LMFDB - Embedded newform 429.2.bb.a.25.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.13
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.a.103.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38149 + 1.90146i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.08900 + 3.35161i) q^{4} +(-0.382487 + 0.526448i) q^{5} +(-1.38149 + 1.90146i) q^{6} +(-0.0445990 - 0.0144911i) q^{7} +(-3.40681 + 1.10694i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.38149 + 1.90146i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.08900 + 3.35161i) q^{4} +(-0.382487 + 0.526448i) q^{5} +(-1.38149 + 1.90146i) q^{6} +(-0.0445990 - 0.0144911i) q^{7} +(-3.40681 + 1.10694i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.52942 q^{10} +(-3.17451 - 0.960445i) q^{11} -3.52409 q^{12} +(-2.64663 + 2.44854i) q^{13} +(-0.0340590 - 0.104823i) q^{14} +(-0.618876 - 0.201085i) q^{15} +(-1.10920 - 0.805882i) q^{16} +(3.05142 + 2.21699i) q^{17} +(-2.23531 - 0.726295i) q^{18} +(3.58016 - 1.16327i) q^{19} +(-1.34792 - 1.85525i) q^{20} -0.0468942i q^{21} +(-2.55932 - 7.36308i) q^{22} +8.92533 q^{23} +(-2.10553 - 2.89801i) q^{24} +(1.41423 + 4.35256i) q^{25} +(-8.31212 - 1.64982i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.0971370 - 0.133698i) q^{28} +(2.04568 - 6.29595i) q^{29} +(-0.472618 - 1.45457i) q^{30} +(-3.43221 - 4.72403i) q^{31} +3.94184i q^{32} +(-0.0675412 - 3.31594i) q^{33} +8.86492i q^{34} +(0.0246873 - 0.0179364i) q^{35} +(-1.08900 - 3.35161i) q^{36} +(-7.33028 - 2.38175i) q^{37} +(7.15788 + 5.20051i) q^{38} +(-3.14656 - 1.76045i) q^{39} +(0.720314 - 2.21690i) q^{40} +(4.14151 - 1.34566i) q^{41} +(0.0891676 - 0.0647840i) q^{42} +3.78727 q^{43} +(6.67610 - 9.59381i) q^{44} -0.650725i q^{45} +(12.3303 + 16.9712i) q^{46} +(1.56990 - 0.510093i) q^{47} +(0.423677 - 1.30394i) q^{48} +(-5.66134 - 4.11320i) q^{49} +(-6.32249 + 8.70216i) q^{50} +(-1.16554 + 3.58716i) q^{51} +(-5.32438 - 11.5369i) q^{52} +(2.06492 - 1.50025i) q^{53} -2.35034i q^{54} +(1.71983 - 1.30386i) q^{55} +0.167981 q^{56} +(2.21266 + 3.04547i) q^{57} +(14.7976 - 4.80804i) q^{58} +(4.38463 + 1.42465i) q^{59} +(1.34792 - 1.85525i) q^{60} +(5.69492 + 4.13760i) q^{61} +(4.24099 - 13.0524i) q^{62} +(0.0445990 - 0.0144911i) q^{63} +(-9.71368 + 7.05740i) q^{64} +(-0.276730 - 2.32985i) q^{65} +(6.21183 - 4.70938i) q^{66} +13.3801i q^{67} +(-10.7535 + 7.81286i) q^{68} +(2.75808 + 8.48849i) q^{69} +(0.0682108 + 0.0221630i) q^{70} +(5.75016 - 7.91442i) q^{71} +(2.10553 - 2.89801i) q^{72} +(-5.01114 - 1.62822i) q^{73} +(-5.59792 - 17.2286i) q^{74} +(-3.70251 + 2.69003i) q^{75} +13.2661i q^{76} +(0.127662 + 0.0888371i) q^{77} +(-0.999516 - 8.41512i) q^{78} +(-0.437587 + 0.317926i) q^{79} +(0.848509 - 0.275697i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.28019 + 6.01591i) q^{82} +(-3.74007 + 5.14776i) q^{83} +(0.157171 + 0.0510680i) q^{84} +(-2.33425 + 0.758445i) q^{85} +(5.23209 + 7.20135i) q^{86} +6.61995 q^{87} +(11.8781 - 0.241942i) q^{88} -15.1434i q^{89} +(1.23733 - 0.898973i) q^{90} +(0.153519 - 0.0708501i) q^{91} +(-9.71973 + 29.9142i) q^{92} +(3.43221 - 4.72403i) q^{93} +(3.13874 + 2.28043i) q^{94} +(-0.756966 + 2.32970i) q^{95} +(-3.74892 + 1.21810i) q^{96} +(-1.67984 - 2.31210i) q^{97} -16.4472i q^{98} +(3.13277 - 1.08892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	$ 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) $ 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.38149	+	1.90146i	0.976864	+	1.34454i	0.938502	+	0.345274i	$0.112214\pi$
$2$	1.38149	+	1.90146i	0.976864	+	1.34454i	0.0383624	+	0.999264i	$0.487786\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−1.08900	+	3.35161i	−0.544502	+	1.67581i
$5$	−0.382487	+	0.526448i	−0.171053	+	0.235435i	−0.885933	−	0.463812i	$-0.846481\pi$
$5$	−0.382487	+	0.526448i	−0.171053	+	0.235435i	0.714880	+	0.699247i	$0.246481\pi$
$6$	−1.38149	+	1.90146i	−0.563993	+	0.776270i
$7$	−0.0445990	−	0.0144911i	−0.0168568	−	0.00547712i	0.300576	−	0.953758i	$-0.402821\pi$
$7$	−0.0445990	−	0.0144911i	−0.0168568	−	0.00547712i	−0.317433	+	0.948281i	$0.602821\pi$
$8$	−3.40681	+	1.10694i	−1.20449	+	0.391363i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.52942			−0.483646
$11$	−3.17451	−	0.960445i	−0.957152	−	0.289585i
$11$	−3.17451	−	0.960445i	−0.957152	−	0.289585i
$12$	−3.52409			−1.01732
$13$	−2.64663	+	2.44854i	−0.734042	+	0.679104i
$13$	−2.64663	+	2.44854i	−0.734042	+	0.679104i
$14$	−0.0340590	−	0.104823i	−0.00910265	−	0.0280151i
$15$	−0.618876	−	0.201085i	−0.159793	−	0.0519199i
$16$	−1.10920	−	0.805882i	−0.277300	−	0.201471i
$17$	3.05142	+	2.21699i	0.740078	+	0.537698i	0.892735	−	0.450581i	$-0.148783\pi$
$17$	3.05142	+	2.21699i	0.740078	+	0.537698i	−0.152658	+	0.988279i	$0.548783\pi$
$18$	−2.23531	−	0.726295i	−0.526867	−	0.171189i
$19$	3.58016	−	1.16327i	0.821346	−	0.266871i	0.131950	−	0.991256i	$-0.457876\pi$
$19$	3.58016	−	1.16327i	0.821346	−	0.266871i	0.689396	+	0.724385i	$0.257876\pi$
$20$	−1.34792	−	1.85525i	−0.301404	−	0.414847i
$21$		−	0.0468942i		−	0.0102331i
$22$	−2.55932	−	7.36308i	−0.545649	−	1.56981i
$23$	8.92533			1.86106			0.930530	−	0.366216i	$-0.119347\pi$
$23$	8.92533			1.86106			0.930530	+	0.366216i	$0.119347\pi$
$24$	−2.10553	−	2.89801i	−0.429789	−	0.591554i
$25$	1.41423	+	4.35256i	0.282847	+	0.870513i
$26$	−8.31212	−	1.64982i	−1.63014	−	0.323556i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.0971370	−	0.133698i	0.0183572	−	0.0252665i
$29$	2.04568	−	6.29595i	0.379873	−	1.16913i	−0.560259	−	0.828317i	$-0.689298\pi$
$29$	2.04568	−	6.29595i	0.379873	−	1.16913i	0.940132	−	0.340811i	$-0.110702\pi$
$30$	−0.472618	−	1.45457i	−0.0862879	−	0.265567i
$31$	−3.43221	−	4.72403i	−0.616442	−	0.848460i	0.380646	−	0.924721i	$-0.375702\pi$
$31$	−3.43221	−	4.72403i	−0.616442	−	0.848460i	−0.997088	+	0.0762609i	$0.975702\pi$
$32$			3.94184i			0.696826i
$33$	−0.0675412	−	3.31594i	−0.0117574	−	0.577231i
$34$			8.86492i			1.52032i
$35$	0.0246873	−	0.0179364i	0.00417292	−	0.00303180i
$36$	−1.08900	−	3.35161i	−0.181501	−	0.558602i
$37$	−7.33028	−	2.38175i	−1.20509	−	0.391557i	−0.363459	−	0.931610i	$-0.618404\pi$
$37$	−7.33028	−	2.38175i	−1.20509	−	0.391557i	−0.841631	+	0.540053i	$0.818404\pi$
$38$	7.15788	+	5.20051i	1.16116	+	0.843633i
$39$	−3.14656	−	1.76045i	−0.503852	−	0.281898i
$40$	0.720314	−	2.21690i	0.113892	−	0.350523i
$41$	4.14151	−	1.34566i	0.646795	−	0.210156i	0.0327944	−	0.999462i	$-0.489559\pi$
$41$	4.14151	−	1.34566i	0.646795	−	0.210156i	0.614000	+	0.789306i	$0.289559\pi$
$42$	0.0891676	−	0.0647840i	0.0137589	−	0.00999639i
$43$	3.78727			0.577553			0.288776	−	0.957397i	$-0.406752\pi$
$43$	3.78727			0.577553			0.288776	+	0.957397i	$0.406752\pi$
$44$	6.67610	−	9.59381i	1.00646	−	1.44632i
$45$		−	0.650725i		−	0.0970044i
$46$	12.3303	+	16.9712i	1.81800	+	2.50227i
$47$	1.56990	−	0.510093i	0.228994	−	0.0744047i	−0.192272	−	0.981342i	$-0.561586\pi$
$47$	1.56990	−	0.510093i	0.228994	−	0.0744047i	0.421266	+	0.906937i	$0.361586\pi$
$48$	0.423677	−	1.30394i	0.0611525	−	0.188208i
$49$	−5.66134	−	4.11320i	−0.808763	−	0.587601i
$50$	−6.32249	+	8.70216i	−0.894135	+	1.23067i
$51$	−1.16554	+	3.58716i	−0.163208	+	0.502303i
$52$	−5.32438	−	11.5369i	−0.738358	−	1.59989i
$53$	2.06492	−	1.50025i	0.283639	−	0.206076i	−0.436864	−	0.899527i	$-0.643911\pi$
$53$	2.06492	−	1.50025i	0.283639	−	0.206076i	0.720503	+	0.693452i	$0.243911\pi$
$54$		−	2.35034i		−	0.319841i
$55$	1.71983	−	1.30386i	0.231902	−	0.175812i
$56$	0.167981			0.0224474
$57$	2.21266	+	3.04547i	0.293074	+	0.403382i
$58$	14.7976	−	4.80804i	1.94302	−	0.631326i
$59$	4.38463	+	1.42465i	0.570830	+	0.185474i	0.580188	−	0.814482i	$-0.302979\pi$
$59$	4.38463	+	1.42465i	0.570830	+	0.185474i	−0.00935859	+	0.999956i	$0.502979\pi$
$60$	1.34792	−	1.85525i	0.174016	−	0.239512i
$61$	5.69492	+	4.13760i	0.729160	+	0.529766i	0.889298	−	0.457329i	$-0.151194\pi$
$61$	5.69492	+	4.13760i	0.729160	+	0.529766i	−0.160138	+	0.987095i	$0.551194\pi$
$62$	4.24099	−	13.0524i	0.538607	−	1.65766i
$63$	0.0445990	−	0.0144911i	0.00561895	−	0.00182571i
$64$	−9.71368	+	7.05740i	−1.21421	+	0.882175i
$65$	−0.276730	−	2.32985i	−0.0343242	−	0.288982i
$66$	6.21183	−	4.70938i	0.764623	−	0.579684i
$67$			13.3801i			1.63464i	0.576184	+	0.817320i	$0.304541\pi$
$67$			13.3801i			1.63464i	−0.576184	+	0.817320i	$0.695459\pi$
$68$	−10.7535	+	7.81286i	−1.30405	+	0.947449i
$69$	2.75808	+	8.48849i	0.332034	+	1.02189i
$70$	0.0682108	+	0.0221630i	0.00815275	+	0.00264899i
$71$	5.75016	−	7.91442i	0.682419	−	0.939269i	−0.317541	−	0.948245i	$-0.602857\pi$
$71$	5.75016	−	7.91442i	0.682419	−	0.939269i	0.999960	+	0.00897557i	$0.00285705\pi$
$72$	2.10553	−	2.89801i	0.248139	−	0.341534i
$73$	−5.01114	−	1.62822i	−0.586510	−	0.190569i	0.000705046	−	1.00000i	$-0.499776\pi$
$73$	−5.01114	−	1.62822i	−0.586510	−	0.190569i	−0.587215	+	0.809431i	$0.699776\pi$
$74$	−5.59792	−	17.2286i	−0.650745	−	2.00279i
$75$	−3.70251	+	2.69003i	−0.427529	+	0.310618i
$76$			13.2661i			1.52173i
$77$	0.127662	+	0.0888371i	0.0145485	+	0.0101239i
$78$	−0.999516	−	8.41512i	−0.113173	−	0.952824i
