LMFDB - Embedded newform 380.2.u.b.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 $ x^18 - 3x^17 + 21x^16 - 30x^15 + 192x^14 - 207x^13 + 1178x^12 - 705x^11 + 4413x^10 - 2224x^9 + 11430x^8 - 4101x^7 + 19237x^6 - 7125x^5 + 21573x^4 - 5266x^3 + 13851x^2 - 3285*x + 5329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			161.1
Root			$1.37427 - 2.38031i$ of defining polynomial
Character	$\chi$	$=$	380.161
Dual form			380.2.u.b.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10551 + 1.76673i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(-1.23778 + 2.14391i) q^{7} +(0.790885 - 4.48533i) q^{9} +O(q^{10})$	\(q+(-2.10551 + 1.76673i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(-1.23778 + 2.14391i) q^{7} +(0.790885 - 4.48533i) q^{9} +(0.186396 + 0.322847i) q^{11} +(-2.64101 - 2.21607i) q^{13} +(2.58279 - 0.940059i) q^{15} +(-0.361680 - 2.05119i) q^{17} +(0.0754994 - 4.35825i) q^{19} +(-1.18154 - 6.70085i) q^{21} +(-0.815458 + 0.296802i) q^{23} +(0.766044 + 0.642788i) q^{25} +(2.13635 + 3.70026i) q^{27} +(1.80276 - 10.2240i) q^{29} +(-0.935507 + 1.62035i) q^{31} +(-0.962842 - 0.350446i) q^{33} +(1.89640 - 1.59127i) q^{35} -6.21229 q^{37} +9.47590 q^{39} +(-6.08529 + 5.10617i) q^{41} +(-3.27429 - 1.19174i) q^{43} +(-2.27726 + 3.94434i) q^{45} +(-0.871070 + 4.94008i) q^{47} +(0.435777 + 0.754789i) q^{49} +(4.38543 + 3.67981i) q^{51} +(7.54214 - 2.74511i) q^{53} +(-0.0647345 - 0.367128i) q^{55} +(7.54089 + 9.30972i) q^{57} +(-1.44337 - 8.18576i) q^{59} +(-12.1477 + 4.42141i) q^{61} +(8.63719 + 7.24746i) q^{63} +(1.72380 + 2.98571i) q^{65} +(-1.28954 + 7.31335i) q^{67} +(1.19258 - 2.06562i) q^{69} +(-2.31925 - 0.844139i) q^{71} +(-3.87343 + 3.25019i) q^{73} -2.74855 q^{75} -0.922870 q^{77} +(-11.9174 + 9.99989i) q^{79} +(1.80409 + 0.656635i) q^{81} +(-3.14735 + 5.45137i) q^{83} +(-0.361680 + 2.05119i) q^{85} +(14.2673 + 24.7117i) q^{87} +(-0.811454 - 0.680891i) q^{89} +(8.02006 - 2.91906i) q^{91} +(-0.892999 - 5.06445i) q^{93} +(-1.56155 + 4.06959i) q^{95} +(-2.49008 - 14.1219i) q^{97} +(1.59549 - 0.580711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 15 * q^9	$ 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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
$3$	−2.10551	+	1.76673i	−1.21562	+	1.02002i	−0.216575	+	0.976266i	$0.569489\pi$
$3$	−2.10551	+	1.76673i	−1.21562	+	1.02002i	−0.999042	+	0.0437583i	$0.986067\pi$
$4$		0			0
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$		0			0
$7$	−1.23778	+	2.14391i	−0.467839	+	0.810320i	−0.999325	−	0.0367467i	$-0.988301\pi$
$7$	−1.23778	+	2.14391i	−0.467839	+	0.810320i	0.531486	+	0.847067i	$0.321634\pi$
$8$		0			0
$9$	0.790885	−	4.48533i	0.263628	−	1.49511i
$10$		0			0
$11$	0.186396	+	0.322847i	0.0562004	+	0.0973419i	0.892757	−	0.450539i	$-0.148768\pi$
$11$	0.186396	+	0.322847i	0.0562004	+	0.0973419i	−0.836556	+	0.547881i	$0.815435\pi$
$12$		0			0
$13$	−2.64101	−	2.21607i	−0.732486	−	0.614628i	0.198322	−	0.980137i	$-0.436451\pi$
$13$	−2.64101	−	2.21607i	−0.732486	−	0.614628i	−0.930808	+	0.365508i	$0.880895\pi$
$14$		0			0
$15$	2.58279	−	0.940059i	0.666874	−	0.242722i
$16$		0			0
$17$	−0.361680	−	2.05119i	−0.0877204	−	0.497487i	−0.996736	−	0.0807258i	$-0.974276\pi$
$17$	−0.361680	−	2.05119i	−0.0877204	−	0.497487i	0.909016	−	0.416761i	$-0.136835\pi$
$18$		0			0
$19$	0.0754994	−	4.35825i	0.0173208	−	0.999850i
$19$	0.0754994	−	4.35825i	0.0173208	−	0.999850i
$20$		0			0
$21$	−1.18154	−	6.70085i	−0.257833	−	1.46225i
$22$		0			0
$23$	−0.815458	+	0.296802i	−0.170035	+	0.0618876i	−0.425635	−	0.904895i	$-0.639949\pi$
$23$	−0.815458	+	0.296802i	−0.170035	+	0.0618876i	0.255600	+	0.966783i	$0.417727\pi$
$24$		0			0
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$		0			0
$27$	2.13635	+	3.70026i	0.411140	+	0.712115i
$28$		0			0
$29$	1.80276	−	10.2240i	0.334764	−	1.89854i	−0.0947830	−	0.995498i	$-0.530216\pi$
$29$	1.80276	−	10.2240i	0.334764	−	1.89854i	0.429547	−	0.903044i	$-0.358673\pi$
$30$		0			0
$31$	−0.935507	+	1.62035i	−0.168022	+	0.291023i	−0.937724	−	0.347380i	$-0.887071\pi$
$31$	−0.935507	+	1.62035i	−0.168022	+	0.291023i	0.769702	+	0.638403i	$0.220405\pi$
$32$		0			0
$33$	−0.962842	−	0.350446i	−0.167609	−	0.0610048i
$34$		0			0
$35$	1.89640	−	1.59127i	0.320549	−	0.268973i
$36$		0			0
$37$	−6.21229			−1.02129			−0.510647	−	0.859790i	$-0.670594\pi$
$37$	−6.21229			−1.02129			−0.510647	+	0.859790i	$0.670594\pi$
$38$		0			0
$39$	9.47590			1.51736
$40$		0			0
$41$	−6.08529	+	5.10617i	−0.950363	+	0.797449i	−0.979359	−	0.202130i	$-0.935214\pi$
$41$	−6.08529	+	5.10617i	−0.950363	+	0.797449i	0.0289956	+	0.999580i	$0.490769\pi$
$42$		0			0
$43$	−3.27429	−	1.19174i	−0.499324	−	0.181739i	0.0800658	−	0.996790i	$-0.474487\pi$
$43$	−3.27429	−	1.19174i	−0.499324	−	0.181739i	−0.579390	+	0.815050i	$0.696709\pi$
$44$		0			0
$45$	−2.27726	+	3.94434i	−0.339474	+	0.587987i
$46$		0			0
$47$	−0.871070	+	4.94008i	−0.127059	+	0.720585i	0.853005	+	0.521902i	$0.174777\pi$
$47$	−0.871070	+	4.94008i	−0.127059	+	0.720585i	−0.980064	+	0.198683i	$0.936334\pi$
$48$		0			0
$49$	0.435777	+	0.754789i	0.0622539	+	0.107827i
$50$		0			0
$51$	4.38543	+	3.67981i	0.614083	+	0.515277i
$52$		0			0
$53$	7.54214	−	2.74511i	1.03599	−	0.377070i	0.232633	−	0.972565i	$-0.425266\pi$
$53$	7.54214	−	2.74511i	1.03599	−	0.377070i	0.803360	+	0.595494i	$0.203044\pi$
$54$		0			0
$55$	−0.0647345	−	0.367128i	−0.00872880	−	0.0495035i
$56$		0			0
$57$	7.54089	+	9.30972i	0.998816	+	1.23310i
$58$		0			0
$59$	−1.44337	−	8.18576i	−0.187911	−	1.06569i	−0.922158	−	0.386813i	$-0.873576\pi$
$59$	−1.44337	−	8.18576i	−0.187911	−	1.06569i	0.734248	−	0.678882i	$-0.237535\pi$
$60$		0			0
$61$	−12.1477	+	4.42141i	−1.55536	+	0.566104i	−0.969667	−	0.244431i	$-0.921399\pi$
$61$	−12.1477	+	4.42141i	−1.55536	+	0.566104i	−0.585691	+	0.810535i	$0.699177\pi$
$62$		0			0
$63$	8.63719	+	7.24746i	1.08818	+	0.913094i
$64$		0			0
$65$	1.72380	+	2.98571i	0.213811	+	0.370332i
$66$		0			0
$67$	−1.28954	+	7.31335i	−0.157543	+	0.893468i	0.798882	+	0.601488i	$0.205425\pi$
$67$	−1.28954	+	7.31335i	−0.157543	+	0.893468i	−0.956424	+	0.291980i	$0.905686\pi$
$68$		0			0
$69$	1.19258	−	2.06562i	0.143570	−	0.248671i
$70$		0			0
$71$	−2.31925	−	0.844139i	−0.275245	−	0.100181i	0.200710	−	0.979651i	$-0.435675\pi$
$71$	−2.31925	−	0.844139i	−0.275245	−	0.100181i	−0.475955	+	0.879470i	$0.657897\pi$
$72$		0			0
$73$	−3.87343	+	3.25019i	−0.453350	+	0.380406i	−0.840677	−	0.541536i	$-0.817843\pi$
$73$	−3.87343	+	3.25019i	−0.453350	+	0.380406i	0.387327	+	0.921942i	$0.373398\pi$
$74$		0			0
$75$	−2.74855			−0.317375
$76$		0			0
$77$	−0.922870			−0.105171
$78$		0			0
