LMFDB - Embedded newform 378.2.z.a.83.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.17
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.419652 + 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.95067 - 1.63681i) q^{5} +(-0.705083 + 1.58204i) q^{6} +(2.43278 + 1.04000i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.419652 + 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.95067 - 1.63681i) q^{5} +(-0.705083 + 1.58204i) q^{6} +(2.43278 + 1.04000i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +(2.20527 - 1.27321i) q^{10} +(3.38986 - 4.03988i) q^{11} +(-0.969090 + 1.43557i) q^{12} +(-4.61346 + 0.813477i) q^{13} +(2.21522 + 1.44665i) q^{14} +(1.93196 + 3.96488i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.45690 + 4.25548i) q^{17} +(-2.36264 - 1.84876i) q^{18} +(-3.75220 - 2.16633i) q^{19} +(2.39285 - 0.870927i) q^{20} +(-2.76858 + 3.65170i) q^{21} +(4.03988 - 3.38986i) q^{22} +(-2.80443 + 7.70512i) q^{23} +(-1.20365 + 1.24548i) q^{24} +(0.257739 - 1.46171i) q^{25} -4.68463 q^{26} +(3.48125 - 3.85757i) q^{27} +(1.93036 + 1.80934i) q^{28} +(-6.32009 - 1.11440i) q^{29} +(1.21411 + 4.24013i) q^{30} +(2.00923 - 5.52031i) q^{31} +(0.642788 + 0.766044i) q^{32} +(5.36622 + 7.39181i) q^{33} +(1.68062 + 4.61746i) q^{34} +(6.44783 - 1.95329i) q^{35} +(-2.00572 - 2.23094i) q^{36} +(0.448119 + 0.776165i) q^{37} +(-3.31901 - 2.78498i) q^{38} +(0.569046 - 8.09404i) q^{39} +(2.50773 - 0.442181i) q^{40} +(-0.918246 - 5.20763i) q^{41} +(-3.36063 + 3.11547i) q^{42} +(-3.13499 - 2.63057i) q^{43} +(4.56714 - 2.63684i) q^{44} +(-7.47352 + 1.58268i) q^{45} +(-4.09981 + 7.10107i) q^{46} +(-2.09624 + 0.762970i) q^{47} +(-1.40164 + 1.01755i) q^{48} +(4.83680 + 5.06018i) q^{49} +(0.507646 - 1.39475i) q^{50} +(-8.18213 + 2.34286i) q^{51} +(-4.61346 - 0.813477i) q^{52} +9.42246i q^{53} +(4.09823 - 3.19445i) q^{54} -13.4290i q^{55} +(1.58685 + 2.11706i) q^{56} +(5.21502 - 5.39625i) q^{57} +(-6.03056 - 2.19494i) q^{58} +(-0.881790 + 0.739910i) q^{59} +(0.459378 + 4.38654i) q^{60} +(-2.05855 - 5.65582i) q^{61} +(2.93730 - 5.08755i) q^{62} +(-4.97464 - 6.18490i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.66784 + 9.13817i) q^{65} +(4.00112 + 8.21135i) q^{66} +(-1.26064 - 7.14945i) q^{67} +(0.853272 + 4.83915i) q^{68} +(-11.7711 - 7.94616i) q^{69} +(6.68906 - 0.803958i) q^{70} +(7.78966 - 4.49736i) q^{71} +(-1.58785 - 2.54534i) q^{72} +(-7.53439 - 4.34998i) q^{73} +(0.306531 + 0.842188i) q^{74} +(2.34816 + 1.04653i) q^{75} +(-2.78498 - 3.31901i) q^{76} +(12.4482 - 6.30266i) q^{77} +(1.96592 - 7.87226i) q^{78} +(1.83651 - 10.4153i) q^{79} +2.54642 q^{80} +(5.02152 + 7.46889i) q^{81} -5.28797i q^{82} +(2.18909 - 12.4150i) q^{83} +(-3.85057 + 2.48457i) q^{84} +(11.7580 + 4.27956i) q^{85} +(-2.63057 - 3.13499i) q^{86} +(4.52493 - 10.1529i) q^{87} +(4.95564 - 1.80371i) q^{88} +(-4.96625 + 8.60180i) q^{89} +(-7.63481 + 0.260870i) q^{90} +(-12.0695 - 2.81899i) q^{91} +(-5.27061 + 6.28127i) q^{92} +(8.43339 + 5.69301i) q^{93} +(-2.19688 + 0.387370i) q^{94} +(-10.8652 + 1.91582i) q^{95} +(-1.55704 + 0.758696i) q^{96} +(-4.09086 + 4.87530i) q^{97} +(3.88462 + 5.82320i) q^{98} +(-14.6735 + 5.91565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.419652	+	1.68044i	−0.242286	+	0.970205i
$3$	−0.419652	+	1.68044i	−0.242286	+	0.970205i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.95067	−	1.63681i	0.872367	−	0.732003i	−0.0922283	−	0.995738i	$-0.529399\pi$
$5$	1.95067	−	1.63681i	0.872367	−	0.732003i	0.964595	+	0.263735i	$0.0849545\pi$
$6$	−0.705083	+	1.58204i	−0.287849	+	0.645866i
$7$	2.43278	+	1.04000i	0.919503	+	0.393083i
$7$	2.43278	+	1.04000i	0.919503	+	0.393083i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.64778	−	1.41040i	−0.882595	−	0.470135i
$10$	2.20527	−	1.27321i	0.697366	−	0.402624i
$11$	3.38986	−	4.03988i	1.02208	−	1.21807i	0.0463888	−	0.998923i	$-0.485229\pi$
$11$	3.38986	−	4.03988i	1.02208	−	1.21807i	0.975692	−	0.219145i	$-0.0703269\pi$
$12$	−0.969090	+	1.43557i	−0.279752	+	0.414414i
$13$	−4.61346	+	0.813477i	−1.27954	+	0.225618i	−0.771786	−	0.635882i	$-0.780636\pi$
$13$	−4.61346	+	0.813477i	−1.27954	+	0.225618i	−0.507757	+	0.861500i	$0.669525\pi$
$14$	2.21522	+	1.44665i	0.592043	+	0.386633i
$15$	1.93196	+	3.96488i	0.498830	+	1.02373i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	2.45690	+	4.25548i	0.595886	+	1.03210i	0.993421	+	0.114518i	$0.0365322\pi$
$17$	2.45690	+	4.25548i	0.595886	+	1.03210i	−0.397535	+	0.917587i	$0.630134\pi$
$18$	−2.36264	−	1.84876i	−0.556880	−	0.435757i
$19$	−3.75220	−	2.16633i	−0.860813	−	0.496991i	0.00347113	−	0.999994i	$-0.498895\pi$
$19$	−3.75220	−	2.16633i	−0.860813	−	0.496991i	−0.864285	+	0.503003i	$0.832228\pi$
$20$	2.39285	−	0.870927i	0.535058	−	0.194745i
$21$	−2.76858	+	3.65170i	−0.604154	+	0.796867i
$22$	4.03988	−	3.38986i	0.861305	−	0.722720i
$23$	−2.80443	+	7.70512i	−0.584765	+	1.60663i	0.195172	+	0.980769i	$0.437474\pi$
$23$	−2.80443	+	7.70512i	−0.584765	+	1.60663i	−0.779937	+	0.625859i	$0.784749\pi$
$24$	−1.20365	+	1.24548i	−0.245694	+	0.254233i
$25$	0.257739	−	1.46171i	0.0515478	−	0.292342i
$26$	−4.68463			−0.918731
$27$	3.48125	−	3.85757i	0.669968	−	0.742390i
$28$	1.93036	+	1.80934i	0.364804	+	0.341933i
$29$	−6.32009	−	1.11440i	−1.17361	−	0.206939i	−0.447351	−	0.894359i	$-0.647632\pi$
$29$	−6.32009	−	1.11440i	−1.17361	−	0.206939i	−0.726261	+	0.687419i	$0.758743\pi$
$30$	1.21411	+	4.24013i	0.221666	+	0.774138i
$31$	2.00923	−	5.52031i	0.360868	−	0.991477i	−0.617855	−	0.786292i	$-0.711998\pi$
$31$	2.00923	−	5.52031i	0.360868	−	0.991477i	0.978723	−	0.205185i	$-0.0657796\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	5.36622	+	7.39181i	0.934140	+	1.28675i
$34$	1.68062	+	4.61746i	0.288224	+	0.791888i
$35$	6.44783	−	1.95329i	1.08988	−	0.330166i
$36$	−2.00572	−	2.23094i	−0.334286	−	0.371824i
$37$	0.448119	+	0.776165i	0.0736703	+	0.127601i	0.900507	−	0.434841i	$-0.143195\pi$
$37$	0.448119	+	0.776165i	0.0736703	+	0.127601i	−0.826837	+	0.562442i	$0.809862\pi$
$38$	−3.31901	−	2.78498i	−0.538415	−	0.451784i
$39$	0.569046	−	8.09404i	0.0911203	−	1.29608i
$40$	2.50773	−	0.442181i	0.396508	−	0.0699150i
$41$	−0.918246	−	5.20763i	−0.143406	−	0.813296i	−0.968633	−	0.248495i	$-0.920064\pi$
$41$	−0.918246	−	5.20763i	−0.143406	−	0.813296i	0.825227	−	0.564801i	$-0.191047\pi$
$42$	−3.36063	+	3.11547i	−0.518557	+	0.480727i
$43$	−3.13499	−	2.63057i	−0.478082	−	0.401158i	0.371650	−	0.928373i	$-0.378792\pi$
$43$	−3.13499	−	2.63057i	−0.478082	−	0.401158i	−0.849732	+	0.527214i	$0.823236\pi$
$44$	4.56714	−	2.63684i	0.688523	−	0.397519i
$45$	−7.47352	+	1.58268i	−1.11409	+	0.235932i
$46$	−4.09981	+	7.10107i	−0.604483	+	1.04700i
$47$	−2.09624	+	0.762970i	−0.305768	+	0.111291i	−0.490347	−	0.871527i	$-0.663130\pi$
$47$	−2.09624	+	0.762970i	−0.305768	+	0.111291i	0.184579	+	0.982818i	$0.440908\pi$
$48$	−1.40164	+	1.01755i	−0.202309	+	0.146870i
$49$	4.83680	+	5.06018i	0.690971	+	0.722883i
$50$	0.507646	−	1.39475i	0.0717920	−	0.197247i
$51$	−8.18213	+	2.34286i	−1.14573	+	0.328066i
$52$	−4.61346	−	0.813477i	−0.639772	−	0.112809i
$53$			9.42246i			1.29427i	0.762373	+	0.647137i	$0.224034\pi$
$53$			9.42246i			1.29427i	−0.762373	+	0.647137i	$0.775966\pi$
$54$	4.09823	−	3.19445i	0.557698	−	0.434710i
$55$		−	13.4290i		−	1.81077i
$56$	1.58685	+	2.11706i	0.212051	+	0.282903i
$57$	5.21502	−	5.39625i	0.690746	−	0.714751i
$58$	−6.03056	−	2.19494i	−0.791851	−	0.288210i
$59$	−0.881790	+	0.739910i	−0.114799	+	0.0963281i	−0.698380	−	0.715727i	$-0.746096\pi$
$59$	−0.881790	+	0.739910i	−0.114799	+	0.0963281i	0.583581	+	0.812055i	$0.301651\pi$
$60$	0.459378	+	4.38654i	0.0593054	+	0.566300i
$61$	−2.05855	−	5.65582i	−0.263570	−	0.724153i	−0.998920	−	0.0464655i	$-0.985204\pi$
$61$	−2.05855	−	5.65582i	−0.263570	−	0.724153i	0.735350	−	0.677688i	$-0.237018\pi$
$62$	2.93730	−	5.08755i	0.373037	−	0.646119i
$63$	−4.97464	−	6.18490i	−0.626746	−	0.779224i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−7.66784	+	9.13817i	−0.951078	+	1.13345i
$66$	4.00112	+	8.21135i	0.492504	+	1.01075i
$67$	−1.26064	−	7.14945i	−0.154012	−	0.873444i	−0.959684	−	0.281082i	$-0.909307\pi$
$67$	−1.26064	−	7.14945i	−0.154012	−	0.873444i	0.805672	−	0.592362i	$-0.201804\pi$
$68$	0.853272	+	4.83915i	0.103474	+	0.586833i
$69$	−11.7711	−	7.94616i	−1.41708	−	0.956605i
$70$	6.68906	−	0.803958i	0.799495	−	0.0960913i
$71$	7.78966	−	4.49736i	0.924463	−	0.533739i	0.0394068	−	0.999223i	$-0.487453\pi$
$71$	7.78966	−	4.49736i	0.924463	−	0.533739i	0.885056	+	0.465484i	$0.154120\pi$
$72$	−1.58785	−	2.54534i	−0.187129	−	0.299971i
$73$	−7.53439	−	4.34998i	−0.881834	−	0.509127i	−0.0105711	−	0.999944i	$-0.503365\pi$
$73$	−7.53439	−	4.34998i	−0.881834	−	0.509127i	−0.871263	+	0.490817i	$0.836698\pi$
$74$	0.306531	+	0.842188i	0.0356335	+	0.0979024i
$75$	2.34816	+	1.04653i	0.271142	+	0.120842i
$76$	−2.78498	−	3.31901i	−0.319460	−	0.380717i
$77$	12.4482	−	6.30266i	1.41861	−	0.718255i
$78$	1.96592	−	7.87226i	0.222596	−	0.891357i
$79$	1.83651	−	10.4153i	0.206623	−	1.17182i	−0.688242	−	0.725481i	$-0.741617\pi$
$79$	1.83651	−	10.4153i	0.206623	−	1.17182i	0.894865	−	0.446337i	$-0.147272\pi$
