LMFDB - Embedded newform 572.2.bg.a.9.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.12
Character	$\chi$	$=$	572.9
Dual form			572.2.bg.a.445.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.251214 + 2.39014i) q^{3} +(-0.900429 - 2.77123i) q^{5} +(0.251542 - 2.39326i) q^{7} +(-2.71524 + 0.577141i) q^{9} +O(q^{10})$	\(q+(0.251214 + 2.39014i) q^{3} +(-0.900429 - 2.77123i) q^{5} +(0.251542 - 2.39326i) q^{7} +(-2.71524 + 0.577141i) q^{9} +(-3.31131 - 0.187635i) q^{11} +(1.68235 - 3.18900i) q^{13} +(6.39745 - 2.84833i) q^{15} +(4.69606 - 5.21550i) q^{17} +(-7.42693 - 3.30668i) q^{19} +5.78343 q^{21} +(0.520623 - 0.901746i) q^{23} +(-2.82388 + 2.05167i) q^{25} +(0.166434 + 0.512231i) q^{27} +(0.884626 - 0.393861i) q^{29} +(-2.19051 + 6.74169i) q^{31} +(-0.383374 - 7.96165i) q^{33} +(-6.85878 + 1.45788i) q^{35} +(3.41024 - 1.51834i) q^{37} +(8.04479 + 3.21994i) q^{39} +(-0.101640 - 0.967044i) q^{41} +(1.77499 + 3.07437i) q^{43} +(4.04427 + 7.00488i) q^{45} +(6.54443 - 4.75481i) q^{47} +(1.18261 + 0.251371i) q^{49} +(13.6455 + 9.91404i) q^{51} +(-0.528337 + 1.62605i) q^{53} +(2.46162 + 9.34538i) q^{55} +(6.03769 - 18.5821i) q^{57} +(1.56462 - 14.8863i) q^{59} +(-2.38157 + 2.64500i) q^{61} +(0.698254 + 6.64344i) q^{63} +(-10.3523 - 1.79073i) q^{65} +(-6.63101 + 11.4852i) q^{67} +(2.28609 + 1.01783i) q^{69} +(3.68254 - 4.08987i) q^{71} +(0.0196023 + 0.0142419i) q^{73} +(-5.61319 - 6.23408i) q^{75} +(-1.28199 + 7.87764i) q^{77} +(-2.95880 + 9.10626i) q^{79} +(-8.79022 + 3.91366i) q^{81} +(-2.56116 - 7.88245i) q^{83} +(-18.6818 - 8.31769i) q^{85} +(1.16361 + 2.01544i) q^{87} +(-5.91521 + 10.2454i) q^{89} +(-7.20892 - 4.82847i) q^{91} +(-16.6639 - 3.54202i) q^{93} +(-2.47617 + 23.5592i) q^{95} +(11.1215 - 2.36395i) q^{97} +(9.09929 - 1.40162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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			0
$2$		0			0
$3$	0.251214	+	2.39014i	0.145039	+	1.37995i	0.788765	+	0.614695i	$0.210721\pi$
$3$	0.251214	+	2.39014i	0.145039	+	1.37995i	−0.643727	+	0.765256i	$0.722613\pi$
$4$		0			0
$5$	−0.900429	−	2.77123i	−0.402684	−	1.23933i	−0.922814	−	0.385246i	$-0.874116\pi$
$5$	−0.900429	−	2.77123i	−0.402684	−	1.23933i	0.520130	−	0.854087i	$-0.325884\pi$
$6$		0			0
$7$	0.251542	−	2.39326i	0.0950739	−	0.904568i	−0.838191	−	0.545378i	$-0.816386\pi$
$7$	0.251542	−	2.39326i	0.0950739	−	0.904568i	0.933264	−	0.359190i	$-0.116947\pi$
$8$		0			0
$9$	−2.71524	+	0.577141i	−0.905079	+	0.192380i
$10$		0			0
$11$	−3.31131	−	0.187635i	−0.998398	−	0.0565741i
$11$	−3.31131	−	0.187635i	−0.998398	−	0.0565741i
$12$		0			0
$13$	1.68235	−	3.18900i	0.466601	−	0.884468i
$13$	1.68235	−	3.18900i	0.466601	−	0.884468i
$14$		0			0
$15$	6.39745	−	2.84833i	1.65181	−	0.735435i
$16$		0			0
$17$	4.69606	−	5.21550i	1.13896	−	1.26494i	0.179297	−	0.983795i	$-0.442618\pi$
$17$	4.69606	−	5.21550i	1.13896	−	1.26494i	0.959664	−	0.281149i	$-0.0907155\pi$
$18$		0			0
$19$	−7.42693	−	3.30668i	−1.70385	−	0.758605i	−0.998775	−	0.0494759i	$-0.984245\pi$
$19$	−7.42693	−	3.30668i	−1.70385	−	0.758605i	−0.705079	−	0.709129i	$-0.749088\pi$
$20$		0			0
$21$	5.78343			1.26205
$22$		0			0
$23$	0.520623	−	0.901746i	0.108557	−	0.188027i	−0.806629	−	0.591059i	$-0.798710\pi$
$23$	0.520623	−	0.901746i	0.108557	−	0.188027i	0.915186	+	0.403032i	$0.132044\pi$
$24$		0			0
$25$	−2.82388	+	2.05167i	−0.564777	+	0.410334i
$26$		0			0
$27$	0.166434	+	0.512231i	0.0320302	+	0.0985790i
$28$		0			0
$29$	0.884626	−	0.393861i	0.164271	−	0.0731381i	−0.322954	−	0.946415i	$-0.604676\pi$
$29$	0.884626	−	0.393861i	0.164271	−	0.0731381i	0.487225	+	0.873277i	$0.338009\pi$
$30$		0			0
$31$	−2.19051	+	6.74169i	−0.393427	+	1.21084i	0.536753	+	0.843740i	$0.319651\pi$
$31$	−2.19051	+	6.74169i	−0.393427	+	1.21084i	−0.930180	+	0.367104i	$0.880349\pi$
$32$		0			0
$33$	−0.383374	−	7.96165i	−0.0667369	−	1.38595i
$34$		0			0
$35$	−6.85878	+	1.45788i	−1.15935	+	0.246427i
$36$		0			0
$37$	3.41024	−	1.51834i	0.560640	−	0.249613i	−0.106795	−	0.994281i	$-0.534059\pi$
$37$	3.41024	−	1.51834i	0.560640	−	0.249613i	0.667435	+	0.744668i	$0.267392\pi$
$38$		0			0
$39$	8.04479	+	3.21994i	1.28820	+	0.515603i
$40$		0			0
$41$	−0.101640	−	0.967044i	−0.0158736	−	0.151027i	0.983714	−	0.179740i	$-0.0575257\pi$
$41$	−0.101640	−	0.967044i	−0.0158736	−	0.151027i	−0.999588	+	0.0287132i	$0.990859\pi$
$42$		0			0
$43$	1.77499	+	3.07437i	0.270684	+	0.468838i	0.969037	−	0.246915i	$-0.0794170\pi$
$43$	1.77499	+	3.07437i	0.270684	+	0.468838i	−0.698354	+	0.715753i	$0.746084\pi$
$44$		0			0
$45$	4.04427	+	7.00488i	0.602884	+	1.04423i
$46$		0			0
$47$	6.54443	−	4.75481i	0.954603	−	0.693560i	0.00271215	−	0.999996i	$-0.499137\pi$
$47$	6.54443	−	4.75481i	0.954603	−	0.693560i	0.951891	+	0.306436i	$0.0991367\pi$
$48$		0			0
$49$	1.18261	+	0.251371i	0.168944	+	0.0359102i
$50$		0			0
$51$	13.6455	+	9.91404i	1.91075	+	1.38824i
$52$		0			0
$53$	−0.528337	+	1.62605i	−0.0725727	+	0.223356i	−0.980763	−	0.195201i	$-0.937464\pi$
$53$	−0.528337	+	1.62605i	−0.0725727	+	0.223356i	0.908191	+	0.418557i	$0.137464\pi$
$54$		0			0
$55$	2.46162	+	9.34538i	0.331925	+	1.26013i
$56$		0			0
$57$	6.03769	−	18.5821i	0.799712	−	2.46126i
$58$		0			0
$59$	1.56462	−	14.8863i	0.203696	−	1.93803i	−0.121936	−	0.992538i	$-0.538910\pi$
$59$	1.56462	−	14.8863i	0.203696	−	1.93803i	0.325631	−	0.945497i	$-0.394423\pi$
$60$		0			0
$61$	−2.38157	+	2.64500i	−0.304929	+	0.338658i	−0.876061	−	0.482200i	$-0.839838\pi$
$61$	−2.38157	+	2.64500i	−0.304929	+	0.338658i	0.571132	+	0.820858i	$0.306504\pi$
$62$		0			0
$63$	0.698254	+	6.64344i	0.0879717	+	0.836995i
$64$		0			0
$65$	−10.3523	−	1.79073i	−1.28404	−	0.222113i
$66$		0			0
$67$	−6.63101	+	11.4852i	−0.810107	+	1.40315i	0.102682	+	0.994714i	$0.467258\pi$
$67$	−6.63101	+	11.4852i	−0.810107	+	1.40315i	−0.912789	+	0.408432i	$0.866076\pi$
$68$		0			0
$69$	2.28609	+	1.01783i	0.275213	+	0.122533i
$70$		0			0
$71$	3.68254	−	4.08987i	0.437037	−	0.485379i	−0.483882	−	0.875133i	$-0.660774\pi$
$71$	3.68254	−	4.08987i	0.437037	−	0.485379i	0.920919	+	0.389755i	$0.127440\pi$
$72$		0			0
$73$	0.0196023	+	0.0142419i	0.00229428	+	0.00166689i	0.588932	−	0.808183i	$-0.299549\pi$
$73$	0.0196023	+	0.0142419i	0.00229428	+	0.00166689i	−0.586638	+	0.809850i	$0.699549\pi$
$74$		0			0
$75$	−5.61319	−	6.23408i	−0.648155	−	0.719849i
$76$		0			0
$77$	−1.28199	+	7.87764i	−0.146097	+	0.897740i
$78$		0			0
$79$	−2.95880	+	9.10626i	−0.332891	+	1.02453i	0.634860	+	0.772627i	$0.281058\pi$
$79$	−2.95880	+	9.10626i	−0.332891	+	1.02453i	−0.967751	+	0.251907i	$0.918942\pi$
$80$		0			0
$81$	−8.79022	+	3.91366i	−0.976691	+	0.434851i
$82$		0			0
$83$	−2.56116	−	7.88245i	−0.281124	−	0.865212i	−0.987534	−	0.157408i	$-0.949686\pi$