$79$	−0.437587	+	0.317926i	−0.0492324	+	0.0357694i	−0.612129	−	0.790758i	$-0.709687\pi$
$79$	−0.437587	+	0.317926i	−0.0492324	+	0.0357694i	0.562897	+	0.826527i	$0.309687\pi$
$80$	0.848509	−	0.275697i	0.0948662	−	0.0308239i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	8.28019	+	6.01591i	0.914394	+	0.664346i
$83$	−3.74007	+	5.14776i	−0.410526	+	0.565040i	−0.963347	−	0.268260i	$-0.913551\pi$
$83$	−3.74007	+	5.14776i	−0.410526	+	0.565040i	0.552821	+	0.833300i	$0.313551\pi$
$84$	0.157171	+	0.0510680i	0.0171488	+	0.00557197i
$85$	−2.33425	+	0.758445i	−0.253185	+	0.0822649i
$86$	5.23209	+	7.20135i	0.564191	+	0.776542i
$87$	6.61995			0.709733
$88$	11.8781	−	0.241942i	1.26621	−	0.0257911i
$89$		−	15.1434i		−	1.60520i	−0.596520	−	0.802598i	$-0.703450\pi$
$89$		−	15.1434i		−	1.60520i	0.596520	−	0.802598i	$-0.296550\pi$
$90$	1.23733	−	0.898973i	0.130426	−	0.0947601i
$91$	0.153519	−	0.0708501i	0.0160932	−	0.00742710i
$92$	−9.71973	+	29.9142i	−1.01335	+	3.11878i
$93$	3.43221	−	4.72403i	0.355903	−	0.489859i
$94$	3.13874	+	2.28043i	0.323736	+	0.235208i
$95$	−0.756966	+	2.32970i	−0.0776631	+	0.239022i
$96$	−3.74892	+	1.21810i	−0.382622	+	0.124322i
$97$	−1.67984	−	2.31210i	−0.170562	−	0.234758i	0.715176	−	0.698945i	$-0.246347\pi$
$97$	−1.67984	−	2.31210i	−0.170562	−	0.234758i	−0.885737	+	0.464187i	$0.846347\pi$
$98$		−	16.4472i		−	1.66142i
$99$	3.13277	−	1.08892i	0.314855	−	0.109440i
$100$	−16.1282			−1.61282
$101$	−3.59625	+	2.61283i	−0.357840	+	0.259986i	−0.752151	−	0.658991i	$-0.770983\pi$
$101$	−3.59625	+	2.61283i	−0.357840	+	0.259986i	0.394311	+	0.918977i	$0.370983\pi$
$102$	−8.43104	+	2.73941i	−0.834797	+	0.271242i
$103$	−3.91338	+	12.0441i	−0.385596	+	1.18674i	0.550450	+	0.834868i	$0.314456\pi$
$103$	−3.91338	+	12.0441i	−0.385596	+	1.18674i	−0.936047	+	0.351876i	$0.885544\pi$
$104$	6.30617	−	11.2714i	0.618371	−	1.10525i
$105$	0.0246873	+	0.0179364i	0.00240924	+	0.00175041i
$106$	5.70536	+	1.85378i	0.554153	+	0.180055i
$107$	−1.41830	−	4.36509i	−0.137113	−	0.421989i	0.858800	−	0.512311i	$-0.171211\pi$
$107$	−1.41830	−	4.36509i	−0.137113	−	0.421989i	−0.995913	+	0.0903216i	$0.971211\pi$
$108$	2.85105	−	2.07141i	0.274343	−	0.199322i
$109$		−	12.9963i		−	1.24482i	−0.782692	−	0.622410i	$-0.786154\pi$
$109$		−	12.9963i		−	1.24482i	0.782692	−	0.622410i	$-0.213846\pi$
$110$	4.85518	+	1.46893i	0.462923	+	0.140057i
$111$		−	7.70751i		−	0.731564i
$112$	0.0377912	+	0.0520151i	0.00357093	+	0.00491496i
$113$	−4.32712	−	13.3175i	−0.407061	−	1.25281i	−0.919162	−	0.393880i	$-0.871133\pi$
$113$	−4.32712	−	13.3175i	−0.407061	−	1.25281i	0.512101	−	0.858925i	$-0.328867\pi$
$114$	−2.73407	+	8.41460i	−0.256069	+	0.788099i
$115$	−3.41382	+	4.69872i	−0.318340	+	0.438158i
$116$	18.8738	+	13.7126i	1.75239	+	1.27319i
$117$	0.701949	−	3.53656i	0.0648952	−	0.326955i
$118$	3.34841	+	10.3054i	0.308246	+	0.948685i
$119$	−0.103964	−	0.143094i	−0.00953033	−	0.0131174i
$120$	2.33099			0.212789
$121$	9.15509	+	6.09790i	0.832281	+	0.554354i
$122$			16.5448i			1.49789i
$123$	2.55959	+	3.52298i	0.230791	+	0.317656i
$124$	19.5708	−	6.35894i	1.75751	−	0.571049i
$125$	−5.92670	−	1.92570i	−0.530101	−	0.172240i
$126$	0.0891676	+	0.0647840i	0.00794368	+	0.00577142i
$127$	−11.4093	−	8.28931i	−1.01241	−	0.735557i	−0.0476949	−	0.998862i	$-0.515188\pi$
$127$	−11.4093	−	8.28931i	−1.01241	−	0.735557i	−0.964713	+	0.263305i	$0.915188\pi$
$128$	−19.3410	−	6.28426i	−1.70952	−	0.555455i
$129$	1.17033	+	3.60191i	0.103042	+	0.317130i
$130$	4.04782	−	3.74486i	0.355017	−	0.328446i
$131$	−11.0486			−0.965323			−0.482662	−	0.875807i	$-0.660330\pi$
$131$	−11.0486			−0.965323			−0.482662	+	0.875807i	$0.660330\pi$
$132$	11.1873	+	3.38470i	0.973728	+	0.294600i
$133$	−0.176529			−0.0153070
$134$	−25.4418	+	18.4845i	−2.19784	+	1.59682i
$135$	0.618876	−	0.201085i	0.0532644	−	0.0173066i
$136$	−12.8497	−	4.17512i	−1.10185	−	0.358013i
$137$	−0.198646	+	0.273412i	−0.0169714	+	0.0233592i	−0.817418	−	0.576044i	$-0.804596\pi$
$137$	−0.198646	+	0.273412i	−0.0169714	+	0.0233592i	0.800447	+	0.599404i	$0.204596\pi$
$138$	−12.3303	+	16.9712i	−1.04962	+	1.44468i
$139$	0.367270	−	1.13034i	0.0311515	−	0.0958744i	−0.934272	−	0.356561i	$-0.883949\pi$
$139$	0.367270	−	1.13034i	0.0311515	−	0.0958744i	0.965423	+	0.260687i	$0.0839491\pi$
$140$	0.0332312	+	0.102275i	0.00280855	+	0.00864383i
$141$	0.970254	+	1.33544i	0.0817101	+	0.112464i
$142$	22.9928			1.92951
$143$	10.7534	−	5.23100i	0.899249	−	0.437438i
$144$	1.37105			0.114254
$145$	2.53204	+	3.48506i	0.210275	+	0.289418i
$146$	−3.82687	−	11.7779i	−0.316714	−	0.974744i
$147$	2.16244	−	6.65530i	0.178355	−	0.548920i
$148$	15.9654	−	21.9745i	1.31235	−	1.80629i
$149$	−6.79036	+	9.34613i	−0.556288	+	0.765665i	−0.990849	−	0.134978i	$-0.956904\pi$
$149$	−6.79036	+	9.34613i	−0.556288	+	0.765665i	0.434561	+	0.900643i	$0.356904\pi$
$150$	−10.2300	−	3.32393i	−0.835276	−	0.271398i
$151$	12.1636	−	3.95221i	0.989864	−	0.321626i	0.231056	−	0.972941i	$-0.425782\pi$
$151$	12.1636	−	3.95221i	0.989864	−	0.321626i	0.758808	+	0.651314i	$0.225782\pi$
$152$	−10.9093	+	7.92606i	−0.884860	+	0.642888i
$153$	−3.77176			−0.304929
$154$	0.00744420	+	0.365473i	0.000599871	+	0.0294507i
$155$	3.79972			0.305201
$156$	9.32696	−	8.62890i	0.746755	−	0.690865i
$157$	0.0799044	+	0.245921i	0.00637707	+	0.0196266i	0.954194	−	0.299187i	$-0.0967155\pi$
$157$	0.0799044	+	0.245921i	0.00637707	+	0.0196266i	−0.947817	+	0.318814i	$0.896716\pi$
$158$	−1.20905	−	0.392844i	−0.0961868	−	0.0312530i
$159$	2.06492	+	1.50025i	0.163759	+	0.118978i
$160$	−2.07517	−	1.50770i	−0.164057	−	0.119194i
$161$	−0.398061	−	0.129338i	−0.0313716	−	0.0101932i
$162$	2.23531	−	0.726295i	0.175622	−	0.0570631i
$163$	3.57021	+	4.91397i	0.279640	+	0.384892i	0.925615	−	0.378467i	$-0.123549\pi$
$163$	3.57021	+	4.91397i	0.279640	+	0.384892i	−0.645974	+	0.763359i	$0.723549\pi$
$164$			15.3462i			1.19833i
$165$	1.77150	+	1.23274i	0.137911	+	0.0959690i
$166$	−14.9552			−1.16075
$167$	15.0776	+	20.7526i	1.16674	+	1.60588i	0.682330	+	0.731044i	$0.260967\pi$
$167$	15.0776	+	20.7526i	1.16674	+	1.60588i	0.484412	+	0.874840i	$0.339033\pi$
$168$	0.0519091	+	0.159760i	0.00400487	+	0.0123257i
$169$	1.00927	−	12.9608i	0.0776362	−	0.996982i
$170$	−4.66691	−	3.39071i	−0.357936	−	0.260056i
$171$	−2.21266	+	3.04547i	−0.169206	+	0.232893i
$172$	−4.12435	+	12.6935i	−0.314479	+	0.967867i
$173$	−0.718243	−	2.21053i	−0.0546070	−	0.168063i	0.920033	−	0.391840i	$-0.128161\pi$
$173$	−0.718243	−	2.21053i	−0.0546070	−	0.168063i	−0.974640	+	0.223777i	$0.928161\pi$
$174$	9.14543	+	12.5876i	0.693313	+	0.954264i
$175$		−	0.214614i		−	0.0162233i
$176$	2.74717	+	3.62361i	0.207076	+	0.273140i
$177$			4.61027i			0.346529i
$178$	28.7946	−	20.9205i	2.15825	−	1.56806i
$179$	−5.85581	−	18.0223i	−0.437684	−	1.34705i	−0.890311	−	0.455353i	$-0.849513\pi$
$179$	−5.85581	−	18.0223i	−0.437684	−	1.34705i	0.452627	−	0.891700i	$-0.350487\pi$
$180$	2.18098	+	0.708643i	0.162560	+	0.0528191i
$181$	−6.14153	−	4.46208i	−0.456496	−	0.331664i	0.335659	−	0.941984i	$-0.391041\pi$
$181$	−6.14153	−	4.46208i	−0.456496	−	0.331664i	−0.792155	+	0.610320i	$0.791041\pi$
$182$	0.346805	+	0.194032i	0.0257069	+	0.0143826i
$183$	−2.17527	+	6.69478i	−0.160800	+	0.494892i
$184$	−30.4069	+	9.87981i	−2.24163	+	0.728350i
$185$	4.05760	−	2.94802i	0.298321	−	0.216743i
$186$	13.7241			1.00630
$187$	−7.55748	−	9.96857i	−0.552658	−	0.728974i
$188$			5.81720i			0.424263i
$189$	0.0275637	+	0.0379382i	0.00200496	+	0.00275960i
$190$	−5.47559	+	1.77913i	−0.397241	+	0.129071i
$191$	2.20839	−	6.79672i	0.159793	−	0.491794i	−0.838822	−	0.544406i	$-0.816755\pi$
$191$	2.20839	−	6.79672i	0.159793	−	0.491794i	0.998615	+	0.0526129i	$0.0167549\pi$
$192$	−9.71368	−	7.05740i	−0.701024	−	0.509324i
$193$	3.44216	−	4.73773i	0.247772	−	0.341029i	−0.666957	−	0.745096i	$-0.732404\pi$
$193$	3.44216	−	4.73773i	0.247772	−	0.341029i	0.914729	+	0.404067i	$0.132404\pi$
$194$	2.07569	−	6.38830i	0.149026	−	0.458653i
$195$	2.13030	−	0.983148i	0.152554	−	0.0704047i
$196$	19.9511	−	14.4953i	1.42508	−	1.03538i
$197$		−	10.4798i		−	0.746654i	−0.927700	−	0.373327i	$-0.878217\pi$
$197$		−	10.4798i		−	0.746654i	0.927700	−	0.373327i	$-0.121783\pi$
$198$	6.39844	+	4.45252i	0.454718	+	0.316427i
$199$	−11.4982			−0.815083			−0.407541	−	0.913187i	$-0.633614\pi$
$199$	−11.4982			−0.815083			−0.407541	+	0.913187i	$0.633614\pi$
$200$	−9.63606	−	13.2629i	−0.681373	−	0.937829i
$201$	−12.7252	+	4.13468i	−0.897569	+	0.291638i
$202$	−9.93639	−	3.22853i	−0.699122	−	0.227159i
$203$	−0.182470	+	0.251149i	−0.0128069	+	0.0176272i
$204$	−10.7535	−	7.81286i	−0.752895	−	0.547010i
$205$	−0.875653	+	2.69498i	−0.0611582	+	0.188226i
$206$	−28.3078	+	9.19776i	−1.97230	+	0.640838i
$207$	−7.22074	+	5.24618i	−0.501876	+	0.364635i
$208$	4.90888	−	0.583059i	0.340370	−	0.0404278i
$209$	−12.4825	+	0.254252i	−0.863435	+	0.0175870i
$210$			0.0717211i			0.00494922i
$211$	−0.388245	+	0.282077i	−0.0267279	+	0.0194190i	−0.601069	−	0.799197i	$-0.705258\pi$
$211$	−0.388245	+	0.282077i	−0.0267279	+	0.0194190i	0.574341	+	0.818616i	$0.305258\pi$
$212$	2.77956	+	8.55460i	0.190901	+	0.587532i
$213$	9.30396	+	3.02304i	0.637497	+	0.207135i
