LMFDB - Embedded newform 156.3.l.c.83.5

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			83.5
Character	$\chi$	$=$	156.83
Dual form			156.3.l.c.47.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89206 - 0.648159i) q^{2} +(-0.777110 + 2.89760i) q^{3} +(3.15978 + 2.45271i) q^{4} +(-0.949668 - 0.949668i) q^{5} +(3.34845 - 4.97875i) q^{6} +(7.87350 - 7.87350i) q^{7} +(-4.38874 - 6.68872i) q^{8} +(-7.79220 - 4.50351i) q^{9} +(1.18129 + 2.41236i) q^{10} +(13.0508 + 13.0508i) q^{11} +(-9.56248 + 7.24976i) 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} +(11.8243 + 13.5715i) q^{18} +(6.48583 + 6.48583i) q^{19} +(-0.671480 - 5.33000i) q^{20} +(16.6957 + 28.9329i) q^{21} +(-16.2339 - 33.1519i) q^{22} +17.0776i q^{23} +(22.7918 - 7.51897i) q^{24} -23.1963i q^{25} +(13.7676 - 22.0557i) q^{26} +(19.1048 - 19.0790i) q^{27} +(44.1900 - 5.56710i) q^{28} +37.2704i q^{29} +(-7.90807 + 1.54824i) q^{30} +(14.6982 + 14.6982i) q^{31} +(2.53803 - 31.8992i) q^{32} +(-47.9580 + 27.6741i) q^{33} +(-19.8427 - 6.79748i) q^{34} -14.9544 q^{35} +(-13.5758 - 33.3421i) 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} +(-12.8362 - 65.5642i) q^{42} +9.70221 q^{43} +(9.22781 + 73.2475i) q^{44} +(3.12316 + 11.6768i) q^{45} +(11.0690 - 32.3119i) q^{46} +(52.2200 + 52.2200i) q^{47} +(-47.9969 - 0.546359i) q^{48} -74.9840i q^{49} +(-15.0349 + 43.8887i) q^{50} +(-8.14984 + 30.3882i) q^{51} +(-40.3447 + 32.8071i) q^{52} -93.7692i q^{53} +(-48.5136 + 23.7156i) q^{54} -24.7879i q^{55} +(-87.2184 - 18.1088i) q^{56} +(-23.8336 + 13.7532i) q^{57} +(24.1572 - 70.5179i) q^{58} +(-27.8906 - 27.8906i) q^{59} +(15.9660 + 2.19632i) 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} +(108.677 - 21.2767i) q^{66} +(-27.3331 - 27.3331i) q^{67} +(33.1378 + 25.7225i) q^{68} +(-49.4842 - 13.2712i) q^{69} +(28.2947 + 9.69285i) q^{70} +(-12.2997 + 12.2997i) q^{71} +(4.07527 + 71.8846i) q^{72} +(3.46448 + 3.46448i) q^{73} +(-22.4179 - 45.7804i) q^{74} +(67.2135 + 18.0260i) q^{75} +(4.58593 + 36.4017i) q^{76} +205.511 q^{77} +(53.2096 + 57.0327i) q^{78} -30.4341i q^{79} +(10.9512 - 18.4886i) q^{80} +(40.4368 + 70.1845i) q^{81} +(33.4683 + 68.3469i) q^{82} +(93.6129 - 93.6129i) q^{83} +(-18.2092 + 132.371i) q^{84} +(-9.95952 - 9.95952i) q^{85} +(-18.3572 - 6.28858i) q^{86} +(-107.995 - 28.9632i) q^{87} +(30.0165 - 144.570i) q^{88} +(-27.0128 + 27.0128i) q^{89} +(1.65924 - 24.1176i) 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} +(90.4589 + 32.1434i) q^{96} +(58.7776 - 58.7776i) q^{97} +(-48.6016 + 141.874i) 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 $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.89206	−	0.648159i	−0.946030	−	0.324080i
$2$	−1.89206	−	0.648159i	−0.946030	−	0.324080i
$3$	−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	0.605734	−	0.795667i	$-0.292880\pi$
$5$	−0.949668	−	0.949668i	−0.189934	−	0.189934i	−0.795667	+	0.605734i	$0.792880\pi$
$6$	3.34845	−	4.97875i	0.558074	−	0.829791i
$7$	7.87350	−	7.87350i	1.12479	−	1.12479i	0.133774	−	0.991012i	$-0.457290\pi$
$7$	7.87350	−	7.87350i	1.12479	−	1.12479i	0.991012	−	0.133774i	$-0.0427096\pi$
$8$	−4.38874	−	6.68872i	−0.548593	−	0.836090i
$9$	−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	0.978046	+	0.208391i	$0.0668227\pi$
$11$	13.0508	+	13.0508i	1.18644	+	1.18644i	0.208391	+	0.978046i	$0.433177\pi$
$12$	−9.56248	+	7.24976i	−0.796873	+	0.604147i
$13$	−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	$0.400189\pi$
$18$	11.8243	+	13.5715i	0.656907	+	0.753972i
$19$	6.48583	+	6.48583i	0.341360	+	0.341360i	0.856878	−	0.515519i	$-0.172401\pi$
$19$	6.48583	+	6.48583i	0.341360	+	0.341360i	−0.515519	+	0.856878i	$0.672401\pi$
$20$	−0.671480	−	5.33000i	−0.0335740	−	0.266500i
$21$	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	$0.878928\pi$
$24$	22.7918	−	7.51897i	0.949657	−	0.313290i
$25$		−	23.1963i		−	0.927850i
$26$	13.7676	−	22.0557i	0.529523	−	0.848295i
$27$	19.1048	−	19.0790i	0.707584	−	0.706629i
$28$	44.1900	−	5.56710i	1.57821	−	0.198825i
$29$			37.2704i			1.28519i	0.766207	+	0.642594i	$0.222142\pi$
$29$			37.2704i			1.28519i	−0.766207	+	0.642594i	$0.777858\pi$
$30$	−7.90807	+	1.54824i	−0.263602	+	0.0516081i
$31$	14.6982	+	14.6982i	0.474136	+	0.474136i	0.903250	−	0.429114i	$-0.141174\pi$
$31$	14.6982	+	14.6982i	0.474136	+	0.474136i	−0.429114	+	0.903250i	$0.641174\pi$
$32$	2.53803	−	31.8992i	0.0793133	−	0.996850i
$33$	−47.9580	+	27.6741i	−1.45327	+	0.838610i
$34$	−19.8427	−	6.79748i	−0.583610	−	0.199926i
$35$	−14.9544			−0.427269
$36$	−13.5758	−	33.3421i	−0.377106	−	0.926170i
$37$	18.0222	+	18.0222i	0.487087	+	0.487087i	0.907386	−	0.420299i	$-0.138075\pi$
$37$	18.0222	+	18.0222i	0.487087	+	0.487087i	−0.420299	+	0.907386i	$0.638075\pi$
$38$	−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	0.298247	−	0.954489i	$-0.403598\pi$
$41$	−26.9059	−	26.9059i	−0.656242	−	0.656242i	−0.954489	+	0.298247i	$0.903598\pi$
$42$	−12.8362	−	65.5642i	−0.305623	−	1.56105i
$43$	9.70221			0.225633			0.112816	−	0.993616i	$-0.464013\pi$
$43$	9.70221			0.225633			0.112816	+	0.993616i	$0.464013\pi$
$44$	9.22781	+	73.2475i	0.209723	+	1.66472i
$45$	3.12316	+	11.6768i	0.0694036	+	0.259485i
$46$	11.0690	−	32.3119i	0.240631	−	0.702433i
$47$	52.2200	+	52.2200i	1.11106	+	1.11106i	0.993007	+	0.118057i	$0.0376666\pi$
$47$	52.2200	+	52.2200i	1.11106	+	1.11106i	0.118057	+	0.993007i	$0.462333\pi$
$48$	−47.9969	−	0.546359i	−0.999935	−	0.0113825i
$49$		−	74.9840i		−	1.53029i
$50$	−15.0349	+	43.8887i	−0.300697	+	0.877774i
$51$	−8.14984	+	30.3882i	−0.159801	+	0.595848i
$52$	−40.3447	+	32.8071i	−0.775860	+	0.630905i
$53$		−	93.7692i		−	1.76923i	−0.466323	−	0.884615i	$-0.654421\pi$
$53$		−	93.7692i		−	1.76923i	0.466323	−	0.884615i	$-0.345579\pi$
$54$	−48.5136	+	23.7156i	−0.898400	+	0.439178i
$55$		−	24.7879i		−	0.450688i
$56$	−87.2184	−	18.1088i	−1.55747	−	0.323372i
$57$	−23.8336	+	13.7532i	−0.418133	+	0.241283i
$58$	24.1572	−	70.5179i	0.416503	−	1.21583i
$59$	−27.8906	−	27.8906i	−0.472722	−	0.472722i	0.430072	−	0.902794i	$-0.358488\pi$
$59$	−27.8906	−	27.8906i	−0.472722	−	0.472722i	−0.902794	+	0.430072i	$0.858488\pi$
$60$	15.9660	+	2.19632i	0.266101	+	0.0366053i
$61$	−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
$66$	108.677	−	21.2767i	1.64661	−	0.322375i
$67$	−27.3331	−	27.3331i	−0.407957	−	0.407957i	0.473069	−	0.881026i	$-0.343146\pi$
$67$	−27.3331	−	27.3331i	−0.407957	−	0.407957i	−0.881026	+	0.473069i	$0.843146\pi$
$68$	33.1378	+	25.7225i	0.487320	+	0.378272i
$69$	−49.4842	−	13.2712i	−0.717162	−	0.192336i
$70$	28.2947	+	9.69285i	0.404209	+	0.138469i
$71$	−12.2997	+	12.2997i	−0.173235	+	0.173235i	−0.788399	−	0.615164i	$-0.789090\pi$
$71$	−12.2997	+	12.2997i	−0.173235	+	0.173235i	0.615164	+	0.788399i	$0.289090\pi$
$72$	4.07527	+	71.8846i	0.0566010	+	0.998397i
$73$	3.46448	+	3.46448i	0.0474586	+	0.0474586i	0.730438	−	0.682979i	$-0.239316\pi$
$73$	3.46448	+	3.46448i	0.0474586	+	0.0474586i	−0.682979	+	0.730438i	$0.739316\pi$
$74$	−22.4179	−	45.7804i	−0.302944	−	0.618654i
