LMFDB - Embedded newform 552.2.t.a.235.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			235.21
Character	$\chi$	$=$	552.235
Dual form			552.2.t.a.451.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25292 + 0.655894i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.13961 + 1.64356i) q^{4} +(-0.329554 + 2.29210i) q^{5} +(1.31618 - 0.517373i) q^{6} +(-0.102068 - 0.223497i) q^{7} +(0.349829 + 2.80671i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(1.25292 + 0.655894i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.13961 + 1.64356i) q^{4} +(-0.329554 + 2.29210i) q^{5} +(1.31618 - 0.517373i) q^{6} +(-0.102068 - 0.223497i) q^{7} +(0.349829 + 2.80671i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.91628 + 2.65565i) q^{10} +(-1.07989 - 3.67777i) q^{11} +(1.98840 + 0.215048i) q^{12} +(4.96634 + 2.26805i) q^{13} +(0.0187080 - 0.346970i) q^{14} +(1.51644 + 1.75006i) q^{15} +(-1.40260 + 3.74603i) q^{16} +(3.16634 + 4.92692i) q^{17} +(0.470909 - 1.33351i) q^{18} +(-2.56041 + 3.98408i) q^{19} +(-4.14276 + 2.07044i) q^{20} +(-0.235748 - 0.0692219i) q^{21} +(1.05921 - 5.31624i) q^{22} +(0.134482 - 4.79395i) q^{23} +(2.35026 + 1.57362i) q^{24} +(-0.347630 - 0.102073i) q^{25} +(4.73481 + 6.09907i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.251015 - 0.422454i) q^{28} +(-5.43786 - 8.46148i) q^{29} +(0.752116 + 3.18731i) q^{30} +(-2.84031 + 2.46114i) q^{31} +(-4.21434 + 3.77351i) q^{32} +(-3.48666 - 1.59230i) q^{33} +(0.735624 + 8.24981i) q^{34} +(0.545914 - 0.160295i) q^{35} +(1.46465 - 1.36191i) q^{36} +(0.0873580 + 0.607588i) q^{37} +(-5.82112 + 3.31236i) q^{38} +(4.96634 - 2.26805i) q^{39} +(-6.54853 - 0.123120i) q^{40} +(1.08039 - 7.51427i) q^{41} +(-0.249971 - 0.241355i) q^{42} +(-4.07515 - 3.53114i) q^{43} +(4.81400 - 5.96608i) q^{44} +2.31567 q^{45} +(3.31282 - 5.91821i) q^{46} -7.48463i q^{47} +(1.91255 + 3.51314i) q^{48} +(4.54449 - 5.24462i) q^{49} +(-0.368602 - 0.355898i) q^{50} +(5.79703 + 0.833487i) q^{51} +(1.93198 + 10.7472i) q^{52} +(3.61923 + 7.92501i) q^{53} +(-0.699418 - 1.22915i) q^{54} +(8.78569 - 1.26319i) q^{55} +(0.591586 - 0.364661i) q^{56} +(1.33425 + 4.54405i) q^{57} +(-1.26336 - 14.1682i) q^{58} +(-2.19586 + 4.80827i) q^{59} +(-1.14820 + 4.48674i) q^{60} +(-2.00820 - 2.31759i) q^{61} +(-5.17293 + 1.22067i) q^{62} +(-0.206697 + 0.132836i) q^{63} +(-7.75524 + 1.96374i) q^{64} +(-6.83526 + 10.6359i) q^{65} +(-3.32411 - 4.28190i) q^{66} +(0.858092 - 2.92239i) q^{67} +(-4.48932 + 10.8188i) q^{68} +(-3.53496 - 3.24100i) q^{69} +(0.789122 + 0.157226i) q^{70} +(4.30935 - 14.6763i) q^{71} +(2.72836 - 0.745705i) q^{72} +(8.82008 + 5.66832i) q^{73} +(-0.289061 + 0.818556i) q^{74} +(-0.304791 + 0.195877i) q^{75} +(-9.46594 + 0.332081i) q^{76} +(-0.711751 + 0.616736i) q^{77} +(7.71001 + 0.415711i) q^{78} +(2.27224 - 4.97551i) q^{79} +(-8.12402 - 4.44940i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(6.28220 - 8.70614i) q^{82} +(0.0564639 - 0.00811829i) q^{83} +(-0.154889 - 0.466353i) q^{84} +(-12.3364 + 5.63387i) q^{85} +(-2.78978 - 7.09710i) q^{86} +(-9.95580 - 1.43143i) q^{87} +(9.94467 - 4.31753i) q^{88} +(-12.4755 - 10.8101i) q^{89} +(2.90134 + 1.51883i) q^{90} -1.34146i q^{91} +(8.03241 - 5.24218i) q^{92} +3.75827i q^{93} +(4.90913 - 9.37763i) q^{94} +(-8.28809 - 7.18167i) q^{95} +(0.0920233 + 5.65611i) q^{96} +(-15.6973 - 2.25693i) q^{97} +(9.13379 - 3.59038i) q^{98} +(-3.48666 + 1.59230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.25292	+	0.655894i	0.885947	+	0.463787i
$2$	1.25292	+	0.655894i	0.885947	+	0.463787i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	1.13961	+	1.64356i	0.569803	+	0.821781i
$5$	−0.329554	+	2.29210i	−0.147381	+	1.02506i	0.773104	+	0.634279i	$0.218703\pi$
$5$	−0.329554	+	2.29210i	−0.147381	+	1.02506i	−0.920485	+	0.390777i	$0.872206\pi$
$6$	1.31618	−	0.517373i	0.537328	−	0.211217i
$7$	−0.102068	−	0.223497i	−0.0385780	−	0.0844741i	0.889362	−	0.457204i	$-0.151149\pi$
$7$	−0.102068	−	0.223497i	−0.0385780	−	0.0844741i	−0.927940	+	0.372730i	$0.878422\pi$
$8$	0.349829	+	2.80671i	0.123683	+	0.992322i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−1.91628	+	2.65565i	−0.605979	+	0.839792i
$11$	−1.07989	−	3.67777i	−0.325600	−	1.10889i	−0.945882	−	0.324512i	$-0.894800\pi$
$11$	−1.07989	−	3.67777i	−0.325600	−	1.10889i	0.620282	−	0.784379i	$-0.287018\pi$
$12$	1.98840	+	0.215048i	0.574003	+	0.0620791i
$13$	4.96634	+	2.26805i	1.37741	+	0.629044i	0.960084	−	0.279712i	$-0.0902388\pi$
$13$	4.96634	+	2.26805i	1.37741	+	0.629044i	0.417329	+	0.908755i	$0.362966\pi$
$14$	0.0187080	−	0.346970i	0.00499993	−	0.0927315i
$15$	1.51644	+	1.75006i	0.391543	+	0.451864i
$16$	−1.40260	+	3.74603i	−0.350649	+	0.936507i
$17$	3.16634	+	4.92692i	0.767950	+	1.19495i	0.976199	+	0.216878i	$0.0695872\pi$
$17$	3.16634	+	4.92692i	0.767950	+	1.19495i	−0.208249	+	0.978076i	$0.566776\pi$
$18$	0.470909	−	1.33351i	0.110994	−	0.314311i
$19$	−2.56041	+	3.98408i	−0.587399	+	0.914010i	0.412596	+	0.910914i	$0.364622\pi$
$19$	−2.56041	+	3.98408i	−0.587399	+	0.914010i	−0.999995	+	0.00309641i	$0.999014\pi$
$20$	−4.14276	+	2.07044i	−0.926350	+	0.462965i
$21$	−0.235748	−	0.0692219i	−0.0514445	−	0.0151055i
$22$	1.05921	−	5.31624i	0.225825	−	1.13343i
$23$	0.134482	−	4.79395i	0.0280413	−	0.999607i
$23$	0.134482	−	4.79395i	0.0280413	−	0.999607i
$24$	2.35026	+	1.57362i	0.479745	+	0.321214i
$25$	−0.347630	−	0.102073i	−0.0695260	−	0.0204147i
$26$	4.73481	+	6.09907i	0.928572	+	1.19613i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	0.251015	−	0.422454i	0.0474374	−	0.0798363i
$29$	−5.43786	−	8.46148i	−1.00979	−	1.57126i	−0.805718	−	0.592300i	$-0.798220\pi$
$29$	−5.43786	−	8.46148i	−1.00979	−	1.57126i	−0.204068	−	0.978957i	$-0.565416\pi$
$30$	0.752116	+	3.18731i	0.137317	+	0.581920i
$31$	−2.84031	+	2.46114i	−0.510135	+	0.442034i	−0.871504	−	0.490388i	$-0.836855\pi$
$31$	−2.84031	+	2.46114i	−0.510135	+	0.442034i	0.361369	+	0.932423i	$0.382309\pi$
$32$	−4.21434	+	3.77351i	−0.744997	+	0.667068i
$33$	−3.48666	−	1.59230i	−0.606949	−	0.277184i
$34$	0.735624	+	8.24981i	0.126159	+	1.41483i
$35$	0.545914	−	0.160295i	0.0922763	−	0.0270948i
$36$	1.46465	−	1.36191i	0.244108	−	0.226985i
$37$	0.0873580	+	0.607588i	0.0143616	+	0.0998869i	0.995741	−	0.0921901i	$-0.0293867\pi$
$37$	0.0873580	+	0.607588i	0.0143616	+	0.0998869i	−0.981380	+	0.192077i	$0.938478\pi$
$38$	−5.82112	+	3.31236i	−0.944310	+	0.537336i
$39$	4.96634	−	2.26805i	0.795250	−	0.363179i
$40$	−6.54853	−	0.123120i	−1.03541	−	0.0194670i
$41$	1.08039	−	7.51427i	0.168728	−	1.17353i	−0.712788	−	0.701379i	$-0.752568\pi$
$41$	1.08039	−	7.51427i	0.168728	−	1.17353i	0.881517	−	0.472153i	$-0.156523\pi$
$42$	−0.249971	−	0.241355i	−0.0385714	−	0.0372419i
$43$	−4.07515	−	3.53114i	−0.621455	−	0.538494i	0.286222	−	0.958163i	$-0.407601\pi$
$43$	−4.07515	−	3.53114i	−0.621455	−	0.538494i	−0.907677	+	0.419670i	$0.862146\pi$
$44$	4.81400	−	5.96608i	0.725738	−	0.899421i
$45$	2.31567			0.345199
$46$	3.31282	−	5.91821i	0.488448	−	0.872593i
$47$		−	7.48463i		−	1.09175i	−0.837868	−	0.545873i	$-0.816198\pi$
$47$		−	7.48463i		−	1.09175i	0.837868	−	0.545873i	$-0.183802\pi$
$48$	1.91255	+	3.51314i	0.276053	+	0.507078i
$49$	4.54449	−	5.24462i	0.649213	−	0.749232i
$50$	−0.368602	−	0.355898i	−0.0521282	−	0.0503316i
$51$	5.79703	+	0.833487i	0.811746	+	0.116711i
$52$	1.93198	+	10.7472i	0.267918	+	1.49036i
$53$	3.61923	+	7.92501i	0.497139	+	1.08858i	0.977389	+	0.211451i	$0.0678190\pi$
$53$	3.61923	+	7.92501i	0.497139	+	1.08858i	−0.480249	+	0.877132i	$0.659454\pi$
$54$	−0.699418	−	1.22915i	−0.0951788	−	0.167266i
$55$	8.78569	−	1.26319i	1.18466	−	0.170329i
$56$	0.591586	−	0.364661i	0.0790540	−	0.0487298i
$57$	1.33425	+	4.54405i	0.176726	+	0.601874i
$58$	−1.26336	−	14.1682i	−0.165887	−	1.86038i
$59$	−2.19586	+	4.80827i	−0.285877	+	0.625983i	−0.997027	−	0.0770573i	$-0.975448\pi$
$59$	−2.19586	+	4.80827i	−0.285877	+	0.625983i	0.711150	+	0.703041i	$0.248175\pi$
$60$	−1.14820	+	4.48674i	−0.148232	+	0.579236i
$61$	−2.00820	−	2.31759i	−0.257124	−	0.296737i	0.612481	−	0.790485i	$-0.290172\pi$
$61$	−2.00820	−	2.31759i	−0.257124	−	0.296737i	−0.869605	+	0.493749i	$0.835626\pi$
$62$	−5.17293	+	1.22067i	−0.656962	+	0.155025i
$63$	−0.206697	+	0.132836i	−0.0260413	+	0.0167358i
$64$	−7.75524	+	1.96374i	−0.969405	+	0.245467i
$65$	−6.83526	+	10.6359i	−0.847809	+	1.31922i
$66$	−3.32411	−	4.28190i	−0.409170	−	0.527065i
$67$	0.858092	−	2.92239i	0.104833	−	0.357027i	−0.890324	−	0.455327i	$-0.849522\pi$
$67$	0.858092	−	2.92239i	0.104833	−	0.357027i	0.995157	+	0.0982999i	$0.0313404\pi$
$68$	−4.48932	+	10.8188i	−0.544411	+	1.31197i
$69$	−3.53496	−	3.24100i	−0.425559	−	0.390171i
$70$	0.789122	+	0.157226i	0.0943181	+	0.0187921i
$71$	4.30935	−	14.6763i	0.511426	−	1.74176i	−0.147024	−	0.989133i	$-0.546970\pi$
$71$	4.30935	−	14.6763i	0.511426	−	1.74176i	0.658450	−	0.752624i	$-0.271212\pi$
$72$	2.72836	−	0.745705i	0.321540	−	0.0878821i
$73$	8.82008	+	5.66832i	1.03231	+	0.663427i	0.943074	−	0.332583i	$-0.107920\pi$
$73$	8.82008	+	5.66832i	1.03231	+	0.663427i	0.0892386	+	0.996010i	$0.471557\pi$
$74$	−0.289061	+	0.818556i	−0.0336027	+	0.0951552i
$75$	−0.304791	+	0.195877i	−0.0351942	+	0.0226180i
$76$	−9.46594	+	0.332081i	−1.08582	+	0.0380923i
$77$	−0.711751	+	0.616736i	−0.0811115	+	0.0702835i