$80$	2.54642			0.284698
$81$	5.02152	+	7.46889i	0.557946	+	0.829877i
$82$		−	5.28797i		−	0.583959i
$83$	2.18909	−	12.4150i	0.240284	−	1.36272i	−0.590910	−	0.806737i	$-0.701231\pi$
$83$	2.18909	−	12.4150i	0.240284	−	1.36272i	0.831194	−	0.555982i	$-0.187658\pi$
$84$	−3.85057	+	2.48457i	−0.420132	+	0.271089i
$85$	11.7580	+	4.27956i	1.27533	+	0.464184i
$86$	−2.63057	−	3.13499i	−0.283662	−	0.338055i
$87$	4.52493	−	10.1529i	0.485124	−	1.08850i
$88$	4.95564	−	1.80371i	0.528273	−	0.192276i
$89$	−4.96625	+	8.60180i	−0.526422	+	0.911789i	0.473104	+	0.881006i	$0.343133\pi$
$89$	−4.96625	+	8.60180i	−0.526422	+	0.911789i	−0.999526	+	0.0307827i	$0.990200\pi$
$90$	−7.63481	+	0.260870i	−0.804779	+	0.0274981i
$91$	−12.0695	−	2.81899i	−1.26523	−	0.295511i
$92$	−5.27061	+	6.28127i	−0.549499	+	0.654867i
$93$	8.43339	+	5.69301i	0.874502	+	0.590337i
$94$	−2.19688	+	0.387370i	−0.226591	+	0.0399542i
$95$	−10.8652	+	1.91582i	−1.11474	+	0.196559i
$96$	−1.55704	+	0.758696i	−0.158915	+	0.0774341i
$97$	−4.09086	+	4.87530i	−0.415364	+	0.495012i	−0.932641	−	0.360806i	$-0.882502\pi$
$97$	−4.09086	+	4.87530i	−0.415364	+	0.495012i	0.517276	+	0.855818i	$0.326946\pi$
$98$	3.88462	+	5.82320i	0.392406	+	0.588232i
$99$	−14.6735	+	5.91565i	−1.47474	+	0.594545i
$100$	0.742129	−	1.28541i	0.0742129	−	0.128541i
$101$	10.0462	−	3.65652i	0.999636	−	0.363838i	0.210192	−	0.977660i	$-0.432591\pi$
$101$	10.0462	−	3.65652i	0.999636	−	0.363838i	0.789444	+	0.613823i	$0.210369\pi$
$102$	−8.46466	+	0.886457i	−0.838126	+	0.0877723i
$103$	1.54935	+	1.84644i	0.152662	+	0.181935i	0.836955	−	0.547272i	$-0.184334\pi$
$103$	1.54935	+	1.84644i	0.152662	+	0.181935i	−0.684293	+	0.729207i	$0.739889\pi$
$104$	−4.40211	−	1.60224i	−0.431662	−	0.157112i
$105$	0.576541	+	11.6549i	0.0562647	+	1.13740i
$106$	−1.63619	+	9.27931i	−0.158921	+	0.901287i
$107$			8.64382i			0.835630i	0.908532	+	0.417815i	$0.137204\pi$
$107$			8.64382i			0.835630i	−0.908532	+	0.417815i	$0.862796\pi$
$108$	4.59068	−	2.43427i	0.441738	−	0.234238i
$109$	−10.0711			−0.964636			−0.482318	−	0.875996i	$-0.660205\pi$
$109$	−10.0711			−0.964636			−0.482318	+	0.875996i	$0.660205\pi$
$110$	2.33192	−	13.2250i	0.222340	−	1.26095i
$111$	−1.49236	+	0.427319i	−0.141648	+	0.0405593i
$112$	1.19511	+	2.36045i	0.112928	+	0.223041i
$113$	−0.126205	−	0.150405i	−0.0118724	−	0.0141489i	0.760076	−	0.649835i	$-0.225162\pi$
$113$	−0.126205	−	0.150405i	−0.0118724	−	0.0141489i	−0.771948	+	0.635686i	$0.780717\pi$
$114$	6.07284	−	4.40869i	0.568774	−	0.412912i
$115$	7.14127	+	19.6205i	0.665926	+	1.82962i
$116$	−5.55779	−	3.20879i	−0.516028	−	0.297929i
$117$	13.3628	+	4.35293i	1.23539	+	0.402429i
$118$	−0.996878	+	0.575548i	−0.0917701	+	0.0529835i
$119$	1.55139	+	12.9078i	0.142215	+	1.18326i
$120$	−0.309316	+	4.39967i	−0.0282366	+	0.401633i
$121$	−2.91933	−	16.5563i	−0.265394	−	1.50512i
$122$	−1.04515	−	5.92736i	−0.0946237	−	0.536638i
$123$	9.13648	+	0.642334i	0.823809	+	0.0579173i
$124$	3.77611	−	4.50020i	0.339105	−	0.404130i
$125$	4.47628	+	7.75314i	0.400370	+	0.693462i
$126$	−3.82507	−	6.95477i	−0.340764	−	0.619580i
$127$	−9.42794	+	16.3297i	−0.836595	+	1.44902i	0.0561306	+	0.998423i	$0.482124\pi$
$127$	−9.42794	+	16.3297i	−0.836595	+	1.44902i	−0.892725	+	0.450601i	$0.851210\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	5.73614	−	4.16425i	0.505039	−	0.366642i
$130$	−9.13817	+	7.66784i	−0.801471	+	0.672514i
$131$	8.02081	+	2.91934i	0.700781	+	0.255064i	0.667744	−	0.744391i	$-0.267260\pi$
$131$	8.02081	+	2.91934i	0.700781	+	0.255064i	0.0330369	+	0.999454i	$0.489482\pi$
$132$	2.51445	+	8.78139i	0.218855	+	0.764322i
$133$	−6.87527	−	9.17249i	−0.596162	−	0.795356i
$134$		−	7.25974i		−	0.627146i
$135$	0.476679	−	13.2230i	0.0410260	−	1.13805i
$136$			4.91380i			0.421355i
$137$	−5.88182	−	1.03712i	−0.502518	−	0.0886075i	−0.0833577	−	0.996520i	$-0.526564\pi$
$137$	−5.88182	−	1.03712i	−0.502518	−	0.0886075i	−0.419160	+	0.907912i	$0.637676\pi$
$138$	−10.2125	−	9.86948i	−0.869342	−	0.840146i
$139$	0.558807	−	1.53531i	0.0473974	−	0.130223i	−0.913735	−	0.406310i	$-0.866815\pi$
$139$	0.558807	−	1.53531i	0.0473974	−	0.130223i	0.961133	+	0.276087i	$0.0890376\pi$
$140$	6.72704	+	0.369799i	0.568539	+	0.0312537i
$141$	−0.402435	−	3.84280i	−0.0338911	−	0.323622i
$142$	8.45228	−	3.07638i	0.709299	−	0.258164i
$143$	−12.3526	+	21.3954i	−1.03298	+	1.78917i
$144$	−1.12173	−	2.78240i	−0.0934775	−	0.231866i
$145$	−14.1525	+	8.17094i	−1.17530	+	0.678560i
$146$	−6.66456	−	5.59223i	−0.551563	−	0.462816i
$147$	−10.5331	+	6.00445i	−0.868757	+	0.495239i
$148$	0.155630	+	0.882622i	0.0127927	+	0.0725511i
$149$	20.7850	−	3.66496i	1.70278	−	0.300246i	0.764114	−	0.645081i	$-0.223176\pi$
$149$	20.7850	−	3.66496i	1.70278	−	0.300246i	0.938663	+	0.344835i	$0.112065\pi$
$150$	2.13076	+	1.43838i	0.173976	+	0.117443i
$151$	16.8405	+	14.1309i	1.37046	+	1.14995i	0.972594	+	0.232511i	$0.0746942\pi$
$151$	16.8405	+	14.1309i	1.37046	+	1.14995i	0.397868	+	0.917443i	$0.369750\pi$
$152$	−2.16633	−	3.75220i	−0.175713	−	0.304344i
$153$	−0.503398	−	14.7328i	−0.0406973	−	1.19108i
$154$	13.3536	−	4.04529i	1.07606	−	0.325979i
$155$	−5.11634	−	14.0570i	−0.410954	−	1.12909i
$156$	3.30305	−	7.41128i	0.264456	−	0.593377i
$157$	6.33840	+	7.55381i	0.505859	+	0.602860i	0.957177	−	0.289504i	$-0.0934903\pi$
$157$	6.33840	+	7.55381i	0.505859	+	0.602860i	−0.451318	+	0.892363i	$0.649046\pi$
$158$	3.61721	−	9.93821i	0.287770	−	0.790641i
$159$	−15.8339	−	3.95416i	−1.25571	−	0.313585i
$160$	2.50773	+	0.442181i	0.198254	+	0.0349575i
$161$	−14.8359	+	15.8282i	−1.16923	+	1.24744i
$162$	3.64827	+	8.22740i	0.286635	+	0.646406i
$163$	−6.19088			−0.484907			−0.242454	−	0.970163i	$-0.577952\pi$
$163$	−6.19088			−0.484907			−0.242454	+	0.970163i	$0.577952\pi$
$164$	0.918246	−	5.20763i	0.0717030	−	0.406648i
$165$	22.5667	+	5.63552i	1.75682	+	0.438725i
$166$	4.31167	−	11.8462i	0.334651	−	0.919445i
$167$	3.15479	−	2.64718i	0.244125	−	0.204845i	−0.512513	−	0.858680i	$-0.671285\pi$
$167$	3.15479	−	2.64718i	0.244125	−	0.204845i	0.756638	+	0.653835i	$0.226841\pi$
$168$	−4.22352	+	1.77818i	−0.325851	+	0.137189i
$169$	8.40625	−	3.05962i	0.646635	−	0.235356i
$170$	10.8362	+	6.25630i	0.831101	+	0.479836i
$171$	6.87961	+	11.0281i	0.526097	+	0.843340i
$172$	−2.04622	−	3.54416i	−0.156023	−	0.270240i
$173$	5.13237	+	4.30657i	0.390207	+	0.327423i	0.816694	−	0.577071i	$-0.195805\pi$
$173$	5.13237	+	4.30657i	0.390207	+	0.327423i	−0.426487	+	0.904494i	$0.640249\pi$
$174$	6.21922	−	9.21290i	0.471478	−	0.698428i
$175$	2.14720	−	3.28796i	0.162313	−	0.248547i
$176$	5.19357	−	0.915766i	0.391480	−	0.0690284i
$177$	−0.873332	−	1.79230i	−0.0656436	−	0.134718i
$178$	−6.38449	+	7.60874i	−0.478538	+	0.570299i
$179$	−0.794596	+	0.458760i	−0.0593909	+	0.0342893i	−0.529401	−	0.848371i	$-0.677583\pi$
$179$	−0.794596	+	0.458760i	−0.0593909	+	0.0342893i	0.470011	+	0.882661i	$0.344250\pi$
$180$	−7.56412	−	1.06886i	−0.563796	−	0.0796684i
$181$	−6.84551	−	3.95226i	−0.508823	−	0.293769i	0.223527	−	0.974698i	$-0.428243\pi$
$181$	−6.84551	−	3.95226i	−0.508823	−	0.293769i	−0.732350	+	0.680929i	$0.761576\pi$
$182$	−11.3967	−	4.87202i	−0.844776	−	0.361138i
$183$	10.3682	−	1.08580i	0.766437	−	0.0802646i
$184$	−6.28127	+	5.27061i	−0.463061	+	0.388554i
$185$	2.14456	+	0.780558i	0.157672	+	0.0573877i
$186$	7.31669	+	7.07096i	0.536486	+	0.518468i
$187$	25.5201	+	4.49989i	1.86622	+	0.329065i
$188$	−2.23078			−0.162696
$189$	12.4810	−	5.76410i	0.907859	−	0.419277i
$190$	−11.0328			−0.800403
$191$	13.9436	+	2.45864i	1.00893	+	0.177901i	0.653598	−	0.756841i	$-0.273259\pi$
$191$	13.9436	+	2.45864i	1.00893	+	0.177901i	0.355327	+	0.934742i	$0.384370\pi$
$192$	−1.66513	+	0.476792i	−0.120171	+	0.0344095i
$193$	−6.23166	−	2.26814i	−0.448565	−	0.163264i	0.107853	−	0.994167i	$-0.465602\pi$
$193$	−6.23166	−	2.26814i	−0.448565	−	0.163264i	−0.556418	+	0.830903i	$0.687825\pi$
$194$	−4.87530	+	4.09086i	−0.350026	+	0.293707i
$195$	−12.1384	−	16.7202i	−0.869246	−	1.19736i
$196$	2.81442	+	6.40929i	0.201030	+	0.457807i
$197$	0.128455	+	0.0741633i	0.00915201	+	0.00528392i	0.504569	−	0.863371i	$-0.331651\pi$
$197$	0.128455	+	0.0741633i	0.00915201	+	0.00528392i	−0.495417	+	0.868655i	$0.664985\pi$
$198$	−15.4778	+	3.27775i	−1.09996	+	0.232940i
$199$	−1.74511	+	1.00754i	−0.123708	+	0.0714226i	−0.560577	−	0.828102i	$-0.689421\pi$
$199$	−1.74511	+	1.00754i	−0.123708	+	0.0714226i	0.436869	+	0.899525i	$0.356087\pi$
$200$	0.954063	−	1.13701i	0.0674625	−	0.0803986i
$201$	12.5433	+	0.881847i	0.884735	+	0.0622007i
$202$	10.5285	−	1.85647i	0.740785	−	0.130620i
$203$	−14.2164	−	9.28399i	−0.997794	−	0.651608i
$204$	−8.48999	−	0.596884i	−0.594419	−	0.0417902i
$205$	−10.3151	−	8.65539i	−0.720437	−	0.604519i
$206$	1.20518	+	2.08743i	0.0839687	+	0.145438i
$207$	18.2929	−	16.4461i	1.27144	−	1.14308i
$208$	−4.05701	−	2.34231i	−0.281303	−	0.162410i
$209$	−21.4711	+	7.81486i	−1.48519	+	0.540565i
$210$	−1.45607	+	11.5780i	−0.100479	+	0.798956i
$211$	−7.67430	+	6.43950i	−0.528320	+	0.443314i	−0.867521	−	0.497401i	$-0.834288\pi$
$211$	−7.67430	+	6.43950i	−0.528320	+	0.443314i	0.339201	+	0.940714i	$0.389843\pi$
