LMFDB - Embedded newform 368.2.m.c.353.1

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)

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")

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);

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			353.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	368.353
Dual form			368.2.m.c.49.1

$q$ -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 $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$ .

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$e\left(\frac{3}{11}\right)$	$1$

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	0.927392	+	0.374091i	$0.122045\pi$
$3$	1.04408	+	2.28621i	0.602799	+	1.31995i	−0.324593	+	0.945854i	$0.605227\pi$
$4$		0			0
$5$	0.809721	+	0.934468i	0.362118	+	0.417907i	0.907348	−	0.420380i	$-0.138103\pi$
$5$	0.809721	+	0.934468i	0.362118	+	0.417907i	−0.545230	+	0.838287i	$0.683558\pi$
$6$		0			0
$7$	1.99611	+	1.28282i	0.754460	+	0.484862i	0.860469	−	0.509503i	$-0.170171\pi$
$7$	1.99611	+	1.28282i	0.754460	+	0.484862i	−0.106009	+	0.994365i	$0.533807\pi$
$8$		0			0
$9$	−2.17208	+	2.50672i	−0.724028	+	0.835573i
$10$		0			0
$11$	−0.272084	−	1.89238i	−0.0820363	−	0.570575i	−0.988835	−	0.149012i	$-0.952391\pi$
$11$	−0.272084	−	1.89238i	−0.0820363	−	0.570575i	0.906799	−	0.421563i	$-0.138518\pi$
$12$		0			0
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	−0.517519	−	0.855672i	$-0.673144\pi$
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	0.563361	+	0.826211i	$0.309508\pi$
$14$		0			0
$15$	−1.29098	+	2.82685i	−0.333330	+	0.729890i
$16$		0			0
$17$	1.49672	−	0.439476i	0.363008	−	0.106589i	−0.0951421	−	0.995464i	$-0.530331\pi$
$17$	1.49672	−	0.439476i	0.363008	−	0.106589i	0.458150	+	0.888875i	$0.348512\pi$
$18$		0			0
$19$	−7.66103	−	2.24948i	−1.75756	−	0.516066i	−0.765678	−	0.643224i	$-0.777597\pi$
$19$	−7.66103	−	2.24948i	−1.75756	−	0.516066i	−0.991883	+	0.127157i	$0.959415\pi$
$20$		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	−0.693256	−	0.720691i	$-0.743825\pi$
$29$	−4.77570	+	1.40227i	−0.886825	+	0.260395i	−0.193569	+	0.981087i	$0.562006\pi$
$30$		0			0
$31$	−0.740552	+	1.62158i	−0.133007	+	0.291245i	−0.964404	−	0.264435i	$-0.914815\pi$
$31$	−0.740552	+	1.62158i	−0.133007	+	0.291245i	0.831397	+	0.555680i	$0.187542\pi$
$32$		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	−0.925246	−	0.379369i	$-0.876141\pi$
$37$	−2.54297	+	2.93475i	−0.418062	+	0.482469i	0.507184	+	0.861838i	$0.330687\pi$
$38$		0			0
$39$	0.415415	+	0.266971i	0.0665196	+	0.0427496i
$40$		0			0
$41$	−0.279295	−	0.322324i	−0.0436186	−	0.0503386i	0.733521	−	0.679667i	$-0.237876\pi$
$41$	−0.279295	−	0.322324i	−0.0436186	−	0.0503386i	−0.777140	+	0.629328i	$0.783330\pi$
$42$		0			0
$43$	−1.84991	−	4.05075i	−0.282109	−	0.617733i	0.714534	−	0.699601i	$-0.246639\pi$
$43$	−1.84991	−	4.05075i	−0.282109	−	0.617733i	−0.996643	+	0.0818677i	$0.973911\pi$
$44$		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	0.966532	−	0.256547i	$-0.0825848\pi$
$53$	8.26060	+	5.30876i	1.13468	+	0.729215i	0.168149	+	0.985762i	$0.446221\pi$
$54$		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	−0.0819173	−	0.996639i	$-0.526104\pi$
$59$	6.07293	−	3.90283i	0.790628	−	0.508106i	0.872545	+	0.488533i	$0.162468\pi$
$60$		0			0
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	−0.602565	−	0.798070i	$-0.705855\pi$
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	0.997737	−	0.0672363i	$-0.0214181\pi$
$62$		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	−0.823800	−	0.566881i	$-0.808150\pi$
$67$	1.03413	−	7.19254i	0.126339	−	0.878708i	0.950139	−	0.311827i	$-0.100941\pi$
$68$		0			0
$69$	2.35404	+	11.8214i	0.283394	+	1.42313i
$70$		0			0
$71$	−0.103930	+	0.722850i	−0.0123342	+	0.0857866i	−0.995059	−	0.0992879i	$-0.968344\pi$
$71$	−0.103930	+	0.722850i	−0.0123342	+	0.0857866i	0.982725	+	0.185074i	$0.0592526\pi$
$72$		0			0
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.622780	−	0.782397i	$-0.286003\pi$
