LMFDB - Embedded newform 430.2.j.a.49.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.8
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.13990 + 0.658124i) q^{3} -1.00000 q^{4} +(-1.72456 - 1.42334i) q^{5} +(0.658124 - 1.13990i) q^{6} +(-3.46526 + 2.00067i) q^{7} +1.00000i q^{8} +(-0.633745 - 1.09768i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.13990 + 0.658124i) q^{3} -1.00000 q^{4} +(-1.72456 - 1.42334i) q^{5} +(0.658124 - 1.13990i) q^{6} +(-3.46526 + 2.00067i) q^{7} +1.00000i q^{8} +(-0.633745 - 1.09768i) q^{9} +(-1.42334 + 1.72456i) q^{10} -4.54340 q^{11} +(-1.13990 - 0.658124i) q^{12} +(0.344070 - 0.198649i) q^{13} +(2.00067 + 3.46526i) q^{14} +(-1.02910 - 2.75745i) q^{15} +1.00000 q^{16} +(-5.13493 + 2.96465i) q^{17} +(-1.09768 + 0.633745i) q^{18} +(3.29530 - 5.70763i) q^{19} +(1.72456 + 1.42334i) q^{20} -5.26676 q^{21} +4.54340i q^{22} +(-0.205900 - 0.118876i) q^{23} +(-0.658124 + 1.13990i) q^{24} +(0.948208 + 4.90927i) q^{25} +(-0.198649 - 0.344070i) q^{26} -5.61708i q^{27} +(3.46526 - 2.00067i) q^{28} +(3.62561 + 6.27974i) q^{29} +(-2.75745 + 1.02910i) q^{30} +(3.00068 - 5.19733i) q^{31} -1.00000i q^{32} +(-5.17904 - 2.99012i) q^{33} +(2.96465 + 5.13493i) q^{34} +(8.82368 + 1.48197i) q^{35} +(0.633745 + 1.09768i) q^{36} +(-5.13633 - 2.96546i) q^{37} +(-5.70763 - 3.29530i) q^{38} +0.522942 q^{39} +(1.42334 - 1.72456i) q^{40} -7.91990 q^{41} +5.26676i q^{42} +(0.0743880 - 6.55702i) q^{43} +4.54340 q^{44} +(-0.469438 + 2.79504i) q^{45} +(-0.118876 + 0.205900i) q^{46} +7.24856i q^{47} +(1.13990 + 0.658124i) q^{48} +(4.50536 - 7.80351i) q^{49} +(4.90927 - 0.948208i) q^{50} -7.80443 q^{51} +(-0.344070 + 0.198649i) q^{52} +(3.99163 + 2.30457i) q^{53} -5.61708 q^{54} +(7.83536 + 6.46680i) q^{55} +(-2.00067 - 3.46526i) q^{56} +(7.51266 - 4.33744i) q^{57} +(6.27974 - 3.62561i) q^{58} -4.15283 q^{59} +(1.02910 + 2.75745i) q^{60} +(1.46507 + 2.53758i) q^{61} +(-5.19733 - 3.00068i) q^{62} +(4.39218 + 2.53583i) q^{63} -1.00000 q^{64} +(-0.876113 - 0.147147i) q^{65} +(-2.99012 + 5.17904i) q^{66} +(3.57089 + 2.06166i) q^{67} +(5.13493 - 2.96465i) q^{68} +(-0.156471 - 0.271015i) q^{69} +(1.48197 - 8.82368i) q^{70} +(1.50077 + 2.59941i) q^{71} +(1.09768 - 0.633745i) q^{72} +(-8.61166 + 4.97194i) q^{73} +(-2.96546 + 5.13633i) q^{74} +(-2.15004 + 6.22014i) q^{75} +(-3.29530 + 5.70763i) q^{76} +(15.7441 - 9.08985i) q^{77} -0.522942i q^{78} +(-5.74385 - 9.94864i) q^{79} +(-1.72456 - 1.42334i) q^{80} +(1.79550 - 3.10990i) q^{81} +7.91990i q^{82} +(-1.52685 - 0.881529i) q^{83} +5.26676 q^{84} +(13.0752 + 2.19603i) q^{85} +(-6.55702 - 0.0743880i) q^{86} +9.54441i q^{87} -4.54340i q^{88} +(-7.40713 + 12.8295i) q^{89} +(2.79504 + 0.469438i) q^{90} +(-0.794861 + 1.37674i) q^{91} +(0.205900 + 0.118876i) q^{92} +(6.84098 - 3.94964i) q^{93} +7.24856 q^{94} +(-13.8068 + 5.15281i) q^{95} +(0.658124 - 1.13990i) q^{96} -7.92017i q^{97} +(-7.80351 - 4.50536i) q^{98} +(2.87936 + 4.98719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.13990	+	0.658124i	0.658124	+	0.379968i	0.791562	−	0.611089i	$-0.209268\pi$
$3$	1.13990	+	0.658124i	0.658124	+	0.379968i	−0.133438	+	0.991057i	$0.542602\pi$
$4$	−1.00000			−0.500000
$5$	−1.72456	−	1.42334i	−0.771246	−	0.636537i
$5$	−1.72456	−	1.42334i	−0.771246	−	0.636537i
$6$	0.658124	−	1.13990i	0.268678	−	0.465364i
$7$	−3.46526	+	2.00067i	−1.30975	+	0.756182i	−0.982054	−	0.188602i	$-0.939604\pi$
$7$	−3.46526	+	2.00067i	−1.30975	+	0.756182i	−0.327692	+	0.944785i	$0.606271\pi$
$8$			1.00000i			0.353553i
$9$	−0.633745	−	1.09768i	−0.211248	−	0.365893i
$10$	−1.42334	+	1.72456i	−0.450100	+	0.545353i
$11$	−4.54340			−1.36989			−0.684944	−	0.728596i	$-0.740173\pi$
$11$	−4.54340			−1.36989			−0.684944	+	0.728596i	$0.740173\pi$
$12$	−1.13990	−	0.658124i	−0.329062	−	0.189984i
$13$	0.344070	−	0.198649i	0.0954278	−	0.0550953i	−0.451527	−	0.892258i	$-0.649120\pi$
$13$	0.344070	−	0.198649i	0.0954278	−	0.0550953i	0.546954	+	0.837162i	$0.315787\pi$
$14$	2.00067	+	3.46526i	0.534701	+	0.926130i
$15$	−1.02910	−	2.75745i	−0.265712	−	0.711970i
$16$	1.00000			0.250000
$17$	−5.13493	+	2.96465i	−1.24540	+	0.719033i	−0.970189	−	0.242350i	$-0.922082\pi$
$17$	−5.13493	+	2.96465i	−1.24540	+	0.719033i	−0.275213	+	0.961383i	$0.588748\pi$
$18$	−1.09768	+	0.633745i	−0.258725	+	0.149375i
$19$	3.29530	−	5.70763i	0.755994	−	1.30942i	−0.188884	−	0.981999i	$-0.560487\pi$
$19$	3.29530	−	5.70763i	0.755994	−	1.30942i	0.944878	−	0.327421i	$-0.106180\pi$
$20$	1.72456	+	1.42334i	0.385623	+	0.318268i
$21$	−5.26676			−1.14930
$22$			4.54340i			0.968656i
$23$	−0.205900	−	0.118876i	−0.0429330	−	0.0247874i	0.478380	−	0.878153i	$-0.341224\pi$
$23$	−0.205900	−	0.118876i	−0.0429330	−	0.0247874i	−0.521313	+	0.853366i	$0.674558\pi$
$24$	−0.658124	+	1.13990i	−0.134339	+	0.232682i
$25$	0.948208	+	4.90927i	0.189642	+	0.981853i
$26$	−0.198649	−	0.344070i	−0.0389582	−	0.0674776i
$27$		−	5.61708i		−	1.08101i
$28$	3.46526	−	2.00067i	0.654873	−	0.378091i
$29$	3.62561	+	6.27974i	0.673259	+	1.16612i	0.976974	+	0.213356i	$0.0684395\pi$
$29$	3.62561	+	6.27974i	0.673259	+	1.16612i	−0.303715	+	0.952763i	$0.598227\pi$
$30$	−2.75745	+	1.02910i	−0.503438	+	0.187887i
$31$	3.00068	−	5.19733i	0.538938	−	0.933468i	−0.460024	−	0.887907i	$-0.652159\pi$
$31$	3.00068	−	5.19733i	0.538938	−	0.933468i	0.998962	−	0.0455613i	$-0.0145076\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.17904	−	2.99012i	−0.901556	−	0.520514i
$34$	2.96465	+	5.13493i	0.508433	+	0.880632i
$35$	8.82368	+	1.48197i	1.49147	+	0.250499i
$36$	0.633745	+	1.09768i	0.105624	+	0.182946i
$37$	−5.13633	−	2.96546i	−0.844407	−	0.487518i	0.0143529	−	0.999897i	$-0.495431\pi$
$37$	−5.13633	−	2.96546i	−0.844407	−	0.487518i	−0.858760	+	0.512379i	$0.828764\pi$
$38$	−5.70763	−	3.29530i	−0.925900	−	0.534569i
$39$	0.522942			0.0837378
$40$	1.42334	−	1.72456i	0.225050	−	0.272677i
$41$	−7.91990			−1.23688			−0.618440	−	0.785832i	$-0.712235\pi$
$41$	−7.91990			−1.23688			−0.618440	+	0.785832i	$0.712235\pi$
$42$			5.26676i			0.812678i
$43$	0.0743880	−	6.55702i	0.0113441	−	0.999936i
$43$	0.0743880	−	6.55702i	0.0113441	−	0.999936i
$44$	4.54340			0.684944
$45$	−0.469438	+	2.79504i	−0.0699798	+	0.416661i
$46$	−0.118876	+	0.205900i	−0.0175273	+	0.0303582i
$47$			7.24856i			1.05731i	0.848836	+	0.528656i	$0.177304\pi$
$47$			7.24856i			1.05731i	−0.848836	+	0.528656i	$0.822696\pi$
$48$	1.13990	+	0.658124i	0.164531	+	0.0949921i
$49$	4.50536	−	7.80351i	0.643623	−	1.11479i
$50$	4.90927	−	0.948208i	0.694275	−	0.134097i
$51$	−7.80443			−1.09284
$52$	−0.344070	+	0.198649i	−0.0477139	+	0.0275476i
$53$	3.99163	+	2.30457i	0.548293	+	0.316557i	0.748433	−	0.663210i	$-0.230806\pi$
$53$	3.99163	+	2.30457i	0.548293	+	0.316557i	−0.200140	+	0.979767i	$0.564140\pi$
$54$	−5.61708			−0.764387
$55$	7.83536	+	6.46680i	1.05652	+	0.871984i
$56$	−2.00067	−	3.46526i	−0.267351	−	0.463065i
$57$	7.51266	−	4.33744i	0.995077	−	0.574508i
$58$	6.27974	−	3.62561i	0.824571	−	0.476066i
$59$	−4.15283			−0.540652			−0.270326	−	0.962769i	$-0.587132\pi$
$59$	−4.15283			−0.540652			−0.270326	+	0.962769i	$0.587132\pi$
$60$	1.02910	+	2.75745i	0.132856	+	0.355985i
$61$	1.46507	+	2.53758i	0.187583	+	0.324904i	0.944444	−	0.328672i	$-0.106601\pi$
$61$	1.46507	+	2.53758i	0.187583	+	0.324904i	−0.756861	+	0.653576i	$0.773268\pi$
$62$	−5.19733	−	3.00068i	−0.660062	−	0.381087i
$63$	4.39218	+	2.53583i	0.553363	+	0.319484i
$64$	−1.00000			−0.125000
$65$	−0.876113	−	0.147147i	−0.108668	−	0.0182513i
$66$	−2.99012	+	5.17904i	−0.368059	+	0.637496i
$67$	3.57089	+	2.06166i	0.436254	+	0.251871i	0.702007	−	0.712170i	$-0.252287\pi$
$67$	3.57089	+	2.06166i	0.436254	+	0.251871i	−0.265753	+	0.964041i	$0.585621\pi$
$68$	5.13493	−	2.96465i	0.622701	−	0.359517i
$69$	−0.156471	−	0.271015i	−0.0188369	−	0.0326264i
$70$	1.48197	−	8.82368i	0.177129	−	1.05463i
$71$	1.50077	+	2.59941i	0.178109	+	0.308493i	0.941233	−	0.337759i	$-0.109669\pi$
$71$	1.50077	+	2.59941i	0.178109	+	0.308493i	−0.763124	+	0.646252i	$0.776335\pi$
$72$	1.09768	−	0.633745i	0.129363	−	0.0746875i
$73$	−8.61166	+	4.97194i	−1.00792	+	0.581922i	−0.910581	−	0.413330i	$-0.864366\pi$
$73$	−8.61166	+	4.97194i	−1.00792	+	0.581922i	−0.0973366	+	0.995252i	$0.531032\pi$
$74$	−2.96546	+	5.13633i	−0.344728	+	0.597086i
$75$	−2.15004	+	6.22014i	−0.248265	+	0.718239i
$76$	−3.29530	+	5.70763i	−0.377997	+	0.654710i
$77$	15.7441	−	9.08985i	1.79420	−	1.03588i
$78$		−	0.522942i		−	0.0592116i
$79$	−5.74385	−	9.94864i	−0.646234	−	1.11931i	−0.984015	−	0.178085i	$-0.943010\pi$