$214$	6.34069	−	8.72721i	0.433440	−	0.596580i
$215$	−1.44858	+	1.99380i	−0.0987923	+	0.135976i
$216$	3.40681	+	1.10694i	0.231804	+	0.0753178i
$217$	0.0846166	+	0.260423i	0.00574415	+	0.0176787i
$218$	24.7120	−	17.9543i	1.67371	−	1.21602i
$219$		−	5.26903i		−	0.356048i
$220$	2.49712	+	7.18412i	0.168356	+	0.484353i
$221$	−13.5044	+	1.60400i	−0.908401	+	0.107897i
$222$	14.6556	−	10.6479i	0.983616	−	0.714639i
$223$	−14.3293	+	4.65586i	−0.959558	+	0.311779i	−0.746593	−	0.665281i	$-0.768312\pi$
$223$	−14.3293	+	4.65586i	−0.959558	+	0.311779i	−0.212964	+	0.977060i	$0.568312\pi$
$224$	0.0571216	−	0.175802i	0.00381660	−	0.0117463i
$225$	−3.70251	−	2.69003i	−0.246834	−	0.179336i
$226$	19.3449	−	26.6259i	1.28680	−	1.77113i
$227$	−11.5324	−	3.74710i	−0.765431	−	0.248704i	−0.0998231	−	0.995005i	$-0.531828\pi$
$227$	−11.5324	−	3.74710i	−0.765431	−	0.248704i	−0.665608	+	0.746302i	$0.731828\pi$
$228$	−12.6168	+	4.09946i	−0.835570	+	0.271493i
$229$	−14.6178	−	20.1197i	−0.965970	−	1.32954i	−0.944056	−	0.329784i	$-0.893024\pi$
$229$	−14.6178	−	20.1197i	−0.965970	−	1.32954i	−0.0219141	−	0.999760i	$-0.506976\pi$
$230$	−13.6506			−0.900095
$231$	−0.0450393	+	0.148866i	−0.00296337	+	0.00979468i
$232$			23.7136i			1.55687i
$233$	14.0748	−	10.2259i	0.922070	−	0.669923i	−0.0219685	−	0.999759i	$-0.506993\pi$
$233$	14.0748	−	10.2259i	0.922070	−	0.669923i	0.944038	+	0.329836i	$0.106993\pi$
$234$	7.69438	−	3.55101i	0.502998	−	0.232137i
$235$	−0.331930	+	1.02158i	−0.0216527	+	0.0666403i
$236$	−9.54976	+	13.1441i	−0.621636	+	0.855609i
$237$	−0.437587	−	0.317926i	−0.0284243	−	0.0206515i
$238$	0.128462	−	0.395366i	0.00832698	−	0.0256278i
$239$	20.4788	−	6.65395i	1.32466	−	0.430408i	0.440568	−	0.897719i	$-0.354777\pi$
$239$	20.4788	−	6.65395i	1.32466	−	0.430408i	0.884093	+	0.467311i	$0.154777\pi$
$240$	0.524408	+	0.721785i	0.0338504	+	0.0465910i
$241$			26.5500i			1.71024i	0.518433	+	0.855118i	$0.326515\pi$
$241$			26.5500i			1.71024i	−0.518433	+	0.855118i	$0.673485\pi$
$242$	1.05277	+	25.8323i	0.0676749	+	1.66056i
$243$	1.00000			0.0641500
$244$	−20.0694	+	14.5813i	−1.28481	+	0.933472i
$245$	4.33077	−	1.40715i	0.276683	−	0.0898997i
$246$	−3.16275	+	9.73395i	−0.201650	+	0.620614i
$247$	−6.62705	+	11.8449i	−0.421669	+	0.753674i
$248$	16.9221	+	12.2946i	1.07455	+	0.780710i
$249$	−6.05155	−	1.96627i	−0.383502	−	0.124607i
$250$	−4.52605	−	13.9298i	−0.286253	−	0.880996i
$251$	−0.960765	+	0.698037i	−0.0606429	+	0.0440597i	−0.617694	−	0.786419i	$-0.711933\pi$
$251$	−0.960765	+	0.698037i	−0.0606429	+	0.0440597i	0.557051	+	0.830478i	$0.311933\pi$
$252$			0.165259i			0.0104104i
$253$	−28.3336	−	8.57229i	−1.78132	−	0.538935i
$254$		−	33.1459i		−	2.07976i
$255$	−1.44265	−	1.98563i	−0.0903421	−	0.124345i
$256$	−7.34955	−	22.6196i	−0.459347	−	1.41372i
$257$	−1.06008	+	3.26259i	−0.0661259	+	0.203515i	−0.978660	−	0.205486i	$-0.934123\pi$
$257$	−1.06008	+	3.26259i	−0.0661259	+	0.203515i	0.912534	+	0.409000i	$0.134123\pi$
$258$	−5.23209	+	7.20135i	−0.325736	+	0.448337i
$259$	0.292409	+	0.212447i	0.0181694	+	0.0132008i
$260$	8.11010	+	1.60972i	0.502967	+	0.0998306i
$261$	2.04568	+	6.29595i	0.126624	+	0.389709i
$262$	−15.2636	−	21.0086i	−0.942990	−	1.29791i
$263$	26.7217			1.64773			0.823865	−	0.566786i	$-0.191814\pi$
$263$	26.7217			1.64773			0.823865	+	0.566786i	$0.191814\pi$
$264$	3.90065	+	11.2220i	0.240068	+	0.690667i
$265$			1.66090i			0.102028i
$266$	−0.243873	−	0.335663i	−0.0149528	−	0.0205808i
$267$	14.4022	−	4.67957i	0.881402	−	0.286385i
$268$	−44.8449	−	14.5710i	−2.73934	−	0.890066i
$269$	0.675283	+	0.490622i	0.0411728	+	0.0299138i	0.608181	−	0.793798i	$-0.291899\pi$
$269$	0.675283	+	0.490622i	0.0411728	+	0.0299138i	−0.567009	+	0.823712i	$0.691899\pi$
$270$	1.23733	+	0.898973i	0.0753015	+	0.0547098i
$271$	24.8599	+	8.07747i	1.51013	+	0.490671i	0.942954	−	0.332924i	$-0.108035\pi$
$271$	24.8599	+	8.07747i	1.51013	+	0.490671i	0.567178	+	0.823596i	$0.308035\pi$
$272$	−1.59801	−	4.91817i	−0.0968936	−	0.298208i
$273$	0.114822	+	0.124111i	0.00694937	+	0.00751156i
$274$	−0.794311			−0.0479861
$275$	−0.309106	−	15.1756i	−0.0186398	−	0.915122i
$276$	−31.4537			−1.89329
$277$	3.05707	−	2.22109i	0.183681	−	0.133452i	−0.492145	−	0.870513i	$-0.663787\pi$
$277$	3.05707	−	2.22109i	0.183681	−	0.133452i	0.675826	+	0.737061i	$0.263787\pi$
$278$	2.65669	−	0.863210i	0.159337	−	0.0517719i
$279$	5.55343	+	1.80442i	0.332475	+	0.108028i
$280$	−0.0642506	+	0.0884333i	−0.00383971	+	0.00528490i
$281$	−8.96471	+	12.3389i	−0.534790	+	0.736075i	−0.987851	−	0.155405i	$-0.950332\pi$
$281$	−8.96471	+	12.3389i	−0.534790	+	0.736075i	0.453061	+	0.891479i	$0.350332\pi$
$282$	−1.19889	+	3.68981i	−0.0713929	+	0.219725i
$283$	4.22329	+	12.9979i	0.251048	+	0.772647i	0.994583	+	0.103949i	$0.0331480\pi$
$283$	4.22329	+	12.9979i	0.251048	+	0.772647i	−0.743534	+	0.668698i	$0.766852\pi$
$284$	20.2641	+	27.8912i	1.20245	+	1.65504i
$285$	−2.44959			−0.145101
$286$	24.8024	+	13.2207i	1.46660	+	0.781757i
$287$	−0.204207			−0.0120540
$288$	−2.31696	−	3.18902i	−0.136528	−	0.187915i
$289$	−0.857157	−	2.63806i	−0.0504210	−	0.155180i
$290$	−3.12871	+	9.62918i	−0.183724	+	0.565445i
$291$	1.67984	−	2.31210i	0.0984738	−	0.135538i
$292$	10.9143	−	15.0223i	0.638712	−	0.879111i
$293$	−1.59544	−	0.518391i	−0.0932068	−	0.0302847i	0.262042	−	0.965056i	$-0.415604\pi$
$293$	−1.59544	−	0.518391i	−0.0932068	−	0.0302847i	−0.355249	+	0.934772i	$0.615604\pi$
$294$	15.6422	−	5.08247i	0.912273	−	0.296415i
$295$	−2.42706	+	1.76337i	−0.141309	+	0.102667i
$296$	27.6093			1.60476
$297$	2.00370	+	2.64295i	0.116267	+	0.153359i
$298$	−27.1522			−1.57288
$299$	−23.6220	+	21.8541i	−1.36610	+	1.26385i
$300$	−4.98389	−	15.3388i	−0.287745	−	0.885589i
$301$	−0.168908	−	0.0548816i	−0.00973571	−	0.00316333i
$302$	24.3190	+	17.6688i	1.39940	+	1.01672i
$303$	−3.59625	−	2.61283i	−0.206599	−	0.150103i
$304$	−4.90858	−	1.59489i	−0.281526	−	0.0914734i
$305$	−4.35646	+	1.41550i	−0.249450	+	0.0810513i
$306$	−5.21067	−	7.17187i	−0.297874	−	0.409988i
$307$			31.3021i			1.78650i	0.449556	+	0.893252i	$0.351582\pi$
$307$			31.3021i			1.78650i	−0.449556	+	0.893252i	$0.648418\pi$
$308$	−0.436772	+	0.331130i	−0.0248874	+	0.0188679i
$309$	−12.6640			−0.720427
$310$	5.24930	+	7.22504i	0.298140	+	0.410355i
$311$	−0.660905	−	2.03406i	−0.0374765	−	0.115341i	0.930568	−	0.366119i	$-0.119314\pi$
$311$	−0.660905	−	2.03406i	−0.0374765	−	0.115341i	−0.968045	+	0.250778i	$0.919314\pi$
$312$	12.6684	+	2.51448i	0.717210	+	0.142354i
$313$	−18.5580	−	13.4832i	−1.04896	−	0.762115i	−0.0769467	−	0.997035i	$-0.524517\pi$
$313$	−18.5580	−	13.4832i	−1.04896	−	0.762115i	−0.972015	+	0.234920i	$0.924517\pi$
$314$	−0.357222	+	0.491673i	−0.0201592	+	0.0277467i
$315$	−0.00942972	+	0.0290217i	−0.000531304	+	0.00163519i
$316$	−0.589029	−	1.81285i	−0.0331355	−	0.101981i
$317$	−2.36718	−	3.25815i	−0.132954	−	0.182996i	0.737349	−	0.675512i	$-0.236077\pi$
$317$	−2.36718	−	3.25815i	−0.132954	−	0.182996i	−0.870303	+	0.492516i	$0.836077\pi$
$318$			5.99897i			0.336405i
$319$	−12.5409	+	18.0218i	−0.702158	+	1.00903i
$320$		−	7.81310i		−	0.436766i
$321$	3.71317	−	2.69778i	0.207249	−	0.150575i
$322$	−0.303988	−	0.935578i	−0.0169406	−	0.0521377i
$323$	13.5035	+	4.38756i	0.751356	+	0.244130i
$324$	2.85105	+	2.07141i	0.158392	+	0.115078i
$325$	−14.4004	−	8.05680i	−0.798790	−	0.446911i
$326$	−4.41151	+	13.5772i	−0.244331	+	0.751974i
$327$	12.3602	−	4.01608i	0.683521	−	0.222089i
$328$	−12.6198	+	9.16881i	−0.696811	+	0.506263i
$329$	−0.0774079			−0.00426764
$330$	0.103299	+	5.07147i	0.00568643	+	0.279176i
$331$		−	10.2861i		−	0.565377i	−0.959212	−	0.282689i	$-0.908774\pi$
$331$		−	10.2861i		−	0.565377i	0.959212	−	0.282689i	$-0.0912263\pi$
$332$	−13.1803	−	18.1412i	−0.723365	−	0.995627i
$333$	7.33028	−	2.38175i	0.401697	−	0.130519i
$334$	−18.6306	+	57.3392i	−1.01942	+	3.13746i
$335$	−7.04393	−	5.11771i	−0.384851	−	0.279610i
$336$	−0.0377912	+	0.0520151i	−0.00206168	+	0.00283765i
$337$	−6.53363	+	20.1085i	−0.355910	+	1.09538i	0.599571	+	0.800322i	$0.295338\pi$
$337$	−6.53363	+	20.1085i	−0.355910	+	1.09538i	−0.955480	+	0.295055i	$0.904662\pi$
$338$	26.0387	−	15.9861i	1.41632	−	0.869531i
$339$	11.3285	−	8.23067i	0.615282	−	0.447029i
$340$		−	8.64946i		−	0.469083i
$341$	6.35842	+	18.2929i	0.344328	+	0.990618i
$342$	−8.84763			−0.478425
$343$	0.385831	+	0.531051i	0.0208329	+	0.0286741i
$344$	−12.9025	+	4.19228i	−0.695657	+	0.226033i
$345$	−5.52367	−	1.79475i	−0.297385	−	0.0966261i
$346$	3.21099	−	4.41954i	0.172624	−	0.237596i
$347$	27.8286	+	20.2187i	1.49392	+	1.08539i	0.972727	+	0.231954i	$0.0745118\pi$
$347$	27.8286	+	20.2187i	1.49392	+	1.08539i	0.521190	+	0.853441i	$0.325488\pi$
$348$	−7.20916	+	22.1875i	−0.386452	+	1.18938i
$349$	−7.56277	+	2.45729i	−0.404826	+	0.131536i	−0.504350	−	0.863499i	$-0.668268\pi$
$349$	−7.56277	+	2.45729i	−0.404826	+	0.131536i	0.0995244	+	0.995035i	$0.468268\pi$
$350$	0.408080	−	0.296488i	0.0218128	−	0.0158479i
$351$	3.58038	−	0.425265i	0.191107	−	0.0226990i
$352$	3.78593	−	12.5134i	0.201791	−	0.666969i
$353$			26.3789i			1.40401i	0.712174	+	0.702003i	$0.247711\pi$