$212$	−3.22267	+	8.85422i	−0.221334	+	0.608110i
$213$	4.28862	+	14.9774i	0.293851	+	1.02624i
$214$	−1.50098	+	8.51250i	−0.102605	+	0.581903i
$215$	−10.4211			−0.710712
$216$	4.94364	−	1.60013i	0.336372	−	0.108875i
$217$	10.6291	−	11.3401i	0.721552	−	0.769815i
$218$	−9.91809	−	1.74883i	−0.671738	−	0.118445i
$219$	10.4717	−	10.8356i	0.707614	−	0.732205i
$220$	4.59300	−	12.6192i	0.309660	−	0.850783i
$221$	−14.7965	−	17.6338i	−0.995323	−	1.18618i
$222$	−1.54389	+	0.161683i	−0.103619	+	0.0108514i
$223$	−6.12585	−	16.8306i	−0.410217	−	1.12706i	−0.957076	−	0.289837i	$-0.906399\pi$
$223$	−6.12585	−	16.8306i	−0.410217	−	1.12706i	0.546859	−	0.837225i	$-0.315823\pi$
$224$	0.767071	+	2.53211i	0.0512521	+	0.169184i
$225$	−2.74404	+	3.50677i	−0.182936	+	0.233785i
$226$	−0.0981700	−	0.170035i	−0.00653017	−	0.0113106i
$227$	3.31314	+	2.78006i	0.219901	+	0.184519i	0.746083	−	0.665853i	$-0.231932\pi$
$227$	3.31314	+	2.78006i	0.219901	+	0.184519i	−0.526182	+	0.850372i	$0.676377\pi$
$228$	6.74614	−	3.28718i	0.446774	−	0.217699i
$229$	−11.5039	+	2.02846i	−0.760202	+	0.134044i	−0.540294	−	0.841476i	$-0.681687\pi$
$229$	−11.5039	+	2.02846i	−0.760202	+	0.134044i	−0.219908	+	0.975521i	$0.570576\pi$
$230$	3.62572	+	20.5625i	0.239073	+	1.35585i
$231$	5.36733	+	23.5635i	0.353144	+	1.55036i
$232$	−4.91616	−	4.12515i	−0.322762	−	0.270829i
$233$	−5.83805	+	3.37060i	−0.382464	+	0.220816i	−0.678890	−	0.734240i	$-0.737539\pi$
$233$	−5.83805	+	3.37060i	−0.382464	+	0.220816i	0.296426	+	0.955056i	$0.404205\pi$
$234$	12.4039	+	6.60722i	0.810867	+	0.431928i
$235$	−2.84025	+	4.91945i	−0.185277	+	0.320910i
$236$	−1.08168	+	0.393698i	−0.0704111	+	0.0256275i
$237$	16.7317	+	7.45697i	1.08684	+	0.484382i
$238$	−0.713596	+	12.9811i	−0.0462556	+	0.841439i
$239$	6.92882	−	19.0368i	0.448188	−	1.23139i	−0.485796	−	0.874072i	$-0.661470\pi$
$239$	6.92882	−	19.0368i	0.448188	−	1.23139i	0.933984	−	0.357315i	$-0.116308\pi$
$240$	−1.06861	+	4.27912i	−0.0689786	+	0.276216i
$241$	1.77571	+	0.313105i	0.114383	+	0.0201689i	0.230547	−	0.973061i	$-0.425949\pi$
$241$	1.77571	+	0.313105i	0.114383	+	0.0201689i	−0.116163	+	0.993230i	$0.537060\pi$
$242$		−	16.8118i		−	1.08070i
$243$	−14.6583	+	5.30404i	−0.940333	+	0.340254i
$244$		−	6.01880i		−	0.385314i
$245$	17.7175	+	1.95384i	1.13193	+	0.124826i
$246$	8.88614	+	2.21911i	0.566559	+	0.141485i
$247$	19.0729	+	6.94196i	1.21358	+	0.441706i
$248$	4.50020	−	3.77611i	0.285763	−	0.239784i
$249$	19.9440	+	8.88862i	1.26390	+	0.563293i
$250$	3.06195	+	8.41265i	0.193655	+	0.532063i
$251$	2.51607	−	4.35797i	0.158813	−	0.275073i	−0.775628	−	0.631191i	$-0.782567\pi$
$251$	2.51607	−	4.35797i	0.158813	−	0.275073i	0.934441	+	0.356118i	$0.115900\pi$
$252$	−2.55928	−	7.51333i	−0.161219	−	0.473295i
$253$	21.6211	+	37.4488i	1.35931	+	2.35439i
$254$	−12.1203	+	14.4444i	−0.760497	+	0.906325i
$255$	−12.1258	+	17.9627i	−0.759349	+	1.12487i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	3.84339	+	21.7969i	0.239744	+	1.35966i	0.832389	+	0.554192i	$0.186973\pi$
$257$	3.84339	+	21.7969i	0.239744	+	1.35966i	−0.592645	+	0.805464i	$0.701916\pi$
$258$	6.37211	−	3.10492i	0.396710	−	0.193304i
$259$	0.282961	+	2.35428i	0.0175823	+	0.146288i
$260$	−10.3308	+	5.96452i	−0.640692	+	0.369904i
$261$	15.1625	+	11.8646i	0.938534	+	0.734399i
$262$	7.39202	+	4.26778i	0.456680	+	0.263665i
$263$	−4.76860	−	13.1016i	−0.294045	−	0.807881i	−0.995465	−	0.0951329i	$-0.969672\pi$
$263$	−4.76860	−	13.1016i	−0.294045	−	0.807881i	0.701420	−	0.712748i	$-0.252550\pi$
$264$	0.951380	+	9.08461i	0.0585534	+	0.559119i
$265$	15.4228	+	18.3801i	0.947413	+	1.12908i
$266$	−5.17803	−	10.2270i	−0.317486	−	0.627059i
$267$	−12.3707	−	11.9553i	−0.757077	−	0.731651i
$268$	1.26064	−	7.14945i	0.0770059	−	0.436722i
$269$	−5.96085			−0.363440			−0.181720	−	0.983350i	$-0.558166\pi$
$269$	−5.96085			−0.363440			−0.181720	+	0.983350i	$0.558166\pi$
$270$	2.76559	−	12.9393i	0.168308	−	0.787463i
$271$			28.5645i			1.73517i	0.497287	+	0.867586i	$0.334330\pi$
$271$			28.5645i			1.73517i	−0.497287	+	0.867586i	$0.665670\pi$
$272$	−0.853272	+	4.83915i	−0.0517372	+	0.293416i
$273$	9.80217	−	19.0992i	0.593254	−	1.15593i
$274$	−5.61237	−	2.04274i	−0.339056	−	0.123406i
$275$	−5.03143	−	5.99622i	−0.303407	−	0.361586i
$276$	−8.34349	−	11.4929i	−0.502219	−	0.691792i
$277$	−19.9590	+	7.26448i	−1.19922	+	0.436480i	−0.862952	−	0.505286i	$-0.831387\pi$
$277$	−19.9590	+	7.26448i	−1.19922	+	0.436480i	−0.336268	+	0.941766i	$0.609165\pi$
$278$	0.816921	−	1.41495i	0.0489957	−	0.0848630i
$279$	−13.1059	+	11.7828i	−0.784628	+	0.705416i
$280$	6.56063	+	1.53232i	0.392072	+	0.0915736i
$281$	0.144779	−	0.172541i	0.00863681	−	0.0102930i	−0.761709	−	0.647920i	$-0.775639\pi$
$281$	0.144779	−	0.172541i	0.00863681	−	0.0102930i	0.770346	+	0.637627i	$0.220084\pi$
$282$	0.270974	−	3.85430i	0.0161363	−	0.229520i
$283$	20.6570	−	3.64238i	1.22793	−	0.216517i	0.478193	−	0.878255i	$-0.341292\pi$
$283$	20.6570	−	3.64238i	1.22793	−	0.216517i	0.749735	+	0.661738i	$0.230181\pi$
$284$	8.85808	−	1.56192i	0.525630	−	0.0926828i
$285$	1.34016	−	19.0623i	0.0793844	−	1.12915i
$286$	−15.8802	+	18.9253i	−0.939018	+	1.11908i
$287$	3.18206	−	13.6240i	0.187831	−	0.804198i
$288$	−0.621530	−	2.93491i	−0.0366240	−	0.172941i
$289$	−3.57271	+	6.18812i	−0.210160	+	0.364007i
$290$	−15.3563	+	5.58925i	−0.901755	+	0.328212i
$291$	−6.47593	−	8.92040i	−0.379626	−	0.522923i
$292$	−5.59223	−	6.66456i	−0.327260	−	0.390014i
$293$	−7.26899	−	2.64570i	−0.424659	−	0.154563i	0.120845	−	0.992671i	$-0.461440\pi$
$293$	−7.26899	−	2.64570i	−0.424659	−	0.154563i	−0.545504	+	0.838108i	$0.683662\pi$
$294$	−11.4158	+	4.08417i	−0.665781	+	0.238194i
$295$	−0.508993	+	2.88664i	−0.0296347	+	0.168067i
$296$			0.896238i			0.0520928i
$297$	−3.78316	−	27.1405i	−0.219521	−	1.57485i
$298$	21.1057			1.22262
$299$	6.67020	−	37.8286i	0.385748	−	2.18768i
$300$	1.84862	+	1.78653i	0.106730	+	0.103145i
$301$	−4.89094	−	9.65999i	−0.281909	−	0.556792i
$302$	14.1309	+	16.8405i	0.813140	+	0.969063i
$303$	1.92866	+	18.4166i	0.110799	+	1.05800i
$304$	−1.48186	−	4.07137i	−0.0849904	−	0.233509i
$305$	−13.2730	−	7.66319i	−0.760012	−	0.438793i
$306$	2.06257	−	14.5964i	0.117910	−	0.834420i
$307$	20.6696	−	11.9336i	1.17968	−	0.681087i	0.223737	−	0.974649i	$-0.428174\pi$
$307$	20.6696	−	11.9336i	1.17968	−	0.681087i	0.955940	+	0.293562i	$0.0948409\pi$
$308$	13.8532	−	1.66501i	0.789357	−	0.0948728i
$309$	−3.75303	+	1.82873i	−0.213502	+	0.104033i
$310$	−2.59763	−	14.7319i	−0.147536	−	0.836717i
$311$	0.0614824	+	0.348684i	0.00348634	+	0.0197720i	0.986501	−	0.163753i	$-0.0523601\pi$
$311$	0.0614824	+	0.348684i	0.00348634	+	0.0197720i	−0.983015	+	0.183525i	$0.941249\pi$
$312$	4.53983	−	6.72512i	0.257017	−	0.380735i
$313$	−6.73049	+	8.02108i	−0.380430	+	0.453378i	−0.921950	−	0.387309i	$-0.873405\pi$
$313$	−6.73049	+	8.02108i	−0.380430	+	0.453378i	0.541520	+	0.840688i	$0.317849\pi$
$314$	4.93040	+	8.53970i	0.278239	+	0.481923i
$315$	−19.8274	−	3.92217i	−1.11715	−	0.220989i
$316$	5.28801	−	9.15910i	0.297474	−	0.515240i
$317$	−3.47766	−	9.55480i	−0.195325	−	0.536651i	0.802906	−	0.596106i	$-0.203286\pi$
$317$	−3.47766	−	9.55480i	−0.195325	−	0.536651i	−0.998231	+	0.0594545i	$0.981064\pi$
$318$	−14.9067	−	6.64362i	−0.835928	−	0.372556i
$319$	−25.9263	+	21.7547i	−1.45159	+	1.21803i
$320$	2.39285	+	0.870927i	0.133765	+	0.0486863i
$321$	−14.5255	−	3.62740i	−0.810732	−	0.202462i
$322$	−17.3590	+	13.0115i	−0.967381	+	0.725103i
$323$		−	21.2899i		−	1.18460i
$324$	2.16417	+	8.73592i	0.120232	+	0.485329i
$325$			6.95320i			0.385694i
$326$	−6.09683	−	1.07503i	−0.337672	−	0.0595407i
$327$	4.22636	−	16.9239i	0.233718	−	0.935894i
$328$	1.80859	−	4.96907i	0.0998628	−	0.274371i
$329$	−5.89318	−	0.323960i	−0.324901	−	0.0178605i
$330$	21.2453	+	9.46857i	1.16951	+	0.521228i
$331$	−16.3609	+	5.95487i	−0.899276	+	0.327310i	−0.749962	−	0.661480i	$-0.769928\pi$
$331$	−16.3609	+	5.95487i	−0.899276	+	0.327310i	−0.149313	+	0.988790i	$0.547706\pi$
$332$	6.30324	−	10.9175i	0.345935	−	0.599178i
$333$	−0.0918157	−	2.68714i	−0.00503147	−	0.147255i
$334$	3.56654	−	2.05914i	0.195152	−	0.112671i
$335$	−14.1614	−	11.8828i	−0.773718	−	0.649227i
$336$	−4.46813	+	1.01776i	−0.243756	+	0.0555232i
$337$	−5.51923	−	31.3011i	−0.300652	−	1.70508i	−0.643298	−	0.765616i	$-0.722435\pi$
$337$	−5.51923	−	31.3011i	−0.300652	−	1.70508i	0.342647	−	0.939464i	$-0.388677\pi$
$338$	8.80984	−	1.55341i	0.479192	−	0.0844945i
$339$	0.305710	−	0.148962i	0.0166039	−	0.00809053i
$340$	9.58521	+	8.04295i	0.519831	+	0.436190i
$341$	−15.4904	−	26.8301i	−0.838851	−	1.45293i
$342$	4.86008	+	12.0552i	0.262803	+	0.651870i
$343$	6.50425	+	17.3406i	0.351196	+	0.936302i
$344$	−1.39970	−	3.84564i	−0.0754666	−	0.207343i
$345$	−35.9679	+	3.76672i	−1.93645	+	0.202793i
$346$	4.30657	+	5.13237i	0.231523	+	0.275918i
$347$	5.65025	−	15.5239i	0.303321	−	0.833369i	−0.690596	−	0.723241i	$-0.742652\pi$
$347$	5.65025	−	15.5239i	0.303321	−	0.833369i	0.993917	−	0.110128i	$-0.0351261\pi$
$348$	7.72454	−	7.99298i	0.414079	−	0.428469i
$349$	22.1665	+	3.90856i	1.18655	+	0.209220i	0.731875	−	0.681439i	$-0.238645\pi$
$349$	22.1665	+	3.90856i	1.18655	+	0.209220i	0.454672	+	0.890659i	$0.349756\pi$