$83$	−2.56116	−	7.88245i	−0.281124	−	0.865212i	0.706409	−	0.707804i	$-0.250314\pi$
$84$		0			0
$85$	−18.6818	−	8.31769i	−2.02633	−	0.902180i
$86$		0			0
$87$	1.16361	+	2.01544i	0.124753	+	0.216078i
$88$		0			0
$89$	−5.91521	+	10.2454i	−0.627011	+	1.08602i	0.361137	+	0.932513i	$0.382389\pi$
$89$	−5.91521	+	10.2454i	−0.627011	+	1.08602i	−0.988148	+	0.153503i	$0.950945\pi$
$90$		0			0
$91$	−7.20892	−	4.82847i	−0.755700	−	0.506162i
$92$		0			0
$93$	−16.6639	−	3.54202i	−1.72797	−	0.367291i
$94$		0			0
$95$	−2.47617	+	23.5592i	−0.254050	+	2.41712i
$96$		0			0
$97$	11.1215	−	2.36395i	1.12922	−	0.240023i	0.394831	−	0.918754i	$-0.370803\pi$
$97$	11.1215	−	2.36395i	1.12922	−	0.240023i	0.734387	+	0.678731i	$0.237470\pi$
$98$		0			0
$99$	9.09929	−	1.40162i	0.914513	−	0.140868i
$100$		0			0
$101$	−3.17442	−	3.52555i	−0.315866	−	0.350805i	0.564215	−	0.825628i	$-0.309179\pi$
$101$	−3.17442	−	3.52555i	−0.315866	−	0.350805i	−0.880081	+	0.474823i	$0.842512\pi$
$102$		0			0
$103$	−6.17257	−	4.48463i	−0.608201	−	0.441884i	0.240579	−	0.970630i	$-0.422663\pi$
$103$	−6.17257	−	4.48463i	−0.608201	−	0.441884i	−0.848780	+	0.528745i	$0.822663\pi$
$104$		0			0
$105$	−5.20756	−	16.0272i	−0.508206	−	1.56410i
$106$		0			0
$107$	−1.28613	−	12.2367i	−0.124335	−	1.18297i	−0.861681	−	0.507451i	$-0.830588\pi$
$107$	−1.28613	−	12.2367i	−0.124335	−	1.18297i	0.737346	−	0.675515i	$-0.236079\pi$
$108$		0			0
$109$	12.2299			1.17142			0.585708	−	0.810522i	$-0.300816\pi$
$109$	12.2299			1.17142			0.585708	+	0.810522i	$0.300816\pi$
$110$		0			0
$111$	4.48574	+	7.76953i	0.425768	+	0.737452i
$112$		0			0
$113$	−9.21416	−	4.10241i	−0.866795	−	0.385922i	−0.0753465	−	0.997157i	$-0.524006\pi$
$113$	−9.21416	−	4.10241i	−0.866795	−	0.385922i	−0.791449	+	0.611235i	$0.790673\pi$
$114$		0			0
$115$	−2.96773	−	0.630811i	−0.276743	−	0.0588234i
$116$		0			0
$117$	−2.72748	+	9.62983i	−0.252156	+	0.890278i
$118$		0			0
$119$	−11.3008	−	12.5508i	−1.03594	−	1.15053i
$120$		0			0
$121$	10.9296	+	1.24264i	0.993599	+	0.112967i
$122$		0			0
$123$	2.28584	−	0.485871i	0.206107	−	0.0438095i
$124$		0			0
$125$	−3.55840	−	2.58533i	−0.318273	−	0.231239i
$126$		0			0
$127$	15.3540	+	3.26360i	1.36245	+	0.289598i	0.830425	−	0.557131i	$-0.188098\pi$
$127$	15.3540	+	3.26360i	1.36245	+	0.289598i	0.532025	+	0.846729i	$0.321431\pi$
$128$		0			0
$129$	−6.90229	+	5.01481i	−0.607713	+	0.441529i
$130$		0			0
$131$	8.19258			0.715789			0.357895	−	0.933762i	$-0.383495\pi$
$131$	8.19258			0.715789			0.357895	+	0.933762i	$0.383495\pi$
$132$		0			0
$133$	−9.78194	+	16.9428i	−0.848201	+	1.46913i
$134$		0			0
$135$	1.26965	−	0.922456i	0.109274	−	0.0793923i
$136$		0			0
$137$	−6.24883	+	6.94002i	−0.533873	+	0.592926i	−0.948386	−	0.317117i	$-0.897285\pi$
$137$	−6.24883	+	6.94002i	−0.533873	+	0.592926i	0.414513	+	0.910043i	$0.363952\pi$
$138$		0			0
$139$	1.43354	−	13.6392i	0.121591	−	1.15686i	−0.748210	−	0.663462i	$-0.769087\pi$
$139$	1.43354	−	13.6392i	0.121591	−	1.15686i	0.869801	−	0.493402i	$-0.164247\pi$
$140$		0			0
$141$	13.0087	+	14.4477i	1.09553	+	1.21671i
$142$		0			0
$143$	−6.16916	+	10.2441i	−0.515891	+	0.856654i
$144$		0			0
$145$	−1.88802	−	2.09686i	−0.156792	−	0.174135i
$146$		0			0
$147$	−0.303725	+	2.88975i	−0.0250508	+	0.238343i
$148$		0			0
$149$	−4.91660	+	5.46044i	−0.402784	+	0.447337i	−0.910078	−	0.414436i	$-0.863979\pi$
$149$	−4.91660	+	5.46044i	−0.402784	+	0.447337i	0.507295	+	0.861773i	$0.330646\pi$
$150$		0			0
$151$	7.77373	−	5.64795i	0.632617	−	0.459623i	−0.224689	−	0.974431i	$-0.572137\pi$
$151$	7.77373	−	5.64795i	0.632617	−	0.459623i	0.857306	+	0.514807i	$0.172137\pi$
$152$		0			0
$153$	−9.74082	+	16.8716i	−0.787499	+	1.36399i
$154$		0			0
$155$	20.6552			1.65907
$156$		0			0
$157$	−17.3216	+	12.5849i	−1.38241	+	1.00438i	−0.385762	+	0.922598i	$0.626061\pi$
$157$	−17.3216	+	12.5849i	−1.38241	+	1.00438i	−0.996650	+	0.0817825i	$0.973939\pi$
$158$		0			0
$159$	−4.01923	−	0.854314i	−0.318746	−	0.0677515i
$160$		0			0
$161$	−2.02715	−	1.47281i	−0.159762	−	0.116074i
$162$		0			0
$163$	−5.51300	+	1.17182i	−0.431811	+	0.0917843i	−0.418689	−	0.908130i	$-0.637510\pi$
$163$	−5.51300	+	1.17182i	−0.431811	+	0.0917843i	−0.0131221	+	0.999914i	$0.504177\pi$
$164$		0			0
$165$	−21.7184	+	8.23132i	−1.69077	+	0.640807i
$166$		0			0
$167$	14.2706	+	15.8491i	1.10429	+	1.22644i	0.971937	+	0.235240i	$0.0755875\pi$
$167$	14.2706	+	15.8491i	1.10429	+	1.22644i	0.132356	+	0.991202i	$0.457746\pi$
$168$		0			0
$169$	−7.33938	−	10.7300i	−0.564568	−	0.825387i
$170$		0			0
$171$	22.0743	+	4.69203i	1.68806	+	0.358809i
$172$		0			0
$173$	12.6262	+	5.62155i	0.959952	+	0.427398i	0.826050	−	0.563596i	$-0.190583\pi$
$173$	12.6262	+	5.62155i	0.959952	+	0.427398i	0.133902	+	0.990995i	$0.457249\pi$
$174$		0			0
$175$	4.19986	+	7.27437i	0.317480	+	0.549891i
$176$		0			0
$177$	35.9735			2.70394
$178$		0			0
$179$	1.60647	+	15.2846i	0.120074	+	1.14242i	0.874157	+	0.485644i	$0.161415\pi$
$179$	1.60647	+	15.2846i	0.120074	+	1.14242i	−0.754083	+	0.656779i	$0.771918\pi$
$180$		0			0
$181$	−0.515614	−	1.58690i	−0.0383253	−	0.117953i	0.930063	−	0.367399i	$-0.119752\pi$
$181$	−0.515614	−	1.58690i	−0.0383253	−	0.117953i	−0.968389	+	0.249446i	$0.919752\pi$
$182$		0			0
$183$	−6.92022	−	5.02784i	−0.511557	−	0.371668i
$184$		0			0
$185$	−7.27834	−	8.08342i	−0.535114	−	0.594305i
$186$		0			0
$187$	−16.5287	+	16.3890i	−1.20870	+	1.19848i
$188$		0			0
$189$	1.26777	−	0.269473i	0.0922166	−	0.0196012i
$190$		0			0
$191$	1.47123	−	13.9978i	0.106455	−	1.01285i	−0.802698	−	0.596385i	$-0.796603\pi$
$191$	1.47123	−	13.9978i	0.106455	−	1.01285i	0.909153	−	0.416462i	$-0.136730\pi$
$192$		0			0
$193$	3.68313	+	0.782873i	0.265117	+	0.0563524i	0.338552	−	0.940948i	$-0.390063\pi$
$193$	3.68313	+	0.782873i	0.265117	+	0.0563524i	−0.0734350	+	0.997300i	$0.523396\pi$
$194$		0			0
$195$	1.67946	−	25.1933i	0.120268	−	1.80413i
$196$		0			0
$197$	11.1360	−	19.2881i	0.793408	−	1.37422i	−0.130437	−	0.991457i	$-0.541638\pi$
$197$	11.1360	−	19.2881i	0.793408	−	1.37422i	0.923845	−	0.382767i	$-0.125029\pi$
$198$		0			0
$199$	−0.763404	−	1.32225i	−0.0541163	−	0.0937322i	0.837698	−	0.546133i	$-0.183901\pi$
$199$	−0.763404	−	1.32225i	−0.0541163	−	0.0937322i	−0.891815	+	0.452401i	$0.850568\pi$
$200$		0			0
$201$	−29.1172	−	12.9638i	−2.05377	−	0.914397i
$202$		0			0
$203$	−0.720091	−	2.21621i	−0.0505405	−	0.155548i
$204$		0			0
$205$	−2.58839	+	1.15242i	−0.180781	+	0.0804888i
$206$		0			0
$207$	−0.893180	+	2.74893i	−0.0620803	+	0.191064i
$208$		0			0
$209$	23.9724	+	12.3430i	1.65821	+	0.853784i
$210$		0			0
$211$	11.4163	+	12.6790i	0.785928	+	0.872862i	0.994456	−	0.105155i	$-0.0335338\pi$