$79$	−5.74385	−	9.94864i	−0.646234	−	1.11931i	0.337782	−	0.941225i	$-0.390323\pi$
$80$	−1.72456	−	1.42334i	−0.192812	−	0.159134i
$81$	1.79550	−	3.10990i	0.199500	−	0.345544i
$82$			7.91990i			0.874607i
$83$	−1.52685	−	0.881529i	−0.167594	−	0.0967604i	0.413857	−	0.910342i	$-0.364181\pi$
$83$	−1.52685	−	0.881529i	−0.167594	−	0.0967604i	−0.581451	+	0.813582i	$0.697515\pi$
$84$	5.26676			0.574650
$85$	13.0752	+	2.19603i	1.41820	+	0.238193i
$86$	−6.55702	−	0.0743880i	−0.707061	−	0.00802147i
$87$			9.54441i			1.02327i
$88$		−	4.54340i		−	0.484328i
$89$	−7.40713	+	12.8295i	−0.785154	+	1.35993i	0.143753	+	0.989614i	$0.454083\pi$
$89$	−7.40713	+	12.8295i	−0.785154	+	1.35993i	−0.928907	+	0.370313i	$0.879251\pi$
$90$	2.79504	+	0.469438i	0.294624	+	0.0494832i
$91$	−0.794861	+	1.37674i	−0.0833241	+	0.144322i
$92$	0.205900	+	0.118876i	0.0214665	+	0.0123937i
$93$	6.84098	−	3.94964i	0.709376	−	0.409559i
$94$	7.24856			0.747632
$95$	−13.8068	+	5.15281i	−1.41655	+	0.528668i
$96$	0.658124	−	1.13990i	0.0671695	−	0.116341i
$97$		−	7.92017i		−	0.804171i	−0.915602	−	0.402086i	$-0.868285\pi$
$97$		−	7.92017i		−	0.804171i	0.915602	−	0.402086i	$-0.131715\pi$
$98$	−7.80351	−	4.50536i	−0.788274	−	0.455110i
$99$	2.87936	+	4.98719i	0.289386	+	0.501232i
$100$	−0.948208	−	4.90927i	−0.0948208	−	0.490927i
$101$	−6.01443	−	10.4173i	−0.598459	−	1.03656i	−0.993049	−	0.117703i	$-0.962447\pi$
$101$	−6.01443	−	10.4173i	−0.598459	−	1.03656i	0.394590	−	0.918857i	$-0.370887\pi$
$102$			7.80443i			0.772754i
$103$	14.6365	−	8.45040i	1.44218	−	0.832642i	0.444184	−	0.895936i	$-0.353494\pi$
$103$	14.6365	−	8.45040i	1.44218	−	0.832642i	0.997995	+	0.0632933i	$0.0201604\pi$
$104$	0.198649	+	0.344070i	0.0194791	+	0.0337388i
$105$	9.08284	+	7.49638i	0.886394	+	0.731572i
$106$	2.30457	−	3.99163i	0.223840	−	0.387702i
$107$		−	14.2763i		−	1.38014i	−0.723743	−	0.690069i	$-0.757580\pi$
$107$		−	14.2763i		−	1.38014i	0.723743	−	0.690069i	$-0.242420\pi$
$108$			5.61708i			0.540504i
$109$	−5.50669	+	9.53787i	−0.527445	+	0.913562i	0.472043	+	0.881576i	$0.343517\pi$
$109$	−5.50669	+	9.53787i	−0.527445	+	0.913562i	−0.999488	+	0.0319867i	$0.989817\pi$
$110$	6.46680	−	7.83536i	0.616586	−	0.747073i
$111$	−3.90328	−	6.76068i	−0.370483	−	0.641696i
$112$	−3.46526	+	2.00067i	−0.327436	+	0.189046i
$113$		−	12.0708i		−	1.13552i	−0.823194	−	0.567761i	$-0.807810\pi$
$113$		−	12.0708i		−	1.13552i	0.823194	−	0.567761i	$-0.192190\pi$
$114$	−4.33744	−	7.51266i	−0.406238	−	0.703625i
$115$	0.185885	+	0.498074i	0.0173339	+	0.0464457i
$116$	−3.62561	−	6.27974i	−0.336630	−	0.583060i
$117$	−0.436105	−	0.251785i	−0.0403179	−	0.0232776i
$118$			4.15283i			0.382299i
$119$	11.8626	−	20.5466i	1.08744	−	1.88350i
$120$	2.75745	−	1.02910i	0.251719	−	0.0939434i
$121$	9.64250			0.876591
$122$	2.53758	−	1.46507i	0.229742	−	0.132642i
$123$	−9.02793	−	5.21228i	−0.814021	−	0.469975i
$124$	−3.00068	+	5.19733i	−0.269469	+	0.466734i
$125$	5.35231	−	9.81594i	0.478725	−	0.877965i
$126$	2.53583	−	4.39218i	0.225909	−	0.391287i
$127$			10.3533i			0.918706i	0.888254	+	0.459353i	$0.151919\pi$
$127$			10.3533i			0.918706i	−0.888254	+	0.459353i	$0.848081\pi$
$128$			1.00000i			0.0883883i
$129$	4.40013	−	7.42542i	0.387410	−	0.653772i
$130$	−0.147147	+	0.876113i	−0.0129056	+	0.0768402i
$131$	−1.81597			−0.158662			−0.0793310	−	0.996848i	$-0.525278\pi$
$131$	−1.81597			−0.158662			−0.0793310	+	0.996848i	$0.525278\pi$
$132$	5.17904	+	2.99012i	0.450778	+	0.260257i
$133$			26.3713i			2.28668i
$134$	2.06166	−	3.57089i	0.178100	−	0.308478i
$135$	−7.99501	+	9.68698i	−0.688101	+	0.833723i
$136$	−2.96465	−	5.13493i	−0.254217	−	0.440316i
$137$		−	12.8025i		−	1.09379i	−0.837200	−	0.546897i	$-0.815809\pi$
$137$		−	12.8025i		−	1.09379i	0.837200	−	0.546897i	$-0.184191\pi$
$138$	−0.271015	+	0.156471i	−0.0230703	+	0.0133197i
$139$	7.03293	−	12.1814i	0.596525	−	1.03321i	−0.396804	−	0.917903i	$-0.629881\pi$
$139$	7.03293	−	12.1814i	0.596525	−	1.03321i	0.993330	−	0.115309i	$-0.0367858\pi$
$140$	−8.82368	−	1.48197i	−0.745737	−	0.125249i
$141$	−4.77045	+	8.26267i	−0.401745	+	0.695842i
$142$	2.59941	−	1.50077i	0.218138	−	0.125942i
$143$	−1.56325	+	0.902541i	−0.130725	+	0.0754743i
$144$	−0.633745	−	1.09768i	−0.0528121	−	0.0914732i
$145$	2.68563	−	15.9903i	0.223029	−	1.32792i
$146$	4.97194	+	8.61166i	0.411481	+	0.712706i
$147$	10.2714	−	5.93017i	0.847167	−	0.489112i
$148$	5.13633	+	2.96546i	0.422203	+	0.243759i
$149$	−3.27337	+	5.66965i	−0.268165	+	0.464476i	−0.968388	−	0.249449i	$-0.919751\pi$
$149$	−3.27337	+	5.66965i	−0.268165	+	0.464476i	0.700223	+	0.713924i	$0.253084\pi$
$150$	6.22014	+	2.15004i	0.507872	+	0.175550i
$151$	−8.97394			−0.730289			−0.365145	−	0.930951i	$-0.618980\pi$
$151$	−8.97394			−0.730289			−0.365145	+	0.930951i	$0.618980\pi$
$152$	5.70763	+	3.29530i	0.462950	+	0.267284i
$153$	6.50846	+	3.75766i	0.526178	+	0.303789i
$154$	−9.08985	−	15.7441i	−0.732481	−	1.26869i
$155$	−12.5724	+	4.69212i	−1.00984	+	0.376880i
$156$	−0.522942			−0.0418689
$157$	−4.74190	+	2.73774i	−0.378445	+	0.218495i	−0.677141	−	0.735853i	$-0.736781\pi$
$157$	−4.74190	+	2.73774i	−0.378445	+	0.218495i	0.298697	+	0.954348i	$0.403448\pi$
$158$	−9.94864	+	5.74385i	−0.791471	+	0.456956i
$159$	3.03339	+	5.25398i	0.240563	+	0.416668i
$160$	−1.42334	+	1.72456i	−0.112525	+	0.136338i
$161$	0.951328			0.0749752
$162$	−3.10990	−	1.79550i	−0.244337	−	0.141068i
$163$	−4.65240	+	2.68607i	−0.364404	+	0.210389i	−0.671011	−	0.741447i	$-0.734140\pi$
$163$	−4.65240	+	2.68607i	−0.364404	+	0.210389i	0.306607	+	0.951836i	$0.400806\pi$
$164$	7.91990			0.618440
$165$	4.67561	+	12.5282i	0.363996	+	0.975318i
$166$	−0.881529	+	1.52685i	−0.0684200	+	0.118507i
$167$	−9.19249	−	5.30729i	−0.711336	−	0.410690i	0.100219	−	0.994965i	$-0.468046\pi$
$167$	−9.19249	−	5.30729i	−0.711336	−	0.410690i	−0.811556	+	0.584275i	$0.801379\pi$
$168$		−	5.26676i		−	0.406339i
$169$	−6.42108	+	11.1216i	−0.493929	+	0.855510i
$170$	2.19603	−	13.0752i	0.168428	−	1.00282i
$171$	−8.35352			−0.638810
$172$	−0.0743880	+	6.55702i	−0.00567204	+	0.499968i
$173$			24.9229i			1.89485i	0.319974	+	0.947426i	$0.396326\pi$
$173$			24.9229i			1.89485i	−0.319974	+	0.947426i	$0.603674\pi$
$174$	9.54441			0.723560
$175$	−13.1076	−	15.1148i	−0.990842	−	1.14257i
$176$	−4.54340			−0.342472
$177$	−4.73383	−	2.73308i	−0.355816	−	0.205431i
$178$	12.8295	+	7.40713i	0.961613	+	0.555188i
$179$	2.34878	+	4.06820i	0.175556	+	0.304072i	0.940354	−	0.340199i	$-0.110494\pi$
$179$	2.34878	+	4.06820i	0.175556	+	0.304072i	−0.764798	+	0.644271i	$0.777161\pi$
$180$	0.469438	−	2.79504i	0.0349899	−	0.208330i
$181$	5.45913	+	9.45550i	0.405774	+	0.702822i	0.994411	−	0.105576i	$-0.0336686\pi$
$181$	5.45913	+	9.45550i	0.405774	+	0.702822i	−0.588637	+	0.808397i	$0.700335\pi$
$182$	1.37674	+	0.794861i	0.102051	+	0.0589190i
$183$			3.85680i			0.285103i
$184$	0.118876	−	0.205900i	0.00876367	−	0.0151791i
$185$	4.63704	+	12.4248i	0.340922	+	0.913493i
$186$	−3.94964	−	6.84098i	−0.289602	−	0.501605i
$187$	23.3300	−	13.4696i	1.70606	−	0.984994i
$188$		−	7.24856i		−	0.528656i
$189$	11.2379	+	19.4646i	0.817438	+	1.41584i
$190$	5.15281	+	13.8068i	0.373824	+	1.00165i
$191$	3.78228	−	6.55110i	0.273676	−	0.474021i	−0.696124	−	0.717922i	$-0.745094\pi$
$191$	3.78228	−	6.55110i	0.273676	−	0.474021i	0.969800	+	0.243900i	$0.0784270\pi$
$192$	−1.13990	−	0.658124i	−0.0822655	−	0.0474960i
$193$			6.28311i			0.452268i	0.974096	+	0.226134i	$0.0726088\pi$
$193$			6.28311i			0.452268i	−0.974096	+	0.226134i	$0.927391\pi$
$194$	−7.92017			−0.568635
$195$	−0.901845	−	0.744325i	−0.0645825	−	0.0533022i
$196$	−4.50536	+	7.80351i	−0.321811	+	0.557394i
$197$	1.75258	−	1.01185i	0.124866	−	0.0720916i	−0.436266	−	0.899818i	$-0.643699\pi$
$197$	1.75258	−	1.01185i	0.124866	−	0.0720916i	0.561132	+	0.827726i	$0.310366\pi$
$198$	4.98719	−	2.87936i	0.354424	−	0.204627i
$199$	12.6142			0.894197			0.447098	−	0.894485i	$-0.352457\pi$
$199$	12.6142			0.894197			0.447098	+	0.894485i	$0.352457\pi$
$200$	−4.90927	+	0.948208i	−0.347138	+	0.0670485i
$201$	2.71365	+	4.70018i	0.191406	+	0.331525i
$202$	−10.4173	+	6.01443i	−0.732959	+	0.423174i
$203$	−25.1274	−	14.5073i	−1.76360	−	1.01821i
$204$	7.80443			0.546420
$205$	13.6583	+	11.2727i	0.953940	+	0.787320i
$206$	−8.45040	−	14.6365i	−0.588767	−	1.01977i
$207$			0.301349i			0.0209452i
$208$	0.344070	−	0.198649i	0.0238569	−	0.0137738i
$209$	−14.9719	+	25.9321i	−1.03563	+	1.79376i
$210$	7.49638	−	9.08284i	0.517300	−	0.626775i
$211$	−26.6725			−1.83621			−0.918104	−	0.396339i	$-0.870280\pi$
