LMFDB - Embedded newform 156.3.l.c.47.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [156,3,Mod(47,156)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("156.47"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(156, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	156.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,-36,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.25069212402$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.20
Character	$\chi$	$=$	156.47
Dual form			156.3.l.c.83.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.648159 + 1.89206i) q^{2} +(0.777110 + 2.89760i) q^{3} +(-3.15978 - 2.45271i) q^{4} +(-0.949668 + 0.949668i) q^{5} +(-5.98613 - 0.407769i) q^{6} +(-7.87350 - 7.87350i) q^{7} +(6.68872 - 4.38874i) q^{8} +(-7.79220 + 4.50351i) q^{9} +(-1.18129 - 2.41236i) q^{10} +(-13.0508 + 13.0508i) q^{11} +(4.65149 - 11.0618i) q^{12} +(-2.93839 - 12.6636i) q^{13} +(20.0004 - 9.79385i) q^{14} +(-3.48976 - 2.01376i) q^{15} +(3.96841 + 15.5001i) q^{16} +10.4874 q^{17} +(-3.47032 - 17.6623i) q^{18} +(-6.48583 + 6.48583i) q^{19} +(5.33000 - 0.671480i) q^{20} +(16.6957 - 28.9329i) q^{21} +(-16.2339 - 33.1519i) q^{22} +17.0776i q^{23} +(17.9147 + 15.9707i) q^{24} +23.1963i q^{25} +(25.8648 + 2.64840i) q^{26} +(-19.1048 - 19.0790i) q^{27} +(5.56710 + 44.1900i) q^{28} -37.2704i q^{29} +(6.07208 - 5.29759i) q^{30} +(-14.6982 + 14.6982i) q^{31} +(-31.8992 - 2.53803i) q^{32} +(-47.9580 - 27.6741i) q^{33} +(-6.79748 + 19.8427i) q^{34} +14.9544 q^{35} +(35.6674 + 4.88192i) q^{36} +(18.0222 - 18.0222i) q^{37} +(-8.06773 - 16.4754i) q^{38} +(34.4105 - 18.3553i) q^{39} +(-2.18421 + 10.5199i) q^{40} +(-26.9059 + 26.9059i) q^{41} +(43.9212 + 50.3424i) q^{42} -9.70221 q^{43} +(73.2475 - 9.22781i) q^{44} +(3.12316 - 11.6768i) q^{45} +(-32.3119 - 11.0690i) q^{46} +(-52.2200 + 52.2200i) q^{47} +(-41.8291 + 23.5441i) q^{48} +74.9840i q^{49} +(-43.8887 - 15.0349i) q^{50} +(8.14984 + 30.3882i) q^{51} +(-21.7754 + 47.2211i) q^{52} +93.7692i q^{53} +(48.4815 - 23.7812i) q^{54} -24.7879i q^{55} +(-87.2184 - 18.1088i) q^{56} +(-23.8336 - 13.7532i) q^{57} +(70.5179 + 24.1572i) q^{58} +(27.8906 - 27.8906i) q^{59} +(6.08768 + 14.9224i) q^{60} -19.9699 q^{61} +(-18.2831 - 37.3367i) q^{62} +(96.8103 + 25.8935i) q^{63} +(25.4778 - 58.7101i) q^{64} +(14.8167 + 9.23569i) q^{65} +(83.4455 - 72.8021i) q^{66} +(27.3331 - 27.3331i) q^{67} +(-33.1378 - 25.7225i) q^{68} +(-49.4842 + 13.2712i) q^{69} +(-9.69285 + 28.2947i) q^{70} +(12.2997 + 12.2997i) q^{71} +(-32.3551 + 64.3207i) q^{72} +(3.46448 - 3.46448i) q^{73} +(22.4179 + 45.7804i) q^{74} +(-67.2135 + 18.0260i) q^{75} +(36.4017 - 4.58593i) q^{76} +205.511 q^{77} +(12.4257 + 77.0039i) q^{78} -30.4341i q^{79} +(-18.4886 - 10.9512i) q^{80} +(40.4368 - 70.1845i) q^{81} +(-33.4683 - 68.3469i) q^{82} +(-93.6129 - 93.6129i) q^{83} +(-123.719 + 50.4717i) q^{84} +(-9.95952 + 9.95952i) q^{85} +(6.28858 - 18.3572i) q^{86} +(107.995 - 28.9632i) q^{87} +(-30.0165 + 144.570i) q^{88} +(-27.0128 - 27.0128i) q^{89} +(20.0690 + 13.4777i) q^{90} +(-76.5712 + 122.842i) q^{91} +(41.8865 - 53.9616i) q^{92} +(-54.0117 - 31.1675i) q^{93} +(-64.9565 - 132.650i) q^{94} -12.3188i q^{95} +(-17.4350 - 94.4035i) q^{96} +(58.7776 + 58.7776i) q^{97} +(-141.874 - 48.6016i) q^{98} +(42.9201 - 160.469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) $ 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.648159	+	1.89206i	−0.324080	+	0.946030i
$2$	−0.648159	+	1.89206i	−0.324080	+	0.946030i
$3$	0.777110	+	2.89760i	0.259037	+	0.965868i
$3$	0.777110	+	2.89760i	0.259037	+	0.965868i
$4$	−3.15978	−	2.45271i	−0.789945	−	0.613178i
$5$	−0.949668	+	0.949668i	−0.189934	+	0.189934i	−0.795667	−	0.605734i	$-0.792880\pi$
$5$	−0.949668	+	0.949668i	−0.189934	+	0.189934i	0.605734	+	0.795667i	$0.292880\pi$
$6$	−5.98613	−	0.407769i	−0.997688	−	0.0679616i
$7$	−7.87350	−	7.87350i	−1.12479	−	1.12479i	−0.991012	−	0.133774i	$-0.957290\pi$
$7$	−7.87350	−	7.87350i	−1.12479	−	1.12479i	−0.133774	−	0.991012i	$-0.542710\pi$
$8$	6.68872	−	4.38874i	0.836090	−	0.548593i
$9$	−7.79220	+	4.50351i	−0.865800	+	0.500390i
$10$	−1.18129	−	2.41236i	−0.118129	−	0.241236i
$11$	−13.0508	+	13.0508i	−1.18644	+	1.18644i	−0.208391	+	0.978046i	$0.566823\pi$
$11$	−13.0508	+	13.0508i	−1.18644	+	1.18644i	−0.978046	+	0.208391i	$0.933177\pi$
$12$	4.65149	−	11.0618i	0.387624	−	0.921818i
$13$	−2.93839	−	12.6636i	−0.226030	−	0.974120i
$13$	−2.93839	−	12.6636i	−0.226030	−	0.974120i
$14$	20.0004	−	9.79385i	1.42860	−	0.699561i
$15$	−3.48976	−	2.01376i	−0.232650	−	0.134251i
$16$	3.96841	+	15.5001i	0.248026	+	0.968753i
$17$	10.4874			0.616904			0.308452	−	0.951240i	$-0.400189\pi$
$17$	10.4874			0.616904			0.308452	+	0.951240i	$0.400189\pi$
$18$	−3.47032	−	17.6623i	−0.192796	−	0.981239i
$19$	−6.48583	+	6.48583i	−0.341360	+	0.341360i	−0.856878	−	0.515519i	$-0.827599\pi$
$19$	−6.48583	+	6.48583i	−0.341360	+	0.341360i	0.515519	+	0.856878i	$0.327599\pi$
$20$	5.33000	−	0.671480i	0.266500	−	0.0335740i
$21$	16.6957	−	28.9329i	0.795033	−	1.37775i
$22$	−16.2339	−	33.1519i	−0.737905	−	1.50690i
$23$			17.0776i			0.742506i	0.928532	+	0.371253i	$0.121072\pi$
$23$			17.0776i			0.742506i	−0.928532	+	0.371253i	$0.878928\pi$
$24$	17.9147	+	15.9707i	0.746446	+	0.665446i
$25$			23.1963i			0.927850i
$26$	25.8648	+	2.64840i	0.994799	+	0.101862i
$27$	−19.1048	−	19.0790i	−0.707584	−	0.706629i
$28$	5.56710	+	44.1900i	0.198825	+	1.57821i
$29$		−	37.2704i		−	1.28519i	−0.766207	−	0.642594i	$-0.777858\pi$
$29$		−	37.2704i		−	1.28519i	0.766207	−	0.642594i	$-0.222142\pi$
$30$	6.07208	−	5.29759i	0.202403	−	0.176586i
$31$	−14.6982	+	14.6982i	−0.474136	+	0.474136i	−0.903250	−	0.429114i	$-0.858826\pi$
$31$	−14.6982	+	14.6982i	−0.474136	+	0.474136i	0.429114	+	0.903250i	$0.358826\pi$
$32$	−31.8992	−	2.53803i	−0.996850	−	0.0793133i
$33$	−47.9580	−	27.6741i	−1.45327	−	0.838610i
$34$	−6.79748	+	19.8427i	−0.199926	+	0.583610i
$35$	14.9544			0.427269
$36$	35.6674	+	4.88192i	0.990762	+	0.135609i
$37$	18.0222	−	18.0222i	0.487087	−	0.487087i	−0.420299	−	0.907386i	$-0.638075\pi$
$37$	18.0222	−	18.0222i	0.487087	−	0.487087i	0.907386	+	0.420299i	$0.138075\pi$
$38$	−8.06773	−	16.4754i	−0.212309	−	0.433564i
$39$	34.4105	−	18.3553i	0.882321	−	0.470648i
$40$	−2.18421	+	10.5199i	−0.0546052	+	0.262998i
$41$	−26.9059	+	26.9059i	−0.656242	+	0.656242i	−0.954489	−	0.298247i	$-0.903598\pi$
$41$	−26.9059	+	26.9059i	−0.656242	+	0.656242i	0.298247	+	0.954489i	$0.403598\pi$
$42$	43.9212	+	50.3424i	1.04574	+	1.19863i
$43$	−9.70221			−0.225633			−0.112816	−	0.993616i	$-0.535987\pi$
$43$	−9.70221			−0.225633			−0.112816	+	0.993616i	$0.535987\pi$
$44$	73.2475	−	9.22781i	1.66472	−	0.209723i
$45$	3.12316	−	11.6768i	0.0694036	−	0.259485i
$46$	−32.3119	−	11.0690i	−0.702433	−	0.240631i
$47$	−52.2200	+	52.2200i	−1.11106	+	1.11106i	−0.118057	+	0.993007i	$0.537667\pi$
$47$	−52.2200	+	52.2200i	−1.11106	+	1.11106i	−0.993007	+	0.118057i	$0.962333\pi$
$48$	−41.8291	+	23.5441i	−0.871440	+	0.490503i
$49$			74.9840i			1.53029i
$50$	−43.8887	−	15.0349i	−0.877774	−	0.300697i
$51$	8.14984	+	30.3882i	0.159801	+	0.595848i
$52$	−21.7754	+	47.2211i	−0.418758	+	0.908098i
$53$			93.7692i			1.76923i	0.466323	+	0.884615i	$0.345579\pi$
$53$			93.7692i			1.76923i	−0.466323	+	0.884615i	$0.654421\pi$
$54$	48.4815	−	23.7812i	0.897806	−	0.440392i
$55$		−	24.7879i		−	0.450688i
$56$	−87.2184	−	18.1088i	−1.55747	−	0.323372i
$57$	−23.8336	−	13.7532i	−0.418133	−	0.241283i
$58$	70.5179	+	24.1572i	1.21583	+	0.416503i
$59$	27.8906	−	27.8906i	0.472722	−	0.472722i	−0.430072	−	0.902794i	$-0.641512\pi$
$59$	27.8906	−	27.8906i	0.472722	−	0.472722i	0.902794	+	0.430072i	$0.141512\pi$
$60$	6.08768	+	14.9224i	0.101461	+	0.248707i
$61$	−19.9699			−0.327375			−0.163688	−	0.986512i	$-0.552339\pi$
$61$	−19.9699			−0.327375			−0.163688	+	0.986512i	$0.552339\pi$
$62$	−18.2831	−	37.3367i	−0.294889	−	0.602205i
$63$	96.8103	+	25.8935i	1.53667	+	0.411008i
$64$	25.4778	−	58.7101i	0.398091	−	0.917346i
$65$	14.8167	+	9.23569i	0.227949	+	0.142088i
$66$	83.4455	−	72.8021i	1.26433	−	1.10306i
$67$	27.3331	−	27.3331i	0.407957	−	0.407957i	−0.473069	−	0.881026i	$-0.656854\pi$
$67$	27.3331	−	27.3331i	0.407957	−	0.407957i	0.881026	+	0.473069i	$0.156854\pi$
$68$	−33.1378	−	25.7225i	−0.487320	−	0.378272i
$69$	−49.4842	+	13.2712i	−0.717162	+	0.192336i
$70$	−9.69285	+	28.2947i	−0.138469	+	0.404209i
$71$	12.2997	+	12.2997i	0.173235	+	0.173235i	0.788399	−	0.615164i	$-0.210910\pi$
$71$	12.2997	+	12.2997i	0.173235	+	0.173235i	−0.615164	+	0.788399i	$0.710910\pi$
$72$	−32.3551	+	64.3207i	−0.449376	+	0.893343i
$73$	3.46448	−	3.46448i	0.0474586	−	0.0474586i	−0.682979	−	0.730438i	$-0.739316\pi$
$73$	3.46448	−	3.46448i	0.0474586	−	0.0474586i	0.730438	+	0.682979i	$0.239316\pi$
$74$	22.4179	+	45.7804i	0.302944	+	0.618654i
$75$	−67.2135	+	18.0260i	−0.896181	+	0.240347i
