LMFDB - Embedded newform 105.3.w.a.38.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(17,105)] 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("105.17"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			38.20
Character	$\chi$	$=$	105.38
Dual form			105.3.w.a.47.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.415874 - 1.55206i) q^{2} +(0.0778404 - 2.99899i) q^{3} +(1.22815 + 0.709073i) q^{4} +(4.73382 - 1.60964i) q^{5} +(-4.62225 - 1.36802i) q^{6} +(3.98085 + 5.75785i) q^{7} +(6.15604 - 6.15604i) q^{8} +(-8.98788 - 0.466885i) q^{9} +(-0.529598 - 8.01660i) q^{10} +(-11.9074 - 6.87474i) q^{11} +(2.22210 - 3.62801i) q^{12} +(-13.4181 + 13.4181i) q^{13} +(10.5921 - 3.78400i) q^{14} +(-4.45883 - 14.3220i) q^{15} +(-4.15814 - 7.20211i) q^{16} +(3.17420 + 11.8463i) q^{17} +(-4.46247 + 13.7556i) q^{18} +(-0.412457 - 0.714396i) q^{19} +(6.95519 + 1.37974i) q^{20} +(17.5776 - 11.4903i) q^{21} +(-15.6220 + 15.6220i) q^{22} +(5.43425 + 1.45610i) q^{23} +(-17.9827 - 18.9411i) q^{24} +(19.8181 - 15.2395i) q^{25} +(15.2455 + 26.4061i) q^{26} +(-2.09980 + 26.9182i) q^{27} +(0.806351 + 9.89421i) q^{28} -4.58981 q^{29} +(-24.0829 + 0.964243i) q^{30} +(4.73029 + 2.73103i) q^{31} +(20.7298 - 5.55454i) q^{32} +(-21.5441 + 35.1750i) q^{33} +19.7063 q^{34} +(28.1127 + 20.8489i) q^{35} +(-10.7074 - 6.94647i) q^{36} +(41.2492 + 11.0527i) q^{37} +(-1.28032 + 0.343060i) q^{38} +(39.1964 + 41.2853i) q^{39} +(19.2325 - 39.0506i) q^{40} -68.0906 q^{41} +(-10.5237 - 32.0601i) q^{42} +(-24.3339 - 24.3339i) q^{43} +(-9.74938 - 16.8864i) q^{44} +(-43.2985 + 12.2571i) q^{45} +(4.51993 - 7.82875i) q^{46} +(24.0846 + 6.45346i) q^{47} +(-21.9227 + 11.9096i) q^{48} +(-17.3056 + 45.8423i) q^{49} +(-15.4109 - 37.0967i) q^{50} +(35.7740 - 8.59728i) q^{51} +(-25.9939 + 6.96505i) q^{52} +(3.61069 + 13.4753i) q^{53} +(40.9056 + 14.4536i) q^{54} +(-67.4333 - 13.3771i) q^{55} +(59.9518 + 10.9393i) q^{56} +(-2.17457 + 1.18134i) q^{57} +(-1.90879 + 7.12369i) q^{58} +(42.3877 + 24.4725i) q^{59} +(4.67921 - 20.7512i) q^{60} +(-11.4199 + 6.59330i) q^{61} +(6.20594 - 6.20594i) q^{62} +(-33.0912 - 53.6095i) q^{63} -67.7492i q^{64} +(-41.9206 + 85.1174i) q^{65} +(45.6342 + 48.0663i) q^{66} +(-6.80245 - 25.3871i) q^{67} +(-4.50148 + 16.7998i) q^{68} +(4.78984 - 16.1839i) q^{69} +(44.0501 - 34.9623i) q^{70} -111.772i q^{71} +(-58.2039 + 52.4556i) q^{72} +(1.34482 + 5.01894i) q^{73} +(34.3090 - 59.4249i) q^{74} +(-44.1606 - 60.6205i) q^{75} -1.16985i q^{76} +(-7.81789 - 95.9283i) q^{77} +(80.3782 - 43.6658i) q^{78} +(49.9119 - 28.8166i) q^{79} +(-31.2767 - 27.4004i) q^{80} +(80.5640 + 8.39262i) q^{81} +(-28.3171 + 105.681i) q^{82} +(-105.311 - 105.311i) q^{83} +(29.7354 - 1.64807i) q^{84} +(34.0944 + 50.9688i) q^{85} +(-47.8876 + 27.6479i) q^{86} +(-0.357273 + 13.7648i) q^{87} +(-115.624 + 30.9813i) q^{88} +(-62.2378 + 35.9330i) q^{89} +(1.01713 + 72.2995i) q^{90} +(-130.675 - 23.8440i) q^{91} +(5.64159 + 5.64159i) q^{92} +(8.55855 - 13.9735i) q^{93} +(20.0324 - 34.6971i) q^{94} +(-3.10242 - 2.71791i) q^{95} +(-15.0444 - 62.6009i) q^{96} +(89.5020 + 89.5020i) q^{97} +(63.9532 + 45.9241i) q^{98} +(103.813 + 67.3487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.415874	−	1.55206i	0.207937	−	0.776032i	−0.780597	−	0.625035i	$-0.785085\pi$
$2$	0.415874	−	1.55206i	0.207937	−	0.776032i	0.988534	−	0.150997i	$-0.0482485\pi$
$3$	0.0778404	−	2.99899i	0.0259468	−	0.999663i
$3$	0.0778404	−	2.99899i	0.0259468	−	0.999663i
$4$	1.22815	+	0.709073i	0.307037	+	0.177268i
$5$	4.73382	−	1.60964i	0.946764	−	0.321929i
$5$	4.73382	−	1.60964i	0.946764	−	0.321929i
$6$	−4.62225	−	1.36802i	−0.770376	−	0.228003i
$7$	3.98085	+	5.75785i	0.568693	+	0.822550i
$7$	3.98085	+	5.75785i	0.568693	+	0.822550i
$8$	6.15604	−	6.15604i	0.769505	−	0.769505i
$9$	−8.98788	−	0.466885i	−0.998654	−	0.0518761i
$10$	−0.529598	−	8.01660i	−0.0529598	−	0.801660i
$11$	−11.9074	−	6.87474i	−1.08249	−	0.624976i	−0.150923	−	0.988545i	$-0.548225\pi$
$11$	−11.9074	−	6.87474i	−1.08249	−	0.624976i	−0.931567	+	0.363569i	$0.881558\pi$
$12$	2.22210	−	3.62801i	0.185175	−	0.302335i
$13$	−13.4181	+	13.4181i	−1.03216	+	1.03216i	−0.0326986	+	0.999465i	$0.510410\pi$
$13$	−13.4181	+	13.4181i	−1.03216	+	1.03216i	−0.999465	+	0.0326986i	$0.989590\pi$
$14$	10.5921	−	3.78400i	0.756577	−	0.270286i
$15$	−4.45883	−	14.3220i	−0.297255	−	0.954798i
$16$	−4.15814	−	7.20211i	−0.259884	−	0.450132i
$17$	3.17420	+	11.8463i	0.186718	+	0.696840i	0.994256	+	0.107025i	$0.0341326\pi$
$17$	3.17420	+	11.8463i	0.186718	+	0.696840i	−0.807539	+	0.589815i	$0.799201\pi$
$18$	−4.46247	+	13.7556i	−0.247915	+	0.764200i
$19$	−0.412457	−	0.714396i	−0.0217082	−	0.0375998i	0.854967	−	0.518682i	$-0.173577\pi$
$19$	−0.412457	−	0.714396i	−0.0217082	−	0.0375998i	−0.876675	+	0.481082i	$0.840244\pi$
$20$	6.95519	+	1.37974i	0.347760	+	0.0689868i
$21$	17.5776	−	11.4903i	0.837029	−	0.547159i
$22$	−15.6220	+	15.6220i	−0.710092	+	0.710092i
$23$	5.43425	+	1.45610i	0.236272	+	0.0633088i	0.375012	−	0.927020i	$-0.377639\pi$
$23$	5.43425	+	1.45610i	0.236272	+	0.0633088i	−0.138740	+	0.990329i	$0.544305\pi$
$24$	−17.9827	−	18.9411i	−0.749280	−	0.789212i
$25$	19.8181	−	15.2395i	0.792724	−	0.609581i
$26$	15.2455	+	26.4061i	0.586367	+	1.01562i
$27$	−2.09980	+	26.9182i	−0.0777706	+	0.996971i
$28$	0.806351	+	9.89421i	0.0287983	+	0.353365i
$29$	−4.58981			−0.158269			−0.0791347	−	0.996864i	$-0.525216\pi$
$29$	−4.58981			−0.158269			−0.0791347	+	0.996864i	$0.525216\pi$
$30$	−24.0829	+	0.964243i	−0.802764	+	0.0321414i
$31$	4.73029	+	2.73103i	0.152590	+	0.0880978i	0.574351	−	0.818609i	$-0.305255\pi$
$31$	4.73029	+	2.73103i	0.152590	+	0.0880978i	−0.421761	+	0.906707i	$0.638588\pi$
$32$	20.7298	−	5.55454i	0.647807	−	0.173579i
$33$	−21.5441	+	35.1750i	−0.652853	+	1.06591i
$34$	19.7063			0.579596
$35$	28.1127	+	20.8489i	0.803221	+	0.595681i
$36$	−10.7074	−	6.94647i	−0.297428	−	0.192957i
$37$	41.2492	+	11.0527i	1.11484	+	0.298721i	0.768795	−	0.639495i	$-0.220857\pi$
$37$	41.2492	+	11.0527i	1.11484	+	0.298721i	0.346048	+	0.938217i	$0.387523\pi$
$38$	−1.28032	+	0.343060i	−0.0336926	+	0.00902790i
$39$	39.1964	+	41.2853i	1.00504	+	1.05860i
$40$	19.2325	−	39.0506i	0.480814	−	0.976266i
$41$	−68.0906			−1.66075			−0.830373	−	0.557208i	$-0.811873\pi$
$41$	−68.0906			−1.66075			−0.830373	+	0.557208i	$0.811873\pi$
$42$	−10.5237	−	32.0601i	−0.250564	−	0.763336i
$43$	−24.3339	−	24.3339i	−0.565905	−	0.565905i	0.365074	−	0.930979i	$-0.381044\pi$
$43$	−24.3339	−	24.3339i	−0.565905	−	0.565905i	−0.930979	+	0.365074i	$0.881044\pi$
$44$	−9.74938	−	16.8864i	−0.221577	−	0.383782i
$45$	−43.2985	+	12.2571i	−0.962189	+	0.272381i
$46$	4.51993	−	7.82875i	0.0982594	−	0.170190i
$47$	24.0846	+	6.45346i	0.512439	+	0.137308i	0.505767	−	0.862670i	$-0.331209\pi$
$47$	24.0846	+	6.45346i	0.512439	+	0.137308i	0.00667218	+	0.999978i	$0.497876\pi$
$48$	−21.9227	+	11.9096i	−0.456724	+	0.248117i
$49$	−17.3056	+	45.8423i	−0.353176	+	0.935557i
$50$	−15.4109	−	37.0967i	−0.308218	−	0.741934i
$51$	35.7740	−	8.59728i	0.701450	−	0.168574i
$52$	−25.9939	+	6.96505i	−0.499883	+	0.133943i
$53$	3.61069	+	13.4753i	0.0681263	+	0.254251i	0.991587	−	0.129442i	$-0.0413187\pi$
$53$	3.61069	+	13.4753i	0.0681263	+	0.254251i	−0.923461	+	0.383693i	$0.874652\pi$
$54$	40.9056	+	14.4536i	0.757510	+	0.267660i
$55$	−67.4333	−	13.3771i	−1.22606	−	0.243220i
$56$	59.9518	+	10.9393i	1.07057	+	0.195344i
$57$	−2.17457	+	1.18134i	−0.0381504	+	0.0207253i
$58$	−1.90879	+	7.12369i	−0.0329101	+	0.122822i
$59$	42.3877	+	24.4725i	0.718435	+	0.414789i	0.814176	−	0.580618i	$-0.197189\pi$
$59$	42.3877	+	24.4725i	0.718435	+	0.414789i	−0.0957414	+	0.995406i	$0.530522\pi$
$60$	4.67921	−	20.7512i	0.0779869	−	0.345853i
$61$	−11.4199	+	6.59330i	−0.187212	+	0.108087i	−0.590677	−	0.806908i	$-0.701139\pi$
$61$	−11.4199	+	6.59330i	−0.187212	+	0.108087i	0.403465	+	0.914995i	$0.367806\pi$
$62$	6.20594	−	6.20594i	0.100096	−	0.100096i
$63$	−33.0912	−	53.6095i	−0.525257	−	0.850944i
$64$		−	67.7492i		−	1.05858i
$65$	−41.9206	+	85.1174i	−0.644932	+	1.30950i
$66$	45.6342	+	48.0663i	0.691428	+	0.728277i
$67$	−6.80245	−	25.3871i	−0.101529	−	0.378912i	0.896399	−	0.443248i	$-0.146174\pi$
$67$	−6.80245	−	25.3871i	−0.101529	−	0.378912i	−0.997928	+	0.0643359i	$0.979507\pi$
$68$	−4.50148	+	16.7998i	−0.0661982	+	0.247055i
$69$	4.78984	−	16.1839i	0.0694180	−	0.234550i
$70$	44.0501	−	34.9623i	0.629287	−	0.499461i
$71$		−	111.772i		−	1.57426i	−0.616790	−	0.787128i	$-0.711567\pi$
$71$		−	111.772i		−	1.57426i	0.616790	−	0.787128i	$-0.288433\pi$
$72$	−58.2039	+	52.4556i	−0.808388	+	0.728550i
$73$	1.34482	+	5.01894i	0.0184222	+	0.0687526i	0.974525	−	0.224279i	$-0.0720026\pi$
$73$	1.34482	+	5.01894i	0.0184222	+	0.0687526i	−0.956103	+	0.293031i	$0.905336\pi$
$74$	34.3090	−	59.4249i	0.463635	−	0.803039i
$75$	−44.1606	−	60.6205i	−0.588807	−	0.808273i
$76$		−	1.16985i		−	0.0153927i
$77$	−7.81789	−	95.9283i	−0.101531	−	1.24582i
$78$	80.3782	−	43.6658i	1.03049	−	0.559818i
$79$	49.9119	−	28.8166i	0.631796	−	0.364767i	−0.149651	−	0.988739i	$-0.547815\pi$
$79$	49.9119	−	28.8166i	0.631796	−	0.364767i	0.781447	+	0.623971i	$0.214482\pi$
