LMFDB - Embedded newform 728.2.cz.a.309.72

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(309,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.309"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.72
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.72

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28678 - 0.586673i) q^{2} +(-1.27132 + 0.733996i) q^{3} +(1.31163 - 1.50984i) q^{4} -3.32694 q^{5} +(-1.20530 + 1.69034i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.802001 - 2.71234i) q^{8} +(-0.422500 + 0.731791i) q^{9} +(-4.28106 + 1.95183i) q^{10} +(1.07297 + 1.85844i) q^{11} +(-0.559280 + 2.88222i) q^{12} +(3.60303 + 0.134708i) q^{13} +(1.40772 + 0.135319i) q^{14} +(4.22960 - 2.44196i) q^{15} +(-0.559254 - 3.96071i) q^{16} +(-3.58968 + 6.21750i) q^{17} +(-0.114344 + 1.18953i) q^{18} +(-2.04773 + 3.54677i) q^{19} +(-4.36372 + 5.02316i) q^{20} -1.46799 q^{21} +(2.47098 + 1.76193i) q^{22} +(2.38394 + 4.12910i) q^{23} +(0.971249 + 4.03691i) q^{24} +6.06855 q^{25} +(4.71536 - 1.94046i) q^{26} -5.64443i q^{27} +(1.89083 - 0.651748i) q^{28} +(0.389432 - 0.224839i) q^{29} +(4.00996 - 5.62367i) q^{30} +8.04759i q^{31} +(-3.04328 - 4.76848i) q^{32} +(-2.72817 - 1.57511i) q^{33} +(-0.971501 + 10.1065i) q^{34} +(-2.88122 - 1.66347i) q^{35} +(0.550727 + 1.59775i) q^{36} +(4.63709 + 8.03168i) q^{37} +(-0.554192 + 5.76527i) q^{38} +(-4.67948 + 2.47336i) q^{39} +(-2.66821 + 9.02380i) q^{40} +(-0.755099 + 0.435957i) q^{41} +(-1.88899 + 0.861231i) q^{42} +(-5.05881 - 2.92071i) q^{43} +(4.21329 + 0.817567i) q^{44} +(1.40563 - 2.43463i) q^{45} +(5.49005 + 3.91467i) q^{46} -7.30129i q^{47} +(3.61814 + 4.62483i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.80892 - 3.56025i) q^{50} -10.5392i q^{51} +(4.92924 - 5.26333i) q^{52} +4.80295i q^{53} +(-3.31143 - 7.26316i) q^{54} +(-3.56971 - 6.18292i) q^{55} +(2.05072 - 1.94796i) q^{56} -6.01209i q^{57} +(0.369209 - 0.517789i) q^{58} +(1.24577 - 2.15774i) q^{59} +(1.86069 - 9.58899i) q^{60} +(4.96788 + 2.86821i) q^{61} +(4.72130 + 10.3555i) q^{62} +(-0.731791 + 0.422500i) q^{63} +(-6.71359 - 4.35060i) q^{64} +(-11.9871 - 0.448166i) q^{65} +(-4.43465 - 0.426284i) q^{66} +(-1.25603 - 2.17551i) q^{67} +(4.67913 + 13.5749i) q^{68} +(-6.06149 - 3.49960i) q^{69} +(-4.68342 - 0.450198i) q^{70} +(-10.6327 - 6.13877i) q^{71} +(1.64602 + 1.73286i) q^{72} -10.1665i q^{73} +(10.6789 + 7.61459i) q^{74} +(-7.71506 + 4.45429i) q^{75} +(2.66920 + 7.74379i) q^{76} +2.14594i q^{77} +(-4.57043 + 5.92800i) q^{78} +2.66373 q^{79} +(1.86061 + 13.1771i) q^{80} +(2.87549 + 4.98049i) q^{81} +(-0.715886 + 1.00398i) q^{82} -15.2629 q^{83} +(-1.92546 + 2.21644i) q^{84} +(11.9426 - 20.6853i) q^{85} +(-8.22310 - 0.790453i) q^{86} +(-0.330062 + 0.571683i) q^{87} +(5.90124 - 1.41979i) q^{88} +(2.59946 - 1.50080i) q^{89} +(0.380417 - 3.95749i) q^{90} +(3.05296 + 1.91818i) q^{91} +(9.36114 + 1.81648i) q^{92} +(-5.90690 - 10.2310i) q^{93} +(-4.28347 - 9.39519i) q^{94} +(6.81267 - 11.7999i) q^{95} +(7.36903 + 3.82850i) q^{96} +(13.7708 + 7.95057i) q^{97} +(1.15147 + 0.821052i) q^{98} -1.81332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) $ 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.28678	−	0.586673i	0.909894	−	0.414840i
$2$	1.28678	−	0.586673i	0.909894	−	0.414840i
$3$	−1.27132	+	0.733996i	−0.733996	+	0.423773i	−0.819882	−	0.572532i	$-0.805961\pi$
$3$	−1.27132	+	0.733996i	−0.733996	+	0.423773i	0.0858863	+	0.996305i	$0.472628\pi$
$4$	1.31163	−	1.50984i	0.655815	−	0.754922i
$5$	−3.32694			−1.48785			−0.743927	−	0.668261i	$-0.767039\pi$
$5$	−3.32694			−1.48785			−0.743927	+	0.668261i	$0.767039\pi$
$6$	−1.20530	+	1.69034i	−0.492061	+	0.690080i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	0.802001	−	2.71234i	0.283550	−	0.958957i
$9$	−0.422500	+	0.731791i	−0.140833	+	0.243930i
$10$	−4.28106	+	1.95183i	−1.35379	+	0.617222i
$11$	1.07297	+	1.85844i	0.323513	+	0.560340i	0.981210	−	0.192942i	$-0.0618028\pi$
$11$	1.07297	+	1.85844i	0.323513	+	0.560340i	−0.657697	+	0.753282i	$0.728469\pi$
$12$	−0.559280	+	2.88222i	−0.161450	+	0.832026i
$13$	3.60303	+	0.134708i	0.999302	+	0.0373613i
$13$	3.60303	+	0.134708i	0.999302	+	0.0373613i
$14$	1.40772	+	0.135319i	0.376230	+	0.0361655i
$15$	4.22960	−	2.44196i	1.09208	−	0.630512i
$16$	−0.559254	−	3.96071i	−0.139813	−	0.990178i
$17$	−3.58968	+	6.21750i	−0.870624	+	1.50797i	−0.00927198	+	0.999957i	$0.502951\pi$
$17$	−3.58968	+	6.21750i	−0.870624	+	1.50797i	−0.861352	+	0.508008i	$0.830382\pi$
$18$	−0.114344	+	1.18953i	−0.0269512	+	0.280374i
$19$	−2.04773	+	3.54677i	−0.469781	+	0.813684i	−0.999403	−	0.0345496i	$-0.989000\pi$
$19$	−2.04773	+	3.54677i	−0.469781	+	0.813684i	0.529622	+	0.848234i	$0.322334\pi$
$20$	−4.36372	+	5.02316i	−0.975757	+	1.12321i
$21$	−1.46799			−0.320342
$22$	2.47098	+	1.76193i	0.526814	+	0.375644i
$23$	2.38394	+	4.12910i	0.497085	+	0.860977i	0.999994	−	0.00336217i	$-0.00107021\pi$
$23$	2.38394	+	4.12910i	0.497085	+	0.860977i	−0.502909	+	0.864339i	$0.667737\pi$
$24$	0.971249	+	4.03691i	0.198255	+	0.824032i
$25$	6.06855			1.21371
$26$	4.71536	−	1.94046i	0.924758	−	0.380556i
$27$		−	5.64443i		−	1.08627i
$28$	1.89083	−	0.651748i	0.357333	−	0.123169i
$29$	0.389432	−	0.224839i	0.0723158	−	0.0417515i	−0.463406	−	0.886146i	$-0.653373\pi$
$29$	0.389432	−	0.224839i	0.0723158	−	0.0417515i	0.535722	+	0.844394i	$0.320040\pi$
$30$	4.00996	−	5.62367i	0.732114	−	1.02674i
$31$			8.04759i			1.44539i	0.691167	+	0.722695i	$0.257097\pi$
$31$			8.04759i			1.44539i	−0.691167	+	0.722695i	$0.742903\pi$
$32$	−3.04328	−	4.76848i	−0.537981	−	0.842957i
$33$	−2.72817	−	1.57511i	−0.474914	−	0.274192i
$34$	−0.971501	+	10.1065i	−0.166611	+	1.73326i
$35$	−2.88122	−	1.66347i	−0.487015	−	0.281178i
$36$	0.550727	+	1.59775i	0.0917878	+	0.266291i
$37$	4.63709	+	8.03168i	0.762334	+	1.32040i	0.941645	+	0.336608i	$0.109280\pi$
$37$	4.63709	+	8.03168i	0.762334	+	1.32040i	−0.179311	+	0.983792i	$0.557387\pi$
$38$	−0.554192	+	5.76527i	−0.0899017	+	0.935250i
$39$	−4.67948	+	2.47336i	−0.749316	+	0.396054i
$40$	−2.66821	+	9.02380i	−0.421881	+	1.42679i
$41$	−0.755099	+	0.435957i	−0.117927	+	0.0680850i	−0.557803	−	0.829973i	$-0.688356\pi$
$41$	−0.755099	+	0.435957i	−0.117927	+	0.0680850i	0.439876	+	0.898058i	$0.355022\pi$
$42$	−1.88899	+	0.861231i	−0.291477	+	0.132891i
$43$	−5.05881	−	2.92071i	−0.771461	−	0.445403i	0.0619342	−	0.998080i	$-0.480273\pi$
$43$	−5.05881	−	2.92071i	−0.771461	−	0.445403i	−0.833396	+	0.552677i	$0.813606\pi$
$44$	4.21329	+	0.817567i	0.635178	+	0.123253i
$45$	1.40563	−	2.43463i	0.209539	−	0.362933i
$46$	5.49005	+	3.91467i	0.809463	+	0.577187i
$47$		−	7.30129i		−	1.06500i	−0.846429	−	0.532502i	$-0.821252\pi$
$47$		−	7.30129i		−	1.06500i	0.846429	−	0.532502i	$-0.178748\pi$
$48$	3.61814	+	4.62483i	0.522233	+	0.667537i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	7.80892	−	3.56025i	1.10435	−	0.503496i
$51$		−	10.5392i		−	1.47579i
$52$	4.92924	−	5.26333i	0.683562	−	0.729893i
$53$			4.80295i			0.659736i	0.944027	+	0.329868i	$0.107004\pi$
$53$			4.80295i			0.659736i	−0.944027	+	0.329868i	$0.892996\pi$
$54$	−3.31143	−	7.26316i	−0.450629	−	0.988391i
$55$	−3.56971	−	6.18292i	−0.481340	−	0.833705i
$56$	2.05072	−	1.94796i	0.274040	−	0.260307i
$57$		−	6.01209i		−	0.796321i
$58$	0.369209	−	0.517789i	0.0484795	−	0.0679890i
$59$	1.24577	−	2.15774i	0.162185	−	0.280913i	−0.773467	−	0.633837i	$-0.781479\pi$
$59$	1.24577	−	2.15774i	0.162185	−	0.280913i	0.935652	+	0.352923i	$0.114812\pi$
$60$	1.86069	−	9.58899i	0.240214	−	1.23793i
$61$	4.96788	+	2.86821i	0.636072	+	0.367237i	0.783100	−	0.621896i	$-0.213637\pi$
$61$	4.96788	+	2.86821i	0.636072	+	0.367237i	−0.147028	+	0.989132i	$0.546971\pi$
$62$	4.72130	+	10.3555i	0.599606	+	1.31515i
$63$	−0.731791	+	0.422500i	−0.0921970	+	0.0532300i
$64$	−6.71359	−	4.35060i	−0.839199	−	0.543825i
$65$	−11.9871	−	0.448166i	−1.48682	−	0.0555882i
$66$	−4.43465	−	0.426284i	−0.545867	−	0.0524720i
$67$	−1.25603	−	2.17551i	−0.153449	−	0.265781i	0.779044	−	0.626969i	$-0.215705\pi$
$67$	−1.25603	−	2.17551i	−0.153449	−	0.265781i	−0.932493	+	0.361188i	$0.882371\pi$
$68$	4.67913	+	13.5749i	0.567427	+	1.64620i
$69$	−6.06149	−	3.49960i	−0.729717	−	0.421303i
$70$	−4.68342	−	0.450198i	−0.559776	−	0.0538089i
$71$	−10.6327	−	6.13877i	−1.26186	−	0.728538i	−0.288429	−	0.957501i	$-0.593133\pi$
$71$	−10.6327	−	6.13877i	−1.26186	−	0.728538i	−0.973435	+	0.228963i	$0.926466\pi$
$72$	1.64602	+	1.73286i	0.193986	+	0.204220i
$73$		−	10.1665i		−	1.18990i	−0.803762	−	0.594951i	$-0.797171\pi$
$73$		−	10.1665i		−	1.18990i	0.803762	−	0.594951i	$-0.202829\pi$
$74$	10.6789	+	7.61459i	1.24140	+	0.885178i
$75$	−7.71506	+	4.45429i	−0.890858	+	0.514337i
$76$	2.66920	+	7.74379i	0.306178	+	0.888274i
$77$			2.14594i			0.244553i
$78$	−4.57043	+	5.92800i	−0.517499	+	0.671214i