$75$	67.2135	+	18.0260i	0.896181	+	0.240347i
$76$	4.58593	+	36.4017i	0.0603411	+	0.478969i
$77$	205.511			2.66897
$78$	53.2096	+	57.0327i	0.682175	+	0.731189i
$79$		−	30.4341i		−	0.385242i	−0.981273	−	0.192621i	$-0.938301\pi$
$79$		−	30.4341i		−	0.385242i	0.981273	−	0.192621i	$-0.0616988\pi$
$80$	10.9512	−	18.4886i	0.136890	−	0.231107i
$81$	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	0.137343	−	0.990524i	$-0.456144\pi$
$83$	93.6129	−	93.6129i	1.12787	−	1.12787i	0.990524	−	0.137343i	$-0.0438561\pi$
$84$	−18.2092	+	132.371i	−0.216776	+	1.57585i
$85$	−9.95952	−	9.95952i	−0.117171	−	0.117171i
$86$	−18.3572	−	6.28858i	−0.213455	−	0.0731230i
$87$	−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	−0.842387	−	0.538872i	$-0.818851\pi$
$89$	−27.0128	+	27.0128i	−0.303515	+	0.303515i	0.538872	+	0.842387i	$0.318851\pi$
$90$	1.65924	−	24.1176i	0.0184360	−	0.267973i
$91$	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
$96$	90.4589	+	32.1434i	0.942280	+	0.334827i
$97$	58.7776	−	58.7776i	0.605954	−	0.605954i	−0.335932	−	0.941886i	$-0.609051\pi$
$97$	58.7776	−	58.7776i	0.605954	−	0.605954i	0.941886	+	0.335932i	$0.109051\pi$
$98$	−48.6016	+	141.874i	−0.495935	+	1.44770i
$99$	−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	$0.479616\pi$
$102$	35.1164	−	52.2139i	0.344278	−	0.511901i
$103$	−24.5921			−0.238758			−0.119379	−	0.992849i	$-0.538090\pi$
$103$	−24.5921			−0.238758			−0.119379	+	0.992849i	$0.538090\pi$
$104$	97.5988	−	35.9231i	0.938450	−	0.345415i
$105$	11.6212	−	43.3320i	0.110678	−	0.412685i
$106$	−60.7773	+	177.417i	−0.573371	+	1.67374i
$107$	−45.2828			−0.423204			−0.211602	−	0.977356i	$-0.567868\pi$
$107$	−45.2828			−0.423204			−0.211602	+	0.977356i	$0.567868\pi$
$108$	107.162	−	13.4269i	0.992242	−	0.124323i
$109$	−127.144	+	127.144i	−1.16646	+	1.16646i	−0.183421	+	0.983035i	$0.558717\pi$
$109$	−127.144	+	127.144i	−1.16646	+	1.16646i	−0.983035	+	0.183421i	$0.941283\pi$
$110$	−16.0665	+	46.9001i	−0.146059	+	0.426365i
$111$	−66.2265	+	38.2160i	−0.596635	+	0.344288i
$112$	153.285	+	90.7944i	1.36862	+	0.810664i
$113$		−	124.896i		−	1.10528i	−0.833421	−	0.552639i	$-0.813621\pi$
$113$		−	124.896i		−	1.10528i	0.833421	−	0.552639i	$-0.186379\pi$
$114$	54.0088	−	10.5739i	0.473761	−	0.0927531i
$115$	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
$120$	−28.7851	−	14.5041i	−0.239876	−	0.120867i
$121$			219.647i			1.81526i
$122$	37.7842	+	12.9437i	0.309707	+	0.106096i
$123$	98.8715	−	57.0538i	0.803833	−	0.463852i
$124$	10.3926	+	82.4936i	0.0838116	+	0.665271i
$125$	−45.7704	+	45.7704i	−0.366164	+	0.366164i
$126$	199.954	+	13.7564i	1.58694	+	0.109178i
$127$	−200.693			−1.58026			−0.790130	−	0.612939i	$-0.789987\pi$
$127$	−200.693			−1.58026			−0.790130	+	0.612939i	$0.789987\pi$
$128$	86.2591	−	94.5694i	0.673899	−	0.738823i
$129$	−7.53968	+	28.1132i	−0.0584472	+	0.217931i
$130$	−34.0202	+	7.87092i	−0.261694	+	0.0605455i
$131$	−137.472			−1.04941			−0.524703	−	0.851285i	$-0.675824\pi$
$131$	−137.472			−1.04941			−0.524703	+	0.851285i	$0.675824\pi$
$132$	−219.413	−	30.1828i	−1.66222	−	0.228658i
$133$	102.132			0.767913
$134$	33.9997	+	69.4321i	0.253729	+	0.518150i
$135$	−36.2619	−	0.0245023i	−0.268607	−	0.000181499i
$136$	−46.0264	−	70.1470i	−0.338429	−	0.515787i
$137$	89.4472	−	89.4472i	0.652900	−	0.652900i	−0.300791	−	0.953690i	$-0.597251\pi$
$137$	89.4472	−	89.4472i	0.652900	−	0.652900i	0.953690	+	0.300791i	$0.0972505\pi$
$138$	85.0252	+	57.1835i	0.616125	+	0.414373i
$139$			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
$144$	38.8820	−	138.651i	0.270014	−	0.962856i
$145$	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
$148$	12.7429	+	101.150i	0.0861010	+	0.683443i
$149$	−74.6323	−	74.6323i	−0.500888	−	0.500888i	0.410826	−	0.911714i	$-0.365240\pi$
$149$	−74.6323	−	74.6323i	−0.500888	−	0.500888i	−0.911714	+	0.410826i	$0.865240\pi$
$150$	−115.488	−	77.6714i	−0.769922	−	0.517809i
$151$	32.3514	−	32.3514i	0.214247	−	0.214247i	−0.591822	−	0.806069i	$-0.701591\pi$
$151$	32.3514	−	32.3514i	0.214247	−	0.214247i	0.806069	+	0.591822i	$0.201591\pi$
$152$	14.9172	−	71.8465i	0.0981397	−	0.472675i
$153$	−81.7197	−	47.2300i	−0.534116	−	0.308693i
$154$	−388.839	−	133.204i	−2.52493	−	0.864960i
$155$		−	27.9168i		−	0.180109i
$156$	−63.7095	−	142.398i	−0.408395	−	0.912806i
$157$	38.4009			0.244592			0.122296	−	0.992494i	$-0.460974\pi$
$157$	38.4009			0.244592			0.122296	+	0.992494i	$0.460974\pi$
$158$	−19.7262	+	57.5832i	−0.124849	+	0.364451i
$159$	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
$162$	−31.0181	−	159.003i	−0.191470	−	0.981499i
$163$	−5.31158	+	5.31158i	−0.0325864	+	0.0325864i	−0.723212	−	0.690626i	$-0.757335\pi$
$163$	−5.31158	+	5.31158i	−0.0325864	+	0.0325864i	0.690626	+	0.723212i	$0.257335\pi$
$164$	−19.0243	−	151.009i	−0.116002	−	0.920788i
$165$	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	$-0.223385\pi$
$167$	19.7239	+	19.7239i	0.118107	+	0.118107i	−0.645583	+	0.763690i	$0.723385\pi$
$168$	120.250	−	238.652i	0.715777	−	1.42055i
$169$	−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	$0.644590\pi$
$174$	185.560	+	124.798i	1.06644	+	0.717230i
$175$	−182.636	−	182.636i	−1.04363	−	1.04363i
$176$	−150.497	+	254.079i	−0.855098	+	1.44363i
$177$	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	$0.844461\pi$
$180$	−18.7714	+	44.5565i	−0.104286	+	0.247536i
$181$		−	161.911i		−	0.894539i	−0.894399	−	0.447269i	$-0.852397\pi$
$181$		−	161.911i		−	0.894539i	0.894399	−	0.447269i	$-0.147603\pi$
$182$	−65.2561	−	282.055i	−0.358550	−	1.54975i
$183$	15.5188	−	57.8648i	0.0848022	−	0.316201i
$184$	114.227	−	74.9494i	0.620801	−	0.407334i
$185$		−	34.2303i		−	0.185028i
$186$	122.395	−	23.9625i	0.658037	−	0.128831i
$187$	136.869	+	136.869i	0.731918	+	0.731918i
$188$	36.9231	+	293.084i	0.196399	+	1.55896i
$189$	0.203144	−	300.640i	0.00107483	−	1.59069i
$190$	−7.98452	+	23.3079i	−0.0420238	+	0.122673i
$191$	89.9885			0.471144			0.235572	−	0.971857i	$-0.424304\pi$
$191$	89.9885			0.471144			0.235572	+	0.971857i	$0.424304\pi$
$192$	−150.320	−	119.449i	−0.782914	−	0.622130i
$193$	−129.472	−	129.472i	−0.670841	−	0.670841i	0.287069	−	0.957910i	$-0.407319\pi$
$193$	−129.472	−	129.472i	−0.670841	−	0.670841i	−0.957910	+	0.287069i	$0.907319\pi$
$194$	−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	0.809763	−	0.586758i	$-0.199596\pi$
$197$	43.9320	+	43.9320i	0.223005	+	0.223005i	−0.586758	+	0.809763i	$0.699596\pi$
$198$	−22.8021	+	331.436i	−0.115162	+	1.67392i
$199$	−170.302			−0.855788			−0.427894	−	0.903829i	$-0.640744\pi$
$199$	−170.302			−0.855788			−0.427894	+	0.903829i	$0.640744\pi$
$200$	−155.153	+	101.802i	−0.775766	+	0.509012i
$201$	100.441	−	57.9597i	0.499708	−	0.288357i
$202$	−24.4580	−	8.37854i	−0.121079	−	0.0414779i
$203$	293.449	+	293.449i	1.44556	+	1.44556i
$204$	−100.285	+	76.0309i	−0.491594	+	0.372700i
$205$			51.1034i			0.249285i
$206$	46.5297	+	15.9396i	0.225872	+	0.0773766i
$207$	76.9093	−	133.072i	0.371543	−	0.642862i
$208$	−207.947	+	4.70912i	−0.999744	+	0.0226400i
$209$			169.291i			0.810003i