$78$	7.71001	+	0.415711i	0.872987	+	0.0470700i
$79$	2.27224	−	4.97551i	0.255647	−	0.559789i	−0.737676	−	0.675155i	$-0.764077\pi$
$79$	2.27224	−	4.97551i	0.255647	−	0.559789i	0.993323	+	0.115366i	$0.0368041\pi$
$80$	−8.12402	−	4.44940i	−0.908293	−	0.497459i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	6.28220	−	8.70614i	0.693753	−	0.961432i
$83$	0.0564639	−	0.00811829i	0.00619772	−	0.000891098i	−0.139215	−	0.990262i	$-0.544458\pi$
$83$	0.0564639	−	0.00811829i	0.00619772	−	0.000891098i	0.145413	+	0.989371i	$0.453549\pi$
$84$	−0.154889	−	0.466353i	−0.0168998	−	0.0508833i
$85$	−12.3364	+	5.63387i	−1.33808	+	0.611079i
$86$	−2.78978	−	7.09710i	−0.300829	−	0.765300i
$87$	−9.95580	−	1.43143i	−1.06737	−	0.153465i
$88$	9.94467	−	4.31753i	1.06011	−	0.460251i
$89$	−12.4755	−	10.8101i	−1.32240	−	1.14586i	−0.978361	−	0.206907i	$-0.933660\pi$
$89$	−12.4755	−	10.8101i	−1.32240	−	1.14586i	−0.344036	−	0.938956i	$-0.611794\pi$
$90$	2.90134	+	1.51883i	0.305828	+	0.160099i
$91$		−	1.34146i		−	0.140623i
$92$	8.03241	−	5.24218i	0.837436	−	0.546535i
$93$			3.75827i			0.389714i
$94$	4.90913	−	9.37763i	0.506338	−	0.967229i
$95$	−8.28809	−	7.18167i	−0.850341	−	0.736824i
$96$	0.0920233	+	5.65611i	0.00939209	+	0.577274i
$97$	−15.6973	−	2.25693i	−1.59382	−	0.229156i	−0.712496	−	0.701676i	$-0.752435\pi$
$97$	−15.6973	−	2.25693i	−1.59382	−	0.229156i	−0.881320	+	0.472520i	$0.843344\pi$
$98$	9.13379	−	3.59038i	0.922652	−	0.362683i
$99$	−3.48666	+	1.59230i	−0.350422	+	0.160032i
$100$	−0.228397	−	0.687675i	−0.0228397	−	0.0687675i
$101$	5.04761	−	0.725736i	0.502256	−	0.0722134i	0.113469	−	0.993541i	$-0.463804\pi$
$101$	5.04761	−	0.725736i	0.502256	−	0.0722134i	0.388786	+	0.921328i	$0.372895\pi$
$102$	6.71652	+	4.84653i	0.665035	+	0.479878i
$103$	10.7481	−	3.15593i	1.05904	−	0.310963i	0.294578	−	0.955628i	$-0.404821\pi$
$103$	10.7481	−	3.15593i	1.05904	−	0.310963i	0.764466	+	0.644664i	$0.223003\pi$
$104$	−4.62839	+	14.7325i	−0.453851	+	1.44464i
$105$	0.236355	−	0.517545i	0.0230659	−	0.0505072i
$106$	−0.663369	+	12.3032i	−0.0644321	+	1.19499i
$107$	−5.42607	+	4.70172i	−0.524558	+	0.454532i	−0.876439	−	0.481512i	$-0.840088\pi$
$107$	−5.42607	+	4.70172i	−0.524558	+	0.454532i	0.351881	+	0.936045i	$0.385542\pi$
$108$	−0.0701201	−	1.99877i	−0.00674731	−	0.192332i
$109$	−4.48661	+	2.88337i	−0.429739	+	0.276177i	−0.737578	−	0.675262i	$-0.764031\pi$
$109$	−4.48661	+	2.88337i	−0.429739	+	0.276177i	0.307839	+	0.951439i	$0.400394\pi$
$110$	11.8363	+	4.17981i	1.12854	+	0.398529i
$111$	0.516392	+	0.331865i	0.0490138	+	0.0314992i
$112$	0.980387	−	0.0688719i	0.0926379	−	0.00650779i
$113$	0.779654	−	2.65526i	0.0733437	−	0.249786i	−0.914658	−	0.404228i	$-0.867540\pi$
$113$	0.779654	−	2.65526i	0.0733437	−	0.249786i	0.988002	+	0.154443i	$0.0493582\pi$
$114$	−1.30871	+	6.56845i	−0.122571	+	0.615191i
$115$	10.9439	+	1.88811i	1.02052	+	0.176067i
$116$	7.70995	−	18.5802i	0.715851	−	1.72513i
$117$	1.53818	−	5.23856i	0.142205	−	0.484305i
$118$	−5.90495	+	4.58411i	−0.543595	+	0.422002i
$119$	0.777972	−	1.21055i	0.0713166	−	0.110971i
$120$	−4.38143	+	4.86842i	−0.399968	+	0.444424i
$121$	−3.10607	+	1.99615i	−0.282370	+	0.181468i
$122$	−0.996018	−	4.22091i	−0.0901753	−	0.382144i
$123$	−4.97140	−	5.73730i	−0.448256	−	0.517315i
$124$	−7.28188	−	1.86350i	−0.653932	−	0.167347i
$125$	−4.46129	+	9.76885i	−0.399030	+	0.873753i
$126$	−0.346100	+	0.0308613i	−0.0308331	+	0.00274934i
$127$	5.61388	+	19.1191i	0.498152	+	1.69655i	0.697470	+	0.716614i	$0.254309\pi$
$127$	5.61388	+	19.1191i	0.498152	+	1.69655i	−0.199318	+	0.979935i	$0.563873\pi$
$128$	−11.0047	−	2.62622i	−0.972685	−	0.232127i
$129$	−5.33732	+	0.767390i	−0.469924	+	0.0675649i
$130$	−15.5400	+	8.84266i	−1.36295	+	0.775553i
$131$	−0.947155	−	2.07398i	−0.0827533	−	0.181205i	0.863732	−	0.503952i	$-0.168121\pi$
$131$	−0.947155	−	2.07398i	−0.0827533	−	0.181205i	−0.946485	+	0.322747i	$0.895394\pi$
$132$	−1.35636	−	7.54513i	−0.118056	−	0.656720i
$133$	1.15177	+	0.165599i	0.0998709	+	0.0143593i
$134$	2.99190	−	3.09870i	0.258461	−	0.267687i
$135$	1.51644	−	1.75006i	0.130514	−	0.150621i
$136$	−12.7208	+	10.6106i	−1.09080	+	0.909849i
$137$			9.20415i			0.786364i	0.919461	+	0.393182i	$0.128626\pi$
$137$			9.20415i			0.786364i	−0.919461	+	0.393182i	$0.871374\pi$
$138$	−2.30325	−	6.37926i	−0.196066	−	0.543039i
$139$	−6.61670			−0.561221			−0.280611	−	0.959822i	$-0.590537\pi$
$139$	−6.61670			−0.561221			−0.280611	+	0.959822i	$0.590537\pi$
$140$	0.885581	+	0.714571i	0.0748453	+	0.0603923i
$141$	−5.65651	−	4.90139i	−0.476364	−	0.412772i
$142$	15.0254	−	15.5617i	1.26090	−	1.30591i
$143$	2.97827	−	20.7143i	0.249055	−	1.73222i
$144$	3.90751	+	0.855206i	0.325626	+	0.0712672i
$145$	21.1866	−	9.67558i	1.75945	−	0.803514i
$146$	7.33302	+	12.8870i	0.606885	+	1.06653i
$147$	−0.987612	−	6.86900i	−0.0814569	−	0.566545i
$148$	−0.899056	+	0.835990i	−0.0739020	+	0.0687179i
$149$	−22.0587	+	6.47702i	−1.80712	+	0.530618i	−0.998345	−	0.0575008i	$-0.981687\pi$
$149$	−22.0587	+	6.47702i	−1.80712	+	0.530618i	−0.808774	+	0.588119i	$0.799869\pi$
$150$	−0.510353	+	0.0455075i	−0.0416701	+	0.00371567i
$151$	11.0322	+	5.03826i	0.897791	+	0.410008i	0.810203	−	0.586149i	$-0.199357\pi$
$151$	11.0322	+	5.03826i	0.897791	+	0.410008i	0.0875883	+	0.996157i	$0.472084\pi$
$152$	−12.0779	−	5.79259i	−0.979644	−	0.469841i
$153$	4.42615	−	3.83528i	0.357833	−	0.310064i
$154$	−1.29628	+	0.305886i	−0.104457	+	0.0246490i
$155$	−4.70514	−	7.32134i	−0.377926	−	0.588064i
$156$	9.38735	+	5.57780i	0.751589	+	0.446582i
$157$	10.4133	+	6.69225i	0.831075	+	0.534099i	0.885619	−	0.464412i	$-0.153734\pi$
$157$	10.4133	+	6.69225i	0.831075	+	0.534099i	−0.0545445	+	0.998511i	$0.517371\pi$
$158$	6.11034	−	4.74356i	0.486112	−	0.377377i
$159$	8.35941	+	2.45454i	0.662944	+	0.194658i
$160$	−7.26039	−	10.9032i	−0.573984	−	0.861976i
$161$	−1.08516	+	0.459251i	−0.0855226	+	0.0361941i
$162$	−1.38695	−	0.276338i	−0.108969	−	0.0217112i
$163$	4.03195	+	1.18389i	0.315807	+	0.0927293i	0.435795	−	0.900046i	$-0.356467\pi$
$163$	4.03195	+	1.18389i	0.315807	+	0.0927293i	−0.119988	+	0.992775i	$0.538286\pi$
$164$	13.5814	−	6.78762i	1.06053	−	0.530024i
$165$	4.79875	−	7.46700i	0.373582	−	0.581305i
$166$	0.0760694	+	0.0268628i	0.00590413	+	0.00208496i
$167$	4.94744	+	7.69837i	0.382845	+	0.595718i	0.978180	−	0.207759i	$-0.0666171\pi$
$167$	4.94744	+	7.69837i	0.382845	+	0.595718i	−0.595335	+	0.803477i	$0.702981\pi$
$168$	0.111814	−	0.685893i	0.00862666	−	0.0529178i
$169$	11.0072	+	12.7030i	0.846711	+	0.977157i
$170$	−19.1518	−	1.03263i	−1.46887	−	0.0791993i
$171$	4.30791	+	1.96736i	0.329434	+	0.150448i
$172$	1.15958	−	10.7219i	0.0884174	−	0.817535i
$173$	0.366594	+	1.24850i	0.0278716	+	0.0949220i	0.972254	−	0.233927i	$-0.0751576\pi$
$173$	0.366594	+	1.24850i	0.0278716	+	0.0949220i	−0.944383	+	0.328849i	$0.893339\pi$
$174$	−11.5349	−	8.32341i	−0.874461	−	0.630996i
$175$	0.0126687	+	0.0881128i	0.000957664	+	0.00666070i
$176$	15.2917	+	1.11313i	1.15265	+	0.0839056i
$177$	2.19586	+	4.80827i	0.165051	+	0.361412i
$178$	−8.54048	−	21.7267i	−0.640136	−	1.62848i
$179$	−3.16016	+	21.9794i	−0.236202	+	1.64282i	0.434198	+	0.900817i	$0.357032\pi$
$179$	−3.16016	+	21.9794i	−0.236202	+	1.64282i	−0.670400	+	0.742000i	$0.733877\pi$
$180$	2.63895	+	3.80594i	0.196695	+	0.283678i
$181$	−4.29493	+	4.95661i	−0.319240	+	0.368422i	−0.892575	−	0.450898i	$-0.851104\pi$
$181$	−4.29493	+	4.95661i	−0.319240	+	0.368422i	0.573336	+	0.819321i	$0.305649\pi$
$182$	0.879854	−	1.68074i	0.0652191	−	0.124584i
$183$	−3.06661			−0.226690
$184$	13.5023	−	1.29961i	0.995400	−	0.0958085i
$185$	−1.42144			−0.104506
$186$	−2.46503	+	4.70880i	−0.180745	+	0.345266i
$187$	14.7008	−	16.9656i	1.07503	−	1.24065i
$188$	12.3015	−	8.52953i	0.897177	−	0.622080i
$189$	−0.0349669	+	0.243200i	−0.00254347	+	0.0176902i
$190$	−5.67388	−	14.4342i	−0.411627	−	1.04716i
$191$	−3.18374	−	6.97143i	−0.230368	−	0.504435i	0.758782	−	0.651344i	$-0.225795\pi$
$191$	−3.18374	−	6.97143i	−0.230368	−	0.504435i	−0.989150	+	0.146910i	$0.953067\pi$
$192$	−3.59451	+	7.14699i	−0.259411	+	0.515790i
$193$	−1.59729	−	11.1094i	−0.114975	−	0.799672i	−0.962959	−	0.269649i	$-0.913092\pi$
$193$	−1.59729	−	11.1094i	−0.114975	−	0.799672i	0.847983	−	0.530023i	$-0.177817\pi$
$194$	−18.1871	−	13.1235i	−1.30576	−	0.942212i
$195$	3.56191	+	12.1308i	0.255074	+	0.868702i
$196$	13.7988	+	1.49236i	0.985628	+	0.106597i
$197$	−15.8981	−	7.26042i	−1.13269	−	0.517284i	−0.241271	−	0.970458i	$-0.577564\pi$
$197$	−15.8981	−	7.26042i	−1.13269	−	0.517284i	−0.891422	+	0.453174i	$0.850292\pi$
$198$	−5.41287	−	0.291853i	−0.384676	−	0.0207411i
$199$	12.5895	+	14.5290i	0.892444	+	1.02994i	0.999364	+	0.0356681i	$0.0113559\pi$
$199$	12.5895	+	14.5290i	0.892444	+	1.02994i	−0.106919	+	0.994268i	$0.534099\pi$
$200$	0.164879	−	1.01140i	0.0116587	−	0.0715171i
$201$	−1.64667	−	2.56226i	−0.116147	−	0.180728i
$202$	6.80024	+	2.40141i	0.478463	+	0.168962i
$203$	−1.33609	+	2.07899i	−0.0937749	+	0.145917i
$204$	5.23644	+	10.4776i	0.366624	+	0.733581i
$205$	16.8674	+	4.95271i	1.17807	+	0.345912i
$206$	15.5365	+	3.09550i	1.08248	+	0.215674i
$207$	−4.76429	+	0.549137i	−0.331141	+	0.0381676i
$208$	−15.4619	+	15.4229i	−1.07209	+	1.06938i
$209$	17.4175	+	5.11424i	1.20479	+	0.353760i
$210$	0.635588	−	0.493418i	0.0438597	−	0.0340491i
