LMFDB - Embedded newform 825.2.cb.a.169.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(169,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("825.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.14
Character	$\chi$	$=$	825.169
Dual form			825.2.cb.a.454.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.75058 - 0.568798i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.12297 + 0.815886i) q^{4} +(2.12442 - 0.697744i) q^{5} +1.84067 q^{6} +(0.161477 - 0.0524671i) q^{7} +(0.662061 + 0.911249i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-4.11584 + 0.0130915i) q^{10} +(-2.62986 + 2.02085i) q^{11} +(-1.32013 - 0.428937i) q^{12} +(3.85838 + 5.31060i) q^{13} -0.312522 q^{14} +(-1.80483 + 1.32008i) q^{15} +(-1.49855 - 4.61206i) q^{16} -1.03771i q^{17} +(-1.75058 + 0.568798i) q^{18} +(-3.38755 + 2.46120i) q^{19} +(2.95494 + 0.949737i) q^{20} +(-0.137361 + 0.0997983i) q^{21} +(5.75324 - 2.04180i) q^{22} +(-5.22698 + 1.69835i) q^{23} +(-0.911249 - 0.662061i) q^{24} +(4.02631 - 2.96460i) q^{25} +(-3.73374 - 11.4913i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.224141 + 0.0728279i) q^{28} +(-0.595847 - 0.432909i) q^{29} +(3.91035 - 1.28432i) q^{30} +(-0.0908653 - 0.279655i) q^{31} +6.67342i q^{32} +(1.87667 - 2.73461i) q^{33} +(-0.590249 + 1.81660i) q^{34} +(0.306436 - 0.224132i) q^{35} +1.38807 q^{36} +3.82856i q^{37} +(7.33012 - 2.38170i) q^{38} +(-5.31060 - 3.85838i) q^{39} +(2.04231 + 1.47392i) q^{40} +(-9.89108 - 7.18629i) q^{41} +(0.297226 - 0.0965746i) q^{42} +1.43140i q^{43} +(-4.60204 + 0.123687i) q^{44} +(1.30857 - 1.81319i) q^{45} +10.1163 q^{46} +(5.74408 - 1.86636i) q^{47} +(2.85041 + 3.92325i) q^{48} +(-5.63980 + 4.09755i) q^{49} +(-8.73464 + 2.89962i) q^{50} +(0.320671 + 0.986923i) q^{51} +9.11164i q^{52} +2.20721i q^{53} +(1.48913 - 1.08192i) q^{54} +(-4.17689 + 6.12810i) q^{55} +(0.154718 + 0.112409i) q^{56} +(2.46120 - 3.38755i) q^{57} +(0.796842 + 1.09676i) q^{58} -14.3049 q^{59} +(-3.10380 + 0.00987244i) q^{60} +(11.1996 + 8.13701i) q^{61} +0.541242i q^{62} +(0.0997983 - 0.137361i) q^{63} +(0.798737 - 2.45826i) q^{64} +(11.9022 + 8.58978i) q^{65} +(-4.84071 + 3.71972i) q^{66} +(-6.82297 + 9.39102i) q^{67} +(0.846655 - 1.16532i) q^{68} +(4.44634 - 3.23045i) q^{69} +(-0.663927 + 0.218060i) q^{70} +(-0.682027 + 2.09906i) q^{71} +(1.07124 + 0.348066i) q^{72} +(8.57381 + 11.8008i) q^{73} +(2.17768 - 6.70220i) q^{74} +(-2.91313 + 4.06370i) q^{75} -5.81218 q^{76} +(-0.318634 + 0.464302i) q^{77} +(7.10200 + 9.77506i) q^{78} +11.1282 q^{79} +(-6.40158 - 8.75234i) q^{80} +(0.309017 - 0.951057i) q^{81} +(13.2276 + 18.2062i) q^{82} +14.1599i q^{83} -0.235676 q^{84} +(-0.724057 - 2.20453i) q^{85} +(0.814181 - 2.50579i) q^{86} +(0.700461 + 0.227593i) q^{87} +(-3.58262 - 1.05853i) q^{88} +(0.142074 + 0.437258i) q^{89} +(-3.32209 + 2.42982i) q^{90} +(0.901671 + 0.655102i) q^{91} +(-7.25541 - 2.35742i) q^{92} +(0.172836 + 0.237888i) q^{93} -11.1171 q^{94} +(-5.47929 + 7.59227i) q^{95} +(-2.06220 - 6.34680i) q^{96} +4.61724i q^{97} +(12.2036 - 3.96519i) q^{98} +(-0.939777 + 3.18069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) $ 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{9}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.75058	−	0.568798i	−1.23785	−	0.402201i	−0.384297	−	0.923210i	$-0.625556\pi$
$2$	−1.75058	−	0.568798i	−1.23785	−	0.402201i	−0.853552	+	0.521008i	$0.825556\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	1.12297	+	0.815886i	0.561485	+	0.407943i
$5$	2.12442	−	0.697744i	0.950069	−	0.312040i
$5$	2.12442	−	0.697744i	0.950069	−	0.312040i
$6$	1.84067			0.751451
$7$	0.161477	−	0.0524671i	0.0610326	−	0.0198307i	−0.278342	−	0.960482i	$-0.589785\pi$
$7$	0.161477	−	0.0524671i	0.0610326	−	0.0198307i	0.339374	+	0.940651i	$0.389785\pi$
$8$	0.662061	+	0.911249i	0.234074	+	0.322175i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−4.11584	+	0.0130915i	−1.30154	+	0.00413990i
$11$	−2.62986	+	2.02085i	−0.792933	+	0.609309i
$11$	−2.62986	+	2.02085i	−0.792933	+	0.609309i
$12$	−1.32013	−	0.428937i	−0.381089	−	0.123823i
$13$	3.85838	+	5.31060i	1.07012	+	1.47290i	0.869954	+	0.493133i	$0.164149\pi$
$13$	3.85838	+	5.31060i	1.07012	+	1.47290i	0.200167	+	0.979762i	$0.435851\pi$
$14$	−0.312522			−0.0835250
$15$	−1.80483	+	1.32008i	−0.466004	+	0.340842i
$16$	−1.49855	−	4.61206i	−0.374637	−	1.15301i
$17$		−	1.03771i		−	0.251682i	−0.992050	−	0.125841i	$-0.959837\pi$
$17$		−	1.03771i		−	0.251682i	0.992050	−	0.125841i	$-0.0401629\pi$
$18$	−1.75058	+	0.568798i	−0.412616	+	0.134067i
$19$	−3.38755	+	2.46120i	−0.777158	+	0.564638i	−0.904125	−	0.427269i	$-0.859476\pi$
$19$	−3.38755	+	2.46120i	−0.777158	+	0.564638i	0.126967	+	0.991907i	$0.459476\pi$
$20$	2.95494	+	0.949737i	0.660744	+	0.212368i
$21$	−0.137361	+	0.0997983i	−0.0299745	+	0.0217778i
$22$	5.75324	−	2.04180i	1.22660	−	0.435313i
$23$	−5.22698	+	1.69835i	−1.08990	+	0.354130i	−0.798208	−	0.602382i	$-0.794219\pi$
$23$	−5.22698	+	1.69835i	−1.08990	+	0.354130i	−0.291693	+	0.956512i	$0.594219\pi$
$24$	−0.911249	−	0.662061i	−0.186008	−	0.135143i
$25$	4.02631	−	2.96460i	0.805261	−	0.592920i
$26$	−3.73374	−	11.4913i	−0.732247	−	2.25362i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	0.224141	+	0.0728279i	0.0423587	+	0.0137632i
$29$	−0.595847	−	0.432909i	−0.110646	−	0.0803891i	0.531086	−	0.847318i	$-0.321784\pi$
$29$	−0.595847	−	0.432909i	−0.110646	−	0.0803891i	−0.641732	+	0.766929i	$0.721784\pi$
$30$	3.91035	−	1.28432i	0.713930	−	0.234483i
$31$	−0.0908653	−	0.279655i	−0.0163199	−	0.0502274i	0.942565	−	0.334023i	$-0.108406\pi$
$31$	−0.0908653	−	0.279655i	−0.0163199	−	0.0502274i	−0.958885	+	0.283796i	$0.908406\pi$
$32$			6.67342i			1.17971i
$33$	1.87667	−	2.73461i	0.326686	−	0.476035i
$34$	−0.590249	+	1.81660i	−0.101227	+	0.311544i
$35$	0.306436	−	0.224132i	0.0517972	−	0.0378852i
$36$	1.38807			0.231345
$37$			3.82856i			0.629411i	0.949189	+	0.314705i	$0.101906\pi$
$37$			3.82856i			0.629411i	−0.949189	+	0.314705i	$0.898094\pi$
$38$	7.33012	−	2.38170i	1.18910	−	0.386363i
$39$	−5.31060	−	3.85838i	−0.850376	−	0.617835i
$40$	2.04231	+	1.47392i	0.322918	+	0.233048i
$41$	−9.89108	−	7.18629i	−1.54473	−	1.12231i	−0.947282	−	0.320400i	$-0.896183\pi$
$41$	−9.89108	−	7.18629i	−1.54473	−	1.12231i	−0.597445	−	0.801910i	$-0.703817\pi$
$42$	0.297226	−	0.0965746i	0.0458630	−	0.0149018i
$43$			1.43140i			0.218287i	0.994026	+	0.109144i	$0.0348108\pi$
$43$			1.43140i			0.218287i	−0.994026	+	0.109144i	$0.965189\pi$
$44$	−4.60204	+	0.123687i	−0.693783	+	0.0186465i
$45$	1.30857	−	1.81319i	0.195070	−	0.270294i
$46$	10.1163			1.49156
$47$	5.74408	−	1.86636i	0.837860	−	0.272237i	0.141508	−	0.989937i	$-0.454805\pi$
$47$	5.74408	−	1.86636i	0.837860	−	0.272237i	0.696353	+	0.717700i	$0.254805\pi$
$48$	2.85041	+	3.92325i	0.411421	+	0.566272i
$49$	−5.63980	+	4.09755i	−0.805685	+	0.585365i
$50$	−8.73464	+	2.89962i	−1.23526	+	0.410068i
$51$	0.320671	+	0.986923i	0.0449029	+	0.138197i
$52$			9.11164i			1.26356i
$53$			2.20721i			0.303183i	0.988443	+	0.151592i	$0.0484398\pi$
$53$			2.20721i			0.303183i	−0.988443	+	0.151592i	$0.951560\pi$
$54$	1.48913	−	1.08192i	0.202645	−	0.147231i
$55$	−4.17689	+	6.12810i	−0.563212	+	0.826313i
$56$	0.154718	+	0.112409i	0.0206751	+	0.0150213i
$57$	2.46120	−	3.38755i	0.325994	−	0.448692i
$58$	0.796842	+	1.09676i	0.104630	+	0.144011i
$59$	−14.3049			−1.86234			−0.931172	−	0.364581i	$-0.881212\pi$
$59$	−14.3049			−1.86234			−0.931172	+	0.364581i	$0.881212\pi$
$60$	−3.10380	+	0.00987244i	−0.400699	+	0.00127453i
$61$	11.1996	+	8.13701i	1.43397	+	1.04184i	0.989261	+	0.146161i	$0.0466916\pi$
$61$	11.1996	+	8.13701i	1.43397	+	1.04184i	0.444705	+	0.895677i	$0.353308\pi$
$62$			0.541242i			0.0687378i
$63$	0.0997983	−	0.137361i	0.0125734	−	0.0173058i
$64$	0.798737	−	2.45826i	0.0998421	−	0.307282i
$65$	11.9022	+	8.58978i	1.47629	+	1.06543i
$66$	−4.84071	+	3.71972i	−0.595850	+	0.457865i
$67$	−6.82297	+	9.39102i	−0.833559	+	1.14730i	0.153691	+	0.988119i	$0.450884\pi$
$67$	−6.82297	+	9.39102i	−0.833559	+	1.14730i	−0.987250	+	0.159176i	$0.949116\pi$
$68$	0.846655	−	1.16532i	0.102672	−	0.141316i
$69$	4.44634	−	3.23045i	0.535276	−	0.388901i
$70$	−0.663927	+	0.218060i	−0.0793545	+	0.0260632i
$71$	−0.682027	+	2.09906i	−0.0809417	+	0.249113i	−0.983336	−	0.181799i	$-0.941808\pi$
$71$	−0.682027	+	2.09906i	−0.0809417	+	0.249113i	0.902394	+	0.430912i	$0.141808\pi$
$72$	1.07124	+	0.348066i	0.126247	+	0.0410200i
$73$	8.57381	+	11.8008i	1.00349	+	1.38118i	0.923160	+	0.384415i	$0.125597\pi$
$73$	8.57381	+	11.8008i	1.00349	+	1.38118i	0.0803281	+	0.996768i	$0.474403\pi$
$74$	2.17768	−	6.70220i	0.253150	−	0.779115i
$75$	−2.91313	+	4.06370i	−0.336380	+	0.469236i
$76$	−5.81218			−0.666703
$77$	−0.318634	+	0.464302i	−0.0363117	+	0.0529121i
$78$	7.10200	+	9.77506i	0.804143	+	1.10681i
$79$	11.1282			1.25202			0.626008	−	0.779817i	$-0.284688\pi$
$79$	11.1282			1.25202			0.626008	+	0.779817i	$0.284688\pi$
$80$	−6.40158	−	8.75234i	−0.715718	−	0.978541i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	13.2276	+	18.2062i	1.46074	+	2.01054i
