	0.534493i	$-0.179497\pi$
$692$			21.6843i			0.824314i
$693$		0			0
$694$	34.3492			1.30388
$695$	16.9056	+	8.48247i	0.641267	+	0.321759i
$696$		0			0
$697$			50.6904i			1.92004i
$698$	1.95233	+	1.12718i	0.0738969	+	0.0426644i
$699$		0			0
$700$	13.0957	+	1.87167i	0.494970	+	0.0707426i
$701$			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
$704$	3.10680	−	1.79371i	0.117092	−	0.0676031i
$705$		0			0
$706$	5.09123	−	2.93942i	0.191611	−	0.110627i
$707$	20.3218	−	20.4336i	0.764282	−	0.768483i
$708$		0			0
$709$	−32.5456			−1.22227			−0.611137	−	0.791525i	$-0.709288\pi$
$709$	−32.5456			−1.22227			−0.611137	+	0.791525i	$0.709288\pi$
$710$	−1.54777	+	1.01881i	−0.0580868	+	0.0382352i
$711$		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
$716$	−15.1142	−	8.72620i	−0.564845	−	0.326113i
$717$		0			0
$718$	−5.91330	+	3.41404i	−0.220682	+	0.127411i
$719$	−1.35013	−	2.33850i	−0.0503515	−	0.0872114i	0.839751	−	0.542971i	$-0.182701\pi$
$719$	−1.35013	−	2.33850i	−0.0503515	−	0.0872114i	−0.890103	+	0.455760i	$0.849367\pi$
$720$		0			0
$721$	1.49415	+	0.395970i	0.0556450	+	0.0147467i
$722$	2.92828	−	5.07193i	0.108979	−	0.188758i
$723$		0			0
$724$		−	24.0491i		−	0.893776i
$725$	−32.3847	+	24.1469i	−1.20274	+	0.896793i
$726$		0			0
$727$	13.0226	−	22.5558i	0.482982	−	0.836549i	−0.516827	−	0.856090i	$-0.672887\pi$
$727$	13.0226	−	22.5558i	0.482982	−	0.836549i	0.999809	+	0.0195409i	$0.00622045\pi$
$728$	−7.57795	+	7.61961i	−0.280858	+	0.282401i
$729$		0			0
$730$	15.6820	−	0.919209i	0.580418	−	0.0340214i
$731$	13.5283	+	23.4317i	0.500363	+	0.866654i
$732$		0			0
$733$	−9.72720	+	16.8480i	−0.359282	+	0.622295i	−0.987841	−	0.155467i	$-0.950312\pi$
$733$	−9.72720	+	16.8480i	−0.359282	+	0.622295i	0.628559	+	0.777762i	$0.283645\pi$
$734$	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	−0.746728	−	0.665130i	$-0.768376\pi$
$739$	5.50909	−	9.54203i	0.202655	−	0.351009i	0.949383	+	0.314120i	$0.101710\pi$
$740$	2.03049	+	1.01881i	0.0746424	+	0.0374522i
$741$		0			0
$742$	29.2219	+	7.74419i	1.07277	+	0.284298i
$743$	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
$745$	2.26713	+	38.6781i	0.0830613	+	1.41706i
$746$	−6.58348	−	3.80098i	−0.241039	−	0.139164i
$747$		0			0
$748$	18.9362			0.692377
$749$	5.01077	−	5.03831i	0.183090	−	0.184096i
$750$		0			0
$751$	−7.79754	+	13.5057i	−0.284536	+	0.492831i	−0.972497	−	0.232917i	$-0.925173\pi$
$751$	−7.79754	+	13.5057i	−0.284536	+	0.492831i	0.687960	+	0.725748i	$0.258506\pi$
$752$		−	11.5014i		−	0.419412i
$753$		0			0
$754$		−	32.8156i		−	1.19507i
$755$	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	$0.988417\pi$
$758$	37.9897			1.37985
$759$		0			0
$760$	7.24569	+	3.63556i	0.262829	+	0.131875i
