LMFDB - Embedded newform 429.2.s.b.166.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.8
Character	$\chi$	$=$	429.166
Dual form			429.2.s.b.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.252478 - 0.145768i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.957503 + 1.65844i) q^{4} -3.62473i q^{5} +(-0.252478 - 0.145768i) q^{6} +(-1.17162 - 0.676437i) q^{7} +1.14137i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.252478 - 0.145768i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.957503 + 1.65844i) q^{4} -3.62473i q^{5} +(-0.252478 - 0.145768i) q^{6} +(-1.17162 - 0.676437i) q^{7} +1.14137i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.528371 - 0.915165i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.91501 q^{12} +(-3.46899 + 0.982920i) q^{13} -0.394413 q^{14} +(-3.13911 + 1.81236i) q^{15} +(-1.74863 - 3.02872i) q^{16} +(-1.50194 + 2.60144i) q^{17} +0.291537i q^{18} +(-6.17022 - 3.56238i) q^{19} +(6.01141 + 3.47069i) q^{20} +1.35287i q^{21} +(0.145768 - 0.252478i) q^{22} +(-0.523583 - 0.906872i) q^{23} +(0.988454 - 0.570684i) q^{24} -8.13867 q^{25} +(-0.732565 + 0.753834i) q^{26} +1.00000 q^{27} +(2.24367 - 1.29538i) q^{28} +(-4.27011 - 7.39605i) q^{29} +(-0.528371 + 0.915165i) q^{30} +6.40036i q^{31} +(-2.85989 - 1.65116i) q^{32} +(-0.866025 - 0.500000i) q^{33} +0.875744i q^{34} +(-2.45190 + 4.24682i) q^{35} +(-0.957503 - 1.65844i) q^{36} +(8.46254 - 4.88585i) q^{37} -2.07713 q^{38} +(2.58573 + 2.51277i) q^{39} +4.13715 q^{40} +(2.16437 - 1.24960i) q^{41} +(0.197206 + 0.341571i) q^{42} +(4.67537 - 8.09798i) q^{43} +1.91501i q^{44} +(3.13911 + 1.81236i) q^{45} +(-0.264387 - 0.152644i) q^{46} +6.55910i q^{47} +(-1.74863 + 3.02872i) q^{48} +(-2.58487 - 4.47712i) q^{49} +(-2.05484 + 1.18636i) q^{50} +3.00389 q^{51} +(1.69145 - 6.69427i) q^{52} -1.69147 q^{53} +(0.252478 - 0.145768i) q^{54} +(-1.81236 - 3.13911i) q^{55} +(0.772064 - 1.33725i) q^{56} +7.12475i q^{57} +(-2.15622 - 1.24489i) q^{58} +(1.63499 + 0.943963i) q^{59} -6.94138i q^{60} +(-3.04389 + 5.27217i) q^{61} +(0.932970 + 1.61595i) q^{62} +(1.17162 - 0.676437i) q^{63} +6.03178 q^{64} +(3.56282 + 12.5741i) q^{65} -0.291537 q^{66} +(-7.65297 + 4.41845i) q^{67} +(-2.87623 - 4.98178i) q^{68} +(-0.523583 + 0.906872i) q^{69} +1.42964i q^{70} +(12.0360 + 6.94898i) q^{71} +(-0.988454 - 0.570684i) q^{72} -4.82119i q^{73} +(1.42440 - 2.46714i) q^{74} +(4.06933 + 7.04829i) q^{75} +(11.8160 - 6.82197i) q^{76} -1.35287 q^{77} +(1.01912 + 0.257503i) q^{78} +7.17375 q^{79} +(-10.9783 + 6.33831i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.364304 - 0.630994i) q^{82} -2.66970i q^{83} +(-2.24367 - 1.29538i) q^{84} +(9.42953 + 5.44414i) q^{85} -2.72609i q^{86} +(-4.27011 + 7.39605i) q^{87} +(0.570684 + 0.988454i) q^{88} +(13.5772 - 7.83880i) q^{89} +1.05674 q^{90} +(4.72923 + 1.19494i) q^{91} +2.00533 q^{92} +(5.54287 - 3.20018i) q^{93} +(0.956110 + 1.65603i) q^{94} +(-12.9127 + 22.3654i) q^{95} +3.30232i q^{96} +(3.66560 + 2.11634i) q^{97} +(-1.30524 - 0.753583i) q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	$ 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) $ 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.252478	−	0.145768i	0.178529	−	0.103074i	−0.408072	−	0.912950i	$-0.633799\pi$
$2$	0.252478	−	0.145768i	0.178529	−	0.103074i	0.586601	+	0.809876i	$0.300466\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.957503	+	1.65844i	−0.478752	+	0.829222i
$5$		−	3.62473i		−	1.62103i	−0.585719	−	0.810514i	$-0.699188\pi$
$5$		−	3.62473i		−	1.62103i	0.585719	−	0.810514i	$-0.300812\pi$
$6$	−0.252478	−	0.145768i	−0.103074	−	0.0595097i
$7$	−1.17162	−	0.676437i	−0.442832	−	0.255669i	0.261966	−	0.965077i	$-0.415629\pi$
$7$	−1.17162	−	0.676437i	−0.442832	−	0.255669i	−0.704798	+	0.709408i	$0.748962\pi$
$8$			1.14137i			0.403535i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.528371	−	0.915165i	−0.167086	−	0.289401i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	1.91501			0.552815
$13$	−3.46899	+	0.982920i	−0.962124	+	0.272613i
$13$	−3.46899	+	0.982920i	−0.962124	+	0.272613i
$14$	−0.394413			−0.105411
$15$	−3.13911	+	1.81236i	−0.810514	+	0.467951i
$16$	−1.74863	−	3.02872i	−0.437158	−	0.757179i
$17$	−1.50194	+	2.60144i	−0.364275	+	0.630943i	−0.988660	−	0.150174i	$-0.952017\pi$
$17$	−1.50194	+	2.60144i	−0.364275	+	0.630943i	0.624385	+	0.781117i	$0.285350\pi$
$18$			0.291537i			0.0687159i
$19$	−6.17022	−	3.56238i	−1.41555	−	0.817265i	−0.419642	−	0.907690i	$-0.637844\pi$
$19$	−6.17022	−	3.56238i	−1.41555	−	0.817265i	−0.995903	+	0.0904245i	$0.971178\pi$
$20$	6.01141	+	3.47069i	1.34419	+	0.776070i
$21$			1.35287i			0.295221i
$22$	0.145768	−	0.252478i	0.0310779	−	0.0538285i
$23$	−0.523583	−	0.906872i	−0.109175	−	0.189096i	0.806262	−	0.591559i	$-0.201487\pi$
$23$	−0.523583	−	0.906872i	−0.109175	−	0.189096i	−0.915436	+	0.402463i	$0.868154\pi$
$24$	0.988454	−	0.570684i	0.201767	−	0.116490i
$25$	−8.13867			−1.62773
$26$	−0.732565	+	0.753834i	−0.143668	+	0.147839i
$27$	1.00000			0.192450
$28$	2.24367	−	1.29538i	0.424013	−	0.244804i
$29$	−4.27011	−	7.39605i	−0.792940	−	1.37341i	−0.924139	−	0.382057i	$-0.875216\pi$
$29$	−4.27011	−	7.39605i	−0.792940	−	1.37341i	0.131199	−	0.991356i	$-0.458117\pi$
$30$	−0.528371	+	0.915165i	−0.0964669	+	0.167086i
$31$			6.40036i			1.14954i	0.818316	+	0.574769i	$0.194908\pi$
$31$			6.40036i			1.14954i	−0.818316	+	0.574769i	$0.805092\pi$
$32$	−2.85989	−	1.65116i	−0.505562	−	0.291886i
$33$	−0.866025	−	0.500000i	−0.150756	−	0.0870388i
$34$			0.875744i			0.150189i
$35$	−2.45190	+	4.24682i	−0.414447	+	0.717843i
$36$	−0.957503	−	1.65844i	−0.159584	−	0.276407i
$37$	8.46254	−	4.88585i	1.39123	−	0.803229i	0.397782	−	0.917480i	$-0.369780\pi$
$37$	8.46254	−	4.88585i	1.39123	−	0.803229i	0.993452	+	0.114251i	$0.0364469\pi$
$38$	−2.07713			−0.336955
$39$	2.58573	+	2.51277i	0.414048	+	0.402365i
$40$	4.13715			0.654141
$41$	2.16437	−	1.24960i	0.338018	−	0.195155i	−0.321377	−	0.946951i	$-0.604146\pi$
$41$	2.16437	−	1.24960i	0.338018	−	0.195155i	0.659395	+	0.751796i	$0.270812\pi$
$42$	0.197206	+	0.341571i	0.0304296	+	0.0527056i
$43$	4.67537	−	8.09798i	0.712988	−	1.23493i	−0.250743	−	0.968054i	$-0.580675\pi$
$43$	4.67537	−	8.09798i	0.712988	−	1.23493i	0.963731	−	0.266877i	$-0.0859918\pi$
$44$			1.91501i			0.288698i
$45$	3.13911	+	1.81236i	0.467951	+	0.270171i
$46$	−0.264387	−	0.152644i	−0.0389817	−	0.0225061i
$47$			6.55910i			0.956744i	0.878157	+	0.478372i	$0.158773\pi$
$47$			6.55910i			0.956744i	−0.878157	+	0.478372i	$0.841227\pi$
$48$	−1.74863	+	3.02872i	−0.252393	+	0.437158i
$49$	−2.58487	−	4.47712i	−0.369267	−	0.639588i
$50$	−2.05484	+	1.18636i	−0.290598	+	0.167777i
$51$	3.00389			0.420629
$52$	1.69145	−	6.69427i	0.234562	−	0.928328i
$53$	−1.69147			−0.232342			−0.116171	−	0.993229i	$-0.537062\pi$
$53$	−1.69147			−0.232342			−0.116171	+	0.993229i	$0.537062\pi$
$54$	0.252478	−	0.145768i	0.0343579	−	0.0198366i
$55$	−1.81236	−	3.13911i	−0.244379	−	0.423277i
$56$	0.772064	−	1.33725i	0.103171	−	0.178698i
$57$			7.12475i			0.943697i
$58$	−2.15622	−	1.24489i	−0.283126	−	0.163463i
$59$	1.63499	+	0.943963i	0.212858	+	0.122894i	0.602639	−	0.798014i	$-0.294116\pi$
$59$	1.63499	+	0.943963i	0.212858	+	0.122894i	−0.389781	+	0.920908i	$0.627449\pi$
$60$		−	6.94138i		−	0.896128i
$61$	−3.04389	+	5.27217i	−0.389730	+	0.675032i	−0.992413	−	0.122949i	$-0.960765\pi$
$61$	−3.04389	+	5.27217i	−0.389730	+	0.675032i	0.602683	+	0.797981i	$0.294098\pi$
$62$	0.932970	+	1.61595i	0.118487	+	0.205226i
$63$	1.17162	−	0.676437i	0.147611	−	0.0852231i
$64$	6.03178			0.753972
$65$	3.56282	+	12.5741i	0.441913	+	1.55963i
$66$	−0.291537			−0.0358857
$67$	−7.65297	+	4.41845i	−0.934959	+	0.539799i	−0.888377	−	0.459115i	$-0.848166\pi$
$67$	−7.65297	+	4.41845i	−0.934959	+	0.539799i	−0.0465827	+	0.998914i	$0.514833\pi$
$68$	−2.87623	−	4.98178i	−0.348794	−	0.604130i
$69$	−0.523583	+	0.906872i	−0.0630320	+	0.109175i
$70$			1.42964i			0.170875i
$71$	12.0360	+	6.94898i	1.42841	+	0.824693i	0.996995	−	0.0774613i	$-0.0246814\pi$
$71$	12.0360	+	6.94898i	1.42841	+	0.824693i	0.431414	+	0.902154i	$0.358015\pi$
$72$	−0.988454	−	0.570684i	−0.116490	−	0.0672558i
$73$		−	4.82119i		−	0.564278i	−0.959374	−	0.282139i	$-0.908956\pi$
$73$		−	4.82119i		−	0.564278i	0.959374	−	0.282139i	$-0.0910439\pi$
$74$	1.42440	−	2.46714i	0.165584	−	0.286799i
$75$	4.06933	+	7.04829i	0.469886	+	0.813867i
$76$	11.8160	−	6.82197i	1.35539	−	0.782534i
$77$	−1.35287			−0.154174
$78$	1.01912	+	0.257503i	0.115393	+	0.0291564i
$79$	7.17375			0.807110			0.403555	−	0.914955i	$-0.367774\pi$
$79$	7.17375			0.807110			0.403555	+	0.914955i	$0.367774\pi$
