LMFDB - Embedded newform 368.2.m.c.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [368,2,Mod(49,368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("368.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(368, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 16])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$368 = 2^{4} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	368.m (of order $11$ , degree $10$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	368.49
Dual form			368.2.m.c.353.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.04408 - 2.28621i) q^{3} +(0.809721 - 0.934468i) q^{5} +(1.99611 - 1.28282i) q^{7} +(-2.17208 - 2.50672i) q^{9} +(-0.272084 + 1.89238i) q^{11} +(0.165284 + 0.106222i) q^{13} +(-1.29098 - 2.82685i) q^{15} +(1.49672 + 0.439476i) q^{17} +(-7.66103 + 2.24948i) q^{19} +(-0.848710 - 5.90291i) q^{21} +(4.66752 - 1.10192i) q^{23} +(0.493992 + 3.43579i) q^{25} +(-0.764125 + 0.224367i) q^{27} +(-4.77570 - 1.40227i) q^{29} +(-0.740552 - 1.62158i) q^{31} +(4.04231 + 2.59784i) q^{33} +(0.417537 - 2.90404i) q^{35} +(-2.54297 - 2.93475i) q^{37} +(0.415415 - 0.266971i) q^{39} +(-0.279295 + 0.322324i) q^{41} +(-1.84991 + 4.05075i) q^{43} -4.10123 q^{45} +2.58842 q^{47} +(-0.569072 + 1.24609i) q^{49} +(2.56743 - 2.96297i) q^{51} +(8.26060 - 5.30876i) q^{53} +(1.54806 + 1.78656i) q^{55} +(-2.85592 + 19.8634i) q^{57} +(6.07293 + 3.90283i) q^{59} +(3.08639 + 6.75826i) q^{61} +(-7.55141 - 2.21729i) q^{63} +(0.233095 - 0.0684429i) q^{65} +(1.03413 + 7.19254i) q^{67} +(2.35404 - 11.8214i) q^{69} +(-0.103930 - 0.722850i) q^{71} +(6.18330 - 1.81558i) q^{73} +(8.37071 + 2.45786i) q^{75} +(1.88449 + 4.12645i) q^{77} +(4.77671 + 3.06980i) q^{79} +(1.13126 - 7.86810i) q^{81} +(-8.44098 - 9.74141i) q^{83} +(1.62260 - 1.04278i) q^{85} +(-8.19209 + 9.45418i) q^{87} +(-5.77436 + 12.6441i) q^{89} +0.466190 q^{91} -4.48047 q^{93} +(-4.10123 + 8.98044i) q^{95} +(-2.83147 + 3.26769i) q^{97} +(5.33466 - 3.42838i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 7 q^{3} - 3 q^{5} + 5 q^{7} - 2 q^{9} - 7 q^{11} - 3 q^{13} - 12 q^{15} - 10 q^{17} - 2 q^{19} - 2 q^{21} + 12 q^{23} - 4 q^{25} + 4 q^{27} + 14 q^{29} - 10 q^{31} + 16 q^{33} - 7 q^{35} - 19 q^{37}+ \cdots + 30 q^{99}+O(q^{100})$ 10 * q + 7 * q^3 - 3 * q^5 + 5 * q^7 - 2 * q^9 - 7 * q^11 - 3 * q^13 - 12 * q^15 - 10 * q^17 - 2 * q^19 - 2 * q^21 + 12 * q^23 - 4 * q^25 + 4 * q^27 + 14 * q^29 - 10 * q^31 + 16 * q^33 - 7 * q^35 - 19 * q^37 - q^39 + 7 * q^41 + 11 * q^43 - 6 * q^45 + 18 * q^47 - 18 * q^49 - 7 * q^51 + 29 * q^53 + q^55 - 8 * q^57 + 21 * q^59 + 3 * q^61 - 34 * q^63 + 2 * q^65 - 45 * q^67 + 26 * q^69 + 14 * q^71 + 19 * q^73 + 28 * q^75 + 2 * q^77 + 15 * q^79 - 44 * q^81 - 18 * q^83 - 19 * q^85 + 23 * q^87 + 25 * q^89 + 4 * q^91 + 4 * q^93 - 6 * q^95 - 34 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$ .

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

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
$3$	1.04408	−	2.28621i	0.602799	−	1.31995i	−0.324593	−	0.945854i	$-0.605227\pi$
$3$	1.04408	−	2.28621i	0.602799	−	1.31995i	0.927392	−	0.374091i	$-0.122045\pi$
$4$		0			0
$5$	0.809721	−	0.934468i	0.362118	−	0.417907i	−0.545230	−	0.838287i	$-0.683558\pi$
$5$	0.809721	−	0.934468i	0.362118	−	0.417907i	0.907348	+	0.420380i	$0.138103\pi$
$6$		0			0
$7$	1.99611	−	1.28282i	0.754460	−	0.484862i	−0.106009	−	0.994365i	$-0.533807\pi$
$7$	1.99611	−	1.28282i	0.754460	−	0.484862i	0.860469	+	0.509503i	$0.170171\pi$
$8$		0			0
$9$	−2.17208	−	2.50672i	−0.724028	−	0.835573i
$10$		0			0
$11$	−0.272084	+	1.89238i	−0.0820363	+	0.570575i	0.906799	+	0.421563i	$0.138518\pi$
$11$	−0.272084	+	1.89238i	−0.0820363	+	0.570575i	−0.988835	+	0.149012i	$0.952391\pi$
$12$		0			0
$13$	0.165284	+	0.106222i	0.0458416	+	0.0294606i	0.563361	−	0.826211i	$-0.309508\pi$
$13$	0.165284	+	0.106222i	0.0458416	+	0.0294606i	−0.517519	+	0.855672i	$0.673144\pi$
$14$		0			0
$15$	−1.29098	−	2.82685i	−0.333330	−	0.729890i
$16$		0			0
$17$	1.49672	+	0.439476i	0.363008	+	0.106589i	0.458150	−	0.888875i	$-0.348512\pi$
$17$	1.49672	+	0.439476i	0.363008	+	0.106589i	−0.0951421	+	0.995464i	$0.530331\pi$
$18$		0			0
$19$	−7.66103	+	2.24948i	−1.75756	+	0.516066i	−0.991883	−	0.127157i	$-0.959415\pi$
$19$	−7.66103	+	2.24948i	−1.75756	+	0.516066i	−0.765678	+	0.643224i	$0.777597\pi$
$20$		0			0
$21$	−0.848710	−	5.90291i	−0.185204	−	1.28812i
$22$		0			0
$23$	4.66752	−	1.10192i	0.973246	−	0.229765i
$23$	4.66752	−	1.10192i	0.973246	−	0.229765i
$24$		0			0
$25$	0.493992	+	3.43579i	0.0987984	+	0.687158i
$26$		0			0
$27$	−0.764125	+	0.224367i	−0.147056	+	0.0431795i
$28$		0			0
$29$	−4.77570	−	1.40227i	−0.886825	−	0.260395i	−0.193569	−	0.981087i	$-0.562006\pi$
$29$	−4.77570	−	1.40227i	−0.886825	−	0.260395i	−0.693256	+	0.720691i	$0.743825\pi$
$30$		0			0
$31$	−0.740552	−	1.62158i	−0.133007	−	0.291245i	0.831397	−	0.555680i	$-0.187542\pi$
$31$	−0.740552	−	1.62158i	−0.133007	−	0.291245i	−0.964404	+	0.264435i	$0.914815\pi$
$32$		0			0
$33$	4.04231	+	2.59784i	0.703677	+	0.452226i
$34$		0			0
$35$	0.417537	−	2.90404i	0.0705767	−	0.490872i
$36$		0			0
$37$	−2.54297	−	2.93475i	−0.418062	−	0.482469i	0.507184	−	0.861838i	$-0.330687\pi$
$37$	−2.54297	−	2.93475i	−0.418062	−	0.482469i	−0.925246	+	0.379369i	$0.876141\pi$
$38$		0			0
$39$	0.415415	−	0.266971i	0.0665196	−	0.0427496i
$40$		0			0
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	−0.777140	−	0.629328i	$-0.783330\pi$
$41$	−0.279295	+	0.322324i	−0.0436186	+	0.0503386i	0.733521	+	0.679667i	$0.237876\pi$
$42$		0			0
$43$	−1.84991	+	4.05075i	−0.282109	+	0.617733i	−0.996643	−	0.0818677i	$-0.973911\pi$
$43$	−1.84991	+	4.05075i	−0.282109	+	0.617733i	0.714534	+	0.699601i	$0.246639\pi$
$44$		0			0
$45$	−4.10123			−0.611375
$46$		0			0
$47$	2.58842			0.377559			0.188780	−	0.982019i	$-0.439547\pi$
$47$	2.58842			0.377559			0.188780	+	0.982019i	$0.439547\pi$
$48$		0			0
$49$	−0.569072	+	1.24609i	−0.0812960	+	0.178013i
$50$		0			0
$51$	2.56743	−	2.96297i	0.359512	−	0.414898i
$52$		0			0
$53$	8.26060	−	5.30876i	1.13468	−	0.729215i	0.168149	−	0.985762i	$-0.446221\pi$
$53$	8.26060	−	5.30876i	1.13468	−	0.729215i	0.966532	+	0.256547i	$0.0825848\pi$
$54$		0			0
$55$	1.54806	+	1.78656i	0.208741	+	0.240899i
$56$		0			0
$57$	−2.85592	+	19.8634i	−0.378276	+	2.63097i
$58$		0			0
$59$	6.07293	+	3.90283i	0.790628	+	0.508106i	0.872545	−	0.488533i	$-0.162468\pi$
$59$	6.07293	+	3.90283i	0.790628	+	0.508106i	−0.0819173	+	0.996639i	$0.526104\pi$
$60$		0			0
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	0.997737	+	0.0672363i	$0.0214181\pi$
$61$	3.08639	+	6.75826i	0.395172	+	0.865306i	−0.602565	+	0.798070i	$0.705855\pi$
$62$		0			0
$63$	−7.55141	−	2.21729i	−0.951388	−	0.279353i
$64$		0			0
$65$	0.233095	−	0.0684429i	0.0289119	−	0.00848929i
$66$		0			0
$67$	1.03413	+	7.19254i	0.126339	+	0.878708i	0.950139	+	0.311827i	$0.100941\pi$