$211$	−26.6725			−1.83621			−0.918104	+	0.396339i	$0.870280\pi$
$212$	−3.99163	−	2.30457i	−0.274146	−	0.158279i
$213$			3.95077i			0.270703i
$214$	−14.2763			−0.975905
$215$	−9.46115	+	11.2021i	−0.645245	+	0.763976i
$216$	5.61708			0.382194
$217$			24.0135i			1.63014i
$218$	9.53787	+	5.50669i	0.645986	+	0.372960i
$219$	−13.0886			−0.884447
$220$	−7.83536	−	6.46680i	−0.528260	−	0.435992i
$221$	−1.17785	+	2.04009i	−0.0792306	+	0.137232i
$222$	−6.76068	+	3.90328i	−0.453747	+	0.261971i
$223$			3.84306i			0.257350i	0.991687	+	0.128675i	$0.0410724\pi$
$223$			3.84306i			0.257350i	−0.991687	+	0.128675i	$0.958928\pi$
$224$	2.00067	+	3.46526i	0.133675	+	0.231533i
$225$	4.78787	−	4.15205i	0.319191	−	0.276803i
$226$	−12.0708			−0.802935
$227$	−19.4469	−	11.2277i	−1.29074	−	0.745208i	−0.311954	−	0.950097i	$-0.600983\pi$
$227$	−19.4469	−	11.2277i	−1.29074	−	0.745208i	−0.978785	+	0.204889i	$0.934317\pi$
$228$	−7.51266	+	4.33744i	−0.497538	+	0.287254i
$229$	−4.29832	−	7.44490i	−0.284041	−	0.491973i	0.688335	−	0.725393i	$-0.258342\pi$
$229$	−4.29832	−	7.44490i	−0.284041	−	0.491973i	−0.972376	+	0.233420i	$0.925008\pi$
$230$	0.498074	−	0.185885i	0.0328420	−	0.0122569i
$231$	23.9290			1.57441
$232$	−6.27974	+	3.62561i	−0.412285	+	0.238033i
$233$	−14.1980	+	8.19720i	−0.930140	+	0.537016i	−0.886856	−	0.462046i	$-0.847115\pi$
$233$	−14.1980	+	8.19720i	−0.930140	+	0.537016i	−0.0432840	+	0.999063i	$0.513782\pi$
$234$	−0.251785	+	0.436105i	−0.0164597	+	0.0285091i
$235$	10.3172	−	12.5006i	0.673018	−	0.815447i
$236$	4.15283			0.270326
$237$		−	15.1207i		−	0.982193i
$238$	−20.5466	−	11.8626i	−1.33184	−	0.768936i
$239$	−13.1099	+	22.7070i	−0.848009	+	1.46879i	0.0349739	+	0.999388i	$0.488865\pi$
$239$	−13.1099	+	22.7070i	−0.848009	+	1.46879i	−0.882983	+	0.469406i	$0.844468\pi$
$240$	−1.02910	−	2.75745i	−0.0664280	−	0.177992i
$241$	−12.1780	−	21.0930i	−0.784456	−	1.35872i	−0.929323	−	0.369267i	$-0.879609\pi$
$241$	−12.1780	−	21.0930i	−0.784456	−	1.35872i	0.144867	−	0.989451i	$-0.453725\pi$
$242$		−	9.64250i		−	0.619843i
$243$	−10.5002	+	6.06229i	−0.673588	+	0.388896i
$244$	−1.46507	−	2.53758i	−0.0937917	−	0.162452i
$245$	−18.8768	+	7.04496i	−1.20599	+	0.450086i
$246$	−5.21228	+	9.02793i	−0.332323	+	0.575600i
$247$		−	2.61843i		−	0.166607i
$248$	5.19733	+	3.00068i	0.330031	+	0.190543i
$249$	−1.16031	−	2.00972i	−0.0735318	−	0.127361i
$250$	−9.81594	−	5.35231i	−0.620815	−	0.338510i
$251$	12.0420	+	20.8574i	0.760085	+	1.31651i	0.942806	+	0.333341i	$0.108176\pi$
$251$	12.0420	+	20.8574i	0.760085	+	1.31651i	−0.182722	+	0.983165i	$0.558491\pi$
$252$	−4.39218	−	2.53583i	−0.276681	−	0.159742i
$253$	0.935485	+	0.540102i	0.0588134	+	0.0339559i
$254$	10.3533			0.649623
$255$	13.4592	+	11.1084i	0.842848	+	0.695633i
$256$	1.00000			0.0625000
$257$		−	3.70281i		−	0.230975i	−0.993309	−	0.115488i	$-0.963157\pi$
$257$		−	3.70281i		−	0.230975i	0.993309	−	0.115488i	$-0.0368430\pi$
$258$	−7.42542	−	4.40013i	−0.462286	−	0.273940i
$259$	23.7316			1.47461
$260$	0.876113	+	0.147147i	0.0543342	+	0.00912564i
$261$	4.59542	−	7.95951i	0.284450	−	0.492681i
$262$			1.81597i			0.112191i
$263$	5.60091	+	3.23369i	0.345367	+	0.199398i	0.662643	−	0.748936i	$-0.269435\pi$
$263$	5.60091	+	3.23369i	0.345367	+	0.199398i	−0.317276	+	0.948333i	$0.602768\pi$
$264$	2.99012	−	5.17904i	0.184029	−	0.318748i
$265$	−3.60362	−	9.65582i	−0.221369	−	0.593152i
$266$	26.3713			1.61693
$267$	−16.8868	+	9.74962i	−1.03346	+	0.596667i
$268$	−3.57089	−	2.06166i	−0.218127	−	0.125936i
$269$	15.4212			0.940250			0.470125	−	0.882600i	$-0.344209\pi$
$269$	15.4212			0.940250			0.470125	+	0.882600i	$0.344209\pi$
$270$	9.68698	+	7.99501i	0.589531	+	0.486561i
$271$	8.99623	+	15.5819i	0.546482	+	0.946535i	0.998512	+	0.0545322i	$0.0173667\pi$
$271$	8.99623	+	15.5819i	0.546482	+	0.946535i	−0.452030	+	0.892003i	$0.649300\pi$
$272$	−5.13493	+	2.96465i	−0.311351	+	0.179758i
$273$	−1.81213	+	1.04623i	−0.109675	+	0.0633210i
$274$	−12.8025			−0.773429
$275$	−4.30809	−	22.3048i	−0.259788	−	1.34503i
$276$	0.156471	+	0.271015i	0.00941843	+	0.0163132i
$277$	6.28827	+	3.63054i	0.377826	+	0.218138i	0.676872	−	0.736101i	$-0.263335\pi$
$277$	6.28827	+	3.63054i	0.377826	+	0.218138i	−0.299046	+	0.954239i	$0.596668\pi$
$278$	−12.1814	−	7.03293i	−0.730591	−	0.421807i
$279$	−7.60666			−0.455399
$280$	−1.48197	+	8.82368i	−0.0885647	+	0.527316i
$281$	7.51100	−	13.0094i	0.448069	−	0.776078i	−0.550192	−	0.835038i	$-0.685445\pi$
$281$	7.51100	−	13.0094i	0.448069	−	0.776078i	0.998260	+	0.0589608i	$0.0187787\pi$
$282$	8.26267	+	4.77045i	0.492035	+	0.284076i
$283$	15.9893	−	9.23142i	0.950465	−	0.548751i	0.0572396	−	0.998360i	$-0.481770\pi$
$283$	15.9893	−	9.23142i	0.950465	−	0.548751i	0.893225	+	0.449609i	$0.148437\pi$
$284$	−1.50077	−	2.59941i	−0.0890543	−	0.154247i
$285$	−19.1297	−	3.21290i	−1.13314	−	0.190316i
$286$	0.902541	+	1.56325i	0.0533684	+	0.0924367i
$287$	27.4445	−	15.8451i	1.62000	−	0.935307i
$288$	−1.09768	+	0.633745i	−0.0646813	+	0.0373438i
$289$	9.07830	−	15.7241i	0.534018	−	0.924946i
$290$	−15.9903	−	2.68563i	−0.938981	−	0.157705i
$291$	5.21245	−	9.02824i	0.305559	−	0.529245i
$292$	8.61166	−	4.97194i	0.503959	−	0.290961i
$293$		−	17.0682i		−	0.997133i	−0.866852	−	0.498566i	$-0.833860\pi$
$293$		−	17.0682i		−	0.997133i	0.866852	−	0.498566i	$-0.166140\pi$
$294$	−5.93017	−	10.2714i	−0.345855	−	0.599038i
$295$	7.16180	+	5.91089i	0.416976	+	0.344145i
$296$	2.96546	−	5.13633i	0.172364	−	0.298543i
$297$			25.5206i			1.48086i
$298$	5.66965	+	3.27337i	0.328434	+	0.189621i
$299$	−0.0944584			−0.00546267
$300$	2.15004	−	6.22014i	0.124133	−	0.359120i
$301$	12.8607	+	22.8706i	0.741276	+	1.31824i
$302$			8.97394i			0.516392i
$303$		−	15.8330i		−	0.909581i
$304$	3.29530	−	5.70763i	0.188999	−	0.327355i
$305$	1.08523	−	6.46151i	0.0621404	−	0.369985i
$306$	3.75766	−	6.50846i	0.214811	−	0.372064i
$307$	4.84036	+	2.79458i	0.276254	+	0.159495i	0.631726	−	0.775191i	$-0.282347\pi$
$307$	4.84036	+	2.79458i	0.276254	+	0.159495i	−0.355472	+	0.934687i	$0.615680\pi$
$308$	−15.7441	+	9.08985i	−0.897102	+	0.517942i
$309$	22.2456			1.26551
$310$	4.69212	+	12.5724i	0.266494	+	0.714065i
$311$	−4.15070	+	7.18923i	−0.235365	+	0.407664i	−0.959379	−	0.282122i	$-0.908962\pi$
$311$	−4.15070	+	7.18923i	−0.235365	+	0.407664i	0.724014	+	0.689785i	$0.242295\pi$
$312$			0.522942i			0.0296058i
$313$	−9.65465	−	5.57411i	−0.545713	−	0.315068i	0.201678	−	0.979452i	$-0.435361\pi$
$313$	−9.65465	−	5.57411i	−0.545713	−	0.315068i	−0.747391	+	0.664384i	$0.768694\pi$
$314$	2.73774	+	4.74190i	0.154499	+	0.267601i
$315$	−3.96523	−	10.6248i	−0.223416	−	0.598637i
$316$	5.74385	+	9.94864i	0.323117	+	0.559655i
$317$		−	18.9910i		−	1.06664i	−0.845914	−	0.533320i	$-0.820944\pi$
$317$		−	18.9910i		−	1.06664i	0.845914	−	0.533320i	$-0.179056\pi$
$318$	5.25398	−	3.03339i	0.294629	−	0.170104i
$319$	−16.4726	−	28.5314i	−0.922289	−	1.59745i
$320$	1.72456	+	1.42334i	0.0964058	+	0.0795671i
$321$	9.39556	−	16.2736i	0.524409	−	0.908303i
$322$		−	0.951328i		−	0.0530154i
$323$			39.0777i			2.17434i
$324$	−1.79550	+	3.10990i	−0.0997501	+	0.172772i
$325$	1.30147	+	1.50077i	0.0721925	+	0.0832477i
$326$	2.68607	+	4.65240i	0.148767	+	0.257673i
$327$	−12.5542	+	7.24818i	−0.694249	+	0.400825i
$328$		−	7.91990i		−	0.437303i
$329$	−14.5020	−	25.1182i	−0.799520	−	1.38481i
$330$	12.5282	−	4.67561i	0.689654	−	0.257384i
$331$	5.59513	+	9.69105i	0.307536	+	0.532668i	0.977823	−	0.209434i	$-0.0671622\pi$
$331$	5.59513	+	9.69105i	0.307536	+	0.532668i	−0.670287	+	0.742102i	$0.733829\pi$
$332$	1.52685	+	0.881529i	0.0837970	+	0.0483802i
$333$			7.51738i			0.411950i
$334$	−5.30729	+	9.19249i	−0.290402	+	0.502991i
$335$	−3.22378	−	8.63804i	−0.176134	−	0.471947i
$336$	−5.26676			−0.287325
$337$	−12.1515	+	7.01564i	−0.661932	+	0.382167i	−0.793013	−	0.609205i	$-0.791489\pi$
$337$	−12.1515	+	7.01564i	−0.661932	+	0.382167i	0.131081	+	0.991372i	$0.458155\pi$
$338$	11.1216	+	6.42108i	0.604937	+	0.349261i
$339$	7.94406	−	13.7595i	0.431462	−	0.747314i
$340$	−13.0752	−	2.19603i	−0.709102	−	0.119096i
$341$	−13.6333	+	23.6136i	−0.738284	+	1.27875i
$342$			8.35352i			0.451707i
$343$			8.04556i			0.434419i
$344$	6.55702	+	0.0743880i	0.353531	+	0.00401073i
$345$	−0.115904	+	0.690092i	−0.00624004	+	0.0371533i
$346$	24.9229			1.33986
$347$	−10.2192	−	5.90007i	−0.548597	−	0.316732i	0.199959	−	0.979804i	$-0.435919\pi$
$347$	−10.2192	−	5.90007i	−0.548597	−	0.316732i	−0.748556	+	0.663072i	$0.769252\pi$
$348$		−	9.54441i		−	0.511634i