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.100920	+	0.994895i	$0.467821\pi$
$74$		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	−0.243608	−	0.969874i	$-0.578331\pi$
$79$	4.77671	−	3.06980i	0.537422	−	0.345380i	0.781030	+	0.624494i	$0.214695\pi$
$80$		0			0
$81$	1.13126	+	7.86810i	0.125696	+	0.874233i
$82$		0			0
$83$	−8.44098	+	9.74141i	−0.926518	+	1.06926i	0.0709025	+	0.997483i	$0.477412\pi$
$83$	−8.44098	+	9.74141i	−0.926518	+	1.06926i	−0.997421	+	0.0717758i	$0.977133\pi$
$84$		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	−0.921141	−	0.389228i	$-0.872742\pi$
$89$	−5.77436	−	12.6441i	−0.612081	−	1.34027i	0.309060	−	0.951043i	$-0.399986\pi$
$90$		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	0.593572	−	0.804781i	$-0.297717\pi$
$97$	−2.83147	−	3.26769i	−0.287492	−	0.331783i	−0.881064	+	0.472998i	$0.843172\pi$
$98$		0			0
$99$	5.33466	+	3.42838i	0.536154	+	0.344565i
$100$		0			0
$101$	1.19203	−	1.37567i	0.118611	−	0.136885i	−0.693338	−	0.720612i	$-0.743861\pi$
$101$	1.19203	−	1.37567i	0.118611	−	0.136885i	0.811950	+	0.583727i	$0.198406\pi$
$102$		0			0
$103$	−2.17930	−	15.1574i	−0.214733	−	1.49350i	−0.757067	−	0.653337i	$-0.773369\pi$
$103$	−2.17930	−	15.1574i	−0.214733	−	1.49350i	0.542335	−	0.840163i	$-0.317541\pi$
$104$		0			0
$105$	−6.20330	+	3.98662i	−0.605380	+	0.389054i
$106$		0			0
$107$	−0.825981	+	1.80865i	−0.0798506	+	0.174848i	−0.945346	−	0.326068i	$-0.894276\pi$
$107$	−0.825981	+	1.80865i	−0.0798506	+	0.174848i	0.865496	+	0.500916i	$0.167004\pi$
$108$		0			0
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.903950	−	0.427638i	$-0.859346\pi$
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.529253	+	0.848464i	$0.677528\pi$
$110$		0			0
$111$	−9.36451	−	2.74967i	−0.888840	−	0.260987i
$112$		0			0
$113$	0.211799	−	1.47310i	0.0199244	−	0.138577i	−0.977431	−	0.211254i	$-0.932245\pi$
$113$	0.211799	−	1.47310i	0.0199244	−	0.138577i	0.997356	+	0.0726771i	$0.0231542\pi$
$114$		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	0.992023	+	0.126061i	$0.0402334\pi$
$127$	0.853087	+	5.93335i	0.0756993	+	0.526500i	−0.916323	+	0.400439i	$0.868858\pi$
$128$		0			0
$129$	7.32941	−	8.45859i	0.645319	−	0.744737i
$130$		0			0
$131$	10.7418	+	6.90335i	0.938517	+	0.603148i	0.917974	−	0.396641i	$-0.129824\pi$
$131$	10.7418	+	6.90335i	0.938517	+	0.603148i	0.0205431	+	0.999789i	$0.493460\pi$
$132$		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	0.821309	+	0.570483i	$0.193244\pi$
$149$	2.36798	+	16.4697i	0.193993	+	1.34925i	−0.627317	+	0.778764i	$0.715847\pi$
$150$		0			0
$151$	−11.0961	+	7.13103i	−0.902988	+	0.580315i	−0.907675	−	0.419674i	$-0.862145\pi$
$151$	−11.0961	+	7.13103i	−0.902988	+	0.580315i	0.00468679	+	0.999989i	$0.498508\pi$
$152$		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	0.119804	−	0.992798i	$-0.461773\pi$
$157$	−3.96143	−	1.16318i	−0.316157	−	0.0928320i	−0.435961	+	0.899965i	$0.643591\pi$
$158$		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	0.724464	+	0.689312i	$0.242087\pi$
$163$	−2.10474	+	14.6388i	−0.164856	+	1.14660i	−0.889320	+	0.457285i	$0.848822\pi$
$164$		0			0
$165$	5.70075	+	1.67389i	0.443802	+	0.130312i
$166$		0			0
$167$	1.27588	−	0.374632i	0.0987306	−	0.0289899i	−0.231994	−	0.972717i	$-0.574525\pi$
$167$	1.27588	−	0.374632i	0.0987306	−	0.0289899i	0.330725	+	0.943727i	$0.392707\pi$
$168$		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	0.849019	+	0.528362i	$0.177194\pi$
$173$	2.41025	+	16.7637i	0.183248	+	1.27452i	−0.665771	+	0.746156i	$0.731897\pi$
$174$		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	0.719638	−	0.694350i	$-0.244308\pi$
$179$	−0.937335	−	1.08174i	−0.0700597	−	0.0808532i	−0.789697	+	0.613497i	$0.789762\pi$
$180$		0			0
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	−0.977083	−	0.212858i	$-0.931723\pi$
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	0.478986	−	0.877822i	$-0.341004\pi$