$67$	1.03413	+	7.19254i	0.126339	+	0.878708i	−0.823800	+	0.566881i	$0.808150\pi$
$68$		0			0
$69$	2.35404	−	11.8214i	0.283394	−	1.42313i
$70$		0			0
$71$	−0.103930	−	0.722850i	−0.0123342	−	0.0857866i	0.982725	−	0.185074i	$-0.0592526\pi$
$71$	−0.103930	−	0.722850i	−0.0123342	−	0.0857866i	−0.995059	+	0.0992879i	$0.968344\pi$
$72$		0			0
$73$	6.18330	−	1.81558i	0.723700	−	0.212498i	0.100920	−	0.994895i	$-0.467821\pi$
$73$	6.18330	−	1.81558i	0.723700	−	0.212498i	0.622780	+	0.782397i	$0.286003\pi$
$74$		0			0
$75$	8.37071	+	2.45786i	0.966566	+	0.283809i
$76$		0			0
$77$	1.88449	+	4.12645i	0.214757	+	0.470253i
$78$		0			0
$79$	4.77671	+	3.06980i	0.537422	+	0.345380i	0.781030	−	0.624494i	$-0.214695\pi$
$79$	4.77671	+	3.06980i	0.537422	+	0.345380i	−0.243608	+	0.969874i	$0.578331\pi$
$80$		0			0
$81$	1.13126	−	7.86810i	0.125696	−	0.874233i
$82$		0			0
$83$	−8.44098	−	9.74141i	−0.926518	−	1.06926i	−0.997421	−	0.0717758i	$-0.977133\pi$
$83$	−8.44098	−	9.74141i	−0.926518	−	1.06926i	0.0709025	−	0.997483i	$-0.477412\pi$
$84$		0			0
$85$	1.62260	−	1.04278i	0.175996	−	0.113106i
$86$		0			0
$87$	−8.19209	+	9.45418i	−0.878284	+	1.01359i
$88$		0			0
$89$	−5.77436	+	12.6441i	−0.612081	+	1.34027i	0.309060	+	0.951043i	$0.399986\pi$
$89$	−5.77436	+	12.6441i	−0.612081	+	1.34027i	−0.921141	+	0.389228i	$0.872742\pi$
$90$		0			0
$91$	0.466190			0.0488700
$92$		0			0
$93$	−4.48047			−0.464603
$94$		0			0
$95$	−4.10123	+	8.98044i	−0.420777	+	0.921374i
$96$		0			0
$97$	−2.83147	+	3.26769i	−0.287492	+	0.331783i	−0.881064	−	0.472998i	$-0.843172\pi$
$97$	−2.83147	+	3.26769i	−0.287492	+	0.331783i	0.593572	+	0.804781i	$0.297717\pi$
$98$		0			0
$99$	5.33466	−	3.42838i	0.536154	−	0.344565i
$100$		0			0
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	0.811950	−	0.583727i	$-0.198406\pi$
$101$	1.19203	+	1.37567i	0.118611	+	0.136885i	−0.693338	+	0.720612i	$0.743861\pi$
$102$		0			0
$103$	−2.17930	+	15.1574i	−0.214733	+	1.49350i	0.542335	+	0.840163i	$0.317541\pi$
$103$	−2.17930	+	15.1574i	−0.214733	+	1.49350i	−0.757067	+	0.653337i	$0.773369\pi$
$104$		0			0
$105$	−6.20330	−	3.98662i	−0.605380	−	0.389054i
$106$		0			0
$107$	−0.825981	−	1.80865i	−0.0798506	−	0.174848i	0.865496	−	0.500916i	$-0.167004\pi$
$107$	−0.825981	−	1.80865i	−0.0798506	−	0.174848i	−0.945346	+	0.326068i	$0.894276\pi$
$108$		0			0
$109$	−14.9631	−	4.39356i	−1.43320	−	0.420826i	−0.529253	−	0.848464i	$-0.677528\pi$
$109$	−14.9631	−	4.39356i	−1.43320	−	0.420826i	−0.903950	+	0.427638i	$0.859346\pi$
$110$		0			0
$111$	−9.36451	+	2.74967i	−0.888840	+	0.260987i
$112$		0			0
$113$	0.211799	+	1.47310i	0.0199244	+	0.138577i	0.997356	−	0.0726771i	$-0.0231542\pi$
$113$	0.211799	+	1.47310i	0.0199244	+	0.138577i	−0.977431	+	0.211254i	$0.932245\pi$
$114$		0			0
$115$	2.74969	−	5.25390i	0.256410	−	0.489929i
$116$		0			0
$117$	−0.0927432	−	0.645043i	−0.00857412	−	0.0596343i
$118$		0			0
$119$	3.55139	−	1.04278i	0.325556	−	0.0955917i
$120$		0			0
$121$	7.04733	+	2.06928i	0.640667	+	0.188117i
$122$		0			0
$123$	0.445295	+	0.975060i	0.0401509	+	0.0879182i
$124$		0			0
$125$	8.81159	+	5.66287i	0.788133	+	0.506502i
$126$		0			0
$127$	0.853087	−	5.93335i	0.0756993	−	0.526500i	−0.916323	−	0.400439i	$-0.868858\pi$
$127$	0.853087	−	5.93335i	0.0756993	−	0.526500i	0.992023	−	0.126061i	$-0.0402334\pi$
$128$		0			0
$129$	7.32941	+	8.45859i	0.645319	+	0.744737i
$130$		0			0
$131$	10.7418	−	6.90335i	0.938517	−	0.603148i	0.0205431	−	0.999789i	$-0.493460\pi$
$131$	10.7418	−	6.90335i	0.938517	−	0.603148i	0.917974	+	0.396641i	$0.129824\pi$
$132$		0			0
$133$	−12.4066	+	14.3180i	−1.07579	+	1.24153i
$134$		0			0
$135$	−0.409064	+	0.895726i	−0.0352067	+	0.0770918i
$136$		0			0
$137$	0.697560			0.0595966			0.0297983	−	0.999556i	$-0.490514\pi$
$137$	0.697560			0.0595966			0.0297983	+	0.999556i	$0.490514\pi$
$138$		0			0
$139$	−13.9559			−1.18372			−0.591862	−	0.806039i	$-0.701607\pi$
$139$	−13.9559			−1.18372			−0.591862	+	0.806039i	$0.701607\pi$
$140$		0			0
$141$	2.70251	−	5.91767i	0.227592	−	0.498358i
$142$		0			0
$143$	−0.245983	+	0.283880i	−0.0205702	+	0.0237392i
$144$		0			0
$145$	−5.17736	+	3.32729i	−0.429957	+	0.276316i
$146$		0			0
$147$	2.25468	+	2.60204i	0.185963	+	0.214613i
$148$		0			0
$149$	2.36798	−	16.4697i	0.193993	−	1.34925i	−0.627317	−	0.778764i	$-0.715847\pi$
$149$	2.36798	−	16.4697i	0.193993	−	1.34925i	0.821309	−	0.570483i	$-0.193244\pi$
$150$		0			0
$151$	−11.0961	−	7.13103i	−0.902988	−	0.580315i	0.00468679	−	0.999989i	$-0.498508\pi$
$151$	−11.0961	−	7.13103i	−0.902988	−	0.580315i	−0.907675	+	0.419674i	$0.862145\pi$
$152$		0			0
$153$	−2.14935	−	4.70643i	−0.173765	−	0.380492i
$154$		0			0
$155$	−2.11496	−	0.621008i	−0.169877	−	0.0498805i
$156$		0			0
$157$	−3.96143	+	1.16318i	−0.316157	+	0.0928320i	−0.435961	−	0.899965i	$-0.643591\pi$
$157$	−3.96143	+	1.16318i	−0.316157	+	0.0928320i	0.119804	+	0.992798i	$0.461773\pi$
$158$		0			0
$159$	−3.51225	−	24.4282i	−0.278540	−	1.93729i
$160$		0			0
$161$	7.90335	−	8.18717i	0.622871	−	0.645239i
$162$		0			0
$163$	−2.10474	−	14.6388i	−0.164856	−	1.14660i	−0.889320	−	0.457285i	$-0.848822\pi$
$163$	−2.10474	−	14.6388i	−0.164856	−	1.14660i	0.724464	−	0.689312i	$-0.242087\pi$
$164$		0			0
$165$	5.70075	−	1.67389i	0.443802	−	0.130312i
$166$		0			0
$167$	1.27588	+	0.374632i	0.0987306	+	0.0289899i	0.330725	−	0.943727i	$-0.392707\pi$
$167$	1.27588	+	0.374632i	0.0987306	+	0.0289899i	−0.231994	+	0.972717i	$0.574525\pi$
$168$		0			0
$169$	−5.38436	−	11.7901i	−0.414181	−	0.906931i
$170$		0			0
$171$	22.2792	+	14.3180i	1.70373	+	1.09492i
$172$		0			0
$173$	2.41025	−	16.7637i	0.183248	−	1.27452i	−0.665771	−	0.746156i	$-0.731897\pi$
$173$	2.41025	−	16.7637i	0.183248	−	1.27452i	0.849019	−	0.528362i	$-0.177194\pi$
$174$		0			0
$175$	5.39358	+	6.22452i	0.407716	+	0.470530i
$176$		0			0
$177$	15.2633	−	9.80914i	1.14726	−	0.737300i
$178$		0			0
$179$	−0.937335	+	1.08174i	−0.0700597	+	0.0808532i	−0.789697	−	0.613497i	$-0.789762\pi$
$179$	−0.937335	+	1.08174i	−0.0700597	+	0.0808532i	0.719638	+	0.694350i	$0.244308\pi$
$180$		0			0
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	0.478986	+	0.877822i	$0.341004\pi$
$181$	−6.70121	+	14.6736i	−0.498097	+	1.09068i	−0.977083	+	0.212858i	$0.931723\pi$
$182$		0			0
$183$	18.6732			1.38037
$184$		0			0
$185$	−4.80153			−0.353015
$186$		0			0
$187$	−1.23889	+	2.71279i	−0.0905967	+	0.198379i
$188$		0			0
$189$	−1.23746	+	1.42810i	−0.0900118	+	0.103879i
$190$		0			0
$191$	17.4514	−	11.2153i	1.26274	−	0.811512i	0.274081	−	0.961707i	$-0.411626\pi$
$191$	17.4514	−	11.2153i	1.26274	−	0.811512i	0.988656	+	0.150195i	$0.0479900\pi$
$192$		0			0
$193$	−9.59519	−	11.0734i	−0.690677	−	0.797083i	0.296785	−	0.954944i	$-0.404086\pi$
$193$	−9.59519	−	11.0734i	−0.690677	−	0.797083i	−0.987461	+	0.157861i	$0.949540\pi$
$194$		0			0
$195$	0.0868945	−	0.604364i	0.00622264	−	0.0432794i
$196$		0			0
$197$	9.82407	+	6.31355i	0.699936	+	0.449822i	0.841606	−	0.540092i	$-0.181611\pi$