$349$	−10.6498	+	18.4460i	−0.570072	+	0.987393i	0.426486	+	0.904494i	$0.359751\pi$
$349$	−10.6498	+	18.4460i	−0.570072	+	0.987393i	−0.996558	+	0.0828992i	$0.973582\pi$
$350$	−15.1148	+	13.1076i	−0.807922	+	0.700631i
$351$	−1.11583	−	1.93267i	−0.0595584	−	0.103158i
$352$			4.54340i			0.242164i
$353$	25.0918	−	14.4868i	1.33550	−	0.771053i	0.349366	−	0.936986i	$-0.386397\pi$
$353$	25.0918	−	14.4868i	1.33550	−	0.771053i	0.986137	+	0.165933i	$0.0530636\pi$
$354$	−2.73308	+	4.73383i	−0.145261	+	0.251600i
$355$	1.11168	−	6.61894i	0.0590017	−	0.351297i
$356$	7.40713	−	12.8295i	0.392577	−	0.679963i
$357$	27.0444	−	15.6141i	1.43134	−	0.826386i
$358$	4.06820	−	2.34878i	0.215011	−	0.124137i
$359$	−11.3758	−	19.7035i	−0.600393	−	1.03991i	−0.992762	−	0.120102i	$-0.961678\pi$
$359$	−11.3758	−	19.7035i	−0.600393	−	1.03991i	0.392369	−	0.919808i	$-0.371656\pi$
$360$	−2.79504	−	0.469438i	−0.147312	−	0.0247416i
$361$	−12.2180	−	21.1623i	−0.643055	−	1.11380i
$362$	9.45550	−	5.45913i	0.496970	−	0.286926i
$363$	10.9915	+	6.34596i	0.576906	+	0.333077i
$364$	0.794861	−	1.37674i	0.0416620	−	0.0721608i
$365$	21.9281	+	3.68290i	1.14777	+	0.192772i
$366$	3.85680			0.201598
$367$	−24.3335	−	14.0490i	−1.27020	−	0.733350i	−0.295174	−	0.955443i	$-0.595378\pi$
$367$	−24.3335	−	14.0490i	−1.27020	−	0.733350i	−0.975025	+	0.222094i	$0.928711\pi$
$368$	−0.205900	−	0.118876i	−0.0107333	−	0.00619685i
$369$	5.01920	+	8.69350i	0.261289	+	0.452566i
$370$	12.4248	−	4.63704i	0.645937	−	0.241068i
$371$	−18.4427			−0.957499
$372$	−6.84098	+	3.94964i	−0.354688	+	0.204779i
$373$	−11.4421	+	6.60611i	−0.592450	+	0.342051i	−0.766066	−	0.642762i	$-0.777788\pi$
$373$	−11.4421	+	6.60611i	−0.592450	+	0.342051i	0.173616	+	0.984813i	$0.444455\pi$
$374$	−13.4696	−	23.3300i	−0.696496	−	1.20637i
$375$	12.5612	−	7.66675i	0.648660	−	0.395909i
$376$	−7.24856			−0.373816
$377$	2.49493	+	1.44045i	0.128495	+	0.0741868i
$378$	19.4646	−	11.2379i	1.00115	−	0.578016i
$379$	8.76993			0.450481			0.225240	−	0.974303i	$-0.427683\pi$
$379$	8.76993			0.450481			0.225240	+	0.974303i	$0.427683\pi$
$380$	13.8068	−	5.15281i	0.708276	−	0.264334i
$381$	−6.81375	+	11.8018i	−0.349079	+	0.604623i
$382$	−6.55110	−	3.78228i	−0.335184	−	0.193518i
$383$		−	21.6170i		−	1.10457i	−0.833654	−	0.552287i	$-0.813755\pi$
$383$		−	21.6170i		−	1.10457i	0.833654	−	0.552287i	$-0.186245\pi$
$384$	−0.658124	+	1.13990i	−0.0335848	+	0.0581705i
$385$	−40.0895	−	6.73319i	−2.04315	−	0.343155i
$386$	6.28311			0.319802
$387$	−7.24464	+	4.07382i	−0.368266	+	0.207084i
$388$			7.92017i			0.402086i
$389$	−1.77743			−0.0901194			−0.0450597	−	0.998984i	$-0.514348\pi$
$389$	−1.77743			−0.0901194			−0.0450597	+	0.998984i	$0.514348\pi$
$390$	−0.744325	+	0.901845i	−0.0376903	+	0.0456667i
$391$	1.40971			0.0712919
$392$	7.80351	+	4.50536i	0.394137	+	0.227555i
$393$	−2.07003	−	1.19513i	−0.104419	−	0.0602865i
$394$	−1.01185	−	1.75258i	−0.0509765	−	0.0882938i
$395$	−4.25468	+	25.3325i	−0.214076	+	1.27461i
$396$	−2.87936	−	4.98719i	−0.144693	−	0.250616i
$397$	−12.1673	−	7.02478i	−0.610658	−	0.352564i	0.162565	−	0.986698i	$-0.448023\pi$
$397$	−12.1673	−	7.02478i	−0.610658	−	0.352564i	−0.773223	+	0.634134i	$0.781357\pi$
$398$		−	12.6142i		−	0.632293i
$399$	−17.3556	+	30.0607i	−0.868865	+	1.50492i
$400$	0.948208	+	4.90927i	0.0474104	+	0.245463i
$401$	−1.32878	−	2.30152i	−0.0663562	−	0.114932i	0.830939	−	0.556364i	$-0.187804\pi$
$401$	−1.32878	−	2.30152i	−0.0663562	−	0.114932i	−0.897295	+	0.441432i	$0.854471\pi$
$402$	4.70018	−	2.71365i	0.234424	−	0.135345i
$403$		−	2.38433i		−	0.118772i
$404$	6.01443	+	10.4173i	0.299229	+	0.518280i
$405$	−7.52289	+	2.80760i	−0.373815	+	0.139511i
$406$	−14.5073	+	25.1274i	−0.719985	+	1.24705i
$407$	23.3364	+	13.4733i	1.15674	+	0.667845i
$408$		−	7.80443i		−	0.386377i
$409$	25.2671			1.24938			0.624689	−	0.780873i	$-0.285226\pi$
$409$	25.2671			1.24938			0.624689	+	0.780873i	$0.285226\pi$
$410$	11.2727	−	13.6583i	0.556719	−	0.674537i
$411$	8.42566	−	14.5937i	0.415607	−	0.719853i
$412$	−14.6365	+	8.45040i	−0.721089	+	0.416321i
$413$	14.3906	−	8.30844i	0.708117	−	0.408832i
$414$	0.301349			0.0148105
$415$	1.37843	+	3.69348i	0.0676647	+	0.181306i
$416$	−0.198649	−	0.344070i	−0.00973956	−	0.0168694i
$417$	16.0337	−	9.25709i	0.785176	−	0.453321i
$418$	25.9321	+	14.9719i	1.26838	+	0.732299i
$419$	−31.5224			−1.53997			−0.769986	−	0.638061i	$-0.779737\pi$
$419$	−31.5224			−1.53997			−0.769986	+	0.638061i	$0.779737\pi$
$420$	−9.08284	−	7.49638i	−0.443197	−	0.365786i
$421$	11.4972	+	19.9137i	0.560340	+	0.970537i	0.997467	+	0.0711368i	$0.0226627\pi$
$421$	11.4972	+	19.9137i	0.560340	+	0.970537i	−0.437127	+	0.899400i	$0.644004\pi$
$422$			26.6725i			1.29840i
$423$	7.95659	−	4.59374i	0.386863	−	0.223355i
$424$	−2.30457	+	3.99163i	−0.111920	+	0.193851i
$425$	−19.4232	−	22.3976i	−0.942166	−	1.08644i
$426$	3.95077			0.191416
$427$	−10.1537	−	5.86226i	−0.491373	−	0.283695i
$428$			14.2763i			0.690069i
$429$	−2.37594			−0.114711
$430$	11.2021	+	9.46115i	0.540212	+	0.456257i
$431$	13.7976			0.664605			0.332303	−	0.943173i	$-0.392174\pi$
$431$	13.7976			0.664605			0.332303	+	0.943173i	$0.392174\pi$
$432$		−	5.61708i		−	0.270252i
$433$	21.9485	+	12.6720i	1.05478	+	0.608977i	0.923984	−	0.382432i	$-0.124913\pi$
$433$	21.9485	+	12.6720i	1.05478	+	0.608977i	0.130796	+	0.991409i	$0.458247\pi$
$434$	24.0135			1.15268
$435$	13.5849	−	16.4599i	0.651348	−	0.789192i
$436$	5.50669	−	9.53787i	0.263723	−	0.456781i
$437$	−1.35700	+	0.783466i	−0.0649143	+	0.0374783i
$438$			13.0886i			0.625399i
$439$	1.15394	+	1.99869i	0.0550747	+	0.0953922i	0.892248	−	0.451545i	$-0.149127\pi$
$439$	1.15394	+	1.99869i	0.0550747	+	0.0953922i	−0.837174	+	0.546937i	$0.815794\pi$
$440$	−6.46680	+	7.83536i	−0.308293	+	0.373536i
$441$	−11.4210			−0.543857
$442$	2.04009	+	1.17785i	0.0970373	+	0.0560245i
$443$	18.2862	−	10.5576i	0.868805	−	0.501605i	0.00185401	−	0.999998i	$-0.499410\pi$
$443$	18.2862	−	10.5576i	0.868805	−	0.501605i	0.866951	+	0.498394i	$0.166077\pi$
$444$	3.90328	+	6.76068i	0.185242	+	0.320848i
$445$	31.0348	−	11.5824i	1.47119	−	0.549059i
$446$	3.84306			0.181974
$447$	−7.46267	+	4.30857i	−0.352972	+	0.203788i
$448$	3.46526	−	2.00067i	0.163718	−	0.0945228i
$449$	10.3179	−	17.8712i	0.486934	−	0.843394i	−0.512953	−	0.858417i	$-0.671449\pi$
$449$	10.3179	−	17.8712i	0.486934	−	0.843394i	0.999887	+	0.0150223i	$0.00478194\pi$
$450$	−4.15205	−	4.78787i	−0.195729	−	0.225702i
$451$	35.9833			1.69439
$452$			12.0708i			0.567761i
$453$	−10.2294	−	5.90597i	−0.480621	−	0.277487i
$454$	−11.2277	+	19.4469i	−0.526942	+	0.912690i
$455$	3.33035	−	1.24291i	0.156129	−	0.0582686i
$456$	4.33744	+	7.51266i	0.203119	+	0.351813i
$457$		−	1.30912i		−	0.0612379i	−0.999531	−	0.0306190i	$-0.990252\pi$
$457$		−	1.30912i		−	0.0612379i	0.999531	−	0.0306190i	$-0.00974784\pi$
$458$	−7.44490	+	4.29832i	−0.347877	+	0.200847i
$459$	16.6527	+	28.8433i	0.777280	+	1.34629i
$460$	−0.185885	−	0.498074i	−0.00866693	−	0.0232228i
$461$	13.3037	−	23.0426i	0.619614	−	1.07320i	−0.369942	−	0.929055i	$-0.620623\pi$
$461$	13.3037	−	23.0426i	0.619614	−	1.07320i	0.989556	−	0.144148i	$-0.0460441\pi$
$462$		−	23.9290i		−	1.11328i
$463$	−5.63102	−	3.25107i	−0.261696	−	0.151090i	0.363412	−	0.931628i	$-0.381612\pi$
$463$	−5.63102	−	3.25107i	−0.261696	−	0.151090i	−0.625108	+	0.780538i	$0.714945\pi$
$464$	3.62561	+	6.27974i	0.168315	+	0.291530i
$465$	−17.4194	−	2.92565i	−0.807803	−	0.135674i
$466$	8.19720	+	14.1980i	0.379728	+	0.657708i
$467$	16.7489	+	9.67000i	0.775048	+	0.447474i	0.834673	−	0.550747i	$-0.185657\pi$
$467$	16.7489	+	9.67000i	0.775048	+	0.447474i	−0.0596242	+	0.998221i	$0.518990\pi$
$468$	0.436105	+	0.251785i	0.0201590	+	0.0116388i
$469$	−16.4988			−0.761842
$470$	−12.5006	−	10.3172i	−0.576608	−	0.475895i
$471$	−7.20708			−0.332085
$472$		−	4.15283i		−	0.191149i
$473$	−0.337975	+	29.7912i	−0.0155401	+	1.36980i
$474$	−15.1207			−0.694515
$475$	31.1449	+	10.7655i	1.42903	+	0.493955i
$476$	−11.8626	+	20.5466i	−0.543720	+	0.941751i
$477$		−	5.84204i		−	0.267488i
$478$	22.7070	+	13.1099i	1.03859	+	0.599633i
$479$	−1.36261	+	2.36011i	−0.0622592	+	0.107836i	−0.895475	−	0.445112i	$-0.853164\pi$
$479$	−1.36261	+	2.36011i	−0.0622592	+	0.107836i	0.833216	+	0.552948i	$0.186497\pi$
$480$	−2.75745	+	1.02910i	−0.125860	+	0.0469717i
$481$	−2.35634			−0.107440
$482$	−21.0930	+	12.1780i	−0.960759	+	0.554694i
$483$	1.08442	+	0.626092i	0.0493430	+	0.0284882i
$484$	−9.64250			−0.438295
$485$	−11.2731	+	13.6588i	−0.511885	+	0.620214i
$486$	6.06229	+	10.5002i	0.274991	+	0.476298i