$79$	−11.9174	+	9.99989i	−1.34081	+	1.12508i	−0.359397	+	0.933185i	$0.617018\pi$
$79$	−11.9174	+	9.99989i	−1.34081	+	1.12508i	−0.981416	+	0.191891i	$0.938538\pi$
$80$		0			0
$81$	1.80409	+	0.656635i	0.200454	+	0.0729594i
$82$		0			0
$83$	−3.14735	+	5.45137i	−0.345467	+	0.598366i	−0.985438	−	0.170033i	$-0.945613\pi$
$83$	−3.14735	+	5.45137i	−0.345467	+	0.598366i	0.639972	+	0.768398i	$0.278946\pi$
$84$		0			0
$85$	−0.361680	+	2.05119i	−0.0392298	+	0.222483i
$86$		0			0
$87$	14.2673	+	24.7117i	1.52961	+	2.64937i
$88$		0			0
$89$	−0.811454	−	0.680891i	−0.0860140	−	0.0721743i	0.598767	−	0.800923i	$-0.295658\pi$
$89$	−0.811454	−	0.680891i	−0.0860140	−	0.0721743i	−0.684781	+	0.728749i	$0.740102\pi$
$90$		0			0
$91$	8.02006	−	2.91906i	0.840731	−	0.306001i
$92$		0			0
$93$	−0.892999	−	5.06445i	−0.0925996	−	0.525159i
$94$		0			0
$95$	−1.56155	+	4.06959i	−0.160212	+	0.417531i
$96$		0			0
$97$	−2.49008	−	14.1219i	−0.252829	−	1.43387i	−0.801584	−	0.597882i	$-0.796009\pi$
$97$	−2.49008	−	14.1219i	−0.252829	−	1.43387i	0.548755	−	0.835983i	$-0.315102\pi$
$98$		0			0
$99$	1.59549	−	0.580711i	0.160353	−	0.0583637i
$100$		0			0
$101$	13.1480	+	11.0324i	1.30827	+	1.09777i	0.988652	+	0.150223i	$0.0479991\pi$
$101$	13.1480	+	11.0324i	1.30827	+	1.09777i	0.319618	+	0.947546i	$0.396445\pi$
$102$		0			0
$103$	−9.36128	−	16.2142i	−0.922394	−	1.59763i	−0.795699	−	0.605692i	$-0.792896\pi$
$103$	−9.36128	−	16.2142i	−0.922394	−	1.59763i	−0.126695	−	0.991942i	$-0.540437\pi$
$104$		0			0
$105$	−1.18154	+	6.70085i	−0.115307	+	0.653936i
$106$		0			0
$107$	0.706719	−	1.22407i	0.0683211	−	0.118336i	−0.829841	−	0.557999i	$-0.811569\pi$
$107$	0.706719	−	1.22407i	0.0683211	−	0.118336i	0.898162	+	0.439664i	$0.144902\pi$
$108$		0			0
$109$	−11.6749	−	4.24930i	−1.11825	−	0.407009i	−0.284236	−	0.958754i	$-0.591740\pi$
$109$	−11.6749	−	4.24930i	−1.11825	−	0.407009i	−0.834013	+	0.551745i	$0.813962\pi$
$110$		0			0
$111$	13.0800	−	10.9755i	1.24150	−	1.04174i
$112$		0			0
$113$	10.6415			1.00107			0.500536	−	0.865716i	$-0.333136\pi$
$113$	10.6415			1.00107			0.500536	+	0.865716i	$0.333136\pi$
$114$		0			0
$115$	0.867792			0.0809220
$116$		0			0
$117$	−12.0286	+	10.0932i	−1.11204	+	0.933114i
$118$		0			0
$119$	4.84525	+	1.76352i	0.444163	+	0.161662i
$120$		0			0
$121$	5.43051	−	9.40593i	0.493683	−	0.855084i
$122$		0			0
$123$	3.79142	−	21.5022i	0.341860	−	1.93879i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−0.188463	−	0.158139i	−0.0167234	−	0.0140326i	0.634388	−	0.773015i	$-0.281252\pi$
$127$	−0.188463	−	0.158139i	−0.0167234	−	0.0140326i	−0.651111	+	0.758983i	$0.725697\pi$
$128$		0			0
$129$	8.99954	−	3.27557i	0.792365	−	0.288397i
$130$		0			0
$131$	−1.50790	−	8.55170i	−0.131745	−	0.747165i	−0.977071	−	0.212914i	$-0.931705\pi$
$131$	−1.50790	−	8.55170i	−0.131745	−	0.747165i	0.845326	−	0.534252i	$-0.179406\pi$
$132$		0			0
$133$	9.25022	+	5.55643i	0.802095	+	0.481804i
$134$		0			0
$135$	−0.741945	−	4.20778i	−0.0638565	−	0.362148i
$136$		0			0
$137$	12.9469	−	4.71230i	1.10613	−	0.402599i	0.276559	−	0.960997i	$-0.410806\pi$
$137$	12.9469	−	4.71230i	1.10613	−	0.402599i	0.829573	+	0.558398i	$0.188584\pi$
$138$		0			0
$139$	3.85051	+	3.23096i	0.326596	+	0.274047i	0.791311	−	0.611414i	$-0.209399\pi$
$139$	3.85051	+	3.23096i	0.326596	+	0.274047i	−0.464715	+	0.885460i	$0.653843\pi$
$140$		0			0
$141$	−6.89376	−	11.9403i	−0.580559	−	1.00556i
$142$		0			0
$143$	0.223179	−	1.26571i	0.0186631	−	0.105844i
$144$		0			0
$145$	−5.19084	+	8.99080i	−0.431076	+	0.746646i
$146$		0			0
$147$	−2.25105	−	0.819313i	−0.185663	−	0.0675758i
$148$		0			0
$149$	−12.1638	+	10.2066i	−0.996496	+	0.836159i	−0.986495	−	0.163791i	$-0.947628\pi$
$149$	−12.1638	+	10.2066i	−0.996496	+	0.836159i	−0.0100007	+	0.999950i	$0.503183\pi$
$150$		0			0
$151$	7.84823			0.638680			0.319340	−	0.947640i	$-0.396539\pi$
$151$	7.84823			0.638680			0.319340	+	0.947640i	$0.396539\pi$
$152$		0			0
$153$	−9.48632			−0.766924
$154$		0			0
$155$	1.43328	−	1.20266i	0.115124	−	0.0966003i
$156$		0			0
$157$	−12.4130	−	4.51795i	−0.990662	−	0.360572i	−0.204686	−	0.978828i	$-0.565617\pi$
$157$	−12.4130	−	4.51795i	−0.990662	−	0.360572i	−0.785977	+	0.618256i	$0.787839\pi$
$158$		0			0
$159$	−11.0302	+	19.1048i	−0.874750	+	1.51511i
$160$		0			0
$161$	0.373045	−	2.11564i	0.0294001	−	0.166736i
$162$		0			0
$163$	−2.03055	−	3.51702i	−0.159045	−	0.275474i	0.775479	−	0.631373i	$-0.217508\pi$
$163$	−2.03055	−	3.51702i	−0.159045	−	0.275474i	−0.934525	+	0.355898i	$0.884175\pi$
$164$		0			0
$165$	0.784916	+	0.658623i	0.0611056	+	0.0512737i
$166$		0			0
$167$	−23.3720	+	8.50671i	−1.80858	+	0.658269i	−0.811294	+	0.584638i	$0.801236\pi$
$167$	−23.3720	+	8.50671i	−1.80858	+	0.658269i	−0.997286	+	0.0736309i	$0.976541\pi$
$168$		0			0
$169$	−0.193455	−	1.09714i	−0.0148811	−	0.0843950i
$170$		0			0
$171$	−19.4885	−	3.78551i	−1.49032	−	0.289485i
$172$		0			0
$173$	−0.714147	−	4.05013i	−0.0542956	−	0.307926i	0.945550	−	0.325476i	$-0.105524\pi$
$173$	−0.714147	−	4.05013i	−0.0542956	−	0.307926i	−0.999846	+	0.0175502i	$0.994413\pi$
$174$		0			0
$175$	−2.32627	+	0.846695i	−0.175850	+	0.0640041i
$176$		0			0
$177$	17.5011	+	14.6852i	1.31546	+	1.10380i
$178$		0			0
$179$	−10.4256	−	18.0577i	−0.779249	−	1.34970i	−0.932375	−	0.361492i	$-0.882267\pi$
$179$	−10.4256	−	18.0577i	−0.779249	−	1.34970i	0.153126	−	0.988207i	$-0.451066\pi$
$180$		0			0
$181$	−3.38402	+	19.1918i	−0.251533	+	1.42651i	0.553286	+	0.832991i	$0.313374\pi$
$181$	−3.38402	+	19.1918i	−0.251533	+	1.42651i	−0.804819	+	0.593521i	$0.797737\pi$
$182$		0			0
$183$	17.7657	−	30.7711i	1.31328	−	2.27467i
$184$		0			0
$185$	5.83764	+	2.12473i	0.429192	+	0.156213i
$186$		0			0
$187$	0.594805	−	0.499100i	0.0434964	−	0.0364978i
$188$		0			0
$189$	−10.5773			−0.769389
$190$		0			0
$191$	6.58959			0.476806			0.238403	−	0.971166i	$-0.423376\pi$
$191$	6.58959			0.476806			0.238403	+	0.971166i	$0.423376\pi$
$192$		0			0
$193$	−15.7958	+	13.2543i	−1.13701	+	0.954064i	−0.999337	−	0.0364135i	$-0.988407\pi$
$193$	−15.7958	+	13.2543i	−1.13701	+	0.954064i	−0.137673	+	0.990478i	$0.543962\pi$
$194$		0			0
$195$	−8.90443	−	3.24095i	−0.637660	−	0.232089i
$196$		0			0
$197$	10.9479	−	18.9623i	0.780004	−	1.35101i	−0.151934	−	0.988391i	$-0.548550\pi$
$197$	10.9479	−	18.9623i	0.780004	−	1.35101i	0.931938	−	0.362616i	$-0.118116\pi$
$198$		0			0
$199$	0.141474	−	0.802338i	0.0100288	−	0.0568762i	−0.979383	−	0.202014i	$-0.935251\pi$
$199$	0.141474	−	0.802338i	0.0100288	−	0.0568762i	0.989411	+	0.145138i	$0.0463625\pi$
$200$		0			0
$201$	−10.2056	−	17.6766i	−0.719848	−	1.24681i
$202$		0			0
$203$	19.6878	+	16.5200i	1.38181	+	1.15948i
$204$		0			0
$205$	7.46472	−	2.71693i	0.521358	−	0.189759i
$206$		0			0