$76$	36.4017	−	4.58593i	0.478969	−	0.0603411i
$77$	205.511			2.66897
$78$	12.4257	+	77.0039i	0.159304	+	0.987230i
$79$		−	30.4341i		−	0.385242i	−0.981273	−	0.192621i	$-0.938301\pi$
$79$		−	30.4341i		−	0.385242i	0.981273	−	0.192621i	$-0.0616988\pi$
$80$	−18.4886	−	10.9512i	−0.231107	−	0.136890i
$81$	40.4368	−	70.1845i	0.499220	−	0.866476i
$82$	−33.4683	−	68.3469i	−0.408150	−	0.833499i
$83$	−93.6129	−	93.6129i	−1.12787	−	1.12787i	−0.990524	−	0.137343i	$-0.956144\pi$
$83$	−93.6129	−	93.6129i	−1.12787	−	1.12787i	−0.137343	−	0.990524i	$-0.543856\pi$
$84$	−123.719	+	50.4717i	−1.47284	+	0.600853i
$85$	−9.95952	+	9.95952i	−0.117171	+	0.117171i
$86$	6.28858	−	18.3572i	0.0731230	−	0.213455i
$87$	107.995	−	28.9632i	1.24132	−	0.332911i
$88$	−30.0165	+	144.570i	−0.341096	+	1.64284i
$89$	−27.0128	−	27.0128i	−0.303515	−	0.303515i	0.538872	−	0.842387i	$-0.318851\pi$
$89$	−27.0128	−	27.0128i	−0.303515	−	0.303515i	−0.842387	+	0.538872i	$0.818851\pi$
$90$	20.0690	+	13.4777i	0.222989	+	0.149752i
$91$	−76.5712	+	122.842i	−0.841442	+	1.34991i
$92$	41.8865	−	53.9616i	0.455288	−	0.586539i
$93$	−54.0117	−	31.1675i	−0.580771	−	0.335134i
$94$	−64.9565	−	132.650i	−0.691027	−	1.41117i
$95$		−	12.3188i		−	0.129671i
$96$	−17.4350	−	94.4035i	−0.181614	−	0.983370i
$97$	58.7776	+	58.7776i	0.605954	+	0.605954i	0.941886	−	0.335932i	$-0.109051\pi$
$97$	58.7776	+	58.7776i	0.605954	+	0.605954i	−0.335932	+	0.941886i	$0.609051\pi$
$98$	−141.874	−	48.6016i	−1.44770	−	0.495935i
$99$	42.9201	−	160.469i	0.433536	−	1.62090i
$100$	56.8937	−	73.2951i	0.568937	−	0.732951i
$101$	12.9267			0.127987			0.0639934	−	0.997950i	$-0.479616\pi$
$101$	12.9267			0.127987			0.0639934	+	0.997950i	$0.479616\pi$
$102$	−62.7787	−	4.27643i	−0.615478	−	0.0419258i
$103$	24.5921			0.238758			0.119379	−	0.992849i	$-0.461910\pi$
$103$	24.5921			0.238758			0.119379	+	0.992849i	$0.461910\pi$
$104$	−75.2312	−	71.8072i	−0.723377	−	0.690454i
$105$	11.6212	+	43.3320i	0.110678	+	0.412685i
$106$	−177.417	−	60.7773i	−1.67374	−	0.573371i
$107$	45.2828			0.423204			0.211602	−	0.977356i	$-0.432132\pi$
$107$	45.2828			0.423204			0.211602	+	0.977356i	$0.432132\pi$
$108$	13.5717	+	107.144i	0.125664	+	0.992073i
$109$	−127.144	−	127.144i	−1.16646	−	1.16646i	−0.983035	−	0.183421i	$-0.941283\pi$
$109$	−127.144	−	127.144i	−1.16646	−	1.16646i	−0.183421	−	0.983035i	$-0.558717\pi$
$110$	46.9001	+	16.0665i	0.426365	+	0.146059i
$111$	66.2265	+	38.2160i	0.596635	+	0.344288i
$112$	90.7944	−	153.285i	0.810664	−	1.36862i
$113$			124.896i			1.10528i	0.833421	+	0.552639i	$0.186379\pi$
$113$			124.896i			1.10528i	−0.833421	+	0.552639i	$0.813621\pi$
$114$	41.4697	−	36.1803i	0.363770	−	0.317371i
$115$	−16.2181	−	16.2181i	−0.141027	−	0.141027i
$116$	−91.4136	+	117.766i	−0.788048	+	1.01523i
$117$	79.9270	+	85.4440i	0.683137	+	0.730291i
$118$	34.6931	+	70.8482i	0.294010	+	0.600409i
$119$	−82.5723	−	82.5723i	−0.693885	−	0.693885i
$120$	−32.1799	+	1.84615i	−0.268166	+	0.0153846i
$121$		−	219.647i		−	1.81526i
$122$	12.9437	−	37.7842i	0.106096	−	0.309707i
$123$	−98.8715	−	57.0538i	−0.803833	−	0.463852i
$124$	82.4936	−	10.3926i	0.665271	−	0.0838116i
$125$	−45.7704	−	45.7704i	−0.366164	−	0.366164i
$126$	−111.741	+	166.388i	−0.886830	+	1.32054i
$127$	200.693			1.58026			0.790130	−	0.612939i	$-0.210013\pi$
$127$	200.693			1.58026			0.790130	+	0.612939i	$0.210013\pi$
$128$	94.5694	+	86.2591i	0.738823	+	0.673899i
$129$	−7.53968	−	28.1132i	−0.0584472	−	0.217931i
$130$	−27.0780	+	22.0478i	−0.208293	+	0.169599i
$131$	137.472			1.04941			0.524703	−	0.851285i	$-0.324176\pi$
$131$	137.472			1.04941			0.524703	+	0.851285i	$0.324176\pi$
$132$	83.6599	+	205.071i	0.633787	+	1.55357i
$133$	102.132			0.767913
$134$	33.9997	+	69.4321i	0.253729	+	0.518150i
$135$	36.2619	−	0.0245023i	0.268607	−	0.000181499i
$136$	70.1470	−	46.0264i	0.515787	−	0.338429i
$137$	89.4472	+	89.4472i	0.652900	+	0.652900i	0.953690	−	0.300791i	$-0.0972505\pi$
$137$	89.4472	+	89.4472i	0.652900	+	0.652900i	−0.300791	+	0.953690i	$0.597251\pi$
$138$	6.96374	−	102.229i	0.0504619	−	0.740789i
$139$			45.2932i			0.325850i	0.986638	+	0.162925i	$0.0520929\pi$
$139$			45.2932i			0.325850i	−0.986638	+	0.162925i	$0.947907\pi$
$140$	−47.2527	−	36.6789i	−0.337519	−	0.261992i
$141$	−191.893	−	110.732i	−1.36095	−	0.785334i
$142$	−31.2440	+	15.2996i	−0.220028	+	0.107744i
$143$	203.618	+	126.921i	1.42390	+	0.887562i
$144$	−100.727	−	102.908i	−0.699495	−	0.714637i
$145$	35.3945	+	35.3945i	0.244100	+	0.244100i
$146$	4.30946	+	8.80053i	0.0295169	+	0.0602776i
$147$	−217.274	+	58.2708i	−1.47805	+	0.396400i
$148$	−101.150	+	12.7429i	−0.683443	+	0.0861010i
$149$	−74.6323	+	74.6323i	−0.500888	+	0.500888i	−0.911714	−	0.410826i	$-0.865240\pi$
$149$	−74.6323	+	74.6323i	−0.500888	+	0.500888i	0.410826	+	0.911714i	$0.365240\pi$
$150$	9.45872	−	138.856i	0.0630582	−	0.925705i
$151$	−32.3514	−	32.3514i	−0.214247	−	0.214247i	0.591822	−	0.806069i	$-0.298409\pi$
$151$	−32.3514	−	32.3514i	−0.214247	−	0.214247i	−0.806069	+	0.591822i	$0.798409\pi$
$152$	−14.9172	+	71.8465i	−0.0981397	+	0.472675i
$153$	−81.7197	+	47.2300i	−0.534116	+	0.308693i
$154$	−133.204	+	388.839i	−0.864960	+	2.52493i
$155$		−	27.9168i		−	0.180109i
$156$	−153.750	−	26.4005i	−0.985576	−	0.169234i
$157$	38.4009			0.244592			0.122296	−	0.992494i	$-0.460974\pi$
$157$	38.4009			0.244592			0.122296	+	0.992494i	$0.460974\pi$
$158$	57.5832	+	19.7262i	0.364451	+	0.124849i
$159$	−271.706	+	72.8689i	−1.70884	+	0.458295i
$160$	32.7039	−	27.8834i	0.204400	−	0.174271i
$161$	134.461	−	134.461i	0.835160	−	0.835160i
$162$	106.584	+	122.000i	0.657925	+	0.753084i
$163$	5.31158	+	5.31158i	0.0325864	+	0.0325864i	0.723212	−	0.690626i	$-0.242665\pi$
$163$	5.31158	+	5.31158i	0.0325864	+	0.0325864i	−0.690626	+	0.723212i	$0.742665\pi$
$164$	151.009	−	19.0243i	0.920788	−	0.116002i
$165$	71.8254	−	19.2629i	0.435305	−	0.116745i
$166$	237.797	−	116.445i	1.43251	−	0.701477i
$167$	−19.7239	+	19.7239i	−0.118107	+	0.118107i	−0.763690	−	0.645583i	$-0.776615\pi$
$167$	−19.7239	+	19.7239i	−0.118107	+	0.118107i	0.645583	+	0.763690i	$0.276615\pi$
$168$	−15.3061	−	266.797i	−0.0911076	−	1.58808i
$169$	−151.732	+	74.4209i	−0.897821	+	0.440360i
$170$	−12.3886	−	25.2994i	−0.0728744	−	0.148820i
$171$	21.3299	−	79.7479i	0.124736	−	0.466362i
$172$	30.6569	+	23.7967i	0.178238	+	0.138353i
$173$	−151.819			−0.877567			−0.438783	−	0.898593i	$-0.644590\pi$
$173$	−151.819			−0.877567			−0.438783	+	0.898593i	$0.644590\pi$
$174$	−15.1977	+	223.106i	−0.0873433	+	1.28222i
$175$	182.636	−	182.636i	1.04363	−	1.04363i
$176$	−254.079	−	150.497i	−1.44363	−	0.855098i
$177$	102.490	+	59.1418i	0.579039	+	0.334134i
$178$	68.6185	−	33.6013i	0.385497	−	0.188771i
$179$			168.054i			0.938850i	0.882972	+	0.469425i	$0.155539\pi$
$179$			168.054i			0.938850i	−0.882972	+	0.469425i	$0.844461\pi$
$180$	−38.5084	+	29.2360i	−0.213936	+	0.162422i
$181$			161.911i			0.894539i	0.894399	+	0.447269i	$0.147603\pi$
$181$			161.911i			0.894539i	−0.894399	+	0.447269i	$0.852397\pi$
$182$	−182.794	−	224.498i	−1.00436	−	1.23351i
$183$	−15.5188	−	57.8648i	−0.0848022	−	0.316201i
$184$	74.9494	+	114.227i	0.407334	+	0.620801i
$185$			34.2303i			0.185028i
$186$	93.9789	−	81.9919i	0.505263	−	0.440817i
$187$	−136.869	+	136.869i	−0.731918	+	0.731918i
$188$	293.084	−	36.9231i	1.55896	−	0.196399i
$189$	0.203144	+	300.640i	0.00107483	+	1.59069i
$190$	23.3079	+	7.98452i	0.122673	+	0.0420238i
$191$	−89.9885			−0.471144			−0.235572	−	0.971857i	$-0.575696\pi$
$191$	−89.9885			−0.471144			−0.235572	+	0.971857i	$0.575696\pi$
$192$	189.918	+	28.2005i	0.989155	+	0.146877i
$193$	−129.472	+	129.472i	−0.670841	+	0.670841i	−0.957910	−	0.287069i	$-0.907319\pi$
$193$	−129.472	+	129.472i	−0.670841	+	0.670841i	0.287069	+	0.957910i	$0.407319\pi$
$194$	−149.308	+	73.1135i	−0.769628	+	0.376874i
$195$	−15.2472	+	50.1100i	−0.0781907	+	0.256974i
$196$	183.914	−	236.933i	0.938338	−	1.20884i
$197$	43.9320	−	43.9320i	0.223005	−	0.223005i	−0.586758	−	0.809763i	$-0.699596\pi$
$197$	43.9320	−	43.9320i	0.223005	−	0.223005i	0.809763	+	0.586758i	$0.199596\pi$
$198$	275.798	+	185.217i	1.39292	+	0.935438i
$199$	170.302			0.855788			0.427894	−	0.903829i	$-0.359256\pi$
$199$	170.302			0.855788			0.427894	+	0.903829i	$0.359256\pi$
$200$	101.802	+	155.153i	0.509012	+	0.775766i
$201$	100.441	+	57.9597i	0.499708	+	0.288357i
$202$	−8.37854	+	24.4580i	−0.0414779	+	0.121079i
$203$	−293.449	+	293.449i	−1.44556	+	1.44556i
$204$	48.7819	−	116.009i	0.239127	−	0.568673i
$205$		−	51.1034i		−	0.249285i
$206$	−15.9396	+	46.5297i	−0.0773766	+	0.225872i
$207$	−76.9093	−	133.072i	−0.371543	−	0.642862i
$208$	184.625	−	95.7994i	0.887621	−	0.460574i
$209$		−	169.291i		−	0.810003i
$210$	−89.5191	−	6.09796i	−0.426281	−	0.0290379i
$211$		−	224.166i		−	1.06240i	−0.847247	−	0.531200i	$-0.821741\pi$
$211$		−	224.166i		−	1.06240i	0.847247	−	0.531200i	$-0.178259\pi$