$211$	11.4163	+	12.6790i	0.785928	+	0.872862i	−0.208528	+	0.978016i	$0.566867\pi$
$212$		0			0
$213$	10.7005	+	7.77436i	0.733186	+	0.532690i
$214$		0			0
$215$	6.92156	−	7.68717i	0.472046	−	0.524261i
$216$		0			0
$217$	15.5836	+	6.93828i	1.05789	+	0.471001i
$218$		0			0
$219$	−0.0291159	+	0.0504302i	−0.00196747	+	0.00340776i
$220$		0			0
$221$	−8.73178	−	23.7500i	−0.587363	−	1.59760i
$222$		0			0
$223$	2.94402	+	28.0104i	0.197146	+	1.87572i	0.429473	+	0.903080i	$0.358699\pi$
$223$	2.94402	+	28.0104i	0.197146	+	1.87572i	−0.232327	+	0.972638i	$0.574634\pi$
$224$		0			0
$225$	6.48340	−	7.20055i	0.432227	−	0.480037i
$226$		0			0
$227$	−0.673035	+	6.40350i	−0.0446709	+	0.425015i	0.949217	+	0.314622i	$0.101878\pi$
$227$	−0.673035	+	6.40350i	−0.0446709	+	0.425015i	−0.993888	+	0.110393i	$0.964789\pi$
$228$		0			0
$229$	−1.13439	+	3.49129i	−0.0749625	+	0.230711i	−0.981516	−	0.191380i	$-0.938704\pi$
$229$	−1.13439	+	3.49129i	−0.0749625	+	0.230711i	0.906554	+	0.422091i	$0.138704\pi$
$230$		0			0
$231$	−19.1507	−	1.08517i	−1.26003	−	0.0713992i
$232$		0			0
$233$	−0.911517	+	2.80536i	−0.0597155	+	0.183785i	−0.976464	−	0.215679i	$-0.930804\pi$
$233$	−0.911517	+	2.80536i	−0.0597155	+	0.183785i	0.916749	+	0.399464i	$0.130804\pi$
$234$		0			0
$235$	−19.0695	−	13.8548i	−1.24396	−	0.903787i
$236$		0			0
$237$	−22.5086	−	4.78434i	−1.46209	−	0.310776i
$238$		0			0
$239$	5.49865	−	3.99500i	0.355678	−	0.258415i	−0.395569	−	0.918436i	$-0.629453\pi$
$239$	5.49865	−	3.99500i	0.355678	−	0.258415i	0.751247	+	0.660021i	$0.229453\pi$
$240$		0			0
$241$	7.87603	+	13.6417i	0.507339	+	0.878738i	0.999964	+	0.00849573i	$0.00270431\pi$
$241$	7.87603	+	13.6417i	0.507339	+	0.878738i	−0.492624	+	0.870242i	$0.663962\pi$
$242$		0			0
$243$	−10.7545	−	18.6274i	−0.689904	−	1.19495i
$244$		0			0
$245$	−0.368246	−	3.50363i	−0.0235264	−	0.223839i
$246$		0			0
$247$	−23.0397	+	18.1214i	−1.46598	+	1.15304i
$248$		0			0
$249$	18.1968	−	8.10174i	1.15318	−	0.513427i
$250$		0			0
$251$	9.36869	−	1.99138i	0.591346	−	0.125695i	0.0974876	−	0.995237i	$-0.468919\pi$
$251$	9.36869	−	1.99138i	0.591346	−	0.125695i	0.493859	+	0.869542i	$0.335586\pi$
$252$		0			0
$253$	−1.89315	+	2.88828i	−0.119021	+	0.181584i
$254$		0			0
$255$	15.1873	−	46.7418i	0.951067	−	2.92708i
$256$		0			0
$257$	20.1495	−	8.97112i	1.25689	−	0.559603i	0.333240	−	0.942842i	$-0.391858\pi$
$257$	20.1495	−	8.97112i	1.25689	−	0.559603i	0.923649	+	0.383239i	$0.125191\pi$
$258$		0			0
$259$	−2.77596	−	8.54352i	−0.172490	−	0.530868i
$260$		0			0
$261$	−2.17465	+	1.57998i	−0.134608	+	0.0977983i
$262$		0			0
$263$	1.77295	−	3.07084i	0.109325	−	0.189356i	−0.806172	−	0.591681i	$-0.798464\pi$
$263$	1.77295	−	3.07084i	0.109325	−	0.189356i	0.915497	+	0.402325i	$0.131798\pi$
$264$		0			0
$265$	4.98191			0.306036
$266$		0			0
$267$	−25.9741	−	11.5644i	−1.58959	−	0.707730i
$268$		0			0
$269$	10.0454	−	11.1566i	0.612481	−	0.680229i	−0.354506	−	0.935054i	$-0.615351\pi$
$269$	10.0454	−	11.1566i	0.612481	−	0.680229i	0.966987	+	0.254825i	$0.0820178\pi$
$270$		0			0
$271$	10.1315	−	4.51082i	0.615443	−	0.274013i	−0.0752460	−	0.997165i	$-0.523974\pi$
$271$	10.1315	−	4.51082i	0.615443	−	0.274013i	0.690689	+	0.723152i	$0.257308\pi$
$272$		0			0
$273$	9.72976	−	18.4433i	0.588872	−	1.11624i
$274$		0			0
$275$	9.73573	−	6.26387i	0.587086	−	0.377725i
$276$		0			0
$277$	14.6924	−	3.12296i	0.882778	−	0.187640i	0.255849	−	0.966717i	$-0.417645\pi$
$277$	14.6924	−	3.12296i	0.882778	−	0.187640i	0.626929	+	0.779077i	$0.284312\pi$
$278$		0			0
$279$	2.05684	−	19.5695i	0.123140	−	1.17160i
$280$		0			0
$281$	−2.66860	−	8.21311i	−0.159195	−	0.489953i	0.839366	−	0.543566i	$-0.182926\pi$
$281$	−2.66860	−	8.21311i	−0.159195	−	0.489953i	−0.998562	+	0.0536130i	$0.982926\pi$
$282$		0			0
$283$	0.712512	+	6.77910i	0.0423545	+	0.402976i	0.995075	+	0.0991271i	$0.0316050\pi$
$283$	0.712512	+	6.77910i	0.0423545	+	0.402976i	−0.952720	+	0.303849i	$0.901728\pi$
$284$		0			0
$285$	−56.9319			−3.37235
$286$		0			0
$287$	−2.33996			−0.138123
$288$		0			0
$289$	−3.37150	−	32.0777i	−0.198323	−	1.88692i
$290$		0			0
$291$	8.44406	+	25.9882i	0.495000	+	1.52345i
$292$		0			0
$293$	−1.61801	+	15.3943i	−0.0945249	+	0.899345i	0.839794	+	0.542906i	$0.182676\pi$
$293$	−1.61801	+	15.3943i	−0.0945249	+	0.899345i	−0.934319	+	0.356439i	$0.883991\pi$
$294$		0			0
$295$	−42.6623	+	9.06816i	−2.48390	+	0.527969i
$296$		0			0
$297$	−0.455003	−	1.72739i	−0.0264019	−	0.100233i
$298$		0			0
$299$	−1.99979	−	3.17732i	−0.115651	−	0.183749i
$300$		0			0
$301$	7.80426	−	3.47468i	0.449830	−	0.200277i
$302$		0			0
$303$	7.62910	−	8.47298i	0.438280	−	0.486760i
$304$		0			0
$305$	9.47436	+	4.21826i	0.542500	+	0.241537i
$306$		0			0
$307$	−3.92363			−0.223933			−0.111967	−	0.993712i	$-0.535715\pi$
$307$	−3.92363			−0.223933			−0.111967	+	0.993712i	$0.535715\pi$
$308$		0			0
$309$	9.16828	−	15.8799i	0.521565	−	0.903378i
$310$		0			0
$311$	6.90309	−	5.01539i	0.391439	−	0.284397i	−0.374606	−	0.927184i	$-0.622222\pi$
$311$	6.90309	−	5.01539i	0.391439	−	0.284397i	0.766045	+	0.642787i	$0.222222\pi$
$312$		0			0
$313$	1.91782	+	5.90243i	0.108401	+	0.333625i	0.990514	−	0.137414i	$-0.0438791\pi$
$313$	1.91782	+	5.90243i	0.108401	+	0.333625i	−0.882112	+	0.471039i	$0.843879\pi$
$314$		0			0
$315$	17.7818	−	7.91697i	1.00189	−	0.446071i
$316$		0			0
$317$	−3.66638	+	11.2840i	−0.205924	+	0.633770i	0.793750	+	0.608244i	$0.208126\pi$
$317$	−3.66638	+	11.2840i	−0.205924	+	0.633770i	−0.999674	+	0.0255257i	$0.991874\pi$
$318$		0			0
$319$	−3.00318	+	1.13821i	−0.168146	+	0.0637275i
$320$		0			0
$321$	28.9244	−	6.14807i	1.61440	−	0.343152i
$322$		0			0
$323$	−52.1233	+	23.2068i	−2.90022	+	1.29126i
$324$		0			0
$325$	1.79200	+	12.4570i	0.0994025	+	0.690989i
$326$		0			0
$327$	3.07234	+	29.2313i	0.169901	+	1.61650i
$328$		0			0
$329$	−9.73330	−	16.8586i	−0.536614	−	0.929443i
$330$		0			0
$331$	16.4483	+	28.4894i	0.904082	+	1.56592i	0.822144	+	0.569279i	$0.192778\pi$
$331$	16.4483	+	28.4894i	0.904082	+	1.56592i	0.0819383	+	0.996637i	$0.473889\pi$
$332$		0			0
$333$	−8.38331	+	6.09083i	−0.459402	+	0.333775i
$334$		0			0
$335$	37.7991	+	8.03444i	2.06518	+	0.438968i
$336$		0			0
$337$	−28.2247	−	20.5064i	−1.53750	−	1.11706i	−0.951882	−	0.306465i	$-0.900854\pi$
$337$	−28.2247	−	20.5064i	−1.53750	−	1.11706i	−0.585614	−	0.810590i	$-0.699146\pi$
$338$		0			0
$339$	7.49062	−	23.0538i	0.406835	−	1.25211i
$340$		0			0
$341$	8.51844	−	21.9128i	0.461299	−	1.18665i
$342$		0			0
$343$	6.10450	−	18.7877i	0.329612	−	1.01444i
$344$		0			0
$345$	0.762192	−	7.25178i	0.0410351	−	0.390423i
$346$		0			0
$347$	−10.4846	+	11.6443i	−0.562842	+	0.625099i	−0.955644	−	0.294524i	$-0.904839\pi$
$347$	−10.4846	+	11.6443i	−0.562842	+	0.625099i	0.392802	+	0.919623i	$0.371506\pi$