$350$	2.68553	−	2.86515i	0.143548	−	0.153149i
$351$	−12.9226	+	20.6287i	−0.689756	+	1.10108i
$352$	5.27368			0.281088
$353$	−6.42145	+	36.4179i	−0.341779	+	1.93833i	0.00394896	+	0.999992i	$0.498743\pi$
$353$	−6.42145	+	36.4179i	−0.341779	+	1.93833i	−0.345728	+	0.938335i	$0.612368\pi$
$354$	−0.548834	−	1.91673i	−0.0291702	−	0.101873i
$355$	7.83375	−	21.5231i	0.415772	−	1.14233i
$356$	−7.60874	+	6.38449i	−0.403262	+	0.338377i
$357$	−22.3419	−	2.80977i	−1.18246	−	0.148709i
$358$	−0.862187	+	0.313810i	−0.0455680	+	0.0165854i
$359$	15.1046	+	8.72065i	0.797191	+	0.460258i	0.842488	−	0.538715i	$-0.181090\pi$
$359$	15.1046	+	8.72065i	0.797191	+	0.460258i	−0.0452971	+	0.998974i	$0.514423\pi$
$360$	−7.26359	−	2.36612i	−0.382825	−	0.124705i
$361$	−0.114002	−	0.197457i	−0.00600009	−	0.0103925i
$362$	−6.05521	−	5.08092i	−0.318255	−	0.267047i
$363$	29.0471	+	2.04214i	1.52458	+	0.107184i
$364$	−10.3775	−	6.77701i	−0.543928	−	0.355212i
$365$	−21.8172	+	3.84696i	−1.14196	+	0.201359i
$366$	10.3992	+	0.731109i	0.543575	+	0.0382157i
$367$	10.2418	−	12.2057i	0.534617	−	0.637131i	−0.429355	−	0.903136i	$-0.641259\pi$
$367$	10.2418	−	12.2057i	0.534617	−	0.637131i	0.963972	+	0.266005i	$0.0857036\pi$
$368$	−7.10107	+	4.09981i	−0.370169	+	0.213717i
$369$	−4.91355	+	15.0838i	−0.255789	+	0.785231i
$370$	1.97644	+	1.14110i	0.102750	+	0.0593229i
$371$	−9.79937	+	22.9227i	−0.508758	+	1.19009i
$372$	5.97768	+	8.23407i	0.309928	+	0.426917i
$373$	17.5072	−	14.6903i	0.906490	−	0.760636i	−0.0649577	−	0.997888i	$-0.520691\pi$
$373$	17.5072	−	14.6903i	0.906490	−	0.760636i	0.971448	+	0.237252i	$0.0762468\pi$
$374$	24.3510	+	8.86305i	1.25916	+	0.458298i
$375$	−14.9072	+	4.26851i	−0.769805	+	0.220425i
$376$	−2.19688	−	0.387370i	−0.113296	−	0.0199771i
$377$	30.0640			1.54838
$378$	13.2923	−	3.50923i	0.683682	−	0.180495i
$379$	−4.48039			−0.230142			−0.115071	−	0.993357i	$-0.536710\pi$
$379$	−4.48039			−0.230142			−0.115071	+	0.993357i	$0.536710\pi$
$380$	−10.8652	−	1.91582i	−0.557372	−	0.0982797i
$381$	−23.4847	−	22.6959i	−1.20316	−	1.16275i
$382$	13.3048	+	4.84257i	0.680735	+	0.247767i
$383$	5.35178	−	4.49067i	0.273463	−	0.229463i	−0.495734	−	0.868474i	$-0.665101\pi$
$383$	5.35178	−	4.49067i	0.273463	−	0.229463i	0.769197	+	0.639012i	$0.220656\pi$
$384$	−1.72263	+	0.180401i	−0.0879076	+	0.00920607i
$385$	13.9662	−	32.6698i	0.711783	−	1.66501i
$386$	−5.74313	−	3.31580i	−0.292318	−	0.168770i
$387$	4.59061	+	11.3868i	0.233354	+	0.578823i
$388$	−5.51161	+	3.18213i	−0.279809	+	0.161548i
$389$	−8.41647	+	10.0304i	−0.426732	+	0.508559i	−0.935976	−	0.352062i	$-0.885480\pi$
$389$	−8.41647	+	10.0304i	−0.426732	+	0.508559i	0.509244	+	0.860622i	$0.329925\pi$
$390$	−9.05051	−	18.5740i	−0.458291	−	0.940532i
$391$	−39.6791	+	6.99650i	−2.00666	+	0.353828i
$392$	1.65870	+	6.80064i	0.0837770	+	0.343484i
$393$	−8.27173	+	12.2534i	−0.417254	+	0.618103i
$394$	0.113625	+	0.0953425i	0.00572434	+	0.00480329i
$395$	−13.4655	−	23.3229i	−0.677523	−	1.17350i
$396$	−15.8118	+	0.540266i	−0.794574	+	0.0271494i
$397$	2.44969	+	1.41433i	0.122946	+	0.0709830i	0.560212	−	0.828349i	$-0.310720\pi$
$397$	2.44969	+	1.41433i	0.122946	+	0.0709830i	−0.437266	+	0.899332i	$0.644053\pi$
$398$	−1.89356	+	0.689198i	−0.0949154	+	0.0345464i
$399$	18.2991	−	7.70425i	0.916100	−	0.385695i
$400$	1.13701	−	0.954063i	0.0568504	−	0.0477032i
$401$	−8.93683	+	24.5537i	−0.446284	+	1.22616i	0.489008	+	0.872279i	$0.337359\pi$
$401$	−8.93683	+	24.5537i	−0.446284	+	1.22616i	−0.935292	+	0.353876i	$0.884863\pi$
$402$	12.1996	+	3.04657i	0.608460	+	0.151949i
$403$	−4.77885	+	27.1022i	−0.238051	+	1.35006i
$404$	10.6910			0.531895
$405$	22.0205	+	6.35010i	1.09421	+	0.315539i
$406$	−12.3883	−	11.6116i	−0.614819	−	0.576274i
$407$	4.65467	+	0.820744i	0.230723	+	0.0406828i
$408$	−8.25736	−	2.06209i	−0.408800	−	0.102089i
$409$	0.298506	−	0.820139i	0.0147602	−	0.0405533i	−0.932094	−	0.362217i	$-0.882020\pi$
$409$	0.298506	−	0.820139i	0.0147602	−	0.0405533i	0.946854	+	0.321664i	$0.104242\pi$
$410$	−8.65539	−	10.3151i	−0.427459	−	0.509426i
$411$	4.21115	−	9.44884i	0.207721	−	0.466077i
$412$	0.824390	+	2.26499i	0.0406148	+	0.111588i
$413$	−2.91471	+	0.882972i	−0.143423	+	0.0434482i
$414$	20.8708	−	13.0197i	1.02574	−	0.639884i
$415$	−16.0507	−	27.8006i	−0.787898	−	1.36468i
$416$	−3.58863	−	3.01122i	−0.175947	−	0.147637i
$417$	2.34550	+	1.58334i	0.114859	+	0.0775365i
$418$	−22.5020	+	3.96771i	−1.10061	+	0.194067i
$419$	−3.55710	−	20.1733i	−0.173776	−	0.985532i	−0.939547	−	0.342419i	$-0.888754\pi$
$419$	−3.55710	−	20.1733i	−0.173776	−	0.985532i	0.765772	−	0.643113i	$-0.222357\pi$
$420$	−3.44444	+	11.1492i	−0.168072	+	0.544027i
$421$	3.29401	+	2.76400i	0.160540	+	0.134709i	0.719519	−	0.694473i	$-0.244362\pi$
$421$	3.29401	+	2.76400i	0.160540	+	0.134709i	−0.558979	+	0.829182i	$0.688807\pi$
$422$	−8.67592	+	5.00904i	−0.422337	+	0.243836i
$423$	6.62649	+	0.936371i	0.322191	+	0.0455279i
$424$	−4.71123	+	8.16009i	−0.228798	+	0.396289i
$425$	6.85351	−	2.49447i	0.332444	−	0.121000i
$426$	1.62266	+	15.4946i	0.0786182	+	0.750715i
$427$	0.874067	−	15.9002i	0.0422991	−	0.769466i
$428$	−2.95636	+	8.12254i	−0.142901	+	0.392618i
$429$	−30.7699	−	29.7365i	−1.48559	−	1.43569i
$430$	−10.2628	−	1.80960i	−0.494914	−	0.0872667i
$431$			5.00891i			0.241271i	0.992697	+	0.120635i	$0.0384932\pi$
$431$			5.00891i			0.241271i	−0.992697	+	0.120635i	$0.961507\pi$
$432$	5.14640	−	0.717365i	0.247606	−	0.0345142i
$433$		−	23.3737i		−	1.12327i	−0.827386	−	0.561633i	$-0.810173\pi$
$433$		−	23.3737i		−	1.12327i	0.827386	−	0.561633i	$-0.189827\pi$
$434$	12.4368	−	9.32207i	0.596987	−	0.447474i
$435$	−7.79168	−	27.2114i	−0.373583	−	1.30469i
$436$	−9.46373	−	3.44452i	−0.453231	−	0.164962i
$437$	27.2146	−	22.8358i	1.30185	−	1.09238i
$438$	12.1942	−	8.85263i	0.582663	−	0.422995i
$439$	7.67296	+	21.0813i	0.366210	+	1.00615i	0.976790	+	0.214200i	$0.0687143\pi$
$439$	7.67296	+	21.0813i	0.366210	+	1.00615i	−0.610580	+	0.791955i	$0.709063\pi$
$440$	6.71451	−	11.6299i	0.320102	−	0.554432i
$441$	−5.66989	−	20.2201i	−0.269995	−	0.962862i
$442$	−11.5097	−	19.9353i	−0.547459	−	0.948227i
$443$	14.4266	−	17.1930i	0.685429	−	0.816863i	−0.305366	−	0.952235i	$-0.598779\pi$
$443$	14.4266	−	17.1930i	0.685429	−	0.816863i	0.990795	+	0.135373i	$0.0432232\pi$
$444$	−1.54851	−	0.108867i	−0.0734889	−	0.00516659i
$445$	4.39197	+	24.9081i	0.208199	+	1.18076i
$446$	−3.11017	−	17.6387i	−0.147271	−	0.835216i
$447$	−2.56373	+	36.4661i	−0.121260	+	1.72479i
$448$	0.315721	+	2.62685i	0.0149164	+	0.124107i
$449$	16.7414	−	9.66565i	0.790075	−	0.456150i	−0.0499138	−	0.998754i	$-0.515895\pi$
$449$	16.7414	−	9.66565i	0.790075	−	0.456150i	0.839989	+	0.542603i	$0.182561\pi$
$450$	−3.31130	+	2.97700i	−0.156096	+	0.140337i
$451$	−24.1509	−	13.9435i	−1.13722	−	0.656576i
$452$	−0.0671522	−	0.184499i	−0.00315858	−	0.00867811i
$453$	−30.8133	+	22.3695i	−1.44773	+	1.05101i
$454$	2.78006	+	3.31314i	0.130475	+	0.155494i
$455$	−28.1578	+	14.2566i	−1.32006	+	0.668358i
$456$	7.21447	−	2.06578i	0.337848	−	0.0967391i
$457$	−0.271050	+	1.53720i	−0.0126792	+	0.0719073i	−0.990491	−	0.137579i	$-0.956068\pi$
$457$	−0.271050	+	1.53720i	−0.0126792	+	0.0719073i	0.977812	+	0.209486i	$0.0671791\pi$
$458$	−11.6814			−0.545837
$459$	24.9689	+	5.33672i	1.16545	+	0.249097i
$460$			20.8797i			0.973519i
$461$	−6.66828	+	37.8177i	−0.310573	+	1.76135i	0.285465	+	0.958389i	$0.407852\pi$
$461$	−6.66828	+	37.8177i	−0.310573	+	1.76135i	−0.596037	+	0.802957i	$0.703259\pi$
$462$	1.19403	+	24.1375i	0.0555512	+	1.12298i
$463$	23.6904	+	8.62262i	1.10099	+	0.400727i	0.827681	−	0.561200i	$-0.189660\pi$
$463$	23.6904	+	8.62262i	1.10099	+	0.400727i	0.273308	+	0.961927i	$0.411882\pi$
$464$	−4.12515	−	4.91616i	−0.191505	−	0.228227i
$465$	25.7691	−	2.69866i	1.19502	−	0.125147i
$466$	−6.33466	+	2.30563i	−0.293447	+	0.106806i
$467$	−15.5985	+	27.0174i	−0.721813	+	1.25022i	0.238459	+	0.971152i	$0.423358\pi$
$467$	−15.5985	+	27.0174i	−0.721813	+	1.25022i	−0.960272	+	0.279064i	$0.909976\pi$
$468$	11.0681	+	8.66075i	0.511624	+	0.400344i
$469$	4.36858	−	18.7041i	0.201722	−	0.863674i
$470$	−3.65135	+	4.35151i	−0.168424	+	0.200720i
$471$	−15.3537	+	7.48135i	−0.707460	+	0.344722i
$472$	−1.13361	+	0.199886i	−0.0521785	+	0.00920048i
$473$	−21.2544	+	3.74772i	−0.977277	+	0.172320i
$474$	15.1826	+	10.2491i	0.697361	+	0.470757i
$475$	−4.13364	+	4.92628i	−0.189664	+	0.226033i
$476$	−2.95690	+	12.6600i	−0.135529	+	0.580269i
$477$	13.2895	−	24.9486i	0.608484	−	1.14232i
$478$	10.1293	−	17.5444i	0.463302	−	0.802462i
$479$	24.8417	−	9.04163i	1.13504	−	0.413123i	0.294923	−	0.955521i	$-0.404706\pi$
$479$	24.8417	−	9.04163i	1.13504	−	0.413123i	0.840121	+	0.542398i	$0.182484\pi$
$480$	−1.79544	+	4.02855i	−0.0819502	+	0.183877i
$481$	−2.69877	−	3.21627i	−0.123053	−	0.146649i
$482$	1.69436	+	0.616696i	0.0771759	+	0.0280897i
$483$	−20.3725	−	31.5732i	−0.926981	−	1.43663i
$484$	2.91933	−	16.5563i	0.132697	−	0.752561i
$485$			16.2061i			0.735880i
$486$	−15.3567	+	2.67807i	−0.696594	+	0.121479i
$487$	−6.11954			−0.277303			−0.138651	−	0.990341i	$-0.544277\pi$
$487$	−6.11954			−0.277303			−0.138651	+	0.990341i	$0.544277\pi$