$353$			26.3789i			1.40401i	−0.712174	+	0.702003i	$0.752289\pi$
$354$	−8.76626	+	6.36906i	−0.465921	+	0.338512i
$355$	1.96717	+	6.05432i	0.104406	+	0.321330i
$356$	50.7548	+	16.4912i	2.69000	+	0.874033i
$357$	0.103964	−	0.143094i	0.00550234	−	0.00757332i
$358$	26.1791	−	36.0324i	1.38361	−	1.90437i
$359$	1.38179	+	0.448971i	0.0729281	+	0.0236958i	0.345254	−	0.938509i	$-0.387793\pi$
$359$	1.38179	+	0.448971i	0.0729281	+	0.0236958i	−0.272326	+	0.962205i	$0.587793\pi$
$360$	0.720314	+	2.21690i	0.0379639	+	0.116841i
$361$	−3.90695	+	2.83856i	−0.205629	+	0.149398i
$362$		−	17.8422i		−	0.937767i
$363$	−2.97037	+	10.5914i	−0.155904	+	0.555902i
$364$	0.0702790	+	0.591692i	0.00368362	+	0.0310131i
$365$	2.77387	−	2.01533i	0.145191	−	0.105487i
$366$	−15.7350	+	5.11261i	−0.822482	+	0.267241i
$367$	8.79511	−	27.0686i	0.459101	−	1.41297i	−0.407151	−	0.913361i	$-0.633478\pi$
$367$	8.79511	−	27.0686i	0.459101	−	1.41297i	0.866252	−	0.499607i	$-0.166522\pi$
$368$	−9.89999	−	7.19276i	−0.516073	−	0.374949i
$369$	−2.55959	+	3.52298i	−0.133247	+	0.183399i
$370$	11.2111	+	3.64271i	0.582838	+	0.189375i
$371$	−0.113834	+	0.0369868i	−0.00590995	+	0.00192026i
$372$	12.0954	+	16.6479i	0.627118	+	0.863154i
$373$	20.4445			1.05858			0.529289	−	0.848442i	$-0.322459\pi$
$373$	20.4445			1.05858			0.529289	+	0.848442i	$0.322459\pi$
$374$	8.51427	−	28.1418i	0.440262	−	1.45518i
$375$		−	6.23171i		−	0.321804i
$376$	−4.78373	+	3.47558i	−0.246702	+	0.179239i
$377$	10.0018	+	21.6720i	0.515117	+	1.11616i
$378$	−0.0340590	+	0.104823i	−0.00175180	+	0.00539150i
$379$	−20.6933	+	28.4819i	−1.06294	+	1.46302i	−0.185921	+	0.982565i	$0.559527\pi$
$379$	−20.6933	+	28.4819i	−1.06294	+	1.46302i	−0.877022	+	0.480450i	$0.840473\pi$
$380$	−6.98392	−	5.07411i	−0.358267	−	0.260296i
$381$	4.35795	−	13.4124i	0.223264	−	0.687137i
$382$	15.9746	−	5.19046i	0.817332	−	0.265567i
$383$	−9.61305	−	13.2312i	−0.491204	−	0.676084i	0.489405	−	0.872056i	$-0.337214\pi$
$383$	−9.61305	−	13.2312i	−0.491204	−	0.676084i	−0.980609	+	0.195972i	$0.937214\pi$
$384$		−	20.3363i		−	1.03778i
$385$	−0.0955972	+	0.0332285i	−0.00487208	+	0.00169348i
$386$	13.7639			0.700566
$387$	−3.06396	+	2.22610i	−0.155750	+	0.113159i
$388$	9.57861	−	3.11228i	0.486280	−	0.158002i
$389$	2.21727	−	6.82405i	0.112420	−	0.345993i	−0.878980	−	0.476858i	$-0.841775\pi$
$389$	2.21727	−	6.82405i	0.112420	−	0.345993i	0.991400	+	0.130865i	$0.0417755\pi$
$390$	4.81242	+	2.69248i	0.243686	+	0.136339i
$391$	27.2349	+	19.7873i	1.37733	+	1.00069i
$392$	23.8402	+	7.74615i	1.20411	+	0.391240i
$393$	−3.41421	−	10.5079i	−0.172224	−	0.530052i
$394$	19.9269	−	14.4778i	1.00390	−	0.729379i
$395$		−	0.351969i		−	0.0177095i
$396$	0.238021	+	11.6857i	0.0119610	+	0.587227i
$397$		−	28.5025i		−	1.43050i	−0.698868	−	0.715251i	$-0.746312\pi$
$397$		−	28.5025i		−	1.43050i	0.698868	−	0.715251i	$-0.253688\pi$
$398$	−15.8846	−	21.8633i	−0.796225	−	1.09591i
$399$	−0.0545503	−	0.167889i	−0.00273093	−	0.00840495i
$400$	1.93898	−	5.96758i	0.0969492	−	0.298379i
$401$	−11.8228	+	16.2726i	−0.590400	+	0.812616i	−0.994787	−	0.101972i	$-0.967485\pi$
$401$	−11.8228	+	16.2726i	−0.590400	+	0.812616i	0.404387	+	0.914588i	$0.367485\pi$
$402$	−25.4418	−	18.4845i	−1.26892	−	0.921925i
$403$	20.6508	+	4.09883i	1.02869	+	0.204177i
$404$	−4.84085	−	14.8986i	−0.240841	−	0.741233i
$405$	0.382487	+	0.526448i	0.0190059	+	0.0261594i
$406$	−0.729632			−0.0362110
$407$	20.9825	+	14.6012i	1.04007	+	0.723756i
$408$		−	13.5110i		−	0.668892i
$409$	−12.8538	−	17.6917i	−0.635578	−	0.874797i	0.362793	−	0.931870i	$-0.381823\pi$
$409$	−12.8538	−	17.6917i	−0.635578	−	0.874797i	−0.998370	+	0.0570726i	$0.981823\pi$
$410$	−6.33412	+	2.05808i	−0.312820	+	0.101641i
$411$	−0.321415	−	0.104434i	−0.0158542	−	0.00515136i
$412$	−36.1056	−	26.2322i	−1.77879	−	1.29237i
$413$	−0.174905	−	0.127076i	−0.00860652	−	0.00625300i
$414$	−19.9508	−	6.48242i	−0.980530	−	0.318594i
$415$	−1.27950	−	3.93790i	−0.0628082	−	0.193304i
$416$	−9.65178	−	10.4326i	−0.473217	−	0.511500i
$417$	1.18851			0.0582017
$418$	−17.7280	−	23.3838i	−0.867105	−	1.14374i
$419$	20.9191			1.02197			0.510983	−	0.859591i	$-0.329282\pi$
$419$	20.9191			1.02197			0.510983	+	0.859591i	$0.329282\pi$
$420$	−0.0870004	+	0.0632095i	−0.00424519	+	0.00308431i
$421$	−21.9005	+	7.11589i	−1.06736	+	0.346807i	−0.789460	−	0.613802i	$-0.789639\pi$
$421$	−21.9005	+	7.11589i	−1.06736	+	0.346807i	−0.277903	+	0.960609i	$0.589639\pi$
$422$	−1.07272	−	0.348547i	−0.0522191	−	0.0169670i
$423$	−0.970254	+	1.33544i	−0.0471754	+	0.0649313i
$424$	−5.37411	+	7.39683i	−0.260990	+	0.359222i
$425$	−5.33415	+	16.4168i	−0.258744	+	0.796333i
$426$	7.10517	+	21.8675i	0.344247	+	1.05948i
$427$	−0.194029	−	0.267058i	−0.00938974	−	0.0129239i
$428$	16.1746			0.781831
$429$	8.29797	+	8.61067i	0.400630	+	0.415727i
$430$	−5.79234			−0.279331
$431$	0.524787	+	0.722308i	0.0252781	+	0.0347923i	0.821469	−	0.570253i	$-0.193155\pi$
$431$	0.524787	+	0.722308i	0.0252781	+	0.0347923i	−0.796191	+	0.605046i	$0.793155\pi$
$432$	0.423677	+	1.30394i	0.0203842	+	0.0627361i
$433$	6.73444	−	20.7265i	0.323636	−	0.996050i	−0.648416	−	0.761286i	$-0.724568\pi$
$433$	6.73444	−	20.7265i	0.323636	−	0.996050i	0.972052	−	0.234764i	$-0.0754318\pi$
$434$	−0.378288	+	0.520669i	−0.0181584	+	0.0249929i
$435$	−2.53204	+	3.48506i	−0.121402	+	0.167096i
$436$	43.5585	+	14.1530i	2.08608	+	0.677807i
$437$	31.9541	−	10.3825i	1.52857	−	0.496664i
$438$	10.0189	−	7.27913i	0.478720	−	0.347810i
$439$	−10.0751			−0.480858			−0.240429	−	0.970667i	$-0.577288\pi$
$439$	−10.0751			−0.480858			−0.240429	+	0.970667i	$0.577288\pi$
$440$	−4.41586	+	6.34576i	−0.210518	+	0.302522i
$441$	6.99780			0.333229
$442$	−21.7061	−	23.4621i	−1.03246	−	1.11598i
$443$	−8.97744	−	27.6297i	−0.426531	−	1.31273i	−0.901520	−	0.432737i	$-0.857548\pi$
$443$	−8.97744	−	27.6297i	−0.426531	−	1.31273i	0.474989	−	0.879992i	$-0.342452\pi$
$444$	25.8326	+	8.39351i	1.22596	+	0.398339i
$445$	7.97220	+	5.79215i	0.377919	+	0.274574i
$446$	−28.6487	−	20.8145i	−1.35656	−	0.985596i
$447$	−10.9870	−	3.56990i	−0.519669	−	0.168851i
$448$	0.535490	−	0.173991i	0.0252995	−	0.00822031i
$449$	9.31013	+	12.8143i	0.439372	+	0.604744i	0.970072	−	0.242816i	$-0.0780710\pi$
$449$	9.31013	+	12.8143i	0.439372	+	0.604744i	−0.530700	+	0.847560i	$0.678071\pi$
$450$		−	10.7565i		−	0.507064i
$451$	−14.4397	+	0.294117i	−0.679939	+	0.0138495i
$452$	49.3474			2.32110
$453$	7.51755	+	10.3470i	0.353205	+	0.486145i
$454$	−8.80695	−	27.1050i	−0.413331	−	1.27210i
$455$	−0.0214201	+	0.107919i	−0.00100419	+	0.00505932i
$456$	−10.9093	−	7.92606i	−0.510874	−	0.371172i
$457$	9.10588	−	12.5332i	0.425955	−	0.586277i	−0.541064	−	0.840982i	$-0.681978\pi$
$457$	9.10588	−	12.5332i	0.425955	−	0.586277i	0.967019	+	0.254705i	$0.0819782\pi$
$458$	18.0624	−	55.5904i	0.844001	−	2.59757i
$459$	−1.16554	−	3.58716i	−0.0544027	−	0.167434i
$460$	−12.0306	−	16.5587i	−0.560930	−	0.772054i
$461$			34.6674i			1.61462i	0.590127	+	0.807310i	$0.299078\pi$
$461$			34.6674i			1.61462i	−0.590127	+	0.807310i	$0.700922\pi$
$462$	−0.345285	+	0.120017i	−0.0160641	+	0.00558371i
$463$		−	5.60212i		−	0.260352i	−0.991491	−	0.130176i	$-0.958446\pi$
$463$		−	5.60212i		−	0.260352i	0.991491	−	0.130176i	$-0.0415543\pi$
$464$	−7.34286	+	5.33490i	−0.340884	+	0.247667i
$465$	1.17418	+	3.61375i	0.0544513	+	0.167584i
$466$	38.8885	+	12.6356i	1.80147	+	0.585334i
$467$	−24.9197	−	18.1052i	−1.15315	−	0.837809i	−0.164249	−	0.986419i	$-0.552520\pi$
$467$	−24.9197	−	18.1052i	−1.15315	−	0.837809i	−0.988896	+	0.148610i	$0.952520\pi$
$468$	11.0888	+	6.20399i	0.512578	+	0.286780i
$469$	0.193892	−	0.596739i	0.00895312	−	0.0275549i
$470$	−2.40105	+	0.780148i	−0.110752	+	0.0359856i
$471$	−0.209192	+	0.151987i	−0.00963908	+	0.00700320i
$472$	−16.5146			−0.760147
$473$	−12.0227	−	3.63746i	−0.552806	−	0.167251i
$474$		−	1.27127i		−	0.0583913i
$475$	10.1264	+	13.9378i	0.464630	+	0.639508i
$476$	0.592812	−	0.192616i	0.0271715	−	0.00882855i
$477$	−0.788730	+	2.42746i	−0.0361135	+	0.111146i
$478$	40.9435	+	29.7472i	1.87271	+	1.36061i
$479$	1.22109	−	1.68069i	0.0557932	−	0.0767927i	−0.780209	−	0.625519i	$-0.784887\pi$
$479$	1.22109	−	1.68069i	0.0557932	−	0.0767927i	0.836002	+	0.548727i	$0.184887\pi$
$480$	0.792646	−	2.43951i	0.0361792	−	0.111348i
$481$	25.2323	−	11.6449i	1.15050	−	0.530961i
$482$	−50.4839	+	36.6787i	−2.29948	+	1.67067i
$483$		−	0.418546i		−	0.0190445i
$484$	−30.4077	+	24.0437i	−1.38217	+	1.09289i
$485$	1.85971			0.0844453
$486$	1.38149	+	1.90146i	0.0626659	+	0.0862522i
$487$	32.9181	−	10.6958i	1.49166	−	0.484671i	0.554089	−	0.832457i	$-0.313067\pi$
$487$	32.9181	−	10.6958i	1.49166	−	0.484671i	0.937574	+	0.347787i	$0.113067\pi$
$488$	−23.9816	−	7.79210i	−1.08560	−	0.352732i
$489$	−3.57021	+	4.91397i	−0.161450	+	0.222217i
$490$	8.65859	+	6.29083i	0.391155	+	0.284191i
$491$	−4.58994	+	14.1264i	−0.207141	+	0.637515i	0.792478	+	0.609901i	$0.208791\pi$
$491$	−4.58994	+	14.1264i	−0.207141	+	0.637515i	−0.999619	+	0.0276136i	$0.991209\pi$
$492$	−14.5951	+	4.74222i	−0.657996	+	0.213796i
$493$	20.2002	−	14.6763i	0.909773	−	0.660989i
$494$	−31.6779	+	3.76259i	−1.42526	+	0.169287i