$348$		0			0
$349$	−0.0181778	−	0.172950i	−0.000973035	−	0.00925781i	0.994025	−	0.109156i	$-0.0348149\pi$
$349$	−0.0181778	−	0.172950i	−0.000973035	−	0.00925781i	−0.994998	+	0.0998984i	$0.968148\pi$
$350$		0			0
$351$	1.91350	+	0.330996i	0.102135	+	0.0176673i
$352$		0			0
$353$	−7.32774	+	12.6920i	−0.390016	+	0.675528i	−0.992451	−	0.122640i	$-0.960864\pi$
$353$	−7.32774	+	12.6920i	−0.390016	+	0.675528i	0.602435	+	0.798168i	$0.294197\pi$
$354$		0			0
$355$	−14.6499	−	6.52254i	−0.777534	−	0.346180i
$356$		0			0
$357$	27.1593	−	30.1635i	1.43742	−	1.59642i
$358$		0			0
$359$	−0.213989	−	0.155472i	−0.0112939	−	0.00820550i	0.582124	−	0.813100i	$-0.302222\pi$
$359$	−0.213989	−	0.155472i	−0.0112939	−	0.00820550i	−0.593418	+	0.804895i	$0.702222\pi$
$360$		0			0
$361$	31.5116	+	34.9972i	1.65851	+	1.84196i
$362$		0			0
$363$	−0.224413	+	26.4355i	−0.0117786	+	1.38750i
$364$		0			0
$365$	0.0218172	−	0.0671465i	0.00114197	−	0.00351461i
$366$		0			0
$367$	28.6850	−	12.7714i	1.49735	−	0.666662i	0.515596	−	0.856832i	$-0.327571\pi$
$367$	28.6850	−	12.7714i	1.49735	−	0.666662i	0.981751	+	0.190170i	$0.0609040\pi$
$368$		0			0
$369$	0.834099	+	2.56709i	0.0434215	+	0.133638i
$370$		0			0
$371$	3.75867	+	1.67347i	0.195141	+	0.0868822i
$372$		0			0
$373$	−5.32154	−	9.21719i	−0.275539	−	0.477248i	0.694732	−	0.719269i	$-0.255523\pi$
$373$	−5.32154	−	9.21719i	−0.275539	−	0.477248i	−0.970271	+	0.242021i	$0.922190\pi$
$374$		0			0
$375$	5.28538	−	9.15455i	0.272936	−	0.472739i
$376$		0			0
$377$	0.232232	−	3.48368i	0.0119606	−	0.179419i
$378$		0			0
$379$	−21.1861	−	4.50324i	−1.08826	−	0.231316i	−0.371355	−	0.928491i	$-0.621107\pi$
$379$	−21.1861	−	4.50324i	−1.08826	−	0.231316i	−0.716901	+	0.697175i	$0.754440\pi$
$380$		0			0
$381$	−3.94332	+	37.5182i	−0.202023	+	1.92212i
$382$		0			0
$383$	31.9957	−	6.80090i	1.63490	−	0.347510i	0.703275	−	0.710918i	$-0.251720\pi$
$383$	31.9957	−	6.80090i	1.63490	−	0.347510i	0.931630	+	0.363408i	$0.118387\pi$
$384$		0			0
$385$	22.9851	−	3.54055i	1.17143	−	0.180443i
$386$		0			0
$387$	−6.59387	−	7.32323i	−0.335185	−	0.372261i
$388$		0			0
$389$	16.3644	+	11.8894i	0.829709	+	0.602819i	0.919477	−	0.393144i	$-0.128613\pi$
$389$	16.3644	+	11.8894i	0.829709	+	0.602819i	−0.0897680	+	0.995963i	$0.528613\pi$
$390$		0			0
$391$	−2.25818	−	6.94996i	−0.114201	−	0.351474i
$392$		0			0
$393$	2.05809	+	19.5814i	0.103817	+	0.987753i
$394$		0			0
$395$	27.8998			1.40379
$396$		0			0
$397$	−4.75767	−	8.24053i	−0.238781	−	0.413580i	0.721584	−	0.692327i	$-0.243414\pi$
$397$	−4.75767	−	8.24053i	−0.238781	−	0.413580i	−0.960365	+	0.278747i	$0.910081\pi$
$398$		0			0
$399$	−42.9531	−	19.1240i	−2.15035	−	0.957395i
$400$		0			0
$401$	10.9688	+	2.33149i	0.547755	+	0.116429i	0.473473	−	0.880808i	$-0.343000\pi$
$401$	10.9688	+	2.33149i	0.547755	+	0.116429i	0.0742819	+	0.997237i	$0.476334\pi$
$402$		0			0
$403$	17.8140	+	18.3274i	0.887380	+	0.912954i
$404$		0			0
$405$	18.7606	+	20.8358i	0.932223	+	1.03534i
$406$		0			0
$407$	−11.5773	+	4.38781i	−0.573864	+	0.217495i
$408$		0			0
$409$	−14.6917	+	3.12283i	−0.726460	+	0.154414i	−0.556275	−	0.830998i	$-0.687770\pi$
$409$	−14.6917	+	3.12283i	−0.726460	+	0.154414i	−0.170185	+	0.985412i	$0.554437\pi$
$410$		0			0
$411$	−18.1574	−	13.1922i	−0.895641	−	0.650721i
$412$		0			0
$413$	−35.2333	−	7.48907i	−1.73372	−	0.368513i
$414$		0			0
$415$	−19.5380	+	14.1952i	−0.959082	+	0.696814i
$416$		0			0
$417$	32.9598			1.61405
$418$		0			0
$419$	3.40945	−	5.90533i	0.166562	−	0.288494i	−0.770647	−	0.637263i	$-0.780067\pi$
$419$	3.40945	−	5.90533i	0.166562	−	0.288494i	0.937209	+	0.348768i	$0.113400\pi$
$420$		0			0
$421$	5.87079	−	4.26538i	0.286125	−	0.207882i	−0.435460	−	0.900208i	$-0.643414\pi$
$421$	5.87079	−	4.26538i	0.286125	−	0.207882i	0.721584	+	0.692326i	$0.243414\pi$
$422$		0			0
$423$	−15.0255	+	16.6875i	−0.730564	+	0.811373i
$424$		0			0
$425$	−2.56062	+	24.3627i	−0.124209	+	1.18177i
$426$		0			0
$427$	5.73112	+	6.36505i	0.277348	+	0.308026i
$428$		0			0
$429$	−26.0346	−	12.1717i	−1.25696	−	0.587656i
$430$		0			0
$431$	−8.46903	−	9.40581i	−0.407939	−	0.453062i	0.503807	−	0.863816i	$-0.331932\pi$
$431$	−8.46903	−	9.40581i	−0.407939	−	0.453062i	−0.911746	+	0.410754i	$0.865265\pi$
$432$		0			0
$433$	−1.60059	+	15.2286i	−0.0769195	+	0.731840i	0.886298	+	0.463116i	$0.153269\pi$
$433$	−1.60059	+	15.2286i	−0.0769195	+	0.731840i	−0.963217	+	0.268724i	$0.913398\pi$
$434$		0			0
$435$	4.53750	−	5.03941i	0.217557	−	0.241621i
$436$		0			0
$437$	−6.84842	+	4.97567i	−0.327604	+	0.238018i
$438$		0			0
$439$	14.2634	−	24.7049i	0.680753	−	1.17910i	−0.293998	−	0.955806i	$-0.594986\pi$
$439$	14.2634	−	24.7049i	0.680753	−	1.17910i	0.974751	−	0.223293i	$-0.0716806\pi$
$440$		0			0
$441$	−3.35614			−0.159816
$442$		0			0
$443$	−7.30827	+	5.30977i	−0.347226	+	0.252275i	−0.747705	−	0.664032i	$-0.768844\pi$
$443$	−7.30827	+	5.30977i	−0.347226	+	0.252275i	0.400478	+	0.916306i	$0.368844\pi$
$444$		0			0
$445$	33.7188	+	7.16715i	1.59842	+	0.339755i
$446$		0			0
$447$	−14.2864	−	10.3796i	−0.675722	−	0.490940i
$448$		0			0
$449$	17.0073	−	3.61501i	0.802624	−	0.170603i	0.211705	−	0.977334i	$-0.432098\pi$
$449$	17.0073	−	3.61501i	0.802624	−	0.170603i	0.590919	+	0.806731i	$0.298765\pi$
$450$		0			0
$451$	0.155112	+	3.22126i	0.00730394	+	0.151683i
$452$		0			0
$453$	15.4523	+	17.1615i	0.726011	+	0.806317i
$454$		0			0
$455$	−6.88972	+	24.3253i	−0.322995	+	1.14039i
$456$		0			0
$457$	0.565847	+	0.120274i	0.0264692	+	0.00562620i	0.221127	−	0.975245i	$-0.429026\pi$
$457$	0.565847	+	0.120274i	0.0264692	+	0.00562620i	−0.194658	+	0.980871i	$0.562360\pi$
$458$		0			0
$459$	3.45313	+	1.53743i	0.161178	+	0.0717611i
$460$		0			0
$461$	12.1976	+	21.1268i	0.568098	+	0.983975i	0.996754	+	0.0805071i	$0.0256540\pi$
$461$	12.1976	+	21.1268i	0.568098	+	0.983975i	−0.428656	+	0.903468i	$0.641013\pi$
$462$		0			0
$463$	−24.6148			−1.14394			−0.571972	−	0.820273i	$-0.693822\pi$
$463$	−24.6148			−1.14394			−0.571972	+	0.820273i	$0.693822\pi$
$464$		0			0
$465$	5.18888	+	49.3689i	0.240629	+	2.28943i
$466$		0			0
$467$	−7.28899	−	22.4332i	−0.337294	−	1.03808i	−0.965581	−	0.260103i	$-0.916244\pi$
$467$	−7.28899	−	22.4332i	−0.337294	−	1.03808i	0.628287	−	0.777982i	$-0.283756\pi$
$468$		0			0
$469$	25.8192	+	18.7588i	1.19222	+	0.866199i
$470$		0			0
$471$	−34.4310	−	38.2395i	−1.58650	−	1.76199i
$472$		0			0
$473$	−5.30069	−	10.5133i	−0.243726	−	0.483400i
$474$		0			0
$475$	27.7570	−	5.89993i	1.27358	−	0.270707i
$476$		0			0
$477$	0.496097	−	4.72005i	0.0227147	−	0.216116i
$478$		0			0
$479$	−7.85207	−	1.66901i	−0.358770	−	0.0762590i	0.0250002	−	0.999687i	$-0.492041\pi$
$479$	−7.85207	−	1.66901i	−0.358770	−	0.0762590i	−0.383771	+	0.923428i	$0.625375\pi$
