LMFDB - Embedded newform 128.2.k.a.117.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,2,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$128 = 2^{7}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	128.k (of order $32$ , degree $16$ , 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:	$1.02208514587$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			117.6
Character	$\chi$	$=$	128.117
Dual form			128.2.k.a.93.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.488178 + 1.32728i) q^{2} +(2.54563 - 0.250723i) q^{3} +(-1.52336 - 1.29590i) q^{4} +(-0.436447 + 0.816534i) q^{5} +(-0.909941 + 3.50117i) q^{6} +(-0.466201 + 2.34375i) q^{7} +(2.46370 - 1.38930i) q^{8} +(3.47501 - 0.691223i) q^{9} +(-0.870709 - 0.977903i) q^{10} +(2.19857 - 1.80432i) q^{11} +(-4.20283 - 2.91694i) q^{12} +(-0.495033 + 0.264601i) q^{13} +(-2.88323 - 1.76295i) q^{14} +(-0.906308 + 2.18802i) q^{15} +(0.641275 + 3.94826i) q^{16} +(-1.59973 - 3.86208i) q^{17} +(-0.778976 + 4.94977i) q^{18} +(-6.93043 - 2.10232i) q^{19} +(1.72302 - 0.678287i) q^{20} +(-0.599143 + 6.08320i) q^{21} +(1.32155 + 3.79896i) q^{22} +(-2.01797 - 1.34836i) q^{23} +(5.92334 - 4.15436i) q^{24} +(2.30161 + 3.44460i) q^{25} +(-0.109536 - 0.786221i) q^{26} +(1.32938 - 0.403263i) q^{27} +(3.74746 - 2.96623i) q^{28} +(6.09406 - 7.42563i) q^{29} +(-2.46168 - 2.27107i) q^{30} +(-6.39173 - 6.39173i) q^{31} +(-5.55352 - 1.07630i) q^{32} +(5.14437 - 5.14437i) q^{33} +(5.90703 - 0.237907i) q^{34} +(-1.71028 - 1.40359i) q^{35} +(-6.18946 - 3.45029i) q^{36} +(2.58509 + 8.52191i) q^{37} +(6.17367 - 8.17234i) q^{38} +(-1.19383 + 0.797691i) q^{39} +(0.0591401 + 2.61806i) q^{40} +(-0.188942 + 0.282772i) q^{41} +(-7.78165 - 3.76492i) q^{42} +(2.72567 + 0.268455i) q^{43} +(-5.68745 - 0.100496i) q^{44} +(-0.952250 + 3.13915i) q^{45} +(2.77478 - 2.02017i) q^{46} +(-4.95618 + 2.05292i) q^{47} +(2.62237 + 9.89003i) q^{48} +(1.19134 + 0.493469i) q^{49} +(-5.69556 + 1.37331i) q^{50} +(-5.04062 - 9.43034i) q^{51} +(1.09701 + 0.238431i) q^{52} +(2.24658 + 2.73747i) q^{53} +(-0.113730 + 1.96133i) q^{54} +(0.513731 + 2.58270i) q^{55} +(2.10760 + 6.42200i) q^{56} +(-18.1694 - 3.61412i) q^{57} +(6.88093 + 11.7136i) q^{58} +(11.5723 + 6.18552i) q^{59} +(4.21610 - 2.15867i) q^{60} +(0.0204700 + 0.207835i) q^{61} +(11.6039 - 5.36333i) q^{62} +8.46680i q^{63} +(4.13966 - 6.84567i) q^{64} -0.519695i q^{65} +(4.31667 + 9.33940i) q^{66} +(1.48710 + 15.0988i) q^{67} +(-2.56791 + 7.95645i) q^{68} +(-5.47506 - 2.92648i) q^{69} +(2.69788 - 1.58482i) q^{70} +(-5.53686 - 1.10135i) q^{71} +(7.60108 - 6.53082i) q^{72} +(-1.09643 - 5.51212i) q^{73} +(-12.5730 - 0.729060i) q^{74} +(6.72268 + 8.19161i) q^{75} +(7.83317 + 12.1838i) q^{76} +(3.20390 + 5.99408i) q^{77} +(-0.475961 - 1.97396i) q^{78} +(-9.47934 - 3.92647i) q^{79} +(-3.50377 - 1.19958i) q^{80} +(-6.53717 + 2.70778i) q^{81} +(-0.283081 - 0.388823i) q^{82} +(-0.837128 + 2.75964i) q^{83} +(8.79595 - 8.49050i) q^{84} +(3.85172 + 0.379361i) q^{85} +(-1.68693 + 3.48668i) q^{86} +(13.6514 - 20.4308i) q^{87} +(2.90988 - 7.49980i) q^{88} +(-6.57935 + 4.39618i) q^{89} +(-3.70167 - 2.79637i) q^{90} +(-0.389373 - 1.28359i) q^{91} +(1.32675 + 4.66913i) q^{92} +(-17.8735 - 14.6684i) q^{93} +(-0.305304 - 7.58045i) q^{94} +(4.74138 - 4.74138i) q^{95} +(-14.4071 - 1.34747i) q^{96} +(0.524236 + 0.524236i) q^{97} +(-1.23656 + 1.34034i) q^{98} +(6.39288 - 7.78974i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100})$ 240 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$ .

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{21}{32}\right)$	$1$

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

)

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

$2$	−0.488178	+	1.32728i	−0.345194	+	0.938531i
$2$	−0.488178	+	1.32728i	−0.345194	+	0.938531i
$3$	2.54563	−	0.250723i	1.46972	−	0.144755i	0.668762	−	0.743476i	$-0.266824\pi$
$3$	2.54563	−	0.250723i	1.46972	−	0.144755i	0.800957	+	0.598721i	$0.204324\pi$
$4$	−1.52336	−	1.29590i	−0.761682	−	0.647951i
$5$	−0.436447	+	0.816534i	−0.195185	+	0.365165i	−0.960407	−	0.278601i	$-0.910129\pi$
$5$	−0.436447	+	0.816534i	−0.195185	+	0.365165i	0.765222	+	0.643767i	$0.222629\pi$
$6$	−0.909941	+	3.50117i	−0.371482	+	1.42935i
$7$	−0.466201	+	2.34375i	−0.176207	+	0.885854i	0.786971	+	0.616990i	$0.211648\pi$
$7$	−0.466201	+	2.34375i	−0.176207	+	0.885854i	−0.963178	+	0.268864i	$0.913352\pi$
$8$	2.46370	−	1.38930i	0.871051	−	0.491193i
$9$	3.47501	−	0.691223i	1.15834	−	0.230408i
$10$	−0.870709	−	0.977903i	−0.275342	−	0.309240i
$11$	2.19857	−	1.80432i	0.662895	−	0.544024i	−0.241671	−	0.970358i	$-0.577695\pi$
$11$	2.19857	−	1.80432i	0.662895	−	0.544024i	0.904565	+	0.426335i	$0.140195\pi$
$12$	−4.20283	−	2.91694i	−1.21325	−	0.842049i
$13$	−0.495033	+	0.264601i	−0.137297	+	0.0733870i	−0.538615	−	0.842552i	$-0.681052\pi$
$13$	−0.495033	+	0.264601i	−0.137297	+	0.0733870i	0.401318	+	0.915939i	$0.368552\pi$
$14$	−2.88323	−	1.76295i	−0.770576	−	0.471168i
$15$	−0.906308	+	2.18802i	−0.234008	+	0.564944i
$16$	0.641275	+	3.94826i	0.160319	+	0.987065i
$17$	−1.59973	−	3.86208i	−0.387991	−	0.936693i	−0.990365	−	0.138479i	$-0.955779\pi$
$17$	−1.59973	−	3.86208i	−0.387991	−	0.936693i	0.602375	−	0.798214i	$-0.294221\pi$
$18$	−0.778976	+	4.94977i	−0.183606	+	1.16667i
$19$	−6.93043	−	2.10232i	−1.58995	−	0.482306i	−0.633388	−	0.773834i	$-0.718336\pi$
$19$	−6.93043	−	2.10232i	−1.58995	−	0.482306i	−0.956562	+	0.291528i	$0.905836\pi$
$20$	1.72302	−	0.678287i	0.385278	−	0.151670i
$21$	−0.599143	+	6.08320i	−0.130744	+	1.32746i
$22$	1.32155	+	3.79896i	0.281756	+	0.809941i
$23$	−2.01797	−	1.34836i	−0.420775	−	0.281153i	0.327104	−	0.944988i	$-0.393927\pi$
$23$	−2.01797	−	1.34836i	−0.420775	−	0.281153i	−0.747878	+	0.663836i	$0.768927\pi$
$24$	5.92334	−	4.15436i	1.20910	−	0.848005i
$25$	2.30161	+	3.44460i	0.460322	+	0.688920i
$26$	−0.109536	−	0.786221i	−0.0214817	−	0.154191i
$27$	1.32938	−	0.403263i	0.255839	−	0.0776079i
$28$	3.74746	−	2.96623i	0.708204	−	0.560565i
$29$	6.09406	−	7.42563i	1.13164	−	1.37890i	0.216247	−	0.976339i	$-0.430618\pi$
$29$	6.09406	−	7.42563i	1.13164	−	1.37890i	0.915391	−	0.402566i	$-0.131882\pi$
$30$	−2.46168	−	2.27107i	−0.449440	−	0.414639i
$31$	−6.39173	−	6.39173i	−1.14799	−	1.14799i	−0.986948	−	0.161040i	$-0.948515\pi$
$31$	−6.39173	−	6.39173i	−1.14799	−	1.14799i	−0.161040	−	0.986948i	$-0.551485\pi$
$32$	−5.55352	−	1.07630i	−0.981733	−	0.190265i
$33$	5.14437	−	5.14437i	0.895519	−	0.895519i
$34$	5.90703	−	0.237907i	1.01305	−	0.0408007i
$35$	−1.71028	−	1.40359i	−0.289090	−	0.237250i
$36$	−6.18946	−	3.45029i	−1.03158	−	0.575048i
$37$	2.58509	+	8.52191i	0.424987	+	1.40099i	0.864443	+	0.502730i	$0.167671\pi$
$37$	2.58509	+	8.52191i	0.424987	+	1.40099i	−0.439457	+	0.898264i	$0.644829\pi$
$38$	6.17367	−	8.17234i	1.00150	−	1.32573i
$39$	−1.19383	+	0.797691i	−0.191166	+	0.127733i
$40$	0.0591401	+	2.61806i	0.00935087	+	0.413951i
$41$	−0.188942	+	0.282772i	−0.0295078	+	0.0441615i	−0.845930	−	0.533294i	$-0.820954\pi$
$41$	−0.188942	+	0.282772i	−0.0295078	+	0.0441615i	0.816422	+	0.577455i	$0.195954\pi$
$42$	−7.78165	−	3.76492i	−1.20073	−	0.580940i
$43$	2.72567	+	0.268455i	0.415660	+	0.0409390i	0.303686	−	0.952772i	$-0.401783\pi$
$43$	2.72567	+	0.268455i	0.415660	+	0.0409390i	0.111974	+	0.993711i	$0.464283\pi$
$44$	−5.68745	−	0.100496i	−0.857415	−	0.0151503i
$45$	−0.952250	+	3.13915i	−0.141953	+	0.467956i
$46$	2.77478	−	2.02017i	0.409120	−	0.297858i
$47$	−4.95618	+	2.05292i	−0.722934	+	0.299449i	−0.713645	−	0.700508i	$-0.752957\pi$
$47$	−4.95618	+	2.05292i	−0.722934	+	0.299449i	−0.00928912	+	0.999957i	$0.502957\pi$
$48$	2.62237	+	9.89003i	0.378506	+	1.42750i
$49$	1.19134	+	0.493469i	0.170191	+	0.0704956i
$50$	−5.69556	+	1.37331i	−0.805474	+	0.194215i
$51$	−5.04062	−	9.43034i	−0.705828	−	1.32051i
$52$	1.09701	+	0.238431i	0.152128	+	0.0330645i
$53$	2.24658	+	2.73747i	0.308592	+	0.376020i	0.904094	−	0.427333i	$-0.140547\pi$
$53$	2.24658	+	2.73747i	0.308592	+	0.376020i	−0.595502	+	0.803354i	$0.703047\pi$
$54$	−0.113730	+	1.96133i	−0.0154767	+	0.266903i
$55$	0.513731	+	2.58270i	0.0692715	+	0.348251i
$56$	2.10760	+	6.42200i	0.281640	+	0.858175i
$57$	−18.1694	−	3.61412i	−2.40660	−	0.478702i
$58$	6.88093	+	11.7136i	0.903510	+	1.53807i
$59$	11.5723	+	6.18552i	1.50659	+	0.805287i	0.998432	−	0.0559800i	$-0.0178283\pi$
$59$	11.5723	+	6.18552i	1.50659	+	0.805287i	0.508153	+	0.861267i	$0.330328\pi$
$60$	4.21610	−	2.15867i	0.544296	−	0.278682i
$61$	0.0204700	+	0.207835i	0.00262091	+	0.0266106i	0.996406	−	0.0847031i	$-0.0269942\pi$
$61$	0.0204700	+	0.207835i	0.00262091	+	0.0266106i	−0.993785	+	0.111314i	$0.964494\pi$
$62$	11.6039	−	5.36333i	1.47370	−	0.681144i
$63$			8.46680i			1.06672i
$64$	4.13966	−	6.84567i	0.517458	−	0.855709i
$65$		−	0.519695i		−	0.0644603i
$66$	4.31667	+	9.33940i	0.531345	+	1.14960i
$67$	1.48710	+	15.0988i	0.181679	+	1.84461i	0.464660	+	0.885489i	$0.346177\pi$
$67$	1.48710	+	15.0988i	0.181679	+	1.84461i	−0.282981	+	0.959125i	$0.591323\pi$