$197$	9.82407	+	6.31355i	0.699936	+	0.449822i	−0.141669	+	0.989914i	$0.545247\pi$
$198$		0			0
$199$	2.37759	+	5.20620i	0.168543	+	0.369057i	0.974990	−	0.222249i	$-0.0713397\pi$
$199$	2.37759	+	5.20620i	0.168543	+	0.369057i	−0.806447	+	0.591306i	$0.798612\pi$
$200$		0			0
$201$	17.5234	+	5.14533i	1.23600	+	0.362923i
$202$		0			0
$203$	−11.3317	+	3.32729i	−0.795330	+	0.233530i
$204$		0			0
$205$	0.0750502	+	0.521985i	0.00524173	+	0.0364570i
$206$		0			0
$207$	−12.9004	−	9.30671i	−0.896643	−	0.646861i
$208$		0			0
$209$	−2.17244	−	15.1097i	−0.150271	−	1.04516i
$210$		0			0
$211$	−13.4979	+	3.96334i	−0.929234	+	0.272848i	−0.711116	−	0.703075i	$-0.751810\pi$
$211$	−13.4979	+	3.96334i	−0.929234	+	0.272848i	−0.218118	+	0.975922i	$0.569992\pi$
$212$		0			0
$213$	−1.76110	−	0.517106i	−0.120669	−	0.0354315i
$214$		0			0
$215$	2.28738	+	5.00866i	0.155998	+	0.341588i
$216$		0			0
$217$	−3.55843	−	2.28687i	−0.241562	−	0.155243i
$218$		0			0
$219$	2.30504	−	16.0319i	0.155760	−	1.08334i
$220$		0			0
$221$	0.200702	+	0.231623i	0.0135007	+	0.0155806i
$222$		0			0
$223$	3.53628	−	2.27263i	0.236807	−	0.152187i	−0.416856	−	0.908973i	$-0.636868\pi$
$223$	3.53628	−	2.27263i	0.236807	−	0.152187i	0.653663	+	0.756786i	$0.273232\pi$
$224$		0			0
$225$	7.53956	−	8.70112i	0.502638	−	0.580075i
$226$		0			0
$227$	−7.65642	+	16.7652i	−0.508174	+	1.11275i	0.465551	+	0.885021i	$0.345856\pi$
$227$	−7.65642	+	16.7652i	−0.508174	+	1.11275i	−0.973725	+	0.227726i	$0.926871\pi$
$228$		0			0
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$		0			0
$231$	11.4015			0.750163
$232$		0			0
$233$	1.73013	−	3.78846i	0.113345	−	0.248190i	−0.844455	−	0.535626i	$-0.820076\pi$
$233$	1.73013	−	3.78846i	0.113345	−	0.248190i	0.957800	+	0.287436i	$0.0928029\pi$
$234$		0			0
$235$	2.09590	−	2.41879i	0.136721	−	0.157785i
$236$		0			0
$237$	12.0055	−	7.71545i	0.779839	−	0.501172i
$238$		0			0
$239$	−14.7456	−	17.0173i	−0.953813	−	1.10076i	−0.994825	−	0.101601i	$-0.967604\pi$
$239$	−14.7456	−	17.0173i	−0.953813	−	1.10076i	0.0410120	−	0.999159i	$-0.486942\pi$
$240$		0			0
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	0.944429	+	0.328717i	$0.106616\pi$
$241$	−0.843804	+	5.86878i	−0.0543542	+	0.378042i	−0.998783	+	0.0493250i	$0.984293\pi$
$242$		0			0
$243$	−18.8169	−	12.0929i	−1.20710	−	0.775759i
$244$		0			0
$245$	0.703646	+	1.54077i	0.0449543	+	0.0984361i
$246$		0			0
$247$	−1.50519	−	0.441964i	−0.0957730	−	0.0281215i
$248$		0			0
$249$	−31.0840	+	9.12708i	−1.96987	+	0.578405i
$250$		0			0
$251$	−0.220675	−	1.53483i	−0.0139289	−	0.0968775i	0.981671	−	0.190583i	$-0.0610379\pi$
$251$	−0.220675	−	1.53483i	−0.0139289	−	0.0968775i	−0.995600	+	0.0937056i	$0.970129\pi$
$252$		0			0
$253$	0.815292	+	9.13256i	0.0512570	+	0.574159i
$254$		0			0
$255$	−0.689900	−	4.79836i	−0.0432032	−	0.300485i
$256$		0			0
$257$	−26.3456	+	7.73578i	−1.64340	+	0.482545i	−0.967166	−	0.254145i	$-0.918206\pi$
$257$	−26.3456	+	7.73578i	−1.64340	+	0.482545i	−0.676230	+	0.736690i	$0.736388\pi$
$258$		0			0
$259$	−8.84083	−	2.59590i	−0.549342	−	0.161301i
$260$		0			0
$261$	6.85812	+	15.0172i	0.424507	+	0.929540i
$262$		0			0
$263$	10.8864	+	6.99627i	0.671285	+	0.431408i	0.831388	−	0.555692i	$-0.187547\pi$
$263$	10.8864	+	6.99627i	0.671285	+	0.431408i	−0.160104	+	0.987100i	$0.551183\pi$
$264$		0			0
$265$	1.72791	−	12.0179i	0.106145	−	0.738253i
$266$		0			0
$267$	22.8782	+	26.4028i	1.40012	+	1.61583i
$268$		0			0
$269$	−8.41057	+	5.40514i	−0.512801	+	0.329557i	−0.771319	−	0.636449i	$-0.780402\pi$
$269$	−8.41057	+	5.40514i	−0.512801	+	0.329557i	0.258517	+	0.966007i	$0.416766\pi$
$270$		0			0
$271$	2.88885	−	3.33391i	0.175485	−	0.202520i	−0.661193	−	0.750216i	$-0.729949\pi$
$271$	2.88885	−	3.33391i	0.175485	−	0.202520i	0.836678	+	0.547696i	$0.184495\pi$
$272$		0			0
$273$	0.486739	−	1.06581i	0.0294588	−	0.0645057i
$274$		0			0
$275$	−6.63624			−0.400180
$276$		0			0
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$		0			0
$279$	−2.45631	+	5.37857i	−0.147055	+	0.322006i
$280$		0			0
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	−0.681516	−	0.731803i	$-0.738679\pi$
$281$	2.34395	−	2.70506i	0.139828	−	0.161370i	0.821344	+	0.570433i	$0.193225\pi$
$282$		0			0
$283$	−12.4341	+	7.99089i	−0.739129	+	0.475009i	−0.855243	−	0.518227i	$-0.826592\pi$
$283$	−12.4341	+	7.99089i	−0.739129	+	0.475009i	0.116115	+	0.993236i	$0.462956\pi$
$284$		0			0
$285$	16.2492	+	18.7526i	0.962519	+	1.11081i
$286$		0			0
$287$	−0.144020	+	1.00168i	−0.00850125	+	0.0591275i
$288$		0			0
$289$	−12.2543	−	7.87535i	−0.720840	−	0.463256i
$290$		0			0
$291$	4.51435	+	9.88506i	0.264636	+	0.579472i
$292$		0			0
$293$	−20.6420	−	6.06104i	−1.20592	−	0.354090i	−0.383806	−	0.923414i	$-0.625387\pi$
$293$	−20.6420	−	6.06104i	−1.20592	−	0.354090i	−0.822113	+	0.569324i	$0.807205\pi$
$294$		0			0
$295$	8.56445	−	2.51475i	0.498642	−	0.146414i
$296$		0			0
$297$	−0.216683	−	1.50707i	−0.0125732	−	0.0874488i
$298$		0			0
$299$	0.888516	+	0.313663i	0.0513842	+	0.0181396i
$300$		0			0
$301$	1.50376	+	10.4589i	0.0866752	+	0.602839i
$302$		0			0
$303$	4.38965	−	1.28892i	0.252179	−	0.0740464i
$304$		0			0
$305$	8.81450	+	2.58817i	0.504717	+	0.148198i
$306$		0			0
$307$	−5.87602	−	12.8667i	−0.335362	−	0.734341i	0.664555	−	0.747240i	$-0.268621\pi$
$307$	−5.87602	−	12.8667i	−0.335362	−	0.734341i	−0.999917	+	0.0128989i	$0.995894\pi$
$308$		0			0
$309$	32.3776	+	20.8078i	1.84190	+	1.18371i
$310$		0			0
$311$	0.0811393	−	0.564336i	0.00460099	−	0.0320006i	−0.987392	−	0.158297i	$-0.949400\pi$
$311$	0.0811393	−	0.564336i	0.00460099	−	0.0320006i	0.991993	+	0.126296i	$0.0403089\pi$
$312$		0			0
$313$	13.8390	+	15.9711i	0.782227	+	0.902738i	0.997268	−	0.0738672i	$-0.0235341\pi$
$313$	13.8390	+	15.9711i	0.782227	+	0.902738i	−0.215041	+	0.976605i	$0.568989\pi$
$314$		0			0
$315$	−8.18653	+	5.26116i	−0.461259	+	0.296433i
$316$		0			0
$317$	5.77072	−	6.65977i	0.324116	−	0.374050i	−0.570185	−	0.821517i	$-0.693128\pi$
$317$	5.77072	−	6.65977i	0.324116	−	0.374050i	0.894301	+	0.447467i	$0.147674\pi$
$318$		0			0
$319$	3.95303	−	8.65592i	0.221327	−	0.484639i
$320$		0			0
$321$	−4.99734			−0.278924
$322$		0			0
$323$	−12.4550			−0.693015
$324$		0			0
$325$	−0.283306	+	0.620354i	−0.0157150	+	0.0344111i
$326$		0			0
$327$	−25.6672	+	29.6216i	−1.41940	+	1.63808i
$328$		0			0
$329$	5.16678	−	3.32049i	0.284854	−	0.183064i
$330$		0			0
$331$	19.7686	+	22.8142i	1.08658	+	1.25398i	0.965239	+	0.261371i	$0.0841744\pi$
$331$	19.7686	+	22.8142i	1.08658	+	1.25398i	0.121342	+	0.992611i	$0.461280\pi$
$332$		0			0
$333$	−1.83303	+	12.7490i	−0.100450	+	0.698642i
$334$		0			0
$335$	7.55856	+	4.85759i	0.412968	+	0.265398i
$336$		0			0
$337$	−2.05870	−	4.50792i	−0.112145	−	0.245562i	0.845235	−	0.534394i	$-0.179460\pi$
$337$	−2.05870	−	4.50792i	−0.112145	−	0.245562i	−0.957380	+	0.288832i	$0.906733\pi$
$338$		0			0