$211$	−15.2536	−	9.80288i	−1.05010	−	0.674858i	−0.102635	−	0.994719i	$-0.532727\pi$
$211$	−15.2536	−	9.80288i	−1.05010	−	0.674858i	−0.947465	+	0.319861i	$0.896364\pi$
$212$	−8.90075	+	14.9798i	−0.611306	+	1.02882i
$213$	−8.26959	−	12.8677i	−0.566623	−	0.881682i
$214$	−9.88225	+	2.33194i	−0.675537	+	0.159408i
$215$	9.43669	−	8.17694i	0.643577	−	0.557663i
$216$	1.22313	−	2.55029i	0.0832233	−	0.173525i
$217$	0.839964	+	0.383599i	0.0570204	+	0.0260404i
$218$	−7.51254	+	0.669883i	−0.508814	+	0.0453702i
$219$	10.0598	−	2.95381i	0.679775	−	0.199600i
$220$	12.0884	+	13.0003i	0.814997	+	0.876480i
$221$	4.55060	+	31.6501i	0.306107	+	2.12902i
$222$	0.429328	+	0.754498i	0.0288146	+	0.0506386i
$223$	−0.259914	+	0.118699i	−0.0174051	+	0.00794866i	−0.424099	−	0.905616i	$-0.639409\pi$
$223$	−0.259914	+	0.118699i	−0.0174051	+	0.00794866i	0.406693	+	0.913565i	$0.366682\pi$
$224$	1.27352	+	0.556740i	0.0850905	+	0.0371987i
$225$	−0.0515615	+	0.358618i	−0.00343743	+	0.0239079i
$226$	2.71841	−	2.81545i	0.180826	−	0.187281i
$227$	−6.25148	−	5.41694i	−0.414925	−	0.359535i	0.422241	−	0.906484i	$-0.361244\pi$
$227$	−6.25148	−	5.41694i	−0.414925	−	0.359535i	−0.837166	+	0.546949i	$0.815789\pi$
$228$	−5.94790	+	7.37135i	−0.393910	+	0.488180i
$229$	6.86772			0.453832			0.226916	−	0.973914i	$-0.427136\pi$
$229$	6.86772			0.453832			0.226916	+	0.973914i	$0.427136\pi$
$230$	12.4734	+	9.54366i	0.822469	+	0.629290i
$231$			0.941781i			0.0619647i
$232$	21.8466	−	18.2226i	1.43430	−	1.19637i
$233$	−6.26603	+	7.23139i	−0.410502	+	0.473744i	−0.922920	−	0.384992i	$-0.874204\pi$
$233$	−6.26603	+	7.23139i	−0.410502	+	0.473744i	0.512418	+	0.858736i	$0.328750\pi$
$234$	5.36316	−	5.55460i	0.350600	−	0.363116i
$235$	17.1555	+	2.46659i	1.11910	+	0.160902i
$236$	−10.4051	+	1.87049i	−0.677315	+	0.121759i
$237$	−2.27224	−	4.97551i	−0.147598	−	0.323194i
$238$	1.76873	−	1.00645i	0.114650	−	0.0652385i
$239$	−18.8926	+	2.71635i	−1.22206	+	0.175706i	−0.722993	−	0.690855i	$-0.757234\pi$
$239$	−18.8926	+	2.71635i	−1.22206	+	0.175706i	−0.499070	+	0.866561i	$0.666325\pi$
$240$	−8.68274	+	3.22598i	−0.560468	+	0.208236i
$241$	−2.54752	−	8.67604i	−0.164100	−	0.558873i	−0.999951	−	0.00991652i	$-0.996843\pi$
$241$	−2.54752	−	8.67604i	−0.164100	−	0.558873i	0.835851	−	0.548957i	$-0.184975\pi$
$242$	−5.20091	+	0.463758i	−0.334327	+	0.0298115i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	1.52054	−	5.94174i	0.0973428	−	0.380381i
$245$	10.5235	+	12.1448i	0.672323	+	0.775902i
$246$	−2.46569	−	10.4491i	−0.157207	−	0.666209i
$247$	−21.7520	+	13.9791i	−1.38404	+	0.889471i
$248$	−7.90134	−	7.11095i	−0.501736	−	0.451546i
$249$	0.0308406	−	0.0479889i	0.00195444	−	0.00304117i
$250$	−11.9970	+	9.31344i	−0.758754	+	0.589034i
$251$	2.65594	−	9.04530i	0.167641	−	0.570934i	−0.832223	−	0.554442i	$-0.812932\pi$
$251$	2.65594	−	9.04530i	0.167641	−	0.570934i	0.999864	−	0.0164924i	$-0.00524994\pi$
$252$	−0.453877	−	0.188339i	−0.0285916	−	0.0118642i
$253$	−17.7763	+	4.68235i	−1.11758	+	0.294377i
$254$	−5.50639	+	27.6368i	−0.345502	+	1.73409i
$255$	−3.82086	+	13.0127i	−0.239272	+	0.814884i
$256$	−12.0654	−	10.5083i	−0.754090	−	0.656771i
$257$	16.8486	+	10.8279i	1.05098	+	0.675426i	0.947679	−	0.319223i	$-0.103422\pi$
$257$	16.8486	+	10.8279i	1.05098	+	0.675426i	0.103304	+	0.994650i	$0.467058\pi$
$258$	−7.19054	−	2.53924i	−0.447664	−	0.158086i
$259$	0.126878	−	0.0815395i	0.00788381	−	0.00506662i
$260$	−25.2702	+	0.886520i	−1.56719	+	0.0549797i
$261$	−7.60146	+	6.58670i	−0.470519	+	0.407707i
$262$	0.173604	−	3.21976i	0.0107253	−	0.198917i
$263$	−4.39390	+	9.62131i	−0.270940	+	0.593275i	−0.995375	−	0.0960678i	$-0.969373\pi$
$263$	−4.39390	+	9.62131i	−0.270940	+	0.593275i	0.724435	+	0.689343i	$0.242101\pi$
$264$	3.24940	−	10.3431i	0.199987	−	0.636571i
$265$	−19.3576	+	5.68390i	−1.18913	+	0.349159i
$266$	1.33445	+	0.962919i	0.0818206	+	0.0590404i
$267$	−16.3394	+	2.34925i	−0.999954	+	0.143772i
$268$	5.78103	−	1.92005i	0.353132	−	0.117286i
$269$	11.8601	−	5.41632i	0.723123	−	0.330239i	−0.0196279	−	0.999807i	$-0.506248\pi$
$269$	11.8601	−	5.41632i	0.723123	−	0.330239i	0.742750	+	0.669568i	$0.233521\pi$
$270$	3.04783	−	1.19806i	0.185485	−	0.0729117i
$271$	−7.53634	−	1.08356i	−0.457800	−	0.0658217i	−0.0904429	−	0.995902i	$-0.528828\pi$
$271$	−7.53634	−	1.08356i	−0.457800	−	0.0658217i	−0.367357	+	0.930080i	$0.619737\pi$
$272$	−22.8975	+	4.95070i	−1.38836	+	0.300181i
$273$	−1.01381	−	0.878468i	−0.0613583	−	0.0531673i
$274$	−6.03695	+	11.5320i	−0.364705	+	0.696676i
$275$			1.38873i			0.0837437i
$276$	1.29833	−	9.50339i	0.0781505	−	0.572037i
$277$		−	2.35003i		−	0.141200i	−0.997505	−	0.0705999i	$-0.977509\pi$
$277$		−	2.35003i		−	0.141200i	0.997505	−	0.0705999i	$-0.0224914\pi$
$278$	−8.29018	−	4.33986i	−0.497212	−	0.260287i
$279$	2.84031	+	2.46114i	0.170045	+	0.147345i
$280$	0.640878	+	1.47615i	0.0382998	+	0.0882166i
$281$	31.7278	+	4.56178i	1.89272	+	0.272133i	0.988069	−	0.154011i	$-0.0492191\pi$
$281$	31.7278	+	4.56178i	1.89272	+	0.272133i	0.904656	+	0.426144i	$0.140128\pi$
$282$	−3.87235	−	9.85111i	−0.230595	−	0.586625i
$283$	−6.61258	+	3.01986i	−0.393077	+	0.179512i	−0.602141	−	0.798390i	$-0.705686\pi$
$283$	−6.61258	+	3.01986i	−0.393077	+	0.179512i	0.209064	+	0.977902i	$0.432958\pi$
$284$	29.0324	−	9.64251i	1.72276	−	0.572178i
$285$	−10.8551	+	1.56073i	−0.643000	+	0.0924495i
$286$	17.3179	−	23.9999i	1.02403	−	1.41914i
$287$	−1.78969	+	0.525501i	−0.105642	+	0.0310194i
$288$	4.33486	+	3.63441i	0.255434	+	0.214160i
$289$	−7.18678	+	15.7368i	−0.422752	+	0.925697i
$290$	32.8912	+	1.77344i	1.93144	+	0.104140i
$291$	−11.9852	+	10.3852i	−0.702585	+	0.608793i
$292$	0.735171	+	20.9560i	0.0430226	+	1.22636i
$293$	5.28346	−	3.39547i	0.308663	−	0.198366i	−0.377134	−	0.926159i	$-0.623090\pi$
$293$	5.28346	−	3.39547i	0.308663	−	0.198366i	0.685797	+	0.727793i	$0.259454\pi$
$294$	3.26794	−	9.25406i	0.190590	−	0.539707i
$295$	−10.2974	−	6.61771i	−0.599535	−	0.385298i
$296$	−1.67476	+	0.457741i	−0.0973437	+	0.0266056i
$297$	−1.07989	+	3.67777i	−0.0626617	+	0.213406i
$298$	−31.8860	−	6.35300i	−1.84711	−	0.368020i
$299$	11.5408	−	23.5033i	0.667421	−	1.35923i
$300$	−0.669278	−	0.277720i	−0.0386408	−	0.0160342i
$301$	−0.373259	+	1.27120i	−0.0215143	+	0.0732709i
$302$	10.5179	+	13.5485i	0.605239	+	0.779629i
$303$	2.75700	−	4.28998i	0.158386	−	0.246453i
$304$	−11.3332	−	15.1794i	−0.650006	−	0.870600i
$305$	5.97394	−	3.83922i	0.342067	−	0.219833i
$306$	8.06115	−	1.90221i	0.460825	−	0.108742i
$307$	17.6507	+	20.3700i	1.00738	+	1.16258i	0.986661	+	0.162790i	$0.0520494\pi$
$307$	17.6507	+	20.3700i	1.00738	+	1.16258i	0.0207169	+	0.999785i	$0.493405\pi$
$308$	−1.82476	−	0.466972i	−0.103975	−	0.0266082i
$309$	4.65343	−	10.1896i	0.264724	−	0.579665i
$310$	−1.09313	−	12.2591i	−0.0620855	−	0.696271i
$311$	2.86856	+	9.76941i	0.162661	+	0.553973i	0.999974	+	0.00724833i	$0.00230723\pi$
$311$	2.86856	+	9.76941i	0.162661	+	0.553973i	−0.837313	+	0.546724i	$0.815875\pi$
$312$	8.10312	+	13.1456i	0.458749	+	0.744225i
$313$	−8.32160	+	1.19647i	−0.470365	+	0.0676282i	−0.373422	−	0.927662i	$-0.621816\pi$
$313$	−8.32160	+	1.19647i	−0.470365	+	0.0676282i	−0.0969430	+	0.995290i	$0.530906\pi$
$314$	8.65765	+	15.2149i	0.488579	+	0.858625i
$315$	−0.236355	−	0.517545i	−0.0133171	−	0.0291604i
$316$	10.7670	−	1.93555i	0.605692	−	0.108883i
$317$	17.8163	+	2.56160i	1.00066	+	0.143874i	0.623126	−	0.782121i	$-0.285862\pi$
$317$	17.8163	+	2.56160i	1.00066	+	0.143874i	0.377536	+	0.925995i	$0.376771\pi$
$318$	8.86373	+	8.55823i	0.497053	+	0.479922i
$319$	−25.2471	+	29.1367i	−1.41357	+	1.63134i
$320$	−1.94530	−	18.4229i	−0.108746	−	1.02987i
$321$			7.17972i			0.400733i
$322$	−1.66084	−	0.136346i	−0.0925548	−	0.00759828i
$323$	−27.7364			−1.54329
$324$	−1.55649	−	1.25592i	−0.0864716	−	0.0697735i
$325$	−1.49494	−	1.29537i	−0.0829243	−	0.0718543i
$326$	4.27520	+	4.12785i	0.236781	+	0.228620i
$327$	−0.759000	+	5.27896i	−0.0419728	+	0.291927i
$328$	21.4683	+	0.403630i	1.18539	+	0.0222867i
$329$	−1.67280	+	0.763940i	−0.0922242	+	0.0421174i
$330$	10.9100	−	6.20806i	0.600575	−	0.341743i
$331$	−0.544538	−	3.78734i	−0.0299305	−	0.208171i	0.969368	−	0.245611i	$-0.0789887\pi$
$331$	−0.544538	−	3.78734i	−0.0299305	−	0.208171i	−0.999299	+	0.0374402i	$0.988080\pi$
$332$	0.0776895	+	0.0835504i	0.00426377	+	0.00458542i
$333$	0.588972	−	0.172938i	0.0322755	−	0.00947693i
$334$	1.14942	+	12.8904i	0.0628936	+	0.705333i
$335$	6.41562	+	2.92992i	0.350523	+	0.160078i
$336$	0.589967	−	0.786029i	0.0321854	−	0.0428814i
$337$	−3.82404	+	3.31355i	−0.208309	+	0.180500i	−0.752766	−	0.658288i	$-0.771281\pi$
$337$	−3.82404	+	3.31355i	−0.208309	+	0.180500i	0.544458	+	0.838788i	$0.316736\pi$
$338$	5.45933	+	23.1355i	0.296948	+	1.25840i
$339$	−1.49615	−	2.32805i	−0.0812595	−	0.126442i
$340$	−23.3183	−	13.8553i	−1.26461	−	0.751411i
$341$	12.1188	+	7.78825i	0.656268	+	0.421758i
$342$	4.10708	+	5.29047i	0.222085	+	0.286076i
$343$	−3.28624	−	0.964928i	−0.177440	−	0.0521012i
$344$	8.48528	−	12.6731i	0.457496	−	0.683286i
$345$	8.59364	−	7.03437i	0.462666	−	0.378718i
$346$	−0.359575	+	1.80472i	−0.0193308	+	0.0970223i
$347$	21.6332	+	6.35207i	1.16133	+	0.340997i	0.804949	−	0.593344i	$-0.202193\pi$
$347$	21.6332	+	6.35207i	1.16133	+	0.340997i	0.356380	+	0.934341i	$0.384011\pi$
$348$	−8.99304	−	17.9942i	−0.482078	−	0.964593i