$68$	−2.56791	+	7.95645i	−0.311405	+	0.964861i
$69$	−5.47506	−	2.92648i	−0.659119	−	0.352307i
$70$	2.69788	−	1.58482i	0.322459	−	0.189423i
$71$	−5.53686	−	1.10135i	−0.657105	−	0.130706i	−0.144734	−	0.989471i	$-0.546233\pi$
$71$	−5.53686	−	1.10135i	−0.657105	−	0.130706i	−0.512371	+	0.858764i	$0.671233\pi$
$72$	7.60108	−	6.53082i	0.895795	−	0.769664i
$73$	−1.09643	−	5.51212i	−0.128327	−	0.645145i	−0.990385	−	0.138336i	$-0.955825\pi$
$73$	−1.09643	−	5.51212i	−0.128327	−	0.645145i	0.862058	−	0.506809i	$-0.169175\pi$
$74$	−12.5730	−	0.729060i	−1.46158	−	0.0847515i
$75$	6.72268	+	8.19161i	0.776268	+	0.945886i
$76$	7.83317	+	12.1838i	0.898526	+	1.39757i
$77$	3.20390	+	5.99408i	0.365119	+	0.683089i
$78$	−0.475961	−	1.97396i	−0.0538920	−	0.223508i
$79$	−9.47934	−	3.92647i	−1.06651	−	0.441763i	−0.220752	−	0.975330i	$-0.570851\pi$
$79$	−9.47934	−	3.92647i	−1.06651	−	0.441763i	−0.845758	+	0.533567i	$0.820851\pi$
$80$	−3.50377	−	1.19958i	−0.391734	−	0.134117i
$81$	−6.53717	+	2.70778i	−0.726352	+	0.300865i
$82$	−0.283081	−	0.388823i	−0.0312611	−	0.0429383i
$83$	−0.837128	+	2.75964i	−0.0918868	+	0.302910i	−0.990822	−	0.135171i	$-0.956842\pi$
$83$	−0.837128	+	2.75964i	−0.0918868	+	0.302910i	0.898936	+	0.438081i	$0.144342\pi$
$84$	8.79595	−	8.49050i	0.959717	−	0.926390i
$85$	3.85172	+	0.379361i	0.417777	+	0.0411475i
$86$	−1.68693	+	3.48668i	−0.181906	+	0.375978i
$87$	13.6514	−	20.4308i	1.46359	−	2.19041i
$88$	2.90988	−	7.49980i	0.310194	−	0.799481i
$89$	−6.57935	+	4.39618i	−0.697409	+	0.465994i	−0.853056	−	0.521819i	$-0.825254\pi$
$89$	−6.57935	+	4.39618i	−0.697409	+	0.465994i	0.155647	+	0.987813i	$0.450254\pi$
$90$	−3.70167	−	2.79637i	−0.390190	−	0.294763i
$91$	−0.389373	−	1.28359i	−0.0408174	−	0.134557i
$92$	1.32675	+	4.66913i	0.138323	+	0.486790i
$93$	−17.8735	−	14.6684i	−1.85340	−	1.52104i
$94$	−0.305304	−	7.58045i	−0.0314897	−	0.781864i
$95$	4.74138	−	4.74138i	0.486456	−	0.486456i
$96$	−14.4071	−	1.34747i	−1.47041	−	0.137526i
$97$	0.524236	+	0.524236i	0.0532281	+	0.0532281i	0.733220	−	0.679992i	$-0.238017\pi$
$97$	0.524236	+	0.524236i	0.0532281	+	0.0532281i	−0.679992	+	0.733220i	$0.738017\pi$
$98$	−1.23656	+	1.34034i	−0.124911	+	0.135395i
$99$	6.39288	−	7.78974i	0.642508	−	0.782899i
$100$	0.957678	−	8.23004i	0.0957678	−	0.823004i
$101$	0.676785	−	0.205301i	0.0673427	−	0.0204282i	−0.256434	−	0.966562i	$-0.582547\pi$
$101$	0.676785	−	0.205301i	0.0673427	−	0.0204282i	0.323776	+	0.946134i	$0.395047\pi$
$102$	14.9775	−	2.08665i	1.48299	−	0.206609i
$103$	0.771936	+	1.15528i	0.0760611	+	0.113834i	0.867550	−	0.497350i	$-0.165694\pi$
$103$	0.771936	+	1.15528i	0.0760611	+	0.113834i	−0.791489	+	0.611184i	$0.790694\pi$
$104$	−0.852003	+	1.33965i	−0.0835458	+	0.131363i
$105$	−4.70565	−	3.14421i	−0.459224	−	0.306844i
$106$	−4.73013	+	1.64548i	−0.459431	+	0.159823i
$107$	0.730345	−	7.41532i	0.0706051	−	0.716866i	−0.893093	−	0.449872i	$-0.851470\pi$
$107$	0.730345	−	7.41532i	0.0706051	−	0.716866i	0.963698	−	0.266994i	$-0.0860304\pi$
$108$	−2.54772	−	1.10843i	−0.245154	−	0.106659i
$109$	12.3210	+	3.73754i	1.18014	+	0.357991i	0.818599	−	0.574366i	$-0.194751\pi$
$109$	12.3210	+	3.73754i	1.18014	+	0.357991i	0.361540	+	0.932357i	$0.382251\pi$
$110$	−3.67877	−	0.578951i	−0.350757	−	0.0552008i
$111$	8.71733	+	21.0455i	0.827412	+	1.99755i
$112$	−9.55270	−	0.337693i	−0.902645	−	0.0319090i
$113$	1.63426	−	3.94544i	0.153738	−	0.371156i	−0.828180	−	0.560462i	$-0.810624\pi$
$113$	1.63426	−	3.94544i	0.153738	−	0.371156i	0.981918	+	0.189306i	$0.0606237\pi$
$114$	13.6669	−	22.3516i	1.28002	−	2.09342i
$115$	1.98172	−	1.05925i	0.184796	−	0.0987756i
$116$	−18.9064	+	3.41464i	−1.75541	+	0.317041i
$117$	−1.53735	+	1.26167i	−0.142128	+	0.116641i
$118$	−13.8593	+	12.3401i	−1.27585	+	1.13600i
$119$	9.79755	−	1.94885i	0.898140	−	0.178651i
$120$	0.806954	+	6.64977i	0.0736645	+	0.607038i
$121$	−0.567850	+	2.85477i	−0.0516227	+	0.259525i
$122$	−0.285849	−	0.0742912i	−0.0258796	−	0.00672601i
$123$	−0.410079	+	0.767204i	−0.0369756	+	0.0691765i
$124$	1.45387	+	18.0200i	0.130562	+	1.61824i
$125$	−8.42416	+	0.829708i	−0.753480	+	0.0742113i
$126$	−11.2378	−	4.13331i	−1.00115	−	0.368224i
$127$	11.2444			0.997782			0.498891	−	0.866665i	$-0.333741\pi$
$127$	11.2444			0.997782			0.498891	+	0.866665i	$0.333741\pi$
$128$	7.06525	+	8.83642i	0.624486	+	0.781036i
$129$	7.00584			0.616830
$130$	0.689783	+	0.253704i	0.0604980	+	0.0222513i
$131$	9.97258	−	0.982213i	0.871308	−	0.0858164i	0.347528	−	0.937670i	$-0.387021\pi$
$131$	9.97258	−	0.982213i	0.871308	−	0.0858164i	0.523780	+	0.851853i	$0.324521\pi$
$132$	−14.5033	+	1.17015i	−1.26235	+	0.101848i
$133$	8.15829	−	15.2631i	0.707414	−	1.32348i
$134$	−20.7664	−	5.39711i	−1.79394	−	0.466239i
$135$	−0.250925	+	1.26149i	−0.0215962	+	0.108571i
$136$	−9.30686	−	7.29252i	−0.798057	−	0.625328i
$137$	17.9530	−	3.57108i	1.53383	−	0.305098i	0.645306	−	0.763924i	$-0.276730\pi$
$137$	17.9530	−	3.57108i	1.53383	−	0.305098i	0.888526	+	0.458826i	$0.151730\pi$
$138$	6.55707	−	5.83831i	0.558175	−	0.496990i
$139$	−12.2300	+	10.0369i	−1.03734	+	0.851320i	−0.989060	−	0.147514i	$-0.952873\pi$
$139$	−12.2300	+	10.0369i	−1.03734	+	0.851320i	−0.0482765	+	0.998834i	$0.515373\pi$
$140$	0.786463	+	4.35453i	0.0664682	+	0.368025i
$141$	−12.1019	+	6.46860i	−1.01916	+	0.544754i
$142$	4.16478	−	6.81133i	0.349501	−	0.571594i
$143$	−0.610941	+	1.47494i	−0.0510895	+	0.123341i
$144$	4.95757	+	13.2770i	0.413131	+	1.10642i
$145$	3.40355	+	8.21690i	0.282649	+	0.682376i
$146$	7.85140	+	1.23563i	0.649787	+	0.102261i
$147$	3.15643	+	0.957493i	0.260338	+	0.0789727i
$148$	7.10553	−	16.3320i	0.584071	−	1.34248i
$149$	−1.13819	+	11.5562i	−0.0932440	+	0.946722i	0.828776	+	0.559580i	$0.189038\pi$
$149$	−1.13819	+	11.5562i	−0.0932440	+	0.946722i	−0.922020	+	0.387142i	$0.873462\pi$
$150$	−14.1545	+	4.92394i	−1.15571	+	0.402038i
$151$	−12.5493	−	8.38519i	−1.02125	−	0.682377i	−0.0721627	−	0.997393i	$-0.522990\pi$
$151$	−12.5493	−	8.38519i	−1.02125	−	0.682377i	−0.949086	+	0.315016i	$0.897990\pi$
$152$	−19.9953	+	4.44898i	−1.62183	+	0.360860i
$153$	−8.22863	−	12.3150i	−0.665245	−	0.995610i
$154$	−9.51992	+	1.32631i	−0.767137	+	0.106877i
$155$	8.00871	−	2.42942i	0.643275	−	0.195135i
$156$	2.85237	+	0.331912i	0.228372	+	0.0265742i
$157$	5.20276	−	6.33958i	0.415225	−	0.505953i	−0.522831	−	0.852436i	$-0.675124\pi$
$157$	5.20276	−	6.33958i	0.415225	−	0.505953i	0.938056	+	0.346483i	$0.112624\pi$
$158$	9.83915	−	10.6650i	0.782761	−	0.848458i
$159$	6.40531	+	6.40531i	0.507974	+	0.507974i
$160$	3.30265	−	4.06489i	0.261097	−	0.321358i
$161$	4.10100	−	4.10100i	0.323204	−	0.323204i
$162$	−0.402694	−	9.99856i	−0.0316386	−	0.785561i
$163$	−6.21670	−	5.10191i	−0.486930	−	0.399613i	0.358642	−	0.933475i	$-0.383240\pi$
$163$	−6.21670	−	5.10191i	−0.486930	−	0.399613i	−0.845571	+	0.533863i	$0.820740\pi$
$164$	0.654272	−	0.185914i	0.0510901	−	0.0145174i
$165$	1.95531	+	6.44579i	0.152221	+	0.501804i
$166$	−3.25416	−	2.45830i	−0.252572	−	0.190801i
$167$	4.05237	−	2.70771i	0.313582	−	0.209529i	−0.388812	−	0.921317i	$-0.627114\pi$
$167$	4.05237	−	2.70771i	0.313582	−	0.209529i	0.702394	+	0.711788i	$0.252114\pi$
$168$	6.97531	+	15.8196i	0.538157	+	1.22051i
$169$	−7.04737	+	10.5471i	−0.542105	+	0.811318i
$170$	−2.38384	+	4.92713i	−0.182833	+	0.377893i
$171$	−25.5365	−	2.51513i	−1.95283	−	0.192337i
$172$	−3.80429	−	3.94115i	−0.290074	−	0.300510i
$173$	3.36416	−	11.0901i	0.255772	−	0.843168i	−0.731184	−	0.682180i	$-0.761032\pi$
$173$	3.36416	−	11.0901i	0.255772	−	0.843168i	0.986956	−	0.160988i	$-0.0514679\pi$
$174$	20.4532	+	28.0932i	1.55055	+	2.12974i
$175$	−9.14629	+	3.78852i	−0.691395	+	0.286385i
$176$	8.53382	+	7.52347i	0.643261	+	0.567103i
$177$	31.0096	+	12.8446i	2.33083	+	0.965460i
$178$	−2.62308	−	10.8788i	−0.196608	−	0.815399i
$179$	−8.59212	−	16.0747i	−0.642205	−	1.20148i	−0.966777	−	0.255620i	$-0.917720\pi$
$179$	−8.59212	−	16.0747i	−0.642205	−	1.20148i	0.324572	−	0.945861i	$-0.394780\pi$
$180$	5.51865	−	3.54804i	0.411336	−	0.264455i
$181$	−12.8587	−	15.6684i	−0.955780	−	1.16462i	−0.986279	−	0.165087i	$-0.947209\pi$
$181$	−12.8587	−	15.6684i	−0.955780	−	1.16462i	0.0304985	−	0.999535i	$-0.490291\pi$
$182$	1.89377	+	0.109813i	0.140376	+	0.00813985i
$183$	0.104218	+	0.523939i	0.00770402	+	0.0387307i
$184$	−6.84495	−	0.518393i	−0.504617	−	0.0382164i
$185$	−8.08669	−	1.60854i	−0.594545	−	0.118262i
$186$	28.1946	−	16.5624i	2.06733	−	1.21442i
$187$	−10.4856	−	5.60465i	−0.766780	−	0.409852i
$188$	10.2105	+	3.29539i	0.744674	+	0.240341i
$189$	0.325389	+	3.30373i	0.0236686	+	0.240311i
$190$	3.97852	+	8.60780i	0.288632	+	0.624476i
$191$			15.2338i			1.10228i	0.834412	+	0.551141i	$0.185807\pi$
$191$			15.2338i			1.10228i	−0.834412	+	0.551141i	$0.814193\pi$
$192$	8.82169	−	18.4644i	0.636650	−	1.33256i
$193$		−	10.5197i		−	0.757222i	−0.925556	−	0.378611i	$-0.876402\pi$
$193$		−	10.5197i		−	0.757222i	0.925556	−	0.378611i	$-0.123598\pi$
$194$	−0.951731	+	0.439889i	−0.0683303	+	0.0315822i