$480$		0			0
$481$	0.895256	−	13.4296i	0.0408201	−	0.612338i
$482$		0			0
$483$	3.01099	−	5.21518i	0.137005	−	0.237299i
$484$		0			0
$485$	−16.5652	−	28.6917i	−0.752186	−	1.30283i
$486$		0			0
$487$	−9.04119	−	4.02540i	−0.409696	−	0.182408i	0.191531	−	0.981486i	$-0.438655\pi$
$487$	−9.04119	−	4.02540i	−0.409696	−	0.182408i	−0.601227	+	0.799078i	$0.705321\pi$
$488$		0			0
$489$	−4.18577	−	12.8825i	−0.189287	−	0.582566i
$490$		0			0
$491$	−11.1180	+	4.95004i	−0.501747	+	0.223392i	−0.641973	−	0.766727i	$-0.721884\pi$
$491$	−11.1180	+	4.95004i	−0.501747	+	0.223392i	0.140226	+	0.990120i	$0.455217\pi$
$492$		0			0
$493$	2.10007	−	6.46336i	0.0945825	−	0.291095i
$494$		0			0
$495$	−12.0775	−	23.9542i	−0.542842	−	1.07666i
$496$		0			0
$497$	−8.86182	−	9.84205i	−0.397507	−	0.441476i
$498$		0			0
$499$	−8.57755	−	6.23196i	−0.383984	−	0.278981i	0.379002	−	0.925396i	$-0.376267\pi$
$499$	−8.57755	−	6.23196i	−0.383984	−	0.278981i	−0.762986	+	0.646415i	$0.776267\pi$
$500$		0			0
$501$	−34.2967	+	38.0903i	−1.53226	+	1.70175i
$502$		0			0
$503$	−15.2834	−	6.80460i	−0.681452	−	0.303402i	0.0366616	−	0.999328i	$-0.488328\pi$
$503$	−15.2834	−	6.80460i	−0.681452	−	0.303402i	−0.718114	+	0.695926i	$0.754994\pi$
$504$		0			0
$505$	−6.91178	+	11.9715i	−0.307570	+	0.532727i
$506$		0			0
$507$	23.8025	−	20.2377i	1.05711	−	0.898788i
$508$		0			0
$509$	−0.244627	−	2.32747i	−0.0108429	−	0.103163i	0.987762	−	0.155970i	$-0.0498502\pi$
$509$	−0.244627	−	2.32747i	−0.0108429	−	0.103163i	−0.998605	+	0.0528060i	$0.983183\pi$
$510$		0			0
$511$	0.0390155	−	0.0433311i	0.00172594	−	0.00191685i
$512$		0			0
$513$	0.457692	−	4.35465i	0.0202076	−	0.192262i
$514$		0			0
$515$	−6.87001	+	21.1437i	−0.302729	+	0.931704i
$516$		0			0
$517$	−22.5628	+	14.5167i	−0.992312	+	0.638443i
$518$		0			0
$519$	−10.2644	+	31.5906i	−0.450558	+	1.38668i
$520$		0			0
$521$	−10.5506	−	7.66546i	−0.462230	−	0.335830i	0.332175	−	0.943218i	$-0.392217\pi$
$521$	−10.5506	−	7.66546i	−0.462230	−	0.335830i	−0.794405	+	0.607388i	$0.792217\pi$
$522$		0			0
$523$	−7.09062	−	1.50716i	−0.310051	−	0.0659034i	0.0502582	−	0.998736i	$-0.483996\pi$
$523$	−7.09062	−	1.50716i	−0.310051	−	0.0659034i	−0.360309	+	0.932833i	$0.617329\pi$
$524$		0			0
$525$	−16.3317	+	11.8657i	−0.712775	+	0.517861i
$526$		0			0
$527$	24.8745	+	43.0840i	1.08355	+	1.87677i
$528$		0			0
$529$	10.9579	+	18.9796i	0.476431	+	0.825202i
$530$		0			0
$531$	4.34321	+	41.3229i	0.188479	+	1.79326i
$532$		0			0
$533$	−3.25490	−	1.30278i	−0.140985	−	0.0564296i
$534$		0			0
$535$	−32.7527	+	14.5824i	−1.41602	+	0.630454i
$536$		0			0
$537$	−36.1288	+	7.67941i	−1.55907	+	0.331391i
$538$		0			0
$539$	−3.86882	−	1.05427i	−0.166642	−	0.0454105i
$540$		0			0
$541$	−0.365911	+	1.12616i	−0.0157317	+	0.0484173i	−0.958614	−	0.284708i	$-0.908103\pi$
$541$	−0.365911	+	1.12616i	−0.0157317	+	0.0484173i	0.942882	+	0.333126i	$0.108103\pi$
$542$		0			0
$543$	3.66338	−	1.63104i	0.157211	−	0.0699948i
$544$		0			0
$545$	−11.0122	−	33.8920i	−0.471711	−	1.45178i
$546$		0			0
$547$	19.2791	−	14.0071i	0.824316	−	0.598900i	−0.0936299	−	0.995607i	$-0.529847\pi$
$547$	19.2791	−	14.0071i	0.824316	−	0.598900i	0.917945	+	0.396707i	$0.129847\pi$
$548$		0			0
$549$	4.93999	−	8.55631i	0.210834	−	0.365174i
$550$		0			0
$551$	−7.87243			−0.335377
$552$		0			0
$553$	21.0494	+	9.37179i	0.895111	+	0.398529i
$554$		0			0
$555$	17.4921	−	19.4270i	0.742499	−	0.824628i
$556$		0			0
$557$	−18.0609	+	8.04122i	−0.765264	+	0.340718i	−0.751973	−	0.659194i	$-0.770898\pi$
$557$	−18.0609	+	8.04122i	−0.765264	+	0.340718i	−0.0132913	+	0.999912i	$0.504231\pi$
$558$		0			0
$559$	12.7903	−	0.488257i	0.540973	−	0.0206511i
$560$		0			0
$561$	−43.3243	−	35.3889i	−1.82915	−	1.49412i
$562$		0			0
$563$	25.8119	−	5.48648i	1.08784	−	0.231228i	0.371118	−	0.928586i	$-0.378975\pi$
$563$	25.8119	−	5.48648i	1.08784	−	0.231228i	0.716723	+	0.697358i	$0.245641\pi$
$564$		0			0
$565$	−3.07204	+	29.2285i	−0.129242	+	1.22965i
$566$		0			0
$567$	7.15529	+	22.0217i	0.300494	+	0.924826i
$568$		0			0
$569$	4.32584	+	41.1577i	0.181349	+	1.72542i	0.585453	+	0.810706i	$0.300917\pi$
$569$	4.32584	+	41.1577i	0.181349	+	1.72542i	−0.404104	+	0.914713i	$0.632417\pi$
$570$		0			0
$571$	−25.4451			−1.06484			−0.532422	−	0.846479i	$-0.678718\pi$
$571$	−25.4451			−1.06484			−0.532422	+	0.846479i	$0.678718\pi$
$572$		0			0
$573$	33.8264			1.41312
$574$		0			0
$575$	0.379907	+	3.61457i	0.0158432	+	0.150738i
$576$		0			0
$577$	−7.02512	−	21.6211i	−0.292460	−	0.900098i	−0.984063	−	0.177821i	$-0.943095\pi$
$577$	−7.02512	−	21.6211i	−0.292460	−	0.900098i	0.691603	−	0.722278i	$-0.256905\pi$
$578$		0			0
$579$	−0.945924	+	8.99987i	−0.0393113	+	0.374022i
$580$		0			0
$581$	−19.5090	+	4.14677i	−0.809370	+	0.172037i
$582$		0			0
$583$	2.05459	−	5.28524i	0.0850926	−	0.218892i
$584$		0			0
$585$	29.1424	−	1.11248i	1.20489	−	0.0459955i
$586$		0			0
$587$	−18.4265	+	8.20400i	−0.760543	+	0.338615i	−0.750095	−	0.661330i	$-0.769992\pi$
$587$	−18.4265	+	8.20400i	−0.760543	+	0.338615i	−0.0104476	+	0.999945i	$0.503326\pi$
$588$		0			0
$589$	38.5614	−	42.8268i	1.58889	−	1.76465i
$590$		0			0
$591$	48.8990	+	21.7712i	2.01143	+	0.895548i
$592$		0			0
$593$	10.6025			0.435390			0.217695	−	0.976017i	$-0.430146\pi$
$593$	10.6025			0.435390			0.217695	+	0.976017i	$0.430146\pi$
$594$		0			0
$595$	−24.6057	+	42.6182i	−1.00873	+	1.74718i
$596$		0			0
$597$	2.96860	−	2.15681i	0.121497	−	0.0882726i
$598$		0			0
$599$	−6.23034	−	19.1750i	−0.254565	−	0.783470i	−0.993915	−	0.110149i	$-0.964867\pi$
$599$	−6.23034	−	19.1750i	−0.254565	−	0.783470i	0.739350	−	0.673321i	$-0.235133\pi$
$600$		0			0
$601$	3.48505	−	1.55165i	0.142158	−	0.0632929i	−0.334425	−	0.942423i	$-0.608542\pi$
$601$	3.48505	−	1.55165i	0.142158	−	0.0632929i	0.476583	+	0.879130i	$0.341875\pi$
$602$		0			0
$603$	11.3761	−	35.0122i	0.463273	−	1.42581i
$604$		0			0
$605$	−6.39767	−	31.4074i	−0.260102	−	1.27689i
$606$		0			0
$607$	−40.1908	+	8.54281i	−1.63129	+	0.346742i	−0.930406	−	0.366530i	$-0.880546\pi$
$607$	−40.1908	+	8.54281i	−1.63129	+	0.346742i	−0.700887	+	0.713272i	$0.747212\pi$
$608$		0			0
$609$	5.11617	−	2.27787i	0.207318	−	0.0923038i
$610$		0			0
$611$	−4.15302	−	28.8694i	−0.168013	−	1.16793i
$612$		0			0
$613$	0.933514	+	8.88179i	0.0377043	+	0.358732i	0.997066	+	0.0765517i	$0.0243910\pi$
$613$	0.933514	+	8.88179i	0.0377043	+	0.358732i	−0.959361	+	0.282180i	$0.908942\pi$
$614$		0			0
$615$	−3.40470	−	5.89711i	−0.137291	−	0.237794i
$616$		0			0
$617$	−8.72271	−	15.1082i	−0.351163	−	0.608232i	0.635290	−	0.772273i	$-0.280880\pi$
$617$	−8.72271	−	15.1082i	−0.351163	−	0.608232i	−0.986454	+	0.164041i	$0.947547\pi$
$618$		0			0