$212$	229.989	−	296.290i	1.08485	−	1.39759i
$213$	−26.0815	+	45.1979i	−0.122448	+	0.212197i
$214$	−29.3505	+	85.6777i	−0.137152	+	0.400363i
$215$	9.21388	−	9.21388i	0.0428553	−	0.0428553i
$216$	−211.519	−	43.7679i	−0.979256	−	0.202629i
$217$	231.453			1.06660
$218$	322.973	−	158.154i	1.48153	−	0.725477i
$219$	12.7310	+	7.34640i	0.0581322	+	0.0335452i
$220$	−60.7975	+	78.3242i	−0.276352	+	0.356019i
$221$	−30.8159	−	132.807i	−0.139439	−	0.600939i
$222$	−115.232	+	100.534i	−0.519064	+	0.452858i
$223$	−177.676	+	177.676i	−0.796752	+	0.796752i	−0.982582	−	0.185830i	$-0.940503\pi$
$223$	−177.676	+	177.676i	−0.796752	+	0.796752i	0.185830	+	0.982582i	$0.440503\pi$
$224$	231.175	+	271.141i	1.03203	+	1.21045i
$225$	−104.465	−	180.750i	−0.464287	−	0.803333i
$226$	−236.311	−	80.9527i	−1.04563	−	0.358198i
$227$	−30.2485	−	30.2485i	−0.133253	−	0.133253i	0.637334	−	0.770588i	$-0.280037\pi$
$227$	−30.2485	−	30.2485i	−0.133253	−	0.133253i	−0.770588	+	0.637334i	$0.780037\pi$
$228$	41.5763	+	101.914i	0.182352	+	0.446990i
$229$	274.828	−	274.828i	1.20012	−	1.20012i	0.225995	−	0.974128i	$-0.427437\pi$
$229$	274.828	−	274.828i	1.20012	−	1.20012i	0.974128	−	0.225995i	$-0.0725634\pi$
$230$	41.1975	−	20.1737i	0.179119	−	0.0877117i
$231$	159.705	+	595.489i	0.691362	+	2.57788i
$232$	−163.570	−	249.291i	−0.705045	−	1.07453i
$233$	−176.505			−0.757532			−0.378766	−	0.925492i	$-0.623652\pi$
$233$	−176.505			−0.757532			−0.378766	+	0.925492i	$0.623652\pi$
$234$	−213.471	+	95.8453i	−0.912267	+	0.409596i
$235$		−	99.1833i		−	0.422057i
$236$	−156.536	+	19.7206i	−0.663287	+	0.0835617i
$237$	88.1860	−	23.6507i	0.372093	−	0.0997918i
$238$	209.752	−	102.712i	0.881310	−	0.431562i
$239$	−82.2545	−	82.2545i	−0.344161	−	0.344161i	0.513768	−	0.857929i	$-0.328249\pi$
$239$	−82.2545	−	82.2545i	−0.344161	−	0.344161i	−0.857929	+	0.513768i	$0.828249\pi$
$240$	17.3647	−	62.0829i	0.0723527	−	0.258679i
$241$	−64.6891	+	64.6891i	−0.268419	+	0.268419i	−0.828463	−	0.560044i	$-0.810784\pi$
$241$	−64.6891	+	64.6891i	−0.268419	+	0.268419i	0.560044	+	0.828463i	$0.310784\pi$
$242$	415.585	+	142.366i	1.71729	+	0.588290i
$243$	234.791	+	62.6287i	0.966217	+	0.257731i
$244$	63.1005	+	48.9804i	0.258608	+	0.200739i
$245$	−71.2099	−	71.2099i	−0.290653	−	0.290653i
$246$	172.034	−	150.091i	0.699324	−	0.610125i
$247$	101.192	+	63.0759i	0.409683	+	0.255368i
$248$	−33.8055	+	162.819i	−0.136312	+	0.656528i
$249$	198.505	−	344.000i	0.797211	−	1.38153i
$250$	116.267	−	56.9339i	0.465068	−	0.227736i
$251$		−	186.767i		−	0.744091i	−0.928215	−	0.372045i	$-0.878657\pi$
$251$		−	186.767i		−	0.744091i	0.928215	−	0.372045i	$-0.121343\pi$
$252$	−242.390	−	319.265i	−0.961865	−	1.26693i
$253$	−222.877	−	222.877i	−0.880936	−	0.880936i
$254$	−130.081	+	379.723i	−0.512130	+	1.49497i
$255$	−36.5984	−	21.1191i	−0.143523	−	0.0828199i
$256$	−224.503	+	123.021i	−0.876966	+	0.480552i
$257$	−440.294			−1.71321			−0.856604	−	0.515975i	$-0.827430\pi$
$257$	−440.294			−1.71321			−0.856604	+	0.515975i	$0.827430\pi$
$258$	58.0787	+	3.95626i	0.225111	+	0.0153344i
$259$	−283.796			−1.09574
$260$	−24.1649	−	65.5238i	−0.0929421	−	0.252015i
$261$	167.848	+	290.419i	0.643095	+	1.11272i
$262$	−89.1039	+	260.106i	−0.340091	+	0.992770i
$263$	−55.8360			−0.212304			−0.106152	−	0.994350i	$-0.533853\pi$
$263$	−55.8360			−0.212304			−0.106152	+	0.994350i	$0.533853\pi$
$264$	−442.232	+	25.3707i	−1.67512	+	0.0961013i
$265$	−89.0496	−	89.0496i	−0.336036	−	0.336036i
$266$	−66.1980	+	193.241i	−0.248865	+	0.726468i
$267$	57.2805	−	99.2644i	0.214534	−	0.371777i
$268$	−153.407	+	19.3264i	−0.572414	+	0.0721133i
$269$		−	139.702i		−	0.519337i	−0.965698	−	0.259668i	$-0.916387\pi$
$269$		−	139.702i		−	0.519337i	0.965698	−	0.259668i	$-0.0836133\pi$
$270$	−23.4571	+	68.6255i	−0.0868782	+	0.254169i
$271$	14.0400	+	14.0400i	0.0518082	+	0.0518082i	0.732536	−	0.680728i	$-0.238336\pi$
$271$	14.0400	+	14.0400i	0.0518082	+	0.0518082i	−0.680728	+	0.732536i	$0.738336\pi$
$272$	41.6182	+	162.555i	0.153008	+	0.597628i
$273$	−415.451	−	126.411i	−1.52180	−	0.463045i
$274$	−227.216	+	111.263i	−0.829254	+	0.406071i
$275$	−302.730	−	302.730i	−1.10084	−	1.10084i
$276$	188.910	+	79.4364i	0.684455	+	0.287813i
$277$			264.498i			0.954868i	0.878668	+	0.477434i	$0.158433\pi$
$277$			264.498i			0.954868i	−0.878668	+	0.477434i	$0.841567\pi$
$278$	−85.6973	−	29.3572i	−0.308264	−	0.105601i
$279$	48.3379	−	180.725i	0.173254	−	0.647760i
$280$	100.026	−	65.6311i	0.357235	−	0.234397i
$281$	−201.246	−	201.246i	−0.716179	−	0.716179i	0.251641	−	0.967821i	$-0.419030\pi$
$281$	−201.246	−	201.246i	−0.716179	−	0.716179i	−0.967821	+	0.251641i	$0.919030\pi$
$282$	333.889	−	291.302i	1.18400	−	1.03299i
$283$	−396.067			−1.39953			−0.699765	−	0.714373i	$-0.746712\pi$
$283$	−396.067			−1.39953			−0.699765	+	0.714373i	$0.746712\pi$
$284$	−8.69674	−	69.0320i	−0.0306223	−	0.243071i
$285$	35.6949	−	9.57304i	0.125245	−	0.0335896i
$286$	−372.120	+	302.992i	−1.30112	+	1.05941i
$287$	423.687			1.47626
$288$	259.995	−	123.882i	0.902760	−	0.430144i
$289$	−179.015			−0.619429
$290$	−89.9099	+	44.0273i	−0.310034	+	0.151818i
$291$	−124.637	+	215.991i	−0.428307	+	0.742236i
$292$	−19.4443	+	2.44962i	−0.0665902	+	0.00838911i
$293$	186.129	+	186.129i	0.635253	+	0.635253i	0.949381	−	0.314128i	$-0.101712\pi$
$293$	186.129	+	186.129i	0.635253	+	0.635253i	−0.314128	+	0.949381i	$0.601712\pi$
$294$	30.5762	−	448.864i	0.104001	−	1.52675i
$295$			52.9736i			0.179572i
$296$	41.4506	−	199.641i	0.140036	−	0.674461i
$297$	498.329	−	0.336723i	1.67787	−	0.00113375i
$298$	−92.8352	−	189.582i	−0.311527	−	0.636183i
$299$	216.264	−	50.1807i	0.723290	−	0.167828i
$300$	256.593	+	107.897i	0.855309	+	0.359657i
$301$	76.3904	+	76.3904i	0.253789	+	0.253789i
$302$	82.1795	−	40.2419i	0.272118	−	0.133251i
$303$	10.0454	+	37.4563i	0.0331533	+	0.123618i
$304$	−126.269	−	74.7923i	−0.415359	−	0.246027i
$305$	18.9648	−	18.9648i	0.0621796	−	0.0621796i
$306$	−36.3946	−	185.231i	−0.118937	−	0.605330i
$307$	−249.313	−	249.313i	−0.812093	−	0.812093i	0.172854	−	0.984947i	$-0.444701\pi$
$307$	−249.313	−	249.313i	−0.812093	−	0.812093i	−0.984947	+	0.172854i	$0.944701\pi$
$308$	−649.370	−	504.059i	−2.10834	−	1.63656i
$309$	19.1107	+	71.2581i	0.0618471	+	0.230609i
$310$	52.8203	+	18.0946i	0.170388	+	0.0583695i
$311$		−	145.007i		−	0.466262i	−0.972445	−	0.233131i	$-0.925103\pi$
$311$		−	145.007i		−	0.466262i	0.972445	−	0.233131i	$-0.0748971\pi$
$312$	149.606	−	273.792i	0.479506	−	0.877539i
$313$	238.458			0.761848			0.380924	−	0.924606i	$-0.375606\pi$
$313$	238.458			0.761848			0.380924	+	0.924606i	$0.375606\pi$
$314$	−24.8899	+	72.6568i	−0.0792672	+	0.231391i
$315$	−116.528	+	67.3474i	−0.369930	+	0.213801i
$316$	−74.6461	+	96.1651i	−0.236222	+	0.304320i
$317$	−313.133	+	313.133i	−0.987801	+	0.987801i	−0.999926	−	0.0121259i	$-0.996140\pi$
$317$	−313.133	+	313.133i	−0.987801	+	0.987801i	0.0121259	+	0.999926i	$0.496140\pi$
$318$	38.2362	−	561.314i	0.120240	−	1.76514i
$319$	486.409	+	486.409i	1.52479	+	1.52479i
$320$	31.5596	+	79.9506i	0.0986239	+	0.249846i
$321$	35.1897	+	131.212i	0.109625	+	0.408759i
$322$	167.256	+	341.560i	0.519428	+	1.06074i
$323$	−68.0193	+	68.0193i	−0.210586	+	0.210586i
$324$	−299.914	+	122.588i	−0.925660	+	0.378358i
$325$	293.747	−	68.1596i	0.903838	−	0.209722i
$326$	−13.4926	+	6.60708i	−0.0413883	+	0.0202671i
$327$	269.607	−	467.216i	0.824487	−	1.42880i
$328$	−61.8828	+	298.049i	−0.188667	+	0.908686i
$329$	822.309			2.49942
$330$	−10.1077	+	148.383i	−0.0306295	+	0.449646i
$331$	−180.560	+	180.560i	−0.545499	+	0.545499i	−0.925136	−	0.379636i	$-0.876049\pi$
$331$	−180.560	+	180.560i	−0.545499	+	0.545499i	0.379636	+	0.925136i	$0.376049\pi$
$332$	66.1907	+	525.401i	0.199370	+	1.58253i
$333$	−59.2695	+	221.596i	−0.177987	+	0.665454i
$334$	−24.5346	−	50.1031i	−0.0734569	−	0.150009i
$335$			51.9148i			0.154969i
$336$	514.716	+	143.967i	1.53189	+	0.428473i
$337$		−	20.9367i		−	0.0621266i	−0.999517	−	0.0310633i	$-0.990111\pi$
$337$		−	20.9367i		−	0.0621266i	0.999517	−	0.0310633i	$-0.00988935\pi$
$338$	−42.4624	−	335.322i	−0.125629	−	0.992077i
$339$	−361.900	+	97.0582i	−1.06755	+	0.286307i
$340$	55.8977	−	7.04206i	0.164405	−	0.0207119i
$341$		−	383.647i		−	1.12506i
$342$	137.063	+	92.0468i	0.400768	+	0.269143i
$343$	204.585	−	204.585i	0.596459	−	0.596459i
$344$	−64.8953	+	42.5805i	−0.188649	+	0.123781i
$345$	34.3903	−	59.5968i	0.0996821	−	0.172744i
$346$	98.4029	−	287.251i	0.284401	−	0.830204i
$347$	304.430			0.877319			0.438659	−	0.898653i	$-0.355453\pi$
$347$	304.430			0.877319			0.438659	+	0.898653i	$0.355453\pi$
$348$	−412.278	−	173.363i	−1.18471	−	0.498169i
$349$	−273.159	+	273.159i	−0.782690	+	0.782690i	−0.980284	−	0.197594i	$-0.936687\pi$
$349$	−273.159	+	273.159i	−0.782690	+	0.782690i	0.197594	+	0.980284i	$0.436687\pi$
$350$	227.181	+	463.935i	0.649088	+	1.32553i
$351$	−185.471	+	297.996i	−0.528406	+	0.848992i