$80$	−31.2767	−	27.4004i	−0.390959	−	0.342505i
$81$	80.5640	+	8.39262i	0.994618	+	0.103613i
$82$	−28.3171	+	105.681i	−0.345331	+	1.28879i
$83$	−105.311	−	105.311i	−1.26881	−	1.26881i	−0.946702	−	0.322110i	$-0.895608\pi$
$83$	−105.311	−	105.311i	−1.26881	−	1.26881i	−0.322110	−	0.946702i	$-0.604392\pi$
$84$	29.7354	−	1.64807i	0.353993	−	0.0196199i
$85$	34.0944	+	50.9688i	0.401111	+	0.599633i
$86$	−47.8876	+	27.6479i	−0.556833	+	0.321488i
$87$	−0.357273	+	13.7648i	−0.00410659	+	0.158216i
$88$	−115.624	+	30.9813i	−1.31390	+	0.352060i
$89$	−62.2378	+	35.9330i	−0.699301	+	0.403742i	−0.807087	−	0.590433i	$-0.798957\pi$
$89$	−62.2378	+	35.9330i	−0.699301	+	0.403742i	0.107786	+	0.994174i	$0.465624\pi$
$90$	1.01713	+	72.2995i	0.0113015	+	0.803328i
$91$	−130.675	−	23.8440i	−1.43599	−	0.262021i
$92$	5.64159	+	5.64159i	0.0613217	+	0.0613217i
$93$	8.55855	−	13.9735i	0.0920274	−	0.150253i
$94$	20.0324	−	34.6971i	0.213110	−	0.369118i
$95$	−3.10242	−	2.71791i	−0.0326570	−	0.0286096i
$96$	−15.0444	−	62.6009i	−0.156712	−	0.652093i
$97$	89.5020	+	89.5020i	0.922701	+	0.922701i	0.997220	−	0.0745185i	$-0.0237420\pi$
$97$	89.5020	+	89.5020i	0.922701	+	0.922701i	−0.0745185	+	0.997220i	$0.523742\pi$
$98$	63.9532	+	45.9241i	0.652584	+	0.468613i
$99$	103.813	+	67.3487i	1.04861	+	0.680290i
$100$	35.1455	−	4.66397i	0.351455	−	0.0466397i
$101$	−12.2793	+	21.2684i	−0.121577	+	0.210578i	−0.920390	−	0.391002i	$-0.872129\pi$
$101$	−12.2793	+	21.2684i	−0.121577	+	0.210578i	0.798813	+	0.601580i	$0.205462\pi$
$102$	1.53394	−	59.0989i	0.0150387	−	0.579401i
$103$	192.555	+	51.5949i	1.86947	+	0.500922i	0.999976	+	0.00697128i	$0.00221905\pi$
$103$	192.555	+	51.5949i	1.86947	+	0.500922i	0.869490	+	0.493951i	$0.164448\pi$
$104$			165.205i			1.58851i
$105$	64.7138	−	82.6869i	0.616322	−	0.787494i
$106$	22.4161			0.211473
$107$	30.0690	−	112.219i	0.281019	−	1.04878i	−0.670681	−	0.741746i	$-0.733998\pi$
$107$	30.0690	−	112.219i	0.281019	−	1.04878i	0.951700	−	0.307031i	$-0.0993354\pi$
$108$	−21.6659	+	31.5707i	−0.200610	+	0.292321i
$109$	−120.456	−	69.5451i	−1.10510	−	0.638028i	−0.167542	−	0.985865i	$-0.553583\pi$
$109$	−120.456	−	69.5451i	−1.10510	−	0.638028i	−0.937555	+	0.347837i	$0.886916\pi$
$110$	−48.8059	+	99.0977i	−0.443690	+	0.900888i
$111$	36.3578	−	122.846i	0.327547	−	1.10672i
$112$	24.9157	−	52.6125i	0.222462	−	0.469754i
$113$	−159.072	+	159.072i	−1.40772	+	1.40772i	−0.636157	+	0.771560i	$0.719477\pi$
$113$	−159.072	+	159.072i	−1.40772	+	1.40772i	−0.771560	+	0.636157i	$0.780523\pi$
$114$	0.929174	+	3.86637i	0.00815065	+	0.0339155i
$115$	28.0686	−	1.85428i	0.244075	−	0.0161242i
$116$	−5.63698	−	3.25451i	−0.0485947	−	0.0280561i
$117$	126.865	−	114.336i	1.08432	−	0.977229i
$118$	55.6109	−	55.6109i	0.471279	−	0.471279i
$119$	−55.5731	+	65.4349i	−0.467001	+	0.549873i
$120$	−115.615	−	60.7179i	−0.963461	−	0.505983i
$121$	34.0241	+	58.9314i	0.281191	+	0.487036i
$122$	5.48397	+	20.4665i	0.0449506	+	0.167758i
$123$	−5.30020	+	204.203i	−0.0430911	+	1.66019i
$124$	3.87300	+	6.70824i	0.0312339	+	0.0540987i
$125$	69.2850	−	104.041i	0.554280	−	0.832330i
$126$	−96.9671	+	29.0648i	−0.769580	+	0.230673i
$127$	−42.9191	+	42.9191i	−0.337946	+	0.337946i	−0.855594	−	0.517648i	$-0.826808\pi$
$127$	−42.9191	+	42.9191i	−0.337946	+	0.337946i	0.517648	+	0.855594i	$0.326808\pi$
$128$	−22.2317	−	5.95697i	−0.173685	−	0.0465388i
$129$	−74.8713	+	71.0830i	−0.580398	+	0.551031i
$130$	114.674	+	100.462i	0.882108	+	0.772781i
$131$	35.8112	+	62.0268i	0.273368	+	0.473487i	0.969722	−	0.244211i	$-0.0785290\pi$
$131$	35.8112	+	62.0268i	0.273368	+	0.473487i	−0.696354	+	0.717698i	$0.745196\pi$
$132$	−51.4011	+	27.9238i	−0.389402	+	0.211544i
$133$	2.47145	−	5.21877i	0.0185824	−	0.0392389i
$134$	−42.2314			−0.315159
$135$	33.3887	+	130.806i	0.247324	+	0.968933i
$136$	92.4667	+	53.3857i	0.679902	+	0.392542i
$137$	−153.123	+	41.0292i	−1.11769	+	0.299483i	−0.769947	−	0.638108i	$-0.779717\pi$
$137$	−153.123	+	41.0292i	−1.11769	+	0.299483i	−0.347739	+	0.937591i	$0.613050\pi$
$138$	−23.1265	−	14.1646i	−0.167583	−	0.102642i
$139$	−154.872			−1.11419			−0.557094	−	0.830449i	$-0.688084\pi$
$139$	−154.872			−1.11419			−0.557094	+	0.830449i	$0.688084\pi$
$140$	19.7433	+	45.5395i	0.141023	+	0.325282i
$141$	21.2286	−	71.7273i	0.150558	−	0.508704i
$142$	−173.478	−	46.4832i	−1.22167	−	0.327346i
$143$	252.021	−	67.5289i	1.76239	−	0.472230i
$144$	34.0103	+	66.6731i	0.236183	+	0.463008i
$145$	−21.7274	+	7.38797i	−0.149844	+	0.0509515i
$146$	8.34900			0.0571849
$147$	136.133	+	55.4678i	0.926078	+	0.377332i
$148$	42.8230	+	42.8230i	0.289345	+	0.289345i
$149$	−72.9664	−	126.382i	−0.489707	−	0.848198i	0.510222	−	0.860042i	$-0.329563\pi$
$149$	−72.9664	−	126.382i	−0.489707	−	0.848198i	−0.999930	+	0.0118444i	$0.996230\pi$
$150$	−112.452	+	43.3295i	−0.749681	+	0.288863i
$151$	−31.3203	+	54.2483i	−0.207419	+	0.359260i	−0.950901	−	0.309496i	$-0.899840\pi$
$151$	−31.3203	+	54.2483i	−0.207419	+	0.359260i	0.743482	+	0.668756i	$0.233173\pi$
$152$	−6.93695	−	1.85875i	−0.0456378	−	0.0122286i
$153$	−22.9985	−	107.955i	−0.150317	−	0.705588i
$154$	−152.138	−	27.7602i	−0.987910	−	0.180261i
$155$	26.7883	+	5.31413i	0.172828	+	0.0342847i
$156$	18.8647	+	78.4976i	0.120928	+	0.503190i
$157$	−57.6901	+	15.4580i	−0.367453	+	0.0984587i	−0.437820	−	0.899062i	$-0.644249\pi$
$157$	−57.6901	+	15.4580i	−0.367453	+	0.0984587i	0.0703676	+	0.997521i	$0.477583\pi$
$158$	−23.9682	−	89.4505i	−0.151697	−	0.566143i
$159$	40.6933	−	9.77951i	0.255933	−	0.0615063i
$160$	89.1904	−	59.6619i	0.557440	−	0.372887i
$161$	13.2489	+	37.0861i	0.0822915	+	0.230349i
$162$	46.5304	−	121.550i	0.287225	−	0.750310i
$163$	71.3765	−	266.381i	0.437893	−	1.63424i	−0.296155	−	0.955140i	$-0.595704\pi$
$163$	71.3765	−	266.381i	0.437893	−	1.63424i	0.734048	−	0.679098i	$-0.237629\pi$
$164$	−83.6254	−	48.2812i	−0.509911	−	0.294397i
$165$	−45.3668	+	201.191i	−0.274950	+	1.21934i
$166$	−207.246	+	119.654i	−1.24847	+	0.720806i
$167$	−14.7856	+	14.7856i	−0.0885368	+	0.0885368i	−0.749988	−	0.661451i	$-0.769941\pi$
$167$	−14.7856	+	14.7856i	−0.0885368	+	0.0885368i	0.661451	+	0.749988i	$0.269941\pi$
$168$	37.4734	−	178.943i	0.223056	−	1.06514i
$169$		−	191.092i		−	1.13072i
$170$	93.2859	−	31.7201i	0.548740	−	0.186589i
$171$	3.37357	+	6.61348i	0.0197285	+	0.0386753i
$172$	−12.6312	−	47.1402i	−0.0734371	−	0.274071i
$173$	60.2642	−	224.909i	0.348348	−	1.30005i	−0.540304	−	0.841470i	$-0.681691\pi$
$173$	60.2642	−	224.909i	0.348348	−	1.30005i	0.888652	−	0.458582i	$-0.151643\pi$
$174$	21.2153	+	6.27894i	0.121927	+	0.0360859i
$175$	166.640	+	53.4432i	0.952227	+	0.305390i
$176$			114.345i			0.649685i
$177$	76.6924	−	125.215i	0.433290	−	0.707431i
$178$	29.8872	+	111.541i	0.167906	+	0.626633i
$179$	86.7280	−	150.217i	0.484514	−	0.839202i	−0.515328	−	0.856993i	$-0.672330\pi$
$179$	86.7280	−	150.217i	0.484514	−	0.839202i	0.999842	+	0.0177906i	$0.00566322\pi$
$180$	−61.8683	−	15.6482i	−0.343713	−	0.0869344i
$181$		−	60.2204i		−	0.332709i	−0.986066	−	0.166355i	$-0.946800\pi$
$181$		−	60.2204i		−	0.332709i	0.986066	−	0.166355i	$-0.0531997\pi$
$182$	−91.3518	+	192.900i	−0.501933	+	1.05989i
$183$	18.8843	+	34.7615i	0.103193	+	0.189953i
$184$	42.4173	−	24.4897i	0.230529	−	0.133096i
$185$	213.057	−	14.0751i	1.15166	−	0.0760818i
$186$	−18.1285	−	19.0946i	−0.0974650	−	0.102659i
$187$	43.6436	−	162.880i	0.233388	−	0.871017i
$188$	25.0036	+	25.0036i	0.132998	+	0.132998i
$189$	−163.350	+	95.0671i	−0.864286	+	0.503001i
$190$	−5.50859	+	3.68484i	−0.0289926	+	0.0193939i
$191$	−90.3163	+	52.1441i	−0.472860	+	0.273006i	−0.717436	−	0.696624i	$-0.754685\pi$
$191$	−90.3163	+	52.1441i	−0.472860	+	0.273006i	0.244576	+	0.969630i	$0.421351\pi$
$192$	−203.179	−	5.27362i	−1.05822	−	0.0274668i
$193$	196.764	−	52.7228i	1.01950	−	0.273175i	0.289908	−	0.957054i	$-0.406375\pi$
$193$	196.764	−	52.7228i	1.01950	−	0.273175i	0.729595	+	0.683879i	$0.239708\pi$
$194$	176.134	−	101.691i	0.907910	−	0.524182i
$195$	252.003	+	132.345i	1.29232	+	0.678692i
$196$	−53.7594	+	44.0303i	−0.274283	+	0.224644i
$197$	189.124	+	189.124i	0.960018	+	0.960018i	0.999231	−	0.0392131i	$-0.0124851\pi$
$197$	189.124	+	189.124i	0.960018	+	0.960018i	−0.0392131	+	0.999231i	$0.512485\pi$
$198$	147.703	−	133.115i	0.745972	−	0.672299i
$199$	49.7166	−	86.1117i	0.249832	−	0.432722i	−0.713647	−	0.700506i	$-0.752958\pi$
$199$	49.7166	−	86.1117i	0.249832	−	0.432722i	0.963479	+	0.267783i	$0.0862912\pi$
$200$	28.1858	−	215.816i	0.140929	−	1.07908i
$201$	−76.6651	+	18.4243i	−0.381419	+	0.0916634i
$202$	27.9032	+	27.9032i	0.138135	+	0.138135i
$203$	−18.2714	−	26.4275i	−0.0900068	−	0.130184i
$204$	50.0319	+	14.8076i	0.245254	+	0.0725862i
$205$	−322.329	+	109.602i	−1.57233	+	0.534642i
$206$	160.157	−	277.401i	0.777463	−	1.34661i
$207$	−48.1626	−	15.6245i	−0.232669	−	0.0754805i
$208$	152.433	+	40.8444i	0.732853	+	0.196367i
$209$			11.3421i			0.0542685i
$210$	−101.423	−	134.827i	−0.482965	−	0.642035i
$211$	3.16077			0.0149799			0.00748997	−	0.999972i	$-0.497616\pi$
$211$	3.16077			0.0149799			0.00748997	+	0.999972i	$0.497616\pi$