$83$			14.1599i			1.55425i	0.629344	+	0.777127i	$0.283324\pi$
$83$			14.1599i			1.55425i	−0.629344	+	0.777127i	$0.716676\pi$
$84$	−0.235676			−0.0257143
$85$	−0.724057	−	2.20453i	−0.0785350	−	0.239115i
$86$	0.814181	−	2.50579i	0.0877954	−	0.270206i
$87$	0.700461	+	0.227593i	0.0750973	+	0.0244006i
$88$	−3.58262	−	1.05853i	−0.381909	−	0.112840i
$89$	0.142074	+	0.437258i	0.0150598	+	0.0463492i	0.958304	−	0.285751i	$-0.0922429\pi$
$89$	0.142074	+	0.437258i	0.0150598	+	0.0463492i	−0.943244	+	0.332100i	$0.892243\pi$
$90$	−3.32209	+	2.42982i	−0.350179	+	0.256126i
$91$	0.901671	+	0.655102i	0.0945208	+	0.0686734i
$92$	−7.25541	−	2.35742i	−0.756429	−	0.245779i
$93$	0.172836	+	0.237888i	0.0179223	+	0.0246679i
$94$	−11.1171			−1.14664
$95$	−5.47929	+	7.59227i	−0.562164	+	0.778950i
$96$	−2.06220	−	6.34680i	−0.210473	−	0.647768i
$97$			4.61724i			0.468810i	0.972139	+	0.234405i	$0.0753141\pi$
$97$			4.61724i			0.468810i	−0.972139	+	0.234405i	$0.924686\pi$
$98$	12.2036	−	3.96519i	1.23275	−	0.400545i
$99$	−0.939777	+	3.18069i	−0.0944512	+	0.319672i
$100$	6.94020	−	0.0441507i	0.694020	−	0.00441507i
$101$	−0.268477	−	0.195060i	−0.0267145	−	0.0194092i	0.574348	−	0.818611i	$-0.305256\pi$
$101$	−0.268477	−	0.195060i	−0.0267145	−	0.0194092i	−0.601062	+	0.799202i	$0.705256\pi$
$102$		−	1.91009i		−	0.189127i
$103$	4.13076	−	5.68551i	0.407016	−	0.560210i	−0.555471	−	0.831536i	$-0.687462\pi$
$103$	4.13076	−	5.68551i	0.407016	−	0.560210i	0.962487	+	0.271326i	$0.0874622\pi$
$104$	−2.28480	+	7.03188i	−0.224043	+	0.689533i
$105$	−0.222178	+	0.307856i	−0.0216823	+	0.0300437i
$106$	1.25546	−	3.86390i	0.121941	−	0.375295i
$107$	0.706648	+	0.229604i	0.0683142	+	0.0221966i	0.342975	−	0.939345i	$-0.388565\pi$
$107$	0.706648	+	0.229604i	0.0683142	+	0.0221966i	−0.274661	+	0.961541i	$0.588565\pi$
$108$	−1.32013	+	0.428937i	−0.127030	+	0.0412744i
$109$	1.47491	−	4.53931i	0.141271	−	0.434787i	−0.855242	−	0.518229i	$-0.826591\pi$
$109$	1.47491	−	4.53931i	0.141271	−	0.434787i	0.996513	+	0.0834422i	$0.0265914\pi$
$110$	10.7976	−	8.35193i	1.02951	−	0.796325i
$111$	−1.18309	−	3.64117i	−0.112294	−	0.345605i
$112$	−0.483962	−	0.666117i	−0.0457301	−	0.0629421i
$113$	5.13705	−	7.07054i	0.483253	−	0.665140i	−0.495873	−	0.868395i	$-0.665152\pi$
$113$	5.13705	−	7.07054i	0.483253	−	0.665140i	0.979126	+	0.203255i	$0.0651520\pi$
$114$	−6.23537	+	4.53026i	−0.583996	+	0.424298i
$115$	−9.91929	+	7.25510i	−0.924978	+	0.676542i
$116$	−0.315915	−	0.972287i	−0.0293320	−	0.0902746i
$117$	6.24298	+	2.02847i	0.577164	+	0.187532i
$118$	25.0419	+	8.13662i	2.30530	+	0.749037i
$119$	−0.0544457	−	0.167567i	−0.00499103	−	0.0153608i
$120$	−2.39782	−	0.770676i	−0.218890	−	0.0703528i
$121$	2.83234	−	10.6291i	0.257485	−	0.966282i
$122$	−14.9776	−	20.6148i	−1.35600	−	1.86638i
$123$	11.6277	+	3.77806i	1.04843	+	0.340656i
$124$	0.126127	−	0.388179i	0.0113266	−	0.0348595i
$125$	6.48503	−	9.10738i	0.580039	−	0.814589i
$126$	−0.252836	+	0.183696i	−0.0225244	+	0.0163649i
$127$	−2.15422	+	2.96504i	−0.191157	+	0.263104i	−0.893828	−	0.448410i	$-0.851990\pi$
$127$	−2.15422	+	2.96504i	−0.191157	+	0.263104i	0.702671	+	0.711515i	$0.251990\pi$
$128$	5.04857	−	6.94876i	0.446235	−	0.614190i
$129$	−0.442328	−	1.36135i	−0.0389448	−	0.119860i
$130$	−15.9500	−	21.8071i	−1.39891	−	1.91261i
$131$	14.5629	+	10.5806i	1.27237	+	0.924430i	0.999294	−	0.0375625i	$-0.0119593\pi$
$131$	14.5629	+	10.5806i	1.27237	+	0.924430i	0.273075	+	0.961993i	$0.411959\pi$
$132$	4.33858	−	1.53974i	0.377625	−	0.134017i
$133$	−0.417880	+	0.575163i	−0.0362348	+	0.0498729i
$134$	17.2858	−	12.5588i	1.49326	−	1.08492i
$135$	−0.684215	+	2.12881i	−0.0588879	+	0.183219i
$136$	0.945614	−	0.687029i	0.0810857	−	0.0589122i
$137$	−12.1727	+	3.95515i	−1.03998	+	0.337911i	−0.778730	−	0.627359i	$-0.784136\pi$
$137$	−12.1727	+	3.95515i	−1.03998	+	0.337911i	−0.261254	+	0.965270i	$0.584136\pi$
$138$	−9.62115	+	3.12610i	−0.819007	+	0.266112i
$139$	−9.79416	+	7.11588i	−0.830730	+	0.603561i	−0.919766	−	0.392468i	$-0.871621\pi$
$139$	−9.79416	+	7.11588i	−0.830730	+	0.603561i	0.0890357	+	0.996028i	$0.471621\pi$
$140$	0.526985	−	0.00167621i	0.0445383	−	0.000141666i
$141$	−4.88621	+	3.55004i	−0.411493	+	0.298967i
$142$	2.38789	−	3.28664i	0.200387	−	0.275809i
$143$	−20.8789	−	6.16894i	−1.74598	−	0.515873i
$144$	−3.92325	−	2.85041i	−0.326937	−	0.237534i
$145$	−1.56789	−	0.503930i	−0.130206	−	0.0418491i
$146$	−8.29686	−	25.5351i	−0.686653	−	2.11330i
$147$	4.09755	−	5.63980i	0.337960	−	0.465163i
$148$	−3.12366	+	4.29936i	−0.256764	+	0.353405i
$149$	−11.8481	+	8.60817i	−0.970636	+	0.705208i	−0.955596	−	0.294679i	$-0.904787\pi$
$149$	−11.8481	+	8.60817i	−0.970636	+	0.705208i	−0.0150396	+	0.999887i	$0.504787\pi$
$150$	7.41111	−	5.45685i	0.605114	−	0.445550i
$151$	3.45685	−	10.6391i	0.281315	−	0.865797i	−0.706165	−	0.708048i	$-0.749576\pi$
$151$	3.45685	−	10.6391i	0.281315	−	0.865797i	0.987479	−	0.157749i	$-0.0504238\pi$
$152$	−4.48553	−	1.45744i	−0.363825	−	0.118214i
$153$	−0.609952	−	0.839527i	−0.0493117	−	0.0678717i
$154$	0.821889	−	0.631560i	0.0662297	−	0.0508925i
$155$	−0.388163	−	0.530703i	−0.0311780	−	0.0426271i
$156$	−2.81565	−	8.66568i	−0.225433	−	0.693810i
$157$	−8.90719	−	2.89412i	−0.710871	−	0.230976i	−0.0688104	−	0.997630i	$-0.521920\pi$
$157$	−8.90719	−	2.89412i	−0.710871	−	0.230976i	−0.642061	+	0.766654i	$0.721920\pi$
$158$	−19.4807	−	6.32968i	−1.54980	−	0.503562i
$159$	−0.682064	−	2.09918i	−0.0540912	−	0.166476i
$160$	4.65634	+	14.1771i	0.368116	+	1.12080i
$161$	−0.754930	+	0.548489i	−0.0594968	+	0.0432270i
$162$	−1.08192	+	1.48913i	−0.0850036	+	0.116997i
$163$	−11.8460	−	16.3046i	−0.927848	−	1.27707i	−0.960693	−	0.277613i	$-0.910457\pi$
$163$	−11.8460	−	16.3046i	−0.927848	−	1.27707i	0.0328447	−	0.999460i	$-0.489543\pi$
$164$	−5.24420	−	16.1400i	−0.409503	−	1.26032i
$165$	2.07877	−	7.11890i	0.161832	−	0.554205i
$166$	8.05415	−	24.7881i	0.625123	−	1.92393i
$167$	21.8120	−	7.08714i	1.68786	−	0.548420i	0.701451	−	0.712717i	$-0.252536\pi$
$167$	21.8120	−	7.08714i	1.68786	−	0.548420i	0.986411	+	0.164298i	$0.0525358\pi$
$168$	−0.181882	−	0.0590971i	−0.0140325	−	0.00455944i
$169$	−9.29817	+	28.6168i	−0.715244	+	2.20129i
$170$	0.0135852	+	4.27106i	0.00104194	+	0.327575i
$171$	−1.29393	+	3.98231i	−0.0989493	+	0.304535i
$172$	−1.16786	+	1.60743i	−0.0890487	+	0.122565i
$173$			15.2451i			1.15907i	0.814949	+	0.579533i	$0.196765\pi$
$173$			15.2451i			1.15907i	−0.814949	+	0.579533i	$0.803235\pi$
$174$	−1.09676	−	0.796842i	−0.0831451	−	0.0604084i
$175$	0.494612	−	0.689963i	0.0373892	−	0.0521563i
$176$	13.2612	+	9.10073i	0.999604	+	0.685993i
$177$	13.6048	−	4.42047i	1.02260	−	0.332263i
$178$		−	0.846267i		−	0.0634304i
$179$	2.87221	+	8.83975i	0.214679	+	0.660714i	0.999176	+	0.0405818i	$0.0129211\pi$
$179$	2.87221	+	8.83975i	0.214679	+	0.660714i	−0.784497	+	0.620132i	$0.787079\pi$
$180$	2.94884	−	0.968516i	0.219793	−	0.0721889i
$181$	3.75534			0.279132			0.139566	−	0.990213i	$-0.455429\pi$
$181$	3.75534			0.279132			0.139566	+	0.990213i	$0.455429\pi$
$182$	−1.20583	−	1.65968i	−0.0893819	−	0.123024i
$183$	−13.1660	−	4.27788i	−0.973256	−	0.316230i
$184$	−5.00820	−	3.63867i	−0.369209	−	0.268246i
$185$	2.67135	+	8.13345i	0.196402	+	0.597983i
$186$	−0.167253	−	0.514752i	−0.0122636	−	0.0377434i
$187$	2.09706	+	2.72904i	0.153352	+	0.199567i
$188$	7.97317	+	2.59064i	0.581503	+	0.188942i
$189$	−0.0524671	+	0.161477i	−0.00381642	+	0.0117457i
$190$	13.9104	−	10.1743i	1.00917	−	0.738119i
$191$	25.4592			1.84216			0.921081	−	0.389371i	$-0.127307\pi$
$191$	25.4592			1.84216			0.921081	+	0.389371i	$0.127307\pi$
$192$			2.58477i			0.186539i
$193$	−4.65416	−	6.40591i	−0.335014	−	0.461107i	0.607963	−	0.793965i	$-0.291987\pi$
$193$	−4.65416	−	6.40591i	−0.335014	−	0.461107i	−0.942977	+	0.332858i	$0.891987\pi$
$194$	2.62628	−	8.08285i	0.188556	−	0.580315i
$195$	−13.9741	−	4.49137i	−1.00071	−	0.321634i
$196$	−9.67646			−0.691176
$197$	4.73782	+	6.52105i	0.337556	+	0.464606i	0.943726	−	0.330730i	$-0.107295\pi$
$197$	4.73782	+	6.52105i	0.337556	+	0.464606i	−0.606170	+	0.795335i	$0.707295\pi$
$198$	3.45433	−	5.03352i	0.245489	−	0.357717i
$199$	−15.2117			−1.07833			−0.539163	−	0.842201i	$-0.681259\pi$
$199$	−15.2117			−1.07833			−0.539163	+	0.842201i	$0.681259\pi$
$200$	5.36715	+	1.70622i	0.379515	+	0.120648i
$201$	3.58705	−	11.0398i	0.253011	−	0.778688i
$202$	0.359042	+	0.494179i	0.0252621	+	0.0347703i
$203$	−0.118929	−	0.0386424i	−0.00834719	−	0.00271217i
$204$	−0.445113	+	1.36992i	−0.0311641	+	0.0959133i
$205$	−26.0270	−	8.36525i	−1.81780	−	0.584254i
$206$	−10.4651	+	7.60337i	−0.729141	+	0.529752i
$207$	−3.23045	+	4.44634i	−0.224532	+	0.309042i
$208$	18.7108	−	25.7532i	1.29736	−	1.78567i
$209$	3.93508	−	13.3184i	0.272195	−	0.921250i
$210$	0.564048	−	0.412552i	0.0389230	−	0.0284688i
$211$	3.33692	−	10.2700i	0.229723	−	0.707016i	−0.768054	−	0.640385i	$-0.778775\pi$
$211$	3.33692	−	10.2700i	0.229723	−	0.707016i	0.997778	−	0.0666311i	$-0.0212251\pi$
$212$	−1.80083	+	2.47863i	−0.123681	+	0.170233i
$213$		−	2.20708i		−	0.151227i
$214$	−1.10645	−	0.803881i	−0.0756351	−	0.0549521i
$215$	0.998754	+	3.04090i	0.0681144	+	0.207388i