$352$	449.433	−	383.187i	1.27680	−	1.08860i
$353$	88.1316	−	88.1316i	0.249665	−	0.249665i	−0.571168	−	0.820833i	$-0.693510\pi$
$353$	88.1316	−	88.1316i	0.249665	−	0.249665i	0.820833	+	0.571168i	$0.193510\pi$
$354$	−178.330	+	155.584i	−0.503756	+	0.439502i
$355$	−23.3613			−0.0658065
$356$	19.0999	+	151.609i	0.0536515	+	0.425869i
$357$	175.094	−	303.429i	0.490459	−	0.849942i
$358$	−317.968	−	108.926i	−0.888180	−	0.304262i
$359$	93.4775	−	93.4775i	0.260383	−	0.260383i	−0.564827	−	0.825210i	$-0.691057\pi$
$359$	93.4775	−	93.4775i	0.260383	−	0.260383i	0.825210	+	0.564827i	$0.191057\pi$
$360$	−30.3567	−	91.8099i	−0.0843242	−	0.255027i
$361$			276.868i			0.766947i
$362$	−306.346	−	104.944i	−0.846260	−	0.289902i
$363$	636.450	−	170.690i	1.75331	−	0.470220i
$364$	543.244	−	200.347i	1.49243	−	0.550402i
$365$			6.58021i			0.0180280i
$366$	119.542	+	8.14311i	0.326618	+	0.0222489i
$367$		−	498.412i		−	1.35807i	−0.734106	−	0.679035i	$-0.762398\pi$
$367$		−	498.412i		−	1.35807i	0.734106	−	0.679035i	$-0.237602\pi$
$368$	−264.704	+	67.7711i	−0.719305	+	0.184161i
$369$	88.4852	−	330.827i	0.239797	−	0.896551i
$370$	−64.7657	−	22.1867i	−0.175042	−	0.0599639i
$371$	738.292	−	738.292i	1.99000	−	1.99000i
$372$	94.2203	+	230.957i	0.253280	+	0.620853i
$373$	−576.578			−1.54579			−0.772893	−	0.634537i	$-0.781191\pi$
$373$	−576.578			−1.54579			−0.772893	+	0.634537i	$0.781191\pi$
$374$	−170.251	−	347.676i	−0.455216	−	0.929615i
$375$	97.0559	−	168.193i	0.258816	−	0.448515i
$376$	−120.105	+	578.465i	−0.319427	+	1.53847i
$377$	−471.977	+	109.515i	−1.25193	+	0.290491i
$378$	−568.960	−	194.478i	−1.50519	−	0.514492i
$379$	−168.149	+	168.149i	−0.443664	+	0.443664i	−0.893241	−	0.449577i	$-0.851575\pi$
$379$	−168.149	+	168.149i	−0.443664	+	0.443664i	0.449577	+	0.893241i	$0.351575\pi$
$380$	−30.2144	+	38.9246i	−0.0795116	+	0.102433i
$381$	155.961	+	581.529i	0.409345	+	1.52632i
$382$	58.3269	−	170.264i	0.152688	−	0.445716i
$383$	199.284	+	199.284i	0.520323	+	0.520323i	0.917669	−	0.397346i	$-0.130069\pi$
$383$	199.284	+	199.284i	0.520323	+	0.520323i	−0.397346	+	0.917669i	$0.630069\pi$
$384$	−176.454	+	341.057i	−0.459515	+	0.888170i
$385$	−195.167	+	195.167i	−0.506928	+	0.506928i
$386$	−161.051	−	328.888i	−0.417230	−	0.852041i
$387$	75.6016	−	43.6940i	0.195353	−	0.112904i
$388$	−41.5598	−	329.889i	−0.107113	−	0.850228i
$389$	−81.1669			−0.208655			−0.104328	−	0.994543i	$-0.533269\pi$
$389$	−81.1669			−0.208655			−0.104328	+	0.994543i	$0.533269\pi$
$390$	−84.9285	−	61.3278i	−0.217765	−	0.157251i
$391$			179.099i			0.458055i
$392$	329.086	+	501.547i	0.839504	+	1.27946i
$393$	106.831	+	398.340i	0.271835	+	1.01359i
$394$	54.6470	+	111.597i	0.138698	+	0.283241i
$395$	28.9023	+	28.9023i	0.0731704	+	0.0731704i
$396$	−529.202	+	401.776i	−1.33637	+	1.01459i
$397$	251.456	−	251.456i	0.633390	−	0.633390i	−0.315527	−	0.948917i	$-0.602181\pi$
$397$	251.456	−	251.456i	0.633390	−	0.633390i	0.948917	+	0.315527i	$0.102181\pi$
$398$	−110.383	+	322.221i	−0.277343	+	0.809601i
$399$	79.3681	+	295.939i	0.198918	+	0.741702i
$400$	−359.543	+	92.0524i	−0.898858	+	0.230131i
$401$	419.266	+	419.266i	1.04555	+	1.04555i	0.998912	+	0.0466382i	$0.0148508\pi$
$401$	419.266	+	419.266i	1.04555	+	1.04555i	0.0466382	+	0.998912i	$0.485149\pi$
$402$	−174.765	+	152.474i	−0.434739	+	0.379288i
$403$	229.321	+	142.943i	0.569034	+	0.354697i
$404$	−40.8454	−	31.7054i	−0.101103	−	0.0784787i
$405$	28.2505	+	105.054i	0.0697542	+	0.259391i
$406$	−365.021	−	745.424i	−0.899067	−	1.83602i
$407$			470.409i			1.15580i
$408$	187.878	+	167.491i	0.460486	+	0.410516i
$409$	474.074	+	474.074i	1.15911	+	1.15911i	0.984668	+	0.174437i	$0.0558104\pi$
$409$	474.074	+	474.074i	1.15911	+	1.15911i	0.174437	+	0.984668i	$0.444190\pi$
$410$	96.6906	+	33.1231i	0.235831	+	0.0807881i
$411$	−189.672	+	328.693i	−0.461490	+	0.799739i
$412$	−77.7056	−	60.3173i	−0.188606	−	0.146401i
$413$	−439.193			−1.06342
$414$	301.630	−	59.2649i	0.728576	−	0.143152i
$415$	177.802			0.428439
$416$	61.5917	+	411.415i	0.148057	+	0.988979i
$417$	−131.242	+	35.1978i	−0.314728	+	0.0844071i
$418$	320.308	+	109.727i	0.766287	+	0.262505i
$419$	−738.508			−1.76255			−0.881274	−	0.472605i	$-0.843314\pi$
$419$	−738.508			−1.76255			−0.881274	+	0.472605i	$0.843314\pi$
$420$	69.5603	−	165.423i	0.165620	−	0.393864i
$421$	18.8649	+	18.8649i	0.0448098	+	0.0448098i	0.729157	−	0.684347i	$-0.239913\pi$
$421$	18.8649	+	18.8649i	0.0448098	+	0.0448098i	−0.684347	+	0.729157i	$0.739913\pi$
$422$	424.136	+	145.295i	1.00506	+	0.344302i
$423$	171.735	−	642.082i	0.405994	−	1.51792i
$424$	411.529	+	627.195i	0.970587	+	1.47923i
$425$			243.268i			0.572395i
$426$	−68.6122	−	78.6431i	−0.161062	−	0.184608i
$427$	157.233	+	157.233i	0.368227	+	0.368227i
$428$	−143.084	−	111.066i	−0.334308	−	0.259499i
$429$	−209.534	+	688.636i	−0.488425	+	1.60521i
$430$	11.4612	+	23.4053i	0.0266538	+	0.0544309i
$431$	−408.414	−	408.414i	−0.947596	−	0.947596i	0.0510979	−	0.998694i	$-0.483728\pi$
$431$	−408.414	−	408.414i	−0.947596	−	0.947596i	−0.998694	+	0.0510979i	$0.983728\pi$
$432$	219.910	−	371.838i	0.509050	−	0.860737i
$433$		−	486.714i		−	1.12405i	−0.827120	−	0.562025i	$-0.810022\pi$
$433$		−	486.714i		−	1.12405i	0.827120	−	0.562025i	$-0.189978\pi$
$434$	−150.018	+	437.923i	−0.345664	+	1.00904i
$435$	−75.0538	+	130.065i	−0.172538	+	0.298999i
$436$	89.8992	+	713.592i	0.206191	+	1.63668i
$437$	−110.763	−	110.763i	−0.253461	−	0.253461i
$438$	−22.1515	+	19.3261i	−0.0505742	+	0.0441235i
$439$	−279.462			−0.636588			−0.318294	−	0.947992i	$-0.603110\pi$
$439$	−279.462			−0.636588			−0.318294	+	0.947992i	$0.603110\pi$
$440$	−108.788	−	165.799i	−0.247245	−	0.376816i
$441$	−337.691	−	584.291i	−0.765740	−	1.32492i
$442$	271.253	+	27.7748i	0.613695	+	0.0628389i
$443$	687.638			1.55223			0.776115	−	0.630592i	$-0.217188\pi$
$443$	687.638			1.55223			0.776115	+	0.630592i	$0.217188\pi$
$444$	−115.528	−	283.189i	−0.260199	−	0.637812i
$445$	51.3065			0.115295
$446$	−221.011	−	451.335i	−0.495540	−	1.01196i
$447$	−274.252	−	158.257i	−0.613540	−	0.354043i
$448$	−662.854	+	261.654i	−1.47959	+	0.584050i
$449$	−332.430	−	332.430i	−0.740378	−	0.740378i	0.232272	−	0.972651i	$-0.425384\pi$
$449$	−332.430	−	332.430i	−0.740378	−	0.740378i	−0.972651	+	0.232272i	$0.925384\pi$
$450$	409.699	−	80.4986i	0.910443	−	0.178886i
$451$		−	702.288i		−	1.55718i
$452$	306.335	−	394.645i	0.677732	−	0.873108i
$453$	68.6008	−	118.882i	0.151437	−	0.262433i
$454$	76.8379	−	37.6262i	0.169246	−	0.0828770i
$455$	−43.9419	−	189.376i	−0.0965755	−	0.416212i
$456$	−219.775	+	12.6084i	−0.481963	+	0.0276501i
$457$	478.742	+	478.742i	1.04758	+	1.04758i	0.998810	+	0.0487647i	$0.0155284\pi$
$457$	478.742	+	478.742i	1.04758	+	1.04758i	0.0487647	+	0.998810i	$0.484472\pi$
$458$	341.859	+	698.124i	0.746417	+	1.52429i
$459$	−200.359	−	200.088i	−0.436512	−	0.435922i
$460$	11.4673	+	91.0238i	0.0249289	+	0.197878i
$461$	222.155	−	222.155i	0.481898	−	0.481898i	−0.423839	−	0.905737i	$-0.639318\pi$
$461$	222.155	−	222.155i	0.481898	−	0.481898i	0.905737	+	0.423839i	$0.139318\pi$
$462$	−1230.22	−	83.8011i	−2.66280	−	0.181388i
$463$	318.982	+	318.982i	0.688945	+	0.688945i	0.961999	−	0.273054i	$-0.0880337\pi$
$463$	318.982	+	318.982i	0.688945	+	0.688945i	−0.273054	+	0.961999i	$0.588034\pi$
$464$	577.694	−	147.904i	1.24503	−	0.318760i
$465$	80.8919	−	21.6945i	0.173961	−	0.0466547i
$466$	114.403	−	333.958i	0.245501	−	0.716648i
$467$			121.753i			0.260714i	0.991467	+	0.130357i	$0.0416123\pi$
$467$			121.753i			0.260714i	−0.991467	+	0.130357i	$0.958388\pi$
$468$	−42.9822	−	466.022i	−0.0918424	−	0.995774i
$469$	−430.415			−0.917728
$470$	187.661	+	64.2866i	0.399278	+	0.136780i
$471$	29.8417	+	111.271i	0.0633582	+	0.236243i
$472$	64.1476	−	308.957i	0.135906	−	0.654570i
$473$	126.622	−	126.622i	0.267699	−	0.267699i
$474$	−12.4101	+	182.183i	−0.0261817	+	0.384351i
$475$	−150.447	−	150.447i	−0.316731	−	0.316731i
$476$	58.3842	+	463.436i	0.122656	+	0.973606i
$477$	−422.290	−	730.668i	−0.885305	−	1.53180i
$478$	208.944	−	102.316i	0.437122	−	0.214051i
$479$	−262.894	+	262.894i	−0.548839	+	0.548839i	−0.926105	−	0.377266i	$-0.876864\pi$
$479$	−262.894	+	262.894i	−0.548839	+	0.548839i	0.377266	+	0.926105i	$0.376864\pi$
$480$	106.209	+	73.0945i	0.221270	+	0.152280i
$481$	−281.182	−	175.269i	−0.584578	−	0.364385i
$482$	−80.4668	−	164.324i	−0.166944	−	0.340922i
$483$	494.105	+	285.123i	1.02299	+	0.590317i
$484$	−538.731	+	694.036i	−1.11308	+	1.43396i
$485$	−111.638			−0.230182
$486$	−270.679	+	403.645i	−0.556952	+	0.830544i
$487$	−222.814	+	222.814i	−0.457524	+	0.457524i	−0.897842	−	0.440318i	$-0.854866\pi$
$487$	−222.814	+	222.814i	−0.457524	+	0.457524i	0.440318	+	0.897842i	$0.354866\pi$
$488$	−133.573	+	87.6428i	−0.273715	+	0.179596i
$489$	−11.2632	+	19.5185i	−0.0230331	+	0.0399152i
$490$	180.889	−	88.5781i	0.369161	−	0.180772i