$212$	−5.12049	+	19.1099i	−0.0241532	+	0.0901411i
$213$	−335.204	−	8.70039i	−1.57373	−	0.0408469i
$214$	−161.666	−	93.3381i	−0.755450	−	0.436159i
$215$	−154.361	−	76.0234i	−0.717959	−	0.353597i
$216$	152.783	+	178.636i	0.707330	+	0.827019i
$217$	3.10571	+	38.1081i	0.0143120	+	0.175613i
$218$	−158.033	+	158.033i	−0.724921	+	0.724921i
$219$	15.1564	−	3.64243i	0.0692075	−	0.0166321i
$220$	−73.3329	−	64.2442i	−0.333331	−	0.292019i
$221$	−201.547	−	116.363i	−0.911977	−	0.526530i
$222$	−175.544	−	107.518i	−0.790739	−	0.484315i
$223$	−90.0928	+	90.0928i	−0.404004	+	0.404004i	−0.879641	−	0.475638i	$-0.842217\pi$
$223$	−90.0928	+	90.0928i	−0.404004	+	0.404004i	0.475638	+	0.879641i	$0.342217\pi$
$224$	114.505	+	97.2474i	0.511181	+	0.434140i
$225$	−185.238	+	127.718i	−0.823279	+	0.567637i
$226$	180.736	+	313.044i	0.799717	+	1.38515i
$227$	38.1818	+	142.497i	0.168202	+	0.627738i	0.997610	+	0.0690950i	$0.0220112\pi$
$227$	38.1818	+	142.497i	0.168202	+	0.627738i	−0.829408	+	0.558643i	$0.811322\pi$
$228$	−3.50836	−	0.0910614i	−0.0153875	−	0.000399392i
$229$	−44.3417	−	76.8022i	−0.193632	−	0.335381i	0.752819	−	0.658227i	$-0.228693\pi$
$229$	−44.3417	−	76.8022i	−0.193632	−	0.335381i	−0.946451	+	0.322847i	$0.895360\pi$
$230$	8.79503	−	44.3354i	0.0382393	−	0.192763i
$231$	−288.297	+	15.9787i	−1.24804	+	0.0691718i
$232$	−28.2551	+	28.2551i	−0.121789	+	0.121789i
$233$	139.034	+	37.2542i	0.596714	+	0.159889i	0.544520	−	0.838748i	$-0.316712\pi$
$233$	139.034	+	37.2542i	0.596714	+	0.159889i	0.0521942	+	0.998637i	$0.483379\pi$
$234$	−124.697	−	244.452i	−0.532891	−	1.04467i
$235$	124.400	−	8.21820i	0.529362	−	0.0349711i
$236$	34.7056	+	60.1119i	0.147058	+	0.254711i
$237$	−82.5356	−	151.928i	−0.348252	−	0.641048i
$238$	78.4477	+	113.466i	0.329612	+	0.476746i
$239$	−3.88680			−0.0162628			−0.00813138	−	0.999967i	$-0.502588\pi$
$239$	−3.88680			−0.0162628			−0.00813138	+	0.999967i	$0.502588\pi$
$240$	−84.6080	+	91.6657i	−0.352533	+	0.381941i
$241$	−158.142	−	91.3034i	−0.656191	−	0.378852i	0.134633	−	0.990896i	$-0.457014\pi$
$241$	−158.142	−	91.3034i	−0.656191	−	0.378852i	−0.790824	+	0.612043i	$0.790348\pi$
$242$	105.615	−	28.2995i	0.436426	−	0.116940i
$243$	31.4405	−	240.957i	0.129385	−	0.991594i
$244$	−18.7005			−0.0766415
$245$	−8.13190	+	244.865i	−0.0331914	+	0.999449i
$246$	314.732	+	93.1490i	1.27940	+	0.378655i
$247$	15.1203	+	4.05146i	0.0612156	+	0.0164027i
$248$	45.9322	−	12.3075i	0.185210	−	0.0496270i
$249$	−324.025	+	307.630i	−1.30131	+	1.23546i
$250$	−132.665	−	150.803i	−0.530660	−	0.603212i
$251$	391.380			1.55928			0.779641	−	0.626227i	$-0.215402\pi$
$251$	391.380			1.55928			0.779641	+	0.626227i	$0.215402\pi$
$252$	−2.62793	−	89.3045i	−0.0104283	−	0.354383i
$253$	−54.6975	−	54.6975i	−0.216196	−	0.216196i
$254$	48.7642	+	84.4621i	0.191985	+	0.332528i
$255$	155.509	−	98.2813i	0.609839	−	0.385417i
$256$	117.007	−	202.662i	0.457059	−	0.791649i
$257$	−175.422	−	47.0043i	−0.682577	−	0.182896i	−0.0991636	−	0.995071i	$-0.531617\pi$
$257$	−175.422	−	47.0043i	−0.682577	−	0.182896i	−0.583414	+	0.812175i	$0.698283\pi$
$258$	79.1883	+	145.767i	0.306931	+	0.564987i
$259$	100.567	+	281.506i	0.388291	+	1.08690i
$260$	−111.839	+	74.8122i	−0.430151	+	0.287739i
$261$	41.2527	+	2.14292i	0.158056	+	0.00821041i
$262$	111.163	−	29.7859i	0.424285	−	0.113687i
$263$	16.3149	+	60.8881i	0.0620339	+	0.231514i	0.989982	−	0.141197i	$-0.0450951\pi$
$263$	16.3149	+	60.8881i	0.0620339	+	0.231514i	−0.927948	+	0.372711i	$0.878428\pi$
$264$	83.9123	+	349.166i	0.317850	+	1.32260i
$265$	38.7828	+	57.9776i	0.146350	+	0.218784i
$266$	−7.07205	−	6.00621i	−0.0265866	−	0.0225797i
$267$	102.918	+	189.448i	0.385461	+	0.709541i
$268$	9.64686	−	36.0026i	0.0359958	−	0.134338i
$269$	71.9710	+	41.5525i	0.267550	+	0.154470i	0.627774	−	0.778396i	$-0.283966\pi$
$269$	71.9710	+	41.5525i	0.267550	+	0.154470i	−0.360224	+	0.932866i	$0.617300\pi$
$270$	216.905	+	2.57746i	0.803351	+	0.00954615i
$271$	−308.322	+	178.010i	−1.13772	+	0.656862i	−0.945865	−	0.324561i	$-0.894783\pi$
$271$	−308.322	+	178.010i	−1.13772	+	0.656862i	−0.191854	+	0.981423i	$0.561450\pi$
$272$	72.1195	−	72.1195i	0.265145	−	0.265145i
$273$	−81.6796	+	390.037i	−0.299193	+	1.42871i
$274$			254.720i			0.929634i
$275$	−340.750	+	45.2190i	−1.23909	+	0.164433i
$276$	17.3582	−	16.4799i	0.0628921	−	0.0597099i
$277$	111.373	+	415.649i	0.402068	+	1.50054i	0.809399	+	0.587259i	$0.199793\pi$
$277$	111.373	+	415.649i	0.402068	+	1.50054i	−0.407331	+	0.913281i	$0.633540\pi$
$278$	−64.4074	+	240.372i	−0.231681	+	0.864646i
$279$	−41.2402	−	26.7547i	−0.147814	−	0.0958950i
$280$	301.410	−	44.7167i	1.07646	−	0.159703i
$281$			332.132i			1.18196i	0.806685	+	0.590982i	$0.201260\pi$
$281$			332.132i			1.18196i	−0.806685	+	0.590982i	$0.798740\pi$
$282$	−102.497	−	62.7777i	−0.363464	−	0.222616i
$283$	−82.3270	−	307.249i	−0.290908	−	1.08568i	−0.944413	−	0.328762i	$-0.893369\pi$
$283$	−82.3270	−	307.249i	−0.290908	−	1.08568i	0.653505	−	0.756923i	$-0.273298\pi$
$284$	79.2546	−	137.273i	0.279065	−	0.483355i
$285$	−8.39248	+	9.09256i	−0.0294473	+	0.0319037i
$286$		−	419.236i		−	1.46586i
$287$	−271.059	−	392.055i	−0.944455	−	1.36605i
$288$	−188.911	+	40.2451i	−0.655940	+	0.139740i
$289$	120.022	−	69.2950i	0.415303	−	0.239775i
$290$	2.43076	+	36.7947i	0.00838192	+	0.126878i
$291$	275.383	−	261.449i	0.946332	−	0.898449i
$292$	−1.90715	+	7.11759i	−0.00653134	+	0.0243753i
$293$	95.6683	+	95.6683i	0.326513	+	0.326513i	0.851259	−	0.524746i	$-0.175840\pi$
$293$	95.6683	+	95.6683i	0.326513	+	0.326513i	−0.524746	+	0.851259i	$0.675840\pi$
$294$	142.704	−	188.220i	0.485388	−	0.640205i
$295$	240.048	+	47.6195i	0.813721	+	0.161422i
$296$	321.973	−	185.891i	1.08775	−	0.628010i
$297$	210.059	−	306.090i	0.707269	−	1.03061i
$298$	−226.497	+	60.6897i	−0.760057	+	0.203657i
$299$	−92.4557	+	53.3793i	−0.309216	+	0.178526i
$300$	−11.2515	−	105.764i	−0.0375048	−	0.352547i
$301$	43.2412	−	236.981i	0.143659	−	0.787311i
$302$	71.1716	+	71.1716i	0.235667	+	0.235667i
$303$	62.8277	+	38.4810i	0.207352	+	0.127000i
$304$	−3.43011	+	5.94112i	−0.0112832	+	0.0195432i
$305$	−43.4470	+	49.5935i	−0.142449	+	0.162602i
$306$	−177.118	−	9.20056i	−0.578816	−	0.0300672i
$307$	4.77318	+	4.77318i	0.0155478	+	0.0155478i	0.714838	−	0.699290i	$-0.246500\pi$
$307$	4.77318	+	4.77318i	0.0155478	+	0.0155478i	−0.699290	+	0.714838i	$0.746500\pi$
$308$	58.4186	−	123.358i	0.189671	−	0.400512i
$309$	169.721	−	573.454i	0.549260	−	1.85584i
$310$	19.3885	−	39.3672i	0.0625434	−	0.126991i
$311$	−99.0019	+	171.476i	−0.318334	+	0.551371i	−0.980141	−	0.198304i	$-0.936457\pi$
$311$	−99.0019	+	171.476i	−0.318334	+	0.551371i	0.661806	+	0.749675i	$0.269790\pi$
$312$	495.449	+	12.8596i	1.58798	+	0.0412168i
$313$	124.012	+	33.2288i	0.396203	+	0.106162i	0.451419	−	0.892312i	$-0.350918\pi$
$313$	124.012	+	33.2288i	0.396203	+	0.106162i	−0.0552157	+	0.998474i	$0.517585\pi$
$314$			95.9673i			0.305628i
$315$	−242.940	−	200.512i	−0.771238	−	0.636547i
$316$	81.7323			0.258647
$317$	−70.3506	+	262.552i	−0.221926	+	0.828239i	0.761687	+	0.647945i	$0.224372\pi$
$317$	−70.3506	+	262.552i	−0.221926	+	0.828239i	−0.983613	+	0.180294i	$0.942295\pi$
$318$	1.74488	−	67.2257i	0.00548704	−	0.211401i
$319$	54.6527	+	31.5538i	0.171325	+	0.0989146i
$320$	−109.052	−	320.712i	−0.340788	−	1.00223i
$321$	−334.203	−	98.9119i	−1.04113	−	0.308137i
$322$	63.0700	−	5.14003i	0.195869	−	0.0159628i
$323$	7.15371	−	7.15371i	0.0221477	−	0.0221477i
$324$	92.9937	+	67.4331i	0.287018	+	0.208127i
$325$	−61.4356	+	470.408i	−0.189033	+	1.44741i
$326$	−383.756	−	221.562i	−1.17717	−	0.679638i
$327$	−217.941	+	355.832i	−0.666487	+	1.08817i
$328$	−419.168	+	419.168i	−1.27795	+	1.27795i
$329$	58.7194	+	164.366i	0.178478	+	0.499593i
$330$	293.394	+	154.082i	0.889072	+	0.466916i
$331$	213.741	+	370.210i	0.645742	+	1.11846i	0.984130	+	0.177451i	$0.0567852\pi$
$331$	213.741	+	370.210i	0.645742	+	1.11846i	−0.338388	+	0.941007i	$0.609882\pi$
$332$	−54.6648	−	204.012i	−0.164653	−	0.614493i
$333$	−365.583	−	118.599i	−1.09785	−	0.356153i
$334$	16.7993	+	29.0972i	0.0502973	+	0.0871175i
$335$	−73.0658	−	109.228i	−0.218107	−	0.326055i
$336$	−155.845	−	78.8174i	−0.463824	−	0.234575i
$337$	85.4690	−	85.4690i	0.253617	−	0.253617i	−0.568835	−	0.822452i	$-0.692606\pi$
$337$	85.4690	−	85.4690i	0.253617	−	0.253617i	0.822452	+	0.568835i	$0.192606\pi$
$338$	−296.588	−	79.4704i	−0.877479	−	0.235120i
$339$	464.673	+	489.437i	1.37072	+	1.44377i
$340$	5.73244	+	86.7728i	0.0168601	+	0.255214i
$341$	−37.5503	−	65.0390i	−0.110118	−	0.190730i
$342$	11.6675	−	2.48562i	0.0341156	−	0.00726790i
$343$	−332.844	+	82.8482i	−0.970391	+	0.241540i
$344$	−299.601			−0.870933
$345$	−3.37611	−	84.3217i	−0.00978583	−	0.244411i
$346$	−324.011	−	187.068i	−0.936448	−	0.540658i
$347$	186.488	−	49.9693i	0.537429	−	0.144004i	0.0201125	−	0.999798i	$-0.493598\pi$
$347$	186.488	−	49.9693i	0.537429	−	0.144004i	0.517317	+	0.855794i	$0.326931\pi$
$348$	−10.1990	+	16.6519i	−0.0293076	+	0.0478503i
$349$	358.922			1.02843			0.514215	−	0.857661i	$-0.328083\pi$
$349$	358.922			1.02843			0.514215	+	0.857661i	$0.328083\pi$