$339$	3.58895	+	1.05381i	0.194925	+	0.0572351i
$340$		0			0
$341$	3.27015	−	0.960202i	0.177088	−	0.0519979i
$342$		0			0
$343$	2.82637	+	19.6578i	0.152609	+	1.06142i
$344$		0			0
$345$	−9.14064	−	11.7719i	−0.492115	−	0.633775i
$346$		0			0
$347$	−0.963038	−	6.69808i	−0.0516986	−	0.359572i	−0.999206	−	0.0398383i	$-0.987316\pi$
$347$	−0.963038	−	6.69808i	−0.0516986	−	0.359572i	0.947508	−	0.319733i	$-0.103593\pi$
$348$		0			0
$349$	−9.68306	+	2.84320i	−0.518322	+	0.152193i	−0.530422	−	0.847734i	$-0.677967\pi$
$349$	−9.68306	+	2.84320i	−0.518322	+	0.152193i	0.0121000	+	0.999927i	$0.496148\pi$
$350$		0			0
$351$	−0.150131	−	0.0440823i	−0.00801338	−	0.00235294i
$352$		0			0
$353$	10.1649	+	22.2580i	0.541023	+	1.18468i	0.960850	+	0.277071i	$0.0893636\pi$
$353$	10.1649	+	22.2580i	0.541023	+	1.18468i	−0.419827	+	0.907604i	$0.637909\pi$
$354$		0			0
$355$	−0.759635	−	0.488188i	−0.0403173	−	0.0259103i
$356$		0			0
$357$	1.32391	−	9.20798i	0.0700686	−	0.487338i
$358$		0			0
$359$	0.274264	+	0.316518i	0.0144751	+	0.0167052i	0.762941	−	0.646468i	$-0.223755\pi$
$359$	0.274264	+	0.316518i	0.0144751	+	0.0167052i	−0.748466	+	0.663173i	$0.769209\pi$
$360$		0			0
$361$	37.6474	−	24.1945i	1.98144	−	1.27340i
$362$		0			0
$363$	12.0888	−	13.9512i	0.634497	−	0.732248i
$364$		0			0
$365$	3.31015	−	7.24821i	0.173261	−	0.379389i
$366$		0			0
$367$	−28.5682			−1.49125			−0.745624	−	0.666367i	$-0.767849\pi$
$367$	−28.5682			−1.49125			−0.745624	+	0.666367i	$0.767849\pi$
$368$		0			0
$369$	1.41463			0.0736426
$370$		0			0
$371$	9.67888	−	21.1938i	0.502503	−	1.10033i
$372$		0			0
$373$	−9.43508	+	10.8887i	−0.488530	+	0.563794i	−0.945472	−	0.325703i	$-0.894399\pi$
$373$	−9.43508	+	10.8887i	−0.488530	+	0.563794i	0.456942	+	0.889496i	$0.348945\pi$
$374$		0			0
$375$	22.1465	−	14.2327i	1.14364	−	0.734973i
$376$		0			0
$377$	−0.640396	−	0.739056i	−0.0329821	−	0.0380633i
$378$		0			0
$379$	−0.800823	+	5.56985i	−0.0411355	+	0.286104i	0.958862	+	0.283873i	$0.0916193\pi$
$379$	−0.800823	+	5.56985i	−0.0411355	+	0.286104i	−0.999998	+	0.00223119i	$0.999290\pi$
$380$		0			0
$381$	−12.6742	−	8.14522i	−0.649320	−	0.417292i
$382$		0			0
$383$	−0.0962350	−	0.210725i	−0.00491738	−	0.0107676i	0.907157	−	0.420792i	$-0.138248\pi$
$383$	−0.0962350	−	0.210725i	−0.00491738	−	0.0107676i	−0.912075	+	0.410024i	$0.865520\pi$
$384$		0			0
$385$	5.38195	+	1.58028i	0.274289	+	0.0805386i
$386$		0			0
$387$	14.1722	−	4.16135i	0.720416	−	0.211533i
$388$		0			0
$389$	4.29361	+	29.8627i	0.217695	+	1.51410i	0.746516	+	0.665367i	$0.231725\pi$
$389$	4.29361	+	29.8627i	0.217695	+	1.51410i	−0.528821	+	0.848733i	$0.677366\pi$
$390$		0			0
$391$	7.47023	+	0.402007i	0.377786	+	0.0203304i
$392$		0			0
$393$	−4.56722	−	31.7657i	−0.230386	−	1.60237i
$394$		0			0
$395$	6.73644	−	1.97800i	0.338947	−	0.0995238i
$396$		0			0
$397$	12.5168	+	3.67528i	0.628202	+	0.184457i	0.580310	−	0.814396i	$-0.302931\pi$
$397$	12.5168	+	3.67528i	0.628202	+	0.184457i	0.0478924	+	0.998853i	$0.484750\pi$
$398$		0			0
$399$	19.7805	+	43.3132i	0.990263	+	2.16837i
$400$		0			0
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	0.00967246	−	0.999953i	$-0.496921\pi$
$401$	−17.9404	−	11.5296i	−0.895899	−	0.575759i	−0.905571	+	0.424194i	$0.860557\pi$
$402$		0			0
$403$	0.0498457	−	0.346685i	0.00248299	−	0.0172696i
$404$		0			0
$405$	−6.43648	−	7.42810i	−0.319831	−	0.369105i
$406$		0			0
$407$	6.24557	−	4.01378i	0.309581	−	0.198956i
$408$		0			0
$409$	5.99134	−	6.91437i	0.296253	−	0.341894i	−0.588036	−	0.808835i	$-0.700099\pi$
$409$	5.99134	−	6.91437i	0.296253	−	0.341894i	0.884288	+	0.466941i	$0.154644\pi$
$410$		0			0
$411$	0.728307	−	1.59477i	0.0359247	−	0.0786642i
$412$		0			0
$413$	17.1289			0.842859
$414$		0			0
$415$	−15.9379			−0.782360
$416$		0			0
$417$	−14.5711	+	31.9062i	−0.713548	+	1.56245i
$418$		0			0
$419$	−5.87685	+	6.78225i	−0.287103	+	0.331334i	−0.880920	−	0.473266i	$-0.843075\pi$
$419$	−5.87685	+	6.78225i	−0.287103	+	0.331334i	0.593817	+	0.804600i	$0.297620\pi$
$420$		0			0
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.298241	−	0.954491i	$-0.403600\pi$
$421$	26.4762	−	17.0152i	1.29037	−	0.829270i	0.992129	+	0.125221i	$0.0399638\pi$
$422$		0			0
$423$	−5.62226	−	6.48843i	−0.273364	−	0.315478i
$424$		0			0
$425$	−0.770581	+	5.35951i	−0.0373787	+	0.259974i
$426$		0			0
$427$	14.8305	+	9.53095i	0.717696	+	0.461235i
$428$		0			0
$429$	0.392184	+	0.858763i	0.0189348	+	0.0414615i
$430$		0			0
$431$	−21.2071	−	6.22697i	−1.02151	−	0.299942i	−0.272256	−	0.962225i	$-0.587770\pi$
$431$	−21.2071	−	6.22697i	−1.02151	−	0.299942i	−0.749254	+	0.662283i	$0.769588\pi$
$432$		0			0
$433$	−12.1810	+	3.57666i	−0.585382	+	0.171884i	−0.560995	−	0.827819i	$-0.689581\pi$
$433$	−12.1810	+	3.57666i	−0.585382	+	0.171884i	−0.0243864	+	0.999703i	$0.507763\pi$
$434$		0			0
$435$	2.20132	+	15.3105i	0.105545	+	0.734082i
$436$		0			0
$437$	−33.2793	+	18.9413i	−1.59196	+	0.906086i
$438$		0			0
$439$	2.62158	+	18.2335i	0.125121	+	0.870238i	0.951615	+	0.307292i	$0.0994229\pi$
$439$	2.62158	+	18.2335i	0.125121	+	0.870238i	−0.826494	+	0.562946i	$0.809668\pi$
$440$		0			0
$441$	4.35968	−	1.28012i	0.207604	−	0.0609580i
$442$		0			0
$443$	−13.3492	−	3.91968i	−0.634240	−	0.186230i	−0.0512201	−	0.998687i	$-0.516311\pi$
$443$	−13.3492	−	3.91968i	−0.634240	−	0.186230i	−0.583020	+	0.812458i	$0.698129\pi$
$444$		0			0
$445$	7.13988	+	15.6342i	0.338463	+	0.741130i
$446$		0			0
$447$	−35.1808	−	22.6093i	−1.66399	−	1.06938i
$448$		0			0
$449$	−4.28260	+	29.7862i	−0.202109	+	1.40570i	0.595904	+	0.803056i	$0.296794\pi$
$449$	−4.28260	+	29.7862i	−0.202109	+	1.40570i	−0.798013	+	0.602641i	$0.794115\pi$
$450$		0			0
$451$	−0.533969	−	0.616233i	−0.0251436	−	0.0290173i
$452$		0			0
$453$	−27.8883	+	17.9227i	−1.31030	+	0.842082i
$454$		0			0
$455$	0.377484	−	0.435640i	0.0176967	−	0.0204231i
$456$		0			0
$457$	15.8055	−	34.6093i	0.739351	−	1.61895i	−0.0452680	−	0.998975i	$-0.514414\pi$
$457$	15.8055	−	34.6093i	0.739351	−	1.61895i	0.784619	−	0.619978i	$-0.212859\pi$
$458$		0			0
$459$	−1.24228			−0.0579849
$460$		0			0
$461$	8.76016			0.408001			0.204001	−	0.978971i	$-0.434606\pi$
$461$	8.76016			0.408001			0.204001	+	0.978971i	$0.434606\pi$
$462$		0			0
$463$	11.5638	−	25.3212i	0.537415	−	1.17677i	−0.425001	−	0.905193i	$-0.639726\pi$
$463$	11.5638	−	25.3212i	0.537415	−	1.17677i	0.962416	−	0.271581i	$-0.0875465\pi$
$464$		0			0
$465$	−3.62794	+	4.18686i	−0.168241	+	0.194161i
$466$		0			0
$467$	14.6095	−	9.38895i	0.676047	−	0.434469i	−0.157054	−	0.987590i	$-0.550200\pi$
$467$	14.6095	−	9.38895i	0.676047	−	0.434469i	0.833101	+	0.553121i	$0.186563\pi$
$468$		0			0
$469$	11.2910	+	13.0305i	0.521370	+	0.601693i
$470$		0			0
$471$	−1.47677	+	10.2711i	−0.0680458	+	0.473269i
$472$		0			0
$473$	−7.16224	−	4.60289i	−0.329320	−	0.211641i
$474$		0			0
$475$	−11.5132	−	25.2105i	−0.528263	−	1.15674i
$476$		0			0
$477$	−31.2503	−	9.17591i	−1.43085	−	0.420136i