$79$	2.66373			0.299693			0.149846	−	0.988709i	$-0.452122\pi$
$79$	2.66373			0.299693			0.149846	+	0.988709i	$0.452122\pi$
$80$	1.86061	+	13.1771i	0.208022	+	1.47324i
$81$	2.87549	+	4.98049i	0.319499	+	0.553388i
$82$	−0.715886	+	1.00398i	−0.0790564	+	0.110871i
$83$	−15.2629			−1.67532			−0.837660	−	0.546192i	$-0.816077\pi$
$83$	−15.2629			−1.67532			−0.837660	+	0.546192i	$0.816077\pi$
$84$	−1.92546	+	2.21644i	−0.210085	+	0.241833i
$85$	11.9426	−	20.6853i	1.29536	−	2.24363i
$86$	−8.22310	−	0.790453i	−0.886720	−	0.0852367i
$87$	−0.330062	+	0.571683i	−0.0353863	+	0.0612909i
$88$	5.90124	−	1.41979i	0.629075	−	0.151350i
$89$	2.59946	−	1.50080i	0.275542	−	0.159084i	−0.355862	−	0.934539i	$-0.615813\pi$
$89$	2.59946	−	1.50080i	0.275542	−	0.159084i	0.631403	+	0.775455i	$0.282479\pi$
$90$	0.380417	−	3.95749i	0.0400995	−	0.417156i
$91$	3.05296	+	1.91818i	0.320038	+	0.201080i
$92$	9.36114	+	1.81648i	0.975966	+	0.189381i
$93$	−5.90690	−	10.2310i	−0.612517	−	1.06091i
$94$	−4.28347	−	9.39519i	−0.441806	−	0.969040i
$95$	6.81267	−	11.7999i	0.698965	−	1.21064i
$96$	7.36903	+	3.82850i	0.752098	+	0.390745i
$97$	13.7708	+	7.95057i	1.39821	+	0.807259i	0.994205	−	0.107497i	$-0.0342837\pi$
$97$	13.7708	+	7.95057i	1.39821	+	0.807259i	0.404007	+	0.914756i	$0.367617\pi$
$98$	1.15147	+	0.821052i	0.116316	+	0.0829388i
$99$	−1.81332			−0.182245
$100$	7.95969	−	9.16256i	0.795969	−	0.916256i
$101$	−1.33891	+	0.773021i	−0.133227	+	0.0769185i	−0.565132	−	0.825000i	$-0.691175\pi$
$101$	−1.33891	+	0.773021i	−0.133227	+	0.0769185i	0.431905	+	0.901919i	$0.357841\pi$
$102$	−6.18308	−	13.5617i	−0.612216	−	1.34281i
$103$	−2.42485			−0.238928			−0.119464	−	0.992839i	$-0.538118\pi$
$103$	−2.42485			−0.238928			−0.119464	+	0.992839i	$0.538118\pi$
$104$	3.25501	−	9.66462i	0.319180	−	0.947694i
$105$	4.88393			0.476622
$106$	2.81776	+	6.18037i	0.273685	+	0.600290i
$107$	−1.49147	+	0.861103i	−0.144186	+	0.0832460i	−0.570358	−	0.821396i	$-0.693195\pi$
$107$	−1.49147	+	0.861103i	−0.144186	+	0.0832460i	0.426171	+	0.904642i	$0.359862\pi$
$108$	−8.52220	−	7.40340i	−0.820049	−	0.712393i
$109$	8.46031			0.810350			0.405175	−	0.914239i	$-0.367211\pi$
$109$	8.46031			0.810350			0.405175	+	0.914239i	$0.367211\pi$
$110$	−8.22080	−	5.86184i	−0.783823	−	0.558904i
$111$	−11.7904	−	6.80722i	−1.11910	−	0.646112i
$112$	1.49603	−	3.70970i	0.141361	−	0.350534i
$113$	−6.80979	+	11.7949i	−0.640611	+	1.10957i	0.344686	+	0.938718i	$0.387986\pi$
$113$	−6.80979	+	11.7949i	−0.640611	+	1.10957i	−0.985297	+	0.170853i	$0.945348\pi$
$114$	−3.52713	−	7.73627i	−0.330346	−	0.724568i
$115$	−7.93123	−	13.7373i	−0.739591	−	1.28101i
$116$	0.171320	−	0.882887i	0.0159066	−	0.0819740i
$117$	−1.62086	+	2.57975i	−0.149849	+	0.238498i
$118$	0.337152	−	3.50740i	0.0310374	−	0.322883i
$119$	−6.21750	+	3.58968i	−0.569957	+	0.329065i
$120$	−3.23129	−	13.4306i	−0.294975	−	1.22604i
$121$	3.19747	−	5.53818i	0.290679	−	0.503471i
$122$	8.07530	+	0.776245i	0.731103	+	0.0702779i
$123$	0.639981	−	1.10848i	0.0577051	−	0.0999482i
$124$	12.1506	+	10.5555i	1.09116	+	0.947908i
$125$	−3.55501			−0.317970
$126$	−0.693789	+	0.972989i	−0.0618076	+	0.0866807i
$127$	−1.79240	−	3.10452i	−0.159049	−	0.275482i	0.775477	−	0.631376i	$-0.217510\pi$
$127$	−1.79240	−	3.10452i	−0.159049	−	0.275482i	−0.934526	+	0.355895i	$0.884176\pi$
$128$	−11.1913	−	1.65961i	−0.989183	−	0.146690i
$129$	8.57515			0.754999
$130$	−15.6877	+	6.45581i	−1.37591	+	0.566212i
$131$			3.91724i			0.342251i	0.985249	+	0.171125i	$0.0547403\pi$
$131$			3.91724i			0.342251i	−0.985249	+	0.171125i	$0.945260\pi$
$132$	−5.95653	+	2.05315i	−0.518449	+	0.178704i
$133$	−3.54677	+	2.04773i	−0.307544	+	0.177560i
$134$	−2.89256	−	2.06254i	−0.249879	−	0.178176i
$135$			18.7787i			1.61621i
$136$	13.9851	+	14.7229i	1.19921	+	1.26248i
$137$	−0.270055	−	0.155916i	−0.0230723	−	0.0133208i	0.488419	−	0.872609i	$-0.337574\pi$
$137$	−0.270055	−	0.155916i	−0.0230723	−	0.0133208i	−0.511492	+	0.859288i	$0.670907\pi$
$138$	−9.85295	−	0.947124i	−0.838739	−	0.0806245i
$139$	−2.25601	−	1.30251i	−0.191353	−	0.110478i	0.401263	−	0.915963i	$-0.368571\pi$
$139$	−2.25601	−	1.30251i	−0.191353	−	0.110478i	−0.592616	+	0.805485i	$0.701905\pi$
$140$	−6.29067	+	2.16833i	−0.531659	+	0.183257i
$141$	5.35912	+	9.28227i	0.451319	+	0.781708i
$142$	−17.2834	−	1.66138i	−1.45039	−	0.139420i
$143$	3.61560	+	6.84056i	0.302352	+	0.572036i
$144$	3.13470	+	1.26414i	0.261225	+	0.105345i
$145$	−1.29562	+	0.748026i	−0.107595	+	0.0621202i
$146$	−5.96443	−	13.0821i	−0.493620	−	1.08269i
$147$	−1.27132	−	0.733996i	−0.104857	−	0.0605390i
$148$	18.2087	+	3.53331i	1.49675	+	0.290436i
$149$	7.75797	−	13.4372i	0.635558	−	1.10082i	−0.350839	−	0.936436i	$-0.614104\pi$
$149$	7.75797	−	13.4372i	0.635558	−	1.10082i	0.986397	−	0.164382i	$-0.0525631\pi$
$150$	−7.31441	+	10.2579i	−0.597219	+	0.837557i
$151$			10.1666i			0.827343i	0.910426	+	0.413671i	$0.135754\pi$
$151$			10.1666i			0.827343i	−0.910426	+	0.413671i	$0.864246\pi$
$152$	7.97776	+	8.39864i	0.647082	+	0.681220i
$153$	−3.03328	−	5.25379i	−0.245226	−	0.424743i
$154$	1.25897	+	2.76136i	0.101450	+	0.222517i
$155$		−	26.7739i		−	2.15053i
$156$	−2.40336	+	10.3094i	−0.192423	+	0.825413i
$157$			19.9529i			1.59241i	0.605025	+	0.796206i	$0.293163\pi$
$157$			19.9529i			1.59241i	−0.605025	+	0.796206i	$0.706837\pi$
$158$	3.42764	−	1.56274i	0.272689	−	0.124325i
$159$	−3.52535	−	6.10608i	−0.279578	−	0.484244i
$160$	10.1248	+	15.8645i	0.800438	+	1.25420i
$161$			4.76788i			0.375761i
$162$	6.62205	+	4.72185i	0.520278	+	0.370983i
$163$	4.14929	−	7.18679i	0.324998	−	0.562913i	−0.656514	−	0.754314i	$-0.727970\pi$
$163$	4.14929	−	7.18679i	0.324998	−	0.562913i	0.981512	+	0.191401i	$0.0613031\pi$
$164$	−0.332184	+	1.71190i	−0.0259392	+	0.133677i
$165$	9.07648	+	5.24031i	0.706603	+	0.407957i
$166$	−19.6400	+	8.95432i	−1.52436	+	0.694990i
$167$	20.3487	−	11.7483i	1.57463	−	0.909112i	0.579038	−	0.815301i	$-0.303428\pi$
$167$	20.3487	−	11.7483i	1.57463	−	0.909112i	0.995590	−	0.0938113i	$-0.0299050\pi$
$168$	−1.17733	+	3.98169i	−0.0908331	+	0.307194i
$169$	12.9637	+	0.970716i	0.997208	+	0.0746705i
$170$	3.23213	−	33.6239i	0.247893	−	2.57884i
$171$	−1.73033	−	2.99702i	−0.132322	−	0.229188i
$172$	−11.0451	+	3.80713i	−0.842181	+	0.290291i
$173$	3.26264	+	1.88369i	0.248054	+	0.143214i	0.618873	−	0.785491i	$-0.287590\pi$
$173$	3.26264	+	1.88369i	0.248054	+	0.143214i	−0.370819	+	0.928705i	$0.620923\pi$
$174$	−0.0893271	+	0.929272i	−0.00677187	+	0.0704479i
$175$	5.25552	+	3.03428i	0.397280	+	0.229370i
$176$	6.76068	−	5.28907i	0.509605	−	0.398678i
$177$			3.65756i			0.274919i
$178$	2.46446	−	3.45623i	0.184719	−	0.259056i
$179$	−12.7370	+	7.35372i	−0.952009	+	0.549643i	−0.893705	−	0.448656i	$-0.851903\pi$
$179$	−12.7370	+	7.35372i	−0.952009	+	0.549643i	−0.0583049	+	0.998299i	$0.518570\pi$
$180$	−1.83224	−	5.31562i	−0.136567	−	0.396203i
$181$		−	18.0696i		−	1.34310i	−0.740960	−	0.671550i	$-0.765629\pi$
$181$		−	18.0696i		−	1.34310i	0.740960	−	0.671550i	$-0.234371\pi$
$182$	5.05385	+	0.677190i	0.374616	+	0.0501967i
$183$	−8.42102			−0.622499
$184$	13.1115	−	3.15451i	0.966589	−	0.232553i
$185$	−15.4274	−	26.7210i	−1.13424	−	1.96456i
$186$	−13.6032	−	9.69974i	−0.997434	−	0.711219i
$187$	−15.4065			−1.12663
$188$	−11.0238	−	9.57659i	−0.803994	−	0.698445i
$189$	2.82221	−	4.88822i	0.205286	−	0.355566i
$190$	1.84376	−	19.1807i	0.133761	−	1.39152i
$191$	−7.22983	+	12.5224i	−0.523132	+	0.906091i	0.476506	+	0.879171i	$0.341903\pi$
$191$	−7.22983	+	12.5224i	−0.523132	+	0.906091i	−0.999638	+	0.0269196i	$0.991430\pi$
$192$	11.7284	+	0.603253i	0.846427	+	0.0435360i
$193$	−0.976789	+	0.563949i	−0.0703108	+	0.0405940i	−0.534743	−	0.845015i	$-0.679592\pi$
$193$	−0.976789	+	0.563949i	−0.0703108	+	0.0405940i	0.464432	+	0.885609i	$0.346258\pi$
$194$	22.3844	+	2.15172i	1.60711	+	0.154485i
$195$	15.5684	−	8.22871i	1.11487	−	0.589270i
$196$	1.96338	+	0.380983i	0.140241	+	0.0272131i
$197$	11.1325	+	19.2821i	0.793159	+	1.37379i	0.924001	+	0.382389i	$0.124899\pi$
$197$	11.1325	+	19.2821i	0.793159	+	1.37379i	−0.130842	+	0.991403i	$0.541768\pi$
$198$	−2.33335	+	1.06383i	−0.165824	+	0.0756028i
$199$	−0.344380	+	0.596484i	−0.0244125	+	0.0422836i	−0.877974	−	0.478709i	$-0.841105\pi$
$199$	−0.344380	+	0.596484i	−0.0244125	+	0.0422836i	0.853561	+	0.520993i	$0.174438\pi$
$200$	4.86699	−	16.4600i	0.344148	−	1.16390i
$201$	3.19363	+	1.84385i	0.225262	+	0.130055i
$202$	−1.26938	+	1.78022i	−0.0893134	+	0.125256i
$203$	0.449678			0.0315612
$204$	−15.9126	−	13.8236i	−1.11410	−	0.967843i
$205$	2.51217	−	1.45040i	0.175458	−	0.101301i
$206$	−3.12026	+	1.42260i	−0.217399	+	0.0991169i
$207$	−4.02885			−0.280025
$208$	−1.48147	−	14.3459i	−0.102722	−	0.994710i
$209$	−8.78860			−0.607920
$210$	6.28456	−	2.86527i	0.433676	−	0.197722i