$195$	−0.130299	−	1.32295i	−0.00933093	−	0.0947385i
$196$	−1.17536	−	2.29559i	−0.0839540	−	0.163971i
$197$	12.1671	+	6.50344i	0.866869	+	0.463351i	0.843972	−	0.536387i	$-0.180211\pi$
$197$	12.1671	+	6.50344i	0.866869	+	0.463351i	0.0228967	+	0.999738i	$0.492711\pi$
$198$	7.21833	+	12.2879i	0.512985	+	0.873266i
$199$	11.3608	+	2.25980i	0.805345	+	0.160193i	0.580562	−	0.814216i	$-0.302833\pi$
$199$	11.3608	+	2.25980i	0.805345	+	0.160193i	0.224783	+	0.974409i	$0.427833\pi$
$200$	10.4561	+	5.28884i	0.739357	+	0.373977i
$201$	7.57123	+	38.0632i	0.534034	+	2.68477i
$202$	−0.0578998	+	0.998510i	−0.00407382	+	0.0702549i
$203$	14.5628	+	17.7448i	1.02211	+	1.24544i
$204$	−4.54210	+	20.8980i	−0.318010	+	1.46315i
$205$	−0.148430	−	0.277693i	−0.0103668	−	0.0193949i
$206$	−1.91023	+	0.460594i	−0.133092	+	0.0320911i
$207$	−7.94447	−	3.29071i	−0.552179	−	0.228720i
$208$	−1.36216	−	1.78484i	−0.0944491	−	0.123756i
$209$	−19.0303	+	7.88262i	−1.31636	+	0.545252i
$210$	6.47046	−	4.71079i	0.446504	−	0.325076i
$211$	−0.823204	+	2.71374i	−0.0566717	+	0.186822i	−0.980706	−	0.195488i	$-0.937371\pi$
$211$	−0.823204	+	2.71374i	−0.0566717	+	0.186822i	0.924034	+	0.382309i	$0.124871\pi$
$212$	0.125129	−	7.08151i	0.00859387	−	0.486360i
$213$	−14.3709	−	1.41541i	−0.984680	−	0.0969825i
$214$	9.48569	+	4.58937i	0.648428	+	0.313723i
$215$	−1.40881	+	2.10843i	−0.0960800	+	0.143794i
$216$	2.71494	−	2.84043i	0.184728	−	0.193267i
$217$	17.9604	−	12.0008i	1.21923	−	0.814666i
$218$	−10.9756	+	14.5289i	−0.743363	+	0.984021i
$219$	−4.17312	−	13.7569i	−0.281993	−	0.929606i
$220$	2.56433	−	4.60014i	0.172887	−	0.310141i
$221$	1.81383	+	1.48857i	0.122011	+	0.100132i
$222$	−32.1889	+	1.29642i	−2.16038	+	0.0870097i
$223$	3.58589	−	3.58589i	0.240129	−	0.240129i	−0.576775	−	0.816903i	$-0.695689\pi$
$223$	3.58589	−	3.58589i	0.240129	−	0.240129i	0.816903	+	0.576775i	$0.195689\pi$
$224$	5.11163	−	12.5143i	0.341535	−	0.836146i
$225$	10.3791	+	10.3791i	0.691940	+	0.691940i
$226$	4.43891	+	4.09520i	0.295272	+	0.272409i
$227$	−1.32993	+	1.62052i	−0.0882704	+	0.107558i	−0.815273	−	0.579077i	$-0.803413\pi$
$227$	−1.32993	+	1.62052i	−0.0882704	+	0.107558i	0.727002	+	0.686635i	$0.240913\pi$
$228$	22.9951	+	29.0514i	1.52289	+	1.92398i
$229$	0.230931	−	0.0700522i	0.0152604	−	0.00462918i	−0.282645	−	0.959225i	$-0.591212\pi$
$229$	0.230931	−	0.0700522i	0.0152604	−	0.00462918i	0.297906	+	0.954595i	$0.403712\pi$
$230$	0.438494	+	3.14740i	0.0289134	+	0.207534i
$231$	9.65880	+	14.4554i	0.635502	+	0.951096i
$232$	4.69748	−	26.7610i	0.308405	−	1.75695i
$233$	−14.6821	−	9.81028i	−0.961858	−	0.642693i	−0.0277239	−	0.999616i	$-0.508826\pi$
$233$	−14.6821	−	9.81028i	−0.961858	−	0.642693i	−0.934134	+	0.356923i	$0.883826\pi$
$234$	−0.924092	−	2.65641i	−0.0604098	−	0.173655i
$235$	0.486832	−	4.94288i	0.0317574	−	0.322438i
$236$	−9.61299	−	24.4194i	−0.625753	−	1.58957i
$237$	−25.1153	−	7.61866i	−1.63142	−	0.494885i
$238$	−2.19627	+	13.9555i	−0.142363	+	0.904601i
$239$	−6.04006	−	14.5820i	−0.390699	−	0.943231i	−0.989788	−	0.142549i	$-0.954470\pi$
$239$	−6.04006	−	14.5820i	−0.390699	−	0.943231i	0.599089	−	0.800683i	$-0.295530\pi$
$240$	−9.22007	−	2.17522i	−0.595153	−	0.140410i
$241$	−3.64595	+	8.80211i	−0.234856	+	0.566994i	−0.996736	−	0.0807246i	$-0.974277\pi$
$241$	−3.64595	+	8.80211i	−0.234856	+	0.566994i	0.761880	+	0.647718i	$0.224277\pi$
$242$	−3.51188	−	2.14734i	−0.225752	−	0.138036i
$243$	−19.6378	+	10.4966i	−1.25977	+	0.673358i
$244$	0.238151	−	0.343136i	0.0152460	−	0.0219670i
$245$	−0.922890	+	0.757397i	−0.0589613	+	0.0483883i
$246$	−0.818106	−	0.918824i	−0.0521605	−	0.0585821i
$247$	3.98707	−	0.793077i	0.253691	−	0.0504623i
$248$	−24.6274	−	6.86726i	−1.56384	−	0.436071i
$249$	−1.43911	+	7.23491i	−0.0912001	+	0.458494i
$250$	3.01124	−	11.5863i	0.190447	−	0.732782i
$251$	4.19977	−	7.85721i	0.265087	−	0.495943i	−0.713799	−	0.700351i	$-0.753027\pi$
$251$	4.19977	−	7.85721i	0.265087	−	0.495943i	0.978886	+	0.204408i	$0.0655269\pi$
$252$	10.9721	−	12.8980i	0.691180	−	0.812499i
$253$	−6.86952	+	0.676589i	−0.431883	+	0.0425368i
$254$	−5.48929	+	14.9246i	−0.344429	+	0.936450i
$255$	9.90016			0.619972
$256$	−15.1775	+	5.06385i	−0.948596	+	0.316490i
$257$	−9.83805			−0.613681			−0.306840	−	0.951761i	$-0.599272\pi$
$257$	−9.83805			−0.613681			−0.306840	+	0.951761i	$0.599272\pi$
$258$	−3.42010	+	9.29874i	−0.212926	+	0.578914i
$259$	−21.1784	+	2.08589i	−1.31596	+	0.129611i
$260$	−0.673474	+	0.791685i	−0.0417671	+	0.0490982i
$261$	16.0442	−	30.0165i	0.993108	−	1.85797i
$262$	−3.56472	+	13.7159i	−0.220229	+	0.847373i
$263$	−0.0956276	+	0.480752i	−0.00589665	+	0.0296445i	−0.983622	−	0.180246i	$-0.942311\pi$
$263$	−0.0956276	+	0.480752i	−0.00589665	+	0.0296445i	0.977725	+	0.209890i	$0.0673107\pi$
$264$	5.52710	−	19.8213i	0.340169	−	1.21992i
$265$	−3.21575	+	0.639652i	−0.197542	+	0.0392935i
$266$	16.2758	+	18.2795i	0.997931	+	1.12079i
$267$	−15.6464	+	12.8406i	−0.957542	+	0.785834i
$268$	17.3012	−	24.9281i	1.05684	−	1.52273i
$269$	23.4464	−	12.5324i	1.42955	−	0.764113i	0.438647	−	0.898659i	$-0.355458\pi$
$269$	23.4464	−	12.5324i	1.42955	−	0.764113i	0.990907	+	0.134547i	$0.0429578\pi$
$270$	−1.55185	−	0.948879i	−0.0944428	−	0.0577469i
$271$	8.05929	−	19.4568i	0.489567	−	1.18192i	−0.465372	−	0.885115i	$-0.654079\pi$
$271$	8.05929	−	19.4568i	0.489567	−	1.18192i	0.954939	−	0.296803i	$-0.0959206\pi$
$272$	14.2226	−	8.79280i	0.862375	−	0.533142i
$273$	−1.31302	−	3.16992i	−0.0794678	−	0.191852i
$274$	−4.02445	+	25.5721i	−0.243126	+	1.54487i
$275$	11.2754	+	3.42036i	0.679934	+	0.206256i
$276$	4.54807	+	11.5532i	0.273762	+	0.695423i
$277$	−0.483782	+	4.91193i	−0.0290677	+	0.295129i	0.969650	+	0.244498i	$0.0786232\pi$
$277$	−0.483782	+	4.91193i	−0.0290677	+	0.295129i	−0.998717	+	0.0506309i	$0.983877\pi$
$278$	−7.35141	−	21.1325i	−0.440908	−	1.26744i
$279$	−26.6294	−	17.7932i	−1.59426	−	1.06525i
$280$	−6.16364	−	1.08193i	−0.368348	−	0.0646577i
$281$	2.23450	+	3.34417i	0.133299	+	0.199496i	0.892114	−	0.451810i	$-0.149221\pi$
$281$	2.23450	+	3.34417i	0.133299	+	0.199496i	−0.758815	+	0.651306i	$0.774221\pi$
$282$	−2.67778	−	19.2205i	−0.159460	−	1.14456i
$283$	−1.04290	+	0.316359i	−0.0619938	+	0.0188056i	−0.321129	−	0.947035i	$-0.604062\pi$
$283$	−1.04290	+	0.316359i	−0.0619938	+	0.0188056i	0.259135	+	0.965841i	$0.416562\pi$
$284$	7.00741	+	8.85299i	0.415813	+	0.525328i
$285$	10.8810	−	13.2586i	0.644537	−	0.785370i
$286$	−1.65942	−	1.53093i	−0.0981235	−	0.0905256i
$287$	−0.574661	−	0.574661i	−0.0339212	−	0.0339212i
$288$	−20.0425	+	0.0985609i	−1.18102	+	0.00580776i
$289$	−0.335741	+	0.335741i	−0.0197495	+	0.0197495i
$290$	−12.5677	+	0.506166i	−0.738000	+	0.0297231i
$291$	1.46595	+	1.20307i	0.0859355	+	0.0705254i
$292$	−5.47291	+	9.81783i	−0.320278	+	0.574545i
$293$	1.66017	+	5.47283i	0.0969879	+	0.319726i	0.991987	−	0.126342i	$-0.0403237\pi$
$293$	1.66017	+	5.47283i	0.0969879	+	0.319726i	−0.894999	+	0.446069i	$0.852824\pi$
$294$	−2.81177	+	3.72205i	−0.163986	+	0.217075i
$295$	−10.1014	+	6.74953i	−0.588125	+	0.392973i
$296$	18.2084	+	17.4040i	1.05834	+	1.01159i
$297$	2.19512	−	3.28523i	0.127374	−	0.190628i
$298$	−14.7827	−	7.15219i	−0.856341	−	0.414315i
$299$	1.35574	+	0.133528i	0.0784042	+	0.00772214i
$300$	0.374436	−	21.1907i	0.0216180	−	1.22345i
$301$	−1.89990	+	6.26312i	−0.109508	+	0.361000i
$302$	17.2558	−	12.5630i	0.992961	−	0.722922i
$303$	1.67137	−	0.692305i	0.0960178	−	0.0397719i
$304$	3.85621	−	28.7113i	0.221169	−	1.64671i
$305$	−0.178639	−	0.0739945i	−0.0102288	−	0.00423692i
$306$	20.3626	−	4.90980i	1.16405	−	0.280675i
$307$	3.50839	+	6.56373i	0.200234	+	0.374612i	0.961918	−	0.273337i	$-0.0881273\pi$
$307$	3.50839	+	6.56373i	0.200234	+	0.374612i	−0.761684	+	0.647948i	$0.775627\pi$
$308$	2.88703	−	13.2831i	0.164504	−	0.756875i
$309$	2.25472	+	2.74738i	0.128267	+	0.156293i
$310$	−0.685155	+	11.8158i	−0.0389142	+	0.671094i
$311$	1.90141	+	9.55903i	0.107819	+	0.542043i	0.996505	+	0.0835275i	$0.0266187\pi$
$311$	1.90141	+	9.55903i	0.107819	+	0.542043i	−0.888686	+	0.458516i	$0.848381\pi$
$312$	−1.83300	+	3.62387i	−0.103773	+	0.205161i
$313$	17.4873	+	3.47845i	0.988442	+	0.196613i	0.662732	−	0.748856i	$-0.269397\pi$
$313$	17.4873	+	3.47845i	0.988442	+	0.196613i	0.325710	+	0.945470i	$0.394397\pi$
$314$	5.87455	+	10.0004i	0.331520	+	0.564354i
$315$	−6.91343	−	3.69531i	−0.389528	−	0.208207i
$316$	9.35216	+	18.2657i	0.526100	+	1.02753i
$317$	1.99479	+	20.2534i	0.112039	+	1.13755i	0.872652	+	0.488342i	$0.162398\pi$
$317$	1.99479	+	20.2534i	0.112039	+	1.13755i	−0.760614	+	0.649205i	$0.775102\pi$
$318$	−11.6286	+	5.37473i	−0.652100	+	0.301400i
$319$		−	27.3214i		−	1.52971i
$320$	3.78298	+	6.36795i	0.211475	+	0.355979i
$321$		−	19.0598i		−	1.06381i
$322$	3.44117	+	7.44520i	0.191769	+	0.414905i
$323$	2.96745	+	30.1291i	0.165113	+	1.67643i
$324$	13.4675	+	4.34659i	0.748195	+	0.241477i
$325$	−2.05082	−	1.09618i	−0.113759	−	0.0608053i
$326$	9.80655	−	5.76068i	0.543134	−	0.319055i
$327$	32.3018	+	6.42523i	1.78629	+	0.355316i