$216$	−1.12637			−0.0766395
$217$	−0.0293453	−	0.0403904i	−0.00199209	−	0.00274188i
$218$	−5.16391	+	7.10751i	−0.349744	+	0.481381i
$219$	−11.8008	−	8.57381i	−0.797427	−	0.579364i
$220$	−9.69035	+	3.47381i	−0.653324	+	0.234204i
$221$	5.51087	−	4.00388i	0.370701	−	0.269330i
$222$			7.04711i			0.472971i
$223$		−	6.72487i		−	0.450331i	−0.974321	−	0.225165i	$-0.927708\pi$
$223$		−	6.72487i		−	0.450331i	0.974321	−	0.225165i	$-0.0722922\pi$
$224$	0.350135	+	1.07760i	0.0233944	+	0.0720005i
$225$	1.51480	−	4.76502i	0.100987	−	0.317668i
$226$	−13.0145	+	9.45561i	−0.865713	+	0.628978i
$227$	−7.99327	−	11.0018i	−0.530532	−	0.730215i	0.456679	−	0.889631i	$-0.349039\pi$
$227$	−7.99327	−	11.0018i	−0.530532	−	0.730215i	−0.987211	+	0.159416i	$0.949039\pi$
$228$	5.52771	−	1.79606i	0.366082	−	0.118947i
$229$	7.24194			0.478561			0.239280	−	0.970951i	$-0.423088\pi$
$229$	7.24194			0.478561			0.239280	+	0.970951i	$0.423088\pi$
$230$	21.4912	−	7.05857i	1.41709	−	0.465428i
$231$	0.159562	−	0.540041i	0.0104984	−	0.0355321i
$232$		−	0.829577i		−	0.0544644i
$233$	−15.5173	+	5.04188i	−1.01657	+	0.330304i	−0.769469	−	0.638685i	$-0.779479\pi$
$233$	−15.5173	+	5.04188i	−1.01657	+	0.330304i	−0.247104	+	0.968989i	$0.579479\pi$
$234$	−9.77506	−	7.10200i	−0.639016	−	0.464272i
$235$	10.9006	−	7.97284i	0.711076	−	0.520090i
$236$	−16.0640	−	11.6712i	−1.04568	−	0.759730i
$237$	−10.5835	+	3.43879i	−0.687472	+	0.223373i
$238$			0.324308i			0.0210218i
$239$	−1.58661			−0.102629			−0.0513145	−	0.998683i	$-0.516341\pi$
$239$	−1.58661			−0.102629			−0.0513145	+	0.998683i	$0.516341\pi$
$240$	8.79288	+	6.34577i	0.567578	+	0.409618i
$241$	6.51807	−	20.0606i	0.419866	−	1.29221i	−0.487960	−	0.872866i	$-0.662259\pi$
$241$	6.51807	−	20.0606i	0.419866	−	1.29221i	0.907825	−	0.419348i	$-0.137741\pi$
$242$	−11.0041	+	16.9961i	−0.707368	+	1.09255i
$243$			1.00000i			0.0641500i
$244$	5.93799	+	18.2752i	0.380141	+	1.16995i
$245$	−9.12225	+	12.6400i	−0.582799	+	0.807543i
$246$	−18.2062	−	13.2276i	−1.16079	−	0.843361i
$247$	−26.1409	−	8.49370i	−1.66331	−	0.540441i
$248$	0.194676	−	0.267949i	0.0123620	−	0.0170148i
$249$	−4.37566	−	13.4669i	−0.277296	−	0.853430i
$250$	−16.5328	+	12.2545i	−1.04563	+	0.775045i
$251$	6.69050	+	4.86093i	0.422301	+	0.306819i	0.778563	−	0.627567i	$-0.215949\pi$
$251$	6.69050	+	4.86093i	0.422301	+	0.306819i	−0.356262	+	0.934386i	$0.615949\pi$
$252$	0.224141	−	0.0728279i	0.0141196	−	0.00458772i
$253$	10.3141	−	15.0294i	0.648444	−	0.944888i
$254$	5.45765	−	3.96522i	0.342444	−	0.248800i
$255$	1.36986	+	1.87289i	0.0857838	+	0.117285i
$256$	−16.9726	+	12.3313i	−1.06079	+	0.770708i
$257$	−2.37472	+	0.771595i	−0.148131	+	0.0481308i	−0.382144	−	0.924103i	$-0.624814\pi$
$257$	−2.37472	+	0.771595i	−0.148131	+	0.0481308i	0.234013	+	0.972233i	$0.424814\pi$
$258$			2.63474i			0.164032i
$259$	0.200873	+	0.618224i	0.0124816	+	0.0384146i
$260$	6.35759	+	19.3569i	0.394281	+	1.20047i
$261$	−0.736508			−0.0455887
$262$	−19.4754	−	26.8056i	−1.20319	−	1.65605i
$263$	−4.74448	−	1.54157i	−0.292557	−	0.0950575i	0.159062	−	0.987269i	$-0.449153\pi$
$263$	−4.74448	−	1.54157i	−0.292557	−	0.0950575i	−0.451618	+	0.892211i	$0.649153\pi$
$264$	3.73438	−	0.100367i	0.229835	−	0.00617719i
$265$	1.54006	+	4.68903i	0.0946054	+	0.288045i
$266$	1.05868	−	0.769180i	0.0649121	−	0.0471614i
$267$	−0.270240	−	0.371954i	−0.0165384	−	0.0227632i
$268$	−15.3240	+	4.97907i	−0.936062	+	0.304145i
$269$	5.18045			0.315858			0.157929	−	0.987450i	$-0.449518\pi$
$269$	5.18045			0.315858			0.157929	+	0.987450i	$0.449518\pi$
$270$	2.40864	−	3.33748i	0.146585	−	0.203113i
$271$	12.8910	+	9.36583i	0.783070	+	0.568934i	0.905899	−	0.423494i	$-0.139197\pi$
$271$	12.8910	+	9.36583i	0.783070	+	0.568934i	−0.122829	+	0.992428i	$0.539197\pi$
$272$	−4.78599	+	1.55506i	−0.290193	+	0.0942894i
$273$	−1.05998	−	0.344408i	−0.0641528	−	0.0208445i
$274$	23.5590			1.42325
$275$	−4.59762	+	15.9330i	−0.277247	+	0.960799i
$276$	7.62879			0.459199
$277$	21.0866	+	6.85147i	1.26697	+	0.411665i	0.863974	−	0.503536i	$-0.167968\pi$
$277$	21.0866	+	6.85147i	1.26697	+	0.411665i	0.402999	+	0.915200i	$0.367968\pi$
$278$	21.1930	−	6.88602i	1.27107	−	0.412996i
$279$	−0.237888	−	0.172836i	−0.0142420	−	0.0103474i
$280$	0.407119	+	0.130851i	0.0243300	+	0.00781983i
$281$	−23.8147			−1.42067			−0.710334	−	0.703865i	$-0.751456\pi$
$281$	−23.8147			−1.42067			−0.710334	+	0.703865i	$0.751456\pi$
$282$	10.5730	−	3.43536i	0.629611	−	0.204573i
$283$	−0.498218	−	0.685738i	−0.0296160	−	0.0407629i	0.793952	−	0.607980i	$-0.208020\pi$
$283$	−0.498218	−	0.685738i	−0.0296160	−	0.0407629i	−0.823568	+	0.567217i	$0.808020\pi$
$284$	−2.47849	+	1.80073i	−0.147071	+	0.106854i
$285$	2.86498	−	8.91387i	0.169707	−	0.528012i
$286$	33.0414	+	22.6751i	1.95378	+	1.34081i
$287$	−1.97423	−	0.641465i	−0.116535	−	0.0378645i
$288$	3.92254	+	5.39891i	0.231138	+	0.318134i
$289$	15.9232			0.936656
$290$	2.45808	+	1.77398i	0.144344	+	0.104172i
$291$	−1.42681	−	4.39125i	−0.0836408	−	0.257420i
$292$			20.2472i			1.18488i
$293$	8.18800	−	2.66044i	0.478348	−	0.155425i	−0.0599118	−	0.998204i	$-0.519082\pi$
$293$	8.18800	−	2.66044i	0.478348	−	0.155425i	0.538260	+	0.842779i	$0.319082\pi$
$294$	−10.3810	+	7.54224i	−0.605433	+	0.439873i
$295$	−30.3897	+	9.98118i	−1.76935	+	0.581126i
$296$	−3.48877	+	2.53474i	−0.202780	+	0.147329i
$297$	−0.0891073	−	3.31543i	−0.00517053	−	0.192381i
$298$	25.6374	−	8.33010i	1.48514	−	0.482550i
$299$	−29.1869	−	21.2055i	−1.68792	−	1.22635i
$300$	−6.58688	+	2.18663i	−0.380294	+	0.126245i
$301$	0.0751016	+	0.231139i	0.00432879	+	0.0133226i
$302$	−12.1030	+	16.6583i	−0.696449	+	0.958580i
$303$	0.315614	+	0.102549i	0.0181316	+	0.00589130i
$304$	16.4276	+	11.9354i	0.942188	+	0.684540i
$305$	29.4703	+	9.47194i	1.68746	+	0.542362i
$306$	0.590249	+	1.81660i	0.0337423	+	0.103848i
$307$			21.6951i			1.23820i	0.785310	+	0.619102i	$0.212503\pi$
$307$			21.6951i			1.23820i	−0.785310	+	0.619102i	$0.787497\pi$
$308$	−0.736634	+	0.261428i	−0.0419736	+	0.0148962i
$309$	−2.17167	+	6.68371i	−0.123542	+	0.380223i
$310$	0.377648	+	1.14982i	0.0214490	+	0.0653057i
$311$	−7.17017			−0.406583			−0.203291	−	0.979118i	$-0.565164\pi$
$311$	−7.17017			−0.406583			−0.203291	+	0.979118i	$0.565164\pi$
$312$		−	7.39376i		−	0.418589i
$313$	12.8673	−	4.18084i	0.727303	−	0.236315i	0.0781165	−	0.996944i	$-0.475109\pi$
$313$	12.8673	−	4.18084i	0.727303	−	0.236315i	0.649187	+	0.760629i	$0.275109\pi$
$314$	13.9466	+	10.1328i	0.787052	+	0.571827i
$315$	0.116171	−	0.361445i	0.00654549	−	0.0203651i
$316$	12.4966	+	9.07930i	0.702988	+	0.510751i
$317$	17.2917	−	5.61840i	0.971196	−	0.315561i	0.219898	−	0.975523i	$-0.429428\pi$
$317$	17.2917	−	5.61840i	0.971196	−	0.315561i	0.751299	+	0.659962i	$0.229428\pi$
$318$			4.06274i			0.227827i
$319$	2.44184	−	0.0656283i	0.136717	−	0.00367448i
$320$	−0.0183838	−	5.77968i	−0.00102768	−	0.323094i
$321$	−0.743014			−0.0414710
$322$	1.63355	−	0.530772i	0.0910340	−	0.0295787i
$323$	2.55402	+	3.51530i	0.142109	+	0.195597i
$324$	1.12297	−	0.815886i	0.0623873	−	0.0453270i
$325$	31.2788	+	9.94356i	1.73504	+	0.551570i
$326$	11.4633	+	35.2805i	0.634895	+	1.95400i
$327$			4.77291i			0.263943i
$328$		−	13.7710i		−	0.760376i
$329$	0.829614	−	0.602750i	0.0457381	−	0.0332307i
$330$	−7.68828	+	11.2798i	−0.423226	+	0.620933i
$331$	−13.4577	−	9.77759i	−0.739702	−	0.537425i	0.152916	−	0.988239i	$-0.451134\pi$
$331$	−13.4577	−	9.77759i	−0.739702	−	0.537425i	−0.892618	+	0.450814i	$0.851134\pi$
$332$	−11.5529	+	15.9012i	−0.634047	+	0.872691i
$333$	2.25037	+	3.09737i	0.123319	+	0.169735i
$334$	−42.2148			−2.30989
$335$	−7.94233	+	24.7111i	−0.433936	+	1.35011i
$336$	0.666117	+	0.483962i	0.0363397	+	0.0264023i
$337$			19.3394i			1.05348i	0.850025	+	0.526742i	$0.176587\pi$
$337$			19.3394i			1.05348i	−0.850025	+	0.526742i	$0.823413\pi$
$338$	32.5544	−	44.8073i	1.77073	−	2.43720i
$339$	−2.70070	+	8.31191i	−0.146682	+	0.451441i
$340$	0.985554	−	3.06638i	0.0534492	−	0.166298i
$341$	0.804103	+	0.551828i	0.0435446	+	0.0298831i
$342$	4.53026	−	6.23537i	0.244968	−	0.337170i
$343$	−1.39430	+	1.91909i	−0.0752851	+	0.103621i
$344$	−1.30437	+	0.947677i	−0.0703267	+	0.0510953i
$345$	7.19185	−	9.96524i	0.387196	−	0.536510i
$346$	8.67141	−	26.6879i	0.466178	−	1.43475i
$347$	−4.09731	−	1.33130i	−0.219955	−	0.0714677i	0.196967	−	0.980410i	$-0.436891\pi$
$347$	−4.09731	−	1.33130i	−0.219955	−	0.0714677i	−0.416921	+	0.908943i	$0.636891\pi$
$348$	0.600906	+	0.827077i	0.0322120	+	0.0443360i
$349$	7.56819	−	23.2925i	0.405116	−	1.24682i	−0.515683	−	0.856780i	$-0.672462\pi$
$349$	7.56819	−	23.2925i	0.405116	−	1.24682i	0.920799	−	0.390038i	$-0.127538\pi$
$350$	−1.25831	+	0.926502i	−0.0672595	+	0.0495236i
$351$	−6.56426			−0.350374
$352$	−13.4860	−	17.5502i	−0.718805	−	0.935428i
$353$	−7.47823	−	10.2929i	−0.398026	−	0.547836i	0.562221	−	0.826987i	$-0.309947\pi$
$353$	−7.47823	−	10.2929i	−0.398026	−	0.547836i	−0.960247	+	0.279151i	$0.909947\pi$
$354$	−26.3307			−1.39946
$355$	0.0156976	+	4.93517i	0.000833141	+	0.261931i
$356$	−0.197208	+	0.606944i	−0.0104520	+	0.0321680i
$357$	0.103562	+	0.142541i	0.00548108	+	0.00754406i