$350$	152.248	−	236.410i	0.434996	−	0.675457i
$351$	−333.017	−	389.368i	−0.948766	−	1.10931i
$352$	−285.024	−	76.3720i	−0.809728	−	0.216966i
$353$	267.173	−	71.5888i	0.756864	−	0.202801i	0.140303	−	0.990109i	$-0.455192\pi$
$353$	267.173	−	71.5888i	0.756864	−	0.202801i	0.616561	+	0.787307i	$0.288526\pi$
$354$	−162.448	−	171.105i	−0.458892	−	0.483348i
$355$	−179.913	−	529.109i	−0.506798	−	1.49045i
$356$	−101.916			−0.286282
$357$	191.913	+	171.757i	0.537571	+	0.481111i
$358$	−197.079	−	197.079i	−0.550500	−	0.550500i
$359$	−83.0240	−	143.802i	−0.231265	−	0.400562i	0.726916	−	0.686726i	$-0.240953\pi$
$359$	−83.0240	−	143.802i	−0.231265	−	0.400562i	−0.958181	+	0.286164i	$0.907620\pi$
$360$	−191.092	+	342.003i	−0.530811	+	0.950008i
$361$	180.160	−	312.046i	0.499058	−	0.864393i
$362$	−93.4659	−	25.0441i	−0.258193	−	0.0691827i
$363$	179.383	−	97.4506i	0.494168	−	0.268459i
$364$	−143.582	−	121.942i	−0.394455	−	0.335006i
$365$	14.4449	+	21.5941i	0.0395750	+	0.0591619i
$366$	61.8056	−	14.8533i	0.168868	−	0.0405827i
$367$	−42.7304	+	11.4496i	−0.116432	+	0.0311978i	−0.316564	−	0.948571i	$-0.602529\pi$
$367$	−42.7304	+	11.4496i	−0.116432	+	0.0311978i	0.200133	+	0.979769i	$0.435863\pi$
$368$	−12.1094	−	45.1928i	−0.0329059	−	0.122806i
$369$	611.990	+	31.7905i	1.65851	+	0.0861531i
$370$	66.7595	−	336.532i	0.180431	−	0.909546i
$371$	−63.2150	+	74.4329i	−0.170391	+	0.200628i
$372$	20.4194	−	11.0929i	0.0548909	−	0.0298197i
$373$	−49.6331	+	185.233i	−0.133065	+	0.496604i	−0.999998	−	0.00181972i	$-0.999421\pi$
$373$	−49.6331	+	185.233i	−0.133065	+	0.496604i	0.866934	+	0.498423i	$0.166087\pi$
$374$	−234.650	−	135.475i	−0.627407	−	0.362234i
$375$	−306.626	−	215.884i	−0.817668	−	0.575690i
$376$	187.994	−	108.538i	0.499984	−	0.288666i
$377$	61.5867	−	61.5867i	0.163360	−	0.163360i
$378$	79.6172	+	293.066i	0.210627	+	0.775306i
$379$			449.389i			1.18572i	0.805304	+	0.592862i	$0.202002\pi$
$379$			449.389i			1.18572i	−0.805304	+	0.592862i	$0.797998\pi$
$380$	−1.88304	−	5.53784i	−0.00495536	−	0.0145733i
$381$	125.373	+	132.055i	0.329063	+	0.346600i
$382$	43.3708	+	161.862i	0.113536	+	0.423723i
$383$	−53.5483	+	199.845i	−0.139813	+	0.521789i	0.860119	+	0.510094i	$0.170389\pi$
$383$	−53.5483	+	199.845i	−0.139813	+	0.521789i	−0.999932	+	0.0116949i	$0.996277\pi$
$384$	−19.5954	+	66.2090i	−0.0510297	+	0.172419i
$385$	−191.419	−	441.523i	−0.497192	−	1.14681i
$386$		−	327.317i		−	0.847971i
$387$	207.349	+	230.071i	0.535786	+	0.594500i
$388$	46.4585	+	173.385i	0.119738	+	0.446869i
$389$	−58.9146	+	102.043i	−0.151451	+	0.262322i	−0.931761	−	0.363072i	$-0.881728\pi$
$389$	−58.9146	+	102.043i	−0.151451	+	0.262322i	0.780310	+	0.625393i	$0.215061\pi$
$390$	310.210	−	336.086i	0.795409	−	0.861760i
$391$			68.9977i			0.176465i
$392$	175.673	+	388.741i	0.448145	+	0.991687i
$393$	188.805	−	102.569i	0.480421	−	0.260991i
$394$	372.183	−	214.880i	0.944628	−	0.545381i
$395$	189.889	−	216.753i	0.480732	−	0.548742i
$396$	79.7422	+	156.325i	0.201369	+	0.394760i
$397$	139.689	−	521.328i	0.351863	−	1.31317i	−0.532524	−	0.846415i	$-0.678756\pi$
$397$	139.689	−	521.328i	0.351863	−	1.31317i	0.884387	−	0.466755i	$-0.154577\pi$
$398$	−112.975	−	112.975i	−0.283857	−	0.283857i
$399$	−15.4587	−	7.81810i	−0.0387435	−	0.0195942i
$400$	−192.163	−	79.3640i	−0.480408	−	0.198410i
$401$	320.784	−	185.205i	0.799961	−	0.461857i	−0.0434968	−	0.999054i	$-0.513850\pi$
$401$	320.784	−	185.205i	0.799961	−	0.461857i	0.843457	+	0.537196i	$0.180517\pi$
$402$	−3.28731	+	126.651i	−0.00817738	+	0.315053i
$403$	−100.117	+	26.8263i	−0.248429	+	0.0665664i
$404$	−30.1616	+	17.4138i	−0.0746575	+	0.0431035i
$405$	394.885	−	89.9503i	0.975024	−	0.222100i
$406$	−48.6157	+	17.3678i	−0.119743	+	0.0427779i
$407$	−415.186	−	415.186i	−1.02011	−	1.02011i
$408$	167.301	−	273.151i	0.410051	−	0.669488i
$409$	−4.27703	+	7.40803i	−0.0104573	+	0.0181125i	−0.871207	−	0.490916i	$-0.836662\pi$
$409$	−4.27703	+	7.40803i	−0.0104573	+	0.0181125i	0.860749	+	0.509029i	$0.169995\pi$
$410$	36.0606	+	545.855i	0.0879528	+	1.33135i
$411$	111.127	+	462.408i	0.270382	+	1.12508i
$412$	199.902	+	199.902i	0.485199	+	0.485199i
$413$	27.8299	+	341.483i	0.0673849	+	0.826836i
$414$	−44.2797	+	68.2536i	−0.106956	+	0.164864i
$415$	−668.039	−	329.011i	−1.60973	−	0.792798i
$416$	−203.624	+	352.687i	−0.489481	+	0.847806i
$417$	−12.0553	+	464.460i	−0.0289096	+	1.11381i
$418$	17.6037	+	4.71690i	0.0421141	+	0.0112844i
$419$		−	335.999i		−	0.801907i	−0.916098	−	0.400953i	$-0.868679\pi$
$419$		−	335.999i		−	0.801907i	0.916098	−	0.400953i	$-0.131321\pi$
$420$	138.109	−	55.6651i	0.328832	−	0.132536i
$421$	549.339			1.30484			0.652421	−	0.757857i	$-0.273753\pi$
$421$	549.339			1.30484			0.652421	+	0.757857i	$0.273753\pi$
$422$	1.31448	−	4.90571i	0.00311489	−	0.0116249i
$423$	−213.457	−	69.2477i	−0.504626	−	0.163706i
$424$	105.182	+	60.7269i	0.248071	+	0.143224i
$425$	243.438	+	186.397i	0.572796	+	0.438582i
$426$	−152.906	+	516.639i	−0.358935	+	1.21277i
$427$	−83.4243	−	39.5073i	−0.195373	−	0.0925229i
$428$	116.501	−	116.501i	0.272198	−	0.272198i
$429$	−182.901	−	761.065i	−0.426343	−	1.77405i
$430$	−182.188	+	207.962i	−0.423693	+	0.483633i
$431$	120.977	+	69.8461i	0.280689	+	0.162056i	0.633735	−	0.773550i	$-0.281521\pi$
$431$	120.977	+	69.8461i	0.280689	+	0.162056i	−0.353046	+	0.935606i	$0.614854\pi$
$432$	202.599	−	96.8068i	0.468980	−	0.224090i
$433$	−60.9485	+	60.9485i	−0.140759	+	0.140759i	−0.773975	−	0.633216i	$-0.781734\pi$
$433$	−60.9485	+	60.9485i	−0.140759	+	0.140759i	0.633216	+	0.773975i	$0.281734\pi$
$434$	60.4378	+	11.0279i	0.139258	+	0.0254100i
$435$	20.4652	+	65.7352i	0.0470464	+	0.151115i
$436$	−98.6250	−	170.824i	−0.226204	−	0.391797i
$437$	−1.20116	−	4.48279i	−0.00274865	−	0.0102581i
$438$	0.649890	−	25.0386i	0.00148377	−	0.0571657i
$439$	287.441	+	497.863i	0.654764	+	1.13408i	0.981953	+	0.189125i	$0.0605653\pi$
$439$	287.441	+	497.863i	0.654764	+	1.13408i	−0.327189	+	0.944959i	$0.606101\pi$
$440$	−497.472	+	332.773i	−1.13062	+	0.756301i
$441$	176.944	−	403.945i	0.401234	−	0.915976i
$442$	−264.421	+	264.421i	−0.598238	+	0.598238i
$443$	−457.750	−	122.654i	−1.03330	−	0.276871i	−0.297964	−	0.954577i	$-0.596307\pi$
$443$	−457.750	−	122.654i	−1.03330	−	0.276871i	−0.735333	+	0.677706i	$0.762974\pi$
$444$	131.759	−	125.093i	0.296755	−	0.281740i
$445$	−236.783	+	270.281i	−0.532097	+	0.607373i
$446$	102.363	+	177.297i	0.229512	+	0.397527i
$447$	−384.697	+	208.988i	−0.860619	+	0.467534i
$448$	390.089	−	269.699i	0.870735	−	0.602008i
$449$	104.385			0.232484			0.116242	−	0.993221i	$-0.462915\pi$
$449$	104.385			0.232484			0.116242	+	0.993221i	$0.462915\pi$
$450$	121.191	+	340.616i	0.269314	+	0.756924i
$451$	810.782	+	468.105i	1.79774	+	1.03793i
$452$	−308.158	+	82.5706i	−0.681765	+	0.182678i
$453$	160.252	+	98.1519i	0.353758	+	0.216671i
$454$	237.043			0.522120
$455$	−656.973	+	97.4676i	−1.44390	+	0.214215i
$456$	−6.11435	+	20.6592i	−0.0134087	+	0.0453052i
$457$	−338.203	−	90.6211i	−0.740050	−	0.198296i	−0.130950	−	0.991389i	$-0.541803\pi$
$457$	−338.203	−	90.6211i	−0.740050	−	0.198296i	−0.609100	+	0.793093i	$0.708469\pi$
$458$	−137.642	+	36.8812i	−0.300529	+	0.0805266i
$459$	−325.546	+	60.5690i	−0.709251	+	0.131959i
$460$	35.7872	+	17.6253i	0.0777984	+	0.0383159i
$461$	−49.3588			−0.107069			−0.0535345	−	0.998566i	$-0.517049\pi$
$461$	−49.3588			−0.107069			−0.0535345	+	0.998566i	$0.517049\pi$
$462$	−95.0952	+	454.100i	−0.205834	+	0.982900i
$463$	−429.745	−	429.745i	−0.928175	−	0.928175i	0.0694132	−	0.997588i	$-0.477887\pi$
$463$	−429.745	−	429.745i	−0.928175	−	0.928175i	−0.997588	+	0.0694132i	$0.977887\pi$
$464$	19.0851	+	33.0564i	0.0411317	+	0.0712421i
$465$	18.0222	−	79.9242i	0.0387575	−	0.171880i
$466$	115.642	−	200.297i	0.248158	−	0.429822i
$467$	782.100	+	209.563i	1.67473	+	0.448743i	0.966380	−	0.257116i	$-0.0827724\pi$
$467$	782.100	+	209.563i	1.67473	+	0.448743i	0.708352	+	0.705860i	$0.249439\pi$
$468$	236.882	−	50.4648i	0.506158	−	0.107831i
$469$	119.095	−	140.230i	0.253935	−	0.298997i
$470$	38.9796	−	196.495i	0.0829354	−	0.418074i
$471$	41.8678	+	174.215i	0.0888913	+	0.369884i
$472$	411.594	−	110.286i	0.872022	−	0.233657i
$473$	122.464	+	457.043i	0.258910	+	0.966264i
$474$	−270.127	+	64.9175i	−0.569888	+	0.136957i
$475$	−19.0612	−	7.87231i	−0.0401288	−	0.0165733i
$476$	−114.650	+	40.9585i	−0.240862	+	0.0860473i
$477$	−26.1611	−	122.800i	−0.0548450	−	0.257442i
$478$	−1.61642	+	6.03257i	−0.00338163	+	0.0126204i
$479$	−217.969	−	125.845i	−0.455051	−	0.262724i	0.254910	−	0.966965i	$-0.417954\pi$
$479$	−217.969	−	125.845i	−0.455051	−	0.262724i	−0.709961	+	0.704241i	$0.751287\pi$
$480$	−171.983	−	272.125i	−0.358297	−	0.566928i
$481$	−701.794	+	405.181i	−1.45903	+	0.842372i
$482$	−207.476	+	207.476i	−0.430448	+	0.430448i
$483$	112.252	−	36.8466i	0.232406	−	0.0762870i
$484$			96.5021i			0.199385i
$485$	567.753	+	279.620i	1.17062	+	0.576536i
$486$	−360.906	−	149.006i	−0.742605	−	0.306596i
$487$	−12.8574	−	47.9846i	−0.0264013	−	0.0985311i	0.951468	−	0.307748i	$-0.0995753\pi$
$487$	−12.8574	−	47.9846i	−0.0264013	−	0.0985311i	−0.977869	+	0.209217i	$0.932909\pi$