$761$	8.46103	−	14.6549i	0.306712	−	0.531241i	−0.670929	−	0.741522i	$-0.734104\pi$
$761$	8.46103	−	14.6549i	0.306712	−	0.531241i	0.977641	+	0.210281i	$0.0674378\pi$
$762$		0			0
$763$	3.16195	+	0.837960i	0.114470	+	0.0303362i
$764$			3.22636i			0.116726i
$765$		0			0
$766$	−10.4289	−	6.02112i	−0.376811	−	0.217552i
$767$	−14.2937	−	24.7574i	−0.516116	−	0.893939i
$768$		0			0
$769$	10.5316	−	6.08042i	0.379779	−	0.219265i	−0.297943	−	0.954584i	$-0.596301\pi$
$769$	10.5316	−	6.08042i	0.379779	−	0.219265i	0.677722	+	0.735318i	$0.262967\pi$
$770$	4.22707	−	20.7983i	0.152333	−	0.749518i
$771$		0			0
$772$			24.2271i			0.871951i
$773$	−19.6768	−	11.3604i	−0.707726	−	0.408606i	0.102492	−	0.994734i	$-0.467318\pi$
$773$	−19.6768	−	11.3604i	−0.707726	−	0.408606i	−0.810219	+	0.586128i	$0.800652\pi$
$774$		0			0
$775$	16.1915	+	6.97008i	0.581615	+	0.250373i
$776$	4.69619	−	8.13404i	0.168583	−	0.291995i
$777$		0			0
$778$	9.93198	−	5.73423i	0.356079	−	0.205582i
$779$	30.1509	+	17.4077i	1.08027	+	0.623694i
$780$		0			0
$781$	1.48642	+	2.57455i	0.0531882	+	0.0921246i
$782$	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
$787$	−28.3169			−1.00939			−0.504695	−	0.863298i	$-0.668395\pi$
$787$	−28.3169			−1.00939			−0.504695	+	0.863298i	$0.668395\pi$
$788$	6.89656			0.245680
$789$		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
$794$	1.89421	+	3.28087i	0.0672231	+	0.116434i
$795$		0			0
$796$	−14.5256	−	8.38638i	−0.514847	−	0.297247i
$797$	2.25578	−	1.30238i	0.0799040	−	0.0461326i	−0.459516	−	0.888170i	$-0.651977\pi$
$797$	2.25578	−	1.30238i	0.0799040	−	0.0461326i	0.539420	+	0.842037i	$0.318644\pi$
$798$		0			0
$799$	30.3550	−	52.5764i	1.07388	−	1.86002i
$800$	1.97699	−	4.59255i	0.0698973	−	0.162371i
$801$		0			0
$802$	10.0319	+	5.79192i	0.354239	+	0.204520i
$803$		−	25.2026i		−	0.889379i
$804$		0			0
$805$	−9.01082	−	26.9124i	−0.317590	−	0.948536i
$806$	−12.4015	+	7.16002i	−0.436825	+	0.252201i
$807$		0			0
$808$	−5.44619	−	9.43308i	−0.191596	−	0.331855i
$809$	21.2398	+	12.2628i	0.746751	+	0.431137i	0.824519	−	0.565835i	$-0.191446\pi$
$809$	21.2398	+	12.2628i	0.746751	+	0.431137i	−0.0777677	+	0.996972i	$0.524779\pi$
$810$		0			0
$811$			9.73361i			0.341793i	0.985289	+	0.170897i	$0.0546664\pi$
$811$			9.73361i			0.341793i	−0.985289	+	0.170897i	$0.945334\pi$
$812$	5.47580	−	20.6623i	0.192163	−	0.725105i
$813$		0			0
$814$	1.82234	−	3.15639i	0.0638730	−	0.110631i
$815$	−10.4735	−	5.25511i	−0.366869	−	0.184078i
$816$		0			0
$817$	18.5831			0.650140
$818$		−	30.2706i		−	1.05839i
$819$		0			0
$820$	9.63012	−	19.1929i	0.336298	−	0.670245i
$821$			2.04290i			0.0712977i	0.999364	+	0.0356488i	$0.0113498\pi$
$821$			2.04290i			0.0712977i	−0.999364	+	0.0356488i	$0.988650\pi$