$478$		0			0
$479$	−24.4458	+	7.17792i	−1.11695	+	0.327968i	−0.787568	−	0.616228i	$-0.788660\pi$
$479$	−24.4458	+	7.17792i	−1.11695	+	0.327968i	−0.329387	+	0.944195i	$0.606842\pi$
$480$		0			0
$481$	−0.108579	−	0.755186i	−0.00495079	−	0.0344335i
$482$		0			0
$483$	−10.4659	−	26.6168i	−0.476214	−	1.21110i
$484$		0			0
$485$	0.760851	+	5.29183i	0.0345485	+	0.240290i
$486$		0			0
$487$	−5.91151	+	1.73577i	−0.267876	+	0.0786555i	−0.412912	−	0.910771i	$-0.635488\pi$
$487$	−5.91151	+	1.73577i	−0.267876	+	0.0786555i	0.145036	+	0.989426i	$0.453670\pi$
$488$		0			0
$489$	−35.6649	−	10.4721i	−1.61282	−	0.473567i
$490$		0			0
$491$	13.5623	+	29.6973i	0.612058	+	1.34022i	0.921157	+	0.389191i	$0.127245\pi$
$491$	13.5623	+	29.6973i	0.612058	+	1.34022i	−0.309099	+	0.951030i	$0.600027\pi$
$492$		0			0
$493$	−6.53161	−	4.19761i	−0.294169	−	0.189051i
$494$		0			0
$495$	1.11588	−	7.76111i	0.0501550	−	0.348836i
$496$		0			0
$497$	−1.13475	−	1.30957i	−0.0509004	−	0.0587421i
$498$		0			0
$499$	7.21265	−	4.63529i	0.322882	−	0.207504i	−0.369151	−	0.929369i	$-0.620351\pi$
$499$	7.21265	−	4.63529i	0.322882	−	0.207504i	0.692033	+	0.721866i	$0.256715\pi$
$500$		0			0
$501$	2.18861	−	2.52579i	0.0977797	−	0.112844i
$502$		0			0
$503$	−2.80635	+	6.14505i	−0.125129	+	0.273994i	−0.961821	−	0.273679i	$-0.911759\pi$
$503$	−2.80635	+	6.14505i	−0.125129	+	0.273994i	0.836692	+	0.547674i	$0.184487\pi$
$504$		0			0
$505$	2.25073			0.100156
$506$		0			0
$507$	−32.5764			−1.44677
$508$		0			0
$509$	17.0206	−	37.2699i	0.754425	−	1.65196i	−0.00382066	−	0.999993i	$-0.501216\pi$
$509$	17.0206	−	37.2699i	0.754425	−	1.65196i	0.758246	−	0.651968i	$-0.226057\pi$
$510$		0			0
$511$	10.0135	−	11.5562i	0.442971	−	0.511216i
$512$		0			0
$513$	5.34928	−	3.43777i	0.236176	−	0.151781i
$514$		0			0
$515$	12.3995	+	14.3097i	0.546385	+	0.630562i
$516$		0			0
$517$	−0.704266	+	4.89828i	−0.0309736	+	0.215426i
$518$		0			0
$519$	−35.8088	−	23.0129i	−1.57183	−	1.01016i
$520$		0			0
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	0.659162	−	0.752001i	$-0.270911\pi$
$521$	−7.77941	−	17.0345i	−0.340822	−	0.746297i	−0.999984	+	0.00570487i	$0.998184\pi$
$522$		0			0
$523$	22.6095	+	6.63875i	0.988644	+	0.290292i	0.735788	−	0.677212i	$-0.236812\pi$
$523$	22.6095	+	6.63875i	0.988644	+	0.290292i	0.252856	+	0.967504i	$0.418630\pi$
$524$		0			0
$525$	19.8619	−	5.83198i	0.866844	−	0.254528i
$526$		0			0
$527$	−0.395751	−	2.75251i	−0.0172392	−	0.119901i
$528$		0			0
$529$	20.5716	−	10.2864i	0.894416	−	0.447237i
$530$		0			0
$531$	−3.40760	−	23.7004i	−0.147877	−	1.02851i
$532$		0			0
$533$	−0.0804009	+	0.0236078i	−0.00348255	+	0.00102257i
$534$		0			0
$535$	−2.35894	−	0.692647i	−0.101986	−	0.0299457i
$536$		0			0
$537$	1.49444	+	3.27237i	0.0644899	+	0.141213i
$538$		0			0
$539$	−2.20325	−	1.41595i	−0.0949009	−	0.0609891i
$540$		0			0
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	−0.992530	−	0.122001i	$-0.961069\pi$
$541$	−0.135667	+	0.943585i	−0.00583278	+	0.0405679i	0.986697	+	0.162569i	$0.0519780\pi$
$542$		0			0
$543$	26.5504	+	30.6408i	1.13939	+	1.31492i
$544$		0			0
$545$	−16.2216	+	10.4250i	−0.694856	+	0.446557i
$546$		0			0
$547$	19.5057	−	22.5108i	0.834003	−	0.962491i	−0.165717	−	0.986173i	$-0.552994\pi$
$547$	19.5057	−	22.5108i	0.834003	−	0.962491i	0.999720	+	0.0236827i	$0.00753914\pi$
$548$		0			0
$549$	10.2371	−	22.4162i	0.436911	−	0.956701i
$550$		0			0
$551$	39.7412			1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$		0			0
$555$	−5.01317	+	10.9773i	−0.212797	+	0.465961i
$556$		0			0
$557$	3.93487	−	4.54108i	0.166726	−	0.192412i	−0.666238	−	0.745739i	$-0.732097\pi$
$557$	3.93487	−	4.54108i	0.166726	−	0.192412i	0.832964	+	0.553327i	$0.186642\pi$
$558$		0			0
$559$	−0.736039	+	0.473023i	−0.0311311	+	0.0200068i
$560$		0			0
$561$	4.90852	+	5.66473i	0.207238	+	0.239165i
$562$		0			0
$563$	0.0126931	−	0.0882822i	0.000534949	−	0.00372065i	−0.989552	−	0.144175i	$-0.953947\pi$
$563$	0.0126931	−	0.0882822i	0.000534949	−	0.00372065i	0.990087	+	0.140454i	$0.0448563\pi$
$564$		0			0
$565$	1.54806	+	0.994879i	0.0651274	+	0.0418549i
$566$		0			0
$567$	−7.83526	−	17.1568i	−0.329050	−	0.720519i
$568$		0			0
$569$	39.6842	+	11.6523i	1.66365	+	0.488491i	0.972243	−	0.233975i	$-0.0751733\pi$
$569$	39.6842	+	11.6523i	1.66365	+	0.488491i	0.691406	+	0.722466i	$0.256991\pi$
$570$		0			0
$571$	24.7458	−	7.26602i	1.03558	−	0.304073i	0.280602	−	0.959824i	$-0.409466\pi$
$571$	24.7458	−	7.26602i	1.03558	−	0.304073i	0.754977	+	0.655751i	$0.227648\pi$
$572$		0			0
$573$	−7.42000	−	51.6072i	−0.309975	−	2.15592i
$574$		0			0
$575$	6.09167	+	15.4923i	0.254040	+	0.646073i
$576$		0			0
$577$	−3.86302	−	26.8679i	−0.160820	−	1.11853i	−0.897093	−	0.441842i	$-0.854325\pi$
$577$	−3.86302	−	26.8679i	−0.160820	−	1.11853i	0.736273	−	0.676684i	$-0.236584\pi$
$578$		0			0
$579$	−35.3343	+	10.3751i	−1.46845	+	0.431174i
$580$		0			0
$581$	−29.3457	−	8.61667i	−1.21746	−	0.357480i
$582$		0			0
$583$	7.79865	+	17.0767i	0.322987	+	0.707243i
$584$		0			0
$585$	−0.677869	−	0.435640i	−0.0280264	−	0.0180115i
$586$		0			0
$587$	4.50210	−	31.3128i	0.185822	−	1.29242i	−0.656863	−	0.754010i	$-0.728117\pi$
$587$	4.50210	−	31.3128i	0.185822	−	1.29242i	0.842685	−	0.538407i	$-0.180974\pi$
$588$		0			0
$589$	9.32111	+	10.7571i	0.384070	+	0.443240i
$590$		0			0
$591$	24.6912	−	15.8681i	1.01566	−	0.652726i
$592$		0			0
$593$	16.8600	−	19.4575i	0.692358	−	0.799024i	−0.295341	−	0.955392i	$-0.595433\pi$
$593$	16.8600	−	19.4575i	0.692358	−	0.799024i	0.987699	+	0.156368i	$0.0499786\pi$
$594$		0			0
$595$	1.90119	−	4.16303i	0.0779412	−	0.170667i
$596$		0			0
$597$	14.3849			0.588733
$598$		0			0
$599$	−16.9434			−0.692289			−0.346144	−	0.938181i	$-0.612509\pi$
$599$	−16.9434			−0.692289			−0.346144	+	0.938181i	$0.612509\pi$
$600$		0			0
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	−0.973624	−	0.228159i	$-0.926729\pi$
$601$	−4.01081	+	8.78246i	−0.163605	+	0.358244i	0.810019	+	0.586403i	$0.199457\pi$
$602$		0			0
$603$	15.7834	−	18.2151i	0.642752	−	0.741775i
$604$		0			0
$605$	7.64006	−	4.90997i	0.310613	−	0.199619i
$606$		0			0
$607$	2.12520	+	2.45261i	0.0862592	+	0.0995484i	0.797238	−	0.603665i	$-0.206293\pi$
$607$	2.12520	+	2.45261i	0.0862592	+	0.0995484i	−0.710979	+	0.703213i	$0.751748\pi$
$608$		0			0
$609$	−4.22430	+	29.3806i	−0.171177	+	1.19056i
$610$		0			0
$611$	0.427825	+	0.274946i	0.0173079	+	0.0111231i
$612$		0			0
$613$	−13.6731	−	29.9399i	−0.552251	−	1.20926i	−0.955723	−	0.294269i	$-0.904924\pi$
$613$	−13.6731	−	29.9399i	−0.552251	−	1.20926i	0.403471	−	0.914992i	$-0.367803\pi$
$614$		0			0
$615$	1.27173	+	0.373413i	0.0512810	+	0.0150575i
$616$		0			0
$617$	−2.90191	+	0.852079i	−0.116827	+	0.0343034i	−0.339623	−	0.940562i	$-0.610300\pi$
$617$	−2.90191	+	0.852079i	−0.116827	+	0.0343034i	0.222797	+	0.974865i	$0.428481\pi$
$618$		0			0
$619$	1.48326	+	10.3163i	0.0596172	+	0.414647i	0.997674	+	0.0681655i	$0.0217146\pi$