$488$	−29.7129	+	110.890i	−0.0608872	+	0.227234i
$489$	−793.317	−	234.793i	−1.62233	−	0.480149i
$490$	376.664	+	114.454i	0.768703	+	0.233580i
$491$		−	0.942475i		−	0.00191950i	−1.00000		0.000959750i	$-0.999695\pi$
$491$		−	0.942475i		−	0.00191950i	1.00000		0.000959750i	$-0.000305498\pi$
$492$	−151.304	+	247.034i	−0.307529	+	0.502101i
$493$	−14.5690	−	54.3722i	−0.0295517	−	0.110289i
$494$	12.5763	−	21.7827i	0.0254580	−	0.0440945i
$495$	599.837	+	151.715i	1.21179	+	0.306496i
$496$		−	45.4241i		−	0.0915808i
$497$	643.567	−	444.948i	1.29490	−	0.895268i
$498$	342.708	+	630.844i	0.688169	+	1.26675i
$499$	−324.659	+	187.442i	−0.650618	+	0.375635i	−0.788693	−	0.614787i	$-0.789242\pi$
$499$	−324.659	+	187.442i	−0.650618	+	0.375635i	0.138075	+	0.990422i	$0.455909\pi$
$500$	158.865	−	78.6502i	0.317730	−	0.157300i
$501$	43.1911	+	45.4929i	0.0862098	+	0.0908042i
$502$	162.765	−	607.447i	0.324233	−	1.21005i
$503$	−8.22946	−	8.22946i	−0.0163608	−	0.0163608i	0.698879	−	0.715240i	$-0.253683\pi$
$503$	−8.22946	−	8.22946i	−0.0163608	−	0.0163608i	−0.715240	+	0.698879i	$0.753683\pi$
$504$	−533.733	−	126.311i	−1.05899	−	0.250618i
$505$	−23.8934	+	120.446i	−0.0473137	+	0.238507i
$506$	−107.641	+	62.1467i	−0.212730	+	0.122820i
$507$	−573.084	−	14.8747i	−1.13034	−	0.0293387i
$508$	−83.1438	+	22.2783i	−0.163669	+	0.0438550i
$509$	−198.079	+	114.361i	−0.389153	+	0.224678i	−0.681793	−	0.731545i	$-0.738800\pi$
$509$	−198.079	+	114.361i	−0.389153	+	0.224678i	0.292640	+	0.956223i	$0.405466\pi$
$510$	−87.8668	−	282.233i	−0.172288	−	0.553397i
$511$	−23.5448	+	27.7230i	−0.0460759	+	0.0542524i
$512$	−330.984	−	330.984i	−0.646452	−	0.646452i
$513$	20.0963	−	9.60251i	0.0391742	−	0.0187183i
$514$	−145.907	+	252.719i	−0.283866	+	0.491671i
$515$	994.570	−	65.7039i	1.93120	−	0.127580i
$516$	−142.356	+	34.2114i	−0.275884	+	0.0663011i
$517$	−242.420	−	242.420i	−0.468897	−	0.468897i
$518$	478.738	−	39.0159i	0.924206	−	0.0753202i
$519$	−669.809	−	198.239i	−1.29058	−	0.381963i
$520$	265.922	+	782.051i	0.511388	+	1.50394i
$521$	−214.530	+	371.577i	−0.411766	+	0.713200i	−0.995083	−	0.0990449i	$-0.968421\pi$
$521$	−214.530	+	371.577i	−0.411766	+	0.713200i	0.583317	+	0.812245i	$0.301755\pi$
$522$	20.4819	−	63.1357i	0.0392373	−	0.120950i
$523$	477.637	+	127.982i	0.913263	+	0.244708i	0.684704	−	0.728822i	$-0.259932\pi$
$523$	477.637	+	127.982i	0.913263	+	0.244708i	0.228560	+	0.973530i	$0.426598\pi$
$524$			101.571i			0.193838i
$525$	173.247	−	495.591i	0.329994	−	0.943983i
$526$	101.287			0.192561
$527$	−17.3377	+	64.7052i	−0.0328989	+	0.122780i
$528$	342.918	+	8.90063i	0.649466	+	0.0168572i
$529$	−430.717	−	248.674i	−0.814209	−	0.470084i
$530$	106.114	−	36.0820i	0.200215	−	0.0680792i
$531$	−369.549	−	239.746i	−0.695950	−	0.451500i
$532$	6.73580	−	4.65699i	0.0126613	−	0.00875374i
$533$	913.648	−	913.648i	1.71416	−	1.71416i
$534$	336.836	−	80.9491i	0.630778	−	0.151590i
$535$	−38.2916	−	579.625i	−0.0715731	−	1.08341i
$536$	−198.160	−	114.408i	−0.369702	−	0.213447i
$537$	−443.749	−	271.789i	−0.826348	−	0.506125i
$538$	94.4230	−	94.4230i	0.175507	−	0.175507i
$539$	521.219	−	426.891i	0.967011	−	0.792005i
$540$	−51.7446	+	184.324i	−0.0958234	+	0.341341i
$541$	−73.6465	−	127.559i	−0.136130	−	0.235785i	0.789898	−	0.613238i	$-0.210133\pi$
$541$	−73.6465	−	127.559i	−0.136130	−	0.235785i	−0.926029	+	0.377453i	$0.876800\pi$
$542$	148.059	+	552.565i	0.273172	+	1.01949i
$543$	−180.600	−	4.68758i	−0.332597	−	0.00863275i
$544$	131.601	+	227.940i	0.241914	+	0.419008i
$545$	−682.158	−	135.323i	−1.25167	−	0.248299i
$546$	571.395	+	288.979i	1.04651	+	0.529265i
$547$	−257.930	+	257.930i	−0.471536	+	0.471536i	−0.902411	−	0.430876i	$-0.858205\pi$
$547$	−257.930	+	257.930i	−0.471536	+	0.471536i	0.430876	+	0.902411i	$0.358205\pi$
$548$	−217.151	−	58.1853i	−0.396260	−	0.106178i
$549$	105.719	−	53.9280i	0.192567	−	0.0982295i
$550$	−71.5262	+	547.671i	−0.130048	+	0.995765i
$551$	1.89310	+	3.27894i	0.00343575	+	0.00595090i
$552$	−70.1424	−	129.115i	−0.127070	−	0.233905i
$553$	364.614	+	172.670i	0.659337	+	0.312243i
$554$	691.432			1.24807
$555$	−25.6267	−	640.052i	−0.0461742	−	1.15325i
$556$	−190.206	−	109.816i	−0.342098	−	0.197510i
$557$	−286.344	+	76.7257i	−0.514083	+	0.137748i	−0.506528	−	0.862223i	$-0.669071\pi$
$557$	−286.344	+	76.7257i	−0.514083	+	0.137748i	−0.00755469	+	0.999971i	$0.502405\pi$
$558$	−58.6758	+	52.8808i	−0.105154	+	0.0947685i
$559$	653.031			1.16821
$560$	33.2591	−	289.163i	0.0593912	−	0.516363i
$561$	−485.079	−	143.565i	−0.864668	−	0.255910i
$562$	515.490	+	138.125i	0.917242	+	0.245774i
$563$	−1056.05	+	282.969i	−1.87576	+	0.502609i	−0.875965	+	0.482374i	$0.839775\pi$
$563$	−1056.05	+	282.969i	−1.87576	+	0.502609i	−0.999795	+	0.0202346i	$0.993559\pi$
$564$	76.9318	−	73.0392i	0.136404	−	0.129502i
$565$	−496.969	+	1009.07i	−0.879590	+	1.78596i
$566$	−511.107			−0.903017
$567$	272.390	+	497.285i	0.480406	+	0.877046i
$568$	−688.074	−	688.074i	−1.21140	−	1.21140i
$569$	450.488	+	780.269i	0.791719	+	1.37130i	0.924902	+	0.380207i	$0.124147\pi$
$569$	450.488	+	780.269i	0.791719	+	1.37130i	−0.133182	+	0.991092i	$0.542520\pi$
$570$	10.6220	+	16.8070i	0.0186351	+	0.0294860i
$571$	179.277	−	310.518i	0.313971	−	0.543814i	−0.665247	−	0.746623i	$-0.731674\pi$
$571$	179.277	−	310.518i	0.313971	−	0.543814i	0.979218	+	0.202809i	$0.0650072\pi$
$572$	357.403	+	95.7657i	0.624830	+	0.167423i
$573$	149.349	+	274.916i	0.260645	+	0.479784i
$574$	−721.221	+	257.655i	−1.25648	+	0.448876i
$575$	129.887	−	53.9583i	0.225890	−	0.0938405i
$576$	−31.6311	+	608.921i	−0.0549151	+	1.05716i
$577$	450.004	−	120.578i	0.779904	−	0.208975i	0.153161	−	0.988201i	$-0.451055\pi$
$577$	450.004	−	120.578i	0.779904	−	0.208975i	0.626742	+	0.779227i	$0.284388\pi$
$578$	−57.6360	−	215.101i	−0.0997163	−	0.372146i
$579$	−142.799	−	594.198i	−0.246630	−	1.02625i
$580$	−31.9230	−	6.33274i	−0.0550397	−	0.0109185i
$581$	187.138	−	1025.60i	0.322096	−	1.76523i
$582$	−291.261	−	536.141i	−0.500448	−	0.921205i
$583$	49.6451	−	185.278i	0.0851546	−	0.317801i
$584$	39.1756	+	22.6180i	0.0670815	+	0.0387295i
$585$	416.517	−	745.453i	0.711995	−	1.27428i
$586$	188.269	−	108.697i	0.321279	−	0.185490i
$587$	359.155	−	359.155i	0.611849	−	0.611849i	−0.331579	−	0.943428i	$-0.607581\pi$
$587$	359.155	−	359.155i	0.611849	−	0.611849i	0.943428	+	0.331579i	$0.107581\pi$
$588$	127.862	+	164.651i	0.217452	+	0.280019i
$589$		−	4.50573i		−	0.00764980i
$590$	173.738	−	352.766i	0.294471	−	0.597908i
$591$	581.901	−	552.458i	0.984604	−	0.934785i
$592$	−91.9173	−	343.040i	−0.155266	−	0.579460i
$593$	222.116	−	828.950i	0.374564	−	1.39789i	−0.479417	−	0.877587i	$-0.659152\pi$
$593$	222.116	−	828.950i	0.374564	−	1.39789i	0.853981	−	0.520305i	$-0.174182\pi$
$594$	−387.714	−	453.320i	−0.652717	−	0.763165i
$595$	−157.746	+	399.210i	−0.265119	+	0.670941i
$596$		−	206.954i		−	0.347238i
$597$	−254.378	−	155.803i	−0.426094	−	0.260976i
$598$	44.3982	+	165.696i	0.0742444	+	0.277084i
$599$	10.8388	−	18.7734i	0.0180949	−	0.0313413i	−0.856836	−	0.515589i	$-0.827573\pi$
$599$	10.8388	−	18.7734i	0.0180949	−	0.0313413i	0.874931	+	0.484248i	$0.160907\pi$
$600$	−645.037	−	101.328i	−1.07506	−	0.168880i
$601$			689.068i			1.14654i	0.819368	+	0.573268i	$0.194325\pi$
$601$			689.068i			1.14654i	−0.819368	+	0.573268i	$0.805675\pi$
$602$	−349.826	−	165.667i	−0.581107	−	0.275195i
$603$	49.2868	+	231.352i	0.0817359	+	0.383669i
$604$	−76.9320	+	44.4167i	−0.127371	+	0.0735376i
$605$	255.922	+	224.204i	0.423012	+	0.370585i
$606$	85.8534	−	81.5094i	0.141672	−	0.134504i
$607$	40.1262	−	149.753i	0.0661058	−	0.246710i	−0.924964	−	0.380055i	$-0.875905\pi$
$607$	40.1262	−	149.753i	0.0661058	−	0.246710i	0.991070	+	0.133345i	$0.0425718\pi$
$608$	−12.5183	−	12.5183i	−0.0205893	−	0.0205893i
$609$	−80.6779	+	52.7385i	−0.132476	+	0.0865986i
$610$	58.9038	+	88.0572i	0.0965637	+	0.144356i
$611$	−409.764	+	236.578i	−0.670645	+	0.387197i
$612$	48.3023	−	148.892i	0.0789254	−	0.243288i
$613$	644.848	−	172.787i	1.05195	−	0.281870i	0.308896	−	0.951096i	$-0.400041\pi$
$613$	644.848	−	172.787i	1.05195	−	0.281870i	0.743059	+	0.669225i	$0.233374\pi$
$614$	9.39332	−	5.42324i	0.0152986	−	0.00883264i
$615$	303.604	+	975.191i	0.493665	+	1.58568i
$616$	−638.666	−	542.411i	−1.03680	−	0.880538i
$617$	433.982	+	433.982i	0.703374	+	0.703374i	0.965133	−	0.261759i	$-0.0843026\pi$
$617$	433.982	+	433.982i	0.703374	+	0.703374i	−0.261759	+	0.965133i	$0.584303\pi$
$618$	−819.455	−	501.903i	−1.32598	−	0.812141i
$619$	129.377	−	224.088i	0.209010	−	0.362016i	−0.742393	−	0.669965i	$-0.766309\pi$
$619$	129.377	−	224.088i	0.209010	−	0.362016i	0.951403	+	0.307949i	$0.0996426\pi$
$620$	29.1320	+	25.5214i	0.0469870	+	0.0411636i
$621$	−50.6066	+	143.223i	−0.0814921	+	0.230633i
$622$	224.970	+	224.970i	0.361688	+	0.361688i
$623$	−454.656	−	215.312i	−0.729785	−	0.345605i
$624$	134.357	−	453.967i	0.215316	−	0.727511i
$625$	160.513	−	604.037i	0.256821	−	0.966459i
$626$	103.147	−	178.655i	0.164771	−	0.285391i
$627$	34.0149	+	0.882876i	0.0542503	+	0.00140810i
$628$	−81.8129	−	21.9217i	−0.130275	−	0.0349072i