$358$		−	17.1084i		−	0.904208i
$359$	31.5526			1.66528			0.832642	−	0.553812i	$-0.186827\pi$
$359$	31.5526			1.66528			0.832642	+	0.553812i	$0.186827\pi$
$360$	2.51862	−	0.00801112i	0.132743	−	0.000422223i
$361$	−0.453318	+	1.39517i	−0.0238589	+	0.0734300i
$362$	−6.57403	−	2.13603i	−0.345524	−	0.112267i
$363$	0.590858	+	10.9841i	0.0310120	+	0.576517i
$364$	0.478061	+	1.47132i	0.0250572	+	0.0771182i
$365$	26.4483	+	19.0876i	1.38437	+	0.999090i
$366$	20.6148	+	14.9776i	1.07755	+	0.782889i
$367$	9.16660	+	2.97841i	0.478493	+	0.155472i	0.538326	−	0.842737i	$-0.319057\pi$
$367$	9.16660	+	2.97841i	0.478493	+	0.155472i	−0.0598333	+	0.998208i	$0.519057\pi$
$368$	15.6658	+	21.5621i	0.816635	+	1.12400i
$369$	−12.2260			−0.636463
$370$	−0.0501216	−	15.7577i	−0.00260570	−	0.819206i
$371$	0.115806	+	0.356413i	0.00601233	+	0.0185041i
$372$			0.408156i			0.0211619i
$373$	−29.3061	+	9.52212i	−1.51741	+	0.493037i	−0.945039	−	0.326957i	$-0.893977\pi$
$373$	−29.3061	+	9.52212i	−1.51741	+	0.493037i	−0.572372	+	0.819994i	$0.693977\pi$
$374$	−2.11880	−	5.97021i	−0.109561	−	0.308712i
$375$	−3.35330	+	10.6656i	−0.173163	+	0.550770i
$376$	5.50365	+	3.99864i	0.283829	+	0.206214i
$377$		−	4.83463i		−	0.248996i
$378$	0.183696	−	0.252836i	0.00944829	−	0.0130045i
$379$	5.02204	−	15.4562i	0.257965	−	0.793934i	−0.735266	−	0.677778i	$-0.762943\pi$
$379$	5.02204	−	15.4562i	0.257965	−	0.793934i	0.993231	−	0.116155i	$-0.0370571\pi$
$380$	−12.3475	+	4.05541i	−0.633414	+	0.208038i
$381$	1.13254	−	3.48561i	0.0580219	−	0.178573i
$382$	−44.5684	−	14.4811i	−2.28032	−	0.740920i
$383$	−11.2220	+	3.64625i	−0.573418	+	0.186315i	−0.581350	−	0.813654i	$-0.697475\pi$
$383$	−11.2220	+	3.64625i	−0.573418	+	0.186315i	0.00793171	+	0.999969i	$0.497475\pi$
$384$	−2.65419	+	8.16876i	−0.135446	+	0.416860i
$385$	−0.352949	+	1.20870i	−0.0179879	+	0.0616009i
$386$	4.50382	+	13.8613i	0.229239	+	0.705524i
$387$	0.841359	+	1.15803i	0.0427687	+	0.0588660i
$388$	−3.76714	+	5.18502i	−0.191248	+	0.263230i
$389$	16.4315	−	11.9382i	0.833111	−	0.605291i	−0.0873265	−	0.996180i	$-0.527832\pi$
$389$	16.4315	−	11.9382i	0.833111	−	0.605291i	0.920438	+	0.390889i	$0.127832\pi$
$390$	21.9081	+	15.8109i	1.10936	+	0.800618i
$391$	1.76240	+	5.42410i	0.0891283	+	0.274309i
$392$	−7.46778	−	2.42643i	−0.377180	−	0.122553i
$393$	−17.1198	−	5.56254i	−0.863577	−	0.280593i
$394$	−4.58478	−	14.1105i	−0.230978	−	0.710877i
$395$	23.6409	−	7.76460i	1.18950	−	0.390679i
$396$	−3.65043	+	2.80508i	−0.183441	+	0.140960i
$397$	11.2736	+	15.5168i	0.565808	+	0.778768i	0.992050	−	0.125841i	$-0.0401630\pi$
$397$	11.2736	+	15.5168i	0.565808	+	0.778768i	−0.426243	+	0.904609i	$0.640163\pi$
$398$	26.6293	+	8.65237i	1.33480	+	0.433704i
$399$	0.219693	−	0.676144i	0.0109984	−	0.0338495i
$400$	−19.7065	−	14.1270i	−0.985326	−	0.706348i
$401$	−3.93580	+	2.85952i	−0.196544	+	0.142798i	−0.681705	−	0.731627i	$-0.738761\pi$
$401$	−3.93580	+	2.85952i	−0.196544	+	0.142798i	0.485161	+	0.874425i	$0.338761\pi$
$402$	−12.5588	+	17.2858i	−0.626378	+	0.862136i
$403$	1.13454	−	1.56156i	0.0565155	−	0.0777869i
$404$	−0.142345	−	0.438094i	−0.00708195	−	0.0217960i
$405$	−0.00711236	−	2.23606i	−0.000353416	−	0.111111i
$406$	0.186215	+	0.135293i	0.00924172	+	0.00671450i
$407$	−7.73693	−	10.0686i	−0.383505	−	0.499080i
$408$	−0.687029	+	0.945614i	−0.0340130	+	0.0468149i
$409$	−20.2251	+	14.6944i	−1.00007	+	0.726592i	−0.962103	−	0.272687i	$-0.912088\pi$
$409$	−20.2251	+	14.6944i	−1.00007	+	0.726592i	−0.0379653	+	0.999279i	$0.512088\pi$
$410$	40.8042	+	29.4482i	2.01518	+	1.45434i
$411$	10.3547	−	7.52314i	0.510761	−	0.371089i
$412$	9.27745	−	3.01443i	0.457067	−	0.148510i
$413$	−2.30992	+	0.750538i	−0.113664	+	0.0369315i
$414$	8.18424	−	5.94620i	0.402234	−	0.292240i
$415$	9.88000	+	30.0816i	0.484990	+	1.47665i
$416$	−35.4399	+	25.7486i	−1.73758	+	1.26243i
$417$	7.11588	−	9.79416i	0.348466	−	0.479622i
$418$	−14.4641	+	21.0766i	−0.707464	+	1.03089i
$419$	15.5801	+	11.3196i	0.761137	+	0.552998i	0.899259	−	0.437417i	$-0.144107\pi$
$419$	15.5801	+	11.3196i	0.761137	+	0.552998i	−0.138122	+	0.990415i	$0.544107\pi$
$420$	−0.500674	+	0.164441i	−0.0244304	+	0.00802392i
$421$	−6.73317	−	20.7226i	−0.328155	−	1.00996i	−0.969996	−	0.243119i	$-0.921829\pi$
$421$	−6.73317	−	20.7226i	−0.328155	−	1.00996i	0.641842	−	0.766837i	$-0.278171\pi$
$422$	−11.6831	+	16.0804i	−0.568725	+	0.782783i
$423$	3.55004	−	4.88621i	0.172609	−	0.237575i
$424$	−2.01131	+	1.46131i	−0.0976781	+	0.0709673i
$425$	−3.07640	−	4.17815i	−0.149227	−	0.202670i
$426$	−1.25539	+	3.86368i	−0.0608237	+	0.187196i
$427$	2.23541	+	0.726328i	0.108179	+	0.0351495i
$428$	0.606214	+	0.834382i	0.0293025	+	0.0403314i
$429$	21.7633	−	0.584924i	1.05074	−	0.0282404i
$430$	−0.0187393	−	5.89144i	−0.000903687	−	0.284110i
$431$	−5.26351	−	16.1994i	−0.253534	−	0.780298i	−0.994115	−	0.108331i	$-0.965449\pi$
$431$	−5.26351	−	16.1994i	−0.253534	−	0.780298i	0.740581	−	0.671967i	$-0.234551\pi$
$432$	4.61206	+	1.49855i	0.221898	+	0.0720989i
$433$	−14.7305	−	4.78624i	−0.707905	−	0.230012i	−0.0671334	−	0.997744i	$-0.521385\pi$
$433$	−14.7305	−	4.78624i	−0.707905	−	0.230012i	−0.640771	+	0.767732i	$0.721385\pi$
$434$	0.0283974	+	0.0873982i	0.00136312	+	0.00419525i
$435$	1.64687	−	0.00523831i	0.0789615	−	0.000251158i
$436$	5.35984	−	3.89415i	0.256690	−	0.186496i
$437$	13.5267	−	18.6179i	0.647070	−	0.890615i
$438$	15.7816	+	21.7215i	0.754072	+	1.03789i
$439$	−0.0733759	−	0.225828i	−0.00350204	−	0.0107782i	0.949290	−	0.314401i	$-0.101804\pi$
$439$	−0.0733759	−	0.225828i	−0.00350204	−	0.0107782i	−0.952792	+	0.303623i	$0.901804\pi$
$440$	−8.34958	+	0.250988i	−0.398050	+	0.0119654i
$441$	−2.15421	+	6.62998i	−0.102581	+	0.315713i
$442$	−11.9246	+	3.87455i	−0.567197	+	0.184293i
$443$	−16.4961	−	5.35991i	−0.783753	−	0.254657i	−0.110311	−	0.993897i	$-0.535185\pi$
$443$	−16.4961	−	5.35991i	−0.783753	−	0.254657i	−0.673442	+	0.739240i	$0.735185\pi$
$444$	1.64221	−	5.05420i	0.0779357	−	0.239861i
$445$	0.606918	+	0.829788i	0.0287707	+	0.0393357i
$446$	−3.82510	+	11.7724i	−0.181124	+	0.557441i
$447$	8.60817	−	11.8481i	0.407152	−	0.560397i
$448$		−	0.438860i		−	0.0207342i
$449$	−31.1915	−	22.6619i	−1.47202	−	1.06948i	−0.980023	−	0.198884i	$-0.936268\pi$
$449$	−31.1915	−	22.6619i	−1.47202	−	1.06948i	−0.491993	−	0.870599i	$-0.663732\pi$
$450$	−5.36212	+	7.47993i	−0.252773	+	0.352607i
$451$	40.5346	−	1.08943i	1.90870	−	0.0512993i
$452$	11.5375	−	3.74876i	0.542678	−	0.176327i
$453$			11.1866i			0.525593i
$454$	7.73507	+	23.8061i	0.363025	+	1.11728i
$455$	2.37262	+	0.762576i	0.111230	+	0.0357501i
$456$	4.71637			0.220864
$457$	5.19064	+	7.14430i	0.242808	+	0.334196i	0.912976	−	0.408013i	$-0.133778\pi$
$457$	5.19064	+	7.14430i	0.242808	+	0.334196i	−0.670168	+	0.742209i	$0.733778\pi$
$458$	−12.6776	−	4.11920i	−0.592386	−	0.192478i
$459$	0.839527	+	0.609952i	0.0391857	+	0.0284701i
$460$	−17.0584	+	0.0542587i	−0.795352	+	0.00252982i
$461$	4.71859	+	14.5223i	0.219766	+	0.676372i	0.998781	+	0.0493655i	$0.0157199\pi$
$461$	4.71859	+	14.5223i	0.219766	+	0.676372i	−0.779014	+	0.627006i	$0.784280\pi$
$462$	−0.586501	+	0.854627i	−0.0272865	+	0.0397608i
$463$	6.31940	+	2.05330i	0.293688	+	0.0954249i	0.452155	−	0.891939i	$-0.350655\pi$
$463$	6.31940	+	2.05330i	0.293688	+	0.0954249i	−0.158468	+	0.987364i	$0.550655\pi$
$464$	−1.10369	+	3.39682i	−0.0512376	+	0.157693i
$465$	0.533161	+	0.384779i	0.0247248	+	0.0178437i
$466$	30.0321			1.39121
$467$		−	20.2368i		−	0.936445i	−0.883611	−	0.468223i	$-0.844895\pi$
$467$		−	20.2368i		−	0.936445i	0.883611	−	0.468223i	$-0.155105\pi$
$468$	5.35569	+	7.37147i	0.247567	+	0.340746i
$469$	−0.609034	+	1.87442i	−0.0281226	+	0.0865524i
$470$	−23.6173	+	7.75686i	−1.08938	+	0.357797i
$471$	9.36558			0.431543
$472$	−9.47073	−	13.0353i	−0.435926	−	0.600001i
$473$	−2.89265	−	3.76440i	−0.133004	−	0.173087i
$474$	20.4833			0.940828
$475$	−6.34285	+	19.9523i	−0.291030	+	0.915474i
$476$	0.0755743	−	0.232594i	0.00346394	−	0.0106609i
$477$	1.29736	+	1.78567i	0.0594022	+	0.0817601i
$478$	2.77748	+	0.902459i	0.127039	+	0.0412775i
$479$	−7.80533	+	24.0223i	−0.356635	+	1.09761i	0.598421	+	0.801182i	$0.295795\pi$
$479$	−7.80533	+	24.0223i	−0.356635	+	1.09761i	−0.955056	+	0.296427i	$0.904205\pi$
$480$	−8.80942	−	12.0444i	−0.402093	−	0.549748i
$481$	−20.3319	+	14.7720i	−0.927056	+	0.673546i
$482$	−22.8208	+	31.4102i	−1.03946	+	1.43069i
$483$	0.548489	−	0.754930i	0.0249571	−	0.0343505i
$484$	11.8528	−	9.62530i	0.538762	−	0.437514i
$485$	3.22165	+	9.80895i	0.146288	+	0.445401i
$486$	0.568798	−	1.75058i	0.0258012	−	0.0794080i
$487$	−7.12353	+	9.80470i	−0.322798	+	0.444293i	−0.939319	−	0.343045i	$-0.888542\pi$
$487$	−7.12353	+	9.80470i	−0.322798	+	0.444293i	0.616521	+	0.787338i	$0.288542\pi$
$488$			15.5929i			0.705855i
$489$	16.3046	+	11.8460i	0.737319	+	0.535693i
$490$	23.1589	−	16.9387i	1.04621	−	0.765213i
$491$	−17.0511			−0.769506			−0.384753	−	0.923019i	$-0.625713\pi$
$491$	−17.0511			−0.769506			−0.384753	+	0.923019i	$0.625713\pi$
$492$	9.97506	+	13.7295i	0.449710	+	0.618973i
$493$	−0.449234	+	0.618318i	−0.0202325	+	0.0278476i
$494$	40.9306	+	29.7378i	1.84155	+	1.33797i