$210$	−50.0741	+	74.4543i	−0.238448	+	0.354544i
$211$		−	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
$214$	85.6777	+	29.3505i	0.400363	+	0.137152i
$215$	−9.21388	−	9.21388i	−0.0428553	−	0.0428553i
$216$	−211.460	−	44.0537i	−0.978981	−	0.203952i
$217$	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
$222$	150.075	−	29.3816i	0.676012	−	0.132350i
$223$	177.676	+	177.676i	0.796752	+	0.796752i	0.982582	−	0.185830i	$-0.0594973\pi$
$223$	177.676	+	177.676i	0.796752	+	0.796752i	−0.185830	+	0.982582i	$0.559497\pi$
$224$	−231.175	−	271.141i	−1.03203	−	1.21045i
$225$	−104.465	+	180.750i	−0.464287	+	0.803333i
$226$	−80.9527	+	236.311i	−0.358198	+	1.04563i
$227$	30.2485	−	30.2485i	0.133253	−	0.133253i	−0.637334	−	0.770588i	$-0.719963\pi$
$227$	30.2485	−	30.2485i	0.133253	−	0.133253i	0.770588	+	0.637334i	$0.219963\pi$
$228$	−109.041	−	14.9999i	−0.478252	−	0.0657891i
$229$	274.828	+	274.828i	1.20012	+	1.20012i	0.974128	+	0.225995i	$0.0725634\pi$
$229$	274.828	+	274.828i	1.20012	+	1.20012i	0.225995	+	0.974128i	$0.427437\pi$
$230$	−41.1975	+	20.1737i	−0.179119	+	0.0877117i
$231$	−159.705	+	595.489i	−0.691362	+	2.57788i
$232$	249.291	−	163.570i	1.07453	−	0.705045i
$233$	−176.505			−0.757532			−0.378766	−	0.925492i	$-0.623652\pi$
$233$	−176.505			−0.757532			−0.378766	+	0.925492i	$0.623652\pi$
$234$	−206.608	+	109.860i	−0.882940	+	0.469486i
$235$		−	99.1833i		−	0.422057i
$236$	−19.7206	−	156.536i	−0.0835617	−	0.663287i
$237$	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	$-0.671751\pi$
$239$	82.2545	−	82.2545i	0.344161	−	0.344161i	0.857929	+	0.513768i	$0.171751\pi$
$240$	45.0622	+	46.1000i	0.187759	+	0.192083i
$241$	−64.6891	−	64.6891i	−0.268419	−	0.268419i	0.560044	−	0.828463i	$-0.310784\pi$
$241$	−64.6891	−	64.6891i	−0.268419	−	0.268419i	−0.828463	+	0.560044i	$0.810784\pi$
$242$	142.366	−	415.585i	0.588290	−	1.71729i
$243$	−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
$246$	−224.051	+	43.8647i	−0.910775	+	0.178312i
$247$	−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	$-0.121343\pi$
$252$	−369.408	−	155.630i	−1.46591	−	0.617579i
$253$	−222.877	+	222.877i	−0.880936	+	0.880936i
$254$	379.723	+	130.081i	1.49497	+	0.512130i
$255$	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	$0.827430\pi$
$258$	32.4873	−	48.3049i	0.125920	−	0.187228i
$259$	283.796			1.09574
$260$	69.4699	+	7.15828i	0.267192	+	0.0275318i
$261$	167.848	−	290.419i	0.643095	−	1.11272i
$262$	260.106	+	89.1039i	0.992770	+	0.340091i
$263$	55.8360			0.212304			0.106152	−	0.994350i	$-0.466147\pi$
$263$	55.8360			0.212304			0.106152	+	0.994350i	$0.466147\pi$
$264$	395.580	+	199.322i	1.49841	+	0.755009i
$265$	−89.0496	+	89.0496i	−0.336036	+	0.336036i
$266$	−193.241	−	66.1980i	−0.726468	−	0.248865i
$267$	−57.2805	−	99.2644i	−0.214534	−	0.371777i
$268$	−19.3264	−	153.407i	−0.0721133	−	0.572414i
$269$			139.702i			0.519337i	0.965698	+	0.259668i	$0.0836133\pi$
$269$			139.702i			0.519337i	−0.965698	+	0.259668i	$0.916387\pi$
$270$	68.5938	+	23.5498i	0.254051	+	0.0872216i
$271$	−14.0400	+	14.0400i	−0.0518082	+	0.0518082i	−0.732536	−	0.680728i	$-0.761664\pi$
$271$	−14.0400	+	14.0400i	−0.0518082	+	0.0518082i	0.680728	+	0.732536i	$0.261664\pi$
$272$	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
$276$	−123.809	−	163.305i	−0.448582	−	0.591683i
$277$		−	264.498i		−	0.954868i	−0.878668	−	0.477434i	$-0.841567\pi$
$277$		−	264.498i		−	0.954868i	0.878668	−	0.477434i	$-0.158433\pi$
$278$	29.3572	−	85.6973i	0.105601	−	0.308264i
$279$	−48.3379	−	180.725i	−0.173254	−	0.647760i
$280$	65.6311	+	100.026i	0.234397	+	0.357235i
$281$	−201.246	+	201.246i	−0.716179	+	0.716179i	−0.967821	−	0.251641i	$-0.919030\pi$
$281$	−201.246	+	201.246i	−0.716179	+	0.716179i	0.251641	+	0.967821i	$0.419030\pi$
$282$	434.846	−	85.1343i	1.54201	−	0.301895i
$283$	396.067			1.39953			0.699765	−	0.714373i	$-0.253288\pi$
$283$	396.067			1.39953			0.699765	+	0.714373i	$0.253288\pi$
$284$	−69.0320	+	8.69674i	−0.243071	+	0.0306223i
$285$	35.6949	+	9.57304i	0.125245	+	0.0335896i
$286$	467.523	−	108.166i	1.63469	−	0.378203i
$287$	−423.687			−1.47626
$288$	−163.435	+	237.135i	−0.567483	+	0.823385i
$289$	−179.015			−0.619429
$290$	−89.9099	+	44.0273i	−0.310034	+	0.151818i
$291$	124.637	+	215.991i	0.428307	+	0.742236i
$292$	2.44962	+	19.4443i	0.00838911	+	0.0665902i
$293$	186.129	−	186.129i	0.635253	−	0.635253i	−0.314128	−	0.949381i	$-0.601712\pi$
$293$	186.129	−	186.129i	0.635253	−	0.635253i	0.949381	+	0.314128i	$0.101712\pi$
$294$	−373.326	−	251.080i	−1.26982	−	0.854013i
$295$			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
$300$	168.167	+	221.814i	0.560558	+	0.739379i
$301$	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
$304$	−74.7923	+	126.269i	−0.246027	+	0.415359i
$305$	18.9648	+	18.9648i	0.0621796	+	0.0621796i
$306$	124.006	+	142.329i	0.405248	+	0.465128i
$307$	249.313	−	249.313i	0.812093	−	0.812093i	−0.172854	−	0.984947i	$-0.555299\pi$
$307$	249.313	−	249.313i	0.812093	−	0.812093i	0.984947	+	0.172854i	$0.0552990\pi$
$308$	649.370	+	504.059i	2.10834	+	1.63656i
$309$	19.1107	−	71.2581i	0.0618471	−	0.230609i
$310$	−18.0946	+	52.8203i	−0.0583695	+	0.170388i
$311$		−	145.007i		−	0.466262i	−0.972445	−	0.233131i	$-0.925103\pi$
$311$		−	145.007i		−	0.466262i	0.972445	−	0.233131i	$-0.0748971\pi$
$312$	28.2459	+	310.719i	0.0905318	+	0.995894i
$313$	238.458			0.761848			0.380924	−	0.924606i	$-0.375606\pi$
$313$	238.458			0.761848			0.380924	+	0.924606i	$0.375606\pi$
$314$	−72.6568	−	24.8899i	−0.231391	−	0.0792672i
$315$	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	0.0121259	−	0.999926i	$-0.496140\pi$
$317$	−313.133	−	313.133i	−0.987801	−	0.987801i	−0.999926	+	0.0121259i	$0.996140\pi$
$318$	−466.853	−	313.981i	−1.46809	−	0.987361i
$319$	−486.409	+	486.409i	−1.52479	+	1.52479i
$320$	79.9506	−	31.5596i	0.249846	−	0.0986239i
$321$	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
$324$	−44.3710	+	320.947i	−0.136948	+	0.990578i
$325$	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
$330$	−123.412	−	83.0008i	−0.373977	−	0.251518i
$331$	180.560	+	180.560i	0.545499	+	0.545499i	0.925136	−	0.379636i	$-0.123951\pi$
$331$	180.560	+	180.560i	0.545499	+	0.545499i	−0.379636	+	0.925136i	$0.623951\pi$
$332$	525.401	−	66.1907i	1.58253	−	0.199370i
$333$	−59.2695	−	221.596i	−0.177987	−	0.665454i
$334$	−24.5346	−	50.1031i	−0.0734569	−	0.150009i
$335$			51.9148i			0.154969i
$336$	−382.205	+	373.602i	−1.13752	+	1.11191i
$337$			20.9367i			0.0621266i	0.999517	+	0.0310633i	$0.00988935\pi$
$337$			20.9367i			0.0621266i	−0.999517	+	0.0310633i	$0.990111\pi$
$338$	238.849	+	239.155i	0.706654	+	0.707559i
$339$	361.900	+	97.0582i	1.06755	+	0.286307i
$340$	−7.04206	−	55.8977i	−0.0207119	−	0.164405i
$341$			383.647i			1.12506i
$342$	−11.3319	+	164.713i	−0.0331342	+	0.481617i
$343$	−204.585	−	204.585i	−0.596459	−	0.596459i
$344$	−42.5805	−	64.8953i	−0.123781	−	0.188649i
$345$	34.3903	+	59.5968i	0.0996821	+	0.172744i
$346$	287.251	+	98.4029i	0.830204	+	0.284401i