$182$		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	0.988656	−	0.150195i	$-0.0479900\pi$
$191$	17.4514	+	11.2153i	1.26274	+	0.811512i	0.274081	+	0.961707i	$0.411626\pi$
$192$		0			0
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	−0.987461	−	0.157861i	$-0.949540\pi$
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	0.296785	+	0.954944i	$0.404086\pi$
$194$		0			0
$195$	0.0868945	+	0.604364i	0.00622264	+	0.0432794i
$196$		0			0
$197$	9.82407	−	6.31355i	0.699936	−	0.449822i	−0.141669	−	0.989914i	$-0.545247\pi$
$197$	9.82407	−	6.31355i	0.699936	−	0.449822i	0.841606	+	0.540092i	$0.181611\pi$
$198$		0			0
$199$	2.37759	−	5.20620i	0.168543	−	0.369057i	−0.806447	−	0.591306i	$-0.798612\pi$
$199$	2.37759	−	5.20620i	0.168543	−	0.369057i	0.974990	+	0.222249i	$0.0713397\pi$
$200$		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	−0.218118	−	0.975922i	$-0.569992\pi$
$211$	−13.4979	−	3.96334i	−0.929234	−	0.272848i	−0.711116	+	0.703075i	$0.751810\pi$
$212$		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	0.653663	−	0.756786i	$-0.273232\pi$
$223$	3.53628	+	2.27263i	0.236807	+	0.152187i	−0.416856	+	0.908973i	$0.636868\pi$
$224$		0			0
$225$	7.53956	+	8.70112i	0.502638	+	0.580075i
$226$		0			0
$227$	−7.65642	−	16.7652i	−0.508174	−	1.11275i	−0.973725	−	0.227726i	$-0.926871\pi$
$227$	−7.65642	−	16.7652i	−0.508174	−	1.11275i	0.465551	−	0.885021i	$-0.345856\pi$
$228$		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	0.957800	−	0.287436i	$-0.0928029\pi$
$233$	1.73013	+	3.78846i	0.113345	+	0.248190i	−0.844455	+	0.535626i	$0.820076\pi$
$234$		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	0.0410120	+	0.999159i	$0.486942\pi$
$239$	−14.7456	+	17.0173i	−0.953813	+	1.10076i	−0.994825	+	0.101601i	$0.967604\pi$
$240$		0			0
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	−0.998783	−	0.0493250i	$-0.984293\pi$
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	0.944429	−	0.328717i	$-0.106616\pi$
$242$		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	−0.995600	−	0.0937056i	$-0.970129\pi$
$251$	−0.220675	+	1.53483i	−0.0139289	+	0.0968775i	0.981671	+	0.190583i	$0.0610379\pi$
$252$		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	−0.676230	−	0.736690i	$-0.736388\pi$
$257$	−26.3456	−	7.73578i	−1.64340	−	0.482545i	−0.967166	+	0.254145i	$0.918206\pi$
$258$		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	−0.160104	−	0.987100i	$-0.551183\pi$
$263$	10.8864	−	6.99627i	0.671285	−	0.431408i	0.831388	+	0.555692i	$0.187547\pi$
$264$		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	0.258517	−	0.966007i	$-0.416766\pi$
$269$	−8.41057	−	5.40514i	−0.512801	−	0.329557i	−0.771319	+	0.636449i	$0.780402\pi$
$270$		0			0
$271$	2.88885	+	3.33391i	0.175485	+	0.202520i	0.836678	−	0.547696i	$-0.184495\pi$
$271$	2.88885	+	3.33391i	0.175485	+	0.202520i	−0.661193	+	0.750216i	$0.729949\pi$
$272$		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	0.821344	−	0.570433i	$-0.193225\pi$
$281$	2.34395	+	2.70506i	0.139828	+	0.161370i	−0.681516	+	0.731803i	$0.738679\pi$
$282$		0			0
$283$	−12.4341	−	7.99089i	−0.739129	−	0.475009i	0.116115	−	0.993236i	$-0.462956\pi$
$283$	−12.4341	−	7.99089i	−0.739129	−	0.475009i	−0.855243	+	0.518227i	$0.826592\pi$
$284$		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	−0.822113	−	0.569324i	$-0.807205\pi$
$293$	−20.6420	+	6.06104i	−1.20592	+	0.354090i	−0.383806	+	0.923414i	$0.625387\pi$
$294$		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	−0.999917	−	0.0128989i	$-0.995894\pi$
$307$	−5.87602	+	12.8667i	−0.335362	+	0.734341i	0.664555	+	0.747240i	$0.268621\pi$
$308$		0			0
$309$	32.3776	−	20.8078i	1.84190	−	1.18371i
$310$		0			0
$311$	0.0811393	+	0.564336i	0.00460099	+	0.0320006i	0.991993	−	0.126296i	$-0.0403089\pi$
$311$	0.0811393	+	0.564336i	0.00460099	+	0.0320006i	−0.987392	+	0.158297i	$0.949400\pi$
$312$		0			0
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	−0.215041	−	0.976605i	$-0.568989\pi$