$495$	0.222830	+	7.41285i	0.0100154	+	0.333183i
$496$	−1.15362	+	0.838151i	−0.0517989	+	0.0376341i
$497$			0.374734i			0.0168091i
$498$			26.0638i			1.16795i
$499$	−8.26293	−	25.4307i	−0.369900	−	1.13843i	−0.946856	−	0.321659i	$-0.895760\pi$
$499$	−8.26293	−	25.4307i	−0.369900	−	1.13843i	0.576956	−	0.816775i	$-0.304240\pi$
$500$	14.7131	−	4.93628i	0.657989	−	0.220757i
$501$	−18.5544	+	13.4805i	−0.828949	+	0.602267i
$502$	−8.94737	−	12.3150i	−0.399341	−	0.549646i
$503$	21.2717	−	6.91161i	0.948460	−	0.308173i	0.206370	−	0.978474i	$-0.433835\pi$
$503$	21.2717	−	6.91161i	0.948460	−	0.308173i	0.742090	+	0.670301i	$0.233835\pi$
$504$	0.191242			0.00851861
$505$	−0.706461	−	0.227061i	−0.0314371	−	0.0101041i
$506$	−26.6044	+	20.4435i	−1.18271	+	0.908823i
$507$		−	30.0895i		−	1.33632i
$508$	−4.83826	+	1.57205i	−0.214663	+	0.0697483i
$509$	19.1469	+	13.9110i	0.848672	+	0.616596i	0.924779	−	0.380504i	$-0.124249\pi$
$509$	19.1469	+	13.9110i	0.848672	+	0.616596i	−0.0761078	+	0.997100i	$0.524249\pi$
$510$	−1.33275	−	4.05782i	−0.0590152	−	0.179683i
$511$	2.00363	+	1.45572i	0.0886353	+	0.0643973i
$512$	20.3885	−	6.62462i	0.901052	−	0.292770i
$513$		−	4.18725i		−	0.184871i
$514$	4.59603			0.202722
$515$	4.80844	−	14.9606i	0.211885	−	0.659243i
$516$	0.613982	−	1.88964i	0.0270290	−	0.0831868i
$517$	−11.3345	+	16.5162i	−0.498490	+	0.726382i
$518$		−	1.19651i		−	0.0525715i
$519$	−4.71101	−	14.4990i	−0.206790	−	0.636435i
$520$	0.0525871	+	16.5329i	0.00230609	+	0.725014i
$521$	−8.39742	−	6.10108i	−0.367898	−	0.267293i	0.388441	−	0.921474i	$-0.373014\pi$
$521$	−8.39742	−	6.10108i	−0.367898	−	0.267293i	−0.756339	+	0.654180i	$0.773014\pi$
$522$	1.28932	+	0.418925i	0.0564319	+	0.0183358i
$523$	−22.1299	+	30.4592i	−0.967672	+	1.33189i	−0.0244586	+	0.999701i	$0.507786\pi$
$523$	−22.1299	+	30.4592i	−0.967672	+	1.33189i	−0.943214	+	0.332186i	$0.892214\pi$
$524$	7.72119	+	23.7634i	0.337302	+	1.03811i
$525$	−0.257194	+	0.809038i	−0.0112249	+	0.0353093i
$526$	7.42875	+	5.39730i	0.323909	+	0.235334i
$527$	−0.290201	+	0.0942920i	−0.0126413	+	0.00410742i
$528$	−15.4245	−	4.55736i	−0.671264	−	0.198334i
$529$	5.82957	−	4.23543i	0.253460	−	0.184149i
$530$	−0.0288957	−	9.08452i	−0.00125515	−	0.394606i
$531$	−11.5729	+	8.40823i	−0.502222	+	0.364886i
$532$	−0.938534	+	0.304948i	−0.0406906	+	0.0132212i
$533$		−	80.2550i		−	3.47623i
$534$	0.261511	+	0.804848i	0.0113167	+	0.0348292i
$535$	1.66142	−	0.00528458i	0.0718295	−	0.000228472i
$536$	−13.0748			−0.564744
$537$	−5.46327	−	7.51954i	−0.235757	−	0.324492i
$538$	−9.06881	−	2.94663i	−0.390984	−	0.127038i
$539$	6.55135	−	22.1732i	0.282187	−	0.955066i
$540$	−2.50522	+	1.83235i	−0.107808	+	0.0788520i
$541$	−12.2679	+	8.91312i	−0.527437	+	0.383205i	−0.819398	−	0.573225i	$-0.805692\pi$
$541$	−12.2679	+	8.91312i	−0.527437	+	0.383205i	0.291961	+	0.956430i	$0.405692\pi$
$542$	−17.2394	−	23.7280i	−0.740496	−	1.01921i
$543$	−3.57154	+	1.16046i	−0.153270	+	0.0498003i
$544$	6.92509			0.296911
$545$	−0.0339467	−	10.6725i	−0.00145412	−	0.457160i
$546$	1.65968	+	1.20583i	0.0710277	+	0.0516046i
$547$	−10.4861	+	3.40715i	−0.448354	+	0.145679i	−0.524487	−	0.851419i	$-0.675743\pi$
$547$	−10.4861	+	3.40715i	−0.448354	+	0.145679i	0.0761327	+	0.997098i	$0.475743\pi$
$548$	−16.8965	−	5.49002i	−0.721784	−	0.234522i
$549$	13.8435			0.590827
$550$	17.1112	−	25.2770i	0.729624	−	1.07781i
$551$	3.08394			0.131380
$552$	5.88749	+	1.91296i	0.250588	+	0.0814211i
$553$	1.79694	−	0.583862i	0.0764137	−	0.0248283i
$554$	−33.0168	−	23.9881i	−1.40275	−	1.01916i
$555$	−5.05398	−	6.90988i	−0.214530	−	0.293308i
$556$	−16.8043			−0.712661
$557$	2.99540	−	0.973265i	0.126919	−	0.0412385i	−0.244869	−	0.969556i	$-0.578745\pi$
$557$	2.99540	−	0.973265i	0.126919	−	0.0412385i	0.371788	+	0.928318i	$0.378745\pi$
$558$	0.318134	+	0.437874i	0.0134677	+	0.0185367i
$559$	−7.60162	+	5.52290i	−0.321514	+	0.233594i
$560$	−1.49292	−	1.07743i	−0.0630873	−	0.0455297i
$561$	−2.83774	−	1.94744i	−0.119810	−	0.0822211i
$562$	41.6896	+	13.5458i	1.75857	+	0.571394i
$563$	−14.1738	−	19.5086i	−0.597354	−	0.822188i	0.398108	−	0.917338i	$-0.369667\pi$
$563$	−14.1738	−	19.5086i	−0.597354	−	0.822188i	−0.995463	+	0.0951505i	$0.969667\pi$
$564$	−8.38349			−0.353009
$565$	5.97981	−	18.6051i	0.251573	−	0.782723i
$566$	0.482124	+	1.48383i	0.0202652	+	0.0623698i
$567$		−	0.169787i		−	0.00713038i
$568$	−2.36431	+	0.768211i	−0.0992043	+	0.0322334i
$569$	12.0524	−	8.75661i	0.505264	−	0.367096i	−0.305760	−	0.952109i	$-0.598910\pi$
$569$	12.0524	−	8.75661i	0.505264	−	0.367096i	0.811024	+	0.585013i	$0.198910\pi$
$570$	−10.0856	+	13.9749i	−0.422438	+	0.585342i
$571$	−20.2290	+	14.6972i	−0.846558	+	0.615060i	−0.924195	−	0.381921i	$-0.875263\pi$
$571$	−20.2290	+	14.6972i	−0.846558	+	0.615060i	0.0776369	+	0.996982i	$0.475263\pi$
$572$	−18.4132	−	23.9623i	−0.769897	−	1.00192i
$573$	−24.2131	+	7.86732i	−1.01152	+	0.328662i
$574$	3.09118	+	2.24587i	0.129023	+	0.0937410i
$575$	−16.0105	+	22.3340i	−0.667685	+	0.931392i
$576$	−0.798737	−	2.45826i	−0.0332807	−	0.102427i
$577$	11.5147	−	15.8486i	0.479362	−	0.659785i	−0.499020	−	0.866590i	$-0.666307\pi$
$577$	11.5147	−	15.8486i	0.479362	−	0.659785i	0.978382	+	0.206806i	$0.0663067\pi$
$578$	−27.8748	−	9.05707i	−1.15944	−	0.376724i
$579$	6.40591	+	4.65416i	0.266220	+	0.193420i
$580$	−1.34954	−	1.84512i	−0.0560367	−	0.0766143i
$581$	0.742930	+	2.28650i	0.0308219	+	0.0948602i
$582$			8.49881i			0.352287i
$583$	−4.46043	−	5.80465i	−0.184732	−	0.240404i
$584$	−5.07711	+	15.6257i	−0.210092	+	0.646598i
$585$	14.6781	−	0.0466874i	0.606863	−	0.00193029i
$586$	−15.8470			−0.654634
$587$			35.4324i			1.46245i	0.682135	+	0.731226i	$0.261052\pi$
$587$			35.4324i			1.46245i	−0.682135	+	0.731226i	$0.738948\pi$
$588$	9.20286	−	2.99019i	0.379520	−	0.123313i
$589$	0.996097	+	0.723707i	0.0410435	+	0.0298198i
$590$	58.8769	−	0.187273i	2.42392	−	0.00770991i
$591$	−6.52105	−	4.73782i	−0.268240	−	0.194888i
$592$	17.6575	−	5.73727i	0.725719	−	0.235801i
$593$		−	14.2924i		−	0.586919i	−0.955971	−	0.293460i	$-0.905193\pi$
$593$		−	14.2924i		−	0.586919i	0.955971	−	0.293460i	$-0.0948066\pi$
$594$	−1.72982	+	5.85461i	−0.0709754	+	0.240218i
$595$	−0.232584	−	0.317993i	−0.00953502	−	0.0130364i
$596$	−20.3284			−0.832683
$597$	14.4672	−	4.70066i	0.592101	−	0.192385i
$598$	39.0324	+	53.7235i	1.59615	+	2.19692i
$599$	−0.110576	+	0.0803381i	−0.00451801	+	0.00328253i	−0.590042	−	0.807373i	$-0.700889\pi$
$599$	−0.110576	+	0.0803381i	−0.00451801	+	0.00328253i	0.585524	+	0.810655i	$0.300889\pi$
$600$	−5.63171	+	0.0358266i	−0.229914	+	0.00146262i
$601$	−6.36934	−	19.6028i	−0.259811	−	0.799616i	−0.992844	−	0.119422i	$-0.961896\pi$
$601$	−6.36934	−	19.6028i	−0.259811	−	0.799616i	0.733033	−	0.680193i	$-0.238104\pi$
$602$		−	0.447345i		−	0.0182324i
$603$			11.6079i			0.472712i
$604$	12.5622	−	9.12699i	0.511150	−	0.371372i
$605$	−1.39931	−	24.5569i	−0.0568902	−	0.998380i
$606$	−0.494179	−	0.359042i	−0.0200746	−	0.0145851i
$607$	16.5997	−	22.8475i	0.673759	−	0.927350i	−0.326079	−	0.945343i	$-0.605727\pi$
$607$	16.5997	−	22.8475i	0.673759	−	0.927350i	0.999838	+	0.0179925i	$0.00572749\pi$
$608$	−16.4246	−	22.6066i	−0.666107	−	0.916818i
$609$	0.125049			0.00506726
$610$	−46.2025	−	33.3440i	−1.87068	−	1.35006i
$611$	32.0743	+	23.3034i	1.29759	+	0.942753i
$612$		−	1.44041i		−	0.0582253i
$613$	25.4451	−	35.0221i	1.02772	−	1.41453i	0.121068	−	0.992644i	$-0.461368\pi$
$613$	25.4451	−	35.0221i	1.02772	−	1.41453i	0.906649	−	0.421886i	$-0.138632\pi$
$614$	12.3401	−	37.9790i	0.498008	−	1.53271i
$615$	27.3381	−	0.0869561i	1.10238	−	0.00350641i
$616$	−0.634050	+	0.0170411i	−0.0255466	+	0.000686605i
$617$	16.9406	−	23.3167i	0.682003	−	0.938696i	−0.317953	−	0.948106i	$-0.602995\pi$
$617$	16.9406	−	23.3167i	0.682003	−	0.938696i	0.999956	+	0.00941037i	$0.00299546\pi$
$618$	7.60337	−	10.4651i	0.305852	−	0.420970i
$619$	−19.8287	+	14.4064i	−0.796981	+	0.579041i	−0.910027	−	0.414549i	$-0.863939\pi$
$619$	−19.8287	+	14.4064i	−0.796981	+	0.579041i	0.113046	+	0.993590i	$0.463939\pi$
$620$	−0.00290295	−	0.912660i	−0.000116585	−	0.0366533i
$621$	1.69835	−	5.22698i	0.0681524	−	0.209752i
$622$	12.5520	+	4.07838i	0.503288	+	0.163528i
$623$	0.0458833	+	0.0631529i	0.00183828	+	0.00253017i
$624$	−9.83686	+	30.2747i	−0.393790	+	1.21196i
$625$	7.42230	−	23.8728i	0.296892	−	0.954911i
$626$	−24.9033			−0.995337
$627$	0.373114	+	13.8825i	0.0149008	+	0.554414i
$628$	−7.64124	−	10.5173i	−0.304919	−	0.419685i
$629$	3.97294			0.158411
$630$	−0.408956	+	0.566661i	−0.0162932	+	0.0225763i
$631$	2.16032	−	6.64878i	0.0860010	−	0.264684i	−0.898803	−	0.438352i	$-0.855562\pi$
$631$	2.16032	−	6.64878i	0.0860010	−	0.264684i	0.984804	+	0.173669i	$0.0555622\pi$
$632$	7.36752	+	10.1405i	0.293064	+	0.403368i
$633$			10.7985i			0.429202i
$634$	−33.4662			−1.32911
$635$	−2.50764	+	7.80207i	−0.0995126	+	0.309616i
$636$	0.946752	−	2.91380i	0.0375411	−	0.115540i
$637$	−43.5209	−	14.1408i	−1.72436	−	0.560279i
$638$	−4.31197	−	1.27403i	−0.170712	−	0.0504392i
$639$	0.682027	+	2.09906i	0.0269806	+	0.0830376i
$640$	5.87682	−	18.2847i	0.232302	−	0.722766i