$495$	−0.624986	+	2.06574i	−0.0280910	+	0.0928479i
$496$			8.00585i			0.359473i
$497$	−0.371140	+	0.269649i	−0.0166479	+	0.0120954i
$498$	−4.62140	−	14.2232i	−0.207090	−	0.637357i
$499$	21.8198	+	7.08969i	0.976789	+	0.317378i	0.753553	−	0.657387i	$-0.228338\pi$
$499$	21.8198	+	7.08969i	0.976789	+	0.317378i	0.223235	+	0.974765i	$0.428338\pi$
$500$	12.9084	−	17.7669i	0.577282	−	0.794561i
$501$	−15.0776	+	20.7526i	−0.673619	+	0.927157i
$502$	−2.65458	−	0.862526i	−0.118480	−	0.0384964i
$503$	3.54031	+	10.8960i	0.157855	+	0.485827i	0.998439	−	0.0558540i	$-0.0177881\pi$
$503$	3.54031	+	10.8960i	0.157855	+	0.485827i	−0.840584	+	0.541681i	$0.817788\pi$
$504$	−0.135900	+	0.0987369i	−0.00605345	+	0.00439809i
$505$		−	2.89261i		−	0.128719i
$506$	−22.8428	−	65.7179i	−1.01549	−	2.92152i
$507$	12.6383	−	3.04522i	0.561287	−	0.135243i
$508$	40.2073	−	29.2123i	1.78391	−	1.29609i
$509$	−30.2552	+	9.83050i	−1.34104	+	0.435729i	−0.889668	−	0.456608i	$-0.849064\pi$
$509$	−30.2552	+	9.83050i	−1.34104	+	0.435729i	−0.451369	+	0.892338i	$0.649064\pi$
$510$	1.78260	−	5.48629i	0.0789350	−	0.242937i
$511$	0.199897	+	0.145234i	0.00884293	+	0.00642477i
$512$	8.95022	−	12.3189i	0.395548	−	0.544425i
$513$	−3.58016	−	1.16327i	−0.158068	−	0.0513594i
$514$	−7.66819	+	2.49155i	−0.338229	+	0.109897i
$515$	−4.84379	−	6.66691i	−0.213443	−	0.293779i
$516$	−13.3467			−0.587555
$517$	−5.47360	+	0.111490i	−0.240729	+	0.00490332i
$518$			0.849500i			0.0373249i
$519$	1.88039	−	1.36618i	0.0825397	−	0.0599686i
$520$	3.52177	+	7.63103i	0.154440	+	0.334643i
$521$	−12.1298	+	37.3318i	−0.531418	+	1.63554i	0.219845	+	0.975535i	$0.429445\pi$
$521$	−12.1298	+	37.3318i	−0.531418	+	1.63554i	−0.751263	+	0.660003i	$0.770555\pi$
$522$	−9.14543	+	12.5876i	−0.400285	+	0.550944i
$523$	12.4917	+	9.07577i	0.546225	+	0.396856i	0.826392	−	0.563096i	$-0.190390\pi$
$523$	12.4917	+	9.07577i	0.546225	+	0.396856i	−0.280167	+	0.959951i	$0.590390\pi$
$524$	12.0320	−	37.0307i	0.525621	−	1.61769i
$525$	0.204110	−	0.0663193i	0.00890808	−	0.00289441i
$526$	36.9159	+	50.8103i	1.60961	+	2.21544i
$527$		−	22.0241i		−	0.959386i
$528$	−2.59734	+	3.73247i	−0.113035	+	0.162435i
$529$	56.6615			2.46354
$530$	−3.15814	+	2.29452i	−0.137181	+	0.0996677i
$531$	−4.38463	+	1.42465i	−0.190277	+	0.0618246i
$532$	0.192241	−	0.591656i	0.00833468	−	0.0256515i
$533$	−7.66613	+	13.7021i	−0.332057	+	0.593504i
$534$	28.7946	+	20.9205i	1.24607	+	0.905319i
$535$	2.84048	+	0.922926i	0.122804	+	0.0399016i
$536$	−14.8110	−	45.5835i	−0.639737	−	1.96891i
$537$	15.3307	−	11.1384i	0.661569	−	0.480658i
$538$			1.96182i			0.0845800i
$539$	14.0215	+	18.4948i	0.603949	+	0.796629i
$540$			2.29322i			0.0986843i
$541$	−13.5752	−	18.6847i	−0.583645	−	0.803319i	0.410444	−	0.911886i	$-0.365374\pi$
$541$	−13.5752	−	18.6847i	−0.583645	−	0.803319i	−0.994089	+	0.108567i	$0.965374\pi$
$542$	18.9848	+	58.4292i	0.815467	+	2.50975i
$543$	2.34585	−	7.21980i	0.100670	−	0.309831i
$544$	−8.73901	+	12.0282i	−0.374682	+	0.515706i
$545$	6.84187	+	4.97091i	0.293073	+	0.212930i
$546$	−0.0773668	+	0.389790i	−0.00331099	+	0.0166815i
$547$	−0.634506	−	1.95281i	−0.0271295	−	0.0834961i	0.936575	−	0.350467i	$-0.113977\pi$
$547$	−0.634506	−	1.95281i	−0.0271295	−	0.0834961i	−0.963705	+	0.266971i	$0.913977\pi$
$548$	−0.700045	−	0.963530i	−0.0299045	−	0.0411600i
$549$	−7.03931			−0.300430
$550$	28.4288	−	21.5527i	1.21221	−	0.919011i
$551$		−	24.9202i		−	1.06164i
$552$	−18.7925	−	25.8657i	−0.799863	−	1.10092i
$553$	0.0241230	−	0.00783805i	0.00102582	−	0.000333308i
$554$	8.44664	+	2.74448i	0.358864	+	0.116602i
$555$	4.05760	+	2.94802i	0.172236	+	0.125136i
$556$	3.38851	+	2.46190i	0.143705	+	0.104408i
$557$	−18.6800	−	6.06951i	−0.791498	−	0.257173i	−0.114756	−	0.993394i	$-0.536609\pi$
$557$	−18.6800	−	6.06951i	−0.791498	−	0.257173i	−0.676742	+	0.736220i	$0.736609\pi$
$558$	4.24099	+	13.0524i	0.179536	+	0.552554i
$559$	−10.0235	+	9.27329i	−0.423948	+	0.392218i
$560$	−0.0418378			−0.00176797
$561$	7.14529	−	10.2681i	0.301674	−	0.433517i
$562$	−35.8466			−1.51210
$563$	−30.2556	+	21.9820i	−1.27512	+	0.926431i	−0.999394	−	0.0348047i	$-0.988919\pi$
$563$	−30.2556	+	21.9820i	−1.27512	+	0.926431i	−0.275729	+	0.961236i	$0.588919\pi$
$564$	−5.53249	+	1.79761i	−0.232960	+	0.0756932i
$565$	8.66603	+	2.81577i	0.364583	+	0.118460i
$566$	−18.8807	+	25.9870i	−0.793614	+	1.09232i
$567$	−0.0275637	+	0.0379382i	−0.00115757	+	0.00159325i
$568$	−10.8289	+	33.3281i	−0.454372	+	1.39841i
$569$	−6.30734	−	19.4120i	−0.264417	−	0.813793i	−0.991827	−	0.127589i	$-0.959276\pi$
$569$	−6.30734	−	19.4120i	−0.264417	−	0.813793i	0.727410	−	0.686203i	$-0.240724\pi$
$570$	−3.38410	−	4.65781i	−0.141744	−	0.195094i
$571$	−16.8352			−0.704533			−0.352267	−	0.935900i	$-0.614589\pi$
$571$	−16.8352			−0.704533			−0.352267	+	0.935900i	$0.614589\pi$
$572$	5.82171	+	41.7380i	0.243418	+	1.74515i
$573$	7.14650			0.298549
$574$	−0.282111	−	0.388293i	−0.0117751	−	0.0162070i
$575$	12.6225	+	38.8481i	0.526395	+	1.62008i
$576$	3.71030	−	11.4191i	0.154596	−	0.475796i
$577$	−11.8882	+	16.3627i	−0.494911	+	0.681187i	−0.981284	−	0.192564i	$-0.938320\pi$
$577$	−11.8882	+	16.3627i	−0.494911	+	0.681187i	0.486373	+	0.873751i	$0.338320\pi$
$578$	3.83201	−	5.27431i	0.159391	−	0.219383i
$579$	5.56953	+	1.80965i	0.231462	+	0.0752065i
$580$	−14.4380	+	4.69118i	−0.599504	+	0.194791i
$581$	0.241400	−	0.175387i	0.0100150	−	0.00727629i
$582$	6.71706			0.278431
$583$	−7.99604	+	2.77933i	−0.331162	+	0.115108i
$584$	18.8744			0.781027
$585$	1.59333	+	1.72223i	0.0658760	+	0.0712053i
$586$	−1.21839	−	3.74983i	−0.0503314	−	0.154904i
$587$	40.8580	+	13.2756i	1.68639	+	0.547942i	0.986134	−	0.165950i	$-0.0530689\pi$
$587$	40.8580	+	13.2756i	1.68639	+	0.547942i	0.700257	+	0.713891i	$0.253069\pi$
$588$	19.9511	+	14.4953i	0.822769	+	0.597777i
$589$	−17.7831	−	12.9202i	−0.732742	−	0.532368i
$590$	−6.70595	−	2.17890i	−0.276080	−	0.0897037i
$591$	9.96687	−	3.23843i	0.409982	−	0.133211i
$592$	6.21134	+	8.54918i	0.255285	+	0.351369i
$593$			16.1293i			0.662353i	0.943569	+	0.331176i	$0.107445\pi$
$593$			16.1293i			0.662353i	−0.943569	+	0.331176i	$0.892555\pi$
$594$	−2.25737	+	7.46119i	−0.0926211	+	0.306136i
$595$	0.115096			0.00471848
$596$	−23.9299	−	32.9366i	−0.980206	−	1.34914i
$597$	−3.55313	−	10.9354i	−0.145420	−	0.447556i
$598$	−74.1884	−	14.7252i	−3.03379	−	0.602157i
$599$	−35.1593	−	25.5447i	−1.43657	−	1.04373i	−0.988746	−	0.149605i	$-0.952200\pi$
$599$	−35.1593	−	25.5447i	−1.43657	−	1.04373i	−0.447822	−	0.894123i	$-0.647800\pi$
$600$	9.63606	−	13.2629i	0.393391	−	0.541456i
$601$	−9.92915	+	30.5588i	−0.405019	+	1.24652i	0.515861	+	0.856672i	$0.327472\pi$
$601$	−9.92915	+	30.5588i	−0.405019	+	1.24652i	−0.920880	+	0.389847i	$0.872528\pi$
$602$	−0.128990	−	0.396992i	−0.00525726	−	0.0161802i
$603$	−7.86463	−	10.8247i	−0.320273	−	0.440817i
$604$			45.0718i			1.83395i
$605$	−6.71192	+	2.48731i	−0.272878	+	0.101124i
$606$		−	10.4477i		−	0.424410i
$607$	12.7028	−	9.22912i	0.515591	−	0.374599i	−0.299350	−	0.954143i	$-0.596770\pi$
$607$	12.7028	−	9.22912i	0.515591	−	0.374599i	0.814940	+	0.579545i	$0.196770\pi$
$608$	4.58541	+	14.1124i	0.185963	+	0.572335i
$609$	−0.295243	−	0.0959303i	−0.0119639	−	0.00388729i
$610$	−8.70995	−	6.32815i	−0.352656	−	0.256219i
$611$	−2.90597	+	5.19400i	−0.117563	+	0.210127i
$612$	4.10747	−	12.6415i	0.166034	−	0.511002i
$613$	−0.0914997	+	0.0297301i	−0.00369564	+	0.00120079i	−0.310864	−	0.950454i	$-0.600618\pi$
$613$	−0.0914997	+	0.0297301i	−0.00369564	+	0.00120079i	0.307169	+	0.951655i	$0.400618\pi$
$614$	−59.5198	+	43.2437i	−2.40202	+	1.74517i
$615$	−2.83367			−0.114265
$616$	−0.533259	−	0.161337i	−0.0214856	−	0.00650045i
$617$		−	38.4857i		−	1.54938i	−0.632344	−	0.774688i	$-0.717907\pi$
$617$		−	38.4857i		−	1.54938i	0.632344	−	0.774688i	$-0.282093\pi$
$618$	−17.4952	−	24.0800i	−0.703759	−	0.968642i
$619$	−23.9440	+	7.77987i	−0.962389	+	0.312699i	−0.747740	−	0.663992i	$-0.768861\pi$
$619$	−23.9440	+	7.77987i	−0.962389	+	0.312699i	−0.214649	+	0.976691i	$0.568861\pi$
$620$	−4.13792	+	12.7352i	−0.166183	+	0.511458i
$621$	−7.22074	−	5.24618i	−0.289758	−	0.210522i
$622$	2.95465	−	4.06672i	0.118471	−	0.163061i
$623$	−0.219444	+	0.675380i	−0.00879185	+	0.0270585i
$624$	2.07145	+	4.48845i	0.0829243	+	0.179682i
$625$	−15.2319	+	11.0666i	−0.609276	+	0.442665i
$626$		−	53.9144i		−	2.15485i
$627$	−4.09912	−	11.7930i	−0.163703	−	0.470968i
$628$	−0.911246			−0.0363627
$629$	−17.0874	−	23.5188i	−0.681321	−	0.937757i
$630$	−0.0682108	+	0.0221630i	−0.00271758	+	0.000882996i
$631$	30.1855	+	9.80788i	1.20167	+	0.390445i	0.840374	−	0.542007i	$-0.182335\pi$
$631$	30.1855	+	9.80788i	1.20167	+	0.390445i	0.361293	+	0.932452i	$0.382335\pi$
$632$	1.13885	−	1.56750i	0.0453012	−	0.0623517i
$633$	−0.388245	−	0.282077i	−0.0154314	−	0.0112115i
$634$	2.92500	−	9.00222i	0.116167	−	0.357524i
$635$	8.72777	−	2.83583i	0.346351	−	0.112536i
$636$	−7.27698	+	5.28703i	−0.288551	+	0.209644i
$637$	25.0548	−	2.97592i	0.992708	−	0.117910i
$638$	−51.5931	+	1.05088i	−2.04259	+	0.0416048i
$639$			9.78276i			0.387000i
$640$	10.7060	−	7.77836i	0.423191	−	0.307467i