$488$	1.04515	−	5.92736i	0.0473119	−	0.268319i
$489$	2.59802	−	10.4034i	0.117486	−	0.470459i
$490$	17.1091	+	5.00078i	0.772910	+	0.225912i
$491$	12.1413	+	14.4695i	0.547930	+	0.652998i	0.966946	−	0.254981i	$-0.0820693\pi$
$491$	12.1413	+	14.4695i	0.547930	+	0.652998i	−0.419016	+	0.907979i	$0.637625\pi$
$492$	8.36579	+	3.72846i	0.377159	+	0.168092i
$493$	−10.7855	−	29.6330i	−0.485755	−	1.33460i
$494$	17.5777	+	10.1485i	0.790856	+	0.456601i
$495$	−18.9404	+	35.5571i	−0.851306	+	1.59817i
$496$	5.08755	−	2.93730i	0.228438	−	0.131888i
$497$	23.6278	−	2.83982i	1.05985	−	0.127383i
$498$	18.0975	+	12.2168i	0.810969	+	0.547449i
$499$	−0.224409	−	1.27269i	−0.0100459	−	0.0569733i	0.979373	−	0.202062i	$-0.0647643\pi$
$499$	−0.224409	−	1.27269i	−0.0100459	−	0.0569733i	−0.989419	+	0.145089i	$0.953653\pi$
$500$	1.55460	+	8.81655i	0.0695236	+	0.394288i
$501$	3.12453	+	6.41235i	0.139594	+	0.286482i
$502$	3.23460	−	3.85485i	0.144367	−	0.172050i
$503$	1.03602	+	1.79445i	0.0461941	+	0.0800105i	0.888198	−	0.459461i	$-0.151957\pi$
$503$	1.03602	+	1.79445i	0.0461941	+	0.0800105i	−0.842004	+	0.539471i	$0.818624\pi$
$504$	−1.21572	−	7.84360i	−0.0541524	−	0.349382i
$505$	13.6118	−	23.5764i	0.605719	−	1.04914i
$506$	14.7897	+	40.6343i	0.657482	+	1.80642i
$507$	1.61383	+	15.4102i	0.0716725	+	0.684391i
$508$	−14.4444	+	12.1203i	−0.640869	+	0.537753i
$509$	26.3345	+	9.58496i	1.16725	+	0.424846i	0.851684	−	0.524056i	$-0.175582\pi$
$509$	26.3345	+	9.58496i	1.16725	+	0.424846i	0.315571	+	0.948902i	$0.397804\pi$
$510$	−15.0608	+	15.5842i	−0.666904	+	0.690080i
$511$	−13.8055	−	18.4183i	−0.610719	−	0.814778i
$512$			1.00000i			0.0441942i
$513$	−21.4191	+	6.93282i	−0.945678	+	0.306092i
$514$			22.1332i			0.976254i
$515$	6.04453	+	1.06581i	0.266354	+	0.0469654i
$516$	6.81446	−	1.95125i	0.299990	−	0.0858988i
$517$	−4.02366	+	11.0549i	−0.176961	+	0.486195i
$518$	−0.130154	+	2.36765i	−0.00571865	+	0.104028i
$519$	−9.39076	+	6.81740i	−0.412209	+	0.299251i
$520$	−11.2096	+	4.07997i	−0.491575	+	0.178919i
$521$	8.50594	−	14.7327i	0.372652	−	0.645452i	−0.617321	−	0.786712i	$-0.711782\pi$
$521$	8.50594	−	14.7327i	0.372652	−	0.645452i	0.989973	+	0.141260i	$0.0451152\pi$
$522$	12.8719	+	14.3173i	0.563386	+	0.626650i
$523$	22.5596	−	13.0248i	0.986461	−	0.569533i	0.0822461	−	0.996612i	$-0.473791\pi$
$523$	22.5596	−	13.0248i	0.986461	−	0.569533i	0.904214	+	0.427079i	$0.140457\pi$
$524$	6.53862	+	5.48656i	0.285641	+	0.239681i
$525$	4.62416	+	4.98805i	0.201815	+	0.217696i
$526$	−2.42108	−	13.7306i	−0.105564	−	0.598685i
$527$	28.4280	−	5.01263i	1.23834	−	0.218353i
$528$	−0.640599	+	9.11180i	−0.0278785	+	0.396540i
$529$	−33.8849	−	28.4328i	−1.47326	−	1.23621i
$530$	11.9968	+	20.7790i	0.521107	+	0.902583i
$531$	3.37836	−	0.715440i	0.146608	−	0.0310475i
$532$	−3.32346	−	10.9708i	−0.144090	−	0.475645i
$533$	8.47258	+	23.2782i	0.366988	+	1.00829i
$534$	−10.1068	−	13.9218i	−0.437364	−	0.602455i
$535$	14.1483	+	16.8613i	0.611683	+	0.728976i
$536$	2.48298	−	6.82193i	0.107248	−	0.294662i
$537$	−0.437467	−	1.52779i	−0.0188781	−	0.0659291i
$538$	−5.87030	−	1.03509i	−0.253086	−	0.0446260i
$539$	36.8386	−	2.38677i	1.58675	−	0.102805i
$540$	4.97046	−	12.2625i	0.213895	−	0.527695i
$541$	4.76276			0.204767			0.102384	−	0.994745i	$-0.467353\pi$
$541$	4.76276			0.204767			0.102384	+	0.994745i	$0.467353\pi$
$542$	−4.96018	+	28.1306i	−0.213058	+	1.20831i
$543$	9.51428	−	9.84492i	0.408297	−	0.422486i
$544$	−1.68062	+	4.61746i	−0.0720559	+	0.197972i
$545$	−19.6454	+	16.4844i	−0.841516	+	0.706116i
$546$	12.9698	−	17.1069i	0.555056	−	0.732107i
$547$	−9.23709	+	3.36202i	−0.394949	+	0.143750i	−0.531857	−	0.846834i	$-0.678506\pi$
$547$	−9.23709	+	3.36202i	−0.394949	+	0.143750i	0.136908	+	0.990584i	$0.456284\pi$
$548$	−5.17239	−	2.98628i	−0.220953	−	0.127568i
$549$	−2.52640	+	17.8788i	−0.107824	+	0.763047i
$550$	−3.91376	−	6.77882i	−0.166883	−	0.289050i
$551$	21.3001	+	17.8729i	0.907413	+	0.761410i
$552$	−6.22101	−	12.7671i	−0.264784	−	0.543406i
$553$	15.2998	−	23.4282i	0.650613	−	0.996270i
$554$	−20.9172	+	3.68827i	−0.888688	+	0.156700i
$555$	−2.21166	+	3.27626i	−0.0938795	+	0.139069i
$556$	1.05021	−	1.25160i	0.0445390	−	0.0530795i
$557$	−18.1232	+	10.4635i	−0.767906	+	0.443351i	−0.832127	−	0.554585i	$-0.812877\pi$
$557$	−18.1232	+	10.4635i	−0.767906	+	0.443351i	0.0642211	+	0.997936i	$0.479544\pi$
$558$	−14.9528	+	9.32794i	−0.633003	+	0.394883i
$559$	16.6031	+	9.58579i	0.702235	+	0.405436i
$560$	6.19487	+	2.64828i	0.261781	+	0.111910i
$561$	−18.2714	+	40.9968i	−0.771419	+	1.73089i
$562$	0.172541	−	0.144779i	0.00727822	−	0.00610715i
$563$	−17.7561	−	6.46269i	−0.748330	−	0.272370i	−0.0604272	−	0.998173i	$-0.519246\pi$
$563$	−17.7561	−	6.46269i	−0.748330	−	0.272370i	−0.687903	+	0.725803i	$0.741469\pi$
$564$	0.936150	−	3.74869i	0.0394190	−	0.157848i
$565$	−0.492369	−	0.0868179i	−0.0207141	−	0.00365246i
$566$	20.9756			0.881671
$567$	4.44857	+	23.3925i	0.186822	+	0.982394i
$568$	8.99473			0.377410
$569$	9.63394	+	1.69872i	0.403876	+	0.0712142i	0.371896	−	0.928274i	$-0.378708\pi$
$569$	9.63394	+	1.69872i	0.403876	+	0.0712142i	0.0319797	+	0.999489i	$0.489819\pi$
$570$	4.62994	−	18.5400i	0.193927	−	0.776555i
$571$	20.3261	+	7.39809i	0.850620	+	0.309601i	0.730293	−	0.683134i	$-0.239383\pi$
$571$	20.3261	+	7.39809i	0.850620	+	0.309601i	0.120327	+	0.992734i	$0.461606\pi$
$572$	−18.9253	+	15.8802i	−0.791307	+	0.663986i
$573$	−9.98308	+	22.3997i	−0.417049	+	0.935761i
$574$	5.49949	−	12.8644i	0.229544	−	0.536952i
$575$	10.5398	+	6.08517i	0.439541	+	0.253769i
$576$	−0.102446	−	2.99825i	−0.00426857	−	0.124927i
$577$	−32.7558	+	18.9115i	−1.36364	+	0.787298i	−0.990106	−	0.140319i	$-0.955187\pi$
$577$	−32.7558	+	18.9115i	−1.36364	+	0.787298i	−0.373534	+	0.927617i	$0.621854\pi$
$578$	−4.59299	+	5.47371i	−0.191043	+	0.227677i
$579$	6.42661	−	9.52013i	0.267081	−	0.395643i
$580$	−16.0936	+	2.83774i	−0.668251	+	0.117831i
$581$	18.2371	−	27.9262i	0.756604	−	1.15857i
$582$	−4.82854	−	9.90941i	−0.200149	−	0.410758i
$583$	38.0656	+	31.9408i	1.57652	+	1.32285i
$584$	−4.34998	−	7.53439i	−0.180004	−	0.311775i
$585$	33.1913	−	13.3812i	1.37229	−	0.553242i
$586$	−6.69914	−	3.86775i	−0.276739	−	0.159775i
$587$	23.0197	−	8.37850i	0.950127	−	0.345818i	0.179970	−	0.983672i	$-0.442400\pi$
$587$	23.0197	−	8.37850i	0.950127	−	0.345818i	0.770157	+	0.637854i	$0.220178\pi$
$588$	−11.9515	+	2.03980i	−0.492873	+	0.0841198i
$589$	−19.4979	+	16.3606i	−0.803395	+	0.674129i
$590$	−1.00252	+	2.75440i	−0.0412731	+	0.113397i
$591$	−0.178534	+	0.184738i	−0.00734389	+	0.00759911i
$592$	−0.155630	+	0.882622i	−0.00639635	+	0.0362755i
$593$	0.129923			0.00533529			0.00266765	−	0.999996i	$-0.499151\pi$
$593$	0.129923			0.00533529			0.00266765	+	0.999996i	$0.499151\pi$
$594$	0.987212	−	27.3851i	0.0405058	−	1.12362i
$595$	24.1538	+	22.6395i	0.990210	+	0.928131i
$596$	20.7850	+	3.66496i	0.851389	+	0.150123i
$597$	−0.960775	−	3.35538i	−0.0393219	−	0.137326i
$598$	13.1377	−	36.0956i	0.537242	−	1.47606i
$599$	17.6534	+	21.0385i	0.721297	+	0.859608i	0.994756	−	0.102276i	$-0.0326124\pi$
$599$	17.6534	+	21.0385i	0.721297	+	0.859608i	−0.273459	+	0.961884i	$0.588168\pi$
$600$	1.51030	+	2.08040i	0.0616579	+	0.0849319i
$601$	4.87437	+	13.3922i	0.198830	+	0.546280i	0.998535	−	0.0541131i	$-0.0172331\pi$
$601$	4.87437	+	13.3922i	0.198830	+	0.546280i	−0.799705	+	0.600393i	$0.795011\pi$
$602$	−3.13919	−	10.3625i	−0.127944	−	0.422345i
$603$	−6.74571	+	20.7082i	−0.274707	+	0.843304i
$604$	10.9919	+	19.0385i	0.447253	+	0.774664i
$605$	−32.7942	−	27.5176i	−1.33327	−	1.11875i
$606$	−1.29864	+	18.4717i	−0.0527536	+	0.750361i
$607$	−21.3829	+	3.77039i	−0.867907	+	0.153035i	−0.589834	−	0.807525i	$-0.700807\pi$
$607$	−21.3829	+	3.77039i	−0.867907	+	0.153035i	−0.278073	+	0.960560i	$0.589696\pi$
$608$	−0.752360	−	4.26684i	−0.0305122	−	0.173043i
$609$	21.5672	−	19.9938i	0.873946	−	0.810189i
$610$	−11.7407	−	9.85161i	−0.475367	−	0.398880i
$611$	9.05027	−	5.22518i	0.366135	−	0.211388i
$612$	4.56588	−	14.0165i	0.184565	−	0.566582i
$613$	4.50406	−	7.80126i	0.181917	−	0.315090i	−0.760616	−	0.649202i	$-0.775103\pi$
$613$	4.50406	−	7.80126i	0.181917	−	0.315090i	0.942533	+	0.334112i	$0.108436\pi$
$614$	22.4278	−	8.16307i	0.905114	−	0.329435i
$615$	18.8737	−	13.7017i	0.761059	−	0.552505i
$616$	13.9318	+	0.765860i	0.561329	+	0.0308574i
$617$	8.72811	−	23.9803i	0.351380	−	0.965410i	−0.630547	−	0.776151i	$-0.717169\pi$
$617$	8.72811	−	23.9803i	0.351380	−	0.965410i	0.981927	−	0.189259i	$-0.0606084\pi$
$618$	−4.01356	+	1.14924i	−0.161449	+	0.0462292i
$619$	−27.0379	−	4.76752i	−1.08675	−	0.191623i	−0.398549	−	0.917147i	$-0.630486\pi$
$619$	−27.0379	−	4.76752i	−1.08675	−	0.191623i	−0.688197	+	0.725524i	$0.741597\pi$
$620$		−	14.9592i		−	0.600775i
$621$	19.9601	+	37.6418i	0.800971	+	1.51051i
$622$			0.354063i			0.0141966i
$623$	−21.0277	+	15.7613i	−0.842455	+	0.631465i
$624$	5.63866	−	5.83462i	0.225727	−	0.233572i
$625$	28.3959	+	10.3353i	1.13584	+	0.413410i
$626$	−8.02108	+	6.73049i	−0.320587	+	0.269004i
$627$	−4.12201	−	39.3606i	−0.164617	−	1.57191i
$628$	3.37259	+	9.26612i	0.134581	+	0.369758i