$349$	−7.37582	+	11.4770i	−0.394818	+	0.614350i	−0.980577	−	0.196136i	$-0.937160\pi$
$349$	−7.37582	+	11.4770i	−0.394818	+	0.614350i	0.585758	+	0.810486i	$0.300797\pi$
$350$	−0.0419198	+	0.118707i	−0.00224071	+	0.00634518i
$351$	−2.95175	−	4.59301i	−0.157553	−	0.245157i
$352$	18.4291	+	11.4244i	0.982276	+	0.608923i
$353$	−20.8656	−	24.0802i	−1.11057	−	1.28166i	−0.955899	−	0.293695i	$-0.905115\pi$
$353$	−20.8656	−	24.0802i	−1.11057	−	1.28166i	−0.154667	−	0.987967i	$-0.549430\pi$
$354$	−0.402480	+	7.46462i	−0.0213916	+	0.396740i
$355$	32.2193	+	14.7141i	1.71002	+	0.780942i
$356$	3.54989	−	32.8234i	0.188144	−	1.73964i
$357$	−0.405408	−	1.38069i	−0.0214565	−	0.0730740i
$358$	−18.3756	+	25.4657i	−0.971180	+	1.34590i
$359$	1.97633	+	13.7456i	0.104306	+	0.725467i	0.973115	+	0.230319i	$0.0739771\pi$
$359$	1.97633	+	13.7456i	0.104306	+	0.725467i	−0.868809	+	0.495148i	$0.835114\pi$
$360$	0.810087	+	6.49940i	0.0426953	+	0.342548i
$361$	−1.42429	−	3.11876i	−0.0749626	−	0.164145i
$362$	−8.63221	+	3.39321i	−0.453699	+	0.178343i
$363$	−0.525453	+	3.65461i	−0.0275792	+	0.191817i
$364$	2.20477	−	1.52873i	0.115561	−	0.0801274i
$365$	−15.8990	+	18.3485i	−0.832193	+	0.960402i
$366$	−3.84221	−	2.01137i	−0.200835	−	0.105136i
$367$	−6.60690			−0.344877			−0.172439	−	0.985020i	$-0.555165\pi$
$367$	−6.60690			−0.344877			−0.172439	+	0.985020i	$0.555165\pi$
$368$	17.7696	+	7.22775i	0.926306	+	0.376772i
$369$	−7.59154			−0.395200
$370$	−1.78095	−	0.932314i	−0.0925870	−	0.0484687i
$371$	1.40181	−	1.61778i	0.0727784	−	0.0839908i
$372$	−6.17695	+	4.28295i	−0.320260	+	0.222060i
$373$	5.13674	−	35.7268i	0.265970	−	1.84986i	−0.219502	−	0.975612i	$-0.570443\pi$
$373$	5.13674	−	35.7268i	0.265970	−	1.84986i	0.485473	−	0.874252i	$-0.338648\pi$
$374$	29.5465	−	11.6144i	1.52781	−	0.600564i
$375$	4.46129	+	9.76885i	0.230380	+	0.504461i
$376$	21.0072	−	2.61834i	1.08336	−	0.135031i
$377$	−7.81519	−	54.3559i	−0.402503	−	2.79947i
$378$	−0.203324	+	0.281775i	−0.0104579	+	0.0144929i
$379$	2.66267	+	9.06822i	0.136772	+	0.465803i	0.999183	−	0.0404050i	$-0.0128648\pi$
$379$	2.66267	+	9.06822i	0.136772	+	0.465803i	−0.862411	+	0.506208i	$0.831047\pi$
$380$	2.35837	−	21.8063i	0.120982	−	1.11864i
$381$	18.1256	+	8.27768i	0.928602	+	0.424078i
$382$	0.583549	−	10.8228i	0.0298570	−	0.553744i
$383$	−15.3049	−	17.6628i	−0.782044	−	0.902527i	0.215211	−	0.976568i	$-0.430956\pi$
$383$	−15.3049	−	17.6628i	−0.782044	−	0.902527i	−0.997255	+	0.0740403i	$0.976411\pi$
$384$	−9.19130	+	6.59698i	−0.469041	+	0.336651i
$385$	−1.17906	−	1.83465i	−0.0600903	−	0.0935023i
$386$	5.28531	−	14.9668i	0.269015	−	0.761791i
$387$	−2.91524	+	4.53621i	−0.148190	+	0.230588i
$388$	−14.1793	−	28.3715i	−0.719845	−	1.44034i
$389$	3.60626	+	1.05889i	0.182844	+	0.0536880i	0.371873	−	0.928284i	$-0.378716\pi$
$389$	3.60626	+	1.05889i	0.182844	+	0.0536880i	−0.189029	+	0.981972i	$0.560534\pi$
$390$	−3.49371	+	17.5351i	−0.176911	+	0.887923i
$391$	24.0452	−	14.5167i	1.21602	−	0.734140i
$392$	16.3099	+	10.9203i	0.823776	+	0.551561i
$393$	−2.18766	−	0.642356i	−0.110353	−	0.0324026i
$394$	−15.1569	−	19.5242i	−0.763596	−	0.983614i
$395$	10.6555	+	6.84789i	0.536137	+	0.344555i
$396$	−6.59046	−	3.91594i	−0.331183	−	0.196783i
$397$	−1.31518	−	2.04646i	−0.0660070	−	0.102709i	0.806681	−	0.590987i	$-0.201262\pi$
$397$	−1.31518	−	2.04646i	−0.0660070	−	0.102709i	−0.872688	+	0.488278i	$0.837625\pi$
$398$	6.24407	+	26.4610i	0.312987	+	1.32637i
$399$	0.879398	−	0.762003i	0.0440250	−	0.0381479i
$400$	0.869955	−	1.15906i	0.0434977	−	0.0579532i
$401$	15.8212	+	7.22529i	0.790072	+	0.360814i	0.769232	−	0.638969i	$-0.220639\pi$
$401$	15.8212	+	7.22529i	0.790072	+	0.360814i	0.0208394	+	0.999783i	$0.493366\pi$
$402$	−0.382564	−	4.29035i	−0.0190806	−	0.213983i
$403$	−19.6879	+	5.78090i	−0.980726	+	0.287967i
$404$	6.94507	+	7.46900i	0.345530	+	0.371597i
$405$	−0.329554	−	2.29210i	−0.0163756	−	0.113895i
$406$	−3.03761	+	1.72847i	−0.150754	+	0.0857827i
$407$	2.14024	−	0.977413i	0.106088	−	0.0484486i
$408$	−0.311388	+	16.5622i	−0.0154160	+	0.819949i
$409$	1.30062	−	9.04602i	0.0643116	−	0.447297i	−0.932068	−	0.362283i	$-0.881997\pi$
$409$	1.30062	−	9.04602i	0.0643116	−	0.447297i	0.996380	−	0.0850140i	$-0.0270935\pi$
$410$	17.8850	+	17.2685i	0.883276	+	0.852833i
$411$	6.95603	+	6.02744i	0.343116	+	0.297312i
$412$	17.4356	+	14.0687i	0.858990	+	0.693115i
$413$	1.29876			0.0639079
$414$	−6.32944	−	2.43685i	−0.311075	−	0.119764i
$415$			0.132096i			0.00648434i
$416$	−29.4883	+	9.18218i	−1.44578	+	0.450194i
$417$	−4.33302	+	5.00057i	−0.212189	+	0.244879i
$418$	18.4683	+	17.8318i	0.903314	+	0.872180i
$419$	9.44017	+	1.35729i	0.461183	+	0.0663080i	0.368990	−	0.929433i	$-0.379704\pi$
$419$	9.44017	+	1.35729i	0.461183	+	0.0663080i	0.0921921	+	0.995741i	$0.470613\pi$
$420$	1.11997	−	0.201333i	0.0546489	−	0.00982405i
$421$	−6.94145	−	15.1997i	−0.338306	−	0.740786i	0.661654	−	0.749810i	$-0.269855\pi$
$421$	−6.94145	−	15.1997i	−0.338306	−	0.740786i	−0.999959	+	0.00902344i	$0.997128\pi$
$422$	−12.6818	−	22.2869i	−0.617342	−	1.08491i
$423$	−7.40845	+	1.06517i	−0.360211	+	0.0517906i
$424$	−20.9771	+	12.9305i	−1.01874	+	0.627962i
$425$	−0.597807	−	2.03594i	−0.0289979	−	0.0987578i
$426$	−1.92124	−	21.5462i	−0.0930846	−	1.04392i
$427$	−0.313002	+	0.685379i	−0.0151472	+	0.0331678i
$428$	−13.9112	−	3.55999i	−0.672421	−	0.172078i
$429$	−13.7045	−	15.8158i	−0.661658	−	0.763595i
$430$	17.1866	−	4.05556i	0.828812	−	0.195577i
$431$	−23.9841	+	15.4137i	−1.15528	+	0.742450i	−0.970683	−	0.240365i	$-0.922733\pi$
$431$	−23.9841	+	15.4137i	−1.15528	+	0.742450i	−0.184593	+	0.982815i	$0.559097\pi$
$432$	3.20520	−	2.39306i	0.154210	−	0.115136i
$433$	−7.70302	+	11.9861i	−0.370184	+	0.576017i	−0.975509	−	0.219961i	$-0.929407\pi$
$433$	−7.70302	+	11.9861i	−0.370184	+	0.576017i	0.605325	+	0.795979i	$0.293043\pi$
$434$	0.800805	+	1.03154i	0.0384399	+	0.0495157i
$435$	6.56194	−	22.3479i	0.314621	−	1.07150i
$436$	−9.85197	−	4.08812i	−0.471824	−	0.195786i
$437$	18.7551	+	12.8103i	0.897179	+	0.612798i
$438$	14.5414	+	2.89725i	0.694817	+	0.138436i
$439$	−6.40785	+	21.8231i	−0.305830	+	1.04156i	0.652947	+	0.757403i	$0.273532\pi$
$439$	−6.40785	+	21.8231i	−0.305830	+	1.04156i	−0.958777	+	0.284158i	$0.908286\pi$
$440$	6.61890	+	24.2170i	0.315544	+	1.15450i
$441$	−5.83799	−	3.75185i	−0.277999	−	0.178659i
$442$	−15.0576	+	42.6397i	−0.716218	+	2.02817i
$443$	−7.07225	+	4.54506i	−0.336013	+	0.215942i	−0.697756	−	0.716336i	$-0.745818\pi$
$443$	−7.07225	+	4.54506i	−0.336013	+	0.215942i	0.361743	+	0.932278i	$0.382182\pi$
$444$	0.0430423	+	1.22692i	0.00204270	+	0.0582270i
$445$	28.8890	−	25.0325i	1.36947	−	1.18665i
$446$	−0.403505	−	0.0217563i	−0.0191065	−	0.00103019i
$447$	−9.55038	+	20.9124i	−0.451717	+	0.989123i
$448$	1.23045	+	1.53284i	0.0581333	+	0.0724200i
$449$	14.5361	−	4.26818i	0.686000	−	0.201428i	0.0798844	−	0.996804i	$-0.474545\pi$
$449$	14.5361	−	4.26818i	0.686000	−	0.201428i	0.606116	+	0.795376i	$0.292727\pi$
$450$	−0.299818	+	0.415500i	−0.0141335	+	0.0195869i
$451$	−28.8025	+	4.14117i	−1.35626	+	0.195000i
$452$	5.25258	−	1.74454i	0.247061	−	0.0820561i
$453$	11.0322	−	5.03826i	0.518340	−	0.236718i
$454$	−4.27965	−	10.8873i	−0.200854	−	0.510966i
$455$	3.07475	+	0.442082i	0.144146	+	0.0207251i
$456$	−12.2871	+	5.33450i	−0.575394	+	0.249811i
$457$	1.87103	+	1.62126i	0.0875233	+	0.0758394i	0.697524	−	0.716562i	$-0.254285\pi$
$457$	1.87103	+	1.62126i	0.0875233	+	0.0758394i	−0.610000	+	0.792401i	$0.708831\pi$
$458$	8.60469	+	4.50450i	0.402071	+	0.210481i
$459$		−	5.85664i		−	0.273365i
$460$	9.36846	+	20.1386i	0.436807	+	0.938968i
$461$			2.76849i			0.128941i	0.997920	+	0.0644707i	$0.0205359\pi$
$461$			2.76849i			0.128941i	−0.997920	+	0.0644707i	$0.979464\pi$
$462$	−0.617709	+	1.17997i	−0.0287384	+	0.0548974i
$463$	−7.58995	−	6.57673i	−0.352735	−	0.305647i	0.460412	−	0.887706i	$-0.347702\pi$
$463$	−7.58995	−	6.57673i	−0.352735	−	0.305647i	−0.813147	+	0.582059i	$0.802247\pi$
$464$	39.3241	−	8.50233i	1.82557	−	0.394711i
$465$	−8.61431	−	1.23855i	−0.399479	−	0.0574364i
$466$	−12.5939	+	4.95048i	−0.583399	+	0.229327i
$467$	32.1428	−	14.6791i	1.48739	−	0.679269i	0.504494	−	0.863415i	$-0.331679\pi$
$467$	32.1428	−	14.6791i	1.48739	−	0.679269i	0.982899	+	0.184146i	$0.0589519\pi$
$468$	10.3628	−	3.44180i	0.479022	−	0.159097i
$469$	−0.740731	+	0.106501i	−0.0342038	+	0.00491776i
$470$	19.8766	+	14.3426i	0.916839	+	0.661576i
$471$	11.8769	−	3.48739i	0.547261	−	0.160690i
$472$	−14.2636	−	4.48108i	−0.656535	−	0.206258i
$473$	−8.58601	+	18.8007i	−0.394785	+	0.864459i
$474$	0.416479	−	7.72425i	0.0191295	−	0.354787i
$475$	1.29674	−	1.12364i	0.0594987	−	0.0515559i
$476$	2.87619	−	0.100902i	0.131830	−	0.00462482i
$477$	7.32927	−	4.71024i	0.335584	−	0.215667i
$478$	−25.4526	−	8.98821i	−1.16417	−	0.411111i
$479$	−3.93364	−	2.52799i	−0.179732	−	0.115507i	0.447681	−	0.894193i	$-0.352250\pi$
$479$	−3.93364	−	2.52799i	−0.179732	−	0.115507i	−0.627413	+	0.778686i	$0.715886\pi$
$480$	−12.9947	−	1.65306i	−0.593122	−	0.0754517i
$481$	−0.944191	+	3.21562i	−0.0430514	+	0.146620i
$482$	2.49874	−	12.5413i	0.113814	−	0.571239i
$483$	−0.363550	+	1.12086i	−0.0165421	+	0.0510007i
$484$	−6.82049	−	2.83020i	−0.310022	−	0.128645i
$485$	10.3462	−	35.2359i	0.469796	−	1.59998i
$486$	−1.11710	+	0.867226i	−0.0506728	+	0.0393382i