$328$	−0.0726409	+	0.959164i	−0.00401092	+	0.0529610i
$329$	−2.50095	−	12.5731i	−0.137882	−	0.693179i
$330$	−9.50994	−	0.551445i	−0.523505	−	0.0303561i
$331$	−1.43755	−	1.75166i	−0.0790150	−	0.0962801i	0.732002	−	0.681302i	$-0.238586\pi$
$331$	−1.43755	−	1.75166i	−0.0790150	−	0.0962801i	−0.811018	+	0.585022i	$0.801086\pi$
$332$	4.85148	−	3.11910i	0.266259	−	0.171183i
$333$	14.8738	+	27.8269i	0.815078	+	1.52490i
$334$	1.61562	+	6.70049i	0.0884027	+	0.366635i
$335$	−12.9777	−	5.37556i	−0.709050	−	0.293698i
$336$	−24.4023	+	1.53543i	−1.33125	+	0.0837648i
$337$	−27.8023	+	11.5161i	−1.51449	+	0.627321i	−0.976478	−	0.215618i	$-0.930823\pi$
$337$	−27.8023	+	11.5161i	−1.51449	+	0.627321i	−0.538009	+	0.842939i	$0.680823\pi$
$338$	−10.5587	−	14.5027i	−0.574316	−	0.788845i
$339$	3.17100	−	10.4534i	0.172225	−	0.567750i
$340$	−5.37595	−	5.56935i	−0.291552	−	0.302041i
$341$	−25.5854	−	2.51994i	−1.38553	−	0.136463i
$342$	15.8047	−	32.6664i	0.854618	−	1.76639i
$343$	−11.0054	+	16.4707i	−0.594234	+	0.889334i
$344$	7.08820	−	3.12539i	0.382170	−	0.168510i
$345$	4.77914	−	3.19332i	0.257300	−	0.171923i
$346$	13.0774	+	9.87915i	0.703048	+	0.531107i
$347$	−1.10518	−	3.64328i	−0.0593290	−	0.195581i	0.922266	−	0.386556i	$-0.126335\pi$
$347$	−1.10518	−	3.64328i	−0.0593290	−	0.195581i	−0.981595	+	0.190974i	$0.938835\pi$
$348$	−47.2724	+	13.4326i	−2.53407	+	0.720065i
$349$	1.61545	+	1.32577i	0.0864732	+	0.0709667i	0.676637	−	0.736317i	$-0.263437\pi$
$349$	1.61545	+	1.32577i	0.0864732	+	0.0709667i	−0.590164	+	0.807284i	$0.700937\pi$
$350$	−0.563417	−	13.9892i	−0.0301159	−	0.747754i
$351$	−0.551383	+	0.551383i	−0.0294306	+	0.0294306i
$352$	−14.1518	+	7.65401i	−0.754294	+	0.407960i
$353$	−18.5474	−	18.5474i	−0.987176	−	0.987176i	0.0127425	−	0.999919i	$-0.495944\pi$
$353$	−18.5474	−	18.5474i	−0.987176	−	0.987176i	−0.999919	+	0.0127425i	$0.995944\pi$
$354$	−32.1867	+	34.8881i	−1.71070	+	1.85428i
$355$	3.31583	−	4.04036i	0.175986	−	0.214440i
$356$	15.7198	+	1.82921i	0.833146	+	0.0969479i
$357$	24.4523	−	7.41752i	1.29415	−	0.392577i
$358$	25.5302	−	3.55685i	1.34931	−	0.187985i
$359$	−12.4033	−	18.5629i	−0.654623	−	0.979713i	−0.999162	−	0.0409405i	$-0.986965\pi$
$359$	−12.4033	−	18.5629i	−0.654623	−	0.979713i	0.344539	−	0.938772i	$-0.388035\pi$
$360$	2.01517	+	9.05689i	0.106209	+	0.477340i
$361$	27.8132	+	18.5842i	1.46385	+	0.978116i
$362$	27.0737	−	9.41819i	1.42296	−	0.495009i
$363$	−0.729779	+	7.40957i	−0.0383034	+	0.388901i
$364$	−1.07025	+	2.45996i	−0.0560964	+	0.128937i
$365$	4.97937	+	1.51047i	0.260632	+	0.0790619i
$366$	−0.746293	−	0.117449i	−0.0390094	−	0.00613915i
$367$	−4.07474	−	9.83729i	−0.212700	−	0.513502i	0.781137	−	0.624360i	$-0.214640\pi$
$367$	−4.07474	−	9.83729i	−0.212700	−	0.513502i	−0.993836	+	0.110858i	$0.964640\pi$
$368$	4.02961	−	8.83212i	0.210058	−	0.460406i
$369$	−0.461118	+	1.11324i	−0.0240048	+	0.0579528i
$370$	6.08274	−	9.94807i	0.316226	−	0.517176i
$371$	−7.46330	+	3.98922i	−0.387475	+	0.207110i
$372$	8.21904	+	45.5077i	0.426137	+	2.35946i
$373$	7.95389	−	6.52759i	0.411837	−	0.337986i	−0.405552	−	0.914072i	$-0.632921\pi$
$373$	7.95389	−	6.52759i	0.411837	−	0.337986i	0.817389	+	0.576086i	$0.195421\pi$
$374$	12.5578	−	11.1812i	0.649347	−	0.578168i
$375$	−21.2368	+	4.22426i	−1.09666	+	0.218140i
$376$	−9.35844	+	11.9434i	−0.482624	+	0.615936i
$377$	−1.05193	+	5.28842i	−0.0541773	+	0.272368i
$378$	−4.54384	−	1.18093i	−0.233710	−	0.0607403i
$379$	−2.63225	+	4.92460i	−0.135210	+	0.252960i	−0.940410	−	0.340044i	$-0.889558\pi$
$379$	−2.63225	+	4.92460i	−0.135210	+	0.252960i	0.805200	+	0.593004i	$0.202058\pi$
$380$	−13.3672	+	1.07848i	−0.685724	+	0.0553251i
$381$	28.6242	−	2.81923i	1.46646	−	0.144434i
$382$	−20.2196	−	7.43683i	−1.03453	−	0.380501i
$383$	19.1509			0.978565			0.489282	−	0.872125i	$-0.337259\pi$
$383$	19.1509			0.978565			0.489282	+	0.872125i	$0.337259\pi$
$384$	20.2010	+	20.7228i	1.03088	+	1.05751i
$385$	−6.29270			−0.320706
$386$	13.9626	+	5.13547i	0.710677	+	0.261389i
$387$	9.65728	−	0.951159i	0.490907	−	0.0483501i
$388$	−0.119244	−	1.47796i	−0.00605368	−	0.0750321i
$389$	−13.0586	+	24.4310i	−0.662099	+	1.23870i	0.296797	+	0.954941i	$0.404081\pi$
$389$	−13.0586	+	24.4310i	−0.662099	+	1.23870i	−0.958896	+	0.283759i	$0.908419\pi$
$390$	1.81954	+	0.472892i	0.0921361	+	0.0239458i
$391$	−1.97929	+	9.95056i	−0.100097	+	0.503221i
$392$	3.62069	−	0.439373i	0.182872	−	0.0221917i
$393$	25.1402	−	5.00070i	1.26816	−	0.252252i
$394$	−14.5716	+	12.9743i	−0.734108	+	0.653638i
$395$	7.34333	−	6.02651i	0.369483	−	0.303227i
$396$	−19.8334	+	3.58207i	−0.996667	+	0.180006i
$397$	30.9813	−	16.5598i	1.55491	−	0.831115i	0.554907	−	0.831913i	$-0.312754\pi$
$397$	30.9813	−	16.5598i	1.55491	−	0.831115i	1.00000		0.000797832i	$0.000253958\pi$
$398$	−8.54549	+	13.9758i	−0.428347	+	0.700544i
$399$	16.9412	−	40.8997i	0.848120	−	2.04754i
$400$	−12.1242	+	11.2963i	−0.606211	+	0.564815i
$401$	4.13360	+	9.97938i	0.206422	+	0.498347i	0.992855	−	0.119329i	$-0.0380744\pi$
$401$	4.13360	+	9.97938i	0.206422	+	0.498347i	−0.786433	+	0.617676i	$0.788074\pi$
$402$	−54.2167	−	8.53243i	−2.70408	−	0.425559i
$403$	4.85537	+	1.47286i	0.241863	+	0.0733684i
$404$	−1.29704	−	0.564300i	−0.0645302	−	0.0280750i
$405$	0.642127	−	6.51963i	0.0319075	−	0.323963i
$406$	−30.6616	+	10.6663i	−1.52171	+	0.529360i
$407$	21.0598	+	14.0717i	1.04390	+	0.697508i
$408$	−25.5202	−	16.2306i	−1.26344	−	0.803535i
$409$	4.24401	+	6.35160i	0.209853	+	0.314067i	0.921432	−	0.388539i	$-0.127020\pi$
$409$	4.24401	+	6.35160i	0.209853	+	0.314067i	−0.711580	+	0.702605i	$0.752020\pi$
$410$	0.441037	−	0.0614449i	0.0217813	−	0.00303455i
$411$	44.8064	−	13.5919i	2.21014	−	0.670438i
$412$	0.321195	−	2.76027i	0.0158242	−	0.135989i
$413$	−19.8923	+	24.2389i	−0.978838	+	1.19272i
$414$	8.24602	−	8.93811i	0.405270	−	0.439284i
$415$	−1.88798	−	1.88798i	−0.0926773	−	0.0926773i
$416$	3.03396	−	0.936660i	0.148752	−	0.0459235i
$417$	−28.6166	+	28.6166i	−1.40136	+	1.40136i
$418$	−1.17228	−	29.1068i	−0.0573381	−	1.42366i
$419$	−6.23702	−	5.11859i	−0.304698	−	0.250059i	0.469601	−	0.882879i	$-0.344398\pi$
$419$	−6.23702	−	5.11859i	−0.304698	−	0.250059i	−0.774300	+	0.632819i	$0.781898\pi$
$420$	3.09382	+	10.8878i	0.150963	+	0.531272i
$421$	−0.386233	−	1.27324i	−0.0188239	−	0.0620540i	0.947025	−	0.321159i	$-0.104072\pi$
$421$	−0.386233	−	1.27324i	−0.0188239	−	0.0620540i	−0.965849	+	0.259105i	$0.916572\pi$
$422$	−3.20003	−	2.41741i	−0.155775	−	0.117678i
$423$	−15.8038	+	10.5597i	−0.768406	+	0.513432i
$424$	9.33809	+	3.62312i	0.453498	+	0.175954i
$425$	9.62139	−	14.3994i	0.466706	−	0.698475i
$426$	8.89423	−	18.3833i	0.430927	−	0.890675i
$427$	−0.496657	−	0.0489164i	−0.0240349	−	0.00236723i
$428$	−10.7221	+	10.3498i	−0.518273	+	0.500275i
$429$	−1.18543	+	3.90783i	−0.0572330	+	0.188672i
$430$	−2.11074	−	2.89918i	−0.101789	−	0.139811i
$431$	−20.7061	+	8.57674i	−0.997376	+	0.413127i	−0.820834	−	0.571166i	$-0.806491\pi$
$431$	−20.7061	+	8.57674i	−0.997376	+	0.413127i	−0.176542	+	0.984293i	$0.556491\pi$
$432$	2.44468	+	4.99013i	0.117620	+	0.240088i
$433$	−6.43606	−	2.66590i	−0.309297	−	0.128115i	0.222635	−	0.974902i	$-0.428534\pi$
$433$	−6.43606	−	2.66590i	−0.309297	−	0.128115i	−0.531933	+	0.846787i	$0.678534\pi$
$434$	7.16054	+	29.6971i	0.343717	+	1.42551i
$435$	10.7243	+	20.0638i	0.514193	+	0.961987i
$436$	−13.9259	−	21.6605i	−0.666930	−	1.03735i
$437$	11.1507	+	13.5871i	0.533409	+	0.649961i
$438$	20.2966	+	1.17692i	0.969807	+	0.0562354i
$439$	6.74059	+	33.8872i	0.321711	+	1.61735i	0.715820	+	0.698285i	$0.246053\pi$
$439$	6.74059	+	33.8872i	0.321711	+	1.61735i	−0.394109	+	0.919064i	$0.628947\pi$
$440$	4.85384	+	5.64928i	0.231398	+	0.269319i
$441$	4.48102	+	0.891329i	0.213382	+	0.0424443i
$442$	−2.86122	+	1.68078i	−0.136095	+	0.0799463i
$443$	7.72345	+	4.12827i	0.366952	+	0.196140i	0.644559	−	0.764555i	$-0.277041\pi$
$443$	7.72345	+	4.12827i	0.366952	+	0.196140i	−0.277607	+	0.960695i	$0.589541\pi$
$444$	13.9932	−	43.3567i	0.664089	−	2.05762i
$445$	−0.718097	−	7.29096i	−0.0340411	−	0.345625i
$446$	3.00894	+	6.51004i	0.142477	+	0.308259i
$447$			29.7032i			1.40491i
$448$	14.1146	+	12.8938i	0.666853	+	0.609174i
$449$		−	34.9143i		−	1.64771i	−0.566804	−	0.823853i	$-0.691820\pi$
$449$		−	34.9143i		−	1.64771i	0.566804	−	0.823853i	$-0.308180\pi$
$450$	−18.8429	+	8.70916i	−0.888261	+	0.410554i
$451$	0.0948085	+	0.962607i	0.00446436	+	0.0453274i
$452$	−7.60247	+	3.89251i	−0.357590	+	0.183088i
$453$	−34.0483	−	18.1992i	−1.59973	−	0.855072i
$454$	−1.50165	−	2.55629i	−0.0704759	−	0.119973i
$455$	1.21804	+	0.242282i	0.0571024	+	0.0113584i
$456$	−49.7852	+	16.3387i	−2.33140	+	0.765131i
$457$	0.727743	+	3.65861i	0.0340424	+	0.171143i	0.994066	−	0.108775i	$-0.0346928\pi$
$457$	0.727743	+	3.65861i	0.0340424	+	0.171143i	−0.960024	+	0.279918i	$0.909693\pi$
$458$	−0.0197564	+	0.340709i	−0.000923157	+	0.0159203i
$459$	−3.68408	−	4.48906i	−0.171958	−	0.209531i
$460$	−4.39156	−	0.954488i	−0.204758	−	0.0445032i