$629$	−2.20197	+	3.81392i	−0.0877981	+	0.152071i
$630$	−18.8451	−	7.30557i	−0.750806	−	0.291061i
$631$	12.0161	+	20.8125i	0.478354	+	0.828533i	0.999692	−	0.0248169i	$-0.00790027\pi$
$631$	12.0161	+	20.8125i	0.478354	+	0.828533i	−0.521338	+	0.853350i	$0.674567\pi$
$632$	6.79813	−	8.10170i	0.270415	−	0.322268i
$633$	−7.60068	−	15.5986i	−0.302100	−	0.619988i
$634$	−1.76566	−	10.0135i	−0.0701232	−	0.397688i
$635$	8.33772	+	47.2856i	0.330872	+	1.87647i
$636$	−13.5266	−	9.13121i	−0.536365	−	0.362076i
$637$	−26.4307	−	19.4103i	−1.04722	−	0.769064i
$638$	−29.3101	+	16.9222i	−1.16040	+	0.669955i
$639$	−26.9684	+	0.921471i	−1.06686	+	0.0364528i
$640$	2.20527	+	1.27321i	0.0871708	+	0.0503281i
$641$	−6.87187	−	18.8803i	−0.271423	−	0.745728i	−0.998263	−	0.0589209i	$-0.981234\pi$
$641$	−6.87187	−	18.8803i	−0.271423	−	0.745728i	0.726840	−	0.686807i	$-0.240988\pi$
$642$	−13.6749	−	6.09461i	−0.539705	−	0.240535i
$643$	25.3998	+	30.2703i	1.00167	+	1.19374i	0.981010	+	0.193958i	$0.0621326\pi$
$643$	25.3998	+	30.2703i	1.00167	+	1.19374i	0.0206609	+	0.999787i	$0.493423\pi$
$644$	−19.3547	+	9.79948i	−0.762683	+	0.386153i
$645$	4.37323	−	17.5120i	0.172196	−	0.689536i
$646$	3.69694	−	20.9664i	0.145454	−	0.824912i
$647$	−10.2344			−0.402357			−0.201178	−	0.979555i	$-0.564477\pi$
$647$	−10.2344			−0.402357			−0.201178	+	0.979555i	$0.564477\pi$
$648$	0.614316	+	8.97901i	0.0241326	+	0.352729i
$649$			6.07051i			0.238289i
$650$	−1.20741	+	6.84757i	−0.0473585	+	0.268584i
$651$	14.5958	+	22.6205i	0.572055	+	0.886569i
$652$	−5.81752	−	2.11741i	−0.227832	−	0.0829240i
$653$	1.38321	+	1.64844i	0.0541290	+	0.0645085i	0.792430	−	0.609963i	$-0.208816\pi$
$653$	1.38321	+	1.64844i	0.0541290	+	0.0645085i	−0.738301	+	0.674472i	$0.764371\pi$
$654$	7.10096	−	15.9329i	0.277669	−	0.623025i
$655$	20.4244	−	7.43386i	0.798046	−	0.290465i
$656$	2.64399	−	4.57952i	0.103230	−	0.178800i
$657$	13.8142	+	22.1444i	0.538943	+	0.863933i
$658$	−5.74739	−	1.34238i	−0.224057	−	0.0523313i
$659$	8.04128	−	9.58322i	0.313244	−	0.373309i	−0.586334	−	0.810069i	$-0.699430\pi$
$659$	8.04128	−	9.58322i	0.313244	−	0.373309i	0.899578	+	0.436760i	$0.143874\pi$
$660$	19.2783	+	13.0139i	0.750407	+	0.506566i
$661$	−30.0972	+	5.30694i	−1.17064	+	0.206416i	−0.724971	−	0.688779i	$-0.758147\pi$
$661$	−30.0972	+	5.30694i	−1.17064	+	0.206416i	−0.445673	+	0.895196i	$0.647036\pi$
$662$	−17.1464	+	3.02337i	−0.666413	+	0.117507i
$663$	35.8421	−	17.4647i	1.39199	−	0.678272i
$664$	8.10329	−	9.65713i	0.314469	−	0.374769i
$665$	−28.4250	−	6.63903i	−1.10227	−	0.257450i
$666$	0.376197	−	2.66226i	0.0145773	−	0.103161i
$667$	26.3109	−	45.5718i	1.01876	−	1.76455i
$668$	3.86992	−	1.40854i	0.149732	−	0.0544979i
$669$	30.8537	−	3.23113i	1.19287	−	0.124923i
$670$	−11.8828	−	14.1614i	−0.459073	−	0.547101i
$671$	−29.8270	−	10.8561i	−1.15146	−	0.419097i
$672$	−4.57698	+	0.226412i	−0.176561	+	0.00873405i
$673$	−2.38731	+	13.5391i	−0.0920239	+	0.521893i	0.903595	+	0.428388i	$0.140918\pi$
$673$	−2.38731	+	13.5391i	−0.0920239	+	0.521893i	−0.995619	+	0.0935053i	$0.970193\pi$
$674$		−	31.7840i		−	1.22427i
$675$	−4.74140	−	6.08283i	−0.182496	−	0.234128i
$676$	8.94574			0.344067
$677$	4.78160	−	27.1178i	0.183772	−	1.04222i	−0.743751	−	0.668457i	$-0.766955\pi$
$677$	4.78160	−	27.1178i	0.183772	−	1.04222i	0.927523	−	0.373766i	$-0.121934\pi$
$678$	0.326932	−	0.0936134i	0.0125558	−	0.00359520i
$679$	−15.0225	+	7.60602i	−0.576510	+	0.291892i
$680$	8.04295	+	9.58521i	0.308433	+	0.367576i
$681$	−6.06210	+	4.40089i	−0.232300	+	0.168643i
$682$	−10.5960	−	29.1124i	−0.405743	−	1.11477i
$683$	−23.1093	−	13.3421i	−0.884251	−	0.510523i	−0.0121934	−	0.999926i	$-0.503881\pi$
$683$	−23.1093	−	13.3421i	−0.884251	−	0.510523i	−0.872058	+	0.489403i	$0.837215\pi$
$684$	2.69288	+	12.7160i	0.102965	+	0.486208i
$685$	−13.1711	+	7.60432i	−0.503241	+	0.290546i
$686$	3.39428	+	18.2066i	0.129594	+	0.695130i
$687$	1.41895	−	20.1830i	0.0541364	−	0.770029i
$688$	−0.710645	−	4.03027i	−0.0270931	−	0.153653i
$689$	−7.66496	−	43.4701i	−0.292012	−	1.65608i
$690$	−36.0756	−	2.53627i	−1.37337	−	0.0965542i
$691$	25.9753	−	30.9562i	0.988148	−	1.17763i	0.00405194	−	0.999992i	$-0.498710\pi$
$691$	25.9753	−	30.9562i	0.988148	−	1.17763i	0.984096	−	0.177637i	$-0.0568453\pi$
$692$	3.34992	+	5.80223i	0.127345	+	0.220568i
$693$	−41.8496	−	0.868984i	−1.58973	−	0.0330100i
$694$	8.26012	−	14.3069i	0.313550	−	0.543084i
$695$	−1.42296	−	3.90954i	−0.0539758	−	0.148297i
$696$	8.99515	−	6.53020i	0.340960	−	0.247527i
$697$	19.9049	−	16.7022i	0.753953	−	0.632641i
$698$	21.1511	+	7.69836i	0.800579	+	0.291387i
$699$	−3.21416	−	11.2250i	−0.121571	−	0.424569i
$700$	3.14226	−	2.35529i	0.118766	−	0.0890216i
$701$		−	2.80042i		−	0.105770i	−0.998601	−	0.0528851i	$-0.983158\pi$
$701$		−	2.80042i		−	0.105770i	0.998601	−	0.0528851i	$-0.0168417\pi$
$702$	−16.3084	+	18.0713i	−0.615520	+	0.682057i
$703$		−	3.88310i		−	0.146454i
$704$	5.19357	+	0.915766i	0.195740	+	0.0345142i
$705$	−7.07494	−	6.83733i	−0.266458	−	0.257509i
$706$	−12.6478	+	34.7495i	−0.476006	+	1.30782i
$707$	28.2430	+	1.55257i	1.06219	+	0.0583905i
$708$	−0.207659	−	1.98291i	−0.00780431	−	0.0745224i
$709$	−1.69734	+	0.617781i	−0.0637450	+	0.0232013i	−0.373696	−	0.927551i	$-0.621910\pi$
$709$	−1.69734	+	0.617781i	−0.0637450	+	0.0232013i	0.309951	+	0.950753i	$0.399687\pi$
$710$	11.4522	−	19.8358i	0.429793	−	0.744423i
$711$	−19.5525	+	24.9874i	−0.733277	+	0.937100i
$712$	−8.60180	+	4.96625i	−0.322366	+	0.186118i
$713$	36.8999	+	30.9627i	1.38191	+	1.15956i
$714$	−21.5145	−	6.64670i	−0.805161	−	0.248747i
$715$	10.9242	+	61.9542i	0.408542	+	2.31696i
$716$	−0.903581	+	0.159326i	−0.0337684	+	0.00595428i
$717$	29.0826	+	19.6323i	1.08611	+	0.733183i
$718$	13.3608	+	11.2111i	0.498621	+	0.418393i
$719$	1.87236	+	3.24302i	0.0698272	+	0.120944i	0.898825	−	0.438307i	$-0.144422\pi$
$719$	1.87236	+	3.24302i	0.0698272	+	0.120944i	−0.828998	+	0.559252i	$0.811089\pi$
$720$	−6.74237	−	3.59148i	−0.251273	−	0.133847i
$721$	1.84891	+	6.10330i	0.0688572	+	0.227299i
$722$	−0.0779817	−	0.214253i	−0.00290218	−	0.00797367i
$723$	−1.27133	+	2.85258i	−0.0472814	+	0.106089i
$724$	−5.08092	−	6.05521i	−0.188831	−	0.225040i
$725$	−3.25787	+	8.95091i	−0.120994	+	0.332428i
$726$	28.2512	+	7.05509i	1.04850	+	0.261839i
$727$	−23.0697	−	4.06780i	−0.855607	−	0.150867i	−0.271395	−	0.962468i	$-0.587485\pi$
$727$	−23.0697	−	4.06780i	−0.855607	−	0.150867i	−0.584211	+	0.811602i	$0.698596\pi$
$728$	−9.04302	−	8.47608i	−0.335157	−	0.314145i
$729$	−2.76173	−	26.8584i	−0.102286	−	0.994755i
$730$	−22.1538			−0.819948
$731$	3.49197	−	19.8039i	0.129155	−	0.732475i
$732$	10.1143	+	2.52580i	0.373833	+	0.0933563i
$733$	14.2849	−	39.2474i	0.527624	−	1.44964i	−0.334236	−	0.942490i	$-0.608478\pi$
$733$	14.2849	−	39.2474i	0.527624	−	1.44964i	0.861860	−	0.507146i	$-0.169300\pi$
$734$	12.2057	−	10.2418i	0.450520	−	0.378031i
$735$	−10.7185	+	28.9534i	−0.395359	+	1.06796i
$736$	−7.70512	+	2.80443i	−0.284014	+	0.103373i
$737$	−33.1563	−	19.1428i	−1.22133	−	0.705134i
$738$	−7.45818	+	14.0014i	−0.274539	+	0.515399i
$739$	12.1995	+	21.1302i	0.448766	+	0.777286i	0.998306	−	0.0581818i	$-0.0185303\pi$
$739$	12.1995	+	21.1302i	0.448766	+	0.777286i	−0.549540	+	0.835467i	$0.685197\pi$
$740$	1.74827	+	1.46697i	0.0642675	+	0.0539268i
$741$	−19.6696	+	29.1377i	−0.722579	+	1.07040i
$742$	−13.6310	+	20.8728i	−0.500409	+	0.766266i
$743$	5.60455	−	0.988234i	0.205611	−	0.0362548i	−0.0698939	−	0.997554i	$-0.522266\pi$
$743$	5.60455	−	0.988234i	0.205611	−	0.0362548i	0.275505	+	0.961300i	$0.411155\pi$
$744$	4.45703	+	9.14699i	0.163403	+	0.335345i
$745$	34.5460	−	41.1703i	1.26567	−	1.50836i
$746$	19.7922	−	11.4270i	0.724644	−	0.418374i
$747$	−23.3064	+	29.7846i	−0.852735	+	1.08976i
$748$	22.4420	+	12.9569i	0.820562	+	0.473752i
$749$	−8.98958	+	21.0285i	−0.328472	+	0.768364i
$750$	−15.4219	+	1.61505i	−0.563130	+	0.0589734i
$751$	−31.5031	+	26.4342i	−1.14956	+	0.964599i	−0.999709	−	0.0241096i	$-0.992325\pi$
$751$	−31.5031	+	26.4342i	−1.14956	+	0.964599i	−0.149854	+	0.988708i	$0.547881\pi$
$752$	−2.09624	−	0.762970i	−0.0764421	−	0.0278227i
$753$	6.26745	+	6.05695i	0.228398	+	0.220728i
$754$	29.6073	+	5.22056i	1.07823	+	0.190122i
$755$	55.9798			2.03731
$756$	13.6997	−	1.14773i	0.498255	−	0.0417426i
$757$	−49.1050			−1.78475			−0.892376	−	0.451292i	$-0.850963\pi$
$757$	−49.1050			−1.78475			−0.892376	+	0.451292i	$0.850963\pi$
$758$	−4.41232	−	0.778011i	−0.160263	−	0.0282586i
$759$	−72.0040	+	20.6175i	−2.61358	+	0.748369i
$760$	−10.3674	−	3.77344i	−0.376066	−	0.136877i
$761$	−7.94534	+	6.66693i	−0.288018	+	0.241676i	−0.775336	−	0.631548i	$-0.782420\pi$
$761$	−7.94534	+	6.66693i	−0.288018	+	0.241676i	0.487318	+	0.873225i	$0.337975\pi$
$762$	−19.1868	−	26.4292i	−0.695063	−	0.957428i
$763$	−24.5007	−	10.4739i	−0.886985	−	0.379182i
$764$	12.2618	+	7.07936i	0.443617	+	0.256122i
$765$	−25.0967	−	27.9149i	−0.907374	−	1.00926i
$766$	6.05027	−	3.49313i	0.218605	−	0.126212i
$767$	3.46620	−	4.13086i	0.125157	−	0.149157i
$768$	−1.72779	−	0.121471i	−0.0623461	−	0.00438320i
$769$	−18.7911	+	3.31338i	−0.677626	+	0.119484i	−0.501861	−	0.864948i	$-0.667351\pi$