$211$	11.1359	−	6.42932i	0.766628	−	0.442613i	−0.0650426	−	0.997882i	$-0.520718\pi$
$211$	11.1359	−	6.42932i	0.766628	−	0.442613i	0.831670	+	0.555270i	$0.187385\pi$
$212$	7.25171	+	6.29970i	0.498049	+	0.432665i
$213$	18.0233			1.23494
$214$	−1.41402	+	1.98306i	−0.0966605	+	0.135559i
$215$	16.8304	+	9.71702i	1.14782	+	0.662695i
$216$	−15.3096	−	4.52684i	−1.04169	−	0.308012i
$217$	−4.02379	+	6.96942i	−0.273153	+	0.473115i
$218$	10.8866	−	4.96343i	0.737333	−	0.336166i
$219$	7.46220	+	12.9249i	0.504248	+	0.873384i
$220$	−14.0174	−	2.72000i	−0.945052	−	0.183382i
$221$	−13.7713	+	21.9183i	−0.926356	+	1.47438i
$222$	−19.1654	−	1.84229i	−1.28630	−	0.123646i
$223$	14.0268	−	8.09840i	0.939307	−	0.542309i	0.0495640	−	0.998771i	$-0.484217\pi$
$223$	14.0268	−	8.09840i	0.939307	−	0.542309i	0.889743	+	0.456462i	$0.150884\pi$
$224$	−0.251317	−	5.65127i	−0.0167918	−	0.377591i
$225$	−2.56396	+	4.44091i	−0.170931	+	0.296061i
$226$	−1.84298	+	19.1726i	−0.122593	+	1.27534i
$227$	−9.26194	+	16.0422i	−0.614737	+	1.06476i	0.375694	+	0.926744i	$0.377404\pi$
$227$	−9.26194	+	16.0422i	−0.614737	+	1.06476i	−0.990431	+	0.138012i	$0.955929\pi$
$228$	−9.07732	−	7.88564i	−0.601160	−	0.522239i
$229$	−9.20999			−0.608613			−0.304307	−	0.952574i	$-0.598425\pi$
$229$	−9.20999			−0.608613			−0.304307	+	0.952574i	$0.598425\pi$
$230$	−18.2651	−	13.0239i	−1.20436	−	0.858770i
$231$	−1.57511	−	2.72817i	−0.103635	−	0.179501i
$232$	−0.297514	−	1.23659i	−0.0195328	−	0.0811864i
$233$	−12.4024			−0.812511			−0.406255	−	0.913760i	$-0.633166\pi$
$233$	−12.4024			−0.812511			−0.406255	+	0.913760i	$0.633166\pi$
$234$	−0.572226	+	4.27050i	−0.0374076	+	0.279172i
$235$			24.2910i			1.58457i
$236$	−1.62386	−	4.71107i	−0.105704	−	0.306665i
$237$	−3.38645	+	1.95517i	−0.219973	+	0.127002i
$238$	−5.89462	+	8.26678i	−0.382091	+	0.535856i
$239$		−	11.2690i		−	0.728934i	−0.931216	−	0.364467i	$-0.881251\pi$
$239$		−	11.2690i		−	0.728934i	0.931216	−	0.364467i	$-0.118749\pi$
$240$	−12.0373	−	15.3866i	−0.777006	−	0.993198i
$241$	−21.6073	−	12.4750i	−1.39185	−	0.803584i	−0.398329	−	0.917243i	$-0.630410\pi$
$241$	−21.6073	−	12.4750i	−1.39185	−	0.803584i	−0.993520	+	0.113658i	$0.963743\pi$
$242$	0.865355	−	9.00231i	0.0556271	−	0.578691i
$243$	7.35334	+	4.24545i	0.471717	+	0.272346i
$244$	10.8466	−	3.73870i	0.694381	−	0.239346i
$245$	−1.66347	−	2.88122i	−0.106275	−	0.184074i
$246$	0.173203	−	1.80183i	0.0110430	−	0.114881i
$247$	−7.85581	+	12.5033i	−0.499853	+	0.795564i
$248$	21.8278	+	6.45418i	1.38607	+	0.409841i
$249$	19.4040	−	11.2029i	1.22968	−	0.709955i
$250$	−4.57453	+	2.08563i	−0.289319	+	0.131907i
$251$	−7.62187	−	4.40049i	−0.481088	−	0.277756i	0.239782	−	0.970827i	$-0.422924\pi$
$251$	−7.62187	−	4.40049i	−0.481088	−	0.277756i	−0.720870	+	0.693071i	$0.756257\pi$
$252$	−0.321931	+	1.65905i	−0.0202797	+	0.104511i
$253$	−5.11579	+	8.86081i	−0.321627	+	0.557074i
$254$	−4.12776	−	2.94330i	−0.258999	−	0.184679i
$255$			35.0634i			2.19576i
$256$	−15.3745	+	4.43009i	−0.960904	+	0.276880i
$257$	14.2572	+	24.6943i	0.889343	+	1.54039i	0.840654	+	0.541573i	$0.182171\pi$
$257$	14.2572	+	24.6943i	0.889343	+	1.54039i	0.0486889	+	0.998814i	$0.484496\pi$
$258$	11.0344	−	5.03081i	0.686970	−	0.313204i
$259$			9.27419i			0.576270i
$260$	−16.3993	+	17.5108i	−1.01704	+	1.08597i
$261$			0.379978i			0.0235200i
$262$	2.29814	+	5.04064i	0.141979	+	0.311412i
$263$	1.26306	+	2.18768i	0.0778836	+	0.134898i	0.902337	−	0.431032i	$-0.141850\pi$
$263$	1.26306	+	2.18768i	0.0778836	+	0.134898i	−0.824453	+	0.565930i	$0.808517\pi$
$264$	−6.46024	+	6.13650i	−0.397600	+	0.377675i
$265$		−	15.9791i		−	0.981591i
$266$	−3.36258	+	4.71577i	−0.206173	+	0.289143i
$267$	−2.20316	+	3.81598i	−0.134831	+	0.233534i
$268$	−4.93213	−	0.957054i	−0.301278	−	0.0584614i
$269$	−22.8267	−	13.1790i	−1.39177	−	0.803537i	−0.398255	−	0.917275i	$-0.630384\pi$
$269$	−22.8267	−	13.1790i	−1.39177	−	0.803537i	−0.993511	+	0.113738i	$0.963718\pi$
$270$	11.0169	+	24.1641i	0.670470	+	1.47058i
$271$	9.51592	−	5.49402i	0.578051	−	0.333738i	−0.182308	−	0.983242i	$-0.558357\pi$
$271$	9.51592	−	5.49402i	0.578051	−	0.333738i	0.760358	+	0.649504i	$0.225023\pi$
$272$	26.6333	+	10.7405i	1.61488	+	0.651239i
$273$	−5.28922	−	0.197750i	−0.320118	−	0.0119684i
$274$	−0.438974	−	0.0421968i	−0.0265194	−	0.00254920i
$275$	6.51138	+	11.2780i	0.392651	+	0.680091i
$276$	−13.2343	+	4.56172i	−0.796610	+	0.274583i
$277$	14.1970	+	8.19662i	0.853012	+	0.492487i	0.861666	−	0.507476i	$-0.169421\pi$
$277$	14.1970	+	8.19662i	0.853012	+	0.492487i	−0.00865373	+	0.999963i	$0.502755\pi$
$278$	−3.66715	−	0.352508i	−0.219941	−	0.0211420i
$279$	−5.88916	−	3.40011i	−0.352575	−	0.203559i
$280$	−6.82264	+	6.48074i	−0.407731	+	0.387298i
$281$			31.8238i			1.89845i	0.314600	+	0.949224i	$0.398130\pi$
$281$			31.8238i			1.89845i	−0.314600	+	0.949224i	$0.601870\pi$
$282$	12.3417	+	8.80023i	0.734937	+	0.524046i
$283$	16.8063	−	9.70312i	0.999031	−	0.576791i	0.0910696	−	0.995845i	$-0.470971\pi$
$283$	16.8063	−	9.70312i	0.999031	−	0.576791i	0.907961	+	0.419054i	$0.137638\pi$
$284$	−23.2147	+	8.00186i	−1.37754	+	0.474823i
$285$			20.0019i			1.18481i
$286$	8.66567	+	6.68115i	0.512412	+	0.395065i
$287$	−0.871913			−0.0514674
$288$	4.77532	−	0.212363i	0.281389	−	0.0125136i
$289$	−17.2715	−	29.9152i	−1.01597	−	1.75972i
$290$	−1.22834	+	1.72265i	−0.0721304	+	0.101158i
$291$	−23.3428			−1.36838
$292$	−15.3499	−	13.3347i	−0.898284	−	0.780356i
$293$	13.9349	−	24.1360i	0.814088	−	1.41004i	−0.0958931	−	0.995392i	$-0.530571\pi$
$293$	13.9349	−	24.1360i	0.814088	−	1.41004i	0.909981	−	0.414650i	$-0.136096\pi$
$294$	−2.06653	−	0.198647i	−0.120522	−	0.0115853i
$295$	−4.14461	+	7.17867i	−0.241308	+	0.417958i
$296$	25.5036	−	6.13596i	1.48237	−	0.356646i
$297$	10.4898	−	6.05630i	0.608682	−	0.351422i
$298$	2.09960	−	21.8422i	0.121626	−	1.26528i
$299$	8.03319	+	15.1984i	0.464571	+	0.878948i
$300$	−3.39402	+	17.4909i	−0.195954	+	1.00984i
$301$	−2.92071	−	5.05881i	−0.168347	−	0.291585i
$302$	5.96444	+	13.0822i	0.343215	+	0.752794i
$303$	1.13479	−	1.96551i	0.0651919	−	0.112916i
$304$	15.1929	+	6.12691i	0.871373	+	0.351402i
$305$	−16.5279	−	9.54237i	−0.946383	−	0.546395i
$306$	−6.98543	−	4.98095i	−0.399330	−	0.284742i
$307$	27.5673			1.57335			0.786674	−	0.617369i	$-0.211801\pi$
$307$	27.5673			1.57335			0.786674	+	0.617369i	$0.211801\pi$
$308$	3.24003	+	2.81468i	0.184618	+	0.160381i
$309$	3.08276	−	1.77983i	0.175372	−	0.101251i
$310$	−15.7075	−	34.4522i	−0.892126	−	1.95675i
$311$	34.1427			1.93605			0.968027	−	0.250845i	$-0.0807085\pi$
$311$	34.1427			1.93605			0.968027	+	0.250845i	$0.0807085\pi$
$312$	2.95564	+	14.6760i	0.167330	+	0.830863i
$313$	−12.7636			−0.721443			−0.360721	−	0.932674i	$-0.617469\pi$
$313$	−12.7636			−0.721443			−0.360721	+	0.932674i	$0.617469\pi$
$314$	11.7058	+	25.6751i	0.660597	+	1.44893i
$315$	2.43463	−	1.40563i	0.137176	−	0.0791985i
$316$	3.49382	−	4.02181i	0.196543	−	0.226245i
$317$	4.88079			0.274132			0.137066	−	0.990562i	$-0.456233\pi$
$317$	4.88079			0.274132			0.137066	+	0.990562i	$0.456233\pi$
$318$	−8.11864	−	5.78899i	−0.455270	−	0.324630i
$319$	0.835699	+	0.482491i	0.0467901	+	0.0270143i
$320$	22.3357	+	14.4742i	1.24861	+	0.809133i
$321$	1.26409	−	2.18947i	0.0705548	−	0.122204i
$322$	2.79718	+	6.13523i	0.155881	+	0.341903i
$323$	−14.7013	−	25.4635i	−0.818005	−	1.41683i
$324$	11.2913	+	2.19102i	0.627296	+	0.121724i
$325$	21.8652	+	0.817483i	1.21286	+	0.0453458i
$326$	1.12295	−	11.6821i	0.0621947	−	0.647013i
$327$	−10.7557	+	6.20983i	−0.594794	+	0.343404i
$328$	0.576873	+	2.39772i	0.0318525	+	0.132392i
$329$	3.65065	−	6.32311i	0.201267	−	0.348604i
$330$	14.7538	+	1.41822i	0.812171	+	0.0780707i
$331$	−10.2628	+	17.7757i	−0.564096	+	0.977043i	0.433037	+	0.901376i	$0.357442\pi$
$331$	−10.2628	+	17.7757i	−0.564096	+	0.977043i	−0.997133	+	0.0756668i	$0.975891\pi$
$332$	−20.0193	+	23.0446i	−1.09870	+	1.26473i
$333$	−7.83669			−0.429448
$334$	19.2920	−	27.0556i	1.05561	−	1.48041i
$335$	4.17875	+	7.23781i	0.228309	+	0.395444i
$336$	0.820980	+	5.81429i	0.0447881	+	0.317196i
$337$	−8.34232			−0.454435			−0.227218	−	0.973844i	$-0.572963\pi$
$337$	−8.34232			−0.454435			−0.227218	+	0.973844i	$0.572963\pi$
$338$	17.2510	−	6.35635i	0.938330	−	0.345740i
$339$		−	19.9934i		−	1.08589i
$340$	−15.5672	−	45.1629i	−0.844249	−	2.44930i
$341$	−14.9560	+	8.63482i	−0.809910	+	0.467602i
$342$	−3.98483	−	2.84138i	−0.215475	−	0.153644i
$343$			1.00000i			0.0539949i
$344$	−11.9791	+	11.3788i	−0.645871	+	0.613504i
$345$	20.1662	+	11.6430i	1.08571	+	0.626837i
$346$	5.30342	+	0.509796i	0.285114	+	0.0274068i
$347$	3.78027	+	2.18254i	0.202935	+	0.117165i	0.598024	−	0.801478i	$-0.295953\pi$
$347$	3.78027	+	2.18254i	0.202935	+	0.117165i	−0.395089	+	0.918643i	$0.629286\pi$
$348$	0.430234	+	1.24818i	0.0230630	+	0.0669094i