$641$	28.7440	+	20.8837i	1.13532	+	0.824858i	0.986460	−	0.164001i	$-0.0524400\pi$
$641$	28.7440	+	20.8837i	1.13532	+	0.824858i	0.148859	+	0.988858i	$0.452440\pi$
$642$	1.30071	+	0.422625i	0.0513348	+	0.0166797i
$643$	−17.8094	−	24.5126i	−0.702336	−	0.966682i	−0.999928	−	0.0119894i	$-0.996184\pi$
$643$	−17.8094	−	24.5126i	−0.702336	−	0.966682i	0.297592	−	0.954693i	$-0.403816\pi$
$644$	−1.29527			−0.0510407
$645$	−1.88956	−	2.58344i	−0.0744014	−	0.101723i
$646$	−2.47152	−	7.60655i	−0.0972406	−	0.299276i
$647$			3.20788i			0.126115i	0.998010	+	0.0630574i	$0.0200851\pi$
$647$			3.20788i			0.126115i	−0.998010	+	0.0630574i	$0.979915\pi$
$648$	1.07124	−	0.348066i	0.0420822	−	0.0136733i
$649$	37.6200	−	28.9081i	1.47671	−	1.13474i
$650$	−49.1002	−	35.1984i	−1.92587	−	1.38059i
$651$	0.0403904	+	0.0293453i	0.00158302	+	0.00115013i
$652$		−	27.9745i		−	1.09557i
$653$	−1.24524	+	1.71393i	−0.0487300	+	0.0670711i	−0.832687	−	0.553744i	$-0.813198\pi$
$653$	−1.24524	+	1.71393i	−0.0487300	+	0.0670711i	0.783957	+	0.620816i	$0.213198\pi$
$654$	2.71483	−	8.35538i	0.106158	−	0.326721i
$655$	38.3203	+	12.3164i	1.49730	+	0.481242i
$656$	−18.3213	+	56.3872i	−0.715327	+	2.20155i
$657$	13.8727	+	4.50752i	0.541226	+	0.175855i
$658$	−1.79515	+	0.583280i	−0.0699823	+	0.0227386i
$659$	11.7034	−	36.0195i	0.455901	−	1.40312i	−0.414172	−	0.910198i	$-0.635929\pi$
$659$	11.7034	−	36.0195i	0.455901	−	1.40312i	0.870074	−	0.492922i	$-0.164071\pi$
$660$	8.14261	−	6.29827i	0.316951	−	0.245160i
$661$	−5.41391	−	16.6623i	−0.210577	−	0.648088i	−0.999438	−	0.0335171i	$-0.989329\pi$
$661$	−5.41391	−	16.6623i	−0.210577	−	0.648088i	0.788862	−	0.614571i	$-0.210671\pi$
$662$	17.9973	+	24.7712i	0.699486	+	0.962760i
$663$	−4.00388	+	5.51087i	−0.155498	+	0.214025i
$664$	−12.9032	+	9.37474i	−0.500742	+	0.363810i
$665$	−0.486436	+	1.51346i	−0.0188632	+	0.0586894i
$666$	−2.17768	−	6.70220i	−0.0843833	−	0.259705i
$667$	3.84971	+	1.25085i	0.149062	+	0.0484330i
$668$	30.2765	+	9.83744i	1.17143	+	0.380622i
$669$	2.07810	+	6.39573i	0.0803440	+	0.247273i
$670$	27.9593	−	38.7413i	1.08016	−	1.49671i
$671$	−45.8972	+	1.23356i	−1.77184	+	0.0476210i
$672$	−0.665996	−	0.916665i	−0.0256914	−	0.0353611i
$673$	24.7789	+	8.05116i	0.955158	+	0.310350i	0.744810	−	0.667277i	$-0.232540\pi$
$673$	24.7789	+	8.05116i	0.955158	+	0.310350i	0.210348	+	0.977627i	$0.432540\pi$
$674$	11.0002	−	33.8552i	0.423713	−	1.30405i
$675$	0.0318073	+	4.99990i	0.00122426	+	0.192446i
$676$	−33.7896	+	24.5496i	−1.29960	+	0.944216i
$677$	−18.0136	+	24.7936i	−0.692320	+	0.952896i	0.307679	+	0.951490i	$0.400448\pi$
$677$	−18.0136	+	24.7936i	−0.692320	+	0.952896i	−0.999999	+	0.00140604i	$0.999552\pi$
$678$	9.45561	−	13.0145i	0.363140	−	0.499820i
$679$	0.242253	+	0.745578i	0.00929682	+	0.0286127i
$680$	1.52951	−	2.11933i	0.0586540	−	0.0812727i
$681$	11.0018	+	7.99327i	0.421590	+	0.306303i
$682$	−1.09377	−	1.42339i	−0.0418826	−	0.0545045i
$683$	−5.48949	+	7.55563i	−0.210049	+	0.289108i	−0.901023	−	0.433772i	$-0.857182\pi$
$683$	−5.48949	+	7.55563i	−0.210049	+	0.289108i	0.690973	+	0.722880i	$0.257182\pi$
$684$	−4.70215	+	3.41631i	−0.179791	+	0.130626i
$685$	−23.1002	+	16.8958i	−0.882614	+	0.645556i
$686$	3.53241	−	2.56645i	0.134868	−	0.0979873i
$687$	−6.88749	+	2.23788i	−0.262774	+	0.0853805i
$688$	6.60172	−	2.14503i	0.251688	−	0.0817785i
$689$	−11.7216	+	8.51623i	−0.446557	+	0.324443i
$690$	−18.2581	+	13.3542i	−0.695075	+	0.508388i
$691$	−5.99100	+	4.35272i	−0.227908	+	0.165585i	−0.695879	−	0.718159i	$-0.744985\pi$
$691$	−5.99100	+	4.35272i	−0.227908	+	0.165585i	0.467971	+	0.883744i	$0.344985\pi$
$692$	−12.4383	+	17.1198i	−0.472833	+	0.650799i
$693$	0.0151293	+	0.562917i	0.000574713	+	0.0213834i
$694$	6.41543	+	4.66108i	0.243526	+	0.176932i
$695$	−15.8418	+	21.9509i	−0.600915	+	0.832646i
$696$	0.256353	+	0.788975i	0.00971705	+	0.0299060i
$697$	−7.45730	+	10.2641i	−0.282465	+	0.388780i
$698$	−26.4975	+	36.4706i	−1.00294	+	1.38043i
$699$	13.1998	−	9.59022i	0.499263	−	0.362736i
$700$	1.11837	−	0.371261i	0.0422703	−	0.0140324i
$701$	2.56749	−	7.90192i	0.0969727	−	0.298451i	−0.890790	−	0.454415i	$-0.849848\pi$
$701$	2.56749	−	7.90192i	0.0969727	−	0.298451i	0.987763	+	0.155964i	$0.0498483\pi$
$702$	11.4913	+	3.73374i	0.433710	+	0.140921i
$703$	−9.42285	−	12.9694i	−0.355389	−	0.489152i
$704$	2.86720	+	8.07901i	0.108062	+	0.304489i
$705$	−7.90333	+	10.9511i	−0.297657	+	0.412442i
$706$	7.23667	+	22.2722i	0.272356	+	0.838225i
$707$	−0.0535872	−	0.0174115i	−0.00201535	−	0.000654828i
$708$	18.8844	+	6.13591i	0.709718	+	0.230602i
$709$	10.2149	+	31.4382i	0.383628	+	1.18069i	0.937470	+	0.348065i	$0.113161\pi$
$709$	10.2149	+	31.4382i	0.383628	+	1.18069i	−0.553842	+	0.832622i	$0.686839\pi$
$710$	2.77964	−	8.64834i	0.104318	−	0.324566i
$711$	9.00287	−	6.54096i	0.337634	−	0.245305i
$712$	−0.304389	+	0.418956i	−0.0114075	+	0.0157010i
$713$	0.949902	+	1.30743i	0.0355741	+	0.0489636i
$714$	−0.100217	−	0.308435i	−0.00375051	−	0.0115429i
$715$	−48.6599	+	1.46271i	−1.81978	+	0.0547023i
$716$	−3.98682	+	12.2702i	−0.148995	+	0.458558i
$717$	1.50895	−	0.490288i	0.0563528	−	0.0183101i
$718$	−55.2354	−	17.9471i	−2.06137	−	0.669779i
$719$	6.90112	−	21.2395i	0.257368	−	0.792098i	−0.735986	−	0.676997i	$-0.763281\pi$
$719$	6.90112	−	21.2395i	0.257368	−	0.792098i	0.993354	−	0.115101i	$-0.0367191\pi$
$720$	−10.3235	−	3.31804i	−0.384733	−	0.123656i
$721$	0.368721	−	1.13481i	0.0137319	−	0.0422624i
$722$	1.58714	−	2.18451i	0.0590673	−	0.0812991i
$723$			21.0929i			0.784454i
$724$	4.21714	+	3.06393i	0.156729	+	0.113870i
$725$	−3.68247	+	0.0234263i	−0.136763	+	0.000870032i
$726$	5.21341	−	19.5647i	0.193488	−	0.726113i
$727$	40.3074	−	13.0967i	1.49492	−	0.485729i	0.556388	−	0.830923i	$-0.312187\pi$
$727$	40.3074	−	13.0967i	1.49492	−	0.485729i	0.938531	+	0.345194i	$0.112187\pi$
$728$			1.25536i			0.0465269i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−35.4430	−	48.4582i	−1.31180	−	1.79352i
$731$	1.48539			0.0549390
$732$	−11.2947	−	15.5459i	−0.417465	−	0.574591i
$733$	−12.6821	−	4.12068i	−0.468425	−	0.152201i	0.0652872	−	0.997867i	$-0.479204\pi$
$733$	−12.6821	−	4.12068i	−0.468425	−	0.152201i	−0.533713	+	0.845666i	$0.679204\pi$
$734$	−14.3528	−	10.4279i	−0.529770	−	0.384901i
$735$	4.76978	−	14.8403i	0.175936	−	0.547394i
$736$	−11.3338	−	34.8819i	−0.417770	−	1.28576i
$737$	−1.03435	−	38.4853i	−0.0381009	−	1.41762i
$738$	21.4027	+	6.95416i	0.787844	+	0.255986i
$739$	7.65463	−	23.5585i	0.281580	−	0.866614i	−0.705823	−	0.708388i	$-0.749423\pi$
$739$	7.65463	−	23.5585i	0.281580	−	0.866614i	0.987403	−	0.158226i	$-0.0505774\pi$
$740$	−3.63612	+	11.3131i	−0.133666	+	0.415880i
$741$	27.4862			1.00973
$742$		−	0.689801i		−	0.0253234i
$743$	10.1482	+	13.9678i	0.372303	+	0.512431i	0.953525	−	0.301314i	$-0.0974253\pi$
$743$	10.1482	+	13.9678i	0.372303	+	0.512431i	−0.581222	+	0.813745i	$0.697425\pi$
$744$	−0.102347	+	0.314993i	−0.00375224	+	0.0115482i
$745$	−19.1641	+	26.5543i	−0.702117	+	0.972874i
$746$	56.7188			2.07662
$747$	8.32300	+	11.4556i	0.304523	+	0.419139i
$748$	0.128352	+	4.77559i	0.00469300	+	0.174613i
$749$	0.126154			0.00460957
$750$	11.9368	−	16.7637i	0.435870	−	0.612123i
$751$	−1.49197	+	4.59180i	−0.0544426	+	0.167557i	−0.974581	−	0.224037i	$-0.928076\pi$
$751$	−1.49197	+	4.59180i	−0.0544426	+	0.167557i	0.920138	+	0.391594i	$0.128076\pi$
$752$	−17.2156	−	23.6952i	−0.627787	−	0.864074i
$753$	−7.86515	−	2.55554i	−0.286622	−	0.0931292i
$754$	−2.74993	+	8.46342i	−0.100147	+	0.308219i
$755$	−0.0795632	−	25.0139i	−0.00289560	−	0.910348i
$756$	−0.190666	+	0.138527i	−0.00693445	+	0.00503817i
$757$	27.7779	−	38.2329i	1.00960	−	1.38960i	0.0903603	−	0.995909i	$-0.471198\pi$
$757$	27.7779	−	38.2329i	1.00960	−	1.38960i	0.919243	−	0.393691i	$-0.128802\pi$
$758$	−17.5830	+	24.2009i	−0.638642	+	0.879016i
$759$	−5.16499	+	17.4810i	−0.187477	+	0.634521i
$760$	−10.5461	+	0.0335445i	−0.382546	+	0.00121679i
$761$	3.00956	−	9.26247i	0.109096	−	0.335764i	−0.881574	−	0.472047i	$-0.843515\pi$
$761$	3.00956	−	9.26247i	0.109096	−	0.335764i	0.990670	+	0.136282i	$0.0435154\pi$
$762$	−3.96522	+	5.45765i	−0.143645	+	0.197710i
$763$		−	0.810379i		−	0.0293377i
$764$	28.5899	+	20.7718i	1.03435	+	0.751497i
$765$	−1.88157	−	1.35792i	−0.0680282	−	0.0490956i
$766$	21.7190			0.784741
$767$	−55.1938	−	75.9677i	−1.99293	−	2.74304i
$768$	12.3313	−	16.9726i	0.444969	−	0.612447i
$769$	0.0643186	+	0.0467302i	0.00231939	+	0.00168513i	0.588944	−	0.808174i	$-0.299544\pi$
$769$	0.0643186	+	0.0467302i	0.00231939	+	0.00168513i	−0.586625	+	0.809859i	$0.699544\pi$
$770$	1.30537	−	1.91517i	0.0470423	−	0.0690178i
$771$	2.02006	−	1.46766i	0.0727507	−	0.0528565i
$772$		−	10.9909i		−	0.395572i
$773$		−	28.5769i		−	1.02784i	−0.857839	−	0.513919i	$-0.828193\pi$
$773$		−	28.5769i		−	1.02784i	0.857839	−	0.513919i	$-0.171807\pi$
$774$	−0.814181	−	2.50579i	−0.0292651	−	0.0900688i
$775$	−1.19492	−	0.856596i	−0.0429226	−	0.0307698i
$776$	−4.20745	+	3.05689i	−0.151039	+	0.109736i
$777$	−0.382083	−	0.525893i	−0.0137072	−	0.0188663i
$778$	−35.5552	+	11.5526i	−1.27471	+	0.414180i
$779$	51.1935			1.83420