$347$	−304.430			−0.877319			−0.438659	−	0.898653i	$-0.644547\pi$
$347$	−304.430			−0.877319			−0.438659	+	0.898653i	$0.644547\pi$
$348$	−270.202	−	356.398i	−0.776441	−	1.02413i
$349$	−273.159	−	273.159i	−0.782690	−	0.782690i	0.197594	−	0.980284i	$-0.436687\pi$
$349$	−273.159	−	273.159i	−0.782690	−	0.782690i	−0.980284	+	0.197594i	$0.936687\pi$
$350$	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	0.820833	−	0.571168i	$-0.193510\pi$
$353$	88.1316	+	88.1316i	0.249665	+	0.249665i	−0.571168	+	0.820833i	$0.693510\pi$
$354$	−232.250	+	45.4700i	−0.656074	+	0.128446i
$355$	23.3613			0.0658065
$356$	−151.609	+	19.0999i	−0.425869	+	0.0536515i
$357$	175.094	+	303.429i	0.490459	+	0.849942i
$358$	108.926	−	317.968i	0.304262	−	0.888180i
$359$	−93.4775	−	93.4775i	−0.260383	−	0.260383i	0.564827	−	0.825210i	$-0.308943\pi$
$359$	−93.4775	−	93.4775i	−0.260383	−	0.260383i	−0.825210	+	0.564827i	$0.808943\pi$
$360$	64.3963	−	72.1366i	0.178879	−	0.200380i
$361$		−	276.868i		−	0.766947i
$362$	−104.944	+	306.346i	−0.289902	+	0.846260i
$363$	−636.450	−	170.690i	−1.75331	−	0.470220i
$364$	−59.3478	+	575.961i	−0.163043	+	1.58231i
$365$		−	6.58021i		−	0.0180280i
$366$	−66.8681	+	99.4250i	−0.182700	+	0.271653i
$367$		−	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
$370$	−22.1867	+	64.7657i	−0.0599639	+	0.175042i
$371$	−738.292	−	738.292i	−1.99000	−	1.99000i
$372$	−247.110	−	33.9928i	−0.664274	−	0.0913786i
$373$	−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
$378$	−195.247	+	568.697i	−0.516526	+	1.50449i
$379$	168.149	+	168.149i	0.443664	+	0.443664i	0.893241	−	0.449577i	$-0.148425\pi$
$379$	168.149	+	168.149i	0.443664	+	0.443664i	−0.449577	+	0.893241i	$0.648425\pi$
$380$	30.2144	−	38.9246i	0.0795116	−	0.102433i
$381$	155.961	−	581.529i	0.409345	−	1.52632i
$382$	−170.264	−	58.3269i	−0.445716	−	0.152688i
$383$	−199.284	+	199.284i	−0.520323	+	0.520323i	−0.917669	−	0.397346i	$-0.869931\pi$
$383$	−199.284	+	199.284i	−0.520323	+	0.520323i	0.397346	+	0.917669i	$0.369931\pi$
$384$	206.992	+	323.435i	0.539041	+	0.842280i
$385$	−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
$388$	329.889	−	41.5598i	0.850228	−	0.107113i
$389$	−81.1669			−0.208655			−0.104328	−	0.994543i	$-0.533269\pi$
$389$	−81.1669			−0.208655			−0.104328	+	0.994543i	$0.533269\pi$
$390$	3.63066	−	104.694i	0.00930940	−	0.268445i
$391$			179.099i			0.458055i
$392$	−501.547	+	329.086i	−1.27946	+	0.839504i
$393$	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
$396$	257.966	−	612.317i	0.651429	−	1.54625i
$397$	251.456	+	251.456i	0.633390	+	0.633390i	0.948917	−	0.315527i	$-0.102181\pi$
$397$	251.456	+	251.456i	0.633390	+	0.633390i	−0.315527	+	0.948917i	$0.602181\pi$
$398$	322.221	+	110.383i	0.809601	+	0.277343i
$399$	−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	0.0466382	−	0.998912i	$-0.485149\pi$
$401$	419.266	−	419.266i	1.04555	−	1.04555i	0.998912	−	0.0466382i	$-0.0148508\pi$
$402$	−227.608	+	44.5612i	−0.566189	+	0.110849i
$403$	−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
$408$	239.026	−	78.8542i	0.585847	−	0.193270i
$409$	474.074	−	474.074i	1.15911	−	1.15911i	0.174437	−	0.984668i	$-0.444190\pi$
$409$	474.074	−	474.074i	1.15911	−	1.15911i	0.984668	−	0.174437i	$-0.0558104\pi$
$410$	33.1231	−	96.6906i	0.0807881	−	0.235831i
$411$	189.672	+	328.693i	0.461490	+	0.799739i
$412$	−77.7056	−	60.3173i	−0.188606	−	0.146401i
$413$	−439.193			−1.06342
$414$	−231.769	+	201.931i	−0.559829	+	0.487757i
$415$	−177.802			−0.428439
$416$	396.500	+	125.873i	0.953125	+	0.302578i
$417$	−131.242	−	35.1978i	−0.314728	−	0.0844071i
$418$	109.727	−	320.308i	0.262505	−	0.766287i
$419$	738.508			1.76255			0.881274	−	0.472605i	$-0.156686\pi$
$419$	738.508			1.76255			0.881274	+	0.472605i	$0.156686\pi$
$420$	143.001	−	108.416i	0.340479	−	0.258133i
$421$	18.8649	−	18.8649i	0.0448098	−	0.0448098i	−0.684347	−	0.729157i	$-0.739913\pi$
$421$	18.8649	−	18.8649i	0.0448098	−	0.0448098i	0.729157	+	0.684347i	$0.239913\pi$
$422$	−145.295	+	424.136i	−0.344302	+	1.00506i
$423$	−171.735	−	642.082i	−0.405994	−	1.51792i
$424$	−627.195	+	411.529i	−1.47923	+	0.970587i
$425$		−	243.268i		−	0.572395i
$426$	20.0522	+	102.422i	0.0470710	+	0.240427i
$427$	−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	$-0.516272\pi$
$431$	408.414	−	408.414i	0.947596	−	0.947596i	0.998694	+	0.0510979i	$0.0162720\pi$
$432$	371.541	+	220.412i	0.860048	+	0.510213i
$433$			486.714i			1.12405i	0.827120	+	0.562025i	$0.189978\pi$
$433$			486.714i			1.12405i	−0.827120	+	0.562025i	$0.810022\pi$
$434$	−437.923	−	150.018i	−1.00904	−	0.345664i
$435$	75.0538	+	130.065i	0.172538	+	0.298999i
$436$	−713.592	+	89.8992i	−1.63668	+	0.206191i
$437$	−110.763	+	110.763i	−0.253461	+	0.253461i
$438$	28.8494	−	5.64814i	0.0658661	−	0.0128953i
$439$	279.462			0.636588			0.318294	−	0.947992i	$-0.396890\pi$
$439$	279.462			0.636588			0.318294	+	0.947992i	$0.396890\pi$
$440$	−165.799	+	108.788i	−0.376816	+	0.247245i
$441$	−337.691	+	584.291i	−0.765740	+	1.32492i
$442$	144.386	−	231.306i	0.326665	−	0.523317i
$443$	−687.638			−1.55223			−0.776115	−	0.630592i	$-0.782812\pi$
$443$	−687.638			−1.55223			−0.776115	+	0.630592i	$0.782812\pi$
$444$	−302.994	−	41.6804i	−0.682419	−	0.0938747i
$445$	51.3065			0.115295
$446$	−221.011	−	451.335i	−0.495540	−	1.01196i
$447$	274.252	−	158.257i	0.613540	−	0.354043i
$448$	261.654	+	662.854i	0.584050	+	1.47959i
$449$	−332.430	+	332.430i	−0.740378	+	0.740378i	−0.972651	−	0.232272i	$-0.925384\pi$
$449$	−332.430	+	332.430i	−0.740378	+	0.740378i	0.232272	+	0.972651i	$0.425384\pi$
$450$	314.808	−	274.280i	0.699573	−	0.609511i
$451$		−	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
$456$	196.590	+	99.0569i	0.431119	+	0.217230i
$457$	478.742	−	478.742i	1.04758	−	1.04758i	0.0487647	−	0.998810i	$-0.484472\pi$
$457$	478.742	−	478.742i	1.04758	−	1.04758i	0.998810	−	0.0487647i	$-0.0155284\pi$
$458$	−341.859	−	698.124i	−0.746417	−	1.52429i
$459$	200.359	−	200.088i	0.436512	−	0.435922i
$460$	91.0238	−	11.4673i	0.197878	−	0.0249289i
$461$	222.155	+	222.155i	0.481898	+	0.481898i	0.905737	−	0.423839i	$-0.139318\pi$
$461$	222.155	+	222.155i	0.481898	+	0.481898i	−0.423839	+	0.905737i	$0.639318\pi$
$462$	688.143	−	1023.19i	1.48949	−	2.21469i
$463$	−318.982	+	318.982i	−0.688945	+	0.688945i	−0.961999	−	0.273054i	$-0.911966\pi$
$463$	−318.982	+	318.982i	−0.688945	+	0.688945i	0.273054	+	0.961999i	$0.411966\pi$
$464$	−577.694	+	147.904i	−1.24503	+	0.318760i
$465$	80.8919	+	21.6945i	0.173961	+	0.0466547i
$466$	333.958	+	114.403i	0.716648	+	0.245501i
$467$			121.753i			0.260714i	0.991467	+	0.130357i	$0.0416123\pi$
$467$			121.753i			0.260714i	−0.991467	+	0.130357i	$0.958388\pi$
$468$	462.121	−	73.9463i	0.987438	−	0.158005i
$469$	−430.415			−0.917728
$470$	−64.2866	+	187.661i	−0.136780	+	0.399278i
$471$	−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
$474$	−151.524	−	101.907i	−0.319670	−	0.214994i
$475$	150.447	−	150.447i	0.316731	−	0.316731i
$476$	463.436	−	58.3842i	0.973606	−	0.122656i
$477$	−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	$-0.123136\pi$