$349$	4.52470	+	7.83700i	0.242201	+	0.419505i	0.961341	−	0.275360i	$-0.0887972\pi$
$349$	4.52470	+	7.83700i	0.242201	+	0.419505i	−0.719140	+	0.694866i	$0.755464\pi$
$350$	8.54285	+	0.821189i	0.456635	+	0.0438944i
$351$	0.760351	−	20.3371i	0.0405845	−	1.08551i
$352$	5.59659	−	10.7722i	0.298299	−	0.574160i
$353$	15.1951	−	8.77287i	0.808751	−	0.466933i	−0.0377708	−	0.999286i	$-0.512026\pi$
$353$	15.1951	−	8.77287i	0.808751	−	0.466933i	0.846522	+	0.532354i	$0.178692\pi$
$354$	2.14579	+	4.70649i	0.114048	+	0.250147i
$355$	35.3743	+	20.4233i	1.87747	+	1.08396i
$356$	1.14356	−	5.89326i	0.0606084	−	0.312342i
$357$	5.26961	−	9.12724i	0.278898	−	0.483065i
$358$	−12.0756	+	16.9351i	−0.638214	+	0.895049i
$359$		−	22.8537i		−	1.20617i	−0.797676	−	0.603086i	$-0.793937\pi$
$359$		−	22.8537i		−	1.20617i	0.797676	−	0.603086i	$-0.206063\pi$
$360$	−5.47622	−	5.76513i	−0.288622	−	0.303849i
$361$	1.11363	+	1.92887i	0.0586123	+	0.101520i
$362$	−10.6009	−	23.2516i	−0.557172	−	1.22208i
$363$			9.38772i			0.492727i
$364$	6.90051	−	2.09356i	0.361685	−	0.109732i
$365$			33.8235i			1.77040i
$366$	−10.8360	+	4.94038i	−0.566409	+	0.258238i
$367$	−12.3303	−	21.3567i	−0.643637	−	1.11481i	−0.984615	−	0.174740i	$-0.944091\pi$
$367$	−12.3303	−	21.3567i	−0.643637	−	1.11481i	0.340978	−	0.940071i	$-0.389242\pi$
$368$	15.0210	−	11.7513i	0.783021	−	0.612579i
$369$		−	0.736767i		−	0.0383545i
$370$	−35.5281	−	25.3333i	−1.84702	−	1.31702i
$371$	−2.40148	+	4.15948i	−0.124678	+	0.215949i
$372$	−23.1949	−	4.50086i	−1.20260	−	0.233359i
$373$	16.3322	+	9.42939i	0.845648	+	0.488235i	0.859180	−	0.511673i	$-0.170974\pi$
$373$	16.3322	+	9.42939i	0.845648	+	0.488235i	−0.0135321	+	0.999908i	$0.504308\pi$
$374$	−19.8248	+	9.03855i	−1.02512	+	0.467372i
$375$	4.51955	−	2.60936i	0.233389	−	0.134747i
$376$	−19.8036	−	5.85565i	−1.02129	−	0.301982i
$377$	1.43343	−	0.757642i	0.0738252	−	0.0390206i
$378$	0.763797	−	7.94580i	0.0392855	−	0.408688i
$379$	−13.6803	−	23.6950i	−0.702711	−	1.21713i	−0.967511	−	0.252828i	$-0.918639\pi$
$379$	−13.6803	−	23.6950i	−0.702711	−	1.21713i	0.264800	−	0.964303i	$-0.414694\pi$
$380$	−8.88028	−	25.7632i	−0.455549	−	1.32162i
$381$	4.55741	+	2.63122i	0.233483	+	0.134802i
$382$	−1.95666	+	20.3552i	−0.100112	+	1.04146i
$383$	14.9043	+	8.60502i	0.761576	+	0.439696i	0.829861	−	0.557970i	$-0.188420\pi$
$383$	14.9043	+	8.60502i	0.761576	+	0.439696i	−0.0682856	+	0.997666i	$0.521753\pi$
$384$	15.4459	−	6.10450i	0.788219	−	0.311519i
$385$		−	7.13942i		−	0.363859i
$386$	−0.926063	+	1.29874i	−0.0471354	+	0.0661040i
$387$	4.27469	−	2.46800i	0.217295	−	0.125455i
$388$	30.0663	−	10.3635i	1.52639	−	0.526129i
$389$			27.6381i			1.40131i	0.713501	+	0.700655i	$0.247109\pi$
$389$			27.6381i			1.40131i	−0.713501	+	0.700655i	$0.752891\pi$
$390$	15.2056	−	19.7221i	0.769964	−	0.998668i
$391$	−34.2303			−1.73110
$392$	2.74996	−	0.661617i	0.138894	−	0.0334167i
$393$	−2.87524	−	4.98006i	−0.145036	−	0.251211i
$394$	25.6374	+	18.2808i	1.29160	+	0.920971i
$395$	−8.86207			−0.445899
$396$	−2.37840	+	2.73783i	−0.119519	+	0.137581i
$397$	−5.23356	+	9.06480i	−0.262665	+	0.454949i	−0.966949	−	0.254969i	$-0.917935\pi$
$397$	−5.23356	+	9.06480i	−0.262665	+	0.454949i	0.704284	+	0.709918i	$0.251268\pi$
$398$	−0.0932022	+	0.969585i	−0.00467180	+	0.0486009i
$399$	3.00605	−	5.20662i	0.150491	−	0.260657i
$400$	−3.39386	−	24.0358i	−0.169693	−	1.20179i
$401$	30.2460	−	17.4626i	1.51041	−	0.872038i	0.510488	−	0.859885i	$-0.329465\pi$
$401$	30.2460	−	17.4626i	1.51041	−	0.872038i	0.999926	−	0.0121537i	$-0.00386873\pi$
$402$	5.19125	+	0.499014i	0.258916	+	0.0248885i
$403$	−1.08408	+	28.9957i	−0.0540017	+	1.44438i
$404$	−0.589016	+	3.03547i	−0.0293047	+	0.151020i
$405$	−9.56658	−	16.5698i	−0.475367	−	0.823361i
$406$	0.578638	−	0.263814i	0.0287173	−	0.0130929i
$407$	−9.95093	+	17.2355i	−0.493249	+	0.854333i
$408$	−28.5860	−	8.45247i	−1.41522	−	0.418460i
$409$	−13.8103	−	7.97339i	−0.682877	−	0.394259i	0.118061	−	0.993006i	$-0.462332\pi$
$409$	−13.8103	−	7.97339i	−0.682877	−	0.394259i	−0.800938	+	0.598747i	$0.795665\pi$
$410$	2.38171	−	3.34018i	0.117624	−	0.164960i
$411$	0.457768			0.0225800
$412$	−3.18051	+	3.66115i	−0.156693	+	0.180372i
$413$	2.15774	−	1.24577i	0.106175	−	0.0613003i
$414$	−5.18427	+	2.36362i	−0.254793	+	0.116166i
$415$	50.7788			2.49263
$416$	−10.3227	−	17.5910i	−0.506112	−	0.862468i
$417$	3.82415			0.187269
$418$	−11.3090	+	5.15603i	−0.553143	+	0.252190i
$419$	26.0223	−	15.0240i	1.27127	−	0.733969i	0.296045	−	0.955174i	$-0.404332\pi$
$419$	26.0223	−	15.0240i	1.27127	−	0.733969i	0.975227	+	0.221205i	$0.0709990\pi$
$420$	6.40590	−	7.37396i	0.312576	−	0.359813i
$421$	32.6204			1.58982			0.794912	−	0.606725i	$-0.207517\pi$
$421$	32.6204			1.58982			0.794912	+	0.606725i	$0.207517\pi$
$422$	10.5576	−	14.8063i	0.513936	−	0.720759i
$423$	5.34302	+	3.08480i	0.259787	+	0.149988i
$424$	13.0272	+	3.85197i	0.632659	+	0.187068i
$425$	−21.7841	+	37.7312i	−1.05669	+	1.83023i
$426$	23.1921	−	10.5738i	1.12366	−	0.512302i
$427$	2.86821	+	4.96788i	0.138802	+	0.240413i
$428$	−0.656132	+	3.38134i	−0.0317153	+	0.163443i
$429$	−9.61752	−	6.04269i	−0.464338	−	0.291744i
$430$	27.3578	+	2.62979i	1.31931	+	0.126820i
$431$	9.86921	−	5.69799i	0.475383	−	0.274463i	−0.243107	−	0.969999i	$-0.578167\pi$
$431$	9.86921	−	5.69799i	0.475383	−	0.274463i	0.718490	+	0.695537i	$0.244833\pi$
$432$	−22.3560	+	3.15667i	−1.07560	+	0.151875i
$433$	−6.81015	+	11.7955i	−0.327275	+	0.566857i	−0.981970	−	0.189036i	$-0.939464\pi$
$433$	−6.81015	+	11.7955i	−0.327275	+	0.566857i	0.654695	+	0.755893i	$0.272797\pi$
$434$	−1.08899	+	11.3288i	−0.0522732	+	0.543799i
$435$	1.09810	−	1.90196i	0.0526497	−	0.0911919i
$436$	11.0968	−	12.7737i	0.531440	−	0.611751i
$437$	−19.5266			−0.934084
$438$	17.1849	+	12.2537i	0.821128	+	0.585504i
$439$	−19.8314	−	34.3489i	−0.946500	−	1.63939i	−0.752720	−	0.658340i	$-0.771259\pi$
$439$	−19.8314	−	34.3489i	−0.946500	−	1.63939i	−0.193779	−	0.981045i	$-0.562075\pi$
$440$	−19.6331	+	4.72356i	−0.935972	+	0.225187i
$441$	−0.845000			−0.0402381
$442$	−4.86179	+	36.2834i	−0.231252	+	1.72582i
$443$		−	20.3617i		−	0.967416i	−0.875230	−	0.483708i	$-0.839290\pi$
$443$		−	20.3617i		−	0.967416i	0.875230	−	0.483708i	$-0.160710\pi$
$444$	−25.7425	+	8.87318i	−1.22169	+	0.421102i
$445$	−8.64825	+	4.99307i	−0.409966	+	0.236694i
$446$	13.2984	−	18.6501i	0.629698	−	0.883106i
$447$			22.7773i			1.07733i
$448$	−3.63884	−	7.12453i	−0.171919	−	0.336602i
$449$	9.60735	+	5.54681i	0.453399	+	0.261770i	0.709265	−	0.704942i	$-0.249027\pi$
$449$	9.60735	+	5.54681i	0.453399	+	0.261770i	−0.255866	+	0.966712i	$0.582360\pi$
$450$	−0.693905	+	7.21871i	−0.0327110	+	0.340293i
$451$	−1.62040	−	0.935537i	−0.0763016	−	0.0440527i
$452$	8.87653	+	25.7523i	0.417517	+	1.21128i
$453$	−7.46221	−	12.9249i	−0.350605	−	0.607266i
$454$	−2.50663	+	26.0765i	−0.117642	+	1.22383i
$455$	−10.1570	−	6.38167i	−0.476169	−	0.299177i
$456$	−16.3068	−	4.82170i	−0.763638	−	0.225797i
$457$	−5.94579	+	3.43280i	−0.278132	+	0.160580i	−0.632578	−	0.774497i	$-0.718003\pi$
$457$	−5.94579	+	3.43280i	−0.278132	+	0.160580i	0.354445	+	0.935077i	$0.384670\pi$
$458$	−11.8513	+	5.40325i	−0.553774	+	0.252477i
$459$	35.0942	+	20.2617i	1.63806	+	0.945734i
$460$	−31.1440	−	6.04333i	−1.45210	−	0.281772i
$461$	7.96326	−	13.7928i	0.370886	−	0.642393i	−0.618816	−	0.785536i	$-0.712387\pi$
$461$	7.96326	−	13.7928i	0.370886	−	0.642393i	0.989702	+	0.143143i	$0.0457208\pi$
$462$	−3.62738	−	2.58650i	−0.168761	−	0.120335i
$463$		−	6.26118i		−	0.290982i	−0.989360	−	0.145491i	$-0.953524\pi$
$463$		−	6.26118i		−	0.290982i	0.989360	−	0.145491i	$-0.0464761\pi$
$464$	−1.10831	−	1.41669i	−0.0514522	−	0.0657680i
$465$	19.6519	+	34.0381i	0.911336	+	1.57848i
$466$	−15.9593	+	7.27617i	−0.739299	+	0.337062i
$467$			41.7902i			1.93382i	0.255118	+	0.966910i	$0.417886\pi$
$467$			41.7902i			1.93382i	−0.255118	+	0.966910i	$0.582114\pi$
$468$	1.76906	+	5.83093i	0.0817747	+	0.269535i
$469$		−	2.51207i		−	0.115996i
$470$	14.2509	+	31.2573i	0.657343	+	1.44179i
$471$	−14.6453	−	25.3665i	−0.674821	−	1.16882i
$472$	−4.85341	−	5.10946i	−0.223396	−	0.235182i
$473$		−	12.5353i		−	0.576375i
$474$	−3.21058	+	4.50261i	−0.147467	+	0.206812i
$475$	−12.4267	+	21.5237i	−0.570178	+	0.987577i
$476$	−2.73521	+	14.0958i	−0.125368	+	0.646079i
$477$	−3.51476	−	2.02925i	−0.160930	−	0.0929128i
$478$	−6.61124	−	14.5008i	−0.302391	−	0.663253i
$479$	10.2981	−	5.94560i	0.470531	−	0.271661i	−0.245931	−	0.969287i	$-0.579094\pi$
$479$	10.2981	−	5.94560i	0.470531	−	0.271661i	0.716462	+	0.697626i	$0.245760\pi$
$480$	−24.5163	−	12.7372i	−1.11901	−	0.581372i
$481$	15.6257	+	29.5631i	0.712469	+	1.34796i
$482$	−35.1227	−	3.37620i	−1.59979	−	0.153782i
$483$	−3.49960	−	6.06149i	−0.159237	−	0.275807i
$484$	−4.16789	−	12.0917i	−0.189449	−	0.549624i
$485$	−45.8147	−	26.4511i	−2.08034	−	1.20108i