$619$	1.48326	+	10.3163i	0.0596172	+	0.414647i	−0.938057	+	0.346482i	$0.887376\pi$
$620$		0			0
$621$	−3.31934	+	1.88924i	−0.133200	+	0.0758127i
$622$		0			0
$623$	4.69386	+	32.6465i	0.188056	+	1.30796i
$624$		0			0
$625$	−4.22587	+	1.24083i	−0.169035	+	0.0496331i
$626$		0			0
$627$	−36.8121	−	10.8090i	−1.47013	−	0.431670i
$628$		0			0
$629$	−2.51636	−	5.51006i	−0.100334	−	0.219701i
$630$		0			0
$631$	−28.6878	−	18.4366i	−1.14205	−	0.733948i	−0.174005	−	0.984745i	$-0.555671\pi$
$631$	−28.6878	−	18.4366i	−1.14205	−	0.733948i	−0.968040	+	0.250797i	$0.919307\pi$
$632$		0			0
$633$	−5.03182	+	34.9971i	−0.199997	+	1.39101i
$634$		0			0
$635$	−4.85377	−	5.60155i	−0.192616	−	0.222291i
$636$		0			0
$637$	−0.226421	+	0.145512i	−0.00897113	+	0.00576539i
$638$		0			0
$639$	−1.58624	+	1.83062i	−0.0627506	+	0.0724180i
$640$		0			0
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	−0.969012	−	0.247013i	$-0.920551\pi$
$641$	−3.74109	+	8.19184i	−0.147764	+	0.323558i	0.821248	+	0.570571i	$0.193278\pi$
$642$		0			0
$643$	22.9522			0.905146			0.452573	−	0.891727i	$-0.350506\pi$
$643$	22.9522			0.905146			0.452573	+	0.891727i	$0.350506\pi$
$644$		0			0
$645$	13.8391			0.544913
$646$		0			0
$647$	18.6747	−	40.8919i	0.734178	−	1.60763i	−0.0587216	−	0.998274i	$-0.518702\pi$
$647$	18.6747	−	40.8919i	0.734178	−	1.60763i	0.792900	−	0.609352i	$-0.208570\pi$
$648$		0			0
$649$	−9.03801	+	10.4304i	−0.354773	+	0.409430i
$650$		0			0
$651$	−8.94354	+	5.74766i	−0.350525	+	0.225269i
$652$		0			0
$653$	19.2289	+	22.1914i	0.752486	+	0.868415i	0.994807	−	0.101781i	$-0.0324542\pi$
$653$	19.2289	+	22.1914i	0.752486	+	0.868415i	−0.242321	+	0.970196i	$0.577909\pi$
$654$		0			0
$655$	2.24692	−	15.6277i	0.0877945	−	0.610624i
$656$		0			0
$657$	−17.9818	−	11.5562i	−0.701536	−	0.450850i
$658$		0			0
$659$	16.6805	+	36.5251i	0.649778	+	1.42282i	0.891748	+	0.452532i	$0.149479\pi$
$659$	16.6805	+	36.5251i	0.649778	+	1.42282i	−0.241970	+	0.970284i	$0.577794\pi$
$660$		0			0
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	0.0904132	−	0.995904i	$-0.471181\pi$
$661$	−9.56288	−	2.80792i	−0.371953	−	0.109215i	−0.462366	+	0.886689i	$0.652999\pi$
$662$		0			0
$663$	0.739087	−	0.217015i	0.0287037	−	0.00842818i
$664$		0			0
$665$	3.33381	+	23.1872i	0.129280	+	0.899159i
$666$		0			0
$667$	−23.8359	−	1.28272i	−0.922929	−	0.0496669i
$668$		0			0
$669$	−1.50356	−	10.4575i	−0.0581310	−	0.404310i
$670$		0			0
$671$	−13.6290	+	4.00183i	−0.526141	+	0.154489i
$672$		0			0
$673$	32.6772	+	9.59489i	1.25961	+	0.369856i	0.842351	−	0.538930i	$-0.181171\pi$
$673$	32.6772	+	9.59489i	1.25961	+	0.369856i	0.417263	+	0.908786i	$0.362989\pi$
$674$		0			0
$675$	−1.14835	−	2.51454i	−0.0442000	−	0.0967846i
$676$		0			0
$677$	−21.0239	−	13.5112i	−0.808012	−	0.519278i	0.0702091	−	0.997532i	$-0.477633\pi$
$677$	−21.0239	−	13.5112i	−0.808012	−	0.519278i	−0.878221	+	0.478254i	$0.841270\pi$
$678$		0			0
$679$	−1.46006	+	10.1550i	−0.0560320	+	0.389711i
$680$		0			0
$681$	30.3349	+	35.0084i	1.16244	+	1.34152i
$682$		0			0
$683$	−29.0032	+	18.6392i	−1.10978	+	0.713210i	−0.961244	−	0.275698i	$-0.911091\pi$
$683$	−29.0032	+	18.6392i	−1.10978	+	0.713210i	−0.148532	+	0.988908i	$0.547455\pi$
$684$		0			0
$685$	0.564829	−	0.651848i	0.0215810	−	0.0249058i
$686$		0			0
$687$	11.4062	−	24.9761i	0.435174	−	0.952898i
$688$		0			0
$689$	1.92925			0.0734987
$690$		0			0
$691$	21.2259			0.807470			0.403735	−	0.914876i	$-0.367712\pi$
$691$	21.2259			0.807470			0.403735	+	0.914876i	$0.367712\pi$
$692$		0			0
$693$	6.25059	−	13.6869i	0.237440	−	0.519921i
$694$		0			0
$695$	−11.3004	+	13.0414i	−0.428649	+	0.494687i
$696$		0			0
$697$	−0.559680	+	0.359685i	−0.0211994	+	0.0136240i
$698$		0			0
$699$	−6.85483	−	7.91090i	−0.259274	−	0.299218i
$700$		0			0
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	−0.816275	−	0.577664i	$-0.803965\pi$
$701$	3.43351	−	23.8806i	0.129682	−	0.901957i	0.945957	−	0.324293i	$-0.105126\pi$
$702$		0			0
$703$	26.0834	+	16.7628i	0.983756	+	0.632221i
$704$		0			0
$705$	−3.34160	−	7.31707i	−0.125852	−	0.275577i
$706$		0			0
$707$	4.14417	+	1.21684i	0.155858	+	0.0457639i
$708$		0			0
$709$	−6.75188	+	1.98253i	−0.253572	+	0.0744556i	−0.406048	−	0.913852i	$-0.633094\pi$
$709$	−6.75188	+	1.98253i	−0.253572	+	0.0744556i	0.152476	+	0.988307i	$0.451275\pi$
$710$		0			0
$711$	−2.68028	−	18.6417i	−0.100518	−	0.699119i
$712$		0			0
$713$	−5.24339	−	6.75275i	−0.196367	−	0.252892i
$714$		0			0
$715$	0.0660988	+	0.459728i	0.00247196	+	0.0171928i
$716$		0			0
$717$	−54.3008	+	15.9441i	−2.02790	+	0.595445i
$718$		0			0
$719$	25.4920	+	7.48514i	0.950693	+	0.279149i	0.720075	−	0.693896i	$-0.244107\pi$
$719$	25.4920	+	7.48514i	0.950693	+	0.279149i	0.230618	+	0.973044i	$0.425925\pi$
$720$		0			0
$721$	15.0941	+	33.0515i	0.562134	+	1.23090i
$722$		0			0
$723$	12.5363	+	8.05658i	0.466230	+	0.299628i
$724$		0			0
$725$	2.45875	−	17.1010i	0.0913158	−	0.635115i
$726$		0			0
$727$	−3.42332	−	3.95072i	−0.126964	−	0.146524i	0.688708	−	0.725039i	$-0.258178\pi$
$727$	−3.42332	−	3.95072i	−0.126964	−	0.146524i	−0.815672	+	0.578514i	$0.803633\pi$
$728$		0			0
$729$	−27.2318	+	17.5008i	−1.00859	+	0.648179i
$730$		0			0
$731$	−4.54901	+	5.24983i	−0.168251	+	0.194172i
$732$		0			0
$733$	−11.0870	+	24.2771i	−0.409506	+	0.896694i	0.586711	+	0.809796i	$0.300422\pi$
$733$	−11.0870	+	24.2771i	−0.409506	+	0.896694i	−0.996217	+	0.0868973i	$0.972305\pi$
$734$		0			0
$735$	4.25719			0.157029
$736$		0			0
$737$	−13.8924			−0.511734
$738$		0			0
$739$	0.930342	−	2.03716i	0.0342232	−	0.0749383i	−0.891748	−	0.452532i	$-0.850521\pi$
$739$	0.930342	−	2.03716i	0.0342232	−	0.0749383i	0.925972	+	0.377593i	$0.123248\pi$
$740$		0			0
$741$	−2.58196	+	2.97974i	−0.0948507	+	0.109464i
$742$		0			0
$743$	−15.2605	+	9.80730i	−0.559852	+	0.359795i	−0.789759	−	0.613418i	$-0.789794\pi$
$743$	−15.2605	+	9.80730i	−0.559852	+	0.359795i	0.229907	+	0.973213i	$0.426158\pi$
$744$		0			0
$745$	−13.4730	−	15.5486i	−0.493612	−	0.569658i
$746$		0			0
$747$	−6.08446	+	42.3183i	−0.222619	+	1.54835i
$748$		0			0
$749$	−3.96893	−	2.55068i	−0.145022	−	0.0931997i
$750$		0			0
$751$	−11.7258	−	25.6759i	−0.427880	−	0.936927i	−0.993666	−	0.112375i	$-0.964154\pi$
$751$	−11.7258	−	25.6759i	−0.427880	−	0.936927i	0.565786	−	0.824552i	$-0.308573\pi$
$752$		0			0
$753$	−3.73935	−	1.09797i	−0.136269	−	0.0400123i
$754$		0			0
$755$	−15.6485	+	4.59481i	−0.569507	+	0.167222i
$756$		0			0
$757$	−0.0173643	−	0.120772i	−0.000631118	−	0.00438952i	0.989503	−	0.144509i	$-0.0461603\pi$
$757$	−0.0173643	−	0.120772i	−0.000631118	−	0.00438952i	−0.990135	+	0.140120i	$0.955251\pi$
$758$		0			0
$759$	21.7302	+	7.67118i	0.788756	+	0.278446i
$760$		0			0
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	0.935027	+	0.354576i	$0.115375\pi$
$761$	3.80057	+	26.4336i	0.137771	+	0.958216i	−0.797257	+	0.603640i	$0.793716\pi$
$762$		0			0