$487$	0.391580	−	0.609311i	0.0177442	−	0.0276105i	−0.832268	−	0.554373i	$-0.812958\pi$
$487$	0.391580	−	0.609311i	0.0177442	−	0.0276105i	0.850012	+	0.526763i	$0.176594\pi$
$488$	5.80227	−	6.44720i	0.262656	−	0.291851i
$489$	3.53509	−	2.27186i	0.159862	−	0.102737i
$490$	5.21941	+	22.1187i	0.235789	+	0.999223i
$491$	11.7670	+	13.5799i	0.531038	+	0.612851i	0.956360	−	0.292191i	$-0.0943844\pi$
$491$	11.7670	+	13.5799i	0.531038	+	0.612851i	−0.425321	+	0.905042i	$0.639839\pi$
$492$	3.76418	−	14.7091i	0.169702	−	0.663136i
$493$	24.4709	−	53.5838i	1.10211	−	2.41329i
$494$	−36.4222	+	3.24772i	−1.63871	+	0.146122i
$495$	−2.50067	−	8.51649i	−0.112397	−	0.382788i
$496$	−5.23570	−	14.0919i	−0.235090	−	0.632744i
$497$	−3.71996	+	0.534850i	−0.166863	+	0.0239913i
$498$	0.0701164	−	0.0398980i	0.00314199	−	0.00178787i
$499$	−15.6642	−	34.2999i	−0.701227	−	1.53547i	−0.838477	−	0.544937i	$-0.816553\pi$
$499$	−15.6642	−	34.2999i	−0.701227	−	1.53547i	0.137249	−	0.990537i	$-0.456174\pi$
$500$	−21.1398	+	3.80024i	−0.945402	+	0.169952i
$501$	9.05793	+	1.30233i	0.404678	+	0.0581840i
$502$	9.26043	−	9.59100i	0.413313	−	0.428067i
$503$	23.9448	−	27.6337i	1.06764	−	1.23213i	0.0960750	−	0.995374i	$-0.469371\pi$
$503$	23.9448	−	27.6337i	1.06764	−	1.23213i	0.971570	−	0.236754i	$-0.0760834\pi$
$504$	−0.445140	−	0.533668i	−0.0198281	−	0.0237715i
$505$			11.8088i			0.525483i
$506$	−25.3433	−	5.79276i	−1.12665	−	0.257519i
$507$	16.8085			0.746493
$508$	−25.0259	+	31.0150i	−1.11034	+	1.37607i
$509$	11.1005	+	9.61865i	0.492022	+	0.426339i	0.865205	−	0.501419i	$-0.167188\pi$
$509$	11.1005	+	9.61865i	0.492022	+	0.426339i	−0.373183	+	0.927758i	$0.621734\pi$
$510$	−13.3222	+	13.7977i	−0.589915	+	0.610973i
$511$	0.366609	−	2.54982i	0.0162178	−	0.112797i
$512$	−8.22464	−	21.0797i	−0.363481	−	0.931601i
$513$	4.30791	−	1.96736i	0.190199	−	0.0868609i
$514$	14.0079	+	24.6173i	0.617862	+	1.08582i
$515$	3.69162	+	25.6758i	0.162672	+	1.13141i
$516$	−7.34369	−	7.89769i	−0.323288	−	0.347676i
$517$	−27.5268	+	8.08260i	−1.21063	+	0.355472i
$518$	0.212449	−	0.0189438i	0.00933447	−	0.000832342i
$519$	1.18362	+	0.540543i	0.0519553	+	0.0237272i
$520$	−32.2430	−	15.4639i	−1.41395	−	0.678135i
$521$	−26.9410	+	23.3445i	−1.18031	+	1.02274i	−0.181079	+	0.983469i	$0.557959\pi$
$521$	−26.9410	+	23.3445i	−1.18031	+	1.02274i	−0.999228	+	0.0392736i	$0.987496\pi$
$522$	−13.8442	+	3.26684i	−0.605944	+	0.142986i
$523$	−3.78195	−	5.88483i	−0.165373	−	0.257325i	0.748670	−	0.662943i	$-0.230693\pi$
$523$	−3.78195	−	5.88483i	−0.165373	−	0.257325i	−0.914043	+	0.405618i	$0.867056\pi$
$524$	2.32933	−	3.92023i	0.101757	−	0.171256i
$525$	0.0748874	+	0.0481272i	0.00326836	+	0.00210044i
$526$	−11.8158	+	9.17277i	−0.515192	+	0.399952i
$527$	−21.1192	−	6.20117i	−0.919969	−	0.270127i
$528$	10.8552	−	10.8277i	0.472411	−	0.471217i
$529$	−22.9638	−	1.28939i	−0.998427	−	0.0560606i
$530$	−27.9815	−	5.57507i	−1.21544	−	0.242166i
$531$	5.07183	+	1.48922i	0.220099	+	0.0646268i
$532$	1.04039	+	2.08172i	0.0451065	+	0.0902540i
$533$	22.4083	−	34.8680i	0.970612	−	1.51030i
$534$	−22.0128	−	7.77349i	−0.952586	−	0.336392i
$535$	−8.98861	−	13.9865i	−0.388611	−	0.604691i
$536$	8.50250	+	1.38608i	0.367252	+	0.0598695i
$537$	14.5415	+	16.7817i	0.627510	+	0.724185i
$538$	18.4123	+	0.992759i	0.793809	+	0.0428009i
$539$	−24.1961	−	11.0500i	−1.04220	−	0.475957i
$540$	4.60448	+	0.497980i	0.198145	+	0.0214296i
$541$	−8.95509	−	30.4982i	−0.385009	−	1.31122i	−0.893077	−	0.449904i	$-0.851458\pi$
$541$	−8.95509	−	30.4982i	−0.385009	−	1.31122i	0.508067	−	0.861317i	$-0.330360\pi$
$542$	−8.73171	−	6.30066i	−0.375059	−	0.270636i
$543$	0.933377	+	6.49178i	0.0400551	+	0.278589i
$544$	−31.9358	−	8.81549i	−1.36924	−	0.377961i
$545$	−5.13038	−	11.2340i	−0.219761	−	0.481210i
$546$	−0.694034	−	1.76560i	−0.0297019	−	0.0755606i
$547$	1.84641	−	12.8421i	0.0789467	−	0.549087i	−0.911512	−	0.411274i	$-0.865084\pi$
$547$	1.84641	−	12.8421i	0.0789467	−	0.549087i	0.990458	−	0.137812i	$-0.0440071\pi$
$548$	−15.1276	+	10.4891i	−0.646219	+	0.448072i
$549$	−2.00820	+	2.31759i	−0.0857079	+	0.0989122i
$550$	−0.910862	+	1.73997i	−0.0388393	+	0.0741925i
$551$	47.6344			2.02929
$552$	7.85992	−	11.0554i	0.334540	−	0.470549i
$553$	−1.34394			−0.0571500
$554$	1.54137	−	2.94440i	0.0654867	−	0.125096i
$555$	−0.930845	+	1.07425i	−0.0395122	+	0.0455995i
$556$	−7.54043	−	10.8750i	−0.319785	−	0.461201i
$557$	−2.22989	+	15.5092i	−0.0944835	+	0.657147i	0.886453	+	0.462819i	$0.153162\pi$
$557$	−2.22989	+	15.5092i	−0.0944835	+	0.657147i	−0.980937	+	0.194328i	$0.937747\pi$
$558$	1.94443	+	4.94655i	0.0823141	+	0.209404i
$559$	−12.2298	−	26.7795i	−0.517264	−	1.13265i
$560$	−0.165229	+	2.26984i	−0.00698220	+	0.0959182i
$561$	−3.19479	−	22.2202i	−0.134884	−	0.938139i
$562$	36.7603	+	26.5256i	1.55064	+	1.11892i
$563$	−0.264712	−	0.901527i	−0.0111563	−	0.0379948i	0.953727	−	0.300675i	$-0.0972119\pi$
$563$	−0.264712	−	0.901527i	−0.0111563	−	0.0379948i	−0.964883	+	0.262680i	$0.915394\pi$
$564$	1.60956	−	14.8825i	0.0677746	−	0.626666i
$565$	5.82917	+	2.66209i	0.245235	+	0.111995i
$566$	−10.2657	−	0.553511i	−0.431501	−	0.0232658i
$567$	0.160900	+	0.185688i	0.00675716	+	0.00779818i
$568$	42.6997	+	6.96091i	1.79164	+	0.292073i
$569$	−13.3941	−	20.8417i	−0.561511	−	0.873728i	0.438173	−	0.898891i	$-0.355626\pi$
$569$	−13.3941	−	20.8417i	−0.561511	−	0.873728i	−0.999683	+	0.0251630i	$0.991990\pi$
$570$	−14.6242	−	5.16433i	−0.612541	−	0.216310i
$571$	−21.1207	+	32.8644i	−0.883872	+	1.37533i	0.0426490	+	0.999090i	$0.486420\pi$
$571$	−21.1207	+	32.8644i	−0.883872	+	1.37533i	−0.926521	+	0.376242i	$0.877216\pi$
$572$	37.4393	−	18.7112i	1.56542	−	0.782353i
$573$	−7.35356	−	2.15920i	−0.307200	−	0.0902019i
$574$	−2.58701	−	0.515439i	−0.107980	−	0.0215140i
$575$	−0.536084	+	1.65279i	−0.0223562	+	0.0689262i
$576$	3.04743	+	7.39683i	0.126976	+	0.308201i
$577$	1.40373	+	0.412173i	0.0584382	+	0.0171590i	0.310821	−	0.950468i	$-0.399396\pi$
$577$	1.40373	+	0.412173i	0.0584382	+	0.0171590i	−0.252383	+	0.967627i	$0.581214\pi$
$578$	−19.3261	+	15.0032i	−0.803862	+	0.624051i
$579$	−9.44192	−	6.06796i	−0.392393	−	0.252176i
$580$	40.0468	+	23.7951i	1.66285	+	0.988038i
$581$	−0.00757757	−	0.0117909i	−0.000314370	−	0.000489170i
$582$	−21.8281	+	5.15082i	−0.904803	+	0.213508i
$583$	25.2380	−	21.8689i	1.04525	−	0.905716i
$584$	−12.8238	+	26.7384i	−0.530653	+	1.10644i
$585$	11.5004	+	5.25204i	0.475482	+	0.217145i
$586$	8.84681	−	0.788858i	0.365458	−	0.0325874i
$587$	−43.8926	+	12.8880i	−1.81164	+	0.531946i	−0.998727	−	0.0504388i	$-0.983938\pi$
$587$	−43.8926	+	12.8880i	−1.81164	+	0.531946i	−0.812913	+	0.582384i	$0.802120\pi$
$588$	10.1641	−	9.45115i	0.419162	−	0.389759i
$589$	−2.53302	−	17.6176i	−0.104371	−	0.725919i
$590$	−8.56122	−	15.0454i	−0.352460	−	0.619410i
$591$	−15.8981	+	7.26042i	−0.653961	+	0.298654i
$592$	−2.39857	−	0.524957i	−0.0985807	−	0.0215756i
$593$	1.70202	−	11.8378i	0.0698937	−	0.486121i	−0.924568	−	0.381018i	$-0.875574\pi$
$593$	1.70202	−	11.8378i	0.0698937	−	0.486121i	0.994461	−	0.105103i	$-0.0335173\pi$
$594$	−3.76525	+	3.89965i	−0.154490	+	0.160005i
$595$	2.51831	+	2.18213i	0.103241	+	0.0894585i
$596$	−35.7836	−	28.8736i	−1.46575	−	1.18271i
$597$	19.2247			0.786813
$598$	29.8754	−	21.8782i	1.22169	−	0.894666i
$599$		−	3.62324i		−	0.148042i	−0.997257	−	0.0740208i	$-0.976417\pi$
$599$		−	3.62324i		−	0.148042i	0.997257	−	0.0740208i	$-0.0235831\pi$
$600$	−0.656396	−	0.786937i	−0.0267972	−	0.0321266i
$601$	6.55041	−	7.55957i	0.267197	−	0.308361i	−0.606257	−	0.795269i	$-0.707330\pi$
$601$	6.55041	−	7.55957i	0.267197	−	0.308361i	0.873454	+	0.486907i	$0.161875\pi$
$602$	−1.30144	+	1.34789i	−0.0530426	+	0.0549360i
$603$	−3.01477	−	0.433458i	−0.122771	−	0.0176518i
$604$	4.29172	+	23.8738i	0.174627	+	0.971412i
$605$	−3.55175	−	7.77724i	−0.144399	−	0.316190i
$606$	6.26807	−	3.56669i	0.254623	−	0.144887i
$607$	−31.2262	+	4.48965i	−1.26743	+	0.182229i	−0.743040	−	0.669247i	$-0.766617\pi$
$607$	−31.2262	+	4.48965i	−1.26743	+	0.182229i	−0.524393	+	0.851476i	$0.675708\pi$
$608$	−4.24351	−	26.4520i	−0.172097	−	1.07277i
$609$	0.696246	+	2.37120i	0.0282133	+	0.0960858i
$610$	10.0030	−	0.891952i	0.405009	−	0.0361141i
$611$	16.9755	−	37.1712i	0.686756	−	1.50379i
$612$	11.3476	+	2.90395i	0.458700	+	0.117385i
$613$	6.02669	+	6.95517i	0.243416	+	0.280917i	0.864290	−	0.502993i	$-0.167768\pi$
$613$	6.02669	+	6.95517i	0.243416	+	0.280917i	−0.620875	+	0.783910i	$0.713222\pi$
$614$	8.75431	+	37.0989i	0.353295	+	1.49719i
$615$	14.7888	−	9.50418i	0.596342	−	0.383245i
$616$	−1.97999	−	1.78193i	−0.0797760	−	0.0717958i
$617$	−3.95322	+	6.15133i	−0.159151	+	0.247643i	−0.911667	−	0.410931i	$-0.865204\pi$
$617$	−3.95322	+	6.15133i	−0.159151	+	0.247643i	0.752516	+	0.658574i	$0.228840\pi$
$618$	12.5136	−	9.71455i	0.503373	−	0.390777i
$619$	−0.659273	+	2.24528i	−0.0264984	+	0.0902453i	−0.971681	−	0.236298i	$-0.924066\pi$
$619$	−0.659273	+	2.24528i	−0.0264984	+	0.0902453i	0.945182	+	0.326544i	$0.105884\pi$
$620$	6.67108	−	16.0766i	0.267917	−	0.645653i
$621$	−2.70494	+	3.96022i	−0.108545	+	0.158918i
$622$	−2.81363	+	14.1217i	−0.112816	+	0.566230i
$623$	−1.14267	+	3.89159i	−0.0457803	+	0.155913i
$624$	1.53040	+	21.7852i	0.0612652	+	0.872105i
$625$	−22.4449	−	14.4244i	−0.897795	−	0.576978i