$207$	0.686324	+	3.89234i	0.0477028	+	0.270536i
$208$		0			0
$209$	1.42112	−	0.787983i	0.0983007	−	0.0545059i
$210$		0			0
$211$	1.55282	+	8.80649i	0.106901	+	0.606264i	0.990444	+	0.137915i	$0.0440400\pi$
$211$	1.55282	+	8.80649i	0.106901	+	0.606264i	−0.883543	+	0.468349i	$0.844849\pi$
$212$		0			0
$213$	6.37458	−	2.32016i	0.436779	−	0.158975i
$214$		0			0
$215$	2.66922	+	2.23974i	0.182040	+	0.152749i
$216$		0			0
$217$	−2.31591	−	4.01128i	−0.157214	−	0.272303i
$218$		0			0
$219$	2.41332	−	13.6866i	0.163077	−	0.924856i
$220$		0			0
$221$	−3.59039	+	6.21874i	−0.241516	+	0.418318i
$222$		0			0
$223$	−7.48167	−	2.72311i	−0.501010	−	0.182353i	0.0791384	−	0.996864i	$-0.474783\pi$
$223$	−7.48167	−	2.72311i	−0.501010	−	0.182353i	−0.580148	+	0.814511i	$0.697005\pi$
$224$		0			0
$225$	3.48897	−	2.92759i	0.232598	−	0.195173i
$226$		0			0
$227$	−11.5327			−0.765453			−0.382727	−	0.923862i	$-0.625015\pi$
$227$	−11.5327			−0.765453			−0.382727	+	0.923862i	$0.625015\pi$
$228$		0			0
$229$	−1.84953			−0.122220			−0.0611102	−	0.998131i	$-0.519464\pi$
$229$	−1.84953			−0.122220			−0.0611102	+	0.998131i	$0.519464\pi$
$230$		0			0
$231$	1.94311	−	1.63047i	0.127848	−	0.107277i
$232$		0			0
$233$	19.4029	+	7.06206i	1.27112	+	0.462651i	0.887487	−	0.460833i	$-0.152449\pi$
$233$	19.4029	+	7.06206i	1.27112	+	0.462651i	0.383637	+	0.923484i	$0.374671\pi$
$234$		0			0
$235$	2.50814	−	4.34423i	0.163613	−	0.283387i
$236$		0			0
$237$	7.42509	−	42.1098i	0.482311	−	2.73532i
$238$		0			0
$239$	12.3934	+	21.4659i	0.801660	+	1.38852i	0.918523	+	0.395368i	$0.129383\pi$
$239$	12.3934	+	21.4659i	0.801660	+	1.38852i	−0.116863	+	0.993148i	$0.537284\pi$
$240$		0			0
$241$	12.3502	+	10.3631i	0.795548	+	0.667544i	0.947112	−	0.320904i	$-0.103987\pi$
$241$	12.3502	+	10.3631i	0.795548	+	0.667544i	−0.151564	+	0.988447i	$0.548431\pi$
$242$		0			0
$243$	−17.0037	+	6.18883i	−1.09079	+	0.397014i
$244$		0			0
$245$	−0.151344	−	0.858314i	−0.00966901	−	0.0548357i
$246$		0			0
$247$	−9.85759	+	11.3429i	−0.627223	+	0.721730i
$248$		0			0
$249$	−3.00434	−	17.0385i	−0.190392	−	1.07977i
$250$		0			0
$251$	−16.0425	+	5.83899i	−1.01259	+	0.368554i	−0.794428	−	0.607358i	$-0.792229\pi$
$251$	−16.0425	+	5.83899i	−1.01259	+	0.368554i	−0.218165	+	0.975912i	$0.570007\pi$
$252$		0			0
$253$	−0.247819	−	0.207945i	−0.0155803	−	0.0130734i
$254$		0			0
$255$	−2.86239	−	4.95780i	−0.179250	−	0.310469i
$256$		0			0
$257$	0.202646	−	1.14926i	0.0126407	−	0.0716890i	−0.977835	−	0.209378i	$-0.932856\pi$
$257$	0.202646	−	1.14926i	0.0126407	−	0.0716890i	0.990476	+	0.137689i	$0.0439673\pi$
$258$		0			0
$259$	7.68948	−	13.3186i	0.477801	−	0.827576i
$260$		0			0
$261$	−44.4321	−	16.1720i	−2.75028	−	1.00102i
$262$		0			0
$263$	7.18738	−	6.03093i	0.443193	−	0.371883i	−0.393710	−	0.919235i	$-0.628809\pi$
$263$	7.18738	−	6.03093i	0.443193	−	0.371883i	0.836903	+	0.547352i	$0.184364\pi$
$264$		0			0
$265$	−8.02618			−0.493044
$266$		0			0
$267$	2.91148			0.178180
$268$		0			0
$269$	5.63696	−	4.72997i	0.343692	−	0.288392i	−0.454559	−	0.890716i	$-0.650203\pi$
$269$	5.63696	−	4.72997i	0.343692	−	0.288392i	0.798251	+	0.602325i	$0.205759\pi$
$270$		0			0
$271$	−10.0761	−	3.66739i	−0.612078	−	0.222778i	0.0173340	−	0.999850i	$-0.494482\pi$
$271$	−10.0761	−	3.66739i	−0.612078	−	0.222778i	−0.629412	+	0.777071i	$0.716704\pi$
$272$		0			0
$273$	−11.7291	+	20.3154i	−0.709879	+	1.22955i
$274$		0			0
$275$	−0.0647345	+	0.367128i	−0.00390364	+	0.0221386i
$276$		0			0
$277$	8.06323	+	13.9659i	0.484472	+	0.839131i	0.999841	−	0.0178380i	$-0.00567832\pi$
$277$	8.06323	+	13.9659i	0.484472	+	0.839131i	−0.515369	+	0.856969i	$0.672345\pi$
$278$		0			0
$279$	6.52791	+	5.47757i	0.390816	+	0.327933i
$280$		0			0
$281$	28.7858	−	10.4772i	1.71722	−	0.625016i	0.719625	−	0.694363i	$-0.244314\pi$
$281$	28.7858	−	10.4772i	1.71722	−	0.625016i	0.997593	+	0.0693473i	$0.0220917\pi$
$282$		0			0
$283$	−0.924150	−	5.24111i	−0.0549350	−	0.311552i	0.944942	−	0.327238i	$-0.106118\pi$
$283$	−0.924150	−	5.24111i	−0.0549350	−	0.311552i	−0.999877	+	0.0156861i	$0.995007\pi$
$284$		0			0
$285$	−3.90201	−	11.3274i	−0.231135	−	0.670978i
$286$		0			0
$287$	−3.41486	−	19.3666i	−0.201573	−	1.14318i
$288$		0			0
$289$	11.8982	−	4.33059i	0.699894	−	0.254741i
$290$		0			0
$291$	30.1926	+	25.3346i	1.76992	+	1.48514i
$292$		0			0
$293$	−1.76580	−	3.05845i	−0.103159	−	0.178677i	0.809826	−	0.586671i	$-0.199562\pi$
$293$	−1.76580	−	3.05845i	−0.103159	−	0.178677i	−0.912985	+	0.407994i	$0.866228\pi$
$294$		0			0
$295$	−1.44337	+	8.18576i	−0.0840362	+	0.476593i
$296$		0			0
$297$	−0.796411	+	1.37942i	−0.0462124	+	0.0800423i
$298$		0			0
$299$	2.81137	+	1.02326i	0.162586	+	0.0591764i
$300$		0			0
$301$	6.60785	−	5.54464i	0.380870	−	0.319588i
$302$		0			0
$303$	−47.1746			−2.71011
$304$		0			0
$305$	12.9273			0.740218
$306$		0			0
$307$	16.1951	−	13.5893i	0.924303	−	0.775582i	−0.0504828	−	0.998725i	$-0.516076\pi$
$307$	16.1951	−	13.5893i	0.924303	−	0.775582i	0.974786	+	0.223143i	$0.0716316\pi$
$308$		0			0
$309$	48.3565	+	17.6003i	2.75090	+	1.00125i
$310$		0			0
$311$	−3.60633	+	6.24635i	−0.204496	+	0.354198i	−0.949972	−	0.312335i	$-0.898889\pi$
$311$	−3.60633	+	6.24635i	−0.204496	+	0.354198i	0.745476	+	0.666533i	$0.232222\pi$
$312$		0			0
$313$	−3.08980	+	17.5231i	−0.174646	+	0.990465i	0.763906	+	0.645327i	$0.223279\pi$
$313$	−3.08980	+	17.5231i	−0.174646	+	0.990465i	−0.938552	+	0.345138i	$0.887832\pi$
$314$		0			0
$315$	−5.63752	−	9.76448i	−0.317638	−	0.550166i
$316$		0			0
$317$	−17.5594	−	14.7341i	−0.986237	−	0.827551i	−0.00121811	−	0.999999i	$-0.500388\pi$
$317$	−17.5594	−	14.7341i	−0.986237	−	0.827551i	−0.985019	+	0.172448i	$0.944832\pi$
$318$		0			0
$319$	3.63680	−	1.32369i	0.203622	−	0.0741122i
$320$		0			0
$321$	0.674606	+	3.82588i	0.0376529	+	0.213540i
$322$		0			0
$323$	−8.96690	+	1.42143i	−0.498932	+	0.0790904i
$324$		0			0
$325$	−0.598669	−	3.39522i	−0.0332082	−	0.188333i
$326$		0			0
$327$	32.0889	−	11.6794i	1.77452	−	0.645873i
$328$		0			0
$329$	−9.51287	−	7.98225i	−0.524462	−	0.440076i
$330$		0			0
$331$	16.0847	+	27.8595i	0.884095	+	1.53130i	0.846747	+	0.531996i	$0.178558\pi$
$331$	16.0847	+	27.8595i	0.884095	+	1.53130i	0.0373483	+	0.999302i	$0.488109\pi$
$332$		0			0
$333$	−4.91321	+	27.8642i	−0.269242	+	1.52695i
$334$		0			0
$335$	3.71309	−	6.43126i	0.202868	−	0.351377i
$336$		0			0
$337$	21.8033	+	7.93577i	1.18770	+	0.432289i	0.858917	−	0.512115i	$-0.171138\pi$
$337$	21.8033	+	7.93577i	1.18770	+	0.432289i	0.328787	+	0.944404i	$0.393360\pi$
$338$		0			0
$339$	−22.4059	+	18.8008i	−1.21692	+	1.02112i
$340$		0			0
$341$	−0.697497			−0.0377716
$342$		0			0
$343$	−19.4866			−1.05218
$344$		0			0