$80$	−10.9783	+	6.33831i	−1.22741	+	0.708645i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.364304	−	0.630994i	0.0402307	−	0.0696816i
$83$		−	2.66970i		−	0.293038i	−0.989208	−	0.146519i	$-0.953193\pi$
$83$		−	2.66970i		−	0.293038i	0.989208	−	0.146519i	$-0.0468069\pi$
$84$	−2.24367	−	1.29538i	−0.244804	−	0.141338i
$85$	9.42953	+	5.44414i	1.02278	+	0.590500i
$86$		−	2.72609i		−	0.293961i
$87$	−4.27011	+	7.39605i	−0.457804	+	0.792940i
$88$	0.570684	+	0.988454i	0.0608351	+	0.105370i
$89$	13.5772	−	7.83880i	1.43918	−	0.830911i	0.441388	−	0.897317i	$-0.354486\pi$
$89$	13.5772	−	7.83880i	1.43918	−	0.830911i	0.997793	+	0.0664054i	$0.0211531\pi$
$90$	1.05674			0.111390
$91$	4.72923	+	1.19494i	0.495758	+	0.125264i
$92$	2.00533			0.209070
$93$	5.54287	−	3.20018i	0.574769	−	0.331843i
$94$	0.956110	+	1.65603i	0.0986152	+	0.170807i
$95$	−12.9127	+	22.3654i	−1.32481	+	2.29464i
$96$			3.30232i			0.337041i
$97$	3.66560	+	2.11634i	0.372186	+	0.214882i	0.674413	−	0.738354i	$-0.264397\pi$
$97$	3.66560	+	2.11634i	0.372186	+	0.214882i	−0.302227	+	0.953236i	$0.597730\pi$
$98$	−1.30524	−	0.753583i	−0.131850	−	0.0761234i
$99$			1.00000i			0.100504i
$100$	7.79280	−	13.4975i	0.779280	−	1.34975i
$101$	−6.29744	−	10.9075i	−0.626619	−	1.08534i	−0.988225	−	0.153005i	$-0.951105\pi$
$101$	−6.29744	−	10.9075i	−0.626619	−	1.08534i	0.361607	−	0.932331i	$-0.382228\pi$
$102$	0.758416	−	0.437872i	0.0750944	−	0.0433558i
$103$	−16.5972			−1.63537			−0.817685	−	0.575666i	$-0.804743\pi$
$103$	−16.5972			−1.63537			−0.817685	+	0.575666i	$0.804743\pi$
$104$	−1.12187	−	3.95939i	−0.110009	−	0.388250i
$105$	4.90380			0.478562
$106$	−0.427060	+	0.246563i	−0.0414797	+	0.0239483i
$107$	−0.00688781	−	0.0119300i	−0.000665870	−	0.00115332i	0.865692	−	0.500577i	$-0.166879\pi$
$107$	−0.00688781	−	0.0119300i	−0.000665870	−	0.00115332i	−0.866358	+	0.499423i	$0.833545\pi$
$108$	−0.957503	+	1.65844i	−0.0921358	+	0.159584i
$109$		−	17.0753i		−	1.63551i	−0.575564	−	0.817756i	$-0.695218\pi$
$109$		−	17.0753i		−	1.63551i	0.575564	−	0.817756i	$-0.304782\pi$
$110$	−0.915165	−	0.528371i	−0.0872576	−	0.0503782i
$111$	−8.46254	−	4.88585i	−0.803229	−	0.463744i
$112$			4.73136i			0.447071i
$113$	6.31431	−	10.9367i	0.594000	−	1.02884i	−0.399687	−	0.916652i	$-0.630881\pi$
$113$	6.31431	−	10.9367i	0.594000	−	1.02884i	0.993687	−	0.112187i	$-0.0357856\pi$
$114$	1.03856	+	1.79884i	0.0972704	+	0.168477i
$115$	−3.28717	+	1.89785i	−0.306530	+	0.176975i
$116$	16.3546			1.51849
$117$	0.883260	−	3.49569i	0.0816574	−	0.323177i
$118$	0.550400			0.0506684
$119$	3.51943	−	2.03194i	0.322625	−	0.186268i
$120$	−2.06858	−	3.58288i	−0.188834	−	0.327070i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$			1.77481i			0.160684i
$123$	−2.16437	−	1.24960i	−0.195155	−	0.112673i
$124$	−10.6146	−	6.12836i	−0.953223	−	0.550343i
$125$			11.3768i			1.01757i
$126$	0.197206	−	0.341571i	0.0175685	−	0.0304296i
$127$	0.0861245	+	0.149172i	0.00764231	+	0.0132369i	0.869821	−	0.493367i	$-0.164234\pi$
$127$	0.0861245	+	0.149172i	0.00764231	+	0.0132369i	−0.862179	+	0.506604i	$0.830901\pi$
$128$	7.24267	−	4.18156i	0.640168	−	0.369601i
$129$	−9.35075			−0.823287
$130$	2.73245	+	2.65535i	0.239651	+	0.232890i
$131$	6.69726			0.585142			0.292571	−	0.956244i	$-0.405489\pi$
$131$	6.69726			0.585142			0.292571	+	0.956244i	$0.405489\pi$
$132$	1.65844	−	0.957503i	0.144349	−	0.0833400i
$133$	4.81945	+	8.34753i	0.417899	+	0.723823i
$134$	−1.28814	+	2.23112i	−0.111278	+	0.192740i
$135$		−	3.62473i		−	0.311967i
$136$	−2.96921	−	1.71427i	−0.254607	−	0.146998i
$137$	13.9866	+	8.07518i	1.19496	+	0.689909i	0.959427	−	0.281958i	$-0.0909837\pi$
$137$	13.9866	+	8.07518i	1.19496	+	0.689909i	0.235531	+	0.971867i	$0.424317\pi$
$138$			0.305287i			0.0259878i
$139$	3.47396	−	6.01707i	0.294657	−	0.510361i	−0.680248	−	0.732982i	$-0.738128\pi$
$139$	3.47396	−	6.01707i	0.294657	−	0.510361i	0.974905	+	0.222621i	$0.0714613\pi$
$140$	−4.69541	−	8.13268i	−0.396834	−	0.687337i
$141$	5.68035	−	3.27955i	0.478372	−	0.276188i
$142$	4.05177			0.340017
$143$	−2.51277	+	2.58573i	−0.210128	+	0.216229i
$144$	3.49726			0.291439
$145$	−26.8087	+	15.4780i	−2.22634	+	1.28538i
$146$	−0.702777	−	1.21725i	−0.0581622	−	0.100740i
$147$	−2.58487	+	4.47712i	−0.213196	+	0.369267i
$148$			18.7129i			1.53819i
$149$	−10.9526	−	6.32349i	−0.897272	−	0.518040i	−0.0209581	−	0.999780i	$-0.506672\pi$
$149$	−10.9526	−	6.32349i	−0.897272	−	0.518040i	−0.876314	+	0.481740i	$0.840005\pi$
$150$	2.05484	+	1.18636i	0.167777	+	0.0968659i
$151$			0.705772i			0.0574349i	0.999588	+	0.0287175i	$0.00914231\pi$
$151$			0.705772i			0.0574349i	−0.999588	+	0.0287175i	$0.990858\pi$
$152$	4.06598	−	7.04249i	0.329795	−	0.571221i
$153$	−1.50194	−	2.60144i	−0.121425	−	0.210314i
$154$	−0.341571	+	0.197206i	−0.0275246	+	0.0158913i
$155$	23.1996			1.86343
$156$	−6.64313	+	1.88230i	−0.531876	+	0.150704i
$157$	−16.4554			−1.31328			−0.656642	−	0.754203i	$-0.728024\pi$
$157$	−16.4554			−1.31328			−0.656642	+	0.754203i	$0.728024\pi$
$158$	1.81121	−	1.04571i	0.144092	−	0.0831918i
$159$	0.845736	+	1.46486i	0.0670712	+	0.116171i
$160$	−5.98500	+	10.3663i	−0.473156	+	0.819530i
$161$			1.41668i			0.111650i
$162$	−0.252478	−	0.145768i	−0.0198366	−	0.0114526i
$163$	−9.36497	−	5.40687i	−0.733521	−	0.423498i	0.0861881	−	0.996279i	$-0.472531\pi$
$163$	−9.36497	−	5.40687i	−0.733521	−	0.423498i	−0.819709	+	0.572780i	$0.805865\pi$
$164$			4.78599i			0.373723i
$165$	−1.81236	+	3.13911i	−0.141092	+	0.244379i
$166$	−0.389158	−	0.674041i	−0.0302045	−	0.0523157i
$167$	−11.5444	+	6.66518i	−0.893334	+	0.515767i	−0.875032	−	0.484066i	$-0.839160\pi$
$167$	−11.5444	+	6.66518i	−0.893334	+	0.515767i	−0.0183026	+	0.999832i	$0.505826\pi$
$168$	−1.54413			−0.119132
$169$	11.0677	−	6.81947i	0.851364	−	0.524575i
$170$	3.17433			0.243460
$171$	6.17022	−	3.56238i	0.471848	−	0.272422i
$172$	8.95337	+	15.5077i	0.682688	+	1.18245i
$173$	−7.12408	+	12.3393i	−0.541634	+	0.938137i	0.457177	+	0.889376i	$0.348861\pi$
$173$	−7.12408	+	12.3393i	−0.541634	+	0.938137i	−0.998810	+	0.0487615i	$0.984473\pi$
$174$			2.48979i			0.188750i
$175$	9.53545	+	5.50530i	0.720812	+	0.416161i
$176$	−3.02872	−	1.74863i	−0.228298	−	0.131808i
$177$		−	1.88793i		−	0.141905i
$178$	2.28530	−	3.95825i	0.171290	−	0.296684i
$179$	8.16083	+	14.1350i	0.609969	+	1.05650i	0.991245	+	0.132036i	$0.0421515\pi$
$179$	8.16083	+	14.1350i	0.609969	+	1.05650i	−0.381276	+	0.924461i	$0.624515\pi$
$180$	−6.01141	+	3.47069i	−0.448064	+	0.258690i
$181$	−7.14758			−0.531275			−0.265638	−	0.964073i	$-0.585582\pi$
$181$	−7.14758			−0.531275			−0.265638	+	0.964073i	$0.585582\pi$
$182$	1.36821	−	0.387676i	0.101419	−	0.0287364i
$183$	6.08777			0.450021
$184$	1.03508	−	0.597601i	0.0763068	−	0.0440557i
$185$	−17.7099	−	30.6744i	−1.30206	−	2.25523i
$186$	0.932970	−	1.61595i	0.0684087	−	0.118487i
$187$			3.00389i			0.219666i
$188$	−10.8779	−	6.28036i	−0.793353	−	0.458043i
$189$	−1.17162	−	0.676437i	−0.0852231	−	0.0492036i
$190$			7.52902i			0.546213i
$191$	2.02649	−	3.50998i	0.146631	−	0.253973i	−0.783349	−	0.621582i	$-0.786490\pi$
$191$	2.02649	−	3.50998i	0.146631	−	0.253973i	0.929980	+	0.367609i	$0.119824\pi$
$192$	−3.01589	−	5.22367i	−0.217653	−	0.376986i
$193$	−17.4339	+	10.0654i	−1.25492	+	0.724526i	−0.972082	−	0.234642i	$-0.924608\pi$
$193$	−17.4339	+	10.0654i	−1.25492	+	0.724526i	−0.282835	+	0.959169i	$0.591275\pi$
$194$	1.23398			0.0885946
$195$	9.10811	−	9.37256i	0.652246	−	0.671183i
$196$	9.90007			0.707148
$197$	−3.53253	+	2.03951i	−0.251682	+	0.145309i	−0.620534	−	0.784179i	$-0.713084\pi$
$197$	−3.53253	+	2.03951i	−0.251682	+	0.145309i	0.368852	+	0.929488i	$0.379751\pi$
$198$	0.145768	+	0.252478i	0.0103593	+	0.0179428i
$199$	−0.0373960	+	0.0647718i	−0.00265093	+	0.00459155i	−0.867348	−	0.497702i	$-0.834177\pi$
$199$	−0.0373960	+	0.0647718i	−0.00265093	+	0.00459155i	0.864697	+	0.502294i	$0.167510\pi$
$200$		−	9.28921i		−	0.656847i
$201$	7.65297	+	4.41845i	0.539799	+	0.311653i
$202$	−3.17993	−	1.83594i	−0.223739	−	0.129176i
$203$			11.5539i			0.810922i
$204$	−2.87623	+	4.98178i	−0.201377	+	0.348794i
$205$	−4.52946	−	7.84526i	−0.316352	−	0.547937i
$206$	−4.19043	+	2.41935i	−0.291961	+	0.168564i
$207$	1.04717			0.0727831
$208$	9.04296	+	8.78782i	0.627017	+	0.609326i
$209$	−7.12475			−0.492830
$210$	1.23810	−	0.714819i	0.0854373	−	0.0493272i
$211$	−5.86439	−	10.1574i	−0.403721	−	0.699266i	0.590450	−	0.807074i	$-0.298950\pi$
$211$	−5.86439	−	10.1574i	−0.403721	−	0.699266i	−0.994172	+	0.107808i	$0.965617\pi$
$212$	1.61959	−	2.80521i	0.111234	−	0.192663i
$213$		−	13.8980i		−	0.952273i
$214$	−0.00347804	−	0.00200805i	−0.000237754	−	0.000137267i
$215$	−29.3530	−	16.9470i	−2.00186	−	1.15577i
$216$			1.14137i			0.0776603i