$491$			972.633i			1.98092i	0.137788	+	0.990462i	$0.456001\pi$
$491$			972.633i			1.98092i	−0.137788	+	0.990462i	$0.543999\pi$
$492$	172.476	+	422.781i	0.350560	+	0.859310i
$493$		−	390.869i		−	0.792837i
$494$	−184.932	+	150.577i	−0.374355	+	0.304813i
$495$	111.632	+	193.152i	0.225520	+	0.390206i
$496$	−286.152	−	169.495i	−0.576919	−	0.341723i
$497$		−	193.684i		−	0.389706i
$498$	522.206	+	598.551i	1.04861	+	1.20191i
$499$	445.893	−	445.893i	0.893574	−	0.893574i	−0.101284	−	0.994858i	$-0.532295\pi$
$499$	445.893	−	445.893i	0.893574	−	0.893574i	0.994858	+	0.101284i	$0.0322951\pi$
$500$	32.3628	+	256.886i	0.0647256	+	0.513772i
$501$	−72.4798	−	41.8245i	−0.144670	−	0.0834819i
$502$	353.374	+	121.055i	0.703932	+	0.241145i
$503$	9.30759			0.0185042			0.00925208	−	0.999957i	$-0.497055\pi$
$503$	9.30759			0.0185042			0.00925208	+	0.999957i	$0.497055\pi$
$504$	761.177	−	251.681i	1.51027	−	0.499368i
$505$	−12.2760	+	12.2760i	−0.0243090	+	0.0243090i
$506$	566.156	−	277.237i	1.11889	−	0.547899i
$507$	−333.554	−	381.825i	−0.657898	−	0.753107i
$508$	−634.146	−	492.242i	−1.24832	−	0.968981i
$509$	336.411	−	336.411i	0.660926	−	0.660926i	−0.294672	−	0.955598i	$-0.595210\pi$
$509$	336.411	−	336.411i	0.660926	−	0.660926i	0.955598	+	0.294672i	$0.0952105\pi$
$510$	63.6801	−	55.5578i	0.124863	−	0.108937i
$511$	−54.5551			−0.106761
$512$	−87.2496	−	504.511i	−0.170409	−	0.985373i
$513$	247.653	−	0.167340i	0.482755	−	0.000326200i
$514$	285.381	−	833.063i	0.555215	−	1.62075i
$515$	−23.3543	+	23.3543i	−0.0453482	+	0.0453482i
$516$	−45.1297	+	107.324i	−0.0874607	+	0.207992i
$517$		−	1363.03i		−	2.63641i
$518$	183.945	−	536.959i	0.355106	−	1.03660i
$519$	−117.980	−	439.911i	−0.227322	−	0.847613i
$520$	139.638	−	3.25168i	0.268534	−	0.00625322i
$521$		−	210.994i		−	0.404979i	−0.979284	−	0.202489i	$-0.935097\pi$
$521$		−	210.994i		−	0.404979i	0.979284	−	0.202489i	$-0.0649031\pi$
$522$	−658.282	+	129.341i	−1.26108	+	0.247779i
$523$			782.435i			1.49605i	0.663670	+	0.748026i	$0.268998\pi$
$523$			782.435i			1.49605i	−0.663670	+	0.748026i	$0.731002\pi$
$524$	−434.382	−	337.180i	−0.828973	−	0.643473i
$525$	671.134	+	387.278i	1.27835	+	0.737672i
$526$	36.1906	−	105.645i	0.0688035	−	0.200846i
$527$	−154.146	+	154.146i	−0.292496	+	0.292496i
$528$	238.634	−	853.173i	0.451958	−	1.61586i
$529$	237.354			0.448685
$530$	226.205	−	110.769i	0.426803	−	0.208998i
$531$	−91.7235	+	342.935i	−0.172737	+	0.645828i
$532$	−322.716	−	250.501i	−0.606609	−	0.470867i
$533$	419.785	+	261.665i	0.787589	+	0.490928i
$534$	150.687	+	172.717i	0.282186	+	0.323441i
$535$	−43.0036	+	43.0036i	−0.0803806	+	0.0803806i
$536$	62.8654	−	302.782i	0.117286	−	0.564891i
$537$	−486.954	+	130.597i	−0.906805	+	0.243197i
$538$	264.324	+	90.5489i	0.491308	+	0.168306i
$539$	−978.602	−	978.602i	−1.81559	−	1.81559i
$540$	−114.640	−	88.8625i	−0.212296	−	0.164560i
$541$	110.852	−	110.852i	0.204903	−	0.204903i	−0.597194	−	0.802097i	$-0.703718\pi$
$541$	110.852	−	110.852i	0.204903	−	0.204903i	0.802097	+	0.597194i	$0.203718\pi$
$542$	−35.6647	+	17.4644i	−0.0658021	+	0.0322221i
$543$	−469.155	+	125.823i	−0.864006	+	0.231718i
$544$	−334.539	−	26.6172i	−0.614961	−	0.0489287i
$545$	241.488			0.443098
$546$	508.456	−	704.124i	0.931238	−	1.28961i
$547$		−	83.0751i		−	0.151874i	−0.997113	−	0.0759370i	$-0.975805\pi$
$547$		−	83.0751i		−	0.151874i	0.997113	−	0.0759370i	$-0.0241948\pi$
$548$	−63.2453	−	502.022i	−0.115411	−	0.916098i
$549$	155.609	−	89.9346i	0.283442	−	0.163815i
$550$	769.000	−	376.566i	1.39818	−	0.684665i
$551$	241.730	+	241.730i	0.438711	+	0.438711i
$552$	−272.742	+	305.941i	−0.494098	+	0.554240i
$553$	−239.623	+	239.623i	−0.433315	+	0.433315i
$554$	−500.447	−	171.437i	−0.903334	−	0.309453i
$555$	−99.1857	+	26.6007i	−0.178713	+	0.0479291i
$556$	111.091	−	143.116i	0.199804	−	0.257404i
$557$	438.392	+	438.392i	0.787060	+	0.787060i	0.981011	−	0.193951i	$-0.0621304\pi$
$557$	438.392	+	438.392i	0.787060	+	0.787060i	−0.193951	+	0.981011i	$0.562130\pi$
$558$	310.612	+	208.597i	0.556652	+	0.373829i
$559$	28.5088	+	122.865i	0.0509997	+	0.219794i
$560$	59.3453	+	231.794i	0.105974	+	0.413919i
$561$	−502.953	−	290.229i	−0.896529	−	0.517342i
$562$	511.210	−	250.330i	0.909626	−	0.445428i
$563$			773.124i			1.37322i	0.727025	+	0.686611i	$0.240902\pi$
$563$			773.124i			1.37322i	−0.727025	+	0.686611i	$0.759098\pi$
$564$	334.747	+	820.549i	0.593523	+	1.45487i
$565$	−118.610	−	118.610i	−0.209929	−	0.209929i
$566$	256.714	−	749.382i	0.453559	−	1.32400i
$567$	−870.977	+	234.219i	−1.53611	+	0.413084i
$568$	136.250	+	28.2890i	0.239876	+	0.0498046i
$569$	−238.618			−0.419364			−0.209682	−	0.977770i	$-0.567243\pi$
$569$	−238.618			−0.419364			−0.209682	+	0.977770i	$0.567243\pi$
$570$	−5.02322	+	73.7417i	−0.00881266	+	0.129371i
$571$	−18.5671			−0.0325168			−0.0162584	−	0.999868i	$-0.505175\pi$
$571$	−18.5671			−0.0325168			−0.0162584	+	0.999868i	$0.505175\pi$
$572$	−332.086	−	900.460i	−0.580571	−	1.57423i
$573$	−69.9309	−	260.751i	−0.122044	−	0.455063i
$574$	−274.617	+	801.642i	−0.478427	+	1.39659i
$575$	−396.137			−0.688934
$576$	65.8732	+	572.221i	0.114363	+	0.993439i
$577$	640.717	+	640.717i	1.11043	+	1.11043i	0.993092	+	0.117336i	$0.0374354\pi$
$577$	640.717	+	640.717i	1.11043	+	1.11043i	0.117336	+	0.993092i	$0.462565\pi$
$578$	116.030	−	338.707i	0.200744	−	0.585999i
$579$	−475.773	−	274.545i	−0.821716	−	0.474171i
$580$	−25.0263	−	198.651i	−0.0431489	−	0.342503i
$581$			1474.12i			2.53722i
$582$	−327.882	−	375.818i	−0.563372	−	0.645735i
$583$	−1223.76	−	1223.76i	−2.09908	−	2.09908i
$584$	7.96820	−	38.3776i	0.0136442	−	0.0657151i
$585$	−157.048	−	5.23931i	−0.268457	−	0.00895609i
$586$	−472.808	+	231.526i	−0.806840	+	0.395095i
$587$	−418.692	−	418.692i	−0.713274	−	0.713274i	0.253945	−	0.967219i	$-0.418272\pi$
$587$	−418.692	−	418.692i	−0.713274	−	0.713274i	−0.967219	+	0.253945i	$0.918272\pi$
$588$	829.459	+	348.787i	1.41064	+	0.593176i
$589$		−	190.660i		−	0.323702i
$590$	−100.229	−	34.3353i	−0.169880	−	0.0581955i
$591$	161.437	+	93.1574i	0.273160	+	0.157627i
$592$	350.865	+	207.826i	0.592678	+	0.351057i
$593$	−213.904	−	213.904i	−0.360715	−	0.360715i	0.503361	−	0.864076i	$-0.332097\pi$
$593$	−213.904	−	213.904i	−0.360715	−	0.360715i	−0.864076	+	0.503361i	$0.832097\pi$
$594$	−322.359	+	943.086i	−0.542692	+	1.58769i
$595$	156.833			0.263584
$596$	418.873	−	52.7701i	0.702807	−	0.0885405i
$597$	132.343	+	493.467i	0.221680	+	0.826578i
$598$	−45.2285	+	441.709i	−0.0756329	+	0.738644i
$599$	−491.097			−0.819862			−0.409931	−	0.912116i	$-0.634447\pi$
$599$	−491.097			−0.819862			−0.409931	+	0.912116i	$0.634447\pi$
$600$	−370.461	+	415.554i	−0.617434	+	0.692590i
$601$	−858.307			−1.42813			−0.714066	−	0.700078i	$-0.753148\pi$
$601$	−858.307			−1.42813			−0.714066	+	0.700078i	$0.753148\pi$
$602$	−194.048	+	95.0220i	−0.322339	+	0.157844i
$603$	−89.8901	+	336.080i	−0.149072	+	0.557347i
$604$	22.8746	+	181.572i	0.0378719	+	0.300615i
$605$	208.592	+	208.592i	0.344780	+	0.344780i
$606$	−77.3807	−	5.27110i	−0.127691	−	0.00869818i
$607$			131.464i			0.216579i	0.994119	+	0.108290i	$0.0345374\pi$
$607$			131.464i			0.216579i	−0.994119	+	0.108290i	$0.965463\pi$
$608$	223.354	−	190.432i	0.367359	−	0.313210i
$609$	−1078.34	−	622.256i	−1.77067	−	1.02177i
$610$	23.5903	+	48.1747i	0.0386726	+	0.0789749i
$611$	814.734	+	507.849i	1.33344	+	0.831177i
$612$	374.058	+	51.1985i	0.611205	+	0.0836576i
$613$	−334.286	−	334.286i	−0.545328	−	0.545328i	0.379758	−	0.925086i	$-0.376007\pi$
$613$	−334.286	−	334.286i	−0.545328	−	0.545328i	−0.925086	+	0.379758i	$0.876007\pi$
$614$	633.308	−	310.120i	1.03145	−	0.505082i
$615$	148.077	−	39.7129i	0.240776	−	0.0645739i
$616$	1374.61	−	901.935i	2.23150	−	1.46418i
$617$	−650.790	+	650.790i	−1.05476	+	1.05476i	−0.0563537	+	0.998411i	$0.517947\pi$
$617$	−650.790	+	650.790i	−1.05476	+	1.05476i	−0.998411	+	0.0563537i	$0.982053\pi$
$618$	−147.211	−	10.0279i	−0.238206	−	0.0162264i
$619$	803.023	+	803.023i	1.29729	+	1.29729i	0.930175	+	0.367116i	$0.119655\pi$
$619$	803.023	+	803.023i	1.29729	+	1.29729i	0.367116	+	0.930175i	$0.380345\pi$
$620$	−68.4720	+	88.2111i	−0.110439	+	0.142276i
$621$	325.824	−	326.264i	0.524676	−	0.525386i
$622$	274.363	+	93.9879i	0.441098	+	0.151106i
$623$			425.371i			0.682779i
$624$	421.063	+	460.524i	0.674780	+	0.738019i
$625$	−492.973			−0.788757
$626$	−154.559	+	451.177i	−0.246899	+	0.720731i
$627$	490.537	−	131.557i	0.782356	−	0.209820i
$628$	−121.338	−	94.1863i	−0.193214	−	0.149978i
$629$	189.006	−	189.006i	0.300486	−	0.300486i
$630$	−51.8967	−	264.130i	−0.0823757	−	0.419253i
$631$	336.411	+	336.411i	0.533140	+	0.533140i	0.921505	−	0.388366i	$-0.126960\pi$
$631$	336.411	+	336.411i	0.533140	+	0.533140i	−0.388366	+	0.921505i	$0.626960\pi$
$632$	−133.568	−	203.565i	−0.211341	−	0.322097i
$633$	649.545	−	174.202i	1.02614	−	0.275200i
$634$	−389.506	−	795.426i	−0.614363	−	1.25461i