$345$	−1.82715	+	1.53316i	−0.0983702	+	0.0825424i
$346$		0			0
$347$	12.9601	+	4.71711i	0.695737	+	0.253228i	0.665590	−	0.746318i	$-0.268180\pi$
$347$	12.9601	+	4.71711i	0.695737	+	0.253228i	0.0301473	+	0.999545i	$0.490402\pi$
$348$		0			0
$349$	−0.487253	+	0.843948i	−0.0260821	+	0.0451755i	−0.878772	−	0.477242i	$-0.841636\pi$
$349$	−0.487253	+	0.843948i	−0.0260821	+	0.0451755i	0.852690	+	0.522418i	$0.174970\pi$
$350$		0			0
$351$	2.55793	−	14.5067i	0.136532	−	0.774312i
$352$		0			0
$353$	7.30765	+	12.6572i	0.388947	+	0.673676i	0.992308	−	0.123792i	$-0.0395057\pi$
$353$	7.30765	+	12.6572i	0.388947	+	0.673676i	−0.603361	+	0.797468i	$0.706172\pi$
$354$		0			0
$355$	1.89067	+	1.58646i	0.100346	+	0.0842007i
$356$		0			0
$357$	−13.3174	+	4.84714i	−0.704831	+	0.256538i
$358$		0			0
$359$	0.311258	+	1.76523i	0.0164276	+	0.0931653i	0.991919	−	0.126871i	$-0.0404935\pi$
$359$	0.311258	+	1.76523i	0.0164276	+	0.0931653i	−0.975492	+	0.220036i	$0.929382\pi$
$360$		0			0
$361$	−18.9886	−	0.658090i	−0.999400	−	0.0346363i
$362$		0			0
$363$	5.18376	+	29.3986i	0.272077	+	1.54302i
$364$		0			0
$365$	4.75146	−	1.72939i	0.248703	−	0.0905204i
$366$		0			0
$367$	−25.2610	−	21.1965i	−1.31861	−	1.10645i	−0.986597	−	0.163173i	$-0.947827\pi$
$367$	−25.2610	−	21.1965i	−1.31861	−	1.10645i	−0.332015	−	0.943274i	$-0.607728\pi$
$368$		0			0
$369$	18.0901	+	31.3330i	0.941732	+	1.63113i
$370$		0			0
$371$	−3.45028	+	19.5675i	−0.179130	+	1.01589i
$372$		0			0
$373$	−9.08808	+	15.7410i	−0.470563	+	0.815039i	−0.999433	−	0.0336640i	$-0.989282\pi$
$373$	−9.08808	+	15.7410i	−0.470563	+	0.815039i	0.528870	+	0.848703i	$0.322616\pi$
$374$		0			0
$375$	2.58279	+	0.940059i	0.133375	+	0.0485445i
$376$		0			0
$377$	−27.4182	+	23.0066i	−1.41211	+	1.18490i
$378$		0			0
$379$	−1.90439			−0.0978220			−0.0489110	−	0.998803i	$-0.515575\pi$
$379$	−1.90439			−0.0978220			−0.0489110	+	0.998803i	$0.515575\pi$
$380$		0			0
$381$	0.676201			0.0346428
$382$		0			0
$383$	1.42516	−	1.19585i	0.0728221	−	0.0611050i	−0.605650	−	0.795731i	$-0.707087\pi$
$383$	1.42516	−	1.19585i	0.0728221	−	0.0611050i	0.678472	+	0.734626i	$0.262642\pi$
$384$		0			0
$385$	0.867214	+	0.315640i	0.0441973	+	0.0160865i
$386$		0			0
$387$	−7.93495	+	13.7437i	−0.403356	+	0.698633i
$388$		0			0
$389$	−1.24054	+	7.03542i	−0.0628976	+	0.356710i	0.937074	+	0.349132i	$0.113523\pi$
$389$	−1.24054	+	7.03542i	−0.0628976	+	0.356710i	−0.999971	+	0.00757846i	$0.997588\pi$
$390$		0			0
$391$	0.903734	+	1.56531i	0.0457038	+	0.0791613i
$392$		0			0
$393$	18.2835	+	15.3417i	0.922279	+	0.773884i
$394$		0			0
$395$	14.6189	−	5.32083i	0.735555	−	0.267720i
$396$		0			0
$397$	4.23145	+	23.9977i	0.212370	+	1.20441i	0.885412	+	0.464807i	$0.153876\pi$
$397$	4.23145	+	23.9977i	0.212370	+	1.20441i	−0.673041	+	0.739605i	$0.735012\pi$
$398$		0			0
$399$	−29.2932	+	4.64354i	−1.46649	+	0.232468i
$400$		0			0
$401$	1.86333	+	10.5675i	0.0930504	+	0.527715i	0.995327	+	0.0965581i	$0.0307833\pi$
$401$	1.86333	+	10.5675i	0.0930504	+	0.527715i	−0.902277	+	0.431157i	$0.858106\pi$
$402$		0			0
$403$	6.06149	−	2.20620i	0.301944	−	0.109899i
$404$		0			0
$405$	−1.47071	−	1.23407i	−0.0730800	−	0.0613214i
$406$		0			0
$407$	−1.15794	−	2.00562i	−0.0573971	−	0.0994147i
$408$		0			0
$409$	−2.17903	+	12.3579i	−0.107746	+	0.611058i	0.882342	+	0.470609i	$0.155966\pi$
$409$	−2.17903	+	12.3579i	−0.107746	+	0.611058i	−0.990088	+	0.140449i	$0.955145\pi$
$410$		0			0
$411$	−18.9346	+	32.7956i	−0.933973	+	1.61769i
$412$		0			0
$413$	19.3361	+	7.03776i	0.951466	+	0.346305i
$414$		0			0
$415$	4.82202	−	4.04616i	0.236704	−	0.198618i
$416$		0			0
$417$	−13.8156			−0.676550
$418$		0			0
$419$	28.0502			1.37034			0.685171	−	0.728383i	$-0.259728\pi$
$419$	28.0502			1.37034			0.685171	+	0.728383i	$0.259728\pi$
$420$		0			0
$421$	16.0840	−	13.4961i	0.783885	−	0.657758i	−0.160339	−	0.987062i	$-0.551259\pi$
$421$	16.0840	−	13.4961i	0.783885	−	0.657758i	0.944224	+	0.329304i	$0.106814\pi$
$422$		0			0
$423$	21.4690	+	7.81407i	1.04386	+	0.379933i
$424$		0			0
$425$	1.04142	−	1.80379i	0.0505162	−	0.0874966i
$426$		0			0
$427$	5.55718	−	31.5164i	0.268931	−	1.52518i
$428$		0			0
$429$	1.76627	+	3.05926i	0.0852761	+	0.147703i
$430$		0			0
$431$	−18.9587	−	15.9082i	−0.913207	−	0.766271i	0.0595196	−	0.998227i	$-0.481043\pi$
$431$	−18.9587	−	15.9082i	−0.913207	−	0.766271i	−0.972726	+	0.231956i	$0.925488\pi$
$432$		0			0
$433$	29.6829	−	10.8037i	1.42647	−	0.519192i	0.490552	−	0.871412i	$-0.336795\pi$
$433$	29.6829	−	10.8037i	1.42647	−	0.519192i	0.935917	+	0.352219i	$0.114573\pi$
$434$		0			0
$435$	−4.95498	−	28.1011i	−0.237573	−	1.34734i
$436$		0			0
$437$	1.23197	+	3.57637i	0.0589332	+	0.171081i
$438$		0			0
$439$	−0.765999	−	4.34420i	−0.0365591	−	0.207337i	0.961056	−	0.276352i	$-0.0891255\pi$
$439$	−0.765999	−	4.34420i	−0.0365591	−	0.207337i	−0.997616	+	0.0690148i	$0.978014\pi$
$440$		0			0
$441$	3.73013	−	1.35766i	0.177625	−	0.0646503i
$442$		0			0
$443$	−20.2239	−	16.9699i	−0.960868	−	0.806264i	0.0202259	−	0.999795i	$-0.493561\pi$
$443$	−20.2239	−	16.9699i	−0.960868	−	0.806264i	−0.981094	+	0.193531i	$0.938006\pi$
$444$		0			0
$445$	0.529639	+	0.917362i	0.0251073	+	0.0434871i
$446$		0			0
$447$	7.57859	−	42.9803i	0.358455	−	2.03290i
$448$		0			0
$449$	−2.30028	+	3.98419i	−0.108557	+	0.188026i	−0.915186	−	0.403032i	$-0.867956\pi$
$449$	−2.30028	+	3.98419i	−0.108557	+	0.188026i	0.806629	+	0.591058i	$0.201290\pi$
$450$		0			0
$451$	−2.78278	−	1.01285i	−0.131036	−	0.0476932i
$452$		0			0
$453$	−16.5245	+	13.8657i	−0.776390	+	0.651469i
$454$		0			0
$455$	−8.53477			−0.400116
$456$		0			0
$457$	−30.9048			−1.44566			−0.722832	−	0.691024i	$-0.757160\pi$
$457$	−30.9048			−1.44566			−0.722832	+	0.691024i	$0.757160\pi$
$458$		0			0
$459$	6.81727	−	5.72037i	0.318203	−	0.267004i
$460$		0			0
$461$	−1.86577	−	0.679084i	−0.0868975	−	0.0316281i	0.298206	−	0.954502i	$-0.403612\pi$
$461$	−1.86577	−	0.679084i	−0.0868975	−	0.0316281i	−0.385103	+	0.922874i	$0.625834\pi$
$462$		0			0
$463$	15.2283	−	26.3762i	0.707719	−	1.22581i	−0.257982	−	0.966150i	$-0.583058\pi$
$463$	15.2283	−	26.3762i	0.707719	−	1.22581i	0.965701	−	0.259656i	$-0.0836091\pi$
$464$		0			0
$465$	−0.892999	+	5.06445i	−0.0414118	+	0.234858i
$466$		0			0
$467$	2.51096	+	4.34911i	0.116193	+	0.201253i	0.918256	−	0.395987i	$-0.129597\pi$
$467$	2.51096	+	4.34911i	0.116193	+	0.201253i	−0.802063	+	0.597240i	$0.796264\pi$
$468$		0			0
$469$	−14.0830	−	11.8170i	−0.650291	−	0.545659i
$470$		0			0
$471$	34.1177	−	12.4178i	1.57206	−	0.572182i
$472$		0			0
$473$	−0.225562	−	1.27923i	−0.0103714	−	0.0588190i
$474$		0			0
$475$	2.85926	−	3.29008i	0.131192	−	0.150959i
$476$		0			0
$477$	−6.34778	−	36.0001i	−0.290645	−	1.64833i