$619$	19.1446	−	13.9094i	0.769487	−	0.559065i	−0.132319	−	0.991207i	$-0.542242\pi$
$619$	19.1446	−	13.9094i	0.769487	−	0.559065i	0.901805	+	0.432143i	$0.142242\pi$
$620$		0			0
$621$	0.548552	+	0.116598i	0.0220126	+	0.00467893i
$622$		0			0
$623$	23.0321	+	16.7338i	0.922762	+	0.670426i
$624$		0			0
$625$	−9.35360	+	28.7874i	−0.374144	+	1.15150i
$626$		0			0
$627$	−23.4794	+	60.3983i	−0.937675	+	2.41208i
$628$		0			0
$629$	8.09579	−	24.9163i	0.322800	−	0.993477i
$630$		0			0
$631$	−0.719880	+	6.84920i	−0.0286580	+	0.272662i	0.970804	+	0.239873i	$0.0771058\pi$
$631$	−0.719880	+	6.84920i	−0.0286580	+	0.272662i	−0.999462	+	0.0327895i	$0.989561\pi$
$632$		0			0
$633$	−27.4368	+	30.4717i	−1.09052	+	1.21114i
$634$		0			0
$635$	−4.78101	−	45.4883i	−0.189729	−	1.80515i
$636$		0			0
$637$	2.79119	−	3.34844i	0.110591	−	0.132670i
$638$		0			0
$639$	−7.63853	+	13.2303i	−0.302175	+	0.523383i
$640$		0			0
$641$	−30.2086	−	13.4498i	−1.19317	−	0.531233i	−0.288555	−	0.957463i	$-0.593175\pi$
$641$	−30.2086	−	13.4498i	−1.19317	−	0.531233i	−0.904615	+	0.426230i	$0.859841\pi$
$642$		0			0
$643$	4.69705	−	5.21661i	0.185234	−	0.205723i	−0.643375	−	0.765551i	$-0.722466\pi$
$643$	4.69705	−	5.21661i	0.185234	−	0.205723i	0.828609	+	0.559828i	$0.189133\pi$
$644$		0			0
$645$	20.1122	+	14.6124i	0.791918	+	0.575362i
$646$		0			0
$647$	−5.86713	−	6.51611i	−0.230661	−	0.256175i	0.616693	−	0.787204i	$-0.288472\pi$
$647$	−5.86713	−	6.51611i	−0.230661	−	0.256175i	−0.847354	+	0.531029i	$0.821805\pi$
$648$		0			0
$649$	−7.97413	+	48.9997i	−0.313012	+	1.92341i
$650$		0			0
$651$	−12.6687	+	38.9901i	−0.496524	+	1.52814i
$652$		0			0
$653$	−5.76414	+	2.56636i	−0.225568	+	0.100429i	−0.516409	−	0.856342i	$-0.672732\pi$
$653$	−5.76414	+	2.56636i	−0.225568	+	0.100429i	0.290841	+	0.956771i	$0.406065\pi$
$654$		0			0
$655$	−7.37683	−	22.7036i	−0.288237	−	0.887101i
$656$		0			0
$657$	−0.0614446	−	0.0273569i	−0.00239718	−	0.00106729i
$658$		0			0
$659$	6.92101	+	11.9875i	0.269604	+	0.466968i	0.968760	−	0.248001i	$-0.0797737\pi$
$659$	6.92101	+	11.9875i	0.269604	+	0.466968i	−0.699155	+	0.714970i	$0.746440\pi$
$660$		0			0
$661$	22.4791	−	38.9350i	0.874337	−	1.51440i	0.0168688	−	0.999858i	$-0.494630\pi$
$661$	22.4791	−	38.9350i	0.874337	−	1.51440i	0.857468	−	0.514538i	$-0.172036\pi$
$662$		0			0
$663$	54.5724	−	26.8365i	2.11942	−	1.04225i
$664$		0			0
$665$	55.7604	+	11.8522i	2.16230	+	0.459610i
$666$		0			0
$667$	0.105394	−	1.00276i	0.00408089	−	0.0388271i
$668$		0			0
$669$	−66.2094	+	14.0732i	−2.55980	+	0.544103i
$670$		0			0
$671$	8.38242	−	8.31157i	0.323600	−	0.320864i
$672$		0			0
$673$	−12.5767	−	13.9678i	−0.484796	−	0.538421i	0.450271	−	0.892892i	$-0.351327\pi$
$673$	−12.5767	−	13.9678i	−0.484796	−	0.538421i	−0.935067	+	0.354471i	$0.884661\pi$
$674$		0			0
$675$	−1.52092	−	1.10501i	−0.0585403	−	0.0425320i
$676$		0			0
$677$	13.7506	+	42.3200i	0.528478	+	1.62649i	0.757334	+	0.653028i	$0.226502\pi$
$677$	13.7506	+	42.3200i	0.528478	+	1.62649i	−0.228855	+	0.973460i	$0.573498\pi$
$678$		0			0
$679$	−2.86002	−	27.2113i	−0.109758	−	1.04427i
$680$		0			0
$681$	−15.4744			−0.592979
$682$		0			0
$683$	−10.0293	−	17.3712i	−0.383760	−	0.664692i	0.607836	−	0.794062i	$-0.292038\pi$
$683$	−10.0293	−	17.3712i	−0.383760	−	0.664692i	−0.991596	+	0.129370i	$0.958704\pi$
$684$		0			0
$685$	24.8591	+	11.0680i	0.949816	+	0.422885i
$686$		0			0
$687$	−8.62965	−	1.83429i	−0.329242	−	0.0699825i
$688$		0			0
$689$	4.29663	+	4.42046i	0.163689	+	0.168406i
$690$		0			0
$691$	−2.70389	−	3.00298i	−0.102861	−	0.114239i	0.689516	−	0.724270i	$-0.257823\pi$
$691$	−2.70389	−	3.00298i	−0.102861	−	0.114239i	−0.792377	+	0.610032i	$0.791157\pi$
$692$		0			0
$693$	−1.06559	−	22.1295i	−0.0404786	−	0.840632i
$694$		0			0
$695$	−39.0883	+	8.30847i	−1.48270	+	0.315158i
$696$		0			0
$697$	−5.52093	−	4.01119i	−0.209120	−	0.151935i
$698$		0			0
$699$	−6.93420	−	1.47391i	−0.262276	−	0.0557484i
$700$		0			0
$701$	−14.1937	+	10.3123i	−0.536089	+	0.389491i	−0.822630	−	0.568576i	$-0.807494\pi$
$701$	−14.1937	+	10.3123i	−0.536089	+	0.389491i	0.286542	+	0.958068i	$0.407494\pi$
$702$		0			0
$703$	−30.3483			−1.14461
$704$		0			0
$705$	28.3244	−	49.0593i	1.06676	−	1.84768i
$706$		0			0
$707$	−9.23605	+	6.71038i	−0.347357	+	0.252370i
$708$		0			0
$709$	−32.0968	+	35.6471i	−1.20542	+	1.33875i	−0.279911	+	0.960026i	$0.590305\pi$
$709$	−32.0968	+	35.6471i	−1.20542	+	1.33875i	−0.925508	+	0.378728i	$0.876362\pi$
$710$		0			0
$711$	2.77825	−	26.4333i	0.104193	−	0.991325i
$712$		0			0
$713$	4.93886	+	5.48517i	0.184962	+	0.205421i
$714$		0			0
$715$	33.9437	+	7.87212i	1.26942	+	0.294401i
$716$		0			0
$717$	10.9300	+	12.1390i	0.408187	+	0.453338i
$718$		0			0
$719$	2.10885	−	20.0643i	0.0786467	−	0.748273i	−0.882141	−	0.470986i	$-0.843898\pi$
$719$	2.10885	−	20.0643i	0.0786467	−	0.748273i	0.960787	−	0.277287i	$-0.0894352\pi$
$720$		0			0
$721$	−12.2856	+	13.6445i	−0.457538	+	0.508148i
$722$		0			0
$723$	−30.6270	+	22.2518i	−1.13903	+	0.827554i
$724$		0			0
$725$	−1.69001	+	2.92718i	−0.0627653	+	0.108713i
$726$		0			0
$727$	9.21747			0.341857			0.170929	−	0.985283i	$-0.445323\pi$
$727$	9.21747			0.341857			0.170929	+	0.985283i	$0.445323\pi$
$728$		0			0
$729$	18.4672	−	13.4172i	0.683970	−	0.496933i
$730$		0			0
$731$	24.3698	+	5.17997i	0.901351	+	0.191588i
$732$		0			0
$733$	25.4198	+	18.4686i	0.938903	+	0.682153i	0.948156	−	0.317804i	$-0.102945\pi$
$733$	25.4198	+	18.4686i	0.938903	+	0.682153i	−0.00925303	+	0.999957i	$0.502945\pi$
$734$		0			0
$735$	8.28166	−	1.76032i	0.305474	−	0.0649305i
$736$		0			0
$737$	24.1124	−	36.7870i	0.888191	−	1.35507i
$738$		0			0
$739$	−6.00046	−	6.66419i	−0.220731	−	0.245146i	0.622601	−	0.782539i	$-0.286076\pi$
$739$	−6.00046	−	6.66419i	−0.220731	−	0.245146i	−0.843332	+	0.537393i	$0.819409\pi$
$740$		0			0
$741$	−49.1007	−	50.5158i	−1.80376	−	1.85575i
$742$		0			0
$743$	28.0636	+	5.96510i	1.02955	+	0.218838i	0.691567	−	0.722312i	$-0.256921\pi$
$743$	28.0636	+	5.96510i	1.02955	+	0.218838i	0.337987	+	0.941151i	$0.390254\pi$
$744$		0			0
$745$	19.5592	+	8.70832i	0.716594	+	0.319048i
$746$		0			0
$747$	11.5035	+	19.9246i	0.420889	+	0.729002i
$748$		0			0
$749$	−29.6091			−1.08189
$750$		0			0
$751$	−4.03081	−	38.3506i	−0.147086	−	1.39943i	−0.780276	−	0.625436i	$-0.784921\pi$
$751$	−4.03081	−	38.3506i	−0.147086	−	1.39943i	0.633190	−	0.773997i	$-0.281745\pi$
$752$		0			0
$753$	7.11322	+	21.8922i	0.259220	+	0.797798i
$754$		0			0
$755$	−22.6515	−	16.4573i	−0.824371	−	0.598941i
$756$		0			0
$757$	−0.280017	−	0.310990i	−0.0101774	−	0.0113031i	0.738035	−	0.674763i	$-0.235754\pi$
$757$	−0.280017	−	0.310990i	−0.0101774	−	0.0113031i	−0.748212	+	0.663460i	$0.769087\pi$
$758$		0			0