$486$	11.9529	+	1.14898i	0.542192	+	0.0521187i
$487$	10.4810	+	6.05124i	0.474942	+	0.274208i	0.718306	−	0.695727i	$-0.244918\pi$
$487$	10.4810	+	6.05124i	0.474942	+	0.274208i	−0.243364	+	0.969935i	$0.578251\pi$
$488$	11.7638	−	11.1743i	0.532523	−	0.505836i
$489$			12.1823i			0.550901i
$490$	−3.83086	−	2.73159i	−0.173061	−	0.123401i
$491$	−14.3555	+	8.28814i	−0.647854	+	0.374039i	−0.787633	−	0.616144i	$-0.788694\pi$
$491$	−14.3555	+	8.28814i	−0.647854	+	0.374039i	0.139780	+	0.990183i	$0.455361\pi$
$492$	−0.834212	−	2.42019i	−0.0376092	−	0.109110i
$493$			3.22839i			0.145400i
$494$	−2.77340	+	20.6978i	−0.124781	+	0.931238i
$495$	6.03281			0.271155
$496$	31.8742	−	4.50065i	1.43119	−	0.202085i
$497$	−6.13877	−	10.6327i	−0.275361	−	0.476940i
$498$	18.3963	−	25.7995i	0.824359	−	1.15610i
$499$	0.611980			0.0273960			0.0136980	−	0.999906i	$-0.495640\pi$
$499$	0.611980			0.0273960			0.0136980	+	0.999906i	$0.495640\pi$
$500$	−4.66286	+	5.36751i	−0.208529	+	0.240042i
$501$	−17.2464	+	29.8717i	−0.770514	+	1.33457i
$502$	−12.3893	−	1.19094i	−0.552964	−	0.0531541i
$503$	−10.1689	+	17.6130i	−0.453408	+	0.785326i	−0.998595	−	0.0529884i	$-0.983125\pi$
$503$	−10.1689	+	17.6130i	−0.453408	+	0.785326i	0.545187	+	0.838315i	$0.316459\pi$
$504$	0.559066	+	2.32371i	0.0249028	+	0.103506i
$505$	4.45449	−	2.57180i	0.198222	−	0.114444i
$506$	−1.38452	+	14.4032i	−0.0615496	+	0.640302i
$507$	−17.1935	+	8.28122i	−0.763590	+	0.367782i
$508$	−7.03830	−	1.36574i	−0.312274	−	0.0605951i
$509$	−9.79932	−	16.9729i	−0.434347	−	0.752312i	0.562895	−	0.826529i	$-0.309688\pi$
$509$	−9.79932	−	16.9729i	−0.434347	−	0.752312i	−0.997242	+	0.0742170i	$0.976354\pi$
$510$	20.5708	+	45.1191i	0.910888	+	1.99791i
$511$	5.08327	−	8.80448i	0.224871	−	0.389487i
$512$	−17.1846	+	14.7204i	−0.759460	+	0.650554i
$513$	20.0195	+	11.5582i	0.883881	+	0.510309i
$514$	32.8335	+	23.4119i	1.44822	+	1.03265i
$515$	8.06735			0.355490
$516$	11.2474	−	12.9471i	0.495140	−	0.569965i
$517$	13.5690	−	7.83407i	0.596764	−	0.344542i
$518$	5.44092	+	11.9339i	0.239060	+	0.524345i
$519$	−5.53047			−0.242761
$520$	−10.8292	+	32.1536i	−0.474894	+	1.41003i
$521$	17.9551			0.786625			0.393313	−	0.919405i	$-0.371329\pi$
$521$	17.9551			0.786625			0.393313	+	0.919405i	$0.371329\pi$
$522$	0.222923	+	0.488949i	0.00975706	+	0.0214007i
$523$	5.89049	−	3.40088i	0.257573	−	0.148710i	−0.365654	−	0.930751i	$-0.619155\pi$
$523$	5.89049	−	3.40088i	0.257573	−	0.148710i	0.623227	+	0.782041i	$0.285821\pi$
$524$	5.91441	+	5.13797i	0.258372	+	0.224453i
$525$	−8.90858			−0.388802
$526$	2.90874	+	2.07408i	0.126827	+	0.0904340i
$527$	−50.0359	−	28.8882i	−2.17960	−	1.25839i
$528$	−4.71282	+	11.6864i	−0.205099	+	0.508585i
$529$	0.133678	−	0.231538i	0.00581211	−	0.0100669i
$530$	−9.37453	−	20.5617i	−0.407204	−	0.893144i
$531$	1.05268	+	1.82329i	0.0456822	+	0.0791239i
$532$	−1.56030	+	8.04092i	−0.0676475	+	0.348618i
$533$	−2.77937	+	1.46905i	−0.120388	+	0.0636316i
$534$	−0.596257	+	6.20288i	−0.0258026	+	0.268425i
$535$	4.96205	−	2.86484i	0.214528	−	0.123858i
$536$	−6.90807	+	1.66203i	−0.298383	+	0.0717886i
$537$	10.7952	−	18.6978i	0.465847	−	0.806871i
$538$	−37.1048	−	3.56673i	−1.59970	−	0.153772i
$539$	−1.07297	+	1.85844i	−0.0462161	+	0.0800486i
$540$	28.3529	+	24.6307i	1.22011	+	1.05994i
$541$	18.9509			0.814764			0.407382	−	0.913258i	$-0.366442\pi$
$541$	18.9509			0.814764			0.407382	+	0.913258i	$0.366442\pi$
$542$	9.02174	−	12.6523i	0.387517	−	0.543465i
$543$	13.2630	+	22.9722i	0.569169	+	0.985830i
$544$	40.5724	−	1.80429i	1.73953	−	0.0773584i
$545$	−28.1470			−1.20568
$546$	−6.92211	+	2.84858i	−0.296239	+	0.121908i
$547$			26.3431i			1.12635i	0.826338	+	0.563174i	$0.190420\pi$
$547$			26.3431i			1.12635i	−0.826338	+	0.563174i	$0.809580\pi$
$548$	−0.589621	+	0.203236i	−0.0251874	+	0.00868182i
$549$	−4.19786	+	2.42364i	−0.179160	+	0.103438i
$550$	14.9953	+	10.6924i	0.639400	+	0.455924i
$551$			1.84163i			0.0784562i
$552$	−14.3534	+	13.6341i	−0.610923	+	0.580307i
$553$	2.30686	+	1.33186i	0.0980975	+	0.0566366i
$554$	23.0772	+	2.21831i	0.980454	+	0.0942470i
$555$	39.2261	+	22.6472i	1.66506	+	0.961321i
$556$	−4.92564	+	1.69782i	−0.208894	+	0.0720035i
$557$	4.50292	+	7.79928i	0.190795	+	0.330466i	0.945514	−	0.325582i	$-0.105560\pi$
$557$	4.50292	+	7.79928i	0.190795	+	0.330466i	−0.754719	+	0.656048i	$0.772227\pi$
$558$	−9.57282	−	0.920196i	−0.405250	−	0.0389550i
$559$	−17.8336	−	11.2049i	−0.754282	−	0.473915i
$560$	−4.97720	+	12.3420i	−0.210325	+	0.521544i
$561$	19.5865	−	11.3083i	0.826943	−	0.477436i
$562$	18.6702	+	40.9504i	0.787553	+	1.72739i
$563$	−10.6074	−	6.12418i	−0.447048	−	0.258103i	0.259535	−	0.965734i	$-0.416431\pi$
$563$	−10.6074	−	6.12418i	−0.447048	−	0.258103i	−0.706583	+	0.707631i	$0.749764\pi$
$564$	21.0440	+	4.08347i	0.886110	+	0.171945i
$565$	22.6558	−	39.2410i	0.953136	−	1.65088i
$566$	15.9335	−	22.3456i	0.669736	−	0.939257i
$567$			5.75098i			0.241518i
$568$	−25.1778	+	23.9161i	−1.05644	+	1.00350i
$569$	−6.93363	−	12.0094i	−0.290673	−	0.503460i	0.683296	−	0.730141i	$-0.260546\pi$
$569$	−6.93363	−	12.0094i	−0.290673	−	0.503460i	−0.973969	+	0.226681i	$0.927212\pi$
$570$	11.7346	+	25.7381i	0.491507	+	1.07805i
$571$		−	16.2837i		−	0.681450i	−0.940163	−	0.340725i	$-0.889328\pi$
$571$		−	16.2837i		−	0.681450i	0.940163	−	0.340725i	$-0.110672\pi$
$572$	15.0705	+	3.51329i	0.630129	+	0.146898i
$573$		−	21.2267i		−	0.886756i
$574$	−1.12196	+	0.511528i	−0.0468299	+	0.0213508i
$575$	14.4671	+	25.0577i	0.603318	+	1.04498i
$576$	6.02022	−	3.07482i	0.250843	−	0.128117i
$577$			2.30321i			0.0958840i	0.998850	+	0.0479420i	$0.0152663\pi$
$577$			2.30321i			0.0958840i	−0.998850	+	0.0479420i	$0.984734\pi$
$578$	−39.7752	−	28.3617i	−1.65443	−	1.17969i
$579$	0.827873	−	1.43392i	0.0344052	−	0.0595916i
$580$	−0.569971	+	2.93732i	−0.0236667	+	0.121965i
$581$	−13.2180	−	7.63144i	−0.548377	−	0.316606i
$582$	−30.0371	+	13.6946i	−1.24508	+	0.567658i
$583$	−8.92599	+	5.15343i	−0.369677	+	0.213433i
$584$	−27.5751	−	8.15357i	−1.14107	−	0.337397i
$585$	5.39251	−	8.58270i	0.222953	−	0.354851i
$586$	3.77132	−	39.2331i	0.155792	−	1.62071i
$587$	−5.98544	−	10.3671i	−0.247045	−	0.427895i	0.715659	−	0.698450i	$-0.246126\pi$
$587$	−5.98544	−	10.3671i	−0.247045	−	0.427895i	−0.962705	+	0.270554i	$0.912793\pi$
$588$	−2.77572	+	0.956760i	−0.114469	+	0.0394561i
$589$	−28.5429	−	16.4793i	−1.17609	−	0.679016i
$590$	−1.12169	+	11.6689i	−0.0461791	+	0.480402i
$591$	−28.3060	−	16.3425i	−1.16435	−	0.672239i
$592$	29.2179	−	22.8579i	1.20085	−	0.939456i
$593$		−	8.67574i		−	0.356270i	−0.984006	−	0.178135i	$-0.942994\pi$
$593$		−	8.67574i		−	0.356270i	0.984006	−	0.178135i	$-0.0570063\pi$
$594$	9.94508	−	13.9473i	0.408052	−	0.572263i
$595$	20.6853	−	11.9426i	0.848013	−	0.489601i
$596$	−10.1125	−	29.3379i	−0.414223	−	1.20173i
$597$		−	1.01109i		−	0.0413813i
$598$	19.2535	+	14.8443i	0.787334	+	0.607027i
$599$	−43.2888			−1.76873			−0.884366	−	0.466794i	$-0.845409\pi$
$599$	−43.2888			−1.76873			−0.884366	+	0.466794i	$0.845409\pi$
$600$	5.89407	+	24.4982i	0.240624	+	1.00014i
$601$	20.2469	+	35.0686i	0.825888	+	1.43048i	0.901239	+	0.433323i	$0.142659\pi$
$601$	20.2469	+	35.0686i	0.825888	+	1.43048i	−0.0753510	+	0.997157i	$0.524008\pi$
$602$	−6.72619	−	4.79610i	−0.274139	−	0.195475i
$603$	2.12269			0.0864428
$604$	15.3499	+	13.3348i	0.624579	+	0.542584i
$605$	−10.6378	+	18.4252i	−0.432488	+	0.749091i
$606$	0.307117	−	3.19494i	0.0124758	−	0.129786i
$607$	−6.31262	+	10.9338i	−0.256221	+	0.443788i	−0.965227	−	0.261415i	$-0.915811\pi$
$607$	−6.31262	+	10.9338i	−0.256221	+	0.443788i	0.709005	+	0.705203i	$0.249144\pi$
$608$	23.1445	−	1.02926i	0.938634	−	0.0417419i
$609$	−0.571683	+	0.330062i	−0.0231658	+	0.0133748i
$610$	−26.8661	−	2.58252i	−1.08778	−	0.104563i
$611$	0.983544	−	26.3068i	0.0397899	−	1.06426i
$612$	−11.9109	−	2.31125i	−0.481471	−	0.0934269i
$613$	−7.90331	−	13.6889i	−0.319212	−	0.552891i	0.661112	−	0.750287i	$-0.270085\pi$
$613$	−7.90331	−	13.6889i	−0.319212	−	0.552891i	−0.980324	+	0.197396i	$0.936751\pi$
$614$	35.4732	−	16.1730i	1.43158	−	0.652688i
$615$	−2.12918	+	3.68785i	−0.0858568	+	0.148708i
$616$	5.82052	+	1.72105i	0.234516	+	0.0693430i
$617$	13.9414	+	8.04909i	0.561261	+	0.324044i	0.753651	−	0.657274i	$-0.228291\pi$
$617$	13.9414	+	8.04909i	0.561261	+	0.324044i	−0.192391	+	0.981318i	$0.561624\pi$
$618$	2.92267	−	4.09883i	0.117567	−	0.164879i
$619$	−1.93623			−0.0778235			−0.0389118	−	0.999243i	$-0.512389\pi$
$619$	−1.93623			−0.0778235			−0.0389118	+	0.999243i	$0.512389\pi$
$620$	−40.4243	−	35.1174i	−1.62348	−	1.41035i
$621$	23.3064	−	13.4560i	0.935254	−	0.539969i
$622$	43.9343	−	20.0306i	1.76160	−	0.803154i
$623$	3.00159			0.120256
$624$	12.4133	+	17.1508i	0.496928	+	0.686583i
$625$	−18.5154			−0.740618
$626$	−16.4240	+	7.48807i	−0.656436	+	0.299284i