$461$	−11.8801	−	22.2261i	−0.553312	−	1.03517i	−0.990721	−	0.135912i	$-0.956604\pi$
$461$	−11.8801	−	22.2261i	−0.553312	−	1.03517i	0.437409	−	0.899263i	$-0.355896\pi$
$462$	−23.9016	+	5.76315i	−1.11201	+	0.268126i
$463$	36.2580	+	15.0186i	1.68505	+	0.697972i	0.999547	−	0.0300934i	$-0.00958046\pi$
$463$	36.2580	+	15.0186i	1.68505	+	0.697972i	0.685507	+	0.728066i	$0.259580\pi$
$464$	33.2263	+	19.2991i	1.54249	+	0.895936i
$465$	19.7781	−	8.19236i	0.917188	−	0.379912i
$466$	20.1885	−	14.6982i	0.935215	−	0.680880i
$467$	8.71932	−	28.7437i	0.403482	−	1.33010i	−0.486331	−	0.873775i	$-0.661665\pi$
$467$	8.71932	−	28.7437i	0.403482	−	1.33010i	0.889812	−	0.456326i	$-0.150835\pi$
$468$	3.97694	+	0.0702716i	0.183834	+	0.00324830i
$469$	−36.0811	−	3.55368i	−1.66607	−	0.164094i
$470$	6.32295	+	3.05917i	0.291656	+	0.141109i
$471$	11.6548	−	17.4427i	0.537026	−	0.803716i
$472$	37.1043	−	0.838161i	1.70786	−	0.0385795i
$473$	6.47695	−	4.32776i	0.297811	−	0.198991i
$474$	22.3729	−	29.6159i	1.02762	−	1.36030i
$475$	−8.70948	−	28.7113i	−0.399618	−	1.31737i
$476$	−17.4508	−	9.72785i	−0.799854	−	0.445875i
$477$	9.69910	+	7.95985i	0.444091	+	0.364456i
$478$	22.3031	−	0.898260i	1.02012	−	0.0410855i
$479$	−10.6380	+	10.6380i	−0.486065	+	0.486065i	−0.907062	−	0.420997i	$-0.861680\pi$
$479$	−10.6380	+	10.6380i	−0.486065	+	0.486065i	0.420997	+	0.907062i	$0.361680\pi$
$480$	7.38817	−	11.1758i	0.337222	−	0.510101i
$481$	−3.53461	−	3.53461i	−0.161164	−	0.161164i
$482$	−9.90302	−	9.13621i	−0.451070	−	0.416143i
$483$	9.41141	−	11.4678i	0.428234	−	0.521804i
$484$	4.56455	−	3.61298i	0.207479	−	0.164226i
$485$	−0.656858	+	0.199256i	−0.0298264	+	0.00904773i
$486$	−4.34525	−	31.1891i	−0.197104	−	1.41477i
$487$	−0.819959	−	1.22716i	−0.0371559	−	0.0556077i	0.812427	−	0.583063i	$-0.198146\pi$
$487$	−0.819959	−	1.22716i	−0.0371559	−	0.0556077i	−0.849583	+	0.527456i	$0.823146\pi$
$488$	0.339178	+	0.483605i	0.0153539	+	0.0218918i
$489$	−17.1046	−	11.4289i	−0.773496	−	0.516833i
$490$	−0.554745	−	1.59468i	−0.0250608	−	0.0720404i
$491$	0.919393	−	9.33475i	0.0414916	−	0.421271i	−0.951892	−	0.306432i	$-0.900865\pi$
$491$	0.919393	−	9.33475i	0.0414916	−	0.421271i	0.993384	−	0.114839i	$-0.0366353\pi$
$492$	1.61892	−	0.637309i	0.0729866	−	0.0287321i
$493$	−38.4272	−	11.6568i	−1.73067	−	0.524995i
$494$	−0.893762	+	5.67913i	−0.0402122	+	0.255516i
$495$	3.57044	+	8.61981i	0.160479	+	0.387432i
$496$	21.1374	−	29.3351i	0.949095	−	1.31718i
$497$	5.16258	−	12.4636i	0.231573	−	0.559067i
$498$	−8.90024	−	5.44204i	−0.398829	−	0.243864i
$499$	18.9859	−	10.1482i	0.849927	−	0.454296i	0.0119034	−	0.999929i	$-0.496211\pi$
$499$	18.9859	−	10.1482i	0.849927	−	0.454296i	0.838024	+	0.545634i	$0.183711\pi$
$500$	13.9083	+	9.65295i	0.621998	+	0.431693i
$501$	9.63696	−	7.90885i	0.430548	−	0.353341i
$502$	8.37852	+	9.41001i	0.373952	+	0.419989i
$503$	−14.1097	+	2.80659i	−0.629120	+	0.125140i	−0.499344	−	0.866404i	$-0.666426\pi$
$503$	−14.1097	+	2.80659i	−0.629120	+	0.125140i	−0.129776	+	0.991543i	$0.541426\pi$
$504$	11.7630	+	20.8597i	0.523964	+	0.929164i
$505$	−0.127746	+	0.642221i	−0.00568461	+	0.0285785i
$506$	2.45553	−	9.44810i	0.109161	−	0.420019i
$507$	−15.2956	+	28.6160i	−0.679301	+	1.27088i
$508$	−17.1294	−	14.5717i	−0.759993	−	0.646514i
$509$	−43.0298	+	4.23806i	−1.90726	+	0.187849i	−0.981659	−	0.190646i	$-0.938942\pi$
$509$	−43.0298	+	4.23806i	−1.90726	+	0.187849i	−0.925603	+	0.378495i	$0.876442\pi$
$510$	−4.83304	+	13.1403i	−0.214011	+	0.581863i
$511$	13.4302			0.594116
$512$	0.688182	−	22.6169i	0.0304136	−	0.999537i
$513$	−10.0610			−0.444202
$514$	4.80272	−	13.0579i	0.211839	−	0.575959i
$515$	−1.28024	+	0.126092i	−0.0564140	+	0.00555630i
$516$	−10.6724	−	9.07889i	−0.469828	−	0.399676i
$517$	−7.19240	+	13.4560i	−0.316322	+	0.591796i
$518$	7.57027	−	29.1280i	0.332618	−	1.27981i
$519$	5.78335	−	29.0748i	0.253861	−	1.27624i
$520$	−0.722015	−	1.28037i	−0.0316625	−	0.0561481i
$521$	−41.2587	+	8.20686i	−1.80757	+	0.359549i	−0.979559	−	0.201156i	$-0.935530\pi$
$521$	−41.2587	+	8.20686i	−1.80757	+	0.359549i	−0.828016	+	0.560705i	$0.810530\pi$
$522$	32.0080	+	35.9485i	1.40095	+	1.57342i
$523$	10.7518	−	8.82381i	0.470145	−	0.385838i	−0.369276	−	0.929320i	$-0.620394\pi$
$523$	10.7518	−	8.82381i	0.470145	−	0.385838i	0.839421	+	0.543481i	$0.182894\pi$
$524$	−16.4647	−	11.4272i	−0.719264	−	0.499200i
$525$	−22.3332	+	11.9373i	−0.974701	+	0.520988i
$526$	−0.591411	−	0.361618i	−0.0257868	−	0.0157673i
$527$	−14.4604	+	34.9104i	−0.629903	+	1.52072i
$528$	23.6103	+	17.0123i	1.02750	+	0.740367i
$529$	−6.54761	−	15.8073i	−0.284679	−	0.687276i
$530$	0.720859	−	4.58048i	0.0313121	−	0.198963i
$531$	44.4894	+	13.4957i	1.93068	+	0.585665i
$532$	−32.2075	+	12.6789i	−1.39637	+	0.549700i
$533$	0.0187110	−	0.189976i	0.000810462	−	0.00822875i
$534$	−9.40495	−	27.0357i	−0.406992	−	1.16995i
$535$	5.73610	+	3.83274i	0.247993	+	0.165704i
$536$	24.6406	+	35.1330i	1.06431	+	1.51751i
$537$	−25.9026	−	38.7661i	−1.11778	−	1.67288i
$538$	5.18798	+	37.2381i	0.223670	+	1.60545i
$539$	3.50962	−	1.06463i	0.151170	−	0.0458570i
$540$	2.01701	−	1.59653i	0.0867984	−	0.0687036i
$541$	11.3014	−	13.7708i	0.485884	−	0.592051i	−0.471141	−	0.882058i	$-0.656158\pi$
$541$	11.3014	−	13.7708i	0.485884	−	0.592051i	0.957025	+	0.290007i	$0.0936576\pi$
$542$	21.8904	+	20.1954i	0.940272	+	0.867465i
$543$	−36.6619	−	36.6619i	−1.57331	−	1.57331i
$544$	4.72735	+	23.1699i	0.202684	+	0.993403i
$545$	−8.42929	+	8.42929i	−0.361071	+	0.361071i
$546$	4.84837	−	0.195269i	0.207491	−	0.00835674i
$547$	25.7519	+	21.1340i	1.10107	+	0.903625i	0.995867	−	0.0908252i	$-0.0289504\pi$
$547$	25.7519	+	21.1340i	1.10107	+	0.903625i	0.105204	+	0.994451i	$0.466450\pi$
$548$	−31.9768	−	17.8253i	−1.36598	−	0.761460i
$549$	0.214794	+	0.708080i	0.00916718	+	0.0302201i
$550$	−10.0442	+	13.2959i	−0.428286	+	0.566941i
$551$	−57.8455	+	38.6512i	−2.46430	+	1.64659i
$552$	−17.5547	+	0.396548i	−0.747177	+	0.0168782i
$553$	13.6219	−	20.3867i	0.579264	−	0.866930i
$554$	−6.28335	−	3.04001i	−0.266954	−	0.129158i
$555$	−20.9890	−	2.06724i	−0.890934	−	0.0877493i
$556$	31.6376	+	0.559030i	1.34173	+	0.0237081i
$557$	−11.8368	+	39.0206i	−0.501540	+	1.65335i	0.231247	+	0.972895i	$0.425720\pi$
$557$	−11.8368	+	39.0206i	−0.501540	+	1.65335i	−0.732786	+	0.680459i	$0.761780\pi$
$558$	36.6166	−	26.6585i	1.55010	−	1.12855i
$559$	−1.42033	+	0.588319i	−0.0600734	+	0.0248832i
$560$	4.44498	−	7.65272i	0.187835	−	0.323386i
$561$	−28.0976	−	11.6384i	−1.18628	−	0.491373i
$562$	−5.52949	+	1.33327i	−0.233247	+	0.0562404i
$563$	−1.00664	−	1.88330i	−0.0424249	−	0.0793715i	0.859815	−	0.510605i	$-0.170579\pi$
$563$	−1.00664	−	1.88330i	−0.0424249	−	0.0793715i	−0.902240	+	0.431233i	$0.858079\pi$
$564$	26.8183	+	5.82884i	1.12925	+	0.245439i
$565$	2.50832	+	3.05640i	0.105526	+	0.128584i
$566$	0.0892210	−	1.53866i	0.00375024	−	0.0646747i
$567$	−3.29873	−	16.5839i	−0.138534	−	0.696456i
$568$	−15.1713	+	4.97899i	−0.636573	+	0.208914i
$569$	−8.23060	−	1.63717i	−0.345045	−	0.0686337i	0.0195260	−	0.999809i	$-0.493784\pi$
$569$	−8.23060	−	1.63717i	−0.345045	−	0.0686337i	−0.364571	+	0.931176i	$0.618784\pi$
$570$	12.2860	+	20.9148i	0.514604	+	0.876023i
$571$	−31.1413	−	16.6454i	−1.30322	−	0.696586i	−0.333952	−	0.942590i	$-0.608382\pi$
$571$	−31.1413	−	16.6454i	−1.30322	−	0.696586i	−0.969269	+	0.246004i	$0.920882\pi$
$572$	2.84207	−	1.45515i	0.118833	−	0.0608430i
$573$	3.81947	+	38.7797i	0.159561	+	1.62005i
$574$	1.04328	−	0.482201i	0.0435455	−	0.0201267i
$575$		−	10.0545i		−	0.419301i
$576$	9.65350	−	26.6502i	0.402229	−	1.11043i
$577$			23.9918i			0.998792i	0.866374	+	0.499396i	$0.166445\pi$
$577$			23.9918i			0.998792i	−0.866374	+	0.499396i	$0.833555\pi$
$578$	−0.281722	−	0.609525i	−0.0117181	−	0.0253529i
$579$	−2.63752	−	26.7792i	−0.109612	−	1.11290i
$580$	5.46345	−	16.9280i	0.226857	−	0.702897i
$581$	−6.07764	−	3.24857i	−0.252143	−	0.134773i
$582$	−2.31246	+	1.35842i	−0.0958547	+	0.0563082i
$583$	9.87855	+	1.96497i	0.409128	+	0.0813806i
$584$	−10.3593	−	12.0570i	−0.428671	−	0.498920i
$585$	−0.359225	−	1.80595i	−0.0148521	−	0.0746667i
$586$	−8.07446	−	0.468207i	−0.333553	−	0.0193415i
$587$	−15.5903	−	18.9969i	−0.643481	−	0.784084i	0.344479	−	0.938794i	$-0.388056\pi$
$587$	−15.5903	−	18.9969i	−0.643481	−	0.784084i	−0.987960	+	0.154710i	$0.950556\pi$
$588$	−3.56758	−	5.54904i	−0.147124	−	0.228839i
$589$	30.8600	+	57.7349i	1.27156	+	2.37893i
$590$	−4.02726	−	16.7024i	−0.165800	−	0.687626i
$591$	32.6035	+	13.5048i	1.34113	+	0.555513i
$592$	−31.9890	+	15.6715i	−1.31474	+	0.644095i
$593$	29.3497	−	12.1570i	1.20525	−	0.499230i	0.312556	−	0.949899i	$-0.398815\pi$
$593$	29.3497	−	12.1570i	1.20525	−	0.499230i	0.892691	+	0.450670i	$0.148815\pi$
$594$	3.28882	+	4.51732i	0.134942	+	0.185348i
$595$	−2.68480	+	8.85060i	−0.110066	+	0.362839i
$596$	16.7096	−	16.1293i	0.684452	−	0.660683i
$597$	29.4869	+	2.90421i	1.20682	+	0.118861i
$598$	−0.839071	+	1.73426i	−0.0343122	+	0.0709192i
$599$	−0.345200	+	0.516628i	−0.0141045	+	0.0211089i	−0.838455	−	0.544971i	$-0.816541\pi$