$487$	16.8125	−	9.70670i	0.761847	−	0.439853i	−0.0681116	−	0.997678i	$-0.521697\pi$
$487$	16.8125	−	9.70670i	0.761847	−	0.439853i	0.829958	+	0.557825i	$0.188364\pi$
$488$	−2.53758	+	1.46507i	−0.114871	+	0.0663208i
$489$	−7.07106			−0.319764
$490$	7.04496	+	18.8768i	0.318259	+	0.852767i
$491$	7.81462	+	13.5353i	0.352669	+	0.610841i	0.986716	−	0.162454i	$-0.0519408\pi$
$491$	7.81462	+	13.5353i	0.352669	+	0.610841i	−0.634047	+	0.773294i	$0.718607\pi$
$492$	9.02793	+	5.21228i	0.407011	+	0.234988i
$493$	−37.2345	−	21.4973i	−1.67696	−	0.968192i
$494$	−2.61843			−0.117809
$495$	2.13285	−	12.6990i	0.0958644	−	0.570778i
$496$	3.00068	−	5.19733i	0.134734	−	0.233367i
$497$	−10.4011	−	6.00509i	−0.466554	−	0.269365i
$498$	−2.00972	+	1.16031i	−0.0900577	+	0.0519948i
$499$	−20.1228	−	34.8536i	−0.900818	−	1.56026i	−0.826434	−	0.563034i	$-0.809634\pi$
$499$	−20.1228	−	34.8536i	−0.900818	−	1.56026i	−0.0743845	−	0.997230i	$-0.523699\pi$
$500$	−5.35231	+	9.81594i	−0.239363	+	0.438982i
$501$	−6.98571	−	12.0996i	−0.312099	−	0.540570i
$502$	20.8574	−	12.0420i	0.930910	−	0.537461i
$503$	24.9597	−	14.4105i	1.11290	−	0.642533i	0.173321	−	0.984865i	$-0.444550\pi$
$503$	24.9597	−	14.4105i	1.11290	−	0.642533i	0.939579	+	0.342333i	$0.111217\pi$
$504$	−2.53583	+	4.39218i	−0.112955	+	0.195643i
$505$	−4.45512	+	26.5258i	−0.198250	+	1.18038i
$506$	0.540102	−	0.935485i	0.0240105	−	0.0415874i
$507$	−14.6388	+	8.45173i	−0.650133	+	0.375355i
$508$		−	10.3533i		−	0.459353i
$509$	−11.0449	−	19.1303i	−0.489557	−	0.847937i	0.510371	−	0.859954i	$-0.329508\pi$
$509$	−11.0449	−	19.1303i	−0.489557	−	0.847937i	−0.999928	+	0.0120170i	$0.996175\pi$
$510$	11.1084	−	13.4592i	0.491886	−	0.595984i
$511$	19.8944	−	34.4582i	0.880078	−	1.52434i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.0602	−	18.5100i	−1.41549	−	0.817235i
$514$	−3.70281			−0.163324
$515$	−37.2693	−	6.25953i	−1.64228	−	0.275828i
$516$	−4.40013	+	7.42542i	−0.193705	+	0.326886i
$517$		−	32.9331i		−	1.44840i
$518$		−	23.7316i		−	1.04271i
$519$	−16.4024	+	28.4097i	−0.719984	+	1.24705i
$520$	0.147147	−	0.876113i	0.00645280	−	0.0384201i
$521$	5.97949	−	10.3568i	0.261966	−	0.453739i	−0.704798	−	0.709408i	$-0.748962\pi$
$521$	5.97949	−	10.3568i	0.261966	−	0.453739i	0.966764	+	0.255669i	$0.0822957\pi$
$522$	−7.95951	−	4.59542i	−0.348378	−	0.201136i
$523$	6.87024	−	3.96653i	0.300415	−	0.173444i	−0.342215	−	0.939622i	$-0.611177\pi$
$523$	6.87024	−	3.96653i	0.300415	−	0.173444i	0.642629	+	0.766177i	$0.277844\pi$
$524$	1.81597			0.0793310
$525$	−4.99398	−	25.8559i	−0.217955	−	1.12844i
$526$	3.23369	−	5.60091i	0.140995	−	0.244211i
$527$			35.5839i			1.55006i
$528$	−5.17904	−	2.99012i	−0.225389	−	0.130128i
$529$	−11.4717	−	19.8696i	−0.498771	−	0.863897i
$530$	−9.65582	+	3.60362i	−0.419422	+	0.156531i
$531$	2.63183	+	4.55847i	0.114212	+	0.197821i
$532$		−	26.3713i		−	1.14334i
$533$	−2.72500	+	1.57328i	−0.118033	+	0.0681463i
$534$	9.74962	+	16.8868i	0.421907	+	0.730765i
$535$	−20.3200	+	24.6203i	−0.878509	+	1.06443i
$536$	−2.06166	+	3.57089i	−0.0890500	+	0.154239i
$537$			6.18315i			0.266823i
$538$		−	15.4212i		−	0.664857i
$539$	−20.4697	+	35.4545i	−0.881690	+	1.52713i
$540$	7.99501	−	9.68698i	0.344050	−	0.416861i
$541$	10.6691	+	18.4795i	0.458702	+	0.794496i	0.998893	−	0.0470473i	$-0.0149811\pi$
$541$	10.6691	+	18.4795i	0.458702	+	0.794496i	−0.540190	+	0.841543i	$0.681648\pi$
$542$	15.5819	−	8.99623i	0.669301	−	0.386421i
$543$			14.3712i			0.616725i
$544$	2.96465	+	5.13493i	0.127108	+	0.220158i
$545$	23.0722	−	8.61073i	0.988306	−	0.368843i
$546$	1.04623	+	1.81213i	0.0447747	+	0.0775521i
$547$	11.4760	+	6.62565i	0.490677	+	0.283292i	0.724855	−	0.688901i	$-0.241907\pi$
$547$	11.4760	+	6.62565i	0.490677	+	0.283292i	−0.234178	+	0.972194i	$0.575240\pi$
$548$			12.8025i			0.546897i
$549$	1.85697	−	3.21636i	0.0792534	−	0.137271i
$550$	−22.3048	+	4.30809i	−0.951079	+	0.183698i
$551$	47.7900			2.03592
$552$	0.271015	−	0.156471i	0.0115352	−	0.00665983i
$553$	39.8079	+	22.9831i	1.69280	+	0.977340i
$554$	3.63054	−	6.28827i	0.154247	−	0.267163i
$555$	−2.89131	+	17.2149i	−0.122729	+	0.730731i
$556$	−7.03293	+	12.1814i	−0.298263	+	0.516606i
$557$			25.8358i			1.09470i	0.836905	+	0.547349i	$0.184363\pi$
$557$			25.8358i			1.09470i	−0.836905	+	0.547349i	$0.815637\pi$
$558$			7.60666i			0.322016i
$559$	−1.27695	−	2.27085i	−0.0540092	−	0.0960466i
$560$	8.82368	+	1.48197i	0.372869	+	0.0626247i
$561$	35.4587			1.49707
$562$	−13.0094	−	7.51100i	−0.548770	−	0.316832i
$563$			3.65957i			0.154233i	0.997022	+	0.0771163i	$0.0245713\pi$
$563$			3.65957i			0.154233i	−0.997022	+	0.0771163i	$0.975429\pi$
$564$	4.77045	−	8.26267i	0.200872	−	0.347921i
$565$	−17.1808	+	20.8167i	−0.722801	+	0.875766i
$566$	−9.23142	−	15.9893i	−0.388026	−	0.672080i
$567$			14.3688i			0.603434i
$568$	−2.59941	+	1.50077i	−0.109069	+	0.0629709i
$569$	8.69584	−	15.0616i	0.364549	−	0.631417i	−0.624155	−	0.781301i	$-0.714557\pi$
$569$	8.69584	−	15.0616i	0.364549	−	0.631417i	0.988704	+	0.149884i	$0.0478899\pi$
$570$	−3.21290	+	19.1297i	−0.134574	+	0.801254i
$571$	−8.67668	+	15.0285i	−0.363108	+	0.628921i	−0.988471	−	0.151413i	$-0.951618\pi$
$571$	−8.67668	+	15.0285i	−0.363108	+	0.628921i	0.625363	+	0.780334i	$0.284951\pi$
$572$	1.56325	−	0.902541i	0.0653626	−	0.0377371i
$573$	8.62288	−	4.97842i	0.360226	−	0.207977i
$574$	−15.8451	−	27.4445i	−0.661362	−	1.14551i
$575$	0.388359	−	1.12354i	0.0161957	−	0.0468547i
$576$	0.633745	+	1.09768i	0.0264060	+	0.0457366i
$577$	−20.4854	+	11.8273i	−0.852820	+	0.492376i	−0.861601	−	0.507586i	$-0.830538\pi$
$577$	−20.4854	+	11.8273i	−0.852820	+	0.492376i	0.00878129	+	0.999961i	$0.497205\pi$
$578$	−15.7241	−	9.07830i	−0.654036	−	0.377608i
$579$	−4.13507	+	7.16215i	−0.171848	+	0.297649i
$580$	−2.68563	+	15.9903i	−0.111515	+	0.663960i
$581$	7.05460			0.292674
$582$	−9.02824	−	5.21245i	−0.374232	−	0.216063i
$583$	−18.1356	−	10.4706i	−0.751099	−	0.433647i
$584$	−4.97194	−	8.61166i	−0.205740	−	0.356353i
$585$	0.393713	+	1.05494i	0.0162780	+	0.0436166i
$586$	−17.0682			−0.705079
$587$	−21.6270	+	12.4864i	−0.892642	+	0.515367i	−0.874806	−	0.484474i	$-0.839011\pi$
$587$	−21.6270	+	12.4864i	−0.892642	+	0.515367i	−0.0178365	+	0.999841i	$0.505678\pi$
$588$	−10.2714	+	5.93017i	−0.423584	+	0.244556i
$589$	−19.7763	−	34.2536i	−0.814868	−	1.41139i
$590$	5.91089	−	7.16180i	0.243347	−	0.294847i
$591$	2.66370			0.109570
$592$	−5.13633	−	2.96546i	−0.211102	−	0.121880i
$593$	1.47706	−	0.852784i	0.0606558	−	0.0350196i	−0.469365	−	0.883004i	$-0.655517\pi$
$593$	1.47706	−	0.852784i	0.0606558	−	0.0350196i	0.530021	+	0.847984i	$0.322184\pi$
$594$	25.5206			1.04712
$595$	−49.7025	+	18.5493i	−2.03760	+	0.760448i
$596$	3.27337	−	5.66965i	0.134083	−	0.232238i
$597$	14.3790	+	8.30171i	0.588493	+	0.339766i
$598$			0.0944584i			0.00386269i
$599$	15.0067	−	25.9924i	0.613158	−	1.06202i	−0.377546	−	0.925991i	$-0.623232\pi$
$599$	15.0067	−	25.9924i	0.613158	−	1.06202i	0.990705	−	0.136030i	$-0.0434345\pi$
$600$	−6.22014	−	2.15004i	−0.253936	−	0.0877750i
$601$	39.9837			1.63097			0.815484	−	0.578780i	$-0.196471\pi$
$601$	39.9837			1.63097			0.815484	+	0.578780i	$0.196471\pi$
$602$	22.8706	−	12.8607i	0.932136	−	0.524161i
$603$		−	5.22625i		−	0.212829i
$604$	8.97394			0.365145
$605$	−16.6291	−	13.7245i	−0.676067	−	0.557982i
$606$	−15.8330			−0.643171
$607$	−1.11505	−	0.643772i	−0.0452583	−	0.0261299i	0.477200	−	0.878795i	$-0.341652\pi$
$607$	−1.11505	−	0.643772i	−0.0452583	−	0.0261299i	−0.522458	+	0.852665i	$0.674985\pi$
$608$	−5.70763	−	3.29530i	−0.231475	−	0.133642i
$609$	−19.0952	−	33.0739i	−0.773777	−	1.34022i
$610$	−6.46151	−	1.08523i	−0.261619	−	0.0439399i
$611$	1.43992	+	2.49401i	0.0582528	+	0.100897i
$612$	−6.50846	−	3.75766i	−0.263089	−	0.151895i
$613$		−	0.820518i		−	0.0331404i	−0.999863	−	0.0165702i	$-0.994725\pi$
$613$		−	0.820518i		−	0.0331404i	0.999863	−	0.0165702i	$-0.00527470\pi$
$614$	2.79458	−	4.84036i	0.112780	−	0.195341i
$615$	8.15036	+	21.8387i	0.328654	+	0.880621i
$616$	9.08985	+	15.7441i	0.366240	+	0.634347i
$617$	−9.12222	+	5.26671i	−0.367247	+	0.212030i	−0.672255	−	0.740320i	$-0.734674\pi$
$617$	−9.12222	+	5.26671i	−0.367247	+	0.212030i	0.305008	+	0.952350i	$0.401341\pi$
$618$		−	22.2456i		−	0.894851i
$619$	13.5520	+	23.4727i	0.544699	+	0.943446i	0.998626	+	0.0524074i	$0.0166894\pi$
$619$	13.5520	+	23.4727i	0.544699	+	0.943446i	−0.453927	+	0.891039i	$0.649977\pi$
$620$	12.5724	−	4.69212i	0.504920	−	0.188440i
$621$	−0.667737	+	1.15655i	−0.0267954	+	0.0464109i
$622$	7.18923	+	4.15070i	0.288262	+	0.166428i