$759$	−7.37898	−	3.79931i	−0.267840	−	0.137906i
$760$		0			0
$761$	52.9143	−	11.2473i	1.91814	−	0.407713i	0.918209	−	0.396097i	$-0.129636\pi$
$761$	52.9143	−	11.2473i	1.91814	−	0.407713i	0.999933	−	0.0116163i	$-0.00369766\pi$
$762$		0			0
$763$	3.07634	−	29.2695i	0.111371	−	1.05963i
$764$		0			0
$765$	55.5260	+	11.8024i	2.00755	+	0.426718i
$766$		0			0
$767$	−44.8402	−	30.0336i	−1.61909	−	1.08445i
$768$		0			0
$769$	18.5216	−	32.0803i	0.667906	−	1.15685i	−0.310583	−	0.950546i	$-0.600524\pi$
$769$	18.5216	−	32.0803i	0.667906	−	1.15685i	0.978489	−	0.206300i	$-0.0661424\pi$
$770$		0			0
$771$	26.5041	+	45.9065i	0.954522	+	1.65328i
$772$		0			0
$773$	37.8017	+	16.8304i	1.35963	+	0.605347i	0.951520	−	0.307586i	$-0.0995211\pi$
$773$	37.8017	+	16.8304i	1.35963	+	0.605347i	0.408111	+	0.912932i	$0.366188\pi$
$774$		0			0
$775$	−7.64600	−	23.5320i	−0.274652	−	0.845293i
$776$		0			0
$777$	19.7229	−	8.78119i	0.707554	−	0.315023i
$778$		0			0
$779$	−2.44283	+	7.51826i	−0.0875235	+	0.269370i
$780$		0			0
$781$	−12.9614	+	12.8519i	−0.463797	+	0.459876i
$782$		0			0
$783$	0.348980	+	0.387581i	0.0124715	+	0.0138510i
$784$		0			0
$785$	50.4724	+	36.6704i	1.80144	+	1.30882i
$786$		0			0
$787$	13.4113	−	14.8947i	0.478060	−	0.530939i	−0.455081	−	0.890450i	$-0.650390\pi$
$787$	13.4113	−	14.8947i	0.478060	−	0.530939i	0.933141	+	0.359511i	$0.117056\pi$
$788$		0			0
$789$	7.78513	+	3.46616i	0.277158	+	0.123399i
$790$		0			0
$791$	−12.1359	+	21.0200i	−0.431502	+	0.747384i
$792$		0			0
$793$	4.42826	+	12.0446i	0.157252	+	0.427718i
$794$		0			0
$795$	1.25153	+	11.9075i	0.0443871	+	0.422315i
$796$		0			0
$797$	−8.69124	+	9.65260i	−0.307859	+	0.341913i	−0.877143	−	0.480228i	$-0.840554\pi$
$797$	−8.69124	+	9.65260i	−0.307859	+	0.341913i	0.569284	+	0.822141i	$0.307220\pi$
$798$		0			0
$799$	5.93432	−	56.4613i	0.209941	−	1.99746i
$800$		0			0
$801$	10.1481	−	31.2327i	0.358566	−	1.10355i
$802$		0			0
$803$	−0.0622372	−	0.0508376i	−0.00219630	−	0.00179402i
$804$		0			0
$805$	−2.25620	+	6.94388i	−0.0795208	+	0.244740i
$806$		0			0
$807$	29.1894	+	21.2073i	1.02752	+	0.746534i
$808$		0			0
$809$	−16.3481	−	3.47489i	−0.574768	−	0.122171i	−0.0886484	−	0.996063i	$-0.528255\pi$
$809$	−16.3481	−	3.47489i	−0.574768	−	0.122171i	−0.486120	+	0.873892i	$0.661588\pi$
$810$		0			0
$811$	−33.2068	+	24.1262i	−1.16605	+	0.847185i	−0.990531	−	0.137291i	$-0.956160\pi$
$811$	−33.2068	+	24.1262i	−1.16605	+	0.847185i	−0.175519	+	0.984476i	$0.556160\pi$
$812$		0			0
$813$	13.3267	+	23.0825i	0.467387	+	0.809538i
$814$		0			0
$815$	8.21146	+	14.2227i	0.287635	+	0.498198i
$816$		0			0
$817$	−3.01675	−	28.7025i	−0.105543	−	1.00417i
$818$		0			0
$819$	22.3606	+	8.94988i	0.781343	+	0.312734i
$820$		0			0
$821$	−37.0874	+	16.5124i	−1.29436	+	0.576286i	−0.934248	−	0.356623i	$-0.883928\pi$
$821$	−37.0874	+	16.5124i	−1.29436	+	0.576286i	−0.360112	+	0.932909i	$0.617261\pi$
$822$		0			0
$823$	27.2853	−	5.79966i	0.951105	−	0.202164i	0.293867	−	0.955846i	$-0.405058\pi$
$823$	27.2853	−	5.79966i	0.951105	−	0.202164i	0.657238	+	0.753683i	$0.271725\pi$
$824$		0			0
$825$	17.4173	+	21.6962i	0.606392	+	0.755365i
$826$		0			0
$827$	−2.64928	+	8.15364i	−0.0921245	+	0.283530i	−0.986494	−	0.163800i	$-0.947625\pi$
$827$	−2.64928	+	8.15364i	−0.0921245	+	0.283530i	0.894369	+	0.447330i	$0.147625\pi$
$828$		0			0
$829$	2.82574	−	1.25810i	0.0981422	−	0.0436957i	−0.357078	−	0.934074i	$-0.616227\pi$
$829$	2.82574	−	1.25810i	0.0981422	−	0.0436957i	0.455221	+	0.890379i	$0.349560\pi$
$830$		0			0
$831$	11.1552	+	34.3323i	0.386971	+	1.19097i
$832$		0			0
$833$	6.86462	−	4.98744i	0.237845	−	0.172805i
$834$		0			0
$835$	31.0720	−	53.8182i	1.07529	−	1.86246i
$836$		0			0
$837$	−3.81788			−0.131965
$838$		0			0
$839$	−6.97278	−	3.10448i	−0.240727	−	0.107179i	0.282827	−	0.959171i	$-0.408728\pi$
$839$	−6.97278	−	3.10448i	−0.240727	−	0.107179i	−0.523554	+	0.851992i	$0.675394\pi$
$840$		0			0
$841$	−18.7774	+	20.8544i	−0.647495	+	0.719116i
$842$		0			0
$843$	18.9601	−	8.44159i	0.653021	−	0.290744i
$844$		0			0
$845$	−23.1268	+	30.0008i	−0.795587	+	1.03206i
$846$		0			0
$847$	5.72320	−	25.8448i	0.196652	−	0.888037i
$848$		0			0
$849$	−16.0240	+	3.40601i	−0.549943	+	0.116894i
$850$		0			0
$851$	0.406296	−	3.86565i	0.0139277	−	0.132513i
$852$		0			0
$853$	3.61106	+	11.1137i	0.123640	+	0.380526i	0.993651	−	0.112507i	$-0.0358882\pi$
$853$	3.61106	+	11.1137i	0.123640	+	0.380526i	−0.870011	+	0.493033i	$0.835888\pi$
$854$		0			0
$855$	−6.87359	−	65.3979i	−0.235072	−	2.23656i
$856$		0			0
$857$	−39.9562			−1.36488			−0.682438	−	0.730943i	$-0.739080\pi$
$857$	−39.9562			−1.36488			−0.682438	+	0.730943i	$0.739080\pi$
$858$		0			0
$859$	10.6074			0.361921			0.180961	−	0.983490i	$-0.442079\pi$
$859$	10.6074			0.361921			0.180961	+	0.983490i	$0.442079\pi$
$860$		0			0
$861$	−0.587830	−	5.59283i	−0.0200332	−	0.190603i
$862$		0			0
$863$	7.41283	+	22.8143i	0.252336	+	0.776609i	0.994343	+	0.106217i	$0.0338740\pi$
$863$	7.41283	+	22.8143i	0.252336	+	0.776609i	−0.742007	+	0.670392i	$0.766126\pi$
$864$		0			0
$865$	4.20963	−	40.0520i	0.143132	−	1.36181i
$866$		0			0
$867$	75.8232	−	16.1167i	2.57509	−	0.547353i
$868$		0			0
$869$	11.5062	−	29.5985i	0.390320	−	1.00406i
$870$		0			0
$871$	25.4707	+	40.4685i	0.863042	+	1.37122i
$872$		0			0
$873$	−28.8332	+	12.8374i	−0.975856	+	0.434479i
$874$		0			0
$875$	−7.08245	+	7.86585i	−0.239430	+	0.265914i
$876$		0			0
$877$	−7.07592	−	3.15040i	−0.238937	−	0.106381i	0.283775	−	0.958891i	$-0.408413\pi$
$877$	−7.07592	−	3.15040i	−0.238937	−	0.106381i	−0.522712	+	0.852509i	$0.675080\pi$
$878$		0			0
$879$	−37.2011			−1.25476
$880$		0			0
$881$	−19.1668	+	33.1978i	−0.645744	+	1.11846i	0.338385	+	0.941008i	$0.390120\pi$
$881$	−19.1668	+	33.1978i	−0.645744	+	1.11846i	−0.984129	+	0.177454i	$0.943214\pi$
$882$		0			0
$883$	41.1525	−	29.8991i	1.38489	−	1.00618i	0.388488	−	0.921454i	$-0.372997\pi$
$883$	41.1525	−	29.8991i	1.38489	−	1.00618i	0.996404	−	0.0847295i	$-0.0270026\pi$
$884$		0			0
$885$	−32.3916	−	99.6910i	−1.08883	−	3.35108i
$886$		0			0
$887$	−27.2484	+	12.1318i	−0.914912	+	0.407345i	−0.809524	−	0.587086i	$-0.800275\pi$
$887$	−27.2484	+	12.1318i	−0.914912	+	0.407345i	−0.105388	+	0.994431i	$0.533608\pi$
$888$		0			0
$889$	11.6728	−	35.9253i	0.391494	−	1.20489i
$890$		0			0
$891$	29.8415	−	11.3100i	0.999728	−	0.378899i
$892$		0			0
$893$	−64.3276	+	13.6733i	−2.15264	+	0.457558i
$894$		0			0
$895$	40.9106	−	18.2146i	1.36749	−	0.608847i
$896$		0			0
$897$	7.09187	−	5.57798i	0.236791	−	0.186243i
$898$		0			0
$899$	0.717508	+	6.82663i	0.0239302	+	0.227681i
$900$		0			0
$901$	5.99958	+	10.3916i	0.199875	+	0.346194i
$902$		0			0
$903$	10.2655	+	17.7804i	0.341615	+	0.591695i