$822$		0			0
$823$			13.0612i			0.455284i	0.973745	+	0.227642i	$0.0731016\pi$
$823$			13.0612i			0.455284i	−0.973745	+	0.227642i	$0.926898\pi$
$824$	0.292115	−	0.505958i	0.0101763	−	0.0176259i
$825$		0			0
$826$	−4.86886	−	17.9736i	−0.169409	−	0.625382i
$827$	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	−0.0350576	−	0.999385i	$-0.511161\pi$
$829$	−26.4337	−	15.2615i	−0.918080	−	0.530053i	−0.883022	+	0.469332i	$0.844495\pi$
$830$	1.04207	+	17.7782i	0.0361709	+	0.617089i
$831$		0			0
$832$	2.03087	+	3.51756i	0.0704076	+	0.121950i
$833$	−36.9489	+	0.202548i	−1.28021	+	0.00701787i
$834$		0			0
$835$	−43.5864	−	21.8697i	−1.50837	−	0.756831i
$836$	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	−0.722250	−	0.691632i	$-0.756892\pi$
$839$	6.88932	−	11.9327i	0.237846	−	0.411961i	0.960096	+	0.279671i	$0.0902253\pi$
$840$		0			0
$841$	18.1368	+	31.4139i	0.625408	+	1.08324i
$842$	12.8685	−	22.2889i	0.443478	−	0.768127i
$843$		0			0
$844$	2.37689	+	4.11690i	0.0818161	+	0.141710i
$845$	7.80766	−	0.457650i	0.268592	−	0.0157436i
$846$		0			0
$847$	−4.78149	−	1.26716i	−0.164294	−	0.0435401i
$848$	5.71305	−	9.89529i	0.196187	−	0.339806i
$849$		0			0
$850$	21.1583	−	15.7762i	0.725725	−	0.541119i
$851$		−	4.87380i		−	0.167072i
$852$		0			0
$853$	−2.66904	+	4.62291i	−0.0913862	+	0.158286i	−0.908095	−	0.418765i	$-0.862463\pi$
$853$	−2.66904	+	4.62291i	−0.0913862	+	0.158286i	0.816708	+	0.577051i	$0.195796\pi$
$854$	28.6605	−	7.76380i	0.980741	−	0.265672i
$855$		0			0
$856$	−1.34287	−	2.32592i	−0.0458984	−	0.0794983i
$857$	−32.1904	+	18.5851i	−1.09960	+	0.634856i	−0.936117	−	0.351690i	$-0.885607\pi$
$857$	−32.1904	+	18.5851i	−1.09960	+	0.634856i	−0.163486	+	0.986546i	$0.552274\pi$
$858$		0			0
$859$	33.7048	+	19.4595i	1.14999	+	0.663949i	0.948885	−	0.315621i	$-0.102213\pi$
$859$	33.7048	+	19.4595i	1.14999	+	0.663949i	0.201107	+	0.979569i	$0.435546\pi$
$860$	−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	0.820541	−	0.571588i	$-0.193672\pi$
$863$	−2.48936	−	4.31171i	−0.0847390	−	0.146772i	−0.905280	+	0.424816i	$0.860339\pi$
$864$		0			0
$865$	40.5009	−	26.6594i	1.37707	−	0.906446i
$866$	−6.29897			−0.214048
$867$		0			0
$868$	−9.00336	+	2.43891i	−0.305594	+	0.0827821i
$869$	0.0931629	−	0.0537876i	0.00316034	−	0.00182462i
$870$		0			0
$871$	24.6068	−	14.2067i	0.833768	−	0.481376i
$872$	0.618180	−	1.07072i	0.0209342	−	0.0362591i
$873$		0			0
$874$		−	17.3918i		−	0.588287i
$875$	−12.6044	−	26.7606i	−0.426107	−	0.904673i
$876$		0			0
$877$	39.7198	+	22.9323i	1.34124	+	0.774367i	0.986990	−	0.160782i	$-0.0514017\pi$
$877$	39.7198	+	22.9323i	1.34124	+	0.774367i	0.354253	+	0.935149i	$0.384735\pi$
$878$			36.3857i			1.22796i