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	0.997268	+	0.0738672i	$0.0235341\pi$
$314$		0			0
$315$	−8.18653	−	5.26116i	−0.461259	−	0.296433i
$316$		0			0
$317$	5.77072	+	6.65977i	0.324116	+	0.374050i	0.894301	−	0.447467i	$-0.147674\pi$
$317$	5.77072	+	6.65977i	0.324116	+	0.374050i	−0.570185	+	0.821517i	$0.693128\pi$
$318$		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	0.121342	−	0.992611i	$-0.461280\pi$
$331$	19.7686	−	22.8142i	1.08658	−	1.25398i	0.965239	−	0.261371i	$-0.0841744\pi$
$332$		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	−0.957380	−	0.288832i	$-0.906733\pi$
$337$	−2.05870	+	4.50792i	−0.112145	+	0.245562i	0.845235	+	0.534394i	$0.179460\pi$
$338$		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	0.947508	+	0.319733i	$0.103593\pi$
$347$	−0.963038	+	6.69808i	−0.0516986	+	0.359572i	−0.999206	+	0.0398383i	$0.987316\pi$
$348$		0			0
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	0.0121000	−	0.999927i	$-0.496148\pi$
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	−0.530422	+	0.847734i	$0.677967\pi$
$350$		0			0
$351$	−0.150131	+	0.0440823i	−0.00801338	+	0.00235294i
$352$		0			0
$353$	10.1649	−	22.2580i	0.541023	−	1.18468i	−0.419827	−	0.907604i	$-0.637909\pi$
$353$	10.1649	−	22.2580i	0.541023	−	1.18468i	0.960850	−	0.277071i	$-0.0893636\pi$
$354$		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	−0.748466	−	0.663173i	$-0.769209\pi$
$359$	0.274264	−	0.316518i	0.0144751	−	0.0167052i	0.762941	+	0.646468i	$0.223755\pi$
$360$		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	0.456942	−	0.889496i	$-0.348945\pi$
$373$	−9.43508	−	10.8887i	−0.488530	−	0.563794i	−0.945472	+	0.325703i	$0.894399\pi$
$374$		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	−0.999998	−	0.00223119i	$-0.999290\pi$
$379$	−0.800823	−	5.56985i	−0.0411355	−	0.286104i	0.958862	−	0.283873i	$-0.0916193\pi$
$380$		0			0
$381$	−12.6742	+	8.14522i	−0.649320	+	0.417292i
$382$		0			0
$383$	−0.0962350	+	0.210725i	−0.00491738	+	0.0107676i	−0.912075	−	0.410024i	$-0.865520\pi$
$383$	−0.0962350	+	0.210725i	−0.00491738	+	0.0107676i	0.907157	+	0.420792i	$0.138248\pi$
$384$		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	−0.528821	−	0.848733i	$-0.677366\pi$
$389$	4.29361	−	29.8627i	0.217695	−	1.51410i	0.746516	−	0.665367i	$-0.231725\pi$
$390$		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	0.0478924	−	0.998853i	$-0.484750\pi$
$397$	12.5168	−	3.67528i	0.628202	−	0.184457i	0.580310	+	0.814396i	$0.302931\pi$
$398$		0			0
$399$	19.7805	−	43.3132i	0.990263	−	2.16837i
$400$		0			0
$401$	−17.9404	+	11.5296i	−0.895899	+	0.575759i	−0.905571	−	0.424194i	$-0.860557\pi$
$401$	−17.9404	+	11.5296i	−0.895899	+	0.575759i	0.00967246	+	0.999953i	$0.496921\pi$
$402$		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	0.884288	−	0.466941i	$-0.154644\pi$
$409$	5.99134	+	6.91437i	0.296253	+	0.341894i	−0.588036	+	0.808835i	$0.700099\pi$
$410$		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	0.593817	−	0.804600i	$-0.297620\pi$
$419$	−5.87685	−	6.78225i	−0.287103	−	0.331334i	−0.880920	+	0.473266i	$0.843075\pi$
$420$		0			0
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.992129	−	0.125221i	$-0.0399638\pi$
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.298241	+	0.954491i	$0.403600\pi$
$422$		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	−0.749254	−	0.662283i	$-0.769588\pi$
$431$	−21.2071	+	6.22697i	−1.02151	+	0.299942i	−0.272256	+	0.962225i	$0.587770\pi$
$432$		0			0
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.0243864	−	0.999703i	$-0.507763\pi$
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.560995	+	0.827819i	$0.689581\pi$
$434$		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	−0.826494	−	0.562946i	$-0.809668\pi$
$439$	2.62158	−	18.2335i	0.125121	−	0.870238i	0.951615	−	0.307292i	$-0.0994229\pi$
$440$		0			0
$441$	4.35968	+	1.28012i	0.207604	+	0.0609580i
$442$		0			0
$443$	−13.3492	+	3.91968i	−0.634240	+	0.186230i	−0.583020	−	0.812458i	$-0.698129\pi$