$904$		0			0
$905$	−3.93339	+	2.85778i	−0.130750	+	0.0949957i
$906$		0			0
$907$	−51.8391	−	11.0187i	−1.72129	−	0.365871i	−0.761841	−	0.647764i	$-0.775704\pi$
$907$	−51.8391	−	11.0187i	−1.72129	−	0.365871i	−0.959446	+	0.281893i	$0.909038\pi$
$908$		0			0
$909$	10.6540	+	7.74060i	0.353372	+	0.256740i
$910$		0			0
$911$	−9.92071	+	30.5328i	−0.328688	+	1.01160i	0.641061	+	0.767490i	$0.278495\pi$
$911$	−9.92071	+	30.5328i	−0.328688	+	1.01160i	−0.969748	+	0.244107i	$0.921505\pi$
$912$		0			0
$913$	7.00179	+	26.5818i	0.231725	+	0.879730i
$914$		0			0
$915$	−7.70214	+	23.7048i	−0.254625	+	0.783655i
$916$		0			0
$917$	2.06078	−	19.6070i	0.0680528	−	0.647480i
$918$		0			0
$919$	21.5739	−	23.9602i	0.711656	−	0.790375i	−0.273530	−	0.961864i	$-0.588191\pi$
$919$	21.5739	−	23.9602i	0.711656	−	0.790375i	0.985186	+	0.171489i	$0.0548578\pi$
$920$		0			0
$921$	−0.985672	−	9.37804i	−0.0324790	−	0.309017i
$922$		0			0
$923$	−6.84726	−	18.6242i	−0.225380	−	0.613023i
$924$		0			0
$925$	−6.51499	+	11.2843i	−0.214212	+	0.371025i
$926$		0			0
$927$	19.3482	+	8.61439i	0.635480	+	0.282934i
$928$		0			0
$929$	23.2901	−	25.8663i	0.764124	−	0.848645i	−0.228032	−	0.973654i	$-0.573229\pi$
$929$	23.2901	−	25.8663i	0.764124	−	0.848645i	0.992156	+	0.125008i	$0.0398958\pi$
$930$		0			0
$931$	−7.95194	−	5.77743i	−0.260614	−	0.189347i
$932$		0			0
$933$	13.7217	+	15.2394i	0.449227	+	0.498917i
$934$		0			0
$935$	60.3007	+	31.0478i	1.97204	+	1.01537i
$936$		0			0
$937$	5.13253	−	15.7963i	0.167672	−	0.516043i	−0.831551	−	0.555449i	$-0.812547\pi$
$937$	5.13253	−	15.7963i	0.167672	−	0.516043i	0.999223	+	0.0394060i	$0.0125466\pi$
$938$		0			0
$939$	−13.6259	+	6.06663i	−0.444664	+	0.197977i
$940$		0			0
$941$	−10.9754	−	33.7788i	−0.357788	−	1.10116i	−0.954375	−	0.298610i	$-0.903477\pi$
$941$	−10.9754	−	33.7788i	−0.357788	−	1.10116i	0.596587	−	0.802548i	$-0.296523\pi$
$942$		0			0
$943$	−0.924945	−	0.411812i	−0.0301203	−	0.0134104i
$944$		0			0
$945$	−1.88831	−	3.27064i	−0.0614266	−	0.106394i
$946$		0			0
$947$	−28.6376	+	49.6018i	−0.930597	+	1.61184i	−0.148293	+	0.988943i	$0.547378\pi$
$947$	−28.6376	+	49.6018i	−0.930597	+	1.61184i	−0.782304	+	0.622897i	$0.785955\pi$
$948$		0			0
$949$	0.0783955	−	0.0385518i	0.00254483	−	0.00125144i
$950$		0			0
$951$	−27.8913	−	5.92848i	−0.904438	−	0.192244i
$952$		0			0
$953$	6.12801	−	58.3041i	0.198506	−	1.88866i	−0.212705	−	0.977116i	$-0.568227\pi$
$953$	6.12801	−	58.3041i	0.198506	−	1.88866i	0.411211	−	0.911540i	$-0.365106\pi$
$954$		0			0
$955$	−40.1160	+	8.52692i	−1.29812	+	0.275925i
$956$		0			0
$957$	−3.47493	−	6.89209i	−0.112328	−	0.222790i
$958$		0			0
$959$	15.0374	+	16.7008i	0.485584	+	0.539296i
$960$		0			0
$961$	−15.5726	−	11.3141i	−0.502342	−	0.364973i
$962$		0			0
$963$	10.5544	+	32.4832i	0.340112	+	1.04676i
$964$		0			0
$965$	−1.14687	−	10.9117i	−0.0369190	−	0.351261i
$966$		0			0
$967$	−41.0545			−1.32022			−0.660112	−	0.751167i	$-0.729491\pi$
$967$	−41.0545			−1.32022			−0.660112	+	0.751167i	$0.729491\pi$
$968$		0			0
$969$	−68.5616	−	118.752i	−2.20252	−	3.81487i
$970$		0			0
$971$	−16.4026	−	7.30292i	−0.526385	−	0.234362i	0.126298	−	0.991992i	$-0.459690\pi$
$971$	−16.4026	−	7.30292i	−0.526385	−	0.234362i	−0.652684	+	0.757630i	$0.726357\pi$
$972$		0			0
$973$	−32.2816	−	6.86167i	−1.03490	−	0.219975i
$974$		0			0
$975$	−29.3238	+	7.41252i	−0.939113	+	0.237391i
$976$		0			0
$977$	7.78068	+	8.64132i	0.248926	+	0.276460i	0.854639	−	0.519223i	$-0.173779\pi$
$977$	7.78068	+	8.64132i	0.248926	+	0.276460i	−0.605713	+	0.795683i	$0.707112\pi$
$978$		0			0
$979$	21.5095	−	32.8160i	0.687447	−	1.04880i
$980$		0			0
$981$	−33.2072	+	7.05841i	−1.06022	+	0.225358i
$982$		0			0
$983$	14.3328	+	10.4134i	0.457144	+	0.332135i	0.792410	−	0.609989i	$-0.208826\pi$
$983$	14.3328	+	10.4134i	0.457144	+	0.332135i	−0.335266	+	0.942124i	$0.608826\pi$
$984$		0			0
$985$	−63.4792	−	13.4929i	−2.02261	−	0.429920i
$986$		0			0
$987$	37.8492	−	27.4991i	1.20475	−	0.875306i
$988$		0			0
$989$	3.69640			0.117539
$990$		0			0
$991$	−19.0390	+	32.9764i	−0.604792	+	1.04753i	0.387292	+	0.921957i	$0.373410\pi$
$991$	−19.0390	+	32.9764i	−0.604792	+	1.04753i	−0.992084	+	0.125574i	$0.959923\pi$
$992$		0			0
$993$	−63.9616	+	46.4708i	−2.02976	+	1.47471i
$994$		0			0
$995$	−2.97689	+	3.30617i	−0.0943737	+	0.104813i
$996$		0			0
$997$	−1.08307	+	10.3047i	−0.0343011	+	0.326353i	0.963893	+	0.266288i	$0.0857973\pi$
$997$	−1.08307	+	10.3047i	−0.0343011	+	0.326353i	−0.998194	+	0.0600645i	$0.980869\pi$
$998$		0			0
$999$	1.34532	+	1.49413i	0.0425640	+	0.0472721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.9.12	✓	112
11.5	even	5	inner	572.2.bg.a.269.3	yes	112
13.3	even	3	inner	572.2.bg.a.185.3	yes	112
143.16	even	15	inner	572.2.bg.a.445.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.9.12	✓	112	1.1	even	1	trivial
572.2.bg.a.185.3	yes	112	13.3	even	3	inner
572.2.bg.a.269.3	yes	112	11.5	even	5	inner
572.2.bg.a.445.12	yes	112	143.16	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.251214 + 2.39014i) q^{3} +(-0.900429 - 2.77123i) q^{5} +(0.251542 - 2.39326i) q^{7} +(-2.71524 + 0.577141i) q^{9} +O(q^{10})\)	\(q+(0.251214 + 2.39014i) q^{3} +(-0.900429 - 2.77123i) q^{5} +(0.251542 - 2.39326i) q^{7} +(-2.71524 + 0.577141i) q^{9} +(-3.31131 - 0.187635i) q^{11} +(1.68235 - 3.18900i) q^{13} +(6.39745 - 2.84833i) q^{15} +(4.69606 - 5.21550i) q^{17} +(-7.42693 - 3.30668i) q^{19} +5.78343 q^{21} +(0.520623 - 0.901746i) q^{23} +(-2.82388 + 2.05167i) q^{25} +(0.166434 + 0.512231i) q^{27} +(0.884626 - 0.393861i) q^{29} +(-2.19051 + 6.74169i) q^{31} +(-0.383374 - 7.96165i) q^{33} +(-6.85878 + 1.45788i) q^{35} +(3.41024 - 1.51834i) q^{37} +(8.04479 + 3.21994i) q^{39} +(-0.101640 - 0.967044i) q^{41} +(1.77499 + 3.07437i) q^{43} +(4.04427 + 7.00488i) q^{45} +(6.54443 - 4.75481i) q^{47} +(1.18261 + 0.251371i) q^{49} +(13.6455 + 9.91404i) q^{51} +(-0.528337 + 1.62605i) q^{53} +(2.46162 + 9.34538i) q^{55} +(6.03769 - 18.5821i) q^{57} +(1.56462 - 14.8863i) q^{59} +(-2.38157 + 2.64500i) q^{61} +(0.698254 + 6.64344i) q^{63} +(-10.3523 - 1.79073i) q^{65} +(-6.63101 + 11.4852i) q^{67} +(2.28609 + 1.01783i) q^{69} +(3.68254 - 4.08987i) q^{71} +(0.0196023 + 0.0142419i) q^{73} +(-5.61319 - 6.23408i) q^{75} +(-1.28199 + 7.87764i) q^{77} +(-2.95880 + 9.10626i) q^{79} +(-8.79022 + 3.91366i) q^{81} +(-2.56116 - 7.88245i) q^{83} +(-18.6818 - 8.31769i) q^{85} +(1.16361 + 2.01544i) q^{87} +(-5.91521 + 10.2454i) q^{89} +(-7.20892 - 4.82847i) q^{91} +(-16.6639 - 3.54202i) q^{93} +(-2.47617 + 23.5592i) q^{95} +(11.1215 - 2.36395i) q^{97} +(9.09929 - 1.40162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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