$599$	−0.345200	+	0.516628i	−0.0141045	+	0.0211089i	0.824350	+	0.566080i	$0.191541\pi$
$600$	27.9433	+	10.8418i	1.14078	+	0.442616i
$601$	24.7101	−	16.5108i	1.00795	−	0.673488i	0.0620886	−	0.998071i	$-0.480224\pi$
$601$	24.7101	−	16.5108i	1.00795	−	0.673488i	0.945857	+	0.324583i	$0.105224\pi$
$602$	−7.38545	−	5.57922i	−0.301009	−	0.227392i
$603$	15.6044	+	51.4407i	0.635458	+	2.09483i
$604$	8.25080	+	29.0364i	0.335720	+	1.18147i
$605$	−2.08318	−	1.70962i	−0.0846934	−	0.0695061i
$606$	0.102958	+	2.55635i	0.00418236	+	0.103845i
$607$	−9.88713	+	9.88713i	−0.401306	+	0.401306i	−0.878693	−	0.477387i	$-0.841584\pi$
$607$	−9.88713	+	9.88713i	−0.401306	+	0.401306i	0.477387	+	0.878693i	$0.341584\pi$
$608$	36.2256	+	19.1345i	1.46914	+	0.776008i
$609$	41.5204	+	41.5204i	1.68249	+	1.68249i
$610$	0.185419	−	0.200982i	0.00750741	−	0.00813751i
$611$	1.91027	−	2.32767i	0.0772813	−	0.0941675i
$612$	−3.42386	+	29.4237i	−0.138401	+	1.18938i
$613$	−6.36607	+	1.93113i	−0.257123	+	0.0779975i	−0.416215	−	0.909266i	$-0.636644\pi$
$613$	−6.36607	+	1.93113i	−0.257123	+	0.0779975i	0.159091	+	0.987264i	$0.449144\pi$
$614$	−10.4246	+	1.45235i	−0.420705	+	0.0586122i
$615$	−0.447471	−	0.669688i	−0.0180438	−	0.0270044i
$616$	16.2211	+	10.3164i	0.653565	+	0.415661i
$617$	−18.2836	−	12.2167i	−0.736070	−	0.491826i	0.130147	−	0.991495i	$-0.458455\pi$
$617$	−18.2836	−	12.2167i	−0.736070	−	0.491826i	−0.866217	+	0.499668i	$0.833455\pi$
$618$	−4.74726	+	1.65144i	−0.190963	+	0.0664306i
$619$	−0.693823	+	7.04450i	−0.0278871	+	0.283142i	0.971120	+	0.238591i	$0.0766857\pi$
$619$	−0.693823	+	7.04450i	−0.0278871	+	0.283142i	−0.999007	+	0.0445509i	$0.985814\pi$
$620$	−15.3485	−	6.67762i	−0.616409	−	0.268180i
$621$	−3.22638	−	0.978713i	−0.129470	−	0.0392744i
$622$	−13.6158	−	2.14280i	−0.545943	−	0.0859185i
$623$	−7.23625	−	17.4698i	−0.289914	−	0.699914i
$624$	−3.91507	−	4.20201i	−0.156728	−	0.168215i
$625$	−4.92767	+	11.8964i	−0.197107	+	0.475857i
$626$	−13.1538	+	21.5125i	−0.525732	+	0.859814i
$627$	−46.4678	+	24.8376i	−1.85575	+	0.991917i
$628$	−16.1412	+	2.91522i	−0.644103	+	0.116330i
$629$	28.7769	−	23.6166i	1.14741	−	0.941655i
$630$	8.27971	−	7.37212i	0.329872	−	0.293712i
$631$	19.5749	−	3.89368i	0.779263	−	0.155005i	0.210596	−	0.977573i	$-0.432459\pi$
$631$	19.5749	−	3.89368i	0.779263	−	0.155005i	0.568667	+	0.822568i	$0.307459\pi$
$632$	−28.8093	+	3.49604i	−1.14597	+	0.139065i
$633$	−1.41518	+	7.11457i	−0.0562482	+	0.282779i
$634$	−27.8559	−	7.23964i	−1.10630	−	0.287523i
$635$	−4.90759	+	9.18146i	−0.194752	+	0.364355i
$636$	−1.45696	−	18.0583i	−0.0577724	−	0.716057i
$637$	−0.720324	+	0.0709458i	−0.0285403	+	0.00281097i
$638$	36.2633	+	13.3377i	1.43568	+	0.528046i
$639$	−20.0019			−0.791264
$640$	−10.2988	+	1.91239i	−0.407097	+	0.0755940i
$641$	16.4932			0.651442			0.325721	−	0.945466i	$-0.394393\pi$
$641$	16.4932			0.651442			0.325721	+	0.945466i	$0.394393\pi$
$642$	25.2977	+	9.30456i	0.998421	+	0.367222i
$643$	34.3686	−	3.38501i	1.35537	−	0.133492i	0.605903	−	0.795539i	$-0.292812\pi$
$643$	34.3686	−	3.38501i	1.35537	−	0.133492i	0.749462	+	0.662047i	$0.230312\pi$
$644$	−11.5618	+	0.932820i	−0.455599	+	0.0367583i
$645$	−3.05768	+	5.72051i	−0.120396	+	0.225245i
$646$	−41.4384	−	10.7697i	−1.63037	−	0.423728i
$647$	0.934703	−	4.69907i	0.0367470	−	0.184739i	−0.958052	−	0.286593i	$-0.907477\pi$
$647$	0.934703	−	4.69907i	0.0367470	−	0.184739i	0.994799	+	0.101853i	$0.0324773\pi$
$648$	−12.3437	+	15.7533i	−0.484907	+	0.618848i
$649$	36.6032	−	7.28083i	1.43680	−	0.285798i
$650$	2.45611	−	2.18688i	0.0963366	−	0.0857765i
$651$	42.7117	−	35.0526i	1.67401	−	1.37382i
$652$	2.85872	+	15.8283i	0.111956	+	0.619884i
$653$	18.3471	−	9.80674i	0.717978	−	0.383767i	−0.0715866	−	0.997434i	$-0.522806\pi$
$653$	18.3471	−	9.80674i	0.717978	−	0.383767i	0.789565	+	0.613667i	$0.210306\pi$
$654$	−24.2971	+	39.7370i	−0.950093	+	1.55384i
$655$	−3.55049	+	8.57163i	−0.138729	+	0.334921i
$656$	−1.23762	−	0.564658i	−0.0483210	−	0.0220462i
$657$	−7.62021	−	18.3968i	−0.297293	−	0.717728i
$658$	17.9090	+	2.81846i	0.698166	+	0.109875i
$659$	7.86079	+	2.38455i	0.306213	+	0.0928887i	0.439652	−	0.898168i	$-0.355102\pi$
$659$	7.86079	+	2.38455i	0.306213	+	0.0928887i	−0.133439	+	0.991057i	$0.542602\pi$
$660$	5.37447	−	12.3532i	0.209201	−	0.480847i
$661$	3.00668	−	30.5273i	0.116946	−	1.18737i	−0.740231	−	0.672353i	$-0.765284\pi$
$661$	3.00668	−	30.5273i	0.116946	−	1.18737i	0.857177	−	0.515022i	$-0.172216\pi$
$662$	3.02674	−	1.05292i	0.117637	−	0.0409228i
$663$	4.99055	+	3.33458i	0.193817	+	0.129504i
$664$	1.77155	+	7.96197i	0.0687494	+	0.308984i
$665$	8.90218	+	13.3231i	0.345212	+	0.516646i
$666$	−44.1952	+	6.15724i	−1.71253	+	0.238588i
$667$	−22.3100	+	6.76767i	−0.863848	+	0.262045i
$668$	−9.68217	−	1.12665i	−0.374614	−	0.0435915i
$669$	8.22927	−	10.0274i	0.318162	−	0.387682i
$670$	13.4703	−	14.6009i	0.520405	−	0.564083i
$671$	0.420006	+	0.420006i	0.0162142	+	0.0162142i
$672$	9.87471	−	33.1383i	0.380925	−	1.27834i
$673$	−3.14379	+	3.14379i	−0.121184	+	0.121184i	−0.765098	−	0.643914i	$-0.777310\pi$
$673$	−3.14379	+	3.14379i	−0.121184	+	0.121184i	0.643914	+	0.765098i	$0.277310\pi$
$674$	−1.71264	−	42.5234i	−0.0659683	−	1.63794i
$675$	4.44879	+	3.65103i	0.171234	+	0.140528i
$676$	24.4038	−	6.93442i	0.938606	−	0.266709i
$677$	−2.12156	−	6.99385i	−0.0815382	−	0.268795i	0.906686	−	0.421805i	$-0.138603\pi$
$677$	−2.12156	−	6.99385i	−0.0815382	−	0.268795i	−0.988225	+	0.153010i	$0.951103\pi$
$678$	12.3266	+	9.31193i	0.473400	+	0.357622i
$679$	−1.47308	+	0.984279i	−0.0565315	+	0.0377732i
$680$	10.0165	−	4.41658i	0.384117	−	0.169368i
$681$	−2.97920	+	4.45869i	−0.114163	+	0.170857i
$682$	15.8349	−	32.7289i	0.606351	−	1.25326i
$683$	12.4509	+	1.22630i	0.476419	+	0.0469232i	0.333377	−	0.942794i	$-0.391812\pi$
$683$	12.4509	+	1.22630i	0.476419	+	0.0469232i	0.143042	+	0.989717i	$0.454312\pi$
$684$	35.6420	+	36.9243i	1.36281	+	1.41183i
$685$	−4.91963	+	16.2179i	−0.187970	+	0.619652i
$686$	−16.4887	−	22.6479i	−0.629541	−	0.864700i
$687$	0.570301	−	0.236227i	0.0217584	−	0.00901261i
$688$	0.687973	+	10.9338i	0.0262287	+	0.416847i
$689$	−1.83647	−	0.760690i	−0.0699639	−	0.0289800i
$690$	1.90537	+	7.90218i	0.0725361	+	0.300831i
$691$	−3.17112	−	5.93274i	−0.120635	−	0.225692i	0.814354	−	0.580368i	$-0.197091\pi$
$691$	−3.17112	−	5.93274i	−0.120635	−	0.225692i	−0.934989	+	0.354676i	$0.884591\pi$
$692$	−19.4966	+	12.5347i	−0.741148	+	0.476498i
$693$	15.2768	+	18.6149i	0.580319	+	0.707121i
$694$	5.37519	+	0.311687i	0.204039	+	0.0118315i
$695$	−2.85774	−	14.3668i	−0.108400	−	0.544964i
$696$	5.24845	−	69.3015i	0.198942	−	2.62687i
$697$	1.39434	+	0.277352i	0.0528145	+	0.0105055i
$698$	−2.54830	+	1.49695i	−0.0964545	+	0.0566605i
$699$	−39.8349	−	21.2922i	−1.50669	−	0.805345i
$700$	18.8427	+	6.08141i	0.712186	+	0.229856i
$701$	−1.98977	−	20.2024i	−0.0751524	−	0.763035i	−0.956726	−	0.290989i	$-0.906016\pi$
$701$	−1.98977	−	20.2024i	−0.0751524	−	0.763035i	0.881574	−	0.472046i	$-0.156484\pi$
$702$	−0.462668	−	1.00101i	−0.0174623	−	0.0377808i
$703$		−	64.4953i		−	2.43248i
$704$	−3.25044	−	22.5200i	−0.122505	−	0.848754i
$705$		−	12.7048i		−	0.478491i
$706$	33.6720	−	15.5632i	1.26726	−	0.585728i
$707$	0.165655	+	1.68193i	0.00623011	+	0.0632554i
$708$	−30.5936	−	59.7525i	−1.14978	−	2.24564i
$709$	−8.16829	−	4.36604i	−0.306767	−	0.163970i	0.310829	−	0.950466i	$-0.399393\pi$
$709$	−8.16829	−	4.36604i	−0.306767	−	0.163970i	−0.617596	+	0.786496i	$0.711893\pi$
$710$	3.74398	+	6.37347i	0.140509	+	0.239192i
$711$	−35.6549	−	7.09220i	−1.33716	−	0.265978i
$712$	−10.1019	+	19.9716i	−0.378586	+	0.748467i
$713$	4.27993	+	21.5166i	0.160284	+	0.805805i
$714$	−2.09192	+	36.0762i	−0.0782883	+	1.35012i
$715$	−0.937698	−	1.14259i	−0.0350679	−	0.0427304i
$716$	−7.74235	+	35.6222i	−0.289345	+	1.33126i
$717$	−19.0318	−	35.6060i	−0.710755	−	1.32973i
$718$	30.6933	−	7.40074i	1.14546	−	0.276193i
$719$	−1.90463	−	0.788923i	−0.0710306	−	0.0294219i	0.346885	−	0.937908i	$-0.387239\pi$
$719$	−1.90463	−	0.788923i	−0.0710306	−	0.0294219i	−0.417916	+	0.908486i	$0.637239\pi$
$720$	−13.0048	−	1.74667i	−0.484661	−	0.0650947i
$721$	−3.06757	+	1.27063i	−0.114242	+	0.0473208i
$722$	−38.2443	+	27.8436i	−1.42331	+	1.03623i
$723$	−7.07436	+	23.3210i	−0.263098	+	0.867318i
$724$	−0.716196	+	40.5323i	−0.0266172	+	1.50637i
$725$	39.6045	+	3.90070i	1.47087	+	0.144868i
$726$	−9.47833	−	4.58581i	−0.351774	−	0.170195i
$727$	−18.3940	+	27.5286i	−0.682197	+	1.02098i	0.315211	+	0.949022i	$0.397925\pi$
$727$	−18.3940	+	27.5286i	−0.682197	+	1.02098i	−0.997408	+	0.0719579i	$0.977075\pi$
$728$	−2.74260	−	2.62143i	−0.101647	−	0.0971565i
$729$	−29.7089	+	19.8509i	−1.10033	+	0.735217i
$730$	−4.43565	+	5.87165i	−0.164171	+	0.217320i
$731$	−3.32353	−	10.9562i	−0.122925	−	0.405230i
$732$	0.520212	−	0.933206i	0.0192276	−	0.0344923i
$733$	27.1769	+	22.3035i	1.00380	+	0.823799i	0.984388	−	0.176012i	$-0.0563198\pi$
$733$	27.1769	+	22.3035i	1.00380	+	0.823799i	0.0194144	+	0.999812i	$0.493820\pi$