$478$		0			0
$479$	−18.3361	+	6.67381i	−0.837800	+	0.304934i	−0.725056	−	0.688690i	$-0.758186\pi$
$479$	−18.3361	+	6.67381i	−0.837800	+	0.304934i	−0.112744	+	0.993624i	$0.535964\pi$
$480$		0			0
$481$	16.4067	+	13.7669i	0.748083	+	0.627716i
$482$		0			0
$483$	2.95233	+	5.11358i	0.134336	+	0.232676i
$484$		0			0
$485$	−2.49008	+	14.1219i	−0.113069	+	0.641244i
$486$		0			0
$487$	20.0327	−	34.6977i	0.907770	−	1.57230i	0.0906158	−	0.995886i	$-0.471116\pi$
$487$	20.0327	−	34.6977i	0.907770	−	1.57230i	0.817155	−	0.576419i	$-0.195550\pi$
$488$		0			0
$489$	10.4890	+	3.81768i	0.474329	+	0.172642i
$490$		0			0
$491$	−19.6384	+	16.4785i	−0.886267	+	0.743666i	−0.967458	−	0.253033i	$-0.918572\pi$
$491$	−19.6384	+	16.4785i	−0.886267	+	0.743666i	0.0811912	+	0.996699i	$0.474128\pi$
$492$		0			0
$493$	−21.6233			−0.973866
$494$		0			0
$495$	−1.69789			−0.0763143
$496$		0			0
$497$	4.68049	−	3.92740i	0.209949	−	0.176168i
$498$		0			0
$499$	−15.9733	−	5.81381i	−0.715064	−	0.260262i	−0.0412351	−	0.999149i	$-0.513129\pi$
$499$	−15.9733	−	5.81381i	−0.715064	−	0.260262i	−0.673829	+	0.738887i	$0.735351\pi$
$500$		0			0
$501$	34.1809	−	59.2031i	1.52709	−	2.64500i
$502$		0			0
$503$	6.12040	−	34.7105i	0.272895	−	1.54767i	−0.472674	−	0.881237i	$-0.656711\pi$
$503$	6.12040	−	34.7105i	0.272895	−	1.54767i	0.745569	−	0.666428i	$-0.232178\pi$
$504$		0			0
$505$	−8.58172	−	14.8640i	−0.381881	−	0.661438i
$506$		0			0
$507$	2.34567	+	1.96825i	0.104175	+	0.0874130i
$508$		0			0
$509$	−13.6138	+	4.95503i	−0.603422	+	0.219628i	−0.625623	−	0.780126i	$-0.715155\pi$
$509$	−13.6138	+	4.95503i	−0.603422	+	0.219628i	0.0222005	+	0.999754i	$0.492933\pi$
$510$		0			0
$511$	−2.17364	−	12.3273i	−0.0961560	−	0.545328i
$512$		0			0
$513$	16.2879	−	9.03135i	0.719130	−	0.398744i
$514$		0			0
$515$	3.25114	+	18.4381i	0.143262	+	0.812481i
$516$		0			0
$517$	−1.75725	+	0.639587i	−0.0772838	+	0.0281290i
$518$		0			0
$519$	8.65914	+	7.26588i	0.380094	+	0.318937i
$520$		0			0
$521$	−12.5675	−	21.7676i	−0.550593	−	0.953655i	−0.998232	−	0.0594407i	$-0.981068\pi$
$521$	−12.5675	−	21.7676i	−0.550593	−	0.953655i	0.447639	−	0.894214i	$-0.352265\pi$
$522$		0			0
$523$	−5.70365	+	32.3470i	−0.249403	+	1.41444i	0.560637	+	0.828062i	$0.310556\pi$
$523$	−5.70365	+	32.3470i	−0.249403	+	1.41444i	−0.810040	+	0.586374i	$0.800555\pi$
$524$		0			0
$525$	3.40211	−	5.89263i	0.148480	−	0.257176i
$526$		0			0
$527$	3.66199	+	1.33286i	0.159519	+	0.0580601i
$528$		0			0
$529$	−17.0421	+	14.3001i	−0.740963	+	0.621742i
$530$		0			0
$531$	−37.8574			−1.64287
$532$		0			0
$533$	27.3870			1.18626
$534$		0			0
$535$	−1.08276	+	0.908540i	−0.0468116	+	0.0392796i
$536$		0			0
$537$	53.8545	+	19.6014i	2.32399	+	0.845865i
$538$		0			0
$539$	−0.162454	+	0.281379i	−0.00699739	+	0.0121198i
$540$		0			0
$541$	−2.04353	+	11.5894i	−0.0878583	+	0.498269i	0.908845	+	0.417134i	$0.136966\pi$
$541$	−2.04353	+	11.5894i	−0.0878583	+	0.498269i	−0.996703	+	0.0811349i	$0.974146\pi$
$542$		0			0
$543$	−26.7816	−	46.3871i	−1.14931	−	1.99066i
$544$		0			0
$545$	9.51744	+	7.98608i	0.407682	+	0.342086i
$546$		0			0
$547$	−3.82799	+	1.39327i	−0.163673	+	0.0595721i	−0.422557	−	0.906336i	$-0.638867\pi$
$547$	−3.82799	+	1.39327i	−0.163673	+	0.0595721i	0.258884	+	0.965908i	$0.416645\pi$
$548$		0			0
$549$	10.2240	+	57.9834i	0.436352	+	2.47467i
$550$		0			0
$551$	−44.4224	−	8.62878i	−1.89246	−	0.367598i
$552$		0			0
$553$	−6.68765	−	37.9275i	−0.284388	−	1.61284i
$554$		0			0
$555$	−16.0451	+	5.83992i	−0.681075	+	0.247891i
$556$		0			0
$557$	−34.2928	−	28.7751i	−1.45303	−	1.21924i	−0.930329	−	0.366726i	$-0.880479\pi$
$557$	−34.2928	−	28.7751i	−1.45303	−	1.21924i	−0.522705	−	0.852514i	$-0.675077\pi$
$558$		0			0
$559$	6.00645	+	10.4035i	0.254046	+	0.440020i
$560$		0			0
$561$	−0.370590	+	2.10172i	−0.0156463	+	0.0887348i
$562$		0			0
$563$	5.16725	−	8.94994i	0.217774	−	0.377195i	−0.736353	−	0.676597i	$-0.763454\pi$
$563$	5.16725	−	8.94994i	0.217774	−	0.377195i	0.954127	+	0.299402i	$0.0967872\pi$
$564$		0			0
$565$	−9.99977	−	3.63962i	−0.420694	−	0.153120i
$566$		0			0
$567$	−3.64084	+	3.05503i	−0.152901	+	0.128299i
$568$		0			0
$569$	−24.2727			−1.01756			−0.508782	−	0.860895i	$-0.669904\pi$
$569$	−24.2727			−1.01756			−0.508782	+	0.860895i	$0.669904\pi$
$570$		0			0
$571$	43.4628			1.81886			0.909431	−	0.415854i	$-0.136517\pi$
$571$	43.4628			1.81886			0.909431	+	0.415854i	$0.136517\pi$
$572$		0			0
$573$	−13.8745	+	11.6421i	−0.579614	+	0.486354i
$574$		0			0
$575$	−0.815458	−	0.296802i	−0.0340069	−	0.0123775i
$576$		0			0
$577$	12.1169	−	20.9871i	0.504434	−	0.873705i	−0.495553	−	0.868578i	$-0.665035\pi$
$577$	12.1169	−	20.9871i	0.504434	−	0.873705i	0.999987	−	0.00512748i	$-0.00163213\pi$
$578$		0			0
$579$	9.84153	−	55.8141i	0.409000	−	2.31955i
$580$		0			0
$581$	−7.79149	−	13.4952i	−0.323245	−	0.559877i
$582$		0			0
$583$	2.29207	+	1.92328i	0.0949279	+	0.0796540i
$584$		0			0
$585$	14.7552	−	5.37046i	0.610053	−	0.222041i
$586$		0			0
$587$	−0.667422	−	3.78514i	−0.0275475	−	0.156229i	0.967931	−	0.251216i	$-0.0808304\pi$
$587$	−0.667422	−	3.78514i	−0.0275475	−	0.156229i	−0.995479	+	0.0949863i	$0.969719\pi$
$588$		0			0
$589$	6.99123	+	4.19950i	0.288069	+	0.173038i
$590$		0			0
$591$	10.4504	+	59.2673i	0.429873	+	2.43793i
$592$		0			0
$593$	19.1592	−	6.97336i	0.786772	−	0.286362i	0.0827786	−	0.996568i	$-0.473621\pi$
$593$	19.1592	−	6.97336i	0.786772	−	0.286362i	0.703994	+	0.710206i	$0.251398\pi$
$594$		0			0
$595$	−3.94988	−	3.31434i	−0.161929	−	0.135875i
$596$		0			0
$597$	1.11964	+	1.93928i	0.0458239	+	0.0793694i
$598$		0			0
$599$	−1.00673	+	5.70947i	−0.0411340	+	0.233283i	−0.998443	−	0.0557846i	$-0.982234\pi$
$599$	−1.00673	+	5.70947i	−0.0411340	+	0.233283i	0.957309	+	0.289067i	$0.0933451\pi$
$600$		0			0
$601$	5.24705	−	9.08816i	0.214032	−	0.370714i	−0.738941	−	0.673770i	$-0.764674\pi$
$601$	5.24705	−	9.08816i	0.214032	−	0.370714i	0.952973	+	0.303056i	$0.0980071\pi$
$602$		0			0
$603$	31.7829	+	11.5680i	1.29430	+	0.471087i
$604$		0			0
$605$	−8.32003	+	6.98133i	−0.338257	+	0.283832i
$606$		0			0
$607$	14.7382			0.598204			0.299102	−	0.954221i	$-0.403313\pi$
$607$	14.7382			0.598204			0.299102	+	0.954221i	$0.403313\pi$
$608$		0			0
$609$	−70.6393			−2.86245
$610$		0			0
$611$	13.2481	−	11.1165i	0.535960	−	0.449724i
$612$		0			0
$613$	−10.8362	−	3.94406i	−0.437671	−	0.159299i	0.113781	−	0.993506i	$-0.463704\pi$
$613$	−10.8362	−	3.94406i	−0.437671	−	0.159299i	−0.551452	+	0.834207i	$0.685926\pi$
$614$		0			0
$615$	−10.9169	+	18.9087i	−0.440214	+	0.762473i
$616$		0			0
$617$	0.153442	−	0.870215i	0.00617736	−	0.0350335i	−0.981563	−	0.191137i	$-0.938782\pi$