$623$		−	59.2768i		−	2.37488i
$624$	0.522942			0.0209344
$625$	−23.2018	+	9.31002i	−0.928072	+	0.372401i
$626$	−5.57411	+	9.65465i	−0.222786	+	0.385877i
$627$	−34.1330	+	19.7067i	−1.36314	+	0.787011i
$628$	4.74190	−	2.73774i	0.189222	−	0.109248i
$629$	35.1662			1.40217
$630$	−10.6248	+	3.96523i	−0.423300	+	0.157979i
$631$	−20.6935	−	35.8422i	−0.823795	−	1.42685i	−0.902837	−	0.429983i	$-0.858519\pi$
$631$	−20.6935	−	35.8422i	−0.823795	−	1.42685i	0.0790419	−	0.996871i	$-0.474814\pi$
$632$	9.94864	−	5.74385i	0.395736	−	0.228478i
$633$	−30.4041	−	17.5538i	−1.20845	−	0.697701i
$634$	−18.9910			−0.754228
$635$	14.7363	−	17.8549i	0.584790	−	0.708549i
$636$	−3.03339	−	5.25398i	−0.120282	−	0.208334i
$637$		−	3.57994i		−	0.141842i
$638$	−28.5314	+	16.4726i	−1.12957	+	0.652157i
$639$	1.90221	−	3.29473i	0.0752503	−	0.130337i
$640$	1.42334	−	1.72456i	0.0562624	−	0.0681692i
$641$	−41.5297			−1.64032			−0.820162	−	0.572131i	$-0.806117\pi$
$641$	−41.5297			−1.64032			−0.820162	+	0.572131i	$0.806117\pi$
$642$	−16.2736	−	9.39556i	−0.642267	−	0.370813i
$643$		−	24.1477i		−	0.952294i	−0.879366	−	0.476147i	$-0.842033\pi$
$643$		−	24.1477i		−	0.952294i	0.879366	−	0.476147i	$-0.157967\pi$
$644$	−0.951328			−0.0374876
$645$	−18.1572	+	6.54270i	−0.714938	+	0.257618i
$646$	39.0777			1.53749
$647$			8.37979i			0.329444i	0.986340	+	0.164722i	$0.0526726\pi$
$647$			8.37979i			0.329444i	−0.986340	+	0.164722i	$0.947327\pi$
$648$	3.10990	+	1.79550i	0.122168	+	0.0705339i
$649$	18.8680			0.740633
$650$	1.50077	−	1.30147i	0.0588650	−	0.0510478i
$651$	−15.8039	+	27.3731i	−0.619402	+	1.07284i
$652$	4.65240	−	2.68607i	0.182202	−	0.105194i
$653$			46.1618i			1.80645i	0.429166	+	0.903226i	$0.358808\pi$
$653$			46.1618i			1.80645i	−0.429166	+	0.903226i	$0.641192\pi$
$654$	7.24818	+	12.5542i	0.283426	+	0.490908i
$655$	3.13175	+	2.58474i	0.122367	+	0.100994i
$656$	−7.91990			−0.309220
$657$	10.9152	+	6.30188i	0.425842	+	0.245860i
$658$	−25.1182	+	14.5020i	−0.979208	+	0.565346i
$659$	17.6588	+	30.5859i	0.687888	+	1.19146i	0.972520	+	0.232820i	$0.0747952\pi$
$659$	17.6588	+	30.5859i	0.687888	+	1.19146i	−0.284632	+	0.958637i	$0.591872\pi$
$660$	−4.67561	−	12.5282i	−0.181998	−	0.487659i
$661$	24.0891			0.936957			0.468479	−	0.883475i	$-0.344802\pi$
$661$	24.0891			0.936957			0.468479	+	0.883475i	$0.344802\pi$
$662$	9.69105	−	5.59513i	0.376653	−	0.217461i
$663$	−2.68527	+	1.55034i	−0.104287	+	0.0602103i
$664$	0.881529	−	1.52685i	0.0342100	−	0.0592534i
$665$	37.5353	−	45.4788i	1.45555	−	1.76359i
$666$	7.51738			0.291292
$667$		−	1.72400i		−	0.0667534i
$668$	9.19249	+	5.30729i	0.355668	+	0.205345i
$669$	−2.52921	+	4.38072i	−0.0977849	+	0.169368i
$670$	−8.63804	+	3.22378i	−0.333717	+	0.124545i
$671$	−6.65642	−	11.5293i	−0.256968	−	0.445082i
$672$			5.26676i			0.203170i
$673$	−31.4540	+	18.1600i	−1.21246	+	0.700015i	−0.963295	−	0.268445i	$-0.913490\pi$
$673$	−31.4540	+	18.1600i	−1.21246	+	0.700015i	−0.249167	+	0.968460i	$0.580157\pi$
$674$	7.01564	+	12.1515i	0.270233	+	0.468056i
$675$	27.5757	−	5.32616i	1.06139	−	0.205004i
$676$	6.42108	−	11.1216i	0.246965	−	0.427755i
$677$			9.39110i			0.360929i	0.983581	+	0.180465i	$0.0577601\pi$
$677$			9.39110i			0.360929i	−0.983581	+	0.180465i	$0.942240\pi$
$678$	−13.7595	−	7.94406i	−0.528431	−	0.305090i
$679$	15.8456	+	27.4454i	0.608100	+	1.05326i
$680$	−2.19603	+	13.0752i	−0.0842138	+	0.501411i
$681$	−14.7784	−	25.5970i	−0.566311	−	0.980880i
$682$	23.6136	+	13.6333i	0.904210	+	0.522046i
$683$	13.6178	+	7.86227i	0.521072	+	0.300841i	0.737373	−	0.675485i	$-0.236066\pi$
$683$	13.6178	+	7.86227i	0.521072	+	0.300841i	−0.216301	+	0.976327i	$0.569399\pi$
$684$	8.35352			0.319405
$685$	−18.2224	+	22.0787i	−0.696240	+	0.843585i
$686$	8.04556			0.307181
$687$		−	11.3153i		−	0.431706i
$688$	0.0743880	−	6.55702i	0.00283602	−	0.249984i
$689$	1.83120			0.0697632
$690$	0.690092	+	0.115904i	0.0262714	+	0.00441238i
$691$	1.65868	−	2.87292i	0.0630993	−	0.109291i	−0.832750	−	0.553649i	$-0.813235\pi$
$691$	1.65868	−	2.87292i	0.0630993	−	0.109291i	0.895849	+	0.444358i	$0.146568\pi$
$692$		−	24.9229i		−	0.947426i
$693$	−19.9554	−	11.5213i	−0.758045	−	0.437657i
$694$	−5.90007	+	10.2192i	−0.223964	+	0.387916i
$695$	−29.4670	+	10.9973i	−1.11775	+	0.417151i
$696$	−9.54441			−0.361780
$697$	40.6681	−	23.4797i	1.54041	−	0.889359i
$698$	18.4460	+	10.6498i	0.698193	+	0.403102i
$699$	−21.5791			−0.816197
$700$	13.1076	+	15.1148i	0.495421	+	0.571287i
$701$	−9.80070	−	16.9753i	−0.370167	−	0.641149i	0.619424	−	0.785057i	$-0.287366\pi$
$701$	−9.80070	−	16.9753i	−0.370167	−	0.641149i	−0.989591	+	0.143908i	$0.954033\pi$
$702$	−1.93267	+	1.11583i	−0.0729438	+	0.0421141i
$703$	−33.8515	+	19.5442i	−1.27673	+	0.737123i
$704$	4.54340			0.171236
$705$	19.9875	−	7.45949i	0.752773	−	0.280940i
$706$	−14.4868	−	25.0918i	−0.545217	−	0.944343i
$707$	41.6832	+	24.0658i	1.56766	+	0.905087i
$708$	4.73383	+	2.73308i	0.177908	+	0.102715i
$709$	−39.4525			−1.48167			−0.740835	−	0.671687i	$-0.765570\pi$
$709$	−39.4525			−1.48167			−0.740835	+	0.671687i	$0.765570\pi$
$710$	−6.61894	−	1.11168i	−0.248405	−	0.0417205i
$711$	−7.28027	+	12.6098i	−0.273031	+	0.472904i
$712$	−12.8295	−	7.40713i	−0.480807	−	0.277594i
$713$	−1.23568	+	0.713419i	−0.0462765	+	0.0267177i
$714$	−15.6141	−	27.0444i	−0.584343	−	1.01211i
$715$	3.98053	+	0.668546i	0.148864	+	0.0250022i
$716$	−2.34878	−	4.06820i	−0.0877779	−	0.152036i
$717$	−29.8881	+	17.2559i	−1.11619	+	0.644433i
$718$	−19.7035	+	11.3758i	−0.735328	+	0.424542i
$719$	6.80616	−	11.7886i	0.253827	−	0.439641i	−0.710749	−	0.703445i	$-0.751644\pi$
$719$	6.80616	−	11.7886i	0.253827	−	0.439641i	0.964576	+	0.263804i	$0.0849773\pi$
$720$	−0.469438	+	2.79504i	−0.0174949	+	0.104165i
$721$	−33.8129	+	58.5657i	−1.25926	+	2.18110i
$722$	−21.1623	+	12.2180i	−0.787579	+	0.454709i
$723$		−	32.0587i		−	1.19227i
$724$	−5.45913	−	9.45550i	−0.202887	−	0.351411i
$725$	−27.3911	+	23.7536i	−1.01728	+	0.882187i
$726$	6.34596	−	10.9915i	0.235521	−	0.407934i
$727$		−	33.5701i		−	1.24505i	−0.782601	−	0.622523i	$-0.786108\pi$
$727$		−	33.5701i		−	1.24505i	0.782601	−	0.622523i	$-0.213892\pi$
$728$	−1.37674	−	0.794861i	−0.0510254	−	0.0294595i
$729$	−26.7320			−0.990073
$730$	3.68290	−	21.9281i	0.136310	−	0.811594i
$731$	19.0573	+	33.8903i	0.704859	+	1.25348i
$732$		−	3.85680i		−	0.142552i
$733$		−	2.67411i		−	0.0987704i	−0.998780	−	0.0493852i	$-0.984274\pi$
$733$		−	2.67411i		−	0.0987704i	0.998780	−	0.0493852i	$-0.0157262\pi$
$734$	−14.0490	+	24.3335i	−0.518557	+	0.898167i
$735$	−26.1542	−	4.39270i	−0.964713	−	0.162027i
$736$	−0.118876	+	0.205900i	−0.00438183	+	0.00758956i
$737$	−16.2240	−	9.36693i	−0.597619	−	0.345035i
$738$	8.69350	−	5.01920i	0.320012	−	0.184759i
$739$	4.86748			0.179053			0.0895265	−	0.995984i	$-0.471465\pi$
$739$	4.86748			0.179053			0.0895265	+	0.995984i	$0.471465\pi$
$740$	−4.63704	−	12.4248i	−0.170461	−	0.456746i
$741$	1.72325	−	2.98476i	0.0633053	−	0.109648i
$742$			18.4427i			0.677054i
$743$	−14.2466	−	8.22531i	−0.522659	−	0.301757i	0.215363	−	0.976534i	$-0.430907\pi$
$743$	−14.2466	−	8.22531i	−0.522659	−	0.301757i	−0.738022	+	0.674777i	$0.764240\pi$
$744$	3.94964	+	6.84098i	0.144801	+	0.250802i
$745$	13.7150	−	5.11852i	0.502477	−	0.187528i
$746$	6.60611	+	11.4421i	0.241867	+	0.418925i
$747$			2.23466i			0.0817619i
$748$	−23.3300	+	13.4696i	−0.853030	+	0.492497i
$749$	28.5621	+	49.4710i	1.04364	+	1.80763i
$750$	−7.66675	−	12.5612i	−0.279950	−	0.458672i
$751$	−19.7485	+	34.2055i	−0.720634	+	1.24817i	0.240112	+	0.970745i	$0.422816\pi$
$751$	−19.7485	+	34.2055i	−0.720634	+	1.24817i	−0.960746	+	0.277430i	$0.910518\pi$
$752$			7.24856i			0.264328i
$753$			31.7006i			1.15523i
$754$	1.44045	−	2.49493i	0.0524580	−	0.0908599i
$755$	15.4761	+	12.7730i	0.563233	+	0.464856i
$756$	−11.2379	−	19.4646i	−0.408719	−	0.707922i
$757$	−28.9104	+	16.6914i	−1.05077	+	0.606661i	−0.922864	−	0.385126i	$-0.874158\pi$
$757$	−28.9104	+	16.6914i	−1.05077	+	0.606661i	−0.127904	+	0.991787i	$0.540825\pi$
$758$		−	8.76993i		−	0.318538i
$759$	0.710909	+	1.23133i	0.0258044	+	0.0446945i
$760$	−5.15281	−	13.8068i	−0.186912	−	0.500827i
$761$	−17.4702	−	30.2593i	−0.633295	−	1.09690i	−0.986874	−	0.161494i	$-0.948369\pi$
$761$	−17.4702	−	30.2593i	−0.633295	−	1.09690i	0.353579	−	0.935405i	$-0.384965\pi$
$762$	11.8018	+	6.81375i	0.427533	+	0.246836i
$763$		−	44.0683i		−	1.59538i
$764$	−3.78228	+	6.55110i	−0.136838	+	0.237011i
$765$	−5.87580	−	15.7441i	−0.212440	−	0.569228i
$766$	−21.6170			−0.781052