$479$	262.894	+	262.894i	0.548839	+	0.548839i	−0.377266	+	0.926105i	$0.623136\pi$
$480$	−55.3804	−	116.431i	−0.115376	−	0.242565i
$481$	−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
$486$	484.831	+	33.6846i	0.997595	+	0.0693098i
$487$	222.814	+	222.814i	0.457524	+	0.457524i	0.897842	−	0.440318i	$-0.145134\pi$
$487$	222.814	+	222.814i	0.457524	+	0.457524i	−0.440318	+	0.897842i	$0.645134\pi$
$488$	87.6428	+	133.573i	0.179596	+	0.273715i
$489$	−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	$0.543999\pi$
$492$	452.349	+	62.2258i	0.919408	+	0.126475i
$493$			390.869i			0.792837i
$494$	232.344	−	53.7550i	0.470332	−	0.108816i
$495$	−111.632	+	193.152i	−0.225520	+	0.390206i
$496$	−169.495	+	286.152i	−0.341723	+	0.576919i
$497$			193.684i			0.389706i
$498$	−152.617	−	779.532i	−0.306460	−	1.56533i
$499$	−445.893	−	445.893i	−0.893574	−	0.893574i	0.101284	−	0.994858i	$-0.467705\pi$
$499$	−445.893	−	445.893i	−0.893574	−	0.893574i	−0.994858	+	0.101284i	$0.967705\pi$
$500$	−256.886	+	32.3628i	−0.513772	+	0.0647256i
$501$	−72.4798	+	41.8245i	−0.144670	+	0.0834819i
$502$	−121.055	+	353.374i	−0.241145	+	0.703932i
$503$	−9.30759			−0.0185042			−0.00925208	−	0.999957i	$-0.502945\pi$
$503$	−9.30759			−0.0185042			−0.00925208	+	0.999957i	$0.502945\pi$
$504$	598.070	+	533.897i	1.18665	+	1.05932i
$505$	−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	0.955598	−	0.294672i	$-0.0952105\pi$
$509$	336.411	+	336.411i	0.660926	+	0.660926i	−0.294672	+	0.955598i	$0.595210\pi$
$510$	−82.9348	+	16.2370i	−0.162617	+	0.0318373i
$511$	54.5551			0.106761
$512$	504.511	−	87.2496i	0.985373	−	0.170409i
$513$	247.653	+	0.167340i	0.482755	+	0.000326200i
$514$	833.063	+	285.381i	1.62075	+	0.555215i
$515$	23.3543	+	23.3543i	0.0453482	+	0.0453482i
$516$	−92.7772	+	70.3387i	−0.179801	+	0.136315i
$517$			1363.03i			2.63641i
$518$	−536.959	−	183.945i	−1.03660	−	0.355106i
$519$	117.980	−	439.911i	0.227322	−	0.847613i
$520$	−126.802	−	58.5714i	−0.243849	−	0.112637i
$521$			210.994i			0.404979i	0.979284	+	0.202489i	$0.0649031\pi$
$521$			210.994i			0.404979i	−0.979284	+	0.202489i	$0.935097\pi$
$522$	−505.816	+	440.697i	−0.968995	+	0.844248i
$523$			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
$526$	−105.645	−	36.1906i	−0.200846	−	0.0688035i
$527$	154.146	+	154.146i	0.292496	+	0.292496i
$528$	−619.268	−	633.528i	−1.17286	−	1.19986i
$529$	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
$534$	44.0391	+	224.941i	0.0824702	+	0.421238i
$535$	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
$538$	90.5489	−	264.324i	0.168306	−	0.491308i
$539$	978.602	−	978.602i	1.81559	−	1.81559i
$540$	−114.519	−	89.0174i	−0.212073	−	0.164847i
$541$	110.852	+	110.852i	0.204903	+	0.204903i	0.802097	−	0.597194i	$-0.203718\pi$
$541$	110.852	+	110.852i	0.204903	+	0.204903i	−0.597194	+	0.802097i	$0.703718\pi$
$542$	35.6647	−	17.4644i	0.0658021	−	0.0322221i
$543$	469.155	+	125.823i	0.864006	+	0.231718i
$544$	26.6172	−	334.539i	0.0489287	−	0.614961i
$545$	241.488			0.443098
$546$	867.994	+	30.1011i	1.58973	+	0.0551302i
$547$		−	83.0751i		−	0.151874i	−0.997113	−	0.0759370i	$-0.975805\pi$
$547$		−	83.0751i		−	0.151874i	0.997113	−	0.0759370i	$-0.0241948\pi$
$548$	502.022	−	63.2453i	0.916098	−	0.115411i
$549$	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
$552$	128.406	+	389.230i	0.232620	+	0.705126i
$553$	−239.623	−	239.623i	−0.433315	−	0.433315i
$554$	−171.437	+	500.447i	−0.309453	+	0.903334i
$555$	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	−0.193951	−	0.981011i	$-0.562130\pi$
$557$	438.392	−	438.392i	0.787060	−	0.787060i	0.981011	+	0.193951i	$0.0621304\pi$
$558$	−25.6804	+	373.273i	−0.0460223	+	0.668948i
$559$	−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	$0.759098\pi$
$564$	−877.935	−	120.770i	−1.55662	−	0.214132i
$565$	−118.610	+	118.610i	−0.209929	+	0.209929i
$566$	−749.382	−	256.714i	−1.32400	−	0.453559i
$567$	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	$0.567243\pi$
$570$	−61.3320	−	41.2487i	−0.107600	−	0.0723662i
$571$	18.5671			0.0325168			0.0162584	−	0.999868i	$-0.494825\pi$
$571$	18.5671			0.0325168			0.0162584	+	0.999868i	$0.494825\pi$
$572$	−954.690	−	98.3726i	−1.66904	−	0.171980i
$573$	−69.9309	+	260.751i	−0.122044	+	0.455063i
$574$	801.642	+	274.617i	1.39659	+	0.478427i
$575$	396.137			0.688934
$576$	462.930	−	342.741i	0.803698	−	0.595037i
$577$	640.717	−	640.717i	1.11043	−	1.11043i	0.117336	−	0.993092i	$-0.462565\pi$
$577$	640.717	−	640.717i	1.11043	−	1.11043i	0.993092	−	0.117336i	$-0.0374354\pi$
$578$	338.707	+	116.030i	0.585999	+	0.200744i
$579$	475.773	−	274.545i	0.821716	−	0.474171i
$580$	198.651	−	25.0263i	0.342503	−	0.0431489i
$581$		−	1474.12i		−	2.53722i
$582$	−95.8251	−	489.452i	−0.164648	−	0.840983i
$583$	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	$-0.581728\pi$
$587$	418.692	−	418.692i	0.713274	−	0.713274i	0.967219	+	0.253945i	$0.0817281\pi$
$588$	543.616	+	717.033i	0.924517	+	1.21944i
$589$			190.660i			0.323702i
$590$	34.3353	−	100.229i	0.0581955	−	0.169880i
$591$	−161.437	+	93.1574i	−0.273160	+	0.157627i
$592$	−207.826	+	350.865i	−0.351057	+	0.592678i
$593$	−213.904	+	213.904i	−0.360715	+	0.360715i	−0.864076	−	0.503361i	$-0.832097\pi$
$593$	−213.904	+	213.904i	−0.360715	+	0.360715i	0.503361	+	0.864076i	$0.332097\pi$
$594$	−942.649	−	323.633i	−1.58695	−	0.544837i
$595$	−156.833			−0.263584
$596$	−52.7701	−	418.873i	−0.0885405	−	0.702807i
$597$	132.343	−	493.467i	0.221680	−	0.826578i
$598$	376.659	+	235.118i	0.629864	+	0.393174i
$599$	491.097			0.819862			0.409931	−	0.912116i	$-0.365553\pi$
$599$	491.097			0.819862			0.409931	+	0.912116i	$0.365553\pi$
$600$	−174.412	−	528.684i	−0.290687	−	0.881140i
$601$	−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
$604$	181.572	−	22.8746i	0.300615	−	0.0378719i
$605$	208.592	−	208.592i	0.344780	−	0.344780i
$606$	43.2842	−	64.3586i	0.0714261	−	0.106202i
$607$			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
$612$	−142.375	−	349.671i	−0.232638	−	0.571358i
$613$	−334.286	+	334.286i	−0.545328	+	0.545328i	−0.925086	−	0.379758i	$-0.876007\pi$
$613$	−334.286	+	334.286i	−0.545328	+	0.545328i	0.379758	+	0.925086i	$0.376007\pi$
$614$	−633.308	+	310.120i	−1.03145	+	0.505082i
$615$	−148.077	−	39.7129i	−0.240776	−	0.0645739i
$616$	−901.935	−	1374.61i	−1.46418	−	2.23150i
$617$	−650.790	−	650.790i	−1.05476	−	1.05476i	−0.998411	−	0.0563537i	$-0.982053\pi$
$617$	−650.790	−	650.790i	−1.05476	−	1.05476i	−0.0563537	−	0.998411i	$-0.517947\pi$
$618$	−82.3453	+	122.438i	−0.133245	+	0.198119i
$619$	−803.023	+	803.023i	−1.29729	+	1.29729i	−0.367116	+	0.930175i	$0.619655\pi$
$619$	−803.023	+	803.023i	−1.29729	+	1.29729i	−0.930175	+	0.367116i	$0.880345\pi$
$620$	68.4720	−	88.2111i	0.110439	−	0.142276i
$621$	325.824	+	326.264i	0.524676	+	0.525386i
$622$	−93.9879	+	274.363i	−0.151106	+	0.441098i
$623$			425.371i			0.682779i
$624$	147.952	−	606.206i	0.237103	−	0.971485i
$625$	−492.973			−0.788757
$626$	−451.177	−	154.559i	−0.720731	−	0.246899i