$617$	0.153442	−	0.870215i	0.00617736	−	0.0350335i	0.987741	+	0.156104i	$0.0498935\pi$
$618$		0			0
$619$	21.0474	+	36.4551i	0.845965	+	1.46525i	0.884781	+	0.466008i	$0.154308\pi$
$619$	21.0474	+	36.4551i	0.845965	+	1.46525i	−0.0388160	+	0.999246i	$0.512359\pi$
$620$		0			0
$621$	−2.84035	−	2.38333i	−0.113979	−	0.0956399i
$622$		0			0
$623$	2.46417	−	0.896885i	0.0987249	−	0.0359329i
$624$		0			0
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$		0			0
$627$	−1.60002	+	4.16984i	−0.0638987	+	0.166527i
$628$		0			0
$629$	2.24686	+	12.7426i	0.0895883	+	0.508081i
$630$		0			0
$631$	−19.6598	+	7.15557i	−0.782643	+	0.284859i	−0.702274	−	0.711906i	$-0.747832\pi$
$631$	−19.6598	+	7.15557i	−0.782643	+	0.284859i	−0.0803687	+	0.996765i	$0.525610\pi$
$632$		0			0
$633$	−18.8282	−	15.7987i	−0.748354	−	0.627944i
$634$		0			0
$635$	0.123011	+	0.213060i	0.00488152	+	0.00845505i
$636$		0			0
$637$	0.521773	−	2.95912i	0.0206734	−	0.117245i
$638$		0			0
$639$	−5.62051	+	9.73500i	−0.222344	+	0.385111i
$640$		0			0
$641$	−43.1639	−	15.7104i	−1.70487	−	0.620523i	−0.708507	−	0.705704i	$-0.750631\pi$
$641$	−43.1639	−	15.7104i	−1.70487	−	0.620523i	−0.996366	+	0.0851809i	$0.972853\pi$
$642$		0			0
$643$	−6.82283	+	5.72504i	−0.269066	+	0.225773i	−0.767331	−	0.641252i	$-0.778415\pi$
$643$	−6.82283	+	5.72504i	−0.269066	+	0.225773i	0.498264	+	0.867025i	$0.333971\pi$
$644$		0			0
$645$	−9.57711			−0.377098
$646$		0			0
$647$	−13.2110			−0.519379			−0.259689	−	0.965692i	$-0.583620\pi$
$647$	−13.2110			−0.519379			−0.259689	+	0.965692i	$0.583620\pi$
$648$		0			0
$649$	2.37371	−	1.99178i	0.0931761	−	0.0781840i
$650$		0			0
$651$	11.9630	+	4.35419i	0.468868	+	0.170654i
$652$		0			0
$653$	−15.6670	+	27.1360i	−0.613095	+	1.06191i	0.377620	+	0.925961i	$0.376743\pi$
$653$	−15.6670	+	27.1360i	−0.613095	+	1.06191i	−0.990715	+	0.135952i	$0.956591\pi$
$654$		0			0
$655$	−1.50790	+	8.55170i	−0.0589183	+	0.334143i
$656$		0			0
$657$	11.5147	+	19.9441i	0.449233	+	0.778095i
$658$		0			0
$659$	5.90427	+	4.95427i	0.229998	+	0.192991i	0.750502	−	0.660868i	$-0.229812\pi$
$659$	5.90427	+	4.95427i	0.229998	+	0.192991i	−0.520504	+	0.853859i	$0.674256\pi$
$660$		0			0
$661$	11.0245	−	4.01257i	0.428801	−	0.156071i	−0.118598	−	0.992942i	$-0.537840\pi$
$661$	11.0245	−	4.01257i	0.428801	−	0.156071i	0.547400	+	0.836871i	$0.315618\pi$
$662$		0			0
$663$	−3.42725	−	19.4369i	−0.133103	−	0.754866i
$664$		0			0
$665$	−6.79195	−	8.38510i	−0.263380	−	0.325160i
$666$		0			0
$667$	1.56442	+	8.87227i	0.0605746	+	0.343536i
$668$		0			0
$669$	20.5637	−	7.48459i	0.795040	−	0.289371i
$670$		0			0
$671$	−3.69172	−	3.09772i	−0.142517	−	0.119586i
$672$		0			0
$673$	−10.9349	−	18.9398i	−0.421509	−	0.730075i	0.574578	−	0.818450i	$-0.305166\pi$
$673$	−10.9349	−	18.9398i	−0.421509	−	0.730075i	−0.996087	+	0.0883747i	$0.971833\pi$
$674$		0			0
$675$	−0.741945	+	4.20778i	−0.0285575	+	0.161958i
$676$		0			0
$677$	9.90091	−	17.1489i	0.380523	−	0.659085i	−0.610614	−	0.791928i	$-0.709077\pi$
$677$	9.90091	−	17.1489i	0.380523	−	0.659085i	0.991137	+	0.132843i	$0.0424107\pi$
$678$		0			0
$679$	33.3583	+	12.1414i	1.28017	+	0.465945i
$680$		0			0
$681$	24.2823	−	20.3752i	0.930499	−	0.780781i
$682$		0			0
$683$	30.3561			1.16154			0.580771	−	0.814067i	$-0.302751\pi$
$683$	30.3561			1.16154			0.580771	+	0.814067i	$0.302751\pi$
$684$		0			0
$685$	−13.7779			−0.526425
$686$		0			0
$687$	3.89421	−	3.26763i	0.148573	−	0.124668i
$688$		0			0
$689$	−26.0023	−	9.46405i	−0.990608	−	0.360552i
$690$		0			0
$691$	23.5595	−	40.8063i	0.896246	−	1.55234i	0.0639920	−	0.997950i	$-0.479617\pi$
$691$	23.5595	−	40.8063i	0.896246	−	1.55234i	0.832254	−	0.554394i	$-0.187050\pi$
$692$		0			0
$693$	−0.729884	+	4.13938i	−0.0277260	+	0.157242i
$694$		0			0
$695$	−2.51324	−	4.35307i	−0.0953328	−	0.165121i
$696$		0			0
$697$	12.6747	+	10.6353i	0.480087	+	0.402841i
$698$		0			0
$699$	−53.3297	+	19.4104i	−2.01712	+	0.734170i
$700$		0			0
$701$	0.348816	+	1.97823i	0.0131746	+	0.0747168i	0.990686	−	0.136165i	$-0.0434777\pi$
$701$	0.348816	+	1.97823i	0.0131746	+	0.0747168i	−0.977512	+	0.210882i	$0.932367\pi$
$702$		0			0
$703$	−0.469024	+	27.0747i	−0.0176896	+	1.02114i
$704$		0			0
$705$	2.39418	+	13.5781i	0.0901700	+	0.511379i
$706$		0			0
$707$	−39.9269	+	14.5322i	−1.50160	+	0.546539i
$708$		0			0
$709$	−12.6356	−	10.6025i	−0.474541	−	0.398187i	0.373907	−	0.927466i	$-0.378018\pi$
$709$	−12.6356	−	10.6025i	−0.474541	−	0.398187i	−0.848448	+	0.529279i	$0.822462\pi$
$710$		0			0
$711$	35.4275	+	61.3623i	1.32864	+	2.30127i
$712$		0			0
$713$	0.281944	−	1.59898i	0.0105589	−	0.0598824i
$714$		0			0
$715$	−0.642617	+	1.11305i	−0.0240325	+	0.0416255i
$716$		0			0
$717$	−64.0189	−	23.3010i	−2.39083	−	0.870191i
$718$		0			0
$719$	15.2913	−	12.8309i	0.570268	−	0.478511i	−0.311467	−	0.950257i	$-0.600820\pi$
$719$	15.2913	−	12.8309i	0.570268	−	0.478511i	0.881735	+	0.471746i	$0.156376\pi$
$720$		0			0
$721$	46.3490			1.72613
$722$		0			0
$723$	−44.3123			−1.64799
$724$		0			0
$725$	7.95283	−	6.67322i	0.295361	−	0.247837i
$726$		0			0
$727$	36.7157	+	13.3634i	1.36171	+	0.495622i	0.916583	−	0.399845i	$-0.130936\pi$
$727$	36.7157	+	13.3634i	1.36171	+	0.495622i	0.445127	+	0.895467i	$0.353158\pi$
$728$		0			0
$729$	21.9876	−	38.0837i	0.814356	−	1.41051i
$730$		0			0
$731$	−1.26025	+	7.14722i	−0.0466120	+	0.264350i
$732$		0			0
$733$	1.22945	+	2.12946i	0.0454106	+	0.0786535i	0.887837	−	0.460157i	$-0.152207\pi$
$733$	1.22945	+	2.12946i	0.0454106	+	0.0786535i	−0.842427	+	0.538811i	$0.818874\pi$
$734$		0			0
$735$	1.83507	+	1.53981i	0.0676875	+	0.0567966i
$736$		0			0
$737$	−2.60146	+	0.946853i	−0.0958259	+	0.0348778i
$738$		0			0
$739$	−6.33250	−	35.9134i	−0.232945	−	1.32110i	−0.846899	−	0.531754i	$-0.821533\pi$
$739$	−6.33250	−	35.9134i	−0.232945	−	1.32110i	0.613954	−	0.789342i	$-0.289578\pi$
$740$		0			0
$741$	0.715425	−	41.2983i	0.0262818	−	1.51713i
$742$		0			0
$743$	6.71560	+	38.0861i	0.246372	+	1.39724i	0.817285	+	0.576233i	$0.195478\pi$
$743$	6.71560	+	38.0861i	0.246372	+	1.39724i	−0.570914	+	0.821010i	$0.693411\pi$
$744$		0			0
$745$	14.9211	−	5.43083i	0.546666	−	0.198970i
$746$		0			0
$747$	21.9620	+	18.4283i	0.803548	+	0.674257i
$748$		0			0
$749$	1.74953	+	3.03028i	0.0639265	+	0.110724i
$750$		0			0
$751$	−3.43069	+	19.4564i	−0.125188	+	0.709975i	0.856008	+	0.516962i	$0.172937\pi$
$751$	−3.43069	+	19.4564i	−0.125188	+	0.709975i	−0.981196	+	0.193013i	$0.938174\pi$
$752$		0			0
$753$	23.4617	−	40.6369i	0.854992	−	1.48089i
$754$		0			0
$755$	−7.37492	−	2.68425i	−0.268401	−	0.0976900i
$756$		0			0
$757$	−14.5962	+	12.2477i	−0.530507	+	0.445149i	−0.868277	−	0.496080i	$-0.834772\pi$