$641$	11.6220	+	35.7688i	0.459041	+	1.41278i	0.866324	+	0.499482i	$0.166476\pi$
$641$	11.6220	+	35.7688i	0.459041	+	1.41278i	−0.407283	+	0.913302i	$0.633524\pi$
$642$	10.2594	+	3.33350i	0.404908	+	0.131563i
$643$	−20.8397	+	28.6834i	−0.821838	+	1.13116i	0.167549	+	0.985864i	$0.446415\pi$
$643$	−20.8397	+	28.6834i	−0.821838	+	1.13116i	−0.989388	+	0.145300i	$0.953585\pi$
$644$	0.866980	−	1.19330i	0.0341638	−	0.0470224i
$645$	−2.34385	−	0.761563i	−0.0922890	−	0.0299865i
$646$	10.3123	+	31.7378i	0.405730	+	1.24871i
$647$	−30.8794	+	22.4352i	−1.21399	+	0.882018i	−0.995587	−	0.0938401i	$-0.970086\pi$
$647$	−30.8794	+	22.4352i	−1.21399	+	0.882018i	−0.218406	+	0.975858i	$0.570086\pi$
$648$			3.58214i			0.140720i
$649$	−12.5508	−	8.73377i	−0.492660	−	0.342830i
$650$	−4.57434	−	38.5123i	−0.179421	−	1.51058i
$651$	−0.221529	+	0.160950i	−0.00868241	+	0.00630814i
$652$	−20.3577	+	6.61462i	−0.797269	+	0.259048i
$653$	−6.50216	+	20.0116i	−0.254449	+	0.783114i	0.739489	+	0.673169i	$0.235067\pi$
$653$	−6.50216	+	20.0116i	−0.254449	+	0.783114i	−0.993938	+	0.109945i	$0.964933\pi$
$654$	24.7120	+	17.9543i	0.966315	+	0.702069i
$655$	4.22595	−	5.81653i	0.165122	−	0.227270i
$656$	−5.67821	−	1.84496i	−0.221697	−	0.0720336i
$657$	5.01114	−	1.62822i	0.195503	−	0.0635228i
$658$	−0.106939	−	0.147188i	−0.00416890	−	0.00573800i
$659$	5.91986			0.230605			0.115302	−	0.993330i	$-0.463216\pi$
$659$	5.91986			0.230605			0.115302	+	0.993330i	$0.463216\pi$
$660$	−6.06085	+	4.59492i	−0.235918	+	0.178857i
$661$			14.8019i			0.575725i	0.957672	+	0.287863i	$0.0929447\pi$
$661$			14.8019i			0.575725i	−0.957672	+	0.287863i	$0.907055\pi$
$662$	19.5587	−	14.2102i	0.760171	−	0.552297i
$663$	−5.69857	−	12.3477i	−0.221314	−	0.479547i
$664$	7.04344	−	21.6775i	0.273339	−	0.841250i
$665$	0.0675198	−	0.0929331i	0.00261831	−	0.00360379i
$666$	14.6556	+	10.6479i	0.567891	+	0.412597i
$667$	18.2583	−	56.1934i	0.706966	−	2.17582i
$668$	−85.9743	+	27.9347i	−3.32644	+	1.08083i
$669$	−8.85596	−	12.1892i	−0.342391	−	0.471261i
$670$		−	20.4639i		−	0.790588i
$671$	−14.1047	−	18.6045i	−0.544505	−	0.718220i
$672$	0.184849			0.00713072
$673$	−32.6342	+	23.7101i	−1.25796	+	0.913958i	−0.998655	−	0.0518387i	$-0.983492\pi$
$673$	−32.6342	+	23.7101i	−1.25796	+	0.913958i	−0.259300	+	0.965797i	$0.583492\pi$
$674$	−47.2617	+	15.3563i	−1.82045	+	0.591501i
$675$	1.41423	−	4.35256i	0.0544339	−	0.167530i
$676$	42.3403	+	17.4970i	1.62847	+	0.672962i
$677$	−26.9485	−	19.5793i	−1.03572	−	0.752492i	−0.0662718	−	0.997802i	$-0.521110\pi$
$677$	−26.9485	−	19.5793i	−1.03572	−	0.752492i	−0.969445	+	0.245309i	$0.921110\pi$
$678$	31.3007	+	10.1702i	1.20209	+	0.390584i
$679$	0.0414142	+	0.127460i	0.00158933	+	0.00489146i
$680$	7.11281	−	5.16776i	0.272764	−	0.198175i
$681$		−	12.1259i		−	0.464664i
$682$	−25.9992	+	37.3619i	−0.995562	+	1.43066i
$683$			22.7581i			0.870815i	0.900233	+	0.435407i	$0.143396\pi$
$683$			22.7581i			0.870815i	−0.900233	+	0.435407i	$0.856604\pi$
$684$	−7.79763	−	10.7325i	−0.298150	−	0.410368i
$685$	−0.0679579	−	0.209153i	−0.00259654	−	0.00799132i
$686$	−0.476751	+	1.46729i	−0.0182024	+	0.0560213i
$687$	14.6178	−	20.1197i	0.557703	−	0.767613i
$688$	−4.20084	−	3.05209i	−0.160156	−	0.116360i
$689$	−1.79164	+	9.02666i	−0.0682561	+	0.343888i
$690$	−4.21827	−	12.9825i	−0.160587	−	0.494236i
$691$	−1.26711	−	1.74403i	−0.0482032	−	0.0663461i	0.784235	−	0.620464i	$-0.213056\pi$
$691$	−1.26711	−	1.74403i	−0.0482032	−	0.0663461i	−0.832438	+	0.554118i	$0.813056\pi$
$692$	8.19099			0.311375
$693$	−0.155498	+	0.00316729i	−0.00590688	+	0.000120315i
$694$			80.8470i			3.06891i
$695$	0.454590	+	0.625689i	0.0172436	+	0.0237337i
$696$	−22.5529	+	7.32790i	−0.854867	+	0.277763i
$697$	15.6208	+	5.07550i	0.591679	+	0.192248i
$698$	−15.1204	−	10.9856i	−0.572315	−	0.415811i
$699$	14.0748	+	10.2259i	0.532357	+	0.386780i
$700$	0.719302	+	0.233715i	0.0271871	+	0.00883361i
$701$	−9.36151	−	28.8118i	−0.353579	−	1.08821i	−0.956829	−	0.290653i	$-0.906128\pi$
$701$	−9.36151	−	28.8118i	−0.353579	−	1.08821i	0.603249	−	0.797553i	$-0.293872\pi$
$702$	5.75491	+	6.22047i	0.217205	+	0.234777i
$703$	−29.0142			−1.09429
$704$	37.6145	−	13.0744i	1.41765	−	0.492759i
$705$	−1.07415			−0.0404548
$706$	−50.1585	+	36.4423i	−1.88774	+	1.37152i
$707$	0.198252	−	0.0644159i	0.00745602	−	0.00242261i
$708$	−15.4518	−	5.02060i	−0.580715	−	0.188686i
$709$	0.319573	−	0.439855i	0.0120018	−	0.0165191i	−0.802974	−	0.596014i	$-0.796750\pi$
$709$	0.319573	−	0.439855i	0.0120018	−	0.0165191i	0.814976	+	0.579495i	$0.196750\pi$
$710$	−8.79444	+	12.1045i	−0.330049	+	0.454274i
$711$	0.167143	−	0.514415i	0.00626837	−	0.0192921i
$712$	16.7628	+	51.5907i	0.628214	+	1.93344i
$713$	−30.6336	−	42.1635i	−1.14724	−	1.57904i
$714$	0.415713			0.0155577
$715$	−1.35920	+	7.66191i	−0.0508314	+	0.286539i
$716$	66.7809			2.49572
$717$	12.6566	+	17.4203i	0.472668	+	0.650572i
$718$	1.05523	+	3.24768i	0.0393810	+	0.121202i
$719$	5.92616	−	18.2388i	0.221008	−	0.680194i	−0.777664	−	0.628680i	$-0.783595\pi$
$719$	5.92616	−	18.2388i	0.221008	−	0.680194i	0.998672	−	0.0515136i	$-0.0164046\pi$
$720$	−0.524408	+	0.721785i	−0.0195435	+	0.0268993i
$721$	0.349065	−	0.480447i	0.0129999	−	0.0178928i
$722$	−10.7948	−	3.50746i	−0.401743	−	0.130534i
$723$	−25.2506	+	8.20440i	−0.939078	+	0.305125i
$724$	21.6433	−	15.7248i	0.804367	−	0.584407i
$725$	30.2966			1.12519
$726$	−24.2426	+	8.98386i	−0.899729	+	0.333422i
$727$	23.1378			0.858133			0.429067	−	0.903273i	$-0.358843\pi$
$727$	23.1378			0.858133			0.429067	+	0.903273i	$0.358843\pi$
$728$	−0.444584	+	0.411309i	−0.0164774	+	0.0152441i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	7.66416	+	2.49024i	0.283663	+	0.0921678i
$731$	11.5565	+	8.39632i	0.427434	+	0.310549i
$732$	−20.0694	−	14.5813i	−0.741788	−	0.538940i
$733$	−8.23060	−	2.67428i	−0.304004	−	0.0987769i	0.153043	−	0.988220i	$-0.451093\pi$
$733$	−8.23060	−	2.67428i	−0.304004	−	0.0987769i	−0.457047	+	0.889443i	$0.651093\pi$
$734$	63.6203	−	20.6715i	2.34827	−	0.762999i
$735$	2.67656	+	3.68398i	0.0987266	+	0.135885i
$736$			35.1823i			1.29684i
$737$	12.8509	−	42.4754i	0.473368	−	1.56460i
$738$	−10.2349			−0.376751
$739$	−12.1472	−	16.7192i	−0.446843	−	0.615027i	0.524872	−	0.851181i	$-0.324113\pi$
$739$	−12.1472	−	16.7192i	−0.446843	−	0.615027i	−0.971716	+	0.236154i	$0.924113\pi$
$740$	5.46187	+	16.8099i	0.200782	+	0.617944i
$741$	−13.3131	−	2.64242i	−0.489067	−	0.0970717i
$742$	−0.227590	−	0.165354i	−0.00835508	−	0.00607032i
$743$	10.8161	−	14.8871i	0.396806	−	0.546156i	−0.563133	−	0.826366i	$-0.690404\pi$
$743$	10.8161	−	14.8871i	0.396806	−	0.546156i	0.959939	+	0.280210i	$0.0904041\pi$
$744$	−6.46367	+	19.8931i	−0.236970	+	0.729317i
$745$	−2.32303	−	7.14954i	−0.0851091	−	0.261939i
$746$	28.2440	+	38.8745i	1.03409	+	1.42330i
$747$		−	6.36298i		−	0.232809i
$748$	41.6409	−	14.4739i	1.52254	−	0.529219i
$749$			0.215232i			0.00786439i
$750$	11.8494	−	8.60907i	0.432678	−	0.314359i
$751$	−1.70350	−	5.24285i	−0.0621618	−	0.191314i	0.915153	−	0.403107i	$-0.132070\pi$
$751$	−1.70350	−	5.24285i	−0.0621618	−	0.191314i	−0.977315	+	0.211793i	$0.932070\pi$
$752$	−2.15241	−	0.699362i	−0.0784905	−	0.0255031i
$753$	−0.960765	−	0.698037i	−0.0350122	−	0.0254379i
$754$	−27.3911	+	48.9577i	−0.997524	+	1.78293i
$755$	−2.57180	+	7.91519i	−0.0935974	+	0.288063i
$756$	−0.157171	+	0.0510680i	−0.00571626	+	0.00185732i
$757$	30.7370	−	22.3317i	1.11715	−	0.811660i	0.133379	−	0.991065i	$-0.457417\pi$
$757$	30.7370	−	22.3317i	1.11715	−	0.811660i	0.983775	+	0.179405i	$0.0574171\pi$
$758$	−82.7449			−3.00543
$759$	−0.602827	−	29.5958i	−0.0218812	−	1.07426i
$760$		−	8.77478i		−	0.318295i
$761$	15.4035	+	21.2011i	0.558376	+	0.768538i	0.991119	−	0.132979i	$-0.0424543\pi$
$761$	15.4035	+	21.2011i	0.558376	+	0.768538i	−0.432743	+	0.901517i	$0.642454\pi$
$762$	31.5236	−	10.2427i	1.14198	−	0.371052i
$763$	−0.188330	+	0.579622i	−0.00681802	+	0.0209837i
$764$	20.3750	+	14.8033i	0.737143	+	0.535566i
$765$	1.44265	−	1.98563i	0.0521590	−	0.0717908i
$766$	11.8783	−	36.5577i	0.429182	−	1.32089i
$767$	−15.0928	+	6.96543i	−0.544969	+	0.251507i
$768$	19.2414	−	13.9797i	0.694313	−	0.504448i
$769$		−	15.0264i		−	0.541866i	−0.962598	−	0.270933i	$-0.912668\pi$
$769$		−	15.0264i		−	0.541866i	0.962598	−	0.270933i	$-0.0873322\pi$
$770$	−0.195250	−	0.135870i	−0.00703631	−	0.00489640i
$771$	−3.43049			−0.123546
$772$	12.1305	+	16.6962i	0.436586	+	0.600909i
$773$	19.8299	−	6.44313i	0.713232	−	0.231743i	0.0701458	−	0.997537i	$-0.477654\pi$
$773$	19.8299	−	6.44313i	0.713232	−	0.231743i	0.643087	+	0.765794i	$0.277654\pi$
$774$	−8.46570	−	2.75067i	−0.304293	−	0.0988709i
$775$	15.7077	−	21.6198i	0.564237	−	0.776605i
$776$	8.28225	+	6.01741i	0.297316	+	0.216012i
$777$	−0.111690	+	0.343747i	−0.00400686	+	0.0123319i
$778$	16.0388	−	5.21134i	0.575020	−	0.186835i
$779$	13.2619	−	9.63534i	0.475157	−	0.345222i
$780$	0.975224	+	8.21059i	0.0349186	+	0.293986i
$781$	−25.8554	+	19.6017i	−0.925177	+	0.701405i
$782$			79.1223i			2.82941i
$783$	−5.35565	+	3.89111i	−0.191395	+	0.139057i
$784$	2.96481	+	9.12474i	0.105886	+	0.325884i
$785$	−0.160027	−	0.0519958i	−0.00571160	−	0.00185581i