$629$			523.733i			0.832644i
$630$	−412.241	+	293.670i	−0.654350	+	0.466143i
$631$	384.244			0.608945			0.304472	−	0.952521i	$-0.401520\pi$
$631$	384.244			0.608945			0.304472	+	0.952521i	$0.401520\pi$
$632$	129.863	−	484.656i	0.205480	−	0.766861i
$633$	0.246035	−	9.47911i	0.000388682	−	0.0149749i
$634$	378.240	+	218.377i	0.596594	+	0.344443i
$635$	−134.087	+	272.256i	−0.211160	+	0.428749i
$636$	56.9119	+	16.8438i	0.0894841	+	0.0264840i
$637$	−382.909	−	847.327i	−0.601113	−	1.33018i
$638$	71.7021	−	71.7021i	0.112386	−	0.112386i
$639$	−52.1848	+	1004.59i	−0.0816663	+	1.57214i
$640$	−114.829	+	7.58594i	−0.179421	+	0.0118530i
$641$	472.114	+	272.575i	0.736528	+	0.425235i	0.820806	−	0.571208i	$-0.193525\pi$
$641$	472.114	+	272.575i	0.736528	+	0.425235i	−0.0842776	+	0.996442i	$0.526858\pi$
$642$	−292.504	+	477.570i	−0.455614	+	0.743879i
$643$	−364.472	+	364.472i	−0.566830	+	0.566830i	−0.931239	−	0.364409i	$-0.881271\pi$
$643$	−364.472	+	364.472i	−0.566830	+	0.566830i	0.364409	+	0.931239i	$0.381271\pi$
$644$	−10.0251	+	54.9418i	−0.0155669	+	0.0853133i
$645$	−240.009	+	457.010i	−0.372107	+	0.708543i
$646$	−8.12798	−	14.0781i	−0.0125820	−	0.0217927i
$647$	51.7389	+	193.092i	0.0799673	+	0.298442i	0.994314	−	0.106491i	$-0.0339615\pi$
$647$	51.7389	+	193.092i	0.0799673	+	0.298442i	−0.914346	+	0.404933i	$0.867295\pi$
$648$	547.621	−	444.290i	0.845094	−	0.685633i
$649$	−336.485	−	582.808i	−0.518466	−	0.898010i
$650$	704.554	+	290.983i	1.08393	+	0.447665i
$651$	114.528	−	6.34763i	0.175926	−	0.00975058i
$652$	276.544	−	276.544i	0.424148	−	0.424148i
$653$	472.271	+	126.545i	0.723233	+	0.193790i	0.601614	−	0.798787i	$-0.294525\pi$
$653$	472.271	+	126.545i	0.723233	+	0.193790i	0.121619	+	0.992577i	$0.461191\pi$
$654$	461.637	+	486.240i	0.705868	+	0.743486i
$655$	269.365	+	235.981i	0.411244	+	0.360276i
$656$	283.130	+	490.396i	0.431601	+	0.747555i
$657$	−9.74383	−	45.7375i	−0.0148308	−	0.0696157i
$658$	279.527	−	22.7806i	0.424812	−	0.0346210i
$659$	−594.519			−0.902153			−0.451076	−	0.892485i	$-0.648960\pi$
$659$	−594.519			−0.902153			−0.451076	+	0.892485i	$0.648960\pi$
$660$	−198.376	+	214.924i	−0.300570	+	0.325642i
$661$	−759.345	−	438.408i	−1.14878	−	0.663250i	−0.200192	−	0.979757i	$-0.564157\pi$
$661$	−759.345	−	438.408i	−1.14878	−	0.663250i	−0.948590	+	0.316507i	$0.897490\pi$
$662$	663.478	−	177.778i	1.00223	−	0.268548i
$663$	−364.660	+	595.379i	−0.550016	+	0.898008i
$664$	−1296.60			−1.95272
$665$	3.29905	−	28.6829i	0.00496098	−	0.0431321i
$666$	−336.110	+	518.086i	−0.504669	+	0.777906i
$667$	−24.9422	−	6.68324i	−0.0373946	−	0.0100199i
$668$	−28.6431	+	7.67489i	−0.0428789	+	0.0114894i
$669$	263.174	+	277.200i	0.393385	+	0.414350i
$670$	−199.916	+	67.9775i	−0.298382	+	0.101459i
$671$	181.309			0.270207
$672$	300.557	−	335.828i	0.447258	−	0.499745i
$673$	429.383	+	429.383i	0.638014	+	0.638014i	0.950065	−	0.312051i	$-0.101016\pi$
$673$	429.383	+	429.383i	0.638014	+	0.638014i	−0.312051	+	0.950065i	$0.601016\pi$
$674$	−97.1090	−	168.198i	−0.144079	−	0.249551i
$675$	368.607	+	565.468i	0.546085	+	0.837730i
$676$	135.498	−	234.690i	0.200441	−	0.347175i
$677$	−1251.15	−	335.245i	−1.84808	−	0.495191i	−0.848650	−	0.528955i	$-0.822584\pi$
$677$	−1251.15	−	335.245i	−1.84808	−	0.495191i	−0.999430	+	0.0337641i	$0.989251\pi$
$678$	952.884	−	517.658i	1.40543	−	0.763507i
$679$	−159.045	+	871.633i	−0.234234	+	1.28370i
$680$	523.653	+	103.880i	0.770078	+	0.152764i
$681$	430.318	−	103.415i	0.631891	−	0.151857i
$682$	−116.561	+	31.2324i	−0.170910	+	0.0457953i
$683$	103.622	+	386.723i	0.151716	+	0.566212i	0.999364	+	0.0356530i	$0.0113511\pi$
$683$	103.622	+	386.723i	0.151716	+	0.566212i	−0.847648	+	0.530559i	$0.821982\pi$
$684$	−0.546184	+	10.5144i	−0.000798515	+	0.0153720i
$685$	−658.814	+	440.698i	−0.961772	+	0.643355i
$686$	−9.83552	+	551.050i	−0.0143375	+	0.803280i
$687$	−233.780	+	127.002i	−0.340292	+	0.184865i
$688$	−74.0717	+	276.439i	−0.107662	+	0.401801i
$689$	−229.262	−	132.364i	−0.332746	−	0.192111i
$690$	−132.277	−	29.8273i	−0.191705	−	0.0432280i
$691$	314.676	−	181.678i	0.455392	−	0.262921i	−0.254712	−	0.967017i	$-0.581981\pi$
$691$	314.676	−	181.678i	0.455392	−	0.262921i	0.710105	+	0.704096i	$0.248647\pi$
$692$	233.490	−	233.490i	0.337414	−	0.337414i
$693$	25.4788	+	865.842i	0.0367659	+	1.24941i
$694$		−	310.222i		−	0.447006i
$695$	−733.137	+	249.289i	−1.05487	+	0.358690i
$696$	82.5373	+	86.9361i	0.118588	+	0.124908i
$697$	−216.133	−	806.620i	−0.310091	−	1.15727i
$698$	149.267	−	557.070i	0.213849	−	0.798095i
$699$	122.547	−	414.063i	0.175318	−	0.592365i
$700$	166.764	+	183.796i	0.238234	+	0.262566i
$701$			424.564i			0.605655i	0.953045	+	0.302827i	$0.0979305\pi$
$701$			424.564i			0.605655i	−0.953045	+	0.302827i	$0.902069\pi$
$702$	−742.817	+	354.935i	−1.05814	+	0.505606i
$703$	−9.11751	−	34.0270i	−0.0129694	−	0.0484026i
$704$	−465.758	+	806.716i	−0.661588	+	1.14590i
$705$	−14.9630	−	373.715i	−0.0212240	−	0.530092i
$706$		−	444.442i		−	0.629521i
$707$	−171.342	+	13.9639i	−0.242351	+	0.0197509i
$708$	182.976	−	99.4026i	0.258441	−	0.140399i
$709$	1075.95	−	621.203i	1.51757	−	0.876168i	0.517780	−	0.855514i	$-0.326759\pi$
$709$	1075.95	−	621.203i	1.51757	−	0.876168i	0.999787	−	0.0206538i	$-0.00657477\pi$
$710$	−896.033	+	59.1943i	−1.26202	+	0.0833723i
$711$	−462.056	+	235.697i	−0.649868	+	0.331501i
$712$	−161.933	+	604.343i	−0.227434	+	0.848797i
$713$	21.7289	+	21.7289i	0.0304753	+	0.0304753i
$714$	346.389	−	226.432i	0.485138	−	0.317131i
$715$	1084.32	−	725.334i	1.51654	−	1.01445i
$716$	213.030	−	122.993i	0.297528	−	0.171778i
$717$	−0.302550	+	11.6565i	−0.000421967	+	0.0162573i
$718$	−257.717	+	69.0551i	−0.358938	+	0.0961770i
$719$	−822.499	+	474.870i	−1.14395	+	0.660459i	−0.947405	−	0.320036i	$-0.896305\pi$
$719$	−822.499	+	474.870i	−1.14395	+	0.660459i	−0.196543	+	0.980495i	$0.562972\pi$
$720$	268.319	+	260.874i	0.372665	+	0.362325i
$721$	469.457	+	1314.09i	0.651119	+	1.82260i
$722$	−409.391	−	409.391i	−0.567024	−	0.567024i
$723$	−286.128	+	467.159i	−0.395751	+	0.646140i
$724$	42.7006	−	73.9597i	0.0589788	−	0.102154i
$725$	−90.9613	+	69.9466i	−0.125464	+	0.0964781i
$726$	−76.6487	−	318.941i	−0.105577	−	0.439313i
$727$	−460.949	−	460.949i	−0.634043	−	0.634043i	0.315037	−	0.949079i	$-0.397983\pi$
$727$	−460.949	−	460.949i	−0.634043	−	0.634043i	−0.949079	+	0.315037i	$0.897983\pi$
$728$	−951.226	+	657.657i	−1.30663	+	0.903375i
$729$	−720.182	−	113.046i	−0.987903	−	0.155070i
$730$	39.5226	−	13.4389i	0.0541406	−	0.0184095i
$731$	211.026	−	365.507i	0.288681	−	0.500010i
$732$	−1.45566	+	56.0827i	−0.00198860	+	0.0766157i
$733$	1056.53	+	283.095i	1.44137	+	0.386214i	0.893014	−	0.450029i	$-0.148586\pi$
$733$	1056.53	+	283.095i	1.44137	+	0.386214i	0.548358	+	0.836244i	$0.315253\pi$
$734$			71.0819i			0.0968419i
$735$	733.715	+	43.4479i	0.998251	+	0.0591128i
$736$	120.739			0.164048
$737$	−93.5301	+	349.059i	−0.126907	+	0.473622i
$738$	303.852	−	936.627i	0.411723	−	1.26914i
$739$	−42.6947	−	24.6498i	−0.0577736	−	0.0333556i	0.470835	−	0.882221i	$-0.343953\pi$
$739$	−42.6947	−	24.6498i	−0.0577736	−	0.0333556i	−0.528609	+	0.848866i	$0.677286\pi$
$740$	271.646	+	133.787i	0.367090	+	0.180793i
$741$	13.3273	−	45.0301i	0.0179855	−	0.0607694i
$742$	89.2352	+	129.069i	0.120263	+	0.173947i
$743$	−155.824	+	155.824i	−0.209723	+	0.209723i	−0.804150	−	0.594427i	$-0.797379\pi$
$743$	−155.824	+	155.824i	−0.209723	+	0.209723i	0.594427	+	0.804150i	$0.297379\pi$
$744$	−33.3347	−	138.708i	−0.0448047	−	0.186436i
$745$	−548.839	−	480.817i	−0.736697	−	0.645392i
$746$	266.853	+	154.067i	0.357711	+	0.206525i
$747$	897.358	+	995.695i	1.20128	+	1.33293i
$748$	169.095	−	169.095i	0.226063	−	0.226063i
$749$	765.841	−	273.595i	1.02248	−	0.365280i
$750$	−462.583	+	386.122i	−0.616777	+	0.514829i
$751$	242.458	+	419.950i	0.322847	+	0.559188i	0.981074	−	0.193631i	$-0.0620266\pi$
$751$	242.458	+	419.950i	0.322847	+	0.559188i	−0.658227	+	0.752820i	$0.728693\pi$
$752$	−53.6688	−	200.295i	−0.0713681	−	0.266349i
$753$	30.4652	−	1173.74i	0.0404584	−	1.55876i
$754$	−69.9742	−	121.199i	−0.0928040	−	0.160741i
$755$	−60.9440	+	307.216i	−0.0807206	+	0.406909i
$756$	−268.028	+	0.929623i	−0.354534	+	0.00122966i
$757$	−675.595	+	675.595i	−0.892464	+	0.892464i	−0.994755	−	0.102291i	$-0.967383\pi$
$757$	−675.595	+	675.595i	−0.892464	+	0.892464i	0.102291	+	0.994755i	$0.467383\pi$
$758$	697.481	+	186.890i	0.920160	+	0.246556i
$759$	−168.295	+	159.779i	−0.221732	+	0.210513i
$760$	−35.8302	+	2.36704i	−0.0471450	+	0.00311452i
$761$	−319.802	−	553.914i	−0.420240	−	0.727876i	0.575723	−	0.817645i	$-0.304721\pi$
$761$	−319.802	−	553.914i	−0.420240	−	0.727876i	−0.995963	+	0.0897683i	$0.971387\pi$
$762$	257.097	−	139.669i	0.337397	−	0.183292i
$763$	−79.0860	−	970.413i	−0.103651	−	1.27184i
$764$	−147.896			−0.193581
$765$	−282.640	−	474.020i	−0.369464	−	0.619634i
$766$	287.903	+	166.221i	0.375852	+	0.216999i
$767$	−897.139	+	240.388i	−1.16967	+	0.313413i
$768$	−598.674	−	366.678i	−0.779524	−	0.477446i
$769$	1079.96			1.40437			0.702187	−	0.711993i	$-0.252207\pi$