$443$	−13.3492	+	3.91968i	−0.634240	+	0.186230i	−0.0512201	+	0.998687i	$0.516311\pi$
$444$		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	−0.798013	−	0.602641i	$-0.794115\pi$
$449$	−4.28260	−	29.7862i	−0.202109	−	1.40570i	0.595904	−	0.803056i	$-0.296794\pi$
$450$		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	0.784619	+	0.619978i	$0.212859\pi$
$457$	15.8055	+	34.6093i	0.739351	+	1.61895i	−0.0452680	+	0.998975i	$0.514414\pi$
$458$		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	0.962416	+	0.271581i	$0.0875465\pi$
$463$	11.5638	+	25.3212i	0.537415	+	1.17677i	−0.425001	+	0.905193i	$0.639726\pi$
$464$		0			0
$465$	−3.62794	−	4.18686i	−0.168241	−	0.194161i
$466$		0			0
$467$	14.6095	+	9.38895i	0.676047	+	0.434469i	0.833101	−	0.553121i	$-0.186563\pi$
$467$	14.6095	+	9.38895i	0.676047	+	0.434469i	−0.157054	+	0.987590i	$0.550200\pi$
$468$		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	−0.329387	−	0.944195i	$-0.606842\pi$
$479$	−24.4458	−	7.17792i	−1.11695	−	0.327968i	−0.787568	+	0.616228i	$0.788660\pi$
$480$		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	0.145036	−	0.989426i	$-0.453670\pi$
$487$	−5.91151	−	1.73577i	−0.267876	−	0.0786555i	−0.412912	+	0.910771i	$0.635488\pi$
$488$		0			0
$489$	−35.6649	+	10.4721i	−1.61282	+	0.473567i
$490$		0			0
$491$	13.5623	−	29.6973i	0.612058	−	1.34022i	−0.309099	−	0.951030i	$-0.600027\pi$
$491$	13.5623	−	29.6973i	0.612058	−	1.34022i	0.921157	−	0.389191i	$-0.127245\pi$
$492$		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	0.692033	−	0.721866i	$-0.256715\pi$
$499$	7.21265	+	4.63529i	0.322882	+	0.207504i	−0.369151	+	0.929369i	$0.620351\pi$
$500$		0			0
$501$	2.18861	+	2.52579i	0.0977797	+	0.112844i
$502$		0			0
$503$	−2.80635	−	6.14505i	−0.125129	−	0.273994i	0.836692	−	0.547674i	$-0.184487\pi$
$503$	−2.80635	−	6.14505i	−0.125129	−	0.273994i	−0.961821	+	0.273679i	$0.911759\pi$
$504$		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	0.758246	+	0.651968i	$0.226057\pi$
$509$	17.0206	+	37.2699i	0.754425	+	1.65196i	−0.00382066	+	0.999993i	$0.501216\pi$
$510$		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	−0.999984	−	0.00570487i	$-0.998184\pi$
$521$	−7.77941	+	17.0345i	−0.340822	+	0.746297i	0.659162	+	0.752001i	$0.270911\pi$
$522$		0			0
$523$	22.6095	−	6.63875i	0.988644	−	0.290292i	0.252856	−	0.967504i	$-0.418630\pi$
$523$	22.6095	−	6.63875i	0.988644	−	0.290292i	0.735788	+	0.677212i	$0.236812\pi$
$524$		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	0.986697	−	0.162569i	$-0.0519780\pi$
$541$	−0.135667	−	0.943585i	−0.00583278	−	0.0405679i	−0.992530	+	0.122001i	$0.961069\pi$
$542$		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	0.999720	−	0.0236827i	$-0.00753914\pi$
$547$	19.5057	+	22.5108i	0.834003	+	0.962491i	−0.165717	+	0.986173i	$0.552994\pi$
$548$		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	0.832964	−	0.553327i	$-0.186642\pi$
$557$	3.93487	+	4.54108i	0.166726	+	0.192412i	−0.666238	+	0.745739i	$0.732097\pi$
$558$		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	0.990087	−	0.140454i	$-0.0448563\pi$
$563$	0.0126931	+	0.0882822i	0.000534949	+	0.00372065i	−0.989552	+	0.144175i	$0.953947\pi$
$564$		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	0.691406	−	0.722466i	$-0.256991\pi$
$569$	39.6842	−	11.6523i	1.66365	−	0.488491i	0.972243	+	0.233975i	$0.0751733\pi$
$570$		0			0
$571$	24.7458	+	7.26602i	1.03558	+	0.304073i	0.754977	−	0.655751i	$-0.227648\pi$
$571$	24.7458	+	7.26602i	1.03558	+	0.304073i	0.280602	+	0.959824i	$0.409466\pi$
$572$		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	0.736273	+	0.676684i	$0.236584\pi$
$577$	−3.86302	+	26.8679i	−0.160820	+	1.11853i	−0.897093	+	0.441842i	$0.854325\pi$
$578$		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	0.842685	+	0.538407i	$0.180974\pi$
$587$	4.50210	+	31.3128i	0.185822	+	1.29242i	−0.656863	+	0.754010i	$0.728117\pi$
$588$		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	0.987699	−	0.156368i	$-0.0499786\pi$