$217$	4.32944	−	7.49881i	0.293902	−	0.509052i
$218$	−2.48903	−	4.31113i	−0.168579	−	0.291987i
$219$	−4.17527	+	2.41060i	−0.282139	+	0.162893i
$220$	6.94138			0.467988
$221$	2.65321	−	10.5007i	0.178475	−	0.706351i
$222$	−2.84881			−0.191200
$223$	−14.6221	+	8.44208i	−0.979169	+	0.565323i	−0.902019	−	0.431696i	$-0.857915\pi$
$223$	−14.6221	+	8.44208i	−0.979169	+	0.565323i	−0.0771495	+	0.997020i	$0.524582\pi$
$224$	2.23381	+	3.86907i	0.149253	+	0.258513i
$225$	4.06933	−	7.04829i	0.271289	−	0.469886i
$226$		−	3.68171i		−	0.244904i
$227$	18.0383	+	10.4144i	1.19725	+	0.691230i	0.959940	−	0.280205i	$-0.0904026\pi$
$227$	18.0383	+	10.4144i	1.19725	+	0.691230i	0.237305	+	0.971435i	$0.423736\pi$
$228$	−11.8160	−	6.82197i	−0.782534	−	0.451796i
$229$		−	8.80483i		−	0.581839i	−0.956747	−	0.290920i	$-0.906039\pi$
$229$		−	8.80483i		−	0.581839i	0.956747	−	0.290920i	$-0.0939612\pi$
$230$	−0.553292	+	0.958330i	−0.0364830	+	0.0631904i
$231$	0.676437	+	1.17162i	0.0445063	+	0.0770872i
$232$	8.44162	−	4.87377i	0.554219	−	0.319979i
$233$	−11.2325			−0.735866			−0.367933	−	0.929852i	$-0.619934\pi$
$233$	−11.2325			−0.735866			−0.367933	+	0.929852i	$0.619934\pi$
$234$	−0.286557	−	1.01134i	−0.0187328	−	0.0661132i
$235$	23.7750			1.55091
$236$	−3.13102	+	1.80769i	−0.203812	+	0.117671i
$237$	−3.58687	−	6.21265i	−0.232992	−	0.403555i
$238$	0.592386	−	1.02604i	0.0383987	−	0.0665084i
$239$			14.7314i			0.952892i	0.879204	+	0.476446i	$0.158075\pi$
$239$			14.7314i			0.952892i	−0.879204	+	0.476446i	$0.841925\pi$
$240$	10.9783	+	6.33831i	0.708645	+	0.409136i
$241$	−2.23515	−	1.29046i	−0.143978	−	0.0831259i	0.426280	−	0.904591i	$-0.359824\pi$
$241$	−2.23515	−	1.29046i	−0.143978	−	0.0831259i	−0.570259	+	0.821465i	$0.693157\pi$
$242$		−	0.291537i		−	0.0187407i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.82906	−	10.0962i	−0.373167	−	0.646345i
$245$	−16.2283	+	9.36944i	−1.03679	+	0.598592i
$246$	−0.728609			−0.0464544
$247$	24.9059	+	6.29301i	1.58473	+	0.400415i
$248$	−7.30516			−0.463878
$249$	−2.31203	+	1.33485i	−0.146519	+	0.0845927i
$250$	1.65838	+	2.87240i	0.104885	+	0.181666i
$251$	10.1745	−	17.6228i	0.642211	−	1.11234i	−0.342727	−	0.939435i	$-0.611351\pi$
$251$	10.1745	−	17.6228i	0.642211	−	1.11234i	0.984938	−	0.172907i	$-0.0553160\pi$
$252$			2.59076i			0.163203i
$253$	−0.906872	−	0.523583i	−0.0570146	−	0.0329174i
$254$	0.0434891	+	0.0251084i	0.00272875	+	0.00157544i
$255$		−	10.8883i		−	0.681851i
$256$	−4.81270	+	8.33584i	−0.300794	+	0.520990i
$257$	−13.4912	−	23.3674i	−0.841557	−	1.45762i	−0.888578	−	0.458725i	$-0.848306\pi$
$257$	−13.4912	−	23.3674i	−0.841557	−	1.45762i	0.0470216	−	0.998894i	$-0.485027\pi$
$258$	−2.36086	+	1.36304i	−0.146981	+	0.0848593i
$259$	−13.2199			−0.821444
$260$	−24.2649	−	6.13104i	−1.50485	−	0.380231i
$261$	8.54023			0.528627
$262$	1.69091	−	0.976248i	0.104465	−	0.0603128i
$263$	−0.922730	−	1.59822i	−0.0568980	−	0.0985502i	0.836173	−	0.548465i	$-0.184788\pi$
$263$	−0.922730	−	1.59822i	−0.0568980	−	0.0985502i	−0.893071	+	0.449915i	$0.851454\pi$
$264$	0.570684	−	0.988454i	0.0351232	−	0.0608351i
$265$			6.13113i			0.376632i
$266$	2.43361	+	1.40505i	0.149214	+	0.0861489i
$267$	−13.5772	−	7.83880i	−0.830911	−	0.479727i
$268$		−	16.9227i		−	1.03372i
$269$	3.21423	−	5.56721i	0.195975	−	0.339439i	−0.751245	−	0.660024i	$-0.770546\pi$
$269$	3.21423	−	5.56721i	0.195975	−	0.339439i	0.947220	+	0.320585i	$0.103880\pi$
$270$	−0.528371	−	0.915165i	−0.0321556	−	0.0556952i
$271$	1.96001	−	1.13161i	0.119062	−	0.0687407i	−0.439286	−	0.898347i	$-0.644769\pi$
$271$	1.96001	−	1.13161i	0.119062	−	0.0687407i	0.558348	+	0.829607i	$0.311435\pi$
$272$	10.5054			0.636983
$273$	−1.32977	−	4.69310i	−0.0804812	−	0.284040i
$274$	4.70842			0.284446
$275$	−7.04829	+	4.06933i	−0.425028	+	0.245390i
$276$	−1.00266	−	1.73667i	−0.0603533	−	0.104535i
$277$	−10.9055	+	18.8889i	−0.655250	+	1.13493i	0.326581	+	0.945169i	$0.394103\pi$
$277$	−10.9055	+	18.8889i	−0.655250	+	1.13493i	−0.981831	+	0.189757i	$0.939230\pi$
$278$		−	2.02557i		−	0.121486i
$279$	−5.54287	−	3.20018i	−0.331843	−	0.191590i
$280$	−4.84718	−	2.79852i	−0.289675	−	0.167244i
$281$		−	7.10283i		−	0.423719i	−0.977300	−	0.211860i	$-0.932048\pi$
$281$		−	7.10283i		−	0.423719i	0.977300	−	0.211860i	$-0.0679519\pi$
$282$	0.956110	−	1.65603i	0.0569355	−	0.0986152i
$283$	−1.18047	−	2.04463i	−0.0701715	−	0.121541i	0.828805	−	0.559538i	$-0.189021\pi$
$283$	−1.18047	−	2.04463i	−0.0701715	−	0.121541i	−0.898976	+	0.437997i	$0.855688\pi$
$284$	−23.0490	+	13.3073i	−1.36771	+	0.789646i
$285$	25.8253			1.52976
$286$	−0.257503	+	1.01912i	−0.0152265	+	0.0602620i
$287$	−3.38111			−0.199580
$288$	2.85989	−	1.65116i	0.168521	−	0.0972954i
$289$	3.98833	+	6.90798i	0.234607	+	0.406352i
$290$	−4.51241	+	7.81572i	−0.264978	+	0.458955i
$291$		−	4.23268i		−	0.248124i
$292$	7.99568	+	4.61631i	0.467912	+	0.270149i
$293$	−5.89952	−	3.40609i	−0.344653	−	0.198986i	0.317674	−	0.948200i	$-0.397098\pi$
$293$	−5.89952	−	3.40609i	−0.344653	−	0.198986i	−0.662328	+	0.749214i	$0.730431\pi$
$294$			1.50717i			0.0878997i
$295$	3.42161	−	5.92640i	0.199214	−	0.345049i
$296$	5.57655	+	9.65888i	0.324131	+	0.561411i
$297$	0.866025	−	0.500000i	0.0502519	−	0.0290129i
$298$	−3.68706			−0.213586
$299$	2.70769	+	2.63129i	0.156589	+	0.152171i
$300$	−15.5856			−0.899835
$301$	−10.9556	+	6.32519i	−0.631468	+	0.364578i
$302$	0.102879	+	0.178192i	0.00592003	+	0.0102538i
$303$	−6.29744	+	10.9075i	−0.361779	+	0.626619i
$304$			24.9171i			1.42910i
$305$	19.1102	+	11.0333i	1.09425	+	0.631763i
$306$	−0.758416	−	0.437872i	−0.0433558	−	0.0250315i
$307$			21.5065i			1.22744i	0.789524	+	0.613720i	$0.210327\pi$
$307$			21.5065i			1.22744i	−0.789524	+	0.613720i	$0.789673\pi$
$308$	1.29538	−	2.24367i	0.0738112	−	0.127845i
$309$	8.29860	+	14.3736i	0.472091	+	0.817685i
$310$	5.85739	−	3.38176i	0.332677	−	0.192071i
$311$	17.1520			0.972602			0.486301	−	0.873791i	$-0.338346\pi$
$311$	17.1520			0.972602			0.486301	+	0.873791i	$0.338346\pi$
$312$	−2.86800	+	2.95127i	−0.162368	+	0.167083i
$313$	6.59696			0.372882			0.186441	−	0.982466i	$-0.440305\pi$
$313$	6.59696			0.372882			0.186441	+	0.982466i	$0.440305\pi$
$314$	−4.15463	+	2.39868i	−0.234459	+	0.135365i
$315$	−2.45190	−	4.24682i	−0.138149	−	0.239281i
$316$	−6.86888	+	11.8973i	−0.386405	+	0.669273i
$317$		−	31.0269i		−	1.74264i	−0.490713	−	0.871321i	$-0.663264\pi$
$317$		−	31.0269i		−	1.74264i	0.490713	−	0.871321i	$-0.336736\pi$
$318$	0.427060	+	0.246563i	0.0239483	+	0.0138266i
$319$	−7.39605	−	4.27011i	−0.414100	−	0.239080i
$320$		−	21.8636i		−	1.22221i
$321$	−0.00688781	+	0.0119300i	−0.000384440	+	0.000665870i
$322$	0.206508	+	0.357682i	0.0115082	+	0.0199328i
$323$	18.5346	−	10.7010i	1.03130	−	0.595419i
$324$	1.91501			0.106389
$325$	28.2329	−	7.99966i	1.56608	−	0.443741i
$326$	−3.15260			−0.174606
$327$	−14.7876	+	8.53763i	−0.817756	+	0.472132i
$328$	1.42625	+	2.47034i	0.0787517	+	0.136402i
$329$	4.43682	−	7.68480i	0.244610	−	0.423677i
$330$			1.05674i			0.0581717i
$331$	17.5574	+	10.1368i	0.965040	+	0.557166i	0.897721	−	0.440565i	$-0.145222\pi$
$331$	17.5574	+	10.1368i	0.965040	+	0.557166i	0.0673197	+	0.997731i	$0.478555\pi$
$332$	4.42755	+	2.55625i	0.242993	+	0.140292i
$333$			9.77170i			0.535486i
$334$	−1.94314	+	3.36562i	−0.106324	+	0.184159i
$335$	16.0157	+	27.7400i	0.875030	+	1.51560i
$336$	4.09747	−	2.36568i	0.223536	−	0.129058i
$337$	−0.168823			−0.00919636			−0.00459818	−	0.999989i	$-0.501464\pi$
$337$	−0.168823			−0.00919636			−0.00459818	+	0.999989i	$0.501464\pi$
$338$	1.80030	−	3.33509i	0.0979234	−	0.181405i
$339$	−12.6286			−0.685893
$340$	−18.0576	+	10.4256i	−0.979312	+	0.565406i
$341$	3.20018	+	5.54287i	0.173299	+	0.300163i
$342$	1.03856	−	1.79884i	0.0561591	−	0.0972704i
$343$			16.4641i			0.888979i
$344$	9.24278	+	5.33632i	0.498337	+	0.287715i
$345$	3.28717	+	1.89785i	0.176975	+	0.102177i
$346$			4.15386i			0.223313i
$347$	−5.68349	+	9.84409i	−0.305106	+	0.528459i	−0.977285	−	0.211930i	$-0.932025\pi$
$347$	−5.68349	+	9.84409i	−0.305106	+	0.528459i	0.672179	+	0.740389i	$0.265358\pi$
$348$	−8.17730	−	14.1635i	−0.438349	−	0.759243i
$349$	−20.8414	+	12.0328i	−1.11561	+	0.644100i	−0.940278	−	0.340408i	$-0.889435\pi$
$349$	−20.8414	+	12.0328i	−1.11561	+	0.644100i	−0.175337	+	0.984509i	$0.556101\pi$
$350$	3.20999			0.171581
$351$	−3.46899	+	0.982920i	−0.185161	+	0.0524644i
$352$	−3.30232			−0.176014
$353$	−9.12917	+	5.27073i	−0.485897	+	0.280533i	−0.722871	−	0.690983i	$-0.757178\pi$
$353$	−9.12917	+	5.27073i	−0.485897	+	0.280533i	0.236974	+	0.971516i	$0.423844\pi$
$354$	−0.275200	−	0.476660i	−0.0146267	−	0.0253342i
$355$	25.1882	−	43.6272i	1.33685	−	2.31549i
$356$			30.0227i			1.59120i