$757$	−14.5962	+	12.2477i	−0.530507	+	0.445149i	0.337769	+	0.941229i	$0.390328\pi$
$758$		0			0
$759$	0.889170			0.0322748
$760$		0			0
$761$	−32.2550			−1.16924			−0.584621	−	0.811307i	$-0.698757\pi$
$761$	−32.2550			−1.16924			−0.584621	+	0.811307i	$0.698757\pi$
$762$		0			0
$763$	23.5611	−	19.7701i	0.852968	−	0.715725i
$764$		0			0
$765$	8.91423	+	3.24451i	0.322295	+	0.117306i
$766$		0			0
$767$	−14.3283	+	24.8173i	−0.517364	+	0.896101i
$768$		0			0
$769$	4.13012	−	23.4231i	0.148936	−	0.844658i	−0.815186	−	0.579199i	$-0.803365\pi$
$769$	4.13012	−	23.4231i	0.148936	−	0.844658i	0.964122	−	0.265459i	$-0.0855234\pi$
$770$		0			0
$771$	1.60377	+	2.77781i	0.0577583	+	0.100040i
$772$		0			0
$773$	−11.4378	−	9.59750i	−0.411391	−	0.345198i	0.413486	−	0.910511i	$-0.364311\pi$
$773$	−11.4378	−	9.59750i	−0.411391	−	0.345198i	−0.824877	+	0.565313i	$0.808756\pi$
$774$		0			0
$775$	−1.75818	+	0.639924i	−0.0631556	+	0.0229868i
$776$		0			0
$777$	7.34008	+	41.6277i	0.263324	+	1.49338i
$778$		0			0
$779$	21.7945	+	26.9067i	0.780869	+	0.964033i
$780$		0			0
$781$	−0.159771	−	0.906107i	−0.00571706	−	0.0324231i
$782$		0			0
$783$	41.6826	−	15.1712i	1.48962	−	0.542176i
$784$		0			0
$785$	10.1191	+	8.49097i	0.361168	+	0.303056i
$786$		0			0
$787$	6.08890	+	10.5463i	0.217046	+	0.375934i	0.953903	−	0.300114i	$-0.0970246\pi$
$787$	6.08890	+	10.5463i	0.217046	+	0.375934i	−0.736858	+	0.676048i	$0.763691\pi$
$788$		0			0
$789$	−4.47807	+	25.3964i	−0.159423	+	0.904135i
$790$		0			0
$791$	−13.1719	+	22.8145i	−0.468340	+	0.811189i
$792$		0			0
$793$	41.8805	+	15.2433i	1.48722	+	0.541304i
$794$		0			0
$795$	16.8992	−	14.1801i	0.599353	−	0.502917i
$796$		0			0
$797$	43.6982			1.54787			0.773935	−	0.633265i	$-0.218286\pi$
$797$	43.6982			1.54787			0.773935	+	0.633265i	$0.218286\pi$
$798$		0			0
$799$	10.4481			0.369627
$800$		0			0
$801$	−3.69579	+	3.10113i	−0.130584	+	0.109573i
$802$		0			0
$803$	−1.77130	−	0.644701i	−0.0625079	−	0.0227510i
$804$		0			0
$805$	−1.07414	+	1.86046i	−0.0378585	+	0.0655728i
$806$		0			0
$807$	−3.51209	+	19.9180i	−0.123631	+	0.701148i
$808$		0			0
$809$	−23.7290	−	41.0998i	−0.834267	−	1.44499i	−0.894626	−	0.446816i	$-0.852558\pi$
$809$	−23.7290	−	41.0998i	−0.834267	−	1.44499i	0.0603588	−	0.998177i	$-0.480776\pi$
$810$		0			0
$811$	19.0737	+	16.0047i	0.669767	+	0.562001i	0.912996	−	0.407968i	$-0.133762\pi$
$811$	19.0737	+	16.0047i	0.669767	+	0.562001i	−0.243230	+	0.969969i	$0.578207\pi$
$812$		0			0
$813$	27.6946	−	10.0800i	0.971293	−	0.353522i
$814$		0			0
$815$	0.705204	+	3.99941i	0.0247022	+	0.140093i
$816$		0			0
$817$	−5.44112	+	14.1802i	−0.190361	+	0.496101i
$818$		0			0
$819$	−6.75002	−	38.2813i	−0.235865	−	1.33766i
$820$		0			0
$821$	−16.0293	+	5.83420i	−0.559428	+	0.203615i	−0.606230	−	0.795289i	$-0.707319\pi$
$821$	−16.0293	+	5.83420i	−0.559428	+	0.203615i	0.0468024	+	0.998904i	$0.485097\pi$
$822$		0			0
$823$	−20.0962	−	16.8627i	−0.700508	−	0.587796i	0.221410	−	0.975181i	$-0.428934\pi$
$823$	−20.0962	−	16.8627i	−0.700508	−	0.587796i	−0.921918	+	0.387385i	$0.873379\pi$
$824$		0			0
$825$	−0.512317	−	0.887360i	−0.0178366	−	0.0308939i
$826$		0			0
$827$	7.85495	−	44.5476i	0.273143	−	1.54907i	−0.471655	−	0.881783i	$-0.656343\pi$
$827$	7.85495	−	44.5476i	0.273143	−	1.54907i	0.744799	−	0.667289i	$-0.232546\pi$
$828$		0			0
$829$	1.06276	−	1.84075i	0.0369111	−	0.0639319i	−0.846980	−	0.531625i	$-0.821581\pi$
$829$	1.06276	−	1.84075i	0.0369111	−	0.0639319i	0.883891	+	0.467693i	$0.154915\pi$
$830$		0			0
$831$	−41.6513	−	15.1598i	−1.44487	−	0.525888i
$832$		0			0
$833$	1.39060	−	1.16686i	0.0481816	−	0.0404291i
$834$		0			0
$835$	24.8720			0.860730
$836$		0			0
$837$	−7.99426			−0.276322
$838$		0			0
$839$	−15.2782	+	12.8199i	−0.527461	+	0.442592i	−0.867224	−	0.497919i	$-0.834098\pi$
$839$	−15.2782	+	12.8199i	−0.527461	+	0.442592i	0.339762	+	0.940511i	$0.389653\pi$
$840$		0			0
$841$	−74.0284	−	26.9441i	−2.55270	−	0.929108i
$842$		0			0
$843$	−42.0985	+	72.9167i	−1.44995	+	2.51138i
$844$		0			0
$845$	−0.193455	+	1.09714i	−0.00665504	+	0.0377426i
$846$		0			0
$847$	13.4436	+	23.2850i	0.461928	+	0.800083i
$848$		0			0
$849$	11.2055	+	9.40250i	0.384570	+	0.322693i
$850$		0			0
$851$	5.06586	−	1.84382i	0.173655	−	0.0632054i
$852$		0			0
$853$	4.75966	+	26.9933i	0.162967	+	0.924235i	0.951135	+	0.308774i	$0.0999188\pi$
$853$	4.75966	+	26.9933i	0.162967	+	0.924235i	−0.788168	+	0.615460i	$0.788970\pi$
$854$		0			0
$855$	17.0184	+	10.2227i	0.582019	+	0.349608i
$856$		0			0
$857$	3.33731	+	18.9268i	0.114000	+	0.646529i	0.987240	+	0.159238i	$0.0509037\pi$
$857$	3.33731	+	18.9268i	0.114000	+	0.646529i	−0.873240	+	0.487291i	$0.837985\pi$
$858$		0			0
$859$	41.7210	−	15.1852i	1.42350	−	0.518113i	0.488441	−	0.872597i	$-0.337566\pi$
$859$	41.7210	−	15.1852i	1.42350	−	0.518113i	0.935062	+	0.354485i	$0.115344\pi$
$860$		0			0
$861$	41.4057	+	34.7435i	1.41110	+	1.18406i
$862$		0			0
$863$	−0.747653	−	1.29497i	−0.0254504	−	0.0440814i	0.853020	−	0.521879i	$-0.174769\pi$
$863$	−0.747653	−	1.29497i	−0.0254504	−	0.0440814i	−0.878470	+	0.477797i	$0.841435\pi$
$864$		0			0
$865$	−0.714147	+	4.05013i	−0.0242817	+	0.137708i
$866$		0			0
$867$	−17.4008	+	30.1391i	−0.590962	+	1.02358i
$868$		0			0
$869$	−5.44978	−	1.98356i	−0.184871	−	0.0672876i
$870$		0			0
$871$	19.6126	−	16.4570i	0.664549	−	0.557623i
$872$		0			0
$873$	−65.3109			−2.21044
$874$		0			0
$875$	2.47557			0.0836895
$876$		0			0
$877$	−21.1135	+	17.7163i	−0.712951	+	0.598237i	−0.925425	−	0.378930i	$-0.876292\pi$
$877$	−21.1135	+	17.7163i	−0.712951	+	0.598237i	0.212475	+	0.977167i	$0.431848\pi$
$878$		0			0
$879$	9.12137	+	3.31991i	0.307656	+	0.111978i
$880$		0			0
$881$	5.10228	−	8.83741i	0.171900	−	0.297740i	−0.767184	−	0.641427i	$-0.778343\pi$
$881$	5.10228	−	8.83741i	0.171900	−	0.297740i	0.939084	+	0.343687i	$0.111676\pi$
$882$		0			0
$883$	1.95162	−	11.0682i	0.0656773	−	0.372475i	−0.934199	−	0.356752i	$-0.883884\pi$
$883$	1.95162	−	11.0682i	0.0656773	−	0.372475i	0.999876	−	0.0157225i	$-0.00500483\pi$
$884$		0			0
$885$	−11.4230	−	19.7853i	−0.383981	−	0.665074i
$886$		0			0
$887$	10.6841	+	8.96500i	0.358736	+	0.301015i	0.804287	−	0.594242i	$-0.202548\pi$
$887$	10.6841	+	8.96500i	0.358736	+	0.301015i	−0.445551	+	0.895257i	$0.646992\pi$
$888$		0			0
$889$	0.572312	−	0.208305i	0.0191947	−	0.00698632i
$890$		0			0
$891$	0.124282	+	0.704838i	0.00416360	+	0.0236130i
$892$		0			0
$893$	21.4643	+	4.16931i	0.718276	+	0.139521i
$894$		0			0
$895$	3.62079	+	20.5345i	0.121030	+	0.686393i
$896$		0			0
$897$	−7.72719	+	2.81247i	−0.258004	+	0.0939056i
$898$		0			0
$899$	14.8799	+	12.4857i	0.496271	+	0.416421i
$900$		0			0
$901$	−8.35860	−	14.4775i	−0.278465	−	0.482316i
$902$		0			0