$879$		0			0
$880$	−7.16981	−	3.59749i	−0.241694	−	0.121271i
$881$	−4.17555			−0.140678			−0.0703390	−	0.997523i	$-0.522408\pi$
$881$	−4.17555			−0.140678			−0.0703390	+	0.997523i	$0.522408\pi$
$882$		0			0
$883$			9.11973i			0.306903i	0.988156	+	0.153452i	$0.0490390\pi$
$883$			9.11973i			0.306903i	−0.988156	+	0.153452i	$0.950961\pi$
$884$			21.4399i			0.721101i
$885$		0			0
$886$	−11.5534			−0.388143
$887$	−6.54685	−	3.77983i	−0.219822	−	0.126914i	0.386046	−	0.922480i	$-0.373841\pi$
$887$	−6.54685	−	3.77983i	−0.219822	−	0.126914i	−0.605868	+	0.795565i	$0.707174\pi$
$888$		0			0
$889$	12.6649	−	3.43078i	0.424767	−	0.115065i
$890$	−1.25353	+	2.49830i	−0.0420185	+	0.0837430i
$891$		0			0
$892$	8.37432	−	14.5048i	0.280393	−	0.485655i
$893$	−20.8485	−	36.1106i	−0.697668	−	1.20840i
$894$		0			0
$895$	2.28353	+	38.9579i	0.0763301	+	1.30222i
$896$	0.691773	+	2.55371i	0.0231105	+	0.0853136i
$897$		0			0
$898$			8.35607i			0.278846i
$899$	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
$905$	−44.9177	+	29.5667i	−1.49311	+	0.982830i
$906$		0			0
$907$	14.6018	−	8.43037i	0.484846	−	0.279926i	−0.237588	−	0.971366i	$-0.576357\pi$
$907$	14.6018	−	8.43037i	0.484846	−	0.279926i	0.722434	+	0.691440i	$0.243023\pi$
$908$	−5.49698	+	3.17368i	−0.182424	+	0.105322i
$909$		0			0
$910$	23.5481	+	4.78594i	0.780612	+	0.158653i
$911$	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
$913$	28.5713			0.945571
$914$			3.77155i			0.124752i
$915$		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	0.687282	−	0.726390i	$-0.258804\pi$
$919$	−8.65286	−	14.9872i	−0.285432	−	0.494382i	−0.972714	+	0.232009i	$0.925470\pi$
$920$	−10.7086	+	0.627687i	−0.353051	+	0.0206942i
$921$		0			0
$922$	−1.39131	+	2.40982i	−0.0458204	+	0.0793632i
$923$	−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
$929$	−10.7008			−0.351083			−0.175542	−	0.984472i	$-0.556168\pi$
$929$	−10.7008			−0.351083			−0.175542	+	0.984472i	$0.556168\pi$
$930$		0			0
$931$	−12.5682	+	22.0470i	−0.411906	+	0.722561i
$932$	−12.2423	−	21.2043i	−0.401010	−	0.694570i
$933$		0			0
$934$	16.4814	−	9.51552i	0.539287	−	0.311357i
$935$	−23.2808	−	35.3682i	−0.761364	−	1.15666i
$936$		0			0
$937$	−12.8760			−0.420639			−0.210320	−	0.977633i	$-0.567450\pi$
$937$	−12.8760			−0.420639			−0.210320	+	0.977633i	$0.567450\pi$
$938$	17.8642	−	4.83923i	0.583288	−	0.158006i
$939$		0			0
$940$	−21.4817	+	14.1402i	−0.700656	+	0.461201i
$941$	33.7847			1.10135			0.550675	−	0.834720i	$-0.314370\pi$
$941$	33.7847			1.10135			0.550675	+	0.834720i	$0.314370\pi$
$942$		0			0
$943$	−46.0687			−1.50020
$944$	−7.03823			−0.229075
$945$		0			0
$946$	−18.3885			−0.597862
$947$	21.1866			0.688472			0.344236	−	0.938883i	$-0.388138\pi$