$769$	−18.7911	+	3.31338i	−0.677626	+	0.119484i	−0.175765	+	0.984432i	$0.556240\pi$
$770$	19.4271	−	29.7483i	0.700103	−	1.07205i
$771$	−38.2414	−	2.68854i	−1.37723	−	0.0968254i
$772$	−5.08010	−	4.26271i	−0.182837	−	0.153418i
$773$	4.01335	+	6.95132i	0.144350	+	0.250022i	0.929130	−	0.369753i	$-0.120558\pi$
$773$	4.01335	+	6.95132i	0.144350	+	0.250022i	−0.784780	+	0.619774i	$0.787224\pi$
$774$	2.54358	+	12.0110i	0.0914269	+	0.431725i
$775$	−7.55123	−	4.35971i	−0.271248	−	0.156605i
$776$	−5.98044	+	2.17670i	−0.214685	+	0.0781391i
$777$	−4.07498	−	0.512479i	−0.146189	−	0.0183851i
$778$	−10.0304	+	8.41647i	−0.359606	+	0.301745i
$779$	−7.83603	+	21.5293i	−0.280755	+	0.771367i
$780$	−5.68767	−	19.8634i	−0.203651	−	0.711225i
$781$	8.23706	−	46.7147i	0.294745	−	1.67158i
$782$	−40.2913			−1.44081
$783$	−26.3007	+	20.5007i	−0.939911	+	0.732635i
$784$	0.452581	+	6.98535i	0.0161636	+	0.249477i
$785$	24.7283	+	4.36026i	0.882590	+	0.155624i
$786$	−10.2738	+	10.6309i	−0.366456	+	0.379191i
$787$	−6.52266	+	17.9209i	−0.232508	+	0.638809i	−0.999997	−	0.00225167i	$-0.999283\pi$
$787$	−6.52266	+	17.9209i	−0.232508	+	0.638809i	0.767490	+	0.641061i	$0.221505\pi$
$788$	0.0953425	+	0.113625i	0.00339644	+	0.00404772i
$789$	24.0177	−	2.51524i	0.855053	−	0.0895449i
$790$	−9.21094	−	25.3069i	−0.327711	−	0.900378i
$791$	−0.150607	−	0.497155i	−0.00535496	−	0.0176768i
$792$	−15.6654	−	2.21364i	−0.556647	−	0.0786581i
$793$	14.0979	+	24.4183i	0.500632	+	0.867119i
$794$	2.16687	+	1.81822i	0.0768995	+	0.0645263i
$795$	−37.3590	+	18.2038i	−1.32499	+	0.645623i
$796$	−1.98447	+	0.349915i	−0.0703376	+	0.0124024i
$797$	−0.0788175	−	0.446997i	−0.00279186	−	0.0158334i	0.983380	−	0.181559i	$-0.0581144\pi$
$797$	−0.0788175	−	0.446997i	−0.00279186	−	0.0158334i	−0.986172	+	0.165726i	$0.947003\pi$
$798$	19.3589	−	4.40960i	0.685298	−	0.156098i
$799$	−8.39706	−	7.04597i	−0.297067	−	0.249268i
$800$	1.28541	−	0.742129i	0.0454460	−	0.0262382i
$801$	25.2816	−	15.7713i	0.893281	−	0.557251i
$802$	−13.0648	+	22.6288i	−0.461333	+	0.799052i
$803$	−43.1139	+	15.6922i	−1.52146	+	0.553765i
$804$	11.4852	+	5.11872i	0.405052	+	0.180523i
$805$	−3.03221	+	55.1591i	−0.106871	+	1.94410i
$806$	−9.41249	+	25.8606i	−0.331541	+	0.910901i
$807$	2.50149	−	10.0169i	0.0880565	−	0.352611i
$808$	10.5285	+	1.85647i	0.370393	+	0.0653102i
$809$			11.4927i			0.404062i	0.979379	+	0.202031i	$0.0647542\pi$
$809$			11.4927i			0.404062i	−0.979379	+	0.202031i	$0.935246\pi$
$810$	20.5832	+	10.0774i	0.723222	+	0.354085i
$811$		−	30.4408i		−	1.06892i	−0.845193	−	0.534461i	$-0.820515\pi$
$811$		−	30.4408i		−	1.06892i	0.845193	−	0.534461i	$-0.179485\pi$
$812$	−10.1837	−	13.5864i	−0.357378	−	0.476789i
$813$	−48.0011	−	11.9872i	−1.68347	−	0.420409i
$814$	4.44143	+	1.61655i	0.155672	+	0.0566600i
$815$	−12.0764	+	10.1333i	−0.423017	+	0.354953i
$816$	−7.77384	−	3.46464i	−0.272139	−	0.121287i
$817$	6.06442	+	16.6619i	0.212167	+	0.582925i
$818$	0.436387	−	0.755844i	0.0152579	−	0.0264275i
$819$	27.9816	+	24.4870i	0.977755	+	0.855645i
$820$	−6.73270	−	11.6614i	−0.235116	−	0.407233i
$821$	27.6443	−	32.9452i	0.964793	−	1.14980i	−0.0238802	−	0.999715i	$-0.507602\pi$
$821$	27.6443	−	32.9452i	0.964793	−	1.14980i	0.988674	−	0.150081i	$-0.0479535\pi$
$822$	5.78795	−	8.57403i	0.201878	−	0.299054i
$823$	−3.48262	−	19.7509i	−0.121396	−	0.688473i	−0.983383	−	0.181542i	$-0.941891\pi$
$823$	−3.48262	−	19.7509i	−0.121396	−	0.688473i	0.861987	−	0.506931i	$-0.169220\pi$
$824$	0.418554	+	2.37374i	0.0145810	+	0.0826931i
$825$	12.1878	−	5.93870i	0.424324	−	0.206759i
$826$	−3.02375	+	0.363425i	−0.105210	+	0.0126452i
$827$	−5.62389	+	3.24696i	−0.195562	+	0.112908i	−0.594584	−	0.804034i	$-0.702683\pi$
$827$	−5.62389	+	3.24696i	−0.195562	+	0.112908i	0.399022	+	0.916941i	$0.369350\pi$
$828$	22.8146	−	9.19775i	0.792861	−	0.319644i
$829$	23.5097	+	13.5733i	0.816525	+	0.471421i	0.849217	−	0.528044i	$-0.177075\pi$
$829$	23.5097	+	13.5733i	0.816525	+	0.471421i	−0.0326915	+	0.999465i	$0.510408\pi$
$830$	−10.9793	−	30.1655i	−0.381098	−	1.04706i
$831$	−3.83171	−	36.5885i	−0.132921	−	1.26924i
$832$	−3.01122	−	3.58863i	−0.104395	−	0.124413i
$833$	−9.64994	+	33.0152i	−0.334351	+	1.14391i
$834$	2.03492	+	1.96658i	0.0704635	+	0.0680970i
$835$	1.82103	−	10.3276i	0.0630193	−	0.357400i
$836$	−22.8491			−0.790253
$837$	−14.3004	−	26.9684i	−0.494293	−	0.932163i
$838$		−	20.4845i		−	0.707627i
$839$	1.52905	−	8.67169i	0.0527888	−	0.299380i	−0.946971	−	0.321320i	$-0.895873\pi$
$839$	1.52905	−	8.67169i	0.0527888	−	0.299380i	0.999759	+	0.0219405i	$0.00698445\pi$
$840$	−5.32816	+	10.3817i	−0.183839	+	0.358203i
$841$	11.4506	+	4.16766i	0.394847	+	0.143712i
$842$	2.76400	+	3.29401i	0.0952538	+	0.113519i
$843$	0.229189	+	0.315701i	0.00789369	+	0.0108733i
$844$	−9.41392	+	3.42639i	−0.324041	+	0.117941i
$845$	11.3898	−	19.7277i	0.391822	−	0.678655i
$846$	6.36322	+	2.07282i	0.218772	+	0.0712652i
$847$	10.1165	−	43.3140i	0.347608	−	1.48829i
$848$	−6.05664	+	7.21802i	−0.207986	+	0.247868i
$849$	−2.54793	+	36.2414i	−0.0874446	+	1.24380i
$850$	7.18255	−	1.26648i	0.246359	−	0.0434398i
$851$	−7.23716	+	1.27611i	−0.248087	+	0.0437443i
$852$	−1.09260	+	15.5410i	−0.0374318	+	0.532425i
$853$	16.3019	−	19.4278i	0.558166	−	0.665196i	−0.410991	−	0.911639i	$-0.634817\pi$
$853$	16.3019	−	19.4278i	0.558166	−	0.665196i	0.969157	+	0.246443i	$0.0792618\pi$
$854$	3.62183	−	15.5069i	0.123937	−	0.530635i
$855$	31.4707	+	10.2516i	1.07628	+	0.350598i
$856$	−4.32191	+	7.48577i	−0.147720	+	0.255858i
$857$	40.2291	−	14.6422i	1.37420	−	0.500168i	0.453786	−	0.891111i	$-0.350073\pi$
$857$	40.2291	−	14.6422i	1.37420	−	0.500168i	0.920415	+	0.390942i	$0.127851\pi$
$858$	−25.1388	−	34.6279i	−0.858223	−	1.18218i
$859$	−27.9961	−	33.3644i	−0.955213	−	1.13838i	−0.990293	−	0.138994i	$-0.955613\pi$
$859$	−27.9961	−	33.3644i	−0.955213	−	1.13838i	0.0350797	−	0.999385i	$-0.488831\pi$
$860$	−9.79261	−	3.56422i	−0.333925	−	0.121539i
$861$	21.5590	+	11.0646i	0.734728	+	0.377081i
$862$	−0.869789	+	4.93282i	−0.0296251	+	0.168012i
$863$		−	2.17856i		−	0.0741589i	−0.999312	−	0.0370795i	$-0.988195\pi$
$863$		−	2.17856i		−	0.0741589i	0.999312	−	0.0370795i	$-0.0118055\pi$
$864$	5.19278	+	0.187196i	0.176662	+	0.00636853i
$865$	17.0606			0.580078
$866$	4.05880	−	23.0186i	0.137923	−	0.782203i
$867$	−8.89949	−	8.60060i	−0.302243	−	0.292092i
$868$	13.8667	−	7.02081i	0.470665	−	0.238302i
$869$	−35.8512	−	42.7258i	−1.21617	−	1.44937i
$870$	−2.94810	−	28.1510i	−0.0999499	−	0.954409i
$871$	11.6318	+	31.9582i	0.394129	+	1.08286i
$872$	−8.72182	−	5.03555i	−0.295358	−	0.170525i
$873$	17.7079	−	7.13897i	0.599321	−	0.241618i
$874$	30.7666	−	17.7631i	1.04070	−	0.600846i
$875$	2.82651	+	23.5170i	0.0955534	+	0.795019i
$876$	13.5462	−	6.60063i	0.457684	−	0.223015i
$877$	2.89582	+	16.4230i	0.0977848	+	0.554565i	0.993858	+	0.110660i	$0.0352964\pi$
$877$	2.89582	+	16.4230i	0.0977848	+	0.554565i	−0.896074	+	0.443906i	$0.853593\pi$
$878$	3.89566	+	22.0934i	0.131472	+	0.745616i
$879$	7.49639	−	11.1049i	0.252847	−	0.374557i
$880$	8.63201	−	10.2872i	0.290985	−	0.346782i
$881$	0.915202	+	1.58518i	0.0308340	+	0.0534060i	0.881031	−	0.473059i	$-0.156850\pi$
$881$	0.915202	+	1.58518i	0.0308340	+	0.0534060i	−0.850197	+	0.526465i	$0.823517\pi$
$882$	−2.07257	−	20.8975i	−0.0697871	−	0.703655i
$883$	20.8174	−	36.0567i	0.700560	−	1.21341i	−0.267710	−	0.963499i	$-0.586267\pi$
$883$	20.8174	−	36.0567i	0.700560	−	1.21341i	0.968270	−	0.249906i	$-0.0803997\pi$
$884$	−7.87307	−	21.6311i	−0.264800	−	0.727532i
$885$	−4.63724	−	2.06672i	−0.155879	−	0.0694720i
$886$	17.1930	−	14.4266i	0.577609	−	0.484672i
$887$	−46.5492	−	16.9425i	−1.56297	−	0.568874i	−0.591555	−	0.806265i	$-0.701486\pi$
$887$	−46.5492	−	16.9425i	−1.56297	−	0.568874i	−0.971414	+	0.237391i	$0.923708\pi$
$888$	−1.50608	−	0.376108i	−0.0505406	−	0.0126214i
$889$	−39.9190	+	29.9214i	−1.33884	+	1.00353i
$890$			25.2923i			0.847801i
$891$	47.1956	+	5.03218i	1.58111	+	0.168584i
$892$		−	17.9108i		−	0.599697i
$893$	9.51837	+	1.67835i	0.318520	+	0.0561637i
$894$	−8.85705	+	35.4669i	−0.296224	+	1.18619i
$895$	−0.799093	+	2.19549i	−0.0267107	+	0.0733872i
$896$	−0.145223	+	2.64176i	−0.00485156	+	0.0882551i
$897$	60.7696	+	27.0837i	2.02904	+	0.904300i
$898$	18.1655	−	6.61169i	0.606190	−	0.220635i
$899$	−18.8504	+	32.6498i	−0.628694	+	1.08893i
$900$	−3.77794	+	2.35677i	−0.125931	+	0.0785591i
$901$	−40.0971	+	23.1500i	−1.33583	+	0.771240i
$902$	−21.3627	−	17.9255i	−0.711302	−	0.596853i
$903$	18.2856	−	4.16511i	0.608505	−	0.138606i
$904$	−0.0340941	−	0.193357i	−0.00113395	−	0.00643096i
$905$	−19.8224	+	3.49523i	−0.658920	+	0.116185i
$906$	−34.2296	+	16.6790i	−1.13720	+	0.554122i
$907$	−30.4725	−	25.5694i	−1.01182	−	0.849019i	−0.0232438	−	0.999730i	$-0.507399\pi$
$907$	−30.4725	−	25.5694i	−1.01182	−	0.849019i	−0.988578	+	0.150711i	$0.951844\pi$
$908$	2.16250	+	3.74556i	0.0717651	+	0.124301i
$909$	−31.7574	−	4.48754i	−1.05333	−	0.148842i
$910$	−30.2057	+	9.15042i	−1.00131	+	0.303333i
$911$	−5.87526	−	16.1421i	−0.194656	−	0.534813i	0.803514	−	0.595286i	$-0.202961\pi$
$911$	−5.87526	−	16.1421i	−0.194656	−	0.534813i	−0.998170	+	0.0604732i	$0.980739\pi$