$780$	−12.0280	−	16.4449i	−0.430673	−	0.588823i
$781$	−2.44825	−	6.89852i	−0.0876053	−	0.246848i
$782$		−	10.4978i		−	0.375400i
$783$	0.700461	−	0.227593i	0.0250324	−	0.00813353i
$784$	27.3496	+	19.8707i	0.976773	+	0.709667i
$785$	−20.9420	+	0.0666113i	−0.747451	+	0.00237746i
$786$	26.8056	+	19.4754i	0.956123	+	0.694664i
$787$	16.5535	−	5.37857i	0.590070	−	0.191725i	0.00126306	−	0.999999i	$-0.499598\pi$
$787$	16.5535	−	5.37857i	0.590070	−	0.191725i	0.588807	+	0.808274i	$0.299598\pi$
$788$			11.1885i			0.398573i
$789$	4.98864			0.177600
$790$	−45.8017	+	0.145684i	−1.62955	+	0.00518322i
$791$	0.458545	−	1.41126i	0.0163040	−	0.0501785i
$792$	−3.52059	+	1.24944i	−0.125099	+	0.0443970i
$793$			90.8724i			3.22697i
$794$	−10.9095	−	33.5759i	−0.387163	−	1.19156i
$795$	−2.91368	−	3.98363i	−0.103338	−	0.141285i
$796$	−17.0822	−	12.4110i	−0.605464	−	0.439896i
$797$	38.6615	+	12.5619i	1.36946	+	0.444965i	0.899191	−	0.437557i	$-0.144156\pi$
$797$	38.6615	+	12.5619i	1.36946	+	0.444965i	0.470271	+	0.882522i	$0.344156\pi$
$798$	−0.769180	+	1.05868i	−0.0272287	+	0.0374770i
$799$	−1.93675	−	5.96070i	−0.0685173	−	0.210874i
$800$	19.7840	+	26.8693i	0.699471	+	0.949971i
$801$	0.371954	+	0.270240i	0.0131423	+	0.00954847i
$802$	8.51643	−	2.76716i	0.300726	−	0.0977116i
$803$	−46.3956	−	13.7082i	−1.63727	−	0.483752i
$804$	13.0354	−	9.47075i	0.459722	−	0.334008i
$805$	−1.22108	+	1.69197i	−0.0430375	+	0.0596340i
$806$	−2.87432	+	2.08832i	−0.101244	+	0.0735578i
$807$	−4.92690	+	1.60085i	−0.173435	+	0.0563525i
$808$		−	0.373792i		−	0.0131499i
$809$	−13.6739	−	42.0839i	−0.480748	−	1.47959i	−0.838046	−	0.545600i	$-0.816302\pi$
$809$	−13.6739	−	42.0839i	−0.480748	−	1.47959i	0.357297	−	0.933991i	$-0.383698\pi$
$810$	−1.25941	+	3.91845i	−0.0442513	+	0.137680i
$811$	48.8543			1.71551			0.857754	−	0.514061i	$-0.171859\pi$
$811$	48.8543			1.71551			0.857754	+	0.514061i	$0.171859\pi$
$812$	−0.102026	−	0.140427i	−0.00358041	−	0.00492802i
$813$	−15.1542	−	4.92391i	−0.531482	−	0.172689i
$814$	7.81714	+	22.0266i	0.273991	+	0.772032i
$815$	−36.5422	−	26.3723i	−1.28002	−	0.923782i
$816$	4.07120	−	2.95790i	0.142521	−	0.103547i
$817$	−3.52298	−	4.84896i	−0.123253	−	0.169644i
$818$	43.7639	−	14.2198i	1.53017	−	0.497182i
$819$	1.11453			0.0389447
$820$	−22.4024	−	30.6290i	−0.782327	−	1.06961i
$821$	8.61385	+	6.25833i	0.300626	+	0.218417i	0.727864	−	0.685722i	$-0.240513\pi$
$821$	8.61385	+	6.25833i	0.300626	+	0.218417i	−0.427238	+	0.904139i	$0.640513\pi$
$822$	−22.4059	+	7.28013i	−0.781497	+	0.253924i
$823$	25.4043	+	8.25436i	0.885538	+	0.287729i	0.716255	−	0.697839i	$-0.245855\pi$
$823$	25.4043	+	8.25436i	0.885538	+	0.287729i	0.169283	+	0.985567i	$0.445855\pi$
$824$	7.91573			0.275757
$825$	−0.550982	−	16.5740i	−0.0191827	−	0.577032i
$826$	4.47060			0.155552
$827$	32.5497	+	10.5761i	1.13187	+	0.367765i	0.814285	−	0.580466i	$-0.197129\pi$
$827$	32.5497	+	10.5761i	1.13187	+	0.367765i	0.317581	+	0.948231i	$0.397129\pi$
$828$	−7.25541	+	2.35742i	−0.252143	+	0.0819262i
$829$	−19.8391	−	14.4139i	−0.689039	−	0.500616i	0.187305	−	0.982302i	$-0.440025\pi$
$829$	−19.8391	−	14.4139i	−0.689039	−	0.500616i	−0.876344	+	0.481685i	$0.840025\pi$
$830$	−0.185375	−	58.2801i	−0.00643446	−	2.02293i
$831$	−22.1718			−0.769132
$832$	16.1367	−	5.24312i	0.559438	−	0.181772i
$833$	4.25208	+	5.85249i	0.147326	+	0.202777i
$834$	−18.0278	+	13.0980i	−0.624253	+	0.453546i
$835$	41.3928	−	30.2752i	1.43246	−	1.04772i
$836$	15.2852	−	11.7455i	0.528651	−	0.406228i
$837$	0.279655	+	0.0908653i	0.00966627	+	0.00314076i
$838$	−20.8356	−	28.6778i	−0.719755	−	0.990658i
$839$	50.0182			1.72682			0.863410	−	0.504503i	$-0.168324\pi$
$839$	50.0182			1.72682			0.863410	+	0.504503i	$0.168324\pi$
$840$	−0.427628	+	0.00136018i	−0.0147546	+	4.69308e-5i
$841$	−8.79387	−	27.0647i	−0.303237	−	0.933267i
$842$			40.1064i			1.38216i
$843$	22.6491	−	7.35915i	0.780078	−	0.253463i
$844$	12.1264	−	8.81036i	0.417408	−	0.303265i
$845$	0.214008	+	67.2819i	0.00736208	+	2.31457i
$846$	−8.99390	+	6.53445i	−0.309217	+	0.224659i
$847$	−0.100320	−	1.86496i	−0.00344704	−	0.0640808i
$848$	10.1798	−	3.30761i	0.349575	−	0.113584i
$849$	0.685738	+	0.498218i	0.0235345	+	0.0170988i
$850$	3.00897	+	9.06404i	0.103207	+	0.310894i
$851$	−6.50223	−	20.0118i	−0.222893	−	0.685996i
$852$	1.80073	−	2.47849i	0.0616920	−	0.0849117i
$853$	−13.9458	−	4.53125i	−0.477494	−	0.155147i	0.0603749	−	0.998176i	$-0.480770\pi$
$853$	−13.9458	−	4.53125i	−0.477494	−	0.155147i	−0.537869	+	0.843029i	$0.680770\pi$
$854$	−3.50013	−	2.54299i	−0.119772	−	0.0870195i
$855$	0.0297812	+	9.36292i	0.00101850	+	0.320205i
$856$	0.258618	+	0.795944i	0.00883937	+	0.0272048i
$857$			33.8924i			1.15774i	0.815419	+	0.578872i	$0.196507\pi$
$857$			33.8924i			1.15774i	−0.815419	+	0.578872i	$0.803493\pi$
$858$	−38.4312	−	11.3550i	−1.31202	−	0.387653i
$859$	8.55901	−	26.3419i	0.292030	−	0.898775i	−0.692173	−	0.721731i	$-0.743347\pi$
$859$	8.55901	−	26.3419i	0.292030	−	0.898775i	0.984203	−	0.177044i	$-0.0566534\pi$
$860$	−1.35946	+	4.22971i	−0.0463571	+	0.144232i
$861$	2.07582			0.0707439
$862$			31.3523i			1.06786i
$863$	−24.9315	+	8.10073i	−0.848678	+	0.275752i	−0.700892	−	0.713267i	$-0.747215\pi$
$863$	−24.9315	+	8.10073i	−0.848678	+	0.275752i	−0.147786	+	0.989019i	$0.547215\pi$
$864$	−5.39891	−	3.92254i	−0.183675	−	0.133448i
$865$	10.6372	+	32.3871i	0.361676	+	1.10119i
$866$	23.0646	+	16.7574i	0.783767	+	0.569440i
$867$	−15.1438	+	4.92053i	−0.514311	+	0.167110i
$868$		−	0.0692996i		−	0.00235218i
$869$	−29.2655	+	22.4883i	−0.992764	+	0.762864i
$870$	−2.88597	−	0.927569i	−0.0978434	−	0.0314475i
$871$	−76.1975			−2.58185
$872$	5.11292	−	1.66129i	0.173145	−	0.0562583i
$873$	2.71394	+	3.73542i	0.0918531	+	0.126425i
$874$	−34.2694	+	24.8982i	−1.15918	+	0.842194i
$875$	0.569346	−	1.81088i	0.0192474	−	0.0612190i
$876$	−6.25674	−	19.2563i	−0.211396	−	0.650609i
$877$		−	18.0791i		−	0.610488i	−0.952274	−	0.305244i	$-0.901262\pi$
$877$		−	18.0791i		−	0.610488i	0.952274	−	0.305244i	$-0.0987380\pi$
$878$			0.437066i			0.0147503i
$879$	−6.96513	+	5.06046i	−0.234928	+	0.170685i
$880$	34.5224	+	10.0808i	1.16375	+	0.339824i
$881$	−1.18473	−	0.860754i	−0.0399144	−	0.0289995i	0.567649	−	0.823271i	$-0.307853\pi$
$881$	−1.18473	−	0.860754i	−0.0399144	−	0.0289995i	−0.607564	+	0.794271i	$0.707853\pi$
$882$	7.54224	−	10.3810i	0.253961	−	0.349547i
$883$	22.7800	+	31.3540i	0.766609	+	1.05515i	0.996635	+	0.0819624i	$0.0261188\pi$
$883$	22.7800	+	31.3540i	0.766609	+	1.05515i	−0.230026	+	0.973184i	$0.573881\pi$
$884$	9.45526			0.318015
$885$	25.8179	−	18.8836i	0.867860	−	0.634765i
$886$	25.8291	+	18.7659i	0.867744	+	0.630453i
$887$			35.4553i			1.19047i	0.803551	+	0.595235i	$0.202941\pi$
$887$			35.4553i			1.19047i	−0.803551	+	0.595235i	$0.797059\pi$
$888$	2.53474	−	3.48877i	0.0850602	−	0.117075i
$889$	−0.192291	+	0.591811i	−0.00644924	+	0.0198487i
$890$	−0.590478	−	1.79783i	−0.0197929	−	0.0602632i
$891$	1.10927	+	3.12562i	0.0371619	+	0.104712i
$892$	5.48673	−	7.55183i	0.183709	−	0.252854i
$893$	−14.8649	+	20.4597i	−0.497434	+	0.684659i
$894$	−21.8085	+	15.8448i	−0.729385	+	0.529929i
$895$	12.2697	+	16.7753i	0.410129	+	0.560735i
$896$	0.450647	−	1.38695i	0.0150551	−	0.0463347i
$897$	34.3113	+	11.1484i	1.14562	+	0.372235i
$898$	41.7131	+	57.4132i	1.39199	+	1.91590i
$899$	−0.0669230	+	0.205968i	−0.00223201	+	0.00686941i
$900$	5.58879	−	4.11507i	0.186293	−	0.137169i
$901$	2.29045			0.0763058
$902$	−71.5788	−	21.1489i	−2.38331	−	0.704180i
$903$	−0.142852	−	0.196619i	−0.00475381	−	0.00654306i
$904$	9.84405			0.327408
$905$	7.97792	−	2.62027i	0.265195	−	0.0871006i
$906$	6.36292	−	19.5831i	0.211394	−	0.650604i
$907$	9.25599	+	12.7398i	0.307340	+	0.423018i	0.934549	−	0.355833i	$-0.115803\pi$
$907$	9.25599	+	12.7398i	0.307340	+	0.423018i	−0.627209	+	0.778851i	$0.715803\pi$
$908$		−	18.8763i		−	0.626432i
$909$	−0.331856			−0.0110070
$910$	−3.71971	−	2.68449i	−0.123307	−	0.0889901i
$911$	−8.97759	+	27.6302i	−0.297441	+	0.915429i	0.684950	+	0.728590i	$0.259824\pi$
$911$	−8.97759	+	27.6302i	−0.297441	+	0.915429i	−0.982391	+	0.186838i	$0.940176\pi$
$912$	−19.3118	−	6.27479i	−0.639478	−	0.207779i
$913$	−28.6151	−	37.2387i	−0.947021	−	1.23242i
$914$	−5.02297	−	15.4591i	−0.166145	−	0.511342i
$915$	−30.9549	+	0.0984600i	−1.02334	+	0.00325499i
$916$	8.13248	+	5.90860i	0.268705	+	0.195226i
$917$	2.90671	+	0.944448i	0.0959881	+	0.0311884i
$918$	−1.12272	−	1.54529i	−0.0370553	−	0.0510022i
$919$	5.35833			0.176755			0.0883774	−	0.996087i	$-0.471832\pi$
$919$	5.35833			0.176755			0.0883774	+	0.996087i	$0.471832\pi$
$920$	−13.1784	−	4.23562i	−0.434478	−	0.139644i
$921$	−6.70416	−	20.6333i	−0.220909	−	0.679889i
$922$		−	28.1064i		−	0.925636i
$923$	−13.7788	+	4.47700i	−0.453534	+	0.147362i
$924$	0.619795	−	0.476265i	0.0203898	−	0.0156680i
$925$	11.3501	+	15.4149i	0.373190	+	0.506840i
$926$	−9.89472	−	7.18893i	−0.325161	−	0.236243i
$927$		−	7.02767i		−	0.230819i
$928$	2.88898	−	3.97634i	0.0948355	−	0.130530i
$929$	−10.8562	+	33.4118i	−0.356179	+	1.09621i	0.599144	+	0.800642i	$0.295508\pi$
$929$	−10.8562	+	33.4118i	−0.356179	+	1.09621i	−0.955323	+	0.295565i	$0.904492\pi$