$357$	−3.51943	−	2.03194i	−0.186268	−	0.107542i
$358$	4.12086	+	2.37918i	0.217794	+	0.125744i
$359$		−	10.0371i		−	0.529739i	−0.964284	−	0.264869i	$-0.914671\pi$
$359$		−	10.0371i		−	0.529739i	0.964284	−	0.264869i	$-0.0853288\pi$
$360$	−2.06858	+	3.58288i	−0.109023	+	0.188834i
$361$	15.8811	+	27.5068i	0.835845	+	1.44773i
$362$	−1.80461	+	1.04189i	−0.0948481	+	0.0547606i
$363$	−1.00000			−0.0524864
$364$	−6.50999	+	6.69901i	−0.341216	+	0.351123i
$365$	−17.4755			−0.914710
$366$	1.53703	−	0.887405i	0.0803418	−	0.0463854i
$367$	1.35284	+	2.34319i	0.0706178	+	0.122314i	0.899172	−	0.437595i	$-0.144170\pi$
$367$	1.35284	+	2.34319i	0.0706178	+	0.122314i	−0.828554	+	0.559909i	$0.810836\pi$
$368$	−1.83111	+	3.17157i	−0.0954531	+	0.165330i
$369$			2.49920i			0.130103i
$370$	−8.94272	−	5.16308i	−0.464910	−	0.268416i
$371$	1.98177	+	1.14417i	0.102888	+	0.0594026i
$372$			12.2567i			0.635482i
$373$	16.7867	−	29.0755i	0.869184	−	1.50547i	0.00635220	−	0.999980i	$-0.497978\pi$
$373$	16.7867	−	29.0755i	0.869184	−	1.50547i	0.862832	−	0.505491i	$-0.168689\pi$
$374$	0.437872	+	0.758416i	0.0226418	+	0.0392168i
$375$	9.85261	−	5.68841i	0.508787	−	0.293748i
$376$	−7.48635			−0.386079
$377$	22.0827	+	21.4596i	1.13732	+	1.10523i
$378$	−0.394413			−0.0202864
$379$	4.91319	−	2.83663i	0.252374	−	0.145708i	−0.368477	−	0.929637i	$-0.620121\pi$
$379$	4.91319	−	2.83663i	0.252374	−	0.145708i	0.620851	+	0.783929i	$0.286787\pi$
$380$	−24.7278	−	42.8298i	−1.26851	−	2.19712i
$381$	0.0861245	−	0.149172i	0.00441229	−	0.00764231i
$382$		−	1.18159i		−	0.0604554i
$383$	7.19972	+	4.15676i	0.367888	+	0.212400i	0.672536	−	0.740065i	$-0.265205\pi$
$383$	7.19972	+	4.15676i	0.367888	+	0.212400i	−0.304647	+	0.952465i	$0.598539\pi$
$384$	−7.24267	−	4.18156i	−0.369601	−	0.213389i
$385$			4.90380i			0.249921i
$386$	−2.93445	+	5.08261i	−0.149359	+	0.258698i
$387$	4.67537	+	8.09798i	0.237663	+	0.411644i
$388$	−7.01966	+	4.05280i	−0.356369	+	0.205750i
$389$	16.5445			0.838841			0.419421	−	0.907792i	$-0.362233\pi$
$389$	16.5445			0.838841			0.419421	+	0.907792i	$0.362233\pi$
$390$	0.933377	−	3.69404i	0.0472634	−	0.187055i
$391$	3.14557			0.159078
$392$	5.11004	−	2.95028i	0.258096	−	0.149012i
$393$	−3.34863	−	5.79999i	−0.168916	−	0.292571i
$394$	−0.594591	+	1.02986i	−0.0299551	+	0.0518837i
$395$		−	26.0029i		−	1.30835i
$396$	−1.65844	−	0.957503i	−0.0833400	−	0.0481163i
$397$	1.85598	+	1.07155i	0.0931489	+	0.0537795i	0.545851	−	0.837882i	$-0.316207\pi$
$397$	1.85598	+	1.07155i	0.0931489	+	0.0537795i	−0.452702	+	0.891662i	$0.649540\pi$
$398$			0.0218046i			0.00109297i
$399$	4.81945	−	8.34753i	0.241274	−	0.417899i
$400$	14.2315	+	24.6497i	0.711576	+	1.23249i
$401$	28.6613	−	16.5476i	1.43128	−	0.826347i	0.434057	−	0.900885i	$-0.357082\pi$
$401$	28.6613	−	16.5476i	1.43128	−	0.826347i	0.997218	+	0.0745383i	$0.0237483\pi$
$402$	2.57628			0.128493
$403$	−6.29104	−	22.2028i	−0.313379	−	1.10600i
$404$	24.1193			1.19998
$405$	−3.13911	+	1.81236i	−0.155984	+	0.0900571i
$406$	1.68419	+	2.91710i	0.0835848	+	0.144773i
$407$	4.88585	−	8.46254i	0.242183	−	0.419473i
$408$			3.42854i			0.169738i
$409$	−14.9540	−	8.63370i	−0.739428	−	0.426909i	0.0824333	−	0.996597i	$-0.473731\pi$
$409$	−14.9540	−	8.63370i	−0.739428	−	0.426909i	−0.821861	+	0.569688i	$0.807064\pi$
$410$	−2.28718	−	1.32051i	−0.112956	−	0.0652151i
$411$		−	16.1504i		−	0.796639i
$412$	15.8919	−	27.5255i	0.782936	−	1.35608i
$413$	−1.27706	−	2.21194i	−0.0628402	−	0.108842i
$414$	0.264387	−	0.152644i	0.0129939	−	0.00750203i
$415$	−9.67694			−0.475022
$416$	11.5439	+	2.91680i	0.565985	+	0.143008i
$417$	−6.94791			−0.340241
$418$	−1.79884	+	1.03856i	−0.0879844	+	0.0507978i
$419$	7.05399	+	12.2179i	0.344610	+	0.596882i	0.985283	−	0.170932i	$-0.0546779\pi$
$419$	7.05399	+	12.2179i	0.344610	+	0.596882i	−0.640673	+	0.767814i	$0.721345\pi$
$420$	−4.69541	+	8.13268i	−0.229112	+	0.396834i
$421$		−	1.67313i		−	0.0815433i	−0.999168	−	0.0407717i	$-0.987018\pi$
$421$		−	1.67313i		−	0.0815433i	0.999168	−	0.0407717i	$-0.0129816\pi$
$422$	−2.96126	−	1.70969i	−0.144152	−	0.0832262i
$423$	−5.68035	−	3.27955i	−0.276188	−	0.159457i
$424$		−	1.93059i		−	0.0937579i
$425$	12.2238	−	21.1723i	0.592943	−	1.02701i
$426$	−2.02588	−	3.50893i	−0.0981544	−	0.170008i
$427$	7.13258	−	4.11800i	0.345170	−	0.199284i
$428$	0.0263804			0.00127514
$429$	3.49569	+	0.883260i	0.168774	+	0.0426442i
$430$	−9.88132			−0.476520
$431$	20.6916	−	11.9463i	0.996680	−	0.575433i	0.0894157	−	0.995994i	$-0.471500\pi$
$431$	20.6916	−	11.9463i	0.996680	−	0.575433i	0.907264	+	0.420561i	$0.138167\pi$
$432$	−1.74863	−	3.02872i	−0.0841310	−	0.145719i
$433$	−7.96445	+	13.7948i	−0.382747	+	0.662937i	−0.991454	−	0.130458i	$-0.958355\pi$
$433$	−7.96445	+	13.7948i	−0.382747	+	0.662937i	0.608707	+	0.793395i	$0.291689\pi$
$434$		−	2.52438i		−	0.121174i
$435$	26.8087	+	15.4780i	1.28538	+	0.742114i
$436$	28.3184	+	16.3496i	1.35620	+	0.783004i
$437$			7.46080i			0.356898i
$438$	−0.702777	+	1.21725i	−0.0335800	+	0.0581622i
$439$	−12.8376	−	22.2353i	−0.612704	−	1.06123i	−0.990783	−	0.135460i	$-0.956749\pi$
$439$	−12.8376	−	22.2353i	−0.612704	−	1.06123i	0.378079	−	0.925773i	$-0.376585\pi$
$440$	3.58288	−	2.06858i	0.170807	−	0.0986155i
$441$	5.16973			0.246178
$442$	−0.860786	−	3.03794i	−0.0409434	−	0.144500i
$443$	−10.2668			−0.487791			−0.243896	−	0.969801i	$-0.578425\pi$
$443$	−10.2668			−0.487791			−0.243896	+	0.969801i	$0.578425\pi$
$444$	16.2058	−	9.35644i	0.769094	−	0.444037i
$445$	−28.4135	−	49.2137i	−1.34693	−	2.33295i
$446$	−2.46118	+	4.26288i	−0.116540	+	0.201853i
$447$			12.6470i			0.598182i
$448$	−7.06697	−	4.08012i	−0.333883	−	0.192767i
$449$	8.55052	+	4.93665i	0.403524	+	0.232975i	0.688003	−	0.725707i	$-0.258487\pi$
$449$	8.55052	+	4.93665i	0.403524	+	0.232975i	−0.284479	+	0.958682i	$0.591821\pi$
$450$		−	2.37272i		−	0.111851i
$451$	1.24960	−	2.16437i	0.0588414	−	0.101916i
$452$	12.0919	+	20.9439i	0.568757	+	0.985117i
$453$	0.611216	−	0.352886i	0.0287175	−	0.0165800i
$454$	6.07238			0.284991
$455$	4.33133	−	17.1422i	0.203056	−	0.803638i
$456$	−8.13197			−0.380814
$457$	0.355945	−	0.205505i	0.0166504	−	0.00961311i	−0.491652	−	0.870792i	$-0.663607\pi$
$457$	0.355945	−	0.205505i	0.0166504	−	0.00961311i	0.508302	+	0.861179i	$0.330273\pi$
$458$	−1.28347	−	2.22303i	−0.0599724	−	0.103875i
$459$	−1.50194	+	2.60144i	−0.0701048	+	0.121425i
$460$		−	7.26878i		−	0.338909i
$461$	32.0898	+	18.5271i	1.49457	+	0.862892i	0.999981	−	0.00623267i	$-0.00198393\pi$
$461$	32.0898	+	18.5271i	1.49457	+	0.862892i	0.494593	+	0.869125i	$0.335317\pi$
$462$	0.341571	+	0.197206i	0.0158913	+	0.00917487i
$463$			25.1563i			1.16911i	0.811354	+	0.584556i	$0.198731\pi$
$463$			25.1563i			1.16911i	−0.811354	+	0.584556i	$0.801269\pi$
$464$	−14.9337	+	25.8659i	−0.693280	+	1.20080i
$465$	−11.5998	−	20.0914i	−0.537927	−	0.931717i
$466$	−2.83596	+	1.63734i	−0.131373	+	0.0758485i
$467$	−25.8359			−1.19554			−0.597771	−	0.801667i	$-0.703947\pi$
$467$	−25.8359			−1.19554			−0.597771	+	0.801667i	$0.703947\pi$
$468$	4.95168	+	4.81197i	0.228892	+	0.222433i
$469$	11.9552			0.552040
$470$	6.00266	−	3.46564i	0.276882	−	0.159858i
$471$	8.22770	+	14.2508i	0.379112	+	0.656642i
$472$	−1.07741	+	1.86613i	−0.0495918	+	0.0858955i
$473$		−	9.35075i		−	0.429948i
$474$	−1.81121	−	1.04571i	−0.0831918	−	0.0480308i
$475$	50.2173	+	28.9930i	2.30413	+	1.33029i
$476$			7.78236i			0.356704i
$477$	0.845736	−	1.46486i	0.0387236	−	0.0670712i
$478$	2.14737	+	3.71935i	0.0982182	+	0.170119i
$479$	12.0096	−	6.93372i	0.548731	−	0.316810i	−0.199879	−	0.979821i	$-0.564055\pi$
$479$	12.0096	−	6.93372i	0.548731	−	0.316810i	0.748610	+	0.663011i	$0.230722\pi$
$480$	11.9700			0.546353
$481$	−24.5540	+	25.2670i	−1.11957	+	1.15207i
$482$	−0.752434			−0.0342724
$483$	1.22688	−	0.708342i	0.0558252	−	0.0322307i
$484$	0.957503	+	1.65844i	0.0435229	+	0.0753838i
$485$	7.67115	−	13.2868i	0.348329	−	0.603324i
$486$			0.291537i			0.0132244i
$487$	−15.8143	−	9.13037i	−0.716612	−	0.413736i	0.0968922	−	0.995295i	$-0.469110\pi$
$487$	−15.8143	−	9.13037i	−0.716612	−	0.413736i	−0.813505	+	0.581559i	$0.802443\pi$
$488$	−6.01748	−	3.47419i	−0.272399	−	0.157269i
$489$			10.8137i			0.489014i
$490$	−2.73154	+	4.73116i	−0.123398	+	0.213732i
$491$	−20.3369	−	35.2246i	−0.917793	−	1.58966i	−0.802759	−	0.596303i	$-0.796636\pi$
$491$	−20.3369	−	35.2246i	−0.917793	−	1.58966i	−0.115034	−	0.993362i	$-0.536698\pi$
$492$	4.14479	−	2.39299i	0.186861	−	0.107884i
$493$	25.6539			1.15539
$494$	7.20553	−	2.04165i	0.324192	−	0.0918582i
$495$	3.62473			0.162919
$496$	19.3849	−	11.1919i	0.870407	−	0.502530i
$497$	−9.40110	−	16.2832i	−0.421697	−	0.730401i
$498$	−0.389158	+	0.674041i	−0.0174386	+	0.0302045i