$635$	−190.592	+	190.592i	−0.300145	+	0.300145i
$636$	1037.26	+	436.166i	1.63091	+	0.685796i
$637$	949.565	−	220.332i	1.49068	−	0.345890i
$638$	−1235.59	+	605.045i	−1.93665	+	0.948346i
$639$	−151.234	−	40.4500i	−0.236673	−	0.0633020i
$640$	−171.727	+	7.89198i	−0.268323	+	0.0123312i
$641$	−135.932			−0.212063			−0.106032	−	0.994363i	$-0.533814\pi$
$641$	−135.932			−0.212063			−0.106032	+	0.994363i	$0.533814\pi$
$642$	−271.069	−	18.4649i	−0.422225	−	0.0287616i
$643$	304.119	−	304.119i	0.472970	−	0.472970i	−0.429905	−	0.902874i	$-0.641453\pi$
$643$	304.119	−	304.119i	0.472970	−	0.472970i	0.902874	+	0.429905i	$0.141453\pi$
$644$	−754.660	+	95.0729i	−1.17183	+	0.147629i
$645$	33.8584	+	19.5380i	0.0524936	+	0.0302914i
$646$	−84.6092	−	172.784i	−0.130974	−	0.267467i
$647$		−	407.010i		−	0.629073i	−0.949245	−	0.314537i	$-0.898151\pi$
$647$		−	407.010i		−	0.629073i	0.949245	−	0.314537i	$-0.101849\pi$
$648$	−37.5517	−	646.911i	−0.0579502	−	0.998319i
$649$			727.989i			1.12171i
$650$	−61.4330	+	599.966i	−0.0945124	+	0.923024i
$651$	179.864	+	670.658i	0.276289	+	1.03020i
$652$	−3.75565	−	29.8112i	−0.00576020	−	0.0457227i
$653$		−	88.1990i		−	0.135067i	−0.997717	−	0.0675337i	$-0.978487\pi$
$653$		−	88.1990i		−	0.135067i	0.997717	−	0.0675337i	$-0.0215130\pi$
$654$	709.253	+	812.943i	1.08448	+	1.24303i
$655$	−130.553	+	130.553i	−0.199318	+	0.199318i
$656$	−523.817	−	310.269i	−0.798501	−	0.472972i
$657$	−11.3936	+	42.5982i	−0.0173418	+	0.0648375i
$658$	−532.987	+	1555.86i	−0.810010	+	2.36452i
$659$	243.877			0.370071			0.185036	−	0.982732i	$-0.440760\pi$
$659$	243.877			0.370071			0.185036	+	0.982732i	$0.440760\pi$
$660$	−274.199	−	115.300i	−0.415452	−	0.174698i
$661$	482.331	−	482.331i	0.729699	−	0.729699i	−0.240861	−	0.970560i	$-0.577430\pi$
$661$	482.331	−	482.331i	0.729699	−	0.729699i	0.970560	+	0.240861i	$0.0774298\pi$
$662$	−224.599	−	458.663i	−0.339274	−	0.692844i
$663$	360.876	−	192.498i	0.544308	−	0.290344i
$664$	−1036.99	−	215.307i	−1.56174	−	0.324258i
$665$	−96.9919	+	96.9919i	−0.145852	+	0.145852i
$666$	−380.857	−	255.771i	−0.571857	−	0.384041i
$667$	636.491			0.954259
$668$	110.700	−	13.9462i	0.165719	−	0.0208775i
$669$	−652.907	−	376.760i	−0.975945	−	0.563169i
$670$	−98.2258	−	33.6490i	−0.146606	−	0.0502224i
$671$	260.623	−	260.623i	0.388410	−	0.388410i
$672$	−606.012	+	880.560i	−0.901803	+	1.31036i
$673$			885.893i			1.31633i	0.752872	+	0.658167i	$0.228668\pi$
$673$			885.893i			1.31633i	−0.752872	+	0.658167i	$0.771332\pi$
$674$	39.6134	+	13.5703i	0.0587737	+	0.0201340i
$675$	442.561	−	443.159i	0.655646	−	0.656533i
$676$	661.972	+	137.001i	0.979248	+	0.202664i
$677$		−	948.372i		−	1.40085i	−0.713728	−	0.700423i	$-0.752995\pi$
$677$		−	948.372i		−	1.40085i	0.713728	−	0.700423i	$-0.247005\pi$
$678$	50.9289	−	747.645i	0.0751164	−	1.10272i
$679$		−	925.571i		−	1.36314i
$680$	−22.9066	+	110.326i	−0.0336862	+	0.162244i
$681$	64.1418	−	111.155i	0.0941876	−	0.163223i
$682$	725.883	+	248.664i	1.06434	+	0.364610i
$683$	−495.730	+	495.730i	−0.725813	+	0.725813i	−0.969783	−	0.243970i	$-0.921550\pi$
$683$	−495.730	+	495.730i	−0.725813	+	0.725813i	0.243970	+	0.969783i	$0.421550\pi$
$684$	−262.996	+	199.670i	−0.384498	+	0.291915i
$685$	−169.890			−0.248015
$686$	254.484	+	519.691i	0.370968	+	0.757568i
$687$	1009.91	+	582.771i	1.47004	+	0.848284i
$688$	−38.5024	−	150.385i	−0.0559628	−	0.218583i
$689$	1187.45	−	275.530i	1.72344	−	0.399898i
$690$	90.4703	+	103.697i	0.131116	+	0.150285i
$691$	842.804	−	842.804i	1.21969	−	1.21969i	0.251946	−	0.967741i	$-0.418929\pi$
$691$	842.804	−	842.804i	1.21969	−	1.21969i	0.967741	−	0.251946i	$-0.0810706\pi$
$692$	479.715	+	372.368i	0.693229	+	0.538104i
$693$	−1601.38	+	925.521i	−2.31080	+	1.33553i
$694$	−197.319	+	575.999i	−0.284321	+	0.829970i
$695$	−43.0135	−	43.0135i	−0.0618899	−	0.0618899i
$696$	595.235	−	667.689i	0.855223	−	0.959323i
$697$	−282.172	+	282.172i	−0.404838	+	0.404838i
$698$	−339.783	−	693.883i	−0.486794	−	0.994102i
$699$	−137.164	−	511.441i	−0.196229	−	0.731676i
$700$	−1025.04	+	129.136i	−1.46435	+	0.184480i
$701$	−435.243			−0.620889			−0.310444	−	0.950592i	$-0.600478\pi$
$701$	−435.243			−0.620889			−0.310444	+	0.950592i	$0.600478\pi$
$702$	−443.612	−	544.070i	−0.631926	−	0.775029i
$703$			233.778i			0.332544i
$704$	433.708	+	1098.72i	0.616063	+	1.56068i
$705$	287.394	−	77.0763i	0.407651	−	0.109328i
$706$	109.627	+	223.874i	0.155279	+	0.317101i
$707$	−101.778	−	101.778i	−0.143958	−	0.143958i
$708$	−178.788	−	438.253i	−0.252525	−	0.619002i
$709$	688.110	−	688.110i	0.970537	−	0.970537i	−0.0290416	−	0.999578i	$-0.509246\pi$
$709$	688.110	−	688.110i	0.970537	−	0.970537i	0.999578	+	0.0290416i	$0.00924553\pi$
$710$	15.1418	−	44.2010i	0.0213265	−	0.0622549i
$711$	137.060	+	237.149i	0.192771	+	0.333543i
$712$	−299.234	−	62.1288i	−0.420272	−	0.0872595i
$713$	−251.011	−	251.011i	−0.352049	−	0.352049i
$714$	460.618	+	527.959i	0.645123	+	0.739438i
$715$	−313.903	+	72.8363i	−0.439025	+	0.101869i
$716$	412.188	−	531.014i	0.575682	−	0.741640i
$717$	174.420	−	302.262i	0.243264	−	0.421564i
$718$	116.277	+	237.453i	0.161945	+	0.330715i
$719$		−	576.024i		−	0.801146i	−0.916265	−	0.400573i	$-0.868811\pi$
$719$		−	576.024i		−	0.801146i	0.916265	−	0.400573i	$-0.131189\pi$
$720$	193.386	+	2.07066i	0.268591	+	0.00287592i
$721$	−193.626	−	193.626i	−0.268552	−	0.268552i
$722$	−523.851	−	179.454i	−0.725555	−	0.248552i
$723$	−237.714	−	137.173i	−0.328788	−	0.189727i
$724$	397.122	−	511.605i	0.548511	−	0.706636i
$725$	864.535			1.19246
$726$	−89.5653	+	1314.84i	−0.123368	+	1.81107i
$727$	−516.927			−0.711041			−0.355520	−	0.934669i	$-0.615696\pi$
$727$	−516.927			−0.711041			−0.355520	+	0.934669i	$0.615696\pi$
$728$	26.9590	+	1157.71i	0.0370316	+	1.59026i
$729$	0.985176	+	728.999i	0.00135141	+	0.999999i
$730$	−12.4501	−	4.26502i	−0.0170550	−	0.00584249i
$731$	−101.751			−0.139194
$732$	−92.8897	+	220.903i	−0.126899	+	0.301780i
$733$	623.462	+	623.462i	0.850563	+	0.850563i	0.990202	−	0.139640i	$-0.0445944\pi$
$733$	623.462	+	623.462i	0.850563	+	0.850563i	−0.139640	+	0.990202i	$0.544594\pi$
$734$	943.025	+	323.050i	1.28477	+	0.440123i
$735$	151.000	−	261.676i	0.205442	−	0.356022i
$736$	43.3435	−	544.763i	0.0588906	−	0.740167i
$737$			713.438i			0.968030i
$738$	568.593	+	381.848i	0.770451	+	0.517409i
$739$	88.1069	+	88.1069i	0.119224	+	0.119224i	0.764202	−	0.644977i	$-0.223133\pi$
$739$	88.1069	+	88.1069i	0.119224	+	0.119224i	−0.644977	+	0.764202i	$0.723133\pi$
$740$	83.9570	−	108.160i	0.113455	−	0.146162i
$741$	−104.132	+	342.230i	−0.140529	+	0.461849i
$742$	918.361	+	1875.42i	1.23768	+	2.52752i
$743$	720.000	+	720.000i	0.969044	+	0.969044i	0.999535	−	0.0304906i	$-0.00970696\pi$
$743$	720.000	+	720.000i	0.969044	+	0.969044i	−0.0304906	+	0.999535i	$0.509707\pi$
$744$	−498.055	+	28.5733i	−0.669429	+	0.0384050i
$745$		−	141.752i		−	0.190271i
$746$	373.714	−	1090.92i	0.500957	−	1.46236i
$747$	1151.04	+	307.864i	1.54088	+	0.412134i
$748$	768.174	−	96.7754i	1.02697	−	0.129379i
$749$	−356.534	−	356.534i	−0.476013	−	0.476013i
$750$	255.324	+	292.652i	0.340432	+	0.390202i
$751$	−863.481			−1.14977			−0.574887	−	0.818233i	$-0.694954\pi$
$751$	−863.481			−1.14977			−0.574887	+	0.818233i	$0.694954\pi$
$752$	−1016.64	−	602.182i	−1.35192	−	0.800774i
$753$	541.176	−	145.138i	0.718693	−	0.192747i
$754$	98.7071	−	963.991i	0.130911	−	1.27850i
$755$	61.4461			0.0813856
$756$	736.741	−	950.454i	0.974525	−	1.25721i
$757$	−1066.15			−1.40839			−0.704195	−	0.710006i	$-0.748692\pi$
$757$	−1066.15			−1.40839			−0.704195	+	0.710006i	$0.748692\pi$
$758$	−209.160	−	427.134i	−0.275937	−	0.563502i
$759$	472.609	−	819.008i	0.622673	−	1.07906i
$760$	−54.0639	−	82.3968i	−0.0711368	−	0.108417i
$761$	913.582	+	913.582i	1.20050	+	1.20050i	0.974014	+	0.226489i	$0.0727247\pi$
$761$	913.582	+	913.582i	1.20050	+	1.20050i	0.226489	+	0.974014i	$0.427275\pi$
$762$	−1201.37	−	81.8365i	−1.57661	−	0.107397i
$763$			2002.13i			2.62402i
$764$	284.344	+	220.716i	0.372178	+	0.288895i
$765$	32.7538	−	122.459i	0.0428154	−	0.160078i
$766$	−506.225	+	247.889i	−0.660868	+	0.323615i
$767$	−435.148	−	271.241i	−0.567337	−	0.353639i
$768$	−530.930	−	554.921i	−0.691316	−	0.722553i
$769$	638.154	+	638.154i	0.829849	+	0.829849i	0.987496	−	0.157646i	$-0.0503905\pi$
$769$	638.154	+	638.154i	0.829849	+	0.829849i	−0.157646	+	0.987496i	$0.550391\pi$
$770$	−242.769	−	495.768i	−0.315284	−	0.643854i
$771$	−342.157	−	1275.80i	−0.443783	−	1.65473i
$772$	726.662	−	91.5457i	0.941272	−	0.118583i
$773$	−92.5067	+	92.5067i	−0.119672	+	0.119672i	−0.764407	−	0.644734i	$-0.776968\pi$
$773$	−92.5067	+	92.5067i	−0.119672	+	0.119672i	0.644734	+	0.764407i	$0.276968\pi$
$774$	33.6698	+	171.363i	0.0435011	+	0.221400i
$775$	−340.944	−	340.944i	−0.439927	−	0.439927i
$776$	651.106	+	135.187i	0.839054	+	0.174210i
$777$	−220.541	−	822.328i	−0.283836	−	1.05834i