$763$	−35.5042	+	10.4250i	−1.28534	+	0.377409i
$764$		0			0
$765$	−6.13839	−	1.80239i	−0.221934	−	0.0651657i
$766$		0			0
$767$	0.589194	+	1.29015i	0.0212745	+	0.0465848i
$768$		0			0
$769$	−6.60471	−	4.24459i	−0.238172	−	0.153064i	0.416111	−	0.909314i	$-0.363393\pi$
$769$	−6.60471	−	4.24459i	−0.238172	−	0.153064i	−0.654283	+	0.756250i	$0.727029\pi$
$770$		0			0
$771$	−9.82128	+	68.3085i	−0.353705	+	2.46007i
$772$		0			0
$773$	22.4497	+	25.9084i	0.807460	+	0.931859i	0.998766	−	0.0496716i	$-0.0158175\pi$
$773$	22.4497	+	25.9084i	0.807460	+	0.931859i	−0.191305	+	0.981531i	$0.561272\pi$
$774$		0			0
$775$	5.20559	−	3.34543i	0.186990	−	0.120171i
$776$		0			0
$777$	−15.1653	+	17.5017i	−0.544052	+	0.627869i
$778$		0			0
$779$	1.41463	−	3.09760i	0.0506843	−	0.110983i
$780$		0			0
$781$	1.39619			0.0499596
$782$		0			0
$783$	3.96386			0.141657
$784$		0			0
$785$	−2.12070	+	4.64369i	−0.0756911	+	0.165740i
$786$		0			0
$787$	10.4860	−	12.1015i	0.373785	−	0.431370i	−0.537426	−	0.843311i	$-0.680603\pi$
$787$	10.4860	−	12.1015i	0.373785	−	0.431370i	0.911211	+	0.411940i	$0.135149\pi$
$788$		0			0
$789$	27.3612	−	17.5840i	0.974085	−	0.626006i
$790$		0			0
$791$	2.31250	+	2.66877i	0.0822231	+	0.0948905i
$792$		0			0
$793$	−0.207742	+	1.44488i	−0.00737712	+	0.0513090i
$794$		0			0
$795$	−25.6714	−	16.4980i	−0.910469	−	0.585123i
$796$		0			0
$797$	8.94128	+	19.5787i	0.316716	+	0.693512i	0.999304	−	0.0372914i	$-0.0118730\pi$
$797$	8.94128	+	19.5787i	0.316716	+	0.693512i	−0.682588	+	0.730803i	$0.739146\pi$
$798$		0			0
$799$	3.87413	+	1.13755i	0.137057	+	0.0402435i
$800$		0			0
$801$	44.2376	−	12.9893i	1.56306	−	0.458955i
$802$		0			0
$803$	1.75340	+	12.1952i	0.0618761	+	0.430358i
$804$		0			0
$805$	−1.25114	−	14.0148i	−0.0440969	−	0.493955i
$806$		0			0
$807$	3.57601	+	24.8717i	0.125882	+	0.875526i
$808$		0			0
$809$	−23.1479	+	6.79683i	−0.813836	+	0.238964i	−0.662060	−	0.749451i	$-0.730318\pi$
$809$	−23.1479	+	6.79683i	−0.813836	+	0.238964i	−0.151776	+	0.988415i	$0.548499\pi$
$810$		0			0
$811$	13.7575	+	4.03956i	0.483091	+	0.141848i	0.514205	−	0.857668i	$-0.328087\pi$
$811$	13.7575	+	4.03956i	0.483091	+	0.141848i	−0.0311137	+	0.999516i	$0.509905\pi$
$812$		0			0
$813$	−4.60584	−	10.0854i	−0.161534	−	0.353710i
$814$		0			0
$815$	−15.3837	−	9.88652i	−0.538868	−	0.346310i
$816$		0			0
$817$	5.06017	−	35.1942i	0.177033	−	1.23129i
$818$		0			0
$819$	−1.01260	−	1.16861i	−0.0353832	−	0.0408344i
$820$		0			0
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	−0.315180	−	0.949032i	$-0.602065\pi$
$821$	11.9529	−	7.68167i	0.417160	−	0.268092i	0.732339	+	0.680940i	$0.238428\pi$
$822$		0			0
$823$	10.4929	−	12.1095i	0.365760	−	0.422109i	−0.542802	−	0.839861i	$-0.682636\pi$
$823$	10.4929	−	12.1095i	0.365760	−	0.422109i	0.908561	+	0.417752i	$0.137182\pi$
$824$		0			0
$825$	−6.92875	+	15.1719i	−0.241228	+	0.528216i
$826$		0			0
$827$	−35.1240			−1.22138			−0.610690	−	0.791870i	$-0.709108\pi$
$827$	−35.1240			−1.22138			−0.610690	+	0.791870i	$0.709108\pi$
$828$		0			0
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$		0			0
$831$	−32.1620	+	70.4250i	−1.11569	+	2.44302i
$832$		0			0
$833$	−1.39937	+	1.61496i	−0.0484853	+	0.0559550i
$834$		0			0
$835$	1.38319	−	0.888922i	0.0478672	−	0.0307624i
$836$		0			0
$837$	0.929704	+	1.07294i	0.0321353	+	0.0370861i
$838$		0			0
$839$	5.49501	−	38.2187i	0.189709	−	1.31945i	−0.643052	−	0.765822i	$-0.722332\pi$
$839$	5.49501	−	38.2187i	0.189709	−	1.31945i	0.832761	−	0.553632i	$-0.186759\pi$
$840$		0			0
$841$	−3.55542	−	2.28493i	−0.122601	−	0.0787906i
$842$		0			0
$843$	−3.73708	−	8.18306i	−0.128712	−	0.281839i
$844$		0			0
$845$	−15.3773	−	4.51519i	−0.528996	−	0.155327i
$846$		0			0
$847$	16.7218	−	4.90997i	0.574568	−	0.168708i
$848$		0			0
$849$	5.28673	+	36.7700i	0.181440	+	1.26194i
$850$		0			0
$851$	−15.1032	−	10.8959i	−0.517732	−	0.373505i
$852$		0			0
$853$	5.46907	+	38.0382i	0.187257	+	1.30240i	0.839070	+	0.544024i	$0.183100\pi$
$853$	5.46907	+	38.0382i	0.187257	+	1.30240i	−0.651812	+	0.758380i	$0.725991\pi$
$854$		0			0
$855$	31.4197	−	9.22564i	1.07453	−	0.315510i
$856$		0			0
$857$	48.8281	+	14.3372i	1.66794	+	0.489750i	0.973286	−	0.229598i	$-0.0737411\pi$
$857$	48.8281	+	14.3372i	1.66794	+	0.489750i	0.694650	+	0.719348i	$0.255559\pi$
$858$		0			0
$859$	−3.79985	−	8.32050i	−0.129649	−	0.283892i	0.833664	−	0.552272i	$-0.186239\pi$
$859$	−3.79985	−	8.32050i	−0.129649	−	0.283892i	−0.963313	+	0.268380i	$0.913512\pi$
$860$		0			0
$861$	2.13969	+	1.37510i	0.0729205	+	0.0468631i
$862$		0			0
$863$	1.75600	−	12.2133i	0.0597750	−	0.415744i	−0.937860	−	0.347013i	$-0.887196\pi$
$863$	1.75600	−	12.2133i	0.0597750	−	0.415744i	0.997635	−	0.0687310i	$-0.0218950\pi$
$864$		0			0
$865$	−13.7135	−	15.8262i	−0.466272	−	0.538107i
$866$		0			0
$867$	−30.7991	+	19.7934i	−1.04599	+	0.672219i
$868$		0			0
$869$	−7.10891	+	8.20412i	−0.241153	+	0.278306i
$870$		0			0
$871$	−0.593078	+	1.29866i	−0.0200957	+	0.0440034i
$872$		0			0
$873$	14.3414			0.485381
$874$		0			0
$875$	24.8534			0.840199
$876$		0			0
$877$	0.958445	−	2.09870i	0.0323644	−	0.0708681i	−0.892759	−	0.450534i	$-0.851234\pi$
$877$	0.958445	−	2.09870i	0.0323644	−	0.0708681i	0.925124	+	0.379666i	$0.123961\pi$
$878$		0			0
$879$	−35.4087	+	40.8638i	−1.19431	+	1.37830i
$880$		0			0
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.937135	−	0.348966i	$-0.886533\pi$
$881$	−29.9489	+	19.2470i	−1.00901	+	0.648448i	−0.0718697	+	0.997414i	$0.522897\pi$
$882$		0			0
$883$	19.9566	+	23.0311i	0.671592	+	0.775059i	0.984625	−	0.174684i	$-0.0558903\pi$
$883$	19.9566	+	23.0311i	0.671592	+	0.775059i	−0.313032	+	0.949742i	$0.601345\pi$
$884$		0			0
$885$	3.19271	−	22.2058i	0.107322	−	0.746438i
$886$		0			0
$887$	−17.4906	−	11.2405i	−0.587278	−	0.377421i	0.212998	−	0.977053i	$-0.431677\pi$
$887$	−17.4906	−	11.2405i	−0.587278	−	0.377421i	−0.800276	+	0.599632i	$0.795314\pi$
$888$		0			0
$889$	−5.90859	−	12.9380i	−0.198168	−	0.433927i
$890$		0			0
$891$	14.5817	+	4.28156i	0.488504	+	0.143438i
$892$		0			0
$893$	−19.8299	+	5.82260i	−0.663584	+	0.194846i
$894$		0			0
$895$	0.251874	+	1.75182i	0.00841920	+	0.0585569i
$896$		0			0
$897$	1.64478	−	1.70385i	0.0549176	−	0.0568898i
$898$		0			0
$899$	1.26275	+	8.78264i	0.0421152	+	0.292918i
$900$		0			0
$901$	14.6969	−	4.31539i	0.489624	−	0.143766i
$902$		0			0
$903$	25.4812	+	7.48196i	0.847962	+	0.248984i
$904$		0			0
$905$	8.28590	+	18.1436i	0.275433	+	0.603114i
$906$		0			0
$907$	19.1064	+	12.2789i	0.634417	+	0.407715i	0.817943	−	0.575300i	$-0.195115\pi$
$907$	19.1064	+	12.2789i	0.634417	+	0.407715i	−0.183525	+	0.983015i	$0.558751\pi$
$908$		0			0
$909$	0.859242	−	5.97616i	0.0284992	−	0.198217i
$910$		0			0
$911$	0.546182	+	0.630328i	0.0180958	+	0.0208837i	0.764725	−	0.644356i	$-0.222875\pi$
$911$	0.546182	+	0.630328i	0.0180958	+	0.0208837i	−0.746630	+	0.665240i	$0.768329\pi$
$912$		0			0
$913$	20.7312	−	13.3231i	0.686101	−	0.440930i