$769$	1079.96			1.40437			0.702187	+	0.711993i	$0.252207\pi$
$770$	−764.879	+	113.476i	−0.993349	+	0.147372i
$771$	−154.620	+	522.431i	−0.200545	+	0.677602i
$772$	279.040	+	74.7686i	0.361451	+	0.0968505i
$773$	−705.759	+	189.108i	−0.913013	+	0.244641i	−0.684596	−	0.728922i	$-0.740022\pi$
$773$	−705.759	+	189.108i	−0.913013	+	0.244641i	−0.228417	+	0.973563i	$0.573355\pi$
$774$	443.317	−	226.138i	0.572761	−	0.292168i
$775$	135.365	−	17.9635i	0.174664	−	0.0231788i
$776$	1101.96			1.42005
$777$	852.061	−	279.688i	1.09660	−	0.359959i
$778$	133.876	+	133.876i	0.172078	+	0.172078i
$779$	28.0844	+	48.6436i	0.0360519	+	0.0624437i
$780$	215.655	+	341.228i	0.276481	+	0.437472i
$781$	−768.404	+	1330.92i	−0.983872	+	1.70412i
$782$	107.089	+	28.6944i	0.136942	+	0.0366936i
$783$	9.63771	−	123.550i	0.0123087	−	0.157790i
$784$	402.121	−	65.9817i	0.512909	−	0.0841603i
$785$	−248.213	+	166.036i	−0.316194	+	0.211511i
$786$	−80.6748	−	335.694i	−0.102640	−	0.427092i
$787$	−741.113	+	198.581i	−0.941694	+	0.252326i	−0.696834	−	0.717232i	$-0.745409\pi$
$787$	−741.113	+	198.581i	−0.941694	+	0.252326i	−0.244860	+	0.969558i	$0.578742\pi$
$788$	98.1697	+	366.374i	0.124581	+	0.464942i
$789$	183.873	−	44.1887i	0.233045	−	0.0560059i
$790$	−257.445	−	384.862i	−0.325879	−	0.487168i
$791$	−1549.15	−	282.670i	−1.95848	−	0.357358i
$792$	1053.68	−	224.473i	1.33040	−	0.283425i
$793$	64.7644	−	241.704i	0.0816701	−	0.304797i
$794$	−751.042	−	433.614i	−0.945896	−	0.546113i
$795$	176.893	−	111.796i	0.222507	−	0.140624i
$796$	122.119	−	70.5054i	0.153416	−	0.0885746i
$797$	−276.684	+	276.684i	−0.347157	+	0.347157i	−0.859050	−	0.511892i	$-0.828945\pi$
$797$	−276.684	+	276.684i	−0.347157	+	0.347157i	0.511892	+	0.859050i	$0.328945\pi$
$798$	−18.5630	+	20.7415i	−0.0232620	+	0.0259918i
$799$			305.798i			0.382726i
$800$	326.177	−	425.993i	0.407721	−	0.532492i
$801$	576.162	−	293.904i	0.719304	−	0.366921i
$802$	−154.044	−	574.900i	−0.192075	−	0.716832i
$803$	18.4906	−	69.0078i	0.0230269	−	0.0859375i
$804$	−107.220	−	31.7333i	−0.133359	−	0.0394693i
$805$	122.414	+	154.233i	0.152067	+	0.191594i
$806$			166.544i			0.206631i
$807$	130.218	−	212.606i	0.161360	−	0.263452i
$808$	55.3370	+	206.521i	0.0684864	+	0.255595i
$809$	545.532	−	944.889i	0.674329	−	1.16797i	−0.302336	−	0.953202i	$-0.597766\pi$
$809$	545.532	−	944.889i	0.674329	−	1.16797i	0.976665	−	0.214770i	$-0.0689003\pi$
$810$	24.6137	−	650.294i	0.0303873	−	0.802833i
$811$		−	1169.06i		−	1.44150i	−0.693194	−	0.720751i	$-0.743797\pi$
$811$		−	1169.06i		−	1.44150i	0.693194	−	0.720751i	$-0.256203\pi$
$812$	−3.70100	−	45.4126i	−0.00455788	−	0.0559268i
$813$	509.849	+	938.510i	0.627121	+	1.15438i
$814$	−817.061	+	471.730i	−1.00376	+	0.579521i
$815$	−90.8949	−	1375.89i	−0.111527	−	1.68821i
$816$	−210.672	−	221.899i	−0.258176	−	0.271936i
$817$	−7.34736	+	27.4207i	−0.00899310	+	0.0335627i
$818$	9.71903	+	9.71903i	0.0118815	+	0.0118815i
$819$	1163.36	+	275.317i	1.42046	+	0.336162i
$820$	−473.583	−	93.9471i	−0.577541	−	0.114570i
$821$	962.475	−	555.685i	1.17232	−	0.676840i	0.218095	−	0.975927i	$-0.430016\pi$
$821$	962.475	−	555.685i	1.17232	−	0.676840i	0.954226	+	0.299088i	$0.0966823\pi$
$822$	763.901	+	19.8275i	0.929321	+	0.0241210i
$823$	−900.608	+	241.317i	−1.09430	+	0.293217i	−0.760441	−	0.649407i	$-0.775017\pi$
$823$	−900.608	+	241.317i	−1.09430	+	0.293217i	−0.333858	+	0.942623i	$0.608351\pi$
$824$	1503.00	−	867.756i	1.82403	−	1.05310i
$825$	109.087	+	1025.42i	0.132227	+	1.24294i
$826$	541.578	+	98.8203i	0.655663	+	0.119637i
$827$	965.882	+	965.882i	1.16793	+	1.16793i	0.982693	+	0.185241i	$0.0593066\pi$
$827$	965.882	+	965.882i	1.16793	+	1.16793i	0.185241	+	0.982693i	$0.440693\pi$
$828$	−48.0720	−	53.3399i	−0.0580580	−	0.0644202i
$829$	82.7727	−	143.367i	0.0998464	−	0.172939i	−0.811775	−	0.583971i	$-0.801498\pi$
$829$	82.7727	−	143.367i	0.0998464	−	0.172939i	0.911621	+	0.411032i	$0.134832\pi$
$830$	−788.467	+	900.012i	−0.949960	+	1.08435i
$831$	1255.20	−	301.652i	1.51047	−	0.362999i
$832$	909.067	+	909.067i	1.09263	+	1.09263i
$833$	−597.992	−	59.4946i	−0.717878	−	0.0714221i
$834$	715.859	+	211.868i	0.858344	+	0.254038i
$835$	−46.1929	+	93.7922i	−0.0553209	+	0.112326i
$836$	−8.04239	+	13.9298i	−0.00962009	+	0.0166625i
$837$	−83.4472	+	121.596i	−0.0996980	+	0.145276i
$838$	−521.492	−	139.733i	−0.622305	−	0.166746i
$839$		−	261.449i		−	0.311620i	−0.987787	−	0.155810i	$-0.950201\pi$
$839$		−	261.449i		−	0.311620i	0.987787	−	0.155810i	$-0.0497987\pi$
$840$	−110.643	−	907.405i	−0.131718	−	1.08024i
$841$	−819.934			−0.974951
$842$	228.456	−	852.609i	0.271325	−	1.01260i
$843$	996.061	+	25.8533i	1.18157	+	0.0306682i
$844$	3.88190	+	2.24121i	0.00459940	+	0.00265547i
$845$	−307.591	−	904.597i	−0.364013	−	1.07053i
$846$	−196.248	+	302.501i	−0.231972	+	0.357566i
$847$	−203.873	+	430.503i	−0.240700	+	0.508267i
$848$	82.0368	−	82.0368i	0.0967415	−	0.0967415i
$849$	−927.844	+	222.982i	−1.09287	+	0.262640i
$850$	390.540	−	300.314i	0.459459	−	0.353311i
$851$	208.065	+	120.126i	0.244494	+	0.141159i
$852$	−405.511	−	248.369i	−0.475952	−	0.291513i
$853$	−324.329	+	324.329i	−0.380221	+	0.380221i	−0.871182	−	0.490960i	$-0.836646\pi$
$853$	−324.329	+	324.329i	−0.380221	+	0.380221i	0.490960	+	0.871182i	$0.336646\pi$
$854$	−96.0118	+	113.050i	−0.112426	+	0.132377i
$855$	26.6152	+	25.8767i	0.0311289	+	0.0302652i
$856$	−505.719	−	875.932i	−0.590794	−	1.02328i
$857$	46.6086	+	173.945i	0.0543857	+	0.202970i	0.987773	−	0.155901i	$-0.0498282\pi$
$857$	46.6086	+	173.945i	0.0543857	+	0.202970i	−0.933387	+	0.358872i	$0.883162\pi$
$858$	−1257.29	−	32.6335i	−1.46537	−	0.0380344i
$859$	−377.574	−	653.978i	−0.439551	−	0.761325i	0.558104	−	0.829771i	$-0.311529\pi$
$859$	−377.574	−	653.978i	−0.439551	−	0.761325i	−0.997655	+	0.0684462i	$0.978196\pi$
$860$	−135.673	−	202.821i	−0.157759	−	0.235839i
$861$	−1196.87	+	782.384i	−1.39009	+	0.908693i
$862$	158.717	−	158.717i	0.184126	−	0.184126i
$863$	−114.394	−	30.6518i	−0.132554	−	0.0355177i	0.191932	−	0.981408i	$-0.438525\pi$
$863$	−114.394	−	30.6518i	−0.132554	−	0.0355177i	−0.324486	+	0.945890i	$0.605191\pi$
$864$	105.990	+	569.674i	0.122673	+	0.659345i
$865$	−76.7438	−	1161.68i	−0.0887212	−	1.34299i
$866$	69.2490	+	119.943i	0.0799642	+	0.138502i
$867$	−198.472	−	365.340i	−0.228919	−	0.421384i
$868$	−23.2071	+	49.0046i	−0.0267363	+	0.0564570i
$869$	−792.427			−0.911884
$870$	110.536	−	4.42570i	0.127053	−	0.00508701i
$871$	431.923	+	249.371i	0.495894	+	0.286304i
$872$	−1169.65	+	313.407i	−1.34134	+	0.359412i
$873$	−762.646	−	846.221i	−0.873593	−	0.969325i
$874$	−7.45710			−0.00853216
$875$	874.867	−	15.2405i	0.999848	−	0.0174177i
$876$	21.1971	+	6.27357i	0.0241976	+	0.00716161i
$877$	1372.82	+	367.846i	1.56536	+	0.419436i	0.934355	−	0.356344i	$-0.115977\pi$
$877$	1372.82	+	367.846i	1.56536	+	0.419436i	0.631003	+	0.775780i	$0.282643\pi$
$878$	892.255	−	239.079i	1.01624	−	0.272299i
$879$	294.355	−	279.461i	0.334875	−	0.317931i
$880$	184.054	+	541.286i	0.209152	+	0.615098i
$881$	−652.322			−0.740434			−0.370217	−	0.928945i	$-0.620717\pi$
$881$	−652.322			−0.740434			−0.370217	+	0.928945i	$0.620717\pi$
$882$	−553.363	−	442.619i	−0.627395	−	0.501836i
$883$	−1013.20	−	1013.20i	−1.14745	−	1.14745i	−0.987053	−	0.160396i	$-0.948723\pi$
$883$	−1013.20	−	1013.20i	−1.14745	−	1.14745i	−0.160396	−	0.987053i	$-0.551277\pi$
$884$	−165.020	−	285.823i	−0.186674	−	0.323329i
$885$	161.496	−	716.194i	0.182481	−	0.809258i
$886$	−380.733	+	659.449i	−0.429721	+	0.744299i
$887$	−410.195	−	109.911i	−0.462452	−	0.123914i	0.0200678	−	0.999799i	$-0.493612\pi$
$887$	−410.195	−	109.911i	−0.462452	−	0.123914i	−0.482520	+	0.875885i	$0.660278\pi$
$888$	−532.423	−	980.063i	−0.599575	−	1.10367i
$889$	−417.976	−	76.2670i	−0.470164	−	0.0857897i
$890$	321.022	+	479.905i	0.360698	+	0.539220i
$891$	−901.611	−	653.791i	−1.01191	−	0.733772i
$892$	−174.530	+	46.7651i	−0.195661	+	0.0524273i
$893$	−5.32355	−	19.8677i	−0.00596142	−	0.0222483i
$894$	164.377	+	683.987i	0.183867	+	0.765086i
$895$	168.758	−	850.702i	0.188557	−	0.950506i
$896$	−54.2018	−	151.721i	−0.0604931	−	0.169331i
$897$	152.887	+	281.429i	0.170443	+	0.313744i
$898$	43.4111	−	162.013i	0.0483420	−	0.180415i
$899$	−21.7111	−	12.5349i	−0.0241503	−	0.0139432i
$900$	−318.061	+	25.5103i	−0.353401	+	0.0283447i
$901$	−148.171	+	85.5466i	−0.164452	+	0.0949462i
$902$	1063.71	−	1063.71i	1.17928	−	1.17928i
$903$	−707.337	−	148.127i	−0.783318	−	0.164038i
$904$			1958.51i			2.16649i
$905$	−96.9335	−	285.073i	−0.107109	−	0.314997i
$906$	218.983	−	207.903i	0.241703	−	0.229473i
$907$	237.458	+	886.205i	0.261806	+	0.977073i	0.964177	+	0.265261i	$0.0854583\pi$
$907$	237.458	+	886.205i	0.261806	+	0.977073i	−0.702371	+	0.711811i	$0.747875\pi$
$908$	−54.1474	+	202.081i	−0.0596337	+	0.222556i
$909$	120.295	−	185.424i	0.132337	−	0.203987i
$910$	−121.942	+	1060.20i	−0.134002	+	1.16505i
$911$		−	1022.80i		−	1.12272i	−0.827570	−	0.561362i	$-0.810278\pi$
$911$		−	1022.80i		−	1.12272i	0.827570	−	0.561362i	$-0.189722\pi$
$912$	17.5504	+	10.7493i	0.0192438	+	0.0117865i
$913$	529.996	+	1977.97i	0.580500	+	2.16646i
$914$	−281.300	+	487.225i	−0.307768	+	0.533069i