$947$	21.1866			0.688472			0.344236	+	0.938883i	$0.388138\pi$
$948$		0			0
$949$	28.5347			0.926276
$950$	−2.11776	−	18.0028i	−0.0687093	−	0.584088i
$951$		0			0
$952$	−3.57758	+	13.4996i	−0.115950	+	0.437524i
$953$	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
$955$	6.02604	−	3.96659i	0.194998	−	0.128356i
$956$	−2.10722	+	1.21660i	−0.0681524	+	0.0393478i
$957$		0			0
$958$	0.146168	+	0.253170i	0.00472247	+	0.00817956i
$959$	−0.0114266	+	0.0114894i	−0.000368983	+	0.000371011i
$960$		0			0
$961$	18.5702			0.599038
$962$	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	$-0.0191563\pi$
$968$	−0.934810	+	1.61914i	−0.0300459	+	0.0520411i
$969$		0			0
$970$	−20.9660	+	1.22893i	−0.673178	+	0.0394586i
$971$	28.9188	+	50.0888i	0.928047	+	1.60743i	0.786586	+	0.617481i	$0.211847\pi$
$971$	28.9188	+	50.0888i	0.928047	+	1.60743i	0.141462	+	0.989944i	$0.454820\pi$
$972$		0			0
$973$	15.8682	+	15.7814i	0.508711	+	0.505930i
$974$	17.4211	+	10.0581i	0.558208	+	0.322281i
$975$		0			0
$976$		−	11.2231i		−	0.359241i
$977$	39.0804			1.25029			0.625146	−	0.780508i	$-0.285039\pi$
$977$	39.0804			1.25029			0.625146	+	0.780508i	$0.285039\pi$
$978$		0			0
$979$	3.88358	+	2.24219i	0.124120	+	0.0716606i
$980$	14.0284	+	6.94283i	0.448122	+	0.221781i
$981$		0			0
$982$	−0.00977625	+	0.00564432i	−0.000311973	+	0.000180118i
$983$	−13.8267	+	7.98287i	−0.441005	+	0.254614i	−0.704024	−	0.710177i	$-0.748615\pi$
$983$	−13.8267	+	7.98287i	−0.441005	+	0.254614i	0.263019	+	0.964791i	$0.415282\pi$
$984$		0			0
$985$	−8.47885	−	12.8811i	−0.270159	−	0.410425i
$986$	−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	−0.487376	−	0.873192i	$-0.662046\pi$
$991$	16.1342	−	27.9452i	0.512519	−	0.887709i	0.999895	−	0.0145163i	$-0.00462085\pi$
$992$			3.52560i			0.111938i
$993$		0			0
$994$	−2.11621	+	0.573259i	−0.0671223	+	0.0181827i
$995$	2.19461	+	37.4407i	0.0695737	+	1.18695i
$996$		0			0
$997$	−19.8570	−	34.3933i	−0.628877	−	1.08925i	−0.987777	−	0.155871i	$-0.950182\pi$
$997$	−19.8570	−	34.3933i	−0.628877	−	1.08925i	0.358901	−	0.933376i	$-0.383152\pi$
$998$	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.bi.a.899.8		48
3.2	odd	2		630.2.bi.b.479.24	yes	48
5.4	even	2		1890.2.bi.b.899.24		48
7.5	odd	6		1890.2.r.b.89.16		48
9.4	even	3		630.2.r.b.59.8	yes	48
9.5	odd	6		1890.2.r.a.1529.16		48
15.14	odd	2		630.2.bi.a.479.1	yes	48
21.5	even	6		630.2.r.a.299.17	yes	48
35.19	odd	6		1890.2.r.a.89.16		48
45.4	even	6		630.2.r.a.59.17	✓	48
45.14	odd	6		1890.2.r.b.1529.16		48
63.5	even	6		1890.2.bi.b.719.24		48
63.40	odd	6		630.2.bi.a.509.1	yes	48
105.89	even	6		630.2.r.b.299.8	yes	48
315.194	even	6	inner	1890.2.bi.a.719.8		48