$499$			1.90505i			0.0852819i	0.999090	+	0.0426409i	$0.0135771\pi$
$499$			1.90505i			0.0852819i	−0.999090	+	0.0426409i	$0.986423\pi$
$500$	−18.8678	−	10.8933i	−0.843794	−	0.487165i
$501$	11.5444	+	6.66518i	0.515767	+	0.297778i
$502$		−	5.93250i		−	0.264780i
$503$	−11.3824	+	19.7149i	−0.507516	+	0.879043i	0.492447	+	0.870343i	$0.336103\pi$
$503$	−11.3824	+	19.7149i	−0.507516	+	0.879043i	−0.999962	+	0.00870003i	$0.997231\pi$
$504$	0.772064	+	1.33725i	0.0343905	+	0.0595660i
$505$	−39.5367	+	22.8265i	−1.75936	+	1.01577i
$506$	−0.305287			−0.0135717
$507$	−11.4397	−	6.17521i	−0.508055	−	0.274251i
$508$	−0.329858			−0.0146351
$509$	−26.2230	+	15.1399i	−1.16232	+	0.671064i	−0.951858	−	0.306539i	$-0.900829\pi$
$509$	−26.2230	+	15.1399i	−1.16232	+	0.671064i	−0.210458	+	0.977603i	$0.567496\pi$
$510$	−1.58717	−	2.74905i	−0.0702810	−	0.121730i
$511$	−3.26123	+	5.64862i	−0.144268	+	0.249880i
$512$			19.5324i			0.863218i
$513$	−6.17022	−	3.56238i	−0.272422	−	0.157283i
$514$	−6.81246	−	3.93317i	−0.300485	−	0.173485i
$515$			60.1603i			2.65098i
$516$	8.95337	−	15.5077i	0.394150	−	0.682688i
$517$	3.27955	+	5.68035i	0.144235	+	0.249822i
$518$	−3.33773	+	1.92704i	−0.146652	+	0.0846693i
$519$	14.2482			0.625425
$520$	−14.3517	+	4.06649i	−0.629365	+	0.178327i
$521$	10.2452			0.448849			0.224424	−	0.974491i	$-0.427950\pi$
$521$	10.2452			0.448849			0.224424	+	0.974491i	$0.427950\pi$
$522$	2.15622	−	1.24489i	0.0943752	−	0.0544876i
$523$	18.1123	+	31.3714i	0.791996	+	1.37178i	0.924729	+	0.380625i	$0.124291\pi$
$523$	18.1123	+	31.3714i	0.791996	+	1.37178i	−0.132734	+	0.991152i	$0.542376\pi$
$524$	−6.41264	+	11.1070i	−0.280138	+	0.485213i
$525$		−	11.0106i		−	0.480542i
$526$	−0.465939	−	0.269010i	−0.0203159	−	0.0117294i
$527$	−16.6502	−	9.61298i	−0.725293	−	0.418748i
$528$			3.49726i			0.152199i
$529$	10.9517	−	18.9689i	0.476162	−	0.824736i
$530$	0.893725	+	1.54798i	0.0388209	+	0.0672398i
$531$	−1.63499	+	0.943963i	−0.0709526	+	0.0409645i
$532$	−18.4585			−0.800280
$533$	−6.27992	+	6.46225i	−0.272014	+	0.279911i
$534$	−4.57060			−0.197789
$535$	−0.0432432	+	0.0249664i	−0.00186956	+	0.00107939i
$536$	−5.04307	−	8.73486i	−0.217828	−	0.377288i
$537$	8.16083	−	14.1350i	0.352166	−	0.609969i
$538$		−	1.87413i		−	0.0807995i
$539$	−4.47712	−	2.58487i	−0.192843	−	0.111338i
$540$	6.01141	+	3.47069i	0.258690	+	0.149355i
$541$			20.1300i			0.865457i	0.901524	+	0.432728i	$0.142449\pi$
$541$			20.1300i			0.865457i	−0.901524	+	0.432728i	$0.857551\pi$
$542$	0.329907	−	0.571416i	0.0141707	−	0.0245444i
$543$	3.57379	+	6.18999i	0.153366	+	0.265638i
$544$	8.59079	−	4.95990i	0.368327	−	0.212654i
$545$	−61.8932			−2.65121
$546$	−1.01984	−	0.991068i	−0.0436453	−	0.0424138i
$547$	36.6440			1.56678			0.783391	−	0.621529i	$-0.213488\pi$
$547$	36.6440			1.56678			0.783391	+	0.621529i	$0.213488\pi$
$548$	−26.7845	+	15.4640i	−1.14418	+	0.660590i
$549$	−3.04389	−	5.27217i	−0.129910	−	0.225011i
$550$	−1.18636	+	2.05484i	−0.0505866	+	0.0876185i
$551$			60.8470i			2.59217i
$552$	−1.03508	−	0.597601i	−0.0440557	−	0.0254356i
$553$	−8.40493	−	4.85259i	−0.357414	−	0.206353i
$554$			6.35873i			0.270156i
$555$	−17.7099	+	30.6744i	−0.751743	+	1.30206i
$556$	6.65265	+	11.5227i	0.282135	+	0.488672i
$557$	34.7681	−	20.0734i	1.47317	−	0.850536i	0.473627	−	0.880725i	$-0.342944\pi$
$557$	34.7681	−	20.0734i	1.47317	−	0.850536i	0.999544	+	0.0301896i	$0.00961112\pi$
$558$	−1.86594			−0.0789915
$559$	−8.25914	+	32.6873i	−0.349324	+	1.38253i
$560$	17.1499			0.724715
$561$	2.60144	−	1.50194i	0.109833	−	0.0634121i
$562$	−1.03537	−	1.79331i	−0.0436743	−	0.0756462i
$563$	−5.64346	+	9.77476i	−0.237843	+	0.411957i	−0.960095	−	0.279673i	$-0.909774\pi$
$563$	−5.64346	+	9.77476i	−0.237843	+	0.411957i	0.722252	+	0.691630i	$0.243107\pi$
$564$			12.5607i			0.528902i
$565$	−39.6426	−	22.8877i	−1.66778	−	0.962892i
$566$	−0.596084	−	0.344149i	−0.0250553	−	0.0144657i
$567$			1.35287i			0.0568154i
$568$	−7.93135	+	13.7375i	−0.332792	+	0.576413i
$569$	−1.93676	−	3.35456i	−0.0811930	−	0.140630i	0.822570	−	0.568664i	$-0.192540\pi$
$569$	−1.93676	−	3.35456i	−0.0811930	−	0.140630i	−0.903763	+	0.428034i	$0.859206\pi$
$570$	6.52033	−	3.76451i	0.273106	−	0.157678i
$571$	−36.5724			−1.53051			−0.765254	−	0.643729i	$-0.777387\pi$
$571$	−36.5724			−1.53051			−0.765254	+	0.643729i	$0.777387\pi$
$572$	−1.88230	−	6.64313i	−0.0787028	−	0.277763i
$573$	−4.05297			−0.169315
$574$	−0.853655	+	0.492858i	−0.0356309	+	0.0205715i
$575$	4.26127	+	7.38073i	0.177707	+	0.307798i
$576$	−3.01589	+	5.22367i	−0.125662	+	0.217653i
$577$		−	4.08847i		−	0.170205i	−0.996372	−	0.0851027i	$-0.972878\pi$
$577$		−	4.08847i		−	0.170205i	0.996372	−	0.0851027i	$-0.0271218\pi$
$578$	2.01393	+	1.16274i	0.0837685	+	0.0483637i
$579$	17.4339	+	10.0654i	0.724526	+	0.418306i
$580$		−	59.2810i		−	2.46151i
$581$	−1.80588	+	3.12788i	−0.0749207	+	0.129766i
$582$	−0.616990	−	1.06866i	−0.0255751	−	0.0442973i
$583$	−1.46486	+	0.845736i	−0.0606682	+	0.0350268i
$584$	5.50275			0.227706
$585$	−12.6709	−	3.20158i	−0.523879	−	0.132369i
$586$	−1.98600			−0.0820409
$587$	11.1153	−	6.41743i	0.458778	−	0.264876i	−0.252752	−	0.967531i	$-0.581336\pi$
$587$	11.1153	−	6.41743i	0.458778	−	0.264876i	0.711530	+	0.702655i	$0.248002\pi$
$588$	−4.95003	−	8.57371i	−0.204136	−	0.353574i
$589$	22.8005	−	39.4916i	0.939478	−	1.62722i
$590$		−	1.99505i		−	0.0821349i
$591$	3.53253	+	2.03951i	0.145309	+	0.0838941i
$592$	−29.5957	−	17.0871i	−1.21638	−	0.702276i
$593$		−	31.7447i		−	1.30360i	−0.758391	−	0.651800i	$-0.774014\pi$
$593$		−	31.7447i		−	1.30360i	0.758391	−	0.651800i	$-0.225986\pi$
$594$	0.145768	−	0.252478i	0.00598095	−	0.0103593i
$595$	−7.36524	−	12.7570i	−0.301945	−	0.522985i
$596$	20.9743	−	12.1095i	0.859141	−	0.496025i
$597$	0.0747920			0.00306103
$598$	1.06719	+	0.269648i	0.0436406	+	0.0110267i
$599$	−23.8296			−0.973650			−0.486825	−	0.873500i	$-0.661845\pi$
$599$	−23.8296			−0.973650			−0.486825	+	0.873500i	$0.661845\pi$
$600$	−8.04469	+	4.64461i	−0.328423	+	0.189615i
$601$	−3.69704	−	6.40347i	−0.150806	−	0.261203i	0.780718	−	0.624883i	$-0.214853\pi$
$601$	−3.69704	−	6.40347i	−0.150806	−	0.261203i	−0.931524	+	0.363680i	$0.881520\pi$
$602$	−1.84403	+	3.19395i	−0.0751569	+	0.130176i
$603$		−	8.83689i		−	0.359866i
$604$	−1.17048	−	0.675779i	−0.0476263	−	0.0274970i
$605$	−3.13911	−	1.81236i	−0.127623	−	0.0736831i
$606$			3.67187i			0.149160i
$607$	14.4096	−	24.9582i	0.584868	−	1.01302i	−0.410024	−	0.912075i	$-0.634480\pi$
$607$	14.4096	−	24.9582i	0.584868	−	1.01302i	0.994892	−	0.100946i	$-0.0321869\pi$
$608$	11.7641	+	20.3760i	0.477097	+	0.826356i
$609$	10.0059	−	5.77693i	0.405461	−	0.234093i
$610$	6.43320			0.260473
$611$	−6.44707	−	22.7534i	−0.260821	−	0.920506i
$612$	5.75247			0.232530
$613$	8.39629	−	4.84760i	0.339123	−	0.195793i	−0.320761	−	0.947160i	$-0.603939\pi$
$613$	8.39629	−	4.84760i	0.339123	−	0.195793i	0.659884	+	0.751367i	$0.270605\pi$
$614$	3.13496	+	5.42992i	0.126517	+	0.219134i
$615$	−4.52946	+	7.84526i	−0.182646	+	0.316352i
$616$		−	1.54413i		−	0.0622147i
$617$	−8.53875	−	4.92985i	−0.343757	−	0.198468i	0.318175	−	0.948032i	$-0.396930\pi$
$617$	−8.53875	−	4.92985i	−0.343757	−	0.198468i	−0.661932	+	0.749564i	$0.730263\pi$
$618$	4.19043	+	2.41935i	0.168564	+	0.0973203i
$619$		−	41.0190i		−	1.64869i	−0.566085	−	0.824347i	$-0.691542\pi$
$619$		−	41.0190i		−	1.64869i	0.566085	−	0.824347i	$-0.308458\pi$
$620$	−22.2137	+	38.4752i	−0.892122	+	1.54520i
$621$	−0.523583	−	0.906872i	−0.0210107	−	0.0363915i
$622$	4.33051	−	2.50022i	0.173638	−	0.100250i
$623$	−21.2098			−0.849754
$624$	3.08899	−	12.2253i	0.123659	−	0.489406i
$625$	0.544553			0.0217821
$626$	1.66559	−	0.961628i	0.0665703	−	0.0384344i
$627$	3.56238	+	6.17022i	0.142268	+	0.246415i
$628$	15.7561	−	27.2904i	0.628736	−	1.08900i
$629$			29.3531i			1.17039i
$630$	−1.23810	−	0.714819i	−0.0493272	−	0.0284791i
$631$	−10.0381	−	5.79547i	−0.399609	−	0.230714i	0.286706	−	0.958018i	$-0.407440\pi$
$631$	−10.0381	−	5.79547i	−0.399609	−	0.230714i	−0.686315	+	0.727304i	$0.740773\pi$
$632$			8.18788i			0.325697i
$633$	−5.86439	+	10.1574i	−0.233089	+	0.403721i
$634$	−4.52274	−	7.83361i	−0.179621	−	0.311112i
$635$	0.540708	−	0.312178i	0.0214573	−	0.0123884i
$636$	−3.23918			−0.128442
$637$	13.3675	+	12.9903i	0.529640	+	0.514696i
$638$	−2.48979			−0.0985717
$639$	−12.0360	+	6.94898i	−0.476137	+	0.274898i
$640$	−15.1570	−	26.2527i	−0.599134	−	1.03773i
$641$	14.3482	−	24.8518i	0.566719	−	0.981587i	−0.430168	−	0.902749i	$-0.641546\pi$
$641$	14.3482	−	24.8518i	0.566719	−	0.981587i	0.996887	−	0.0788380i	$-0.0251210\pi$
$642$			0.00401610i			0.000158503i
$643$	−30.3338	−	17.5132i	−1.19625	−	0.690654i	−0.236532	−	0.971624i	$-0.576011\pi$