$767$	−1.42886	+	0.824954i	−0.0515932	+	0.0297874i
$768$	1.13990	+	0.658124i	0.0411328	+	0.0237480i
$769$	21.2623	−	36.8274i	0.766739	−	1.32803i	−0.172584	−	0.984995i	$-0.555212\pi$
$769$	21.2623	−	36.8274i	0.766739	−	1.32803i	0.939322	−	0.343035i	$-0.111455\pi$
$770$	−6.73319	+	40.0895i	−0.242647	+	1.44473i
$771$	2.43691	−	4.22085i	0.0877632	−	0.152010i
$772$		−	6.28311i		−	0.226134i
$773$			10.8438i			0.390023i	0.980801	+	0.195011i	$0.0624744\pi$
$773$			10.8438i			0.390023i	−0.980801	+	0.195011i	$0.937526\pi$
$774$	4.07382	+	7.24464i	0.146430	+	0.260403i
$775$	28.3603	+	9.80298i	1.01873	+	0.352134i
$776$	7.92017			0.284317
$777$	27.0518	+	15.6184i	0.970477	+	0.560305i
$778$			1.77743i			0.0637241i
$779$	−26.0985	+	45.2039i	−0.935075	+	1.61960i
$780$	0.901845	+	0.744325i	0.0322912	+	0.0266511i
$781$	−6.81860	−	11.8102i	−0.243989	−	0.422601i
$782$		−	1.40971i		−	0.0504110i
$783$	35.2738	−	20.3653i	1.26058	−	0.727798i
$784$	4.50536	−	7.80351i	0.160906	−	0.278697i
$785$	12.0744	+	2.02794i	0.430954	+	0.0723804i
$786$	−1.19513	+	2.07003i	−0.0426290	+	0.0738356i
$787$	38.9833	−	22.5070i	1.38960	−	0.802289i	0.396334	−	0.918106i	$-0.370282\pi$
$787$	38.9833	−	22.5070i	1.38960	−	0.802289i	0.993270	+	0.115818i	$0.0369488\pi$
$788$	−1.75258	+	1.01185i	−0.0624332	+	0.0360458i
$789$	4.25634	+	7.37219i	0.151530	+	0.262457i
$790$	25.3325	+	4.25468i	0.901289	+	0.151375i
$791$	24.1496	+	41.8283i	0.858661	+	1.48724i
$792$	−4.98719	+	2.87936i	−0.177212	+	0.102313i
$793$	1.00818	+	0.582070i	0.0358013	+	0.0206699i
$794$	−7.02478	+	12.1673i	−0.249300	+	0.431801i
$795$	2.24694	−	13.3783i	0.0796909	−	0.474481i
$796$	−12.6142			−0.447098
$797$	13.8151	+	7.97613i	0.489355	+	0.282529i	0.724307	−	0.689478i	$-0.242160\pi$
$797$	13.8151	+	7.97613i	0.489355	+	0.282529i	−0.234952	+	0.972007i	$0.575493\pi$
$798$	30.0607	+	17.3556i	1.06414	+	0.614380i
$799$	−21.4895	−	37.2208i	−0.760242	−	1.31678i
$800$	4.90927	−	0.948208i	0.173569	−	0.0335242i
$801$	18.7769			0.663449
$802$	−2.30152	+	1.32878i	−0.0812694	+	0.0469209i
$803$	39.1262	−	22.5895i	1.38073	−	0.797167i
$804$	−2.71365	−	4.70018i	−0.0957031	−	0.165763i
$805$	−1.64062	−	1.35406i	−0.0578243	−	0.0477244i
$806$	−2.38433			−0.0839843
$807$	17.5787	+	10.1491i	0.618801	+	0.357265i
$808$	10.4173	−	6.01443i	0.366480	−	0.211587i
$809$	23.6724			0.832277			0.416138	−	0.909301i	$-0.363383\pi$
$809$	23.6724			0.832277			0.416138	+	0.909301i	$0.363383\pi$
$810$	2.80760	+	7.52289i	0.0986489	+	0.264327i
$811$	−12.8249	+	22.2134i	−0.450343	+	0.780018i	−0.998407	−	0.0564189i	$-0.982032\pi$
$811$	−12.8249	+	22.2134i	−0.450343	+	0.780018i	0.548064	+	0.836437i	$0.315365\pi$
$812$	25.1274	+	14.5073i	0.881798	+	0.509106i
$813$			23.6826i			0.830584i
$814$	13.4733	−	23.3364i	0.472238	−	0.817940i
$815$	11.8465	+	1.98967i	0.414966	+	0.0696951i
$816$	−7.80443			−0.273210
$817$	−37.1799	−	22.0319i	−1.30076	−	0.770800i
$818$		−	25.2671i		−	0.883444i
$819$	2.01496			0.0704083
$820$	−13.6583	−	11.2727i	−0.476970	−	0.393660i
$821$	−14.9160			−0.520572			−0.260286	−	0.965532i	$-0.583817\pi$
$821$	−14.9160			−0.520572			−0.260286	+	0.965532i	$0.583817\pi$
$822$	−14.5937	−	8.42566i	−0.509013	−	0.293879i
$823$	−18.8328	−	10.8731i	−0.656469	−	0.379012i	0.134461	−	0.990919i	$-0.457070\pi$
$823$	−18.8328	−	10.8731i	−0.656469	−	0.379012i	−0.790930	+	0.611906i	$0.790403\pi$
$824$	8.45040	+	14.6365i	0.294384	+	0.509887i
$825$	9.76850	−	28.2606i	0.340095	−	0.983907i
$826$	−8.30844	−	14.3906i	−0.289088	−	0.500714i
$827$	−5.35165	−	3.08977i	−0.186095	−	0.107442i	0.404058	−	0.914733i	$-0.367599\pi$
$827$	−5.35165	−	3.08977i	−0.186095	−	0.107442i	−0.590153	+	0.807291i	$0.700933\pi$
$828$		−	0.301349i		−	0.0104726i
$829$	16.9896	−	29.4269i	0.590074	−	1.02204i	−0.404147	−	0.914694i	$-0.632432\pi$
$829$	16.9896	−	29.4269i	0.590074	−	1.02204i	0.994222	−	0.107345i	$-0.0342349\pi$
$830$	3.69348	−	1.37843i	0.128203	−	0.0478461i
$831$	4.77869	+	8.27693i	0.165771	+	0.287124i
$832$	−0.344070	+	0.198649i	−0.0119285	+	0.00688691i
$833$			53.4273i			1.85114i
$834$	−9.25709	−	16.0337i	−0.320547	−	0.555203i
$835$	8.29892	+	22.2368i	0.287196	+	0.769535i
$836$	14.9719	−	25.9321i	0.517814	−	0.896879i
$837$	−29.1938	−	16.8550i	−1.00909	−	0.582596i
$838$			31.5224i			1.08892i
$839$	−13.0338			−0.449976			−0.224988	−	0.974362i	$-0.572234\pi$
$839$	−13.0338			−0.449976			−0.224988	+	0.974362i	$0.572234\pi$
$840$	−7.49638	+	9.08284i	−0.258650	+	0.313388i
$841$	−11.7901	+	20.4211i	−0.406556	+	0.704175i
$842$	19.9137	−	11.4972i	0.686273	−	0.396220i
$843$	17.1236	−	9.88634i	0.589770	−	0.340504i
$844$	26.6725			0.918104
$845$	26.9034	−	10.0405i	0.925505	−	0.345405i
$846$	−4.59374	−	7.95659i	−0.157936	−	0.273553i
$847$	−33.4138	+	19.2914i	−1.14811	+	0.662862i
$848$	3.99163	+	2.30457i	0.137073	+	0.0791393i
$849$	24.3017			0.834032
$850$	−22.3976	+	19.4232i	−0.768232	+	0.666212i
$851$	0.705045	+	1.22117i	0.0241686	+	0.0418613i
$852$		−	3.95077i		−	0.135351i
$853$	31.9003	−	18.4176i	1.09224	−	0.630607i	0.158071	−	0.987428i	$-0.449473\pi$
$853$	31.9003	−	18.4176i	1.09224	−	0.630607i	0.934173	+	0.356820i	$0.116139\pi$
$854$	−5.86226	+	10.1537i	−0.200602	+	0.347453i
$855$	14.4061	+	11.8899i	0.492680	+	0.406626i
$856$	14.2763			0.487953
$857$	30.4431	+	17.5763i	1.03992	+	0.600397i	0.919810	−	0.392364i	$-0.128343\pi$
$857$	30.4431	+	17.5763i	1.03992	+	0.600397i	0.120107	+	0.992761i	$0.461676\pi$
$858$			2.37594i			0.0811131i
$859$	16.9803			0.579360			0.289680	−	0.957124i	$-0.406451\pi$
$859$	16.9803			0.579360			0.289680	+	0.957124i	$0.406451\pi$
$860$	9.46115	−	11.2021i	0.322622	−	0.381988i
$861$	41.7122			1.42155
$862$		−	13.7976i		−	0.469947i
$863$	−21.3072	−	12.3017i	−0.725304	−	0.418755i	0.0913976	−	0.995814i	$-0.470867\pi$
$863$	−21.3072	−	12.3017i	−0.725304	−	0.418755i	−0.816702	+	0.577060i	$0.804200\pi$
$864$	−5.61708			−0.191097
$865$	35.4737	−	42.9810i	1.20614	−	1.46140i
$866$	12.6720	−	21.9485i	0.430612	−	0.745842i
$867$	20.6968	−	11.9493i	0.702900	−	0.405820i
$868$		−	24.0135i		−	0.815070i
$869$	26.0966	+	45.2007i	0.885267	+	1.53333i
$870$	−16.4599	−	13.5849i	−0.558043	−	0.460573i
$871$	1.63818			0.0555077
$872$	−9.53787	−	5.50669i	−0.322993	−	0.186480i
$873$	−8.69379	+	5.01936i	−0.294240	+	0.169880i
$874$	0.783466	+	1.35700i	0.0265011	+	0.0459013i
$875$	1.09130	+	44.7230i	0.0368926	+	1.51191i
$876$	13.0886			0.442224
$877$	39.5938	−	22.8595i	1.33699	−	0.771911i	0.350629	−	0.936514i	$-0.385968\pi$
$877$	39.5938	−	22.8595i	1.33699	−	0.771911i	0.986360	+	0.164604i	$0.0526345\pi$
$878$	1.99869	−	1.15394i	0.0674525	−	0.0389437i
$879$	11.2330	−	19.4561i	0.378879	−	0.656237i
$880$	7.83536	+	6.46680i	0.264130	+	0.217996i
$881$	−25.8020			−0.869292			−0.434646	−	0.900601i	$-0.643127\pi$
$881$	−25.8020			−0.869292			−0.434646	+	0.900601i	$0.643127\pi$
$882$			11.4210i			0.384565i
$883$	27.0549	+	15.6202i	0.910471	+	0.525661i	0.880583	−	0.473893i	$-0.157151\pi$
$883$	27.0549	+	15.6202i	0.910471	+	0.525661i	0.0298884	+	0.999553i	$0.490485\pi$
$884$	1.17785	−	2.04009i	0.0396153	−	0.0686158i
$885$	4.27367	+	11.4512i	0.143658	+	0.384928i
$886$	−10.5576	−	18.2862i	−0.354688	−	0.614338i
$887$		−	2.27964i		−	0.0765429i	−0.999267	−	0.0382715i	$-0.987815\pi$
$887$		−	2.27964i		−	0.0765429i	0.999267	−	0.0382715i	$-0.0121852\pi$
$888$	6.76068	−	3.90328i	0.226874	−	0.130986i
$889$	−20.7135	−	35.8769i	−0.694709	−	1.20327i
$890$	−11.5824	−	31.0348i	−0.388243	−	1.04029i
$891$	−8.15768	+	14.1295i	−0.273293	+	0.473357i
$892$		−	3.84306i		−	0.128675i
$893$	41.3721	+	23.8862i	1.38447	+	0.799322i
$894$	4.30857	+	7.46267i	0.144100	+	0.249589i
$895$	1.73983	−	10.3590i	0.0581560	−	0.346262i
$896$	−2.00067	−	3.46526i	−0.0668377	−	0.115766i
$897$	−0.107674	−	0.0621654i	−0.00359512	−	0.00207564i
$898$	−17.8712	−	10.3179i	−0.596370	−	0.344314i
$899$	43.5172			1.45138
$900$	−4.78787	+	4.15205i	−0.159596	+	0.138402i
$901$	−27.3290			−0.910460
$902$		−	35.9833i		−	1.19811i
$903$	−0.391784	+	34.5342i	−0.0130377	+	1.14923i
$904$	12.0708			0.401467
$905$	4.04378	−	24.0768i	0.134420	−	0.800339i
$906$	−5.90597	+	10.2294i	−0.196213	+	0.339850i
$907$			28.6607i			0.951662i	0.879537	+	0.475831i	$0.157853\pi$
$907$			28.6607i			0.951662i	−0.879537	+	0.475831i	$0.842147\pi$
$908$	19.4469	+	11.2277i	0.645369	+	0.372604i
$909$	−7.62323	+	13.2038i	−0.252847	+	0.437943i
$910$	−1.24291	−	3.33035i	−0.0412021	−	0.110400i
$911$	−19.3711			−0.641792			−0.320896	−	0.947114i	$-0.603984\pi$
$911$	−19.3711			−0.641792			−0.320896	+	0.947114i	$0.603984\pi$