$627$	−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
$630$	−176.826	−	202.954i	−0.280676	−	0.322149i
$631$	−336.411	+	336.411i	−0.533140	+	0.533140i	−0.921505	−	0.388366i	$-0.873040\pi$
$631$	−336.411	+	336.411i	−0.533140	+	0.533140i	0.388366	+	0.921505i	$0.373040\pi$
$632$	−203.565	+	133.568i	−0.322097	+	0.211341i
$633$	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
$636$	679.804	+	896.666i	1.06887	+	1.40985i
$637$	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	$0.533814\pi$
$642$	−151.627	+	225.452i	−0.236179	+	0.351171i
$643$	−304.119	−	304.119i	−0.472970	−	0.472970i	0.429905	−	0.902874i	$-0.358547\pi$
$643$	−304.119	−	304.119i	−0.472970	−	0.472970i	−0.902874	+	0.429905i	$0.858547\pi$
$644$	95.0729	+	754.660i	0.147629	+	1.17183i
$645$	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	$-0.101849\pi$
$648$	291.978	−	578.492i	0.450583	−	0.892735i
$649$		−	727.989i		−	1.12171i
$650$	−511.609	−	319.357i	−0.787091	−	0.491318i
$651$	−179.864	+	670.658i	−0.276289	+	1.03020i
$652$	−29.8112	+	3.75565i	−0.0457227	+	0.00576020i
$653$			88.1990i			0.135067i	0.997717	+	0.0675337i	$0.0215130\pi$
$653$			88.1990i			0.135067i	−0.997717	+	0.0675337i	$0.978487\pi$
$654$	207.282	+	1058.75i	0.316945	+	1.61888i
$655$	130.553	+	130.553i	0.199318	+	0.199318i
$656$	310.269	−	523.817i	0.472972	−	0.798501i
$657$	−11.3936	−	42.5982i	−0.0173418	−	0.0648375i
$658$	−1555.86	−	532.987i	−2.36452	−	0.810010i
$659$	−243.877			−0.370071			−0.185036	−	0.982732i	$-0.559240\pi$
$659$	−243.877			−0.370071			−0.185036	+	0.982732i	$0.559240\pi$
$660$	179.706	+	237.033i	0.272282	+	0.359142i
$661$	482.331	+	482.331i	0.729699	+	0.729699i	0.970560	−	0.240861i	$-0.0774298\pi$
$661$	482.331	+	482.331i	0.729699	+	0.729699i	−0.240861	+	0.970560i	$0.577430\pi$
$662$	−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
$666$	−31.4881	+	457.689i	−0.0472794	+	0.687221i
$667$	−636.491			−0.954259
$668$	13.9462	+	110.700i	0.0208775	+	0.165719i
$669$	−652.907	+	376.760i	−0.975945	+	0.563169i
$670$	33.6490	−	98.2258i	0.0502224	−	0.146606i
$671$	−260.623	−	260.623i	−0.388410	−	0.388410i
$672$	965.309	−	459.147i	1.43647	−	0.683255i
$673$		−	885.893i		−	1.31633i	−0.752872	−	0.658167i	$-0.771332\pi$
$673$		−	885.893i		−	1.31633i	0.752872	−	0.658167i	$-0.228668\pi$
$674$	13.5703	−	39.6134i	0.0201340	−	0.0587737i
$675$	−442.561	−	443.159i	−0.655646	−	0.656533i
$676$	−296.906	−	607.308i	−0.439210	−	0.898384i
$677$			948.372i			1.40085i	0.713728	+	0.700423i	$0.247005\pi$
$677$			948.372i			1.40085i	−0.713728	+	0.700423i	$0.752995\pi$
$678$	−621.827	−	418.209i	−0.917149	−	0.616827i
$679$		−	925.571i		−	1.36314i
$680$	−22.9066	+	110.326i	−0.0336862	+	0.162244i
$681$	64.1418	+	111.155i	0.0941876	+	0.163223i
$682$	248.664	−	725.883i	0.364610	−	1.06434i
$683$	495.730	+	495.730i	0.725813	+	0.725813i	0.969783	−	0.243970i	$-0.0784499\pi$
$683$	495.730	+	495.730i	0.725813	+	0.725813i	−0.243970	+	0.969783i	$0.578450\pi$
$684$	128.201	−	304.302i	0.187428	−	0.444886i
$685$	−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
$690$	−26.4403	−	135.051i	−0.0383193	−	0.195726i
$691$	−842.804	−	842.804i	−1.21969	−	1.21969i	−0.967741	−	0.251946i	$-0.918929\pi$
$691$	−842.804	−	842.804i	−1.21969	−	1.21969i	−0.251946	−	0.967741i	$-0.581071\pi$
$692$	−479.715	−	372.368i	−0.693229	−	0.538104i
$693$	−1601.38	−	925.521i	−2.31080	−	1.33553i
$694$	575.999	+	197.319i	0.829970	+	0.284321i
$695$	43.0135	−	43.0135i	0.0618899	−	0.0618899i
$696$	280.235	+	849.459i	0.402637	+	1.22049i
$697$	−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
$700$	−129.136	−	1025.04i	−0.184480	−	1.46435i
$701$	−435.243			−0.620889			−0.310444	−	0.950592i	$-0.600478\pi$
$701$	−435.243			−0.620889			−0.310444	+	0.950592i	$0.600478\pi$
$702$	−157.773	−	684.041i	−0.224747	−	0.974417i
$703$			233.778i			0.332544i
$704$	−1098.72	+	433.708i	−1.56068	+	0.616063i
$705$	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
$708$	468.903	+	64.5031i	0.662293	+	0.0911061i
$709$	688.110	+	688.110i	0.970537	+	0.970537i	0.999578	−	0.0290416i	$-0.00924553\pi$
$709$	688.110	+	688.110i	0.970537	+	0.970537i	−0.0290416	+	0.999578i	$0.509246\pi$
$710$	−44.2010	−	15.1418i	−0.0622549	−	0.0213265i
$711$	−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
$714$	−134.618	−	687.595i	−0.188540	−	0.963019i
$715$	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	$-0.131189\pi$
$720$	−168.598	+	94.7478i	−0.234163	+	0.131594i
$721$	−193.626	+	193.626i	−0.268552	+	0.268552i
$722$	−179.454	+	523.851i	−0.248552	+	0.725555i
$723$	237.714	−	137.173i	0.328788	−	0.189727i
$724$	397.122	−	511.605i	0.548511	−	0.706636i
$725$	864.535			1.19246
$726$	1093.57	+	735.476i	1.50629	+	1.01305i
$727$	516.927			0.711041			0.355520	−	0.934669i	$-0.384304\pi$
$727$	516.927			0.711041			0.355520	+	0.934669i	$0.384304\pi$
$728$	485.604	−	1051.29i	0.667038	−	1.44407i
$729$	0.985176	−	728.999i	0.00135141	−	0.999999i
$730$	−4.26502	+	12.4501i	−0.00584249	+	0.0170550i
$731$	101.751			0.139194
$732$	190.962	−	144.777i	0.260877	−	0.197783i
$733$	623.462	−	623.462i	0.850563	−	0.850563i	−0.139640	−	0.990202i	$-0.544594\pi$
$733$	623.462	−	623.462i	0.850563	−	0.850563i	0.990202	+	0.139640i	$0.0445944\pi$
$734$	−323.050	+	943.025i	−0.440123	+	1.28477i
$735$	−151.000	−	261.676i	−0.205442	−	0.356022i
$736$	544.763	+	43.3435i	0.740167	+	0.0588906i
$737$		−	713.438i		−	0.968030i
$738$	47.0095	−	683.298i	0.0636984	−	0.925877i
$739$	−88.1069	+	88.1069i	−0.119224	+	0.119224i	−0.764202	−	0.644977i	$-0.776867\pi$
$739$	−88.1069	+	88.1069i	−0.119224	+	0.119224i	0.644977	+	0.764202i	$0.276867\pi$
$740$	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	$-0.990293\pi$
$743$	−720.000	+	720.000i	−0.969044	+	0.969044i	0.0304906	+	0.999535i	$0.490293\pi$
$744$	445.514	+	224.483i	0.598809	+	0.301724i
$745$			141.752i			0.190271i
$746$	1090.92	+	373.714i	1.46236	+	0.500957i
$747$	−1151.04	+	307.864i	−1.54088	+	0.412134i
$748$	96.7754	+	768.174i	0.129379	+	1.02697i
$749$	−356.534	+	356.534i	−0.476013	+	0.476013i
$750$	74.6196	+	381.139i	0.0994928	+	0.508186i
$751$	863.481			1.14977			0.574887	−	0.818233i	$-0.305046\pi$
$751$	863.481			1.14977			0.574887	+	0.818233i	$0.305046\pi$
$752$	−602.182	+	1016.64i	−0.800774	+	1.35192i
$753$	541.176	+	145.138i	0.718693	+	0.192747i
$754$	822.025	+	513.125i	1.09022	+	0.680537i
$755$	−61.4461			−0.0813856
$756$	738.025	−	949.457i	0.976223	−	1.25590i
$757$	−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
$760$	−82.3968	+	54.0639i	−0.108417	+	0.0711368i
$761$	913.582	−	913.582i	1.20050	−	1.20050i	0.226489	−	0.974014i	$-0.427275\pi$
$761$	913.582	−	913.582i	1.20050	−	1.20050i	0.974014	−	0.226489i	$-0.0727247\pi$
$762$	−672.010	+	999.200i	−0.881903	+	1.31129i
$763$			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
$768$	−182.003	−	746.123i	−0.236983	−	0.971514i
$769$	638.154	−	638.154i	0.829849	−	0.829849i	−0.157646	−	0.987496i	$-0.550391\pi$
$769$	638.154	−	638.154i	0.829849	−	0.829849i	0.987496	+	0.157646i	$0.0503905\pi$