$627$	11.1731	−	6.45080i	0.446211	−	0.257620i
$628$	30.1257	+	26.1708i	1.20215	+	1.04433i
$629$	−66.5827			−2.65482
$630$	2.30820	−	3.23708i	0.0919607	−	0.128968i
$631$	−2.33947	−	1.35069i	−0.0931327	−	0.0537702i	0.452710	−	0.891658i	$-0.350457\pi$
$631$	−2.33947	−	1.35069i	−0.0931327	−	0.0537702i	−0.545843	+	0.837887i	$0.683791\pi$
$632$	2.13631	−	7.22494i	0.0849780	−	0.287393i
$633$	−9.43819	+	16.3474i	−0.375134	+	0.649752i
$634$	6.28053	−	2.86343i	0.249432	−	0.113721i
$635$	5.96320	+	10.3286i	0.236642	+	0.409876i
$636$	−13.8432	−	2.68620i	−0.548918	−	0.106515i
$637$	1.68486	+	3.18767i	0.0667564	+	0.126300i
$638$	1.35843	+	0.130580i	0.0537807	+	0.00516972i
$639$	8.98460	−	5.18726i	0.355425	−	0.205205i
$640$	37.2329	+	5.52142i	1.47176	+	0.218253i
$641$	−11.2541	+	19.4926i	−0.444509	+	0.769912i	−0.998018	−	0.0629309i	$-0.979955\pi$
$641$	−11.2541	+	19.4926i	−0.444509	+	0.769912i	0.553509	+	0.832843i	$0.313289\pi$
$642$	0.342111	−	3.55899i	0.0135020	−	0.140462i
$643$	−22.5435	+	39.0466i	−0.889031	+	1.53985i	−0.0480079	+	0.998847i	$0.515287\pi$
$643$	−22.5435	+	39.0466i	−0.889031	+	1.53985i	−0.841023	+	0.541000i	$0.818046\pi$
$644$	7.19875	+	6.25369i	0.283670	+	0.246430i
$645$	−28.5290			−1.12333
$646$	−33.8562	−	24.1411i	−1.33205	−	0.949820i
$647$	−10.5316	−	18.2413i	−0.414041	−	0.717140i	0.581286	−	0.813699i	$-0.302550\pi$
$647$	−10.5316	−	18.2413i	−0.414041	−	0.717140i	−0.995327	+	0.0965590i	$0.969216\pi$
$648$	15.8149	−	3.80494i	0.621269	−	0.149472i
$649$	5.34670			0.209876
$650$	28.6154	−	11.7758i	1.12239	−	0.461885i
$651$		−	11.8138i		−	0.463019i
$652$	−5.40859	−	15.6912i	−0.211817	−	0.614514i
$653$	−32.2840	+	18.6392i	−1.26337	+	0.729406i	−0.973725	−	0.227728i	$-0.926870\pi$
$653$	−32.2840	+	18.6392i	−1.26337	+	0.729406i	−0.289644	+	0.957134i	$0.593537\pi$
$654$	−10.1972	+	14.3008i	−0.398741	+	0.559206i
$655$		−	13.0324i		−	0.509219i
$656$	2.14899	+	2.74692i	0.0839040	+	0.107249i
$657$	7.43978	+	4.29536i	0.290254	+	0.167578i
$658$	0.988002	−	10.2782i	0.0385163	−	0.400686i
$659$	−16.6375	−	9.60567i	−0.648105	−	0.374184i	0.139625	−	0.990204i	$-0.455410\pi$
$659$	−16.6375	−	9.60567i	−0.648105	−	0.374184i	−0.787730	+	0.616021i	$0.788744\pi$
$660$	19.8170	−	6.83072i	0.771377	−	0.265885i
$661$	−16.2763	−	28.1914i	−0.633076	−	1.09652i	−0.986919	−	0.161215i	$-0.948459\pi$
$661$	−16.2763	−	28.1914i	−0.633076	−	1.09652i	0.353844	−	0.935305i	$-0.384874\pi$
$662$	−2.77751	+	28.8945i	−0.107951	+	1.12302i
$663$	1.41972	−	37.9732i	0.0551374	−	1.47476i
$664$	−12.2409	+	41.3982i	−0.475037	+	1.60656i
$665$	11.7999	−	6.81267i	0.457580	−	0.264184i
$666$	−10.0841	+	4.59757i	−0.390752	+	0.178152i
$667$	1.85677	+	1.07200i	0.0718942	+	0.0415082i
$668$	8.95182	−	46.1328i	0.346356	−	1.78493i
$669$	−11.8884	+	20.5913i	−0.459632	+	0.796105i
$670$	9.62337	+	6.86194i	0.371783	+	0.265100i
$671$			12.3100i			0.475223i
$672$	4.46751	+	7.00010i	0.172338	+	0.270035i
$673$	−0.672703	−	1.16516i	−0.0259308	−	0.0449135i	0.852769	−	0.522289i	$-0.174922\pi$
$673$	−0.672703	−	1.16516i	−0.0259308	−	0.0449135i	−0.878700	+	0.477375i	$0.841588\pi$
$674$	−10.7348	+	4.89421i	−0.413488	+	0.188518i
$675$		−	34.2535i		−	1.31842i
$676$	18.4692	−	18.2999i	0.710354	−	0.703844i
$677$		−	16.6699i		−	0.640675i	−0.947303	−	0.320338i	$-0.896204\pi$
$677$		−	16.6699i		−	0.640675i	0.947303	−	0.320338i	$-0.103796\pi$
$678$	−11.7296	−	25.7272i	−0.450473	−	0.988049i
$679$	7.95057	+	13.7708i	0.305115	+	0.528475i
$680$	−46.5275	−	48.9821i	−1.78425	−	1.87838i
$681$		−	27.1929i		−	1.04203i
$682$	−14.1793	+	19.8854i	−0.542952	+	0.761452i
$683$	16.8113	−	29.1180i	0.643265	−	1.11417i	−0.341434	−	0.939906i	$-0.610913\pi$
$683$	16.8113	−	29.1180i	0.643265	−	1.11417i	0.984699	−	0.174262i	$-0.0557540\pi$
$684$	−6.79458	−	1.31845i	−0.259797	−	0.0504123i
$685$	0.898457	+	0.518725i	0.0343283	+	0.0198194i
$686$	0.586673	+	1.28678i	0.0223993	+	0.0491297i
$687$	11.7088	−	6.76009i	0.446720	−	0.257914i
$688$	−8.73891	+	21.6699i	−0.333168	+	0.826157i
$689$	−0.646997	+	17.3052i	−0.0246486	+	0.659276i
$690$	32.7802	+	3.15103i	1.24792	+	0.119958i
$691$	−5.38504	−	9.32717i	−0.204857	−	0.354822i	0.745230	−	0.666807i	$-0.232339\pi$
$691$	−5.38504	−	9.32717i	−0.204857	−	0.354822i	−0.950087	+	0.311985i	$0.899006\pi$
$692$	7.12345	−	2.45538i	0.270793	−	0.0933394i
$693$	−1.57038	−	0.906660i	−0.0596538	−	0.0344412i
$694$	6.14483	+	0.590677i	0.233255	+	0.0224218i
$695$	7.50563	+	4.33338i	0.284705	+	0.164374i
$696$	1.28589	+	1.35373i	0.0487416	+	0.0513130i
$697$		−	6.25977i		−	0.237106i
$698$	10.4201	+	7.43002i	0.394405	+	0.281230i
$699$	15.7674	−	9.10334i	0.596380	−	0.344320i
$700$	11.4746	−	3.95516i	0.433698	−	0.149491i
$701$		−	10.6340i		−	0.401640i	−0.979628	−	0.200820i	$-0.935639\pi$
$701$		−	10.6340i		−	0.401640i	0.979628	−	0.200820i	$-0.0643606\pi$
$702$	−10.9528	−	26.6155i	−0.413387	−	1.00454i
$703$	−37.9820			−1.43252
$704$	0.881848	−	17.1449i	0.0332359	−	0.646171i
$705$	−17.8295	−	30.8816i	−0.671497	−	1.16307i
$706$	14.4060	−	20.2033i	0.542176	−	0.760362i
$707$	−1.54604			−0.0581449
$708$	5.52234	+	4.79737i	0.207542	+	0.180296i
$709$	12.4081	−	21.4915i	0.465998	−	0.807132i	−0.533248	−	0.845959i	$-0.679029\pi$
$709$	12.4081	−	21.4915i	0.465998	−	0.807132i	0.999246	+	0.0388270i	$0.0123621\pi$
$710$	57.5009	+	5.52732i	2.15797	+	0.207437i
$711$	−1.12542	+	1.94929i	−0.0422067	+	0.0731042i
$712$	−1.98591	−	8.25425i	−0.0744250	−	0.309341i
$713$	−33.2293	+	19.1850i	−1.24445	+	0.718482i
$714$	1.42616	−	14.8363i	0.0533725	−	0.555236i
$715$	−12.0289	−	22.7581i	−0.449855	−	0.851106i
$716$	−5.60329	+	28.8763i	−0.209405	+	1.07916i
$717$	8.27143	+	14.3265i	0.308902	+	0.535035i
$718$	−13.4077	−	29.4078i	−0.500369	−	1.09749i
$719$	18.5886	−	32.1964i	0.693238	−	1.20072i	−0.277533	−	0.960716i	$-0.589517\pi$
$719$	18.5886	−	32.1964i	0.693238	−	1.20072i	0.970771	−	0.240008i	$-0.0771500\pi$
$720$	−10.4290	−	4.20573i	−0.388665	−	0.156738i
$721$	−2.09998	−	1.21243i	−0.0782075	−	0.0451531i
$722$	2.56462	+	1.82870i	0.0954454	+	0.0680573i
$723$	36.6263			1.36215
$724$	−27.2822	−	23.7006i	−1.01393	−	0.880825i
$725$	2.36329	−	1.36445i	0.0877704	−	0.0506743i
$726$	5.50752	+	12.0800i	0.204403	+	0.448330i
$727$	19.5319			0.724398			0.362199	−	0.932101i	$-0.382026\pi$
$727$	19.5319			0.724398			0.362199	+	0.932101i	$0.382026\pi$
$728$	7.65123	−	6.74230i	0.283574	−	0.249886i
$729$	−29.7175			−1.10065
$730$	19.8433	+	43.5235i	0.734434	+	1.61088i
$731$	36.3190	−	20.9688i	1.34331	−	0.775558i
$732$	−11.0453	+	12.7144i	−0.408244	+	0.469938i
$733$	10.7156			0.395791			0.197895	−	0.980223i	$-0.436589\pi$
$733$	10.7156			0.395791			0.197895	+	0.980223i	$0.436589\pi$
$734$	−28.3959	−	20.2476i	−1.04811	−	0.747354i
$735$	4.22960	+	2.44196i	0.156011	+	0.0900732i
$736$	12.4346	−	23.9338i	0.458344	−	0.882211i
$737$	2.69537	−	4.66852i	0.0992853	−	0.171967i
$738$	−0.432241	−	0.948060i	−0.0159110	−	0.0348986i
$739$	−18.9606	−	32.8407i	−0.697477	−	1.20807i	−0.969338	−	0.245730i	$-0.920972\pi$
$739$	−18.9606	−	32.8407i	−0.697477	−	1.20807i	0.271861	−	0.962337i	$-0.412361\pi$
$740$	−60.5794	−	11.7551i	−2.22694	−	0.432127i
$741$	0.809878	−	21.6618i	0.0297516	−	0.795765i
$742$	−0.649930	+	6.76123i	−0.0238597	+	0.248213i
$743$	−7.81743	+	4.51340i	−0.286794	+	0.165580i	−0.636495	−	0.771281i	$-0.719616\pi$
$743$	−7.81743	+	4.51340i	−0.286794	+	0.165580i	0.349701	+	0.936861i	$0.386283\pi$
$744$	−32.4874	+	7.81621i	−1.19105	+	0.286556i
$745$	−25.8103	+	44.7048i	−0.945617	+	1.63786i
$746$	26.5480	+	2.55195i	0.971990	+	0.0934334i
$747$	6.44857	−	11.1692i	0.235941	−	0.408661i
$748$	−20.2076	+	23.2613i	−0.738862	+	0.850519i
$749$	−1.72221			−0.0629281
$750$	4.28484	−	6.00919i	0.156460	−	0.219424i
$751$	1.19524	+	2.07022i	0.0436150	+	0.0755434i	0.887009	−	0.461753i	$-0.152779\pi$
$751$	1.19524	+	2.07022i	0.0436150	+	0.0755434i	−0.843394	+	0.537296i	$0.819446\pi$
$752$	−28.9183	+	4.08328i	−1.05454	+	0.148902i
$753$	12.9198			0.470822
$754$	1.40002	−	1.81587i	0.0509858	−	0.0661302i
$755$		−	33.8236i		−	1.23097i
$756$	−3.67874	−	10.6726i	−0.133795	−	0.388160i
$757$	34.0758	−	19.6737i	1.23851	−	0.715051i	0.269717	−	0.962940i	$-0.413070\pi$
$757$	34.0758	−	19.6737i	1.23851	−	0.715051i	0.968789	+	0.247888i	$0.0797366\pi$
$758$	−31.5049	−	22.4645i	−1.14431	−	0.815948i
$759$		−	15.0199i		−	0.545187i
$760$	−26.5416	−	27.9418i	−0.962763	−	1.01356i
$761$	−6.51631	−	3.76219i	−0.236216	−	0.136379i	0.377220	−	0.926124i	$-0.376880\pi$
$761$	−6.51631	−	3.76219i	−0.236216	−	0.136379i	−0.613436	+	0.789744i	$0.710213\pi$
$762$	7.40807	+	0.712107i	0.268366	+	0.0257969i
$763$	7.32684	+	4.23015i	0.265249	+	0.153142i
$764$	9.42405	+	27.3407i	0.340950	+	0.989152i
$765$	10.0915	+	17.4791i	0.364860	+	0.631956i
$766$	24.2270	+	2.32884i	0.875357	+	0.0841444i
$767$	4.77922	−	7.60658i	0.172568	−	0.274658i