315.229	odd	6		630.2.bi.b.509.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.17	✓	48	45.4	even	6
630.2.r.a.299.17	yes	48	21.5	even	6
630.2.r.b.59.8	yes	48	9.4	even	3
630.2.r.b.299.8	yes	48	105.89	even	6
630.2.bi.a.479.1	yes	48	15.14	odd	2
630.2.bi.a.509.1	yes	48	63.40	odd	6
630.2.bi.b.479.24	yes	48	3.2	odd	2
630.2.bi.b.509.24	yes	48	315.229	odd	6
1890.2.r.a.89.16		48	35.19	odd	6
1890.2.r.a.1529.16		48	9.5	odd	6
1890.2.r.b.89.16		48	7.5	odd	6
1890.2.r.b.1529.16		48	45.14	odd	6
1890.2.bi.a.719.8		48	315.194	even	6	inner
1890.2.bi.a.899.8		48	1.1	even	1	trivial
1890.2.bi.b.719.24		48	63.5	even	6
1890.2.bi.b.899.24		48	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.22943 - 1.86775i) q^{5} +(-0.691773 - 2.55371i) q^{7} -1.00000 q^{8} +(1.22943 + 1.86775i) q^{10} +(3.10680 - 1.79371i) q^{11} +(2.03087 + 3.51756i) q^{13} +(0.691773 + 2.55371i) q^{14} +1.00000 q^{16} +(4.57132 + 2.63925i) q^{17} +(3.13968 - 1.81269i) q^{19} +(-1.22943 - 1.86775i) q^{20} +(-3.10680 + 1.79371i) q^{22} +(-2.39862 + 4.15452i) q^{23} +(-1.97699 + 4.59255i) q^{25} +(-2.03087 - 3.51756i) q^{26} +(-0.691773 - 2.55371i) q^{28} +(6.99680 + 4.03961i) q^{29} -3.52560i q^{31} -1.00000 q^{32} +(-4.57132 - 2.63925i) q^{34} +(-3.91921 + 4.43168i) q^{35} +(-0.879847 + 0.507980i) q^{37} +(-3.13968 + 1.81269i) q^{38} +(1.22943 + 1.86775i) q^{40} +(4.80160 + 8.31661i) q^{41} +(4.43909 + 2.56291i) q^{43} +(3.10680 - 1.79371i) q^{44} +(2.39862 - 4.15452i) q^{46} -11.5014i q^{47} +(-6.04290 + 3.53318i) q^{49} +(1.97699 - 4.59255i) q^{50} +(2.03087 + 3.51756i) q^{52} +(5.71305 - 9.89529i) q^{53} +(-7.16981 - 3.59749i) q^{55} +(0.691773 + 2.55371i) q^{56} +(-6.99680 - 4.03961i) q^{58} -7.03823 q^{59} -11.2231i q^{61} +3.52560i q^{62} +1.00000 q^{64} +(4.07312 - 8.11776i) q^{65} -6.99540i q^{67} +(4.57132 + 2.63925i) q^{68} +(3.91921 - 4.43168i) q^{70} +0.828681i q^{71} +(3.51263 - 6.08405i) q^{73} +(0.879847 - 0.507980i) q^{74} +(3.13968 - 1.81269i) q^{76} +(-6.72983 - 6.69304i) q^{77} +0.0299868 q^{79} +(-1.22943 - 1.86775i) q^{80} +(-4.80160 - 8.31661i) q^{82} +(6.89727 + 3.98214i) q^{83} +(-0.690658 - 11.7829i) q^{85} +(-4.43909 - 2.56291i) q^{86} +(-3.10680 + 1.79371i) q^{88} +(0.625013 + 1.08255i) q^{89} +(7.57795 - 7.61961i) q^{91} +(-2.39862 + 4.15452i) q^{92} +11.5014i q^{94} +(-7.24569 - 3.63556i) q^{95} +(-4.69619 + 8.13404i) q^{97} +(6.04290 - 3.53318i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49}+ \cdots - 3 q^{98}+O(q^{100}) \) 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 + 12 * 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 - 12 * 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

Introduction

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