$626$	−11.2110	−	3.95902i	−0.448083	−	0.158234i
$627$	15.2711	−	9.81416i	0.609870	−	0.391940i
$628$	0.867972	+	24.7415i	0.0346359	+	0.987293i
$629$	−2.71693	+	2.35424i	−0.108331	+	0.0938696i
$630$	0.0433215	−	0.803465i	0.00172597	−	0.0320108i
$631$	3.97806	−	8.71073i	0.158364	−	0.346769i	−0.813773	−	0.581183i	$-0.802590\pi$
$631$	3.97806	−	8.71073i	0.158364	−	0.346769i	0.972137	+	0.234415i	$0.0753173\pi$
$632$	14.7597	+	4.63694i	0.587110	+	0.184448i
$633$	−17.3975	+	5.10837i	−0.691488	+	0.203039i
$634$	20.6422	+	14.8951i	0.819807	+	0.591559i
$635$	−45.6729	+	6.56678i	−1.81248	+	0.260595i
$636$	5.49223	+	16.5364i	0.217781	+	0.655712i
$637$	34.4645	−	15.7394i	1.36553	−	0.623619i
$638$	−50.7431	+	19.9465i	−2.00894	+	0.789688i
$639$	−15.1402	−	2.17683i	−0.598937	−	0.0861142i
$640$	9.64617	−	24.3583i	0.381298	−	0.962846i
$641$	2.11100	+	1.82919i	0.0833794	+	0.0722486i	0.695553	−	0.718475i	$-0.255159\pi$
$641$	2.11100	+	1.82919i	0.0833794	+	0.0722486i	−0.612174	+	0.790723i	$0.709705\pi$
$642$	−4.70914	+	8.99560i	−0.185855	+	0.355028i
$643$		−	21.9936i		−	0.867344i	−0.901071	−	0.433672i	$-0.857218\pi$
$643$		−	21.9936i		−	0.867344i	0.901071	−	0.433672i	$-0.142782\pi$
$644$	−1.99146	−	1.26016i	−0.0784747	−	0.0496574i
$645$		−	12.4865i		−	0.491657i
$646$	−34.7514	−	18.1921i	−1.36727	−	0.715759i
$647$	−24.7258	−	21.4250i	−0.972070	−	0.842303i	0.0154368	−	0.999881i	$-0.495086\pi$
$647$	−24.7258	−	21.4250i	−0.972070	−	0.842303i	−0.987507	+	0.157578i	$0.949632\pi$
$648$	−1.12640	−	2.59446i	−0.0442492	−	0.101920i
$649$	20.0550	+	2.88348i	0.787229	+	0.113186i
$650$	−1.02341	−	2.60352i	−0.0401414	−	0.102118i
$651$	0.839964	−	0.383599i	0.0329208	−	0.0150344i
$652$	2.64904	+	7.97593i	0.103744	+	0.312362i
$653$	−25.1880	+	3.62149i	−0.985682	+	0.141720i	−0.616261	−	0.787542i	$-0.711353\pi$
$653$	−25.1880	+	3.62149i	−0.985682	+	0.141720i	−0.369421	+	0.929262i	$0.620444\pi$
$654$	−4.41340	+	6.11628i	−0.172578	+	0.239165i
$655$	5.06590	−	1.48748i	0.197941	−	0.0581207i
$656$	26.6333	+	14.5867i	1.03986	+	0.569514i
$657$	4.35540	−	9.53699i	0.169920	−	0.372074i
$658$	−2.59694	−	0.140023i	−0.101239	−	0.00545866i
$659$	1.51932	−	1.31650i	0.0591843	−	0.0512835i	−0.624766	−	0.780812i	$-0.714806\pi$
$659$	1.51932	−	1.31650i	0.0591843	−	0.0512835i	0.683951	+	0.729528i	$0.260260\pi$
$660$	17.7412	−	0.622389i	0.690574	−	0.0242264i
$661$	−35.0333	+	22.5146i	−1.36264	+	0.875715i	−0.998453	−	0.0556109i	$-0.982289\pi$
$661$	−35.0333	+	22.5146i	−1.36264	+	0.875715i	−0.364187	+	0.931326i	$0.618653\pi$
$662$	1.80184	−	5.10239i	0.0700303	−	0.198310i
$663$	26.8996	+	17.2873i	1.04469	+	0.671384i
$664$	0.0425384	+	0.155638i	0.00165081	+	0.00603992i
$665$	−0.759138	+	2.58539i	−0.0294381	+	0.100257i
$666$	0.851362	+	0.169626i	0.0329896	+	0.00657289i
$667$	−41.2952	+	24.9309i	−1.59895	+	0.965328i
$668$	−7.01463	+	16.9045i	−0.271404	+	0.654057i
$669$	−0.0805010	+	0.274161i	−0.00311235	+	0.0105997i
$670$	6.11653	+	7.87891i	0.236302	+	0.304389i
$671$	−6.35492	+	9.88845i	−0.245329	+	0.381739i
$672$	1.25473	−	0.597873i	0.0484023	−	0.0230635i
$673$	−6.37562	+	4.09736i	−0.245762	+	0.157942i	−0.657723	−	0.753260i	$-0.728480\pi$
$673$	−6.37562	+	4.09736i	−0.245762	+	0.157942i	0.411961	+	0.911201i	$0.364844\pi$
$674$	−6.96454	+	1.64344i	−0.268264	+	0.0633029i
$675$	0.237260	+	0.273812i	0.00913214	+	0.0105390i
$676$	−8.33433	+	32.5676i	−0.320551	+	1.25260i
$677$	−1.67051	+	3.65791i	−0.0642030	+	0.140585i	−0.939013	−	0.343880i	$-0.888259\pi$
$677$	−1.67051	+	3.65791i	−0.0642030	+	0.140585i	0.874810	+	0.484465i	$0.160986\pi$
$678$	−0.347594	−	3.89817i	−0.0133493	−	0.149708i
$679$	1.09777	+	3.73866i	0.0421285	+	0.143477i
$680$	−20.1283	−	32.6539i	−0.771884	−	1.25222i
$681$	−8.18770	+	1.17721i	−0.313753	+	0.0451109i
$682$	10.0755	+	17.7067i	0.385812	+	0.678023i
$683$	0.944631	+	2.06845i	0.0361453	+	0.0791471i	0.926843	−	0.375448i	$-0.122511\pi$
$683$	0.944631	+	2.06845i	0.0361453	+	0.0791471i	−0.890698	+	0.454595i	$0.849784\pi$
$684$	1.67584	+	9.32233i	0.0640775	+	0.356448i
$685$	−21.0968	−	3.03326i	−0.806067	−	0.115895i
$686$	−3.48450	−	3.36440i	−0.133039	−	0.128454i
$687$	4.49740	−	5.19028i	0.171586	−	0.198021i
$688$	18.9435	−	10.3129i	0.722216	−	0.393174i
$689$			47.5668i			1.81215i
$690$	15.3809	−	3.17697i	0.585542	−	0.120945i
$691$	−27.9299			−1.06250			−0.531251	−	0.847214i	$-0.678278\pi$
$691$	−27.9299			−1.06250			−0.531251	+	0.847214i	$0.678278\pi$
$692$	−1.63422	+	2.02532i	−0.0621238	+	0.0769912i
$693$	0.711751	+	0.616736i	0.0270372	+	0.0234278i
$694$	22.9383	+	22.1477i	0.870725	+	0.840714i
$695$	2.18056	−	15.1661i	0.0827132	−	0.575283i
$696$	0.534777	−	28.4438i	0.0202707	−	1.07816i
$697$	40.4431	−	18.4697i	1.53189	−	0.699591i
$698$	−16.7690	+	9.54198i	−0.634716	+	0.361169i
$699$	1.36174	+	9.47111i	0.0515057	+	0.358230i
$700$	−0.130382	+	0.121236i	−0.00492796	+	0.00458228i
$701$	41.9637	−	12.3217i	1.58495	−	0.465382i	0.633640	−	0.773628i	$-0.281560\pi$
$701$	41.9637	−	12.3217i	1.58495	−	0.465382i	0.951307	+	0.308245i	$0.0997418\pi$
$702$	−0.685769	−	7.69069i	−0.0258827	−	0.290267i
$703$	−2.64435	−	1.20764i	−0.0997337	−	0.0455468i
$704$	15.5970	+	26.4014i	0.587834	+	0.995040i
$705$	13.0986	−	11.3500i	0.493321	−	0.427465i
$706$	−10.3488	−	43.8562i	−0.389484	−	1.65055i
$707$	−0.677398	−	1.05405i	−0.0254762	−	0.0396417i
$708$	−5.40027	+	9.08857i	−0.202955	+	0.341569i
$709$	17.0653	+	10.9672i	0.640902	+	0.411883i	0.820332	−	0.571888i	$-0.193789\pi$
$709$	17.0653	+	10.9672i	0.640902	+	0.411883i	−0.179430	+	0.983771i	$0.557425\pi$
$710$	30.7173	+	39.5680i	1.15280	+	1.48496i
$711$	−5.24824	−	1.54102i	−0.196824	−	0.0577929i
$712$	25.9764	−	38.7967i	0.973507	−	1.45397i
$713$	11.4166	+	13.9473i	0.427556	+	0.522330i
$714$	0.397646	−	1.99580i	0.0148815	−	0.0746909i
$715$	46.4977	+	13.6529i	1.73891	+	0.510591i
$716$	−39.7259	+	19.8539i	−1.48463	+	0.741976i
$717$	−10.3192	+	16.0569i	−0.385376	+	0.599657i
$718$	−6.53951	+	18.5184i	−0.244053	+	0.691101i
$719$	15.1905	+	23.6369i	0.566510	+	0.881506i	0.999805	−	0.0197458i	$-0.00628569\pi$
$719$	15.1905	+	23.6369i	0.566510	+	0.881506i	−0.433295	+	0.901252i	$0.642649\pi$
$720$	−3.24795	+	8.67455i	−0.121044	+	0.323281i
$721$	−1.80238	−	2.08006i	−0.0671241	−	0.0774654i
$722$	0.261058	−	4.84173i	0.00971558	−	0.180190i
$723$	−8.22518	−	3.75632i	−0.305898	−	0.139699i
$724$	−13.0410	−	1.41040i	−0.484666	−	0.0524172i
$725$	1.02667	+	3.49652i	0.0381296	+	0.129858i
$726$	−3.05539	+	4.23428i	−0.113396	+	0.157149i
$727$	3.80952	+	26.4958i	0.141287	+	0.982676i	0.929907	+	0.367794i	$0.119887\pi$
$727$	3.80952	+	26.4958i	0.141287	+	0.982676i	−0.788620	+	0.614881i	$0.789204\pi$
$728$	3.76508	−	0.469281i	0.139543	−	0.0173927i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−31.9548	+	12.5610i	−1.18270	+	0.464904i
$731$	4.49433	−	31.2587i	0.166229	−	1.15615i
$732$	−3.49472	−	5.04016i	−0.129169	−	0.186290i
$733$	21.2943	−	24.5749i	0.786522	−	0.907694i	−0.211040	−	0.977477i	$-0.567685\pi$
$733$	21.2943	−	24.5749i	0.786522	−	0.907694i	0.997562	+	0.0697828i	$0.0222306\pi$
$734$	−8.27790	−	4.33343i	−0.305543	−	0.159950i
$735$	16.0699			0.592746
$736$	17.5232	+	20.7108i	0.645915	+	0.763409i
$737$	−11.6746			−0.430038
$738$	−9.51158	−	4.97925i	−0.350126	−	0.183289i
$739$	24.2312	−	27.9643i	0.891358	−	1.02868i	−0.108046	−	0.994146i	$-0.534459\pi$
$739$	24.2312	−	27.9643i	0.891358	−	1.02868i	0.999403	−	0.0345357i	$-0.0109952\pi$
$740$	−1.61988	−	2.33623i	−0.0595480	−	0.0858814i
$741$	−3.67978	+	25.5934i	−0.135180	+	0.940197i
$742$	2.81744	−	1.10750i	0.103432	−	0.0406576i
$743$	14.3515	+	31.4254i	0.526505	+	1.15289i	0.966917	+	0.255090i	$0.0821049\pi$
$743$	14.3515	+	31.4254i	0.526505	+	1.15289i	−0.440412	+	0.897796i	$0.645168\pi$
$744$	−10.5484	+	1.31475i	−0.386722	+	0.0482011i
$745$	−7.57642	−	52.6952i	−0.277579	−	1.93060i
$746$	29.8689	−	41.3936i	1.09358	−	1.51553i
$747$	−0.0160713	−	0.0547338i	−0.000588018	−	0.00200261i
$748$	44.6372	+	4.82756i	1.63210	+	0.176513i
$749$	1.60465	+	0.732819i	0.0586326	+	0.0267766i
$750$	−0.817710	+	15.1657i	−0.0298585	+	0.553773i
$751$	16.5892	+	19.1449i	0.605348	+	0.698609i	0.972856	−	0.231412i	$-0.0743344\pi$
$751$	16.5892	+	19.1449i	0.605348	+	0.698609i	−0.367508	+	0.930020i	$0.619789\pi$
$752$	28.0376	+	10.4979i	1.02243	+	0.382820i
$753$	−5.09671	−	7.93063i	−0.185734	−	0.289008i
$754$	25.8599	−	73.2294i	0.941762	−	2.66686i
$755$	−15.1839	+	23.6266i	−0.552598	+	0.859859i
$756$	−0.439563	+	0.219682i	−0.0159868	+	0.00798975i
$757$	−8.85149	−	2.59903i	−0.321713	−	0.0944634i	0.116889	−	0.993145i	$-0.462708\pi$
$757$	−8.85149	−	2.59903i	−0.321713	−	0.0944634i	−0.438602	+	0.898682i	$0.644526\pi$
$758$	−2.61169	+	13.1082i	−0.0948608	+	0.476110i
$759$	−8.10230	+	16.5007i	−0.294095	+	0.598937i
$760$	17.2575	−	25.7746i	0.625994	−	0.934944i
$761$	−3.10797	−	0.912583i	−0.112664	−	0.0330811i	0.224915	−	0.974378i	$-0.427790\pi$
$761$	−3.10797	−	0.912583i	−0.112664	−	0.0330811i	−0.337579	+	0.941297i	$0.609608\pi$
$762$	17.2806	+	22.2597i	0.626010	+	0.806384i
$763$	1.10236	+	0.708447i	0.0399083	+	0.0256475i
$764$	7.82977	−	13.1774i	0.283271	−	0.476740i
$765$	7.33218	+	11.4091i	0.265096	+	0.412497i
$766$	−7.59086	−	32.1684i	−0.274269	−	1.16229i
$767$	−21.8108	+	18.8992i	−0.787542	+	0.682409i
$768$	−15.8429	+	2.23695i	−0.571680	+	0.0807190i