$914$		0			0
$915$	15.1201	−	17.4496i	0.499856	−	0.576864i
$916$		0			0
$917$	12.5861	−	27.5597i	0.415630	−	0.910103i
$918$		0			0
$919$	45.3320			1.49537			0.747683	−	0.664056i	$-0.231166\pi$
$919$	45.3320			1.49537			0.747683	+	0.664056i	$0.231166\pi$
$920$		0			0
$921$	−35.5510			−1.17145
$922$		0			0
$923$	0.0596044	−	0.130515i	0.00196190	−	0.00429597i
$924$		0			0
$925$	8.82696	−	10.1869i	0.290229	−	0.334942i
$926$		0			0
$927$	42.7289	−	27.4602i	1.40340	−	0.901910i
$928$		0			0
$929$	11.5958	+	13.3822i	0.380445	+	0.439056i	0.913385	−	0.407096i	$-0.133459\pi$
$929$	11.5958	+	13.3822i	0.380445	+	0.439056i	−0.532941	+	0.846153i	$0.678913\pi$
$930$		0			0
$931$	1.55661	−	10.8265i	0.0510159	−	0.354824i
$932$		0			0
$933$	−1.20548	−	0.774713i	−0.0394655	−	0.0253630i
$934$		0			0
$935$	1.53186	+	3.35431i	0.0500972	+	0.109698i
$936$		0			0
$937$	22.3812	+	6.57170i	0.731161	+	0.214688i	0.626062	−	0.779774i	$-0.284666\pi$
$937$	22.3812	+	6.57170i	0.731161	+	0.214688i	0.105099	+	0.994462i	$0.466484\pi$
$938$		0			0
$939$	50.9622	−	14.9639i	1.66309	−	0.488327i
$940$		0			0
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	−0.998864	−	0.0476470i	$-0.984828\pi$
$941$	−1.65295	−	11.4965i	−0.0538847	−	0.374776i	0.944980	−	0.327130i	$-0.106081\pi$
$942$		0			0
$943$	−0.948444	+	1.81222i	−0.0308856	+	0.0590139i
$944$		0			0
$945$	0.332520	+	2.31273i	0.0108169	+	0.0752331i
$946$		0			0
$947$	5.75498	−	1.68981i	0.187012	−	0.0549116i	−0.186886	−	0.982382i	$-0.559839\pi$
$947$	5.75498	−	1.68981i	0.187012	−	0.0549116i	0.373897	+	0.927470i	$0.378021\pi$
$948$		0			0
$949$	1.21486	+	0.356714i	0.0394359	+	0.0115794i
$950$		0			0
$951$	−9.20056	−	20.1464i	−0.298348	−	0.653292i
$952$		0			0
$953$	−15.0640	−	9.68107i	−0.487972	−	0.313601i	0.273417	−	0.961896i	$-0.411846\pi$
$953$	−15.0640	−	9.68107i	−0.487972	−	0.313601i	−0.761389	+	0.648295i	$0.775482\pi$
$954$		0			0
$955$	3.65039	−	25.3890i	0.118124	−	0.821570i
$956$		0			0
$957$	−15.6620	−	18.0749i	−0.506281	−	0.584279i
$958$		0			0
$959$	1.39241	−	0.894847i	0.0449632	−	0.0288961i
$960$		0			0
$961$	18.2196	−	21.0265i	0.587728	−	0.678274i
$962$		0			0
$963$	−2.73967	+	5.99903i	−0.0882845	+	0.193316i
$964$		0			0
$965$	−18.1172			−0.583213
$966$		0			0
$967$	−33.5068			−1.07751			−0.538753	−	0.842464i	$-0.681104\pi$
$967$	−33.5068			−1.07751			−0.538753	+	0.842464i	$0.681104\pi$
$968$		0			0
$969$	−13.0040	+	28.4748i	−0.417748	+	0.914741i
$970$		0			0
$971$	38.8241	−	44.8054i	1.24592	−	1.43787i	0.389964	−	0.920830i	$-0.372487\pi$
$971$	38.8241	−	44.8054i	1.24592	−	1.43787i	0.855960	−	0.517042i	$-0.172967\pi$
$972$		0			0
$973$	−27.8576	+	17.9030i	−0.893073	+	0.573943i
$974$		0			0
$975$	1.12247	+	1.29540i	0.0359477	+	0.0414859i
$976$		0			0
$977$	1.79914	−	12.5133i	0.0575596	−	0.400336i	−0.940591	−	0.339542i	$-0.889728\pi$
$977$	1.79914	−	12.5133i	0.0575596	−	0.400336i	0.998150	−	0.0607934i	$-0.0193631\pi$
$978$		0			0
$979$	−22.3564	−	14.3676i	−0.714513	−	0.459189i
$980$		0			0
$981$	21.4877	+	47.0514i	0.686048	+	1.50224i
$982$		0			0
$983$	−56.0008	−	16.4433i	−1.78615	−	0.524461i	−0.790077	−	0.613008i	$-0.789960\pi$
$983$	−56.0008	−	16.4433i	−1.78615	−	0.524461i	−0.996072	+	0.0885469i	$0.971778\pi$
$984$		0			0
$985$	13.8546	−	4.06807i	0.441444	−	0.129620i
$986$		0			0
$987$	−2.19682	−	15.2792i	−0.0699254	−	0.486342i
$988$		0			0
$989$	−4.17093	+	20.9454i	−0.132628	+	0.666025i
$990$		0			0
$991$	−6.51675	−	45.3250i	−0.207011	−	1.43980i	−0.782839	−	0.622224i	$-0.786229\pi$
$991$	−6.51675	−	45.3250i	−0.207011	−	1.43980i	0.575828	−	0.817571i	$-0.304680\pi$
$992$		0			0
$993$	72.7980	−	21.3754i	2.31018	−	0.678329i
$994$		0			0
$995$	6.79021	+	1.99379i	0.215264	+	0.0632073i
$996$		0			0
$997$	−16.3475	−	35.7959i	−0.517729	−	1.13367i	−0.970292	−	0.241936i	$-0.922218\pi$
$997$	−16.3475	−	35.7959i	−0.517729	−	1.13367i	0.452563	−	0.891732i	$-0.350510\pi$
$998$		0			0
$999$	2.60161	+	1.67195i	0.0823113	+	0.0528983i

Display

a_p

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p

up to: 50 250 1000 (See

a_n

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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

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.m.c.49.1		10
4.3	odd	2		23.2.c.a.3.1	✓	10
12.11	even	2		207.2.i.c.118.1		10
20.3	even	4		575.2.p.b.49.1		20
20.7	even	4		575.2.p.b.49.2		20
20.19	odd	2		575.2.k.b.26.1		10
23.8	even	11	inner	368.2.m.c.353.1		10
23.10	odd	22		8464.2.a.bt.1.5		5
23.13	even	11		8464.2.a.bs.1.5		5
92.3	odd	22		529.2.c.g.487.1		10
92.7	even	22		529.2.c.c.170.1		10
92.11	even	22		529.2.c.c.501.1		10
92.15	even	22		529.2.c.a.399.1		10
92.19	even	22		529.2.c.h.255.1		10
92.27	odd	22		529.2.c.i.255.1		10
92.31	odd	22		23.2.c.a.8.1	yes	10
92.35	odd	22		529.2.c.b.501.1		10
92.39	odd	22		529.2.c.b.170.1		10
92.43	even	22		529.2.c.f.487.1		10
92.51	even	22		529.2.c.f.466.1		10
92.55	odd	22		529.2.c.d.266.1		10
92.59	odd	22		529.2.a.i.1.5		5
92.63	even	22		529.2.c.e.177.1		10
92.67	even	22		529.2.c.h.334.1		10
92.71	odd	22		529.2.c.i.334.1		10
92.75	odd	22		529.2.c.d.177.1		10
92.79	even	22		529.2.a.j.1.5		5
92.83	even	22		529.2.c.e.266.1		10
92.87	odd	22		529.2.c.g.466.1		10
92.91	even	2		529.2.c.a.118.1		10
276.59	even	22		4761.2.a.bo.1.1		5
276.215	even	22		207.2.i.c.100.1		10
276.263	odd	22		4761.2.a.bn.1.1		5
460.123	even	44		575.2.p.b.399.2		20
460.307	even	44		575.2.p.b.399.1		20
460.399	odd	22		575.2.k.b.376.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	4.3	odd	2
23.2.c.a.8.1	yes	10	92.31	odd	22
207.2.i.c.100.1		10	276.215	even	22
207.2.i.c.118.1		10	12.11	even	2
368.2.m.c.49.1		10	1.1	even	1	trivial
368.2.m.c.353.1		10	23.8	even	11	inner
529.2.a.i.1.5		5	92.59	odd	22
529.2.a.j.1.5		5	92.79	even	22
529.2.c.a.118.1		10	92.91	even	2
529.2.c.a.399.1		10	92.15	even	22
529.2.c.b.170.1		10	92.39	odd	22
529.2.c.b.501.1		10	92.35	odd	22
529.2.c.c.170.1		10	92.7	even	22
529.2.c.c.501.1		10	92.11	even	22
529.2.c.d.177.1		10	92.75	odd	22
529.2.c.d.266.1		10	92.55	odd	22
529.2.c.e.177.1		10	92.63	even	22
529.2.c.e.266.1		10	92.83	even	22
529.2.c.f.466.1		10	92.51	even	22
529.2.c.f.487.1		10	92.43	even	22
529.2.c.g.466.1		10	92.87	odd	22
529.2.c.g.487.1		10	92.3	odd	22
529.2.c.h.255.1		10	92.19	even	22
529.2.c.h.334.1		10	92.67	even	22
529.2.c.i.255.1		10	92.27	odd	22
529.2.c.i.334.1		10	92.71	odd	22
575.2.k.b.26.1		10	20.19	odd	2
575.2.k.b.376.1		10	460.399	odd	22
575.2.p.b.49.1		20	20.3	even	4
575.2.p.b.49.2		20	20.7	even	4
575.2.p.b.399.1		20	460.307	even	44
575.2.p.b.399.2		20	460.123	even	44
4761.2.a.bn.1.1		5	276.263	odd	22
4761.2.a.bo.1.1		5	276.59	even	22
8464.2.a.bs.1.5		5	23.13	even	11
8464.2.a.bt.1.5		5	23.10	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	368.2.m.c.49.1

Level	$368$
Weight	$2$
Character	368.49
Analytic conductor	$2.938$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$