$593$	16.8600	+	19.4575i	0.692358	+	0.799024i	−0.295341	+	0.955392i	$0.595433\pi$
$594$		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	0.810019	−	0.586403i	$-0.199457\pi$
$601$	−4.01081	−	8.78246i	−0.163605	−	0.358244i	−0.973624	+	0.228159i	$0.926729\pi$
$602$		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	−0.710979	−	0.703213i	$-0.751748\pi$
$607$	2.12520	−	2.45261i	0.0862592	−	0.0995484i	0.797238	+	0.603665i	$0.206293\pi$
$608$		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	0.403471	+	0.914992i	$0.367803\pi$
$613$	−13.6731	+	29.9399i	−0.552251	+	1.20926i	−0.955723	+	0.294269i	$0.904924\pi$
$614$		0			0
$615$	1.27173	−	0.373413i	0.0512810	−	0.0150575i
$616$		0			0
$617$	−2.90191	−	0.852079i	−0.116827	−	0.0343034i	0.222797	−	0.974865i	$-0.428481\pi$
$617$	−2.90191	−	0.852079i	−0.116827	−	0.0343034i	−0.339623	+	0.940562i	$0.610300\pi$
$618$		0			0
$619$	1.48326	−	10.3163i	0.0596172	−	0.414647i	−0.938057	−	0.346482i	$-0.887376\pi$
$619$	1.48326	−	10.3163i	0.0596172	−	0.414647i	0.997674	−	0.0681655i	$-0.0217146\pi$
$620$		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	−0.968040	−	0.250797i	$-0.919307\pi$
$631$	−28.6878	+	18.4366i	−1.14205	+	0.733948i	−0.174005	+	0.984745i	$0.555671\pi$
$632$		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	0.821248	−	0.570571i	$-0.193278\pi$
$641$	−3.74109	−	8.19184i	−0.147764	−	0.323558i	−0.969012	+	0.247013i	$0.920551\pi$
$642$		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	0.792900	+	0.609352i	$0.208570\pi$
$647$	18.6747	+	40.8919i	0.734178	+	1.60763i	−0.0587216	+	0.998274i	$0.518702\pi$
$648$		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	−0.242321	−	0.970196i	$-0.577909\pi$
$653$	19.2289	−	22.1914i	0.752486	−	0.868415i	0.994807	+	0.101781i	$0.0324542\pi$
$654$		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	−0.241970	−	0.970284i	$-0.577794\pi$
$659$	16.6805	−	36.5251i	0.649778	−	1.42282i	0.891748	−	0.452532i	$-0.149479\pi$
$660$		0			0
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	−0.462366	−	0.886689i	$-0.652999\pi$
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	0.0904132	+	0.995904i	$0.471181\pi$
$662$		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	0.417263	−	0.908786i	$-0.362989\pi$
$673$	32.6772	−	9.59489i	1.25961	−	0.369856i	0.842351	+	0.538930i	$0.181171\pi$
$674$		0			0
$675$	−1.14835	+	2.51454i	−0.0442000	+	0.0967846i
$676$		0			0
$677$	−21.0239	+	13.5112i	−0.808012	+	0.519278i	−0.878221	−	0.478254i	$-0.841270\pi$
$677$	−21.0239	+	13.5112i	−0.808012	+	0.519278i	0.0702091	+	0.997532i	$0.477633\pi$
$678$		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	−0.148532	−	0.988908i	$-0.547455\pi$
$683$	−29.0032	−	18.6392i	−1.10978	−	0.713210i	−0.961244	+	0.275698i	$0.911091\pi$
$684$		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	0.945957	+	0.324293i	$0.105126\pi$
$701$	3.43351	+	23.8806i	0.129682	+	0.901957i	−0.816275	+	0.577664i	$0.803965\pi$
$702$		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	0.152476	−	0.988307i	$-0.451275\pi$
$709$	−6.75188	−	1.98253i	−0.253572	−	0.0744556i	−0.406048	+	0.913852i	$0.633094\pi$
$710$		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	0.230618	−	0.973044i	$-0.425925\pi$
$719$	25.4920	−	7.48514i	0.950693	−	0.279149i	0.720075	+	0.693896i	$0.244107\pi$
$720$		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	−0.815672	−	0.578514i	$-0.803633\pi$
$727$	−3.42332	+	3.95072i	−0.126964	+	0.146524i	0.688708	+	0.725039i	$0.258178\pi$
$728$		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	−0.996217	−	0.0868973i	$-0.972305\pi$
$733$	−11.0870	−	24.2771i	−0.409506	−	0.896694i	0.586711	−	0.809796i	$-0.300422\pi$
$734$		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	0.925972	−	0.377593i	$-0.123248\pi$
$739$	0.930342	+	2.03716i	0.0342232	+	0.0749383i	−0.891748	+	0.452532i	$0.850521\pi$
$740$		0			0
$741$	−2.58196	−	2.97974i	−0.0948507	−	0.109464i
$742$		0			0