$768$	16.2942	−	16.9168i	0.587966	−	0.610434i
$769$	4.03351	−	2.32875i	0.145452	−	0.0839768i	−0.425508	−	0.904955i	$-0.639904\pi$
$769$	4.03351	−	2.32875i	0.145452	−	0.0839768i	0.570960	+	0.820978i	$0.306571\pi$
$770$	−4.18851	−	9.18690i	−0.150943	−	0.331073i
$771$	−36.2510	−	20.9295i	−1.30555	−	0.753758i
$772$	−0.429710	+	2.21449i	−0.0154656	+	0.0797013i
$773$	20.5288	−	35.5569i	0.738370	−	1.27889i	−0.214859	−	0.976645i	$-0.568929\pi$
$773$	20.5288	−	35.5569i	0.738370	−	1.27889i	0.953229	−	0.302249i	$-0.0977374\pi$
$774$	4.05271	−	5.68363i	0.145671	−	0.204294i
$775$			48.8372i			1.75428i
$776$	32.6089	−	30.9747i	1.17059	−	1.11193i
$777$	−6.80722	−	11.7904i	−0.244208	−	0.422980i
$778$	16.2145	+	35.5643i	0.581320	+	1.27504i
$779$		−	3.57088i		−	0.127940i
$780$	7.99586	−	34.2988i	0.286298	−	1.22809i
$781$		−	26.3469i		−	0.942765i
$782$	−44.0470	+	20.0820i	−1.57512	+	0.718129i
$783$	−1.26909	−	2.19812i	−0.0453535	−	0.0785545i
$784$	3.15045	−	2.46468i	0.112516	−	0.0880244i
$785$		−	66.3821i		−	2.36928i
$786$	−6.62147	−	4.72144i	−0.236180	−	0.168408i
$787$	−22.9518	+	39.7537i	−0.818144	+	1.41707i	0.0889037	+	0.996040i	$0.471664\pi$
$787$	−22.9518	+	39.7537i	−0.818144	+	1.41707i	−0.907048	+	0.421027i	$0.861670\pi$
$788$	43.7147	+	8.48261i	1.55727	+	0.302180i
$789$	−3.21150	−	1.85416i	−0.114333	−	0.0660099i
$790$	−11.4036	+	5.19914i	−0.405721	+	0.184977i
$791$	−11.7949	+	6.80979i	−0.419378	+	0.242128i
$792$	−1.45428	+	4.91834i	−0.0516758	+	0.174766i
$793$	17.5131	+	11.0035i	0.621908	+	0.390745i
$794$	−1.41640	+	14.7348i	−0.0502661	+	0.522920i
$795$	11.7286	+	20.3146i	0.415972	+	0.720484i
$796$	0.448898	+	1.30233i	0.0159108	+	0.0461597i
$797$	−33.6967	−	19.4548i	−1.19360	−	0.689125i	−0.234478	−	0.972121i	$-0.575338\pi$
$797$	−33.6967	−	19.4548i	−1.19360	−	0.689125i	−0.959121	+	0.282997i	$0.908671\pi$
$798$	0.813549	−	8.46337i	0.0287993	−	0.299600i
$799$	45.3958	+	26.2093i	1.60599	+	0.927217i
$800$	−18.4683	−	28.9378i	−0.652953	−	1.02311i
$801$			2.53635i			0.0896174i
$802$	28.6753	−	40.2151i	1.01256	−	1.42004i
$803$	18.8939	−	10.9084i	0.666751	−	0.384949i
$804$	6.97278	−	2.40344i	0.245911	−	0.0847630i
$805$		−	15.8625i		−	0.559078i
$806$	15.6160	+	37.9473i	0.550051	+	1.33664i
$807$	38.6933			1.36207
$808$	1.02289	+	4.25155i	0.0359851	+	0.149569i
$809$	−8.66971	−	15.0164i	−0.304811	−	0.527948i	0.672408	−	0.740180i	$-0.265260\pi$
$809$	−8.66971	−	15.0164i	−0.304811	−	0.527948i	−0.977219	+	0.212233i	$0.931927\pi$
$810$	−22.0312	−	15.7093i	−0.774097	−	0.551969i
$811$	48.1308			1.69010			0.845050	−	0.534687i	$-0.179571\pi$
$811$	48.1308			1.69010			0.845050	+	0.534687i	$0.179571\pi$
$812$	0.589811	−	0.678943i	0.0206983	−	0.0238262i
$813$	−8.06517	+	13.9693i	−0.282858	+	0.489924i
$814$	−2.69310	+	28.0163i	−0.0943929	+	0.981972i
$815$	−13.8045	+	23.9100i	−0.483549	+	0.837532i
$816$	−41.7428	+	5.89411i	−1.46129	+	0.206335i
$817$	20.7181	−	11.9616i	0.724835	−	0.418484i
$818$	−22.4487	−	2.15790i	−0.784900	−	0.0754492i
$819$	−2.69358	+	1.42370i	−0.0941214	+	0.0497482i
$820$	1.10516	−	5.69538i	0.0385938	−	0.198891i
$821$	−17.9770	−	31.1370i	−0.627401	−	1.08669i	−0.988071	−	0.153997i	$-0.950785\pi$
$821$	−17.9770	−	31.1370i	−0.627401	−	1.08669i	0.360670	−	0.932693i	$-0.382548\pi$
$822$	0.589048	−	0.268560i	0.0205454	−	0.00936710i
$823$	−6.38185	+	11.0537i	−0.222457	+	0.385307i	−0.955554	−	0.294818i	$-0.904741\pi$
$823$	−6.38185	+	11.0537i	−0.222457	+	0.385307i	0.733096	+	0.680125i	$0.238074\pi$
$824$	−1.94474	+	6.57703i	−0.0677481	+	0.229122i
$825$	−16.5561	−	9.55865i	−0.576408	−	0.332789i
$826$	2.04568	−	2.86892i	0.0711784	−	0.0998226i
$827$	4.87643			0.169570			0.0847851	−	0.996399i	$-0.472980\pi$
$827$	4.87643			0.169570			0.0847851	+	0.996399i	$0.472980\pi$
$828$	−5.28437	+	6.08294i	−0.183644	+	0.211397i
$829$	1.73551	−	1.00200i	0.0602768	−	0.0348009i	−0.469559	−	0.882901i	$-0.655587\pi$
$829$	1.73551	−	1.00200i	0.0602768	−	0.0348009i	0.529836	+	0.848100i	$0.322254\pi$
$830$	65.3413	−	29.7905i	2.26803	−	1.03404i
$831$	−24.0651			−0.834810
$832$	−23.6032	−	16.5797i	−0.818295	−	0.574799i
$833$	−7.17935			−0.248750
$834$	4.92086	−	2.24353i	0.170395	−	0.0776869i
$835$	−67.6989	+	39.0860i	−2.34282	+	1.35263i
$836$	−11.5274	+	13.2694i	−0.398683	+	0.458932i
$837$	45.4240			1.57008
$838$	24.6709	−	34.5992i	0.852243	−	1.19521i
$839$	37.6971	+	21.7645i	1.30145	+	0.751393i	0.980653	−	0.195755i	$-0.0627158\pi$
$839$	37.6971	+	21.7645i	1.30145	+	0.751393i	0.320797	+	0.947148i	$0.396049\pi$
$840$	3.91691	−	13.2469i	0.135146	−	0.457061i
$841$	−14.3989	+	24.9396i	−0.496514	+	0.859987i
$842$	41.9755	−	19.1375i	1.44657	−	0.659523i
$843$	−23.3585	−	40.4582i	−0.804511	−	1.39345i
$844$	4.89893	−	25.2464i	0.168628	−	0.869016i
$845$	−43.1295	−	3.22952i	−1.48370	−	0.111099i
$846$	8.68509	+	0.834862i	0.298599	+	0.0287031i
$847$	5.53818	−	3.19747i	0.190294	−	0.109866i
$848$	19.0231	−	2.68607i	0.653256	−	0.0922400i
$849$	−14.2441	+	24.6715i	−0.488857	+	0.846724i
$850$	−5.89560	+	61.3321i	−0.202218	+	2.10367i
$851$	−22.1091	+	38.2941i	−0.757890	+	1.31270i
$852$	23.6399	−	27.2124i	0.809891	−	0.932281i
$853$	12.5852			0.430908			0.215454	−	0.976514i	$-0.430877\pi$
$853$	12.5852			0.430908			0.215454	+	0.976514i	$0.430877\pi$
$854$	6.60529	+	4.70990i	0.226028	+	0.161169i
$855$	5.75670	+	9.97090i	0.196875	+	0.340998i
$856$	1.13944	+	4.73599i	0.0389453	+	0.161873i
$857$	−0.909554			−0.0310698			−0.0155349	−	0.999879i	$-0.504945\pi$
$857$	−0.909554			−0.0310698			−0.0155349	+	0.999879i	$0.504945\pi$
$858$	−15.9208	−	2.13330i	−0.543526	−	0.0728297i
$859$			33.5753i			1.14557i	0.819704	+	0.572787i	$0.194138\pi$
$859$			33.5753i			1.14557i	−0.819704	+	0.572787i	$0.805862\pi$
$860$	36.7464	−	12.6661i	1.25304	−	0.431910i
$861$	1.10848	−	0.639981i	0.0377769	−	0.0218105i
$862$	9.35669	−	13.1221i	0.318690	−	0.446940i
$863$			41.7483i			1.42113i	0.703633	+	0.710564i	$0.251560\pi$
$863$			41.7483i			1.42113i	−0.703633	+	0.710564i	$0.748440\pi$
$864$	−26.9154	+	17.1776i	−0.915679	+	0.584393i
$865$	−10.8546	−	6.26692i	−0.369068	−	0.213082i
$866$	−1.84308	+	19.1736i	−0.0626305	+	0.651547i
$867$	43.9152	+	25.3545i	1.49144	+	0.861083i
$868$	5.24500	+	15.2166i	0.178027	+	0.516485i
$869$	2.85810	+	4.95038i	0.0969544	+	0.167930i
$870$	0.297186	−	3.09163i	0.0100756	−	0.104816i
$871$	−4.23247	−	8.00764i	−0.143412	−	0.271329i
$872$	6.78518	−	22.9472i	0.229775	−	0.777091i
$873$	−11.6363	+	6.71823i	−0.393830	+	0.227378i
$874$	−25.1265	+	11.4557i	−0.849918	+	0.387496i
$875$	−3.07873	−	1.77751i	−0.104080	−	0.0600906i
$876$	29.3022	+	5.68594i	0.990030	+	0.192110i
$877$	−21.8270	+	37.8054i	−0.737045	+	1.27660i	0.216776	+	0.976221i	$0.430446\pi$
$877$	−21.8270	+	37.8054i	−0.737045	+	1.27660i	−0.953820	+	0.300377i	$0.902887\pi$
$878$	−45.6703	−	32.5652i	−1.54130	−	1.09902i
$879$			40.9128i			1.37995i
$880$	−22.4924	+	17.5964i	−0.758218	+	0.593175i
$881$	−8.10121	−	14.0317i	−0.272937	−	0.472740i	0.696676	−	0.717386i	$-0.254662\pi$
$881$	−8.10121	−	14.0317i	−0.272937	−	0.472740i	−0.969612	+	0.244646i	$0.921328\pi$
$882$	−1.08733	+	0.495738i	−0.0366124	+	0.0166924i
$883$		−	16.5826i		−	0.558048i	−0.960284	−	0.279024i	$-0.909989\pi$
$883$		−	16.5826i		−	0.558048i	0.960284	−	0.279024i	$-0.0900109\pi$
$884$	15.0304	+	49.5412i	0.505527	+	1.66625i
$885$		−	12.1685i		−	0.409040i
$886$	−11.9457	−	26.2012i	−0.401323	−	0.880246i
$887$	9.62465	+	16.6704i	0.323164	+	0.559737i	0.981139	−	0.193303i	$-0.0619201\pi$
$887$	9.62465	+	16.6704i	0.323164	+	0.559737i	−0.657975	+	0.753040i	$0.728587\pi$
$888$	−27.9194	+	26.5203i	−0.936915	+	0.889963i
$889$		−	3.58479i		−	0.120230i
$890$	−8.19913	+	11.4987i	−0.274836	+	0.385437i
$891$	−6.17063	+	10.6878i	−0.206724	+	0.358056i
$892$	6.17071	−	31.8004i	0.206611	−	1.06476i
$893$	25.8960	+	14.9511i	0.866576	+	0.500318i
$894$	13.3628	+	29.3094i	0.446919	+	0.980254i
$895$	42.3753	−	24.4654i	1.41645	−	0.817789i
$896$	−8.86217	−	7.03292i	−0.296064	−	0.234953i
$897$	−21.3683	−	13.4257i	−0.713468	−	0.448272i
$898$	15.6168	+	1.50117i	0.521138	+	0.0500948i
$899$	1.80941	+	3.13399i	0.0603472	+	0.104524i
$900$	3.34211	+	9.69602i	0.111404	+	0.323201i
$901$	−29.8624	−	17.2410i	−0.994859	−	0.574382i
$902$	−2.63396	−	0.253191i	−0.0877012	−	0.00843035i
$903$	7.42629	+	4.28757i	0.247132	+	0.142681i
$904$	26.5303	+	27.9300i	0.882386	+	0.928938i
$905$			60.1164i			1.99834i
$906$	−17.1850	−	12.2537i	−0.570932	−	0.407103i
$907$	−8.26168	+	4.76989i	−0.274325	+	0.158381i	−0.630851	−	0.775904i	$-0.717294\pi$
$907$	−8.26168	+	4.76989i	−0.274325	+	0.158381i	0.356527	+	0.934285i	$0.383961\pi$
$908$	12.0729	+	35.0255i	0.400653	+	1.16236i
$909$		−	1.30641i		−	0.0433308i
$910$	−16.8139	−	2.25297i	−0.557375	−	0.0746853i
$911$	11.7284			0.388580			0.194290	−	0.980944i	$-0.437760\pi$