$769$	46.5847	+	21.2745i	1.67989	+	0.767179i	0.999408	+	0.0344138i	$0.0109564\pi$
$769$	46.5847	+	21.2745i	1.67989	+	0.767179i	0.680481	+	0.732766i	$0.261771\pi$
$770$	−0.273926	−	3.07200i	−0.00987161	−	0.110707i
$771$	19.2166	−	5.64252i	0.692071	−	0.203210i
$772$	16.4387	−	15.2856i	0.591642	−	0.550140i
$773$	−3.61887	−	25.1698i	−0.130162	−	0.905294i	−0.945341	−	0.326085i	$-0.894270\pi$
$773$	−3.61887	−	25.1698i	−0.130162	−	0.905294i	0.815179	−	0.579209i	$-0.196639\pi$
$774$	−6.62783	+	3.77140i	−0.238233	+	0.135560i
$775$	1.23859	−	0.565647i	0.0444916	−	0.0203186i
$776$	0.843180	−	44.8472i	0.0302684	−	1.60992i
$777$	0.0214639	−	0.149285i	0.000770015	−	0.00535557i
$778$	3.82382	+	3.69203i	0.137091	+	0.132366i
$779$	27.1712	+	23.5440i	0.973509	+	0.843551i
$780$	−15.8785	+	19.6785i	−0.568541	+	0.704603i
$781$	−58.6298			−2.09794
$782$	39.6481	−	2.41710i	1.41781	−	0.0864352i
$783$			10.0582i			0.359450i
$784$	13.2724	+	24.3799i	0.474015	+	0.870710i
$785$	−18.7710	+	21.6629i	−0.669966	+	0.773182i
$786$	−2.31965	−	2.23970i	−0.0827390	−	0.0798873i
$787$	20.9552	+	3.01290i	0.746973	+	0.107398i	0.505281	−	0.862955i	$-0.331389\pi$
$787$	20.9552	+	3.01290i	0.746973	+	0.107398i	0.241691	+	0.970353i	$0.422298\pi$
$788$	−6.18461	−	34.4035i	−0.220318	−	1.22558i
$789$	4.39390	+	9.62131i	0.156427	+	0.342528i
$790$	8.85900	+	15.5687i	0.315189	+	0.553911i
$791$	−0.673021	+	0.0967658i	−0.0239299	+	0.00344060i
$792$	−5.68886	−	9.22900i	−0.202145	−	0.327938i
$793$	−4.71700	−	16.0646i	−0.167505	−	0.570471i
$794$	−0.305551	−	3.42667i	−0.0108436	−	0.121608i
$795$	−8.38092	+	18.3517i	−0.297241	+	0.650866i
$796$	−9.53234	+	37.2490i	−0.337865	+	1.32025i
$797$	−14.2101	−	16.3994i	−0.503349	−	0.580896i	0.446034	−	0.895016i	$-0.352836\pi$
$797$	−14.2101	−	16.3994i	−0.503349	−	0.580896i	−0.949383	+	0.314120i	$0.898290\pi$
$798$	1.60161	−	0.377935i	0.0566963	−	0.0133787i
$799$	36.8762	−	23.6989i	1.30459	−	0.838406i
$800$	1.85020	−	0.881613i	0.0654146	−	0.0311697i
$801$	−8.92458	+	13.8869i	−0.315335	+	0.490670i
$802$	15.0836	+	19.4297i	0.532621	+	0.686087i
$803$	11.3221	−	38.5594i	0.399547	−	1.36073i
$804$	2.33469	−	5.62637i	0.0823382	−	0.198427i
$805$	−0.695029	−	2.63864i	−0.0244966	−	0.0929998i
$806$	−28.4590	−	5.67021i	−1.00243	−	0.199725i
$807$	3.67333	−	12.5102i	0.129307	−	0.440380i
$808$	3.80273	+	13.9133i	0.133780	+	0.489468i
$809$	4.67455	+	3.00415i	0.164348	+	0.105620i	0.620230	−	0.784420i	$-0.287039\pi$
$809$	4.67455	+	3.00415i	0.164348	+	0.105620i	−0.455881	+	0.890041i	$0.650676\pi$
$810$	1.09047	−	3.08796i	0.0383152	−	0.108500i
$811$	26.1612	−	16.8128i	0.918643	−	0.590376i	0.00637917	−	0.999980i	$-0.497969\pi$
$811$	26.1612	−	16.8128i	0.918643	−	0.590376i	0.912263	+	0.409604i	$0.134333\pi$
$812$	−4.93957	+	0.173288i	−0.173345	+	0.00608122i
$813$	−5.75416	+	4.98600i	−0.201807	+	0.174867i
$814$	3.32262	+	0.179150i	0.116458	+	0.00627921i
$815$	−4.04233	+	8.85147i	−0.141597	+	0.310053i
$816$	−11.2532	+	20.5468i	−0.393940	+	0.719281i
$817$	24.5024	−	7.19456i	0.857231	−	0.251706i
$818$	7.56280	−	10.4809i	0.264427	−	0.366454i
$819$	−1.32780	+	0.190909i	−0.0463972	+	0.00667091i
$820$	11.0821	+	33.3667i	0.387003	+	1.16522i
$821$	−42.9116	+	19.5971i	−1.49763	+	0.683943i	−0.984663	−	0.174468i	$-0.944180\pi$
$821$	−42.9116	+	19.5971i	−1.49763	+	0.683943i	−0.512963	+	0.858411i	$0.671452\pi$
$822$	4.76198	+	12.1143i	0.166093	+	0.422535i
$823$	29.7617	+	4.27909i	1.03743	+	0.149160i	0.639922	−	0.768440i	$-0.278967\pi$
$823$	29.7617	+	4.27909i	1.03743	+	0.149160i	0.397506	+	0.917600i	$0.369876\pi$
$824$	12.6178	+	29.0628i	0.439561	+	1.01245i
$825$	1.04953	+	0.909426i	0.0365401	+	0.0316622i
$826$	1.62724	+	0.851851i	0.0566190	+	0.0296397i
$827$			53.1681i			1.84884i	0.381379	+	0.924419i	$0.375449\pi$
$827$			53.1681i			1.84884i	−0.381379	+	0.924419i	$0.624551\pi$
$828$	−6.33195	−	7.20461i	−0.220051	−	0.250377i
$829$			24.7194i			0.858540i	0.903176	+	0.429270i	$0.141229\pi$
$829$			24.7194i			0.858540i	−0.903176	+	0.429270i	$0.858771\pi$
$830$	−0.0866411	+	0.165506i	−0.00300735	+	0.00574478i
$831$	−1.77604	−	1.53894i	−0.0616100	−	0.0533854i
$832$	−42.9690	−	7.83669i	−1.48968	−	0.271688i
$833$	40.2292	+	5.78409i	1.39386	+	0.200407i
$834$	−8.70876	+	3.42330i	−0.301560	+	0.118539i
$835$	−19.2759	+	8.80299i	−0.667068	+	0.304640i
$836$	11.4435	+	34.4550i	0.395782	+	1.19165i
$837$	3.72002	−	0.534858i	0.128583	−	0.0184874i
$838$	10.9375	+	7.89233i	0.377830	+	0.272636i
$839$	−33.4076	+	9.80936i	−1.15336	+	0.338657i	−0.801849	−	0.597527i	$-0.796150\pi$
$839$	−33.4076	+	9.80936i	−1.15336	+	0.338657i	−0.351511	+	0.936184i	$0.614332\pi$
$840$	1.53528	+	0.482328i	0.0529723	+	0.0166419i
$841$	−29.9792	+	65.6453i	−1.03377	+	2.26363i
$842$	1.27230	−	23.5968i	0.0438464	−	0.813199i
$843$	24.2249	−	20.9910i	0.834349	−	0.722968i
$844$	−1.27142	−	36.2416i	−0.0437639	−	1.24749i
$845$	−32.7441	+	21.0433i	−1.12643	+	0.723913i
$846$	−9.98082	−	3.52458i	−0.343148	−	0.121178i
$847$	0.763164	+	0.490456i	0.0262226	+	0.0168523i
$848$	−34.7636	+	2.44213i	−1.19379	+	0.0838632i
$849$	−2.04806	+	6.97504i	−0.0702892	+	0.239383i
$850$	0.586361	−	2.94297i	0.0201120	−	0.100943i
$851$	2.92449	−	0.337080i	0.100250	−	0.0115550i
$852$	11.7249	−	28.2557i	0.401687	−	0.968025i
$853$	6.78171	−	23.0964i	0.232201	−	0.790806i	−0.758132	−	0.652101i	$-0.773888\pi$
$853$	6.78171	−	23.0964i	0.232201	−	0.790806i	0.990334	−	0.138705i	$-0.0442939\pi$
$854$	−0.841702	+	0.653427i	−0.0288024	+	0.0223598i
$855$	−5.92906	+	9.22579i	−0.202769	+	0.315515i
$856$	−15.0946	−	13.5846i	−0.515921	−	0.464313i
$857$	−5.22283	+	3.35651i	−0.178409	+	0.114656i	−0.626797	−	0.779183i	$-0.715634\pi$
$857$	−5.22283	+	3.35651i	−0.178409	+	0.114656i	0.448388	+	0.893839i	$0.351998\pi$
$858$	−6.79709	−	28.8046i	−0.232049	−	0.983373i
$859$	5.18658	+	5.98564i	0.176964	+	0.204227i	0.837301	−	0.546742i	$-0.184132\pi$
$859$	5.18658	+	5.98564i	0.176964	+	0.204227i	−0.660337	+	0.750969i	$0.729587\pi$
$860$	24.1934	+	6.19131i	0.824989	+	0.211122i
$861$	−0.774852	+	1.69669i	−0.0264069	+	0.0578230i
$862$	−40.1599	+	3.58100i	−1.36785	+	0.121969i
$863$	2.74038	+	9.33289i	0.0932838	+	0.317695i	0.992895	−	0.118997i	$-0.0379680\pi$
$863$	2.74038	+	9.33289i	0.0932838	+	0.317695i	−0.899611	+	0.436693i	$0.856150\pi$
$864$	5.58544	−	0.896034i	0.190020	−	0.0304837i
$865$	−2.98250	+	0.428819i	−0.101408	+	0.0145803i
$866$	−17.5129	+	9.96528i	−0.595112	+	0.338634i
$867$	7.18678	+	15.7368i	0.244076	+	0.534451i
$868$	0.326759	+	1.81768i	0.0110909	+	0.0616962i
$869$	−20.7526	−	2.98377i	−0.703983	−	0.101217i
$870$	22.8794	−	23.6962i	0.775685	−	0.803375i
$871$	10.8897	−	12.5674i	0.368984	−	0.425830i
$872$	−9.66233	−	11.5839i	−0.327208	−	0.392281i
$873$			15.8587i			0.536735i
$874$	15.0965	+	28.3516i	0.510645	+	0.959007i
$875$	2.63867			0.0892032
$876$	16.3189	+	13.1677i	0.551366	+	0.444894i
$877$	28.0371	+	24.2943i	0.946745	+	0.820359i	0.983858	−	0.178952i	$-0.0572708\pi$
$877$	28.0371	+	24.2943i	0.946745	+	0.820359i	−0.0371132	+	0.999311i	$0.511816\pi$
$878$	−22.3422	+	23.1397i	−0.754012	+	0.780928i
$879$	0.893802	−	6.21653i	0.0301472	−	0.209678i
$880$	−7.59084	+	34.6832i	−0.255887	+	1.16917i
$881$	26.2752	−	11.9995i	0.885234	−	0.404273i	0.0796974	−	0.996819i	$-0.474605\pi$
$881$	26.2752	−	11.9995i	0.885234	−	0.404273i	0.805536	+	0.592546i	$0.201877\pi$
$882$	−4.85371	−	8.52986i	−0.163433	−	0.287215i
$883$	−3.23119	−	22.4734i	−0.108738	−	0.756291i	−0.969111	−	0.246626i	$-0.920678\pi$
$883$	−3.23119	−	22.4734i	−0.108738	−	0.756291i	0.860373	−	0.509666i	$-0.170231\pi$
$884$	−46.8331	+	43.5479i	−1.57517	+	1.46467i
$885$	−11.7447	+	3.44854i	−0.394793	+	0.115922i
$886$	−11.8420	+	1.05594i	−0.397840	+	0.0354749i
$887$	−20.5751	−	9.39633i	−0.690844	−	0.315498i	0.0388759	−	0.999244i	$-0.487622\pi$
$887$	−20.5751	−	9.39633i	−0.690844	−	0.315498i	−0.729720	+	0.683746i	$0.760350\pi$
$888$	−0.750800	+	1.56546i	−0.0251952	+	0.0525334i
$889$	3.70008	−	3.20614i	0.124097	−	0.107530i
$890$	52.6142	−	12.4155i	1.76363	−	0.416168i
$891$	2.07230	+	3.22456i	0.0694246	+	0.108027i
$892$	−0.491288	−	0.291915i	−0.0164496	−	0.00977405i
$893$	29.8194	+	19.1637i	0.997867	+	0.641290i
$894$	−25.6822	+	19.9375i	−0.858940	+	0.666809i
$895$	−49.3374	−	14.4868i	−1.64917	−	0.484240i
$896$	0.536271	+	2.72757i	0.0179156	+	0.0911217i
$897$	−10.2050	−	24.1134i	−0.340736	−	0.805121i
$898$	21.0120	+	4.18646i	0.701179	+	0.139704i
$899$	36.2701	+	10.6499i	1.20968	+	0.355193i
$900$	−0.648171	+	0.323939i	−0.0216057	+	0.0107980i
$901$	−27.5862	+	42.9249i	−0.919028	+	1.43004i
$902$	−38.8033	−	13.7028i	−1.29201	−	0.456255i
$903$	0.716278	+	1.11455i	0.0238362	+	0.0370899i
$904$	7.72528	+	1.25938i	0.256939	+	0.0418863i
$905$	−9.94562	−	11.4779i	−0.330604	−	0.381537i
$906$	17.1271	+	0.923463i	0.569008	+	0.0306800i
$907$	−51.6205	−	23.5743i	−1.71403	−	0.782771i	−0.996252	−	0.0864989i	$-0.972432\pi$
$907$	−51.6205	−	23.5743i	−1.71403	−	0.782771i	−0.717778	−	0.696272i	$-0.754841\pi$
$908$	1.77886	−	16.4479i	0.0590334	−	0.545842i
$909$	−1.43670	−	4.89295i	−0.0476523	−	0.162289i
$910$	3.56245	+	2.57060i	0.118094	+	0.0852146i
$911$	−4.76175	−	33.1187i	−0.157764	−	1.09727i	−0.902742	−	0.430182i	$-0.858449\pi$
$911$	−4.76175	−	33.1187i	−0.157764	−	1.09727i	0.744978	−	0.667089i	$-0.232460\pi$