$734$	15.0461	−	0.605983i	0.555361	−	0.0223672i
$735$	−2.15944	+	2.15944i	−0.0796522	+	0.0796522i
$736$	9.75557	+	9.66009i	0.359595	+	0.356076i
$737$	30.5126	+	30.5126i	1.12395	+	1.12395i
$738$	−1.25247	−	1.15549i	−0.0461042	−	0.0425342i
$739$	4.80182	−	5.85104i	0.176638	−	0.215234i	−0.677164	−	0.735832i	$-0.736791\pi$
$739$	4.80182	−	5.85104i	0.176638	−	0.215234i	0.853802	+	0.520598i	$0.174291\pi$
$740$	10.2345	+	12.9300i	0.376226	+	0.475314i
$741$	9.95076	−	3.01853i	0.365550	−	0.110888i
$742$	−1.65140	−	11.8534i	−0.0606249	−	0.435151i
$743$	−9.98759	−	14.9475i	−0.366409	−	0.548370i	0.601757	−	0.798679i	$-0.294468\pi$
$743$	−9.98759	−	14.9475i	−0.366409	−	0.548370i	−0.968166	+	0.250309i	$0.919468\pi$
$744$	−64.4140	−	11.3069i	−2.36153	−	0.414530i
$745$	−8.93928	−	5.97304i	−0.327510	−	0.218835i
$746$	4.78105	+	13.7437i	0.175047	+	0.503193i
$747$	−1.00150	+	10.1684i	−0.0366431	+	0.372043i
$748$	8.71025	+	22.1262i	0.318478	+	0.809013i
$749$	17.0392	+	5.16877i	0.622597	+	0.188863i
$750$	4.76054	−	30.2494i	0.173830	−	1.10455i
$751$	17.9080	+	43.2336i	0.653471	+	1.57762i	0.807707	+	0.589584i	$0.200708\pi$
$751$	17.9080	+	43.2336i	0.653471	+	1.57762i	−0.154237	+	0.988034i	$0.549292\pi$
$752$	−11.2837	−	18.2518i	−0.411476	−	0.665576i
$753$	8.72107	−	21.0545i	0.317814	−	0.767270i
$754$	−6.50570	−	3.97790i	−0.236924	−	0.144867i
$755$	12.3239	−	6.58726i	0.448513	−	0.239735i
$756$	3.78563	−	5.45446i	0.137682	−	0.198377i
$757$	32.8117	−	26.9279i	1.19256	−	0.978711i	0.192566	−	0.981284i	$-0.438319\pi$
$757$	32.8117	−	26.9279i	1.19256	−	0.978711i	0.999997	+	0.00257362i	$0.000819209\pi$
$758$	−5.25133	−	5.89783i	−0.190737	−	0.214219i
$759$	−17.3176	+	3.44469i	−0.628590	+	0.125034i
$760$	5.09413	−	18.2686i	0.184784	−	0.662671i
$761$	−7.80425	+	39.2346i	−0.282904	+	1.42225i	0.534002	+	0.845483i	$0.320687\pi$
$761$	−7.80425	+	39.2346i	−0.282904	+	1.42225i	−0.816906	+	0.576771i	$0.804313\pi$
$762$	−10.2318	+	39.3687i	−0.370658	+	1.42618i
$763$	−14.5039	+	27.1349i	−0.525077	+	0.982350i
$764$	19.7416	−	23.2067i	0.714225	−	0.839588i
$765$	13.6470	−	1.34411i	0.493408	−	0.0485964i
$766$	−9.34905	+	25.4187i	−0.337795	+	0.918413i
$767$	−7.36536			−0.265948
$768$	−37.3667	+	16.6960i	−1.34836	+	0.602466i
$769$	5.59080			0.201609			0.100805	−	0.994906i	$-0.467858\pi$
$769$	5.59080			0.201609			0.100805	+	0.994906i	$0.467858\pi$
$770$	3.07196	−	8.35220i	0.110706	−	0.300992i
$771$	−25.0440	+	2.46662i	−0.901939	+	0.0888332i
$772$	−13.6325	+	16.0253i	−0.490643	+	0.576762i
$773$	−7.39473	+	13.8346i	−0.265970	+	0.497595i	−0.979085	−	0.203452i	$-0.934784\pi$
$773$	−7.39473	+	13.8346i	−0.265970	+	0.497595i	0.713115	+	0.701047i	$0.247284\pi$
$774$	−3.45202	+	13.2823i	−0.124080	+	0.477422i
$775$	7.30569	−	36.7282i	0.262428	−	1.31932i
$776$	2.01989	+	0.563238i	0.0725097	+	0.0202191i
$777$	−53.3894	+	10.6198i	−1.91533	+	0.380983i
$778$	−26.0519	−	29.2592i	−0.934005	−	1.04899i
$779$	1.90393	−	1.56251i	0.0682153	−	0.0559829i
$780$	−1.51592	+	2.18419i	−0.0542787	+	0.0782066i
$781$	−14.1604	+	7.56888i	−0.506698	+	0.270836i
$782$	−12.2410	−	7.48472i	−0.437736	−	0.267653i
$783$	5.10683	−	12.3290i	0.182503	−	0.440602i
$784$	−1.18437	+	5.02017i	−0.0422988	+	0.179292i
$785$	2.90576	+	7.01512i	0.103711	+	0.250380i
$786$	−5.63556	+	35.8094i	−0.201014	+	1.27728i
$787$	−18.9238	−	5.74049i	−0.674562	−	0.204626i	−0.0656248	−	0.997844i	$-0.520904\pi$
$787$	−18.9238	−	5.74049i	−0.674562	−	0.204626i	−0.608938	+	0.793218i	$0.708404\pi$
$788$	−10.1071	−	25.6745i	−0.360050	−	0.914615i
$789$	−0.122897	+	1.24779i	−0.00437525	+	0.0444226i
$790$	4.41404	+	12.6887i	0.157044	+	0.451443i
$791$	8.48524	+	5.66965i	0.301700	+	0.201590i
$792$	4.92782	−	28.0733i	0.175102	−	0.997540i
$793$	−0.0651266	−	0.0974689i	−0.00231271	−	0.00346122i
$794$	6.85522	+	49.2051i	0.243283	+	1.74622i
$795$	−8.02573	+	2.43458i	−0.284643	+	0.0863456i
$796$	−14.3781	−	18.1650i	−0.509620	−	0.643840i
$797$	−0.264433	+	0.322213i	−0.00936670	+	0.0114134i	−0.777673	−	0.628669i	$-0.783600\pi$
$797$	−0.264433	+	0.322213i	−0.00936670	+	0.0114134i	0.768306	+	0.640083i	$0.221100\pi$
$798$	46.0151	+	42.4521i	1.62892	+	1.50279i
$799$	15.8571	+	15.8571i	0.560983	+	0.560983i
$800$	−9.07460	−	21.6069i	−0.320836	−	0.763919i
$801$	−19.8246	+	19.8246i	−0.700467	+	0.700467i
$802$	−15.2634	+	0.614736i	−0.538969	+	0.0217071i
$803$	−12.3562	−	10.1405i	−0.436042	−	0.357850i
$804$	37.7924	−	67.7956i	1.33283	−	2.39097i
$805$	1.55874	+	5.13847i	0.0549383	+	0.181107i
$806$	−4.32519	+	5.72544i	−0.152348	+	0.201670i
$807$	56.5438	−	37.7813i	1.99044	−	1.32997i
$808$	1.38217	−	1.44606i	0.0486247	−	0.0508723i
$809$	17.5024	−	26.1942i	0.615352	−	0.920939i	−0.384646	−	0.923064i	$-0.625676\pi$
$809$	17.5024	−	26.1942i	0.615352	−	0.920939i	0.999998	+	0.00212495i	$0.000676394\pi$
$810$	8.33992	+	4.03502i	0.293035	+	0.141776i
$811$	1.09421	+	0.107770i	0.0384229	+	0.00378433i	0.117210	−	0.993107i	$-0.462605\pi$
$811$	1.09421	+	0.107770i	0.0384229	+	0.00378433i	−0.0787874	+	0.996891i	$0.525105\pi$
$812$	0.811107	−	45.9037i	0.0284643	−	1.61090i
$813$	15.6377	−	51.5505i	0.548438	−	1.80796i
$814$	−28.9581	+	21.0828i	−1.01498	+	0.738952i
$815$	6.87914	−	2.84944i	0.240966	−	0.0998114i
$816$	34.0010	−	25.9491i	1.19027	−	0.908402i
$817$	−18.3257	−	7.59074i	−0.641134	−	0.265566i
$818$	−10.5022	+	2.53228i	−0.367201	+	0.0885393i
$819$	−2.24032	−	4.19135i	−0.0782831	−	0.146457i
$820$	−0.133750	+	0.615377i	−0.00467075	+	0.0214899i
$821$	16.6394	+	20.2751i	0.580718	+	0.707607i	0.977650	−	0.210241i	$-0.0674250\pi$
$821$	16.6394	+	20.2751i	0.580718	+	0.707607i	−0.396932	+	0.917848i	$0.629925\pi$
$822$	−3.83324	+	66.1061i	−0.133700	+	2.30572i
$823$	−5.89454	−	29.6339i	−0.205471	−	1.03297i	−0.936511	−	0.350637i	$-0.885965\pi$
$823$	−5.89454	−	29.6339i	−0.205471	−	1.03297i	0.731040	−	0.682334i	$-0.239035\pi$
$824$	3.50686	+	1.77382i	0.122167	+	0.0617940i
$825$	29.5606	+	5.87997i	1.02917	+	0.204714i
$826$	−22.4609	−	38.2357i	−0.781513	−	1.33039i
$827$	28.6663	+	15.3225i	0.996827	+	0.532815i	0.887312	−	0.461170i	$-0.152570\pi$
$827$	28.6663	+	15.3225i	0.996827	+	0.532815i	0.109515	+	0.993985i	$0.465070\pi$
$828$	7.83788	+	15.3082i	0.272385	+	0.531997i
$829$	−0.915971	−	9.30001i	−0.0318130	−	0.323003i	−0.997899	−	0.0647836i	$-0.979364\pi$
$829$	−0.915971	−	9.30001i	−0.0318130	−	0.323003i	0.966086	−	0.258219i	$-0.0831357\pi$
$830$	3.42756	−	1.58421i	0.118972	−	0.0549889i
$831$			12.6252i			0.437965i
$832$	−0.237902	+	4.48419i	−0.00824776	+	0.155461i
$833$		−	5.39047i		−	0.186769i
$834$	−24.0124	−	51.9524i	−0.831480	−	1.79896i
$835$	0.442293	+	4.49067i	0.0153062	+	0.155406i
$836$	39.2052	+	12.6533i	1.35594	+	0.437625i
$837$	−11.0746	−	5.91948i	−0.382793	−	0.204607i
$838$	9.83859	−	5.77951i	0.339869	−	0.199650i
$839$	7.87316	+	1.56607i	0.271812	+	0.0540667i	0.329114	−	0.944290i	$-0.393250\pi$
$839$	7.87316	+	1.56607i	0.271812	+	0.0540667i	−0.0573024	+	0.998357i	$0.518250\pi$
$840$	−15.9616	−	1.20883i	−0.550727	−	0.0417086i
$841$	−12.3448	−	62.0616i	−0.425684	−	2.14006i
$842$	1.87850	+	0.108927i	0.0647375	+	0.00375388i
$843$	6.52667	+	7.95277i	0.224790	+	0.273908i
$844$	4.77078	−	3.06722i	0.164217	−	0.105578i
$845$	−5.53629	−	10.3577i	−0.190454	−	0.356315i
$846$	−6.30072	−	26.1311i	−0.216623	−	0.898407i
$847$	−6.42614	−	2.66179i	−0.220805	−	0.0914603i
$848$	−9.36756	+	10.6256i	−0.321683	+	0.364883i
$849$	−2.57551	+	1.06681i	−0.0883913	+	0.0366129i
$850$	14.4152	+	19.7998i	0.494436	+	0.679127i
$851$	6.27399	−	20.6826i	0.215069	−	0.708989i
$852$	20.0579	+	20.7795i	0.687173	+	0.711894i
$853$	−44.7112	−	4.40367i	−1.53088	−	0.150779i	−0.702801	−	0.711386i	$-0.748068\pi$
$853$	−44.7112	−	4.40367i	−1.53088	−	0.150779i	−0.828082	+	0.560607i	$0.810568\pi$
$854$	0.307383	−	0.635325i	0.0105184	−	0.0217404i
$855$	13.1990	−	19.7537i	0.451397	−	0.675563i
$856$	−8.50278	−	19.2838i	−0.290619	−	0.659107i
$857$	29.9367	−	20.0031i	1.02262	−	0.683292i	0.0732037	−	0.997317i	$-0.476678\pi$
$857$	29.9367	−	20.0031i	1.02262	−	0.683292i	0.949415	+	0.314025i	$0.101678\pi$
$858$	−4.60810	−	3.48112i	−0.157318	−	0.118843i
$859$	14.4160	+	47.5232i	0.491868	+	1.62147i	0.754306	+	0.656523i	$0.227973\pi$
$859$	14.4160	+	47.5232i	0.491868	+	1.62147i	−0.262438	+	0.964949i	$0.584527\pi$
$860$	4.87845	−	1.38623i	0.166354	−	0.0472701i
$861$	−1.60696	−	1.31879i	−0.0547649	−	0.0449444i
$862$	−1.27551	−	31.6698i	−0.0434439	−	1.07868i
$863$	−35.7353	+	35.7353i	−1.21645	+	1.21645i	−0.247577	+	0.968868i	$0.579634\pi$
$863$	−35.7353	+	35.7353i	−1.21645	+	1.21645i	−0.968868	+	0.247577i	$0.920366\pi$
$864$	−7.81676	+	0.808715i	−0.265932	+	0.0275130i
$865$	7.58720	+	7.58720i	0.257973	+	0.257973i
$866$	6.68035	−	7.24104i	0.227008	−	0.246061i
$867$	−0.770494	+	0.938849i	−0.0261673	+	0.0318850i
$868$	−42.9121	−	4.99341i	−1.45653	−	0.169487i
$869$	−27.9256	+	8.47115i	−0.947312	+	0.287364i
$870$	−31.8658	+	4.43952i	−1.08035	+	0.150514i
$871$	−4.73132	−	7.08092i	−0.160315	−	0.239928i
$872$	35.5479	−	7.90946i	1.20380	−	0.267848i