$778$	52.6091	−	153.573i	0.0676209	−	0.197394i
$779$		−	349.014i		−	0.448029i
$780$	171.083	−	120.940i	0.219337	−	0.155051i
$781$	−321.042			−0.411066
$782$	−338.867	−	116.085i	−0.433334	−	0.148446i
$783$	−711.082	+	712.043i	−0.908150	+	0.909378i
$784$	−1162.26	+	297.568i	−1.48247	+	0.379551i
$785$	−36.4681	+	36.4681i	−0.0464562	+	0.0464562i
$786$	−822.926	−	56.0570i	−1.04698	−	0.0713193i
$787$	−226.028	−	226.028i	−0.287202	−	0.287202i	0.548771	−	0.835973i	$-0.315096\pi$
$787$	−226.028	−	226.028i	−0.287202	−	0.287202i	−0.835973	+	0.548771i	$0.815096\pi$
$788$	−246.568	+	31.0629i	−0.312903	+	0.0394199i
$789$	−43.3907	−	161.791i	−0.0549946	−	0.205058i
$790$	−73.4182	+	35.9516i	−0.0929344	+	0.0455084i
$791$	983.371	−	983.371i	1.24320	−	1.24320i
$792$	−417.177	−	1261.70i	−0.526739	−	1.59305i
$793$	58.6793	+	252.890i	0.0739966	+	0.318903i
$794$	312.786	+	638.753i	0.393937	+	0.804475i
$795$	188.829	−	327.232i	0.237521	−	0.411612i
$796$	−538.116	−	417.701i	−0.676025	−	0.524750i
$797$	834.278			1.04677			0.523387	−	0.852095i	$-0.324668\pi$
$797$	834.278			1.04677			0.523387	+	0.852095i	$0.324668\pi$
$798$	−611.378	−	41.6465i	−0.766137	−	0.0521885i
$799$	−547.650	+	547.650i	−0.685420	+	0.685420i
$800$	58.8727	−	739.942i	0.0735909	−	0.924927i
$801$	332.142	+	88.8369i	0.414659	+	0.110907i
$802$	−1065.03	+	521.525i	−1.32796	+	0.650280i
$803$			90.4284i			0.112613i
$804$	−175.214	−	429.493i	−0.217928	−	0.534196i
$805$			255.386i			0.317250i
$806$	−419.093	+	341.239i	−0.519966	+	0.423374i
$807$	404.800	−	108.563i	0.501611	−	0.134527i
$808$	86.4628	−	56.7318i	0.107008	−	0.0702127i
$809$		−	775.968i		−	0.959169i	−0.877496	−	0.479585i	$-0.840787\pi$
$809$		−	775.968i		−	0.959169i	0.877496	−	0.479585i	$-0.159213\pi$
$810$	−217.078	−	14.6398i	−0.267998	−	0.0180738i
$811$	627.437	−	627.437i	0.773658	−	0.773658i	−0.205086	−	0.978744i	$-0.565747\pi$
$811$	627.437	−	627.437i	0.773658	−	0.773658i	0.978744	+	0.205086i	$0.0657474\pi$
$812$	1646.98	−	207.488i	2.02830	−	0.255527i
$813$	−29.7718	+	51.5931i	−0.0366197	+	0.0634601i
$814$	−890.042	−	304.900i	−1.09342	−	0.374570i
$815$	−10.0885			−0.0123785
$816$	−438.677	+	246.916i	−0.537595	+	0.302593i
$817$	62.9269	−	62.9269i	0.0770219	−	0.0770219i
$818$	−1204.25	+	589.701i	−1.47219	+	0.720906i
$819$	43.4380	−	1302.05i	0.0530379	−	1.58980i
$820$	−125.342	+	161.475i	−0.152856	+	0.196921i
$821$	−845.820	+	845.820i	−1.03023	+	1.03023i	−0.0307022	+	0.999529i	$0.509774\pi$
$821$	−845.820	+	845.820i	−1.03023	+	1.03023i	−0.999529	+	0.0307022i	$0.990226\pi$
$822$	−498.969	−	571.916i	−0.607018	−	0.695762i
$823$	632.140			0.768092			0.384046	−	0.923314i	$-0.374530\pi$
$823$	632.140			0.768092			0.384046	+	0.923314i	$0.374530\pi$
$824$	164.489	−	107.928i	0.199623	−	0.130981i
$825$	641.937	−	1112.45i	0.778105	−	1.34842i
$826$	284.667	−	830.980i	0.344633	−	1.00603i
$827$	533.580	−	533.580i	0.645200	−	0.645200i	−0.306629	−	0.951829i	$-0.599201\pi$
$827$	533.580	−	533.580i	0.645200	−	0.645200i	0.951829	+	0.306629i	$0.0992012\pi$
$828$	−83.3716	+	609.116i	−0.100690	+	0.735647i
$829$		−	34.0426i		−	0.0410646i	−0.999789	−	0.0205323i	$-0.993464\pi$
$829$		−	34.0426i		−	0.0410646i	0.999789	−	0.0205323i	$-0.00653610\pi$
$830$	−115.244	+	336.413i	−0.138848	+	0.405316i
$831$	−766.411	+	205.544i	−0.922276	+	0.247346i
$832$	−818.343	−	150.127i	−0.983586	−	0.180442i
$833$			786.385i			0.944040i
$834$	18.4692	−	271.131i	0.0221453	−	0.325097i
$835$		−	37.4624i		−	0.0448651i
$836$	−415.221	+	534.921i	−0.496676	+	0.639858i
$837$	561.233	−	0.379228i	0.670529	−	0.000453079i
$838$	478.671	−	1397.30i	0.571206	−	1.66742i
$839$	63.4338	−	63.4338i	0.0756064	−	0.0756064i	−0.668292	−	0.743899i	$-0.732974\pi$
$839$	63.4338	−	63.4338i	0.0756064	−	0.0756064i	0.743899	+	0.668292i	$0.232974\pi$
$840$	267.904	+	238.833i	0.318933	+	0.284325i
$841$	−548.085			−0.651706
$842$	−47.9211	+	23.4661i	−0.0569134	+	0.0278695i
$843$	426.741	−	739.522i	0.506217	−	0.877251i
$844$	−549.815	+	708.316i	−0.651440	+	0.839237i
$845$	73.4197	−	214.770i	0.0868872	−	0.254166i
$846$	1103.55	+	741.105i	1.30443	+	0.876011i
$847$	−1729.39	+	1729.39i	−2.04178	+	2.04178i
$848$	−1453.43	+	372.115i	−1.71395	+	0.438815i
$849$	−307.787	−	1147.64i	−0.362529	−	1.35176i
$850$	−460.277	−	157.676i	−0.541502	−	0.185501i
$851$	307.777	+	307.777i	0.361665	+	0.361665i
$852$	193.269	−	78.8452i	0.226842	−	0.0925413i
$853$	−529.185	+	529.185i	−0.620381	+	0.620381i	−0.945629	−	0.325248i	$-0.894552\pi$
$853$	−529.185	+	529.185i	−0.620381	+	0.620381i	0.325248	+	0.945629i	$0.394552\pi$
$854$	−399.406	+	195.582i	−0.467689	+	0.229019i
$855$	55.4777	+	95.9904i	0.0648862	+	0.112269i
$856$	302.884	−	198.735i	0.353836	−	0.232167i
$857$	941.964			1.09914			0.549571	−	0.835447i	$-0.314791\pi$
$857$	941.964			1.09914			0.549571	+	0.835447i	$0.314791\pi$
$858$	−1167.13	−	842.797i	−1.36029	−	0.982281i
$859$		−	51.4741i		−	0.0599233i	−0.999551	−	0.0299617i	$-0.990461\pi$
$859$		−	51.4741i		−	0.0599233i	0.999551	−	0.0299617i	$-0.00953852\pi$
$860$	−51.7128	+	6.51484i	−0.0601312	+	0.00757540i
$861$	329.252	+	1227.68i	0.382406	+	1.42587i
$862$	1037.46	−	508.026i	1.20355	−	0.589357i
$863$	182.144	+	182.144i	0.211059	+	0.211059i	0.804717	−	0.593658i	$-0.202317\pi$
$863$	182.144	+	182.144i	0.211059	+	0.211059i	−0.593658	+	0.804717i	$0.702317\pi$
$864$	561.004	+	657.092i	0.649310	+	0.760524i
$865$	144.178	−	144.178i	0.166679	−	0.166679i
$866$	920.892	+	315.468i	1.06339	+	0.364282i
$867$	−139.114	−	518.715i	−0.160455	−	0.598287i
$868$	−731.340	−	567.687i	−0.842558	−	0.654017i
$869$	397.190	+	397.190i	0.457065	+	0.457065i
$870$	−197.443	−	226.309i	−0.226946	−	0.260125i
$871$	−426.450	−	265.819i	−0.489610	−	0.305189i
$872$	−1408.43	−	292.427i	−1.61517	−	0.335352i
$873$	−722.712	−	193.301i	−0.827849	−	0.221422i
$874$	281.361	−	137.778i	0.321924	−	0.157640i
$875$			720.747i			0.823711i
$876$	−22.2084	−	54.4384i	−0.0253521	−	0.0621442i
$877$	−646.826	−	646.826i	−0.737544	−	0.737544i	0.234558	−	0.972102i	$-0.424636\pi$
$877$	−646.826	−	646.826i	−0.737544	−	0.737544i	−0.972102	+	0.234558i	$0.924636\pi$
$878$	181.136	−	528.759i	0.206305	−	0.602231i
$879$	−394.685	+	683.970i	−0.449016	+	0.778123i
$880$	384.213	−	98.3685i	0.436606	−	0.111782i
$881$	82.3758			0.0935026			0.0467513	−	0.998907i	$-0.485113\pi$
$881$	82.3758			0.0935026			0.0467513	+	0.998907i	$0.485113\pi$
$882$	1324.39	−	260.219i	1.50158	−	0.295033i
$883$	−128.459			−0.145481			−0.0727403	−	0.997351i	$-0.523174\pi$
$883$	−128.459			−0.145481			−0.0727403	+	0.997351i	$0.523174\pi$
$884$	−228.367	+	495.225i	−0.258334	+	0.560209i
$885$	−153.496	+	41.1663i	−0.173442	+	0.0465156i
$886$	−445.699	+	1301.05i	−0.503046	+	1.46846i
$887$	1047.33			1.18076			0.590380	−	0.807126i	$-0.298978\pi$
$887$	1047.33			1.18076			0.590380	+	0.807126i	$0.298978\pi$
$888$	610.691	−	35.0352i	0.687715	−	0.0394540i
$889$	−1580.16	−	1580.16i	−1.77745	−	1.77745i
$890$	−33.2548	+	97.0749i	−0.0373649	+	0.109073i
$891$	388.232	+	1443.70i	0.435726	+	1.62031i
$892$	997.203	−	125.629i	1.11794	−	0.140840i
$893$		−	677.380i		−	0.758545i
$894$	477.191	−	416.326i	0.533771	−	0.465689i
$895$	−159.596	−	159.596i	−0.178319	−	0.178319i
$896$	−65.4308	−	1423.75i	−0.0730255	−	1.58901i
$897$	313.464	+	587.650i	0.349459	+	0.655129i
$898$	844.445	−	413.510i	0.940361	−	0.460478i
$899$	547.809	+	547.809i	0.609354	+	0.609354i
$900$	−113.242	+	827.351i	−0.125825	+	0.919279i
$901$			983.392i			1.09144i
$902$	1328.77	+	455.194i	1.47314	+	0.504650i
$903$	−161.985	+	280.713i	−0.179386	+	0.310867i
$904$	548.138	+	835.396i	0.606347	+	0.924111i
$905$	−153.762	−	153.762i	−0.169903	−	0.169903i
$906$	180.467	+	206.851i	0.199191	+	0.228313i
$907$	1213.59			1.33803			0.669014	−	0.743250i	$-0.266717\pi$
$907$	1213.59			1.33803			0.669014	+	0.743250i	$0.266717\pi$
$908$	21.3878	+	169.770i	0.0235548	+	0.186971i
$909$	−100.727	+	58.2154i	−0.110811	+	0.0640433i
$910$	386.793	+	39.6053i	0.425047	+	0.0435223i
$911$	−1249.62			−1.37170			−0.685849	−	0.727744i	$-0.740569\pi$
$911$	−1249.62			−1.37170			−0.685849	+	0.727744i	$0.740569\pi$
$912$	118.593	−	424.000i	0.130036	−	0.464912i
$913$	2443.45			2.67628
$914$	−1216.11	+	595.507i	−1.33053	+	0.651540i
$915$	69.6901	+	40.2147i	0.0761640	+	0.0439504i
$916$	−1542.47	+	194.322i	−1.68392	+	0.212142i
$917$	−1082.39	−	1082.39i	−1.18036	−	1.18036i
$918$	508.443	−	249.402i	0.553860	−	0.271680i
$919$		−	1693.18i		−	1.84241i	−0.389076	−	0.921205i	$-0.627206\pi$
$919$		−	1693.18i		−	1.84241i	0.389076	−	0.921205i	$-0.372794\pi$
$920$	−179.655	−	37.3011i	−0.195277	−	0.0405447i
$921$	528.665	−	916.152i	0.574012	−	0.994736i
$922$	276.339	+	564.322i	0.299717	+	0.612063i
$923$	119.617	−	191.900i	0.129596	−	0.207909i
$924$	955.932	−	2273.32i	1.03456	−	2.46031i
$925$	418.048	+	418.048i	0.451944	+	0.451944i
$926$	−810.283	+	396.781i	−0.875036	+	0.428490i