$643$	−30.3338	−	17.5132i	−1.19625	−	0.690654i	−0.959717	+	0.280969i	$0.909344\pi$
$644$	−2.34949	−	1.35648i	−0.0925829	−	0.0534528i
$645$			33.8939i			1.33457i
$646$	3.11973	−	5.40353i	0.122744	−	0.212599i
$647$	−23.8802	−	41.3617i	−0.938827	−	1.62610i	−0.767664	−	0.640853i	$-0.778581\pi$
$647$	−23.8802	−	41.3617i	−0.938827	−	1.62610i	−0.171163	−	0.985243i	$-0.554753\pi$
$648$	0.988454	−	0.570684i	0.0388301	−	0.0224186i
$649$	1.88793			0.0741076
$650$	5.96210	−	6.13521i	0.233853	−	0.240643i
$651$	−8.65888			−0.339368
$652$	17.9340	−	10.3542i	0.702348	−	0.405501i
$653$	4.02337	+	6.96867i	0.157446	+	0.272705i	0.933947	−	0.357411i	$-0.116340\pi$
$653$	4.02337	+	6.96867i	0.157446	+	0.272705i	−0.776501	+	0.630116i	$0.783007\pi$
$654$	−2.48903	+	4.31113i	−0.0973288	+	0.168579i
$655$		−	24.2757i		−	0.948532i
$656$	−7.56938	−	4.37018i	−0.295534	−	0.170627i
$657$	4.17527	+	2.41060i	0.162893	+	0.0940463i
$658$		−	2.58699i		−	0.100851i
$659$	−11.1834	+	19.3702i	−0.435644	+	0.754557i	−0.997348	−	0.0727810i	$-0.976813\pi$
$659$	−11.1834	+	19.3702i	−0.435644	+	0.754557i	0.561704	+	0.827338i	$0.310146\pi$
$660$	−3.47069	−	6.01141i	−0.135096	−	0.233994i
$661$	8.57530	−	4.95095i	0.333540	−	0.192570i	−0.323871	−	0.946101i	$-0.604985\pi$
$661$	8.57530	−	4.95095i	0.333540	−	0.192570i	0.657412	+	0.753531i	$0.271651\pi$
$662$	5.91047			0.229717
$663$	−10.4205	+	2.95258i	−0.404697	+	0.114669i
$664$	3.04711			0.118251
$665$	30.2575	−	17.4692i	1.17334	−	0.677426i
$666$	1.42440	+	2.46714i	0.0551946	+	0.0955998i
$667$	−4.47152	+	7.74490i	−0.173138	+	0.299884i
$668$		−	25.5277i		−	0.987697i
$669$	14.6221	+	8.44208i	0.565323	+	0.326390i
$670$	8.08721	+	4.66916i	0.312436	+	0.180385i
$671$			6.08777i			0.235016i
$672$	2.23381	−	3.86907i	0.0861711	−	0.149253i
$673$	−1.66499	−	2.88385i	−0.0641806	−	0.111164i	0.832150	−	0.554551i	$-0.187110\pi$
$673$	−1.66499	−	2.88385i	−0.0641806	−	0.111164i	−0.896330	+	0.443387i	$0.853777\pi$
$674$	−0.0426240	+	0.0246090i	−0.00164182	+	0.000947904i
$675$	−8.13867			−0.313257
$676$	0.712319	+	24.8849i	0.0273969	+	0.957111i
$677$	15.1408			0.581906			0.290953	−	0.956737i	$-0.406028\pi$
$677$	15.1408			0.581906			0.290953	+	0.956737i	$0.406028\pi$
$678$	−3.18845	+	1.84085i	−0.122452	+	0.0706976i
$679$	−2.86314	−	4.95910i	−0.109877	−	0.190313i
$680$	−6.21377	+	10.7626i	−0.238287	+	0.412726i
$681$		−	20.8289i		−	0.798163i
$682$	1.61595	+	0.932970i	0.0618780	+	0.0357253i
$683$	−29.1977	−	16.8573i	−1.11722	−	0.645026i	−0.176529	−	0.984295i	$-0.556487\pi$
$683$	−29.1977	−	16.8573i	−1.11722	−	0.645026i	−0.940689	+	0.339269i	$0.889820\pi$
$684$			13.6439i			0.521689i
$685$	29.2703	−	50.6977i	1.11836	−	1.93706i
$686$	2.39995	+	4.15683i	0.0916304	+	0.158709i
$687$	−7.62520	+	4.40241i	−0.290920	+	0.167963i
$688$	−32.7020			−1.24675
$689$	5.86769	−	1.66258i	0.223541	−	0.0633393i
$690$	1.10658			0.0421269
$691$	1.95393	−	1.12810i	0.0743309	−	0.0429150i	−0.462374	−	0.886685i	$-0.653002\pi$
$691$	1.95393	−	1.12810i	0.0743309	−	0.0429150i	0.536705	+	0.843770i	$0.319669\pi$
$692$	−13.6427	−	23.6298i	−0.518616	−	0.898270i
$693$	0.676437	−	1.17162i	0.0256957	−	0.0445063i
$694$			3.31389i			0.125794i
$695$	−21.8102	−	12.5921i	−0.827310	−	0.477647i
$696$	−8.44162	−	4.87377i	−0.319979	−	0.184740i
$697$			7.50732i			0.284360i
$698$	−3.50800	+	6.07603i	−0.132780	+	0.229981i
$699$	5.61625	+	9.72763i	0.212426	+	0.367933i
$700$	−18.2605	+	10.5427i	−0.690180	+	0.398476i
$701$	−41.5303			−1.56858			−0.784289	−	0.620395i	$-0.786972\pi$
$701$	−41.5303			−1.56858			−0.784289	+	0.620395i	$0.786972\pi$
$702$	−0.732565	+	0.753834i	−0.0276489	+	0.0284516i
$703$	−69.6210			−2.62580
$704$	5.22367	−	3.01589i	0.196875	−	0.113666i
$705$	−11.8875	−	20.5897i	−0.447709	−	0.775454i
$706$	−1.53661	+	2.66149i	−0.0578311	+	0.100166i
$707$			17.0393i			0.640829i
$708$	3.13102	+	1.80769i	0.117671	+	0.0679373i
$709$	2.74460	+	1.58460i	0.103076	+	0.0595108i	0.550652	−	0.834735i	$-0.314379\pi$
$709$	2.74460	+	1.58460i	0.103076	+	0.0595108i	−0.447576	+	0.894246i	$0.647713\pi$
$710$		−	14.6866i		−	0.551177i
$711$	−3.58687	+	6.21265i	−0.134518	+	0.232992i
$712$	8.94696	+	15.4966i	0.335301	+	0.580759i
$713$	5.80431	−	3.35112i	0.217373	−	0.125500i
$714$	−1.18477			−0.0443390
$715$	9.37256	+	9.10811i	0.350514	+	0.340624i
$716$	−31.2561			−1.16809
$717$	12.7577	−	7.36568i	0.476446	−	0.275076i
$718$	−1.46309	−	2.53415i	−0.0546022	−	0.0945737i
$719$	9.62159	−	16.6651i	0.358825	−	0.621503i	−0.628940	−	0.777454i	$-0.716511\pi$
$719$	9.62159	−	16.6651i	0.358825	−	0.621503i	0.987765	+	0.155951i	$0.0498442\pi$
$720$		−	12.6766i		−	0.472430i
$721$	19.4457	+	11.2270i	0.724194	+	0.418114i
$722$	8.01924	+	4.62991i	0.298445	+	0.172307i
$723$			2.58092i			0.0959856i
$724$	6.84383	−	11.8539i	0.254349	−	0.440545i
$725$	34.7530	+	60.1940i	1.29070	+	2.23555i
$726$	−0.252478	+	0.145768i	−0.00937034	+	0.00540997i
$727$	−9.70728			−0.360023			−0.180012	−	0.983664i	$-0.557614\pi$
$727$	−9.70728			−0.360023			−0.180012	+	0.983664i	$0.557614\pi$
$728$	−1.36387	+	5.39779i	−0.0505482	+	0.200055i
$729$	1.00000			0.0370370
$730$	−4.41219	+	2.54738i	−0.163302	+	0.0942826i
$731$	14.0443	+	24.3254i	0.519447	+	0.899709i
$732$	−5.82906	+	10.0962i	−0.215448	+	0.373167i
$733$			31.3082i			1.15639i	0.815897	+	0.578197i	$0.196244\pi$
$733$			31.3082i			1.15639i	−0.815897	+	0.578197i	$0.803756\pi$
$734$	0.683127	+	0.394403i	0.0252147	+	0.0145577i
$735$	16.2283	+	9.36944i	0.598592	+	0.345597i
$736$			3.45807i			0.127466i
$737$	−4.41845	+	7.65297i	−0.162756	+	0.281901i
$738$	0.364304	+	0.630994i	0.0134102	+	0.0232272i
$739$	13.8147	−	7.97594i	0.508183	−	0.293400i	−0.223903	−	0.974611i	$-0.571880\pi$
$739$	13.8147	−	7.97594i	0.508183	−	0.293400i	0.732086	+	0.681212i	$0.238547\pi$
$740$	67.8291			2.49345
$741$	−7.00306	−	24.7157i	−0.257264	−	0.907953i
$742$	0.667138			0.0244914
$743$	26.6225	−	15.3705i	0.976685	−	0.563889i	0.0754174	−	0.997152i	$-0.475971\pi$
$743$	26.6225	−	15.3705i	0.976685	−	0.563889i	0.901268	+	0.433263i	$0.142638\pi$
$744$	3.65258	+	6.32646i	0.133910	+	0.231939i
$745$	−22.9209	+	39.7002i	−0.839758	+	1.45450i
$746$		−	9.78790i		−	0.358360i
$747$	2.31203	+	1.33485i	0.0845927	+	0.0488396i
$748$	−4.98178	−	2.87623i	−0.182152	−	0.105165i
$749$			0.0186367i			0.000680970i
$750$	1.65838	−	2.87240i	0.0605555	−	0.104885i
$751$	−2.46920	−	4.27679i	−0.0901025	−	0.156062i	0.817452	−	0.575997i	$-0.195386\pi$
$751$	−2.46920	−	4.27679i	−0.0901025	−	0.156062i	−0.907554	+	0.419935i	$0.862053\pi$
$752$	19.8657	−	11.4695i	0.724427	−	0.418248i
$753$	−20.3491			−0.741561
$754$	8.70353	+	2.19913i	0.316964	+	0.0800876i
$755$	2.55823			0.0931036
$756$	2.24367	−	1.29538i	0.0816014	−	0.0471126i
$757$	2.49104	+	4.31460i	0.0905383	+	0.156817i	0.907738	−	0.419538i	$-0.137808\pi$
$757$	2.49104	+	4.31460i	0.0905383	+	0.156817i	−0.817199	+	0.576355i	$0.804475\pi$
$758$	0.826982	−	1.43238i	0.0300374	−	0.0520262i
$759$			1.04717i			0.0380097i
$760$	−25.5271	−	14.7381i	−0.925966	−	0.534607i
$761$	28.5619	+	16.4902i	1.03537	+	0.597769i	0.918517	−	0.395380i	$-0.129387\pi$
$761$	28.5619	+	16.4902i	1.03537	+	0.597769i	0.116849	+	0.993150i	$0.462721\pi$
$762$		−	0.0502169i		−	0.00181917i
$763$	−11.5503	+	20.0058i	−0.418150	+	0.724258i
$764$	3.88074	+	6.72163i	0.140400	+	0.243180i
$765$	−9.42953	+	5.44414i	−0.340925	+	0.196833i
$766$	2.42370			0.0875717
$767$	−6.59960	−	1.66753i	−0.238298	−	0.0602110i
$768$	9.62540			0.347327
$769$	5.88095	−	3.39537i	0.212072	−	0.122440i	−0.390202	−	0.920729i	$-0.627595\pi$
$769$	5.88095	−	3.39537i	0.212072	−	0.122440i	0.602274	+	0.798289i	$0.294261\pi$
$770$	0.714819	+	1.23810i	0.0257603	+	0.0446182i
$771$	−13.4912	+	23.3674i	−0.485873	+	0.841557i
$772$		−	38.5508i		−	1.38747i
$773$	26.5342	+	15.3195i	0.954368	+	0.551005i	0.894435	−	0.447198i	$-0.147578\pi$
$773$	26.5342	+	15.3195i	0.954368	+	0.551005i	0.0599329	+	0.998202i	$0.480911\pi$
$774$	2.36086	+	1.36304i	0.0848593	+	0.0489936i
$775$		−	52.0904i		−	1.87114i
$776$	−2.41552	+	4.18380i	−0.0867121	+	0.150190i
$777$	6.60994	+	11.4488i	0.237130	+	0.410722i
$778$	4.17713	−	2.41167i	0.149757	−	0.0864625i
$779$	−17.8062			−0.637973
$780$	6.82282	+	24.0796i	0.244296	+	0.862186i
$781$	13.8980			0.497308
$782$	0.794188	−	0.458525i	0.0284001	−	0.0163968i
$783$	−4.27011	−	7.39605i	−0.152601	−	0.264313i
$784$	−9.03995	+	15.6577i	−0.322855	+	0.559202i
$785$			59.6464i			2.12887i
$786$	−1.69091	−	0.976248i	−0.0603128	−	0.0348216i
$787$	30.3716	+	17.5351i	1.08263	+	0.625058i	0.931605	−	0.363472i	$-0.118409\pi$
$787$	30.3716	+	17.5351i	1.08263	+	0.625058i	0.151027	+	0.988530i	$0.451742\pi$
$788$		−	7.81133i		−	0.278267i
$789$	−0.922730	+	1.59822i	−0.0328501	+	0.0568980i