$743$	−15.2605	−	9.80730i	−0.559852	−	0.359795i	0.229907	−	0.973213i	$-0.426158\pi$
$743$	−15.2605	−	9.80730i	−0.559852	−	0.359795i	−0.789759	+	0.613418i	$0.789794\pi$
$744$		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	0.565786	+	0.824552i	$0.308573\pi$
$751$	−11.7258	+	25.6759i	−0.427880	+	0.936927i	−0.993666	+	0.112375i	$0.964154\pi$
$752$		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	−0.990135	−	0.140120i	$-0.955251\pi$
$757$	−0.0173643	+	0.120772i	−0.000631118	+	0.00438952i	0.989503	+	0.144509i	$0.0461603\pi$
$758$		0			0
$759$	21.7302	−	7.67118i	0.788756	−	0.278446i
$760$		0			0
$761$	3.80057	−	26.4336i	0.137771	−	0.958216i	−0.797257	−	0.603640i	$-0.793716\pi$
$761$	3.80057	−	26.4336i	0.137771	−	0.958216i	0.935027	−	0.354576i	$-0.115375\pi$
$762$		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	−0.654283	−	0.756250i	$-0.727029\pi$
$769$	−6.60471	+	4.24459i	−0.238172	+	0.153064i	0.416111	+	0.909314i	$0.363393\pi$
$770$		0			0
$771$	−9.82128	−	68.3085i	−0.353705	−	2.46007i
$772$		0			0
$773$	22.4497	−	25.9084i	0.807460	−	0.931859i	−0.191305	−	0.981531i	$-0.561272\pi$
$773$	22.4497	−	25.9084i	0.807460	−	0.931859i	0.998766	+	0.0496716i	$0.0158175\pi$
$774$		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	0.911211	−	0.411940i	$-0.135149\pi$
$787$	10.4860	+	12.1015i	0.373785	+	0.431370i	−0.537426	+	0.843311i	$0.680603\pi$
$788$		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	−0.682588	−	0.730803i	$-0.739146\pi$
$797$	8.94128	−	19.5787i	0.316716	−	0.693512i	0.999304	+	0.0372914i	$0.0118730\pi$
$798$		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	−0.151776	−	0.988415i	$-0.548499\pi$
$809$	−23.1479	−	6.79683i	−0.813836	−	0.238964i	−0.662060	+	0.749451i	$0.730318\pi$
$810$		0			0
$811$	13.7575	−	4.03956i	0.483091	−	0.141848i	−0.0311137	−	0.999516i	$-0.509905\pi$
$811$	13.7575	−	4.03956i	0.483091	−	0.141848i	0.514205	+	0.857668i	$0.328087\pi$
$812$		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	0.732339	−	0.680940i	$-0.238428\pi$
$821$	11.9529	+	7.68167i	0.417160	+	0.268092i	−0.315180	+	0.949032i	$0.602065\pi$
$822$		0			0
$823$	10.4929	+	12.1095i	0.365760	+	0.422109i	0.908561	−	0.417752i	$-0.137182\pi$
$823$	10.4929	+	12.1095i	0.365760	+	0.422109i	−0.542802	+	0.839861i	$0.682636\pi$
$824$		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	0.832761	+	0.553632i	$0.186759\pi$
$839$	5.49501	+	38.2187i	0.189709	+	1.31945i	−0.643052	+	0.765822i	$0.722332\pi$
$840$		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	−0.651812	−	0.758380i	$-0.725991\pi$
$853$	5.46907	−	38.0382i	0.187257	−	1.30240i	0.839070	−	0.544024i	$-0.183100\pi$
$854$		0			0
$855$	31.4197	+	9.22564i	1.07453	+	0.315510i
$856$		0			0
$857$	48.8281	−	14.3372i	1.66794	−	0.489750i	0.694650	−	0.719348i	$-0.255559\pi$
$857$	48.8281	−	14.3372i	1.66794	−	0.489750i	0.973286	+	0.229598i	$0.0737411\pi$
$858$		0			0
$859$	−3.79985	+	8.32050i	−0.129649	+	0.283892i	−0.963313	−	0.268380i	$-0.913512\pi$
$859$	−3.79985	+	8.32050i	−0.129649	+	0.283892i	0.833664	+	0.552272i	$0.186239\pi$
$860$		0			0
$861$	2.13969	−	1.37510i	0.0729205	−	0.0468631i
$862$		0			0
$863$	1.75600	+	12.2133i	0.0597750	+	0.415744i	0.997635	+	0.0687310i	$0.0218950\pi$
$863$	1.75600	+	12.2133i	0.0597750	+	0.415744i	−0.937860	+	0.347013i	$0.887196\pi$
$864$		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	0.925124	−	0.379666i	$-0.123961\pi$
$877$	0.958445	+	2.09870i	0.0323644	+	0.0708681i	−0.892759	+	0.450534i	$0.851234\pi$
$878$		0			0
$879$	−35.4087	−	40.8638i	−1.19431	−	1.37830i
$880$		0			0
$881$	−29.9489	−	19.2470i	−1.00901	−	0.648448i	−0.0718697	−	0.997414i	$-0.522897\pi$
$881$	−29.9489	−	19.2470i	−1.00901	−	0.648448i	−0.937135	+	0.348966i	$0.886533\pi$
$882$		0			0
$883$	19.9566	−	23.0311i	0.671592	−	0.775059i	−0.313032	−	0.949742i	$-0.601345\pi$
$883$	19.9566	−	23.0311i	0.671592	−	0.775059i	0.984625	+	0.174684i	$0.0558903\pi$
$884$		0			0
$885$	3.19271	+	22.2058i	0.107322	+	0.746438i
$886$		0			0