$770$	242.769	+	495.768i	0.315284	+	0.643854i
$771$	342.157	−	1275.80i	0.443783	−	1.65473i
$772$	−91.5457	−	726.662i	−0.118583	−	0.941272i
$773$	−92.5067	−	92.5067i	−0.119672	−	0.119672i	0.644734	−	0.764407i	$-0.276968\pi$
$773$	−92.5067	−	92.5067i	−0.119672	−	0.119672i	−0.764407	+	0.644734i	$0.776968\pi$
$774$	114.722	+	131.674i	0.148220	+	0.170121i
$775$	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
$778$	153.573	+	52.6091i	0.197394	+	0.0676209i
$779$		−	349.014i		−	0.448029i
$780$	−74.7276	+	195.733i	−0.0958046	+	0.250940i
$781$	−321.042			−0.411066
$782$	116.085	−	338.867i	0.148446	−	0.433334i
$783$	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
$786$	−460.318	+	684.439i	−0.585647	+	0.870788i
$787$	226.028	−	226.028i	0.287202	−	0.287202i	−0.548771	−	0.835973i	$-0.684904\pi$
$787$	226.028	−	226.028i	0.287202	−	0.287202i	0.835973	+	0.548771i	$0.184904\pi$
$788$	31.0629	+	246.568i	0.0394199	+	0.312903i
$789$	−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
$792$	−884.966	+	991.337i	−1.11738	+	1.25169i
$793$	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	$0.324668\pi$
$798$	341.985	−	508.491i	0.428552	−	0.637207i
$799$	547.650	+	547.650i	0.685420	+	0.685420i
$800$	−739.942	−	58.8727i	−0.924927	−	0.0735909i
$801$	332.142	−	88.8369i	0.414659	−	0.110907i
$802$	−1065.03	+	521.525i	−1.32796	+	0.650280i
$803$			90.4284i			0.112613i
$804$	459.531	+	63.2138i	0.571556	+	0.0786242i
$805$		−	255.386i		−	0.317250i
$806$	526.538	−	121.820i	0.653273	−	0.151141i
$807$	−404.800	−	108.563i	−0.501611	−	0.134527i
$808$	−56.7318	−	86.4628i	−0.0702127	−	0.107008i
$809$			775.968i			0.959169i	0.877496	+	0.479585i	$0.159213\pi$
$809$			775.968i			0.959169i	−0.877496	+	0.479585i	$0.840787\pi$
$810$	−121.543	+	180.457i	−0.150053	+	0.222786i
$811$	−627.437	−	627.437i	−0.773658	−	0.773658i	0.205086	−	0.978744i	$-0.434253\pi$
$811$	−627.437	−	627.437i	−0.773658	−	0.773658i	−0.978744	+	0.205086i	$0.934253\pi$
$812$	207.488	+	1646.98i	0.255527	+	2.02830i
$813$	−29.7718	−	51.5931i	−0.0366197	−	0.0634601i
$814$	304.900	−	890.042i	0.374570	−	1.09342i
$815$	10.0885			0.0123785
$816$	−503.361	−	5.72986i	−0.616864	−	0.00702189i
$817$	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	−0.999529	−	0.0307022i	$-0.990226\pi$
$821$	−845.820	−	845.820i	−1.03023	−	1.03023i	−0.0307022	−	0.999529i	$-0.509774\pi$
$822$	−145.826	−	744.844i	−0.177404	−	0.906137i
$823$	−632.140			−0.768092			−0.384046	−	0.923314i	$-0.625470\pi$
$823$	−632.140			−0.768092			−0.384046	+	0.923314i	$0.625470\pi$
$824$	107.928	+	164.489i	0.130981	+	0.199623i
$825$	641.937	+	1112.45i	0.778105	+	1.34842i
$826$	830.980	+	284.667i	1.00603	+	0.344633i
$827$	−533.580	−	533.580i	−0.645200	−	0.645200i	0.306629	−	0.951829i	$-0.400799\pi$
$827$	−533.580	−	533.580i	−0.645200	−	0.645200i	−0.951829	+	0.306629i	$0.900799\pi$
$828$	569.405	−	231.843i	0.687687	−	0.280004i
$829$			34.0426i			0.0410646i	0.999789	+	0.0205323i	$0.00653610\pi$
$829$			34.0426i			0.0410646i	−0.999789	+	0.0205323i	$0.993464\pi$
$830$	336.413	+	115.244i	0.405316	+	0.138848i
$831$	766.411	+	205.544i	0.922276	+	0.247346i
$832$	−668.616	−	495.153i	−0.803625	−	0.595136i
$833$		−	786.385i		−	0.944040i
$834$	225.503	+	151.662i	0.270387	+	0.181849i
$835$		−	37.4624i		−	0.0448651i
$836$	−415.221	+	534.921i	−0.496676	+	0.639858i
$837$	561.233	+	0.379228i	0.670529	+	0.000453079i
$838$	−1397.30	−	478.671i	−1.66742	−	0.571206i
$839$	−63.4338	−	63.4338i	−0.0756064	−	0.0756064i	0.668292	−	0.743899i	$-0.267026\pi$
$839$	−63.4338	−	63.4338i	−0.0756064	−	0.0756064i	−0.743899	+	0.668292i	$0.767026\pi$
$840$	−340.838	+	112.442i	−0.405759	+	0.133859i
$841$	−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
$846$	−91.2377	+	1326.17i	−0.107846	+	1.56758i
$847$	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
$850$	−157.676	+	460.277i	−0.185501	+	0.541502i
$851$	−307.777	+	307.777i	−0.361665	+	0.361665i
$852$	28.4458	−	206.786i	0.0333871	−	0.242706i
$853$	−529.185	−	529.185i	−0.620381	−	0.620381i	0.325248	−	0.945629i	$-0.394552\pi$
$853$	−529.185	−	529.185i	−0.620381	−	0.620381i	−0.945629	+	0.325248i	$0.894552\pi$
$854$	399.406	−	195.582i	0.467689	−	0.229019i
$855$	−55.4777	+	95.9904i	−0.0648862	+	0.112269i
$856$	198.735	+	302.884i	0.232167	+	0.353836i
$857$	941.964			1.09914			0.549571	−	0.835447i	$-0.314791\pi$
$857$	941.964			1.09914			0.549571	+	0.835447i	$0.314791\pi$
$858$	−49.8944	+	1438.75i	−0.0581520	+	1.67687i
$859$		−	51.4741i		−	0.0599233i	−0.999551	−	0.0299617i	$-0.990461\pi$
$859$		−	51.4741i		−	0.0599233i	0.999551	−	0.0299617i	$-0.00953852\pi$
$860$	−6.51484	−	51.7128i	−0.00757540	−	0.0601312i
$861$	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	$-0.797683\pi$
$863$	−182.144	+	182.144i	−0.211059	+	0.211059i	0.593658	+	0.804717i	$0.297683\pi$
$864$	−560.116	−	657.850i	−0.648282	−	0.761400i
$865$	144.178	+	144.178i	0.166679	+	0.166679i
$866$	315.468	−	920.892i	0.364282	−	1.06339i
$867$	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
$870$	−57.7037	−	294.737i	−0.0663261	−	0.338778i
$871$	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
$876$	−58.2456	−	8.01236i	−0.0664904	−	0.00914653i
$877$	−646.826	+	646.826i	−0.737544	+	0.737544i	−0.972102	−	0.234558i	$-0.924636\pi$
$877$	−646.826	+	646.826i	−0.737544	+	0.737544i	0.234558	+	0.972102i	$0.424636\pi$
$878$	−528.759	−	181.136i	−0.602231	−	0.206305i
$879$	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	$0.485113\pi$
$882$	1017.65	−	886.635i	1.15379	−	1.00526i
$883$	128.459			0.145481			0.0727403	−	0.997351i	$-0.476826\pi$
$883$	128.459			0.145481			0.0727403	+	0.997351i	$0.476826\pi$
$884$	−423.110	+	344.060i	−0.478631	+	0.389208i
$885$	−153.496	−	41.1663i	−0.173442	−	0.0465156i
$886$	1301.05	+	445.699i	1.46846	+	0.503046i
$887$	−1047.33			−1.18076			−0.590380	−	0.807126i	$-0.701022\pi$
$887$	−1047.33			−1.18076			−0.590380	+	0.807126i	$0.701022\pi$
$888$	546.267	+	275.250i	0.615166	+	0.309966i
$889$	−1580.16	+	1580.16i	−1.77745	+	1.77745i
$890$	−97.0749	−	33.2548i	−0.109073	−	0.0373649i
$891$	−388.232	+	1443.70i	−0.435726	+	1.62031i
$892$	125.629	+	997.203i	0.140840	+	1.11794i
$893$			677.380i			0.758545i
$894$	−621.478	+	121.673i	−0.695165	+	0.136100i
$895$	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
$900$	−773.413	+	314.908i	−0.859347	+	0.349898i
$901$		−	983.392i		−	1.09144i
$902$	−455.194	+	1328.77i	−0.504650	+	1.47314i
$903$	161.985	+	280.713i	0.179386	+	0.310867i
$904$	−835.396	+	548.138i	−0.924111	+	0.606347i
$905$	−153.762	+	153.762i	−0.169903	+	0.169903i
$906$	−52.7424	−	269.396i	−0.0582146	−	0.297347i
$907$	−1213.59			−1.33803			−0.669014	−	0.743250i	$-0.733283\pi$
$907$	−1213.59			−1.33803			−0.669014	+	0.743250i	$0.733283\pi$
$908$	169.770	−	21.3878i	0.186971	−	0.0235548i
$909$	−100.727	−	58.2154i	−0.110811	−	0.0640433i
$910$	−205.887	+	329.830i	−0.226249	+	0.362450i
$911$	1249.62			1.37170			0.685849	−	0.727744i	$-0.259431\pi$
$911$	1249.62			1.37170			0.685849	+	0.727744i	$0.259431\pi$
$912$	−307.756	−	314.843i	−0.337452	−	0.345223i