$911$	11.7284			0.388580			0.194290	+	0.980944i	$0.437760\pi$
$912$	−23.8122	+	3.36229i	−0.788499	+	0.111336i
$913$	−16.3766	−	28.3651i	−0.541987	−	0.938749i
$914$	−5.63702	+	7.90551i	−0.186456	+	0.261491i
$915$	28.0162			0.926188
$916$	−12.0801	+	13.9056i	−0.399138	+	0.459455i
$917$	−1.95862	+	3.39243i	−0.0646793	+	0.112028i
$918$	57.0457	+	5.48357i	1.88279	+	0.180985i
$919$	6.21888	−	10.7714i	0.205142	−	0.355316i	−0.745036	−	0.667024i	$-0.767568\pi$
$919$	6.21888	−	10.7714i	0.205142	−	0.355316i	0.950178	+	0.311708i	$0.100901\pi$
$920$	−43.6211	+	10.4949i	−1.43814	+	0.346006i
$921$	−35.0468	+	20.2343i	−1.15483	+	0.666742i
$922$	2.15516	−	22.4201i	0.0709763	−	0.738368i
$923$	−37.4829	−	23.5505i	−1.23376	−	0.775174i
$924$	−6.18508	−	1.20018i	−0.203474	−	0.0394831i
$925$	28.1404	+	48.7407i	0.925252	+	1.60258i
$926$	−3.67326	−	8.05679i	−0.120711	−	0.264763i
$927$	1.02450	−	1.77449i	0.0336490	−	0.0582818i
$928$	−2.25729	−	1.17275i	−0.0740993	−	0.0384975i
$929$	51.8001	+	29.9068i	1.69951	+	0.981210i	0.946224	+	0.323512i	$0.104864\pi$
$929$	51.8001	+	29.9068i	1.69951	+	0.981210i	0.753282	+	0.657698i	$0.228470\pi$
$930$	45.2570	+	32.2705i	1.48404	+	1.05819i
$931$	−4.09545			−0.134223
$932$	−16.2674	+	18.7257i	−0.532857	+	0.613382i
$933$	−43.4062	+	25.0606i	−1.42106	+	0.820447i
$934$	24.5172	+	53.7750i	0.802227	+	1.75957i
$935$	51.2564			1.67626
$936$	5.69724	+	6.46529i	0.186220	+	0.211325i
$937$	13.6334			0.445385			0.222693	−	0.974889i	$-0.428515\pi$
$937$	13.6334			0.445385			0.222693	+	0.974889i	$0.428515\pi$
$938$	−1.47376	−	3.23249i	−0.0481200	−	0.105544i
$939$	16.2266	−	9.36845i	0.529536	−	0.305728i
$940$	36.6756	+	31.8608i	1.19623	+	1.03918i
$941$	−15.6606			−0.510522			−0.255261	−	0.966872i	$-0.582161\pi$
$941$	−15.6606			−0.510522			−0.255261	+	0.966872i	$0.582161\pi$
$942$	−33.7272	−	24.0491i	−1.09889	−	0.783564i
$943$	−3.60022	−	2.07859i	−0.117239	−	0.0676881i
$944$	−9.24288	−	3.72741i	−0.300830	−	0.121317i
$945$	−9.38935	+	16.2628i	−0.305435	+	0.529030i
$946$	−7.35413	−	16.1303i	−0.239104	−	0.524440i
$947$	29.2783	+	50.7115i	0.951417	+	1.64790i	0.742362	+	0.669999i	$0.233705\pi$
$947$	29.2783	+	50.7115i	0.951417	+	1.64790i	0.209055	+	0.977904i	$0.432961\pi$
$948$	−1.48977	+	7.67745i	−0.0483855	+	0.249352i
$949$	1.36952	−	36.6304i	0.0444563	−	1.18907i
$950$	−3.36314	+	34.9868i	−0.109115	+	1.13512i
$951$	−6.20504	+	3.58248i	−0.201212	+	0.116170i
$952$	4.74998	+	19.7429i	0.153948	+	0.639871i
$953$	28.6620	−	49.6440i	0.928453	−	1.60813i	0.142542	−	0.989789i	$-0.454472\pi$
$953$	28.6620	−	49.6440i	0.928453	−	1.60813i	0.785911	−	0.618339i	$-0.212194\pi$
$954$	−5.71324	−	0.549190i	−0.184973	−	0.0177807i
$955$	24.0532	−	41.6614i	0.778344	−	1.34813i
$956$	−17.0145	−	14.7808i	−0.550288	−	0.478046i
$957$	−1.41659			−0.0457917
$958$	9.76329	−	13.6923i	0.315438	−	0.442379i
$959$	−0.155916	−	0.270055i	−0.00503480	−	0.00872053i
$960$	−39.0198	−	2.00699i	−1.25936	−	0.0647753i
$961$	−33.7637			−1.08915
$962$	37.4507	+	28.8742i	1.20746	+	0.930940i
$963$		−	1.45526i		−	0.0468952i
$964$	−47.1761	+	16.2611i	−1.51944	+	0.523734i
$965$	3.24972	−	1.87623i	0.104612	−	0.0603979i
$966$	−8.05934	−	5.74671i	−0.259305	−	0.184897i
$967$			35.8951i			1.15431i	0.816635	+	0.577154i	$0.195837\pi$
$967$			35.8951i			1.15431i	−0.816635	+	0.577154i	$0.804163\pi$
$968$	−12.4571	−	13.1143i	−0.400385	−	0.421508i
$969$	37.3802	+	21.5815i	1.20082	+	0.693296i
$970$	−74.4718	−	7.15866i	−2.39114	−	0.229851i
$971$	−31.1026	−	17.9571i	−0.998131	−	0.576271i	−0.0904359	−	0.995902i	$-0.528826\pi$
$971$	−31.1026	−	17.9571i	−0.998131	−	0.576271i	−0.907695	+	0.419631i	$0.862159\pi$
$972$	16.0548	−	5.53393i	0.514959	−	0.177501i
$973$	−1.30251	−	2.25601i	−0.0417566	−	0.0723245i
$974$	17.0370	+	1.63769i	0.545899	+	0.0524750i
$975$	−28.3977	+	15.0097i	−0.909453	+	0.480695i
$976$	8.58184	−	21.2804i	0.274698	−	0.681170i
$977$	0.0470932	−	0.0271893i	0.00150664	−	0.000869861i	−0.499246	−	0.866460i	$-0.666390\pi$
$977$	0.0470932	−	0.0271893i	0.00150664	−	0.000869861i	0.500753	+	0.865590i	$0.333056\pi$
$978$	7.14700	+	15.6759i	0.228536	+	0.501261i
$979$	5.57828	+	3.22062i	0.178283	+	0.102932i
$980$	−6.53205	−	1.26751i	−0.208659	−	0.0404891i
$981$	−3.57448	+	6.19118i	−0.114124	+	0.197669i
$982$	−13.6100	+	19.0870i	−0.434312	+	0.609091i
$983$			25.5289i			0.814246i	0.913373	+	0.407123i	$0.133468\pi$
$983$			25.5289i			0.814246i	−0.913373	+	0.407123i	$0.866532\pi$
$984$	−2.49331	−	2.62485i	−0.0794838	−	0.0836771i
$985$	−37.0373	−	64.1504i	−1.18011	−	2.04400i
$986$	1.89401	+	4.15425i	0.0603176	+	0.132298i
$987$			10.7182i			0.341165i
$988$	8.57407	+	28.2607i	0.272778	+	0.899093i
$989$		−	27.8511i		−	0.885614i
$990$	7.76293	−	3.53929i	0.246722	−	0.112486i
$991$	3.29918	+	5.71435i	0.104802	+	0.181522i	0.913657	−	0.406485i	$-0.133246\pi$
$991$	3.29918	+	5.71435i	0.104802	+	0.181522i	−0.808855	+	0.588008i	$0.799912\pi$
$992$	38.3748	−	24.4911i	1.21840	−	0.777592i
$993$		−	30.1315i		−	0.956194i
$994$	−14.1372	−	10.0805i	−0.448404	−	0.319734i
$995$	1.14573	−	1.98447i	0.0363222	−	0.0629119i
$996$	8.53623	−	43.9910i	0.270481	−	1.39391i
$997$	4.02201	+	2.32211i	0.127378	+	0.0735418i	0.562335	−	0.826909i	$-0.309903\pi$
$997$	4.02201	+	2.32211i	0.127378	+	0.0735418i	−0.434957	+	0.900451i	$0.643236\pi$
$998$	0.787487	−	0.359032i	0.0249275	−	0.0113650i
$999$	45.3343	−	26.1737i	1.43431	−	0.828101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cz.a.309.72	yes	168
8.5	even	2	inner	728.2.cz.a.309.68	✓	168
13.4	even	6	inner	728.2.cz.a.589.68	yes	168
104.69	even	6	inner	728.2.cz.a.589.72	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.68	✓	168	8.5	even	2	inner
728.2.cz.a.309.72	yes	168	1.1	even	1	trivial
728.2.cz.a.589.68	yes	168	13.4	even	6	inner
728.2.cz.a.589.72	yes	168	104.69	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28678 - 0.586673i) q^{2} +(-1.27132 + 0.733996i) q^{3} +(1.31163 - 1.50984i) q^{4} -3.32694 q^{5} +(-1.20530 + 1.69034i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.802001 - 2.71234i) q^{8} +(-0.422500 + 0.731791i) q^{9} +(-4.28106 + 1.95183i) q^{10} +(1.07297 + 1.85844i) q^{11} +(-0.559280 + 2.88222i) q^{12} +(3.60303 + 0.134708i) q^{13} +(1.40772 + 0.135319i) q^{14} +(4.22960 - 2.44196i) q^{15} +(-0.559254 - 3.96071i) q^{16} +(-3.58968 + 6.21750i) q^{17} +(-0.114344 + 1.18953i) q^{18} +(-2.04773 + 3.54677i) q^{19} +(-4.36372 + 5.02316i) q^{20} -1.46799 q^{21} +(2.47098 + 1.76193i) q^{22} +(2.38394 + 4.12910i) q^{23} +(0.971249 + 4.03691i) q^{24} +6.06855 q^{25} +(4.71536 - 1.94046i) q^{26} -5.64443i q^{27} +(1.89083 - 0.651748i) q^{28} +(0.389432 - 0.224839i) q^{29} +(4.00996 - 5.62367i) q^{30} +8.04759i q^{31} +(-3.04328 - 4.76848i) q^{32} +(-2.72817 - 1.57511i) q^{33} +(-0.971501 + 10.1065i) q^{34} +(-2.88122 - 1.66347i) q^{35} +(0.550727 + 1.59775i) q^{36} +(4.63709 + 8.03168i) q^{37} +(-0.554192 + 5.76527i) q^{38} +(-4.67948 + 2.47336i) q^{39} +(-2.66821 + 9.02380i) q^{40} +(-0.755099 + 0.435957i) q^{41} +(-1.88899 + 0.861231i) q^{42} +(-5.05881 - 2.92071i) q^{43} +(4.21329 + 0.817567i) q^{44} +(1.40563 - 2.43463i) q^{45} +(5.49005 + 3.91467i) q^{46} -7.30129i q^{47} +(3.61814 + 4.62483i) q^{48} +(0.500000 + 0.866025i) q^{49} +(7.80892 - 3.56025i) q^{50} -10.5392i q^{51} +(4.92924 - 5.26333i) q^{52} +4.80295i q^{53} +(-3.31143 - 7.26316i) q^{54} +(-3.56971 - 6.18292i) q^{55} +(2.05072 - 1.94796i) q^{56} -6.01209i q^{57} +(0.369209 - 0.517789i) q^{58} +(1.24577 - 2.15774i) q^{59} +(1.86069 - 9.58899i) q^{60} +(4.96788 + 2.86821i) q^{61} +(4.72130 + 10.3555i) q^{62} +(-0.731791 + 0.422500i) q^{63} +(-6.71359 - 4.35060i) q^{64} +(-11.9871 - 0.448166i) q^{65} +(-4.43465 - 0.426284i) q^{66} +(-1.25603 - 2.17551i) q^{67} +(4.67913 + 13.5749i) q^{68} +(-6.06149 - 3.49960i) q^{69} +(-4.68342 - 0.450198i) q^{70} +(-10.6327 - 6.13877i) q^{71} +(1.64602 + 1.73286i) q^{72} -10.1665i q^{73} +(10.6789 + 7.61459i) q^{74} +(-7.71506 + 4.45429i) q^{75} +(2.66920 + 7.74379i) q^{76} +2.14594i q^{77} +(-4.57043 + 5.92800i) q^{78} +2.66373 q^{79} +(1.86061 + 13.1771i) q^{80} +(2.87549 + 4.98049i) q^{81} +(-0.715886 + 1.00398i) q^{82} -15.2629 q^{83} +(-1.92546 + 2.21644i) q^{84} +(11.9426 - 20.6853i) q^{85} +(-8.22310 - 0.790453i) q^{86} +(-0.330062 + 0.571683i) q^{87} +(5.90124 - 1.41979i) q^{88} +(2.59946 - 1.50080i) q^{89} +(0.380417 - 3.95749i) q^{90} +(3.05296 + 1.91818i) q^{91} +(9.36114 + 1.81648i) q^{92} +(-5.90690 - 10.2310i) q^{93} +(-4.28347 - 9.39519i) q^{94} +(6.81267 - 11.7999i) q^{95} +(7.36903 + 3.82850i) q^{96} +(13.7708 + 7.95057i) q^{97} +(1.15147 + 0.821052i) q^{98} -1.81332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) \) 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Introduction

L-functions

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