$786$	15.2636	−	21.0086i	0.544435	−	0.749351i
$787$	9.35411	−	12.8748i	0.333438	−	0.458938i	−0.609073	−	0.793115i	$-0.708458\pi$
$787$	9.35411	−	12.8748i	0.333438	−	0.458938i	0.942510	+	0.334177i	$0.108458\pi$
$788$	35.1242	+	11.4125i	1.25125	+	0.406555i
$789$	8.25745	+	25.4138i	0.293973	+	0.904756i
$790$	0.669257	−	0.486243i	0.0238111	−	0.0172998i
$791$			0.656652i			0.0233479i
$792$	−9.46741	+	7.17753i	−0.336410	+	0.255042i
$793$	−25.2034	+	2.99357i	−0.895000	+	0.106305i
$794$	54.1966	−	39.3761i	1.92336	−	1.39741i
$795$	−1.57961	+	0.513246i	−0.0560230	+	0.0182030i
$796$	12.5216	−	38.5374i	0.443815	−	1.36592i
$797$	−1.72434	−	1.25281i	−0.0610793	−	0.0443767i	0.556827	−	0.830629i	$-0.312019\pi$
$797$	−1.72434	−	1.25281i	−0.0610793	−	0.0443767i	−0.617906	+	0.786252i	$0.712019\pi$
$798$	0.243873	−	0.335663i	0.00863302	−	0.0118823i
$799$	5.92130	+	1.92395i	0.209481	+	0.0680644i
$800$	−17.1571	+	5.57469i	−0.606596	+	0.197095i
$801$	8.90106	+	12.2513i	0.314504	+	0.432877i
$802$	−47.2749			−1.66933
$803$	14.3441	+	9.98173i	0.506193	+	0.352248i
$804$		−	47.1528i		−	1.66295i
$805$	0.220342	−	0.160088i	0.00776605	−	0.00564237i
$806$	20.7351	+	44.9292i	0.730364	+	1.58256i
$807$	−0.257935	+	0.793843i	−0.00907975	+	0.0279446i
$808$	9.35950	−	12.8822i	0.329266	−	0.453196i
$809$	−25.4935	−	18.5221i	−0.896302	−	0.651202i	0.0412113	−	0.999150i	$-0.486878\pi$
$809$	−25.4935	−	18.5221i	−0.896302	−	0.651202i	−0.937514	+	0.347949i	$0.886878\pi$
$810$	−0.472618	+	1.45457i	−0.0166061	+	0.0511083i
$811$	−22.4184	+	7.28419i	−0.787218	+	0.255783i	−0.674919	−	0.737892i	$-0.735821\pi$
$811$	−22.4184	+	7.28419i	−0.787218	+	0.255783i	−0.112299	+	0.993674i	$0.535821\pi$
$812$	−0.643043	−	0.885072i	−0.0225664	−	0.0310599i
$813$			26.1392i			0.916743i
$814$	1.22353	+	60.0691i	0.0428846	+	2.10542i
$815$	−3.95250			−0.138450
$816$	4.18364	−	3.03959i	0.146457	−	0.106407i
$817$	13.5590	−	4.40560i	0.474371	−	0.154132i
$818$	15.8827	−	48.8819i	0.555326	−	1.70912i
$819$	−0.0825548	+	0.147555i	−0.00288470	+	0.00515599i
$820$	−8.07895	−	5.86970i	−0.282129	−	0.204979i
$821$	27.5707	+	8.95825i	0.962223	+	0.312645i	0.747673	−	0.664068i	$-0.231171\pi$
$821$	27.5707	+	8.95825i	0.962223	+	0.312645i	0.214551	+	0.976713i	$0.431171\pi$
$822$	−0.245456	−	0.755435i	−0.00856125	−	0.0263488i
$823$	7.14222	−	5.18913i	0.248962	−	0.180882i	−0.456305	−	0.889824i	$-0.650827\pi$
$823$	7.14222	−	5.18913i	0.248962	−	0.180882i	0.705267	+	0.708942i	$0.250827\pi$
$824$		−	45.3640i		−	1.58033i
$825$	14.3373	−	4.98349i	0.499161	−	0.173503i
$826$		−	0.508131i		−	0.0176801i
$827$	2.45367	+	3.37719i	0.0853225	+	0.117436i	0.849545	−	0.527517i	$-0.176877\pi$
$827$	2.45367	+	3.37719i	0.0853225	+	0.117436i	−0.764222	+	0.644953i	$0.776877\pi$
$828$	−9.71973	−	29.9142i	−0.337784	−	1.03959i
$829$	0.611595	−	1.88230i	0.0212416	−	0.0653749i	−0.939874	−	0.341522i	$-0.889058\pi$
$829$	0.611595	−	1.88230i	0.0212416	−	0.0653749i	0.961115	+	0.276147i	$0.0890577\pi$
$830$	5.72015	−	7.87311i	0.198549	−	0.273280i
$831$	3.05707	+	2.22109i	0.106048	+	0.0770487i
$832$	8.42813	−	42.4627i	0.292193	−	1.47213i
$833$	−8.15621	−	25.1022i	−0.282596	−	0.869740i
$834$	1.64192	+	2.25991i	0.0568551	+	0.0782544i
$835$	−16.6921			−0.577656
$836$	12.7414	−	42.1135i	0.440670	−	1.45653i
$837$			5.83922i			0.201833i
$838$	28.8996	+	39.7769i	0.998321	+	1.37407i
$839$	26.1845	−	8.50786i	0.903989	−	0.293724i	0.180107	−	0.983647i	$-0.442356\pi$
$839$	26.1845	−	8.50786i	0.903989	−	0.293724i	0.723883	+	0.689923i	$0.242356\pi$
$840$	−0.103960	−	0.0337785i	−0.00358695	−	0.00116547i
$841$	−11.9927	−	8.71319i	−0.413541	−	0.300455i
$842$	−43.7860	−	31.8124i	−1.50896	−	1.09633i
$843$	−14.5052	−	4.71302i	−0.499586	−	0.162325i
$844$	−0.522611	−	1.60843i	−0.0179890	−	0.0553645i
$845$	6.43713	+	5.48865i	0.221444	+	0.188815i
$846$	−3.87969			−0.133387
$847$	−0.319943	−	0.404627i	−0.0109934	−	0.0139032i
$848$	−3.49944			−0.120171
$849$	−11.0567	+	8.03317i	−0.379465	+	0.275698i
$850$	−38.5851	+	12.5371i	−1.32346	+	0.430018i
$851$	−65.4251	−	21.2579i	−2.24274	−	0.728712i
$852$	−20.2641	+	27.8912i	−0.694237	+	0.955535i
$853$	22.8140	−	31.4008i	0.781137	−	1.07514i	−0.214019	−	0.976829i	$-0.568655\pi$
$853$	22.8140	−	31.4008i	0.781137	−	1.07514i	0.995156	−	0.0983127i	$-0.0313445\pi$
$854$	0.239752	−	0.737880i	0.00820413	−	0.0252497i
$855$	−0.756966	−	2.32970i	−0.0258877	−	0.0796741i
$856$	9.66380	+	13.3011i	0.330302	+	0.454622i
$857$	3.96699			0.135510			0.0677548	−	0.997702i	$-0.478416\pi$
$857$	3.96699			0.135510			0.0677548	+	0.997702i	$0.478416\pi$
$858$	−4.90928	+	27.6739i	−0.167600	+	0.944771i
$859$	17.4336			0.594828			0.297414	−	0.954749i	$-0.403876\pi$
$859$	17.4336			0.594828			0.297414	+	0.954749i	$0.403876\pi$
$860$	−5.10493	−	7.02633i	−0.174077	−	0.239596i
$861$	−0.0631035	−	0.194213i	−0.00215056	−	0.00661874i
$862$	−0.648451	+	1.99573i	−0.0220863	+	0.0679748i
$863$	15.7022	−	21.6122i	0.534508	−	0.735688i	−0.453301	−	0.891358i	$-0.649754\pi$
$863$	15.7022	−	21.6122i	0.534508	−	0.735688i	0.987809	+	0.155670i	$0.0497536\pi$
$864$	2.31696	−	3.18902i	0.0788245	−	0.108493i
$865$	1.43844	+	0.467379i	0.0489086	+	0.0158914i
$866$	48.7142	−	15.8282i	1.65538	−	0.537864i
$867$	2.24407	−	1.63041i	0.0762125	−	0.0553716i
$868$	−0.964986			−0.0327537
$869$	1.69448	−	0.588981i	0.0574812	−	0.0199798i
$870$	−10.1247			−0.343260
$871$	−32.7618	−	35.4122i	−1.11009	−	1.19990i
$872$	14.3861	+	44.2760i	0.487176	+	1.49937i
$873$	2.71803	+	0.883143i	0.0919915	+	0.0298899i
$874$	63.8865	+	46.4162i	2.16099	+	1.57005i
$875$	0.236420	+	0.171769i	0.00799244	+	0.00580685i
$876$	17.6597	+	5.73799i	0.596667	+	0.193869i
$877$	7.86694	−	2.55612i	0.265648	−	0.0863141i	−0.173165	−	0.984893i	$-0.555399\pi$
$877$	7.86694	−	2.55612i	0.265648	−	0.0863141i	0.438812	+	0.898579i	$0.355399\pi$
$878$	−13.9187	−	19.1574i	−0.469733	−	0.646532i
$879$		−	1.67755i		−	0.0565823i
$880$	−2.95840	+	0.0602586i	−0.0997276	+	0.00203132i
$881$	−9.10210			−0.306658			−0.153329	−	0.988175i	$-0.548999\pi$
$881$	−9.10210			−0.306658			−0.153329	+	0.988175i	$0.548999\pi$
$882$	9.66742	+	13.3061i	0.325519	+	0.448039i
$883$	−11.4293	−	35.1757i	−0.384626	−	1.18376i	−0.936751	−	0.349996i	$-0.886183\pi$
$883$	−11.4293	−	35.1757i	−0.384626	−	1.18376i	0.552125	−	0.833761i	$-0.313817\pi$
$884$	9.33033	−	47.0081i	0.313813	−	1.58105i
$885$	−2.42706	−	1.76337i	−0.0815849	−	0.0592749i
$886$	40.1347	−	55.2406i	1.34835	−	1.85584i
$887$	8.44325	−	25.9857i	0.283497	−	0.872513i	−0.703349	−	0.710845i	$-0.748313\pi$
$887$	8.44325	−	25.9857i	0.283497	−	0.872513i	0.986845	−	0.161668i	$-0.0516873\pi$
$888$	8.53176	+	26.2581i	0.286307	+	0.881163i
$889$	0.388720	+	0.535027i	0.0130373	+	0.0179442i
$890$			23.1607i			0.776348i
$891$	−1.89442	+	2.72235i	−0.0634654	+	0.0912021i
$892$		−	53.0963i		−	1.77780i
$893$	5.02714	−	3.65243i	0.168227	−	0.122224i
$894$	−8.39049	−	25.8233i	−0.280620	−	0.863659i
$895$	11.7276	+	3.81052i	0.392010	+	0.127372i
$896$	0.771522	+	0.560543i	0.0257747	+	0.0187264i
$897$	−28.0840	−	15.7126i	−0.937699	−	0.524628i
$898$	−11.5040	+	35.4058i	−0.383894	+	1.18151i
$899$	−36.7634	+	11.9452i	−1.22613	+	0.398393i
$900$	13.0480	−	9.47993i	0.434933	−	0.315998i
$901$	9.62698			0.320721
$902$	−20.5076	−	27.0503i	−0.682829	−	0.900675i
$903$		−	0.177601i		−	0.00591018i
$904$	29.4834	+	40.5804i	0.980603	+	1.34968i
$905$	4.69810	−	1.52651i	0.156170	−	0.0507428i
$906$	−9.28903	+	28.5887i	−0.308607	+	0.949796i
$907$	−35.3094	−	25.6538i	−1.17243	−	0.851821i	−0.181133	−	0.983459i	$-0.557976\pi$
$907$	−35.3094	−	25.6538i	−1.17243	−	0.851821i	−0.991298	+	0.131638i	$0.957976\pi$
$908$	25.1176	−	34.5715i	0.833558	−	1.14729i
$909$	1.37364	−	4.22764i	0.0455609	−	0.140222i
$910$	−0.234796	+	0.108360i	−0.00778340	+	0.00359209i
$911$	7.64929	−	5.55754i	0.253432	−	0.184129i	−0.453814	−	0.891096i	$-0.649937\pi$
$911$	7.64929	−	5.55754i	0.253432	−	0.184129i	0.707247	+	0.706967i	$0.249937\pi$
$912$		−	5.16118i		−	0.170904i
$913$	16.8170	−	12.7495i	0.556563	−	0.421947i
$914$	36.4111			1.20437
$915$	−2.69244	−	3.70583i	−0.0890093	−	0.122511i
$916$	83.3521	−	27.0827i	2.75403	−	0.894839i
$917$	0.492758	+	0.160107i	0.0162723	+	0.00528719i
$918$	5.21067	−	7.17187i	0.171978	−	0.236707i
$919$	13.6480	+	9.91582i	0.450205	+	0.327093i	0.789677	−	0.613523i	$-0.210248\pi$
$919$	13.6480	+	9.91582i	0.450205	+	0.327093i	−0.339472	+	0.940616i	$0.610248\pi$
$920$	6.42904	−	19.7866i	0.211959	−	0.652343i
$921$	−29.7701	+	9.67288i	−0.980957	+	0.318732i
$922$	−65.9188	+	47.8928i	−2.17092	+	1.57726i
$923$	4.16026	+	35.0260i	0.136937	+	1.15290i
$924$	−0.449894	−	0.313070i	−0.0148004	−	0.0102993i
$925$		−	35.2739i		−	1.15980i
$926$	10.6522	−	7.73929i	0.350054	−	0.254329i
$927$	−3.91338	−	12.0441i	−0.128532	−	0.395581i
$928$	24.8177	+	8.06374i	0.814679	+	0.264705i
$929$	−1.84510	+	2.53956i	−0.0605357	+	0.0833203i	−0.838212	−	0.545345i	$-0.816399\pi$
$929$	−1.84510	+	2.53956i	−0.0605357	+	0.0833203i	0.777676	+	0.628666i	$0.216399\pi$
$930$	−5.24930	+	7.22504i	−0.172131	+	0.236918i
$931$	−25.0533	−	8.14030i	−0.821088	−	0.266788i