$912$	7.51266	−	4.33744i	0.248769	−	0.143627i
$913$	6.93711	+	4.00514i	0.229585	+	0.132551i
$914$	−1.30912			−0.0433018
$915$	5.48954	−	6.65128i	0.181479	−	0.219885i
$916$	4.29832	+	7.44490i	0.142020	+	0.245986i
$917$	6.29281	−	3.63315i	0.207807	−	0.119977i
$918$	28.8433	−	16.6527i	0.951970	−	0.549620i
$919$	12.3502			0.407394			0.203697	−	0.979034i	$-0.434704\pi$
$919$	12.3502			0.407394			0.203697	+	0.979034i	$0.434704\pi$
$920$	−0.498074	+	0.185885i	−0.0164210	+	0.00612844i
$921$	3.67837	+	6.37112i	0.121206	+	0.209936i
$922$	−23.0426	−	13.3037i	−0.758869	−	0.438133i
$923$	1.03274	+	0.596252i	0.0339930	+	0.0196259i
$924$	−23.9290			−0.787206
$925$	9.68792	−	28.0275i	0.318537	−	0.921537i
$926$	−3.25107	+	5.63102i	−0.106837	+	0.185047i
$927$	−18.5516	−	10.7108i	−0.609315	−	0.351788i
$928$	6.27974	−	3.62561i	0.206143	−	0.119017i
$929$	−20.1781	−	34.9495i	−0.662022	−	1.14666i	−0.980083	−	0.198586i	$-0.936365\pi$
$929$	−20.1781	−	34.9495i	−0.662022	−	1.14666i	0.318061	−	0.948070i	$-0.396968\pi$
$930$	−2.92565	+	17.4194i	−0.0959357	+	0.571203i
$931$	−29.6930	−	51.4299i	−0.973150	−	1.68555i
$932$	14.1980	−	8.19720i	0.465070	−	0.268508i
$933$	−9.46281	+	5.46336i	−0.309799	+	0.178862i
$934$	9.67000	−	16.7489i	0.316412	−	0.548042i
$935$	−59.4058	−	9.97743i	−1.94278	−	0.326297i
$936$	0.251785	−	0.436105i	0.00822986	−	0.0142545i
$937$	−31.2029	+	18.0150i	−1.01935	+	0.588524i	−0.913917	−	0.405902i	$-0.866958\pi$
$937$	−31.2029	+	18.0150i	−1.01935	+	0.588524i	−0.105437	+	0.994426i	$0.533624\pi$
$938$			16.4988i			0.538704i
$939$	−7.33692	−	12.7079i	−0.239431	−	0.414707i
$940$	−10.3172	+	12.5006i	−0.336509	+	0.407724i
$941$	−10.5368	+	18.2502i	−0.343489	+	0.594940i	−0.985078	−	0.172108i	$-0.944942\pi$
$941$	−10.5368	+	18.2502i	−0.343489	+	0.594940i	0.641589	+	0.767049i	$0.278275\pi$
$942$			7.20708i			0.234819i
$943$	1.63070	+	0.941488i	0.0531031	+	0.0306591i
$944$	−4.15283			−0.135163
$945$	8.32435	−	49.5633i	0.270791	−	1.61229i
$946$	29.7912	+	0.337975i	0.968594	+	0.0109885i
$947$			18.7358i			0.608832i	0.952539	+	0.304416i	$0.0984614\pi$
$947$			18.7358i			0.608832i	−0.952539	+	0.304416i	$0.901539\pi$
$948$			15.1207i			0.491096i
$949$	−1.97534	+	3.42139i	−0.0641223	+	0.111063i
$950$	10.7655	−	31.1449i	0.349279	−	1.01047i
$951$	12.4984	−	21.6479i	0.405289	−	0.701981i
$952$	20.5466	+	11.8626i	0.665918	+	0.384468i
$953$	9.16995	−	5.29427i	0.297044	−	0.171498i	−0.344070	−	0.938944i	$-0.611806\pi$
$953$	9.16995	−	5.29427i	0.297044	−	0.171498i	0.641114	+	0.767446i	$0.278473\pi$
$954$	−5.84204			−0.189143
$955$	−15.8472	+	5.91429i	−0.512804	+	0.191382i
$956$	13.1099	−	22.7070i	0.424004	−	0.734397i
$957$		−	43.3641i		−	1.40176i
$958$	2.36011	+	1.36261i	0.0762516	+	0.0440239i
$959$	25.6136	+	44.3641i	0.827108	+	1.43259i
$960$	1.02910	+	2.75745i	0.0332140	+	0.0889962i
$961$	−2.50816	−	4.34425i	−0.0809083	−	0.140137i
$962$			2.35634i			0.0759714i
$963$	−15.6707	+	9.04751i	−0.504983	+	0.291552i
$964$	12.1780	+	21.0930i	0.392228	+	0.679359i
$965$	8.94301	−	10.8356i	0.287886	−	0.348810i
$966$	0.626092	−	1.08442i	0.0201442	−	0.0348908i
$967$			45.2957i			1.45661i	0.685252	+	0.728306i	$0.259692\pi$
$967$			45.2957i			1.45661i	−0.685252	+	0.728306i	$0.740308\pi$
$968$			9.64250i			0.309922i
$969$	−25.7180	+	44.5448i	−0.826181	+	1.43099i
$970$	13.6588	+	11.2731i	0.438558	+	0.361957i
$971$	−24.5555	−	42.5313i	−0.788022	−	1.36489i	−0.927177	−	0.374623i	$-0.877772\pi$
$971$	−24.5555	−	42.5313i	−0.788022	−	1.36489i	0.139155	−	0.990271i	$-0.455561\pi$
$972$	10.5002	−	6.06229i	0.336794	−	0.194448i
$973$			56.2823i			1.80433i
$974$	−9.70670	−	16.8125i	−0.311023	−	0.538707i
$975$	0.495858	+	2.56726i	0.0158802	+	0.0822182i
$976$	1.46507	+	2.53758i	0.0468959	+	0.0812260i
$977$	−13.5573	−	7.82732i	−0.433737	−	0.250418i	0.267200	−	0.963641i	$-0.413901\pi$
$977$	−13.5573	−	7.82732i	−0.433737	−	0.250418i	−0.700937	+	0.713223i	$0.747235\pi$
$978$			7.07106i			0.226108i
$979$	33.6535	−	58.2897i	1.07557	−	1.86295i
$980$	18.8768	−	7.04496i	0.602997	−	0.225043i
$981$	13.9593			0.445688
$982$	13.5353	−	7.81462i	0.431930	−	0.249375i
$983$	48.7707	+	28.1578i	1.55554	+	0.898093i	0.997674	+	0.0681633i	$0.0217139\pi$
$983$	48.7707	+	28.1578i	1.55554	+	0.898093i	0.557868	+	0.829930i	$0.311619\pi$
$984$	5.21228	−	9.02793i	0.166161	−	0.287800i
$985$	−4.46264	−	0.749518i	−0.142192	−	0.0238816i
$986$	−21.4973	+	37.2345i	−0.684615	+	1.18579i
$987$		−	38.1764i		−	1.21517i
$988$			2.61843i			0.0833034i
$989$	−0.794790	+	1.34124i	−0.0252728	+	0.0426491i
$990$	−12.6990	−	2.13285i	−0.403601	−	0.0677863i
$991$	9.24196			0.293581			0.146790	−	0.989168i	$-0.453106\pi$
$991$	9.24196			0.293581			0.146790	+	0.989168i	$0.453106\pi$
$992$	−5.19733	−	3.00068i	−0.165015	−	0.0952717i
$993$			14.7292i			0.467416i
$994$	−6.00509	+	10.4011i	−0.190470	+	0.329904i
$995$	−21.7539	−	17.9543i	−0.689646	−	0.569189i
$996$	1.16031	+	2.00972i	0.0367659	+	0.0636804i
$997$			20.4649i			0.648131i	0.946035	+	0.324066i	$0.105050\pi$
$997$			20.4649i			0.648131i	−0.946035	+	0.324066i	$0.894950\pi$
$998$	−34.8536	+	20.1228i	−1.10327	+	0.636975i
$999$	−16.6572	+	28.8511i	−0.527011	+	0.912810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.8	✓	44
5.4	even	2	inner	430.2.j.a.49.15	yes	44
43.36	even	3	inner	430.2.j.a.79.4	yes	44
215.79	even	6	inner	430.2.j.a.79.19	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.8	✓	44	1.1	even	1	trivial
430.2.j.a.49.15	yes	44	5.4	even	2	inner
430.2.j.a.79.4	yes	44	43.36	even	3	inner
430.2.j.a.79.19	yes	44	215.79	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.13990 + 0.658124i) q^{3} -1.00000 q^{4} +(-1.72456 - 1.42334i) q^{5} +(0.658124 - 1.13990i) q^{6} +(-3.46526 + 2.00067i) q^{7} +1.00000i q^{8} +(-0.633745 - 1.09768i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.13990 + 0.658124i) q^{3} -1.00000 q^{4} +(-1.72456 - 1.42334i) q^{5} +(0.658124 - 1.13990i) q^{6} +(-3.46526 + 2.00067i) q^{7} +1.00000i q^{8} +(-0.633745 - 1.09768i) q^{9} +(-1.42334 + 1.72456i) q^{10} -4.54340 q^{11} +(-1.13990 - 0.658124i) q^{12} +(0.344070 - 0.198649i) q^{13} +(2.00067 + 3.46526i) q^{14} +(-1.02910 - 2.75745i) q^{15} +1.00000 q^{16} +(-5.13493 + 2.96465i) q^{17} +(-1.09768 + 0.633745i) q^{18} +(3.29530 - 5.70763i) q^{19} +(1.72456 + 1.42334i) q^{20} -5.26676 q^{21} +4.54340i q^{22} +(-0.205900 - 0.118876i) q^{23} +(-0.658124 + 1.13990i) q^{24} +(0.948208 + 4.90927i) q^{25} +(-0.198649 - 0.344070i) q^{26} -5.61708i q^{27} +(3.46526 - 2.00067i) q^{28} +(3.62561 + 6.27974i) q^{29} +(-2.75745 + 1.02910i) q^{30} +(3.00068 - 5.19733i) q^{31} -1.00000i q^{32} +(-5.17904 - 2.99012i) q^{33} +(2.96465 + 5.13493i) q^{34} +(8.82368 + 1.48197i) q^{35} +(0.633745 + 1.09768i) q^{36} +(-5.13633 - 2.96546i) q^{37} +(-5.70763 - 3.29530i) q^{38} +0.522942 q^{39} +(1.42334 - 1.72456i) q^{40} -7.91990 q^{41} +5.26676i q^{42} +(0.0743880 - 6.55702i) q^{43} +4.54340 q^{44} +(-0.469438 + 2.79504i) q^{45} +(-0.118876 + 0.205900i) q^{46} +7.24856i q^{47} +(1.13990 + 0.658124i) q^{48} +(4.50536 - 7.80351i) q^{49} +(4.90927 - 0.948208i) q^{50} -7.80443 q^{51} +(-0.344070 + 0.198649i) q^{52} +(3.99163 + 2.30457i) q^{53} -5.61708 q^{54} +(7.83536 + 6.46680i) q^{55} +(-2.00067 - 3.46526i) q^{56} +(7.51266 - 4.33744i) q^{57} +(6.27974 - 3.62561i) q^{58} -4.15283 q^{59} +(1.02910 + 2.75745i) q^{60} +(1.46507 + 2.53758i) q^{61} +(-5.19733 - 3.00068i) q^{62} +(4.39218 + 2.53583i) q^{63} -1.00000 q^{64} +(-0.876113 - 0.147147i) q^{65} +(-2.99012 + 5.17904i) q^{66} +(3.57089 + 2.06166i) q^{67} +(5.13493 - 2.96465i) q^{68} +(-0.156471 - 0.271015i) q^{69} +(1.48197 - 8.82368i) q^{70} +(1.50077 + 2.59941i) q^{71} +(1.09768 - 0.633745i) q^{72} +(-8.61166 + 4.97194i) q^{73} +(-2.96546 + 5.13633i) q^{74} +(-2.15004 + 6.22014i) q^{75} +(-3.29530 + 5.70763i) q^{76} +(15.7441 - 9.08985i) q^{77} -0.522942i q^{78} +(-5.74385 - 9.94864i) q^{79} +(-1.72456 - 1.42334i) q^{80} +(1.79550 - 3.10990i) q^{81} +7.91990i q^{82} +(-1.52685 - 0.881529i) q^{83} +5.26676 q^{84} +(13.0752 + 2.19603i) q^{85} +(-6.55702 - 0.0743880i) q^{86} +9.54441i q^{87} -4.54340i q^{88} +(-7.40713 + 12.8295i) q^{89} +(2.79504 + 0.469438i) q^{90} +(-0.794861 + 1.37674i) q^{91} +(0.205900 + 0.118876i) q^{92} +(6.84098 - 3.94964i) q^{93} +7.24856 q^{94} +(-13.8068 + 5.15281i) q^{95} +(0.658124 - 1.13990i) q^{96} -7.92017i q^{97} +(-7.80351 - 4.50536i) q^{98} +(2.87936 + 4.98719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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