$873$	2.18409	+	1.45936i	0.0739203	+	0.0493920i
$874$	−23.4775	+	8.16717i	−0.794139	+	0.276259i
$875$	1.98272	−	20.1309i	0.0670283	−	0.680550i
$876$	−11.4704	+	26.3647i	−0.387550	+	0.890782i
$877$	−6.00501	−	1.82160i	−0.202775	−	0.0615111i	0.187263	−	0.982310i	$-0.440038\pi$
$877$	−6.00501	−	1.82160i	−0.202775	−	0.0615111i	−0.390038	+	0.920799i	$0.627538\pi$
$878$	−48.2686	−	7.59633i	−1.62899	−	0.256364i
$879$	5.59833	+	13.5156i	0.188827	+	0.455869i
$880$	−9.86773	+	3.68457i	−0.332641	+	0.124207i
$881$	10.0917	−	24.3636i	0.339999	−	0.820831i	−0.657716	−	0.753266i	$-0.728477\pi$
$881$	10.0917	−	24.3636i	0.339999	−	0.820831i	0.997715	−	0.0675645i	$-0.0215228\pi$
$882$	−3.37058	+	5.51245i	−0.113493	+	0.185614i
$883$	24.5908	−	13.1440i	0.827545	−	0.442332i	−0.00252125	−	0.999997i	$-0.500803\pi$
$883$	24.5908	−	13.1440i	0.827545	−	0.442332i	0.830066	+	0.557665i	$0.188303\pi$
$884$	−0.834078	−	4.61817i	−0.0280531	−	0.155326i
$885$	−24.0221	+	19.7144i	−0.807495	+	0.662694i
$886$	−9.24980	+	8.23588i	−0.310753	+	0.276690i
$887$	44.6216	−	8.87580i	1.49825	−	0.298020i	0.623203	−	0.782060i	$-0.285831\pi$
$887$	44.6216	−	8.87580i	1.49825	−	0.298020i	0.875046	+	0.484040i	$0.160831\pi$
$888$	50.7155	+	39.7388i	1.70190	+	1.33355i
$889$	−5.24216	+	26.3541i	−0.175816	+	0.883889i
$890$	10.0277	+	2.60617i	0.336130	+	0.0873590i
$891$	−9.48673	+	17.7484i	−0.317817	+	0.594594i
$892$	−10.1096	+	0.815652i	−0.338493	+	0.0273100i
$893$	38.6644	−	3.80811i	1.29386	−	0.127434i
$894$	−39.4246	−	14.5005i	−1.31856	−	0.484968i
$895$	16.8756			0.564088
$896$	−24.0042	+	12.4396i	−0.801923	+	0.415579i
$897$	3.48468			0.116350
$898$	46.3411	+	17.0444i	1.54642	+	0.568778i
$899$	−86.4142	+	8.51105i	−2.88207	+	0.283859i
$900$	−2.36085	−	29.2615i	−0.0786950	−	0.975382i
$901$	6.97841	−	13.0557i	0.232485	−	0.434948i
$902$	−1.32394	−	0.344086i	−0.0440822	−	0.0114568i
$903$	−3.26613	+	16.4199i	−0.108690	+	0.546421i
$904$	−1.45510	−	11.9909i	−0.0483960	−	0.398811i
$905$	18.4059	−	3.66116i	0.611833	−	0.121701i
$906$	40.7771	−	36.3073i	1.35473	−	1.20623i
$907$	0.707031	−	0.580245i	0.0234766	−	0.0192667i	−0.622582	−	0.782555i	$-0.713916\pi$
$907$	0.707031	−	0.580245i	0.0234766	−	0.0192667i	0.646058	+	0.763288i	$0.276416\pi$
$908$	4.12600	−	0.745188i	0.136926	−	0.0247299i
$909$	2.20993	−	1.18123i	0.0732987	−	0.0391790i
$910$	−0.916196	+	1.49840i	−0.0303716	+	0.0496715i
$911$	8.47162	−	20.4523i	0.280677	−	0.677615i	−0.719174	−	0.694830i	$-0.755480\pi$
$911$	8.47162	−	20.4523i	0.280677	−	0.677615i	0.999852	+	0.0172145i	$0.00547981\pi$
$912$	2.61790	−	74.0553i	0.0866872	−	2.45221i
$913$	3.13880	+	7.57772i	0.103879	+	0.250786i
$914$	−5.21129	−	0.820133i	−0.172374	−	0.0271276i
$915$	−0.473300	−	0.143574i	−0.0156468	−	0.00474641i
$916$	−0.442573	−	0.192549i	−0.0146230	−	0.00636200i
$917$	−2.34716	+	23.8311i	−0.0775101	+	0.786973i
$918$	7.75674	−	2.69835i	0.256011	−	0.0890589i
$919$	28.4575	+	19.0147i	0.938728	+	0.627238i	0.927950	−	0.372704i	$-0.121569\pi$
$919$	28.4575	+	19.0147i	0.938728	+	0.627238i	0.0107776	+	0.999942i	$0.496569\pi$
$920$	3.41074	−	5.36289i	0.112449	−	0.176809i
$921$	10.5767	+	15.8292i	0.348515	+	0.521590i
$922$	35.3000	−	4.91797i	1.16254	−	0.161965i
$923$	3.03235	−	0.919852i	0.0998109	−	0.0302773i
$924$	4.01894	−	34.5377i	0.132213	−	1.13621i
$925$	−23.4047	+	28.5187i	−0.769542	+	0.937690i
$926$	−37.6343	+	40.7930i	−1.23674	+	1.34054i
$927$	3.48105	+	3.48105i	0.114333	+	0.114333i
$928$	−41.8357	+	34.6793i	−1.37332	+	1.13840i
$929$	5.92992	−	5.92992i	0.194554	−	0.194554i	−0.603106	−	0.797661i	$-0.706071\pi$
$929$	5.92992	−	5.92992i	0.194554	−	0.194554i	0.797661	+	0.603106i	$0.206071\pi$
$930$	1.21834	+	30.2505i	0.0399511	+	0.991953i
$931$	−7.21907	−	5.92454i	−0.236595	−	0.194169i
$932$	9.65305	+	33.9712i	0.316196	+	1.11276i
$933$	7.23695	+	23.8570i	0.236927	+	0.781044i
$934$	33.8945	+	25.6051i	1.10906	+	0.837823i
$935$	9.15277	−	6.11569i	0.299328	−	0.200004i
$936$	−2.03472	+	5.24422i	−0.0665070	+	0.171413i
$937$	−29.2574	+	43.7868i	−0.955798	+	1.43045i	−0.0538791	+	0.998547i	$0.517159\pi$
$937$	−29.2574	+	43.7868i	−0.955798	+	1.43045i	−0.901919	+	0.431905i	$0.857841\pi$
$938$	22.3308	−	46.1551i	0.729126	−	1.50702i
$939$	45.3884	+	4.47037i	1.48119	+	0.145885i
$940$	−7.14711	+	6.89892i	−0.233113	+	0.225018i
$941$	14.3359	−	47.2590i	0.467336	−	1.54060i	−0.334110	−	0.942534i	$-0.608436\pi$
$941$	14.3359	−	47.2590i	0.467336	−	1.54060i	0.801446	−	0.598067i	$-0.204064\pi$
$942$	17.4617	+	23.9844i	0.568934	+	0.781453i
$943$	0.762557	−	0.315862i	0.0248323	−	0.0102859i
$944$	−17.0010	+	49.6571i	−0.553336	+	1.61620i
$945$	−2.83962	−	1.17621i	−0.0923730	−	0.0382621i
$946$	2.58226	+	10.7095i	0.0839565	+	0.348195i
$947$	−8.39371	−	15.7035i	−0.272759	−	0.510296i	0.707827	−	0.706386i	$-0.249676\pi$
$947$	−8.39371	−	15.7035i	−0.272759	−	0.510296i	−0.980586	+	0.196090i	$0.937176\pi$
$948$	28.3868	+	44.1530i	0.921960	+	1.43402i
$949$	2.00128	+	2.43857i	0.0649643	+	0.0791592i
$950$	42.3598	+	2.45629i	1.37433	+	0.0796924i
$951$	10.1560	+	51.0576i	0.329331	+	1.65566i
$952$	21.4307	−	18.4132i	0.694573	−	0.596774i
$953$	−8.04912	−	1.60107i	−0.260737	−	0.0518637i	0.0629909	−	0.998014i	$-0.479936\pi$
$953$	−8.04912	−	1.60107i	−0.260737	−	0.0518637i	−0.323727	+	0.946150i	$0.604936\pi$
$954$	−15.2999	+	8.98763i	−0.495351	+	0.290985i
$955$	−12.4390	−	6.64876i	−0.402515	−	0.215149i
$956$	−9.69563	+	30.0410i	−0.313579	+	0.971596i
$957$	−6.85010	−	69.5502i	−0.221432	−	2.24824i
$958$	−8.92644	−	19.3130i	−0.288400	−	0.623974i
$959$			43.7423i			1.41251i
$960$	11.2267	+	15.2620i	0.362339	+	0.492577i
$961$			50.7084i			1.63575i
$962$	6.41695	−	2.96591i	0.206891	−	0.0956248i
$963$	−2.58768	−	26.2731i	−0.0833868	−	0.846640i
$964$	16.9608	−	8.68402i	0.546270	−	0.279693i
$965$	8.58967	+	4.59127i	0.276511	+	0.147798i
$966$	10.6266	+	18.0900i	0.341906	+	0.582035i
$967$	−4.52016	−	0.899116i	−0.145359	−	0.0289136i	0.121875	−	0.992545i	$-0.461109\pi$
$967$	−4.52016	−	0.899116i	−0.145359	−	0.0289136i	−0.267233	+	0.963632i	$0.586109\pi$
$968$	2.56714	+	7.82223i	0.0825109	+	0.251416i
$969$	15.1081	+	75.9534i	0.485341	+	2.43997i
$970$	0.0561950	−	0.969109i	0.00180431	−	0.0311162i
$971$	−3.20136	−	3.90087i	−0.102737	−	0.125185i	0.719104	−	0.694903i	$-0.244553\pi$
$971$	−3.20136	−	3.90087i	−0.102737	−	0.125185i	−0.821840	+	0.569718i	$0.807053\pi$
$972$	43.5181	+	9.45849i	1.39584	+	0.303381i
$973$	−17.8224	−	33.3433i	−0.571359	−	1.06894i
$974$	2.02907	−	0.489248i	0.0650156	−	0.0156765i
$975$	−5.49545	−	2.27629i	−0.175995	−	0.0728997i
$976$	−0.807461	+	0.214100i	−0.0258462	+	0.00685319i
$977$	−1.33346	+	0.552337i	−0.0426611	+	0.0176708i	−0.403912	−	0.914798i	$-0.632350\pi$
$977$	−1.33346	+	0.552337i	−0.0426611	+	0.0176708i	0.361251	+	0.932469i	$0.382350\pi$
$978$	23.5195	−	17.1233i	0.752071	−	0.547542i
$979$	−6.53305	+	21.5366i	−0.208797	+	0.688312i
$980$	2.38741	+	0.0421850i	0.0762630	+	0.00134755i
$981$	45.3991	+	4.47142i	1.44948	+	0.142762i
$982$	11.9410	+	5.77732i	0.381054	+	0.184362i
$983$	−3.93079	+	5.88284i	−0.125373	+	0.187634i	−0.888846	−	0.458206i	$-0.848492\pi$
$983$	−3.93079	+	5.88284i	−0.125373	+	0.187634i	0.763474	+	0.645839i	$0.223492\pi$
$984$	0.0555672	+	2.45989i	0.00177142	+	0.0784184i
$985$	−10.6206	+	7.09644i	−0.338399	+	0.226111i
$986$	34.2312	−	45.3132i	1.09014	−	1.44307i
$987$	−9.51886	−	31.3795i	−0.302989	−	0.998820i
$988$	−7.10151	−	3.95871i	−0.225929	−	0.125943i
$989$	−5.13832	−	4.21691i	−0.163389	−	0.134090i
$990$	−13.1839	+	0.530986i	−0.419013	+	0.0168758i
$991$	8.98450	−	8.98450i	0.285402	−	0.285402i	−0.549857	−	0.835259i	$-0.685318\pi$
$991$	8.98450	−	8.98450i	0.285402	−	0.285402i	0.835259	+	0.549857i	$0.185318\pi$
$992$	28.6172	+	42.3760i	0.908596	+	1.34544i
$993$	−4.09866	−	4.09866i	−0.130067	−	0.130067i
$994$	14.0224	+	12.9366i	0.444764	+	0.410325i
$995$	−6.80358	+	8.29019i	−0.215688	+	0.262817i
$996$	11.5680	−	9.15646i	0.366547	−	0.290133i
$997$	−31.1782	+	9.45781i	−0.987424	+	0.299532i	−0.742379	−	0.669980i	$-0.766303\pi$
$997$	−31.1782	+	9.45781i	−0.987424	+	0.299532i	−0.245045	+	0.969512i	$0.578803\pi$
$998$	4.20101	+	30.1539i	0.132981	+	0.954503i
$999$	6.87314	+	10.2864i	0.217456	+	0.325447i

Display

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a_n

instead) (See

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a_n

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a_p

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.2.k.a.117.6	yes	240
4.3	odd	2		512.2.k.a.305.2		240
128.35	odd	32		512.2.k.a.465.2		240
128.93	even	32	inner	128.2.k.a.93.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.93.6	✓	240	128.93	even	32	inner
128.2.k.a.117.6	yes	240	1.1	even	1	trivial
512.2.k.a.305.2		240	4.3	odd	2
512.2.k.a.465.2		240	128.35	odd	32

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	128.2.k.a.117.6

Level	$128$
Weight	$2$
Character	128.117
Analytic conductor	$1.022$
Analytic rank	$0$
Dimension	$240$
Inner twists	$2$