$790$	−3.79040	−	6.56516i	−0.134856	−	0.233578i
$791$	−14.7960	+	8.54247i	−0.526085	+	0.303735i
$792$	−1.14137			−0.0405567
$793$	5.37709	−	21.2810i	0.190946	−	0.755709i
$794$	0.624792			0.0221730
$795$	5.30971	−	3.06556i	0.188316	−	0.108724i
$796$	−0.0716136	−	0.124038i	−0.00253828	−	0.00439642i
$797$	−6.54920	+	11.3436i	−0.231985	+	0.401809i	−0.958392	−	0.285455i	$-0.907855\pi$
$797$	−6.54920	+	11.3436i	−0.231985	+	0.401809i	0.726407	+	0.687264i	$0.241189\pi$
$798$		−	2.81009i		−	0.0994762i
$799$	−17.0631	−	9.85141i	−0.603651	−	0.348518i
$800$	23.2757	+	13.4382i	0.822920	+	0.475113i
$801$			15.6776i			0.553941i
$802$	4.82423	−	8.35581i	0.170349	−	0.295054i
$803$	−2.41060	−	4.17527i	−0.0850681	−	0.147342i
$804$	−14.6555	+	8.46135i	−0.516859	+	0.298409i
$805$	5.13510			0.180988
$806$	−4.82481	−	4.68868i	−0.169947	−	0.165152i
$807$	−6.42846			−0.226292
$808$	12.4495	−	7.18770i	0.437970	−	0.252862i
$809$	26.0459	+	45.1128i	0.915724	+	1.58608i	0.805838	+	0.592136i	$0.201715\pi$
$809$	26.0459	+	45.1128i	0.915724	+	1.58608i	0.109886	+	0.993944i	$0.464952\pi$
$810$	−0.528371	+	0.915165i	−0.0185651	+	0.0321556i
$811$		−	16.9990i		−	0.596916i	−0.954423	−	0.298458i	$-0.903528\pi$
$811$		−	16.9990i		−	0.596916i	0.954423	−	0.298458i	$-0.0964722\pi$
$812$	−19.1614	−	11.0629i	−0.672434	−	0.388230i
$813$	−1.96001	−	1.13161i	−0.0687407	−	0.0396874i
$814$		−	2.84881i		−	0.0998507i
$815$	−19.5984	+	33.9455i	−0.686503	+	1.18906i
$816$	−5.25269	−	9.09793i	−0.183881	−	0.318491i
$817$	−57.6961	+	33.3109i	−2.01853	+	1.16540i
$818$	−5.03408			−0.176012
$819$	−3.39946	+	3.49816i	−0.118787	+	0.122236i
$820$	17.3479			0.605815
$821$	−18.2062	+	10.5114i	−0.635402	+	0.366849i	−0.782841	−	0.622222i	$-0.786230\pi$
$821$	−18.2062	+	10.5114i	−0.635402	+	0.366849i	0.147439	+	0.989071i	$0.452897\pi$
$822$	−2.35421	−	4.07761i	−0.0821126	−	0.142223i
$823$	−9.30277	+	16.1129i	−0.324274	+	0.561659i	−0.981365	−	0.192152i	$-0.938453\pi$
$823$	−9.30277	+	16.1129i	−0.324274	+	0.561659i	0.657091	+	0.753811i	$0.271787\pi$
$824$		−	18.9435i		−	0.659928i
$825$	7.04829	+	4.06933i	0.245390	+	0.141676i
$826$	−0.644861	−	0.372311i	−0.0224376	−	0.0129543i
$827$			20.6881i			0.719396i	0.933069	+	0.359698i	$0.117120\pi$
$827$			20.6881i			0.719396i	−0.933069	+	0.359698i	$0.882880\pi$
$828$	−1.00266	+	1.73667i	−0.0348450	+	0.0603533i
$829$	−21.2223	−	36.7582i	−0.737082	−	1.27666i	−0.953804	−	0.300430i	$-0.902870\pi$
$829$	−21.2223	−	36.7582i	−0.737082	−	1.27666i	0.216722	−	0.976233i	$-0.430464\pi$
$830$	−2.44322	+	1.41059i	−0.0848053	+	0.0489624i
$831$	21.8111			0.756618
$832$	−20.9242	+	5.92875i	−0.725415	+	0.205543i
$833$	15.5293			0.538058
$834$	−1.75420	+	1.01279i	−0.0607428	+	0.0350699i
$835$	24.1595	+	41.8454i	0.836073	+	1.44812i
$836$	6.82197	−	11.8160i	0.235943	−	0.408665i
$837$			6.40036i			0.221229i
$838$	3.56196	+	2.05650i	0.123046	+	0.0710405i
$839$	−23.6975	−	13.6817i	−0.818127	−	0.472346i	0.0316430	−	0.999499i	$-0.489926\pi$
$839$	−23.6975	−	13.6817i	−0.818127	−	0.472346i	−0.849770	+	0.527153i	$0.823259\pi$
$840$			5.59704i			0.193116i
$841$	−21.9677	+	38.0493i	−0.757508	+	1.31204i
$842$	−0.243889	−	0.422429i	−0.00840498	−	0.0145579i
$843$	−6.15123	+	3.55141i	−0.211860	+	0.122317i
$844$	22.4607			0.773129
$845$	−24.7187	−	40.1176i	−0.850351	−	1.38009i
$846$	−1.91222			−0.0657435
$847$	−1.17162	+	0.676437i	−0.0402575	+	0.0232427i
$848$	2.95776	+	5.12299i	0.101570	+	0.175924i
$849$	−1.18047	+	2.04463i	−0.0405135	+	0.0701715i
$850$		−	7.12739i		−	0.244467i
$851$	−8.86169	−	5.11630i	−0.303775	−	0.175384i
$852$	23.0490	+	13.3073i	0.789646	+	0.455902i
$853$		−	7.41283i		−	0.253811i	−0.991915	−	0.126905i	$-0.959496\pi$
$853$		−	7.41283i		−	0.253811i	0.991915	−	0.126905i	$-0.0405044\pi$
$854$	1.20055	−	2.07941i	0.0410819	−	0.0711559i
$855$	−12.9127	−	22.3654i	−0.441603	−	0.764880i
$856$	0.0136166	−	0.00786153i	0.000465404	−	0.000268701i
$857$	45.2655			1.54624			0.773121	−	0.634259i	$-0.218695\pi$
$857$	45.2655			1.54624			0.773121	+	0.634259i	$0.218695\pi$
$858$	1.01134	−	0.286557i	0.0345265	−	0.00978290i
$859$	18.4545			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$859$	18.4545			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$860$	56.2112	−	32.4535i	1.91679	−	1.10666i
$861$	1.69055	+	2.92812i	0.0576139	+	0.0997902i
$862$	3.48279	−	6.03236i	0.118624	−	0.205463i
$863$		−	24.9328i		−	0.848724i	−0.905493	−	0.424362i	$-0.860498\pi$
$863$		−	24.9328i		−	0.848724i	0.905493	−	0.424362i	$-0.139502\pi$
$864$	−2.85989	−	1.65116i	−0.0972954	−	0.0561735i
$865$	44.7265	+	25.8229i	1.52075	+	0.878004i
$866$			4.64386i			0.157805i
$867$	3.98833	−	6.90798i	0.135451	−	0.234607i
$868$	8.29091	+	14.3603i	0.281412	+	0.487419i
$869$	6.21265	−	3.58687i	0.210750	−	0.121676i
$870$	9.02482			0.305970
$871$	22.2051	−	22.8498i	0.752390	−	0.774235i
$872$	19.4892			0.659986
$873$	−3.66560	+	2.11634i	−0.124062	+	0.0716272i
$874$	1.08755	+	1.88369i	0.0367869	+	0.0637167i
$875$	7.69570	−	13.3293i	0.260162	−	0.450614i
$876$		−	9.23261i		−	0.311941i
$877$	−35.0515	−	20.2370i	−1.18360	−	0.683354i	−0.226759	−	0.973951i	$-0.572813\pi$
$877$	−35.0515	−	20.2370i	−1.18360	−	0.683354i	−0.956846	+	0.290596i	$0.906146\pi$
$878$	−6.48241	−	3.74262i	−0.218771	−	0.126307i
$879$			6.81218i			0.229769i
$880$	−6.33831	+	10.9783i	−0.213665	+	0.370078i
$881$	−19.6371	−	34.0125i	−0.661592	−	1.14591i	−0.980197	−	0.198023i	$-0.936548\pi$
$881$	−19.6371	−	34.0125i	−0.661592	−	1.14591i	0.318605	−	0.947887i	$-0.396786\pi$
$882$	1.30524	−	0.753583i	0.0439499	−	0.0253745i
$883$	56.5727			1.90382			0.951912	−	0.306371i	$-0.0991147\pi$
$883$	56.5727			1.90382			0.951912	+	0.306371i	$0.0991147\pi$
$884$	14.8743	+	14.4546i	0.500277	+	0.486162i
$885$	−6.84322			−0.230032
$886$	−2.59215	+	1.49658i	−0.0870849	+	0.0502785i
$887$	3.51799	+	6.09333i	0.118122	+	0.204594i	0.919024	−	0.394202i	$-0.128979\pi$
$887$	3.51799	+	6.09333i	0.118122	+	0.204594i	−0.800901	+	0.598797i	$0.795646\pi$
$888$	5.57655	−	9.65888i	0.187137	−	0.324131i
$889$		−	0.233031i		−	0.00781561i
$890$	−14.3476	−	8.28359i	−0.480932	−	0.277666i
$891$	−0.866025	−	0.500000i	−0.0290129	−	0.0167506i
$892$		−	32.3333i		−	1.08260i
$893$	23.3660	−	40.4711i	0.781913	−	1.35431i
$894$	1.84353	+	3.19309i	0.0616568	+	0.106793i
$895$	51.2355	−	29.5808i	1.71261	−	0.988777i
$896$	−11.3142			−0.377982
$897$	0.924920	−	3.66057i	0.0308822	−	0.122223i
$898$	2.87843			0.0960544
$899$	47.3374	−	27.3303i	1.57879	−	0.911515i
$900$	7.79280	+	13.4975i	0.259760	+	0.449917i
$901$	2.54050	−	4.40027i	0.0846362	−	0.146594i
$902$		−	0.728609i		−	0.0242600i
$903$	10.9556	+	6.32519i	0.364578	+	0.210489i
$904$	12.4828	+	7.20695i	0.415172	+	0.239700i
$905$			25.9080i			0.861212i
$906$	0.102879	−	0.178192i	0.00341793	−	0.00592003i
$907$	18.4641	+	31.9808i	0.613091	+	1.06190i	0.990716	+	0.135946i	$0.0434074\pi$
$907$	18.4641	+	31.9808i	0.613091	+	1.06190i	−0.377625	+	0.925959i	$0.623259\pi$
$908$	−34.5435	+	19.9437i	−1.14637	+	0.661855i
$909$	12.5949			0.417746
$910$	−1.40522	−	4.95940i	−0.0465826	−	0.164402i
$911$	−33.9405			−1.12450			−0.562249	−	0.826968i	$-0.690064\pi$
$911$	−33.9405			−1.12450			−0.562249	+	0.826968i	$0.690064\pi$
$912$	21.5789	−	12.4586i	0.714548	−	0.412544i
$913$	−1.33485	−	2.31203i	−0.0441771	−	0.0765170i
$914$	0.0599122	−	0.103771i	0.00198172	−	0.00343244i
$915$		−	22.0665i		−	0.729497i
$916$	14.6023	+	8.43065i	0.482474	+	0.278557i
$917$	−7.84666	−	4.53027i	−0.259120	−	0.149603i
$918$			0.875744i			0.0289039i
$919$	−2.98928	+	5.17758i	−0.0986071	+	0.170793i	−0.911108	−	0.412167i	$-0.864772\pi$
$919$	−2.98928	+	5.17758i	−0.0986071	+	0.170793i	0.812501	+	0.582960i	$0.198105\pi$
$920$	−2.16614	−	3.75187i	−0.0714156	−	0.123695i
$921$	18.6252	−	10.7532i	0.613720	−	0.354331i
$922$	10.8026			0.355766
$923$	−48.5830	−	12.2755i	−1.59913	−	0.404054i
$924$	−2.59076			−0.0852298
$925$	−68.8738	+	39.7643i	−2.26456	+	1.30744i
$926$	3.66699	+	6.35141i	0.120505	+	0.208720i
$927$	8.29860	−	14.3736i	0.272562	−	0.472091i
$928$			28.2025i			0.925794i
$929$	23.3925	+	13.5057i	0.767484	+	0.443107i	0.831976	−	0.554811i	$-0.187209\pi$
$929$	23.3925	+	13.5057i	0.767484	+	0.443107i	−0.0644924	+	0.997918i	$0.520543\pi$
$930$	−5.85739	−	3.38176i	−0.192071	−	0.110892i
$931$			36.8331i			1.20715i
$932$	10.7552	−	18.6285i	0.352297	−	0.610196i
$933$	−8.57601	−	14.8541i	−0.280766	−	0.486301i
$934$	−6.52300	+	3.76606i	−0.213439	+	0.123229i
$935$	10.8883			0.356085
$936$	3.98987	+	1.00812i	0.130413	+	0.0329516i
$937$	10.5115			0.343394			0.171697	−	0.985150i	$-0.445075\pi$
$937$	10.5115			0.343394			0.171697	+	0.985150i	$0.445075\pi$
$938$	3.01843	−	1.74269i	0.0985552	−	0.0569008i