$915$	145.349	+	134.158i	0.158851	+	0.146620i
$916$		−	125.766i		−	0.137299i
$917$	−214.582	+	453.115i	−0.234004	+	0.494128i
$918$	−41.3793	+	530.458i	−0.0450755	+	0.577840i
$919$	44.4702	−	25.6749i	0.0483898	−	0.0279379i	−0.475610	−	0.879656i	$-0.657773\pi$
$919$	44.4702	−	25.6749i	0.0483898	−	0.0279379i	0.524000	+	0.851718i	$0.324439\pi$
$920$	161.376	−	184.206i	0.175409	−	0.200224i
$921$	14.6863	−	13.9432i	0.0159460	−	0.0151392i
$922$	−20.5271	+	76.6080i	−0.0222636	+	0.0830890i
$923$	1499.77	+	1499.77i	1.62489	+	1.62489i
$924$	−365.401	−	184.799i	−0.395456	−	0.199999i
$925$	985.918	−	409.576i	1.06586	−	0.442784i
$926$	−845.712	+	488.272i	−0.913295	+	0.527291i
$927$	−1706.57	−	553.630i	−1.84096	−	0.597228i
$928$	−95.1461	+	25.4943i	−0.102528	+	0.0274723i
$929$	−254.572	+	146.977i	−0.274028	+	0.158210i	−0.630717	−	0.776013i	$-0.717239\pi$
$929$	−254.572	+	146.977i	−0.274028	+	0.158210i	0.356689	+	0.934223i	$0.383906\pi$
$930$	−116.553	−	61.2101i	−0.125325	−	0.0658173i
$931$	39.8874	−	6.54489i	0.0428436	−	0.00702996i
$932$	144.339	+	144.339i	0.154870	+	0.154870i
$933$	506.549	+	310.254i	0.542926	+	0.332533i
$934$	650.511	−	1126.72i	0.696478	−	1.20634i
$935$	−55.5783	−	841.296i	−0.0594420	−	0.899782i
$936$	77.1319	−	1484.84i	0.0824058	−	1.58637i
$937$	259.320	+	259.320i	0.276755	+	0.276755i	0.831812	−	0.555057i	$-0.187304\pi$
$937$	259.320	+	259.320i	0.276755	+	0.276755i	−0.555057	+	0.831812i	$0.687304\pi$
$938$	−168.117	−	243.162i	−0.179229	−	0.259234i
$939$	109.306	−	369.323i	0.116407	−	0.393315i
$940$	158.609	+	78.1156i	0.168733	+	0.0831017i
$941$	−714.684	+	1237.87i	−0.759494	+	1.31548i	0.183615	+	0.982998i	$0.441220\pi$
$941$	−714.684	+	1237.87i	−0.759494	+	1.31548i	−0.943109	+	0.332484i	$0.892113\pi$
$942$	287.805	+	7.47014i	0.305526	+	0.00793008i
$943$	−370.021	−	99.1469i	−0.392388	−	0.105140i
$944$		−	407.041i		−	0.431187i
$945$	−620.245	+	712.966i	−0.656344	+	0.754462i
$946$	760.289			0.803688
$947$	−371.310	+	1385.75i	−0.392091	+	1.46330i	0.434587	+	0.900630i	$0.356894\pi$
$947$	−371.310	+	1385.75i	−0.392091	+	1.46330i	−0.826678	+	0.562675i	$0.809772\pi$
$948$	6.36208	−	245.114i	0.00671105	−	0.258560i
$949$	−85.3898	−	49.2998i	−0.0899787	−	0.0519492i
$950$	−20.1454	+	26.3103i	−0.0212057	+	0.0276950i
$951$	781.914	+	231.418i	0.822202	+	0.243341i
$952$	60.7097	+	744.930i	0.0637707	+	0.782489i
$953$	−441.938	+	441.938i	−0.463733	+	0.463733i	−0.899877	−	0.436144i	$-0.856344\pi$
$953$	−441.938	+	441.938i	−0.463733	+	0.463733i	0.436144	+	0.899877i	$0.356344\pi$
$954$	−201.473	−	10.4657i	−0.211188	−	0.0109704i
$955$	−343.607	+	392.218i	−0.359798	+	0.410699i
$956$	−4.77357	−	2.75602i	−0.00499328	−	0.00288287i
$957$	98.8836	−	161.447i	0.103327	−	0.168701i
$958$	−285.967	+	285.967i	−0.298504	+	0.298504i
$959$	−845.799	−	718.327i	−0.881960	−	0.749038i
$960$	−970.301	+	302.082i	−1.01073	+	0.314668i
$961$	−465.583	−	806.413i	−0.484478	−	0.839140i
$962$	337.009	+	1257.73i	0.350321	+	1.30742i
$963$	−322.650	+	994.573i	−0.335047	+	1.03279i
$964$	−129.481	−	224.268i	−0.134317	−	0.232644i
$965$	846.581	−	566.301i	0.877286	−	0.586840i
$966$	−10.5055	−	189.546i	−0.0108753	−	0.196218i
$967$	86.8779	−	86.8779i	0.0898427	−	0.0898427i	−0.660757	−	0.750600i	$-0.729765\pi$
$967$	86.8779	−	86.8779i	0.0898427	−	0.0898427i	0.750600	+	0.660757i	$0.229765\pi$
$968$	572.238	+	153.331i	0.591155	+	0.158399i
$969$	−20.8971	−	22.0108i	−0.0215656	−	0.0227149i
$970$	670.102	−	764.902i	0.690827	−	0.788559i
$971$	−441.199	−	764.180i	−0.454376	−	0.787003i	0.544276	−	0.838906i	$-0.316805\pi$
$971$	−441.199	−	764.180i	−0.454376	−	0.787003i	−0.998652	+	0.0519034i	$0.983471\pi$
$972$	209.470	−	273.638i	0.215504	−	0.281521i
$973$	−616.524	−	891.731i	−0.633632	−	0.916476i
$974$	−79.8223			−0.0819531
$975$	1405.97	+	220.862i	1.44202	+	0.226525i
$976$	94.9714	+	54.8318i	0.0973067	+	0.0561801i
$977$	590.426	−	158.204i	0.604325	−	0.161928i	0.0563331	−	0.998412i	$-0.482059\pi$
$977$	590.426	−	158.204i	0.604325	−	0.161928i	0.547992	+	0.836484i	$0.315392\pi$
$978$	−694.334	+	1133.64i	−0.709953	+	1.15914i
$979$	988.120			1.00932
$980$	−183.614	+	294.965i	−0.187361	+	0.300985i
$981$	1050.17	+	681.302i	1.07051	+	0.694497i
$982$	−1.46278	−	0.391951i	−0.00148959	−	0.000399135i
$983$	823.815	−	220.740i	0.838062	−	0.224558i	0.185834	−	0.982581i	$-0.440501\pi$
$983$	823.815	−	220.740i	0.838062	−	0.224558i	0.652228	+	0.758023i	$0.273835\pi$
$984$	1224.45	+	1289.71i	1.24436	+	1.31068i
$985$	1199.70	+	590.855i	1.21797	+	0.599853i
$986$	−90.4481			−0.0917323
$987$	497.503	−	163.305i	0.504056	−	0.165455i
$988$	15.6972	+	15.6972i	0.0158878	+	0.0158878i
$989$	−96.8039	−	167.669i	−0.0978806	−	0.169534i
$990$	484.929	−	867.892i	0.489827	−	0.876658i
$991$	104.543	−	181.074i	0.105493	−	0.182718i	−0.808447	−	0.588569i	$-0.799691\pi$
$991$	104.543	−	181.074i	0.105493	−	0.182718i	0.913939	+	0.405851i	$0.133025\pi$
$992$	113.228	+	30.3393i	0.114141	+	0.0305839i
$993$	1126.89	−	612.189i	1.13484	−	0.616504i
$994$	−422.946	−	1183.90i	−0.425499	−	1.19105i
$995$	96.7403	−	487.664i	0.0972264	−	0.490114i
$996$	−616.084	+	148.059i	−0.618558	+	0.148653i
$997$	−328.709	+	88.0773i	−0.329698	+	0.0883424i	−0.419871	−	0.907584i	$-0.637925\pi$
$997$	−328.709	+	88.0773i	−0.329698	+	0.0883424i	0.0901729	+	0.995926i	$0.471258\pi$
$998$	155.904	+	581.843i	0.156217	+	0.583009i
$999$	−384.134	+	1087.15i	−0.384519	+	1.08824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.38.20	yes	112
3.2	odd	2	inner	105.3.w.a.38.9	yes	112
5.2	odd	4	inner	105.3.w.a.17.20	yes	112
7.5	odd	6	inner	105.3.w.a.68.9	yes	112
15.2	even	4	inner	105.3.w.a.17.9	✓	112
21.5	even	6	inner	105.3.w.a.68.20	yes	112
35.12	even	12	inner	105.3.w.a.47.9	yes	112
105.47	odd	12	inner	105.3.w.a.47.20	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.9	✓	112	15.2	even	4	inner
105.3.w.a.17.20	yes	112	5.2	odd	4	inner
105.3.w.a.38.9	yes	112	3.2	odd	2	inner
105.3.w.a.38.20	yes	112	1.1	even	1	trivial
105.3.w.a.47.9	yes	112	35.12	even	12	inner
105.3.w.a.47.20	yes	112	105.47	odd	12	inner
105.3.w.a.68.9	yes	112	7.5	odd	6	inner
105.3.w.a.68.20	yes	112	21.5	even	6	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415874 - 1.55206i) q^{2} +(0.0778404 - 2.99899i) q^{3} +(1.22815 + 0.709073i) q^{4} +(4.73382 - 1.60964i) q^{5} +(-4.62225 - 1.36802i) q^{6} +(3.98085 + 5.75785i) q^{7} +(6.15604 - 6.15604i) q^{8} +(-8.98788 - 0.466885i) q^{9} +(-0.529598 - 8.01660i) q^{10} +(-11.9074 - 6.87474i) q^{11} +(2.22210 - 3.62801i) q^{12} +(-13.4181 + 13.4181i) q^{13} +(10.5921 - 3.78400i) q^{14} +(-4.45883 - 14.3220i) q^{15} +(-4.15814 - 7.20211i) q^{16} +(3.17420 + 11.8463i) q^{17} +(-4.46247 + 13.7556i) q^{18} +(-0.412457 - 0.714396i) q^{19} +(6.95519 + 1.37974i) q^{20} +(17.5776 - 11.4903i) q^{21} +(-15.6220 + 15.6220i) q^{22} +(5.43425 + 1.45610i) q^{23} +(-17.9827 - 18.9411i) q^{24} +(19.8181 - 15.2395i) q^{25} +(15.2455 + 26.4061i) q^{26} +(-2.09980 + 26.9182i) q^{27} +(0.806351 + 9.89421i) q^{28} -4.58981 q^{29} +(-24.0829 + 0.964243i) q^{30} +(4.73029 + 2.73103i) q^{31} +(20.7298 - 5.55454i) q^{32} +(-21.5441 + 35.1750i) q^{33} +19.7063 q^{34} +(28.1127 + 20.8489i) q^{35} +(-10.7074 - 6.94647i) q^{36} +(41.2492 + 11.0527i) q^{37} +(-1.28032 + 0.343060i) q^{38} +(39.1964 + 41.2853i) q^{39} +(19.2325 - 39.0506i) q^{40} -68.0906 q^{41} +(-10.5237 - 32.0601i) q^{42} +(-24.3339 - 24.3339i) q^{43} +(-9.74938 - 16.8864i) q^{44} +(-43.2985 + 12.2571i) q^{45} +(4.51993 - 7.82875i) q^{46} +(24.0846 + 6.45346i) q^{47} +(-21.9227 + 11.9096i) q^{48} +(-17.3056 + 45.8423i) q^{49} +(-15.4109 - 37.0967i) q^{50} +(35.7740 - 8.59728i) q^{51} +(-25.9939 + 6.96505i) q^{52} +(3.61069 + 13.4753i) q^{53} +(40.9056 + 14.4536i) q^{54} +(-67.4333 - 13.3771i) q^{55} +(59.9518 + 10.9393i) q^{56} +(-2.17457 + 1.18134i) q^{57} +(-1.90879 + 7.12369i) q^{58} +(42.3877 + 24.4725i) q^{59} +(4.67921 - 20.7512i) q^{60} +(-11.4199 + 6.59330i) q^{61} +(6.20594 - 6.20594i) q^{62} +(-33.0912 - 53.6095i) q^{63} -67.7492i q^{64} +(-41.9206 + 85.1174i) q^{65} +(45.6342 + 48.0663i) q^{66} +(-6.80245 - 25.3871i) q^{67} +(-4.50148 + 16.7998i) q^{68} +(4.78984 - 16.1839i) q^{69} +(44.0501 - 34.9623i) q^{70} -111.772i q^{71} +(-58.2039 + 52.4556i) q^{72} +(1.34482 + 5.01894i) q^{73} +(34.3090 - 59.4249i) q^{74} +(-44.1606 - 60.6205i) q^{75} -1.16985i q^{76} +(-7.81789 - 95.9283i) q^{77} +(80.3782 - 43.6658i) q^{78} +(49.9119 - 28.8166i) q^{79} +(-31.2767 - 27.4004i) q^{80} +(80.5640 + 8.39262i) q^{81} +(-28.3171 + 105.681i) q^{82} +(-105.311 - 105.311i) q^{83} +(29.7354 - 1.64807i) q^{84} +(34.0944 + 50.9688i) q^{85} +(-47.8876 + 27.6479i) q^{86} +(-0.357273 + 13.7648i) q^{87} +(-115.624 + 30.9813i) q^{88} +(-62.2378 + 35.9330i) q^{89} +(1.01713 + 72.2995i) q^{90} +(-130.675 - 23.8440i) q^{91} +(5.64159 + 5.64159i) q^{92} +(8.55855 - 13.9735i) q^{93} +(20.0324 - 34.6971i) q^{94} +(-3.10242 - 2.71791i) q^{95} +(-15.0444 - 62.6009i) q^{96} +(89.5020 + 89.5020i) q^{97} +(63.9532 + 45.9241i) q^{98} +(103.813 + 67.3487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more