$932$	18.9458	+	58.3093i	0.620592	+	1.90998i
$933$	1.73027	−	1.25712i	0.0566465	−	0.0411561i
$934$		−	72.3961i		−	2.36887i
$935$	8.13857	−	0.165772i	0.266160	−	0.00542131i
$936$	1.52336	+	12.8254i	0.0497925	+	0.419212i
$937$	41.4549	−	30.1187i	1.35427	−	0.983936i	0.355486	−	0.934682i	$-0.384315\pi$
$937$	41.4549	−	30.1187i	1.35427	−	0.983936i	0.998786	−	0.0492544i	$-0.0156845\pi$
$938$	1.40254	−	0.455713i	0.0457946	−	0.0148796i
$939$	7.08853	−	21.8163i	0.231326	−	0.711947i
$940$	−3.06245	−	2.22500i	−0.0998862	−	0.0725716i
$941$	8.27354	−	11.3875i	0.269710	−	0.371224i	−0.652582	−	0.757718i	$-0.726314\pi$
$941$	8.27354	−	11.3875i	0.269710	−	0.371224i	0.922292	+	0.386495i	$0.126314\pi$
$942$	−0.577997	−	0.187802i	−0.0188321	−	0.00611894i
$943$	36.9643	−	12.0104i	1.20372	−	0.391114i
$944$	−3.71533	−	5.11372i	−0.120924	−	0.166437i
$945$	−0.0305152			−0.000992660
$946$	−9.69284	−	27.8859i	−0.315141	−	0.906650i
$947$			5.72315i			0.185977i	0.995667	+	0.0929887i	$0.0296420\pi$
$947$			5.72315i			0.185977i	−0.995667	+	0.0929887i	$0.970358\pi$
$948$	1.54210	−	1.12040i	0.0500850	−	0.0363889i
$949$	17.2494	−	7.96071i	0.559939	−	0.258416i
$950$	−12.5126	+	38.5099i	−0.405963	+	1.24943i
$951$	2.36718	−	3.25815i	0.0767611	−	0.105653i
$952$	0.512581	+	0.372412i	0.0166129	+	0.0120699i
$953$	−10.0270	+	30.8601i	−0.324808	+	0.999656i	0.646719	+	0.762728i	$0.276141\pi$
$953$	−10.0270	+	30.8601i	−0.324808	+	0.999656i	−0.971527	+	0.236928i	$0.923859\pi$
$954$	−5.70536	+	1.85378i	−0.184718	+	0.0600184i
$955$	2.73344	+	3.76226i	0.0884520	+	0.121744i
$956$			75.8830i			2.45423i
$957$	−21.0151	−	6.35810i	−0.679323	−	0.205528i
$958$	4.88271			0.157753
$959$	0.0128214	−	0.00931531i	0.000414026	−	0.000300807i
$960$	7.43070	−	2.41438i	0.239825	−	0.0779238i
$961$	−0.956858	+	2.94491i	−0.0308664	+	0.0949970i
$962$	57.0007	+	31.8910i	1.83778	+	1.02821i
$963$	3.71317	+	2.69778i	0.119655	+	0.0869346i
$964$	−88.9853	−	28.9131i	−2.86602	−	0.931228i
$965$	1.17759	+	3.62423i	0.0379078	+	0.116668i
$966$	0.795850	−	0.578219i	0.0256061	−	0.0186039i
$967$		−	2.65178i		−	0.0852754i	−0.999091	−	0.0426377i	$-0.986424\pi$
$967$		−	2.65178i		−	0.0852754i	0.999091	−	0.0426377i	$-0.0135761\pi$
$968$	−37.9397	−	10.6403i	−1.21943	−	0.341991i
$969$			14.1984i			0.456120i
$970$	2.56918	+	3.53618i	0.0824915	+	0.113540i
$971$	−6.30193	−	19.3953i	−0.202238	−	0.622426i	−0.999815	−	0.0192088i	$-0.993885\pi$
$971$	−6.30193	−	19.3953i	−0.202238	−	0.622426i	0.797577	−	0.603217i	$-0.206115\pi$
$972$	−1.08900	+	3.35161i	−0.0349298	+	0.107503i
$973$	−0.0327598	+	0.0450900i	−0.00105023	+	0.00144552i
$974$	65.8138	+	47.8165i	2.10881	+	1.53214i
$975$	3.21251	−	16.1853i	0.102883	−	0.518344i
$976$	−2.98239	−	9.17887i	−0.0954641	−	0.293808i
$977$	10.2373	+	14.0904i	0.327520	+	0.450792i	0.940745	−	0.339116i	$-0.110128\pi$
$977$	10.2373	+	14.0904i	0.327520	+	0.450792i	−0.613225	+	0.789909i	$0.710128\pi$
$978$	−14.2760			−0.456495
$979$	−14.5444	+	48.0729i	−0.464841	+	1.53642i
$980$			16.0475i			0.512618i
$981$	7.63903	+	10.5142i	0.243895	+	0.335693i
$982$	−33.2018	+	10.7879i	−1.05951	+	0.344256i
$983$	−58.7521	−	19.0897i	−1.87390	−	0.608868i	−0.989975	−	0.141243i	$-0.954890\pi$
$983$	−58.7521	−	19.0897i	−1.87390	−	0.608868i	−0.883927	−	0.467625i	$-0.845110\pi$
$984$	−12.6198	−	9.16881i	−0.402304	−	0.292291i
$985$	5.51706	+	4.00838i	0.175788	+	0.127717i
$986$	55.8131	+	18.1348i	1.77745	+	0.577529i
$987$	−0.0239204	−	0.0736193i	−0.000761394	−	0.00234333i
$988$	−32.4827	−	35.1105i	−1.03341	−	1.11701i
$989$	33.8026			1.07486
$990$	−4.79134	+	1.66542i	−0.152279	+	0.0529304i
$991$	−17.4208			−0.553391			−0.276695	−	0.960958i	$-0.589239\pi$
$991$	−17.4208			−0.553391			−0.276695	+	0.960958i	$0.589239\pi$
$992$	18.6214	−	13.5292i	0.591229	−	0.429553i
$993$	9.78270	−	3.17859i	0.310445	−	0.100870i
$994$	−1.02546	−	0.333191i	−0.0325255	−	0.0105682i
$995$	4.39789	−	6.05318i	0.139423	−	0.191899i
$996$	13.1803	−	18.1412i	0.417635	−	0.574825i
$997$	−18.1117	+	55.7422i	−0.573604	+	1.76537i	0.0672795	+	0.997734i	$0.478568\pi$
$997$	−18.1117	+	55.7422i	−0.573604	+	1.76537i	−0.640884	+	0.767638i	$0.721432\pi$
$998$	16.6632	+	51.2839i	0.527463	+	1.62336i
$999$	4.53036	+	6.23551i	0.143334	+	0.197283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.a.25.13	yes	56
11.4	even	5	inner	429.2.bb.a.103.2	yes	56
13.12	even	2	inner	429.2.bb.a.25.2	✓	56
143.103	even	10	inner	429.2.bb.a.103.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.a.25.2	✓	56	13.12	even	2	inner
429.2.bb.a.25.13	yes	56	1.1	even	1	trivial
429.2.bb.a.103.2	yes	56	11.4	even	5	inner
429.2.bb.a.103.13	yes	56	143.103	even	10	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38149 + 1.90146i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.08900 + 3.35161i) q^{4} +(-0.382487 + 0.526448i) q^{5} +(-1.38149 + 1.90146i) q^{6} +(-0.0445990 - 0.0144911i) q^{7} +(-3.40681 + 1.10694i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.38149 + 1.90146i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.08900 + 3.35161i) q^{4} +(-0.382487 + 0.526448i) q^{5} +(-1.38149 + 1.90146i) q^{6} +(-0.0445990 - 0.0144911i) q^{7} +(-3.40681 + 1.10694i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.52942 q^{10} +(-3.17451 - 0.960445i) q^{11} -3.52409 q^{12} +(-2.64663 + 2.44854i) q^{13} +(-0.0340590 - 0.104823i) q^{14} +(-0.618876 - 0.201085i) q^{15} +(-1.10920 - 0.805882i) q^{16} +(3.05142 + 2.21699i) q^{17} +(-2.23531 - 0.726295i) q^{18} +(3.58016 - 1.16327i) q^{19} +(-1.34792 - 1.85525i) q^{20} -0.0468942i q^{21} +(-2.55932 - 7.36308i) q^{22} +8.92533 q^{23} +(-2.10553 - 2.89801i) q^{24} +(1.41423 + 4.35256i) q^{25} +(-8.31212 - 1.64982i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.0971370 - 0.133698i) q^{28} +(2.04568 - 6.29595i) q^{29} +(-0.472618 - 1.45457i) q^{30} +(-3.43221 - 4.72403i) q^{31} +3.94184i q^{32} +(-0.0675412 - 3.31594i) q^{33} +8.86492i q^{34} +(0.0246873 - 0.0179364i) q^{35} +(-1.08900 - 3.35161i) q^{36} +(-7.33028 - 2.38175i) q^{37} +(7.15788 + 5.20051i) q^{38} +(-3.14656 - 1.76045i) q^{39} +(0.720314 - 2.21690i) q^{40} +(4.14151 - 1.34566i) q^{41} +(0.0891676 - 0.0647840i) q^{42} +3.78727 q^{43} +(6.67610 - 9.59381i) q^{44} -0.650725i q^{45} +(12.3303 + 16.9712i) q^{46} +(1.56990 - 0.510093i) q^{47} +(0.423677 - 1.30394i) q^{48} +(-5.66134 - 4.11320i) q^{49} +(-6.32249 + 8.70216i) q^{50} +(-1.16554 + 3.58716i) q^{51} +(-5.32438 - 11.5369i) q^{52} +(2.06492 - 1.50025i) q^{53} -2.35034i q^{54} +(1.71983 - 1.30386i) q^{55} +0.167981 q^{56} +(2.21266 + 3.04547i) q^{57} +(14.7976 - 4.80804i) q^{58} +(4.38463 + 1.42465i) q^{59} +(1.34792 - 1.85525i) q^{60} +(5.69492 + 4.13760i) q^{61} +(4.24099 - 13.0524i) q^{62} +(0.0445990 - 0.0144911i) q^{63} +(-9.71368 + 7.05740i) q^{64} +(-0.276730 - 2.32985i) q^{65} +(6.21183 - 4.70938i) q^{66} +13.3801i q^{67} +(-10.7535 + 7.81286i) q^{68} +(2.75808 + 8.48849i) q^{69} +(0.0682108 + 0.0221630i) q^{70} +(5.75016 - 7.91442i) q^{71} +(2.10553 - 2.89801i) q^{72} +(-5.01114 - 1.62822i) q^{73} +(-5.59792 - 17.2286i) q^{74} +(-3.70251 + 2.69003i) q^{75} +13.2661i q^{76} +(0.127662 + 0.0888371i) q^{77} +(-0.999516 - 8.41512i) q^{78} +(-0.437587 + 0.317926i) q^{79} +(0.848509 - 0.275697i) q^{80} +(0.309017 - 0.951057i) q^{81} +(8.28019 + 6.01591i) q^{82} +(-3.74007 + 5.14776i) q^{83} +(0.157171 + 0.0510680i) q^{84} +(-2.33425 + 0.758445i) q^{85} +(5.23209 + 7.20135i) q^{86} +6.61995 q^{87} +(11.8781 - 0.241942i) q^{88} -15.1434i q^{89} +(1.23733 - 0.898973i) q^{90} +(0.153519 - 0.0708501i) q^{91} +(-9.71973 + 29.9142i) q^{92} +(3.43221 - 4.72403i) q^{93} +(3.13874 + 2.28043i) q^{94} +(-0.756966 + 2.32970i) q^{95} +(-3.74892 + 1.21810i) q^{96} +(-1.67984 - 2.31210i) q^{97} -16.4472i q^{98} +(3.13277 - 1.08892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9	\( 56 q - 14 q^{3} + 8 q^{4} - 14 q^{9} + 40 q^{10} - 52 q^{12} + 5 q^{13} - 6 q^{14} + 16 q^{16} - 14 q^{17} - 36 q^{22} + 28 q^{23} + 36 q^{25} + 6 q^{26} - 14 q^{27} + 34 q^{29} - 10 q^{30} + 18 q^{35} + 8 q^{36} - 18 q^{38} + 5 q^{39} + 40 q^{40} - 6 q^{42} + 48 q^{43} - 14 q^{48} - 14 q^{49} - 4 q^{51} + 11 q^{52} + 10 q^{53} + 8 q^{55} - 68 q^{56} + 10 q^{61} - 132 q^{62} - 52 q^{64} - 42 q^{65} + 14 q^{66} + 50 q^{68} - 2 q^{69} + 10 q^{74} + 6 q^{75} - 88 q^{77} + 26 q^{78} + 48 q^{79} - 14 q^{81} - 30 q^{82} - 36 q^{87} - 10 q^{88} - 10 q^{90} - 11 q^{91} - 126 q^{92} - 34 q^{94} + 36 q^{95}+O(q^{100}) \) 56 * q - 14 * q^3 + 8 * q^4 - 14 * q^9 + 40 * q^10 - 52 * q^12 + 5 * q^13 - 6 * q^14 + 16 * q^16 - 14 * q^17 - 36 * q^22 + 28 * q^23 + 36 * q^25 + 6 * q^26 - 14 * q^27 + 34 * q^29 - 10 * q^30 + 18 * q^35 + 8 * q^36 - 18 * q^38 + 5 * q^39 + 40 * q^40 - 6 * q^42 + 48 * q^43 - 14 * q^48 - 14 * q^49 - 4 * q^51 + 11 * q^52 + 10 * q^53 + 8 * q^55 - 68 * q^56 + 10 * q^61 - 132 * q^62 - 52 * q^64 - 42 * q^65 + 14 * q^66 + 50 * q^68 - 2 * q^69 + 10 * q^74 + 6 * q^75 - 88 * q^77 + 26 * q^78 + 48 * q^79 - 14 * q^81 - 30 * q^82 - 36 * q^87 - 10 * q^88 - 10 * q^90 - 11 * q^91 - 126 * q^92 - 34 * q^94 + 36 * q^95

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