$930$	−0.714480	−	0.976849i	−0.0234287	−	0.0320321i
$931$	9.02021	−	27.7614i	0.295625	−	0.909842i
$932$	−21.5391	−	6.99847i	−0.705536	−	0.229243i
$933$	6.81924	−	2.21570i	0.223252	−	0.0725389i
$934$	−11.5106	+	35.4261i	−0.376639	+	1.15918i
$935$	6.35920	+	4.33441i	0.207968	+	0.141750i
$936$	2.28480	+	7.03188i	0.0746809	+	0.229844i
$937$	−2.57505	−	3.54425i	−0.0841231	−	0.115785i	0.764881	−	0.644171i	$-0.222798\pi$
$937$	−2.57505	−	3.54425i	−0.0841231	−	0.115785i	−0.849004	+	0.528386i	$0.822798\pi$
$938$	2.13233	−	2.93490i	0.0696230	−	0.0958278i
$939$	−10.9456	+	7.95243i	−0.357196	+	0.259518i
$940$	18.7460	−	0.0596264i	0.611426	−	0.00194480i
$941$	3.53728	+	10.8866i	0.115312	+	0.354894i	0.992012	−	0.126144i	$-0.0402601\pi$
$941$	3.53728	+	10.8866i	0.115312	+	0.354894i	−0.876700	+	0.481038i	$0.840260\pi$
$942$	−16.3952	−	5.32712i	−0.534185	−	0.173567i
$943$	63.9053	+	20.7641i	2.08104	+	0.676172i
$944$	21.4366	+	65.9751i	0.697703	+	2.14731i
$945$	0.00120759	+	0.379653i	3.92828e−5	+	0.0123501i
$946$	2.92264	+	8.23522i	0.0950233	+	0.267750i
$947$	0.266870	+	0.367315i	0.00867211	+	0.0119361i	0.813331	−	0.581801i	$-0.197652\pi$
$947$	0.266870	+	0.367315i	0.00867211	+	0.0119361i	−0.804659	+	0.593737i	$0.797652\pi$
$948$	−14.6906	−	4.77327i	−0.477129	−	0.155029i
$949$	−29.5885	+	91.0641i	−0.960484	+	2.95607i
$950$	22.4525	−	31.3203i	0.728456	−	1.01617i
$951$	−14.7092	+	10.6868i	−0.476977	+	0.346544i
$952$	0.116649	−	0.160553i	0.00378060	−	0.00520355i
$953$	4.89019	−	6.73076i	0.158409	−	0.218031i	−0.722434	−	0.691440i	$-0.756977\pi$
$953$	4.89019	−	6.73076i	0.158409	−	0.218031i	0.880843	+	0.473409i	$0.156977\pi$
$954$	−1.25546	−	3.86390i	−0.0406469	−	0.125098i
$955$	54.0860	−	17.7640i	1.75018	−	0.574829i
$956$	−1.78171	−	1.29449i	−0.0576247	−	0.0418668i
$957$	−2.30205	+	0.816986i	−0.0744146	+	0.0264094i
$958$	27.3277	−	37.6134i	0.882919	−	1.21523i
$959$	−1.75810	+	1.27733i	−0.0567719	+	0.0412472i
$960$	1.80350	+	5.49112i	0.0582079	+	0.177225i
$961$	25.0096	−	18.1705i	0.806761	−	0.586146i
$962$	43.9950	−	14.2948i	1.41846	−	0.460884i
$963$	0.706648	−	0.229604i	0.0227714	−	0.00739888i
$964$	23.6867	−	17.2094i	0.762898	−	0.554278i
$965$	−14.3571	−	10.3614i	−0.462170	−	0.333546i
$966$	−1.38958	+	1.00959i	−0.0447089	+	0.0324829i
$967$	−29.3942	+	40.4576i	−0.945253	+	1.30103i	0.00835079	+	0.999965i	$0.497342\pi$
$967$	−29.3942	+	40.4576i	−0.945253	+	1.30103i	−0.953604	+	0.301064i	$0.902658\pi$
$968$	11.5609	−	4.45615i	0.371583	−	0.143226i
$969$	−3.51530	−	2.55402i	−0.112928	−	0.0820469i
$970$	−0.0604466	−	19.0038i	−0.00194082	−	0.610176i
$971$	1.13395	+	3.48995i	0.0363903	+	0.111998i	0.967602	−	0.252482i	$-0.0812468\pi$
$971$	1.13395	+	3.48995i	0.0363903	+	0.111998i	−0.931211	+	0.364480i	$0.881247\pi$
$972$	−0.815886	+	1.12297i	−0.0261696	+	0.0360193i
$973$	−1.20818	+	1.66292i	−0.0387326	+	0.0533108i
$974$	18.0472	−	13.1121i	0.578270	−	0.420138i
$975$	−32.8206	+	0.208791i	−1.05110	+	0.00668667i
$976$	20.7452	−	63.8471i	0.664037	−	2.04369i
$977$	29.7646	+	9.67111i	0.952254	+	0.309406i	0.743631	−	0.668590i	$-0.233102\pi$
$977$	29.7646	+	9.67111i	0.952254	+	0.309406i	0.208623	+	0.977996i	$0.433102\pi$
$978$	−21.8045	−	30.0114i	−0.697232	−	0.959658i
$979$	−1.25727	−	0.862818i	−0.0401824	−	0.0275758i
$980$	−20.5569	+	6.75169i	−0.656665	+	0.215675i
$981$	−1.47491	−	4.53931i	−0.0470903	−	0.144929i
$982$	29.8494	+	9.69865i	0.952532	+	0.309496i
$983$	−3.12263	−	1.01460i	−0.0995964	−	0.0323608i	0.258795	−	0.965932i	$-0.416675\pi$
$983$	−3.12263	−	1.01460i	−0.0995964	−	0.0323608i	−0.358391	+	0.933571i	$0.616675\pi$
$984$	4.25547	+	13.0970i	0.135659	+	0.417517i
$985$	14.6151	+	10.5477i	0.465677	+	0.336076i
$986$	1.13812	−	0.826893i	0.0362451	−	0.0263336i
$987$	−0.602750	+	0.829614i	−0.0191857	+	0.0264069i
$988$	−22.4256	−	30.8662i	−0.713453	−	0.981984i
$989$	−2.43103	−	7.48193i	−0.0773021	−	0.237911i
$990$	3.82634	−	13.1035i	0.121609	−	0.416458i
$991$	−12.6780	+	39.0188i	−0.402729	+	1.23947i	0.520047	+	0.854138i	$0.325914\pi$
$991$	−12.6780	+	39.0188i	−0.402729	+	1.23947i	−0.922776	+	0.385336i	$0.874086\pi$
$992$	1.86625	−	0.606382i	0.0592536	−	0.0192527i
$993$	15.8205	+	5.14039i	0.502048	+	0.163125i
$994$	0.213148	−	0.656003i	0.00676065	−	0.0208072i
$995$	−32.3159	+	10.6138i	−1.02448	+	0.336481i
$996$	6.07371	−	18.6930i	0.192453	−	0.592309i
$997$	−12.8104	+	17.6320i	−0.405709	+	0.558411i	−0.962165	−	0.272466i	$-0.912161\pi$
$997$	−12.8104	+	17.6320i	−0.405709	+	0.558411i	0.556456	+	0.830877i	$0.312161\pi$
$998$			49.2184i			1.55798i
$999$	−3.09737	−	2.25037i	−0.0979963	−	0.0711985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cb.a.169.14	yes	240
11.3	even	5		825.2.by.a.619.14	yes	240
25.4	even	10		825.2.by.a.4.14	✓	240
275.179	even	10	inner	825.2.cb.a.454.14	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.by.a.4.14	✓	240	25.4	even	10
825.2.by.a.619.14	yes	240	11.3	even	5
825.2.cb.a.169.14	yes	240	1.1	even	1	trivial
825.2.cb.a.454.14	yes	240	275.179	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75058 - 0.568798i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(1.12297 + 0.815886i) q^{4} +(2.12442 - 0.697744i) q^{5} +1.84067 q^{6} +(0.161477 - 0.0524671i) q^{7} +(0.662061 + 0.911249i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-4.11584 + 0.0130915i) q^{10} +(-2.62986 + 2.02085i) q^{11} +(-1.32013 - 0.428937i) q^{12} +(3.85838 + 5.31060i) q^{13} -0.312522 q^{14} +(-1.80483 + 1.32008i) q^{15} +(-1.49855 - 4.61206i) q^{16} -1.03771i q^{17} +(-1.75058 + 0.568798i) q^{18} +(-3.38755 + 2.46120i) q^{19} +(2.95494 + 0.949737i) q^{20} +(-0.137361 + 0.0997983i) q^{21} +(5.75324 - 2.04180i) q^{22} +(-5.22698 + 1.69835i) q^{23} +(-0.911249 - 0.662061i) q^{24} +(4.02631 - 2.96460i) q^{25} +(-3.73374 - 11.4913i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.224141 + 0.0728279i) q^{28} +(-0.595847 - 0.432909i) q^{29} +(3.91035 - 1.28432i) q^{30} +(-0.0908653 - 0.279655i) q^{31} +6.67342i q^{32} +(1.87667 - 2.73461i) q^{33} +(-0.590249 + 1.81660i) q^{34} +(0.306436 - 0.224132i) q^{35} +1.38807 q^{36} +3.82856i q^{37} +(7.33012 - 2.38170i) q^{38} +(-5.31060 - 3.85838i) q^{39} +(2.04231 + 1.47392i) q^{40} +(-9.89108 - 7.18629i) q^{41} +(0.297226 - 0.0965746i) q^{42} +1.43140i q^{43} +(-4.60204 + 0.123687i) q^{44} +(1.30857 - 1.81319i) q^{45} +10.1163 q^{46} +(5.74408 - 1.86636i) q^{47} +(2.85041 + 3.92325i) q^{48} +(-5.63980 + 4.09755i) q^{49} +(-8.73464 + 2.89962i) q^{50} +(0.320671 + 0.986923i) q^{51} +9.11164i q^{52} +2.20721i q^{53} +(1.48913 - 1.08192i) q^{54} +(-4.17689 + 6.12810i) q^{55} +(0.154718 + 0.112409i) q^{56} +(2.46120 - 3.38755i) q^{57} +(0.796842 + 1.09676i) q^{58} -14.3049 q^{59} +(-3.10380 + 0.00987244i) q^{60} +(11.1996 + 8.13701i) q^{61} +0.541242i q^{62} +(0.0997983 - 0.137361i) q^{63} +(0.798737 - 2.45826i) q^{64} +(11.9022 + 8.58978i) q^{65} +(-4.84071 + 3.71972i) q^{66} +(-6.82297 + 9.39102i) q^{67} +(0.846655 - 1.16532i) q^{68} +(4.44634 - 3.23045i) q^{69} +(-0.663927 + 0.218060i) q^{70} +(-0.682027 + 2.09906i) q^{71} +(1.07124 + 0.348066i) q^{72} +(8.57381 + 11.8008i) q^{73} +(2.17768 - 6.70220i) q^{74} +(-2.91313 + 4.06370i) q^{75} -5.81218 q^{76} +(-0.318634 + 0.464302i) q^{77} +(7.10200 + 9.77506i) q^{78} +11.1282 q^{79} +(-6.40158 - 8.75234i) q^{80} +(0.309017 - 0.951057i) q^{81} +(13.2276 + 18.2062i) q^{82} +14.1599i q^{83} -0.235676 q^{84} +(-0.724057 - 2.20453i) q^{85} +(0.814181 - 2.50579i) q^{86} +(0.700461 + 0.227593i) q^{87} +(-3.58262 - 1.05853i) q^{88} +(0.142074 + 0.437258i) q^{89} +(-3.32209 + 2.42982i) q^{90} +(0.901671 + 0.655102i) q^{91} +(-7.25541 - 2.35742i) q^{92} +(0.172836 + 0.237888i) q^{93} -11.1171 q^{94} +(-5.47929 + 7.59227i) q^{95} +(-2.06220 - 6.34680i) q^{96} +4.61724i q^{97} +(12.2036 - 3.96519i) q^{98} +(-0.939777 + 3.18069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 60 q^{4} + 6 q^{5} - 16 q^{6} + 10 q^{7} + 60 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 64 q^{16} - 24 q^{19} - 44 q^{20} + 8 q^{21} - 40 q^{22} + 40 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{26} + 30 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) \) 240 * q + 60 * q^4 + 6 * q^5 - 16 * q^6 + 10 * q^7 + 60 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 - 64 * q^16 - 24 * q^19 - 44 * q^20 + 8 * q^21 - 40 * q^22 + 40 * q^23 - 12 * q^24 + 4 * q^25 + 40 * q^26 + 30 * q^28 + 4 * q^30 - 2 * q^31 + 30 * q^35 + 240 * q^36 - 16 * q^39 + 68 * q^40 - 6 * q^41 - 10 * q^42 + 26 * q^44 + 4 * q^45 - 48 * q^46 - 40 * q^47 + 40 * q^48 + 58 * q^49 - 78 * q^50 + 16 * q^51 - 4 * q^54 - 10 * q^55 - 40 * q^57 + 60 * q^58 - 24 * q^59 + 8 * q^60 + 28 * q^61 - 10 * q^63 + 44 * q^64 + 60 * q^65 + 8 * q^66 - 40 * q^67 - 250 * q^68 + 2 * q^69 - 44 * q^70 - 16 * q^71 + 22 * q^74 + 20 * q^75 - 168 * q^76 - 30 * q^77 + 172 * q^79 - 118 * q^80 - 60 * q^81 + 40 * q^82 + 96 * q^84 + 40 * q^85 - 72 * q^86 - 40 * q^87 - 100 * q^88 + 2 * q^90 - 30 * q^91 + 100 * q^92 + 56 * q^94 - 122 * q^95 + 28 * q^96 - 140 * q^98 - 4 * q^99

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