$927$	−191.626	+	110.751i	−0.206717	+	0.119472i
$928$	−94.5933	+	1188.90i	−0.101932	+	1.28114i
$929$	−871.599	+	871.599i	−0.938212	+	0.938212i	−0.998199	−	0.0599867i	$-0.980894\pi$
$929$	−871.599	+	871.599i	−0.938212	+	0.938212i	0.0599867	+	0.998199i	$0.480894\pi$
$930$	−11.3836	+	167.114i	−0.0122405	+	0.179692i
$931$	−486.334	−	486.334i	−0.522378	−	0.522378i
$932$	557.717	+	432.916i	0.598409	+	0.464502i
$933$	420.174	−	112.687i	0.450347	−	0.120779i
$934$	−230.365	−	78.9155i	−0.246643	−	0.0844920i
$935$		−	259.959i		−	0.278031i
$936$	909.601	+	220.731i	0.971796	+	0.235824i
$937$	565.122			0.603119			0.301559	−	0.953447i	$-0.402493\pi$
$937$	565.122			0.603119			0.301559	+	0.953447i	$0.402493\pi$
$938$	278.977	−	814.370i	0.297417	−	0.868198i
$939$	185.308	+	690.957i	0.197346	+	0.735844i
$940$	−243.268	+	313.397i	−0.258796	+	0.333402i
$941$	−1134.28	+	1134.28i	−1.20540	+	1.20540i	−0.232893	+	0.972502i	$0.574819\pi$
$941$	−1134.28	+	1134.28i	−1.20540	+	1.20540i	−0.972502	+	0.232893i	$0.925181\pi$
$942$	−229.873	−	15.6587i	−0.244026	−	0.0166228i
$943$	−459.489	−	459.489i	−0.487263	−	0.487263i
$944$	542.987	+	321.624i	0.575198	+	0.340704i
$945$	−285.701	−	285.315i	−0.302329	−	0.301921i
$946$	157.505	+	321.647i	0.166496	+	0.340007i
$947$	−456.667	+	456.667i	−0.482225	+	0.482225i	−0.905842	−	0.423617i	$-0.860760\pi$
$947$	−456.667	+	456.667i	−0.482225	+	0.482225i	0.423617	+	0.905842i	$0.360760\pi$
$948$	−336.657	−	141.564i	−0.355123	−	0.149329i
$949$	−54.0526	−	33.6927i	−0.0569574	−	0.0355033i
$950$	382.168	−	187.141i	0.402283	−	0.196991i
$951$	−1150.67	−	663.996i	−1.20996	−	0.698208i
$952$	−914.691	−	189.914i	−0.960810	−	0.199489i
$953$	883.026			0.926575			0.463288	−	0.886208i	$-0.346670\pi$
$953$	883.026			0.926575			0.463288	+	0.886208i	$0.346670\pi$
$954$	1656.18	−	325.409i	1.73604	−	0.341100i
$955$	85.4592	−	85.4592i	0.0894861	−	0.0894861i
$956$	58.1595	+	461.652i	0.0608363	+	0.482900i
$957$	−1031.43	+	1787.41i	−1.07777	+	1.86773i
$958$	−327.014	−	667.808i	−0.341351	−	0.697086i
$959$		−	1408.53i		−	1.46874i
$960$	−207.140	+	153.578i	−0.215771	+	0.159977i
$961$			528.925i			0.550390i
$962$	513.871	−	418.411i	0.534169	−	0.434938i
$963$	−352.853	+	203.932i	−0.366410	+	0.211767i
$964$	363.067	−	45.7396i	0.376625	−	0.0474477i
$965$		−	245.911i		−	0.254830i
$966$	−859.728	+	750.070i	−0.889988	+	0.776470i
$967$	−556.304	+	556.304i	−0.575289	+	0.575289i	−0.933602	−	0.358313i	$-0.883352\pi$
$967$	−556.304	+	556.304i	−0.575289	+	0.575289i	0.358313	+	0.933602i	$0.383352\pi$
$968$	−963.975	−	1469.16i	−0.995841	−	1.51772i
$969$	−249.951	−	144.234i	−0.257948	−	0.148849i
$970$	72.3594	−	211.226i	0.0745973	−	0.217759i
$971$	−1135.92			−1.16985			−0.584924	−	0.811088i	$-0.698876\pi$
$971$	−1135.92			−1.16985			−0.584924	+	0.811088i	$0.698876\pi$
$972$	−588.277	−	773.766i	−0.605223	−	0.796056i
$973$	356.616	−	356.616i	0.366511	−	0.366511i
$974$	−277.159	−	565.997i	−0.284557	−	0.581106i
$975$	425.773	+	798.196i	0.436691	+	0.818662i
$976$	−79.2488	−	309.534i	−0.0811976	−	0.317146i
$977$	−302.818	+	302.818i	−0.309947	+	0.309947i	−0.844889	−	0.534942i	$-0.820333\pi$
$977$	−302.818	+	302.818i	−0.309947	+	0.309947i	0.534942	+	0.844889i	$0.320333\pi$
$978$	−29.6299	−	33.9617i	−0.0302964	−	0.0347257i
$979$	705.079			0.720203
$980$	50.3503	+	399.665i	0.0513778	+	0.407822i
$981$	1563.32	+	418.136i	1.59360	+	0.426234i
$982$	−1840.28	−	630.421i	−1.87401	−	0.641977i
$983$	859.837	−	859.837i	0.874707	−	0.874707i	−0.118274	−	0.992981i	$-0.537736\pi$
$983$	859.837	−	859.837i	0.874707	−	0.874707i	0.992981	+	0.118274i	$0.0377362\pi$
$984$	−911.718	+	52.3051i	−0.926542	+	0.0531555i
$985$			83.4416i			0.0847123i
$986$	739.547	+	253.345i	0.750048	+	0.256942i
$987$	639.024	+	2382.72i	0.647441	+	2.41411i
$988$	−165.036	−	447.500i	−0.167041	−	0.452935i
$989$		−	165.691i		−	0.167534i
$990$	−437.811	+	86.0219i	−0.442233	+	0.0868908i
$991$			29.9709i			0.0302431i	0.999886	+	0.0151216i	$0.00481352\pi$
$991$			29.9709i			0.0302431i	−0.999886	+	0.0151216i	$0.995186\pi$
$992$	506.166	−	431.557i	0.510248	−	0.435037i
$993$	−663.507	−	382.877i	−0.668185	−	0.385576i
$994$	366.461	+	125.538i	0.368673	+	0.126296i
$995$	−161.730	+	161.730i	−0.162543	+	0.162543i
$996$	−1470.97	+	600.089i	−1.47687	+	0.602499i
$997$	−558.581			−0.560262			−0.280131	−	0.959962i	$-0.590378\pi$
$997$	−558.581			−0.560262			−0.280131	+	0.959962i	$0.590378\pi$
$998$	554.647	+	1132.67i	0.555758	+	1.13494i
$999$	−688.156	+	0.464990i	−0.688845	+	0.000465456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.3.l.c.47.20	yes	96
3.2	odd	2	inner	156.3.l.c.47.29	yes	96
4.3	odd	2	inner	156.3.l.c.47.5	✓	96
12.11	even	2	inner	156.3.l.c.47.44	yes	96
13.5	odd	4	inner	156.3.l.c.83.44	yes	96
39.5	even	4	inner	156.3.l.c.83.5	yes	96
52.31	even	4	inner	156.3.l.c.83.29	yes	96
156.83	odd	4	inner	156.3.l.c.83.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.5	✓	96	4.3	odd	2	inner
156.3.l.c.47.20	yes	96	1.1	even	1	trivial
156.3.l.c.47.29	yes	96	3.2	odd	2	inner
156.3.l.c.47.44	yes	96	12.11	even	2	inner
156.3.l.c.83.5	yes	96	39.5	even	4	inner
156.3.l.c.83.20	yes	96	156.83	odd	4	inner
156.3.l.c.83.29	yes	96	52.31	even	4	inner
156.3.l.c.83.44	yes	96	13.5	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	156.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.648159 + 1.89206i) q^{2} +(0.777110 + 2.89760i) q^{3} +(-3.15978 - 2.45271i) q^{4} +(-0.949668 + 0.949668i) q^{5} +(-5.98613 - 0.407769i) q^{6} +(-7.87350 - 7.87350i) q^{7} +(6.68872 - 4.38874i) q^{8} +(-7.79220 + 4.50351i) q^{9} +(-1.18129 - 2.41236i) q^{10} +(-13.0508 + 13.0508i) q^{11} +(4.65149 - 11.0618i) q^{12} +(-2.93839 - 12.6636i) q^{13} +(20.0004 - 9.79385i) q^{14} +(-3.48976 - 2.01376i) q^{15} +(3.96841 + 15.5001i) q^{16} +10.4874 q^{17} +(-3.47032 - 17.6623i) q^{18} +(-6.48583 + 6.48583i) q^{19} +(5.33000 - 0.671480i) q^{20} +(16.6957 - 28.9329i) q^{21} +(-16.2339 - 33.1519i) q^{22} +17.0776i q^{23} +(17.9147 + 15.9707i) q^{24} +23.1963i q^{25} +(25.8648 + 2.64840i) q^{26} +(-19.1048 - 19.0790i) q^{27} +(5.56710 + 44.1900i) q^{28} -37.2704i q^{29} +(6.07208 - 5.29759i) q^{30} +(-14.6982 + 14.6982i) q^{31} +(-31.8992 - 2.53803i) q^{32} +(-47.9580 - 27.6741i) q^{33} +(-6.79748 + 19.8427i) q^{34} +14.9544 q^{35} +(35.6674 + 4.88192i) q^{36} +(18.0222 - 18.0222i) q^{37} +(-8.06773 - 16.4754i) q^{38} +(34.4105 - 18.3553i) q^{39} +(-2.18421 + 10.5199i) q^{40} +(-26.9059 + 26.9059i) q^{41} +(43.9212 + 50.3424i) q^{42} -9.70221 q^{43} +(73.2475 - 9.22781i) q^{44} +(3.12316 - 11.6768i) q^{45} +(-32.3119 - 11.0690i) q^{46} +(-52.2200 + 52.2200i) q^{47} +(-41.8291 + 23.5441i) q^{48} +74.9840i q^{49} +(-43.8887 - 15.0349i) q^{50} +(8.14984 + 30.3882i) q^{51} +(-21.7754 + 47.2211i) q^{52} +93.7692i q^{53} +(48.4815 - 23.7812i) q^{54} -24.7879i q^{55} +(-87.2184 - 18.1088i) q^{56} +(-23.8336 - 13.7532i) q^{57} +(70.5179 + 24.1572i) q^{58} +(27.8906 - 27.8906i) q^{59} +(6.08768 + 14.9224i) q^{60} -19.9699 q^{61} +(-18.2831 - 37.3367i) q^{62} +(96.8103 + 25.8935i) q^{63} +(25.4778 - 58.7101i) q^{64} +(14.8167 + 9.23569i) q^{65} +(83.4455 - 72.8021i) q^{66} +(27.3331 - 27.3331i) q^{67} +(-33.1378 - 25.7225i) q^{68} +(-49.4842 + 13.2712i) q^{69} +(-9.69285 + 28.2947i) q^{70} +(12.2997 + 12.2997i) q^{71} +(-32.3551 + 64.3207i) q^{72} +(3.46448 - 3.46448i) q^{73} +(22.4179 + 45.7804i) q^{74} +(-67.2135 + 18.0260i) q^{75} +(36.4017 - 4.58593i) q^{76} +205.511 q^{77} +(12.4257 + 77.0039i) q^{78} -30.4341i q^{79} +(-18.4886 - 10.9512i) q^{80} +(40.4368 - 70.1845i) q^{81} +(-33.4683 - 68.3469i) q^{82} +(-93.6129 - 93.6129i) q^{83} +(-123.719 + 50.4717i) q^{84} +(-9.95952 + 9.95952i) q^{85} +(6.28858 - 18.3572i) q^{86} +(107.995 - 28.9632i) q^{87} +(-30.0165 + 144.570i) q^{88} +(-27.0128 - 27.0128i) q^{89} +(20.0690 + 13.4777i) q^{90} +(-76.5712 + 122.842i) q^{91} +(41.8865 - 53.9616i) q^{92} +(-54.0117 - 31.1675i) q^{93} +(-64.9565 - 132.650i) q^{94} -12.3188i q^{95} +(-17.4350 - 94.4035i) q^{96} +(58.7776 + 58.7776i) q^{97} +(-141.874 - 48.6016i) q^{98} +(42.9201 - 160.469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 36 q^{6} - 64 q^{9} - 8 q^{13} + 80 q^{16} + 48 q^{18} + 8 q^{21} + 124 q^{24} - 8 q^{28} + 24 q^{33} + 64 q^{34} - 128 q^{37} - 136 q^{40} - 140 q^{42} - 160 q^{45} + 88 q^{46} - 108 q^{48} - 320 q^{52}+ \cdots + 336 q^{97}+O(q^{100}) \) 96 * q - 36 * q^6 - 64 * q^9 - 8 * q^13 + 80 * q^16 + 48 * q^18 + 8 * q^21 + 124 * q^24 - 8 * q^28 + 24 * q^33 + 64 * q^34 - 128 * q^37 - 136 * q^40 - 140 * q^42 - 160 * q^45 + 88 * q^46 - 108 * q^48 - 320 * q^52 - 216 * q^54 + 136 * q^57 + 280 * q^58 + 80 * q^60 - 464 * q^61 - 240 * q^66 - 120 * q^70 - 32 * q^72 + 288 * q^73 + 88 * q^76 - 296 * q^78 - 144 * q^81 + 204 * q^84 + 848 * q^85 - 392 * q^93 + 1384 * q^94 - 204 * q^96 + 336 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more