$912$	7.46358	−	0.781619i	0.247144	−	0.0258820i
$913$	−42.7342	−	50.9286i	−1.41430	−	1.68549i
$914$	−0.533865	+	1.46678i	−0.0176587	+	0.0485168i
$915$	18.4476	−	19.0887i	0.609860	−	0.631054i
$916$	−11.5039	−	2.02846i	−0.380101	−	0.0670221i
$917$	16.4767	+	15.4437i	0.544109	+	0.509997i
$918$	23.6629	+	9.59145i	0.780991	+	0.316565i
$919$	30.8418			1.01738			0.508688	−	0.860951i	$-0.330131\pi$
$919$	30.8418			1.01738			0.508688	+	0.860951i	$0.330131\pi$
$920$	−3.62572	+	20.5625i	−0.119536	+	0.677924i
$921$	11.3797	+	39.7421i	0.374974	+	1.30955i
$922$	−13.1339	+	36.0852i	−0.432544	+	1.18840i
$923$	−32.2788	+	27.0851i	−1.06247	+	0.891517i
$924$	−3.01555	+	23.9782i	−0.0992044	+	0.788824i
$925$	1.25002	−	0.454972i	0.0411006	−	0.0149594i
$926$	21.8332	+	12.6054i	0.717485	+	0.414240i
$927$	−1.49811	−	7.07418i	−0.0492043	−	0.232347i
$928$	−3.20879	−	5.55779i	−0.105334	−	0.182444i
$929$	−23.3958	−	19.6314i	−0.767592	−	0.644086i	0.172499	−	0.985010i	$-0.444816\pi$
$929$	−23.3958	−	19.6314i	−0.767592	−	0.644086i	−0.940091	+	0.340923i	$0.889260\pi$
$930$	25.8463	+	1.81710i	0.847532	+	0.0595852i
$931$	−7.18659	−	29.4649i	−0.235531	−	0.965673i
$932$	−6.63879	+	1.17060i	−0.217461	+	0.0383442i
$933$	−0.611745	−	0.0430083i	−0.0200276	−	0.00140803i
$934$	−20.0531	+	23.8983i	−0.656156	+	0.781976i
$935$	57.1469	−	32.9938i	1.86890	−	1.07901i
$936$	9.39603	+	10.4511i	0.307119	+	0.341606i
$937$	−2.37693	−	1.37232i	−0.0776510	−	0.0448318i	0.460672	−	0.887571i	$-0.347609\pi$
$937$	−2.37693	−	1.37232i	−0.0776510	−	0.0448318i	−0.538323	+	0.842739i	$0.680942\pi$
$938$	7.55014	−	17.6613i	0.246521	−	0.576663i
$939$	−10.6545	−	14.6763i	−0.347697	−	0.478942i
$940$	−4.35151	+	3.65135i	−0.141931	+	0.119094i
$941$	−18.7249	−	6.81530i	−0.610414	−	0.222173i	0.0182704	−	0.999833i	$-0.494184\pi$
$941$	−18.7249	−	6.81530i	−0.610414	−	0.222173i	−0.628684	+	0.777661i	$0.716406\pi$
$942$	−16.4195	+	4.70155i	−0.534978	+	0.153185i
$943$	42.7006	+	7.52926i	1.39052	+	0.245187i
$944$	−1.15110			−0.0374650
$945$	14.9116	−	31.6729i	0.485074	−	1.03032i
$946$	−21.5823			−0.701700
$947$	−5.62577	−	0.991976i	−0.182813	−	0.0322349i	0.0814920	−	0.996674i	$-0.474031\pi$
$947$	−5.62577	−	0.991976i	−0.182813	−	0.0322349i	−0.264305	+	0.964439i	$0.585143\pi$
$948$	13.1722	+	12.7298i	0.427814	+	0.413446i
$949$	38.2982	+	13.9394i	1.24321	+	0.452492i
$950$	−4.92628	+	4.13364i	−0.159830	+	0.134113i
$951$	17.5157	−	1.83432i	0.567986	−	0.0594820i
$952$	−5.11036	+	11.9542i	−0.165628	+	0.387437i
$953$	−28.4693	−	16.4368i	−0.922211	−	0.532439i	−0.0378713	−	0.999283i	$-0.512058\pi$
$953$	−28.4693	−	16.4368i	−0.922211	−	0.532439i	−0.884340	+	0.466844i	$0.845391\pi$
$954$	17.4199	−	22.2619i	0.563989	−	0.720756i
$955$	31.2237	−	18.0270i	1.01038	−	0.583341i
$956$	13.0219	−	15.5189i	0.421159	−	0.501918i
$957$	−25.6776	−	52.6971i	−0.830038	−	1.70345i
$958$	26.0343	−	4.59056i	0.841131	−	0.148314i
$959$	−13.2305	−	8.64019i	−0.427237	−	0.279006i
$960$	−2.46771	+	3.65557i	−0.0796450	+	0.117983i
$961$	−2.68945	−	2.25671i	−0.0867563	−	0.0727972i
$962$	−2.09927	−	3.63604i	−0.0676832	−	0.117231i
$963$	12.1913	−	22.8870i	0.392859	−	0.737522i
$964$	1.56153	+	0.901550i	0.0502935	+	0.0290370i
$965$	−15.8684	+	5.77564i	−0.510823	+	0.185924i
$966$	−14.5804	−	34.6312i	−0.469116	−	1.11424i
$967$	2.62559	−	2.20313i	0.0844332	−	0.0708479i	−0.599594	−	0.800304i	$-0.704671\pi$
$967$	2.62559	−	2.20313i	0.0844332	−	0.0708479i	0.684027	+	0.729456i	$0.260227\pi$
$968$	5.74996	−	15.7979i	0.184811	−	0.507763i
$969$	35.7764	+	8.93434i	1.14930	+	0.287012i
$970$	−2.81416	+	15.9599i	−0.0903571	+	0.512440i
$971$	−47.4770			−1.52361			−0.761805	−	0.647806i	$-0.775687\pi$
$971$	−47.4770			−1.52361			−0.761805	+	0.647806i	$0.775687\pi$
$972$	−15.5884	−	0.0292822i	−0.499999	−	0.000939227i
$973$	2.95617	−	3.15390i	0.0947706	−	0.101109i
$974$	−6.02657	−	1.06265i	−0.193104	−	0.0340494i
$975$	−11.6845	−	2.91793i	−0.374202	−	0.0934485i
$976$	2.05855	−	5.65582i	0.0658926	−	0.181038i
$977$	31.3920	+	37.4115i	1.00432	+	1.19690i	0.980366	+	0.197188i	$0.0631808\pi$
$977$	31.3920	+	37.4115i	1.00432	+	1.19690i	0.0239533	+	0.999713i	$0.492375\pi$
$978$	4.36508	−	9.79423i	0.139580	−	0.313185i
$979$	17.9153	+	49.2219i	0.572576	+	1.57314i
$980$	15.9808	+	7.89576i	0.510488	+	0.252221i
$981$	26.6661	+	14.2043i	0.851382	+	0.453509i
$982$	9.44427	+	16.3580i	0.301379	+	0.522003i
$983$	18.3269	+	15.3781i	0.584537	+	0.490484i	0.886433	−	0.462856i	$-0.153175\pi$
$983$	18.3269	+	15.3781i	0.584537	+	0.490484i	−0.301897	+	0.953341i	$0.597620\pi$
$984$	7.59126	+	5.12452i	0.242000	+	0.163364i
$985$	0.371964	−	0.0655873i	0.0118518	−	0.00208978i
$986$	−5.47595	−	31.0557i	−0.174390	−	0.989014i
$987$	3.01748	−	9.76721i	0.0960475	−	0.310894i
$988$	15.5484	+	13.0466i	0.494659	+	0.415068i
$989$	29.0607	−	16.7782i	0.924078	−	0.533516i
$990$	−24.8270	+	31.7280i	−0.789055	+	1.00838i
$991$	−23.9239	+	41.4373i	−0.759966	+	1.31630i	0.182901	+	0.983131i	$0.441451\pi$
$991$	−23.9239	+	41.4373i	−0.759966	+	1.31630i	−0.942867	+	0.333169i	$0.891882\pi$
$992$	5.52031	−	2.00923i	0.175270	−	0.0637931i
$993$	−3.14095	−	29.9925i	−0.0996750	−	0.951784i
$994$	23.7619	+	1.30624i	0.753683	+	0.0414314i
$995$	−1.75499	+	4.82179i	−0.0556369	+	0.152861i
$996$	15.7011	+	15.1738i	0.497510	+	0.480801i
$997$	58.9417	+	10.3930i	1.86670	+	0.329150i	0.988747	−	0.149596i	$-0.0477973\pi$
$997$	58.9417	+	10.3930i	1.86670	+	0.329150i	0.877954	+	0.478746i	$0.158908\pi$
$998$		−	1.29232i		−	0.0409077i
$999$	4.55413	+	0.973376i	0.144086	+	0.0307962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.83.17	yes	144
7.6	odd	2	inner	378.2.z.a.83.20	yes	144
27.14	odd	18	inner	378.2.z.a.41.20	yes	144
189.41	even	18	inner	378.2.z.a.41.17	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.17	✓	144	189.41	even	18	inner
378.2.z.a.41.20	yes	144	27.14	odd	18	inner
378.2.z.a.83.17	yes	144	1.1	even	1	trivial
378.2.z.a.83.20	yes	144	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.419652 + 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.95067 - 1.63681i) q^{5} +(-0.705083 + 1.58204i) q^{6} +(2.43278 + 1.04000i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.419652 + 1.68044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.95067 - 1.63681i) q^{5} +(-0.705083 + 1.58204i) q^{6} +(2.43278 + 1.04000i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.64778 - 1.41040i) q^{9} +(2.20527 - 1.27321i) q^{10} +(3.38986 - 4.03988i) q^{11} +(-0.969090 + 1.43557i) q^{12} +(-4.61346 + 0.813477i) q^{13} +(2.21522 + 1.44665i) q^{14} +(1.93196 + 3.96488i) q^{15} +(0.766044 + 0.642788i) q^{16} +(2.45690 + 4.25548i) q^{17} +(-2.36264 - 1.84876i) q^{18} +(-3.75220 - 2.16633i) q^{19} +(2.39285 - 0.870927i) q^{20} +(-2.76858 + 3.65170i) q^{21} +(4.03988 - 3.38986i) q^{22} +(-2.80443 + 7.70512i) q^{23} +(-1.20365 + 1.24548i) q^{24} +(0.257739 - 1.46171i) q^{25} -4.68463 q^{26} +(3.48125 - 3.85757i) q^{27} +(1.93036 + 1.80934i) q^{28} +(-6.32009 - 1.11440i) q^{29} +(1.21411 + 4.24013i) q^{30} +(2.00923 - 5.52031i) q^{31} +(0.642788 + 0.766044i) q^{32} +(5.36622 + 7.39181i) q^{33} +(1.68062 + 4.61746i) q^{34} +(6.44783 - 1.95329i) q^{35} +(-2.00572 - 2.23094i) q^{36} +(0.448119 + 0.776165i) q^{37} +(-3.31901 - 2.78498i) q^{38} +(0.569046 - 8.09404i) q^{39} +(2.50773 - 0.442181i) q^{40} +(-0.918246 - 5.20763i) q^{41} +(-3.36063 + 3.11547i) q^{42} +(-3.13499 - 2.63057i) q^{43} +(4.56714 - 2.63684i) q^{44} +(-7.47352 + 1.58268i) q^{45} +(-4.09981 + 7.10107i) q^{46} +(-2.09624 + 0.762970i) q^{47} +(-1.40164 + 1.01755i) q^{48} +(4.83680 + 5.06018i) q^{49} +(0.507646 - 1.39475i) q^{50} +(-8.18213 + 2.34286i) q^{51} +(-4.61346 - 0.813477i) q^{52} +9.42246i q^{53} +(4.09823 - 3.19445i) q^{54} -13.4290i q^{55} +(1.58685 + 2.11706i) q^{56} +(5.21502 - 5.39625i) q^{57} +(-6.03056 - 2.19494i) q^{58} +(-0.881790 + 0.739910i) q^{59} +(0.459378 + 4.38654i) q^{60} +(-2.05855 - 5.65582i) q^{61} +(2.93730 - 5.08755i) q^{62} +(-4.97464 - 6.18490i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.66784 + 9.13817i) q^{65} +(4.00112 + 8.21135i) q^{66} +(-1.26064 - 7.14945i) q^{67} +(0.853272 + 4.83915i) q^{68} +(-11.7711 - 7.94616i) q^{69} +(6.68906 - 0.803958i) q^{70} +(7.78966 - 4.49736i) q^{71} +(-1.58785 - 2.54534i) q^{72} +(-7.53439 - 4.34998i) q^{73} +(0.306531 + 0.842188i) q^{74} +(2.34816 + 1.04653i) q^{75} +(-2.78498 - 3.31901i) q^{76} +(12.4482 - 6.30266i) q^{77} +(1.96592 - 7.87226i) q^{78} +(1.83651 - 10.4153i) q^{79} +2.54642 q^{80} +(5.02152 + 7.46889i) q^{81} -5.28797i q^{82} +(2.18909 - 12.4150i) q^{83} +(-3.85057 + 2.48457i) q^{84} +(11.7580 + 4.27956i) q^{85} +(-2.63057 - 3.13499i) q^{86} +(4.52493 - 10.1529i) q^{87} +(4.95564 - 1.80371i) q^{88} +(-4.96625 + 8.60180i) q^{89} +(-7.63481 + 0.260870i) q^{90} +(-12.0695 - 2.81899i) q^{91} +(-5.27061 + 6.28127i) q^{92} +(8.43339 + 5.69301i) q^{93} +(-2.19688 + 0.387370i) q^{94} +(-10.8652 + 1.91582i) q^{95} +(-1.55704 + 0.758696i) q^{96} +(-4.09086 + 4.87530i) q^{97} +(3.88462 + 5.82320i) q^{98} +(-14.6735 + 5.91565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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