$912$	−18.8935	−	1.37532i	−0.625628	−	0.0455415i
$913$	−0.0908322	−	0.198895i	−0.00300611	−	0.00658245i
$914$	1.28088	+	3.25851i	0.0423676	+	0.107782i
$915$	1.01061	−	7.02896i	0.0334098	−	0.232370i
$916$	7.82649	+	11.2875i	0.258595	+	0.372950i
$917$	−0.366855	+	0.423373i	−0.0121146	+	0.0139810i
$918$	3.84134	−	7.33789i	0.126783	−	0.242186i
$919$	−12.1795			−0.401766			−0.200883	−	0.979615i	$-0.564381\pi$
$919$	−12.1795			−0.401766			−0.200883	+	0.979615i	$0.564381\pi$
$920$	−1.47089	+	31.3768i	−0.0484938	+	1.03446i
$921$	26.9533			0.888143
$922$	−1.81584	+	3.46869i	−0.0598014	+	0.114235i
$923$	54.6883	−	63.1136i	1.80009	−	2.07741i
$924$	−1.54788	+	1.07326i	−0.0509214	+	0.0353076i
$925$	0.0316503	−	0.220133i	0.00104066	−	0.00723792i
$926$	−5.19595	−	13.2183i	−0.170749	−	0.434380i
$927$	−4.65343	−	10.1896i	−0.152839	−	0.334670i
$928$	54.8464	+	15.1397i	1.80042	+	0.496985i
$929$	0.429550	+	2.98759i	0.0140931	+	0.0980196i	0.995654	−	0.0931305i	$-0.0296874\pi$
$929$	0.429550	+	2.98759i	0.0140931	+	0.0980196i	−0.981561	+	0.191150i	$0.938778\pi$
$930$	−9.98067	−	7.20188i	−0.327279	−	0.236159i
$931$	9.25922	+	31.5340i	0.303459	+	1.03349i
$932$	−19.0261	−	2.05769i	−0.623219	−	0.0674019i
$933$	9.26174	+	4.22969i	0.303216	+	0.138474i
$934$	49.9003	+	2.69054i	1.63279	+	0.0880372i
$935$	34.0421	+	39.2867i	1.11330	+	1.28481i
$936$	15.2412	+	2.48463i	0.498175	+	0.0812126i
$937$	20.3496	+	31.6646i	0.664794	+	1.03444i	0.995866	+	0.0908336i	$0.0289531\pi$
$937$	20.3496	+	31.6646i	0.664794	+	1.03444i	−0.331073	+	0.943605i	$0.607410\pi$
$938$	−0.997929	−	0.352404i	−0.0325835	−	0.0115064i
$939$	−4.54526	+	7.07256i	−0.148329	+	0.230804i
$940$	15.4965	+	31.0071i	0.505440	+	1.01134i
$941$	−36.5227	−	10.7240i	−1.19061	−	0.349594i	−0.374353	−	0.927286i	$-0.622135\pi$
$941$	−36.5227	−	10.7240i	−1.19061	−	0.349594i	−0.816254	+	0.577693i	$0.803953\pi$
$942$	17.1682	+	3.42061i	0.559370	+	0.111450i
$943$	−35.8777	−	6.18986i	−1.16834	−	0.201569i
$944$	−14.9320	−	14.9698i	−0.485995	−	0.487226i
$945$	−0.545914	−	0.160295i	−0.0177586	−	0.00521439i
$946$	−23.0889	+	17.9243i	−0.750684	+	0.582768i
$947$	−12.9933	−	8.35026i	−0.422224	−	0.271347i	0.312228	−	0.950007i	$-0.398925\pi$
$947$	−12.9933	−	8.35026i	−0.422224	−	0.271347i	−0.734452	+	0.678660i	$0.762561\pi$
$948$	5.58811	−	9.40469i	0.181493	−	0.305450i
$949$	30.9474	+	48.1552i	1.00460	+	1.56318i
$950$	2.36170	−	0.557295i	0.0766236	−	0.0180811i
$951$	13.6031	−	11.7872i	0.441111	−	0.382225i
$952$	3.66982	+	1.76006i	0.118939	+	0.0570438i
$953$	−29.5971	−	13.5166i	−0.958745	−	0.437844i	−0.126325	−	0.991989i	$-0.540318\pi$
$953$	−29.5971	−	13.5166i	−0.958745	−	0.437844i	−0.832420	+	0.554145i	$0.813045\pi$
$954$	12.2724	−	1.09431i	0.397333	−	0.0354297i
$955$	17.0284	−	4.99999i	0.551026	−	0.161796i
$956$	−25.9947	−	27.9557i	−0.840727	−	0.904151i
$957$	5.48672	+	38.1610i	0.177360	+	1.23357i
$958$	−3.27043	−	5.74742i	−0.105663	−	0.185691i
$959$	2.05710	−	0.939448i	0.0664273	−	0.0303363i
$960$	−15.1970	−	10.5943i	−0.490481	−	0.341929i
$961$	−2.40162	+	16.7036i	−0.0774716	+	0.538827i
$962$	−3.29210	+	3.40962i	−0.106142	+	0.109931i
$963$	5.42607	+	4.70172i	0.174853	+	0.151511i
$964$	11.3565	−	14.0743i	0.365767	−	0.453302i
$965$	25.9902			0.836654
$966$	−1.19066	+	1.16589i	−0.0383089	+	0.0375119i
$967$			28.8772i			0.928627i	0.885671	+	0.464314i	$0.153699\pi$
$967$			28.8772i			0.928627i	−0.885671	+	0.464314i	$0.846301\pi$
$968$	−6.68920	−	8.01952i	−0.214999	−	0.257757i
$969$	−18.1635	+	20.9617i	−0.583494	+	0.673388i
$970$	36.0739	−	37.3616i	1.15826	−	1.19961i
$971$	5.71633	+	0.821885i	0.183446	+	0.0263755i	0.233425	−	0.972375i	$-0.425007\pi$
$971$	5.71633	+	0.821885i	0.183446	+	0.0263755i	−0.0499796	+	0.998750i	$0.515916\pi$
$972$	−1.96845	+	0.353861i	−0.0631380	+	0.0113501i
$973$	0.675352	+	1.47882i	0.0216508	+	0.0474086i
$974$	0.890262	−	0.506581i	0.0285258	−	0.0162319i
$975$	−1.95795	+	0.281511i	−0.0627047	+	0.00901558i
$976$	11.4984	−	4.27213i	0.368056	−	0.136748i
$977$	−8.09022	−	27.5527i	−0.258829	−	0.881491i	−0.981688	−	0.190495i	$-0.938991\pi$
$977$	−8.09022	−	27.5527i	−0.258829	−	0.881491i	0.722859	−	0.690995i	$-0.242828\pi$
$978$	5.91928	−	0.527814i	0.189278	−	0.0168776i
$979$	−26.2848	+	57.5556i	−0.840065	+	1.83949i
$980$	−7.96806	+	31.1363i	−0.254530	+	0.994614i
$981$	3.49253	+	4.03060i	0.111508	+	0.128687i
$982$	5.83616	+	24.7324i	0.186239	+	0.789242i
$983$	50.2722	−	32.3080i	1.60343	−	1.03046i	0.637924	−	0.770099i	$-0.279793\pi$
$983$	50.2722	−	32.3080i	1.60343	−	1.03046i	0.965510	−	0.260366i	$-0.0838432\pi$
$984$	14.3638	−	15.9604i	0.457901	−	0.508798i
$985$	21.8809	−	34.0473i	0.697182	−	1.08484i
$986$	65.8053	−	51.0858i	2.09567	−	1.62690i
$987$	−0.518101	+	1.76449i	−0.0164913	+	0.0561643i
$988$	−47.7642	−	19.8200i	−1.51958	−	0.630558i
$989$	−17.4761	+	19.0612i	−0.555708	+	0.606111i
$990$	2.45279	−	12.3106i	0.0779547	−	0.391258i
$991$	1.17398	−	3.99822i	0.0372928	−	0.127008i	−0.938743	−	0.344619i	$-0.888008\pi$
$991$	1.17398	−	3.99822i	0.0372928	−	0.127008i	0.976036	+	0.217611i	$0.0698264\pi$
$992$	2.68288	−	21.0900i	0.0851816	−	0.669609i
$993$	−3.21888	−	2.06865i	−0.102148	−	0.0656466i
$994$	−5.01161	−	1.76978i	−0.158959	−	0.0561340i
$995$	−37.4508	+	24.0682i	−1.18727	+	0.763013i
$996$	0.114019	−	0.00399997i	0.00361283	−	0.000126744i
$997$	−7.28974	+	6.31659i	−0.230868	+	0.200049i	−0.762611	−	0.646858i	$-0.776083\pi$
$997$	−7.28974	+	6.31659i	−0.230868	+	0.200049i	0.531743	+	0.846906i	$0.321537\pi$
$998$	2.87110	−	53.2490i	0.0908831	−	1.68557i
$999$	0.254997	−	0.558365i	0.00806774	−	0.0176659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.235.21	✓	240
8.3	odd	2	inner	552.2.t.a.235.23	yes	240
23.14	odd	22	inner	552.2.t.a.451.23	yes	240
184.83	even	22	inner	552.2.t.a.451.21	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.21	✓	240	1.1	even	1	trivial
552.2.t.a.235.23	yes	240	8.3	odd	2	inner
552.2.t.a.451.21	yes	240	184.83	even	22	inner
552.2.t.a.451.23	yes	240	23.14	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25292 + 0.655894i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.13961 + 1.64356i) q^{4} +(-0.329554 + 2.29210i) q^{5} +(1.31618 - 0.517373i) q^{6} +(-0.102068 - 0.223497i) q^{7} +(0.349829 + 2.80671i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.25292 + 0.655894i) q^{2} +(0.654861 - 0.755750i) q^{3} +(1.13961 + 1.64356i) q^{4} +(-0.329554 + 2.29210i) q^{5} +(1.31618 - 0.517373i) q^{6} +(-0.102068 - 0.223497i) q^{7} +(0.349829 + 2.80671i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.91628 + 2.65565i) q^{10} +(-1.07989 - 3.67777i) q^{11} +(1.98840 + 0.215048i) q^{12} +(4.96634 + 2.26805i) q^{13} +(0.0187080 - 0.346970i) q^{14} +(1.51644 + 1.75006i) q^{15} +(-1.40260 + 3.74603i) q^{16} +(3.16634 + 4.92692i) q^{17} +(0.470909 - 1.33351i) q^{18} +(-2.56041 + 3.98408i) q^{19} +(-4.14276 + 2.07044i) q^{20} +(-0.235748 - 0.0692219i) q^{21} +(1.05921 - 5.31624i) q^{22} +(0.134482 - 4.79395i) q^{23} +(2.35026 + 1.57362i) q^{24} +(-0.347630 - 0.102073i) q^{25} +(4.73481 + 6.09907i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(0.251015 - 0.422454i) q^{28} +(-5.43786 - 8.46148i) q^{29} +(0.752116 + 3.18731i) q^{30} +(-2.84031 + 2.46114i) q^{31} +(-4.21434 + 3.77351i) q^{32} +(-3.48666 - 1.59230i) q^{33} +(0.735624 + 8.24981i) q^{34} +(0.545914 - 0.160295i) q^{35} +(1.46465 - 1.36191i) q^{36} +(0.0873580 + 0.607588i) q^{37} +(-5.82112 + 3.31236i) q^{38} +(4.96634 - 2.26805i) q^{39} +(-6.54853 - 0.123120i) q^{40} +(1.08039 - 7.51427i) q^{41} +(-0.249971 - 0.241355i) q^{42} +(-4.07515 - 3.53114i) q^{43} +(4.81400 - 5.96608i) q^{44} +2.31567 q^{45} +(3.31282 - 5.91821i) q^{46} -7.48463i q^{47} +(1.91255 + 3.51314i) q^{48} +(4.54449 - 5.24462i) q^{49} +(-0.368602 - 0.355898i) q^{50} +(5.79703 + 0.833487i) q^{51} +(1.93198 + 10.7472i) q^{52} +(3.61923 + 7.92501i) q^{53} +(-0.699418 - 1.22915i) q^{54} +(8.78569 - 1.26319i) q^{55} +(0.591586 - 0.364661i) q^{56} +(1.33425 + 4.54405i) q^{57} +(-1.26336 - 14.1682i) q^{58} +(-2.19586 + 4.80827i) q^{59} +(-1.14820 + 4.48674i) q^{60} +(-2.00820 - 2.31759i) q^{61} +(-5.17293 + 1.22067i) q^{62} +(-0.206697 + 0.132836i) q^{63} +(-7.75524 + 1.96374i) q^{64} +(-6.83526 + 10.6359i) q^{65} +(-3.32411 - 4.28190i) q^{66} +(0.858092 - 2.92239i) q^{67} +(-4.48932 + 10.8188i) q^{68} +(-3.53496 - 3.24100i) q^{69} +(0.789122 + 0.157226i) q^{70} +(4.30935 - 14.6763i) q^{71} +(2.72836 - 0.745705i) q^{72} +(8.82008 + 5.66832i) q^{73} +(-0.289061 + 0.818556i) q^{74} +(-0.304791 + 0.195877i) q^{75} +(-9.46594 + 0.332081i) q^{76} +(-0.711751 + 0.616736i) q^{77} +(7.71001 + 0.415711i) q^{78} +(2.27224 - 4.97551i) q^{79} +(-8.12402 - 4.44940i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(6.28220 - 8.70614i) q^{82} +(0.0564639 - 0.00811829i) q^{83} +(-0.154889 - 0.466353i) q^{84} +(-12.3364 + 5.63387i) q^{85} +(-2.78978 - 7.09710i) q^{86} +(-9.95580 - 1.43143i) q^{87} +(9.94467 - 4.31753i) q^{88} +(-12.4755 - 10.8101i) q^{89} +(2.90134 + 1.51883i) q^{90} -1.34146i q^{91} +(8.03241 - 5.24218i) q^{92} +3.75827i q^{93} +(4.90913 - 9.37763i) q^{94} +(-8.28809 - 7.18167i) q^{95} +(0.0920233 + 5.65611i) q^{96} +(-15.6973 - 2.25693i) q^{97} +(9.13379 - 3.59038i) q^{98} +(-3.48666 + 1.59230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more