$939$	−3.29848	−	5.71313i	−0.107642	−	0.186441i
$940$	−22.7646	+	39.4295i	−0.742500	+	1.28605i
$941$		−	37.9757i		−	1.23797i	−0.785402	−	0.618986i	$-0.787544\pi$
$941$		−	37.9757i		−	1.23797i	0.785402	−	0.618986i	$-0.212456\pi$
$942$	4.15463	+	2.39868i	0.135365	+	0.0781531i
$943$	−2.26646	−	1.30854i	−0.0738060	−	0.0426119i
$944$		−	6.60257i		−	0.214895i
$945$	−2.45190	+	4.24682i	−0.0797604	+	0.138149i
$946$	−1.36304	−	2.36086i	−0.0443163	−	0.0767582i
$947$	−5.43433	+	3.13751i	−0.176592	+	0.101955i	−0.585691	−	0.810535i	$-0.699177\pi$
$947$	−5.43433	+	3.13751i	−0.176592	+	0.101955i	0.409098	+	0.912490i	$0.365843\pi$
$948$	13.7378			0.446182
$949$	4.73884	+	16.7246i	0.153829	+	0.542905i
$950$	16.9050			0.548472
$951$	−26.8701	+	15.5134i	−0.871321	+	0.503058i
$952$	2.31919	+	4.01696i	0.0751655	+	0.130190i
$953$	−10.1668	+	17.6095i	−0.329336	+	0.570427i	−0.982380	−	0.186893i	$-0.940158\pi$
$953$	−10.1668	+	17.6095i	−0.329336	+	0.570427i	0.653044	+	0.757320i	$0.273492\pi$
$954$		−	0.493126i		−	0.0159656i
$955$	−12.7227	−	7.34547i	−0.411698	−	0.237694i
$956$	−24.4311	−	14.1053i	−0.790159	−	0.456199i
$957$			8.54023i			0.276066i
$958$	2.02143	−	3.50123i	0.0653096	−	0.113120i
$959$	−10.9247	−	18.9221i	−0.352777	−	0.611028i
$960$	−18.9344	+	10.9318i	−0.611105	+	0.352822i
$961$	−9.96459			−0.321438
$962$	−2.51624	+	9.95856i	−0.0811268	+	0.321077i
$963$	0.0137756			0.000443913
$964$	4.28032	−	2.47124i	0.137860	−	0.0795934i
$965$	36.4845	+	63.1930i	1.17448	+	2.03426i
$966$	0.206508	−	0.357682i	0.00664428	−	0.0115082i
$967$		−	22.4521i		−	0.722012i	−0.932563	−	0.361006i	$-0.882433\pi$
$967$		−	22.4521i		−	0.722012i	0.932563	−	0.361006i	$-0.117567\pi$
$968$	0.988454	+	0.570684i	0.0317701	+	0.0183425i
$969$	−18.5346	−	10.7010i	−0.595419	−	0.343765i
$970$		−	4.47284i		−	0.143614i
$971$	−20.9931	+	36.3611i	−0.673701	+	1.16688i	0.303146	+	0.952944i	$0.401963\pi$
$971$	−20.9931	+	36.3611i	−0.673701	+	1.16688i	−0.976847	+	0.213940i	$0.931370\pi$
$972$	−0.957503	−	1.65844i	−0.0307119	−	0.0531946i
$973$	−8.14034	+	4.69982i	−0.260967	+	0.150669i
$974$	−5.32367			−0.170581
$975$	−21.0444	−	20.4506i	−0.673959	−	0.654943i
$976$	21.2905			0.681494
$977$	−20.0684	+	11.5865i	−0.642045	+	0.370685i	−0.785402	−	0.618986i	$-0.787544\pi$
$977$	−20.0684	+	11.5865i	−0.642045	+	0.370685i	0.143357	+	0.989671i	$0.454210\pi$
$978$	1.57630	+	2.73023i	0.0504045	+	0.0873032i
$979$	7.83880	−	13.5772i	0.250529	−	0.433929i
$980$		−	35.8851i		−	1.14631i
$981$	14.7876	+	8.53763i	0.472132	+	0.272585i
$982$	−10.2693	−	5.92897i	−0.327706	−	0.189201i
$983$		−	52.2582i		−	1.66678i	−0.552688	−	0.833388i	$-0.686398\pi$
$983$		−	52.2582i		−	1.66678i	0.552688	−	0.833388i	$-0.313602\pi$
$984$	1.42625	−	2.47034i	0.0454673	−	0.0787517i
$985$	7.39266	+	12.8045i	0.235550	+	0.407984i
$986$	6.47705	−	3.73953i	0.206271	−	0.119091i
$987$	−8.87364			−0.282451
$988$	−34.2841	+	35.2795i	−1.09072	+	1.12239i
$989$	−9.79178			−0.311361
$990$	0.915165	−	0.528371i	0.0290859	−	0.0167927i
$991$	12.4245	+	21.5199i	0.394678	+	0.683602i	0.993060	−	0.117609i	$-0.0375229\pi$
$991$	12.4245	+	21.5199i	0.394678	+	0.683602i	−0.598382	+	0.801211i	$0.704190\pi$
$992$	10.5680	−	18.3043i	0.335534	−	0.581163i
$993$		−	20.2735i		−	0.643360i
$994$	−4.74715	−	2.74077i	−0.150570	−	0.0869318i
$995$	0.234780	+	0.135550i	0.00744303	+	0.00429724i
$996$		−	5.11249i		−	0.161996i
$997$	29.9505	−	51.8758i	0.948543	−	1.64292i	0.200046	−	0.979787i	$-0.435891\pi$
$997$	29.9505	−	51.8758i	0.948543	−	1.64292i	0.748497	−	0.663138i	$-0.230776\pi$
$998$	0.277696	+	0.480984i	0.00879033	+	0.0152253i
$999$	8.46254	−	4.88585i	0.267743	−	0.154581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.b.166.8	✓	28
13.2	odd	12		5577.2.a.bf.1.9		14
13.4	even	6	inner	429.2.s.b.199.8	yes	28
13.11	odd	12		5577.2.a.bg.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.8	✓	28	1.1	even	1	trivial
429.2.s.b.199.8	yes	28	13.4	even	6	inner
5577.2.a.bf.1.9		14	13.2	odd	12
5577.2.a.bg.1.6		14	13.11	odd	12

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.252478 - 0.145768i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.957503 + 1.65844i) q^{4} -3.62473i q^{5} +(-0.252478 - 0.145768i) q^{6} +(-1.17162 - 0.676437i) q^{7} +1.14137i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.252478 - 0.145768i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.957503 + 1.65844i) q^{4} -3.62473i q^{5} +(-0.252478 - 0.145768i) q^{6} +(-1.17162 - 0.676437i) q^{7} +1.14137i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.528371 - 0.915165i) q^{10} +(0.866025 - 0.500000i) q^{11} +1.91501 q^{12} +(-3.46899 + 0.982920i) q^{13} -0.394413 q^{14} +(-3.13911 + 1.81236i) q^{15} +(-1.74863 - 3.02872i) q^{16} +(-1.50194 + 2.60144i) q^{17} +0.291537i q^{18} +(-6.17022 - 3.56238i) q^{19} +(6.01141 + 3.47069i) q^{20} +1.35287i q^{21} +(0.145768 - 0.252478i) q^{22} +(-0.523583 - 0.906872i) q^{23} +(0.988454 - 0.570684i) q^{24} -8.13867 q^{25} +(-0.732565 + 0.753834i) q^{26} +1.00000 q^{27} +(2.24367 - 1.29538i) q^{28} +(-4.27011 - 7.39605i) q^{29} +(-0.528371 + 0.915165i) q^{30} +6.40036i q^{31} +(-2.85989 - 1.65116i) q^{32} +(-0.866025 - 0.500000i) q^{33} +0.875744i q^{34} +(-2.45190 + 4.24682i) q^{35} +(-0.957503 - 1.65844i) q^{36} +(8.46254 - 4.88585i) q^{37} -2.07713 q^{38} +(2.58573 + 2.51277i) q^{39} +4.13715 q^{40} +(2.16437 - 1.24960i) q^{41} +(0.197206 + 0.341571i) q^{42} +(4.67537 - 8.09798i) q^{43} +1.91501i q^{44} +(3.13911 + 1.81236i) q^{45} +(-0.264387 - 0.152644i) q^{46} +6.55910i q^{47} +(-1.74863 + 3.02872i) q^{48} +(-2.58487 - 4.47712i) q^{49} +(-2.05484 + 1.18636i) q^{50} +3.00389 q^{51} +(1.69145 - 6.69427i) q^{52} -1.69147 q^{53} +(0.252478 - 0.145768i) q^{54} +(-1.81236 - 3.13911i) q^{55} +(0.772064 - 1.33725i) q^{56} +7.12475i q^{57} +(-2.15622 - 1.24489i) q^{58} +(1.63499 + 0.943963i) q^{59} -6.94138i q^{60} +(-3.04389 + 5.27217i) q^{61} +(0.932970 + 1.61595i) q^{62} +(1.17162 - 0.676437i) q^{63} +6.03178 q^{64} +(3.56282 + 12.5741i) q^{65} -0.291537 q^{66} +(-7.65297 + 4.41845i) q^{67} +(-2.87623 - 4.98178i) q^{68} +(-0.523583 + 0.906872i) q^{69} +1.42964i q^{70} +(12.0360 + 6.94898i) q^{71} +(-0.988454 - 0.570684i) q^{72} -4.82119i q^{73} +(1.42440 - 2.46714i) q^{74} +(4.06933 + 7.04829i) q^{75} +(11.8160 - 6.82197i) q^{76} -1.35287 q^{77} +(1.01912 + 0.257503i) q^{78} +7.17375 q^{79} +(-10.9783 + 6.33831i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.364304 - 0.630994i) q^{82} -2.66970i q^{83} +(-2.24367 - 1.29538i) q^{84} +(9.42953 + 5.44414i) q^{85} -2.72609i q^{86} +(-4.27011 + 7.39605i) q^{87} +(0.570684 + 0.988454i) q^{88} +(13.5772 - 7.83880i) q^{89} +1.05674 q^{90} +(4.72923 + 1.19494i) q^{91} +2.00533 q^{92} +(5.54287 - 3.20018i) q^{93} +(0.956110 + 1.65603i) q^{94} +(-12.9127 + 22.3654i) q^{95} +3.30232i q^{96} +(3.66560 + 2.11634i) q^{97} +(-1.30524 - 0.753583i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9}+O(q^{10}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9	\( 28 q - 14 q^{3} + 18 q^{4} - 14 q^{9} - 36 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - 22 q^{16} + 2 q^{17} + 12 q^{19} + 18 q^{20} - 6 q^{22} + 2 q^{23} - 40 q^{25} - 18 q^{26} + 28 q^{27} - 18 q^{28} - 30 q^{32} + 2 q^{35} + 18 q^{36} + 20 q^{38} + 6 q^{39} + 20 q^{40} + 18 q^{41} + 2 q^{42} - 2 q^{43} - 6 q^{45} + 48 q^{46} - 22 q^{48} + 10 q^{49} + 24 q^{50} - 4 q^{51} - 28 q^{52} + 16 q^{53} - 12 q^{55} - 10 q^{56} - 48 q^{58} - 12 q^{59} - 4 q^{61} - 6 q^{62} - 32 q^{64} + 6 q^{65} + 12 q^{66} + 12 q^{67} - 22 q^{68} + 2 q^{69} - 18 q^{71} + 48 q^{74} + 20 q^{75} + 96 q^{76} - 24 q^{77} + 6 q^{78} - 48 q^{79} + 66 q^{80} - 14 q^{81} + 46 q^{82} + 18 q^{84} - 66 q^{85} + 12 q^{88} + 8 q^{91} + 72 q^{92} + 6 q^{93} + 50 q^{94} - 60 q^{95} - 36 q^{97} + 18 q^{98}+O(q^{100}) \) 28 * q - 14 * q^3 + 18 * q^4 - 14 * q^9 - 36 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - 22 * q^16 + 2 * q^17 + 12 * q^19 + 18 * q^20 - 6 * q^22 + 2 * q^23 - 40 * q^25 - 18 * q^26 + 28 * q^27 - 18 * q^28 - 30 * q^32 + 2 * q^35 + 18 * q^36 + 20 * q^38 + 6 * q^39 + 20 * q^40 + 18 * q^41 + 2 * q^42 - 2 * q^43 - 6 * q^45 + 48 * q^46 - 22 * q^48 + 10 * q^49 + 24 * q^50 - 4 * q^51 - 28 * q^52 + 16 * q^53 - 12 * q^55 - 10 * q^56 - 48 * q^58 - 12 * q^59 - 4 * q^61 - 6 * q^62 - 32 * q^64 + 6 * q^65 + 12 * q^66 + 12 * q^67 - 22 * q^68 + 2 * q^69 - 18 * q^71 + 48 * q^74 + 20 * q^75 + 96 * q^76 - 24 * q^77 + 6 * q^78 - 48 * q^79 + 66 * q^80 - 14 * q^81 + 46 * q^82 + 18 * q^84 - 66 * q^85 + 12 * q^88 + 8 * q^91 + 72 * q^92 + 6 * q^93 + 50 * q^94 - 60 * q^95 - 36 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more