$913$	2443.45			2.67628
$914$	−1216.11	+	595.507i	−1.33053	+	0.651540i
$915$	−69.6901	+	40.2147i	−0.0761640	+	0.0439504i
$916$	194.322	+	1542.47i	0.212142	+	1.68392i
$917$	−1082.39	+	1082.39i	−1.18036	+	1.18036i
$918$	−508.780	+	248.715i	−0.554227	+	0.270931i
$919$		−	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
$924$	−1965.19	+	1489.91i	−2.12683	+	1.61245i
$925$	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
$928$	1188.90	+	94.5933i	1.28114	+	0.101932i
$929$	−871.599	−	871.599i	−0.938212	−	0.938212i	0.0599867	−	0.998199i	$-0.480894\pi$
$929$	−871.599	−	871.599i	−0.938212	−	0.938212i	−0.998199	+	0.0599867i	$0.980894\pi$
$930$	−138.991	−	93.4781i	−0.149453	−	0.100514i
$931$	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
$934$	78.9155	−	230.365i	0.0844920	−	0.246643i
$935$		−	259.959i		−	0.278031i
$936$	−922.290	−	159.617i	−0.985352	−	0.170531i
$937$	565.122			0.603119			0.301559	−	0.953447i	$-0.402493\pi$
$937$	565.122			0.603119			0.301559	+	0.953447i	$0.402493\pi$
$938$	814.370	+	278.977i	0.868198	+	0.297417i
$939$	−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	−0.972502	−	0.232893i	$-0.925181\pi$
$941$	−1134.28	−	1134.28i	−1.20540	−	1.20540i	−0.232893	−	0.972502i	$-0.574819\pi$
$942$	128.583	−	191.188i	0.136500	−	0.202960i
$943$	459.489	−	459.489i	0.487263	−	0.487263i
$944$	321.624	−	542.987i	0.340704	−	0.575198i
$945$	−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	$-0.139240\pi$
$947$	456.667	+	456.667i	0.482225	+	0.482225i	−0.423617	+	0.905842i	$0.639240\pi$
$948$	220.640	+	291.026i	0.232743	+	0.306989i
$949$	−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	$0.346670\pi$
$954$	1272.59	−	1108.76i	1.33395	−	1.16222i
$955$	−85.4592	−	85.4592i	−0.0894861	−	0.0894861i
$956$	461.652	−	58.1595i	0.482900	−	0.0608363i
$957$	−1031.43	−	1787.41i	−1.07777	−	1.86773i
$958$	−327.014	−	667.808i	−0.341351	−	0.697086i
$959$		−	1408.53i		−	1.46874i
$960$	29.3169	+	256.190i	0.0305384	+	0.266865i
$961$		−	528.925i		−	0.550390i
$962$	645.615	−	149.370i	0.671118	−	0.155270i
$963$	352.853	+	203.932i	0.366410	+	0.211767i
$964$	−45.7396	−	363.067i	−0.0474477	−	0.376625i
$965$			245.911i			0.254830i
$966$	1119.68	−	219.211i	1.15909	−	0.226927i
$967$	556.304	+	556.304i	0.575289	+	0.575289i	0.933602	−	0.358313i	$-0.116648\pi$
$967$	556.304	+	556.304i	0.575289	+	0.575289i	−0.358313	+	0.933602i	$0.616648\pi$
$968$	1469.16	−	963.975i	1.51772	−	0.995841i
$969$	−249.951	+	144.234i	−0.257948	+	0.148849i
$970$	211.226	+	72.3594i	0.217759	+	0.0745973i
$971$	1135.92			1.16985			0.584924	−	0.811088i	$-0.301124\pi$
$971$	1135.92			1.16985			0.584924	+	0.811088i	$0.301124\pi$
$972$	−895.497	−	377.981i	−0.921293	−	0.388869i
$973$	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	0.534942	−	0.844889i	$-0.320333\pi$
$977$	−302.818	−	302.818i	−0.309947	−	0.309947i	−0.844889	+	0.534942i	$0.820333\pi$
$978$	8.65948	+	44.2306i	0.00885427	+	0.0452255i
$979$	−705.079			−0.720203
$980$	−399.665	+	50.3503i	−0.407822	+	0.0513778i
$981$	1563.32	−	418.136i	1.59360	−	0.426234i
$982$	630.421	−	1840.28i	0.641977	−	1.87401i
$983$	−859.837	−	859.837i	−0.874707	−	0.874707i	0.118274	−	0.992981i	$-0.462264\pi$
$983$	−859.837	−	859.837i	−0.874707	−	0.874707i	−0.992981	+	0.118274i	$0.962264\pi$
$984$	−815.538	−	410.929i	−0.828799	−	0.417611i
$985$		−	83.4416i		−	0.0847123i
$986$	253.345	−	739.547i	0.256942	−	0.750048i
$987$	−639.024	+	2382.72i	−0.647441	+	2.41411i
$988$	−474.450	−	48.8880i	−0.480213	−	0.0494818i
$989$			165.691i			0.167534i
$990$	336.408	−	293.100i	0.339806	−	0.296060i
$991$			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
$994$	125.538	−	366.461i	0.126296	−	0.368673i
$995$	161.730	+	161.730i	0.162543	+	0.162543i
$996$	−216.500	+	1573.84i	−0.217370	+	1.58016i
$997$	−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.83.5	yes	96
3.2	odd	2	inner	156.3.l.c.83.44	yes	96
4.3	odd	2	inner	156.3.l.c.83.20	yes	96
12.11	even	2	inner	156.3.l.c.83.29	yes	96
13.8	odd	4	inner	156.3.l.c.47.29	yes	96
39.8	even	4	inner	156.3.l.c.47.20	yes	96
52.47	even	4	inner	156.3.l.c.47.44	yes	96
156.47	odd	4	inner	156.3.l.c.47.5	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.3.l.c.47.5	✓	96	156.47	odd	4	inner
156.3.l.c.47.20	yes	96	39.8	even	4	inner
156.3.l.c.47.29	yes	96	13.8	odd	4	inner
156.3.l.c.47.44	yes	96	52.47	even	4	inner
156.3.l.c.83.5	yes	96	1.1	even	1	trivial
156.3.l.c.83.20	yes	96	4.3	odd	2	inner
156.3.l.c.83.29	yes	96	12.11	even	2	inner
156.3.l.c.83.44	yes	96	3.2	odd	2	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+(-1.89206 - 0.648159i) q^{2} +(-0.777110 + 2.89760i) q^{3} +(3.15978 + 2.45271i) q^{4} +(-0.949668 - 0.949668i) q^{5} +(3.34845 - 4.97875i) q^{6} +(7.87350 - 7.87350i) q^{7} +(-4.38874 - 6.68872i) q^{8} +(-7.79220 - 4.50351i) q^{9} +(1.18129 + 2.41236i) q^{10} +(13.0508 + 13.0508i) q^{11} +(-9.56248 + 7.24976i) 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} +(11.8243 + 13.5715i) q^{18} +(6.48583 + 6.48583i) q^{19} +(-0.671480 - 5.33000i) q^{20} +(16.6957 + 28.9329i) q^{21} +(-16.2339 - 33.1519i) q^{22} +17.0776i q^{23} +(22.7918 - 7.51897i) q^{24} -23.1963i q^{25} +(13.7676 - 22.0557i) q^{26} +(19.1048 - 19.0790i) q^{27} +(44.1900 - 5.56710i) q^{28} +37.2704i q^{29} +(-7.90807 + 1.54824i) q^{30} +(14.6982 + 14.6982i) q^{31} +(2.53803 - 31.8992i) q^{32} +(-47.9580 + 27.6741i) q^{33} +(-19.8427 - 6.79748i) q^{34} -14.9544 q^{35} +(-13.5758 - 33.3421i) 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} +(-12.8362 - 65.5642i) q^{42} +9.70221 q^{43} +(9.22781 + 73.2475i) q^{44} +(3.12316 + 11.6768i) q^{45} +(11.0690 - 32.3119i) q^{46} +(52.2200 + 52.2200i) q^{47} +(-47.9969 - 0.546359i) q^{48} -74.9840i q^{49} +(-15.0349 + 43.8887i) q^{50} +(-8.14984 + 30.3882i) q^{51} +(-40.3447 + 32.8071i) q^{52} -93.7692i q^{53} +(-48.5136 + 23.7156i) q^{54} -24.7879i q^{55} +(-87.2184 - 18.1088i) q^{56} +(-23.8336 + 13.7532i) q^{57} +(24.1572 - 70.5179i) q^{58} +(-27.8906 - 27.8906i) q^{59} +(15.9660 + 2.19632i) 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} +(108.677 - 21.2767i) q^{66} +(-27.3331 - 27.3331i) q^{67} +(33.1378 + 25.7225i) q^{68} +(-49.4842 - 13.2712i) q^{69} +(28.2947 + 9.69285i) q^{70} +(-12.2997 + 12.2997i) q^{71} +(4.07527 + 71.8846i) q^{72} +(3.46448 + 3.46448i) q^{73} +(-22.4179 - 45.7804i) q^{74} +(67.2135 + 18.0260i) q^{75} +(4.58593 + 36.4017i) q^{76} +205.511 q^{77} +(53.2096 + 57.0327i) q^{78} -30.4341i q^{79} +(10.9512 - 18.4886i) q^{80} +(40.4368 + 70.1845i) q^{81} +(33.4683 + 68.3469i) q^{82} +(93.6129 - 93.6129i) q^{83} +(-18.2092 + 132.371i) q^{84} +(-9.95952 - 9.95952i) q^{85} +(-18.3572 - 6.28858i) q^{86} +(-107.995 - 28.9632i) q^{87} +(30.0165 - 144.570i) q^{88} +(-27.0128 + 27.0128i) q^{89} +(1.65924 - 24.1176i) 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} +(90.4589 + 32.1434i) q^{96} +(58.7776 - 58.7776i) q^{97} +(-48.6016 + 141.874i) 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

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