$887$	−17.4906	+	11.2405i	−0.587278	+	0.377421i	−0.800276	−	0.599632i	$-0.795314\pi$
$887$	−17.4906	+	11.2405i	−0.587278	+	0.377421i	0.212998	+	0.977053i	$0.431677\pi$
$888$		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	−0.183525	−	0.983015i	$-0.558751\pi$
$907$	19.1064	−	12.2789i	0.634417	−	0.407715i	0.817943	+	0.575300i	$0.195115\pi$
$908$		0			0
$909$	0.859242	+	5.97616i	0.0284992	+	0.198217i
$910$		0			0
$911$	0.546182	−	0.630328i	0.0180958	−	0.0208837i	−0.746630	−	0.665240i	$-0.768329\pi$
$911$	0.546182	−	0.630328i	0.0180958	−	0.0208837i	0.764725	+	0.644356i	$0.222875\pi$
$912$		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	−0.532941	−	0.846153i	$-0.678913\pi$
$929$	11.5958	−	13.3822i	0.380445	−	0.439056i	0.913385	+	0.407096i	$0.133459\pi$
$930$		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	0.105099	−	0.994462i	$-0.466484\pi$
$937$	22.3812	−	6.57170i	0.731161	−	0.214688i	0.626062	+	0.779774i	$0.284666\pi$
$938$		0			0
$939$	50.9622	+	14.9639i	1.66309	+	0.488327i
$940$		0			0
$941$	−1.65295	+	11.4965i	−0.0538847	+	0.374776i	0.944980	+	0.327130i	$0.106081\pi$
$941$	−1.65295	+	11.4965i	−0.0538847	+	0.374776i	−0.998864	+	0.0476470i	$0.984828\pi$
$942$		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	0.373897	−	0.927470i	$-0.378021\pi$
$947$	5.75498	+	1.68981i	0.187012	+	0.0549116i	−0.186886	+	0.982382i	$0.559839\pi$
$948$		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	−0.761389	−	0.648295i	$-0.775482\pi$
$953$	−15.0640	+	9.68107i	−0.487972	+	0.313601i	0.273417	+	0.961896i	$0.411846\pi$
$954$		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	0.855960	+	0.517042i	$0.172967\pi$
$971$	38.8241	+	44.8054i	1.24592	+	1.43787i	0.389964	+	0.920830i	$0.372487\pi$
$972$		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	0.998150	+	0.0607934i	$0.0193631\pi$
$977$	1.79914	+	12.5133i	0.0575596	+	0.400336i	−0.940591	+	0.339542i	$0.889728\pi$
$978$		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	−0.996072	−	0.0885469i	$-0.971778\pi$
$983$	−56.0008	+	16.4433i	−1.78615	+	0.524461i	−0.790077	+	0.613008i	$0.789960\pi$
$984$		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	0.575828	+	0.817571i	$0.304680\pi$
$991$	−6.51675	+	45.3250i	−0.207011	+	1.43980i	−0.782839	+	0.622224i	$0.786229\pi$
$992$		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	0.452563	+	0.891732i	$0.350510\pi$
$997$	−16.3475	+	35.7959i	−0.517729	+	1.13367i	−0.970292	+	0.241936i	$0.922218\pi$
$998$		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

) (See only

a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	92.3	odd	22
23.2.c.a.8.1	yes	10	4.3	odd	2
207.2.i.c.100.1		10	12.11	even	2
207.2.i.c.118.1		10	276.95	even	22
368.2.m.c.49.1		10	23.3	even	11	inner
368.2.m.c.353.1		10	1.1	even	1	trivial
529.2.a.i.1.5		5	92.39	odd	22
529.2.a.j.1.5		5	92.7	even	22
529.2.c.a.118.1		10	92.43	even	22
529.2.c.a.399.1		10	92.91	even	2
529.2.c.b.170.1		10	92.71	odd	22
529.2.c.b.501.1		10	92.59	odd	22
529.2.c.c.170.1		10	92.67	even	22
529.2.c.c.501.1		10	92.79	even	22
529.2.c.d.177.1		10	92.87	odd	22
529.2.c.d.266.1		10	92.27	odd	22
529.2.c.e.177.1		10	92.51	even	22
529.2.c.e.266.1		10	92.19	even	22
529.2.c.f.466.1		10	92.15	even	22
529.2.c.f.487.1		10	92.83	even	22
529.2.c.g.466.1		10	92.31	odd	22
529.2.c.g.487.1		10	92.55	odd	22
529.2.c.h.255.1		10	92.11	even	22
529.2.c.h.334.1		10	92.63	even	22
529.2.c.i.255.1		10	92.35	odd	22
529.2.c.i.334.1		10	92.75	odd	22
575.2.k.b.26.1		10	460.279	odd	22
575.2.k.b.376.1		10	20.19	odd	2
575.2.p.b.49.1		20	460.3	even	44
575.2.p.b.49.2		20	460.187	even	44
575.2.p.b.399.1		20	20.7	even	4
575.2.p.b.399.2		20	20.3	even	4
4761.2.a.bn.1.1		5	276.191	odd	22
4761.2.a.bo.1.1		5	276.131	even	22
8464.2.a.bs.1.5		5	23.16	even	11
8464.2.a.bt.1.5		5	23.7	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.353.1

Level	$368$
Weight	$2$
Character	368.353
Analytic conductor	$2.938$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$