$903$	−4.11699	+	23.3486i	−0.137005	+	0.776993i
$904$		0			0
$905$	9.74391	−	16.8769i	0.323899	−	0.561009i
$906$		0			0
$907$	3.45607	+	1.25791i	0.114757	+	0.0417681i	0.398760	−	0.917055i	$-0.369441\pi$
$907$	3.45607	+	1.25791i	0.114757	+	0.0417681i	−0.284004	+	0.958823i	$0.591663\pi$
$908$		0			0
$909$	59.8827	−	50.2476i	1.98618	−	1.66661i
$910$		0			0
$911$	−20.6699			−0.684826			−0.342413	−	0.939550i	$-0.611244\pi$
$911$	−20.6699			−0.684826			−0.342413	+	0.939550i	$0.611244\pi$
$912$		0			0
$913$	−2.34661			−0.0776614
$914$		0			0
$915$	−27.2187	+	22.8392i	−0.899821	+	0.755040i
$916$		0			0
$917$	20.2005	+	7.35238i	0.667079	+	0.242797i
$918$		0			0
$919$	14.1812	−	24.5625i	0.467793	−	0.810242i	−0.531529	−	0.847040i	$-0.678382\pi$
$919$	14.1812	−	24.5625i	0.467793	−	0.810242i	0.999323	+	0.0367979i	$0.0117158\pi$
$920$		0			0
$921$	−10.0903	+	57.2249i	−0.332486	+	1.88562i
$922$		0			0
$923$	4.25451	+	7.36902i	0.140039	+	0.242554i
$924$		0			0
$925$	−4.75889	−	3.99318i	−0.156471	−	0.131295i
$926$		0			0
$927$	−80.1298	+	29.1649i	−2.63181	+	0.957900i
$928$		0			0
$929$	0.469159	+	2.66073i	0.0153926	+	0.0872959i	0.991536	−	0.129830i	$-0.0414430\pi$
$929$	0.469159	+	2.66073i	0.0153926	+	0.0872959i	−0.976144	+	0.217125i	$0.930332\pi$
$930$		0			0
$931$	3.32246	−	1.84224i	0.108889	−	0.0603769i
$932$		0			0
$933$	−3.44247	−	19.5232i	−0.112701	−	0.639161i
$934$		0			0
$935$	−0.729636	+	0.265566i	−0.0238616	+	0.00868493i
$936$		0			0
$937$	13.8164	+	11.5933i	0.451361	+	0.378737i	0.839941	−	0.542678i	$-0.182590\pi$
$937$	13.8164	+	11.5933i	0.451361	+	0.378737i	−0.388580	+	0.921415i	$0.627034\pi$
$938$		0			0
$939$	−24.4531	−	42.3540i	−0.797996	−	1.38217i
$940$		0			0
$941$	−3.39940	+	19.2790i	−0.110817	+	0.628476i	0.877919	+	0.478809i	$0.158931\pi$
$941$	−3.39940	+	19.2790i	−0.110817	+	0.628476i	−0.988736	+	0.149667i	$0.952180\pi$
$942$		0			0
$943$	3.44678	−	5.96999i	0.112243	−	0.194410i
$944$		0			0
$945$	9.93945	+	3.61767i	0.323330	+	0.117683i
$946$		0			0
$947$	−41.5661	+	34.8781i	−1.35072	+	1.13339i	−0.371985	+	0.928239i	$0.621323\pi$
$947$	−41.5661	+	34.8781i	−1.35072	+	1.13339i	−0.978731	+	0.205147i	$0.934233\pi$
$948$		0			0
$949$	17.4324			0.565881
$950$		0			0
$951$	63.0029			2.04301
$952$		0			0
$953$	−19.9282	+	16.7218i	−0.645538	+	0.541671i	−0.905713	−	0.423891i	$-0.860664\pi$
$953$	−19.9282	+	16.7218i	−0.645538	+	0.541671i	0.260175	+	0.965561i	$0.416220\pi$
$954$		0			0
$955$	−6.19219	−	2.25377i	−0.200375	−	0.0729304i
$956$		0			0
$957$	−5.31872	+	9.21229i	−0.171930	+	0.297791i
$958$		0			0
$959$	−5.92280	+	33.5899i	−0.191257	+	1.08467i
$960$		0			0
$961$	13.7497	+	23.8151i	0.443537	+	0.768229i
$962$		0			0
$963$	−4.93144	−	4.13797i	−0.158913	−	0.133344i
$964$		0			0
$965$	19.3765	−	7.05246i	0.623751	−	0.227027i
$966$		0			0
$967$	6.63034	+	37.6025i	0.213217	+	1.20922i	0.883973	+	0.467538i	$0.154859\pi$
$967$	6.63034	+	37.6025i	0.213217	+	1.20922i	−0.670756	+	0.741678i	$0.734030\pi$
$968$		0			0
$969$	16.3686	−	18.8350i	0.525836	−	0.605066i
$970$		0			0
$971$	−10.3072	−	58.4549i	−0.330773	−	1.87591i	−0.465537	−	0.885028i	$-0.654139\pi$
$971$	−10.3072	−	58.4549i	−0.330773	−	1.87591i	0.134764	−	0.990878i	$-0.456972\pi$
$972$		0			0
$973$	−11.6930	+	4.25590i	−0.374860	+	0.136438i
$974$		0			0
$975$	7.25896	+	6.09099i	0.232473	+	0.195068i
$976$		0			0
$977$	0.735809	+	1.27446i	0.0235406	+	0.0407735i	0.877556	−	0.479475i	$-0.159173\pi$
$977$	0.735809	+	1.27446i	0.0235406	+	0.0407735i	−0.854015	+	0.520248i	$0.825839\pi$
$978$		0			0
$979$	0.0685718	−	0.388890i	0.00219157	−	0.0124290i
$980$		0			0
$981$	−28.2930	+	49.0049i	−0.903326	+	1.56461i
$982$		0			0
$983$	35.3932	+	12.8821i	1.12887	+	0.410874i	0.837881	−	0.545853i	$-0.183794\pi$
$983$	35.3932	+	12.8821i	1.12887	+	0.410874i	0.290986	+	0.956727i	$0.406017\pi$
$984$		0			0
$985$	−16.7731	+	14.0743i	−0.534436	+	0.448445i
$986$		0			0
$987$	34.1320			1.08643
$988$		0			0
$989$	3.02376			0.0961498
$990$		0			0
$991$	15.0832	−	12.6563i	0.479133	−	0.402040i	−0.370980	−	0.928641i	$-0.620978\pi$
$991$	15.0832	−	12.6563i	0.479133	−	0.402040i	0.850113	+	0.526601i	$0.176534\pi$
$992$		0			0
$993$	−83.0869	−	30.2412i	−2.63668	−	0.959674i
$994$		0			0
$995$	−0.407358	+	0.705564i	−0.0129141	+	0.0223679i
$996$		0			0
$997$	0.991547	−	5.62334i	0.0314026	−	0.178093i	−0.965072	−	0.261983i	$-0.915623\pi$
$997$	0.991547	−	5.62334i	0.0314026	−	0.178093i	0.996475	+	0.0838903i	$0.0267345\pi$
$998$		0			0
$999$	−13.2716	−	22.9871i	−0.419895	−	0.727279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.161.1	✓	18
19.6	even	9		7220.2.a.w.1.2		9
19.13	odd	18		7220.2.a.y.1.8		9
19.17	even	9	inner	380.2.u.b.321.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.161.1	✓	18	1.1	even	1	trivial
380.2.u.b.321.1	yes	18	19.17	even	9	inner
7220.2.a.w.1.2		9	19.6	even	9
7220.2.a.y.1.8		9	19.13	odd	18

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10551 + 1.76673i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(-1.23778 + 2.14391i) q^{7} +(0.790885 - 4.48533i) q^{9} +O(q^{10})\)	\(q+(-2.10551 + 1.76673i) q^{3} +(-0.939693 - 0.342020i) q^{5} +(-1.23778 + 2.14391i) q^{7} +(0.790885 - 4.48533i) q^{9} +(0.186396 + 0.322847i) q^{11} +(-2.64101 - 2.21607i) q^{13} +(2.58279 - 0.940059i) q^{15} +(-0.361680 - 2.05119i) q^{17} +(0.0754994 - 4.35825i) q^{19} +(-1.18154 - 6.70085i) q^{21} +(-0.815458 + 0.296802i) q^{23} +(0.766044 + 0.642788i) q^{25} +(2.13635 + 3.70026i) q^{27} +(1.80276 - 10.2240i) q^{29} +(-0.935507 + 1.62035i) q^{31} +(-0.962842 - 0.350446i) q^{33} +(1.89640 - 1.59127i) q^{35} -6.21229 q^{37} +9.47590 q^{39} +(-6.08529 + 5.10617i) q^{41} +(-3.27429 - 1.19174i) q^{43} +(-2.27726 + 3.94434i) q^{45} +(-0.871070 + 4.94008i) q^{47} +(0.435777 + 0.754789i) q^{49} +(4.38543 + 3.67981i) q^{51} +(7.54214 - 2.74511i) q^{53} +(-0.0647345 - 0.367128i) q^{55} +(7.54089 + 9.30972i) q^{57} +(-1.44337 - 8.18576i) q^{59} +(-12.1477 + 4.42141i) q^{61} +(8.63719 + 7.24746i) q^{63} +(1.72380 + 2.98571i) q^{65} +(-1.28954 + 7.31335i) q^{67} +(1.19258 - 2.06562i) q^{69} +(-2.31925 - 0.844139i) q^{71} +(-3.87343 + 3.25019i) q^{73} -2.74855 q^{75} -0.922870 q^{77} +(-11.9174 + 9.99989i) q^{79} +(1.80409 + 0.656635i) q^{81} +(-3.14735 + 5.45137i) q^{83} +(-0.361680 + 2.05119i) q^{85} +(14.2673 + 24.7117i) q^{87} +(-0.811454 - 0.680891i) q^{89} +(8.02006 - 2.91906i) q^{91} +(-0.892999 - 5.06445i) q^{93} +(-1.56155 + 4.06959i) q^{95} +(-2.49008 - 14.1219i) q^{97} +(1.59549 - 0.580711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 15 * q^9	\( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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